id	sid	tid	token	lemma	pos
ejpam-3914	1	1	european	european	PROPN
ejpam-3914	1	2	journal	journal	PROPN
ejpam-3914	1	3	of	of	ADP
ejpam-3914	1	4	pure	pure	ADJ
ejpam-3914	1	5	and	and	CCONJ
ejpam-3914	1	6	applied	apply	VERB
ejpam-3914	1	7	mathematics	mathematic	NOUN
ejpam-3914	1	8	vol	vol	NOUN
ejpam-3914	1	9	.	.	PUNCT
ejpam-3914	2	1	14	14	NUM
ejpam-3914	2	2	,	,	PUNCT
ejpam-3914	2	3	no	no	INTJ
ejpam-3914	2	4	.	.	NOUN
ejpam-3914	2	5	2	2	NUM
ejpam-3914	2	6	,	,	PUNCT
ejpam-3914	2	7	2021	2021	NUM
ejpam-3914	2	8	,	,	PUNCT
ejpam-3914	2	9	451	451	NUM
ejpam-3914	2	10	-	-	SYM
ejpam-3914	2	11	470	470	NUM
ejpam-3914	2	12	issn	issn	PROPN
ejpam-3914	2	13	1307	1307	NUM
ejpam-3914	2	14	-	-	SYM
ejpam-3914	2	15	5543	5543	NUM
ejpam-3914	2	16	–	–	PUNCT
ejpam-3914	2	17	ejpam.com	ejpam.com	X
ejpam-3914	2	18	published	publish	VERB
ejpam-3914	2	19	by	by	ADP
ejpam-3914	2	20	new	new	PROPN
ejpam-3914	2	21	york	york	PROPN
ejpam-3914	2	22	business	business	PROPN
ejpam-3914	2	23	global	global	ADJ
ejpam-3914	2	24	forcing	force	VERB
ejpam-3914	2	25	subsets	subset	NOUN
ejpam-3914	2	26	for	for	ADP
ejpam-3914	2	27	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	2	28	-sets	-set	NOUN
ejpam-3914	2	29	in	in	ADP
ejpam-3914	2	30	graphs	graph	NOUN
ejpam-3914	2	31	cris	cris	PROPN
ejpam-3914	2	32	l.	l.	PROPN
ejpam-3914	2	33	armada1	armada1	PROPN
ejpam-3914	2	34	1	1	NUM
ejpam-3914	2	35	mathematics	mathematics	PROPN
ejpam-3914	2	36	department	department	NOUN
ejpam-3914	2	37	,	,	PUNCT
ejpam-3914	2	38	college	college	NOUN
ejpam-3914	2	39	of	of	ADP
ejpam-3914	2	40	arts	art	NOUN
ejpam-3914	2	41	and	and	CCONJ
ejpam-3914	2	42	sciences	science	NOUN
ejpam-3914	2	43	,	,	PUNCT
ejpam-3914	2	44	cebu	cebu	NOUN
ejpam-3914	2	45	normal	normal	ADJ
ejpam-3914	2	46	university	university	NOUN
ejpam-3914	2	47	,	,	PUNCT
ejpam-3914	2	48	cebu	cebu	NOUN
ejpam-3914	2	49	city	city	NOUN
ejpam-3914	2	50	,	,	PUNCT
ejpam-3914	3	1	philippines	philippine	NOUN
ejpam-3914	3	2	6000	6000	NUM
ejpam-3914	3	3	abstract	abstract	NOUN
ejpam-3914	3	4	.	.	PUNCT
ejpam-3914	4	1	in	in	ADP
ejpam-3914	4	2	this	this	DET
ejpam-3914	4	3	paper	paper	NOUN
ejpam-3914	4	4	,	,	PUNCT
ejpam-3914	4	5	the	the	DET
ejpam-3914	4	6	lower	low	ADJ
ejpam-3914	4	7	and	and	CCONJ
ejpam-3914	4	8	upper	upper	ADJ
ejpam-3914	4	9	bounds	bound	NOUN
ejpam-3914	4	10	of	of	ADP
ejpam-3914	4	11	the	the	DET
ejpam-3914	4	12	forcing	force	VERB
ejpam-3914	4	13	total	total	ADJ
ejpam-3914	4	14	dr	dr	PROPN
ejpam-3914	4	15	-	-	PUNCT
ejpam-3914	4	16	power	power	NOUN
ejpam-3914	4	17	domination	domination	NOUN
ejpam-3914	4	18	number	number	NOUN
ejpam-3914	4	19	of	of	ADP
ejpam-3914	4	20	any	any	DET
ejpam-3914	4	21	graph	graph	NOUN
ejpam-3914	4	22	are	be	AUX
ejpam-3914	4	23	determined	determine	VERB
ejpam-3914	4	24	.	.	PUNCT
ejpam-3914	5	1	total	total	ADJ
ejpam-3914	5	2	dr	dr	PROPN
ejpam-3914	5	3	-	-	PUNCT
ejpam-3914	5	4	power	power	NOUN
ejpam-3914	5	5	domination	domination	NOUN
ejpam-3914	5	6	number	number	NOUN
ejpam-3914	5	7	of	of	ADP
ejpam-3914	5	8	some	some	DET
ejpam-3914	5	9	special	special	ADJ
ejpam-3914	5	10	graphs	graph	NOUN
ejpam-3914	5	11	such	such	ADJ
ejpam-3914	5	12	as	as	ADP
ejpam-3914	5	13	complete	complete	ADJ
ejpam-3914	5	14	graphs	graph	NOUN
ejpam-3914	5	15	,	,	PUNCT
ejpam-3914	5	16	star	star	NOUN
ejpam-3914	5	17	,	,	PUNCT
ejpam-3914	5	18	fan	fan	NOUN
ejpam-3914	5	19	and	and	CCONJ
ejpam-3914	5	20	wheel	wheel	NOUN
ejpam-3914	5	21	graphs	graph	NOUN
ejpam-3914	5	22	are	be	AUX
ejpam-3914	5	23	shown	show	VERB
ejpam-3914	5	24	.	.	PUNCT
ejpam-3914	6	1	moreover	moreover	ADV
ejpam-3914	6	2	,	,	PUNCT
ejpam-3914	6	3	the	the	DET
ejpam-3914	6	4	forcing	force	VERB
ejpam-3914	6	5	total	total	ADJ
ejpam-3914	6	6	dr	dr	PROPN
ejpam-3914	6	7	-	-	PUNCT
ejpam-3914	6	8	power	power	NOUN
ejpam-3914	6	9	domination	domination	NOUN
ejpam-3914	6	10	number	number	NOUN
ejpam-3914	6	11	of	of	ADP
ejpam-3914	6	12	these	these	DET
ejpam-3914	6	13	graphs	graph	NOUN
ejpam-3914	6	14	,	,	PUNCT
ejpam-3914	6	15	together	together	ADV
ejpam-3914	6	16	with	with	ADP
ejpam-3914	6	17	paths	path	NOUN
ejpam-3914	6	18	and	and	CCONJ
ejpam-3914	6	19	cycles	cycle	NOUN
ejpam-3914	6	20	,	,	PUNCT
ejpam-3914	6	21	are	be	AUX
ejpam-3914	6	22	determined	determine	VERB
ejpam-3914	6	23	.	.	PUNCT
ejpam-3914	7	1	2020	2020	NUM
ejpam-3914	7	2	mathematics	mathematic	NOUN
ejpam-3914	7	3	subject	subject	NOUN
ejpam-3914	7	4	classifications	classification	NOUN
ejpam-3914	7	5	:	:	PUNCT
ejpam-3914	7	6	05c38	05c38	NUM
ejpam-3914	7	7	,	,	PUNCT
ejpam-3914	7	8	05c69	05c69	X
ejpam-3914	7	9	key	key	ADJ
ejpam-3914	7	10	words	word	NOUN
ejpam-3914	7	11	and	and	CCONJ
ejpam-3914	7	12	phrases	phrase	NOUN
ejpam-3914	7	13	:	:	PUNCT
ejpam-3914	7	14	forcing	force	VERB
ejpam-3914	7	15	,	,	PUNCT
ejpam-3914	7	16	total	total	NOUN
ejpam-3914	7	17	,	,	PUNCT
ejpam-3914	7	18	dr	dr	PROPN
ejpam-3914	7	19	-	-	PUNCT
ejpam-3914	7	20	power	power	NOUN
ejpam-3914	7	21	domination	domination	NOUN
ejpam-3914	7	22	,	,	PUNCT
ejpam-3914	7	23	paths	path	NOUN
ejpam-3914	7	24	,	,	PUNCT
ejpam-3914	7	25	cycles	cycle	VERB
ejpam-3914	7	26	1	1	NUM
ejpam-3914	7	27	.	.	PUNCT
ejpam-3914	7	28	introduction	introduction	NOUN
ejpam-3914	7	29	let	let	VERB
ejpam-3914	7	30	g	g	PROPN
ejpam-3914	7	31	=	=	SYM
ejpam-3914	7	32	(	(	PUNCT
ejpam-3914	7	33	v	v	NOUN
ejpam-3914	7	34	,	,	PUNCT
ejpam-3914	7	35	e	e	NOUN
ejpam-3914	7	36	)	)	PUNCT
ejpam-3914	7	37	be	be	AUX
ejpam-3914	7	38	a	a	DET
ejpam-3914	7	39	graph	graph	NOUN
ejpam-3914	7	40	representing	represent	VERB
ejpam-3914	7	41	the	the	DET
ejpam-3914	7	42	electrical	electrical	ADJ
ejpam-3914	7	43	power	power	NOUN
ejpam-3914	7	44	system	system	NOUN
ejpam-3914	7	45	,	,	PUNCT
ejpam-3914	7	46	where	where	SCONJ
ejpam-3914	7	47	a	a	DET
ejpam-3914	7	48	vertex	vertex	NOUN
ejpam-3914	7	49	represents	represent	VERB
ejpam-3914	7	50	an	an	DET
ejpam-3914	7	51	electrical	electrical	ADJ
ejpam-3914	7	52	node	node	NOUN
ejpam-3914	7	53	and	and	CCONJ
ejpam-3914	7	54	an	an	DET
ejpam-3914	7	55	edge	edge	NOUN
ejpam-3914	7	56	represents	represent	VERB
ejpam-3914	7	57	a	a	DET
ejpam-3914	7	58	transmission	transmission	NOUN
ejpam-3914	7	59	line	line	NOUN
ejpam-3914	7	60	joining	join	VERB
ejpam-3914	7	61	two	two	NUM
ejpam-3914	7	62	electrical	electrical	ADJ
ejpam-3914	7	63	nodes	node	NOUN
ejpam-3914	7	64	.	.	PUNCT
ejpam-3914	8	1	in	in	ADP
ejpam-3914	8	2	order	order	NOUN
ejpam-3914	8	3	to	to	PART
ejpam-3914	8	4	monitor	monitor	VERB
ejpam-3914	8	5	the	the	DET
ejpam-3914	8	6	power	power	NOUN
ejpam-3914	8	7	system	system	NOUN
ejpam-3914	8	8	,	,	PUNCT
ejpam-3914	8	9	some	some	DET
ejpam-3914	8	10	measurement	measurement	NOUN
ejpam-3914	8	11	devices	device	NOUN
ejpam-3914	8	12	must	must	AUX
ejpam-3914	8	13	be	be	AUX
ejpam-3914	8	14	placed	place	VERB
ejpam-3914	8	15	at	at	ADP
ejpam-3914	8	16	selected	select	VERB
ejpam-3914	8	17	locations	location	NOUN
ejpam-3914	8	18	so	so	SCONJ
ejpam-3914	8	19	that	that	SCONJ
ejpam-3914	8	20	all	all	DET
ejpam-3914	8	21	the	the	DET
ejpam-3914	8	22	state	state	NOUN
ejpam-3914	8	23	variables	variable	NOUN
ejpam-3914	8	24	of	of	ADP
ejpam-3914	8	25	the	the	DET
ejpam-3914	8	26	system	system	NOUN
ejpam-3914	8	27	can	can	AUX
ejpam-3914	8	28	be	be	AUX
ejpam-3914	8	29	measured	measure	VERB
ejpam-3914	8	30	.	.	PUNCT
ejpam-3914	9	1	a	a	DET
ejpam-3914	9	2	phase	phase	NOUN
ejpam-3914	9	3	measurement	measurement	NOUN
ejpam-3914	9	4	unit	unit	NOUN
ejpam-3914	9	5	(	(	PUNCT
ejpam-3914	9	6	pmu	pmu	PROPN
ejpam-3914	9	7	)	)	PUNCT
ejpam-3914	9	8	is	be	AUX
ejpam-3914	9	9	a	a	DET
ejpam-3914	9	10	measurement	measurement	NOUN
ejpam-3914	9	11	device	device	NOUN
ejpam-3914	9	12	placed	place	VERB
ejpam-3914	9	13	on	on	ADP
ejpam-3914	9	14	a	a	DET
ejpam-3914	9	15	vertex	vertex	NOUN
ejpam-3914	9	16	and	and	CCONJ
ejpam-3914	9	17	has	have	VERB
ejpam-3914	9	18	the	the	DET
ejpam-3914	9	19	ability	ability	NOUN
ejpam-3914	9	20	to	to	PART
ejpam-3914	9	21	measure	measure	VERB
ejpam-3914	9	22	the	the	DET
ejpam-3914	9	23	state	state	NOUN
ejpam-3914	9	24	of	of	ADP
ejpam-3914	9	25	the	the	DET
ejpam-3914	9	26	vertex	vertex	NOUN
ejpam-3914	9	27	and	and	CCONJ
ejpam-3914	9	28	the	the	DET
ejpam-3914	9	29	edges	edge	NOUN
ejpam-3914	9	30	connected	connect	VERB
ejpam-3914	9	31	to	to	ADP
ejpam-3914	9	32	the	the	DET
ejpam-3914	9	33	vertex	vertex	NOUN
ejpam-3914	9	34	.	.	PUNCT
ejpam-3914	10	1	the	the	DET
ejpam-3914	10	2	vertices	vertex	NOUN
ejpam-3914	10	3	and	and	CCONJ
ejpam-3914	10	4	edges	edge	NOUN
ejpam-3914	10	5	that	that	PRON
ejpam-3914	10	6	are	be	AUX
ejpam-3914	10	7	measured	measure	VERB
ejpam-3914	10	8	by	by	ADP
ejpam-3914	10	9	pmu	pmu	PROPN
ejpam-3914	10	10	’s	’s	PART
ejpam-3914	10	11	are	be	AUX
ejpam-3914	10	12	said	say	VERB
ejpam-3914	10	13	to	to	PART
ejpam-3914	10	14	be	be	AUX
ejpam-3914	10	15	observed	observe	VERB
ejpam-3914	10	16	.	.	PUNCT
ejpam-3914	11	1	in	in	ADP
ejpam-3914	11	2	this	this	DET
ejpam-3914	11	3	study	study	NOUN
ejpam-3914	11	4	,	,	PUNCT
ejpam-3914	11	5	it	it	PRON
ejpam-3914	11	6	is	be	AUX
ejpam-3914	11	7	necessary	necessary	ADJ
ejpam-3914	11	8	that	that	SCONJ
ejpam-3914	11	9	each	each	DET
ejpam-3914	11	10	vertex	vertex	NOUN
ejpam-3914	11	11	with	with	ADP
ejpam-3914	11	12	pmu	pmu	NOUN
ejpam-3914	11	13	is	be	AUX
ejpam-3914	11	14	adjacent	adjacent	ADJ
ejpam-3914	11	15	to	to	ADP
ejpam-3914	11	16	another	another	DET
ejpam-3914	11	17	vertex	vertex	NOUN
ejpam-3914	11	18	with	with	ADP
ejpam-3914	11	19	pmu	pmu	NOUN
ejpam-3914	11	20	also	also	ADV
ejpam-3914	11	21	.	.	PUNCT
ejpam-3914	12	1	but	but	CCONJ
ejpam-3914	12	2	because	because	SCONJ
ejpam-3914	12	3	of	of	ADP
ejpam-3914	12	4	the	the	DET
ejpam-3914	12	5	high	high	ADJ
ejpam-3914	12	6	cost	cost	NOUN
ejpam-3914	12	7	value	value	NOUN
ejpam-3914	12	8	of	of	ADP
ejpam-3914	12	9	a	a	DET
ejpam-3914	12	10	pmu	pmu	NOUN
ejpam-3914	12	11	,	,	PUNCT
ejpam-3914	12	12	it	it	PRON
ejpam-3914	12	13	is	be	AUX
ejpam-3914	12	14	desirable	desirable	ADJ
ejpam-3914	12	15	to	to	PART
ejpam-3914	12	16	minimize	minimize	VERB
ejpam-3914	12	17	their	their	PRON
ejpam-3914	12	18	number	number	NOUN
ejpam-3914	12	19	while	while	SCONJ
ejpam-3914	12	20	maintaining	maintain	VERB
ejpam-3914	12	21	the	the	DET
ejpam-3914	12	22	ability	ability	NOUN
ejpam-3914	12	23	to	to	PART
ejpam-3914	12	24	monitor	monitor	VERB
ejpam-3914	12	25	the	the	DET
ejpam-3914	12	26	entire	entire	ADJ
ejpam-3914	12	27	power	power	NOUN
ejpam-3914	12	28	system	system	NOUN
ejpam-3914	12	29	.	.	PUNCT
ejpam-3914	13	1	all	all	DET
ejpam-3914	13	2	graphs	graph	NOUN
ejpam-3914	13	3	considered	consider	VERB
ejpam-3914	13	4	in	in	ADP
ejpam-3914	13	5	this	this	DET
ejpam-3914	13	6	study	study	NOUN
ejpam-3914	13	7	are	be	AUX
ejpam-3914	13	8	simple	simple	ADJ
ejpam-3914	13	9	,	,	PUNCT
ejpam-3914	13	10	undirected	undirected	ADJ
ejpam-3914	13	11	and	and	CCONJ
ejpam-3914	13	12	without	without	ADP
ejpam-3914	13	13	loops	loop	NOUN
ejpam-3914	13	14	or	or	CCONJ
ejpam-3914	13	15	multiple	multiple	ADJ
ejpam-3914	13	16	edges	edge	NOUN
ejpam-3914	13	17	.	.	PUNCT
ejpam-3914	14	1	let	let	VERB
ejpam-3914	14	2	g	g	PROPN
ejpam-3914	14	3	=	=	SYM
ejpam-3914	14	4	(	(	PUNCT
ejpam-3914	14	5	v	v	NOUN
ejpam-3914	14	6	(	(	PUNCT
ejpam-3914	14	7	g	g	NOUN
ejpam-3914	14	8	)	)	PUNCT
ejpam-3914	14	9	,	,	PUNCT
ejpam-3914	14	10	e(g	e(g	PROPN
ejpam-3914	14	11	)	)	PUNCT
ejpam-3914	14	12	)	)	PUNCT
ejpam-3914	15	1	be	be	AUX
ejpam-3914	15	2	a	a	DET
ejpam-3914	15	3	graph	graph	NOUN
ejpam-3914	15	4	and	and	CCONJ
ejpam-3914	15	5	v	v	ADP
ejpam-3914	15	6	∈	∈	PROPN
ejpam-3914	15	7	v	v	NOUN
ejpam-3914	15	8	(	(	PUNCT
ejpam-3914	15	9	g	g	NOUN
ejpam-3914	15	10	)	)	PUNCT
ejpam-3914	15	11	.	.	PUNCT
ejpam-3914	16	1	the	the	DET
ejpam-3914	16	2	open	open	ADJ
ejpam-3914	16	3	neighborhood	neighborhood	NOUN
ejpam-3914	16	4	of	of	ADP
ejpam-3914	16	5	v	v	NOUN
ejpam-3914	16	6	in	in	ADP
ejpam-3914	16	7	g	g	PROPN
ejpam-3914	16	8	is	be	AUX
ejpam-3914	16	9	the	the	DET
ejpam-3914	16	10	set	set	NOUN
ejpam-3914	16	11	n(v	n(v	PROPN
ejpam-3914	16	12	)	)	PUNCT
ejpam-3914	16	13	=	=	PRON
ejpam-3914	17	1	{	{	PUNCT
ejpam-3914	17	2	u	u	NOUN
ejpam-3914	17	3	∈	∈	PROPN
ejpam-3914	17	4	v	v	NOUN
ejpam-3914	17	5	(	(	PUNCT
ejpam-3914	17	6	g	g	NOUN
ejpam-3914	17	7	)	)	PUNCT
ejpam-3914	17	8	:	:	PUNCT
ejpam-3914	17	9	uv	uv	PROPN
ejpam-3914	17	10	∈	∈	PROPN
ejpam-3914	17	11	e(g	e(g	PROPN
ejpam-3914	17	12	)	)	PUNCT
ejpam-3914	17	13	}	}	PUNCT
ejpam-3914	17	14	and	and	CCONJ
ejpam-3914	17	15	the	the	DET
ejpam-3914	17	16	closed	closed	ADJ
ejpam-3914	17	17	neighborhood	neighborhood	NOUN
ejpam-3914	17	18	of	of	ADP
ejpam-3914	17	19	v	v	NOUN
ejpam-3914	17	20	is	be	AUX
ejpam-3914	17	21	the	the	DET
ejpam-3914	17	22	set	set	ADJ
ejpam-3914	17	23	n	n	PROPN
ejpam-3914	17	24	[	[	X
ejpam-3914	17	25	v	v	X
ejpam-3914	17	26	]	]	X
ejpam-3914	17	27	=	=	PUNCT
ejpam-3914	17	28	n(v	n(v	PROPN
ejpam-3914	17	29	)	)	PUNCT
ejpam-3914	17	30	∪	∪	NOUN
ejpam-3914	17	31	{	{	PUNCT
ejpam-3914	17	32	v	v	NOUN
ejpam-3914	17	33	}	}	PUNCT
ejpam-3914	17	34	.	.	PUNCT
ejpam-3914	18	1	for	for	ADP
ejpam-3914	18	2	x	x	SYM
ejpam-3914	18	3	⊆	⊆	NUM
ejpam-3914	18	4	v	v	ADP
ejpam-3914	18	5	(	(	PUNCT
ejpam-3914	18	6	g	g	NOUN
ejpam-3914	18	7	)	)	PUNCT
ejpam-3914	18	8	,	,	PUNCT
ejpam-3914	18	9	the	the	DET
ejpam-3914	18	10	open	open	ADJ
ejpam-3914	18	11	neighborhood	neighborhood	NOUN
ejpam-3914	18	12	of	of	ADP
ejpam-3914	18	13	x	x	SYM
ejpam-3914	18	14	is	be	AUX
ejpam-3914	18	15	the	the	DET
ejpam-3914	18	16	set	set	NOUN
ejpam-3914	18	17	n(x	n(x	NOUN
ejpam-3914	18	18	)	)	PUNCT
ejpam-3914	18	19	=	=	PUNCT
ejpam-3914	18	20	∪v∈xng(v	∪v∈xng(v	PROPN
ejpam-3914	18	21	)	)	PUNCT
ejpam-3914	18	22	and	and	CCONJ
ejpam-3914	18	23	its	its	PRON
ejpam-3914	18	24	closed	closed	ADJ
ejpam-3914	18	25	neighborhood	neighborhood	NOUN
ejpam-3914	18	26	is	be	AUX
ejpam-3914	18	27	the	the	DET
ejpam-3914	18	28	set	set	ADJ
ejpam-3914	18	29	n	n	NOUN
ejpam-3914	18	30	[	[	X
ejpam-3914	18	31	x	x	X
ejpam-3914	18	32	]	]	X
ejpam-3914	18	33	=	=	SYM
ejpam-3914	18	34	n(x	n(x	X
ejpam-3914	18	35	)	)	PUNCT
ejpam-3914	18	36	∪x	∪x	NUM
ejpam-3914	18	37	.	.	PUNCT
ejpam-3914	19	1	a	a	DET
ejpam-3914	19	2	set	set	NOUN
ejpam-3914	19	3	s	s	NOUN
ejpam-3914	19	4	⊆	⊆	NUM
ejpam-3914	19	5	v	v	NOUN
ejpam-3914	19	6	(	(	PUNCT
ejpam-3914	19	7	g	g	NOUN
ejpam-3914	19	8	)	)	PUNCT
ejpam-3914	19	9	is	be	AUX
ejpam-3914	19	10	a	a	DET
ejpam-3914	19	11	dominating	dominating	NOUN
ejpam-3914	19	12	set	set	NOUN
ejpam-3914	19	13	(	(	PUNCT
ejpam-3914	19	14	resp	resp	NOUN
ejpam-3914	19	15	.	.	PUNCT
ejpam-3914	20	1	total	total	ADJ
ejpam-3914	20	2	dominating	dominating	NOUN
ejpam-3914	20	3	set	set	NOUN
ejpam-3914	20	4	)	)	PUNCT
ejpam-3914	20	5	of	of	ADP
ejpam-3914	20	6	g	g	PROPN
ejpam-3914	20	7	if	if	SCONJ
ejpam-3914	20	8	n	n	PROPN
ejpam-3914	20	9	[	[	X
ejpam-3914	20	10	s	s	X
ejpam-3914	20	11	]	]	X
ejpam-3914	20	12	=	=	SYM
ejpam-3914	20	13	v	v	X
ejpam-3914	20	14	(	(	PUNCT
ejpam-3914	20	15	g	g	NOUN
ejpam-3914	20	16	)	)	PUNCT
ejpam-3914	20	17	(	(	PUNCT
ejpam-3914	20	18	resp	resp	NOUN
ejpam-3914	20	19	.	.	PUNCT
ejpam-3914	21	1	n(s	n(s	PROPN
ejpam-3914	21	2	)	)	PUNCT
ejpam-3914	21	3	=	=	SYM
ejpam-3914	21	4	v	v	NOUN
ejpam-3914	21	5	(	(	PUNCT
ejpam-3914	21	6	g	g	NOUN
ejpam-3914	21	7	)	)	PUNCT
ejpam-3914	21	8	)	)	PUNCT
ejpam-3914	21	9	.	.	PUNCT
ejpam-3914	22	1	the	the	DET
ejpam-3914	22	2	domination	domination	NOUN
ejpam-3914	22	3	number	number	NOUN
ejpam-3914	22	4	γ(g	γ(g	PROPN
ejpam-3914	22	5	)	)	PUNCT
ejpam-3914	22	6	(	(	PUNCT
ejpam-3914	22	7	resp	resp	NOUN
ejpam-3914	22	8	.	.	PUNCT
ejpam-3914	23	1	total	total	ADJ
ejpam-3914	23	2	domination	domination	NOUN
ejpam-3914	23	3	number	number	NOUN
ejpam-3914	23	4	doi	doi	NOUN
ejpam-3914	23	5	:	:	PUNCT
ejpam-3914	23	6	https://doi.org/10.29020/nybg.ejpam.v14i2.3914	https://doi.org/10.29020/nybg.ejpam.v14i2.3914	PROPN
ejpam-3914	23	7	email	email	NOUN
ejpam-3914	23	8	addresses	address	NOUN
ejpam-3914	23	9	:	:	PUNCT
ejpam-3914	23	10	armadac@cnu.edu.ph	armadac@cnu.edu.ph	PROPN
ejpam-3914	23	11	/	/	SYM
ejpam-3914	23	12	cris.armada@g.msuiit.edu.ph	cris.armada@g.msuiit.edu.ph	PROPN
ejpam-3914	23	13	(	(	PUNCT
ejpam-3914	23	14	c.	c.	PROPN
ejpam-3914	23	15	armada	armada	PROPN
ejpam-3914	23	16	)	)	PUNCT
ejpam-3914	23	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3914	24	1	451	451	NUM
ejpam-3914	25	1	c	c	X
ejpam-3914	25	2	©	©	PROPN
ejpam-3914	25	3	2021	2021	NUM
ejpam-3914	25	4	ejpam	ejpam	VERB
ejpam-3914	25	5	all	all	DET
ejpam-3914	25	6	rights	right	NOUN
ejpam-3914	25	7	reserved	reserve	VERB
ejpam-3914	25	8	.	.	PUNCT
ejpam-3914	26	1	c.	c.	PROPN
ejpam-3914	26	2	armada	armada	PROPN
ejpam-3914	26	3	/	/	SYM
ejpam-3914	26	4	eur	eur	PROPN
ejpam-3914	26	5	.	.	PUNCT
ejpam-3914	27	1	j.	j.	PROPN
ejpam-3914	27	2	pure	pure	PROPN
ejpam-3914	27	3	appl	appl	PROPN
ejpam-3914	27	4	.	.	PROPN
ejpam-3914	27	5	math	math	PROPN
ejpam-3914	27	6	,	,	PUNCT
ejpam-3914	27	7	14	14	NUM
ejpam-3914	27	8	(	(	PUNCT
ejpam-3914	27	9	2	2	NUM
ejpam-3914	27	10	)	)	PUNCT
ejpam-3914	27	11	(	(	PUNCT
ejpam-3914	27	12	2021	2021	NUM
ejpam-3914	27	13	)	)	PUNCT
ejpam-3914	27	14	,	,	PUNCT
ejpam-3914	27	15	451	451	NUM
ejpam-3914	27	16	-	-	SYM
ejpam-3914	27	17	470	470	NUM
ejpam-3914	27	18	452	452	NUM
ejpam-3914	27	19	γt(g	γt(g	NOUN
ejpam-3914	27	20	)	)	PUNCT
ejpam-3914	27	21	)	)	PUNCT
ejpam-3914	27	22	of	of	ADP
ejpam-3914	27	23	g	g	PROPN
ejpam-3914	27	24	is	be	AUX
ejpam-3914	27	25	the	the	DET
ejpam-3914	27	26	minimum	minimum	ADJ
ejpam-3914	27	27	cardinality	cardinality	NOUN
ejpam-3914	27	28	of	of	ADP
ejpam-3914	27	29	a	a	DET
ejpam-3914	27	30	dominating	dominating	NOUN
ejpam-3914	27	31	set	set	NOUN
ejpam-3914	27	32	(	(	PUNCT
ejpam-3914	27	33	resp	resp	NOUN
ejpam-3914	27	34	.	.	PUNCT
ejpam-3914	28	1	total	total	ADJ
ejpam-3914	28	2	dominating	dominating	NOUN
ejpam-3914	28	3	set	set	NOUN
ejpam-3914	28	4	)	)	PUNCT
ejpam-3914	28	5	.	.	PUNCT
ejpam-3914	29	1	if	if	SCONJ
ejpam-3914	29	2	s	s	NOUN
ejpam-3914	29	3	is	be	AUX
ejpam-3914	29	4	a	a	DET
ejpam-3914	29	5	dominating	dominating	NOUN
ejpam-3914	29	6	set	set	NOUN
ejpam-3914	29	7	(	(	PUNCT
ejpam-3914	29	8	resp	resp	NOUN
ejpam-3914	29	9	.	.	PUNCT
ejpam-3914	30	1	a	a	DET
ejpam-3914	30	2	total	total	ADJ
ejpam-3914	30	3	dominating	dominating	NOUN
ejpam-3914	30	4	set	set	NOUN
ejpam-3914	30	5	)	)	PUNCT
ejpam-3914	30	6	with	with	ADP
ejpam-3914	30	7	|s|	|s|	PROPN
ejpam-3914	30	8	=	=	SYM
ejpam-3914	30	9	γ(g	γ(g	PROPN
ejpam-3914	30	10	)	)	PUNCT
ejpam-3914	30	11	(	(	PUNCT
ejpam-3914	30	12	resp	resp	NOUN
ejpam-3914	30	13	.	.	PUNCT
ejpam-3914	30	14	|s|	|s|	PROPN
ejpam-3914	30	15	=	=	SYM
ejpam-3914	30	16	γt(g	γt(g	NUM
ejpam-3914	30	17	)	)	PUNCT
ejpam-3914	30	18	)	)	PUNCT
ejpam-3914	30	19	,	,	PUNCT
ejpam-3914	30	20	then	then	ADV
ejpam-3914	30	21	we	we	PRON
ejpam-3914	30	22	call	call	VERB
ejpam-3914	30	23	s	s	PRON
ejpam-3914	30	24	a	a	DET
ejpam-3914	30	25	γ	γ	X
ejpam-3914	30	26	-	-	PUNCT
ejpam-3914	30	27	set	set	ADJ
ejpam-3914	30	28	(	(	PUNCT
ejpam-3914	30	29	resp	resp	NOUN
ejpam-3914	30	30	.	.	PUNCT
ejpam-3914	31	1	a	a	DET
ejpam-3914	31	2	γt	γt	NOUN
ejpam-3914	31	3	-	-	NOUN
ejpam-3914	31	4	set	set	NOUN
ejpam-3914	31	5	)	)	PUNCT
ejpam-3914	31	6	of	of	ADP
ejpam-3914	31	7	g.	g.	PROPN
ejpam-3914	31	8	let	let	VERB
ejpam-3914	31	9	g	g	PROPN
ejpam-3914	31	10	=	=	SYM
ejpam-3914	31	11	(	(	PUNCT
ejpam-3914	31	12	v	v	NOUN
ejpam-3914	31	13	,	,	PUNCT
ejpam-3914	31	14	e	e	NOUN
ejpam-3914	31	15	)	)	PUNCT
ejpam-3914	31	16	be	be	AUX
ejpam-3914	31	17	a	a	DET
ejpam-3914	31	18	simple	simple	ADJ
ejpam-3914	31	19	graph	graph	NOUN
ejpam-3914	31	20	.	.	PUNCT
ejpam-3914	32	1	let	let	VERB
ejpam-3914	32	2	p	p	PRON
ejpam-3914	32	3	⊆	⊆	NUM
ejpam-3914	32	4	v	v	NOUN
ejpam-3914	32	5	(	(	PUNCT
ejpam-3914	32	6	g	g	NOUN
ejpam-3914	32	7	)	)	PUNCT
ejpam-3914	32	8	.	.	PUNCT
ejpam-3914	33	1	an	an	DET
ejpam-3914	33	2	edge	edge	NOUN
ejpam-3914	33	3	e	e	NOUN
ejpam-3914	33	4	=	=	NOUN
ejpam-3914	33	5	uv	uv	NOUN
ejpam-3914	33	6	of	of	ADP
ejpam-3914	33	7	g	g	PROPN
ejpam-3914	33	8	is	be	AUX
ejpam-3914	33	9	directly	directly	ADV
ejpam-3914	33	10	observed	observe	VERB
ejpam-3914	33	11	by	by	ADP
ejpam-3914	33	12	p	p	NOUN
ejpam-3914	33	13	if	if	SCONJ
ejpam-3914	33	14	u	u	PROPN
ejpam-3914	33	15	∈	∈	PROPN
ejpam-3914	33	16	p	p	NOUN
ejpam-3914	33	17	or	or	CCONJ
ejpam-3914	33	18	v	v	ADP
ejpam-3914	33	19	∈	∈	PROPN
ejpam-3914	33	20	p	p	NOUN
ejpam-3914	33	21	.	.	PUNCT
ejpam-3914	34	1	a	a	DET
ejpam-3914	34	2	vertex	vertex	NOUN
ejpam-3914	34	3	u	u	NOUN
ejpam-3914	34	4	of	of	ADP
ejpam-3914	34	5	g	g	PROPN
ejpam-3914	34	6	is	be	AUX
ejpam-3914	34	7	directly	directly	ADV
ejpam-3914	34	8	observed	observe	VERB
ejpam-3914	34	9	if	if	SCONJ
ejpam-3914	34	10	u	u	NOUN
ejpam-3914	34	11	is	be	AUX
ejpam-3914	34	12	incident	incident	NOUN
ejpam-3914	34	13	to	to	ADP
ejpam-3914	34	14	a	a	DET
ejpam-3914	34	15	directly	directly	ADV
ejpam-3914	34	16	observed	observe	VERB
ejpam-3914	34	17	edge	edge	NOUN
ejpam-3914	34	18	.	.	PUNCT
ejpam-3914	35	1	an	an	DET
ejpam-3914	35	2	edge	edge	NOUN
ejpam-3914	35	3	e′	e′	X
ejpam-3914	35	4	=	=	SYM
ejpam-3914	36	1	xy	xy	PROPN
ejpam-3914	36	2	is	be	AUX
ejpam-3914	36	3	remotely	remotely	ADV
ejpam-3914	36	4	observed	observe	VERB
ejpam-3914	36	5	by	by	ADP
ejpam-3914	36	6	p	p	PRON
ejpam-3914	36	7	if	if	SCONJ
ejpam-3914	36	8	x	x	PROPN
ejpam-3914	36	9	,	,	PUNCT
ejpam-3914	36	10	y	y	PROPN
ejpam-3914	36	11	/∈	/∈	PUNCT
ejpam-3914	37	1	p	p	NOUN
ejpam-3914	37	2	and	and	CCONJ
ejpam-3914	37	3	x	x	X
ejpam-3914	37	4	,	,	PUNCT
ejpam-3914	37	5	y	y	PROPN
ejpam-3914	37	6	are	be	AUX
ejpam-3914	37	7	directly	directly	ADV
ejpam-3914	37	8	observed	observe	VERB
ejpam-3914	37	9	vertices	vertex	NOUN
ejpam-3914	37	10	or	or	CCONJ
ejpam-3914	37	11	at	at	ADP
ejpam-3914	37	12	least	least	ADJ
ejpam-3914	37	13	one	one	NUM
ejpam-3914	37	14	of	of	ADP
ejpam-3914	37	15	x	x	PUNCT
ejpam-3914	37	16	and	and	CCONJ
ejpam-3914	37	17	y	y	PROPN
ejpam-3914	37	18	is	be	AUX
ejpam-3914	37	19	incident	incident	NOUN
ejpam-3914	37	20	to	to	ADP
ejpam-3914	37	21	k	k	PROPN
ejpam-3914	37	22	edges	edge	NOUN
ejpam-3914	37	23	where	where	SCONJ
ejpam-3914	37	24	k	k	PROPN
ejpam-3914	37	25	−	−	PROPN
ejpam-3914	37	26	1	1	NUM
ejpam-3914	37	27	of	of	ADP
ejpam-3914	37	28	these	these	DET
ejpam-3914	37	29	edges	edge	NOUN
ejpam-3914	37	30	are	be	AUX
ejpam-3914	37	31	directly	directly	ADV
ejpam-3914	37	32	observed	observe	VERB
ejpam-3914	37	33	by	by	ADP
ejpam-3914	37	34	p	p	PROPN
ejpam-3914	37	35	.	.	PUNCT
ejpam-3914	38	1	clearly	clearly	ADV
ejpam-3914	38	2	,	,	PUNCT
ejpam-3914	38	3	k	k	PROPN
ejpam-3914	38	4	is	be	AUX
ejpam-3914	38	5	a	a	DET
ejpam-3914	38	6	positive	positive	ADJ
ejpam-3914	38	7	integer	integer	NOUN
ejpam-3914	38	8	,	,	PUNCT
ejpam-3914	38	9	k	k	PROPN
ejpam-3914	38	10	>	>	X
ejpam-3914	38	11	1	1	NUM
ejpam-3914	38	12	,	,	PUNCT
ejpam-3914	38	13	and	and	CCONJ
ejpam-3914	38	14	k	k	PROPN
ejpam-3914	38	15	is	be	AUX
ejpam-3914	38	16	not	not	PART
ejpam-3914	38	17	constant	constant	ADJ
ejpam-3914	38	18	for	for	ADP
ejpam-3914	38	19	any	any	DET
ejpam-3914	38	20	pair	pair	NOUN
ejpam-3914	38	21	of	of	ADP
ejpam-3914	38	22	vertices	vertex	NOUN
ejpam-3914	38	23	x	x	PUNCT
ejpam-3914	38	24	and	and	CCONJ
ejpam-3914	38	25	y.	y.	PROPN
ejpam-3914	38	26	a	a	DET
ejpam-3914	38	27	non	non	ADJ
ejpam-3914	38	28	-	-	ADJ
ejpam-3914	38	29	directly	directly	ADV
ejpam-3914	38	30	observed	observe	VERB
ejpam-3914	38	31	vertex	vertex	NOUN
ejpam-3914	38	32	u	u	NOUN
ejpam-3914	38	33	of	of	ADP
ejpam-3914	38	34	g	g	NOUN
ejpam-3914	38	35	which	which	PRON
ejpam-3914	38	36	is	be	AUX
ejpam-3914	38	37	incident	incident	NOUN
ejpam-3914	38	38	to	to	ADP
ejpam-3914	38	39	a	a	DET
ejpam-3914	38	40	remotely	remotely	ADV
ejpam-3914	38	41	observed	observe	VERB
ejpam-3914	38	42	edge	edge	NOUN
ejpam-3914	38	43	is	be	AUX
ejpam-3914	38	44	called	call	VERB
ejpam-3914	38	45	remotely	remotely	ADV
ejpam-3914	38	46	observed	observe	VERB
ejpam-3914	38	47	vertex	vertex	NOUN
ejpam-3914	38	48	.	.	PUNCT
ejpam-3914	39	1	let	let	VERB
ejpam-3914	39	2	op	op	NOUN
ejpam-3914	39	3	v	v	NOUN
ejpam-3914	39	4	(	(	PUNCT
ejpam-3914	39	5	g	g	NOUN
ejpam-3914	39	6	)	)	PUNCT
ejpam-3914	39	7	be	be	VERB
ejpam-3914	39	8	the	the	DET
ejpam-3914	39	9	set	set	NOUN
ejpam-3914	39	10	of	of	ADP
ejpam-3914	39	11	all	all	DET
ejpam-3914	39	12	directly	directly	ADV
ejpam-3914	39	13	and	and	CCONJ
ejpam-3914	39	14	remotely	remotely	ADV
ejpam-3914	39	15	observed	observe	VERB
ejpam-3914	39	16	vertices	vertex	NOUN
ejpam-3914	39	17	and	and	CCONJ
ejpam-3914	39	18	op	op	PROPN
ejpam-3914	39	19	e(g	e(g	PROPN
ejpam-3914	39	20	)	)	PUNCT
ejpam-3914	39	21	be	be	VERB
ejpam-3914	39	22	the	the	DET
ejpam-3914	39	23	set	set	NOUN
ejpam-3914	39	24	of	of	ADP
ejpam-3914	39	25	all	all	DET
ejpam-3914	39	26	directly	directly	ADV
ejpam-3914	39	27	and	and	CCONJ
ejpam-3914	39	28	remotely	remotely	ADV
ejpam-3914	39	29	observed	observe	VERB
ejpam-3914	39	30	edges	edge	NOUN
ejpam-3914	39	31	.	.	PUNCT
ejpam-3914	40	1	then	then	ADV
ejpam-3914	40	2	p	p	X
ejpam-3914	40	3	⊆	⊆	NUM
ejpam-3914	40	4	v	v	NOUN
ejpam-3914	40	5	(	(	PUNCT
ejpam-3914	40	6	g	g	NOUN
ejpam-3914	40	7	)	)	PUNCT
ejpam-3914	40	8	is	be	AUX
ejpam-3914	40	9	a	a	DET
ejpam-3914	40	10	dr	dr	PROPN
ejpam-3914	40	11	-	-	PUNCT
ejpam-3914	40	12	power	power	NOUN
ejpam-3914	40	13	dominating	dominating	NOUN
ejpam-3914	40	14	set	set	NOUN
ejpam-3914	40	15	(	(	PUNCT
ejpam-3914	40	16	dr	dr	NOUN
ejpam-3914	40	17	-	-	PUNCT
ejpam-3914	40	18	pds	pds	NOUN
ejpam-3914	40	19	)	)	PUNCT
ejpam-3914	40	20	of	of	ADP
ejpam-3914	40	21	g	g	PROPN
ejpam-3914	40	22	if	if	SCONJ
ejpam-3914	40	23	op	op	NOUN
ejpam-3914	40	24	v	v	X
ejpam-3914	40	25	(	(	PUNCT
ejpam-3914	40	26	g	g	NOUN
ejpam-3914	40	27	)	)	PUNCT
ejpam-3914	40	28	=	=	NOUN
ejpam-3914	40	29	v	v	X
ejpam-3914	40	30	(	(	PUNCT
ejpam-3914	40	31	g	g	NOUN
ejpam-3914	40	32	)	)	PUNCT
ejpam-3914	40	33	and	and	CCONJ
ejpam-3914	40	34	op	op	PROPN
ejpam-3914	40	35	e(g	e(g	PROPN
ejpam-3914	40	36	)	)	PUNCT
ejpam-3914	41	1	=	=	SYM
ejpam-3914	41	2	e(g	e(g	PROPN
ejpam-3914	41	3	)	)	PUNCT
ejpam-3914	41	4	.	.	PUNCT
ejpam-3914	42	1	the	the	DET
ejpam-3914	42	2	minimum	minimum	ADJ
ejpam-3914	42	3	cardinality	cardinality	NOUN
ejpam-3914	42	4	of	of	ADP
ejpam-3914	42	5	a	a	DET
ejpam-3914	42	6	dr	dr	NOUN
ejpam-3914	42	7	-	-	PUNCT
ejpam-3914	42	8	power	power	NOUN
ejpam-3914	42	9	dominating	dominating	NOUN
ejpam-3914	42	10	set	set	NOUN
ejpam-3914	42	11	is	be	AUX
ejpam-3914	42	12	called	call	VERB
ejpam-3914	42	13	the	the	DET
ejpam-3914	42	14	dr	dr	PROPN
ejpam-3914	42	15	-	-	PUNCT
ejpam-3914	42	16	power	power	NOUN
ejpam-3914	42	17	domination	domination	NOUN
ejpam-3914	42	18	number	number	NOUN
ejpam-3914	42	19	of	of	ADP
ejpam-3914	42	20	g	g	NOUN
ejpam-3914	42	21	and	and	CCONJ
ejpam-3914	42	22	is	be	AUX
ejpam-3914	42	23	denoted	denote	VERB
ejpam-3914	42	24	by	by	ADP
ejpam-3914	42	25	γ∗pw(g	γ∗pw(g	NOUN
ejpam-3914	42	26	)	)	PUNCT
ejpam-3914	42	27	.	.	PUNCT
ejpam-3914	43	1	a	a	DET
ejpam-3914	43	2	subset	subset	NOUN
ejpam-3914	43	3	p	p	NOUN
ejpam-3914	43	4	of	of	ADP
ejpam-3914	43	5	v	v	NOUN
ejpam-3914	43	6	(	(	PUNCT
ejpam-3914	43	7	g	g	NOUN
ejpam-3914	43	8	)	)	PUNCT
ejpam-3914	43	9	with	with	ADP
ejpam-3914	43	10	cardinality	cardinality	PROPN
ejpam-3914	43	11	γ∗pw(g	γ∗pw(g	PROPN
ejpam-3914	43	12	)	)	PUNCT
ejpam-3914	43	13	is	be	AUX
ejpam-3914	43	14	called	call	VERB
ejpam-3914	43	15	a	a	DET
ejpam-3914	43	16	γ∗pw	γ∗pw	NOUN
ejpam-3914	43	17	-	-	PUNCT
ejpam-3914	43	18	set	set	NOUN
ejpam-3914	43	19	of	of	ADP
ejpam-3914	43	20	g.	g.	PROPN
ejpam-3914	43	21	a	a	DET
ejpam-3914	43	22	dr	dr	PROPN
ejpam-3914	43	23	-	-	PUNCT
ejpam-3914	43	24	power	power	NOUN
ejpam-3914	43	25	dominating	dominating	NOUN
ejpam-3914	43	26	set	set	NOUN
ejpam-3914	43	27	d	d	NOUN
ejpam-3914	43	28	is	be	AUX
ejpam-3914	43	29	said	say	VERB
ejpam-3914	43	30	to	to	PART
ejpam-3914	43	31	be	be	AUX
ejpam-3914	43	32	a	a	DET
ejpam-3914	43	33	total	total	ADJ
ejpam-3914	43	34	dr	dr	NOUN
ejpam-3914	43	35	-	-	PUNCT
ejpam-3914	43	36	power	power	NOUN
ejpam-3914	43	37	dominating	dominating	NOUN
ejpam-3914	43	38	set(tdr	set(tdr	PROPN
ejpam-3914	43	39	-	-	PUNCT
ejpam-3914	43	40	pds	pds	NOUN
ejpam-3914	43	41	)	)	PUNCT
ejpam-3914	43	42	if	if	SCONJ
ejpam-3914	43	43	the	the	DET
ejpam-3914	43	44	induced	induced	ADJ
ejpam-3914	43	45	subgraph	subgraph	NOUN
ejpam-3914	43	46	〈	〈	PROPN
ejpam-3914	43	47	d	d	PROPN
ejpam-3914	43	48	〉	〉	PROPN
ejpam-3914	43	49	has	have	VERB
ejpam-3914	43	50	no	no	DET
ejpam-3914	43	51	isolated	isolated	ADJ
ejpam-3914	43	52	vertex	vertex	NOUN
ejpam-3914	43	53	.	.	PUNCT
ejpam-3914	44	1	the	the	DET
ejpam-3914	44	2	minimum	minimum	ADJ
ejpam-3914	44	3	cardinality	cardinality	NOUN
ejpam-3914	44	4	of	of	ADP
ejpam-3914	44	5	a	a	DET
ejpam-3914	44	6	total	total	ADJ
ejpam-3914	44	7	dr	dr	PROPN
ejpam-3914	44	8	-	-	PUNCT
ejpam-3914	44	9	power	power	NOUN
ejpam-3914	44	10	dominating	dominating	NOUN
ejpam-3914	44	11	set	set	NOUN
ejpam-3914	44	12	(	(	PUNCT
ejpam-3914	44	13	tdr	tdr	PROPN
ejpam-3914	44	14	-	-	PUNCT
ejpam-3914	44	15	pds	pds	NOUN
ejpam-3914	44	16	)	)	PUNCT
ejpam-3914	44	17	is	be	AUX
ejpam-3914	44	18	called	call	VERB
ejpam-3914	44	19	the	the	DET
ejpam-3914	44	20	total	total	ADJ
ejpam-3914	44	21	dr	dr	PROPN
ejpam-3914	44	22	-	-	PUNCT
ejpam-3914	44	23	power	power	NOUN
ejpam-3914	44	24	domination	domination	NOUN
ejpam-3914	44	25	number	number	NOUN
ejpam-3914	44	26	of	of	ADP
ejpam-3914	44	27	g	g	NOUN
ejpam-3914	44	28	and	and	CCONJ
ejpam-3914	44	29	is	be	AUX
ejpam-3914	44	30	denoted	denote	VERB
ejpam-3914	44	31	by	by	ADP
ejpam-3914	44	32	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	44	33	(	(	PUNCT
ejpam-3914	44	34	g	g	NOUN
ejpam-3914	44	35	)	)	PUNCT
ejpam-3914	44	36	.	.	PUNCT
ejpam-3914	45	1	a	a	DET
ejpam-3914	45	2	subset	subset	NOUN
ejpam-3914	45	3	t	t	NOUN
ejpam-3914	45	4	of	of	ADP
ejpam-3914	45	5	v	v	PROPN
ejpam-3914	45	6	(	(	PUNCT
ejpam-3914	45	7	g	g	NOUN
ejpam-3914	45	8	)	)	PUNCT
ejpam-3914	45	9	with	with	ADP
ejpam-3914	45	10	cardinality	cardinality	NOUN
ejpam-3914	45	11	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	45	12	(	(	PUNCT
ejpam-3914	45	13	g	g	NOUN
ejpam-3914	45	14	)	)	PUNCT
ejpam-3914	45	15	is	be	AUX
ejpam-3914	45	16	called	call	VERB
ejpam-3914	45	17	a	a	DET
ejpam-3914	45	18	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	45	19	-set	-set	PROPN
ejpam-3914	45	20	of	of	ADP
ejpam-3914	45	21	g.	g.	PROPN
ejpam-3914	45	22	moreover	moreover	ADV
ejpam-3914	45	23	,	,	PUNCT
ejpam-3914	45	24	there	there	PRON
ejpam-3914	45	25	exists	exist	VERB
ejpam-3914	45	26	a	a	DET
ejpam-3914	45	27	connected	connected	ADJ
ejpam-3914	45	28	graph	graph	NOUN
ejpam-3914	45	29	g	g	ADP
ejpam-3914	45	30	such	such	ADJ
ejpam-3914	45	31	that	that	DET
ejpam-3914	45	32	2	2	NUM
ejpam-3914	45	33	≤	≤	NOUN
ejpam-3914	45	34	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	45	35	(	(	PUNCT
ejpam-3914	45	36	g	g	NOUN
ejpam-3914	45	37	)	)	PUNCT
ejpam-3914	45	38	≤	≤	NOUN
ejpam-3914	45	39	γt(g	γt(g	PUNCT
ejpam-3914	45	40	)	)	PUNCT
ejpam-3914	45	41	.	.	PUNCT
ejpam-3914	46	1	let	let	VERB
ejpam-3914	46	2	s	s	PRON
ejpam-3914	46	3	be	be	AUX
ejpam-3914	46	4	a	a	DET
ejpam-3914	46	5	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	46	6	-set	-set	PUNCT
ejpam-3914	46	7	of	of	ADP
ejpam-3914	46	8	a	a	DET
ejpam-3914	46	9	graph	graph	NOUN
ejpam-3914	46	10	g.	g.	NOUN
ejpam-3914	46	11	a	a	DET
ejpam-3914	46	12	subset	subset	NOUN
ejpam-3914	46	13	d	d	NOUN
ejpam-3914	46	14	of	of	ADP
ejpam-3914	46	15	s	s	NOUN
ejpam-3914	46	16	is	be	AUX
ejpam-3914	46	17	said	say	VERB
ejpam-3914	46	18	to	to	PART
ejpam-3914	46	19	be	be	AUX
ejpam-3914	46	20	a	a	DET
ejpam-3914	46	21	forcing	forcing	NOUN
ejpam-3914	46	22	subset	subset	NOUN
ejpam-3914	46	23	for	for	ADP
ejpam-3914	46	24	s	s	PRON
ejpam-3914	46	25	if	if	SCONJ
ejpam-3914	46	26	s	s	VERB
ejpam-3914	46	27	is	be	AUX
ejpam-3914	46	28	the	the	DET
ejpam-3914	46	29	unique	unique	ADJ
ejpam-3914	46	30	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	46	31	-set	-set	PUNCT
ejpam-3914	46	32	containing	contain	VERB
ejpam-3914	46	33	d.	d.	PROPN
ejpam-3914	46	34	the	the	DET
ejpam-3914	46	35	forcing	force	VERB
ejpam-3914	46	36	total	total	ADJ
ejpam-3914	46	37	dr	dr	PROPN
ejpam-3914	46	38	-	-	PUNCT
ejpam-3914	46	39	power	power	NOUN
ejpam-3914	46	40	domination	domination	NOUN
ejpam-3914	46	41	number	number	NOUN
ejpam-3914	46	42	of	of	ADP
ejpam-3914	46	43	s	s	NOUN
ejpam-3914	46	44	is	be	AUX
ejpam-3914	46	45	given	give	VERB
ejpam-3914	46	46	by	by	ADP
ejpam-3914	46	47	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	46	48	(	(	PUNCT
ejpam-3914	46	49	s	s	NOUN
ejpam-3914	46	50	)	)	PUNCT
ejpam-3914	46	51	=	=	SYM
ejpam-3914	46	52	min{|d|	min{|d|	NOUN
ejpam-3914	46	53	:	:	PUNCT
ejpam-3914	47	1	d	d	X
ejpam-3914	47	2	is	be	AUX
ejpam-3914	47	3	a	a	DET
ejpam-3914	47	4	forcing	forcing	NOUN
ejpam-3914	47	5	subset	subset	NOUN
ejpam-3914	47	6	for	for	ADP
ejpam-3914	47	7	s	s	NOUN
ejpam-3914	47	8	}	}	PUNCT
ejpam-3914	47	9	.	.	PUNCT
ejpam-3914	48	1	the	the	DET
ejpam-3914	48	2	forcing	force	VERB
ejpam-3914	48	3	total	total	ADJ
ejpam-3914	48	4	dr	dr	PROPN
ejpam-3914	48	5	-	-	PUNCT
ejpam-3914	48	6	power	power	NOUN
ejpam-3914	48	7	domination	domination	NOUN
ejpam-3914	48	8	number	number	NOUN
ejpam-3914	48	9	of	of	ADP
ejpam-3914	48	10	g	g	PROPN
ejpam-3914	48	11	is	be	AUX
ejpam-3914	48	12	given	give	VERB
ejpam-3914	48	13	by	by	ADP
ejpam-3914	48	14	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	48	15	(	(	PUNCT
ejpam-3914	48	16	g	g	NOUN
ejpam-3914	48	17	)	)	PUNCT
ejpam-3914	48	18	=	=	SYM
ejpam-3914	48	19	min{fγ∗tpw	min{fγ∗tpw	PROPN
ejpam-3914	48	20	(	(	PUNCT
ejpam-3914	48	21	s	s	NOUN
ejpam-3914	48	22	)	)	PUNCT
ejpam-3914	48	23	:	:	PUNCT
ejpam-3914	48	24	s	s	VERB
ejpam-3914	48	25	is	be	AUX
ejpam-3914	48	26	a	a	DET
ejpam-3914	48	27	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	48	28	-set	-set	PROPN
ejpam-3914	48	29	of	of	ADP
ejpam-3914	48	30	g	g	NOUN
ejpam-3914	48	31	}	}	PUNCT
ejpam-3914	48	32	.	.	PUNCT
ejpam-3914	49	1	the	the	DET
ejpam-3914	49	2	join	join	NOUN
ejpam-3914	49	3	of	of	ADP
ejpam-3914	49	4	two	two	NUM
ejpam-3914	49	5	graphs	graph	NOUN
ejpam-3914	49	6	g	g	NOUN
ejpam-3914	49	7	and	and	CCONJ
ejpam-3914	49	8	h	h	NOUN
ejpam-3914	49	9	,	,	PUNCT
ejpam-3914	49	10	denoted	denote	VERB
ejpam-3914	49	11	by	by	ADP
ejpam-3914	49	12	g+h	g+h	PROPN
ejpam-3914	49	13	is	be	AUX
ejpam-3914	49	14	the	the	DET
ejpam-3914	49	15	graph	graph	NOUN
ejpam-3914	49	16	with	with	ADP
ejpam-3914	49	17	vertex	vertex	NOUN
ejpam-3914	49	18	set	set	VERB
ejpam-3914	49	19	v	v	NOUN
ejpam-3914	49	20	(	(	PUNCT
ejpam-3914	49	21	g+h	g+h	NOUN
ejpam-3914	49	22	)	)	PUNCT
ejpam-3914	49	23	=	=	SYM
ejpam-3914	49	24	v	v	X
ejpam-3914	49	25	(	(	PUNCT
ejpam-3914	49	26	g	g	NOUN
ejpam-3914	49	27	)	)	PUNCT
ejpam-3914	49	28	∪	∪	NOUN
ejpam-3914	49	29	v	v	NOUN
ejpam-3914	49	30	(	(	PUNCT
ejpam-3914	49	31	h	h	NOUN
ejpam-3914	49	32	)	)	PUNCT
ejpam-3914	49	33	and	and	CCONJ
ejpam-3914	49	34	edge	edge	NOUN
ejpam-3914	49	35	set	set	VERB
ejpam-3914	49	36	e(g+h	e(g+h	NUM
ejpam-3914	49	37	)	)	PUNCT
ejpam-3914	49	38	=	=	SYM
ejpam-3914	49	39	e(g	e(g	NOUN
ejpam-3914	49	40	)	)	PUNCT
ejpam-3914	49	41	∪	∪	ADP
ejpam-3914	49	42	e(h	e(h	PROPN
ejpam-3914	49	43	)	)	PUNCT
ejpam-3914	49	44	∪	∪	NOUN
ejpam-3914	49	45	{	{	PUNCT
ejpam-3914	49	46	uv	uv	NOUN
ejpam-3914	49	47	:	:	PUNCT
ejpam-3914	49	48	u	u	PROPN
ejpam-3914	49	49	∈	∈	PROPN
ejpam-3914	49	50	v	v	ADP
ejpam-3914	49	51	(	(	PUNCT
ejpam-3914	49	52	g	g	NOUN
ejpam-3914	49	53	)	)	PUNCT
ejpam-3914	49	54	,	,	PUNCT
ejpam-3914	49	55	v	v	X
ejpam-3914	49	56	∈	∈	PROPN
ejpam-3914	49	57	v	v	NOUN
ejpam-3914	49	58	(	(	PUNCT
ejpam-3914	49	59	h	h	NOUN
ejpam-3914	49	60	)	)	PUNCT
ejpam-3914	49	61	}	}	PUNCT
ejpam-3914	49	62	.	.	PUNCT
ejpam-3914	50	1	the	the	DET
ejpam-3914	50	2	total	total	ADJ
ejpam-3914	50	3	domination	domination	NOUN
ejpam-3914	50	4	is	be	AUX
ejpam-3914	50	5	studied	study	VERB
ejpam-3914	50	6	by	by	ADP
ejpam-3914	50	7	amos	amos	PROPN
ejpam-3914	51	1	[	[	X
ejpam-3914	51	2	1	1	NUM
ejpam-3914	51	3	]	]	PUNCT
ejpam-3914	51	4	.	.	PUNCT
ejpam-3914	52	1	chartrand	chartrand	PROPN
ejpam-3914	52	2	et	et	PROPN
ejpam-3914	52	3	al	al	PROPN
ejpam-3914	52	4	.	.	PUNCT
ejpam-3914	53	1	[	[	X
ejpam-3914	53	2	5	5	NUM
ejpam-3914	53	3	]	]	PUNCT
ejpam-3914	53	4	investigated	investigate	VERB
ejpam-3914	53	5	the	the	DET
ejpam-3914	53	6	relation	relation	NOUN
ejpam-3914	53	7	between	between	ADP
ejpam-3914	53	8	forcing	force	VERB
ejpam-3914	53	9	and	and	CCONJ
ejpam-3914	53	10	domination	domination	NOUN
ejpam-3914	53	11	concepts	concept	NOUN
ejpam-3914	53	12	and	and	CCONJ
ejpam-3914	53	13	defined	define	VERB
ejpam-3914	53	14	"	"	PUNCT
ejpam-3914	53	15	forcing	force	VERB
ejpam-3914	53	16	domination	domination	NOUN
ejpam-3914	53	17	number	number	NOUN
ejpam-3914	53	18	"	"	PUNCT
ejpam-3914	53	19	.	.	PUNCT
ejpam-3914	54	1	canoy	canoy	PROPN
ejpam-3914	54	2	,	,	PUNCT
ejpam-3914	54	3	et	et	PROPN
ejpam-3914	54	4	al	al	PROPN
ejpam-3914	54	5	studied	study	VERB
ejpam-3914	54	6	the	the	DET
ejpam-3914	54	7	following	follow	VERB
ejpam-3914	54	8	concepts	concept	NOUN
ejpam-3914	54	9	:	:	PUNCT
ejpam-3914	54	10	total	total	ADJ
ejpam-3914	54	11	dr	dr	PROPN
ejpam-3914	54	12	-	-	PUNCT
ejpam-3914	54	13	power	power	NOUN
ejpam-3914	54	14	domination	domination	NOUN
ejpam-3914	54	15	[	[	X
ejpam-3914	54	16	6	6	NUM
ejpam-3914	54	17	]	]	PUNCT
ejpam-3914	54	18	,	,	PUNCT
ejpam-3914	54	19	forcing	force	VERB
ejpam-3914	54	20	domination	domination	NOUN
ejpam-3914	54	21	number	number	NOUN
ejpam-3914	54	22	of	of	ADP
ejpam-3914	54	23	graphs	graph	NOUN
ejpam-3914	54	24	under	under	ADP
ejpam-3914	54	25	some	some	DET
ejpam-3914	54	26	binary	binary	ADJ
ejpam-3914	54	27	operations	operation	NOUN
ejpam-3914	54	28	[	[	X
ejpam-3914	54	29	7	7	NUM
ejpam-3914	54	30	]	]	PUNCT
ejpam-3914	54	31	,	,	PUNCT
ejpam-3914	54	32	forcing	force	VERB
ejpam-3914	54	33	total	total	ADJ
ejpam-3914	54	34	domination	domination	NOUN
ejpam-3914	54	35	number	number	NOUN
ejpam-3914	54	36	and	and	CCONJ
ejpam-3914	54	37	forcing	force	VERB
ejpam-3914	54	38	connected	connected	ADJ
ejpam-3914	54	39	domination	domination	NOUN
ejpam-3914	54	40	number	number	NOUN
ejpam-3914	54	41	under	under	ADP
ejpam-3914	54	42	the	the	DET
ejpam-3914	54	43	lexicographic	lexicographic	ADJ
ejpam-3914	54	44	product	product	NOUN
ejpam-3914	54	45	of	of	ADP
ejpam-3914	54	46	graphs	graph	NOUN
ejpam-3914	54	47	[	[	X
ejpam-3914	54	48	8	8	NUM
ejpam-3914	54	49	]	]	PUNCT
ejpam-3914	54	50	,	,	PUNCT
ejpam-3914	54	51	forcing	force	VERB
ejpam-3914	54	52	independent	independent	ADJ
ejpam-3914	54	53	domination	domination	NOUN
ejpam-3914	54	54	number	number	NOUN
ejpam-3914	54	55	of	of	ADP
ejpam-3914	54	56	a	a	DET
ejpam-3914	54	57	graph	graph	NOUN
ejpam-3914	54	58	[	[	X
ejpam-3914	54	59	4	4	NUM
ejpam-3914	54	60	]	]	PUNCT
ejpam-3914	54	61	,	,	PUNCT
ejpam-3914	54	62	and	and	CCONJ
ejpam-3914	54	63	a	a	DET
ejpam-3914	54	64	-	-	PUNCT
ejpam-3914	54	65	differential	differential	NOUN
ejpam-3914	54	66	of	of	ADP
ejpam-3914	54	67	graphs	graph	NOUN
ejpam-3914	54	68	[	[	X
ejpam-3914	54	69	3	3	NUM
ejpam-3914	54	70	]	]	PUNCT
ejpam-3914	54	71	.	.	PUNCT
ejpam-3914	55	1	also	also	ADV
ejpam-3914	55	2	,	,	PUNCT
ejpam-3914	55	3	armada	armada	PROPN
ejpam-3914	56	1	[	[	X
ejpam-3914	56	2	2	2	X
ejpam-3914	56	3	]	]	PUNCT
ejpam-3914	56	4	studied	study	VERB
ejpam-3914	56	5	the	the	DET
ejpam-3914	56	6	forcing	force	VERB
ejpam-3914	56	7	total	total	ADJ
ejpam-3914	56	8	dr	dr	PROPN
ejpam-3914	56	9	-	-	PUNCT
ejpam-3914	56	10	power	power	NOUN
ejpam-3914	56	11	domination	domination	NOUN
ejpam-3914	56	12	of	of	ADP
ejpam-3914	56	13	graphs	graph	NOUN
ejpam-3914	56	14	under	under	ADP
ejpam-3914	56	15	some	some	DET
ejpam-3914	56	16	binary	binary	ADJ
ejpam-3914	56	17	operations	operation	NOUN
ejpam-3914	56	18	.	.	PUNCT
ejpam-3914	57	1	c.	c.	PROPN
ejpam-3914	57	2	armada	armada	PROPN
ejpam-3914	57	3	/	/	SYM
ejpam-3914	57	4	eur	eur	PROPN
ejpam-3914	57	5	.	.	PUNCT
ejpam-3914	58	1	j.	j.	PROPN
ejpam-3914	58	2	pure	pure	PROPN
ejpam-3914	58	3	appl	appl	PROPN
ejpam-3914	58	4	.	.	PROPN
ejpam-3914	58	5	math	math	PROPN
ejpam-3914	58	6	,	,	PUNCT
ejpam-3914	58	7	14	14	NUM
ejpam-3914	58	8	(	(	PUNCT
ejpam-3914	58	9	2	2	NUM
ejpam-3914	58	10	)	)	PUNCT
ejpam-3914	58	11	(	(	PUNCT
ejpam-3914	58	12	2021	2021	NUM
ejpam-3914	58	13	)	)	PUNCT
ejpam-3914	58	14	,	,	PUNCT
ejpam-3914	58	15	451	451	NUM
ejpam-3914	58	16	-	-	SYM
ejpam-3914	58	17	470	470	NUM
ejpam-3914	58	18	453	453	NUM
ejpam-3914	58	19	illustration	illustration	NOUN
ejpam-3914	58	20	1.1	1.1	NUM
ejpam-3914	58	21	.	.	PUNCT
ejpam-3914	59	1	consider	consider	VERB
ejpam-3914	59	2	the	the	DET
ejpam-3914	59	3	cycle	cycle	NOUN
ejpam-3914	59	4	graph	graph	NOUN
ejpam-3914	59	5	c5	c5	PROPN
ejpam-3914	59	6	=	=	PUNCT
ejpam-3914	60	1	[	[	X
ejpam-3914	60	2	u1	u1	NOUN
ejpam-3914	60	3	,	,	PUNCT
ejpam-3914	60	4	u2	u2	NOUN
ejpam-3914	60	5	,	,	PUNCT
ejpam-3914	60	6	u3	u3	PROPN
ejpam-3914	60	7	,	,	PUNCT
ejpam-3914	60	8	u4	u4	PROPN
ejpam-3914	60	9	,	,	PUNCT
ejpam-3914	60	10	u5	u5	PROPN
ejpam-3914	60	11	,	,	PUNCT
ejpam-3914	60	12	u1	u1	NOUN
ejpam-3914	60	13	]	]	PUNCT
ejpam-3914	60	14	.	.	PUNCT
ejpam-3914	61	1	let	let	VERB
ejpam-3914	61	2	p	p	PRON
ejpam-3914	61	3	⊆	⊆	NUM
ejpam-3914	61	4	v	v	NOUN
ejpam-3914	61	5	(	(	PUNCT
ejpam-3914	61	6	c5	c5	PROPN
ejpam-3914	61	7	)	)	PUNCT
ejpam-3914	61	8	.	.	PUNCT
ejpam-3914	62	1	pick	pick	VERB
ejpam-3914	62	2	u2	u2	NOUN
ejpam-3914	62	3	,	,	PUNCT
ejpam-3914	62	4	u3	u3	NOUN
ejpam-3914	62	5	∈	∈	PROPN
ejpam-3914	62	6	p	p	PROPN
ejpam-3914	62	7	.	.	PUNCT
ejpam-3914	63	1	then	then	ADV
ejpam-3914	63	2	u1u2	u1u2	NOUN
ejpam-3914	63	3	,	,	PUNCT
ejpam-3914	63	4	u2u3	u2u3	X
ejpam-3914	63	5	and	and	CCONJ
ejpam-3914	63	6	u3u4	u3u4	NOUN
ejpam-3914	63	7	are	be	AUX
ejpam-3914	63	8	directly	directly	ADV
ejpam-3914	63	9	observed	observe	VERB
ejpam-3914	63	10	edges	edge	NOUN
ejpam-3914	63	11	in	in	ADP
ejpam-3914	63	12	c5	c5	PROPN
ejpam-3914	63	13	.	.	PUNCT
ejpam-3914	64	1	clearly	clearly	ADV
ejpam-3914	64	2	,	,	PUNCT
ejpam-3914	64	3	u1	u1	PROPN
ejpam-3914	64	4	,	,	PUNCT
ejpam-3914	64	5	u2	u2	NOUN
ejpam-3914	64	6	,	,	PUNCT
ejpam-3914	64	7	u3	u3	NOUN
ejpam-3914	64	8	and	and	CCONJ
ejpam-3914	64	9	u4	u4	PROPN
ejpam-3914	64	10	are	be	AUX
ejpam-3914	64	11	incident	incident	NOUN
ejpam-3914	64	12	to	to	ADP
ejpam-3914	64	13	a	a	DET
ejpam-3914	64	14	directly	directly	ADV
ejpam-3914	64	15	observed	observe	VERB
ejpam-3914	64	16	edge	edge	NOUN
ejpam-3914	64	17	,	,	PUNCT
ejpam-3914	64	18	and	and	CCONJ
ejpam-3914	64	19	so	so	ADV
ejpam-3914	64	20	,	,	PUNCT
ejpam-3914	64	21	u1	u1	NOUN
ejpam-3914	64	22	,	,	PUNCT
ejpam-3914	64	23	u2	u2	NOUN
ejpam-3914	64	24	,	,	PUNCT
ejpam-3914	64	25	u3	u3	NOUN
ejpam-3914	64	26	and	and	CCONJ
ejpam-3914	64	27	u4	u4	PROPN
ejpam-3914	64	28	are	be	AUX
ejpam-3914	64	29	directly	directly	ADV
ejpam-3914	64	30	observed	observe	VERB
ejpam-3914	64	31	vertices	vertex	NOUN
ejpam-3914	64	32	.	.	PUNCT
ejpam-3914	65	1	the	the	DET
ejpam-3914	65	2	edges	edge	NOUN
ejpam-3914	65	3	u1u5	u1u5	NOUN
ejpam-3914	65	4	and	and	CCONJ
ejpam-3914	65	5	u4u5	u4u5	PRON
ejpam-3914	65	6	are	be	AUX
ejpam-3914	65	7	remotely	remotely	ADV
ejpam-3914	65	8	observed	observe	VERB
ejpam-3914	65	9	edges	edge	NOUN
ejpam-3914	65	10	since	since	SCONJ
ejpam-3914	65	11	u1	u1	NOUN
ejpam-3914	65	12	,	,	PUNCT
ejpam-3914	65	13	u4	u4	PROPN
ejpam-3914	65	14	,	,	PUNCT
ejpam-3914	65	15	u5	u5	PROPN
ejpam-3914	65	16	/∈	/∈	PUNCT
ejpam-3914	65	17	p	p	NOUN
ejpam-3914	66	1	and	and	CCONJ
ejpam-3914	66	2	there	there	PRON
ejpam-3914	66	3	are	be	VERB
ejpam-3914	66	4	k	k	PROPN
ejpam-3914	66	5	=	=	SYM
ejpam-3914	66	6	2	2	NUM
ejpam-3914	66	7	incident	incident	NOUN
ejpam-3914	66	8	edges	edge	NOUN
ejpam-3914	66	9	to	to	ADP
ejpam-3914	66	10	the	the	DET
ejpam-3914	66	11	vertices	vertex	NOUN
ejpam-3914	66	12	u1	u1	NOUN
ejpam-3914	66	13	and	and	CCONJ
ejpam-3914	66	14	u4	u4	PROPN
ejpam-3914	66	15	such	such	ADJ
ejpam-3914	66	16	that	that	SCONJ
ejpam-3914	66	17	k	k	PROPN
ejpam-3914	67	1	−	−	NOUN
ejpam-3914	67	2	1	1	NUM
ejpam-3914	67	3	=	=	SYM
ejpam-3914	67	4	2−	2−	NUM
ejpam-3914	67	5	1	1	NUM
ejpam-3914	67	6	=	=	SYM
ejpam-3914	67	7	1	1	NUM
ejpam-3914	67	8	edge	edge	NOUN
ejpam-3914	67	9	is	be	AUX
ejpam-3914	67	10	directly	directly	ADV
ejpam-3914	67	11	observed	observe	VERB
ejpam-3914	67	12	by	by	ADP
ejpam-3914	67	13	p	p	PRON
ejpam-3914	67	14	which	which	PRON
ejpam-3914	67	15	are	be	AUX
ejpam-3914	67	16	u1u2	u1u2	X
ejpam-3914	67	17	and	and	CCONJ
ejpam-3914	67	18	u3u4	u3u4	NOUN
ejpam-3914	67	19	.	.	PROPN
ejpam-3914	68	1	since	since	SCONJ
ejpam-3914	68	2	u5	u5	PROPN
ejpam-3914	68	3	is	be	AUX
ejpam-3914	68	4	incident	incident	NOUN
ejpam-3914	68	5	to	to	ADP
ejpam-3914	68	6	a	a	DET
ejpam-3914	68	7	remotely	remotely	ADV
ejpam-3914	68	8	observed	observe	VERB
ejpam-3914	68	9	edge	edge	NOUN
ejpam-3914	68	10	u1u5	u1u5	ADP
ejpam-3914	68	11	or	or	CCONJ
ejpam-3914	68	12	u4u5	u4u5	PROPN
ejpam-3914	68	13	,	,	PUNCT
ejpam-3914	68	14	then	then	ADV
ejpam-3914	68	15	u5	u5	PROPN
ejpam-3914	68	16	is	be	AUX
ejpam-3914	68	17	a	a	DET
ejpam-3914	68	18	remotely	remotely	ADV
ejpam-3914	68	19	observed	observe	VERB
ejpam-3914	68	20	vertex	vertex	NOUN
ejpam-3914	68	21	.	.	PUNCT
ejpam-3914	69	1	clearly	clearly	ADV
ejpam-3914	69	2	,	,	PUNCT
ejpam-3914	69	3	op	op	NOUN
ejpam-3914	69	4	v	v	NOUN
ejpam-3914	69	5	(	(	PUNCT
ejpam-3914	69	6	c5	c5	PROPN
ejpam-3914	69	7	)	)	PUNCT
ejpam-3914	69	8	=	=	SYM
ejpam-3914	69	9	v	v	X
ejpam-3914	69	10	(	(	PUNCT
ejpam-3914	69	11	c5	c5	PROPN
ejpam-3914	69	12	)	)	PUNCT
ejpam-3914	69	13	and	and	CCONJ
ejpam-3914	69	14	op	op	NOUN
ejpam-3914	69	15	e(c5	e(c5	ADJ
ejpam-3914	69	16	)	)	PUNCT
ejpam-3914	69	17	=	=	SYM
ejpam-3914	69	18	e(c5	e(c5	NOUN
ejpam-3914	69	19	)	)	PUNCT
ejpam-3914	69	20	,	,	PUNCT
ejpam-3914	69	21	that	that	ADV
ejpam-3914	69	22	is	is	ADV
ejpam-3914	69	23	,	,	PUNCT
ejpam-3914	69	24	p	p	PRON
ejpam-3914	69	25	is	be	AUX
ejpam-3914	69	26	a	a	DET
ejpam-3914	69	27	dr	dr	ADJ
ejpam-3914	69	28	-	-	PUNCT
ejpam-3914	69	29	power	power	NOUN
ejpam-3914	69	30	dominating	dominating	NOUN
ejpam-3914	69	31	set	set	NOUN
ejpam-3914	69	32	of	of	ADP
ejpam-3914	69	33	c5	c5	PROPN
ejpam-3914	69	34	.	.	PUNCT
ejpam-3914	70	1	since	since	SCONJ
ejpam-3914	70	2	the	the	DET
ejpam-3914	70	3	induced	induced	ADJ
ejpam-3914	70	4	subgraph	subgraph	NOUN
ejpam-3914	70	5	〈	〈	PROPN
ejpam-3914	70	6	p	p	PROPN
ejpam-3914	70	7	〉	〉	PROPN
ejpam-3914	70	8	has	have	VERB
ejpam-3914	70	9	no	no	DET
ejpam-3914	70	10	isolated	isolated	ADJ
ejpam-3914	70	11	vertex	vertex	NOUN
ejpam-3914	70	12	,	,	PUNCT
ejpam-3914	70	13	p	p	PROPN
ejpam-3914	70	14	is	be	AUX
ejpam-3914	70	15	a	a	DET
ejpam-3914	70	16	total	total	ADJ
ejpam-3914	70	17	dr	dr	ADJ
ejpam-3914	70	18	-	-	PUNCT
ejpam-3914	70	19	power	power	NOUN
ejpam-3914	70	20	dominating	dominating	NOUN
ejpam-3914	70	21	set	set	NOUN
ejpam-3914	70	22	of	of	ADP
ejpam-3914	70	23	c5	c5	PROPN
ejpam-3914	70	24	.	.	PUNCT
ejpam-3914	71	1	note	note	VERB
ejpam-3914	71	2	that	that	SCONJ
ejpam-3914	71	3	for	for	ADP
ejpam-3914	71	4	any	any	DET
ejpam-3914	71	5	connected	connected	ADJ
ejpam-3914	71	6	graph	graph	NOUN
ejpam-3914	71	7	g	g	NOUN
ejpam-3914	71	8	,	,	PUNCT
ejpam-3914	71	9	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	71	10	(	(	PUNCT
ejpam-3914	71	11	g	g	NOUN
ejpam-3914	71	12	)	)	PUNCT
ejpam-3914	71	13	≥	≥	NOUN
ejpam-3914	71	14	2	2	NUM
ejpam-3914	71	15	and	and	CCONJ
ejpam-3914	71	16	since	since	SCONJ
ejpam-3914	71	17	|p	|p	X
ejpam-3914	71	18	|	|	ADV
ejpam-3914	71	19	=	=	SYM
ejpam-3914	71	20	2	2	NUM
ejpam-3914	71	21	,	,	PUNCT
ejpam-3914	71	22	p	p	PRON
ejpam-3914	71	23	is	be	AUX
ejpam-3914	71	24	a	a	DET
ejpam-3914	71	25	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	71	26	-set	-set	PROPN
ejpam-3914	71	27	of	of	ADP
ejpam-3914	71	28	c5	c5	PROPN
ejpam-3914	71	29	and	and	CCONJ
ejpam-3914	71	30	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	71	31	(	(	PUNCT
ejpam-3914	71	32	c5	c5	PROPN
ejpam-3914	71	33	)	)	PUNCT
ejpam-3914	71	34	=	=	SYM
ejpam-3914	72	1	2	2	X
ejpam-3914	72	2	.	.	PUNCT
ejpam-3914	72	3	clearly	clearly	ADV
ejpam-3914	72	4	,	,	PUNCT
ejpam-3914	72	5	any	any	DET
ejpam-3914	72	6	pair	pair	NOUN
ejpam-3914	72	7	of	of	ADP
ejpam-3914	72	8	adjacent	adjacent	ADJ
ejpam-3914	72	9	vertices	vertex	NOUN
ejpam-3914	72	10	in	in	ADP
ejpam-3914	72	11	c5	c5	PROPN
ejpam-3914	72	12	is	be	AUX
ejpam-3914	72	13	a	a	DET
ejpam-3914	72	14	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	72	15	-set	-set	PROPN
ejpam-3914	72	16	of	of	ADP
ejpam-3914	72	17	c5	c5	PROPN
ejpam-3914	72	18	,	,	PUNCT
ejpam-3914	72	19	that	that	ADV
ejpam-3914	72	20	is	is	ADV
ejpam-3914	72	21	,	,	PUNCT
ejpam-3914	72	22	s1	s1	PROPN
ejpam-3914	72	23	=	=	SYM
ejpam-3914	72	24	{	{	PUNCT
ejpam-3914	72	25	u1	u1	NOUN
ejpam-3914	72	26	,	,	PUNCT
ejpam-3914	72	27	u2	u2	PROPN
ejpam-3914	72	28	}	}	PUNCT
ejpam-3914	72	29	,	,	PUNCT
ejpam-3914	72	30	s2	s2	NOUN
ejpam-3914	72	31	=	=	PUNCT
ejpam-3914	73	1	p	p	NOUN
ejpam-3914	73	2	=	=	X
ejpam-3914	73	3	{	{	PUNCT
ejpam-3914	73	4	u2	u2	NOUN
ejpam-3914	73	5	,	,	PUNCT
ejpam-3914	73	6	u3	u3	NOUN
ejpam-3914	73	7	}	}	PUNCT
ejpam-3914	73	8	,	,	PUNCT
ejpam-3914	73	9	s3	s3	PROPN
ejpam-3914	73	10	=	=	SYM
ejpam-3914	73	11	{	{	PUNCT
ejpam-3914	73	12	u3	u3	PROPN
ejpam-3914	73	13	,	,	PUNCT
ejpam-3914	73	14	u4	u4	PROPN
ejpam-3914	73	15	}	}	PUNCT
ejpam-3914	73	16	,	,	PUNCT
ejpam-3914	73	17	s4	s4	PROPN
ejpam-3914	73	18	=	=	SYM
ejpam-3914	73	19	{	{	PUNCT
ejpam-3914	73	20	u4	u4	PROPN
ejpam-3914	73	21	,	,	PUNCT
ejpam-3914	73	22	u5	u5	PROPN
ejpam-3914	73	23	}	}	PUNCT
ejpam-3914	73	24	,	,	PUNCT
ejpam-3914	73	25	s5	s5	X
ejpam-3914	73	26	=	=	PUNCT
ejpam-3914	73	27	{	{	PUNCT
ejpam-3914	73	28	u5	u5	PROPN
ejpam-3914	73	29	,	,	PUNCT
ejpam-3914	73	30	u1	u1	NOUN
ejpam-3914	73	31	}	}	PUNCT
ejpam-3914	73	32	,	,	PUNCT
ejpam-3914	73	33	are	be	AUX
ejpam-3914	73	34	the	the	DET
ejpam-3914	73	35	only	only	ADJ
ejpam-3914	73	36	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	73	37	-sets	-set	NOUN
ejpam-3914	73	38	of	of	ADP
ejpam-3914	73	39	c5	c5	PROPN
ejpam-3914	73	40	.	.	PUNCT
ejpam-3914	74	1	clearly	clearly	ADV
ejpam-3914	74	2	,	,	PUNCT
ejpam-3914	74	3	for	for	ADP
ejpam-3914	74	4	all	all	DET
ejpam-3914	74	5	i	i	PRON
ejpam-3914	74	6	=	=	NOUN
ejpam-3914	74	7	1	1	NUM
ejpam-3914	74	8	,	,	PUNCT
ejpam-3914	74	9	2	2	NUM
ejpam-3914	74	10	,	,	PUNCT
ejpam-3914	74	11	.	.	PUNCT
ejpam-3914	74	12	.	.	PUNCT
ejpam-3914	74	13	.	.	PUNCT
ejpam-3914	75	1	,	,	PUNCT
ejpam-3914	75	2	5	5	NUM
ejpam-3914	75	3	,	,	PUNCT
ejpam-3914	75	4	no	no	DET
ejpam-3914	75	5	subset	subset	NOUN
ejpam-3914	75	6	{	{	PUNCT
ejpam-3914	75	7	ui	ui	NOUN
ejpam-3914	75	8	}	}	PUNCT
ejpam-3914	75	9	is	be	AUX
ejpam-3914	75	10	contained	contain	VERB
ejpam-3914	75	11	in	in	ADP
ejpam-3914	75	12	a	a	DET
ejpam-3914	75	13	unique	unique	ADJ
ejpam-3914	75	14	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	75	15	-set	-set	PUNCT
ejpam-3914	75	16	sj	sj	VERB
ejpam-3914	75	17	for	for	ADP
ejpam-3914	75	18	all	all	DET
ejpam-3914	75	19	j	j	NOUN
ejpam-3914	75	20	=	=	SYM
ejpam-3914	75	21	1	1	NUM
ejpam-3914	75	22	,	,	PUNCT
ejpam-3914	75	23	2	2	NUM
ejpam-3914	75	24	,	,	PUNCT
ejpam-3914	75	25	.	.	PUNCT
ejpam-3914	75	26	.	.	PUNCT
ejpam-3914	76	1	.	.	PUNCT
ejpam-3914	77	1	,	,	PUNCT
ejpam-3914	78	1	5	5	NUM
ejpam-3914	78	2	and	and	CCONJ
ejpam-3914	78	3	so	so	ADV
ejpam-3914	78	4	,	,	PUNCT
ejpam-3914	78	5	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	78	6	(	(	PUNCT
ejpam-3914	78	7	sj	sj	NOUN
ejpam-3914	78	8	)	)	PUNCT
ejpam-3914	78	9	6=	6=	ADP
ejpam-3914	78	10	1	1	X
ejpam-3914	78	11	.	.	PUNCT
ejpam-3914	79	1	therefore	therefore	ADV
ejpam-3914	79	2	,	,	PUNCT
ejpam-3914	79	3	for	for	ADP
ejpam-3914	79	4	all	all	DET
ejpam-3914	79	5	j	j	NOUN
ejpam-3914	79	6	=	=	SYM
ejpam-3914	79	7	1	1	NUM
ejpam-3914	79	8	,	,	PUNCT
ejpam-3914	79	9	2	2	NUM
ejpam-3914	79	10	,	,	PUNCT
ejpam-3914	79	11	.	.	PUNCT
ejpam-3914	79	12	.	.	PUNCT
ejpam-3914	79	13	.	.	PUNCT
ejpam-3914	80	1	,	,	PUNCT
ejpam-3914	80	2	5	5	NUM
ejpam-3914	80	3	,	,	PUNCT
ejpam-3914	80	4	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	80	5	(	(	PUNCT
ejpam-3914	80	6	sj	sj	NOUN
ejpam-3914	80	7	)	)	PUNCT
ejpam-3914	80	8	=	=	SYM
ejpam-3914	80	9	|sj	|sj	NUM
ejpam-3914	80	10	|	|	NOUN
ejpam-3914	80	11	=	=	SYM
ejpam-3914	80	12	2	2	NUM
ejpam-3914	80	13	=	=	NOUN
ejpam-3914	80	14	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	80	15	(	(	PUNCT
ejpam-3914	80	16	c5	c5	PROPN
ejpam-3914	80	17	)	)	PUNCT
ejpam-3914	80	18	.	.	PUNCT
ejpam-3914	81	1	2	2	X
ejpam-3914	81	2	.	.	X
ejpam-3914	81	3	known	know	VERB
ejpam-3914	81	4	results	result	NOUN
ejpam-3914	81	5	this	this	DET
ejpam-3914	81	6	section	section	NOUN
ejpam-3914	81	7	contains	contain	VERB
ejpam-3914	81	8	known	know	VERB
ejpam-3914	81	9	results	result	NOUN
ejpam-3914	81	10	involving	involve	VERB
ejpam-3914	81	11	dr	dr	PROPN
ejpam-3914	81	12	-	-	PUNCT
ejpam-3914	81	13	power	power	NOUN
ejpam-3914	81	14	domination	domination	NOUN
ejpam-3914	81	15	,	,	PUNCT
ejpam-3914	81	16	total	total	ADJ
ejpam-3914	81	17	domination	domination	NOUN
ejpam-3914	81	18	and	and	CCONJ
ejpam-3914	81	19	total	total	ADJ
ejpam-3914	81	20	dr	dr	PROPN
ejpam-3914	81	21	-	-	PUNCT
ejpam-3914	81	22	power	power	NOUN
ejpam-3914	81	23	domination	domination	NOUN
ejpam-3914	81	24	numbers	number	NOUN
ejpam-3914	81	25	of	of	ADP
ejpam-3914	81	26	a	a	DET
ejpam-3914	81	27	graph	graph	NOUN
ejpam-3914	81	28	g	g	NOUN
ejpam-3914	81	29	that	that	PRON
ejpam-3914	81	30	are	be	AUX
ejpam-3914	81	31	useful	useful	ADJ
ejpam-3914	81	32	in	in	ADP
ejpam-3914	81	33	proving	prove	VERB
ejpam-3914	81	34	the	the	DET
ejpam-3914	81	35	main	main	ADJ
ejpam-3914	81	36	results	result	NOUN
ejpam-3914	81	37	of	of	ADP
ejpam-3914	81	38	this	this	DET
ejpam-3914	81	39	study	study	NOUN
ejpam-3914	81	40	.	.	PUNCT
ejpam-3914	82	1	remark	remark	VERB
ejpam-3914	82	2	2.1	2.1	NUM
ejpam-3914	82	3	.	.	PUNCT
ejpam-3914	83	1	[	[	X
ejpam-3914	83	2	6	6	NUM
ejpam-3914	83	3	]	]	PUNCT
ejpam-3914	83	4	for	for	ADP
ejpam-3914	83	5	any	any	DET
ejpam-3914	83	6	graph	graph	NOUN
ejpam-3914	83	7	g	g	NOUN
ejpam-3914	83	8	without	without	ADP
ejpam-3914	83	9	isolated	isolated	ADJ
ejpam-3914	83	10	vertices	vertex	NOUN
ejpam-3914	83	11	,	,	PUNCT
ejpam-3914	83	12	γ∗pw(g	γ∗pw(g	ADJ
ejpam-3914	83	13	)	)	PUNCT
ejpam-3914	83	14	≤	≤	NOUN
ejpam-3914	83	15	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	83	16	(	(	PUNCT
ejpam-3914	83	17	g	g	NOUN
ejpam-3914	83	18	)	)	PUNCT
ejpam-3914	83	19	≤	≤	NOUN
ejpam-3914	83	20	γt(g	γt(g	PUNCT
ejpam-3914	83	21	)	)	PUNCT
ejpam-3914	83	22	.	.	PUNCT
ejpam-3914	83	23	theorem	theorem	VERB
ejpam-3914	83	24	2.2	2.2	NUM
ejpam-3914	83	25	.	.	PUNCT
ejpam-3914	84	1	[	[	X
ejpam-3914	84	2	6	6	NUM
ejpam-3914	84	3	]	]	PUNCT
ejpam-3914	84	4	let	let	VERB
ejpam-3914	84	5	n	n	PRON
ejpam-3914	84	6	be	be	AUX
ejpam-3914	84	7	a	a	DET
ejpam-3914	84	8	positive	positive	ADJ
ejpam-3914	84	9	integer	integer	NOUN
ejpam-3914	84	10	with	with	ADP
ejpam-3914	84	11	n	n	PRON
ejpam-3914	84	12	≥	≥	NUM
ejpam-3914	84	13	5	5	NUM
ejpam-3914	84	14	.	.	PUNCT
ejpam-3914	85	1	then	then	ADV
ejpam-3914	85	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	85	3	(	(	PUNCT
ejpam-3914	85	4	pn	pn	NOUN
ejpam-3914	85	5	)	)	PUNCT
ejpam-3914	85	6	=	=	SYM
ejpam-3914	85	7			NUM
ejpam-3914	85	8	2n	2n	NUM
ejpam-3914	85	9	5	5	NUM
ejpam-3914	85	10	,	,	PUNCT
ejpam-3914	85	11	n	n	PRON
ejpam-3914	85	12	≡	≡	PROPN
ejpam-3914	85	13	0(mod	0(mod	NOUN
ejpam-3914	85	14	5	5	X
ejpam-3914	85	15	)	)	PUNCT
ejpam-3914	85	16	2n−2	2n−2	NUM
ejpam-3914	85	17	5	5	NUM
ejpam-3914	85	18	,	,	PUNCT
ejpam-3914	85	19	n	n	PRON
ejpam-3914	85	20	≡	≡	PROPN
ejpam-3914	85	21	1(mod	1(mod	NUM
ejpam-3914	85	22	5	5	X
ejpam-3914	85	23	)	)	PUNCT
ejpam-3914	85	24	2n+1	2n+1	NOUN
ejpam-3914	85	25	5	5	NUM
ejpam-3914	85	26	,	,	PUNCT
ejpam-3914	85	27	n	n	PRON
ejpam-3914	85	28	≡	≡	PROPN
ejpam-3914	85	29	2(mod	2(mod	NUM
ejpam-3914	85	30	5	5	X
ejpam-3914	85	31	)	)	PUNCT
ejpam-3914	85	32	2n+4	2n+4	PROPN
ejpam-3914	85	33	5	5	NUM
ejpam-3914	85	34	,	,	PUNCT
ejpam-3914	85	35	n	n	PRON
ejpam-3914	85	36	≡	≡	PROPN
ejpam-3914	85	37	3(mod	3(mod	NUM
ejpam-3914	85	38	5	5	NUM
ejpam-3914	85	39	)	)	PUNCT
ejpam-3914	85	40	2n+2	2n+2	NUM
ejpam-3914	85	41	5	5	NUM
ejpam-3914	85	42	,	,	PUNCT
ejpam-3914	85	43	n	n	PRON
ejpam-3914	85	44	≡	≡	PROPN
ejpam-3914	85	45	4(mod	4(mod	NUM
ejpam-3914	85	46	5	5	NUM
ejpam-3914	85	47	)	)	PUNCT
ejpam-3914	85	48	theorem	theorem	VERB
ejpam-3914	85	49	2.3	2.3	NUM
ejpam-3914	85	50	.	.	PUNCT
ejpam-3914	86	1	[	[	X
ejpam-3914	86	2	6	6	NUM
ejpam-3914	86	3	]	]	PUNCT
ejpam-3914	86	4	let	let	VERB
ejpam-3914	86	5	n	n	PRON
ejpam-3914	86	6	be	be	AUX
ejpam-3914	86	7	a	a	DET
ejpam-3914	86	8	positive	positive	ADJ
ejpam-3914	86	9	integer	integer	NOUN
ejpam-3914	86	10	with	with	ADP
ejpam-3914	86	11	n	n	PRON
ejpam-3914	86	12	≥	≥	NUM
ejpam-3914	86	13	5	5	NUM
ejpam-3914	86	14	.	.	PUNCT
ejpam-3914	87	1	then	then	ADV
ejpam-3914	87	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	87	3	(	(	PUNCT
ejpam-3914	87	4	cn	cn	PROPN
ejpam-3914	87	5	)	)	PUNCT
ejpam-3914	87	6	=	=	SYM
ejpam-3914	87	7			NUM
ejpam-3914	87	8	2n	2n	NUM
ejpam-3914	87	9	5	5	NUM
ejpam-3914	87	10	,	,	PUNCT
ejpam-3914	87	11	n	n	PRON
ejpam-3914	87	12	≡	≡	PROPN
ejpam-3914	87	13	0(mod	0(mod	NOUN
ejpam-3914	87	14	5	5	X
ejpam-3914	87	15	)	)	PUNCT
ejpam-3914	87	16	2n+3	2n+3	NOUN
ejpam-3914	87	17	5	5	NUM
ejpam-3914	87	18	,	,	PUNCT
ejpam-3914	87	19	n	n	PRON
ejpam-3914	87	20	≡	≡	PROPN
ejpam-3914	87	21	1(mod	1(mod	NUM
ejpam-3914	87	22	5	5	X
ejpam-3914	87	23	)	)	PUNCT
ejpam-3914	87	24	2n+6	2n+6	NOUN
ejpam-3914	87	25	5	5	NUM
ejpam-3914	87	26	,	,	PUNCT
ejpam-3914	87	27	n	n	PRON
ejpam-3914	87	28	≡	≡	PROPN
ejpam-3914	87	29	2(mod	2(mod	NUM
ejpam-3914	87	30	5	5	X
ejpam-3914	87	31	)	)	PUNCT
ejpam-3914	87	32	2n+4	2n+4	PROPN
ejpam-3914	87	33	5	5	NUM
ejpam-3914	87	34	,	,	PUNCT
ejpam-3914	87	35	n	n	PRON
ejpam-3914	87	36	≡	≡	PROPN
ejpam-3914	87	37	3(mod	3(mod	NUM
ejpam-3914	87	38	5	5	NUM
ejpam-3914	87	39	)	)	PUNCT
ejpam-3914	87	40	2n+2	2n+2	NUM
ejpam-3914	87	41	5	5	NUM
ejpam-3914	87	42	,	,	PUNCT
ejpam-3914	87	43	n	n	PRON
ejpam-3914	87	44	≡	≡	PROPN
ejpam-3914	87	45	4(mod	4(mod	NUM
ejpam-3914	87	46	5	5	X
ejpam-3914	87	47	)	)	PUNCT
ejpam-3914	87	48	c.	c.	PROPN
ejpam-3914	87	49	armada	armada	PROPN
ejpam-3914	87	50	/	/	SYM
ejpam-3914	87	51	eur	eur	PROPN
ejpam-3914	87	52	.	.	PUNCT
ejpam-3914	88	1	j.	j.	PROPN
ejpam-3914	88	2	pure	pure	PROPN
ejpam-3914	88	3	appl	appl	PROPN
ejpam-3914	88	4	.	.	PROPN
ejpam-3914	88	5	math	math	PROPN
ejpam-3914	88	6	,	,	PUNCT
ejpam-3914	88	7	14	14	NUM
ejpam-3914	88	8	(	(	PUNCT
ejpam-3914	88	9	2	2	NUM
ejpam-3914	88	10	)	)	PUNCT
ejpam-3914	88	11	(	(	PUNCT
ejpam-3914	88	12	2021	2021	NUM
ejpam-3914	88	13	)	)	PUNCT
ejpam-3914	88	14	,	,	PUNCT
ejpam-3914	88	15	451	451	NUM
ejpam-3914	88	16	-	-	SYM
ejpam-3914	88	17	470	470	NUM
ejpam-3914	88	18	454	454	NUM
ejpam-3914	88	19	proposition	proposition	NOUN
ejpam-3914	88	20	2.4	2.4	NUM
ejpam-3914	88	21	.	.	PUNCT
ejpam-3914	89	1	[	[	X
ejpam-3914	89	2	1	1	X
ejpam-3914	89	3	]	]	PUNCT
ejpam-3914	89	4	the	the	DET
ejpam-3914	89	5	total	total	ADJ
ejpam-3914	89	6	domination	domination	NOUN
ejpam-3914	89	7	number	number	NOUN
ejpam-3914	89	8	of	of	ADP
ejpam-3914	89	9	a	a	DET
ejpam-3914	89	10	cycle	cycle	NOUN
ejpam-3914	89	11	cn	cn	NOUN
ejpam-3914	89	12	or	or	CCONJ
ejpam-3914	89	13	a	a	DET
ejpam-3914	89	14	path	path	NOUN
ejpam-3914	89	15	pn	pn	NOUN
ejpam-3914	89	16	on	on	ADP
ejpam-3914	89	17	n	n	PRON
ejpam-3914	89	18	≥	≥	NUM
ejpam-3914	89	19	3	3	NUM
ejpam-3914	89	20	vertices	vertex	NOUN
ejpam-3914	89	21	is	be	AUX
ejpam-3914	89	22	given	give	VERB
ejpam-3914	89	23	by	by	ADP
ejpam-3914	89	24	γt(cn	γt(cn	PROPN
ejpam-3914	89	25	)	)	PUNCT
ejpam-3914	90	1	=	=	SYM
ejpam-3914	90	2	γt(pn	γt(pn	NOUN
ejpam-3914	90	3	)	)	PUNCT
ejpam-3914	90	4	=	=	SYM
ejpam-3914	90	5			PROPN
ejpam-3914	90	6	n	n	ADV
ejpam-3914	90	7	2	2	NUM
ejpam-3914	90	8	,	,	PUNCT
ejpam-3914	90	9	n	n	PRON
ejpam-3914	90	10	≡	≡	PROPN
ejpam-3914	90	11	0(mod	0(mod	NOUN
ejpam-3914	90	12	4	4	NUM
ejpam-3914	90	13	)	)	PUNCT
ejpam-3914	90	14	,	,	PUNCT
ejpam-3914	90	15	n+2	n+2	ADV
ejpam-3914	90	16	2	2	NUM
ejpam-3914	90	17	,	,	PUNCT
ejpam-3914	90	18	n	n	PRON
ejpam-3914	90	19	≡	≡	PROPN
ejpam-3914	90	20	2(mod	2(mod	NUM
ejpam-3914	90	21	4	4	NUM
ejpam-3914	90	22	)	)	PUNCT
ejpam-3914	90	23	,	,	PUNCT
ejpam-3914	90	24	n+1	n+1	PROPN
ejpam-3914	90	25	2	2	NUM
ejpam-3914	90	26	,	,	PUNCT
ejpam-3914	90	27	otherwise	otherwise	ADV
ejpam-3914	90	28	.	.	PUNCT
ejpam-3914	91	1	theorem	theorem	VERB
ejpam-3914	91	2	2.5	2.5	NUM
ejpam-3914	91	3	.	.	PUNCT
ejpam-3914	92	1	[	[	X
ejpam-3914	92	2	6	6	NUM
ejpam-3914	92	3	]	]	PUNCT
ejpam-3914	92	4	let	let	VERB
ejpam-3914	92	5	g	g	NOUN
ejpam-3914	92	6	and	and	CCONJ
ejpam-3914	92	7	h	h	NOUN
ejpam-3914	92	8	be	be	VERB
ejpam-3914	92	9	any	any	DET
ejpam-3914	92	10	graphs	graph	NOUN
ejpam-3914	92	11	.	.	PUNCT
ejpam-3914	93	1	then	then	ADV
ejpam-3914	93	2	p	p	X
ejpam-3914	93	3	⊆	⊆	NUM
ejpam-3914	93	4	v	v	NOUN
ejpam-3914	93	5	(	(	PUNCT
ejpam-3914	93	6	g+h	g+h	NOUN
ejpam-3914	93	7	)	)	PUNCT
ejpam-3914	93	8	is	be	AUX
ejpam-3914	93	9	a	a	DET
ejpam-3914	93	10	total	total	ADJ
ejpam-3914	93	11	dr	dr	ADJ
ejpam-3914	93	12	-	-	PUNCT
ejpam-3914	93	13	power	power	NOUN
ejpam-3914	93	14	dominating	dominating	NOUN
ejpam-3914	93	15	set	set	NOUN
ejpam-3914	93	16	of	of	ADP
ejpam-3914	93	17	g+h	g+h	PROPN
ejpam-3914	93	18	if	if	SCONJ
ejpam-3914	93	19	and	and	CCONJ
ejpam-3914	93	20	only	only	ADV
ejpam-3914	93	21	if	if	SCONJ
ejpam-3914	93	22	it	it	PRON
ejpam-3914	93	23	satisfies	satisfy	VERB
ejpam-3914	93	24	one	one	NUM
ejpam-3914	93	25	of	of	ADP
ejpam-3914	93	26	the	the	DET
ejpam-3914	93	27	following	following	ADJ
ejpam-3914	93	28	conditions	condition	NOUN
ejpam-3914	93	29	:	:	PUNCT
ejpam-3914	93	30	(	(	PUNCT
ejpam-3914	93	31	i	i	NOUN
ejpam-3914	93	32	)	)	PUNCT
ejpam-3914	93	33	p	p	PROPN
ejpam-3914	93	34	⊆	⊆	NUM
ejpam-3914	93	35	v	v	NOUN
ejpam-3914	93	36	(	(	PUNCT
ejpam-3914	93	37	g	g	NOUN
ejpam-3914	93	38	)	)	PUNCT
ejpam-3914	93	39	and	and	CCONJ
ejpam-3914	93	40	is	be	AUX
ejpam-3914	93	41	a	a	DET
ejpam-3914	93	42	total	total	ADJ
ejpam-3914	93	43	dominating	dominating	NOUN
ejpam-3914	93	44	set	set	NOUN
ejpam-3914	93	45	,	,	PUNCT
ejpam-3914	93	46	provided	provide	VERB
ejpam-3914	93	47	that	that	SCONJ
ejpam-3914	93	48	g	g	PROPN
ejpam-3914	93	49	is	be	AUX
ejpam-3914	93	50	a	a	DET
ejpam-3914	93	51	graph	graph	NOUN
ejpam-3914	93	52	with	with	ADP
ejpam-3914	93	53	no	no	DET
ejpam-3914	93	54	isolated	isolated	ADJ
ejpam-3914	93	55	vertex	vertex	NOUN
ejpam-3914	93	56	;	;	PUNCT
ejpam-3914	93	57	(	(	PUNCT
ejpam-3914	93	58	ii	ii	NOUN
ejpam-3914	93	59	)	)	PUNCT
ejpam-3914	93	60	p	p	NOUN
ejpam-3914	93	61	⊆	⊆	NUM
ejpam-3914	93	62	v	v	NOUN
ejpam-3914	93	63	(	(	PUNCT
ejpam-3914	93	64	h	h	NOUN
ejpam-3914	93	65	)	)	PUNCT
ejpam-3914	93	66	and	and	CCONJ
ejpam-3914	93	67	is	be	AUX
ejpam-3914	93	68	a	a	DET
ejpam-3914	93	69	total	total	ADJ
ejpam-3914	93	70	dominating	dominating	NOUN
ejpam-3914	93	71	set	set	NOUN
ejpam-3914	93	72	,	,	PUNCT
ejpam-3914	93	73	provided	provide	VERB
ejpam-3914	93	74	that	that	SCONJ
ejpam-3914	93	75	h	h	NOUN
ejpam-3914	93	76	is	be	AUX
ejpam-3914	93	77	a	a	DET
ejpam-3914	93	78	graph	graph	NOUN
ejpam-3914	93	79	with	with	ADP
ejpam-3914	93	80	no	no	DET
ejpam-3914	93	81	isolated	isolated	ADJ
ejpam-3914	93	82	vertex	vertex	NOUN
ejpam-3914	93	83	;	;	PUNCT
ejpam-3914	93	84	or	or	CCONJ
ejpam-3914	93	85	(	(	PUNCT
ejpam-3914	93	86	iii	iii	NOUN
ejpam-3914	93	87	)	)	PUNCT
ejpam-3914	93	88	p	p	NOUN
ejpam-3914	93	89	=	=	SYM
ejpam-3914	93	90	p1	p1	PROPN
ejpam-3914	93	91	∪	∪	ADJ
ejpam-3914	93	92	p2	p2	NOUN
ejpam-3914	93	93	,	,	PUNCT
ejpam-3914	93	94	where	where	SCONJ
ejpam-3914	93	95	∅	∅	NOUN
ejpam-3914	93	96	6=	6=	NUM
ejpam-3914	93	97	p1	p1	PROPN
ejpam-3914	93	98	⊆	⊆	NUM
ejpam-3914	93	99	v	v	NOUN
ejpam-3914	93	100	(	(	PUNCT
ejpam-3914	93	101	g	g	NOUN
ejpam-3914	93	102	)	)	PUNCT
ejpam-3914	93	103	and	and	CCONJ
ejpam-3914	93	104	∅	∅	NOUN
ejpam-3914	93	105	6=	6=	X
ejpam-3914	93	106	p2	p2	PROPN
ejpam-3914	93	107	⊆	⊆	NUM
ejpam-3914	93	108	v	v	NOUN
ejpam-3914	93	109	(	(	PUNCT
ejpam-3914	93	110	g	g	NOUN
ejpam-3914	93	111	)	)	PUNCT
ejpam-3914	93	112	.	.	PUNCT
ejpam-3914	94	1	corollary	corollary	ADJ
ejpam-3914	94	2	2.6	2.6	NUM
ejpam-3914	94	3	.	.	PUNCT
ejpam-3914	95	1	[	[	X
ejpam-3914	95	2	6	6	NUM
ejpam-3914	95	3	]	]	PUNCT
ejpam-3914	95	4	let	let	VERB
ejpam-3914	95	5	g	g	NOUN
ejpam-3914	95	6	and	and	CCONJ
ejpam-3914	95	7	h	h	NOUN
ejpam-3914	95	8	be	be	VERB
ejpam-3914	95	9	any	any	DET
ejpam-3914	95	10	graphs	graph	NOUN
ejpam-3914	95	11	.	.	PUNCT
ejpam-3914	96	1	then	then	ADV
ejpam-3914	96	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	96	3	(	(	PUNCT
ejpam-3914	96	4	g+h	g+h	NOUN
ejpam-3914	96	5	)	)	PUNCT
ejpam-3914	96	6	=	=	SYM
ejpam-3914	96	7	2	2	NUM
ejpam-3914	96	8	.	.	NOUN
ejpam-3914	96	9	3	3	NUM
ejpam-3914	96	10	.	.	X
ejpam-3914	96	11	main	main	ADJ
ejpam-3914	96	12	results	result	NOUN
ejpam-3914	96	13	this	this	DET
ejpam-3914	96	14	section	section	NOUN
ejpam-3914	96	15	contains	contain	VERB
ejpam-3914	96	16	the	the	DET
ejpam-3914	96	17	lower	low	ADJ
ejpam-3914	96	18	and	and	CCONJ
ejpam-3914	96	19	upper	upper	ADJ
ejpam-3914	96	20	bounds	bound	NOUN
ejpam-3914	96	21	of	of	ADP
ejpam-3914	96	22	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	96	23	(	(	PUNCT
ejpam-3914	96	24	g	g	NOUN
ejpam-3914	96	25	)	)	PUNCT
ejpam-3914	96	26	and	and	CCONJ
ejpam-3914	96	27	the	the	DET
ejpam-3914	96	28	forcing	force	VERB
ejpam-3914	96	29	total	total	ADJ
ejpam-3914	96	30	dr	dr	PROPN
ejpam-3914	96	31	-	-	PUNCT
ejpam-3914	96	32	power	power	NOUN
ejpam-3914	96	33	domination	domination	NOUN
ejpam-3914	96	34	number	number	NOUN
ejpam-3914	96	35	of	of	ADP
ejpam-3914	96	36	some	some	DET
ejpam-3914	96	37	special	special	ADJ
ejpam-3914	96	38	graphs	graph	NOUN
ejpam-3914	96	39	such	such	ADJ
ejpam-3914	96	40	as	as	ADP
ejpam-3914	96	41	path	path	NOUN
ejpam-3914	96	42	,	,	PUNCT
ejpam-3914	96	43	cycle	cycle	NOUN
ejpam-3914	96	44	,	,	PUNCT
ejpam-3914	96	45	complete	complete	ADJ
ejpam-3914	96	46	graph	graph	NOUN
ejpam-3914	96	47	,	,	PUNCT
ejpam-3914	96	48	fan	fan	NOUN
ejpam-3914	96	49	,	,	PUNCT
ejpam-3914	96	50	star	star	NOUN
ejpam-3914	96	51	and	and	CCONJ
ejpam-3914	96	52	wheel	wheel	NOUN
ejpam-3914	96	53	graphs	graph	NOUN
ejpam-3914	96	54	.	.	PUNCT
ejpam-3914	97	1	theorem	theorem	VERB
ejpam-3914	97	2	3.1	3.1	NUM
ejpam-3914	97	3	.	.	PUNCT
ejpam-3914	98	1	let	let	VERB
ejpam-3914	98	2	g	g	PRON
ejpam-3914	98	3	be	be	AUX
ejpam-3914	98	4	a	a	DET
ejpam-3914	98	5	graph	graph	NOUN
ejpam-3914	98	6	.	.	PUNCT
ejpam-3914	99	1	then	then	ADV
ejpam-3914	99	2	(	(	PUNCT
ejpam-3914	99	3	i	i	NOUN
ejpam-3914	99	4	)	)	PUNCT
ejpam-3914	99	5	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	99	6	(	(	PUNCT
ejpam-3914	99	7	g	g	NOUN
ejpam-3914	99	8	)	)	PUNCT
ejpam-3914	99	9	=	=	SYM
ejpam-3914	99	10	0	0	PUNCT
ejpam-3914	100	1	if	if	SCONJ
ejpam-3914	100	2	and	and	CCONJ
ejpam-3914	100	3	only	only	ADV
ejpam-3914	100	4	if	if	SCONJ
ejpam-3914	100	5	g	g	PROPN
ejpam-3914	100	6	has	have	VERB
ejpam-3914	100	7	a	a	DET
ejpam-3914	100	8	unique	unique	ADJ
ejpam-3914	100	9	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	100	10	-set	-set	NUM
ejpam-3914	100	11	.	.	PUNCT
ejpam-3914	101	1	(	(	PUNCT
ejpam-3914	101	2	ii	ii	NOUN
ejpam-3914	101	3	)	)	PUNCT
ejpam-3914	101	4	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	101	5	(	(	PUNCT
ejpam-3914	101	6	g	g	NOUN
ejpam-3914	101	7	)	)	PUNCT
ejpam-3914	101	8	=	=	SYM
ejpam-3914	101	9	1	1	NUM
ejpam-3914	101	10	if	if	SCONJ
ejpam-3914	101	11	and	and	CCONJ
ejpam-3914	101	12	only	only	ADV
ejpam-3914	101	13	if	if	SCONJ
ejpam-3914	101	14	g	g	PROPN
ejpam-3914	101	15	has	have	VERB
ejpam-3914	101	16	at	at	ADV
ejpam-3914	101	17	least	least	ADV
ejpam-3914	101	18	two	two	NUM
ejpam-3914	101	19	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	101	20	-sets	-set	NOUN
ejpam-3914	101	21	and	and	CCONJ
ejpam-3914	101	22	there	there	PRON
ejpam-3914	101	23	exists	exist	VERB
ejpam-3914	101	24	a	a	DET
ejpam-3914	101	25	vertex	vertex	NOUN
ejpam-3914	101	26	v	v	NOUN
ejpam-3914	101	27	which	which	PRON
ejpam-3914	101	28	is	be	AUX
ejpam-3914	101	29	contained	contain	VERB
ejpam-3914	101	30	in	in	ADP
ejpam-3914	101	31	exactly	exactly	ADV
ejpam-3914	101	32	one	one	NUM
ejpam-3914	101	33	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	101	34	-set	-set	PUNCT
ejpam-3914	101	35	of	of	ADP
ejpam-3914	101	36	g.	g.	PROPN
ejpam-3914	101	37	proof	proof	NOUN
ejpam-3914	101	38	.	.	PUNCT
ejpam-3914	102	1	(	(	PUNCT
ejpam-3914	102	2	i	i	NOUN
ejpam-3914	102	3	)	)	PUNCT
ejpam-3914	102	4	suppose	suppose	VERB
ejpam-3914	103	1	that	that	SCONJ
ejpam-3914	103	2	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	103	3	(	(	PUNCT
ejpam-3914	103	4	g	g	NOUN
ejpam-3914	103	5	)	)	PUNCT
ejpam-3914	103	6	=	=	SYM
ejpam-3914	103	7	0	0	X
ejpam-3914	103	8	.	.	PUNCT
ejpam-3914	104	1	it	it	PRON
ejpam-3914	104	2	follows	follow	VERB
ejpam-3914	104	3	that	that	SCONJ
ejpam-3914	104	4	∅	∅	NOUN
ejpam-3914	104	5	is	be	AUX
ejpam-3914	104	6	the	the	DET
ejpam-3914	104	7	forcing	forcing	NOUN
ejpam-3914	104	8	subset	subset	NOUN
ejpam-3914	104	9	for	for	ADP
ejpam-3914	104	10	a	a	DET
ejpam-3914	104	11	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	104	12	-set	-set	NUM
ejpam-3914	104	13	,	,	PUNCT
ejpam-3914	104	14	say	say	VERB
ejpam-3914	104	15	p	p	NOUN
ejpam-3914	104	16	,	,	PUNCT
ejpam-3914	104	17	in	in	ADP
ejpam-3914	104	18	g.	g.	PROPN
ejpam-3914	104	19	suppose	suppose	VERB
ejpam-3914	104	20	that	that	SCONJ
ejpam-3914	104	21	there	there	PRON
ejpam-3914	104	22	is	be	VERB
ejpam-3914	104	23	another	another	DET
ejpam-3914	104	24	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	104	25	-set	-set	PROPN
ejpam-3914	104	26	of	of	ADP
ejpam-3914	104	27	g	g	PROPN
ejpam-3914	104	28	,	,	PUNCT
ejpam-3914	104	29	say	say	VERB
ejpam-3914	104	30	r.	r.	PROPN
ejpam-3914	104	31	note	note	VERB
ejpam-3914	104	32	that	that	SCONJ
ejpam-3914	104	33	∅	∅	NOUN
ejpam-3914	104	34	is	be	AUX
ejpam-3914	104	35	also	also	ADV
ejpam-3914	104	36	a	a	DET
ejpam-3914	104	37	subset	subset	NOUN
ejpam-3914	104	38	for	for	ADP
ejpam-3914	104	39	r	r	NOUN
ejpam-3914	104	40	,	,	PUNCT
ejpam-3914	104	41	a	a	DET
ejpam-3914	104	42	contradiction	contradiction	NOUN
ejpam-3914	104	43	since	since	SCONJ
ejpam-3914	104	44	∅	∅	NOUN
ejpam-3914	104	45	is	be	AUX
ejpam-3914	104	46	a	a	DET
ejpam-3914	104	47	forcing	forcing	NOUN
ejpam-3914	104	48	subset	subset	NOUN
ejpam-3914	104	49	for	for	ADP
ejpam-3914	104	50	p	p	PROPN
ejpam-3914	104	51	.	.	PUNCT
ejpam-3914	105	1	thus	thus	ADV
ejpam-3914	105	2	,	,	PUNCT
ejpam-3914	105	3	g	g	PROPN
ejpam-3914	105	4	has	have	VERB
ejpam-3914	105	5	a	a	DET
ejpam-3914	105	6	unique	unique	ADJ
ejpam-3914	105	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	105	8	-set	-set	NUM
ejpam-3914	105	9	.	.	PUNCT
ejpam-3914	106	1	conversely	conversely	ADV
ejpam-3914	106	2	,	,	PUNCT
ejpam-3914	106	3	if	if	SCONJ
ejpam-3914	106	4	g	g	PROPN
ejpam-3914	106	5	has	have	VERB
ejpam-3914	106	6	a	a	DET
ejpam-3914	106	7	unique	unique	ADJ
ejpam-3914	106	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	106	9	-set	-set	NUM
ejpam-3914	106	10	,	,	PUNCT
ejpam-3914	106	11	say	say	VERB
ejpam-3914	106	12	q.	q.	PROPN
ejpam-3914	106	13	clearly	clearly	ADV
ejpam-3914	106	14	,	,	PUNCT
ejpam-3914	106	15	∅	∅	NOUN
ejpam-3914	106	16	is	be	AUX
ejpam-3914	106	17	a	a	DET
ejpam-3914	106	18	forcing	forcing	NOUN
ejpam-3914	106	19	subset	subset	NOUN
ejpam-3914	106	20	for	for	ADP
ejpam-3914	106	21	q.	q.	PROPN
ejpam-3914	106	22	consequently	consequently	ADV
ejpam-3914	106	23	,	,	PUNCT
ejpam-3914	106	24	|∅|	|∅|	PROPN
ejpam-3914	106	25	=	=	SYM
ejpam-3914	107	1	0	0	NUM
ejpam-3914	107	2	=	=	NOUN
ejpam-3914	107	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	107	4	(	(	PUNCT
ejpam-3914	107	5	q	q	X
ejpam-3914	107	6	)	)	PUNCT
ejpam-3914	107	7	=	=	NOUN
ejpam-3914	107	8	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	107	9	(	(	PUNCT
ejpam-3914	107	10	g	g	NOUN
ejpam-3914	107	11	)	)	PUNCT
ejpam-3914	107	12	.	.	PUNCT
ejpam-3914	108	1	(	(	PUNCT
ejpam-3914	108	2	ii	ii	NOUN
ejpam-3914	108	3	)	)	PUNCT
ejpam-3914	108	4	suppose	suppose	VERB
ejpam-3914	108	5	that	that	SCONJ
ejpam-3914	108	6	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	108	7	(	(	PUNCT
ejpam-3914	108	8	g	g	NOUN
ejpam-3914	108	9	)	)	PUNCT
ejpam-3914	108	10	=	=	SYM
ejpam-3914	108	11	1	1	X
ejpam-3914	108	12	.	.	PUNCT
ejpam-3914	108	13	hence	hence	ADV
ejpam-3914	108	14	,	,	PUNCT
ejpam-3914	108	15	g	g	PROPN
ejpam-3914	108	16	has	have	VERB
ejpam-3914	108	17	at	at	ADV
ejpam-3914	108	18	least	least	ADV
ejpam-3914	108	19	two	two	NUM
ejpam-3914	108	20	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	108	21	-sets	-set	NOUN
ejpam-3914	108	22	by	by	ADP
ejpam-3914	108	23	part	part	NOUN
ejpam-3914	108	24	(	(	PUNCT
ejpam-3914	108	25	i	i	NOUN
ejpam-3914	108	26	)	)	PUNCT
ejpam-3914	108	27	and	and	CCONJ
ejpam-3914	108	28	there	there	PRON
ejpam-3914	108	29	exists	exist	VERB
ejpam-3914	108	30	a	a	DET
ejpam-3914	108	31	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	108	32	-set	-set	NUM
ejpam-3914	108	33	,	,	PUNCT
ejpam-3914	108	34	say	say	VERB
ejpam-3914	108	35	p	p	NOUN
ejpam-3914	108	36	,	,	PUNCT
ejpam-3914	108	37	and	and	CCONJ
ejpam-3914	108	38	v	v	ADP
ejpam-3914	108	39	∈	∈	NOUN
ejpam-3914	108	40	p	p	NOUN
ejpam-3914	108	41	such	such	ADJ
ejpam-3914	108	42	that	that	SCONJ
ejpam-3914	108	43	{	{	PUNCT
ejpam-3914	108	44	v	v	NOUN
ejpam-3914	108	45	}	}	PUNCT
ejpam-3914	108	46	is	be	AUX
ejpam-3914	108	47	a	a	DET
ejpam-3914	108	48	forcing	forcing	NOUN
ejpam-3914	108	49	subset	subset	NOUN
ejpam-3914	108	50	for	for	ADP
ejpam-3914	108	51	p	p	NOUN
ejpam-3914	108	52	and	and	CCONJ
ejpam-3914	108	53	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	108	54	(	(	PUNCT
ejpam-3914	108	55	p	p	NOUN
ejpam-3914	108	56	)	)	PUNCT
ejpam-3914	108	57	=	=	PUNCT
ejpam-3914	109	1	|{v}|	|{v}|	PUNCT
ejpam-3914	109	2	=	=	SYM
ejpam-3914	109	3	1	1	NUM
ejpam-3914	109	4	,	,	PUNCT
ejpam-3914	109	5	that	that	ADV
ejpam-3914	109	6	is	is	ADV
ejpam-3914	109	7	,	,	PUNCT
ejpam-3914	109	8	there	there	PRON
ejpam-3914	109	9	exists	exist	VERB
ejpam-3914	109	10	a	a	DET
ejpam-3914	109	11	vertex	vertex	NOUN
ejpam-3914	109	12	which	which	PRON
ejpam-3914	109	13	is	be	AUX
ejpam-3914	109	14	contained	contain	VERB
ejpam-3914	109	15	in	in	ADP
ejpam-3914	109	16	exactly	exactly	ADV
ejpam-3914	109	17	one	one	NUM
ejpam-3914	109	18	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	109	19	-set	-set	PUNCT
ejpam-3914	109	20	of	of	ADP
ejpam-3914	109	21	g.	g.	PROPN
ejpam-3914	109	22	conversely	conversely	ADV
ejpam-3914	109	23	,	,	PUNCT
ejpam-3914	109	24	if	if	SCONJ
ejpam-3914	109	25	g	g	PROPN
ejpam-3914	109	26	has	have	VERB
ejpam-3914	109	27	at	at	ADV
ejpam-3914	109	28	least	least	ADV
ejpam-3914	109	29	two	two	NUM
ejpam-3914	109	30	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	109	31	-sets	-set	NOUN
ejpam-3914	109	32	,	,	PUNCT
ejpam-3914	109	33	then	then	ADV
ejpam-3914	109	34	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	109	35	(	(	PUNCT
ejpam-3914	109	36	g	g	NOUN
ejpam-3914	109	37	)	)	PUNCT
ejpam-3914	109	38	>	>	X
ejpam-3914	109	39	0	0	PUNCT
ejpam-3914	110	1	by	by	ADP
ejpam-3914	110	2	part	part	NOUN
ejpam-3914	110	3	(	(	PUNCT
ejpam-3914	110	4	i	i	NOUN
ejpam-3914	110	5	)	)	PUNCT
ejpam-3914	110	6	.	.	PUNCT
ejpam-3914	111	1	by	by	ADP
ejpam-3914	111	2	assumption	assumption	NOUN
ejpam-3914	111	3	,	,	PUNCT
ejpam-3914	111	4	there	there	PRON
ejpam-3914	111	5	exists	exist	VERB
ejpam-3914	111	6	a	a	DET
ejpam-3914	111	7	vertex	vertex	NOUN
ejpam-3914	111	8	,	,	PUNCT
ejpam-3914	111	9	say	say	VERB
ejpam-3914	111	10	x	x	X
ejpam-3914	111	11	,	,	PUNCT
ejpam-3914	111	12	which	which	PRON
ejpam-3914	111	13	is	be	AUX
ejpam-3914	111	14	contained	contain	VERB
ejpam-3914	111	15	in	in	ADP
ejpam-3914	111	16	exactly	exactly	ADV
ejpam-3914	111	17	one	one	NUM
ejpam-3914	111	18	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	111	19	-set	-set	PUNCT
ejpam-3914	111	20	of	of	ADP
ejpam-3914	111	21	g	g	PROPN
ejpam-3914	111	22	,	,	PUNCT
ejpam-3914	111	23	say	say	VERB
ejpam-3914	111	24	t	t	PROPN
ejpam-3914	111	25	,	,	PUNCT
ejpam-3914	111	26	that	that	ADV
ejpam-3914	111	27	is	is	ADV
ejpam-3914	111	28	,	,	PUNCT
ejpam-3914	111	29	{	{	PUNCT
ejpam-3914	111	30	x	x	X
ejpam-3914	111	31	}	}	PUNCT
ejpam-3914	111	32	is	be	AUX
ejpam-3914	111	33	a	a	DET
ejpam-3914	111	34	forcing	forcing	NOUN
ejpam-3914	111	35	subset	subset	NOUN
ejpam-3914	111	36	for	for	ADP
ejpam-3914	111	37	t	t	PROPN
ejpam-3914	111	38	.	.	PUNCT
ejpam-3914	112	1	therefore	therefore	ADV
ejpam-3914	112	2	,	,	PUNCT
ejpam-3914	112	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	112	4	(	(	PUNCT
ejpam-3914	112	5	t	t	NOUN
ejpam-3914	112	6	)	)	PUNCT
ejpam-3914	112	7	=	=	PUNCT
ejpam-3914	113	1	|{x}|	|{x}|	ADV
ejpam-3914	113	2	=	=	SYM
ejpam-3914	113	3	1	1	NUM
ejpam-3914	113	4	=	=	NOUN
ejpam-3914	113	5	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	113	6	(	(	PUNCT
ejpam-3914	113	7	g	g	NOUN
ejpam-3914	113	8	)	)	PUNCT
ejpam-3914	113	9	.	.	PUNCT
ejpam-3914	114	1	the	the	DET
ejpam-3914	114	2	next	next	ADJ
ejpam-3914	114	3	result	result	NOUN
ejpam-3914	114	4	is	be	AUX
ejpam-3914	114	5	a	a	DET
ejpam-3914	114	6	direct	direct	ADJ
ejpam-3914	114	7	consequence	consequence	NOUN
ejpam-3914	114	8	of	of	ADP
ejpam-3914	114	9	theorem	theorem	ADJ
ejpam-3914	114	10	3.1	3.1	NUM
ejpam-3914	114	11	and	and	CCONJ
ejpam-3914	114	12	definition	definition	NOUN
ejpam-3914	114	13	of	of	ADP
ejpam-3914	114	14	forcing	force	VERB
ejpam-3914	114	15	total	total	ADJ
ejpam-3914	114	16	dr	dr	PROPN
ejpam-3914	114	17	-	-	PUNCT
ejpam-3914	114	18	power	power	NOUN
ejpam-3914	114	19	domination	domination	NOUN
ejpam-3914	114	20	.	.	PUNCT
ejpam-3914	115	1	c.	c.	PROPN
ejpam-3914	115	2	armada	armada	PROPN
ejpam-3914	115	3	/	/	SYM
ejpam-3914	115	4	eur	eur	PROPN
ejpam-3914	115	5	.	.	PUNCT
ejpam-3914	116	1	j.	j.	PROPN
ejpam-3914	116	2	pure	pure	PROPN
ejpam-3914	116	3	appl	appl	PROPN
ejpam-3914	116	4	.	.	PROPN
ejpam-3914	116	5	math	math	PROPN
ejpam-3914	116	6	,	,	PUNCT
ejpam-3914	116	7	14	14	NUM
ejpam-3914	116	8	(	(	PUNCT
ejpam-3914	116	9	2	2	NUM
ejpam-3914	116	10	)	)	PUNCT
ejpam-3914	116	11	(	(	PUNCT
ejpam-3914	116	12	2021	2021	NUM
ejpam-3914	116	13	)	)	PUNCT
ejpam-3914	116	14	,	,	PUNCT
ejpam-3914	116	15	451	451	NUM
ejpam-3914	116	16	-	-	SYM
ejpam-3914	116	17	470	470	NUM
ejpam-3914	116	18	455	455	NUM
ejpam-3914	116	19	corollary	corollary	ADJ
ejpam-3914	116	20	3.2	3.2	NUM
ejpam-3914	116	21	.	.	PUNCT
ejpam-3914	117	1	let	let	VERB
ejpam-3914	117	2	g	g	PRON
ejpam-3914	117	3	be	be	AUX
ejpam-3914	117	4	a	a	DET
ejpam-3914	117	5	connected	connected	ADJ
ejpam-3914	117	6	graph	graph	NOUN
ejpam-3914	117	7	.	.	PUNCT
ejpam-3914	118	1	then	then	ADV
ejpam-3914	118	2	0	0	NUM
ejpam-3914	118	3	≤	≤	NOUN
ejpam-3914	118	4	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	118	5	(	(	PUNCT
ejpam-3914	118	6	g	g	NOUN
ejpam-3914	118	7	)	)	PUNCT
ejpam-3914	118	8	≤	≤	NOUN
ejpam-3914	118	9	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	118	10	(	(	PUNCT
ejpam-3914	118	11	g	g	NOUN
ejpam-3914	118	12	)	)	PUNCT
ejpam-3914	118	13	.	.	PUNCT
ejpam-3914	119	1	theorem	theorem	VERB
ejpam-3914	119	2	3.3	3.3	NUM
ejpam-3914	119	3	.	.	PUNCT
ejpam-3914	120	1	let	let	VERB
ejpam-3914	120	2	g	g	PRON
ejpam-3914	120	3	be	be	AUX
ejpam-3914	120	4	a	a	DET
ejpam-3914	120	5	nontrivial	nontrivial	ADJ
ejpam-3914	120	6	graph	graph	NOUN
ejpam-3914	120	7	.	.	PUNCT
ejpam-3914	121	1	then	then	ADV
ejpam-3914	121	2	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3914	121	3	(	(	PUNCT
ejpam-3914	121	4	g	g	NOUN
ejpam-3914	121	5	)	)	PUNCT
ejpam-3914	121	6	=	=	SYM
ejpam-3914	121	7	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	121	8	(	(	PUNCT
ejpam-3914	121	9	g	g	NOUN
ejpam-3914	121	10	)	)	PUNCT
ejpam-3914	121	11	if	if	SCONJ
ejpam-3914	121	12	and	and	CCONJ
ejpam-3914	121	13	only	only	ADV
ejpam-3914	121	14	if	if	SCONJ
ejpam-3914	121	15	for	for	ADP
ejpam-3914	121	16	every	every	PRON
ejpam-3914	121	17	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	121	18	-set	-set	PUNCT
ejpam-3914	122	1	p	p	NOUN
ejpam-3914	122	2	of	of	ADP
ejpam-3914	122	3	g	g	PROPN
ejpam-3914	122	4	and	and	CCONJ
ejpam-3914	122	5	for	for	ADP
ejpam-3914	122	6	each	each	PRON
ejpam-3914	122	7	v	v	ADP
ejpam-3914	122	8	∈	∈	PROPN
ejpam-3914	122	9	p	p	NOUN
ejpam-3914	122	10	,	,	PUNCT
ejpam-3914	122	11	there	there	PRON
ejpam-3914	122	12	exists	exist	VERB
ejpam-3914	122	13	u	u	PROPN
ejpam-3914	122	14	∈	∈	PROPN
ejpam-3914	122	15	v	v	NOUN
ejpam-3914	122	16	(	(	PUNCT
ejpam-3914	122	17	g)\p	g)\p	VERB
ejpam-3914	122	18	such	such	ADJ
ejpam-3914	122	19	that	that	SCONJ
ejpam-3914	122	20	[	[	X
ejpam-3914	122	21	p\{v}]∪{u	p\{v}]∪{u	VERB
ejpam-3914	122	22	}	}	PUNCT
ejpam-3914	122	23	is	be	AUX
ejpam-3914	122	24	a	a	DET
ejpam-3914	122	25	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	122	26	-set	-set	PROPN
ejpam-3914	122	27	of	of	ADP
ejpam-3914	122	28	g.	g.	PROPN
ejpam-3914	122	29	proof	proof	PROPN
ejpam-3914	122	30	.	.	PUNCT
ejpam-3914	123	1	suppose	suppose	VERB
ejpam-3914	123	2	that	that	SCONJ
ejpam-3914	123	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	123	4	(	(	PUNCT
ejpam-3914	123	5	g	g	NOUN
ejpam-3914	123	6	)	)	PUNCT
ejpam-3914	123	7	=	=	SYM
ejpam-3914	123	8	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	123	9	(	(	PUNCT
ejpam-3914	123	10	g	g	NOUN
ejpam-3914	123	11	)	)	PUNCT
ejpam-3914	123	12	.	.	PUNCT
ejpam-3914	124	1	let	let	VERB
ejpam-3914	124	2	p	p	PRON
ejpam-3914	124	3	be	be	AUX
ejpam-3914	124	4	a	a	DET
ejpam-3914	124	5	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	124	6	-set	-set	PUNCT
ejpam-3914	124	7	of	of	ADP
ejpam-3914	124	8	g	g	PROPN
ejpam-3914	124	9	such	such	ADJ
ejpam-3914	124	10	that	that	SCONJ
ejpam-3914	124	11	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	124	12	(	(	PUNCT
ejpam-3914	124	13	g	g	NOUN
ejpam-3914	124	14	)	)	PUNCT
ejpam-3914	124	15	=	=	SYM
ejpam-3914	124	16	|p	|p	X
ejpam-3914	124	17	|	|	NOUN
ejpam-3914	124	18	=	=	SYM
ejpam-3914	124	19	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	125	1	(	(	PUNCT
ejpam-3914	125	2	g	g	NOUN
ejpam-3914	125	3	)	)	PUNCT
ejpam-3914	125	4	,	,	PUNCT
ejpam-3914	125	5	that	that	ADV
ejpam-3914	125	6	is	is	ADV
ejpam-3914	125	7	,	,	PUNCT
ejpam-3914	125	8	p	p	PRON
ejpam-3914	125	9	is	be	AUX
ejpam-3914	125	10	the	the	DET
ejpam-3914	125	11	only	only	ADJ
ejpam-3914	125	12	forcing	forcing	NOUN
ejpam-3914	125	13	subset	subset	NOUN
ejpam-3914	125	14	for	for	ADP
ejpam-3914	125	15	p	p	PROPN
ejpam-3914	125	16	.	.	PUNCT
ejpam-3914	126	1	let	let	VERB
ejpam-3914	126	2	v	v	NUM
ejpam-3914	126	3	∈	∈	PROPN
ejpam-3914	126	4	p	p	NOUN
ejpam-3914	126	5	.	.	PUNCT
ejpam-3914	127	1	since	since	SCONJ
ejpam-3914	127	2	p\{v	p\{v	VERB
ejpam-3914	127	3	}	}	PUNCT
ejpam-3914	127	4	is	be	AUX
ejpam-3914	127	5	not	not	PART
ejpam-3914	127	6	a	a	DET
ejpam-3914	127	7	forcing	forcing	NOUN
ejpam-3914	127	8	subset	subset	NOUN
ejpam-3914	127	9	for	for	ADP
ejpam-3914	127	10	p	p	NOUN
ejpam-3914	127	11	,	,	PUNCT
ejpam-3914	127	12	there	there	PRON
ejpam-3914	127	13	exists	exist	VERB
ejpam-3914	127	14	a	a	DET
ejpam-3914	127	15	u	u	NOUN
ejpam-3914	127	16	∈	∈	PROPN
ejpam-3914	127	17	v	v	NOUN
ejpam-3914	127	18	(	(	PUNCT
ejpam-3914	127	19	g)\p	g)\p	VERB
ejpam-3914	127	20	such	such	ADJ
ejpam-3914	127	21	that	that	SCONJ
ejpam-3914	127	22	[	[	X
ejpam-3914	127	23	p\{v	p\{v	NOUN
ejpam-3914	127	24	}	}	PUNCT
ejpam-3914	127	25	]	]	PUNCT
ejpam-3914	127	26	∪	∪	X
ejpam-3914	127	27	{	{	PUNCT
ejpam-3914	127	28	u	u	NOUN
ejpam-3914	127	29	}	}	PUNCT
ejpam-3914	127	30	is	be	AUX
ejpam-3914	127	31	a	a	DET
ejpam-3914	127	32	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	127	33	-set	-set	PROPN
ejpam-3914	127	34	of	of	ADP
ejpam-3914	127	35	g.	g.	PROPN
ejpam-3914	127	36	conversely	conversely	ADV
ejpam-3914	127	37	,	,	PUNCT
ejpam-3914	127	38	suppose	suppose	VERB
ejpam-3914	127	39	that	that	SCONJ
ejpam-3914	127	40	every	every	DET
ejpam-3914	127	41	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	127	42	-set	-set	PUNCT
ejpam-3914	127	43	p	p	X
ejpam-3914	127	44	′	′	NOUN
ejpam-3914	127	45	of	of	ADP
ejpam-3914	127	46	g	g	PROPN
ejpam-3914	127	47	satisfies	satisfy	VERB
ejpam-3914	127	48	the	the	DET
ejpam-3914	127	49	given	give	VERB
ejpam-3914	127	50	condition	condition	NOUN
ejpam-3914	127	51	.	.	PUNCT
ejpam-3914	128	1	let	let	VERB
ejpam-3914	128	2	p	p	PRON
ejpam-3914	128	3	be	be	AUX
ejpam-3914	128	4	a	a	DET
ejpam-3914	128	5	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	128	6	-set	-set	PUNCT
ejpam-3914	128	7	of	of	ADP
ejpam-3914	128	8	g	g	PROPN
ejpam-3914	128	9	such	such	ADJ
ejpam-3914	128	10	that	that	SCONJ
ejpam-3914	128	11	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	128	12	(	(	PUNCT
ejpam-3914	128	13	g	g	NOUN
ejpam-3914	128	14	)	)	PUNCT
ejpam-3914	128	15	=	=	NOUN
ejpam-3914	129	1	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	129	2	(	(	PUNCT
ejpam-3914	129	3	p	p	NOUN
ejpam-3914	129	4	)	)	PUNCT
ejpam-3914	129	5	.	.	PUNCT
ejpam-3914	130	1	moreover	moreover	ADV
ejpam-3914	130	2	,	,	PUNCT
ejpam-3914	130	3	suppose	suppose	VERB
ejpam-3914	130	4	that	that	SCONJ
ejpam-3914	130	5	p	p	PROPN
ejpam-3914	130	6	has	have	VERB
ejpam-3914	130	7	a	a	DET
ejpam-3914	130	8	forcing	force	VERB
ejpam-3914	130	9	subset	subset	NOUN
ejpam-3914	130	10	r	r	NOUN
ejpam-3914	130	11	with	with	ADP
ejpam-3914	130	12	|r|	|r|	PROPN
ejpam-3914	130	13	<	<	X
ejpam-3914	130	14	|p	|p	X
ejpam-3914	130	15	|	|	ADV
ejpam-3914	130	16	,	,	PUNCT
ejpam-3914	130	17	that	that	ADV
ejpam-3914	130	18	is	is	ADV
ejpam-3914	130	19	,	,	PUNCT
ejpam-3914	130	20	p	p	X
ejpam-3914	130	21	=	=	PUNCT
ejpam-3914	130	22	r	r	NOUN
ejpam-3914	130	23	∪	∪	X
ejpam-3914	130	24	s	s	PROPN
ejpam-3914	130	25	,	,	PUNCT
ejpam-3914	130	26	where	where	SCONJ
ejpam-3914	130	27	s	s	VERB
ejpam-3914	130	28	=	=	PUNCT
ejpam-3914	130	29	{	{	PUNCT
ejpam-3914	130	30	u	u	NOUN
ejpam-3914	130	31	∈	∈	PROPN
ejpam-3914	130	32	p	p	X
ejpam-3914	130	33	:	:	PUNCT
ejpam-3914	130	34	u	u	NOUN
ejpam-3914	130	35	/∈	/∈	PUNCT
ejpam-3914	130	36	r	r	NOUN
ejpam-3914	130	37	}	}	PUNCT
ejpam-3914	130	38	.	.	PUNCT
ejpam-3914	131	1	pick	pick	VERB
ejpam-3914	131	2	u	u	PRON
ejpam-3914	131	3	∈	∈	PROPN
ejpam-3914	131	4	s.	s.	PROPN
ejpam-3914	131	5	by	by	ADP
ejpam-3914	131	6	assumption	assumption	NOUN
ejpam-3914	131	7	,	,	PUNCT
ejpam-3914	131	8	there	there	PRON
ejpam-3914	131	9	exists	exist	VERB
ejpam-3914	131	10	v	v	ADP
ejpam-3914	131	11	∈	∈	PROPN
ejpam-3914	131	12	v	v	NOUN
ejpam-3914	131	13	(	(	PUNCT
ejpam-3914	131	14	g)\p	g)\p	VERB
ejpam-3914	131	15	such	such	ADJ
ejpam-3914	131	16	that	that	SCONJ
ejpam-3914	132	1	[	[	X
ejpam-3914	132	2	p\{u	p\{u	X
ejpam-3914	132	3	}	}	PUNCT
ejpam-3914	132	4	]	]	PUNCT
ejpam-3914	132	5	∪	∪	X
ejpam-3914	132	6	{	{	PUNCT
ejpam-3914	132	7	v	v	NOUN
ejpam-3914	132	8	}	}	PUNCT
ejpam-3914	132	9	=	=	PUNCT
ejpam-3914	132	10	q	q	X
ejpam-3914	132	11	is	be	AUX
ejpam-3914	132	12	a	a	DET
ejpam-3914	132	13	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	132	14	-set	-set	PROPN
ejpam-3914	132	15	of	of	ADP
ejpam-3914	132	16	g.	g.	PROPN
ejpam-3914	132	17	thus	thus	ADV
ejpam-3914	132	18	,	,	PUNCT
ejpam-3914	132	19	q	q	X
ejpam-3914	132	20	=	=	PUNCT
ejpam-3914	132	21	r	r	NOUN
ejpam-3914	132	22	∪	∪	NOUN
ejpam-3914	132	23	t	t	NOUN
ejpam-3914	132	24	,	,	PUNCT
ejpam-3914	132	25	where	where	SCONJ
ejpam-3914	132	26	t	t	NOUN
ejpam-3914	132	27	=	=	PUNCT
ejpam-3914	132	28	[	[	X
ejpam-3914	132	29	s\{u	s\{u	X
ejpam-3914	132	30	}	}	PUNCT
ejpam-3914	132	31	]	]	PUNCT
ejpam-3914	132	32	∪	∪	X
ejpam-3914	132	33	{	{	PUNCT
ejpam-3914	132	34	v	v	NOUN
ejpam-3914	132	35	}	}	PUNCT
ejpam-3914	132	36	,	,	PUNCT
ejpam-3914	132	37	that	that	ADV
ejpam-3914	132	38	is	is	ADV
ejpam-3914	132	39	,	,	PUNCT
ejpam-3914	132	40	q	q	X
ejpam-3914	132	41	is	be	AUX
ejpam-3914	132	42	a	a	DET
ejpam-3914	132	43	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	132	44	-set	-set	PUNCT
ejpam-3914	132	45	containing	contain	VERB
ejpam-3914	132	46	r	r	NOUN
ejpam-3914	132	47	,	,	PUNCT
ejpam-3914	132	48	a	a	DET
ejpam-3914	132	49	contradiction	contradiction	NOUN
ejpam-3914	132	50	.	.	PUNCT
ejpam-3914	133	1	thus	thus	ADV
ejpam-3914	133	2	,	,	PUNCT
ejpam-3914	133	3	|r|	|r|	PROPN
ejpam-3914	133	4	=	=	SYM
ejpam-3914	133	5	|p	|p	PROPN
ejpam-3914	133	6	|	|	ADV
ejpam-3914	133	7	and	and	CCONJ
ejpam-3914	133	8	p	p	NOUN
ejpam-3914	133	9	is	be	AUX
ejpam-3914	133	10	the	the	DET
ejpam-3914	133	11	only	only	ADJ
ejpam-3914	133	12	forcing	forcing	NOUN
ejpam-3914	133	13	subset	subset	NOUN
ejpam-3914	133	14	for	for	ADP
ejpam-3914	133	15	p	p	PROPN
ejpam-3914	133	16	.	.	PUNCT
ejpam-3914	134	1	therefore	therefore	ADV
ejpam-3914	134	2	,	,	PUNCT
ejpam-3914	134	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	134	4	(	(	PUNCT
ejpam-3914	134	5	g	g	NOUN
ejpam-3914	134	6	)	)	PUNCT
ejpam-3914	134	7	=	=	SYM
ejpam-3914	134	8	|p	|p	X
ejpam-3914	134	9	|	|	NOUN
ejpam-3914	134	10	=	=	SYM
ejpam-3914	134	11	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	134	12	(	(	PUNCT
ejpam-3914	134	13	g	g	NOUN
ejpam-3914	134	14	)	)	PUNCT
ejpam-3914	134	15	.	.	PUNCT
ejpam-3914	135	1	theorem	theorem	VERB
ejpam-3914	135	2	3.4	3.4	NUM
ejpam-3914	135	3	.	.	PUNCT
ejpam-3914	136	1	let	let	VERB
ejpam-3914	136	2	n	n	PRON
ejpam-3914	136	3	be	be	AUX
ejpam-3914	136	4	a	a	DET
ejpam-3914	136	5	positive	positive	ADJ
ejpam-3914	136	6	integer	integer	NOUN
ejpam-3914	136	7	with	with	ADP
ejpam-3914	136	8	n	n	PRON
ejpam-3914	136	9	≥	≥	NUM
ejpam-3914	136	10	5	5	NUM
ejpam-3914	136	11	.	.	PUNCT
ejpam-3914	137	1	then	then	ADV
ejpam-3914	137	2	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3914	137	3	(	(	PUNCT
ejpam-3914	137	4	pn	pn	NOUN
ejpam-3914	137	5	)	)	PUNCT
ejpam-3914	137	6	=	=	PUNCT
ejpam-3914	137	7			X
ejpam-3914	137	8	0	0	NUM
ejpam-3914	137	9	,	,	PUNCT
ejpam-3914	137	10	n	n	NOUN
ejpam-3914	137	11	=	=	SYM
ejpam-3914	137	12	7	7	NUM
ejpam-3914	137	13	or	or	CCONJ
ejpam-3914	137	14	n	n	PRON
ejpam-3914	137	15	≡	≡	PROPN
ejpam-3914	137	16	1(mod	1(mod	NUM
ejpam-3914	137	17	5	5	NUM
ejpam-3914	137	18	)	)	PUNCT
ejpam-3914	137	19	2	2	NUM
ejpam-3914	137	20	,	,	PUNCT
ejpam-3914	137	21	n	n	PRON
ejpam-3914	137	22	≡	≡	PROPN
ejpam-3914	137	23	3(mod	3(mod	NUM
ejpam-3914	137	24	5	5	NUM
ejpam-3914	137	25	)	)	PUNCT
ejpam-3914	137	26	1	1	NUM
ejpam-3914	137	27	,	,	PUNCT
ejpam-3914	137	28	otherwise	otherwise	ADV
ejpam-3914	137	29	.	.	PUNCT
ejpam-3914	138	1	proof	proof	NOUN
ejpam-3914	138	2	.	.	PUNCT
ejpam-3914	139	1	let	let	VERB
ejpam-3914	139	2	the	the	DET
ejpam-3914	139	3	path	path	NOUN
ejpam-3914	139	4	pn	pn	NOUN
ejpam-3914	140	1	=	=	PUNCT
ejpam-3914	141	1	[	[	X
ejpam-3914	141	2	u1	u1	NOUN
ejpam-3914	141	3	,	,	PUNCT
ejpam-3914	141	4	u2	u2	NOUN
ejpam-3914	141	5	,	,	PUNCT
ejpam-3914	141	6	.	.	PUNCT
ejpam-3914	141	7	.	.	PUNCT
ejpam-3914	141	8	.	.	PUNCT
ejpam-3914	142	1	,	,	PUNCT
ejpam-3914	142	2	un	un	PROPN
ejpam-3914	142	3	]	]	X
ejpam-3914	142	4	.	.	PUNCT
ejpam-3914	143	1	note	note	VERB
ejpam-3914	143	2	that	that	SCONJ
ejpam-3914	143	3	deg(u1	deg(u1	NOUN
ejpam-3914	143	4	)	)	PUNCT
ejpam-3914	143	5	=	=	SYM
ejpam-3914	143	6	1	1	NUM
ejpam-3914	143	7	=	=	SYM
ejpam-3914	143	8	deg(un	deg(un	NOUN
ejpam-3914	143	9	)	)	PUNCT
ejpam-3914	143	10	and	and	CCONJ
ejpam-3914	143	11	deg(ui	deg(ui	X
ejpam-3914	143	12	)	)	PUNCT
ejpam-3914	143	13	=	=	SYM
ejpam-3914	143	14	2	2	NUM
ejpam-3914	143	15	for	for	ADP
ejpam-3914	143	16	all	all	DET
ejpam-3914	143	17	i	i	PRON
ejpam-3914	143	18	=	=	NOUN
ejpam-3914	143	19	2	2	NUM
ejpam-3914	143	20	,	,	PUNCT
ejpam-3914	143	21	3	3	NUM
ejpam-3914	143	22	,	,	PUNCT
ejpam-3914	143	23	.	.	PUNCT
ejpam-3914	143	24	.	.	PUNCT
ejpam-3914	144	1	.	.	PUNCT
ejpam-3914	145	1	,	,	PUNCT
ejpam-3914	146	1	n	n	CCONJ
ejpam-3914	146	2	−	−	PROPN
ejpam-3914	146	3	1	1	NUM
ejpam-3914	146	4	.	.	PUNCT
ejpam-3914	147	1	by	by	ADP
ejpam-3914	147	2	definition	definition	NOUN
ejpam-3914	147	3	of	of	ADP
ejpam-3914	147	4	total	total	ADJ
ejpam-3914	147	5	dr	dr	PROPN
ejpam-3914	147	6	-	-	PUNCT
ejpam-3914	147	7	power	power	NOUN
ejpam-3914	147	8	dominating	dominating	NOUN
ejpam-3914	147	9	set	set	NOUN
ejpam-3914	147	10	,	,	PUNCT
ejpam-3914	147	11	a	a	DET
ejpam-3914	147	12	choosen	choosen	ADJ
ejpam-3914	147	13	vertex	vertex	NOUN
ejpam-3914	147	14	in	in	ADP
ejpam-3914	147	15	a	a	DET
ejpam-3914	147	16	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	147	17	-set	-set	NUM
ejpam-3914	147	18	,	,	PUNCT
ejpam-3914	147	19	say	say	VERB
ejpam-3914	147	20	d	d	X
ejpam-3914	147	21	,	,	PUNCT
ejpam-3914	147	22	of	of	ADP
ejpam-3914	147	23	pn	pn	PROPN
ejpam-3914	147	24	must	must	AUX
ejpam-3914	147	25	always	always	ADV
ejpam-3914	147	26	have	have	VERB
ejpam-3914	147	27	an	an	DET
ejpam-3914	147	28	adjacent	adjacent	ADJ
ejpam-3914	147	29	vertex	vertex	NOUN
ejpam-3914	147	30	in	in	ADP
ejpam-3914	147	31	d	d	PROPN
ejpam-3914	147	32	,	,	PUNCT
ejpam-3914	147	33	say	say	VERB
ejpam-3914	147	34	ui	ui	NOUN
ejpam-3914	147	35	and	and	CCONJ
ejpam-3914	147	36	ui+1	ui+1	PROPN
ejpam-3914	147	37	and	and	CCONJ
ejpam-3914	147	38	by	by	ADP
ejpam-3914	147	39	theorem	theorem	NOUN
ejpam-3914	147	40	2.2	2.2	NUM
ejpam-3914	147	41	,	,	PUNCT
ejpam-3914	147	42	the	the	DET
ejpam-3914	147	43	choosen	choosen	ADJ
ejpam-3914	147	44	vertex	vertex	NOUN
ejpam-3914	147	45	ui+1	ui+1	PROPN
ejpam-3914	147	46	must	must	AUX
ejpam-3914	147	47	be	be	AUX
ejpam-3914	147	48	of	of	ADP
ejpam-3914	147	49	at	at	ADP
ejpam-3914	147	50	most	most	ADJ
ejpam-3914	147	51	distance	distance	NOUN
ejpam-3914	147	52	4	4	NUM
ejpam-3914	147	53	to	to	ADP
ejpam-3914	147	54	the	the	DET
ejpam-3914	147	55	next	next	ADJ
ejpam-3914	147	56	choosen	choosen	ADJ
ejpam-3914	147	57	vertex	vertex	NOUN
ejpam-3914	147	58	in	in	ADP
ejpam-3914	147	59	d	d	NOUN
ejpam-3914	147	60	since	since	SCONJ
ejpam-3914	147	61	if	if	SCONJ
ejpam-3914	147	62	the	the	DET
ejpam-3914	147	63	next	next	ADJ
ejpam-3914	147	64	vertex	vertex	NOUN
ejpam-3914	147	65	to	to	PART
ejpam-3914	147	66	be	be	AUX
ejpam-3914	147	67	choosen	choosen	VERB
ejpam-3914	147	68	is	be	AUX
ejpam-3914	147	69	of	of	ADP
ejpam-3914	147	70	distance	distance	NOUN
ejpam-3914	147	71	5	5	NUM
ejpam-3914	147	72	,	,	PUNCT
ejpam-3914	147	73	say	say	VERB
ejpam-3914	147	74	u1	u1	NOUN
ejpam-3914	147	75	,	,	PUNCT
ejpam-3914	147	76	u2	u2	PROPN
ejpam-3914	147	77	∈	∈	PROPN
ejpam-3914	147	78	d	d	NOUN
ejpam-3914	147	79	and	and	CCONJ
ejpam-3914	147	80	choose	choose	VERB
ejpam-3914	147	81	u7	u7	PROPN
ejpam-3914	147	82	to	to	PART
ejpam-3914	147	83	be	be	AUX
ejpam-3914	147	84	the	the	DET
ejpam-3914	147	85	next	next	ADJ
ejpam-3914	147	86	vertex	vertex	NOUN
ejpam-3914	147	87	,	,	PUNCT
ejpam-3914	147	88	then	then	ADV
ejpam-3914	147	89	u3	u3	NOUN
ejpam-3914	147	90	and	and	CCONJ
ejpam-3914	147	91	u6	u6	NOUN
ejpam-3914	147	92	are	be	AUX
ejpam-3914	147	93	directly	directly	ADV
ejpam-3914	147	94	observed	observe	VERB
ejpam-3914	147	95	vertices	vertex	NOUN
ejpam-3914	147	96	while	while	SCONJ
ejpam-3914	147	97	u4	u4	PROPN
ejpam-3914	147	98	and	and	CCONJ
ejpam-3914	147	99	u5	u5	PROPN
ejpam-3914	147	100	are	be	AUX
ejpam-3914	147	101	remotely	remotely	ADV
ejpam-3914	147	102	observed	observe	VERB
ejpam-3914	147	103	vertices	vertex	NOUN
ejpam-3914	147	104	but	but	CCONJ
ejpam-3914	147	105	the	the	DET
ejpam-3914	147	106	edge	edge	NOUN
ejpam-3914	147	107	u4u5	u4u5	NUM
ejpam-3914	147	108	is	be	AUX
ejpam-3914	147	109	neither	neither	CCONJ
ejpam-3914	147	110	directly	directly	ADV
ejpam-3914	147	111	nor	nor	CCONJ
ejpam-3914	147	112	remotely	remotely	ADV
ejpam-3914	147	113	observed	observe	VERB
ejpam-3914	147	114	edge	edge	NOUN
ejpam-3914	147	115	which	which	PRON
ejpam-3914	147	116	is	be	AUX
ejpam-3914	147	117	a	a	DET
ejpam-3914	147	118	contradiction	contradiction	NOUN
ejpam-3914	147	119	.	.	PUNCT
ejpam-3914	148	1	also	also	ADV
ejpam-3914	148	2	,	,	PUNCT
ejpam-3914	148	3	the	the	DET
ejpam-3914	148	4	starting	start	VERB
ejpam-3914	148	5	vertex	vertex	NOUN
ejpam-3914	148	6	of	of	ADP
ejpam-3914	148	7	a	a	PRON
ejpam-3914	148	8	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	148	9	-set	-set	PUNCT
ejpam-3914	149	1	d	d	NOUN
ejpam-3914	149	2	,	,	PUNCT
ejpam-3914	149	3	of	of	ADP
ejpam-3914	149	4	pn	pn	PROPN
ejpam-3914	149	5	must	must	AUX
ejpam-3914	149	6	be	be	AUX
ejpam-3914	149	7	u1	u1	NOUN
ejpam-3914	149	8	,	,	PUNCT
ejpam-3914	149	9	u2	u2	NOUN
ejpam-3914	149	10	or	or	CCONJ
ejpam-3914	149	11	u3	u3	NOUN
ejpam-3914	149	12	since	since	SCONJ
ejpam-3914	149	13	if	if	SCONJ
ejpam-3914	149	14	it	it	PRON
ejpam-3914	149	15	starts	start	VERB
ejpam-3914	149	16	with	with	ADP
ejpam-3914	149	17	u4	u4	PROPN
ejpam-3914	149	18	,	,	PUNCT
ejpam-3914	149	19	then	then	ADV
ejpam-3914	149	20	u3	u3	NOUN
ejpam-3914	149	21	is	be	AUX
ejpam-3914	149	22	a	a	DET
ejpam-3914	149	23	directly	directly	ADV
ejpam-3914	149	24	observed	observe	VERB
ejpam-3914	149	25	vertex	vertex	NOUN
ejpam-3914	149	26	while	while	SCONJ
ejpam-3914	149	27	u2	u2	NOUN
ejpam-3914	149	28	becomes	become	VERB
ejpam-3914	149	29	a	a	DET
ejpam-3914	149	30	remotely	remotely	ADV
ejpam-3914	149	31	observed	observe	VERB
ejpam-3914	149	32	vertex	vertex	NOUN
ejpam-3914	149	33	but	but	CCONJ
ejpam-3914	149	34	the	the	DET
ejpam-3914	149	35	vertex	vertex	NOUN
ejpam-3914	149	36	u1	u1	NOUN
ejpam-3914	149	37	is	be	AUX
ejpam-3914	149	38	neither	neither	CCONJ
ejpam-3914	149	39	directly	directly	ADV
ejpam-3914	149	40	nor	nor	CCONJ
ejpam-3914	149	41	remotely	remotely	ADV
ejpam-3914	149	42	observed	observe	VERB
ejpam-3914	149	43	vertex	vertex	NOUN
ejpam-3914	149	44	which	which	PRON
ejpam-3914	149	45	is	be	AUX
ejpam-3914	149	46	a	a	DET
ejpam-3914	149	47	contradiction	contradiction	NOUN
ejpam-3914	149	48	.	.	PUNCT
ejpam-3914	150	1	now	now	ADV
ejpam-3914	150	2	,	,	PUNCT
ejpam-3914	150	3	consider	consider	VERB
ejpam-3914	150	4	the	the	DET
ejpam-3914	150	5	following	follow	VERB
ejpam-3914	150	6	cases	case	NOUN
ejpam-3914	150	7	:	:	PUNCT
ejpam-3914	150	8	case	case	NOUN
ejpam-3914	150	9	1	1	NUM
ejpam-3914	150	10	:	:	PUNCT
ejpam-3914	150	11	suppose	suppose	VERB
ejpam-3914	150	12	that	that	SCONJ
ejpam-3914	150	13	n	n	NOUN
ejpam-3914	150	14	=	=	SYM
ejpam-3914	150	15	7	7	X
ejpam-3914	150	16	.	.	PUNCT
ejpam-3914	150	17	by	by	ADP
ejpam-3914	150	18	theorem	theorem	ADJ
ejpam-3914	150	19	2.2	2.2	NUM
ejpam-3914	150	20	,	,	PUNCT
ejpam-3914	150	21	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	150	22	(	(	PUNCT
ejpam-3914	150	23	p7	p7	PROPN
ejpam-3914	150	24	)	)	PUNCT
ejpam-3914	150	25	=	=	SYM
ejpam-3914	150	26	2(7)+1	2(7)+1	NUM
ejpam-3914	150	27	5	5	NUM
ejpam-3914	150	28	=	=	SYM
ejpam-3914	150	29	3	3	X
ejpam-3914	150	30	.	.	PUNCT
ejpam-3914	150	31	clearly	clearly	ADV
ejpam-3914	150	32	,	,	PUNCT
ejpam-3914	150	33	s	s	PART
ejpam-3914	150	34	=	=	SYM
ejpam-3914	150	35	{	{	PUNCT
ejpam-3914	150	36	u3	u3	PROPN
ejpam-3914	150	37	,	,	PUNCT
ejpam-3914	150	38	u4	u4	PROPN
ejpam-3914	150	39	,	,	PUNCT
ejpam-3914	150	40	u5	u5	PROPN
ejpam-3914	150	41	}	}	PUNCT
ejpam-3914	150	42	is	be	AUX
ejpam-3914	150	43	the	the	DET
ejpam-3914	150	44	only	only	ADJ
ejpam-3914	150	45	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	150	46	-set	-set	PUNCT
ejpam-3914	150	47	of	of	ADP
ejpam-3914	150	48	p7	p7	NOUN
ejpam-3914	150	49	since	since	SCONJ
ejpam-3914	150	50	u2	u2	NOUN
ejpam-3914	150	51	and	and	CCONJ
ejpam-3914	150	52	u6	u6	NOUN
ejpam-3914	150	53	are	be	AUX
ejpam-3914	150	54	the	the	DET
ejpam-3914	150	55	directly	directly	ADV
ejpam-3914	150	56	observed	observe	VERB
ejpam-3914	150	57	vertices	vertex	NOUN
ejpam-3914	150	58	while	while	SCONJ
ejpam-3914	150	59	u1	u1	NOUN
ejpam-3914	150	60	and	and	CCONJ
ejpam-3914	150	61	u7	u7	PROPN
ejpam-3914	150	62	are	be	AUX
ejpam-3914	150	63	the	the	DET
ejpam-3914	150	64	remotely	remotely	ADV
ejpam-3914	150	65	observed	observe	VERB
ejpam-3914	150	66	vertices	vertex	NOUN
ejpam-3914	150	67	,	,	PUNCT
ejpam-3914	150	68	that	that	ADV
ejpam-3914	150	69	is	is	ADV
ejpam-3914	150	70	,	,	PUNCT
ejpam-3914	150	71	os	os	ADV
ejpam-3914	150	72	v	v	X
ejpam-3914	150	73	(	(	PUNCT
ejpam-3914	150	74	p7	p7	PROPN
ejpam-3914	150	75	)	)	PUNCT
ejpam-3914	150	76	=	=	SYM
ejpam-3914	150	77	v	v	NOUN
ejpam-3914	150	78	(	(	PUNCT
ejpam-3914	150	79	p7	p7	PROPN
ejpam-3914	150	80	)	)	PUNCT
ejpam-3914	150	81	,	,	PUNCT
ejpam-3914	150	82	os	os	NOUN
ejpam-3914	150	83	e(p7	e(p7	ADV
ejpam-3914	150	84	)	)	PUNCT
ejpam-3914	150	85	=	=	SYM
ejpam-3914	150	86	e(p7	e(p7	X
ejpam-3914	150	87	)	)	PUNCT
ejpam-3914	150	88	and	and	CCONJ
ejpam-3914	150	89	the	the	DET
ejpam-3914	150	90	induced	induced	ADJ
ejpam-3914	150	91	subgraph	subgraph	NOUN
ejpam-3914	150	92	〈	〈	PROPN
ejpam-3914	150	93	s	s	PROPN
ejpam-3914	150	94	〉	〉	PROPN
ejpam-3914	150	95	has	have	VERB
ejpam-3914	150	96	no	no	DET
ejpam-3914	150	97	isolated	isolated	ADJ
ejpam-3914	150	98	vertex	vertex	NOUN
ejpam-3914	150	99	.	.	PUNCT
ejpam-3914	151	1	by	by	ADP
ejpam-3914	151	2	theorem	theorem	NOUN
ejpam-3914	151	3	3.1(i	3.1(i	NUM
ejpam-3914	151	4	)	)	PUNCT
ejpam-3914	151	5	,	,	PUNCT
ejpam-3914	151	6	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	151	7	(	(	PUNCT
ejpam-3914	151	8	p7	p7	ADJ
ejpam-3914	151	9	)	)	PUNCT
ejpam-3914	151	10	=	=	SYM
ejpam-3914	151	11	0	0	X
ejpam-3914	151	12	.	.	PUNCT
ejpam-3914	151	13	c.	c.	PROPN
ejpam-3914	151	14	armada	armada	PROPN
ejpam-3914	151	15	/	/	SYM
ejpam-3914	151	16	eur	eur	PROPN
ejpam-3914	151	17	.	.	PUNCT
ejpam-3914	152	1	j.	j.	PROPN
ejpam-3914	152	2	pure	pure	PROPN
ejpam-3914	152	3	appl	appl	PROPN
ejpam-3914	152	4	.	.	PROPN
ejpam-3914	152	5	math	math	PROPN
ejpam-3914	152	6	,	,	PUNCT
ejpam-3914	152	7	14	14	NUM
ejpam-3914	152	8	(	(	PUNCT
ejpam-3914	152	9	2	2	NUM
ejpam-3914	152	10	)	)	PUNCT
ejpam-3914	152	11	(	(	PUNCT
ejpam-3914	152	12	2021	2021	NUM
ejpam-3914	152	13	)	)	PUNCT
ejpam-3914	152	14	,	,	PUNCT
ejpam-3914	152	15	451	451	NUM
ejpam-3914	152	16	-	-	SYM
ejpam-3914	152	17	470	470	NUM
ejpam-3914	152	18	456	456	NUM
ejpam-3914	152	19	case	case	NOUN
ejpam-3914	152	20	2	2	NUM
ejpam-3914	152	21	:	:	PUNCT
ejpam-3914	152	22	suppose	suppose	VERB
ejpam-3914	152	23	that	that	SCONJ
ejpam-3914	152	24	n	n	NUM
ejpam-3914	152	25	≡	≡	PROPN
ejpam-3914	152	26	1(mod	1(mod	NUM
ejpam-3914	152	27	5	5	NUM
ejpam-3914	152	28	)	)	PUNCT
ejpam-3914	152	29	.	.	PUNCT
ejpam-3914	153	1	by	by	ADP
ejpam-3914	153	2	theorem	theorem	ADJ
ejpam-3914	153	3	2.2	2.2	NUM
ejpam-3914	153	4	,	,	PUNCT
ejpam-3914	153	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	153	6	(	(	PUNCT
ejpam-3914	153	7	pn	pn	NOUN
ejpam-3914	153	8	)	)	PUNCT
ejpam-3914	153	9	=	=	SYM
ejpam-3914	154	1	2n−2	2n−2	PROPN
ejpam-3914	154	2	5	5	NUM
ejpam-3914	154	3	.	.	PUNCT
ejpam-3914	155	1	let	let	VERB
ejpam-3914	155	2	n	n	NOUN
ejpam-3914	155	3	=	=	SYM
ejpam-3914	155	4	6	6	NUM
ejpam-3914	155	5	.	.	PUNCT
ejpam-3914	156	1	then	then	ADV
ejpam-3914	156	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	156	3	(	(	PUNCT
ejpam-3914	156	4	p6	p6	PROPN
ejpam-3914	156	5	)	)	PUNCT
ejpam-3914	156	6	=	=	SYM
ejpam-3914	156	7	2(6)−2	2(6)−2	NUM
ejpam-3914	156	8	5	5	NUM
ejpam-3914	156	9	=	=	SYM
ejpam-3914	156	10	2	2	X
ejpam-3914	156	11	.	.	PUNCT
ejpam-3914	156	12	clearly	clearly	ADV
ejpam-3914	156	13	,	,	PUNCT
ejpam-3914	156	14	s	s	PART
ejpam-3914	156	15	=	=	SYM
ejpam-3914	156	16	{	{	PUNCT
ejpam-3914	156	17	u3	u3	PROPN
ejpam-3914	156	18	,	,	PUNCT
ejpam-3914	156	19	u4	u4	PROPN
ejpam-3914	156	20	}	}	PUNCT
ejpam-3914	156	21	is	be	AUX
ejpam-3914	156	22	the	the	DET
ejpam-3914	156	23	only	only	ADJ
ejpam-3914	156	24	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	156	25	-set	-set	PUNCT
ejpam-3914	156	26	of	of	ADP
ejpam-3914	156	27	p6	p6	PROPN
ejpam-3914	156	28	since	since	SCONJ
ejpam-3914	156	29	u2	u2	NOUN
ejpam-3914	156	30	and	and	CCONJ
ejpam-3914	156	31	u5	u5	PROPN
ejpam-3914	156	32	are	be	AUX
ejpam-3914	156	33	the	the	DET
ejpam-3914	156	34	directly	directly	ADV
ejpam-3914	156	35	observed	observe	VERB
ejpam-3914	156	36	vertices	vertex	NOUN
ejpam-3914	156	37	while	while	SCONJ
ejpam-3914	156	38	u1	u1	NOUN
ejpam-3914	156	39	and	and	CCONJ
ejpam-3914	156	40	u6	u6	NOUN
ejpam-3914	156	41	are	be	AUX
ejpam-3914	156	42	the	the	DET
ejpam-3914	156	43	remotely	remotely	ADV
ejpam-3914	156	44	observed	observe	VERB
ejpam-3914	156	45	vertices	vertex	NOUN
ejpam-3914	156	46	,	,	PUNCT
ejpam-3914	156	47	that	that	ADV
ejpam-3914	156	48	is	is	ADV
ejpam-3914	156	49	,	,	PUNCT
ejpam-3914	156	50	os	os	ADV
ejpam-3914	156	51	v	v	X
ejpam-3914	156	52	(	(	PUNCT
ejpam-3914	156	53	p6	p6	PROPN
ejpam-3914	156	54	)	)	PUNCT
ejpam-3914	156	55	=	=	SYM
ejpam-3914	156	56	v	v	X
ejpam-3914	156	57	(	(	PUNCT
ejpam-3914	156	58	p6	p6	PROPN
ejpam-3914	156	59	)	)	PUNCT
ejpam-3914	156	60	and	and	CCONJ
ejpam-3914	156	61	os	os	PROPN
ejpam-3914	156	62	e(p6	e(p6	NOUN
ejpam-3914	156	63	)	)	PUNCT
ejpam-3914	156	64	=	=	SYM
ejpam-3914	156	65	e(p6	e(p6	NOUN
ejpam-3914	156	66	)	)	PUNCT
ejpam-3914	156	67	and	and	CCONJ
ejpam-3914	156	68	the	the	DET
ejpam-3914	156	69	induced	induced	ADJ
ejpam-3914	156	70	subgraph	subgraph	NOUN
ejpam-3914	156	71	〈	〈	PROPN
ejpam-3914	156	72	s	s	PROPN
ejpam-3914	156	73	〉	〉	PROPN
ejpam-3914	156	74	has	have	VERB
ejpam-3914	156	75	no	no	DET
ejpam-3914	156	76	isolated	isolated	ADJ
ejpam-3914	156	77	vertex	vertex	NOUN
ejpam-3914	156	78	.	.	PUNCT
ejpam-3914	157	1	by	by	ADP
ejpam-3914	157	2	theorem	theorem	NOUN
ejpam-3914	157	3	3.1(i	3.1(i	NUM
ejpam-3914	157	4	)	)	PUNCT
ejpam-3914	157	5	,	,	PUNCT
ejpam-3914	157	6	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	157	7	(	(	PUNCT
ejpam-3914	157	8	p6	p6	PROPN
ejpam-3914	157	9	)	)	PUNCT
ejpam-3914	157	10	=	=	SYM
ejpam-3914	158	1	0	0	X
ejpam-3914	158	2	.	.	PUNCT
ejpam-3914	159	1	now	now	ADV
ejpam-3914	159	2	,	,	PUNCT
ejpam-3914	159	3	suppose	suppose	VERB
ejpam-3914	159	4	that	that	SCONJ
ejpam-3914	159	5	n	n	PROPN
ejpam-3914	159	6	>	>	X
ejpam-3914	159	7	6	6	NUM
ejpam-3914	159	8	.	.	PUNCT
ejpam-3914	160	1	let	let	VERB
ejpam-3914	160	2	p	p	NOUN
ejpam-3914	160	3	=	=	PUNCT
ejpam-3914	160	4	n−1	n−1	PROPN
ejpam-3914	160	5	5	5	NUM
ejpam-3914	160	6	and	and	CCONJ
ejpam-3914	160	7	j	j	NOUN
ejpam-3914	160	8	=	=	SYM
ejpam-3914	160	9	0	0	NUM
ejpam-3914	160	10	,	,	PUNCT
ejpam-3914	160	11	1	1	NUM
ejpam-3914	160	12	,	,	PUNCT
ejpam-3914	160	13	2	2	NUM
ejpam-3914	160	14	,	,	PUNCT
ejpam-3914	160	15	.	.	PUNCT
ejpam-3914	160	16	.	.	PUNCT
ejpam-3914	161	1	.	.	PUNCT
ejpam-3914	162	1	,	,	PUNCT
ejpam-3914	162	2	p−	p−	NOUN
ejpam-3914	162	3	1	1	NUM
ejpam-3914	162	4	,	,	PUNCT
ejpam-3914	162	5	p.	p.	NOUN
ejpam-3914	162	6	group	group	NOUN
ejpam-3914	162	7	the	the	DET
ejpam-3914	162	8	vertices	vertex	NOUN
ejpam-3914	162	9	of	of	ADP
ejpam-3914	162	10	pn	pn	PROPN
ejpam-3914	162	11	into	into	ADP
ejpam-3914	162	12	p+	p+	NOUN
ejpam-3914	162	13	1	1	NUM
ejpam-3914	162	14	disjoint	disjoint	NOUN
ejpam-3914	162	15	subsets	subset	NOUN
ejpam-3914	162	16	rj	rj	PROPN
ejpam-3914	162	17	r0	r0	PROPN
ejpam-3914	162	18	=	=	PUNCT
ejpam-3914	162	19	{	{	PUNCT
ejpam-3914	162	20	u1	u1	NOUN
ejpam-3914	162	21	}	}	PUNCT
ejpam-3914	162	22	r1	r1	NOUN
ejpam-3914	162	23	=	=	SYM
ejpam-3914	162	24	{	{	PUNCT
ejpam-3914	162	25	u2	u2	PROPN
ejpam-3914	162	26	,	,	PUNCT
ejpam-3914	162	27	u3	u3	PROPN
ejpam-3914	162	28	,	,	PUNCT
ejpam-3914	162	29	u4	u4	PROPN
ejpam-3914	162	30	,	,	PUNCT
ejpam-3914	162	31	u5	u5	PROPN
ejpam-3914	162	32	,	,	PUNCT
ejpam-3914	162	33	u6	u6	NOUN
ejpam-3914	162	34	}	}	PUNCT
ejpam-3914	162	35	r2	r2	NOUN
ejpam-3914	162	36	=	=	SYM
ejpam-3914	162	37	{	{	PUNCT
ejpam-3914	162	38	u7	u7	PROPN
ejpam-3914	162	39	,	,	PUNCT
ejpam-3914	162	40	u8	u8	PROPN
ejpam-3914	162	41	,	,	PUNCT
ejpam-3914	162	42	u9	u9	PROPN
ejpam-3914	162	43	,	,	PUNCT
ejpam-3914	162	44	u10	u10	PROPN
ejpam-3914	162	45	,	,	PUNCT
ejpam-3914	162	46	u11	u11	PROPN
ejpam-3914	162	47	}	}	PUNCT
ejpam-3914	162	48	...	...	PUNCT
ejpam-3914	163	1	rp−1	rp−1	NOUN
ejpam-3914	163	2	=	=	SYM
ejpam-3914	163	3	{	{	PUNCT
ejpam-3914	163	4	un−9	un−9	PROPN
ejpam-3914	163	5	,	,	PUNCT
ejpam-3914	163	6	un−8	un−8	ADJ
ejpam-3914	163	7	,	,	PUNCT
ejpam-3914	163	8	un−7	un−7	PROPN
ejpam-3914	163	9	,	,	PUNCT
ejpam-3914	163	10	un−6	un−6	PROPN
ejpam-3914	163	11	,	,	PUNCT
ejpam-3914	163	12	un−5	un−5	PROPN
ejpam-3914	163	13	}	}	PUNCT
ejpam-3914	163	14	rp	rp	NOUN
ejpam-3914	163	15	=	=	SYM
ejpam-3914	163	16	{	{	PUNCT
ejpam-3914	163	17	un−4	un−4	NOUN
ejpam-3914	163	18	,	,	PUNCT
ejpam-3914	163	19	un−3	un−3	ADJ
ejpam-3914	163	20	,	,	PUNCT
ejpam-3914	163	21	un−2	un−2	PROPN
ejpam-3914	163	22	,	,	PUNCT
ejpam-3914	163	23	un−1	un−1	PROPN
ejpam-3914	163	24	,	,	PUNCT
ejpam-3914	163	25	un	un	ADJ
ejpam-3914	163	26	}	}	PUNCT
ejpam-3914	163	27	let	let	VERB
ejpam-3914	163	28	i	i	PRON
ejpam-3914	163	29	=	=	NOUN
ejpam-3914	163	30	2	2	NUM
ejpam-3914	163	31	,	,	PUNCT
ejpam-3914	163	32	7	7	NUM
ejpam-3914	163	33	,	,	PUNCT
ejpam-3914	163	34	12	12	NUM
ejpam-3914	163	35	,	,	PUNCT
ejpam-3914	163	36	.	.	PUNCT
ejpam-3914	163	37	.	.	PUNCT
ejpam-3914	164	1	.	.	PUNCT
ejpam-3914	165	1	,	,	PUNCT
ejpam-3914	165	2	n−	n−	NOUN
ejpam-3914	165	3	4	4	NUM
ejpam-3914	165	4	.	.	PUNCT
ejpam-3914	166	1	for	for	ADP
ejpam-3914	166	2	every	every	DET
ejpam-3914	166	3	induced	induced	ADJ
ejpam-3914	166	4	subgraph	subgraph	NOUN
ejpam-3914	166	5	〈	〈	PROPN
ejpam-3914	166	6	ui	ui	PROPN
ejpam-3914	166	7	,	,	PUNCT
ejpam-3914	166	8	ui+1	ui+1	PROPN
ejpam-3914	166	9	,	,	PUNCT
ejpam-3914	166	10	ui+2	ui+2	NUM
ejpam-3914	166	11	,	,	PUNCT
ejpam-3914	166	12	ui+3	ui+3	NOUN
ejpam-3914	166	13	,	,	PUNCT
ejpam-3914	166	14	ui+4	ui+4	PROPN
ejpam-3914	166	15	〉	〉	NOUN
ejpam-3914	166	16	,	,	PUNCT
ejpam-3914	166	17	the	the	DET
ejpam-3914	166	18	vertices	vertex	NOUN
ejpam-3914	166	19	ui+1	ui+1	PROPN
ejpam-3914	166	20	,	,	PUNCT
ejpam-3914	166	21	ui+2	ui+2	PRON
ejpam-3914	166	22	form	form	VERB
ejpam-3914	166	23	a	a	DET
ejpam-3914	166	24	total	total	ADJ
ejpam-3914	166	25	dr	dr	ADJ
ejpam-3914	166	26	-	-	PUNCT
ejpam-3914	166	27	power	power	NOUN
ejpam-3914	166	28	dominating	dominating	NOUN
ejpam-3914	166	29	set	set	VERB
ejpam-3914	166	30	since	since	SCONJ
ejpam-3914	166	31	ui	ui	PROPN
ejpam-3914	166	32	and	and	CCONJ
ejpam-3914	166	33	ui+3	ui+3	NOUN
ejpam-3914	166	34	are	be	AUX
ejpam-3914	166	35	directly	directly	ADV
ejpam-3914	166	36	observed	observe	VERB
ejpam-3914	166	37	vertices	vertex	NOUN
ejpam-3914	166	38	while	while	SCONJ
ejpam-3914	166	39	u1	u1	NOUN
ejpam-3914	166	40	and	and	CCONJ
ejpam-3914	166	41	ui+4	ui+4	PRON
ejpam-3914	166	42	are	be	AUX
ejpam-3914	166	43	remotely	remotely	ADV
ejpam-3914	166	44	observed	observe	VERB
ejpam-3914	166	45	vertices	vertex	NOUN
ejpam-3914	166	46	for	for	ADP
ejpam-3914	166	47	all	all	DET
ejpam-3914	166	48	i	i	PRON
ejpam-3914	166	49	=	=	NOUN
ejpam-3914	166	50	2	2	NUM
ejpam-3914	166	51	,	,	PUNCT
ejpam-3914	166	52	7	7	NUM
ejpam-3914	166	53	,	,	PUNCT
ejpam-3914	166	54	12	12	NUM
ejpam-3914	166	55	,	,	PUNCT
ejpam-3914	166	56	.	.	PUNCT
ejpam-3914	166	57	.	.	PUNCT
ejpam-3914	167	1	.	.	PUNCT
ejpam-3914	168	1	,	,	PUNCT
ejpam-3914	168	2	n−	n−	NOUN
ejpam-3914	168	3	9	9	NUM
ejpam-3914	168	4	,	,	PUNCT
ejpam-3914	168	5	n−	n−	NOUN
ejpam-3914	168	6	4	4	NUM
ejpam-3914	168	7	.	.	PUNCT
ejpam-3914	168	8	let	let	VERB
ejpam-3914	168	9	the	the	DET
ejpam-3914	168	10	set	set	NOUN
ejpam-3914	168	11	r	r	NOUN
ejpam-3914	168	12	=	=	SYM
ejpam-3914	168	13	{	{	PUNCT
ejpam-3914	168	14	ui+1	ui+1	PROPN
ejpam-3914	168	15	,	,	PUNCT
ejpam-3914	168	16	ui+2	ui+2	NUM
ejpam-3914	168	17	:	:	PUNCT
ejpam-3914	169	1	i	i	NOUN
ejpam-3914	169	2	=	=	NOUN
ejpam-3914	169	3	2	2	NUM
ejpam-3914	169	4	,	,	PUNCT
ejpam-3914	169	5	7	7	NUM
ejpam-3914	169	6	,	,	PUNCT
ejpam-3914	169	7	12	12	NUM
ejpam-3914	169	8	,	,	PUNCT
ejpam-3914	169	9	.	.	PUNCT
ejpam-3914	169	10	.	.	PUNCT
ejpam-3914	169	11	.	.	PUNCT
ejpam-3914	170	1	,	,	PUNCT
ejpam-3914	170	2	n−	n−	NOUN
ejpam-3914	170	3	9	9	NUM
ejpam-3914	170	4	,	,	PUNCT
ejpam-3914	170	5	n−	n−	NOUN
ejpam-3914	170	6	4	4	NUM
ejpam-3914	170	7	}	}	PUNCT
ejpam-3914	170	8	=	=	SYM
ejpam-3914	170	9	{	{	PUNCT
ejpam-3914	170	10	u3	u3	PROPN
ejpam-3914	170	11	,	,	PUNCT
ejpam-3914	170	12	u4	u4	PROPN
ejpam-3914	170	13	,	,	PUNCT
ejpam-3914	170	14	u8	u8	PROPN
ejpam-3914	170	15	,	,	PUNCT
ejpam-3914	170	16	u9	u9	PROPN
ejpam-3914	170	17	,	,	PUNCT
ejpam-3914	170	18	.	.	PUNCT
ejpam-3914	170	19	.	.	PUNCT
ejpam-3914	171	1	.	.	PUNCT
ejpam-3914	172	1	,	,	PUNCT
ejpam-3914	172	2	un−8	un−8	ADJ
ejpam-3914	172	3	,	,	PUNCT
ejpam-3914	172	4	un−7	un−7	NOUN
ejpam-3914	172	5	,	,	PUNCT
ejpam-3914	172	6	un−3	un−3	ADJ
ejpam-3914	172	7	,	,	PUNCT
ejpam-3914	172	8	un−2	un−2	VERB
ejpam-3914	172	9	}	}	PUNCT
ejpam-3914	172	10	where	where	SCONJ
ejpam-3914	172	11	|r|	|r|	NOUN
ejpam-3914	173	1	=	=	NOUN
ejpam-3914	173	2	2p	2p	NUM
ejpam-3914	173	3	=	=	SYM
ejpam-3914	173	4	2n−2	2n−2	NUM
ejpam-3914	173	5	5	5	NUM
ejpam-3914	173	6	,	,	PUNCT
ejpam-3914	173	7	or	or	CCONJ
ejpam-3914	173	8	v	v	NOUN
ejpam-3914	173	9	(	(	PUNCT
ejpam-3914	173	10	pn	pn	NOUN
ejpam-3914	173	11	)	)	PUNCT
ejpam-3914	173	12	=	=	NOUN
ejpam-3914	173	13	v	v	X
ejpam-3914	173	14	(	(	PUNCT
ejpam-3914	173	15	pn	pn	NOUN
ejpam-3914	173	16	)	)	PUNCT
ejpam-3914	173	17	,	,	PUNCT
ejpam-3914	173	18	or	or	CCONJ
ejpam-3914	173	19	e(pn	e(pn	NUM
ejpam-3914	173	20	)	)	PUNCT
ejpam-3914	173	21	=	=	SYM
ejpam-3914	173	22	e(pn	e(pn	NUM
ejpam-3914	173	23	)	)	PUNCT
ejpam-3914	173	24	,	,	PUNCT
ejpam-3914	173	25	and	and	CCONJ
ejpam-3914	173	26	the	the	DET
ejpam-3914	173	27	induced	induced	ADJ
ejpam-3914	173	28	subgraph	subgraph	NOUN
ejpam-3914	173	29	〈	〈	PROPN
ejpam-3914	173	30	r	r	PROPN
ejpam-3914	173	31	〉	〉	PROPN
ejpam-3914	173	32	has	have	VERB
ejpam-3914	173	33	no	no	DET
ejpam-3914	173	34	isolated	isolated	ADJ
ejpam-3914	173	35	vertex	vertex	NOUN
ejpam-3914	173	36	.	.	PUNCT
ejpam-3914	174	1	by	by	ADP
ejpam-3914	174	2	theorem	theorem	NOUN
ejpam-3914	174	3	2.2	2.2	NUM
ejpam-3914	174	4	,	,	PUNCT
ejpam-3914	174	5	r	r	NOUN
ejpam-3914	174	6	is	be	AUX
ejpam-3914	174	7	a	a	DET
ejpam-3914	174	8	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	174	9	-set	-set	PROPN
ejpam-3914	174	10	of	of	ADP
ejpam-3914	174	11	pn	pn	PROPN
ejpam-3914	174	12	.	.	PROPN
ejpam-3914	174	13	note	note	VERB
ejpam-3914	174	14	that	that	SCONJ
ejpam-3914	174	15	the	the	DET
ejpam-3914	174	16	set	set	NOUN
ejpam-3914	174	17	r	r	NOUN
ejpam-3914	174	18	contains	contain	VERB
ejpam-3914	174	19	pairs	pair	NOUN
ejpam-3914	174	20	of	of	ADP
ejpam-3914	174	21	adjacent	adjacent	ADJ
ejpam-3914	174	22	vertices	vertex	NOUN
ejpam-3914	174	23	in	in	ADP
ejpam-3914	174	24	each	each	DET
ejpam-3914	174	25	rj	rj	PROPN
ejpam-3914	174	26	’s	’s	ADV
ejpam-3914	174	27	except	except	SCONJ
ejpam-3914	174	28	in	in	ADP
ejpam-3914	174	29	r0	r0	NOUN
ejpam-3914	174	30	and	and	CCONJ
ejpam-3914	174	31	the	the	DET
ejpam-3914	174	32	distance	distance	NOUN
ejpam-3914	174	33	between	between	ADP
ejpam-3914	174	34	the	the	DET
ejpam-3914	174	35	last	last	ADJ
ejpam-3914	174	36	choosen	choosen	ADJ
ejpam-3914	174	37	vertex	vertex	NOUN
ejpam-3914	174	38	in	in	ADP
ejpam-3914	174	39	rj	rj	PROPN
ejpam-3914	174	40	and	and	CCONJ
ejpam-3914	174	41	the	the	DET
ejpam-3914	174	42	first	first	ADJ
ejpam-3914	174	43	choosen	choosen	ADJ
ejpam-3914	174	44	vertex	vertex	NOUN
ejpam-3914	174	45	in	in	ADP
ejpam-3914	174	46	rj+1	rj+1	NOUN
ejpam-3914	174	47	is	be	AUX
ejpam-3914	174	48	always	always	ADV
ejpam-3914	174	49	4	4	NUM
ejpam-3914	174	50	.	.	PUNCT
ejpam-3914	175	1	let	let	AUX
ejpam-3914	175	2	t	t	PROPN
ejpam-3914	175	3	be	be	AUX
ejpam-3914	175	4	a	a	DET
ejpam-3914	175	5	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	175	6	-set	-set	PUNCT
ejpam-3914	175	7	of	of	ADP
ejpam-3914	175	8	pn	pn	PROPN
ejpam-3914	175	9	different	different	ADJ
ejpam-3914	175	10	from	from	ADP
ejpam-3914	175	11	r.	r.	PROPN
ejpam-3914	175	12	consider	consider	VERB
ejpam-3914	175	13	the	the	DET
ejpam-3914	175	14	following	follow	VERB
ejpam-3914	175	15	subcases	subcase	NOUN
ejpam-3914	175	16	:	:	PUNCT
ejpam-3914	175	17	subcase	subcase	NOUN
ejpam-3914	175	18	1	1	NUM
ejpam-3914	175	19	:	:	PUNCT
ejpam-3914	175	20	let	let	VERB
ejpam-3914	175	21	u2	u2	NOUN
ejpam-3914	175	22	,	,	PUNCT
ejpam-3914	175	23	u3	u3	NOUN
ejpam-3914	175	24	∈	∈	PROPN
ejpam-3914	175	25	t	t	PROPN
ejpam-3914	175	26	.	.	PUNCT
ejpam-3914	176	1	then	then	ADV
ejpam-3914	176	2	the	the	DET
ejpam-3914	176	3	next	next	ADJ
ejpam-3914	176	4	vertex	vertex	NOUN
ejpam-3914	176	5	to	to	PART
ejpam-3914	176	6	be	be	AUX
ejpam-3914	176	7	chosen	choose	VERB
ejpam-3914	176	8	must	must	AUX
ejpam-3914	176	9	be	be	AUX
ejpam-3914	176	10	of	of	ADP
ejpam-3914	176	11	distance	distance	NOUN
ejpam-3914	176	12	4	4	NUM
ejpam-3914	176	13	from	from	ADP
ejpam-3914	176	14	u3	u3	NOUN
ejpam-3914	176	15	,	,	PUNCT
ejpam-3914	176	16	that	that	ADV
ejpam-3914	176	17	is	is	ADV
ejpam-3914	176	18	,	,	PUNCT
ejpam-3914	176	19	the	the	DET
ejpam-3914	176	20	vertex	vertex	NOUN
ejpam-3914	176	21	u7	u7	PROPN
ejpam-3914	176	22	,	,	PUNCT
ejpam-3914	176	23	together	together	ADV
ejpam-3914	176	24	with	with	ADP
ejpam-3914	176	25	u8	u8	PROPN
ejpam-3914	176	26	,	,	PUNCT
ejpam-3914	176	27	must	must	AUX
ejpam-3914	176	28	be	be	AUX
ejpam-3914	176	29	in	in	ADP
ejpam-3914	176	30	t	t	PROPN
ejpam-3914	176	31	.	.	PUNCT
ejpam-3914	177	1	thus	thus	ADV
ejpam-3914	177	2	,	,	PUNCT
ejpam-3914	177	3	ui	ui	PROPN
ejpam-3914	177	4	,	,	PUNCT
ejpam-3914	177	5	ui+1	ui+1	PROPN
ejpam-3914	177	6	∈	∈	PROPN
ejpam-3914	177	7	t	t	NOUN
ejpam-3914	177	8	for	for	ADP
ejpam-3914	177	9	all	all	DET
ejpam-3914	177	10	i	i	PRON
ejpam-3914	177	11	=	=	NOUN
ejpam-3914	177	12	2	2	NUM
ejpam-3914	177	13	,	,	PUNCT
ejpam-3914	177	14	7	7	NUM
ejpam-3914	177	15	,	,	PUNCT
ejpam-3914	177	16	.	.	PUNCT
ejpam-3914	177	17	.	.	PUNCT
ejpam-3914	177	18	.	.	PUNCT
ejpam-3914	178	1	,	,	PUNCT
ejpam-3914	178	2	n−	n−	NOUN
ejpam-3914	178	3	9	9	NUM
ejpam-3914	178	4	,	,	PUNCT
ejpam-3914	178	5	n−	n−	NOUN
ejpam-3914	178	6	4	4	NUM
ejpam-3914	178	7	.	.	PUNCT
ejpam-3914	179	1	it	it	PRON
ejpam-3914	179	2	follows	follow	VERB
ejpam-3914	179	3	that	that	DET
ejpam-3914	179	4	t	t	NOUN
ejpam-3914	179	5	=	=	SYM
ejpam-3914	179	6	{	{	PUNCT
ejpam-3914	179	7	u2	u2	PROPN
ejpam-3914	179	8	,	,	PUNCT
ejpam-3914	179	9	u3	u3	PROPN
ejpam-3914	179	10	,	,	PUNCT
ejpam-3914	179	11	u7	u7	PROPN
ejpam-3914	179	12	,	,	PUNCT
ejpam-3914	179	13	u8	u8	PROPN
ejpam-3914	179	14	,	,	PUNCT
ejpam-3914	179	15	.	.	PUNCT
ejpam-3914	179	16	.	.	PUNCT
ejpam-3914	180	1	.	.	PUNCT
ejpam-3914	181	1	,	,	PUNCT
ejpam-3914	181	2	un−9	un−9	PROPN
ejpam-3914	181	3	,	,	PUNCT
ejpam-3914	181	4	un−8	un−8	ADJ
ejpam-3914	181	5	,	,	PUNCT
ejpam-3914	181	6	un−4	un−4	NOUN
ejpam-3914	181	7	,	,	PUNCT
ejpam-3914	181	8	un−3	un−3	ADJ
ejpam-3914	181	9	}	}	PUNCT
ejpam-3914	181	10	and	and	CCONJ
ejpam-3914	181	11	|t	|t	VERB
ejpam-3914	181	12	|	|	ADV
ejpam-3914	181	13	=	=	SYM
ejpam-3914	181	14	|r|	|r|	PROPN
ejpam-3914	181	15	.	.	PUNCT
ejpam-3914	181	16	since	since	SCONJ
ejpam-3914	181	17	un−3	un−3	PROPN
ejpam-3914	181	18	is	be	AUX
ejpam-3914	181	19	the	the	DET
ejpam-3914	181	20	last	last	ADJ
ejpam-3914	181	21	vertex	vertex	NOUN
ejpam-3914	181	22	in	in	ADP
ejpam-3914	181	23	t	t	PROPN
ejpam-3914	181	24	,	,	PUNCT
ejpam-3914	181	25	the	the	DET
ejpam-3914	181	26	vertex	vertex	NOUN
ejpam-3914	181	27	un−2	un−2	NOUN
ejpam-3914	181	28	is	be	AUX
ejpam-3914	181	29	a	a	DET
ejpam-3914	181	30	directly	directly	ADV
ejpam-3914	181	31	observed	observe	VERB
ejpam-3914	181	32	vertex	vertex	NOUN
ejpam-3914	181	33	and	and	CCONJ
ejpam-3914	181	34	un−1	un−1	PROPN
ejpam-3914	181	35	is	be	AUX
ejpam-3914	181	36	a	a	DET
ejpam-3914	181	37	remotely	remotely	ADV
ejpam-3914	181	38	observed	observe	VERB
ejpam-3914	181	39	vertex	vertex	NOUN
ejpam-3914	181	40	.	.	PUNCT
ejpam-3914	182	1	hence	hence	ADV
ejpam-3914	182	2	,	,	PUNCT
ejpam-3914	182	3	un	un	PROPN
ejpam-3914	182	4	is	be	AUX
ejpam-3914	182	5	neither	neither	CCONJ
ejpam-3914	182	6	a	a	PRON
ejpam-3914	182	7	directly	directly	ADV
ejpam-3914	182	8	or	or	CCONJ
ejpam-3914	182	9	a	a	DET
ejpam-3914	182	10	remotely	remotely	ADV
ejpam-3914	182	11	observed	observe	VERB
ejpam-3914	182	12	vertex	vertex	NOUN
ejpam-3914	182	13	.	.	PUNCT
ejpam-3914	183	1	thus	thus	ADV
ejpam-3914	183	2	,	,	PUNCT
ejpam-3914	183	3	ot	ot	NOUN
ejpam-3914	183	4	v	v	X
ejpam-3914	183	5	(	(	PUNCT
ejpam-3914	183	6	pn	pn	NOUN
ejpam-3914	183	7	)	)	PUNCT
ejpam-3914	183	8	6=	6=	ADP
ejpam-3914	183	9	v	v	PROPN
ejpam-3914	183	10	(	(	PUNCT
ejpam-3914	183	11	pn	pn	NOUN
ejpam-3914	183	12	)	)	PUNCT
ejpam-3914	183	13	,	,	PUNCT
ejpam-3914	183	14	a	a	DET
ejpam-3914	183	15	contradiction	contradiction	NOUN
ejpam-3914	183	16	,	,	PUNCT
ejpam-3914	183	17	that	that	ADV
ejpam-3914	183	18	is	is	ADV
ejpam-3914	183	19	,	,	PUNCT
ejpam-3914	183	20	t	t	PROPN
ejpam-3914	183	21	is	be	AUX
ejpam-3914	183	22	not	not	PART
ejpam-3914	183	23	a	a	DET
ejpam-3914	183	24	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	183	25	-set	-set	PROPN
ejpam-3914	183	26	of	of	ADP
ejpam-3914	183	27	pn	pn	PROPN
ejpam-3914	183	28	.	.	PROPN
ejpam-3914	184	1	hence	hence	ADV
ejpam-3914	184	2	,	,	PUNCT
ejpam-3914	184	3	it	it	PRON
ejpam-3914	184	4	is	be	AUX
ejpam-3914	184	5	not	not	PART
ejpam-3914	184	6	possible	possible	ADJ
ejpam-3914	184	7	to	to	PART
ejpam-3914	184	8	start	start	VERB
ejpam-3914	184	9	with	with	ADP
ejpam-3914	184	10	the	the	DET
ejpam-3914	184	11	vertex	vertex	NOUN
ejpam-3914	184	12	u2	u2	NOUN
ejpam-3914	184	13	to	to	PART
ejpam-3914	184	14	form	form	VERB
ejpam-3914	184	15	a	a	DET
ejpam-3914	184	16	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	184	17	-set	-set	PROPN
ejpam-3914	184	18	t	t	PROPN
ejpam-3914	184	19	.	.	PUNCT
ejpam-3914	185	1	similarly	similarly	ADV
ejpam-3914	185	2	,	,	PUNCT
ejpam-3914	185	3	it	it	PRON
ejpam-3914	185	4	is	be	AUX
ejpam-3914	185	5	not	not	PART
ejpam-3914	185	6	possible	possible	ADJ
ejpam-3914	185	7	to	to	PART
ejpam-3914	185	8	start	start	VERB
ejpam-3914	185	9	with	with	ADP
ejpam-3914	185	10	the	the	DET
ejpam-3914	185	11	vertex	vertex	NOUN
ejpam-3914	185	12	u1	u1	NOUN
ejpam-3914	185	13	.	.	PUNCT
ejpam-3914	186	1	subcase	subcase	PROPN
ejpam-3914	186	2	2	2	NUM
ejpam-3914	186	3	:	:	PUNCT
ejpam-3914	186	4	suppose	suppose	VERB
ejpam-3914	186	5	that	that	SCONJ
ejpam-3914	186	6	u3	u3	PROPN
ejpam-3914	186	7	,	,	PUNCT
ejpam-3914	186	8	u4	u4	PROPN
ejpam-3914	186	9	∈	∈	PROPN
ejpam-3914	186	10	t	t	PROPN
ejpam-3914	186	11	.	.	PUNCT
ejpam-3914	187	1	now	now	ADV
ejpam-3914	187	2	,	,	PUNCT
ejpam-3914	187	3	replace	replace	VERB
ejpam-3914	187	4	u8	u8	PROPN
ejpam-3914	187	5	∈	∈	PROPN
ejpam-3914	187	6	r	r	NOUN
ejpam-3914	187	7	by	by	ADP
ejpam-3914	187	8	u7	u7	PROPN
ejpam-3914	187	9	to	to	PART
ejpam-3914	187	10	form	form	VERB
ejpam-3914	187	11	t	t	PROPN
ejpam-3914	187	12	.	.	PUNCT
ejpam-3914	188	1	then	then	ADV
ejpam-3914	188	2	the	the	DET
ejpam-3914	188	3	next	next	ADJ
ejpam-3914	188	4	vertex	vertex	NOUN
ejpam-3914	188	5	to	to	PART
ejpam-3914	188	6	be	be	AUX
ejpam-3914	188	7	chosen	choose	VERB
ejpam-3914	188	8	must	must	AUX
ejpam-3914	188	9	be	be	AUX
ejpam-3914	188	10	u8	u8	PROPN
ejpam-3914	188	11	,	,	PUNCT
ejpam-3914	188	12	that	that	ADV
ejpam-3914	188	13	is	is	ADV
ejpam-3914	188	14	,	,	PUNCT
ejpam-3914	188	15	the	the	DET
ejpam-3914	188	16	vertex	vertex	NOUN
ejpam-3914	188	17	ui	ui	PROPN
ejpam-3914	188	18	,	,	PUNCT
ejpam-3914	188	19	ui+1	ui+1	PROPN
ejpam-3914	188	20	must	must	AUX
ejpam-3914	188	21	be	be	AUX
ejpam-3914	188	22	in	in	ADP
ejpam-3914	188	23	t	t	PROPN
ejpam-3914	188	24	for	for	ADP
ejpam-3914	188	25	all	all	DET
ejpam-3914	188	26	i	i	PRON
ejpam-3914	188	27	=	=	NOUN
ejpam-3914	188	28	7	7	NUM
ejpam-3914	188	29	,	,	PUNCT
ejpam-3914	188	30	12	12	NUM
ejpam-3914	188	31	,	,	PUNCT
ejpam-3914	188	32	.	.	PUNCT
ejpam-3914	188	33	.	.	PUNCT
ejpam-3914	189	1	.	.	PUNCT
ejpam-3914	190	1	,	,	PUNCT
ejpam-3914	190	2	n	n	CCONJ
ejpam-3914	190	3	−	−	PROPN
ejpam-3914	190	4	9	9	NUM
ejpam-3914	190	5	,	,	PUNCT
ejpam-3914	190	6	n	n	CCONJ
ejpam-3914	190	7	−	−	PROPN
ejpam-3914	190	8	4	4	NUM
ejpam-3914	190	9	.	.	PUNCT
ejpam-3914	191	1	then	then	ADV
ejpam-3914	191	2	t	t	PROPN
ejpam-3914	191	3	=	=	SYM
ejpam-3914	191	4	{	{	PUNCT
ejpam-3914	191	5	u3	u3	PROPN
ejpam-3914	191	6	,	,	PUNCT
ejpam-3914	191	7	u4	u4	PROPN
ejpam-3914	191	8	,	,	PUNCT
ejpam-3914	191	9	u7	u7	PROPN
ejpam-3914	191	10	,	,	PUNCT
ejpam-3914	191	11	u8	u8	PROPN
ejpam-3914	191	12	,	,	PUNCT
ejpam-3914	191	13	u13	u13	NOUN
ejpam-3914	191	14	,	,	PUNCT
ejpam-3914	191	15	u14	u14	NOUN
ejpam-3914	191	16	,	,	PUNCT
ejpam-3914	191	17	.	.	PUNCT
ejpam-3914	191	18	.	.	PUNCT
ejpam-3914	192	1	.	.	PUNCT
ejpam-3914	193	1	,	,	PUNCT
ejpam-3914	193	2	un−4	un−4	NOUN
ejpam-3914	193	3	,	,	PUNCT
ejpam-3914	193	4	un−3	un−3	ADJ
ejpam-3914	193	5	}	}	PUNCT
ejpam-3914	193	6	and	and	CCONJ
ejpam-3914	193	7	|t	|t	VERB
ejpam-3914	194	1	|	|	ADV
ejpam-3914	194	2	=	=	SYM
ejpam-3914	194	3	|r|	|r|	PROPN
ejpam-3914	194	4	.	.	PUNCT
ejpam-3914	194	5	since	since	SCONJ
ejpam-3914	194	6	un−3	un−3	PROPN
ejpam-3914	194	7	is	be	AUX
ejpam-3914	194	8	the	the	DET
ejpam-3914	194	9	last	last	ADJ
ejpam-3914	194	10	vertex	vertex	NOUN
ejpam-3914	194	11	in	in	ADP
ejpam-3914	194	12	t	t	PROPN
ejpam-3914	194	13	,	,	PUNCT
ejpam-3914	194	14	by	by	ADP
ejpam-3914	194	15	previous	previous	ADJ
ejpam-3914	194	16	subcase	subcase	NOUN
ejpam-3914	194	17	,	,	PUNCT
ejpam-3914	194	18	t	t	PROPN
ejpam-3914	194	19	is	be	AUX
ejpam-3914	194	20	not	not	PART
ejpam-3914	194	21	a	a	DET
ejpam-3914	194	22	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	194	23	-set	-set	PROPN
ejpam-3914	194	24	of	of	ADP
ejpam-3914	194	25	pn	pn	PROPN
ejpam-3914	194	26	.	.	PROPN
ejpam-3914	195	1	since	since	SCONJ
ejpam-3914	195	2	u8	u8	PROPN
ejpam-3914	195	3	is	be	AUX
ejpam-3914	195	4	arbitrarily	arbitrarily	ADV
ejpam-3914	195	5	replaced	replace	VERB
ejpam-3914	195	6	from	from	ADP
ejpam-3914	195	7	r	r	NOUN
ejpam-3914	195	8	,	,	PUNCT
ejpam-3914	195	9	we	we	PRON
ejpam-3914	195	10	can	can	AUX
ejpam-3914	195	11	not	not	PART
ejpam-3914	195	12	replace	replace	VERB
ejpam-3914	195	13	the	the	DET
ejpam-3914	195	14	vertex	vertex	NOUN
ejpam-3914	195	15	ui+1	ui+1	NOUN
ejpam-3914	195	16	in	in	ADP
ejpam-3914	195	17	r	r	NOUN
ejpam-3914	195	18	,	,	PUNCT
ejpam-3914	195	19	where	where	SCONJ
ejpam-3914	195	20	i	i	PRON
ejpam-3914	195	21	=	=	NOUN
ejpam-3914	195	22	7	7	NUM
ejpam-3914	195	23	,	,	PUNCT
ejpam-3914	195	24	12	12	NUM
ejpam-3914	195	25	,	,	PUNCT
ejpam-3914	195	26	.	.	PUNCT
ejpam-3914	195	27	.	.	PUNCT
ejpam-3914	196	1	.	.	PUNCT
ejpam-3914	197	1	,	,	PUNCT
ejpam-3914	197	2	n−	n−	NOUN
ejpam-3914	197	3	9	9	NUM
ejpam-3914	197	4	,	,	PUNCT
ejpam-3914	197	5	n−	n−	NOUN
ejpam-3914	197	6	4	4	NUM
ejpam-3914	197	7	to	to	PART
ejpam-3914	197	8	form	form	VERB
ejpam-3914	197	9	c.	c.	PROPN
ejpam-3914	197	10	armada	armada	PROPN
ejpam-3914	197	11	/	/	SYM
ejpam-3914	197	12	eur	eur	PROPN
ejpam-3914	197	13	.	.	PUNCT
ejpam-3914	198	1	j.	j.	PROPN
ejpam-3914	198	2	pure	pure	PROPN
ejpam-3914	198	3	appl	appl	PROPN
ejpam-3914	198	4	.	.	PROPN
ejpam-3914	198	5	math	math	PROPN
ejpam-3914	198	6	,	,	PUNCT
ejpam-3914	198	7	14	14	NUM
ejpam-3914	198	8	(	(	PUNCT
ejpam-3914	198	9	2	2	NUM
ejpam-3914	198	10	)	)	PUNCT
ejpam-3914	198	11	(	(	PUNCT
ejpam-3914	198	12	2021	2021	NUM
ejpam-3914	198	13	)	)	PUNCT
ejpam-3914	198	14	,	,	PUNCT
ejpam-3914	198	15	451	451	NUM
ejpam-3914	198	16	-	-	SYM
ejpam-3914	198	17	470	470	NUM
ejpam-3914	198	18	457	457	NUM
ejpam-3914	198	19	another	another	PRON
ejpam-3914	198	20	γ∗tpw	γ∗tpw	SYM
ejpam-3914	198	21	-set	-set	PROPN
ejpam-3914	198	22	of	of	ADP
ejpam-3914	198	23	pn	pn	PROPN
ejpam-3914	198	24	.	.	PUNCT
ejpam-3914	199	1	thus	thus	ADV
ejpam-3914	199	2	,	,	PUNCT
ejpam-3914	199	3	either	either	PRON
ejpam-3914	199	4	of	of	ADP
ejpam-3914	199	5	the	the	DET
ejpam-3914	199	6	subcases	subcase	NOUN
ejpam-3914	199	7	,	,	PUNCT
ejpam-3914	199	8	it	it	PRON
ejpam-3914	199	9	is	be	AUX
ejpam-3914	199	10	not	not	PART
ejpam-3914	199	11	possible	possible	ADJ
ejpam-3914	199	12	to	to	PART
ejpam-3914	199	13	form	form	VERB
ejpam-3914	199	14	another	another	DET
ejpam-3914	199	15	γ∗tpw	γ∗tpw	SYM
ejpam-3914	199	16	-set	-set	PUNCT
ejpam-3914	199	17	t	t	PROPN
ejpam-3914	199	18	of	of	ADP
ejpam-3914	199	19	pn	pn	PROPN
ejpam-3914	199	20	which	which	PRON
ejpam-3914	199	21	is	be	AUX
ejpam-3914	199	22	different	different	ADJ
ejpam-3914	199	23	from	from	ADP
ejpam-3914	199	24	r.	r.	PROPN
ejpam-3914	199	25	therefore	therefore	ADV
ejpam-3914	199	26	,	,	PUNCT
ejpam-3914	199	27	r	r	NOUN
ejpam-3914	199	28	is	be	AUX
ejpam-3914	199	29	a	a	DET
ejpam-3914	199	30	unique	unique	ADJ
ejpam-3914	199	31	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	199	32	-set	-set	NUM
ejpam-3914	199	33	of	of	ADP
ejpam-3914	199	34	pn	pn	PROPN
ejpam-3914	199	35	.	.	PROPN
ejpam-3914	199	36	by	by	ADP
ejpam-3914	199	37	theorem	theorem	NOUN
ejpam-3914	199	38	3.1(i	3.1(i	NUM
ejpam-3914	199	39	)	)	PUNCT
ejpam-3914	199	40	,	,	PUNCT
ejpam-3914	199	41	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	199	42	(	(	PUNCT
ejpam-3914	199	43	pn	pn	NOUN
ejpam-3914	199	44	)	)	PUNCT
ejpam-3914	199	45	=	=	SYM
ejpam-3914	200	1	0	0	X
ejpam-3914	200	2	.	.	PUNCT
ejpam-3914	200	3	case	case	NOUN
ejpam-3914	200	4	3	3	X
ejpam-3914	200	5	:	:	PUNCT
ejpam-3914	200	6	suppose	suppose	VERB
ejpam-3914	200	7	that	that	SCONJ
ejpam-3914	200	8	n	n	PROPN
ejpam-3914	200	9	6=	6=	NUM
ejpam-3914	200	10	7	7	NUM
ejpam-3914	200	11	and	and	CCONJ
ejpam-3914	200	12	n	n	PRON
ejpam-3914	200	13	≡	≡	PROPN
ejpam-3914	200	14	2(mod	2(mod	NUM
ejpam-3914	200	15	5	5	NUM
ejpam-3914	200	16	)	)	PUNCT
ejpam-3914	200	17	.	.	PUNCT
ejpam-3914	201	1	by	by	ADP
ejpam-3914	201	2	theorem	theorem	ADJ
ejpam-3914	201	3	2.2	2.2	NUM
ejpam-3914	201	4	,	,	PUNCT
ejpam-3914	201	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	201	6	(	(	PUNCT
ejpam-3914	201	7	pn	pn	NOUN
ejpam-3914	201	8	)	)	PUNCT
ejpam-3914	201	9	=	=	SYM
ejpam-3914	202	1	2n+1	2n+1	NOUN
ejpam-3914	202	2	5	5	NUM
ejpam-3914	202	3	.	.	PUNCT
ejpam-3914	203	1	let	let	VERB
ejpam-3914	203	2	n	n	NOUN
ejpam-3914	203	3	=	=	NOUN
ejpam-3914	203	4	12	12	NUM
ejpam-3914	203	5	.	.	PUNCT
ejpam-3914	204	1	then	then	ADV
ejpam-3914	204	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	204	3	(	(	PUNCT
ejpam-3914	204	4	p12	p12	NOUN
ejpam-3914	204	5	)	)	PUNCT
ejpam-3914	204	6	=	=	SYM
ejpam-3914	204	7	2(12)+1	2(12)+1	NUM
ejpam-3914	204	8	5	5	NUM
ejpam-3914	204	9	=	=	SYM
ejpam-3914	204	10	5	5	X
ejpam-3914	204	11	.	.	PUNCT
ejpam-3914	204	12	clearly	clearly	ADV
ejpam-3914	204	13	,	,	PUNCT
ejpam-3914	204	14	s1	s1	PROPN
ejpam-3914	204	15	=	=	SYM
ejpam-3914	204	16	{	{	PUNCT
ejpam-3914	204	17	u3	u3	PROPN
ejpam-3914	204	18	,	,	PUNCT
ejpam-3914	204	19	u4	u4	PROPN
ejpam-3914	204	20	,	,	PUNCT
ejpam-3914	204	21	u5	u5	PROPN
ejpam-3914	204	22	,	,	PUNCT
ejpam-3914	204	23	u9	u9	PROPN
ejpam-3914	204	24	,	,	PUNCT
ejpam-3914	204	25	u10	u10	PROPN
ejpam-3914	204	26	}	}	PUNCT
ejpam-3914	204	27	and	and	CCONJ
ejpam-3914	204	28	s2	s2	PROPN
ejpam-3914	204	29	=	=	SYM
ejpam-3914	204	30	{	{	PUNCT
ejpam-3914	204	31	u3	u3	PROPN
ejpam-3914	204	32	,	,	PUNCT
ejpam-3914	204	33	u4	u4	PROPN
ejpam-3914	204	34	,	,	PUNCT
ejpam-3914	204	35	u8	u8	PROPN
ejpam-3914	204	36	,	,	PUNCT
ejpam-3914	204	37	u9	u9	PROPN
ejpam-3914	204	38	,	,	PUNCT
ejpam-3914	204	39	u10	u10	PROPN
ejpam-3914	204	40	}	}	PUNCT
ejpam-3914	204	41	are	be	AUX
ejpam-3914	204	42	the	the	DET
ejpam-3914	204	43	only	only	ADJ
ejpam-3914	204	44	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	204	45	-sets	-set	NOUN
ejpam-3914	204	46	of	of	ADP
ejpam-3914	204	47	p12	p12	NOUN
ejpam-3914	204	48	.	.	PUNCT
ejpam-3914	205	1	since	since	SCONJ
ejpam-3914	205	2	u5	u5	PROPN
ejpam-3914	205	3	∈	∈	PROPN
ejpam-3914	205	4	s1	s1	NOUN
ejpam-3914	205	5	and	and	CCONJ
ejpam-3914	205	6	u5	u5	PROPN
ejpam-3914	205	7	/∈	/∈	PROPN
ejpam-3914	205	8	s2	s2	PROPN
ejpam-3914	205	9	,	,	PUNCT
ejpam-3914	205	10	by	by	ADP
ejpam-3914	205	11	theorem	theorem	NOUN
ejpam-3914	205	12	3.1(ii	3.1(ii	NUM
ejpam-3914	205	13	)	)	PUNCT
ejpam-3914	205	14	,	,	PUNCT
ejpam-3914	205	15	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	205	16	(	(	PUNCT
ejpam-3914	205	17	p12	p12	NOUN
ejpam-3914	205	18	)	)	PUNCT
ejpam-3914	205	19	=	=	SYM
ejpam-3914	205	20	1	1	X
ejpam-3914	205	21	.	.	PUNCT
ejpam-3914	205	22	now	now	ADV
ejpam-3914	205	23	,	,	PUNCT
ejpam-3914	205	24	suppose	suppose	VERB
ejpam-3914	205	25	that	that	SCONJ
ejpam-3914	205	26	n	n	PROPN
ejpam-3914	205	27	>	>	X
ejpam-3914	205	28	12	12	NUM
ejpam-3914	205	29	.	.	PUNCT
ejpam-3914	206	1	let	let	VERB
ejpam-3914	206	2	p	p	NOUN
ejpam-3914	206	3	=	=	PUNCT
ejpam-3914	206	4	n−2	n−2	PROPN
ejpam-3914	206	5	5	5	NUM
ejpam-3914	206	6	and	and	CCONJ
ejpam-3914	206	7	j	j	NOUN
ejpam-3914	206	8	=	=	SYM
ejpam-3914	206	9	0	0	NUM
ejpam-3914	206	10	,	,	PUNCT
ejpam-3914	206	11	1	1	NUM
ejpam-3914	206	12	,	,	PUNCT
ejpam-3914	206	13	2	2	NUM
ejpam-3914	206	14	,	,	PUNCT
ejpam-3914	206	15	.	.	PUNCT
ejpam-3914	206	16	.	.	PUNCT
ejpam-3914	207	1	.	.	PUNCT
ejpam-3914	208	1	,	,	PUNCT
ejpam-3914	208	2	p−	p−	NOUN
ejpam-3914	208	3	1	1	NUM
ejpam-3914	208	4	,	,	PUNCT
ejpam-3914	208	5	p.	p.	NOUN
ejpam-3914	208	6	group	group	NOUN
ejpam-3914	208	7	the	the	DET
ejpam-3914	208	8	vertices	vertex	NOUN
ejpam-3914	208	9	of	of	ADP
ejpam-3914	208	10	pn	pn	PROPN
ejpam-3914	208	11	into	into	ADP
ejpam-3914	208	12	p+	p+	NOUN
ejpam-3914	208	13	1	1	NUM
ejpam-3914	208	14	disjoint	disjoint	NOUN
ejpam-3914	208	15	subsets	subset	NOUN
ejpam-3914	208	16	rj	rj	PROPN
ejpam-3914	208	17	r0	r0	PROPN
ejpam-3914	208	18	=	=	PUNCT
ejpam-3914	208	19	{	{	PUNCT
ejpam-3914	208	20	u1	u1	NOUN
ejpam-3914	208	21	,	,	PUNCT
ejpam-3914	208	22	u2	u2	NOUN
ejpam-3914	208	23	}	}	PUNCT
ejpam-3914	208	24	r1	r1	NOUN
ejpam-3914	208	25	=	=	SYM
ejpam-3914	208	26	{	{	PUNCT
ejpam-3914	208	27	u3	u3	PROPN
ejpam-3914	208	28	,	,	PUNCT
ejpam-3914	208	29	u4	u4	PROPN
ejpam-3914	208	30	,	,	PUNCT
ejpam-3914	208	31	u5	u5	PROPN
ejpam-3914	208	32	,	,	PUNCT
ejpam-3914	208	33	u6	u6	PROPN
ejpam-3914	208	34	,	,	PUNCT
ejpam-3914	208	35	u7	u7	PROPN
ejpam-3914	208	36	}	}	PUNCT
ejpam-3914	208	37	r2	r2	PROPN
ejpam-3914	208	38	=	=	SYM
ejpam-3914	208	39	{	{	PUNCT
ejpam-3914	208	40	u8	u8	PROPN
ejpam-3914	208	41	,	,	PUNCT
ejpam-3914	208	42	u9	u9	PROPN
ejpam-3914	208	43	,	,	PUNCT
ejpam-3914	208	44	u10	u10	PROPN
ejpam-3914	208	45	,	,	PUNCT
ejpam-3914	208	46	u11	u11	PROPN
ejpam-3914	208	47	,	,	PUNCT
ejpam-3914	208	48	u12	u12	PROPN
ejpam-3914	208	49	}	}	PUNCT
ejpam-3914	208	50	r3	r3	PROPN
ejpam-3914	208	51	=	=	SYM
ejpam-3914	208	52	{	{	PUNCT
ejpam-3914	208	53	u13	u13	PROPN
ejpam-3914	208	54	,	,	PUNCT
ejpam-3914	208	55	u14	u14	NOUN
ejpam-3914	208	56	,	,	PUNCT
ejpam-3914	208	57	u15	u15	NOUN
ejpam-3914	208	58	,	,	PUNCT
ejpam-3914	208	59	u16	u16	NOUN
ejpam-3914	208	60	,	,	PUNCT
ejpam-3914	208	61	u17	u17	NOUN
ejpam-3914	208	62	}	}	PUNCT
ejpam-3914	208	63	...	...	PUNCT
ejpam-3914	209	1	rp−1	rp−1	NOUN
ejpam-3914	209	2	=	=	SYM
ejpam-3914	209	3	{	{	PUNCT
ejpam-3914	209	4	un−9	un−9	PROPN
ejpam-3914	209	5	,	,	PUNCT
ejpam-3914	209	6	un−8	un−8	ADJ
ejpam-3914	209	7	,	,	PUNCT
ejpam-3914	209	8	un−7	un−7	PROPN
ejpam-3914	209	9	,	,	PUNCT
ejpam-3914	209	10	un−6	un−6	PROPN
ejpam-3914	209	11	,	,	PUNCT
ejpam-3914	209	12	un−5	un−5	PROPN
ejpam-3914	209	13	}	}	PUNCT
ejpam-3914	209	14	rp	rp	NOUN
ejpam-3914	209	15	=	=	SYM
ejpam-3914	209	16	{	{	PUNCT
ejpam-3914	209	17	un−4	un−4	NOUN
ejpam-3914	209	18	,	,	PUNCT
ejpam-3914	209	19	un−3	un−3	ADJ
ejpam-3914	209	20	,	,	PUNCT
ejpam-3914	209	21	un−2	un−2	PROPN
ejpam-3914	209	22	,	,	PUNCT
ejpam-3914	209	23	un−1	un−1	PROPN
ejpam-3914	209	24	,	,	PUNCT
ejpam-3914	209	25	un	un	ADJ
ejpam-3914	209	26	}	}	PUNCT
ejpam-3914	209	27	let	let	VERB
ejpam-3914	209	28	i	i	PRON
ejpam-3914	209	29	=	=	NOUN
ejpam-3914	209	30	3	3	NUM
ejpam-3914	209	31	,	,	PUNCT
ejpam-3914	209	32	8	8	NUM
ejpam-3914	209	33	,	,	PUNCT
ejpam-3914	209	34	13	13	NUM
ejpam-3914	209	35	,	,	PUNCT
ejpam-3914	209	36	.	.	PUNCT
ejpam-3914	209	37	.	.	PUNCT
ejpam-3914	210	1	.	.	PUNCT
ejpam-3914	211	1	,	,	PUNCT
ejpam-3914	212	1	n	n	CCONJ
ejpam-3914	212	2	−	−	PROPN
ejpam-3914	212	3	4	4	NUM
ejpam-3914	212	4	.	.	PUNCT
ejpam-3914	212	5	for	for	ADP
ejpam-3914	212	6	every	every	DET
ejpam-3914	212	7	induced	induced	ADJ
ejpam-3914	212	8	subgraph	subgraph	NOUN
ejpam-3914	212	9	〈	〈	PROPN
ejpam-3914	212	10	ui	ui	PROPN
ejpam-3914	212	11	,	,	PUNCT
ejpam-3914	212	12	ui+1	ui+1	PROPN
ejpam-3914	212	13	,	,	PUNCT
ejpam-3914	212	14	ui+2	ui+2	NUM
ejpam-3914	212	15	,	,	PUNCT
ejpam-3914	212	16	ui+3	ui+3	NOUN
ejpam-3914	212	17	,	,	PUNCT
ejpam-3914	212	18	ui+4	ui+4	PROPN
ejpam-3914	212	19	〉	〉	NOUN
ejpam-3914	212	20	,	,	PUNCT
ejpam-3914	212	21	the	the	DET
ejpam-3914	212	22	vertices	vertex	NOUN
ejpam-3914	212	23	u3	u3	NOUN
ejpam-3914	212	24	,	,	PUNCT
ejpam-3914	212	25	ui+1	ui+1	PROPN
ejpam-3914	212	26	,	,	PUNCT
ejpam-3914	212	27	ui+2	ui+2	PRON
ejpam-3914	212	28	form	form	VERB
ejpam-3914	212	29	a	a	DET
ejpam-3914	212	30	total	total	ADJ
ejpam-3914	212	31	dr	dr	ADJ
ejpam-3914	212	32	-	-	PUNCT
ejpam-3914	212	33	power	power	NOUN
ejpam-3914	212	34	dominating	dominating	NOUN
ejpam-3914	212	35	set	set	VERB
ejpam-3914	212	36	since	since	SCONJ
ejpam-3914	212	37	u2	u2	NOUN
ejpam-3914	212	38	,	,	PUNCT
ejpam-3914	212	39	ui	ui	PROPN
ejpam-3914	212	40	and	and	CCONJ
ejpam-3914	212	41	ui+3	ui+3	NOUN
ejpam-3914	212	42	are	be	AUX
ejpam-3914	212	43	directly	directly	ADV
ejpam-3914	212	44	observed	observe	VERB
ejpam-3914	212	45	vertices	vertex	NOUN
ejpam-3914	212	46	while	while	SCONJ
ejpam-3914	212	47	u1	u1	NOUN
ejpam-3914	212	48	and	and	CCONJ
ejpam-3914	212	49	ui+4	ui+4	PRON
ejpam-3914	212	50	are	be	AUX
ejpam-3914	212	51	remotely	remotely	ADV
ejpam-3914	212	52	observed	observe	VERB
ejpam-3914	212	53	vertices	vertex	NOUN
ejpam-3914	212	54	for	for	ADP
ejpam-3914	212	55	all	all	DET
ejpam-3914	212	56	i	i	PRON
ejpam-3914	212	57	=	=	NOUN
ejpam-3914	212	58	3	3	NUM
ejpam-3914	212	59	,	,	PUNCT
ejpam-3914	212	60	8	8	NUM
ejpam-3914	212	61	,	,	PUNCT
ejpam-3914	212	62	13	13	NUM
ejpam-3914	212	63	,	,	PUNCT
ejpam-3914	212	64	.	.	PUNCT
ejpam-3914	212	65	.	.	PUNCT
ejpam-3914	213	1	.	.	PUNCT
ejpam-3914	214	1	,	,	PUNCT
ejpam-3914	214	2	n−	n−	NOUN
ejpam-3914	214	3	9	9	NUM
ejpam-3914	214	4	,	,	PUNCT
ejpam-3914	214	5	n−	n−	NOUN
ejpam-3914	214	6	4	4	NUM
ejpam-3914	214	7	.	.	PUNCT
ejpam-3914	214	8	let	let	VERB
ejpam-3914	214	9	the	the	DET
ejpam-3914	214	10	set	set	NOUN
ejpam-3914	214	11	r	r	NOUN
ejpam-3914	214	12	=	=	SYM
ejpam-3914	214	13	{	{	PUNCT
ejpam-3914	214	14	u3	u3	PROPN
ejpam-3914	214	15	,	,	PUNCT
ejpam-3914	214	16	ui+1	ui+1	PROPN
ejpam-3914	214	17	,	,	PUNCT
ejpam-3914	214	18	ui+2	ui+2	NUM
ejpam-3914	214	19	:	:	PUNCT
ejpam-3914	215	1	i	i	NOUN
ejpam-3914	215	2	=	=	NOUN
ejpam-3914	215	3	3	3	NUM
ejpam-3914	215	4	,	,	PUNCT
ejpam-3914	215	5	8	8	NUM
ejpam-3914	215	6	,	,	PUNCT
ejpam-3914	215	7	13	13	NUM
ejpam-3914	215	8	,	,	PUNCT
ejpam-3914	215	9	.	.	PUNCT
ejpam-3914	215	10	.	.	PUNCT
ejpam-3914	215	11	.	.	PUNCT
ejpam-3914	216	1	,	,	PUNCT
ejpam-3914	216	2	n−	n−	NOUN
ejpam-3914	216	3	9	9	NUM
ejpam-3914	216	4	,	,	PUNCT
ejpam-3914	216	5	n−	n−	NOUN
ejpam-3914	216	6	4	4	NUM
ejpam-3914	216	7	}	}	PUNCT
ejpam-3914	216	8	=	=	SYM
ejpam-3914	216	9	{	{	PUNCT
ejpam-3914	216	10	u3	u3	PROPN
ejpam-3914	216	11	,	,	PUNCT
ejpam-3914	216	12	u4	u4	PROPN
ejpam-3914	216	13	,	,	PUNCT
ejpam-3914	216	14	u5	u5	PROPN
ejpam-3914	216	15	,	,	PUNCT
ejpam-3914	216	16	u9	u9	PROPN
ejpam-3914	216	17	,	,	PUNCT
ejpam-3914	216	18	u10	u10	PROPN
ejpam-3914	216	19	,	,	PUNCT
ejpam-3914	216	20	u14	u14	NOUN
ejpam-3914	216	21	,	,	PUNCT
ejpam-3914	216	22	u15	u15	NOUN
ejpam-3914	216	23	,	,	PUNCT
ejpam-3914	216	24	.	.	PUNCT
ejpam-3914	216	25	.	.	PUNCT
ejpam-3914	217	1	.	.	PUNCT
ejpam-3914	218	1	,	,	PUNCT
ejpam-3914	218	2	un−8	un−8	ADJ
ejpam-3914	218	3	,	,	PUNCT
ejpam-3914	218	4	un−7	un−7	NOUN
ejpam-3914	218	5	,	,	PUNCT
ejpam-3914	218	6	un−3	un−3	ADJ
ejpam-3914	218	7	,	,	PUNCT
ejpam-3914	218	8	un−2	un−2	VERB
ejpam-3914	218	9	}	}	PUNCT
ejpam-3914	218	10	where	where	SCONJ
ejpam-3914	218	11	|r|	|r|	NOUN
ejpam-3914	219	1	=	=	NOUN
ejpam-3914	219	2	2p	2p	NOUN
ejpam-3914	219	3	+	+	CCONJ
ejpam-3914	219	4	1	1	NUM
ejpam-3914	219	5	=	=	SYM
ejpam-3914	219	6	2	2	NUM
ejpam-3914	219	7	(	(	PUNCT
ejpam-3914	219	8	n−2	n−2	PROPN
ejpam-3914	219	9	5	5	NUM
ejpam-3914	219	10	)	)	PUNCT
ejpam-3914	219	11	+	+	CCONJ
ejpam-3914	219	12	1	1	NUM
ejpam-3914	219	13	=	=	SYM
ejpam-3914	219	14	2n+1	2n+1	NUM
ejpam-3914	219	15	5	5	NUM
ejpam-3914	219	16	,	,	PUNCT
ejpam-3914	219	17	or	or	CCONJ
ejpam-3914	219	18	v	v	NOUN
ejpam-3914	219	19	(	(	PUNCT
ejpam-3914	219	20	pn	pn	NOUN
ejpam-3914	219	21	)	)	PUNCT
ejpam-3914	219	22	=	=	NOUN
ejpam-3914	219	23	v	v	X
ejpam-3914	219	24	(	(	PUNCT
ejpam-3914	219	25	pn	pn	NOUN
ejpam-3914	219	26	)	)	PUNCT
ejpam-3914	219	27	,	,	PUNCT
ejpam-3914	219	28	or	or	CCONJ
ejpam-3914	219	29	e(pn	e(pn	NUM
ejpam-3914	219	30	)	)	PUNCT
ejpam-3914	219	31	=	=	SYM
ejpam-3914	219	32	e(pn	e(pn	NUM
ejpam-3914	219	33	)	)	PUNCT
ejpam-3914	219	34	,	,	PUNCT
ejpam-3914	219	35	and	and	CCONJ
ejpam-3914	219	36	the	the	DET
ejpam-3914	219	37	induced	induced	ADJ
ejpam-3914	219	38	subgraph	subgraph	NOUN
ejpam-3914	219	39	〈	〈	PROPN
ejpam-3914	219	40	r	r	PROPN
ejpam-3914	219	41	〉	〉	PROPN
ejpam-3914	219	42	has	have	VERB
ejpam-3914	219	43	no	no	DET
ejpam-3914	219	44	isolated	isolated	ADJ
ejpam-3914	219	45	vertex	vertex	NOUN
ejpam-3914	219	46	.	.	PUNCT
ejpam-3914	220	1	by	by	ADP
ejpam-3914	220	2	theorem	theorem	NOUN
ejpam-3914	220	3	2.2	2.2	NUM
ejpam-3914	220	4	,	,	PUNCT
ejpam-3914	220	5	r	r	NOUN
ejpam-3914	220	6	is	be	AUX
ejpam-3914	220	7	a	a	DET
ejpam-3914	220	8	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	220	9	-set	-set	PROPN
ejpam-3914	220	10	of	of	ADP
ejpam-3914	220	11	pn	pn	PROPN
ejpam-3914	220	12	.	.	PROPN
ejpam-3914	221	1	let	let	VERB
ejpam-3914	221	2	m+	m+	PRON
ejpam-3914	221	3	1	1	NUM
ejpam-3914	221	4	be	be	AUX
ejpam-3914	221	5	the	the	DET
ejpam-3914	221	6	number	number	NOUN
ejpam-3914	221	7	of	of	ADP
ejpam-3914	221	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	221	9	-sets	-set	NOUN
ejpam-3914	221	10	of	of	ADP
ejpam-3914	221	11	pn	pn	NOUN
ejpam-3914	221	12	where	where	SCONJ
ejpam-3914	221	13	m	m	PROPN
ejpam-3914	221	14	is	be	AUX
ejpam-3914	221	15	a	a	DET
ejpam-3914	221	16	positive	positive	ADJ
ejpam-3914	221	17	integer	integer	NOUN
ejpam-3914	221	18	.	.	PUNCT
ejpam-3914	222	1	let	let	VERB
ejpam-3914	222	2	k	k	NOUN
ejpam-3914	222	3	=	=	SYM
ejpam-3914	222	4	1	1	NUM
ejpam-3914	222	5	,	,	PUNCT
ejpam-3914	222	6	2	2	NUM
ejpam-3914	222	7	,	,	PUNCT
ejpam-3914	222	8	.	.	PUNCT
ejpam-3914	222	9	.	.	PUNCT
ejpam-3914	223	1	.	.	PUNCT
ejpam-3914	224	1	,	,	PUNCT
ejpam-3914	224	2	m	m	VERB
ejpam-3914	224	3	and	and	CCONJ
ejpam-3914	224	4	tk	tk	PROPN
ejpam-3914	224	5	be	be	AUX
ejpam-3914	224	6	a	a	DET
ejpam-3914	224	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	224	8	-set	-set	PUNCT
ejpam-3914	224	9	of	of	ADP
ejpam-3914	224	10	pn	pn	PROPN
ejpam-3914	224	11	different	different	ADJ
ejpam-3914	224	12	from	from	ADP
ejpam-3914	224	13	r.	r.	PROPN
ejpam-3914	224	14	note	note	VERB
ejpam-3914	224	15	that	that	SCONJ
ejpam-3914	224	16	in	in	ADP
ejpam-3914	224	17	forming	form	VERB
ejpam-3914	224	18	r	r	NOUN
ejpam-3914	224	19	,	,	PUNCT
ejpam-3914	224	20	there	there	PRON
ejpam-3914	224	21	are	be	VERB
ejpam-3914	224	22	three	three	NUM
ejpam-3914	224	23	vertices	vertex	NOUN
ejpam-3914	224	24	in	in	ADP
ejpam-3914	224	25	r1	r1	NOUN
ejpam-3914	224	26	such	such	ADJ
ejpam-3914	224	27	that	that	SCONJ
ejpam-3914	224	28	the	the	DET
ejpam-3914	224	29	induced	induced	ADJ
ejpam-3914	224	30	subgraph	subgraph	NOUN
ejpam-3914	224	31	is	be	AUX
ejpam-3914	224	32	a	a	DET
ejpam-3914	224	33	graph	graph	NOUN
ejpam-3914	224	34	p3	p3	NOUN
ejpam-3914	224	35	and	and	CCONJ
ejpam-3914	224	36	two	two	NUM
ejpam-3914	224	37	adjacent	adjacent	ADJ
ejpam-3914	224	38	vertices	vertex	NOUN
ejpam-3914	224	39	in	in	ADP
ejpam-3914	224	40	the	the	DET
ejpam-3914	224	41	other	other	ADJ
ejpam-3914	224	42	rj	rj	PROPN
ejpam-3914	224	43	’s	’s	ADV
ejpam-3914	224	44	with	with	ADP
ejpam-3914	224	45	j	j	PROPN
ejpam-3914	224	46	>	>	X
ejpam-3914	224	47	1	1	NUM
ejpam-3914	224	48	.	.	PUNCT
ejpam-3914	225	1	thus	thus	ADV
ejpam-3914	225	2	,	,	PUNCT
ejpam-3914	225	3	tk	tk	PROPN
ejpam-3914	225	4	can	can	AUX
ejpam-3914	225	5	be	be	AUX
ejpam-3914	225	6	formed	form	VERB
ejpam-3914	225	7	by	by	ADP
ejpam-3914	225	8	getting	get	VERB
ejpam-3914	225	9	3	3	NUM
ejpam-3914	225	10	vertices	vertex	NOUN
ejpam-3914	225	11	in	in	ADP
ejpam-3914	225	12	any	any	DET
ejpam-3914	225	13	one	one	NUM
ejpam-3914	225	14	of	of	ADP
ejpam-3914	225	15	the	the	DET
ejpam-3914	225	16	rj	rj	PROPN
ejpam-3914	225	17	’s	’	VERB
ejpam-3914	225	18	where	where	SCONJ
ejpam-3914	225	19	j	j	PROPN
ejpam-3914	225	20	>	>	X
ejpam-3914	225	21	1	1	NUM
ejpam-3914	225	22	such	such	ADJ
ejpam-3914	225	23	that	that	SCONJ
ejpam-3914	225	24	the	the	DET
ejpam-3914	225	25	induced	induced	ADJ
ejpam-3914	225	26	subgraph	subgraph	NOUN
ejpam-3914	225	27	is	be	AUX
ejpam-3914	225	28	a	a	DET
ejpam-3914	225	29	graph	graph	NOUN
ejpam-3914	225	30	p3	p3	NOUN
ejpam-3914	225	31	and	and	CCONJ
ejpam-3914	225	32	two	two	NUM
ejpam-3914	225	33	adjacent	adjacent	ADJ
ejpam-3914	225	34	vertices	vertex	NOUN
ejpam-3914	225	35	in	in	ADP
ejpam-3914	225	36	the	the	DET
ejpam-3914	225	37	other	other	ADJ
ejpam-3914	225	38	rl	rl	X
ejpam-3914	225	39	’s	’s	NOUN
ejpam-3914	225	40	where	where	SCONJ
ejpam-3914	225	41	l	l	PROPN
ejpam-3914	225	42	6=	6=	PROPN
ejpam-3914	226	1	j	j	PROPN
ejpam-3914	227	1	and	and	CCONJ
ejpam-3914	227	2	l	l	PROPN
ejpam-3914	227	3	6=	6=	ADP
ejpam-3914	227	4	0	0	X
ejpam-3914	227	5	.	.	PUNCT
ejpam-3914	227	6	consider	consider	VERB
ejpam-3914	227	7	the	the	DET
ejpam-3914	227	8	following	follow	VERB
ejpam-3914	227	9	subcases	subcase	NOUN
ejpam-3914	227	10	.	.	PUNCT
ejpam-3914	228	1	subcase	subcase	PROPN
ejpam-3914	228	2	1	1	NUM
ejpam-3914	228	3	:	:	PUNCT
ejpam-3914	228	4	choose	choose	VERB
ejpam-3914	228	5	3	3	NUM
ejpam-3914	228	6	vertices	vertex	NOUN
ejpam-3914	228	7	in	in	ADP
ejpam-3914	228	8	r2	r2	PROPN
ejpam-3914	228	9	to	to	PART
ejpam-3914	228	10	form	form	VERB
ejpam-3914	228	11	another	another	DET
ejpam-3914	228	12	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	228	13	set	set	NOUN
ejpam-3914	228	14	,	,	PUNCT
ejpam-3914	228	15	say	say	VERB
ejpam-3914	228	16	t1	t1	NOUN
ejpam-3914	228	17	,	,	PUNCT
ejpam-3914	228	18	that	that	ADV
ejpam-3914	228	19	is	is	ADV
ejpam-3914	228	20	,	,	PUNCT
ejpam-3914	228	21	replaced	replace	VERB
ejpam-3914	228	22	u5	u5	PROPN
ejpam-3914	228	23	∈	∈	PROPN
ejpam-3914	228	24	r1	r1	NOUN
ejpam-3914	228	25	in	in	ADP
ejpam-3914	228	26	r	r	NOUN
ejpam-3914	228	27	by	by	ADP
ejpam-3914	228	28	u8	u8	PROPN
ejpam-3914	228	29	∈	∈	PROPN
ejpam-3914	228	30	r2	r2	NOUN
ejpam-3914	228	31	.	.	PUNCT
ejpam-3914	229	1	it	it	PRON
ejpam-3914	229	2	follows	follow	VERB
ejpam-3914	229	3	that	that	PRON
ejpam-3914	229	4	t1	t1	NOUN
ejpam-3914	229	5	=	=	PUNCT
ejpam-3914	229	6	{	{	PUNCT
ejpam-3914	229	7	u3	u3	PROPN
ejpam-3914	229	8	,	,	PUNCT
ejpam-3914	229	9	u4	u4	PROPN
ejpam-3914	229	10	,	,	PUNCT
ejpam-3914	229	11	u8	u8	PROPN
ejpam-3914	229	12	,	,	PUNCT
ejpam-3914	229	13	u9	u9	PROPN
ejpam-3914	229	14	,	,	PUNCT
ejpam-3914	229	15	u10	u10	PROPN
ejpam-3914	229	16	,	,	PUNCT
ejpam-3914	229	17	u14	u14	NOUN
ejpam-3914	229	18	,	,	PUNCT
ejpam-3914	229	19	u15	u15	NOUN
ejpam-3914	229	20	,	,	PUNCT
ejpam-3914	229	21	.	.	PUNCT
ejpam-3914	229	22	.	.	PUNCT
ejpam-3914	230	1	.	.	PUNCT
ejpam-3914	231	1	,	,	PUNCT
ejpam-3914	231	2	un−8	un−8	ADJ
ejpam-3914	231	3	,	,	PUNCT
ejpam-3914	231	4	un−7	un−7	NOUN
ejpam-3914	231	5	,	,	PUNCT
ejpam-3914	231	6	un−3	un−3	ADJ
ejpam-3914	231	7	,	,	PUNCT
ejpam-3914	231	8	un−2	un−2	PROPN
ejpam-3914	231	9	}	}	PUNCT
ejpam-3914	231	10	,	,	PUNCT
ejpam-3914	231	11	where	where	SCONJ
ejpam-3914	231	12	|t1|	|t1|	NOUN
ejpam-3914	231	13	=	=	SYM
ejpam-3914	231	14	|r|	|r|	PROPN
ejpam-3914	231	15	,	,	PUNCT
ejpam-3914	231	16	ot1	ot1	NOUN
ejpam-3914	231	17	v	v	INTJ
ejpam-3914	231	18	(	(	PUNCT
ejpam-3914	231	19	pn	pn	NOUN
ejpam-3914	231	20	)	)	PUNCT
ejpam-3914	231	21	=	=	NOUN
ejpam-3914	231	22	v	v	X
ejpam-3914	231	23	(	(	PUNCT
ejpam-3914	231	24	pn	pn	NOUN
ejpam-3914	231	25	)	)	PUNCT
ejpam-3914	231	26	,	,	PUNCT
ejpam-3914	231	27	ot1	ot1	PROPN
ejpam-3914	231	28	e	e	X
ejpam-3914	231	29	(	(	PUNCT
ejpam-3914	231	30	pn	pn	NOUN
ejpam-3914	231	31	)	)	PUNCT
ejpam-3914	231	32	=	=	PUNCT
ejpam-3914	231	33	e(pn	e(pn	NUM
ejpam-3914	231	34	)	)	PUNCT
ejpam-3914	231	35	,	,	PUNCT
ejpam-3914	231	36	and	and	CCONJ
ejpam-3914	231	37	the	the	DET
ejpam-3914	231	38	induced	induced	ADJ
ejpam-3914	231	39	subgraph	subgraph	NOUN
ejpam-3914	231	40	〈	〈	PROPN
ejpam-3914	231	41	t1	t1	PROPN
ejpam-3914	231	42	〉	〉	PROPN
ejpam-3914	231	43	has	have	VERB
ejpam-3914	231	44	no	no	DET
ejpam-3914	231	45	isolated	isolated	ADJ
ejpam-3914	231	46	vertex	vertex	NOUN
ejpam-3914	231	47	,	,	PUNCT
ejpam-3914	231	48	that	that	ADV
ejpam-3914	231	49	is	is	ADV
ejpam-3914	231	50	,	,	PUNCT
ejpam-3914	231	51	t1	t1	PROPN
ejpam-3914	231	52	is	be	AUX
ejpam-3914	231	53	a	a	DET
ejpam-3914	231	54	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	231	55	-set	-set	PROPN
ejpam-3914	231	56	of	of	ADP
ejpam-3914	231	57	pn	pn	PROPN
ejpam-3914	231	58	.	.	PROPN
ejpam-3914	232	1	clearly	clearly	ADV
ejpam-3914	232	2	,	,	PUNCT
ejpam-3914	232	3	u5	u5	PROPN
ejpam-3914	232	4	/∈	/∈	PROPN
ejpam-3914	232	5	t1	t1	PROPN
ejpam-3914	232	6	.	.	PUNCT
ejpam-3914	233	1	subcase	subcase	PROPN
ejpam-3914	233	2	2	2	NUM
ejpam-3914	233	3	:	:	PUNCT
ejpam-3914	233	4	choose	choose	VERB
ejpam-3914	233	5	3	3	NUM
ejpam-3914	233	6	vertices	vertex	NOUN
ejpam-3914	233	7	in	in	ADP
ejpam-3914	233	8	r3	r3	PROPN
ejpam-3914	233	9	to	to	PART
ejpam-3914	233	10	form	form	VERB
ejpam-3914	233	11	another	another	DET
ejpam-3914	233	12	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	233	13	set	set	NOUN
ejpam-3914	233	14	,	,	PUNCT
ejpam-3914	233	15	say	say	VERB
ejpam-3914	233	16	t2	t2	PROPN
ejpam-3914	233	17	,	,	PUNCT
ejpam-3914	233	18	c.	c.	PROPN
ejpam-3914	233	19	armada	armada	PROPN
ejpam-3914	233	20	/	/	SYM
ejpam-3914	233	21	eur	eur	PROPN
ejpam-3914	233	22	.	.	PUNCT
ejpam-3914	234	1	j.	j.	PROPN
ejpam-3914	234	2	pure	pure	PROPN
ejpam-3914	234	3	appl	appl	PROPN
ejpam-3914	234	4	.	.	PROPN
ejpam-3914	234	5	math	math	PROPN
ejpam-3914	234	6	,	,	PUNCT
ejpam-3914	234	7	14	14	NUM
ejpam-3914	234	8	(	(	PUNCT
ejpam-3914	234	9	2	2	NUM
ejpam-3914	234	10	)	)	PUNCT
ejpam-3914	234	11	(	(	PUNCT
ejpam-3914	234	12	2021	2021	NUM
ejpam-3914	234	13	)	)	PUNCT
ejpam-3914	234	14	,	,	PUNCT
ejpam-3914	234	15	451	451	NUM
ejpam-3914	234	16	-	-	SYM
ejpam-3914	234	17	470	470	NUM
ejpam-3914	234	18	458	458	NUM
ejpam-3914	234	19	that	that	PRON
ejpam-3914	234	20	is	be	AUX
ejpam-3914	234	21	,	,	PUNCT
ejpam-3914	234	22	replaced	replace	VERB
ejpam-3914	234	23	u10	u10	PROPN
ejpam-3914	234	24	∈	∈	PROPN
ejpam-3914	234	25	r2	r2	PROPN
ejpam-3914	234	26	in	in	ADP
ejpam-3914	234	27	t1	t1	NUM
ejpam-3914	234	28	by	by	ADP
ejpam-3914	234	29	u13	u13	PROPN
ejpam-3914	234	30	∈	∈	PROPN
ejpam-3914	234	31	r3	r3	PROPN
ejpam-3914	234	32	.	.	PUNCT
ejpam-3914	235	1	it	it	PRON
ejpam-3914	235	2	follows	follow	VERB
ejpam-3914	235	3	that	that	SCONJ
ejpam-3914	235	4	t2	t2	NOUN
ejpam-3914	235	5	=	=	SYM
ejpam-3914	235	6	{	{	PUNCT
ejpam-3914	235	7	u3	u3	PROPN
ejpam-3914	235	8	,	,	PUNCT
ejpam-3914	235	9	u4	u4	PROPN
ejpam-3914	235	10	,	,	PUNCT
ejpam-3914	235	11	u8	u8	PROPN
ejpam-3914	235	12	,	,	PUNCT
ejpam-3914	235	13	u9	u9	PROPN
ejpam-3914	235	14	,	,	PUNCT
ejpam-3914	235	15	u13	u13	NOUN
ejpam-3914	235	16	,	,	PUNCT
ejpam-3914	235	17	u14	u14	NOUN
ejpam-3914	235	18	,	,	PUNCT
ejpam-3914	235	19	u15	u15	NOUN
ejpam-3914	235	20	,	,	PUNCT
ejpam-3914	235	21	u19	u19	PROPN
ejpam-3914	235	22	,	,	PUNCT
ejpam-3914	235	23	u20	u20	PROPN
ejpam-3914	235	24	,	,	PUNCT
ejpam-3914	235	25	.	.	PUNCT
ejpam-3914	235	26	.	.	PUNCT
ejpam-3914	236	1	.	.	PUNCT
ejpam-3914	237	1	,	,	PUNCT
ejpam-3914	237	2	un−8	un−8	ADJ
ejpam-3914	237	3	,	,	PUNCT
ejpam-3914	237	4	un−7	un−7	NOUN
ejpam-3914	237	5	,	,	PUNCT
ejpam-3914	237	6	un−3	un−3	ADJ
ejpam-3914	237	7	,	,	PUNCT
ejpam-3914	237	8	un−2	un−2	PROPN
ejpam-3914	237	9	}	}	PUNCT
ejpam-3914	237	10	,	,	PUNCT
ejpam-3914	238	1	where	where	SCONJ
ejpam-3914	238	2	|t2|	|t2|	NOUN
ejpam-3914	238	3	=	=	SYM
ejpam-3914	238	4	|r|	|r|	PROPN
ejpam-3914	238	5	,	,	PUNCT
ejpam-3914	238	6	ot2	ot2	NOUN
ejpam-3914	238	7	v	v	NOUN
ejpam-3914	238	8	(	(	PUNCT
ejpam-3914	238	9	pn	pn	NOUN
ejpam-3914	238	10	)	)	PUNCT
ejpam-3914	238	11	=	=	NOUN
ejpam-3914	238	12	v	v	X
ejpam-3914	238	13	(	(	PUNCT
ejpam-3914	238	14	pn	pn	NOUN
ejpam-3914	238	15	)	)	PUNCT
ejpam-3914	238	16	,	,	PUNCT
ejpam-3914	238	17	ot2	ot2	NOUN
ejpam-3914	238	18	e	e	X
ejpam-3914	238	19	(	(	PUNCT
ejpam-3914	238	20	pn	pn	NOUN
ejpam-3914	238	21	)	)	PUNCT
ejpam-3914	238	22	=	=	PUNCT
ejpam-3914	238	23	e(pn	e(pn	NUM
ejpam-3914	238	24	)	)	PUNCT
ejpam-3914	238	25	,	,	PUNCT
ejpam-3914	238	26	and	and	CCONJ
ejpam-3914	238	27	the	the	DET
ejpam-3914	238	28	induced	induced	ADJ
ejpam-3914	238	29	subgraph	subgraph	NOUN
ejpam-3914	238	30	〈	〈	PROPN
ejpam-3914	238	31	t2	t2	PROPN
ejpam-3914	238	32	〉	〉	PROPN
ejpam-3914	238	33	has	have	VERB
ejpam-3914	238	34	no	no	DET
ejpam-3914	238	35	isolated	isolated	ADJ
ejpam-3914	238	36	vertex	vertex	NOUN
ejpam-3914	238	37	,	,	PUNCT
ejpam-3914	238	38	that	that	ADV
ejpam-3914	238	39	is	is	ADV
ejpam-3914	238	40	,	,	PUNCT
ejpam-3914	238	41	t2	t2	PROPN
ejpam-3914	238	42	is	be	AUX
ejpam-3914	238	43	a	a	DET
ejpam-3914	238	44	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	238	45	-set	-set	PROPN
ejpam-3914	238	46	of	of	ADP
ejpam-3914	238	47	pn	pn	PROPN
ejpam-3914	238	48	.	.	PROPN
ejpam-3914	239	1	clearly	clearly	ADV
ejpam-3914	239	2	,	,	PUNCT
ejpam-3914	239	3	u5	u5	PROPN
ejpam-3914	239	4	/∈	/∈	PROPN
ejpam-3914	239	5	t2	t2	PROPN
ejpam-3914	239	6	.	.	PUNCT
ejpam-3914	240	1	continuing	continue	VERB
ejpam-3914	240	2	in	in	ADP
ejpam-3914	240	3	this	this	DET
ejpam-3914	240	4	manner	manner	NOUN
ejpam-3914	240	5	and	and	CCONJ
ejpam-3914	240	6	in	in	ADP
ejpam-3914	240	7	any	any	DET
ejpam-3914	240	8	subcase	subcase	NOUN
ejpam-3914	240	9	,	,	PUNCT
ejpam-3914	240	10	u5	u5	PROPN
ejpam-3914	240	11	/∈	/∈	PROPN
ejpam-3914	240	12	tk	tk	PROPN
ejpam-3914	240	13	for	for	ADP
ejpam-3914	240	14	all	all	PRON
ejpam-3914	240	15	k	k	NOUN
ejpam-3914	240	16	=	=	SYM
ejpam-3914	240	17	1	1	NUM
ejpam-3914	240	18	,	,	PUNCT
ejpam-3914	240	19	2	2	NUM
ejpam-3914	240	20	,	,	PUNCT
ejpam-3914	240	21	.	.	PUNCT
ejpam-3914	240	22	.	.	PUNCT
ejpam-3914	241	1	.	.	PUNCT
ejpam-3914	242	1	,	,	PUNCT
ejpam-3914	242	2	m	m	PROPN
ejpam-3914	242	3	,	,	PUNCT
ejpam-3914	242	4	and	and	CCONJ
ejpam-3914	242	5	so	so	ADV
ejpam-3914	242	6	,	,	PUNCT
ejpam-3914	242	7	the	the	DET
ejpam-3914	242	8	vertex	vertex	NOUN
ejpam-3914	242	9	u5	u5	PROPN
ejpam-3914	242	10	is	be	AUX
ejpam-3914	242	11	contained	contain	VERB
ejpam-3914	242	12	in	in	ADP
ejpam-3914	242	13	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	242	14	-set	-set	PUNCT
ejpam-3914	243	1	r	r	NOUN
ejpam-3914	243	2	only	only	ADV
ejpam-3914	243	3	.	.	PUNCT
ejpam-3914	244	1	by	by	ADP
ejpam-3914	244	2	theorem	theorem	NOUN
ejpam-3914	244	3	3.1(ii	3.1(ii	NUM
ejpam-3914	244	4	)	)	PUNCT
ejpam-3914	244	5	,	,	PUNCT
ejpam-3914	244	6	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	244	7	(	(	PUNCT
ejpam-3914	244	8	pn	pn	NOUN
ejpam-3914	244	9	)	)	PUNCT
ejpam-3914	244	10	=	=	SYM
ejpam-3914	244	11	1	1	X
ejpam-3914	244	12	.	.	X
ejpam-3914	244	13	case	case	NOUN
ejpam-3914	244	14	4	4	NUM
ejpam-3914	244	15	:	:	PUNCT
ejpam-3914	244	16	suppose	suppose	VERB
ejpam-3914	244	17	that	that	SCONJ
ejpam-3914	244	18	n	n	PROPN
ejpam-3914	244	19	≡	≡	PROPN
ejpam-3914	244	20	3(mod	3(mod	NUM
ejpam-3914	244	21	5	5	NUM
ejpam-3914	244	22	)	)	PUNCT
ejpam-3914	244	23	.	.	PUNCT
ejpam-3914	245	1	by	by	ADP
ejpam-3914	245	2	theorem	theorem	ADJ
ejpam-3914	245	3	2.2	2.2	NUM
ejpam-3914	245	4	,	,	PUNCT
ejpam-3914	245	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	245	6	(	(	PUNCT
ejpam-3914	245	7	pn	pn	NOUN
ejpam-3914	245	8	)	)	PUNCT
ejpam-3914	245	9	=	=	SYM
ejpam-3914	246	1	2n+4	2n+4	NOUN
ejpam-3914	246	2	5	5	NUM
ejpam-3914	246	3	.	.	PUNCT
ejpam-3914	246	4	suppose	suppose	VERB
ejpam-3914	246	5	that	that	SCONJ
ejpam-3914	246	6	n	n	PROPN
ejpam-3914	246	7	=	=	SYM
ejpam-3914	246	8	8	8	NUM
ejpam-3914	246	9	.	.	PUNCT
ejpam-3914	247	1	then	then	ADV
ejpam-3914	247	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	247	3	(	(	PUNCT
ejpam-3914	247	4	p8	p8	PROPN
ejpam-3914	247	5	)	)	PUNCT
ejpam-3914	247	6	=	=	NOUN
ejpam-3914	247	7	2(8)+4	2(8)+4	NUM
ejpam-3914	247	8	5	5	NUM
ejpam-3914	247	9	=	=	SYM
ejpam-3914	247	10	4	4	NUM
ejpam-3914	247	11	.	.	PUNCT
ejpam-3914	247	12	clearly	clearly	ADV
ejpam-3914	247	13	,	,	PUNCT
ejpam-3914	247	14	s1	s1	PROPN
ejpam-3914	247	15	=	=	SYM
ejpam-3914	247	16	{	{	PUNCT
ejpam-3914	247	17	u1	u1	NOUN
ejpam-3914	247	18	,	,	PUNCT
ejpam-3914	247	19	u2	u2	PROPN
ejpam-3914	247	20	,	,	PUNCT
ejpam-3914	247	21	u5	u5	PROPN
ejpam-3914	247	22	,	,	PUNCT
ejpam-3914	247	23	u6	u6	NOUN
ejpam-3914	247	24	}	}	PUNCT
ejpam-3914	247	25	,	,	PUNCT
ejpam-3914	247	26	s2	s2	NOUN
ejpam-3914	247	27	=	=	SYM
ejpam-3914	247	28	{	{	PUNCT
ejpam-3914	247	29	u1	u1	NOUN
ejpam-3914	247	30	,	,	PUNCT
ejpam-3914	247	31	u2	u2	NOUN
ejpam-3914	247	32	,	,	PUNCT
ejpam-3914	247	33	u6	u6	PROPN
ejpam-3914	247	34	,	,	PUNCT
ejpam-3914	247	35	u7	u7	PROPN
ejpam-3914	247	36	}	}	PUNCT
ejpam-3914	247	37	,	,	PUNCT
ejpam-3914	247	38	s3	s3	PROPN
ejpam-3914	247	39	=	=	SYM
ejpam-3914	247	40	{	{	PUNCT
ejpam-3914	247	41	u2	u2	PROPN
ejpam-3914	247	42	,	,	PUNCT
ejpam-3914	247	43	u3	u3	PROPN
ejpam-3914	247	44	,	,	PUNCT
ejpam-3914	247	45	u5	u5	PROPN
ejpam-3914	247	46	,	,	PUNCT
ejpam-3914	247	47	u6	u6	NOUN
ejpam-3914	247	48	}	}	PUNCT
ejpam-3914	247	49	,	,	PUNCT
ejpam-3914	247	50	s4	s4	PROPN
ejpam-3914	247	51	=	=	SYM
ejpam-3914	247	52	{	{	PUNCT
ejpam-3914	247	53	u2	u2	PROPN
ejpam-3914	247	54	,	,	PUNCT
ejpam-3914	247	55	u3	u3	NOUN
ejpam-3914	247	56	,	,	PUNCT
ejpam-3914	247	57	u6	u6	PROPN
ejpam-3914	247	58	,	,	PUNCT
ejpam-3914	247	59	u7	u7	PROPN
ejpam-3914	247	60	}	}	PUNCT
ejpam-3914	247	61	,	,	PUNCT
ejpam-3914	247	62	s5	s5	X
ejpam-3914	247	63	=	=	PUNCT
ejpam-3914	247	64	{	{	PUNCT
ejpam-3914	247	65	u2	u2	PROPN
ejpam-3914	247	66	,	,	PUNCT
ejpam-3914	247	67	u3	u3	PROPN
ejpam-3914	247	68	,	,	PUNCT
ejpam-3914	247	69	u7	u7	PROPN
ejpam-3914	247	70	,	,	PUNCT
ejpam-3914	247	71	u8	u8	PROPN
ejpam-3914	247	72	}	}	PUNCT
ejpam-3914	247	73	,	,	PUNCT
ejpam-3914	247	74	s6	s6	PROPN
ejpam-3914	247	75	=	=	SYM
ejpam-3914	247	76	{	{	PUNCT
ejpam-3914	247	77	u3	u3	PROPN
ejpam-3914	247	78	,	,	PUNCT
ejpam-3914	247	79	u4	u4	PROPN
ejpam-3914	247	80	,	,	PUNCT
ejpam-3914	247	81	u5	u5	PROPN
ejpam-3914	247	82	,	,	PUNCT
ejpam-3914	247	83	u6	u6	NOUN
ejpam-3914	247	84	}	}	PUNCT
ejpam-3914	247	85	,	,	PUNCT
ejpam-3914	247	86	s7	s7	PROPN
ejpam-3914	247	87	=	=	SYM
ejpam-3914	247	88	{	{	PUNCT
ejpam-3914	247	89	u3	u3	PROPN
ejpam-3914	247	90	,	,	PUNCT
ejpam-3914	247	91	u4	u4	PROPN
ejpam-3914	247	92	,	,	PUNCT
ejpam-3914	247	93	u6	u6	PROPN
ejpam-3914	247	94	,	,	PUNCT
ejpam-3914	247	95	u7	u7	PROPN
ejpam-3914	247	96	}	}	PUNCT
ejpam-3914	247	97	,	,	PUNCT
ejpam-3914	247	98	and	and	CCONJ
ejpam-3914	247	99	s8	s8	PROPN
ejpam-3914	247	100	=	=	SYM
ejpam-3914	247	101	{	{	PUNCT
ejpam-3914	247	102	u3	u3	PROPN
ejpam-3914	247	103	,	,	PUNCT
ejpam-3914	247	104	u4	u4	PROPN
ejpam-3914	247	105	,	,	PUNCT
ejpam-3914	247	106	u7	u7	PROPN
ejpam-3914	247	107	,	,	PUNCT
ejpam-3914	247	108	u8	u8	PROPN
ejpam-3914	247	109	}	}	PUNCT
ejpam-3914	247	110	are	be	AUX
ejpam-3914	247	111	the	the	DET
ejpam-3914	247	112	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	247	113	-sets	-set	NOUN
ejpam-3914	247	114	of	of	ADP
ejpam-3914	247	115	p8	p8	PROPN
ejpam-3914	247	116	.	.	PUNCT
ejpam-3914	248	1	clearly	clearly	ADV
ejpam-3914	248	2	,	,	PUNCT
ejpam-3914	248	3	for	for	ADP
ejpam-3914	248	4	i	i	PROPN
ejpam-3914	248	5	=	=	SYM
ejpam-3914	248	6	1	1	NUM
ejpam-3914	248	7	,	,	PUNCT
ejpam-3914	248	8	2	2	NUM
ejpam-3914	248	9	,	,	PUNCT
ejpam-3914	248	10	.	.	PUNCT
ejpam-3914	248	11	.	.	PUNCT
ejpam-3914	248	12	.	.	PUNCT
ejpam-3914	249	1	,	,	PUNCT
ejpam-3914	249	2	8	8	NUM
ejpam-3914	249	3	,	,	PUNCT
ejpam-3914	249	4	no	no	DET
ejpam-3914	249	5	subset	subset	NOUN
ejpam-3914	249	6	{	{	PUNCT
ejpam-3914	249	7	ui	ui	NOUN
ejpam-3914	249	8	}	}	PUNCT
ejpam-3914	249	9	is	be	AUX
ejpam-3914	249	10	contained	contain	VERB
ejpam-3914	249	11	in	in	ADP
ejpam-3914	249	12	exactly	exactly	ADV
ejpam-3914	249	13	one	one	NUM
ejpam-3914	249	14	of	of	ADP
ejpam-3914	249	15	the	the	DET
ejpam-3914	249	16	sl	sl	NOUN
ejpam-3914	249	17	’s	’s	NOUN
ejpam-3914	249	18	,	,	PUNCT
ejpam-3914	249	19	for	for	ADP
ejpam-3914	249	20	l	l	NOUN
ejpam-3914	249	21	=	=	SYM
ejpam-3914	249	22	1	1	NUM
ejpam-3914	249	23	,	,	PUNCT
ejpam-3914	249	24	2	2	NUM
ejpam-3914	249	25	,	,	PUNCT
ejpam-3914	249	26	.	.	PUNCT
ejpam-3914	249	27	.	.	PUNCT
ejpam-3914	250	1	.	.	PUNCT
ejpam-3914	251	1	,	,	PUNCT
ejpam-3914	251	2	8	8	NUM
ejpam-3914	251	3	,	,	PUNCT
ejpam-3914	251	4	that	that	ADV
ejpam-3914	251	5	is	is	ADV
ejpam-3914	251	6	,	,	PUNCT
ejpam-3914	251	7	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3914	251	8	(	(	PUNCT
ejpam-3914	251	9	sl	sl	NOUN
ejpam-3914	251	10	)	)	PUNCT
ejpam-3914	251	11	>	>	X
ejpam-3914	252	1	1	1	X
ejpam-3914	252	2	.	.	PUNCT
ejpam-3914	252	3	clearly	clearly	ADV
ejpam-3914	252	4	,	,	PUNCT
ejpam-3914	252	5	{	{	PUNCT
ejpam-3914	252	6	u1	u1	NOUN
ejpam-3914	252	7	,	,	PUNCT
ejpam-3914	252	8	u5	u5	PROPN
ejpam-3914	252	9	}	}	PUNCT
ejpam-3914	252	10	is	be	AUX
ejpam-3914	252	11	forcing	force	VERB
ejpam-3914	252	12	subset	subset	NOUN
ejpam-3914	252	13	for	for	ADP
ejpam-3914	252	14	s1	s1	PROPN
ejpam-3914	252	15	since	since	SCONJ
ejpam-3914	252	16	{	{	PUNCT
ejpam-3914	252	17	u1	u1	PROPN
ejpam-3914	252	18	,	,	PUNCT
ejpam-3914	252	19	u5	u5	PROPN
ejpam-3914	252	20	}	}	PUNCT
ejpam-3914	252	21	*	*	PUNCT
ejpam-3914	252	22	sl	sl	INTJ
ejpam-3914	252	23	for	for	ADP
ejpam-3914	252	24	all	all	DET
ejpam-3914	252	25	l	l	NOUN
ejpam-3914	252	26	6=	6=	NUM
ejpam-3914	252	27	1	1	NUM
ejpam-3914	252	28	.	.	PUNCT
ejpam-3914	253	1	thus	thus	ADV
ejpam-3914	253	2	,	,	PUNCT
ejpam-3914	253	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	253	4	(	(	PUNCT
ejpam-3914	253	5	s1	s1	NOUN
ejpam-3914	253	6	)	)	PUNCT
ejpam-3914	253	7	=	=	SYM
ejpam-3914	253	8	2	2	NUM
ejpam-3914	253	9	=	=	NOUN
ejpam-3914	253	10	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	253	11	(	(	PUNCT
ejpam-3914	253	12	p8	p8	PROPN
ejpam-3914	253	13	)	)	PUNCT
ejpam-3914	253	14	.	.	PUNCT
ejpam-3914	254	1	now	now	ADV
ejpam-3914	254	2	,	,	PUNCT
ejpam-3914	254	3	suppose	suppose	VERB
ejpam-3914	254	4	that	that	SCONJ
ejpam-3914	254	5	n	n	PROPN
ejpam-3914	254	6	>	>	X
ejpam-3914	254	7	8	8	NUM
ejpam-3914	254	8	.	.	PUNCT
ejpam-3914	255	1	since	since	SCONJ
ejpam-3914	255	2	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	255	3	(	(	PUNCT
ejpam-3914	255	4	p8	p8	PROPN
ejpam-3914	255	5	)	)	PUNCT
ejpam-3914	255	6	=	=	SYM
ejpam-3914	255	7	2	2	NUM
ejpam-3914	255	8	,	,	PUNCT
ejpam-3914	255	9	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	255	10	(	(	PUNCT
ejpam-3914	255	11	pn	pn	NOUN
ejpam-3914	255	12	)	)	PUNCT
ejpam-3914	255	13	≥	≥	NOUN
ejpam-3914	255	14	2	2	NUM
ejpam-3914	255	15	.	.	PUNCT
ejpam-3914	255	16	let	let	VERB
ejpam-3914	255	17	p	p	NOUN
ejpam-3914	255	18	=	=	PUNCT
ejpam-3914	255	19	n−3	n−3	PROPN
ejpam-3914	255	20	5	5	NUM
ejpam-3914	255	21	and	and	CCONJ
ejpam-3914	255	22	j	j	NOUN
ejpam-3914	255	23	=	=	SYM
ejpam-3914	255	24	0	0	NUM
ejpam-3914	255	25	,	,	PUNCT
ejpam-3914	255	26	1	1	NUM
ejpam-3914	255	27	,	,	PUNCT
ejpam-3914	255	28	2	2	NUM
ejpam-3914	255	29	,	,	PUNCT
ejpam-3914	255	30	.	.	PUNCT
ejpam-3914	255	31	.	.	PUNCT
ejpam-3914	256	1	.	.	PUNCT
ejpam-3914	257	1	,	,	PUNCT
ejpam-3914	257	2	p−	p−	NOUN
ejpam-3914	257	3	1	1	NUM
ejpam-3914	257	4	,	,	PUNCT
ejpam-3914	257	5	p.	p.	NOUN
ejpam-3914	257	6	group	group	NOUN
ejpam-3914	257	7	the	the	DET
ejpam-3914	257	8	vertices	vertex	NOUN
ejpam-3914	257	9	of	of	ADP
ejpam-3914	257	10	pn	pn	PROPN
ejpam-3914	257	11	into	into	ADP
ejpam-3914	257	12	p+	p+	NOUN
ejpam-3914	257	13	1	1	NUM
ejpam-3914	257	14	disjoint	disjoint	NOUN
ejpam-3914	257	15	subsets	subset	NOUN
ejpam-3914	257	16	rj	rj	PROPN
ejpam-3914	257	17	r0	r0	PROPN
ejpam-3914	257	18	=	=	PUNCT
ejpam-3914	257	19	{	{	PUNCT
ejpam-3914	257	20	u1	u1	NOUN
ejpam-3914	257	21	,	,	PUNCT
ejpam-3914	257	22	u2	u2	NOUN
ejpam-3914	257	23	,	,	PUNCT
ejpam-3914	257	24	u3	u3	NOUN
ejpam-3914	257	25	}	}	PUNCT
ejpam-3914	257	26	r1	r1	NOUN
ejpam-3914	257	27	=	=	SYM
ejpam-3914	257	28	{	{	PUNCT
ejpam-3914	257	29	u4	u4	PROPN
ejpam-3914	257	30	,	,	PUNCT
ejpam-3914	257	31	u5	u5	PROPN
ejpam-3914	257	32	,	,	PUNCT
ejpam-3914	257	33	u6	u6	PROPN
ejpam-3914	257	34	,	,	PUNCT
ejpam-3914	257	35	u7	u7	PROPN
ejpam-3914	257	36	,	,	PUNCT
ejpam-3914	257	37	u8	u8	PROPN
ejpam-3914	257	38	}	}	PUNCT
ejpam-3914	257	39	r2	r2	NOUN
ejpam-3914	257	40	=	=	SYM
ejpam-3914	257	41	{	{	PUNCT
ejpam-3914	257	42	u9	u9	PROPN
ejpam-3914	257	43	,	,	PUNCT
ejpam-3914	257	44	u10	u10	PROPN
ejpam-3914	257	45	,	,	PUNCT
ejpam-3914	257	46	u11	u11	PROPN
ejpam-3914	257	47	,	,	PUNCT
ejpam-3914	257	48	u12	u12	PROPN
ejpam-3914	257	49	,	,	PUNCT
ejpam-3914	257	50	u13	u13	NOUN
ejpam-3914	257	51	}	}	PUNCT
ejpam-3914	257	52	r3	r3	PROPN
ejpam-3914	257	53	=	=	PUNCT
ejpam-3914	257	54	{	{	PUNCT
ejpam-3914	257	55	u14	u14	NOUN
ejpam-3914	257	56	,	,	PUNCT
ejpam-3914	257	57	u15	u15	NOUN
ejpam-3914	257	58	,	,	PUNCT
ejpam-3914	257	59	u16	u16	NOUN
ejpam-3914	257	60	,	,	PUNCT
ejpam-3914	257	61	u17	u17	ADJ
ejpam-3914	257	62	,	,	PUNCT
ejpam-3914	257	63	u18	u18	PROPN
ejpam-3914	257	64	}	}	PUNCT
ejpam-3914	257	65	...	...	PUNCT
ejpam-3914	258	1	rp−1	rp−1	NOUN
ejpam-3914	258	2	=	=	SYM
ejpam-3914	258	3	{	{	PUNCT
ejpam-3914	258	4	un−9	un−9	PROPN
ejpam-3914	258	5	,	,	PUNCT
ejpam-3914	258	6	un−8	un−8	ADJ
ejpam-3914	258	7	,	,	PUNCT
ejpam-3914	258	8	un−7	un−7	PROPN
ejpam-3914	258	9	,	,	PUNCT
ejpam-3914	258	10	un−6	un−6	PROPN
ejpam-3914	258	11	,	,	PUNCT
ejpam-3914	258	12	un−5	un−5	PROPN
ejpam-3914	258	13	}	}	PUNCT
ejpam-3914	258	14	rp	rp	NOUN
ejpam-3914	258	15	=	=	SYM
ejpam-3914	258	16	{	{	PUNCT
ejpam-3914	258	17	un−4	un−4	NOUN
ejpam-3914	258	18	,	,	PUNCT
ejpam-3914	258	19	un−3	un−3	ADJ
ejpam-3914	258	20	,	,	PUNCT
ejpam-3914	258	21	un−2	un−2	PROPN
ejpam-3914	258	22	,	,	PUNCT
ejpam-3914	258	23	un−1	un−1	PROPN
ejpam-3914	258	24	,	,	PUNCT
ejpam-3914	258	25	un	un	ADJ
ejpam-3914	258	26	}	}	PUNCT
ejpam-3914	258	27	let	let	VERB
ejpam-3914	258	28	i	i	PRON
ejpam-3914	258	29	=	=	NOUN
ejpam-3914	258	30	4	4	NUM
ejpam-3914	258	31	,	,	PUNCT
ejpam-3914	258	32	9	9	NUM
ejpam-3914	258	33	,	,	PUNCT
ejpam-3914	258	34	14	14	NUM
ejpam-3914	258	35	,	,	PUNCT
ejpam-3914	258	36	.	.	PUNCT
ejpam-3914	258	37	.	.	PUNCT
ejpam-3914	259	1	.	.	PUNCT
ejpam-3914	260	1	,	,	PUNCT
ejpam-3914	261	1	n	n	CCONJ
ejpam-3914	261	2	−	−	PROPN
ejpam-3914	261	3	4	4	NUM
ejpam-3914	261	4	.	.	PUNCT
ejpam-3914	261	5	for	for	ADP
ejpam-3914	261	6	every	every	DET
ejpam-3914	261	7	induced	induced	ADJ
ejpam-3914	261	8	subgraph	subgraph	NOUN
ejpam-3914	261	9	〈	〈	PROPN
ejpam-3914	261	10	ui	ui	PROPN
ejpam-3914	261	11	,	,	PUNCT
ejpam-3914	261	12	ui+1	ui+1	PROPN
ejpam-3914	261	13	,	,	PUNCT
ejpam-3914	261	14	ui+2	ui+2	NUM
ejpam-3914	261	15	,	,	PUNCT
ejpam-3914	261	16	ui+3	ui+3	NOUN
ejpam-3914	261	17	,	,	PUNCT
ejpam-3914	261	18	ui+4	ui+4	PROPN
ejpam-3914	261	19	〉	〉	NOUN
ejpam-3914	261	20	,	,	PUNCT
ejpam-3914	261	21	the	the	DET
ejpam-3914	261	22	vertices	vertex	NOUN
ejpam-3914	261	23	u1	u1	NOUN
ejpam-3914	261	24	,	,	PUNCT
ejpam-3914	261	25	u2	u2	NOUN
ejpam-3914	261	26	,	,	PUNCT
ejpam-3914	261	27	ui+1	ui+1	PROPN
ejpam-3914	261	28	,	,	PUNCT
ejpam-3914	261	29	ui+2	ui+2	PRON
ejpam-3914	261	30	form	form	VERB
ejpam-3914	261	31	a	a	DET
ejpam-3914	261	32	total	total	ADJ
ejpam-3914	261	33	dr	dr	ADJ
ejpam-3914	261	34	-	-	PUNCT
ejpam-3914	261	35	power	power	NOUN
ejpam-3914	261	36	dominating	dominating	NOUN
ejpam-3914	261	37	set	set	VERB
ejpam-3914	261	38	since	since	SCONJ
ejpam-3914	261	39	u3	u3	NOUN
ejpam-3914	261	40	,	,	PUNCT
ejpam-3914	261	41	ui	ui	PROPN
ejpam-3914	261	42	and	and	CCONJ
ejpam-3914	261	43	ui+3	ui+3	NOUN
ejpam-3914	261	44	are	be	AUX
ejpam-3914	261	45	directly	directly	ADV
ejpam-3914	261	46	observed	observe	VERB
ejpam-3914	261	47	vertices	vertex	NOUN
ejpam-3914	261	48	while	while	SCONJ
ejpam-3914	261	49	ui+4	ui+4	PRON
ejpam-3914	261	50	are	be	AUX
ejpam-3914	261	51	remotely	remotely	ADV
ejpam-3914	261	52	observed	observe	VERB
ejpam-3914	261	53	vertices	vertex	NOUN
ejpam-3914	261	54	for	for	ADP
ejpam-3914	261	55	all	all	DET
ejpam-3914	261	56	i	i	PRON
ejpam-3914	261	57	=	=	NOUN
ejpam-3914	261	58	4	4	NUM
ejpam-3914	261	59	,	,	PUNCT
ejpam-3914	261	60	9	9	NUM
ejpam-3914	261	61	,	,	PUNCT
ejpam-3914	261	62	14	14	NUM
ejpam-3914	261	63	,	,	PUNCT
ejpam-3914	261	64	.	.	PUNCT
ejpam-3914	261	65	.	.	PUNCT
ejpam-3914	262	1	.	.	PUNCT
ejpam-3914	263	1	,	,	PUNCT
ejpam-3914	263	2	n−	n−	NOUN
ejpam-3914	263	3	9	9	NUM
ejpam-3914	263	4	,	,	PUNCT
ejpam-3914	263	5	n−	n−	NOUN
ejpam-3914	263	6	4	4	NUM
ejpam-3914	263	7	.	.	PUNCT
ejpam-3914	263	8	let	let	VERB
ejpam-3914	263	9	the	the	DET
ejpam-3914	263	10	set	set	NOUN
ejpam-3914	263	11	r	r	NOUN
ejpam-3914	263	12	=	=	SYM
ejpam-3914	263	13	{	{	PUNCT
ejpam-3914	263	14	u1	u1	NOUN
ejpam-3914	263	15	,	,	PUNCT
ejpam-3914	263	16	u2	u2	NOUN
ejpam-3914	263	17	,	,	PUNCT
ejpam-3914	263	18	ui+1	ui+1	PROPN
ejpam-3914	263	19	,	,	PUNCT
ejpam-3914	263	20	ui+2	ui+2	NUM
ejpam-3914	263	21	:	:	PUNCT
ejpam-3914	263	22	i	i	NOUN
ejpam-3914	263	23	=	=	NOUN
ejpam-3914	263	24	4	4	NUM
ejpam-3914	263	25	,	,	PUNCT
ejpam-3914	263	26	9	9	NUM
ejpam-3914	263	27	,	,	PUNCT
ejpam-3914	263	28	14	14	NUM
ejpam-3914	263	29	,	,	PUNCT
ejpam-3914	263	30	.	.	PUNCT
ejpam-3914	263	31	.	.	PUNCT
ejpam-3914	264	1	.	.	PUNCT
ejpam-3914	265	1	,	,	PUNCT
ejpam-3914	265	2	n−	n−	NOUN
ejpam-3914	265	3	9	9	NUM
ejpam-3914	265	4	,	,	PUNCT
ejpam-3914	265	5	n−	n−	NOUN
ejpam-3914	265	6	4	4	NUM
ejpam-3914	265	7	}	}	PUNCT
ejpam-3914	265	8	=	=	NOUN
ejpam-3914	265	9	{	{	PUNCT
ejpam-3914	265	10	u1	u1	NOUN
ejpam-3914	265	11	,	,	PUNCT
ejpam-3914	265	12	u2	u2	PROPN
ejpam-3914	265	13	,	,	PUNCT
ejpam-3914	265	14	u5	u5	PROPN
ejpam-3914	265	15	,	,	PUNCT
ejpam-3914	265	16	u6	u6	PROPN
ejpam-3914	265	17	,	,	PUNCT
ejpam-3914	265	18	u10	u10	PROPN
ejpam-3914	265	19	,	,	PUNCT
ejpam-3914	265	20	u11	u11	PROPN
ejpam-3914	265	21	,	,	PUNCT
ejpam-3914	265	22	u15	u15	NOUN
ejpam-3914	265	23	,	,	PUNCT
ejpam-3914	265	24	u16	u16	NOUN
ejpam-3914	265	25	,	,	PUNCT
ejpam-3914	265	26	.	.	PUNCT
ejpam-3914	265	27	.	.	PUNCT
ejpam-3914	266	1	.	.	PUNCT
ejpam-3914	267	1	,	,	PUNCT
ejpam-3914	267	2	un−8	un−8	ADJ
ejpam-3914	267	3	,	,	PUNCT
ejpam-3914	267	4	un−7	un−7	NOUN
ejpam-3914	267	5	,	,	PUNCT
ejpam-3914	267	6	un−3	un−3	ADJ
ejpam-3914	267	7	,	,	PUNCT
ejpam-3914	267	8	un−2	un−2	VERB
ejpam-3914	267	9	}	}	PUNCT
ejpam-3914	267	10	where	where	SCONJ
ejpam-3914	267	11	|r|	|r|	NOUN
ejpam-3914	268	1	=	=	NOUN
ejpam-3914	268	2	2p	2p	NOUN
ejpam-3914	268	3	+	+	CCONJ
ejpam-3914	268	4	2	2	NUM
ejpam-3914	268	5	=	=	SYM
ejpam-3914	268	6	2	2	NUM
ejpam-3914	268	7	(	(	PUNCT
ejpam-3914	268	8	n−3	n−3	PROPN
ejpam-3914	268	9	5	5	NUM
ejpam-3914	268	10	)	)	PUNCT
ejpam-3914	268	11	+	+	CCONJ
ejpam-3914	268	12	2	2	X
ejpam-3914	268	13	=	=	SYM
ejpam-3914	268	14	2n+4	2n+4	NUM
ejpam-3914	268	15	5	5	NUM
ejpam-3914	268	16	,	,	PUNCT
ejpam-3914	268	17	or	or	CCONJ
ejpam-3914	268	18	v	v	NOUN
ejpam-3914	268	19	(	(	PUNCT
ejpam-3914	268	20	pn	pn	NOUN
ejpam-3914	268	21	)	)	PUNCT
ejpam-3914	268	22	=	=	NOUN
ejpam-3914	268	23	v	v	X
ejpam-3914	268	24	(	(	PUNCT
ejpam-3914	268	25	pn	pn	NOUN
ejpam-3914	268	26	)	)	PUNCT
ejpam-3914	268	27	,	,	PUNCT
ejpam-3914	268	28	or	or	CCONJ
ejpam-3914	268	29	e(pn	e(pn	NUM
ejpam-3914	268	30	)	)	PUNCT
ejpam-3914	268	31	=	=	SYM
ejpam-3914	268	32	e(pn	e(pn	NUM
ejpam-3914	268	33	)	)	PUNCT
ejpam-3914	268	34	,	,	PUNCT
ejpam-3914	268	35	and	and	CCONJ
ejpam-3914	268	36	the	the	DET
ejpam-3914	268	37	induced	induced	ADJ
ejpam-3914	268	38	subgraph	subgraph	NOUN
ejpam-3914	268	39	〈	〈	PROPN
ejpam-3914	268	40	r	r	PROPN
ejpam-3914	268	41	〉	〉	PROPN
ejpam-3914	268	42	has	have	VERB
ejpam-3914	268	43	no	no	DET
ejpam-3914	268	44	isolated	isolated	ADJ
ejpam-3914	268	45	vertex	vertex	NOUN
ejpam-3914	268	46	.	.	PUNCT
ejpam-3914	269	1	by	by	ADP
ejpam-3914	269	2	theorem	theorem	NOUN
ejpam-3914	269	3	2.2	2.2	NUM
ejpam-3914	269	4	,	,	PUNCT
ejpam-3914	269	5	r	r	NOUN
ejpam-3914	269	6	is	be	AUX
ejpam-3914	269	7	a	a	DET
ejpam-3914	269	8	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	269	9	-set	-set	PROPN
ejpam-3914	269	10	of	of	ADP
ejpam-3914	269	11	pn	pn	PROPN
ejpam-3914	269	12	.	.	PROPN
ejpam-3914	270	1	let	let	VERB
ejpam-3914	270	2	m+	m+	PRON
ejpam-3914	270	3	1	1	NUM
ejpam-3914	270	4	be	be	AUX
ejpam-3914	270	5	the	the	DET
ejpam-3914	270	6	number	number	NOUN
ejpam-3914	270	7	of	of	ADP
ejpam-3914	270	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	270	9	-sets	-set	NOUN
ejpam-3914	270	10	of	of	ADP
ejpam-3914	270	11	pn	pn	NOUN
ejpam-3914	270	12	where	where	SCONJ
ejpam-3914	270	13	m	m	PROPN
ejpam-3914	270	14	is	be	AUX
ejpam-3914	270	15	a	a	DET
ejpam-3914	270	16	positive	positive	ADJ
ejpam-3914	270	17	integer	integer	NOUN
ejpam-3914	270	18	.	.	PUNCT
ejpam-3914	271	1	let	let	VERB
ejpam-3914	271	2	k	k	NOUN
ejpam-3914	271	3	=	=	SYM
ejpam-3914	271	4	1	1	NUM
ejpam-3914	271	5	,	,	PUNCT
ejpam-3914	271	6	2	2	NUM
ejpam-3914	271	7	,	,	PUNCT
ejpam-3914	271	8	.	.	PUNCT
ejpam-3914	271	9	.	.	PUNCT
ejpam-3914	272	1	.	.	PUNCT
ejpam-3914	273	1	,	,	PUNCT
ejpam-3914	273	2	m	m	VERB
ejpam-3914	273	3	and	and	CCONJ
ejpam-3914	273	4	tk	tk	PROPN
ejpam-3914	273	5	be	be	AUX
ejpam-3914	273	6	a	a	DET
ejpam-3914	273	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	273	8	-set	-set	PUNCT
ejpam-3914	273	9	of	of	ADP
ejpam-3914	273	10	pn	pn	PROPN
ejpam-3914	273	11	different	different	ADJ
ejpam-3914	273	12	from	from	ADP
ejpam-3914	273	13	r.	r.	PROPN
ejpam-3914	273	14	consider	consider	VERB
ejpam-3914	273	15	the	the	DET
ejpam-3914	273	16	following	follow	VERB
ejpam-3914	273	17	subcases	subcase	NOUN
ejpam-3914	273	18	:	:	PUNCT
ejpam-3914	273	19	subcase	subcase	NOUN
ejpam-3914	273	20	1	1	NUM
ejpam-3914	273	21	:	:	PUNCT
ejpam-3914	273	22	tk	tk	PROPN
ejpam-3914	273	23	,	,	PUNCT
ejpam-3914	273	24	say	say	VERB
ejpam-3914	273	25	t1	t1	NOUN
ejpam-3914	273	26	and	and	CCONJ
ejpam-3914	273	27	t2	t2	NOUN
ejpam-3914	273	28	,	,	PUNCT
ejpam-3914	273	29	can	can	AUX
ejpam-3914	273	30	be	be	AUX
ejpam-3914	273	31	formed	form	VERB
ejpam-3914	273	32	by	by	ADP
ejpam-3914	273	33	replacing	replace	VERB
ejpam-3914	273	34	u1	u1	NOUN
ejpam-3914	273	35	,	,	PUNCT
ejpam-3914	273	36	u2	u2	NOUN
ejpam-3914	273	37	in	in	ADP
ejpam-3914	273	38	r	r	NOUN
ejpam-3914	273	39	by	by	ADP
ejpam-3914	273	40	either	either	CCONJ
ejpam-3914	273	41	u2	u2	NOUN
ejpam-3914	273	42	,	,	PUNCT
ejpam-3914	273	43	u3	u3	NOUN
ejpam-3914	273	44	or	or	CCONJ
ejpam-3914	273	45	u3	u3	PROPN
ejpam-3914	273	46	,	,	PUNCT
ejpam-3914	273	47	u4	u4	PROPN
ejpam-3914	273	48	.	.	PUNCT
ejpam-3914	274	1	it	it	PRON
ejpam-3914	274	2	follows	follow	VERB
ejpam-3914	274	3	that	that	PRON
ejpam-3914	274	4	t1	t1	NOUN
ejpam-3914	274	5	=	=	PUNCT
ejpam-3914	274	6	{	{	PUNCT
ejpam-3914	274	7	u2	u2	PROPN
ejpam-3914	274	8	,	,	PUNCT
ejpam-3914	274	9	u3	u3	PROPN
ejpam-3914	274	10	,	,	PUNCT
ejpam-3914	274	11	u5	u5	PROPN
ejpam-3914	274	12	,	,	PUNCT
ejpam-3914	274	13	u6	u6	PROPN
ejpam-3914	274	14	,	,	PUNCT
ejpam-3914	274	15	u10	u10	PROPN
ejpam-3914	274	16	,	,	PUNCT
ejpam-3914	274	17	u11	u11	PROPN
ejpam-3914	274	18	,	,	PUNCT
ejpam-3914	274	19	.	.	PUNCT
ejpam-3914	274	20	.	.	PUNCT
ejpam-3914	275	1	.	.	PUNCT
ejpam-3914	276	1	,	,	PUNCT
ejpam-3914	276	2	un−8	un−8	ADJ
ejpam-3914	276	3	,	,	PUNCT
ejpam-3914	276	4	un−7	un−7	NOUN
ejpam-3914	276	5	,	,	PUNCT
ejpam-3914	276	6	un−3	un−3	ADJ
ejpam-3914	276	7	,	,	PUNCT
ejpam-3914	276	8	un−2	un−2	VERB
ejpam-3914	276	9	}	}	PUNCT
ejpam-3914	276	10	and	and	CCONJ
ejpam-3914	276	11	the	the	DET
ejpam-3914	276	12	set	set	NOUN
ejpam-3914	276	13	t2	t2	NOUN
ejpam-3914	276	14	=	=	SYM
ejpam-3914	276	15	{	{	PUNCT
ejpam-3914	276	16	u3	u3	PROPN
ejpam-3914	276	17	,	,	PUNCT
ejpam-3914	276	18	u4	u4	PROPN
ejpam-3914	276	19	,	,	PUNCT
ejpam-3914	276	20	u5	u5	PROPN
ejpam-3914	276	21	,	,	PUNCT
ejpam-3914	276	22	u6	u6	PROPN
ejpam-3914	276	23	,	,	PUNCT
ejpam-3914	276	24	u10	u10	PROPN
ejpam-3914	276	25	,	,	PUNCT
ejpam-3914	276	26	u11	u11	PROPN
ejpam-3914	276	27	,	,	PUNCT
ejpam-3914	276	28	.	.	PUNCT
ejpam-3914	276	29	.	.	PUNCT
ejpam-3914	277	1	.	.	PUNCT
ejpam-3914	278	1	,	,	PUNCT
ejpam-3914	278	2	un−8	un−8	ADJ
ejpam-3914	278	3	,	,	PUNCT
ejpam-3914	278	4	un−7	un−7	NOUN
ejpam-3914	278	5	,	,	PUNCT
ejpam-3914	278	6	un−3	un−3	ADJ
ejpam-3914	278	7	,	,	PUNCT
ejpam-3914	278	8	un−2	un−2	PROPN
ejpam-3914	278	9	}	}	PUNCT
ejpam-3914	278	10	are	be	AUX
ejpam-3914	278	11	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	278	12	-sets	-set	NOUN
ejpam-3914	278	13	of	of	ADP
ejpam-3914	278	14	pn	pn	PROPN
ejpam-3914	278	15	.	.	PUNCT
ejpam-3914	279	1	clearly	clearly	ADV
ejpam-3914	279	2	,	,	PUNCT
ejpam-3914	279	3	c.	c.	PROPN
ejpam-3914	279	4	armada	armada	PROPN
ejpam-3914	279	5	/	/	SYM
ejpam-3914	279	6	eur	eur	PROPN
ejpam-3914	279	7	.	.	PUNCT
ejpam-3914	280	1	j.	j.	PROPN
ejpam-3914	280	2	pure	pure	PROPN
ejpam-3914	280	3	appl	appl	PROPN
ejpam-3914	280	4	.	.	PROPN
ejpam-3914	280	5	math	math	PROPN
ejpam-3914	280	6	,	,	PUNCT
ejpam-3914	280	7	14	14	NUM
ejpam-3914	280	8	(	(	PUNCT
ejpam-3914	280	9	2	2	NUM
ejpam-3914	280	10	)	)	PUNCT
ejpam-3914	280	11	(	(	PUNCT
ejpam-3914	280	12	2021	2021	NUM
ejpam-3914	280	13	)	)	PUNCT
ejpam-3914	280	14	,	,	PUNCT
ejpam-3914	280	15	451	451	NUM
ejpam-3914	280	16	-	-	SYM
ejpam-3914	280	17	470	470	NUM
ejpam-3914	280	18	459	459	NUM
ejpam-3914	280	19	{	{	PUNCT
ejpam-3914	280	20	u1	u1	PROPN
ejpam-3914	280	21	,	,	PUNCT
ejpam-3914	280	22	u5	u5	PROPN
ejpam-3914	280	23	}	}	PUNCT
ejpam-3914	280	24	*	*	PUNCT
ejpam-3914	280	25	t1	t1	NOUN
ejpam-3914	280	26	and	and	CCONJ
ejpam-3914	280	27	{	{	PUNCT
ejpam-3914	280	28	u1	u1	PROPN
ejpam-3914	280	29	,	,	PUNCT
ejpam-3914	280	30	u5	u5	PROPN
ejpam-3914	280	31	}	}	PUNCT
ejpam-3914	280	32	*	*	PROPN
ejpam-3914	280	33	t2	t2	PROPN
ejpam-3914	280	34	.	.	PUNCT
ejpam-3914	281	1	subcase	subcase	PROPN
ejpam-3914	281	2	2	2	NUM
ejpam-3914	281	3	:	:	PUNCT
ejpam-3914	281	4	tk	tk	PROPN
ejpam-3914	281	5	,	,	PUNCT
ejpam-3914	281	6	say	say	VERB
ejpam-3914	281	7	t3	t3	PROPN
ejpam-3914	281	8	,	,	PUNCT
ejpam-3914	281	9	can	can	AUX
ejpam-3914	281	10	be	be	AUX
ejpam-3914	281	11	formed	form	VERB
ejpam-3914	281	12	by	by	ADP
ejpam-3914	281	13	replacing	replace	VERB
ejpam-3914	281	14	u5	u5	NOUN
ejpam-3914	281	15	in	in	ADP
ejpam-3914	281	16	r	r	NOUN
ejpam-3914	281	17	by	by	ADP
ejpam-3914	281	18	u7	u7	PROPN
ejpam-3914	281	19	.	.	PUNCT
ejpam-3914	282	1	thus	thus	ADV
ejpam-3914	282	2	,	,	PUNCT
ejpam-3914	282	3	the	the	DET
ejpam-3914	282	4	set	set	ADJ
ejpam-3914	282	5	t3	t3	NOUN
ejpam-3914	282	6	=	=	PUNCT
ejpam-3914	282	7	{	{	PUNCT
ejpam-3914	282	8	u1	u1	NOUN
ejpam-3914	282	9	,	,	PUNCT
ejpam-3914	282	10	u2	u2	NOUN
ejpam-3914	282	11	,	,	PUNCT
ejpam-3914	282	12	u6	u6	PROPN
ejpam-3914	282	13	,	,	PUNCT
ejpam-3914	282	14	u7	u7	PROPN
ejpam-3914	282	15	,	,	PUNCT
ejpam-3914	282	16	u10	u10	PROPN
ejpam-3914	282	17	,	,	PUNCT
ejpam-3914	282	18	u11	u11	PROPN
ejpam-3914	282	19	,	,	PUNCT
ejpam-3914	282	20	.	.	PUNCT
ejpam-3914	282	21	.	.	PUNCT
ejpam-3914	282	22	.	.	PUNCT
ejpam-3914	283	1	,	,	PUNCT
ejpam-3914	283	2	un−8	un−8	ADJ
ejpam-3914	283	3	,	,	PUNCT
ejpam-3914	283	4	un−7	un−7	NOUN
ejpam-3914	283	5	,	,	PUNCT
ejpam-3914	283	6	un−3	un−3	ADJ
ejpam-3914	283	7	,	,	PUNCT
ejpam-3914	283	8	un−2	un−2	PROPN
ejpam-3914	283	9	}	}	PUNCT
ejpam-3914	283	10	is	be	AUX
ejpam-3914	283	11	a	a	DET
ejpam-3914	283	12	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	283	13	-set	-set	PROPN
ejpam-3914	283	14	of	of	ADP
ejpam-3914	283	15	pn	pn	PROPN
ejpam-3914	283	16	.	.	PROPN
ejpam-3914	284	1	by	by	ADP
ejpam-3914	284	2	the	the	DET
ejpam-3914	284	3	previous	previous	ADJ
ejpam-3914	284	4	subcase	subcase	NOUN
ejpam-3914	284	5	,	,	PUNCT
ejpam-3914	284	6	tk	tk	PROPN
ejpam-3914	284	7	can	can	AUX
ejpam-3914	284	8	be	be	AUX
ejpam-3914	284	9	formed	form	VERB
ejpam-3914	284	10	by	by	ADP
ejpam-3914	284	11	replacing	replace	VERB
ejpam-3914	284	12	u1	u1	NOUN
ejpam-3914	284	13	,	,	PUNCT
ejpam-3914	284	14	u2	u2	PROPN
ejpam-3914	284	15	in	in	ADP
ejpam-3914	284	16	t3	t3	PROPN
ejpam-3914	284	17	by	by	ADP
ejpam-3914	284	18	either	either	CCONJ
ejpam-3914	284	19	u2	u2	PROPN
ejpam-3914	284	20	,	,	PUNCT
ejpam-3914	284	21	u3	u3	NOUN
ejpam-3914	284	22	or	or	CCONJ
ejpam-3914	284	23	u3	u3	PROPN
ejpam-3914	284	24	,	,	PUNCT
ejpam-3914	284	25	u4	u4	PROPN
ejpam-3914	284	26	.	.	PUNCT
ejpam-3914	285	1	it	it	PRON
ejpam-3914	285	2	follows	follow	VERB
ejpam-3914	285	3	that	that	SCONJ
ejpam-3914	285	4	t4	t4	PROPN
ejpam-3914	285	5	=	=	PROPN
ejpam-3914	285	6	{	{	PUNCT
ejpam-3914	285	7	u2	u2	PROPN
ejpam-3914	285	8	,	,	PUNCT
ejpam-3914	285	9	u3	u3	NOUN
ejpam-3914	285	10	,	,	PUNCT
ejpam-3914	285	11	u6	u6	PROPN
ejpam-3914	285	12	,	,	PUNCT
ejpam-3914	285	13	u7	u7	PROPN
ejpam-3914	285	14	,	,	PUNCT
ejpam-3914	285	15	u10	u10	PROPN
ejpam-3914	285	16	,	,	PUNCT
ejpam-3914	285	17	u11	u11	PROPN
ejpam-3914	285	18	,	,	PUNCT
ejpam-3914	285	19	.	.	PUNCT
ejpam-3914	285	20	.	.	PUNCT
ejpam-3914	286	1	.	.	PUNCT
ejpam-3914	287	1	,	,	PUNCT
ejpam-3914	287	2	un−8	un−8	ADJ
ejpam-3914	287	3	,	,	PUNCT
ejpam-3914	287	4	un−7	un−7	NOUN
ejpam-3914	287	5	,	,	PUNCT
ejpam-3914	287	6	un−3	un−3	ADJ
ejpam-3914	287	7	,	,	PUNCT
ejpam-3914	287	8	un−2	un−2	VERB
ejpam-3914	287	9	}	}	PUNCT
ejpam-3914	287	10	and	and	CCONJ
ejpam-3914	287	11	the	the	DET
ejpam-3914	287	12	set	set	NOUN
ejpam-3914	287	13	t5	t5	PROPN
ejpam-3914	287	14	=	=	SYM
ejpam-3914	287	15	{	{	PUNCT
ejpam-3914	287	16	u3	u3	PROPN
ejpam-3914	287	17	,	,	PUNCT
ejpam-3914	287	18	u4	u4	PROPN
ejpam-3914	287	19	,	,	PUNCT
ejpam-3914	287	20	u6	u6	PROPN
ejpam-3914	287	21	,	,	PUNCT
ejpam-3914	287	22	u7	u7	PROPN
ejpam-3914	287	23	,	,	PUNCT
ejpam-3914	287	24	u10	u10	PROPN
ejpam-3914	287	25	,	,	PUNCT
ejpam-3914	287	26	u11	u11	PROPN
ejpam-3914	287	27	,	,	PUNCT
ejpam-3914	287	28	.	.	PUNCT
ejpam-3914	287	29	.	.	PUNCT
ejpam-3914	288	1	.	.	PUNCT
ejpam-3914	289	1	,	,	PUNCT
ejpam-3914	289	2	un−8	un−8	ADJ
ejpam-3914	289	3	,	,	PUNCT
ejpam-3914	289	4	un−7	un−7	NOUN
ejpam-3914	289	5	,	,	PUNCT
ejpam-3914	289	6	un−3	un−3	ADJ
ejpam-3914	289	7	,	,	PUNCT
ejpam-3914	289	8	un−2	un−2	PROPN
ejpam-3914	289	9	}	}	PUNCT
ejpam-3914	289	10	are	be	AUX
ejpam-3914	289	11	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	289	12	-sets	-set	NOUN
ejpam-3914	289	13	of	of	ADP
ejpam-3914	289	14	pn	pn	PROPN
ejpam-3914	289	15	.	.	PUNCT
ejpam-3914	290	1	clearly	clearly	ADV
ejpam-3914	290	2	,	,	PUNCT
ejpam-3914	290	3	{	{	PUNCT
ejpam-3914	290	4	u1	u1	NOUN
ejpam-3914	290	5	,	,	PUNCT
ejpam-3914	290	6	u5	u5	PROPN
ejpam-3914	290	7	}	}	PUNCT
ejpam-3914	290	8	*	*	NOUN
ejpam-3914	290	9	t3	t3	PROPN
ejpam-3914	290	10	,	,	PUNCT
ejpam-3914	290	11	{	{	PUNCT
ejpam-3914	290	12	u1	u1	NOUN
ejpam-3914	290	13	,	,	PUNCT
ejpam-3914	290	14	u5	u5	PROPN
ejpam-3914	290	15	}	}	PUNCT
ejpam-3914	290	16	*	*	PUNCT
ejpam-3914	290	17	t4	t4	PROPN
ejpam-3914	290	18	and	and	CCONJ
ejpam-3914	290	19	{	{	PUNCT
ejpam-3914	290	20	u1	u1	PROPN
ejpam-3914	290	21	,	,	PUNCT
ejpam-3914	290	22	u5	u5	PROPN
ejpam-3914	290	23	}	}	PUNCT
ejpam-3914	290	24	*	*	PUNCT
ejpam-3914	290	25	t5	t5	PROPN
ejpam-3914	290	26	.	.	PUNCT
ejpam-3914	290	27	subcase	subcase	PROPN
ejpam-3914	290	28	3	3	NUM
ejpam-3914	290	29	:	:	PUNCT
ejpam-3914	290	30	suppose	suppose	VERB
ejpam-3914	290	31	that	that	SCONJ
ejpam-3914	290	32	{	{	PUNCT
ejpam-3914	290	33	u1	u1	PROPN
ejpam-3914	290	34	,	,	PUNCT
ejpam-3914	290	35	u5	u5	PROPN
ejpam-3914	290	36	}	}	PUNCT
ejpam-3914	290	37	is	be	AUX
ejpam-3914	290	38	a	a	DET
ejpam-3914	290	39	subset	subset	NOUN
ejpam-3914	290	40	in	in	ADP
ejpam-3914	290	41	one	one	NUM
ejpam-3914	290	42	of	of	ADP
ejpam-3914	290	43	the	the	DET
ejpam-3914	290	44	tk	tk	PROPN
ejpam-3914	290	45	’s	’s	NOUN
ejpam-3914	290	46	with	with	ADP
ejpam-3914	290	47	k	k	PROPN
ejpam-3914	290	48	>	>	X
ejpam-3914	290	49	5	5	NUM
ejpam-3914	290	50	,	,	PUNCT
ejpam-3914	290	51	say	say	VERB
ejpam-3914	290	52	t6	t6	PROPN
ejpam-3914	290	53	,	,	PUNCT
ejpam-3914	290	54	that	that	ADV
ejpam-3914	290	55	is	is	ADV
ejpam-3914	290	56	,	,	PUNCT
ejpam-3914	290	57	u2	u2	PROPN
ejpam-3914	290	58	must	must	AUX
ejpam-3914	290	59	be	be	AUX
ejpam-3914	290	60	in	in	ADP
ejpam-3914	290	61	t6	t6	PROPN
ejpam-3914	290	62	and	and	CCONJ
ejpam-3914	290	63	either	either	CCONJ
ejpam-3914	290	64	u4	u4	PROPN
ejpam-3914	290	65	or	or	CCONJ
ejpam-3914	290	66	u6	u6	NOUN
ejpam-3914	290	67	is	be	AUX
ejpam-3914	290	68	in	in	ADP
ejpam-3914	290	69	t6	t6	PROPN
ejpam-3914	290	70	.	.	PUNCT
ejpam-3914	290	71	suppose	suppose	VERB
ejpam-3914	290	72	that	that	SCONJ
ejpam-3914	290	73	u4	u4	PROPN
ejpam-3914	290	74	∈	∈	PROPN
ejpam-3914	290	75	t6	t6	PROPN
ejpam-3914	290	76	.	.	PUNCT
ejpam-3914	291	1	then	then	ADV
ejpam-3914	291	2	the	the	DET
ejpam-3914	291	3	next	next	ADJ
ejpam-3914	291	4	pair	pair	NOUN
ejpam-3914	291	5	to	to	PART
ejpam-3914	291	6	be	be	AUX
ejpam-3914	291	7	choosen	choosen	VERB
ejpam-3914	291	8	must	must	AUX
ejpam-3914	291	9	be	be	AUX
ejpam-3914	291	10	u9	u9	ADJ
ejpam-3914	291	11	and	and	CCONJ
ejpam-3914	291	12	u10	u10	PROPN
ejpam-3914	291	13	since	since	SCONJ
ejpam-3914	291	14	the	the	DET
ejpam-3914	291	15	distance	distance	NOUN
ejpam-3914	291	16	between	between	ADP
ejpam-3914	291	17	u5	u5	PROPN
ejpam-3914	291	18	and	and	CCONJ
ejpam-3914	291	19	u9	u9	PROPN
ejpam-3914	291	20	is	be	AUX
ejpam-3914	291	21	4	4	NUM
ejpam-3914	291	22	,	,	PUNCT
ejpam-3914	291	23	that	that	ADV
ejpam-3914	291	24	is	is	ADV
ejpam-3914	291	25	,	,	PUNCT
ejpam-3914	291	26	ui	ui	PROPN
ejpam-3914	291	27	and	and	CCONJ
ejpam-3914	291	28	ui+1	ui+1	PROPN
ejpam-3914	291	29	must	must	AUX
ejpam-3914	291	30	be	be	AUX
ejpam-3914	291	31	in	in	ADP
ejpam-3914	291	32	t6	t6	PROPN
ejpam-3914	291	33	.	.	PUNCT
ejpam-3914	292	1	thus	thus	ADV
ejpam-3914	292	2	,	,	PUNCT
ejpam-3914	292	3	t6	t6	PROPN
ejpam-3914	292	4	=	=	SYM
ejpam-3914	292	5	{	{	PUNCT
ejpam-3914	292	6	u1	u1	NOUN
ejpam-3914	292	7	,	,	PUNCT
ejpam-3914	292	8	u2	u2	PROPN
ejpam-3914	292	9	,	,	PUNCT
ejpam-3914	292	10	u4	u4	PROPN
ejpam-3914	292	11	,	,	PUNCT
ejpam-3914	292	12	u5	u5	PROPN
ejpam-3914	292	13	,	,	PUNCT
ejpam-3914	292	14	u9	u9	PROPN
ejpam-3914	292	15	,	,	PUNCT
ejpam-3914	292	16	u10	u10	PROPN
ejpam-3914	292	17	,	,	PUNCT
ejpam-3914	292	18	u14	u14	NOUN
ejpam-3914	292	19	,	,	PUNCT
ejpam-3914	292	20	u15	u15	NOUN
ejpam-3914	292	21	,	,	PUNCT
ejpam-3914	292	22	.	.	PUNCT
ejpam-3914	292	23	.	.	PUNCT
ejpam-3914	292	24	.	.	PUNCT
ejpam-3914	293	1	,	,	PUNCT
ejpam-3914	293	2	un−4	un−4	NOUN
ejpam-3914	293	3	,	,	PUNCT
ejpam-3914	293	4	un−3	un−3	ADJ
ejpam-3914	293	5	}	}	PUNCT
ejpam-3914	293	6	.	.	PUNCT
ejpam-3914	294	1	since	since	SCONJ
ejpam-3914	294	2	un−3	un−3	PROPN
ejpam-3914	294	3	is	be	AUX
ejpam-3914	294	4	the	the	DET
ejpam-3914	294	5	last	last	ADJ
ejpam-3914	294	6	vertex	vertex	NOUN
ejpam-3914	294	7	in	in	ADP
ejpam-3914	294	8	t6	t6	PROPN
ejpam-3914	294	9	,	,	PUNCT
ejpam-3914	294	10	by	by	ADP
ejpam-3914	294	11	subcase	subcase	NOUN
ejpam-3914	294	12	1	1	NUM
ejpam-3914	294	13	of	of	ADP
ejpam-3914	294	14	case	case	NOUN
ejpam-3914	294	15	2	2	NUM
ejpam-3914	294	16	,	,	PUNCT
ejpam-3914	294	17	t6	t6	PROPN
ejpam-3914	294	18	is	be	AUX
ejpam-3914	294	19	not	not	PART
ejpam-3914	294	20	a	a	DET
ejpam-3914	294	21	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	294	22	-set	-set	PROPN
ejpam-3914	294	23	of	of	ADP
ejpam-3914	294	24	pn	pn	PROPN
ejpam-3914	294	25	.	.	PUNCT
ejpam-3914	295	1	now	now	ADV
ejpam-3914	295	2	,	,	PUNCT
ejpam-3914	295	3	suppose	suppose	VERB
ejpam-3914	295	4	that	that	SCONJ
ejpam-3914	295	5	u6	u6	PROPN
ejpam-3914	295	6	∈	∈	PROPN
ejpam-3914	295	7	t6	t6	PROPN
ejpam-3914	295	8	.	.	PUNCT
ejpam-3914	296	1	then	then	ADV
ejpam-3914	296	2	the	the	DET
ejpam-3914	296	3	first	first	ADJ
ejpam-3914	296	4	four	four	NUM
ejpam-3914	296	5	vertices	vertex	NOUN
ejpam-3914	296	6	u1	u1	NOUN
ejpam-3914	296	7	,	,	PUNCT
ejpam-3914	296	8	u2	u2	PROPN
ejpam-3914	296	9	,	,	PUNCT
ejpam-3914	296	10	u5	u5	PROPN
ejpam-3914	296	11	,	,	PUNCT
ejpam-3914	296	12	u6	u6	NOUN
ejpam-3914	296	13	in	in	ADP
ejpam-3914	296	14	t6	t6	PROPN
ejpam-3914	296	15	are	be	AUX
ejpam-3914	296	16	the	the	DET
ejpam-3914	296	17	same	same	ADJ
ejpam-3914	296	18	with	with	ADP
ejpam-3914	296	19	r.	r.	PROPN
ejpam-3914	296	20	replace	replace	VERB
ejpam-3914	296	21	u10	u10	PROPN
ejpam-3914	296	22	∈	∈	PROPN
ejpam-3914	296	23	r	r	NOUN
ejpam-3914	296	24	by	by	ADP
ejpam-3914	296	25	u9	u9	NOUN
ejpam-3914	296	26	to	to	PART
ejpam-3914	296	27	form	form	VERB
ejpam-3914	296	28	t6	t6	PROPN
ejpam-3914	296	29	.	.	PUNCT
ejpam-3914	297	1	then	then	ADV
ejpam-3914	297	2	the	the	DET
ejpam-3914	297	3	next	next	ADJ
ejpam-3914	297	4	vertex	vertex	NOUN
ejpam-3914	297	5	to	to	PART
ejpam-3914	297	6	be	be	AUX
ejpam-3914	297	7	chosen	choose	VERB
ejpam-3914	297	8	must	must	AUX
ejpam-3914	297	9	be	be	AUX
ejpam-3914	297	10	u10	u10	PROPN
ejpam-3914	297	11	,	,	PUNCT
ejpam-3914	297	12	that	that	ADV
ejpam-3914	297	13	is	is	ADV
ejpam-3914	297	14	,	,	PUNCT
ejpam-3914	297	15	the	the	DET
ejpam-3914	297	16	vertex	vertex	NOUN
ejpam-3914	297	17	ui	ui	PROPN
ejpam-3914	297	18	,	,	PUNCT
ejpam-3914	297	19	ui+1	ui+1	PROPN
ejpam-3914	297	20	must	must	AUX
ejpam-3914	297	21	be	be	AUX
ejpam-3914	297	22	in	in	ADP
ejpam-3914	297	23	t6	t6	PROPN
ejpam-3914	297	24	for	for	ADP
ejpam-3914	297	25	all	all	DET
ejpam-3914	297	26	i	i	PRON
ejpam-3914	297	27	=	=	NOUN
ejpam-3914	297	28	9	9	NUM
ejpam-3914	297	29	,	,	PUNCT
ejpam-3914	297	30	.	.	PUNCT
ejpam-3914	297	31	.	.	PUNCT
ejpam-3914	298	1	.	.	PUNCT
ejpam-3914	299	1	,	,	PUNCT
ejpam-3914	299	2	n	n	CCONJ
ejpam-3914	299	3	−	−	PROPN
ejpam-3914	299	4	9	9	NUM
ejpam-3914	299	5	,	,	PUNCT
ejpam-3914	299	6	n	n	CCONJ
ejpam-3914	299	7	−	−	PROPN
ejpam-3914	299	8	4	4	NUM
ejpam-3914	299	9	.	.	PUNCT
ejpam-3914	300	1	then	then	ADV
ejpam-3914	300	2	t6	t6	PROPN
ejpam-3914	300	3	=	=	SYM
ejpam-3914	300	4	{	{	PUNCT
ejpam-3914	300	5	u1	u1	NOUN
ejpam-3914	300	6	,	,	PUNCT
ejpam-3914	300	7	u2	u2	PROPN
ejpam-3914	300	8	,	,	PUNCT
ejpam-3914	300	9	u5	u5	PROPN
ejpam-3914	300	10	,	,	PUNCT
ejpam-3914	300	11	u6	u6	PROPN
ejpam-3914	300	12	,	,	PUNCT
ejpam-3914	300	13	u9	u9	PROPN
ejpam-3914	300	14	,	,	PUNCT
ejpam-3914	300	15	u10	u10	PROPN
ejpam-3914	300	16	,	,	PUNCT
ejpam-3914	300	17	u14	u14	NOUN
ejpam-3914	300	18	,	,	PUNCT
ejpam-3914	300	19	u15	u15	NOUN
ejpam-3914	300	20	,	,	PUNCT
ejpam-3914	300	21	.	.	PUNCT
ejpam-3914	300	22	.	.	PUNCT
ejpam-3914	301	1	.	.	PUNCT
ejpam-3914	302	1	,	,	PUNCT
ejpam-3914	302	2	un−4	un−4	NOUN
ejpam-3914	302	3	,	,	PUNCT
ejpam-3914	302	4	un−3	un−3	ADJ
ejpam-3914	302	5	}	}	PUNCT
ejpam-3914	302	6	.	.	PUNCT
ejpam-3914	303	1	since	since	SCONJ
ejpam-3914	303	2	un−3	un−3	PROPN
ejpam-3914	303	3	is	be	AUX
ejpam-3914	303	4	the	the	DET
ejpam-3914	303	5	last	last	ADJ
ejpam-3914	303	6	vertex	vertex	NOUN
ejpam-3914	303	7	in	in	ADP
ejpam-3914	303	8	t6	t6	PROPN
ejpam-3914	303	9	,	,	PUNCT
ejpam-3914	303	10	by	by	ADP
ejpam-3914	303	11	subcase	subcase	NOUN
ejpam-3914	303	12	1	1	NUM
ejpam-3914	303	13	of	of	ADP
ejpam-3914	303	14	case	case	NOUN
ejpam-3914	303	15	2	2	NUM
ejpam-3914	303	16	,	,	PUNCT
ejpam-3914	303	17	t6	t6	PROPN
ejpam-3914	303	18	is	be	AUX
ejpam-3914	303	19	not	not	PART
ejpam-3914	303	20	a	a	DET
ejpam-3914	303	21	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	303	22	-set	-set	PROPN
ejpam-3914	303	23	of	of	ADP
ejpam-3914	303	24	pn	pn	PROPN
ejpam-3914	303	25	.	.	PROPN
ejpam-3914	304	1	since	since	SCONJ
ejpam-3914	304	2	u10	u10	PROPN
ejpam-3914	304	3	is	be	AUX
ejpam-3914	304	4	arbitrarily	arbitrarily	ADV
ejpam-3914	304	5	replaced	replace	VERB
ejpam-3914	304	6	from	from	ADP
ejpam-3914	304	7	r	r	NOUN
ejpam-3914	304	8	,	,	PUNCT
ejpam-3914	304	9	we	we	PRON
ejpam-3914	304	10	can	can	AUX
ejpam-3914	304	11	not	not	PART
ejpam-3914	304	12	replace	replace	VERB
ejpam-3914	304	13	the	the	DET
ejpam-3914	304	14	vertex	vertex	NOUN
ejpam-3914	304	15	ui+1	ui+1	NOUN
ejpam-3914	304	16	in	in	ADP
ejpam-3914	304	17	r	r	NOUN
ejpam-3914	304	18	,	,	PUNCT
ejpam-3914	304	19	where	where	SCONJ
ejpam-3914	304	20	i	i	PRON
ejpam-3914	304	21	=	=	NOUN
ejpam-3914	304	22	9	9	NUM
ejpam-3914	304	23	,	,	PUNCT
ejpam-3914	304	24	14	14	NUM
ejpam-3914	304	25	,	,	PUNCT
ejpam-3914	304	26	.	.	PUNCT
ejpam-3914	304	27	.	.	PUNCT
ejpam-3914	305	1	.	.	PUNCT
ejpam-3914	306	1	,	,	PUNCT
ejpam-3914	306	2	n−	n−	NOUN
ejpam-3914	306	3	9	9	NUM
ejpam-3914	306	4	,	,	PUNCT
ejpam-3914	306	5	n−	n−	NOUN
ejpam-3914	306	6	4	4	NUM
ejpam-3914	306	7	to	to	PART
ejpam-3914	306	8	form	form	VERB
ejpam-3914	306	9	another	another	PRON
ejpam-3914	306	10	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	306	11	-set	-set	PROPN
ejpam-3914	306	12	of	of	ADP
ejpam-3914	306	13	pn	pn	PROPN
ejpam-3914	306	14	.	.	PROPN
ejpam-3914	306	15	hence	hence	ADV
ejpam-3914	306	16	,	,	PUNCT
ejpam-3914	306	17	{	{	PUNCT
ejpam-3914	306	18	u1	u1	NOUN
ejpam-3914	306	19	,	,	PUNCT
ejpam-3914	306	20	u5	u5	PROPN
ejpam-3914	306	21	}	}	PUNCT
ejpam-3914	306	22	is	be	AUX
ejpam-3914	306	23	not	not	PART
ejpam-3914	306	24	a	a	DET
ejpam-3914	306	25	subset	subset	NOUN
ejpam-3914	306	26	of	of	ADP
ejpam-3914	306	27	tk	tk	PROPN
ejpam-3914	306	28	for	for	ADP
ejpam-3914	306	29	all	all	PRON
ejpam-3914	306	30	k	k	PROPN
ejpam-3914	306	31	>	>	X
ejpam-3914	306	32	5	5	X
ejpam-3914	306	33	.	.	PUNCT
ejpam-3914	307	1	therefore	therefore	ADV
ejpam-3914	307	2	,	,	PUNCT
ejpam-3914	307	3	in	in	ADP
ejpam-3914	307	4	any	any	DET
ejpam-3914	307	5	subcase	subcase	NOUN
ejpam-3914	307	6	,	,	PUNCT
ejpam-3914	307	7	{	{	PUNCT
ejpam-3914	307	8	u1	u1	NOUN
ejpam-3914	307	9	,	,	PUNCT
ejpam-3914	307	10	u5	u5	PROPN
ejpam-3914	307	11	}	}	PUNCT
ejpam-3914	307	12	*	*	PUNCT
ejpam-3914	307	13	tk	tk	PROPN
ejpam-3914	307	14	for	for	ADP
ejpam-3914	307	15	all	all	PRON
ejpam-3914	307	16	k	k	NOUN
ejpam-3914	307	17	=	=	SYM
ejpam-3914	307	18	1	1	NUM
ejpam-3914	307	19	,	,	PUNCT
ejpam-3914	307	20	2	2	NUM
ejpam-3914	307	21	,	,	PUNCT
ejpam-3914	307	22	.	.	PUNCT
ejpam-3914	307	23	.	.	PUNCT
ejpam-3914	307	24	.	.	PUNCT
ejpam-3914	308	1	,	,	PUNCT
ejpam-3914	308	2	m	m	PROPN
ejpam-3914	308	3	,	,	PUNCT
ejpam-3914	308	4	that	that	ADV
ejpam-3914	308	5	is	is	ADV
ejpam-3914	308	6	,	,	PUNCT
ejpam-3914	308	7	{	{	PUNCT
ejpam-3914	308	8	u1	u1	NOUN
ejpam-3914	308	9	,	,	PUNCT
ejpam-3914	308	10	u5	u5	PROPN
ejpam-3914	308	11	}	}	PUNCT
ejpam-3914	308	12	is	be	AUX
ejpam-3914	308	13	a	a	DET
ejpam-3914	308	14	forcing	forcing	NOUN
ejpam-3914	308	15	subset	subset	NOUN
ejpam-3914	308	16	for	for	ADP
ejpam-3914	308	17	r.	r.	PROPN
ejpam-3914	308	18	thus	thus	ADV
ejpam-3914	308	19	,	,	PUNCT
ejpam-3914	308	20	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	308	21	(	(	PUNCT
ejpam-3914	308	22	r	r	NOUN
ejpam-3914	308	23	)	)	PUNCT
ejpam-3914	308	24	=	=	SYM
ejpam-3914	309	1	2	2	NUM
ejpam-3914	309	2	=	=	NOUN
ejpam-3914	309	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	309	4	(	(	PUNCT
ejpam-3914	309	5	pn	pn	NOUN
ejpam-3914	309	6	)	)	PUNCT
ejpam-3914	309	7	.	.	PUNCT
ejpam-3914	310	1	case	case	NOUN
ejpam-3914	310	2	5	5	NUM
ejpam-3914	310	3	:	:	PUNCT
ejpam-3914	310	4	suppose	suppose	VERB
ejpam-3914	310	5	that	that	SCONJ
ejpam-3914	310	6	n	n	PROPN
ejpam-3914	310	7	≡	≡	PROPN
ejpam-3914	310	8	4(mod	4(mod	NUM
ejpam-3914	310	9	5	5	NUM
ejpam-3914	310	10	)	)	PUNCT
ejpam-3914	310	11	.	.	PUNCT
ejpam-3914	311	1	by	by	ADP
ejpam-3914	311	2	theorem	theorem	ADJ
ejpam-3914	311	3	2.2	2.2	NUM
ejpam-3914	311	4	,	,	PUNCT
ejpam-3914	311	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	311	6	(	(	PUNCT
ejpam-3914	311	7	pn	pn	NOUN
ejpam-3914	311	8	)	)	PUNCT
ejpam-3914	311	9	=	=	PUNCT
ejpam-3914	312	1	2n+2	2n+2	NUM
ejpam-3914	312	2	5	5	NUM
ejpam-3914	312	3	.	.	PUNCT
ejpam-3914	313	1	let	let	VERB
ejpam-3914	313	2	n	n	NOUN
ejpam-3914	313	3	=	=	SYM
ejpam-3914	313	4	9	9	NUM
ejpam-3914	313	5	.	.	PUNCT
ejpam-3914	314	1	then	then	ADV
ejpam-3914	314	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	314	3	(	(	PUNCT
ejpam-3914	314	4	p9	p9	PROPN
ejpam-3914	314	5	)	)	PUNCT
ejpam-3914	314	6	=	=	NOUN
ejpam-3914	314	7	2(9)+2	2(9)+2	NUM
ejpam-3914	314	8	5	5	NUM
ejpam-3914	314	9	=	=	SYM
ejpam-3914	314	10	4	4	NUM
ejpam-3914	314	11	.	.	PUNCT
ejpam-3914	314	12	clearly	clearly	ADV
ejpam-3914	314	13	,	,	PUNCT
ejpam-3914	314	14	s1	s1	PROPN
ejpam-3914	314	15	=	=	SYM
ejpam-3914	314	16	{	{	PUNCT
ejpam-3914	314	17	u1	u1	NOUN
ejpam-3914	314	18	,	,	PUNCT
ejpam-3914	314	19	u2	u2	NOUN
ejpam-3914	314	20	,	,	PUNCT
ejpam-3914	314	21	u6	u6	PROPN
ejpam-3914	314	22	,	,	PUNCT
ejpam-3914	314	23	u7	u7	PROPN
ejpam-3914	314	24	}	}	PUNCT
ejpam-3914	314	25	,	,	PUNCT
ejpam-3914	314	26	s2	s2	NOUN
ejpam-3914	314	27	=	=	SYM
ejpam-3914	314	28	{	{	PUNCT
ejpam-3914	314	29	u2	u2	PROPN
ejpam-3914	314	30	,	,	PUNCT
ejpam-3914	314	31	u3	u3	NOUN
ejpam-3914	314	32	,	,	PUNCT
ejpam-3914	314	33	u6	u6	PROPN
ejpam-3914	314	34	,	,	PUNCT
ejpam-3914	314	35	u7	u7	PROPN
ejpam-3914	314	36	}	}	PUNCT
ejpam-3914	314	37	,	,	PUNCT
ejpam-3914	314	38	s3	s3	PROPN
ejpam-3914	314	39	=	=	SYM
ejpam-3914	314	40	{	{	PUNCT
ejpam-3914	314	41	u2	u2	PROPN
ejpam-3914	314	42	,	,	PUNCT
ejpam-3914	314	43	u3	u3	PROPN
ejpam-3914	314	44	,	,	PUNCT
ejpam-3914	314	45	u7	u7	PROPN
ejpam-3914	314	46	,	,	PUNCT
ejpam-3914	314	47	u8	u8	PROPN
ejpam-3914	314	48	}	}	PUNCT
ejpam-3914	314	49	,	,	PUNCT
ejpam-3914	314	50	s4	s4	PROPN
ejpam-3914	314	51	=	=	SYM
ejpam-3914	314	52	{	{	PUNCT
ejpam-3914	314	53	u3	u3	PROPN
ejpam-3914	314	54	,	,	PUNCT
ejpam-3914	314	55	u4	u4	PROPN
ejpam-3914	314	56	,	,	PUNCT
ejpam-3914	314	57	u7	u7	PROPN
ejpam-3914	314	58	,	,	PUNCT
ejpam-3914	314	59	u8	u8	PROPN
ejpam-3914	314	60	}	}	PUNCT
ejpam-3914	314	61	,	,	PUNCT
ejpam-3914	314	62	and	and	CCONJ
ejpam-3914	314	63	s5	s5	PROPN
ejpam-3914	314	64	=	=	SYM
ejpam-3914	314	65	{	{	PUNCT
ejpam-3914	314	66	u3	u3	PROPN
ejpam-3914	314	67	,	,	PUNCT
ejpam-3914	314	68	u4	u4	PROPN
ejpam-3914	314	69	,	,	PUNCT
ejpam-3914	314	70	u8	u8	PROPN
ejpam-3914	314	71	,	,	PUNCT
ejpam-3914	314	72	u9	u9	PROPN
ejpam-3914	314	73	}	}	PUNCT
ejpam-3914	314	74	are	be	AUX
ejpam-3914	314	75	the	the	DET
ejpam-3914	314	76	only	only	ADJ
ejpam-3914	314	77	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	314	78	-sets	-set	NOUN
ejpam-3914	314	79	of	of	ADP
ejpam-3914	314	80	p9	p9	PROPN
ejpam-3914	314	81	.	.	PUNCT
ejpam-3914	315	1	since	since	SCONJ
ejpam-3914	315	2	u1	u1	PROPN
ejpam-3914	315	3	∈	∈	PROPN
ejpam-3914	315	4	s1	s1	NOUN
ejpam-3914	315	5	and	and	CCONJ
ejpam-3914	315	6	u1	u1	NOUN
ejpam-3914	315	7	/∈	/∈	PUNCT
ejpam-3914	315	8	sl	sl	VERB
ejpam-3914	315	9	for	for	ADP
ejpam-3914	315	10	l	l	NOUN
ejpam-3914	315	11	=	=	SYM
ejpam-3914	315	12	2	2	NUM
ejpam-3914	315	13	,	,	PUNCT
ejpam-3914	315	14	3	3	NUM
ejpam-3914	315	15	,	,	PUNCT
ejpam-3914	315	16	4	4	NUM
ejpam-3914	315	17	,	,	PUNCT
ejpam-3914	315	18	5	5	NUM
ejpam-3914	315	19	,	,	PUNCT
ejpam-3914	315	20	by	by	ADP
ejpam-3914	315	21	theorem	theorem	NOUN
ejpam-3914	315	22	3.1(ii	3.1(ii	NUM
ejpam-3914	315	23	)	)	PUNCT
ejpam-3914	315	24	,	,	PUNCT
ejpam-3914	315	25	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	315	26	(	(	PUNCT
ejpam-3914	315	27	p9	p9	PROPN
ejpam-3914	315	28	)	)	PUNCT
ejpam-3914	315	29	=	=	SYM
ejpam-3914	316	1	1	1	X
ejpam-3914	316	2	.	.	PUNCT
ejpam-3914	316	3	now	now	ADV
ejpam-3914	316	4	,	,	PUNCT
ejpam-3914	316	5	suppose	suppose	VERB
ejpam-3914	316	6	that	that	SCONJ
ejpam-3914	316	7	n	n	PROPN
ejpam-3914	316	8	>	>	X
ejpam-3914	316	9	9	9	X
ejpam-3914	316	10	.	.	PUNCT
ejpam-3914	317	1	let	let	VERB
ejpam-3914	317	2	p	p	NOUN
ejpam-3914	317	3	=	=	PUNCT
ejpam-3914	317	4	n−4	n−4	PROPN
ejpam-3914	317	5	5	5	NUM
ejpam-3914	317	6	and	and	CCONJ
ejpam-3914	317	7	j	j	NOUN
ejpam-3914	317	8	=	=	SYM
ejpam-3914	317	9	0	0	NUM
ejpam-3914	317	10	,	,	PUNCT
ejpam-3914	317	11	1	1	NUM
ejpam-3914	317	12	,	,	PUNCT
ejpam-3914	317	13	2	2	NUM
ejpam-3914	317	14	,	,	PUNCT
ejpam-3914	317	15	.	.	PUNCT
ejpam-3914	317	16	.	.	PUNCT
ejpam-3914	318	1	.	.	PUNCT
ejpam-3914	319	1	,	,	PUNCT
ejpam-3914	319	2	p−	p−	NOUN
ejpam-3914	319	3	1	1	NUM
ejpam-3914	319	4	,	,	PUNCT
ejpam-3914	319	5	p.	p.	NOUN
ejpam-3914	319	6	group	group	NOUN
ejpam-3914	319	7	the	the	DET
ejpam-3914	319	8	vertices	vertex	NOUN
ejpam-3914	319	9	of	of	ADP
ejpam-3914	319	10	pn	pn	PROPN
ejpam-3914	319	11	into	into	ADP
ejpam-3914	319	12	p+	p+	NOUN
ejpam-3914	319	13	1	1	NUM
ejpam-3914	319	14	disjoint	disjoint	NOUN
ejpam-3914	319	15	subsets	subset	NOUN
ejpam-3914	319	16	rj	rj	PROPN
ejpam-3914	319	17	r0	r0	PROPN
ejpam-3914	319	18	=	=	PUNCT
ejpam-3914	319	19	{	{	PUNCT
ejpam-3914	319	20	u1	u1	NOUN
ejpam-3914	319	21	,	,	PUNCT
ejpam-3914	319	22	u2	u2	NOUN
ejpam-3914	319	23	,	,	PUNCT
ejpam-3914	319	24	u3	u3	NOUN
ejpam-3914	319	25	,	,	PUNCT
ejpam-3914	319	26	u4	u4	PROPN
ejpam-3914	319	27	}	}	PUNCT
ejpam-3914	319	28	r1	r1	NOUN
ejpam-3914	319	29	=	=	SYM
ejpam-3914	319	30	{	{	PUNCT
ejpam-3914	319	31	u5	u5	PROPN
ejpam-3914	319	32	,	,	PUNCT
ejpam-3914	319	33	u6	u6	PROPN
ejpam-3914	319	34	,	,	PUNCT
ejpam-3914	319	35	u7	u7	PROPN
ejpam-3914	319	36	,	,	PUNCT
ejpam-3914	319	37	u8	u8	PROPN
ejpam-3914	319	38	,	,	PUNCT
ejpam-3914	319	39	u9	u9	PROPN
ejpam-3914	319	40	}	}	PUNCT
ejpam-3914	319	41	r2	r2	NOUN
ejpam-3914	319	42	=	=	SYM
ejpam-3914	319	43	{	{	PUNCT
ejpam-3914	319	44	u10	u10	PROPN
ejpam-3914	319	45	,	,	PUNCT
ejpam-3914	319	46	u11	u11	PROPN
ejpam-3914	319	47	,	,	PUNCT
ejpam-3914	319	48	u12	u12	PROPN
ejpam-3914	319	49	,	,	PUNCT
ejpam-3914	319	50	u13	u13	NOUN
ejpam-3914	319	51	,	,	PUNCT
ejpam-3914	319	52	u14	u14	NOUN
ejpam-3914	319	53	}	}	PUNCT
ejpam-3914	319	54	r3	r3	PROPN
ejpam-3914	319	55	=	=	SYM
ejpam-3914	319	56	{	{	PUNCT
ejpam-3914	319	57	u15	u15	PROPN
ejpam-3914	319	58	,	,	PUNCT
ejpam-3914	319	59	u16	u16	NOUN
ejpam-3914	319	60	,	,	PUNCT
ejpam-3914	319	61	u17	u17	PROPN
ejpam-3914	319	62	,	,	PUNCT
ejpam-3914	319	63	u18	u18	PROPN
ejpam-3914	319	64	,	,	PUNCT
ejpam-3914	319	65	u13	u13	NOUN
ejpam-3914	319	66	}	}	PUNCT
ejpam-3914	319	67	...	...	PUNCT
ejpam-3914	320	1	rp−1	rp−1	NOUN
ejpam-3914	320	2	=	=	SYM
ejpam-3914	320	3	{	{	PUNCT
ejpam-3914	320	4	un−9	un−9	PROPN
ejpam-3914	320	5	,	,	PUNCT
ejpam-3914	320	6	un−8	un−8	ADJ
ejpam-3914	320	7	,	,	PUNCT
ejpam-3914	320	8	un−7	un−7	PROPN
ejpam-3914	320	9	,	,	PUNCT
ejpam-3914	320	10	un−6	un−6	PROPN
ejpam-3914	320	11	,	,	PUNCT
ejpam-3914	320	12	un−5	un−5	PROPN
ejpam-3914	320	13	}	}	PUNCT
ejpam-3914	320	14	rp	rp	NOUN
ejpam-3914	320	15	=	=	SYM
ejpam-3914	320	16	{	{	PUNCT
ejpam-3914	320	17	un−4	un−4	NOUN
ejpam-3914	320	18	,	,	PUNCT
ejpam-3914	320	19	un−3	un−3	ADJ
ejpam-3914	320	20	,	,	PUNCT
ejpam-3914	320	21	un−2	un−2	PROPN
ejpam-3914	320	22	,	,	PUNCT
ejpam-3914	320	23	un−1	un−1	PROPN
ejpam-3914	320	24	,	,	PUNCT
ejpam-3914	320	25	un	un	ADJ
ejpam-3914	320	26	}	}	PUNCT
ejpam-3914	320	27	let	let	VERB
ejpam-3914	320	28	i	i	PRON
ejpam-3914	320	29	=	=	NOUN
ejpam-3914	320	30	5	5	NUM
ejpam-3914	320	31	,	,	PUNCT
ejpam-3914	320	32	10	10	NUM
ejpam-3914	320	33	,	,	PUNCT
ejpam-3914	320	34	15	15	NUM
ejpam-3914	320	35	,	,	PUNCT
ejpam-3914	320	36	.	.	PUNCT
ejpam-3914	320	37	.	.	PUNCT
ejpam-3914	321	1	.	.	PUNCT
ejpam-3914	322	1	,	,	PUNCT
ejpam-3914	323	1	n	n	CCONJ
ejpam-3914	323	2	−	−	PROPN
ejpam-3914	323	3	4	4	NUM
ejpam-3914	323	4	.	.	PUNCT
ejpam-3914	323	5	for	for	ADP
ejpam-3914	323	6	every	every	DET
ejpam-3914	323	7	induced	induced	ADJ
ejpam-3914	323	8	subgraph	subgraph	NOUN
ejpam-3914	323	9	〈	〈	PROPN
ejpam-3914	323	10	ui	ui	PROPN
ejpam-3914	323	11	,	,	PUNCT
ejpam-3914	323	12	ui+1	ui+1	PROPN
ejpam-3914	323	13	,	,	PUNCT
ejpam-3914	323	14	ui+2	ui+2	NUM
ejpam-3914	323	15	,	,	PUNCT
ejpam-3914	323	16	ui+3	ui+3	NOUN
ejpam-3914	323	17	,	,	PUNCT
ejpam-3914	323	18	ui+4	ui+4	PROPN
ejpam-3914	323	19	〉	〉	NOUN
ejpam-3914	323	20	,	,	PUNCT
ejpam-3914	323	21	the	the	DET
ejpam-3914	323	22	vertices	vertex	NOUN
ejpam-3914	323	23	u1	u1	NOUN
ejpam-3914	323	24	,	,	PUNCT
ejpam-3914	323	25	u2	u2	NOUN
ejpam-3914	323	26	,	,	PUNCT
ejpam-3914	323	27	ui+1	ui+1	PROPN
ejpam-3914	323	28	,	,	PUNCT
ejpam-3914	323	29	ui+2	ui+2	PRON
ejpam-3914	323	30	form	form	VERB
ejpam-3914	323	31	a	a	DET
ejpam-3914	323	32	total	total	ADJ
ejpam-3914	323	33	dr	dr	ADJ
ejpam-3914	323	34	-	-	PUNCT
ejpam-3914	323	35	power	power	NOUN
ejpam-3914	323	36	dominating	dominating	NOUN
ejpam-3914	323	37	set	set	VERB
ejpam-3914	323	38	since	since	SCONJ
ejpam-3914	323	39	u3	u3	NOUN
ejpam-3914	323	40	,	,	PUNCT
ejpam-3914	323	41	ui	ui	NOUN
ejpam-3914	323	42	and	and	CCONJ
ejpam-3914	323	43	ui+3	ui+3	PROPN
ejpam-3914	323	44	c.	c.	PROPN
ejpam-3914	323	45	armada	armada	PROPN
ejpam-3914	323	46	/	/	SYM
ejpam-3914	323	47	eur	eur	PROPN
ejpam-3914	323	48	.	.	PUNCT
ejpam-3914	324	1	j.	j.	PROPN
ejpam-3914	324	2	pure	pure	PROPN
ejpam-3914	324	3	appl	appl	PROPN
ejpam-3914	324	4	.	.	PROPN
ejpam-3914	324	5	math	math	PROPN
ejpam-3914	324	6	,	,	PUNCT
ejpam-3914	324	7	14	14	NUM
ejpam-3914	324	8	(	(	PUNCT
ejpam-3914	324	9	2	2	NUM
ejpam-3914	324	10	)	)	PUNCT
ejpam-3914	324	11	(	(	PUNCT
ejpam-3914	324	12	2021	2021	NUM
ejpam-3914	324	13	)	)	PUNCT
ejpam-3914	325	1	,	,	PUNCT
ejpam-3914	325	2	451	451	NUM
ejpam-3914	325	3	-	-	SYM
ejpam-3914	325	4	470	470	NUM
ejpam-3914	325	5	460	460	NUM
ejpam-3914	325	6	are	be	AUX
ejpam-3914	325	7	directly	directly	ADV
ejpam-3914	325	8	observed	observe	VERB
ejpam-3914	325	9	vertices	vertex	NOUN
ejpam-3914	325	10	while	while	SCONJ
ejpam-3914	325	11	u4	u4	PROPN
ejpam-3914	325	12	and	and	CCONJ
ejpam-3914	325	13	ui+4	ui+4	PRON
ejpam-3914	325	14	are	be	AUX
ejpam-3914	325	15	remotely	remotely	ADV
ejpam-3914	325	16	observed	observe	VERB
ejpam-3914	325	17	vertices	vertex	NOUN
ejpam-3914	325	18	for	for	ADP
ejpam-3914	325	19	all	all	DET
ejpam-3914	325	20	i	i	PRON
ejpam-3914	325	21	=	=	NOUN
ejpam-3914	325	22	5	5	NUM
ejpam-3914	325	23	,	,	PUNCT
ejpam-3914	325	24	10	10	NUM
ejpam-3914	325	25	,	,	PUNCT
ejpam-3914	325	26	15	15	NUM
ejpam-3914	325	27	,	,	PUNCT
ejpam-3914	325	28	.	.	PUNCT
ejpam-3914	325	29	.	.	PUNCT
ejpam-3914	326	1	.	.	PUNCT
ejpam-3914	327	1	,	,	PUNCT
ejpam-3914	327	2	n−	n−	NOUN
ejpam-3914	327	3	9	9	NUM
ejpam-3914	327	4	,	,	PUNCT
ejpam-3914	327	5	n−	n−	NOUN
ejpam-3914	327	6	4	4	NUM
ejpam-3914	327	7	.	.	PUNCT
ejpam-3914	327	8	let	let	VERB
ejpam-3914	327	9	the	the	DET
ejpam-3914	327	10	set	set	NOUN
ejpam-3914	327	11	r	r	NOUN
ejpam-3914	327	12	=	=	SYM
ejpam-3914	327	13	{	{	PUNCT
ejpam-3914	327	14	u1	u1	NOUN
ejpam-3914	327	15	,	,	PUNCT
ejpam-3914	327	16	u2	u2	NOUN
ejpam-3914	327	17	,	,	PUNCT
ejpam-3914	327	18	ui+1	ui+1	PROPN
ejpam-3914	327	19	,	,	PUNCT
ejpam-3914	327	20	ui+2	ui+2	NUM
ejpam-3914	327	21	:	:	PUNCT
ejpam-3914	327	22	i	i	NOUN
ejpam-3914	327	23	=	=	NOUN
ejpam-3914	327	24	5	5	NUM
ejpam-3914	327	25	,	,	PUNCT
ejpam-3914	327	26	10	10	NUM
ejpam-3914	327	27	,	,	PUNCT
ejpam-3914	327	28	15	15	NUM
ejpam-3914	327	29	,	,	PUNCT
ejpam-3914	327	30	.	.	PUNCT
ejpam-3914	327	31	.	.	PUNCT
ejpam-3914	328	1	.	.	PUNCT
ejpam-3914	329	1	,	,	PUNCT
ejpam-3914	329	2	n−	n−	NOUN
ejpam-3914	329	3	9	9	NUM
ejpam-3914	329	4	,	,	PUNCT
ejpam-3914	329	5	n−	n−	NOUN
ejpam-3914	329	6	4	4	NUM
ejpam-3914	329	7	}	}	PUNCT
ejpam-3914	329	8	=	=	NOUN
ejpam-3914	329	9	{	{	PUNCT
ejpam-3914	329	10	u1	u1	NOUN
ejpam-3914	329	11	,	,	PUNCT
ejpam-3914	329	12	u2	u2	NOUN
ejpam-3914	329	13	,	,	PUNCT
ejpam-3914	329	14	u6	u6	PROPN
ejpam-3914	329	15	,	,	PUNCT
ejpam-3914	329	16	u7	u7	PROPN
ejpam-3914	329	17	,	,	PUNCT
ejpam-3914	329	18	u11	u11	PROPN
ejpam-3914	329	19	,	,	PUNCT
ejpam-3914	329	20	u12	u12	PROPN
ejpam-3914	329	21	,	,	PUNCT
ejpam-3914	329	22	u16	u16	PROPN
ejpam-3914	329	23	,	,	PUNCT
ejpam-3914	329	24	u17	u17	NOUN
ejpam-3914	329	25	,	,	PUNCT
ejpam-3914	329	26	.	.	PUNCT
ejpam-3914	329	27	.	.	PUNCT
ejpam-3914	330	1	.	.	PUNCT
ejpam-3914	331	1	,	,	PUNCT
ejpam-3914	331	2	un−8	un−8	ADJ
ejpam-3914	331	3	,	,	PUNCT
ejpam-3914	331	4	un−7	un−7	NOUN
ejpam-3914	331	5	,	,	PUNCT
ejpam-3914	331	6	un−3	un−3	ADJ
ejpam-3914	331	7	,	,	PUNCT
ejpam-3914	331	8	un−2	un−2	VERB
ejpam-3914	331	9	}	}	PUNCT
ejpam-3914	331	10	where	where	SCONJ
ejpam-3914	331	11	|r|	|r|	NOUN
ejpam-3914	332	1	=	=	NOUN
ejpam-3914	332	2	2p	2p	NOUN
ejpam-3914	332	3	+	+	CCONJ
ejpam-3914	332	4	2	2	NUM
ejpam-3914	332	5	=	=	SYM
ejpam-3914	332	6	2	2	NUM
ejpam-3914	332	7	(	(	PUNCT
ejpam-3914	332	8	n−4	n−4	PROPN
ejpam-3914	332	9	5	5	NUM
ejpam-3914	332	10	)	)	PUNCT
ejpam-3914	333	1	+	+	CCONJ
ejpam-3914	333	2	2	2	X
ejpam-3914	333	3	=	=	SYM
ejpam-3914	333	4	2n+2	2n+2	NUM
ejpam-3914	333	5	5	5	NUM
ejpam-3914	333	6	,	,	PUNCT
ejpam-3914	333	7	or	or	CCONJ
ejpam-3914	333	8	v	v	NOUN
ejpam-3914	333	9	(	(	PUNCT
ejpam-3914	333	10	pn	pn	NOUN
ejpam-3914	333	11	)	)	PUNCT
ejpam-3914	333	12	=	=	NOUN
ejpam-3914	333	13	v	v	X
ejpam-3914	333	14	(	(	PUNCT
ejpam-3914	333	15	pn	pn	NOUN
ejpam-3914	333	16	)	)	PUNCT
ejpam-3914	333	17	,	,	PUNCT
ejpam-3914	333	18	or	or	CCONJ
ejpam-3914	333	19	e(pn	e(pn	NUM
ejpam-3914	333	20	)	)	PUNCT
ejpam-3914	333	21	=	=	SYM
ejpam-3914	333	22	e(pn	e(pn	NUM
ejpam-3914	333	23	)	)	PUNCT
ejpam-3914	333	24	,	,	PUNCT
ejpam-3914	333	25	and	and	CCONJ
ejpam-3914	333	26	the	the	DET
ejpam-3914	333	27	induced	induced	ADJ
ejpam-3914	333	28	subgraph	subgraph	NOUN
ejpam-3914	333	29	〈	〈	PROPN
ejpam-3914	333	30	r	r	PROPN
ejpam-3914	333	31	〉	〉	PROPN
ejpam-3914	333	32	has	have	VERB
ejpam-3914	333	33	no	no	DET
ejpam-3914	333	34	isolated	isolated	ADJ
ejpam-3914	333	35	vertex	vertex	NOUN
ejpam-3914	333	36	.	.	PUNCT
ejpam-3914	334	1	by	by	ADP
ejpam-3914	334	2	theorem	theorem	NOUN
ejpam-3914	334	3	2.2	2.2	NUM
ejpam-3914	334	4	,	,	PUNCT
ejpam-3914	334	5	r	r	NOUN
ejpam-3914	334	6	is	be	AUX
ejpam-3914	334	7	a	a	DET
ejpam-3914	334	8	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	334	9	-set	-set	PROPN
ejpam-3914	334	10	of	of	ADP
ejpam-3914	334	11	pn	pn	PROPN
ejpam-3914	334	12	.	.	PROPN
ejpam-3914	335	1	let	let	VERB
ejpam-3914	335	2	m+	m+	PRON
ejpam-3914	335	3	1	1	NUM
ejpam-3914	335	4	be	be	AUX
ejpam-3914	335	5	the	the	DET
ejpam-3914	335	6	number	number	NOUN
ejpam-3914	335	7	of	of	ADP
ejpam-3914	335	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	335	9	-sets	-set	NOUN
ejpam-3914	335	10	of	of	ADP
ejpam-3914	335	11	pn	pn	NOUN
ejpam-3914	335	12	where	where	SCONJ
ejpam-3914	335	13	m	m	PROPN
ejpam-3914	335	14	is	be	AUX
ejpam-3914	335	15	a	a	DET
ejpam-3914	335	16	positive	positive	ADJ
ejpam-3914	335	17	integer	integer	NOUN
ejpam-3914	335	18	.	.	PUNCT
ejpam-3914	336	1	let	let	VERB
ejpam-3914	336	2	k	k	NOUN
ejpam-3914	336	3	=	=	SYM
ejpam-3914	336	4	1	1	NUM
ejpam-3914	336	5	,	,	PUNCT
ejpam-3914	336	6	2	2	NUM
ejpam-3914	336	7	,	,	PUNCT
ejpam-3914	336	8	.	.	PUNCT
ejpam-3914	336	9	.	.	PUNCT
ejpam-3914	337	1	.	.	PUNCT
ejpam-3914	338	1	,	,	PUNCT
ejpam-3914	338	2	m	m	VERB
ejpam-3914	338	3	and	and	CCONJ
ejpam-3914	338	4	tk	tk	PROPN
ejpam-3914	338	5	be	be	AUX
ejpam-3914	338	6	a	a	DET
ejpam-3914	338	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	338	8	-set	-set	PUNCT
ejpam-3914	338	9	of	of	ADP
ejpam-3914	338	10	pn	pn	PROPN
ejpam-3914	338	11	different	different	ADJ
ejpam-3914	338	12	from	from	ADP
ejpam-3914	338	13	r.	r.	PROPN
ejpam-3914	338	14	consider	consider	VERB
ejpam-3914	338	15	the	the	DET
ejpam-3914	338	16	following	follow	VERB
ejpam-3914	338	17	subcases	subcase	NOUN
ejpam-3914	338	18	:	:	PUNCT
ejpam-3914	338	19	subcase	subcase	NOUN
ejpam-3914	338	20	1	1	NUM
ejpam-3914	338	21	:	:	PUNCT
ejpam-3914	338	22	tk	tk	PROPN
ejpam-3914	338	23	,	,	PUNCT
ejpam-3914	338	24	say	say	VERB
ejpam-3914	338	25	t1	t1	NOUN
ejpam-3914	338	26	and	and	CCONJ
ejpam-3914	338	27	t2	t2	NOUN
ejpam-3914	338	28	,	,	PUNCT
ejpam-3914	338	29	can	can	AUX
ejpam-3914	338	30	be	be	AUX
ejpam-3914	338	31	formed	form	VERB
ejpam-3914	338	32	by	by	ADP
ejpam-3914	338	33	replacing	replace	VERB
ejpam-3914	338	34	u1	u1	NOUN
ejpam-3914	338	35	,	,	PUNCT
ejpam-3914	338	36	u2	u2	NOUN
ejpam-3914	338	37	in	in	ADP
ejpam-3914	338	38	r	r	NOUN
ejpam-3914	338	39	by	by	ADP
ejpam-3914	338	40	either	either	CCONJ
ejpam-3914	338	41	u2	u2	NOUN
ejpam-3914	338	42	,	,	PUNCT
ejpam-3914	338	43	u3	u3	NOUN
ejpam-3914	338	44	or	or	CCONJ
ejpam-3914	338	45	u3	u3	PROPN
ejpam-3914	338	46	,	,	PUNCT
ejpam-3914	338	47	u4	u4	PROPN
ejpam-3914	338	48	.	.	PUNCT
ejpam-3914	339	1	it	it	PRON
ejpam-3914	339	2	follows	follow	VERB
ejpam-3914	339	3	that	that	PRON
ejpam-3914	339	4	t1	t1	NOUN
ejpam-3914	339	5	=	=	PUNCT
ejpam-3914	339	6	{	{	PUNCT
ejpam-3914	339	7	u2	u2	PROPN
ejpam-3914	339	8	,	,	PUNCT
ejpam-3914	339	9	u3	u3	NOUN
ejpam-3914	339	10	,	,	PUNCT
ejpam-3914	339	11	u6	u6	PROPN
ejpam-3914	339	12	,	,	PUNCT
ejpam-3914	339	13	u7	u7	PROPN
ejpam-3914	339	14	,	,	PUNCT
ejpam-3914	339	15	u11	u11	PROPN
ejpam-3914	339	16	,	,	PUNCT
ejpam-3914	339	17	u12	u12	PROPN
ejpam-3914	339	18	,	,	PUNCT
ejpam-3914	339	19	.	.	PUNCT
ejpam-3914	339	20	.	.	PUNCT
ejpam-3914	340	1	.	.	PUNCT
ejpam-3914	341	1	,	,	PUNCT
ejpam-3914	341	2	un−8	un−8	ADJ
ejpam-3914	341	3	,	,	PUNCT
ejpam-3914	341	4	un−7	un−7	NOUN
ejpam-3914	341	5	,	,	PUNCT
ejpam-3914	341	6	un−3	un−3	ADJ
ejpam-3914	341	7	,	,	PUNCT
ejpam-3914	341	8	un−2	un−2	VERB
ejpam-3914	341	9	}	}	PUNCT
ejpam-3914	341	10	and	and	CCONJ
ejpam-3914	341	11	the	the	DET
ejpam-3914	341	12	set	set	NOUN
ejpam-3914	341	13	t2	t2	NOUN
ejpam-3914	341	14	=	=	SYM
ejpam-3914	341	15	{	{	PUNCT
ejpam-3914	341	16	u3	u3	PROPN
ejpam-3914	341	17	,	,	PUNCT
ejpam-3914	341	18	u4	u4	PROPN
ejpam-3914	341	19	,	,	PUNCT
ejpam-3914	341	20	u6	u6	PROPN
ejpam-3914	341	21	,	,	PUNCT
ejpam-3914	341	22	u7	u7	PROPN
ejpam-3914	341	23	,	,	PUNCT
ejpam-3914	341	24	u11	u11	PROPN
ejpam-3914	341	25	,	,	PUNCT
ejpam-3914	341	26	u12	u12	PROPN
ejpam-3914	341	27	,	,	PUNCT
ejpam-3914	341	28	.	.	PUNCT
ejpam-3914	341	29	.	.	PUNCT
ejpam-3914	342	1	.	.	PUNCT
ejpam-3914	343	1	,	,	PUNCT
ejpam-3914	343	2	un−8	un−8	ADJ
ejpam-3914	343	3	,	,	PUNCT
ejpam-3914	343	4	un−7	un−7	NOUN
ejpam-3914	343	5	,	,	PUNCT
ejpam-3914	343	6	un−3	un−3	ADJ
ejpam-3914	343	7	,	,	PUNCT
ejpam-3914	343	8	un−2	un−2	PROPN
ejpam-3914	343	9	}	}	PUNCT
ejpam-3914	343	10	are	be	AUX
ejpam-3914	343	11	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	343	12	-sets	-set	NOUN
ejpam-3914	343	13	of	of	ADP
ejpam-3914	343	14	pn	pn	PROPN
ejpam-3914	343	15	.	.	PUNCT
ejpam-3914	344	1	clearly	clearly	ADV
ejpam-3914	344	2	,	,	PUNCT
ejpam-3914	344	3	u1	u1	PROPN
ejpam-3914	344	4	/∈	/∈	PUNCT
ejpam-3914	345	1	t1	t1	NOUN
ejpam-3914	345	2	and	and	CCONJ
ejpam-3914	345	3	u1	u1	PROPN
ejpam-3914	345	4	/∈	/∈	PUNCT
ejpam-3914	345	5	t2	t2	PROPN
ejpam-3914	345	6	.	.	PUNCT
ejpam-3914	346	1	subcase	subcase	PROPN
ejpam-3914	346	2	2	2	NUM
ejpam-3914	346	3	:	:	PUNCT
ejpam-3914	346	4	let	let	VERB
ejpam-3914	346	5	k	k	NOUN
ejpam-3914	346	6	=	=	PUNCT
ejpam-3914	346	7	3	3	NUM
ejpam-3914	346	8	and	and	CCONJ
ejpam-3914	346	9	let	let	VERB
ejpam-3914	346	10	u1	u1	NOUN
ejpam-3914	346	11	,	,	PUNCT
ejpam-3914	346	12	u2	u2	PROPN
ejpam-3914	346	13	∈	∈	PROPN
ejpam-3914	346	14	t3	t3	PROPN
ejpam-3914	346	15	.	.	PUNCT
ejpam-3914	347	1	now	now	ADV
ejpam-3914	347	2	,	,	PUNCT
ejpam-3914	347	3	replace	replace	VERB
ejpam-3914	347	4	u6	u6	ADJ
ejpam-3914	347	5	∈	∈	NOUN
ejpam-3914	347	6	r	r	NOUN
ejpam-3914	347	7	by	by	ADP
ejpam-3914	347	8	u5	u5	PROPN
ejpam-3914	347	9	to	to	PART
ejpam-3914	347	10	form	form	VERB
ejpam-3914	347	11	t3	t3	PROPN
ejpam-3914	347	12	.	.	PUNCT
ejpam-3914	348	1	then	then	ADV
ejpam-3914	348	2	the	the	DET
ejpam-3914	348	3	next	next	ADJ
ejpam-3914	348	4	vertex	vertex	NOUN
ejpam-3914	348	5	to	to	PART
ejpam-3914	348	6	be	be	AUX
ejpam-3914	348	7	chosen	choose	VERB
ejpam-3914	348	8	must	must	AUX
ejpam-3914	348	9	be	be	AUX
ejpam-3914	348	10	u6	u6	ADJ
ejpam-3914	348	11	,	,	PUNCT
ejpam-3914	348	12	that	that	ADV
ejpam-3914	348	13	is	is	ADV
ejpam-3914	348	14	,	,	PUNCT
ejpam-3914	348	15	the	the	DET
ejpam-3914	348	16	vertex	vertex	NOUN
ejpam-3914	348	17	ui	ui	PROPN
ejpam-3914	348	18	,	,	PUNCT
ejpam-3914	348	19	ui+1	ui+1	PROPN
ejpam-3914	348	20	must	must	AUX
ejpam-3914	348	21	be	be	AUX
ejpam-3914	348	22	in	in	ADP
ejpam-3914	348	23	t3	t3	PROPN
ejpam-3914	348	24	for	for	ADP
ejpam-3914	348	25	all	all	DET
ejpam-3914	348	26	i	i	PRON
ejpam-3914	348	27	=	=	NOUN
ejpam-3914	348	28	5	5	NUM
ejpam-3914	348	29	,	,	PUNCT
ejpam-3914	348	30	10	10	NUM
ejpam-3914	348	31	,	,	PUNCT
ejpam-3914	348	32	15	15	NUM
ejpam-3914	348	33	,	,	PUNCT
ejpam-3914	348	34	.	.	PUNCT
ejpam-3914	348	35	.	.	PUNCT
ejpam-3914	349	1	.	.	PUNCT
ejpam-3914	350	1	,	,	PUNCT
ejpam-3914	350	2	n−	n−	NOUN
ejpam-3914	350	3	9	9	NUM
ejpam-3914	350	4	,	,	PUNCT
ejpam-3914	350	5	n−	n−	NOUN
ejpam-3914	350	6	4	4	NUM
ejpam-3914	350	7	.	.	PUNCT
ejpam-3914	351	1	then	then	ADV
ejpam-3914	351	2	t3	t3	PROPN
ejpam-3914	351	3	=	=	PUNCT
ejpam-3914	351	4	{	{	PUNCT
ejpam-3914	351	5	u1	u1	NOUN
ejpam-3914	351	6	,	,	PUNCT
ejpam-3914	351	7	u2	u2	PROPN
ejpam-3914	351	8	,	,	PUNCT
ejpam-3914	351	9	u5	u5	PROPN
ejpam-3914	351	10	,	,	PUNCT
ejpam-3914	351	11	u6	u6	PROPN
ejpam-3914	351	12	,	,	PUNCT
ejpam-3914	351	13	u10	u10	PROPN
ejpam-3914	351	14	,	,	PUNCT
ejpam-3914	351	15	u11	u11	PROPN
ejpam-3914	351	16	,	,	PUNCT
ejpam-3914	351	17	.	.	PUNCT
ejpam-3914	351	18	.	.	PUNCT
ejpam-3914	352	1	.	.	PUNCT
ejpam-3914	353	1	,	,	PUNCT
ejpam-3914	353	2	un−4	un−4	NOUN
ejpam-3914	353	3	,	,	PUNCT
ejpam-3914	353	4	un−3	un−3	ADJ
ejpam-3914	353	5	}	}	PUNCT
ejpam-3914	353	6	such	such	ADJ
ejpam-3914	353	7	that	that	SCONJ
ejpam-3914	353	8	|t3|	|t3|	PROPN
ejpam-3914	353	9	=	=	SYM
ejpam-3914	353	10	|r|	|r|	PROPN
ejpam-3914	353	11	.	.	PUNCT
ejpam-3914	354	1	since	since	SCONJ
ejpam-3914	354	2	un−3	un−3	PROPN
ejpam-3914	354	3	is	be	AUX
ejpam-3914	354	4	the	the	DET
ejpam-3914	354	5	last	last	ADJ
ejpam-3914	354	6	vertex	vertex	NOUN
ejpam-3914	354	7	in	in	ADP
ejpam-3914	354	8	t3	t3	PROPN
ejpam-3914	354	9	,	,	PUNCT
ejpam-3914	354	10	by	by	ADP
ejpam-3914	354	11	subcase	subcase	NOUN
ejpam-3914	354	12	1	1	NUM
ejpam-3914	354	13	of	of	ADP
ejpam-3914	354	14	case	case	NOUN
ejpam-3914	354	15	2	2	NUM
ejpam-3914	354	16	,	,	PUNCT
ejpam-3914	354	17	t3	t3	PROPN
ejpam-3914	354	18	is	be	AUX
ejpam-3914	354	19	not	not	PART
ejpam-3914	354	20	a	a	DET
ejpam-3914	354	21	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	354	22	-set	-set	PROPN
ejpam-3914	354	23	of	of	ADP
ejpam-3914	354	24	pn	pn	PROPN
ejpam-3914	354	25	.	.	PROPN
ejpam-3914	355	1	since	since	SCONJ
ejpam-3914	355	2	u6	u6	PROPN
ejpam-3914	355	3	is	be	AUX
ejpam-3914	355	4	arbitrarily	arbitrarily	ADV
ejpam-3914	355	5	replaced	replace	VERB
ejpam-3914	355	6	from	from	ADP
ejpam-3914	355	7	r	r	NOUN
ejpam-3914	355	8	,	,	PUNCT
ejpam-3914	355	9	we	we	PRON
ejpam-3914	355	10	can	can	AUX
ejpam-3914	355	11	not	not	PART
ejpam-3914	355	12	replace	replace	VERB
ejpam-3914	355	13	the	the	DET
ejpam-3914	355	14	vertex	vertex	NOUN
ejpam-3914	355	15	ui+1	ui+1	NOUN
ejpam-3914	355	16	in	in	ADP
ejpam-3914	355	17	r	r	NOUN
ejpam-3914	355	18	,	,	PUNCT
ejpam-3914	355	19	where	where	SCONJ
ejpam-3914	355	20	i	i	PRON
ejpam-3914	355	21	=	=	NOUN
ejpam-3914	355	22	10	10	NUM
ejpam-3914	355	23	,	,	PUNCT
ejpam-3914	355	24	15	15	NUM
ejpam-3914	355	25	,	,	PUNCT
ejpam-3914	355	26	.	.	PUNCT
ejpam-3914	355	27	.	.	PUNCT
ejpam-3914	356	1	.	.	PUNCT
ejpam-3914	357	1	,	,	PUNCT
ejpam-3914	357	2	n−9	n−9	PROPN
ejpam-3914	357	3	,	,	PUNCT
ejpam-3914	357	4	n−4	n−4	PROPN
ejpam-3914	357	5	to	to	PART
ejpam-3914	357	6	form	form	VERB
ejpam-3914	357	7	another	another	PRON
ejpam-3914	357	8	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	357	9	-set	-set	PROPN
ejpam-3914	357	10	of	of	ADP
ejpam-3914	357	11	pn	pn	PROPN
ejpam-3914	357	12	.	.	PUNCT
ejpam-3914	358	1	thus	thus	ADV
ejpam-3914	358	2	,	,	PUNCT
ejpam-3914	358	3	u1	u1	PROPN
ejpam-3914	358	4	/∈	/∈	PROPN
ejpam-3914	358	5	tk	tk	PROPN
ejpam-3914	359	1	for	for	ADP
ejpam-3914	359	2	all	all	DET
ejpam-3914	359	3	k	k	PROPN
ejpam-3914	359	4	≥	≥	NUM
ejpam-3914	359	5	3	3	NUM
ejpam-3914	359	6	.	.	PUNCT
ejpam-3914	360	1	therefore	therefore	ADV
ejpam-3914	360	2	,	,	PUNCT
ejpam-3914	360	3	in	in	ADP
ejpam-3914	360	4	any	any	DET
ejpam-3914	360	5	subcase	subcase	NOUN
ejpam-3914	360	6	,	,	PUNCT
ejpam-3914	360	7	u1	u1	PROPN
ejpam-3914	360	8	/∈	/∈	PROPN
ejpam-3914	360	9	tk	tk	PROPN
ejpam-3914	360	10	for	for	ADP
ejpam-3914	360	11	all	all	PRON
ejpam-3914	360	12	k	k	NOUN
ejpam-3914	360	13	=	=	SYM
ejpam-3914	360	14	1	1	NUM
ejpam-3914	360	15	,	,	PUNCT
ejpam-3914	360	16	2	2	NUM
ejpam-3914	360	17	,	,	PUNCT
ejpam-3914	360	18	.	.	PUNCT
ejpam-3914	360	19	.	.	PUNCT
ejpam-3914	361	1	.	.	PUNCT
ejpam-3914	362	1	,	,	PUNCT
ejpam-3914	362	2	m	m	VERB
ejpam-3914	362	3	and	and	CCONJ
ejpam-3914	362	4	so	so	ADV
ejpam-3914	362	5	,	,	PUNCT
ejpam-3914	362	6	the	the	DET
ejpam-3914	362	7	vertex	vertex	NOUN
ejpam-3914	362	8	u1	u1	NOUN
ejpam-3914	362	9	is	be	AUX
ejpam-3914	362	10	contained	contain	VERB
ejpam-3914	362	11	in	in	ADP
ejpam-3914	362	12	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	362	13	-set	-set	PUNCT
ejpam-3914	363	1	r	r	NOUN
ejpam-3914	363	2	only	only	ADV
ejpam-3914	363	3	.	.	PUNCT
ejpam-3914	364	1	by	by	ADP
ejpam-3914	364	2	theorem	theorem	NOUN
ejpam-3914	364	3	3.1(ii	3.1(ii	NUM
ejpam-3914	364	4	)	)	PUNCT
ejpam-3914	364	5	,	,	PUNCT
ejpam-3914	364	6	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	364	7	(	(	PUNCT
ejpam-3914	364	8	pn	pn	NOUN
ejpam-3914	364	9	)	)	PUNCT
ejpam-3914	364	10	=	=	SYM
ejpam-3914	364	11	1	1	X
ejpam-3914	364	12	.	.	X
ejpam-3914	364	13	case	case	NOUN
ejpam-3914	364	14	6	6	NUM
ejpam-3914	364	15	:	:	PUNCT
ejpam-3914	364	16	suppose	suppose	VERB
ejpam-3914	364	17	that	that	SCONJ
ejpam-3914	364	18	n	n	NUM
ejpam-3914	364	19	≡	≡	ADJ
ejpam-3914	364	20	0(mod	0(mod	NOUN
ejpam-3914	364	21	5	5	NUM
ejpam-3914	364	22	)	)	PUNCT
ejpam-3914	364	23	.	.	PUNCT
ejpam-3914	365	1	by	by	ADP
ejpam-3914	365	2	theorem	theorem	ADJ
ejpam-3914	365	3	2.2	2.2	NUM
ejpam-3914	365	4	,	,	PUNCT
ejpam-3914	365	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	365	6	(	(	PUNCT
ejpam-3914	365	7	pn	pn	NOUN
ejpam-3914	365	8	)	)	PUNCT
ejpam-3914	365	9	=	=	SYM
ejpam-3914	365	10	2n	2n	NUM
ejpam-3914	365	11	5	5	X
ejpam-3914	365	12	.	.	PUNCT
ejpam-3914	366	1	let	let	VERB
ejpam-3914	366	2	n	n	NOUN
ejpam-3914	366	3	=	=	SYM
ejpam-3914	366	4	5	5	X
ejpam-3914	366	5	.	.	PUNCT
ejpam-3914	366	6	then	then	ADV
ejpam-3914	366	7	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	366	8	(	(	PUNCT
ejpam-3914	366	9	p5	p5	ADJ
ejpam-3914	366	10	)	)	PUNCT
ejpam-3914	366	11	=	=	SYM
ejpam-3914	366	12	2(5	2(5	NOUN
ejpam-3914	366	13	)	)	PUNCT
ejpam-3914	366	14	5	5	NUM
ejpam-3914	366	15	=	=	SYM
ejpam-3914	366	16	2	2	X
ejpam-3914	366	17	.	.	PUNCT
ejpam-3914	366	18	clearly	clearly	ADV
ejpam-3914	366	19	,	,	PUNCT
ejpam-3914	366	20	s1	s1	PROPN
ejpam-3914	366	21	=	=	PUNCT
ejpam-3914	366	22	{	{	PUNCT
ejpam-3914	366	23	u2	u2	PROPN
ejpam-3914	366	24	,	,	PUNCT
ejpam-3914	366	25	u3	u3	NOUN
ejpam-3914	366	26	}	}	PUNCT
ejpam-3914	366	27	and	and	CCONJ
ejpam-3914	366	28	s2	s2	PROPN
ejpam-3914	366	29	=	=	SYM
ejpam-3914	366	30	{	{	PUNCT
ejpam-3914	366	31	u3	u3	PROPN
ejpam-3914	366	32	,	,	PUNCT
ejpam-3914	366	33	u4	u4	PROPN
ejpam-3914	366	34	}	}	PUNCT
ejpam-3914	366	35	are	be	AUX
ejpam-3914	366	36	the	the	DET
ejpam-3914	366	37	only	only	ADJ
ejpam-3914	366	38	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	366	39	-sets	-set	NOUN
ejpam-3914	366	40	of	of	ADP
ejpam-3914	366	41	p5	p5	NOUN
ejpam-3914	366	42	.	.	PUNCT
ejpam-3914	367	1	since	since	SCONJ
ejpam-3914	367	2	u2	u2	PROPN
ejpam-3914	367	3	∈	∈	PROPN
ejpam-3914	367	4	s1	s1	NOUN
ejpam-3914	367	5	and	and	CCONJ
ejpam-3914	367	6	u2	u2	PROPN
ejpam-3914	367	7	/∈	/∈	PUNCT
ejpam-3914	367	8	s2	s2	PROPN
ejpam-3914	367	9	,	,	PUNCT
ejpam-3914	367	10	by	by	ADP
ejpam-3914	367	11	theorem	theorem	NOUN
ejpam-3914	367	12	3.1(ii	3.1(ii	NUM
ejpam-3914	367	13	)	)	PUNCT
ejpam-3914	367	14	,	,	PUNCT
ejpam-3914	367	15	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	367	16	(	(	PUNCT
ejpam-3914	367	17	p5	p5	ADJ
ejpam-3914	367	18	)	)	PUNCT
ejpam-3914	367	19	=	=	SYM
ejpam-3914	367	20	1	1	X
ejpam-3914	367	21	.	.	PUNCT
ejpam-3914	367	22	now	now	ADV
ejpam-3914	367	23	,	,	PUNCT
ejpam-3914	367	24	suppose	suppose	VERB
ejpam-3914	367	25	that	that	SCONJ
ejpam-3914	367	26	n	n	PROPN
ejpam-3914	367	27	>	>	X
ejpam-3914	367	28	5	5	X
ejpam-3914	367	29	.	.	PUNCT
ejpam-3914	367	30	let	let	VERB
ejpam-3914	367	31	p	p	NOUN
ejpam-3914	367	32	=	=	PUNCT
ejpam-3914	367	33	n	n	NUM
ejpam-3914	367	34	5	5	NUM
ejpam-3914	367	35	and	and	CCONJ
ejpam-3914	367	36	j	j	NOUN
ejpam-3914	367	37	=	=	SYM
ejpam-3914	367	38	1	1	NUM
ejpam-3914	367	39	,	,	PUNCT
ejpam-3914	367	40	2	2	NUM
ejpam-3914	367	41	,	,	PUNCT
ejpam-3914	367	42	.	.	PUNCT
ejpam-3914	367	43	.	.	PUNCT
ejpam-3914	368	1	.	.	PUNCT
ejpam-3914	369	1	,	,	PUNCT
ejpam-3914	369	2	p−	p−	NOUN
ejpam-3914	369	3	1	1	NUM
ejpam-3914	369	4	,	,	PUNCT
ejpam-3914	369	5	p.	p.	NOUN
ejpam-3914	369	6	group	group	NOUN
ejpam-3914	369	7	the	the	DET
ejpam-3914	369	8	vertices	vertex	NOUN
ejpam-3914	369	9	of	of	ADP
ejpam-3914	369	10	pn	pn	NOUN
ejpam-3914	369	11	into	into	ADP
ejpam-3914	369	12	p	p	PROPN
ejpam-3914	369	13	disjoint	disjoint	PROPN
ejpam-3914	369	14	subsets	subset	NOUN
ejpam-3914	369	15	rj	rj	PROPN
ejpam-3914	369	16	c.	c.	PROPN
ejpam-3914	369	17	armada	armada	PROPN
ejpam-3914	369	18	/	/	SYM
ejpam-3914	369	19	eur	eur	PROPN
ejpam-3914	369	20	.	.	PUNCT
ejpam-3914	370	1	j.	j.	PROPN
ejpam-3914	370	2	pure	pure	PROPN
ejpam-3914	370	3	appl	appl	PROPN
ejpam-3914	370	4	.	.	PROPN
ejpam-3914	370	5	math	math	PROPN
ejpam-3914	370	6	,	,	PUNCT
ejpam-3914	370	7	14	14	NUM
ejpam-3914	370	8	(	(	PUNCT
ejpam-3914	370	9	2	2	NUM
ejpam-3914	370	10	)	)	PUNCT
ejpam-3914	370	11	(	(	PUNCT
ejpam-3914	370	12	2021	2021	NUM
ejpam-3914	370	13	)	)	PUNCT
ejpam-3914	370	14	,	,	PUNCT
ejpam-3914	370	15	451	451	NUM
ejpam-3914	370	16	-	-	SYM
ejpam-3914	370	17	470	470	NUM
ejpam-3914	370	18	461	461	NUM
ejpam-3914	370	19	r1	r1	NOUN
ejpam-3914	370	20	=	=	SYM
ejpam-3914	370	21	{	{	PUNCT
ejpam-3914	370	22	u1	u1	NOUN
ejpam-3914	370	23	,	,	PUNCT
ejpam-3914	370	24	u2	u2	NOUN
ejpam-3914	370	25	,	,	PUNCT
ejpam-3914	370	26	u3	u3	PROPN
ejpam-3914	370	27	,	,	PUNCT
ejpam-3914	370	28	u4	u4	PROPN
ejpam-3914	370	29	,	,	PUNCT
ejpam-3914	370	30	u5	u5	PROPN
ejpam-3914	370	31	}	}	PUNCT
ejpam-3914	370	32	r2	r2	NOUN
ejpam-3914	370	33	=	=	SYM
ejpam-3914	370	34	{	{	PUNCT
ejpam-3914	370	35	u6	u6	PROPN
ejpam-3914	370	36	,	,	PUNCT
ejpam-3914	370	37	u7	u7	PROPN
ejpam-3914	370	38	,	,	PUNCT
ejpam-3914	370	39	u8	u8	PROPN
ejpam-3914	370	40	,	,	PUNCT
ejpam-3914	370	41	u9	u9	PROPN
ejpam-3914	370	42	,	,	PUNCT
ejpam-3914	370	43	u10	u10	PROPN
ejpam-3914	370	44	}	}	PUNCT
ejpam-3914	370	45	r3	r3	PROPN
ejpam-3914	370	46	=	=	SYM
ejpam-3914	370	47	{	{	PUNCT
ejpam-3914	370	48	u11	u11	PROPN
ejpam-3914	370	49	,	,	PUNCT
ejpam-3914	370	50	u12	u12	PROPN
ejpam-3914	370	51	,	,	PUNCT
ejpam-3914	370	52	u13	u13	NOUN
ejpam-3914	370	53	,	,	PUNCT
ejpam-3914	370	54	u14	u14	NOUN
ejpam-3914	370	55	,	,	PUNCT
ejpam-3914	370	56	u15	u15	NOUN
ejpam-3914	370	57	}	}	PUNCT
ejpam-3914	370	58	...	...	PUNCT
ejpam-3914	371	1	rp−1	rp−1	NOUN
ejpam-3914	371	2	=	=	SYM
ejpam-3914	371	3	{	{	PUNCT
ejpam-3914	371	4	un−9	un−9	PROPN
ejpam-3914	371	5	,	,	PUNCT
ejpam-3914	371	6	un−8	un−8	ADJ
ejpam-3914	371	7	,	,	PUNCT
ejpam-3914	371	8	un−7	un−7	PROPN
ejpam-3914	371	9	,	,	PUNCT
ejpam-3914	371	10	un−6	un−6	PROPN
ejpam-3914	371	11	,	,	PUNCT
ejpam-3914	371	12	un−5	un−5	PROPN
ejpam-3914	371	13	}	}	PUNCT
ejpam-3914	371	14	rp	rp	NOUN
ejpam-3914	371	15	=	=	SYM
ejpam-3914	371	16	{	{	PUNCT
ejpam-3914	371	17	un−4	un−4	NOUN
ejpam-3914	371	18	,	,	PUNCT
ejpam-3914	371	19	un−3	un−3	ADJ
ejpam-3914	371	20	,	,	PUNCT
ejpam-3914	371	21	un−2	un−2	PROPN
ejpam-3914	371	22	,	,	PUNCT
ejpam-3914	371	23	un−1	un−1	PROPN
ejpam-3914	371	24	,	,	PUNCT
ejpam-3914	371	25	un	un	ADJ
ejpam-3914	371	26	}	}	PUNCT
ejpam-3914	371	27	let	let	VERB
ejpam-3914	371	28	i	i	PRON
ejpam-3914	371	29	=	=	NOUN
ejpam-3914	371	30	1	1	NUM
ejpam-3914	371	31	,	,	PUNCT
ejpam-3914	371	32	6	6	NUM
ejpam-3914	371	33	,	,	PUNCT
ejpam-3914	371	34	11	11	NUM
ejpam-3914	371	35	,	,	PUNCT
ejpam-3914	371	36	.	.	PUNCT
ejpam-3914	371	37	.	.	PUNCT
ejpam-3914	372	1	.	.	PUNCT
ejpam-3914	373	1	,	,	PUNCT
ejpam-3914	373	2	n−	n−	NOUN
ejpam-3914	373	3	4	4	NUM
ejpam-3914	373	4	.	.	PUNCT
ejpam-3914	374	1	for	for	ADP
ejpam-3914	374	2	every	every	DET
ejpam-3914	374	3	induced	induced	ADJ
ejpam-3914	374	4	subgraph	subgraph	NOUN
ejpam-3914	374	5	〈	〈	PROPN
ejpam-3914	374	6	ui	ui	PROPN
ejpam-3914	374	7	,	,	PUNCT
ejpam-3914	374	8	ui+1	ui+1	PROPN
ejpam-3914	374	9	,	,	PUNCT
ejpam-3914	374	10	ui+2	ui+2	NUM
ejpam-3914	374	11	,	,	PUNCT
ejpam-3914	374	12	ui+3	ui+3	NOUN
ejpam-3914	374	13	,	,	PUNCT
ejpam-3914	374	14	ui+4	ui+4	PROPN
ejpam-3914	374	15	〉	〉	NOUN
ejpam-3914	374	16	,	,	PUNCT
ejpam-3914	374	17	the	the	DET
ejpam-3914	374	18	vertices	vertex	NOUN
ejpam-3914	374	19	ui+1	ui+1	PROPN
ejpam-3914	374	20	,	,	PUNCT
ejpam-3914	374	21	ui+2	ui+2	PRON
ejpam-3914	374	22	form	form	VERB
ejpam-3914	374	23	a	a	DET
ejpam-3914	374	24	total	total	ADJ
ejpam-3914	374	25	dr	dr	ADJ
ejpam-3914	374	26	-	-	PUNCT
ejpam-3914	374	27	power	power	NOUN
ejpam-3914	374	28	dominating	dominating	NOUN
ejpam-3914	374	29	set	set	VERB
ejpam-3914	374	30	since	since	SCONJ
ejpam-3914	374	31	ui	ui	PROPN
ejpam-3914	374	32	and	and	CCONJ
ejpam-3914	374	33	ui+3	ui+3	NOUN
ejpam-3914	374	34	are	be	AUX
ejpam-3914	374	35	directly	directly	ADV
ejpam-3914	374	36	observed	observe	VERB
ejpam-3914	374	37	vertices	vertex	NOUN
ejpam-3914	374	38	while	while	SCONJ
ejpam-3914	374	39	ui+4	ui+4	PRON
ejpam-3914	374	40	is	be	VERB
ejpam-3914	374	41	a	a	DET
ejpam-3914	374	42	remotely	remotely	ADV
ejpam-3914	374	43	observed	observe	VERB
ejpam-3914	374	44	vertex	vertex	NOUN
ejpam-3914	374	45	for	for	ADP
ejpam-3914	374	46	all	all	DET
ejpam-3914	374	47	i	i	PRON
ejpam-3914	374	48	=	=	NOUN
ejpam-3914	374	49	1	1	NUM
ejpam-3914	374	50	,	,	PUNCT
ejpam-3914	374	51	6	6	NUM
ejpam-3914	374	52	,	,	PUNCT
ejpam-3914	374	53	11	11	NUM
ejpam-3914	374	54	,	,	PUNCT
ejpam-3914	374	55	.	.	PUNCT
ejpam-3914	374	56	.	.	PUNCT
ejpam-3914	375	1	.	.	PUNCT
ejpam-3914	376	1	,	,	PUNCT
ejpam-3914	376	2	n−9	n−9	PROPN
ejpam-3914	376	3	,	,	PUNCT
ejpam-3914	376	4	n−4	n−4	PROPN
ejpam-3914	376	5	.	.	PUNCT
ejpam-3914	377	1	let	let	VERB
ejpam-3914	377	2	the	the	DET
ejpam-3914	377	3	set	set	NOUN
ejpam-3914	377	4	r	r	NOUN
ejpam-3914	377	5	=	=	SYM
ejpam-3914	377	6	{	{	PUNCT
ejpam-3914	377	7	ui+1	ui+1	PROPN
ejpam-3914	377	8	,	,	PUNCT
ejpam-3914	377	9	ui+2	ui+2	NUM
ejpam-3914	377	10	:	:	PUNCT
ejpam-3914	378	1	i	i	NOUN
ejpam-3914	378	2	=	=	NOUN
ejpam-3914	378	3	1	1	NUM
ejpam-3914	378	4	,	,	PUNCT
ejpam-3914	378	5	6	6	NUM
ejpam-3914	378	6	,	,	PUNCT
ejpam-3914	378	7	11	11	NUM
ejpam-3914	378	8	,	,	PUNCT
ejpam-3914	378	9	.	.	PUNCT
ejpam-3914	378	10	.	.	PUNCT
ejpam-3914	378	11	.	.	PUNCT
ejpam-3914	379	1	,	,	PUNCT
ejpam-3914	379	2	n−	n−	NOUN
ejpam-3914	379	3	9	9	NUM
ejpam-3914	379	4	,	,	PUNCT
ejpam-3914	379	5	n−	n−	NOUN
ejpam-3914	379	6	4	4	NUM
ejpam-3914	379	7	}	}	PUNCT
ejpam-3914	379	8	=	=	SYM
ejpam-3914	379	9	{	{	PUNCT
ejpam-3914	379	10	u2	u2	NOUN
ejpam-3914	379	11	,	,	PUNCT
ejpam-3914	379	12	u3	u3	PROPN
ejpam-3914	379	13	,	,	PUNCT
ejpam-3914	379	14	u7	u7	PROPN
ejpam-3914	379	15	,	,	PUNCT
ejpam-3914	379	16	u8	u8	PROPN
ejpam-3914	379	17	,	,	PUNCT
ejpam-3914	379	18	u12	u12	PROPN
ejpam-3914	379	19	,	,	PUNCT
ejpam-3914	379	20	u13	u13	NOUN
ejpam-3914	379	21	,	,	PUNCT
ejpam-3914	379	22	.	.	PUNCT
ejpam-3914	379	23	.	.	PUNCT
ejpam-3914	379	24	.	.	PUNCT
ejpam-3914	380	1	,	,	PUNCT
ejpam-3914	380	2	un−8	un−8	ADJ
ejpam-3914	380	3	,	,	PUNCT
ejpam-3914	380	4	un−7	un−7	NOUN
ejpam-3914	380	5	,	,	PUNCT
ejpam-3914	380	6	un−3	un−3	ADJ
ejpam-3914	380	7	,	,	PUNCT
ejpam-3914	380	8	un−2	un−2	VERB
ejpam-3914	380	9	}	}	PUNCT
ejpam-3914	380	10	,	,	PUNCT
ejpam-3914	380	11	where	where	SCONJ
ejpam-3914	380	12	|r|	|r|	NOUN
ejpam-3914	380	13	=	=	NOUN
ejpam-3914	380	14	2p	2p	NUM
ejpam-3914	380	15	=	=	SYM
ejpam-3914	380	16	2n	2n	NUM
ejpam-3914	380	17	5	5	NUM
ejpam-3914	380	18	,	,	PUNCT
ejpam-3914	380	19	or	or	CCONJ
ejpam-3914	380	20	v	v	NOUN
ejpam-3914	380	21	(	(	PUNCT
ejpam-3914	380	22	pn	pn	NOUN
ejpam-3914	380	23	)	)	PUNCT
ejpam-3914	380	24	=	=	NOUN
ejpam-3914	380	25	v	v	X
ejpam-3914	380	26	(	(	PUNCT
ejpam-3914	380	27	pn	pn	NOUN
ejpam-3914	380	28	)	)	PUNCT
ejpam-3914	380	29	,	,	PUNCT
ejpam-3914	380	30	or	or	CCONJ
ejpam-3914	380	31	e(pn	e(pn	NUM
ejpam-3914	380	32	)	)	PUNCT
ejpam-3914	380	33	=	=	SYM
ejpam-3914	380	34	e(pn	e(pn	NUM
ejpam-3914	380	35	)	)	PUNCT
ejpam-3914	380	36	,	,	PUNCT
ejpam-3914	380	37	and	and	CCONJ
ejpam-3914	380	38	the	the	DET
ejpam-3914	380	39	induced	induced	ADJ
ejpam-3914	380	40	subgraph	subgraph	NOUN
ejpam-3914	380	41	〈	〈	PROPN
ejpam-3914	380	42	r	r	PROPN
ejpam-3914	380	43	〉	〉	PROPN
ejpam-3914	380	44	has	have	VERB
ejpam-3914	380	45	no	no	DET
ejpam-3914	380	46	isolated	isolated	ADJ
ejpam-3914	380	47	vertex	vertex	NOUN
ejpam-3914	380	48	.	.	PUNCT
ejpam-3914	381	1	by	by	ADP
ejpam-3914	381	2	theorem	theorem	NOUN
ejpam-3914	381	3	2.2	2.2	NUM
ejpam-3914	381	4	,	,	PUNCT
ejpam-3914	381	5	r	r	NOUN
ejpam-3914	381	6	is	be	AUX
ejpam-3914	381	7	a	a	DET
ejpam-3914	381	8	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	381	9	-set	-set	PROPN
ejpam-3914	381	10	of	of	ADP
ejpam-3914	381	11	pn	pn	PROPN
ejpam-3914	381	12	.	.	PROPN
ejpam-3914	382	1	let	let	VERB
ejpam-3914	382	2	m+	m+	PRON
ejpam-3914	382	3	1	1	NUM
ejpam-3914	382	4	be	be	AUX
ejpam-3914	382	5	the	the	DET
ejpam-3914	382	6	number	number	NOUN
ejpam-3914	382	7	of	of	ADP
ejpam-3914	382	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	382	9	-sets	-set	NOUN
ejpam-3914	382	10	of	of	ADP
ejpam-3914	382	11	pn	pn	NOUN
ejpam-3914	382	12	where	where	SCONJ
ejpam-3914	382	13	m	m	PROPN
ejpam-3914	382	14	is	be	AUX
ejpam-3914	382	15	a	a	DET
ejpam-3914	382	16	positive	positive	ADJ
ejpam-3914	382	17	integer	integer	NOUN
ejpam-3914	382	18	.	.	PUNCT
ejpam-3914	383	1	let	let	VERB
ejpam-3914	383	2	k	k	NOUN
ejpam-3914	383	3	=	=	SYM
ejpam-3914	383	4	1	1	NUM
ejpam-3914	383	5	,	,	PUNCT
ejpam-3914	383	6	2	2	NUM
ejpam-3914	383	7	,	,	PUNCT
ejpam-3914	383	8	.	.	PUNCT
ejpam-3914	383	9	.	.	PUNCT
ejpam-3914	384	1	.	.	PUNCT
ejpam-3914	385	1	,	,	PUNCT
ejpam-3914	385	2	m	m	VERB
ejpam-3914	385	3	and	and	CCONJ
ejpam-3914	385	4	tk	tk	PROPN
ejpam-3914	385	5	be	be	AUX
ejpam-3914	385	6	a	a	DET
ejpam-3914	385	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	385	8	-set	-set	PUNCT
ejpam-3914	385	9	of	of	ADP
ejpam-3914	385	10	pn	pn	PROPN
ejpam-3914	385	11	different	different	ADJ
ejpam-3914	385	12	from	from	ADP
ejpam-3914	385	13	r.	r.	PROPN
ejpam-3914	385	14	consider	consider	VERB
ejpam-3914	385	15	the	the	DET
ejpam-3914	385	16	following	follow	VERB
ejpam-3914	385	17	subcases	subcase	NOUN
ejpam-3914	385	18	:	:	PUNCT
ejpam-3914	385	19	subcase	subcase	NOUN
ejpam-3914	385	20	1	1	NUM
ejpam-3914	385	21	:	:	PUNCT
ejpam-3914	385	22	let	let	VERB
ejpam-3914	385	23	k	k	NOUN
ejpam-3914	385	24	=	=	SYM
ejpam-3914	385	25	1	1	X
ejpam-3914	385	26	.	.	PUNCT
ejpam-3914	385	27	t1	t1	NOUN
ejpam-3914	385	28	can	can	AUX
ejpam-3914	385	29	be	be	AUX
ejpam-3914	385	30	formed	form	VERB
ejpam-3914	385	31	by	by	ADP
ejpam-3914	385	32	replacing	replace	VERB
ejpam-3914	385	33	u2	u2	NOUN
ejpam-3914	385	34	in	in	ADP
ejpam-3914	385	35	r	r	NOUN
ejpam-3914	385	36	by	by	ADP
ejpam-3914	385	37	u4	u4	PROPN
ejpam-3914	385	38	.	.	PUNCT
ejpam-3914	386	1	it	it	PRON
ejpam-3914	386	2	follows	follow	VERB
ejpam-3914	386	3	that	that	PRON
ejpam-3914	386	4	t1	t1	NOUN
ejpam-3914	386	5	=	=	PUNCT
ejpam-3914	386	6	{	{	PUNCT
ejpam-3914	386	7	u3	u3	PROPN
ejpam-3914	386	8	,	,	PUNCT
ejpam-3914	386	9	u4	u4	PROPN
ejpam-3914	386	10	,	,	PUNCT
ejpam-3914	386	11	u7	u7	PROPN
ejpam-3914	386	12	,	,	PUNCT
ejpam-3914	386	13	u8	u8	PROPN
ejpam-3914	386	14	,	,	PUNCT
ejpam-3914	386	15	u12	u12	PROPN
ejpam-3914	386	16	,	,	PUNCT
ejpam-3914	386	17	u13	u13	NOUN
ejpam-3914	386	18	,	,	PUNCT
ejpam-3914	386	19	.	.	PUNCT
ejpam-3914	386	20	.	.	PUNCT
ejpam-3914	387	1	.	.	PUNCT
ejpam-3914	388	1	,	,	PUNCT
ejpam-3914	388	2	un−8	un−8	ADJ
ejpam-3914	388	3	,	,	PUNCT
ejpam-3914	388	4	un−7	un−7	NOUN
ejpam-3914	388	5	,	,	PUNCT
ejpam-3914	388	6	un−3	un−3	ADJ
ejpam-3914	388	7	,	,	PUNCT
ejpam-3914	388	8	un−2	un−2	PROPN
ejpam-3914	388	9	}	}	PUNCT
ejpam-3914	388	10	is	be	AUX
ejpam-3914	388	11	a	a	DET
ejpam-3914	388	12	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	388	13	-set	-set	PROPN
ejpam-3914	388	14	of	of	ADP
ejpam-3914	388	15	pn	pn	PROPN
ejpam-3914	388	16	.	.	PUNCT
ejpam-3914	389	1	clearly	clearly	ADV
ejpam-3914	389	2	,	,	PUNCT
ejpam-3914	389	3	u2	u2	PROPN
ejpam-3914	389	4	/∈	/∈	PROPN
ejpam-3914	389	5	t1	t1	PROPN
ejpam-3914	389	6	.	.	PUNCT
ejpam-3914	390	1	subcase	subcase	PROPN
ejpam-3914	390	2	2	2	NUM
ejpam-3914	390	3	:	:	PUNCT
ejpam-3914	390	4	let	let	VERB
ejpam-3914	390	5	k	k	NOUN
ejpam-3914	390	6	=	=	SYM
ejpam-3914	390	7	2	2	NUM
ejpam-3914	390	8	and	and	CCONJ
ejpam-3914	390	9	let	let	VERB
ejpam-3914	390	10	u2	u2	NOUN
ejpam-3914	390	11	,	,	PUNCT
ejpam-3914	390	12	u3	u3	NOUN
ejpam-3914	390	13	∈	∈	PROPN
ejpam-3914	390	14	t2	t2	NOUN
ejpam-3914	390	15	.	.	PUNCT
ejpam-3914	391	1	now	now	ADV
ejpam-3914	391	2	,	,	PUNCT
ejpam-3914	391	3	replace	replace	VERB
ejpam-3914	391	4	u7	u7	PROPN
ejpam-3914	391	5	∈	∈	PROPN
ejpam-3914	391	6	r	r	NOUN
ejpam-3914	391	7	by	by	ADP
ejpam-3914	391	8	u6	u6	NOUN
ejpam-3914	391	9	to	to	PART
ejpam-3914	391	10	form	form	VERB
ejpam-3914	391	11	t2	t2	NOUN
ejpam-3914	391	12	.	.	PUNCT
ejpam-3914	392	1	then	then	ADV
ejpam-3914	392	2	the	the	DET
ejpam-3914	392	3	next	next	ADJ
ejpam-3914	392	4	vertex	vertex	NOUN
ejpam-3914	392	5	to	to	PART
ejpam-3914	392	6	be	be	AUX
ejpam-3914	392	7	chosen	choose	VERB
ejpam-3914	392	8	must	must	AUX
ejpam-3914	392	9	be	be	AUX
ejpam-3914	392	10	u7	u7	PROPN
ejpam-3914	392	11	,	,	PUNCT
ejpam-3914	392	12	that	that	ADV
ejpam-3914	392	13	is	is	ADV
ejpam-3914	392	14	,	,	PUNCT
ejpam-3914	392	15	the	the	DET
ejpam-3914	392	16	vertices	vertex	NOUN
ejpam-3914	392	17	ui	ui	PROPN
ejpam-3914	392	18	,	,	PUNCT
ejpam-3914	392	19	ui+1	ui+1	PROPN
ejpam-3914	392	20	must	must	AUX
ejpam-3914	392	21	be	be	AUX
ejpam-3914	392	22	in	in	ADP
ejpam-3914	392	23	t2	t2	NOUN
ejpam-3914	392	24	for	for	ADP
ejpam-3914	392	25	all	all	DET
ejpam-3914	392	26	i	i	NOUN
ejpam-3914	392	27	=	=	NOUN
ejpam-3914	392	28	6	6	NUM
ejpam-3914	392	29	,	,	PUNCT
ejpam-3914	392	30	11	11	NUM
ejpam-3914	392	31	,	,	PUNCT
ejpam-3914	392	32	16	16	NUM
ejpam-3914	392	33	,	,	PUNCT
ejpam-3914	392	34	.	.	PUNCT
ejpam-3914	392	35	.	.	PUNCT
ejpam-3914	393	1	.	.	PUNCT
ejpam-3914	394	1	,	,	PUNCT
ejpam-3914	394	2	n−	n−	NOUN
ejpam-3914	394	3	9	9	NUM
ejpam-3914	394	4	,	,	PUNCT
ejpam-3914	394	5	n−	n−	NOUN
ejpam-3914	394	6	4	4	NUM
ejpam-3914	394	7	.	.	PUNCT
ejpam-3914	395	1	then	then	ADV
ejpam-3914	395	2	t2	t2	PROPN
ejpam-3914	395	3	=	=	SYM
ejpam-3914	395	4	{	{	PUNCT
ejpam-3914	395	5	u2	u2	PROPN
ejpam-3914	395	6	,	,	PUNCT
ejpam-3914	395	7	u3	u3	NOUN
ejpam-3914	395	8	,	,	PUNCT
ejpam-3914	395	9	u6	u6	PROPN
ejpam-3914	395	10	,	,	PUNCT
ejpam-3914	395	11	u7	u7	PROPN
ejpam-3914	395	12	,	,	PUNCT
ejpam-3914	395	13	u11	u11	PROPN
ejpam-3914	395	14	,	,	PUNCT
ejpam-3914	395	15	u12	u12	PROPN
ejpam-3914	395	16	,	,	PUNCT
ejpam-3914	395	17	.	.	PUNCT
ejpam-3914	395	18	.	.	PUNCT
ejpam-3914	395	19	.	.	PUNCT
ejpam-3914	396	1	,	,	PUNCT
ejpam-3914	396	2	un−4	un−4	NOUN
ejpam-3914	396	3	,	,	PUNCT
ejpam-3914	396	4	un−3	un−3	ADJ
ejpam-3914	396	5	}	}	PUNCT
ejpam-3914	396	6	such	such	ADJ
ejpam-3914	396	7	that	that	DET
ejpam-3914	396	8	|t2|	|t2|	NOUN
ejpam-3914	396	9	=	=	SYM
ejpam-3914	396	10	|r|	|r|	PROPN
ejpam-3914	396	11	.	.	PUNCT
ejpam-3914	397	1	since	since	SCONJ
ejpam-3914	397	2	un−3	un−3	PROPN
ejpam-3914	397	3	is	be	AUX
ejpam-3914	397	4	the	the	DET
ejpam-3914	397	5	last	last	ADJ
ejpam-3914	397	6	vertex	vertex	NOUN
ejpam-3914	397	7	in	in	ADP
ejpam-3914	397	8	t2	t2	NOUN
ejpam-3914	397	9	,	,	PUNCT
ejpam-3914	397	10	by	by	ADP
ejpam-3914	397	11	subcase	subcase	NOUN
ejpam-3914	397	12	1	1	NUM
ejpam-3914	397	13	of	of	ADP
ejpam-3914	397	14	case	case	NOUN
ejpam-3914	397	15	2	2	NUM
ejpam-3914	397	16	,	,	PUNCT
ejpam-3914	397	17	t3	t3	PROPN
ejpam-3914	397	18	is	be	AUX
ejpam-3914	397	19	not	not	PART
ejpam-3914	397	20	a	a	DET
ejpam-3914	397	21	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	397	22	-set	-set	PROPN
ejpam-3914	397	23	of	of	ADP
ejpam-3914	397	24	pn	pn	PROPN
ejpam-3914	397	25	.	.	PROPN
ejpam-3914	398	1	since	since	SCONJ
ejpam-3914	398	2	u7	u7	PROPN
ejpam-3914	398	3	is	be	AUX
ejpam-3914	398	4	arbitrarily	arbitrarily	ADV
ejpam-3914	398	5	replaced	replace	VERB
ejpam-3914	398	6	from	from	ADP
ejpam-3914	398	7	r	r	NOUN
ejpam-3914	398	8	,	,	PUNCT
ejpam-3914	398	9	we	we	PRON
ejpam-3914	398	10	can	can	AUX
ejpam-3914	398	11	not	not	PART
ejpam-3914	398	12	replace	replace	VERB
ejpam-3914	398	13	the	the	DET
ejpam-3914	398	14	vertex	vertex	NOUN
ejpam-3914	398	15	ui+1	ui+1	NOUN
ejpam-3914	398	16	in	in	ADP
ejpam-3914	398	17	r	r	NOUN
ejpam-3914	398	18	,	,	PUNCT
ejpam-3914	398	19	where	where	SCONJ
ejpam-3914	398	20	i	i	PRON
ejpam-3914	398	21	=	=	NOUN
ejpam-3914	398	22	6	6	NUM
ejpam-3914	398	23	,	,	PUNCT
ejpam-3914	398	24	11	11	NUM
ejpam-3914	398	25	,	,	PUNCT
ejpam-3914	398	26	16	16	NUM
ejpam-3914	398	27	,	,	PUNCT
ejpam-3914	398	28	.	.	PUNCT
ejpam-3914	398	29	.	.	PUNCT
ejpam-3914	399	1	.	.	PUNCT
ejpam-3914	400	1	,	,	PUNCT
ejpam-3914	400	2	n−	n−	NOUN
ejpam-3914	400	3	9	9	NUM
ejpam-3914	400	4	,	,	PUNCT
ejpam-3914	400	5	n−	n−	NOUN
ejpam-3914	400	6	4	4	NUM
ejpam-3914	400	7	to	to	PART
ejpam-3914	400	8	form	form	VERB
ejpam-3914	400	9	another	another	PRON
ejpam-3914	400	10	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	400	11	-set	-set	PROPN
ejpam-3914	400	12	of	of	ADP
ejpam-3914	400	13	pn	pn	PROPN
ejpam-3914	400	14	.	.	PUNCT
ejpam-3914	401	1	thus	thus	ADV
ejpam-3914	401	2	,	,	PUNCT
ejpam-3914	401	3	it	it	PRON
ejpam-3914	401	4	is	be	AUX
ejpam-3914	401	5	not	not	PART
ejpam-3914	401	6	possible	possible	ADJ
ejpam-3914	401	7	to	to	PART
ejpam-3914	401	8	start	start	VERB
ejpam-3914	401	9	with	with	ADP
ejpam-3914	401	10	vertex	vertex	NOUN
ejpam-3914	401	11	u2	u2	NOUN
ejpam-3914	401	12	to	to	PART
ejpam-3914	401	13	form	form	VERB
ejpam-3914	401	14	tk	tk	PROPN
ejpam-3914	401	15	for	for	ADP
ejpam-3914	401	16	all	all	DET
ejpam-3914	401	17	k	k	PROPN
ejpam-3914	401	18	≥	≥	NUM
ejpam-3914	401	19	2	2	NUM
ejpam-3914	401	20	,	,	PUNCT
ejpam-3914	401	21	that	that	ADV
ejpam-3914	401	22	is	is	ADV
ejpam-3914	401	23	,	,	PUNCT
ejpam-3914	401	24	u2	u2	PROPN
ejpam-3914	401	25	/∈	/∈	PROPN
ejpam-3914	401	26	tk	tk	PROPN
ejpam-3914	401	27	for	for	ADP
ejpam-3914	401	28	all	all	DET
ejpam-3914	401	29	k	k	PROPN
ejpam-3914	401	30	≥	≥	NUM
ejpam-3914	401	31	2	2	NUM
ejpam-3914	401	32	.	.	PUNCT
ejpam-3914	402	1	therefore	therefore	ADV
ejpam-3914	402	2	,	,	PUNCT
ejpam-3914	402	3	in	in	ADP
ejpam-3914	402	4	any	any	DET
ejpam-3914	402	5	subcase	subcase	NOUN
ejpam-3914	402	6	,	,	PUNCT
ejpam-3914	402	7	u2	u2	PROPN
ejpam-3914	402	8	/∈	/∈	PROPN
ejpam-3914	402	9	tk	tk	PROPN
ejpam-3914	402	10	for	for	ADP
ejpam-3914	402	11	all	all	PRON
ejpam-3914	402	12	k	k	NOUN
ejpam-3914	402	13	=	=	SYM
ejpam-3914	402	14	1	1	NUM
ejpam-3914	402	15	,	,	PUNCT
ejpam-3914	402	16	2	2	NUM
ejpam-3914	402	17	,	,	PUNCT
ejpam-3914	402	18	.	.	PUNCT
ejpam-3914	402	19	.	.	PUNCT
ejpam-3914	403	1	.	.	PUNCT
ejpam-3914	404	1	,	,	PUNCT
ejpam-3914	404	2	m	m	PROPN
ejpam-3914	404	3	,	,	PUNCT
ejpam-3914	404	4	and	and	CCONJ
ejpam-3914	404	5	so	so	ADV
ejpam-3914	404	6	,	,	PUNCT
ejpam-3914	404	7	the	the	DET
ejpam-3914	404	8	vertex	vertex	NOUN
ejpam-3914	404	9	u2	u2	NOUN
ejpam-3914	404	10	is	be	AUX
ejpam-3914	404	11	contained	contain	VERB
ejpam-3914	404	12	in	in	ADP
ejpam-3914	404	13	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	404	14	-set	-set	PUNCT
ejpam-3914	405	1	r	r	NOUN
ejpam-3914	405	2	only	only	ADV
ejpam-3914	405	3	.	.	PUNCT
ejpam-3914	406	1	by	by	ADP
ejpam-3914	406	2	theorem	theorem	NOUN
ejpam-3914	406	3	3.1(ii	3.1(ii	NUM
ejpam-3914	406	4	)	)	PUNCT
ejpam-3914	406	5	,	,	PUNCT
ejpam-3914	406	6	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	406	7	(	(	PUNCT
ejpam-3914	406	8	pn	pn	NOUN
ejpam-3914	406	9	)	)	PUNCT
ejpam-3914	406	10	=	=	SYM
ejpam-3914	406	11	1	1	X
ejpam-3914	406	12	.	.	PUNCT
ejpam-3914	406	13	c.	c.	PROPN
ejpam-3914	406	14	armada	armada	PROPN
ejpam-3914	406	15	/	/	SYM
ejpam-3914	406	16	eur	eur	PROPN
ejpam-3914	406	17	.	.	PUNCT
ejpam-3914	407	1	j.	j.	PROPN
ejpam-3914	407	2	pure	pure	PROPN
ejpam-3914	407	3	appl	appl	PROPN
ejpam-3914	407	4	.	.	PROPN
ejpam-3914	407	5	math	math	PROPN
ejpam-3914	407	6	,	,	PUNCT
ejpam-3914	407	7	14	14	NUM
ejpam-3914	407	8	(	(	PUNCT
ejpam-3914	407	9	2	2	NUM
ejpam-3914	407	10	)	)	PUNCT
ejpam-3914	407	11	(	(	PUNCT
ejpam-3914	407	12	2021	2021	NUM
ejpam-3914	407	13	)	)	PUNCT
ejpam-3914	407	14	,	,	PUNCT
ejpam-3914	407	15	451	451	NUM
ejpam-3914	407	16	-	-	SYM
ejpam-3914	407	17	470	470	NUM
ejpam-3914	407	18	462	462	NUM
ejpam-3914	407	19	theorem	theorem	VERB
ejpam-3914	407	20	3.5	3.5	NUM
ejpam-3914	407	21	.	.	PUNCT
ejpam-3914	408	1	let	let	VERB
ejpam-3914	408	2	n	n	PRON
ejpam-3914	408	3	be	be	AUX
ejpam-3914	408	4	a	a	DET
ejpam-3914	408	5	positive	positive	ADJ
ejpam-3914	408	6	integer	integer	NOUN
ejpam-3914	408	7	with	with	ADP
ejpam-3914	408	8	n	n	PRON
ejpam-3914	408	9	≥	≥	NUM
ejpam-3914	408	10	5	5	NUM
ejpam-3914	408	11	.	.	PUNCT
ejpam-3914	409	1	then	then	ADV
ejpam-3914	409	2	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3914	409	3	(	(	PUNCT
ejpam-3914	409	4	cn	cn	NOUN
ejpam-3914	409	5	)	)	PUNCT
ejpam-3914	409	6	=	=	NOUN
ejpam-3914	409	7	{	{	PUNCT
ejpam-3914	409	8	4	4	NUM
ejpam-3914	409	9	,	,	PUNCT
ejpam-3914	409	10	n	n	PRON
ejpam-3914	409	11	≡	≡	PROPN
ejpam-3914	409	12	2(mod	2(mod	NUM
ejpam-3914	409	13	5	5	X
ejpam-3914	409	14	)	)	PUNCT
ejpam-3914	409	15	2	2	NUM
ejpam-3914	409	16	,	,	PUNCT
ejpam-3914	409	17	otherwise	otherwise	ADV
ejpam-3914	409	18	.	.	PUNCT
ejpam-3914	410	1	proof	proof	NOUN
ejpam-3914	410	2	.	.	PUNCT
ejpam-3914	411	1	let	let	VERB
ejpam-3914	411	2	the	the	DET
ejpam-3914	411	3	cycle	cycle	NOUN
ejpam-3914	411	4	cn	cn	NOUN
ejpam-3914	412	1	=	=	PUNCT
ejpam-3914	413	1	[	[	X
ejpam-3914	413	2	u1	u1	NOUN
ejpam-3914	413	3	,	,	PUNCT
ejpam-3914	413	4	u2	u2	NOUN
ejpam-3914	413	5	,	,	PUNCT
ejpam-3914	413	6	.	.	PUNCT
ejpam-3914	413	7	.	.	PUNCT
ejpam-3914	413	8	.	.	PUNCT
ejpam-3914	414	1	,	,	PUNCT
ejpam-3914	414	2	un	un	PROPN
ejpam-3914	414	3	,	,	PUNCT
ejpam-3914	414	4	u1	u1	NOUN
ejpam-3914	414	5	]	]	PUNCT
ejpam-3914	414	6	.	.	PUNCT
ejpam-3914	415	1	note	note	VERB
ejpam-3914	415	2	that	that	PRON
ejpam-3914	415	3	and	and	CCONJ
ejpam-3914	415	4	deg(ui	deg(ui	PRON
ejpam-3914	415	5	)	)	PUNCT
ejpam-3914	415	6	=	=	SYM
ejpam-3914	415	7	2	2	NUM
ejpam-3914	415	8	for	for	ADP
ejpam-3914	415	9	all	all	DET
ejpam-3914	415	10	i	i	PRON
ejpam-3914	415	11	=	=	NOUN
ejpam-3914	415	12	1	1	NUM
ejpam-3914	415	13	,	,	PUNCT
ejpam-3914	415	14	2	2	NUM
ejpam-3914	415	15	,	,	PUNCT
ejpam-3914	415	16	3	3	NUM
ejpam-3914	415	17	,	,	PUNCT
ejpam-3914	415	18	.	.	PUNCT
ejpam-3914	415	19	.	.	PUNCT
ejpam-3914	416	1	.	.	PUNCT
ejpam-3914	417	1	,	,	PUNCT
ejpam-3914	417	2	n−	n−	NOUN
ejpam-3914	417	3	1	1	NUM
ejpam-3914	417	4	,	,	PUNCT
ejpam-3914	417	5	n.	n.	NOUN
ejpam-3914	417	6	by	by	ADP
ejpam-3914	417	7	definition	definition	NOUN
ejpam-3914	417	8	of	of	ADP
ejpam-3914	417	9	total	total	ADJ
ejpam-3914	417	10	dr	dr	PROPN
ejpam-3914	417	11	-	-	PUNCT
ejpam-3914	417	12	power	power	NOUN
ejpam-3914	417	13	dominating	dominating	NOUN
ejpam-3914	417	14	set	set	NOUN
ejpam-3914	417	15	,	,	PUNCT
ejpam-3914	417	16	a	a	DET
ejpam-3914	417	17	choosen	choosen	ADJ
ejpam-3914	417	18	vertex	vertex	NOUN
ejpam-3914	417	19	in	in	ADP
ejpam-3914	417	20	a	a	DET
ejpam-3914	417	21	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	417	22	-set	-set	NUM
ejpam-3914	417	23	,	,	PUNCT
ejpam-3914	417	24	say	say	VERB
ejpam-3914	417	25	d	d	X
ejpam-3914	417	26	,	,	PUNCT
ejpam-3914	417	27	of	of	ADP
ejpam-3914	417	28	cn	cn	PROPN
ejpam-3914	417	29	must	must	AUX
ejpam-3914	417	30	always	always	ADV
ejpam-3914	417	31	have	have	VERB
ejpam-3914	417	32	an	an	DET
ejpam-3914	417	33	adjacent	adjacent	ADJ
ejpam-3914	417	34	vertex	vertex	NOUN
ejpam-3914	417	35	in	in	ADP
ejpam-3914	417	36	d	d	PROPN
ejpam-3914	417	37	,	,	PUNCT
ejpam-3914	417	38	say	say	VERB
ejpam-3914	417	39	ui	ui	NOUN
ejpam-3914	417	40	and	and	CCONJ
ejpam-3914	417	41	ui+1	ui+1	PROPN
ejpam-3914	417	42	and	and	CCONJ
ejpam-3914	417	43	by	by	ADP
ejpam-3914	417	44	theorem	theorem	NOUN
ejpam-3914	417	45	2.3	2.3	NUM
ejpam-3914	417	46	,	,	PUNCT
ejpam-3914	417	47	the	the	DET
ejpam-3914	417	48	distance	distance	NOUN
ejpam-3914	417	49	of	of	ADP
ejpam-3914	417	50	the	the	DET
ejpam-3914	417	51	choosen	choosen	ADJ
ejpam-3914	417	52	vertex	vertex	NOUN
ejpam-3914	417	53	ui+1	ui+1	PROPN
ejpam-3914	417	54	must	must	AUX
ejpam-3914	417	55	be	be	AUX
ejpam-3914	417	56	of	of	ADP
ejpam-3914	417	57	at	at	ADV
ejpam-3914	417	58	most	most	ADV
ejpam-3914	417	59	4	4	NUM
ejpam-3914	417	60	to	to	ADP
ejpam-3914	417	61	the	the	DET
ejpam-3914	417	62	next	next	ADJ
ejpam-3914	417	63	choosen	choosen	ADJ
ejpam-3914	417	64	vertex	vertex	NOUN
ejpam-3914	417	65	in	in	ADP
ejpam-3914	417	66	d	d	NOUN
ejpam-3914	417	67	since	since	SCONJ
ejpam-3914	417	68	if	if	SCONJ
ejpam-3914	417	69	the	the	DET
ejpam-3914	417	70	next	next	ADJ
ejpam-3914	417	71	vertex	vertex	NOUN
ejpam-3914	417	72	to	to	PART
ejpam-3914	417	73	be	be	AUX
ejpam-3914	417	74	choosen	choosen	VERB
ejpam-3914	417	75	is	be	AUX
ejpam-3914	417	76	of	of	ADP
ejpam-3914	417	77	distance	distance	NOUN
ejpam-3914	417	78	5	5	NUM
ejpam-3914	417	79	,	,	PUNCT
ejpam-3914	417	80	say	say	VERB
ejpam-3914	417	81	u1	u1	NOUN
ejpam-3914	417	82	,	,	PUNCT
ejpam-3914	417	83	u2	u2	PROPN
ejpam-3914	417	84	∈	∈	PROPN
ejpam-3914	417	85	d	d	NOUN
ejpam-3914	417	86	and	and	CCONJ
ejpam-3914	417	87	choose	choose	VERB
ejpam-3914	417	88	u7	u7	PROPN
ejpam-3914	417	89	to	to	PART
ejpam-3914	417	90	be	be	AUX
ejpam-3914	417	91	the	the	DET
ejpam-3914	417	92	next	next	ADJ
ejpam-3914	417	93	vertex	vertex	NOUN
ejpam-3914	417	94	,	,	PUNCT
ejpam-3914	417	95	then	then	ADV
ejpam-3914	417	96	u3	u3	NOUN
ejpam-3914	417	97	and	and	CCONJ
ejpam-3914	417	98	u6	u6	NOUN
ejpam-3914	417	99	are	be	AUX
ejpam-3914	417	100	directly	directly	ADV
ejpam-3914	417	101	observed	observe	VERB
ejpam-3914	417	102	vertices	vertex	NOUN
ejpam-3914	417	103	while	while	SCONJ
ejpam-3914	417	104	u4	u4	PROPN
ejpam-3914	417	105	and	and	CCONJ
ejpam-3914	417	106	u5	u5	PROPN
ejpam-3914	417	107	are	be	AUX
ejpam-3914	417	108	remotely	remotely	ADV
ejpam-3914	417	109	observed	observe	VERB
ejpam-3914	417	110	vertices	vertex	NOUN
ejpam-3914	417	111	but	but	CCONJ
ejpam-3914	417	112	the	the	DET
ejpam-3914	417	113	edge	edge	NOUN
ejpam-3914	417	114	u4u5	u4u5	NUM
ejpam-3914	417	115	is	be	AUX
ejpam-3914	417	116	neither	neither	CCONJ
ejpam-3914	417	117	directly	directly	ADV
ejpam-3914	417	118	nor	nor	CCONJ
ejpam-3914	417	119	remotely	remotely	ADV
ejpam-3914	417	120	observed	observe	VERB
ejpam-3914	417	121	edge	edge	NOUN
ejpam-3914	417	122	which	which	PRON
ejpam-3914	417	123	is	be	AUX
ejpam-3914	417	124	a	a	DET
ejpam-3914	417	125	contradiction	contradiction	NOUN
ejpam-3914	417	126	.	.	PUNCT
ejpam-3914	418	1	note	note	VERB
ejpam-3914	418	2	that	that	SCONJ
ejpam-3914	418	3	ui	ui	PROPN
ejpam-3914	418	4	is	be	AUX
ejpam-3914	418	5	contained	contain	VERB
ejpam-3914	418	6	in	in	ADP
ejpam-3914	418	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	418	8	-sets	-set	NOUN
ejpam-3914	418	9	containing	contain	VERB
ejpam-3914	418	10	the	the	DET
ejpam-3914	418	11	pairs	pair	NOUN
ejpam-3914	418	12	of	of	ADP
ejpam-3914	418	13	sets	set	NOUN
ejpam-3914	418	14	{	{	PUNCT
ejpam-3914	418	15	ui−1	ui−1	PROPN
ejpam-3914	418	16	,	,	PUNCT
ejpam-3914	418	17	ui	ui	NOUN
ejpam-3914	418	18	}	}	PUNCT
ejpam-3914	418	19	and	and	CCONJ
ejpam-3914	418	20	{	{	PUNCT
ejpam-3914	418	21	ui	ui	PROPN
ejpam-3914	418	22	,	,	PUNCT
ejpam-3914	418	23	ui+1	ui+1	PROPN
ejpam-3914	418	24	}	}	PUNCT
ejpam-3914	418	25	for	for	ADP
ejpam-3914	418	26	all	all	DET
ejpam-3914	418	27	i	i	PRON
ejpam-3914	418	28	=	=	NOUN
ejpam-3914	418	29	1	1	NUM
ejpam-3914	418	30	,	,	PUNCT
ejpam-3914	418	31	2	2	NUM
ejpam-3914	418	32	,	,	PUNCT
ejpam-3914	418	33	.	.	PUNCT
ejpam-3914	418	34	.	.	PUNCT
ejpam-3914	418	35	.	.	PUNCT
ejpam-3914	419	1	n	n	CCONJ
ejpam-3914	419	2	,	,	PUNCT
ejpam-3914	419	3	and	and	CCONJ
ejpam-3914	419	4	so	so	ADV
ejpam-3914	419	5	,	,	PUNCT
ejpam-3914	419	6	the	the	DET
ejpam-3914	419	7	set	set	NOUN
ejpam-3914	419	8	{	{	PUNCT
ejpam-3914	419	9	ui	ui	NOUN
ejpam-3914	419	10	}	}	PUNCT
ejpam-3914	419	11	is	be	AUX
ejpam-3914	419	12	not	not	PART
ejpam-3914	419	13	a	a	DET
ejpam-3914	419	14	forcing	force	VERB
ejpam-3914	419	15	subset	subset	NOUN
ejpam-3914	419	16	of	of	ADP
ejpam-3914	419	17	any	any	DET
ejpam-3914	419	18	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	419	19	-set	-set	PROPN
ejpam-3914	419	20	of	of	ADP
ejpam-3914	419	21	cn	cn	PROPN
ejpam-3914	419	22	,	,	PUNCT
ejpam-3914	419	23	that	that	ADV
ejpam-3914	419	24	is	is	ADV
ejpam-3914	419	25	,	,	PUNCT
ejpam-3914	419	26	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3914	419	27	(	(	PUNCT
ejpam-3914	419	28	cn	cn	PROPN
ejpam-3914	419	29	)	)	PUNCT
ejpam-3914	419	30	≥	≥	NOUN
ejpam-3914	419	31	2	2	NUM
ejpam-3914	419	32	.	.	PUNCT
ejpam-3914	420	1	now	now	ADV
ejpam-3914	420	2	,	,	PUNCT
ejpam-3914	420	3	consider	consider	VERB
ejpam-3914	420	4	the	the	DET
ejpam-3914	420	5	following	follow	VERB
ejpam-3914	420	6	cases	case	NOUN
ejpam-3914	420	7	:	:	PUNCT
ejpam-3914	420	8	case	case	NOUN
ejpam-3914	420	9	1	1	NUM
ejpam-3914	420	10	:	:	PUNCT
ejpam-3914	420	11	suppose	suppose	VERB
ejpam-3914	420	12	that	that	SCONJ
ejpam-3914	420	13	n	n	NUM
ejpam-3914	420	14	≡	≡	PROPN
ejpam-3914	420	15	2(mod	2(mod	NUM
ejpam-3914	420	16	5	5	NUM
ejpam-3914	420	17	)	)	PUNCT
ejpam-3914	420	18	.	.	PUNCT
ejpam-3914	421	1	by	by	ADP
ejpam-3914	421	2	theorem	theorem	NOUN
ejpam-3914	421	3	2.3	2.3	NUM
ejpam-3914	421	4	,	,	PUNCT
ejpam-3914	421	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	421	6	(	(	PUNCT
ejpam-3914	421	7	cn	cn	NOUN
ejpam-3914	421	8	)	)	PUNCT
ejpam-3914	421	9	=	=	SYM
ejpam-3914	421	10	2n+6	2n+6	NOUN
ejpam-3914	421	11	5	5	NUM
ejpam-3914	421	12	.	.	PUNCT
ejpam-3914	421	13	suppose	suppose	VERB
ejpam-3914	421	14	that	that	SCONJ
ejpam-3914	421	15	n	n	NOUN
ejpam-3914	421	16	=	=	SYM
ejpam-3914	421	17	7	7	X
ejpam-3914	421	18	.	.	PUNCT
ejpam-3914	422	1	then	then	ADV
ejpam-3914	422	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	422	3	(	(	PUNCT
ejpam-3914	422	4	c7	c7	PROPN
ejpam-3914	422	5	)	)	PUNCT
ejpam-3914	422	6	=	=	PRON
ejpam-3914	422	7	2(7)+6	2(7)+6	NUM
ejpam-3914	422	8	5	5	NUM
ejpam-3914	422	9	=	=	SYM
ejpam-3914	422	10	4	4	NUM
ejpam-3914	422	11	.	.	PUNCT
ejpam-3914	422	12	clearly	clearly	ADV
ejpam-3914	422	13	,	,	PUNCT
ejpam-3914	422	14	s1	s1	PROPN
ejpam-3914	422	15	=	=	SYM
ejpam-3914	422	16	{	{	PUNCT
ejpam-3914	422	17	u1	u1	NOUN
ejpam-3914	422	18	,	,	PUNCT
ejpam-3914	422	19	u2	u2	NOUN
ejpam-3914	422	20	,	,	PUNCT
ejpam-3914	422	21	u3	u3	NOUN
ejpam-3914	422	22	,	,	PUNCT
ejpam-3914	422	23	u4	u4	PROPN
ejpam-3914	422	24	}	}	PUNCT
ejpam-3914	422	25	,	,	PUNCT
ejpam-3914	422	26	s2	s2	X
ejpam-3914	422	27	=	=	SYM
ejpam-3914	422	28	{	{	PUNCT
ejpam-3914	422	29	u1	u1	NOUN
ejpam-3914	422	30	,	,	PUNCT
ejpam-3914	422	31	u2	u2	PROPN
ejpam-3914	422	32	,	,	PUNCT
ejpam-3914	422	33	u4	u4	PROPN
ejpam-3914	422	34	,	,	PUNCT
ejpam-3914	422	35	u5	u5	PROPN
ejpam-3914	422	36	}	}	PUNCT
ejpam-3914	422	37	,	,	PUNCT
ejpam-3914	422	38	s3	s3	PROPN
ejpam-3914	422	39	=	=	SYM
ejpam-3914	422	40	{	{	PUNCT
ejpam-3914	422	41	u1	u1	NOUN
ejpam-3914	422	42	,	,	PUNCT
ejpam-3914	422	43	u2	u2	PROPN
ejpam-3914	422	44	,	,	PUNCT
ejpam-3914	422	45	u5	u5	PROPN
ejpam-3914	422	46	,	,	PUNCT
ejpam-3914	422	47	u6	u6	NOUN
ejpam-3914	422	48	}	}	PUNCT
ejpam-3914	422	49	,	,	PUNCT
ejpam-3914	422	50	s4	s4	PROPN
ejpam-3914	422	51	=	=	SYM
ejpam-3914	422	52	{	{	PUNCT
ejpam-3914	422	53	u1	u1	NOUN
ejpam-3914	422	54	,	,	PUNCT
ejpam-3914	422	55	u2	u2	NOUN
ejpam-3914	422	56	,	,	PUNCT
ejpam-3914	422	57	u6	u6	PROPN
ejpam-3914	422	58	,	,	PUNCT
ejpam-3914	422	59	u7	u7	PROPN
ejpam-3914	422	60	}	}	PUNCT
ejpam-3914	422	61	,	,	PUNCT
ejpam-3914	422	62	s5	s5	X
ejpam-3914	422	63	=	=	PUNCT
ejpam-3914	422	64	{	{	PUNCT
ejpam-3914	422	65	u2	u2	PROPN
ejpam-3914	422	66	,	,	PUNCT
ejpam-3914	422	67	u3	u3	PROPN
ejpam-3914	422	68	,	,	PUNCT
ejpam-3914	422	69	u4	u4	PROPN
ejpam-3914	422	70	,	,	PUNCT
ejpam-3914	422	71	u5	u5	PROPN
ejpam-3914	422	72	}	}	PUNCT
ejpam-3914	422	73	,	,	PUNCT
ejpam-3914	422	74	s6	s6	PROPN
ejpam-3914	422	75	=	=	SYM
ejpam-3914	422	76	{	{	PUNCT
ejpam-3914	422	77	u2	u2	PROPN
ejpam-3914	422	78	,	,	PUNCT
ejpam-3914	422	79	u3	u3	PROPN
ejpam-3914	422	80	,	,	PUNCT
ejpam-3914	422	81	u5	u5	PROPN
ejpam-3914	422	82	,	,	PUNCT
ejpam-3914	422	83	u6	u6	NOUN
ejpam-3914	422	84	}	}	PUNCT
ejpam-3914	422	85	,	,	PUNCT
ejpam-3914	422	86	s7	s7	PROPN
ejpam-3914	422	87	=	=	PUNCT
ejpam-3914	422	88	{	{	PUNCT
ejpam-3914	422	89	u2	u2	PROPN
ejpam-3914	422	90	,	,	PUNCT
ejpam-3914	422	91	u3	u3	NOUN
ejpam-3914	422	92	,	,	PUNCT
ejpam-3914	422	93	u6	u6	PROPN
ejpam-3914	422	94	,	,	PUNCT
ejpam-3914	422	95	u7	u7	PROPN
ejpam-3914	422	96	}	}	PUNCT
ejpam-3914	422	97	,	,	PUNCT
ejpam-3914	422	98	s8	s8	PROPN
ejpam-3914	422	99	=	=	SYM
ejpam-3914	422	100	{	{	PUNCT
ejpam-3914	422	101	u3	u3	PROPN
ejpam-3914	422	102	,	,	PUNCT
ejpam-3914	422	103	u4	u4	PROPN
ejpam-3914	422	104	,	,	PUNCT
ejpam-3914	422	105	u5	u5	PROPN
ejpam-3914	422	106	,	,	PUNCT
ejpam-3914	422	107	u6	u6	NOUN
ejpam-3914	422	108	}	}	PUNCT
ejpam-3914	422	109	,	,	PUNCT
ejpam-3914	423	1	s9	s9	NOUN
ejpam-3914	423	2	=	=	SYM
ejpam-3914	423	3	{	{	PUNCT
ejpam-3914	423	4	u3	u3	PROPN
ejpam-3914	423	5	,	,	PUNCT
ejpam-3914	423	6	u4	u4	PROPN
ejpam-3914	423	7	,	,	PUNCT
ejpam-3914	423	8	u6	u6	PROPN
ejpam-3914	423	9	,	,	PUNCT
ejpam-3914	423	10	u7	u7	PROPN
ejpam-3914	423	11	}	}	PUNCT
ejpam-3914	423	12	,	,	PUNCT
ejpam-3914	423	13	s10	s10	PROPN
ejpam-3914	423	14	=	=	SYM
ejpam-3914	423	15	{	{	PUNCT
ejpam-3914	423	16	u4	u4	PROPN
ejpam-3914	423	17	,	,	PUNCT
ejpam-3914	423	18	u5	u5	PROPN
ejpam-3914	423	19	,	,	PUNCT
ejpam-3914	423	20	u6	u6	PROPN
ejpam-3914	423	21	,	,	PUNCT
ejpam-3914	423	22	u7	u7	PROPN
ejpam-3914	423	23	}	}	PUNCT
ejpam-3914	423	24	,	,	PUNCT
ejpam-3914	423	25	s11	s11	PROPN
ejpam-3914	423	26	=	=	SYM
ejpam-3914	423	27	{	{	PUNCT
ejpam-3914	423	28	u7	u7	PROPN
ejpam-3914	423	29	,	,	PUNCT
ejpam-3914	423	30	u1	u1	PROPN
ejpam-3914	423	31	,	,	PUNCT
ejpam-3914	423	32	u2	u2	NOUN
ejpam-3914	423	33	,	,	PUNCT
ejpam-3914	423	34	u3	u3	NOUN
ejpam-3914	423	35	}	}	PUNCT
ejpam-3914	423	36	,	,	PUNCT
ejpam-3914	423	37	s12	s12	NOUN
ejpam-3914	423	38	=	=	SYM
ejpam-3914	423	39	{	{	PUNCT
ejpam-3914	423	40	u7	u7	PROPN
ejpam-3914	423	41	,	,	PUNCT
ejpam-3914	423	42	u1	u1	NOUN
ejpam-3914	423	43	,	,	PUNCT
ejpam-3914	423	44	u3	u3	PROPN
ejpam-3914	423	45	,	,	PUNCT
ejpam-3914	423	46	u4	u4	PROPN
ejpam-3914	423	47	}	}	PUNCT
ejpam-3914	423	48	,	,	PUNCT
ejpam-3914	423	49	s13	s13	NOUN
ejpam-3914	423	50	=	=	SYM
ejpam-3914	423	51	{	{	PUNCT
ejpam-3914	423	52	u7	u7	PROPN
ejpam-3914	423	53	,	,	PUNCT
ejpam-3914	423	54	u1	u1	PROPN
ejpam-3914	423	55	,	,	PUNCT
ejpam-3914	423	56	u4	u4	PROPN
ejpam-3914	423	57	,	,	PUNCT
ejpam-3914	423	58	u5	u5	PROPN
ejpam-3914	423	59	}	}	PUNCT
ejpam-3914	423	60	and	and	CCONJ
ejpam-3914	423	61	s14	s14	NOUN
ejpam-3914	423	62	=	=	SYM
ejpam-3914	423	63	{	{	PUNCT
ejpam-3914	423	64	u7	u7	PROPN
ejpam-3914	423	65	,	,	PUNCT
ejpam-3914	423	66	u1	u1	PROPN
ejpam-3914	423	67	,	,	PUNCT
ejpam-3914	423	68	u5	u5	PROPN
ejpam-3914	423	69	,	,	PUNCT
ejpam-3914	423	70	u6	u6	PROPN
ejpam-3914	423	71	}	}	PUNCT
ejpam-3914	423	72	are	be	AUX
ejpam-3914	423	73	the	the	DET
ejpam-3914	423	74	only	only	ADJ
ejpam-3914	423	75	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	423	76	-sets	-set	NOUN
ejpam-3914	423	77	of	of	ADP
ejpam-3914	423	78	c7	c7	PROPN
ejpam-3914	423	79	.	.	PUNCT
ejpam-3914	424	1	note	note	VERB
ejpam-3914	424	2	that	that	SCONJ
ejpam-3914	424	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	424	4	(	(	PUNCT
ejpam-3914	424	5	c7	c7	PROPN
ejpam-3914	424	6	)	)	PUNCT
ejpam-3914	424	7	≥	≥	NOUN
ejpam-3914	424	8	2	2	NUM
ejpam-3914	424	9	and	and	CCONJ
ejpam-3914	424	10	each	each	DET
ejpam-3914	424	11	pair	pair	NOUN
ejpam-3914	424	12	of	of	ADP
ejpam-3914	424	13	vertices	vertex	NOUN
ejpam-3914	424	14	in	in	ADP
ejpam-3914	424	15	c7	c7	PROPN
ejpam-3914	424	16	is	be	AUX
ejpam-3914	424	17	contained	contain	VERB
ejpam-3914	424	18	in	in	ADP
ejpam-3914	424	19	more	more	ADJ
ejpam-3914	424	20	than	than	ADP
ejpam-3914	424	21	one	one	NUM
ejpam-3914	424	22	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	424	23	-sets	-set	NOUN
ejpam-3914	424	24	of	of	ADP
ejpam-3914	424	25	c7	c7	PROPN
ejpam-3914	424	26	,	,	PUNCT
ejpam-3914	424	27	that	that	ADV
ejpam-3914	424	28	is	is	ADV
ejpam-3914	424	29	,	,	PUNCT
ejpam-3914	424	30	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3914	424	31	(	(	PUNCT
ejpam-3914	424	32	c7	c7	PROPN
ejpam-3914	424	33	)	)	PUNCT
ejpam-3914	424	34	≥	≥	NOUN
ejpam-3914	425	1	3	3	NUM
ejpam-3914	425	2	.	.	X
ejpam-3914	425	3	note	note	VERB
ejpam-3914	425	4	that	that	SCONJ
ejpam-3914	425	5	each	each	PRON
ejpam-3914	425	6	of	of	ADP
ejpam-3914	425	7	the	the	DET
ejpam-3914	425	8	vertices	vertex	NOUN
ejpam-3914	425	9	u1	u1	NOUN
ejpam-3914	425	10	,	,	PUNCT
ejpam-3914	425	11	u2	u2	NOUN
ejpam-3914	425	12	,	,	PUNCT
ejpam-3914	425	13	u3	u3	NOUN
ejpam-3914	425	14	,	,	PUNCT
ejpam-3914	425	15	and	and	CCONJ
ejpam-3914	425	16	u4	u4	PROPN
ejpam-3914	425	17	in	in	ADP
ejpam-3914	425	18	s1	s1	PROPN
ejpam-3914	425	19	can	can	AUX
ejpam-3914	425	20	be	be	AUX
ejpam-3914	425	21	replaced	replace	VERB
ejpam-3914	425	22	by	by	ADP
ejpam-3914	425	23	u5	u5	PROPN
ejpam-3914	425	24	,	,	PUNCT
ejpam-3914	425	25	u7	u7	PROPN
ejpam-3914	425	26	,	,	PUNCT
ejpam-3914	425	27	u5	u5	PROPN
ejpam-3914	425	28	and	and	CCONJ
ejpam-3914	425	29	u7	u7	PROPN
ejpam-3914	425	30	,	,	PUNCT
ejpam-3914	425	31	respectively	respectively	ADV
ejpam-3914	425	32	to	to	PART
ejpam-3914	425	33	form	form	VERB
ejpam-3914	425	34	another	another	DET
ejpam-3914	425	35	γ∗tpw	γ∗tpw	SYM
ejpam-3914	425	36	-sets	-set	NOUN
ejpam-3914	425	37	of	of	ADP
ejpam-3914	425	38	c7	c7	PROPN
ejpam-3914	425	39	which	which	PRON
ejpam-3914	425	40	are	be	AUX
ejpam-3914	425	41	s5	s5	PROPN
ejpam-3914	425	42	,	,	PUNCT
ejpam-3914	425	43	s12	s12	PROPN
ejpam-3914	425	44	,	,	PUNCT
ejpam-3914	425	45	s2	s2	PROPN
ejpam-3914	425	46	,	,	PUNCT
ejpam-3914	425	47	and	and	CCONJ
ejpam-3914	425	48	s11	s11	PROPN
ejpam-3914	425	49	,	,	PUNCT
ejpam-3914	425	50	respectively	respectively	ADV
ejpam-3914	425	51	,	,	PUNCT
ejpam-3914	425	52	that	that	ADV
ejpam-3914	425	53	is	is	ADV
ejpam-3914	425	54	,	,	PUNCT
ejpam-3914	425	55	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	425	56	(	(	PUNCT
ejpam-3914	425	57	s1	s1	NOUN
ejpam-3914	425	58	)	)	PUNCT
ejpam-3914	425	59	=	=	SYM
ejpam-3914	426	1	4	4	X
ejpam-3914	426	2	.	.	PUNCT
ejpam-3914	426	3	clearly	clearly	ADV
ejpam-3914	426	4	,	,	PUNCT
ejpam-3914	426	5	for	for	ADP
ejpam-3914	426	6	all	all	DET
ejpam-3914	426	7	l	l	NOUN
ejpam-3914	426	8	=	=	SYM
ejpam-3914	426	9	1	1	NUM
ejpam-3914	426	10	,	,	PUNCT
ejpam-3914	426	11	2	2	NUM
ejpam-3914	426	12	,	,	PUNCT
ejpam-3914	426	13	.	.	PUNCT
ejpam-3914	426	14	.	.	PUNCT
ejpam-3914	426	15	.	.	PUNCT
ejpam-3914	427	1	,	,	PUNCT
ejpam-3914	427	2	14	14	NUM
ejpam-3914	427	3	and	and	CCONJ
ejpam-3914	427	4	for	for	ADP
ejpam-3914	427	5	every	every	DET
ejpam-3914	427	6	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	427	7	-set	-set	PUNCT
ejpam-3914	427	8	sl	sl	NOUN
ejpam-3914	427	9	of	of	ADP
ejpam-3914	427	10	c7	c7	PROPN
ejpam-3914	427	11	and	and	CCONJ
ejpam-3914	427	12	for	for	ADP
ejpam-3914	427	13	each	each	DET
ejpam-3914	427	14	ui	ui	PROPN
ejpam-3914	427	15	∈	∈	PROPN
ejpam-3914	427	16	sl	sl	INTJ
ejpam-3914	427	17	,	,	PUNCT
ejpam-3914	427	18	there	there	PRON
ejpam-3914	427	19	exists	exist	VERB
ejpam-3914	427	20	uj	uj	PROPN
ejpam-3914	427	21	∈	∈	PROPN
ejpam-3914	427	22	v	v	NOUN
ejpam-3914	427	23	(	(	PUNCT
ejpam-3914	427	24	c7)\sl	c7)\sl	NOUN
ejpam-3914	427	25	and	and	CCONJ
ejpam-3914	427	26	j	j	PROPN
ejpam-3914	427	27	6=	6=	PROPN
ejpam-3914	427	28	i	i	PRON
ejpam-3914	427	29	such	such	ADJ
ejpam-3914	427	30	that	that	SCONJ
ejpam-3914	427	31	[	[	X
ejpam-3914	427	32	sl\{ui	sl\{ui	X
ejpam-3914	427	33	}	}	PUNCT
ejpam-3914	427	34	]	]	PUNCT
ejpam-3914	427	35	∪	∪	X
ejpam-3914	427	36	{	{	PUNCT
ejpam-3914	427	37	uj	uj	PROPN
ejpam-3914	427	38	}	}	PUNCT
ejpam-3914	427	39	is	be	AUX
ejpam-3914	427	40	a	a	DET
ejpam-3914	427	41	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	427	42	-set	-set	PROPN
ejpam-3914	427	43	of	of	ADP
ejpam-3914	427	44	c7	c7	PROPN
ejpam-3914	427	45	.	.	PUNCT
ejpam-3914	428	1	by	by	ADP
ejpam-3914	428	2	theorem	theorem	NOUN
ejpam-3914	428	3	3.3	3.3	NUM
ejpam-3914	428	4	,	,	PUNCT
ejpam-3914	428	5	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	428	6	(	(	PUNCT
ejpam-3914	428	7	c7	c7	PROPN
ejpam-3914	428	8	)	)	PUNCT
ejpam-3914	428	9	=	=	SYM
ejpam-3914	428	10	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	428	11	(	(	PUNCT
ejpam-3914	428	12	c7	c7	PROPN
ejpam-3914	428	13	)	)	PUNCT
ejpam-3914	428	14	=	=	PUNCT
ejpam-3914	429	1	4	4	X
ejpam-3914	429	2	.	.	PUNCT
ejpam-3914	429	3	now	now	ADV
ejpam-3914	429	4	,	,	PUNCT
ejpam-3914	429	5	suppose	suppose	VERB
ejpam-3914	429	6	that	that	SCONJ
ejpam-3914	429	7	n	n	PROPN
ejpam-3914	429	8	>	>	X
ejpam-3914	429	9	7	7	X
ejpam-3914	429	10	.	.	PUNCT
ejpam-3914	429	11	since	since	SCONJ
ejpam-3914	429	12	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	429	13	(	(	PUNCT
ejpam-3914	429	14	c7	c7	PROPN
ejpam-3914	429	15	)	)	PUNCT
ejpam-3914	429	16	=	=	PUNCT
ejpam-3914	429	17	4	4	NUM
ejpam-3914	429	18	,	,	PUNCT
ejpam-3914	429	19	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	429	20	(	(	PUNCT
ejpam-3914	429	21	cn	cn	PROPN
ejpam-3914	429	22	)	)	PUNCT
ejpam-3914	429	23	≥	≥	NOUN
ejpam-3914	429	24	4	4	NUM
ejpam-3914	429	25	.	.	PUNCT
ejpam-3914	430	1	let	let	VERB
ejpam-3914	430	2	p	p	NOUN
ejpam-3914	430	3	=	=	PUNCT
ejpam-3914	430	4	n−2	n−2	PROPN
ejpam-3914	430	5	5	5	NUM
ejpam-3914	430	6	and	and	CCONJ
ejpam-3914	430	7	j	j	NOUN
ejpam-3914	430	8	=	=	SYM
ejpam-3914	430	9	0	0	NUM
ejpam-3914	430	10	,	,	PUNCT
ejpam-3914	430	11	1	1	NUM
ejpam-3914	430	12	,	,	PUNCT
ejpam-3914	430	13	2	2	NUM
ejpam-3914	430	14	,	,	PUNCT
ejpam-3914	430	15	.	.	PUNCT
ejpam-3914	430	16	.	.	PUNCT
ejpam-3914	431	1	.	.	PUNCT
ejpam-3914	432	1	,	,	PUNCT
ejpam-3914	432	2	p−	p−	NOUN
ejpam-3914	432	3	1	1	NUM
ejpam-3914	432	4	,	,	PUNCT
ejpam-3914	432	5	p.	p.	NOUN
ejpam-3914	432	6	group	group	NOUN
ejpam-3914	432	7	the	the	DET
ejpam-3914	432	8	vertices	vertex	NOUN
ejpam-3914	432	9	of	of	ADP
ejpam-3914	432	10	cn	cn	PROPN
ejpam-3914	432	11	into	into	ADP
ejpam-3914	432	12	p+	p+	NOUN
ejpam-3914	432	13	1	1	NUM
ejpam-3914	432	14	disjoint	disjoint	NOUN
ejpam-3914	432	15	subsets	subset	NOUN
ejpam-3914	432	16	rj	rj	PROPN
ejpam-3914	432	17	r0	r0	PROPN
ejpam-3914	432	18	=	=	PUNCT
ejpam-3914	432	19	{	{	PUNCT
ejpam-3914	432	20	u1	u1	NOUN
ejpam-3914	432	21	,	,	PUNCT
ejpam-3914	432	22	u2	u2	NOUN
ejpam-3914	432	23	}	}	PUNCT
ejpam-3914	432	24	r1	r1	NOUN
ejpam-3914	432	25	=	=	SYM
ejpam-3914	432	26	{	{	PUNCT
ejpam-3914	432	27	u3	u3	PROPN
ejpam-3914	432	28	,	,	PUNCT
ejpam-3914	432	29	u4	u4	PROPN
ejpam-3914	432	30	,	,	PUNCT
ejpam-3914	432	31	u5	u5	PROPN
ejpam-3914	432	32	,	,	PUNCT
ejpam-3914	432	33	u6	u6	PROPN
ejpam-3914	432	34	,	,	PUNCT
ejpam-3914	432	35	u7	u7	PROPN
ejpam-3914	432	36	}	}	PUNCT
ejpam-3914	432	37	r2	r2	PROPN
ejpam-3914	432	38	=	=	SYM
ejpam-3914	432	39	{	{	PUNCT
ejpam-3914	432	40	u8	u8	PROPN
ejpam-3914	432	41	,	,	PUNCT
ejpam-3914	432	42	u9	u9	PROPN
ejpam-3914	432	43	,	,	PUNCT
ejpam-3914	432	44	u10	u10	PROPN
ejpam-3914	432	45	,	,	PUNCT
ejpam-3914	432	46	u11	u11	PROPN
ejpam-3914	432	47	,	,	PUNCT
ejpam-3914	432	48	u12	u12	PROPN
ejpam-3914	432	49	}	}	PUNCT
ejpam-3914	432	50	r3	r3	PROPN
ejpam-3914	432	51	=	=	SYM
ejpam-3914	432	52	{	{	PUNCT
ejpam-3914	432	53	u13	u13	PROPN
ejpam-3914	432	54	,	,	PUNCT
ejpam-3914	432	55	u14	u14	NOUN
ejpam-3914	432	56	,	,	PUNCT
ejpam-3914	432	57	u15	u15	NOUN
ejpam-3914	432	58	,	,	PUNCT
ejpam-3914	432	59	u16	u16	NOUN
ejpam-3914	432	60	,	,	PUNCT
ejpam-3914	432	61	u17	u17	NOUN
ejpam-3914	432	62	}	}	PUNCT
ejpam-3914	432	63	...	...	PUNCT
ejpam-3914	433	1	rp−1	rp−1	NOUN
ejpam-3914	433	2	=	=	SYM
ejpam-3914	433	3	{	{	PUNCT
ejpam-3914	433	4	un−9	un−9	PROPN
ejpam-3914	433	5	,	,	PUNCT
ejpam-3914	433	6	un−8	un−8	ADJ
ejpam-3914	433	7	,	,	PUNCT
ejpam-3914	433	8	un−7	un−7	PROPN
ejpam-3914	433	9	,	,	PUNCT
ejpam-3914	433	10	un−6	un−6	PROPN
ejpam-3914	433	11	,	,	PUNCT
ejpam-3914	433	12	un−5	un−5	PROPN
ejpam-3914	433	13	}	}	PUNCT
ejpam-3914	433	14	rp	rp	NOUN
ejpam-3914	433	15	=	=	SYM
ejpam-3914	433	16	{	{	PUNCT
ejpam-3914	433	17	un−4	un−4	NOUN
ejpam-3914	433	18	,	,	PUNCT
ejpam-3914	433	19	un−3	un−3	ADJ
ejpam-3914	433	20	,	,	PUNCT
ejpam-3914	433	21	un−2	un−2	PROPN
ejpam-3914	433	22	,	,	PUNCT
ejpam-3914	433	23	un−1	un−1	PROPN
ejpam-3914	433	24	,	,	PUNCT
ejpam-3914	433	25	un	un	ADJ
ejpam-3914	433	26	}	}	PUNCT
ejpam-3914	433	27	let	let	VERB
ejpam-3914	433	28	i	i	PRON
ejpam-3914	433	29	=	=	NOUN
ejpam-3914	433	30	3	3	NUM
ejpam-3914	433	31	,	,	PUNCT
ejpam-3914	433	32	8	8	NUM
ejpam-3914	433	33	,	,	PUNCT
ejpam-3914	433	34	13	13	NUM
ejpam-3914	433	35	,	,	PUNCT
ejpam-3914	433	36	.	.	PUNCT
ejpam-3914	433	37	.	.	PUNCT
ejpam-3914	434	1	.	.	PUNCT
ejpam-3914	435	1	,	,	PUNCT
ejpam-3914	436	1	n	n	CCONJ
ejpam-3914	436	2	−	−	PROPN
ejpam-3914	436	3	4	4	NUM
ejpam-3914	436	4	.	.	PUNCT
ejpam-3914	436	5	for	for	ADP
ejpam-3914	436	6	every	every	DET
ejpam-3914	436	7	induced	induced	ADJ
ejpam-3914	436	8	subgraph	subgraph	NOUN
ejpam-3914	436	9	〈	〈	PROPN
ejpam-3914	436	10	ui	ui	PROPN
ejpam-3914	436	11	,	,	PUNCT
ejpam-3914	436	12	ui+1	ui+1	PROPN
ejpam-3914	436	13	,	,	PUNCT
ejpam-3914	436	14	ui+2	ui+2	NUM
ejpam-3914	436	15	,	,	PUNCT
ejpam-3914	436	16	ui+3	ui+3	NOUN
ejpam-3914	436	17	,	,	PUNCT
ejpam-3914	436	18	ui+4	ui+4	PROPN
ejpam-3914	436	19	〉	〉	NOUN
ejpam-3914	436	20	,	,	PUNCT
ejpam-3914	436	21	the	the	DET
ejpam-3914	436	22	vertices	vertex	NOUN
ejpam-3914	436	23	u1	u1	NOUN
ejpam-3914	436	24	,	,	PUNCT
ejpam-3914	436	25	u2	u2	PROPN
ejpam-3914	436	26	,	,	PUNCT
ejpam-3914	436	27	ui	ui	NOUN
ejpam-3914	436	28	,	,	PUNCT
ejpam-3914	436	29	ui+1	ui+1	PROPN
ejpam-3914	436	30	form	form	NOUN
ejpam-3914	436	31	a	a	DET
ejpam-3914	436	32	total	total	ADJ
ejpam-3914	436	33	dr	dr	ADJ
ejpam-3914	436	34	-	-	PUNCT
ejpam-3914	436	35	power	power	NOUN
ejpam-3914	436	36	dominating	dominating	NOUN
ejpam-3914	436	37	set	set	VERB
ejpam-3914	436	38	since	since	SCONJ
ejpam-3914	436	39	ui+2	ui+2	NUM
ejpam-3914	436	40	and	and	CCONJ
ejpam-3914	436	41	ui+4	ui+4	PRON
ejpam-3914	436	42	are	be	AUX
ejpam-3914	436	43	directly	directly	ADV
ejpam-3914	436	44	observed	observe	VERB
ejpam-3914	436	45	vertices	vertex	NOUN
ejpam-3914	436	46	while	while	SCONJ
ejpam-3914	436	47	ui+3	ui+3	NOUN
ejpam-3914	436	48	is	be	AUX
ejpam-3914	436	49	a	a	DET
ejpam-3914	436	50	remotely	remotely	ADV
ejpam-3914	436	51	observed	observe	VERB
ejpam-3914	436	52	vertex	vertex	NOUN
ejpam-3914	436	53	for	for	ADP
ejpam-3914	436	54	all	all	DET
ejpam-3914	436	55	i	i	PRON
ejpam-3914	436	56	=	=	NOUN
ejpam-3914	436	57	3	3	NUM
ejpam-3914	436	58	,	,	PUNCT
ejpam-3914	436	59	8	8	NUM
ejpam-3914	436	60	,	,	PUNCT
ejpam-3914	436	61	13	13	NUM
ejpam-3914	436	62	,	,	PUNCT
ejpam-3914	436	63	.	.	PUNCT
ejpam-3914	436	64	.	.	PUNCT
ejpam-3914	437	1	.	.	PUNCT
ejpam-3914	438	1	,	,	PUNCT
ejpam-3914	438	2	n−9	n−9	PROPN
ejpam-3914	438	3	,	,	PUNCT
ejpam-3914	438	4	n−4	n−4	PROPN
ejpam-3914	438	5	.	.	PUNCT
ejpam-3914	438	6	c.	c.	PROPN
ejpam-3914	438	7	armada	armada	PROPN
ejpam-3914	438	8	/	/	SYM
ejpam-3914	438	9	eur	eur	PROPN
ejpam-3914	438	10	.	.	PUNCT
ejpam-3914	439	1	j.	j.	PROPN
ejpam-3914	439	2	pure	pure	PROPN
ejpam-3914	439	3	appl	appl	PROPN
ejpam-3914	439	4	.	.	PROPN
ejpam-3914	439	5	math	math	PROPN
ejpam-3914	439	6	,	,	PUNCT
ejpam-3914	439	7	14	14	NUM
ejpam-3914	439	8	(	(	PUNCT
ejpam-3914	439	9	2	2	NUM
ejpam-3914	439	10	)	)	PUNCT
ejpam-3914	439	11	(	(	PUNCT
ejpam-3914	439	12	2021	2021	NUM
ejpam-3914	439	13	)	)	PUNCT
ejpam-3914	439	14	,	,	PUNCT
ejpam-3914	439	15	451	451	NUM
ejpam-3914	439	16	-	-	SYM
ejpam-3914	439	17	470	470	NUM
ejpam-3914	439	18	463	463	NUM
ejpam-3914	439	19	let	let	VERB
ejpam-3914	439	20	the	the	DET
ejpam-3914	439	21	set	set	NOUN
ejpam-3914	439	22	r	r	NOUN
ejpam-3914	439	23	=	=	SYM
ejpam-3914	439	24	{	{	PUNCT
ejpam-3914	439	25	u1	u1	NOUN
ejpam-3914	439	26	,	,	PUNCT
ejpam-3914	439	27	u2	u2	PROPN
ejpam-3914	439	28	,	,	PUNCT
ejpam-3914	439	29	ui	ui	NOUN
ejpam-3914	439	30	,	,	PUNCT
ejpam-3914	439	31	ui+1	ui+1	PROPN
ejpam-3914	439	32	:	:	PUNCT
ejpam-3914	439	33	i	i	NOUN
ejpam-3914	439	34	=	=	NOUN
ejpam-3914	439	35	3	3	NUM
ejpam-3914	439	36	,	,	PUNCT
ejpam-3914	439	37	8	8	NUM
ejpam-3914	439	38	,	,	PUNCT
ejpam-3914	439	39	13	13	NUM
ejpam-3914	439	40	,	,	PUNCT
ejpam-3914	439	41	.	.	PUNCT
ejpam-3914	439	42	.	.	PUNCT
ejpam-3914	439	43	.	.	PUNCT
ejpam-3914	440	1	,	,	PUNCT
ejpam-3914	440	2	n−	n−	NOUN
ejpam-3914	440	3	9	9	NUM
ejpam-3914	440	4	,	,	PUNCT
ejpam-3914	440	5	n−	n−	NOUN
ejpam-3914	440	6	4	4	NUM
ejpam-3914	440	7	}	}	PUNCT
ejpam-3914	440	8	=	=	NOUN
ejpam-3914	440	9	{	{	PUNCT
ejpam-3914	440	10	u1	u1	NOUN
ejpam-3914	440	11	,	,	PUNCT
ejpam-3914	440	12	u2	u2	NOUN
ejpam-3914	440	13	,	,	PUNCT
ejpam-3914	440	14	u3	u3	PROPN
ejpam-3914	440	15	,	,	PUNCT
ejpam-3914	440	16	u4	u4	PROPN
ejpam-3914	440	17	,	,	PUNCT
ejpam-3914	440	18	u8	u8	PROPN
ejpam-3914	440	19	,	,	PUNCT
ejpam-3914	440	20	u9	u9	PROPN
ejpam-3914	440	21	,	,	PUNCT
ejpam-3914	440	22	u13	u13	NOUN
ejpam-3914	440	23	,	,	PUNCT
ejpam-3914	440	24	u14	u14	NOUN
ejpam-3914	440	25	,	,	PUNCT
ejpam-3914	440	26	.	.	PUNCT
ejpam-3914	440	27	.	.	PUNCT
ejpam-3914	441	1	.	.	PUNCT
ejpam-3914	442	1	,	,	PUNCT
ejpam-3914	442	2	un−9	un−9	PROPN
ejpam-3914	442	3	,	,	PUNCT
ejpam-3914	442	4	un−8	un−8	ADJ
ejpam-3914	442	5	,	,	PUNCT
ejpam-3914	442	6	un−4	un−4	NOUN
ejpam-3914	442	7	,	,	PUNCT
ejpam-3914	442	8	un−3	un−3	ADJ
ejpam-3914	442	9	}	}	PUNCT
ejpam-3914	442	10	,	,	PUNCT
ejpam-3914	442	11	where	where	SCONJ
ejpam-3914	443	1	|r|	|r|	NOUN
ejpam-3914	443	2	=	=	NOUN
ejpam-3914	443	3	2p+	2p+	NUM
ejpam-3914	443	4	2	2	NUM
ejpam-3914	443	5	=	=	SYM
ejpam-3914	443	6	2(n−2	2(n−2	NUM
ejpam-3914	443	7	5	5	NUM
ejpam-3914	443	8	)	)	PUNCT
ejpam-3914	443	9	+	+	CCONJ
ejpam-3914	443	10	2	2	NUM
ejpam-3914	443	11	=	=	SYM
ejpam-3914	443	12	2n+6	2n+6	NOUN
ejpam-3914	443	13	5	5	NUM
ejpam-3914	443	14	,	,	PUNCT
ejpam-3914	443	15	or	or	CCONJ
ejpam-3914	443	16	v	v	NOUN
ejpam-3914	443	17	(	(	PUNCT
ejpam-3914	443	18	cn	cn	PROPN
ejpam-3914	443	19	)	)	PUNCT
ejpam-3914	443	20	=	=	NOUN
ejpam-3914	443	21	v	v	X
ejpam-3914	443	22	(	(	PUNCT
ejpam-3914	443	23	cn	cn	PROPN
ejpam-3914	443	24	)	)	PUNCT
ejpam-3914	443	25	,	,	PUNCT
ejpam-3914	443	26	or	or	CCONJ
ejpam-3914	443	27	e(cn	e(cn	NOUN
ejpam-3914	443	28	)	)	PUNCT
ejpam-3914	443	29	=	=	SYM
ejpam-3914	443	30	e(cn	e(cn	NOUN
ejpam-3914	443	31	)	)	PUNCT
ejpam-3914	443	32	,	,	PUNCT
ejpam-3914	443	33	and	and	CCONJ
ejpam-3914	443	34	the	the	DET
ejpam-3914	443	35	induced	induced	ADJ
ejpam-3914	443	36	subgraph	subgraph	NOUN
ejpam-3914	443	37	〈	〈	PROPN
ejpam-3914	443	38	r	r	PROPN
ejpam-3914	443	39	〉	〉	PROPN
ejpam-3914	443	40	has	have	VERB
ejpam-3914	443	41	no	no	DET
ejpam-3914	443	42	isolated	isolated	ADJ
ejpam-3914	443	43	vertex	vertex	NOUN
ejpam-3914	443	44	.	.	PUNCT
ejpam-3914	444	1	by	by	ADP
ejpam-3914	444	2	theorem	theorem	NOUN
ejpam-3914	444	3	2.3	2.3	NUM
ejpam-3914	444	4	,	,	PUNCT
ejpam-3914	444	5	r	r	NOUN
ejpam-3914	444	6	is	be	AUX
ejpam-3914	444	7	a	a	DET
ejpam-3914	444	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	444	9	-set	-set	PROPN
ejpam-3914	444	10	of	of	ADP
ejpam-3914	444	11	cn	cn	PROPN
ejpam-3914	444	12	.	.	PUNCT
ejpam-3914	445	1	let	let	VERB
ejpam-3914	445	2	m+1	m+1	PRON
ejpam-3914	445	3	be	be	AUX
ejpam-3914	445	4	the	the	DET
ejpam-3914	445	5	number	number	NOUN
ejpam-3914	445	6	of	of	ADP
ejpam-3914	445	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	445	8	-sets	-set	NOUN
ejpam-3914	445	9	of	of	ADP
ejpam-3914	445	10	cn	cn	PROPN
ejpam-3914	445	11	where	where	SCONJ
ejpam-3914	445	12	m	m	PROPN
ejpam-3914	445	13	is	be	AUX
ejpam-3914	445	14	a	a	DET
ejpam-3914	445	15	positive	positive	ADJ
ejpam-3914	445	16	integer	integer	NOUN
ejpam-3914	445	17	.	.	PUNCT
ejpam-3914	446	1	let	let	VERB
ejpam-3914	446	2	k	k	NOUN
ejpam-3914	446	3	=	=	SYM
ejpam-3914	446	4	1	1	NUM
ejpam-3914	446	5	,	,	PUNCT
ejpam-3914	446	6	2	2	NUM
ejpam-3914	446	7	,	,	PUNCT
ejpam-3914	446	8	.	.	PUNCT
ejpam-3914	446	9	.	.	PUNCT
ejpam-3914	447	1	.	.	PUNCT
ejpam-3914	448	1	,	,	PUNCT
ejpam-3914	448	2	m+1	m+1	NUM
ejpam-3914	448	3	and	and	CCONJ
ejpam-3914	448	4	tk	tk	PROPN
ejpam-3914	448	5	be	be	AUX
ejpam-3914	448	6	a	a	DET
ejpam-3914	448	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	448	8	-set	-set	PUNCT
ejpam-3914	448	9	of	of	ADP
ejpam-3914	448	10	cn	cn	PROPN
ejpam-3914	448	11	and	and	CCONJ
ejpam-3914	448	12	one	one	NUM
ejpam-3914	448	13	of	of	ADP
ejpam-3914	448	14	the	the	DET
ejpam-3914	448	15	tk	tk	PROPN
ejpam-3914	448	16	’s	’s	PART
ejpam-3914	448	17	is	be	AUX
ejpam-3914	448	18	equal	equal	ADJ
ejpam-3914	448	19	to	to	ADP
ejpam-3914	448	20	r.	r.	PROPN
ejpam-3914	448	21	note	note	VERB
ejpam-3914	448	22	that	that	SCONJ
ejpam-3914	448	23	in	in	ADP
ejpam-3914	448	24	forming	form	VERB
ejpam-3914	448	25	r	r	NOUN
ejpam-3914	448	26	,	,	PUNCT
ejpam-3914	448	27	there	there	PRON
ejpam-3914	448	28	are	be	VERB
ejpam-3914	448	29	four	four	NUM
ejpam-3914	448	30	vertices	vertex	NOUN
ejpam-3914	448	31	taken	take	VERB
ejpam-3914	448	32	both	both	PRON
ejpam-3914	448	33	from	from	ADP
ejpam-3914	448	34	r0	r0	NOUN
ejpam-3914	448	35	and	and	CCONJ
ejpam-3914	448	36	r1	r1	NOUN
ejpam-3914	448	37	such	such	ADJ
ejpam-3914	448	38	that	that	SCONJ
ejpam-3914	448	39	the	the	DET
ejpam-3914	448	40	induced	induced	ADJ
ejpam-3914	448	41	subgraph	subgraph	NOUN
ejpam-3914	448	42	is	be	AUX
ejpam-3914	448	43	a	a	DET
ejpam-3914	448	44	graph	graph	NOUN
ejpam-3914	448	45	p4	p4	ADJ
ejpam-3914	448	46	and	and	CCONJ
ejpam-3914	448	47	two	two	NUM
ejpam-3914	448	48	adjacent	adjacent	ADJ
ejpam-3914	448	49	vertices	vertex	NOUN
ejpam-3914	448	50	in	in	ADP
ejpam-3914	448	51	the	the	DET
ejpam-3914	448	52	other	other	ADJ
ejpam-3914	448	53	rj	rj	PROPN
ejpam-3914	448	54	’s	’	VERB
ejpam-3914	448	55	where	where	SCONJ
ejpam-3914	448	56	j	j	PROPN
ejpam-3914	448	57	>	>	X
ejpam-3914	448	58	1	1	X
ejpam-3914	448	59	.	.	PUNCT
ejpam-3914	449	1	now	now	ADV
ejpam-3914	449	2	,	,	PUNCT
ejpam-3914	449	3	tk	tk	PROPN
ejpam-3914	449	4	can	can	AUX
ejpam-3914	449	5	be	be	AUX
ejpam-3914	449	6	formed	form	VERB
ejpam-3914	449	7	by	by	ADP
ejpam-3914	449	8	starting	start	VERB
ejpam-3914	449	9	all	all	DET
ejpam-3914	449	10	the	the	DET
ejpam-3914	449	11	vertices	vertex	NOUN
ejpam-3914	449	12	of	of	ADP
ejpam-3914	449	13	sl	sl	NOUN
ejpam-3914	449	14	for	for	ADP
ejpam-3914	449	15	l	l	NOUN
ejpam-3914	449	16	=	=	SYM
ejpam-3914	449	17	1	1	NUM
ejpam-3914	449	18	,	,	PUNCT
ejpam-3914	449	19	2	2	NUM
ejpam-3914	449	20	,	,	PUNCT
ejpam-3914	449	21	.	.	PUNCT
ejpam-3914	449	22	.	.	PUNCT
ejpam-3914	450	1	.	.	PUNCT
ejpam-3914	451	1	,	,	PUNCT
ejpam-3914	451	2	14	14	NUM
ejpam-3914	451	3	and	and	CCONJ
ejpam-3914	451	4	replacing	replace	VERB
ejpam-3914	451	5	u7	u7	PROPN
ejpam-3914	451	6	by	by	ADP
ejpam-3914	451	7	un	un	PROPN
ejpam-3914	451	8	in	in	ADP
ejpam-3914	451	9	s11	s11	PROPN
ejpam-3914	451	10	,	,	PUNCT
ejpam-3914	451	11	s12	s12	PROPN
ejpam-3914	451	12	,	,	PUNCT
ejpam-3914	451	13	s13	s13	NOUN
ejpam-3914	451	14	,	,	PUNCT
ejpam-3914	451	15	and	and	CCONJ
ejpam-3914	451	16	s14	s14	NOUN
ejpam-3914	451	17	,	,	PUNCT
ejpam-3914	451	18	that	that	ADV
ejpam-3914	451	19	is	is	ADV
ejpam-3914	451	20	,	,	PUNCT
ejpam-3914	451	21	tk	tk	PROPN
ejpam-3914	452	1	=	=	NOUN
ejpam-3914	452	2	sl	sl	PROPN
ejpam-3914	452	3	∪h	∪h	NUM
ejpam-3914	452	4	for	for	ADP
ejpam-3914	452	5	some	some	DET
ejpam-3914	452	6	set	set	VERB
ejpam-3914	452	7	h.	h.	NOUN
ejpam-3914	452	8	if	if	SCONJ
ejpam-3914	452	9	tk	tk	PROPN
ejpam-3914	452	10	starts	start	VERB
ejpam-3914	452	11	with	with	ADP
ejpam-3914	452	12	s11	s11	PROPN
ejpam-3914	452	13	=	=	SYM
ejpam-3914	452	14	{	{	PUNCT
ejpam-3914	452	15	un	un	PROPN
ejpam-3914	452	16	,	,	PUNCT
ejpam-3914	452	17	u1	u1	NOUN
ejpam-3914	452	18	,	,	PUNCT
ejpam-3914	452	19	u2	u2	NOUN
ejpam-3914	452	20	,	,	PUNCT
ejpam-3914	452	21	u3	u3	NOUN
ejpam-3914	452	22	}	}	PUNCT
ejpam-3914	452	23	,	,	PUNCT
ejpam-3914	452	24	say	say	VERB
ejpam-3914	452	25	t1	t1	NOUN
ejpam-3914	452	26	,	,	PUNCT
ejpam-3914	452	27	note	note	VERB
ejpam-3914	452	28	that	that	SCONJ
ejpam-3914	452	29	s11	s11	PROPN
ejpam-3914	452	30	is	be	AUX
ejpam-3914	452	31	the	the	DET
ejpam-3914	452	32	only	only	ADJ
ejpam-3914	452	33	set	set	NOUN
ejpam-3914	452	34	in	in	ADP
ejpam-3914	452	35	the	the	DET
ejpam-3914	452	36	sl	sl	NOUN
ejpam-3914	452	37	’s	’s	NOUN
ejpam-3914	452	38	that	that	PRON
ejpam-3914	452	39	ends	end	VERB
ejpam-3914	452	40	with	with	ADP
ejpam-3914	452	41	u3	u3	NOUN
ejpam-3914	452	42	and	and	CCONJ
ejpam-3914	452	43	its	its	PRON
ejpam-3914	452	44	induced	induced	ADJ
ejpam-3914	452	45	subgraph	subgraph	NOUN
ejpam-3914	452	46	is	be	AUX
ejpam-3914	452	47	a	a	DET
ejpam-3914	452	48	graph	graph	NOUN
ejpam-3914	452	49	p4	p4	ADJ
ejpam-3914	452	50	,	,	PUNCT
ejpam-3914	452	51	then	then	ADV
ejpam-3914	452	52	the	the	DET
ejpam-3914	452	53	next	next	ADJ
ejpam-3914	452	54	pairs	pair	NOUN
ejpam-3914	452	55	of	of	ADP
ejpam-3914	452	56	vertices	vertex	NOUN
ejpam-3914	452	57	must	must	AUX
ejpam-3914	452	58	be	be	AUX
ejpam-3914	452	59	choosen	choosen	VERB
ejpam-3914	452	60	are	be	AUX
ejpam-3914	452	61	u7	u7	PROPN
ejpam-3914	452	62	,	,	PUNCT
ejpam-3914	452	63	u8	u8	PROPN
ejpam-3914	452	64	,	,	PUNCT
ejpam-3914	452	65	u12	u12	PROPN
ejpam-3914	452	66	,	,	PUNCT
ejpam-3914	452	67	u13	u13	NOUN
ejpam-3914	452	68	,	,	PUNCT
ejpam-3914	452	69	.	.	PUNCT
ejpam-3914	452	70	.	.	PUNCT
ejpam-3914	453	1	.	.	PUNCT
ejpam-3914	454	1	,	,	PUNCT
ejpam-3914	455	1	un−5	un−5	PROPN
ejpam-3914	455	2	,	,	PUNCT
ejpam-3914	455	3	un−4	un−4	NOUN
ejpam-3914	455	4	,	,	PUNCT
ejpam-3914	455	5	that	that	ADV
ejpam-3914	455	6	is	is	ADV
ejpam-3914	455	7	,	,	PUNCT
ejpam-3914	455	8	t1	t1	NOUN
ejpam-3914	455	9	=	=	PUNCT
ejpam-3914	455	10	{	{	PUNCT
ejpam-3914	455	11	un	un	PROPN
ejpam-3914	455	12	,	,	PUNCT
ejpam-3914	455	13	u1	u1	NOUN
ejpam-3914	455	14	,	,	PUNCT
ejpam-3914	455	15	u2	u2	NOUN
ejpam-3914	455	16	,	,	PUNCT
ejpam-3914	455	17	u3	u3	PROPN
ejpam-3914	455	18	,	,	PUNCT
ejpam-3914	455	19	u7	u7	PROPN
ejpam-3914	455	20	,	,	PUNCT
ejpam-3914	455	21	u8	u8	PROPN
ejpam-3914	455	22	,	,	PUNCT
ejpam-3914	455	23	u12	u12	PROPN
ejpam-3914	455	24	,	,	PUNCT
ejpam-3914	455	25	u13	u13	NOUN
ejpam-3914	455	26	,	,	PUNCT
ejpam-3914	455	27	.	.	PUNCT
ejpam-3914	455	28	.	.	PUNCT
ejpam-3914	456	1	.	.	PUNCT
ejpam-3914	457	1	,	,	PUNCT
ejpam-3914	458	1	un−5	un−5	PROPN
ejpam-3914	458	2	,	,	PUNCT
ejpam-3914	458	3	un−4	un−4	NOUN
ejpam-3914	458	4	}	}	PUNCT
ejpam-3914	458	5	such	such	ADJ
ejpam-3914	458	6	that	that	DET
ejpam-3914	458	7	|t1|	|t1|	NOUN
ejpam-3914	458	8	=	=	SYM
ejpam-3914	458	9	|r|	|r|	PROPN
ejpam-3914	458	10	,	,	PUNCT
ejpam-3914	458	11	ot1	ot1	NOUN
ejpam-3914	458	12	v	v	NOUN
ejpam-3914	458	13	(	(	PUNCT
ejpam-3914	458	14	cn	cn	PROPN
ejpam-3914	458	15	)	)	PUNCT
ejpam-3914	458	16	=	=	NOUN
ejpam-3914	458	17	v	v	X
ejpam-3914	458	18	(	(	PUNCT
ejpam-3914	458	19	cn	cn	PROPN
ejpam-3914	458	20	)	)	PUNCT
ejpam-3914	458	21	,	,	PUNCT
ejpam-3914	458	22	ot1	ot1	PROPN
ejpam-3914	458	23	e	e	PROPN
ejpam-3914	458	24	(	(	PUNCT
ejpam-3914	458	25	cn	cn	NOUN
ejpam-3914	458	26	)	)	PUNCT
ejpam-3914	458	27	=	=	SYM
ejpam-3914	458	28	e(cn	e(cn	NOUN
ejpam-3914	458	29	)	)	PUNCT
ejpam-3914	458	30	,	,	PUNCT
ejpam-3914	458	31	and	and	CCONJ
ejpam-3914	458	32	the	the	DET
ejpam-3914	458	33	induced	induced	ADJ
ejpam-3914	458	34	subgraph	subgraph	NOUN
ejpam-3914	458	35	〈	〈	PROPN
ejpam-3914	458	36	t1	t1	PROPN
ejpam-3914	458	37	〉	〉	PROPN
ejpam-3914	458	38	has	have	VERB
ejpam-3914	458	39	no	no	DET
ejpam-3914	458	40	isolated	isolated	ADJ
ejpam-3914	458	41	vertex	vertex	NOUN
ejpam-3914	458	42	,	,	PUNCT
ejpam-3914	458	43	that	that	ADV
ejpam-3914	458	44	is	is	ADV
ejpam-3914	458	45	,	,	PUNCT
ejpam-3914	458	46	t1	t1	PROPN
ejpam-3914	458	47	is	be	AUX
ejpam-3914	458	48	a	a	DET
ejpam-3914	458	49	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	458	50	-set	-set	PROPN
ejpam-3914	458	51	of	of	ADP
ejpam-3914	458	52	cn	cn	PROPN
ejpam-3914	458	53	.	.	PROPN
ejpam-3914	458	54	note	note	NOUN
ejpam-3914	458	55	also	also	ADV
ejpam-3914	458	56	that	that	SCONJ
ejpam-3914	458	57	if	if	SCONJ
ejpam-3914	458	58	tk	tk	PROPN
ejpam-3914	458	59	starts	start	VERB
ejpam-3914	458	60	with	with	ADP
ejpam-3914	458	61	s14	s14	NOUN
ejpam-3914	458	62	=	=	SYM
ejpam-3914	458	63	{	{	PUNCT
ejpam-3914	458	64	un	un	PROPN
ejpam-3914	458	65	,	,	PUNCT
ejpam-3914	458	66	u1	u1	PROPN
ejpam-3914	458	67	,	,	PUNCT
ejpam-3914	458	68	u5	u5	PROPN
ejpam-3914	458	69	,	,	PUNCT
ejpam-3914	458	70	u6	u6	NOUN
ejpam-3914	458	71	}	}	PUNCT
ejpam-3914	458	72	,	,	PUNCT
ejpam-3914	458	73	say	say	VERB
ejpam-3914	458	74	t2	t2	NOUN
ejpam-3914	458	75	,	,	PUNCT
ejpam-3914	458	76	then	then	ADV
ejpam-3914	458	77	the	the	DET
ejpam-3914	458	78	next	next	ADJ
ejpam-3914	458	79	pairs	pair	NOUN
ejpam-3914	458	80	of	of	ADP
ejpam-3914	458	81	vertices	vertex	NOUN
ejpam-3914	458	82	must	must	AUX
ejpam-3914	458	83	be	be	AUX
ejpam-3914	458	84	choosen	choosen	VERB
ejpam-3914	458	85	are	be	AUX
ejpam-3914	458	86	u7	u7	PROPN
ejpam-3914	458	87	,	,	PUNCT
ejpam-3914	458	88	u8	u8	PROPN
ejpam-3914	458	89	,	,	PUNCT
ejpam-3914	458	90	u12	u12	PROPN
ejpam-3914	458	91	,	,	PUNCT
ejpam-3914	458	92	u13	u13	NOUN
ejpam-3914	458	93	,	,	PUNCT
ejpam-3914	458	94	.	.	PUNCT
ejpam-3914	458	95	.	.	PUNCT
ejpam-3914	459	1	.	.	PUNCT
ejpam-3914	460	1	,	,	PUNCT
ejpam-3914	460	2	un−5	un−5	NOUN
ejpam-3914	460	3	,	,	PUNCT
ejpam-3914	460	4	un−4	un−4	VERB
ejpam-3914	460	5	such	such	ADJ
ejpam-3914	460	6	that	that	DET
ejpam-3914	460	7	induced	induce	VERB
ejpam-3914	460	8	subgraph	subgraph	NOUN
ejpam-3914	460	9	of	of	ADP
ejpam-3914	460	10	{	{	PUNCT
ejpam-3914	460	11	u5	u5	PROPN
ejpam-3914	460	12	,	,	PUNCT
ejpam-3914	460	13	u6	u6	PROPN
ejpam-3914	460	14	,	,	PUNCT
ejpam-3914	460	15	u7	u7	PROPN
ejpam-3914	460	16	,	,	PUNCT
ejpam-3914	460	17	u8	u8	PROPN
ejpam-3914	460	18	}	}	PUNCT
ejpam-3914	460	19	⊆	⊆	NUM
ejpam-3914	460	20	t2	t2	NOUN
ejpam-3914	460	21	is	be	AUX
ejpam-3914	460	22	a	a	DET
ejpam-3914	460	23	graph	graph	NOUN
ejpam-3914	460	24	p4	p4	ADJ
ejpam-3914	460	25	,	,	PUNCT
ejpam-3914	460	26	that	that	ADV
ejpam-3914	460	27	is	is	ADV
ejpam-3914	460	28	,	,	PUNCT
ejpam-3914	460	29	t2	t2	PROPN
ejpam-3914	460	30	=	=	SYM
ejpam-3914	460	31	{	{	PUNCT
ejpam-3914	460	32	un	un	PROPN
ejpam-3914	460	33	,	,	PUNCT
ejpam-3914	460	34	u1	u1	PROPN
ejpam-3914	460	35	,	,	PUNCT
ejpam-3914	460	36	u5	u5	PROPN
ejpam-3914	460	37	,	,	PUNCT
ejpam-3914	460	38	u6	u6	PROPN
ejpam-3914	460	39	,	,	PUNCT
ejpam-3914	460	40	u7	u7	PROPN
ejpam-3914	460	41	,	,	PUNCT
ejpam-3914	460	42	u8	u8	PROPN
ejpam-3914	460	43	,	,	PUNCT
ejpam-3914	460	44	u12	u12	PROPN
ejpam-3914	460	45	,	,	PUNCT
ejpam-3914	460	46	u13	u13	NOUN
ejpam-3914	460	47	,	,	PUNCT
ejpam-3914	460	48	.	.	PUNCT
ejpam-3914	460	49	.	.	PUNCT
ejpam-3914	461	1	.	.	PUNCT
ejpam-3914	462	1	,	,	PUNCT
ejpam-3914	463	1	un−5	un−5	PROPN
ejpam-3914	463	2	,	,	PUNCT
ejpam-3914	463	3	un−4	un−4	NOUN
ejpam-3914	463	4	}	}	PUNCT
ejpam-3914	463	5	such	such	ADJ
ejpam-3914	463	6	that	that	DET
ejpam-3914	463	7	|t2|	|t2|	NOUN
ejpam-3914	463	8	=	=	SYM
ejpam-3914	463	9	|r|	|r|	PROPN
ejpam-3914	463	10	,	,	PUNCT
ejpam-3914	463	11	ot2	ot2	NOUN
ejpam-3914	463	12	v	v	NOUN
ejpam-3914	463	13	(	(	PUNCT
ejpam-3914	463	14	cn	cn	PROPN
ejpam-3914	463	15	)	)	PUNCT
ejpam-3914	463	16	=	=	NOUN
ejpam-3914	463	17	v	v	X
ejpam-3914	463	18	(	(	PUNCT
ejpam-3914	463	19	cn	cn	PROPN
ejpam-3914	463	20	)	)	PUNCT
ejpam-3914	463	21	,	,	PUNCT
ejpam-3914	463	22	ot2	ot2	NOUN
ejpam-3914	463	23	e	e	X
ejpam-3914	463	24	(	(	PUNCT
ejpam-3914	463	25	cn	cn	NOUN
ejpam-3914	463	26	)	)	PUNCT
ejpam-3914	463	27	=	=	SYM
ejpam-3914	463	28	e(cn	e(cn	NOUN
ejpam-3914	463	29	)	)	PUNCT
ejpam-3914	463	30	,	,	PUNCT
ejpam-3914	463	31	and	and	CCONJ
ejpam-3914	463	32	the	the	DET
ejpam-3914	463	33	induced	induced	ADJ
ejpam-3914	463	34	subgraph	subgraph	NOUN
ejpam-3914	463	35	〈	〈	PROPN
ejpam-3914	463	36	t2	t2	PROPN
ejpam-3914	463	37	〉	〉	PROPN
ejpam-3914	463	38	has	have	VERB
ejpam-3914	463	39	no	no	DET
ejpam-3914	463	40	isolated	isolated	ADJ
ejpam-3914	463	41	vertex	vertex	NOUN
ejpam-3914	463	42	,	,	PUNCT
ejpam-3914	463	43	that	that	ADV
ejpam-3914	463	44	is	is	ADV
ejpam-3914	463	45	,	,	PUNCT
ejpam-3914	463	46	t2	t2	PROPN
ejpam-3914	463	47	is	be	AUX
ejpam-3914	463	48	a	a	DET
ejpam-3914	463	49	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	463	50	-set	-set	PROPN
ejpam-3914	463	51	of	of	ADP
ejpam-3914	463	52	cn	cn	PROPN
ejpam-3914	463	53	.	.	PUNCT
ejpam-3914	463	54	clearly	clearly	ADV
ejpam-3914	463	55	,	,	PUNCT
ejpam-3914	463	56	t1\s11	t1\s11	X
ejpam-3914	463	57	=	=	SYM
ejpam-3914	463	58	t2\s14	t2\s14	PROPN
ejpam-3914	463	59	.	.	PUNCT
ejpam-3914	464	1	now	now	ADV
ejpam-3914	464	2	,	,	PUNCT
ejpam-3914	464	3	since	since	SCONJ
ejpam-3914	464	4	none	none	NOUN
ejpam-3914	464	5	of	of	ADP
ejpam-3914	464	6	the	the	DET
ejpam-3914	464	7	other	other	ADJ
ejpam-3914	464	8	sl	sl	PROPN
ejpam-3914	464	9	’s	’	VERB
ejpam-3914	464	10	ended	end	VERB
ejpam-3914	464	11	with	with	ADP
ejpam-3914	464	12	a	a	DET
ejpam-3914	464	13	unique	unique	ADJ
ejpam-3914	464	14	vertex	vertex	NOUN
ejpam-3914	464	15	,	,	PUNCT
ejpam-3914	464	16	the	the	DET
ejpam-3914	464	17	set	set	NOUN
ejpam-3914	464	18	of	of	ADP
ejpam-3914	464	19	vertices	vertex	NOUN
ejpam-3914	464	20	in	in	ADP
ejpam-3914	464	21	tk\sl	tk\sl	NOUN
ejpam-3914	464	22	must	must	AUX
ejpam-3914	464	23	be	be	AUX
ejpam-3914	464	24	contained	contain	VERB
ejpam-3914	464	25	in	in	ADP
ejpam-3914	464	26	tr	tr	VERB
ejpam-3914	464	27	for	for	ADP
ejpam-3914	464	28	some	some	DET
ejpam-3914	464	29	r	r	NOUN
ejpam-3914	464	30	6=	6=	NUM
ejpam-3914	464	31	k.	k.	PROPN
ejpam-3914	464	32	hence	hence	ADV
ejpam-3914	464	33	,	,	PUNCT
ejpam-3914	464	34	tk\sl	tk\sl	PROPN
ejpam-3914	464	35	is	be	AUX
ejpam-3914	464	36	not	not	PART
ejpam-3914	464	37	a	a	DET
ejpam-3914	464	38	forcing	forcing	NOUN
ejpam-3914	464	39	subset	subset	NOUN
ejpam-3914	464	40	for	for	ADP
ejpam-3914	464	41	tk	tk	PROPN
ejpam-3914	464	42	.	.	PROPN
ejpam-3914	465	1	therefore	therefore	ADV
ejpam-3914	465	2	,	,	PUNCT
ejpam-3914	465	3	either	either	CCONJ
ejpam-3914	465	4	the	the	DET
ejpam-3914	465	5	sets	set	NOUN
ejpam-3914	465	6	sl	sl	INTJ
ejpam-3914	465	7	or	or	CCONJ
ejpam-3914	465	8	tk	tk	PROPN
ejpam-3914	465	9	must	must	AUX
ejpam-3914	465	10	be	be	AUX
ejpam-3914	465	11	the	the	DET
ejpam-3914	465	12	forcing	forcing	NOUN
ejpam-3914	465	13	subset	subset	NOUN
ejpam-3914	465	14	for	for	ADP
ejpam-3914	465	15	tk	tk	PROPN
ejpam-3914	465	16	for	for	ADP
ejpam-3914	465	17	some	some	DET
ejpam-3914	465	18	l	l	NOUN
ejpam-3914	465	19	=	=	SYM
ejpam-3914	465	20	1	1	NUM
ejpam-3914	465	21	,	,	PUNCT
ejpam-3914	465	22	2	2	NUM
ejpam-3914	465	23	,	,	PUNCT
ejpam-3914	465	24	.	.	PUNCT
ejpam-3914	465	25	.	.	PUNCT
ejpam-3914	466	1	.	.	PUNCT
ejpam-3914	467	1	,	,	PUNCT
ejpam-3914	467	2	14	14	NUM
ejpam-3914	467	3	and	and	CCONJ
ejpam-3914	467	4	for	for	ADP
ejpam-3914	467	5	some	some	PRON
ejpam-3914	467	6	k	k	NOUN
ejpam-3914	467	7	=	=	SYM
ejpam-3914	467	8	1	1	NUM
ejpam-3914	467	9	,	,	PUNCT
ejpam-3914	467	10	2	2	NUM
ejpam-3914	467	11	,	,	PUNCT
ejpam-3914	467	12	.	.	PUNCT
ejpam-3914	467	13	.	.	PUNCT
ejpam-3914	467	14	.	.	PUNCT
ejpam-3914	468	1	,	,	PUNCT
ejpam-3914	468	2	m+1	m+1	X
ejpam-3914	468	3	.	.	PUNCT
ejpam-3914	469	1	now	now	ADV
ejpam-3914	469	2	,	,	PUNCT
ejpam-3914	469	3	if	if	SCONJ
ejpam-3914	469	4	tk	tk	PROPN
ejpam-3914	469	5	starts	start	VERB
ejpam-3914	469	6	with	with	ADP
ejpam-3914	469	7	s1	s1	NOUN
ejpam-3914	469	8	,	,	PUNCT
ejpam-3914	469	9	then	then	ADV
ejpam-3914	469	10	let	let	VERB
ejpam-3914	469	11	k	k	PROPN
ejpam-3914	469	12	=	=	SYM
ejpam-3914	469	13	3	3	NUM
ejpam-3914	469	14	and	and	CCONJ
ejpam-3914	469	15	{	{	PUNCT
ejpam-3914	469	16	u1	u1	NOUN
ejpam-3914	469	17	,	,	PUNCT
ejpam-3914	469	18	u2	u2	NOUN
ejpam-3914	469	19	,	,	PUNCT
ejpam-3914	469	20	u3	u3	NOUN
ejpam-3914	469	21	,	,	PUNCT
ejpam-3914	469	22	u4	u4	PROPN
ejpam-3914	469	23	}	}	PUNCT
ejpam-3914	469	24	⊆	⊆	NUM
ejpam-3914	469	25	t3	t3	NOUN
ejpam-3914	469	26	such	such	ADJ
ejpam-3914	469	27	that	that	SCONJ
ejpam-3914	469	28	t3	t3	PROPN
ejpam-3914	469	29	is	be	AUX
ejpam-3914	469	30	a	a	DET
ejpam-3914	469	31	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	469	32	-set	-set	PUNCT
ejpam-3914	469	33	of	of	ADP
ejpam-3914	469	34	cn	cn	PROPN
ejpam-3914	469	35	different	different	ADJ
ejpam-3914	469	36	from	from	ADP
ejpam-3914	469	37	r.	r.	PROPN
ejpam-3914	469	38	replace	replace	PROPN
ejpam-3914	469	39	u8	u8	PROPN
ejpam-3914	469	40	∈	∈	PROPN
ejpam-3914	469	41	r	r	NOUN
ejpam-3914	469	42	by	by	ADP
ejpam-3914	469	43	u7	u7	PROPN
ejpam-3914	469	44	to	to	PART
ejpam-3914	469	45	form	form	VERB
ejpam-3914	469	46	t3	t3	PROPN
ejpam-3914	469	47	.	.	PUNCT
ejpam-3914	470	1	then	then	ADV
ejpam-3914	470	2	the	the	DET
ejpam-3914	470	3	next	next	ADJ
ejpam-3914	470	4	vertex	vertex	NOUN
ejpam-3914	470	5	to	to	PART
ejpam-3914	470	6	be	be	AUX
ejpam-3914	470	7	chosen	choose	VERB
ejpam-3914	470	8	must	must	AUX
ejpam-3914	470	9	be	be	AUX
ejpam-3914	470	10	u8	u8	PROPN
ejpam-3914	470	11	,	,	PUNCT
ejpam-3914	470	12	that	that	ADV
ejpam-3914	470	13	is	is	ADV
ejpam-3914	470	14	,	,	PUNCT
ejpam-3914	470	15	the	the	DET
ejpam-3914	470	16	vertex	vertex	NOUN
ejpam-3914	470	17	ui+4	ui+4	PROPN
ejpam-3914	470	18	,	,	PUNCT
ejpam-3914	470	19	ui	ui	PROPN
ejpam-3914	470	20	must	must	AUX
ejpam-3914	470	21	be	be	AUX
ejpam-3914	470	22	in	in	ADP
ejpam-3914	470	23	t3	t3	PROPN
ejpam-3914	470	24	for	for	ADP
ejpam-3914	470	25	all	all	DET
ejpam-3914	470	26	i	i	PRON
ejpam-3914	470	27	=	=	NOUN
ejpam-3914	470	28	3	3	NUM
ejpam-3914	470	29	,	,	PUNCT
ejpam-3914	470	30	8	8	NUM
ejpam-3914	470	31	,	,	PUNCT
ejpam-3914	470	32	13	13	NUM
ejpam-3914	470	33	,	,	PUNCT
ejpam-3914	470	34	.	.	PUNCT
ejpam-3914	470	35	.	.	PUNCT
ejpam-3914	471	1	.	.	PUNCT
ejpam-3914	472	1	,	,	PUNCT
ejpam-3914	472	2	n	n	CCONJ
ejpam-3914	472	3	−	−	PROPN
ejpam-3914	472	4	9	9	NUM
ejpam-3914	472	5	,	,	PUNCT
ejpam-3914	472	6	n	n	CCONJ
ejpam-3914	472	7	−	−	PROPN
ejpam-3914	472	8	4	4	NUM
ejpam-3914	472	9	.	.	PUNCT
ejpam-3914	473	1	then	then	ADV
ejpam-3914	473	2	t3	t3	PROPN
ejpam-3914	473	3	=	=	PUNCT
ejpam-3914	473	4	{	{	PUNCT
ejpam-3914	473	5	u1	u1	NOUN
ejpam-3914	473	6	,	,	PUNCT
ejpam-3914	473	7	u2	u2	NOUN
ejpam-3914	473	8	,	,	PUNCT
ejpam-3914	473	9	u3	u3	PROPN
ejpam-3914	473	10	,	,	PUNCT
ejpam-3914	473	11	u4	u4	PROPN
ejpam-3914	473	12	,	,	PUNCT
ejpam-3914	473	13	u7	u7	PROPN
ejpam-3914	473	14	,	,	PUNCT
ejpam-3914	473	15	u8	u8	PROPN
ejpam-3914	473	16	,	,	PUNCT
ejpam-3914	473	17	u12	u12	PROPN
ejpam-3914	473	18	,	,	PUNCT
ejpam-3914	473	19	u13	u13	NOUN
ejpam-3914	473	20	,	,	PUNCT
ejpam-3914	473	21	.	.	PUNCT
ejpam-3914	473	22	.	.	PUNCT
ejpam-3914	474	1	.	.	PUNCT
ejpam-3914	475	1	,	,	PUNCT
ejpam-3914	476	1	un−5	un−5	PROPN
ejpam-3914	476	2	,	,	PUNCT
ejpam-3914	476	3	un−4	un−4	NOUN
ejpam-3914	476	4	}	}	PUNCT
ejpam-3914	476	5	such	such	ADJ
ejpam-3914	476	6	that	that	SCONJ
ejpam-3914	476	7	|t3|	|t3|	PROPN
ejpam-3914	476	8	=	=	SYM
ejpam-3914	476	9	|r|	|r|	PROPN
ejpam-3914	476	10	.	.	PUNCT
ejpam-3914	477	1	since	since	SCONJ
ejpam-3914	477	2	u1	u1	PROPN
ejpam-3914	477	3	∈	∈	PROPN
ejpam-3914	477	4	t3	t3	NOUN
ejpam-3914	477	5	and	and	CCONJ
ejpam-3914	477	6	un−4	un−4	NOUN
ejpam-3914	477	7	is	be	AUX
ejpam-3914	477	8	the	the	DET
ejpam-3914	477	9	last	last	ADJ
ejpam-3914	477	10	vertex	vertex	NOUN
ejpam-3914	477	11	in	in	ADP
ejpam-3914	477	12	t3	t3	PROPN
ejpam-3914	477	13	,	,	PUNCT
ejpam-3914	477	14	the	the	DET
ejpam-3914	477	15	vertices	vertex	NOUN
ejpam-3914	477	16	un	un	PROPN
ejpam-3914	477	17	and	and	CCONJ
ejpam-3914	477	18	un−3	un−3	PROPN
ejpam-3914	477	19	are	be	AUX
ejpam-3914	477	20	directly	directly	ADV
ejpam-3914	477	21	observed	observe	VERB
ejpam-3914	477	22	vertices	vertex	NOUN
ejpam-3914	477	23	while	while	SCONJ
ejpam-3914	477	24	un−1	un−1	ADJ
ejpam-3914	477	25	and	and	CCONJ
ejpam-3914	477	26	un−2	un−2	NOUN
ejpam-3914	477	27	are	be	AUX
ejpam-3914	477	28	remotely	remotely	ADV
ejpam-3914	477	29	observed	observe	VERB
ejpam-3914	477	30	vertices	vertex	NOUN
ejpam-3914	477	31	.	.	PUNCT
ejpam-3914	478	1	hence	hence	ADV
ejpam-3914	478	2	,	,	PUNCT
ejpam-3914	478	3	by	by	ADP
ejpam-3914	478	4	definition	definition	NOUN
ejpam-3914	478	5	,	,	PUNCT
ejpam-3914	478	6	the	the	DET
ejpam-3914	478	7	edge	edge	NOUN
ejpam-3914	478	8	un−1un−2	un−1un−2	PRON
ejpam-3914	478	9	is	be	AUX
ejpam-3914	478	10	neither	neither	CCONJ
ejpam-3914	478	11	a	a	PRON
ejpam-3914	478	12	directly	directly	ADV
ejpam-3914	478	13	or	or	CCONJ
ejpam-3914	478	14	a	a	DET
ejpam-3914	478	15	remotely	remotely	ADV
ejpam-3914	478	16	observed	observe	VERB
ejpam-3914	478	17	edge	edge	NOUN
ejpam-3914	478	18	.	.	PUNCT
ejpam-3914	479	1	thus	thus	ADV
ejpam-3914	479	2	,	,	PUNCT
ejpam-3914	479	3	ot3	ot3	PROPN
ejpam-3914	479	4	e	e	X
ejpam-3914	479	5	(	(	PUNCT
ejpam-3914	479	6	cn	cn	PROPN
ejpam-3914	479	7	)	)	PUNCT
ejpam-3914	479	8	6=	6=	ADP
ejpam-3914	479	9	e(cn	e(cn	NOUN
ejpam-3914	479	10	)	)	PUNCT
ejpam-3914	479	11	,	,	PUNCT
ejpam-3914	479	12	a	a	DET
ejpam-3914	479	13	contradiction	contradiction	NOUN
ejpam-3914	479	14	,	,	PUNCT
ejpam-3914	479	15	that	that	ADV
ejpam-3914	479	16	is	is	ADV
ejpam-3914	479	17	,	,	PUNCT
ejpam-3914	479	18	t3	t3	PROPN
ejpam-3914	479	19	is	be	AUX
ejpam-3914	479	20	not	not	PART
ejpam-3914	479	21	a	a	DET
ejpam-3914	479	22	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	479	23	-set	-set	PROPN
ejpam-3914	479	24	of	of	ADP
ejpam-3914	479	25	cn	cn	PROPN
ejpam-3914	479	26	.	.	PUNCT
ejpam-3914	480	1	since	since	SCONJ
ejpam-3914	480	2	u8	u8	PROPN
ejpam-3914	480	3	is	be	AUX
ejpam-3914	480	4	arbitrarily	arbitrarily	ADV
ejpam-3914	480	5	replaced	replace	VERB
ejpam-3914	480	6	from	from	ADP
ejpam-3914	480	7	r	r	NOUN
ejpam-3914	480	8	,	,	PUNCT
ejpam-3914	480	9	we	we	PRON
ejpam-3914	480	10	can	can	AUX
ejpam-3914	480	11	not	not	PART
ejpam-3914	480	12	replace	replace	VERB
ejpam-3914	480	13	the	the	DET
ejpam-3914	480	14	vertex	vertex	NOUN
ejpam-3914	480	15	ui	ui	NOUN
ejpam-3914	480	16	in	in	ADP
ejpam-3914	480	17	r	r	NOUN
ejpam-3914	480	18	,	,	PUNCT
ejpam-3914	480	19	where	where	SCONJ
ejpam-3914	480	20	i	i	PRON
ejpam-3914	480	21	=	=	NOUN
ejpam-3914	480	22	8	8	NUM
ejpam-3914	480	23	,	,	PUNCT
ejpam-3914	480	24	13	13	NUM
ejpam-3914	480	25	,	,	PUNCT
ejpam-3914	480	26	.	.	PUNCT
ejpam-3914	480	27	.	.	PUNCT
ejpam-3914	481	1	.	.	PUNCT
ejpam-3914	482	1	,	,	PUNCT
ejpam-3914	482	2	n−	n−	NOUN
ejpam-3914	482	3	9	9	NUM
ejpam-3914	482	4	,	,	PUNCT
ejpam-3914	482	5	n−	n−	NOUN
ejpam-3914	482	6	4	4	NUM
ejpam-3914	482	7	to	to	PART
ejpam-3914	482	8	form	form	VERB
ejpam-3914	482	9	another	another	PRON
ejpam-3914	482	10	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	482	11	-set	-set	PROPN
ejpam-3914	482	12	of	of	ADP
ejpam-3914	482	13	cn	cn	PROPN
ejpam-3914	482	14	.	.	PUNCT
ejpam-3914	482	15	therefore	therefore	ADV
ejpam-3914	482	16	,	,	PUNCT
ejpam-3914	482	17	only	only	ADV
ejpam-3914	482	18	the	the	DET
ejpam-3914	482	19	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	482	20	-set	-set	PUNCT
ejpam-3914	482	21	r	r	NOUN
ejpam-3914	482	22	starts	start	VERB
ejpam-3914	482	23	with	with	ADP
ejpam-3914	482	24	s1	s1	NOUN
ejpam-3914	482	25	and	and	CCONJ
ejpam-3914	482	26	so	so	ADV
ejpam-3914	482	27	,	,	PUNCT
ejpam-3914	482	28	{	{	PUNCT
ejpam-3914	482	29	u1	u1	NOUN
ejpam-3914	482	30	,	,	PUNCT
ejpam-3914	482	31	u2	u2	NOUN
ejpam-3914	482	32	,	,	PUNCT
ejpam-3914	482	33	u3	u3	NOUN
ejpam-3914	482	34	,	,	PUNCT
ejpam-3914	482	35	u4	u4	PROPN
ejpam-3914	482	36	}	}	PUNCT
ejpam-3914	482	37	*	*	PUNCT
ejpam-3914	482	38	tk	tk	PROPN
ejpam-3914	482	39	for	for	ADP
ejpam-3914	482	40	all	all	DET
ejpam-3914	482	41	tk	tk	PROPN
ejpam-3914	482	42	6=	6=	PROPN
ejpam-3914	482	43	r.	r.	PROPN
ejpam-3914	482	44	hence	hence	ADV
ejpam-3914	482	45	,	,	PUNCT
ejpam-3914	482	46	{	{	PUNCT
ejpam-3914	482	47	u1	u1	NOUN
ejpam-3914	482	48	,	,	PUNCT
ejpam-3914	482	49	u2	u2	NOUN
ejpam-3914	482	50	,	,	PUNCT
ejpam-3914	482	51	u3	u3	PROPN
ejpam-3914	482	52	,	,	PUNCT
ejpam-3914	482	53	u4	u4	PROPN
ejpam-3914	482	54	}	}	PUNCT
ejpam-3914	482	55	is	be	AUX
ejpam-3914	482	56	a	a	DET
ejpam-3914	482	57	forcing	forcing	NOUN
ejpam-3914	482	58	subset	subset	NOUN
ejpam-3914	482	59	for	for	ADP
ejpam-3914	482	60	r.	r.	PROPN
ejpam-3914	482	61	therefore	therefore	ADV
ejpam-3914	482	62	,	,	PUNCT
ejpam-3914	482	63	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	482	64	(	(	PUNCT
ejpam-3914	482	65	r	r	NOUN
ejpam-3914	482	66	)	)	PUNCT
ejpam-3914	482	67	=	=	SYM
ejpam-3914	483	1	4	4	NUM
ejpam-3914	483	2	=	=	NOUN
ejpam-3914	483	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	483	4	(	(	PUNCT
ejpam-3914	483	5	cn	cn	NOUN
ejpam-3914	483	6	)	)	PUNCT
ejpam-3914	483	7	.	.	PUNCT
ejpam-3914	484	1	case	case	NOUN
ejpam-3914	484	2	2	2	NUM
ejpam-3914	484	3	:	:	PUNCT
ejpam-3914	484	4	suppose	suppose	VERB
ejpam-3914	484	5	that	that	SCONJ
ejpam-3914	484	6	n	n	NUM
ejpam-3914	484	7	≡	≡	ADJ
ejpam-3914	484	8	0(mod	0(mod	NOUN
ejpam-3914	484	9	5	5	NUM
ejpam-3914	484	10	)	)	PUNCT
ejpam-3914	484	11	.	.	PUNCT
ejpam-3914	485	1	by	by	ADP
ejpam-3914	485	2	theorem	theorem	NOUN
ejpam-3914	485	3	2.3	2.3	NUM
ejpam-3914	485	4	,	,	PUNCT
ejpam-3914	485	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	485	6	(	(	PUNCT
ejpam-3914	485	7	cn	cn	NOUN
ejpam-3914	485	8	)	)	PUNCT
ejpam-3914	485	9	=	=	SYM
ejpam-3914	485	10	2n	2n	NUM
ejpam-3914	485	11	5	5	NUM
ejpam-3914	485	12	.	.	PUNCT
ejpam-3914	485	13	suppose	suppose	VERB
ejpam-3914	485	14	that	that	SCONJ
ejpam-3914	485	15	n	n	NOUN
ejpam-3914	485	16	=	=	SYM
ejpam-3914	485	17	5	5	NUM
ejpam-3914	485	18	.	.	PUNCT
ejpam-3914	485	19	then	then	ADV
ejpam-3914	485	20	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	485	21	(	(	PUNCT
ejpam-3914	485	22	c5	c5	PROPN
ejpam-3914	485	23	)	)	PUNCT
ejpam-3914	485	24	=	=	SYM
ejpam-3914	485	25	2(5	2(5	NOUN
ejpam-3914	485	26	)	)	PUNCT
ejpam-3914	485	27	5	5	NUM
ejpam-3914	485	28	=	=	SYM
ejpam-3914	485	29	2	2	X
ejpam-3914	485	30	.	.	PUNCT
ejpam-3914	485	31	clearly	clearly	ADV
ejpam-3914	485	32	,	,	PUNCT
ejpam-3914	485	33	s1	s1	PROPN
ejpam-3914	485	34	=	=	SYM
ejpam-3914	485	35	{	{	PUNCT
ejpam-3914	485	36	u1	u1	NOUN
ejpam-3914	485	37	,	,	PUNCT
ejpam-3914	485	38	u2	u2	PROPN
ejpam-3914	485	39	}	}	PUNCT
ejpam-3914	485	40	,	,	PUNCT
ejpam-3914	485	41	s2	s2	X
ejpam-3914	485	42	=	=	SYM
ejpam-3914	485	43	{	{	PUNCT
ejpam-3914	485	44	u2	u2	NOUN
ejpam-3914	485	45	,	,	PUNCT
ejpam-3914	485	46	u3	u3	NOUN
ejpam-3914	485	47	}	}	PUNCT
ejpam-3914	485	48	,	,	PUNCT
ejpam-3914	485	49	s3	s3	PROPN
ejpam-3914	485	50	=	=	SYM
ejpam-3914	485	51	{	{	PUNCT
ejpam-3914	485	52	u3	u3	PROPN
ejpam-3914	485	53	,	,	PUNCT
ejpam-3914	485	54	u4	u4	PROPN
ejpam-3914	485	55	}	}	PUNCT
ejpam-3914	485	56	,	,	PUNCT
ejpam-3914	485	57	s4	s4	PROPN
ejpam-3914	485	58	=	=	SYM
ejpam-3914	485	59	{	{	PUNCT
ejpam-3914	485	60	u4	u4	PROPN
ejpam-3914	485	61	,	,	PUNCT
ejpam-3914	485	62	u5	u5	PROPN
ejpam-3914	485	63	}	}	PUNCT
ejpam-3914	485	64	,	,	PUNCT
ejpam-3914	485	65	s5	s5	X
ejpam-3914	485	66	=	=	PUNCT
ejpam-3914	485	67	{	{	PUNCT
ejpam-3914	485	68	u5	u5	PROPN
ejpam-3914	485	69	,	,	PUNCT
ejpam-3914	485	70	u1	u1	NOUN
ejpam-3914	485	71	}	}	PUNCT
ejpam-3914	485	72	,	,	PUNCT
ejpam-3914	485	73	are	be	AUX
ejpam-3914	485	74	the	the	DET
ejpam-3914	485	75	only	only	ADJ
ejpam-3914	485	76	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	485	77	-sets	-set	NOUN
ejpam-3914	485	78	of	of	ADP
ejpam-3914	485	79	c5	c5	PROPN
ejpam-3914	485	80	.	.	PUNCT
ejpam-3914	486	1	note	note	VERB
ejpam-3914	486	2	that	that	SCONJ
ejpam-3914	486	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	486	4	(	(	PUNCT
ejpam-3914	486	5	c5	c5	PROPN
ejpam-3914	486	6	)	)	PUNCT
ejpam-3914	486	7	≥	≥	NOUN
ejpam-3914	486	8	2	2	NUM
ejpam-3914	486	9	.	.	PUNCT
ejpam-3914	487	1	it	it	PRON
ejpam-3914	487	2	follows	follow	VERB
ejpam-3914	487	3	that	that	SCONJ
ejpam-3914	487	4	c.	c.	PROPN
ejpam-3914	487	5	armada	armada	PROPN
ejpam-3914	487	6	/	/	SYM
ejpam-3914	487	7	eur	eur	PROPN
ejpam-3914	487	8	.	.	PUNCT
ejpam-3914	488	1	j.	j.	PROPN
ejpam-3914	488	2	pure	pure	PROPN
ejpam-3914	488	3	appl	appl	PROPN
ejpam-3914	488	4	.	.	PROPN
ejpam-3914	488	5	math	math	PROPN
ejpam-3914	488	6	,	,	PUNCT
ejpam-3914	488	7	14	14	NUM
ejpam-3914	488	8	(	(	PUNCT
ejpam-3914	488	9	2	2	NUM
ejpam-3914	488	10	)	)	PUNCT
ejpam-3914	488	11	(	(	PUNCT
ejpam-3914	488	12	2021	2021	NUM
ejpam-3914	488	13	)	)	PUNCT
ejpam-3914	488	14	,	,	PUNCT
ejpam-3914	488	15	451	451	NUM
ejpam-3914	488	16	-	-	SYM
ejpam-3914	488	17	470	470	NUM
ejpam-3914	488	18	464	464	NUM
ejpam-3914	488	19	2	2	NUM
ejpam-3914	488	20	≤	≤	NOUN
ejpam-3914	488	21	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	488	22	(	(	PUNCT
ejpam-3914	488	23	c5	c5	PROPN
ejpam-3914	488	24	)	)	PUNCT
ejpam-3914	488	25	≤	≤	PROPN
ejpam-3914	488	26	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	488	27	(	(	PUNCT
ejpam-3914	488	28	c5	c5	PROPN
ejpam-3914	488	29	)	)	PUNCT
ejpam-3914	488	30	=	=	SYM
ejpam-3914	489	1	2	2	NUM
ejpam-3914	489	2	,	,	PUNCT
ejpam-3914	489	3	that	that	ADV
ejpam-3914	489	4	is	is	ADV
ejpam-3914	489	5	,	,	PUNCT
ejpam-3914	489	6	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3914	489	7	(	(	PUNCT
ejpam-3914	489	8	c5	c5	PROPN
ejpam-3914	489	9	)	)	PUNCT
ejpam-3914	489	10	=	=	SYM
ejpam-3914	490	1	2	2	X
ejpam-3914	490	2	.	.	PUNCT
ejpam-3914	490	3	now	now	ADV
ejpam-3914	490	4	,	,	PUNCT
ejpam-3914	490	5	suppose	suppose	VERB
ejpam-3914	490	6	that	that	SCONJ
ejpam-3914	490	7	n	n	PROPN
ejpam-3914	490	8	>	>	X
ejpam-3914	490	9	5	5	X
ejpam-3914	490	10	.	.	PUNCT
ejpam-3914	490	11	let	let	VERB
ejpam-3914	490	12	p	p	NOUN
ejpam-3914	490	13	=	=	PUNCT
ejpam-3914	490	14	n	n	NUM
ejpam-3914	490	15	5	5	NUM
ejpam-3914	490	16	and	and	CCONJ
ejpam-3914	490	17	j	j	NOUN
ejpam-3914	490	18	=	=	SYM
ejpam-3914	490	19	1	1	NUM
ejpam-3914	490	20	,	,	PUNCT
ejpam-3914	490	21	2	2	NUM
ejpam-3914	490	22	,	,	PUNCT
ejpam-3914	490	23	.	.	PUNCT
ejpam-3914	490	24	.	.	PUNCT
ejpam-3914	491	1	.	.	PUNCT
ejpam-3914	492	1	,	,	PUNCT
ejpam-3914	492	2	p−	p−	NOUN
ejpam-3914	492	3	1	1	NUM
ejpam-3914	492	4	,	,	PUNCT
ejpam-3914	492	5	p.	p.	NOUN
ejpam-3914	492	6	group	group	NOUN
ejpam-3914	492	7	the	the	DET
ejpam-3914	492	8	vertices	vertex	NOUN
ejpam-3914	492	9	of	of	ADP
ejpam-3914	492	10	cn	cn	PROPN
ejpam-3914	492	11	into	into	ADP
ejpam-3914	492	12	p	p	PROPN
ejpam-3914	492	13	disjoint	disjoint	NOUN
ejpam-3914	492	14	subsets	subset	NOUN
ejpam-3914	492	15	rj	rj	PROPN
ejpam-3914	492	16	r1	r1	PROPN
ejpam-3914	492	17	=	=	SYM
ejpam-3914	492	18	{	{	PUNCT
ejpam-3914	492	19	u1	u1	NOUN
ejpam-3914	492	20	,	,	PUNCT
ejpam-3914	492	21	u2	u2	NOUN
ejpam-3914	492	22	,	,	PUNCT
ejpam-3914	492	23	u3	u3	PROPN
ejpam-3914	492	24	,	,	PUNCT
ejpam-3914	492	25	u4	u4	PROPN
ejpam-3914	492	26	,	,	PUNCT
ejpam-3914	492	27	u5	u5	PROPN
ejpam-3914	492	28	}	}	PUNCT
ejpam-3914	492	29	r2	r2	NOUN
ejpam-3914	492	30	=	=	SYM
ejpam-3914	492	31	{	{	PUNCT
ejpam-3914	492	32	u6	u6	PROPN
ejpam-3914	492	33	,	,	PUNCT
ejpam-3914	492	34	u7	u7	PROPN
ejpam-3914	492	35	,	,	PUNCT
ejpam-3914	492	36	u8	u8	PROPN
ejpam-3914	492	37	,	,	PUNCT
ejpam-3914	492	38	u9	u9	PROPN
ejpam-3914	492	39	,	,	PUNCT
ejpam-3914	492	40	u10	u10	PROPN
ejpam-3914	492	41	}	}	PUNCT
ejpam-3914	492	42	r3	r3	PROPN
ejpam-3914	492	43	=	=	SYM
ejpam-3914	492	44	{	{	PUNCT
ejpam-3914	492	45	u11	u11	PROPN
ejpam-3914	492	46	,	,	PUNCT
ejpam-3914	492	47	u12	u12	PROPN
ejpam-3914	492	48	,	,	PUNCT
ejpam-3914	492	49	u13	u13	NOUN
ejpam-3914	492	50	,	,	PUNCT
ejpam-3914	492	51	u14	u14	NOUN
ejpam-3914	492	52	,	,	PUNCT
ejpam-3914	492	53	u15	u15	NOUN
ejpam-3914	492	54	}	}	PUNCT
ejpam-3914	492	55	...	...	PUNCT
ejpam-3914	492	56	rp−1	rp−1	NOUN
ejpam-3914	492	57	=	=	SYM
ejpam-3914	492	58	{	{	PUNCT
ejpam-3914	492	59	un−9	un−9	PROPN
ejpam-3914	492	60	,	,	PUNCT
ejpam-3914	492	61	un−8	un−8	ADJ
ejpam-3914	492	62	,	,	PUNCT
ejpam-3914	492	63	un−7	un−7	PROPN
ejpam-3914	492	64	,	,	PUNCT
ejpam-3914	492	65	un−6	un−6	PROPN
ejpam-3914	492	66	,	,	PUNCT
ejpam-3914	492	67	un−5	un−5	PROPN
ejpam-3914	492	68	}	}	PUNCT
ejpam-3914	492	69	rp	rp	NOUN
ejpam-3914	492	70	=	=	SYM
ejpam-3914	492	71	{	{	PUNCT
ejpam-3914	492	72	un−4	un−4	NOUN
ejpam-3914	492	73	,	,	PUNCT
ejpam-3914	492	74	un−3	un−3	ADJ
ejpam-3914	492	75	,	,	PUNCT
ejpam-3914	492	76	un−2	un−2	PROPN
ejpam-3914	492	77	,	,	PUNCT
ejpam-3914	492	78	un−1	un−1	PROPN
ejpam-3914	492	79	,	,	PUNCT
ejpam-3914	492	80	un	un	ADJ
ejpam-3914	492	81	}	}	PUNCT
ejpam-3914	492	82	let	let	VERB
ejpam-3914	492	83	i	i	PRON
ejpam-3914	492	84	=	=	NOUN
ejpam-3914	492	85	1	1	NUM
ejpam-3914	492	86	,	,	PUNCT
ejpam-3914	492	87	6	6	NUM
ejpam-3914	492	88	,	,	PUNCT
ejpam-3914	492	89	11	11	NUM
ejpam-3914	492	90	,	,	PUNCT
ejpam-3914	492	91	.	.	PUNCT
ejpam-3914	492	92	.	.	PUNCT
ejpam-3914	493	1	.	.	PUNCT
ejpam-3914	494	1	,	,	PUNCT
ejpam-3914	495	1	n	n	CCONJ
ejpam-3914	495	2	−	−	PROPN
ejpam-3914	495	3	4	4	NUM
ejpam-3914	495	4	.	.	PUNCT
ejpam-3914	495	5	for	for	ADP
ejpam-3914	495	6	every	every	DET
ejpam-3914	495	7	induced	induced	ADJ
ejpam-3914	495	8	subgraph	subgraph	NOUN
ejpam-3914	495	9	〈	〈	PROPN
ejpam-3914	495	10	ui	ui	PROPN
ejpam-3914	495	11	,	,	PUNCT
ejpam-3914	495	12	ui+1	ui+1	PROPN
ejpam-3914	495	13	,	,	PUNCT
ejpam-3914	495	14	ui+2	ui+2	NUM
ejpam-3914	495	15	,	,	PUNCT
ejpam-3914	495	16	ui+3	ui+3	NOUN
ejpam-3914	495	17	,	,	PUNCT
ejpam-3914	495	18	ui+4	ui+4	PROPN
ejpam-3914	495	19	〉	〉	NOUN
ejpam-3914	495	20	,	,	PUNCT
ejpam-3914	495	21	the	the	DET
ejpam-3914	495	22	vertices	vertex	NOUN
ejpam-3914	495	23	ui	ui	NOUN
ejpam-3914	495	24	,	,	PUNCT
ejpam-3914	495	25	ui+1	ui+1	PROPN
ejpam-3914	495	26	form	form	VERB
ejpam-3914	495	27	a	a	DET
ejpam-3914	495	28	total	total	ADJ
ejpam-3914	495	29	dr	dr	ADJ
ejpam-3914	495	30	-	-	PUNCT
ejpam-3914	495	31	power	power	NOUN
ejpam-3914	495	32	dominating	dominating	NOUN
ejpam-3914	495	33	set	set	VERB
ejpam-3914	495	34	since	since	SCONJ
ejpam-3914	495	35	ui+2	ui+2	NUM
ejpam-3914	495	36	and	and	CCONJ
ejpam-3914	495	37	ui+4	ui+4	PRON
ejpam-3914	495	38	are	be	AUX
ejpam-3914	495	39	directly	directly	ADV
ejpam-3914	495	40	observed	observe	VERB
ejpam-3914	495	41	vertices	vertex	NOUN
ejpam-3914	495	42	while	while	SCONJ
ejpam-3914	495	43	ui+3	ui+3	NOUN
ejpam-3914	495	44	is	be	AUX
ejpam-3914	495	45	a	a	DET
ejpam-3914	495	46	remotely	remotely	ADV
ejpam-3914	495	47	observed	observe	VERB
ejpam-3914	495	48	vertex	vertex	NOUN
ejpam-3914	495	49	for	for	ADP
ejpam-3914	495	50	all	all	DET
ejpam-3914	495	51	i	i	PRON
ejpam-3914	495	52	=	=	NOUN
ejpam-3914	495	53	1	1	NUM
ejpam-3914	495	54	,	,	PUNCT
ejpam-3914	495	55	6	6	NUM
ejpam-3914	495	56	,	,	PUNCT
ejpam-3914	495	57	11	11	NUM
ejpam-3914	495	58	,	,	PUNCT
ejpam-3914	495	59	.	.	PUNCT
ejpam-3914	495	60	.	.	PUNCT
ejpam-3914	496	1	.	.	PUNCT
ejpam-3914	497	1	,	,	PUNCT
ejpam-3914	497	2	n−9	n−9	PROPN
ejpam-3914	497	3	,	,	PUNCT
ejpam-3914	497	4	n−4	n−4	PROPN
ejpam-3914	497	5	.	.	PUNCT
ejpam-3914	498	1	let	let	VERB
ejpam-3914	498	2	the	the	DET
ejpam-3914	498	3	set	set	NOUN
ejpam-3914	498	4	r	r	NOUN
ejpam-3914	498	5	=	=	PUNCT
ejpam-3914	498	6	{	{	PUNCT
ejpam-3914	498	7	ui	ui	PROPN
ejpam-3914	498	8	,	,	PUNCT
ejpam-3914	498	9	ui+1	ui+1	PROPN
ejpam-3914	498	10	:	:	PUNCT
ejpam-3914	498	11	i	i	NOUN
ejpam-3914	498	12	=	=	NOUN
ejpam-3914	498	13	1	1	NUM
ejpam-3914	498	14	,	,	PUNCT
ejpam-3914	498	15	6	6	NUM
ejpam-3914	498	16	,	,	PUNCT
ejpam-3914	498	17	11	11	NUM
ejpam-3914	498	18	,	,	PUNCT
ejpam-3914	498	19	.	.	PUNCT
ejpam-3914	498	20	.	.	PUNCT
ejpam-3914	499	1	.	.	PUNCT
ejpam-3914	500	1	,	,	PUNCT
ejpam-3914	500	2	n−	n−	NOUN
ejpam-3914	500	3	9	9	NUM
ejpam-3914	500	4	,	,	PUNCT
ejpam-3914	500	5	n−	n−	NOUN
ejpam-3914	500	6	4	4	NUM
ejpam-3914	500	7	}	}	PUNCT
ejpam-3914	500	8	=	=	NOUN
ejpam-3914	500	9	{	{	PUNCT
ejpam-3914	500	10	u1	u1	NOUN
ejpam-3914	500	11	,	,	PUNCT
ejpam-3914	500	12	u2	u2	NOUN
ejpam-3914	500	13	,	,	PUNCT
ejpam-3914	500	14	u6	u6	PROPN
ejpam-3914	500	15	,	,	PUNCT
ejpam-3914	500	16	u7	u7	PROPN
ejpam-3914	500	17	,	,	PUNCT
ejpam-3914	500	18	u11	u11	PROPN
ejpam-3914	500	19	,	,	PUNCT
ejpam-3914	500	20	u12	u12	PROPN
ejpam-3914	500	21	,	,	PUNCT
ejpam-3914	500	22	.	.	PUNCT
ejpam-3914	500	23	.	.	PUNCT
ejpam-3914	501	1	.	.	PUNCT
ejpam-3914	502	1	,	,	PUNCT
ejpam-3914	502	2	un−9	un−9	PROPN
ejpam-3914	502	3	,	,	PUNCT
ejpam-3914	502	4	un−8	un−8	ADJ
ejpam-3914	502	5	,	,	PUNCT
ejpam-3914	502	6	un−4	un−4	NOUN
ejpam-3914	502	7	,	,	PUNCT
ejpam-3914	502	8	un−3	un−3	ADJ
ejpam-3914	502	9	}	}	PUNCT
ejpam-3914	502	10	,	,	PUNCT
ejpam-3914	502	11	where	where	SCONJ
ejpam-3914	502	12	|r|	|r|	NOUN
ejpam-3914	503	1	=	=	NOUN
ejpam-3914	503	2	2p	2p	NOUN
ejpam-3914	503	3	=	=	SYM
ejpam-3914	503	4	2(n	2(n	NUM
ejpam-3914	503	5	5	5	NUM
ejpam-3914	503	6	)	)	PUNCT
ejpam-3914	503	7	=	=	SYM
ejpam-3914	503	8	2n	2n	NUM
ejpam-3914	503	9	5	5	NUM
ejpam-3914	503	10	,	,	PUNCT
ejpam-3914	503	11	or	or	CCONJ
ejpam-3914	503	12	v	v	NOUN
ejpam-3914	503	13	(	(	PUNCT
ejpam-3914	503	14	cn	cn	PROPN
ejpam-3914	503	15	)	)	PUNCT
ejpam-3914	503	16	=	=	NOUN
ejpam-3914	503	17	v	v	X
ejpam-3914	503	18	(	(	PUNCT
ejpam-3914	503	19	cn	cn	PROPN
ejpam-3914	503	20	)	)	PUNCT
ejpam-3914	503	21	,	,	PUNCT
ejpam-3914	503	22	or	or	CCONJ
ejpam-3914	503	23	e(cn	e(cn	NOUN
ejpam-3914	503	24	)	)	PUNCT
ejpam-3914	503	25	=	=	SYM
ejpam-3914	503	26	e(cn	e(cn	NOUN
ejpam-3914	503	27	)	)	PUNCT
ejpam-3914	503	28	,	,	PUNCT
ejpam-3914	503	29	and	and	CCONJ
ejpam-3914	503	30	the	the	DET
ejpam-3914	503	31	induced	induced	ADJ
ejpam-3914	503	32	subgraph	subgraph	NOUN
ejpam-3914	503	33	〈	〈	PROPN
ejpam-3914	503	34	r	r	PROPN
ejpam-3914	503	35	〉	〉	PROPN
ejpam-3914	503	36	has	have	VERB
ejpam-3914	503	37	no	no	DET
ejpam-3914	503	38	isolated	isolated	ADJ
ejpam-3914	503	39	vertex	vertex	NOUN
ejpam-3914	503	40	.	.	PUNCT
ejpam-3914	504	1	by	by	ADP
ejpam-3914	504	2	theorem	theorem	NOUN
ejpam-3914	504	3	2.3	2.3	NUM
ejpam-3914	504	4	,	,	PUNCT
ejpam-3914	504	5	r	r	NOUN
ejpam-3914	504	6	is	be	AUX
ejpam-3914	504	7	a	a	DET
ejpam-3914	504	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	504	9	-set	-set	PROPN
ejpam-3914	504	10	of	of	ADP
ejpam-3914	504	11	cn	cn	PROPN
ejpam-3914	504	12	.	.	PUNCT
ejpam-3914	505	1	let	let	VERB
ejpam-3914	505	2	m+	m+	PRON
ejpam-3914	505	3	1	1	NUM
ejpam-3914	505	4	be	be	AUX
ejpam-3914	505	5	the	the	DET
ejpam-3914	505	6	number	number	NOUN
ejpam-3914	505	7	of	of	ADP
ejpam-3914	505	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	505	9	-sets	-set	NOUN
ejpam-3914	505	10	of	of	ADP
ejpam-3914	505	11	cn	cn	PROPN
ejpam-3914	505	12	where	where	SCONJ
ejpam-3914	505	13	m	m	PROPN
ejpam-3914	505	14	is	be	AUX
ejpam-3914	505	15	a	a	DET
ejpam-3914	505	16	positive	positive	ADJ
ejpam-3914	505	17	integer	integer	NOUN
ejpam-3914	505	18	.	.	PUNCT
ejpam-3914	506	1	let	let	VERB
ejpam-3914	506	2	k	k	NOUN
ejpam-3914	506	3	=	=	SYM
ejpam-3914	506	4	1	1	NUM
ejpam-3914	506	5	,	,	PUNCT
ejpam-3914	506	6	2	2	NUM
ejpam-3914	506	7	,	,	PUNCT
ejpam-3914	506	8	.	.	PUNCT
ejpam-3914	506	9	.	.	PUNCT
ejpam-3914	507	1	.	.	PUNCT
ejpam-3914	508	1	,	,	PUNCT
ejpam-3914	508	2	m	m	VERB
ejpam-3914	508	3	and	and	CCONJ
ejpam-3914	508	4	tk	tk	PROPN
ejpam-3914	508	5	be	be	AUX
ejpam-3914	508	6	a	a	DET
ejpam-3914	508	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	508	8	-set	-set	PUNCT
ejpam-3914	508	9	of	of	ADP
ejpam-3914	508	10	cn	cn	PROPN
ejpam-3914	508	11	different	different	ADJ
ejpam-3914	508	12	from	from	ADP
ejpam-3914	508	13	r.	r.	PROPN
ejpam-3914	508	14	note	note	PROPN
ejpam-3914	508	15	that	that	SCONJ
ejpam-3914	508	16	tk	tk	PROPN
ejpam-3914	508	17	can	can	AUX
ejpam-3914	508	18	be	be	AUX
ejpam-3914	508	19	formed	form	VERB
ejpam-3914	508	20	by	by	ADP
ejpam-3914	508	21	starting	start	VERB
ejpam-3914	508	22	all	all	DET
ejpam-3914	508	23	the	the	DET
ejpam-3914	508	24	vertices	vertex	NOUN
ejpam-3914	508	25	of	of	ADP
ejpam-3914	508	26	sl	sl	NOUN
ejpam-3914	508	27	for	for	ADP
ejpam-3914	508	28	l	l	NOUN
ejpam-3914	508	29	=	=	SYM
ejpam-3914	508	30	1	1	NUM
ejpam-3914	508	31	,	,	PUNCT
ejpam-3914	508	32	2	2	NUM
ejpam-3914	508	33	,	,	PUNCT
ejpam-3914	508	34	.	.	PUNCT
ejpam-3914	508	35	.	.	PUNCT
ejpam-3914	509	1	.	.	PUNCT
ejpam-3914	510	1	,	,	PUNCT
ejpam-3914	510	2	5	5	NUM
ejpam-3914	510	3	and	and	CCONJ
ejpam-3914	510	4	replacing	replace	VERB
ejpam-3914	510	5	u5	u5	NOUN
ejpam-3914	510	6	by	by	ADP
ejpam-3914	510	7	un	un	PROPN
ejpam-3914	510	8	in	in	ADP
ejpam-3914	510	9	s5	s5	PROPN
ejpam-3914	510	10	.	.	PUNCT
ejpam-3914	511	1	now	now	ADV
ejpam-3914	511	2	,	,	PUNCT
ejpam-3914	511	3	if	if	SCONJ
ejpam-3914	511	4	tk	tk	PROPN
ejpam-3914	511	5	starts	start	VERB
ejpam-3914	511	6	with	with	ADP
ejpam-3914	511	7	s1	s1	NOUN
ejpam-3914	511	8	,	,	PUNCT
ejpam-3914	511	9	then	then	ADV
ejpam-3914	511	10	let	let	VERB
ejpam-3914	511	11	k	k	NOUN
ejpam-3914	511	12	=	=	SYM
ejpam-3914	511	13	1	1	NUM
ejpam-3914	511	14	and	and	CCONJ
ejpam-3914	511	15	{	{	PUNCT
ejpam-3914	511	16	u1	u1	NOUN
ejpam-3914	511	17	,	,	PUNCT
ejpam-3914	511	18	u2	u2	PROPN
ejpam-3914	511	19	}	}	PUNCT
ejpam-3914	511	20	⊆	⊆	NUM
ejpam-3914	511	21	t1	t1	NOUN
ejpam-3914	511	22	.	.	PUNCT
ejpam-3914	512	1	replace	replace	VERB
ejpam-3914	512	2	u6	u6	NOUN
ejpam-3914	512	3	∈	∈	NOUN
ejpam-3914	512	4	r	r	NOUN
ejpam-3914	512	5	by	by	ADP
ejpam-3914	512	6	u5	u5	PROPN
ejpam-3914	512	7	to	to	PART
ejpam-3914	512	8	form	form	VERB
ejpam-3914	512	9	t1	t1	PROPN
ejpam-3914	512	10	.	.	PUNCT
ejpam-3914	513	1	then	then	ADV
ejpam-3914	513	2	the	the	DET
ejpam-3914	513	3	next	next	ADJ
ejpam-3914	513	4	vertex	vertex	NOUN
ejpam-3914	513	5	to	to	PART
ejpam-3914	513	6	be	be	AUX
ejpam-3914	513	7	choosen	choosen	VERB
ejpam-3914	513	8	must	must	AUX
ejpam-3914	513	9	be	be	AUX
ejpam-3914	513	10	u6	u6	ADJ
ejpam-3914	513	11	,	,	PUNCT
ejpam-3914	513	12	that	that	ADV
ejpam-3914	513	13	is	is	ADV
ejpam-3914	513	14	,	,	PUNCT
ejpam-3914	513	15	the	the	DET
ejpam-3914	513	16	vertex	vertex	NOUN
ejpam-3914	513	17	ui+4	ui+4	PROPN
ejpam-3914	513	18	,	,	PUNCT
ejpam-3914	513	19	ui	ui	PROPN
ejpam-3914	513	20	must	must	AUX
ejpam-3914	513	21	be	be	AUX
ejpam-3914	513	22	in	in	ADP
ejpam-3914	513	23	t1	t1	NOUN
ejpam-3914	513	24	for	for	ADP
ejpam-3914	513	25	all	all	DET
ejpam-3914	513	26	i	i	PRON
ejpam-3914	513	27	=	=	NOUN
ejpam-3914	513	28	1	1	NUM
ejpam-3914	513	29	,	,	PUNCT
ejpam-3914	513	30	6	6	NUM
ejpam-3914	513	31	,	,	PUNCT
ejpam-3914	513	32	11	11	NUM
ejpam-3914	513	33	,	,	PUNCT
ejpam-3914	513	34	.	.	PUNCT
ejpam-3914	513	35	.	.	PUNCT
ejpam-3914	514	1	.	.	PUNCT
ejpam-3914	515	1	,	,	PUNCT
ejpam-3914	515	2	n	n	CCONJ
ejpam-3914	515	3	−	−	PROPN
ejpam-3914	515	4	9	9	NUM
ejpam-3914	515	5	,	,	PUNCT
ejpam-3914	515	6	n	n	CCONJ
ejpam-3914	515	7	−	−	PROPN
ejpam-3914	515	8	4	4	NUM
ejpam-3914	515	9	.	.	PUNCT
ejpam-3914	516	1	it	it	PRON
ejpam-3914	516	2	follows	follow	VERB
ejpam-3914	516	3	that	that	PRON
ejpam-3914	516	4	t1	t1	NOUN
ejpam-3914	516	5	=	=	PUNCT
ejpam-3914	516	6	{	{	PUNCT
ejpam-3914	516	7	u1	u1	NOUN
ejpam-3914	516	8	,	,	PUNCT
ejpam-3914	516	9	u2	u2	PROPN
ejpam-3914	516	10	,	,	PUNCT
ejpam-3914	516	11	u5	u5	PROPN
ejpam-3914	516	12	,	,	PUNCT
ejpam-3914	516	13	u6	u6	PROPN
ejpam-3914	516	14	,	,	PUNCT
ejpam-3914	516	15	u10	u10	PROPN
ejpam-3914	516	16	,	,	PUNCT
ejpam-3914	516	17	u11	u11	PROPN
ejpam-3914	516	18	,	,	PUNCT
ejpam-3914	516	19	u15	u15	NOUN
ejpam-3914	516	20	,	,	PUNCT
ejpam-3914	516	21	u16	u16	NOUN
ejpam-3914	516	22	,	,	PUNCT
ejpam-3914	516	23	.	.	PUNCT
ejpam-3914	516	24	.	.	PUNCT
ejpam-3914	517	1	.	.	PUNCT
ejpam-3914	518	1	,	,	PUNCT
ejpam-3914	519	1	un−5	un−5	PROPN
ejpam-3914	519	2	,	,	PUNCT
ejpam-3914	519	3	un−4	un−4	NOUN
ejpam-3914	519	4	}	}	PUNCT
ejpam-3914	519	5	such	such	ADJ
ejpam-3914	519	6	that	that	DET
ejpam-3914	519	7	|t1|	|t1|	NOUN
ejpam-3914	519	8	=	=	SYM
ejpam-3914	519	9	|r|	|r|	PROPN
ejpam-3914	519	10	.	.	PUNCT
ejpam-3914	520	1	since	since	SCONJ
ejpam-3914	520	2	u1	u1	PROPN
ejpam-3914	520	3	∈	∈	PROPN
ejpam-3914	520	4	t1	t1	NOUN
ejpam-3914	520	5	and	and	CCONJ
ejpam-3914	520	6	un−4	un−4	NOUN
ejpam-3914	520	7	is	be	AUX
ejpam-3914	520	8	the	the	DET
ejpam-3914	520	9	last	last	ADJ
ejpam-3914	520	10	vertex	vertex	NOUN
ejpam-3914	520	11	in	in	ADP
ejpam-3914	520	12	t1	t1	PROPN
ejpam-3914	520	13	,	,	PUNCT
ejpam-3914	520	14	by	by	ADP
ejpam-3914	520	15	the	the	DET
ejpam-3914	520	16	same	same	ADJ
ejpam-3914	520	17	argument	argument	NOUN
ejpam-3914	520	18	in	in	ADP
ejpam-3914	520	19	case	case	NOUN
ejpam-3914	520	20	1	1	NUM
ejpam-3914	520	21	,	,	PUNCT
ejpam-3914	520	22	t1	t1	PROPN
ejpam-3914	520	23	is	be	AUX
ejpam-3914	520	24	not	not	PART
ejpam-3914	520	25	a	a	DET
ejpam-3914	520	26	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	520	27	-set	-set	PROPN
ejpam-3914	520	28	of	of	ADP
ejpam-3914	520	29	cn	cn	PROPN
ejpam-3914	520	30	.	.	PUNCT
ejpam-3914	521	1	since	since	SCONJ
ejpam-3914	521	2	u6	u6	PROPN
ejpam-3914	521	3	is	be	AUX
ejpam-3914	521	4	arbitrarily	arbitrarily	ADV
ejpam-3914	521	5	replaced	replace	VERB
ejpam-3914	521	6	from	from	ADP
ejpam-3914	521	7	r	r	NOUN
ejpam-3914	521	8	,	,	PUNCT
ejpam-3914	521	9	we	we	PRON
ejpam-3914	521	10	can	can	AUX
ejpam-3914	521	11	not	not	PART
ejpam-3914	521	12	replace	replace	VERB
ejpam-3914	521	13	the	the	DET
ejpam-3914	521	14	vertex	vertex	NOUN
ejpam-3914	521	15	ui	ui	NOUN
ejpam-3914	521	16	in	in	ADP
ejpam-3914	521	17	r	r	NOUN
ejpam-3914	521	18	,	,	PUNCT
ejpam-3914	521	19	where	where	SCONJ
ejpam-3914	521	20	i	i	PRON
ejpam-3914	521	21	=	=	NOUN
ejpam-3914	521	22	6	6	NUM
ejpam-3914	521	23	,	,	PUNCT
ejpam-3914	521	24	11	11	NUM
ejpam-3914	521	25	,	,	PUNCT
ejpam-3914	521	26	.	.	PUNCT
ejpam-3914	521	27	.	.	PUNCT
ejpam-3914	522	1	.	.	PUNCT
ejpam-3914	523	1	,	,	PUNCT
ejpam-3914	523	2	n−	n−	NOUN
ejpam-3914	523	3	9	9	NUM
ejpam-3914	523	4	,	,	PUNCT
ejpam-3914	523	5	n−	n−	NOUN
ejpam-3914	523	6	4	4	NUM
ejpam-3914	523	7	to	to	PART
ejpam-3914	523	8	form	form	VERB
ejpam-3914	523	9	another	another	PRON
ejpam-3914	523	10	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	523	11	-set	-set	PROPN
ejpam-3914	523	12	of	of	ADP
ejpam-3914	523	13	cn	cn	PROPN
ejpam-3914	523	14	.	.	PUNCT
ejpam-3914	523	15	therefore	therefore	ADV
ejpam-3914	523	16	,	,	PUNCT
ejpam-3914	523	17	only	only	ADV
ejpam-3914	523	18	the	the	DET
ejpam-3914	523	19	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	523	20	-set	-set	PUNCT
ejpam-3914	523	21	r	r	NOUN
ejpam-3914	523	22	starts	start	VERB
ejpam-3914	523	23	with	with	ADP
ejpam-3914	523	24	s1	s1	NOUN
ejpam-3914	523	25	and	and	CCONJ
ejpam-3914	523	26	so	so	ADV
ejpam-3914	523	27	,	,	PUNCT
ejpam-3914	523	28	{	{	PUNCT
ejpam-3914	523	29	u1	u1	NOUN
ejpam-3914	523	30	,	,	PUNCT
ejpam-3914	523	31	u2	u2	PROPN
ejpam-3914	523	32	}	}	PUNCT
ejpam-3914	523	33	*	*	PUNCT
ejpam-3914	523	34	tk	tk	PROPN
ejpam-3914	523	35	for	for	ADP
ejpam-3914	523	36	all	all	PRON
ejpam-3914	523	37	k	k	NOUN
ejpam-3914	523	38	=	=	SYM
ejpam-3914	523	39	1	1	NUM
ejpam-3914	523	40	,	,	PUNCT
ejpam-3914	523	41	2	2	NUM
ejpam-3914	523	42	,	,	PUNCT
ejpam-3914	523	43	.	.	PUNCT
ejpam-3914	523	44	.	.	PUNCT
ejpam-3914	523	45	.	.	PUNCT
ejpam-3914	524	1	,	,	PUNCT
ejpam-3914	524	2	m.	m.	NOUN
ejpam-3914	524	3	hence	hence	ADV
ejpam-3914	524	4	,	,	PUNCT
ejpam-3914	524	5	{	{	PUNCT
ejpam-3914	524	6	u1	u1	NOUN
ejpam-3914	524	7	,	,	PUNCT
ejpam-3914	524	8	u2	u2	PROPN
ejpam-3914	524	9	}	}	PUNCT
ejpam-3914	524	10	is	be	AUX
ejpam-3914	524	11	a	a	DET
ejpam-3914	524	12	forcing	forcing	NOUN
ejpam-3914	524	13	subset	subset	NOUN
ejpam-3914	524	14	for	for	ADP
ejpam-3914	524	15	r.	r.	PROPN
ejpam-3914	524	16	therefore	therefore	ADV
ejpam-3914	524	17	,	,	PUNCT
ejpam-3914	524	18	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	524	19	(	(	PUNCT
ejpam-3914	524	20	r	r	NOUN
ejpam-3914	524	21	)	)	PUNCT
ejpam-3914	524	22	=	=	SYM
ejpam-3914	525	1	2	2	NUM
ejpam-3914	525	2	=	=	NOUN
ejpam-3914	525	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	525	4	(	(	PUNCT
ejpam-3914	525	5	cn	cn	NOUN
ejpam-3914	525	6	)	)	PUNCT
ejpam-3914	525	7	.	.	PUNCT
ejpam-3914	526	1	case	case	NOUN
ejpam-3914	526	2	3	3	X
ejpam-3914	526	3	:	:	PUNCT
ejpam-3914	526	4	suppose	suppose	VERB
ejpam-3914	526	5	that	that	SCONJ
ejpam-3914	526	6	n	n	NUM
ejpam-3914	526	7	≡	≡	PROPN
ejpam-3914	526	8	1(mod	1(mod	NUM
ejpam-3914	526	9	5	5	NUM
ejpam-3914	526	10	)	)	PUNCT
ejpam-3914	526	11	.	.	PUNCT
ejpam-3914	527	1	by	by	ADP
ejpam-3914	527	2	theorem	theorem	NOUN
ejpam-3914	527	3	2.3	2.3	NUM
ejpam-3914	527	4	,	,	PUNCT
ejpam-3914	527	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	527	6	(	(	PUNCT
ejpam-3914	527	7	cn	cn	NOUN
ejpam-3914	527	8	)	)	PUNCT
ejpam-3914	527	9	=	=	SYM
ejpam-3914	527	10	2n+3	2n+3	NOUN
ejpam-3914	527	11	5	5	NUM
ejpam-3914	527	12	.	.	PUNCT
ejpam-3914	527	13	suppose	suppose	VERB
ejpam-3914	527	14	that	that	SCONJ
ejpam-3914	527	15	n	n	PROPN
ejpam-3914	527	16	=	=	SYM
ejpam-3914	527	17	6	6	NUM
ejpam-3914	527	18	.	.	PUNCT
ejpam-3914	528	1	then	then	ADV
ejpam-3914	528	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	528	3	(	(	PUNCT
ejpam-3914	528	4	c6	c6	PROPN
ejpam-3914	528	5	)	)	PUNCT
ejpam-3914	528	6	=	=	SYM
ejpam-3914	528	7	2(6)+3	2(6)+3	NUM
ejpam-3914	528	8	5	5	NUM
ejpam-3914	528	9	=	=	SYM
ejpam-3914	528	10	3	3	X
ejpam-3914	528	11	.	.	PUNCT
ejpam-3914	529	1	clearly	clearly	ADV
ejpam-3914	529	2	,	,	PUNCT
ejpam-3914	529	3	s1	s1	PROPN
ejpam-3914	529	4	=	=	SYM
ejpam-3914	529	5	{	{	PUNCT
ejpam-3914	529	6	u1	u1	NOUN
ejpam-3914	529	7	,	,	PUNCT
ejpam-3914	529	8	u2	u2	NOUN
ejpam-3914	529	9	,	,	PUNCT
ejpam-3914	529	10	u3	u3	NOUN
ejpam-3914	529	11	}	}	PUNCT
ejpam-3914	529	12	,	,	PUNCT
ejpam-3914	529	13	s2	s2	X
ejpam-3914	529	14	=	=	SYM
ejpam-3914	529	15	{	{	PUNCT
ejpam-3914	529	16	u2	u2	PROPN
ejpam-3914	529	17	,	,	PUNCT
ejpam-3914	529	18	u3	u3	NOUN
ejpam-3914	529	19	,	,	PUNCT
ejpam-3914	529	20	u4	u4	PROPN
ejpam-3914	529	21	}	}	PUNCT
ejpam-3914	529	22	,	,	PUNCT
ejpam-3914	529	23	s3	s3	PROPN
ejpam-3914	529	24	=	=	SYM
ejpam-3914	529	25	{	{	PUNCT
ejpam-3914	529	26	u3	u3	PROPN
ejpam-3914	529	27	,	,	PUNCT
ejpam-3914	529	28	u4	u4	PROPN
ejpam-3914	529	29	,	,	PUNCT
ejpam-3914	529	30	u5	u5	PROPN
ejpam-3914	529	31	}	}	PUNCT
ejpam-3914	529	32	,	,	PUNCT
ejpam-3914	529	33	s4	s4	PROPN
ejpam-3914	529	34	=	=	SYM
ejpam-3914	529	35	{	{	PUNCT
ejpam-3914	529	36	u4	u4	PROPN
ejpam-3914	529	37	,	,	PUNCT
ejpam-3914	529	38	u5	u5	PROPN
ejpam-3914	529	39	,	,	PUNCT
ejpam-3914	529	40	u6	u6	NOUN
ejpam-3914	529	41	}	}	PUNCT
ejpam-3914	529	42	,	,	PUNCT
ejpam-3914	529	43	s5	s5	X
ejpam-3914	529	44	=	=	PUNCT
ejpam-3914	529	45	{	{	PUNCT
ejpam-3914	529	46	u5	u5	PROPN
ejpam-3914	529	47	,	,	PUNCT
ejpam-3914	529	48	u6	u6	NOUN
ejpam-3914	529	49	,	,	PUNCT
ejpam-3914	529	50	u1	u1	NOUN
ejpam-3914	529	51	}	}	PUNCT
ejpam-3914	529	52	,	,	PUNCT
ejpam-3914	529	53	s6	s6	PROPN
ejpam-3914	529	54	=	=	SYM
ejpam-3914	529	55	{	{	PUNCT
ejpam-3914	529	56	u6	u6	PROPN
ejpam-3914	529	57	,	,	PUNCT
ejpam-3914	529	58	u1	u1	NOUN
ejpam-3914	529	59	,	,	PUNCT
ejpam-3914	529	60	u2	u2	PROPN
ejpam-3914	529	61	}	}	PUNCT
ejpam-3914	529	62	,	,	PUNCT
ejpam-3914	529	63	are	be	AUX
ejpam-3914	529	64	the	the	DET
ejpam-3914	529	65	only	only	ADJ
ejpam-3914	529	66	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	529	67	-sets	-set	NOUN
ejpam-3914	529	68	of	of	ADP
ejpam-3914	529	69	c6	c6	PROPN
ejpam-3914	529	70	.	.	PUNCT
ejpam-3914	530	1	clearly	clearly	ADV
ejpam-3914	530	2	,	,	PUNCT
ejpam-3914	530	3	for	for	ADP
ejpam-3914	530	4	l	l	NOUN
ejpam-3914	530	5	=	=	SYM
ejpam-3914	530	6	1	1	NUM
ejpam-3914	530	7	,	,	PUNCT
ejpam-3914	530	8	2	2	NUM
ejpam-3914	530	9	,	,	PUNCT
ejpam-3914	530	10	.	.	PUNCT
ejpam-3914	530	11	.	.	PUNCT
ejpam-3914	530	12	.	.	PUNCT
ejpam-3914	531	1	,	,	PUNCT
ejpam-3914	531	2	6	6	NUM
ejpam-3914	531	3	,	,	PUNCT
ejpam-3914	531	4	{	{	PUNCT
ejpam-3914	531	5	u1	u1	NOUN
ejpam-3914	531	6	,	,	PUNCT
ejpam-3914	531	7	u3	u3	NOUN
ejpam-3914	531	8	}	}	PUNCT
ejpam-3914	531	9	⊆	⊆	NUM
ejpam-3914	531	10	s1	s1	NOUN
ejpam-3914	531	11	and	and	CCONJ
ejpam-3914	531	12	{	{	PUNCT
ejpam-3914	531	13	u1	u1	NOUN
ejpam-3914	531	14	,	,	PUNCT
ejpam-3914	531	15	u3	u3	NOUN
ejpam-3914	531	16	}	}	PUNCT
ejpam-3914	531	17	*	*	PUNCT
ejpam-3914	531	18	sl	sl	INTJ
ejpam-3914	531	19	for	for	ADP
ejpam-3914	531	20	all	all	DET
ejpam-3914	531	21	l	l	NOUN
ejpam-3914	531	22	6=	6=	NUM
ejpam-3914	531	23	1	1	NUM
ejpam-3914	531	24	.	.	PUNCT
ejpam-3914	532	1	thus	thus	ADV
ejpam-3914	532	2	,	,	PUNCT
ejpam-3914	532	3	{	{	PUNCT
ejpam-3914	532	4	u1	u1	NOUN
ejpam-3914	532	5	,	,	PUNCT
ejpam-3914	532	6	u3	u3	PROPN
ejpam-3914	532	7	}	}	PUNCT
ejpam-3914	532	8	is	be	AUX
ejpam-3914	532	9	a	a	DET
ejpam-3914	532	10	forcing	forcing	NOUN
ejpam-3914	532	11	subset	subset	NOUN
ejpam-3914	532	12	for	for	ADP
ejpam-3914	532	13	s1	s1	NOUN
ejpam-3914	532	14	,	,	PUNCT
ejpam-3914	532	15	that	that	ADV
ejpam-3914	532	16	is	is	ADV
ejpam-3914	532	17	,	,	PUNCT
ejpam-3914	532	18	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	532	19	(	(	PUNCT
ejpam-3914	532	20	s1	s1	NOUN
ejpam-3914	532	21	)	)	PUNCT
ejpam-3914	532	22	=	=	SYM
ejpam-3914	533	1	2	2	NUM
ejpam-3914	533	2	=	=	NOUN
ejpam-3914	533	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	533	4	(	(	PUNCT
ejpam-3914	533	5	c6	c6	PROPN
ejpam-3914	533	6	)	)	PUNCT
ejpam-3914	533	7	.	.	PUNCT
ejpam-3914	534	1	now	now	ADV
ejpam-3914	534	2	,	,	PUNCT
ejpam-3914	534	3	suppose	suppose	VERB
ejpam-3914	534	4	that	that	SCONJ
ejpam-3914	534	5	n	n	PROPN
ejpam-3914	534	6	>	>	X
ejpam-3914	534	7	6	6	NUM
ejpam-3914	534	8	.	.	PUNCT
ejpam-3914	535	1	let	let	VERB
ejpam-3914	535	2	p	p	NOUN
ejpam-3914	535	3	=	=	PUNCT
ejpam-3914	535	4	n−1	n−1	PROPN
ejpam-3914	535	5	5	5	NUM
ejpam-3914	535	6	and	and	CCONJ
ejpam-3914	535	7	j	j	NOUN
ejpam-3914	535	8	=	=	SYM
ejpam-3914	535	9	0	0	NUM
ejpam-3914	535	10	,	,	PUNCT
ejpam-3914	535	11	1	1	NUM
ejpam-3914	535	12	,	,	PUNCT
ejpam-3914	535	13	2	2	NUM
ejpam-3914	535	14	,	,	PUNCT
ejpam-3914	535	15	.	.	PUNCT
ejpam-3914	535	16	.	.	PUNCT
ejpam-3914	536	1	.	.	PUNCT
ejpam-3914	537	1	,	,	PUNCT
ejpam-3914	537	2	p−	p−	NOUN
ejpam-3914	537	3	1	1	NUM
ejpam-3914	537	4	,	,	PUNCT
ejpam-3914	537	5	p.	p.	NOUN
ejpam-3914	537	6	group	group	NOUN
ejpam-3914	537	7	the	the	DET
ejpam-3914	537	8	vertices	vertex	NOUN
ejpam-3914	537	9	of	of	ADP
ejpam-3914	537	10	cn	cn	PROPN
ejpam-3914	537	11	into	into	ADP
ejpam-3914	537	12	p+	p+	NOUN
ejpam-3914	537	13	1	1	NUM
ejpam-3914	537	14	disjoint	disjoint	NOUN
ejpam-3914	537	15	subsets	subset	NOUN
ejpam-3914	537	16	rj	rj	PROPN
ejpam-3914	537	17	c.	c.	PROPN
ejpam-3914	537	18	armada	armada	PROPN
ejpam-3914	537	19	/	/	SYM
ejpam-3914	537	20	eur	eur	PROPN
ejpam-3914	537	21	.	.	PUNCT
ejpam-3914	538	1	j.	j.	PROPN
ejpam-3914	538	2	pure	pure	PROPN
ejpam-3914	538	3	appl	appl	PROPN
ejpam-3914	538	4	.	.	PROPN
ejpam-3914	538	5	math	math	PROPN
ejpam-3914	538	6	,	,	PUNCT
ejpam-3914	538	7	14	14	NUM
ejpam-3914	538	8	(	(	PUNCT
ejpam-3914	538	9	2	2	NUM
ejpam-3914	538	10	)	)	PUNCT
ejpam-3914	538	11	(	(	PUNCT
ejpam-3914	538	12	2021	2021	NUM
ejpam-3914	538	13	)	)	PUNCT
ejpam-3914	538	14	,	,	PUNCT
ejpam-3914	538	15	451	451	NUM
ejpam-3914	538	16	-	-	SYM
ejpam-3914	538	17	470	470	NUM
ejpam-3914	538	18	465	465	NUM
ejpam-3914	538	19	r0	r0	NOUN
ejpam-3914	538	20	=	=	SYM
ejpam-3914	538	21	{	{	PUNCT
ejpam-3914	538	22	u1	u1	NOUN
ejpam-3914	538	23	}	}	PUNCT
ejpam-3914	538	24	r1	r1	NOUN
ejpam-3914	538	25	=	=	SYM
ejpam-3914	538	26	{	{	PUNCT
ejpam-3914	538	27	u2	u2	PROPN
ejpam-3914	538	28	,	,	PUNCT
ejpam-3914	538	29	u3	u3	PROPN
ejpam-3914	538	30	,	,	PUNCT
ejpam-3914	538	31	u4	u4	PROPN
ejpam-3914	538	32	,	,	PUNCT
ejpam-3914	538	33	u5	u5	PROPN
ejpam-3914	538	34	,	,	PUNCT
ejpam-3914	538	35	u6	u6	NOUN
ejpam-3914	538	36	}	}	PUNCT
ejpam-3914	538	37	r2	r2	NOUN
ejpam-3914	538	38	=	=	SYM
ejpam-3914	538	39	{	{	PUNCT
ejpam-3914	538	40	u7	u7	PROPN
ejpam-3914	538	41	,	,	PUNCT
ejpam-3914	538	42	u8	u8	PROPN
ejpam-3914	538	43	,	,	PUNCT
ejpam-3914	538	44	u9	u9	PROPN
ejpam-3914	538	45	,	,	PUNCT
ejpam-3914	538	46	u10	u10	PROPN
ejpam-3914	538	47	,	,	PUNCT
ejpam-3914	538	48	u11	u11	ADJ
ejpam-3914	538	49	}	}	PUNCT
ejpam-3914	538	50	r3	r3	PROPN
ejpam-3914	538	51	=	=	SYM
ejpam-3914	538	52	{	{	PUNCT
ejpam-3914	538	53	u12	u12	PROPN
ejpam-3914	538	54	,	,	PUNCT
ejpam-3914	538	55	u13	u13	NOUN
ejpam-3914	538	56	,	,	PUNCT
ejpam-3914	538	57	u14	u14	NOUN
ejpam-3914	538	58	,	,	PUNCT
ejpam-3914	538	59	u15	u15	NOUN
ejpam-3914	538	60	,	,	PUNCT
ejpam-3914	538	61	u16	u16	NOUN
ejpam-3914	538	62	}	}	PUNCT
ejpam-3914	538	63	...	...	PUNCT
ejpam-3914	539	1	rp−1	rp−1	NOUN
ejpam-3914	539	2	=	=	SYM
ejpam-3914	539	3	{	{	PUNCT
ejpam-3914	539	4	un−9	un−9	PROPN
ejpam-3914	539	5	,	,	PUNCT
ejpam-3914	539	6	un−8	un−8	ADJ
ejpam-3914	539	7	,	,	PUNCT
ejpam-3914	539	8	un−7	un−7	PROPN
ejpam-3914	539	9	,	,	PUNCT
ejpam-3914	539	10	un−6	un−6	PROPN
ejpam-3914	539	11	,	,	PUNCT
ejpam-3914	539	12	un−5	un−5	PROPN
ejpam-3914	539	13	}	}	PUNCT
ejpam-3914	539	14	rp	rp	NOUN
ejpam-3914	539	15	=	=	SYM
ejpam-3914	539	16	{	{	PUNCT
ejpam-3914	539	17	un−4	un−4	NOUN
ejpam-3914	539	18	,	,	PUNCT
ejpam-3914	539	19	un−3	un−3	ADJ
ejpam-3914	539	20	,	,	PUNCT
ejpam-3914	539	21	un−2	un−2	PROPN
ejpam-3914	539	22	,	,	PUNCT
ejpam-3914	539	23	un−1	un−1	PROPN
ejpam-3914	539	24	,	,	PUNCT
ejpam-3914	539	25	un	un	ADJ
ejpam-3914	539	26	}	}	PUNCT
ejpam-3914	539	27	let	let	VERB
ejpam-3914	539	28	i	i	PRON
ejpam-3914	539	29	=	=	NOUN
ejpam-3914	539	30	2	2	NUM
ejpam-3914	539	31	,	,	PUNCT
ejpam-3914	539	32	7	7	NUM
ejpam-3914	539	33	,	,	PUNCT
ejpam-3914	539	34	12	12	NUM
ejpam-3914	539	35	,	,	PUNCT
ejpam-3914	539	36	.	.	PUNCT
ejpam-3914	539	37	.	.	PUNCT
ejpam-3914	540	1	.	.	PUNCT
ejpam-3914	541	1	,	,	PUNCT
ejpam-3914	542	1	n	n	CCONJ
ejpam-3914	542	2	−	−	PROPN
ejpam-3914	542	3	4	4	NUM
ejpam-3914	542	4	.	.	PUNCT
ejpam-3914	542	5	for	for	ADP
ejpam-3914	542	6	every	every	DET
ejpam-3914	542	7	induced	induced	ADJ
ejpam-3914	542	8	subgraph	subgraph	NOUN
ejpam-3914	542	9	〈	〈	PROPN
ejpam-3914	542	10	ui	ui	PROPN
ejpam-3914	542	11	,	,	PUNCT
ejpam-3914	542	12	ui+1	ui+1	PROPN
ejpam-3914	542	13	,	,	PUNCT
ejpam-3914	542	14	ui+2	ui+2	NUM
ejpam-3914	542	15	,	,	PUNCT
ejpam-3914	542	16	ui+3	ui+3	NOUN
ejpam-3914	542	17	,	,	PUNCT
ejpam-3914	542	18	ui+4	ui+4	PROPN
ejpam-3914	542	19	〉	〉	NOUN
ejpam-3914	542	20	,	,	PUNCT
ejpam-3914	542	21	the	the	DET
ejpam-3914	542	22	vertices	vertex	NOUN
ejpam-3914	542	23	u1	u1	NOUN
ejpam-3914	542	24	,	,	PUNCT
ejpam-3914	542	25	ui	ui	NOUN
ejpam-3914	542	26	,	,	PUNCT
ejpam-3914	542	27	ui+1	ui+1	PROPN
ejpam-3914	542	28	form	form	NOUN
ejpam-3914	542	29	a	a	DET
ejpam-3914	542	30	total	total	ADJ
ejpam-3914	542	31	dr	dr	ADJ
ejpam-3914	542	32	-	-	PUNCT
ejpam-3914	542	33	power	power	NOUN
ejpam-3914	542	34	dominating	dominating	NOUN
ejpam-3914	542	35	set	set	VERB
ejpam-3914	542	36	since	since	SCONJ
ejpam-3914	542	37	ui+2	ui+2	NUM
ejpam-3914	542	38	and	and	CCONJ
ejpam-3914	542	39	ui+4	ui+4	PRON
ejpam-3914	542	40	are	be	AUX
ejpam-3914	542	41	directly	directly	ADV
ejpam-3914	542	42	observed	observe	VERB
ejpam-3914	542	43	vertices	vertex	NOUN
ejpam-3914	542	44	while	while	SCONJ
ejpam-3914	542	45	ui+3	ui+3	NOUN
ejpam-3914	542	46	is	be	AUX
ejpam-3914	542	47	a	a	DET
ejpam-3914	542	48	remotely	remotely	ADV
ejpam-3914	542	49	observed	observe	VERB
ejpam-3914	542	50	vertex	vertex	NOUN
ejpam-3914	542	51	for	for	ADP
ejpam-3914	542	52	all	all	DET
ejpam-3914	542	53	i	i	PRON
ejpam-3914	542	54	=	=	NOUN
ejpam-3914	542	55	2	2	NUM
ejpam-3914	542	56	,	,	PUNCT
ejpam-3914	542	57	7	7	NUM
ejpam-3914	542	58	,	,	PUNCT
ejpam-3914	542	59	12	12	NUM
ejpam-3914	542	60	,	,	PUNCT
ejpam-3914	542	61	.	.	PUNCT
ejpam-3914	542	62	.	.	PUNCT
ejpam-3914	543	1	.	.	PUNCT
ejpam-3914	544	1	,	,	PUNCT
ejpam-3914	544	2	n−9	n−9	PROPN
ejpam-3914	544	3	,	,	PUNCT
ejpam-3914	544	4	n−4	n−4	PROPN
ejpam-3914	544	5	.	.	PUNCT
ejpam-3914	545	1	let	let	VERB
ejpam-3914	545	2	the	the	DET
ejpam-3914	545	3	set	set	NOUN
ejpam-3914	545	4	r	r	NOUN
ejpam-3914	545	5	=	=	SYM
ejpam-3914	545	6	{	{	PUNCT
ejpam-3914	545	7	u1	u1	NOUN
ejpam-3914	545	8	,	,	PUNCT
ejpam-3914	545	9	ui	ui	NOUN
ejpam-3914	545	10	,	,	PUNCT
ejpam-3914	545	11	ui+1	ui+1	PROPN
ejpam-3914	545	12	:	:	PUNCT
ejpam-3914	545	13	i	i	NOUN
ejpam-3914	545	14	=	=	NOUN
ejpam-3914	545	15	2	2	NUM
ejpam-3914	545	16	,	,	PUNCT
ejpam-3914	545	17	7	7	NUM
ejpam-3914	545	18	,	,	PUNCT
ejpam-3914	545	19	12	12	NUM
ejpam-3914	545	20	,	,	PUNCT
ejpam-3914	545	21	.	.	PUNCT
ejpam-3914	545	22	.	.	PUNCT
ejpam-3914	546	1	.	.	PUNCT
ejpam-3914	547	1	,	,	PUNCT
ejpam-3914	547	2	n−	n−	NOUN
ejpam-3914	547	3	9	9	NUM
ejpam-3914	547	4	,	,	PUNCT
ejpam-3914	547	5	n−	n−	NOUN
ejpam-3914	547	6	4	4	NUM
ejpam-3914	547	7	}	}	PUNCT
ejpam-3914	547	8	=	=	NOUN
ejpam-3914	547	9	{	{	PUNCT
ejpam-3914	547	10	u1	u1	NOUN
ejpam-3914	547	11	,	,	PUNCT
ejpam-3914	547	12	u2	u2	NOUN
ejpam-3914	547	13	,	,	PUNCT
ejpam-3914	547	14	u3	u3	PROPN
ejpam-3914	547	15	,	,	PUNCT
ejpam-3914	547	16	u7	u7	PROPN
ejpam-3914	547	17	,	,	PUNCT
ejpam-3914	547	18	u8	u8	PROPN
ejpam-3914	547	19	,	,	PUNCT
ejpam-3914	547	20	u12	u12	PROPN
ejpam-3914	547	21	,	,	PUNCT
ejpam-3914	547	22	u13	u13	NOUN
ejpam-3914	547	23	,	,	PUNCT
ejpam-3914	547	24	.	.	PUNCT
ejpam-3914	547	25	.	.	PUNCT
ejpam-3914	548	1	.	.	PUNCT
ejpam-3914	549	1	,	,	PUNCT
ejpam-3914	549	2	un−9	un−9	PROPN
ejpam-3914	549	3	,	,	PUNCT
ejpam-3914	549	4	un−8	un−8	ADJ
ejpam-3914	549	5	,	,	PUNCT
ejpam-3914	549	6	un−4	un−4	NOUN
ejpam-3914	549	7	,	,	PUNCT
ejpam-3914	549	8	un−3	un−3	ADJ
ejpam-3914	549	9	}	}	PUNCT
ejpam-3914	549	10	,	,	PUNCT
ejpam-3914	549	11	where	where	SCONJ
ejpam-3914	549	12	|r|	|r|	NOUN
ejpam-3914	549	13	=	=	NOUN
ejpam-3914	549	14	2p+	2p+	NUM
ejpam-3914	549	15	1	1	X
ejpam-3914	549	16	=	=	SYM
ejpam-3914	549	17	2(n−1	2(n−1	NUM
ejpam-3914	549	18	5	5	NUM
ejpam-3914	549	19	)	)	PUNCT
ejpam-3914	549	20	+	+	CCONJ
ejpam-3914	549	21	1	1	X
ejpam-3914	549	22	=	=	SYM
ejpam-3914	549	23	2n+3	2n+3	NOUN
ejpam-3914	549	24	5	5	NUM
ejpam-3914	549	25	,	,	PUNCT
ejpam-3914	549	26	or	or	CCONJ
ejpam-3914	549	27	v	v	NOUN
ejpam-3914	549	28	(	(	PUNCT
ejpam-3914	549	29	cn	cn	PROPN
ejpam-3914	549	30	)	)	PUNCT
ejpam-3914	549	31	=	=	NOUN
ejpam-3914	549	32	v	v	X
ejpam-3914	549	33	(	(	PUNCT
ejpam-3914	549	34	cn	cn	PROPN
ejpam-3914	549	35	)	)	PUNCT
ejpam-3914	549	36	,	,	PUNCT
ejpam-3914	549	37	or	or	CCONJ
ejpam-3914	549	38	e(cn	e(cn	NOUN
ejpam-3914	549	39	)	)	PUNCT
ejpam-3914	549	40	=	=	SYM
ejpam-3914	549	41	e(cn	e(cn	NOUN
ejpam-3914	549	42	)	)	PUNCT
ejpam-3914	549	43	,	,	PUNCT
ejpam-3914	549	44	and	and	CCONJ
ejpam-3914	549	45	the	the	DET
ejpam-3914	549	46	induced	induced	ADJ
ejpam-3914	549	47	subgraph	subgraph	NOUN
ejpam-3914	549	48	〈	〈	PROPN
ejpam-3914	549	49	r	r	PROPN
ejpam-3914	549	50	〉	〉	PROPN
ejpam-3914	549	51	has	have	VERB
ejpam-3914	549	52	no	no	DET
ejpam-3914	549	53	isolated	isolated	ADJ
ejpam-3914	549	54	vertex	vertex	NOUN
ejpam-3914	549	55	,	,	PUNCT
ejpam-3914	549	56	that	that	ADV
ejpam-3914	549	57	is	is	ADV
ejpam-3914	549	58	,	,	PUNCT
ejpam-3914	549	59	r	r	NOUN
ejpam-3914	549	60	is	be	AUX
ejpam-3914	549	61	a	a	DET
ejpam-3914	549	62	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	549	63	-set	-set	PROPN
ejpam-3914	549	64	of	of	ADP
ejpam-3914	549	65	cn	cn	PROPN
ejpam-3914	549	66	.	.	PUNCT
ejpam-3914	550	1	let	let	VERB
ejpam-3914	550	2	m+	m+	PRON
ejpam-3914	550	3	1	1	NUM
ejpam-3914	550	4	be	be	AUX
ejpam-3914	550	5	the	the	DET
ejpam-3914	550	6	number	number	NOUN
ejpam-3914	550	7	of	of	ADP
ejpam-3914	550	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	550	9	-sets	-set	NOUN
ejpam-3914	550	10	of	of	ADP
ejpam-3914	550	11	cn	cn	PROPN
ejpam-3914	550	12	where	where	SCONJ
ejpam-3914	550	13	m	m	PROPN
ejpam-3914	550	14	is	be	AUX
ejpam-3914	550	15	a	a	DET
ejpam-3914	550	16	positive	positive	ADJ
ejpam-3914	550	17	integer	integer	NOUN
ejpam-3914	550	18	.	.	PUNCT
ejpam-3914	551	1	let	let	VERB
ejpam-3914	551	2	k	k	NOUN
ejpam-3914	551	3	=	=	SYM
ejpam-3914	551	4	1	1	NUM
ejpam-3914	551	5	,	,	PUNCT
ejpam-3914	551	6	2	2	NUM
ejpam-3914	551	7	,	,	PUNCT
ejpam-3914	551	8	.	.	PUNCT
ejpam-3914	551	9	.	.	PUNCT
ejpam-3914	552	1	.	.	PUNCT
ejpam-3914	553	1	,	,	PUNCT
ejpam-3914	553	2	m	m	VERB
ejpam-3914	553	3	and	and	CCONJ
ejpam-3914	553	4	tk	tk	PROPN
ejpam-3914	553	5	be	be	AUX
ejpam-3914	553	6	a	a	DET
ejpam-3914	553	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	553	8	-set	-set	PUNCT
ejpam-3914	553	9	of	of	ADP
ejpam-3914	553	10	cn	cn	PROPN
ejpam-3914	553	11	different	different	ADJ
ejpam-3914	553	12	from	from	ADP
ejpam-3914	553	13	r.	r.	PROPN
ejpam-3914	553	14	note	note	PROPN
ejpam-3914	553	15	that	that	SCONJ
ejpam-3914	553	16	tk	tk	PROPN
ejpam-3914	553	17	can	can	AUX
ejpam-3914	553	18	be	be	AUX
ejpam-3914	553	19	formed	form	VERB
ejpam-3914	553	20	by	by	ADP
ejpam-3914	553	21	starting	start	VERB
ejpam-3914	553	22	all	all	DET
ejpam-3914	553	23	the	the	DET
ejpam-3914	553	24	vertices	vertex	NOUN
ejpam-3914	553	25	of	of	ADP
ejpam-3914	553	26	sl	sl	NOUN
ejpam-3914	553	27	for	for	ADP
ejpam-3914	553	28	l	l	NOUN
ejpam-3914	553	29	=	=	SYM
ejpam-3914	553	30	1	1	NUM
ejpam-3914	553	31	,	,	PUNCT
ejpam-3914	553	32	2	2	NUM
ejpam-3914	553	33	,	,	PUNCT
ejpam-3914	553	34	.	.	PUNCT
ejpam-3914	553	35	.	.	PUNCT
ejpam-3914	554	1	.	.	PUNCT
ejpam-3914	555	1	,	,	PUNCT
ejpam-3914	555	2	5	5	NUM
ejpam-3914	555	3	and	and	CCONJ
ejpam-3914	555	4	replacing	replace	VERB
ejpam-3914	555	5	u6	u6	NOUN
ejpam-3914	555	6	by	by	ADP
ejpam-3914	555	7	un	un	PROPN
ejpam-3914	555	8	in	in	ADP
ejpam-3914	555	9	s5	s5	PROPN
ejpam-3914	555	10	and	and	CCONJ
ejpam-3914	555	11	s6	s6	PROPN
ejpam-3914	555	12	and	and	CCONJ
ejpam-3914	555	13	also	also	ADV
ejpam-3914	555	14	,	,	PUNCT
ejpam-3914	555	15	tk	tk	PROPN
ejpam-3914	555	16	can	can	AUX
ejpam-3914	555	17	be	be	AUX
ejpam-3914	555	18	formed	form	VERB
ejpam-3914	555	19	by	by	ADP
ejpam-3914	555	20	having	have	VERB
ejpam-3914	555	21	three	three	NUM
ejpam-3914	555	22	vertices	vertex	NOUN
ejpam-3914	555	23	in	in	ADP
ejpam-3914	555	24	any	any	DET
ejpam-3914	555	25	one	one	NUM
ejpam-3914	555	26	or	or	CCONJ
ejpam-3914	555	27	two	two	NUM
ejpam-3914	555	28	of	of	ADP
ejpam-3914	555	29	the	the	DET
ejpam-3914	555	30	rj	rj	PROPN
ejpam-3914	555	31	’s	’	VERB
ejpam-3914	555	32	where	where	SCONJ
ejpam-3914	555	33	j	j	PROPN
ejpam-3914	555	34	≥	≥	X
ejpam-3914	555	35	0	0	NUM
ejpam-3914	555	36	such	such	ADJ
ejpam-3914	555	37	that	that	SCONJ
ejpam-3914	555	38	the	the	DET
ejpam-3914	555	39	induced	induced	ADJ
ejpam-3914	555	40	subgraph	subgraph	NOUN
ejpam-3914	555	41	is	be	AUX
ejpam-3914	555	42	a	a	DET
ejpam-3914	555	43	graph	graph	NOUN
ejpam-3914	555	44	p3	p3	NOUN
ejpam-3914	555	45	and	and	CCONJ
ejpam-3914	555	46	two	two	NUM
ejpam-3914	555	47	vertices	vertex	NOUN
ejpam-3914	555	48	in	in	ADP
ejpam-3914	555	49	the	the	DET
ejpam-3914	555	50	other	other	ADJ
ejpam-3914	555	51	rl	rl	X
ejpam-3914	555	52	’s	’s	NOUN
ejpam-3914	555	53	where	where	SCONJ
ejpam-3914	555	54	l	l	NOUN
ejpam-3914	555	55	6=	6=	PUNCT
ejpam-3914	555	56	j.	j.	PROPN
ejpam-3914	555	57	replacing	replace	VERB
ejpam-3914	555	58	u3	u3	NOUN
ejpam-3914	555	59	∈	∈	NOUN
ejpam-3914	555	60	r	r	NOUN
ejpam-3914	555	61	by	by	ADP
ejpam-3914	555	62	u6	u6	NOUN
ejpam-3914	555	63	to	to	PART
ejpam-3914	555	64	form	form	VERB
ejpam-3914	555	65	tk	tk	PROPN
ejpam-3914	555	66	,	,	PUNCT
ejpam-3914	555	67	say	say	VERB
ejpam-3914	555	68	t1	t1	NOUN
ejpam-3914	555	69	,	,	PUNCT
ejpam-3914	555	70	that	that	ADV
ejpam-3914	555	71	is	is	ADV
ejpam-3914	555	72	,	,	PUNCT
ejpam-3914	555	73	t1	t1	NOUN
ejpam-3914	555	74	=	=	PUNCT
ejpam-3914	555	75	{	{	PUNCT
ejpam-3914	555	76	u1	u1	NOUN
ejpam-3914	555	77	,	,	PUNCT
ejpam-3914	555	78	u2	u2	NOUN
ejpam-3914	555	79	,	,	PUNCT
ejpam-3914	555	80	u6	u6	PROPN
ejpam-3914	555	81	,	,	PUNCT
ejpam-3914	555	82	u7	u7	PROPN
ejpam-3914	555	83	,	,	PUNCT
ejpam-3914	555	84	u8	u8	PROPN
ejpam-3914	555	85	,	,	PUNCT
ejpam-3914	555	86	u12	u12	PROPN
ejpam-3914	555	87	,	,	PUNCT
ejpam-3914	555	88	u13	u13	NOUN
ejpam-3914	555	89	,	,	PUNCT
ejpam-3914	555	90	.	.	PUNCT
ejpam-3914	555	91	.	.	PUNCT
ejpam-3914	556	1	.	.	PUNCT
ejpam-3914	557	1	,	,	PUNCT
ejpam-3914	557	2	un−9	un−9	PROPN
ejpam-3914	557	3	,	,	PUNCT
ejpam-3914	557	4	un−8	un−8	ADJ
ejpam-3914	557	5	,	,	PUNCT
ejpam-3914	557	6	un−4	un−4	NOUN
ejpam-3914	557	7	,	,	PUNCT
ejpam-3914	557	8	un−3	un−3	ADJ
ejpam-3914	557	9	}	}	PUNCT
ejpam-3914	557	10	is	be	AUX
ejpam-3914	557	11	a	a	DET
ejpam-3914	557	12	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	557	13	-set	-set	PROPN
ejpam-3914	557	14	of	of	ADP
ejpam-3914	557	15	cn	cn	PROPN
ejpam-3914	557	16	.	.	PUNCT
ejpam-3914	558	1	clearly	clearly	ADV
ejpam-3914	558	2	,	,	PUNCT
ejpam-3914	558	3	{	{	PUNCT
ejpam-3914	558	4	u1	u1	NOUN
ejpam-3914	558	5	,	,	PUNCT
ejpam-3914	558	6	u3	u3	NOUN
ejpam-3914	558	7	}	}	PUNCT
ejpam-3914	558	8	*	*	PUNCT
ejpam-3914	558	9	t1	t1	NOUN
ejpam-3914	558	10	.	.	PUNCT
ejpam-3914	559	1	replacing	replace	VERB
ejpam-3914	559	2	u8	u8	PROPN
ejpam-3914	559	3	∈	∈	PROPN
ejpam-3914	559	4	t1	t1	NOUN
ejpam-3914	559	5	by	by	ADP
ejpam-3914	559	6	u11	u11	PROPN
ejpam-3914	559	7	to	to	PART
ejpam-3914	559	8	form	form	NOUN
ejpam-3914	559	9	tk	tk	PROPN
ejpam-3914	559	10	,	,	PUNCT
ejpam-3914	559	11	say	say	AUX
ejpam-3914	559	12	t2	t2	NOUN
ejpam-3914	559	13	,	,	PUNCT
ejpam-3914	559	14	that	that	ADV
ejpam-3914	559	15	is	is	ADV
ejpam-3914	559	16	,	,	PUNCT
ejpam-3914	559	17	t2	t2	NOUN
ejpam-3914	559	18	=	=	SYM
ejpam-3914	559	19	{	{	PUNCT
ejpam-3914	559	20	u1	u1	NOUN
ejpam-3914	559	21	,	,	PUNCT
ejpam-3914	559	22	u2	u2	NOUN
ejpam-3914	559	23	,	,	PUNCT
ejpam-3914	559	24	u6	u6	PROPN
ejpam-3914	559	25	,	,	PUNCT
ejpam-3914	559	26	u7	u7	PROPN
ejpam-3914	559	27	,	,	PUNCT
ejpam-3914	559	28	u11	u11	PROPN
ejpam-3914	559	29	,	,	PUNCT
ejpam-3914	559	30	u12	u12	PROPN
ejpam-3914	559	31	,	,	PUNCT
ejpam-3914	559	32	u13	u13	NOUN
ejpam-3914	559	33	,	,	PUNCT
ejpam-3914	559	34	.	.	PUNCT
ejpam-3914	559	35	.	.	PUNCT
ejpam-3914	560	1	.	.	PUNCT
ejpam-3914	561	1	,	,	PUNCT
ejpam-3914	561	2	un−9	un−9	PROPN
ejpam-3914	561	3	,	,	PUNCT
ejpam-3914	561	4	un−8	un−8	ADJ
ejpam-3914	561	5	,	,	PUNCT
ejpam-3914	561	6	un−4	un−4	NOUN
ejpam-3914	561	7	,	,	PUNCT
ejpam-3914	561	8	un−3	un−3	ADJ
ejpam-3914	561	9	}	}	PUNCT
ejpam-3914	561	10	is	be	AUX
ejpam-3914	561	11	a	a	DET
ejpam-3914	561	12	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	561	13	-set	-set	PROPN
ejpam-3914	561	14	of	of	ADP
ejpam-3914	561	15	cn	cn	PROPN
ejpam-3914	561	16	.	.	PUNCT
ejpam-3914	562	1	clearly	clearly	ADV
ejpam-3914	562	2	,	,	PUNCT
ejpam-3914	562	3	{	{	PUNCT
ejpam-3914	562	4	u1	u1	NOUN
ejpam-3914	562	5	,	,	PUNCT
ejpam-3914	562	6	u3	u3	NOUN
ejpam-3914	562	7	}	}	PUNCT
ejpam-3914	562	8	*	*	PUNCT
ejpam-3914	562	9	t2	t2	NOUN
ejpam-3914	562	10	.	.	PUNCT
ejpam-3914	563	1	continuing	continue	VERB
ejpam-3914	563	2	in	in	ADP
ejpam-3914	563	3	this	this	DET
ejpam-3914	563	4	manner	manner	NOUN
ejpam-3914	563	5	,	,	PUNCT
ejpam-3914	563	6	{	{	PUNCT
ejpam-3914	563	7	u1	u1	NOUN
ejpam-3914	563	8	,	,	PUNCT
ejpam-3914	563	9	u3	u3	PROPN
ejpam-3914	563	10	}	}	PUNCT
ejpam-3914	563	11	*	*	PUNCT
ejpam-3914	563	12	tk	tk	PROPN
ejpam-3914	563	13	for	for	ADP
ejpam-3914	563	14	some	some	PRON
ejpam-3914	563	15	k.	k.	NOUN
ejpam-3914	564	1	now	now	ADV
ejpam-3914	564	2	,	,	PUNCT
ejpam-3914	564	3	if	if	SCONJ
ejpam-3914	564	4	tk	tk	PROPN
ejpam-3914	564	5	starts	start	VERB
ejpam-3914	564	6	with	with	ADP
ejpam-3914	564	7	s1	s1	NOUN
ejpam-3914	564	8	,	,	PUNCT
ejpam-3914	564	9	then	then	ADV
ejpam-3914	564	10	let	let	VERB
ejpam-3914	564	11	k	k	PROPN
ejpam-3914	564	12	=	=	SYM
ejpam-3914	564	13	3	3	NUM
ejpam-3914	564	14	and	and	CCONJ
ejpam-3914	564	15	{	{	PUNCT
ejpam-3914	564	16	u1	u1	NOUN
ejpam-3914	564	17	,	,	PUNCT
ejpam-3914	564	18	u3	u3	NOUN
ejpam-3914	564	19	}	}	PUNCT
ejpam-3914	564	20	⊆	⊆	NUM
ejpam-3914	564	21	t3	t3	NOUN
ejpam-3914	564	22	.	.	PUNCT
ejpam-3914	565	1	then	then	ADV
ejpam-3914	565	2	u2	u2	PROPN
ejpam-3914	565	3	must	must	AUX
ejpam-3914	565	4	be	be	AUX
ejpam-3914	565	5	in	in	ADP
ejpam-3914	565	6	t3	t3	PROPN
ejpam-3914	565	7	.	.	PUNCT
ejpam-3914	566	1	replace	replace	VERB
ejpam-3914	566	2	u7	u7	PROPN
ejpam-3914	566	3	∈	∈	PROPN
ejpam-3914	566	4	r	r	NOUN
ejpam-3914	566	5	by	by	ADP
ejpam-3914	566	6	u6	u6	NOUN
ejpam-3914	566	7	to	to	PART
ejpam-3914	566	8	form	form	VERB
ejpam-3914	566	9	t3	t3	PROPN
ejpam-3914	566	10	.	.	PUNCT
ejpam-3914	567	1	then	then	ADV
ejpam-3914	567	2	the	the	DET
ejpam-3914	567	3	next	next	ADJ
ejpam-3914	567	4	vertex	vertex	NOUN
ejpam-3914	567	5	to	to	PART
ejpam-3914	567	6	be	be	AUX
ejpam-3914	567	7	choosen	choosen	VERB
ejpam-3914	567	8	must	must	AUX
ejpam-3914	567	9	be	be	AUX
ejpam-3914	567	10	u7	u7	PROPN
ejpam-3914	567	11	,	,	PUNCT
ejpam-3914	567	12	that	that	ADV
ejpam-3914	567	13	is	is	ADV
ejpam-3914	567	14	,	,	PUNCT
ejpam-3914	567	15	the	the	DET
ejpam-3914	567	16	vertex	vertex	NOUN
ejpam-3914	567	17	ui+4	ui+4	PROPN
ejpam-3914	567	18	,	,	PUNCT
ejpam-3914	567	19	ui	ui	PROPN
ejpam-3914	567	20	must	must	AUX
ejpam-3914	567	21	be	be	AUX
ejpam-3914	567	22	in	in	ADP
ejpam-3914	567	23	t3	t3	PROPN
ejpam-3914	567	24	for	for	ADP
ejpam-3914	567	25	all	all	DET
ejpam-3914	567	26	i	i	PRON
ejpam-3914	567	27	=	=	NOUN
ejpam-3914	567	28	2	2	NUM
ejpam-3914	567	29	,	,	PUNCT
ejpam-3914	567	30	7	7	NUM
ejpam-3914	567	31	,	,	PUNCT
ejpam-3914	567	32	12	12	NUM
ejpam-3914	567	33	,	,	PUNCT
ejpam-3914	567	34	.	.	PUNCT
ejpam-3914	567	35	.	.	PUNCT
ejpam-3914	568	1	.	.	PUNCT
ejpam-3914	569	1	,	,	PUNCT
ejpam-3914	569	2	n	n	CCONJ
ejpam-3914	569	3	−	−	PROPN
ejpam-3914	569	4	9	9	NUM
ejpam-3914	569	5	,	,	PUNCT
ejpam-3914	569	6	n	n	CCONJ
ejpam-3914	569	7	−	−	PROPN
ejpam-3914	569	8	4	4	NUM
ejpam-3914	569	9	.	.	PUNCT
ejpam-3914	570	1	then	then	ADV
ejpam-3914	570	2	t3	t3	PROPN
ejpam-3914	570	3	=	=	PUNCT
ejpam-3914	570	4	{	{	PUNCT
ejpam-3914	570	5	u1	u1	NOUN
ejpam-3914	570	6	,	,	PUNCT
ejpam-3914	570	7	u2	u2	NOUN
ejpam-3914	570	8	,	,	PUNCT
ejpam-3914	570	9	u3	u3	NOUN
ejpam-3914	570	10	,	,	PUNCT
ejpam-3914	570	11	u6	u6	PROPN
ejpam-3914	570	12	,	,	PUNCT
ejpam-3914	570	13	u7	u7	PROPN
ejpam-3914	570	14	,	,	PUNCT
ejpam-3914	570	15	u11	u11	PROPN
ejpam-3914	570	16	,	,	PUNCT
ejpam-3914	570	17	u12	u12	PROPN
ejpam-3914	570	18	,	,	PUNCT
ejpam-3914	570	19	u16	u16	PROPN
ejpam-3914	570	20	,	,	PUNCT
ejpam-3914	570	21	u17	u17	NOUN
ejpam-3914	570	22	,	,	PUNCT
ejpam-3914	570	23	.	.	PUNCT
ejpam-3914	570	24	.	.	PUNCT
ejpam-3914	571	1	.	.	PUNCT
ejpam-3914	572	1	,	,	PUNCT
ejpam-3914	573	1	un−5	un−5	PROPN
ejpam-3914	573	2	,	,	PUNCT
ejpam-3914	573	3	un−4	un−4	NOUN
ejpam-3914	573	4	}	}	PUNCT
ejpam-3914	573	5	such	such	ADJ
ejpam-3914	573	6	that	that	SCONJ
ejpam-3914	573	7	|t3|	|t3|	PROPN
ejpam-3914	573	8	=	=	SYM
ejpam-3914	573	9	|r|	|r|	PROPN
ejpam-3914	573	10	.	.	PUNCT
ejpam-3914	574	1	since	since	SCONJ
ejpam-3914	574	2	u1	u1	PROPN
ejpam-3914	574	3	∈	∈	PROPN
ejpam-3914	574	4	t3	t3	NOUN
ejpam-3914	574	5	and	and	CCONJ
ejpam-3914	574	6	un−4	un−4	NOUN
ejpam-3914	574	7	is	be	AUX
ejpam-3914	574	8	the	the	DET
ejpam-3914	574	9	last	last	ADJ
ejpam-3914	574	10	vertex	vertex	NOUN
ejpam-3914	574	11	in	in	ADP
ejpam-3914	574	12	t3	t3	PROPN
ejpam-3914	574	13	,	,	PUNCT
ejpam-3914	574	14	by	by	ADP
ejpam-3914	574	15	the	the	DET
ejpam-3914	574	16	same	same	ADJ
ejpam-3914	574	17	argument	argument	NOUN
ejpam-3914	574	18	in	in	ADP
ejpam-3914	574	19	case	case	NOUN
ejpam-3914	574	20	1	1	NUM
ejpam-3914	574	21	,	,	PUNCT
ejpam-3914	574	22	t3	t3	PROPN
ejpam-3914	574	23	is	be	AUX
ejpam-3914	574	24	not	not	PART
ejpam-3914	574	25	a	a	DET
ejpam-3914	574	26	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	574	27	-set	-set	PROPN
ejpam-3914	574	28	of	of	ADP
ejpam-3914	574	29	cn	cn	PROPN
ejpam-3914	574	30	.	.	PUNCT
ejpam-3914	575	1	since	since	SCONJ
ejpam-3914	575	2	u7	u7	PROPN
ejpam-3914	575	3	is	be	AUX
ejpam-3914	575	4	arbitrarily	arbitrarily	ADV
ejpam-3914	575	5	replaced	replace	VERB
ejpam-3914	575	6	from	from	ADP
ejpam-3914	575	7	r	r	NOUN
ejpam-3914	575	8	,	,	PUNCT
ejpam-3914	575	9	we	we	PRON
ejpam-3914	575	10	can	can	AUX
ejpam-3914	575	11	not	not	PART
ejpam-3914	575	12	replace	replace	VERB
ejpam-3914	575	13	the	the	DET
ejpam-3914	575	14	vertex	vertex	NOUN
ejpam-3914	575	15	ui	ui	NOUN
ejpam-3914	575	16	in	in	ADP
ejpam-3914	575	17	r	r	NOUN
ejpam-3914	575	18	,	,	PUNCT
ejpam-3914	575	19	where	where	SCONJ
ejpam-3914	575	20	i	i	PRON
ejpam-3914	575	21	=	=	NOUN
ejpam-3914	575	22	7	7	NUM
ejpam-3914	575	23	,	,	PUNCT
ejpam-3914	575	24	12	12	NUM
ejpam-3914	575	25	,	,	PUNCT
ejpam-3914	575	26	.	.	PUNCT
ejpam-3914	575	27	.	.	PUNCT
ejpam-3914	576	1	.	.	PUNCT
ejpam-3914	577	1	,	,	PUNCT
ejpam-3914	577	2	n−	n−	NOUN
ejpam-3914	577	3	9	9	NUM
ejpam-3914	577	4	,	,	PUNCT
ejpam-3914	577	5	n−	n−	NOUN
ejpam-3914	577	6	4	4	NUM
ejpam-3914	577	7	to	to	PART
ejpam-3914	577	8	form	form	VERB
ejpam-3914	577	9	another	another	PRON
ejpam-3914	577	10	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	577	11	-set	-set	PROPN
ejpam-3914	577	12	of	of	ADP
ejpam-3914	577	13	cn	cn	PROPN
ejpam-3914	577	14	.	.	PUNCT
ejpam-3914	577	15	therefore	therefore	ADV
ejpam-3914	577	16	,	,	PUNCT
ejpam-3914	577	17	only	only	ADV
ejpam-3914	577	18	the	the	DET
ejpam-3914	577	19	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	577	20	-set	-set	PUNCT
ejpam-3914	577	21	r	r	NOUN
ejpam-3914	577	22	starts	start	VERB
ejpam-3914	577	23	with	with	ADP
ejpam-3914	577	24	s1	s1	NOUN
ejpam-3914	577	25	and	and	CCONJ
ejpam-3914	577	26	so	so	ADV
ejpam-3914	577	27	,	,	PUNCT
ejpam-3914	577	28	{	{	PUNCT
ejpam-3914	577	29	u1	u1	NOUN
ejpam-3914	577	30	,	,	PUNCT
ejpam-3914	577	31	u3	u3	PROPN
ejpam-3914	577	32	}	}	PUNCT
ejpam-3914	577	33	*	*	PUNCT
ejpam-3914	577	34	tk	tk	PROPN
ejpam-3914	577	35	for	for	ADP
ejpam-3914	577	36	all	all	PRON
ejpam-3914	577	37	k	k	NOUN
ejpam-3914	577	38	=	=	SYM
ejpam-3914	577	39	1	1	NUM
ejpam-3914	577	40	,	,	PUNCT
ejpam-3914	577	41	2	2	NUM
ejpam-3914	577	42	,	,	PUNCT
ejpam-3914	577	43	.	.	PUNCT
ejpam-3914	577	44	.	.	PUNCT
ejpam-3914	577	45	.	.	PUNCT
ejpam-3914	578	1	,	,	PUNCT
ejpam-3914	578	2	m.	m.	NOUN
ejpam-3914	578	3	hence	hence	ADV
ejpam-3914	578	4	,	,	PUNCT
ejpam-3914	578	5	{	{	PUNCT
ejpam-3914	578	6	u1	u1	NOUN
ejpam-3914	578	7	,	,	PUNCT
ejpam-3914	578	8	u3	u3	PROPN
ejpam-3914	578	9	}	}	PUNCT
ejpam-3914	578	10	is	be	AUX
ejpam-3914	578	11	a	a	DET
ejpam-3914	578	12	forcing	forcing	NOUN
ejpam-3914	578	13	subset	subset	NOUN
ejpam-3914	578	14	for	for	ADP
ejpam-3914	578	15	r.	r.	PROPN
ejpam-3914	578	16	therefore	therefore	ADV
ejpam-3914	578	17	,	,	PUNCT
ejpam-3914	578	18	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	578	19	(	(	PUNCT
ejpam-3914	578	20	r	r	NOUN
ejpam-3914	578	21	)	)	PUNCT
ejpam-3914	578	22	=	=	SYM
ejpam-3914	579	1	2	2	NUM
ejpam-3914	579	2	=	=	NOUN
ejpam-3914	579	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	579	4	(	(	PUNCT
ejpam-3914	579	5	cn	cn	NOUN
ejpam-3914	579	6	)	)	PUNCT
ejpam-3914	579	7	.	.	PUNCT
ejpam-3914	580	1	case	case	NOUN
ejpam-3914	580	2	4	4	NUM
ejpam-3914	580	3	:	:	PUNCT
ejpam-3914	580	4	suppose	suppose	VERB
ejpam-3914	580	5	that	that	SCONJ
ejpam-3914	580	6	n	n	PROPN
ejpam-3914	580	7	≡	≡	PROPN
ejpam-3914	580	8	3(mod	3(mod	NUM
ejpam-3914	580	9	5	5	NUM
ejpam-3914	580	10	)	)	PUNCT
ejpam-3914	580	11	.	.	PUNCT
ejpam-3914	581	1	by	by	ADP
ejpam-3914	581	2	theorem	theorem	NOUN
ejpam-3914	581	3	2.3	2.3	NUM
ejpam-3914	581	4	,	,	PUNCT
ejpam-3914	581	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	581	6	(	(	PUNCT
ejpam-3914	581	7	cn	cn	NOUN
ejpam-3914	581	8	)	)	PUNCT
ejpam-3914	581	9	=	=	SYM
ejpam-3914	581	10	2n+4	2n+4	NOUN
ejpam-3914	581	11	5	5	NUM
ejpam-3914	581	12	.	.	PUNCT
ejpam-3914	581	13	suppose	suppose	VERB
ejpam-3914	581	14	that	that	SCONJ
ejpam-3914	581	15	n	n	PROPN
ejpam-3914	581	16	=	=	SYM
ejpam-3914	581	17	8	8	NUM
ejpam-3914	581	18	.	.	PUNCT
ejpam-3914	582	1	then	then	ADV
ejpam-3914	582	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	582	3	(	(	PUNCT
ejpam-3914	582	4	c8	c8	PROPN
ejpam-3914	582	5	)	)	PUNCT
ejpam-3914	582	6	=	=	NOUN
ejpam-3914	582	7	2(8)+4	2(8)+4	NUM
ejpam-3914	582	8	5	5	NUM
ejpam-3914	582	9	=	=	SYM
ejpam-3914	582	10	4	4	NUM
ejpam-3914	582	11	.	.	PUNCT
ejpam-3914	582	12	clearly	clearly	ADV
ejpam-3914	582	13	,	,	PUNCT
ejpam-3914	582	14	s1	s1	PROPN
ejpam-3914	582	15	=	=	SYM
ejpam-3914	582	16	{	{	PUNCT
ejpam-3914	582	17	u1	u1	NOUN
ejpam-3914	582	18	,	,	PUNCT
ejpam-3914	582	19	u2	u2	PROPN
ejpam-3914	582	20	,	,	PUNCT
ejpam-3914	582	21	u4	u4	PROPN
ejpam-3914	582	22	,	,	PUNCT
ejpam-3914	582	23	u5	u5	PROPN
ejpam-3914	582	24	}	}	PUNCT
ejpam-3914	582	25	,	,	PUNCT
ejpam-3914	582	26	s2	s2	NOUN
ejpam-3914	582	27	=	=	SYM
ejpam-3914	582	28	{	{	PUNCT
ejpam-3914	582	29	u1	u1	NOUN
ejpam-3914	582	30	,	,	PUNCT
ejpam-3914	582	31	u2	u2	PROPN
ejpam-3914	582	32	,	,	PUNCT
ejpam-3914	582	33	u5	u5	PROPN
ejpam-3914	582	34	,	,	PUNCT
ejpam-3914	582	35	u6	u6	NOUN
ejpam-3914	582	36	}	}	PUNCT
ejpam-3914	582	37	,	,	PUNCT
ejpam-3914	582	38	s3	s3	PROPN
ejpam-3914	582	39	=	=	SYM
ejpam-3914	582	40	{	{	PUNCT
ejpam-3914	582	41	u1	u1	NOUN
ejpam-3914	582	42	,	,	PUNCT
ejpam-3914	582	43	u2	u2	NOUN
ejpam-3914	582	44	,	,	PUNCT
ejpam-3914	582	45	u6	u6	PROPN
ejpam-3914	582	46	,	,	PUNCT
ejpam-3914	582	47	u7	u7	PROPN
ejpam-3914	582	48	}	}	PUNCT
ejpam-3914	582	49	,	,	PUNCT
ejpam-3914	582	50	s4	s4	PROPN
ejpam-3914	582	51	=	=	SYM
ejpam-3914	582	52	{	{	PUNCT
ejpam-3914	582	53	u2	u2	PROPN
ejpam-3914	582	54	,	,	PUNCT
ejpam-3914	582	55	u3	u3	PROPN
ejpam-3914	582	56	,	,	PUNCT
ejpam-3914	582	57	u5	u5	PROPN
ejpam-3914	582	58	,	,	PUNCT
ejpam-3914	582	59	u6	u6	NOUN
ejpam-3914	582	60	}	}	PUNCT
ejpam-3914	582	61	,	,	PUNCT
ejpam-3914	582	62	s5	s5	X
ejpam-3914	582	63	=	=	PUNCT
ejpam-3914	582	64	{	{	PUNCT
ejpam-3914	582	65	u2	u2	PROPN
ejpam-3914	582	66	,	,	PUNCT
ejpam-3914	582	67	u3	u3	NOUN
ejpam-3914	582	68	,	,	PUNCT
ejpam-3914	582	69	u6	u6	PROPN
ejpam-3914	582	70	,	,	PUNCT
ejpam-3914	582	71	u7	u7	PROPN
ejpam-3914	582	72	}	}	PUNCT
ejpam-3914	582	73	,	,	PUNCT
ejpam-3914	582	74	s6	s6	PROPN
ejpam-3914	582	75	=	=	SYM
ejpam-3914	582	76	{	{	PUNCT
ejpam-3914	582	77	u2	u2	PROPN
ejpam-3914	582	78	,	,	PUNCT
ejpam-3914	582	79	u3	u3	PROPN
ejpam-3914	582	80	,	,	PUNCT
ejpam-3914	582	81	u7	u7	PROPN
ejpam-3914	582	82	,	,	PUNCT
ejpam-3914	582	83	u8	u8	PROPN
ejpam-3914	582	84	}	}	PUNCT
ejpam-3914	582	85	,	,	PUNCT
ejpam-3914	582	86	s7	s7	PROPN
ejpam-3914	582	87	=	=	SYM
ejpam-3914	582	88	{	{	PUNCT
ejpam-3914	582	89	u3	u3	PROPN
ejpam-3914	582	90	,	,	PUNCT
ejpam-3914	582	91	u4	u4	PROPN
ejpam-3914	582	92	,	,	PUNCT
ejpam-3914	582	93	u6	u6	PROPN
ejpam-3914	582	94	,	,	PUNCT
ejpam-3914	582	95	u7	u7	PROPN
ejpam-3914	582	96	}	}	PUNCT
ejpam-3914	582	97	,	,	PUNCT
ejpam-3914	582	98	s8	s8	PROPN
ejpam-3914	582	99	=	=	SYM
ejpam-3914	582	100	{	{	PUNCT
ejpam-3914	582	101	u3	u3	PROPN
ejpam-3914	582	102	,	,	PUNCT
ejpam-3914	582	103	u4	u4	PROPN
ejpam-3914	582	104	,	,	PUNCT
ejpam-3914	582	105	u7	u7	PROPN
ejpam-3914	582	106	,	,	PUNCT
ejpam-3914	582	107	u8	u8	PROPN
ejpam-3914	582	108	}	}	PUNCT
ejpam-3914	582	109	,	,	PUNCT
ejpam-3914	582	110	s9	s9	NOUN
ejpam-3914	582	111	=	=	SYM
ejpam-3914	582	112	{	{	PUNCT
ejpam-3914	582	113	u8	u8	PROPN
ejpam-3914	582	114	,	,	PUNCT
ejpam-3914	582	115	u1	u1	NOUN
ejpam-3914	582	116	,	,	PUNCT
ejpam-3914	582	117	u3	u3	PROPN
ejpam-3914	582	118	,	,	PUNCT
ejpam-3914	582	119	u4	u4	PROPN
ejpam-3914	582	120	}	}	PUNCT
ejpam-3914	582	121	,	,	PUNCT
ejpam-3914	582	122	s10	s10	NOUN
ejpam-3914	582	123	=	=	SYM
ejpam-3914	582	124	{	{	PUNCT
ejpam-3914	582	125	u4	u4	PROPN
ejpam-3914	582	126	,	,	PUNCT
ejpam-3914	582	127	u5	u5	PROPN
ejpam-3914	582	128	,	,	PUNCT
ejpam-3914	582	129	u7	u7	PROPN
ejpam-3914	582	130	,	,	PUNCT
ejpam-3914	582	131	u8	u8	PROPN
ejpam-3914	582	132	}	}	PUNCT
ejpam-3914	582	133	,	,	PUNCT
ejpam-3914	582	134	s11	s11	PROPN
ejpam-3914	582	135	=	=	SYM
ejpam-3914	582	136	{	{	PUNCT
ejpam-3914	582	137	u8	u8	PROPN
ejpam-3914	582	138	,	,	PUNCT
ejpam-3914	582	139	u1	u1	PROPN
ejpam-3914	582	140	,	,	PUNCT
ejpam-3914	582	141	u4	u4	PROPN
ejpam-3914	582	142	,	,	PUNCT
ejpam-3914	582	143	u5	u5	PROPN
ejpam-3914	582	144	}	}	PUNCT
ejpam-3914	582	145	,	,	PUNCT
ejpam-3914	582	146	and	and	CCONJ
ejpam-3914	582	147	s12	s12	NUM
ejpam-3914	582	148	=	=	SYM
ejpam-3914	582	149	{	{	PUNCT
ejpam-3914	582	150	u8	u8	PROPN
ejpam-3914	582	151	,	,	PUNCT
ejpam-3914	582	152	u1	u1	PROPN
ejpam-3914	582	153	,	,	PUNCT
ejpam-3914	582	154	u5	u5	PROPN
ejpam-3914	582	155	,	,	PUNCT
ejpam-3914	582	156	u6	u6	NOUN
ejpam-3914	582	157	}	}	PUNCT
ejpam-3914	582	158	,	,	PUNCT
ejpam-3914	582	159	are	be	AUX
ejpam-3914	582	160	the	the	DET
ejpam-3914	582	161	only	only	ADJ
ejpam-3914	582	162	c.	c.	PROPN
ejpam-3914	582	163	armada	armada	PROPN
ejpam-3914	582	164	/	/	SYM
ejpam-3914	582	165	eur	eur	PROPN
ejpam-3914	582	166	.	.	PUNCT
ejpam-3914	583	1	j.	j.	PROPN
ejpam-3914	583	2	pure	pure	PROPN
ejpam-3914	583	3	appl	appl	PROPN
ejpam-3914	583	4	.	.	PROPN
ejpam-3914	583	5	math	math	PROPN
ejpam-3914	583	6	,	,	PUNCT
ejpam-3914	583	7	14	14	NUM
ejpam-3914	583	8	(	(	PUNCT
ejpam-3914	583	9	2	2	NUM
ejpam-3914	583	10	)	)	PUNCT
ejpam-3914	583	11	(	(	PUNCT
ejpam-3914	583	12	2021	2021	NUM
ejpam-3914	583	13	)	)	PUNCT
ejpam-3914	583	14	,	,	PUNCT
ejpam-3914	583	15	451	451	NUM
ejpam-3914	583	16	-	-	SYM
ejpam-3914	583	17	470	470	NUM
ejpam-3914	583	18	466	466	NUM
ejpam-3914	583	19	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	583	20	-sets	-set	NOUN
ejpam-3914	583	21	of	of	ADP
ejpam-3914	583	22	c8	c8	PROPN
ejpam-3914	583	23	.	.	PUNCT
ejpam-3914	584	1	clearly	clearly	ADV
ejpam-3914	584	2	,	,	PUNCT
ejpam-3914	584	3	for	for	ADP
ejpam-3914	584	4	l	l	NOUN
ejpam-3914	584	5	=	=	SYM
ejpam-3914	584	6	1	1	NUM
ejpam-3914	584	7	,	,	PUNCT
ejpam-3914	584	8	2	2	NUM
ejpam-3914	584	9	.	.	PUNCT
ejpam-3914	584	10	.	.	PUNCT
ejpam-3914	584	11	.	.	PUNCT
ejpam-3914	585	1	,	,	PUNCT
ejpam-3914	585	2	12	12	NUM
ejpam-3914	585	3	,	,	PUNCT
ejpam-3914	585	4	{	{	PUNCT
ejpam-3914	585	5	u2	u2	NOUN
ejpam-3914	585	6	,	,	PUNCT
ejpam-3914	585	7	u4	u4	PROPN
ejpam-3914	585	8	}	}	PUNCT
ejpam-3914	585	9	⊆	⊆	NUM
ejpam-3914	585	10	s1	s1	NOUN
ejpam-3914	585	11	and	and	CCONJ
ejpam-3914	585	12	{	{	PUNCT
ejpam-3914	585	13	u2	u2	PROPN
ejpam-3914	585	14	,	,	PUNCT
ejpam-3914	585	15	u4	u4	PROPN
ejpam-3914	585	16	}	}	PUNCT
ejpam-3914	585	17	*	*	PUNCT
ejpam-3914	585	18	sl	sl	INTJ
ejpam-3914	585	19	for	for	ADP
ejpam-3914	585	20	all	all	DET
ejpam-3914	585	21	l	l	NOUN
ejpam-3914	585	22	6=	6=	NUM
ejpam-3914	585	23	1	1	NUM
ejpam-3914	585	24	.	.	PUNCT
ejpam-3914	586	1	thus	thus	ADV
ejpam-3914	586	2	,	,	PUNCT
ejpam-3914	586	3	{	{	PUNCT
ejpam-3914	586	4	u2	u2	NOUN
ejpam-3914	586	5	,	,	PUNCT
ejpam-3914	586	6	u4	u4	PROPN
ejpam-3914	586	7	}	}	PUNCT
ejpam-3914	586	8	is	be	AUX
ejpam-3914	586	9	a	a	DET
ejpam-3914	586	10	forcing	forcing	NOUN
ejpam-3914	586	11	subset	subset	NOUN
ejpam-3914	586	12	for	for	ADP
ejpam-3914	586	13	s1	s1	NOUN
ejpam-3914	586	14	,	,	PUNCT
ejpam-3914	586	15	that	that	ADV
ejpam-3914	586	16	is	is	ADV
ejpam-3914	586	17	,	,	PUNCT
ejpam-3914	586	18	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	586	19	(	(	PUNCT
ejpam-3914	586	20	s1	s1	NOUN
ejpam-3914	586	21	)	)	PUNCT
ejpam-3914	586	22	=	=	SYM
ejpam-3914	587	1	2	2	NUM
ejpam-3914	587	2	=	=	NOUN
ejpam-3914	587	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	587	4	(	(	PUNCT
ejpam-3914	587	5	c8	c8	PROPN
ejpam-3914	587	6	)	)	PUNCT
ejpam-3914	587	7	.	.	PUNCT
ejpam-3914	588	1	now	now	ADV
ejpam-3914	588	2	,	,	PUNCT
ejpam-3914	588	3	suppose	suppose	VERB
ejpam-3914	588	4	that	that	SCONJ
ejpam-3914	588	5	n	n	PROPN
ejpam-3914	588	6	>	>	X
ejpam-3914	588	7	8	8	NUM
ejpam-3914	588	8	.	.	PUNCT
ejpam-3914	589	1	let	let	VERB
ejpam-3914	589	2	p	p	NOUN
ejpam-3914	589	3	=	=	PUNCT
ejpam-3914	589	4	n−3	n−3	PROPN
ejpam-3914	589	5	5	5	NUM
ejpam-3914	589	6	and	and	CCONJ
ejpam-3914	589	7	j	j	NOUN
ejpam-3914	589	8	=	=	SYM
ejpam-3914	589	9	0	0	NUM
ejpam-3914	589	10	,	,	PUNCT
ejpam-3914	589	11	1	1	NUM
ejpam-3914	589	12	,	,	PUNCT
ejpam-3914	589	13	2	2	NUM
ejpam-3914	589	14	,	,	PUNCT
ejpam-3914	589	15	.	.	PUNCT
ejpam-3914	589	16	.	.	PUNCT
ejpam-3914	590	1	.	.	PUNCT
ejpam-3914	591	1	,	,	PUNCT
ejpam-3914	591	2	p−	p−	NOUN
ejpam-3914	591	3	1	1	NUM
ejpam-3914	591	4	,	,	PUNCT
ejpam-3914	591	5	p.	p.	NOUN
ejpam-3914	591	6	group	group	NOUN
ejpam-3914	591	7	the	the	DET
ejpam-3914	591	8	vertices	vertex	NOUN
ejpam-3914	591	9	of	of	ADP
ejpam-3914	591	10	cn	cn	PROPN
ejpam-3914	591	11	into	into	ADP
ejpam-3914	591	12	p+	p+	NOUN
ejpam-3914	591	13	1	1	NUM
ejpam-3914	591	14	disjoint	disjoint	NOUN
ejpam-3914	591	15	subsets	subset	NOUN
ejpam-3914	591	16	rj	rj	PROPN
ejpam-3914	591	17	r0	r0	PROPN
ejpam-3914	591	18	=	=	PUNCT
ejpam-3914	591	19	{	{	PUNCT
ejpam-3914	591	20	u1	u1	NOUN
ejpam-3914	591	21	,	,	PUNCT
ejpam-3914	591	22	u2	u2	NOUN
ejpam-3914	591	23	,	,	PUNCT
ejpam-3914	591	24	u3	u3	NOUN
ejpam-3914	591	25	}	}	PUNCT
ejpam-3914	591	26	r1	r1	NOUN
ejpam-3914	591	27	=	=	SYM
ejpam-3914	591	28	{	{	PUNCT
ejpam-3914	591	29	u4	u4	PROPN
ejpam-3914	591	30	,	,	PUNCT
ejpam-3914	591	31	u5	u5	PROPN
ejpam-3914	591	32	,	,	PUNCT
ejpam-3914	591	33	u6	u6	PROPN
ejpam-3914	591	34	,	,	PUNCT
ejpam-3914	591	35	u7	u7	PROPN
ejpam-3914	591	36	,	,	PUNCT
ejpam-3914	591	37	u8	u8	PROPN
ejpam-3914	591	38	}	}	PUNCT
ejpam-3914	591	39	r2	r2	NOUN
ejpam-3914	591	40	=	=	SYM
ejpam-3914	591	41	{	{	PUNCT
ejpam-3914	591	42	u9	u9	PROPN
ejpam-3914	591	43	,	,	PUNCT
ejpam-3914	591	44	u10	u10	PROPN
ejpam-3914	591	45	,	,	PUNCT
ejpam-3914	591	46	u11	u11	PROPN
ejpam-3914	591	47	,	,	PUNCT
ejpam-3914	591	48	u12	u12	PROPN
ejpam-3914	591	49	,	,	PUNCT
ejpam-3914	591	50	u13	u13	NOUN
ejpam-3914	591	51	}	}	PUNCT
ejpam-3914	591	52	r3	r3	PROPN
ejpam-3914	591	53	=	=	PUNCT
ejpam-3914	591	54	{	{	PUNCT
ejpam-3914	591	55	u14	u14	NOUN
ejpam-3914	591	56	,	,	PUNCT
ejpam-3914	591	57	u15	u15	NOUN
ejpam-3914	591	58	,	,	PUNCT
ejpam-3914	591	59	u16	u16	NOUN
ejpam-3914	591	60	,	,	PUNCT
ejpam-3914	591	61	u17	u17	ADJ
ejpam-3914	591	62	,	,	PUNCT
ejpam-3914	591	63	u18	u18	PROPN
ejpam-3914	591	64	}	}	PUNCT
ejpam-3914	591	65	...	...	PUNCT
ejpam-3914	592	1	rp−1	rp−1	NOUN
ejpam-3914	592	2	=	=	SYM
ejpam-3914	592	3	{	{	PUNCT
ejpam-3914	592	4	un−9	un−9	PROPN
ejpam-3914	592	5	,	,	PUNCT
ejpam-3914	592	6	un−8	un−8	ADJ
ejpam-3914	592	7	,	,	PUNCT
ejpam-3914	592	8	un−7	un−7	PROPN
ejpam-3914	592	9	,	,	PUNCT
ejpam-3914	592	10	un−6	un−6	PROPN
ejpam-3914	592	11	,	,	PUNCT
ejpam-3914	592	12	un−5	un−5	PROPN
ejpam-3914	592	13	}	}	PUNCT
ejpam-3914	592	14	rp	rp	NOUN
ejpam-3914	592	15	=	=	SYM
ejpam-3914	592	16	{	{	PUNCT
ejpam-3914	592	17	un−4	un−4	NOUN
ejpam-3914	592	18	,	,	PUNCT
ejpam-3914	592	19	un−3	un−3	ADJ
ejpam-3914	592	20	,	,	PUNCT
ejpam-3914	592	21	un−2	un−2	PROPN
ejpam-3914	592	22	,	,	PUNCT
ejpam-3914	592	23	un−1	un−1	PROPN
ejpam-3914	592	24	,	,	PUNCT
ejpam-3914	592	25	un	un	ADJ
ejpam-3914	592	26	}	}	PUNCT
ejpam-3914	592	27	let	let	VERB
ejpam-3914	592	28	i	i	PRON
ejpam-3914	592	29	=	=	NOUN
ejpam-3914	592	30	4	4	NUM
ejpam-3914	592	31	,	,	PUNCT
ejpam-3914	592	32	9	9	NUM
ejpam-3914	592	33	,	,	PUNCT
ejpam-3914	592	34	14	14	NUM
ejpam-3914	592	35	.	.	PUNCT
ejpam-3914	592	36	.	.	PUNCT
ejpam-3914	593	1	.	.	PUNCT
ejpam-3914	594	1	,	,	PUNCT
ejpam-3914	594	2	n−4	n−4	PROPN
ejpam-3914	594	3	.	.	PROPN
ejpam-3914	595	1	for	for	ADP
ejpam-3914	595	2	every	every	DET
ejpam-3914	595	3	induced	induced	ADJ
ejpam-3914	595	4	subgraph	subgraph	NOUN
ejpam-3914	595	5	〈	〈	PROPN
ejpam-3914	595	6	ui	ui	PROPN
ejpam-3914	595	7	,	,	PUNCT
ejpam-3914	595	8	ui+1	ui+1	PROPN
ejpam-3914	595	9	,	,	PUNCT
ejpam-3914	595	10	ui+2	ui+2	NUM
ejpam-3914	595	11	,	,	PUNCT
ejpam-3914	595	12	ui+3	ui+3	NOUN
ejpam-3914	595	13	,	,	PUNCT
ejpam-3914	595	14	ui+4	ui+4	PROPN
ejpam-3914	595	15	〉	〉	NOUN
ejpam-3914	595	16	,	,	PUNCT
ejpam-3914	595	17	the	the	DET
ejpam-3914	595	18	vertices	vertex	NOUN
ejpam-3914	595	19	u1	u1	NOUN
ejpam-3914	595	20	,	,	PUNCT
ejpam-3914	595	21	u2	u2	PROPN
ejpam-3914	595	22	,	,	PUNCT
ejpam-3914	595	23	ui	ui	NOUN
ejpam-3914	595	24	,	,	PUNCT
ejpam-3914	595	25	ui+1	ui+1	PROPN
ejpam-3914	595	26	form	form	NOUN
ejpam-3914	595	27	a	a	DET
ejpam-3914	595	28	total	total	ADJ
ejpam-3914	595	29	dr	dr	ADJ
ejpam-3914	595	30	-	-	PUNCT
ejpam-3914	595	31	power	power	NOUN
ejpam-3914	595	32	dominating	dominating	NOUN
ejpam-3914	595	33	set	set	VERB
ejpam-3914	595	34	since	since	SCONJ
ejpam-3914	595	35	u3	u3	NOUN
ejpam-3914	595	36	,	,	PUNCT
ejpam-3914	595	37	ui+2	ui+2	NUM
ejpam-3914	595	38	and	and	CCONJ
ejpam-3914	595	39	ui+4	ui+4	PRON
ejpam-3914	595	40	are	be	AUX
ejpam-3914	595	41	directly	directly	ADV
ejpam-3914	595	42	observed	observe	VERB
ejpam-3914	595	43	vertices	vertex	NOUN
ejpam-3914	595	44	while	while	SCONJ
ejpam-3914	595	45	ui+3	ui+3	NOUN
ejpam-3914	595	46	is	be	AUX
ejpam-3914	595	47	a	a	DET
ejpam-3914	595	48	remotely	remotely	ADV
ejpam-3914	595	49	observed	observe	VERB
ejpam-3914	595	50	vertex	vertex	NOUN
ejpam-3914	595	51	for	for	ADP
ejpam-3914	595	52	all	all	DET
ejpam-3914	595	53	i	i	PRON
ejpam-3914	595	54	=	=	NOUN
ejpam-3914	595	55	4	4	NUM
ejpam-3914	595	56	,	,	PUNCT
ejpam-3914	595	57	9	9	NUM
ejpam-3914	595	58	,	,	PUNCT
ejpam-3914	595	59	14	14	NUM
ejpam-3914	595	60	,	,	PUNCT
ejpam-3914	595	61	.	.	PUNCT
ejpam-3914	595	62	.	.	PUNCT
ejpam-3914	596	1	.	.	PUNCT
ejpam-3914	597	1	,	,	PUNCT
ejpam-3914	597	2	n−9	n−9	PROPN
ejpam-3914	597	3	,	,	PUNCT
ejpam-3914	597	4	n−4	n−4	PROPN
ejpam-3914	597	5	.	.	PUNCT
ejpam-3914	598	1	let	let	VERB
ejpam-3914	598	2	the	the	DET
ejpam-3914	598	3	set	set	NOUN
ejpam-3914	598	4	r	r	NOUN
ejpam-3914	598	5	=	=	SYM
ejpam-3914	598	6	{	{	PUNCT
ejpam-3914	598	7	u1	u1	NOUN
ejpam-3914	598	8	,	,	PUNCT
ejpam-3914	598	9	u2	u2	PROPN
ejpam-3914	598	10	,	,	PUNCT
ejpam-3914	598	11	ui	ui	NOUN
ejpam-3914	598	12	,	,	PUNCT
ejpam-3914	598	13	ui+1	ui+1	PROPN
ejpam-3914	599	1	:	:	PUNCT
ejpam-3914	599	2	i	i	NOUN
ejpam-3914	599	3	=	=	NOUN
ejpam-3914	599	4	4	4	NUM
ejpam-3914	599	5	,	,	PUNCT
ejpam-3914	599	6	9	9	NUM
ejpam-3914	599	7	,	,	PUNCT
ejpam-3914	599	8	14	14	NUM
ejpam-3914	599	9	,	,	PUNCT
ejpam-3914	599	10	.	.	PUNCT
ejpam-3914	599	11	.	.	PUNCT
ejpam-3914	599	12	.	.	PUNCT
ejpam-3914	600	1	,	,	PUNCT
ejpam-3914	600	2	n−	n−	NOUN
ejpam-3914	600	3	9	9	NUM
ejpam-3914	600	4	,	,	PUNCT
ejpam-3914	600	5	n−	n−	NOUN
ejpam-3914	600	6	4	4	NUM
ejpam-3914	600	7	}	}	PUNCT
ejpam-3914	600	8	=	=	NOUN
ejpam-3914	600	9	{	{	PUNCT
ejpam-3914	600	10	u1	u1	NOUN
ejpam-3914	600	11	,	,	PUNCT
ejpam-3914	600	12	u2	u2	PROPN
ejpam-3914	600	13	,	,	PUNCT
ejpam-3914	600	14	u4	u4	PROPN
ejpam-3914	600	15	,	,	PUNCT
ejpam-3914	600	16	u5	u5	PROPN
ejpam-3914	600	17	,	,	PUNCT
ejpam-3914	600	18	u9	u9	PROPN
ejpam-3914	600	19	,	,	PUNCT
ejpam-3914	600	20	u10	u10	PROPN
ejpam-3914	600	21	,	,	PUNCT
ejpam-3914	600	22	u14	u14	NOUN
ejpam-3914	600	23	,	,	PUNCT
ejpam-3914	600	24	u15	u15	NOUN
ejpam-3914	600	25	,	,	PUNCT
ejpam-3914	600	26	.	.	PUNCT
ejpam-3914	600	27	.	.	PUNCT
ejpam-3914	601	1	.	.	PUNCT
ejpam-3914	602	1	,	,	PUNCT
ejpam-3914	602	2	un−9	un−9	PROPN
ejpam-3914	602	3	,	,	PUNCT
ejpam-3914	602	4	un−8	un−8	ADJ
ejpam-3914	602	5	,	,	PUNCT
ejpam-3914	602	6	un−4	un−4	NOUN
ejpam-3914	602	7	,	,	PUNCT
ejpam-3914	602	8	un−3	un−3	ADJ
ejpam-3914	602	9	}	}	PUNCT
ejpam-3914	602	10	,	,	PUNCT
ejpam-3914	602	11	where	where	SCONJ
ejpam-3914	602	12	|r|	|r|	NOUN
ejpam-3914	603	1	=	=	NOUN
ejpam-3914	603	2	2p	2p	NOUN
ejpam-3914	603	3	+	+	CCONJ
ejpam-3914	603	4	2	2	NUM
ejpam-3914	603	5	=	=	SYM
ejpam-3914	603	6	2(n−3	2(n−3	NOUN
ejpam-3914	603	7	5	5	NUM
ejpam-3914	603	8	)	)	PUNCT
ejpam-3914	603	9	+	+	CCONJ
ejpam-3914	603	10	2	2	X
ejpam-3914	603	11	=	=	SYM
ejpam-3914	603	12	2n+4	2n+4	NUM
ejpam-3914	603	13	5	5	NUM
ejpam-3914	603	14	,	,	PUNCT
ejpam-3914	603	15	or	or	CCONJ
ejpam-3914	603	16	v	v	NOUN
ejpam-3914	603	17	(	(	PUNCT
ejpam-3914	603	18	cn	cn	PROPN
ejpam-3914	603	19	)	)	PUNCT
ejpam-3914	603	20	=	=	NOUN
ejpam-3914	603	21	v	v	X
ejpam-3914	603	22	(	(	PUNCT
ejpam-3914	603	23	cn	cn	PROPN
ejpam-3914	603	24	)	)	PUNCT
ejpam-3914	603	25	,	,	PUNCT
ejpam-3914	603	26	or	or	CCONJ
ejpam-3914	603	27	e(cn	e(cn	NOUN
ejpam-3914	603	28	)	)	PUNCT
ejpam-3914	603	29	=	=	SYM
ejpam-3914	603	30	e(cn	e(cn	NOUN
ejpam-3914	603	31	)	)	PUNCT
ejpam-3914	603	32	,	,	PUNCT
ejpam-3914	603	33	and	and	CCONJ
ejpam-3914	603	34	the	the	DET
ejpam-3914	603	35	induced	induced	ADJ
ejpam-3914	603	36	subgraph	subgraph	NOUN
ejpam-3914	603	37	〈	〈	PROPN
ejpam-3914	603	38	r	r	PROPN
ejpam-3914	603	39	〉	〉	PROPN
ejpam-3914	603	40	has	have	VERB
ejpam-3914	603	41	no	no	DET
ejpam-3914	603	42	isolated	isolated	ADJ
ejpam-3914	603	43	vertex	vertex	NOUN
ejpam-3914	603	44	.	.	PUNCT
ejpam-3914	604	1	by	by	ADP
ejpam-3914	604	2	theorem	theorem	NOUN
ejpam-3914	604	3	2.3	2.3	NUM
ejpam-3914	604	4	,	,	PUNCT
ejpam-3914	604	5	r	r	NOUN
ejpam-3914	604	6	is	be	AUX
ejpam-3914	604	7	a	a	DET
ejpam-3914	604	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	604	9	-set	-set	PROPN
ejpam-3914	604	10	of	of	ADP
ejpam-3914	604	11	cn	cn	PROPN
ejpam-3914	604	12	.	.	PUNCT
ejpam-3914	605	1	let	let	VERB
ejpam-3914	606	1	m	m	PRON
ejpam-3914	606	2	+	+	ADJ
ejpam-3914	606	3	1	1	NUM
ejpam-3914	606	4	be	be	VERB
ejpam-3914	606	5	the	the	DET
ejpam-3914	606	6	number	number	NOUN
ejpam-3914	606	7	of	of	ADP
ejpam-3914	606	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	606	9	-sets	-set	NOUN
ejpam-3914	606	10	of	of	ADP
ejpam-3914	606	11	cn	cn	PROPN
ejpam-3914	606	12	where	where	SCONJ
ejpam-3914	606	13	m	m	PROPN
ejpam-3914	606	14	is	be	AUX
ejpam-3914	606	15	a	a	DET
ejpam-3914	606	16	positive	positive	ADJ
ejpam-3914	606	17	integer	integer	NOUN
ejpam-3914	606	18	.	.	PUNCT
ejpam-3914	607	1	let	let	VERB
ejpam-3914	607	2	k	k	NOUN
ejpam-3914	607	3	=	=	SYM
ejpam-3914	607	4	1	1	NUM
ejpam-3914	607	5	,	,	PUNCT
ejpam-3914	607	6	2	2	NUM
ejpam-3914	607	7	,	,	PUNCT
ejpam-3914	607	8	.	.	PUNCT
ejpam-3914	607	9	.	.	PUNCT
ejpam-3914	608	1	.	.	PUNCT
ejpam-3914	609	1	,	,	PUNCT
ejpam-3914	609	2	m	m	VERB
ejpam-3914	609	3	and	and	CCONJ
ejpam-3914	609	4	tk	tk	PROPN
ejpam-3914	609	5	be	be	AUX
ejpam-3914	609	6	a	a	DET
ejpam-3914	609	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	609	8	-set	-set	PUNCT
ejpam-3914	609	9	of	of	ADP
ejpam-3914	609	10	cn	cn	PROPN
ejpam-3914	609	11	different	different	ADJ
ejpam-3914	609	12	from	from	ADP
ejpam-3914	609	13	r.	r.	PROPN
ejpam-3914	609	14	note	note	PROPN
ejpam-3914	609	15	that	that	SCONJ
ejpam-3914	609	16	tk	tk	PROPN
ejpam-3914	609	17	can	can	AUX
ejpam-3914	609	18	be	be	AUX
ejpam-3914	609	19	formed	form	VERB
ejpam-3914	609	20	by	by	ADP
ejpam-3914	609	21	starting	start	VERB
ejpam-3914	609	22	all	all	DET
ejpam-3914	609	23	the	the	DET
ejpam-3914	609	24	vertices	vertex	NOUN
ejpam-3914	609	25	of	of	ADP
ejpam-3914	609	26	sl	sl	NOUN
ejpam-3914	609	27	for	for	ADP
ejpam-3914	609	28	l	l	NOUN
ejpam-3914	609	29	=	=	SYM
ejpam-3914	609	30	1	1	NUM
ejpam-3914	609	31	,	,	PUNCT
ejpam-3914	609	32	2	2	NUM
ejpam-3914	609	33	,	,	PUNCT
ejpam-3914	609	34	.	.	PUNCT
ejpam-3914	609	35	.	.	PUNCT
ejpam-3914	610	1	.	.	PUNCT
ejpam-3914	611	1	,	,	PUNCT
ejpam-3914	611	2	12	12	NUM
ejpam-3914	611	3	and	and	CCONJ
ejpam-3914	611	4	replacing	replace	VERB
ejpam-3914	611	5	u8	u8	PROPN
ejpam-3914	611	6	by	by	ADP
ejpam-3914	611	7	un	un	PROPN
ejpam-3914	611	8	in	in	ADP
ejpam-3914	611	9	s9	s9	PROPN
ejpam-3914	611	10	,	,	PUNCT
ejpam-3914	611	11	s11	s11	PROPN
ejpam-3914	611	12	and	and	CCONJ
ejpam-3914	611	13	s12	s12	PROPN
ejpam-3914	611	14	.	.	PUNCT
ejpam-3914	612	1	now	now	ADV
ejpam-3914	612	2	,	,	PUNCT
ejpam-3914	612	3	if	if	SCONJ
ejpam-3914	612	4	tk	tk	PROPN
ejpam-3914	612	5	starts	start	VERB
ejpam-3914	612	6	with	with	ADP
ejpam-3914	612	7	s1	s1	NOUN
ejpam-3914	612	8	,	,	PUNCT
ejpam-3914	612	9	then	then	ADV
ejpam-3914	612	10	let	let	VERB
ejpam-3914	612	11	k	k	NOUN
ejpam-3914	612	12	=	=	SYM
ejpam-3914	612	13	1	1	NUM
ejpam-3914	612	14	and	and	CCONJ
ejpam-3914	612	15	{	{	PUNCT
ejpam-3914	612	16	u2	u2	PROPN
ejpam-3914	612	17	,	,	PUNCT
ejpam-3914	612	18	u4	u4	PROPN
ejpam-3914	612	19	}	}	PUNCT
ejpam-3914	612	20	⊆	⊆	NUM
ejpam-3914	612	21	{	{	PUNCT
ejpam-3914	612	22	u1	u1	NOUN
ejpam-3914	612	23	,	,	PUNCT
ejpam-3914	612	24	u2	u2	PROPN
ejpam-3914	612	25	,	,	PUNCT
ejpam-3914	612	26	u4	u4	PROPN
ejpam-3914	612	27	,	,	PUNCT
ejpam-3914	612	28	u5	u5	PROPN
ejpam-3914	612	29	}	}	PUNCT
ejpam-3914	612	30	⊆	⊆	NUM
ejpam-3914	612	31	t1	t1	NOUN
ejpam-3914	612	32	.	.	PUNCT
ejpam-3914	613	1	replace	replace	VERB
ejpam-3914	613	2	u9	u9	PROPN
ejpam-3914	613	3	∈	∈	PROPN
ejpam-3914	613	4	r	r	NOUN
ejpam-3914	613	5	by	by	ADP
ejpam-3914	613	6	u8	u8	PROPN
ejpam-3914	613	7	to	to	PART
ejpam-3914	613	8	form	form	VERB
ejpam-3914	613	9	t1	t1	PROPN
ejpam-3914	613	10	.	.	PUNCT
ejpam-3914	614	1	then	then	ADV
ejpam-3914	614	2	the	the	DET
ejpam-3914	614	3	next	next	ADJ
ejpam-3914	614	4	vertex	vertex	NOUN
ejpam-3914	614	5	to	to	PART
ejpam-3914	614	6	be	be	AUX
ejpam-3914	614	7	choosen	choosen	VERB
ejpam-3914	614	8	must	must	AUX
ejpam-3914	614	9	be	be	AUX
ejpam-3914	614	10	u9	u9	ADJ
ejpam-3914	614	11	,	,	PUNCT
ejpam-3914	614	12	that	that	ADV
ejpam-3914	614	13	is	is	ADV
ejpam-3914	614	14	,	,	PUNCT
ejpam-3914	614	15	the	the	DET
ejpam-3914	614	16	vertex	vertex	NOUN
ejpam-3914	614	17	ui+4	ui+4	PROPN
ejpam-3914	614	18	,	,	PUNCT
ejpam-3914	614	19	ui	ui	PROPN
ejpam-3914	614	20	must	must	AUX
ejpam-3914	614	21	be	be	AUX
ejpam-3914	614	22	in	in	ADP
ejpam-3914	614	23	t1	t1	NOUN
ejpam-3914	614	24	for	for	ADP
ejpam-3914	614	25	all	all	DET
ejpam-3914	614	26	i	i	PRON
ejpam-3914	614	27	=	=	NOUN
ejpam-3914	614	28	4	4	NUM
ejpam-3914	614	29	,	,	PUNCT
ejpam-3914	614	30	9	9	NUM
ejpam-3914	614	31	,	,	PUNCT
ejpam-3914	614	32	14	14	NUM
ejpam-3914	614	33	,	,	PUNCT
ejpam-3914	614	34	.	.	PUNCT
ejpam-3914	614	35	.	.	PUNCT
ejpam-3914	615	1	.	.	PUNCT
ejpam-3914	616	1	,	,	PUNCT
ejpam-3914	616	2	n	n	CCONJ
ejpam-3914	616	3	−	−	PROPN
ejpam-3914	616	4	9	9	NUM
ejpam-3914	616	5	,	,	PUNCT
ejpam-3914	616	6	n	n	CCONJ
ejpam-3914	616	7	−	−	PROPN
ejpam-3914	616	8	4	4	NUM
ejpam-3914	616	9	.	.	PUNCT
ejpam-3914	617	1	then	then	ADV
ejpam-3914	617	2	t1	t1	NOUN
ejpam-3914	617	3	=	=	PUNCT
ejpam-3914	617	4	{	{	PUNCT
ejpam-3914	617	5	u1	u1	NOUN
ejpam-3914	617	6	,	,	PUNCT
ejpam-3914	617	7	u2	u2	PROPN
ejpam-3914	617	8	,	,	PUNCT
ejpam-3914	617	9	u4	u4	PROPN
ejpam-3914	617	10	,	,	PUNCT
ejpam-3914	617	11	u5	u5	PROPN
ejpam-3914	617	12	,	,	PUNCT
ejpam-3914	617	13	u8	u8	PROPN
ejpam-3914	617	14	,	,	PUNCT
ejpam-3914	617	15	u9	u9	PROPN
ejpam-3914	617	16	,	,	PUNCT
ejpam-3914	617	17	u13	u13	NOUN
ejpam-3914	617	18	,	,	PUNCT
ejpam-3914	617	19	u14	u14	NOUN
ejpam-3914	617	20	,	,	PUNCT
ejpam-3914	617	21	u18	u18	PROPN
ejpam-3914	617	22	,	,	PUNCT
ejpam-3914	617	23	u19	u19	PROPN
ejpam-3914	617	24	,	,	PUNCT
ejpam-3914	617	25	.	.	PUNCT
ejpam-3914	617	26	.	.	PUNCT
ejpam-3914	618	1	.	.	PUNCT
ejpam-3914	619	1	,	,	PUNCT
ejpam-3914	620	1	un−5	un−5	PROPN
ejpam-3914	620	2	,	,	PUNCT
ejpam-3914	620	3	un−4	un−4	NOUN
ejpam-3914	620	4	}	}	PUNCT
ejpam-3914	620	5	such	such	ADJ
ejpam-3914	620	6	that	that	DET
ejpam-3914	620	7	|t1|	|t1|	NOUN
ejpam-3914	620	8	=	=	SYM
ejpam-3914	620	9	|r|	|r|	PROPN
ejpam-3914	620	10	.	.	PUNCT
ejpam-3914	621	1	since	since	SCONJ
ejpam-3914	621	2	u1	u1	PROPN
ejpam-3914	621	3	∈	∈	PROPN
ejpam-3914	621	4	t1	t1	NOUN
ejpam-3914	621	5	and	and	CCONJ
ejpam-3914	621	6	un−4	un−4	NOUN
ejpam-3914	621	7	is	be	AUX
ejpam-3914	621	8	the	the	DET
ejpam-3914	621	9	last	last	ADJ
ejpam-3914	621	10	vertex	vertex	NOUN
ejpam-3914	621	11	in	in	ADP
ejpam-3914	621	12	t1	t1	PROPN
ejpam-3914	621	13	,	,	PUNCT
ejpam-3914	621	14	by	by	ADP
ejpam-3914	621	15	the	the	DET
ejpam-3914	621	16	same	same	ADJ
ejpam-3914	621	17	argument	argument	NOUN
ejpam-3914	621	18	in	in	ADP
ejpam-3914	621	19	case	case	NOUN
ejpam-3914	621	20	1	1	NUM
ejpam-3914	621	21	,	,	PUNCT
ejpam-3914	621	22	t1	t1	PROPN
ejpam-3914	621	23	is	be	AUX
ejpam-3914	621	24	not	not	PART
ejpam-3914	621	25	a	a	DET
ejpam-3914	621	26	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	621	27	-set	-set	PROPN
ejpam-3914	621	28	of	of	ADP
ejpam-3914	621	29	cn	cn	PROPN
ejpam-3914	621	30	.	.	PUNCT
ejpam-3914	622	1	since	since	SCONJ
ejpam-3914	622	2	u9	u9	PROPN
ejpam-3914	622	3	is	be	AUX
ejpam-3914	622	4	arbitrarily	arbitrarily	ADV
ejpam-3914	622	5	replaced	replace	VERB
ejpam-3914	622	6	from	from	ADP
ejpam-3914	622	7	r	r	NOUN
ejpam-3914	622	8	,	,	PUNCT
ejpam-3914	622	9	we	we	PRON
ejpam-3914	622	10	can	can	AUX
ejpam-3914	622	11	not	not	PART
ejpam-3914	622	12	replace	replace	VERB
ejpam-3914	622	13	the	the	DET
ejpam-3914	622	14	vertex	vertex	NOUN
ejpam-3914	622	15	ui	ui	NOUN
ejpam-3914	622	16	in	in	ADP
ejpam-3914	622	17	r	r	NOUN
ejpam-3914	622	18	,	,	PUNCT
ejpam-3914	622	19	where	where	SCONJ
ejpam-3914	622	20	i	i	PRON
ejpam-3914	622	21	=	=	NOUN
ejpam-3914	622	22	9	9	NUM
ejpam-3914	622	23	,	,	PUNCT
ejpam-3914	622	24	14	14	NUM
ejpam-3914	622	25	,	,	PUNCT
ejpam-3914	622	26	.	.	PUNCT
ejpam-3914	622	27	.	.	PUNCT
ejpam-3914	623	1	.	.	PUNCT
ejpam-3914	624	1	,	,	PUNCT
ejpam-3914	624	2	n−	n−	NOUN
ejpam-3914	624	3	9	9	NUM
ejpam-3914	624	4	,	,	PUNCT
ejpam-3914	624	5	n−	n−	NOUN
ejpam-3914	624	6	4	4	NUM
ejpam-3914	624	7	to	to	PART
ejpam-3914	624	8	form	form	VERB
ejpam-3914	624	9	another	another	PRON
ejpam-3914	624	10	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	624	11	-set	-set	PROPN
ejpam-3914	624	12	of	of	ADP
ejpam-3914	624	13	cn	cn	PROPN
ejpam-3914	624	14	.	.	PUNCT
ejpam-3914	624	15	therefore	therefore	ADV
ejpam-3914	624	16	,	,	PUNCT
ejpam-3914	624	17	only	only	ADV
ejpam-3914	624	18	the	the	DET
ejpam-3914	624	19	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	624	20	-set	-set	PUNCT
ejpam-3914	624	21	r	r	NOUN
ejpam-3914	624	22	starts	start	VERB
ejpam-3914	624	23	with	with	ADP
ejpam-3914	624	24	s1	s1	NOUN
ejpam-3914	624	25	and	and	CCONJ
ejpam-3914	624	26	so	so	ADV
ejpam-3914	624	27	,	,	PUNCT
ejpam-3914	624	28	{	{	PUNCT
ejpam-3914	624	29	u2	u2	NOUN
ejpam-3914	624	30	,	,	PUNCT
ejpam-3914	624	31	u4	u4	PROPN
ejpam-3914	624	32	}	}	PUNCT
ejpam-3914	624	33	*	*	PUNCT
ejpam-3914	624	34	tk	tk	PROPN
ejpam-3914	624	35	for	for	ADP
ejpam-3914	624	36	all	all	PRON
ejpam-3914	624	37	k	k	NOUN
ejpam-3914	624	38	=	=	SYM
ejpam-3914	624	39	1	1	NUM
ejpam-3914	624	40	,	,	PUNCT
ejpam-3914	624	41	2	2	NUM
ejpam-3914	624	42	,	,	PUNCT
ejpam-3914	624	43	.	.	PUNCT
ejpam-3914	624	44	.	.	PUNCT
ejpam-3914	624	45	.	.	PUNCT
ejpam-3914	625	1	,	,	PUNCT
ejpam-3914	625	2	m.	m.	NOUN
ejpam-3914	625	3	hence	hence	ADV
ejpam-3914	625	4	,	,	PUNCT
ejpam-3914	625	5	{	{	PUNCT
ejpam-3914	625	6	u2	u2	NOUN
ejpam-3914	625	7	,	,	PUNCT
ejpam-3914	625	8	u4	u4	PROPN
ejpam-3914	625	9	}	}	PUNCT
ejpam-3914	625	10	is	be	AUX
ejpam-3914	625	11	a	a	DET
ejpam-3914	625	12	forcing	forcing	NOUN
ejpam-3914	625	13	subset	subset	NOUN
ejpam-3914	625	14	for	for	ADP
ejpam-3914	625	15	r.	r.	PROPN
ejpam-3914	625	16	therefore	therefore	ADV
ejpam-3914	625	17	,	,	PUNCT
ejpam-3914	625	18	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	625	19	(	(	PUNCT
ejpam-3914	625	20	r	r	NOUN
ejpam-3914	625	21	)	)	PUNCT
ejpam-3914	625	22	=	=	SYM
ejpam-3914	626	1	2	2	NUM
ejpam-3914	626	2	=	=	NOUN
ejpam-3914	626	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	626	4	(	(	PUNCT
ejpam-3914	626	5	cn	cn	NOUN
ejpam-3914	626	6	)	)	PUNCT
ejpam-3914	626	7	.	.	PUNCT
ejpam-3914	627	1	case	case	NOUN
ejpam-3914	627	2	5	5	NUM
ejpam-3914	627	3	:	:	PUNCT
ejpam-3914	627	4	suppose	suppose	VERB
ejpam-3914	627	5	that	that	SCONJ
ejpam-3914	627	6	n	n	PROPN
ejpam-3914	627	7	≡	≡	PROPN
ejpam-3914	627	8	4(mod	4(mod	NUM
ejpam-3914	627	9	5	5	NUM
ejpam-3914	627	10	)	)	PUNCT
ejpam-3914	627	11	.	.	PUNCT
ejpam-3914	628	1	by	by	ADP
ejpam-3914	628	2	theorem	theorem	NOUN
ejpam-3914	628	3	2.3	2.3	NUM
ejpam-3914	628	4	,	,	PUNCT
ejpam-3914	628	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	628	6	(	(	PUNCT
ejpam-3914	628	7	cn	cn	NOUN
ejpam-3914	628	8	)	)	PUNCT
ejpam-3914	628	9	=	=	PUNCT
ejpam-3914	628	10	2n+2	2n+2	NUM
ejpam-3914	628	11	5	5	NUM
ejpam-3914	628	12	.	.	PUNCT
ejpam-3914	628	13	suppose	suppose	VERB
ejpam-3914	628	14	that	that	SCONJ
ejpam-3914	628	15	n	n	NOUN
ejpam-3914	628	16	=	=	SYM
ejpam-3914	628	17	9	9	NUM
ejpam-3914	628	18	.	.	PUNCT
ejpam-3914	629	1	then	then	ADV
ejpam-3914	629	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	629	3	(	(	PUNCT
ejpam-3914	629	4	c9	c9	NOUN
ejpam-3914	629	5	)	)	PUNCT
ejpam-3914	629	6	=	=	NOUN
ejpam-3914	629	7	2(9)+2	2(9)+2	NUM
ejpam-3914	629	8	5	5	NUM
ejpam-3914	629	9	=	=	SYM
ejpam-3914	629	10	4	4	NUM
ejpam-3914	629	11	.	.	PUNCT
ejpam-3914	629	12	clearly	clearly	ADV
ejpam-3914	629	13	,	,	PUNCT
ejpam-3914	629	14	s1	s1	PROPN
ejpam-3914	629	15	=	=	SYM
ejpam-3914	629	16	{	{	PUNCT
ejpam-3914	629	17	u1	u1	NOUN
ejpam-3914	629	18	,	,	PUNCT
ejpam-3914	629	19	u2	u2	PROPN
ejpam-3914	629	20	,	,	PUNCT
ejpam-3914	629	21	u5	u5	PROPN
ejpam-3914	629	22	,	,	PUNCT
ejpam-3914	629	23	u6	u6	NOUN
ejpam-3914	629	24	}	}	PUNCT
ejpam-3914	629	25	,	,	PUNCT
ejpam-3914	629	26	s2	s2	NOUN
ejpam-3914	629	27	=	=	SYM
ejpam-3914	629	28	{	{	PUNCT
ejpam-3914	629	29	u1	u1	NOUN
ejpam-3914	629	30	,	,	PUNCT
ejpam-3914	629	31	u2	u2	NOUN
ejpam-3914	629	32	,	,	PUNCT
ejpam-3914	629	33	u6	u6	PROPN
ejpam-3914	629	34	,	,	PUNCT
ejpam-3914	629	35	u7	u7	PROPN
ejpam-3914	629	36	}	}	PUNCT
ejpam-3914	629	37	,	,	PUNCT
ejpam-3914	629	38	s3	s3	PROPN
ejpam-3914	629	39	=	=	SYM
ejpam-3914	629	40	{	{	PUNCT
ejpam-3914	629	41	u2	u2	PROPN
ejpam-3914	629	42	,	,	PUNCT
ejpam-3914	629	43	u3	u3	NOUN
ejpam-3914	629	44	,	,	PUNCT
ejpam-3914	629	45	u6	u6	PROPN
ejpam-3914	629	46	,	,	PUNCT
ejpam-3914	629	47	u7	u7	PROPN
ejpam-3914	629	48	}	}	PUNCT
ejpam-3914	629	49	,	,	PUNCT
ejpam-3914	629	50	s4	s4	PROPN
ejpam-3914	629	51	=	=	SYM
ejpam-3914	629	52	{	{	PUNCT
ejpam-3914	629	53	u2	u2	PROPN
ejpam-3914	629	54	,	,	PUNCT
ejpam-3914	629	55	u3	u3	PROPN
ejpam-3914	629	56	,	,	PUNCT
ejpam-3914	629	57	u7	u7	PROPN
ejpam-3914	629	58	,	,	PUNCT
ejpam-3914	629	59	u8	u8	PROPN
ejpam-3914	629	60	}	}	PUNCT
ejpam-3914	629	61	,	,	PUNCT
ejpam-3914	629	62	s5	s5	X
ejpam-3914	629	63	=	=	PUNCT
ejpam-3914	629	64	{	{	PUNCT
ejpam-3914	629	65	u3	u3	PROPN
ejpam-3914	629	66	,	,	PUNCT
ejpam-3914	629	67	u4	u4	PROPN
ejpam-3914	629	68	,	,	PUNCT
ejpam-3914	629	69	u7	u7	PROPN
ejpam-3914	629	70	,	,	PUNCT
ejpam-3914	629	71	u8	u8	PROPN
ejpam-3914	629	72	}	}	PUNCT
ejpam-3914	629	73	,	,	PUNCT
ejpam-3914	629	74	s6	s6	PROPN
ejpam-3914	629	75	=	=	SYM
ejpam-3914	629	76	{	{	PUNCT
ejpam-3914	629	77	u3	u3	PROPN
ejpam-3914	629	78	,	,	PUNCT
ejpam-3914	629	79	u4	u4	PROPN
ejpam-3914	629	80	,	,	PUNCT
ejpam-3914	629	81	u8	u8	PROPN
ejpam-3914	629	82	,	,	PUNCT
ejpam-3914	629	83	u9	u9	PROPN
ejpam-3914	629	84	}	}	PUNCT
ejpam-3914	629	85	,	,	PUNCT
ejpam-3914	629	86	s7	s7	PROPN
ejpam-3914	629	87	=	=	SYM
ejpam-3914	629	88	{	{	PUNCT
ejpam-3914	629	89	u4	u4	PROPN
ejpam-3914	629	90	,	,	PUNCT
ejpam-3914	629	91	u5	u5	PROPN
ejpam-3914	629	92	,	,	PUNCT
ejpam-3914	629	93	u8	u8	PROPN
ejpam-3914	629	94	,	,	PUNCT
ejpam-3914	629	95	u9	u9	PROPN
ejpam-3914	629	96	}	}	PUNCT
ejpam-3914	629	97	,	,	PUNCT
ejpam-3914	629	98	s8	s8	PROPN
ejpam-3914	629	99	=	=	SYM
ejpam-3914	629	100	{	{	PUNCT
ejpam-3914	629	101	u4	u4	PROPN
ejpam-3914	629	102	,	,	PUNCT
ejpam-3914	629	103	u5	u5	PROPN
ejpam-3914	629	104	,	,	PUNCT
ejpam-3914	629	105	u9	u9	PROPN
ejpam-3914	629	106	,	,	PUNCT
ejpam-3914	629	107	u1	u1	NOUN
ejpam-3914	629	108	}	}	PUNCT
ejpam-3914	629	109	,	,	PUNCT
ejpam-3914	629	110	and	and	CCONJ
ejpam-3914	629	111	s9	s9	NOUN
ejpam-3914	629	112	=	=	SYM
ejpam-3914	629	113	{	{	PUNCT
ejpam-3914	629	114	u5	u5	PROPN
ejpam-3914	629	115	,	,	PUNCT
ejpam-3914	629	116	u6	u6	PROPN
ejpam-3914	629	117	,	,	PUNCT
ejpam-3914	629	118	u9	u9	PROPN
ejpam-3914	629	119	,	,	PUNCT
ejpam-3914	629	120	u1	u1	PROPN
ejpam-3914	629	121	}	}	PUNCT
ejpam-3914	629	122	are	be	AUX
ejpam-3914	629	123	the	the	DET
ejpam-3914	629	124	only	only	ADJ
ejpam-3914	629	125	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	629	126	-sets	-set	NOUN
ejpam-3914	629	127	of	of	ADP
ejpam-3914	629	128	c9	c9	NOUN
ejpam-3914	629	129	.	.	PUNCT
ejpam-3914	630	1	clearly	clearly	ADV
ejpam-3914	630	2	,	,	PUNCT
ejpam-3914	630	3	for	for	ADP
ejpam-3914	630	4	l	l	NOUN
ejpam-3914	630	5	=	=	SYM
ejpam-3914	630	6	1	1	NUM
ejpam-3914	630	7	,	,	PUNCT
ejpam-3914	630	8	2	2	NUM
ejpam-3914	630	9	,	,	PUNCT
ejpam-3914	630	10	.	.	PUNCT
ejpam-3914	630	11	.	.	PUNCT
ejpam-3914	630	12	.	.	PUNCT
ejpam-3914	631	1	,	,	PUNCT
ejpam-3914	631	2	9	9	NUM
ejpam-3914	631	3	,	,	PUNCT
ejpam-3914	631	4	{	{	PUNCT
ejpam-3914	631	5	u2	u2	NOUN
ejpam-3914	631	6	,	,	PUNCT
ejpam-3914	631	7	u5	u5	PROPN
ejpam-3914	631	8	}	}	PUNCT
ejpam-3914	631	9	⊆	⊆	NUM
ejpam-3914	631	10	s1	s1	NOUN
ejpam-3914	631	11	and	and	CCONJ
ejpam-3914	631	12	{	{	PUNCT
ejpam-3914	631	13	u2	u2	PROPN
ejpam-3914	631	14	,	,	PUNCT
ejpam-3914	631	15	u5	u5	PROPN
ejpam-3914	631	16	}	}	PUNCT
ejpam-3914	631	17	*	*	PUNCT
ejpam-3914	631	18	sl	sl	INTJ
ejpam-3914	631	19	for	for	ADP
ejpam-3914	631	20	all	all	DET
ejpam-3914	631	21	l	l	NOUN
ejpam-3914	631	22	6=	6=	NUM
ejpam-3914	631	23	1	1	NUM
ejpam-3914	631	24	.	.	PUNCT
ejpam-3914	632	1	thus	thus	ADV
ejpam-3914	632	2	,	,	PUNCT
ejpam-3914	632	3	{	{	PUNCT
ejpam-3914	632	4	u2	u2	NOUN
ejpam-3914	632	5	,	,	PUNCT
ejpam-3914	632	6	u5	u5	PROPN
ejpam-3914	632	7	}	}	PUNCT
ejpam-3914	632	8	is	be	AUX
ejpam-3914	632	9	a	a	DET
ejpam-3914	632	10	forcing	forcing	NOUN
ejpam-3914	632	11	subset	subset	NOUN
ejpam-3914	632	12	for	for	ADP
ejpam-3914	632	13	s1	s1	NOUN
ejpam-3914	632	14	,	,	PUNCT
ejpam-3914	632	15	that	that	ADV
ejpam-3914	632	16	is	is	ADV
ejpam-3914	632	17	,	,	PUNCT
ejpam-3914	632	18	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	632	19	(	(	PUNCT
ejpam-3914	632	20	s1	s1	NOUN
ejpam-3914	632	21	)	)	PUNCT
ejpam-3914	632	22	=	=	SYM
ejpam-3914	633	1	2	2	NUM
ejpam-3914	633	2	=	=	NOUN
ejpam-3914	633	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	633	4	(	(	PUNCT
ejpam-3914	633	5	c9	c9	NOUN
ejpam-3914	633	6	)	)	PUNCT
ejpam-3914	633	7	.	.	PUNCT
ejpam-3914	634	1	now	now	ADV
ejpam-3914	634	2	,	,	PUNCT
ejpam-3914	634	3	suppose	suppose	VERB
ejpam-3914	634	4	that	that	SCONJ
ejpam-3914	634	5	n	n	PROPN
ejpam-3914	634	6	>	>	X
ejpam-3914	634	7	9	9	X
ejpam-3914	634	8	.	.	PUNCT
ejpam-3914	635	1	let	let	VERB
ejpam-3914	635	2	p	p	NOUN
ejpam-3914	635	3	=	=	PUNCT
ejpam-3914	635	4	n−4	n−4	PROPN
ejpam-3914	635	5	5	5	NUM
ejpam-3914	635	6	and	and	CCONJ
ejpam-3914	635	7	j	j	NOUN
ejpam-3914	635	8	=	=	SYM
ejpam-3914	635	9	0	0	NUM
ejpam-3914	635	10	,	,	PUNCT
ejpam-3914	635	11	1	1	NUM
ejpam-3914	635	12	,	,	PUNCT
ejpam-3914	635	13	2	2	NUM
ejpam-3914	635	14	,	,	PUNCT
ejpam-3914	635	15	.	.	PUNCT
ejpam-3914	635	16	.	.	PUNCT
ejpam-3914	636	1	.	.	PUNCT
ejpam-3914	637	1	,	,	PUNCT
ejpam-3914	637	2	p−	p−	NOUN
ejpam-3914	637	3	1	1	NUM
ejpam-3914	637	4	,	,	PUNCT
ejpam-3914	637	5	p.	p.	NOUN
ejpam-3914	637	6	group	group	NOUN
ejpam-3914	637	7	the	the	DET
ejpam-3914	637	8	vertices	vertex	NOUN
ejpam-3914	637	9	of	of	ADP
ejpam-3914	637	10	c.	c.	PROPN
ejpam-3914	637	11	armada	armada	PROPN
ejpam-3914	637	12	/	/	SYM
ejpam-3914	637	13	eur	eur	PROPN
ejpam-3914	637	14	.	.	PUNCT
ejpam-3914	638	1	j.	j.	PROPN
ejpam-3914	638	2	pure	pure	PROPN
ejpam-3914	638	3	appl	appl	PROPN
ejpam-3914	638	4	.	.	PROPN
ejpam-3914	638	5	math	math	PROPN
ejpam-3914	638	6	,	,	PUNCT
ejpam-3914	638	7	14	14	NUM
ejpam-3914	638	8	(	(	PUNCT
ejpam-3914	638	9	2	2	NUM
ejpam-3914	638	10	)	)	PUNCT
ejpam-3914	638	11	(	(	PUNCT
ejpam-3914	638	12	2021	2021	NUM
ejpam-3914	638	13	)	)	PUNCT
ejpam-3914	638	14	,	,	PUNCT
ejpam-3914	638	15	451	451	NUM
ejpam-3914	638	16	-	-	SYM
ejpam-3914	638	17	470	470	NUM
ejpam-3914	638	18	467	467	NUM
ejpam-3914	638	19	cn	cn	NOUN
ejpam-3914	638	20	into	into	ADP
ejpam-3914	638	21	p+	p+	NOUN
ejpam-3914	638	22	1	1	NUM
ejpam-3914	638	23	disjoint	disjoint	NOUN
ejpam-3914	638	24	subsets	subset	NOUN
ejpam-3914	638	25	rj	rj	PROPN
ejpam-3914	638	26	r0	r0	PROPN
ejpam-3914	638	27	=	=	PUNCT
ejpam-3914	638	28	{	{	PUNCT
ejpam-3914	638	29	u1	u1	NOUN
ejpam-3914	638	30	,	,	PUNCT
ejpam-3914	638	31	u2	u2	NOUN
ejpam-3914	638	32	,	,	PUNCT
ejpam-3914	638	33	u3	u3	NOUN
ejpam-3914	638	34	,	,	PUNCT
ejpam-3914	638	35	u4	u4	PROPN
ejpam-3914	638	36	}	}	PUNCT
ejpam-3914	638	37	r1	r1	NOUN
ejpam-3914	638	38	=	=	SYM
ejpam-3914	638	39	{	{	PUNCT
ejpam-3914	638	40	u5	u5	PROPN
ejpam-3914	638	41	,	,	PUNCT
ejpam-3914	638	42	u6	u6	PROPN
ejpam-3914	638	43	,	,	PUNCT
ejpam-3914	638	44	u7	u7	PROPN
ejpam-3914	638	45	,	,	PUNCT
ejpam-3914	638	46	u8	u8	PROPN
ejpam-3914	638	47	,	,	PUNCT
ejpam-3914	638	48	u9	u9	PROPN
ejpam-3914	638	49	}	}	PUNCT
ejpam-3914	638	50	r2	r2	NOUN
ejpam-3914	638	51	=	=	SYM
ejpam-3914	638	52	{	{	PUNCT
ejpam-3914	638	53	u10	u10	PROPN
ejpam-3914	638	54	,	,	PUNCT
ejpam-3914	638	55	u11	u11	PROPN
ejpam-3914	638	56	,	,	PUNCT
ejpam-3914	638	57	u12	u12	PROPN
ejpam-3914	638	58	,	,	PUNCT
ejpam-3914	638	59	u13	u13	NOUN
ejpam-3914	638	60	,	,	PUNCT
ejpam-3914	638	61	u14	u14	NOUN
ejpam-3914	638	62	}	}	PUNCT
ejpam-3914	638	63	r3	r3	PROPN
ejpam-3914	638	64	=	=	SYM
ejpam-3914	638	65	{	{	PUNCT
ejpam-3914	638	66	u15	u15	PROPN
ejpam-3914	638	67	,	,	PUNCT
ejpam-3914	638	68	u16	u16	NOUN
ejpam-3914	638	69	,	,	PUNCT
ejpam-3914	638	70	u17	u17	PROPN
ejpam-3914	638	71	,	,	PUNCT
ejpam-3914	638	72	u18	u18	PROPN
ejpam-3914	638	73	,	,	PUNCT
ejpam-3914	638	74	u19	u19	PROPN
ejpam-3914	638	75	}	}	PUNCT
ejpam-3914	638	76	...	...	PUNCT
ejpam-3914	639	1	rp−1	rp−1	NOUN
ejpam-3914	639	2	=	=	SYM
ejpam-3914	639	3	{	{	PUNCT
ejpam-3914	639	4	un−9	un−9	PROPN
ejpam-3914	639	5	,	,	PUNCT
ejpam-3914	639	6	un−8	un−8	ADJ
ejpam-3914	639	7	,	,	PUNCT
ejpam-3914	639	8	un−7	un−7	PROPN
ejpam-3914	639	9	,	,	PUNCT
ejpam-3914	639	10	un−6	un−6	PROPN
ejpam-3914	639	11	,	,	PUNCT
ejpam-3914	639	12	un−5	un−5	PROPN
ejpam-3914	639	13	}	}	PUNCT
ejpam-3914	639	14	rp	rp	NOUN
ejpam-3914	639	15	=	=	SYM
ejpam-3914	639	16	{	{	PUNCT
ejpam-3914	639	17	un−4	un−4	NOUN
ejpam-3914	639	18	,	,	PUNCT
ejpam-3914	639	19	un−3	un−3	ADJ
ejpam-3914	639	20	,	,	PUNCT
ejpam-3914	639	21	un−2	un−2	PROPN
ejpam-3914	639	22	,	,	PUNCT
ejpam-3914	639	23	un−1	un−1	PROPN
ejpam-3914	639	24	,	,	PUNCT
ejpam-3914	639	25	un	un	ADJ
ejpam-3914	639	26	}	}	PUNCT
ejpam-3914	639	27	let	let	VERB
ejpam-3914	639	28	i	i	PRON
ejpam-3914	639	29	=	=	NOUN
ejpam-3914	639	30	5	5	NUM
ejpam-3914	639	31	,	,	PUNCT
ejpam-3914	639	32	10	10	NUM
ejpam-3914	639	33	,	,	PUNCT
ejpam-3914	639	34	15	15	NUM
ejpam-3914	639	35	,	,	PUNCT
ejpam-3914	639	36	.	.	PUNCT
ejpam-3914	639	37	.	.	PUNCT
ejpam-3914	640	1	.	.	PUNCT
ejpam-3914	641	1	,	,	PUNCT
ejpam-3914	642	1	n	n	CCONJ
ejpam-3914	642	2	−	−	PROPN
ejpam-3914	642	3	4	4	NUM
ejpam-3914	642	4	.	.	PUNCT
ejpam-3914	642	5	for	for	ADP
ejpam-3914	642	6	every	every	DET
ejpam-3914	642	7	induced	induced	ADJ
ejpam-3914	642	8	subgraph	subgraph	NOUN
ejpam-3914	642	9	〈	〈	PROPN
ejpam-3914	642	10	ui	ui	PROPN
ejpam-3914	642	11	,	,	PUNCT
ejpam-3914	642	12	ui+1	ui+1	PROPN
ejpam-3914	642	13	,	,	PUNCT
ejpam-3914	642	14	ui+2	ui+2	NUM
ejpam-3914	642	15	,	,	PUNCT
ejpam-3914	642	16	ui+3	ui+3	NOUN
ejpam-3914	642	17	,	,	PUNCT
ejpam-3914	642	18	ui+4	ui+4	PROPN
ejpam-3914	642	19	〉	〉	NOUN
ejpam-3914	642	20	,	,	PUNCT
ejpam-3914	642	21	the	the	DET
ejpam-3914	642	22	vertices	vertex	NOUN
ejpam-3914	642	23	u1	u1	NOUN
ejpam-3914	642	24	,	,	PUNCT
ejpam-3914	642	25	u2	u2	PROPN
ejpam-3914	642	26	,	,	PUNCT
ejpam-3914	642	27	ui	ui	NOUN
ejpam-3914	642	28	,	,	PUNCT
ejpam-3914	642	29	ui+1	ui+1	PROPN
ejpam-3914	642	30	form	form	NOUN
ejpam-3914	642	31	a	a	DET
ejpam-3914	642	32	total	total	ADJ
ejpam-3914	642	33	dr	dr	ADJ
ejpam-3914	642	34	-	-	PUNCT
ejpam-3914	642	35	power	power	NOUN
ejpam-3914	642	36	dominating	dominating	NOUN
ejpam-3914	642	37	set	set	VERB
ejpam-3914	642	38	since	since	SCONJ
ejpam-3914	642	39	u3,u4,ui+2	u3,u4,ui+2	NOUN
ejpam-3914	642	40	and	and	CCONJ
ejpam-3914	642	41	ui+4	ui+4	PRON
ejpam-3914	642	42	are	be	AUX
ejpam-3914	642	43	directly	directly	ADV
ejpam-3914	642	44	observed	observe	VERB
ejpam-3914	642	45	vertices	vertex	NOUN
ejpam-3914	642	46	while	while	SCONJ
ejpam-3914	642	47	ui+3	ui+3	NOUN
ejpam-3914	642	48	is	be	AUX
ejpam-3914	642	49	a	a	DET
ejpam-3914	642	50	remotely	remotely	ADV
ejpam-3914	642	51	observed	observe	VERB
ejpam-3914	642	52	vertex	vertex	NOUN
ejpam-3914	642	53	∀	∀	NOUN
ejpam-3914	643	1	i	i	NOUN
ejpam-3914	643	2	=	=	NOUN
ejpam-3914	643	3	5	5	NUM
ejpam-3914	643	4	,	,	PUNCT
ejpam-3914	643	5	10	10	NUM
ejpam-3914	643	6	,	,	PUNCT
ejpam-3914	643	7	15	15	NUM
ejpam-3914	643	8	,	,	PUNCT
ejpam-3914	643	9	.	.	PUNCT
ejpam-3914	643	10	.	.	PUNCT
ejpam-3914	643	11	.	.	PUNCT
ejpam-3914	644	1	,	,	PUNCT
ejpam-3914	644	2	n−	n−	NOUN
ejpam-3914	644	3	4	4	NUM
ejpam-3914	644	4	.	.	PUNCT
ejpam-3914	645	1	let	let	VERB
ejpam-3914	645	2	the	the	DET
ejpam-3914	645	3	set	set	NOUN
ejpam-3914	645	4	r	r	NOUN
ejpam-3914	645	5	=	=	SYM
ejpam-3914	645	6	{	{	PUNCT
ejpam-3914	645	7	u1	u1	NOUN
ejpam-3914	645	8	,	,	PUNCT
ejpam-3914	645	9	u2	u2	PROPN
ejpam-3914	645	10	,	,	PUNCT
ejpam-3914	645	11	ui	ui	NOUN
ejpam-3914	645	12	,	,	PUNCT
ejpam-3914	645	13	ui+1	ui+1	PROPN
ejpam-3914	646	1	:	:	PUNCT
ejpam-3914	646	2	i	i	NOUN
ejpam-3914	646	3	=	=	NOUN
ejpam-3914	646	4	5	5	NUM
ejpam-3914	646	5	,	,	PUNCT
ejpam-3914	646	6	10	10	NUM
ejpam-3914	646	7	,	,	PUNCT
ejpam-3914	646	8	15	15	NUM
ejpam-3914	646	9	,	,	PUNCT
ejpam-3914	646	10	.	.	PUNCT
ejpam-3914	646	11	.	.	PUNCT
ejpam-3914	646	12	.	.	PUNCT
ejpam-3914	647	1	,	,	PUNCT
ejpam-3914	647	2	n−	n−	NOUN
ejpam-3914	647	3	9	9	NUM
ejpam-3914	647	4	,	,	PUNCT
ejpam-3914	647	5	n−	n−	NOUN
ejpam-3914	647	6	4	4	NUM
ejpam-3914	647	7	}	}	PUNCT
ejpam-3914	647	8	=	=	NOUN
ejpam-3914	647	9	{	{	PUNCT
ejpam-3914	647	10	u1	u1	NOUN
ejpam-3914	647	11	,	,	PUNCT
ejpam-3914	647	12	u2	u2	PROPN
ejpam-3914	647	13	,	,	PUNCT
ejpam-3914	647	14	u5	u5	PROPN
ejpam-3914	647	15	,	,	PUNCT
ejpam-3914	647	16	u6	u6	PROPN
ejpam-3914	647	17	,	,	PUNCT
ejpam-3914	647	18	u10	u10	PROPN
ejpam-3914	647	19	,	,	PUNCT
ejpam-3914	647	20	u11	u11	PROPN
ejpam-3914	647	21	,	,	PUNCT
ejpam-3914	647	22	u15	u15	NOUN
ejpam-3914	647	23	,	,	PUNCT
ejpam-3914	647	24	u16	u16	NOUN
ejpam-3914	647	25	,	,	PUNCT
ejpam-3914	647	26	.	.	PUNCT
ejpam-3914	647	27	.	.	PUNCT
ejpam-3914	648	1	.	.	PUNCT
ejpam-3914	649	1	,	,	PUNCT
ejpam-3914	649	2	un−9	un−9	PROPN
ejpam-3914	649	3	,	,	PUNCT
ejpam-3914	649	4	un−8	un−8	ADJ
ejpam-3914	649	5	,	,	PUNCT
ejpam-3914	649	6	un−4	un−4	NOUN
ejpam-3914	649	7	,	,	PUNCT
ejpam-3914	649	8	un−3	un−3	ADJ
ejpam-3914	649	9	}	}	PUNCT
ejpam-3914	649	10	,	,	PUNCT
ejpam-3914	649	11	where	where	SCONJ
ejpam-3914	649	12	|r|	|r|	NOUN
ejpam-3914	649	13	=	=	NOUN
ejpam-3914	649	14	2p+	2p+	NUM
ejpam-3914	649	15	2	2	NUM
ejpam-3914	649	16	=	=	SYM
ejpam-3914	649	17	2(n−4	2(n−4	NUM
ejpam-3914	649	18	5	5	NUM
ejpam-3914	649	19	)	)	PUNCT
ejpam-3914	649	20	+	+	CCONJ
ejpam-3914	649	21	2	2	X
ejpam-3914	649	22	=	=	SYM
ejpam-3914	649	23	2n+2	2n+2	NUM
ejpam-3914	649	24	5	5	NUM
ejpam-3914	649	25	,	,	PUNCT
ejpam-3914	649	26	or	or	CCONJ
ejpam-3914	649	27	v	v	NOUN
ejpam-3914	649	28	(	(	PUNCT
ejpam-3914	649	29	cn	cn	PROPN
ejpam-3914	649	30	)	)	PUNCT
ejpam-3914	649	31	=	=	NOUN
ejpam-3914	649	32	v	v	X
ejpam-3914	649	33	(	(	PUNCT
ejpam-3914	649	34	cn	cn	PROPN
ejpam-3914	649	35	)	)	PUNCT
ejpam-3914	649	36	,	,	PUNCT
ejpam-3914	649	37	or	or	CCONJ
ejpam-3914	649	38	e(cn	e(cn	NOUN
ejpam-3914	649	39	)	)	PUNCT
ejpam-3914	649	40	=	=	SYM
ejpam-3914	649	41	e(cn	e(cn	NOUN
ejpam-3914	649	42	)	)	PUNCT
ejpam-3914	649	43	,	,	PUNCT
ejpam-3914	649	44	and	and	CCONJ
ejpam-3914	649	45	the	the	DET
ejpam-3914	649	46	induced	induced	ADJ
ejpam-3914	649	47	subgraph	subgraph	NOUN
ejpam-3914	649	48	〈	〈	PROPN
ejpam-3914	649	49	r	r	PROPN
ejpam-3914	649	50	〉	〉	PROPN
ejpam-3914	649	51	has	have	VERB
ejpam-3914	649	52	no	no	DET
ejpam-3914	649	53	isolated	isolated	ADJ
ejpam-3914	649	54	vertex	vertex	NOUN
ejpam-3914	649	55	.	.	PUNCT
ejpam-3914	650	1	by	by	ADP
ejpam-3914	650	2	theorem	theorem	NOUN
ejpam-3914	650	3	2.3	2.3	NUM
ejpam-3914	650	4	,	,	PUNCT
ejpam-3914	650	5	r	r	NOUN
ejpam-3914	650	6	is	be	AUX
ejpam-3914	650	7	a	a	DET
ejpam-3914	650	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	650	9	-set	-set	PROPN
ejpam-3914	650	10	of	of	ADP
ejpam-3914	650	11	cn	cn	PROPN
ejpam-3914	650	12	.	.	PUNCT
ejpam-3914	651	1	let	let	VERB
ejpam-3914	651	2	m+	m+	PRON
ejpam-3914	651	3	1	1	NUM
ejpam-3914	651	4	be	be	AUX
ejpam-3914	651	5	the	the	DET
ejpam-3914	651	6	number	number	NOUN
ejpam-3914	651	7	of	of	ADP
ejpam-3914	651	8	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	651	9	-sets	-set	NOUN
ejpam-3914	651	10	of	of	ADP
ejpam-3914	651	11	cn	cn	PROPN
ejpam-3914	651	12	where	where	SCONJ
ejpam-3914	651	13	m	m	PROPN
ejpam-3914	651	14	is	be	AUX
ejpam-3914	651	15	a	a	DET
ejpam-3914	651	16	positive	positive	ADJ
ejpam-3914	651	17	integer	integer	NOUN
ejpam-3914	651	18	.	.	PUNCT
ejpam-3914	652	1	let	let	VERB
ejpam-3914	652	2	k	k	NOUN
ejpam-3914	652	3	=	=	SYM
ejpam-3914	652	4	1	1	NUM
ejpam-3914	652	5	,	,	PUNCT
ejpam-3914	652	6	2	2	NUM
ejpam-3914	652	7	,	,	PUNCT
ejpam-3914	652	8	.	.	PUNCT
ejpam-3914	652	9	.	.	PUNCT
ejpam-3914	653	1	.	.	PUNCT
ejpam-3914	654	1	,	,	PUNCT
ejpam-3914	654	2	m	m	VERB
ejpam-3914	654	3	and	and	CCONJ
ejpam-3914	654	4	tk	tk	PROPN
ejpam-3914	654	5	be	be	AUX
ejpam-3914	654	6	a	a	DET
ejpam-3914	654	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	654	8	-set	-set	PUNCT
ejpam-3914	654	9	of	of	ADP
ejpam-3914	654	10	cn	cn	PROPN
ejpam-3914	654	11	different	different	ADJ
ejpam-3914	654	12	from	from	ADP
ejpam-3914	654	13	r.	r.	PROPN
ejpam-3914	654	14	note	note	PROPN
ejpam-3914	654	15	that	that	SCONJ
ejpam-3914	654	16	tk	tk	PROPN
ejpam-3914	654	17	can	can	AUX
ejpam-3914	654	18	be	be	AUX
ejpam-3914	654	19	formed	form	VERB
ejpam-3914	654	20	by	by	ADP
ejpam-3914	654	21	starting	start	VERB
ejpam-3914	654	22	all	all	DET
ejpam-3914	654	23	the	the	DET
ejpam-3914	654	24	vertices	vertex	NOUN
ejpam-3914	654	25	of	of	ADP
ejpam-3914	654	26	sl	sl	NOUN
ejpam-3914	654	27	for	for	ADP
ejpam-3914	654	28	l	l	NOUN
ejpam-3914	654	29	=	=	SYM
ejpam-3914	654	30	1	1	NUM
ejpam-3914	654	31	,	,	PUNCT
ejpam-3914	654	32	2	2	NUM
ejpam-3914	654	33	,	,	PUNCT
ejpam-3914	654	34	.	.	PUNCT
ejpam-3914	654	35	.	.	PUNCT
ejpam-3914	655	1	.	.	PUNCT
ejpam-3914	656	1	,	,	PUNCT
ejpam-3914	656	2	9	9	NUM
ejpam-3914	656	3	and	and	CCONJ
ejpam-3914	656	4	replacing	replace	VERB
ejpam-3914	656	5	u9	u9	NOUN
ejpam-3914	656	6	by	by	ADP
ejpam-3914	656	7	un	un	PROPN
ejpam-3914	656	8	in	in	ADP
ejpam-3914	656	9	s8	s8	PROPN
ejpam-3914	656	10	and	and	CCONJ
ejpam-3914	656	11	s9	s9	NOUN
ejpam-3914	656	12	.	.	PUNCT
ejpam-3914	657	1	now	now	ADV
ejpam-3914	657	2	,	,	PUNCT
ejpam-3914	657	3	if	if	SCONJ
ejpam-3914	657	4	tk	tk	PROPN
ejpam-3914	657	5	starts	start	VERB
ejpam-3914	657	6	with	with	ADP
ejpam-3914	657	7	s1	s1	NOUN
ejpam-3914	657	8	,	,	PUNCT
ejpam-3914	657	9	then	then	ADV
ejpam-3914	657	10	let	let	VERB
ejpam-3914	657	11	k	k	NOUN
ejpam-3914	657	12	=	=	SYM
ejpam-3914	657	13	1	1	NUM
ejpam-3914	657	14	and	and	CCONJ
ejpam-3914	657	15	{	{	PUNCT
ejpam-3914	657	16	u2	u2	PROPN
ejpam-3914	657	17	,	,	PUNCT
ejpam-3914	657	18	u5	u5	PROPN
ejpam-3914	657	19	}	}	PUNCT
ejpam-3914	657	20	⊆	⊆	NUM
ejpam-3914	657	21	{	{	PUNCT
ejpam-3914	657	22	u1	u1	NOUN
ejpam-3914	657	23	,	,	PUNCT
ejpam-3914	657	24	u2	u2	PROPN
ejpam-3914	657	25	,	,	PUNCT
ejpam-3914	657	26	u5	u5	PROPN
ejpam-3914	657	27	,	,	PUNCT
ejpam-3914	657	28	u6	u6	NOUN
ejpam-3914	657	29	}	}	PUNCT
ejpam-3914	657	30	⊆	⊆	NUM
ejpam-3914	657	31	t1	t1	NOUN
ejpam-3914	657	32	.	.	PUNCT
ejpam-3914	658	1	replace	replace	VERB
ejpam-3914	658	2	u10	u10	PROPN
ejpam-3914	658	3	∈	∈	PROPN
ejpam-3914	658	4	r	r	NOUN
ejpam-3914	658	5	by	by	ADP
ejpam-3914	658	6	u9	u9	NOUN
ejpam-3914	658	7	to	to	PART
ejpam-3914	658	8	form	form	VERB
ejpam-3914	658	9	t1	t1	PROPN
ejpam-3914	658	10	.	.	PUNCT
ejpam-3914	659	1	then	then	ADV
ejpam-3914	659	2	the	the	DET
ejpam-3914	659	3	next	next	ADJ
ejpam-3914	659	4	vertex	vertex	NOUN
ejpam-3914	659	5	to	to	PART
ejpam-3914	659	6	be	be	AUX
ejpam-3914	659	7	choosen	choosen	VERB
ejpam-3914	659	8	must	must	AUX
ejpam-3914	659	9	be	be	AUX
ejpam-3914	659	10	u10	u10	PROPN
ejpam-3914	659	11	,	,	PUNCT
ejpam-3914	659	12	that	that	ADV
ejpam-3914	659	13	is	is	ADV
ejpam-3914	659	14	,	,	PUNCT
ejpam-3914	659	15	the	the	DET
ejpam-3914	659	16	vertex	vertex	NOUN
ejpam-3914	659	17	ui+4	ui+4	PROPN
ejpam-3914	659	18	,	,	PUNCT
ejpam-3914	659	19	ui	ui	PROPN
ejpam-3914	659	20	must	must	AUX
ejpam-3914	659	21	be	be	AUX
ejpam-3914	659	22	in	in	ADP
ejpam-3914	659	23	t1	t1	NOUN
ejpam-3914	659	24	for	for	ADP
ejpam-3914	659	25	all	all	DET
ejpam-3914	659	26	i	i	PRON
ejpam-3914	659	27	=	=	NOUN
ejpam-3914	659	28	5	5	NUM
ejpam-3914	659	29	,	,	PUNCT
ejpam-3914	659	30	10	10	NUM
ejpam-3914	659	31	,	,	PUNCT
ejpam-3914	659	32	15	15	NUM
ejpam-3914	659	33	,	,	PUNCT
ejpam-3914	659	34	.	.	PUNCT
ejpam-3914	659	35	.	.	PUNCT
ejpam-3914	660	1	.	.	PUNCT
ejpam-3914	661	1	,	,	PUNCT
ejpam-3914	661	2	n−9	n−9	PROPN
ejpam-3914	661	3	,	,	PUNCT
ejpam-3914	661	4	n−4	n−4	PROPN
ejpam-3914	661	5	.	.	PUNCT
ejpam-3914	662	1	then	then	ADV
ejpam-3914	662	2	t1	t1	NOUN
ejpam-3914	662	3	=	=	PUNCT
ejpam-3914	662	4	{	{	PUNCT
ejpam-3914	662	5	u1	u1	NOUN
ejpam-3914	662	6	,	,	PUNCT
ejpam-3914	662	7	u2	u2	PROPN
ejpam-3914	662	8	,	,	PUNCT
ejpam-3914	662	9	u5	u5	PROPN
ejpam-3914	662	10	,	,	PUNCT
ejpam-3914	662	11	u6	u6	PROPN
ejpam-3914	662	12	,	,	PUNCT
ejpam-3914	662	13	u9	u9	PROPN
ejpam-3914	662	14	,	,	PUNCT
ejpam-3914	662	15	u10	u10	PROPN
ejpam-3914	662	16	,	,	PUNCT
ejpam-3914	662	17	u14	u14	NOUN
ejpam-3914	662	18	,	,	PUNCT
ejpam-3914	662	19	u15	u15	NOUN
ejpam-3914	662	20	,	,	PUNCT
ejpam-3914	662	21	.	.	PUNCT
ejpam-3914	662	22	.	.	PUNCT
ejpam-3914	663	1	.	.	PUNCT
ejpam-3914	664	1	,	,	PUNCT
ejpam-3914	665	1	un−5	un−5	PROPN
ejpam-3914	665	2	,	,	PUNCT
ejpam-3914	665	3	un−4	un−4	NOUN
ejpam-3914	665	4	}	}	PUNCT
ejpam-3914	665	5	such	such	ADJ
ejpam-3914	665	6	that	that	DET
ejpam-3914	665	7	|t1|	|t1|	NOUN
ejpam-3914	665	8	=	=	SYM
ejpam-3914	665	9	|r|	|r|	PROPN
ejpam-3914	665	10	.	.	PUNCT
ejpam-3914	666	1	since	since	SCONJ
ejpam-3914	666	2	u1	u1	PROPN
ejpam-3914	666	3	∈	∈	PROPN
ejpam-3914	666	4	t1	t1	NOUN
ejpam-3914	666	5	and	and	CCONJ
ejpam-3914	666	6	un−4	un−4	NOUN
ejpam-3914	666	7	is	be	AUX
ejpam-3914	666	8	the	the	DET
ejpam-3914	666	9	last	last	ADJ
ejpam-3914	666	10	vertex	vertex	NOUN
ejpam-3914	666	11	in	in	ADP
ejpam-3914	666	12	t1	t1	PROPN
ejpam-3914	666	13	,	,	PUNCT
ejpam-3914	666	14	by	by	ADP
ejpam-3914	666	15	the	the	DET
ejpam-3914	666	16	same	same	ADJ
ejpam-3914	666	17	argument	argument	NOUN
ejpam-3914	666	18	in	in	ADP
ejpam-3914	666	19	case	case	NOUN
ejpam-3914	666	20	1	1	NUM
ejpam-3914	666	21	,	,	PUNCT
ejpam-3914	666	22	t1	t1	PROPN
ejpam-3914	666	23	is	be	AUX
ejpam-3914	666	24	not	not	PART
ejpam-3914	666	25	a	a	DET
ejpam-3914	666	26	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	666	27	-set	-set	PROPN
ejpam-3914	666	28	of	of	ADP
ejpam-3914	666	29	cn	cn	PROPN
ejpam-3914	666	30	.	.	PUNCT
ejpam-3914	667	1	since	since	SCONJ
ejpam-3914	667	2	u10	u10	PROPN
ejpam-3914	667	3	is	be	AUX
ejpam-3914	667	4	arbitrarily	arbitrarily	ADV
ejpam-3914	667	5	replaced	replace	VERB
ejpam-3914	667	6	from	from	ADP
ejpam-3914	667	7	r	r	NOUN
ejpam-3914	667	8	,	,	PUNCT
ejpam-3914	667	9	we	we	PRON
ejpam-3914	667	10	can	can	AUX
ejpam-3914	667	11	not	not	PART
ejpam-3914	667	12	replace	replace	VERB
ejpam-3914	667	13	the	the	DET
ejpam-3914	667	14	vertex	vertex	NOUN
ejpam-3914	667	15	ui	ui	NOUN
ejpam-3914	667	16	in	in	ADP
ejpam-3914	667	17	r	r	NOUN
ejpam-3914	667	18	,	,	PUNCT
ejpam-3914	667	19	where	where	SCONJ
ejpam-3914	667	20	i	i	PRON
ejpam-3914	667	21	=	=	NOUN
ejpam-3914	667	22	10	10	NUM
ejpam-3914	667	23	,	,	PUNCT
ejpam-3914	667	24	15	15	NUM
ejpam-3914	667	25	,	,	PUNCT
ejpam-3914	667	26	.	.	PUNCT
ejpam-3914	667	27	.	.	PUNCT
ejpam-3914	668	1	.	.	PUNCT
ejpam-3914	669	1	,	,	PUNCT
ejpam-3914	669	2	n−	n−	NOUN
ejpam-3914	669	3	9	9	NUM
ejpam-3914	669	4	,	,	PUNCT
ejpam-3914	669	5	n−	n−	NOUN
ejpam-3914	669	6	4	4	NUM
ejpam-3914	669	7	to	to	PART
ejpam-3914	669	8	form	form	VERB
ejpam-3914	669	9	another	another	PRON
ejpam-3914	669	10	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	669	11	-set	-set	PROPN
ejpam-3914	669	12	of	of	ADP
ejpam-3914	669	13	cn	cn	PROPN
ejpam-3914	669	14	.	.	PUNCT
ejpam-3914	669	15	therefore	therefore	ADV
ejpam-3914	669	16	,	,	PUNCT
ejpam-3914	669	17	only	only	ADV
ejpam-3914	669	18	the	the	DET
ejpam-3914	669	19	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	669	20	-set	-set	PUNCT
ejpam-3914	669	21	r	r	NOUN
ejpam-3914	669	22	starts	start	VERB
ejpam-3914	669	23	with	with	ADP
ejpam-3914	669	24	s1	s1	NOUN
ejpam-3914	669	25	and	and	CCONJ
ejpam-3914	669	26	so	so	ADV
ejpam-3914	669	27	,	,	PUNCT
ejpam-3914	669	28	{	{	PUNCT
ejpam-3914	669	29	u2	u2	NOUN
ejpam-3914	669	30	,	,	PUNCT
ejpam-3914	669	31	u5	u5	PROPN
ejpam-3914	669	32	}	}	PUNCT
ejpam-3914	669	33	*	*	PUNCT
ejpam-3914	669	34	tk	tk	PROPN
ejpam-3914	669	35	for	for	ADP
ejpam-3914	669	36	all	all	PRON
ejpam-3914	669	37	k	k	NOUN
ejpam-3914	669	38	=	=	SYM
ejpam-3914	669	39	1	1	NUM
ejpam-3914	669	40	,	,	PUNCT
ejpam-3914	669	41	2	2	NUM
ejpam-3914	669	42	,	,	PUNCT
ejpam-3914	669	43	.	.	PUNCT
ejpam-3914	669	44	.	.	PUNCT
ejpam-3914	669	45	.	.	PUNCT
ejpam-3914	670	1	,	,	PUNCT
ejpam-3914	670	2	m.	m.	NOUN
ejpam-3914	670	3	hence	hence	ADV
ejpam-3914	670	4	,	,	PUNCT
ejpam-3914	670	5	{	{	PUNCT
ejpam-3914	670	6	u2	u2	NOUN
ejpam-3914	670	7	,	,	PUNCT
ejpam-3914	670	8	u5	u5	PROPN
ejpam-3914	670	9	}	}	PUNCT
ejpam-3914	670	10	is	be	AUX
ejpam-3914	670	11	a	a	DET
ejpam-3914	670	12	forcing	forcing	NOUN
ejpam-3914	670	13	subset	subset	NOUN
ejpam-3914	670	14	for	for	ADP
ejpam-3914	670	15	r.	r.	PROPN
ejpam-3914	670	16	therefore	therefore	ADV
ejpam-3914	670	17	,	,	PUNCT
ejpam-3914	670	18	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	670	19	(	(	PUNCT
ejpam-3914	670	20	r	r	NOUN
ejpam-3914	670	21	)	)	PUNCT
ejpam-3914	670	22	=	=	SYM
ejpam-3914	671	1	2	2	NUM
ejpam-3914	671	2	=	=	NOUN
ejpam-3914	671	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	671	4	(	(	PUNCT
ejpam-3914	671	5	cn	cn	NOUN
ejpam-3914	671	6	)	)	PUNCT
ejpam-3914	671	7	.	.	PUNCT
ejpam-3914	672	1	theorem	theorem	VERB
ejpam-3914	672	2	3.6	3.6	NUM
ejpam-3914	672	3	.	.	PUNCT
ejpam-3914	673	1	let	let	VERB
ejpam-3914	673	2	n	n	PRON
ejpam-3914	673	3	be	be	AUX
ejpam-3914	673	4	a	a	DET
ejpam-3914	673	5	positive	positive	ADJ
ejpam-3914	673	6	integer	integer	NOUN
ejpam-3914	673	7	with	with	ADP
ejpam-3914	673	8	n	n	PRON
ejpam-3914	673	9	≥	≥	NUM
ejpam-3914	673	10	2	2	NUM
ejpam-3914	673	11	.	.	PUNCT
ejpam-3914	674	1	then	then	ADV
ejpam-3914	674	2	the	the	DET
ejpam-3914	674	3	total	total	ADJ
ejpam-3914	674	4	dr	dr	PROPN
ejpam-3914	674	5	-	-	PUNCT
ejpam-3914	674	6	power	power	NOUN
ejpam-3914	674	7	domination	domination	NOUN
ejpam-3914	674	8	number	number	NOUN
ejpam-3914	674	9	of	of	ADP
ejpam-3914	674	10	the	the	DET
ejpam-3914	674	11	complete	complete	ADJ
ejpam-3914	674	12	graph	graph	NOUN
ejpam-3914	674	13	kn	kn	PROPN
ejpam-3914	674	14	is	be	AUX
ejpam-3914	674	15	given	give	VERB
ejpam-3914	674	16	by	by	ADP
ejpam-3914	674	17	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	674	18	(	(	PUNCT
ejpam-3914	674	19	kn	kn	PROPN
ejpam-3914	674	20	)	)	PUNCT
ejpam-3914	674	21	=	=	SYM
ejpam-3914	674	22	2	2	NUM
ejpam-3914	674	23	and	and	CCONJ
ejpam-3914	674	24	its	its	PRON
ejpam-3914	674	25	forcing	force	VERB
ejpam-3914	674	26	total	total	ADJ
ejpam-3914	674	27	dr	dr	PROPN
ejpam-3914	674	28	-	-	PUNCT
ejpam-3914	674	29	power	power	NOUN
ejpam-3914	674	30	domination	domination	NOUN
ejpam-3914	674	31	number	number	NOUN
ejpam-3914	674	32	is	be	AUX
ejpam-3914	674	33	given	give	VERB
ejpam-3914	674	34	by	by	ADP
ejpam-3914	674	35	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	674	36	(	(	PUNCT
ejpam-3914	674	37	kn	kn	PROPN
ejpam-3914	674	38	)	)	PUNCT
ejpam-3914	674	39	=	=	PRON
ejpam-3914	674	40	{	{	PUNCT
ejpam-3914	674	41	0	0	NUM
ejpam-3914	674	42	,	,	PUNCT
ejpam-3914	674	43	n	n	NOUN
ejpam-3914	674	44	=	=	SYM
ejpam-3914	674	45	2	2	NUM
ejpam-3914	674	46	2	2	NUM
ejpam-3914	674	47	,	,	PUNCT
ejpam-3914	674	48	n	n	CCONJ
ejpam-3914	674	49	>	>	X
ejpam-3914	674	50	2	2	X
ejpam-3914	674	51	.	.	PUNCT
ejpam-3914	674	52	proof	proof	NOUN
ejpam-3914	674	53	.	.	PUNCT
ejpam-3914	675	1	let	let	VERB
ejpam-3914	675	2	v	v	X
ejpam-3914	675	3	(	(	PUNCT
ejpam-3914	675	4	kn	kn	PROPN
ejpam-3914	675	5	)	)	PUNCT
ejpam-3914	675	6	=	=	PRON
ejpam-3914	675	7	{	{	PUNCT
ejpam-3914	675	8	u1	u1	NOUN
ejpam-3914	675	9	,	,	PUNCT
ejpam-3914	675	10	u2	u2	NOUN
ejpam-3914	675	11	,	,	PUNCT
ejpam-3914	675	12	u3	u3	NOUN
ejpam-3914	675	13	,	,	PUNCT
ejpam-3914	675	14	.	.	PUNCT
ejpam-3914	675	15	.	.	PUNCT
ejpam-3914	676	1	.	.	PUNCT
ejpam-3914	677	1	,	,	PUNCT
ejpam-3914	677	2	un	un	PROPN
ejpam-3914	677	3	}	}	PUNCT
ejpam-3914	677	4	.	.	PUNCT
ejpam-3914	678	1	clearly	clearly	ADV
ejpam-3914	678	2	,	,	PUNCT
ejpam-3914	678	3	each	each	DET
ejpam-3914	678	4	pair	pair	NOUN
ejpam-3914	678	5	of	of	ADP
ejpam-3914	678	6	vertices	vertex	NOUN
ejpam-3914	678	7	ui	ui	PROPN
ejpam-3914	678	8	,	,	PUNCT
ejpam-3914	678	9	uj	uj	NOUN
ejpam-3914	678	10	such	such	ADJ
ejpam-3914	678	11	that	that	SCONJ
ejpam-3914	678	12	i	i	PRON
ejpam-3914	678	13	6=	6=	PROPN
ejpam-3914	678	14	j	j	PROPN
ejpam-3914	678	15	in	in	ADP
ejpam-3914	678	16	kn	kn	PROPN
ejpam-3914	678	17	forms	form	VERB
ejpam-3914	678	18	a	a	DET
ejpam-3914	678	19	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	678	20	-set	-set	PROPN
ejpam-3914	678	21	of	of	ADP
ejpam-3914	678	22	kn	kn	PROPN
ejpam-3914	678	23	,	,	PUNCT
ejpam-3914	678	24	and	and	CCONJ
ejpam-3914	678	25	so	so	ADV
ejpam-3914	678	26	,	,	PUNCT
ejpam-3914	678	27	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	678	28	(	(	PUNCT
ejpam-3914	678	29	kn	kn	PROPN
ejpam-3914	678	30	)	)	PUNCT
ejpam-3914	678	31	=	=	PUNCT
ejpam-3914	679	1	2	2	X
ejpam-3914	679	2	.	.	X
ejpam-3914	680	1	if	if	SCONJ
ejpam-3914	680	2	n	n	NOUN
ejpam-3914	680	3	=	=	SYM
ejpam-3914	680	4	2	2	NUM
ejpam-3914	680	5	,	,	PUNCT
ejpam-3914	680	6	then	then	ADV
ejpam-3914	680	7	k2	k2	PROPN
ejpam-3914	680	8	has	have	VERB
ejpam-3914	680	9	exactly	exactly	ADV
ejpam-3914	680	10	one	one	NUM
ejpam-3914	680	11	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	680	12	-set	-set	PUNCT
ejpam-3914	681	1	which	which	PRON
ejpam-3914	681	2	is	be	AUX
ejpam-3914	681	3	v	v	NOUN
ejpam-3914	681	4	(	(	PUNCT
ejpam-3914	681	5	k2	k2	NOUN
ejpam-3914	681	6	)	)	PUNCT
ejpam-3914	681	7	.	.	PUNCT
ejpam-3914	682	1	by	by	ADP
ejpam-3914	682	2	theorem	theorem	ADJ
ejpam-3914	682	3	3.1	3.1	NUM
ejpam-3914	682	4	(	(	PUNCT
ejpam-3914	682	5	i	i	NOUN
ejpam-3914	682	6	)	)	PUNCT
ejpam-3914	682	7	,	,	PUNCT
ejpam-3914	682	8	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	682	9	(	(	PUNCT
ejpam-3914	682	10	k2	k2	NOUN
ejpam-3914	682	11	)	)	PUNCT
ejpam-3914	682	12	=	=	SYM
ejpam-3914	682	13	0	0	X
ejpam-3914	682	14	.	.	PUNCT
ejpam-3914	682	15	suppose	suppose	VERB
ejpam-3914	682	16	that	that	SCONJ
ejpam-3914	682	17	n	n	PROPN
ejpam-3914	682	18	>	>	X
ejpam-3914	682	19	2	2	X
ejpam-3914	682	20	.	.	X
ejpam-3914	682	21	note	note	VERB
ejpam-3914	682	22	that	that	SCONJ
ejpam-3914	682	23	for	for	ADP
ejpam-3914	682	24	all	all	DET
ejpam-3914	682	25	i	i	PRON
ejpam-3914	682	26	=	=	NOUN
ejpam-3914	682	27	1	1	NUM
ejpam-3914	682	28	,	,	PUNCT
ejpam-3914	682	29	2	2	NUM
ejpam-3914	682	30	,	,	PUNCT
ejpam-3914	682	31	.	.	PUNCT
ejpam-3914	682	32	.	.	PUNCT
ejpam-3914	682	33	.	.	PUNCT
ejpam-3914	683	1	n	n	CCONJ
ejpam-3914	683	2	,	,	PUNCT
ejpam-3914	683	3	ui	ui	PROPN
ejpam-3914	683	4	is	be	AUX
ejpam-3914	683	5	contained	contain	VERB
ejpam-3914	683	6	in	in	ADP
ejpam-3914	683	7	γ∗tpw	γ∗tpw	NOUN
ejpam-3914	683	8	-sets	-sets	PROPN
ejpam-3914	683	9	{	{	PUNCT
ejpam-3914	683	10	ui	ui	NOUN
ejpam-3914	683	11	,	,	PUNCT
ejpam-3914	683	12	uj	uj	PROPN
ejpam-3914	683	13	}	}	PUNCT
ejpam-3914	683	14	and	and	CCONJ
ejpam-3914	683	15	{	{	PUNCT
ejpam-3914	683	16	ui	ui	PROPN
ejpam-3914	683	17	,	,	PUNCT
ejpam-3914	683	18	uk	uk	PROPN
ejpam-3914	683	19	}	}	PUNCT
ejpam-3914	683	20	such	such	ADJ
ejpam-3914	683	21	that	that	SCONJ
ejpam-3914	683	22	i	i	PRON
ejpam-3914	683	23	6=	6=	PROPN
ejpam-3914	683	24	j	j	PROPN
ejpam-3914	683	25	6=	6=	PROPN
ejpam-3914	684	1	k	k	PROPN
ejpam-3914	684	2	6=	6=	PROPN
ejpam-3914	685	1	i	i	PRON
ejpam-3914	685	2	and	and	CCONJ
ejpam-3914	685	3	so	so	ADV
ejpam-3914	685	4	,	,	PUNCT
ejpam-3914	685	5	the	the	DET
ejpam-3914	685	6	set	set	NOUN
ejpam-3914	685	7	{	{	PUNCT
ejpam-3914	685	8	ui	ui	NOUN
ejpam-3914	685	9	}	}	PUNCT
ejpam-3914	685	10	is	be	AUX
ejpam-3914	685	11	not	not	PART
ejpam-3914	685	12	a	a	DET
ejpam-3914	685	13	forcing	forcing	NOUN
ejpam-3914	685	14	subset	subset	NOUN
ejpam-3914	685	15	for	for	ADP
ejpam-3914	685	16	any	any	DET
ejpam-3914	685	17	γ∗tpw	γ∗tpw	SYM
ejpam-3914	685	18	-set	-set	PROPN
ejpam-3914	685	19	of	of	ADP
ejpam-3914	685	20	kn	kn	PROPN
ejpam-3914	685	21	,	,	PUNCT
ejpam-3914	685	22	that	that	ADV
ejpam-3914	685	23	is	is	ADV
ejpam-3914	685	24	,	,	PUNCT
ejpam-3914	685	25	c.	c.	PROPN
ejpam-3914	685	26	armada	armada	PROPN
ejpam-3914	685	27	/	/	SYM
ejpam-3914	685	28	eur	eur	PROPN
ejpam-3914	685	29	.	.	PUNCT
ejpam-3914	686	1	j.	j.	PROPN
ejpam-3914	686	2	pure	pure	PROPN
ejpam-3914	686	3	appl	appl	PROPN
ejpam-3914	686	4	.	.	PROPN
ejpam-3914	686	5	math	math	PROPN
ejpam-3914	686	6	,	,	PUNCT
ejpam-3914	686	7	14	14	NUM
ejpam-3914	686	8	(	(	PUNCT
ejpam-3914	686	9	2	2	NUM
ejpam-3914	686	10	)	)	PUNCT
ejpam-3914	686	11	(	(	PUNCT
ejpam-3914	686	12	2021	2021	NUM
ejpam-3914	686	13	)	)	PUNCT
ejpam-3914	686	14	,	,	PUNCT
ejpam-3914	686	15	451	451	NUM
ejpam-3914	686	16	-	-	SYM
ejpam-3914	686	17	470	470	NUM
ejpam-3914	686	18	468	468	NUM
ejpam-3914	686	19	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	686	20	(	(	PUNCT
ejpam-3914	686	21	kn	kn	PROPN
ejpam-3914	686	22	)	)	PUNCT
ejpam-3914	686	23	≥	≥	NOUN
ejpam-3914	686	24	2	2	NUM
ejpam-3914	686	25	.	.	PUNCT
ejpam-3914	687	1	consequently	consequently	ADV
ejpam-3914	687	2	,	,	PUNCT
ejpam-3914	687	3	by	by	ADP
ejpam-3914	687	4	corollary	corollary	ADJ
ejpam-3914	687	5	3.2	3.2	NUM
ejpam-3914	687	6	,	,	PUNCT
ejpam-3914	687	7	2	2	NUM
ejpam-3914	687	8	≤	≤	NOUN
ejpam-3914	687	9	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	687	10	(	(	PUNCT
ejpam-3914	687	11	kn	kn	NOUN
ejpam-3914	687	12	)	)	PUNCT
ejpam-3914	687	13	≤	≤	NOUN
ejpam-3914	687	14	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	687	15	(	(	PUNCT
ejpam-3914	687	16	kn	kn	PROPN
ejpam-3914	687	17	)	)	PUNCT
ejpam-3914	687	18	=	=	PUNCT
ejpam-3914	687	19	2	2	X
ejpam-3914	687	20	.	.	X
ejpam-3914	687	21	therefore	therefore	ADV
ejpam-3914	687	22	,	,	PUNCT
ejpam-3914	687	23	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3914	687	24	(	(	PUNCT
ejpam-3914	687	25	kn	kn	PROPN
ejpam-3914	687	26	)	)	PUNCT
ejpam-3914	687	27	=	=	SYM
ejpam-3914	687	28	2	2	NUM
ejpam-3914	687	29	for	for	ADP
ejpam-3914	687	30	all	all	DET
ejpam-3914	687	31	n	n	CCONJ
ejpam-3914	687	32	>	>	X
ejpam-3914	687	33	2	2	X
ejpam-3914	687	34	.	.	PUNCT
ejpam-3914	687	35	theorem	theorem	VERB
ejpam-3914	687	36	3.7	3.7	NUM
ejpam-3914	687	37	.	.	PUNCT
ejpam-3914	688	1	let	let	VERB
ejpam-3914	688	2	n	n	PRON
ejpam-3914	688	3	be	be	AUX
ejpam-3914	688	4	a	a	DET
ejpam-3914	688	5	positive	positive	ADJ
ejpam-3914	688	6	integer	integer	NOUN
ejpam-3914	688	7	with	with	ADP
ejpam-3914	688	8	n	n	PRON
ejpam-3914	688	9	≥	≥	NUM
ejpam-3914	688	10	2	2	NUM
ejpam-3914	688	11	.	.	PUNCT
ejpam-3914	689	1	then	then	ADV
ejpam-3914	689	2	the	the	DET
ejpam-3914	689	3	total	total	ADJ
ejpam-3914	689	4	dr	dr	PROPN
ejpam-3914	689	5	-	-	PUNCT
ejpam-3914	689	6	power	power	NOUN
ejpam-3914	689	7	domination	domination	NOUN
ejpam-3914	689	8	number	number	NOUN
ejpam-3914	689	9	of	of	ADP
ejpam-3914	689	10	the	the	DET
ejpam-3914	689	11	fan	fan	NOUN
ejpam-3914	689	12	graph	graph	NOUN
ejpam-3914	689	13	fn	fn	NOUN
ejpam-3914	689	14	=	=	NOUN
ejpam-3914	689	15	k1	k1	PROPN
ejpam-3914	689	16	+	+	CCONJ
ejpam-3914	689	17	pn	pn	X
ejpam-3914	689	18	of	of	ADP
ejpam-3914	689	19	order	order	NOUN
ejpam-3914	689	20	n	n	NOUN
ejpam-3914	689	21	+	+	CCONJ
ejpam-3914	689	22	1	1	NUM
ejpam-3914	689	23	is	be	AUX
ejpam-3914	689	24	given	give	VERB
ejpam-3914	689	25	by	by	ADP
ejpam-3914	689	26	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	689	27	(	(	PUNCT
ejpam-3914	689	28	fn	fn	NOUN
ejpam-3914	689	29	)	)	PUNCT
ejpam-3914	689	30	=	=	SYM
ejpam-3914	689	31	2	2	NUM
ejpam-3914	689	32	and	and	CCONJ
ejpam-3914	689	33	its	its	PRON
ejpam-3914	689	34	forcing	force	VERB
ejpam-3914	689	35	total	total	ADJ
ejpam-3914	689	36	dr	dr	PROPN
ejpam-3914	689	37	-	-	PUNCT
ejpam-3914	689	38	power	power	NOUN
ejpam-3914	689	39	domination	domination	NOUN
ejpam-3914	689	40	number	number	NOUN
ejpam-3914	689	41	is	be	AUX
ejpam-3914	689	42	given	give	VERB
ejpam-3914	689	43	by	by	ADP
ejpam-3914	689	44	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	689	45	(	(	PUNCT
ejpam-3914	689	46	fn	fn	NOUN
ejpam-3914	689	47	)	)	PUNCT
ejpam-3914	689	48	=	=	PRON
ejpam-3914	689	49	{	{	PUNCT
ejpam-3914	689	50	2	2	NUM
ejpam-3914	689	51	,	,	PUNCT
ejpam-3914	689	52	n	n	NOUN
ejpam-3914	689	53	=	=	SYM
ejpam-3914	689	54	2	2	NUM
ejpam-3914	689	55	,	,	PUNCT
ejpam-3914	689	56	3	3	NUM
ejpam-3914	689	57	,	,	PUNCT
ejpam-3914	689	58	1	1	NUM
ejpam-3914	689	59	,	,	PUNCT
ejpam-3914	689	60	n	n	PRON
ejpam-3914	689	61	≥	≥	NOUN
ejpam-3914	689	62	4	4	NUM
ejpam-3914	689	63	.	.	PUNCT
ejpam-3914	690	1	proof	proof	NOUN
ejpam-3914	690	2	.	.	PUNCT
ejpam-3914	691	1	by	by	ADP
ejpam-3914	691	2	corollary	corollary	ADJ
ejpam-3914	691	3	2.6	2.6	NUM
ejpam-3914	691	4	,	,	PUNCT
ejpam-3914	691	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	691	6	(	(	PUNCT
ejpam-3914	691	7	fn	fn	NOUN
ejpam-3914	691	8	)	)	PUNCT
ejpam-3914	691	9	=	=	SYM
ejpam-3914	691	10	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	691	11	(	(	PUNCT
ejpam-3914	691	12	k1	k1	NOUN
ejpam-3914	691	13	+	+	CCONJ
ejpam-3914	691	14	pn	pn	NOUN
ejpam-3914	691	15	)	)	PUNCT
ejpam-3914	691	16	=	=	SYM
ejpam-3914	691	17	2	2	X
ejpam-3914	691	18	.	.	X
ejpam-3914	691	19	let	let	VERB
ejpam-3914	691	20	v	v	NOUN
ejpam-3914	691	21	(	(	PUNCT
ejpam-3914	691	22	fn	fn	NOUN
ejpam-3914	691	23	)	)	PUNCT
ejpam-3914	691	24	=	=	PRON
ejpam-3914	691	25	{	{	PUNCT
ejpam-3914	691	26	v	v	NOUN
ejpam-3914	691	27	,	,	PUNCT
ejpam-3914	691	28	u1	u1	NOUN
ejpam-3914	691	29	,	,	PUNCT
ejpam-3914	691	30	u2	u2	NOUN
ejpam-3914	691	31	,	,	PUNCT
ejpam-3914	691	32	u3	u3	NOUN
ejpam-3914	691	33	,	,	PUNCT
ejpam-3914	691	34	.	.	PUNCT
ejpam-3914	691	35	.	.	PUNCT
ejpam-3914	692	1	.	.	PUNCT
ejpam-3914	693	1	,	,	PUNCT
ejpam-3914	693	2	un	un	AUX
ejpam-3914	693	3	}	}	PUNCT
ejpam-3914	693	4	such	such	ADJ
ejpam-3914	693	5	that	that	SCONJ
ejpam-3914	693	6	deg(v	deg(v	PROPN
ejpam-3914	693	7	)	)	PUNCT
ejpam-3914	693	8	=	=	SYM
ejpam-3914	693	9	n.	n.	NOUN
ejpam-3914	693	10	note	note	VERB
ejpam-3914	693	11	that	that	SCONJ
ejpam-3914	693	12	the	the	DET
ejpam-3914	693	13	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	693	14	-sets	-set	NOUN
ejpam-3914	693	15	of	of	ADP
ejpam-3914	693	16	fn	fn	NOUN
ejpam-3914	693	17	are	be	AUX
ejpam-3914	693	18	of	of	ADP
ejpam-3914	693	19	the	the	DET
ejpam-3914	693	20	form	form	NOUN
ejpam-3914	693	21	{	{	PUNCT
ejpam-3914	693	22	v	v	NOUN
ejpam-3914	693	23	,	,	PUNCT
ejpam-3914	693	24	ui	ui	NOUN
ejpam-3914	693	25	}	}	PUNCT
ejpam-3914	693	26	for	for	ADP
ejpam-3914	693	27	all	all	DET
ejpam-3914	693	28	ui	ui	NOUN
ejpam-3914	693	29	∈	∈	PROPN
ejpam-3914	693	30	v	v	ADP
ejpam-3914	693	31	(	(	PUNCT
ejpam-3914	693	32	fn	fn	NOUN
ejpam-3914	693	33	)	)	PUNCT
ejpam-3914	693	34	and	and	CCONJ
ejpam-3914	693	35	of	of	ADP
ejpam-3914	693	36	the	the	DET
ejpam-3914	693	37	form	form	NOUN
ejpam-3914	693	38	{	{	PUNCT
ejpam-3914	693	39	ui	ui	PROPN
ejpam-3914	693	40	,	,	PUNCT
ejpam-3914	693	41	uj	uj	PROPN
ejpam-3914	693	42	}	}	PUNCT
ejpam-3914	693	43	such	such	ADJ
ejpam-3914	693	44	that	that	SCONJ
ejpam-3914	693	45	i	i	PRON
ejpam-3914	693	46	6=	6=	PROPN
ejpam-3914	693	47	j	j	PROPN
ejpam-3914	693	48	and	and	CCONJ
ejpam-3914	693	49	{	{	PUNCT
ejpam-3914	693	50	ui	ui	PROPN
ejpam-3914	693	51	,	,	PUNCT
ejpam-3914	693	52	uj	uj	PROPN
ejpam-3914	693	53	}	}	PUNCT
ejpam-3914	693	54	is	be	AUX
ejpam-3914	693	55	a	a	DET
ejpam-3914	693	56	γt	γt	NOUN
ejpam-3914	693	57	-	-	NOUN
ejpam-3914	693	58	set	set	NOUN
ejpam-3914	693	59	of	of	ADP
ejpam-3914	693	60	pn	pn	PROPN
ejpam-3914	693	61	by	by	ADP
ejpam-3914	693	62	theorem	theorem	ADJ
ejpam-3914	693	63	2.5	2.5	NUM
ejpam-3914	693	64	and	and	CCONJ
ejpam-3914	693	65	corollary	corollary	ADJ
ejpam-3914	693	66	2.6	2.6	NUM
ejpam-3914	693	67	.	.	PUNCT
ejpam-3914	694	1	consider	consider	VERB
ejpam-3914	694	2	the	the	DET
ejpam-3914	694	3	following	follow	VERB
ejpam-3914	694	4	cases	case	NOUN
ejpam-3914	694	5	:	:	PUNCT
ejpam-3914	694	6	case	case	NOUN
ejpam-3914	694	7	1	1	NUM
ejpam-3914	694	8	:	:	PUNCT
ejpam-3914	694	9	suppose	suppose	VERB
ejpam-3914	694	10	that	that	SCONJ
ejpam-3914	694	11	either	either	CCONJ
ejpam-3914	694	12	n	n	PROPN
ejpam-3914	694	13	=	=	SYM
ejpam-3914	694	14	2	2	NUM
ejpam-3914	694	15	or	or	CCONJ
ejpam-3914	694	16	n	n	NOUN
ejpam-3914	694	17	=	=	SYM
ejpam-3914	694	18	3	3	X
ejpam-3914	694	19	.	.	PUNCT
ejpam-3914	694	20	by	by	ADP
ejpam-3914	694	21	proposition	proposition	NOUN
ejpam-3914	694	22	2.4	2.4	NUM
ejpam-3914	694	23	,	,	PUNCT
ejpam-3914	694	24	γt(pn	γt(pn	NOUN
ejpam-3914	694	25	)	)	PUNCT
ejpam-3914	694	26	=	=	SYM
ejpam-3914	694	27	2	2	NUM
ejpam-3914	694	28	for	for	ADP
ejpam-3914	694	29	n	n	NOUN
ejpam-3914	694	30	=	=	SYM
ejpam-3914	694	31	2	2	NUM
ejpam-3914	694	32	,	,	PUNCT
ejpam-3914	694	33	3	3	NUM
ejpam-3914	694	34	.	.	PUNCT
ejpam-3914	695	1	if	if	SCONJ
ejpam-3914	695	2	n	n	NOUN
ejpam-3914	695	3	=	=	SYM
ejpam-3914	695	4	2	2	NUM
ejpam-3914	695	5	,	,	PUNCT
ejpam-3914	695	6	then	then	ADV
ejpam-3914	695	7	r1	r1	PROPN
ejpam-3914	695	8	=	=	SYM
ejpam-3914	695	9	{	{	PUNCT
ejpam-3914	695	10	v	v	NOUN
ejpam-3914	695	11	,	,	PUNCT
ejpam-3914	695	12	u1	u1	NOUN
ejpam-3914	695	13	}	}	PUNCT
ejpam-3914	695	14	,	,	PUNCT
ejpam-3914	695	15	r2	r2	PROPN
ejpam-3914	695	16	=	=	PUNCT
ejpam-3914	695	17	{	{	PUNCT
ejpam-3914	695	18	v	v	NOUN
ejpam-3914	695	19	,	,	PUNCT
ejpam-3914	695	20	u2	u2	NOUN
ejpam-3914	695	21	}	}	PUNCT
ejpam-3914	695	22	and	and	CCONJ
ejpam-3914	695	23	r3	r3	PROPN
ejpam-3914	695	24	=	=	SYM
ejpam-3914	695	25	{	{	PUNCT
ejpam-3914	695	26	u1	u1	NOUN
ejpam-3914	695	27	,	,	PUNCT
ejpam-3914	695	28	u2	u2	PROPN
ejpam-3914	695	29	}	}	PUNCT
ejpam-3914	695	30	are	be	AUX
ejpam-3914	695	31	the	the	DET
ejpam-3914	695	32	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	695	33	-sets	-set	NOUN
ejpam-3914	695	34	of	of	ADP
ejpam-3914	695	35	f2	f2	PROPN
ejpam-3914	695	36	.	.	PUNCT
ejpam-3914	696	1	if	if	SCONJ
ejpam-3914	696	2	n	n	NUM
ejpam-3914	696	3	=	=	SYM
ejpam-3914	696	4	3	3	NUM
ejpam-3914	696	5	,	,	PUNCT
ejpam-3914	696	6	then	then	ADV
ejpam-3914	696	7	r1	r1	PROPN
ejpam-3914	696	8	=	=	SYM
ejpam-3914	696	9	{	{	PUNCT
ejpam-3914	696	10	v	v	NOUN
ejpam-3914	696	11	,	,	PUNCT
ejpam-3914	696	12	u1	u1	NOUN
ejpam-3914	696	13	}	}	PUNCT
ejpam-3914	696	14	,	,	PUNCT
ejpam-3914	696	15	r2	r2	PROPN
ejpam-3914	696	16	=	=	PUNCT
ejpam-3914	696	17	{	{	PUNCT
ejpam-3914	696	18	v	v	NOUN
ejpam-3914	696	19	,	,	PUNCT
ejpam-3914	696	20	u2	u2	NOUN
ejpam-3914	696	21	}	}	PUNCT
ejpam-3914	696	22	,	,	PUNCT
ejpam-3914	696	23	r3	r3	PROPN
ejpam-3914	696	24	=	=	SYM
ejpam-3914	696	25	{	{	PUNCT
ejpam-3914	696	26	v	v	NOUN
ejpam-3914	696	27	,	,	PUNCT
ejpam-3914	696	28	u3	u3	NOUN
ejpam-3914	696	29	}	}	PUNCT
ejpam-3914	696	30	,	,	PUNCT
ejpam-3914	696	31	r4	r4	NOUN
ejpam-3914	696	32	=	=	SYM
ejpam-3914	696	33	{	{	PUNCT
ejpam-3914	696	34	u1	u1	NOUN
ejpam-3914	696	35	,	,	PUNCT
ejpam-3914	696	36	u2	u2	PROPN
ejpam-3914	696	37	}	}	PUNCT
ejpam-3914	696	38	and	and	CCONJ
ejpam-3914	696	39	r5	r5	PROPN
ejpam-3914	696	40	=	=	PUNCT
ejpam-3914	696	41	{	{	PUNCT
ejpam-3914	696	42	u2	u2	PROPN
ejpam-3914	696	43	,	,	PUNCT
ejpam-3914	696	44	u3	u3	PROPN
ejpam-3914	696	45	}	}	PUNCT
ejpam-3914	696	46	are	be	AUX
ejpam-3914	696	47	the	the	DET
ejpam-3914	696	48	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	696	49	-sets	-set	NOUN
ejpam-3914	696	50	of	of	ADP
ejpam-3914	696	51	f3	f3	NOUN
ejpam-3914	696	52	.	.	PUNCT
ejpam-3914	697	1	clearly	clearly	ADV
ejpam-3914	697	2	,	,	PUNCT
ejpam-3914	697	3	for	for	ADP
ejpam-3914	697	4	all	all	DET
ejpam-3914	697	5	ui	ui	NOUN
ejpam-3914	697	6	∈	∈	PROPN
ejpam-3914	697	7	v	v	ADP
ejpam-3914	697	8	(	(	PUNCT
ejpam-3914	697	9	fn	fn	NOUN
ejpam-3914	697	10	)	)	PUNCT
ejpam-3914	697	11	and	and	CCONJ
ejpam-3914	697	12	n	n	CCONJ
ejpam-3914	697	13	=	=	SYM
ejpam-3914	697	14	2	2	NUM
ejpam-3914	697	15	,	,	PUNCT
ejpam-3914	697	16	3	3	NUM
ejpam-3914	697	17	,	,	PUNCT
ejpam-3914	697	18	the	the	DET
ejpam-3914	697	19	singleton	singleton	NOUN
ejpam-3914	697	20	{	{	PUNCT
ejpam-3914	697	21	ui	ui	PROPN
ejpam-3914	697	22	}	}	PUNCT
ejpam-3914	697	23	,	,	PUNCT
ejpam-3914	697	24	together	together	ADV
ejpam-3914	697	25	with	with	ADP
ejpam-3914	697	26	{	{	PUNCT
ejpam-3914	697	27	v	v	NOUN
ejpam-3914	697	28	}	}	PUNCT
ejpam-3914	697	29	,	,	PUNCT
ejpam-3914	697	30	is	be	AUX
ejpam-3914	697	31	not	not	PART
ejpam-3914	697	32	contained	contain	VERB
ejpam-3914	697	33	in	in	ADP
ejpam-3914	697	34	exactly	exactly	ADV
ejpam-3914	697	35	one	one	NUM
ejpam-3914	697	36	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	697	37	-set	-set	PUNCT
ejpam-3914	697	38	of	of	ADP
ejpam-3914	697	39	fn	fn	NOUN
ejpam-3914	697	40	,	,	PUNCT
ejpam-3914	697	41	that	that	ADV
ejpam-3914	697	42	is	is	ADV
ejpam-3914	697	43	,	,	PUNCT
ejpam-3914	697	44	the	the	DET
ejpam-3914	697	45	sets	set	NOUN
ejpam-3914	697	46	{	{	PUNCT
ejpam-3914	697	47	ui	ui	NOUN
ejpam-3914	697	48	}	}	PUNCT
ejpam-3914	697	49	and	and	CCONJ
ejpam-3914	697	50	{	{	PUNCT
ejpam-3914	697	51	v	v	NOUN
ejpam-3914	697	52	}	}	PUNCT
ejpam-3914	697	53	are	be	AUX
ejpam-3914	697	54	not	not	PART
ejpam-3914	697	55	forcing	force	VERB
ejpam-3914	697	56	subsets	subset	NOUN
ejpam-3914	697	57	for	for	ADP
ejpam-3914	697	58	any	any	DET
ejpam-3914	697	59	γ∗tpw	γ∗tpw	SYM
ejpam-3914	697	60	-set	-set	PROPN
ejpam-3914	697	61	of	of	ADP
ejpam-3914	697	62	fn	fn	PROPN
ejpam-3914	697	63	.	.	PUNCT
ejpam-3914	698	1	thus	thus	ADV
ejpam-3914	698	2	,	,	PUNCT
ejpam-3914	698	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	698	4	(	(	PUNCT
ejpam-3914	698	5	fn	fn	NOUN
ejpam-3914	698	6	)	)	PUNCT
ejpam-3914	698	7	≥	≥	NOUN
ejpam-3914	698	8	2	2	NUM
ejpam-3914	698	9	.	.	PUNCT
ejpam-3914	698	10	then	then	ADV
ejpam-3914	698	11	2	2	NUM
ejpam-3914	698	12	≤	≤	NOUN
ejpam-3914	698	13	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	698	14	(	(	PUNCT
ejpam-3914	698	15	fn	fn	NOUN
ejpam-3914	698	16	)	)	PUNCT
ejpam-3914	698	17	≤	≤	NOUN
ejpam-3914	698	18	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	698	19	(	(	PUNCT
ejpam-3914	698	20	fn	fn	NOUN
ejpam-3914	698	21	)	)	PUNCT
ejpam-3914	698	22	=	=	SYM
ejpam-3914	698	23	2	2	X
ejpam-3914	698	24	.	.	X
ejpam-3914	698	25	therefore	therefore	ADV
ejpam-3914	698	26	,	,	PUNCT
ejpam-3914	698	27	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	698	28	(	(	PUNCT
ejpam-3914	698	29	fn	fn	NOUN
ejpam-3914	698	30	)	)	PUNCT
ejpam-3914	698	31	=	=	SYM
ejpam-3914	698	32	2	2	NUM
ejpam-3914	698	33	for	for	ADP
ejpam-3914	698	34	n	n	NOUN
ejpam-3914	698	35	=	=	SYM
ejpam-3914	698	36	2	2	NUM
ejpam-3914	698	37	,	,	PUNCT
ejpam-3914	698	38	3	3	NUM
ejpam-3914	698	39	.	.	X
ejpam-3914	698	40	case	case	NOUN
ejpam-3914	698	41	2	2	NUM
ejpam-3914	698	42	:	:	PUNCT
ejpam-3914	698	43	suppose	suppose	VERB
ejpam-3914	698	44	that	that	SCONJ
ejpam-3914	698	45	n	n	PROPN
ejpam-3914	698	46	≥	≥	NUM
ejpam-3914	698	47	4	4	NUM
ejpam-3914	698	48	.	.	PUNCT
ejpam-3914	698	49	by	by	ADP
ejpam-3914	698	50	proposition	proposition	NOUN
ejpam-3914	698	51	2.4	2.4	NUM
ejpam-3914	698	52	,	,	PUNCT
ejpam-3914	698	53	γt(p4	γt(p4	NOUN
ejpam-3914	698	54	)	)	PUNCT
ejpam-3914	698	55	=	=	SYM
ejpam-3914	698	56	2	2	X
ejpam-3914	698	57	.	.	X
ejpam-3914	699	1	if	if	SCONJ
ejpam-3914	699	2	n	n	NOUN
ejpam-3914	699	3	=	=	SYM
ejpam-3914	699	4	4	4	NUM
ejpam-3914	699	5	,	,	PUNCT
ejpam-3914	699	6	then	then	ADV
ejpam-3914	699	7	r1	r1	PROPN
ejpam-3914	699	8	=	=	SYM
ejpam-3914	699	9	{	{	PUNCT
ejpam-3914	699	10	v	v	NOUN
ejpam-3914	699	11	,	,	PUNCT
ejpam-3914	699	12	u1	u1	NOUN
ejpam-3914	699	13	}	}	PUNCT
ejpam-3914	699	14	,	,	PUNCT
ejpam-3914	699	15	r2	r2	PROPN
ejpam-3914	699	16	=	=	PUNCT
ejpam-3914	699	17	{	{	PUNCT
ejpam-3914	699	18	v	v	NOUN
ejpam-3914	699	19	,	,	PUNCT
ejpam-3914	699	20	u2	u2	NOUN
ejpam-3914	699	21	}	}	PUNCT
ejpam-3914	699	22	,	,	PUNCT
ejpam-3914	699	23	r3	r3	PROPN
ejpam-3914	699	24	=	=	SYM
ejpam-3914	699	25	{	{	PUNCT
ejpam-3914	699	26	v	v	NOUN
ejpam-3914	699	27	,	,	PUNCT
ejpam-3914	699	28	u3	u3	NOUN
ejpam-3914	699	29	}	}	PUNCT
ejpam-3914	699	30	,	,	PUNCT
ejpam-3914	699	31	r4	r4	NOUN
ejpam-3914	699	32	=	=	PUNCT
ejpam-3914	699	33	{	{	PUNCT
ejpam-3914	699	34	v	v	NOUN
ejpam-3914	699	35	,	,	PUNCT
ejpam-3914	699	36	u4	u4	PROPN
ejpam-3914	699	37	}	}	PUNCT
ejpam-3914	699	38	,	,	PUNCT
ejpam-3914	699	39	and	and	CCONJ
ejpam-3914	699	40	r5	r5	PROPN
ejpam-3914	699	41	=	=	PUNCT
ejpam-3914	699	42	{	{	PUNCT
ejpam-3914	699	43	u2	u2	PROPN
ejpam-3914	699	44	,	,	PUNCT
ejpam-3914	699	45	u3	u3	PROPN
ejpam-3914	699	46	}	}	PUNCT
ejpam-3914	699	47	are	be	AUX
ejpam-3914	699	48	the	the	DET
ejpam-3914	699	49	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	699	50	-sets	-set	NOUN
ejpam-3914	699	51	of	of	ADP
ejpam-3914	699	52	f4	f4	PROPN
ejpam-3914	699	53	.	.	PUNCT
ejpam-3914	700	1	clearly	clearly	ADV
ejpam-3914	700	2	,	,	PUNCT
ejpam-3914	700	3	{	{	PUNCT
ejpam-3914	700	4	u1	u1	NOUN
ejpam-3914	700	5	}	}	PUNCT
ejpam-3914	700	6	⊆	⊆	NUM
ejpam-3914	700	7	r1	r1	NOUN
ejpam-3914	700	8	and	and	CCONJ
ejpam-3914	700	9	{	{	PUNCT
ejpam-3914	700	10	u1	u1	NOUN
ejpam-3914	700	11	}	}	PUNCT
ejpam-3914	700	12	*	*	PUNCT
ejpam-3914	700	13	rl	rl	X
ejpam-3914	700	14	for	for	ADP
ejpam-3914	700	15	l	l	NOUN
ejpam-3914	700	16	=	=	SYM
ejpam-3914	700	17	2	2	NUM
ejpam-3914	700	18	,	,	PUNCT
ejpam-3914	700	19	3	3	NUM
ejpam-3914	700	20	,	,	PUNCT
ejpam-3914	700	21	4	4	NUM
ejpam-3914	700	22	,	,	PUNCT
ejpam-3914	700	23	5	5	NUM
ejpam-3914	700	24	,	,	PUNCT
ejpam-3914	700	25	that	that	ADV
ejpam-3914	700	26	is	is	ADV
ejpam-3914	700	27	,	,	PUNCT
ejpam-3914	700	28	{	{	PUNCT
ejpam-3914	700	29	u1	u1	NOUN
ejpam-3914	700	30	}	}	PUNCT
ejpam-3914	700	31	is	be	AUX
ejpam-3914	700	32	a	a	DET
ejpam-3914	700	33	forcing	forcing	NOUN
ejpam-3914	700	34	subset	subset	NOUN
ejpam-3914	700	35	for	for	ADP
ejpam-3914	700	36	r1	r1	NOUN
ejpam-3914	700	37	and	and	CCONJ
ejpam-3914	700	38	so	so	ADV
ejpam-3914	700	39	,	,	PUNCT
ejpam-3914	700	40	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	700	41	(	(	PUNCT
ejpam-3914	700	42	r1	r1	PROPN
ejpam-3914	700	43	)	)	PUNCT
ejpam-3914	700	44	=	=	SYM
ejpam-3914	701	1	1	1	NUM
ejpam-3914	701	2	=	=	NOUN
ejpam-3914	701	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	701	4	(	(	PUNCT
ejpam-3914	701	5	f4	f4	NOUN
ejpam-3914	701	6	)	)	PUNCT
ejpam-3914	701	7	.	.	PUNCT
ejpam-3914	702	1	if	if	SCONJ
ejpam-3914	702	2	n	n	PROPN
ejpam-3914	702	3	>	>	X
ejpam-3914	702	4	4	4	NUM
ejpam-3914	702	5	,	,	PUNCT
ejpam-3914	702	6	then	then	ADV
ejpam-3914	702	7	γt(pn	γt(pn	PROPN
ejpam-3914	702	8	)	)	PUNCT
ejpam-3914	702	9	>	>	X
ejpam-3914	702	10	2	2	NUM
ejpam-3914	702	11	by	by	ADP
ejpam-3914	702	12	proposition	proposition	NOUN
ejpam-3914	702	13	2.4	2.4	NUM
ejpam-3914	702	14	and	and	CCONJ
ejpam-3914	702	15	so	so	ADV
ejpam-3914	702	16	,	,	PUNCT
ejpam-3914	702	17	the	the	DET
ejpam-3914	702	18	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	702	19	-sets	-set	NOUN
ejpam-3914	702	20	of	of	ADP
ejpam-3914	702	21	fn	fn	NOUN
ejpam-3914	702	22	are	be	AUX
ejpam-3914	702	23	of	of	ADP
ejpam-3914	702	24	the	the	DET
ejpam-3914	702	25	form	form	NOUN
ejpam-3914	702	26	{	{	PUNCT
ejpam-3914	702	27	v	v	NOUN
ejpam-3914	702	28	,	,	PUNCT
ejpam-3914	702	29	ui	ui	NOUN
ejpam-3914	702	30	}	}	PUNCT
ejpam-3914	702	31	for	for	ADP
ejpam-3914	702	32	all	all	DET
ejpam-3914	702	33	ui	ui	NOUN
ejpam-3914	702	34	∈	∈	PROPN
ejpam-3914	702	35	v	v	ADP
ejpam-3914	702	36	(	(	PUNCT
ejpam-3914	702	37	fn	fn	NOUN
ejpam-3914	702	38	)	)	PUNCT
ejpam-3914	702	39	.	.	PUNCT
ejpam-3914	703	1	clearly	clearly	ADV
ejpam-3914	703	2	,	,	PUNCT
ejpam-3914	703	3	r	r	NOUN
ejpam-3914	703	4	=	=	SYM
ejpam-3914	703	5	{	{	PUNCT
ejpam-3914	703	6	v	v	NOUN
ejpam-3914	703	7	,	,	PUNCT
ejpam-3914	703	8	u1	u1	NOUN
ejpam-3914	703	9	}	}	PUNCT
ejpam-3914	703	10	is	be	AUX
ejpam-3914	703	11	the	the	DET
ejpam-3914	703	12	only	only	ADJ
ejpam-3914	703	13	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	703	14	-set	-set	PUNCT
ejpam-3914	703	15	of	of	ADP
ejpam-3914	703	16	fn	fn	NOUN
ejpam-3914	703	17	containing	contain	VERB
ejpam-3914	703	18	u1	u1	NOUN
ejpam-3914	703	19	.	.	PUNCT
ejpam-3914	704	1	thus	thus	ADV
ejpam-3914	704	2	,	,	PUNCT
ejpam-3914	704	3	{	{	PUNCT
ejpam-3914	704	4	u1	u1	NOUN
ejpam-3914	704	5	}	}	PUNCT
ejpam-3914	704	6	is	be	AUX
ejpam-3914	704	7	a	a	DET
ejpam-3914	704	8	forcing	forcing	NOUN
ejpam-3914	704	9	subset	subset	NOUN
ejpam-3914	704	10	for	for	ADP
ejpam-3914	704	11	r	r	NOUN
ejpam-3914	704	12	,	,	PUNCT
ejpam-3914	704	13	that	that	ADV
ejpam-3914	704	14	is	is	ADV
ejpam-3914	704	15	,	,	PUNCT
ejpam-3914	704	16	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	704	17	(	(	PUNCT
ejpam-3914	704	18	r	r	NOUN
ejpam-3914	704	19	)	)	PUNCT
ejpam-3914	704	20	=	=	SYM
ejpam-3914	705	1	1	1	NUM
ejpam-3914	705	2	=	=	NOUN
ejpam-3914	705	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	705	4	(	(	PUNCT
ejpam-3914	705	5	fn	fn	NOUN
ejpam-3914	705	6	)	)	PUNCT
ejpam-3914	705	7	for	for	ADP
ejpam-3914	705	8	n	n	X
ejpam-3914	705	9	>	>	X
ejpam-3914	705	10	4	4	NUM
ejpam-3914	705	11	.	.	PUNCT
ejpam-3914	705	12	theorem	theorem	VERB
ejpam-3914	705	13	3.8	3.8	NUM
ejpam-3914	705	14	.	.	PUNCT
ejpam-3914	706	1	let	let	VERB
ejpam-3914	706	2	n	n	PRON
ejpam-3914	706	3	be	be	AUX
ejpam-3914	706	4	a	a	DET
ejpam-3914	706	5	positive	positive	ADJ
ejpam-3914	706	6	integer	integer	NOUN
ejpam-3914	706	7	with	with	ADP
ejpam-3914	706	8	n	n	PRON
ejpam-3914	706	9	≥	≥	NUM
ejpam-3914	706	10	3	3	NUM
ejpam-3914	706	11	.	.	PUNCT
ejpam-3914	707	1	then	then	ADV
ejpam-3914	707	2	the	the	DET
ejpam-3914	707	3	total	total	ADJ
ejpam-3914	707	4	dr	dr	PROPN
ejpam-3914	707	5	-	-	PUNCT
ejpam-3914	707	6	power	power	NOUN
ejpam-3914	707	7	domination	domination	NOUN
ejpam-3914	707	8	number	number	NOUN
ejpam-3914	707	9	of	of	ADP
ejpam-3914	707	10	the	the	DET
ejpam-3914	707	11	wheel	wheel	NOUN
ejpam-3914	707	12	graph	graph	NOUN
ejpam-3914	707	13	wn	wn	PROPN
ejpam-3914	707	14	=	=	PROPN
ejpam-3914	707	15	k1	k1	PROPN
ejpam-3914	707	16	+	+	CCONJ
ejpam-3914	707	17	cn	cn	NOUN
ejpam-3914	707	18	of	of	ADP
ejpam-3914	707	19	order	order	NOUN
ejpam-3914	707	20	n+	n+	ADP
ejpam-3914	707	21	1	1	NUM
ejpam-3914	707	22	is	be	AUX
ejpam-3914	707	23	given	give	VERB
ejpam-3914	707	24	by	by	ADP
ejpam-3914	707	25	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	707	26	(	(	PUNCT
ejpam-3914	707	27	wn	wn	PROPN
ejpam-3914	707	28	)	)	PUNCT
ejpam-3914	707	29	=	=	SYM
ejpam-3914	707	30	2	2	NUM
ejpam-3914	707	31	and	and	CCONJ
ejpam-3914	707	32	its	its	PRON
ejpam-3914	707	33	forcing	force	VERB
ejpam-3914	707	34	total	total	ADJ
ejpam-3914	707	35	dr	dr	PROPN
ejpam-3914	707	36	-	-	PUNCT
ejpam-3914	707	37	power	power	NOUN
ejpam-3914	707	38	domination	domination	NOUN
ejpam-3914	707	39	number	number	NOUN
ejpam-3914	707	40	is	be	AUX
ejpam-3914	707	41	given	give	VERB
ejpam-3914	707	42	by	by	ADP
ejpam-3914	707	43	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	707	44	(	(	PUNCT
ejpam-3914	707	45	wn	wn	NOUN
ejpam-3914	707	46	)	)	PUNCT
ejpam-3914	707	47	=	=	PRON
ejpam-3914	707	48	{	{	PUNCT
ejpam-3914	707	49	2	2	NUM
ejpam-3914	707	50	,	,	PUNCT
ejpam-3914	707	51	n	n	NOUN
ejpam-3914	707	52	=	=	SYM
ejpam-3914	707	53	3	3	NUM
ejpam-3914	707	54	,	,	PUNCT
ejpam-3914	707	55	4	4	NUM
ejpam-3914	707	56	1	1	NUM
ejpam-3914	707	57	,	,	PUNCT
ejpam-3914	707	58	n	n	PRON
ejpam-3914	707	59	≥	≥	NOUN
ejpam-3914	707	60	5	5	NUM
ejpam-3914	707	61	.	.	PUNCT
ejpam-3914	708	1	proof	proof	NOUN
ejpam-3914	708	2	.	.	PUNCT
ejpam-3914	709	1	by	by	ADP
ejpam-3914	709	2	corollary	corollary	ADJ
ejpam-3914	709	3	2.6	2.6	NUM
ejpam-3914	709	4	,	,	PUNCT
ejpam-3914	709	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	709	6	(	(	PUNCT
ejpam-3914	709	7	wn	wn	PROPN
ejpam-3914	709	8	)	)	PUNCT
ejpam-3914	709	9	=	=	SYM
ejpam-3914	709	10	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	709	11	(	(	PUNCT
ejpam-3914	709	12	k1	k1	NOUN
ejpam-3914	709	13	+	+	CCONJ
ejpam-3914	709	14	cn	cn	PROPN
ejpam-3914	709	15	)	)	PUNCT
ejpam-3914	709	16	=	=	SYM
ejpam-3914	709	17	2	2	X
ejpam-3914	709	18	.	.	X
ejpam-3914	709	19	let	let	VERB
ejpam-3914	709	20	v	v	X
ejpam-3914	709	21	(	(	PUNCT
ejpam-3914	709	22	wn	wn	PROPN
ejpam-3914	709	23	)	)	PUNCT
ejpam-3914	709	24	=	=	SYM
ejpam-3914	709	25	{	{	PUNCT
ejpam-3914	709	26	v	v	NOUN
ejpam-3914	709	27	,	,	PUNCT
ejpam-3914	709	28	u1	u1	NOUN
ejpam-3914	709	29	,	,	PUNCT
ejpam-3914	709	30	u2	u2	NOUN
ejpam-3914	709	31	,	,	PUNCT
ejpam-3914	709	32	u3	u3	NOUN
ejpam-3914	709	33	,	,	PUNCT
ejpam-3914	709	34	.	.	PUNCT
ejpam-3914	709	35	.	.	PUNCT
ejpam-3914	710	1	.	.	PUNCT
ejpam-3914	711	1	,	,	PUNCT
ejpam-3914	711	2	un	un	AUX
ejpam-3914	711	3	}	}	PUNCT
ejpam-3914	711	4	such	such	ADJ
ejpam-3914	711	5	that	that	SCONJ
ejpam-3914	711	6	deg(v	deg(v	PROPN
ejpam-3914	711	7	)	)	PUNCT
ejpam-3914	711	8	=	=	SYM
ejpam-3914	711	9	n.	n.	NOUN
ejpam-3914	711	10	note	note	VERB
ejpam-3914	711	11	that	that	SCONJ
ejpam-3914	711	12	the	the	DET
ejpam-3914	711	13	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	711	14	-sets	-set	NOUN
ejpam-3914	711	15	of	of	ADP
ejpam-3914	711	16	wn	wn	PROPN
ejpam-3914	711	17	are	be	AUX
ejpam-3914	711	18	of	of	ADP
ejpam-3914	711	19	the	the	DET
ejpam-3914	711	20	form	form	NOUN
ejpam-3914	711	21	{	{	PUNCT
ejpam-3914	711	22	v	v	NOUN
ejpam-3914	711	23	,	,	PUNCT
ejpam-3914	711	24	ui	ui	NOUN
ejpam-3914	711	25	}	}	PUNCT
ejpam-3914	711	26	for	for	ADP
ejpam-3914	711	27	all	all	DET
ejpam-3914	711	28	ui	ui	NOUN
ejpam-3914	711	29	∈	∈	PROPN
ejpam-3914	711	30	v	v	NOUN
ejpam-3914	711	31	(	(	PUNCT
ejpam-3914	711	32	wn	wn	PROPN
ejpam-3914	711	33	)	)	PUNCT
ejpam-3914	711	34	and	and	CCONJ
ejpam-3914	711	35	of	of	ADP
ejpam-3914	711	36	the	the	DET
ejpam-3914	711	37	form	form	NOUN
ejpam-3914	711	38	{	{	PUNCT
ejpam-3914	711	39	ui	ui	PROPN
ejpam-3914	711	40	,	,	PUNCT
ejpam-3914	711	41	uj	uj	PROPN
ejpam-3914	711	42	}	}	PUNCT
ejpam-3914	711	43	such	such	ADJ
ejpam-3914	711	44	that	that	SCONJ
ejpam-3914	711	45	i	i	PRON
ejpam-3914	711	46	6=	6=	PROPN
ejpam-3914	711	47	j	j	PROPN
ejpam-3914	711	48	and	and	CCONJ
ejpam-3914	711	49	{	{	PUNCT
ejpam-3914	711	50	ui	ui	PROPN
ejpam-3914	711	51	,	,	PUNCT
ejpam-3914	711	52	uj	uj	PROPN
ejpam-3914	711	53	}	}	PUNCT
ejpam-3914	711	54	is	be	AUX
ejpam-3914	711	55	a	a	DET
ejpam-3914	711	56	γt	γt	NOUN
ejpam-3914	711	57	-	-	NOUN
ejpam-3914	711	58	set	set	NOUN
ejpam-3914	711	59	of	of	ADP
ejpam-3914	711	60	cn	cn	PROPN
ejpam-3914	711	61	by	by	ADP
ejpam-3914	711	62	theorem	theorem	ADJ
ejpam-3914	711	63	2.5	2.5	NUM
ejpam-3914	711	64	and	and	CCONJ
ejpam-3914	711	65	corollary	corollary	ADJ
ejpam-3914	711	66	2.6	2.6	NUM
ejpam-3914	711	67	.	.	PUNCT
ejpam-3914	712	1	consider	consider	VERB
ejpam-3914	712	2	the	the	DET
ejpam-3914	712	3	following	follow	VERB
ejpam-3914	712	4	cases	case	NOUN
ejpam-3914	712	5	:	:	PUNCT
ejpam-3914	712	6	references	reference	NOUN
ejpam-3914	712	7	469	469	NUM
ejpam-3914	712	8	case	case	NOUN
ejpam-3914	712	9	1	1	NUM
ejpam-3914	712	10	:	:	PUNCT
ejpam-3914	712	11	suppose	suppose	VERB
ejpam-3914	712	12	that	that	SCONJ
ejpam-3914	712	13	either	either	CCONJ
ejpam-3914	712	14	n	n	PROPN
ejpam-3914	712	15	=	=	SYM
ejpam-3914	712	16	3	3	NUM
ejpam-3914	712	17	or	or	CCONJ
ejpam-3914	712	18	n	n	NOUN
ejpam-3914	712	19	=	=	SYM
ejpam-3914	712	20	4	4	X
ejpam-3914	712	21	.	.	PUNCT
ejpam-3914	712	22	by	by	ADP
ejpam-3914	712	23	proposition	proposition	NOUN
ejpam-3914	712	24	2.4	2.4	NUM
ejpam-3914	712	25	,	,	PUNCT
ejpam-3914	712	26	γt(cn	γt(cn	PROPN
ejpam-3914	712	27	)	)	PUNCT
ejpam-3914	713	1	=	=	SYM
ejpam-3914	713	2	2	2	NUM
ejpam-3914	713	3	for	for	ADP
ejpam-3914	713	4	n	n	NOUN
ejpam-3914	713	5	=	=	SYM
ejpam-3914	713	6	3	3	NUM
ejpam-3914	713	7	,	,	PUNCT
ejpam-3914	713	8	4	4	NUM
ejpam-3914	713	9	.	.	PUNCT
ejpam-3914	714	1	if	if	SCONJ
ejpam-3914	714	2	n	n	NOUN
ejpam-3914	714	3	=	=	SYM
ejpam-3914	714	4	3	3	NUM
ejpam-3914	714	5	,	,	PUNCT
ejpam-3914	714	6	then	then	ADV
ejpam-3914	714	7	r1	r1	PROPN
ejpam-3914	714	8	=	=	SYM
ejpam-3914	714	9	{	{	PUNCT
ejpam-3914	714	10	v	v	NOUN
ejpam-3914	714	11	,	,	PUNCT
ejpam-3914	714	12	u1	u1	NOUN
ejpam-3914	714	13	}	}	PUNCT
ejpam-3914	714	14	,	,	PUNCT
ejpam-3914	714	15	r2	r2	PROPN
ejpam-3914	714	16	=	=	PUNCT
ejpam-3914	714	17	{	{	PUNCT
ejpam-3914	714	18	v	v	NOUN
ejpam-3914	714	19	,	,	PUNCT
ejpam-3914	714	20	u2	u2	NOUN
ejpam-3914	714	21	}	}	PUNCT
ejpam-3914	714	22	,	,	PUNCT
ejpam-3914	714	23	r3	r3	PROPN
ejpam-3914	714	24	=	=	SYM
ejpam-3914	714	25	{	{	PUNCT
ejpam-3914	714	26	v	v	NOUN
ejpam-3914	714	27	,	,	PUNCT
ejpam-3914	714	28	u3	u3	NOUN
ejpam-3914	714	29	}	}	PUNCT
ejpam-3914	714	30	,	,	PUNCT
ejpam-3914	714	31	r4	r4	NOUN
ejpam-3914	714	32	=	=	SYM
ejpam-3914	714	33	{	{	PUNCT
ejpam-3914	714	34	u1	u1	NOUN
ejpam-3914	714	35	,	,	PUNCT
ejpam-3914	714	36	u2	u2	PROPN
ejpam-3914	714	37	}	}	PUNCT
ejpam-3914	714	38	,	,	PUNCT
ejpam-3914	714	39	r5	r5	PROPN
ejpam-3914	714	40	=	=	PUNCT
ejpam-3914	714	41	{	{	PUNCT
ejpam-3914	714	42	u2	u2	PROPN
ejpam-3914	714	43	,	,	PUNCT
ejpam-3914	714	44	u3	u3	NOUN
ejpam-3914	714	45	}	}	PUNCT
ejpam-3914	714	46	and	and	CCONJ
ejpam-3914	714	47	r6	r6	NOUN
ejpam-3914	714	48	=	=	SYM
ejpam-3914	714	49	{	{	PUNCT
ejpam-3914	714	50	u1	u1	NOUN
ejpam-3914	714	51	,	,	PUNCT
ejpam-3914	714	52	u3	u3	PROPN
ejpam-3914	714	53	}	}	PUNCT
ejpam-3914	714	54	are	be	AUX
ejpam-3914	714	55	the	the	DET
ejpam-3914	714	56	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	714	57	-sets	-set	NOUN
ejpam-3914	714	58	of	of	ADP
ejpam-3914	714	59	w3	w3	NOUN
ejpam-3914	714	60	.	.	PUNCT
ejpam-3914	715	1	if	if	SCONJ
ejpam-3914	715	2	n	n	NOUN
ejpam-3914	715	3	=	=	SYM
ejpam-3914	715	4	4	4	NUM
ejpam-3914	715	5	,	,	PUNCT
ejpam-3914	715	6	then	then	ADV
ejpam-3914	715	7	r1	r1	PROPN
ejpam-3914	715	8	=	=	SYM
ejpam-3914	715	9	{	{	PUNCT
ejpam-3914	715	10	v	v	NOUN
ejpam-3914	715	11	,	,	PUNCT
ejpam-3914	715	12	u1	u1	NOUN
ejpam-3914	715	13	}	}	PUNCT
ejpam-3914	715	14	,	,	PUNCT
ejpam-3914	715	15	r2	r2	PROPN
ejpam-3914	715	16	=	=	PUNCT
ejpam-3914	715	17	{	{	PUNCT
ejpam-3914	715	18	v	v	NOUN
ejpam-3914	715	19	,	,	PUNCT
ejpam-3914	715	20	u2	u2	NOUN
ejpam-3914	715	21	}	}	PUNCT
ejpam-3914	715	22	,	,	PUNCT
ejpam-3914	715	23	r3	r3	PROPN
ejpam-3914	715	24	=	=	SYM
ejpam-3914	715	25	{	{	PUNCT
ejpam-3914	715	26	v	v	NOUN
ejpam-3914	715	27	,	,	PUNCT
ejpam-3914	715	28	u3	u3	NOUN
ejpam-3914	715	29	}	}	PUNCT
ejpam-3914	715	30	,	,	PUNCT
ejpam-3914	715	31	r4	r4	NOUN
ejpam-3914	715	32	=	=	PUNCT
ejpam-3914	715	33	{	{	PUNCT
ejpam-3914	715	34	v	v	NOUN
ejpam-3914	715	35	,	,	PUNCT
ejpam-3914	715	36	u4	u4	PROPN
ejpam-3914	715	37	}	}	PUNCT
ejpam-3914	715	38	,	,	PUNCT
ejpam-3914	715	39	r5	r5	PROPN
ejpam-3914	715	40	=	=	SYM
ejpam-3914	715	41	{	{	PUNCT
ejpam-3914	715	42	u1	u1	NOUN
ejpam-3914	715	43	,	,	PUNCT
ejpam-3914	715	44	u2	u2	PROPN
ejpam-3914	715	45	}	}	PUNCT
ejpam-3914	715	46	,	,	PUNCT
ejpam-3914	715	47	r6	r6	NOUN
ejpam-3914	715	48	=	=	SYM
ejpam-3914	715	49	{	{	PUNCT
ejpam-3914	715	50	u2	u2	NOUN
ejpam-3914	715	51	,	,	PUNCT
ejpam-3914	715	52	u3	u3	NOUN
ejpam-3914	715	53	}	}	PUNCT
ejpam-3914	715	54	,	,	PUNCT
ejpam-3914	716	1	r7	r7	NOUN
ejpam-3914	716	2	=	=	SYM
ejpam-3914	716	3	{	{	PUNCT
ejpam-3914	716	4	u3	u3	PROPN
ejpam-3914	716	5	,	,	PUNCT
ejpam-3914	716	6	u4	u4	PROPN
ejpam-3914	716	7	}	}	PUNCT
ejpam-3914	716	8	and	and	CCONJ
ejpam-3914	716	9	r8	r8	PROPN
ejpam-3914	716	10	=	=	SYM
ejpam-3914	716	11	{	{	PUNCT
ejpam-3914	716	12	u4	u4	PROPN
ejpam-3914	716	13	,	,	PUNCT
ejpam-3914	716	14	u1	u1	PROPN
ejpam-3914	716	15	}	}	PUNCT
ejpam-3914	716	16	are	be	AUX
ejpam-3914	716	17	the	the	DET
ejpam-3914	716	18	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	716	19	-sets	-set	NOUN
ejpam-3914	716	20	of	of	ADP
ejpam-3914	716	21	w4	w4	NOUN
ejpam-3914	716	22	.	.	PUNCT
ejpam-3914	717	1	clearly	clearly	ADV
ejpam-3914	717	2	,	,	PUNCT
ejpam-3914	717	3	for	for	ADP
ejpam-3914	717	4	all	all	DET
ejpam-3914	717	5	ui	ui	NOUN
ejpam-3914	717	6	∈	∈	PROPN
ejpam-3914	717	7	v	v	NOUN
ejpam-3914	717	8	(	(	PUNCT
ejpam-3914	717	9	wn	wn	PROPN
ejpam-3914	717	10	)	)	PUNCT
ejpam-3914	717	11	and	and	CCONJ
ejpam-3914	717	12	for	for	ADP
ejpam-3914	717	13	n	n	NOUN
ejpam-3914	717	14	=	=	SYM
ejpam-3914	717	15	3	3	NUM
ejpam-3914	717	16	,	,	PUNCT
ejpam-3914	717	17	4	4	NUM
ejpam-3914	717	18	,	,	PUNCT
ejpam-3914	717	19	the	the	DET
ejpam-3914	717	20	singleton	singleton	NOUN
ejpam-3914	717	21	{	{	PUNCT
ejpam-3914	717	22	ui	ui	PROPN
ejpam-3914	717	23	}	}	PUNCT
ejpam-3914	717	24	,	,	PUNCT
ejpam-3914	717	25	together	together	ADV
ejpam-3914	717	26	with	with	ADP
ejpam-3914	717	27	{	{	PUNCT
ejpam-3914	717	28	v	v	NOUN
ejpam-3914	717	29	}	}	PUNCT
ejpam-3914	717	30	,	,	PUNCT
ejpam-3914	717	31	is	be	AUX
ejpam-3914	717	32	not	not	PART
ejpam-3914	717	33	contained	contain	VERB
ejpam-3914	717	34	in	in	ADP
ejpam-3914	717	35	exactly	exactly	ADV
ejpam-3914	717	36	one	one	NUM
ejpam-3914	717	37	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	717	38	-set	-set	PUNCT
ejpam-3914	717	39	of	of	ADP
ejpam-3914	717	40	wn	wn	PROPN
ejpam-3914	717	41	,	,	PUNCT
ejpam-3914	717	42	that	that	ADV
ejpam-3914	717	43	is	is	ADV
ejpam-3914	717	44	,	,	PUNCT
ejpam-3914	717	45	the	the	DET
ejpam-3914	717	46	sets	set	NOUN
ejpam-3914	717	47	{	{	PUNCT
ejpam-3914	717	48	ui	ui	NOUN
ejpam-3914	717	49	}	}	PUNCT
ejpam-3914	717	50	and	and	CCONJ
ejpam-3914	717	51	{	{	PUNCT
ejpam-3914	717	52	v	v	NOUN
ejpam-3914	717	53	}	}	PUNCT
ejpam-3914	717	54	are	be	AUX
ejpam-3914	717	55	not	not	PART
ejpam-3914	717	56	forcing	force	VERB
ejpam-3914	717	57	subsets	subset	NOUN
ejpam-3914	717	58	for	for	ADP
ejpam-3914	717	59	any	any	DET
ejpam-3914	717	60	γ∗tpw	γ∗tpw	SYM
ejpam-3914	717	61	-set	-set	PROPN
ejpam-3914	717	62	of	of	ADP
ejpam-3914	717	63	wn	wn	PROPN
ejpam-3914	717	64	.	.	PUNCT
ejpam-3914	718	1	thus	thus	ADV
ejpam-3914	718	2	,	,	PUNCT
ejpam-3914	718	3	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3914	718	4	(	(	PUNCT
ejpam-3914	718	5	wn	wn	PROPN
ejpam-3914	718	6	)	)	PUNCT
ejpam-3914	718	7	≥	≥	NOUN
ejpam-3914	718	8	2	2	NUM
ejpam-3914	718	9	.	.	PUNCT
ejpam-3914	718	10	then	then	ADV
ejpam-3914	718	11	2	2	NUM
ejpam-3914	718	12	≤	≤	NOUN
ejpam-3914	718	13	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	718	14	(	(	PUNCT
ejpam-3914	718	15	wn	wn	NOUN
ejpam-3914	718	16	)	)	PUNCT
ejpam-3914	718	17	≤	≤	NOUN
ejpam-3914	718	18	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	718	19	(	(	PUNCT
ejpam-3914	718	20	wn	wn	PROPN
ejpam-3914	718	21	)	)	PUNCT
ejpam-3914	718	22	=	=	SYM
ejpam-3914	718	23	2	2	X
ejpam-3914	718	24	.	.	X
ejpam-3914	718	25	therefore	therefore	ADV
ejpam-3914	718	26	,	,	PUNCT
ejpam-3914	718	27	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3914	718	28	(	(	PUNCT
ejpam-3914	718	29	wn	wn	NOUN
ejpam-3914	718	30	)	)	PUNCT
ejpam-3914	718	31	=	=	SYM
ejpam-3914	718	32	2	2	NUM
ejpam-3914	718	33	for	for	ADP
ejpam-3914	718	34	n	n	NOUN
ejpam-3914	718	35	=	=	SYM
ejpam-3914	718	36	3	3	NUM
ejpam-3914	718	37	,	,	PUNCT
ejpam-3914	718	38	4	4	NUM
ejpam-3914	718	39	.	.	PUNCT
ejpam-3914	718	40	case	case	NOUN
ejpam-3914	718	41	2	2	NUM
ejpam-3914	718	42	:	:	PUNCT
ejpam-3914	718	43	suppose	suppose	VERB
ejpam-3914	718	44	that	that	SCONJ
ejpam-3914	718	45	n	n	PROPN
ejpam-3914	718	46	≥	≥	NUM
ejpam-3914	718	47	5	5	NUM
ejpam-3914	718	48	.	.	PUNCT
ejpam-3914	718	49	then	then	ADV
ejpam-3914	718	50	γt(cn	γt(cn	PROPN
ejpam-3914	718	51	)	)	PUNCT
ejpam-3914	718	52	>	>	X
ejpam-3914	719	1	2	2	NUM
ejpam-3914	719	2	by	by	ADP
ejpam-3914	719	3	proposition	proposition	NOUN
ejpam-3914	719	4	2.4	2.4	NUM
ejpam-3914	719	5	and	and	CCONJ
ejpam-3914	719	6	so	so	ADV
ejpam-3914	719	7	,	,	PUNCT
ejpam-3914	719	8	the	the	DET
ejpam-3914	719	9	γ∗tpw	γ∗tpw	PUNCT
ejpam-3914	719	10	-sets	-set	NOUN
ejpam-3914	719	11	of	of	ADP
ejpam-3914	719	12	wn	wn	PROPN
ejpam-3914	719	13	are	be	AUX
ejpam-3914	719	14	of	of	ADP
ejpam-3914	719	15	the	the	DET
ejpam-3914	719	16	form	form	NOUN
ejpam-3914	719	17	{	{	PUNCT
ejpam-3914	719	18	v	v	NOUN
ejpam-3914	719	19	,	,	PUNCT
ejpam-3914	719	20	ui	ui	NOUN
ejpam-3914	719	21	}	}	PUNCT
ejpam-3914	719	22	for	for	ADP
ejpam-3914	719	23	all	all	DET
ejpam-3914	719	24	ui	ui	NOUN
ejpam-3914	719	25	∈	∈	PROPN
ejpam-3914	719	26	v	v	NOUN
ejpam-3914	719	27	(	(	PUNCT
ejpam-3914	719	28	wn	wn	PROPN
ejpam-3914	719	29	)	)	PUNCT
ejpam-3914	719	30	.	.	PUNCT
ejpam-3914	720	1	clearly	clearly	ADV
ejpam-3914	720	2	,	,	PUNCT
ejpam-3914	720	3	r	r	NOUN
ejpam-3914	720	4	=	=	SYM
ejpam-3914	720	5	{	{	PUNCT
ejpam-3914	720	6	v	v	NOUN
ejpam-3914	720	7	,	,	PUNCT
ejpam-3914	720	8	u1	u1	NOUN
ejpam-3914	720	9	}	}	PUNCT
ejpam-3914	720	10	is	be	AUX
ejpam-3914	720	11	the	the	DET
ejpam-3914	720	12	only	only	ADJ
ejpam-3914	720	13	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	720	14	-set	-set	PROPN
ejpam-3914	720	15	of	of	ADP
ejpam-3914	720	16	wn	wn	PROPN
ejpam-3914	720	17	containing	contain	VERB
ejpam-3914	720	18	u1	u1	NOUN
ejpam-3914	720	19	.	.	PUNCT
ejpam-3914	721	1	thus	thus	ADV
ejpam-3914	721	2	,	,	PUNCT
ejpam-3914	721	3	{	{	PUNCT
ejpam-3914	721	4	u1	u1	NOUN
ejpam-3914	721	5	}	}	PUNCT
ejpam-3914	721	6	is	be	AUX
ejpam-3914	721	7	a	a	DET
ejpam-3914	721	8	forcing	forcing	NOUN
ejpam-3914	721	9	subset	subset	NOUN
ejpam-3914	721	10	for	for	ADP
ejpam-3914	721	11	r	r	NOUN
ejpam-3914	721	12	,	,	PUNCT
ejpam-3914	721	13	that	that	ADV
ejpam-3914	721	14	is	is	ADV
ejpam-3914	721	15	,	,	PUNCT
ejpam-3914	721	16	for	for	ADP
ejpam-3914	721	17	all	all	DET
ejpam-3914	721	18	n	n	PRON
ejpam-3914	721	19	≥	≥	NUM
ejpam-3914	721	20	5	5	NUM
ejpam-3914	721	21	,	,	PUNCT
ejpam-3914	721	22	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	721	23	(	(	PUNCT
ejpam-3914	721	24	r	r	NOUN
ejpam-3914	721	25	)	)	PUNCT
ejpam-3914	721	26	=	=	SYM
ejpam-3914	722	1	1	1	NUM
ejpam-3914	722	2	=	=	NOUN
ejpam-3914	722	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	722	4	(	(	PUNCT
ejpam-3914	722	5	wn	wn	NOUN
ejpam-3914	722	6	)	)	PUNCT
ejpam-3914	722	7	.	.	PUNCT
ejpam-3914	723	1	theorem	theorem	VERB
ejpam-3914	723	2	3.9	3.9	NUM
ejpam-3914	723	3	.	.	PUNCT
ejpam-3914	724	1	let	let	VERB
ejpam-3914	724	2	n	n	PRON
ejpam-3914	724	3	be	be	AUX
ejpam-3914	724	4	a	a	DET
ejpam-3914	724	5	positive	positive	ADJ
ejpam-3914	724	6	integer	integer	NOUN
ejpam-3914	724	7	with	with	ADP
ejpam-3914	724	8	n	n	PRON
ejpam-3914	724	9	≥	≥	NUM
ejpam-3914	724	10	1	1	NUM
ejpam-3914	724	11	.	.	PUNCT
ejpam-3914	725	1	then	then	ADV
ejpam-3914	725	2	the	the	DET
ejpam-3914	725	3	total	total	ADJ
ejpam-3914	725	4	dr	dr	PROPN
ejpam-3914	725	5	-	-	PUNCT
ejpam-3914	725	6	power	power	NOUN
ejpam-3914	725	7	domination	domination	NOUN
ejpam-3914	725	8	number	number	NOUN
ejpam-3914	725	9	of	of	ADP
ejpam-3914	725	10	the	the	DET
ejpam-3914	725	11	star	star	NOUN
ejpam-3914	725	12	graph	graph	NOUN
ejpam-3914	725	13	sn	sn	PROPN
ejpam-3914	725	14	=	=	SYM
ejpam-3914	725	15	k1	k1	PROPN
ejpam-3914	726	1	+	+	NOUN
ejpam-3914	726	2	kn	kn	NOUN
ejpam-3914	726	3	of	of	ADP
ejpam-3914	726	4	order	order	NOUN
ejpam-3914	726	5	n+	n+	ADP
ejpam-3914	726	6	1	1	NUM
ejpam-3914	726	7	is	be	AUX
ejpam-3914	726	8	given	give	VERB
ejpam-3914	726	9	by	by	ADP
ejpam-3914	726	10	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	726	11	(	(	PUNCT
ejpam-3914	726	12	sn	sn	PROPN
ejpam-3914	726	13	)	)	PUNCT
ejpam-3914	726	14	=	=	SYM
ejpam-3914	726	15	2	2	NUM
ejpam-3914	726	16	and	and	CCONJ
ejpam-3914	726	17	its	its	PRON
ejpam-3914	726	18	forcing	force	VERB
ejpam-3914	726	19	total	total	ADJ
ejpam-3914	726	20	dr	dr	PROPN
ejpam-3914	726	21	-	-	PUNCT
ejpam-3914	726	22	power	power	NOUN
ejpam-3914	726	23	domination	domination	NOUN
ejpam-3914	726	24	number	number	NOUN
ejpam-3914	726	25	is	be	AUX
ejpam-3914	726	26	given	give	VERB
ejpam-3914	726	27	by	by	ADP
ejpam-3914	726	28	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	726	29	(	(	PUNCT
ejpam-3914	726	30	sn	sn	NOUN
ejpam-3914	726	31	)	)	PUNCT
ejpam-3914	726	32	=	=	PRON
ejpam-3914	726	33	{	{	PUNCT
ejpam-3914	726	34	0	0	NUM
ejpam-3914	726	35	,	,	PUNCT
ejpam-3914	726	36	n	n	NOUN
ejpam-3914	726	37	=	=	SYM
ejpam-3914	726	38	1	1	NUM
ejpam-3914	726	39	1	1	NUM
ejpam-3914	726	40	,	,	PUNCT
ejpam-3914	726	41	n	n	CCONJ
ejpam-3914	726	42	>	>	X
ejpam-3914	726	43	1	1	X
ejpam-3914	726	44	.	.	PUNCT
ejpam-3914	726	45	proof	proof	NOUN
ejpam-3914	726	46	.	.	PUNCT
ejpam-3914	727	1	by	by	ADP
ejpam-3914	727	2	corollary	corollary	ADJ
ejpam-3914	727	3	2.6	2.6	NUM
ejpam-3914	727	4	,	,	PUNCT
ejpam-3914	727	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	727	6	(	(	PUNCT
ejpam-3914	727	7	sn	sn	PROPN
ejpam-3914	727	8	)	)	PUNCT
ejpam-3914	727	9	=	=	SYM
ejpam-3914	727	10	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	727	11	(	(	PUNCT
ejpam-3914	727	12	k1	k1	NOUN
ejpam-3914	727	13	+	+	CCONJ
ejpam-3914	727	14	kn	kn	PROPN
ejpam-3914	727	15	)	)	PUNCT
ejpam-3914	727	16	=	=	SYM
ejpam-3914	727	17	2	2	X
ejpam-3914	727	18	.	.	X
ejpam-3914	727	19	let	let	VERB
ejpam-3914	727	20	v	v	NOUN
ejpam-3914	727	21	(	(	PUNCT
ejpam-3914	727	22	sn	sn	PROPN
ejpam-3914	727	23	)	)	PUNCT
ejpam-3914	727	24	=	=	PRON
ejpam-3914	727	25	{	{	PUNCT
ejpam-3914	727	26	v	v	NOUN
ejpam-3914	727	27	,	,	PUNCT
ejpam-3914	727	28	u1	u1	NOUN
ejpam-3914	727	29	,	,	PUNCT
ejpam-3914	727	30	u2	u2	NOUN
ejpam-3914	727	31	,	,	PUNCT
ejpam-3914	727	32	u3	u3	NOUN
ejpam-3914	727	33	,	,	PUNCT
ejpam-3914	727	34	.	.	PUNCT
ejpam-3914	727	35	.	.	PUNCT
ejpam-3914	728	1	.	.	PUNCT
ejpam-3914	729	1	,	,	PUNCT
ejpam-3914	729	2	un	un	PROPN
ejpam-3914	729	3	}	}	PUNCT
ejpam-3914	729	4	such	such	ADJ
ejpam-3914	729	5	that	that	SCONJ
ejpam-3914	729	6	deg(v	deg(v	PROPN
ejpam-3914	729	7	)	)	PUNCT
ejpam-3914	729	8	=	=	VERB
ejpam-3914	729	9	n.	n.	NOUN
ejpam-3914	729	10	if	if	SCONJ
ejpam-3914	729	11	n	n	NOUN
ejpam-3914	729	12	=	=	SYM
ejpam-3914	729	13	1	1	NUM
ejpam-3914	729	14	,	,	PUNCT
ejpam-3914	729	15	then	then	ADV
ejpam-3914	729	16	r	r	NOUN
ejpam-3914	729	17	=	=	PUNCT
ejpam-3914	729	18	{	{	PUNCT
ejpam-3914	729	19	v	v	NOUN
ejpam-3914	729	20	,	,	PUNCT
ejpam-3914	729	21	u1	u1	NOUN
ejpam-3914	729	22	}	}	PUNCT
ejpam-3914	729	23	is	be	AUX
ejpam-3914	729	24	the	the	DET
ejpam-3914	729	25	only	only	ADJ
ejpam-3914	729	26	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	729	27	-set	-set	PROPN
ejpam-3914	729	28	of	of	ADP
ejpam-3914	729	29	s1	s1	PROPN
ejpam-3914	729	30	.	.	PUNCT
ejpam-3914	730	1	by	by	ADP
ejpam-3914	730	2	theorem	theorem	NOUN
ejpam-3914	730	3	3.1(i	3.1(i	NUM
ejpam-3914	730	4	)	)	PUNCT
ejpam-3914	730	5	,	,	PUNCT
ejpam-3914	730	6	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	730	7	(	(	PUNCT
ejpam-3914	730	8	s1	s1	NOUN
ejpam-3914	730	9	)	)	PUNCT
ejpam-3914	730	10	=	=	SYM
ejpam-3914	731	1	0	0	X
ejpam-3914	731	2	.	.	PUNCT
ejpam-3914	732	1	if	if	SCONJ
ejpam-3914	732	2	n	n	PROPN
ejpam-3914	732	3	>	>	X
ejpam-3914	732	4	1	1	NUM
ejpam-3914	732	5	,	,	PUNCT
ejpam-3914	732	6	then	then	ADV
ejpam-3914	732	7	the	the	DET
ejpam-3914	732	8	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	732	9	-sets	-set	NOUN
ejpam-3914	732	10	of	of	ADP
ejpam-3914	732	11	sn	sn	NOUN
ejpam-3914	732	12	are	be	AUX
ejpam-3914	732	13	of	of	ADP
ejpam-3914	732	14	the	the	DET
ejpam-3914	732	15	form	form	NOUN
ejpam-3914	732	16	{	{	PUNCT
ejpam-3914	732	17	v	v	NOUN
ejpam-3914	732	18	,	,	PUNCT
ejpam-3914	732	19	ui	ui	NOUN
ejpam-3914	732	20	}	}	PUNCT
ejpam-3914	732	21	for	for	ADP
ejpam-3914	732	22	all	all	PRON
ejpam-3914	732	23	ui	ui	NOUN
ejpam-3914	732	24	∈	∈	PROPN
ejpam-3914	732	25	v	v	NOUN
ejpam-3914	732	26	(	(	PUNCT
ejpam-3914	732	27	sn	sn	PROPN
ejpam-3914	732	28	)	)	PUNCT
ejpam-3914	732	29	by	by	ADP
ejpam-3914	732	30	theorem	theorem	VERB
ejpam-3914	732	31	2.5	2.5	NUM
ejpam-3914	732	32	.	.	PUNCT
ejpam-3914	733	1	clearly	clearly	ADV
ejpam-3914	733	2	,	,	PUNCT
ejpam-3914	733	3	r	r	NOUN
ejpam-3914	733	4	=	=	SYM
ejpam-3914	733	5	{	{	PUNCT
ejpam-3914	733	6	v	v	NOUN
ejpam-3914	733	7	,	,	PUNCT
ejpam-3914	733	8	u1	u1	NOUN
ejpam-3914	733	9	}	}	PUNCT
ejpam-3914	733	10	is	be	AUX
ejpam-3914	733	11	the	the	DET
ejpam-3914	733	12	only	only	ADJ
ejpam-3914	733	13	γ∗tpw	γ∗tpw	PROPN
ejpam-3914	733	14	-set	-set	PROPN
ejpam-3914	733	15	of	of	ADP
ejpam-3914	733	16	sn	sn	NOUN
ejpam-3914	733	17	containing	contain	VERB
ejpam-3914	733	18	u1	u1	NOUN
ejpam-3914	733	19	.	.	PUNCT
ejpam-3914	734	1	thus	thus	ADV
ejpam-3914	734	2	,	,	PUNCT
ejpam-3914	734	3	{	{	PUNCT
ejpam-3914	734	4	u1	u1	NOUN
ejpam-3914	734	5	}	}	PUNCT
ejpam-3914	734	6	is	be	AUX
ejpam-3914	734	7	a	a	DET
ejpam-3914	734	8	forcing	forcing	NOUN
ejpam-3914	734	9	subset	subset	NOUN
ejpam-3914	734	10	for	for	ADP
ejpam-3914	734	11	r	r	NOUN
ejpam-3914	734	12	,	,	PUNCT
ejpam-3914	734	13	that	that	ADV
ejpam-3914	734	14	is	is	ADV
ejpam-3914	734	15	,	,	PUNCT
ejpam-3914	734	16	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	734	17	(	(	PUNCT
ejpam-3914	734	18	r	r	NOUN
ejpam-3914	734	19	)	)	PUNCT
ejpam-3914	734	20	=	=	SYM
ejpam-3914	735	1	1	1	NUM
ejpam-3914	735	2	=	=	NOUN
ejpam-3914	735	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3914	735	4	(	(	PUNCT
ejpam-3914	735	5	sn	sn	NOUN
ejpam-3914	735	6	)	)	PUNCT
ejpam-3914	735	7	for	for	ADP
ejpam-3914	735	8	all	all	PRON
ejpam-3914	735	9	n	n	CCONJ
ejpam-3914	735	10	>	>	X
ejpam-3914	735	11	1	1	X
ejpam-3914	735	12	.	.	PUNCT
ejpam-3914	735	13	acknowledgements	acknowledgement	VERB
ejpam-3914	735	14	the	the	DET
ejpam-3914	735	15	author	author	NOUN
ejpam-3914	735	16	thanks	thank	NOUN
ejpam-3914	735	17	the	the	DET
ejpam-3914	735	18	peer	peer	NOUN
ejpam-3914	735	19	reviewers	reviewer	NOUN
ejpam-3914	735	20	of	of	ADP
ejpam-3914	735	21	the	the	DET
ejpam-3914	735	22	paper	paper	NOUN
ejpam-3914	735	23	and	and	CCONJ
ejpam-3914	735	24	readers	reader	NOUN
ejpam-3914	735	25	of	of	ADP
ejpam-3914	735	26	european	european	PROPN
ejpam-3914	735	27	journal	journal	PROPN
ejpam-3914	735	28	of	of	ADP
ejpam-3914	735	29	pure	pure	ADJ
ejpam-3914	735	30	and	and	CCONJ
ejpam-3914	735	31	applied	applied	ADJ
ejpam-3914	735	32	mathematics	mathematic	NOUN
ejpam-3914	735	33	,	,	PUNCT
ejpam-3914	735	34	for	for	ADP
ejpam-3914	735	35	making	make	VERB
ejpam-3914	735	36	the	the	DET
ejpam-3914	735	37	journal	journal	NOUN
ejpam-3914	735	38	successful	successful	ADJ
ejpam-3914	735	39	and	and	CCONJ
ejpam-3914	735	40	to	to	ADP
ejpam-3914	735	41	the	the	DET
ejpam-3914	735	42	cebu	cebu	NOUN
ejpam-3914	735	43	normal	normal	ADJ
ejpam-3914	735	44	university	university	NOUN
ejpam-3914	735	45	for	for	ADP
ejpam-3914	735	46	the	the	DET
ejpam-3914	735	47	financial	financial	ADJ
ejpam-3914	735	48	support	support	NOUN
ejpam-3914	735	49	.	.	PUNCT
ejpam-3914	736	1	the	the	DET
ejpam-3914	736	2	author	author	NOUN
ejpam-3914	736	3	also	also	ADV
ejpam-3914	736	4	expresses	express	VERB
ejpam-3914	736	5	warm	warm	ADJ
ejpam-3914	736	6	gratitude	gratitude	NOUN
ejpam-3914	736	7	to	to	ADP
ejpam-3914	736	8	ho	ho	PROPN
ejpam-3914	736	9	jc	jc	PROPN
ejpam-3914	736	10	for	for	ADP
ejpam-3914	736	11	the	the	DET
ejpam-3914	736	12	emotional	emotional	ADJ
ejpam-3914	736	13	and	and	CCONJ
ejpam-3914	736	14	moral	moral	ADJ
ejpam-3914	736	15	support	support	NOUN
ejpam-3914	736	16	.	.	PUNCT
ejpam-3914	737	1	references	reference	NOUN
ejpam-3914	737	2	[	[	X
ejpam-3914	737	3	1	1	NUM
ejpam-3914	737	4	]	]	X
ejpam-3914	737	5	d	d	PROPN
ejpam-3914	737	6	amos	amos	PROPN
ejpam-3914	737	7	.	.	PUNCT
ejpam-3914	738	1	on	on	ADP
ejpam-3914	738	2	total	total	ADJ
ejpam-3914	738	3	domination	domination	NOUN
ejpam-3914	738	4	in	in	ADP
ejpam-3914	738	5	graphs	graph	NOUN
ejpam-3914	738	6	.	.	PUNCT
ejpam-3914	739	1	university	university	NOUN
ejpam-3914	739	2	of	of	ADP
ejpam-3914	739	3	houston	houston	PROPN
ejpam-3914	739	4	-	-	PUNCT
ejpam-3914	739	5	downtown	downtown	NOUN
ejpam-3914	739	6	,	,	PUNCT
ejpam-3914	739	7	2012	2012	NUM
ejpam-3914	739	8	.	.	PUNCT
ejpam-3914	740	1	[	[	X
ejpam-3914	740	2	2	2	NUM
ejpam-3914	740	3	]	]	X
ejpam-3914	740	4	c	c	PROPN
ejpam-3914	740	5	armada	armada	PROPN
ejpam-3914	740	6	.	.	PUNCT
ejpam-3914	741	1	forcing	force	VERB
ejpam-3914	741	2	total	total	ADJ
ejpam-3914	741	3	dr	dr	PROPN
ejpam-3914	741	4	-	-	PUNCT
ejpam-3914	741	5	power	power	NOUN
ejpam-3914	741	6	domination	domination	NOUN
ejpam-3914	741	7	number	number	NOUN
ejpam-3914	741	8	of	of	ADP
ejpam-3914	741	9	graphs	graph	NOUN
ejpam-3914	741	10	under	under	ADP
ejpam-3914	741	11	some	some	DET
ejpam-3914	741	12	binary	binary	ADJ
ejpam-3914	741	13	operations	operation	NOUN
ejpam-3914	741	14	.	.	PUNCT
ejpam-3914	742	1	european	european	ADJ
ejpam-3914	742	2	journal	journal	PROPN
ejpam-3914	742	3	of	of	ADP
ejpam-3914	742	4	pure	pure	ADJ
ejpam-3914	742	5	and	and	CCONJ
ejpam-3914	742	6	applied	applied	ADJ
ejpam-3914	742	7	mathematics	mathematic	NOUN
ejpam-3914	742	8	,	,	PUNCT
ejpam-3914	742	9	accepted	accept	VERB
ejpam-3914	742	10	for	for	ADP
ejpam-3914	742	11	publication	publication	NOUN
ejpam-3914	742	12	.	.	PUNCT
ejpam-3914	743	1	references	reference	NOUN
ejpam-3914	743	2	470	470	NUM
ejpam-3914	744	1	[	[	X
ejpam-3914	744	2	3	3	NUM
ejpam-3914	744	3	]	]	X
ejpam-3914	744	4	c	c	PROPN
ejpam-3914	744	5	armada	armada	PROPN
ejpam-3914	744	6	and	and	CCONJ
ejpam-3914	744	7	s	s	VERB
ejpam-3914	744	8	canoy	canoy	PROPN
ejpam-3914	744	9	jr	jr	PROPN
ejpam-3914	744	10	.	.	PROPN
ejpam-3914	745	1	a	a	X
ejpam-3914	745	2	-	-	PUNCT
ejpam-3914	745	3	differential	differential	NOUN
ejpam-3914	745	4	of	of	ADP
ejpam-3914	745	5	graphs	graph	NOUN
ejpam-3914	745	6	.	.	PUNCT
ejpam-3914	746	1	international	international	ADJ
ejpam-3914	746	2	journal	journal	PROPN
ejpam-3914	746	3	of	of	ADP
ejpam-3914	746	4	mathematical	mathematical	ADJ
ejpam-3914	746	5	analysis	analysis	NOUN
ejpam-3914	746	6	,	,	PUNCT
ejpam-3914	746	7	9(44):2171–2180	9(44):2171–2180	NUM
ejpam-3914	746	8	,	,	PUNCT
ejpam-3914	746	9	2015	2015	NUM
ejpam-3914	746	10	.	.	PUNCT
ejpam-3914	747	1	[	[	X
ejpam-3914	747	2	4	4	NUM
ejpam-3914	747	3	]	]	X
ejpam-3914	747	4	c	c	X
ejpam-3914	747	5	armada	armada	PROPN
ejpam-3914	747	6	and	and	CCONJ
ejpam-3914	747	7	s	s	VERB
ejpam-3914	747	8	canoy	canoy	PROPN
ejpam-3914	747	9	jr	jr	PROPN
ejpam-3914	747	10	.	.	PUNCT
ejpam-3914	747	11	forcing	force	VERB
ejpam-3914	747	12	independent	independent	ADJ
ejpam-3914	747	13	domination	domination	NOUN
ejpam-3914	747	14	number	number	NOUN
ejpam-3914	747	15	of	of	ADP
ejpam-3914	747	16	a	a	DET
ejpam-3914	747	17	graph	graph	NOUN
ejpam-3914	747	18	.	.	PUNCT
ejpam-3914	748	1	european	european	ADJ
ejpam-3914	748	2	journal	journal	PROPN
ejpam-3914	748	3	of	of	ADP
ejpam-3914	748	4	pure	pure	ADJ
ejpam-3914	748	5	and	and	CCONJ
ejpam-3914	748	6	applied	applied	ADJ
ejpam-3914	748	7	mathematics	mathematic	NOUN
ejpam-3914	748	8	,	,	PUNCT
ejpam-3914	748	9	12(4):1371–1381	12(4):1371–1381	NUM
ejpam-3914	748	10	,	,	PUNCT
ejpam-3914	748	11	2019	2019	NUM
ejpam-3914	748	12	.	.	PUNCT
ejpam-3914	749	1	[	[	X
ejpam-3914	749	2	5	5	X
ejpam-3914	749	3	]	]	PUNCT
ejpam-3914	749	4	g	g	PROPN
ejpam-3914	749	5	chartrand	chartrand	PROPN
ejpam-3914	749	6	h	h	PROPN
ejpam-3914	749	7	gavlas	gavlas	PROPN
ejpam-3914	749	8	k	k	PROPN
ejpam-3914	749	9	c	c	PROPN
ejpam-3914	749	10	vandell	vandell	NOUN
ejpam-3914	749	11	and	and	CCONJ
ejpam-3914	749	12	f	f	PROPN
ejpam-3914	749	13	harary	harary	NOUN
ejpam-3914	749	14	.	.	PUNCT
ejpam-3914	750	1	the	the	DET
ejpam-3914	750	2	forcing	force	VERB
ejpam-3914	750	3	domination	domination	NOUN
ejpam-3914	750	4	number	number	NOUN
ejpam-3914	750	5	of	of	ADP
ejpam-3914	750	6	a	a	DET
ejpam-3914	750	7	graph	graph	NOUN
ejpam-3914	750	8	.	.	PUNCT
ejpam-3914	751	1	j.	j.	PROPN
ejpam-3914	751	2	combin	combin	PROPN
ejpam-3914	751	3	.	.	PUNCT
ejpam-3914	752	1	math	math	NOUN
ejpam-3914	752	2	.	.	PUNCT
ejpam-3914	753	1	combin	combin	NOUN
ejpam-3914	753	2	.	.	PUNCT
ejpam-3914	754	1	comput	comput	NOUN
ejpam-3914	754	2	.	.	PUNCT
ejpam-3914	754	3	,	,	PUNCT
ejpam-3914	755	1	25:161–174	25:161–174	NUM
ejpam-3914	755	2	,	,	PUNCT
ejpam-3914	755	3	1997	1997	NUM
ejpam-3914	755	4	.	.	PUNCT
ejpam-3914	756	1	[	[	X
ejpam-3914	756	2	6	6	NUM
ejpam-3914	756	3	]	]	PUNCT
ejpam-3914	756	4	i	i	PRON
ejpam-3914	756	5	cabahug	cabahug	VERB
ejpam-3914	756	6	jr	jr	PROPN
ejpam-3914	756	7	.	.	PUNCT
ejpam-3914	756	8	and	and	CCONJ
ejpam-3914	756	9	s	s	VERB
ejpam-3914	756	10	canoy	canoy	PROPN
ejpam-3914	756	11	jr	jr	PROPN
ejpam-3914	756	12	.	.	PROPN
ejpam-3914	756	13	total	total	PROPN
ejpam-3914	756	14	dr	dr	PROPN
ejpam-3914	756	15	-	-	PUNCT
ejpam-3914	756	16	power	power	NOUN
ejpam-3914	756	17	dominating	dominating	NOUN
ejpam-3914	756	18	sets	set	NOUN
ejpam-3914	756	19	in	in	ADP
ejpam-3914	756	20	graphs	graph	NOUN
ejpam-3914	756	21	.	.	PUNCT
ejpam-3914	757	1	accepted	accept	VERB
ejpam-3914	757	2	for	for	ADP
ejpam-3914	757	3	publication	publication	NOUN
ejpam-3914	757	4	.	.	PUNCT
ejpam-3914	758	1	[	[	X
ejpam-3914	758	2	7	7	NUM
ejpam-3914	758	3	]	]	X
ejpam-3914	758	4	c	c	PROPN
ejpam-3914	758	5	armada	armada	PROPN
ejpam-3914	758	6	s	s	PART
ejpam-3914	758	7	canoy	canoy	PROPN
ejpam-3914	758	8	jr	jr	PROPN
ejpam-3914	758	9	.	.	PROPN
ejpam-3914	758	10	and	and	CCONJ
ejpam-3914	758	11	c	c	PROPN
ejpam-3914	758	12	go	go	VERB
ejpam-3914	758	13	.	.	PUNCT
ejpam-3914	759	1	forcing	force	VERB
ejpam-3914	759	2	domination	domination	NOUN
ejpam-3914	759	3	numbers	number	NOUN
ejpam-3914	759	4	of	of	ADP
ejpam-3914	759	5	graphs	graph	NOUN
ejpam-3914	759	6	under	under	ADP
ejpam-3914	759	7	some	some	DET
ejpam-3914	759	8	binary	binary	ADJ
ejpam-3914	759	9	operations	operation	NOUN
ejpam-3914	759	10	.	.	PUNCT
ejpam-3914	760	1	advances	advance	NOUN
ejpam-3914	760	2	and	and	CCONJ
ejpam-3914	760	3	applications	application	NOUN
ejpam-3914	760	4	in	in	ADP
ejpam-3914	760	5	discrete	discrete	ADJ
ejpam-3914	760	6	mathematics	mathematic	NOUN
ejpam-3914	760	7	,	,	PUNCT
ejpam-3914	760	8	19:213–228	19:213–228	NUM
ejpam-3914	760	9	,	,	PUNCT
ejpam-3914	760	10	2018	2018	NUM
ejpam-3914	760	11	.	.	PUNCT
ejpam-3914	761	1	[	[	X
ejpam-3914	761	2	8	8	NUM
ejpam-3914	761	3	]	]	X
ejpam-3914	761	4	c	c	PROPN
ejpam-3914	761	5	armada	armada	PROPN
ejpam-3914	761	6	s	s	PART
ejpam-3914	761	7	canoy	canoy	PROPN
ejpam-3914	761	8	jr	jr	PROPN
ejpam-3914	761	9	.	.	PROPN
ejpam-3914	762	1	and	and	CCONJ
ejpam-3914	762	2	c	c	PROPN
ejpam-3914	762	3	go	go	VERB
ejpam-3914	762	4	.	.	PUNCT
ejpam-3914	763	1	forcing	force	VERB
ejpam-3914	763	2	subsets	subset	NOUN
ejpam-3914	763	3	for	for	ADP
ejpam-3914	763	4	γc	γc	NOUN
ejpam-3914	763	5	-	-	PUNCT
ejpam-3914	763	6	sets	set	NOUN
ejpam-3914	763	7	and	and	CCONJ
ejpam-3914	763	8	γt	γt	NOUN
ejpam-3914	763	9	-	-	NOUN
ejpam-3914	763	10	sets	set	NOUN
ejpam-3914	763	11	in	in	ADP
ejpam-3914	763	12	the	the	DET
ejpam-3914	763	13	lexicographic	lexicographic	ADJ
ejpam-3914	763	14	product	product	NOUN
ejpam-3914	763	15	of	of	ADP
ejpam-3914	763	16	graphs	graph	NOUN
ejpam-3914	763	17	.	.	PUNCT
ejpam-3914	764	1	european	european	ADJ
ejpam-3914	764	2	journal	journal	PROPN
ejpam-3914	764	3	of	of	ADP
ejpam-3914	764	4	pure	pure	ADJ
ejpam-3914	764	5	and	and	CCONJ
ejpam-3914	764	6	applied	applied	ADJ
ejpam-3914	764	7	mathematics	mathematic	NOUN
ejpam-3914	764	8	,	,	PUNCT
ejpam-3914	764	9	12(4):1779–1786	12(4):1779–1786	NUM
ejpam-3914	764	10	,	,	PUNCT
ejpam-3914	764	11	2019	2019	NUM
ejpam-3914	764	12	.	.	PUNCT