id	sid	tid	token	lemma	pos
ejpam-6939	1	1	european	european	PROPN
ejpam-6939	1	2	journal	journal	PROPN
ejpam-6939	1	3	of	of	ADP
ejpam-6939	1	4	pure	pure	ADJ
ejpam-6939	1	5	and	and	CCONJ
ejpam-6939	1	6	applied	applied	ADJ
ejpam-6939	1	7	mathematics	mathematic	NOUN
ejpam-6939	1	8	2025	2025	NUM
ejpam-6939	1	9	,	,	PUNCT
ejpam-6939	1	10	vol	vol	NOUN
ejpam-6939	1	11	.	.	PROPN
ejpam-6939	1	12	18	18	NUM
ejpam-6939	1	13	,	,	PUNCT
ejpam-6939	1	14	issue	issue	NOUN
ejpam-6939	1	15	4	4	NUM
ejpam-6939	1	16	,	,	PUNCT
ejpam-6939	1	17	article	article	NOUN
ejpam-6939	1	18	number	number	NOUN
ejpam-6939	1	19	6939	6939	NUM
ejpam-6939	1	20	issn	issn	PROPN
ejpam-6939	1	21	1307	1307	NUM
ejpam-6939	1	22	-	-	SYM
ejpam-6939	1	23	5543	5543	NUM
ejpam-6939	1	24	–	–	PUNCT
ejpam-6939	1	25	ejpam.com	ejpam.com	X
ejpam-6939	1	26	published	publish	VERB
ejpam-6939	1	27	by	by	ADP
ejpam-6939	1	28	new	new	PROPN
ejpam-6939	1	29	york	york	PROPN
ejpam-6939	1	30	business	business	PROPN
ejpam-6939	1	31	global	global	ADJ
ejpam-6939	1	32	connected	connect	VERB
ejpam-6939	1	33	disjunctive	disjunctive	ADJ
ejpam-6939	1	34	domination	domination	NOUN
ejpam-6939	1	35	in	in	ADP
ejpam-6939	1	36	graphs	graph	NOUN
ejpam-6939	1	37	alkajim	alkajim	NOUN
ejpam-6939	1	38	ahadi	ahadi	NOUN
ejpam-6939	1	39	aradais1,3,∗	aradais1,3,∗	PROPN
ejpam-6939	1	40	,	,	PUNCT
ejpam-6939	2	1	ferdinand	ferdinand	PROPN
ejpam-6939	2	2	p.	p.	PROPN
ejpam-6939	2	3	jamil2,3	jamil2,3	PROPN
ejpam-6939	2	4	,	,	PUNCT
ejpam-6939	2	5	sergio	sergio	PROPN
ejpam-6939	2	6	r.	r.	PROPN
ejpam-6939	2	7	canoy	canoy	PROPN
ejpam-6939	2	8	,	,	PUNCT
ejpam-6939	2	9	jr.2,3	jr.2,3	PROPN
ejpam-6939	2	10	1	1	NUM
ejpam-6939	2	11	department	department	NOUN
ejpam-6939	2	12	of	of	ADP
ejpam-6939	2	13	mathematics	mathematic	NOUN
ejpam-6939	2	14	,	,	PUNCT
ejpam-6939	2	15	college	college	NOUN
ejpam-6939	2	16	of	of	ADP
ejpam-6939	2	17	arts	art	NOUN
ejpam-6939	2	18	and	and	CCONJ
ejpam-6939	2	19	sciences	science	NOUN
ejpam-6939	2	20	,	,	PUNCT
ejpam-6939	2	21	msu	msu	PROPN
ejpam-6939	2	22	-	-	PUNCT
ejpam-6939	2	23	tawi	tawi	NOUN
ejpam-6939	2	24	-	-	PUNCT
ejpam-6939	2	25	tawi	tawi	NOUN
ejpam-6939	2	26	college	college	PROPN
ejpam-6939	2	27	of	of	ADP
ejpam-6939	2	28	technology	technology	NOUN
ejpam-6939	2	29	and	and	CCONJ
ejpam-6939	2	30	oceanography	oceanography	NOUN
ejpam-6939	2	31	,	,	PUNCT
ejpam-6939	2	32	7500	7500	NUM
ejpam-6939	2	33	bongao	bongao	NOUN
ejpam-6939	2	34	,	,	PUNCT
ejpam-6939	2	35	tawi	tawi	NOUN
ejpam-6939	2	36	-	-	PUNCT
ejpam-6939	2	37	tawi	tawi	NOUN
ejpam-6939	2	38	,	,	PUNCT
ejpam-6939	2	39	2	2	NUM
ejpam-6939	2	40	department	department	NOUN
ejpam-6939	2	41	of	of	ADP
ejpam-6939	2	42	mathematics	mathematic	NOUN
ejpam-6939	2	43	and	and	CCONJ
ejpam-6939	2	44	statistics	statistic	NOUN
ejpam-6939	2	45	,	,	PUNCT
ejpam-6939	2	46	college	college	NOUN
ejpam-6939	2	47	of	of	ADP
ejpam-6939	2	48	science	science	NOUN
ejpam-6939	2	49	and	and	CCONJ
ejpam-6939	2	50	mathematics	mathematics	PROPN
ejpam-6939	2	51	3	3	NUM
ejpam-6939	2	52	center	center	NOUN
ejpam-6939	2	53	for	for	ADP
ejpam-6939	2	54	mathematical	mathematical	ADJ
ejpam-6939	2	55	and	and	CCONJ
ejpam-6939	2	56	theoretical	theoretical	ADJ
ejpam-6939	2	57	physical	physical	ADJ
ejpam-6939	2	58	sciences	science	NOUN
ejpam-6939	2	59	,	,	PUNCT
ejpam-6939	2	60	premier	premier	PROPN
ejpam-6939	2	61	research	research	PROPN
ejpam-6939	2	62	institute	institute	PROPN
ejpam-6939	2	63	of	of	ADP
ejpam-6939	2	64	science	science	NOUN
ejpam-6939	2	65	and	and	CCONJ
ejpam-6939	2	66	mathematics	mathematic	NOUN
ejpam-6939	2	67	,	,	PUNCT
ejpam-6939	2	68	msu	msu	PROPN
ejpam-6939	2	69	-	-	PUNCT
ejpam-6939	2	70	iligan	iligan	PROPN
ejpam-6939	2	71	institute	institute	PROPN
ejpam-6939	2	72	of	of	ADP
ejpam-6939	2	73	technology	technology	PROPN
ejpam-6939	2	74	,	,	PUNCT
ejpam-6939	2	75	9200	9200	NUM
ejpam-6939	2	76	iligan	iligan	ADJ
ejpam-6939	2	77	city	city	NOUN
ejpam-6939	2	78	,	,	PUNCT
ejpam-6939	2	79	philippines	philippine	NOUN
ejpam-6939	2	80	abstract	abstract	ADJ
ejpam-6939	2	81	.	.	PUNCT
ejpam-6939	3	1	a	a	DET
ejpam-6939	3	2	set	set	NOUN
ejpam-6939	3	3	s	s	NOUN
ejpam-6939	3	4	of	of	ADP
ejpam-6939	3	5	vertices	vertex	NOUN
ejpam-6939	3	6	of	of	ADP
ejpam-6939	3	7	a	a	DET
ejpam-6939	3	8	graph	graph	NOUN
ejpam-6939	3	9	g	g	NOUN
ejpam-6939	3	10	is	be	AUX
ejpam-6939	3	11	a	a	DET
ejpam-6939	3	12	disjunctive	disjunctive	ADJ
ejpam-6939	3	13	dominating	dominating	NOUN
ejpam-6939	3	14	set	set	VERB
ejpam-6939	3	15	if	if	SCONJ
ejpam-6939	3	16	for	for	ADP
ejpam-6939	3	17	every	every	DET
ejpam-6939	3	18	v	v	NUM
ejpam-6939	3	19	∈	∈	NOUN
ejpam-6939	3	20	v	v	NOUN
ejpam-6939	3	21	(	(	PUNCT
ejpam-6939	3	22	g)\s	g)\s	NOUN
ejpam-6939	3	23	,	,	PUNCT
ejpam-6939	3	24	v	v	NOUN
ejpam-6939	3	25	is	be	AUX
ejpam-6939	3	26	adjacent	adjacent	ADJ
ejpam-6939	3	27	to	to	ADP
ejpam-6939	3	28	a	a	DET
ejpam-6939	3	29	vertex	vertex	NOUN
ejpam-6939	3	30	in	in	ADP
ejpam-6939	3	31	s	s	PRON
ejpam-6939	3	32	or	or	CCONJ
ejpam-6939	3	33	s	s	NOUN
ejpam-6939	3	34	contains	contain	VERB
ejpam-6939	3	35	two	two	NUM
ejpam-6939	3	36	vertices	vertex	NOUN
ejpam-6939	3	37	each	each	PRON
ejpam-6939	3	38	of	of	ADP
ejpam-6939	3	39	distance	distance	NOUN
ejpam-6939	3	40	two	two	NUM
ejpam-6939	3	41	from	from	ADP
ejpam-6939	3	42	v.	v.	ADP
ejpam-6939	3	43	a	a	DET
ejpam-6939	3	44	disjunctive	disjunctive	ADJ
ejpam-6939	3	45	dominating	dominating	NOUN
ejpam-6939	3	46	set	set	NOUN
ejpam-6939	3	47	s	s	VERB
ejpam-6939	3	48	is	be	AUX
ejpam-6939	3	49	a	a	DET
ejpam-6939	3	50	connected	connected	ADJ
ejpam-6939	3	51	disjunctive	disjunctive	ADJ
ejpam-6939	3	52	dominating	dominating	NOUN
ejpam-6939	3	53	set	set	VERB
ejpam-6939	3	54	if	if	SCONJ
ejpam-6939	3	55	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	3	56	is	be	AUX
ejpam-6939	3	57	connected	connect	VERB
ejpam-6939	3	58	.	.	PUNCT
ejpam-6939	4	1	in	in	ADP
ejpam-6939	4	2	this	this	DET
ejpam-6939	4	3	paper	paper	NOUN
ejpam-6939	4	4	,	,	PUNCT
ejpam-6939	4	5	we	we	PRON
ejpam-6939	4	6	study	study	VERB
ejpam-6939	4	7	the	the	DET
ejpam-6939	4	8	concept	concept	NOUN
ejpam-6939	4	9	of	of	ADP
ejpam-6939	4	10	connected	connected	ADJ
ejpam-6939	4	11	disjunctive	disjunctive	ADJ
ejpam-6939	4	12	dominating	dominating	NOUN
ejpam-6939	4	13	set	set	NOUN
ejpam-6939	4	14	.	.	PUNCT
ejpam-6939	5	1	2020	2020	NUM
ejpam-6939	5	2	mathematics	mathematics	PROPN
ejpam-6939	5	3	subject	subject	NOUN
ejpam-6939	5	4	classifications	classification	NOUN
ejpam-6939	5	5	:	:	PUNCT
ejpam-6939	5	6	05c69	05c69	X
ejpam-6939	5	7	key	key	ADJ
ejpam-6939	5	8	words	word	NOUN
ejpam-6939	5	9	and	and	CCONJ
ejpam-6939	5	10	phrases	phrase	NOUN
ejpam-6939	5	11	:	:	PUNCT
ejpam-6939	5	12	connected	connect	VERB
ejpam-6939	5	13	disjunctive	disjunctive	ADJ
ejpam-6939	5	14	dominating	dominating	NOUN
ejpam-6939	5	15	set	set	NOUN
ejpam-6939	5	16	,	,	PUNCT
ejpam-6939	5	17	connected	connect	VERB
ejpam-6939	5	18	disjunctive	disjunctive	ADJ
ejpam-6939	5	19	domination	domination	NOUN
ejpam-6939	5	20	number	number	NOUN
ejpam-6939	5	21	,	,	PUNCT
ejpam-6939	5	22	join	join	NOUN
ejpam-6939	5	23	,	,	PUNCT
ejpam-6939	5	24	corona	corona	PROPN
ejpam-6939	5	25	,	,	PUNCT
ejpam-6939	5	26	lexicographic	lexicographic	ADJ
ejpam-6939	5	27	product	product	NOUN
ejpam-6939	5	28	1	1	NUM
ejpam-6939	5	29	.	.	PUNCT
ejpam-6939	5	30	introduction	introduction	NOUN
ejpam-6939	5	31	in	in	ADP
ejpam-6939	5	32	2014	2014	NUM
ejpam-6939	5	33	,	,	PUNCT
ejpam-6939	5	34	goddard	goddard	PROPN
ejpam-6939	5	35	et	et	PROPN
ejpam-6939	5	36	al.[1	al.[1	PROPN
ejpam-6939	5	37	]	]	PUNCT
ejpam-6939	5	38	introduced	introduce	VERB
ejpam-6939	5	39	the	the	DET
ejpam-6939	5	40	concept	concept	NOUN
ejpam-6939	5	41	of	of	ADP
ejpam-6939	5	42	disjunctive	disjunctive	ADJ
ejpam-6939	5	43	,	,	PUNCT
ejpam-6939	5	44	specifically	specifically	ADV
ejpam-6939	5	45	b	b	NOUN
ejpam-6939	5	46	-	-	PUNCT
ejpam-6939	5	47	disjunctive	disjunctive	ADJ
ejpam-6939	5	48	,	,	PUNCT
ejpam-6939	5	49	domination	domination	NOUN
ejpam-6939	5	50	in	in	ADP
ejpam-6939	5	51	graphs	graph	NOUN
ejpam-6939	5	52	.	.	PUNCT
ejpam-6939	6	1	while	while	SCONJ
ejpam-6939	6	2	most	most	ADJ
ejpam-6939	6	3	of	of	ADP
ejpam-6939	6	4	the	the	DET
ejpam-6939	6	5	variations	variation	NOUN
ejpam-6939	6	6	on	on	ADP
ejpam-6939	6	7	dominating	dominating	NOUN
ejpam-6939	6	8	sets	set	NOUN
ejpam-6939	6	9	tend	tend	VERB
ejpam-6939	6	10	to	to	PART
ejpam-6939	6	11	increase	increase	VERB
ejpam-6939	6	12	the	the	DET
ejpam-6939	6	13	domination	domination	NOUN
ejpam-6939	6	14	number	number	NOUN
ejpam-6939	6	15	,	,	PUNCT
ejpam-6939	6	16	which	which	PRON
ejpam-6939	6	17	in	in	ADP
ejpam-6939	6	18	effect	effect	NOUN
ejpam-6939	6	19	raise	raise	VERB
ejpam-6939	6	20	implementation	implementation	NOUN
ejpam-6939	6	21	costs	cost	NOUN
ejpam-6939	6	22	,	,	PUNCT
ejpam-6939	6	23	disjunctive	disjunctive	ADJ
ejpam-6939	6	24	domination	domination	NOUN
ejpam-6939	6	25	is	be	AUX
ejpam-6939	6	26	a	a	DET
ejpam-6939	6	27	relaxation	relaxation	NOUN
ejpam-6939	6	28	of	of	ADP
ejpam-6939	6	29	the	the	DET
ejpam-6939	6	30	domination	domination	NOUN
ejpam-6939	6	31	number	number	NOUN
ejpam-6939	6	32	[	[	X
ejpam-6939	6	33	2	2	NUM
ejpam-6939	6	34	]	]	PUNCT
ejpam-6939	6	35	.	.	PUNCT
ejpam-6939	7	1	in	in	ADP
ejpam-6939	7	2	[	[	X
ejpam-6939	7	3	1	1	NUM
ejpam-6939	7	4	]	]	PUNCT
ejpam-6939	7	5	,	,	PUNCT
ejpam-6939	7	6	sharp	sharp	ADJ
ejpam-6939	7	7	bounds	bound	NOUN
ejpam-6939	7	8	for	for	ADP
ejpam-6939	7	9	the	the	DET
ejpam-6939	7	10	disjunctive	disjunctive	ADJ
ejpam-6939	7	11	domination	domination	NOUN
ejpam-6939	7	12	number	number	NOUN
ejpam-6939	7	13	were	be	AUX
ejpam-6939	7	14	established	establish	VERB
ejpam-6939	7	15	for	for	ADP
ejpam-6939	7	16	general	general	ADJ
ejpam-6939	7	17	graphs	graph	NOUN
ejpam-6939	7	18	,	,	PUNCT
ejpam-6939	7	19	and	and	CCONJ
ejpam-6939	7	20	exact	exact	ADJ
ejpam-6939	7	21	values	value	NOUN
ejpam-6939	7	22	were	be	AUX
ejpam-6939	7	23	determined	determine	VERB
ejpam-6939	7	24	for	for	ADP
ejpam-6939	7	25	specific	specific	ADJ
ejpam-6939	7	26	graphs	graph	NOUN
ejpam-6939	7	27	.	.	PUNCT
ejpam-6939	8	1	in	in	ADP
ejpam-6939	8	2	2016	2016	NUM
ejpam-6939	8	3	,	,	PUNCT
ejpam-6939	8	4	henning	henning	NOUN
ejpam-6939	8	5	and	and	CCONJ
ejpam-6939	8	6	naicker	naicker	NOUN
ejpam-6939	8	7	[	[	X
ejpam-6939	8	8	2	2	NUM
ejpam-6939	8	9	]	]	PUNCT
ejpam-6939	8	10	introduced	introduce	VERB
ejpam-6939	8	11	the	the	DET
ejpam-6939	8	12	disjunctive	disjunctive	ADJ
ejpam-6939	8	13	total	total	ADJ
ejpam-6939	8	14	domination	domination	NOUN
ejpam-6939	8	15	.	.	PUNCT
ejpam-6939	9	1	accordingly	accordingly	ADV
ejpam-6939	9	2	,	,	PUNCT
ejpam-6939	9	3	it	it	PRON
ejpam-6939	9	4	allows	allow	VERB
ejpam-6939	9	5	for	for	ADP
ejpam-6939	9	6	greater	great	ADJ
ejpam-6939	9	7	flexibility	flexibility	NOUN
ejpam-6939	9	8	by	by	ADP
ejpam-6939	9	9	modeling	model	VERB
ejpam-6939	9	10	networks	network	NOUN
ejpam-6939	9	11	where	where	SCONJ
ejpam-6939	9	12	one	one	NUM
ejpam-6939	9	13	trades	trade	VERB
ejpam-6939	9	14	off	off	ADP
ejpam-6939	9	15	redundancy	redundancy	NOUN
ejpam-6939	9	16	and	and	CCONJ
ejpam-6939	9	17	backup	backup	ADJ
ejpam-6939	9	18	capability	capability	NOUN
ejpam-6939	9	19	with	with	ADP
ejpam-6939	9	20	resource	resource	NOUN
ejpam-6939	9	21	optimization	optimization	NOUN
ejpam-6939	9	22	.	.	PUNCT
ejpam-6939	10	1	the	the	DET
ejpam-6939	10	2	above	above	ADV
ejpam-6939	10	3	-	-	PUNCT
ejpam-6939	10	4	mentioned	mention	VERB
ejpam-6939	10	5	authors	author	NOUN
ejpam-6939	10	6	established	establish	VERB
ejpam-6939	10	7	in	in	ADP
ejpam-6939	10	8	[	[	X
ejpam-6939	10	9	2	2	NUM
ejpam-6939	10	10	]	]	X
ejpam-6939	10	11	tight	tight	ADJ
ejpam-6939	10	12	upper	upper	ADJ
ejpam-6939	10	13	bound	bind	VERB
ejpam-6939	10	14	on	on	ADP
ejpam-6939	10	15	the	the	DET
ejpam-6939	10	16	disjunctive	disjunctive	ADJ
ejpam-6939	10	17	total	total	ADJ
ejpam-6939	10	18	domination	domination	NOUN
ejpam-6939	10	19	number	number	NOUN
ejpam-6939	10	20	of	of	ADP
ejpam-6939	10	21	a	a	DET
ejpam-6939	10	22	graph	graph	NOUN
ejpam-6939	10	23	in	in	ADP
ejpam-6939	10	24	terms	term	NOUN
ejpam-6939	10	25	of	of	ADP
ejpam-6939	10	26	its	its	PRON
ejpam-6939	10	27	order	order	NOUN
ejpam-6939	10	28	and	and	CCONJ
ejpam-6939	10	29	characterized	characterize	VERB
ejpam-6939	10	30	the	the	DET
ejpam-6939	10	31	extremal	extremal	ADJ
ejpam-6939	10	32	graphs	graph	NOUN
ejpam-6939	10	33	,	,	PUNCT
ejpam-6939	10	34	and	and	CCONJ
ejpam-6939	10	35	then	then	ADV
ejpam-6939	10	36	proved	prove	VERB
ejpam-6939	10	37	that	that	SCONJ
ejpam-6939	10	38	this	this	PRON
ejpam-6939	10	39	bound	bind	VERB
ejpam-6939	10	40	can	can	AUX
ejpam-6939	10	41	be	be	AUX
ejpam-6939	10	42	significantly	significantly	ADV
ejpam-6939	10	43	improved	improve	VERB
ejpam-6939	10	44	if	if	SCONJ
ejpam-6939	10	45	claw	claw	NOUN
ejpam-6939	10	46	-	-	PUNCT
ejpam-6939	10	47	freeness	freeness	NOUN
ejpam-6939	10	48	of	of	ADP
ejpam-6939	10	49	a	a	DET
ejpam-6939	10	50	graph	graph	NOUN
ejpam-6939	10	51	is	be	AUX
ejpam-6939	10	52	imposed	impose	VERB
ejpam-6939	10	53	.	.	PUNCT
ejpam-6939	11	1	the	the	DET
ejpam-6939	11	2	same	same	ADJ
ejpam-6939	11	3	authors	author	NOUN
ejpam-6939	11	4	also	also	ADV
ejpam-6939	11	5	investigated	investigate	VERB
ejpam-6939	11	6	the	the	DET
ejpam-6939	11	7	variant	variant	NOUN
ejpam-6939	11	8	on	on	ADP
ejpam-6939	11	9	the	the	DET
ejpam-6939	11	10	class	class	NOUN
ejpam-6939	11	11	of	of	ADP
ejpam-6939	11	12	trees	tree	NOUN
ejpam-6939	11	13	in	in	ADP
ejpam-6939	11	14	[	[	X
ejpam-6939	11	15	3	3	NUM
ejpam-6939	11	16	]	]	PUNCT
ejpam-6939	11	17	.	.	PUNCT
ejpam-6939	12	1	in	in	ADP
ejpam-6939	12	2	[	[	X
ejpam-6939	12	3	4	4	NUM
ejpam-6939	12	4	,	,	PUNCT
ejpam-6939	12	5	5	5	NUM
ejpam-6939	12	6	]	]	PUNCT
ejpam-6939	12	7	,	,	PUNCT
ejpam-6939	12	8	malalay	malalay	NOUN
ejpam-6939	12	9	and	and	CCONJ
ejpam-6939	12	10	jamil	jamil	PROPN
ejpam-6939	12	11	explored	explore	VERB
ejpam-6939	12	12	∗corresponding	∗corresponde	VERB
ejpam-6939	12	13	author	author	NOUN
ejpam-6939	12	14	.	.	PUNCT
ejpam-6939	13	1	doi	doi	NOUN
ejpam-6939	13	2	:	:	PUNCT
ejpam-6939	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6939	https://doi.org/10.29020/nybg.ejpam.v18i4.6939	PROPN
ejpam-6939	13	4	email	email	NOUN
ejpam-6939	13	5	addresses	address	VERB
ejpam-6939	13	6	:	:	PUNCT
ejpam-6939	13	7	alkajimaradais@msutawi-tawi.edu.ph	alkajimaradais@msutawi-tawi.edu.ph	PROPN
ejpam-6939	13	8	(	(	PUNCT
ejpam-6939	13	9	a.	a.	PROPN
ejpam-6939	13	10	aradais	aradais	PROPN
ejpam-6939	13	11	)	)	PUNCT
ejpam-6939	14	1	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-6939	14	2	(	(	PUNCT
ejpam-6939	14	3	f.	f.	PROPN
ejpam-6939	14	4	jamil	jamil	PROPN
ejpam-6939	14	5	)	)	PUNCT
ejpam-6939	14	6	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-6939	14	7	(	(	PUNCT
ejpam-6939	14	8	s.	s.	PROPN
ejpam-6939	14	9	canoy	canoy	PROPN
ejpam-6939	14	10	)	)	PUNCT
ejpam-6939	14	11	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6939	15	1	1	1	NUM
ejpam-6939	15	2	copyright	copyright	NOUN
ejpam-6939	15	3	:	:	PUNCT
ejpam-6939	15	4	©	©	PROPN
ejpam-6939	15	5	2025	2025	NUM
ejpam-6939	15	6	the	the	DET
ejpam-6939	15	7	author(s	author(s	NOUN
ejpam-6939	15	8	)	)	PUNCT
ejpam-6939	15	9	.	.	PUNCT
ejpam-6939	16	1	(	(	PUNCT
ejpam-6939	16	2	cc	cc	NOUN
ejpam-6939	16	3	by	by	ADP
ejpam-6939	16	4	-	-	PUNCT
ejpam-6939	16	5	nc	nc	PROPN
ejpam-6939	16	6	4.0	4.0	NUM
ejpam-6939	16	7	)	)	PUNCT
ejpam-6939	16	8	a.	a.	NOUN
ejpam-6939	16	9	aradais	aradais	PROPN
ejpam-6939	16	10	,	,	PUNCT
ejpam-6939	16	11	f.	f.	PROPN
ejpam-6939	16	12	jamil	jamil	PROPN
ejpam-6939	16	13	,	,	PUNCT
ejpam-6939	16	14	s.	s.	PROPN
ejpam-6939	16	15	canoy	canoy	PROPN
ejpam-6939	16	16	/	/	SYM
ejpam-6939	16	17	eur	eur	PROPN
ejpam-6939	16	18	.	.	PUNCT
ejpam-6939	17	1	j.	j.	PROPN
ejpam-6939	17	2	pure	pure	PROPN
ejpam-6939	17	3	appl	appl	PROPN
ejpam-6939	17	4	.	.	PROPN
ejpam-6939	17	5	math	math	PROPN
ejpam-6939	17	6	,	,	PUNCT
ejpam-6939	17	7	18	18	NUM
ejpam-6939	17	8	(	(	PUNCT
ejpam-6939	17	9	4	4	NUM
ejpam-6939	17	10	)	)	PUNCT
ejpam-6939	17	11	(	(	PUNCT
ejpam-6939	17	12	2025	2025	NUM
ejpam-6939	17	13	)	)	PUNCT
ejpam-6939	17	14	,	,	PUNCT
ejpam-6939	17	15	6939	6939	NUM
ejpam-6939	17	16	2	2	NUM
ejpam-6939	17	17	of	of	ADP
ejpam-6939	17	18	14	14	NUM
ejpam-6939	17	19	both	both	CCONJ
ejpam-6939	17	20	the	the	DET
ejpam-6939	17	21	disjunctive	disjunctive	ADJ
ejpam-6939	17	22	domination	domination	NOUN
ejpam-6939	17	23	and	and	CCONJ
ejpam-6939	17	24	disjunctive	disjunctive	ADJ
ejpam-6939	17	25	total	total	ADJ
ejpam-6939	17	26	domination	domination	NOUN
ejpam-6939	17	27	,	,	PUNCT
ejpam-6939	17	28	and	and	CCONJ
ejpam-6939	17	29	initiated	initiate	VERB
ejpam-6939	17	30	the	the	DET
ejpam-6939	17	31	study	study	NOUN
ejpam-6939	17	32	of	of	ADP
ejpam-6939	17	33	restrained	restrained	ADJ
ejpam-6939	17	34	disjunctive	disjunctive	ADJ
ejpam-6939	17	35	domination	domination	NOUN
ejpam-6939	17	36	in	in	ADP
ejpam-6939	17	37	graphs	graph	NOUN
ejpam-6939	17	38	under	under	ADP
ejpam-6939	17	39	some	some	DET
ejpam-6939	17	40	binary	binary	ADJ
ejpam-6939	17	41	operations	operation	NOUN
ejpam-6939	17	42	.	.	PUNCT
ejpam-6939	18	1	in	in	ADP
ejpam-6939	18	2	this	this	DET
ejpam-6939	18	3	present	present	ADJ
ejpam-6939	18	4	paper	paper	NOUN
ejpam-6939	18	5	,	,	PUNCT
ejpam-6939	18	6	we	we	PRON
ejpam-6939	18	7	introduce	introduce	VERB
ejpam-6939	18	8	and	and	CCONJ
ejpam-6939	18	9	initiate	initiate	VERB
ejpam-6939	18	10	the	the	DET
ejpam-6939	18	11	study	study	NOUN
ejpam-6939	18	12	of	of	ADP
ejpam-6939	18	13	connected	connected	ADJ
ejpam-6939	18	14	disjunctive	disjunctive	ADJ
ejpam-6939	18	15	domination	domination	NOUN
ejpam-6939	18	16	.	.	PUNCT
ejpam-6939	19	1	first	first	ADV
ejpam-6939	19	2	,	,	PUNCT
ejpam-6939	19	3	we	we	PRON
ejpam-6939	19	4	investigate	investigate	VERB
ejpam-6939	19	5	the	the	DET
ejpam-6939	19	6	concept	concept	NOUN
ejpam-6939	19	7	for	for	ADP
ejpam-6939	19	8	some	some	DET
ejpam-6939	19	9	special	special	ADJ
ejpam-6939	19	10	graphs	graph	NOUN
ejpam-6939	19	11	,	,	PUNCT
ejpam-6939	19	12	and	and	CCONJ
ejpam-6939	19	13	characterize	characterize	VERB
ejpam-6939	19	14	the	the	DET
ejpam-6939	19	15	graphs	graph	NOUN
ejpam-6939	19	16	which	which	PRON
ejpam-6939	19	17	give	give	VERB
ejpam-6939	19	18	small	small	ADJ
ejpam-6939	19	19	values	value	NOUN
ejpam-6939	19	20	for	for	ADP
ejpam-6939	19	21	the	the	DET
ejpam-6939	19	22	corresponding	corresponding	ADJ
ejpam-6939	19	23	parameter	parameter	NOUN
ejpam-6939	19	24	.	.	PUNCT
ejpam-6939	20	1	then	then	ADV
ejpam-6939	20	2	we	we	PRON
ejpam-6939	20	3	study	study	VERB
ejpam-6939	20	4	connected	connect	VERB
ejpam-6939	20	5	disjunctive	disjunctive	ADJ
ejpam-6939	20	6	domination	domination	NOUN
ejpam-6939	20	7	for	for	ADP
ejpam-6939	20	8	families	family	NOUN
ejpam-6939	20	9	of	of	ADP
ejpam-6939	20	10	graphs	graph	NOUN
ejpam-6939	20	11	involving	involve	VERB
ejpam-6939	20	12	some	some	DET
ejpam-6939	20	13	binary	binary	ADJ
ejpam-6939	20	14	operations	operation	NOUN
ejpam-6939	20	15	.	.	PUNCT
ejpam-6939	21	1	2	2	X
ejpam-6939	21	2	.	.	X
ejpam-6939	21	3	terminology	terminology	NOUN
ejpam-6939	21	4	and	and	CCONJ
ejpam-6939	21	5	notations	notation	NOUN
ejpam-6939	21	6	throughout	throughout	ADP
ejpam-6939	21	7	this	this	DET
ejpam-6939	21	8	paper	paper	NOUN
ejpam-6939	21	9	,	,	PUNCT
ejpam-6939	21	10	we	we	PRON
ejpam-6939	21	11	only	only	ADV
ejpam-6939	21	12	consider	consider	VERB
ejpam-6939	21	13	graphs	graph	NOUN
ejpam-6939	21	14	which	which	PRON
ejpam-6939	21	15	are	be	AUX
ejpam-6939	21	16	finite	finite	ADJ
ejpam-6939	21	17	,	,	PUNCT
ejpam-6939	21	18	simple	simple	ADJ
ejpam-6939	21	19	and	and	CCONJ
ejpam-6939	21	20	undirected	undirected	ADJ
ejpam-6939	21	21	.	.	PUNCT
ejpam-6939	22	1	all	all	DET
ejpam-6939	22	2	basic	basic	ADJ
ejpam-6939	22	3	terminologies	terminology	NOUN
ejpam-6939	22	4	which	which	PRON
ejpam-6939	22	5	are	be	AUX
ejpam-6939	22	6	not	not	PART
ejpam-6939	22	7	defined	define	VERB
ejpam-6939	22	8	but	but	CCONJ
ejpam-6939	22	9	are	be	AUX
ejpam-6939	22	10	being	be	AUX
ejpam-6939	22	11	used	use	VERB
ejpam-6939	22	12	here	here	ADV
ejpam-6939	22	13	are	be	AUX
ejpam-6939	22	14	adapted	adapt	VERB
ejpam-6939	22	15	from	from	ADP
ejpam-6939	22	16	[	[	X
ejpam-6939	22	17	6	6	NUM
ejpam-6939	22	18	]	]	PUNCT
ejpam-6939	22	19	.	.	PUNCT
ejpam-6939	23	1	for	for	ADP
ejpam-6939	23	2	a	a	DET
ejpam-6939	23	3	graph	graph	NOUN
ejpam-6939	23	4	g	g	NOUN
ejpam-6939	23	5	,	,	PUNCT
ejpam-6939	23	6	the	the	DET
ejpam-6939	23	7	symbols	symbol	NOUN
ejpam-6939	23	8	v	v	ADP
ejpam-6939	23	9	(	(	PUNCT
ejpam-6939	23	10	g	g	NOUN
ejpam-6939	23	11	)	)	PUNCT
ejpam-6939	23	12	and	and	CCONJ
ejpam-6939	23	13	e(g	e(g	PROPN
ejpam-6939	23	14	)	)	PUNCT
ejpam-6939	23	15	refer	refer	VERB
ejpam-6939	23	16	to	to	ADP
ejpam-6939	23	17	the	the	DET
ejpam-6939	23	18	vertex	vertex	NOUN
ejpam-6939	23	19	-	-	PUNCT
ejpam-6939	23	20	set	set	VERB
ejpam-6939	23	21	and	and	CCONJ
ejpam-6939	23	22	edge	edge	NOUN
ejpam-6939	23	23	-	-	PUNCT
ejpam-6939	23	24	set	set	NOUN
ejpam-6939	23	25	,	,	PUNCT
ejpam-6939	23	26	respectively	respectively	ADV
ejpam-6939	23	27	,	,	PUNCT
ejpam-6939	23	28	of	of	ADP
ejpam-6939	23	29	g.	g.	NOUN
ejpam-6939	23	30	for	for	ADP
ejpam-6939	23	31	s	s	PROPN
ejpam-6939	23	32	⊆	⊆	NUM
ejpam-6939	23	33	v	v	NOUN
ejpam-6939	23	34	(	(	PUNCT
ejpam-6939	23	35	g	g	NOUN
ejpam-6939	23	36	)	)	PUNCT
ejpam-6939	23	37	,	,	PUNCT
ejpam-6939	23	38	|s|	|s|	PROPN
ejpam-6939	23	39	is	be	AUX
ejpam-6939	23	40	the	the	DET
ejpam-6939	23	41	cardinality	cardinality	NOUN
ejpam-6939	23	42	of	of	ADP
ejpam-6939	23	43	s.	s.	PROPN
ejpam-6939	23	44	in	in	ADP
ejpam-6939	23	45	particular	particular	ADJ
ejpam-6939	23	46	,	,	PUNCT
ejpam-6939	23	47	|v	|v	PROPN
ejpam-6939	23	48	(	(	PUNCT
ejpam-6939	23	49	g)|	g)|	PROPN
ejpam-6939	23	50	is	be	AUX
ejpam-6939	23	51	called	call	VERB
ejpam-6939	23	52	the	the	DET
ejpam-6939	23	53	order	order	NOUN
ejpam-6939	23	54	of	of	ADP
ejpam-6939	23	55	g.	g.	PROPN
ejpam-6939	23	56	a	a	DET
ejpam-6939	23	57	graph	graph	NOUN
ejpam-6939	23	58	g	g	NOUN
ejpam-6939	23	59	is	be	AUX
ejpam-6939	23	60	connected	connect	VERB
ejpam-6939	23	61	if	if	SCONJ
ejpam-6939	23	62	for	for	ADP
ejpam-6939	23	63	every	every	DET
ejpam-6939	23	64	pair	pair	NOUN
ejpam-6939	23	65	of	of	ADP
ejpam-6939	23	66	distinct	distinct	ADJ
ejpam-6939	23	67	vertices	vertex	NOUN
ejpam-6939	23	68	u	u	NOUN
ejpam-6939	23	69	and	and	CCONJ
ejpam-6939	23	70	v	v	NOUN
ejpam-6939	23	71	of	of	ADP
ejpam-6939	23	72	g	g	NOUN
ejpam-6939	23	73	,	,	PUNCT
ejpam-6939	23	74	g	g	PROPN
ejpam-6939	23	75	contains	contain	VERB
ejpam-6939	23	76	a	a	DET
ejpam-6939	23	77	path	path	NOUN
ejpam-6939	23	78	from	from	ADP
ejpam-6939	23	79	u	u	PRON
ejpam-6939	23	80	to	to	ADP
ejpam-6939	23	81	v.	v.	NOUN
ejpam-6939	23	82	if	if	SCONJ
ejpam-6939	23	83	g	g	PROPN
ejpam-6939	23	84	is	be	AUX
ejpam-6939	23	85	connected	connect	VERB
ejpam-6939	23	86	and	and	CCONJ
ejpam-6939	23	87	u	u	NOUN
ejpam-6939	23	88	,	,	PUNCT
ejpam-6939	23	89	v	v	NOUN
ejpam-6939	23	90	∈	∈	PROPN
ejpam-6939	23	91	v	v	NOUN
ejpam-6939	23	92	(	(	PUNCT
ejpam-6939	23	93	g	g	NOUN
ejpam-6939	23	94	)	)	PUNCT
ejpam-6939	23	95	,	,	PUNCT
ejpam-6939	23	96	then	then	ADV
ejpam-6939	23	97	dg(u	dg(u	X
ejpam-6939	23	98	,	,	PUNCT
ejpam-6939	23	99	v	v	NOUN
ejpam-6939	23	100	)	)	PUNCT
ejpam-6939	23	101	,	,	PUNCT
ejpam-6939	23	102	the	the	DET
ejpam-6939	23	103	distance	distance	NOUN
ejpam-6939	23	104	from	from	ADP
ejpam-6939	23	105	u	u	PRON
ejpam-6939	23	106	to	to	ADP
ejpam-6939	23	107	v	v	NOUN
ejpam-6939	23	108	,	,	PUNCT
ejpam-6939	23	109	is	be	AUX
ejpam-6939	23	110	the	the	DET
ejpam-6939	23	111	length	length	NOUN
ejpam-6939	23	112	of	of	ADP
ejpam-6939	23	113	the	the	DET
ejpam-6939	23	114	shortest	short	ADJ
ejpam-6939	23	115	path	path	NOUN
ejpam-6939	23	116	connecting	connect	VERB
ejpam-6939	23	117	u	u	NOUN
ejpam-6939	23	118	and	and	CCONJ
ejpam-6939	23	119	v.	v.	ADP
ejpam-6939	23	120	a	a	DET
ejpam-6939	23	121	vertex	vertex	NOUN
ejpam-6939	23	122	u	u	NOUN
ejpam-6939	23	123	is	be	AUX
ejpam-6939	23	124	a	a	DET
ejpam-6939	23	125	cut	cut	NOUN
ejpam-6939	23	126	-	-	PUNCT
ejpam-6939	23	127	vertex	vertex	NOUN
ejpam-6939	23	128	if	if	SCONJ
ejpam-6939	23	129	the	the	DET
ejpam-6939	23	130	removal	removal	NOUN
ejpam-6939	23	131	of	of	ADP
ejpam-6939	23	132	u	u	NOUN
ejpam-6939	23	133	from	from	ADP
ejpam-6939	23	134	g	g	PROPN
ejpam-6939	23	135	increases	increase	VERB
ejpam-6939	23	136	the	the	DET
ejpam-6939	23	137	number	number	NOUN
ejpam-6939	23	138	of	of	ADP
ejpam-6939	23	139	components	component	NOUN
ejpam-6939	23	140	of	of	ADP
ejpam-6939	23	141	g.	g.	PROPN
ejpam-6939	23	142	given	give	VERB
ejpam-6939	23	143	graphs	graph	NOUN
ejpam-6939	23	144	g	g	PROPN
ejpam-6939	23	145	and	and	CCONJ
ejpam-6939	23	146	h	h	NOUN
ejpam-6939	23	147	,	,	PUNCT
ejpam-6939	23	148	the	the	DET
ejpam-6939	23	149	join	join	NOUN
ejpam-6939	23	150	of	of	ADP
ejpam-6939	23	151	g	g	PROPN
ejpam-6939	23	152	and	and	CCONJ
ejpam-6939	23	153	h	h	NOUN
ejpam-6939	23	154	is	be	AUX
ejpam-6939	23	155	the	the	DET
ejpam-6939	23	156	graph	graph	NOUN
ejpam-6939	23	157	g	g	NOUN
ejpam-6939	23	158	+	+	CCONJ
ejpam-6939	23	159	h	h	NOUN
ejpam-6939	23	160	with	with	ADP
ejpam-6939	23	161	vertex	vertex	NOUN
ejpam-6939	23	162	set	set	VERB
ejpam-6939	23	163	v	v	NOUN
ejpam-6939	23	164	(	(	PUNCT
ejpam-6939	23	165	g	g	NOUN
ejpam-6939	23	166	)	)	PUNCT
ejpam-6939	23	167	∪	∪	NOUN
ejpam-6939	23	168	v	v	NOUN
ejpam-6939	23	169	(	(	PUNCT
ejpam-6939	23	170	h	h	NOUN
ejpam-6939	23	171	)	)	PUNCT
ejpam-6939	23	172	and	and	CCONJ
ejpam-6939	23	173	edge	edge	VERB
ejpam-6939	23	174	set	set	VERB
ejpam-6939	23	175	e(g	e(g	NOUN
ejpam-6939	23	176	)	)	PUNCT
ejpam-6939	23	177	∪	∪	ADP
ejpam-6939	23	178	e(h	e(h	PROPN
ejpam-6939	23	179	)	)	PUNCT
ejpam-6939	23	180	∪	∪	NOUN
ejpam-6939	23	181	{	{	PUNCT
ejpam-6939	23	182	uv	uv	NOUN
ejpam-6939	23	183	:	:	PUNCT
ejpam-6939	23	184	u	u	PROPN
ejpam-6939	23	185	∈	∈	PROPN
ejpam-6939	23	186	v	v	ADP
ejpam-6939	23	187	(	(	PUNCT
ejpam-6939	23	188	g	g	NOUN
ejpam-6939	23	189	)	)	PUNCT
ejpam-6939	23	190	,	,	PUNCT
ejpam-6939	23	191	v	v	X
ejpam-6939	23	192	∈	∈	PROPN
ejpam-6939	23	193	v	v	NOUN
ejpam-6939	23	194	(	(	PUNCT
ejpam-6939	23	195	h	h	NOUN
ejpam-6939	23	196	)	)	PUNCT
ejpam-6939	23	197	}	}	PUNCT
ejpam-6939	23	198	.	.	PUNCT
ejpam-6939	24	1	the	the	DET
ejpam-6939	24	2	corona	corona	NOUN
ejpam-6939	24	3	of	of	ADP
ejpam-6939	24	4	g	g	PROPN
ejpam-6939	24	5	and	and	CCONJ
ejpam-6939	24	6	h	h	NOUN
ejpam-6939	24	7	is	be	AUX
ejpam-6939	24	8	the	the	DET
ejpam-6939	24	9	graph	graph	NOUN
ejpam-6939	24	10	g	g	PROPN
ejpam-6939	24	11	◦	◦	NOUN
ejpam-6939	24	12	h	h	NOUN
ejpam-6939	24	13	obtained	obtain	VERB
ejpam-6939	24	14	by	by	ADP
ejpam-6939	24	15	taking	take	VERB
ejpam-6939	24	16	one	one	NUM
ejpam-6939	24	17	copy	copy	NOUN
ejpam-6939	24	18	of	of	ADP
ejpam-6939	24	19	g	g	PROPN
ejpam-6939	24	20	and	and	CCONJ
ejpam-6939	24	21	|v	|v	PROPN
ejpam-6939	24	22	(	(	PUNCT
ejpam-6939	24	23	g)|	g)|	NOUN
ejpam-6939	24	24	copies	copy	NOUN
ejpam-6939	24	25	of	of	ADP
ejpam-6939	24	26	h	h	NOUN
ejpam-6939	24	27	,	,	PUNCT
ejpam-6939	24	28	and	and	CCONJ
ejpam-6939	24	29	then	then	ADV
ejpam-6939	24	30	joining	join	VERB
ejpam-6939	24	31	the	the	DET
ejpam-6939	24	32	ith	ith	PROPN
ejpam-6939	24	33	vertex	vertex	NOUN
ejpam-6939	24	34	of	of	ADP
ejpam-6939	24	35	g	g	NOUN
ejpam-6939	24	36	to	to	ADP
ejpam-6939	24	37	every	every	DET
ejpam-6939	24	38	vertex	vertex	NOUN
ejpam-6939	24	39	in	in	ADP
ejpam-6939	24	40	the	the	DET
ejpam-6939	24	41	ith	ith	PROPN
ejpam-6939	24	42	copy	copy	NOUN
ejpam-6939	24	43	of	of	ADP
ejpam-6939	24	44	h.	h.	PROPN
ejpam-6939	24	45	in	in	ADP
ejpam-6939	24	46	particular	particular	ADJ
ejpam-6939	24	47	,	,	PUNCT
ejpam-6939	24	48	we	we	PRON
ejpam-6939	24	49	call	call	VERB
ejpam-6939	24	50	g	g	PROPN
ejpam-6939	24	51	◦	◦	NOUN
ejpam-6939	24	52	k1	k1	NOUN
ejpam-6939	24	53	the	the	DET
ejpam-6939	24	54	corona	corona	NOUN
ejpam-6939	24	55	of	of	ADP
ejpam-6939	24	56	g	g	PROPN
ejpam-6939	24	57	,	,	PUNCT
ejpam-6939	24	58	and	and	CCONJ
ejpam-6939	24	59	write	write	VERB
ejpam-6939	24	60	cor(g	cor(g	PROPN
ejpam-6939	24	61	)	)	PUNCT
ejpam-6939	25	1	=	=	SYM
ejpam-6939	25	2	g	g	PROPN
ejpam-6939	25	3	◦	◦	NOUN
ejpam-6939	25	4	k1	k1	NOUN
ejpam-6939	25	5	.	.	PUNCT
ejpam-6939	26	1	the	the	DET
ejpam-6939	26	2	composition	composition	NOUN
ejpam-6939	26	3	(	(	PUNCT
ejpam-6939	26	4	or	or	CCONJ
ejpam-6939	26	5	lexicographic	lexicographic	ADJ
ejpam-6939	26	6	product	product	NOUN
ejpam-6939	26	7	)	)	PUNCT
ejpam-6939	26	8	of	of	ADP
ejpam-6939	26	9	g	g	PROPN
ejpam-6939	26	10	and	and	CCONJ
ejpam-6939	26	11	h	h	NOUN
ejpam-6939	26	12	is	be	AUX
ejpam-6939	26	13	the	the	DET
ejpam-6939	26	14	graph	graph	NOUN
ejpam-6939	26	15	g[h	g[h	PROPN
ejpam-6939	26	16	]	]	PUNCT
ejpam-6939	26	17	with	with	ADP
ejpam-6939	26	18	v	v	NOUN
ejpam-6939	26	19	(	(	PUNCT
ejpam-6939	26	20	g[h	g[h	PROPN
ejpam-6939	26	21	]	]	PUNCT
ejpam-6939	26	22	)	)	PUNCT
ejpam-6939	26	23	=	=	SYM
ejpam-6939	26	24	v	v	X
ejpam-6939	26	25	(	(	PUNCT
ejpam-6939	26	26	g	g	NOUN
ejpam-6939	26	27	)	)	PUNCT
ejpam-6939	26	28	×	×	NOUN
ejpam-6939	26	29	v	v	NOUN
ejpam-6939	26	30	(	(	PUNCT
ejpam-6939	26	31	h	h	NOUN
ejpam-6939	26	32	)	)	PUNCT
ejpam-6939	26	33	and	and	CCONJ
ejpam-6939	26	34	(	(	PUNCT
ejpam-6939	26	35	u	u	NOUN
ejpam-6939	26	36	,	,	PUNCT
ejpam-6939	26	37	v)(u′	v)(u′	NOUN
ejpam-6939	26	38	,	,	PUNCT
ejpam-6939	26	39	v′	v′	NOUN
ejpam-6939	26	40	)	)	PUNCT
ejpam-6939	26	41	∈	∈	NOUN
ejpam-6939	26	42	e(g[h	e(g[h	NOUN
ejpam-6939	26	43	]	]	PUNCT
ejpam-6939	26	44	)	)	PUNCT
ejpam-6939	26	45	if	if	SCONJ
ejpam-6939	26	46	and	and	CCONJ
ejpam-6939	26	47	only	only	ADV
ejpam-6939	26	48	if	if	SCONJ
ejpam-6939	26	49	either	either	CCONJ
ejpam-6939	26	50	uu′	uu′	PROPN
ejpam-6939	26	51	∈	∈	PROPN
ejpam-6939	26	52	e(g	e(g	PROPN
ejpam-6939	26	53	)	)	PUNCT
ejpam-6939	26	54	or	or	CCONJ
ejpam-6939	26	55	u	u	X
ejpam-6939	26	56	=	=	PUNCT
ejpam-6939	26	57	u′	u′	PROPN
ejpam-6939	26	58	and	and	CCONJ
ejpam-6939	26	59	vv′	vv′	NOUN
ejpam-6939	26	60	∈	∈	PROPN
ejpam-6939	26	61	e(h	e(h	PROPN
ejpam-6939	26	62	)	)	PUNCT
ejpam-6939	26	63	.	.	PUNCT
ejpam-6939	27	1	in	in	ADP
ejpam-6939	27	2	any	any	PRON
ejpam-6939	27	3	of	of	ADP
ejpam-6939	27	4	these	these	DET
ejpam-6939	27	5	graphs	graph	NOUN
ejpam-6939	27	6	,	,	PUNCT
ejpam-6939	27	7	g	g	PROPN
ejpam-6939	27	8	and	and	CCONJ
ejpam-6939	27	9	h	h	NOUN
ejpam-6939	27	10	are	be	AUX
ejpam-6939	27	11	referred	refer	VERB
ejpam-6939	27	12	to	to	ADP
ejpam-6939	27	13	as	as	ADP
ejpam-6939	27	14	their	their	PRON
ejpam-6939	27	15	basic	basic	ADJ
ejpam-6939	27	16	component	component	NOUN
ejpam-6939	27	17	graphs	graph	NOUN
ejpam-6939	27	18	.	.	PUNCT
ejpam-6939	28	1	vertices	vertice	VERB
ejpam-6939	28	2	u	u	NOUN
ejpam-6939	28	3	and	and	CCONJ
ejpam-6939	28	4	v	v	NOUN
ejpam-6939	28	5	of	of	ADP
ejpam-6939	28	6	a	a	DET
ejpam-6939	28	7	graph	graph	NOUN
ejpam-6939	28	8	g	g	NOUN
ejpam-6939	28	9	are	be	AUX
ejpam-6939	28	10	neighbors	neighbor	NOUN
ejpam-6939	28	11	if	if	SCONJ
ejpam-6939	28	12	uv	uv	PROPN
ejpam-6939	28	13	∈	∈	PROPN
ejpam-6939	28	14	e(g	e(g	PROPN
ejpam-6939	28	15	)	)	PUNCT
ejpam-6939	28	16	.	.	PUNCT
ejpam-6939	29	1	the	the	DET
ejpam-6939	29	2	open	open	ADJ
ejpam-6939	29	3	neighborhood	neighborhood	NOUN
ejpam-6939	29	4	of	of	ADP
ejpam-6939	29	5	v	v	NOUN
ejpam-6939	29	6	refers	refer	VERB
ejpam-6939	29	7	to	to	ADP
ejpam-6939	29	8	the	the	DET
ejpam-6939	29	9	set	set	NOUN
ejpam-6939	29	10	ng(v	ng(v	PUNCT
ejpam-6939	29	11	)	)	PUNCT
ejpam-6939	29	12	consisting	consist	VERB
ejpam-6939	29	13	of	of	ADP
ejpam-6939	29	14	all	all	DET
ejpam-6939	29	15	neighbors	neighbor	NOUN
ejpam-6939	29	16	of	of	ADP
ejpam-6939	29	17	v.	v.	ADP
ejpam-6939	29	18	the	the	DET
ejpam-6939	29	19	degree	degree	NOUN
ejpam-6939	29	20	of	of	ADP
ejpam-6939	29	21	v	v	NOUN
ejpam-6939	29	22	,	,	PUNCT
ejpam-6939	29	23	denoted	denote	VERB
ejpam-6939	29	24	degg(v	degg(v	PROPN
ejpam-6939	29	25	)	)	PUNCT
ejpam-6939	29	26	,	,	PUNCT
ejpam-6939	29	27	refers	refer	VERB
ejpam-6939	29	28	to	to	ADP
ejpam-6939	29	29	the	the	DET
ejpam-6939	29	30	cardinality	cardinality	NOUN
ejpam-6939	29	31	|ng(v)|	|ng(v)|	NOUN
ejpam-6939	29	32	of	of	ADP
ejpam-6939	29	33	the	the	DET
ejpam-6939	29	34	open	open	ADJ
ejpam-6939	29	35	neighborhood	neighborhood	NOUN
ejpam-6939	29	36	of	of	ADP
ejpam-6939	29	37	v.	v.	ADP
ejpam-6939	29	38	vertex	vertex	PROPN
ejpam-6939	29	39	v	v	NOUN
ejpam-6939	29	40	is	be	AUX
ejpam-6939	29	41	an	an	DET
ejpam-6939	29	42	end	end	NOUN
ejpam-6939	29	43	-	-	PUNCT
ejpam-6939	29	44	vertex	vertex	NOUN
ejpam-6939	29	45	if	if	SCONJ
ejpam-6939	29	46	degg(v	degg(v	VERB
ejpam-6939	29	47	)	)	PUNCT
ejpam-6939	29	48	=	=	SYM
ejpam-6939	30	1	1	1	X
ejpam-6939	30	2	.	.	PUNCT
ejpam-6939	31	1	the	the	DET
ejpam-6939	31	2	closed	closed	ADJ
ejpam-6939	31	3	neighborhood	neighborhood	NOUN
ejpam-6939	31	4	of	of	ADP
ejpam-6939	31	5	v	v	NOUN
ejpam-6939	31	6	is	be	AUX
ejpam-6939	31	7	the	the	DET
ejpam-6939	31	8	set	set	NOUN
ejpam-6939	31	9	ng[v	ng[v	NOUN
ejpam-6939	31	10	]	]	X
ejpam-6939	31	11	=	=	SYM
ejpam-6939	31	12	ng(v)∪{v	ng(v)∪{v	PROPN
ejpam-6939	31	13	}	}	PUNCT
ejpam-6939	31	14	.	.	PUNCT
ejpam-6939	32	1	customarily	customarily	ADV
ejpam-6939	32	2	,	,	PUNCT
ejpam-6939	32	3	for	for	ADP
ejpam-6939	32	4	s	s	PROPN
ejpam-6939	32	5	⊆	⊆	NUM
ejpam-6939	32	6	v	v	NOUN
ejpam-6939	32	7	(	(	PUNCT
ejpam-6939	32	8	g	g	NOUN
ejpam-6939	32	9	)	)	PUNCT
ejpam-6939	32	10	,	,	PUNCT
ejpam-6939	32	11	ng(s	ng(s	NUM
ejpam-6939	32	12	)	)	PUNCT
ejpam-6939	32	13	=	=	SYM
ejpam-6939	32	14	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-6939	32	15	)	)	PUNCT
ejpam-6939	32	16	and	and	CCONJ
ejpam-6939	32	17	ng[s	ng[s	PROPN
ejpam-6939	32	18	]	]	PUNCT
ejpam-6939	32	19	=	=	SYM
ejpam-6939	32	20	∪v∈sng[v	∪v∈sng[v	X
ejpam-6939	32	21	]	]	PUNCT
ejpam-6939	32	22	.	.	PUNCT
ejpam-6939	33	1	a	a	DET
ejpam-6939	33	2	subset	subset	NOUN
ejpam-6939	33	3	s	s	VERB
ejpam-6939	33	4	⊆	⊆	NUM
ejpam-6939	33	5	v	v	NOUN
ejpam-6939	33	6	(	(	PUNCT
ejpam-6939	33	7	g	g	NOUN
ejpam-6939	33	8	)	)	PUNCT
ejpam-6939	33	9	is	be	AUX
ejpam-6939	33	10	a	a	DET
ejpam-6939	33	11	dominating	dominating	NOUN
ejpam-6939	33	12	set	set	NOUN
ejpam-6939	33	13	of	of	ADP
ejpam-6939	33	14	g	g	PROPN
ejpam-6939	33	15	if	if	SCONJ
ejpam-6939	33	16	ng[s	ng[	NOUN
ejpam-6939	33	17	]	]	PUNCT
ejpam-6939	33	18	=	=	SYM
ejpam-6939	33	19	v	v	NOUN
ejpam-6939	33	20	(	(	PUNCT
ejpam-6939	33	21	g	g	NOUN
ejpam-6939	33	22	)	)	PUNCT
ejpam-6939	33	23	.	.	PUNCT
ejpam-6939	34	1	if	if	SCONJ
ejpam-6939	34	2	ng(s	ng(s	NUM
ejpam-6939	34	3	)	)	PUNCT
ejpam-6939	34	4	=	=	SYM
ejpam-6939	34	5	v	v	X
ejpam-6939	34	6	(	(	PUNCT
ejpam-6939	34	7	g	g	NOUN
ejpam-6939	34	8	)	)	PUNCT
ejpam-6939	34	9	,	,	PUNCT
ejpam-6939	34	10	then	then	ADV
ejpam-6939	34	11	s	s	VERB
ejpam-6939	34	12	is	be	AUX
ejpam-6939	34	13	a	a	DET
ejpam-6939	34	14	total	total	ADJ
ejpam-6939	34	15	dominating	dominating	NOUN
ejpam-6939	34	16	set	set	NOUN
ejpam-6939	34	17	of	of	ADP
ejpam-6939	34	18	g.	g.	PROPN
ejpam-6939	34	19	the	the	DET
ejpam-6939	34	20	minimum	minimum	ADJ
ejpam-6939	34	21	cardinality	cardinality	NOUN
ejpam-6939	34	22	of	of	ADP
ejpam-6939	34	23	a	a	DET
ejpam-6939	34	24	dominating	dominating	NOUN
ejpam-6939	34	25	set	set	NOUN
ejpam-6939	34	26	of	of	ADP
ejpam-6939	34	27	g	g	PROPN
ejpam-6939	34	28	is	be	AUX
ejpam-6939	34	29	the	the	DET
ejpam-6939	34	30	domination	domination	NOUN
ejpam-6939	34	31	number	number	NOUN
ejpam-6939	34	32	of	of	ADP
ejpam-6939	34	33	g	g	NOUN
ejpam-6939	34	34	,	,	PUNCT
ejpam-6939	34	35	and	and	CCONJ
ejpam-6939	34	36	the	the	DET
ejpam-6939	34	37	minimum	minimum	ADJ
ejpam-6939	34	38	cardinality	cardinality	NOUN
ejpam-6939	34	39	of	of	ADP
ejpam-6939	34	40	a	a	DET
ejpam-6939	34	41	total	total	ADJ
ejpam-6939	34	42	dominating	dominating	NOUN
ejpam-6939	34	43	set	set	NOUN
ejpam-6939	34	44	is	be	AUX
ejpam-6939	34	45	the	the	DET
ejpam-6939	34	46	total	total	ADJ
ejpam-6939	34	47	domination	domination	NOUN
ejpam-6939	34	48	number	number	NOUN
ejpam-6939	34	49	of	of	ADP
ejpam-6939	34	50	g.	g.	PROPN
ejpam-6939	34	51	we	we	PRON
ejpam-6939	34	52	write	write	VERB
ejpam-6939	34	53	γ(g	γ(g	PROPN
ejpam-6939	34	54	)	)	PUNCT
ejpam-6939	34	55	and	and	CCONJ
ejpam-6939	34	56	γt(g	γt(g	PUNCT
ejpam-6939	34	57	)	)	PUNCT
ejpam-6939	34	58	to	to	PART
ejpam-6939	34	59	denote	denote	VERB
ejpam-6939	34	60	the	the	DET
ejpam-6939	34	61	domination	domination	NOUN
ejpam-6939	34	62	number	number	NOUN
ejpam-6939	34	63	and	and	CCONJ
ejpam-6939	34	64	total	total	ADJ
ejpam-6939	34	65	domination	domination	NOUN
ejpam-6939	34	66	number	number	NOUN
ejpam-6939	34	67	,	,	PUNCT
ejpam-6939	34	68	respectively	respectively	ADV
ejpam-6939	34	69	,	,	PUNCT
ejpam-6939	34	70	of	of	ADP
ejpam-6939	34	71	g.	g.	PROPN
ejpam-6939	34	72	a	a	DET
ejpam-6939	34	73	dominating	dominating	NOUN
ejpam-6939	34	74	set	set	NOUN
ejpam-6939	34	75	of	of	ADP
ejpam-6939	34	76	cardinality	cardinality	PROPN
ejpam-6939	34	77	γ(g	γ(g	PROPN
ejpam-6939	34	78	)	)	PUNCT
ejpam-6939	34	79	is	be	AUX
ejpam-6939	34	80	called	call	VERB
ejpam-6939	34	81	a	a	DET
ejpam-6939	34	82	γ	γ	NOUN
ejpam-6939	34	83	-	-	PUNCT
ejpam-6939	34	84	set	set	NOUN
ejpam-6939	34	85	of	of	ADP
ejpam-6939	34	86	g.	g.	PROPN
ejpam-6939	34	87	similarly	similarly	ADV
ejpam-6939	34	88	,	,	PUNCT
ejpam-6939	34	89	a	a	DET
ejpam-6939	34	90	γt	γt	NOUN
ejpam-6939	34	91	-	-	ADJ
ejpam-6939	34	92	set	set	ADJ
ejpam-6939	34	93	is	be	AUX
ejpam-6939	34	94	a	a	DET
ejpam-6939	34	95	total	total	ADJ
ejpam-6939	34	96	dominating	dominating	NOUN
ejpam-6939	34	97	set	set	NOUN
ejpam-6939	34	98	of	of	ADP
ejpam-6939	34	99	cardinality	cardinality	NOUN
ejpam-6939	34	100	γt(g	γt(g	NUM
ejpam-6939	34	101	)	)	PUNCT
ejpam-6939	34	102	.	.	PUNCT
ejpam-6939	35	1	the	the	DET
ejpam-6939	35	2	reader	reader	NOUN
ejpam-6939	35	3	is	be	AUX
ejpam-6939	35	4	referred	refer	VERB
ejpam-6939	35	5	to	to	ADP
ejpam-6939	35	6	[	[	X
ejpam-6939	35	7	7–10	7–10	X
ejpam-6939	35	8	]	]	PUNCT
ejpam-6939	35	9	for	for	ADP
ejpam-6939	35	10	the	the	DET
ejpam-6939	35	11	history	history	NOUN
ejpam-6939	35	12	,	,	PUNCT
ejpam-6939	35	13	fundamental	fundamental	ADJ
ejpam-6939	35	14	concepts	concept	NOUN
ejpam-6939	35	15	and	and	CCONJ
ejpam-6939	35	16	recent	recent	ADJ
ejpam-6939	35	17	developments	development	NOUN
ejpam-6939	35	18	of	of	ADP
ejpam-6939	35	19	domination	domination	NOUN
ejpam-6939	35	20	in	in	ADP
ejpam-6939	35	21	graphs	graph	NOUN
ejpam-6939	35	22	as	as	ADV
ejpam-6939	35	23	well	well	ADV
ejpam-6939	35	24	as	as	ADP
ejpam-6939	35	25	its	its	PRON
ejpam-6939	35	26	various	various	ADJ
ejpam-6939	35	27	applications	application	NOUN
ejpam-6939	35	28	,	,	PUNCT
ejpam-6939	35	29	and	and	CCONJ
ejpam-6939	35	30	to	to	ADP
ejpam-6939	35	31	[	[	X
ejpam-6939	35	32	11–13	11–13	NUM
ejpam-6939	35	33	]	]	PUNCT
ejpam-6939	35	34	for	for	ADP
ejpam-6939	35	35	studies	study	NOUN
ejpam-6939	35	36	whose	whose	DET
ejpam-6939	35	37	primary	primary	ADJ
ejpam-6939	35	38	emphasis	emphasis	NOUN
ejpam-6939	35	39	is	be	AUX
ejpam-6939	35	40	on	on	ADP
ejpam-6939	35	41	total	total	ADJ
ejpam-6939	35	42	domination	domination	NOUN
ejpam-6939	35	43	in	in	ADP
ejpam-6939	35	44	graphs	graph	NOUN
ejpam-6939	35	45	.	.	PUNCT
ejpam-6939	36	1	a	a	DET
ejpam-6939	36	2	dominating	dominating	NOUN
ejpam-6939	36	3	set	set	NOUN
ejpam-6939	36	4	s	s	VERB
ejpam-6939	36	5	is	be	AUX
ejpam-6939	36	6	a	a	DET
ejpam-6939	36	7	connected	connected	ADJ
ejpam-6939	36	8	dominating	dominating	NOUN
ejpam-6939	36	9	set	set	NOUN
ejpam-6939	36	10	of	of	ADP
ejpam-6939	36	11	g	g	PROPN
ejpam-6939	36	12	provided	provide	VERB
ejpam-6939	36	13	the	the	DET
ejpam-6939	36	14	subgraph	subgraph	NOUN
ejpam-6939	36	15	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	36	16	induced	induce	VERB
ejpam-6939	36	17	by	by	ADP
ejpam-6939	36	18	s	s	PROPN
ejpam-6939	36	19	is	be	AUX
ejpam-6939	36	20	connected	connect	VERB
ejpam-6939	36	21	.	.	PUNCT
ejpam-6939	37	1	the	the	DET
ejpam-6939	37	2	minimum	minimum	ADJ
ejpam-6939	37	3	cardinality	cardinality	NOUN
ejpam-6939	37	4	of	of	ADP
ejpam-6939	37	5	a	a	DET
ejpam-6939	37	6	connected	connect	VERB
ejpam-6939	37	7	dominating	dominating	NOUN
ejpam-6939	37	8	set	set	NOUN
ejpam-6939	37	9	,	,	PUNCT
ejpam-6939	37	10	a.	a.	PROPN
ejpam-6939	37	11	aradais	aradais	PROPN
ejpam-6939	37	12	,	,	PUNCT
ejpam-6939	37	13	f.	f.	PROPN
ejpam-6939	37	14	jamil	jamil	PROPN
ejpam-6939	37	15	,	,	PUNCT
ejpam-6939	37	16	s.	s.	PROPN
ejpam-6939	37	17	canoy	canoy	PROPN
ejpam-6939	37	18	/	/	SYM
ejpam-6939	37	19	eur	eur	PROPN
ejpam-6939	37	20	.	.	PUNCT
ejpam-6939	38	1	j.	j.	PROPN
ejpam-6939	38	2	pure	pure	PROPN
ejpam-6939	38	3	appl	appl	PROPN
ejpam-6939	38	4	.	.	PROPN
ejpam-6939	38	5	math	math	PROPN
ejpam-6939	38	6	,	,	PUNCT
ejpam-6939	38	7	18	18	NUM
ejpam-6939	38	8	(	(	PUNCT
ejpam-6939	38	9	4	4	NUM
ejpam-6939	38	10	)	)	PUNCT
ejpam-6939	38	11	(	(	PUNCT
ejpam-6939	38	12	2025	2025	NUM
ejpam-6939	38	13	)	)	PUNCT
ejpam-6939	38	14	,	,	PUNCT
ejpam-6939	38	15	6939	6939	NUM
ejpam-6939	38	16	3	3	NUM
ejpam-6939	38	17	of	of	ADP
ejpam-6939	38	18	14	14	NUM
ejpam-6939	38	19	which	which	PRON
ejpam-6939	38	20	is	be	AUX
ejpam-6939	38	21	denoted	denote	VERB
ejpam-6939	38	22	by	by	ADP
ejpam-6939	38	23	γc(g	γc(g	NOUN
ejpam-6939	38	24	)	)	PUNCT
ejpam-6939	38	25	,	,	PUNCT
ejpam-6939	38	26	is	be	AUX
ejpam-6939	38	27	the	the	DET
ejpam-6939	38	28	connected	connected	ADJ
ejpam-6939	38	29	domination	domination	NOUN
ejpam-6939	38	30	number	number	NOUN
ejpam-6939	38	31	of	of	ADP
ejpam-6939	38	32	g.	g.	PROPN
ejpam-6939	38	33	the	the	DET
ejpam-6939	38	34	problem	problem	NOUN
ejpam-6939	38	35	of	of	ADP
ejpam-6939	38	36	connected	connected	ADJ
ejpam-6939	38	37	domination	domination	NOUN
ejpam-6939	38	38	would	would	AUX
ejpam-6939	38	39	arise	arise	VERB
ejpam-6939	38	40	in	in	ADP
ejpam-6939	38	41	real	real	ADJ
ejpam-6939	38	42	life	life	NOUN
ejpam-6939	38	43	in	in	ADP
ejpam-6939	38	44	the	the	DET
ejpam-6939	38	45	following	follow	VERB
ejpam-6939	38	46	scenario	scenario	NOUN
ejpam-6939	38	47	.	.	PUNCT
ejpam-6939	39	1	an	an	DET
ejpam-6939	39	2	existing	exist	VERB
ejpam-6939	39	3	computer	computer	NOUN
ejpam-6939	39	4	network	network	NOUN
ejpam-6939	39	5	with	with	ADP
ejpam-6939	39	6	direct	direct	ADJ
ejpam-6939	39	7	connections	connection	NOUN
ejpam-6939	39	8	described	describe	VERB
ejpam-6939	39	9	by	by	ADP
ejpam-6939	39	10	a	a	DET
ejpam-6939	39	11	graph	graph	NOUN
ejpam-6939	39	12	g	g	NOUN
ejpam-6939	39	13	must	must	AUX
ejpam-6939	39	14	have	have	VERB
ejpam-6939	39	15	the	the	DET
ejpam-6939	39	16	property	property	NOUN
ejpam-6939	39	17	that	that	PRON
ejpam-6939	39	18	any	any	DET
ejpam-6939	39	19	computer	computer	NOUN
ejpam-6939	39	20	turned	turn	VERB
ejpam-6939	39	21	on	on	ADP
ejpam-6939	39	22	must	must	AUX
ejpam-6939	39	23	always	always	ADV
ejpam-6939	39	24	be	be	AUX
ejpam-6939	39	25	able	able	ADJ
ejpam-6939	39	26	to	to	PART
ejpam-6939	39	27	send	send	VERB
ejpam-6939	39	28	a	a	DET
ejpam-6939	39	29	message	message	NOUN
ejpam-6939	39	30	to	to	ADP
ejpam-6939	39	31	any	any	DET
ejpam-6939	39	32	other	other	ADJ
ejpam-6939	39	33	computer	computer	NOUN
ejpam-6939	39	34	turned	turn	VERB
ejpam-6939	39	35	on	on	ADP
ejpam-6939	39	36	.	.	PUNCT
ejpam-6939	40	1	one	one	PRON
ejpam-6939	40	2	can	can	AUX
ejpam-6939	40	3	make	make	VERB
ejpam-6939	40	4	sure	sure	ADJ
ejpam-6939	40	5	a	a	DET
ejpam-6939	40	6	computer	computer	NOUN
ejpam-6939	40	7	is	be	AUX
ejpam-6939	40	8	always	always	ADV
ejpam-6939	40	9	on	on	ADV
ejpam-6939	40	10	by	by	ADP
ejpam-6939	40	11	connecting	connect	VERB
ejpam-6939	40	12	it	it	PRON
ejpam-6939	40	13	to	to	ADP
ejpam-6939	40	14	an	an	DET
ejpam-6939	40	15	(	(	PUNCT
ejpam-6939	40	16	expensive	expensive	ADJ
ejpam-6939	40	17	)	)	PUNCT
ejpam-6939	40	18	unlimited	unlimited	ADJ
ejpam-6939	40	19	power	power	NOUN
ejpam-6939	40	20	supply	supply	NOUN
ejpam-6939	40	21	(	(	PUNCT
ejpam-6939	40	22	ups	up	NOUN
ejpam-6939	40	23	)	)	PUNCT
ejpam-6939	40	24	source	source	NOUN
ejpam-6939	40	25	.	.	PUNCT
ejpam-6939	41	1	the	the	DET
ejpam-6939	41	2	requirement	requirement	NOUN
ejpam-6939	41	3	is	be	AUX
ejpam-6939	41	4	met	meet	VERB
ejpam-6939	41	5	by	by	ADP
ejpam-6939	41	6	connecting	connect	VERB
ejpam-6939	41	7	only	only	ADV
ejpam-6939	41	8	the	the	DET
ejpam-6939	41	9	computers	computer	NOUN
ejpam-6939	41	10	in	in	ADP
ejpam-6939	41	11	a	a	DET
ejpam-6939	41	12	connected	connect	VERB
ejpam-6939	41	13	dominating	dominating	NOUN
ejpam-6939	41	14	set	set	VERB
ejpam-6939	41	15	to	to	ADP
ejpam-6939	41	16	such	such	ADJ
ejpam-6939	41	17	power	power	NOUN
ejpam-6939	41	18	sources	source	NOUN
ejpam-6939	41	19	.	.	PUNCT
ejpam-6939	42	1	a	a	DET
ejpam-6939	42	2	set	set	NOUN
ejpam-6939	42	3	s	s	NOUN
ejpam-6939	42	4	⊆	⊆	NUM
ejpam-6939	42	5	v	v	NOUN
ejpam-6939	42	6	(	(	PUNCT
ejpam-6939	42	7	g	g	NOUN
ejpam-6939	42	8	)	)	PUNCT
ejpam-6939	42	9	is	be	AUX
ejpam-6939	42	10	a	a	DET
ejpam-6939	42	11	2	2	NUM
ejpam-6939	42	12	-	-	PUNCT
ejpam-6939	42	13	dominating	dominating	NOUN
ejpam-6939	42	14	set	set	NOUN
ejpam-6939	42	15	of	of	ADP
ejpam-6939	42	16	g	g	PROPN
ejpam-6939	42	17	if	if	SCONJ
ejpam-6939	42	18	for	for	ADP
ejpam-6939	42	19	each	each	PRON
ejpam-6939	42	20	v	v	NUM
ejpam-6939	42	21	∈	∈	PROPN
ejpam-6939	42	22	v	v	NOUN
ejpam-6939	42	23	(	(	PUNCT
ejpam-6939	42	24	g	g	NOUN
ejpam-6939	42	25	)	)	PUNCT
ejpam-6939	42	26	\	\	PROPN
ejpam-6939	43	1	s	s	X
ejpam-6939	43	2	,	,	PUNCT
ejpam-6939	43	3	|ng(v	|ng(v	ADJ
ejpam-6939	43	4	)	)	PUNCT
ejpam-6939	43	5	∩	∩	NOUN
ejpam-6939	43	6	s|	s|	VERB
ejpam-6939	43	7	≥	≥	NOUN
ejpam-6939	43	8	2	2	X
ejpam-6939	43	9	.	.	PUNCT
ejpam-6939	44	1	it	it	PRON
ejpam-6939	44	2	is	be	AUX
ejpam-6939	44	3	a	a	DET
ejpam-6939	44	4	connected	connected	ADJ
ejpam-6939	44	5	2	2	NUM
ejpam-6939	44	6	-	-	PUNCT
ejpam-6939	44	7	dominating	dominate	VERB
ejpam-6939	44	8	set	set	NOUN
ejpam-6939	44	9	of	of	ADP
ejpam-6939	44	10	g	g	PROPN
ejpam-6939	44	11	if	if	SCONJ
ejpam-6939	44	12	it	it	PRON
ejpam-6939	44	13	is	be	AUX
ejpam-6939	44	14	a	a	DET
ejpam-6939	44	15	2	2	NUM
ejpam-6939	44	16	-	-	PUNCT
ejpam-6939	44	17	dominating	dominating	NOUN
ejpam-6939	44	18	set	set	NOUN
ejpam-6939	44	19	and	and	CCONJ
ejpam-6939	44	20	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	44	21	is	be	AUX
ejpam-6939	44	22	connected	connect	VERB
ejpam-6939	44	23	.	.	PUNCT
ejpam-6939	45	1	the	the	DET
ejpam-6939	45	2	minimum	minimum	ADJ
ejpam-6939	45	3	cardinality	cardinality	NOUN
ejpam-6939	45	4	of	of	ADP
ejpam-6939	45	5	a	a	DET
ejpam-6939	45	6	2	2	NUM
ejpam-6939	45	7	-	-	PUNCT
ejpam-6939	45	8	dominating	dominating	NOUN
ejpam-6939	45	9	set	set	NOUN
ejpam-6939	45	10	(	(	PUNCT
ejpam-6939	45	11	resp	resp	NOUN
ejpam-6939	45	12	.	.	PUNCT
ejpam-6939	46	1	connected	connect	VERB
ejpam-6939	46	2	2	2	NUM
ejpam-6939	46	3	-	-	PUNCT
ejpam-6939	46	4	dominating	dominating	NOUN
ejpam-6939	46	5	set	set	NOUN
ejpam-6939	46	6	)	)	PUNCT
ejpam-6939	46	7	is	be	AUX
ejpam-6939	46	8	the	the	DET
ejpam-6939	46	9	2	2	NUM
ejpam-6939	46	10	-	-	PUNCT
ejpam-6939	46	11	domination	domination	NOUN
ejpam-6939	46	12	number	number	NOUN
ejpam-6939	46	13	(	(	PUNCT
ejpam-6939	46	14	resp	resp	NOUN
ejpam-6939	46	15	.	.	PUNCT
ejpam-6939	47	1	connected	connect	VERB
ejpam-6939	47	2	2	2	NUM
ejpam-6939	47	3	-	-	PUNCT
ejpam-6939	47	4	domination	domination	NOUN
ejpam-6939	47	5	number	number	NOUN
ejpam-6939	47	6	)	)	PUNCT
ejpam-6939	47	7	of	of	ADP
ejpam-6939	47	8	g	g	NOUN
ejpam-6939	47	9	,	,	PUNCT
ejpam-6939	47	10	denoted	denote	VERB
ejpam-6939	47	11	by	by	ADP
ejpam-6939	47	12	γ×2(g	γ×2(g	NOUN
ejpam-6939	47	13	)	)	PUNCT
ejpam-6939	47	14	(	(	PUNCT
ejpam-6939	47	15	resp	resp	NOUN
ejpam-6939	47	16	.	.	PUNCT
ejpam-6939	47	17	γ×2,c(g	γ×2,c(g	ADJ
ejpam-6939	47	18	)	)	PUNCT
ejpam-6939	47	19	)	)	PUNCT
ejpam-6939	47	20	.	.	PUNCT
ejpam-6939	48	1	any	any	DET
ejpam-6939	48	2	2	2	NUM
ejpam-6939	48	3	-	-	PUNCT
ejpam-6939	48	4	dominating	dominate	VERB
ejpam-6939	48	5	(	(	PUNCT
ejpam-6939	48	6	resp	resp	NOUN
ejpam-6939	48	7	.	.	PUNCT
ejpam-6939	49	1	connected	connect	VERB
ejpam-6939	49	2	2	2	NUM
ejpam-6939	49	3	-	-	PUNCT
ejpam-6939	49	4	dominating	dominating	NOUN
ejpam-6939	49	5	)	)	PUNCT
ejpam-6939	49	6	set	set	VERB
ejpam-6939	49	7	with	with	ADP
ejpam-6939	49	8	cardinality	cardinality	NOUN
ejpam-6939	49	9	γ×2(g	γ×2(g	PROPN
ejpam-6939	49	10	)	)	PUNCT
ejpam-6939	49	11	(	(	PUNCT
ejpam-6939	49	12	resp	resp	NOUN
ejpam-6939	49	13	.	.	PUNCT
ejpam-6939	49	14	γ×2,c(g	γ×2,c(g	X
ejpam-6939	49	15	)	)	PUNCT
ejpam-6939	49	16	)	)	PUNCT
ejpam-6939	49	17	is	be	AUX
ejpam-6939	49	18	called	call	VERB
ejpam-6939	49	19	a	a	DET
ejpam-6939	49	20	γ×2	γ×2	NOUN
ejpam-6939	49	21	-	-	PUNCT
ejpam-6939	49	22	set	set	VERB
ejpam-6939	49	23	(	(	PUNCT
ejpam-6939	49	24	resp	resp	NOUN
ejpam-6939	49	25	.	.	PUNCT
ejpam-6939	50	1	γ×2,c	γ×2,c	ADJ
ejpam-6939	50	2	-	-	PUNCT
ejpam-6939	50	3	set	set	NOUN
ejpam-6939	50	4	)	)	PUNCT
ejpam-6939	50	5	of	of	ADP
ejpam-6939	50	6	g.	g.	PROPN
ejpam-6939	50	7	excellent	excellent	ADJ
ejpam-6939	50	8	references	reference	NOUN
ejpam-6939	50	9	for	for	ADP
ejpam-6939	50	10	studies	study	NOUN
ejpam-6939	50	11	of	of	ADP
ejpam-6939	50	12	2	2	NUM
ejpam-6939	50	13	-	-	PUNCT
ejpam-6939	50	14	domination	domination	NOUN
ejpam-6939	50	15	include	include	VERB
ejpam-6939	50	16	[	[	X
ejpam-6939	50	17	14–19	14–19	NUM
ejpam-6939	50	18	]	]	PUNCT
ejpam-6939	50	19	.	.	PUNCT
ejpam-6939	51	1	for	for	ADP
ejpam-6939	51	2	a	a	DET
ejpam-6939	51	3	vertex	vertex	NOUN
ejpam-6939	51	4	v	v	NOUN
ejpam-6939	51	5	of	of	ADP
ejpam-6939	51	6	g	g	NOUN
ejpam-6939	51	7	,	,	PUNCT
ejpam-6939	51	8	ng(v	ng(v	X
ejpam-6939	51	9	,	,	PUNCT
ejpam-6939	51	10	2	2	X
ejpam-6939	51	11	)	)	PUNCT
ejpam-6939	51	12	=	=	PRON
ejpam-6939	51	13	{	{	PUNCT
ejpam-6939	51	14	u	u	NOUN
ejpam-6939	51	15	∈	∈	PROPN
ejpam-6939	51	16	v	v	NOUN
ejpam-6939	51	17	(	(	PUNCT
ejpam-6939	51	18	g	g	NOUN
ejpam-6939	51	19	)	)	PUNCT
ejpam-6939	51	20	\	\	NOUN
ejpam-6939	51	21	{	{	PUNCT
ejpam-6939	51	22	v	v	NOUN
ejpam-6939	51	23	}	}	PUNCT
ejpam-6939	51	24	:	:	PUNCT
ejpam-6939	51	25	dg(u	dg(u	X
ejpam-6939	51	26	,	,	PUNCT
ejpam-6939	51	27	v	v	NOUN
ejpam-6939	51	28	)	)	PUNCT
ejpam-6939	51	29	≤	≤	NOUN
ejpam-6939	51	30	2	2	NUM
ejpam-6939	51	31	}	}	PUNCT
ejpam-6939	51	32	.	.	PUNCT
ejpam-6939	52	1	for	for	ADP
ejpam-6939	52	2	s	s	PROPN
ejpam-6939	52	3	⊆	⊆	NUM
ejpam-6939	52	4	v	v	NOUN
ejpam-6939	52	5	(	(	PUNCT
ejpam-6939	52	6	g	g	NOUN
ejpam-6939	52	7	)	)	PUNCT
ejpam-6939	52	8	,	,	PUNCT
ejpam-6939	52	9	ng(s	ng(s	CCONJ
ejpam-6939	52	10	,	,	PUNCT
ejpam-6939	52	11	2	2	X
ejpam-6939	52	12	)	)	PUNCT
ejpam-6939	52	13	=	=	SYM
ejpam-6939	52	14	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-6939	52	15	,	,	PUNCT
ejpam-6939	52	16	2	2	NUM
ejpam-6939	52	17	)	)	PUNCT
ejpam-6939	52	18	.	.	PUNCT
ejpam-6939	53	1	a	a	DET
ejpam-6939	53	2	set	set	NOUN
ejpam-6939	53	3	s	s	NOUN
ejpam-6939	53	4	⊆	⊆	NUM
ejpam-6939	53	5	v	v	NOUN
ejpam-6939	53	6	(	(	PUNCT
ejpam-6939	53	7	g	g	NOUN
ejpam-6939	53	8	)	)	PUNCT
ejpam-6939	53	9	is	be	AUX
ejpam-6939	53	10	a	a	DET
ejpam-6939	53	11	distance	distance	NOUN
ejpam-6939	53	12	-	-	PUNCT
ejpam-6939	53	13	two	two	NUM
ejpam-6939	53	14	dominating	dominating	NOUN
ejpam-6939	53	15	set	set	NOUN
ejpam-6939	53	16	of	of	ADP
ejpam-6939	53	17	g	g	NOUN
ejpam-6939	53	18	provided	provide	VERB
ejpam-6939	53	19	v	v	ADP
ejpam-6939	53	20	(	(	PUNCT
ejpam-6939	53	21	g	g	NOUN
ejpam-6939	53	22	)	)	PUNCT
ejpam-6939	53	23	\	\	PUNCT
ejpam-6939	53	24	s	s	PART
ejpam-6939	53	25	⊆	⊆	NUM
ejpam-6939	53	26	ng(s	ng(s	NUM
ejpam-6939	53	27	,	,	PUNCT
ejpam-6939	53	28	2	2	NUM
ejpam-6939	53	29	)	)	PUNCT
ejpam-6939	53	30	,	,	PUNCT
ejpam-6939	53	31	i.e.	i.e.	X
ejpam-6939	53	32	,	,	PUNCT
ejpam-6939	53	33	if	if	SCONJ
ejpam-6939	53	34	for	for	ADP
ejpam-6939	53	35	every	every	PRON
ejpam-6939	53	36	v	v	NUM
ejpam-6939	53	37	∈	∈	NOUN
ejpam-6939	53	38	v	v	NOUN
ejpam-6939	53	39	(	(	PUNCT
ejpam-6939	53	40	g	g	NOUN
ejpam-6939	53	41	)	)	PUNCT
ejpam-6939	53	42	\	\	PROPN
ejpam-6939	54	1	s	s	VERB
ejpam-6939	54	2	there	there	PRON
ejpam-6939	54	3	exists	exist	VERB
ejpam-6939	54	4	u	u	PROPN
ejpam-6939	54	5	∈	∈	PROPN
ejpam-6939	54	6	s	s	VERB
ejpam-6939	54	7	such	such	ADJ
ejpam-6939	54	8	that	that	PRON
ejpam-6939	54	9	dg(u	dg(u	ADJ
ejpam-6939	54	10	,	,	PUNCT
ejpam-6939	54	11	v	v	NOUN
ejpam-6939	54	12	)	)	PUNCT
ejpam-6939	54	13	≤	≤	NOUN
ejpam-6939	54	14	2	2	NUM
ejpam-6939	54	15	.	.	PUNCT
ejpam-6939	54	16	a	a	DET
ejpam-6939	54	17	distance	distance	NOUN
ejpam-6939	54	18	-	-	PUNCT
ejpam-6939	54	19	two	two	NUM
ejpam-6939	54	20	dominating	dominating	NOUN
ejpam-6939	54	21	set	set	NOUN
ejpam-6939	54	22	s	s	VERB
ejpam-6939	54	23	is	be	AUX
ejpam-6939	54	24	a	a	DET
ejpam-6939	54	25	connected	connected	ADJ
ejpam-6939	54	26	distance	distance	NOUN
ejpam-6939	54	27	-	-	PUNCT
ejpam-6939	54	28	two	two	NUM
ejpam-6939	54	29	dominating	dominating	NOUN
ejpam-6939	54	30	set	set	NOUN
ejpam-6939	54	31	if	if	SCONJ
ejpam-6939	54	32	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	54	33	is	be	AUX
ejpam-6939	54	34	connected	connect	VERB
ejpam-6939	54	35	.	.	PUNCT
ejpam-6939	55	1	the	the	DET
ejpam-6939	55	2	minimum	minimum	ADJ
ejpam-6939	55	3	cardinality	cardinality	NOUN
ejpam-6939	55	4	of	of	ADP
ejpam-6939	55	5	a	a	DET
ejpam-6939	55	6	distance	distance	NOUN
ejpam-6939	55	7	-	-	PUNCT
ejpam-6939	55	8	two	two	NUM
ejpam-6939	55	9	dominating	dominating	NOUN
ejpam-6939	55	10	set	set	NOUN
ejpam-6939	55	11	(	(	PUNCT
ejpam-6939	55	12	resp	resp	NOUN
ejpam-6939	55	13	.	.	PUNCT
ejpam-6939	56	1	connected	connected	ADJ
ejpam-6939	56	2	distance	distance	NOUN
ejpam-6939	56	3	-	-	PUNCT
ejpam-6939	56	4	two	two	NUM
ejpam-6939	56	5	dominating	dominating	NOUN
ejpam-6939	56	6	set	set	NOUN
ejpam-6939	56	7	)	)	PUNCT
ejpam-6939	56	8	is	be	AUX
ejpam-6939	56	9	the	the	DET
ejpam-6939	56	10	distance	distance	NOUN
ejpam-6939	56	11	-	-	PUNCT
ejpam-6939	56	12	two	two	NUM
ejpam-6939	56	13	domination	domination	NOUN
ejpam-6939	56	14	number	number	NOUN
ejpam-6939	56	15	(	(	PUNCT
ejpam-6939	56	16	respectively	respectively	ADV
ejpam-6939	56	17	connected	connect	VERB
ejpam-6939	56	18	distance	distance	NOUN
ejpam-6939	56	19	-	-	PUNCT
ejpam-6939	56	20	two	two	NUM
ejpam-6939	56	21	domination	domination	NOUN
ejpam-6939	56	22	number	number	NOUN
ejpam-6939	56	23	)	)	PUNCT
ejpam-6939	56	24	of	of	ADP
ejpam-6939	56	25	g.	g.	NOUN
ejpam-6939	56	26	we	we	PRON
ejpam-6939	56	27	use	use	VERB
ejpam-6939	56	28	the	the	DET
ejpam-6939	56	29	symbols	symbol	NOUN
ejpam-6939	56	30	γ2(g	γ2(g	ADP
ejpam-6939	56	31	)	)	PUNCT
ejpam-6939	56	32	and	and	CCONJ
ejpam-6939	56	33	γ2,c(g	γ2,c(g	ADP
ejpam-6939	56	34	)	)	PUNCT
ejpam-6939	56	35	for	for	ADP
ejpam-6939	56	36	the	the	DET
ejpam-6939	56	37	distance	distance	NOUN
ejpam-6939	56	38	-	-	PUNCT
ejpam-6939	56	39	two	two	NUM
ejpam-6939	56	40	domination	domination	NOUN
ejpam-6939	56	41	number	number	NOUN
ejpam-6939	56	42	and	and	CCONJ
ejpam-6939	56	43	connected	connected	ADJ
ejpam-6939	56	44	distance	distance	NOUN
ejpam-6939	56	45	-	-	PUNCT
ejpam-6939	56	46	two	two	NUM
ejpam-6939	56	47	domination	domination	NOUN
ejpam-6939	56	48	number	number	NOUN
ejpam-6939	56	49	,	,	PUNCT
ejpam-6939	56	50	respectively	respectively	ADV
ejpam-6939	56	51	,	,	PUNCT
ejpam-6939	56	52	of	of	ADP
ejpam-6939	56	53	g.	g.	PROPN
ejpam-6939	56	54	a	a	DET
ejpam-6939	56	55	distance	distance	NOUN
ejpam-6939	56	56	-	-	PUNCT
ejpam-6939	56	57	two	two	NUM
ejpam-6939	56	58	dominating	dominating	NOUN
ejpam-6939	56	59	set	set	NOUN
ejpam-6939	56	60	(	(	PUNCT
ejpam-6939	56	61	resp	resp	NOUN
ejpam-6939	56	62	.	.	PUNCT
ejpam-6939	57	1	connected	connected	ADJ
ejpam-6939	57	2	distance	distance	NOUN
ejpam-6939	57	3	-	-	PUNCT
ejpam-6939	57	4	two	two	NUM
ejpam-6939	57	5	dominating	dominating	NOUN
ejpam-6939	57	6	set	set	NOUN
ejpam-6939	57	7	)	)	PUNCT
ejpam-6939	57	8	of	of	ADP
ejpam-6939	57	9	cardinality	cardinality	NOUN
ejpam-6939	57	10	γ2(g	γ2(g	NUM
ejpam-6939	57	11	)	)	PUNCT
ejpam-6939	57	12	(	(	PUNCT
ejpam-6939	57	13	resp	resp	NOUN
ejpam-6939	57	14	.	.	PUNCT
ejpam-6939	58	1	γ2,c(g	γ2,c(g	X
ejpam-6939	58	2	)	)	PUNCT
ejpam-6939	58	3	)	)	PUNCT
ejpam-6939	58	4	is	be	AUX
ejpam-6939	58	5	called	call	VERB
ejpam-6939	58	6	a	a	DET
ejpam-6939	58	7	γ2	γ2	NOUN
ejpam-6939	58	8	-	-	PUNCT
ejpam-6939	58	9	set	set	VERB
ejpam-6939	58	10	(	(	PUNCT
ejpam-6939	58	11	resp	resp	NOUN
ejpam-6939	58	12	.	.	PUNCT
ejpam-6939	59	1	γ2,c	γ2,c	NOUN
ejpam-6939	59	2	-	-	PUNCT
ejpam-6939	59	3	set	set	NOUN
ejpam-6939	59	4	)	)	PUNCT
ejpam-6939	59	5	.	.	PUNCT
ejpam-6939	60	1	the	the	DET
ejpam-6939	60	2	articles	article	NOUN
ejpam-6939	60	3	in	in	ADP
ejpam-6939	60	4	[	[	X
ejpam-6939	60	5	20	20	NUM
ejpam-6939	60	6	,	,	PUNCT
ejpam-6939	60	7	21	21	NUM
ejpam-6939	60	8	]	]	PUNCT
ejpam-6939	60	9	are	be	AUX
ejpam-6939	60	10	good	good	ADJ
ejpam-6939	60	11	references	reference	NOUN
ejpam-6939	60	12	for	for	ADP
ejpam-6939	60	13	studies	study	NOUN
ejpam-6939	60	14	in	in	ADP
ejpam-6939	60	15	distance	distance	NOUN
ejpam-6939	60	16	-	-	PUNCT
ejpam-6939	60	17	two	two	NUM
ejpam-6939	60	18	domination	domination	NOUN
ejpam-6939	60	19	.	.	PUNCT
ejpam-6939	61	1	in	in	ADP
ejpam-6939	61	2	[	[	X
ejpam-6939	61	3	21	21	NUM
ejpam-6939	61	4	]	]	PUNCT
ejpam-6939	61	5	the	the	DET
ejpam-6939	61	6	connected	connected	ADJ
ejpam-6939	61	7	distance	distance	NOUN
ejpam-6939	61	8	-	-	PUNCT
ejpam-6939	61	9	two	two	NUM
ejpam-6939	61	10	domination	domination	NOUN
ejpam-6939	61	11	is	be	AUX
ejpam-6939	61	12	called	call	VERB
ejpam-6939	61	13	connected	connected	ADJ
ejpam-6939	61	14	2	2	NUM
ejpam-6939	61	15	-	-	PUNCT
ejpam-6939	61	16	distance	distance	NOUN
ejpam-6939	61	17	domination	domination	NOUN
ejpam-6939	61	18	.	.	PUNCT
ejpam-6939	62	1	a	a	DET
ejpam-6939	62	2	subset	subset	NOUN
ejpam-6939	62	3	s	s	VERB
ejpam-6939	62	4	⊆	⊆	NUM
ejpam-6939	62	5	v	v	NOUN
ejpam-6939	62	6	(	(	PUNCT
ejpam-6939	62	7	g	g	NOUN
ejpam-6939	62	8	)	)	PUNCT
ejpam-6939	62	9	is	be	AUX
ejpam-6939	62	10	a	a	DET
ejpam-6939	62	11	connected	connected	ADJ
ejpam-6939	62	12	distance	distance	NOUN
ejpam-6939	62	13	-	-	PUNCT
ejpam-6939	62	14	two	two	NUM
ejpam-6939	62	15	dominating	dominating	NOUN
ejpam-6939	62	16	set	set	NOUN
ejpam-6939	62	17	of	of	ADP
ejpam-6939	62	18	g	g	PROPN
ejpam-6939	62	19	if	if	SCONJ
ejpam-6939	62	20	s	s	VERB
ejpam-6939	62	21	is	be	AUX
ejpam-6939	62	22	a	a	DET
ejpam-6939	62	23	distancetwo	distancetwo	ADJ
ejpam-6939	62	24	dominating	dominating	NOUN
ejpam-6939	62	25	set	set	NOUN
ejpam-6939	62	26	of	of	ADP
ejpam-6939	62	27	g	g	NOUN
ejpam-6939	62	28	for	for	ADP
ejpam-6939	62	29	which	which	PRON
ejpam-6939	62	30	⟨s⟩	⟨s⟩	VERB
ejpam-6939	62	31	is	be	AUX
ejpam-6939	62	32	connected	connect	VERB
ejpam-6939	62	33	.	.	PUNCT
ejpam-6939	63	1	in	in	ADP
ejpam-6939	63	2	[	[	X
ejpam-6939	63	3	21	21	NUM
ejpam-6939	63	4	]	]	PUNCT
ejpam-6939	63	5	,	,	PUNCT
ejpam-6939	63	6	the	the	DET
ejpam-6939	63	7	same	same	ADJ
ejpam-6939	63	8	is	be	AUX
ejpam-6939	63	9	called	call	VERB
ejpam-6939	63	10	connected	connected	ADJ
ejpam-6939	63	11	2	2	NUM
ejpam-6939	63	12	-	-	PUNCT
ejpam-6939	63	13	distance	distance	NOUN
ejpam-6939	63	14	dominating	dominating	NOUN
ejpam-6939	63	15	set	set	NOUN
ejpam-6939	63	16	.	.	PUNCT
ejpam-6939	64	1	we	we	PRON
ejpam-6939	64	2	used	use	VERB
ejpam-6939	64	3	γ2,c(g	γ2,c(g	ADP
ejpam-6939	64	4	)	)	PUNCT
ejpam-6939	64	5	to	to	PART
ejpam-6939	64	6	denote	denote	VERB
ejpam-6939	64	7	the	the	DET
ejpam-6939	64	8	minimum	minimum	ADJ
ejpam-6939	64	9	cardinality	cardinality	NOUN
ejpam-6939	64	10	of	of	ADP
ejpam-6939	64	11	a	a	DET
ejpam-6939	64	12	connected	connected	ADJ
ejpam-6939	64	13	distance	distance	NOUN
ejpam-6939	64	14	-	-	PUNCT
ejpam-6939	64	15	two	two	NUM
ejpam-6939	64	16	dominating	dominating	NOUN
ejpam-6939	64	17	set	set	NOUN
ejpam-6939	64	18	of	of	ADP
ejpam-6939	64	19	g.	g.	PROPN
ejpam-6939	64	20	a	a	DET
ejpam-6939	64	21	set	set	NOUN
ejpam-6939	64	22	s	s	PROPN
ejpam-6939	64	23	⊆	⊆	NUM
ejpam-6939	64	24	v	v	NOUN
ejpam-6939	64	25	(	(	PUNCT
ejpam-6939	64	26	g	g	NOUN
ejpam-6939	64	27	)	)	PUNCT
ejpam-6939	64	28	is	be	AUX
ejpam-6939	64	29	a	a	DET
ejpam-6939	64	30	disjunctive	disjunctive	ADJ
ejpam-6939	64	31	dominating	dominating	NOUN
ejpam-6939	64	32	set	set	NOUN
ejpam-6939	64	33	of	of	ADP
ejpam-6939	64	34	g	g	PROPN
ejpam-6939	65	1	if	if	SCONJ
ejpam-6939	65	2	for	for	ADP
ejpam-6939	65	3	every	every	PRON
ejpam-6939	65	4	v	v	NUM
ejpam-6939	65	5	∈	∈	NOUN
ejpam-6939	65	6	v	v	NOUN
ejpam-6939	65	7	(	(	PUNCT
ejpam-6939	65	8	g	g	NOUN
ejpam-6939	65	9	)	)	PUNCT
ejpam-6939	65	10	\	\	PROPN
ejpam-6939	66	1	s	s	X
ejpam-6939	66	2	,	,	PUNCT
ejpam-6939	66	3	v	v	NOUN
ejpam-6939	66	4	is	be	AUX
ejpam-6939	66	5	a	a	DET
ejpam-6939	66	6	neighbor	neighbor	NOUN
ejpam-6939	66	7	of	of	ADP
ejpam-6939	66	8	a	a	DET
ejpam-6939	66	9	vertex	vertex	NOUN
ejpam-6939	66	10	in	in	ADP
ejpam-6939	66	11	s	s	PRON
ejpam-6939	66	12	or	or	CCONJ
ejpam-6939	66	13	s	s	NOUN
ejpam-6939	66	14	has	have	AUX
ejpam-6939	66	15	at	at	ADV
ejpam-6939	66	16	least	least	ADV
ejpam-6939	66	17	two	two	NUM
ejpam-6939	66	18	vertices	vertex	NOUN
ejpam-6939	66	19	each	each	PRON
ejpam-6939	66	20	at	at	ADP
ejpam-6939	66	21	distance	distance	NOUN
ejpam-6939	66	22	2	2	NUM
ejpam-6939	66	23	from	from	ADP
ejpam-6939	66	24	v.	v.	ADP
ejpam-6939	66	25	provided	provide	VERB
ejpam-6939	66	26	g	g	PROPN
ejpam-6939	66	27	has	have	VERB
ejpam-6939	66	28	no	no	DET
ejpam-6939	66	29	isolated	isolated	ADJ
ejpam-6939	66	30	vertex	vertex	NOUN
ejpam-6939	66	31	,	,	PUNCT
ejpam-6939	66	32	s	s	VERB
ejpam-6939	66	33	⊆	⊆	NUM
ejpam-6939	66	34	v	v	NOUN
ejpam-6939	66	35	(	(	PUNCT
ejpam-6939	66	36	g	g	NOUN
ejpam-6939	66	37	)	)	PUNCT
ejpam-6939	66	38	is	be	AUX
ejpam-6939	66	39	a	a	DET
ejpam-6939	66	40	disjunctive	disjunctive	ADJ
ejpam-6939	66	41	total	total	ADJ
ejpam-6939	66	42	dominating	dominating	NOUN
ejpam-6939	66	43	set	set	VERB
ejpam-6939	66	44	if	if	SCONJ
ejpam-6939	66	45	for	for	ADP
ejpam-6939	66	46	every	every	DET
ejpam-6939	66	47	v	v	NUM
ejpam-6939	66	48	∈	∈	NOUN
ejpam-6939	66	49	v	v	NOUN
ejpam-6939	66	50	(	(	PUNCT
ejpam-6939	66	51	g	g	NOUN
ejpam-6939	66	52	)	)	PUNCT
ejpam-6939	66	53	,	,	PUNCT
ejpam-6939	66	54	v	v	NOUN
ejpam-6939	66	55	is	be	AUX
ejpam-6939	66	56	adjacent	adjacent	ADJ
ejpam-6939	66	57	to	to	ADP
ejpam-6939	66	58	a	a	DET
ejpam-6939	66	59	vertex	vertex	NOUN
ejpam-6939	66	60	of	of	ADP
ejpam-6939	66	61	s	s	PRON
ejpam-6939	66	62	or	or	CCONJ
ejpam-6939	66	63	s	s	NOUN
ejpam-6939	66	64	has	have	AUX
ejpam-6939	66	65	at	at	ADV
ejpam-6939	66	66	least	least	ADV
ejpam-6939	66	67	two	two	NUM
ejpam-6939	66	68	vertices	vertex	NOUN
ejpam-6939	66	69	each	each	PRON
ejpam-6939	66	70	at	at	ADP
ejpam-6939	66	71	distance	distance	NOUN
ejpam-6939	66	72	2	2	NUM
ejpam-6939	66	73	from	from	ADP
ejpam-6939	66	74	v.	v.	ADP
ejpam-6939	66	75	the	the	DET
ejpam-6939	66	76	minimum	minimum	ADJ
ejpam-6939	66	77	cardinality	cardinality	NOUN
ejpam-6939	66	78	of	of	ADP
ejpam-6939	66	79	a	a	DET
ejpam-6939	66	80	disjunctive	disjunctive	ADJ
ejpam-6939	66	81	dominating	dominating	NOUN
ejpam-6939	66	82	set	set	NOUN
ejpam-6939	66	83	(	(	PUNCT
ejpam-6939	66	84	resp	resp	NOUN
ejpam-6939	66	85	.	.	PUNCT
ejpam-6939	67	1	disjunctive	disjunctive	ADJ
ejpam-6939	67	2	total	total	ADJ
ejpam-6939	67	3	dominating	dominating	NOUN
ejpam-6939	67	4	set	set	NOUN
ejpam-6939	67	5	)	)	PUNCT
ejpam-6939	67	6	is	be	AUX
ejpam-6939	67	7	the	the	DET
ejpam-6939	67	8	disjunctive	disjunctive	ADJ
ejpam-6939	67	9	domination	domination	NOUN
ejpam-6939	67	10	number	number	NOUN
ejpam-6939	67	11	(	(	PUNCT
ejpam-6939	67	12	resp	resp	NOUN
ejpam-6939	67	13	.	.	PUNCT
ejpam-6939	68	1	disjunctive	disjunctive	ADJ
ejpam-6939	68	2	total	total	ADJ
ejpam-6939	68	3	domination	domination	NOUN
ejpam-6939	68	4	number	number	NOUN
ejpam-6939	68	5	)	)	PUNCT
ejpam-6939	68	6	of	of	ADP
ejpam-6939	68	7	g.	g.	PROPN
ejpam-6939	68	8	we	we	PRON
ejpam-6939	68	9	write	write	VERB
ejpam-6939	68	10	γd(g	γd(g	PRON
ejpam-6939	68	11	)	)	PUNCT
ejpam-6939	68	12	and	and	CCONJ
ejpam-6939	68	13	γdt	γdt	NOUN
ejpam-6939	68	14	(	(	PUNCT
ejpam-6939	68	15	g	g	NOUN
ejpam-6939	68	16	)	)	PUNCT
ejpam-6939	68	17	to	to	PART
ejpam-6939	68	18	denote	denote	VERB
ejpam-6939	68	19	the	the	DET
ejpam-6939	68	20	disjunctive	disjunctive	ADJ
ejpam-6939	68	21	domination	domination	NOUN
ejpam-6939	68	22	number	number	NOUN
ejpam-6939	68	23	and	and	CCONJ
ejpam-6939	68	24	disjunctive	disjunctive	ADJ
ejpam-6939	68	25	total	total	ADJ
ejpam-6939	68	26	domination	domination	NOUN
ejpam-6939	68	27	number	number	NOUN
ejpam-6939	68	28	,	,	PUNCT
ejpam-6939	68	29	respectively	respectively	ADV
ejpam-6939	68	30	,	,	PUNCT
ejpam-6939	68	31	of	of	ADP
ejpam-6939	68	32	g.	g.	PROPN
ejpam-6939	68	33	a	a	DET
ejpam-6939	68	34	disjunctive	disjunctive	ADJ
ejpam-6939	68	35	dominating	dominating	NOUN
ejpam-6939	68	36	set	set	NOUN
ejpam-6939	68	37	of	of	ADP
ejpam-6939	68	38	cardinality	cardinality	NOUN
ejpam-6939	68	39	γd(g	γd(g	NUM
ejpam-6939	68	40	)	)	PUNCT
ejpam-6939	68	41	is	be	AUX
ejpam-6939	68	42	called	call	VERB
ejpam-6939	68	43	a	a	DET
ejpam-6939	68	44	γd	γd	NOUN
ejpam-6939	68	45	-	-	PUNCT
ejpam-6939	68	46	set	set	NOUN
ejpam-6939	68	47	.	.	PUNCT
ejpam-6939	69	1	any	any	DET
ejpam-6939	69	2	disjunctive	disjunctive	ADJ
ejpam-6939	69	3	total	total	ADJ
ejpam-6939	69	4	dominating	dominating	NOUN
ejpam-6939	69	5	set	set	NOUN
ejpam-6939	69	6	of	of	ADP
ejpam-6939	69	7	cardinality	cardinality	PROPN
ejpam-6939	69	8	γdt	γdt	PROPN
ejpam-6939	69	9	(	(	PUNCT
ejpam-6939	69	10	g	g	NOUN
ejpam-6939	69	11	)	)	PUNCT
ejpam-6939	69	12	is	be	AUX
ejpam-6939	69	13	called	call	VERB
ejpam-6939	69	14	γdt	γdt	PROPN
ejpam-6939	69	15	-set	-set	NOUN
ejpam-6939	69	16	.	.	PUNCT
ejpam-6939	70	1	for	for	ADP
ejpam-6939	70	2	convenience	convenience	NOUN
ejpam-6939	70	3	,	,	PUNCT
ejpam-6939	70	4	the	the	DET
ejpam-6939	70	5	symbol	symbol	NOUN
ejpam-6939	70	6	nd	nd	PRON
ejpam-6939	70	7	g(s	g(s	PROPN
ejpam-6939	70	8	)	)	PUNCT
ejpam-6939	70	9	denotes	denote	VERB
ejpam-6939	70	10	the	the	DET
ejpam-6939	70	11	set	set	NOUN
ejpam-6939	70	12	of	of	ADP
ejpam-6939	70	13	all	all	PRON
ejpam-6939	70	14	x	x	SYM
ejpam-6939	70	15	∈	∈	PROPN
ejpam-6939	70	16	v	v	NOUN
ejpam-6939	70	17	(	(	PUNCT
ejpam-6939	70	18	g	g	NOUN
ejpam-6939	70	19	)	)	PUNCT
ejpam-6939	70	20	such	such	ADJ
ejpam-6939	70	21	that	that	SCONJ
ejpam-6939	70	22	xy	xy	PROPN
ejpam-6939	70	23	∈	∈	PROPN
ejpam-6939	70	24	a.	a.	PROPN
ejpam-6939	70	25	aradais	aradais	PROPN
ejpam-6939	70	26	,	,	PUNCT
ejpam-6939	70	27	f.	f.	PROPN
ejpam-6939	70	28	jamil	jamil	PROPN
ejpam-6939	70	29	,	,	PUNCT
ejpam-6939	70	30	s.	s.	PROPN
ejpam-6939	70	31	canoy	canoy	PROPN
ejpam-6939	70	32	/	/	SYM
ejpam-6939	70	33	eur	eur	PROPN
ejpam-6939	70	34	.	.	PUNCT
ejpam-6939	71	1	j.	j.	PROPN
ejpam-6939	71	2	pure	pure	PROPN
ejpam-6939	71	3	appl	appl	PROPN
ejpam-6939	71	4	.	.	PROPN
ejpam-6939	71	5	math	math	PROPN
ejpam-6939	71	6	,	,	PUNCT
ejpam-6939	71	7	18	18	NUM
ejpam-6939	71	8	(	(	PUNCT
ejpam-6939	71	9	4	4	NUM
ejpam-6939	71	10	)	)	PUNCT
ejpam-6939	71	11	(	(	PUNCT
ejpam-6939	71	12	2025	2025	NUM
ejpam-6939	71	13	)	)	PUNCT
ejpam-6939	71	14	,	,	PUNCT
ejpam-6939	71	15	6939	6939	NUM
ejpam-6939	71	16	4	4	NUM
ejpam-6939	71	17	of	of	ADP
ejpam-6939	71	18	14	14	NUM
ejpam-6939	71	19	e(g	e(g	NOUN
ejpam-6939	71	20	)	)	PUNCT
ejpam-6939	71	21	for	for	ADP
ejpam-6939	71	22	some	some	DET
ejpam-6939	71	23	y	y	PROPN
ejpam-6939	71	24	∈	∈	PROPN
ejpam-6939	71	25	s	s	PART
ejpam-6939	71	26	or	or	CCONJ
ejpam-6939	71	27	there	there	ADV
ejpam-6939	71	28	exist	exist	VERB
ejpam-6939	71	29	distinct	distinct	ADJ
ejpam-6939	71	30	u	u	NOUN
ejpam-6939	71	31	,	,	PUNCT
ejpam-6939	71	32	v	v	PROPN
ejpam-6939	71	33	∈	∈	NOUN
ejpam-6939	71	34	s	s	VERB
ejpam-6939	71	35	with	with	ADP
ejpam-6939	71	36	dg(x	dg(x	NUM
ejpam-6939	71	37	,	,	PUNCT
ejpam-6939	71	38	u	u	NOUN
ejpam-6939	71	39	)	)	PUNCT
ejpam-6939	71	40	=	=	SYM
ejpam-6939	71	41	2	2	NUM
ejpam-6939	71	42	=	=	SYM
ejpam-6939	71	43	dg(x	dg(x	NUM
ejpam-6939	71	44	,	,	PUNCT
ejpam-6939	71	45	v	v	NOUN
ejpam-6939	71	46	)	)	PUNCT
ejpam-6939	71	47	.	.	PUNCT
ejpam-6939	72	1	precisely	precisely	ADV
ejpam-6939	72	2	,	,	PUNCT
ejpam-6939	72	3	s	s	VERB
ejpam-6939	72	4	is	be	AUX
ejpam-6939	72	5	a	a	DET
ejpam-6939	72	6	disjunctive	disjunctive	ADJ
ejpam-6939	72	7	dominating	dominating	NOUN
ejpam-6939	72	8	set	set	NOUN
ejpam-6939	72	9	(	(	PUNCT
ejpam-6939	72	10	resp	resp	NOUN
ejpam-6939	72	11	.	.	PUNCT
ejpam-6939	73	1	disjunctive	disjunctive	ADJ
ejpam-6939	73	2	total	total	ADJ
ejpam-6939	73	3	dominating	dominating	NOUN
ejpam-6939	73	4	set	set	NOUN
ejpam-6939	73	5	)	)	PUNCT
ejpam-6939	73	6	of	of	ADP
ejpam-6939	73	7	g	g	PROPN
ejpam-6939	73	8	if	if	SCONJ
ejpam-6939	74	1	and	and	CCONJ
ejpam-6939	74	2	only	only	ADV
ejpam-6939	74	3	if	if	SCONJ
ejpam-6939	74	4	v	v	INTJ
ejpam-6939	74	5	(	(	PUNCT
ejpam-6939	74	6	g	g	NOUN
ejpam-6939	74	7	)	)	PUNCT
ejpam-6939	74	8	\	\	PUNCT
ejpam-6939	75	1	s	s	PART
ejpam-6939	75	2	⊆	⊆	NUM
ejpam-6939	75	3	nd	nd	PRON
ejpam-6939	75	4	g(s	g(s	PROPN
ejpam-6939	75	5	)	)	PUNCT
ejpam-6939	75	6	(	(	PUNCT
ejpam-6939	75	7	resp	resp	NOUN
ejpam-6939	75	8	.	.	PUNCT
ejpam-6939	76	1	v	v	X
ejpam-6939	76	2	(	(	PUNCT
ejpam-6939	76	3	g	g	NOUN
ejpam-6939	76	4	)	)	PUNCT
ejpam-6939	76	5	=	=	NOUN
ejpam-6939	76	6	nd	nd	PRON
ejpam-6939	76	7	g(s	g(s	PROPN
ejpam-6939	76	8	)	)	PUNCT
ejpam-6939	76	9	.	.	PUNCT
ejpam-6939	77	1	since	since	SCONJ
ejpam-6939	77	2	ng(s	ng(s	NUM
ejpam-6939	77	3	)	)	PUNCT
ejpam-6939	77	4	⊆	⊆	NUM
ejpam-6939	77	5	nd	nd	PRON
ejpam-6939	77	6	g(s	g(s	PROPN
ejpam-6939	77	7	)	)	PUNCT
ejpam-6939	77	8	,	,	PUNCT
ejpam-6939	77	9	dominating	dominating	NOUN
ejpam-6939	77	10	sets	set	NOUN
ejpam-6939	77	11	are	be	AUX
ejpam-6939	77	12	disjunctive	disjunctive	ADJ
ejpam-6939	77	13	dominating	dominating	NOUN
ejpam-6939	77	14	sets	set	NOUN
ejpam-6939	77	15	.	.	PUNCT
ejpam-6939	78	1	in	in	ADP
ejpam-6939	78	2	particular	particular	ADJ
ejpam-6939	78	3	,	,	PUNCT
ejpam-6939	78	4	γd(g	γd(g	NUM
ejpam-6939	78	5	)	)	PUNCT
ejpam-6939	78	6	=	=	SYM
ejpam-6939	78	7	1	1	NUM
ejpam-6939	78	8	if	if	SCONJ
ejpam-6939	78	9	and	and	CCONJ
ejpam-6939	78	10	only	only	ADV
ejpam-6939	78	11	if	if	SCONJ
ejpam-6939	78	12	γ(g	γ(g	NOUN
ejpam-6939	78	13	)	)	PUNCT
ejpam-6939	78	14	=	=	PUNCT
ejpam-6939	79	1	1	1	NUM
ejpam-6939	79	2	;	;	PUNCT
ejpam-6939	79	3	and	and	CCONJ
ejpam-6939	79	4	if	if	SCONJ
ejpam-6939	79	5	γ(g	γ(g	PROPN
ejpam-6939	79	6	)	)	PUNCT
ejpam-6939	79	7	=	=	SYM
ejpam-6939	80	1	2	2	NUM
ejpam-6939	80	2	,	,	PUNCT
ejpam-6939	80	3	then	then	ADV
ejpam-6939	80	4	γd(g	γd(g	NUM
ejpam-6939	80	5	)	)	PUNCT
ejpam-6939	80	6	=	=	SYM
ejpam-6939	80	7	2	2	NUM
ejpam-6939	80	8	,	,	PUNCT
ejpam-6939	80	9	but	but	CCONJ
ejpam-6939	80	10	not	not	PART
ejpam-6939	80	11	conversely	conversely	ADV
ejpam-6939	80	12	.	.	PUNCT
ejpam-6939	81	1	note	note	NOUN
ejpam-6939	81	2	,	,	PUNCT
ejpam-6939	81	3	for	for	ADP
ejpam-6939	81	4	example	example	NOUN
ejpam-6939	81	5	,	,	PUNCT
ejpam-6939	81	6	that	that	SCONJ
ejpam-6939	81	7	for	for	ADP
ejpam-6939	81	8	path	path	NOUN
ejpam-6939	81	9	p3	p3	PROPN
ejpam-6939	81	10	on	on	ADP
ejpam-6939	81	11	3	3	NUM
ejpam-6939	81	12	vertices	vertex	NOUN
ejpam-6939	81	13	and	and	CCONJ
ejpam-6939	81	14	any	any	DET
ejpam-6939	81	15	graph	graph	NOUN
ejpam-6939	81	16	g	g	NOUN
ejpam-6939	81	17	,	,	PUNCT
ejpam-6939	81	18	γd(p3	γd(p3	NOUN
ejpam-6939	81	19	◦	◦	NOUN
ejpam-6939	81	20	g	g	NOUN
ejpam-6939	81	21	)	)	PUNCT
ejpam-6939	81	22	=	=	SYM
ejpam-6939	81	23	2	2	NUM
ejpam-6939	81	24	while	while	SCONJ
ejpam-6939	81	25	γ(p3	γ(p3	ADP
ejpam-6939	81	26	◦	◦	NOUN
ejpam-6939	81	27	g	g	NOUN
ejpam-6939	81	28	)	)	PUNCT
ejpam-6939	81	29	=	=	SYM
ejpam-6939	82	1	3	3	X
ejpam-6939	82	2	.	.	PUNCT
ejpam-6939	82	3	also	also	ADV
ejpam-6939	82	4	,	,	PUNCT
ejpam-6939	82	5	since	since	SCONJ
ejpam-6939	82	6	total	total	ADJ
ejpam-6939	82	7	dominating	dominating	NOUN
ejpam-6939	82	8	sets	set	NOUN
ejpam-6939	82	9	are	be	AUX
ejpam-6939	82	10	disjunctive	disjunctive	ADJ
ejpam-6939	82	11	total	total	ADJ
ejpam-6939	82	12	dominating	dominating	NOUN
ejpam-6939	82	13	sets	set	NOUN
ejpam-6939	82	14	,	,	PUNCT
ejpam-6939	82	15	γdt	γdt	NOUN
ejpam-6939	82	16	(	(	PUNCT
ejpam-6939	82	17	g	g	NOUN
ejpam-6939	82	18	)	)	PUNCT
ejpam-6939	82	19	≤	≤	NOUN
ejpam-6939	82	20	γt(g	γt(g	PUNCT
ejpam-6939	82	21	)	)	PUNCT
ejpam-6939	82	22	for	for	ADP
ejpam-6939	82	23	all	all	DET
ejpam-6939	82	24	graphs	graph	NOUN
ejpam-6939	82	25	g	g	NOUN
ejpam-6939	82	26	without	without	ADP
ejpam-6939	82	27	isolated	isolated	ADJ
ejpam-6939	82	28	vertices	vertex	NOUN
ejpam-6939	82	29	.	.	PUNCT
ejpam-6939	83	1	in	in	ADP
ejpam-6939	83	2	particular	particular	ADJ
ejpam-6939	83	3	,	,	PUNCT
ejpam-6939	83	4	if	if	SCONJ
ejpam-6939	83	5	γt(g	γt(g	NOUN
ejpam-6939	83	6	)	)	PUNCT
ejpam-6939	83	7	=	=	SYM
ejpam-6939	83	8	2	2	NUM
ejpam-6939	83	9	,	,	PUNCT
ejpam-6939	83	10	then	then	ADV
ejpam-6939	83	11	γdt	γdt	NOUN
ejpam-6939	83	12	(	(	PUNCT
ejpam-6939	83	13	g	g	NOUN
ejpam-6939	83	14	)	)	PUNCT
ejpam-6939	83	15	=	=	SYM
ejpam-6939	83	16	2	2	X
ejpam-6939	83	17	.	.	PUNCT
ejpam-6939	83	18	the	the	DET
ejpam-6939	83	19	converse	converse	NOUN
ejpam-6939	83	20	,	,	PUNCT
ejpam-6939	83	21	however	however	ADV
ejpam-6939	83	22	,	,	PUNCT
ejpam-6939	83	23	need	need	AUX
ejpam-6939	83	24	not	not	PART
ejpam-6939	83	25	be	be	AUX
ejpam-6939	83	26	true	true	ADJ
ejpam-6939	83	27	.	.	PUNCT
ejpam-6939	84	1	note	note	VERB
ejpam-6939	84	2	that	that	SCONJ
ejpam-6939	84	3	for	for	ADP
ejpam-6939	84	4	cycle	cycle	NOUN
ejpam-6939	84	5	c5	c5	PROPN
ejpam-6939	84	6	,	,	PUNCT
ejpam-6939	84	7	γt(c5	γt(c5	NOUN
ejpam-6939	84	8	)	)	PUNCT
ejpam-6939	84	9	=	=	SYM
ejpam-6939	84	10	3	3	NUM
ejpam-6939	84	11	but	but	CCONJ
ejpam-6939	84	12	γdt	γdt	PROPN
ejpam-6939	84	13	(	(	PUNCT
ejpam-6939	84	14	c5	c5	PROPN
ejpam-6939	84	15	)	)	PUNCT
ejpam-6939	84	16	=	=	SYM
ejpam-6939	85	1	2	2	NUM
ejpam-6939	85	2	.	.	NOUN
ejpam-6939	85	3	3	3	NUM
ejpam-6939	85	4	.	.	NOUN
ejpam-6939	85	5	results	result	VERB
ejpam-6939	85	6	a	a	DET
ejpam-6939	85	7	disjunctive	disjunctive	ADJ
ejpam-6939	85	8	dominating	dominating	NOUN
ejpam-6939	85	9	set	set	NOUN
ejpam-6939	85	10	s	s	VERB
ejpam-6939	85	11	is	be	AUX
ejpam-6939	85	12	a	a	DET
ejpam-6939	85	13	connected	connected	ADJ
ejpam-6939	85	14	disjunctive	disjunctive	ADJ
ejpam-6939	85	15	dominating	dominating	NOUN
ejpam-6939	85	16	set	set	NOUN
ejpam-6939	85	17	provided	provide	VERB
ejpam-6939	85	18	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	85	19	is	be	AUX
ejpam-6939	85	20	connected	connect	VERB
ejpam-6939	85	21	.	.	PUNCT
ejpam-6939	86	1	the	the	DET
ejpam-6939	86	2	minimum	minimum	ADJ
ejpam-6939	86	3	cardinality	cardinality	NOUN
ejpam-6939	86	4	of	of	ADP
ejpam-6939	86	5	a	a	DET
ejpam-6939	86	6	connected	connected	ADJ
ejpam-6939	86	7	disjunctive	disjunctive	ADJ
ejpam-6939	86	8	dominating	dominating	NOUN
ejpam-6939	86	9	set	set	NOUN
ejpam-6939	86	10	of	of	ADP
ejpam-6939	86	11	g	g	NOUN
ejpam-6939	86	12	,	,	PUNCT
ejpam-6939	86	13	denoted	denote	VERB
ejpam-6939	86	14	by	by	ADP
ejpam-6939	86	15	γdc	γdc	PROPN
ejpam-6939	86	16	(	(	PUNCT
ejpam-6939	86	17	g	g	NOUN
ejpam-6939	86	18	)	)	PUNCT
ejpam-6939	86	19	,	,	PUNCT
ejpam-6939	86	20	is	be	AUX
ejpam-6939	86	21	the	the	DET
ejpam-6939	86	22	connected	connect	VERB
ejpam-6939	86	23	disjunctive	disjunctive	ADJ
ejpam-6939	86	24	domination	domination	NOUN
ejpam-6939	86	25	number	number	NOUN
ejpam-6939	86	26	of	of	ADP
ejpam-6939	86	27	g.	g.	PROPN
ejpam-6939	86	28	any	any	DET
ejpam-6939	86	29	connected	connected	ADJ
ejpam-6939	86	30	disjunctive	disjunctive	ADJ
ejpam-6939	86	31	dominating	dominating	NOUN
ejpam-6939	86	32	set	set	NOUN
ejpam-6939	86	33	of	of	ADP
ejpam-6939	86	34	cardinality	cardinality	PROPN
ejpam-6939	86	35	γdc	γdc	PROPN
ejpam-6939	86	36	(	(	PUNCT
ejpam-6939	86	37	g	g	NOUN
ejpam-6939	86	38	)	)	PUNCT
ejpam-6939	86	39	is	be	AUX
ejpam-6939	86	40	called	call	VERB
ejpam-6939	86	41	a	a	DET
ejpam-6939	86	42	γdc	γdc	NOUN
ejpam-6939	86	43	-set	-set	PUNCT
ejpam-6939	86	44	of	of	ADP
ejpam-6939	86	45	g.	g.	PROPN
ejpam-6939	86	46	we	we	PRON
ejpam-6939	86	47	denote	denote	VERB
ejpam-6939	86	48	by	by	ADP
ejpam-6939	86	49	pn	pn	PROPN
ejpam-6939	86	50	,	,	PUNCT
ejpam-6939	86	51	cn	cn	PROPN
ejpam-6939	86	52	,	,	PUNCT
ejpam-6939	86	53	kn	kn	PROPN
ejpam-6939	86	54	and	and	CCONJ
ejpam-6939	86	55	kn	kn	PROPN
ejpam-6939	86	56	the	the	DET
ejpam-6939	86	57	path	path	NOUN
ejpam-6939	86	58	,	,	PUNCT
ejpam-6939	86	59	cycle	cycle	NOUN
ejpam-6939	86	60	,	,	PUNCT
ejpam-6939	86	61	complete	complete	ADJ
ejpam-6939	86	62	graph	graph	NOUN
ejpam-6939	86	63	and	and	CCONJ
ejpam-6939	86	64	empty	empty	ADJ
ejpam-6939	86	65	graph	graph	NOUN
ejpam-6939	86	66	on	on	ADP
ejpam-6939	86	67	n	n	DET
ejpam-6939	86	68	vertices	vertex	NOUN
ejpam-6939	86	69	.	.	PUNCT
ejpam-6939	87	1	for	for	ADP
ejpam-6939	87	2	positive	positive	ADJ
ejpam-6939	87	3	integers	integer	NOUN
ejpam-6939	87	4	n1	n1	NOUN
ejpam-6939	87	5	,	,	PUNCT
ejpam-6939	87	6	n2	n2	NOUN
ejpam-6939	87	7	,	,	PUNCT
ejpam-6939	87	8	.	.	PUNCT
ejpam-6939	87	9	.	.	PUNCT
ejpam-6939	87	10	.	.	PUNCT
ejpam-6939	88	1	,	,	PUNCT
ejpam-6939	88	2	nk	nk	PROPN
ejpam-6939	88	3	,	,	PUNCT
ejpam-6939	88	4	we	we	PRON
ejpam-6939	88	5	denote	denote	VERB
ejpam-6939	88	6	by	by	ADP
ejpam-6939	88	7	kn1,n2,	kn1,n2,	NOUN
ejpam-6939	88	8	...	...	PUNCT
ejpam-6939	88	9	,nk	,nk	PUNCT
ejpam-6939	88	10	the	the	DET
ejpam-6939	88	11	complete	complete	ADJ
ejpam-6939	88	12	multipartite	multipartite	ADJ
ejpam-6939	88	13	graph	graph	NOUN
ejpam-6939	88	14	with	with	ADP
ejpam-6939	88	15	partite	partite	ADJ
ejpam-6939	88	16	sets	set	NOUN
ejpam-6939	88	17	un1	un1	PROPN
ejpam-6939	88	18	,	,	PUNCT
ejpam-6939	88	19	un2	un2	ADJ
ejpam-6939	88	20	,	,	PUNCT
ejpam-6939	88	21	.	.	PUNCT
ejpam-6939	88	22	.	.	PUNCT
ejpam-6939	89	1	.	.	PUNCT
ejpam-6939	89	2	,	,	PUNCT
ejpam-6939	89	3	unk	unk	NOUN
ejpam-6939	89	4	with	with	ADP
ejpam-6939	89	5	|unj	|unj	NOUN
ejpam-6939	89	6	|	|	NOUN
ejpam-6939	89	7	=	=	SYM
ejpam-6939	89	8	nj	nj	PROPN
ejpam-6939	89	9	for	for	ADP
ejpam-6939	89	10	each	each	DET
ejpam-6939	89	11	j	j	PROPN
ejpam-6939	89	12	∈	∈	PROPN
ejpam-6939	89	13	{	{	PUNCT
ejpam-6939	89	14	1	1	NUM
ejpam-6939	89	15	,	,	PUNCT
ejpam-6939	89	16	2	2	NUM
ejpam-6939	89	17	,	,	PUNCT
ejpam-6939	89	18	.	.	PUNCT
ejpam-6939	89	19	.	.	PUNCT
ejpam-6939	90	1	.	.	PUNCT
ejpam-6939	91	1	,	,	PUNCT
ejpam-6939	91	2	k	k	X
ejpam-6939	91	3	}	}	PUNCT
ejpam-6939	91	4	.	.	PUNCT
ejpam-6939	92	1	in	in	ADP
ejpam-6939	92	2	particular	particular	ADJ
ejpam-6939	92	3	,	,	PUNCT
ejpam-6939	92	4	a	a	DET
ejpam-6939	92	5	star	star	NOUN
ejpam-6939	92	6	on	on	ADP
ejpam-6939	92	7	n+	n+	PRON
ejpam-6939	92	8	1	1	NUM
ejpam-6939	92	9	vertices	vertex	NOUN
ejpam-6939	92	10	is	be	AUX
ejpam-6939	92	11	denoted	denote	VERB
ejpam-6939	92	12	by	by	ADP
ejpam-6939	92	13	k1,n	k1,n	PROPN
ejpam-6939	92	14	.	.	PUNCT
ejpam-6939	93	1	a	a	DET
ejpam-6939	93	2	subdivision	subdivision	NOUN
ejpam-6939	93	3	of	of	ADP
ejpam-6939	93	4	an	an	DET
ejpam-6939	93	5	edge	edge	NOUN
ejpam-6939	93	6	uv	uv	PROPN
ejpam-6939	93	7	∈	∈	PROPN
ejpam-6939	93	8	e(g	e(g	PROPN
ejpam-6939	93	9	)	)	PUNCT
ejpam-6939	93	10	is	be	AUX
ejpam-6939	93	11	obtained	obtain	VERB
ejpam-6939	93	12	by	by	ADP
ejpam-6939	93	13	inserting	insert	VERB
ejpam-6939	93	14	in	in	ADP
ejpam-6939	93	15	g	g	PROPN
ejpam-6939	93	16	a	a	DET
ejpam-6939	93	17	new	new	ADJ
ejpam-6939	93	18	vertex	vertex	NOUN
ejpam-6939	93	19	w	w	NOUN
ejpam-6939	93	20	and	and	CCONJ
ejpam-6939	93	21	replacing	replace	VERB
ejpam-6939	93	22	the	the	DET
ejpam-6939	93	23	edge	edge	NOUN
ejpam-6939	93	24	uv	uv	NOUN
ejpam-6939	93	25	by	by	ADP
ejpam-6939	93	26	the	the	DET
ejpam-6939	93	27	edges	edge	NOUN
ejpam-6939	93	28	uw	uw	PROPN
ejpam-6939	93	29	and	and	CCONJ
ejpam-6939	93	30	wv	wv	PROPN
ejpam-6939	93	31	.	.	PUNCT
ejpam-6939	94	1	a	a	DET
ejpam-6939	94	2	spider	spider	NOUN
ejpam-6939	94	3	is	be	AUX
ejpam-6939	94	4	the	the	DET
ejpam-6939	94	5	graph	graph	NOUN
ejpam-6939	94	6	obtained	obtain	VERB
ejpam-6939	94	7	from	from	ADP
ejpam-6939	94	8	a	a	DET
ejpam-6939	94	9	star	star	NOUN
ejpam-6939	94	10	by	by	ADP
ejpam-6939	94	11	subdividing	subdivide	VERB
ejpam-6939	94	12	all	all	PRON
ejpam-6939	94	13	of	of	ADP
ejpam-6939	94	14	the	the	DET
ejpam-6939	94	15	edges	edge	NOUN
ejpam-6939	94	16	.	.	PUNCT
ejpam-6939	95	1	a	a	DET
ejpam-6939	95	2	wounded	wound	VERB
ejpam-6939	95	3	spider	spider	NOUN
ejpam-6939	95	4	is	be	AUX
ejpam-6939	95	5	any	any	DET
ejpam-6939	95	6	graph	graph	NOUN
ejpam-6939	95	7	obtained	obtain	VERB
ejpam-6939	95	8	from	from	ADP
ejpam-6939	95	9	a	a	DET
ejpam-6939	95	10	spider	spider	NOUN
ejpam-6939	95	11	by	by	ADP
ejpam-6939	95	12	removing	remove	VERB
ejpam-6939	95	13	at	at	ADV
ejpam-6939	95	14	least	least	ADV
ejpam-6939	95	15	one	one	NUM
ejpam-6939	95	16	endvertex	endvertex	NOUN
ejpam-6939	95	17	.	.	PUNCT
ejpam-6939	96	1	for	for	ADP
ejpam-6939	96	2	convenience	convenience	NOUN
ejpam-6939	96	3	,	,	PUNCT
ejpam-6939	96	4	let	let	VERB
ejpam-6939	96	5	sk,0	sk,0	PROPN
ejpam-6939	96	6	denote	denote	VERB
ejpam-6939	96	7	any	any	DET
ejpam-6939	96	8	spider	spider	NOUN
ejpam-6939	96	9	with	with	ADP
ejpam-6939	96	10	k	k	PROPN
ejpam-6939	96	11	endvertices	endvertice	NOUN
ejpam-6939	96	12	,	,	PUNCT
ejpam-6939	96	13	and	and	CCONJ
ejpam-6939	96	14	let	let	VERB
ejpam-6939	96	15	sk	sk	VERB
ejpam-6939	96	16	,	,	PUNCT
ejpam-6939	96	17	j	j	PROPN
ejpam-6939	96	18	(	(	PUNCT
ejpam-6939	96	19	1	1	NUM
ejpam-6939	96	20	≤	≤	NUM
ejpam-6939	96	21	j	j	PROPN
ejpam-6939	96	22	≤	≤	PROPN
ejpam-6939	96	23	k	k	NOUN
ejpam-6939	96	24	)	)	PUNCT
ejpam-6939	96	25	denote	denote	VERB
ejpam-6939	96	26	the	the	DET
ejpam-6939	96	27	wounded	wounded	ADJ
ejpam-6939	96	28	spider	spider	NOUN
ejpam-6939	96	29	obtained	obtain	VERB
ejpam-6939	96	30	from	from	ADP
ejpam-6939	96	31	sk,0	sk,0	PROPN
ejpam-6939	96	32	by	by	ADP
ejpam-6939	96	33	removing	remove	VERB
ejpam-6939	96	34	j	j	PROPN
ejpam-6939	96	35	end	end	NOUN
ejpam-6939	96	36	-	-	PUNCT
ejpam-6939	96	37	vertices	vertex	NOUN
ejpam-6939	96	38	.	.	PUNCT
ejpam-6939	97	1	observation	observation	NOUN
ejpam-6939	97	2	1	1	NUM
ejpam-6939	97	3	.	.	PUNCT
ejpam-6939	98	1	for	for	ADP
ejpam-6939	98	2	paths	path	NOUN
ejpam-6939	98	3	,	,	PUNCT
ejpam-6939	98	4	cycles	cycle	NOUN
ejpam-6939	98	5	,	,	PUNCT
ejpam-6939	98	6	complete	complete	ADJ
ejpam-6939	98	7	multipartite	multipartite	ADJ
ejpam-6939	98	8	graphs	graph	NOUN
ejpam-6939	98	9	and	and	CCONJ
ejpam-6939	98	10	spiders	spider	NOUN
ejpam-6939	98	11	,	,	PUNCT
ejpam-6939	98	12	(	(	PUNCT
ejpam-6939	98	13	i	i	NOUN
ejpam-6939	98	14	)	)	PUNCT
ejpam-6939	98	15	γdc	γdc	PROPN
ejpam-6939	98	16	(	(	PUNCT
ejpam-6939	98	17	pn	pn	NOUN
ejpam-6939	98	18	)	)	PUNCT
ejpam-6939	98	19	=	=	SYM
ejpam-6939	98	20	®	®	NOUN
ejpam-6939	98	21	1	1	NUM
ejpam-6939	98	22	,	,	PUNCT
ejpam-6939	98	23	if	if	SCONJ
ejpam-6939	98	24	n	n	NOUN
ejpam-6939	98	25	=	=	SYM
ejpam-6939	98	26	1	1	NUM
ejpam-6939	98	27	,	,	PUNCT
ejpam-6939	98	28	2	2	NUM
ejpam-6939	98	29	;	;	PUNCT
ejpam-6939	98	30	n−	n−	NOUN
ejpam-6939	98	31	2	2	NUM
ejpam-6939	98	32	,	,	PUNCT
ejpam-6939	98	33	if	if	SCONJ
ejpam-6939	98	34	n	n	PRON
ejpam-6939	98	35	≥	≥	NOUN
ejpam-6939	98	36	3	3	NUM
ejpam-6939	98	37	.	.	PUNCT
ejpam-6939	98	38	(	(	PUNCT
ejpam-6939	98	39	ii	ii	PROPN
ejpam-6939	98	40	)	)	PUNCT
ejpam-6939	98	41	γdc	γdc	NOUN
ejpam-6939	98	42	(	(	PUNCT
ejpam-6939	98	43	cn	cn	PROPN
ejpam-6939	98	44	)	)	PUNCT
ejpam-6939	98	45	=	=	SYM
ejpam-6939	98	46			NOUN
ejpam-6939	98	47	1	1	NUM
ejpam-6939	98	48	,	,	PUNCT
ejpam-6939	98	49	if	if	SCONJ
ejpam-6939	98	50	n	n	NOUN
ejpam-6939	98	51	=	=	SYM
ejpam-6939	98	52	3	3	NUM
ejpam-6939	98	53	;	;	PUNCT
ejpam-6939	98	54	2	2	NUM
ejpam-6939	98	55	,	,	PUNCT
ejpam-6939	98	56	if	if	SCONJ
ejpam-6939	98	57	n	n	NOUN
ejpam-6939	98	58	=	=	SYM
ejpam-6939	98	59	4	4	NUM
ejpam-6939	98	60	;	;	PUNCT
ejpam-6939	98	61	n−	n−	NOUN
ejpam-6939	98	62	3	3	NUM
ejpam-6939	98	63	,	,	PUNCT
ejpam-6939	98	64	if	if	SCONJ
ejpam-6939	98	65	n	n	PRON
ejpam-6939	98	66	≥	≥	NOUN
ejpam-6939	98	67	5	5	NUM
ejpam-6939	98	68	.	.	PUNCT
ejpam-6939	98	69	(	(	PUNCT
ejpam-6939	98	70	iii	iii	X
ejpam-6939	98	71	)	)	PUNCT
ejpam-6939	98	72	if	if	SCONJ
ejpam-6939	98	73	k	k	PROPN
ejpam-6939	98	74	≥	≥	NUM
ejpam-6939	98	75	2	2	NUM
ejpam-6939	98	76	and	and	CCONJ
ejpam-6939	98	77	n1	n1	ADJ
ejpam-6939	98	78	≤	≤	NOUN
ejpam-6939	98	79	n2	n2	ADJ
ejpam-6939	98	80	≤	≤	NOUN
ejpam-6939	98	81	.	.	PUNCT
ejpam-6939	98	82	.	.	PUNCT
ejpam-6939	98	83	.	.	PUNCT
ejpam-6939	99	1	≤	≤	PROPN
ejpam-6939	99	2	nk	nk	PROPN
ejpam-6939	99	3	,	,	PUNCT
ejpam-6939	99	4	then	then	ADV
ejpam-6939	99	5	γdc	γdc	PROPN
ejpam-6939	99	6	(	(	PUNCT
ejpam-6939	99	7	kn1,n2,	kn1,n2,	NOUN
ejpam-6939	99	8	...	...	PUNCT
ejpam-6939	99	9	,nk	,nk	PUNCT
ejpam-6939	99	10	)	)	PUNCT
ejpam-6939	99	11	=	=	SYM
ejpam-6939	99	12	®	®	NOUN
ejpam-6939	99	13	1	1	NUM
ejpam-6939	99	14	,	,	PUNCT
ejpam-6939	99	15	if	if	SCONJ
ejpam-6939	99	16	n1	n1	ADJ
ejpam-6939	99	17	=	=	SYM
ejpam-6939	99	18	1	1	NUM
ejpam-6939	99	19	2	2	NUM
ejpam-6939	99	20	,	,	PUNCT
ejpam-6939	99	21	otherwise	otherwise	ADV
ejpam-6939	99	22	.	.	PUNCT
ejpam-6939	100	1	a.	a.	PROPN
ejpam-6939	100	2	aradais	aradais	PROPN
ejpam-6939	100	3	,	,	PUNCT
ejpam-6939	100	4	f.	f.	PROPN
ejpam-6939	100	5	jamil	jamil	PROPN
ejpam-6939	100	6	,	,	PUNCT
ejpam-6939	100	7	s.	s.	PROPN
ejpam-6939	100	8	canoy	canoy	PROPN
ejpam-6939	100	9	/	/	SYM
ejpam-6939	100	10	eur	eur	PROPN
ejpam-6939	100	11	.	.	PUNCT
ejpam-6939	101	1	j.	j.	PROPN
ejpam-6939	101	2	pure	pure	PROPN
ejpam-6939	101	3	appl	appl	PROPN
ejpam-6939	101	4	.	.	PROPN
ejpam-6939	101	5	math	math	PROPN
ejpam-6939	101	6	,	,	PUNCT
ejpam-6939	101	7	18	18	NUM
ejpam-6939	101	8	(	(	PUNCT
ejpam-6939	101	9	4	4	NUM
ejpam-6939	101	10	)	)	PUNCT
ejpam-6939	101	11	(	(	PUNCT
ejpam-6939	101	12	2025	2025	NUM
ejpam-6939	101	13	)	)	PUNCT
ejpam-6939	101	14	,	,	PUNCT
ejpam-6939	101	15	6939	6939	NUM
ejpam-6939	101	16	5	5	NUM
ejpam-6939	101	17	of	of	ADP
ejpam-6939	101	18	14	14	NUM
ejpam-6939	101	19	(	(	PUNCT
ejpam-6939	101	20	iv	iv	NOUN
ejpam-6939	101	21	)	)	PUNCT
ejpam-6939	101	22	for	for	ADP
ejpam-6939	101	23	n	n	X
ejpam-6939	101	24	≥	≥	NUM
ejpam-6939	101	25	2	2	NUM
ejpam-6939	101	26	and	and	CCONJ
ejpam-6939	101	27	k	k	PROPN
ejpam-6939	101	28	∈	∈	PROPN
ejpam-6939	101	29	{	{	PUNCT
ejpam-6939	101	30	0	0	NUM
ejpam-6939	101	31	,	,	PUNCT
ejpam-6939	101	32	1	1	NUM
ejpam-6939	101	33	,	,	PUNCT
ejpam-6939	101	34	.	.	PUNCT
ejpam-6939	101	35	.	.	PUNCT
ejpam-6939	102	1	.	.	PUNCT
ejpam-6939	102	2	,	,	PUNCT
ejpam-6939	103	1	n	n	CCONJ
ejpam-6939	103	2	}	}	PUNCT
ejpam-6939	104	1	,	,	PUNCT
ejpam-6939	104	2	γdc	γdc	PROPN
ejpam-6939	104	3	(	(	PUNCT
ejpam-6939	104	4	sn	sn	PROPN
ejpam-6939	104	5	,	,	PUNCT
ejpam-6939	104	6	k	k	NOUN
ejpam-6939	104	7	)	)	PUNCT
ejpam-6939	104	8	=	=	SYM
ejpam-6939	104	9	®	®	NOUN
ejpam-6939	104	10	n+	n+	PUNCT
ejpam-6939	104	11	1	1	X
ejpam-6939	104	12	,	,	PUNCT
ejpam-6939	104	13	if	if	SCONJ
ejpam-6939	104	14	k	k	PROPN
ejpam-6939	104	15	=	=	SYM
ejpam-6939	104	16	0	0	NUM
ejpam-6939	105	1	n−	n−	PROPN
ejpam-6939	105	2	k	k	NOUN
ejpam-6939	106	1	+	+	CCONJ
ejpam-6939	106	2	1	1	NUM
ejpam-6939	106	3	,	,	PUNCT
ejpam-6939	106	4	otherwise	otherwise	ADV
ejpam-6939	106	5	.	.	PUNCT
ejpam-6939	107	1	proposition	proposition	NOUN
ejpam-6939	107	2	1	1	NUM
ejpam-6939	107	3	.	.	PUNCT
ejpam-6939	108	1	let	let	VERB
ejpam-6939	108	2	g	g	PRON
ejpam-6939	108	3	be	be	AUX
ejpam-6939	108	4	a	a	DET
ejpam-6939	108	5	connected	connected	ADJ
ejpam-6939	108	6	graph	graph	NOUN
ejpam-6939	108	7	.	.	PUNCT
ejpam-6939	109	1	then	then	ADV
ejpam-6939	109	2	γd(g	γd(g	NUM
ejpam-6939	109	3	)	)	PUNCT
ejpam-6939	109	4	≤	≤	NUM
ejpam-6939	109	5	γdc	γdc	NOUN
ejpam-6939	109	6	(	(	PUNCT
ejpam-6939	109	7	g	g	NOUN
ejpam-6939	109	8	)	)	PUNCT
ejpam-6939	109	9	≤	≤	NOUN
ejpam-6939	109	10	min{γc(g	min{γc(g	NOUN
ejpam-6939	109	11	)	)	PUNCT
ejpam-6939	109	12	,	,	PUNCT
ejpam-6939	109	13	5γd(g)−	5γd(g)−	NUM
ejpam-6939	109	14	4	4	NUM
ejpam-6939	109	15	}	}	PUNCT
ejpam-6939	109	16	.	.	PUNCT
ejpam-6939	110	1	(	(	PUNCT
ejpam-6939	110	2	1	1	X
ejpam-6939	110	3	)	)	PUNCT
ejpam-6939	110	4	proof	proof	NOUN
ejpam-6939	110	5	.	.	PUNCT
ejpam-6939	111	1	since	since	SCONJ
ejpam-6939	111	2	connected	connect	VERB
ejpam-6939	111	3	disjunctive	disjunctive	ADJ
ejpam-6939	111	4	dominating	dominating	NOUN
ejpam-6939	111	5	sets	set	NOUN
ejpam-6939	111	6	are	be	AUX
ejpam-6939	111	7	disjunctive	disjunctive	ADJ
ejpam-6939	111	8	dominating	dominating	NOUN
ejpam-6939	111	9	sets	set	NOUN
ejpam-6939	111	10	,	,	PUNCT
ejpam-6939	111	11	the	the	DET
ejpam-6939	111	12	left	leave	VERB
ejpam-6939	111	13	-	-	PUNCT
ejpam-6939	111	14	hand	hand	NOUN
ejpam-6939	111	15	inequality	inequality	NOUN
ejpam-6939	111	16	in	in	ADP
ejpam-6939	111	17	(	(	PUNCT
ejpam-6939	111	18	1	1	X
ejpam-6939	111	19	)	)	PUNCT
ejpam-6939	111	20	follows	follow	VERB
ejpam-6939	111	21	immediately	immediately	ADV
ejpam-6939	111	22	.	.	PUNCT
ejpam-6939	112	1	also	also	ADV
ejpam-6939	112	2	,	,	PUNCT
ejpam-6939	112	3	since	since	SCONJ
ejpam-6939	112	4	connected	connect	VERB
ejpam-6939	112	5	dominating	dominating	NOUN
ejpam-6939	112	6	sets	set	NOUN
ejpam-6939	112	7	are	be	AUX
ejpam-6939	112	8	connected	connect	VERB
ejpam-6939	112	9	disjunctive	disjunctive	ADJ
ejpam-6939	112	10	dominating	dominating	NOUN
ejpam-6939	112	11	sets	set	NOUN
ejpam-6939	112	12	,	,	PUNCT
ejpam-6939	112	13	γdc	γdc	PROPN
ejpam-6939	112	14	(	(	PUNCT
ejpam-6939	112	15	g	g	NOUN
ejpam-6939	112	16	)	)	PUNCT
ejpam-6939	112	17	≤	≤	NOUN
ejpam-6939	112	18	γc(g	γc(g	NUM
ejpam-6939	112	19	)	)	PUNCT
ejpam-6939	112	20	.	.	PUNCT
ejpam-6939	113	1	let	let	VERB
ejpam-6939	113	2	s	s	PRON
ejpam-6939	113	3	⊆	⊆	NUM
ejpam-6939	113	4	v	v	NOUN
ejpam-6939	113	5	(	(	PUNCT
ejpam-6939	113	6	g	g	NOUN
ejpam-6939	113	7	)	)	PUNCT
ejpam-6939	113	8	be	be	AUX
ejpam-6939	113	9	a	a	DET
ejpam-6939	113	10	γd	γd	ADV
ejpam-6939	113	11	-	-	PUNCT
ejpam-6939	113	12	set	set	NOUN
ejpam-6939	113	13	of	of	ADP
ejpam-6939	113	14	g	g	NOUN
ejpam-6939	113	15	,	,	PUNCT
ejpam-6939	113	16	and	and	CCONJ
ejpam-6939	113	17	letm	letm	NOUN
ejpam-6939	113	18	be	be	AUX
ejpam-6939	113	19	the	the	DET
ejpam-6939	113	20	number	number	NOUN
ejpam-6939	113	21	of	of	ADP
ejpam-6939	113	22	components	component	NOUN
ejpam-6939	113	23	in	in	ADP
ejpam-6939	113	24	⟨s⟩.	⟨s⟩.	PROPN
ejpam-6939	113	25	we	we	PRON
ejpam-6939	113	26	claim	claim	VERB
ejpam-6939	113	27	that	that	SCONJ
ejpam-6939	113	28	γdc	γdc	NOUN
ejpam-6939	113	29	(	(	PUNCT
ejpam-6939	113	30	g	g	NOUN
ejpam-6939	113	31	)	)	PUNCT
ejpam-6939	113	32	≤	≤	NUM
ejpam-6939	113	33	γd(g)+4(m−1	γd(g)+4(m−1	NOUN
ejpam-6939	113	34	)	)	PUNCT
ejpam-6939	113	35	.	.	PUNCT
ejpam-6939	114	1	if	if	SCONJ
ejpam-6939	114	2	m	m	VERB
ejpam-6939	114	3	=	=	NOUN
ejpam-6939	114	4	1	1	NUM
ejpam-6939	114	5	,	,	PUNCT
ejpam-6939	114	6	then	then	ADV
ejpam-6939	114	7	s	s	VERB
ejpam-6939	114	8	is	be	AUX
ejpam-6939	114	9	a	a	DET
ejpam-6939	114	10	connected	connected	ADJ
ejpam-6939	114	11	disjunctive	disjunctive	ADJ
ejpam-6939	114	12	dominating	dominating	NOUN
ejpam-6939	114	13	set	set	NOUN
ejpam-6939	114	14	of	of	ADP
ejpam-6939	114	15	g	g	PROPN
ejpam-6939	114	16	so	so	SCONJ
ejpam-6939	114	17	that	that	SCONJ
ejpam-6939	114	18	γdc	γdc	NOUN
ejpam-6939	114	19	(	(	PUNCT
ejpam-6939	114	20	g	g	NOUN
ejpam-6939	114	21	)	)	PUNCT
ejpam-6939	114	22	=	=	SYM
ejpam-6939	114	23	γd(g	γd(g	PRON
ejpam-6939	114	24	)	)	PUNCT
ejpam-6939	114	25	=	=	SYM
ejpam-6939	114	26	|s|	|s|	PROPN
ejpam-6939	114	27	,	,	PUNCT
ejpam-6939	114	28	and	and	CCONJ
ejpam-6939	114	29	the	the	DET
ejpam-6939	114	30	desired	desire	VERB
ejpam-6939	114	31	inequality	inequality	NOUN
ejpam-6939	114	32	holds	hold	VERB
ejpam-6939	114	33	.	.	PUNCT
ejpam-6939	115	1	suppose	suppose	VERB
ejpam-6939	115	2	that	that	SCONJ
ejpam-6939	115	3	m	m	PROPN
ejpam-6939	115	4	≥	≥	NOUN
ejpam-6939	115	5	2	2	NUM
ejpam-6939	115	6	.	.	X
ejpam-6939	116	1	for	for	ADP
ejpam-6939	116	2	distinct	distinct	ADJ
ejpam-6939	116	3	components	component	NOUN
ejpam-6939	116	4	ci	ci	PROPN
ejpam-6939	116	5	and	and	CCONJ
ejpam-6939	116	6	cj	cj	NOUN
ejpam-6939	116	7	of	of	ADP
ejpam-6939	116	8	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	116	9	,	,	PUNCT
ejpam-6939	116	10	define	define	VERB
ejpam-6939	116	11	dg(ci	dg(ci	PROPN
ejpam-6939	116	12	,	,	PUNCT
ejpam-6939	116	13	cj	cj	X
ejpam-6939	116	14	)	)	PUNCT
ejpam-6939	116	15	=	=	SYM
ejpam-6939	116	16	min{dg(u	min{dg(u	ADJ
ejpam-6939	116	17	,	,	PUNCT
ejpam-6939	116	18	v	v	NOUN
ejpam-6939	116	19	)	)	PUNCT
ejpam-6939	116	20	:	:	PUNCT
ejpam-6939	117	1	u	u	PROPN
ejpam-6939	117	2	∈	∈	PROPN
ejpam-6939	117	3	v	v	ADP
ejpam-6939	117	4	(	(	PUNCT
ejpam-6939	117	5	ci	ci	NOUN
ejpam-6939	117	6	)	)	PUNCT
ejpam-6939	117	7	,	,	PUNCT
ejpam-6939	117	8	v	v	X
ejpam-6939	117	9	∈	∈	PROPN
ejpam-6939	117	10	v	v	NOUN
ejpam-6939	117	11	(	(	PUNCT
ejpam-6939	117	12	cj	cj	NOUN
ejpam-6939	117	13	)	)	PUNCT
ejpam-6939	117	14	}	}	PUNCT
ejpam-6939	117	15	.	.	PUNCT
ejpam-6939	118	1	let	let	VERB
ejpam-6939	118	2	ci	ci	NOUN
ejpam-6939	118	3	and	and	CCONJ
ejpam-6939	118	4	cj	cj	NOUN
ejpam-6939	118	5	be	be	AUX
ejpam-6939	118	6	distinct	distinct	ADJ
ejpam-6939	118	7	components	component	NOUN
ejpam-6939	118	8	of	of	ADP
ejpam-6939	118	9	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	118	10	for	for	ADP
ejpam-6939	118	11	which	which	DET
ejpam-6939	118	12	dg(ci	dg(ci	PROPN
ejpam-6939	118	13	,	,	PUNCT
ejpam-6939	118	14	cj	cj	NOUN
ejpam-6939	118	15	)	)	PUNCT
ejpam-6939	118	16	is	be	AUX
ejpam-6939	118	17	minimum	minimum	ADJ
ejpam-6939	118	18	.	.	PUNCT
ejpam-6939	119	1	let	let	VERB
ejpam-6939	119	2	u	u	PRON
ejpam-6939	119	3	∈	∈	PROPN
ejpam-6939	119	4	v	v	ADP
ejpam-6939	119	5	(	(	PUNCT
ejpam-6939	119	6	ci	ci	NOUN
ejpam-6939	119	7	)	)	PUNCT
ejpam-6939	119	8	and	and	CCONJ
ejpam-6939	119	9	v	v	ADP
ejpam-6939	119	10	∈	∈	PROPN
ejpam-6939	119	11	v	v	NOUN
ejpam-6939	119	12	(	(	PUNCT
ejpam-6939	119	13	cj	cj	NOUN
ejpam-6939	119	14	)	)	PUNCT
ejpam-6939	119	15	for	for	ADP
ejpam-6939	119	16	which	which	PRON
ejpam-6939	119	17	dg(ci	dg(ci	PROPN
ejpam-6939	119	18	,	,	PUNCT
ejpam-6939	119	19	cj	cj	X
ejpam-6939	119	20	)	)	PUNCT
ejpam-6939	119	21	=	=	SYM
ejpam-6939	119	22	dg(u	dg(u	X
ejpam-6939	119	23	,	,	PUNCT
ejpam-6939	119	24	v	v	NOUN
ejpam-6939	119	25	)	)	PUNCT
ejpam-6939	119	26	.	.	PUNCT
ejpam-6939	120	1	suppose	suppose	VERB
ejpam-6939	120	2	that	that	SCONJ
ejpam-6939	120	3	dg(u	dg(u	ADJ
ejpam-6939	120	4	,	,	PUNCT
ejpam-6939	120	5	v	v	NOUN
ejpam-6939	120	6	)	)	PUNCT
ejpam-6939	120	7	≥	≥	NOUN
ejpam-6939	120	8	6	6	NUM
ejpam-6939	120	9	,	,	PUNCT
ejpam-6939	120	10	and	and	CCONJ
ejpam-6939	120	11	let	let	VERB
ejpam-6939	120	12	p	p	PRON
ejpam-6939	120	13	be	be	AUX
ejpam-6939	120	14	a	a	DET
ejpam-6939	120	15	u	u	NOUN
ejpam-6939	120	16	-	-	NOUN
ejpam-6939	120	17	v	v	ADJ
ejpam-6939	120	18	geodesic	geodesic	NOUN
ejpam-6939	121	1	[	[	X
ejpam-6939	121	2	u	u	X
ejpam-6939	121	3	=	=	SYM
ejpam-6939	121	4	x1	x1	PROPN
ejpam-6939	121	5	,	,	PUNCT
ejpam-6939	121	6	x2	x2	PROPN
ejpam-6939	121	7	,	,	PUNCT
ejpam-6939	121	8	x3	x3	PROPN
ejpam-6939	121	9	,	,	PUNCT
ejpam-6939	121	10	x4	x4	PROPN
ejpam-6939	121	11	,	,	PUNCT
ejpam-6939	121	12	x5	x5	PROPN
ejpam-6939	121	13	,	,	PUNCT
ejpam-6939	121	14	x6	x6	PROPN
ejpam-6939	121	15	,	,	PUNCT
ejpam-6939	121	16	x7	x7	NOUN
ejpam-6939	121	17	,	,	PUNCT
ejpam-6939	121	18	.	.	PUNCT
ejpam-6939	121	19	.	.	PUNCT
ejpam-6939	122	1	.	.	PUNCT
ejpam-6939	123	1	,	,	PUNCT
ejpam-6939	123	2	xn	xn	PUNCT
ejpam-6939	124	1	=	=	SYM
ejpam-6939	124	2	v	v	NOUN
ejpam-6939	124	3	]	]	PUNCT
ejpam-6939	124	4	in	in	ADP
ejpam-6939	124	5	g.	g.	PROPN
ejpam-6939	124	6	since	since	SCONJ
ejpam-6939	124	7	s	s	PROPN
ejpam-6939	124	8	is	be	AUX
ejpam-6939	124	9	a	a	DET
ejpam-6939	124	10	disjunctive	disjunctive	ADJ
ejpam-6939	124	11	dominating	dominating	NOUN
ejpam-6939	124	12	set	set	NOUN
ejpam-6939	124	13	of	of	ADP
ejpam-6939	124	14	g	g	NOUN
ejpam-6939	124	15	,	,	PUNCT
ejpam-6939	124	16	in	in	ADP
ejpam-6939	124	17	particular	particular	ADJ
ejpam-6939	124	18	,	,	PUNCT
ejpam-6939	124	19	there	there	PRON
ejpam-6939	124	20	exists	exist	VERB
ejpam-6939	124	21	w	w	PROPN
ejpam-6939	124	22	∈	∈	PROPN
ejpam-6939	124	23	s	s	VERB
ejpam-6939	124	24	such	such	ADJ
ejpam-6939	124	25	that	that	SCONJ
ejpam-6939	124	26	dg(w	dg(w	NUM
ejpam-6939	124	27	,	,	PUNCT
ejpam-6939	124	28	x4	x4	PROPN
ejpam-6939	124	29	)	)	PUNCT
ejpam-6939	124	30	≤	≤	NUM
ejpam-6939	124	31	2	2	NUM
ejpam-6939	124	32	.	.	PUNCT
ejpam-6939	125	1	if	if	SCONJ
ejpam-6939	125	2	w	w	PROPN
ejpam-6939	125	3	∈	∈	PROPN
ejpam-6939	125	4	ci	ci	PROPN
ejpam-6939	125	5	,	,	PUNCT
ejpam-6939	125	6	then	then	ADV
ejpam-6939	125	7	there	there	PRON
ejpam-6939	125	8	exists	exist	VERB
ejpam-6939	125	9	a	a	DET
ejpam-6939	125	10	w	w	NOUN
ejpam-6939	125	11	-	-	PUNCT
ejpam-6939	125	12	v	v	NOUN
ejpam-6939	125	13	geodesic	geodesic	NOUN
ejpam-6939	125	14	joining	join	VERB
ejpam-6939	125	15	ci	ci	PROPN
ejpam-6939	125	16	and	and	CCONJ
ejpam-6939	125	17	cj	cj	NOUN
ejpam-6939	125	18	of	of	ADP
ejpam-6939	125	19	length	length	NOUN
ejpam-6939	125	20	less	less	ADV
ejpam-6939	125	21	than	than	ADP
ejpam-6939	125	22	the	the	DET
ejpam-6939	125	23	length	length	NOUN
ejpam-6939	125	24	of	of	ADP
ejpam-6939	125	25	p	p	NOUN
ejpam-6939	125	26	.	.	PUNCT
ejpam-6939	126	1	if	if	SCONJ
ejpam-6939	126	2	w	w	PROPN
ejpam-6939	126	3	/∈	/∈	PROPN
ejpam-6939	126	4	ci	ci	NOUN
ejpam-6939	126	5	,	,	PUNCT
ejpam-6939	126	6	then	then	ADV
ejpam-6939	126	7	there	there	PRON
ejpam-6939	126	8	is	be	VERB
ejpam-6939	126	9	a	a	DET
ejpam-6939	126	10	w	w	NOUN
ejpam-6939	126	11	-	-	PUNCT
ejpam-6939	126	12	u	u	NOUN
ejpam-6939	126	13	geodesic	geodesic	NOUN
ejpam-6939	126	14	that	that	PRON
ejpam-6939	126	15	joins	join	VERB
ejpam-6939	126	16	two	two	NUM
ejpam-6939	126	17	distinct	distinct	ADJ
ejpam-6939	126	18	components	component	NOUN
ejpam-6939	126	19	of	of	ADP
ejpam-6939	126	20	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	126	21	with	with	ADP
ejpam-6939	126	22	length	length	NOUN
ejpam-6939	126	23	shorter	short	ADJ
ejpam-6939	126	24	than	than	ADP
ejpam-6939	126	25	the	the	DET
ejpam-6939	126	26	length	length	NOUN
ejpam-6939	126	27	of	of	ADP
ejpam-6939	126	28	p	p	PROPN
ejpam-6939	126	29	.	.	PUNCT
ejpam-6939	127	1	either	either	DET
ejpam-6939	127	2	case	case	NOUN
ejpam-6939	127	3	is	be	AUX
ejpam-6939	127	4	a	a	DET
ejpam-6939	127	5	contradiction	contradiction	NOUN
ejpam-6939	127	6	to	to	ADP
ejpam-6939	127	7	the	the	DET
ejpam-6939	127	8	definitions	definition	NOUN
ejpam-6939	127	9	of	of	ADP
ejpam-6939	127	10	ci	ci	NOUN
ejpam-6939	127	11	and	and	CCONJ
ejpam-6939	127	12	cj	cj	NOUN
ejpam-6939	127	13	.	.	PUNCT
ejpam-6939	128	1	thus	thus	ADV
ejpam-6939	128	2	,	,	PUNCT
ejpam-6939	128	3	dg(u	dg(u	X
ejpam-6939	128	4	,	,	PUNCT
ejpam-6939	128	5	v	v	NOUN
ejpam-6939	128	6	)	)	PUNCT
ejpam-6939	128	7	≤	≤	NOUN
ejpam-6939	128	8	5	5	NUM
ejpam-6939	128	9	.	.	PUNCT
ejpam-6939	128	10	put	put	VERB
ejpam-6939	128	11	s1	s1	NOUN
ejpam-6939	128	12	=	=	X
ejpam-6939	128	13	s	s	NOUN
ejpam-6939	128	14	∪	∪	X
ejpam-6939	128	15	(	(	PUNCT
ejpam-6939	128	16	v	v	NOUN
ejpam-6939	128	17	(	(	PUNCT
ejpam-6939	128	18	p	p	NOUN
ejpam-6939	128	19	)	)	PUNCT
ejpam-6939	128	20	\	\	NOUN
ejpam-6939	129	1	{	{	PUNCT
ejpam-6939	129	2	u	u	NOUN
ejpam-6939	129	3	,	,	PUNCT
ejpam-6939	129	4	v	v	NOUN
ejpam-6939	129	5	}	}	PUNCT
ejpam-6939	129	6	.	.	PUNCT
ejpam-6939	130	1	then	then	ADV
ejpam-6939	130	2	s1	s1	PROPN
ejpam-6939	130	3	is	be	AUX
ejpam-6939	130	4	a	a	DET
ejpam-6939	130	5	disjunctive	disjunctive	ADJ
ejpam-6939	130	6	dominating	dominating	NOUN
ejpam-6939	130	7	set	set	NOUN
ejpam-6939	130	8	of	of	ADP
ejpam-6939	130	9	g	g	NOUN
ejpam-6939	130	10	with	with	ADP
ejpam-6939	130	11	|s1|	|s1|	NOUN
ejpam-6939	130	12	≤	≤	VERB
ejpam-6939	130	13	|s|+	|s|+	NOUN
ejpam-6939	130	14	4	4	NUM
ejpam-6939	130	15	and	and	CCONJ
ejpam-6939	130	16	⟨s1⟩	⟨s1⟩	NOUN
ejpam-6939	130	17	having	have	VERB
ejpam-6939	130	18	at	at	ADP
ejpam-6939	130	19	most	most	ADJ
ejpam-6939	130	20	m−	m−	PROPN
ejpam-6939	130	21	1	1	NUM
ejpam-6939	130	22	components	component	NOUN
ejpam-6939	130	23	.	.	PUNCT
ejpam-6939	131	1	repeating	repeat	VERB
ejpam-6939	131	2	the	the	DET
ejpam-6939	131	3	same	same	ADJ
ejpam-6939	131	4	process	process	NOUN
ejpam-6939	131	5	in	in	ADP
ejpam-6939	131	6	at	at	ADV
ejpam-6939	131	7	most	most	ADV
ejpam-6939	131	8	(	(	PUNCT
ejpam-6939	131	9	m−	m−	PROPN
ejpam-6939	131	10	1	1	NUM
ejpam-6939	131	11	)	)	PUNCT
ejpam-6939	131	12	times	time	NOUN
ejpam-6939	131	13	yields	yield	VERB
ejpam-6939	131	14	a	a	DET
ejpam-6939	131	15	connected	connected	ADJ
ejpam-6939	131	16	disjunctive	disjunctive	ADJ
ejpam-6939	131	17	dominating	dominating	NOUN
ejpam-6939	131	18	set	set	VERB
ejpam-6939	131	19	sm−1	sm−1	NOUN
ejpam-6939	131	20	with	with	ADP
ejpam-6939	131	21	|sm−1|	|sm−1|	PROPN
ejpam-6939	131	22	≤	≤	X
ejpam-6939	131	23	|s|+	|s|+	NOUN
ejpam-6939	131	24	4(m−	4(m−	NUM
ejpam-6939	131	25	1	1	NUM
ejpam-6939	131	26	)	)	PUNCT
ejpam-6939	131	27	.	.	PUNCT
ejpam-6939	132	1	thus	thus	ADV
ejpam-6939	132	2	,	,	PUNCT
ejpam-6939	132	3	γdc	γdc	PROPN
ejpam-6939	132	4	(	(	PUNCT
ejpam-6939	132	5	g	g	NOUN
ejpam-6939	132	6	)	)	PUNCT
ejpam-6939	132	7	≤	≤	NOUN
ejpam-6939	132	8	γd(g	γd(g	NUM
ejpam-6939	132	9	)	)	PUNCT
ejpam-6939	132	10	+	+	CCONJ
ejpam-6939	132	11	4(m−	4(m−	NUM
ejpam-6939	132	12	1	1	NUM
ejpam-6939	132	13	)	)	PUNCT
ejpam-6939	132	14	,	,	PUNCT
ejpam-6939	132	15	and	and	CCONJ
ejpam-6939	132	16	the	the	DET
ejpam-6939	132	17	claim	claim	NOUN
ejpam-6939	132	18	is	be	AUX
ejpam-6939	132	19	established	establish	VERB
ejpam-6939	132	20	.	.	PUNCT
ejpam-6939	133	1	since	since	SCONJ
ejpam-6939	133	2	m	m	NOUN
ejpam-6939	133	3	≤	≤	NUM
ejpam-6939	133	4	γd(g	γd(g	NUM
ejpam-6939	133	5	)	)	PUNCT
ejpam-6939	133	6	,	,	PUNCT
ejpam-6939	133	7	we	we	PRON
ejpam-6939	133	8	have	have	VERB
ejpam-6939	133	9	γdc	γdc	NOUN
ejpam-6939	133	10	(	(	PUNCT
ejpam-6939	133	11	g	g	NOUN
ejpam-6939	133	12	)	)	PUNCT
ejpam-6939	133	13	≤	≤	NOUN
ejpam-6939	133	14	γd(g	γd(g	NUM
ejpam-6939	133	15	)	)	PUNCT
ejpam-6939	134	1	+	+	CCONJ
ejpam-6939	135	1	4(γd(g)−	4(γd(g)−	NUM
ejpam-6939	135	2	1	1	X
ejpam-6939	135	3	)	)	PUNCT
ejpam-6939	135	4	=	=	PUNCT
ejpam-6939	135	5	5γd(g)−	5γd(g)−	NOUN
ejpam-6939	135	6	4	4	NUM
ejpam-6939	135	7	.	.	PUNCT
ejpam-6939	136	1	if	if	SCONJ
ejpam-6939	136	2	α	α	NUM
ejpam-6939	136	3	=	=	PUNCT
ejpam-6939	136	4	min{γc(g	min{γc(g	NOUN
ejpam-6939	136	5	)	)	PUNCT
ejpam-6939	136	6	,	,	PUNCT
ejpam-6939	136	7	5γd(g)−	5γd(g)−	NUM
ejpam-6939	136	8	4	4	NUM
ejpam-6939	136	9	}	}	PUNCT
ejpam-6939	136	10	,	,	PUNCT
ejpam-6939	136	11	then	then	ADV
ejpam-6939	136	12	for	for	ADP
ejpam-6939	136	13	g	g	PROPN
ejpam-6939	136	14	=	=	SYM
ejpam-6939	136	15	c5	c5	PROPN
ejpam-6939	136	16	,	,	PUNCT
ejpam-6939	136	17	α	α	NOUN
ejpam-6939	136	18	=	=	SYM
ejpam-6939	136	19	γc(g	γc(g	NUM
ejpam-6939	136	20	)	)	PUNCT
ejpam-6939	136	21	.	.	PUNCT
ejpam-6939	137	1	for	for	ADP
ejpam-6939	137	2	the	the	DET
ejpam-6939	137	3	graph	graph	NOUN
ejpam-6939	137	4	g	g	NOUN
ejpam-6939	137	5	given	give	VERB
ejpam-6939	137	6	in	in	ADP
ejpam-6939	137	7	figure	figure	NOUN
ejpam-6939	137	8	1	1	NUM
ejpam-6939	137	9	,	,	PUNCT
ejpam-6939	137	10	α	α	NOUN
ejpam-6939	137	11	=	=	SYM
ejpam-6939	137	12	5γd(g)−	5γd(g)−	NUM
ejpam-6939	137	13	4	4	NUM
ejpam-6939	137	14	.	.	PUNCT
ejpam-6939	137	15	.............................................................................................................................................................................................	.............................................................................................................................................................................................	PROPN
ejpam-6939	137	16	.............................................................................................................................................................................................	.............................................................................................................................................................................................	PROPN
ejpam-6939	138	1	.............................................................................................................................................................................................	.............................................................................................................................................................................................	PROPN
ejpam-6939	138	2	.............................................................................................................................................................................................	.............................................................................................................................................................................................	PUNCT
ejpam-6939	138	3	....................................	....................................	PUNCT
ejpam-6939	138	4	...............	...............	PUNCT
ejpam-6939	139	1	..............	..............	PUNCT
ejpam-6939	139	2	..............	..............	PUNCT
ejpam-6939	140	1	..............	..............	PUNCT
ejpam-6939	140	2	..............	..............	PUNCT
ejpam-6939	141	1	..............	..............	PUNCT
ejpam-6939	141	2	..............	..............	PUNCT
ejpam-6939	142	1	..............	..............	PUNCT
ejpam-6939	142	2	..............	..............	PUNCT
ejpam-6939	143	1	..............	..............	PUNCT
ejpam-6939	143	2	..............	..............	PUNCT
ejpam-6939	144	1	..............	..............	PUNCT
ejpam-6939	144	2	..............	..............	PUNCT
ejpam-6939	145	1	....	....	PUNCT
ejpam-6939	145	2	....................................	....................................	PUNCT
ejpam-6939	146	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-6939	146	2	....................................	....................................	PUNCT
ejpam-6939	147	1	..........................	..........................	PUNCT
ejpam-6939	147	2	.........................	.........................	PUNCT
ejpam-6939	147	3	.........................	.........................	PUNCT
ejpam-6939	147	4	.........................	.........................	PUNCT
ejpam-6939	147	5	.........................	.........................	PUNCT
ejpam-6939	147	6	.........................	.........................	PUNCT
ejpam-6939	147	7	...........	...........	PUNCT
ejpam-6939	147	8	....................................	....................................	PUNCT
ejpam-6939	148	1	...........................................................................................................................................................................................	...........................................................................................................................................................................................	PUNCT
ejpam-6939	148	2	....................................	....................................	PUNCT
ejpam-6939	149	1	....................................	....................................	PUNCT
ejpam-6939	149	2	............	............	PUNCT
ejpam-6939	149	3	...........	...........	PUNCT
ejpam-6939	149	4	...........	...........	PUNCT
ejpam-6939	149	5	...........	...........	PUNCT
ejpam-6939	149	6	...........	...........	PUNCT
ejpam-6939	149	7	...........	...........	PUNCT
ejpam-6939	149	8	...........	...........	PUNCT
ejpam-6939	149	9	...........	...........	PUNCT
ejpam-6939	149	10	...........	...........	PUNCT
ejpam-6939	149	11	...........	...........	PUNCT
ejpam-6939	149	12	...........	...........	PUNCT
ejpam-6939	149	13	...........	...........	PUNCT
ejpam-6939	149	14	...........	...........	PUNCT
ejpam-6939	149	15	...........	...........	PUNCT
ejpam-6939	149	16	...........	...........	PUNCT
ejpam-6939	149	17	...........	...........	PUNCT
ejpam-6939	149	18	...........	...........	PUNCT
ejpam-6939	149	19	...........	...........	PUNCT
ejpam-6939	149	20	...........	...........	PUNCT
ejpam-6939	149	21	...........	...........	PUNCT
ejpam-6939	149	22	....................................	....................................	PUNCT
ejpam-6939	150	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-6939	150	2	....................................	....................................	PUNCT
ejpam-6939	151	1	..........................	..........................	PUNCT
ejpam-6939	151	2	.........................	.........................	PUNCT
ejpam-6939	151	3	.........................	.........................	PUNCT
ejpam-6939	151	4	.........................	.........................	PUNCT
ejpam-6939	151	5	.........................	.........................	PUNCT
ejpam-6939	151	6	.........................	.........................	PUNCT
ejpam-6939	151	7	...........	...........	PUNCT
ejpam-6939	152	1	....................................	....................................	PUNCT
ejpam-6939	152	2	.............................................................................................................................................................................................................................	.............................................................................................................................................................................................................................	PUNCT
ejpam-6939	153	1	....................................	....................................	PUNCT
ejpam-6939	154	1	....................................	....................................	PUNCT
ejpam-6939	155	1	•	•	NUM
ejpam-6939	156	1	•	•	NUM
ejpam-6939	156	2	•	•	NUM
ejpam-6939	156	3	•	•	NUM
ejpam-6939	156	4	•	•	NUM
ejpam-6939	156	5	•	•	NUM
ejpam-6939	156	6	•	•	NUM
ejpam-6939	156	7	•	•	NUM
ejpam-6939	156	8	•	•	NUM
ejpam-6939	156	9	•	•	NUM
ejpam-6939	156	10	•	•	NUM
ejpam-6939	156	11	•	•	NUM
ejpam-6939	156	12	•	•	NOUN
ejpam-6939	156	13	•	•	NOUN
ejpam-6939	157	1	x1	x1	NOUN
ejpam-6939	157	2	x2	x2	PROPN
ejpam-6939	158	1	xk	xk	PROPN
ejpam-6939	158	2	g	g	PROPN
ejpam-6939	158	3	:	:	PUNCT
ejpam-6939	158	4	...	...	PUNCT
ejpam-6939	158	5	...	...	PUNCT
ejpam-6939	158	6	...	...	PUNCT
ejpam-6939	158	7	...........	...........	PUNCT
ejpam-6939	158	8	..........	..........	PUNCT
ejpam-6939	159	1	..........	..........	PUNCT
ejpam-6939	159	2	..........	..........	PUNCT
ejpam-6939	160	1	..........	..........	PUNCT
ejpam-6939	160	2	..........	..........	PUNCT
ejpam-6939	161	1	..........	..........	PUNCT
ejpam-6939	161	2	..........	..........	PUNCT
ejpam-6939	162	1	..........	..........	PUNCT
ejpam-6939	162	2	..........	..........	PUNCT
ejpam-6939	163	1	..........	..........	PUNCT
ejpam-6939	163	2	..........	..........	PUNCT
ejpam-6939	164	1	..........	..........	PUNCT
ejpam-6939	164	2	..........	..........	PUNCT
ejpam-6939	165	1	..........	..........	PUNCT
ejpam-6939	165	2	..........	..........	PUNCT
ejpam-6939	166	1	..........	..........	PUNCT
ejpam-6939	166	2	..........	..........	PUNCT
ejpam-6939	167	1	..........	..........	PUNCT
ejpam-6939	167	2	..........	..........	PUNCT
ejpam-6939	168	1	..........	..........	PUNCT
ejpam-6939	168	2	..........	..........	PUNCT
ejpam-6939	169	1	..........	..........	PUNCT
ejpam-6939	169	2	..........	..........	PUNCT
ejpam-6939	170	1	..........	..........	PUNCT
ejpam-6939	170	2	..........	..........	PUNCT
ejpam-6939	171	1	..........	..........	PUNCT
ejpam-6939	171	2	..........	..........	PUNCT
ejpam-6939	172	1	..........	..........	PUNCT
ejpam-6939	172	2	..........	..........	PUNCT
ejpam-6939	172	3	.......	.......	PUNCT
ejpam-6939	173	1	....................................	....................................	PUNCT
ejpam-6939	173	2	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-6939	174	1	....................................	....................................	PUNCT
ejpam-6939	174	2	..........................	..........................	PUNCT
ejpam-6939	175	1	.........................	.........................	PUNCT
ejpam-6939	175	2	.........................	.........................	PUNCT
ejpam-6939	175	3	.........................	.........................	PUNCT
ejpam-6939	175	4	.........................	.........................	PUNCT
ejpam-6939	175	5	.........................	.........................	PUNCT
ejpam-6939	175	6	...........	...........	PUNCT
ejpam-6939	175	7	....................................	....................................	PUNCT
ejpam-6939	175	8	....................................................................................................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6939	176	1	....................................	....................................	PUNCT
ejpam-6939	177	1	....................................	....................................	PUNCT
ejpam-6939	178	1	figure	figure	NOUN
ejpam-6939	178	2	1	1	NUM
ejpam-6939	178	3	:	:	PUNCT
ejpam-6939	178	4	a	a	DET
ejpam-6939	178	5	graph	graph	NOUN
ejpam-6939	178	6	g	g	NOUN
ejpam-6939	178	7	with	with	ADP
ejpam-6939	178	8	γc(g	γc(g	PUNCT
ejpam-6939	178	9	)	)	PUNCT
ejpam-6939	178	10	=	=	SYM
ejpam-6939	179	1	5	5	NUM
ejpam-6939	179	2	+	+	CCONJ
ejpam-6939	179	3	k	k	NOUN
ejpam-6939	179	4	,	,	PUNCT
ejpam-6939	179	5	5γd(g)−	5γd(g)−	NUM
ejpam-6939	179	6	4	4	NUM
ejpam-6939	179	7	=	=	SYM
ejpam-6939	179	8	6	6	NUM
ejpam-6939	179	9	and	and	CCONJ
ejpam-6939	179	10	γd	γd	ADP
ejpam-6939	179	11	c	c	PROPN
ejpam-6939	179	12	(	(	PUNCT
ejpam-6939	179	13	g	g	NOUN
ejpam-6939	179	14	)	)	PUNCT
ejpam-6939	179	15	=	=	SYM
ejpam-6939	179	16	5	5	NUM
ejpam-6939	179	17	proposition	proposition	NOUN
ejpam-6939	179	18	2	2	NUM
ejpam-6939	179	19	.	.	PUNCT
ejpam-6939	180	1	let	let	VERB
ejpam-6939	180	2	g	g	PRON
ejpam-6939	180	3	be	be	AUX
ejpam-6939	180	4	a	a	DET
ejpam-6939	180	5	connected	connected	ADJ
ejpam-6939	180	6	graph	graph	NOUN
ejpam-6939	180	7	.	.	PUNCT
ejpam-6939	181	1	then	then	ADV
ejpam-6939	181	2	a.	a.	PROPN
ejpam-6939	181	3	aradais	aradais	PROPN
ejpam-6939	181	4	,	,	PUNCT
ejpam-6939	181	5	f.	f.	PROPN
ejpam-6939	181	6	jamil	jamil	PROPN
ejpam-6939	181	7	,	,	PUNCT
ejpam-6939	181	8	s.	s.	PROPN
ejpam-6939	181	9	canoy	canoy	PROPN
ejpam-6939	181	10	/	/	SYM
ejpam-6939	181	11	eur	eur	PROPN
ejpam-6939	181	12	.	.	PUNCT
ejpam-6939	182	1	j.	j.	PROPN
ejpam-6939	182	2	pure	pure	PROPN
ejpam-6939	182	3	appl	appl	PROPN
ejpam-6939	182	4	.	.	PROPN
ejpam-6939	182	5	math	math	PROPN
ejpam-6939	182	6	,	,	PUNCT
ejpam-6939	182	7	18	18	NUM
ejpam-6939	182	8	(	(	PUNCT
ejpam-6939	182	9	4	4	NUM
ejpam-6939	182	10	)	)	PUNCT
ejpam-6939	182	11	(	(	PUNCT
ejpam-6939	182	12	2025	2025	NUM
ejpam-6939	182	13	)	)	PUNCT
ejpam-6939	182	14	,	,	PUNCT
ejpam-6939	182	15	6939	6939	NUM
ejpam-6939	182	16	6	6	NUM
ejpam-6939	182	17	of	of	ADP
ejpam-6939	182	18	14	14	NUM
ejpam-6939	182	19	(	(	PUNCT
ejpam-6939	182	20	i	i	NOUN
ejpam-6939	182	21	)	)	PUNCT
ejpam-6939	182	22	γdc	γdc	NOUN
ejpam-6939	182	23	(	(	PUNCT
ejpam-6939	182	24	g	g	NOUN
ejpam-6939	182	25	)	)	PUNCT
ejpam-6939	182	26	=	=	SYM
ejpam-6939	183	1	1	1	NUM
ejpam-6939	183	2	if	if	SCONJ
ejpam-6939	183	3	and	and	CCONJ
ejpam-6939	183	4	only	only	ADV
ejpam-6939	183	5	if	if	SCONJ
ejpam-6939	183	6	γ(g	γ(g	NOUN
ejpam-6939	183	7	)	)	PUNCT
ejpam-6939	183	8	=	=	SYM
ejpam-6939	184	1	1	1	X
ejpam-6939	184	2	.	.	PUNCT
ejpam-6939	184	3	(	(	PUNCT
ejpam-6939	184	4	ii	ii	PROPN
ejpam-6939	184	5	)	)	PUNCT
ejpam-6939	184	6	γdc	γdc	NOUN
ejpam-6939	184	7	(	(	PUNCT
ejpam-6939	184	8	g	g	NOUN
ejpam-6939	184	9	)	)	PUNCT
ejpam-6939	184	10	=	=	SYM
ejpam-6939	184	11	2	2	NUM
ejpam-6939	184	12	if	if	SCONJ
ejpam-6939	184	13	and	and	CCONJ
ejpam-6939	184	14	only	only	ADV
ejpam-6939	184	15	if	if	SCONJ
ejpam-6939	184	16	γ(g	γ(g	NOUN
ejpam-6939	184	17	)	)	PUNCT
ejpam-6939	184	18	̸=	̸=	PROPN
ejpam-6939	184	19	1	1	NUM
ejpam-6939	184	20	and	and	CCONJ
ejpam-6939	184	21	there	there	PRON
ejpam-6939	184	22	exist	exist	VERB
ejpam-6939	184	23	u	u	NOUN
ejpam-6939	184	24	,	,	PUNCT
ejpam-6939	184	25	v	v	NOUN
ejpam-6939	184	26	∈	∈	PROPN
ejpam-6939	184	27	v	v	NOUN
ejpam-6939	184	28	(	(	PUNCT
ejpam-6939	184	29	g	g	NOUN
ejpam-6939	184	30	)	)	PUNCT
ejpam-6939	184	31	for	for	ADP
ejpam-6939	184	32	which	which	PRON
ejpam-6939	184	33	uv	uv	NOUN
ejpam-6939	184	34	∈	∈	PROPN
ejpam-6939	184	35	e(g	e(g	PROPN
ejpam-6939	184	36	)	)	PUNCT
ejpam-6939	184	37	and	and	CCONJ
ejpam-6939	184	38	dg(u	dg(u	X
ejpam-6939	184	39	,	,	PUNCT
ejpam-6939	184	40	z	z	NOUN
ejpam-6939	184	41	)	)	PUNCT
ejpam-6939	184	42	≤	≤	NUM
ejpam-6939	184	43	2	2	NUM
ejpam-6939	184	44	and	and	CCONJ
ejpam-6939	184	45	dg(v	dg(v	NOUN
ejpam-6939	184	46	,	,	PUNCT
ejpam-6939	184	47	z	z	NOUN
ejpam-6939	184	48	)	)	PUNCT
ejpam-6939	184	49	≤	≤	NUM
ejpam-6939	184	50	2	2	NUM
ejpam-6939	184	51	for	for	ADP
ejpam-6939	184	52	all	all	DET
ejpam-6939	184	53	z	z	NOUN
ejpam-6939	184	54	∈	∈	PROPN
ejpam-6939	184	55	v	v	NOUN
ejpam-6939	184	56	(	(	PUNCT
ejpam-6939	184	57	g	g	NOUN
ejpam-6939	184	58	)	)	PUNCT
ejpam-6939	184	59	.	.	PUNCT
ejpam-6939	185	1	in	in	ADP
ejpam-6939	185	2	particular	particular	ADJ
ejpam-6939	185	3	,	,	PUNCT
ejpam-6939	185	4	if	if	SCONJ
ejpam-6939	185	5	γc(g	γc(g	PUNCT
ejpam-6939	186	1	)	)	PUNCT
ejpam-6939	186	2	=	=	SYM
ejpam-6939	186	3	2	2	NUM
ejpam-6939	186	4	,	,	PUNCT
ejpam-6939	186	5	then	then	ADV
ejpam-6939	186	6	γdc	γdc	PROPN
ejpam-6939	186	7	(	(	PUNCT
ejpam-6939	186	8	g	g	NOUN
ejpam-6939	186	9	)	)	PUNCT
ejpam-6939	186	10	=	=	SYM
ejpam-6939	186	11	2	2	X
ejpam-6939	186	12	.	.	PUNCT
ejpam-6939	186	13	(	(	PUNCT
ejpam-6939	186	14	iii	iii	X
ejpam-6939	186	15	)	)	PUNCT
ejpam-6939	186	16	if	if	SCONJ
ejpam-6939	186	17	g	g	PROPN
ejpam-6939	186	18	is	be	AUX
ejpam-6939	186	19	a	a	DET
ejpam-6939	186	20	tree	tree	NOUN
ejpam-6939	186	21	,	,	PUNCT
ejpam-6939	186	22	then	then	ADV
ejpam-6939	186	23	γdc	γdc	PROPN
ejpam-6939	186	24	(	(	PUNCT
ejpam-6939	186	25	g	g	NOUN
ejpam-6939	186	26	)	)	PUNCT
ejpam-6939	186	27	=	=	NOUN
ejpam-6939	186	28	γc(g	γc(g	X
ejpam-6939	186	29	)	)	PUNCT
ejpam-6939	186	30	.	.	PUNCT
ejpam-6939	187	1	proof	proof	NOUN
ejpam-6939	187	2	.	.	PUNCT
ejpam-6939	188	1	the	the	DET
ejpam-6939	188	2	proof	proof	NOUN
ejpam-6939	188	3	of	of	ADP
ejpam-6939	188	4	statement	statement	NOUN
ejpam-6939	188	5	(	(	PUNCT
ejpam-6939	188	6	i	i	NOUN
ejpam-6939	188	7	)	)	PUNCT
ejpam-6939	188	8	utilizes	utilize	VERB
ejpam-6939	188	9	(	(	PUNCT
ejpam-6939	188	10	1	1	NUM
ejpam-6939	188	11	)	)	PUNCT
ejpam-6939	188	12	in	in	ADP
ejpam-6939	188	13	proposition	proposition	NOUN
ejpam-6939	188	14	1	1	NUM
ejpam-6939	188	15	.	.	PUNCT
ejpam-6939	189	1	if	if	SCONJ
ejpam-6939	189	2	γdc	γdc	PROPN
ejpam-6939	189	3	(	(	PUNCT
ejpam-6939	189	4	g	g	NOUN
ejpam-6939	189	5	)	)	PUNCT
ejpam-6939	189	6	=	=	SYM
ejpam-6939	189	7	1	1	NUM
ejpam-6939	189	8	,	,	PUNCT
ejpam-6939	189	9	then	then	ADV
ejpam-6939	189	10	γd(g	γd(g	NUM
ejpam-6939	189	11	)	)	PUNCT
ejpam-6939	189	12	=	=	SYM
ejpam-6939	190	1	1	1	NUM
ejpam-6939	190	2	so	so	SCONJ
ejpam-6939	190	3	that	that	PRON
ejpam-6939	190	4	γ(g	γ(g	PROPN
ejpam-6939	190	5	)	)	PUNCT
ejpam-6939	190	6	=	=	PUNCT
ejpam-6939	191	1	1	1	X
ejpam-6939	191	2	.	.	PUNCT
ejpam-6939	192	1	conversely	conversely	ADV
ejpam-6939	192	2	,	,	PUNCT
ejpam-6939	192	3	if	if	SCONJ
ejpam-6939	192	4	γ(g	γ(g	PROPN
ejpam-6939	192	5	)	)	PUNCT
ejpam-6939	192	6	=	=	SYM
ejpam-6939	192	7	1	1	NUM
ejpam-6939	192	8	,	,	PUNCT
ejpam-6939	192	9	then	then	ADV
ejpam-6939	192	10	γc(g	γc(g	PUNCT
ejpam-6939	192	11	)	)	PUNCT
ejpam-6939	192	12	=	=	SYM
ejpam-6939	193	1	1	1	NUM
ejpam-6939	193	2	so	so	SCONJ
ejpam-6939	193	3	that	that	PRON
ejpam-6939	193	4	γdc	γdc	NOUN
ejpam-6939	193	5	(	(	PUNCT
ejpam-6939	193	6	g	g	NOUN
ejpam-6939	193	7	)	)	PUNCT
ejpam-6939	193	8	=	=	SYM
ejpam-6939	193	9	1	1	NUM
ejpam-6939	193	10	,	,	PUNCT
ejpam-6939	193	11	and	and	CCONJ
ejpam-6939	193	12	(	(	PUNCT
ejpam-6939	193	13	i	i	NOUN
ejpam-6939	193	14	)	)	PUNCT
ejpam-6939	193	15	holds	hold	VERB
ejpam-6939	193	16	.	.	PUNCT
ejpam-6939	194	1	suppose	suppose	VERB
ejpam-6939	195	1	that	that	SCONJ
ejpam-6939	195	2	γdc	γdc	PROPN
ejpam-6939	195	3	(	(	PUNCT
ejpam-6939	195	4	g	g	NOUN
ejpam-6939	195	5	)	)	PUNCT
ejpam-6939	195	6	=	=	SYM
ejpam-6939	195	7	2	2	X
ejpam-6939	195	8	.	.	PUNCT
ejpam-6939	195	9	by	by	ADP
ejpam-6939	195	10	(	(	PUNCT
ejpam-6939	195	11	i	i	NOUN
ejpam-6939	195	12	)	)	PUNCT
ejpam-6939	195	13	,	,	PUNCT
ejpam-6939	195	14	γ(g	γ(g	PROPN
ejpam-6939	195	15	)	)	PUNCT
ejpam-6939	195	16	>	>	X
ejpam-6939	196	1	1	1	X
ejpam-6939	196	2	.	.	PUNCT
ejpam-6939	197	1	let	let	VERB
ejpam-6939	197	2	{	{	PUNCT
ejpam-6939	197	3	u	u	NOUN
ejpam-6939	197	4	,	,	PUNCT
ejpam-6939	197	5	v	v	NOUN
ejpam-6939	197	6	}	}	PUNCT
ejpam-6939	197	7	be	be	AUX
ejpam-6939	197	8	a	a	DET
ejpam-6939	197	9	γdc	γdc	NOUN
ejpam-6939	197	10	-set	-set	PUNCT
ejpam-6939	197	11	of	of	ADP
ejpam-6939	197	12	g	g	NOUN
ejpam-6939	197	13	,	,	PUNCT
ejpam-6939	197	14	and	and	CCONJ
ejpam-6939	197	15	let	let	VERB
ejpam-6939	197	16	z	z	NOUN
ejpam-6939	197	17	∈	∈	PROPN
ejpam-6939	197	18	v	v	ADP
ejpam-6939	197	19	(	(	PUNCT
ejpam-6939	197	20	g	g	NOUN
ejpam-6939	197	21	)	)	PUNCT
ejpam-6939	197	22	.	.	PUNCT
ejpam-6939	198	1	if	if	SCONJ
ejpam-6939	198	2	z	z	PROPN
ejpam-6939	198	3	∈	∈	PROPN
ejpam-6939	198	4	ng[u	ng[u	PROPN
ejpam-6939	198	5	]	]	PUNCT
ejpam-6939	198	6	,	,	PUNCT
ejpam-6939	198	7	then	then	ADV
ejpam-6939	198	8	dg(u	dg(u	X
ejpam-6939	198	9	,	,	PUNCT
ejpam-6939	198	10	z	z	NOUN
ejpam-6939	198	11	)	)	PUNCT
ejpam-6939	198	12	≤	≤	NUM
ejpam-6939	198	13	1	1	NUM
ejpam-6939	198	14	so	so	SCONJ
ejpam-6939	198	15	that	that	PRON
ejpam-6939	198	16	dg(v	dg(v	VERB
ejpam-6939	198	17	,	,	PUNCT
ejpam-6939	198	18	z	z	NOUN
ejpam-6939	198	19	)	)	PUNCT
ejpam-6939	198	20	≤	≤	NUM
ejpam-6939	198	21	2	2	NUM
ejpam-6939	198	22	.	.	PUNCT
ejpam-6939	199	1	similarly	similarly	ADV
ejpam-6939	199	2	,	,	PUNCT
ejpam-6939	199	3	if	if	SCONJ
ejpam-6939	199	4	z	z	NOUN
ejpam-6939	199	5	∈	∈	PROPN
ejpam-6939	199	6	ng[v	ng[v	X
ejpam-6939	199	7	]	]	PUNCT
ejpam-6939	199	8	,	,	PUNCT
ejpam-6939	199	9	then	then	ADV
ejpam-6939	199	10	dg(v	dg(v	NOUN
ejpam-6939	199	11	,	,	PUNCT
ejpam-6939	199	12	z	z	NOUN
ejpam-6939	199	13	)	)	PUNCT
ejpam-6939	199	14	≤	≤	NUM
ejpam-6939	199	15	1	1	NUM
ejpam-6939	199	16	so	so	SCONJ
ejpam-6939	199	17	that	that	PRON
ejpam-6939	199	18	dg(u	dg(u	ADJ
ejpam-6939	199	19	,	,	PUNCT
ejpam-6939	199	20	z	z	NOUN
ejpam-6939	199	21	)	)	PUNCT
ejpam-6939	199	22	≤	≤	NUM
ejpam-6939	199	23	2	2	NUM
ejpam-6939	199	24	.	.	PUNCT
ejpam-6939	199	25	suppose	suppose	VERB
ejpam-6939	200	1	that	that	SCONJ
ejpam-6939	200	2	z	z	AUX
ejpam-6939	200	3	/∈	/∈	PUNCT
ejpam-6939	200	4	ng[u]∪ng[v	ng[u]∪ng[v	ADV
ejpam-6939	200	5	]	]	PUNCT
ejpam-6939	200	6	.	.	PUNCT
ejpam-6939	201	1	then	then	ADV
ejpam-6939	201	2	since	since	SCONJ
ejpam-6939	201	3	{	{	PUNCT
ejpam-6939	201	4	u	u	NOUN
ejpam-6939	201	5	,	,	PUNCT
ejpam-6939	201	6	v	v	NOUN
ejpam-6939	201	7	}	}	PUNCT
ejpam-6939	201	8	is	be	AUX
ejpam-6939	201	9	a	a	DET
ejpam-6939	201	10	disjunctive	disjunctive	ADJ
ejpam-6939	201	11	dominating	dominating	NOUN
ejpam-6939	201	12	set	set	NOUN
ejpam-6939	201	13	,	,	PUNCT
ejpam-6939	201	14	dg(z	dg(z	NUM
ejpam-6939	201	15	,	,	PUNCT
ejpam-6939	201	16	u	u	NOUN
ejpam-6939	201	17	)	)	PUNCT
ejpam-6939	201	18	=	=	SYM
ejpam-6939	201	19	2	2	NUM
ejpam-6939	201	20	=	=	SYM
ejpam-6939	201	21	dg(v	dg(v	X
ejpam-6939	201	22	,	,	PUNCT
ejpam-6939	201	23	z	z	NOUN
ejpam-6939	201	24	)	)	PUNCT
ejpam-6939	201	25	.	.	PUNCT
ejpam-6939	202	1	conversely	conversely	ADV
ejpam-6939	202	2	,	,	PUNCT
ejpam-6939	202	3	by	by	ADP
ejpam-6939	202	4	(	(	PUNCT
ejpam-6939	202	5	i	i	NOUN
ejpam-6939	202	6	)	)	PUNCT
ejpam-6939	202	7	,	,	PUNCT
ejpam-6939	202	8	γdc	γdc	PROPN
ejpam-6939	202	9	(	(	PUNCT
ejpam-6939	202	10	g	g	NOUN
ejpam-6939	202	11	)	)	PUNCT
ejpam-6939	202	12	≥	≥	NOUN
ejpam-6939	202	13	2	2	NUM
ejpam-6939	202	14	.	.	PUNCT
ejpam-6939	202	15	further	far	ADV
ejpam-6939	202	16	,	,	PUNCT
ejpam-6939	202	17	since	since	SCONJ
ejpam-6939	202	18	u	u	PRON
ejpam-6939	202	19	and	and	CCONJ
ejpam-6939	202	20	v	v	NOUN
ejpam-6939	202	21	constitute	constitute	VERB
ejpam-6939	202	22	a	a	DET
ejpam-6939	202	23	connected	connected	ADJ
ejpam-6939	202	24	disjunctive	disjunctive	ADJ
ejpam-6939	202	25	dominating	dominating	NOUN
ejpam-6939	202	26	set	set	NOUN
ejpam-6939	202	27	,	,	PUNCT
ejpam-6939	202	28	γdc	γdc	PROPN
ejpam-6939	202	29	(	(	PUNCT
ejpam-6939	202	30	g	g	NOUN
ejpam-6939	202	31	)	)	PUNCT
ejpam-6939	202	32	=	=	SYM
ejpam-6939	202	33	2	2	NUM
ejpam-6939	202	34	,	,	PUNCT
ejpam-6939	202	35	and	and	CCONJ
ejpam-6939	202	36	(	(	PUNCT
ejpam-6939	202	37	ii	ii	NOUN
ejpam-6939	202	38	)	)	PUNCT
ejpam-6939	202	39	holds	hold	VERB
ejpam-6939	202	40	.	.	PUNCT
ejpam-6939	203	1	to	to	PART
ejpam-6939	203	2	prove	prove	VERB
ejpam-6939	203	3	(	(	PUNCT
ejpam-6939	203	4	iii	iii	NOUN
ejpam-6939	203	5	)	)	PUNCT
ejpam-6939	203	6	,	,	PUNCT
ejpam-6939	203	7	we	we	PRON
ejpam-6939	203	8	only	only	ADV
ejpam-6939	203	9	have	have	VERB
ejpam-6939	203	10	to	to	PART
ejpam-6939	203	11	show	show	VERB
ejpam-6939	203	12	that	that	SCONJ
ejpam-6939	203	13	γc(g	γc(g	PUNCT
ejpam-6939	203	14	)	)	PUNCT
ejpam-6939	203	15	≤	≤	NUM
ejpam-6939	203	16	γdc	γdc	NOUN
ejpam-6939	203	17	(	(	PUNCT
ejpam-6939	203	18	g	g	NOUN
ejpam-6939	203	19	)	)	PUNCT
ejpam-6939	203	20	.	.	PUNCT
ejpam-6939	204	1	let	let	VERB
ejpam-6939	204	2	s	s	PRON
ejpam-6939	204	3	⊆	⊆	NUM
ejpam-6939	204	4	v	v	NOUN
ejpam-6939	204	5	(	(	PUNCT
ejpam-6939	204	6	g	g	NOUN
ejpam-6939	204	7	)	)	PUNCT
ejpam-6939	204	8	be	be	AUX
ejpam-6939	204	9	a	a	DET
ejpam-6939	204	10	γdc	γdc	NOUN
ejpam-6939	204	11	-set	-set	PUNCT
ejpam-6939	204	12	of	of	ADP
ejpam-6939	204	13	g.	g.	PROPN
ejpam-6939	204	14	suppose	suppose	VERB
ejpam-6939	204	15	ng[s	ng[	NOUN
ejpam-6939	204	16	]	]	PUNCT
ejpam-6939	204	17	̸=	̸=	PROPN
ejpam-6939	204	18	v	v	NOUN
ejpam-6939	204	19	(	(	PUNCT
ejpam-6939	204	20	g	g	NOUN
ejpam-6939	204	21	)	)	PUNCT
ejpam-6939	204	22	,	,	PUNCT
ejpam-6939	204	23	and	and	CCONJ
ejpam-6939	204	24	let	let	VERB
ejpam-6939	204	25	x	x	SYM
ejpam-6939	204	26	∈	∈	PROPN
ejpam-6939	204	27	v	v	X
ejpam-6939	204	28	(	(	PUNCT
ejpam-6939	204	29	g	g	NOUN
ejpam-6939	204	30	)	)	PUNCT
ejpam-6939	204	31	\ng[s	\ng[s	PROPN
ejpam-6939	204	32	]	]	PUNCT
ejpam-6939	204	33	.	.	PUNCT
ejpam-6939	205	1	since	since	SCONJ
ejpam-6939	205	2	s	s	PROPN
ejpam-6939	205	3	is	be	AUX
ejpam-6939	205	4	a	a	DET
ejpam-6939	205	5	disjunctive	disjunctive	ADJ
ejpam-6939	205	6	dominating	dominating	NOUN
ejpam-6939	205	7	set	set	NOUN
ejpam-6939	205	8	,	,	PUNCT
ejpam-6939	205	9	there	there	PRON
ejpam-6939	205	10	exist	exist	VERB
ejpam-6939	205	11	distinct	distinct	ADJ
ejpam-6939	205	12	vertices	vertex	NOUN
ejpam-6939	205	13	u	u	NOUN
ejpam-6939	205	14	,	,	PUNCT
ejpam-6939	205	15	v	v	PROPN
ejpam-6939	205	16	∈	∈	NOUN
ejpam-6939	205	17	s	s	NOUN
ejpam-6939	205	18	for	for	ADP
ejpam-6939	205	19	which	which	PRON
ejpam-6939	205	20	dg(x	dg(x	NUM
ejpam-6939	205	21	,	,	PUNCT
ejpam-6939	205	22	u	u	NOUN
ejpam-6939	205	23	)	)	PUNCT
ejpam-6939	205	24	=	=	SYM
ejpam-6939	205	25	2	2	NUM
ejpam-6939	205	26	=	=	SYM
ejpam-6939	205	27	dg(x	dg(x	NUM
ejpam-6939	205	28	,	,	PUNCT
ejpam-6939	205	29	v	v	NOUN
ejpam-6939	205	30	)	)	PUNCT
ejpam-6939	205	31	.	.	PUNCT
ejpam-6939	206	1	since	since	SCONJ
ejpam-6939	206	2	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	206	3	does	do	AUX
ejpam-6939	206	4	not	not	PART
ejpam-6939	206	5	contain	contain	VERB
ejpam-6939	206	6	a	a	DET
ejpam-6939	206	7	u	u	NOUN
ejpam-6939	206	8	-	-	NOUN
ejpam-6939	206	9	v	v	ADJ
ejpam-6939	206	10	path	path	NOUN
ejpam-6939	206	11	,	,	PUNCT
ejpam-6939	206	12	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	206	13	is	be	AUX
ejpam-6939	206	14	not	not	PART
ejpam-6939	206	15	connected	connect	VERB
ejpam-6939	206	16	,	,	PUNCT
ejpam-6939	206	17	a	a	DET
ejpam-6939	206	18	contradiction	contradiction	NOUN
ejpam-6939	206	19	.	.	PUNCT
ejpam-6939	207	1	this	this	PRON
ejpam-6939	207	2	shows	show	VERB
ejpam-6939	207	3	that	that	SCONJ
ejpam-6939	207	4	s	s	VERB
ejpam-6939	207	5	is	be	AUX
ejpam-6939	207	6	a	a	DET
ejpam-6939	207	7	connected	connected	ADJ
ejpam-6939	207	8	dominating	dominating	NOUN
ejpam-6939	207	9	set	set	NOUN
ejpam-6939	207	10	of	of	ADP
ejpam-6939	207	11	g.	g.	PROPN
ejpam-6939	207	12	consequently	consequently	ADV
ejpam-6939	207	13	,	,	PUNCT
ejpam-6939	207	14	γc(g	γc(g	NUM
ejpam-6939	207	15	)	)	PUNCT
ejpam-6939	207	16	≤	≤	NUM
ejpam-6939	207	17	|s|	|s|	PROPN
ejpam-6939	207	18	=	=	SYM
ejpam-6939	207	19	γdc	γdc	NOUN
ejpam-6939	207	20	(	(	PUNCT
ejpam-6939	207	21	g	g	NOUN
ejpam-6939	207	22	)	)	PUNCT
ejpam-6939	207	23	.	.	PUNCT
ejpam-6939	208	1	remark	remark	PROPN
ejpam-6939	208	2	1	1	NUM
ejpam-6939	208	3	.	.	PUNCT
ejpam-6939	209	1	the	the	DET
ejpam-6939	209	2	bound	bind	VERB
ejpam-6939	209	3	given	give	VERB
ejpam-6939	209	4	for	for	ADP
ejpam-6939	209	5	γdc	γdc	NOUN
ejpam-6939	209	6	(	(	PUNCT
ejpam-6939	209	7	g	g	NOUN
ejpam-6939	209	8	)	)	PUNCT
ejpam-6939	209	9	in	in	ADP
ejpam-6939	209	10	proposition	proposition	NOUN
ejpam-6939	209	11	1	1	NUM
ejpam-6939	209	12	is	be	AUX
ejpam-6939	209	13	tight	tight	ADJ
ejpam-6939	209	14	.	.	PUNCT
ejpam-6939	210	1	indeed	indeed	ADV
ejpam-6939	210	2	,	,	PUNCT
ejpam-6939	210	3	if	if	SCONJ
ejpam-6939	210	4	γ(g	γ(g	PROPN
ejpam-6939	210	5	)	)	PUNCT
ejpam-6939	210	6	=	=	SYM
ejpam-6939	210	7	1	1	NUM
ejpam-6939	210	8	,	,	PUNCT
ejpam-6939	210	9	then	then	ADV
ejpam-6939	210	10	γdc	γdc	PROPN
ejpam-6939	210	11	(	(	PUNCT
ejpam-6939	210	12	g	g	NOUN
ejpam-6939	210	13	)	)	PUNCT
ejpam-6939	210	14	=	=	SYM
ejpam-6939	210	15	5γd(g)−	5γd(g)−	NUM
ejpam-6939	210	16	4	4	NUM
ejpam-6939	210	17	=	=	NOUN
ejpam-6939	210	18	γc(g	γc(g	X
ejpam-6939	210	19	)	)	PUNCT
ejpam-6939	210	20	=	=	SYM
ejpam-6939	210	21	1	1	X
ejpam-6939	210	22	.	.	X
ejpam-6939	210	23	proposition	proposition	NOUN
ejpam-6939	210	24	3	3	NUM
ejpam-6939	210	25	.	.	PUNCT
ejpam-6939	210	26	for	for	ADP
ejpam-6939	210	27	every	every	DET
ejpam-6939	210	28	pair	pair	NOUN
ejpam-6939	210	29	of	of	ADP
ejpam-6939	210	30	positive	positive	ADJ
ejpam-6939	210	31	integers	integer	NOUN
ejpam-6939	210	32	a	a	PRON
ejpam-6939	210	33	and	and	CCONJ
ejpam-6939	210	34	b	b	NOUN
ejpam-6939	210	35	with	with	ADP
ejpam-6939	210	36	2	2	NUM
ejpam-6939	210	37	≤	≤	NOUN
ejpam-6939	210	38	a	a	DET
ejpam-6939	210	39	≤	≤	NUM
ejpam-6939	210	40	b	b	NOUN
ejpam-6939	210	41	≤	≤	NOUN
ejpam-6939	210	42	2a−	2a−	NUM
ejpam-6939	210	43	1	1	NUM
ejpam-6939	210	44	,	,	PUNCT
ejpam-6939	210	45	there	there	PRON
ejpam-6939	210	46	exists	exist	VERB
ejpam-6939	210	47	a	a	DET
ejpam-6939	210	48	connected	connected	ADJ
ejpam-6939	210	49	graph	graph	NOUN
ejpam-6939	210	50	g	g	NOUN
ejpam-6939	210	51	for	for	ADP
ejpam-6939	210	52	which	which	PRON
ejpam-6939	210	53	γd(g	γd(g	PUNCT
ejpam-6939	210	54	)	)	PUNCT
ejpam-6939	210	55	=	=	SYM
ejpam-6939	210	56	a	a	PRON
ejpam-6939	210	57	and	and	CCONJ
ejpam-6939	210	58	γdc	γdc	ADJ
ejpam-6939	210	59	(	(	PUNCT
ejpam-6939	210	60	g	g	NOUN
ejpam-6939	210	61	)	)	PUNCT
ejpam-6939	210	62	=	=	SYM
ejpam-6939	210	63	b.	b.	NOUN
ejpam-6939	210	64	proof	proof	NOUN
ejpam-6939	210	65	.	.	PUNCT
ejpam-6939	211	1	if	if	SCONJ
ejpam-6939	211	2	a	a	DET
ejpam-6939	211	3	=	=	SYM
ejpam-6939	211	4	b	b	NOUN
ejpam-6939	211	5	=	=	SYM
ejpam-6939	211	6	2	2	NUM
ejpam-6939	211	7	,	,	PUNCT
ejpam-6939	211	8	then	then	ADV
ejpam-6939	211	9	we	we	PRON
ejpam-6939	211	10	take	take	VERB
ejpam-6939	211	11	g	g	NOUN
ejpam-6939	211	12	=	=	SYM
ejpam-6939	211	13	p4	p4	ADJ
ejpam-6939	211	14	.	.	PUNCT
ejpam-6939	212	1	suppose	suppose	VERB
ejpam-6939	212	2	that	that	SCONJ
ejpam-6939	212	3	a	a	DET
ejpam-6939	212	4	=	=	SYM
ejpam-6939	212	5	b	b	NOUN
ejpam-6939	212	6	≥	≥	NUM
ejpam-6939	212	7	3	3	NUM
ejpam-6939	212	8	.	.	PUNCT
ejpam-6939	213	1	let	let	VERB
ejpam-6939	213	2	pa	pa	PROPN
ejpam-6939	213	3	=	=	PUNCT
ejpam-6939	214	1	[	[	X
ejpam-6939	214	2	x1	x1	PROPN
ejpam-6939	214	3	,	,	PUNCT
ejpam-6939	214	4	x2	x2	PROPN
ejpam-6939	214	5	,	,	PUNCT
ejpam-6939	214	6	.	.	PUNCT
ejpam-6939	214	7	.	.	PUNCT
ejpam-6939	215	1	.	.	PUNCT
ejpam-6939	216	1	,	,	PUNCT
ejpam-6939	216	2	xa	xa	PROPN
ejpam-6939	216	3	]	]	PUNCT
ejpam-6939	216	4	be	be	AUX
ejpam-6939	216	5	a	a	DET
ejpam-6939	216	6	path	path	NOUN
ejpam-6939	216	7	on	on	ADP
ejpam-6939	216	8	a	a	DET
ejpam-6939	216	9	vertices	vertex	NOUN
ejpam-6939	216	10	.	.	PUNCT
ejpam-6939	217	1	obtain	obtain	VERB
ejpam-6939	217	2	g	g	NOUN
ejpam-6939	217	3	as	as	ADP
ejpam-6939	217	4	the	the	DET
ejpam-6939	217	5	graph	graph	NOUN
ejpam-6939	217	6	g1	g1	NOUN
ejpam-6939	217	7	in	in	ADP
ejpam-6939	217	8	figure	figure	NOUN
ejpam-6939	217	9	2	2	NUM
ejpam-6939	217	10	by	by	ADP
ejpam-6939	217	11	adding	add	VERB
ejpam-6939	217	12	•	•	NOUN
ejpam-6939	217	13	•	•	NOUN
ejpam-6939	217	14	•	•	NUM
ejpam-6939	217	15	•	•	NOUN
ejpam-6939	217	16	•	•	NOUN
ejpam-6939	217	17	•	•	NOUN
ejpam-6939	217	18	.......................................................................................................................................	.......................................................................................................................................	NUM
ejpam-6939	217	19	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6939	217	20	....................................	....................................	PUNCT
ejpam-6939	218	1	....................................	....................................	PUNCT
ejpam-6939	218	2	....................................	....................................	PUNCT
ejpam-6939	219	1	....................................	....................................	PUNCT
ejpam-6939	219	2	..........	..........	PUNCT
ejpam-6939	220	1	.........	.........	PUNCT
ejpam-6939	220	2	.........	.........	PUNCT
ejpam-6939	221	1	.........	.........	PUNCT
ejpam-6939	221	2	.........	.........	PUNCT
ejpam-6939	221	3	.	.	PUNCT
ejpam-6939	222	1	....................................	....................................	PUNCT
ejpam-6939	222	2	...............	...............	PUNCT
ejpam-6939	223	1	..............	..............	PUNCT
ejpam-6939	223	2	........	........	PUNCT
ejpam-6939	223	3	....................................	....................................	PUNCT
ejpam-6939	223	4	.....................................	.....................................	PUNCT
ejpam-6939	224	1	....................................	....................................	PUNCT
ejpam-6939	224	2	...............................................	...............................................	PUNCT
ejpam-6939	225	1	....................................	....................................	PUNCT
ejpam-6939	225	2	.......................................	.......................................	PUNCT
ejpam-6939	225	3	.................................	.................................	PUNCT
ejpam-6939	226	1	....................................	....................................	PUNCT
ejpam-6939	226	2	....................................	....................................	PUNCT
ejpam-6939	227	1	....................................	....................................	PUNCT
ejpam-6939	227	2	..........	..........	PUNCT
ejpam-6939	228	1	.........	.........	PUNCT
ejpam-6939	228	2	.........	.........	PUNCT
ejpam-6939	229	1	.........	.........	PUNCT
ejpam-6939	229	2	.........	.........	PUNCT
ejpam-6939	229	3	.	.	PUNCT
ejpam-6939	230	1	....................................	....................................	PUNCT
ejpam-6939	230	2	...............	...............	PUNCT
ejpam-6939	231	1	..............	..............	PUNCT
ejpam-6939	231	2	........	........	PUNCT
ejpam-6939	231	3	....................................	....................................	PUNCT
ejpam-6939	231	4	.....................................	.....................................	PUNCT
ejpam-6939	232	1	....................................	....................................	PUNCT
ejpam-6939	232	2	...............................................	...............................................	PUNCT
ejpam-6939	233	1	....................................	....................................	PUNCT
ejpam-6939	233	2	................................................................................	................................................................................	PUNCT
ejpam-6939	234	1	............................................	............................................	PUNCT
ejpam-6939	234	2	....................................	....................................	PUNCT
ejpam-6939	235	1	....................................	....................................	PUNCT
ejpam-6939	235	2	..........	..........	PUNCT
ejpam-6939	236	1	.........	.........	PUNCT
ejpam-6939	236	2	.........	.........	PUNCT
ejpam-6939	237	1	.........	.........	PUNCT
ejpam-6939	237	2	.........	.........	PUNCT
ejpam-6939	237	3	.	.	PUNCT
ejpam-6939	238	1	....................................	....................................	PUNCT
ejpam-6939	238	2	...............	...............	PUNCT
ejpam-6939	239	1	..............	..............	PUNCT
ejpam-6939	239	2	........	........	PUNCT
ejpam-6939	240	1	....................................	....................................	PUNCT
ejpam-6939	240	2	..........................................................	..........................................................	PUNCT
ejpam-6939	240	3	.	.	PUNCT
ejpam-6939	240	4	.	.	PUNCT
ejpam-6939	240	5	.	.	PUNCT
ejpam-6939	240	6	.	.	PUNCT
ejpam-6939	240	7	.	.	PUNCT
ejpam-6939	240	8	.	.	PUNCT
ejpam-6939	241	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6939	241	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6939	242	1	....................................	....................................	PUNCT
ejpam-6939	242	2	....................................	....................................	PUNCT
ejpam-6939	243	1	....................................	....................................	PUNCT
ejpam-6939	243	2	....................................	....................................	PUNCT
ejpam-6939	244	1	....................................	....................................	PUNCT
ejpam-6939	244	2	....................................	....................................	PUNCT
ejpam-6939	245	1	....................................	....................................	PUNCT
ejpam-6939	245	2	..........	..........	PUNCT
ejpam-6939	246	1	.........	.........	PUNCT
ejpam-6939	246	2	.........	.........	PUNCT
ejpam-6939	247	1	.........	.........	PUNCT
ejpam-6939	247	2	.........	.........	PUNCT
ejpam-6939	247	3	.	.	PUNCT
ejpam-6939	248	1	....................................	....................................	PUNCT
ejpam-6939	248	2	...............	...............	PUNCT
ejpam-6939	249	1	..............	..............	PUNCT
ejpam-6939	249	2	........	........	PUNCT
ejpam-6939	249	3	....................................	....................................	PUNCT
ejpam-6939	249	4	.....................................	.....................................	PUNCT
ejpam-6939	250	1	....................................	....................................	PUNCT
ejpam-6939	250	2	...............................................	...............................................	PUNCT
ejpam-6939	251	1	....................................	....................................	PUNCT
ejpam-6939	251	2	....................................	....................................	PUNCT
ejpam-6939	252	1	..........	..........	PUNCT
ejpam-6939	252	2	.........	.........	PUNCT
ejpam-6939	253	1	.........	.........	PUNCT
ejpam-6939	253	2	.........	.........	PUNCT
ejpam-6939	253	3	.........	.........	PUNCT
ejpam-6939	253	4	.	.	PUNCT
ejpam-6939	254	1	....................................	....................................	PUNCT
ejpam-6939	254	2	...............	...............	PUNCT
ejpam-6939	255	1	..............	..............	PUNCT
ejpam-6939	255	2	........	........	PUNCT
ejpam-6939	255	3	....................................	....................................	PUNCT
ejpam-6939	255	4	.....................................	.....................................	PUNCT
ejpam-6939	256	1	....................................	....................................	PUNCT
ejpam-6939	256	2	...............................................	...............................................	PUNCT
ejpam-6939	257	1	....................................	....................................	PUNCT
ejpam-6939	257	2	....................................	....................................	PUNCT
ejpam-6939	258	1	....................................	....................................	PUNCT
ejpam-6939	258	2	....................................	....................................	PUNCT
ejpam-6939	258	3	.....................................	.....................................	PUNCT
ejpam-6939	259	1	....................................	....................................	PUNCT
ejpam-6939	259	2	...............................................	...............................................	PUNCT
ejpam-6939	260	1	....................................	....................................	PUNCT
ejpam-6939	260	2	....................................	....................................	PUNCT
ejpam-6939	261	1	.................	.................	PUNCT
ejpam-6939	262	1	.....	.....	PUNCT
ejpam-6939	263	1	x1	x1	NUM
ejpam-6939	264	1	x2	x2	NOUN
ejpam-6939	264	2	x3	x3	PROPN
ejpam-6939	264	3	xa−2	xa−2	PROPN
ejpam-6939	264	4	xa−1	xa−1	PROPN
ejpam-6939	264	5	xa	xa	PROPN
ejpam-6939	264	6	g1	g1	PROPN
ejpam-6939	264	7	:	:	PUNCT
ejpam-6939	264	8	a1	a1	NOUN
ejpam-6939	264	9	b1	b1	PROPN
ejpam-6939	264	10	c1	c1	PROPN
ejpam-6939	264	11	figure	figure	NOUN
ejpam-6939	264	12	2	2	NUM
ejpam-6939	264	13	:	:	PUNCT
ejpam-6939	264	14	graph	graph	VERB
ejpam-6939	264	15	g	g	NOUN
ejpam-6939	264	16	for	for	ADP
ejpam-6939	264	17	which	which	PRON
ejpam-6939	264	18	γd(g	γd(g	PUNCT
ejpam-6939	264	19	)	)	PUNCT
ejpam-6939	264	20	=	=	PUNCT
ejpam-6939	264	21	γd	γd	ADP
ejpam-6939	264	22	c	c	PROPN
ejpam-6939	264	23	(	(	PUNCT
ejpam-6939	264	24	g	g	NOUN
ejpam-6939	264	25	)	)	PUNCT
ejpam-6939	264	26	to	to	ADP
ejpam-6939	264	27	pa	pa	PROPN
ejpam-6939	264	28	the	the	DET
ejpam-6939	264	29	path	path	NOUN
ejpam-6939	265	1	p	p	X
ejpam-6939	265	2	j	j	PROPN
ejpam-6939	265	3	=	=	PUNCT
ejpam-6939	266	1	[	[	X
ejpam-6939	266	2	xj	xj	PROPN
ejpam-6939	266	3	,	,	PUNCT
ejpam-6939	266	4	aj	aj	PROPN
ejpam-6939	266	5	,	,	PUNCT
ejpam-6939	266	6	bj	bj	VERB
ejpam-6939	266	7	,	,	PUNCT
ejpam-6939	266	8	cj	cj	X
ejpam-6939	266	9	,	,	PUNCT
ejpam-6939	266	10	xj+1	xj+1	X
ejpam-6939	266	11	]	]	PUNCT
ejpam-6939	266	12	for	for	ADP
ejpam-6939	266	13	each	each	DET
ejpam-6939	266	14	j	j	PROPN
ejpam-6939	266	15	=	=	SYM
ejpam-6939	266	16	1	1	NUM
ejpam-6939	266	17	,	,	PUNCT
ejpam-6939	266	18	2	2	NUM
ejpam-6939	266	19	,	,	PUNCT
ejpam-6939	266	20	.	.	PUNCT
ejpam-6939	266	21	.	.	PUNCT
ejpam-6939	267	1	.	.	PUNCT
ejpam-6939	268	1	,	,	PUNCT
ejpam-6939	268	2	a−	a−	PROPN
ejpam-6939	268	3	1	1	NUM
ejpam-6939	268	4	such	such	ADJ
ejpam-6939	268	5	that	that	SCONJ
ejpam-6939	268	6	two	two	NUM
ejpam-6939	268	7	distinct	distinct	ADJ
ejpam-6939	268	8	p	p	DET
ejpam-6939	268	9	js	js	PROPN
ejpam-6939	268	10	may	may	AUX
ejpam-6939	268	11	intersect	intersect	ADJ
ejpam-6939	268	12	but	but	CCONJ
ejpam-6939	268	13	only	only	ADV
ejpam-6939	268	14	at	at	ADP
ejpam-6939	268	15	a	a	DET
ejpam-6939	268	16	vertex	vertex	NOUN
ejpam-6939	268	17	on	on	ADP
ejpam-6939	268	18	pa	pa	PROPN
ejpam-6939	268	19	.	.	PUNCT
ejpam-6939	269	1	then	then	ADV
ejpam-6939	269	2	v	v	INTJ
ejpam-6939	269	3	(	(	PUNCT
ejpam-6939	269	4	pa	pa	PROPN
ejpam-6939	269	5	)	)	PUNCT
ejpam-6939	269	6	is	be	AUX
ejpam-6939	269	7	both	both	PRON
ejpam-6939	269	8	a	a	DET
ejpam-6939	269	9	γd	γd	ADV
ejpam-6939	269	10	-	-	PUNCT
ejpam-6939	269	11	set	set	VERB
ejpam-6939	269	12	and	and	CCONJ
ejpam-6939	269	13	γdc	γdc	NOUN
ejpam-6939	269	14	-set	-set	PROPN
ejpam-6939	269	15	of	of	ADP
ejpam-6939	269	16	g.	g.	PROPN
ejpam-6939	269	17	thus	thus	ADV
ejpam-6939	269	18	,	,	PUNCT
ejpam-6939	269	19	γd(g	γd(g	NUM
ejpam-6939	269	20	)	)	PUNCT
ejpam-6939	270	1	=	=	SYM
ejpam-6939	270	2	γdc	γdc	NOUN
ejpam-6939	270	3	(	(	PUNCT
ejpam-6939	270	4	g	g	NOUN
ejpam-6939	270	5	)	)	PUNCT
ejpam-6939	270	6	=	=	VERB
ejpam-6939	270	7	a.	a.	NOUN
ejpam-6939	270	8	now	now	ADV
ejpam-6939	270	9	,	,	PUNCT
ejpam-6939	270	10	assume	assume	VERB
ejpam-6939	270	11	that	that	SCONJ
ejpam-6939	270	12	a	a	DET
ejpam-6939	270	13	<	<	X
ejpam-6939	270	14	b	b	NOUN
ejpam-6939	270	15	,	,	PUNCT
ejpam-6939	270	16	and	and	CCONJ
ejpam-6939	270	17	let	let	VERB
ejpam-6939	270	18	b	b	NOUN
ejpam-6939	270	19	=	=	PUNCT
ejpam-6939	270	20	a	a	PROPN
ejpam-6939	270	21	+	+	X
ejpam-6939	270	22	k	k	NOUN
ejpam-6939	270	23	,	,	PUNCT
ejpam-6939	270	24	where	where	SCONJ
ejpam-6939	270	25	k	k	PROPN
ejpam-6939	270	26	≤	≤	VERB
ejpam-6939	270	27	a	a	DET
ejpam-6939	270	28	−	−	NOUN
ejpam-6939	270	29	1	1	NUM
ejpam-6939	270	30	.	.	PUNCT
ejpam-6939	271	1	if	if	SCONJ
ejpam-6939	271	2	a	a	DET
ejpam-6939	271	3	=	=	X
ejpam-6939	271	4	k	k	PROPN
ejpam-6939	272	1	+	+	PROPN
ejpam-6939	272	2	1	1	NUM
ejpam-6939	272	3	,	,	PUNCT
ejpam-6939	272	4	then	then	ADV
ejpam-6939	272	5	b	b	X
ejpam-6939	272	6	=	=	SYM
ejpam-6939	272	7	2k	2k	PROPN
ejpam-6939	272	8	+	+	CCONJ
ejpam-6939	272	9	1	1	X
ejpam-6939	272	10	.	.	X
ejpam-6939	272	11	in	in	ADP
ejpam-6939	272	12	this	this	DET
ejpam-6939	272	13	case	case	NOUN
ejpam-6939	272	14	,	,	PUNCT
ejpam-6939	272	15	obtain	obtain	VERB
ejpam-6939	272	16	g	g	NOUN
ejpam-6939	272	17	from	from	ADP
ejpam-6939	272	18	p2k+1	p2k+1	NOUN
ejpam-6939	272	19	as	as	ADP
ejpam-6939	272	20	the	the	DET
ejpam-6939	272	21	graph	graph	NOUN
ejpam-6939	272	22	g2	g2	PROPN
ejpam-6939	272	23	in	in	ADP
ejpam-6939	272	24	figure	figure	NOUN
ejpam-6939	272	25	3	3	NUM
ejpam-6939	272	26	by	by	ADP
ejpam-6939	272	27	adding	add	VERB
ejpam-6939	272	28	to	to	ADP
ejpam-6939	272	29	p2k+1	p2k+1	NOUN
ejpam-6939	272	30	=	=	PUNCT
ejpam-6939	273	1	[	[	X
ejpam-6939	273	2	x1	x1	X
ejpam-6939	273	3	,	,	PUNCT
ejpam-6939	273	4	x2	x2	PROPN
ejpam-6939	273	5	,	,	PUNCT
ejpam-6939	273	6	.	.	PUNCT
ejpam-6939	273	7	.	.	PUNCT
ejpam-6939	273	8	.	.	PUNCT
ejpam-6939	274	1	,	,	PUNCT
ejpam-6939	274	2	x2k+1	x2k+1	X
ejpam-6939	274	3	]	]	X
ejpam-6939	274	4	the	the	DET
ejpam-6939	274	5	path	path	NOUN
ejpam-6939	275	1	p	p	X
ejpam-6939	275	2	j	j	PROPN
ejpam-6939	275	3	=	=	PUNCT
ejpam-6939	276	1	[	[	X
ejpam-6939	276	2	xj	xj	PROPN
ejpam-6939	276	3	,	,	PUNCT
ejpam-6939	276	4	aj	aj	PROPN
ejpam-6939	276	5	,	,	PUNCT
ejpam-6939	276	6	bj	bj	VERB
ejpam-6939	276	7	,	,	PUNCT
ejpam-6939	276	8	cj	cj	X
ejpam-6939	276	9	,	,	PUNCT
ejpam-6939	276	10	xj+2	xj+2	X
ejpam-6939	276	11	]	]	PUNCT
ejpam-6939	276	12	for	for	ADP
ejpam-6939	276	13	each	each	DET
ejpam-6939	276	14	j	j	PROPN
ejpam-6939	276	15	=	=	SYM
ejpam-6939	276	16	1	1	NUM
ejpam-6939	276	17	,	,	PUNCT
ejpam-6939	276	18	2	2	NUM
ejpam-6939	276	19	,	,	PUNCT
ejpam-6939	276	20	.	.	PUNCT
ejpam-6939	276	21	.	.	PUNCT
ejpam-6939	276	22	.	.	PUNCT
ejpam-6939	277	1	,	,	PUNCT
ejpam-6939	277	2	2k	2k	NOUN
ejpam-6939	277	3	−	−	NOUN
ejpam-6939	277	4	1	1	NUM
ejpam-6939	277	5	such	such	ADJ
ejpam-6939	277	6	that	that	SCONJ
ejpam-6939	277	7	two	two	NUM
ejpam-6939	277	8	distinct	distinct	ADJ
ejpam-6939	277	9	p	p	DET
ejpam-6939	277	10	js	js	PROPN
ejpam-6939	277	11	may	may	AUX
ejpam-6939	277	12	intersect	intersect	ADJ
ejpam-6939	277	13	but	but	CCONJ
ejpam-6939	277	14	only	only	ADV
ejpam-6939	277	15	at	at	ADP
ejpam-6939	277	16	a	a	DET
ejpam-6939	277	17	vertex	vertex	NOUN
ejpam-6939	277	18	on	on	ADP
ejpam-6939	277	19	p2k+1	p2k+1	PROPN
ejpam-6939	277	20	.	.	PUNCT
ejpam-6939	278	1	then	then	ADV
ejpam-6939	278	2	γd(g	γd(g	NUM
ejpam-6939	278	3	)	)	PUNCT
ejpam-6939	278	4	=	=	SYM
ejpam-6939	278	5	a.	a.	NOUN
ejpam-6939	278	6	aradais	aradais	PROPN
ejpam-6939	278	7	,	,	PUNCT
ejpam-6939	278	8	f.	f.	PROPN
ejpam-6939	278	9	jamil	jamil	PROPN
ejpam-6939	278	10	,	,	PUNCT
ejpam-6939	278	11	s.	s.	PROPN
ejpam-6939	278	12	canoy	canoy	PROPN
ejpam-6939	278	13	/	/	SYM
ejpam-6939	278	14	eur	eur	PROPN
ejpam-6939	278	15	.	.	PUNCT
ejpam-6939	279	1	j.	j.	PROPN
ejpam-6939	279	2	pure	pure	PROPN
ejpam-6939	279	3	appl	appl	PROPN
ejpam-6939	279	4	.	.	PROPN
ejpam-6939	279	5	math	math	PROPN
ejpam-6939	279	6	,	,	PUNCT
ejpam-6939	279	7	18	18	NUM
ejpam-6939	279	8	(	(	PUNCT
ejpam-6939	279	9	4	4	NUM
ejpam-6939	279	10	)	)	PUNCT
ejpam-6939	279	11	(	(	PUNCT
ejpam-6939	279	12	2025	2025	NUM
ejpam-6939	279	13	)	)	PUNCT
ejpam-6939	279	14	,	,	PUNCT
ejpam-6939	279	15	6939	6939	NUM
ejpam-6939	279	16	7	7	NUM
ejpam-6939	279	17	of	of	ADP
ejpam-6939	279	18	14	14	NUM
ejpam-6939	279	19	•	•	NUM
ejpam-6939	279	20	•	•	NUM
ejpam-6939	279	21	•	•	NUM
ejpam-6939	279	22	•	•	NOUN
ejpam-6939	279	23	•	•	NOUN
ejpam-6939	279	24	•	•	NOUN
ejpam-6939	279	25	....................................	....................................	PUNCT
ejpam-6939	279	26	....................................	....................................	PUNCT
ejpam-6939	279	27	....................................	....................................	PUNCT
ejpam-6939	279	28	....................................................................................................................	....................................................................................................................	PUNCT
ejpam-6939	279	29	................................................................................	................................................................................	PUNCT
ejpam-6939	280	1	................................................................................	................................................................................	PUNCT
ejpam-6939	280	2	................................................................................	................................................................................	PUNCT
ejpam-6939	281	1	....................................	....................................	PUNCT
ejpam-6939	281	2	....................................	....................................	PUNCT
ejpam-6939	282	1	....................................	....................................	PUNCT
ejpam-6939	282	2	....................................	....................................	PUNCT
ejpam-6939	283	1	..........	..........	PUNCT
ejpam-6939	283	2	.........	.........	PUNCT
ejpam-6939	284	1	.........	.........	PUNCT
ejpam-6939	284	2	.........	.........	PUNCT
ejpam-6939	284	3	.........	.........	PUNCT
ejpam-6939	284	4	.	.	PUNCT
ejpam-6939	285	1	....................................	....................................	PUNCT
ejpam-6939	285	2	...............	...............	PUNCT
ejpam-6939	286	1	..............	..............	PUNCT
ejpam-6939	286	2	........	........	PUNCT
ejpam-6939	286	3	....................................	....................................	PUNCT
ejpam-6939	286	4	.....................................	.....................................	PUNCT
ejpam-6939	287	1	....................................	....................................	PUNCT
ejpam-6939	287	2	...............................................	...............................................	PUNCT
ejpam-6939	288	1	....................................	....................................	PUNCT
ejpam-6939	288	2	.......................................	.......................................	PUNCT
ejpam-6939	288	3	.................................	.................................	PUNCT
ejpam-6939	289	1	....................................	....................................	PUNCT
ejpam-6939	289	2	....................................	....................................	PUNCT
ejpam-6939	290	1	....................................	....................................	PUNCT
ejpam-6939	290	2	..........	..........	PUNCT
ejpam-6939	291	1	.........	.........	PUNCT
ejpam-6939	291	2	.........	.........	PUNCT
ejpam-6939	292	1	.........	.........	PUNCT
ejpam-6939	292	2	.........	.........	PUNCT
ejpam-6939	292	3	.	.	PUNCT
ejpam-6939	293	1	....................................	....................................	PUNCT
ejpam-6939	293	2	...............	...............	PUNCT
ejpam-6939	294	1	..............	..............	PUNCT
ejpam-6939	294	2	........	........	PUNCT
ejpam-6939	294	3	....................................	....................................	PUNCT
ejpam-6939	294	4	.....................................	.....................................	PUNCT
ejpam-6939	295	1	....................................	....................................	PUNCT
ejpam-6939	295	2	...............................................	...............................................	PUNCT
ejpam-6939	296	1	....................................	....................................	PUNCT
ejpam-6939	296	2	................................................................................	................................................................................	PUNCT
ejpam-6939	297	1	............................................	............................................	PUNCT
ejpam-6939	297	2	....................................	....................................	PUNCT
ejpam-6939	298	1	....................................	....................................	PUNCT
ejpam-6939	298	2	..........	..........	PUNCT
ejpam-6939	299	1	.........	.........	PUNCT
ejpam-6939	299	2	.........	.........	PUNCT
ejpam-6939	300	1	.........	.........	PUNCT
ejpam-6939	300	2	.........	.........	PUNCT
ejpam-6939	300	3	.	.	PUNCT
ejpam-6939	301	1	....................................	....................................	PUNCT
ejpam-6939	301	2	...............	...............	PUNCT
ejpam-6939	302	1	..............	..............	PUNCT
ejpam-6939	302	2	........	........	PUNCT
ejpam-6939	303	1	....................................	....................................	PUNCT
ejpam-6939	303	2	..........................................................	..........................................................	PUNCT
ejpam-6939	303	3	.	.	PUNCT
ejpam-6939	303	4	.	.	PUNCT
ejpam-6939	303	5	.	.	PUNCT
ejpam-6939	303	6	.	.	PUNCT
ejpam-6939	303	7	.	.	PUNCT
ejpam-6939	303	8	.	.	PUNCT
ejpam-6939	304	1	................................................................................	................................................................................	PUNCT
ejpam-6939	304	2	................................................................................	................................................................................	PUNCT
ejpam-6939	305	1	................................................................................	................................................................................	PUNCT
ejpam-6939	305	2	................................................................................	................................................................................	PUNCT
ejpam-6939	306	1	....................................	....................................	PUNCT
ejpam-6939	306	2	....................................	....................................	PUNCT
ejpam-6939	307	1	....................................	....................................	PUNCT
ejpam-6939	307	2	....................................	....................................	PUNCT
ejpam-6939	308	1	....................................	....................................	PUNCT
ejpam-6939	308	2	....................................	....................................	PUNCT
ejpam-6939	309	1	....................................	....................................	PUNCT
ejpam-6939	309	2	..........	..........	PUNCT
ejpam-6939	310	1	.........	.........	PUNCT
ejpam-6939	310	2	.........	.........	PUNCT
ejpam-6939	311	1	.........	.........	PUNCT
ejpam-6939	311	2	.........	.........	PUNCT
ejpam-6939	311	3	.	.	PUNCT
ejpam-6939	312	1	....................................	....................................	PUNCT
ejpam-6939	312	2	...............	...............	PUNCT
ejpam-6939	313	1	..............	..............	PUNCT
ejpam-6939	313	2	........	........	PUNCT
ejpam-6939	313	3	....................................	....................................	PUNCT
ejpam-6939	313	4	.....................................	.....................................	PUNCT
ejpam-6939	314	1	....................................	....................................	PUNCT
ejpam-6939	314	2	...............................................	...............................................	PUNCT
ejpam-6939	315	1	....................................	....................................	PUNCT
ejpam-6939	315	2	....................................	....................................	PUNCT
ejpam-6939	316	1	..........	..........	PUNCT
ejpam-6939	316	2	.........	.........	PUNCT
ejpam-6939	317	1	.........	.........	PUNCT
ejpam-6939	317	2	.........	.........	PUNCT
ejpam-6939	317	3	.........	.........	PUNCT
ejpam-6939	317	4	.	.	PUNCT
ejpam-6939	318	1	....................................	....................................	PUNCT
ejpam-6939	318	2	...............	...............	PUNCT
ejpam-6939	319	1	..............	..............	PUNCT
ejpam-6939	319	2	........	........	PUNCT
ejpam-6939	319	3	....................................	....................................	PUNCT
ejpam-6939	319	4	.....................................	.....................................	PUNCT
ejpam-6939	320	1	....................................	....................................	PUNCT
ejpam-6939	320	2	...............................................	...............................................	PUNCT
ejpam-6939	321	1	....................................	....................................	PUNCT
ejpam-6939	321	2	....................................	....................................	PUNCT
ejpam-6939	322	1	....................................	....................................	PUNCT
ejpam-6939	322	2	....................................	....................................	PUNCT
ejpam-6939	322	3	.....................................	.....................................	PUNCT
ejpam-6939	323	1	....................................	....................................	PUNCT
ejpam-6939	323	2	...............................................	...............................................	PUNCT
ejpam-6939	324	1	....................................	....................................	PUNCT
ejpam-6939	324	2	....................................	....................................	PUNCT
ejpam-6939	325	1	.................	.................	PUNCT
ejpam-6939	326	1	.....	.....	PUNCT
ejpam-6939	327	1	x1	x1	NUM
ejpam-6939	328	1	x2	x2	INTJ
ejpam-6939	329	1	x3	x3	INTJ
ejpam-6939	329	2	x2k+1	x2k+1	PROPN
ejpam-6939	329	3	g2	g2	PROPN
ejpam-6939	329	4	:	:	PUNCT
ejpam-6939	329	5	a1	a1	PROPN
ejpam-6939	329	6	b1	b1	PROPN
ejpam-6939	329	7	c1	c1	PROPN
ejpam-6939	329	8	figure	figure	VERB
ejpam-6939	329	9	3	3	NUM
ejpam-6939	329	10	:	:	PUNCT
ejpam-6939	329	11	graph	graph	VERB
ejpam-6939	329	12	g	g	NOUN
ejpam-6939	329	13	with	with	ADP
ejpam-6939	329	14	γd(g	γd(g	NUM
ejpam-6939	329	15	)	)	PUNCT
ejpam-6939	329	16	=	=	SYM
ejpam-6939	330	1	k	k	PROPN
ejpam-6939	331	1	+	+	CCONJ
ejpam-6939	331	2	1	1	NUM
ejpam-6939	331	3	and	and	CCONJ
ejpam-6939	331	4	γd	γd	ADP
ejpam-6939	331	5	c	c	PROPN
ejpam-6939	331	6	(	(	PUNCT
ejpam-6939	331	7	g	g	NOUN
ejpam-6939	331	8	)	)	PUNCT
ejpam-6939	331	9	=	=	SYM
ejpam-6939	331	10	γd(g	γd(g	X
ejpam-6939	331	11	)	)	PUNCT
ejpam-6939	332	1	+	+	CCONJ
ejpam-6939	333	1	k	k	PROPN
ejpam-6939	333	2	k	k	X
ejpam-6939	333	3	+	+	PROPN
ejpam-6939	333	4	1	1	NUM
ejpam-6939	333	5	=	=	SYM
ejpam-6939	333	6	a	a	NOUN
ejpam-6939	333	7	,	,	PUNCT
ejpam-6939	333	8	which	which	PRON
ejpam-6939	333	9	is	be	AUX
ejpam-6939	333	10	determined	determine	VERB
ejpam-6939	333	11	by	by	ADP
ejpam-6939	333	12	the	the	DET
ejpam-6939	333	13	γd	γd	ADV
ejpam-6939	333	14	-	-	PUNCT
ejpam-6939	333	15	set	set	VERB
ejpam-6939	333	16	{	{	PUNCT
ejpam-6939	333	17	x1	x1	PROPN
ejpam-6939	333	18	,	,	PUNCT
ejpam-6939	333	19	x3	x3	ADJ
ejpam-6939	333	20	,	,	PUNCT
ejpam-6939	333	21	x5	x5	NOUN
ejpam-6939	333	22	,	,	PUNCT
ejpam-6939	333	23	.	.	PUNCT
ejpam-6939	333	24	.	.	PUNCT
ejpam-6939	333	25	.	.	PUNCT
ejpam-6939	334	1	,	,	PUNCT
ejpam-6939	334	2	x2k+1	x2k+1	PROPN
ejpam-6939	334	3	}	}	PUNCT
ejpam-6939	334	4	.	.	PUNCT
ejpam-6939	335	1	also	also	ADV
ejpam-6939	335	2	,	,	PUNCT
ejpam-6939	335	3	γdc	γdc	PROPN
ejpam-6939	335	4	(	(	PUNCT
ejpam-6939	335	5	g	g	NOUN
ejpam-6939	335	6	)	)	PUNCT
ejpam-6939	335	7	=	=	SYM
ejpam-6939	335	8	2k	2k	NUM
ejpam-6939	335	9	+	+	CCONJ
ejpam-6939	335	10	1	1	NUM
ejpam-6939	335	11	=	=	SYM
ejpam-6939	335	12	b	b	NOUN
ejpam-6939	335	13	,	,	PUNCT
ejpam-6939	335	14	and	and	CCONJ
ejpam-6939	335	15	v	v	NOUN
ejpam-6939	335	16	(	(	PUNCT
ejpam-6939	335	17	p2k+1	p2k+1	NOUN
ejpam-6939	335	18	)	)	PUNCT
ejpam-6939	335	19	is	be	AUX
ejpam-6939	335	20	a	a	DET
ejpam-6939	335	21	γdc	γdc	NOUN
ejpam-6939	335	22	-set	-set	PUNCT
ejpam-6939	335	23	of	of	ADP
ejpam-6939	335	24	g.	g.	PROPN
ejpam-6939	335	25	suppose	suppose	VERB
ejpam-6939	335	26	that	that	SCONJ
ejpam-6939	335	27	a	a	PRON
ejpam-6939	335	28	=	=	X
ejpam-6939	335	29	k	k	X
ejpam-6939	335	30	+	+	PROPN
ejpam-6939	335	31	2	2	X
ejpam-6939	335	32	.	.	PUNCT
ejpam-6939	335	33	extend	extend	VERB
ejpam-6939	335	34	the	the	DET
ejpam-6939	335	35	graph	graph	NOUN
ejpam-6939	335	36	g2	g2	PROPN
ejpam-6939	335	37	in	in	ADP
ejpam-6939	335	38	figure	figure	NOUN
ejpam-6939	335	39	3	3	NUM
ejpam-6939	335	40	to	to	ADP
ejpam-6939	335	41	a	a	DET
ejpam-6939	335	42	graph	graph	NOUN
ejpam-6939	335	43	g	g	PROPN
ejpam-6939	335	44	=	=	PROPN
ejpam-6939	335	45	g3	g3	PROPN
ejpam-6939	335	46	as	as	ADP
ejpam-6939	335	47	in	in	ADP
ejpam-6939	335	48	figure	figure	NOUN
ejpam-6939	335	49	4	4	NUM
ejpam-6939	335	50	by	by	ADP
ejpam-6939	335	51	adding	add	VERB
ejpam-6939	335	52	p3	p3	PROPN
ejpam-6939	335	53	=	=	PUNCT
ejpam-6939	336	1	[	[	X
ejpam-6939	336	2	u	u	NOUN
ejpam-6939	336	3	,	,	PUNCT
ejpam-6939	336	4	v	v	NOUN
ejpam-6939	336	5	,	,	PUNCT
ejpam-6939	336	6	x1	x1	PROPN
ejpam-6939	336	7	]	]	PUNCT
ejpam-6939	336	8	through	through	ADP
ejpam-6939	336	9	................................................................................	................................................................................	PUNCT
ejpam-6939	336	10	................................................................................	................................................................................	PUNCT
ejpam-6939	337	1	....................................	....................................	PUNCT
ejpam-6939	338	1	•	•	NUM
ejpam-6939	339	1	•	•	NUM
ejpam-6939	339	2	•	•	NUM
ejpam-6939	339	3	•	•	NUM
ejpam-6939	339	4	•	•	NOUN
ejpam-6939	339	5	•	•	NOUN
ejpam-6939	339	6	•	•	NOUN
ejpam-6939	339	7	....................................	....................................	PUNCT
ejpam-6939	339	8	....................................	....................................	PUNCT
ejpam-6939	339	9	....................................	....................................	PUNCT
ejpam-6939	339	10	....................................................................................................................	....................................................................................................................	PUNCT
ejpam-6939	339	11	................................................................................	................................................................................	PUNCT
ejpam-6939	339	12	................................................................................	................................................................................	PUNCT
ejpam-6939	339	13	................................................................................	................................................................................	PUNCT
ejpam-6939	340	1	....................................	....................................	PUNCT
ejpam-6939	340	2	....................................	....................................	PUNCT
ejpam-6939	341	1	....................................	....................................	PUNCT
ejpam-6939	341	2	....................................	....................................	PUNCT
ejpam-6939	342	1	..........	..........	PUNCT
ejpam-6939	342	2	.........	.........	PUNCT
ejpam-6939	343	1	.........	.........	PUNCT
ejpam-6939	343	2	.........	.........	PUNCT
ejpam-6939	343	3	.........	.........	PUNCT
ejpam-6939	343	4	.	.	PUNCT
ejpam-6939	344	1	....................................	....................................	PUNCT
ejpam-6939	344	2	...............	...............	PUNCT
ejpam-6939	345	1	..............	..............	PUNCT
ejpam-6939	345	2	........	........	PUNCT
ejpam-6939	345	3	....................................	....................................	PUNCT
ejpam-6939	345	4	.....................................	.....................................	PUNCT
ejpam-6939	346	1	....................................	....................................	PUNCT
ejpam-6939	346	2	...............................................	...............................................	PUNCT
ejpam-6939	347	1	....................................	....................................	PUNCT
ejpam-6939	347	2	.......................................	.......................................	PUNCT
ejpam-6939	347	3	.................................	.................................	PUNCT
ejpam-6939	348	1	....................................	....................................	PUNCT
ejpam-6939	348	2	....................................	....................................	PUNCT
ejpam-6939	349	1	....................................	....................................	PUNCT
ejpam-6939	349	2	..........	..........	PUNCT
ejpam-6939	350	1	.........	.........	PUNCT
ejpam-6939	350	2	.........	.........	PUNCT
ejpam-6939	351	1	.........	.........	PUNCT
ejpam-6939	351	2	.........	.........	PUNCT
ejpam-6939	351	3	.	.	PUNCT
ejpam-6939	352	1	....................................	....................................	PUNCT
ejpam-6939	352	2	...............	...............	PUNCT
ejpam-6939	353	1	..............	..............	PUNCT
ejpam-6939	353	2	........	........	PUNCT
ejpam-6939	353	3	....................................	....................................	PUNCT
ejpam-6939	353	4	.....................................	.....................................	PUNCT
ejpam-6939	354	1	....................................	....................................	PUNCT
ejpam-6939	354	2	...............................................	...............................................	PUNCT
ejpam-6939	355	1	....................................	....................................	PUNCT
ejpam-6939	355	2	................................................................................	................................................................................	PUNCT
ejpam-6939	356	1	............................................	............................................	PUNCT
ejpam-6939	356	2	....................................	....................................	PUNCT
ejpam-6939	357	1	....................................	....................................	PUNCT
ejpam-6939	357	2	..........	..........	PUNCT
ejpam-6939	358	1	.........	.........	PUNCT
ejpam-6939	358	2	.........	.........	PUNCT
ejpam-6939	359	1	.........	.........	PUNCT
ejpam-6939	359	2	.........	.........	PUNCT
ejpam-6939	359	3	.	.	PUNCT
ejpam-6939	360	1	....................................	....................................	PUNCT
ejpam-6939	360	2	...............	...............	PUNCT
ejpam-6939	361	1	..............	..............	PUNCT
ejpam-6939	361	2	........	........	PUNCT
ejpam-6939	362	1	....................................	....................................	PUNCT
ejpam-6939	362	2	..........................................................	..........................................................	PUNCT
ejpam-6939	362	3	.	.	PUNCT
ejpam-6939	362	4	.	.	PUNCT
ejpam-6939	362	5	.	.	PUNCT
ejpam-6939	362	6	.	.	PUNCT
ejpam-6939	362	7	.	.	PUNCT
ejpam-6939	362	8	.	.	PUNCT
ejpam-6939	363	1	................................................................................	................................................................................	PUNCT
ejpam-6939	363	2	................................................................................	................................................................................	PUNCT
ejpam-6939	364	1	................................................................................	................................................................................	PUNCT
ejpam-6939	364	2	................................................................................	................................................................................	PUNCT
ejpam-6939	365	1	....................................	....................................	PUNCT
ejpam-6939	365	2	....................................	....................................	PUNCT
ejpam-6939	366	1	....................................	....................................	PUNCT
ejpam-6939	366	2	....................................	....................................	PUNCT
ejpam-6939	367	1	....................................	....................................	PUNCT
ejpam-6939	367	2	....................................	....................................	PUNCT
ejpam-6939	368	1	....................................	....................................	PUNCT
ejpam-6939	368	2	..........	..........	PUNCT
ejpam-6939	369	1	.........	.........	PUNCT
ejpam-6939	369	2	.........	.........	PUNCT
ejpam-6939	370	1	.........	.........	PUNCT
ejpam-6939	370	2	.........	.........	PUNCT
ejpam-6939	370	3	.	.	PUNCT
ejpam-6939	371	1	....................................	....................................	PUNCT
ejpam-6939	371	2	...............	...............	PUNCT
ejpam-6939	372	1	..............	..............	PUNCT
ejpam-6939	372	2	........	........	PUNCT
ejpam-6939	372	3	....................................	....................................	PUNCT
ejpam-6939	372	4	.....................................	.....................................	PUNCT
ejpam-6939	373	1	....................................	....................................	PUNCT
ejpam-6939	373	2	...............................................	...............................................	PUNCT
ejpam-6939	374	1	....................................	....................................	PUNCT
ejpam-6939	374	2	....................................	....................................	PUNCT
ejpam-6939	375	1	..........	..........	PUNCT
ejpam-6939	375	2	.........	.........	PUNCT
ejpam-6939	376	1	.........	.........	PUNCT
ejpam-6939	376	2	.........	.........	PUNCT
ejpam-6939	376	3	.........	.........	PUNCT
ejpam-6939	376	4	.	.	PUNCT
ejpam-6939	377	1	....................................	....................................	PUNCT
ejpam-6939	377	2	...............	...............	PUNCT
ejpam-6939	378	1	..............	..............	PUNCT
ejpam-6939	378	2	........	........	PUNCT
ejpam-6939	378	3	....................................	....................................	PUNCT
ejpam-6939	378	4	.....................................	.....................................	PUNCT
ejpam-6939	379	1	....................................	....................................	PUNCT
ejpam-6939	379	2	...............................................	...............................................	PUNCT
ejpam-6939	380	1	....................................	....................................	PUNCT
ejpam-6939	380	2	....................................	....................................	PUNCT
ejpam-6939	381	1	....................................	....................................	PUNCT
ejpam-6939	381	2	....................................	....................................	PUNCT
ejpam-6939	381	3	.....................................	.....................................	PUNCT
ejpam-6939	382	1	....................................	....................................	PUNCT
ejpam-6939	382	2	...............................................	...............................................	PUNCT
ejpam-6939	383	1	....................................	....................................	PUNCT
ejpam-6939	383	2	....................................	....................................	PUNCT
ejpam-6939	384	1	.................	.................	PUNCT
ejpam-6939	385	1	.....	.....	PUNCT
ejpam-6939	386	1	x1	x1	NUM
ejpam-6939	387	1	x2	x2	NOUN
ejpam-6939	387	2	x3	x3	VERB
ejpam-6939	387	3	x2k+1u	x2k+1u	PROPN
ejpam-6939	387	4	v	v	ADP
ejpam-6939	387	5	g3	g3	NOUN
ejpam-6939	387	6	:	:	PUNCT
ejpam-6939	387	7	figure	figure	NOUN
ejpam-6939	387	8	4	4	NUM
ejpam-6939	387	9	:	:	PUNCT
ejpam-6939	387	10	graph	graph	VERB
ejpam-6939	387	11	g	g	NOUN
ejpam-6939	387	12	with	with	ADP
ejpam-6939	387	13	γd(g	γd(g	NUM
ejpam-6939	387	14	)	)	PUNCT
ejpam-6939	387	15	=	=	SYM
ejpam-6939	388	1	k	k	PROPN
ejpam-6939	389	1	+	+	CCONJ
ejpam-6939	389	2	2	2	NUM
ejpam-6939	389	3	and	and	CCONJ
ejpam-6939	389	4	γd	γd	ADP
ejpam-6939	389	5	c	c	PROPN
ejpam-6939	389	6	(	(	PUNCT
ejpam-6939	389	7	g	g	NOUN
ejpam-6939	389	8	)	)	PUNCT
ejpam-6939	389	9	=	=	SYM
ejpam-6939	389	10	γd(g	γd(g	X
ejpam-6939	389	11	)	)	PUNCT
ejpam-6939	390	1	+	+	CCONJ
ejpam-6939	391	1	k	k	PROPN
ejpam-6939	391	2	x1	x1	PROPN
ejpam-6939	391	3	.	.	PUNCT
ejpam-6939	392	1	then	then	ADV
ejpam-6939	392	2	{	{	PUNCT
ejpam-6939	392	3	v	v	NOUN
ejpam-6939	392	4	,	,	PUNCT
ejpam-6939	392	5	x1	x1	PROPN
ejpam-6939	392	6	,	,	PUNCT
ejpam-6939	392	7	x3	x3	ADJ
ejpam-6939	392	8	,	,	PUNCT
ejpam-6939	392	9	x5	x5	NOUN
ejpam-6939	392	10	,	,	PUNCT
ejpam-6939	392	11	.	.	PUNCT
ejpam-6939	392	12	.	.	PUNCT
ejpam-6939	392	13	.	.	PUNCT
ejpam-6939	393	1	,	,	PUNCT
ejpam-6939	393	2	x2k+1	x2k+1	PROPN
ejpam-6939	393	3	}	}	PUNCT
ejpam-6939	393	4	is	be	AUX
ejpam-6939	393	5	a	a	DET
ejpam-6939	393	6	γd	γd	ADV
ejpam-6939	393	7	-	-	PUNCT
ejpam-6939	393	8	set	set	NOUN
ejpam-6939	393	9	of	of	ADP
ejpam-6939	393	10	g	g	NOUN
ejpam-6939	393	11	and	and	CCONJ
ejpam-6939	393	12	v	v	NOUN
ejpam-6939	393	13	(	(	PUNCT
ejpam-6939	393	14	p2k+1	p2k+1	NOUN
ejpam-6939	393	15	)	)	PUNCT
ejpam-6939	393	16	∪	∪	ADP
ejpam-6939	393	17	{	{	PUNCT
ejpam-6939	393	18	v	v	NOUN
ejpam-6939	393	19	}	}	PUNCT
ejpam-6939	393	20	is	be	AUX
ejpam-6939	393	21	a	a	DET
ejpam-6939	393	22	γdc	γdc	NOUN
ejpam-6939	393	23	-set	-set	PUNCT
ejpam-6939	393	24	of	of	ADP
ejpam-6939	393	25	g.	g.	PROPN
ejpam-6939	393	26	thus	thus	ADV
ejpam-6939	393	27	,	,	PUNCT
ejpam-6939	393	28	γd(g	γd(g	NUM
ejpam-6939	393	29	)	)	PUNCT
ejpam-6939	394	1	=	=	SYM
ejpam-6939	394	2	k	k	X
ejpam-6939	395	1	+	+	CCONJ
ejpam-6939	395	2	2	2	NUM
ejpam-6939	395	3	=	=	SYM
ejpam-6939	395	4	a	a	DET
ejpam-6939	395	5	and	and	CCONJ
ejpam-6939	395	6	γdc	γdc	ADJ
ejpam-6939	395	7	(	(	PUNCT
ejpam-6939	395	8	g	g	NOUN
ejpam-6939	395	9	)	)	PUNCT
ejpam-6939	395	10	=	=	SYM
ejpam-6939	395	11	2k	2k	NUM
ejpam-6939	395	12	+	+	CCONJ
ejpam-6939	395	13	2	2	NUM
ejpam-6939	395	14	=	=	SYM
ejpam-6939	395	15	b.	b.	PROPN
ejpam-6939	395	16	finally	finally	ADV
ejpam-6939	395	17	,	,	PUNCT
ejpam-6939	395	18	suppose	suppose	VERB
ejpam-6939	395	19	that	that	SCONJ
ejpam-6939	395	20	a	a	DET
ejpam-6939	395	21	≥	≥	NOUN
ejpam-6939	395	22	k	k	NOUN
ejpam-6939	395	23	+	+	CCONJ
ejpam-6939	395	24	3	3	X
ejpam-6939	395	25	.	.	NOUN
ejpam-6939	395	26	•	•	NUM
ejpam-6939	395	27	•	•	NUM
ejpam-6939	395	28	•	•	NUM
ejpam-6939	395	29	•	•	NOUN
ejpam-6939	395	30	•	•	NOUN
ejpam-6939	395	31	•	•	NOUN
ejpam-6939	395	32	....................................................................................................	....................................................................................................	PUNCT
ejpam-6939	395	33	....................................................................................................	....................................................................................................	PUNCT
ejpam-6939	395	34	....................................	....................................	PUNCT
ejpam-6939	395	35	....................................	....................................	PUNCT
ejpam-6939	395	36	....................................	....................................	PUNCT
ejpam-6939	395	37	....................................	....................................	PUNCT
ejpam-6939	396	1	..........	..........	PUNCT
ejpam-6939	396	2	.........	.........	PUNCT
ejpam-6939	397	1	.........	.........	PUNCT
ejpam-6939	397	2	.	.	PUNCT
ejpam-6939	398	1	....................................	....................................	PUNCT
ejpam-6939	398	2	...............	...............	PUNCT
ejpam-6939	398	3	.......	.......	PUNCT
ejpam-6939	399	1	....................................	....................................	PUNCT
ejpam-6939	399	2	......................	......................	PUNCT
ejpam-6939	400	1	....................................	....................................	PUNCT
ejpam-6939	400	2	.............................	.............................	PUNCT
ejpam-6939	401	1	....................................	....................................	PUNCT
ejpam-6939	401	2	.......................................	.......................................	PUNCT
ejpam-6939	401	3	.................................	.................................	PUNCT
ejpam-6939	402	1	....................................	....................................	PUNCT
ejpam-6939	402	2	....................................	....................................	PUNCT
ejpam-6939	403	1	....................................	....................................	PUNCT
ejpam-6939	403	2	..........	..........	PUNCT
ejpam-6939	404	1	.........	.........	PUNCT
ejpam-6939	404	2	.........	.........	PUNCT
ejpam-6939	404	3	.	.	PUNCT
ejpam-6939	405	1	....................................	....................................	PUNCT
ejpam-6939	405	2	...............	...............	PUNCT
ejpam-6939	405	3	.......	.......	PUNCT
ejpam-6939	406	1	....................................	....................................	PUNCT
ejpam-6939	406	2	......................	......................	PUNCT
ejpam-6939	407	1	....................................	....................................	PUNCT
ejpam-6939	407	2	.............................	.............................	PUNCT
ejpam-6939	408	1	....................................	....................................	PUNCT
ejpam-6939	408	2	...............................................................	...............................................................	PUNCT
ejpam-6939	408	3	...........................	...........................	PUNCT
ejpam-6939	409	1	....................................	....................................	PUNCT
ejpam-6939	409	2	....................................	....................................	PUNCT
ejpam-6939	410	1	..........	..........	PUNCT
ejpam-6939	410	2	.........	.........	PUNCT
ejpam-6939	411	1	.........	.........	PUNCT
ejpam-6939	411	2	.	.	PUNCT
ejpam-6939	412	1	....................................	....................................	PUNCT
ejpam-6939	412	2	...............	...............	PUNCT
ejpam-6939	413	1	.......	.......	PUNCT
ejpam-6939	413	2	....................................	....................................	PUNCT
ejpam-6939	414	1	................................................	................................................	PUNCT
ejpam-6939	414	2	.	.	PUNCT
ejpam-6939	414	3	.	.	PUNCT
ejpam-6939	414	4	.	.	PUNCT
ejpam-6939	414	5	.	.	PUNCT
ejpam-6939	414	6	.	.	PUNCT
ejpam-6939	414	7	.	.	PUNCT
ejpam-6939	415	1	....................................................................................................	....................................................................................................	PUNCT
ejpam-6939	415	2	....................................................................................................	....................................................................................................	PUNCT
ejpam-6939	416	1	....................................	....................................	PUNCT
ejpam-6939	416	2	....................................	....................................	PUNCT
ejpam-6939	417	1	....................................	....................................	PUNCT
ejpam-6939	417	2	....................................	....................................	PUNCT
ejpam-6939	418	1	....................................	....................................	PUNCT
ejpam-6939	418	2	....................................	....................................	PUNCT
ejpam-6939	419	1	....................................	....................................	PUNCT
ejpam-6939	419	2	..........	..........	PUNCT
ejpam-6939	420	1	.........	.........	PUNCT
ejpam-6939	420	2	.........	.........	PUNCT
ejpam-6939	420	3	.	.	PUNCT
ejpam-6939	421	1	....................................	....................................	PUNCT
ejpam-6939	421	2	...............	...............	PUNCT
ejpam-6939	421	3	.......	.......	PUNCT
ejpam-6939	422	1	....................................	....................................	PUNCT
ejpam-6939	422	2	......................	......................	PUNCT
ejpam-6939	423	1	....................................	....................................	PUNCT
ejpam-6939	423	2	.............................	.............................	PUNCT
ejpam-6939	424	1	....................................	....................................	PUNCT
ejpam-6939	424	2	....................................	....................................	PUNCT
ejpam-6939	425	1	..........	..........	PUNCT
ejpam-6939	425	2	.........	.........	PUNCT
ejpam-6939	426	1	.........	.........	PUNCT
ejpam-6939	426	2	.	.	PUNCT
ejpam-6939	427	1	....................................	....................................	PUNCT
ejpam-6939	427	2	...............	...............	PUNCT
ejpam-6939	427	3	.......	.......	PUNCT
ejpam-6939	428	1	....................................	....................................	PUNCT
ejpam-6939	428	2	......................	......................	PUNCT
ejpam-6939	429	1	....................................	....................................	PUNCT
ejpam-6939	429	2	.............................	.............................	PUNCT
ejpam-6939	430	1	....................................	....................................	PUNCT
ejpam-6939	430	2	....................................	....................................	PUNCT
ejpam-6939	431	1	....................................	....................................	PUNCT
ejpam-6939	431	2	....................................	....................................	PUNCT
ejpam-6939	432	1	......................	......................	PUNCT
ejpam-6939	432	2	....................................	....................................	PUNCT
ejpam-6939	432	3	.............................	.............................	PUNCT
ejpam-6939	433	1	....................................	....................................	PUNCT
ejpam-6939	433	2	....................................	....................................	PUNCT
ejpam-6939	433	3	............	............	PUNCT
ejpam-6939	434	1	y1	y1	INTJ
ejpam-6939	434	2	y2	y2	NOUN
ejpam-6939	434	3	y3	y3	NOUN
ejpam-6939	434	4	................................................................	................................................................	PUNCT
ejpam-6939	434	5	ya−k−1	ya−k−1	NOUN
ejpam-6939	435	1	•	•	NUM
ejpam-6939	435	2	•	•	NUM
ejpam-6939	435	3	•	•	NUM
ejpam-6939	435	4	•	•	NOUN
ejpam-6939	435	5	•	•	NOUN
ejpam-6939	435	6	•	•	NOUN
ejpam-6939	435	7	....................................	....................................	PUNCT
ejpam-6939	435	8	....................................	....................................	PUNCT
ejpam-6939	435	9	....................................	....................................	PUNCT
ejpam-6939	435	10	...................................................................................................	...................................................................................................	PUNCT
ejpam-6939	436	1	...............................................................	...............................................................	PUNCT
ejpam-6939	436	2	...............................................................	...............................................................	PUNCT
ejpam-6939	437	1	...............................................................	...............................................................	PUNCT
ejpam-6939	437	2	....................................	....................................	PUNCT
ejpam-6939	438	1	....................................	....................................	PUNCT
ejpam-6939	438	2	....................................	....................................	PUNCT
ejpam-6939	439	1	....................................	....................................	PUNCT
ejpam-6939	439	2	..........	..........	PUNCT
ejpam-6939	440	1	.........	.........	PUNCT
ejpam-6939	440	2	.........	.........	PUNCT
ejpam-6939	440	3	.	.	PUNCT
ejpam-6939	441	1	....................................	....................................	PUNCT
ejpam-6939	441	2	...............	...............	PUNCT
ejpam-6939	441	3	.......	.......	PUNCT
ejpam-6939	442	1	....................................	....................................	PUNCT
ejpam-6939	442	2	......................	......................	PUNCT
ejpam-6939	443	1	....................................	....................................	PUNCT
ejpam-6939	443	2	.............................	.............................	PUNCT
ejpam-6939	444	1	....................................	....................................	PUNCT
ejpam-6939	444	2	.......................................	.......................................	PUNCT
ejpam-6939	444	3	.................................	.................................	PUNCT
ejpam-6939	445	1	....................................	....................................	PUNCT
ejpam-6939	445	2	....................................	....................................	PUNCT
ejpam-6939	446	1	....................................	....................................	PUNCT
ejpam-6939	446	2	..........	..........	PUNCT
ejpam-6939	447	1	.........	.........	PUNCT
ejpam-6939	447	2	.........	.........	PUNCT
ejpam-6939	447	3	.	.	PUNCT
ejpam-6939	448	1	....................................	....................................	PUNCT
ejpam-6939	448	2	...............	...............	PUNCT
ejpam-6939	448	3	.......	.......	PUNCT
ejpam-6939	449	1	....................................	....................................	PUNCT
ejpam-6939	449	2	......................	......................	PUNCT
ejpam-6939	450	1	....................................	....................................	PUNCT
ejpam-6939	450	2	.............................	.............................	PUNCT
ejpam-6939	451	1	....................................	....................................	PUNCT
ejpam-6939	451	2	...............................................................	...............................................................	PUNCT
ejpam-6939	451	3	...........................	...........................	PUNCT
ejpam-6939	452	1	....................................	....................................	PUNCT
ejpam-6939	452	2	....................................	....................................	PUNCT
ejpam-6939	453	1	..........	..........	PUNCT
ejpam-6939	453	2	.........	.........	PUNCT
ejpam-6939	454	1	.........	.........	PUNCT
ejpam-6939	454	2	.	.	PUNCT
ejpam-6939	455	1	....................................	....................................	PUNCT
ejpam-6939	455	2	...............	...............	PUNCT
ejpam-6939	456	1	.......	.......	PUNCT
ejpam-6939	456	2	....................................	....................................	PUNCT
ejpam-6939	457	1	................................................	................................................	PUNCT
ejpam-6939	457	2	.	.	PUNCT
ejpam-6939	457	3	.	.	PUNCT
ejpam-6939	457	4	.	.	PUNCT
ejpam-6939	457	5	.	.	PUNCT
ejpam-6939	457	6	.	.	PUNCT
ejpam-6939	458	1	.	.	PUNCT
ejpam-6939	459	1	...............................................................	...............................................................	PUNCT
ejpam-6939	459	2	...............................................................	...............................................................	PUNCT
ejpam-6939	460	1	...............................................................	...............................................................	PUNCT
ejpam-6939	460	2	...............................................................	...............................................................	PUNCT
ejpam-6939	461	1	....................................	....................................	PUNCT
ejpam-6939	461	2	....................................	....................................	PUNCT
ejpam-6939	462	1	....................................	....................................	PUNCT
ejpam-6939	462	2	....................................	....................................	PUNCT
ejpam-6939	463	1	....................................	....................................	PUNCT
ejpam-6939	463	2	....................................	....................................	PUNCT
ejpam-6939	464	1	....................................	....................................	PUNCT
ejpam-6939	464	2	..........	..........	PUNCT
ejpam-6939	465	1	.........	.........	PUNCT
ejpam-6939	465	2	.........	.........	PUNCT
ejpam-6939	465	3	.	.	PUNCT
ejpam-6939	466	1	....................................	....................................	PUNCT
ejpam-6939	466	2	...............	...............	PUNCT
ejpam-6939	466	3	.......	.......	PUNCT
ejpam-6939	467	1	....................................	....................................	PUNCT
ejpam-6939	467	2	......................	......................	PUNCT
ejpam-6939	468	1	....................................	....................................	PUNCT
ejpam-6939	468	2	.............................	.............................	PUNCT
ejpam-6939	469	1	....................................	....................................	PUNCT
ejpam-6939	469	2	....................................	....................................	PUNCT
ejpam-6939	470	1	..........	..........	PUNCT
ejpam-6939	470	2	.........	.........	PUNCT
ejpam-6939	471	1	.........	.........	PUNCT
ejpam-6939	471	2	.	.	PUNCT
ejpam-6939	472	1	....................................	....................................	PUNCT
ejpam-6939	472	2	...............	...............	PUNCT
ejpam-6939	472	3	.......	.......	PUNCT
ejpam-6939	473	1	....................................	....................................	PUNCT
ejpam-6939	473	2	......................	......................	PUNCT
ejpam-6939	474	1	....................................	....................................	PUNCT
ejpam-6939	474	2	.............................	.............................	PUNCT
ejpam-6939	475	1	....................................	....................................	PUNCT
ejpam-6939	475	2	....................................	....................................	PUNCT
ejpam-6939	476	1	....................................	....................................	PUNCT
ejpam-6939	476	2	....................................	....................................	PUNCT
ejpam-6939	477	1	......................	......................	PUNCT
ejpam-6939	477	2	....................................	....................................	PUNCT
ejpam-6939	477	3	.............................	.............................	PUNCT
ejpam-6939	478	1	....................................	....................................	PUNCT
ejpam-6939	478	2	....................................	....................................	PUNCT
ejpam-6939	479	1	............	............	PUNCT
ejpam-6939	480	1	x1	x1	NUM
ejpam-6939	481	1	x2	x2	NOUN
ejpam-6939	481	2	x3	x3	INTJ
ejpam-6939	481	3	x2k+1	x2k+1	VERB
ejpam-6939	481	4	g4	g4	NOUN
ejpam-6939	481	5	:	:	PUNCT
ejpam-6939	481	6	figure	figure	NOUN
ejpam-6939	481	7	5	5	NUM
ejpam-6939	481	8	:	:	PUNCT
ejpam-6939	481	9	graph	graph	VERB
ejpam-6939	481	10	g	g	NOUN
ejpam-6939	481	11	with	with	ADP
ejpam-6939	481	12	γd(g	γd(g	NUM
ejpam-6939	481	13	)	)	PUNCT
ejpam-6939	481	14	≥	≥	X
ejpam-6939	481	15	k	k	NOUN
ejpam-6939	482	1	+	+	CCONJ
ejpam-6939	482	2	3	3	NUM
ejpam-6939	482	3	and	and	CCONJ
ejpam-6939	482	4	γd	γd	ADP
ejpam-6939	482	5	c	c	PROPN
ejpam-6939	482	6	(	(	PUNCT
ejpam-6939	482	7	g	g	NOUN
ejpam-6939	482	8	)	)	PUNCT
ejpam-6939	482	9	=	=	SYM
ejpam-6939	482	10	γd(g	γd(g	X
ejpam-6939	482	11	)	)	PUNCT
ejpam-6939	483	1	+	+	CCONJ
ejpam-6939	484	1	k	k	X
ejpam-6939	484	2	then	then	ADV
ejpam-6939	484	3	a	a	DET
ejpam-6939	484	4	−	−	PROPN
ejpam-6939	484	5	(	(	PUNCT
ejpam-6939	484	6	k	k	PROPN
ejpam-6939	484	7	+	+	PROPN
ejpam-6939	484	8	1	1	X
ejpam-6939	484	9	)	)	PUNCT
ejpam-6939	484	10	≥	≥	NOUN
ejpam-6939	484	11	2	2	NUM
ejpam-6939	484	12	.	.	PUNCT
ejpam-6939	484	13	form	form	VERB
ejpam-6939	484	14	a	a	DET
ejpam-6939	484	15	graph	graph	NOUN
ejpam-6939	484	16	g∗	g∗	NOUN
ejpam-6939	484	17	1	1	NUM
ejpam-6939	484	18	similar	similar	ADJ
ejpam-6939	484	19	to	to	ADP
ejpam-6939	484	20	the	the	DET
ejpam-6939	484	21	graph	graph	NOUN
ejpam-6939	484	22	g1	g1	NOUN
ejpam-6939	484	23	in	in	ADP
ejpam-6939	484	24	figure	figure	NOUN
ejpam-6939	484	25	2	2	NUM
ejpam-6939	484	26	but	but	CCONJ
ejpam-6939	484	27	using	use	VERB
ejpam-6939	484	28	pa−k−1	pa−k−1	NOUN
ejpam-6939	484	29	and	and	CCONJ
ejpam-6939	484	30	obtain	obtain	VERB
ejpam-6939	484	31	g	g	NOUN
ejpam-6939	484	32	as	as	ADP
ejpam-6939	484	33	the	the	DET
ejpam-6939	484	34	graph	graph	NOUN
ejpam-6939	484	35	g4	g4	NOUN
ejpam-6939	484	36	in	in	ADP
ejpam-6939	484	37	figure	figure	NOUN
ejpam-6939	484	38	5	5	NUM
ejpam-6939	484	39	by	by	ADP
ejpam-6939	484	40	combining	combine	VERB
ejpam-6939	484	41	g∗	g∗	PROPN
ejpam-6939	484	42	1	1	NUM
ejpam-6939	484	43	and	and	CCONJ
ejpam-6939	484	44	the	the	DET
ejpam-6939	484	45	graph	graph	NOUN
ejpam-6939	484	46	g2	g2	PROPN
ejpam-6939	484	47	in	in	ADP
ejpam-6939	484	48	figure	figure	NOUN
ejpam-6939	484	49	3	3	NUM
ejpam-6939	484	50	by	by	ADP
ejpam-6939	484	51	adding	add	VERB
ejpam-6939	484	52	the	the	DET
ejpam-6939	484	53	edge	edge	NOUN
ejpam-6939	484	54	y(a−k−1)x1	y(a−k−1)x1	NOUN
ejpam-6939	484	55	.	.	PUNCT
ejpam-6939	485	1	then	then	ADV
ejpam-6939	485	2	γd(g	γd(g	NUM
ejpam-6939	485	3	)	)	PUNCT
ejpam-6939	486	1	=	=	SYM
ejpam-6939	486	2	(	(	PUNCT
ejpam-6939	486	3	a	a	DET
ejpam-6939	486	4	−	−	PROPN
ejpam-6939	486	5	k	k	NOUN
ejpam-6939	486	6	−	−	PROPN
ejpam-6939	486	7	1	1	NUM
ejpam-6939	486	8	)	)	PUNCT
ejpam-6939	486	9	+	+	CCONJ
ejpam-6939	486	10	(	(	PUNCT
ejpam-6939	486	11	k	k	X
ejpam-6939	486	12	+	+	PROPN
ejpam-6939	486	13	1	1	X
ejpam-6939	486	14	)	)	PUNCT
ejpam-6939	486	15	=	=	PUNCT
ejpam-6939	486	16	a	a	DET
ejpam-6939	486	17	and	and	CCONJ
ejpam-6939	486	18	γdc	γdc	ADJ
ejpam-6939	486	19	(	(	PUNCT
ejpam-6939	486	20	g	g	NOUN
ejpam-6939	486	21	)	)	PUNCT
ejpam-6939	486	22	=	=	SYM
ejpam-6939	486	23	(	(	PUNCT
ejpam-6939	486	24	a−	a−	PROPN
ejpam-6939	486	25	k	k	PROPN
ejpam-6939	486	26	−	−	NOUN
ejpam-6939	486	27	1	1	NUM
ejpam-6939	486	28	)	)	PUNCT
ejpam-6939	486	29	+	+	CCONJ
ejpam-6939	486	30	(	(	PUNCT
ejpam-6939	486	31	2k	2k	NUM
ejpam-6939	486	32	+	+	CCONJ
ejpam-6939	486	33	1	1	X
ejpam-6939	486	34	)	)	PUNCT
ejpam-6939	486	35	=	=	PRON
ejpam-6939	486	36	a+	a+	PUNCT
ejpam-6939	486	37	k	k	PROPN
ejpam-6939	486	38	=	=	PROPN
ejpam-6939	486	39	b.	b.	PROPN
ejpam-6939	486	40	corollary	corollary	NOUN
ejpam-6939	486	41	1	1	NUM
ejpam-6939	486	42	.	.	PUNCT
ejpam-6939	487	1	the	the	DET
ejpam-6939	487	2	difference	difference	NOUN
ejpam-6939	487	3	γdc	γdc	NOUN
ejpam-6939	487	4	(	(	PUNCT
ejpam-6939	487	5	g)−	g)−	PROPN
ejpam-6939	487	6	γd(g	γd(g	NUM
ejpam-6939	487	7	)	)	PUNCT
ejpam-6939	487	8	can	can	AUX
ejpam-6939	487	9	be	be	AUX
ejpam-6939	487	10	made	make	VERB
ejpam-6939	487	11	arbitrarily	arbitrarily	ADV
ejpam-6939	487	12	large	large	ADJ
ejpam-6939	487	13	.	.	PUNCT
ejpam-6939	488	1	proposition	proposition	NOUN
ejpam-6939	488	2	4	4	NUM
ejpam-6939	488	3	.	.	PUNCT
ejpam-6939	489	1	for	for	ADP
ejpam-6939	489	2	every	every	DET
ejpam-6939	489	3	pair	pair	NOUN
ejpam-6939	489	4	of	of	ADP
ejpam-6939	489	5	positive	positive	ADJ
ejpam-6939	489	6	integers	integer	NOUN
ejpam-6939	489	7	a	a	PRON
ejpam-6939	489	8	and	and	CCONJ
ejpam-6939	489	9	b	b	NOUN
ejpam-6939	489	10	with	with	ADP
ejpam-6939	489	11	a	a	DET
ejpam-6939	489	12	≤	≤	NUM
ejpam-6939	489	13	b	b	NOUN
ejpam-6939	489	14	,	,	PUNCT
ejpam-6939	489	15	there	there	PRON
ejpam-6939	489	16	exists	exist	VERB
ejpam-6939	489	17	a	a	DET
ejpam-6939	489	18	connected	connected	ADJ
ejpam-6939	489	19	graph	graph	NOUN
ejpam-6939	489	20	g	g	NOUN
ejpam-6939	489	21	for	for	ADP
ejpam-6939	489	22	which	which	PRON
ejpam-6939	489	23	γdc	γdc	NOUN
ejpam-6939	489	24	(	(	PUNCT
ejpam-6939	489	25	g	g	NOUN
ejpam-6939	489	26	)	)	PUNCT
ejpam-6939	489	27	=	=	SYM
ejpam-6939	489	28	a	a	PRON
ejpam-6939	489	29	and	and	CCONJ
ejpam-6939	489	30	γc(g	γc(g	NUM
ejpam-6939	489	31	)	)	PUNCT
ejpam-6939	489	32	=	=	SYM
ejpam-6939	489	33	b.	b.	NOUN
ejpam-6939	489	34	proof	proof	NOUN
ejpam-6939	489	35	.	.	PUNCT
ejpam-6939	490	1	if	if	SCONJ
ejpam-6939	490	2	a	a	DET
ejpam-6939	490	3	=	=	SYM
ejpam-6939	490	4	b	b	NOUN
ejpam-6939	490	5	,	,	PUNCT
ejpam-6939	490	6	then	then	ADV
ejpam-6939	490	7	we	we	PRON
ejpam-6939	490	8	take	take	VERB
ejpam-6939	490	9	,	,	PUNCT
ejpam-6939	490	10	in	in	ADP
ejpam-6939	490	11	particular	particular	ADJ
ejpam-6939	490	12	,	,	PUNCT
ejpam-6939	490	13	g	g	PROPN
ejpam-6939	490	14	=	=	PUNCT
ejpam-6939	490	15	pa+2	pa+2	X
ejpam-6939	490	16	.	.	PUNCT
ejpam-6939	490	17	by	by	ADP
ejpam-6939	490	18	observation	observation	NOUN
ejpam-6939	490	19	1	1	NUM
ejpam-6939	490	20	and	and	CCONJ
ejpam-6939	490	21	proposition	proposition	NOUN
ejpam-6939	490	22	2(iii	2(iii	NUM
ejpam-6939	490	23	)	)	PUNCT
ejpam-6939	490	24	,	,	PUNCT
ejpam-6939	490	25	γdc	γdc	NOUN
ejpam-6939	490	26	(	(	PUNCT
ejpam-6939	490	27	g	g	NOUN
ejpam-6939	490	28	)	)	PUNCT
ejpam-6939	490	29	=	=	PUNCT
ejpam-6939	490	30	γc(g	γc(g	X
ejpam-6939	490	31	)	)	PUNCT
ejpam-6939	490	32	=	=	SYM
ejpam-6939	491	1	a	a	DET
ejpam-6939	491	2	=	=	X
ejpam-6939	491	3	b.	b.	PROPN
ejpam-6939	491	4	suppose	suppose	VERB
ejpam-6939	491	5	that	that	SCONJ
ejpam-6939	491	6	a	a	DET
ejpam-6939	491	7	<	<	X
ejpam-6939	491	8	b	b	NOUN
ejpam-6939	491	9	,	,	PUNCT
ejpam-6939	491	10	say	say	VERB
ejpam-6939	491	11	b	b	NOUN
ejpam-6939	491	12	=	=	PUNCT
ejpam-6939	491	13	a+k	a+k	PROPN
ejpam-6939	491	14	,	,	PUNCT
ejpam-6939	491	15	where	where	SCONJ
ejpam-6939	491	16	k	k	PROPN
ejpam-6939	491	17	≥	≥	PROPN
ejpam-6939	491	18	1	1	NUM
ejpam-6939	491	19	.	.	PUNCT
ejpam-6939	492	1	obtain	obtain	VERB
ejpam-6939	492	2	the	the	DET
ejpam-6939	492	3	graph	graph	NOUN
ejpam-6939	492	4	g	g	NOUN
ejpam-6939	492	5	from	from	ADP
ejpam-6939	492	6	pa	pa	PROPN
ejpam-6939	492	7	=	=	PUNCT
ejpam-6939	493	1	[	[	X
ejpam-6939	493	2	x1	x1	PROPN
ejpam-6939	493	3	,	,	PUNCT
ejpam-6939	493	4	x2	x2	PROPN
ejpam-6939	493	5	,	,	PUNCT
ejpam-6939	493	6	.	.	PUNCT
ejpam-6939	493	7	.	.	PUNCT
ejpam-6939	494	1	.	.	PUNCT
ejpam-6939	495	1	,	,	PUNCT
ejpam-6939	495	2	xa	xa	PROPN
ejpam-6939	495	3	]	]	PUNCT
ejpam-6939	495	4	,	,	PUNCT
ejpam-6939	495	5	as	as	SCONJ
ejpam-6939	495	6	provided	provide	VERB
ejpam-6939	495	7	in	in	ADP
ejpam-6939	495	8	figure	figure	NOUN
ejpam-6939	495	9	6	6	NUM
ejpam-6939	495	10	,	,	PUNCT
ejpam-6939	495	11	by	by	ADP
ejpam-6939	495	12	adding	add	VERB
ejpam-6939	495	13	to	to	ADP
ejpam-6939	495	14	pa	pa	PROPN
ejpam-6939	495	15	the	the	DET
ejpam-6939	495	16	path	path	NOUN
ejpam-6939	496	1	[	[	X
ejpam-6939	496	2	x1	x1	PROPN
ejpam-6939	496	3	,	,	PUNCT
ejpam-6939	496	4	aj	aj	PROPN
ejpam-6939	496	5	,	,	PUNCT
ejpam-6939	496	6	bj	bj	VERB
ejpam-6939	496	7	,	,	PUNCT
ejpam-6939	496	8	cj	cj	INTJ
ejpam-6939	496	9	,	,	PUNCT
ejpam-6939	496	10	x2	x2	PROPN
ejpam-6939	496	11	]	]	PUNCT
ejpam-6939	496	12	for	for	ADP
ejpam-6939	496	13	all	all	DET
ejpam-6939	496	14	j	j	NOUN
ejpam-6939	496	15	=	=	SYM
ejpam-6939	496	16	1	1	NUM
ejpam-6939	496	17	,	,	PUNCT
ejpam-6939	496	18	2	2	NUM
ejpam-6939	496	19	,	,	PUNCT
ejpam-6939	496	20	.	.	PUNCT
ejpam-6939	496	21	.	.	PUNCT
ejpam-6939	497	1	.	.	PUNCT
ejpam-6939	498	1	,	,	PUNCT
ejpam-6939	498	2	k.	k.	PROPN
ejpam-6939	498	3	then	then	ADV
ejpam-6939	498	4	v	v	INTJ
ejpam-6939	498	5	(	(	PUNCT
ejpam-6939	498	6	pa	pa	PROPN
ejpam-6939	498	7	)	)	PUNCT
ejpam-6939	498	8	and	and	CCONJ
ejpam-6939	498	9	v	v	NOUN
ejpam-6939	498	10	(	(	PUNCT
ejpam-6939	498	11	pa)∪{cj	pa)∪{cj	PROPN
ejpam-6939	498	12	:	:	PUNCT
ejpam-6939	498	13	j	j	PROPN
ejpam-6939	498	14	=	=	SYM
ejpam-6939	498	15	1	1	NUM
ejpam-6939	498	16	,	,	PUNCT
ejpam-6939	498	17	2	2	NUM
ejpam-6939	498	18	,	,	PUNCT
ejpam-6939	498	19	.	.	PUNCT
ejpam-6939	498	20	.	.	PUNCT
ejpam-6939	498	21	.	.	PUNCT
ejpam-6939	499	1	,	,	PUNCT
ejpam-6939	499	2	k	k	X
ejpam-6939	499	3	}	}	PUNCT
ejpam-6939	499	4	are	be	AUX
ejpam-6939	499	5	a	a	DET
ejpam-6939	499	6	γdc	γdc	NOUN
ejpam-6939	499	7	-set	-set	PUNCT
ejpam-6939	499	8	and	and	CCONJ
ejpam-6939	499	9	a	a	DET
ejpam-6939	499	10	γc	γc	NOUN
ejpam-6939	499	11	-	-	PUNCT
ejpam-6939	499	12	set	set	ADJ
ejpam-6939	499	13	,	,	PUNCT
ejpam-6939	499	14	respectively	respectively	ADV
ejpam-6939	499	15	,	,	PUNCT
ejpam-6939	499	16	of	of	ADP
ejpam-6939	499	17	g.	g.	PROPN
ejpam-6939	499	18	thus	thus	ADV
ejpam-6939	499	19	,	,	PUNCT
ejpam-6939	499	20	γdc	γdc	PROPN
ejpam-6939	499	21	(	(	PUNCT
ejpam-6939	499	22	g	g	NOUN
ejpam-6939	499	23	)	)	PUNCT
ejpam-6939	499	24	=	=	SYM
ejpam-6939	499	25	a	a	PRON
ejpam-6939	499	26	and	and	CCONJ
ejpam-6939	499	27	γc(g	γc(g	NUM
ejpam-6939	499	28	)	)	PUNCT
ejpam-6939	499	29	=	=	SYM
ejpam-6939	499	30	a+	a+	PUNCT
ejpam-6939	500	1	k	k	PROPN
ejpam-6939	500	2	=	=	PROPN
ejpam-6939	500	3	b.	b.	PROPN
ejpam-6939	500	4	corollary	corollary	NOUN
ejpam-6939	500	5	2	2	NUM
ejpam-6939	500	6	.	.	PUNCT
ejpam-6939	501	1	the	the	DET
ejpam-6939	501	2	difference	difference	NOUN
ejpam-6939	501	3	γc(g)−	γc(g)−	VERB
ejpam-6939	501	4	γdc	γdc	NOUN
ejpam-6939	501	5	(	(	PUNCT
ejpam-6939	501	6	g	g	NOUN
ejpam-6939	501	7	)	)	PUNCT
ejpam-6939	501	8	can	can	AUX
ejpam-6939	501	9	be	be	AUX
ejpam-6939	501	10	made	make	VERB
ejpam-6939	501	11	arbitrarily	arbitrarily	ADV
ejpam-6939	501	12	large	large	ADJ
ejpam-6939	501	13	.	.	PUNCT
ejpam-6939	502	1	a.	a.	PROPN
ejpam-6939	502	2	aradais	aradais	PROPN
ejpam-6939	502	3	,	,	PUNCT
ejpam-6939	502	4	f.	f.	PROPN
ejpam-6939	502	5	jamil	jamil	PROPN
ejpam-6939	502	6	,	,	PUNCT
ejpam-6939	502	7	s.	s.	PROPN
ejpam-6939	502	8	canoy	canoy	PROPN
ejpam-6939	502	9	/	/	SYM
ejpam-6939	502	10	eur	eur	PROPN
ejpam-6939	502	11	.	.	PUNCT
ejpam-6939	503	1	j.	j.	PROPN
ejpam-6939	503	2	pure	pure	PROPN
ejpam-6939	503	3	appl	appl	PROPN
ejpam-6939	503	4	.	.	PROPN
ejpam-6939	503	5	math	math	PROPN
ejpam-6939	503	6	,	,	PUNCT
ejpam-6939	503	7	18	18	NUM
ejpam-6939	503	8	(	(	PUNCT
ejpam-6939	503	9	4	4	NUM
ejpam-6939	503	10	)	)	PUNCT
ejpam-6939	503	11	(	(	PUNCT
ejpam-6939	503	12	2025	2025	NUM
ejpam-6939	503	13	)	)	PUNCT
ejpam-6939	503	14	,	,	PUNCT
ejpam-6939	503	15	6939	6939	NUM
ejpam-6939	503	16	8	8	NUM
ejpam-6939	503	17	of	of	ADP
ejpam-6939	503	18	14	14	NUM
ejpam-6939	503	19	•	•	NUM
ejpam-6939	503	20	•	•	NUM
ejpam-6939	503	21	•	•	NUM
ejpam-6939	503	22	•	•	NUM
ejpam-6939	503	23	•	•	NUM
ejpam-6939	503	24	•	•	NUM
ejpam-6939	503	25	•	•	NOUN
ejpam-6939	503	26	•	•	NOUN
ejpam-6939	503	27	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6939	503	28	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6939	503	29	....................................	....................................	PUNCT
ejpam-6939	504	1	....................................	....................................	PUNCT
ejpam-6939	504	2	....................................	....................................	PUNCT
ejpam-6939	505	1	....................................	....................................	PUNCT
ejpam-6939	505	2	..........	..........	PUNCT
ejpam-6939	506	1	.........	.........	PUNCT
ejpam-6939	506	2	.........	.........	PUNCT
ejpam-6939	507	1	.........	.........	PUNCT
ejpam-6939	507	2	.........	.........	PUNCT
ejpam-6939	507	3	.	.	PUNCT
ejpam-6939	508	1	....................................	....................................	PUNCT
ejpam-6939	508	2	...............	...............	PUNCT
ejpam-6939	509	1	..............	..............	PUNCT
ejpam-6939	509	2	........	........	PUNCT
ejpam-6939	509	3	....................................	....................................	PUNCT
ejpam-6939	509	4	.....................................	.....................................	PUNCT
ejpam-6939	510	1	....................................	....................................	PUNCT
ejpam-6939	510	2	...............................................	...............................................	PUNCT
ejpam-6939	511	1	....................................	....................................	PUNCT
ejpam-6939	511	2	....................................	....................................	PUNCT
ejpam-6939	512	1	............................................	............................................	PUNCT
ejpam-6939	512	2	.............................................	.............................................	PUNCT
ejpam-6939	512	3	.	.	PUNCT
ejpam-6939	512	4	.	.	PUNCT
ejpam-6939	513	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-6939	513	2	....................................	....................................	PUNCT
ejpam-6939	514	1	....................................	....................................	PUNCT
ejpam-6939	514	2	....................................	....................................	PUNCT
ejpam-6939	515	1	....................................	....................................	PUNCT
ejpam-6939	515	2	.........	.........	PUNCT
ejpam-6939	515	3	........	........	PUNCT
ejpam-6939	515	4	........	........	PUNCT
ejpam-6939	515	5	........	........	PUNCT
ejpam-6939	515	6	........	........	PUNCT
ejpam-6939	515	7	........	........	PUNCT
ejpam-6939	515	8	........	........	PUNCT
ejpam-6939	515	9	........	........	PUNCT
ejpam-6939	515	10	.......	.......	PUNCT
ejpam-6939	515	11	....................................	....................................	PUNCT
ejpam-6939	516	1	.................	.................	PUNCT
ejpam-6939	516	2	................	................	PUNCT
ejpam-6939	516	3	.............	.............	PUNCT
ejpam-6939	517	1	....................................	....................................	PUNCT
ejpam-6939	517	2	..............................................	..............................................	PUNCT
ejpam-6939	518	1	....................................	....................................	PUNCT
ejpam-6939	518	2	........................................................................	........................................................................	PUNCT
ejpam-6939	519	1	....................................	....................................	PUNCT
ejpam-6939	519	2	....................................	....................................	PUNCT
ejpam-6939	519	3	...	...	PUNCT
ejpam-6939	520	1	....................................	....................................	PUNCT
ejpam-6939	520	2	....................................	....................................	PUNCT
ejpam-6939	521	1	................................................................................................................................................................................................................	................................................................................................................................................................................................................	PUNCT
ejpam-6939	521	2	....................................	....................................	PUNCT
ejpam-6939	521	3	......................	......................	PUNCT
ejpam-6939	522	1	.....................	.....................	PUNCT
ejpam-6939	522	2	.....................	.....................	PUNCT
ejpam-6939	522	3	.....................	.....................	PUNCT
ejpam-6939	522	4	.....................	.....................	PUNCT
ejpam-6939	523	1	.....................	.....................	PUNCT
ejpam-6939	523	2	.........	.........	PUNCT
ejpam-6939	524	1	....................................	....................................	PUNCT
ejpam-6939	524	2	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-6939	525	1	....................................	....................................	PUNCT
ejpam-6939	525	2	..........	..........	PUNCT
ejpam-6939	526	1	.........	.........	PUNCT
ejpam-6939	526	2	.........	.........	PUNCT
ejpam-6939	527	1	.........	.........	PUNCT
ejpam-6939	527	2	.........	.........	PUNCT
ejpam-6939	528	1	.........	.........	PUNCT
ejpam-6939	528	2	.........	.........	PUNCT
ejpam-6939	529	1	.........	.........	PUNCT
ejpam-6939	529	2	.........	.........	PUNCT
ejpam-6939	530	1	.........	.........	PUNCT
ejpam-6939	530	2	.........	.........	PUNCT
ejpam-6939	531	1	.........	.........	PUNCT
ejpam-6939	531	2	.........	.........	PUNCT
ejpam-6939	532	1	.........	.........	PUNCT
ejpam-6939	532	2	.........	.........	PUNCT
ejpam-6939	533	1	.........	.........	PUNCT
ejpam-6939	533	2	.........	.........	PUNCT
ejpam-6939	534	1	.........	.........	PUNCT
ejpam-6939	534	2	.........	.........	PUNCT
ejpam-6939	535	1	....................................	....................................	PUNCT
ejpam-6939	535	2	....................................	....................................	PUNCT
ejpam-6939	535	3	.	.	PUNCT
ejpam-6939	535	4	.	.	PUNCT
ejpam-6939	535	5	.	.	PUNCT
ejpam-6939	535	6	.	.	PUNCT
ejpam-6939	535	7	.	.	PUNCT
ejpam-6939	536	1	.	.	PUNCT
ejpam-6939	537	1	x1	x1	NUM
ejpam-6939	538	1	x2	x2	PROPN
ejpam-6939	538	2	x3	x3	PROPN
ejpam-6939	538	3	xa−1	xa−1	PROPN
ejpam-6939	539	1	xa	xa	PROPN
ejpam-6939	540	1	g	g	PROPN
ejpam-6939	540	2	:	:	PUNCT
ejpam-6939	540	3	a1	a1	PROPN
ejpam-6939	540	4	b1	b1	PROPN
ejpam-6939	540	5	c1	c1	PROPN
ejpam-6939	540	6	a2	a2	PROPN
ejpam-6939	540	7	b2	b2	PROPN
ejpam-6939	540	8	c2	c2	PROPN
ejpam-6939	540	9	ak	ak	PROPN
ejpam-6939	540	10	bk	bk	PROPN
ejpam-6939	540	11	ck	ck	PROPN
ejpam-6939	540	12	figure	figure	NOUN
ejpam-6939	540	13	6	6	NUM
ejpam-6939	540	14	:	:	PUNCT
ejpam-6939	540	15	graph	graph	VERB
ejpam-6939	540	16	g	g	NOUN
ejpam-6939	540	17	for	for	ADP
ejpam-6939	540	18	which	which	PRON
ejpam-6939	540	19	γc(g	γc(g	PUNCT
ejpam-6939	540	20	)	)	PUNCT
ejpam-6939	540	21	=	=	PUNCT
ejpam-6939	540	22	γd	γd	ADP
ejpam-6939	540	23	c	c	PROPN
ejpam-6939	540	24	(	(	PUNCT
ejpam-6939	540	25	g	g	NOUN
ejpam-6939	540	26	)	)	PUNCT
ejpam-6939	540	27	+	+	CCONJ
ejpam-6939	541	1	k	k	PROPN
ejpam-6939	541	2	4	4	X
ejpam-6939	541	3	.	.	PUNCT
ejpam-6939	542	1	in	in	ADP
ejpam-6939	542	2	the	the	DET
ejpam-6939	542	3	join	join	NOUN
ejpam-6939	542	4	of	of	ADP
ejpam-6939	542	5	graphs	graph	NOUN
ejpam-6939	542	6	observation	observation	NOUN
ejpam-6939	542	7	2	2	NUM
ejpam-6939	542	8	.	.	PUNCT
ejpam-6939	542	9	for	for	ADP
ejpam-6939	542	10	any	any	DET
ejpam-6939	542	11	graphs	graph	NOUN
ejpam-6939	542	12	g	g	NOUN
ejpam-6939	542	13	and	and	CCONJ
ejpam-6939	542	14	h	h	NOUN
ejpam-6939	542	15	,	,	PUNCT
ejpam-6939	542	16	if	if	SCONJ
ejpam-6939	542	17	s	s	VERB
ejpam-6939	542	18	⊆	⊆	NUM
ejpam-6939	542	19	v	v	NOUN
ejpam-6939	542	20	(	(	PUNCT
ejpam-6939	542	21	g	g	PROPN
ejpam-6939	542	22	+	+	NOUN
ejpam-6939	542	23	h	h	NOUN
ejpam-6939	542	24	)	)	PUNCT
ejpam-6939	542	25	intersects	intersect	NOUN
ejpam-6939	542	26	both	both	PRON
ejpam-6939	542	27	v	v	NOUN
ejpam-6939	542	28	(	(	PUNCT
ejpam-6939	542	29	g	g	NOUN
ejpam-6939	542	30	)	)	PUNCT
ejpam-6939	542	31	and	and	CCONJ
ejpam-6939	542	32	v	v	NOUN
ejpam-6939	542	33	(	(	PUNCT
ejpam-6939	542	34	h	h	NOUN
ejpam-6939	542	35	)	)	PUNCT
ejpam-6939	542	36	,	,	PUNCT
ejpam-6939	542	37	then	then	ADV
ejpam-6939	542	38	s	s	VERB
ejpam-6939	542	39	is	be	AUX
ejpam-6939	542	40	a	a	DET
ejpam-6939	542	41	connected	connected	ADJ
ejpam-6939	542	42	dominating	dominating	NOUN
ejpam-6939	542	43	set	set	NOUN
ejpam-6939	542	44	,	,	PUNCT
ejpam-6939	542	45	hence	hence	ADV
ejpam-6939	542	46	is	be	AUX
ejpam-6939	542	47	a	a	DET
ejpam-6939	542	48	connected	connected	ADJ
ejpam-6939	542	49	disjunctive	disjunctive	ADJ
ejpam-6939	542	50	dominating	dominating	NOUN
ejpam-6939	542	51	set	set	NOUN
ejpam-6939	542	52	of	of	ADP
ejpam-6939	542	53	g+h	g+h	PROPN
ejpam-6939	542	54	.	.	PUNCT
ejpam-6939	543	1	theorem	theorem	NOUN
ejpam-6939	543	2	1	1	NUM
ejpam-6939	543	3	.	.	PUNCT
ejpam-6939	544	1	let	let	VERB
ejpam-6939	544	2	g	g	NOUN
ejpam-6939	545	1	and	and	CCONJ
ejpam-6939	545	2	h	h	NOUN
ejpam-6939	545	3	be	be	VERB
ejpam-6939	545	4	any	any	DET
ejpam-6939	545	5	graphs	graph	NOUN
ejpam-6939	545	6	,	,	PUNCT
ejpam-6939	545	7	and	and	CCONJ
ejpam-6939	545	8	s	s	VERB
ejpam-6939	545	9	⊆	⊆	NUM
ejpam-6939	545	10	v	v	NOUN
ejpam-6939	545	11	(	(	PUNCT
ejpam-6939	545	12	g	g	PROPN
ejpam-6939	545	13	+	+	NOUN
ejpam-6939	545	14	h	h	NOUN
ejpam-6939	545	15	)	)	PUNCT
ejpam-6939	545	16	.	.	PUNCT
ejpam-6939	546	1	then	then	ADV
ejpam-6939	546	2	s	s	VERB
ejpam-6939	546	3	is	be	AUX
ejpam-6939	546	4	a	a	DET
ejpam-6939	546	5	connected	connected	ADJ
ejpam-6939	546	6	disjunctive	disjunctive	ADJ
ejpam-6939	546	7	dominating	dominating	NOUN
ejpam-6939	546	8	set	set	NOUN
ejpam-6939	546	9	of	of	ADP
ejpam-6939	546	10	g+h	g+h	PROPN
ejpam-6939	546	11	if	if	SCONJ
ejpam-6939	546	12	and	and	CCONJ
ejpam-6939	546	13	only	only	ADV
ejpam-6939	546	14	if	if	SCONJ
ejpam-6939	546	15	one	one	NUM
ejpam-6939	546	16	of	of	ADP
ejpam-6939	546	17	the	the	DET
ejpam-6939	546	18	following	follow	VERB
ejpam-6939	546	19	holds	hold	VERB
ejpam-6939	546	20	:	:	PUNCT
ejpam-6939	546	21	(	(	PUNCT
ejpam-6939	546	22	i	i	NOUN
ejpam-6939	546	23	)	)	PUNCT
ejpam-6939	546	24	s	s	VERB
ejpam-6939	546	25	⊆	⊆	NUM
ejpam-6939	546	26	v	v	NOUN
ejpam-6939	546	27	(	(	PUNCT
ejpam-6939	546	28	g	g	NOUN
ejpam-6939	546	29	)	)	PUNCT
ejpam-6939	546	30	(	(	PUNCT
ejpam-6939	546	31	resp	resp	NOUN
ejpam-6939	546	32	.	.	PUNCT
ejpam-6939	547	1	s	s	PART
ejpam-6939	547	2	⊆	⊆	NUM
ejpam-6939	547	3	v	v	NOUN
ejpam-6939	547	4	(	(	PUNCT
ejpam-6939	547	5	h	h	NOUN
ejpam-6939	547	6	)	)	PUNCT
ejpam-6939	547	7	)	)	PUNCT
ejpam-6939	547	8	for	for	ADP
ejpam-6939	547	9	which	which	PRON
ejpam-6939	547	10	either	either	CCONJ
ejpam-6939	547	11	|s|	|s|	PROPN
ejpam-6939	547	12	≥	≥	NOUN
ejpam-6939	547	13	2	2	NUM
ejpam-6939	547	14	and	and	CCONJ
ejpam-6939	547	15	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	547	16	is	be	AUX
ejpam-6939	547	17	connected	connect	VERB
ejpam-6939	547	18	or	or	CCONJ
ejpam-6939	547	19	s	s	VERB
ejpam-6939	547	20	=	=	X
ejpam-6939	547	21	{	{	PUNCT
ejpam-6939	547	22	x	x	NOUN
ejpam-6939	547	23	}	}	PUNCT
ejpam-6939	547	24	where	where	SCONJ
ejpam-6939	547	25	ng[x	ng[x	PROPN
ejpam-6939	547	26	]	]	X
ejpam-6939	547	27	=	=	SYM
ejpam-6939	547	28	v	v	X
ejpam-6939	547	29	(	(	PUNCT
ejpam-6939	547	30	g	g	NOUN
ejpam-6939	547	31	)	)	PUNCT
ejpam-6939	547	32	(	(	PUNCT
ejpam-6939	547	33	resp	resp	NOUN
ejpam-6939	547	34	.	.	PUNCT
ejpam-6939	548	1	nh	nh	PROPN
ejpam-6939	549	1	[	[	X
ejpam-6939	549	2	x	x	X
ejpam-6939	549	3	]	]	X
ejpam-6939	549	4	=	=	SYM
ejpam-6939	549	5	v	v	ADJ
ejpam-6939	549	6	(	(	PUNCT
ejpam-6939	549	7	h	h	NOUN
ejpam-6939	549	8	)	)	PUNCT
ejpam-6939	549	9	)	)	PUNCT
ejpam-6939	549	10	.	.	PUNCT
ejpam-6939	550	1	(	(	PUNCT
ejpam-6939	550	2	ii	ii	X
ejpam-6939	550	3	)	)	PUNCT
ejpam-6939	550	4	s	s	PART
ejpam-6939	550	5	∩	∩	ADJ
ejpam-6939	550	6	v	v	ADJ
ejpam-6939	550	7	(	(	PUNCT
ejpam-6939	550	8	g	g	NOUN
ejpam-6939	550	9	)	)	PUNCT
ejpam-6939	550	10	̸=	̸=	PROPN
ejpam-6939	550	11	∅	∅	NOUN
ejpam-6939	550	12	and	and	CCONJ
ejpam-6939	550	13	s	s	VERB
ejpam-6939	550	14	∩	∩	ADJ
ejpam-6939	550	15	v	v	ADJ
ejpam-6939	550	16	(	(	PUNCT
ejpam-6939	550	17	h	h	NOUN
ejpam-6939	550	18	)	)	PUNCT
ejpam-6939	550	19	̸=	̸=	PROPN
ejpam-6939	550	20	∅.	∅.	PRON
ejpam-6939	550	21	proof	proof	NOUN
ejpam-6939	550	22	.	.	PUNCT
ejpam-6939	551	1	let	let	VERB
ejpam-6939	551	2	s	s	PRON
ejpam-6939	551	3	be	be	AUX
ejpam-6939	551	4	a	a	DET
ejpam-6939	551	5	connected	connected	ADJ
ejpam-6939	551	6	disjunctive	disjunctive	ADJ
ejpam-6939	551	7	dominating	dominating	NOUN
ejpam-6939	551	8	set	set	NOUN
ejpam-6939	551	9	of	of	ADP
ejpam-6939	551	10	g	g	PROPN
ejpam-6939	551	11	+	+	PROPN
ejpam-6939	551	12	h.	h.	PROPN
ejpam-6939	551	13	suppose	suppose	VERB
ejpam-6939	551	14	that	that	SCONJ
ejpam-6939	551	15	(	(	PUNCT
ejpam-6939	551	16	ii	ii	NOUN
ejpam-6939	551	17	)	)	PUNCT
ejpam-6939	551	18	does	do	AUX
ejpam-6939	551	19	not	not	PART
ejpam-6939	551	20	hold	hold	VERB
ejpam-6939	551	21	for	for	ADP
ejpam-6939	551	22	s	s	NOUN
ejpam-6939	551	23	,	,	PUNCT
ejpam-6939	551	24	say	say	VERB
ejpam-6939	551	25	s	s	PRON
ejpam-6939	551	26	⊆	⊆	NUM
ejpam-6939	551	27	v	v	NOUN
ejpam-6939	551	28	(	(	PUNCT
ejpam-6939	551	29	g	g	NOUN
ejpam-6939	551	30	)	)	PUNCT
ejpam-6939	551	31	.	.	PUNCT
ejpam-6939	552	1	the	the	DET
ejpam-6939	552	2	conclusion	conclusion	NOUN
ejpam-6939	552	3	is	be	AUX
ejpam-6939	552	4	obvious	obvious	ADJ
ejpam-6939	552	5	for	for	ADP
ejpam-6939	552	6	a	a	DET
ejpam-6939	552	7	trivial	trivial	ADJ
ejpam-6939	552	8	graph	graph	NOUN
ejpam-6939	552	9	g.	g.	NOUN
ejpam-6939	552	10	suppose	suppose	VERB
ejpam-6939	552	11	that	that	SCONJ
ejpam-6939	552	12	|v	|v	PROPN
ejpam-6939	552	13	(	(	PUNCT
ejpam-6939	552	14	g)|	g)|	X
ejpam-6939	552	15	≥	≥	NOUN
ejpam-6939	552	16	2	2	NUM
ejpam-6939	552	17	.	.	PUNCT
ejpam-6939	552	18	if	if	SCONJ
ejpam-6939	552	19	|s|	|s|	NOUN
ejpam-6939	552	20	≥	≥	NOUN
ejpam-6939	552	21	2	2	NUM
ejpam-6939	552	22	,	,	PUNCT
ejpam-6939	552	23	then	then	ADV
ejpam-6939	552	24	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	552	25	is	be	AUX
ejpam-6939	552	26	connected	connect	VERB
ejpam-6939	552	27	subgraph	subgraph	NOUN
ejpam-6939	552	28	of	of	ADP
ejpam-6939	552	29	g.	g.	PROPN
ejpam-6939	552	30	suppose	suppose	VERB
ejpam-6939	552	31	that	that	SCONJ
ejpam-6939	552	32	|s|	|s|	NOUN
ejpam-6939	552	33	=	=	SYM
ejpam-6939	552	34	1	1	NUM
ejpam-6939	552	35	,	,	PUNCT
ejpam-6939	552	36	say	say	VERB
ejpam-6939	552	37	s	s	X
ejpam-6939	552	38	=	=	PUNCT
ejpam-6939	552	39	{	{	PUNCT
ejpam-6939	552	40	x	x	NOUN
ejpam-6939	552	41	}	}	PUNCT
ejpam-6939	552	42	.	.	PUNCT
ejpam-6939	553	1	since	since	SCONJ
ejpam-6939	553	2	s	s	PROPN
ejpam-6939	553	3	is	be	AUX
ejpam-6939	553	4	a	a	DET
ejpam-6939	553	5	disjunctive	disjunctive	ADJ
ejpam-6939	553	6	dominating	dominating	NOUN
ejpam-6939	553	7	set	set	NOUN
ejpam-6939	553	8	,	,	PUNCT
ejpam-6939	553	9	v	v	X
ejpam-6939	553	10	(	(	PUNCT
ejpam-6939	553	11	g	g	NOUN
ejpam-6939	553	12	)	)	PUNCT
ejpam-6939	553	13	=	=	SYM
ejpam-6939	553	14	ng[x	ng[x	PROPN
ejpam-6939	553	15	]	]	PUNCT
ejpam-6939	553	16	.	.	PUNCT
ejpam-6939	554	1	this	this	PRON
ejpam-6939	554	2	proves	prove	VERB
ejpam-6939	554	3	(	(	PUNCT
ejpam-6939	554	4	i	i	NOUN
ejpam-6939	554	5	)	)	PUNCT
ejpam-6939	554	6	.	.	PUNCT
ejpam-6939	555	1	conversely	conversely	ADV
ejpam-6939	555	2	,	,	PUNCT
ejpam-6939	555	3	suppose	suppose	VERB
ejpam-6939	555	4	that	that	SCONJ
ejpam-6939	555	5	s	s	VERB
ejpam-6939	555	6	⊆	⊆	NUM
ejpam-6939	555	7	v	v	NOUN
ejpam-6939	555	8	(	(	PUNCT
ejpam-6939	555	9	g	g	NOUN
ejpam-6939	555	10	)	)	PUNCT
ejpam-6939	555	11	satisfying	satisfy	VERB
ejpam-6939	555	12	property	property	NOUN
ejpam-6939	555	13	(	(	PUNCT
ejpam-6939	555	14	i	i	NOUN
ejpam-6939	555	15	)	)	PUNCT
ejpam-6939	555	16	.	.	PUNCT
ejpam-6939	556	1	then	then	ADV
ejpam-6939	556	2	v	v	X
ejpam-6939	556	3	(	(	PUNCT
ejpam-6939	556	4	h	h	NOUN
ejpam-6939	556	5	)	)	PUNCT
ejpam-6939	556	6	⊆	⊆	NUM
ejpam-6939	556	7	ng+h(s	ng+h(s	NUM
ejpam-6939	556	8	)	)	PUNCT
ejpam-6939	556	9	.	.	PUNCT
ejpam-6939	557	1	if	if	SCONJ
ejpam-6939	557	2	s	s	VERB
ejpam-6939	557	3	=	=	X
ejpam-6939	557	4	{	{	PUNCT
ejpam-6939	557	5	x	x	NOUN
ejpam-6939	557	6	}	}	PUNCT
ejpam-6939	557	7	for	for	ADP
ejpam-6939	557	8	which	which	PRON
ejpam-6939	557	9	ng[x	ng[x	PROPN
ejpam-6939	557	10	]	]	X
ejpam-6939	557	11	=	=	SYM
ejpam-6939	557	12	v	v	X
ejpam-6939	557	13	(	(	PUNCT
ejpam-6939	557	14	g	g	NOUN
ejpam-6939	557	15	)	)	PUNCT
ejpam-6939	557	16	,	,	PUNCT
ejpam-6939	557	17	then	then	ADV
ejpam-6939	557	18	s	s	VERB
ejpam-6939	557	19	is	be	AUX
ejpam-6939	557	20	a	a	DET
ejpam-6939	557	21	dominating	dominating	NOUN
ejpam-6939	557	22	set	set	NOUN
ejpam-6939	557	23	,	,	PUNCT
ejpam-6939	557	24	hence	hence	ADV
ejpam-6939	557	25	a	a	DET
ejpam-6939	557	26	connected	connected	ADJ
ejpam-6939	557	27	disjunctive	disjunctive	ADJ
ejpam-6939	557	28	dominating	dominating	NOUN
ejpam-6939	557	29	set	set	NOUN
ejpam-6939	557	30	of	of	ADP
ejpam-6939	557	31	g+h	g+h	PROPN
ejpam-6939	557	32	.	.	PUNCT
ejpam-6939	558	1	suppose	suppose	VERB
ejpam-6939	558	2	that	that	SCONJ
ejpam-6939	558	3	|s|	|s|	NOUN
ejpam-6939	558	4	≥	≥	NOUN
ejpam-6939	558	5	2	2	NUM
ejpam-6939	558	6	.	.	PUNCT
ejpam-6939	559	1	let	let	VERB
ejpam-6939	559	2	x	x	SYM
ejpam-6939	559	3	∈	∈	PROPN
ejpam-6939	559	4	v	v	X
ejpam-6939	559	5	(	(	PUNCT
ejpam-6939	559	6	g)\s	g)\s	NOUN
ejpam-6939	559	7	,	,	PUNCT
ejpam-6939	559	8	and	and	CCONJ
ejpam-6939	559	9	suppose	suppose	VERB
ejpam-6939	559	10	that	that	SCONJ
ejpam-6939	559	11	x	x	SYM
ejpam-6939	559	12	/∈	/∈	NOUN
ejpam-6939	559	13	ng(s	ng(s	NUM
ejpam-6939	559	14	)	)	PUNCT
ejpam-6939	559	15	.	.	PUNCT
ejpam-6939	560	1	pick	pick	VERB
ejpam-6939	560	2	any	any	DET
ejpam-6939	560	3	distinct	distinct	ADJ
ejpam-6939	560	4	u	u	NOUN
ejpam-6939	560	5	,	,	PUNCT
ejpam-6939	560	6	v	v	PROPN
ejpam-6939	560	7	∈	∈	PROPN
ejpam-6939	560	8	s.	s.	PROPN
ejpam-6939	560	9	then	then	ADV
ejpam-6939	560	10	dg+h(x	dg+h(x	PROPN
ejpam-6939	560	11	,	,	PUNCT
ejpam-6939	560	12	u	u	NOUN
ejpam-6939	560	13	)	)	PUNCT
ejpam-6939	560	14	=	=	SYM
ejpam-6939	560	15	2	2	NUM
ejpam-6939	560	16	=	=	SYM
ejpam-6939	560	17	dg+h(x	dg+h(x	PROPN
ejpam-6939	560	18	,	,	PUNCT
ejpam-6939	560	19	v	v	NOUN
ejpam-6939	560	20	)	)	PUNCT
ejpam-6939	560	21	.	.	PUNCT
ejpam-6939	561	1	thus	thus	ADV
ejpam-6939	561	2	,	,	PUNCT
ejpam-6939	561	3	s	s	VERB
ejpam-6939	561	4	is	be	AUX
ejpam-6939	561	5	a	a	DET
ejpam-6939	561	6	disjunctive	disjunctive	ADJ
ejpam-6939	561	7	dominating	dominating	NOUN
ejpam-6939	561	8	set	set	NOUN
ejpam-6939	561	9	of	of	ADP
ejpam-6939	561	10	g	g	PROPN
ejpam-6939	561	11	+	+	PROPN
ejpam-6939	561	12	h.	h.	PROPN
ejpam-6939	561	13	since	since	SCONJ
ejpam-6939	561	14	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	561	15	is	be	AUX
ejpam-6939	561	16	connected	connect	VERB
ejpam-6939	561	17	,	,	PUNCT
ejpam-6939	561	18	the	the	DET
ejpam-6939	561	19	conclusion	conclusion	NOUN
ejpam-6939	561	20	follows	follow	VERB
ejpam-6939	561	21	.	.	PUNCT
ejpam-6939	562	1	similarly	similarly	ADV
ejpam-6939	562	2	,	,	PUNCT
ejpam-6939	562	3	if	if	SCONJ
ejpam-6939	562	4	s	s	VERB
ejpam-6939	562	5	⊆	⊆	NUM
ejpam-6939	562	6	v	v	NOUN
ejpam-6939	562	7	(	(	PUNCT
ejpam-6939	562	8	h	h	NOUN
ejpam-6939	562	9	)	)	PUNCT
ejpam-6939	562	10	for	for	ADP
ejpam-6939	562	11	which	which	PRON
ejpam-6939	562	12	either	either	CCONJ
ejpam-6939	562	13	|s|	|s|	PROPN
ejpam-6939	562	14	≥	≥	NOUN
ejpam-6939	562	15	2	2	NUM
ejpam-6939	562	16	and	and	CCONJ
ejpam-6939	562	17	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	562	18	is	be	AUX
ejpam-6939	562	19	connected	connect	VERB
ejpam-6939	562	20	or	or	CCONJ
ejpam-6939	562	21	s	s	AUX
ejpam-6939	562	22	=	=	X
ejpam-6939	562	23	{	{	PUNCT
ejpam-6939	562	24	x	x	NOUN
ejpam-6939	562	25	}	}	PUNCT
ejpam-6939	562	26	where	where	SCONJ
ejpam-6939	562	27	nh	nh	PROPN
ejpam-6939	563	1	[	[	X
ejpam-6939	563	2	x	x	X
ejpam-6939	563	3	]	]	X
ejpam-6939	563	4	=	=	SYM
ejpam-6939	563	5	v	v	ADJ
ejpam-6939	563	6	(	(	PUNCT
ejpam-6939	563	7	h	h	NOUN
ejpam-6939	563	8	)	)	PUNCT
ejpam-6939	563	9	,	,	PUNCT
ejpam-6939	563	10	then	then	ADV
ejpam-6939	563	11	s	s	VERB
ejpam-6939	563	12	is	be	AUX
ejpam-6939	563	13	a	a	DET
ejpam-6939	563	14	connected	connected	ADJ
ejpam-6939	563	15	disjunctive	disjunctive	ADJ
ejpam-6939	563	16	dominating	dominating	NOUN
ejpam-6939	563	17	set	set	NOUN
ejpam-6939	563	18	of	of	ADP
ejpam-6939	563	19	g+h	g+h	PROPN
ejpam-6939	563	20	.	.	PUNCT
ejpam-6939	564	1	observation	observation	NOUN
ejpam-6939	564	2	2	2	NUM
ejpam-6939	564	3	finally	finally	ADV
ejpam-6939	564	4	establishes	establish	VERB
ejpam-6939	564	5	the	the	DET
ejpam-6939	564	6	necessity	necessity	NOUN
ejpam-6939	564	7	proof	proof	NOUN
ejpam-6939	564	8	.	.	PUNCT
ejpam-6939	565	1	corollary	corollary	ADJ
ejpam-6939	565	2	3	3	NUM
ejpam-6939	565	3	.	.	PUNCT
ejpam-6939	566	1	for	for	ADP
ejpam-6939	566	2	nontrivial	nontrivial	ADJ
ejpam-6939	566	3	graphs	graph	NOUN
ejpam-6939	566	4	g	g	NOUN
ejpam-6939	566	5	and	and	CCONJ
ejpam-6939	566	6	h	h	NOUN
ejpam-6939	566	7	,	,	PUNCT
ejpam-6939	566	8	γdc	γdc	PROPN
ejpam-6939	566	9	(	(	PUNCT
ejpam-6939	566	10	g+h	g+h	PROPN
ejpam-6939	566	11	)	)	PUNCT
ejpam-6939	567	1	=	=	SYM
ejpam-6939	567	2	min{γ(g	min{γ(g	PROPN
ejpam-6939	567	3	)	)	PUNCT
ejpam-6939	567	4	,	,	PUNCT
ejpam-6939	567	5	γ(h	γ(h	NOUN
ejpam-6939	567	6	)	)	PUNCT
ejpam-6939	567	7	,	,	PUNCT
ejpam-6939	567	8	2	2	NUM
ejpam-6939	567	9	}	}	PUNCT
ejpam-6939	567	10	.	.	PUNCT
ejpam-6939	568	1	5	5	X
ejpam-6939	568	2	.	.	X
ejpam-6939	568	3	in	in	ADP
ejpam-6939	568	4	the	the	DET
ejpam-6939	568	5	corona	corona	NOUN
ejpam-6939	568	6	of	of	ADP
ejpam-6939	568	7	graphs	graph	NOUN
ejpam-6939	568	8	in	in	ADP
ejpam-6939	568	9	a	a	DET
ejpam-6939	568	10	corona	corona	NOUN
ejpam-6939	568	11	g	g	ADP
ejpam-6939	568	12	◦	◦	NOUN
ejpam-6939	568	13	h	h	NOUN
ejpam-6939	568	14	,	,	PUNCT
ejpam-6939	568	15	we	we	PRON
ejpam-6939	568	16	denote	denote	VERB
ejpam-6939	568	17	by	by	ADP
ejpam-6939	568	18	hv	hv	PROPN
ejpam-6939	568	19	that	that	DET
ejpam-6939	568	20	copy	copy	NOUN
ejpam-6939	568	21	of	of	ADP
ejpam-6939	568	22	h	h	PRON
ejpam-6939	568	23	which	which	PRON
ejpam-6939	568	24	is	be	AUX
ejpam-6939	568	25	being	be	AUX
ejpam-6939	568	26	joined	join	VERB
ejpam-6939	568	27	to	to	ADP
ejpam-6939	568	28	the	the	DET
ejpam-6939	568	29	vertex	vertex	NOUN
ejpam-6939	568	30	v	v	NOUN
ejpam-6939	568	31	of	of	ADP
ejpam-6939	568	32	g.	g.	PROPN
ejpam-6939	568	33	we	we	PRON
ejpam-6939	568	34	also	also	ADV
ejpam-6939	568	35	denote	denote	VERB
ejpam-6939	568	36	by	by	ADP
ejpam-6939	568	37	hv	hv	PROPN
ejpam-6939	568	38	+	+	NOUN
ejpam-6939	568	39	v	v	ADP
ejpam-6939	568	40	that	that	DET
ejpam-6939	568	41	subgraph	subgraph	PROPN
ejpam-6939	568	42	⟨{v	⟨{v	PROPN
ejpam-6939	568	43	}	}	PUNCT
ejpam-6939	568	44	∪	∪	VERB
ejpam-6939	568	45	v	v	NOUN
ejpam-6939	568	46	(	(	PUNCT
ejpam-6939	568	47	hv)⟩	hv)⟩	NOUN
ejpam-6939	568	48	of	of	ADP
ejpam-6939	568	49	g	g	PROPN
ejpam-6939	568	50	◦	◦	NOUN
ejpam-6939	568	51	h	h	NOUN
ejpam-6939	568	52	induced	induce	VERB
ejpam-6939	568	53	by	by	ADP
ejpam-6939	568	54	a.	a.	PROPN
ejpam-6939	568	55	aradais	aradais	PROPN
ejpam-6939	568	56	,	,	PUNCT
ejpam-6939	568	57	f.	f.	PROPN
ejpam-6939	568	58	jamil	jamil	PROPN
ejpam-6939	568	59	,	,	PUNCT
ejpam-6939	568	60	s.	s.	PROPN
ejpam-6939	568	61	canoy	canoy	PROPN
ejpam-6939	568	62	/	/	SYM
ejpam-6939	568	63	eur	eur	PROPN
ejpam-6939	568	64	.	.	PUNCT
ejpam-6939	569	1	j.	j.	PROPN
ejpam-6939	569	2	pure	pure	PROPN
ejpam-6939	569	3	appl	appl	PROPN
ejpam-6939	569	4	.	.	PROPN
ejpam-6939	569	5	math	math	PROPN
ejpam-6939	569	6	,	,	PUNCT
ejpam-6939	569	7	18	18	NUM
ejpam-6939	569	8	(	(	PUNCT
ejpam-6939	569	9	4	4	NUM
ejpam-6939	569	10	)	)	PUNCT
ejpam-6939	569	11	(	(	PUNCT
ejpam-6939	569	12	2025	2025	NUM
ejpam-6939	569	13	)	)	PUNCT
ejpam-6939	569	14	,	,	PUNCT
ejpam-6939	569	15	6939	6939	NUM
ejpam-6939	569	16	9	9	NUM
ejpam-6939	569	17	of	of	ADP
ejpam-6939	569	18	14	14	NUM
ejpam-6939	569	19	{	{	PUNCT
ejpam-6939	569	20	v	v	NOUN
ejpam-6939	569	21	}	}	PUNCT
ejpam-6939	569	22	∪	∪	NOUN
ejpam-6939	569	23	v	v	NOUN
ejpam-6939	569	24	(	(	PUNCT
ejpam-6939	569	25	hv	hv	PROPN
ejpam-6939	569	26	)	)	PUNCT
ejpam-6939	569	27	.	.	PUNCT
ejpam-6939	570	1	thus	thus	ADV
ejpam-6939	570	2	,	,	PUNCT
ejpam-6939	570	3	v	v	INTJ
ejpam-6939	570	4	(	(	PUNCT
ejpam-6939	570	5	g	g	PROPN
ejpam-6939	570	6	◦	◦	NOUN
ejpam-6939	570	7	h	h	NOUN
ejpam-6939	570	8	)	)	PUNCT
ejpam-6939	570	9	=	=	NOUN
ejpam-6939	570	10	v	v	X
ejpam-6939	570	11	(	(	PUNCT
ejpam-6939	570	12	g	g	NOUN
ejpam-6939	570	13	)	)	PUNCT
ejpam-6939	570	14	∪	∪	NOUN
ejpam-6939	570	15	(	(	PUNCT
ejpam-6939	570	16	∪v∈v	∪v∈v	X
ejpam-6939	570	17	(	(	PUNCT
ejpam-6939	570	18	g)v	g)v	X
ejpam-6939	570	19	(	(	PUNCT
ejpam-6939	570	20	hv	hv	NOUN
ejpam-6939	570	21	)	)	PUNCT
ejpam-6939	570	22	)	)	PUNCT
ejpam-6939	570	23	.	.	PUNCT
ejpam-6939	571	1	theorem	theorem	NOUN
ejpam-6939	571	2	2	2	NUM
ejpam-6939	571	3	.	.	PUNCT
ejpam-6939	572	1	[	[	X
ejpam-6939	572	2	4	4	X
ejpam-6939	572	3	]	]	PUNCT
ejpam-6939	572	4	let	let	VERB
ejpam-6939	572	5	g	g	PRON
ejpam-6939	572	6	be	be	AUX
ejpam-6939	572	7	a	a	DET
ejpam-6939	572	8	nontrivial	nontrivial	ADJ
ejpam-6939	572	9	connected	connect	VERB
ejpam-6939	572	10	graph	graph	NOUN
ejpam-6939	572	11	and	and	CCONJ
ejpam-6939	572	12	h	h	NOUN
ejpam-6939	572	13	any	any	DET
ejpam-6939	572	14	graph	graph	NOUN
ejpam-6939	572	15	,	,	PUNCT
ejpam-6939	572	16	and	and	CCONJ
ejpam-6939	572	17	let	let	VERB
ejpam-6939	572	18	s	s	PRON
ejpam-6939	572	19	⊆	⊆	NUM
ejpam-6939	572	20	v	v	NOUN
ejpam-6939	572	21	(	(	PUNCT
ejpam-6939	572	22	g	g	PROPN
ejpam-6939	572	23	◦	◦	NOUN
ejpam-6939	572	24	h	h	NOUN
ejpam-6939	572	25	)	)	PUNCT
ejpam-6939	572	26	.	.	PUNCT
ejpam-6939	573	1	then	then	ADV
ejpam-6939	573	2	s	s	VERB
ejpam-6939	573	3	is	be	AUX
ejpam-6939	573	4	a	a	DET
ejpam-6939	573	5	disjunctive	disjunctive	ADJ
ejpam-6939	573	6	dominating	dominating	NOUN
ejpam-6939	573	7	set	set	NOUN
ejpam-6939	573	8	of	of	ADP
ejpam-6939	573	9	g	g	PROPN
ejpam-6939	573	10	◦	◦	NOUN
ejpam-6939	573	11	h	h	NOUN
ejpam-6939	573	12	if	if	SCONJ
ejpam-6939	574	1	and	and	CCONJ
ejpam-6939	574	2	only	only	ADV
ejpam-6939	574	3	if	if	SCONJ
ejpam-6939	574	4	each	each	PRON
ejpam-6939	574	5	of	of	ADP
ejpam-6939	574	6	the	the	DET
ejpam-6939	574	7	following	following	NOUN
ejpam-6939	574	8	holds	hold	VERB
ejpam-6939	574	9	for	for	ADP
ejpam-6939	574	10	s	s	PRON
ejpam-6939	574	11	:	:	PUNCT
ejpam-6939	574	12	(	(	PUNCT
ejpam-6939	574	13	i	i	NOUN
ejpam-6939	574	14	)	)	PUNCT
ejpam-6939	574	15	|s	|s	PROPN
ejpam-6939	575	1	∩ng(v)|	∩ng(v)|	PROPN
ejpam-6939	575	2	≥	≥	NUM
ejpam-6939	575	3	2	2	NUM
ejpam-6939	575	4	for	for	ADP
ejpam-6939	575	5	all	all	PRON
ejpam-6939	575	6	v	v	ADP
ejpam-6939	575	7	∈	∈	NOUN
ejpam-6939	575	8	v	v	NOUN
ejpam-6939	575	9	(	(	PUNCT
ejpam-6939	575	10	g	g	NOUN
ejpam-6939	575	11	)	)	PUNCT
ejpam-6939	575	12	\	\	PUNCT
ejpam-6939	576	1	s	s	PART
ejpam-6939	576	2	with	with	ADP
ejpam-6939	576	3	s	s	PROPN
ejpam-6939	576	4	∩	∩	ADJ
ejpam-6939	576	5	v	v	X
ejpam-6939	576	6	(	(	PUNCT
ejpam-6939	576	7	hv	hv	NOUN
ejpam-6939	576	8	)	)	PUNCT
ejpam-6939	576	9	=	=	NOUN
ejpam-6939	576	10	∅	∅	NOUN
ejpam-6939	576	11	;	;	PUNCT
ejpam-6939	576	12	(	(	PUNCT
ejpam-6939	576	13	ii	ii	X
ejpam-6939	576	14	)	)	PUNCT
ejpam-6939	576	15	|s	|s	PROPN
ejpam-6939	576	16	∩	∩	PROPN
ejpam-6939	576	17	v	v	NOUN
ejpam-6939	576	18	(	(	PUNCT
ejpam-6939	576	19	hv)|	hv)|	X
ejpam-6939	576	20	≥	≥	NOUN
ejpam-6939	576	21	1	1	NUM
ejpam-6939	576	22	for	for	ADP
ejpam-6939	576	23	all	all	PRON
ejpam-6939	576	24	v	v	ADP
ejpam-6939	576	25	∈	∈	NUM
ejpam-6939	576	26	v	v	NOUN
ejpam-6939	576	27	(	(	PUNCT
ejpam-6939	576	28	g	g	NOUN
ejpam-6939	576	29	)	)	PUNCT
ejpam-6939	576	30	\	\	PROPN
ejpam-6939	577	1	s	s	PART
ejpam-6939	577	2	with	with	ADP
ejpam-6939	577	3	|s	|s	PROPN
ejpam-6939	578	1	∩ng(v)|	∩ng(v)|	PROPN
ejpam-6939	578	2	=	=	SYM
ejpam-6939	578	3	1	1	NUM
ejpam-6939	578	4	;	;	PUNCT
ejpam-6939	578	5	and	and	CCONJ
ejpam-6939	578	6	(	(	PUNCT
ejpam-6939	578	7	iii	iii	X
ejpam-6939	578	8	)	)	PUNCT
ejpam-6939	578	9	s	s	PART
ejpam-6939	578	10	∩	∩	ADJ
ejpam-6939	578	11	v	v	X
ejpam-6939	578	12	(	(	PUNCT
ejpam-6939	578	13	hv	hv	X
ejpam-6939	578	14	)	)	PUNCT
ejpam-6939	578	15	is	be	AUX
ejpam-6939	578	16	a	a	DET
ejpam-6939	578	17	disjunctive	disjunctive	ADJ
ejpam-6939	578	18	dominating	dominating	NOUN
ejpam-6939	578	19	set	set	NOUN
ejpam-6939	578	20	of	of	ADP
ejpam-6939	578	21	hv	hv	PROPN
ejpam-6939	578	22	+	+	X
ejpam-6939	578	23	v	v	NOUN
ejpam-6939	578	24	for	for	ADP
ejpam-6939	578	25	all	all	PRON
ejpam-6939	578	26	v	v	ADP
ejpam-6939	578	27	∈	∈	NUM
ejpam-6939	578	28	v	v	NOUN
ejpam-6939	578	29	(	(	PUNCT
ejpam-6939	578	30	g	g	NOUN
ejpam-6939	578	31	)	)	PUNCT
ejpam-6939	578	32	\	\	PUNCT
ejpam-6939	579	1	s	s	PART
ejpam-6939	579	2	with	with	ADP
ejpam-6939	579	3	s	s	PROPN
ejpam-6939	579	4	∩ng(v	∩ng(v	PROPN
ejpam-6939	579	5	)	)	PUNCT
ejpam-6939	580	1	=	=	PUNCT
ejpam-6939	580	2	∅.	∅.	NOUN
ejpam-6939	580	3	in	in	ADP
ejpam-6939	580	4	particular	particular	ADJ
ejpam-6939	580	5	,	,	PUNCT
ejpam-6939	580	6	if	if	SCONJ
ejpam-6939	580	7	γ(h	γ(h	NOUN
ejpam-6939	580	8	)	)	PUNCT
ejpam-6939	580	9	>	>	X
ejpam-6939	581	1	1	1	NUM
ejpam-6939	581	2	,	,	PUNCT
ejpam-6939	581	3	then	then	ADV
ejpam-6939	581	4	|s	|s	PROPN
ejpam-6939	581	5	∩	∩	ADJ
ejpam-6939	581	6	v	v	X
ejpam-6939	581	7	(	(	PUNCT
ejpam-6939	581	8	hv)|	hv)|	X
ejpam-6939	581	9	≥	≥	NOUN
ejpam-6939	581	10	2	2	NUM
ejpam-6939	581	11	.	.	PUNCT
ejpam-6939	581	12	proposition	proposition	NOUN
ejpam-6939	581	13	5	5	NUM
ejpam-6939	581	14	.	.	PUNCT
ejpam-6939	582	1	let	let	VERB
ejpam-6939	582	2	g	g	PRON
ejpam-6939	582	3	be	be	AUX
ejpam-6939	582	4	a	a	DET
ejpam-6939	582	5	nontrivial	nontrivial	ADJ
ejpam-6939	582	6	connected	connect	VERB
ejpam-6939	582	7	graph	graph	NOUN
ejpam-6939	582	8	and	and	CCONJ
ejpam-6939	582	9	let	let	VERB
ejpam-6939	582	10	h	h	NOUN
ejpam-6939	582	11	be	be	AUX
ejpam-6939	582	12	any	any	DET
ejpam-6939	582	13	graph	graph	NOUN
ejpam-6939	582	14	.	.	PUNCT
ejpam-6939	583	1	then	then	ADV
ejpam-6939	583	2	a	a	DET
ejpam-6939	583	3	set	set	NOUN
ejpam-6939	583	4	s	s	NOUN
ejpam-6939	583	5	⊆	⊆	NUM
ejpam-6939	583	6	v	v	NOUN
ejpam-6939	583	7	(	(	PUNCT
ejpam-6939	583	8	g	g	PROPN
ejpam-6939	583	9	◦	◦	NOUN
ejpam-6939	583	10	h	h	NOUN
ejpam-6939	583	11	)	)	PUNCT
ejpam-6939	583	12	is	be	AUX
ejpam-6939	583	13	a	a	DET
ejpam-6939	583	14	connected	connected	ADJ
ejpam-6939	583	15	disjunctive	disjunctive	ADJ
ejpam-6939	583	16	dominating	dominating	NOUN
ejpam-6939	583	17	set	set	NOUN
ejpam-6939	583	18	of	of	ADP
ejpam-6939	583	19	g	g	PROPN
ejpam-6939	583	20	◦	◦	NOUN
ejpam-6939	583	21	h	h	NOUN
ejpam-6939	583	22	if	if	SCONJ
ejpam-6939	584	1	and	and	CCONJ
ejpam-6939	584	2	only	only	ADV
ejpam-6939	584	3	if	if	SCONJ
ejpam-6939	584	4	s	s	VERB
ejpam-6939	584	5	=	=	NOUN
ejpam-6939	584	6	a	a	DET
ejpam-6939	584	7	∪	∪	ADJ
ejpam-6939	584	8	(	(	PUNCT
ejpam-6939	584	9	∪v∈asv	∪v∈asv	NOUN
ejpam-6939	584	10	)	)	PUNCT
ejpam-6939	584	11	,	,	PUNCT
ejpam-6939	584	12	(	(	PUNCT
ejpam-6939	584	13	2	2	X
ejpam-6939	584	14	)	)	PUNCT
ejpam-6939	584	15	where	where	SCONJ
ejpam-6939	584	16	a	a	PRON
ejpam-6939	584	17	is	be	AUX
ejpam-6939	584	18	a	a	DET
ejpam-6939	584	19	connected	connected	ADJ
ejpam-6939	584	20	2	2	NUM
ejpam-6939	584	21	-	-	PUNCT
ejpam-6939	584	22	dominating	dominate	VERB
ejpam-6939	584	23	set	set	NOUN
ejpam-6939	584	24	of	of	ADP
ejpam-6939	584	25	g	g	PROPN
ejpam-6939	584	26	and	and	CCONJ
ejpam-6939	584	27	sv	sv	PROPN
ejpam-6939	584	28	⊆	⊆	NUM
ejpam-6939	584	29	v	v	PROPN
ejpam-6939	584	30	(	(	PUNCT
ejpam-6939	584	31	hv	hv	NOUN
ejpam-6939	584	32	)	)	PUNCT
ejpam-6939	584	33	for	for	ADP
ejpam-6939	584	34	all	all	DET
ejpam-6939	584	35	v	v	NOUN
ejpam-6939	584	36	∈	∈	NOUN
ejpam-6939	584	37	a.	a.	NOUN
ejpam-6939	584	38	proof	proof	NOUN
ejpam-6939	584	39	.	.	PUNCT
ejpam-6939	585	1	let	let	VERB
ejpam-6939	585	2	s	s	PRON
ejpam-6939	585	3	⊆	⊆	NUM
ejpam-6939	585	4	v	v	NOUN
ejpam-6939	585	5	(	(	PUNCT
ejpam-6939	585	6	g	g	PROPN
ejpam-6939	585	7	◦	◦	NOUN
ejpam-6939	585	8	h	h	NOUN
ejpam-6939	585	9	)	)	PUNCT
ejpam-6939	585	10	be	be	VERB
ejpam-6939	585	11	a	a	DET
ejpam-6939	585	12	connected	connected	ADJ
ejpam-6939	585	13	disjunctive	disjunctive	ADJ
ejpam-6939	585	14	dominating	dominating	NOUN
ejpam-6939	585	15	set	set	NOUN
ejpam-6939	585	16	of	of	ADP
ejpam-6939	585	17	g	g	PROPN
ejpam-6939	585	18	◦	◦	PROPN
ejpam-6939	585	19	h.	h.	PROPN
ejpam-6939	585	20	put	put	VERB
ejpam-6939	585	21	a	a	DET
ejpam-6939	585	22	=	=	SYM
ejpam-6939	585	23	s	s	NOUN
ejpam-6939	585	24	∩	∩	ADJ
ejpam-6939	585	25	v	v	X
ejpam-6939	585	26	(	(	PUNCT
ejpam-6939	585	27	g	g	NOUN
ejpam-6939	585	28	)	)	PUNCT
ejpam-6939	585	29	and	and	CCONJ
ejpam-6939	585	30	sv	sv	X
ejpam-6939	585	31	=	=	SYM
ejpam-6939	585	32	s	s	PROPN
ejpam-6939	585	33	∩	∩	ADJ
ejpam-6939	585	34	v	v	X
ejpam-6939	585	35	(	(	PUNCT
ejpam-6939	585	36	hv	hv	PROPN
ejpam-6939	585	37	)	)	PUNCT
ejpam-6939	585	38	for	for	ADP
ejpam-6939	585	39	each	each	DET
ejpam-6939	585	40	v	v	NUM
ejpam-6939	585	41	∈	∈	PROPN
ejpam-6939	585	42	v	v	NOUN
ejpam-6939	585	43	(	(	PUNCT
ejpam-6939	585	44	g	g	NOUN
ejpam-6939	585	45	)	)	PUNCT
ejpam-6939	585	46	.	.	PUNCT
ejpam-6939	586	1	then	then	ADV
ejpam-6939	586	2	s	s	VERB
ejpam-6939	586	3	=	=	PUNCT
ejpam-6939	586	4	a	a	DET
ejpam-6939	586	5	∪	∪	ADJ
ejpam-6939	586	6	(	(	PUNCT
ejpam-6939	586	7	∪v∈asv	∪v∈asv	NOUN
ejpam-6939	586	8	)	)	PUNCT
ejpam-6939	586	9	∪	∪	NOUN
ejpam-6939	586	10	(	(	PUNCT
ejpam-6939	586	11	∪v∈v	∪v∈v	X
ejpam-6939	586	12	(	(	PUNCT
ejpam-6939	586	13	g)\asv	g)\asv	PROPN
ejpam-6939	586	14	)	)	PUNCT
ejpam-6939	586	15	.	.	PUNCT
ejpam-6939	587	1	since	since	SCONJ
ejpam-6939	587	2	g	g	PROPN
ejpam-6939	587	3	is	be	AUX
ejpam-6939	587	4	nontrivial	nontrivial	ADJ
ejpam-6939	587	5	and	and	CCONJ
ejpam-6939	587	6	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	587	7	is	be	AUX
ejpam-6939	587	8	connected	connect	VERB
ejpam-6939	587	9	,	,	PUNCT
ejpam-6939	587	10	a	a	DET
ejpam-6939	587	11	̸=	̸=	PROPN
ejpam-6939	587	12	∅	∅	NOUN
ejpam-6939	587	13	and	and	CCONJ
ejpam-6939	587	14	⟨a⟩	⟨a⟩	PROPN
ejpam-6939	587	15	is	be	AUX
ejpam-6939	587	16	connected	connect	VERB
ejpam-6939	587	17	.	.	PUNCT
ejpam-6939	588	1	we	we	PRON
ejpam-6939	588	2	claim	claim	VERB
ejpam-6939	588	3	that	that	SCONJ
ejpam-6939	588	4	sv	sv	INTJ
ejpam-6939	589	1	=	=	NOUN
ejpam-6939	589	2	∅	∅	NOUN
ejpam-6939	589	3	for	for	ADP
ejpam-6939	589	4	all	all	PRON
ejpam-6939	589	5	v	v	ADP
ejpam-6939	589	6	∈	∈	NUM
ejpam-6939	589	7	v	v	NOUN
ejpam-6939	589	8	(	(	PUNCT
ejpam-6939	589	9	g	g	NOUN
ejpam-6939	589	10	)	)	PUNCT
ejpam-6939	589	11	\	\	PROPN
ejpam-6939	590	1	a	a	PRON
ejpam-6939	590	2	,	,	PUNCT
ejpam-6939	590	3	and	and	CCONJ
ejpam-6939	590	4	equation	equation	NOUN
ejpam-6939	590	5	(	(	PUNCT
ejpam-6939	590	6	2	2	X
ejpam-6939	590	7	)	)	PUNCT
ejpam-6939	590	8	holds	hold	VERB
ejpam-6939	590	9	.	.	PUNCT
ejpam-6939	591	1	suppose	suppose	VERB
ejpam-6939	591	2	v	v	NUM
ejpam-6939	591	3	∈	∈	PROPN
ejpam-6939	591	4	v	v	NOUN
ejpam-6939	591	5	(	(	PUNCT
ejpam-6939	591	6	g	g	NOUN
ejpam-6939	591	7	)	)	PUNCT
ejpam-6939	591	8	\	\	PROPN
ejpam-6939	591	9	a	a	DET
ejpam-6939	591	10	for	for	ADP
ejpam-6939	591	11	which	which	PRON
ejpam-6939	591	12	sv	sv	NOUN
ejpam-6939	591	13	̸=	̸=	PROPN
ejpam-6939	591	14	∅.	∅.	ADV
ejpam-6939	591	15	since	since	SCONJ
ejpam-6939	591	16	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	591	17	is	be	AUX
ejpam-6939	591	18	connected	connect	VERB
ejpam-6939	591	19	,	,	PUNCT
ejpam-6939	591	20	s	s	NOUN
ejpam-6939	591	21	=	=	NOUN
ejpam-6939	591	22	sv	sv	PROPN
ejpam-6939	591	23	.	.	PUNCT
ejpam-6939	592	1	this	this	PRON
ejpam-6939	592	2	is	be	AUX
ejpam-6939	592	3	impossible	impossible	ADJ
ejpam-6939	592	4	because	because	SCONJ
ejpam-6939	592	5	a	a	DET
ejpam-6939	592	6	̸=	̸=	PROPN
ejpam-6939	592	7	∅.	∅.	PRON
ejpam-6939	592	8	hence	hence	ADV
ejpam-6939	592	9	,	,	PUNCT
ejpam-6939	592	10	sv	sv	NOUN
ejpam-6939	592	11	=	=	PUNCT
ejpam-6939	592	12	∅.	∅.	VERB
ejpam-6939	592	13	consequently	consequently	ADV
ejpam-6939	592	14	,	,	PUNCT
ejpam-6939	592	15	|a	|a	PRON
ejpam-6939	592	16	∩ng(v)|	∩ng(v)|	PROPN
ejpam-6939	592	17	≥	≥	NUM
ejpam-6939	592	18	2	2	NUM
ejpam-6939	592	19	by	by	ADP
ejpam-6939	592	20	theorem	theorem	NOUN
ejpam-6939	592	21	2(i	2(i	NUM
ejpam-6939	592	22	)	)	PUNCT
ejpam-6939	592	23	.	.	PUNCT
ejpam-6939	593	1	thus	thus	ADV
ejpam-6939	593	2	,	,	PUNCT
ejpam-6939	593	3	s	s	VERB
ejpam-6939	593	4	=	=	PUNCT
ejpam-6939	593	5	a	a	DET
ejpam-6939	593	6	∪	∪	ADJ
ejpam-6939	593	7	(	(	PUNCT
ejpam-6939	593	8	∪v∈asv	∪v∈asv	NOUN
ejpam-6939	593	9	)	)	PUNCT
ejpam-6939	593	10	and	and	CCONJ
ejpam-6939	593	11	a	a	PRON
ejpam-6939	593	12	is	be	AUX
ejpam-6939	593	13	a	a	DET
ejpam-6939	593	14	(	(	PUNCT
ejpam-6939	593	15	connected	connected	ADJ
ejpam-6939	593	16	)	)	PUNCT
ejpam-6939	593	17	2	2	NUM
ejpam-6939	593	18	-	-	PUNCT
ejpam-6939	593	19	dominating	dominate	VERB
ejpam-6939	593	20	set	set	NOUN
ejpam-6939	593	21	of	of	ADP
ejpam-6939	593	22	g.	g.	PROPN
ejpam-6939	593	23	conversely	conversely	ADV
ejpam-6939	593	24	,	,	PUNCT
ejpam-6939	593	25	assume	assume	VERB
ejpam-6939	593	26	that	that	SCONJ
ejpam-6939	593	27	s	s	VERB
ejpam-6939	593	28	has	have	VERB
ejpam-6939	593	29	the	the	DET
ejpam-6939	593	30	form	form	NOUN
ejpam-6939	593	31	given	give	VERB
ejpam-6939	593	32	in	in	ADP
ejpam-6939	593	33	equation	equation	NOUN
ejpam-6939	593	34	2	2	NUM
ejpam-6939	593	35	,	,	PUNCT
ejpam-6939	593	36	where	where	SCONJ
ejpam-6939	593	37	a	a	PRON
ejpam-6939	593	38	is	be	AUX
ejpam-6939	593	39	a	a	DET
ejpam-6939	593	40	connected	connected	ADJ
ejpam-6939	593	41	2dominating	2dominating	NUM
ejpam-6939	593	42	set	set	NOUN
ejpam-6939	593	43	of	of	ADP
ejpam-6939	593	44	g	g	PROPN
ejpam-6939	593	45	and	and	CCONJ
ejpam-6939	593	46	sv	sv	PROPN
ejpam-6939	593	47	⊆	⊆	NUM
ejpam-6939	593	48	v	v	PROPN
ejpam-6939	593	49	(	(	PUNCT
ejpam-6939	593	50	hv	hv	PROPN
ejpam-6939	593	51	)	)	PUNCT
ejpam-6939	593	52	for	for	ADP
ejpam-6939	593	53	each	each	DET
ejpam-6939	593	54	v	v	NOUN
ejpam-6939	593	55	∈	∈	PROPN
ejpam-6939	593	56	a.	a.	NOUN
ejpam-6939	593	57	then	then	ADV
ejpam-6939	593	58	|s∩ng(v)|	|s∩ng(v)|	ADP
ejpam-6939	593	59	=	=	SYM
ejpam-6939	593	60	|a∩ng(v)|	|a∩ng(v)|	X
ejpam-6939	593	61	≥	≥	NOUN
ejpam-6939	593	62	2	2	NUM
ejpam-6939	593	63	for	for	ADP
ejpam-6939	593	64	each	each	PRON
ejpam-6939	593	65	v	v	NUM
ejpam-6939	593	66	∈	∈	PROPN
ejpam-6939	593	67	v	v	NOUN
ejpam-6939	593	68	(	(	PUNCT
ejpam-6939	593	69	g	g	NOUN
ejpam-6939	593	70	)	)	PUNCT
ejpam-6939	593	71	\	\	PUNCT
ejpam-6939	594	1	s.	s.	PROPN
ejpam-6939	594	2	by	by	ADP
ejpam-6939	594	3	theorem	theorem	NOUN
ejpam-6939	594	4	2	2	NUM
ejpam-6939	594	5	,	,	PUNCT
ejpam-6939	594	6	s	s	VERB
ejpam-6939	594	7	is	be	AUX
ejpam-6939	594	8	a	a	DET
ejpam-6939	594	9	disjunctive	disjunctive	ADJ
ejpam-6939	594	10	dominating	dominating	NOUN
ejpam-6939	594	11	set	set	NOUN
ejpam-6939	594	12	of	of	ADP
ejpam-6939	594	13	g	g	PROPN
ejpam-6939	594	14	◦	◦	NOUN
ejpam-6939	594	15	h.	h.	PROPN
ejpam-6939	594	16	since	since	SCONJ
ejpam-6939	594	17	sw	sw	PROPN
ejpam-6939	594	18	=	=	NOUN
ejpam-6939	594	19	∅	∅	NOUN
ejpam-6939	594	20	for	for	ADP
ejpam-6939	594	21	all	all	DET
ejpam-6939	594	22	w	w	NOUN
ejpam-6939	594	23	∈	∈	PROPN
ejpam-6939	594	24	v	v	ADP
ejpam-6939	594	25	(	(	PUNCT
ejpam-6939	594	26	g	g	NOUN
ejpam-6939	594	27	)	)	PUNCT
ejpam-6939	594	28	\	\	PROPN
ejpam-6939	595	1	a	a	PRON
ejpam-6939	595	2	and	and	CCONJ
ejpam-6939	595	3	⟨a⟩	⟨a⟩	PROPN
ejpam-6939	595	4	is	be	AUX
ejpam-6939	595	5	connected	connect	VERB
ejpam-6939	595	6	,	,	PUNCT
ejpam-6939	595	7	it	it	PRON
ejpam-6939	595	8	follows	follow	VERB
ejpam-6939	595	9	that	that	SCONJ
ejpam-6939	595	10	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	595	11	is	be	AUX
ejpam-6939	595	12	connected	connect	VERB
ejpam-6939	595	13	.	.	PUNCT
ejpam-6939	596	1	therefore	therefore	ADV
ejpam-6939	596	2	,	,	PUNCT
ejpam-6939	596	3	s	s	VERB
ejpam-6939	596	4	is	be	AUX
ejpam-6939	596	5	a	a	DET
ejpam-6939	596	6	connected	connected	ADJ
ejpam-6939	596	7	disjunctive	disjunctive	ADJ
ejpam-6939	596	8	dominating	dominating	NOUN
ejpam-6939	596	9	set	set	NOUN
ejpam-6939	596	10	of	of	ADP
ejpam-6939	596	11	g	g	PROPN
ejpam-6939	596	12	◦	◦	PROPN
ejpam-6939	596	13	h.	h.	PROPN
ejpam-6939	596	14	lemma	lemma	PROPN
ejpam-6939	597	1	1	1	X
ejpam-6939	597	2	.	.	PUNCT
ejpam-6939	598	1	let	let	VERB
ejpam-6939	598	2	g	g	PRON
ejpam-6939	598	3	be	be	AUX
ejpam-6939	598	4	a	a	DET
ejpam-6939	598	5	connected	connected	ADJ
ejpam-6939	598	6	graph	graph	NOUN
ejpam-6939	598	7	of	of	ADP
ejpam-6939	598	8	order	order	NOUN
ejpam-6939	598	9	n	n	PRON
ejpam-6939	598	10	≥	≥	NOUN
ejpam-6939	598	11	2	2	NUM
ejpam-6939	598	12	.	.	PUNCT
ejpam-6939	599	1	(	(	PUNCT
ejpam-6939	599	2	i	i	NOUN
ejpam-6939	599	3	)	)	PUNCT
ejpam-6939	599	4	γ×2,c(g	γ×2,c(g	PUNCT
ejpam-6939	599	5	)	)	PUNCT
ejpam-6939	599	6	=	=	SYM
ejpam-6939	599	7	2	2	NUM
ejpam-6939	599	8	if	if	SCONJ
ejpam-6939	599	9	and	and	CCONJ
ejpam-6939	599	10	only	only	ADV
ejpam-6939	599	11	if	if	SCONJ
ejpam-6939	599	12	g	g	PROPN
ejpam-6939	599	13	=	=	SYM
ejpam-6939	599	14	k2	k2	PROPN
ejpam-6939	599	15	or	or	CCONJ
ejpam-6939	599	16	g	g	PROPN
ejpam-6939	599	17	=	=	PROPN
ejpam-6939	599	18	k2	k2	PROPN
ejpam-6939	599	19	+	+	PROPN
ejpam-6939	599	20	h	h	NOUN
ejpam-6939	599	21	for	for	ADP
ejpam-6939	599	22	some	some	DET
ejpam-6939	599	23	graph	graph	NOUN
ejpam-6939	599	24	h.	h.	PROPN
ejpam-6939	599	25	(	(	PUNCT
ejpam-6939	599	26	ii	ii	PROPN
ejpam-6939	599	27	)	)	PUNCT
ejpam-6939	599	28	γ×2,c(g	γ×2,c(g	PROPN
ejpam-6939	599	29	)	)	PUNCT
ejpam-6939	599	30	=	=	SYM
ejpam-6939	600	1	n	n	NOUN
ejpam-6939	600	2	if	if	SCONJ
ejpam-6939	600	3	and	and	CCONJ
ejpam-6939	600	4	only	only	ADV
ejpam-6939	600	5	if	if	SCONJ
ejpam-6939	600	6	for	for	ADP
ejpam-6939	600	7	every	every	DET
ejpam-6939	600	8	v	v	NUM
ejpam-6939	600	9	∈	∈	NOUN
ejpam-6939	600	10	v	v	NOUN
ejpam-6939	600	11	(	(	PUNCT
ejpam-6939	600	12	g	g	NOUN
ejpam-6939	600	13	)	)	PUNCT
ejpam-6939	600	14	,	,	PUNCT
ejpam-6939	600	15	v	v	NOUN
ejpam-6939	600	16	is	be	AUX
ejpam-6939	600	17	either	either	CCONJ
ejpam-6939	600	18	an	an	DET
ejpam-6939	600	19	end	end	NOUN
ejpam-6939	600	20	-	-	PUNCT
ejpam-6939	600	21	vertex	vertex	NOUN
ejpam-6939	600	22	or	or	CCONJ
ejpam-6939	600	23	a	a	DET
ejpam-6939	600	24	cut	cut	NOUN
ejpam-6939	600	25	-	-	PUNCT
ejpam-6939	600	26	vertex	vertex	NOUN
ejpam-6939	600	27	.	.	PUNCT
ejpam-6939	601	1	(	(	PUNCT
ejpam-6939	601	2	iii	iii	NOUN
ejpam-6939	601	3	)	)	PUNCT
ejpam-6939	601	4	γ×2,c(g	γ×2,c(g	PUNCT
ejpam-6939	601	5	)	)	PUNCT
ejpam-6939	602	1	=	=	PUNCT
ejpam-6939	602	2	n−	n−	NOUN
ejpam-6939	602	3	1	1	NUM
ejpam-6939	602	4	if	if	SCONJ
ejpam-6939	602	5	and	and	CCONJ
ejpam-6939	602	6	only	only	ADV
ejpam-6939	602	7	if	if	SCONJ
ejpam-6939	602	8	(	(	PUNCT
ejpam-6939	602	9	a	a	X
ejpam-6939	602	10	)	)	PUNCT
ejpam-6939	602	11	g	g	NOUN
ejpam-6939	602	12	has	have	VERB
ejpam-6939	602	13	a	a	DET
ejpam-6939	602	14	non	non	ADJ
ejpam-6939	602	15	-	-	ADJ
ejpam-6939	602	16	cut	cut	ADJ
ejpam-6939	602	17	vertex	vertex	NOUN
ejpam-6939	602	18	with	with	ADP
ejpam-6939	602	19	degree	degree	NOUN
ejpam-6939	602	20	at	at	ADV
ejpam-6939	602	21	least	least	ADJ
ejpam-6939	602	22	two	two	NUM
ejpam-6939	602	23	,	,	PUNCT
ejpam-6939	602	24	and	and	CCONJ
ejpam-6939	602	25	a.	a.	PROPN
ejpam-6939	602	26	aradais	aradais	PROPN
ejpam-6939	602	27	,	,	PUNCT
ejpam-6939	602	28	f.	f.	PROPN
ejpam-6939	602	29	jamil	jamil	PROPN
ejpam-6939	602	30	,	,	PUNCT
ejpam-6939	602	31	s.	s.	PROPN
ejpam-6939	602	32	canoy	canoy	PROPN
ejpam-6939	602	33	/	/	SYM
ejpam-6939	602	34	eur	eur	PROPN
ejpam-6939	602	35	.	.	PUNCT
ejpam-6939	603	1	j.	j.	PROPN
ejpam-6939	603	2	pure	pure	PROPN
ejpam-6939	603	3	appl	appl	PROPN
ejpam-6939	603	4	.	.	PROPN
ejpam-6939	603	5	math	math	PROPN
ejpam-6939	603	6	,	,	PUNCT
ejpam-6939	603	7	18	18	NUM
ejpam-6939	603	8	(	(	PUNCT
ejpam-6939	603	9	4	4	NUM
ejpam-6939	603	10	)	)	PUNCT
ejpam-6939	603	11	(	(	PUNCT
ejpam-6939	603	12	2025	2025	NUM
ejpam-6939	603	13	)	)	PUNCT
ejpam-6939	603	14	,	,	PUNCT
ejpam-6939	603	15	6939	6939	NUM
ejpam-6939	603	16	10	10	NUM
ejpam-6939	603	17	of	of	ADP
ejpam-6939	603	18	14	14	NUM
ejpam-6939	603	19	(	(	PUNCT
ejpam-6939	603	20	b	b	NOUN
ejpam-6939	603	21	)	)	PUNCT
ejpam-6939	603	22	for	for	ADP
ejpam-6939	603	23	each	each	DET
ejpam-6939	603	24	non	non	ADJ
ejpam-6939	603	25	-	-	ADJ
ejpam-6939	603	26	cut	cut	ADJ
ejpam-6939	603	27	vertex	vertex	NOUN
ejpam-6939	603	28	v	v	ADP
ejpam-6939	603	29	∈	∈	PROPN
ejpam-6939	603	30	v	v	NOUN
ejpam-6939	603	31	(	(	PUNCT
ejpam-6939	603	32	g	g	NOUN
ejpam-6939	603	33	)	)	PUNCT
ejpam-6939	603	34	with	with	ADP
ejpam-6939	603	35	degg(v	degg(v	PROPN
ejpam-6939	603	36	)	)	PUNCT
ejpam-6939	603	37	≥	≥	NOUN
ejpam-6939	603	38	2	2	NUM
ejpam-6939	603	39	,	,	PUNCT
ejpam-6939	603	40	if	if	SCONJ
ejpam-6939	603	41	w	w	NOUN
ejpam-6939	603	42	is	be	AUX
ejpam-6939	603	43	a	a	DET
ejpam-6939	603	44	non	non	ADJ
ejpam-6939	603	45	-	-	ADJ
ejpam-6939	603	46	cut	cut	ADJ
ejpam-6939	603	47	vertex	vertex	NOUN
ejpam-6939	603	48	of	of	ADP
ejpam-6939	603	49	h	h	NOUN
ejpam-6939	603	50	=	=	SYM
ejpam-6939	603	51	⟨v	⟨v	PUNCT
ejpam-6939	603	52	(	(	PUNCT
ejpam-6939	603	53	g	g	NOUN
ejpam-6939	603	54	)	)	PUNCT
ejpam-6939	603	55	\	\	NOUN
ejpam-6939	604	1	{	{	PUNCT
ejpam-6939	604	2	v}⟩	v}⟩	NOUN
ejpam-6939	604	3	with	with	ADP
ejpam-6939	604	4	degh(w	degh(w	PROPN
ejpam-6939	604	5	)	)	PUNCT
ejpam-6939	604	6	≥	≥	NOUN
ejpam-6939	604	7	2	2	NUM
ejpam-6939	604	8	,	,	PUNCT
ejpam-6939	604	9	then	then	ADV
ejpam-6939	604	10	degg(v	degg(v	PROPN
ejpam-6939	604	11	)	)	PUNCT
ejpam-6939	604	12	=	=	SYM
ejpam-6939	604	13	2	2	NUM
ejpam-6939	604	14	and	and	CCONJ
ejpam-6939	604	15	w	w	NOUN
ejpam-6939	604	16	∈	∈	PROPN
ejpam-6939	604	17	ng(v	ng(v	NOUN
ejpam-6939	604	18	)	)	PUNCT
ejpam-6939	604	19	.	.	PUNCT
ejpam-6939	605	1	proof	proof	NOUN
ejpam-6939	605	2	.	.	PUNCT
ejpam-6939	606	1	(	(	PUNCT
ejpam-6939	606	2	i	i	NOUN
ejpam-6939	606	3	)	)	PUNCT
ejpam-6939	606	4	suppose	suppose	VERB
ejpam-6939	606	5	γ×2,c(g	γ×2,c(g	PUNCT
ejpam-6939	606	6	)	)	PUNCT
ejpam-6939	606	7	=	=	SYM
ejpam-6939	607	1	2	2	X
ejpam-6939	607	2	.	.	X
ejpam-6939	608	1	if	if	SCONJ
ejpam-6939	608	2	n	n	NOUN
ejpam-6939	608	3	=	=	SYM
ejpam-6939	608	4	2	2	NUM
ejpam-6939	608	5	,	,	PUNCT
ejpam-6939	608	6	then	then	ADV
ejpam-6939	608	7	g	g	PROPN
ejpam-6939	608	8	=	=	PROPN
ejpam-6939	608	9	k2	k2	PROPN
ejpam-6939	608	10	.	.	PUNCT
ejpam-6939	609	1	suppose	suppose	VERB
ejpam-6939	609	2	n	n	PRON
ejpam-6939	609	3	≥	≥	NUM
ejpam-6939	609	4	3	3	X
ejpam-6939	609	5	.	.	PUNCT
ejpam-6939	610	1	let	let	VERB
ejpam-6939	610	2	s	s	VERB
ejpam-6939	610	3	=	=	X
ejpam-6939	610	4	{	{	PUNCT
ejpam-6939	610	5	a	a	PRON
ejpam-6939	610	6	,	,	PUNCT
ejpam-6939	610	7	b	b	AUX
ejpam-6939	610	8	}	}	PUNCT
ejpam-6939	610	9	be	be	AUX
ejpam-6939	610	10	a	a	DET
ejpam-6939	610	11	γ×2,c	γ×2,c	ADV
ejpam-6939	610	12	-	-	PUNCT
ejpam-6939	610	13	set	set	NOUN
ejpam-6939	610	14	of	of	ADP
ejpam-6939	610	15	g.	g.	PROPN
ejpam-6939	610	16	since	since	SCONJ
ejpam-6939	610	17	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	610	18	is	be	AUX
ejpam-6939	610	19	connected	connect	VERB
ejpam-6939	610	20	,	,	PUNCT
ejpam-6939	610	21	it	it	PRON
ejpam-6939	610	22	follows	follow	VERB
ejpam-6939	610	23	that	that	SCONJ
ejpam-6939	610	24	ab	ab	PROPN
ejpam-6939	610	25	∈	∈	PROPN
ejpam-6939	610	26	e(g	e(g	PROPN
ejpam-6939	610	27	)	)	PUNCT
ejpam-6939	610	28	.	.	PUNCT
ejpam-6939	611	1	let	let	VERB
ejpam-6939	611	2	g1	g1	PROPN
ejpam-6939	611	3	=	=	SYM
ejpam-6939	611	4	⟨{a	⟨{a	PROPN
ejpam-6939	611	5	,	,	PUNCT
ejpam-6939	611	6	b}⟩	b}⟩	PROPN
ejpam-6939	611	7	and	and	CCONJ
ejpam-6939	611	8	h	h	NOUN
ejpam-6939	611	9	=	=	SYM
ejpam-6939	611	10	⟨v	⟨v	PUNCT
ejpam-6939	611	11	(	(	PUNCT
ejpam-6939	611	12	g	g	NOUN
ejpam-6939	611	13	)	)	PUNCT
ejpam-6939	611	14	\	\	NOUN
ejpam-6939	611	15	{	{	PUNCT
ejpam-6939	611	16	a	a	PRON
ejpam-6939	611	17	,	,	PUNCT
ejpam-6939	611	18	b}⟩.	b}⟩.	NOUN
ejpam-6939	611	19	let	let	VERB
ejpam-6939	611	20	h	h	NOUN
ejpam-6939	611	21	∈	∈	PROPN
ejpam-6939	611	22	v	v	PROPN
ejpam-6939	611	23	(	(	PUNCT
ejpam-6939	611	24	h	h	NOUN
ejpam-6939	611	25	)	)	PUNCT
ejpam-6939	611	26	.	.	PUNCT
ejpam-6939	612	1	since	since	SCONJ
ejpam-6939	612	2	s	s	PROPN
ejpam-6939	612	3	is	be	AUX
ejpam-6939	612	4	a	a	DET
ejpam-6939	612	5	2	2	NUM
ejpam-6939	612	6	-	-	PUNCT
ejpam-6939	612	7	dominating	dominating	NOUN
ejpam-6939	612	8	set	set	NOUN
ejpam-6939	612	9	,	,	PUNCT
ejpam-6939	612	10	h	h	NOUN
ejpam-6939	612	11	∈	∈	PROPN
ejpam-6939	612	12	ng(a	ng(a	NOUN
ejpam-6939	612	13	)	)	PUNCT
ejpam-6939	612	14	∩ng(b	∩ng(b	NOUN
ejpam-6939	612	15	)	)	PUNCT
ejpam-6939	612	16	.	.	PUNCT
ejpam-6939	613	1	thus	thus	ADV
ejpam-6939	613	2	,	,	PUNCT
ejpam-6939	613	3	g	g	PROPN
ejpam-6939	613	4	=	=	PUNCT
ejpam-6939	613	5	g1	g1	PROPN
ejpam-6939	613	6	+	+	NOUN
ejpam-6939	613	7	h	h	NOUN
ejpam-6939	613	8	∼=	∼=	PART
ejpam-6939	613	9	k2	k2	NOUN
ejpam-6939	613	10	+	+	PROPN
ejpam-6939	613	11	h.	h.	NOUN
ejpam-6939	613	12	the	the	DET
ejpam-6939	613	13	converse	converse	NOUN
ejpam-6939	613	14	is	be	AUX
ejpam-6939	613	15	clear	clear	ADJ
ejpam-6939	613	16	.	.	PUNCT
ejpam-6939	614	1	(	(	PUNCT
ejpam-6939	614	2	ii	ii	NOUN
ejpam-6939	614	3	)	)	PUNCT
ejpam-6939	614	4	suppose	suppose	VERB
ejpam-6939	614	5	γ×2,c(g	γ×2,c(g	PUNCT
ejpam-6939	614	6	)	)	PUNCT
ejpam-6939	614	7	=	=	VERB
ejpam-6939	615	1	n.	n.	NOUN
ejpam-6939	615	2	let	let	VERB
ejpam-6939	615	3	v	v	ADP
ejpam-6939	615	4	∈	∈	PROPN
ejpam-6939	615	5	v	v	NOUN
ejpam-6939	615	6	(	(	PUNCT
ejpam-6939	615	7	g	g	NOUN
ejpam-6939	615	8	)	)	PUNCT
ejpam-6939	615	9	.	.	PUNCT
ejpam-6939	616	1	suppose	suppose	VERB
ejpam-6939	616	2	v	v	NOUN
ejpam-6939	616	3	is	be	AUX
ejpam-6939	616	4	neither	neither	CCONJ
ejpam-6939	616	5	an	an	DET
ejpam-6939	616	6	end	end	NOUN
ejpam-6939	616	7	-	-	PUNCT
ejpam-6939	616	8	vertex	vertex	NOUN
ejpam-6939	616	9	nor	nor	CCONJ
ejpam-6939	616	10	a	a	DET
ejpam-6939	616	11	cut	cut	NOUN
ejpam-6939	616	12	-	-	PUNCT
ejpam-6939	616	13	vertex	vertex	NOUN
ejpam-6939	616	14	.	.	PUNCT
ejpam-6939	617	1	then	then	ADV
ejpam-6939	617	2	s	s	VERB
ejpam-6939	617	3	=	=	SYM
ejpam-6939	617	4	v	v	PROPN
ejpam-6939	617	5	(	(	PUNCT
ejpam-6939	617	6	g	g	NOUN
ejpam-6939	617	7	)	)	PUNCT
ejpam-6939	617	8	\	\	NOUN
ejpam-6939	617	9	{	{	PUNCT
ejpam-6939	617	10	v	v	NOUN
ejpam-6939	617	11	}	}	PUNCT
ejpam-6939	617	12	is	be	AUX
ejpam-6939	617	13	a	a	DET
ejpam-6939	617	14	connected	connected	ADJ
ejpam-6939	617	15	2	2	NUM
ejpam-6939	617	16	-	-	PUNCT
ejpam-6939	617	17	dominating	dominate	VERB
ejpam-6939	617	18	set	set	NOUN
ejpam-6939	617	19	of	of	ADP
ejpam-6939	617	20	g.	g.	PROPN
ejpam-6939	617	21	this	this	PRON
ejpam-6939	617	22	implies	imply	VERB
ejpam-6939	617	23	that	that	SCONJ
ejpam-6939	617	24	γc2(g	γc2(g	ADV
ejpam-6939	617	25	)	)	PUNCT
ejpam-6939	617	26	≤	≤	NUM
ejpam-6939	617	27	|s|	|s|	PROPN
ejpam-6939	617	28	=	=	SYM
ejpam-6939	617	29	n−	n−	NOUN
ejpam-6939	617	30	1	1	NUM
ejpam-6939	617	31	,	,	PUNCT
ejpam-6939	617	32	contrary	contrary	ADV
ejpam-6939	617	33	to	to	ADP
ejpam-6939	617	34	our	our	PRON
ejpam-6939	617	35	assumption	assumption	NOUN
ejpam-6939	617	36	.	.	PUNCT
ejpam-6939	618	1	thus	thus	ADV
ejpam-6939	618	2	,	,	PUNCT
ejpam-6939	618	3	v	v	NOUN
ejpam-6939	618	4	is	be	AUX
ejpam-6939	618	5	end	end	NOUN
ejpam-6939	618	6	-	-	PUNCT
ejpam-6939	618	7	vertex	vertex	NOUN
ejpam-6939	618	8	or	or	CCONJ
ejpam-6939	618	9	a	a	DET
ejpam-6939	618	10	cut	cut	NOUN
ejpam-6939	618	11	-	-	PUNCT
ejpam-6939	618	12	vertex	vertex	NOUN
ejpam-6939	618	13	of	of	ADP
ejpam-6939	618	14	g.	g.	PROPN
ejpam-6939	618	15	for	for	ADP
ejpam-6939	618	16	the	the	DET
ejpam-6939	618	17	converse	converse	NOUN
ejpam-6939	618	18	,	,	PUNCT
ejpam-6939	618	19	suppose	suppose	VERB
ejpam-6939	618	20	that	that	SCONJ
ejpam-6939	618	21	every	every	DET
ejpam-6939	618	22	v	v	NOUN
ejpam-6939	618	23	∈	∈	NOUN
ejpam-6939	618	24	v	v	NOUN
ejpam-6939	618	25	(	(	PUNCT
ejpam-6939	618	26	g	g	NOUN
ejpam-6939	618	27	)	)	PUNCT
ejpam-6939	618	28	is	be	AUX
ejpam-6939	618	29	either	either	CCONJ
ejpam-6939	618	30	an	an	DET
ejpam-6939	618	31	end	end	NOUN
ejpam-6939	618	32	-	-	PUNCT
ejpam-6939	618	33	vertex	vertex	NOUN
ejpam-6939	618	34	or	or	CCONJ
ejpam-6939	618	35	a	a	DET
ejpam-6939	618	36	cut	cut	NOUN
ejpam-6939	618	37	-	-	PUNCT
ejpam-6939	618	38	vertex	vertex	NOUN
ejpam-6939	618	39	.	.	PUNCT
ejpam-6939	619	1	let	let	AUX
ejpam-6939	619	2	end(g	end(g	PROPN
ejpam-6939	619	3	)	)	PUNCT
ejpam-6939	619	4	denote	denote	VERB
ejpam-6939	619	5	the	the	DET
ejpam-6939	619	6	set	set	NOUN
ejpam-6939	619	7	of	of	ADP
ejpam-6939	619	8	all	all	DET
ejpam-6939	619	9	end	end	NOUN
ejpam-6939	619	10	-	-	PUNCT
ejpam-6939	619	11	vertices	vertex	NOUN
ejpam-6939	619	12	of	of	ADP
ejpam-6939	619	13	g	g	NOUN
ejpam-6939	619	14	and	and	CCONJ
ejpam-6939	619	15	let	let	VERB
ejpam-6939	619	16	s	s	PRON
ejpam-6939	619	17	be	be	AUX
ejpam-6939	619	18	a	a	DET
ejpam-6939	619	19	γ×2,c	γ×2,c	ADV
ejpam-6939	619	20	-	-	PUNCT
ejpam-6939	619	21	set	set	NOUN
ejpam-6939	619	22	of	of	ADP
ejpam-6939	619	23	g.	g.	PROPN
ejpam-6939	619	24	since	since	SCONJ
ejpam-6939	619	25	s	s	PROPN
ejpam-6939	619	26	is	be	AUX
ejpam-6939	619	27	a	a	DET
ejpam-6939	619	28	2	2	NUM
ejpam-6939	619	29	-	-	PUNCT
ejpam-6939	619	30	dominating	dominating	NOUN
ejpam-6939	619	31	set	set	NOUN
ejpam-6939	619	32	,	,	PUNCT
ejpam-6939	619	33	end(g	end(g	PROPN
ejpam-6939	619	34	)	)	PUNCT
ejpam-6939	620	1	⊆	⊆	NUM
ejpam-6939	620	2	s.	s.	PROPN
ejpam-6939	620	3	suppose	suppose	VERB
ejpam-6939	620	4	s	s	VERB
ejpam-6939	620	5	̸=	̸=	PROPN
ejpam-6939	620	6	v	v	NOUN
ejpam-6939	620	7	(	(	PUNCT
ejpam-6939	620	8	g	g	NOUN
ejpam-6939	620	9	)	)	PUNCT
ejpam-6939	620	10	,	,	PUNCT
ejpam-6939	620	11	say	say	VERB
ejpam-6939	620	12	x	x	X
ejpam-6939	620	13	∈	∈	PROPN
ejpam-6939	620	14	v	v	ADP
ejpam-6939	620	15	(	(	PUNCT
ejpam-6939	620	16	g	g	NOUN
ejpam-6939	620	17	)	)	PUNCT
ejpam-6939	620	18	\	\	PUNCT
ejpam-6939	621	1	s.	s.	PROPN
ejpam-6939	621	2	then	then	ADV
ejpam-6939	621	3	x	x	PRON
ejpam-6939	621	4	is	be	AUX
ejpam-6939	621	5	a	a	DET
ejpam-6939	621	6	cut	cut	NOUN
ejpam-6939	621	7	-	-	PUNCT
ejpam-6939	621	8	vertex	vertex	NOUN
ejpam-6939	621	9	of	of	ADP
ejpam-6939	621	10	g.	g.	PROPN
ejpam-6939	621	11	since	since	SCONJ
ejpam-6939	621	12	s	s	PROPN
ejpam-6939	621	13	⊆	⊆	NUM
ejpam-6939	621	14	v	v	NOUN
ejpam-6939	621	15	(	(	PUNCT
ejpam-6939	621	16	g	g	NOUN
ejpam-6939	621	17	)	)	PUNCT
ejpam-6939	621	18	\	\	NOUN
ejpam-6939	621	19	{	{	PUNCT
ejpam-6939	621	20	x	x	NOUN
ejpam-6939	621	21	}	}	PUNCT
ejpam-6939	621	22	and	and	CCONJ
ejpam-6939	621	23	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	621	24	is	be	AUX
ejpam-6939	621	25	connected	connect	VERB
ejpam-6939	621	26	,	,	PUNCT
ejpam-6939	621	27	s	s	VERB
ejpam-6939	621	28	⊆	⊆	NUM
ejpam-6939	621	29	v	v	NOUN
ejpam-6939	621	30	(	(	PUNCT
ejpam-6939	621	31	cs	cs	PROPN
ejpam-6939	621	32	)	)	PUNCT
ejpam-6939	621	33	for	for	ADP
ejpam-6939	621	34	some	some	DET
ejpam-6939	621	35	component	component	NOUN
ejpam-6939	621	36	cs	c	NOUN
ejpam-6939	621	37	of	of	ADP
ejpam-6939	621	38	⟨v	⟨v	PROPN
ejpam-6939	621	39	(	(	PUNCT
ejpam-6939	621	40	g	g	NOUN
ejpam-6939	621	41	)	)	PUNCT
ejpam-6939	621	42	\	\	PROPN
ejpam-6939	621	43	s⟩.	s⟩.	PROPN
ejpam-6939	621	44	let	let	VERB
ejpam-6939	621	45	c	c	PRON
ejpam-6939	621	46	be	be	AUX
ejpam-6939	621	47	a	a	DET
ejpam-6939	621	48	component	component	NOUN
ejpam-6939	621	49	of	of	ADP
ejpam-6939	621	50	⟨v	⟨v	PROPN
ejpam-6939	621	51	(	(	PUNCT
ejpam-6939	621	52	g	g	NOUN
ejpam-6939	621	53	)	)	PUNCT
ejpam-6939	621	54	\	\	NOUN
ejpam-6939	621	55	s⟩	s⟩	VERB
ejpam-6939	621	56	different	different	ADJ
ejpam-6939	621	57	from	from	ADP
ejpam-6939	621	58	cs	cs	PROPN
ejpam-6939	621	59	and	and	CCONJ
ejpam-6939	621	60	let	let	VERB
ejpam-6939	621	61	z	z	NOUN
ejpam-6939	621	62	∈	∈	PROPN
ejpam-6939	621	63	v	v	NOUN
ejpam-6939	621	64	(	(	PUNCT
ejpam-6939	621	65	c	c	NOUN
ejpam-6939	621	66	)	)	PUNCT
ejpam-6939	621	67	.	.	PUNCT
ejpam-6939	622	1	then	then	ADV
ejpam-6939	622	2	ng(z)∩	ng(z)∩	X
ejpam-6939	622	3	s	s	X
ejpam-6939	622	4	=	=	SYM
ejpam-6939	622	5	∅	∅	NOUN
ejpam-6939	622	6	,	,	PUNCT
ejpam-6939	622	7	contrary	contrary	ADJ
ejpam-6939	622	8	to	to	ADP
ejpam-6939	622	9	the	the	DET
ejpam-6939	622	10	assumption	assumption	NOUN
ejpam-6939	622	11	that	that	SCONJ
ejpam-6939	622	12	s	s	VERB
ejpam-6939	622	13	is	be	AUX
ejpam-6939	622	14	a	a	DET
ejpam-6939	622	15	2	2	NUM
ejpam-6939	622	16	-	-	PUNCT
ejpam-6939	622	17	dominating	dominating	NOUN
ejpam-6939	622	18	set	set	NOUN
ejpam-6939	622	19	.	.	PUNCT
ejpam-6939	623	1	thus	thus	ADV
ejpam-6939	623	2	,	,	PUNCT
ejpam-6939	623	3	s	s	VERB
ejpam-6939	623	4	=	=	SYM
ejpam-6939	623	5	v	v	X
ejpam-6939	623	6	(	(	PUNCT
ejpam-6939	623	7	g	g	NOUN
ejpam-6939	623	8	)	)	PUNCT
ejpam-6939	623	9	and	and	CCONJ
ejpam-6939	623	10	γ×2,c(g	γ×2,c(g	PUNCT
ejpam-6939	623	11	)	)	PUNCT
ejpam-6939	623	12	=	=	SYM
ejpam-6939	623	13	n	n	CCONJ
ejpam-6939	623	14	,	,	PUNCT
ejpam-6939	623	15	showing	show	VERB
ejpam-6939	623	16	that	that	SCONJ
ejpam-6939	623	17	(	(	PUNCT
ejpam-6939	623	18	ii	ii	NOUN
ejpam-6939	623	19	)	)	PUNCT
ejpam-6939	623	20	holds	hold	VERB
ejpam-6939	623	21	.	.	PUNCT
ejpam-6939	624	1	(	(	PUNCT
ejpam-6939	624	2	iii	iii	NOUN
ejpam-6939	624	3	)	)	PUNCT
ejpam-6939	624	4	suppose	suppose	VERB
ejpam-6939	624	5	γ×2,c(g	γ×2,c(g	PUNCT
ejpam-6939	624	6	)	)	PUNCT
ejpam-6939	625	1	=	=	PUNCT
ejpam-6939	625	2	n−	n−	NOUN
ejpam-6939	625	3	1	1	NUM
ejpam-6939	625	4	and	and	CCONJ
ejpam-6939	625	5	let	let	VERB
ejpam-6939	625	6	s	s	PRON
ejpam-6939	625	7	=	=	VERB
ejpam-6939	625	8	v	v	ADJ
ejpam-6939	625	9	(	(	PUNCT
ejpam-6939	625	10	g	g	NOUN
ejpam-6939	625	11	)	)	PUNCT
ejpam-6939	625	12	\	\	NOUN
ejpam-6939	625	13	{	{	PUNCT
ejpam-6939	625	14	v	v	AUX
ejpam-6939	625	15	}	}	PUNCT
ejpam-6939	625	16	be	be	AUX
ejpam-6939	625	17	a	a	DET
ejpam-6939	625	18	γ×2,c	γ×2,c	ADV
ejpam-6939	625	19	-	-	PUNCT
ejpam-6939	625	20	set	set	NOUN
ejpam-6939	625	21	of	of	ADP
ejpam-6939	625	22	g.	g.	PROPN
ejpam-6939	625	23	then	then	ADV
ejpam-6939	625	24	v	v	NOUN
ejpam-6939	625	25	is	be	AUX
ejpam-6939	625	26	a	a	DET
ejpam-6939	625	27	non	non	ADJ
ejpam-6939	625	28	-	-	ADJ
ejpam-6939	625	29	cut	cut	ADJ
ejpam-6939	625	30	vertex	vertex	NOUN
ejpam-6939	625	31	and	and	CCONJ
ejpam-6939	625	32	degg(v	degg(v	PROPN
ejpam-6939	625	33	)	)	PUNCT
ejpam-6939	625	34	≥	≥	NOUN
ejpam-6939	625	35	2	2	NUM
ejpam-6939	625	36	.	.	PUNCT
ejpam-6939	626	1	let	let	VERB
ejpam-6939	626	2	h	h	NOUN
ejpam-6939	626	3	=	=	PUNCT
ejpam-6939	626	4	⟨v	⟨v	X
ejpam-6939	626	5	(	(	PUNCT
ejpam-6939	626	6	g)\{v}⟩	g)\{v}⟩	VERB
ejpam-6939	626	7	and	and	CCONJ
ejpam-6939	626	8	suppose	suppose	VERB
ejpam-6939	626	9	there	there	PRON
ejpam-6939	626	10	exists	exist	VERB
ejpam-6939	626	11	a	a	DET
ejpam-6939	626	12	non	non	ADJ
ejpam-6939	626	13	-	-	NOUN
ejpam-6939	626	14	cutvertex	cutvertex	NOUN
ejpam-6939	626	15	w	w	PROPN
ejpam-6939	626	16	∈	∈	PROPN
ejpam-6939	626	17	v	v	ADP
ejpam-6939	626	18	(	(	PUNCT
ejpam-6939	626	19	h	h	NOUN
ejpam-6939	626	20	)	)	PUNCT
ejpam-6939	626	21	with	with	ADP
ejpam-6939	626	22	degh(w	degh(w	PROPN
ejpam-6939	626	23	)	)	PUNCT
ejpam-6939	626	24	≥	≥	NOUN
ejpam-6939	626	25	2	2	NUM
ejpam-6939	626	26	.	.	PUNCT
ejpam-6939	626	27	suppose	suppose	VERB
ejpam-6939	626	28	that	that	SCONJ
ejpam-6939	626	29	w	w	PROPN
ejpam-6939	626	30	/∈	/∈	PUNCT
ejpam-6939	626	31	ng(v	ng(v	NUM
ejpam-6939	626	32	)	)	PUNCT
ejpam-6939	626	33	.	.	PUNCT
ejpam-6939	627	1	then	then	ADV
ejpam-6939	627	2	s′	s′	ADJ
ejpam-6939	627	3	=	=	SYM
ejpam-6939	627	4	v	v	ADJ
ejpam-6939	627	5	(	(	PUNCT
ejpam-6939	627	6	g	g	NOUN
ejpam-6939	627	7	)	)	PUNCT
ejpam-6939	627	8	\	\	NOUN
ejpam-6939	627	9	{	{	PUNCT
ejpam-6939	627	10	v	v	NOUN
ejpam-6939	627	11	,	,	PUNCT
ejpam-6939	627	12	w	w	NOUN
ejpam-6939	627	13	}	}	PUNCT
ejpam-6939	627	14	is	be	AUX
ejpam-6939	627	15	a	a	DET
ejpam-6939	627	16	connected	connected	ADJ
ejpam-6939	627	17	2	2	NUM
ejpam-6939	627	18	-	-	PUNCT
ejpam-6939	627	19	dominating	dominate	VERB
ejpam-6939	627	20	set	set	NOUN
ejpam-6939	627	21	of	of	ADP
ejpam-6939	627	22	g	g	PROPN
ejpam-6939	627	23	,	,	PUNCT
ejpam-6939	627	24	contrary	contrary	ADV
ejpam-6939	627	25	to	to	ADP
ejpam-6939	627	26	the	the	DET
ejpam-6939	627	27	assumption	assumption	NOUN
ejpam-6939	627	28	that	that	SCONJ
ejpam-6939	627	29	s	s	VERB
ejpam-6939	627	30	is	be	AUX
ejpam-6939	627	31	a	a	DET
ejpam-6939	627	32	γ×2,c	γ×2,c	ADV
ejpam-6939	627	33	-	-	PUNCT
ejpam-6939	627	34	set	set	NOUN
ejpam-6939	627	35	.	.	PUNCT
ejpam-6939	628	1	hence	hence	ADV
ejpam-6939	628	2	,	,	PUNCT
ejpam-6939	628	3	w	w	PROPN
ejpam-6939	628	4	∈	∈	PROPN
ejpam-6939	628	5	ng(v	ng(v	NOUN
ejpam-6939	628	6	)	)	PUNCT
ejpam-6939	628	7	.	.	PUNCT
ejpam-6939	629	1	suppose	suppose	VERB
ejpam-6939	629	2	degg(v	degg(v	X
ejpam-6939	629	3	)	)	PUNCT
ejpam-6939	629	4	≥	≥	NOUN
ejpam-6939	629	5	3	3	NUM
ejpam-6939	629	6	.	.	PUNCT
ejpam-6939	630	1	then	then	ADV
ejpam-6939	630	2	,	,	PUNCT
ejpam-6939	630	3	again	again	ADV
ejpam-6939	630	4	,	,	PUNCT
ejpam-6939	630	5	v	v	X
ejpam-6939	630	6	(	(	PUNCT
ejpam-6939	630	7	g	g	NOUN
ejpam-6939	630	8	)	)	PUNCT
ejpam-6939	630	9	\	\	NOUN
ejpam-6939	630	10	{	{	PUNCT
ejpam-6939	630	11	v	v	NOUN
ejpam-6939	630	12	,	,	PUNCT
ejpam-6939	630	13	w	w	NOUN
ejpam-6939	630	14	}	}	PUNCT
ejpam-6939	630	15	is	be	AUX
ejpam-6939	630	16	a	a	DET
ejpam-6939	630	17	connected	connected	ADJ
ejpam-6939	630	18	2	2	NUM
ejpam-6939	630	19	-	-	PUNCT
ejpam-6939	630	20	dominating	dominate	VERB
ejpam-6939	630	21	set	set	NOUN
ejpam-6939	630	22	of	of	ADP
ejpam-6939	630	23	g	g	PROPN
ejpam-6939	630	24	,	,	PUNCT
ejpam-6939	630	25	a	a	DET
ejpam-6939	630	26	contradiction	contradiction	NOUN
ejpam-6939	630	27	.	.	PUNCT
ejpam-6939	631	1	therefore	therefore	ADV
ejpam-6939	631	2	,	,	PUNCT
ejpam-6939	631	3	degg(v	degg(v	PROPN
ejpam-6939	631	4	)	)	PUNCT
ejpam-6939	631	5	=	=	SYM
ejpam-6939	632	1	2	2	X
ejpam-6939	632	2	.	.	X
ejpam-6939	632	3	for	for	ADP
ejpam-6939	632	4	the	the	DET
ejpam-6939	632	5	converse	converse	NOUN
ejpam-6939	632	6	,	,	PUNCT
ejpam-6939	632	7	suppose	suppose	VERB
ejpam-6939	632	8	g	g	PROPN
ejpam-6939	632	9	satisfies	satisfie	NOUN
ejpam-6939	632	10	(	(	PUNCT
ejpam-6939	632	11	a	a	X
ejpam-6939	632	12	)	)	PUNCT
ejpam-6939	632	13	and	and	CCONJ
ejpam-6939	632	14	(	(	PUNCT
ejpam-6939	632	15	b	b	NOUN
ejpam-6939	632	16	)	)	PUNCT
ejpam-6939	632	17	.	.	PUNCT
ejpam-6939	633	1	if	if	SCONJ
ejpam-6939	633	2	n	n	NUM
ejpam-6939	633	3	=	=	SYM
ejpam-6939	633	4	3	3	NUM
ejpam-6939	633	5	,	,	PUNCT
ejpam-6939	633	6	then	then	ADV
ejpam-6939	633	7	g	g	PROPN
ejpam-6939	633	8	=	=	PROPN
ejpam-6939	633	9	c3	c3	PROPN
ejpam-6939	633	10	=	=	PUNCT
ejpam-6939	633	11	k3	k3	X
ejpam-6939	633	12	and	and	CCONJ
ejpam-6939	633	13	γ×2,c(g	γ×2,c(g	PUNCT
ejpam-6939	633	14	)	)	PUNCT
ejpam-6939	633	15	=	=	SYM
ejpam-6939	634	1	2	2	X
ejpam-6939	634	2	.	.	X
ejpam-6939	634	3	suppose	suppose	VERB
ejpam-6939	634	4	n	n	DET
ejpam-6939	634	5	≥	≥	X
ejpam-6939	634	6	4	4	NUM
ejpam-6939	634	7	and	and	CCONJ
ejpam-6939	634	8	let	let	VERB
ejpam-6939	634	9	s	s	PRON
ejpam-6939	634	10	be	be	AUX
ejpam-6939	634	11	a	a	DET
ejpam-6939	634	12	γ×2,c	γ×2,c	ADV
ejpam-6939	634	13	-	-	PUNCT
ejpam-6939	634	14	set	set	NOUN
ejpam-6939	634	15	of	of	ADP
ejpam-6939	634	16	g.	g.	PROPN
ejpam-6939	634	17	by	by	ADP
ejpam-6939	634	18	(	(	PUNCT
ejpam-6939	634	19	a	a	NOUN
ejpam-6939	634	20	)	)	PUNCT
ejpam-6939	634	21	,	,	PUNCT
ejpam-6939	634	22	|s|	|s|	NOUN
ejpam-6939	634	23	≤	≤	PROPN
ejpam-6939	634	24	n	n	CCONJ
ejpam-6939	634	25	−	−	PROPN
ejpam-6939	634	26	1	1	NUM
ejpam-6939	634	27	.	.	PUNCT
ejpam-6939	635	1	let	let	VERB
ejpam-6939	635	2	v	v	NUM
ejpam-6939	635	3	∈	∈	PROPN
ejpam-6939	635	4	v	v	NOUN
ejpam-6939	635	5	(	(	PUNCT
ejpam-6939	635	6	g	g	NOUN
ejpam-6939	635	7	)	)	PUNCT
ejpam-6939	635	8	\	\	PUNCT
ejpam-6939	636	1	s.	s.	PROPN
ejpam-6939	636	2	since	since	SCONJ
ejpam-6939	636	3	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	636	4	is	be	AUX
ejpam-6939	636	5	a	a	DET
ejpam-6939	636	6	connected	connected	ADJ
ejpam-6939	636	7	2	2	NUM
ejpam-6939	636	8	-	-	PUNCT
ejpam-6939	636	9	dominating	dominating	NOUN
ejpam-6939	636	10	set	set	NOUN
ejpam-6939	636	11	,	,	PUNCT
ejpam-6939	636	12	it	it	PRON
ejpam-6939	636	13	follows	follow	VERB
ejpam-6939	636	14	that	that	SCONJ
ejpam-6939	636	15	v	v	NOUN
ejpam-6939	636	16	is	be	AUX
ejpam-6939	636	17	a	a	DET
ejpam-6939	636	18	noncut	noncut	ADJ
ejpam-6939	636	19	-	-	PUNCT
ejpam-6939	636	20	vertex	vertex	NOUN
ejpam-6939	636	21	of	of	ADP
ejpam-6939	636	22	g	g	PROPN
ejpam-6939	636	23	and	and	CCONJ
ejpam-6939	636	24	degg(v	degg(v	PROPN
ejpam-6939	636	25	)	)	PUNCT
ejpam-6939	636	26	≥	≥	NOUN
ejpam-6939	636	27	2	2	NUM
ejpam-6939	636	28	.	.	PUNCT
ejpam-6939	636	29	suppose	suppose	VERB
ejpam-6939	636	30	there	there	PRON
ejpam-6939	636	31	exists	exist	VERB
ejpam-6939	636	32	w	w	PROPN
ejpam-6939	636	33	∈	∈	PROPN
ejpam-6939	636	34	v	v	ADP
ejpam-6939	636	35	(	(	PUNCT
ejpam-6939	636	36	g	g	NOUN
ejpam-6939	636	37	)	)	PUNCT
ejpam-6939	636	38	\	\	PUNCT
ejpam-6939	637	1	(	(	PUNCT
ejpam-6939	637	2	s	s	NOUN
ejpam-6939	637	3	∪	∪	X
ejpam-6939	637	4	{	{	PUNCT
ejpam-6939	637	5	v	v	NOUN
ejpam-6939	637	6	}	}	PUNCT
ejpam-6939	637	7	)	)	PUNCT
ejpam-6939	637	8	.	.	PUNCT
ejpam-6939	638	1	then	then	ADV
ejpam-6939	638	2	w	w	PROPN
ejpam-6939	638	3	is	be	AUX
ejpam-6939	638	4	also	also	ADV
ejpam-6939	638	5	non	non	ADJ
ejpam-6939	638	6	-	-	ADJ
ejpam-6939	638	7	cut	cut	ADJ
ejpam-6939	638	8	-	-	PUNCT
ejpam-6939	638	9	vertex	vertex	NOUN
ejpam-6939	638	10	of	of	ADP
ejpam-6939	638	11	g	g	PROPN
ejpam-6939	638	12	and	and	CCONJ
ejpam-6939	638	13	|ng(w	|ng(w	NOUN
ejpam-6939	638	14	)	)	PUNCT
ejpam-6939	638	15	∩	∩	NOUN
ejpam-6939	638	16	s|	s|	VERB
ejpam-6939	638	17	≥	≥	NOUN
ejpam-6939	638	18	2	2	NUM
ejpam-6939	638	19	.	.	PUNCT
ejpam-6939	639	1	hence	hence	ADV
ejpam-6939	639	2	,	,	PUNCT
ejpam-6939	639	3	w	w	PROPN
ejpam-6939	639	4	is	be	AUX
ejpam-6939	639	5	a	a	DET
ejpam-6939	639	6	non	non	ADJ
ejpam-6939	639	7	-	-	ADJ
ejpam-6939	639	8	cut	cut	ADJ
ejpam-6939	639	9	-	-	PUNCT
ejpam-6939	639	10	vertex	vertex	NOUN
ejpam-6939	639	11	of	of	ADP
ejpam-6939	639	12	h	h	NOUN
ejpam-6939	639	13	=	=	SYM
ejpam-6939	639	14	⟨v	⟨v	PUNCT
ejpam-6939	639	15	(	(	PUNCT
ejpam-6939	639	16	g	g	NOUN
ejpam-6939	639	17	)	)	PUNCT
ejpam-6939	639	18	\	\	NOUN
ejpam-6939	639	19	{	{	PUNCT
ejpam-6939	639	20	v}⟩	v}⟩	PROPN
ejpam-6939	639	21	and	and	CCONJ
ejpam-6939	639	22	deg(w	deg(w	NUM
ejpam-6939	639	23	)	)	PUNCT
ejpam-6939	639	24	≥	≥	NOUN
ejpam-6939	639	25	2	2	NUM
ejpam-6939	639	26	.	.	PUNCT
ejpam-6939	640	1	by	by	ADP
ejpam-6939	640	2	(	(	PUNCT
ejpam-6939	640	3	b	b	NOUN
ejpam-6939	640	4	)	)	PUNCT
ejpam-6939	640	5	,	,	PUNCT
ejpam-6939	640	6	it	it	PRON
ejpam-6939	640	7	follows	follow	VERB
ejpam-6939	640	8	that	that	SCONJ
ejpam-6939	640	9	vw	vw	PROPN
ejpam-6939	640	10	∈	∈	PROPN
ejpam-6939	640	11	e(g	e(g	PROPN
ejpam-6939	640	12	)	)	PUNCT
ejpam-6939	640	13	and	and	CCONJ
ejpam-6939	640	14	degg(v	degg(v	PROPN
ejpam-6939	640	15	)	)	PUNCT
ejpam-6939	640	16	=	=	SYM
ejpam-6939	640	17	2	2	X
ejpam-6939	640	18	.	.	PUNCT
ejpam-6939	640	19	thus	thus	ADV
ejpam-6939	640	20	,	,	PUNCT
ejpam-6939	640	21	|ng(v)∩s|	|ng(v)∩s|	PROPN
ejpam-6939	640	22	≤	≤	ADV
ejpam-6939	640	23	1	1	NUM
ejpam-6939	640	24	,	,	PUNCT
ejpam-6939	640	25	contrary	contrary	ADV
ejpam-6939	640	26	to	to	ADP
ejpam-6939	640	27	the	the	DET
ejpam-6939	640	28	assumption	assumption	NOUN
ejpam-6939	640	29	that	that	SCONJ
ejpam-6939	640	30	s	s	VERB
ejpam-6939	640	31	is	be	AUX
ejpam-6939	640	32	a	a	DET
ejpam-6939	640	33	2	2	NUM
ejpam-6939	640	34	-	-	PUNCT
ejpam-6939	640	35	dominating	dominating	NOUN
ejpam-6939	640	36	set	set	NOUN
ejpam-6939	640	37	.	.	PUNCT
ejpam-6939	641	1	therefore	therefore	ADV
ejpam-6939	641	2	,	,	PUNCT
ejpam-6939	641	3	s	s	NOUN
ejpam-6939	641	4	=	=	SYM
ejpam-6939	641	5	v	v	X
ejpam-6939	641	6	(	(	PUNCT
ejpam-6939	641	7	g	g	NOUN
ejpam-6939	641	8	)	)	PUNCT
ejpam-6939	641	9	\	\	NOUN
ejpam-6939	641	10	{	{	PUNCT
ejpam-6939	641	11	v	v	NOUN
ejpam-6939	641	12	}	}	PUNCT
ejpam-6939	641	13	and	and	CCONJ
ejpam-6939	641	14	γ×2,c(g	γ×2,c(g	ADJ
ejpam-6939	641	15	)	)	PUNCT
ejpam-6939	641	16	=	=	SYM
ejpam-6939	641	17	|s|	|s|	NOUN
ejpam-6939	641	18	=	=	SYM
ejpam-6939	641	19	n−	n−	PROPN
ejpam-6939	641	20	1	1	NUM
ejpam-6939	641	21	.	.	PUNCT
ejpam-6939	642	1	the	the	DET
ejpam-6939	642	2	next	next	ADJ
ejpam-6939	642	3	result	result	NOUN
ejpam-6939	642	4	is	be	AUX
ejpam-6939	642	5	immediate	immediate	ADJ
ejpam-6939	642	6	from	from	ADP
ejpam-6939	642	7	proposition	proposition	NOUN
ejpam-6939	642	8	5	5	NUM
ejpam-6939	642	9	and	and	CCONJ
ejpam-6939	642	10	lemma	lemma	PROPN
ejpam-6939	642	11	1	1	NUM
ejpam-6939	642	12	.	.	PUNCT
ejpam-6939	642	13	corollary	corollary	ADJ
ejpam-6939	642	14	4	4	NUM
ejpam-6939	642	15	.	.	PUNCT
ejpam-6939	643	1	let	let	VERB
ejpam-6939	643	2	g	g	PRON
ejpam-6939	643	3	be	be	AUX
ejpam-6939	643	4	a	a	DET
ejpam-6939	643	5	connected	connected	ADJ
ejpam-6939	643	6	graph	graph	NOUN
ejpam-6939	643	7	of	of	ADP
ejpam-6939	643	8	order	order	NOUN
ejpam-6939	643	9	n	n	NOUN
ejpam-6939	643	10	and	and	CCONJ
ejpam-6939	643	11	let	let	VERB
ejpam-6939	643	12	h	h	NOUN
ejpam-6939	643	13	be	be	AUX
ejpam-6939	643	14	any	any	DET
ejpam-6939	643	15	graph	graph	NOUN
ejpam-6939	643	16	.	.	PUNCT
ejpam-6939	644	1	then	then	ADV
ejpam-6939	644	2	γdc	γdc	PROPN
ejpam-6939	644	3	(	(	PUNCT
ejpam-6939	644	4	g	g	PROPN
ejpam-6939	644	5	◦	◦	NOUN
ejpam-6939	644	6	h	h	NOUN
ejpam-6939	644	7	)	)	PUNCT
ejpam-6939	644	8	=	=	SYM
ejpam-6939	644	9	γ×2,c(g	γ×2,c(g	NOUN
ejpam-6939	644	10	)	)	PUNCT
ejpam-6939	644	11	.	.	PUNCT
ejpam-6939	645	1	in	in	ADP
ejpam-6939	645	2	particular	particular	ADJ
ejpam-6939	645	3	,	,	PUNCT
ejpam-6939	645	4	the	the	DET
ejpam-6939	645	5	following	follow	VERB
ejpam-6939	645	6	hold	hold	NOUN
ejpam-6939	645	7	:	:	PUNCT
ejpam-6939	645	8	(	(	PUNCT
ejpam-6939	645	9	i	i	NOUN
ejpam-6939	645	10	)	)	PUNCT
ejpam-6939	645	11	if	if	SCONJ
ejpam-6939	645	12	g	g	PROPN
ejpam-6939	645	13	=	=	PROPN
ejpam-6939	645	14	kn	kn	PROPN
ejpam-6939	645	15	with	with	ADP
ejpam-6939	645	16	n	n	PRON
ejpam-6939	645	17	≥	≥	NUM
ejpam-6939	645	18	2	2	NUM
ejpam-6939	645	19	,	,	PUNCT
ejpam-6939	645	20	then	then	ADV
ejpam-6939	645	21	γdc	γdc	PROPN
ejpam-6939	645	22	(	(	PUNCT
ejpam-6939	645	23	g	g	PROPN
ejpam-6939	645	24	◦	◦	NOUN
ejpam-6939	645	25	h	h	NOUN
ejpam-6939	645	26	)	)	PUNCT
ejpam-6939	645	27	=	=	SYM
ejpam-6939	646	1	2	2	X
ejpam-6939	646	2	.	.	PUNCT
ejpam-6939	646	3	(	(	PUNCT
ejpam-6939	646	4	ii	ii	NOUN
ejpam-6939	646	5	)	)	PUNCT
ejpam-6939	646	6	if	if	SCONJ
ejpam-6939	646	7	g	g	PROPN
ejpam-6939	646	8	is	be	AUX
ejpam-6939	646	9	a	a	DET
ejpam-6939	646	10	tree	tree	NOUN
ejpam-6939	646	11	,	,	PUNCT
ejpam-6939	646	12	then	then	ADV
ejpam-6939	646	13	γdc	γdc	PROPN
ejpam-6939	646	14	(	(	PUNCT
ejpam-6939	646	15	g	g	PROPN
ejpam-6939	646	16	◦	◦	NOUN
ejpam-6939	646	17	h	h	NOUN
ejpam-6939	646	18	)	)	PUNCT
ejpam-6939	646	19	=	=	VERB
ejpam-6939	647	1	n.	n.	NOUN
ejpam-6939	647	2	(	(	PUNCT
ejpam-6939	647	3	iii	iii	NOUN
ejpam-6939	647	4	)	)	PUNCT
ejpam-6939	647	5	if	if	SCONJ
ejpam-6939	647	6	g	g	PROPN
ejpam-6939	647	7	=	=	SYM
ejpam-6939	647	8	cn	cn	PROPN
ejpam-6939	647	9	with	with	ADP
ejpam-6939	647	10	n	n	NUM
ejpam-6939	647	11	≥	≥	NUM
ejpam-6939	647	12	3	3	NUM
ejpam-6939	647	13	,	,	PUNCT
ejpam-6939	647	14	then	then	ADV
ejpam-6939	647	15	γdc	γdc	PROPN
ejpam-6939	647	16	(	(	PUNCT
ejpam-6939	647	17	g	g	PROPN
ejpam-6939	647	18	◦	◦	NOUN
ejpam-6939	647	19	h	h	NOUN
ejpam-6939	647	20	)	)	PUNCT
ejpam-6939	647	21	=	=	PUNCT
ejpam-6939	647	22	n−	n−	NOUN
ejpam-6939	647	23	1	1	NUM
ejpam-6939	647	24	.	.	PUNCT
ejpam-6939	647	25	a.	a.	PROPN
ejpam-6939	647	26	aradais	aradais	PROPN
ejpam-6939	647	27	,	,	PUNCT
ejpam-6939	647	28	f.	f.	PROPN
ejpam-6939	647	29	jamil	jamil	PROPN
ejpam-6939	647	30	,	,	PUNCT
ejpam-6939	647	31	s.	s.	PROPN
ejpam-6939	647	32	canoy	canoy	PROPN
ejpam-6939	647	33	/	/	SYM
ejpam-6939	647	34	eur	eur	PROPN
ejpam-6939	647	35	.	.	PUNCT
ejpam-6939	648	1	j.	j.	PROPN
ejpam-6939	648	2	pure	pure	PROPN
ejpam-6939	648	3	appl	appl	PROPN
ejpam-6939	648	4	.	.	PROPN
ejpam-6939	648	5	math	math	PROPN
ejpam-6939	648	6	,	,	PUNCT
ejpam-6939	648	7	18	18	NUM
ejpam-6939	648	8	(	(	PUNCT
ejpam-6939	648	9	4	4	NUM
ejpam-6939	648	10	)	)	PUNCT
ejpam-6939	648	11	(	(	PUNCT
ejpam-6939	648	12	2025	2025	NUM
ejpam-6939	648	13	)	)	PUNCT
ejpam-6939	648	14	,	,	PUNCT
ejpam-6939	648	15	6939	6939	NUM
ejpam-6939	648	16	11	11	NUM
ejpam-6939	648	17	of	of	ADP
ejpam-6939	648	18	14	14	NUM
ejpam-6939	648	19	6	6	NUM
ejpam-6939	648	20	.	.	PUNCT
ejpam-6939	649	1	in	in	ADP
ejpam-6939	649	2	the	the	DET
ejpam-6939	649	3	lexicographic	lexicographic	ADJ
ejpam-6939	649	4	product	product	NOUN
ejpam-6939	649	5	of	of	ADP
ejpam-6939	649	6	graphs	graph	NOUN
ejpam-6939	649	7	for	for	ADP
ejpam-6939	649	8	any	any	DET
ejpam-6939	649	9	graphs	graph	NOUN
ejpam-6939	649	10	g	g	NOUN
ejpam-6939	649	11	and	and	CCONJ
ejpam-6939	649	12	h	h	NOUN
ejpam-6939	649	13	and	and	CCONJ
ejpam-6939	649	14	for	for	ADP
ejpam-6939	649	15	any	any	DET
ejpam-6939	649	16	c	c	NOUN
ejpam-6939	649	17	⊆	⊆	NUM
ejpam-6939	649	18	v	v	NOUN
ejpam-6939	649	19	(	(	PUNCT
ejpam-6939	649	20	g[h	g[h	PROPN
ejpam-6939	649	21	]	]	PUNCT
ejpam-6939	649	22	)	)	PUNCT
ejpam-6939	649	23	,	,	PUNCT
ejpam-6939	649	24	there	there	PRON
ejpam-6939	649	25	exists	exist	VERB
ejpam-6939	649	26	s	s	PROPN
ejpam-6939	649	27	⊆	⊆	NUM
ejpam-6939	649	28	v	v	NOUN
ejpam-6939	649	29	(	(	PUNCT
ejpam-6939	649	30	g	g	NOUN
ejpam-6939	649	31	)	)	PUNCT
ejpam-6939	649	32	for	for	ADP
ejpam-6939	649	33	which	which	PRON
ejpam-6939	649	34	c	c	NOUN
ejpam-6939	649	35	=	=	SYM
ejpam-6939	649	36	∪x∈s	∪x∈s	PROPN
ejpam-6939	649	37	(	(	PUNCT
ejpam-6939	649	38	{	{	PUNCT
ejpam-6939	649	39	x	x	NOUN
ejpam-6939	649	40	}	}	PUNCT
ejpam-6939	649	41	×	×	PROPN
ejpam-6939	649	42	tx	tx	PROPN
ejpam-6939	649	43	)	)	PUNCT
ejpam-6939	649	44	,	,	PUNCT
ejpam-6939	649	45	where	where	SCONJ
ejpam-6939	649	46	tx	tx	PROPN
ejpam-6939	649	47	⊆	⊆	NUM
ejpam-6939	649	48	v	v	NOUN
ejpam-6939	649	49	(	(	PUNCT
ejpam-6939	649	50	h	h	NOUN
ejpam-6939	649	51	)	)	PUNCT
ejpam-6939	649	52	for	for	ADP
ejpam-6939	649	53	each	each	DET
ejpam-6939	649	54	x	x	PROPN
ejpam-6939	649	55	∈	∈	PROPN
ejpam-6939	649	56	s.	s.	PROPN
ejpam-6939	649	57	moreover	moreover	ADV
ejpam-6939	649	58	,	,	PUNCT
ejpam-6939	649	59	if	if	SCONJ
ejpam-6939	649	60	⟨c⟩	⟨c⟩	PROPN
ejpam-6939	649	61	is	be	AUX
ejpam-6939	649	62	connected	connect	VERB
ejpam-6939	649	63	,	,	PUNCT
ejpam-6939	649	64	then	then	ADV
ejpam-6939	649	65	so	so	ADV
ejpam-6939	649	66	is	be	AUX
ejpam-6939	649	67	⟨s⟩.	⟨s⟩.	PROPN
ejpam-6939	649	68	provided	provide	VERB
ejpam-6939	649	69	|s|	|s|	PROPN
ejpam-6939	649	70	≥	≥	NOUN
ejpam-6939	649	71	2	2	NUM
ejpam-6939	649	72	,	,	PUNCT
ejpam-6939	649	73	the	the	DET
ejpam-6939	649	74	converse	converse	NOUN
ejpam-6939	649	75	is	be	AUX
ejpam-6939	649	76	also	also	ADV
ejpam-6939	649	77	true	true	ADJ
ejpam-6939	649	78	.	.	PUNCT
ejpam-6939	650	1	for	for	ADP
ejpam-6939	650	2	convenience	convenience	NOUN
ejpam-6939	650	3	,	,	PUNCT
ejpam-6939	650	4	we	we	PRON
ejpam-6939	650	5	write	write	VERB
ejpam-6939	650	6	nd	nd	ADV
ejpam-6939	650	7	g[s	g[s	PROPN
ejpam-6939	650	8	]	]	PUNCT
ejpam-6939	650	9	=	=	SYM
ejpam-6939	650	10	s	s	PROPN
ejpam-6939	650	11	∪nd	∪nd	NOUN
ejpam-6939	650	12	g(s	g(s	PROPN
ejpam-6939	650	13	)	)	PUNCT
ejpam-6939	650	14	.	.	PUNCT
ejpam-6939	651	1	theorem	theorem	NOUN
ejpam-6939	651	2	3	3	NUM
ejpam-6939	651	3	.	.	PUNCT
ejpam-6939	652	1	[	[	X
ejpam-6939	652	2	4	4	X
ejpam-6939	652	3	]	]	PUNCT
ejpam-6939	652	4	let	let	VERB
ejpam-6939	652	5	g	g	NOUN
ejpam-6939	652	6	and	and	CCONJ
ejpam-6939	652	7	h	h	NOUN
ejpam-6939	652	8	be	be	AUX
ejpam-6939	652	9	nontrivial	nontrivial	ADJ
ejpam-6939	652	10	connected	connected	ADJ
ejpam-6939	652	11	graphs	graph	NOUN
ejpam-6939	652	12	,	,	PUNCT
ejpam-6939	652	13	and	and	CCONJ
ejpam-6939	652	14	let	let	VERB
ejpam-6939	652	15	c	c	NOUN
ejpam-6939	652	16	=	=	SYM
ejpam-6939	652	17	∪x∈s	∪x∈s	PROPN
ejpam-6939	652	18	(	(	PUNCT
ejpam-6939	652	19	{	{	PUNCT
ejpam-6939	652	20	x	x	NOUN
ejpam-6939	652	21	}	}	PUNCT
ejpam-6939	652	22	×	×	PROPN
ejpam-6939	652	23	tx	tx	PROPN
ejpam-6939	652	24	)	)	PUNCT
ejpam-6939	652	25	.	.	PUNCT
ejpam-6939	653	1	then	then	ADV
ejpam-6939	653	2	c	c	PROPN
ejpam-6939	653	3	is	be	AUX
ejpam-6939	653	4	a	a	DET
ejpam-6939	653	5	disjunctive	disjunctive	ADJ
ejpam-6939	653	6	dominating	dominating	NOUN
ejpam-6939	653	7	set	set	NOUN
ejpam-6939	653	8	of	of	ADP
ejpam-6939	653	9	g[h	g[h	PROPN
ejpam-6939	653	10	]	]	PUNCT
ejpam-6939	653	11	if	if	SCONJ
ejpam-6939	653	12	and	and	CCONJ
ejpam-6939	653	13	only	only	ADV
ejpam-6939	653	14	if	if	SCONJ
ejpam-6939	653	15	one	one	NUM
ejpam-6939	653	16	of	of	ADP
ejpam-6939	653	17	the	the	DET
ejpam-6939	653	18	following	follow	VERB
ejpam-6939	653	19	holds	hold	VERB
ejpam-6939	653	20	:	:	PUNCT
ejpam-6939	653	21	(	(	PUNCT
ejpam-6939	653	22	i	i	NOUN
ejpam-6939	653	23	)	)	PUNCT
ejpam-6939	653	24	s	s	VERB
ejpam-6939	653	25	is	be	AUX
ejpam-6939	653	26	a	a	DET
ejpam-6939	653	27	disjunctive	disjunctive	ADJ
ejpam-6939	653	28	total	total	ADJ
ejpam-6939	653	29	dominating	dominating	NOUN
ejpam-6939	653	30	set	set	VERB
ejpam-6939	653	31	in	in	ADP
ejpam-6939	653	32	g	g	NOUN
ejpam-6939	653	33	;	;	PUNCT
ejpam-6939	653	34	(	(	PUNCT
ejpam-6939	653	35	ii	ii	NOUN
ejpam-6939	653	36	)	)	PUNCT
ejpam-6939	653	37	s	s	VERB
ejpam-6939	653	38	is	be	AUX
ejpam-6939	653	39	a	a	DET
ejpam-6939	653	40	distance	distance	NOUN
ejpam-6939	653	41	-	-	PUNCT
ejpam-6939	653	42	two	two	NUM
ejpam-6939	653	43	dominating	dominating	NOUN
ejpam-6939	653	44	set	set	NOUN
ejpam-6939	653	45	of	of	ADP
ejpam-6939	653	46	g	g	PROPN
ejpam-6939	653	47	satisfying	satisfy	VERB
ejpam-6939	653	48	the	the	DET
ejpam-6939	653	49	following	following	NOUN
ejpam-6939	653	50	:	:	PUNCT
ejpam-6939	653	51	(	(	PUNCT
ejpam-6939	653	52	a	a	X
ejpam-6939	653	53	)	)	PUNCT
ejpam-6939	653	54	for	for	ADP
ejpam-6939	653	55	each	each	DET
ejpam-6939	653	56	x	x	SYM
ejpam-6939	653	57	∈	∈	PROPN
ejpam-6939	653	58	v	v	ADP
ejpam-6939	653	59	(	(	PUNCT
ejpam-6939	653	60	g	g	NOUN
ejpam-6939	653	61	)	)	PUNCT
ejpam-6939	653	62	\	\	PROPN
ejpam-6939	653	63	nd	nd	NUM
ejpam-6939	653	64	g[s	g[s	PROPN
ejpam-6939	653	65	]	]	PUNCT
ejpam-6939	653	66	there	there	PRON
ejpam-6939	653	67	exists	exist	VERB
ejpam-6939	653	68	u	u	PROPN
ejpam-6939	653	69	∈	∈	PROPN
ejpam-6939	653	70	s	s	X
ejpam-6939	653	71	for	for	ADP
ejpam-6939	653	72	which	which	PRON
ejpam-6939	653	73	dg(u	dg(u	NOUN
ejpam-6939	653	74	,	,	PUNCT
ejpam-6939	653	75	x	x	X
ejpam-6939	653	76	)	)	PUNCT
ejpam-6939	653	77	=	=	SYM
ejpam-6939	653	78	2	2	NUM
ejpam-6939	653	79	and	and	CCONJ
ejpam-6939	653	80	|tu|	|tu|	NOUN
ejpam-6939	653	81	≥	≥	NOUN
ejpam-6939	653	82	2	2	NUM
ejpam-6939	653	83	.	.	PUNCT
ejpam-6939	654	1	(	(	PUNCT
ejpam-6939	654	2	b	b	NOUN
ejpam-6939	654	3	)	)	PUNCT
ejpam-6939	654	4	for	for	ADP
ejpam-6939	654	5	each	each	DET
ejpam-6939	654	6	x	x	SYM
ejpam-6939	654	7	∈	∈	PROPN
ejpam-6939	654	8	s	s	PART
ejpam-6939	654	9	\	\	NOUN
ejpam-6939	654	10	ng(s	ng(s	NUM
ejpam-6939	654	11	,	,	PUNCT
ejpam-6939	654	12	2	2	NUM
ejpam-6939	654	13	)	)	PUNCT
ejpam-6939	654	14	,	,	PUNCT
ejpam-6939	654	15	either	either	CCONJ
ejpam-6939	654	16	tx	tx	PROPN
ejpam-6939	654	17	=	=	SYM
ejpam-6939	654	18	{	{	PUNCT
ejpam-6939	654	19	y	y	NOUN
ejpam-6939	654	20	}	}	PUNCT
ejpam-6939	654	21	and	and	CCONJ
ejpam-6939	654	22	is	be	AUX
ejpam-6939	654	23	a	a	DET
ejpam-6939	654	24	dominating	dominating	NOUN
ejpam-6939	654	25	set	set	NOUN
ejpam-6939	654	26	of	of	ADP
ejpam-6939	654	27	h	h	NOUN
ejpam-6939	654	28	or	or	CCONJ
ejpam-6939	654	29	|tx|	|tx|	PROPN
ejpam-6939	654	30	≥	≥	NUM
ejpam-6939	654	31	2	2	NUM
ejpam-6939	654	32	.	.	PUNCT
ejpam-6939	654	33	theorem	theorem	NOUN
ejpam-6939	654	34	4	4	NUM
ejpam-6939	654	35	.	.	PUNCT
ejpam-6939	655	1	let	let	VERB
ejpam-6939	655	2	g	g	NOUN
ejpam-6939	655	3	and	and	CCONJ
ejpam-6939	655	4	h	h	NOUN
ejpam-6939	655	5	be	be	AUX
ejpam-6939	655	6	nontrivial	nontrivial	ADJ
ejpam-6939	655	7	connected	connected	ADJ
ejpam-6939	655	8	graphs	graph	NOUN
ejpam-6939	655	9	,	,	PUNCT
ejpam-6939	655	10	and	and	CCONJ
ejpam-6939	655	11	let	let	VERB
ejpam-6939	655	12	c	c	NOUN
ejpam-6939	655	13	=	=	SYM
ejpam-6939	655	14	∪x∈s	∪x∈s	PROPN
ejpam-6939	655	15	(	(	PUNCT
ejpam-6939	655	16	{	{	PUNCT
ejpam-6939	655	17	x	x	NOUN
ejpam-6939	655	18	}	}	PUNCT
ejpam-6939	655	19	×	×	PROPN
ejpam-6939	655	20	tx	tx	PROPN
ejpam-6939	655	21	)	)	PUNCT
ejpam-6939	655	22	.	.	PUNCT
ejpam-6939	656	1	then	then	ADV
ejpam-6939	656	2	c	c	PROPN
ejpam-6939	656	3	is	be	AUX
ejpam-6939	656	4	a	a	DET
ejpam-6939	656	5	connected	connected	ADJ
ejpam-6939	656	6	disjunctive	disjunctive	ADJ
ejpam-6939	656	7	dominating	dominating	NOUN
ejpam-6939	656	8	set	set	NOUN
ejpam-6939	656	9	of	of	ADP
ejpam-6939	656	10	g[h	g[h	PROPN
ejpam-6939	656	11	]	]	PUNCT
ejpam-6939	656	12	if	if	SCONJ
ejpam-6939	656	13	and	and	CCONJ
ejpam-6939	656	14	only	only	ADV
ejpam-6939	656	15	if	if	SCONJ
ejpam-6939	656	16	one	one	NUM
ejpam-6939	656	17	of	of	ADP
ejpam-6939	656	18	the	the	DET
ejpam-6939	656	19	following	following	NOUN
ejpam-6939	656	20	holds	hold	VERB
ejpam-6939	656	21	for	for	ADP
ejpam-6939	656	22	s	s	PRON
ejpam-6939	656	23	:	:	PUNCT
ejpam-6939	656	24	(	(	PUNCT
ejpam-6939	656	25	i	i	NOUN
ejpam-6939	656	26	)	)	PUNCT
ejpam-6939	656	27	|s|	|s|	VERB
ejpam-6939	656	28	≥	≥	NOUN
ejpam-6939	656	29	2	2	NUM
ejpam-6939	656	30	and	and	CCONJ
ejpam-6939	656	31	s	s	VERB
ejpam-6939	656	32	is	be	AUX
ejpam-6939	656	33	a	a	DET
ejpam-6939	656	34	connected	connected	ADJ
ejpam-6939	656	35	disjunctive	disjunctive	ADJ
ejpam-6939	656	36	dominating	dominating	NOUN
ejpam-6939	656	37	set	set	NOUN
ejpam-6939	656	38	of	of	ADP
ejpam-6939	656	39	g	g	NOUN
ejpam-6939	656	40	;	;	PUNCT
ejpam-6939	656	41	(	(	PUNCT
ejpam-6939	656	42	ii	ii	NOUN
ejpam-6939	656	43	)	)	PUNCT
ejpam-6939	656	44	s	s	VERB
ejpam-6939	656	45	is	be	AUX
ejpam-6939	656	46	a	a	DET
ejpam-6939	656	47	connected	connected	ADJ
ejpam-6939	656	48	distance	distance	NOUN
ejpam-6939	656	49	-	-	PUNCT
ejpam-6939	656	50	two	two	NUM
ejpam-6939	656	51	dominating	dominating	NOUN
ejpam-6939	656	52	set	set	NOUN
ejpam-6939	656	53	of	of	ADP
ejpam-6939	656	54	g	g	NOUN
ejpam-6939	656	55	satisfying	satisfy	VERB
ejpam-6939	656	56	exactly	exactly	ADV
ejpam-6939	656	57	one	one	NUM
ejpam-6939	656	58	of	of	ADP
ejpam-6939	656	59	the	the	DET
ejpam-6939	656	60	following	following	NOUN
ejpam-6939	656	61	:	:	PUNCT
ejpam-6939	656	62	(	(	PUNCT
ejpam-6939	656	63	a	a	X
ejpam-6939	656	64	)	)	PUNCT
ejpam-6939	656	65	|s|	|s|	PROPN
ejpam-6939	656	66	≥	≥	NOUN
ejpam-6939	656	67	2	2	NUM
ejpam-6939	656	68	and	and	CCONJ
ejpam-6939	656	69	for	for	ADP
ejpam-6939	656	70	each	each	DET
ejpam-6939	656	71	x	x	SYM
ejpam-6939	656	72	∈	∈	PROPN
ejpam-6939	656	73	v	v	X
ejpam-6939	656	74	(	(	PUNCT
ejpam-6939	656	75	g)\nd	g)\nd	PROPN
ejpam-6939	656	76	g[s	g[s	PROPN
ejpam-6939	656	77	]	]	PUNCT
ejpam-6939	656	78	there	there	PRON
ejpam-6939	656	79	exists	exist	VERB
ejpam-6939	656	80	u	u	PROPN
ejpam-6939	656	81	∈	∈	PROPN
ejpam-6939	656	82	s	s	X
ejpam-6939	656	83	for	for	ADP
ejpam-6939	656	84	which	which	PRON
ejpam-6939	656	85	dg(u	dg(u	NOUN
ejpam-6939	656	86	,	,	PUNCT
ejpam-6939	656	87	x	x	X
ejpam-6939	656	88	)	)	PUNCT
ejpam-6939	656	89	=	=	SYM
ejpam-6939	656	90	2	2	NUM
ejpam-6939	656	91	and	and	CCONJ
ejpam-6939	656	92	|tu|	|tu|	NOUN
ejpam-6939	656	93	≥	≥	NOUN
ejpam-6939	656	94	2	2	NUM
ejpam-6939	656	95	.	.	PUNCT
ejpam-6939	657	1	(	(	PUNCT
ejpam-6939	657	2	b	b	X
ejpam-6939	657	3	)	)	PUNCT
ejpam-6939	657	4	s	s	PART
ejpam-6939	657	5	=	=	PUNCT
ejpam-6939	657	6	{	{	PUNCT
ejpam-6939	657	7	x	x	NOUN
ejpam-6939	657	8	}	}	PUNCT
ejpam-6939	657	9	for	for	ADP
ejpam-6939	657	10	some	some	DET
ejpam-6939	657	11	x	x	SYM
ejpam-6939	657	12	∈	∈	PROPN
ejpam-6939	657	13	v	v	NOUN
ejpam-6939	657	14	(	(	PUNCT
ejpam-6939	657	15	g	g	NOUN
ejpam-6939	657	16	)	)	PUNCT
ejpam-6939	657	17	,	,	PUNCT
ejpam-6939	657	18	where	where	SCONJ
ejpam-6939	657	19	⟨tx⟩	⟨tx⟩	NOUN
ejpam-6939	657	20	is	be	AUX
ejpam-6939	657	21	a	a	DET
ejpam-6939	657	22	connected	connected	ADJ
ejpam-6939	657	23	graph	graph	NOUN
ejpam-6939	657	24	satisfying	satisfy	VERB
ejpam-6939	657	25	the	the	DET
ejpam-6939	657	26	following	following	NOUN
ejpam-6939	657	27	:	:	PUNCT
ejpam-6939	657	28	(	(	PUNCT
ejpam-6939	657	29	b.1	b.1	X
ejpam-6939	657	30	)	)	PUNCT
ejpam-6939	657	31	if	if	SCONJ
ejpam-6939	657	32	s	s	NOUN
ejpam-6939	657	33	is	be	AUX
ejpam-6939	657	34	a	a	DET
ejpam-6939	657	35	non	non	ADJ
ejpam-6939	657	36	-	-	ADJ
ejpam-6939	657	37	dominating	dominating	ADJ
ejpam-6939	657	38	set	set	NOUN
ejpam-6939	657	39	of	of	ADP
ejpam-6939	657	40	g	g	NOUN
ejpam-6939	657	41	,	,	PUNCT
ejpam-6939	657	42	then	then	ADV
ejpam-6939	657	43	|tx|	|tx|	NOUN
ejpam-6939	657	44	≥	≥	NUM
ejpam-6939	657	45	2	2	NUM
ejpam-6939	657	46	;	;	PUNCT
ejpam-6939	657	47	and	and	CCONJ
ejpam-6939	657	48	(	(	PUNCT
ejpam-6939	657	49	b.2	b.2	X
ejpam-6939	657	50	)	)	PUNCT
ejpam-6939	657	51	if	if	SCONJ
ejpam-6939	657	52	|tx|	|tx|	NUM
ejpam-6939	657	53	=	=	SYM
ejpam-6939	657	54	1	1	NUM
ejpam-6939	657	55	,	,	PUNCT
ejpam-6939	657	56	then	then	ADV
ejpam-6939	657	57	s	s	PART
ejpam-6939	657	58	and	and	CCONJ
ejpam-6939	657	59	tx	tx	PROPN
ejpam-6939	657	60	are	be	AUX
ejpam-6939	657	61	dominating	dominate	VERB
ejpam-6939	657	62	sets	set	NOUN
ejpam-6939	657	63	of	of	ADP
ejpam-6939	657	64	g	g	PROPN
ejpam-6939	657	65	and	and	CCONJ
ejpam-6939	657	66	h	h	NOUN
ejpam-6939	657	67	,	,	PUNCT
ejpam-6939	657	68	respectively	respectively	ADV
ejpam-6939	657	69	.	.	PUNCT
ejpam-6939	658	1	proof	proof	NOUN
ejpam-6939	658	2	.	.	PUNCT
ejpam-6939	659	1	suppose	suppose	VERB
ejpam-6939	659	2	that	that	SCONJ
ejpam-6939	659	3	c	c	PROPN
ejpam-6939	659	4	is	be	AUX
ejpam-6939	659	5	a	a	DET
ejpam-6939	659	6	connected	connected	ADJ
ejpam-6939	659	7	disjunctive	disjunctive	ADJ
ejpam-6939	659	8	dominating	dominating	NOUN
ejpam-6939	659	9	set	set	VERB
ejpam-6939	659	10	ofg[h	ofg[h	PROPN
ejpam-6939	659	11	]	]	PUNCT
ejpam-6939	659	12	.	.	PUNCT
ejpam-6939	660	1	as	as	SCONJ
ejpam-6939	660	2	previously	previously	ADV
ejpam-6939	660	3	remarked	remark	VERB
ejpam-6939	660	4	,	,	PUNCT
ejpam-6939	660	5	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	660	6	is	be	AUX
ejpam-6939	660	7	a	a	DET
ejpam-6939	660	8	connected	connected	ADJ
ejpam-6939	660	9	graph	graph	NOUN
ejpam-6939	660	10	.	.	PUNCT
ejpam-6939	661	1	first	first	ADV
ejpam-6939	661	2	,	,	PUNCT
ejpam-6939	661	3	if	if	SCONJ
ejpam-6939	661	4	theorem	theorem	VERB
ejpam-6939	661	5	3(i	3(i	NUM
ejpam-6939	661	6	)	)	PUNCT
ejpam-6939	661	7	holds	hold	VERB
ejpam-6939	661	8	for	for	ADP
ejpam-6939	661	9	s	s	PROPN
ejpam-6939	661	10	,	,	PUNCT
ejpam-6939	661	11	then	then	ADV
ejpam-6939	661	12	|s|	|s|	PROPN
ejpam-6939	661	13	≥	≥	NOUN
ejpam-6939	661	14	2	2	NUM
ejpam-6939	661	15	and	and	CCONJ
ejpam-6939	661	16	s	s	VERB
ejpam-6939	661	17	is	be	AUX
ejpam-6939	661	18	a	a	DET
ejpam-6939	661	19	disjunctive	disjunctive	ADJ
ejpam-6939	661	20	dominating	dominating	NOUN
ejpam-6939	661	21	set	set	NOUN
ejpam-6939	661	22	of	of	ADP
ejpam-6939	661	23	g.	g.	PROPN
ejpam-6939	661	24	in	in	ADP
ejpam-6939	661	25	this	this	DET
ejpam-6939	661	26	case	case	NOUN
ejpam-6939	661	27	,	,	PUNCT
ejpam-6939	661	28	(	(	PUNCT
ejpam-6939	661	29	i	i	NOUN
ejpam-6939	661	30	)	)	PUNCT
ejpam-6939	661	31	holds	hold	VERB
ejpam-6939	661	32	.	.	PUNCT
ejpam-6939	662	1	next	next	ADV
ejpam-6939	662	2	,	,	PUNCT
ejpam-6939	662	3	suppose	suppose	VERB
ejpam-6939	662	4	that	that	SCONJ
ejpam-6939	662	5	theorem	theorem	VERB
ejpam-6939	662	6	3(ii	3(ii	NUM
ejpam-6939	662	7	)	)	PUNCT
ejpam-6939	662	8	holds	hold	VERB
ejpam-6939	662	9	for	for	ADP
ejpam-6939	662	10	s.	s.	PROPN
ejpam-6939	663	1	then	then	ADV
ejpam-6939	663	2	s	s	VERB
ejpam-6939	663	3	is	be	AUX
ejpam-6939	663	4	a	a	DET
ejpam-6939	663	5	connected	connected	ADJ
ejpam-6939	663	6	distance	distance	NOUN
ejpam-6939	663	7	-	-	PUNCT
ejpam-6939	663	8	two	two	NUM
ejpam-6939	663	9	dominating	dominating	NOUN
ejpam-6939	663	10	set	set	NOUN
ejpam-6939	663	11	of	of	ADP
ejpam-6939	663	12	g.	g.	PROPN
ejpam-6939	663	13	if	if	SCONJ
ejpam-6939	663	14	|s|	|s|	NOUN
ejpam-6939	663	15	≥	≥	NOUN
ejpam-6939	663	16	2	2	NUM
ejpam-6939	663	17	,	,	PUNCT
ejpam-6939	663	18	then	then	ADV
ejpam-6939	663	19	condition	condition	NOUN
ejpam-6939	663	20	(	(	PUNCT
ejpam-6939	663	21	ii)(a	ii)(a	PROPN
ejpam-6939	663	22	)	)	PUNCT
ejpam-6939	663	23	follows	follow	VERB
ejpam-6939	663	24	immediately	immediately	ADV
ejpam-6939	663	25	from	from	ADP
ejpam-6939	663	26	theorem	theorem	ADJ
ejpam-6939	663	27	3(ii)(a	3(ii)(a	NUM
ejpam-6939	663	28	)	)	PUNCT
ejpam-6939	663	29	.	.	PUNCT
ejpam-6939	664	1	assume	assume	VERB
ejpam-6939	664	2	that	that	SCONJ
ejpam-6939	664	3	s	s	VERB
ejpam-6939	664	4	=	=	X
ejpam-6939	664	5	{	{	PUNCT
ejpam-6939	664	6	x	x	NOUN
ejpam-6939	664	7	}	}	PUNCT
ejpam-6939	664	8	for	for	ADP
ejpam-6939	664	9	some	some	DET
ejpam-6939	664	10	x	x	SYM
ejpam-6939	664	11	∈	∈	PROPN
ejpam-6939	664	12	v	v	NOUN
ejpam-6939	664	13	(	(	PUNCT
ejpam-6939	664	14	g	g	NOUN
ejpam-6939	664	15	)	)	PUNCT
ejpam-6939	664	16	.	.	PUNCT
ejpam-6939	665	1	clearly	clearly	ADV
ejpam-6939	665	2	,	,	PUNCT
ejpam-6939	665	3	⟨tx⟩	⟨tx⟩	PROPN
ejpam-6939	665	4	is	be	AUX
ejpam-6939	665	5	connected	connect	VERB
ejpam-6939	665	6	as	as	ADP
ejpam-6939	665	7	⟨c⟩	⟨c⟩	PROPN
ejpam-6939	665	8	is	be	AUX
ejpam-6939	665	9	connected	connect	VERB
ejpam-6939	665	10	.	.	PUNCT
ejpam-6939	666	1	suppose	suppose	VERB
ejpam-6939	666	2	s	s	PRON
ejpam-6939	666	3	is	be	AUX
ejpam-6939	666	4	a	a	DET
ejpam-6939	666	5	nondominating	nondominate	VERB
ejpam-6939	666	6	set	set	NOUN
ejpam-6939	666	7	of	of	ADP
ejpam-6939	666	8	g	g	NOUN
ejpam-6939	666	9	,	,	PUNCT
ejpam-6939	666	10	and	and	CCONJ
ejpam-6939	666	11	choose	choose	VERB
ejpam-6939	666	12	u	u	PROPN
ejpam-6939	666	13	∈	∈	PROPN
ejpam-6939	666	14	v	v	ADP
ejpam-6939	666	15	(	(	PUNCT
ejpam-6939	666	16	g	g	NOUN
ejpam-6939	666	17	)	)	PUNCT
ejpam-6939	666	18	\	\	PUNCT
ejpam-6939	667	1	ng[x	ng[x	PROPN
ejpam-6939	667	2	]	]	PUNCT
ejpam-6939	667	3	.	.	PUNCT
ejpam-6939	668	1	for	for	ADP
ejpam-6939	668	2	any	any	DET
ejpam-6939	668	3	v	v	NUM
ejpam-6939	668	4	∈	∈	PROPN
ejpam-6939	668	5	v	v	NOUN
ejpam-6939	668	6	(	(	PUNCT
ejpam-6939	668	7	h	h	NOUN
ejpam-6939	668	8	)	)	PUNCT
ejpam-6939	668	9	,	,	PUNCT
ejpam-6939	668	10	there	there	PRON
ejpam-6939	668	11	exist	exist	VERB
ejpam-6939	668	12	distinct	distinct	ADJ
ejpam-6939	668	13	y	y	NOUN
ejpam-6939	668	14	,	,	PUNCT
ejpam-6939	668	15	z	z	PROPN
ejpam-6939	668	16	∈	∈	PROPN
ejpam-6939	668	17	tx	tx	ADP
ejpam-6939	668	18	such	such	ADJ
ejpam-6939	668	19	that	that	DET
ejpam-6939	668	20	dg[h	dg[h	PROPN
ejpam-6939	668	21	]	]	X
ejpam-6939	668	22	(	(	PUNCT
ejpam-6939	668	23	(	(	PUNCT
ejpam-6939	668	24	u	u	NOUN
ejpam-6939	668	25	,	,	PUNCT
ejpam-6939	668	26	v	v	NOUN
ejpam-6939	668	27	)	)	PUNCT
ejpam-6939	668	28	,	,	PUNCT
ejpam-6939	668	29	(	(	PUNCT
ejpam-6939	668	30	x	x	X
ejpam-6939	668	31	,	,	PUNCT
ejpam-6939	668	32	y	y	NOUN
ejpam-6939	668	33	)	)	PUNCT
ejpam-6939	668	34	)	)	PUNCT
ejpam-6939	669	1	=	=	SYM
ejpam-6939	669	2	2	2	NUM
ejpam-6939	669	3	=	=	SYM
ejpam-6939	669	4	dg[h	dg[h	PROPN
ejpam-6939	669	5	]	]	X
ejpam-6939	669	6	(	(	PUNCT
ejpam-6939	669	7	(	(	PUNCT
ejpam-6939	669	8	u	u	NOUN
ejpam-6939	669	9	,	,	PUNCT
ejpam-6939	669	10	v	v	NOUN
ejpam-6939	669	11	)	)	PUNCT
ejpam-6939	669	12	,	,	PUNCT
ejpam-6939	669	13	(	(	PUNCT
ejpam-6939	669	14	x	x	X
ejpam-6939	669	15	,	,	PUNCT
ejpam-6939	669	16	z	z	NOUN
ejpam-6939	669	17	)	)	PUNCT
ejpam-6939	669	18	)	)	PUNCT
ejpam-6939	669	19	.	.	PUNCT
ejpam-6939	670	1	thus	thus	ADV
ejpam-6939	670	2	,	,	PUNCT
ejpam-6939	670	3	|tx|	|tx|	NOUN
ejpam-6939	670	4	≥	≥	NOUN
ejpam-6939	670	5	2	2	NUM
ejpam-6939	670	6	,	,	PUNCT
ejpam-6939	670	7	and	and	CCONJ
ejpam-6939	670	8	(	(	PUNCT
ejpam-6939	670	9	ii)(b)(b.1	ii)(b)(b.1	NOUN
ejpam-6939	670	10	)	)	PUNCT
ejpam-6939	670	11	holds	hold	VERB
ejpam-6939	670	12	.	.	PUNCT
ejpam-6939	671	1	now	now	ADV
ejpam-6939	671	2	,	,	PUNCT
ejpam-6939	671	3	if	if	SCONJ
ejpam-6939	671	4	|tx|	|tx|	NOUN
ejpam-6939	671	5	=	=	SYM
ejpam-6939	671	6	1	1	NUM
ejpam-6939	671	7	,	,	PUNCT
ejpam-6939	671	8	say	say	VERB
ejpam-6939	671	9	tx	tx	ADV
ejpam-6939	671	10	=	=	SYM
ejpam-6939	671	11	{	{	PUNCT
ejpam-6939	671	12	y	y	NOUN
ejpam-6939	671	13	}	}	PUNCT
ejpam-6939	671	14	,	,	PUNCT
ejpam-6939	671	15	then	then	ADV
ejpam-6939	671	16	c	c	X
ejpam-6939	671	17	=	=	PRON
ejpam-6939	671	18	{	{	PUNCT
ejpam-6939	671	19	(	(	PUNCT
ejpam-6939	671	20	x	x	NOUN
ejpam-6939	671	21	,	,	PUNCT
ejpam-6939	671	22	y	y	NOUN
ejpam-6939	671	23	)	)	PUNCT
ejpam-6939	671	24	}	}	PUNCT
ejpam-6939	671	25	is	be	AUX
ejpam-6939	671	26	a	a	DET
ejpam-6939	671	27	dominating	dominating	NOUN
ejpam-6939	671	28	set	set	NOUN
ejpam-6939	671	29	of	of	ADP
ejpam-6939	671	30	g[h	g[h	NOUN
ejpam-6939	671	31	]	]	PUNCT
ejpam-6939	671	32	.	.	PUNCT
ejpam-6939	672	1	necessarily	necessarily	ADV
ejpam-6939	672	2	,	,	PUNCT
ejpam-6939	672	3	s	s	X
ejpam-6939	672	4	and	and	CCONJ
ejpam-6939	672	5	{	{	PUNCT
ejpam-6939	672	6	y	y	NOUN
ejpam-6939	672	7	}	}	PUNCT
ejpam-6939	672	8	are	be	AUX
ejpam-6939	672	9	dominating	dominate	VERB
ejpam-6939	672	10	sets	set	NOUN
ejpam-6939	672	11	of	of	ADP
ejpam-6939	672	12	g	g	PROPN
ejpam-6939	672	13	and	and	CCONJ
ejpam-6939	672	14	h	h	NOUN
ejpam-6939	672	15	,	,	PUNCT
ejpam-6939	672	16	respectively	respectively	ADV
ejpam-6939	672	17	.	.	PUNCT
ejpam-6939	673	1	a.	a.	PROPN
ejpam-6939	673	2	aradais	aradais	PROPN
ejpam-6939	673	3	,	,	PUNCT
ejpam-6939	673	4	f.	f.	PROPN
ejpam-6939	673	5	jamil	jamil	PROPN
ejpam-6939	673	6	,	,	PUNCT
ejpam-6939	673	7	s.	s.	PROPN
ejpam-6939	673	8	canoy	canoy	PROPN
ejpam-6939	673	9	/	/	SYM
ejpam-6939	673	10	eur	eur	PROPN
ejpam-6939	673	11	.	.	PUNCT
ejpam-6939	674	1	j.	j.	PROPN
ejpam-6939	674	2	pure	pure	PROPN
ejpam-6939	674	3	appl	appl	PROPN
ejpam-6939	674	4	.	.	PROPN
ejpam-6939	674	5	math	math	PROPN
ejpam-6939	674	6	,	,	PUNCT
ejpam-6939	674	7	18	18	NUM
ejpam-6939	674	8	(	(	PUNCT
ejpam-6939	674	9	4	4	NUM
ejpam-6939	674	10	)	)	PUNCT
ejpam-6939	674	11	(	(	PUNCT
ejpam-6939	674	12	2025	2025	NUM
ejpam-6939	674	13	)	)	PUNCT
ejpam-6939	674	14	,	,	PUNCT
ejpam-6939	674	15	6939	6939	NUM
ejpam-6939	674	16	12	12	NUM
ejpam-6939	674	17	of	of	ADP
ejpam-6939	674	18	14	14	NUM
ejpam-6939	674	19	conversely	conversely	ADV
ejpam-6939	674	20	,	,	PUNCT
ejpam-6939	674	21	if	if	SCONJ
ejpam-6939	674	22	(	(	PUNCT
ejpam-6939	674	23	i	i	NOUN
ejpam-6939	674	24	)	)	PUNCT
ejpam-6939	674	25	holds	hold	VERB
ejpam-6939	674	26	for	for	ADP
ejpam-6939	674	27	s	s	PROPN
ejpam-6939	674	28	,	,	PUNCT
ejpam-6939	674	29	then	then	ADV
ejpam-6939	674	30	s	s	VERB
ejpam-6939	674	31	is	be	AUX
ejpam-6939	674	32	a	a	DET
ejpam-6939	674	33	disjunctive	disjunctive	ADJ
ejpam-6939	674	34	total	total	ADJ
ejpam-6939	674	35	dominating	dominating	NOUN
ejpam-6939	674	36	set	set	NOUN
ejpam-6939	674	37	of	of	ADP
ejpam-6939	674	38	g.	g.	PROPN
ejpam-6939	674	39	consequently	consequently	ADV
ejpam-6939	674	40	,	,	PUNCT
ejpam-6939	674	41	c	c	PROPN
ejpam-6939	674	42	is	be	AUX
ejpam-6939	674	43	a	a	DET
ejpam-6939	674	44	disjunctive	disjunctive	ADJ
ejpam-6939	674	45	dominating	dominating	NOUN
ejpam-6939	674	46	set	set	NOUN
ejpam-6939	674	47	of	of	ADP
ejpam-6939	674	48	g[h	g[h	PROPN
ejpam-6939	674	49	]	]	PUNCT
ejpam-6939	674	50	by	by	ADP
ejpam-6939	674	51	theorem	theorem	NOUN
ejpam-6939	674	52	3	3	NUM
ejpam-6939	674	53	.	.	PUNCT
ejpam-6939	674	54	since	since	SCONJ
ejpam-6939	674	55	⟨s⟩	⟨s⟩	PROPN
ejpam-6939	674	56	is	be	AUX
ejpam-6939	674	57	connected	connect	VERB
ejpam-6939	674	58	,	,	PUNCT
ejpam-6939	674	59	⟨c⟩	⟨c⟩	PROPN
ejpam-6939	674	60	is	be	AUX
ejpam-6939	674	61	connected	connect	VERB
ejpam-6939	674	62	.	.	PUNCT
ejpam-6939	675	1	assume	assume	VERB
ejpam-6939	675	2	that	that	SCONJ
ejpam-6939	675	3	s	s	VERB
ejpam-6939	675	4	is	be	AUX
ejpam-6939	675	5	a	a	DET
ejpam-6939	675	6	connected	connected	ADJ
ejpam-6939	675	7	distance	distance	NOUN
ejpam-6939	675	8	-	-	PUNCT
ejpam-6939	675	9	two	two	NUM
ejpam-6939	675	10	dominating	dominating	NOUN
ejpam-6939	675	11	set	set	NOUN
ejpam-6939	675	12	of	of	ADP
ejpam-6939	675	13	g.	g.	PROPN
ejpam-6939	675	14	suppose	suppose	VERB
ejpam-6939	675	15	that	that	SCONJ
ejpam-6939	675	16	condition	condition	NOUN
ejpam-6939	675	17	(	(	PUNCT
ejpam-6939	675	18	ii)(a	ii)(a	NOUN
ejpam-6939	675	19	)	)	PUNCT
ejpam-6939	675	20	holds	hold	VERB
ejpam-6939	675	21	for	for	ADP
ejpam-6939	675	22	s.	s.	PROPN
ejpam-6939	675	23	then	then	ADV
ejpam-6939	675	24	⟨c⟩	⟨c⟩	PROPN
ejpam-6939	675	25	is	be	AUX
ejpam-6939	675	26	connected	connect	VERB
ejpam-6939	675	27	.	.	PUNCT
ejpam-6939	676	1	let	let	VERB
ejpam-6939	676	2	(	(	PUNCT
ejpam-6939	676	3	x	x	NOUN
ejpam-6939	676	4	,	,	PUNCT
ejpam-6939	676	5	y	y	NOUN
ejpam-6939	676	6	)	)	PUNCT
ejpam-6939	676	7	∈	∈	PROPN
ejpam-6939	676	8	v	v	NOUN
ejpam-6939	676	9	(	(	PUNCT
ejpam-6939	676	10	g[h	g[h	PROPN
ejpam-6939	676	11	]	]	PUNCT
ejpam-6939	676	12	)	)	PUNCT
ejpam-6939	676	13	\	\	PROPN
ejpam-6939	677	1	c.	c.	NOUN
ejpam-6939	677	2	case	case	NOUN
ejpam-6939	677	3	1	1	NUM
ejpam-6939	677	4	:	:	PUNCT
ejpam-6939	677	5	x	x	SYM
ejpam-6939	677	6	∈	∈	NOUN
ejpam-6939	677	7	nd	nd	NOUN
ejpam-6939	677	8	g[s	g[s	PROPN
ejpam-6939	677	9	]	]	PUNCT
ejpam-6939	677	10	if	if	SCONJ
ejpam-6939	677	11	u	u	PROPN
ejpam-6939	677	12	∈	∈	PROPN
ejpam-6939	677	13	s	s	PART
ejpam-6939	677	14	∩ng(x	∩ng(x	NOUN
ejpam-6939	677	15	)	)	PUNCT
ejpam-6939	677	16	,	,	PUNCT
ejpam-6939	677	17	then	then	ADV
ejpam-6939	677	18	(	(	PUNCT
ejpam-6939	677	19	x	x	X
ejpam-6939	677	20	,	,	PUNCT
ejpam-6939	677	21	y)(u	y)(u	ADJ
ejpam-6939	677	22	,	,	PUNCT
ejpam-6939	677	23	v	v	NOUN
ejpam-6939	677	24	)	)	PUNCT
ejpam-6939	677	25	∈	∈	PROPN
ejpam-6939	677	26	e(g	e(g	PROPN
ejpam-6939	677	27	)	)	PUNCT
ejpam-6939	677	28	for	for	ADP
ejpam-6939	677	29	any	any	PRON
ejpam-6939	677	30	v	v	PROPN
ejpam-6939	677	31	∈	∈	PROPN
ejpam-6939	677	32	tu	tu	PROPN
ejpam-6939	677	33	.	.	PROPN
ejpam-6939	677	34	suppose	suppose	VERB
ejpam-6939	677	35	that	that	SCONJ
ejpam-6939	677	36	x	x	SYM
ejpam-6939	677	37	/∈	/∈	NOUN
ejpam-6939	677	38	ng(s	ng(s	NUM
ejpam-6939	677	39	)	)	PUNCT
ejpam-6939	677	40	.	.	PUNCT
ejpam-6939	678	1	then	then	ADV
ejpam-6939	678	2	there	there	PRON
ejpam-6939	678	3	exist	exist	VERB
ejpam-6939	678	4	distinct	distinct	ADJ
ejpam-6939	678	5	u	u	NOUN
ejpam-6939	678	6	,	,	PUNCT
ejpam-6939	678	7	w	w	PROPN
ejpam-6939	678	8	∈	∈	PROPN
ejpam-6939	678	9	s	s	X
ejpam-6939	678	10	for	for	ADP
ejpam-6939	678	11	which	which	PRON
ejpam-6939	678	12	dg(x	dg(x	NUM
ejpam-6939	678	13	,	,	PUNCT
ejpam-6939	678	14	u	u	NOUN
ejpam-6939	678	15	)	)	PUNCT
ejpam-6939	678	16	=	=	SYM
ejpam-6939	678	17	2	2	NUM
ejpam-6939	678	18	=	=	SYM
ejpam-6939	678	19	dg(x	dg(x	NUM
ejpam-6939	678	20	,	,	PUNCT
ejpam-6939	678	21	w	w	NOUN
ejpam-6939	678	22	)	)	PUNCT
ejpam-6939	678	23	.	.	PUNCT
ejpam-6939	679	1	pick	pick	VERB
ejpam-6939	679	2	v	v	ADP
ejpam-6939	679	3	∈	∈	PROPN
ejpam-6939	679	4	tu	tu	X
ejpam-6939	679	5	and	and	CCONJ
ejpam-6939	679	6	z	z	PROPN
ejpam-6939	679	7	∈	∈	PROPN
ejpam-6939	679	8	tw	tw	PROPN
ejpam-6939	679	9	.	.	PUNCT
ejpam-6939	680	1	then	then	ADV
ejpam-6939	680	2	(	(	PUNCT
ejpam-6939	680	3	u	u	NOUN
ejpam-6939	680	4	,	,	PUNCT
ejpam-6939	680	5	v	v	NOUN
ejpam-6939	680	6	)	)	PUNCT
ejpam-6939	680	7	,	,	PUNCT
ejpam-6939	680	8	(	(	PUNCT
ejpam-6939	680	9	w	w	PROPN
ejpam-6939	680	10	,	,	PUNCT
ejpam-6939	680	11	z	z	NOUN
ejpam-6939	680	12	)	)	PUNCT
ejpam-6939	680	13	∈	∈	PROPN
ejpam-6939	680	14	c	c	PROPN
ejpam-6939	680	15	and	and	CCONJ
ejpam-6939	680	16	dg[h	dg[h	PROPN
ejpam-6939	680	17	]	]	X
ejpam-6939	680	18	(	(	PUNCT
ejpam-6939	680	19	(	(	PUNCT
ejpam-6939	680	20	x	x	NOUN
ejpam-6939	680	21	,	,	PUNCT
ejpam-6939	680	22	y	y	PROPN
ejpam-6939	680	23	)	)	PUNCT
ejpam-6939	680	24	,	,	PUNCT
ejpam-6939	680	25	(	(	PUNCT
ejpam-6939	680	26	u	u	NOUN
ejpam-6939	680	27	,	,	PUNCT
ejpam-6939	680	28	v	v	NOUN
ejpam-6939	680	29	)	)	PUNCT
ejpam-6939	680	30	)	)	PUNCT
ejpam-6939	680	31	=	=	SYM
ejpam-6939	680	32	2	2	NUM
ejpam-6939	680	33	=	=	SYM
ejpam-6939	680	34	dg[h	dg[h	PROPN
ejpam-6939	680	35	]	]	X
ejpam-6939	680	36	(	(	PUNCT
ejpam-6939	680	37	(	(	PUNCT
ejpam-6939	680	38	x	x	NOUN
ejpam-6939	680	39	,	,	PUNCT
ejpam-6939	680	40	y	y	PROPN
ejpam-6939	680	41	)	)	PUNCT
ejpam-6939	680	42	,	,	PUNCT
ejpam-6939	680	43	(	(	PUNCT
ejpam-6939	680	44	w	w	PROPN
ejpam-6939	680	45	,	,	PUNCT
ejpam-6939	680	46	z	z	NOUN
ejpam-6939	680	47	)	)	PUNCT
ejpam-6939	680	48	)	)	PUNCT
ejpam-6939	680	49	.	.	PUNCT
ejpam-6939	681	1	case	case	NOUN
ejpam-6939	681	2	2	2	NUM
ejpam-6939	681	3	:	:	PUNCT
ejpam-6939	681	4	x	x	X
ejpam-6939	681	5	/∈	/∈	PROPN
ejpam-6939	681	6	nd	nd	SYM
ejpam-6939	681	7	g[s	g[	NOUN
ejpam-6939	681	8	]	]	PUNCT
ejpam-6939	681	9	by	by	ADP
ejpam-6939	681	10	the	the	DET
ejpam-6939	681	11	hypothesis	hypothesis	NOUN
ejpam-6939	681	12	,	,	PUNCT
ejpam-6939	681	13	there	there	PRON
ejpam-6939	681	14	exists	exist	VERB
ejpam-6939	681	15	u	u	PROPN
ejpam-6939	681	16	∈	∈	PROPN
ejpam-6939	681	17	s	s	X
ejpam-6939	681	18	for	for	ADP
ejpam-6939	681	19	which	which	PRON
ejpam-6939	681	20	dg(u	dg(u	NOUN
ejpam-6939	681	21	,	,	PUNCT
ejpam-6939	681	22	x	x	X
ejpam-6939	681	23	)	)	PUNCT
ejpam-6939	681	24	=	=	SYM
ejpam-6939	681	25	2	2	NUM
ejpam-6939	681	26	and	and	CCONJ
ejpam-6939	681	27	|tu|	|tu|	NOUN
ejpam-6939	681	28	≥	≥	NOUN
ejpam-6939	681	29	2	2	NUM
ejpam-6939	681	30	,	,	PUNCT
ejpam-6939	681	31	say	say	VERB
ejpam-6939	681	32	v	v	ADP
ejpam-6939	681	33	,	,	PUNCT
ejpam-6939	682	1	z	z	PROPN
ejpam-6939	682	2	∈	∈	PROPN
ejpam-6939	682	3	tu	tu	PROPN
ejpam-6939	682	4	.	.	PUNCT
ejpam-6939	683	1	then	then	ADV
ejpam-6939	683	2	(	(	PUNCT
ejpam-6939	683	3	u	u	NOUN
ejpam-6939	683	4	,	,	PUNCT
ejpam-6939	683	5	v	v	NOUN
ejpam-6939	683	6	)	)	PUNCT
ejpam-6939	683	7	and	and	CCONJ
ejpam-6939	683	8	(	(	PUNCT
ejpam-6939	683	9	u	u	NOUN
ejpam-6939	683	10	,	,	PUNCT
ejpam-6939	683	11	z	z	NOUN
ejpam-6939	683	12	)	)	PUNCT
ejpam-6939	683	13	are	be	AUX
ejpam-6939	683	14	distinct	distinct	ADJ
ejpam-6939	683	15	vertices	vertex	NOUN
ejpam-6939	683	16	in	in	ADP
ejpam-6939	683	17	c	c	PROPN
ejpam-6939	683	18	and	and	CCONJ
ejpam-6939	683	19	dg[h	dg[h	PROPN
ejpam-6939	683	20	]	]	X
ejpam-6939	683	21	(	(	PUNCT
ejpam-6939	683	22	(	(	PUNCT
ejpam-6939	683	23	x	x	NOUN
ejpam-6939	683	24	,	,	PUNCT
ejpam-6939	683	25	y	y	PROPN
ejpam-6939	683	26	)	)	PUNCT
ejpam-6939	683	27	,	,	PUNCT
ejpam-6939	683	28	(	(	PUNCT
ejpam-6939	683	29	u	u	NOUN
ejpam-6939	683	30	,	,	PUNCT
ejpam-6939	683	31	v	v	NOUN
ejpam-6939	683	32	)	)	PUNCT
ejpam-6939	683	33	)	)	PUNCT
ejpam-6939	684	1	=	=	SYM
ejpam-6939	684	2	2	2	NUM
ejpam-6939	684	3	=	=	SYM
ejpam-6939	684	4	dg[h	dg[h	PROPN
ejpam-6939	684	5	]	]	X
ejpam-6939	684	6	(	(	PUNCT
ejpam-6939	684	7	(	(	PUNCT
ejpam-6939	684	8	x	x	NOUN
ejpam-6939	684	9	,	,	PUNCT
ejpam-6939	684	10	y	y	PROPN
ejpam-6939	684	11	)	)	PUNCT
ejpam-6939	684	12	,	,	PUNCT
ejpam-6939	684	13	(	(	PUNCT
ejpam-6939	684	14	u	u	NOUN
ejpam-6939	684	15	,	,	PUNCT
ejpam-6939	684	16	z	z	NOUN
ejpam-6939	684	17	)	)	PUNCT
ejpam-6939	684	18	)	)	PUNCT
ejpam-6939	684	19	.	.	PUNCT
ejpam-6939	685	1	the	the	DET
ejpam-6939	685	2	above	above	ADJ
ejpam-6939	685	3	cases	case	NOUN
ejpam-6939	685	4	imply	imply	VERB
ejpam-6939	685	5	that	that	SCONJ
ejpam-6939	685	6	c	c	PROPN
ejpam-6939	685	7	is	be	AUX
ejpam-6939	685	8	a	a	DET
ejpam-6939	685	9	connected	connected	ADJ
ejpam-6939	685	10	disjunctive	disjunctive	ADJ
ejpam-6939	685	11	dominating	dominating	NOUN
ejpam-6939	685	12	set	set	NOUN
ejpam-6939	685	13	of	of	ADP
ejpam-6939	685	14	g[h	g[h	NOUN
ejpam-6939	685	15	]	]	PUNCT
ejpam-6939	685	16	.	.	PUNCT
ejpam-6939	686	1	finally	finally	ADV
ejpam-6939	686	2	,	,	PUNCT
ejpam-6939	686	3	suppose	suppose	VERB
ejpam-6939	686	4	that	that	SCONJ
ejpam-6939	686	5	|s|	|s|	PROPN
ejpam-6939	686	6	=	=	SYM
ejpam-6939	686	7	1	1	NUM
ejpam-6939	686	8	,	,	PUNCT
ejpam-6939	686	9	say	say	VERB
ejpam-6939	686	10	s	s	X
ejpam-6939	686	11	=	=	PUNCT
ejpam-6939	686	12	{	{	PUNCT
ejpam-6939	686	13	x	x	NOUN
ejpam-6939	686	14	}	}	PUNCT
ejpam-6939	686	15	,	,	PUNCT
ejpam-6939	686	16	satisfying	satisfy	VERB
ejpam-6939	686	17	condition	condition	NOUN
ejpam-6939	686	18	(	(	PUNCT
ejpam-6939	686	19	ii)(b	ii)(b	PROPN
ejpam-6939	686	20	)	)	PUNCT
ejpam-6939	686	21	.	.	PUNCT
ejpam-6939	687	1	then	then	ADV
ejpam-6939	687	2	⟨c⟩	⟨c⟩	PROPN
ejpam-6939	687	3	=	=	SYM
ejpam-6939	687	4	⟨{x	⟨{x	PROPN
ejpam-6939	687	5	}	}	PUNCT
ejpam-6939	687	6	×	×	PROPN
ejpam-6939	687	7	tx⟩	tx⟩	PROPN
ejpam-6939	687	8	is	be	AUX
ejpam-6939	687	9	connected	connect	VERB
ejpam-6939	687	10	.	.	PUNCT
ejpam-6939	688	1	let	let	VERB
ejpam-6939	688	2	(	(	PUNCT
ejpam-6939	688	3	u	u	NOUN
ejpam-6939	688	4	,	,	PUNCT
ejpam-6939	688	5	v	v	NOUN
ejpam-6939	688	6	)	)	PUNCT
ejpam-6939	688	7	∈	∈	NOUN
ejpam-6939	688	8	v	v	NOUN
ejpam-6939	688	9	(	(	PUNCT
ejpam-6939	688	10	g[h	g[h	PROPN
ejpam-6939	688	11	]	]	PUNCT
ejpam-6939	688	12	)	)	PUNCT
ejpam-6939	688	13	\	\	PROPN
ejpam-6939	689	1	c.	c.	NOUN
ejpam-6939	689	2	case	case	NOUN
ejpam-6939	689	3	1	1	NUM
ejpam-6939	689	4	:	:	PUNCT
ejpam-6939	689	5	u	u	PROPN
ejpam-6939	689	6	̸=	̸=	PROPN
ejpam-6939	689	7	x	x	PUNCT
ejpam-6939	689	8	if	if	SCONJ
ejpam-6939	689	9	ux	ux	PROPN
ejpam-6939	689	10	∈	∈	PROPN
ejpam-6939	689	11	e(g	e(g	PROPN
ejpam-6939	689	12	)	)	PUNCT
ejpam-6939	689	13	,	,	PUNCT
ejpam-6939	689	14	then	then	ADV
ejpam-6939	689	15	(	(	PUNCT
ejpam-6939	689	16	u	u	NOUN
ejpam-6939	689	17	,	,	PUNCT
ejpam-6939	689	18	v)(x	v)(x	NOUN
ejpam-6939	689	19	,	,	PUNCT
ejpam-6939	689	20	y	y	NOUN
ejpam-6939	689	21	)	)	PUNCT
ejpam-6939	689	22	∈	∈	NOUN
ejpam-6939	689	23	e(g[h	e(g[h	NOUN
ejpam-6939	689	24	]	]	PUNCT
ejpam-6939	689	25	)	)	PUNCT
ejpam-6939	689	26	for	for	ADP
ejpam-6939	689	27	any	any	DET
ejpam-6939	689	28	y	y	PROPN
ejpam-6939	689	29	∈	∈	PROPN
ejpam-6939	689	30	tx	tx	PROPN
ejpam-6939	689	31	.	.	PUNCT
ejpam-6939	690	1	if	if	SCONJ
ejpam-6939	690	2	dg(u	dg(u	NOUN
ejpam-6939	690	3	,	,	PUNCT
ejpam-6939	690	4	x	x	X
ejpam-6939	690	5	)	)	PUNCT
ejpam-6939	690	6	=	=	SYM
ejpam-6939	690	7	2	2	NUM
ejpam-6939	690	8	,	,	PUNCT
ejpam-6939	690	9	then	then	ADV
ejpam-6939	690	10	by	by	ADP
ejpam-6939	690	11	condition	condition	NOUN
ejpam-6939	690	12	(	(	PUNCT
ejpam-6939	690	13	b.1	b.1	NOUN
ejpam-6939	690	14	)	)	PUNCT
ejpam-6939	690	15	,	,	PUNCT
ejpam-6939	690	16	|tx|	|tx|	NOUN
ejpam-6939	690	17	≥	≥	NUM
ejpam-6939	690	18	2	2	NUM
ejpam-6939	690	19	,	,	PUNCT
ejpam-6939	690	20	say	say	VERB
ejpam-6939	690	21	y	y	NOUN
ejpam-6939	690	22	,	,	PUNCT
ejpam-6939	690	23	z	z	PROPN
ejpam-6939	690	24	∈	∈	PROPN
ejpam-6939	690	25	tx	tx	PROPN
ejpam-6939	690	26	.	.	PUNCT
ejpam-6939	691	1	then	then	ADV
ejpam-6939	691	2	(	(	PUNCT
ejpam-6939	691	3	x	x	X
ejpam-6939	691	4	,	,	PUNCT
ejpam-6939	691	5	y	y	PROPN
ejpam-6939	691	6	)	)	PUNCT
ejpam-6939	691	7	,	,	PUNCT
ejpam-6939	691	8	(	(	PUNCT
ejpam-6939	691	9	x	x	X
ejpam-6939	691	10	,	,	PUNCT
ejpam-6939	691	11	z	z	NOUN
ejpam-6939	691	12	)	)	PUNCT
ejpam-6939	691	13	are	be	AUX
ejpam-6939	691	14	distinct	distinct	ADJ
ejpam-6939	691	15	vertices	vertex	NOUN
ejpam-6939	691	16	in	in	ADP
ejpam-6939	691	17	c	c	PROPN
ejpam-6939	691	18	with	with	ADP
ejpam-6939	691	19	dg[h	dg[h	PROPN
ejpam-6939	691	20	]	]	X
ejpam-6939	691	21	(	(	PUNCT
ejpam-6939	691	22	(	(	PUNCT
ejpam-6939	691	23	x	x	NOUN
ejpam-6939	691	24	,	,	PUNCT
ejpam-6939	691	25	y	y	PROPN
ejpam-6939	691	26	)	)	PUNCT
ejpam-6939	691	27	,	,	PUNCT
ejpam-6939	691	28	(	(	PUNCT
ejpam-6939	691	29	u	u	NOUN
ejpam-6939	691	30	,	,	PUNCT
ejpam-6939	691	31	v	v	NOUN
ejpam-6939	691	32	)	)	PUNCT
ejpam-6939	691	33	)	)	PUNCT
ejpam-6939	692	1	=	=	SYM
ejpam-6939	692	2	2	2	NUM
ejpam-6939	692	3	=	=	SYM
ejpam-6939	692	4	dg[h	dg[h	PROPN
ejpam-6939	692	5	]	]	X
ejpam-6939	692	6	(	(	PUNCT
ejpam-6939	692	7	(	(	PUNCT
ejpam-6939	692	8	x	x	X
ejpam-6939	692	9	,	,	PUNCT
ejpam-6939	692	10	z	z	NOUN
ejpam-6939	692	11	)	)	PUNCT
ejpam-6939	692	12	,	,	PUNCT
ejpam-6939	692	13	(	(	PUNCT
ejpam-6939	692	14	u	u	NOUN
ejpam-6939	692	15	,	,	PUNCT
ejpam-6939	692	16	v	v	NOUN
ejpam-6939	692	17	)	)	PUNCT
ejpam-6939	692	18	)	)	PUNCT
ejpam-6939	692	19	.	.	PUNCT
ejpam-6939	693	1	case	case	NOUN
ejpam-6939	693	2	2	2	NUM
ejpam-6939	693	3	:	:	PUNCT
ejpam-6939	693	4	u	u	NOUN
ejpam-6939	693	5	=	=	NOUN
ejpam-6939	693	6	x	x	PART
ejpam-6939	693	7	note	note	VERB
ejpam-6939	693	8	that	that	SCONJ
ejpam-6939	693	9	since	since	SCONJ
ejpam-6939	693	10	g	g	PROPN
ejpam-6939	693	11	is	be	AUX
ejpam-6939	693	12	nontrivial	nontrivial	ADJ
ejpam-6939	693	13	,	,	PUNCT
ejpam-6939	693	14	dg[h	dg[h	PROPN
ejpam-6939	693	15	]	]	X
ejpam-6939	693	16	(	(	PUNCT
ejpam-6939	693	17	(	(	PUNCT
ejpam-6939	693	18	u	u	NOUN
ejpam-6939	693	19	,	,	PUNCT
ejpam-6939	693	20	v	v	NOUN
ejpam-6939	693	21	)	)	PUNCT
ejpam-6939	693	22	,	,	PUNCT
ejpam-6939	693	23	(	(	PUNCT
ejpam-6939	693	24	x	x	X
ejpam-6939	693	25	,	,	PUNCT
ejpam-6939	693	26	y	y	NOUN
ejpam-6939	693	27	)	)	PUNCT
ejpam-6939	693	28	)	)	PUNCT
ejpam-6939	693	29	≤	≤	ADV
ejpam-6939	693	30	2	2	NUM
ejpam-6939	693	31	for	for	ADP
ejpam-6939	693	32	all	all	DET
ejpam-6939	693	33	y	y	PROPN
ejpam-6939	693	34	∈	∈	PROPN
ejpam-6939	693	35	tx	tx	PROPN
ejpam-6939	693	36	.	.	PUNCT
ejpam-6939	694	1	if	if	SCONJ
ejpam-6939	694	2	|tx|	|tx|	PROPN
ejpam-6939	694	3	≥	≥	NOUN
ejpam-6939	694	4	2	2	NUM
ejpam-6939	694	5	,	,	PUNCT
ejpam-6939	694	6	then	then	ADV
ejpam-6939	694	7	(	(	PUNCT
ejpam-6939	694	8	u	u	NOUN
ejpam-6939	694	9	,	,	PUNCT
ejpam-6939	694	10	v	v	NOUN
ejpam-6939	694	11	)	)	PUNCT
ejpam-6939	694	12	∈	∈	PROPN
ejpam-6939	694	13	nd	nd	NOUN
ejpam-6939	694	14	g[h](c	g[h](c	NOUN
ejpam-6939	694	15	)	)	PUNCT
ejpam-6939	694	16	.	.	PUNCT
ejpam-6939	695	1	on	on	ADP
ejpam-6939	695	2	the	the	DET
ejpam-6939	695	3	other	other	ADJ
ejpam-6939	695	4	hand	hand	NOUN
ejpam-6939	695	5	,	,	PUNCT
ejpam-6939	695	6	if	if	SCONJ
ejpam-6939	695	7	tx	tx	VERB
ejpam-6939	695	8	=	=	PUNCT
ejpam-6939	695	9	{	{	PUNCT
ejpam-6939	695	10	y	y	NOUN
ejpam-6939	695	11	}	}	PUNCT
ejpam-6939	695	12	,	,	PUNCT
ejpam-6939	695	13	then	then	ADV
ejpam-6939	695	14	by	by	ADP
ejpam-6939	695	15	condition	condition	NOUN
ejpam-6939	695	16	(	(	PUNCT
ejpam-6939	695	17	b.2	b.2	NOUN
ejpam-6939	695	18	)	)	PUNCT
ejpam-6939	695	19	,	,	PUNCT
ejpam-6939	695	20	vy	vy	NOUN
ejpam-6939	695	21	∈	∈	PROPN
ejpam-6939	695	22	e(h	e(h	PROPN
ejpam-6939	695	23	)	)	PUNCT
ejpam-6939	696	1	so	so	SCONJ
ejpam-6939	696	2	that	that	SCONJ
ejpam-6939	696	3	(	(	PUNCT
ejpam-6939	696	4	u	u	NOUN
ejpam-6939	696	5	,	,	PUNCT
ejpam-6939	696	6	v)(x	v)(x	NOUN
ejpam-6939	696	7	,	,	PUNCT
ejpam-6939	696	8	y	y	NOUN
ejpam-6939	696	9	)	)	PUNCT
ejpam-6939	696	10	∈	∈	NOUN
ejpam-6939	696	11	e(g[h	e(g[h	NOUN
ejpam-6939	696	12	]	]	PUNCT
ejpam-6939	696	13	)	)	PUNCT
ejpam-6939	696	14	.	.	PUNCT
ejpam-6939	696	15	accordingly	accordingly	ADV
ejpam-6939	696	16	,	,	PUNCT
ejpam-6939	696	17	c	c	PROPN
ejpam-6939	696	18	is	be	AUX
ejpam-6939	696	19	a	a	DET
ejpam-6939	696	20	connected	connected	ADJ
ejpam-6939	696	21	disjunctive	disjunctive	ADJ
ejpam-6939	696	22	dominating	dominating	NOUN
ejpam-6939	696	23	set	set	NOUN
ejpam-6939	696	24	of	of	ADP
ejpam-6939	696	25	g[h	g[h	PROPN
ejpam-6939	696	26	]	]	PUNCT
ejpam-6939	696	27	.	.	PUNCT
ejpam-6939	697	1	let	let	VERB
ejpam-6939	697	2	s	s	PRON
ejpam-6939	697	3	⊆	⊆	NUM
ejpam-6939	697	4	v	v	NOUN
ejpam-6939	697	5	(	(	PUNCT
ejpam-6939	697	6	g	g	NOUN
ejpam-6939	697	7	)	)	PUNCT
ejpam-6939	697	8	be	be	AUX
ejpam-6939	697	9	a	a	DET
ejpam-6939	697	10	distance	distance	NOUN
ejpam-6939	697	11	-	-	PUNCT
ejpam-6939	697	12	two	two	NUM
ejpam-6939	697	13	dominating	dominating	NOUN
ejpam-6939	697	14	set	set	NOUN
ejpam-6939	697	15	of	of	ADP
ejpam-6939	697	16	g.	g.	PROPN
ejpam-6939	697	17	for	for	ADP
ejpam-6939	697	18	each	each	DET
ejpam-6939	697	19	x	x	SYM
ejpam-6939	697	20	∈	∈	PROPN
ejpam-6939	697	21	v	v	ADP
ejpam-6939	697	22	(	(	PUNCT
ejpam-6939	697	23	g	g	NOUN
ejpam-6939	697	24	)	)	PUNCT
ejpam-6939	697	25	\nd	\nd	PROPN
ejpam-6939	697	26	g[s	g[	NOUN
ejpam-6939	697	27	]	]	PUNCT
ejpam-6939	697	28	,	,	PUNCT
ejpam-6939	697	29	let	let	VERB
ejpam-6939	697	30	sx	sx	PROPN
ejpam-6939	697	31	∈	∈	PROPN
ejpam-6939	697	32	s	s	PART
ejpam-6939	697	33	∩ng(x	∩ng(x	NOUN
ejpam-6939	697	34	,	,	PUNCT
ejpam-6939	697	35	2	2	NUM
ejpam-6939	697	36	)	)	PUNCT
ejpam-6939	697	37	.	.	PUNCT
ejpam-6939	698	1	we	we	PRON
ejpam-6939	698	2	define	define	VERB
ejpam-6939	698	3	for	for	ADP
ejpam-6939	698	4	s	s	NOUN
ejpam-6939	698	5	,	,	PUNCT
ejpam-6939	698	6	sd	sd	ADV
ejpam-6939	698	7	=	=	SYM
ejpam-6939	698	8	{	{	PUNCT
ejpam-6939	698	9	sx	sx	NOUN
ejpam-6939	698	10	:	:	PUNCT
ejpam-6939	698	11	x	x	SYM
ejpam-6939	698	12	∈	∈	NOUN
ejpam-6939	698	13	v	v	ADP
ejpam-6939	698	14	(	(	PUNCT
ejpam-6939	698	15	g	g	NOUN
ejpam-6939	698	16	)	)	PUNCT
ejpam-6939	698	17	\nd	\nd	NOUN
ejpam-6939	698	18	g[s	g[	NOUN
ejpam-6939	698	19	]	]	PUNCT
ejpam-6939	698	20	}	}	PUNCT
ejpam-6939	698	21	.	.	PUNCT
ejpam-6939	699	1	denote	denote	VERB
ejpam-6939	699	2	by	by	ADP
ejpam-6939	699	3	cd2d(g	cd2d(g	NOUN
ejpam-6939	699	4	)	)	PUNCT
ejpam-6939	699	5	the	the	DET
ejpam-6939	699	6	families	family	NOUN
ejpam-6939	699	7	of	of	ADP
ejpam-6939	699	8	all	all	DET
ejpam-6939	699	9	connected	connected	ADJ
ejpam-6939	699	10	distance	distance	NOUN
ejpam-6939	699	11	-	-	PUNCT
ejpam-6939	699	12	two	two	NUM
ejpam-6939	699	13	dominating	dominating	NOUN
ejpam-6939	699	14	sets	set	NOUN
ejpam-6939	699	15	of	of	ADP
ejpam-6939	699	16	g.	g.	PROPN
ejpam-6939	699	17	corollary	corollary	PROPN
ejpam-6939	699	18	5	5	NUM
ejpam-6939	699	19	.	.	PUNCT
ejpam-6939	700	1	let	let	VERB
ejpam-6939	700	2	g	g	NOUN
ejpam-6939	700	3	and	and	CCONJ
ejpam-6939	700	4	h	h	NOUN
ejpam-6939	700	5	be	be	AUX
ejpam-6939	700	6	nontrivial	nontrivial	ADJ
ejpam-6939	700	7	connected	connected	ADJ
ejpam-6939	700	8	graphs	graph	NOUN
ejpam-6939	700	9	.	.	PUNCT
ejpam-6939	701	1	then	then	ADV
ejpam-6939	701	2	(	(	PUNCT
ejpam-6939	701	3	i	i	NOUN
ejpam-6939	701	4	)	)	PUNCT
ejpam-6939	701	5	provided	provide	VERB
ejpam-6939	701	6	γ2,c(g	γ2,c(g	ADP
ejpam-6939	701	7	)	)	PUNCT
ejpam-6939	701	8	=	=	SYM
ejpam-6939	701	9	1	1	NUM
ejpam-6939	701	10	,	,	PUNCT
ejpam-6939	701	11	γdc	γdc	NOUN
ejpam-6939	701	12	(	(	PUNCT
ejpam-6939	701	13	g[h	g[h	PROPN
ejpam-6939	701	14	]	]	PUNCT
ejpam-6939	701	15	)	)	PUNCT
ejpam-6939	702	1	=	=	SYM
ejpam-6939	702	2	®	®	NOUN
ejpam-6939	702	3	1	1	NUM
ejpam-6939	702	4	,	,	PUNCT
ejpam-6939	702	5	if	if	SCONJ
ejpam-6939	702	6	γ(h	γ(h	NOUN
ejpam-6939	702	7	)	)	PUNCT
ejpam-6939	702	8	=	=	SYM
ejpam-6939	702	9	1	1	NUM
ejpam-6939	702	10	=	=	SYM
ejpam-6939	702	11	γ(g	γ(g	PROPN
ejpam-6939	702	12	)	)	PUNCT
ejpam-6939	702	13	2	2	NUM
ejpam-6939	702	14	,	,	PUNCT
ejpam-6939	702	15	if	if	SCONJ
ejpam-6939	702	16	γ(g	γ(g	PROPN
ejpam-6939	702	17	)	)	PUNCT
ejpam-6939	702	18	≥	≥	NOUN
ejpam-6939	702	19	2	2	NUM
ejpam-6939	702	20	.	.	PUNCT
ejpam-6939	702	21	(	(	PUNCT
ejpam-6939	702	22	ii	ii	NOUN
ejpam-6939	702	23	)	)	PUNCT
ejpam-6939	702	24	provided	provide	VERB
ejpam-6939	702	25	γ2,c(g	γ2,c(g	ADP
ejpam-6939	702	26	)	)	PUNCT
ejpam-6939	702	27	≥	≥	NOUN
ejpam-6939	702	28	2	2	NUM
ejpam-6939	702	29	,	,	PUNCT
ejpam-6939	702	30	γdc	γdc	NOUN
ejpam-6939	702	31	(	(	PUNCT
ejpam-6939	702	32	g[h	g[h	PROPN
ejpam-6939	702	33	]	]	PUNCT
ejpam-6939	702	34	)	)	PUNCT
ejpam-6939	703	1	=	=	SYM
ejpam-6939	703	2	min{γdc	min{γdc	NOUN
ejpam-6939	703	3	(	(	PUNCT
ejpam-6939	703	4	g	g	NOUN
ejpam-6939	703	5	)	)	PUNCT
ejpam-6939	703	6	,	,	PUNCT
ejpam-6939	703	7	α(g	α(g	NUM
ejpam-6939	703	8	)	)	PUNCT
ejpam-6939	703	9	}	}	PUNCT
ejpam-6939	703	10	,	,	PUNCT
ejpam-6939	703	11	where	where	SCONJ
ejpam-6939	703	12	α(g	α(g	NUM
ejpam-6939	703	13	)	)	PUNCT
ejpam-6939	703	14	=	=	SYM
ejpam-6939	703	15	min{|s	min{|s	X
ejpam-6939	703	16	\	\	NOUN
ejpam-6939	703	17	sd|+	sd|+	PROPN
ejpam-6939	703	18	2|sd|	2|sd|	PROPN
ejpam-6939	703	19	:	:	PUNCT
ejpam-6939	703	20	s	s	X
ejpam-6939	703	21	∈	∈	PROPN
ejpam-6939	703	22	cd2d(g	cd2d(g	NOUN
ejpam-6939	703	23	)	)	PUNCT
ejpam-6939	703	24	}	}	PUNCT
ejpam-6939	703	25	.	.	PUNCT
ejpam-6939	704	1	for	for	ADP
ejpam-6939	704	2	all	all	DET
ejpam-6939	704	3	nontrivial	nontrivial	ADJ
ejpam-6939	704	4	connected	connect	VERB
ejpam-6939	704	5	graphs	graph	NOUN
ejpam-6939	704	6	h	h	NOUN
ejpam-6939	704	7	,	,	PUNCT
ejpam-6939	704	8	γdc	γdc	PROPN
ejpam-6939	704	9	(	(	PUNCT
ejpam-6939	704	10	c4[h	c4[h	PROPN
ejpam-6939	704	11	]	]	PUNCT
ejpam-6939	704	12	)	)	PUNCT
ejpam-6939	704	13	=	=	SYM
ejpam-6939	704	14	2	2	NUM
ejpam-6939	704	15	,	,	PUNCT
ejpam-6939	704	16	γdc	γdc	NOUN
ejpam-6939	704	17	(	(	PUNCT
ejpam-6939	704	18	c6[h	c6[h	NOUN
ejpam-6939	704	19	]	]	PUNCT
ejpam-6939	704	20	)	)	PUNCT
ejpam-6939	704	21	=	=	SYM
ejpam-6939	704	22	γdc	γdc	PROPN
ejpam-6939	704	23	(	(	PUNCT
ejpam-6939	704	24	c6	c6	PROPN
ejpam-6939	704	25	)	)	PUNCT
ejpam-6939	704	26	=	=	SYM
ejpam-6939	704	27	3	3	NUM
ejpam-6939	704	28	and	and	CCONJ
ejpam-6939	704	29	γdc	γdc	PROPN
ejpam-6939	704	30	(	(	PUNCT
ejpam-6939	704	31	p6[h	p6[h	NOUN
ejpam-6939	704	32	]	]	PUNCT
ejpam-6939	704	33	)	)	PUNCT
ejpam-6939	704	34	=	=	SYM
ejpam-6939	704	35	α(p6	α(p6	NOUN
ejpam-6939	704	36	)	)	PUNCT
ejpam-6939	704	37	=	=	SYM
ejpam-6939	705	1	4	4	X
ejpam-6939	705	2	.	.	PUNCT
ejpam-6939	705	3	a.	a.	PROPN
ejpam-6939	705	4	aradais	aradais	PROPN
ejpam-6939	705	5	,	,	PUNCT
ejpam-6939	705	6	f.	f.	PROPN
ejpam-6939	705	7	jamil	jamil	PROPN
ejpam-6939	705	8	,	,	PUNCT
ejpam-6939	705	9	s.	s.	PROPN
ejpam-6939	705	10	canoy	canoy	PROPN
ejpam-6939	705	11	/	/	SYM
ejpam-6939	705	12	eur	eur	PROPN
ejpam-6939	705	13	.	.	PUNCT
ejpam-6939	706	1	j.	j.	PROPN
ejpam-6939	706	2	pure	pure	PROPN
ejpam-6939	706	3	appl	appl	PROPN
ejpam-6939	706	4	.	.	PROPN
ejpam-6939	706	5	math	math	PROPN
ejpam-6939	706	6	,	,	PUNCT
ejpam-6939	706	7	18	18	NUM
ejpam-6939	706	8	(	(	PUNCT
ejpam-6939	706	9	4	4	NUM
ejpam-6939	706	10	)	)	PUNCT
ejpam-6939	706	11	(	(	PUNCT
ejpam-6939	706	12	2025	2025	NUM
ejpam-6939	706	13	)	)	PUNCT
ejpam-6939	706	14	,	,	PUNCT
ejpam-6939	706	15	6939	6939	NUM
ejpam-6939	706	16	13	13	NUM
ejpam-6939	706	17	of	of	ADP
ejpam-6939	706	18	14	14	NUM
ejpam-6939	706	19	acknowledgements	acknowledgement	NOUN
ejpam-6939	706	20	this	this	DET
ejpam-6939	706	21	research	research	NOUN
ejpam-6939	706	22	work	work	NOUN
ejpam-6939	706	23	is	be	AUX
ejpam-6939	706	24	fully	fully	ADV
ejpam-6939	706	25	supported	support	VERB
ejpam-6939	706	26	by	by	ADP
ejpam-6939	706	27	the	the	DET
ejpam-6939	706	28	department	department	PROPN
ejpam-6939	706	29	of	of	ADP
ejpam-6939	706	30	science	science	NOUN
ejpam-6939	706	31	and	and	CCONJ
ejpam-6939	706	32	technology	technology	NOUN
ejpam-6939	706	33	accelerated	accelerate	VERB
ejpam-6939	706	34	science	science	NOUN
ejpam-6939	706	35	and	and	CCONJ
ejpam-6939	706	36	technology	technology	NOUN
ejpam-6939	706	37	human	human	ADJ
ejpam-6939	706	38	resource	resource	NOUN
ejpam-6939	706	39	development	development	NOUN
ejpam-6939	706	40	program	program	NOUN
ejpam-6939	706	41	(	(	PUNCT
ejpam-6939	706	42	dostasthrdp	dostasthrdp	PROPN
ejpam-6939	706	43	)	)	PUNCT
ejpam-6939	706	44	,	,	PUNCT
ejpam-6939	706	45	philippines	philippine	NOUN
ejpam-6939	706	46	;	;	PUNCT
ejpam-6939	706	47	the	the	DET
ejpam-6939	706	48	office	office	NOUN
ejpam-6939	706	49	of	of	ADP
ejpam-6939	706	50	the	the	DET
ejpam-6939	706	51	vice	vice	NOUN
ejpam-6939	706	52	chancellor	chancellor	NOUN
ejpam-6939	706	53	for	for	ADP
ejpam-6939	706	54	research	research	NOUN
ejpam-6939	706	55	and	and	CCONJ
ejpam-6939	706	56	enterprise	enterprise	NOUN
ejpam-6939	706	57	(	(	PUNCT
ejpam-6939	706	58	ovcre	ovcre	NOUN
ejpam-6939	706	59	)	)	PUNCT
ejpam-6939	706	60	of	of	ADP
ejpam-6939	706	61	the	the	DET
ejpam-6939	706	62	msu	msu	PROPN
ejpam-6939	706	63	-	-	PUNCT
ejpam-6939	706	64	iligan	iligan	PROPN
ejpam-6939	706	65	institute	institute	PROPN
ejpam-6939	706	66	of	of	ADP
ejpam-6939	706	67	technology	technology	NOUN
ejpam-6939	706	68	of	of	ADP
ejpam-6939	706	69	the	the	DET
ejpam-6939	706	70	philippines	philippine	NOUN
ejpam-6939	706	71	;	;	PUNCT
ejpam-6939	706	72	and	and	CCONJ
ejpam-6939	706	73	the	the	DET
ejpam-6939	706	74	msu	msu	PROPN
ejpam-6939	706	75	tawi	tawi	PROPN
ejpam-6939	706	76	-	-	PUNCT
ejpam-6939	706	77	tawi	tawi	PROPN
ejpam-6939	706	78	college	college	PROPN
ejpam-6939	706	79	of	of	ADP
ejpam-6939	706	80	technology	technology	NOUN
ejpam-6939	706	81	and	and	CCONJ
ejpam-6939	706	82	oceanography	oceanography	NOUN
ejpam-6939	706	83	,	,	PUNCT
ejpam-6939	706	84	philippines	philippine	NOUN
ejpam-6939	706	85	.	.	PUNCT
ejpam-6939	707	1	the	the	DET
ejpam-6939	707	2	authors	author	NOUN
ejpam-6939	707	3	would	would	AUX
ejpam-6939	707	4	also	also	ADV
ejpam-6939	707	5	like	like	VERB
ejpam-6939	707	6	to	to	PART
ejpam-6939	707	7	recognize	recognize	VERB
ejpam-6939	707	8	the	the	DET
ejpam-6939	707	9	efforts	effort	NOUN
ejpam-6939	707	10	of	of	ADP
ejpam-6939	707	11	the	the	DET
ejpam-6939	707	12	anonymous	anonymous	ADJ
ejpam-6939	707	13	reviewers	reviewer	NOUN
ejpam-6939	707	14	whose	whose	DET
ejpam-6939	707	15	suggestions	suggestion	NOUN
ejpam-6939	707	16	and	and	CCONJ
ejpam-6939	707	17	recommendations	recommendation	NOUN
ejpam-6939	707	18	contributed	contribute	VERB
ejpam-6939	707	19	to	to	ADP
ejpam-6939	707	20	the	the	DET
ejpam-6939	707	21	improvement	improvement	NOUN
ejpam-6939	707	22	of	of	ADP
ejpam-6939	707	23	the	the	DET
ejpam-6939	707	24	paper	paper	NOUN
ejpam-6939	707	25	.	.	PUNCT
ejpam-6939	708	1	references	reference	NOUN
ejpam-6939	708	2	[	[	X
ejpam-6939	708	3	1	1	NUM
ejpam-6939	708	4	]	]	PUNCT
ejpam-6939	708	5	w.	w.	PROPN
ejpam-6939	708	6	goddard	goddard	PROPN
ejpam-6939	708	7	,	,	PUNCT
ejpam-6939	708	8	m.	m.	NOUN
ejpam-6939	708	9	a.	a.	PROPN
ejpam-6939	708	10	henning	henning	PROPN
ejpam-6939	708	11	,	,	PUNCT
ejpam-6939	708	12	and	and	CCONJ
ejpam-6939	708	13	c.	c.	PROPN
ejpam-6939	708	14	a.	a.	PROPN
ejpam-6939	708	15	mcpillan	mcpillan	PROPN
ejpam-6939	708	16	.	.	PUNCT
ejpam-6939	709	1	the	the	DET
ejpam-6939	709	2	disjunctive	disjunctive	ADJ
ejpam-6939	709	3	domination	domination	NOUN
ejpam-6939	709	4	number	number	NOUN
ejpam-6939	709	5	of	of	ADP
ejpam-6939	709	6	a	a	DET
ejpam-6939	709	7	graph	graph	NOUN
ejpam-6939	709	8	.	.	PUNCT
ejpam-6939	710	1	quaestiones	quaestione	NOUN
ejpam-6939	710	2	mathematicae	mathematicae	PROPN
ejpam-6939	710	3	,	,	PUNCT
ejpam-6939	710	4	37:547–561	37:547–561	PROPN
ejpam-6939	710	5	,	,	PUNCT
ejpam-6939	710	6	2014	2014	NUM
ejpam-6939	710	7	.	.	PUNCT
ejpam-6939	711	1	[	[	X
ejpam-6939	711	2	2	2	X
ejpam-6939	711	3	]	]	PUNCT
ejpam-6939	711	4	m.	m.	NOUN
ejpam-6939	711	5	a.	a.	PROPN
ejpam-6939	711	6	henning	henning	PROPN
ejpam-6939	711	7	and	and	CCONJ
ejpam-6939	711	8	v.	v.	ADP
ejpam-6939	711	9	naicker	naicker	PROPN
ejpam-6939	711	10	.	.	PUNCT
ejpam-6939	712	1	disjunctive	disjunctive	ADJ
ejpam-6939	712	2	total	total	ADJ
ejpam-6939	712	3	domination	domination	NOUN
ejpam-6939	712	4	in	in	ADP
ejpam-6939	712	5	graphs	graph	NOUN
ejpam-6939	712	6	.	.	PUNCT
ejpam-6939	713	1	combinatorial	combinatorial	ADJ
ejpam-6939	713	2	optimization	optimization	NOUN
ejpam-6939	713	3	,	,	PUNCT
ejpam-6939	713	4	31:1090–1110	31:1090–1110	PROPN
ejpam-6939	713	5	,	,	PUNCT
ejpam-6939	713	6	2016	2016	NUM
ejpam-6939	713	7	.	.	PUNCT
ejpam-6939	714	1	[	[	X
ejpam-6939	714	2	3	3	X
ejpam-6939	714	3	]	]	X
ejpam-6939	714	4	m.	m.	NOUN
ejpam-6939	714	5	a.	a.	PROPN
ejpam-6939	714	6	henning	henning	PROPN
ejpam-6939	714	7	and	and	CCONJ
ejpam-6939	714	8	v.	v.	ADP
ejpam-6939	714	9	naicker	naicker	NOUN
ejpam-6939	714	10	.	.	PUNCT
ejpam-6939	715	1	bounds	bound	NOUN
ejpam-6939	715	2	on	on	ADP
ejpam-6939	715	3	the	the	DET
ejpam-6939	715	4	disjunctive	disjunctive	ADJ
ejpam-6939	715	5	total	total	ADJ
ejpam-6939	715	6	domination	domination	NOUN
ejpam-6939	715	7	number	number	NOUN
ejpam-6939	715	8	of	of	ADP
ejpam-6939	715	9	a	a	DET
ejpam-6939	715	10	tree	tree	NOUN
ejpam-6939	715	11	.	.	PUNCT
ejpam-6939	716	1	discussiones	discussione	NOUN
ejpam-6939	716	2	mathematicae	mathematicae	PROPN
ejpam-6939	716	3	graph	graph	NOUN
ejpam-6939	716	4	theory	theory	NOUN
ejpam-6939	716	5	,	,	PUNCT
ejpam-6939	716	6	36:153–171	36:153–171	NUM
ejpam-6939	716	7	,	,	PUNCT
ejpam-6939	716	8	2016	2016	NUM
ejpam-6939	716	9	.	.	PUNCT
ejpam-6939	717	1	[	[	X
ejpam-6939	717	2	4	4	X
ejpam-6939	717	3	]	]	X
ejpam-6939	717	4	f.	f.	PROPN
ejpam-6939	717	5	jamil	jamil	PROPN
ejpam-6939	717	6	and	and	CCONJ
ejpam-6939	717	7	r.	r.	PROPN
ejpam-6939	717	8	malalay	malalay	PROPN
ejpam-6939	717	9	.	.	PUNCT
ejpam-6939	718	1	on	on	ADP
ejpam-6939	718	2	disjunctive	disjunctive	ADJ
ejpam-6939	718	3	domination	domination	NOUN
ejpam-6939	718	4	in	in	ADP
ejpam-6939	718	5	graphs	graph	NOUN
ejpam-6939	718	6	.	.	PUNCT
ejpam-6939	719	1	quaestiones	quaestione	NOUN
ejpam-6939	719	2	mathematicae	mathematicae	PROPN
ejpam-6939	719	3	,	,	PUNCT
ejpam-6939	719	4	43(2):149–168	43(2):149–168	PROPN
ejpam-6939	719	5	,	,	PUNCT
ejpam-6939	719	6	2020	2020	NUM
ejpam-6939	719	7	.	.	PUNCT
ejpam-6939	720	1	[	[	X
ejpam-6939	720	2	5	5	NUM
ejpam-6939	720	3	]	]	PUNCT
ejpam-6939	720	4	r.	r.	PROPN
ejpam-6939	720	5	malalay	malalay	PROPN
ejpam-6939	720	6	and	and	CCONJ
ejpam-6939	720	7	f.	f.	PROPN
ejpam-6939	720	8	p.	p.	PROPN
ejpam-6939	720	9	jamil	jamil	PROPN
ejpam-6939	720	10	.	.	PUNCT
ejpam-6939	721	1	restrained	restrained	ADJ
ejpam-6939	721	2	disjunctive	disjunctive	ADJ
ejpam-6939	721	3	domination	domination	NOUN
ejpam-6939	721	4	in	in	ADP
ejpam-6939	721	5	graphs	graph	NOUN
ejpam-6939	721	6	under	under	ADP
ejpam-6939	721	7	some	some	DET
ejpam-6939	721	8	binary	binary	ADJ
ejpam-6939	721	9	operations	operation	NOUN
ejpam-6939	721	10	.	.	PUNCT
ejpam-6939	722	1	european	european	ADJ
ejpam-6939	722	2	journal	journal	PROPN
ejpam-6939	722	3	of	of	ADP
ejpam-6939	722	4	pure	pure	ADJ
ejpam-6939	722	5	and	and	CCONJ
ejpam-6939	722	6	applied	applied	ADJ
ejpam-6939	722	7	mathematics	mathematic	NOUN
ejpam-6939	722	8	,	,	PUNCT
ejpam-6939	722	9	15(1):207	15(1):207	NOUN
ejpam-6939	722	10	–	–	PUNCT
ejpam-6939	722	11	223	223	NUM
ejpam-6939	722	12	,	,	PUNCT
ejpam-6939	722	13	2022	2022	NUM
ejpam-6939	722	14	.	.	PUNCT
ejpam-6939	723	1	[	[	X
ejpam-6939	723	2	6	6	NUM
ejpam-6939	723	3	]	]	X
ejpam-6939	723	4	f.	f.	PROPN
ejpam-6939	723	5	buckley	buckley	PROPN
ejpam-6939	723	6	and	and	CCONJ
ejpam-6939	723	7	f.	f.	PROPN
ejpam-6939	723	8	harary	harary	PROPN
ejpam-6939	723	9	.	.	PUNCT
ejpam-6939	724	1	distance	distance	NOUN
ejpam-6939	724	2	in	in	ADP
ejpam-6939	724	3	graphs	graph	NOUN
ejpam-6939	724	4	.	.	PUNCT
ejpam-6939	725	1	addison	addison	PROPN
ejpam-6939	725	2	-	-	PUNCT
ejpam-6939	725	3	wesley	wesley	PROPN
ejpam-6939	725	4	,	,	PUNCT
ejpam-6939	725	5	redwood	redwood	NOUN
ejpam-6939	725	6	city	city	NOUN
ejpam-6939	725	7	,	,	PUNCT
ejpam-6939	725	8	ca	ca	NOUN
ejpam-6939	725	9	,	,	PUNCT
ejpam-6939	725	10	1990	1990	NUM
ejpam-6939	725	11	.	.	PUNCT
ejpam-6939	726	1	[	[	X
ejpam-6939	726	2	7	7	X
ejpam-6939	726	3	]	]	X
ejpam-6939	726	4	c.	c.	PROPN
ejpam-6939	726	5	berge	berge	PROPN
ejpam-6939	726	6	.	.	PUNCT
ejpam-6939	727	1	théorie	théorie	PROPN
ejpam-6939	727	2	des	des	PROPN
ejpam-6939	727	3	graphes	graphes	PROPN
ejpam-6939	727	4	et	et	PROPN
ejpam-6939	727	5	ses	ses	PROPN
ejpam-6939	727	6	applications	application	NOUN
ejpam-6939	727	7	.	.	PUNCT
ejpam-6939	728	1	dunod	dunod	PROPN
ejpam-6939	728	2	,	,	PUNCT
ejpam-6939	728	3	paris	paris	PROPN
ejpam-6939	728	4	,	,	PUNCT
ejpam-6939	728	5	1958	1958	NUM
ejpam-6939	728	6	.	.	PUNCT
ejpam-6939	729	1	translation	translation	NOUN
ejpam-6939	729	2	:	:	PUNCT
ejpam-6939	729	3	the	the	DET
ejpam-6939	729	4	theory	theory	NOUN
ejpam-6939	729	5	of	of	ADP
ejpam-6939	729	6	graphs	graph	NOUN
ejpam-6939	729	7	and	and	CCONJ
ejpam-6939	729	8	its	its	PRON
ejpam-6939	729	9	applications	application	NOUN
ejpam-6939	729	10	,	,	PUNCT
ejpam-6939	729	11	methuen	methuen	PROPN
ejpam-6939	729	12	(	(	PUNCT
ejpam-6939	729	13	london	london	PROPN
ejpam-6939	729	14	)	)	PUNCT
ejpam-6939	729	15	and	and	CCONJ
ejpam-6939	729	16	wiley	wiley	PROPN
ejpam-6939	729	17	(	(	PUNCT
ejpam-6939	729	18	new	new	PROPN
ejpam-6939	729	19	york	york	PROPN
ejpam-6939	729	20	)	)	PUNCT
ejpam-6939	729	21	,	,	PUNCT
ejpam-6939	729	22	1962	1962	NUM
ejpam-6939	729	23	.	.	PUNCT
ejpam-6939	730	1	[	[	X
ejpam-6939	730	2	8	8	NUM
ejpam-6939	730	3	]	]	X
ejpam-6939	730	4	e.	e.	PROPN
ejpam-6939	730	5	cockayne	cockayne	PROPN
ejpam-6939	730	6	and	and	CCONJ
ejpam-6939	730	7	s.	s.	PROPN
ejpam-6939	730	8	hedetniemi	hedetniemi	PROPN
ejpam-6939	730	9	.	.	PUNCT
ejpam-6939	731	1	towards	towards	ADP
ejpam-6939	731	2	a	a	DET
ejpam-6939	731	3	theory	theory	NOUN
ejpam-6939	731	4	of	of	ADP
ejpam-6939	731	5	domination	domination	NOUN
ejpam-6939	731	6	in	in	ADP
ejpam-6939	731	7	graphs	graph	NOUN
ejpam-6939	731	8	.	.	PUNCT
ejpam-6939	732	1	networks	network	NOUN
ejpam-6939	732	2	,	,	PUNCT
ejpam-6939	732	3	7(3):247–261	7(3):247–261	NUM
ejpam-6939	732	4	,	,	PUNCT
ejpam-6939	732	5	1977	1977	NUM
ejpam-6939	732	6	.	.	PUNCT
ejpam-6939	733	1	[	[	X
ejpam-6939	733	2	9	9	X
ejpam-6939	733	3	]	]	PUNCT
ejpam-6939	733	4	t.	t.	PROPN
ejpam-6939	733	5	w.	w.	PROPN
ejpam-6939	733	6	haynes	haynes	PROPN
ejpam-6939	733	7	,	,	PUNCT
ejpam-6939	733	8	s.	s.	PROPN
ejpam-6939	733	9	t.	t.	PROPN
ejpam-6939	733	10	hedetniemi	hedetniemi	PROPN
ejpam-6939	733	11	,	,	PUNCT
ejpam-6939	733	12	and	and	CCONJ
ejpam-6939	733	13	p.	p.	PROPN
ejpam-6939	733	14	j.	j.	PROPN
ejpam-6939	733	15	slater	slater	PROPN
ejpam-6939	733	16	.	.	PUNCT
ejpam-6939	734	1	fundamentals	fundamental	NOUN
ejpam-6939	734	2	of	of	ADP
ejpam-6939	734	3	domination	domination	NOUN
ejpam-6939	734	4	in	in	ADP
ejpam-6939	734	5	graphs	graph	NOUN
ejpam-6939	734	6	.	.	PUNCT
ejpam-6939	735	1	marcel	marcel	PROPN
ejpam-6939	735	2	dekker	dekker	PROPN
ejpam-6939	735	3	,	,	PUNCT
ejpam-6939	735	4	inc	inc	PROPN
ejpam-6939	735	5	.	.	PROPN
ejpam-6939	735	6	,	,	PUNCT
ejpam-6939	735	7	new	new	PROPN
ejpam-6939	735	8	york	york	PROPN
ejpam-6939	735	9	,	,	PUNCT
ejpam-6939	735	10	1998	1998	NUM
ejpam-6939	735	11	.	.	PUNCT
ejpam-6939	736	1	[	[	X
ejpam-6939	736	2	10	10	NUM
ejpam-6939	736	3	]	]	X
ejpam-6939	736	4	o.	o.	NOUN
ejpam-6939	736	5	ore	ore	PROPN
ejpam-6939	736	6	.	.	PUNCT
ejpam-6939	737	1	theory	theory	NOUN
ejpam-6939	737	2	of	of	ADP
ejpam-6939	737	3	graphs	graph	NOUN
ejpam-6939	737	4	,	,	PUNCT
ejpam-6939	737	5	volume	volume	NOUN
ejpam-6939	737	6	38	38	NUM
ejpam-6939	737	7	of	of	ADP
ejpam-6939	737	8	amer	amer	PROPN
ejpam-6939	737	9	.	.	PUNCT
ejpam-6939	737	10	math	math	PROPN
ejpam-6939	737	11	.	.	PUNCT
ejpam-6939	738	1	soc	soc	PROPN
ejpam-6939	738	2	.	.	PUNCT
ejpam-6939	739	1	colloq	colloq	PROPN
ejpam-6939	739	2	.	.	PUNCT
ejpam-6939	740	1	publ	publ	PROPN
ejpam-6939	740	2	.	.	PUNCT
ejpam-6939	741	1	amer	amer	PROPN
ejpam-6939	741	2	.	.	PUNCT
ejpam-6939	741	3	math	math	PROPN
ejpam-6939	741	4	.	.	PUNCT
ejpam-6939	742	1	soc	soc	PROPN
ejpam-6939	742	2	.	.	PUNCT
ejpam-6939	742	3	,	,	PUNCT
ejpam-6939	742	4	providence	providence	NOUN
ejpam-6939	742	5	,	,	PUNCT
ejpam-6939	742	6	ri	ri	PROPN
ejpam-6939	742	7	,	,	PUNCT
ejpam-6939	742	8	1962	1962	NUM
ejpam-6939	742	9	.	.	PUNCT
ejpam-6939	743	1	[	[	X
ejpam-6939	743	2	11	11	NUM
ejpam-6939	743	3	]	]	X
ejpam-6939	743	4	e.	e.	PROPN
ejpam-6939	743	5	cockayne	cockayne	PROPN
ejpam-6939	743	6	,	,	PUNCT
ejpam-6939	743	7	r.	r.	PROPN
ejpam-6939	743	8	m.	m.	PROPN
ejpam-6939	743	9	dawes	dawes	PROPN
ejpam-6939	743	10	,	,	PUNCT
ejpam-6939	743	11	and	and	CCONJ
ejpam-6939	743	12	s.	s.	PROPN
ejpam-6939	743	13	t.	t.	PROPN
ejpam-6939	743	14	hedetniemi	hedetniemi	PROPN
ejpam-6939	743	15	.	.	PUNCT
ejpam-6939	744	1	total	total	ADJ
ejpam-6939	744	2	domination	domination	NOUN
ejpam-6939	744	3	in	in	ADP
ejpam-6939	744	4	graphs	graph	NOUN
ejpam-6939	744	5	.	.	PUNCT
ejpam-6939	745	1	networks	network	NOUN
ejpam-6939	745	2	,	,	PUNCT
ejpam-6939	745	3	10(3):211–219	10(3):211–219	NUM
ejpam-6939	745	4	,	,	PUNCT
ejpam-6939	745	5	2006	2006	NUM
ejpam-6939	745	6	.	.	PUNCT
ejpam-6939	746	1	[	[	X
ejpam-6939	746	2	12	12	NUM
ejpam-6939	746	3	]	]	PUNCT
ejpam-6939	746	4	w.	w.	PROPN
ejpam-6939	746	5	j.	j.	PROPN
ejpam-6939	746	6	desormeaux	desormeaux	PROPN
ejpam-6939	746	7	,	,	PUNCT
ejpam-6939	746	8	t.	t.	PROPN
ejpam-6939	746	9	w.	w.	PROPN
ejpam-6939	746	10	haynes	haynes	PROPN
ejpam-6939	746	11	,	,	PUNCT
ejpam-6939	746	12	and	and	CCONJ
ejpam-6939	746	13	m.	m.	PROPN
ejpam-6939	746	14	a.	a.	PROPN
ejpam-6939	746	15	henning	henning	PROPN
ejpam-6939	746	16	.	.	PUNCT
ejpam-6939	747	1	an	an	DET
ejpam-6939	747	2	extremal	extremal	ADJ
ejpam-6939	747	3	problem	problem	NOUN
ejpam-6939	747	4	for	for	ADP
ejpam-6939	747	5	total	total	ADJ
ejpam-6939	747	6	domination	domination	NOUN
ejpam-6939	747	7	stable	stable	ADJ
ejpam-6939	747	8	graphs	graph	NOUN
ejpam-6939	747	9	upon	upon	SCONJ
ejpam-6939	747	10	edge	edge	NOUN
ejpam-6939	747	11	removal	removal	NOUN
ejpam-6939	747	12	.	.	PUNCT
ejpam-6939	748	1	discrete	discrete	ADJ
ejpam-6939	748	2	applied	applied	ADJ
ejpam-6939	748	3	mathematics	mathematic	NOUN
ejpam-6939	748	4	,	,	PUNCT
ejpam-6939	748	5	159:1048–1052	159:1048–1052	NUM
ejpam-6939	748	6	,	,	PUNCT
ejpam-6939	748	7	2011	2011	NUM
ejpam-6939	748	8	.	.	PUNCT
ejpam-6939	749	1	[	[	X
ejpam-6939	749	2	13	13	NUM
ejpam-6939	749	3	]	]	PUNCT
ejpam-6939	749	4	m.	m.	NOUN
ejpam-6939	749	5	henning	henning	PROPN
ejpam-6939	749	6	and	and	CCONJ
ejpam-6939	749	7	a.	a.	PROPN
ejpam-6939	749	8	yeo	yeo	PROPN
ejpam-6939	749	9	.	.	PROPN
ejpam-6939	750	1	total	total	ADJ
ejpam-6939	750	2	domination	domination	NOUN
ejpam-6939	750	3	in	in	ADP
ejpam-6939	750	4	graphs	graph	NOUN
ejpam-6939	750	5	.	.	PUNCT
ejpam-6939	751	1	springer	springer	NOUN
ejpam-6939	751	2	,	,	PUNCT
ejpam-6939	751	3	new	new	PROPN
ejpam-6939	751	4	york	york	PROPN
ejpam-6939	751	5	,	,	PUNCT
ejpam-6939	751	6	2013	2013	NUM
ejpam-6939	751	7	.	.	PUNCT
ejpam-6939	752	1	[	[	X
ejpam-6939	752	2	14	14	NUM
ejpam-6939	752	3	]	]	X
ejpam-6939	752	4	s.	s.	PROPN
ejpam-6939	752	5	bermudo	bermudo	PROPN
ejpam-6939	752	6	,	,	PUNCT
ejpam-6939	752	7	j.	j.	PROPN
ejpam-6939	752	8	c.	c.	PROPN
ejpam-6939	752	9	hernandez	hernandez	PROPN
ejpam-6939	752	10	-	-	PUNCT
ejpam-6939	752	11	gomez	gomez	PROPN
ejpam-6939	752	12	,	,	PUNCT
ejpam-6939	752	13	and	and	CCONJ
ejpam-6939	752	14	j.	j.	PROPN
ejpam-6939	752	15	m.	m.	PROPN
ejpam-6939	752	16	sigarreta	sigarreta	PROPN
ejpam-6939	752	17	.	.	PUNCT
ejpam-6939	753	1	on	on	ADP
ejpam-6939	753	2	the	the	DET
ejpam-6939	753	3	total	total	ADJ
ejpam-6939	753	4	k	k	NOUN
ejpam-6939	753	5	-	-	NOUN
ejpam-6939	753	6	domination	domination	NOUN
ejpam-6939	753	7	in	in	ADP
ejpam-6939	753	8	graphs	graph	NOUN
ejpam-6939	753	9	.	.	PUNCT
ejpam-6939	754	1	discussiones	discussione	NOUN
ejpam-6939	754	2	mathematicae	mathematicae	PROPN
ejpam-6939	754	3	graph	graph	NOUN
ejpam-6939	754	4	theory	theory	NOUN
ejpam-6939	754	5	,	,	PUNCT
ejpam-6939	754	6	38:301–317	38:301–317	NUM
ejpam-6939	754	7	,	,	PUNCT
ejpam-6939	754	8	2018	2018	NUM
ejpam-6939	754	9	.	.	PUNCT
ejpam-6939	755	1	a.	a.	PROPN
ejpam-6939	755	2	aradais	aradais	PROPN
ejpam-6939	755	3	,	,	PUNCT
ejpam-6939	755	4	f.	f.	PROPN
ejpam-6939	755	5	jamil	jamil	PROPN
ejpam-6939	755	6	,	,	PUNCT
ejpam-6939	755	7	s.	s.	PROPN
ejpam-6939	755	8	canoy	canoy	PROPN
ejpam-6939	755	9	/	/	SYM
ejpam-6939	755	10	eur	eur	PROPN
ejpam-6939	755	11	.	.	PUNCT
ejpam-6939	756	1	j.	j.	PROPN
ejpam-6939	756	2	pure	pure	PROPN
ejpam-6939	756	3	appl	appl	PROPN
ejpam-6939	756	4	.	.	PROPN
ejpam-6939	756	5	math	math	PROPN
ejpam-6939	756	6	,	,	PUNCT
ejpam-6939	756	7	18	18	NUM
ejpam-6939	756	8	(	(	PUNCT
ejpam-6939	756	9	4	4	NUM
ejpam-6939	756	10	)	)	PUNCT
ejpam-6939	756	11	(	(	PUNCT
ejpam-6939	756	12	2025	2025	NUM
ejpam-6939	756	13	)	)	PUNCT
ejpam-6939	756	14	,	,	PUNCT
ejpam-6939	756	15	6939	6939	NUM
ejpam-6939	756	16	14	14	NUM
ejpam-6939	756	17	of	of	ADP
ejpam-6939	756	18	14	14	NUM
ejpam-6939	756	19	[	[	SYM
ejpam-6939	756	20	15	15	NUM
ejpam-6939	756	21	]	]	X
ejpam-6939	756	22	m.	m.	NOUN
ejpam-6939	756	23	chellali	chellali	PROPN
ejpam-6939	756	24	.	.	PUNCT
ejpam-6939	757	1	bounds	bound	VERB
ejpam-6939	757	2	on	on	ADP
ejpam-6939	757	3	the	the	DET
ejpam-6939	757	4	2	2	NUM
ejpam-6939	757	5	-	-	PUNCT
ejpam-6939	757	6	domination	domination	NOUN
ejpam-6939	757	7	number	number	NOUN
ejpam-6939	757	8	in	in	ADP
ejpam-6939	757	9	cactus	cactus	NOUN
ejpam-6939	757	10	graphs	graph	NOUN
ejpam-6939	757	11	.	.	PUNCT
ejpam-6939	758	1	opuscula	opuscula	PROPN
ejpam-6939	758	2	mathematica	mathematica	PROPN
ejpam-6939	758	3	,	,	PUNCT
ejpam-6939	758	4	26(1	26(1	NUM
ejpam-6939	758	5	)	)	PUNCT
ejpam-6939	758	6	,	,	PUNCT
ejpam-6939	758	7	2006	2006	NUM
ejpam-6939	758	8	.	.	PUNCT
ejpam-6939	759	1	[	[	X
ejpam-6939	759	2	16	16	NUM
ejpam-6939	759	3	]	]	X
ejpam-6939	759	4	b.	b.	PROPN
ejpam-6939	759	5	d.	d.	PROPN
ejpam-6939	759	6	domolan	domolan	PROPN
ejpam-6939	759	7	and	and	CCONJ
ejpam-6939	759	8	s.	s.	PROPN
ejpam-6939	759	9	r.	r.	PROPN
ejpam-6939	759	10	canoy	canoy	PROPN
ejpam-6939	759	11	jr	jr	PROPN
ejpam-6939	759	12	.	.	PROPN
ejpam-6939	759	13	2	2	NUM
ejpam-6939	759	14	-	-	PUNCT
ejpam-6939	759	15	domination	domination	NOUN
ejpam-6939	759	16	and	and	CCONJ
ejpam-6939	759	17	restrained	restrain	VERB
ejpam-6939	759	18	2	2	NUM
ejpam-6939	759	19	-	-	PUNCT
ejpam-6939	759	20	domination	domination	NOUN
ejpam-6939	759	21	in	in	ADP
ejpam-6939	759	22	graphs	graph	NOUN
ejpam-6939	759	23	.	.	PUNCT
ejpam-6939	760	1	applied	apply	VERB
ejpam-6939	760	2	mathematical	mathematical	ADJ
ejpam-6939	760	3	sciences	science	NOUN
ejpam-6939	760	4	,	,	PUNCT
ejpam-6939	760	5	9(114):5651–5659	9(114):5651–5659	NUM
ejpam-6939	760	6	,	,	PUNCT
ejpam-6939	760	7	2015	2015	NUM
ejpam-6939	760	8	.	.	PUNCT
ejpam-6939	761	1	[	[	X
ejpam-6939	761	2	17	17	NUM
ejpam-6939	761	3	]	]	PUNCT
ejpam-6939	761	4	a.	a.	NOUN
ejpam-6939	761	5	hansberg	hansberg	PROPN
ejpam-6939	761	6	and	and	CCONJ
ejpam-6939	761	7	l.	l.	PROPN
ejpam-6939	761	8	volkmann	volkmann	PROPN
ejpam-6939	761	9	.	.	PUNCT
ejpam-6939	762	1	note	note	VERB
ejpam-6939	762	2	on	on	ADP
ejpam-6939	762	3	graphs	graph	NOUN
ejpam-6939	762	4	with	with	ADP
ejpam-6939	762	5	equal	equal	ADJ
ejpam-6939	762	6	domination	domination	NOUN
ejpam-6939	762	7	and	and	CCONJ
ejpam-6939	762	8	2domination	2domination	NUM
ejpam-6939	762	9	numbers	number	NOUN
ejpam-6939	762	10	.	.	PUNCT
ejpam-6939	763	1	discrete	discrete	ADJ
ejpam-6939	763	2	mathematics	mathematic	NOUN
ejpam-6939	763	3	,	,	PUNCT
ejpam-6939	763	4	308:2277–2281	308:2277–2281	NUM
ejpam-6939	763	5	,	,	PUNCT
ejpam-6939	763	6	2008	2008	NUM
ejpam-6939	763	7	.	.	PUNCT
ejpam-6939	764	1	[	[	X
ejpam-6939	764	2	18	18	NUM
ejpam-6939	764	3	]	]	PUNCT
ejpam-6939	764	4	a.	a.	NOUN
ejpam-6939	764	5	p.	p.	PROPN
ejpam-6939	764	6	kazemi	kazemi	PROPN
ejpam-6939	764	7	.	.	PUNCT
ejpam-6939	765	1	on	on	ADP
ejpam-6939	765	2	the	the	DET
ejpam-6939	765	3	total	total	ADJ
ejpam-6939	765	4	k	k	ADJ
ejpam-6939	765	5	-	-	PUNCT
ejpam-6939	765	6	domination	domination	NOUN
ejpam-6939	765	7	number	number	NOUN
ejpam-6939	765	8	of	of	ADP
ejpam-6939	765	9	graphs	graph	NOUN
ejpam-6939	765	10	.	.	PUNCT
ejpam-6939	766	1	discussiones	discussione	NOUN
ejpam-6939	766	2	mathematicae	mathematicae	PROPN
ejpam-6939	766	3	graph	graph	NOUN
ejpam-6939	766	4	theory	theory	NOUN
ejpam-6939	766	5	,	,	PUNCT
ejpam-6939	766	6	32:419–426	32:419–426	NUM
ejpam-6939	766	7	,	,	PUNCT
ejpam-6939	766	8	2012	2012	NUM
ejpam-6939	766	9	.	.	PUNCT
ejpam-6939	767	1	[	[	X
ejpam-6939	767	2	19	19	NUM
ejpam-6939	767	3	]	]	X
ejpam-6939	767	4	c.	c.	PROPN
ejpam-6939	767	5	sivagnanam	sivagnanam	PROPN
ejpam-6939	767	6	.	.	PUNCT
ejpam-6939	768	1	neighborhood	neighborhood	NOUN
ejpam-6939	768	2	total	total	ADJ
ejpam-6939	768	3	2	2	NUM
ejpam-6939	768	4	-	-	PUNCT
ejpam-6939	768	5	domination	domination	NOUN
ejpam-6939	768	6	in	in	ADP
ejpam-6939	768	7	graphs	graph	NOUN
ejpam-6939	768	8	.	.	PUNCT
ejpam-6939	769	1	international	international	ADJ
ejpam-6939	769	2	journal	journal	NOUN
ejpam-6939	769	3	of	of	ADP
ejpam-6939	769	4	mathematics	mathematics	PROPN
ejpam-6939	769	5	and	and	CCONJ
ejpam-6939	769	6	combinatorics	combinatoric	NOUN
ejpam-6939	769	7	,	,	PUNCT
ejpam-6939	769	8	4:108–119	4:108–119	PROPN
ejpam-6939	769	9	,	,	PUNCT
ejpam-6939	769	10	2014	2014	NUM
ejpam-6939	769	11	.	.	PUNCT
ejpam-6939	770	1	[	[	X
ejpam-6939	770	2	20	20	NUM
ejpam-6939	770	3	]	]	X
ejpam-6939	770	4	n.	n.	NOUN
ejpam-6939	770	5	sridharan	sridharan	ADJ
ejpam-6939	770	6	,	,	PUNCT
ejpam-6939	770	7	v.	v.	PROPN
ejpam-6939	770	8	s.	s.	PROPN
ejpam-6939	770	9	a.	a.	PROPN
ejpam-6939	770	10	subramanian	subramanian	PROPN
ejpam-6939	770	11	,	,	PUNCT
ejpam-6939	770	12	and	and	CCONJ
ejpam-6939	770	13	m.	m.	PROPN
ejpam-6939	770	14	d.	d.	PROPN
ejpam-6939	770	15	elias	elias	PROPN
ejpam-6939	770	16	.	.	PROPN
ejpam-6939	771	1	bounds	bound	NOUN
ejpam-6939	771	2	on	on	ADP
ejpam-6939	771	3	the	the	DET
ejpam-6939	771	4	distance	distance	NOUN
ejpam-6939	771	5	twodomination	twodomination	NOUN
ejpam-6939	771	6	number	number	NOUN
ejpam-6939	771	7	of	of	ADP
ejpam-6939	771	8	a	a	DET
ejpam-6939	771	9	graph	graph	NOUN
ejpam-6939	771	10	.	.	PUNCT
ejpam-6939	772	1	graphs	graph	NOUN
ejpam-6939	772	2	and	and	CCONJ
ejpam-6939	772	3	combinatorics	combinatoric	NOUN
ejpam-6939	772	4	,	,	PUNCT
ejpam-6939	772	5	18:667–675	18:667–675	NUM
ejpam-6939	772	6	,	,	PUNCT
ejpam-6939	772	7	2002	2002	NUM
ejpam-6939	772	8	.	.	PUNCT
ejpam-6939	773	1	[	[	X
ejpam-6939	773	2	21	21	NUM
ejpam-6939	773	3	]	]	X
ejpam-6939	773	4	f.	f.	PROPN
ejpam-6939	773	5	tian	tian	PROPN
ejpam-6939	773	6	and	and	CCONJ
ejpam-6939	773	7	j	j	PROPN
ejpam-6939	773	8	-	-	PROPN
ejpam-6939	773	9	m	m	PROPN
ejpam-6939	773	10	xu	xu	PROPN
ejpam-6939	773	11	.	.	PUNCT
ejpam-6939	774	1	on	on	ADP
ejpam-6939	774	2	distance	distance	NOUN
ejpam-6939	774	3	connected	connect	VERB
ejpam-6939	774	4	domination	domination	NOUN
ejpam-6939	774	5	numbers	number	NOUN
ejpam-6939	774	6	of	of	ADP
ejpam-6939	774	7	graphs	graph	NOUN
ejpam-6939	774	8	.	.	PUNCT
ejpam-6939	775	1	ars	ar	NOUN
ejpam-6939	775	2	combinatoria	combinatoria	PROPN
ejpam-6939	775	3	,	,	PUNCT
ejpam-6939	775	4	84	84	NUM
ejpam-6939	775	5	,	,	PUNCT
ejpam-6939	775	6	2007	2007	NUM
ejpam-6939	775	7	.	.	PUNCT