id	sid	tid	token	lemma	pos
ejpam-3915	1	1	european	european	PROPN
ejpam-3915	1	2	journal	journal	PROPN
ejpam-3915	1	3	of	of	ADP
ejpam-3915	1	4	pure	pure	ADJ
ejpam-3915	1	5	and	and	CCONJ
ejpam-3915	1	6	applied	apply	VERB
ejpam-3915	1	7	mathematics	mathematic	NOUN
ejpam-3915	1	8	vol	vol	NOUN
ejpam-3915	1	9	.	.	PUNCT
ejpam-3915	2	1	14	14	NUM
ejpam-3915	2	2	,	,	PUNCT
ejpam-3915	2	3	no	no	INTJ
ejpam-3915	2	4	.	.	NOUN
ejpam-3915	2	5	3	3	NUM
ejpam-3915	2	6	,	,	PUNCT
ejpam-3915	2	7	2021	2021	NUM
ejpam-3915	2	8	,	,	PUNCT
ejpam-3915	2	9	1098	1098	NUM
ejpam-3915	2	10	-	-	PUNCT
ejpam-3915	2	11	1107	1107	NUM
ejpam-3915	2	12	issn	issn	PROPN
ejpam-3915	2	13	1307	1307	NUM
ejpam-3915	2	14	-	-	SYM
ejpam-3915	2	15	5543	5543	NUM
ejpam-3915	2	16	–	–	PUNCT
ejpam-3915	2	17	ejpam.com	ejpam.com	X
ejpam-3915	2	18	published	publish	VERB
ejpam-3915	2	19	by	by	ADP
ejpam-3915	2	20	new	new	PROPN
ejpam-3915	2	21	york	york	PROPN
ejpam-3915	2	22	business	business	PROPN
ejpam-3915	2	23	global	global	ADJ
ejpam-3915	2	24	forcing	force	VERB
ejpam-3915	2	25	total	total	ADJ
ejpam-3915	2	26	dr	dr	PROPN
ejpam-3915	2	27	-	-	PUNCT
ejpam-3915	2	28	power	power	NOUN
ejpam-3915	2	29	domination	domination	NOUN
ejpam-3915	2	30	number	number	NOUN
ejpam-3915	2	31	of	of	ADP
ejpam-3915	2	32	graphs	graph	NOUN
ejpam-3915	2	33	under	under	ADP
ejpam-3915	2	34	some	some	DET
ejpam-3915	2	35	binary	binary	ADJ
ejpam-3915	2	36	operations	operation	NOUN
ejpam-3915	2	37	cris	cris	PROPN
ejpam-3915	2	38	l.	l.	PROPN
ejpam-3915	2	39	armada1,∗	armada1,∗	PROPN
ejpam-3915	2	40	1	1	NUM
ejpam-3915	2	41	mathematics	mathematics	PROPN
ejpam-3915	2	42	department	department	NOUN
ejpam-3915	2	43	,	,	PUNCT
ejpam-3915	2	44	college	college	NOUN
ejpam-3915	2	45	of	of	ADP
ejpam-3915	2	46	arts	art	NOUN
ejpam-3915	2	47	and	and	CCONJ
ejpam-3915	2	48	sciences	science	NOUN
ejpam-3915	2	49	,	,	PUNCT
ejpam-3915	2	50	cebu	cebu	NOUN
ejpam-3915	2	51	normal	normal	ADJ
ejpam-3915	2	52	university	university	NOUN
ejpam-3915	2	53	,	,	PUNCT
ejpam-3915	2	54	cebu	cebu	NOUN
ejpam-3915	2	55	city	city	NOUN
ejpam-3915	2	56	,	,	PUNCT
ejpam-3915	3	1	philippines	philippine	NOUN
ejpam-3915	3	2	6000	6000	NUM
ejpam-3915	3	3	abstract	abstract	NOUN
ejpam-3915	3	4	.	.	PUNCT
ejpam-3915	4	1	in	in	ADP
ejpam-3915	4	2	this	this	DET
ejpam-3915	4	3	paper	paper	NOUN
ejpam-3915	4	4	,	,	PUNCT
ejpam-3915	4	5	the	the	DET
ejpam-3915	4	6	total	total	ADJ
ejpam-3915	4	7	dr	dr	PROPN
ejpam-3915	4	8	-	-	PUNCT
ejpam-3915	4	9	power	power	NOUN
ejpam-3915	4	10	domination	domination	NOUN
ejpam-3915	4	11	number	number	NOUN
ejpam-3915	4	12	of	of	ADP
ejpam-3915	4	13	graphs	graph	NOUN
ejpam-3915	4	14	such	such	ADJ
ejpam-3915	4	15	as	as	ADP
ejpam-3915	4	16	complete	complete	ADJ
ejpam-3915	4	17	bipartite	bipartite	NOUN
ejpam-3915	4	18	graph	graph	NOUN
ejpam-3915	4	19	,	,	PUNCT
ejpam-3915	4	20	generalized	generalized	ADJ
ejpam-3915	4	21	fan	fan	NOUN
ejpam-3915	4	22	and	and	CCONJ
ejpam-3915	4	23	generalized	generalized	ADJ
ejpam-3915	4	24	wheel	wheel	NOUN
ejpam-3915	4	25	are	be	AUX
ejpam-3915	4	26	obtained	obtain	VERB
ejpam-3915	4	27	.	.	PUNCT
ejpam-3915	5	1	the	the	DET
ejpam-3915	5	2	forcing	force	VERB
ejpam-3915	5	3	total	total	ADJ
ejpam-3915	5	4	dr	dr	PROPN
ejpam-3915	5	5	-	-	PUNCT
ejpam-3915	5	6	power	power	NOUN
ejpam-3915	5	7	domination	domination	NOUN
ejpam-3915	5	8	number	number	NOUN
ejpam-3915	5	9	of	of	ADP
ejpam-3915	5	10	graphs	graph	NOUN
ejpam-3915	5	11	resulting	result	VERB
ejpam-3915	5	12	from	from	ADP
ejpam-3915	5	13	some	some	DET
ejpam-3915	5	14	binary	binary	ADJ
ejpam-3915	5	15	operations	operation	NOUN
ejpam-3915	5	16	such	such	ADJ
ejpam-3915	5	17	as	as	ADP
ejpam-3915	5	18	join	join	NOUN
ejpam-3915	5	19	,	,	PUNCT
ejpam-3915	5	20	corona	corona	NOUN
ejpam-3915	5	21	and	and	CCONJ
ejpam-3915	5	22	lexicographic	lexicographic	ADJ
ejpam-3915	5	23	product	product	NOUN
ejpam-3915	5	24	of	of	ADP
ejpam-3915	5	25	graphs	graph	NOUN
ejpam-3915	5	26	were	be	AUX
ejpam-3915	5	27	determined	determine	VERB
ejpam-3915	5	28	.	.	PUNCT
ejpam-3915	6	1	2020	2020	NUM
ejpam-3915	6	2	mathematics	mathematic	NOUN
ejpam-3915	6	3	subject	subject	NOUN
ejpam-3915	6	4	classifications	classification	NOUN
ejpam-3915	6	5	:	:	PUNCT
ejpam-3915	6	6	05c69	05c69	X
ejpam-3915	6	7	key	key	ADJ
ejpam-3915	6	8	words	word	NOUN
ejpam-3915	6	9	and	and	CCONJ
ejpam-3915	6	10	phrases	phrase	NOUN
ejpam-3915	6	11	:	:	PUNCT
ejpam-3915	6	12	forcing	force	VERB
ejpam-3915	6	13	,	,	PUNCT
ejpam-3915	6	14	total	total	NOUN
ejpam-3915	6	15	,	,	PUNCT
ejpam-3915	6	16	dr	dr	PROPN
ejpam-3915	6	17	-	-	PUNCT
ejpam-3915	6	18	power	power	NOUN
ejpam-3915	6	19	domination	domination	NOUN
ejpam-3915	6	20	,	,	PUNCT
ejpam-3915	6	21	join	join	NOUN
ejpam-3915	6	22	,	,	PUNCT
ejpam-3915	6	23	corona	corona	PROPN
ejpam-3915	6	24	,	,	PUNCT
ejpam-3915	6	25	lexicographic	lexicographic	ADJ
ejpam-3915	6	26	product	product	NOUN
ejpam-3915	6	27	1	1	NUM
ejpam-3915	6	28	.	.	PUNCT
ejpam-3915	7	1	introduction	introduction	NOUN
ejpam-3915	7	2	let	let	VERB
ejpam-3915	7	3	g	g	PROPN
ejpam-3915	7	4	=	=	SYM
ejpam-3915	7	5	(	(	PUNCT
ejpam-3915	7	6	v	v	NOUN
ejpam-3915	7	7	,	,	PUNCT
ejpam-3915	7	8	e	e	NOUN
ejpam-3915	7	9	)	)	PUNCT
ejpam-3915	7	10	be	be	AUX
ejpam-3915	7	11	a	a	DET
ejpam-3915	7	12	graph	graph	NOUN
ejpam-3915	7	13	representing	represent	VERB
ejpam-3915	7	14	the	the	DET
ejpam-3915	7	15	electrical	electrical	ADJ
ejpam-3915	7	16	power	power	NOUN
ejpam-3915	7	17	system	system	NOUN
ejpam-3915	7	18	,	,	PUNCT
ejpam-3915	7	19	where	where	SCONJ
ejpam-3915	7	20	a	a	DET
ejpam-3915	7	21	vertex	vertex	NOUN
ejpam-3915	7	22	represents	represent	VERB
ejpam-3915	7	23	an	an	DET
ejpam-3915	7	24	electrical	electrical	ADJ
ejpam-3915	7	25	node	node	NOUN
ejpam-3915	7	26	and	and	CCONJ
ejpam-3915	7	27	an	an	DET
ejpam-3915	7	28	edge	edge	NOUN
ejpam-3915	7	29	represents	represent	VERB
ejpam-3915	7	30	a	a	DET
ejpam-3915	7	31	transmission	transmission	NOUN
ejpam-3915	7	32	line	line	NOUN
ejpam-3915	7	33	joining	join	VERB
ejpam-3915	7	34	two	two	NUM
ejpam-3915	7	35	electrical	electrical	ADJ
ejpam-3915	7	36	nodes	node	NOUN
ejpam-3915	7	37	.	.	PUNCT
ejpam-3915	8	1	some	some	DET
ejpam-3915	8	2	measurement	measurement	NOUN
ejpam-3915	8	3	devices	device	NOUN
ejpam-3915	8	4	must	must	AUX
ejpam-3915	8	5	be	be	AUX
ejpam-3915	8	6	placed	place	VERB
ejpam-3915	8	7	at	at	ADP
ejpam-3915	8	8	selected	select	VERB
ejpam-3915	8	9	locations	location	NOUN
ejpam-3915	8	10	so	so	SCONJ
ejpam-3915	8	11	that	that	SCONJ
ejpam-3915	8	12	all	all	DET
ejpam-3915	8	13	the	the	DET
ejpam-3915	8	14	state	state	NOUN
ejpam-3915	8	15	variables	variable	NOUN
ejpam-3915	8	16	of	of	ADP
ejpam-3915	8	17	the	the	DET
ejpam-3915	8	18	system	system	NOUN
ejpam-3915	8	19	can	can	AUX
ejpam-3915	8	20	be	be	AUX
ejpam-3915	8	21	measured	measure	VERB
ejpam-3915	8	22	in	in	ADP
ejpam-3915	8	23	order	order	NOUN
ejpam-3915	8	24	to	to	PART
ejpam-3915	8	25	monitor	monitor	VERB
ejpam-3915	8	26	the	the	DET
ejpam-3915	8	27	power	power	NOUN
ejpam-3915	8	28	system	system	NOUN
ejpam-3915	8	29	.	.	PUNCT
ejpam-3915	9	1	a	a	DET
ejpam-3915	9	2	phase	phase	NOUN
ejpam-3915	9	3	measurement	measurement	NOUN
ejpam-3915	9	4	unit	unit	NOUN
ejpam-3915	9	5	(	(	PUNCT
ejpam-3915	9	6	pmu	pmu	PROPN
ejpam-3915	9	7	)	)	PUNCT
ejpam-3915	9	8	is	be	AUX
ejpam-3915	9	9	a	a	DET
ejpam-3915	9	10	measurement	measurement	NOUN
ejpam-3915	9	11	device	device	NOUN
ejpam-3915	9	12	placed	place	VERB
ejpam-3915	9	13	on	on	ADP
ejpam-3915	9	14	a	a	DET
ejpam-3915	9	15	vertex	vertex	NOUN
ejpam-3915	9	16	and	and	CCONJ
ejpam-3915	9	17	has	have	VERB
ejpam-3915	9	18	the	the	DET
ejpam-3915	9	19	ability	ability	NOUN
ejpam-3915	9	20	to	to	PART
ejpam-3915	9	21	measure	measure	VERB
ejpam-3915	9	22	the	the	DET
ejpam-3915	9	23	state	state	NOUN
ejpam-3915	9	24	of	of	ADP
ejpam-3915	9	25	the	the	DET
ejpam-3915	9	26	vertex	vertex	NOUN
ejpam-3915	9	27	and	and	CCONJ
ejpam-3915	9	28	the	the	DET
ejpam-3915	9	29	edges	edge	NOUN
ejpam-3915	9	30	connected	connect	VERB
ejpam-3915	9	31	to	to	ADP
ejpam-3915	9	32	the	the	DET
ejpam-3915	9	33	vertex	vertex	NOUN
ejpam-3915	9	34	.	.	PUNCT
ejpam-3915	10	1	the	the	DET
ejpam-3915	10	2	vertices	vertex	NOUN
ejpam-3915	10	3	and	and	CCONJ
ejpam-3915	10	4	edges	edge	NOUN
ejpam-3915	10	5	that	that	PRON
ejpam-3915	10	6	are	be	AUX
ejpam-3915	10	7	measured	measure	VERB
ejpam-3915	10	8	by	by	ADP
ejpam-3915	10	9	pmu	pmu	PROPN
ejpam-3915	10	10	’s	’s	PART
ejpam-3915	10	11	are	be	AUX
ejpam-3915	10	12	said	say	VERB
ejpam-3915	10	13	to	to	PART
ejpam-3915	10	14	be	be	AUX
ejpam-3915	10	15	observed	observe	VERB
ejpam-3915	10	16	.	.	PUNCT
ejpam-3915	11	1	in	in	ADP
ejpam-3915	11	2	this	this	DET
ejpam-3915	11	3	study	study	NOUN
ejpam-3915	11	4	,	,	PUNCT
ejpam-3915	11	5	it	it	PRON
ejpam-3915	11	6	is	be	AUX
ejpam-3915	11	7	necessary	necessary	ADJ
ejpam-3915	11	8	that	that	SCONJ
ejpam-3915	11	9	each	each	DET
ejpam-3915	11	10	vertex	vertex	NOUN
ejpam-3915	11	11	with	with	ADP
ejpam-3915	11	12	pmu	pmu	NOUN
ejpam-3915	11	13	is	be	AUX
ejpam-3915	11	14	adjacent	adjacent	ADJ
ejpam-3915	11	15	to	to	ADP
ejpam-3915	11	16	another	another	DET
ejpam-3915	11	17	vertex	vertex	NOUN
ejpam-3915	11	18	with	with	ADP
ejpam-3915	11	19	pmu	pmu	NOUN
ejpam-3915	11	20	also	also	ADV
ejpam-3915	11	21	.	.	PUNCT
ejpam-3915	12	1	but	but	CCONJ
ejpam-3915	12	2	because	because	SCONJ
ejpam-3915	12	3	of	of	ADP
ejpam-3915	12	4	the	the	DET
ejpam-3915	12	5	high	high	ADJ
ejpam-3915	12	6	cost	cost	NOUN
ejpam-3915	12	7	value	value	NOUN
ejpam-3915	12	8	of	of	ADP
ejpam-3915	12	9	a	a	DET
ejpam-3915	12	10	pmu	pmu	NOUN
ejpam-3915	12	11	,	,	PUNCT
ejpam-3915	12	12	it	it	PRON
ejpam-3915	12	13	is	be	AUX
ejpam-3915	12	14	desirable	desirable	ADJ
ejpam-3915	12	15	to	to	PART
ejpam-3915	12	16	minimize	minimize	VERB
ejpam-3915	12	17	their	their	PRON
ejpam-3915	12	18	number	number	NOUN
ejpam-3915	12	19	while	while	SCONJ
ejpam-3915	12	20	maintaining	maintain	VERB
ejpam-3915	12	21	the	the	DET
ejpam-3915	12	22	ability	ability	NOUN
ejpam-3915	12	23	to	to	PART
ejpam-3915	12	24	monitor	monitor	VERB
ejpam-3915	12	25	the	the	DET
ejpam-3915	12	26	entire	entire	ADJ
ejpam-3915	12	27	power	power	NOUN
ejpam-3915	12	28	system	system	NOUN
ejpam-3915	12	29	.	.	PUNCT
ejpam-3915	13	1	the	the	DET
ejpam-3915	13	2	graphs	graph	NOUN
ejpam-3915	13	3	considered	consider	VERB
ejpam-3915	13	4	in	in	ADP
ejpam-3915	13	5	this	this	DET
ejpam-3915	13	6	paper	paper	NOUN
ejpam-3915	13	7	are	be	AUX
ejpam-3915	13	8	simple	simple	ADJ
ejpam-3915	13	9	,	,	PUNCT
ejpam-3915	13	10	connected	connected	ADJ
ejpam-3915	13	11	,	,	PUNCT
ejpam-3915	13	12	undirected	undirected	ADJ
ejpam-3915	13	13	and	and	CCONJ
ejpam-3915	13	14	without	without	ADP
ejpam-3915	13	15	loops	loop	NOUN
ejpam-3915	13	16	or	or	CCONJ
ejpam-3915	13	17	multiple	multiple	ADJ
ejpam-3915	13	18	edges	edge	NOUN
ejpam-3915	13	19	.	.	PUNCT
ejpam-3915	14	1	let	let	VERB
ejpam-3915	14	2	g	g	PROPN
ejpam-3915	14	3	=	=	SYM
ejpam-3915	14	4	(	(	PUNCT
ejpam-3915	14	5	v	v	NOUN
ejpam-3915	14	6	(	(	PUNCT
ejpam-3915	14	7	g	g	NOUN
ejpam-3915	14	8	)	)	PUNCT
ejpam-3915	14	9	,	,	PUNCT
ejpam-3915	14	10	e(g	e(g	PROPN
ejpam-3915	14	11	)	)	PUNCT
ejpam-3915	14	12	)	)	PUNCT
ejpam-3915	15	1	be	be	AUX
ejpam-3915	15	2	a	a	DET
ejpam-3915	15	3	graph	graph	NOUN
ejpam-3915	15	4	and	and	CCONJ
ejpam-3915	15	5	v	v	ADP
ejpam-3915	15	6	∈	∈	PROPN
ejpam-3915	15	7	v	v	NOUN
ejpam-3915	15	8	(	(	PUNCT
ejpam-3915	15	9	g	g	NOUN
ejpam-3915	15	10	)	)	PUNCT
ejpam-3915	15	11	.	.	PUNCT
ejpam-3915	16	1	the	the	DET
ejpam-3915	16	2	open	open	ADJ
ejpam-3915	16	3	neighborhood	neighborhood	NOUN
ejpam-3915	16	4	of	of	ADP
ejpam-3915	16	5	v	v	NOUN
ejpam-3915	16	6	in	in	ADP
ejpam-3915	16	7	g	g	PROPN
ejpam-3915	16	8	is	be	AUX
ejpam-3915	16	9	the	the	DET
ejpam-3915	16	10	set	set	NOUN
ejpam-3915	16	11	n(v	n(v	PROPN
ejpam-3915	16	12	)	)	PUNCT
ejpam-3915	16	13	=	=	PRON
ejpam-3915	17	1	{	{	PUNCT
ejpam-3915	17	2	u	u	NOUN
ejpam-3915	17	3	∈	∈	PROPN
ejpam-3915	17	4	v	v	NOUN
ejpam-3915	17	5	(	(	PUNCT
ejpam-3915	17	6	g	g	NOUN
ejpam-3915	17	7	)	)	PUNCT
ejpam-3915	17	8	:	:	PUNCT
ejpam-3915	17	9	uv	uv	PROPN
ejpam-3915	17	10	∈	∈	PROPN
ejpam-3915	17	11	e(g	e(g	PROPN
ejpam-3915	17	12	)	)	PUNCT
ejpam-3915	17	13	}	}	PUNCT
ejpam-3915	17	14	and	and	CCONJ
ejpam-3915	17	15	the	the	DET
ejpam-3915	17	16	closed	closed	ADJ
ejpam-3915	17	17	neighborhood	neighborhood	NOUN
ejpam-3915	17	18	of	of	ADP
ejpam-3915	17	19	v	v	NOUN
ejpam-3915	17	20	is	be	AUX
ejpam-3915	17	21	the	the	DET
ejpam-3915	17	22	set	set	ADJ
ejpam-3915	17	23	n	n	PROPN
ejpam-3915	17	24	[	[	X
ejpam-3915	17	25	v	v	X
ejpam-3915	17	26	]	]	X
ejpam-3915	17	27	=	=	PUNCT
ejpam-3915	17	28	n(v	n(v	PROPN
ejpam-3915	17	29	)	)	PUNCT
ejpam-3915	17	30	∪	∪	NOUN
ejpam-3915	17	31	{	{	PUNCT
ejpam-3915	17	32	v	v	NOUN
ejpam-3915	17	33	}	}	PUNCT
ejpam-3915	17	34	.	.	PUNCT
ejpam-3915	18	1	for	for	ADP
ejpam-3915	18	2	x	x	SYM
ejpam-3915	18	3	⊆	⊆	NUM
ejpam-3915	18	4	v	v	ADP
ejpam-3915	18	5	(	(	PUNCT
ejpam-3915	18	6	g	g	NOUN
ejpam-3915	18	7	)	)	PUNCT
ejpam-3915	18	8	,	,	PUNCT
ejpam-3915	18	9	the	the	DET
ejpam-3915	18	10	open	open	ADJ
ejpam-3915	18	11	neighborhood	neighborhood	NOUN
ejpam-3915	18	12	of	of	ADP
ejpam-3915	18	13	x	x	SYM
ejpam-3915	18	14	is	be	AUX
ejpam-3915	18	15	the	the	DET
ejpam-3915	18	16	set	set	NOUN
ejpam-3915	18	17	n(x	n(x	NOUN
ejpam-3915	18	18	)	)	PUNCT
ejpam-3915	18	19	=	=	PUNCT
ejpam-3915	18	20	∪v∈xng(v	∪v∈xng(v	PROPN
ejpam-3915	18	21	)	)	PUNCT
ejpam-3915	18	22	and	and	CCONJ
ejpam-3915	18	23	its	its	PRON
ejpam-3915	18	24	closed	closed	ADJ
ejpam-3915	18	25	neighborhood	neighborhood	NOUN
ejpam-3915	18	26	is	be	AUX
ejpam-3915	18	27	the	the	DET
ejpam-3915	18	28	set	set	ADJ
ejpam-3915	18	29	n	n	NOUN
ejpam-3915	18	30	[	[	X
ejpam-3915	18	31	x	x	X
ejpam-3915	18	32	]	]	X
ejpam-3915	18	33	=	=	SYM
ejpam-3915	18	34	n(x	n(x	X
ejpam-3915	18	35	)	)	PUNCT
ejpam-3915	19	1	∪x	∪x	PRON
ejpam-3915	19	2	.	.	PUNCT
ejpam-3915	19	3	∗corresponding	∗corresponde	VERB
ejpam-3915	19	4	author	author	NOUN
ejpam-3915	19	5	.	.	PUNCT
ejpam-3915	20	1	doi	doi	NOUN
ejpam-3915	20	2	:	:	PUNCT
ejpam-3915	20	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3915	https://doi.org/10.29020/nybg.ejpam.v14i3.3915	NOUN
ejpam-3915	20	4	email	email	NOUN
ejpam-3915	20	5	addresses	address	NOUN
ejpam-3915	20	6	:	:	PUNCT
ejpam-3915	20	7	armadac@cnu.edu.ph	armadac@cnu.edu.ph	PROPN
ejpam-3915	20	8	/	/	SYM
ejpam-3915	20	9	cris.armada@g.msuiit.edu.ph	cris.armada@g.msuiit.edu.ph	PROPN
ejpam-3915	20	10	(	(	PUNCT
ejpam-3915	20	11	c.	c.	PROPN
ejpam-3915	20	12	armada	armada	PROPN
ejpam-3915	20	13	)	)	PUNCT
ejpam-3915	20	14	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3915	21	1	1098	1098	NUM
ejpam-3915	21	2	c	c	X
ejpam-3915	21	3	©	©	PROPN
ejpam-3915	21	4	2021	2021	NUM
ejpam-3915	21	5	ejpam	ejpam	VERB
ejpam-3915	21	6	all	all	DET
ejpam-3915	21	7	rights	right	NOUN
ejpam-3915	21	8	reserved	reserve	VERB
ejpam-3915	21	9	.	.	PUNCT
ejpam-3915	22	1	c.	c.	PROPN
ejpam-3915	22	2	armada	armada	PROPN
ejpam-3915	22	3	/	/	SYM
ejpam-3915	22	4	eur	eur	PROPN
ejpam-3915	22	5	.	.	PUNCT
ejpam-3915	23	1	j.	j.	PROPN
ejpam-3915	23	2	pure	pure	PROPN
ejpam-3915	23	3	appl	appl	PROPN
ejpam-3915	23	4	.	.	PROPN
ejpam-3915	23	5	math	math	PROPN
ejpam-3915	23	6	,	,	PUNCT
ejpam-3915	23	7	14	14	NUM
ejpam-3915	23	8	(	(	PUNCT
ejpam-3915	23	9	3	3	NUM
ejpam-3915	23	10	)	)	PUNCT
ejpam-3915	23	11	(	(	PUNCT
ejpam-3915	23	12	2021	2021	NUM
ejpam-3915	23	13	)	)	PUNCT
ejpam-3915	23	14	,	,	PUNCT
ejpam-3915	23	15	1098	1098	NUM
ejpam-3915	23	16	-	-	SYM
ejpam-3915	23	17	1107	1107	NUM
ejpam-3915	23	18	1099	1099	NUM
ejpam-3915	23	19	a	a	DET
ejpam-3915	23	20	set	set	NOUN
ejpam-3915	23	21	s	s	NOUN
ejpam-3915	23	22	⊆	⊆	NUM
ejpam-3915	23	23	v	v	NOUN
ejpam-3915	23	24	(	(	PUNCT
ejpam-3915	23	25	g	g	NOUN
ejpam-3915	23	26	)	)	PUNCT
ejpam-3915	23	27	is	be	AUX
ejpam-3915	23	28	a	a	DET
ejpam-3915	23	29	dominating	dominating	NOUN
ejpam-3915	23	30	set	set	NOUN
ejpam-3915	23	31	(	(	PUNCT
ejpam-3915	23	32	resp	resp	NOUN
ejpam-3915	23	33	.	.	PUNCT
ejpam-3915	24	1	total	total	ADJ
ejpam-3915	24	2	dominating	dominating	NOUN
ejpam-3915	24	3	set	set	NOUN
ejpam-3915	24	4	)	)	PUNCT
ejpam-3915	24	5	of	of	ADP
ejpam-3915	24	6	g	g	PROPN
ejpam-3915	24	7	if	if	SCONJ
ejpam-3915	24	8	n	n	PROPN
ejpam-3915	24	9	[	[	X
ejpam-3915	24	10	s	s	X
ejpam-3915	24	11	]	]	X
ejpam-3915	24	12	=	=	SYM
ejpam-3915	24	13	v	v	X
ejpam-3915	24	14	(	(	PUNCT
ejpam-3915	24	15	g	g	NOUN
ejpam-3915	24	16	)	)	PUNCT
ejpam-3915	24	17	(	(	PUNCT
ejpam-3915	24	18	resp	resp	NOUN
ejpam-3915	24	19	.	.	PUNCT
ejpam-3915	25	1	n(s	n(s	PROPN
ejpam-3915	25	2	)	)	PUNCT
ejpam-3915	25	3	=	=	SYM
ejpam-3915	25	4	v	v	NOUN
ejpam-3915	25	5	(	(	PUNCT
ejpam-3915	25	6	g	g	NOUN
ejpam-3915	25	7	)	)	PUNCT
ejpam-3915	25	8	)	)	PUNCT
ejpam-3915	25	9	.	.	PUNCT
ejpam-3915	26	1	the	the	DET
ejpam-3915	26	2	domination	domination	NOUN
ejpam-3915	26	3	number	number	NOUN
ejpam-3915	26	4	γ(g	γ(g	PROPN
ejpam-3915	26	5	)	)	PUNCT
ejpam-3915	26	6	(	(	PUNCT
ejpam-3915	26	7	resp	resp	NOUN
ejpam-3915	26	8	.	.	PUNCT
ejpam-3915	27	1	total	total	ADJ
ejpam-3915	27	2	domination	domination	NOUN
ejpam-3915	27	3	number	number	NOUN
ejpam-3915	27	4	γt(g	γt(g	NUM
ejpam-3915	27	5	)	)	PUNCT
ejpam-3915	27	6	)	)	PUNCT
ejpam-3915	27	7	of	of	ADP
ejpam-3915	27	8	g	g	PROPN
ejpam-3915	27	9	is	be	AUX
ejpam-3915	27	10	the	the	DET
ejpam-3915	27	11	minimum	minimum	ADJ
ejpam-3915	27	12	cardinality	cardinality	NOUN
ejpam-3915	27	13	of	of	ADP
ejpam-3915	27	14	a	a	DET
ejpam-3915	27	15	dominating	dominating	NOUN
ejpam-3915	27	16	set	set	NOUN
ejpam-3915	27	17	(	(	PUNCT
ejpam-3915	27	18	resp	resp	NOUN
ejpam-3915	27	19	.	.	PUNCT
ejpam-3915	28	1	total	total	ADJ
ejpam-3915	28	2	dominating	dominating	NOUN
ejpam-3915	28	3	set	set	NOUN
ejpam-3915	28	4	)	)	PUNCT
ejpam-3915	28	5	.	.	PUNCT
ejpam-3915	29	1	if	if	SCONJ
ejpam-3915	29	2	s	s	NOUN
ejpam-3915	29	3	is	be	AUX
ejpam-3915	29	4	a	a	DET
ejpam-3915	29	5	dominating	dominating	NOUN
ejpam-3915	29	6	set	set	NOUN
ejpam-3915	29	7	(	(	PUNCT
ejpam-3915	29	8	resp	resp	NOUN
ejpam-3915	29	9	.	.	PUNCT
ejpam-3915	30	1	a	a	DET
ejpam-3915	30	2	total	total	ADJ
ejpam-3915	30	3	dominating	dominating	NOUN
ejpam-3915	30	4	set	set	NOUN
ejpam-3915	30	5	)	)	PUNCT
ejpam-3915	30	6	with	with	ADP
ejpam-3915	30	7	|s|	|s|	PROPN
ejpam-3915	30	8	=	=	SYM
ejpam-3915	30	9	γ(g	γ(g	PROPN
ejpam-3915	30	10	)	)	PUNCT
ejpam-3915	30	11	(	(	PUNCT
ejpam-3915	30	12	resp	resp	NOUN
ejpam-3915	30	13	.	.	PUNCT
ejpam-3915	30	14	|s|	|s|	PROPN
ejpam-3915	30	15	=	=	SYM
ejpam-3915	30	16	γt(g	γt(g	NUM
ejpam-3915	30	17	)	)	PUNCT
ejpam-3915	30	18	)	)	PUNCT
ejpam-3915	30	19	,	,	PUNCT
ejpam-3915	30	20	then	then	ADV
ejpam-3915	30	21	we	we	PRON
ejpam-3915	30	22	call	call	VERB
ejpam-3915	30	23	s	s	PRON
ejpam-3915	30	24	a	a	DET
ejpam-3915	30	25	γ	γ	X
ejpam-3915	30	26	-	-	PUNCT
ejpam-3915	30	27	set	set	ADJ
ejpam-3915	30	28	(	(	PUNCT
ejpam-3915	30	29	resp	resp	NOUN
ejpam-3915	30	30	.	.	PUNCT
ejpam-3915	31	1	a	a	DET
ejpam-3915	31	2	γt	γt	NOUN
ejpam-3915	31	3	-	-	NOUN
ejpam-3915	31	4	set	set	NOUN
ejpam-3915	31	5	)	)	PUNCT
ejpam-3915	31	6	of	of	ADP
ejpam-3915	31	7	g.	g.	PROPN
ejpam-3915	31	8	let	let	VERB
ejpam-3915	31	9	g	g	PROPN
ejpam-3915	31	10	=	=	SYM
ejpam-3915	31	11	(	(	PUNCT
ejpam-3915	31	12	v	v	NOUN
ejpam-3915	31	13	,	,	PUNCT
ejpam-3915	31	14	e	e	NOUN
ejpam-3915	31	15	)	)	PUNCT
ejpam-3915	31	16	be	be	AUX
ejpam-3915	31	17	a	a	DET
ejpam-3915	31	18	simple	simple	ADJ
ejpam-3915	31	19	graph	graph	NOUN
ejpam-3915	31	20	.	.	PUNCT
ejpam-3915	32	1	let	let	VERB
ejpam-3915	32	2	p	p	PRON
ejpam-3915	32	3	⊆	⊆	NUM
ejpam-3915	32	4	v	v	NOUN
ejpam-3915	32	5	(	(	PUNCT
ejpam-3915	32	6	g	g	NOUN
ejpam-3915	32	7	)	)	PUNCT
ejpam-3915	32	8	.	.	PUNCT
ejpam-3915	33	1	an	an	DET
ejpam-3915	33	2	edge	edge	NOUN
ejpam-3915	33	3	e	e	NOUN
ejpam-3915	33	4	=	=	NOUN
ejpam-3915	33	5	uv	uv	NOUN
ejpam-3915	33	6	of	of	ADP
ejpam-3915	33	7	g	g	PROPN
ejpam-3915	33	8	is	be	AUX
ejpam-3915	33	9	directly	directly	ADV
ejpam-3915	33	10	observed	observe	VERB
ejpam-3915	33	11	by	by	ADP
ejpam-3915	33	12	p	p	NOUN
ejpam-3915	33	13	if	if	SCONJ
ejpam-3915	33	14	u	u	PROPN
ejpam-3915	33	15	∈	∈	PROPN
ejpam-3915	33	16	p	p	NOUN
ejpam-3915	33	17	or	or	CCONJ
ejpam-3915	33	18	v	v	ADP
ejpam-3915	33	19	∈	∈	PROPN
ejpam-3915	33	20	p	p	NOUN
ejpam-3915	33	21	.	.	PUNCT
ejpam-3915	34	1	a	a	DET
ejpam-3915	34	2	vertex	vertex	NOUN
ejpam-3915	34	3	u	u	NOUN
ejpam-3915	34	4	of	of	ADP
ejpam-3915	34	5	g	g	PROPN
ejpam-3915	34	6	is	be	AUX
ejpam-3915	34	7	directly	directly	ADV
ejpam-3915	34	8	observed	observe	VERB
ejpam-3915	34	9	if	if	SCONJ
ejpam-3915	34	10	u	u	NOUN
ejpam-3915	34	11	is	be	AUX
ejpam-3915	34	12	incident	incident	NOUN
ejpam-3915	34	13	to	to	ADP
ejpam-3915	34	14	a	a	DET
ejpam-3915	34	15	directly	directly	ADV
ejpam-3915	34	16	observed	observe	VERB
ejpam-3915	34	17	edge	edge	NOUN
ejpam-3915	34	18	.	.	PUNCT
ejpam-3915	35	1	an	an	DET
ejpam-3915	35	2	edge	edge	NOUN
ejpam-3915	35	3	e′	e′	X
ejpam-3915	35	4	=	=	SYM
ejpam-3915	36	1	xy	xy	PROPN
ejpam-3915	36	2	is	be	AUX
ejpam-3915	36	3	remotely	remotely	ADV
ejpam-3915	36	4	observed	observe	VERB
ejpam-3915	36	5	by	by	ADP
ejpam-3915	36	6	p	p	PRON
ejpam-3915	36	7	if	if	SCONJ
ejpam-3915	36	8	x	x	PROPN
ejpam-3915	36	9	,	,	PUNCT
ejpam-3915	36	10	y	y	PROPN
ejpam-3915	36	11	/∈	/∈	PUNCT
ejpam-3915	37	1	p	p	NOUN
ejpam-3915	37	2	and	and	CCONJ
ejpam-3915	37	3	x	x	X
ejpam-3915	37	4	,	,	PUNCT
ejpam-3915	37	5	y	y	PROPN
ejpam-3915	37	6	are	be	AUX
ejpam-3915	37	7	directly	directly	ADV
ejpam-3915	37	8	observed	observe	VERB
ejpam-3915	37	9	vertices	vertex	NOUN
ejpam-3915	37	10	or	or	CCONJ
ejpam-3915	37	11	at	at	ADP
ejpam-3915	37	12	least	least	ADJ
ejpam-3915	37	13	one	one	NUM
ejpam-3915	37	14	of	of	ADP
ejpam-3915	37	15	x	x	PUNCT
ejpam-3915	37	16	and	and	CCONJ
ejpam-3915	37	17	y	y	PROPN
ejpam-3915	37	18	is	be	AUX
ejpam-3915	37	19	incident	incident	NOUN
ejpam-3915	37	20	to	to	ADP
ejpam-3915	37	21	k	k	PROPN
ejpam-3915	37	22	edges	edge	NOUN
ejpam-3915	37	23	where	where	SCONJ
ejpam-3915	37	24	k	k	PROPN
ejpam-3915	37	25	−	−	PROPN
ejpam-3915	37	26	1	1	NUM
ejpam-3915	37	27	of	of	ADP
ejpam-3915	37	28	these	these	DET
ejpam-3915	37	29	edges	edge	NOUN
ejpam-3915	37	30	are	be	AUX
ejpam-3915	37	31	directly	directly	ADV
ejpam-3915	37	32	observed	observe	VERB
ejpam-3915	37	33	by	by	ADP
ejpam-3915	37	34	p	p	PROPN
ejpam-3915	37	35	.	.	PUNCT
ejpam-3915	38	1	a	a	DET
ejpam-3915	38	2	non	non	ADJ
ejpam-3915	38	3	-	-	ADJ
ejpam-3915	38	4	directly	directly	ADV
ejpam-3915	38	5	observed	observe	VERB
ejpam-3915	38	6	vertex	vertex	NOUN
ejpam-3915	38	7	u	u	NOUN
ejpam-3915	38	8	of	of	ADP
ejpam-3915	38	9	g	g	NOUN
ejpam-3915	38	10	which	which	PRON
ejpam-3915	38	11	is	be	AUX
ejpam-3915	38	12	incident	incident	NOUN
ejpam-3915	38	13	to	to	ADP
ejpam-3915	38	14	a	a	DET
ejpam-3915	38	15	remotely	remotely	ADV
ejpam-3915	38	16	observed	observe	VERB
ejpam-3915	38	17	edge	edge	NOUN
ejpam-3915	38	18	is	be	AUX
ejpam-3915	38	19	called	call	VERB
ejpam-3915	38	20	remotely	remotely	ADV
ejpam-3915	38	21	observed	observe	VERB
ejpam-3915	38	22	vertex	vertex	NOUN
ejpam-3915	38	23	.	.	PUNCT
ejpam-3915	39	1	let	let	VERB
ejpam-3915	39	2	op	op	NOUN
ejpam-3915	39	3	v	v	NOUN
ejpam-3915	39	4	(	(	PUNCT
ejpam-3915	39	5	g	g	NOUN
ejpam-3915	39	6	)	)	PUNCT
ejpam-3915	39	7	be	be	VERB
ejpam-3915	39	8	the	the	DET
ejpam-3915	39	9	set	set	NOUN
ejpam-3915	39	10	of	of	ADP
ejpam-3915	39	11	all	all	DET
ejpam-3915	39	12	directly	directly	ADV
ejpam-3915	39	13	and	and	CCONJ
ejpam-3915	39	14	remotely	remotely	ADV
ejpam-3915	39	15	observed	observe	VERB
ejpam-3915	39	16	vertices	vertex	NOUN
ejpam-3915	39	17	and	and	CCONJ
ejpam-3915	39	18	op	op	PROPN
ejpam-3915	39	19	e(g	e(g	PROPN
ejpam-3915	39	20	)	)	PUNCT
ejpam-3915	39	21	be	be	VERB
ejpam-3915	39	22	the	the	DET
ejpam-3915	39	23	set	set	NOUN
ejpam-3915	39	24	of	of	ADP
ejpam-3915	39	25	all	all	DET
ejpam-3915	39	26	directly	directly	ADV
ejpam-3915	39	27	and	and	CCONJ
ejpam-3915	39	28	remotely	remotely	ADV
ejpam-3915	39	29	observed	observe	VERB
ejpam-3915	39	30	edges	edge	NOUN
ejpam-3915	39	31	.	.	PUNCT
ejpam-3915	40	1	then	then	ADV
ejpam-3915	40	2	p	p	X
ejpam-3915	40	3	⊆	⊆	NUM
ejpam-3915	40	4	v	v	NOUN
ejpam-3915	40	5	(	(	PUNCT
ejpam-3915	40	6	g	g	NOUN
ejpam-3915	40	7	)	)	PUNCT
ejpam-3915	40	8	is	be	AUX
ejpam-3915	40	9	a	a	DET
ejpam-3915	40	10	dr	dr	PROPN
ejpam-3915	40	11	-	-	PUNCT
ejpam-3915	40	12	power	power	NOUN
ejpam-3915	40	13	dominating	dominating	NOUN
ejpam-3915	40	14	set	set	NOUN
ejpam-3915	40	15	(	(	PUNCT
ejpam-3915	40	16	dr	dr	NOUN
ejpam-3915	40	17	-	-	PUNCT
ejpam-3915	40	18	pds	pds	NOUN
ejpam-3915	40	19	)	)	PUNCT
ejpam-3915	40	20	of	of	ADP
ejpam-3915	40	21	g	g	PROPN
ejpam-3915	40	22	if	if	SCONJ
ejpam-3915	40	23	op	op	NOUN
ejpam-3915	40	24	v	v	X
ejpam-3915	40	25	(	(	PUNCT
ejpam-3915	40	26	g	g	NOUN
ejpam-3915	40	27	)	)	PUNCT
ejpam-3915	40	28	=	=	NOUN
ejpam-3915	40	29	v	v	X
ejpam-3915	40	30	(	(	PUNCT
ejpam-3915	40	31	g	g	NOUN
ejpam-3915	40	32	)	)	PUNCT
ejpam-3915	40	33	and	and	CCONJ
ejpam-3915	40	34	op	op	PROPN
ejpam-3915	40	35	e(g	e(g	PROPN
ejpam-3915	40	36	)	)	PUNCT
ejpam-3915	41	1	=	=	SYM
ejpam-3915	41	2	e(g	e(g	PROPN
ejpam-3915	41	3	)	)	PUNCT
ejpam-3915	41	4	.	.	PUNCT
ejpam-3915	42	1	the	the	DET
ejpam-3915	42	2	minimum	minimum	ADJ
ejpam-3915	42	3	cardinality	cardinality	NOUN
ejpam-3915	42	4	of	of	ADP
ejpam-3915	42	5	a	a	DET
ejpam-3915	42	6	dr	dr	NOUN
ejpam-3915	42	7	-	-	PUNCT
ejpam-3915	42	8	power	power	NOUN
ejpam-3915	42	9	dominating	dominating	NOUN
ejpam-3915	42	10	set	set	NOUN
ejpam-3915	42	11	is	be	AUX
ejpam-3915	42	12	called	call	VERB
ejpam-3915	42	13	the	the	DET
ejpam-3915	42	14	dr	dr	PROPN
ejpam-3915	42	15	-	-	PUNCT
ejpam-3915	42	16	power	power	NOUN
ejpam-3915	42	17	domination	domination	NOUN
ejpam-3915	42	18	number	number	NOUN
ejpam-3915	42	19	of	of	ADP
ejpam-3915	42	20	g	g	NOUN
ejpam-3915	42	21	and	and	CCONJ
ejpam-3915	42	22	is	be	AUX
ejpam-3915	42	23	denoted	denote	VERB
ejpam-3915	42	24	by	by	ADP
ejpam-3915	42	25	γ∗pw(g	γ∗pw(g	NOUN
ejpam-3915	42	26	)	)	PUNCT
ejpam-3915	42	27	.	.	PUNCT
ejpam-3915	43	1	a	a	DET
ejpam-3915	43	2	subset	subset	NOUN
ejpam-3915	43	3	p	p	NOUN
ejpam-3915	43	4	of	of	ADP
ejpam-3915	43	5	v	v	NOUN
ejpam-3915	43	6	(	(	PUNCT
ejpam-3915	43	7	g	g	NOUN
ejpam-3915	43	8	)	)	PUNCT
ejpam-3915	43	9	with	with	ADP
ejpam-3915	43	10	cardinality	cardinality	PROPN
ejpam-3915	43	11	γ∗pw(g	γ∗pw(g	PROPN
ejpam-3915	43	12	)	)	PUNCT
ejpam-3915	43	13	is	be	AUX
ejpam-3915	43	14	called	call	VERB
ejpam-3915	43	15	a	a	DET
ejpam-3915	43	16	γ∗pw	γ∗pw	NOUN
ejpam-3915	43	17	-	-	PUNCT
ejpam-3915	43	18	set	set	NOUN
ejpam-3915	43	19	of	of	ADP
ejpam-3915	43	20	g.	g.	PROPN
ejpam-3915	43	21	a	a	DET
ejpam-3915	43	22	dr	dr	PROPN
ejpam-3915	43	23	-	-	PUNCT
ejpam-3915	43	24	power	power	NOUN
ejpam-3915	43	25	dominating	dominating	NOUN
ejpam-3915	43	26	set	set	NOUN
ejpam-3915	43	27	d	d	NOUN
ejpam-3915	43	28	is	be	AUX
ejpam-3915	43	29	said	say	VERB
ejpam-3915	43	30	to	to	PART
ejpam-3915	43	31	be	be	AUX
ejpam-3915	43	32	a	a	DET
ejpam-3915	43	33	total	total	ADJ
ejpam-3915	43	34	dr	dr	NOUN
ejpam-3915	43	35	-	-	PUNCT
ejpam-3915	43	36	power	power	NOUN
ejpam-3915	43	37	dominating	dominating	NOUN
ejpam-3915	43	38	set(tdr	set(tdr	PROPN
ejpam-3915	43	39	-	-	PUNCT
ejpam-3915	43	40	pds	pds	NOUN
ejpam-3915	43	41	)	)	PUNCT
ejpam-3915	43	42	if	if	SCONJ
ejpam-3915	43	43	the	the	DET
ejpam-3915	43	44	induced	induced	ADJ
ejpam-3915	43	45	subgraph	subgraph	NOUN
ejpam-3915	43	46	〈	〈	PROPN
ejpam-3915	43	47	d	d	PROPN
ejpam-3915	43	48	〉	〉	PROPN
ejpam-3915	43	49	has	have	VERB
ejpam-3915	43	50	no	no	DET
ejpam-3915	43	51	isolated	isolated	ADJ
ejpam-3915	43	52	vertex	vertex	NOUN
ejpam-3915	43	53	.	.	PUNCT
ejpam-3915	44	1	the	the	DET
ejpam-3915	44	2	minimum	minimum	ADJ
ejpam-3915	44	3	cardinality	cardinality	NOUN
ejpam-3915	44	4	of	of	ADP
ejpam-3915	44	5	a	a	DET
ejpam-3915	44	6	total	total	ADJ
ejpam-3915	44	7	dr	dr	PROPN
ejpam-3915	44	8	-	-	PUNCT
ejpam-3915	44	9	power	power	NOUN
ejpam-3915	44	10	dominating	dominating	NOUN
ejpam-3915	44	11	set	set	NOUN
ejpam-3915	44	12	(	(	PUNCT
ejpam-3915	44	13	tdr	tdr	PROPN
ejpam-3915	44	14	-	-	PUNCT
ejpam-3915	44	15	pds	pds	NOUN
ejpam-3915	44	16	)	)	PUNCT
ejpam-3915	44	17	is	be	AUX
ejpam-3915	44	18	called	call	VERB
ejpam-3915	44	19	the	the	DET
ejpam-3915	44	20	total	total	ADJ
ejpam-3915	44	21	dr	dr	PROPN
ejpam-3915	44	22	-	-	PUNCT
ejpam-3915	44	23	power	power	NOUN
ejpam-3915	44	24	domination	domination	NOUN
ejpam-3915	44	25	number	number	NOUN
ejpam-3915	44	26	of	of	ADP
ejpam-3915	44	27	g	g	NOUN
ejpam-3915	44	28	and	and	CCONJ
ejpam-3915	44	29	is	be	AUX
ejpam-3915	44	30	denoted	denote	VERB
ejpam-3915	44	31	by	by	ADP
ejpam-3915	44	32	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	44	33	(	(	PUNCT
ejpam-3915	44	34	g	g	NOUN
ejpam-3915	44	35	)	)	PUNCT
ejpam-3915	44	36	.	.	PUNCT
ejpam-3915	45	1	a	a	DET
ejpam-3915	45	2	subset	subset	NOUN
ejpam-3915	45	3	t	t	NOUN
ejpam-3915	45	4	of	of	ADP
ejpam-3915	45	5	v	v	PROPN
ejpam-3915	45	6	(	(	PUNCT
ejpam-3915	45	7	g	g	NOUN
ejpam-3915	45	8	)	)	PUNCT
ejpam-3915	45	9	with	with	ADP
ejpam-3915	45	10	cardinality	cardinality	NOUN
ejpam-3915	45	11	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	45	12	(	(	PUNCT
ejpam-3915	45	13	g	g	NOUN
ejpam-3915	45	14	)	)	PUNCT
ejpam-3915	45	15	is	be	AUX
ejpam-3915	45	16	called	call	VERB
ejpam-3915	45	17	a	a	DET
ejpam-3915	45	18	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	45	19	-set	-set	PROPN
ejpam-3915	45	20	of	of	ADP
ejpam-3915	45	21	g.	g.	PROPN
ejpam-3915	45	22	moreover	moreover	ADV
ejpam-3915	45	23	,	,	PUNCT
ejpam-3915	45	24	there	there	PRON
ejpam-3915	45	25	exists	exist	VERB
ejpam-3915	45	26	a	a	DET
ejpam-3915	45	27	connected	connected	ADJ
ejpam-3915	45	28	graph	graph	NOUN
ejpam-3915	45	29	g	g	ADP
ejpam-3915	45	30	such	such	ADJ
ejpam-3915	45	31	that	that	PRON
ejpam-3915	45	32	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	45	33	(	(	PUNCT
ejpam-3915	45	34	g	g	NOUN
ejpam-3915	45	35	)	)	PUNCT
ejpam-3915	45	36	≤	≤	NOUN
ejpam-3915	45	37	γt(g	γt(g	PUNCT
ejpam-3915	45	38	)	)	PUNCT
ejpam-3915	45	39	.	.	PUNCT
ejpam-3915	46	1	let	let	VERB
ejpam-3915	46	2	s	s	PRON
ejpam-3915	46	3	be	be	AUX
ejpam-3915	46	4	a	a	DET
ejpam-3915	46	5	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	46	6	-set	-set	PUNCT
ejpam-3915	46	7	of	of	ADP
ejpam-3915	46	8	a	a	DET
ejpam-3915	46	9	graph	graph	NOUN
ejpam-3915	46	10	g.	g.	NOUN
ejpam-3915	46	11	a	a	DET
ejpam-3915	46	12	subset	subset	NOUN
ejpam-3915	46	13	d	d	NOUN
ejpam-3915	46	14	of	of	ADP
ejpam-3915	46	15	s	s	NOUN
ejpam-3915	46	16	is	be	AUX
ejpam-3915	46	17	said	say	VERB
ejpam-3915	46	18	to	to	PART
ejpam-3915	46	19	be	be	AUX
ejpam-3915	46	20	a	a	DET
ejpam-3915	46	21	forcing	forcing	NOUN
ejpam-3915	46	22	subset	subset	NOUN
ejpam-3915	46	23	for	for	ADP
ejpam-3915	46	24	s	s	PRON
ejpam-3915	46	25	if	if	SCONJ
ejpam-3915	46	26	s	s	VERB
ejpam-3915	46	27	is	be	AUX
ejpam-3915	46	28	the	the	DET
ejpam-3915	46	29	unique	unique	ADJ
ejpam-3915	46	30	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	46	31	-set	-set	PUNCT
ejpam-3915	46	32	containing	contain	VERB
ejpam-3915	46	33	d.	d.	PROPN
ejpam-3915	46	34	the	the	DET
ejpam-3915	46	35	forcing	force	VERB
ejpam-3915	46	36	total	total	ADJ
ejpam-3915	46	37	dr	dr	PROPN
ejpam-3915	46	38	-	-	PUNCT
ejpam-3915	46	39	power	power	NOUN
ejpam-3915	46	40	domination	domination	NOUN
ejpam-3915	46	41	number	number	NOUN
ejpam-3915	46	42	of	of	ADP
ejpam-3915	46	43	s	s	NOUN
ejpam-3915	46	44	is	be	AUX
ejpam-3915	46	45	given	give	VERB
ejpam-3915	46	46	by	by	ADP
ejpam-3915	46	47	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	46	48	(	(	PUNCT
ejpam-3915	46	49	s	s	NOUN
ejpam-3915	46	50	)	)	PUNCT
ejpam-3915	46	51	=	=	SYM
ejpam-3915	46	52	min{|d|	min{|d|	NOUN
ejpam-3915	46	53	:	:	PUNCT
ejpam-3915	47	1	d	d	X
ejpam-3915	47	2	is	be	AUX
ejpam-3915	47	3	a	a	DET
ejpam-3915	47	4	forcing	forcing	NOUN
ejpam-3915	47	5	subset	subset	NOUN
ejpam-3915	47	6	for	for	ADP
ejpam-3915	47	7	s	s	NOUN
ejpam-3915	47	8	}	}	PUNCT
ejpam-3915	47	9	.	.	PUNCT
ejpam-3915	48	1	the	the	DET
ejpam-3915	48	2	forcing	force	VERB
ejpam-3915	48	3	total	total	ADJ
ejpam-3915	48	4	dr	dr	PROPN
ejpam-3915	48	5	-	-	PUNCT
ejpam-3915	48	6	power	power	NOUN
ejpam-3915	48	7	domination	domination	NOUN
ejpam-3915	48	8	number	number	NOUN
ejpam-3915	48	9	of	of	ADP
ejpam-3915	48	10	g	g	PROPN
ejpam-3915	48	11	is	be	AUX
ejpam-3915	48	12	given	give	VERB
ejpam-3915	48	13	by	by	ADP
ejpam-3915	48	14	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	48	15	(	(	PUNCT
ejpam-3915	48	16	g	g	NOUN
ejpam-3915	48	17	)	)	PUNCT
ejpam-3915	48	18	=	=	SYM
ejpam-3915	48	19	min{fγ∗tpw	min{fγ∗tpw	PROPN
ejpam-3915	48	20	(	(	PUNCT
ejpam-3915	48	21	s	s	NOUN
ejpam-3915	48	22	)	)	PUNCT
ejpam-3915	48	23	:	:	PUNCT
ejpam-3915	48	24	s	s	VERB
ejpam-3915	48	25	is	be	AUX
ejpam-3915	48	26	a	a	DET
ejpam-3915	48	27	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	48	28	-set	-set	PROPN
ejpam-3915	48	29	of	of	ADP
ejpam-3915	48	30	g	g	NOUN
ejpam-3915	48	31	}	}	PUNCT
ejpam-3915	48	32	.	.	PUNCT
ejpam-3915	49	1	the	the	DET
ejpam-3915	49	2	join	join	NOUN
ejpam-3915	49	3	of	of	ADP
ejpam-3915	49	4	two	two	NUM
ejpam-3915	49	5	graphs	graph	NOUN
ejpam-3915	49	6	g	g	NOUN
ejpam-3915	49	7	and	and	CCONJ
ejpam-3915	49	8	h	h	NOUN
ejpam-3915	49	9	,	,	PUNCT
ejpam-3915	49	10	denoted	denote	VERB
ejpam-3915	49	11	by	by	ADP
ejpam-3915	49	12	g+h	g+h	PROPN
ejpam-3915	49	13	is	be	AUX
ejpam-3915	49	14	the	the	DET
ejpam-3915	49	15	graph	graph	NOUN
ejpam-3915	49	16	with	with	ADP
ejpam-3915	49	17	vertex	vertex	NOUN
ejpam-3915	49	18	set	set	VERB
ejpam-3915	49	19	v	v	NOUN
ejpam-3915	49	20	(	(	PUNCT
ejpam-3915	49	21	g+h	g+h	NOUN
ejpam-3915	49	22	)	)	PUNCT
ejpam-3915	49	23	=	=	SYM
ejpam-3915	49	24	v	v	X
ejpam-3915	49	25	(	(	PUNCT
ejpam-3915	49	26	g	g	NOUN
ejpam-3915	49	27	)	)	PUNCT
ejpam-3915	49	28	∪	∪	NOUN
ejpam-3915	49	29	v	v	NOUN
ejpam-3915	49	30	(	(	PUNCT
ejpam-3915	49	31	h	h	NOUN
ejpam-3915	49	32	)	)	PUNCT
ejpam-3915	49	33	and	and	CCONJ
ejpam-3915	49	34	edge	edge	NOUN
ejpam-3915	49	35	set	set	VERB
ejpam-3915	49	36	e(g+h	e(g+h	NUM
ejpam-3915	49	37	)	)	PUNCT
ejpam-3915	49	38	=	=	SYM
ejpam-3915	49	39	e(g	e(g	NOUN
ejpam-3915	49	40	)	)	PUNCT
ejpam-3915	49	41	∪	∪	ADP
ejpam-3915	49	42	e(h	e(h	PROPN
ejpam-3915	49	43	)	)	PUNCT
ejpam-3915	49	44	∪	∪	NOUN
ejpam-3915	49	45	{	{	PUNCT
ejpam-3915	49	46	uv	uv	NOUN
ejpam-3915	49	47	:	:	PUNCT
ejpam-3915	49	48	u	u	PROPN
ejpam-3915	49	49	∈	∈	PROPN
ejpam-3915	49	50	v	v	ADP
ejpam-3915	49	51	(	(	PUNCT
ejpam-3915	49	52	g	g	NOUN
ejpam-3915	49	53	)	)	PUNCT
ejpam-3915	49	54	,	,	PUNCT
ejpam-3915	49	55	v	v	X
ejpam-3915	49	56	∈	∈	PROPN
ejpam-3915	49	57	v	v	NOUN
ejpam-3915	49	58	(	(	PUNCT
ejpam-3915	49	59	h	h	NOUN
ejpam-3915	49	60	)	)	PUNCT
ejpam-3915	49	61	}	}	PUNCT
ejpam-3915	49	62	.	.	PUNCT
ejpam-3915	50	1	the	the	DET
ejpam-3915	50	2	corona	corona	NOUN
ejpam-3915	50	3	g	g	PROPN
ejpam-3915	50	4	◦	◦	NOUN
ejpam-3915	50	5	h	h	NOUN
ejpam-3915	50	6	of	of	ADP
ejpam-3915	50	7	two	two	NUM
ejpam-3915	50	8	graphs	graph	NOUN
ejpam-3915	50	9	g	g	NOUN
ejpam-3915	50	10	and	and	CCONJ
ejpam-3915	50	11	h	h	NOUN
ejpam-3915	50	12	is	be	AUX
ejpam-3915	50	13	the	the	DET
ejpam-3915	50	14	graph	graph	NOUN
ejpam-3915	50	15	obtained	obtain	VERB
ejpam-3915	50	16	by	by	ADP
ejpam-3915	50	17	taking	take	VERB
ejpam-3915	50	18	one	one	NUM
ejpam-3915	50	19	copy	copy	NOUN
ejpam-3915	50	20	of	of	ADP
ejpam-3915	50	21	g	g	PROPN
ejpam-3915	50	22	and	and	CCONJ
ejpam-3915	50	23	|v	|v	PROPN
ejpam-3915	50	24	(	(	PUNCT
ejpam-3915	50	25	g)|	g)|	NOUN
ejpam-3915	50	26	copies	copy	NOUN
ejpam-3915	50	27	of	of	ADP
ejpam-3915	50	28	h	h	NOUN
ejpam-3915	50	29	,	,	PUNCT
ejpam-3915	50	30	and	and	CCONJ
ejpam-3915	50	31	then	then	ADV
ejpam-3915	50	32	forming	form	VERB
ejpam-3915	50	33	the	the	DET
ejpam-3915	50	34	join	join	NOUN
ejpam-3915	50	35	〈	〈	PROPN
ejpam-3915	50	36	{	{	PUNCT
ejpam-3915	50	37	v}〉+hv	v}〉+hv	PROPN
ejpam-3915	50	38	=	=	SYM
ejpam-3915	50	39	v	v	PROPN
ejpam-3915	50	40	+	+	PROPN
ejpam-3915	50	41	hv	hv	PROPN
ejpam-3915	50	42	,	,	PUNCT
ejpam-3915	50	43	where	where	SCONJ
ejpam-3915	50	44	hv	hv	PROPN
ejpam-3915	50	45	is	be	AUX
ejpam-3915	50	46	a	a	DET
ejpam-3915	50	47	copy	copy	NOUN
ejpam-3915	50	48	of	of	ADP
ejpam-3915	50	49	h	h	NOUN
ejpam-3915	50	50	,	,	PUNCT
ejpam-3915	50	51	for	for	ADP
ejpam-3915	50	52	each	each	DET
ejpam-3915	50	53	v	v	NUM
ejpam-3915	50	54	∈	∈	PROPN
ejpam-3915	50	55	v	v	NOUN
ejpam-3915	50	56	(	(	PUNCT
ejpam-3915	50	57	g	g	NOUN
ejpam-3915	50	58	)	)	PUNCT
ejpam-3915	50	59	.	.	PUNCT
ejpam-3915	51	1	c.	c.	PROPN
ejpam-3915	51	2	armada	armada	PROPN
ejpam-3915	51	3	/	/	SYM
ejpam-3915	51	4	eur	eur	PROPN
ejpam-3915	51	5	.	.	PUNCT
ejpam-3915	52	1	j.	j.	PROPN
ejpam-3915	52	2	pure	pure	PROPN
ejpam-3915	52	3	appl	appl	PROPN
ejpam-3915	52	4	.	.	PROPN
ejpam-3915	52	5	math	math	PROPN
ejpam-3915	52	6	,	,	PUNCT
ejpam-3915	52	7	14	14	NUM
ejpam-3915	52	8	(	(	PUNCT
ejpam-3915	52	9	3	3	NUM
ejpam-3915	52	10	)	)	PUNCT
ejpam-3915	52	11	(	(	PUNCT
ejpam-3915	52	12	2021	2021	NUM
ejpam-3915	52	13	)	)	PUNCT
ejpam-3915	52	14	,	,	PUNCT
ejpam-3915	52	15	1098	1098	NUM
ejpam-3915	52	16	-	-	SYM
ejpam-3915	52	17	1107	1107	NUM
ejpam-3915	52	18	1100	1100	NUM
ejpam-3915	52	19	the	the	DET
ejpam-3915	52	20	lexicographic	lexicographic	ADJ
ejpam-3915	52	21	product	product	NOUN
ejpam-3915	52	22	(	(	PUNCT
ejpam-3915	52	23	composition	composition	NOUN
ejpam-3915	52	24	)	)	PUNCT
ejpam-3915	52	25	g[h	g[h	PROPN
ejpam-3915	52	26	]	]	PUNCT
ejpam-3915	52	27	of	of	ADP
ejpam-3915	52	28	two	two	NUM
ejpam-3915	52	29	graphs	graph	NOUN
ejpam-3915	52	30	g	g	NOUN
ejpam-3915	52	31	and	and	CCONJ
ejpam-3915	52	32	h	h	NOUN
ejpam-3915	52	33	is	be	AUX
ejpam-3915	52	34	the	the	DET
ejpam-3915	52	35	graph	graph	NOUN
ejpam-3915	52	36	with	with	ADP
ejpam-3915	52	37	v	v	NOUN
ejpam-3915	52	38	(	(	PUNCT
ejpam-3915	52	39	g[h	g[h	PROPN
ejpam-3915	52	40	]	]	PUNCT
ejpam-3915	52	41	)	)	PUNCT
ejpam-3915	52	42	=	=	SYM
ejpam-3915	52	43	v	v	X
ejpam-3915	52	44	(	(	PUNCT
ejpam-3915	52	45	g)×	g)×	NOUN
ejpam-3915	52	46	v	v	NOUN
ejpam-3915	52	47	(	(	PUNCT
ejpam-3915	52	48	h	h	NOUN
ejpam-3915	52	49	)	)	PUNCT
ejpam-3915	52	50	,	,	PUNCT
ejpam-3915	52	51	and	and	CCONJ
ejpam-3915	52	52	(	(	PUNCT
ejpam-3915	52	53	u	u	NOUN
ejpam-3915	52	54	,	,	PUNCT
ejpam-3915	52	55	u′)(v	u′)(v	NOUN
ejpam-3915	52	56	,	,	PUNCT
ejpam-3915	52	57	v′	v′	NOUN
ejpam-3915	52	58	)	)	PUNCT
ejpam-3915	52	59	∈	∈	NOUN
ejpam-3915	52	60	e(g[h	e(g[h	NOUN
ejpam-3915	52	61	]	]	PUNCT
ejpam-3915	52	62	)	)	PUNCT
ejpam-3915	52	63	if	if	SCONJ
ejpam-3915	52	64	and	and	CCONJ
ejpam-3915	52	65	only	only	ADV
ejpam-3915	52	66	if	if	SCONJ
ejpam-3915	52	67	either	either	DET
ejpam-3915	52	68	uv	uv	PROPN
ejpam-3915	52	69	∈	∈	PROPN
ejpam-3915	52	70	e(g	e(g	PROPN
ejpam-3915	52	71	)	)	PUNCT
ejpam-3915	52	72	or	or	CCONJ
ejpam-3915	52	73	u	u	X
ejpam-3915	52	74	=	=	NOUN
ejpam-3915	52	75	v	v	PROPN
ejpam-3915	52	76	and	and	CCONJ
ejpam-3915	52	77	u′v′	u′v′	PROPN
ejpam-3915	52	78	∈	∈	PROPN
ejpam-3915	52	79	e(h	e(h	PROPN
ejpam-3915	52	80	)	)	PUNCT
ejpam-3915	52	81	.	.	PUNCT
ejpam-3915	53	1	amos	amos	PROPN
ejpam-3915	54	1	[	[	X
ejpam-3915	54	2	1	1	NUM
ejpam-3915	54	3	]	]	PUNCT
ejpam-3915	54	4	studied	study	VERB
ejpam-3915	54	5	total	total	ADJ
ejpam-3915	54	6	domination	domination	NOUN
ejpam-3915	54	7	.	.	PUNCT
ejpam-3915	55	1	the	the	DET
ejpam-3915	55	2	relation	relation	NOUN
ejpam-3915	55	3	between	between	ADP
ejpam-3915	55	4	forcing	force	VERB
ejpam-3915	55	5	and	and	CCONJ
ejpam-3915	55	6	domination	domination	NOUN
ejpam-3915	55	7	concepts	concept	NOUN
ejpam-3915	55	8	was	be	AUX
ejpam-3915	55	9	investigated	investigate	VERB
ejpam-3915	55	10	by	by	ADP
ejpam-3915	55	11	chartrand	chartrand	PROPN
ejpam-3915	55	12	et	et	PROPN
ejpam-3915	55	13	al	al	PROPN
ejpam-3915	55	14	.	.	PUNCT
ejpam-3915	56	1	[	[	X
ejpam-3915	56	2	5	5	NUM
ejpam-3915	56	3	]	]	PUNCT
ejpam-3915	56	4	and	and	CCONJ
ejpam-3915	56	5	they	they	PRON
ejpam-3915	56	6	defined	define	VERB
ejpam-3915	56	7	"	"	PUNCT
ejpam-3915	56	8	forcing	force	VERB
ejpam-3915	56	9	domination	domination	NOUN
ejpam-3915	56	10	number	number	NOUN
ejpam-3915	56	11	"	"	PUNCT
ejpam-3915	56	12	.	.	PUNCT
ejpam-3915	57	1	the	the	DET
ejpam-3915	57	2	following	follow	VERB
ejpam-3915	57	3	concepts	concept	NOUN
ejpam-3915	57	4	:	:	PUNCT
ejpam-3915	57	5	total	total	ADJ
ejpam-3915	57	6	dr	dr	PROPN
ejpam-3915	57	7	-	-	PUNCT
ejpam-3915	57	8	power	power	NOUN
ejpam-3915	57	9	domination	domination	NOUN
ejpam-3915	57	10	[	[	X
ejpam-3915	57	11	6	6	NUM
ejpam-3915	57	12	]	]	PUNCT
ejpam-3915	57	13	,	,	PUNCT
ejpam-3915	57	14	forcing	force	VERB
ejpam-3915	57	15	domination	domination	NOUN
ejpam-3915	57	16	number	number	NOUN
ejpam-3915	57	17	of	of	ADP
ejpam-3915	57	18	graphs	graph	NOUN
ejpam-3915	57	19	under	under	ADP
ejpam-3915	57	20	some	some	DET
ejpam-3915	57	21	binary	binary	ADJ
ejpam-3915	57	22	operations	operation	NOUN
ejpam-3915	57	23	[	[	X
ejpam-3915	57	24	7	7	NUM
ejpam-3915	57	25	]	]	PUNCT
ejpam-3915	57	26	,	,	PUNCT
ejpam-3915	57	27	forcing	force	VERB
ejpam-3915	57	28	total	total	ADJ
ejpam-3915	57	29	domination	domination	NOUN
ejpam-3915	57	30	number	number	NOUN
ejpam-3915	57	31	and	and	CCONJ
ejpam-3915	57	32	forcing	force	VERB
ejpam-3915	57	33	connected	connected	ADJ
ejpam-3915	57	34	domination	domination	NOUN
ejpam-3915	57	35	number	number	NOUN
ejpam-3915	57	36	under	under	ADP
ejpam-3915	57	37	the	the	DET
ejpam-3915	57	38	lexicographic	lexicographic	ADJ
ejpam-3915	57	39	product	product	NOUN
ejpam-3915	57	40	of	of	ADP
ejpam-3915	57	41	graphs	graph	NOUN
ejpam-3915	57	42	[	[	X
ejpam-3915	57	43	8	8	NUM
ejpam-3915	57	44	]	]	PUNCT
ejpam-3915	57	45	,	,	PUNCT
ejpam-3915	57	46	forcing	force	VERB
ejpam-3915	57	47	independent	independent	ADJ
ejpam-3915	57	48	domination	domination	NOUN
ejpam-3915	57	49	number	number	NOUN
ejpam-3915	57	50	of	of	ADP
ejpam-3915	57	51	a	a	DET
ejpam-3915	57	52	graph	graph	NOUN
ejpam-3915	57	53	[	[	X
ejpam-3915	57	54	4	4	NUM
ejpam-3915	57	55	]	]	PUNCT
ejpam-3915	57	56	,	,	PUNCT
ejpam-3915	57	57	and	and	CCONJ
ejpam-3915	57	58	a	a	DET
ejpam-3915	57	59	-	-	PUNCT
ejpam-3915	57	60	differential	differential	NOUN
ejpam-3915	57	61	of	of	ADP
ejpam-3915	57	62	graphs	graph	NOUN
ejpam-3915	57	63	[	[	X
ejpam-3915	57	64	3	3	NUM
ejpam-3915	57	65	]	]	PUNCT
ejpam-3915	57	66	was	be	AUX
ejpam-3915	57	67	studied	study	VERB
ejpam-3915	57	68	by	by	ADP
ejpam-3915	57	69	canoy	canoy	NOUN
ejpam-3915	57	70	,	,	PUNCT
ejpam-3915	57	71	et	et	PROPN
ejpam-3915	57	72	al	al	PROPN
ejpam-3915	57	73	.	.	PUNCT
ejpam-3915	58	1	the	the	DET
ejpam-3915	58	2	total	total	ADJ
ejpam-3915	58	3	dr	dr	PROPN
ejpam-3915	58	4	-	-	PUNCT
ejpam-3915	58	5	power	power	NOUN
ejpam-3915	58	6	domination	domination	NOUN
ejpam-3915	58	7	number	number	NOUN
ejpam-3915	58	8	of	of	ADP
ejpam-3915	58	9	some	some	DET
ejpam-3915	58	10	special	special	ADJ
ejpam-3915	58	11	graphs	graph	NOUN
ejpam-3915	58	12	such	such	ADJ
ejpam-3915	58	13	as	as	ADP
ejpam-3915	58	14	paths	path	NOUN
ejpam-3915	58	15	and	and	CCONJ
ejpam-3915	58	16	cycles	cycle	NOUN
ejpam-3915	58	17	was	be	AUX
ejpam-3915	58	18	studied	study	VERB
ejpam-3915	58	19	by	by	ADP
ejpam-3915	58	20	armada	armada	PROPN
ejpam-3915	59	1	[	[	X
ejpam-3915	59	2	2	2	NUM
ejpam-3915	59	3	]	]	PUNCT
ejpam-3915	59	4	.	.	PUNCT
ejpam-3915	60	1	2	2	X
ejpam-3915	60	2	.	.	X
ejpam-3915	60	3	known	know	VERB
ejpam-3915	60	4	results	result	NOUN
ejpam-3915	60	5	this	this	DET
ejpam-3915	60	6	section	section	NOUN
ejpam-3915	60	7	contains	contain	VERB
ejpam-3915	60	8	known	know	VERB
ejpam-3915	60	9	results	result	NOUN
ejpam-3915	60	10	involving	involve	VERB
ejpam-3915	60	11	total	total	ADJ
ejpam-3915	60	12	dr	dr	PROPN
ejpam-3915	60	13	-	-	PUNCT
ejpam-3915	60	14	power	power	NOUN
ejpam-3915	60	15	domination	domination	NOUN
ejpam-3915	60	16	,	,	PUNCT
ejpam-3915	60	17	dr	dr	PROPN
ejpam-3915	60	18	-	-	PUNCT
ejpam-3915	60	19	power	power	NOUN
ejpam-3915	60	20	domination	domination	NOUN
ejpam-3915	60	21	,	,	PUNCT
ejpam-3915	60	22	total	total	ADJ
ejpam-3915	60	23	domination	domination	NOUN
ejpam-3915	60	24	numbers	number	NOUN
ejpam-3915	60	25	of	of	ADP
ejpam-3915	60	26	a	a	DET
ejpam-3915	60	27	graph	graph	NOUN
ejpam-3915	60	28	g	g	NOUN
ejpam-3915	60	29	that	that	PRON
ejpam-3915	60	30	are	be	AUX
ejpam-3915	60	31	very	very	ADV
ejpam-3915	60	32	useful	useful	ADJ
ejpam-3915	60	33	in	in	ADP
ejpam-3915	60	34	proving	prove	VERB
ejpam-3915	60	35	the	the	DET
ejpam-3915	60	36	main	main	ADJ
ejpam-3915	60	37	results	result	NOUN
ejpam-3915	60	38	of	of	ADP
ejpam-3915	60	39	this	this	DET
ejpam-3915	60	40	paper	paper	NOUN
ejpam-3915	60	41	.	.	PUNCT
ejpam-3915	61	1	remark	remark	NOUN
ejpam-3915	61	2	2.1	2.1	NUM
ejpam-3915	61	3	.	.	PUNCT
ejpam-3915	62	1	[	[	X
ejpam-3915	62	2	6	6	NUM
ejpam-3915	62	3	]	]	PUNCT
ejpam-3915	62	4	for	for	ADP
ejpam-3915	62	5	a	a	DET
ejpam-3915	62	6	graph	graph	NOUN
ejpam-3915	62	7	g	g	NOUN
ejpam-3915	62	8	without	without	ADP
ejpam-3915	62	9	isolated	isolated	ADJ
ejpam-3915	62	10	vertices	vertex	NOUN
ejpam-3915	62	11	,	,	PUNCT
ejpam-3915	62	12	γ∗pw(g	γ∗pw(g	ADJ
ejpam-3915	62	13	)	)	PUNCT
ejpam-3915	62	14	≤	≤	NOUN
ejpam-3915	62	15	γ∗tpw	γ∗tpw	PUNCT
ejpam-3915	62	16	(	(	PUNCT
ejpam-3915	62	17	g	g	NOUN
ejpam-3915	62	18	)	)	PUNCT
ejpam-3915	62	19	≤	≤	NOUN
ejpam-3915	62	20	γt(g	γt(g	PUNCT
ejpam-3915	62	21	)	)	PUNCT
ejpam-3915	62	22	.	.	PUNCT
ejpam-3915	63	1	proposition	proposition	NOUN
ejpam-3915	63	2	2.2	2.2	NUM
ejpam-3915	63	3	.	.	PUNCT
ejpam-3915	64	1	[	[	X
ejpam-3915	64	2	1	1	X
ejpam-3915	64	3	]	]	PUNCT
ejpam-3915	64	4	the	the	DET
ejpam-3915	64	5	total	total	ADJ
ejpam-3915	64	6	domination	domination	NOUN
ejpam-3915	64	7	number	number	NOUN
ejpam-3915	64	8	of	of	ADP
ejpam-3915	64	9	a	a	DET
ejpam-3915	64	10	cycle	cycle	NOUN
ejpam-3915	64	11	cn	cn	NOUN
ejpam-3915	64	12	or	or	CCONJ
ejpam-3915	64	13	a	a	DET
ejpam-3915	64	14	path	path	NOUN
ejpam-3915	64	15	pn	pn	NOUN
ejpam-3915	64	16	on	on	ADP
ejpam-3915	64	17	n	n	PRON
ejpam-3915	64	18	≥	≥	NUM
ejpam-3915	64	19	3	3	NUM
ejpam-3915	64	20	vertices	vertex	NOUN
ejpam-3915	64	21	is	be	AUX
ejpam-3915	64	22	given	give	VERB
ejpam-3915	64	23	by	by	ADP
ejpam-3915	64	24	γt(cn	γt(cn	PROPN
ejpam-3915	64	25	)	)	PUNCT
ejpam-3915	65	1	=	=	SYM
ejpam-3915	65	2	γt(pn	γt(pn	NOUN
ejpam-3915	65	3	)	)	PUNCT
ejpam-3915	65	4	=	=	SYM
ejpam-3915	65	5			PROPN
ejpam-3915	65	6	n	n	ADV
ejpam-3915	65	7	2	2	NUM
ejpam-3915	65	8	,	,	PUNCT
ejpam-3915	65	9	n	n	PRON
ejpam-3915	65	10	≡	≡	PROPN
ejpam-3915	65	11	0(mod	0(mod	NOUN
ejpam-3915	65	12	4	4	NUM
ejpam-3915	65	13	)	)	PUNCT
ejpam-3915	65	14	,	,	PUNCT
ejpam-3915	65	15	n+2	n+2	ADV
ejpam-3915	65	16	2	2	NUM
ejpam-3915	65	17	,	,	PUNCT
ejpam-3915	65	18	n	n	PRON
ejpam-3915	65	19	≡	≡	PROPN
ejpam-3915	65	20	2(mod	2(mod	NUM
ejpam-3915	65	21	4	4	NUM
ejpam-3915	65	22	)	)	PUNCT
ejpam-3915	65	23	,	,	PUNCT
ejpam-3915	65	24	n+1	n+1	PROPN
ejpam-3915	65	25	2	2	NUM
ejpam-3915	65	26	,	,	PUNCT
ejpam-3915	65	27	otherwise	otherwise	ADV
ejpam-3915	65	28	.	.	PUNCT
ejpam-3915	66	1	theorem	theorem	VERB
ejpam-3915	66	2	2.3	2.3	NUM
ejpam-3915	66	3	.	.	PUNCT
ejpam-3915	67	1	[	[	X
ejpam-3915	67	2	6	6	NUM
ejpam-3915	67	3	]	]	PUNCT
ejpam-3915	67	4	let	let	VERB
ejpam-3915	67	5	g	g	NOUN
ejpam-3915	67	6	and	and	CCONJ
ejpam-3915	67	7	h	h	NOUN
ejpam-3915	67	8	be	be	VERB
ejpam-3915	67	9	any	any	DET
ejpam-3915	67	10	graphs	graph	NOUN
ejpam-3915	67	11	.	.	PUNCT
ejpam-3915	68	1	then	then	ADV
ejpam-3915	68	2	p	p	X
ejpam-3915	68	3	⊆	⊆	NUM
ejpam-3915	68	4	v	v	NOUN
ejpam-3915	68	5	(	(	PUNCT
ejpam-3915	68	6	g+h	g+h	NOUN
ejpam-3915	68	7	)	)	PUNCT
ejpam-3915	68	8	is	be	AUX
ejpam-3915	68	9	a	a	DET
ejpam-3915	68	10	total	total	ADJ
ejpam-3915	68	11	dr	dr	ADJ
ejpam-3915	68	12	-	-	PUNCT
ejpam-3915	68	13	power	power	NOUN
ejpam-3915	68	14	dominating	dominating	NOUN
ejpam-3915	68	15	set	set	NOUN
ejpam-3915	68	16	of	of	ADP
ejpam-3915	68	17	g+h	g+h	PROPN
ejpam-3915	68	18	if	if	SCONJ
ejpam-3915	68	19	and	and	CCONJ
ejpam-3915	68	20	only	only	ADV
ejpam-3915	68	21	if	if	SCONJ
ejpam-3915	68	22	it	it	PRON
ejpam-3915	68	23	satisfies	satisfy	VERB
ejpam-3915	68	24	one	one	NUM
ejpam-3915	68	25	of	of	ADP
ejpam-3915	68	26	the	the	DET
ejpam-3915	68	27	following	following	ADJ
ejpam-3915	68	28	conditions	condition	NOUN
ejpam-3915	68	29	:	:	PUNCT
ejpam-3915	68	30	(	(	PUNCT
ejpam-3915	68	31	i	i	NOUN
ejpam-3915	68	32	)	)	PUNCT
ejpam-3915	68	33	p	p	PROPN
ejpam-3915	68	34	⊆	⊆	NUM
ejpam-3915	68	35	v	v	NOUN
ejpam-3915	68	36	(	(	PUNCT
ejpam-3915	68	37	g	g	NOUN
ejpam-3915	68	38	)	)	PUNCT
ejpam-3915	68	39	and	and	CCONJ
ejpam-3915	68	40	is	be	AUX
ejpam-3915	68	41	a	a	DET
ejpam-3915	68	42	total	total	ADJ
ejpam-3915	68	43	dominating	dominating	NOUN
ejpam-3915	68	44	set	set	NOUN
ejpam-3915	68	45	,	,	PUNCT
ejpam-3915	68	46	provided	provide	VERB
ejpam-3915	68	47	that	that	SCONJ
ejpam-3915	68	48	g	g	PROPN
ejpam-3915	68	49	is	be	AUX
ejpam-3915	68	50	a	a	DET
ejpam-3915	68	51	graph	graph	NOUN
ejpam-3915	68	52	with	with	ADP
ejpam-3915	68	53	no	no	DET
ejpam-3915	68	54	isolated	isolated	ADJ
ejpam-3915	68	55	vertex	vertex	NOUN
ejpam-3915	68	56	;	;	PUNCT
ejpam-3915	68	57	(	(	PUNCT
ejpam-3915	68	58	ii	ii	NOUN
ejpam-3915	68	59	)	)	PUNCT
ejpam-3915	68	60	p	p	NOUN
ejpam-3915	68	61	⊆	⊆	NUM
ejpam-3915	68	62	v	v	NOUN
ejpam-3915	68	63	(	(	PUNCT
ejpam-3915	68	64	h	h	NOUN
ejpam-3915	68	65	)	)	PUNCT
ejpam-3915	68	66	and	and	CCONJ
ejpam-3915	68	67	is	be	AUX
ejpam-3915	68	68	a	a	DET
ejpam-3915	68	69	total	total	ADJ
ejpam-3915	68	70	dominating	dominating	NOUN
ejpam-3915	68	71	set	set	NOUN
ejpam-3915	68	72	,	,	PUNCT
ejpam-3915	68	73	provided	provide	VERB
ejpam-3915	68	74	that	that	SCONJ
ejpam-3915	68	75	h	h	NOUN
ejpam-3915	68	76	is	be	AUX
ejpam-3915	68	77	a	a	DET
ejpam-3915	68	78	graph	graph	NOUN
ejpam-3915	68	79	with	with	ADP
ejpam-3915	68	80	no	no	DET
ejpam-3915	68	81	isolated	isolated	ADJ
ejpam-3915	68	82	vertex	vertex	NOUN
ejpam-3915	68	83	;	;	PUNCT
ejpam-3915	68	84	or	or	CCONJ
ejpam-3915	68	85	(	(	PUNCT
ejpam-3915	68	86	iii	iii	NOUN
ejpam-3915	68	87	)	)	PUNCT
ejpam-3915	68	88	p	p	NOUN
ejpam-3915	68	89	=	=	SYM
ejpam-3915	68	90	p1	p1	PROPN
ejpam-3915	68	91	∪	∪	ADJ
ejpam-3915	68	92	p2	p2	NOUN
ejpam-3915	68	93	,	,	PUNCT
ejpam-3915	68	94	where	where	SCONJ
ejpam-3915	68	95	∅	∅	NOUN
ejpam-3915	68	96	6=	6=	NUM
ejpam-3915	68	97	p1	p1	PROPN
ejpam-3915	68	98	⊆	⊆	NUM
ejpam-3915	68	99	v	v	NOUN
ejpam-3915	68	100	(	(	PUNCT
ejpam-3915	68	101	g	g	NOUN
ejpam-3915	68	102	)	)	PUNCT
ejpam-3915	68	103	and	and	CCONJ
ejpam-3915	68	104	∅	∅	NOUN
ejpam-3915	68	105	6=	6=	X
ejpam-3915	68	106	p2	p2	PROPN
ejpam-3915	68	107	⊆	⊆	NUM
ejpam-3915	68	108	v	v	NOUN
ejpam-3915	68	109	(	(	PUNCT
ejpam-3915	68	110	g	g	NOUN
ejpam-3915	68	111	)	)	PUNCT
ejpam-3915	68	112	.	.	PUNCT
ejpam-3915	69	1	corollary	corollary	ADJ
ejpam-3915	69	2	2.4	2.4	NUM
ejpam-3915	69	3	.	.	PUNCT
ejpam-3915	70	1	[	[	X
ejpam-3915	70	2	6	6	NUM
ejpam-3915	70	3	]	]	PUNCT
ejpam-3915	70	4	let	let	VERB
ejpam-3915	70	5	g	g	NOUN
ejpam-3915	70	6	and	and	CCONJ
ejpam-3915	70	7	h	h	NOUN
ejpam-3915	70	8	be	be	VERB
ejpam-3915	70	9	any	any	DET
ejpam-3915	70	10	graphs	graph	NOUN
ejpam-3915	70	11	.	.	PUNCT
ejpam-3915	71	1	then	then	ADV
ejpam-3915	71	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	71	3	(	(	PUNCT
ejpam-3915	71	4	g+h	g+h	NOUN
ejpam-3915	71	5	)	)	PUNCT
ejpam-3915	72	1	=	=	SYM
ejpam-3915	72	2	2	2	X
ejpam-3915	72	3	.	.	PUNCT
ejpam-3915	72	4	c.	c.	PROPN
ejpam-3915	72	5	armada	armada	PROPN
ejpam-3915	72	6	/	/	SYM
ejpam-3915	72	7	eur	eur	PROPN
ejpam-3915	72	8	.	.	PUNCT
ejpam-3915	73	1	j.	j.	PROPN
ejpam-3915	73	2	pure	pure	PROPN
ejpam-3915	73	3	appl	appl	PROPN
ejpam-3915	73	4	.	.	PROPN
ejpam-3915	73	5	math	math	PROPN
ejpam-3915	73	6	,	,	PUNCT
ejpam-3915	73	7	14	14	NUM
ejpam-3915	73	8	(	(	PUNCT
ejpam-3915	73	9	3	3	NUM
ejpam-3915	73	10	)	)	PUNCT
ejpam-3915	73	11	(	(	PUNCT
ejpam-3915	73	12	2021	2021	NUM
ejpam-3915	73	13	)	)	PUNCT
ejpam-3915	73	14	,	,	PUNCT
ejpam-3915	73	15	1098	1098	NUM
ejpam-3915	73	16	-	-	SYM
ejpam-3915	73	17	1107	1107	NUM
ejpam-3915	73	18	1101	1101	NUM
ejpam-3915	73	19	theorem	theorem	VERB
ejpam-3915	73	20	2.5	2.5	NUM
ejpam-3915	73	21	.	.	PUNCT
ejpam-3915	74	1	[	[	X
ejpam-3915	74	2	6	6	NUM
ejpam-3915	74	3	]	]	PUNCT
ejpam-3915	74	4	let	let	VERB
ejpam-3915	74	5	g	g	PRON
ejpam-3915	74	6	be	be	AUX
ejpam-3915	74	7	a	a	DET
ejpam-3915	74	8	nontrivial	nontrivial	ADJ
ejpam-3915	74	9	connected	connect	VERB
ejpam-3915	74	10	graph	graph	NOUN
ejpam-3915	74	11	and	and	CCONJ
ejpam-3915	74	12	h	h	NOUN
ejpam-3915	74	13	be	be	AUX
ejpam-3915	74	14	a	a	DET
ejpam-3915	74	15	graph	graph	NOUN
ejpam-3915	74	16	with	with	ADP
ejpam-3915	74	17	no	no	DET
ejpam-3915	74	18	isolated	isolated	ADJ
ejpam-3915	74	19	vertex	vertex	NOUN
ejpam-3915	74	20	.	.	PUNCT
ejpam-3915	75	1	then	then	ADV
ejpam-3915	75	2	p	p	X
ejpam-3915	75	3	⊆	⊆	NUM
ejpam-3915	75	4	v	v	NOUN
ejpam-3915	75	5	(	(	PUNCT
ejpam-3915	75	6	g	g	PROPN
ejpam-3915	75	7	◦	◦	NOUN
ejpam-3915	75	8	h	h	NOUN
ejpam-3915	75	9	)	)	PUNCT
ejpam-3915	75	10	is	be	AUX
ejpam-3915	75	11	a	a	DET
ejpam-3915	75	12	total	total	ADJ
ejpam-3915	75	13	dr	dr	ADJ
ejpam-3915	75	14	-	-	PUNCT
ejpam-3915	75	15	power	power	NOUN
ejpam-3915	75	16	dominating	dominating	NOUN
ejpam-3915	75	17	set	set	VERB
ejpam-3915	75	18	if	if	SCONJ
ejpam-3915	75	19	and	and	CCONJ
ejpam-3915	75	20	only	only	ADV
ejpam-3915	75	21	if	if	SCONJ
ejpam-3915	75	22	p	p	X
ejpam-3915	75	23	=	=	PUNCT
ejpam-3915	75	24	a	a	DET
ejpam-3915	75	25	⋃(⋃	⋃(⋃	PROPN
ejpam-3915	75	26	v∈a	v∈a	NOUN
ejpam-3915	75	27	bv	bv	PROPN
ejpam-3915	75	28	)	)	PUNCT
ejpam-3915	75	29	⋃⋃	⋃⋃	PUNCT
ejpam-3915	75	30	u/∈a	u/∈a	VERB
ejpam-3915	75	31	du	du	PROPN
ejpam-3915	75	32			PROPN
ejpam-3915	75	33	where	where	SCONJ
ejpam-3915	75	34	a	a	DET
ejpam-3915	75	35	⊆	⊆	NUM
ejpam-3915	75	36	v	v	NOUN
ejpam-3915	75	37	(	(	PUNCT
ejpam-3915	75	38	g	g	NOUN
ejpam-3915	75	39	)	)	PUNCT
ejpam-3915	75	40	,	,	PUNCT
ejpam-3915	75	41	bv	bv	PROPN
ejpam-3915	75	42	⊆	⊆	NUM
ejpam-3915	75	43	v	v	PROPN
ejpam-3915	75	44	(	(	PUNCT
ejpam-3915	75	45	hv	hv	PROPN
ejpam-3915	75	46	)	)	PUNCT
ejpam-3915	75	47	for	for	ADP
ejpam-3915	75	48	each	each	DET
ejpam-3915	75	49	v	v	ADP
ejpam-3915	75	50	∈	∈	PROPN
ejpam-3915	75	51	a	a	PRON
ejpam-3915	75	52	and	and	CCONJ
ejpam-3915	75	53	bv	bv	PROPN
ejpam-3915	75	54	6=	6=	PROPN
ejpam-3915	75	55	∅	∅	NOUN
ejpam-3915	75	56	for	for	ADP
ejpam-3915	75	57	each	each	DET
ejpam-3915	75	58	v	v	NOUN
ejpam-3915	75	59	/∈	/∈	PUNCT
ejpam-3915	75	60	ng(a	ng(a	NUM
ejpam-3915	75	61	)	)	PUNCT
ejpam-3915	75	62	,	,	PUNCT
ejpam-3915	75	63	and	and	CCONJ
ejpam-3915	75	64	du	du	PROPN
ejpam-3915	75	65	⊆	⊆	NUM
ejpam-3915	75	66	v	v	NOUN
ejpam-3915	75	67	(	(	PUNCT
ejpam-3915	75	68	hu	hu	PROPN
ejpam-3915	75	69	)	)	PUNCT
ejpam-3915	75	70	is	be	AUX
ejpam-3915	75	71	a	a	DET
ejpam-3915	75	72	total	total	ADJ
ejpam-3915	75	73	dominating	dominating	NOUN
ejpam-3915	75	74	set	set	NOUN
ejpam-3915	75	75	of	of	ADP
ejpam-3915	75	76	hu	hu	PROPN
ejpam-3915	75	77	for	for	ADP
ejpam-3915	75	78	each	each	DET
ejpam-3915	75	79	u	u	NOUN
ejpam-3915	75	80	/∈	/∈	PUNCT
ejpam-3915	75	81	a.	a.	NOUN
ejpam-3915	75	82	corollary	corollary	NOUN
ejpam-3915	75	83	2.6	2.6	NUM
ejpam-3915	75	84	.	.	PUNCT
ejpam-3915	76	1	[	[	X
ejpam-3915	76	2	6	6	NUM
ejpam-3915	76	3	]	]	PUNCT
ejpam-3915	76	4	let	let	VERB
ejpam-3915	76	5	g	g	PRON
ejpam-3915	76	6	be	be	AUX
ejpam-3915	76	7	a	a	DET
ejpam-3915	76	8	nontrivial	nontrivial	ADJ
ejpam-3915	76	9	connected	connect	VERB
ejpam-3915	76	10	graph	graph	NOUN
ejpam-3915	76	11	of	of	ADP
ejpam-3915	76	12	order	order	NOUN
ejpam-3915	76	13	m	m	VERB
ejpam-3915	76	14	and	and	CCONJ
ejpam-3915	76	15	h	h	NOUN
ejpam-3915	76	16	be	be	VERB
ejpam-3915	76	17	any	any	DET
ejpam-3915	76	18	graph	graph	NOUN
ejpam-3915	76	19	with	with	ADP
ejpam-3915	76	20	no	no	DET
ejpam-3915	76	21	isolated	isolated	ADJ
ejpam-3915	76	22	vertex	vertex	NOUN
ejpam-3915	76	23	.	.	PUNCT
ejpam-3915	77	1	then	then	ADV
ejpam-3915	77	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	77	3	(	(	PUNCT
ejpam-3915	77	4	g	g	PROPN
ejpam-3915	77	5	◦	◦	NOUN
ejpam-3915	77	6	h	h	NOUN
ejpam-3915	77	7	)	)	PUNCT
ejpam-3915	77	8	=	=	SYM
ejpam-3915	77	9	m.	m.	NOUN
ejpam-3915	77	10	theorem	theorem	VERB
ejpam-3915	77	11	2.7	2.7	NUM
ejpam-3915	77	12	.	.	PUNCT
ejpam-3915	78	1	[	[	X
ejpam-3915	78	2	6	6	NUM
ejpam-3915	78	3	]	]	PUNCT
ejpam-3915	78	4	let	let	VERB
ejpam-3915	78	5	g	g	NOUN
ejpam-3915	78	6	and	and	CCONJ
ejpam-3915	78	7	h	h	NOUN
ejpam-3915	78	8	be	be	AUX
ejpam-3915	78	9	nontrivial	nontrivial	ADJ
ejpam-3915	78	10	connected	connected	ADJ
ejpam-3915	78	11	graphs	graph	NOUN
ejpam-3915	78	12	.	.	PUNCT
ejpam-3915	79	1	then	then	ADV
ejpam-3915	79	2	p	p	X
ejpam-3915	79	3	=	=	X
ejpam-3915	79	4	⋃	⋃	PROPN
ejpam-3915	79	5	x∈s	x∈s	NOUN
ejpam-3915	79	6	(	(	PUNCT
ejpam-3915	79	7	{	{	PUNCT
ejpam-3915	79	8	x	x	NOUN
ejpam-3915	79	9	}	}	PUNCT
ejpam-3915	79	10	×	×	PROPN
ejpam-3915	79	11	tx	tx	PROPN
ejpam-3915	79	12	)	)	PUNCT
ejpam-3915	79	13	,	,	PUNCT
ejpam-3915	79	14	where	where	SCONJ
ejpam-3915	79	15	s	s	VERB
ejpam-3915	79	16	⊆	⊆	NUM
ejpam-3915	79	17	v	v	NOUN
ejpam-3915	79	18	(	(	PUNCT
ejpam-3915	79	19	g	g	NOUN
ejpam-3915	79	20	)	)	PUNCT
ejpam-3915	79	21	and	and	CCONJ
ejpam-3915	79	22	tx	tx	VERB
ejpam-3915	79	23	⊆	⊆	NUM
ejpam-3915	79	24	v	v	NOUN
ejpam-3915	79	25	(	(	PUNCT
ejpam-3915	79	26	h	h	NOUN
ejpam-3915	79	27	)	)	PUNCT
ejpam-3915	79	28	for	for	ADP
ejpam-3915	79	29	all	all	PRON
ejpam-3915	79	30	x	x	SYM
ejpam-3915	79	31	∈	∈	PROPN
ejpam-3915	79	32	s	s	NOUN
ejpam-3915	79	33	,	,	PUNCT
ejpam-3915	79	34	is	be	AUX
ejpam-3915	79	35	a	a	DET
ejpam-3915	79	36	total	total	ADJ
ejpam-3915	79	37	drpower	drpower	NOUN
ejpam-3915	79	38	dominating	dominating	NOUN
ejpam-3915	79	39	set	set	NOUN
ejpam-3915	79	40	of	of	ADP
ejpam-3915	79	41	g[h	g[h	PROPN
ejpam-3915	79	42	]	]	PUNCT
ejpam-3915	79	43	if	if	SCONJ
ejpam-3915	80	1	and	and	CCONJ
ejpam-3915	80	2	only	only	ADV
ejpam-3915	80	3	if	if	SCONJ
ejpam-3915	80	4	s	s	NOUN
ejpam-3915	80	5	is	be	AUX
ejpam-3915	80	6	a	a	DET
ejpam-3915	80	7	dominating	dominating	NOUN
ejpam-3915	80	8	set	set	NOUN
ejpam-3915	80	9	of	of	ADP
ejpam-3915	80	10	g	g	NOUN
ejpam-3915	80	11	,	,	PUNCT
ejpam-3915	80	12	and	and	CCONJ
ejpam-3915	80	13	tx	tx	PROPN
ejpam-3915	80	14	is	be	AUX
ejpam-3915	80	15	a	a	DET
ejpam-3915	80	16	total	total	ADJ
ejpam-3915	80	17	dominating	dominating	NOUN
ejpam-3915	80	18	set	set	NOUN
ejpam-3915	80	19	of	of	ADP
ejpam-3915	80	20	h	h	NOUN
ejpam-3915	80	21	for	for	ADP
ejpam-3915	80	22	each	each	DET
ejpam-3915	80	23	x	x	PROPN
ejpam-3915	80	24	∈	∈	PROPN
ejpam-3915	80	25	s\n(s	s\n(s	NOUN
ejpam-3915	80	26	)	)	PUNCT
ejpam-3915	80	27	.	.	PUNCT
ejpam-3915	81	1	corollary	corollary	ADJ
ejpam-3915	81	2	2.8	2.8	NUM
ejpam-3915	81	3	.	.	PUNCT
ejpam-3915	82	1	[	[	X
ejpam-3915	82	2	6	6	NUM
ejpam-3915	82	3	]	]	PUNCT
ejpam-3915	82	4	let	let	VERB
ejpam-3915	82	5	g	g	NOUN
ejpam-3915	82	6	and	and	CCONJ
ejpam-3915	82	7	h	h	NOUN
ejpam-3915	82	8	be	be	AUX
ejpam-3915	82	9	nontrivial	nontrivial	ADJ
ejpam-3915	82	10	connected	connected	ADJ
ejpam-3915	82	11	graphs	graph	NOUN
ejpam-3915	82	12	.	.	PUNCT
ejpam-3915	83	1	then	then	ADV
ejpam-3915	83	2	p	p	NOUN
ejpam-3915	83	3	is	be	AUX
ejpam-3915	83	4	a	a	DET
ejpam-3915	83	5	total	total	ADJ
ejpam-3915	83	6	dr	dr	ADJ
ejpam-3915	83	7	-	-	PUNCT
ejpam-3915	83	8	power	power	NOUN
ejpam-3915	83	9	dominating	dominating	NOUN
ejpam-3915	83	10	set	set	NOUN
ejpam-3915	83	11	of	of	ADP
ejpam-3915	83	12	g[h	g[h	PROPN
ejpam-3915	83	13	]	]	PUNCT
ejpam-3915	83	14	if	if	SCONJ
ejpam-3915	84	1	and	and	CCONJ
ejpam-3915	84	2	only	only	ADV
ejpam-3915	84	3	if	if	SCONJ
ejpam-3915	84	4	p	p	NOUN
ejpam-3915	84	5	is	be	AUX
ejpam-3915	84	6	a	a	DET
ejpam-3915	84	7	total	total	ADJ
ejpam-3915	84	8	dominating	dominating	NOUN
ejpam-3915	84	9	set	set	NOUN
ejpam-3915	84	10	of	of	ADP
ejpam-3915	84	11	g[h	g[h	NOUN
ejpam-3915	84	12	]	]	PUNCT
ejpam-3915	84	13	.	.	PUNCT
ejpam-3915	85	1	moreover	moreover	ADV
ejpam-3915	85	2	,	,	PUNCT
ejpam-3915	85	3	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	85	4	(	(	PUNCT
ejpam-3915	85	5	g[h	g[h	NOUN
ejpam-3915	85	6	]	]	PUNCT
ejpam-3915	85	7	)	)	PUNCT
ejpam-3915	85	8	=	=	SYM
ejpam-3915	85	9	γt(g	γt(g	NUM
ejpam-3915	85	10	)	)	PUNCT
ejpam-3915	85	11	.	.	PUNCT
ejpam-3915	86	1	theorem	theorem	VERB
ejpam-3915	86	2	2.9	2.9	NUM
ejpam-3915	86	3	.	.	PUNCT
ejpam-3915	87	1	[	[	X
ejpam-3915	87	2	2	2	X
ejpam-3915	87	3	]	]	PUNCT
ejpam-3915	87	4	let	let	VERB
ejpam-3915	87	5	g	g	PRON
ejpam-3915	87	6	be	be	AUX
ejpam-3915	87	7	a	a	DET
ejpam-3915	87	8	graph	graph	NOUN
ejpam-3915	87	9	.	.	PUNCT
ejpam-3915	88	1	then	then	ADV
ejpam-3915	88	2	(	(	PUNCT
ejpam-3915	88	3	i	i	NOUN
ejpam-3915	88	4	)	)	PUNCT
ejpam-3915	88	5	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	88	6	(	(	PUNCT
ejpam-3915	88	7	g	g	NOUN
ejpam-3915	88	8	)	)	PUNCT
ejpam-3915	88	9	=	=	SYM
ejpam-3915	88	10	0	0	PUNCT
ejpam-3915	89	1	if	if	SCONJ
ejpam-3915	89	2	and	and	CCONJ
ejpam-3915	89	3	only	only	ADV
ejpam-3915	89	4	if	if	SCONJ
ejpam-3915	89	5	g	g	PROPN
ejpam-3915	89	6	has	have	VERB
ejpam-3915	89	7	a	a	DET
ejpam-3915	89	8	unique	unique	ADJ
ejpam-3915	89	9	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	89	10	-set	-set	NUM
ejpam-3915	89	11	.	.	PUNCT
ejpam-3915	90	1	(	(	PUNCT
ejpam-3915	90	2	ii	ii	NOUN
ejpam-3915	90	3	)	)	PUNCT
ejpam-3915	90	4	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	90	5	(	(	PUNCT
ejpam-3915	90	6	g	g	NOUN
ejpam-3915	90	7	)	)	PUNCT
ejpam-3915	90	8	=	=	SYM
ejpam-3915	90	9	1	1	NUM
ejpam-3915	90	10	if	if	SCONJ
ejpam-3915	90	11	and	and	CCONJ
ejpam-3915	90	12	only	only	ADV
ejpam-3915	90	13	if	if	SCONJ
ejpam-3915	90	14	g	g	PROPN
ejpam-3915	90	15	has	have	VERB
ejpam-3915	90	16	at	at	ADV
ejpam-3915	90	17	least	least	ADV
ejpam-3915	90	18	two	two	NUM
ejpam-3915	90	19	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	90	20	-sets	-set	NOUN
ejpam-3915	90	21	and	and	CCONJ
ejpam-3915	90	22	there	there	PRON
ejpam-3915	90	23	exists	exist	VERB
ejpam-3915	90	24	a	a	DET
ejpam-3915	90	25	vertex	vertex	NOUN
ejpam-3915	90	26	v	v	NOUN
ejpam-3915	90	27	which	which	PRON
ejpam-3915	90	28	is	be	AUX
ejpam-3915	90	29	contained	contain	VERB
ejpam-3915	90	30	in	in	ADP
ejpam-3915	90	31	exactly	exactly	ADV
ejpam-3915	90	32	one	one	NUM
ejpam-3915	90	33	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	90	34	-set	-set	PUNCT
ejpam-3915	90	35	of	of	ADP
ejpam-3915	90	36	g.	g.	PROPN
ejpam-3915	90	37	corollary	corollary	PROPN
ejpam-3915	90	38	2.10	2.10	NUM
ejpam-3915	90	39	.	.	PUNCT
ejpam-3915	91	1	[	[	X
ejpam-3915	91	2	2	2	X
ejpam-3915	91	3	]	]	PUNCT
ejpam-3915	91	4	let	let	VERB
ejpam-3915	91	5	g	g	PRON
ejpam-3915	91	6	be	be	AUX
ejpam-3915	91	7	a	a	DET
ejpam-3915	91	8	connected	connected	ADJ
ejpam-3915	91	9	graph	graph	NOUN
ejpam-3915	91	10	.	.	PUNCT
ejpam-3915	92	1	then	then	ADV
ejpam-3915	92	2	0	0	NUM
ejpam-3915	92	3	≤	≤	NOUN
ejpam-3915	92	4	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	92	5	(	(	PUNCT
ejpam-3915	92	6	g	g	NOUN
ejpam-3915	92	7	)	)	PUNCT
ejpam-3915	92	8	≤	≤	NOUN
ejpam-3915	92	9	γ∗tpw	γ∗tpw	PUNCT
ejpam-3915	92	10	(	(	PUNCT
ejpam-3915	92	11	g	g	NOUN
ejpam-3915	92	12	)	)	PUNCT
ejpam-3915	92	13	.	.	PUNCT
ejpam-3915	93	1	theorem	theorem	VERB
ejpam-3915	93	2	2.11	2.11	NUM
ejpam-3915	93	3	.	.	PUNCT
ejpam-3915	94	1	[	[	X
ejpam-3915	94	2	2	2	X
ejpam-3915	94	3	]	]	PUNCT
ejpam-3915	94	4	let	let	VERB
ejpam-3915	94	5	g	g	PRON
ejpam-3915	94	6	be	be	AUX
ejpam-3915	94	7	a	a	DET
ejpam-3915	94	8	nontrivial	nontrivial	ADJ
ejpam-3915	94	9	graph	graph	NOUN
ejpam-3915	94	10	.	.	PUNCT
ejpam-3915	95	1	then	then	ADV
ejpam-3915	95	2	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3915	95	3	(	(	PUNCT
ejpam-3915	95	4	g	g	NOUN
ejpam-3915	95	5	)	)	PUNCT
ejpam-3915	95	6	=	=	SYM
ejpam-3915	95	7	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	95	8	(	(	PUNCT
ejpam-3915	95	9	g	g	NOUN
ejpam-3915	95	10	)	)	PUNCT
ejpam-3915	95	11	if	if	SCONJ
ejpam-3915	95	12	and	and	CCONJ
ejpam-3915	95	13	only	only	ADV
ejpam-3915	95	14	if	if	SCONJ
ejpam-3915	95	15	for	for	ADP
ejpam-3915	95	16	every	every	PRON
ejpam-3915	95	17	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	95	18	-set	-set	PUNCT
ejpam-3915	96	1	p	p	NOUN
ejpam-3915	96	2	of	of	ADP
ejpam-3915	96	3	g	g	PROPN
ejpam-3915	96	4	and	and	CCONJ
ejpam-3915	96	5	for	for	ADP
ejpam-3915	96	6	each	each	PRON
ejpam-3915	96	7	v	v	ADP
ejpam-3915	96	8	∈	∈	PROPN
ejpam-3915	96	9	p	p	NOUN
ejpam-3915	96	10	,	,	PUNCT
ejpam-3915	96	11	there	there	PRON
ejpam-3915	96	12	exists	exist	VERB
ejpam-3915	96	13	u	u	PROPN
ejpam-3915	96	14	∈	∈	PROPN
ejpam-3915	96	15	v	v	NOUN
ejpam-3915	96	16	(	(	PUNCT
ejpam-3915	96	17	g)\p	g)\p	VERB
ejpam-3915	96	18	such	such	ADJ
ejpam-3915	96	19	that	that	SCONJ
ejpam-3915	96	20	[	[	X
ejpam-3915	96	21	p\{v	p\{v	NOUN
ejpam-3915	96	22	}	}	PUNCT
ejpam-3915	96	23	]	]	PUNCT
ejpam-3915	96	24	∪	∪	X
ejpam-3915	96	25	{	{	PUNCT
ejpam-3915	96	26	u	u	NOUN
ejpam-3915	96	27	}	}	PUNCT
ejpam-3915	96	28	is	be	AUX
ejpam-3915	96	29	a	a	DET
ejpam-3915	96	30	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	96	31	-set	-set	PROPN
ejpam-3915	96	32	of	of	ADP
ejpam-3915	96	33	g.	g.	PROPN
ejpam-3915	96	34	c.	c.	PROPN
ejpam-3915	96	35	armada	armada	PROPN
ejpam-3915	96	36	/	/	SYM
ejpam-3915	96	37	eur	eur	PROPN
ejpam-3915	96	38	.	.	PUNCT
ejpam-3915	97	1	j.	j.	PROPN
ejpam-3915	97	2	pure	pure	PROPN
ejpam-3915	97	3	appl	appl	PROPN
ejpam-3915	97	4	.	.	PROPN
ejpam-3915	97	5	math	math	PROPN
ejpam-3915	97	6	,	,	PUNCT
ejpam-3915	97	7	14	14	NUM
ejpam-3915	97	8	(	(	PUNCT
ejpam-3915	97	9	3	3	NUM
ejpam-3915	97	10	)	)	PUNCT
ejpam-3915	97	11	(	(	PUNCT
ejpam-3915	97	12	2021	2021	NUM
ejpam-3915	97	13	)	)	PUNCT
ejpam-3915	97	14	,	,	PUNCT
ejpam-3915	97	15	1098	1098	NUM
ejpam-3915	97	16	-	-	SYM
ejpam-3915	97	17	1107	1107	NUM
ejpam-3915	97	18	1102	1102	NUM
ejpam-3915	97	19	3	3	NUM
ejpam-3915	97	20	.	.	PUNCT
ejpam-3915	98	1	forcing	force	VERB
ejpam-3915	98	2	total	total	ADJ
ejpam-3915	98	3	dr	dr	PROPN
ejpam-3915	98	4	-	-	PUNCT
ejpam-3915	98	5	power	power	NOUN
ejpam-3915	98	6	domination	domination	NOUN
ejpam-3915	98	7	number	number	NOUN
ejpam-3915	98	8	of	of	ADP
ejpam-3915	98	9	the	the	DET
ejpam-3915	98	10	join	join	NOUN
ejpam-3915	98	11	of	of	ADP
ejpam-3915	98	12	graphs	graph	NOUN
ejpam-3915	98	13	this	this	DET
ejpam-3915	98	14	section	section	NOUN
ejpam-3915	98	15	contains	contain	VERB
ejpam-3915	98	16	the	the	DET
ejpam-3915	98	17	total	total	ADJ
ejpam-3915	98	18	dr	dr	PROPN
ejpam-3915	98	19	-	-	PUNCT
ejpam-3915	98	20	power	power	NOUN
ejpam-3915	98	21	domination	domination	NOUN
ejpam-3915	98	22	number	number	NOUN
ejpam-3915	98	23	of	of	ADP
ejpam-3915	98	24	the	the	DET
ejpam-3915	98	25	complete	complete	ADJ
ejpam-3915	98	26	bipartite	bipartite	PROPN
ejpam-3915	98	27	graphs	graph	NOUN
ejpam-3915	98	28	,	,	PUNCT
ejpam-3915	98	29	generalized	generalized	ADJ
ejpam-3915	98	30	fan	fan	NOUN
ejpam-3915	98	31	graphs	graph	NOUN
ejpam-3915	98	32	,	,	PUNCT
ejpam-3915	98	33	generalized	generalized	ADJ
ejpam-3915	98	34	wheel	wheel	NOUN
ejpam-3915	98	35	graphs	graph	NOUN
ejpam-3915	98	36	,	,	PUNCT
ejpam-3915	98	37	pn	pn	PROPN
ejpam-3915	98	38	+	+	CCONJ
ejpam-3915	98	39	pm	pm	PROPN
ejpam-3915	98	40	,	,	PUNCT
ejpam-3915	98	41	pn	pn	PROPN
ejpam-3915	98	42	+	+	NOUN
ejpam-3915	98	43	cm	cm	NOUN
ejpam-3915	98	44	and	and	CCONJ
ejpam-3915	98	45	cn	cn	PROPN
ejpam-3915	99	1	+	+	NOUN
ejpam-3915	99	2	cm	cm	NOUN
ejpam-3915	99	3	and	and	CCONJ
ejpam-3915	99	4	their	their	PRON
ejpam-3915	99	5	forcing	force	VERB
ejpam-3915	99	6	total	total	ADJ
ejpam-3915	99	7	dr	dr	PROPN
ejpam-3915	99	8	-	-	PUNCT
ejpam-3915	99	9	power	power	NOUN
ejpam-3915	99	10	domination	domination	NOUN
ejpam-3915	99	11	numbers	number	NOUN
ejpam-3915	99	12	.	.	PUNCT
ejpam-3915	100	1	corollary	corollary	ADJ
ejpam-3915	100	2	3.1	3.1	NUM
ejpam-3915	100	3	.	.	PUNCT
ejpam-3915	101	1	let	let	VERB
ejpam-3915	101	2	g	g	NOUN
ejpam-3915	102	1	and	and	CCONJ
ejpam-3915	102	2	h	h	NOUN
ejpam-3915	102	3	be	be	VERB
ejpam-3915	102	4	any	any	DET
ejpam-3915	102	5	graphs	graph	NOUN
ejpam-3915	102	6	.	.	PUNCT
ejpam-3915	103	1	then	then	ADV
ejpam-3915	103	2	r	r	NOUN
ejpam-3915	103	3	⊆	⊆	NUM
ejpam-3915	103	4	v	v	NOUN
ejpam-3915	103	5	(	(	PUNCT
ejpam-3915	103	6	g+h	g+h	PROPN
ejpam-3915	103	7	)	)	PUNCT
ejpam-3915	103	8	is	be	AUX
ejpam-3915	103	9	a	a	DET
ejpam-3915	103	10	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	103	11	-set	-set	PUNCT
ejpam-3915	103	12	of	of	ADP
ejpam-3915	103	13	g+h	g+h	PROPN
ejpam-3915	104	1	if	if	SCONJ
ejpam-3915	104	2	and	and	CCONJ
ejpam-3915	104	3	only	only	ADV
ejpam-3915	104	4	if	if	SCONJ
ejpam-3915	104	5	at	at	ADV
ejpam-3915	104	6	least	least	ADJ
ejpam-3915	104	7	one	one	NUM
ejpam-3915	104	8	of	of	ADP
ejpam-3915	104	9	the	the	DET
ejpam-3915	104	10	following	follow	VERB
ejpam-3915	104	11	holds	hold	VERB
ejpam-3915	104	12	:	:	PUNCT
ejpam-3915	104	13	(	(	PUNCT
ejpam-3915	104	14	i	i	NOUN
ejpam-3915	104	15	)	)	PUNCT
ejpam-3915	104	16	r	r	NOUN
ejpam-3915	104	17	is	be	AUX
ejpam-3915	104	18	a	a	DET
ejpam-3915	104	19	γt	γt	NOUN
ejpam-3915	104	20	-	-	NOUN
ejpam-3915	104	21	set	set	NOUN
ejpam-3915	104	22	of	of	ADP
ejpam-3915	104	23	g	g	NOUN
ejpam-3915	104	24	and	and	CCONJ
ejpam-3915	104	25	|r|	|r|	NOUN
ejpam-3915	104	26	=	=	SYM
ejpam-3915	104	27	2	2	NUM
ejpam-3915	104	28	,	,	PUNCT
ejpam-3915	104	29	(	(	PUNCT
ejpam-3915	104	30	ii	ii	NOUN
ejpam-3915	104	31	)	)	PUNCT
ejpam-3915	104	32	r	r	NOUN
ejpam-3915	104	33	is	be	AUX
ejpam-3915	104	34	a	a	DET
ejpam-3915	104	35	γt	γt	NOUN
ejpam-3915	104	36	-	-	NOUN
ejpam-3915	104	37	set	set	NOUN
ejpam-3915	104	38	of	of	ADP
ejpam-3915	104	39	h	h	NOUN
ejpam-3915	104	40	and	and	CCONJ
ejpam-3915	104	41	|r|	|r|	NOUN
ejpam-3915	104	42	=	=	SYM
ejpam-3915	104	43	2	2	NUM
ejpam-3915	104	44	,	,	PUNCT
ejpam-3915	104	45	(	(	PUNCT
ejpam-3915	104	46	iii	iii	X
ejpam-3915	104	47	)	)	PUNCT
ejpam-3915	104	48	|r	|r	PROPN
ejpam-3915	104	49	∩	∩	PROPN
ejpam-3915	104	50	v	v	X
ejpam-3915	104	51	(	(	PUNCT
ejpam-3915	104	52	g)|	g)|	NOUN
ejpam-3915	104	53	=	=	SYM
ejpam-3915	104	54	1	1	NUM
ejpam-3915	104	55	and	and	CCONJ
ejpam-3915	104	56	|r	|r	PROPN
ejpam-3915	104	57	∩	∩	PROPN
ejpam-3915	104	58	v	v	X
ejpam-3915	104	59	(	(	PUNCT
ejpam-3915	104	60	h)|	h)|	NOUN
ejpam-3915	104	61	=	=	SYM
ejpam-3915	104	62	1	1	X
ejpam-3915	104	63	.	.	PUNCT
ejpam-3915	104	64	theorem	theorem	VERB
ejpam-3915	104	65	3.2	3.2	NUM
ejpam-3915	104	66	.	.	PUNCT
ejpam-3915	105	1	for	for	ADP
ejpam-3915	105	2	any	any	DET
ejpam-3915	105	3	graphs	graph	NOUN
ejpam-3915	105	4	g	g	NOUN
ejpam-3915	105	5	and	and	CCONJ
ejpam-3915	105	6	h	h	NOUN
ejpam-3915	105	7	,	,	PUNCT
ejpam-3915	105	8	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	105	9	(	(	PUNCT
ejpam-3915	105	10	g+h	g+h	NOUN
ejpam-3915	105	11	)	)	PUNCT
ejpam-3915	105	12	=	=	SYM
ejpam-3915	105	13			NUM
ejpam-3915	105	14	0	0	NUM
ejpam-3915	105	15	,	,	PUNCT
ejpam-3915	105	16	if	if	SCONJ
ejpam-3915	105	17	g	g	PROPN
ejpam-3915	105	18	and	and	CCONJ
ejpam-3915	105	19	h	h	NOUN
ejpam-3915	105	20	are	be	AUX
ejpam-3915	105	21	both	both	ADV
ejpam-3915	105	22	trivial	trivial	ADJ
ejpam-3915	105	23	,	,	PUNCT
ejpam-3915	105	24	1	1	NUM
ejpam-3915	105	25	,	,	PUNCT
ejpam-3915	105	26	if	if	SCONJ
ejpam-3915	105	27	g	g	PROPN
ejpam-3915	105	28	is	be	AUX
ejpam-3915	105	29	trivial	trivial	ADJ
ejpam-3915	105	30	and	and	CCONJ
ejpam-3915	105	31	(	(	PUNCT
ejpam-3915	105	32	i	i	NOUN
ejpam-3915	105	33	)	)	PUNCT
ejpam-3915	105	34	h	h	PROPN
ejpam-3915	105	35	has	have	VERB
ejpam-3915	105	36	an	an	DET
ejpam-3915	105	37	isolated	isolated	ADJ
ejpam-3915	105	38	vertex	vertex	NOUN
ejpam-3915	105	39	or	or	CCONJ
ejpam-3915	105	40	(	(	PUNCT
ejpam-3915	105	41	ii	ii	NOUN
ejpam-3915	105	42	)	)	PUNCT
ejpam-3915	105	43	γt(h	γt(h	NUM
ejpam-3915	105	44	)	)	PUNCT
ejpam-3915	105	45	>	>	SYM
ejpam-3915	105	46	2	2	NUM
ejpam-3915	105	47	or	or	CCONJ
ejpam-3915	105	48	(	(	PUNCT
ejpam-3915	105	49	iii	iii	NOUN
ejpam-3915	105	50	)	)	PUNCT
ejpam-3915	105	51	γt(h	γt(h	NUM
ejpam-3915	105	52	)	)	PUNCT
ejpam-3915	106	1	=	=	SYM
ejpam-3915	106	2	2	2	NUM
ejpam-3915	106	3	and	and	CCONJ
ejpam-3915	106	4	there	there	PRON
ejpam-3915	106	5	exists	exist	VERB
ejpam-3915	106	6	a	a	DET
ejpam-3915	106	7	vertex	vertex	NOUN
ejpam-3915	106	8	in	in	ADP
ejpam-3915	106	9	h	h	NOUN
ejpam-3915	106	10	which	which	PRON
ejpam-3915	106	11	is	be	AUX
ejpam-3915	106	12	not	not	PART
ejpam-3915	106	13	in	in	ADP
ejpam-3915	106	14	any	any	DET
ejpam-3915	106	15	γt	γt	NOUN
ejpam-3915	106	16	-	-	NOUN
ejpam-3915	106	17	set	set	NOUN
ejpam-3915	106	18	of	of	ADP
ejpam-3915	106	19	h	h	NOUN
ejpam-3915	106	20	,	,	PUNCT
ejpam-3915	106	21	or	or	CCONJ
ejpam-3915	106	22	if	if	SCONJ
ejpam-3915	106	23	h	h	NOUN
ejpam-3915	106	24	is	be	AUX
ejpam-3915	106	25	trivial	trivial	ADJ
ejpam-3915	106	26	and	and	CCONJ
ejpam-3915	106	27	(	(	PUNCT
ejpam-3915	106	28	i	i	NOUN
ejpam-3915	106	29	)	)	PUNCT
ejpam-3915	106	30	g	g	PROPN
ejpam-3915	106	31	has	have	VERB
ejpam-3915	106	32	an	an	DET
ejpam-3915	106	33	isolated	isolated	ADJ
ejpam-3915	106	34	vertex	vertex	NOUN
ejpam-3915	106	35	or	or	CCONJ
ejpam-3915	106	36	(	(	PUNCT
ejpam-3915	106	37	ii	ii	NOUN
ejpam-3915	106	38	)	)	PUNCT
ejpam-3915	106	39	γt(g	γt(g	PUNCT
ejpam-3915	106	40	)	)	PUNCT
ejpam-3915	106	41	>	>	SYM
ejpam-3915	106	42	2	2	NUM
ejpam-3915	106	43	or	or	CCONJ
ejpam-3915	106	44	(	(	PUNCT
ejpam-3915	106	45	iii	iii	NOUN
ejpam-3915	106	46	)	)	PUNCT
ejpam-3915	106	47	γt(g	γt(g	PUNCT
ejpam-3915	106	48	)	)	PUNCT
ejpam-3915	106	49	=	=	SYM
ejpam-3915	106	50	2	2	NUM
ejpam-3915	106	51	and	and	CCONJ
ejpam-3915	106	52	there	there	PRON
ejpam-3915	106	53	exists	exist	VERB
ejpam-3915	106	54	a	a	DET
ejpam-3915	106	55	vertex	vertex	NOUN
ejpam-3915	106	56	in	in	ADP
ejpam-3915	106	57	h	h	NOUN
ejpam-3915	106	58	which	which	PRON
ejpam-3915	106	59	is	be	AUX
ejpam-3915	106	60	not	not	PART
ejpam-3915	106	61	in	in	ADP
ejpam-3915	106	62	any	any	DET
ejpam-3915	106	63	γt	γt	NOUN
ejpam-3915	106	64	-	-	NOUN
ejpam-3915	106	65	set	set	NOUN
ejpam-3915	106	66	of	of	ADP
ejpam-3915	106	67	g	g	NOUN
ejpam-3915	106	68	,	,	PUNCT
ejpam-3915	106	69	2	2	NUM
ejpam-3915	106	70	,	,	PUNCT
ejpam-3915	106	71	otherwise	otherwise	ADV
ejpam-3915	106	72	.	.	PUNCT
ejpam-3915	107	1	proof	proof	NOUN
ejpam-3915	107	2	.	.	PUNCT
ejpam-3915	108	1	consider	consider	VERB
ejpam-3915	108	2	the	the	DET
ejpam-3915	108	3	following	follow	VERB
ejpam-3915	108	4	cases	case	NOUN
ejpam-3915	108	5	:	:	PUNCT
ejpam-3915	108	6	case	case	NOUN
ejpam-3915	108	7	1	1	NUM
ejpam-3915	108	8	:	:	PUNCT
ejpam-3915	108	9	g	g	NOUN
ejpam-3915	108	10	and	and	CCONJ
ejpam-3915	108	11	h	h	NOUN
ejpam-3915	108	12	are	be	AUX
ejpam-3915	108	13	both	both	PRON
ejpam-3915	108	14	trivial	trivial	ADJ
ejpam-3915	108	15	graphs	graph	NOUN
ejpam-3915	108	16	.	.	PUNCT
ejpam-3915	109	1	{	{	PUNCT
ejpam-3915	109	2	x	x	X
ejpam-3915	109	3	,	,	PUNCT
ejpam-3915	109	4	y	y	NOUN
ejpam-3915	109	5	}	}	PUNCT
ejpam-3915	109	6	such	such	ADJ
ejpam-3915	109	7	that	that	SCONJ
ejpam-3915	109	8	x	x	SYM
ejpam-3915	109	9	∈	∈	NOUN
ejpam-3915	109	10	v	v	X
ejpam-3915	109	11	(	(	PUNCT
ejpam-3915	109	12	g	g	NOUN
ejpam-3915	109	13	)	)	PUNCT
ejpam-3915	109	14	and	and	CCONJ
ejpam-3915	109	15	y	y	PROPN
ejpam-3915	109	16	∈	∈	PROPN
ejpam-3915	109	17	v	v	ADP
ejpam-3915	109	18	(	(	PUNCT
ejpam-3915	109	19	h	h	NOUN
ejpam-3915	109	20	)	)	PUNCT
ejpam-3915	109	21	is	be	AUX
ejpam-3915	109	22	the	the	DET
ejpam-3915	109	23	only	only	ADJ
ejpam-3915	109	24	γt	γt	NOUN
ejpam-3915	109	25	-	-	NOUN
ejpam-3915	109	26	set	set	NOUN
ejpam-3915	109	27	of	of	ADP
ejpam-3915	109	28	g	g	PROPN
ejpam-3915	109	29	+	+	CCONJ
ejpam-3915	109	30	h	h	NOUN
ejpam-3915	109	31	by	by	ADP
ejpam-3915	109	32	corollary	corollary	ADJ
ejpam-3915	109	33	3.1	3.1	NUM
ejpam-3915	109	34	.	.	PUNCT
ejpam-3915	110	1	thus	thus	ADV
ejpam-3915	110	2	,	,	PUNCT
ejpam-3915	110	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	110	4	(	(	PUNCT
ejpam-3915	110	5	g+h	g+h	NOUN
ejpam-3915	110	6	)	)	PUNCT
ejpam-3915	110	7	=	=	SYM
ejpam-3915	110	8	0	0	PUNCT
ejpam-3915	110	9	by	by	ADP
ejpam-3915	110	10	theorem	theorem	NOUN
ejpam-3915	110	11	2.9(i	2.9(i	NUM
ejpam-3915	110	12	)	)	PUNCT
ejpam-3915	110	13	.	.	PUNCT
ejpam-3915	111	1	case	case	NOUN
ejpam-3915	111	2	2	2	NUM
ejpam-3915	111	3	:	:	PUNCT
ejpam-3915	111	4	g	g	PROPN
ejpam-3915	111	5	is	be	AUX
ejpam-3915	111	6	trivial	trivial	ADJ
ejpam-3915	111	7	and	and	CCONJ
ejpam-3915	111	8	(	(	PUNCT
ejpam-3915	111	9	i	i	NOUN
ejpam-3915	111	10	)	)	PUNCT
ejpam-3915	111	11	h	h	PROPN
ejpam-3915	111	12	has	have	VERB
ejpam-3915	111	13	an	an	DET
ejpam-3915	111	14	isolated	isolated	ADJ
ejpam-3915	111	15	vertex	vertex	NOUN
ejpam-3915	111	16	or	or	CCONJ
ejpam-3915	111	17	(	(	PUNCT
ejpam-3915	111	18	ii	ii	NOUN
ejpam-3915	111	19	)	)	PUNCT
ejpam-3915	111	20	γt(h	γt(h	NUM
ejpam-3915	111	21	)	)	PUNCT
ejpam-3915	111	22	>	>	SYM
ejpam-3915	111	23	2	2	NUM
ejpam-3915	111	24	or	or	CCONJ
ejpam-3915	111	25	(	(	PUNCT
ejpam-3915	111	26	iii	iii	NOUN
ejpam-3915	111	27	)	)	PUNCT
ejpam-3915	111	28	γt(h	γt(h	NUM
ejpam-3915	111	29	)	)	PUNCT
ejpam-3915	111	30	=	=	SYM
ejpam-3915	111	31	2	2	NUM
ejpam-3915	111	32	and	and	CCONJ
ejpam-3915	111	33	h	h	NOUN
ejpam-3915	111	34	contains	contain	VERB
ejpam-3915	111	35	a	a	DET
ejpam-3915	111	36	vertex	vertex	NOUN
ejpam-3915	111	37	which	which	PRON
ejpam-3915	111	38	is	be	AUX
ejpam-3915	111	39	not	not	PART
ejpam-3915	111	40	in	in	ADP
ejpam-3915	111	41	any	any	DET
ejpam-3915	111	42	γt	γt	NOUN
ejpam-3915	111	43	-	-	NOUN
ejpam-3915	111	44	set	set	NOUN
ejpam-3915	111	45	of	of	ADP
ejpam-3915	111	46	h	h	NOUN
ejpam-3915	111	47	let	let	VERB
ejpam-3915	111	48	v	v	X
ejpam-3915	111	49	(	(	PUNCT
ejpam-3915	111	50	g	g	NOUN
ejpam-3915	111	51	)	)	PUNCT
ejpam-3915	111	52	=	=	PRON
ejpam-3915	111	53	{	{	PUNCT
ejpam-3915	111	54	x	x	NOUN
ejpam-3915	111	55	}	}	PUNCT
ejpam-3915	111	56	.	.	PUNCT
ejpam-3915	112	1	suppose	suppose	VERB
ejpam-3915	112	2	that	that	SCONJ
ejpam-3915	112	3	h	h	NOUN
ejpam-3915	112	4	has	have	VERB
ejpam-3915	112	5	an	an	DET
ejpam-3915	112	6	isolated	isolated	ADJ
ejpam-3915	112	7	vertex	vertex	NOUN
ejpam-3915	112	8	,	,	PUNCT
ejpam-3915	112	9	say	say	VERB
ejpam-3915	112	10	w.	w.	PROPN
ejpam-3915	112	11	by	by	ADP
ejpam-3915	112	12	corollary	corollary	ADJ
ejpam-3915	112	13	3.1	3.1	NUM
ejpam-3915	112	14	,	,	PUNCT
ejpam-3915	112	15	rw	rw	NOUN
ejpam-3915	112	16	=	=	PRON
ejpam-3915	112	17	{	{	PUNCT
ejpam-3915	112	18	x	x	NOUN
ejpam-3915	112	19	,	,	PUNCT
ejpam-3915	112	20	w	w	NOUN
ejpam-3915	112	21	}	}	PUNCT
ejpam-3915	112	22	is	be	AUX
ejpam-3915	112	23	the	the	DET
ejpam-3915	112	24	only	only	ADJ
ejpam-3915	112	25	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	112	26	-set	-set	PUNCT
ejpam-3915	112	27	of	of	ADP
ejpam-3915	112	28	g+h	g+h	PROPN
ejpam-3915	112	29	containing	contain	VERB
ejpam-3915	112	30	w.	w.	NOUN
ejpam-3915	112	31	if	if	SCONJ
ejpam-3915	112	32	γt(h	γt(h	NUM
ejpam-3915	112	33	)	)	PUNCT
ejpam-3915	112	34	>	>	X
ejpam-3915	113	1	2	2	NUM
ejpam-3915	113	2	,	,	PUNCT
ejpam-3915	113	3	then	then	ADV
ejpam-3915	113	4	by	by	ADP
ejpam-3915	113	5	corollary	corollary	ADJ
ejpam-3915	113	6	3.1	3.1	NUM
ejpam-3915	113	7	,	,	PUNCT
ejpam-3915	113	8	for	for	ADP
ejpam-3915	113	9	each	each	DET
ejpam-3915	113	10	u	u	PROPN
ejpam-3915	113	11	∈	∈	PROPN
ejpam-3915	113	12	v	v	NOUN
ejpam-3915	113	13	(	(	PUNCT
ejpam-3915	113	14	h	h	NOUN
ejpam-3915	113	15	)	)	PUNCT
ejpam-3915	113	16	,	,	PUNCT
ejpam-3915	113	17	ru	ru	NOUN
ejpam-3915	113	18	=	=	SYM
ejpam-3915	113	19	{	{	PUNCT
ejpam-3915	113	20	x	x	NOUN
ejpam-3915	113	21	,	,	PUNCT
ejpam-3915	113	22	u	u	NOUN
ejpam-3915	113	23	}	}	PUNCT
ejpam-3915	113	24	is	be	AUX
ejpam-3915	113	25	the	the	DET
ejpam-3915	113	26	only	only	ADJ
ejpam-3915	113	27	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	113	28	-set	-set	PUNCT
ejpam-3915	113	29	of	of	ADP
ejpam-3915	113	30	g+h	g+h	PROPN
ejpam-3915	113	31	containing	contain	VERB
ejpam-3915	113	32	u.	u.	NOUN
ejpam-3915	113	33	if	if	SCONJ
ejpam-3915	113	34	γt(h	γt(h	NUM
ejpam-3915	113	35	)	)	PUNCT
ejpam-3915	113	36	=	=	SYM
ejpam-3915	113	37	2	2	NUM
ejpam-3915	113	38	and	and	CCONJ
ejpam-3915	113	39	there	there	PRON
ejpam-3915	113	40	exists	exist	VERB
ejpam-3915	113	41	a	a	DET
ejpam-3915	113	42	vertex	vertex	NOUN
ejpam-3915	113	43	,	,	PUNCT
ejpam-3915	113	44	say	say	VERB
ejpam-3915	113	45	v	v	ADP
ejpam-3915	113	46	,	,	PUNCT
ejpam-3915	113	47	in	in	ADP
ejpam-3915	113	48	h	h	NOUN
ejpam-3915	113	49	which	which	PRON
ejpam-3915	113	50	is	be	AUX
ejpam-3915	113	51	not	not	PART
ejpam-3915	113	52	in	in	ADP
ejpam-3915	113	53	any	any	DET
ejpam-3915	113	54	γt	γt	NOUN
ejpam-3915	113	55	-	-	NOUN
ejpam-3915	113	56	set	set	NOUN
ejpam-3915	113	57	of	of	ADP
ejpam-3915	113	58	h	h	NOUN
ejpam-3915	113	59	,	,	PUNCT
ejpam-3915	113	60	then	then	ADV
ejpam-3915	113	61	by	by	ADP
ejpam-3915	113	62	corollary	corollary	ADJ
ejpam-3915	113	63	3.1	3.1	NUM
ejpam-3915	113	64	,	,	PUNCT
ejpam-3915	113	65	rv	rv	NOUN
ejpam-3915	113	66	=	=	SYM
ejpam-3915	113	67	{	{	PUNCT
ejpam-3915	113	68	x	x	NOUN
ejpam-3915	113	69	,	,	PUNCT
ejpam-3915	113	70	v	v	NOUN
ejpam-3915	113	71	}	}	PUNCT
ejpam-3915	113	72	is	be	AUX
ejpam-3915	113	73	the	the	DET
ejpam-3915	113	74	only	only	ADJ
ejpam-3915	113	75	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	113	76	-set	-set	PUNCT
ejpam-3915	113	77	of	of	ADP
ejpam-3915	113	78	g	g	PROPN
ejpam-3915	113	79	+	+	CCONJ
ejpam-3915	113	80	h	h	NOUN
ejpam-3915	113	81	containing	contain	VERB
ejpam-3915	113	82	v.	v.	ADV
ejpam-3915	113	83	thus	thus	ADV
ejpam-3915	113	84	,	,	PUNCT
ejpam-3915	113	85	in	in	ADP
ejpam-3915	113	86	any	any	PRON
ejpam-3915	113	87	of	of	ADP
ejpam-3915	113	88	the	the	DET
ejpam-3915	113	89	three	three	NUM
ejpam-3915	113	90	cases	case	NOUN
ejpam-3915	113	91	,	,	PUNCT
ejpam-3915	113	92	there	there	PRON
ejpam-3915	113	93	always	always	ADV
ejpam-3915	113	94	exists	exist	VERB
ejpam-3915	113	95	a	a	DET
ejpam-3915	113	96	vertex	vertex	NOUN
ejpam-3915	113	97	which	which	PRON
ejpam-3915	113	98	is	be	AUX
ejpam-3915	113	99	contained	contain	VERB
ejpam-3915	113	100	in	in	ADP
ejpam-3915	113	101	exactly	exactly	ADV
ejpam-3915	113	102	one	one	NUM
ejpam-3915	113	103	γ∗tpw	γ∗tpw	PUNCT
ejpam-3915	113	104	-set	-set	PUNCT
ejpam-3915	113	105	of	of	ADP
ejpam-3915	113	106	g	g	PROPN
ejpam-3915	113	107	+	+	CCONJ
ejpam-3915	113	108	h.	h.	PROPN
ejpam-3915	113	109	by	by	ADP
ejpam-3915	113	110	theorem	theorem	NOUN
ejpam-3915	113	111	2.9(ii	2.9(ii	NUM
ejpam-3915	113	112	)	)	PUNCT
ejpam-3915	113	113	,	,	PUNCT
ejpam-3915	113	114	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	113	115	(	(	PUNCT
ejpam-3915	113	116	g+h	g+h	NOUN
ejpam-3915	113	117	)	)	PUNCT
ejpam-3915	113	118	=	=	SYM
ejpam-3915	114	1	1	1	X
ejpam-3915	114	2	.	.	X
ejpam-3915	114	3	similarly	similarly	ADV
ejpam-3915	114	4	,	,	PUNCT
ejpam-3915	114	5	if	if	SCONJ
ejpam-3915	114	6	h	h	NOUN
ejpam-3915	114	7	is	be	AUX
ejpam-3915	114	8	trivial	trivial	ADJ
ejpam-3915	114	9	and	and	CCONJ
ejpam-3915	114	10	(	(	PUNCT
ejpam-3915	114	11	i	i	NOUN
ejpam-3915	114	12	)	)	PUNCT
ejpam-3915	114	13	g	g	PROPN
ejpam-3915	114	14	has	have	VERB
ejpam-3915	114	15	an	an	DET
ejpam-3915	114	16	isolated	isolated	ADJ
ejpam-3915	114	17	vertex	vertex	NOUN
ejpam-3915	114	18	or	or	CCONJ
ejpam-3915	114	19	(	(	PUNCT
ejpam-3915	114	20	ii	ii	NOUN
ejpam-3915	114	21	)	)	PUNCT
ejpam-3915	114	22	γt(g	γt(g	PUNCT
ejpam-3915	114	23	)	)	PUNCT
ejpam-3915	114	24	>	>	SYM
ejpam-3915	114	25	2	2	NUM
ejpam-3915	114	26	or	or	CCONJ
ejpam-3915	114	27	(	(	PUNCT
ejpam-3915	114	28	iii	iii	NOUN
ejpam-3915	114	29	)	)	PUNCT
ejpam-3915	114	30	γt(g	γt(g	PUNCT
ejpam-3915	114	31	)	)	PUNCT
ejpam-3915	114	32	=	=	SYM
ejpam-3915	114	33	2	2	NUM
ejpam-3915	114	34	and	and	CCONJ
ejpam-3915	114	35	there	there	PRON
ejpam-3915	114	36	exists	exist	VERB
ejpam-3915	114	37	a	a	DET
ejpam-3915	114	38	vertex	vertex	NOUN
ejpam-3915	114	39	in	in	ADP
ejpam-3915	114	40	g	g	NOUN
ejpam-3915	114	41	which	which	PRON
ejpam-3915	114	42	is	be	AUX
ejpam-3915	114	43	not	not	PART
ejpam-3915	114	44	in	in	ADP
ejpam-3915	114	45	any	any	DET
ejpam-3915	114	46	γt	γt	NOUN
ejpam-3915	114	47	-	-	NOUN
ejpam-3915	114	48	set	set	NOUN
ejpam-3915	114	49	of	of	ADP
ejpam-3915	114	50	g	g	NOUN
ejpam-3915	114	51	,	,	PUNCT
ejpam-3915	114	52	then	then	ADV
ejpam-3915	114	53	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3915	114	54	(	(	PUNCT
ejpam-3915	114	55	g+h	g+h	NOUN
ejpam-3915	114	56	)	)	PUNCT
ejpam-3915	115	1	=	=	SYM
ejpam-3915	115	2	1	1	X
ejpam-3915	115	3	.	.	PUNCT
ejpam-3915	115	4	c.	c.	PROPN
ejpam-3915	115	5	armada	armada	PROPN
ejpam-3915	115	6	/	/	SYM
ejpam-3915	115	7	eur	eur	PROPN
ejpam-3915	115	8	.	.	PUNCT
ejpam-3915	116	1	j.	j.	PROPN
ejpam-3915	116	2	pure	pure	PROPN
ejpam-3915	116	3	appl	appl	PROPN
ejpam-3915	116	4	.	.	PROPN
ejpam-3915	116	5	math	math	PROPN
ejpam-3915	116	6	,	,	PUNCT
ejpam-3915	116	7	14	14	NUM
ejpam-3915	116	8	(	(	PUNCT
ejpam-3915	116	9	3	3	NUM
ejpam-3915	116	10	)	)	PUNCT
ejpam-3915	116	11	(	(	PUNCT
ejpam-3915	116	12	2021	2021	NUM
ejpam-3915	116	13	)	)	PUNCT
ejpam-3915	116	14	,	,	PUNCT
ejpam-3915	116	15	1098	1098	NUM
ejpam-3915	116	16	-	-	SYM
ejpam-3915	116	17	1107	1107	NUM
ejpam-3915	116	18	1103	1103	NUM
ejpam-3915	116	19	case	case	NOUN
ejpam-3915	116	20	3	3	NUM
ejpam-3915	116	21	:	:	PUNCT
ejpam-3915	116	22	g	g	PROPN
ejpam-3915	116	23	is	be	AUX
ejpam-3915	116	24	trivial	trivial	ADJ
ejpam-3915	116	25	,	,	PUNCT
ejpam-3915	116	26	γt(h	γt(h	NUM
ejpam-3915	116	27	)	)	PUNCT
ejpam-3915	116	28	=	=	SYM
ejpam-3915	116	29	2	2	NUM
ejpam-3915	116	30	and	and	CCONJ
ejpam-3915	116	31	every	every	DET
ejpam-3915	116	32	vertex	vertex	NOUN
ejpam-3915	116	33	v	v	ADP
ejpam-3915	116	34	∈	∈	PROPN
ejpam-3915	116	35	v	v	NOUN
ejpam-3915	116	36	(	(	PUNCT
ejpam-3915	116	37	h	h	NOUN
ejpam-3915	116	38	)	)	PUNCT
ejpam-3915	116	39	is	be	AUX
ejpam-3915	116	40	contained	contain	VERB
ejpam-3915	116	41	in	in	ADP
ejpam-3915	116	42	a	a	DET
ejpam-3915	116	43	γt	γt	NOUN
ejpam-3915	116	44	-	-	NOUN
ejpam-3915	116	45	set	set	NOUN
ejpam-3915	116	46	of	of	ADP
ejpam-3915	116	47	h	h	NOUN
ejpam-3915	116	48	let	let	VERB
ejpam-3915	116	49	v	v	X
ejpam-3915	116	50	(	(	PUNCT
ejpam-3915	116	51	g	g	NOUN
ejpam-3915	116	52	)	)	PUNCT
ejpam-3915	116	53	=	=	PRON
ejpam-3915	116	54	{	{	PUNCT
ejpam-3915	116	55	x	x	NOUN
ejpam-3915	116	56	}	}	PUNCT
ejpam-3915	116	57	.	.	PUNCT
ejpam-3915	117	1	by	by	ADP
ejpam-3915	117	2	corollary	corollary	ADJ
ejpam-3915	117	3	3.1	3.1	NUM
ejpam-3915	117	4	,	,	PUNCT
ejpam-3915	117	5	for	for	ADP
ejpam-3915	117	6	each	each	DET
ejpam-3915	117	7	u	u	PROPN
ejpam-3915	117	8	∈	∈	PROPN
ejpam-3915	117	9	v	v	NOUN
ejpam-3915	117	10	(	(	PUNCT
ejpam-3915	117	11	h	h	NOUN
ejpam-3915	117	12	)	)	PUNCT
ejpam-3915	117	13	,	,	PUNCT
ejpam-3915	117	14	ru	ru	NOUN
ejpam-3915	117	15	=	=	SYM
ejpam-3915	117	16	{	{	PUNCT
ejpam-3915	117	17	x	x	NOUN
ejpam-3915	117	18	,	,	PUNCT
ejpam-3915	117	19	u	u	NOUN
ejpam-3915	117	20	}	}	PUNCT
ejpam-3915	117	21	is	be	AUX
ejpam-3915	117	22	a	a	DET
ejpam-3915	117	23	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	117	24	-set	-set	PROPN
ejpam-3915	117	25	of	of	ADP
ejpam-3915	117	26	g+h	g+h	PROPN
ejpam-3915	117	27	.	.	PUNCT
ejpam-3915	118	1	also	also	ADV
ejpam-3915	118	2	by	by	ADP
ejpam-3915	118	3	assumption	assumption	NOUN
ejpam-3915	118	4	and	and	CCONJ
ejpam-3915	118	5	corollary	corollary	ADJ
ejpam-3915	118	6	3.1	3.1	NUM
ejpam-3915	118	7	,	,	PUNCT
ejpam-3915	118	8	for	for	ADP
ejpam-3915	118	9	all	all	DET
ejpam-3915	118	10	v	v	NOUN
ejpam-3915	118	11	,	,	PUNCT
ejpam-3915	118	12	w	w	PROPN
ejpam-3915	118	13	∈	∈	PROPN
ejpam-3915	118	14	v	v	ADP
ejpam-3915	118	15	(	(	PUNCT
ejpam-3915	118	16	h	h	NOUN
ejpam-3915	118	17	)	)	PUNCT
ejpam-3915	118	18	such	such	ADJ
ejpam-3915	118	19	that	that	PRON
ejpam-3915	118	20	v	v	NOUN
ejpam-3915	118	21	6=	6=	PROPN
ejpam-3915	118	22	w	w	PROPN
ejpam-3915	118	23	,	,	PUNCT
ejpam-3915	118	24	r	r	NOUN
ejpam-3915	118	25	=	=	SYM
ejpam-3915	118	26	{	{	PUNCT
ejpam-3915	118	27	v	v	NOUN
ejpam-3915	118	28	,	,	PUNCT
ejpam-3915	118	29	w	w	NOUN
ejpam-3915	118	30	}	}	PUNCT
ejpam-3915	118	31	is	be	AUX
ejpam-3915	118	32	a	a	DET
ejpam-3915	118	33	γt	γt	NOUN
ejpam-3915	118	34	-	-	NOUN
ejpam-3915	118	35	set	set	NOUN
ejpam-3915	118	36	of	of	ADP
ejpam-3915	118	37	h	h	NOUN
ejpam-3915	118	38	and	and	CCONJ
ejpam-3915	118	39	a	a	DET
ejpam-3915	118	40	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	118	41	-set	-set	PROPN
ejpam-3915	118	42	of	of	ADP
ejpam-3915	118	43	g	g	PROPN
ejpam-3915	118	44	+	+	CCONJ
ejpam-3915	118	45	h.	h.	PROPN
ejpam-3915	118	46	clearly	clearly	ADV
ejpam-3915	118	47	,	,	PUNCT
ejpam-3915	118	48	no	no	DET
ejpam-3915	118	49	single	single	ADJ
ejpam-3915	118	50	element	element	NOUN
ejpam-3915	118	51	is	be	AUX
ejpam-3915	118	52	contained	contain	VERB
ejpam-3915	118	53	in	in	ADP
ejpam-3915	118	54	exactly	exactly	ADV
ejpam-3915	118	55	one	one	NUM
ejpam-3915	118	56	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	118	57	-set	-set	PUNCT
ejpam-3915	118	58	of	of	ADP
ejpam-3915	118	59	g+h	g+h	PROPN
ejpam-3915	118	60	,	,	PUNCT
ejpam-3915	118	61	that	that	ADV
ejpam-3915	118	62	is	is	ADV
ejpam-3915	118	63	,	,	PUNCT
ejpam-3915	118	64	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3915	118	65	(	(	PUNCT
ejpam-3915	118	66	g+h	g+h	NOUN
ejpam-3915	118	67	)	)	PUNCT
ejpam-3915	118	68	≥	≥	NOUN
ejpam-3915	119	1	2	2	NUM
ejpam-3915	119	2	.	.	PUNCT
ejpam-3915	119	3	consequently	consequently	ADV
ejpam-3915	119	4	,	,	PUNCT
ejpam-3915	119	5	by	by	ADP
ejpam-3915	119	6	corollary	corollary	ADJ
ejpam-3915	119	7	2.10	2.10	NUM
ejpam-3915	119	8	,	,	PUNCT
ejpam-3915	119	9	2	2	NUM
ejpam-3915	119	10	≤	≤	NOUN
ejpam-3915	119	11	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	119	12	(	(	PUNCT
ejpam-3915	119	13	g+h	g+h	NOUN
ejpam-3915	119	14	)	)	PUNCT
ejpam-3915	119	15	≤	≤	NOUN
ejpam-3915	119	16	γ∗tpw	γ∗tpw	PUNCT
ejpam-3915	119	17	(	(	PUNCT
ejpam-3915	119	18	g+h	g+h	NOUN
ejpam-3915	119	19	)	)	PUNCT
ejpam-3915	119	20	=	=	SYM
ejpam-3915	119	21	2	2	X
ejpam-3915	119	22	.	.	X
ejpam-3915	119	23	therefore	therefore	ADV
ejpam-3915	119	24	,	,	PUNCT
ejpam-3915	119	25	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	119	26	(	(	PUNCT
ejpam-3915	119	27	g+h	g+h	NOUN
ejpam-3915	119	28	)	)	PUNCT
ejpam-3915	119	29	=	=	SYM
ejpam-3915	120	1	2	2	X
ejpam-3915	120	2	.	.	X
ejpam-3915	120	3	similarly	similarly	ADV
ejpam-3915	120	4	,	,	PUNCT
ejpam-3915	120	5	ifh	ifh	ADJ
ejpam-3915	120	6	is	be	AUX
ejpam-3915	120	7	trivial	trivial	ADJ
ejpam-3915	120	8	,	,	PUNCT
ejpam-3915	120	9	γt(g	γt(g	NUM
ejpam-3915	120	10	)	)	PUNCT
ejpam-3915	120	11	=	=	SYM
ejpam-3915	120	12	2	2	NUM
ejpam-3915	120	13	and	and	CCONJ
ejpam-3915	120	14	every	every	DET
ejpam-3915	120	15	vertex	vertex	NOUN
ejpam-3915	120	16	v	v	ADP
ejpam-3915	120	17	∈	∈	PROPN
ejpam-3915	120	18	v	v	NOUN
ejpam-3915	120	19	(	(	PUNCT
ejpam-3915	120	20	g	g	NOUN
ejpam-3915	120	21	)	)	PUNCT
ejpam-3915	120	22	is	be	AUX
ejpam-3915	120	23	contained	contain	VERB
ejpam-3915	120	24	in	in	ADP
ejpam-3915	120	25	a	a	DET
ejpam-3915	120	26	γt	γt	NOUN
ejpam-3915	120	27	-	-	NOUN
ejpam-3915	120	28	set	set	NOUN
ejpam-3915	120	29	of	of	ADP
ejpam-3915	120	30	g	g	NOUN
ejpam-3915	120	31	,	,	PUNCT
ejpam-3915	120	32	then	then	ADV
ejpam-3915	120	33	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3915	120	34	(	(	PUNCT
ejpam-3915	120	35	g+h	g+h	NOUN
ejpam-3915	120	36	)	)	PUNCT
ejpam-3915	120	37	=	=	SYM
ejpam-3915	120	38	2	2	X
ejpam-3915	120	39	.	.	X
ejpam-3915	120	40	case	case	NOUN
ejpam-3915	120	41	4	4	NUM
ejpam-3915	120	42	:	:	PUNCT
ejpam-3915	120	43	g	g	NOUN
ejpam-3915	120	44	and	and	CCONJ
ejpam-3915	120	45	h	h	NOUN
ejpam-3915	120	46	are	be	AUX
ejpam-3915	120	47	both	both	PRON
ejpam-3915	120	48	nontrivial	nontrivial	ADJ
ejpam-3915	120	49	graphs	graph	NOUN
ejpam-3915	120	50	.	.	PUNCT
ejpam-3915	121	1	by	by	ADP
ejpam-3915	121	2	corollary	corollary	ADJ
ejpam-3915	121	3	3.1	3.1	NUM
ejpam-3915	121	4	,	,	PUNCT
ejpam-3915	121	5	for	for	ADP
ejpam-3915	121	6	each	each	DET
ejpam-3915	121	7	x	x	SYM
ejpam-3915	121	8	∈	∈	PROPN
ejpam-3915	121	9	v	v	ADP
ejpam-3915	121	10	(	(	PUNCT
ejpam-3915	121	11	g	g	NOUN
ejpam-3915	121	12	)	)	PUNCT
ejpam-3915	121	13	and	and	CCONJ
ejpam-3915	121	14	for	for	ADP
ejpam-3915	121	15	each	each	DET
ejpam-3915	121	16	u	u	PROPN
ejpam-3915	121	17	∈	∈	PROPN
ejpam-3915	121	18	v	v	NOUN
ejpam-3915	121	19	(	(	PUNCT
ejpam-3915	121	20	h	h	NOUN
ejpam-3915	121	21	)	)	PUNCT
ejpam-3915	121	22	,	,	PUNCT
ejpam-3915	121	23	r	r	NOUN
ejpam-3915	121	24	=	=	SYM
ejpam-3915	121	25	{	{	PUNCT
ejpam-3915	121	26	x	x	NOUN
ejpam-3915	121	27	,	,	PUNCT
ejpam-3915	121	28	u	u	NOUN
ejpam-3915	121	29	}	}	PUNCT
ejpam-3915	121	30	is	be	AUX
ejpam-3915	121	31	a	a	DET
ejpam-3915	121	32	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	121	33	-set	-set	PROPN
ejpam-3915	121	34	of	of	ADP
ejpam-3915	121	35	g+h	g+h	PROPN
ejpam-3915	121	36	.	.	PUNCT
ejpam-3915	122	1	thus	thus	ADV
ejpam-3915	122	2	,	,	PUNCT
ejpam-3915	122	3	for	for	ADP
ejpam-3915	122	4	each	each	DET
ejpam-3915	122	5	u	u	PROPN
ejpam-3915	122	6	∈	∈	PROPN
ejpam-3915	122	7	r	r	NOUN
ejpam-3915	122	8	,	,	PUNCT
ejpam-3915	122	9	there	there	PRON
ejpam-3915	122	10	exists	exist	VERB
ejpam-3915	122	11	uy	uy	PROPN
ejpam-3915	122	12	∈	∈	PROPN
ejpam-3915	122	13	v	v	NOUN
ejpam-3915	122	14	(	(	PUNCT
ejpam-3915	122	15	g+h)\r	g+h)\r	NOUN
ejpam-3915	122	16	such	such	ADJ
ejpam-3915	122	17	that	that	SCONJ
ejpam-3915	122	18	[	[	NOUN
ejpam-3915	122	19	r\{u	r\{u	NOUN
ejpam-3915	122	20	}	}	PUNCT
ejpam-3915	122	21	]	]	PUNCT
ejpam-3915	122	22	∪	∪	X
ejpam-3915	122	23	{	{	PUNCT
ejpam-3915	122	24	uy	uy	NOUN
ejpam-3915	122	25	}	}	PUNCT
ejpam-3915	122	26	is	be	AUX
ejpam-3915	122	27	a	a	DET
ejpam-3915	122	28	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	122	29	-set	-set	PROPN
ejpam-3915	122	30	of	of	ADP
ejpam-3915	122	31	g+h	g+h	PROPN
ejpam-3915	122	32	.	.	PUNCT
ejpam-3915	123	1	by	by	ADP
ejpam-3915	123	2	theorem	theorem	NOUN
ejpam-3915	123	3	2.11	2.11	NUM
ejpam-3915	123	4	,	,	PUNCT
ejpam-3915	123	5	it	it	PRON
ejpam-3915	123	6	follows	follow	VERB
ejpam-3915	123	7	that	that	SCONJ
ejpam-3915	123	8	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	123	9	(	(	PUNCT
ejpam-3915	123	10	g+h	g+h	NOUN
ejpam-3915	123	11	)	)	PUNCT
ejpam-3915	123	12	=	=	SYM
ejpam-3915	124	1	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	124	2	(	(	PUNCT
ejpam-3915	124	3	g+h	g+h	NOUN
ejpam-3915	124	4	)	)	PUNCT
ejpam-3915	124	5	=	=	SYM
ejpam-3915	125	1	2	2	X
ejpam-3915	125	2	.	.	PUNCT
ejpam-3915	125	3	the	the	DET
ejpam-3915	125	4	next	next	ADJ
ejpam-3915	125	5	result	result	NOUN
ejpam-3915	125	6	is	be	AUX
ejpam-3915	125	7	a	a	DET
ejpam-3915	125	8	direct	direct	ADJ
ejpam-3915	125	9	consequence	consequence	NOUN
ejpam-3915	125	10	of	of	ADP
ejpam-3915	125	11	corollary	corollary	ADJ
ejpam-3915	125	12	2.4	2.4	NUM
ejpam-3915	125	13	and	and	CCONJ
ejpam-3915	125	14	theorem	theorem	VERB
ejpam-3915	125	15	3.2	3.2	NUM
ejpam-3915	125	16	.	.	PUNCT
ejpam-3915	126	1	corollary	corollary	ADJ
ejpam-3915	126	2	3.3	3.3	NUM
ejpam-3915	126	3	.	.	PUNCT
ejpam-3915	127	1	for	for	ADP
ejpam-3915	127	2	any	any	DET
ejpam-3915	127	3	graph	graph	NOUN
ejpam-3915	127	4	h	h	NOUN
ejpam-3915	127	5	,	,	PUNCT
ejpam-3915	127	6	the	the	DET
ejpam-3915	127	7	total	total	ADJ
ejpam-3915	127	8	dr	dr	PROPN
ejpam-3915	127	9	-	-	PUNCT
ejpam-3915	127	10	power	power	NOUN
ejpam-3915	127	11	domination	domination	NOUN
ejpam-3915	127	12	number	number	NOUN
ejpam-3915	127	13	of	of	ADP
ejpam-3915	127	14	the	the	DET
ejpam-3915	127	15	join	join	NOUN
ejpam-3915	127	16	k1+h	k1+h	PROPN
ejpam-3915	127	17	is	be	AUX
ejpam-3915	127	18	given	give	VERB
ejpam-3915	127	19	by	by	ADP
ejpam-3915	127	20	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	127	21	(	(	PUNCT
ejpam-3915	127	22	k1	k1	NOUN
ejpam-3915	127	23	+	+	NOUN
ejpam-3915	127	24	h	h	NOUN
ejpam-3915	127	25	)	)	PUNCT
ejpam-3915	127	26	=	=	SYM
ejpam-3915	127	27	2	2	NUM
ejpam-3915	127	28	and	and	CCONJ
ejpam-3915	127	29	its	its	PRON
ejpam-3915	127	30	forcing	force	VERB
ejpam-3915	127	31	total	total	ADJ
ejpam-3915	127	32	dr	dr	PROPN
ejpam-3915	127	33	-	-	PUNCT
ejpam-3915	127	34	power	power	NOUN
ejpam-3915	127	35	domination	domination	NOUN
ejpam-3915	127	36	number	number	NOUN
ejpam-3915	127	37	is	be	AUX
ejpam-3915	127	38	given	give	VERB
ejpam-3915	127	39	by	by	ADP
ejpam-3915	127	40	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	127	41	(	(	PUNCT
ejpam-3915	127	42	k1	k1	NOUN
ejpam-3915	127	43	+	+	NOUN
ejpam-3915	127	44	h	h	NOUN
ejpam-3915	127	45	)	)	PUNCT
ejpam-3915	127	46	=	=	SYM
ejpam-3915	127	47			NUM
ejpam-3915	128	1	0	0	PUNCT
ejpam-3915	128	2	,	,	PUNCT
ejpam-3915	128	3	if	if	SCONJ
ejpam-3915	128	4	h	h	NOUN
ejpam-3915	128	5	is	be	AUX
ejpam-3915	128	6	trivial	trivial	ADJ
ejpam-3915	128	7	,	,	PUNCT
ejpam-3915	128	8	1	1	NUM
ejpam-3915	128	9	,	,	PUNCT
ejpam-3915	128	10	if	if	SCONJ
ejpam-3915	128	11	h	h	NOUN
ejpam-3915	128	12	has	have	VERB
ejpam-3915	128	13	an	an	DET
ejpam-3915	128	14	isolated	isolated	ADJ
ejpam-3915	128	15	vertex	vertex	NOUN
ejpam-3915	128	16	,	,	PUNCT
ejpam-3915	128	17	or	or	CCONJ
ejpam-3915	128	18	γt(h	γt(h	NUM
ejpam-3915	128	19	)	)	PUNCT
ejpam-3915	128	20	>	>	X
ejpam-3915	129	1	2	2	NUM
ejpam-3915	129	2	,	,	PUNCT
ejpam-3915	129	3	or	or	CCONJ
ejpam-3915	129	4	γt(h	γt(h	NUM
ejpam-3915	129	5	)	)	PUNCT
ejpam-3915	129	6	=	=	SYM
ejpam-3915	129	7	2	2	NUM
ejpam-3915	129	8	and	and	CCONJ
ejpam-3915	129	9	there	there	PRON
ejpam-3915	129	10	exists	exist	VERB
ejpam-3915	129	11	a	a	DET
ejpam-3915	129	12	vertex	vertex	NOUN
ejpam-3915	129	13	in	in	ADP
ejpam-3915	129	14	h	h	NOUN
ejpam-3915	129	15	which	which	PRON
ejpam-3915	129	16	is	be	AUX
ejpam-3915	129	17	not	not	PART
ejpam-3915	129	18	in	in	ADP
ejpam-3915	129	19	any	any	DET
ejpam-3915	129	20	γt	γt	NOUN
ejpam-3915	129	21	-	-	NOUN
ejpam-3915	129	22	set	set	NOUN
ejpam-3915	129	23	of	of	ADP
ejpam-3915	129	24	h	h	NOUN
ejpam-3915	129	25	,	,	PUNCT
ejpam-3915	129	26	2	2	NUM
ejpam-3915	129	27	,	,	PUNCT
ejpam-3915	129	28	otherwise	otherwise	ADV
ejpam-3915	129	29	.	.	PUNCT
ejpam-3915	130	1	corollary	corollary	ADJ
ejpam-3915	130	2	3.4	3.4	NUM
ejpam-3915	130	3	.	.	PUNCT
ejpam-3915	131	1	the	the	DET
ejpam-3915	131	2	total	total	ADJ
ejpam-3915	131	3	dr	dr	PROPN
ejpam-3915	131	4	-	-	PUNCT
ejpam-3915	131	5	power	power	NOUN
ejpam-3915	131	6	domination	domination	NOUN
ejpam-3915	131	7	number	number	NOUN
ejpam-3915	131	8	of	of	ADP
ejpam-3915	131	9	the	the	DET
ejpam-3915	131	10	complete	complete	ADJ
ejpam-3915	131	11	bipartite	bipartite	PROPN
ejpam-3915	131	12	kn	kn	PROPN
ejpam-3915	131	13	,	,	PUNCT
ejpam-3915	131	14	m	m	VERB
ejpam-3915	131	15	=	=	ADJ
ejpam-3915	131	16	kn	kn	PROPN
ejpam-3915	132	1	+	+	CCONJ
ejpam-3915	132	2	km	km	NOUN
ejpam-3915	132	3	such	such	ADJ
ejpam-3915	132	4	that	that	SCONJ
ejpam-3915	132	5	n	n	CCONJ
ejpam-3915	132	6	,	,	PUNCT
ejpam-3915	132	7	m	m	VERB
ejpam-3915	132	8	≥	≥	NOUN
ejpam-3915	132	9	1	1	NUM
ejpam-3915	132	10	,	,	PUNCT
ejpam-3915	132	11	is	be	AUX
ejpam-3915	132	12	given	give	VERB
ejpam-3915	132	13	by	by	ADP
ejpam-3915	132	14	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	132	15	(	(	PUNCT
ejpam-3915	132	16	kn	kn	PROPN
ejpam-3915	132	17	,	,	PUNCT
ejpam-3915	132	18	m	m	PROPN
ejpam-3915	132	19	)	)	PUNCT
ejpam-3915	132	20	=	=	SYM
ejpam-3915	132	21	2	2	NUM
ejpam-3915	132	22	and	and	CCONJ
ejpam-3915	132	23	its	its	PRON
ejpam-3915	132	24	forcing	force	VERB
ejpam-3915	132	25	total	total	ADJ
ejpam-3915	132	26	dr	dr	PROPN
ejpam-3915	132	27	-	-	PUNCT
ejpam-3915	132	28	power	power	NOUN
ejpam-3915	132	29	domination	domination	NOUN
ejpam-3915	132	30	number	number	NOUN
ejpam-3915	132	31	is	be	AUX
ejpam-3915	132	32	given	give	VERB
ejpam-3915	132	33	by	by	ADP
ejpam-3915	132	34	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	132	35	(	(	PUNCT
ejpam-3915	132	36	kn	kn	PROPN
ejpam-3915	132	37	,	,	PUNCT
ejpam-3915	132	38	m	m	PROPN
ejpam-3915	132	39	)	)	PUNCT
ejpam-3915	132	40	=	=	SYM
ejpam-3915	132	41			X
ejpam-3915	132	42	0	0	NUM
ejpam-3915	132	43	,	,	PUNCT
ejpam-3915	132	44	n	n	NOUN
ejpam-3915	132	45	=	=	SYM
ejpam-3915	132	46	1	1	NUM
ejpam-3915	132	47	and	and	CCONJ
ejpam-3915	132	48	m	m	PROPN
ejpam-3915	132	49	=	=	ADJ
ejpam-3915	132	50	1	1	NUM
ejpam-3915	132	51	,	,	PUNCT
ejpam-3915	132	52	1	1	NUM
ejpam-3915	132	53	,	,	PUNCT
ejpam-3915	132	54	n	n	NOUN
ejpam-3915	132	55	=	=	SYM
ejpam-3915	132	56	1	1	NUM
ejpam-3915	132	57	and	and	CCONJ
ejpam-3915	132	58	m	m	PROPN
ejpam-3915	132	59	≥	≥	NOUN
ejpam-3915	132	60	2	2	NUM
ejpam-3915	132	61	or	or	CCONJ
ejpam-3915	132	62	m	m	NOUN
ejpam-3915	132	63	=	=	NOUN
ejpam-3915	132	64	1	1	NUM
ejpam-3915	132	65	and	and	CCONJ
ejpam-3915	132	66	n	n	PRON
ejpam-3915	132	67	≥	≥	NOUN
ejpam-3915	132	68	2	2	NUM
ejpam-3915	132	69	,	,	PUNCT
ejpam-3915	132	70	2	2	NUM
ejpam-3915	132	71	,	,	PUNCT
ejpam-3915	132	72	n	n	PRON
ejpam-3915	132	73	≥	≥	NOUN
ejpam-3915	132	74	2	2	NUM
ejpam-3915	132	75	and	and	CCONJ
ejpam-3915	132	76	m	m	PROPN
ejpam-3915	132	77	≥	≥	NOUN
ejpam-3915	132	78	2	2	NUM
ejpam-3915	132	79	.	.	PUNCT
ejpam-3915	133	1	proof	proof	NOUN
ejpam-3915	133	2	.	.	PUNCT
ejpam-3915	134	1	by	by	ADP
ejpam-3915	134	2	corollary	corollary	ADJ
ejpam-3915	134	3	2.4	2.4	NUM
ejpam-3915	134	4	,	,	PUNCT
ejpam-3915	134	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	134	6	(	(	PUNCT
ejpam-3915	134	7	kn	kn	PROPN
ejpam-3915	134	8	,	,	PUNCT
ejpam-3915	134	9	m	m	PROPN
ejpam-3915	134	10	)	)	PUNCT
ejpam-3915	134	11	=	=	SYM
ejpam-3915	134	12	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	134	13	(	(	PUNCT
ejpam-3915	134	14	kn	kn	NOUN
ejpam-3915	134	15	+	+	PROPN
ejpam-3915	134	16	km	km	NOUN
ejpam-3915	134	17	)	)	PUNCT
ejpam-3915	134	18	=	=	SYM
ejpam-3915	134	19	2	2	X
ejpam-3915	134	20	.	.	X
ejpam-3915	135	1	if	if	SCONJ
ejpam-3915	135	2	n	n	NOUN
ejpam-3915	135	3	=	=	SYM
ejpam-3915	135	4	1	1	NUM
ejpam-3915	135	5	and	and	CCONJ
ejpam-3915	135	6	m	m	PROPN
ejpam-3915	135	7	=	=	ADJ
ejpam-3915	135	8	1	1	NUM
ejpam-3915	135	9	,	,	PUNCT
ejpam-3915	135	10	then	then	ADV
ejpam-3915	135	11	k1	k1	PROPN
ejpam-3915	135	12	=	=	SYM
ejpam-3915	135	13	k1	k1	PROPN
ejpam-3915	135	14	is	be	AUX
ejpam-3915	135	15	trivial	trivial	ADJ
ejpam-3915	135	16	,	,	PUNCT
ejpam-3915	135	17	and	and	CCONJ
ejpam-3915	135	18	so	so	ADV
ejpam-3915	135	19	by	by	ADP
ejpam-3915	135	20	corollary	corollary	ADJ
ejpam-3915	135	21	3.3	3.3	NUM
ejpam-3915	135	22	,	,	PUNCT
ejpam-3915	135	23	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	135	24	(	(	PUNCT
ejpam-3915	135	25	k1,1	k1,1	NOUN
ejpam-3915	135	26	)	)	PUNCT
ejpam-3915	135	27	=	=	SYM
ejpam-3915	136	1	0	0	X
ejpam-3915	136	2	.	.	PUNCT
ejpam-3915	137	1	if	if	SCONJ
ejpam-3915	137	2	n	n	NOUN
ejpam-3915	137	3	=	=	SYM
ejpam-3915	137	4	1	1	NUM
ejpam-3915	137	5	and	and	CCONJ
ejpam-3915	137	6	m	m	PROPN
ejpam-3915	137	7	≥	≥	NOUN
ejpam-3915	137	8	2	2	NUM
ejpam-3915	137	9	,	,	PUNCT
ejpam-3915	137	10	then	then	ADV
ejpam-3915	137	11	km	km	PROPN
ejpam-3915	137	12	has	have	VERB
ejpam-3915	137	13	an	an	DET
ejpam-3915	137	14	isolated	isolated	ADJ
ejpam-3915	137	15	vertex	vertex	NOUN
ejpam-3915	137	16	,	,	PUNCT
ejpam-3915	137	17	and	and	CCONJ
ejpam-3915	137	18	so	so	ADV
ejpam-3915	137	19	by	by	ADP
ejpam-3915	137	20	corollary	corollary	ADJ
ejpam-3915	137	21	3.3	3.3	NUM
ejpam-3915	137	22	,	,	PUNCT
ejpam-3915	137	23	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	137	24	(	(	PUNCT
ejpam-3915	137	25	k1,m	k1,m	PROPN
ejpam-3915	137	26	)	)	PUNCT
ejpam-3915	137	27	=	=	SYM
ejpam-3915	138	1	1	1	X
ejpam-3915	138	2	.	.	X
ejpam-3915	138	3	similarly	similarly	ADV
ejpam-3915	138	4	,	,	PUNCT
ejpam-3915	138	5	if	if	SCONJ
ejpam-3915	138	6	m	m	ADV
ejpam-3915	138	7	=	=	SYM
ejpam-3915	138	8	1	1	NUM
ejpam-3915	138	9	and	and	CCONJ
ejpam-3915	138	10	n	n	PRON
ejpam-3915	138	11	≥	≥	NOUN
ejpam-3915	138	12	2	2	NUM
ejpam-3915	138	13	,	,	PUNCT
ejpam-3915	138	14	then	then	ADV
ejpam-3915	138	15	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3915	138	16	(	(	PUNCT
ejpam-3915	138	17	kn,1	kn,1	PROPN
ejpam-3915	138	18	)	)	PUNCT
ejpam-3915	138	19	=	=	PUNCT
ejpam-3915	139	1	1	1	X
ejpam-3915	139	2	.	.	PUNCT
ejpam-3915	140	1	if	if	SCONJ
ejpam-3915	140	2	n	n	NUM
ejpam-3915	140	3	≥	≥	NOUN
ejpam-3915	140	4	2	2	NUM
ejpam-3915	140	5	and	and	CCONJ
ejpam-3915	140	6	m	m	PROPN
ejpam-3915	140	7	≥	≥	NOUN
ejpam-3915	140	8	2	2	NUM
ejpam-3915	140	9	,	,	PUNCT
ejpam-3915	140	10	then	then	ADV
ejpam-3915	140	11	kn	kn	PROPN
ejpam-3915	140	12	and	and	CCONJ
ejpam-3915	140	13	km	km	PROPN
ejpam-3915	140	14	are	be	AUX
ejpam-3915	140	15	nontrivial	nontrivial	ADJ
ejpam-3915	140	16	graphs	graph	NOUN
ejpam-3915	140	17	and	and	CCONJ
ejpam-3915	140	18	so	so	ADV
ejpam-3915	140	19	,	,	PUNCT
ejpam-3915	140	20	by	by	ADP
ejpam-3915	140	21	theorem	theorem	NOUN
ejpam-3915	140	22	3.2	3.2	NUM
ejpam-3915	140	23	,	,	PUNCT
ejpam-3915	140	24	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	140	25	(	(	PUNCT
ejpam-3915	140	26	kn	kn	PROPN
ejpam-3915	140	27	,	,	PUNCT
ejpam-3915	140	28	m	m	PROPN
ejpam-3915	140	29	)	)	PUNCT
ejpam-3915	141	1	=	=	SYM
ejpam-3915	141	2	2	2	X
ejpam-3915	141	3	.	.	PUNCT
ejpam-3915	141	4	c.	c.	PROPN
ejpam-3915	141	5	armada	armada	PROPN
ejpam-3915	141	6	/	/	SYM
ejpam-3915	141	7	eur	eur	PROPN
ejpam-3915	141	8	.	.	PUNCT
ejpam-3915	142	1	j.	j.	PROPN
ejpam-3915	142	2	pure	pure	PROPN
ejpam-3915	142	3	appl	appl	PROPN
ejpam-3915	142	4	.	.	PROPN
ejpam-3915	142	5	math	math	PROPN
ejpam-3915	142	6	,	,	PUNCT
ejpam-3915	142	7	14	14	NUM
ejpam-3915	142	8	(	(	PUNCT
ejpam-3915	142	9	3	3	NUM
ejpam-3915	142	10	)	)	PUNCT
ejpam-3915	142	11	(	(	PUNCT
ejpam-3915	142	12	2021	2021	NUM
ejpam-3915	142	13	)	)	PUNCT
ejpam-3915	142	14	,	,	PUNCT
ejpam-3915	142	15	1098	1098	NUM
ejpam-3915	142	16	-	-	SYM
ejpam-3915	142	17	1107	1107	NUM
ejpam-3915	142	18	1104	1104	NUM
ejpam-3915	142	19	corollary	corollary	ADJ
ejpam-3915	142	20	3.5	3.5	NUM
ejpam-3915	142	21	.	.	PUNCT
ejpam-3915	143	1	the	the	DET
ejpam-3915	143	2	total	total	ADJ
ejpam-3915	143	3	dr	dr	PROPN
ejpam-3915	143	4	-	-	PUNCT
ejpam-3915	143	5	power	power	NOUN
ejpam-3915	143	6	domination	domination	NOUN
ejpam-3915	143	7	number	number	NOUN
ejpam-3915	143	8	of	of	ADP
ejpam-3915	143	9	the	the	DET
ejpam-3915	143	10	generalized	generalized	ADJ
ejpam-3915	143	11	fan	fan	NOUN
ejpam-3915	143	12	fn	fn	PROPN
ejpam-3915	143	13	,	,	PUNCT
ejpam-3915	143	14	m	m	VERB
ejpam-3915	143	15	=	=	ADJ
ejpam-3915	143	16	kn	kn	PROPN
ejpam-3915	143	17	+	+	CCONJ
ejpam-3915	143	18	pm	pm	PROPN
ejpam-3915	143	19	,	,	PUNCT
ejpam-3915	143	20	where	where	SCONJ
ejpam-3915	143	21	n	n	PRON
ejpam-3915	143	22	≥	≥	NOUN
ejpam-3915	143	23	1	1	NUM
ejpam-3915	143	24	and	and	CCONJ
ejpam-3915	143	25	m	m	PROPN
ejpam-3915	143	26	≥	≥	NOUN
ejpam-3915	143	27	2	2	NUM
ejpam-3915	143	28	,	,	PUNCT
ejpam-3915	143	29	is	be	AUX
ejpam-3915	143	30	given	give	VERB
ejpam-3915	143	31	by	by	ADP
ejpam-3915	143	32	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	143	33	(	(	PUNCT
ejpam-3915	143	34	fn	fn	NOUN
ejpam-3915	143	35	,	,	PUNCT
ejpam-3915	143	36	m	m	NOUN
ejpam-3915	143	37	)	)	PUNCT
ejpam-3915	143	38	=	=	SYM
ejpam-3915	143	39	2	2	NUM
ejpam-3915	143	40	and	and	CCONJ
ejpam-3915	143	41	its	its	PRON
ejpam-3915	143	42	forcing	force	VERB
ejpam-3915	143	43	total	total	ADJ
ejpam-3915	143	44	dr	dr	PROPN
ejpam-3915	143	45	-	-	PUNCT
ejpam-3915	143	46	power	power	NOUN
ejpam-3915	143	47	domination	domination	NOUN
ejpam-3915	143	48	number	number	NOUN
ejpam-3915	143	49	is	be	AUX
ejpam-3915	143	50	given	give	VERB
ejpam-3915	143	51	by	by	ADP
ejpam-3915	143	52	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	143	53	(	(	PUNCT
ejpam-3915	143	54	fn	fn	NOUN
ejpam-3915	143	55	,	,	PUNCT
ejpam-3915	143	56	m	m	NOUN
ejpam-3915	143	57	)	)	PUNCT
ejpam-3915	143	58	=	=	PRON
ejpam-3915	143	59	{	{	PUNCT
ejpam-3915	143	60	1	1	NUM
ejpam-3915	143	61	,	,	PUNCT
ejpam-3915	143	62	n	n	NOUN
ejpam-3915	143	63	=	=	SYM
ejpam-3915	143	64	1	1	NUM
ejpam-3915	143	65	and	and	CCONJ
ejpam-3915	143	66	m	m	PRON
ejpam-3915	143	67	≥	≥	NOUN
ejpam-3915	143	68	4	4	NUM
ejpam-3915	143	69	,	,	PUNCT
ejpam-3915	143	70	2	2	NUM
ejpam-3915	143	71	,	,	PUNCT
ejpam-3915	143	72	otherwise	otherwise	ADV
ejpam-3915	143	73	.	.	PUNCT
ejpam-3915	144	1	proof	proof	NOUN
ejpam-3915	144	2	.	.	PUNCT
ejpam-3915	145	1	by	by	ADP
ejpam-3915	145	2	corollary	corollary	ADJ
ejpam-3915	145	3	2.4	2.4	NUM
ejpam-3915	145	4	,	,	PUNCT
ejpam-3915	145	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	145	6	(	(	PUNCT
ejpam-3915	145	7	fn	fn	NOUN
ejpam-3915	145	8	,	,	PUNCT
ejpam-3915	145	9	m	m	NOUN
ejpam-3915	145	10	)	)	PUNCT
ejpam-3915	145	11	=	=	SYM
ejpam-3915	145	12	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	145	13	(	(	PUNCT
ejpam-3915	145	14	kn	kn	NOUN
ejpam-3915	145	15	+	+	CCONJ
ejpam-3915	145	16	pm	pm	NOUN
ejpam-3915	145	17	)	)	PUNCT
ejpam-3915	145	18	=	=	SYM
ejpam-3915	145	19	2	2	X
ejpam-3915	145	20	.	.	X
ejpam-3915	145	21	let	let	VERB
ejpam-3915	145	22	pn	pn	VERB
ejpam-3915	145	23	=	=	PUNCT
ejpam-3915	146	1	[	[	X
ejpam-3915	146	2	u1	u1	NOUN
ejpam-3915	146	3	,	,	PUNCT
ejpam-3915	146	4	u2	u2	NOUN
ejpam-3915	146	5	,	,	PUNCT
ejpam-3915	146	6	.	.	PUNCT
ejpam-3915	146	7	.	.	PUNCT
ejpam-3915	146	8	.	.	PUNCT
ejpam-3915	147	1	,	,	PUNCT
ejpam-3915	147	2	un	un	PROPN
ejpam-3915	147	3	]	]	X
ejpam-3915	147	4	.	.	PUNCT
ejpam-3915	148	1	if	if	SCONJ
ejpam-3915	148	2	n	n	NUM
ejpam-3915	148	3	=	=	SYM
ejpam-3915	148	4	1	1	NUM
ejpam-3915	148	5	and	and	CCONJ
ejpam-3915	148	6	m	m	PROPN
ejpam-3915	148	7	=	=	ADJ
ejpam-3915	148	8	4	4	NUM
ejpam-3915	148	9	,	,	PUNCT
ejpam-3915	148	10	then	then	ADV
ejpam-3915	148	11	by	by	ADP
ejpam-3915	148	12	proposition	proposition	NOUN
ejpam-3915	148	13	2.2	2.2	NUM
ejpam-3915	148	14	,	,	PUNCT
ejpam-3915	148	15	γt(p4	γt(p4	NOUN
ejpam-3915	148	16	)	)	PUNCT
ejpam-3915	148	17	=	=	SYM
ejpam-3915	148	18	2	2	NUM
ejpam-3915	148	19	and	and	CCONJ
ejpam-3915	148	20	p4	p4	NOUN
ejpam-3915	148	21	has	have	VERB
ejpam-3915	148	22	exactly	exactly	ADV
ejpam-3915	148	23	one	one	NUM
ejpam-3915	148	24	γt	γt	NOUN
ejpam-3915	148	25	-	-	VERB
ejpam-3915	148	26	set	set	NOUN
ejpam-3915	148	27	which	which	PRON
ejpam-3915	148	28	is	be	AUX
ejpam-3915	148	29	{	{	PUNCT
ejpam-3915	148	30	u2	u2	NOUN
ejpam-3915	148	31	,	,	PUNCT
ejpam-3915	148	32	u3	u3	NOUN
ejpam-3915	148	33	}	}	PUNCT
ejpam-3915	148	34	,	,	PUNCT
ejpam-3915	148	35	that	that	ADV
ejpam-3915	148	36	is	is	ADV
ejpam-3915	148	37	,	,	PUNCT
ejpam-3915	148	38	u1	u1	PROPN
ejpam-3915	148	39	is	be	AUX
ejpam-3915	148	40	a	a	DET
ejpam-3915	148	41	vertex	vertex	NOUN
ejpam-3915	148	42	not	not	PART
ejpam-3915	148	43	in	in	ADP
ejpam-3915	148	44	a	a	DET
ejpam-3915	148	45	γt	γt	NOUN
ejpam-3915	148	46	-	-	NOUN
ejpam-3915	148	47	set	set	NOUN
ejpam-3915	148	48	of	of	ADP
ejpam-3915	148	49	p4	p4	NOUN
ejpam-3915	148	50	.	.	PUNCT
ejpam-3915	149	1	by	by	ADP
ejpam-3915	149	2	corollary	corollary	ADJ
ejpam-3915	149	3	3.3	3.3	NUM
ejpam-3915	149	4	,	,	PUNCT
ejpam-3915	149	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	149	6	(	(	PUNCT
ejpam-3915	149	7	f1,4	f1,4	ADV
ejpam-3915	149	8	)	)	PUNCT
ejpam-3915	149	9	=	=	SYM
ejpam-3915	149	10	1	1	X
ejpam-3915	149	11	.	.	PUNCT
ejpam-3915	150	1	if	if	SCONJ
ejpam-3915	150	2	n	n	NOUN
ejpam-3915	150	3	=	=	SYM
ejpam-3915	150	4	1	1	NUM
ejpam-3915	150	5	and	and	CCONJ
ejpam-3915	150	6	m	m	VERB
ejpam-3915	150	7	>	>	X
ejpam-3915	150	8	4	4	NUM
ejpam-3915	150	9	,	,	PUNCT
ejpam-3915	150	10	then	then	ADV
ejpam-3915	150	11	by	by	ADP
ejpam-3915	150	12	proposition	proposition	NOUN
ejpam-3915	150	13	2.2	2.2	NUM
ejpam-3915	150	14	,	,	PUNCT
ejpam-3915	150	15	γt(pm	γt(pm	PROPN
ejpam-3915	150	16	)	)	PUNCT
ejpam-3915	150	17	>	>	X
ejpam-3915	151	1	2	2	X
ejpam-3915	151	2	.	.	PUNCT
ejpam-3915	151	3	by	by	ADP
ejpam-3915	151	4	corollary	corollary	ADJ
ejpam-3915	151	5	3.3	3.3	NUM
ejpam-3915	151	6	,	,	PUNCT
ejpam-3915	151	7	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	151	8	(	(	PUNCT
ejpam-3915	151	9	f1,m	f1,m	PROPN
ejpam-3915	151	10	)	)	PUNCT
ejpam-3915	151	11	=	=	NOUN
ejpam-3915	151	12	1	1	X
ejpam-3915	151	13	.	.	PUNCT
ejpam-3915	152	1	if	if	SCONJ
ejpam-3915	152	2	n	n	NOUN
ejpam-3915	152	3	=	=	SYM
ejpam-3915	152	4	1	1	NUM
ejpam-3915	152	5	and	and	CCONJ
ejpam-3915	152	6	m	m	VERB
ejpam-3915	152	7	<	<	X
ejpam-3915	152	8	4	4	NUM
ejpam-3915	152	9	,	,	PUNCT
ejpam-3915	152	10	then	then	ADV
ejpam-3915	152	11	by	by	ADP
ejpam-3915	152	12	proposition	proposition	NOUN
ejpam-3915	152	13	2.2	2.2	NUM
ejpam-3915	152	14	,	,	PUNCT
ejpam-3915	152	15	γt(p2	γt(p2	NOUN
ejpam-3915	152	16	)	)	PUNCT
ejpam-3915	152	17	=	=	SYM
ejpam-3915	153	1	γt(p3	γt(p3	NOUN
ejpam-3915	153	2	)	)	PUNCT
ejpam-3915	153	3	=	=	SYM
ejpam-3915	153	4	2	2	NUM
ejpam-3915	153	5	and	and	CCONJ
ejpam-3915	153	6	so	so	ADV
ejpam-3915	153	7	,	,	PUNCT
ejpam-3915	153	8	{	{	PUNCT
ejpam-3915	153	9	u1	u1	NOUN
ejpam-3915	153	10	,	,	PUNCT
ejpam-3915	153	11	u2	u2	PROPN
ejpam-3915	153	12	}	}	PUNCT
ejpam-3915	153	13	is	be	AUX
ejpam-3915	153	14	the	the	DET
ejpam-3915	153	15	γt	γt	NOUN
ejpam-3915	153	16	-	-	NOUN
ejpam-3915	153	17	set	set	NOUN
ejpam-3915	153	18	of	of	ADP
ejpam-3915	153	19	p2	p2	PROPN
ejpam-3915	153	20	while	while	SCONJ
ejpam-3915	153	21	{	{	PUNCT
ejpam-3915	153	22	u1	u1	NOUN
ejpam-3915	153	23	,	,	PUNCT
ejpam-3915	153	24	u2	u2	PROPN
ejpam-3915	153	25	}	}	PUNCT
ejpam-3915	153	26	and	and	CCONJ
ejpam-3915	153	27	{	{	PUNCT
ejpam-3915	153	28	u2	u2	NOUN
ejpam-3915	153	29	,	,	PUNCT
ejpam-3915	153	30	u3	u3	PROPN
ejpam-3915	153	31	}	}	PUNCT
ejpam-3915	153	32	are	be	AUX
ejpam-3915	153	33	γt	γt	NOUN
ejpam-3915	153	34	-	-	NOUN
ejpam-3915	153	35	sets	set	NOUN
ejpam-3915	153	36	of	of	ADP
ejpam-3915	153	37	p3	p3	PROPN
ejpam-3915	153	38	.	.	PUNCT
ejpam-3915	154	1	clearly	clearly	ADV
ejpam-3915	154	2	,	,	PUNCT
ejpam-3915	154	3	for	for	ADP
ejpam-3915	154	4	m	m	PROPN
ejpam-3915	154	5	=	=	SYM
ejpam-3915	154	6	2	2	NUM
ejpam-3915	154	7	,	,	PUNCT
ejpam-3915	154	8	3	3	NUM
ejpam-3915	154	9	,	,	PUNCT
ejpam-3915	154	10	every	every	DET
ejpam-3915	154	11	vertex	vertex	NOUN
ejpam-3915	154	12	ui	ui	PROPN
ejpam-3915	154	13	∈	∈	PROPN
ejpam-3915	154	14	v	v	ADP
ejpam-3915	154	15	(	(	PUNCT
ejpam-3915	154	16	pm	pm	NOUN
ejpam-3915	154	17	)	)	PUNCT
ejpam-3915	154	18	is	be	AUX
ejpam-3915	154	19	contained	contain	VERB
ejpam-3915	154	20	in	in	ADP
ejpam-3915	154	21	a	a	DET
ejpam-3915	154	22	γt	γt	NOUN
ejpam-3915	154	23	-	-	NOUN
ejpam-3915	154	24	set	set	NOUN
ejpam-3915	154	25	of	of	ADP
ejpam-3915	154	26	pm	pm	NOUN
ejpam-3915	154	27	.	.	PUNCT
ejpam-3915	155	1	by	by	ADP
ejpam-3915	155	2	corollary	corollary	ADJ
ejpam-3915	155	3	3.3	3.3	NUM
ejpam-3915	155	4	,	,	PUNCT
ejpam-3915	155	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	155	6	(	(	PUNCT
ejpam-3915	155	7	f1,m	f1,m	PROPN
ejpam-3915	155	8	)	)	PUNCT
ejpam-3915	155	9	=	=	SYM
ejpam-3915	155	10	2	2	X
ejpam-3915	155	11	.	.	X
ejpam-3915	156	1	if	if	SCONJ
ejpam-3915	156	2	n	n	NUM
ejpam-3915	156	3	≥	≥	NOUN
ejpam-3915	156	4	2	2	NUM
ejpam-3915	156	5	and	and	CCONJ
ejpam-3915	156	6	m	m	PROPN
ejpam-3915	156	7	≥	≥	NOUN
ejpam-3915	156	8	2	2	NUM
ejpam-3915	156	9	,	,	PUNCT
ejpam-3915	156	10	then	then	ADV
ejpam-3915	156	11	kn	kn	PROPN
ejpam-3915	156	12	and	and	CCONJ
ejpam-3915	156	13	pm	pm	NOUN
ejpam-3915	156	14	are	be	AUX
ejpam-3915	156	15	nontrivial	nontrivial	ADJ
ejpam-3915	156	16	graphs	graph	NOUN
ejpam-3915	156	17	.	.	PUNCT
ejpam-3915	157	1	by	by	ADP
ejpam-3915	157	2	corollary	corollary	ADJ
ejpam-3915	157	3	3.3	3.3	NUM
ejpam-3915	157	4	,	,	PUNCT
ejpam-3915	157	5	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	157	6	(	(	PUNCT
ejpam-3915	157	7	fn	fn	NOUN
ejpam-3915	157	8	,	,	PUNCT
ejpam-3915	157	9	m	m	NOUN
ejpam-3915	157	10	)	)	PUNCT
ejpam-3915	157	11	=	=	SYM
ejpam-3915	157	12	2	2	X
ejpam-3915	157	13	.	.	PUNCT
ejpam-3915	157	14	corollary	corollary	ADJ
ejpam-3915	157	15	3.6	3.6	NUM
ejpam-3915	157	16	.	.	PUNCT
ejpam-3915	158	1	the	the	DET
ejpam-3915	158	2	total	total	ADJ
ejpam-3915	158	3	dr	dr	PROPN
ejpam-3915	158	4	-	-	PUNCT
ejpam-3915	158	5	power	power	NOUN
ejpam-3915	158	6	domination	domination	NOUN
ejpam-3915	158	7	number	number	NOUN
ejpam-3915	158	8	of	of	ADP
ejpam-3915	158	9	the	the	DET
ejpam-3915	158	10	generalized	generalize	VERB
ejpam-3915	158	11	wheel	wheel	NOUN
ejpam-3915	158	12	wn	wn	PROPN
ejpam-3915	158	13	,	,	PUNCT
ejpam-3915	158	14	m	m	VERB
ejpam-3915	158	15	=	=	ADJ
ejpam-3915	158	16	kn	kn	PROPN
ejpam-3915	158	17	+	+	CCONJ
ejpam-3915	158	18	cm	cm	NOUN
ejpam-3915	158	19	,	,	PUNCT
ejpam-3915	158	20	where	where	SCONJ
ejpam-3915	158	21	n	n	PRON
ejpam-3915	158	22	≥	≥	NOUN
ejpam-3915	158	23	1	1	NUM
ejpam-3915	158	24	and	and	CCONJ
ejpam-3915	158	25	m	m	PROPN
ejpam-3915	158	26	≥	≥	NOUN
ejpam-3915	158	27	3	3	NUM
ejpam-3915	158	28	,	,	PUNCT
ejpam-3915	158	29	is	be	AUX
ejpam-3915	158	30	given	give	VERB
ejpam-3915	158	31	by	by	ADP
ejpam-3915	158	32	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	158	33	(	(	PUNCT
ejpam-3915	158	34	wn	wn	PROPN
ejpam-3915	158	35	,	,	PUNCT
ejpam-3915	158	36	m	m	PROPN
ejpam-3915	158	37	)	)	PUNCT
ejpam-3915	158	38	=	=	SYM
ejpam-3915	158	39	2	2	NUM
ejpam-3915	158	40	and	and	CCONJ
ejpam-3915	158	41	its	its	PRON
ejpam-3915	158	42	forcing	force	VERB
ejpam-3915	158	43	total	total	ADJ
ejpam-3915	158	44	dr	dr	PROPN
ejpam-3915	158	45	-	-	PUNCT
ejpam-3915	158	46	power	power	NOUN
ejpam-3915	158	47	domination	domination	NOUN
ejpam-3915	158	48	number	number	NOUN
ejpam-3915	158	49	is	be	AUX
ejpam-3915	158	50	given	give	VERB
ejpam-3915	158	51	by	by	ADP
ejpam-3915	158	52	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	158	53	(	(	PUNCT
ejpam-3915	158	54	wn	wn	PROPN
ejpam-3915	158	55	,	,	PUNCT
ejpam-3915	158	56	m	m	PROPN
ejpam-3915	158	57	)	)	PUNCT
ejpam-3915	159	1	=	=	PRON
ejpam-3915	159	2	{	{	PUNCT
ejpam-3915	159	3	1	1	NUM
ejpam-3915	159	4	,	,	PUNCT
ejpam-3915	159	5	n	n	NOUN
ejpam-3915	159	6	=	=	SYM
ejpam-3915	159	7	1	1	NUM
ejpam-3915	159	8	and	and	CCONJ
ejpam-3915	159	9	m	m	PRON
ejpam-3915	159	10	≥	≥	NOUN
ejpam-3915	159	11	5	5	NUM
ejpam-3915	159	12	,	,	PUNCT
ejpam-3915	159	13	2	2	NUM
ejpam-3915	159	14	,	,	PUNCT
ejpam-3915	159	15	otherwise	otherwise	ADV
ejpam-3915	159	16	.	.	PUNCT
ejpam-3915	160	1	proof	proof	NOUN
ejpam-3915	160	2	.	.	PUNCT
ejpam-3915	161	1	by	by	ADP
ejpam-3915	161	2	corollary	corollary	ADJ
ejpam-3915	161	3	2.4	2.4	NUM
ejpam-3915	161	4	,	,	PUNCT
ejpam-3915	161	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	161	6	(	(	PUNCT
ejpam-3915	161	7	wn	wn	PROPN
ejpam-3915	161	8	,	,	PUNCT
ejpam-3915	161	9	m	m	PROPN
ejpam-3915	161	10	)	)	PUNCT
ejpam-3915	161	11	=	=	SYM
ejpam-3915	161	12	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	161	13	(	(	PUNCT
ejpam-3915	161	14	kn	kn	PROPN
ejpam-3915	161	15	+	+	PROPN
ejpam-3915	161	16	cm	cm	NOUN
ejpam-3915	161	17	)	)	PUNCT
ejpam-3915	161	18	=	=	SYM
ejpam-3915	161	19	2	2	X
ejpam-3915	161	20	.	.	PUNCT
ejpam-3915	161	21	let	let	VERB
ejpam-3915	161	22	cn	cn	PROPN
ejpam-3915	161	23	=	=	PUNCT
ejpam-3915	162	1	[	[	X
ejpam-3915	162	2	un	un	NOUN
ejpam-3915	162	3	,	,	PUNCT
ejpam-3915	162	4	u1	u1	NOUN
ejpam-3915	162	5	,	,	PUNCT
ejpam-3915	162	6	u2	u2	NOUN
ejpam-3915	162	7	,	,	PUNCT
ejpam-3915	162	8	.	.	PUNCT
ejpam-3915	162	9	.	.	PUNCT
ejpam-3915	163	1	.	.	PUNCT
ejpam-3915	164	1	,	,	PUNCT
ejpam-3915	164	2	un	un	PROPN
ejpam-3915	164	3	]	]	X
ejpam-3915	164	4	.	.	PUNCT
ejpam-3915	165	1	if	if	SCONJ
ejpam-3915	165	2	n	n	NUM
ejpam-3915	165	3	=	=	SYM
ejpam-3915	165	4	1	1	NUM
ejpam-3915	165	5	and	and	CCONJ
ejpam-3915	165	6	m	m	PROPN
ejpam-3915	165	7	≥	≥	NOUN
ejpam-3915	165	8	5	5	NUM
ejpam-3915	165	9	,	,	PUNCT
ejpam-3915	165	10	then	then	ADV
ejpam-3915	165	11	by	by	ADP
ejpam-3915	165	12	proposition	proposition	NOUN
ejpam-3915	165	13	2.2	2.2	NUM
ejpam-3915	165	14	,	,	PUNCT
ejpam-3915	165	15	γt(cm	γt(cm	PROPN
ejpam-3915	165	16	)	)	PUNCT
ejpam-3915	165	17	>	>	X
ejpam-3915	166	1	2	2	X
ejpam-3915	166	2	.	.	PUNCT
ejpam-3915	166	3	by	by	ADP
ejpam-3915	166	4	corollary	corollary	ADJ
ejpam-3915	166	5	3.3	3.3	NUM
ejpam-3915	166	6	,	,	PUNCT
ejpam-3915	166	7	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	166	8	(	(	PUNCT
ejpam-3915	166	9	w1,m	w1,m	PROPN
ejpam-3915	166	10	)	)	PUNCT
ejpam-3915	166	11	=	=	PUNCT
ejpam-3915	167	1	1	1	X
ejpam-3915	167	2	.	.	PUNCT
ejpam-3915	168	1	if	if	SCONJ
ejpam-3915	168	2	n	n	NOUN
ejpam-3915	168	3	=	=	SYM
ejpam-3915	168	4	1	1	NUM
ejpam-3915	168	5	and	and	CCONJ
ejpam-3915	168	6	m	m	PRON
ejpam-3915	168	7	<	<	X
ejpam-3915	168	8	5	5	NUM
ejpam-3915	168	9	,	,	PUNCT
ejpam-3915	168	10	then	then	ADV
ejpam-3915	168	11	by	by	ADP
ejpam-3915	168	12	proposition	proposition	NOUN
ejpam-3915	168	13	2.2	2.2	NUM
ejpam-3915	168	14	,	,	PUNCT
ejpam-3915	168	15	γt(c3	γt(c3	NOUN
ejpam-3915	168	16	)	)	PUNCT
ejpam-3915	168	17	=	=	NOUN
ejpam-3915	168	18	γt(c4	γt(c4	NOUN
ejpam-3915	168	19	)	)	PUNCT
ejpam-3915	168	20	=	=	SYM
ejpam-3915	168	21	2	2	NUM
ejpam-3915	168	22	and	and	CCONJ
ejpam-3915	168	23	so	so	ADV
ejpam-3915	168	24	,	,	PUNCT
ejpam-3915	168	25	{	{	PUNCT
ejpam-3915	168	26	u1	u1	NOUN
ejpam-3915	168	27	,	,	PUNCT
ejpam-3915	168	28	u2	u2	PROPN
ejpam-3915	168	29	}	}	PUNCT
ejpam-3915	168	30	,	,	PUNCT
ejpam-3915	168	31	{	{	PUNCT
ejpam-3915	168	32	u2	u2	NOUN
ejpam-3915	168	33	,	,	PUNCT
ejpam-3915	168	34	u3	u3	NOUN
ejpam-3915	168	35	}	}	PUNCT
ejpam-3915	168	36	and	and	CCONJ
ejpam-3915	168	37	{	{	PUNCT
ejpam-3915	168	38	u3	u3	NOUN
ejpam-3915	168	39	,	,	PUNCT
ejpam-3915	168	40	u1	u1	PROPN
ejpam-3915	168	41	}	}	PUNCT
ejpam-3915	168	42	are	be	AUX
ejpam-3915	168	43	the	the	DET
ejpam-3915	168	44	γt	γt	NOUN
ejpam-3915	168	45	-	-	NOUN
ejpam-3915	168	46	sets	set	NOUN
ejpam-3915	168	47	of	of	ADP
ejpam-3915	168	48	c3	c3	PROPN
ejpam-3915	168	49	while	while	SCONJ
ejpam-3915	168	50	{	{	PUNCT
ejpam-3915	168	51	u1	u1	NOUN
ejpam-3915	168	52	,	,	PUNCT
ejpam-3915	168	53	u2	u2	PROPN
ejpam-3915	168	54	}	}	PUNCT
ejpam-3915	168	55	,	,	PUNCT
ejpam-3915	168	56	{	{	PUNCT
ejpam-3915	168	57	u2	u2	NOUN
ejpam-3915	168	58	,	,	PUNCT
ejpam-3915	168	59	u3	u3	NOUN
ejpam-3915	168	60	}	}	PUNCT
ejpam-3915	168	61	,	,	PUNCT
ejpam-3915	168	62	{	{	PUNCT
ejpam-3915	168	63	u3	u3	PROPN
ejpam-3915	168	64	,	,	PUNCT
ejpam-3915	168	65	u4	u4	PROPN
ejpam-3915	168	66	}	}	PUNCT
ejpam-3915	168	67	and	and	CCONJ
ejpam-3915	168	68	{	{	PUNCT
ejpam-3915	168	69	u4	u4	PROPN
ejpam-3915	168	70	,	,	PUNCT
ejpam-3915	168	71	u1	u1	PROPN
ejpam-3915	168	72	}	}	PUNCT
ejpam-3915	168	73	are	be	AUX
ejpam-3915	168	74	γt	γt	NOUN
ejpam-3915	168	75	-	-	NOUN
ejpam-3915	168	76	sets	set	NOUN
ejpam-3915	168	77	of	of	ADP
ejpam-3915	168	78	c4	c4	NOUN
ejpam-3915	168	79	.	.	PUNCT
ejpam-3915	169	1	clearly	clearly	ADV
ejpam-3915	169	2	,	,	PUNCT
ejpam-3915	169	3	form	form	NOUN
ejpam-3915	169	4	=	=	SYM
ejpam-3915	169	5	3	3	NUM
ejpam-3915	169	6	,	,	PUNCT
ejpam-3915	169	7	4	4	NUM
ejpam-3915	169	8	,	,	PUNCT
ejpam-3915	169	9	every	every	DET
ejpam-3915	169	10	vertex	vertex	NOUN
ejpam-3915	169	11	ui	ui	PROPN
ejpam-3915	169	12	∈	∈	PROPN
ejpam-3915	169	13	v	v	ADP
ejpam-3915	169	14	(	(	PUNCT
ejpam-3915	169	15	cm	cm	NOUN
ejpam-3915	169	16	)	)	PUNCT
ejpam-3915	169	17	is	be	AUX
ejpam-3915	169	18	contained	contain	VERB
ejpam-3915	169	19	in	in	ADP
ejpam-3915	169	20	a	a	DET
ejpam-3915	169	21	γt	γt	NOUN
ejpam-3915	169	22	-	-	NOUN
ejpam-3915	169	23	set	set	NOUN
ejpam-3915	169	24	of	of	ADP
ejpam-3915	169	25	cm	cm	PROPN
ejpam-3915	169	26	.	.	PUNCT
ejpam-3915	170	1	by	by	ADP
ejpam-3915	170	2	corollary	corollary	ADJ
ejpam-3915	170	3	3.3	3.3	NUM
ejpam-3915	170	4	,	,	PUNCT
ejpam-3915	170	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	170	6	(	(	PUNCT
ejpam-3915	170	7	w1,m	w1,m	PROPN
ejpam-3915	170	8	)	)	PUNCT
ejpam-3915	170	9	=	=	SYM
ejpam-3915	170	10	2	2	X
ejpam-3915	170	11	.	.	X
ejpam-3915	170	12	if	if	SCONJ
ejpam-3915	170	13	n	n	NUM
ejpam-3915	170	14	≥	≥	NOUN
ejpam-3915	170	15	2	2	NUM
ejpam-3915	170	16	and	and	CCONJ
ejpam-3915	170	17	m	m	PROPN
ejpam-3915	170	18	≥	≥	NOUN
ejpam-3915	170	19	3	3	NUM
ejpam-3915	170	20	,	,	PUNCT
ejpam-3915	170	21	then	then	ADV
ejpam-3915	170	22	kn	kn	PROPN
ejpam-3915	170	23	and	and	CCONJ
ejpam-3915	170	24	cm	cm	PROPN
ejpam-3915	170	25	are	be	AUX
ejpam-3915	170	26	nontrivial	nontrivial	ADJ
ejpam-3915	170	27	graphs	graph	NOUN
ejpam-3915	170	28	.	.	PUNCT
ejpam-3915	171	1	by	by	ADP
ejpam-3915	171	2	corollary	corollary	ADJ
ejpam-3915	171	3	3.3	3.3	NUM
ejpam-3915	171	4	,	,	PUNCT
ejpam-3915	171	5	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	171	6	(	(	PUNCT
ejpam-3915	171	7	wn	wn	PROPN
ejpam-3915	171	8	,	,	PUNCT
ejpam-3915	171	9	m	m	PROPN
ejpam-3915	171	10	)	)	PUNCT
ejpam-3915	171	11	=	=	SYM
ejpam-3915	171	12	2	2	X
ejpam-3915	171	13	.	.	X
ejpam-3915	171	14	corollary	corollary	ADJ
ejpam-3915	171	15	3.7	3.7	NUM
ejpam-3915	171	16	.	.	PUNCT
ejpam-3915	172	1	the	the	DET
ejpam-3915	172	2	total	total	ADJ
ejpam-3915	172	3	dr	dr	PROPN
ejpam-3915	172	4	-	-	PUNCT
ejpam-3915	172	5	power	power	NOUN
ejpam-3915	172	6	domination	domination	NOUN
ejpam-3915	172	7	number	number	NOUN
ejpam-3915	172	8	of	of	ADP
ejpam-3915	172	9	the	the	DET
ejpam-3915	172	10	join	join	NOUN
ejpam-3915	172	11	pn	pn	PROPN
ejpam-3915	172	12	+	+	CCONJ
ejpam-3915	172	13	pm	pm	PROPN
ejpam-3915	172	14	,	,	PUNCT
ejpam-3915	172	15	where	where	SCONJ
ejpam-3915	172	16	n	n	PRON
ejpam-3915	172	17	≥	≥	NOUN
ejpam-3915	172	18	1	1	NUM
ejpam-3915	172	19	and	and	CCONJ
ejpam-3915	172	20	m	m	PROPN
ejpam-3915	172	21	≥	≥	NOUN
ejpam-3915	172	22	1	1	NUM
ejpam-3915	172	23	,	,	PUNCT
ejpam-3915	172	24	is	be	AUX
ejpam-3915	172	25	given	give	VERB
ejpam-3915	172	26	by	by	ADP
ejpam-3915	172	27	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	172	28	(	(	PUNCT
ejpam-3915	172	29	pn	pn	NOUN
ejpam-3915	172	30	+	+	CCONJ
ejpam-3915	172	31	pm	pm	NOUN
ejpam-3915	172	32	)	)	PUNCT
ejpam-3915	172	33	=	=	SYM
ejpam-3915	172	34	2	2	NUM
ejpam-3915	172	35	and	and	CCONJ
ejpam-3915	172	36	its	its	PRON
ejpam-3915	172	37	forcing	force	VERB
ejpam-3915	172	38	total	total	ADJ
ejpam-3915	172	39	dr	dr	PROPN
ejpam-3915	172	40	-	-	PUNCT
ejpam-3915	172	41	power	power	NOUN
ejpam-3915	172	42	domination	domination	NOUN
ejpam-3915	172	43	number	number	NOUN
ejpam-3915	172	44	is	be	AUX
ejpam-3915	172	45	given	give	VERB
ejpam-3915	172	46	by	by	ADP
ejpam-3915	172	47	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	172	48	(	(	PUNCT
ejpam-3915	172	49	pn	pn	NOUN
ejpam-3915	172	50	+	+	CCONJ
ejpam-3915	172	51	pm	pm	NOUN
ejpam-3915	172	52	)	)	PUNCT
ejpam-3915	172	53	=	=	SYM
ejpam-3915	172	54			X
ejpam-3915	172	55	0	0	NUM
ejpam-3915	172	56	,	,	PUNCT
ejpam-3915	172	57	n	n	NOUN
ejpam-3915	172	58	=	=	SYM
ejpam-3915	172	59	1	1	NUM
ejpam-3915	172	60	and	and	CCONJ
ejpam-3915	172	61	m	m	PROPN
ejpam-3915	172	62	=	=	ADJ
ejpam-3915	172	63	1	1	NUM
ejpam-3915	172	64	,	,	PUNCT
ejpam-3915	172	65	1	1	NUM
ejpam-3915	172	66	,	,	PUNCT
ejpam-3915	172	67	either	either	CCONJ
ejpam-3915	172	68	n	n	CCONJ
ejpam-3915	172	69	=	=	SYM
ejpam-3915	172	70	1	1	NUM
ejpam-3915	172	71	and	and	CCONJ
ejpam-3915	172	72	m	m	PROPN
ejpam-3915	172	73	≥	≥	NOUN
ejpam-3915	172	74	4	4	NUM
ejpam-3915	172	75	,	,	PUNCT
ejpam-3915	172	76	or	or	CCONJ
ejpam-3915	172	77	m	m	PROPN
ejpam-3915	172	78	=	=	NOUN
ejpam-3915	172	79	1	1	NUM
ejpam-3915	172	80	and	and	CCONJ
ejpam-3915	172	81	n	n	PRON
ejpam-3915	172	82	≥	≥	NOUN
ejpam-3915	172	83	4	4	NUM
ejpam-3915	172	84	,	,	PUNCT
ejpam-3915	172	85	2	2	NUM
ejpam-3915	172	86	,	,	PUNCT
ejpam-3915	172	87	otherwise	otherwise	ADV
ejpam-3915	172	88	.	.	PUNCT
ejpam-3915	173	1	proof	proof	NOUN
ejpam-3915	173	2	.	.	PUNCT
ejpam-3915	174	1	by	by	ADP
ejpam-3915	174	2	corollary	corollary	ADJ
ejpam-3915	174	3	2.4	2.4	NUM
ejpam-3915	174	4	,	,	PUNCT
ejpam-3915	174	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	174	6	(	(	PUNCT
ejpam-3915	174	7	pn	pn	NOUN
ejpam-3915	174	8	+	+	CCONJ
ejpam-3915	174	9	pm	pm	NOUN
ejpam-3915	174	10	)	)	PUNCT
ejpam-3915	174	11	=	=	SYM
ejpam-3915	174	12	2	2	X
ejpam-3915	174	13	.	.	X
ejpam-3915	175	1	if	if	SCONJ
ejpam-3915	175	2	n	n	NOUN
ejpam-3915	175	3	=	=	SYM
ejpam-3915	175	4	1	1	NUM
ejpam-3915	175	5	and	and	CCONJ
ejpam-3915	175	6	m	m	PROPN
ejpam-3915	175	7	=	=	ADJ
ejpam-3915	175	8	1	1	NUM
ejpam-3915	175	9	,	,	PUNCT
ejpam-3915	175	10	then	then	ADV
ejpam-3915	175	11	p1	p1	PROPN
ejpam-3915	175	12	=	=	SYM
ejpam-3915	175	13	k1	k1	PROPN
ejpam-3915	175	14	is	be	AUX
ejpam-3915	175	15	a	a	DET
ejpam-3915	175	16	trivial	trivial	ADJ
ejpam-3915	175	17	graph	graph	NOUN
ejpam-3915	175	18	and	and	CCONJ
ejpam-3915	175	19	so	so	ADV
ejpam-3915	175	20	,	,	PUNCT
ejpam-3915	175	21	by	by	ADP
ejpam-3915	175	22	corollary	corollary	ADJ
ejpam-3915	175	23	3.3	3.3	NUM
ejpam-3915	175	24	,	,	PUNCT
ejpam-3915	175	25	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	175	26	(	(	PUNCT
ejpam-3915	175	27	p1	p1	PROPN
ejpam-3915	175	28	+	+	CCONJ
ejpam-3915	175	29	p1	p1	NOUN
ejpam-3915	175	30	)	)	PUNCT
ejpam-3915	175	31	=	=	SYM
ejpam-3915	176	1	0	0	X
ejpam-3915	176	2	.	.	PUNCT
ejpam-3915	177	1	if	if	SCONJ
ejpam-3915	177	2	n	n	NOUN
ejpam-3915	177	3	=	=	SYM
ejpam-3915	177	4	1	1	NUM
ejpam-3915	177	5	and	and	CCONJ
ejpam-3915	177	6	m	m	PROPN
ejpam-3915	177	7	≥	≥	NOUN
ejpam-3915	177	8	4	4	NUM
ejpam-3915	177	9	,	,	PUNCT
ejpam-3915	177	10	then	then	ADV
ejpam-3915	177	11	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3915	177	12	(	(	PUNCT
ejpam-3915	177	13	p1	p1	NOUN
ejpam-3915	177	14	+	+	CCONJ
ejpam-3915	177	15	pm	pm	NOUN
ejpam-3915	177	16	)	)	PUNCT
ejpam-3915	177	17	=	=	NOUN
ejpam-3915	177	18	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	177	19	(	(	PUNCT
ejpam-3915	177	20	f1,m	f1,m	PROPN
ejpam-3915	177	21	)	)	PUNCT
ejpam-3915	177	22	=	=	SYM
ejpam-3915	177	23	1	1	NUM
ejpam-3915	177	24	by	by	ADP
ejpam-3915	177	25	corollary	corollary	ADJ
ejpam-3915	177	26	3.5	3.5	NUM
ejpam-3915	177	27	.	.	PUNCT
ejpam-3915	178	1	similarly	similarly	ADV
ejpam-3915	178	2	,	,	PUNCT
ejpam-3915	178	3	if	if	SCONJ
ejpam-3915	178	4	m	m	ADV
ejpam-3915	178	5	=	=	SYM
ejpam-3915	178	6	1	1	NUM
ejpam-3915	178	7	and	and	CCONJ
ejpam-3915	178	8	n	n	PRON
ejpam-3915	178	9	≥	≥	NOUN
ejpam-3915	178	10	4	4	NUM
ejpam-3915	178	11	,	,	PUNCT
ejpam-3915	178	12	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	178	13	(	(	PUNCT
ejpam-3915	178	14	pn	pn	NOUN
ejpam-3915	178	15	+	+	CCONJ
ejpam-3915	178	16	p1	p1	NOUN
ejpam-3915	178	17	)	)	PUNCT
ejpam-3915	178	18	=	=	SYM
ejpam-3915	178	19	1	1	X
ejpam-3915	178	20	.	.	PUNCT
ejpam-3915	179	1	if	if	SCONJ
ejpam-3915	179	2	n	n	NOUN
ejpam-3915	179	3	=	=	SYM
ejpam-3915	179	4	1	1	NUM
ejpam-3915	179	5	and	and	CCONJ
ejpam-3915	179	6	either	either	CCONJ
ejpam-3915	179	7	m	m	PROPN
ejpam-3915	179	8	=	=	SYM
ejpam-3915	179	9	2	2	NUM
ejpam-3915	179	10	or	or	CCONJ
ejpam-3915	179	11	m	m	PROPN
ejpam-3915	179	12	=	=	NOUN
ejpam-3915	179	13	3	3	NUM
ejpam-3915	179	14	,	,	PUNCT
ejpam-3915	179	15	then	then	ADV
ejpam-3915	179	16	by	by	ADP
ejpam-3915	179	17	corollary	corollary	ADJ
ejpam-3915	179	18	3.5	3.5	NUM
ejpam-3915	179	19	,	,	PUNCT
ejpam-3915	179	20	c.	c.	PROPN
ejpam-3915	179	21	armada	armada	PROPN
ejpam-3915	179	22	/	/	SYM
ejpam-3915	179	23	eur	eur	PROPN
ejpam-3915	179	24	.	.	PUNCT
ejpam-3915	180	1	j.	j.	PROPN
ejpam-3915	180	2	pure	pure	PROPN
ejpam-3915	180	3	appl	appl	PROPN
ejpam-3915	180	4	.	.	PROPN
ejpam-3915	180	5	math	math	PROPN
ejpam-3915	180	6	,	,	PUNCT
ejpam-3915	180	7	14	14	NUM
ejpam-3915	180	8	(	(	PUNCT
ejpam-3915	180	9	3	3	NUM
ejpam-3915	180	10	)	)	PUNCT
ejpam-3915	180	11	(	(	PUNCT
ejpam-3915	180	12	2021	2021	NUM
ejpam-3915	180	13	)	)	PUNCT
ejpam-3915	180	14	,	,	PUNCT
ejpam-3915	180	15	1098	1098	NUM
ejpam-3915	180	16	-	-	SYM
ejpam-3915	180	17	1107	1107	NUM
ejpam-3915	180	18	1105	1105	NUM
ejpam-3915	180	19	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	180	20	(	(	PUNCT
ejpam-3915	180	21	p1	p1	NOUN
ejpam-3915	180	22	+	+	CCONJ
ejpam-3915	180	23	pm	pm	NOUN
ejpam-3915	180	24	)	)	PUNCT
ejpam-3915	180	25	=	=	NOUN
ejpam-3915	180	26	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	180	27	(	(	PUNCT
ejpam-3915	180	28	f1,m	f1,m	PROPN
ejpam-3915	180	29	)	)	PUNCT
ejpam-3915	180	30	=	=	SYM
ejpam-3915	181	1	2	2	X
ejpam-3915	181	2	.	.	X
ejpam-3915	181	3	similarly	similarly	ADV
ejpam-3915	181	4	,	,	PUNCT
ejpam-3915	181	5	if	if	SCONJ
ejpam-3915	181	6	m	m	ADV
ejpam-3915	181	7	=	=	NOUN
ejpam-3915	181	8	1	1	NUM
ejpam-3915	181	9	and	and	CCONJ
ejpam-3915	181	10	either	either	CCONJ
ejpam-3915	181	11	n	n	CCONJ
ejpam-3915	181	12	=	=	SYM
ejpam-3915	181	13	2	2	NUM
ejpam-3915	181	14	or	or	CCONJ
ejpam-3915	181	15	n	n	NOUN
ejpam-3915	181	16	=	=	SYM
ejpam-3915	181	17	3	3	NUM
ejpam-3915	181	18	,	,	PUNCT
ejpam-3915	181	19	then	then	ADV
ejpam-3915	181	20	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3915	181	21	(	(	PUNCT
ejpam-3915	181	22	pn	pn	NOUN
ejpam-3915	181	23	+	+	CCONJ
ejpam-3915	181	24	p1	p1	NOUN
ejpam-3915	181	25	)	)	PUNCT
ejpam-3915	181	26	=	=	SYM
ejpam-3915	182	1	2	2	X
ejpam-3915	182	2	.	.	X
ejpam-3915	182	3	if	if	SCONJ
ejpam-3915	182	4	n	n	NUM
ejpam-3915	182	5	≥	≥	NOUN
ejpam-3915	182	6	2	2	NUM
ejpam-3915	182	7	and	and	CCONJ
ejpam-3915	182	8	m	m	PROPN
ejpam-3915	182	9	≥	≥	NOUN
ejpam-3915	182	10	2	2	NUM
ejpam-3915	182	11	,	,	PUNCT
ejpam-3915	182	12	then	then	ADV
ejpam-3915	182	13	pn	pn	PROPN
ejpam-3915	182	14	and	and	CCONJ
ejpam-3915	182	15	pm	pm	NOUN
ejpam-3915	182	16	are	be	AUX
ejpam-3915	182	17	nontrivial	nontrivial	ADJ
ejpam-3915	182	18	graphs	graph	NOUN
ejpam-3915	182	19	.	.	PUNCT
ejpam-3915	183	1	by	by	ADP
ejpam-3915	183	2	corollary	corollary	ADJ
ejpam-3915	183	3	3.3	3.3	NUM
ejpam-3915	183	4	,	,	PUNCT
ejpam-3915	183	5	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	183	6	(	(	PUNCT
ejpam-3915	183	7	pn	pn	NOUN
ejpam-3915	183	8	+	+	CCONJ
ejpam-3915	183	9	pm	pm	NOUN
ejpam-3915	183	10	)	)	PUNCT
ejpam-3915	183	11	=	=	SYM
ejpam-3915	183	12	2	2	X
ejpam-3915	183	13	.	.	X
ejpam-3915	183	14	corollary	corollary	ADJ
ejpam-3915	183	15	3.8	3.8	NUM
ejpam-3915	183	16	.	.	PUNCT
ejpam-3915	184	1	the	the	DET
ejpam-3915	184	2	total	total	ADJ
ejpam-3915	184	3	dr	dr	PROPN
ejpam-3915	184	4	-	-	PUNCT
ejpam-3915	184	5	power	power	NOUN
ejpam-3915	184	6	domination	domination	NOUN
ejpam-3915	184	7	number	number	NOUN
ejpam-3915	184	8	of	of	ADP
ejpam-3915	184	9	the	the	DET
ejpam-3915	184	10	join	join	NOUN
ejpam-3915	184	11	pn	pn	PROPN
ejpam-3915	184	12	+	+	CCONJ
ejpam-3915	184	13	cm	cm	NOUN
ejpam-3915	184	14	,	,	PUNCT
ejpam-3915	184	15	where	where	SCONJ
ejpam-3915	184	16	n	n	PRON
ejpam-3915	184	17	≥	≥	NOUN
ejpam-3915	184	18	1	1	NUM
ejpam-3915	184	19	and	and	CCONJ
ejpam-3915	184	20	m	m	PROPN
ejpam-3915	184	21	≥	≥	NOUN
ejpam-3915	184	22	3	3	NUM
ejpam-3915	184	23	,	,	PUNCT
ejpam-3915	184	24	is	be	AUX
ejpam-3915	184	25	given	give	VERB
ejpam-3915	184	26	by	by	ADP
ejpam-3915	184	27	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	184	28	(	(	PUNCT
ejpam-3915	184	29	pn	pn	NOUN
ejpam-3915	184	30	+	+	CCONJ
ejpam-3915	184	31	cm	cm	NOUN
ejpam-3915	184	32	)	)	PUNCT
ejpam-3915	184	33	=	=	SYM
ejpam-3915	184	34	2	2	NUM
ejpam-3915	184	35	and	and	CCONJ
ejpam-3915	184	36	its	its	PRON
ejpam-3915	184	37	forcing	force	VERB
ejpam-3915	184	38	total	total	ADJ
ejpam-3915	184	39	dr	dr	PROPN
ejpam-3915	184	40	-	-	PUNCT
ejpam-3915	184	41	power	power	NOUN
ejpam-3915	184	42	domination	domination	NOUN
ejpam-3915	184	43	number	number	NOUN
ejpam-3915	184	44	is	be	AUX
ejpam-3915	184	45	given	give	VERB
ejpam-3915	184	46	by	by	ADP
ejpam-3915	184	47	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	184	48	(	(	PUNCT
ejpam-3915	184	49	pn	pn	NOUN
ejpam-3915	184	50	+	+	CCONJ
ejpam-3915	184	51	cm	cm	NOUN
ejpam-3915	184	52	)	)	PUNCT
ejpam-3915	184	53	=	=	PRON
ejpam-3915	184	54	{	{	PUNCT
ejpam-3915	184	55	1	1	NUM
ejpam-3915	184	56	,	,	PUNCT
ejpam-3915	184	57	n	n	NOUN
ejpam-3915	184	58	=	=	SYM
ejpam-3915	184	59	1	1	NUM
ejpam-3915	184	60	and	and	CCONJ
ejpam-3915	184	61	m	m	PRON
ejpam-3915	184	62	≥	≥	NUM
ejpam-3915	184	63	5	5	NUM
ejpam-3915	184	64	2	2	NUM
ejpam-3915	184	65	,	,	PUNCT
ejpam-3915	184	66	otherwise	otherwise	ADV
ejpam-3915	184	67	.	.	PUNCT
ejpam-3915	185	1	proof	proof	NOUN
ejpam-3915	185	2	.	.	PUNCT
ejpam-3915	186	1	by	by	ADP
ejpam-3915	186	2	corollary	corollary	ADJ
ejpam-3915	186	3	2.4	2.4	NUM
ejpam-3915	186	4	,	,	PUNCT
ejpam-3915	186	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	186	6	(	(	PUNCT
ejpam-3915	186	7	pn	pn	NOUN
ejpam-3915	186	8	+	+	CCONJ
ejpam-3915	186	9	cm	cm	NOUN
ejpam-3915	186	10	)	)	PUNCT
ejpam-3915	186	11	=	=	SYM
ejpam-3915	186	12	2	2	X
ejpam-3915	186	13	.	.	X
ejpam-3915	187	1	if	if	SCONJ
ejpam-3915	187	2	n	n	NOUN
ejpam-3915	187	3	=	=	SYM
ejpam-3915	187	4	1	1	NUM
ejpam-3915	187	5	and	and	CCONJ
ejpam-3915	187	6	m	m	PROPN
ejpam-3915	187	7	≥	≥	NOUN
ejpam-3915	187	8	5	5	NUM
ejpam-3915	187	9	,	,	PUNCT
ejpam-3915	187	10	then	then	ADV
ejpam-3915	187	11	by	by	ADP
ejpam-3915	187	12	corollary	corollary	ADJ
ejpam-3915	187	13	3.6	3.6	NUM
ejpam-3915	187	14	,	,	PUNCT
ejpam-3915	187	15	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	187	16	(	(	PUNCT
ejpam-3915	187	17	p1	p1	NOUN
ejpam-3915	187	18	+	+	CCONJ
ejpam-3915	187	19	cm	cm	NOUN
ejpam-3915	187	20	)	)	PUNCT
ejpam-3915	188	1	=	=	NOUN
ejpam-3915	188	2	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	188	3	(	(	PUNCT
ejpam-3915	188	4	w1,m	w1,m	PROPN
ejpam-3915	188	5	)	)	PUNCT
ejpam-3915	188	6	=	=	PUNCT
ejpam-3915	189	1	1	1	X
ejpam-3915	189	2	.	.	PUNCT
ejpam-3915	190	1	if	if	SCONJ
ejpam-3915	190	2	n	n	NOUN
ejpam-3915	190	3	=	=	SYM
ejpam-3915	190	4	1	1	NUM
ejpam-3915	190	5	and	and	CCONJ
ejpam-3915	190	6	m	m	PRON
ejpam-3915	190	7	<	<	X
ejpam-3915	190	8	5	5	NUM
ejpam-3915	190	9	,	,	PUNCT
ejpam-3915	190	10	then	then	ADV
ejpam-3915	190	11	by	by	ADP
ejpam-3915	190	12	corollary	corollary	ADJ
ejpam-3915	190	13	3.6	3.6	NUM
ejpam-3915	190	14	,	,	PUNCT
ejpam-3915	190	15	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	190	16	(	(	PUNCT
ejpam-3915	190	17	p1	p1	NOUN
ejpam-3915	190	18	+	+	CCONJ
ejpam-3915	190	19	cm	cm	NOUN
ejpam-3915	190	20	)	)	PUNCT
ejpam-3915	191	1	=	=	NOUN
ejpam-3915	191	2	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	191	3	(	(	PUNCT
ejpam-3915	191	4	w1,m	w1,m	PROPN
ejpam-3915	191	5	)	)	PUNCT
ejpam-3915	191	6	=	=	SYM
ejpam-3915	192	1	2	2	X
ejpam-3915	192	2	.	.	X
ejpam-3915	192	3	if	if	SCONJ
ejpam-3915	192	4	n	n	NUM
ejpam-3915	192	5	≥	≥	NOUN
ejpam-3915	192	6	2	2	NUM
ejpam-3915	192	7	and	and	CCONJ
ejpam-3915	192	8	m	m	PROPN
ejpam-3915	192	9	≥	≥	NOUN
ejpam-3915	192	10	2	2	NUM
ejpam-3915	192	11	,	,	PUNCT
ejpam-3915	192	12	then	then	ADV
ejpam-3915	192	13	pn	pn	PROPN
ejpam-3915	192	14	and	and	CCONJ
ejpam-3915	192	15	cm	cm	PROPN
ejpam-3915	192	16	are	be	AUX
ejpam-3915	192	17	nontrivial	nontrivial	ADJ
ejpam-3915	192	18	graphs	graph	NOUN
ejpam-3915	192	19	.	.	PUNCT
ejpam-3915	193	1	by	by	ADP
ejpam-3915	193	2	corollary	corollary	ADJ
ejpam-3915	193	3	3.3	3.3	NUM
ejpam-3915	193	4	,	,	PUNCT
ejpam-3915	193	5	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	193	6	(	(	PUNCT
ejpam-3915	193	7	pn	pn	NOUN
ejpam-3915	193	8	+	+	CCONJ
ejpam-3915	193	9	cm	cm	NOUN
ejpam-3915	193	10	)	)	PUNCT
ejpam-3915	193	11	=	=	SYM
ejpam-3915	193	12	2	2	X
ejpam-3915	193	13	.	.	X
ejpam-3915	193	14	corollary	corollary	ADJ
ejpam-3915	193	15	3.9	3.9	NUM
ejpam-3915	193	16	.	.	PUNCT
ejpam-3915	194	1	the	the	DET
ejpam-3915	194	2	total	total	ADJ
ejpam-3915	194	3	dr	dr	PROPN
ejpam-3915	194	4	-	-	PUNCT
ejpam-3915	194	5	power	power	NOUN
ejpam-3915	194	6	domination	domination	NOUN
ejpam-3915	194	7	number	number	NOUN
ejpam-3915	194	8	of	of	ADP
ejpam-3915	194	9	the	the	DET
ejpam-3915	194	10	join	join	NOUN
ejpam-3915	194	11	cn	cn	PROPN
ejpam-3915	194	12	+	+	PROPN
ejpam-3915	194	13	cm	cm	NOUN
ejpam-3915	194	14	,	,	PUNCT
ejpam-3915	194	15	where	where	SCONJ
ejpam-3915	194	16	n	n	PRON
ejpam-3915	194	17	≥	≥	X
ejpam-3915	194	18	3	3	NUM
ejpam-3915	194	19	and	and	CCONJ
ejpam-3915	194	20	m	m	PROPN
ejpam-3915	194	21	≥	≥	NOUN
ejpam-3915	194	22	3	3	NUM
ejpam-3915	194	23	,	,	PUNCT
ejpam-3915	194	24	and	and	CCONJ
ejpam-3915	194	25	its	its	PRON
ejpam-3915	194	26	forcing	force	VERB
ejpam-3915	194	27	total	total	ADJ
ejpam-3915	194	28	dr	dr	PROPN
ejpam-3915	194	29	-	-	PUNCT
ejpam-3915	194	30	power	power	NOUN
ejpam-3915	194	31	domination	domination	NOUN
ejpam-3915	194	32	number	number	NOUN
ejpam-3915	194	33	is	be	AUX
ejpam-3915	194	34	given	give	VERB
ejpam-3915	194	35	by	by	ADP
ejpam-3915	194	36	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	194	37	(	(	PUNCT
ejpam-3915	194	38	cn	cn	X
ejpam-3915	194	39	+	+	NOUN
ejpam-3915	194	40	cm	cm	NOUN
ejpam-3915	194	41	)	)	PUNCT
ejpam-3915	195	1	=	=	SYM
ejpam-3915	195	2	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	195	3	(	(	PUNCT
ejpam-3915	195	4	cn	cn	X
ejpam-3915	195	5	+	+	NOUN
ejpam-3915	195	6	cm	cm	NOUN
ejpam-3915	195	7	)	)	PUNCT
ejpam-3915	195	8	=	=	SYM
ejpam-3915	195	9	2	2	X
ejpam-3915	195	10	.	.	PUNCT
ejpam-3915	195	11	proof	proof	NOUN
ejpam-3915	195	12	.	.	PUNCT
ejpam-3915	196	1	by	by	ADP
ejpam-3915	196	2	corollary	corollary	ADJ
ejpam-3915	196	3	2.4	2.4	NUM
ejpam-3915	196	4	,	,	PUNCT
ejpam-3915	196	5	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	196	6	(	(	PUNCT
ejpam-3915	196	7	cn	cn	X
ejpam-3915	196	8	+	+	NOUN
ejpam-3915	196	9	cm	cm	NOUN
ejpam-3915	196	10	)	)	PUNCT
ejpam-3915	196	11	=	=	SYM
ejpam-3915	196	12	2	2	X
ejpam-3915	196	13	.	.	X
ejpam-3915	196	14	note	note	VERB
ejpam-3915	196	15	that	that	SCONJ
ejpam-3915	196	16	the	the	DET
ejpam-3915	196	17	cycles	cycle	NOUN
ejpam-3915	196	18	cn	cn	PROPN
ejpam-3915	196	19	and	and	CCONJ
ejpam-3915	196	20	cm	cm	PROPN
ejpam-3915	196	21	are	be	AUX
ejpam-3915	196	22	nontrivial	nontrivial	ADJ
ejpam-3915	196	23	graphs	graph	NOUN
ejpam-3915	196	24	.	.	PUNCT
ejpam-3915	197	1	by	by	ADP
ejpam-3915	197	2	theorem	theorem	NOUN
ejpam-3915	197	3	3.2	3.2	NUM
ejpam-3915	197	4	,	,	PUNCT
ejpam-3915	197	5	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	197	6	(	(	PUNCT
ejpam-3915	197	7	cn	cn	X
ejpam-3915	197	8	+	+	NOUN
ejpam-3915	197	9	cm	cm	NOUN
ejpam-3915	197	10	)	)	PUNCT
ejpam-3915	197	11	=	=	SYM
ejpam-3915	197	12	2	2	NUM
ejpam-3915	197	13	.	.	NOUN
ejpam-3915	197	14	4	4	NUM
ejpam-3915	197	15	.	.	X
ejpam-3915	197	16	forcing	force	VERB
ejpam-3915	197	17	total	total	ADJ
ejpam-3915	197	18	dr	dr	PROPN
ejpam-3915	197	19	-	-	PUNCT
ejpam-3915	197	20	power	power	NOUN
ejpam-3915	197	21	domination	domination	NOUN
ejpam-3915	197	22	number	number	NOUN
ejpam-3915	197	23	of	of	ADP
ejpam-3915	197	24	the	the	DET
ejpam-3915	197	25	corona	corona	NOUN
ejpam-3915	197	26	of	of	ADP
ejpam-3915	197	27	graphs	graph	NOUN
ejpam-3915	197	28	this	this	DET
ejpam-3915	197	29	section	section	NOUN
ejpam-3915	197	30	contains	contain	VERB
ejpam-3915	197	31	the	the	DET
ejpam-3915	197	32	forcing	force	VERB
ejpam-3915	197	33	total	total	ADJ
ejpam-3915	197	34	dr	dr	PROPN
ejpam-3915	197	35	-	-	PUNCT
ejpam-3915	197	36	power	power	NOUN
ejpam-3915	197	37	domination	domination	NOUN
ejpam-3915	197	38	number	number	NOUN
ejpam-3915	197	39	of	of	ADP
ejpam-3915	197	40	the	the	DET
ejpam-3915	197	41	coronas	coronas	PROPN
ejpam-3915	197	42	g	g	PROPN
ejpam-3915	197	43	◦	◦	NOUN
ejpam-3915	197	44	h	h	NOUN
ejpam-3915	197	45	and	and	CCONJ
ejpam-3915	197	46	km	km	PROPN
ejpam-3915	197	47	◦	◦	NOUN
ejpam-3915	197	48	h	h	NOUN
ejpam-3915	197	49	such	such	ADJ
ejpam-3915	197	50	that	that	SCONJ
ejpam-3915	197	51	g	g	PROPN
ejpam-3915	197	52	is	be	AUX
ejpam-3915	197	53	a	a	DET
ejpam-3915	197	54	nontrivial	nontrivial	ADJ
ejpam-3915	197	55	connected	connect	VERB
ejpam-3915	197	56	graph	graph	NOUN
ejpam-3915	197	57	,	,	PUNCT
ejpam-3915	197	58	km	km	PROPN
ejpam-3915	197	59	is	be	AUX
ejpam-3915	197	60	a	a	DET
ejpam-3915	197	61	complete	complete	ADJ
ejpam-3915	197	62	graph	graph	NOUN
ejpam-3915	197	63	and	and	CCONJ
ejpam-3915	197	64	h	h	NOUN
ejpam-3915	197	65	is	be	AUX
ejpam-3915	197	66	any	any	DET
ejpam-3915	197	67	graph	graph	NOUN
ejpam-3915	197	68	.	.	PUNCT
ejpam-3915	198	1	theorem	theorem	NOUN
ejpam-3915	198	2	4.1	4.1	NUM
ejpam-3915	198	3	.	.	PUNCT
ejpam-3915	199	1	let	let	VERB
ejpam-3915	199	2	g	g	PRON
ejpam-3915	199	3	be	be	AUX
ejpam-3915	199	4	a	a	DET
ejpam-3915	199	5	nontrivial	nontrivial	ADJ
ejpam-3915	199	6	connected	connect	VERB
ejpam-3915	199	7	graph	graph	NOUN
ejpam-3915	199	8	and	and	CCONJ
ejpam-3915	199	9	let	let	VERB
ejpam-3915	199	10	h	h	NOUN
ejpam-3915	199	11	be	be	AUX
ejpam-3915	199	12	any	any	DET
ejpam-3915	199	13	graph	graph	NOUN
ejpam-3915	199	14	.	.	PUNCT
ejpam-3915	200	1	then	then	ADV
ejpam-3915	200	2	r	r	NOUN
ejpam-3915	200	3	⊆	⊆	NUM
ejpam-3915	200	4	v	v	NOUN
ejpam-3915	200	5	(	(	PUNCT
ejpam-3915	200	6	g	g	PROPN
ejpam-3915	200	7	◦	◦	NOUN
ejpam-3915	200	8	h	h	NOUN
ejpam-3915	200	9	)	)	PUNCT
ejpam-3915	200	10	is	be	AUX
ejpam-3915	200	11	a	a	DET
ejpam-3915	200	12	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	200	13	-set	-set	PUNCT
ejpam-3915	200	14	of	of	ADP
ejpam-3915	200	15	g	g	PROPN
ejpam-3915	200	16	◦	◦	NOUN
ejpam-3915	200	17	h	h	NOUN
ejpam-3915	201	1	if	if	SCONJ
ejpam-3915	202	1	and	and	CCONJ
ejpam-3915	202	2	only	only	ADV
ejpam-3915	202	3	if	if	SCONJ
ejpam-3915	202	4	r	r	NOUN
ejpam-3915	202	5	=	=	SYM
ejpam-3915	202	6	v	v	NOUN
ejpam-3915	202	7	(	(	PUNCT
ejpam-3915	202	8	g	g	NOUN
ejpam-3915	202	9	)	)	PUNCT
ejpam-3915	202	10	.	.	PUNCT
ejpam-3915	203	1	in	in	ADP
ejpam-3915	203	2	particular	particular	ADJ
ejpam-3915	203	3	,	,	PUNCT
ejpam-3915	203	4	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	203	5	(	(	PUNCT
ejpam-3915	203	6	g	g	PROPN
ejpam-3915	203	7	◦	◦	NOUN
ejpam-3915	203	8	h	h	NOUN
ejpam-3915	203	9	)	)	PUNCT
ejpam-3915	203	10	=	=	SYM
ejpam-3915	204	1	0	0	X
ejpam-3915	204	2	.	.	PUNCT
ejpam-3915	204	3	proof	proof	NOUN
ejpam-3915	204	4	.	.	PUNCT
ejpam-3915	205	1	suppose	suppose	VERB
ejpam-3915	205	2	that	that	SCONJ
ejpam-3915	205	3	r	r	NOUN
ejpam-3915	205	4	⊆	⊆	NUM
ejpam-3915	205	5	v	v	NOUN
ejpam-3915	205	6	(	(	PUNCT
ejpam-3915	205	7	g	g	PROPN
ejpam-3915	205	8	◦	◦	NOUN
ejpam-3915	205	9	h	h	NOUN
ejpam-3915	205	10	)	)	PUNCT
ejpam-3915	205	11	is	be	AUX
ejpam-3915	205	12	a	a	DET
ejpam-3915	205	13	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	205	14	-set	-set	PROPN
ejpam-3915	205	15	of	of	ADP
ejpam-3915	205	16	g	g	PROPN
ejpam-3915	205	17	◦	◦	PROPN
ejpam-3915	205	18	h.	h.	PROPN
ejpam-3915	205	19	note	note	VERB
ejpam-3915	205	20	that	that	SCONJ
ejpam-3915	205	21	v	v	X
ejpam-3915	205	22	(	(	PUNCT
ejpam-3915	205	23	g	g	NOUN
ejpam-3915	205	24	)	)	PUNCT
ejpam-3915	205	25	is	be	AUX
ejpam-3915	205	26	a	a	DET
ejpam-3915	205	27	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	205	28	-set	-set	PROPN
ejpam-3915	205	29	of	of	ADP
ejpam-3915	205	30	g	g	PROPN
ejpam-3915	205	31	◦	◦	NOUN
ejpam-3915	205	32	h	h	NOUN
ejpam-3915	205	33	by	by	ADP
ejpam-3915	205	34	corollary	corollary	ADJ
ejpam-3915	205	35	2.6	2.6	NUM
ejpam-3915	205	36	.	.	PUNCT
ejpam-3915	205	37	suppose	suppose	VERB
ejpam-3915	205	38	that	that	SCONJ
ejpam-3915	205	39	r	r	PROPN
ejpam-3915	205	40	6=	6=	ADP
ejpam-3915	205	41	v	v	ADP
ejpam-3915	205	42	(	(	PUNCT
ejpam-3915	205	43	g	g	NOUN
ejpam-3915	205	44	)	)	PUNCT
ejpam-3915	205	45	and	and	CCONJ
ejpam-3915	205	46	let	let	VERB
ejpam-3915	205	47	a	a	DET
ejpam-3915	205	48	=	=	PUNCT
ejpam-3915	205	49	r∩v	r∩v	NOUN
ejpam-3915	205	50	(	(	PUNCT
ejpam-3915	205	51	g	g	NOUN
ejpam-3915	205	52	)	)	PUNCT
ejpam-3915	205	53	,	,	PUNCT
ejpam-3915	205	54	that	that	ADV
ejpam-3915	205	55	is	is	ADV
ejpam-3915	205	56	,	,	PUNCT
ejpam-3915	205	57	|a|	|a|	PROPN
ejpam-3915	205	58	<	<	X
ejpam-3915	205	59	|v	|v	X
ejpam-3915	205	60	(	(	PUNCT
ejpam-3915	205	61	g)|	g)|	PROPN
ejpam-3915	205	62	.	.	PUNCT
ejpam-3915	206	1	since	since	SCONJ
ejpam-3915	206	2	r	r	NOUN
ejpam-3915	206	3	is	be	AUX
ejpam-3915	206	4	a	a	DET
ejpam-3915	206	5	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	206	6	-set	-set	PUNCT
ejpam-3915	206	7	of	of	ADP
ejpam-3915	206	8	g	g	PROPN
ejpam-3915	206	9	◦	◦	NOUN
ejpam-3915	206	10	h	h	NOUN
ejpam-3915	206	11	,	,	PUNCT
ejpam-3915	207	1	r	r	NOUN
ejpam-3915	207	2	=	=	PUNCT
ejpam-3915	207	3	a	a	DET
ejpam-3915	207	4	∪	∪	ADJ
ejpam-3915	207	5	(	(	PUNCT
ejpam-3915	207	6	⋃	⋃	PROPN
ejpam-3915	207	7	v∈a	v∈a	NOUN
ejpam-3915	207	8	bv	bv	NOUN
ejpam-3915	207	9	)	)	PUNCT
ejpam-3915	207	10	∪	∪	ADP
ejpam-3915	207	11	⋃	⋃	SYM
ejpam-3915	207	12	u/∈a	u/∈a	ADJ
ejpam-3915	207	13	du	du	NOUN
ejpam-3915	207	14			PROPN
ejpam-3915	207	15	as	as	SCONJ
ejpam-3915	207	16	described	describe	VERB
ejpam-3915	207	17	in	in	ADP
ejpam-3915	207	18	theorem	theorem	ADJ
ejpam-3915	207	19	2.5	2.5	NUM
ejpam-3915	207	20	where	where	SCONJ
ejpam-3915	207	21	|bv|	|bv|	PROPN
ejpam-3915	207	22	=	=	PUNCT
ejpam-3915	207	23	0	0	NUM
ejpam-3915	207	24	for	for	ADP
ejpam-3915	207	25	each	each	DET
ejpam-3915	207	26	v	v	ADP
ejpam-3915	207	27	∈	∈	PROPN
ejpam-3915	207	28	a	a	PRON
ejpam-3915	207	29	and	and	CCONJ
ejpam-3915	207	30	|du|	|du|	NOUN
ejpam-3915	207	31	=	=	PUNCT
ejpam-3915	207	32	γt(h	γt(h	X
ejpam-3915	207	33	)	)	PUNCT
ejpam-3915	207	34	for	for	ADP
ejpam-3915	207	35	each	each	DET
ejpam-3915	207	36	u	u	NOUN
ejpam-3915	207	37	/∈	/∈	PROPN
ejpam-3915	208	1	a	a	PRON
ejpam-3915	208	2	or	or	CCONJ
ejpam-3915	208	3	u	u	NOUN
ejpam-3915	208	4	∈	∈	PROPN
ejpam-3915	208	5	v	v	NOUN
ejpam-3915	208	6	(	(	PUNCT
ejpam-3915	208	7	g)\a	g)\a	NOUN
ejpam-3915	208	8	.	.	PUNCT
ejpam-3915	209	1	hence	hence	ADV
ejpam-3915	209	2	,	,	PUNCT
ejpam-3915	209	3	c.	c.	PROPN
ejpam-3915	209	4	armada	armada	PROPN
ejpam-3915	209	5	/	/	SYM
ejpam-3915	209	6	eur	eur	PROPN
ejpam-3915	209	7	.	.	PUNCT
ejpam-3915	210	1	j.	j.	PROPN
ejpam-3915	210	2	pure	pure	PROPN
ejpam-3915	210	3	appl	appl	PROPN
ejpam-3915	210	4	.	.	PROPN
ejpam-3915	210	5	math	math	PROPN
ejpam-3915	210	6	,	,	PUNCT
ejpam-3915	210	7	14	14	NUM
ejpam-3915	210	8	(	(	PUNCT
ejpam-3915	210	9	3	3	NUM
ejpam-3915	210	10	)	)	PUNCT
ejpam-3915	210	11	(	(	PUNCT
ejpam-3915	210	12	2021	2021	NUM
ejpam-3915	210	13	)	)	PUNCT
ejpam-3915	210	14	,	,	PUNCT
ejpam-3915	210	15	1098	1098	NUM
ejpam-3915	210	16	-	-	SYM
ejpam-3915	210	17	1107	1107	NUM
ejpam-3915	210	18	1106	1106	NUM
ejpam-3915	210	19	|r|	|r|	NOUN
ejpam-3915	210	20	=	=	PUNCT
ejpam-3915	210	21	|a|+	|a|+	VERB
ejpam-3915	210	22	γt(h)(|v	γt(h)(|v	NUM
ejpam-3915	210	23	(	(	PUNCT
ejpam-3915	210	24	g)|	g)|	NOUN
ejpam-3915	210	25	−	−	PROPN
ejpam-3915	210	26	|a|	|a|	NOUN
ejpam-3915	210	27	)	)	PUNCT
ejpam-3915	210	28	≥	≥	NOUN
ejpam-3915	210	29	|a|+	|a|+	NOUN
ejpam-3915	210	30	2|v	2|v	PROPN
ejpam-3915	210	31	(	(	PUNCT
ejpam-3915	210	32	g)|	g)|	VERB
ejpam-3915	210	33	−	−	PROPN
ejpam-3915	210	34	2|a|	2|a|	NUM
ejpam-3915	210	35	since	since	SCONJ
ejpam-3915	210	36	γt(h	γt(h	NUM
ejpam-3915	210	37	)	)	PUNCT
ejpam-3915	210	38	≥	≥	NUM
ejpam-3915	210	39	2	2	NUM
ejpam-3915	210	40	≥	≥	NOUN
ejpam-3915	210	41	2|v	2|v	NUM
ejpam-3915	210	42	(	(	PUNCT
ejpam-3915	210	43	g)|	g)|	NOUN
ejpam-3915	210	44	−	−	PROPN
ejpam-3915	210	45	|a|	|a|	PROPN
ejpam-3915	210	46	>	>	X
ejpam-3915	210	47	|v	|v	PROPN
ejpam-3915	210	48	(	(	PUNCT
ejpam-3915	210	49	g)|	g)|	NOUN
ejpam-3915	210	50	=	=	NOUN
ejpam-3915	210	51	m	m	PROPN
ejpam-3915	210	52	since	since	SCONJ
ejpam-3915	210	53	|v	|v	PROPN
ejpam-3915	210	54	(	(	PUNCT
ejpam-3915	210	55	g)|	g)|	PROPN
ejpam-3915	210	56	>	>	X
ejpam-3915	210	57	|a|	|a|	NOUN
ejpam-3915	210	58	this	this	PRON
ejpam-3915	210	59	is	be	AUX
ejpam-3915	210	60	a	a	DET
ejpam-3915	210	61	contradiction	contradiction	NOUN
ejpam-3915	210	62	since	since	SCONJ
ejpam-3915	210	63	|r|	|r|	NOUN
ejpam-3915	210	64	=	=	NOUN
ejpam-3915	210	65	m	m	VERB
ejpam-3915	210	66	by	by	ADP
ejpam-3915	210	67	corollary	corollary	ADJ
ejpam-3915	210	68	2.6	2.6	NUM
ejpam-3915	210	69	.	.	PUNCT
ejpam-3915	211	1	thus	thus	ADV
ejpam-3915	211	2	,	,	PUNCT
ejpam-3915	211	3	r	r	NOUN
ejpam-3915	211	4	=	=	SYM
ejpam-3915	211	5	v	v	NOUN
ejpam-3915	211	6	(	(	PUNCT
ejpam-3915	211	7	g	g	NOUN
ejpam-3915	211	8	)	)	PUNCT
ejpam-3915	211	9	.	.	PUNCT
ejpam-3915	212	1	the	the	DET
ejpam-3915	212	2	converse	converse	NOUN
ejpam-3915	212	3	is	be	AUX
ejpam-3915	212	4	clear	clear	ADJ
ejpam-3915	212	5	.	.	PUNCT
ejpam-3915	213	1	in	in	ADP
ejpam-3915	213	2	particular	particular	ADJ
ejpam-3915	213	3	,	,	PUNCT
ejpam-3915	213	4	since	since	SCONJ
ejpam-3915	213	5	v	v	NOUN
ejpam-3915	213	6	(	(	PUNCT
ejpam-3915	213	7	g	g	NOUN
ejpam-3915	213	8	)	)	PUNCT
ejpam-3915	213	9	is	be	AUX
ejpam-3915	213	10	the	the	DET
ejpam-3915	213	11	unique	unique	ADJ
ejpam-3915	213	12	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	213	13	-set	-set	PUNCT
ejpam-3915	213	14	of	of	ADP
ejpam-3915	213	15	g	g	PROPN
ejpam-3915	213	16	◦	◦	NOUN
ejpam-3915	213	17	h	h	NOUN
ejpam-3915	213	18	,	,	PUNCT
ejpam-3915	213	19	by	by	ADP
ejpam-3915	213	20	theorem	theorem	NOUN
ejpam-3915	213	21	2.9(i	2.9(i	NUM
ejpam-3915	213	22	)	)	PUNCT
ejpam-3915	213	23	,	,	PUNCT
ejpam-3915	213	24	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	213	25	(	(	PUNCT
ejpam-3915	213	26	g	g	PROPN
ejpam-3915	213	27	◦	◦	NOUN
ejpam-3915	213	28	h	h	NOUN
ejpam-3915	213	29	)	)	PUNCT
ejpam-3915	213	30	=	=	SYM
ejpam-3915	214	1	0	0	X
ejpam-3915	214	2	.	.	PUNCT
ejpam-3915	215	1	the	the	DET
ejpam-3915	215	2	next	next	ADJ
ejpam-3915	215	3	result	result	NOUN
ejpam-3915	215	4	follows	follow	VERB
ejpam-3915	215	5	directly	directly	ADV
ejpam-3915	215	6	from	from	ADP
ejpam-3915	215	7	corollary	corollary	ADJ
ejpam-3915	215	8	3.3	3.3	NUM
ejpam-3915	215	9	and	and	CCONJ
ejpam-3915	215	10	theorem	theorem	VERB
ejpam-3915	215	11	4.1	4.1	NUM
ejpam-3915	215	12	.	.	PUNCT
ejpam-3915	216	1	note	note	VERB
ejpam-3915	216	2	that	that	SCONJ
ejpam-3915	216	3	k1	k1	NOUN
ejpam-3915	216	4	◦	◦	NOUN
ejpam-3915	216	5	h	h	NOUN
ejpam-3915	216	6	=	=	PROPN
ejpam-3915	216	7	k1	k1	PROPN
ejpam-3915	217	1	+	+	NOUN
ejpam-3915	217	2	h.	h.	PROPN
ejpam-3915	217	3	corollary	corollary	ADJ
ejpam-3915	217	4	4.2	4.2	NUM
ejpam-3915	217	5	.	.	PUNCT
ejpam-3915	218	1	let	let	VERB
ejpam-3915	218	2	km	km	PROPN
ejpam-3915	218	3	be	be	AUX
ejpam-3915	218	4	a	a	DET
ejpam-3915	218	5	complete	complete	ADJ
ejpam-3915	218	6	graph	graph	NOUN
ejpam-3915	218	7	of	of	ADP
ejpam-3915	218	8	order	order	NOUN
ejpam-3915	218	9	m	m	VERB
ejpam-3915	218	10	≥	≥	NOUN
ejpam-3915	218	11	1	1	NUM
ejpam-3915	218	12	and	and	CCONJ
ejpam-3915	218	13	let	let	VERB
ejpam-3915	218	14	h	h	NOUN
ejpam-3915	218	15	be	be	AUX
ejpam-3915	218	16	any	any	DET
ejpam-3915	218	17	graph	graph	NOUN
ejpam-3915	218	18	.	.	PUNCT
ejpam-3915	219	1	then	then	ADV
ejpam-3915	219	2	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3915	219	3	(	(	PUNCT
ejpam-3915	219	4	km	km	NOUN
ejpam-3915	219	5	◦	◦	NOUN
ejpam-3915	219	6	h	h	NOUN
ejpam-3915	219	7	)	)	PUNCT
ejpam-3915	219	8	=	=	SYM
ejpam-3915	219	9			X
ejpam-3915	219	10	0	0	NUM
ejpam-3915	219	11	,	,	PUNCT
ejpam-3915	219	12	if	if	SCONJ
ejpam-3915	219	13	either	either	PRON
ejpam-3915	219	14	m	m	VERB
ejpam-3915	219	15	=	=	SYM
ejpam-3915	219	16	1	1	NUM
ejpam-3915	219	17	and	and	CCONJ
ejpam-3915	219	18	h	h	NOUN
ejpam-3915	219	19	is	be	AUX
ejpam-3915	219	20	trivial	trivial	ADJ
ejpam-3915	219	21	,	,	PUNCT
ejpam-3915	219	22	or	or	CCONJ
ejpam-3915	219	23	m	m	VERB
ejpam-3915	219	24	>	>	X
ejpam-3915	219	25	1	1	NUM
ejpam-3915	219	26	,	,	PUNCT
ejpam-3915	219	27	1	1	NUM
ejpam-3915	219	28	,	,	PUNCT
ejpam-3915	219	29	if	if	SCONJ
ejpam-3915	219	30	m	m	VERB
ejpam-3915	219	31	=	=	NOUN
ejpam-3915	219	32	1	1	NUM
ejpam-3915	219	33	and	and	CCONJ
ejpam-3915	219	34	either	either	CCONJ
ejpam-3915	219	35	(	(	PUNCT
ejpam-3915	219	36	i	i	NOUN
ejpam-3915	219	37	)	)	PUNCT
ejpam-3915	219	38	h	h	PROPN
ejpam-3915	219	39	has	have	VERB
ejpam-3915	219	40	an	an	DET
ejpam-3915	219	41	isolated	isolated	ADJ
ejpam-3915	219	42	vertex	vertex	NOUN
ejpam-3915	219	43	,	,	PUNCT
ejpam-3915	219	44	or	or	CCONJ
ejpam-3915	219	45	(	(	PUNCT
ejpam-3915	219	46	ii	ii	NOUN
ejpam-3915	219	47	)	)	PUNCT
ejpam-3915	219	48	γt(h	γt(h	NUM
ejpam-3915	219	49	)	)	PUNCT
ejpam-3915	219	50	>	>	X
ejpam-3915	220	1	2	2	NUM
ejpam-3915	220	2	,	,	PUNCT
ejpam-3915	220	3	or	or	CCONJ
ejpam-3915	220	4	(	(	PUNCT
ejpam-3915	220	5	iii	iii	NOUN
ejpam-3915	220	6	)	)	PUNCT
ejpam-3915	220	7	γt(h	γt(h	NUM
ejpam-3915	220	8	)	)	PUNCT
ejpam-3915	220	9	=	=	SYM
ejpam-3915	220	10	2	2	NUM
ejpam-3915	220	11	and	and	CCONJ
ejpam-3915	220	12	there	there	PRON
ejpam-3915	220	13	exists	exist	VERB
ejpam-3915	220	14	a	a	DET
ejpam-3915	220	15	vertex	vertex	NOUN
ejpam-3915	220	16	in	in	ADP
ejpam-3915	220	17	h	h	NOUN
ejpam-3915	220	18	which	which	PRON
ejpam-3915	220	19	is	be	AUX
ejpam-3915	220	20	not	not	PART
ejpam-3915	220	21	in	in	ADP
ejpam-3915	220	22	any	any	DET
ejpam-3915	220	23	γt	γt	NOUN
ejpam-3915	220	24	-	-	NOUN
ejpam-3915	220	25	set	set	NOUN
ejpam-3915	220	26	of	of	ADP
ejpam-3915	220	27	h	h	NOUN
ejpam-3915	220	28	,	,	PUNCT
ejpam-3915	220	29	2	2	NUM
ejpam-3915	220	30	,	,	PUNCT
ejpam-3915	220	31	if	if	SCONJ
ejpam-3915	220	32	m	m	ADV
ejpam-3915	220	33	=	=	NOUN
ejpam-3915	220	34	1	1	NUM
ejpam-3915	220	35	,	,	PUNCT
ejpam-3915	220	36	γt(h	γt(h	NUM
ejpam-3915	220	37	)	)	PUNCT
ejpam-3915	220	38	=	=	SYM
ejpam-3915	220	39	2	2	NUM
ejpam-3915	220	40	and	and	CCONJ
ejpam-3915	220	41	every	every	DET
ejpam-3915	220	42	vertex	vertex	NOUN
ejpam-3915	220	43	in	in	ADP
ejpam-3915	220	44	h	h	NOUN
ejpam-3915	220	45	is	be	AUX
ejpam-3915	220	46	contained	contain	VERB
ejpam-3915	220	47	in	in	ADP
ejpam-3915	220	48	any	any	DET
ejpam-3915	220	49	γt	γt	NOUN
ejpam-3915	220	50	-	-	NOUN
ejpam-3915	220	51	set	set	NOUN
ejpam-3915	220	52	of	of	ADP
ejpam-3915	220	53	h.	h.	PROPN
ejpam-3915	220	54	5	5	NUM
ejpam-3915	220	55	.	.	PUNCT
ejpam-3915	220	56	forcing	force	VERB
ejpam-3915	220	57	total	total	ADJ
ejpam-3915	220	58	dr	dr	PROPN
ejpam-3915	220	59	-	-	PUNCT
ejpam-3915	220	60	power	power	NOUN
ejpam-3915	220	61	domination	domination	NOUN
ejpam-3915	220	62	number	number	NOUN
ejpam-3915	220	63	of	of	ADP
ejpam-3915	220	64	the	the	DET
ejpam-3915	220	65	lexicographic	lexicographic	ADJ
ejpam-3915	220	66	product	product	NOUN
ejpam-3915	220	67	of	of	ADP
ejpam-3915	220	68	graphs	graph	NOUN
ejpam-3915	220	69	this	this	DET
ejpam-3915	220	70	section	section	NOUN
ejpam-3915	220	71	contains	contain	VERB
ejpam-3915	220	72	the	the	DET
ejpam-3915	220	73	forcing	force	VERB
ejpam-3915	220	74	total	total	ADJ
ejpam-3915	220	75	dr	dr	PROPN
ejpam-3915	220	76	-	-	PUNCT
ejpam-3915	220	77	power	power	NOUN
ejpam-3915	220	78	domination	domination	NOUN
ejpam-3915	220	79	number	number	NOUN
ejpam-3915	220	80	of	of	ADP
ejpam-3915	220	81	the	the	DET
ejpam-3915	220	82	graphs	graph	NOUN
ejpam-3915	220	83	g[h	g[h	VERB
ejpam-3915	220	84	]	]	PUNCT
ejpam-3915	220	85	,	,	PUNCT
ejpam-3915	220	86	pn[h	pn[h	PROPN
ejpam-3915	220	87	]	]	X
ejpam-3915	220	88	and	and	CCONJ
ejpam-3915	220	89	cn[h	cn[h	PROPN
ejpam-3915	220	90	]	]	PUNCT
ejpam-3915	220	91	where	where	SCONJ
ejpam-3915	220	92	g	g	PROPN
ejpam-3915	220	93	and	and	CCONJ
ejpam-3915	220	94	h	h	NOUN
ejpam-3915	220	95	are	be	AUX
ejpam-3915	220	96	nontrivial	nontrivial	ADJ
ejpam-3915	220	97	connected	connected	ADJ
ejpam-3915	220	98	graphs	graph	NOUN
ejpam-3915	220	99	.	.	PUNCT
ejpam-3915	221	1	theorem	theorem	VERB
ejpam-3915	221	2	5.1	5.1	NUM
ejpam-3915	221	3	.	.	PUNCT
ejpam-3915	222	1	let	let	VERB
ejpam-3915	222	2	g	g	NOUN
ejpam-3915	222	3	and	and	CCONJ
ejpam-3915	222	4	h	h	NOUN
ejpam-3915	222	5	be	be	AUX
ejpam-3915	222	6	nontrivial	nontrivial	ADJ
ejpam-3915	222	7	connected	connected	ADJ
ejpam-3915	222	8	graphs	graph	NOUN
ejpam-3915	222	9	.	.	PUNCT
ejpam-3915	223	1	then	then	ADV
ejpam-3915	223	2	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3915	223	3	(	(	PUNCT
ejpam-3915	223	4	g[h	g[h	NOUN
ejpam-3915	223	5	]	]	PUNCT
ejpam-3915	223	6	)	)	PUNCT
ejpam-3915	223	7	=	=	SYM
ejpam-3915	223	8	γt(g	γt(g	NUM
ejpam-3915	223	9	)	)	PUNCT
ejpam-3915	223	10	.	.	PUNCT
ejpam-3915	224	1	proof	proof	NOUN
ejpam-3915	224	2	.	.	PUNCT
ejpam-3915	225	1	note	note	VERB
ejpam-3915	225	2	that	that	SCONJ
ejpam-3915	225	3	γ∗tpw	γ∗tpw	PROPN
ejpam-3915	225	4	(	(	PUNCT
ejpam-3915	225	5	g[h	g[h	NOUN
ejpam-3915	225	6	]	]	PUNCT
ejpam-3915	225	7	)	)	PUNCT
ejpam-3915	225	8	=	=	SYM
ejpam-3915	225	9	γt(g	γt(g	NOUN
ejpam-3915	225	10	)	)	PUNCT
ejpam-3915	225	11	by	by	ADP
ejpam-3915	225	12	corollary	corollary	ADJ
ejpam-3915	225	13	2.8	2.8	NUM
ejpam-3915	225	14	.	.	PUNCT
ejpam-3915	226	1	now	now	ADV
ejpam-3915	226	2	,	,	PUNCT
ejpam-3915	226	3	suppose	suppose	VERB
ejpam-3915	226	4	that	that	SCONJ
ejpam-3915	226	5	p	p	X
ejpam-3915	226	6	=	=	PUNCT
ejpam-3915	226	7	⋃	⋃	NOUN
ejpam-3915	226	8	u∈s	u∈s	ADJ
ejpam-3915	226	9	(	(	PUNCT
ejpam-3915	226	10	{	{	PUNCT
ejpam-3915	226	11	u	u	NOUN
ejpam-3915	226	12	}	}	PUNCT
ejpam-3915	226	13	×	×	PROPN
ejpam-3915	226	14	tu	tu	PROPN
ejpam-3915	226	15	)	)	PUNCT
ejpam-3915	226	16	,	,	PUNCT
ejpam-3915	226	17	where	where	SCONJ
ejpam-3915	226	18	s	s	NOUN
ejpam-3915	226	19	is	be	AUX
ejpam-3915	226	20	a	a	DET
ejpam-3915	226	21	γt	γt	NOUN
ejpam-3915	226	22	-	-	NOUN
ejpam-3915	226	23	set	set	NOUN
ejpam-3915	226	24	of	of	ADP
ejpam-3915	226	25	g	g	PROPN
ejpam-3915	226	26	and	and	CCONJ
ejpam-3915	226	27	tu	tu	PROPN
ejpam-3915	227	1	⊆	⊆	NUM
ejpam-3915	227	2	v	v	X
ejpam-3915	227	3	(	(	PUNCT
ejpam-3915	227	4	h	h	NOUN
ejpam-3915	227	5	)	)	PUNCT
ejpam-3915	227	6	.	.	PUNCT
ejpam-3915	228	1	consequently	consequently	ADV
ejpam-3915	228	2	,	,	PUNCT
ejpam-3915	228	3	|p	|p	ADJ
ejpam-3915	228	4	|	|	NOUN
ejpam-3915	228	5	=	=	SYM
ejpam-3915	228	6	|s|	|s|	NOUN
ejpam-3915	228	7	=	=	SYM
ejpam-3915	228	8	γt(g	γt(g	NUM
ejpam-3915	228	9	)	)	PUNCT
ejpam-3915	228	10	.	.	PUNCT
ejpam-3915	229	1	by	by	ADP
ejpam-3915	229	2	theorem	theorem	ADJ
ejpam-3915	229	3	2.7	2.7	NUM
ejpam-3915	229	4	and	and	CCONJ
ejpam-3915	229	5	corollary	corollary	ADJ
ejpam-3915	229	6	2.8	2.8	NUM
ejpam-3915	229	7	,	,	PUNCT
ejpam-3915	229	8	p	p	NOUN
ejpam-3915	229	9	is	be	AUX
ejpam-3915	229	10	a	a	DET
ejpam-3915	229	11	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	229	12	-set	-set	PROPN
ejpam-3915	229	13	of	of	ADP
ejpam-3915	229	14	g[h	g[h	NOUN
ejpam-3915	229	15	]	]	PUNCT
ejpam-3915	229	16	.	.	PUNCT
ejpam-3915	230	1	suppose	suppose	VERB
ejpam-3915	230	2	that	that	SCONJ
ejpam-3915	230	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	230	4	(	(	PUNCT
ejpam-3915	230	5	g[h	g[h	NOUN
ejpam-3915	230	6	]	]	PUNCT
ejpam-3915	230	7	)	)	PUNCT
ejpam-3915	231	1	=	=	SYM
ejpam-3915	231	2	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	231	3	(	(	PUNCT
ejpam-3915	231	4	p	p	NOUN
ejpam-3915	231	5	)	)	PUNCT
ejpam-3915	231	6	.	.	PUNCT
ejpam-3915	232	1	moreover	moreover	ADV
ejpam-3915	232	2	,	,	PUNCT
ejpam-3915	232	3	suppose	suppose	VERB
ejpam-3915	232	4	that	that	SCONJ
ejpam-3915	232	5	p	p	PROPN
ejpam-3915	232	6	has	have	VERB
ejpam-3915	232	7	a	a	DET
ejpam-3915	232	8	forcing	force	VERB
ejpam-3915	232	9	subset	subset	NOUN
ejpam-3915	232	10	r	r	NOUN
ejpam-3915	232	11	with	with	ADP
ejpam-3915	232	12	|r|	|r|	PROPN
ejpam-3915	232	13	<	<	X
ejpam-3915	232	14	|p	|p	X
ejpam-3915	232	15	|	|	ADV
ejpam-3915	232	16	,	,	PUNCT
ejpam-3915	232	17	that	that	ADV
ejpam-3915	232	18	is	is	ADV
ejpam-3915	232	19	,	,	PUNCT
ejpam-3915	232	20	p	p	X
ejpam-3915	232	21	=	=	PUNCT
ejpam-3915	232	22	r	r	NOUN
ejpam-3915	232	23	∪	∪	NOUN
ejpam-3915	232	24	n	n	NOUN
ejpam-3915	232	25	,	,	PUNCT
ejpam-3915	232	26	where	where	SCONJ
ejpam-3915	232	27	n	n	X
ejpam-3915	232	28	=	=	PRON
ejpam-3915	232	29	{	{	PUNCT
ejpam-3915	232	30	(	(	PUNCT
ejpam-3915	232	31	u	u	NOUN
ejpam-3915	232	32	,	,	PUNCT
ejpam-3915	232	33	v	v	NOUN
ejpam-3915	232	34	)	)	PUNCT
ejpam-3915	232	35	∈	∈	PROPN
ejpam-3915	232	36	p	p	NOUN
ejpam-3915	232	37	:	:	PUNCT
ejpam-3915	232	38	(	(	PUNCT
ejpam-3915	232	39	u	u	NOUN
ejpam-3915	232	40	,	,	PUNCT
ejpam-3915	232	41	v	v	NOUN
ejpam-3915	232	42	)	)	PUNCT
ejpam-3915	232	43	/∈	/∈	PUNCT
ejpam-3915	233	1	r	r	NOUN
ejpam-3915	233	2	}	}	PUNCT
ejpam-3915	233	3	.	.	PUNCT
ejpam-3915	234	1	pick	pick	VERB
ejpam-3915	234	2	(	(	PUNCT
ejpam-3915	234	3	u	u	NOUN
ejpam-3915	234	4	,	,	PUNCT
ejpam-3915	234	5	v	v	NOUN
ejpam-3915	234	6	)	)	PUNCT
ejpam-3915	234	7	∈	∈	PROPN
ejpam-3915	234	8	n	n	X
ejpam-3915	234	9	.	.	PUNCT
ejpam-3915	235	1	note	note	VERB
ejpam-3915	235	2	that	that	SCONJ
ejpam-3915	235	3	there	there	PRON
ejpam-3915	235	4	always	always	ADV
ejpam-3915	235	5	exists	exist	VERB
ejpam-3915	235	6	a	a	DET
ejpam-3915	235	7	vertex	vertex	NOUN
ejpam-3915	235	8	(	(	PUNCT
ejpam-3915	235	9	u	u	NOUN
ejpam-3915	235	10	,	,	PUNCT
ejpam-3915	235	11	w	w	NOUN
ejpam-3915	235	12	)	)	PUNCT
ejpam-3915	235	13	∈	∈	NOUN
ejpam-3915	235	14	v	v	NOUN
ejpam-3915	235	15	(	(	PUNCT
ejpam-3915	235	16	g[h])\p	g[h])\p	ADP
ejpam-3915	235	17	such	such	ADJ
ejpam-3915	235	18	that	that	DET
ejpam-3915	235	19	w	w	PROPN
ejpam-3915	235	20	6=	6=	PROPN
ejpam-3915	235	21	v	v	NOUN
ejpam-3915	235	22	and	and	CCONJ
ejpam-3915	235	23	[	[	X
ejpam-3915	235	24	p\{(u	p\{(u	PROPN
ejpam-3915	235	25	,	,	PUNCT
ejpam-3915	235	26	v	v	NOUN
ejpam-3915	235	27	)	)	PUNCT
ejpam-3915	235	28	}	}	PUNCT
ejpam-3915	235	29	]	]	PUNCT
ejpam-3915	235	30	∪	∪	X
ejpam-3915	235	31	{	{	PUNCT
ejpam-3915	235	32	(	(	PUNCT
ejpam-3915	235	33	u	u	NOUN
ejpam-3915	235	34	,	,	PUNCT
ejpam-3915	235	35	w	w	NOUN
ejpam-3915	235	36	)	)	PUNCT
ejpam-3915	235	37	}	}	PUNCT
ejpam-3915	236	1	=	=	PUNCT
ejpam-3915	236	2	q	q	X
ejpam-3915	236	3	is	be	AUX
ejpam-3915	236	4	a	a	DET
ejpam-3915	236	5	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	236	6	-set	-set	PROPN
ejpam-3915	236	7	of	of	ADP
ejpam-3915	236	8	g[h	g[h	NOUN
ejpam-3915	236	9	]	]	PUNCT
ejpam-3915	236	10	since	since	SCONJ
ejpam-3915	236	11	all	all	DET
ejpam-3915	236	12	adjacent	adjacent	ADJ
ejpam-3915	236	13	vertices	vertex	NOUN
ejpam-3915	236	14	(	(	PUNCT
ejpam-3915	236	15	r	r	NOUN
ejpam-3915	236	16	,	,	PUNCT
ejpam-3915	236	17	s	s	NOUN
ejpam-3915	236	18	)	)	PUNCT
ejpam-3915	236	19	references	reference	NOUN
ejpam-3915	236	20	1107	1107	NUM
ejpam-3915	236	21	of	of	ADP
ejpam-3915	236	22	(	(	PUNCT
ejpam-3915	236	23	u	u	NOUN
ejpam-3915	236	24	,	,	PUNCT
ejpam-3915	236	25	v	v	NOUN
ejpam-3915	236	26	)	)	PUNCT
ejpam-3915	236	27	with	with	ADP
ejpam-3915	236	28	u	u	PROPN
ejpam-3915	236	29	6=	6=	PROPN
ejpam-3915	236	30	r	r	NOUN
ejpam-3915	236	31	are	be	AUX
ejpam-3915	236	32	adjacent	adjacent	ADJ
ejpam-3915	236	33	vertices	vertex	NOUN
ejpam-3915	236	34	of	of	ADP
ejpam-3915	236	35	(	(	PUNCT
ejpam-3915	236	36	u	u	NOUN
ejpam-3915	236	37	,	,	PUNCT
ejpam-3915	236	38	w	w	NOUN
ejpam-3915	236	39	)	)	PUNCT
ejpam-3915	236	40	also	also	ADV
ejpam-3915	236	41	.	.	PUNCT
ejpam-3915	237	1	thus	thus	ADV
ejpam-3915	237	2	,	,	PUNCT
ejpam-3915	237	3	q	q	X
ejpam-3915	237	4	=	=	PUNCT
ejpam-3915	237	5	r	r	NOUN
ejpam-3915	237	6	∪	∪	VERB
ejpam-3915	237	7	m	m	PROPN
ejpam-3915	237	8	,	,	PUNCT
ejpam-3915	237	9	where	where	SCONJ
ejpam-3915	237	10	m	m	VERB
ejpam-3915	237	11	=	=	PUNCT
ejpam-3915	238	1	[	[	X
ejpam-3915	238	2	n\{(u	n\{(u	ADJ
ejpam-3915	238	3	,	,	PUNCT
ejpam-3915	238	4	v	v	NOUN
ejpam-3915	238	5	)	)	PUNCT
ejpam-3915	238	6	}	}	PUNCT
ejpam-3915	238	7	]	]	PUNCT
ejpam-3915	238	8	∪	∪	X
ejpam-3915	238	9	{	{	PUNCT
ejpam-3915	238	10	(	(	PUNCT
ejpam-3915	238	11	u	u	NOUN
ejpam-3915	238	12	,	,	PUNCT
ejpam-3915	238	13	w	w	NOUN
ejpam-3915	238	14	)	)	PUNCT
ejpam-3915	238	15	}	}	PUNCT
ejpam-3915	238	16	,	,	PUNCT
ejpam-3915	238	17	oq	oq	INTJ
ejpam-3915	238	18	v	v	INTJ
ejpam-3915	238	19	(	(	PUNCT
ejpam-3915	238	20	g[h	g[h	PROPN
ejpam-3915	238	21	]	]	PUNCT
ejpam-3915	238	22	)	)	PUNCT
ejpam-3915	238	23	=	=	SYM
ejpam-3915	238	24	v	v	X
ejpam-3915	238	25	(	(	PUNCT
ejpam-3915	238	26	g[h	g[h	PROPN
ejpam-3915	238	27	]	]	PUNCT
ejpam-3915	238	28	)	)	PUNCT
ejpam-3915	238	29	and	and	CCONJ
ejpam-3915	238	30	oq	oq	ADJ
ejpam-3915	238	31	e(g[h	e(g[h	X
ejpam-3915	238	32	]	]	PUNCT
ejpam-3915	238	33	)	)	PUNCT
ejpam-3915	238	34	=	=	SYM
ejpam-3915	238	35	e(g[h	e(g[h	X
ejpam-3915	238	36	]	]	PUNCT
ejpam-3915	238	37	)	)	PUNCT
ejpam-3915	238	38	,	,	PUNCT
ejpam-3915	238	39	that	that	ADV
ejpam-3915	238	40	is	is	ADV
ejpam-3915	238	41	,	,	PUNCT
ejpam-3915	238	42	q	q	X
ejpam-3915	238	43	is	be	AUX
ejpam-3915	238	44	a	a	DET
ejpam-3915	238	45	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	238	46	-set	-set	PUNCT
ejpam-3915	238	47	containing	contain	VERB
ejpam-3915	238	48	r	r	NOUN
ejpam-3915	238	49	,	,	PUNCT
ejpam-3915	238	50	a	a	DET
ejpam-3915	238	51	contradiction	contradiction	NOUN
ejpam-3915	238	52	.	.	PUNCT
ejpam-3915	239	1	thus,|r|	thus,|r|	NOUN
ejpam-3915	239	2	=	=	SYM
ejpam-3915	239	3	|p	|p	X
ejpam-3915	240	1	|	|	ADV
ejpam-3915	240	2	and	and	CCONJ
ejpam-3915	240	3	p	p	NOUN
ejpam-3915	240	4	is	be	AUX
ejpam-3915	240	5	the	the	DET
ejpam-3915	240	6	only	only	ADJ
ejpam-3915	240	7	forcing	forcing	NOUN
ejpam-3915	240	8	subset	subset	NOUN
ejpam-3915	240	9	for	for	ADP
ejpam-3915	240	10	p	p	PROPN
ejpam-3915	240	11	.	.	PUNCT
ejpam-3915	241	1	therefore	therefore	ADV
ejpam-3915	241	2	,	,	PUNCT
ejpam-3915	241	3	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	241	4	(	(	PUNCT
ejpam-3915	241	5	g[h	g[h	NOUN
ejpam-3915	241	6	]	]	PUNCT
ejpam-3915	241	7	)	)	PUNCT
ejpam-3915	242	1	=	=	SYM
ejpam-3915	242	2	|p	|p	PUNCT
ejpam-3915	242	3	|	|	ADV
ejpam-3915	242	4	=	=	SYM
ejpam-3915	242	5	γt(g	γt(g	NUM
ejpam-3915	242	6	)	)	PUNCT
ejpam-3915	242	7	.	.	PUNCT
ejpam-3915	243	1	the	the	DET
ejpam-3915	243	2	next	next	ADJ
ejpam-3915	243	3	result	result	NOUN
ejpam-3915	243	4	follows	follow	VERB
ejpam-3915	243	5	from	from	ADP
ejpam-3915	243	6	theorem	theorem	ADJ
ejpam-3915	243	7	5.1	5.1	NUM
ejpam-3915	243	8	and	and	CCONJ
ejpam-3915	243	9	corollary	corollary	ADJ
ejpam-3915	243	10	2.2	2.2	NUM
ejpam-3915	243	11	.	.	PUNCT
ejpam-3915	244	1	corollary	corollary	ADJ
ejpam-3915	244	2	5.2	5.2	NUM
ejpam-3915	244	3	.	.	PUNCT
ejpam-3915	245	1	let	let	VERB
ejpam-3915	245	2	h	h	PRON
ejpam-3915	245	3	be	be	AUX
ejpam-3915	245	4	a	a	DET
ejpam-3915	245	5	nontrivial	nontrivial	ADJ
ejpam-3915	245	6	connected	connect	VERB
ejpam-3915	245	7	graph	graph	NOUN
ejpam-3915	245	8	and	and	CCONJ
ejpam-3915	245	9	n	n	PRON
ejpam-3915	245	10	≥	≥	NOUN
ejpam-3915	245	11	3	3	NUM
ejpam-3915	245	12	.	.	PUNCT
ejpam-3915	246	1	then	then	ADV
ejpam-3915	246	2	fγ∗tpw	fγ∗tpw	PROPN
ejpam-3915	246	3	(	(	PUNCT
ejpam-3915	246	4	pn[h	pn[h	PROPN
ejpam-3915	246	5	]	]	X
ejpam-3915	246	6	)	)	PUNCT
ejpam-3915	247	1	=	=	SYM
ejpam-3915	247	2	fγ∗tpw	fγ∗tpw	NOUN
ejpam-3915	247	3	(	(	PUNCT
ejpam-3915	247	4	cn[h	cn[h	PROPN
ejpam-3915	247	5	]	]	PUNCT
ejpam-3915	247	6	)	)	PUNCT
ejpam-3915	247	7	=	=	SYM
ejpam-3915	247	8			PROPN
ejpam-3915	247	9	n	n	ADV
ejpam-3915	247	10	2	2	NUM
ejpam-3915	247	11	,	,	PUNCT
ejpam-3915	247	12	n	n	PRON
ejpam-3915	247	13	≡	≡	PROPN
ejpam-3915	247	14	0(mod	0(mod	NOUN
ejpam-3915	247	15	4	4	NUM
ejpam-3915	247	16	)	)	PUNCT
ejpam-3915	247	17	,	,	PUNCT
ejpam-3915	247	18	n+2	n+2	ADV
ejpam-3915	247	19	2	2	NUM
ejpam-3915	247	20	,	,	PUNCT
ejpam-3915	247	21	n	n	PRON
ejpam-3915	247	22	≡	≡	PROPN
ejpam-3915	247	23	2(mod	2(mod	NUM
ejpam-3915	247	24	4	4	NUM
ejpam-3915	247	25	)	)	PUNCT
ejpam-3915	247	26	,	,	PUNCT
ejpam-3915	247	27	n+1	n+1	PROPN
ejpam-3915	247	28	2	2	NUM
ejpam-3915	247	29	,	,	PUNCT
ejpam-3915	247	30	otherwise	otherwise	ADV
ejpam-3915	247	31	.	.	PUNCT
ejpam-3915	248	1	acknowledgements	acknowledgement	VERB
ejpam-3915	248	2	the	the	DET
ejpam-3915	248	3	author	author	NOUN
ejpam-3915	248	4	thanks	thank	NOUN
ejpam-3915	248	5	the	the	DET
ejpam-3915	248	6	peer	peer	NOUN
ejpam-3915	248	7	reviewers	reviewer	NOUN
ejpam-3915	248	8	of	of	ADP
ejpam-3915	248	9	the	the	DET
ejpam-3915	248	10	paper	paper	NOUN
ejpam-3915	248	11	and	and	CCONJ
ejpam-3915	248	12	readers	reader	NOUN
ejpam-3915	248	13	of	of	ADP
ejpam-3915	248	14	european	european	PROPN
ejpam-3915	248	15	journal	journal	PROPN
ejpam-3915	248	16	of	of	ADP
ejpam-3915	248	17	pure	pure	ADJ
ejpam-3915	248	18	and	and	CCONJ
ejpam-3915	248	19	applied	applied	ADJ
ejpam-3915	248	20	mathematics	mathematic	NOUN
ejpam-3915	248	21	,	,	PUNCT
ejpam-3915	248	22	for	for	ADP
ejpam-3915	248	23	making	make	VERB
ejpam-3915	248	24	the	the	DET
ejpam-3915	248	25	journal	journal	NOUN
ejpam-3915	248	26	successful	successful	ADJ
ejpam-3915	248	27	and	and	CCONJ
ejpam-3915	248	28	to	to	ADP
ejpam-3915	248	29	the	the	DET
ejpam-3915	248	30	cebu	cebu	NOUN
ejpam-3915	248	31	normal	normal	ADJ
ejpam-3915	248	32	university	university	NOUN
ejpam-3915	248	33	for	for	ADP
ejpam-3915	248	34	the	the	DET
ejpam-3915	248	35	financial	financial	ADJ
ejpam-3915	248	36	support	support	NOUN
ejpam-3915	248	37	.	.	PUNCT
ejpam-3915	249	1	the	the	DET
ejpam-3915	249	2	author	author	NOUN
ejpam-3915	249	3	also	also	ADV
ejpam-3915	249	4	expresses	express	VERB
ejpam-3915	249	5	warm	warm	ADJ
ejpam-3915	249	6	gratitude	gratitude	NOUN
ejpam-3915	249	7	to	to	ADP
ejpam-3915	249	8	ho	ho	PROPN
ejpam-3915	249	9	jc	jc	PROPN
ejpam-3915	249	10	for	for	ADP
ejpam-3915	249	11	the	the	DET
ejpam-3915	249	12	emotional	emotional	ADJ
ejpam-3915	249	13	and	and	CCONJ
ejpam-3915	249	14	moral	moral	ADJ
ejpam-3915	249	15	support	support	NOUN
ejpam-3915	249	16	.	.	PUNCT
ejpam-3915	250	1	references	reference	NOUN
ejpam-3915	250	2	[	[	X
ejpam-3915	250	3	1	1	NUM
ejpam-3915	250	4	]	]	X
ejpam-3915	250	5	d	d	PROPN
ejpam-3915	250	6	amos	amos	PROPN
ejpam-3915	250	7	.	.	PUNCT
ejpam-3915	251	1	on	on	ADP
ejpam-3915	251	2	total	total	ADJ
ejpam-3915	251	3	domination	domination	NOUN
ejpam-3915	251	4	in	in	ADP
ejpam-3915	251	5	graphs	graph	NOUN
ejpam-3915	251	6	.	.	PUNCT
ejpam-3915	252	1	university	university	NOUN
ejpam-3915	252	2	of	of	ADP
ejpam-3915	252	3	houston	houston	PROPN
ejpam-3915	252	4	-	-	PUNCT
ejpam-3915	252	5	downtown	downtown	NOUN
ejpam-3915	252	6	,	,	PUNCT
ejpam-3915	252	7	2012	2012	NUM
ejpam-3915	252	8	.	.	PUNCT
ejpam-3915	253	1	[	[	X
ejpam-3915	253	2	2	2	NUM
ejpam-3915	253	3	]	]	X
ejpam-3915	253	4	c	c	PROPN
ejpam-3915	253	5	armada	armada	PROPN
ejpam-3915	253	6	.	.	PUNCT
ejpam-3915	254	1	forcing	force	VERB
ejpam-3915	254	2	subsets	subset	NOUN
ejpam-3915	254	3	for	for	ADP
ejpam-3915	254	4	γ∗tpw	γ∗tpw	NOUN
ejpam-3915	254	5	-sets	-set	NOUN
ejpam-3915	254	6	in	in	ADP
ejpam-3915	254	7	graphs	graph	NOUN
ejpam-3915	254	8	.	.	PUNCT
ejpam-3915	255	1	european	european	ADJ
ejpam-3915	255	2	journal	journal	PROPN
ejpam-3915	255	3	of	of	ADP
ejpam-3915	255	4	pure	pure	ADJ
ejpam-3915	255	5	and	and	CCONJ
ejpam-3915	255	6	applied	applied	ADJ
ejpam-3915	255	7	mathematics	mathematic	NOUN
ejpam-3915	255	8	,	,	PUNCT
ejpam-3915	255	9	14(2):451–470	14(2):451–470	PROPN
ejpam-3915	255	10	,	,	PUNCT
ejpam-3915	255	11	2021	2021	NUM
ejpam-3915	255	12	.	.	PUNCT
ejpam-3915	256	1	[	[	X
ejpam-3915	256	2	3	3	NUM
ejpam-3915	256	3	]	]	X
ejpam-3915	256	4	c	c	PROPN
ejpam-3915	256	5	armada	armada	PROPN
ejpam-3915	256	6	and	and	CCONJ
ejpam-3915	256	7	s	s	VERB
ejpam-3915	256	8	canoy	canoy	PROPN
ejpam-3915	256	9	jr	jr	PROPN
ejpam-3915	256	10	.	.	PROPN
ejpam-3915	257	1	a	a	X
ejpam-3915	257	2	-	-	PUNCT
ejpam-3915	257	3	differential	differential	NOUN
ejpam-3915	257	4	of	of	ADP
ejpam-3915	257	5	graphs	graph	NOUN
ejpam-3915	257	6	.	.	PUNCT
ejpam-3915	258	1	international	international	ADJ
ejpam-3915	258	2	journal	journal	PROPN
ejpam-3915	258	3	of	of	ADP
ejpam-3915	258	4	mathematical	mathematical	ADJ
ejpam-3915	258	5	analysis	analysis	NOUN
ejpam-3915	258	6	,	,	PUNCT
ejpam-3915	258	7	9(44):2171–2180	9(44):2171–2180	NUM
ejpam-3915	258	8	,	,	PUNCT
ejpam-3915	258	9	2015	2015	NUM
ejpam-3915	258	10	.	.	PUNCT
ejpam-3915	259	1	[	[	X
ejpam-3915	259	2	4	4	NUM
ejpam-3915	259	3	]	]	X
ejpam-3915	259	4	c	c	X
ejpam-3915	259	5	armada	armada	PROPN
ejpam-3915	259	6	and	and	CCONJ
ejpam-3915	259	7	s	s	VERB
ejpam-3915	259	8	canoy	canoy	PROPN
ejpam-3915	259	9	jr	jr	PROPN
ejpam-3915	259	10	.	.	PUNCT
ejpam-3915	259	11	forcing	force	VERB
ejpam-3915	259	12	independent	independent	ADJ
ejpam-3915	259	13	domination	domination	NOUN
ejpam-3915	259	14	number	number	NOUN
ejpam-3915	259	15	of	of	ADP
ejpam-3915	259	16	a	a	DET
ejpam-3915	259	17	graph	graph	NOUN
ejpam-3915	259	18	.	.	PUNCT
ejpam-3915	260	1	european	european	ADJ
ejpam-3915	260	2	journal	journal	PROPN
ejpam-3915	260	3	of	of	ADP
ejpam-3915	260	4	pure	pure	ADJ
ejpam-3915	260	5	and	and	CCONJ
ejpam-3915	260	6	applied	applied	ADJ
ejpam-3915	260	7	mathematics	mathematic	NOUN
ejpam-3915	260	8	,	,	PUNCT
ejpam-3915	260	9	12(4):1371–1381	12(4):1371–1381	NUM
ejpam-3915	260	10	,	,	PUNCT
ejpam-3915	260	11	2019	2019	NUM
ejpam-3915	260	12	.	.	PUNCT
ejpam-3915	261	1	[	[	X
ejpam-3915	261	2	5	5	NUM
ejpam-3915	261	3	]	]	X
ejpam-3915	261	4	h	h	NOUN
ejpam-3915	261	5	gavlas	gavlas	PROPN
ejpam-3915	261	6	,	,	PUNCT
ejpam-3915	261	7	k	k	PROPN
ejpam-3915	261	8	c	c	NOUN
ejpam-3915	261	9	vandell	vandell	NOUN
ejpam-3915	261	10	,	,	PUNCT
ejpam-3915	261	11	g	g	PROPN
ejpam-3915	261	12	chartrand	chartrand	NOUN
ejpam-3915	261	13	,	,	PUNCT
ejpam-3915	261	14	and	and	CCONJ
ejpam-3915	261	15	f	f	PROPN
ejpam-3915	261	16	harary	harary	NOUN
ejpam-3915	261	17	.	.	PUNCT
ejpam-3915	262	1	the	the	DET
ejpam-3915	262	2	forcing	force	VERB
ejpam-3915	262	3	domination	domination	NOUN
ejpam-3915	262	4	number	number	NOUN
ejpam-3915	262	5	of	of	ADP
ejpam-3915	262	6	a	a	DET
ejpam-3915	262	7	graph	graph	NOUN
ejpam-3915	262	8	.	.	PUNCT
ejpam-3915	263	1	j.	j.	PROPN
ejpam-3915	263	2	combin	combin	PROPN
ejpam-3915	263	3	.	.	PUNCT
ejpam-3915	264	1	math	math	NOUN
ejpam-3915	264	2	.	.	PUNCT
ejpam-3915	265	1	combin	combin	NOUN
ejpam-3915	265	2	.	.	PUNCT
ejpam-3915	266	1	comput	comput	NOUN
ejpam-3915	266	2	.	.	PUNCT
ejpam-3915	266	3	,	,	PUNCT
ejpam-3915	267	1	25:161–174	25:161–174	NUM
ejpam-3915	267	2	,	,	PUNCT
ejpam-3915	267	3	1997	1997	NUM
ejpam-3915	267	4	.	.	PUNCT
ejpam-3915	268	1	[	[	X
ejpam-3915	268	2	6	6	NUM
ejpam-3915	268	3	]	]	PUNCT
ejpam-3915	268	4	i	i	PRON
ejpam-3915	268	5	cabahug	cabahug	VERB
ejpam-3915	268	6	jr	jr	PROPN
ejpam-3915	268	7	.	.	PUNCT
ejpam-3915	268	8	and	and	CCONJ
ejpam-3915	268	9	s	s	VERB
ejpam-3915	268	10	canoy	canoy	PROPN
ejpam-3915	268	11	jr	jr	PROPN
ejpam-3915	268	12	.	.	PROPN
ejpam-3915	268	13	total	total	PROPN
ejpam-3915	268	14	dr	dr	PROPN
ejpam-3915	268	15	-	-	PUNCT
ejpam-3915	268	16	power	power	NOUN
ejpam-3915	268	17	dominating	dominating	NOUN
ejpam-3915	268	18	sets	set	NOUN
ejpam-3915	268	19	in	in	ADP
ejpam-3915	268	20	graphs	graph	NOUN
ejpam-3915	268	21	.	.	PUNCT
ejpam-3915	269	1	accepted	accept	VERB
ejpam-3915	269	2	for	for	ADP
ejpam-3915	269	3	publication	publication	NOUN
ejpam-3915	269	4	.	.	PUNCT
ejpam-3915	270	1	[	[	X
ejpam-3915	270	2	7	7	NUM
ejpam-3915	270	3	]	]	X
ejpam-3915	270	4	s	s	PART
ejpam-3915	270	5	canoy	canoy	PROPN
ejpam-3915	270	6	jr	jr	PROPN
ejpam-3915	270	7	.	.	PROPN
ejpam-3915	270	8	,	,	PUNCT
ejpam-3915	270	9	c	c	PROPN
ejpam-3915	270	10	armada	armada	PROPN
ejpam-3915	270	11	,	,	PUNCT
ejpam-3915	270	12	and	and	CCONJ
ejpam-3915	270	13	c	c	PROPN
ejpam-3915	270	14	go	go	VERB
ejpam-3915	270	15	.	.	PUNCT
ejpam-3915	271	1	forcing	force	VERB
ejpam-3915	271	2	domination	domination	NOUN
ejpam-3915	271	3	numbers	number	NOUN
ejpam-3915	271	4	of	of	ADP
ejpam-3915	271	5	graphs	graph	NOUN
ejpam-3915	271	6	under	under	ADP
ejpam-3915	271	7	some	some	DET
ejpam-3915	271	8	binary	binary	ADJ
ejpam-3915	271	9	operations	operation	NOUN
ejpam-3915	271	10	.	.	PUNCT
ejpam-3915	272	1	advances	advance	NOUN
ejpam-3915	272	2	and	and	CCONJ
ejpam-3915	272	3	applications	application	NOUN
ejpam-3915	272	4	in	in	ADP
ejpam-3915	272	5	discrete	discrete	ADJ
ejpam-3915	272	6	mathematics	mathematic	NOUN
ejpam-3915	272	7	,	,	PUNCT
ejpam-3915	272	8	19:213–228	19:213–228	NUM
ejpam-3915	272	9	,	,	PUNCT
ejpam-3915	272	10	2018	2018	NUM
ejpam-3915	272	11	.	.	PUNCT
ejpam-3915	273	1	[	[	X
ejpam-3915	273	2	8	8	NUM
ejpam-3915	273	3	]	]	X
ejpam-3915	273	4	s	s	PART
ejpam-3915	273	5	canoy	canoy	PROPN
ejpam-3915	273	6	jr	jr	PROPN
ejpam-3915	273	7	.	.	PROPN
ejpam-3915	273	8	,	,	PUNCT
ejpam-3915	273	9	c	c	PROPN
ejpam-3915	273	10	armada	armada	PROPN
ejpam-3915	273	11	,	,	PUNCT
ejpam-3915	273	12	and	and	CCONJ
ejpam-3915	273	13	c	c	PROPN
ejpam-3915	273	14	go	go	VERB
ejpam-3915	273	15	.	.	PUNCT
ejpam-3915	274	1	forcing	force	VERB
ejpam-3915	274	2	subsets	subset	NOUN
ejpam-3915	274	3	for	for	ADP
ejpam-3915	274	4	γc	γc	NOUN
ejpam-3915	274	5	-	-	PUNCT
ejpam-3915	274	6	sets	set	NOUN
ejpam-3915	274	7	and	and	CCONJ
ejpam-3915	274	8	γt	γt	NOUN
ejpam-3915	274	9	-	-	NOUN
ejpam-3915	274	10	sets	set	NOUN
ejpam-3915	274	11	in	in	ADP
ejpam-3915	274	12	the	the	DET
ejpam-3915	274	13	lexicographic	lexicographic	ADJ
ejpam-3915	274	14	product	product	NOUN
ejpam-3915	274	15	of	of	ADP
ejpam-3915	274	16	graphs	graph	NOUN
ejpam-3915	274	17	.	.	PUNCT
ejpam-3915	275	1	european	european	ADJ
ejpam-3915	275	2	journal	journal	PROPN
ejpam-3915	275	3	of	of	ADP
ejpam-3915	275	4	pure	pure	ADJ
ejpam-3915	275	5	and	and	CCONJ
ejpam-3915	275	6	applied	applied	ADJ
ejpam-3915	275	7	mathematics	mathematic	NOUN
ejpam-3915	275	8	,	,	PUNCT
ejpam-3915	275	9	12(4):1779–1786	12(4):1779–1786	NUM
ejpam-3915	275	10	,	,	PUNCT
ejpam-3915	275	11	2019	2019	NUM
ejpam-3915	275	12	.	.	PUNCT