id	sid	tid	token	lemma	pos
ejpam-4610	1	1	european	european	PROPN
ejpam-4610	1	2	journal	journal	PROPN
ejpam-4610	1	3	of	of	ADP
ejpam-4610	1	4	pure	pure	ADJ
ejpam-4610	1	5	and	and	CCONJ
ejpam-4610	1	6	applied	apply	VERB
ejpam-4610	1	7	mathematics	mathematic	NOUN
ejpam-4610	1	8	vol	vol	NOUN
ejpam-4610	1	9	.	.	PUNCT
ejpam-4610	2	1	16	16	NUM
ejpam-4610	2	2	,	,	PUNCT
ejpam-4610	2	3	no	no	INTJ
ejpam-4610	2	4	.	.	NOUN
ejpam-4610	2	5	1	1	NUM
ejpam-4610	2	6	,	,	PUNCT
ejpam-4610	2	7	2023	2023	NUM
ejpam-4610	2	8	,	,	PUNCT
ejpam-4610	2	9	192	192	NUM
ejpam-4610	2	10	-	-	SYM
ejpam-4610	2	11	206	206	NUM
ejpam-4610	2	12	issn	issn	PROPN
ejpam-4610	2	13	1307	1307	NUM
ejpam-4610	2	14	-	-	SYM
ejpam-4610	2	15	5543	5543	NUM
ejpam-4610	2	16	–	–	PUNCT
ejpam-4610	2	17	ejpam.com	ejpam.com	X
ejpam-4610	2	18	published	publish	VERB
ejpam-4610	2	19	by	by	ADP
ejpam-4610	2	20	new	new	PROPN
ejpam-4610	2	21	york	york	PROPN
ejpam-4610	2	22	business	business	PROPN
ejpam-4610	2	23	global	global	ADJ
ejpam-4610	2	24	transversal	transversal	NOUN
ejpam-4610	2	25	hop	hop	NOUN
ejpam-4610	2	26	domination	domination	NOUN
ejpam-4610	2	27	in	in	ADP
ejpam-4610	2	28	graphs	graph	NOUN
ejpam-4610	2	29	maria	maria	PROPN
ejpam-4610	2	30	andrea	andrea	PROPN
ejpam-4610	2	31	o.	o.	PROPN
ejpam-4610	2	32	bonsocan	bonsocan	PROPN
ejpam-4610	2	33	1	1	NUM
ejpam-4610	2	34	,	,	PUNCT
ejpam-4610	3	1	ferdinand	ferdinand	PROPN
ejpam-4610	3	2	p.	p.	PROPN
ejpam-4610	3	3	jamil	jamil	PROPN
ejpam-4610	3	4	2	2	NUM
ejpam-4610	3	5	1	1	NUM
ejpam-4610	3	6	department	department	NOUN
ejpam-4610	3	7	of	of	ADP
ejpam-4610	3	8	mathematics	mathematic	NOUN
ejpam-4610	3	9	and	and	CCONJ
ejpam-4610	3	10	statistics	statistic	NOUN
ejpam-4610	3	11	,	,	PUNCT
ejpam-4610	3	12	college	college	NOUN
ejpam-4610	3	13	of	of	ADP
ejpam-4610	3	14	science	science	NOUN
ejpam-4610	3	15	and	and	CCONJ
ejpam-4610	3	16	mathematics	mathematic	NOUN
ejpam-4610	3	17	,	,	PUNCT
ejpam-4610	3	18	mindanao	mindanao	PROPN
ejpam-4610	3	19	state	state	PROPN
ejpam-4610	3	20	university	university	PROPN
ejpam-4610	3	21	-	-	PUNCT
ejpam-4610	3	22	iligan	iligan	PROPN
ejpam-4610	3	23	institute	institute	PROPN
ejpam-4610	3	24	of	of	ADP
ejpam-4610	3	25	technology	technology	PROPN
ejpam-4610	3	26	,	,	PUNCT
ejpam-4610	3	27	9200	9200	NUM
ejpam-4610	3	28	iligan	iligan	ADJ
ejpam-4610	3	29	city	city	NOUN
ejpam-4610	3	30	,	,	PUNCT
ejpam-4610	3	31	philippines	philippines	PROPN
ejpam-4610	3	32	2	2	NUM
ejpam-4610	3	33	department	department	NOUN
ejpam-4610	3	34	of	of	ADP
ejpam-4610	3	35	mathematics	mathematic	NOUN
ejpam-4610	3	36	and	and	CCONJ
ejpam-4610	3	37	statistics	statistic	NOUN
ejpam-4610	3	38	,	,	PUNCT
ejpam-4610	3	39	college	college	NOUN
ejpam-4610	3	40	of	of	ADP
ejpam-4610	3	41	science	science	NOUN
ejpam-4610	3	42	and	and	CCONJ
ejpam-4610	3	43	mathematics	mathematic	NOUN
ejpam-4610	3	44	,	,	PUNCT
ejpam-4610	3	45	center	center	NOUN
ejpam-4610	3	46	of	of	ADP
ejpam-4610	3	47	graph	graph	NOUN
ejpam-4610	3	48	theory	theory	NOUN
ejpam-4610	3	49	,	,	PUNCT
ejpam-4610	3	50	algebra	algebra	NOUN
ejpam-4610	3	51	,	,	PUNCT
ejpam-4610	3	52	and	and	CCONJ
ejpam-4610	3	53	analysis	analysis	NOUN
ejpam-4610	3	54	-	-	PUNCT
ejpam-4610	3	55	premier	premier	NOUN
ejpam-4610	3	56	research	research	NOUN
ejpam-4610	3	57	institute	institute	PROPN
ejpam-4610	3	58	of	of	ADP
ejpam-4610	3	59	science	science	NOUN
ejpam-4610	3	60	and	and	CCONJ
ejpam-4610	3	61	mathematics	mathematic	NOUN
ejpam-4610	3	62	,	,	PUNCT
ejpam-4610	3	63	mindanao	mindanao	PROPN
ejpam-4610	3	64	state	state	PROPN
ejpam-4610	3	65	university	university	PROPN
ejpam-4610	3	66	-	-	PUNCT
ejpam-4610	3	67	iligan	iligan	PROPN
ejpam-4610	3	68	institute	institute	PROPN
ejpam-4610	3	69	of	of	ADP
ejpam-4610	3	70	technology	technology	PROPN
ejpam-4610	3	71	,	,	PUNCT
ejpam-4610	3	72	9200	9200	NUM
ejpam-4610	3	73	iligan	iligan	ADJ
ejpam-4610	3	74	city	city	NOUN
ejpam-4610	3	75	,	,	PUNCT
ejpam-4610	3	76	philippines	philippine	NOUN
ejpam-4610	3	77	abstract	abstract	ADJ
ejpam-4610	3	78	.	.	PUNCT
ejpam-4610	4	1	letg	letg	NOUN
ejpam-4610	4	2	be	be	AUX
ejpam-4610	4	3	a	a	DET
ejpam-4610	4	4	graph	graph	NOUN
ejpam-4610	4	5	.	.	PUNCT
ejpam-4610	5	1	a	a	DET
ejpam-4610	5	2	set	set	NOUN
ejpam-4610	5	3	s	s	NOUN
ejpam-4610	5	4	⊆	⊆	NUM
ejpam-4610	5	5	v	v	NOUN
ejpam-4610	5	6	(	(	PUNCT
ejpam-4610	5	7	g	g	NOUN
ejpam-4610	5	8	)	)	PUNCT
ejpam-4610	5	9	is	be	AUX
ejpam-4610	5	10	a	a	DET
ejpam-4610	5	11	hop	hop	NOUN
ejpam-4610	5	12	dominating	dominating	NOUN
ejpam-4610	5	13	set	set	VERB
ejpam-4610	5	14	ofg	ofg	PROPN
ejpam-4610	5	15	if	if	SCONJ
ejpam-4610	5	16	for	for	ADP
ejpam-4610	5	17	every	every	DET
ejpam-4610	5	18	v	v	NUM
ejpam-4610	5	19	∈	∈	NOUN
ejpam-4610	5	20	v	v	NOUN
ejpam-4610	5	21	(	(	PUNCT
ejpam-4610	5	22	g)\s	g)\s	NOUN
ejpam-4610	5	23	,	,	PUNCT
ejpam-4610	5	24	there	there	PRON
ejpam-4610	5	25	exists	exist	VERB
ejpam-4610	5	26	u	u	PROPN
ejpam-4610	5	27	∈	∈	PROPN
ejpam-4610	5	28	s	s	VERB
ejpam-4610	5	29	such	such	ADJ
ejpam-4610	5	30	that	that	DET
ejpam-4610	5	31	dg(u	dg(u	ADJ
ejpam-4610	5	32	,	,	PUNCT
ejpam-4610	5	33	v	v	NOUN
ejpam-4610	5	34	)	)	PUNCT
ejpam-4610	6	1	=	=	SYM
ejpam-4610	6	2	2	2	X
ejpam-4610	6	3	.	.	PUNCT
ejpam-4610	7	1	the	the	DET
ejpam-4610	7	2	minimum	minimum	ADJ
ejpam-4610	7	3	cardinality	cardinality	NOUN
ejpam-4610	7	4	γh(g	γh(g	NOUN
ejpam-4610	7	5	)	)	PUNCT
ejpam-4610	7	6	of	of	ADP
ejpam-4610	7	7	a	a	DET
ejpam-4610	7	8	hop	hop	NOUN
ejpam-4610	7	9	dominating	dominating	NOUN
ejpam-4610	7	10	set	set	NOUN
ejpam-4610	7	11	is	be	AUX
ejpam-4610	7	12	the	the	DET
ejpam-4610	7	13	hop	hop	NOUN
ejpam-4610	7	14	domination	domination	NOUN
ejpam-4610	7	15	number	number	NOUN
ejpam-4610	7	16	of	of	ADP
ejpam-4610	7	17	g.	g.	PROPN
ejpam-4610	7	18	any	any	DET
ejpam-4610	7	19	hop	hop	NOUN
ejpam-4610	7	20	dominating	dominating	NOUN
ejpam-4610	7	21	set	set	NOUN
ejpam-4610	7	22	of	of	ADP
ejpam-4610	7	23	g	g	PROPN
ejpam-4610	7	24	of	of	ADP
ejpam-4610	7	25	cardinality	cardinality	NOUN
ejpam-4610	7	26	γh(g	γh(g	PUNCT
ejpam-4610	7	27	)	)	PUNCT
ejpam-4610	7	28	is	be	AUX
ejpam-4610	7	29	a	a	DET
ejpam-4610	7	30	γh	γh	ADV
ejpam-4610	7	31	-	-	PUNCT
ejpam-4610	7	32	set	set	NOUN
ejpam-4610	7	33	of	of	ADP
ejpam-4610	7	34	g.	g.	PROPN
ejpam-4610	7	35	a	a	DET
ejpam-4610	7	36	hop	hop	NOUN
ejpam-4610	7	37	dominating	dominating	NOUN
ejpam-4610	7	38	set	set	NOUN
ejpam-4610	7	39	s	s	PROPN
ejpam-4610	7	40	of	of	ADP
ejpam-4610	7	41	g	g	NOUN
ejpam-4610	7	42	which	which	PRON
ejpam-4610	7	43	intersects	intersect	VERB
ejpam-4610	7	44	every	every	DET
ejpam-4610	7	45	γh	γh	ADV
ejpam-4610	7	46	-	-	PUNCT
ejpam-4610	7	47	set	set	NOUN
ejpam-4610	7	48	of	of	ADP
ejpam-4610	7	49	g	g	PROPN
ejpam-4610	7	50	is	be	AUX
ejpam-4610	7	51	a	a	DET
ejpam-4610	7	52	transversal	transversal	ADJ
ejpam-4610	7	53	hop	hop	NOUN
ejpam-4610	7	54	dominating	dominating	NOUN
ejpam-4610	7	55	set	set	NOUN
ejpam-4610	7	56	.	.	PUNCT
ejpam-4610	8	1	the	the	DET
ejpam-4610	8	2	minimum	minimum	ADJ
ejpam-4610	8	3	cardinality	cardinality	NOUN
ejpam-4610	8	4	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	8	5	)	)	PUNCT
ejpam-4610	8	6	of	of	ADP
ejpam-4610	8	7	a	a	DET
ejpam-4610	8	8	transversal	transversal	ADJ
ejpam-4610	8	9	hop	hop	NOUN
ejpam-4610	8	10	dominating	dominating	NOUN
ejpam-4610	8	11	set	set	NOUN
ejpam-4610	8	12	in	in	ADP
ejpam-4610	8	13	g	g	PROPN
ejpam-4610	8	14	is	be	AUX
ejpam-4610	8	15	the	the	DET
ejpam-4610	8	16	transversal	transversal	ADJ
ejpam-4610	8	17	hop	hop	NOUN
ejpam-4610	8	18	domination	domination	NOUN
ejpam-4610	8	19	number	number	NOUN
ejpam-4610	8	20	of	of	ADP
ejpam-4610	8	21	g.	g.	PROPN
ejpam-4610	8	22	in	in	ADP
ejpam-4610	8	23	this	this	DET
ejpam-4610	8	24	paper	paper	NOUN
ejpam-4610	8	25	,	,	PUNCT
ejpam-4610	8	26	we	we	PRON
ejpam-4610	8	27	initiate	initiate	VERB
ejpam-4610	8	28	the	the	DET
ejpam-4610	8	29	study	study	NOUN
ejpam-4610	8	30	of	of	ADP
ejpam-4610	8	31	transversal	transversal	ADJ
ejpam-4610	8	32	hop	hop	NOUN
ejpam-4610	8	33	domination	domination	NOUN
ejpam-4610	8	34	.	.	PUNCT
ejpam-4610	9	1	first	first	ADV
ejpam-4610	9	2	,	,	PUNCT
ejpam-4610	9	3	we	we	PRON
ejpam-4610	9	4	characterize	characterize	VERB
ejpam-4610	9	5	graphs	graph	NOUN
ejpam-4610	9	6	g	g	ADP
ejpam-4610	9	7	whose	whose	DET
ejpam-4610	9	8	values	value	NOUN
ejpam-4610	9	9	for	for	ADP
ejpam-4610	9	10	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	9	11	)	)	PUNCT
ejpam-4610	9	12	are	be	AUX
ejpam-4610	9	13	either	either	CCONJ
ejpam-4610	9	14	n	n	CCONJ
ejpam-4610	9	15	or	or	CCONJ
ejpam-4610	9	16	n	n	CCONJ
ejpam-4610	9	17	−	−	PROPN
ejpam-4610	9	18	1	1	NUM
ejpam-4610	9	19	,	,	PUNCT
ejpam-4610	9	20	and	and	CCONJ
ejpam-4610	9	21	we	we	PRON
ejpam-4610	9	22	determine	determine	VERB
ejpam-4610	9	23	the	the	DET
ejpam-4610	9	24	specific	specific	ADJ
ejpam-4610	9	25	values	value	NOUN
ejpam-4610	9	26	of	of	ADP
ejpam-4610	9	27	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	9	28	)	)	PUNCT
ejpam-4610	9	29	for	for	ADP
ejpam-4610	9	30	some	some	DET
ejpam-4610	9	31	specific	specific	ADJ
ejpam-4610	9	32	graphs	graph	NOUN
ejpam-4610	9	33	.	.	PUNCT
ejpam-4610	10	1	next	next	ADV
ejpam-4610	10	2	,	,	PUNCT
ejpam-4610	10	3	we	we	PRON
ejpam-4610	10	4	show	show	VERB
ejpam-4610	10	5	that	that	SCONJ
ejpam-4610	10	6	for	for	ADP
ejpam-4610	10	7	every	every	DET
ejpam-4610	10	8	positive	positive	ADJ
ejpam-4610	10	9	integers	integer	NOUN
ejpam-4610	10	10	a	a	PRON
ejpam-4610	10	11	and	and	CCONJ
ejpam-4610	10	12	b	b	NOUN
ejpam-4610	10	13	with	with	ADP
ejpam-4610	10	14	a	a	DET
ejpam-4610	10	15	≥	≥	NUM
ejpam-4610	10	16	2	2	NUM
ejpam-4610	10	17	and	and	CCONJ
ejpam-4610	10	18	b	b	NOUN
ejpam-4610	10	19	≥	≥	X
ejpam-4610	10	20	3a	3a	NUM
ejpam-4610	10	21	,	,	PUNCT
ejpam-4610	10	22	there	there	PRON
ejpam-4610	10	23	exists	exist	VERB
ejpam-4610	10	24	a	a	DET
ejpam-4610	10	25	connected	connected	ADJ
ejpam-4610	10	26	graph	graph	NOUN
ejpam-4610	10	27	g	g	NOUN
ejpam-4610	10	28	on	on	ADP
ejpam-4610	10	29	b	b	NOUN
ejpam-4610	10	30	vertices	vertex	NOUN
ejpam-4610	10	31	such	such	ADJ
ejpam-4610	10	32	that	that	SCONJ
ejpam-4610	10	33	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	10	34	)	)	PUNCT
ejpam-4610	10	35	=	=	SYM
ejpam-4610	11	1	a.	a.	NOUN
ejpam-4610	11	2	we	we	PRON
ejpam-4610	11	3	also	also	ADV
ejpam-4610	11	4	show	show	VERB
ejpam-4610	11	5	that	that	SCONJ
ejpam-4610	11	6	for	for	ADP
ejpam-4610	11	7	every	every	DET
ejpam-4610	11	8	positive	positive	ADJ
ejpam-4610	11	9	integers	integer	NOUN
ejpam-4610	11	10	a	a	PRON
ejpam-4610	11	11	and	and	CCONJ
ejpam-4610	11	12	b	b	NOUN
ejpam-4610	11	13	with	with	ADP
ejpam-4610	11	14	2	2	NUM
ejpam-4610	11	15	≤	≤	NOUN
ejpam-4610	11	16	a	a	DET
ejpam-4610	11	17	≤	≤	NUM
ejpam-4610	11	18	b	b	NOUN
ejpam-4610	11	19	,	,	PUNCT
ejpam-4610	11	20	there	there	PRON
ejpam-4610	11	21	exists	exist	VERB
ejpam-4610	11	22	a	a	DET
ejpam-4610	11	23	connected	connected	ADJ
ejpam-4610	11	24	graph	graph	NOUN
ejpam-4610	11	25	g	g	NOUN
ejpam-4610	11	26	for	for	ADP
ejpam-4610	11	27	which	which	PRON
ejpam-4610	11	28	γh(g	γh(g	NOUN
ejpam-4610	11	29	)	)	PUNCT
ejpam-4610	11	30	=	=	SYM
ejpam-4610	11	31	a	a	PRON
ejpam-4610	11	32	and	and	CCONJ
ejpam-4610	11	33	γ̂h(g	γ̂h(g	PROPN
ejpam-4610	11	34	)	)	PUNCT
ejpam-4610	11	35	=	=	SYM
ejpam-4610	11	36	b.	b.	PROPN
ejpam-4610	12	1	finally	finally	ADV
ejpam-4610	12	2	,	,	PUNCT
ejpam-4610	12	3	we	we	PRON
ejpam-4610	12	4	investigate	investigate	VERB
ejpam-4610	12	5	the	the	DET
ejpam-4610	12	6	transversal	transversal	ADJ
ejpam-4610	12	7	hop	hop	NOUN
ejpam-4610	12	8	dominating	dominating	NOUN
ejpam-4610	12	9	sets	set	NOUN
ejpam-4610	12	10	in	in	ADP
ejpam-4610	12	11	the	the	DET
ejpam-4610	12	12	join	join	NOUN
ejpam-4610	12	13	and	and	CCONJ
ejpam-4610	12	14	corona	corona	NOUN
ejpam-4610	12	15	of	of	ADP
ejpam-4610	12	16	two	two	NUM
ejpam-4610	12	17	graphs	graph	NOUN
ejpam-4610	12	18	,	,	PUNCT
ejpam-4610	12	19	and	and	CCONJ
ejpam-4610	12	20	determine	determine	VERB
ejpam-4610	12	21	their	their	PRON
ejpam-4610	12	22	corresponding	corresponding	ADJ
ejpam-4610	12	23	transversal	transversal	ADJ
ejpam-4610	12	24	hop	hop	NOUN
ejpam-4610	12	25	domination	domination	NOUN
ejpam-4610	12	26	numbers	number	NOUN
ejpam-4610	12	27	.	.	PUNCT
ejpam-4610	13	1	2020	2020	NUM
ejpam-4610	13	2	mathematics	mathematic	NOUN
ejpam-4610	13	3	subject	subject	NOUN
ejpam-4610	13	4	classifications	classification	NOUN
ejpam-4610	13	5	:	:	PUNCT
ejpam-4610	13	6	05c69	05c69	X
ejpam-4610	13	7	key	key	ADJ
ejpam-4610	13	8	words	word	NOUN
ejpam-4610	13	9	and	and	CCONJ
ejpam-4610	13	10	phrases	phrase	NOUN
ejpam-4610	13	11	:	:	PUNCT
ejpam-4610	13	12	hop	hop	NOUN
ejpam-4610	13	13	dominating	dominating	NOUN
ejpam-4610	13	14	set	set	NOUN
ejpam-4610	13	15	,	,	PUNCT
ejpam-4610	13	16	transversal	transversal	ADJ
ejpam-4610	13	17	hop	hop	NOUN
ejpam-4610	13	18	dominating	dominating	NOUN
ejpam-4610	13	19	set	set	NOUN
ejpam-4610	13	20	,	,	PUNCT
ejpam-4610	13	21	transversal	transversal	ADJ
ejpam-4610	13	22	hop	hop	NOUN
ejpam-4610	13	23	domination	domination	NOUN
ejpam-4610	13	24	number	number	NOUN
ejpam-4610	13	25	1	1	NUM
ejpam-4610	13	26	.	.	PUNCT
ejpam-4610	13	27	introduction	introduction	NOUN
ejpam-4610	13	28	the	the	DET
ejpam-4610	13	29	concept	concept	NOUN
ejpam-4610	13	30	of	of	ADP
ejpam-4610	13	31	domination	domination	NOUN
ejpam-4610	13	32	in	in	ADP
ejpam-4610	13	33	graphs	graph	NOUN
ejpam-4610	13	34	was	be	AUX
ejpam-4610	13	35	first	first	ADV
ejpam-4610	13	36	introduced	introduce	VERB
ejpam-4610	13	37	by	by	ADP
ejpam-4610	13	38	ore	ore	NOUN
ejpam-4610	13	39	[	[	X
ejpam-4610	13	40	16	16	NUM
ejpam-4610	13	41	]	]	PUNCT
ejpam-4610	13	42	in	in	ADP
ejpam-4610	13	43	1958	1958	NUM
ejpam-4610	13	44	and	and	CCONJ
ejpam-4610	13	45	c.	c.	PROPN
ejpam-4610	13	46	berge	berge	NOUN
ejpam-4610	14	1	[	[	X
ejpam-4610	14	2	2	2	X
ejpam-4610	14	3	]	]	PUNCT
ejpam-4610	14	4	in	in	ADP
ejpam-4610	14	5	1962	1962	NUM
ejpam-4610	14	6	.	.	PUNCT
ejpam-4610	15	1	thereafter	thereafter	ADV
ejpam-4610	15	2	,	,	PUNCT
ejpam-4610	15	3	domination	domination	NOUN
ejpam-4610	15	4	as	as	ADV
ejpam-4610	15	5	well	well	ADV
ejpam-4610	15	6	as	as	ADP
ejpam-4610	15	7	its	its	PRON
ejpam-4610	15	8	numerous	numerous	ADJ
ejpam-4610	15	9	variations	variation	NOUN
ejpam-4610	15	10	have	have	AUX
ejpam-4610	15	11	become	become	VERB
ejpam-4610	15	12	among	among	ADP
ejpam-4610	15	13	the	the	DET
ejpam-4610	15	14	most	most	ADV
ejpam-4610	15	15	extensively	extensively	ADV
ejpam-4610	15	16	studied	study	VERB
ejpam-4610	15	17	research	research	NOUN
ejpam-4610	15	18	areas	area	NOUN
ejpam-4610	15	19	in	in	ADP
ejpam-4610	15	20	graph	graph	NOUN
ejpam-4610	15	21	theory	theory	NOUN
ejpam-4610	15	22	.	.	PUNCT
ejpam-4610	16	1	given	give	VERB
ejpam-4610	16	2	a	a	DET
ejpam-4610	16	3	family	family	NOUN
ejpam-4610	16	4	c	c	NOUN
ejpam-4610	16	5	of	of	ADP
ejpam-4610	16	6	sets	set	NOUN
ejpam-4610	16	7	,	,	PUNCT
ejpam-4610	16	8	a	a	DET
ejpam-4610	16	9	transversal	transversal	NOUN
ejpam-4610	16	10	of	of	ADP
ejpam-4610	16	11	c	c	PROPN
ejpam-4610	16	12	is	be	AUX
ejpam-4610	16	13	a	a	DET
ejpam-4610	16	14	set	set	NOUN
ejpam-4610	16	15	containing	contain	VERB
ejpam-4610	16	16	at	at	ADV
ejpam-4610	16	17	least	least	ADV
ejpam-4610	16	18	one	one	NUM
ejpam-4610	16	19	element	element	NOUN
ejpam-4610	16	20	from	from	ADP
ejpam-4610	16	21	each	each	DET
ejpam-4610	16	22	member	member	NOUN
ejpam-4610	16	23	of	of	ADP
ejpam-4610	16	24	c	c	PROPN
ejpam-4610	16	25	.	.	PUNCT
ejpam-4610	17	1	transversals	transversal	NOUN
ejpam-4610	17	2	in	in	ADP
ejpam-4610	17	3	graphs	graph	NOUN
ejpam-4610	17	4	have	have	AUX
ejpam-4610	17	5	received	receive	VERB
ejpam-4610	17	6	high	high	ADJ
ejpam-4610	17	7	attention	attention	NOUN
ejpam-4610	17	8	since	since	SCONJ
ejpam-4610	17	9	the	the	DET
ejpam-4610	17	10	last	last	ADJ
ejpam-4610	17	11	30	30	NUM
ejpam-4610	17	12	years	year	NOUN
ejpam-4610	17	13	.	.	PUNCT
ejpam-4610	18	1	in	in	ADP
ejpam-4610	18	2	1991	1991	NUM
ejpam-4610	18	3	,	,	PUNCT
ejpam-4610	18	4	t.	t.	PROPN
ejpam-4610	18	5	andreae	andreae	ADP
ejpam-4610	18	6	et	et	PROPN
ejpam-4610	18	7	al	al	PROPN
ejpam-4610	18	8	.	.	PUNCT
ejpam-4610	19	1	[	[	X
ejpam-4610	19	2	21	21	NUM
ejpam-4610	19	3	]	]	PUNCT
ejpam-4610	19	4	studied	study	VERB
ejpam-4610	19	5	the	the	DET
ejpam-4610	19	6	clique	clique	NOUN
ejpam-4610	19	7	-	-	PUNCT
ejpam-4610	19	8	transversal	transversal	ADJ
ejpam-4610	19	9	sets	set	NOUN
ejpam-4610	19	10	of	of	ADP
ejpam-4610	19	11	line	line	NOUN
ejpam-4610	19	12	graphs	graph	NOUN
ejpam-4610	19	13	.	.	PUNCT
ejpam-4610	20	1	doi	doi	NOUN
ejpam-4610	20	2	:	:	PUNCT
ejpam-4610	20	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4610	https://doi.org/10.29020/nybg.ejpam.v16i1.4610	ADJ
ejpam-4610	20	4	email	email	NOUN
ejpam-4610	20	5	addresses	address	VERB
ejpam-4610	20	6	:	:	PUNCT
ejpam-4610	20	7	mariaandrea.bonsocan@g.msuiit.edu.ph	mariaandrea.bonsocan@g.msuiit.edu.ph	PROPN
ejpam-4610	20	8	(	(	PUNCT
ejpam-4610	20	9	m.a	m.a	PROPN
ejpam-4610	20	10	.	.	PROPN
ejpam-4610	20	11	bonsocan	bonsocan	PROPN
ejpam-4610	20	12	)	)	PUNCT
ejpam-4610	20	13	,	,	PUNCT
ejpam-4610	20	14	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-4610	20	15	(	(	PUNCT
ejpam-4610	20	16	f.	f.	PROPN
ejpam-4610	20	17	jamil	jamil	PROPN
ejpam-4610	20	18	)	)	PUNCT
ejpam-4610	20	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4610	21	1	192	192	NUM
ejpam-4610	21	2	©	©	PROPN
ejpam-4610	21	3	2023	2023	NUM
ejpam-4610	21	4	ejpam	ejpam	NOUN
ejpam-4610	21	5	all	all	DET
ejpam-4610	21	6	rights	right	NOUN
ejpam-4610	21	7	reserved	reserve	VERB
ejpam-4610	21	8	.	.	PUNCT
ejpam-4610	22	1	m.a	m.a	PROPN
ejpam-4610	22	2	.	.	PROPN
ejpam-4610	22	3	bonsocan	bonsocan	PROPN
ejpam-4610	22	4	,	,	PUNCT
ejpam-4610	22	5	f.	f.	PROPN
ejpam-4610	22	6	jamil	jamil	PROPN
ejpam-4610	22	7	/	/	SYM
ejpam-4610	22	8	eur	eur	PROPN
ejpam-4610	22	9	.	.	PUNCT
ejpam-4610	23	1	j.	j.	PROPN
ejpam-4610	23	2	pure	pure	PROPN
ejpam-4610	23	3	appl	appl	PROPN
ejpam-4610	23	4	.	.	PROPN
ejpam-4610	23	5	math	math	PROPN
ejpam-4610	23	6	,	,	PUNCT
ejpam-4610	23	7	16	16	NUM
ejpam-4610	23	8	(	(	PUNCT
ejpam-4610	23	9	1	1	NUM
ejpam-4610	23	10	)	)	PUNCT
ejpam-4610	23	11	(	(	PUNCT
ejpam-4610	23	12	2023	2023	NUM
ejpam-4610	23	13	)	)	PUNCT
ejpam-4610	23	14	,	,	PUNCT
ejpam-4610	23	15	192	192	NUM
ejpam-4610	23	16	-	-	SYM
ejpam-4610	23	17	206	206	NUM
ejpam-4610	23	18	193	193	NUM
ejpam-4610	23	19	in	in	ADP
ejpam-4610	23	20	1996	1996	NUM
ejpam-4610	23	21	,	,	PUNCT
ejpam-4610	23	22	the	the	DET
ejpam-4610	23	23	vertex	vertex	NOUN
ejpam-4610	23	24	transversals	transversal	NOUN
ejpam-4610	23	25	that	that	PRON
ejpam-4610	23	26	dominate	dominate	VERB
ejpam-4610	23	27	is	be	AUX
ejpam-4610	23	28	introduced	introduce	VERB
ejpam-4610	23	29	in	in	ADP
ejpam-4610	23	30	[	[	X
ejpam-4610	23	31	5	5	NUM
ejpam-4610	23	32	]	]	PUNCT
ejpam-4610	23	33	.	.	PUNCT
ejpam-4610	24	1	the	the	DET
ejpam-4610	24	2	independent	independent	ADJ
ejpam-4610	24	3	transversal	transversal	ADJ
ejpam-4610	24	4	domination	domination	NOUN
ejpam-4610	24	5	is	be	AUX
ejpam-4610	24	6	being	be	AUX
ejpam-4610	24	7	investigated	investigate	VERB
ejpam-4610	24	8	in	in	ADP
ejpam-4610	24	9	[	[	X
ejpam-4610	24	10	6	6	NUM
ejpam-4610	24	11	,	,	PUNCT
ejpam-4610	24	12	20	20	NUM
ejpam-4610	24	13	,	,	PUNCT
ejpam-4610	24	14	22	22	NUM
ejpam-4610	24	15	]	]	PUNCT
ejpam-4610	24	16	.	.	PUNCT
ejpam-4610	25	1	recently	recently	ADV
ejpam-4610	25	2	,	,	PUNCT
ejpam-4610	25	3	a.	a.	PROPN
ejpam-4610	25	4	alwardi	alwardi	PROPN
ejpam-4610	25	5	et	et	PROPN
ejpam-4610	25	6	al.[18	al.[18	PROPN
ejpam-4610	25	7	,	,	PUNCT
ejpam-4610	25	8	19	19	NUM
ejpam-4610	25	9	]	]	PUNCT
ejpam-4610	25	10	investigated	investigate	VERB
ejpam-4610	25	11	the	the	DET
ejpam-4610	25	12	transversal	transversal	ADJ
ejpam-4610	25	13	domination	domination	NOUN
ejpam-4610	25	14	in	in	ADP
ejpam-4610	25	15	graphs	graph	NOUN
ejpam-4610	25	16	.	.	PUNCT
ejpam-4610	26	1	in	in	ADP
ejpam-4610	26	2	this	this	DET
ejpam-4610	26	3	paper	paper	NOUN
ejpam-4610	26	4	,	,	PUNCT
ejpam-4610	26	5	we	we	PRON
ejpam-4610	26	6	introduce	introduce	VERB
ejpam-4610	26	7	and	and	CCONJ
ejpam-4610	26	8	initiate	initiate	VERB
ejpam-4610	26	9	the	the	DET
ejpam-4610	26	10	study	study	NOUN
ejpam-4610	26	11	of	of	ADP
ejpam-4610	26	12	transversal	transversal	ADJ
ejpam-4610	26	13	hop	hop	NOUN
ejpam-4610	26	14	domination	domination	NOUN
ejpam-4610	26	15	.	.	PUNCT
ejpam-4610	27	1	all	all	DET
ejpam-4610	27	2	graphs	graph	NOUN
ejpam-4610	27	3	considered	consider	VERB
ejpam-4610	27	4	here	here	ADV
ejpam-4610	27	5	are	be	AUX
ejpam-4610	27	6	finite	finite	ADJ
ejpam-4610	27	7	,	,	PUNCT
ejpam-4610	27	8	simple	simple	ADJ
ejpam-4610	27	9	and	and	CCONJ
ejpam-4610	27	10	undirected	undirected	ADJ
ejpam-4610	27	11	.	.	PUNCT
ejpam-4610	28	1	for	for	ADP
ejpam-4610	28	2	basic	basic	ADJ
ejpam-4610	28	3	graph	graph	NOUN
ejpam-4610	28	4	terminologies	terminology	NOUN
ejpam-4610	28	5	,	,	PUNCT
ejpam-4610	28	6	we	we	PRON
ejpam-4610	28	7	refer	refer	VERB
ejpam-4610	28	8	the	the	DET
ejpam-4610	28	9	readers	reader	NOUN
ejpam-4610	28	10	to	to	ADP
ejpam-4610	28	11	[	[	X
ejpam-4610	28	12	3	3	NUM
ejpam-4610	28	13	]	]	PUNCT
ejpam-4610	28	14	.	.	PUNCT
ejpam-4610	29	1	for	for	ADP
ejpam-4610	29	2	a	a	DET
ejpam-4610	29	3	graph	graph	NOUN
ejpam-4610	29	4	g	g	NOUN
ejpam-4610	29	5	=	=	PUNCT
ejpam-4610	29	6	(	(	PUNCT
ejpam-4610	29	7	v	v	NOUN
ejpam-4610	29	8	(	(	PUNCT
ejpam-4610	29	9	g	g	NOUN
ejpam-4610	29	10	)	)	PUNCT
ejpam-4610	29	11	,	,	PUNCT
ejpam-4610	29	12	e(g	e(g	PROPN
ejpam-4610	29	13	)	)	PUNCT
ejpam-4610	29	14	)	)	PUNCT
ejpam-4610	29	15	,	,	PUNCT
ejpam-4610	29	16	v	v	X
ejpam-4610	29	17	(	(	PUNCT
ejpam-4610	29	18	g	g	NOUN
ejpam-4610	29	19	)	)	PUNCT
ejpam-4610	29	20	and	and	CCONJ
ejpam-4610	29	21	e(g	e(g	PROPN
ejpam-4610	29	22	)	)	PUNCT
ejpam-4610	29	23	are	be	AUX
ejpam-4610	29	24	its	its	PRON
ejpam-4610	29	25	vertex	vertex	NOUN
ejpam-4610	29	26	set	set	NOUN
ejpam-4610	29	27	and	and	CCONJ
ejpam-4610	29	28	edge	edge	NOUN
ejpam-4610	29	29	set	set	NOUN
ejpam-4610	29	30	,	,	PUNCT
ejpam-4610	29	31	respectively	respectively	ADV
ejpam-4610	29	32	.	.	PUNCT
ejpam-4610	30	1	for	for	ADP
ejpam-4610	30	2	s	s	PROPN
ejpam-4610	30	3	⊆	⊆	NUM
ejpam-4610	30	4	v	v	NOUN
ejpam-4610	30	5	(	(	PUNCT
ejpam-4610	30	6	g	g	NOUN
ejpam-4610	30	7	)	)	PUNCT
ejpam-4610	30	8	,	,	PUNCT
ejpam-4610	30	9	|s|	|s|	PROPN
ejpam-4610	30	10	refers	refer	VERB
ejpam-4610	30	11	to	to	ADP
ejpam-4610	30	12	the	the	DET
ejpam-4610	30	13	cardinality	cardinality	NOUN
ejpam-4610	30	14	of	of	ADP
ejpam-4610	30	15	s.	s.	PROPN
ejpam-4610	30	16	in	in	ADP
ejpam-4610	30	17	particular	particular	ADJ
ejpam-4610	30	18	,	,	PUNCT
ejpam-4610	30	19	|v	|v	PROPN
ejpam-4610	30	20	(	(	PUNCT
ejpam-4610	30	21	g)|	g)|	PROPN
ejpam-4610	30	22	is	be	AUX
ejpam-4610	30	23	the	the	DET
ejpam-4610	30	24	order	order	NOUN
ejpam-4610	30	25	of	of	ADP
ejpam-4610	30	26	g.	g.	NOUN
ejpam-4610	30	27	given	give	VERB
ejpam-4610	30	28	two	two	NUM
ejpam-4610	30	29	graphs	graph	NOUN
ejpam-4610	30	30	g	g	NOUN
ejpam-4610	30	31	and	and	CCONJ
ejpam-4610	30	32	h	h	NOUN
ejpam-4610	30	33	with	with	ADP
ejpam-4610	30	34	disjoint	disjoint	ADJ
ejpam-4610	30	35	vertex	vertex	NOUN
ejpam-4610	30	36	sets	set	NOUN
ejpam-4610	30	37	,	,	PUNCT
ejpam-4610	30	38	the	the	DET
ejpam-4610	30	39	union	union	NOUN
ejpam-4610	30	40	of	of	ADP
ejpam-4610	30	41	g	g	PROPN
ejpam-4610	30	42	and	and	CCONJ
ejpam-4610	30	43	h	h	NOUN
ejpam-4610	30	44	is	be	AUX
ejpam-4610	30	45	the	the	DET
ejpam-4610	30	46	graph	graph	NOUN
ejpam-4610	30	47	g∪h	g∪h	NOUN
ejpam-4610	30	48	whose	whose	DET
ejpam-4610	30	49	vertex	vertex	NOUN
ejpam-4610	30	50	set	set	NOUN
ejpam-4610	30	51	is	be	AUX
ejpam-4610	30	52	v	v	NOUN
ejpam-4610	30	53	(	(	PUNCT
ejpam-4610	30	54	g∪h	g∪h	NOUN
ejpam-4610	30	55	)	)	PUNCT
ejpam-4610	30	56	=	=	SYM
ejpam-4610	30	57	v	v	X
ejpam-4610	30	58	(	(	PUNCT
ejpam-4610	30	59	g)∪v	g)∪v	NOUN
ejpam-4610	30	60	(	(	PUNCT
ejpam-4610	30	61	h	h	NOUN
ejpam-4610	30	62	)	)	PUNCT
ejpam-4610	30	63	and	and	CCONJ
ejpam-4610	30	64	edge	edge	VERB
ejpam-4610	30	65	set	set	NOUN
ejpam-4610	30	66	e(g∪h	e(g∪h	NOUN
ejpam-4610	30	67	)	)	PUNCT
ejpam-4610	30	68	=	=	PUNCT
ejpam-4610	30	69	e(g)∪e(h	e(g)∪e(h	PROPN
ejpam-4610	30	70	)	)	PUNCT
ejpam-4610	30	71	.	.	PUNCT
ejpam-4610	31	1	the	the	DET
ejpam-4610	31	2	join	join	NOUN
ejpam-4610	31	3	of	of	ADP
ejpam-4610	31	4	g	g	PROPN
ejpam-4610	31	5	and	and	CCONJ
ejpam-4610	31	6	h	h	NOUN
ejpam-4610	31	7	is	be	AUX
ejpam-4610	31	8	the	the	DET
ejpam-4610	31	9	graph	graph	NOUN
ejpam-4610	31	10	g	g	NOUN
ejpam-4610	31	11	+	+	CCONJ
ejpam-4610	31	12	h	h	NOUN
ejpam-4610	31	13	with	with	ADP
ejpam-4610	31	14	vertex	vertex	NOUN
ejpam-4610	31	15	set	set	VERB
ejpam-4610	31	16	v	v	NOUN
ejpam-4610	31	17	(	(	PUNCT
ejpam-4610	31	18	g	g	NOUN
ejpam-4610	31	19	)	)	PUNCT
ejpam-4610	31	20	∪	∪	NOUN
ejpam-4610	31	21	v	v	NOUN
ejpam-4610	31	22	(	(	PUNCT
ejpam-4610	31	23	h	h	NOUN
ejpam-4610	31	24	)	)	PUNCT
ejpam-4610	31	25	and	and	CCONJ
ejpam-4610	31	26	edge	edge	VERB
ejpam-4610	31	27	set	set	VERB
ejpam-4610	31	28	e(g	e(g	NOUN
ejpam-4610	31	29	)	)	PUNCT
ejpam-4610	31	30	∪	∪	ADP
ejpam-4610	31	31	e(h	e(h	PROPN
ejpam-4610	31	32	)	)	PUNCT
ejpam-4610	31	33	∪	∪	NOUN
ejpam-4610	31	34	{	{	PUNCT
ejpam-4610	31	35	uv	uv	NOUN
ejpam-4610	31	36	:	:	PUNCT
ejpam-4610	31	37	u	u	PROPN
ejpam-4610	31	38	∈	∈	PROPN
ejpam-4610	31	39	v	v	ADP
ejpam-4610	31	40	(	(	PUNCT
ejpam-4610	31	41	g	g	NOUN
ejpam-4610	31	42	)	)	PUNCT
ejpam-4610	31	43	,	,	PUNCT
ejpam-4610	31	44	v	v	X
ejpam-4610	31	45	∈	∈	PROPN
ejpam-4610	31	46	v	v	NOUN
ejpam-4610	31	47	(	(	PUNCT
ejpam-4610	31	48	h	h	NOUN
ejpam-4610	31	49	)	)	PUNCT
ejpam-4610	31	50	}	}	PUNCT
ejpam-4610	31	51	.	.	PUNCT
ejpam-4610	32	1	the	the	DET
ejpam-4610	32	2	corona	corona	NOUN
ejpam-4610	32	3	of	of	ADP
ejpam-4610	32	4	g	g	PROPN
ejpam-4610	32	5	and	and	CCONJ
ejpam-4610	32	6	h	h	NOUN
ejpam-4610	32	7	is	be	AUX
ejpam-4610	32	8	the	the	DET
ejpam-4610	32	9	graph	graph	NOUN
ejpam-4610	32	10	g	g	PROPN
ejpam-4610	32	11	◦	◦	NOUN
ejpam-4610	32	12	h	h	NOUN
ejpam-4610	32	13	obtained	obtain	VERB
ejpam-4610	32	14	by	by	ADP
ejpam-4610	32	15	taking	take	VERB
ejpam-4610	32	16	one	one	NUM
ejpam-4610	32	17	copy	copy	NOUN
ejpam-4610	32	18	of	of	ADP
ejpam-4610	32	19	g	g	PROPN
ejpam-4610	32	20	and	and	CCONJ
ejpam-4610	32	21	|v	|v	PROPN
ejpam-4610	32	22	(	(	PUNCT
ejpam-4610	32	23	g)|	g)|	NOUN
ejpam-4610	32	24	copies	copy	NOUN
ejpam-4610	32	25	of	of	ADP
ejpam-4610	32	26	h	h	NOUN
ejpam-4610	32	27	,	,	PUNCT
ejpam-4610	32	28	and	and	CCONJ
ejpam-4610	32	29	then	then	ADV
ejpam-4610	32	30	joining	join	VERB
ejpam-4610	32	31	the	the	DET
ejpam-4610	32	32	ith	ith	PROPN
ejpam-4610	32	33	vertex	vertex	NOUN
ejpam-4610	32	34	of	of	ADP
ejpam-4610	32	35	g	g	NOUN
ejpam-4610	32	36	to	to	ADP
ejpam-4610	32	37	every	every	DET
ejpam-4610	32	38	vertex	vertex	NOUN
ejpam-4610	32	39	in	in	ADP
ejpam-4610	32	40	the	the	DET
ejpam-4610	32	41	ith	ith	PROPN
ejpam-4610	32	42	copy	copy	NOUN
ejpam-4610	32	43	of	of	ADP
ejpam-4610	32	44	h.	h.	PROPN
ejpam-4610	32	45	in	in	ADP
ejpam-4610	32	46	g	g	PROPN
ejpam-4610	32	47	◦	◦	NOUN
ejpam-4610	32	48	h	h	NOUN
ejpam-4610	32	49	,	,	PUNCT
ejpam-4610	32	50	we	we	PRON
ejpam-4610	32	51	denote	denote	VERB
ejpam-4610	32	52	by	by	ADP
ejpam-4610	32	53	hv	hv	PROPN
ejpam-4610	32	54	that	that	DET
ejpam-4610	32	55	copy	copy	NOUN
ejpam-4610	32	56	of	of	ADP
ejpam-4610	32	57	h	h	PRON
ejpam-4610	32	58	which	which	PRON
ejpam-4610	32	59	is	be	AUX
ejpam-4610	32	60	being	be	AUX
ejpam-4610	32	61	joined	join	VERB
ejpam-4610	32	62	to	to	ADP
ejpam-4610	32	63	the	the	DET
ejpam-4610	32	64	vertex	vertex	NOUN
ejpam-4610	32	65	v	v	NOUN
ejpam-4610	32	66	of	of	ADP
ejpam-4610	32	67	g.	g.	PROPN
ejpam-4610	32	68	we	we	PRON
ejpam-4610	32	69	also	also	ADV
ejpam-4610	32	70	denote	denote	VERB
ejpam-4610	32	71	by	by	ADP
ejpam-4610	32	72	hv	hv	PROPN
ejpam-4610	32	73	+	+	NOUN
ejpam-4610	32	74	v	v	ADP
ejpam-4610	32	75	that	that	DET
ejpam-4610	32	76	subgraph	subgraph	PROPN
ejpam-4610	32	77	⟨{v	⟨{v	PROPN
ejpam-4610	32	78	}	}	PUNCT
ejpam-4610	32	79	∪	∪	VERB
ejpam-4610	32	80	v	v	NOUN
ejpam-4610	32	81	(	(	PUNCT
ejpam-4610	32	82	hv)⟩	hv)⟩	NOUN
ejpam-4610	32	83	of	of	ADP
ejpam-4610	32	84	g	g	PROPN
ejpam-4610	32	85	◦	◦	NOUN
ejpam-4610	32	86	h	h	NOUN
ejpam-4610	32	87	induced	induce	VERB
ejpam-4610	32	88	by	by	ADP
ejpam-4610	32	89	{	{	PUNCT
ejpam-4610	32	90	v	v	NOUN
ejpam-4610	32	91	}	}	PUNCT
ejpam-4610	32	92	∪	∪	NOUN
ejpam-4610	32	93	v	v	NOUN
ejpam-4610	32	94	(	(	PUNCT
ejpam-4610	32	95	hv	hv	PROPN
ejpam-4610	32	96	)	)	PUNCT
ejpam-4610	32	97	.	.	PUNCT
ejpam-4610	33	1	for	for	ADP
ejpam-4610	33	2	a	a	DET
ejpam-4610	33	3	vertex	vertex	NOUN
ejpam-4610	33	4	v	v	NOUN
ejpam-4610	33	5	of	of	ADP
ejpam-4610	33	6	g	g	NOUN
ejpam-4610	33	7	,	,	PUNCT
ejpam-4610	33	8	the	the	DET
ejpam-4610	33	9	open	open	ADJ
ejpam-4610	33	10	neighborhood	neighborhood	NOUN
ejpam-4610	33	11	of	of	ADP
ejpam-4610	33	12	v	v	NOUN
ejpam-4610	33	13	in	in	ADP
ejpam-4610	33	14	g	g	PROPN
ejpam-4610	33	15	is	be	AUX
ejpam-4610	33	16	the	the	DET
ejpam-4610	33	17	set	set	NOUN
ejpam-4610	33	18	ng(v	ng(v	PUNCT
ejpam-4610	33	19	)	)	PUNCT
ejpam-4610	33	20	=	=	SYM
ejpam-4610	34	1	{	{	PUNCT
ejpam-4610	34	2	u	u	NOUN
ejpam-4610	34	3	∈	∈	PROPN
ejpam-4610	34	4	v	v	NOUN
ejpam-4610	34	5	(	(	PUNCT
ejpam-4610	34	6	g	g	NOUN
ejpam-4610	34	7	)	)	PUNCT
ejpam-4610	34	8	:	:	PUNCT
ejpam-4610	34	9	uv	uv	PROPN
ejpam-4610	34	10	∈	∈	PROPN
ejpam-4610	34	11	e(g	e(g	PROPN
ejpam-4610	34	12	)	)	PUNCT
ejpam-4610	34	13	}	}	PUNCT
ejpam-4610	34	14	,	,	PUNCT
ejpam-4610	34	15	while	while	SCONJ
ejpam-4610	34	16	the	the	DET
ejpam-4610	34	17	closed	closed	ADJ
ejpam-4610	34	18	neighborhood	neighborhood	NOUN
ejpam-4610	34	19	of	of	ADP
ejpam-4610	34	20	v	v	NOUN
ejpam-4610	34	21	in	in	ADP
ejpam-4610	34	22	g	g	PROPN
ejpam-4610	34	23	is	be	AUX
ejpam-4610	34	24	the	the	DET
ejpam-4610	34	25	set	set	NOUN
ejpam-4610	34	26	ng[v	ng[v	NOUN
ejpam-4610	34	27	]	]	X
ejpam-4610	34	28	=	=	SYM
ejpam-4610	34	29	ng(v	ng(v	X
ejpam-4610	34	30	)	)	PUNCT
ejpam-4610	34	31	∪	∪	ADP
ejpam-4610	34	32	{	{	PUNCT
ejpam-4610	34	33	v	v	NOUN
ejpam-4610	34	34	}	}	PUNCT
ejpam-4610	34	35	.	.	PUNCT
ejpam-4610	35	1	any	any	DET
ejpam-4610	35	2	vertex	vertex	NOUN
ejpam-4610	35	3	u	u	NOUN
ejpam-4610	35	4	∈	∈	PROPN
ejpam-4610	35	5	ng(v	ng(v	PUNCT
ejpam-4610	35	6	)	)	PUNCT
ejpam-4610	35	7	is	be	AUX
ejpam-4610	35	8	called	call	VERB
ejpam-4610	35	9	a	a	DET
ejpam-4610	35	10	neighbor	neighbor	NOUN
ejpam-4610	35	11	of	of	ADP
ejpam-4610	35	12	v.	v.	ADP
ejpam-4610	35	13	the	the	DET
ejpam-4610	35	14	degree	degree	NOUN
ejpam-4610	35	15	of	of	ADP
ejpam-4610	35	16	a	a	DET
ejpam-4610	35	17	vertex	vertex	NOUN
ejpam-4610	35	18	v	v	NOUN
ejpam-4610	35	19	of	of	ADP
ejpam-4610	35	20	g	g	NOUN
ejpam-4610	35	21	,	,	PUNCT
ejpam-4610	35	22	denoted	denote	VERB
ejpam-4610	35	23	by	by	ADP
ejpam-4610	35	24	degg(v	degg(v	PROPN
ejpam-4610	35	25	)	)	PUNCT
ejpam-4610	35	26	,	,	PUNCT
ejpam-4610	35	27	is	be	AUX
ejpam-4610	35	28	the	the	DET
ejpam-4610	35	29	number	number	NOUN
ejpam-4610	35	30	|ng(v)|	|ng(v)|	NOUN
ejpam-4610	35	31	of	of	ADP
ejpam-4610	35	32	neighbors	neighbor	NOUN
ejpam-4610	35	33	of	of	ADP
ejpam-4610	35	34	v.	v.	ADP
ejpam-4610	35	35	the	the	DET
ejpam-4610	35	36	distance	distance	NOUN
ejpam-4610	35	37	between	between	ADP
ejpam-4610	35	38	two	two	NUM
ejpam-4610	35	39	vertices	vertex	NOUN
ejpam-4610	35	40	u	u	NOUN
ejpam-4610	35	41	,	,	PUNCT
ejpam-4610	35	42	v	v	NOUN
ejpam-4610	35	43	∈	∈	PROPN
ejpam-4610	35	44	v	v	NOUN
ejpam-4610	35	45	(	(	PUNCT
ejpam-4610	35	46	g	g	NOUN
ejpam-4610	35	47	)	)	PUNCT
ejpam-4610	35	48	is	be	AUX
ejpam-4610	35	49	the	the	DET
ejpam-4610	35	50	number	number	NOUN
ejpam-4610	35	51	of	of	ADP
ejpam-4610	35	52	edges	edge	NOUN
ejpam-4610	35	53	in	in	ADP
ejpam-4610	35	54	a	a	DET
ejpam-4610	35	55	shortest	short	ADJ
ejpam-4610	35	56	path	path	NOUN
ejpam-4610	35	57	that	that	PRON
ejpam-4610	35	58	joins	join	VERB
ejpam-4610	35	59	vertex	vertex	NOUN
ejpam-4610	35	60	u	u	NOUN
ejpam-4610	35	61	to	to	PART
ejpam-4610	35	62	vertex	vertex	NOUN
ejpam-4610	35	63	v	v	NOUN
ejpam-4610	35	64	,	,	PUNCT
ejpam-4610	35	65	and	and	CCONJ
ejpam-4610	35	66	is	be	AUX
ejpam-4610	35	67	denoted	denote	VERB
ejpam-4610	35	68	by	by	ADP
ejpam-4610	35	69	dg(u	dg(u	NOUN
ejpam-4610	35	70	,	,	PUNCT
ejpam-4610	35	71	v	v	NOUN
ejpam-4610	35	72	)	)	PUNCT
ejpam-4610	35	73	.	.	PUNCT
ejpam-4610	36	1	such	such	ADJ
ejpam-4610	36	2	shortest	short	ADJ
ejpam-4610	36	3	u	u	ADJ
ejpam-4610	36	4	-	-	NOUN
ejpam-4610	36	5	v	v	ADJ
ejpam-4610	36	6	path	path	NOUN
ejpam-4610	36	7	is	be	AUX
ejpam-4610	36	8	called	call	VERB
ejpam-4610	36	9	u	u	NOUN
ejpam-4610	36	10	-	-	NOUN
ejpam-4610	36	11	v	v	NOUN
ejpam-4610	36	12	geodesic	geodesic	NOUN
ejpam-4610	36	13	.	.	PUNCT
ejpam-4610	37	1	we	we	PRON
ejpam-4610	37	2	define	define	VERB
ejpam-4610	37	3	diam(g	diam(g	NOUN
ejpam-4610	37	4	)	)	PUNCT
ejpam-4610	37	5	=	=	SYM
ejpam-4610	37	6	max{dg(u	max{dg(u	X
ejpam-4610	37	7	,	,	PUNCT
ejpam-4610	37	8	v	v	NOUN
ejpam-4610	37	9	)	)	PUNCT
ejpam-4610	37	10	:	:	PUNCT
ejpam-4610	37	11	u	u	NOUN
ejpam-4610	37	12	,	,	PUNCT
ejpam-4610	37	13	v	v	PROPN
ejpam-4610	37	14	∈	∈	PROPN
ejpam-4610	37	15	v	v	NOUN
ejpam-4610	37	16	(	(	PUNCT
ejpam-4610	37	17	g	g	NOUN
ejpam-4610	37	18	)	)	PUNCT
ejpam-4610	37	19	}	}	PUNCT
ejpam-4610	37	20	.	.	PUNCT
ejpam-4610	38	1	any	any	DET
ejpam-4610	38	2	geodesic	geodesic	NOUN
ejpam-4610	38	3	of	of	ADP
ejpam-4610	38	4	length	length	NOUN
ejpam-4610	38	5	equal	equal	ADJ
ejpam-4610	38	6	to	to	ADP
ejpam-4610	38	7	diam(g	diam(g	PROPN
ejpam-4610	38	8	)	)	PUNCT
ejpam-4610	38	9	is	be	AUX
ejpam-4610	38	10	called	call	VERB
ejpam-4610	38	11	a	a	DET
ejpam-4610	38	12	diametral	diametral	ADJ
ejpam-4610	38	13	path	path	NOUN
ejpam-4610	38	14	.	.	PUNCT
ejpam-4610	39	1	for	for	ADP
ejpam-4610	39	2	s	s	PROPN
ejpam-4610	39	3	⊆	⊆	NUM
ejpam-4610	39	4	v	v	NOUN
ejpam-4610	39	5	(	(	PUNCT
ejpam-4610	39	6	g	g	NOUN
ejpam-4610	39	7	)	)	PUNCT
ejpam-4610	39	8	,	,	PUNCT
ejpam-4610	39	9	ng(s	ng(s	NUM
ejpam-4610	39	10	)	)	PUNCT
ejpam-4610	39	11	=	=	SYM
ejpam-4610	39	12	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-4610	39	13	)	)	PUNCT
ejpam-4610	39	14	and	and	CCONJ
ejpam-4610	39	15	ng[s	ng[s	PROPN
ejpam-4610	39	16	]	]	X
ejpam-4610	39	17	=	=	SYM
ejpam-4610	39	18	ng(s	ng(s	X
ejpam-4610	39	19	)	)	PUNCT
ejpam-4610	39	20	∪	∪	ADP
ejpam-4610	39	21	s.	s.	PROPN
ejpam-4610	39	22	if	if	SCONJ
ejpam-4610	39	23	ng[s	ng[	NOUN
ejpam-4610	39	24	]	]	PUNCT
ejpam-4610	39	25	=	=	SYM
ejpam-4610	39	26	v	v	X
ejpam-4610	39	27	(	(	PUNCT
ejpam-4610	39	28	g	g	NOUN
ejpam-4610	39	29	)	)	PUNCT
ejpam-4610	39	30	(	(	PUNCT
ejpam-4610	39	31	resp	resp	NOUN
ejpam-4610	39	32	.	.	PUNCT
ejpam-4610	39	33	ng(s	ng(s	NUM
ejpam-4610	39	34	)	)	PUNCT
ejpam-4610	39	35	=	=	SYM
ejpam-4610	39	36	v	v	X
ejpam-4610	39	37	(	(	PUNCT
ejpam-4610	39	38	g	g	NOUN
ejpam-4610	39	39	)	)	PUNCT
ejpam-4610	39	40	)	)	PUNCT
ejpam-4610	39	41	,	,	PUNCT
ejpam-4610	39	42	then	then	ADV
ejpam-4610	39	43	s	s	VERB
ejpam-4610	39	44	is	be	AUX
ejpam-4610	39	45	a	a	DET
ejpam-4610	39	46	dominating	dominating	NOUN
ejpam-4610	39	47	set	set	NOUN
ejpam-4610	39	48	(	(	PUNCT
ejpam-4610	39	49	resp	resp	NOUN
ejpam-4610	39	50	.	.	PUNCT
ejpam-4610	40	1	total	total	ADJ
ejpam-4610	40	2	dominating	dominating	NOUN
ejpam-4610	40	3	set	set	NOUN
ejpam-4610	40	4	)	)	PUNCT
ejpam-4610	40	5	of	of	ADP
ejpam-4610	40	6	g.	g.	PROPN
ejpam-4610	40	7	for	for	ADP
ejpam-4610	40	8	total	total	ADJ
ejpam-4610	40	9	dominating	dominating	NOUN
ejpam-4610	40	10	sets	set	NOUN
ejpam-4610	40	11	,	,	PUNCT
ejpam-4610	40	12	g	g	NOUN
ejpam-4610	40	13	necessarily	necessarily	ADV
ejpam-4610	40	14	has	have	VERB
ejpam-4610	40	15	no	no	DET
ejpam-4610	40	16	isolated	isolated	ADJ
ejpam-4610	40	17	vertex	vertex	NOUN
ejpam-4610	40	18	.	.	PUNCT
ejpam-4610	41	1	the	the	DET
ejpam-4610	41	2	smallest	small	ADJ
ejpam-4610	41	3	cardinality	cardinality	NOUN
ejpam-4610	41	4	of	of	ADP
ejpam-4610	41	5	a	a	DET
ejpam-4610	41	6	dominating	dominating	NOUN
ejpam-4610	41	7	(	(	PUNCT
ejpam-4610	41	8	resp	resp	NOUN
ejpam-4610	41	9	.	.	PUNCT
ejpam-4610	42	1	total	total	ADJ
ejpam-4610	42	2	dominating	dominating	NOUN
ejpam-4610	42	3	)	)	PUNCT
ejpam-4610	42	4	set	set	NOUN
ejpam-4610	42	5	s	s	NOUN
ejpam-4610	42	6	of	of	ADP
ejpam-4610	42	7	g	g	NOUN
ejpam-4610	42	8	,	,	PUNCT
ejpam-4610	42	9	denoted	denote	VERB
ejpam-4610	42	10	by	by	ADP
ejpam-4610	42	11	γ(g	γ(g	PROPN
ejpam-4610	42	12	)	)	PUNCT
ejpam-4610	42	13	(	(	PUNCT
ejpam-4610	42	14	resp	resp	NOUN
ejpam-4610	42	15	.	.	PUNCT
ejpam-4610	42	16	γt(g	γt(g	PUNCT
ejpam-4610	42	17	)	)	PUNCT
ejpam-4610	42	18	)	)	PUNCT
ejpam-4610	42	19	is	be	AUX
ejpam-4610	42	20	called	call	VERB
ejpam-4610	42	21	the	the	DET
ejpam-4610	42	22	domination	domination	NOUN
ejpam-4610	42	23	number	number	NOUN
ejpam-4610	42	24	(	(	PUNCT
ejpam-4610	42	25	resp	resp	NOUN
ejpam-4610	42	26	.	.	PUNCT
ejpam-4610	43	1	total	total	ADJ
ejpam-4610	43	2	domination	domination	NOUN
ejpam-4610	43	3	number	number	NOUN
ejpam-4610	43	4	)	)	PUNCT
ejpam-4610	43	5	.	.	PUNCT
ejpam-4610	44	1	a	a	DET
ejpam-4610	44	2	dominating	dominating	NOUN
ejpam-4610	44	3	(	(	PUNCT
ejpam-4610	44	4	resp	resp	NOUN
ejpam-4610	44	5	.	.	PUNCT
ejpam-4610	45	1	total	total	ADJ
ejpam-4610	45	2	dominating	dominating	NOUN
ejpam-4610	45	3	)	)	PUNCT
ejpam-4610	45	4	set	set	NOUN
ejpam-4610	45	5	s	s	PRON
ejpam-4610	45	6	of	of	ADP
ejpam-4610	45	7	g	g	NOUN
ejpam-4610	45	8	with	with	ADP
ejpam-4610	45	9	|s|	|s|	PROPN
ejpam-4610	45	10	=	=	SYM
ejpam-4610	45	11	γ(g	γ(g	PROPN
ejpam-4610	45	12	)	)	PUNCT
ejpam-4610	45	13	(	(	PUNCT
ejpam-4610	45	14	resp	resp	NOUN
ejpam-4610	45	15	.	.	PUNCT
ejpam-4610	46	1	|s|	|s|	PROPN
ejpam-4610	46	2	=	=	SYM
ejpam-4610	46	3	γt(g	γt(g	NUM
ejpam-4610	46	4	)	)	PUNCT
ejpam-4610	46	5	)	)	PUNCT
ejpam-4610	46	6	is	be	AUX
ejpam-4610	46	7	called	call	VERB
ejpam-4610	46	8	a	a	DET
ejpam-4610	46	9	γ	γ	NOUN
ejpam-4610	46	10	-	-	PUNCT
ejpam-4610	46	11	set	set	ADJ
ejpam-4610	46	12	(	(	PUNCT
ejpam-4610	46	13	resp	resp	NOUN
ejpam-4610	46	14	.	.	PUNCT
ejpam-4610	47	1	γt	γt	NOUN
ejpam-4610	47	2	-	-	PUNCT
ejpam-4610	47	3	set	set	NOUN
ejpam-4610	47	4	)	)	PUNCT
ejpam-4610	47	5	of	of	ADP
ejpam-4610	47	6	g.	g.	PROPN
ejpam-4610	47	7	the	the	DET
ejpam-4610	47	8	reader	reader	NOUN
ejpam-4610	47	9	is	be	AUX
ejpam-4610	47	10	referred	refer	VERB
ejpam-4610	47	11	to	to	ADP
ejpam-4610	47	12	the	the	DET
ejpam-4610	47	13	following	following	ADJ
ejpam-4610	47	14	references	reference	NOUN
ejpam-4610	47	15	,	,	PUNCT
ejpam-4610	47	16	namely	namely	ADV
ejpam-4610	47	17	[	[	X
ejpam-4610	47	18	4	4	NUM
ejpam-4610	47	19	,	,	PUNCT
ejpam-4610	47	20	7–12	7–12	PROPN
ejpam-4610	47	21	,	,	PUNCT
ejpam-4610	47	22	14	14	NUM
ejpam-4610	47	23	]	]	PUNCT
ejpam-4610	47	24	,	,	PUNCT
ejpam-4610	47	25	for	for	ADP
ejpam-4610	47	26	the	the	DET
ejpam-4610	47	27	history	history	NOUN
ejpam-4610	47	28	and	and	CCONJ
ejpam-4610	47	29	a	a	DET
ejpam-4610	47	30	bit	bit	NOUN
ejpam-4610	47	31	of	of	ADP
ejpam-4610	47	32	the	the	DET
ejpam-4610	47	33	succeeding	succeed	VERB
ejpam-4610	47	34	developments	development	NOUN
ejpam-4610	47	35	of	of	ADP
ejpam-4610	47	36	the	the	DET
ejpam-4610	47	37	theory	theory	NOUN
ejpam-4610	47	38	of	of	ADP
ejpam-4610	47	39	domination	domination	NOUN
ejpam-4610	47	40	in	in	ADP
ejpam-4610	47	41	graphs	graph	NOUN
ejpam-4610	47	42	.	.	PUNCT
ejpam-4610	48	1	for	for	ADP
ejpam-4610	48	2	two	two	NUM
ejpam-4610	48	3	vertices	vertex	NOUN
ejpam-4610	48	4	u	u	NOUN
ejpam-4610	48	5	and	and	CCONJ
ejpam-4610	48	6	v	v	NOUN
ejpam-4610	48	7	of	of	ADP
ejpam-4610	48	8	g	g	NOUN
ejpam-4610	48	9	,	,	PUNCT
ejpam-4610	48	10	v	v	NOUN
ejpam-4610	48	11	is	be	AUX
ejpam-4610	48	12	a	a	DET
ejpam-4610	48	13	hop	hop	NOUN
ejpam-4610	48	14	neighbor	neighbor	NOUN
ejpam-4610	48	15	of	of	ADP
ejpam-4610	48	16	vertex	vertex	NOUN
ejpam-4610	48	17	u	u	PROPN
ejpam-4610	48	18	if	if	SCONJ
ejpam-4610	48	19	dg(u	dg(u	NOUN
ejpam-4610	48	20	,	,	PUNCT
ejpam-4610	48	21	v	v	NOUN
ejpam-4610	48	22	)	)	PUNCT
ejpam-4610	48	23	=	=	SYM
ejpam-4610	48	24	2	2	X
ejpam-4610	48	25	.	.	X
ejpam-4610	48	26	the	the	DET
ejpam-4610	48	27	set	set	NOUN
ejpam-4610	48	28	ng(u	ng(u	NOUN
ejpam-4610	48	29	,	,	PUNCT
ejpam-4610	48	30	2	2	NUM
ejpam-4610	48	31	)	)	PUNCT
ejpam-4610	48	32	=	=	PRON
ejpam-4610	48	33	{	{	PUNCT
ejpam-4610	48	34	v	v	NUM
ejpam-4610	48	35	∈	∈	NOUN
ejpam-4610	48	36	v	v	NOUN
ejpam-4610	48	37	(	(	PUNCT
ejpam-4610	48	38	g	g	NOUN
ejpam-4610	48	39	)	)	PUNCT
ejpam-4610	48	40	:	:	PUNCT
ejpam-4610	48	41	dg(v	dg(v	X
ejpam-4610	48	42	,	,	PUNCT
ejpam-4610	48	43	u	u	NOUN
ejpam-4610	48	44	)	)	PUNCT
ejpam-4610	48	45	=	=	SYM
ejpam-4610	48	46	2	2	X
ejpam-4610	48	47	}	}	PUNCT
ejpam-4610	48	48	is	be	AUX
ejpam-4610	48	49	called	call	VERB
ejpam-4610	48	50	the	the	DET
ejpam-4610	48	51	open	open	ADJ
ejpam-4610	48	52	hop	hop	NOUN
ejpam-4610	48	53	neighborhood	neighborhood	NOUN
ejpam-4610	48	54	of	of	ADP
ejpam-4610	48	55	u.	u.	PROPN
ejpam-4610	48	56	the	the	DET
ejpam-4610	48	57	closed	closed	ADJ
ejpam-4610	48	58	hop	hop	NOUN
ejpam-4610	48	59	neighborhood	neighborhood	NOUN
ejpam-4610	48	60	of	of	ADP
ejpam-4610	48	61	u	u	PROPN
ejpam-4610	48	62	ing	e	VERB
ejpam-4610	48	63	refers	refer	VERB
ejpam-4610	48	64	tong[u	tong[u	NOUN
ejpam-4610	48	65	,	,	PUNCT
ejpam-4610	48	66	2	2	NUM
ejpam-4610	48	67	]	]	PUNCT
ejpam-4610	48	68	=	=	SYM
ejpam-4610	48	69	ng(u	ng(u	NOUN
ejpam-4610	48	70	,	,	PUNCT
ejpam-4610	48	71	2)∪{u	2)∪{u	NUM
ejpam-4610	48	72	}	}	PUNCT
ejpam-4610	48	73	.	.	PUNCT
ejpam-4610	49	1	for	for	ADP
ejpam-4610	49	2	s	s	PROPN
ejpam-4610	49	3	⊆	⊆	NUM
ejpam-4610	49	4	v	v	NOUN
ejpam-4610	49	5	(	(	PUNCT
ejpam-4610	49	6	g	g	NOUN
ejpam-4610	49	7	)	)	PUNCT
ejpam-4610	49	8	,	,	PUNCT
ejpam-4610	49	9	the	the	DET
ejpam-4610	49	10	open	open	ADJ
ejpam-4610	49	11	hop	hop	NOUN
ejpam-4610	49	12	neighborhood	neighborhood	NOUN
ejpam-4610	49	13	and	and	CCONJ
ejpam-4610	49	14	closed	close	VERB
ejpam-4610	49	15	hop	hop	NOUN
ejpam-4610	49	16	neighborhood	neighborhood	NOUN
ejpam-4610	49	17	of	of	ADP
ejpam-4610	49	18	s	s	PRON
ejpam-4610	49	19	refer	refer	NOUN
ejpam-4610	49	20	to	to	ADP
ejpam-4610	49	21	the	the	DET
ejpam-4610	49	22	sets	set	NOUN
ejpam-4610	49	23	ng(s	ng(s	ADV
ejpam-4610	49	24	,	,	PUNCT
ejpam-4610	49	25	2	2	X
ejpam-4610	49	26	)	)	PUNCT
ejpam-4610	49	27	=	=	SYM
ejpam-4610	49	28	∪u∈sng(u	∪u∈sng(u	PROPN
ejpam-4610	49	29	,	,	PUNCT
ejpam-4610	49	30	2	2	NUM
ejpam-4610	49	31	)	)	PUNCT
ejpam-4610	49	32	and	and	CCONJ
ejpam-4610	49	33	ng[s	ng[s	PROPN
ejpam-4610	49	34	,	,	PUNCT
ejpam-4610	49	35	2	2	NUM
ejpam-4610	49	36	]	]	PUNCT
ejpam-4610	49	37	=	=	PUNCT
ejpam-4610	49	38	ng(s	ng(s	NOUN
ejpam-4610	49	39	,	,	PUNCT
ejpam-4610	49	40	2	2	X
ejpam-4610	49	41	)	)	PUNCT
ejpam-4610	49	42	∪	∪	ADP
ejpam-4610	49	43	s	s	PROPN
ejpam-4610	49	44	,	,	PUNCT
ejpam-4610	49	45	respectively	respectively	ADV
ejpam-4610	49	46	.	.	PUNCT
ejpam-4610	50	1	in	in	ADP
ejpam-4610	50	2	case	case	NOUN
ejpam-4610	50	3	ng[s	ng[s	PROPN
ejpam-4610	50	4	,	,	PUNCT
ejpam-4610	50	5	2	2	NUM
ejpam-4610	50	6	]	]	PUNCT
ejpam-4610	50	7	=	=	SYM
ejpam-4610	50	8	v	v	NOUN
ejpam-4610	50	9	(	(	PUNCT
ejpam-4610	50	10	g	g	NOUN
ejpam-4610	50	11	)	)	PUNCT
ejpam-4610	50	12	,	,	PUNCT
ejpam-4610	50	13	then	then	ADV
ejpam-4610	50	14	s	s	VERB
ejpam-4610	50	15	is	be	AUX
ejpam-4610	50	16	a	a	DET
ejpam-4610	50	17	hop	hop	NOUN
ejpam-4610	50	18	dominating	dominating	NOUN
ejpam-4610	50	19	set	set	NOUN
ejpam-4610	50	20	(	(	PUNCT
ejpam-4610	50	21	or	or	CCONJ
ejpam-4610	50	22	hd	hd	NOUN
ejpam-4610	50	23	-	-	PUNCT
ejpam-4610	50	24	set	set	NOUN
ejpam-4610	50	25	)	)	PUNCT
ejpam-4610	50	26	of	of	ADP
ejpam-4610	50	27	g.	g.	PROPN
ejpam-4610	50	28	provided	provide	VERB
ejpam-4610	50	29	g	g	PROPN
ejpam-4610	50	30	has	have	VERB
ejpam-4610	50	31	no	no	DET
ejpam-4610	50	32	isolated	isolated	ADJ
ejpam-4610	50	33	vertex	vertex	NOUN
ejpam-4610	50	34	,	,	PUNCT
ejpam-4610	50	35	s	s	PART
ejpam-4610	50	36	is	be	AUX
ejpam-4610	50	37	a	a	DET
ejpam-4610	50	38	total	total	ADJ
ejpam-4610	50	39	hop	hop	NOUN
ejpam-4610	50	40	dominating	dominating	NOUN
ejpam-4610	50	41	set	set	NOUN
ejpam-4610	50	42	(	(	PUNCT
ejpam-4610	50	43	or	or	CCONJ
ejpam-4610	50	44	thd	thd	NOUN
ejpam-4610	50	45	-	-	PUNCT
ejpam-4610	50	46	set	set	NOUN
ejpam-4610	50	47	)	)	PUNCT
ejpam-4610	50	48	of	of	ADP
ejpam-4610	50	49	g	g	PROPN
ejpam-4610	50	50	if	if	SCONJ
ejpam-4610	50	51	ng(s	ng(s	NUM
ejpam-4610	50	52	,	,	PUNCT
ejpam-4610	50	53	2	2	X
ejpam-4610	50	54	)	)	PUNCT
ejpam-4610	50	55	=	=	NOUN
ejpam-4610	50	56	v	v	NOUN
ejpam-4610	50	57	(	(	PUNCT
ejpam-4610	50	58	g	g	NOUN
ejpam-4610	50	59	)	)	PUNCT
ejpam-4610	50	60	.	.	PUNCT
ejpam-4610	51	1	the	the	DET
ejpam-4610	51	2	minimum	minimum	ADJ
ejpam-4610	51	3	cardinality	cardinality	NOUN
ejpam-4610	51	4	of	of	ADP
ejpam-4610	51	5	a	a	DET
ejpam-4610	51	6	hdset	hdset	NOUN
ejpam-4610	51	7	(	(	PUNCT
ejpam-4610	51	8	resp	resp	NOUN
ejpam-4610	51	9	.	.	PUNCT
ejpam-4610	52	1	thd	thd	NOUN
ejpam-4610	52	2	-	-	PUNCT
ejpam-4610	52	3	set	set	NOUN
ejpam-4610	52	4	)	)	PUNCT
ejpam-4610	52	5	of	of	ADP
ejpam-4610	52	6	g	g	NOUN
ejpam-4610	52	7	,	,	PUNCT
ejpam-4610	52	8	denoted	denote	VERB
ejpam-4610	52	9	by	by	ADP
ejpam-4610	52	10	γh(g	γh(g	NOUN
ejpam-4610	52	11	)	)	PUNCT
ejpam-4610	52	12	(	(	PUNCT
ejpam-4610	52	13	resp	resp	NOUN
ejpam-4610	52	14	.	.	PUNCT
ejpam-4610	53	1	γth(g	γth(g	NOUN
ejpam-4610	53	2	)	)	PUNCT
ejpam-4610	53	3	)	)	PUNCT
ejpam-4610	53	4	,	,	PUNCT
ejpam-4610	53	5	is	be	AUX
ejpam-4610	53	6	called	call	VERB
ejpam-4610	53	7	the	the	DET
ejpam-4610	53	8	hop	hop	NOUN
ejpam-4610	53	9	domination	domination	NOUN
ejpam-4610	53	10	number	number	NOUN
ejpam-4610	53	11	(	(	PUNCT
ejpam-4610	53	12	resp	resp	NOUN
ejpam-4610	53	13	.	.	PUNCT
ejpam-4610	54	1	total	total	ADJ
ejpam-4610	54	2	hop	hop	PROPN
ejpam-4610	54	3	domination	domination	NOUN
ejpam-4610	54	4	number	number	NOUN
ejpam-4610	54	5	)	)	PUNCT
ejpam-4610	54	6	of	of	ADP
ejpam-4610	54	7	g.	g.	PROPN
ejpam-4610	54	8	any	any	DET
ejpam-4610	54	9	hd	hd	NOUN
ejpam-4610	54	10	-	-	PUNCT
ejpam-4610	54	11	set	set	ADJ
ejpam-4610	54	12	(	(	PUNCT
ejpam-4610	54	13	resp	resp	NOUN
ejpam-4610	54	14	.	.	PUNCT
ejpam-4610	55	1	thd	thd	NOUN
ejpam-4610	55	2	-	-	PUNCT
ejpam-4610	55	3	set	set	NOUN
ejpam-4610	55	4	)	)	PUNCT
ejpam-4610	55	5	with	with	ADP
ejpam-4610	55	6	cardinality	cardinality	NOUN
ejpam-4610	55	7	γh(g	γh(g	NOUN
ejpam-4610	55	8	)	)	PUNCT
ejpam-4610	55	9	(	(	PUNCT
ejpam-4610	55	10	resp	resp	NOUN
ejpam-4610	55	11	.	.	PUNCT
ejpam-4610	56	1	γth(g	γth(g	NOUN
ejpam-4610	56	2	)	)	PUNCT
ejpam-4610	56	3	)	)	PUNCT
ejpam-4610	56	4	is	be	AUX
ejpam-4610	56	5	called	call	VERB
ejpam-4610	56	6	a	a	DET
ejpam-4610	56	7	γh	γh	ADV
ejpam-4610	56	8	-	-	PUNCT
ejpam-4610	56	9	set	set	VERB
ejpam-4610	56	10	(	(	PUNCT
ejpam-4610	56	11	resp	resp	NOUN
ejpam-4610	56	12	.	.	PUNCT
ejpam-4610	57	1	γth	γth	ADJ
ejpam-4610	57	2	-	-	PUNCT
ejpam-4610	57	3	set	set	NOUN
ejpam-4610	57	4	)	)	PUNCT
ejpam-4610	57	5	.	.	PUNCT
ejpam-4610	58	1	references	reference	NOUN
ejpam-4610	58	2	[	[	X
ejpam-4610	58	3	15	15	NUM
ejpam-4610	58	4	]	]	PUNCT
ejpam-4610	58	5	and	and	CCONJ
ejpam-4610	58	6	[	[	X
ejpam-4610	58	7	17	17	NUM
ejpam-4610	58	8	]	]	PUNCT
ejpam-4610	58	9	are	be	AUX
ejpam-4610	58	10	excellent	excellent	ADJ
ejpam-4610	58	11	references	reference	NOUN
ejpam-4610	58	12	for	for	ADP
ejpam-4610	58	13	hop	hop	NOUN
ejpam-4610	58	14	domination	domination	NOUN
ejpam-4610	58	15	and	and	CCONJ
ejpam-4610	58	16	total	total	ADJ
ejpam-4610	58	17	hop	hop	NOUN
ejpam-4610	58	18	domination	domination	NOUN
ejpam-4610	58	19	,	,	PUNCT
ejpam-4610	58	20	respectively	respectively	ADV
ejpam-4610	58	21	.	.	PUNCT
ejpam-4610	59	1	m.a	m.a	PROPN
ejpam-4610	59	2	.	.	PROPN
ejpam-4610	59	3	bonsocan	bonsocan	PROPN
ejpam-4610	59	4	,	,	PUNCT
ejpam-4610	59	5	f.	f.	PROPN
ejpam-4610	59	6	jamil	jamil	PROPN
ejpam-4610	59	7	/	/	SYM
ejpam-4610	59	8	eur	eur	PROPN
ejpam-4610	59	9	.	.	PUNCT
ejpam-4610	60	1	j.	j.	PROPN
ejpam-4610	60	2	pure	pure	PROPN
ejpam-4610	60	3	appl	appl	PROPN
ejpam-4610	60	4	.	.	PROPN
ejpam-4610	60	5	math	math	PROPN
ejpam-4610	60	6	,	,	PUNCT
ejpam-4610	60	7	16	16	NUM
ejpam-4610	60	8	(	(	PUNCT
ejpam-4610	60	9	1	1	NUM
ejpam-4610	60	10	)	)	PUNCT
ejpam-4610	60	11	(	(	PUNCT
ejpam-4610	60	12	2023	2023	NUM
ejpam-4610	60	13	)	)	PUNCT
ejpam-4610	60	14	,	,	PUNCT
ejpam-4610	60	15	192	192	NUM
ejpam-4610	60	16	-	-	SYM
ejpam-4610	60	17	206	206	NUM
ejpam-4610	60	18	194	194	NUM
ejpam-4610	60	19	a	a	DET
ejpam-4610	60	20	set	set	NOUN
ejpam-4610	60	21	s	s	NOUN
ejpam-4610	60	22	⊆	⊆	NUM
ejpam-4610	60	23	v	v	NOUN
ejpam-4610	60	24	(	(	PUNCT
ejpam-4610	60	25	g	g	NOUN
ejpam-4610	60	26	)	)	PUNCT
ejpam-4610	60	27	is	be	AUX
ejpam-4610	60	28	a	a	DET
ejpam-4610	60	29	(	(	PUNCT
ejpam-4610	60	30	1	1	NUM
ejpam-4610	60	31	,	,	PUNCT
ejpam-4610	60	32	2)∗-dominating	2)∗-dominate	VERB
ejpam-4610	60	33	set	set	NOUN
ejpam-4610	60	34	of	of	ADP
ejpam-4610	60	35	g	g	PROPN
ejpam-4610	60	36	(	(	PUNCT
ejpam-4610	60	37	resp	resp	NOUN
ejpam-4610	60	38	.	.	PUNCT
ejpam-4610	61	1	(	(	PUNCT
ejpam-4610	61	2	1	1	NUM
ejpam-4610	61	3	,	,	PUNCT
ejpam-4610	61	4	2)∗-total	2)∗-total	ADJ
ejpam-4610	61	5	dominating	dominating	NOUN
ejpam-4610	61	6	set	set	NOUN
ejpam-4610	61	7	)	)	PUNCT
ejpam-4610	61	8	if	if	SCONJ
ejpam-4610	61	9	it	it	PRON
ejpam-4610	61	10	is	be	AUX
ejpam-4610	61	11	both	both	CCONJ
ejpam-4610	61	12	a	a	DET
ejpam-4610	61	13	dominating	dominating	NOUN
ejpam-4610	61	14	(	(	PUNCT
ejpam-4610	61	15	resp	resp	NOUN
ejpam-4610	61	16	.	.	PUNCT
ejpam-4610	62	1	a	a	DET
ejpam-4610	62	2	total	total	ADJ
ejpam-4610	62	3	dominating	dominating	NOUN
ejpam-4610	62	4	)	)	PUNCT
ejpam-4610	62	5	set	set	NOUN
ejpam-4610	62	6	and	and	CCONJ
ejpam-4610	62	7	a	a	DET
ejpam-4610	62	8	hop	hop	NOUN
ejpam-4610	62	9	dominating	dominating	NOUN
ejpam-4610	62	10	set	set	NOUN
ejpam-4610	62	11	of	of	ADP
ejpam-4610	62	12	g.	g.	PROPN
ejpam-4610	62	13	the	the	DET
ejpam-4610	62	14	smallest	small	ADJ
ejpam-4610	62	15	cardinality	cardinality	NOUN
ejpam-4610	62	16	of	of	ADP
ejpam-4610	62	17	a	a	DET
ejpam-4610	62	18	(	(	PUNCT
ejpam-4610	62	19	1	1	NUM
ejpam-4610	62	20	,	,	PUNCT
ejpam-4610	62	21	2)∗	2)∗	NOUN
ejpam-4610	62	22	-dominating	-dominating	NOUN
ejpam-4610	62	23	(	(	PUNCT
ejpam-4610	62	24	resp	resp	NOUN
ejpam-4610	62	25	.	.	PUNCT
ejpam-4610	63	1	(	(	PUNCT
ejpam-4610	63	2	1	1	NUM
ejpam-4610	63	3	,	,	PUNCT
ejpam-4610	63	4	2)∗-total	2)∗-total	ADJ
ejpam-4610	63	5	dominating	dominating	NOUN
ejpam-4610	63	6	)	)	PUNCT
ejpam-4610	63	7	set	set	NOUN
ejpam-4610	63	8	of	of	ADP
ejpam-4610	63	9	g	g	NOUN
ejpam-4610	63	10	,	,	PUNCT
ejpam-4610	63	11	denoted	denote	VERB
ejpam-4610	63	12	by	by	ADP
ejpam-4610	63	13	γ∗1,2(g	γ∗1,2(g	NOUN
ejpam-4610	63	14	)	)	PUNCT
ejpam-4610	63	15	(	(	PUNCT
ejpam-4610	63	16	resp.γ∗t1,2(g	resp.γ∗t1,2(g	NOUN
ejpam-4610	63	17	)	)	PUNCT
ejpam-4610	63	18	)	)	PUNCT
ejpam-4610	63	19	is	be	AUX
ejpam-4610	63	20	called	call	VERB
ejpam-4610	63	21	the	the	DET
ejpam-4610	63	22	(	(	PUNCT
ejpam-4610	63	23	1	1	NUM
ejpam-4610	63	24	,	,	PUNCT
ejpam-4610	63	25	2)∗	2)∗	NOUN
ejpam-4610	63	26	-domination	-domination	NOUN
ejpam-4610	63	27	number	number	NOUN
ejpam-4610	63	28	(	(	PUNCT
ejpam-4610	63	29	resp	resp	NOUN
ejpam-4610	63	30	.	.	PUNCT
ejpam-4610	64	1	(	(	PUNCT
ejpam-4610	64	2	1	1	NUM
ejpam-4610	64	3	,	,	PUNCT
ejpam-4610	64	4	2)∗total	2)∗total	NUM
ejpam-4610	64	5	domination	domination	NOUN
ejpam-4610	64	6	number	number	NOUN
ejpam-4610	64	7	)	)	PUNCT
ejpam-4610	64	8	of	of	ADP
ejpam-4610	64	9	g.	g.	PROPN
ejpam-4610	64	10	a	a	PRON
ejpam-4610	64	11	(	(	PUNCT
ejpam-4610	64	12	1	1	NUM
ejpam-4610	64	13	,	,	PUNCT
ejpam-4610	64	14	2)∗	2)∗	NOUN
ejpam-4610	64	15	-dominating	-dominating	NOUN
ejpam-4610	64	16	(	(	PUNCT
ejpam-4610	64	17	resp	resp	NOUN
ejpam-4610	64	18	.	.	PUNCT
ejpam-4610	65	1	(	(	PUNCT
ejpam-4610	65	2	1	1	NUM
ejpam-4610	65	3	,	,	PUNCT
ejpam-4610	65	4	2)∗	2)∗	NOUN
ejpam-4610	65	5	-total	-total	ADJ
ejpam-4610	65	6	dominating	dominating	NOUN
ejpam-4610	65	7	)	)	PUNCT
ejpam-4610	65	8	set	set	VERB
ejpam-4610	65	9	s	s	PRON
ejpam-4610	65	10	with	with	ADP
ejpam-4610	65	11	|s|	|s|	PROPN
ejpam-4610	65	12	=	=	PUNCT
ejpam-4610	65	13	γ∗1,2(g	γ∗1,2(g	NOUN
ejpam-4610	65	14	)	)	PUNCT
ejpam-4610	65	15	(	(	PUNCT
ejpam-4610	65	16	resp	resp	NOUN
ejpam-4610	65	17	.	.	PUNCT
ejpam-4610	66	1	|s|	|s|	PROPN
ejpam-4610	66	2	=	=	SYM
ejpam-4610	66	3	γ∗t1,2(g	γ∗t1,2(g	PROPN
ejpam-4610	66	4	)	)	PUNCT
ejpam-4610	66	5	)	)	PUNCT
ejpam-4610	66	6	is	be	AUX
ejpam-4610	66	7	called	call	VERB
ejpam-4610	66	8	a	a	DET
ejpam-4610	66	9	γ∗1,2	γ∗1,2	NOUN
ejpam-4610	66	10	-	-	PUNCT
ejpam-4610	66	11	set	set	VERB
ejpam-4610	66	12	(	(	PUNCT
ejpam-4610	66	13	resp	resp	NOUN
ejpam-4610	66	14	.	.	PUNCT
ejpam-4610	67	1	γ∗t1,2	γ∗t1,2	ADJ
ejpam-4610	67	2	-	-	PUNCT
ejpam-4610	67	3	set	set	NOUN
ejpam-4610	67	4	)	)	PUNCT
ejpam-4610	67	5	of	of	ADP
ejpam-4610	67	6	g.	g.	PROPN
ejpam-4610	67	7	the	the	DET
ejpam-4610	67	8	concept	concept	NOUN
ejpam-4610	67	9	of	of	ADP
ejpam-4610	67	10	(	(	PUNCT
ejpam-4610	67	11	1	1	NUM
ejpam-4610	67	12	,	,	PUNCT
ejpam-4610	67	13	2)∗-domination	2)∗-domination	NOUN
ejpam-4610	67	14	(	(	PUNCT
ejpam-4610	67	15	a	a	DET
ejpam-4610	67	16	variation	variation	NOUN
ejpam-4610	67	17	of	of	ADP
ejpam-4610	67	18	(	(	PUNCT
ejpam-4610	67	19	1	1	NUM
ejpam-4610	67	20	,	,	PUNCT
ejpam-4610	67	21	2)-domination	2)-domination	NUM
ejpam-4610	67	22	)	)	PUNCT
ejpam-4610	67	23	is	be	AUX
ejpam-4610	67	24	introduced	introduce	VERB
ejpam-4610	67	25	in	in	ADP
ejpam-4610	67	26	[	[	X
ejpam-4610	67	27	1	1	NUM
ejpam-4610	67	28	]	]	PUNCT
ejpam-4610	67	29	.	.	PUNCT
ejpam-4610	68	1	a	a	DET
ejpam-4610	68	2	subset	subset	NOUN
ejpam-4610	68	3	s	s	X
ejpam-4610	68	4	of	of	ADP
ejpam-4610	68	5	v	v	NOUN
ejpam-4610	68	6	(	(	PUNCT
ejpam-4610	68	7	g	g	NOUN
ejpam-4610	68	8	)	)	PUNCT
ejpam-4610	68	9	is	be	AUX
ejpam-4610	68	10	a	a	DET
ejpam-4610	68	11	point	point	NOUN
ejpam-4610	68	12	-	-	PUNCT
ejpam-4610	68	13	wise	wise	ADJ
ejpam-4610	68	14	non	non	ADJ
ejpam-4610	68	15	-	-	ADJ
ejpam-4610	68	16	dominating	dominating	ADJ
ejpam-4610	68	17	set	set	NOUN
ejpam-4610	68	18	(	(	PUNCT
ejpam-4610	68	19	or	or	CCONJ
ejpam-4610	68	20	pnd	pnd	NOUN
ejpam-4610	68	21	-	-	PUNCT
ejpam-4610	68	22	set	set	NOUN
ejpam-4610	68	23	)	)	PUNCT
ejpam-4610	68	24	of	of	ADP
ejpam-4610	68	25	g	g	PROPN
ejpam-4610	68	26	if	if	SCONJ
ejpam-4610	68	27	for	for	ADP
ejpam-4610	68	28	each	each	PRON
ejpam-4610	68	29	v	v	NUM
ejpam-4610	68	30	∈	∈	PROPN
ejpam-4610	68	31	v	v	NOUN
ejpam-4610	68	32	(	(	PUNCT
ejpam-4610	68	33	g	g	NOUN
ejpam-4610	68	34	)	)	PUNCT
ejpam-4610	68	35	\	\	PROPN
ejpam-4610	69	1	s	s	X
ejpam-4610	69	2	,	,	PUNCT
ejpam-4610	69	3	there	there	PRON
ejpam-4610	69	4	exists	exist	VERB
ejpam-4610	69	5	u	u	PROPN
ejpam-4610	69	6	∈	∈	PROPN
ejpam-4610	69	7	s	s	VERB
ejpam-4610	69	8	such	such	ADJ
ejpam-4610	69	9	that	that	DET
ejpam-4610	69	10	v	v	NOUN
ejpam-4610	69	11	/∈	/∈	PUNCT
ejpam-4610	69	12	ng(u	ng(u	NOUN
ejpam-4610	69	13	)	)	PUNCT
ejpam-4610	69	14	.	.	PUNCT
ejpam-4610	70	1	the	the	DET
ejpam-4610	70	2	smallest	small	ADJ
ejpam-4610	70	3	cardinality	cardinality	NOUN
ejpam-4610	70	4	of	of	ADP
ejpam-4610	70	5	a	a	DET
ejpam-4610	70	6	pnd	pnd	NOUN
ejpam-4610	70	7	-	-	PUNCT
ejpam-4610	70	8	set	set	NOUN
ejpam-4610	70	9	of	of	ADP
ejpam-4610	70	10	g	g	NOUN
ejpam-4610	70	11	,	,	PUNCT
ejpam-4610	70	12	denoted	denote	VERB
ejpam-4610	70	13	pnd(g	pnd(g	ADP
ejpam-4610	70	14	)	)	PUNCT
ejpam-4610	70	15	,	,	PUNCT
ejpam-4610	70	16	is	be	AUX
ejpam-4610	70	17	called	call	VERB
ejpam-4610	70	18	the	the	DET
ejpam-4610	70	19	point	point	NOUN
ejpam-4610	70	20	-	-	PUNCT
ejpam-4610	70	21	wise	wise	ADJ
ejpam-4610	70	22	non	non	ADJ
ejpam-4610	70	23	-	-	ADJ
ejpam-4610	70	24	domination	domination	ADJ
ejpam-4610	70	25	number	number	NOUN
ejpam-4610	70	26	of	of	ADP
ejpam-4610	70	27	g.	g.	PROPN
ejpam-4610	70	28	any	any	DET
ejpam-4610	70	29	point	point	NOUN
ejpam-4610	70	30	-	-	PUNCT
ejpam-4610	70	31	wise	wise	ADJ
ejpam-4610	70	32	non	non	ADJ
ejpam-4610	70	33	-	-	ADJ
ejpam-4610	70	34	dominating	dominating	ADJ
ejpam-4610	70	35	set	set	NOUN
ejpam-4610	70	36	s	s	NOUN
ejpam-4610	70	37	of	of	ADP
ejpam-4610	70	38	g	g	NOUN
ejpam-4610	70	39	with	with	ADP
ejpam-4610	70	40	|s|	|s|	NOUN
ejpam-4610	70	41	=	=	SYM
ejpam-4610	70	42	pnd(g	pnd(g	PROPN
ejpam-4610	70	43	)	)	PUNCT
ejpam-4610	70	44	is	be	AUX
ejpam-4610	70	45	called	call	VERB
ejpam-4610	70	46	a	a	DET
ejpam-4610	70	47	pnd	pnd	NOUN
ejpam-4610	70	48	-	-	PUNCT
ejpam-4610	70	49	set	set	NOUN
ejpam-4610	70	50	of	of	ADP
ejpam-4610	70	51	g.	g.	PROPN
ejpam-4610	70	52	the	the	DET
ejpam-4610	70	53	concept	concept	NOUN
ejpam-4610	70	54	of	of	ADP
ejpam-4610	70	55	point	point	NOUN
ejpam-4610	70	56	-	-	PUNCT
ejpam-4610	70	57	wise	wise	ADJ
ejpam-4610	70	58	non	non	ADJ
ejpam-4610	70	59	-	-	ADJ
ejpam-4610	70	60	domination	domination	NOUN
ejpam-4610	70	61	was	be	AUX
ejpam-4610	70	62	introduced	introduce	VERB
ejpam-4610	70	63	in	in	ADP
ejpam-4610	70	64	[	[	X
ejpam-4610	70	65	1	1	NUM
ejpam-4610	70	66	]	]	PUNCT
ejpam-4610	70	67	.	.	PUNCT
ejpam-4610	71	1	a	a	DET
ejpam-4610	71	2	hop	hop	NOUN
ejpam-4610	71	3	dominating	dominating	NOUN
ejpam-4610	71	4	set	set	NOUN
ejpam-4610	71	5	s	s	PROPN
ejpam-4610	71	6	of	of	ADP
ejpam-4610	71	7	g	g	NOUN
ejpam-4610	71	8	which	which	PRON
ejpam-4610	71	9	intersects	intersect	VERB
ejpam-4610	71	10	every	every	DET
ejpam-4610	71	11	γh	γh	ADV
ejpam-4610	71	12	-	-	PUNCT
ejpam-4610	71	13	set	set	NOUN
ejpam-4610	71	14	of	of	ADP
ejpam-4610	71	15	g	g	PROPN
ejpam-4610	71	16	is	be	AUX
ejpam-4610	71	17	called	call	VERB
ejpam-4610	71	18	a	a	DET
ejpam-4610	71	19	transversal	transversal	ADJ
ejpam-4610	71	20	hop	hop	NOUN
ejpam-4610	71	21	dominating	dominating	NOUN
ejpam-4610	71	22	set	set	NOUN
ejpam-4610	71	23	or	or	CCONJ
ejpam-4610	71	24	(	(	PUNCT
ejpam-4610	71	25	thd	thd	NOUN
ejpam-4610	71	26	-	-	PUNCT
ejpam-4610	71	27	set	set	NOUN
ejpam-4610	71	28	)	)	PUNCT
ejpam-4610	71	29	.	.	PUNCT
ejpam-4610	72	1	in	in	ADP
ejpam-4610	72	2	other	other	ADJ
ejpam-4610	72	3	words	word	NOUN
ejpam-4610	72	4	,	,	PUNCT
ejpam-4610	72	5	a	a	DET
ejpam-4610	72	6	thd	thd	NOUN
ejpam-4610	72	7	-	-	PUNCT
ejpam-4610	72	8	set	set	NOUN
ejpam-4610	72	9	is	be	AUX
ejpam-4610	72	10	a	a	DET
ejpam-4610	72	11	hop	hop	NOUN
ejpam-4610	72	12	dominating	dominating	NOUN
ejpam-4610	72	13	set	set	NOUN
ejpam-4610	72	14	of	of	ADP
ejpam-4610	72	15	g	g	PROPN
ejpam-4610	72	16	which	which	PRON
ejpam-4610	72	17	is	be	AUX
ejpam-4610	72	18	represented	represent	VERB
ejpam-4610	72	19	by	by	ADP
ejpam-4610	72	20	every	every	DET
ejpam-4610	72	21	γh	γh	ADV
ejpam-4610	72	22	-	-	PUNCT
ejpam-4610	72	23	set	set	NOUN
ejpam-4610	72	24	of	of	ADP
ejpam-4610	72	25	g.	g.	PROPN
ejpam-4610	72	26	the	the	DET
ejpam-4610	72	27	minimum	minimum	ADJ
ejpam-4610	72	28	cardinality	cardinality	NOUN
ejpam-4610	72	29	of	of	ADP
ejpam-4610	72	30	a	a	DET
ejpam-4610	72	31	thd	thd	NOUN
ejpam-4610	72	32	-	-	PUNCT
ejpam-4610	72	33	set	set	NOUN
ejpam-4610	72	34	of	of	ADP
ejpam-4610	72	35	g	g	PROPN
ejpam-4610	72	36	is	be	AUX
ejpam-4610	72	37	called	call	VERB
ejpam-4610	72	38	the	the	DET
ejpam-4610	72	39	transversal	transversal	ADJ
ejpam-4610	72	40	hop	hop	NOUN
ejpam-4610	72	41	domination	domination	NOUN
ejpam-4610	72	42	number	number	NOUN
ejpam-4610	72	43	of	of	ADP
ejpam-4610	72	44	g	g	NOUN
ejpam-4610	72	45	and	and	CCONJ
ejpam-4610	72	46	is	be	AUX
ejpam-4610	72	47	denoted	denote	VERB
ejpam-4610	72	48	by	by	ADP
ejpam-4610	72	49	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	72	50	)	)	PUNCT
ejpam-4610	72	51	.	.	PUNCT
ejpam-4610	73	1	any	any	DET
ejpam-4610	73	2	thd	thd	NOUN
ejpam-4610	73	3	-	-	PUNCT
ejpam-4610	73	4	set	set	VERB
ejpam-4610	73	5	s	s	NOUN
ejpam-4610	73	6	of	of	ADP
ejpam-4610	73	7	g	g	NOUN
ejpam-4610	73	8	with	with	ADP
ejpam-4610	73	9	|s|	|s|	NOUN
ejpam-4610	73	10	=	=	PUNCT
ejpam-4610	73	11	γ̂h(g	γ̂h(g	PROPN
ejpam-4610	73	12	)	)	PUNCT
ejpam-4610	73	13	is	be	AUX
ejpam-4610	73	14	called	call	VERB
ejpam-4610	73	15	a	a	DET
ejpam-4610	73	16	γ̂h	γ̂h	NOUN
ejpam-4610	73	17	-	-	PUNCT
ejpam-4610	73	18	set	set	NOUN
ejpam-4610	73	19	.	.	PUNCT
ejpam-4610	74	1	2	2	X
ejpam-4610	74	2	.	.	X
ejpam-4610	74	3	preliminary	preliminary	ADJ
ejpam-4610	74	4	results	result	NOUN
ejpam-4610	74	5	clearly	clearly	ADV
ejpam-4610	74	6	,	,	PUNCT
ejpam-4610	74	7	γh(g	γh(g	NOUN
ejpam-4610	74	8	)	)	PUNCT
ejpam-4610	74	9	≤	≤	NUM
ejpam-4610	74	10	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	74	11	)	)	PUNCT
ejpam-4610	74	12	≤	≤	NOUN
ejpam-4610	74	13	n	n	CCONJ
ejpam-4610	74	14	for	for	ADP
ejpam-4610	74	15	all	all	DET
ejpam-4610	74	16	connected	connected	ADJ
ejpam-4610	74	17	graphs	graph	NOUN
ejpam-4610	74	18	g	g	ADP
ejpam-4610	74	19	of	of	ADP
ejpam-4610	74	20	order	order	NOUN
ejpam-4610	74	21	n.	n.	NOUN
ejpam-4610	74	22	in	in	ADP
ejpam-4610	74	23	particular	particular	ADJ
ejpam-4610	74	24	,	,	PUNCT
ejpam-4610	74	25	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	74	26	)	)	PUNCT
ejpam-4610	74	27	=	=	SYM
ejpam-4610	74	28	1	1	NUM
ejpam-4610	74	29	if	if	SCONJ
ejpam-4610	74	30	and	and	CCONJ
ejpam-4610	74	31	only	only	ADV
ejpam-4610	74	32	if	if	SCONJ
ejpam-4610	74	33	g	g	PROPN
ejpam-4610	74	34	=	=	SYM
ejpam-4610	74	35	k1	k1	PROPN
ejpam-4610	74	36	.	.	PUNCT
ejpam-4610	75	1	proposition	proposition	NOUN
ejpam-4610	75	2	1	1	NUM
ejpam-4610	75	3	.	.	PUNCT
ejpam-4610	76	1	let	let	VERB
ejpam-4610	76	2	g	g	PRON
ejpam-4610	76	3	be	be	AUX
ejpam-4610	76	4	a	a	DET
ejpam-4610	76	5	connected	connected	ADJ
ejpam-4610	76	6	graph	graph	NOUN
ejpam-4610	76	7	of	of	ADP
ejpam-4610	76	8	order	order	NOUN
ejpam-4610	76	9	n.	n.	NOUN
ejpam-4610	76	10	then	then	ADV
ejpam-4610	76	11	(	(	PUNCT
ejpam-4610	76	12	i	i	NOUN
ejpam-4610	76	13	)	)	PUNCT
ejpam-4610	76	14	γ̂h(g	γ̂h(g	PROPN
ejpam-4610	76	15	)	)	PUNCT
ejpam-4610	77	1	=	=	SYM
ejpam-4610	77	2	n	n	NOUN
ejpam-4610	77	3	if	if	SCONJ
ejpam-4610	77	4	and	and	CCONJ
ejpam-4610	77	5	only	only	ADV
ejpam-4610	77	6	if	if	SCONJ
ejpam-4610	77	7	g	g	PROPN
ejpam-4610	77	8	is	be	AUX
ejpam-4610	77	9	a	a	DET
ejpam-4610	77	10	complete	complete	ADJ
ejpam-4610	77	11	graph	graph	NOUN
ejpam-4610	77	12	.	.	PUNCT
ejpam-4610	78	1	(	(	PUNCT
ejpam-4610	78	2	ii	ii	NOUN
ejpam-4610	78	3	)	)	PUNCT
ejpam-4610	78	4	for	for	ADP
ejpam-4610	78	5	n	n	X
ejpam-4610	78	6	≥	≥	NUM
ejpam-4610	78	7	3	3	NUM
ejpam-4610	78	8	,	,	PUNCT
ejpam-4610	78	9	γ̂h(g	γ̂h(g	PROPN
ejpam-4610	78	10	)	)	PUNCT
ejpam-4610	79	1	=	=	SYM
ejpam-4610	79	2	n−1	n−1	PROPN
ejpam-4610	79	3	if	if	SCONJ
ejpam-4610	79	4	and	and	CCONJ
ejpam-4610	79	5	only	only	ADV
ejpam-4610	79	6	if	if	SCONJ
ejpam-4610	79	7	g	g	PROPN
ejpam-4610	79	8	is	be	AUX
ejpam-4610	79	9	one	one	NUM
ejpam-4610	79	10	of	of	ADP
ejpam-4610	79	11	the	the	DET
ejpam-4610	79	12	graphs	graph	NOUN
ejpam-4610	79	13	p4	p4	ADJ
ejpam-4610	79	14	,	,	PUNCT
ejpam-4610	79	15	c4	c4	NOUN
ejpam-4610	79	16	and	and	CCONJ
ejpam-4610	79	17	k2+kn−2	k2+kn−2	NOUN
ejpam-4610	79	18	.	.	PUNCT
ejpam-4610	79	19	proof	proof	NOUN
ejpam-4610	79	20	.	.	PUNCT
ejpam-4610	80	1	it	it	PRON
ejpam-4610	80	2	is	be	AUX
ejpam-4610	80	3	clear	clear	ADJ
ejpam-4610	80	4	that	that	SCONJ
ejpam-4610	80	5	if	if	SCONJ
ejpam-4610	80	6	g	g	PROPN
ejpam-4610	80	7	=	=	PROPN
ejpam-4610	80	8	kn	kn	PROPN
ejpam-4610	80	9	,	,	PUNCT
ejpam-4610	80	10	then	then	ADV
ejpam-4610	80	11	γh(g	γh(g	PUNCT
ejpam-4610	80	12	)	)	PUNCT
ejpam-4610	80	13	=	=	SYM
ejpam-4610	80	14	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	80	15	)	)	PUNCT
ejpam-4610	80	16	=	=	VERB
ejpam-4610	80	17	n.	n.	NOUN
ejpam-4610	80	18	conversely	conversely	ADV
ejpam-4610	80	19	,	,	PUNCT
ejpam-4610	80	20	suppose	suppose	VERB
ejpam-4610	80	21	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	80	22	)	)	PUNCT
ejpam-4610	80	23	=	=	VERB
ejpam-4610	80	24	n.	n.	VERB
ejpam-4610	80	25	the	the	DET
ejpam-4610	80	26	conclusion	conclusion	NOUN
ejpam-4610	80	27	is	be	AUX
ejpam-4610	80	28	clear	clear	ADJ
ejpam-4610	80	29	if	if	SCONJ
ejpam-4610	80	30	n	n	NOUN
ejpam-4610	80	31	=	=	SYM
ejpam-4610	80	32	1	1	NUM
ejpam-4610	80	33	,	,	PUNCT
ejpam-4610	80	34	2	2	NUM
ejpam-4610	80	35	.	.	X
ejpam-4610	80	36	assume	assume	VERB
ejpam-4610	80	37	n	n	PRON
ejpam-4610	80	38	≥	≥	NUM
ejpam-4610	80	39	3	3	X
ejpam-4610	80	40	.	.	PUNCT
ejpam-4610	81	1	suppose	suppose	VERB
ejpam-4610	81	2	g	g	PROPN
ejpam-4610	81	3	is	be	AUX
ejpam-4610	81	4	not	not	PART
ejpam-4610	81	5	complete	complete	ADJ
ejpam-4610	81	6	.	.	PUNCT
ejpam-4610	82	1	since	since	SCONJ
ejpam-4610	82	2	g	g	PROPN
ejpam-4610	82	3	is	be	AUX
ejpam-4610	82	4	connected	connect	VERB
ejpam-4610	82	5	,	,	PUNCT
ejpam-4610	82	6	there	there	PRON
ejpam-4610	82	7	exist	exist	VERB
ejpam-4610	82	8	u	u	NOUN
ejpam-4610	82	9	,	,	PUNCT
ejpam-4610	82	10	v	v	NOUN
ejpam-4610	82	11	∈	∈	PROPN
ejpam-4610	82	12	v	v	NOUN
ejpam-4610	82	13	(	(	PUNCT
ejpam-4610	82	14	g	g	NOUN
ejpam-4610	82	15	)	)	PUNCT
ejpam-4610	82	16	such	such	ADJ
ejpam-4610	82	17	that	that	SCONJ
ejpam-4610	82	18	dg(u	dg(u	ADJ
ejpam-4610	82	19	,	,	PUNCT
ejpam-4610	82	20	v	v	NOUN
ejpam-4610	82	21	)	)	PUNCT
ejpam-4610	82	22	=	=	SYM
ejpam-4610	82	23	2	2	X
ejpam-4610	82	24	.	.	X
ejpam-4610	82	25	let	let	VERB
ejpam-4610	82	26	s	s	NOUN
ejpam-4610	82	27	=	=	X
ejpam-4610	82	28	v	v	ADJ
ejpam-4610	82	29	(	(	PUNCT
ejpam-4610	82	30	g	g	NOUN
ejpam-4610	82	31	)	)	PUNCT
ejpam-4610	82	32	\	\	NOUN
ejpam-4610	82	33	{	{	PUNCT
ejpam-4610	82	34	v	v	NOUN
ejpam-4610	82	35	}	}	PUNCT
ejpam-4610	82	36	,	,	PUNCT
ejpam-4610	82	37	and	and	CCONJ
ejpam-4610	82	38	let	let	VERB
ejpam-4610	82	39	t	t	PROPN
ejpam-4610	82	40	be	be	AUX
ejpam-4610	82	41	a	a	DET
ejpam-4610	82	42	γ̂h	γ̂h	NOUN
ejpam-4610	82	43	-	-	PUNCT
ejpam-4610	82	44	set	set	NOUN
ejpam-4610	82	45	of	of	ADP
ejpam-4610	82	46	g.	g.	PROPN
ejpam-4610	82	47	clearly	clearly	ADV
ejpam-4610	82	48	,	,	PUNCT
ejpam-4610	82	49	s	s	VERB
ejpam-4610	82	50	is	be	AUX
ejpam-4610	82	51	an	an	DET
ejpam-4610	82	52	hd	hd	NOUN
ejpam-4610	82	53	-	-	PUNCT
ejpam-4610	82	54	set	set	NOUN
ejpam-4610	82	55	of	of	ADP
ejpam-4610	82	56	g.	g.	PROPN
ejpam-4610	83	1	if	if	SCONJ
ejpam-4610	83	2	v	v	PROPN
ejpam-4610	83	3	/∈	/∈	PROPN
ejpam-4610	84	1	t	t	PROPN
ejpam-4610	84	2	,	,	PUNCT
ejpam-4610	84	3	then	then	ADV
ejpam-4610	84	4	t	t	PROPN
ejpam-4610	84	5	⊆	⊆	NUM
ejpam-4610	84	6	s.	s.	PROPN
ejpam-4610	84	7	suppose	suppose	VERB
ejpam-4610	84	8	that	that	SCONJ
ejpam-4610	84	9	v	v	PROPN
ejpam-4610	84	10	∈	∈	PROPN
ejpam-4610	84	11	t	t	NOUN
ejpam-4610	84	12	.	.	PUNCT
ejpam-4610	85	1	since	since	SCONJ
ejpam-4610	85	2	{	{	PUNCT
ejpam-4610	85	3	v	v	NOUN
ejpam-4610	85	4	}	}	PUNCT
ejpam-4610	85	5	is	be	AUX
ejpam-4610	85	6	not	not	PART
ejpam-4610	85	7	a	a	DET
ejpam-4610	85	8	hop	hop	NOUN
ejpam-4610	85	9	dominating	dominating	NOUN
ejpam-4610	85	10	set	set	NOUN
ejpam-4610	85	11	of	of	ADP
ejpam-4610	85	12	g	g	NOUN
ejpam-4610	85	13	,	,	PUNCT
ejpam-4610	85	14	there	there	PRON
ejpam-4610	85	15	exists	exist	VERB
ejpam-4610	85	16	w	w	PROPN
ejpam-4610	85	17	∈	∈	PROPN
ejpam-4610	85	18	t	t	NOUN
ejpam-4610	85	19	with	with	ADP
ejpam-4610	85	20	w	w	PROPN
ejpam-4610	85	21	̸=	̸=	PROPN
ejpam-4610	85	22	v.	v.	CCONJ
ejpam-4610	85	23	thus	thus	ADV
ejpam-4610	85	24	,	,	PUNCT
ejpam-4610	85	25	w	w	PROPN
ejpam-4610	85	26	∈	∈	PROPN
ejpam-4610	85	27	s	s	PART
ejpam-4610	85	28	∩	∩	ADJ
ejpam-4610	85	29	t	t	NOUN
ejpam-4610	85	30	.	.	PUNCT
ejpam-4610	86	1	since	since	SCONJ
ejpam-4610	86	2	t	t	PROPN
ejpam-4610	86	3	is	be	AUX
ejpam-4610	86	4	arbitrary	arbitrary	ADJ
ejpam-4610	86	5	,	,	PUNCT
ejpam-4610	86	6	s	s	PART
ejpam-4610	86	7	is	be	AUX
ejpam-4610	86	8	a	a	DET
ejpam-4610	86	9	thd	thd	NOUN
ejpam-4610	86	10	-	-	PUNCT
ejpam-4610	86	11	set	set	NOUN
ejpam-4610	86	12	of	of	ADP
ejpam-4610	86	13	g.	g.	PROPN
ejpam-4610	86	14	consequently	consequently	ADV
ejpam-4610	86	15	,	,	PUNCT
ejpam-4610	86	16	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	86	17	)	)	PUNCT
ejpam-4610	86	18	≤	≤	NUM
ejpam-4610	86	19	|s|	|s|	PROPN
ejpam-4610	86	20	=	=	SYM
ejpam-4610	86	21	n−	n−	NOUN
ejpam-4610	86	22	1	1	NUM
ejpam-4610	86	23	,	,	PUNCT
ejpam-4610	86	24	a	a	DET
ejpam-4610	86	25	contradiction	contradiction	NOUN
ejpam-4610	86	26	.	.	PUNCT
ejpam-4610	87	1	thus	thus	ADV
ejpam-4610	87	2	,	,	PUNCT
ejpam-4610	87	3	g	g	PROPN
ejpam-4610	87	4	is	be	AUX
ejpam-4610	87	5	a	a	DET
ejpam-4610	87	6	complete	complete	ADJ
ejpam-4610	87	7	graph	graph	NOUN
ejpam-4610	87	8	.	.	PUNCT
ejpam-4610	88	1	if	if	SCONJ
ejpam-4610	88	2	g	g	PROPN
ejpam-4610	88	3	is	be	AUX
ejpam-4610	88	4	one	one	NUM
ejpam-4610	88	5	of	of	ADP
ejpam-4610	88	6	the	the	DET
ejpam-4610	88	7	graphs	graph	NOUN
ejpam-4610	88	8	p4	p4	ADJ
ejpam-4610	88	9	,	,	PUNCT
ejpam-4610	88	10	c4	c4	NOUN
ejpam-4610	88	11	and	and	CCONJ
ejpam-4610	88	12	k2	k2	NOUN
ejpam-4610	88	13	+	+	CCONJ
ejpam-4610	88	14	kn−2	kn−2	PROPN
ejpam-4610	88	15	where	where	SCONJ
ejpam-4610	88	16	n	n	NUM
ejpam-4610	88	17	≥	≥	NOUN
ejpam-4610	88	18	3	3	NUM
ejpam-4610	88	19	,	,	PUNCT
ejpam-4610	88	20	then	then	ADV
ejpam-4610	88	21	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	88	22	)	)	PUNCT
ejpam-4610	88	23	=	=	SYM
ejpam-4610	89	1	n	n	CCONJ
ejpam-4610	90	1	−	−	NOUN
ejpam-4610	90	2	1	1	NUM
ejpam-4610	90	3	.	.	PUNCT
ejpam-4610	91	1	conversely	conversely	ADV
ejpam-4610	91	2	,	,	PUNCT
ejpam-4610	91	3	assume	assume	VERB
ejpam-4610	91	4	that	that	SCONJ
ejpam-4610	91	5	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	91	6	)	)	PUNCT
ejpam-4610	92	1	=	=	PUNCT
ejpam-4610	92	2	n−	n−	NOUN
ejpam-4610	92	3	1	1	X
ejpam-4610	92	4	.	.	PUNCT
ejpam-4610	92	5	suppose	suppose	VERB
ejpam-4610	92	6	diam(g	diam(g	NOUN
ejpam-4610	92	7	)	)	PUNCT
ejpam-4610	92	8	≥	≥	NOUN
ejpam-4610	92	9	4	4	NUM
ejpam-4610	92	10	.	.	PUNCT
ejpam-4610	93	1	then	then	ADV
ejpam-4610	93	2	g	g	PROPN
ejpam-4610	93	3	has	have	VERB
ejpam-4610	93	4	order	order	NOUN
ejpam-4610	93	5	n	n	DET
ejpam-4610	93	6	≥	≥	NOUN
ejpam-4610	93	7	5	5	NUM
ejpam-4610	93	8	.	.	PUNCT
ejpam-4610	94	1	let	let	VERB
ejpam-4610	94	2	u	u	NOUN
ejpam-4610	94	3	,	,	PUNCT
ejpam-4610	94	4	v	v	PROPN
ejpam-4610	94	5	∈	∈	PROPN
ejpam-4610	94	6	v	v	NOUN
ejpam-4610	94	7	(	(	PUNCT
ejpam-4610	94	8	g	g	NOUN
ejpam-4610	94	9	)	)	PUNCT
ejpam-4610	94	10	such	such	ADJ
ejpam-4610	94	11	that	that	SCONJ
ejpam-4610	94	12	dg(u	dg(u	ADJ
ejpam-4610	94	13	,	,	PUNCT
ejpam-4610	94	14	v	v	NOUN
ejpam-4610	94	15	)	)	PUNCT
ejpam-4610	94	16	=	=	SYM
ejpam-4610	94	17	4	4	X
ejpam-4610	94	18	.	.	PUNCT
ejpam-4610	94	19	then	then	ADV
ejpam-4610	94	20	{	{	PUNCT
ejpam-4610	94	21	u	u	NOUN
ejpam-4610	94	22	,	,	PUNCT
ejpam-4610	94	23	v	v	NOUN
ejpam-4610	94	24	}	}	PUNCT
ejpam-4610	94	25	is	be	AUX
ejpam-4610	94	26	not	not	PART
ejpam-4610	94	27	a	a	DET
ejpam-4610	94	28	γh	γh	ADV
ejpam-4610	94	29	-	-	PUNCT
ejpam-4610	94	30	set	set	NOUN
ejpam-4610	94	31	of	of	ADP
ejpam-4610	94	32	g.	g.	PROPN
ejpam-4610	95	1	it	it	PRON
ejpam-4610	95	2	follows	follow	VERB
ejpam-4610	95	3	that	that	PRON
ejpam-4610	95	4	s	s	VERB
ejpam-4610	95	5	=	=	SYM
ejpam-4610	95	6	v	v	X
ejpam-4610	95	7	(	(	PUNCT
ejpam-4610	95	8	g	g	NOUN
ejpam-4610	95	9	)	)	PUNCT
ejpam-4610	95	10	\	\	NOUN
ejpam-4610	95	11	{	{	PUNCT
ejpam-4610	95	12	u	u	NOUN
ejpam-4610	95	13	,	,	PUNCT
ejpam-4610	95	14	v	v	NOUN
ejpam-4610	95	15	}	}	PUNCT
ejpam-4610	95	16	is	be	AUX
ejpam-4610	95	17	a	a	DET
ejpam-4610	95	18	thd	thd	NOUN
ejpam-4610	95	19	-	-	PUNCT
ejpam-4610	95	20	set	set	NOUN
ejpam-4610	95	21	of	of	ADP
ejpam-4610	95	22	g.	g.	PROPN
ejpam-4610	95	23	thus	thus	ADV
ejpam-4610	95	24	,	,	PUNCT
ejpam-4610	95	25	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	95	26	)	)	PUNCT
ejpam-4610	95	27	≤	≤	NUM
ejpam-4610	95	28	|s|	|s|	PROPN
ejpam-4610	95	29	=	=	SYM
ejpam-4610	95	30	n−	n−	NOUN
ejpam-4610	95	31	2	2	NUM
ejpam-4610	95	32	,	,	PUNCT
ejpam-4610	95	33	a	a	DET
ejpam-4610	95	34	contradiction	contradiction	NOUN
ejpam-4610	95	35	.	.	PUNCT
ejpam-4610	96	1	hence	hence	ADV
ejpam-4610	96	2	,	,	PUNCT
ejpam-4610	96	3	diam(g	diam(g	PROPN
ejpam-4610	96	4	)	)	PUNCT
ejpam-4610	96	5	≤	≤	NOUN
ejpam-4610	96	6	3	3	NUM
ejpam-4610	96	7	.	.	PUNCT
ejpam-4610	97	1	consider	consider	VERB
ejpam-4610	97	2	the	the	DET
ejpam-4610	97	3	following	follow	VERB
ejpam-4610	97	4	cases	case	NOUN
ejpam-4610	97	5	:	:	PUNCT
ejpam-4610	97	6	case	case	NOUN
ejpam-4610	97	7	1	1	NUM
ejpam-4610	97	8	:	:	PUNCT
ejpam-4610	97	9	suppose	suppose	VERB
ejpam-4610	97	10	that	that	SCONJ
ejpam-4610	97	11	diam(g	diam(g	NOUN
ejpam-4610	97	12	)	)	PUNCT
ejpam-4610	97	13	=	=	SYM
ejpam-4610	98	1	3	3	X
ejpam-4610	98	2	.	.	PUNCT
ejpam-4610	98	3	then	then	ADV
ejpam-4610	98	4	g	g	PROPN
ejpam-4610	98	5	has	have	VERB
ejpam-4610	98	6	order	order	NOUN
ejpam-4610	98	7	n	n	DET
ejpam-4610	98	8	≥	≥	NOUN
ejpam-4610	98	9	4	4	NUM
ejpam-4610	98	10	.	.	PUNCT
ejpam-4610	99	1	let	let	VERB
ejpam-4610	99	2	p	p	NOUN
ejpam-4610	99	3	=	=	PUNCT
ejpam-4610	100	1	[	[	X
ejpam-4610	100	2	u	u	NOUN
ejpam-4610	100	3	,	,	PUNCT
ejpam-4610	100	4	w	w	PROPN
ejpam-4610	100	5	,	,	PUNCT
ejpam-4610	100	6	x	x	NOUN
ejpam-4610	100	7	,	,	PUNCT
ejpam-4610	100	8	v	v	PART
ejpam-4610	100	9	]	]	PUNCT
ejpam-4610	100	10	be	be	AUX
ejpam-4610	100	11	a	a	DET
ejpam-4610	100	12	diametral	diametral	ADJ
ejpam-4610	100	13	path	path	NOUN
ejpam-4610	100	14	in	in	ADP
ejpam-4610	100	15	g.	g.	PROPN
ejpam-4610	100	16	let	let	VERB
ejpam-4610	100	17	y	y	PROPN
ejpam-4610	100	18	∈	∈	PROPN
ejpam-4610	100	19	v	v	ADP
ejpam-4610	100	20	(	(	PUNCT
ejpam-4610	100	21	g	g	NOUN
ejpam-4610	100	22	)	)	PUNCT
ejpam-4610	100	23	\	\	PROPN
ejpam-4610	100	24	v	v	X
ejpam-4610	100	25	(	(	PUNCT
ejpam-4610	100	26	p	p	NOUN
ejpam-4610	100	27	)	)	PUNCT
ejpam-4610	100	28	that	that	PRON
ejpam-4610	100	29	is	be	AUX
ejpam-4610	100	30	adjacent	adjacent	ADJ
ejpam-4610	100	31	to	to	ADP
ejpam-4610	100	32	any	any	PRON
ejpam-4610	100	33	of	of	ADP
ejpam-4610	100	34	the	the	DET
ejpam-4610	100	35	vertices	vertex	NOUN
ejpam-4610	100	36	in	in	ADP
ejpam-4610	100	37	p	p	NOUN
ejpam-4610	100	38	.	.	PUNCT
ejpam-4610	101	1	if	if	SCONJ
ejpam-4610	101	2	wy	wy	PROPN
ejpam-4610	101	3	∈	∈	PROPN
ejpam-4610	101	4	e(g	e(g	PROPN
ejpam-4610	101	5	)	)	PUNCT
ejpam-4610	101	6	,	,	PUNCT
ejpam-4610	101	7	then	then	ADV
ejpam-4610	101	8	s	s	VERB
ejpam-4610	101	9	=	=	SYM
ejpam-4610	101	10	v	v	PROPN
ejpam-4610	101	11	(	(	PUNCT
ejpam-4610	101	12	g	g	NOUN
ejpam-4610	101	13	)	)	PUNCT
ejpam-4610	101	14	\	\	NOUN
ejpam-4610	101	15	{	{	PUNCT
ejpam-4610	101	16	u	u	NOUN
ejpam-4610	101	17	,	,	PUNCT
ejpam-4610	101	18	y	y	PROPN
ejpam-4610	101	19	}	}	PUNCT
ejpam-4610	101	20	is	be	AUX
ejpam-4610	101	21	a	a	DET
ejpam-4610	101	22	hd	hd	NOUN
ejpam-4610	101	23	-	-	PUNCT
ejpam-4610	101	24	set	set	NOUN
ejpam-4610	101	25	of	of	ADP
ejpam-4610	101	26	g.	g.	PROPN
ejpam-4610	101	27	since	since	SCONJ
ejpam-4610	101	28	{	{	PUNCT
ejpam-4610	101	29	u	u	NOUN
ejpam-4610	101	30	,	,	PUNCT
ejpam-4610	101	31	y	y	NOUN
ejpam-4610	101	32	}	}	PUNCT
ejpam-4610	101	33	is	be	AUX
ejpam-4610	101	34	not	not	PART
ejpam-4610	101	35	m.a	m.a	PROPN
ejpam-4610	101	36	.	.	PROPN
ejpam-4610	101	37	bonsocan	bonsocan	PROPN
ejpam-4610	101	38	,	,	PUNCT
ejpam-4610	101	39	f.	f.	PROPN
ejpam-4610	101	40	jamil	jamil	PROPN
ejpam-4610	101	41	/	/	SYM
ejpam-4610	101	42	eur	eur	PROPN
ejpam-4610	101	43	.	.	PUNCT
ejpam-4610	102	1	j.	j.	PROPN
ejpam-4610	102	2	pure	pure	PROPN
ejpam-4610	102	3	appl	appl	PROPN
ejpam-4610	102	4	.	.	PROPN
ejpam-4610	102	5	math	math	PROPN
ejpam-4610	102	6	,	,	PUNCT
ejpam-4610	102	7	16	16	NUM
ejpam-4610	102	8	(	(	PUNCT
ejpam-4610	102	9	1	1	NUM
ejpam-4610	102	10	)	)	PUNCT
ejpam-4610	102	11	(	(	PUNCT
ejpam-4610	102	12	2023	2023	NUM
ejpam-4610	102	13	)	)	PUNCT
ejpam-4610	102	14	,	,	PUNCT
ejpam-4610	102	15	192	192	NUM
ejpam-4610	102	16	-	-	SYM
ejpam-4610	102	17	206	206	NUM
ejpam-4610	102	18	195	195	NUM
ejpam-4610	102	19	a	a	DET
ejpam-4610	102	20	hd	hd	NOUN
ejpam-4610	102	21	-	-	NOUN
ejpam-4610	102	22	set	set	NOUN
ejpam-4610	102	23	of	of	ADP
ejpam-4610	102	24	g	g	NOUN
ejpam-4610	102	25	,	,	PUNCT
ejpam-4610	102	26	s	s	PART
ejpam-4610	102	27	is	be	AUX
ejpam-4610	102	28	a	a	DET
ejpam-4610	102	29	thd	thd	NOUN
ejpam-4610	102	30	-	-	PUNCT
ejpam-4610	102	31	set	set	NOUN
ejpam-4610	102	32	of	of	ADP
ejpam-4610	102	33	g.	g.	PROPN
ejpam-4610	102	34	thus	thus	ADV
ejpam-4610	102	35	,	,	PUNCT
ejpam-4610	102	36	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	102	37	)	)	PUNCT
ejpam-4610	102	38	≤	≤	NUM
ejpam-4610	102	39	|s|	|s|	PROPN
ejpam-4610	102	40	=	=	PUNCT
ejpam-4610	102	41	n	n	CCONJ
ejpam-4610	102	42	−	−	PROPN
ejpam-4610	102	43	2	2	NUM
ejpam-4610	102	44	,	,	PUNCT
ejpam-4610	102	45	a	a	DET
ejpam-4610	102	46	contradiction	contradiction	NOUN
ejpam-4610	102	47	.	.	PUNCT
ejpam-4610	103	1	similar	similar	ADJ
ejpam-4610	103	2	contradiction	contradiction	NOUN
ejpam-4610	103	3	is	be	AUX
ejpam-4610	103	4	attained	attain	VERB
ejpam-4610	103	5	if	if	SCONJ
ejpam-4610	103	6	xy	xy	PROPN
ejpam-4610	103	7	∈	∈	PROPN
ejpam-4610	103	8	e(g	e(g	PROPN
ejpam-4610	103	9	)	)	PUNCT
ejpam-4610	103	10	.	.	PUNCT
ejpam-4610	104	1	suppose	suppose	VERB
ejpam-4610	104	2	that	that	SCONJ
ejpam-4610	104	3	uy	uy	PROPN
ejpam-4610	104	4	∈	∈	PROPN
ejpam-4610	104	5	e(g	e(g	PROPN
ejpam-4610	104	6	)	)	PUNCT
ejpam-4610	104	7	.	.	PUNCT
ejpam-4610	105	1	necessarily	necessarily	ADV
ejpam-4610	105	2	,	,	PUNCT
ejpam-4610	105	3	2	2	NUM
ejpam-4610	105	4	≤	≤	NOUN
ejpam-4610	105	5	dg(y	dg(y	ADJ
ejpam-4610	105	6	,	,	PUNCT
ejpam-4610	105	7	v	v	NOUN
ejpam-4610	105	8	)	)	PUNCT
ejpam-4610	105	9	≤	≤	NOUN
ejpam-4610	105	10	3	3	NUM
ejpam-4610	105	11	.	.	PUNCT
ejpam-4610	106	1	since	since	SCONJ
ejpam-4610	106	2	{	{	PUNCT
ejpam-4610	106	3	w	w	PROPN
ejpam-4610	106	4	,	,	PUNCT
ejpam-4610	106	5	y	y	NOUN
ejpam-4610	106	6	}	}	PUNCT
ejpam-4610	106	7	is	be	AUX
ejpam-4610	106	8	not	not	PART
ejpam-4610	106	9	a	a	DET
ejpam-4610	106	10	hd	hd	NOUN
ejpam-4610	106	11	-	-	NOUN
ejpam-4610	106	12	set	set	NOUN
ejpam-4610	106	13	of	of	ADP
ejpam-4610	106	14	g	g	NOUN
ejpam-4610	106	15	,	,	PUNCT
ejpam-4610	106	16	s	s	PART
ejpam-4610	106	17	=	=	SYM
ejpam-4610	106	18	v	v	X
ejpam-4610	106	19	(	(	PUNCT
ejpam-4610	106	20	g	g	NOUN
ejpam-4610	106	21	)	)	PUNCT
ejpam-4610	106	22	\	\	NOUN
ejpam-4610	106	23	{	{	PUNCT
ejpam-4610	106	24	w	w	PROPN
ejpam-4610	106	25	,	,	PUNCT
ejpam-4610	106	26	y	y	NOUN
ejpam-4610	106	27	}	}	PUNCT
ejpam-4610	106	28	is	be	AUX
ejpam-4610	106	29	a	a	DET
ejpam-4610	106	30	thd	thd	NOUN
ejpam-4610	106	31	-	-	PUNCT
ejpam-4610	106	32	set	set	NOUN
ejpam-4610	106	33	of	of	ADP
ejpam-4610	106	34	g.	g.	PROPN
ejpam-4610	106	35	thus	thus	ADV
ejpam-4610	106	36	,	,	PUNCT
ejpam-4610	106	37	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	106	38	)	)	PUNCT
ejpam-4610	106	39	≤	≤	NUM
ejpam-4610	106	40	|s|	|s|	PROPN
ejpam-4610	106	41	=	=	PUNCT
ejpam-4610	106	42	n	n	CCONJ
ejpam-4610	106	43	−	−	PROPN
ejpam-4610	106	44	2	2	NUM
ejpam-4610	106	45	,	,	PUNCT
ejpam-4610	106	46	a	a	DET
ejpam-4610	106	47	contradiction	contradiction	NOUN
ejpam-4610	106	48	.	.	PUNCT
ejpam-4610	107	1	a	a	DET
ejpam-4610	107	2	similar	similar	ADJ
ejpam-4610	107	3	contradiction	contradiction	NOUN
ejpam-4610	107	4	is	be	AUX
ejpam-4610	107	5	attained	attain	VERB
ejpam-4610	107	6	if	if	SCONJ
ejpam-4610	107	7	yv	yv	PROPN
ejpam-4610	107	8	∈	∈	PROPN
ejpam-4610	107	9	e(g	e(g	PROPN
ejpam-4610	107	10	)	)	PUNCT
ejpam-4610	107	11	.	.	PUNCT
ejpam-4610	108	1	therefore	therefore	ADV
ejpam-4610	108	2	,	,	PUNCT
ejpam-4610	108	3	g	g	PROPN
ejpam-4610	108	4	=	=	PUNCT
ejpam-4610	108	5	p	p	NOUN
ejpam-4610	108	6	=	=	NOUN
ejpam-4610	108	7	p4	p4	ADJ
ejpam-4610	108	8	.	.	PUNCT
ejpam-4610	109	1	case	case	NOUN
ejpam-4610	109	2	2	2	NUM
ejpam-4610	109	3	:	:	PUNCT
ejpam-4610	109	4	suppose	suppose	VERB
ejpam-4610	109	5	that	that	SCONJ
ejpam-4610	109	6	diam(g	diam(g	NOUN
ejpam-4610	109	7	)	)	PUNCT
ejpam-4610	109	8	=	=	SYM
ejpam-4610	109	9	2	2	NUM
ejpam-4610	109	10	and	and	CCONJ
ejpam-4610	109	11	g	g	PROPN
ejpam-4610	109	12	̸=	̸=	PROPN
ejpam-4610	109	13	c4	c4	NOUN
ejpam-4610	109	14	.	.	PUNCT
ejpam-4610	110	1	then	then	ADV
ejpam-4610	110	2	g	g	PROPN
ejpam-4610	110	3	has	have	VERB
ejpam-4610	110	4	order	order	NOUN
ejpam-4610	110	5	n	n	DET
ejpam-4610	110	6	≥	≥	NOUN
ejpam-4610	110	7	3	3	X
ejpam-4610	110	8	.	.	PUNCT
ejpam-4610	111	1	let	let	VERB
ejpam-4610	111	2	u	u	NOUN
ejpam-4610	111	3	,	,	PUNCT
ejpam-4610	111	4	v	v	PROPN
ejpam-4610	111	5	∈	∈	PROPN
ejpam-4610	111	6	v	v	NOUN
ejpam-4610	111	7	(	(	PUNCT
ejpam-4610	111	8	g	g	NOUN
ejpam-4610	111	9	)	)	PUNCT
ejpam-4610	111	10	such	such	ADJ
ejpam-4610	111	11	that	that	SCONJ
ejpam-4610	111	12	dg(u	dg(u	ADJ
ejpam-4610	111	13	,	,	PUNCT
ejpam-4610	111	14	v	v	NOUN
ejpam-4610	111	15	)	)	PUNCT
ejpam-4610	111	16	=	=	SYM
ejpam-4610	111	17	2	2	X
ejpam-4610	111	18	.	.	X
ejpam-4610	112	1	first	first	ADV
ejpam-4610	112	2	,	,	PUNCT
ejpam-4610	112	3	we	we	PRON
ejpam-4610	112	4	claim	claim	VERB
ejpam-4610	112	5	that	that	SCONJ
ejpam-4610	112	6	ux	ux	PROPN
ejpam-4610	112	7	,	,	PUNCT
ejpam-4610	112	8	vx	vx	PROPN
ejpam-4610	112	9	∈	∈	PROPN
ejpam-4610	112	10	e(g	e(g	PROPN
ejpam-4610	112	11	)	)	PUNCT
ejpam-4610	112	12	for	for	ADP
ejpam-4610	112	13	all	all	PRON
ejpam-4610	112	14	x	x	SYM
ejpam-4610	112	15	∈	∈	PROPN
ejpam-4610	112	16	v	v	NOUN
ejpam-4610	112	17	(	(	PUNCT
ejpam-4610	112	18	g)\{u	g)\{u	PROPN
ejpam-4610	112	19	,	,	PUNCT
ejpam-4610	112	20	v	v	NOUN
ejpam-4610	112	21	}	}	PUNCT
ejpam-4610	112	22	.	.	PUNCT
ejpam-4610	113	1	this	this	PRON
ejpam-4610	113	2	is	be	AUX
ejpam-4610	113	3	clear	clear	ADJ
ejpam-4610	113	4	if	if	SCONJ
ejpam-4610	113	5	n	n	PROPN
ejpam-4610	113	6	=	=	SYM
ejpam-4610	113	7	3	3	NUM
ejpam-4610	113	8	i.e.	i.e.	X
ejpam-4610	113	9	,	,	PUNCT
ejpam-4610	113	10	g	g	PROPN
ejpam-4610	113	11	=	=	PROPN
ejpam-4610	113	12	p3	p3	PROPN
ejpam-4610	113	13	.	.	PUNCT
ejpam-4610	114	1	assume	assume	VERB
ejpam-4610	114	2	n	n	PRON
ejpam-4610	114	3	≥	≥	NOUN
ejpam-4610	114	4	4	4	NUM
ejpam-4610	114	5	.	.	PUNCT
ejpam-4610	115	1	let	let	VERB
ejpam-4610	115	2	[	[	X
ejpam-4610	115	3	u	u	NOUN
ejpam-4610	115	4	,	,	PUNCT
ejpam-4610	115	5	w	w	PROPN
ejpam-4610	115	6	,	,	PUNCT
ejpam-4610	115	7	v	v	NOUN
ejpam-4610	115	8	]	]	PUNCT
ejpam-4610	115	9	be	be	AUX
ejpam-4610	115	10	a	a	DET
ejpam-4610	115	11	geodesic	geodesic	NOUN
ejpam-4610	115	12	in	in	ADP
ejpam-4610	115	13	g	g	NOUN
ejpam-4610	115	14	,	,	PUNCT
ejpam-4610	115	15	and	and	CCONJ
ejpam-4610	115	16	let	let	VERB
ejpam-4610	115	17	y	y	PROPN
ejpam-4610	115	18	∈	∈	PROPN
ejpam-4610	115	19	v	v	ADP
ejpam-4610	115	20	(	(	PUNCT
ejpam-4610	115	21	g	g	NOUN
ejpam-4610	115	22	)	)	PUNCT
ejpam-4610	115	23	\	\	NOUN
ejpam-4610	115	24	{	{	PUNCT
ejpam-4610	115	25	u	u	NOUN
ejpam-4610	115	26	,	,	PUNCT
ejpam-4610	115	27	w	w	PROPN
ejpam-4610	115	28	,	,	PUNCT
ejpam-4610	115	29	v	v	NOUN
ejpam-4610	115	30	}	}	PUNCT
ejpam-4610	115	31	.	.	PUNCT
ejpam-4610	116	1	suppose	suppose	VERB
ejpam-4610	116	2	that	that	SCONJ
ejpam-4610	116	3	uy	uy	PROPN
ejpam-4610	116	4	/∈	/∈	PROPN
ejpam-4610	116	5	e(g	e(g	PROPN
ejpam-4610	116	6	)	)	PUNCT
ejpam-4610	116	7	.	.	PUNCT
ejpam-4610	117	1	then	then	ADV
ejpam-4610	117	2	dg(u	dg(u	X
ejpam-4610	117	3	,	,	PUNCT
ejpam-4610	117	4	y	y	NOUN
ejpam-4610	117	5	)	)	PUNCT
ejpam-4610	117	6	=	=	SYM
ejpam-4610	117	7	2	2	NUM
ejpam-4610	117	8	,	,	PUNCT
ejpam-4610	117	9	and	and	CCONJ
ejpam-4610	117	10	say	say	VERB
ejpam-4610	117	11	[	[	X
ejpam-4610	117	12	u	u	NOUN
ejpam-4610	117	13	,	,	PUNCT
ejpam-4610	117	14	z	z	PROPN
ejpam-4610	117	15	,	,	PUNCT
ejpam-4610	117	16	y	y	PROPN
ejpam-4610	117	17	]	]	X
ejpam-4610	117	18	is	be	AUX
ejpam-4610	117	19	a	a	DET
ejpam-4610	117	20	u	u	NOUN
ejpam-4610	117	21	-	-	PROPN
ejpam-4610	117	22	y	y	ADJ
ejpam-4610	117	23	geodesic	geodesic	NOUN
ejpam-4610	117	24	in	in	ADP
ejpam-4610	117	25	g.	g.	PROPN
ejpam-4610	118	1	the	the	DET
ejpam-4610	118	2	desired	desire	VERB
ejpam-4610	118	3	contradiction	contradiction	NOUN
ejpam-4610	118	4	is	be	AUX
ejpam-4610	118	5	attained	attain	VERB
ejpam-4610	118	6	as	as	SCONJ
ejpam-4610	118	7	we	we	PRON
ejpam-4610	118	8	consider	consider	VERB
ejpam-4610	118	9	the	the	DET
ejpam-4610	118	10	following	follow	VERB
ejpam-4610	118	11	subcases	subcase	NOUN
ejpam-4610	118	12	:	:	PUNCT
ejpam-4610	118	13	subcase	subcase	NOUN
ejpam-4610	118	14	2.1	2.1	NUM
ejpam-4610	118	15	:	:	PUNCT
ejpam-4610	118	16	suppose	suppose	VERB
ejpam-4610	118	17	that	that	SCONJ
ejpam-4610	118	18	z	z	NOUN
ejpam-4610	118	19	=	=	SYM
ejpam-4610	118	20	w.	w.	PROPN
ejpam-4610	118	21	observe	observe	VERB
ejpam-4610	118	22	that	that	SCONJ
ejpam-4610	118	23	s	s	VERB
ejpam-4610	118	24	=	=	X
ejpam-4610	118	25	v	v	X
ejpam-4610	118	26	(	(	PUNCT
ejpam-4610	118	27	g	g	NOUN
ejpam-4610	118	28	)	)	PUNCT
ejpam-4610	118	29	\	\	NOUN
ejpam-4610	118	30	{	{	PUNCT
ejpam-4610	118	31	v	v	NOUN
ejpam-4610	118	32	,	,	PUNCT
ejpam-4610	118	33	y	y	NOUN
ejpam-4610	118	34	}	}	PUNCT
ejpam-4610	118	35	is	be	AUX
ejpam-4610	118	36	a	a	DET
ejpam-4610	118	37	hd	hd	NOUN
ejpam-4610	118	38	-	-	PUNCT
ejpam-4610	118	39	set	set	NOUN
ejpam-4610	118	40	of	of	ADP
ejpam-4610	118	41	g.	g.	PROPN
ejpam-4610	118	42	since	since	SCONJ
ejpam-4610	118	43	t	t	PROPN
ejpam-4610	118	44	=	=	SYM
ejpam-4610	118	45	{	{	PUNCT
ejpam-4610	118	46	v	v	NOUN
ejpam-4610	118	47	,	,	PUNCT
ejpam-4610	118	48	y	y	PROPN
ejpam-4610	118	49	}	}	PUNCT
ejpam-4610	118	50	does	do	AUX
ejpam-4610	118	51	not	not	PART
ejpam-4610	118	52	hop	hop	NOUN
ejpam-4610	118	53	-	-	PUNCT
ejpam-4610	118	54	dominate	dominate	VERB
ejpam-4610	118	55	w	w	PROPN
ejpam-4610	118	56	,	,	PUNCT
ejpam-4610	118	57	t	t	PROPN
ejpam-4610	118	58	is	be	AUX
ejpam-4610	118	59	not	not	PART
ejpam-4610	118	60	a	a	DET
ejpam-4610	118	61	hd	hd	NOUN
ejpam-4610	118	62	-	-	PUNCT
ejpam-4610	118	63	set	set	NOUN
ejpam-4610	118	64	of	of	ADP
ejpam-4610	118	65	g.	g.	PROPN
ejpam-4610	118	66	thus	thus	ADV
ejpam-4610	118	67	,	,	PUNCT
ejpam-4610	118	68	s	s	VERB
ejpam-4610	118	69	is	be	AUX
ejpam-4610	118	70	a	a	DET
ejpam-4610	118	71	thd	thd	NOUN
ejpam-4610	118	72	-	-	PUNCT
ejpam-4610	118	73	set	set	NOUN
ejpam-4610	118	74	of	of	ADP
ejpam-4610	118	75	g.	g.	PROPN
ejpam-4610	118	76	consequently	consequently	ADV
ejpam-4610	118	77	,	,	PUNCT
ejpam-4610	118	78	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	118	79	)	)	PUNCT
ejpam-4610	118	80	≤	≤	NUM
ejpam-4610	118	81	|s|	|s|	PROPN
ejpam-4610	118	82	=	=	SYM
ejpam-4610	118	83	n−	n−	NOUN
ejpam-4610	118	84	2	2	NUM
ejpam-4610	118	85	,	,	PUNCT
ejpam-4610	118	86	a	a	DET
ejpam-4610	118	87	contradiction	contradiction	NOUN
ejpam-4610	118	88	.	.	PUNCT
ejpam-4610	119	1	subcase	subcase	PROPN
ejpam-4610	119	2	2.2	2.2	NUM
ejpam-4610	119	3	:	:	PUNCT
ejpam-4610	119	4	suppose	suppose	VERB
ejpam-4610	119	5	that	that	SCONJ
ejpam-4610	119	6	w	w	PROPN
ejpam-4610	119	7	̸=	̸=	PROPN
ejpam-4610	119	8	z	z	PROPN
ejpam-4610	119	9	and	and	CCONJ
ejpam-4610	119	10	wy	wy	PROPN
ejpam-4610	119	11	∈	∈	PROPN
ejpam-4610	119	12	e(g	e(g	PROPN
ejpam-4610	119	13	)	)	PUNCT
ejpam-4610	119	14	.	.	PUNCT
ejpam-4610	120	1	then	then	ADV
ejpam-4610	120	2	s	s	VERB
ejpam-4610	120	3	=	=	SYM
ejpam-4610	120	4	v	v	PROPN
ejpam-4610	120	5	(	(	PUNCT
ejpam-4610	120	6	g	g	NOUN
ejpam-4610	120	7	)	)	PUNCT
ejpam-4610	120	8	\	\	NOUN
ejpam-4610	120	9	{	{	PUNCT
ejpam-4610	120	10	v	v	NOUN
ejpam-4610	120	11	,	,	PUNCT
ejpam-4610	120	12	y	y	NOUN
ejpam-4610	120	13	}	}	PUNCT
ejpam-4610	120	14	is	be	AUX
ejpam-4610	120	15	a	a	DET
ejpam-4610	120	16	hd	hd	NOUN
ejpam-4610	120	17	-	-	PUNCT
ejpam-4610	120	18	set	set	NOUN
ejpam-4610	120	19	of	of	ADP
ejpam-4610	120	20	g.	g.	PROPN
ejpam-4610	120	21	since	since	SCONJ
ejpam-4610	120	22	t	t	PROPN
ejpam-4610	120	23	=	=	SYM
ejpam-4610	120	24	{	{	PUNCT
ejpam-4610	120	25	v	v	NOUN
ejpam-4610	120	26	,	,	PUNCT
ejpam-4610	120	27	y	y	NOUN
ejpam-4610	120	28	}	}	PUNCT
ejpam-4610	120	29	is	be	AUX
ejpam-4610	120	30	not	not	PART
ejpam-4610	120	31	a	a	DET
ejpam-4610	120	32	hd	hd	NOUN
ejpam-4610	120	33	-	-	NOUN
ejpam-4610	120	34	set	set	NOUN
ejpam-4610	120	35	of	of	ADP
ejpam-4610	120	36	g	g	NOUN
ejpam-4610	120	37	,	,	PUNCT
ejpam-4610	120	38	s	s	PART
ejpam-4610	120	39	is	be	AUX
ejpam-4610	120	40	a	a	DET
ejpam-4610	120	41	thd	thd	NOUN
ejpam-4610	120	42	-	-	PUNCT
ejpam-4610	120	43	set	set	NOUN
ejpam-4610	120	44	of	of	ADP
ejpam-4610	120	45	g.	g.	PROPN
ejpam-4610	120	46	this	this	PRON
ejpam-4610	120	47	means	mean	VERB
ejpam-4610	120	48	that	that	SCONJ
ejpam-4610	120	49	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	120	50	)	)	PUNCT
ejpam-4610	120	51	≤	≤	NUM
ejpam-4610	120	52	|s|	|s|	PROPN
ejpam-4610	120	53	=	=	SYM
ejpam-4610	120	54	n−	n−	NOUN
ejpam-4610	120	55	2	2	NUM
ejpam-4610	120	56	,	,	PUNCT
ejpam-4610	120	57	a	a	DET
ejpam-4610	120	58	contradiction	contradiction	NOUN
ejpam-4610	120	59	.	.	PUNCT
ejpam-4610	121	1	subcase	subcase	PROPN
ejpam-4610	121	2	2.3	2.3	NUM
ejpam-4610	121	3	:	:	PUNCT
ejpam-4610	121	4	suppose	suppose	VERB
ejpam-4610	121	5	that	that	SCONJ
ejpam-4610	121	6	w	w	PROPN
ejpam-4610	121	7	̸=	̸=	PROPN
ejpam-4610	121	8	z	z	NOUN
ejpam-4610	121	9	and	and	CCONJ
ejpam-4610	121	10	dg(y	dg(y	ADJ
ejpam-4610	121	11	,	,	PUNCT
ejpam-4610	121	12	w	w	NOUN
ejpam-4610	121	13	)	)	PUNCT
ejpam-4610	121	14	=	=	SYM
ejpam-4610	121	15	2	2	X
ejpam-4610	121	16	.	.	X
ejpam-4610	121	17	let	let	VERB
ejpam-4610	121	18	[	[	X
ejpam-4610	121	19	y	y	PROPN
ejpam-4610	121	20	,	,	PUNCT
ejpam-4610	121	21	x	x	X
ejpam-4610	121	22	,	,	PUNCT
ejpam-4610	121	23	w	w	PROPN
ejpam-4610	121	24	]	]	PUNCT
ejpam-4610	121	25	be	be	AUX
ejpam-4610	121	26	a	a	DET
ejpam-4610	121	27	y	y	PROPN
ejpam-4610	121	28	-	-	PUNCT
ejpam-4610	121	29	w	w	NOUN
ejpam-4610	121	30	geodesic	geodesic	NOUN
ejpam-4610	121	31	in	in	ADP
ejpam-4610	121	32	g.	g.	PROPN
ejpam-4610	121	33	if	if	SCONJ
ejpam-4610	121	34	x	x	PROPN
ejpam-4610	121	35	=	=	SYM
ejpam-4610	121	36	z	z	NOUN
ejpam-4610	121	37	,	,	PUNCT
ejpam-4610	121	38	then	then	ADV
ejpam-4610	121	39	s	s	VERB
ejpam-4610	121	40	=	=	SYM
ejpam-4610	121	41	v	v	PROPN
ejpam-4610	121	42	(	(	PUNCT
ejpam-4610	121	43	g)\{u	g)\{u	PROPN
ejpam-4610	121	44	,	,	PUNCT
ejpam-4610	121	45	y	y	PROPN
ejpam-4610	121	46	}	}	PUNCT
ejpam-4610	121	47	is	be	AUX
ejpam-4610	121	48	a	a	DET
ejpam-4610	121	49	thd	thd	NOUN
ejpam-4610	121	50	-	-	PUNCT
ejpam-4610	121	51	set	set	NOUN
ejpam-4610	121	52	of	of	ADP
ejpam-4610	121	53	g	g	NOUN
ejpam-4610	121	54	as	as	ADP
ejpam-4610	121	55	{	{	PUNCT
ejpam-4610	121	56	u	u	NOUN
ejpam-4610	121	57	,	,	PUNCT
ejpam-4610	121	58	y	y	PROPN
ejpam-4610	121	59	}	}	PUNCT
ejpam-4610	121	60	does	do	AUX
ejpam-4610	121	61	not	not	PART
ejpam-4610	121	62	hop	hop	NOUN
ejpam-4610	121	63	-	-	PUNCT
ejpam-4610	121	64	dominate	dominate	VERB
ejpam-4610	121	65	z.	z.	NOUN
ejpam-4610	121	66	if	if	SCONJ
ejpam-4610	121	67	x	x	PROPN
ejpam-4610	121	68	̸=	̸=	PROPN
ejpam-4610	121	69	z	z	PROPN
ejpam-4610	121	70	,	,	PUNCT
ejpam-4610	121	71	then	then	ADV
ejpam-4610	121	72	s	s	VERB
ejpam-4610	121	73	=	=	SYM
ejpam-4610	121	74	v	v	PROPN
ejpam-4610	121	75	(	(	PUNCT
ejpam-4610	121	76	g	g	NOUN
ejpam-4610	121	77	)	)	PUNCT
ejpam-4610	121	78	\	\	NOUN
ejpam-4610	121	79	{	{	PUNCT
ejpam-4610	121	80	w	w	PROPN
ejpam-4610	121	81	,	,	PUNCT
ejpam-4610	121	82	y	y	NOUN
ejpam-4610	121	83	}	}	PUNCT
ejpam-4610	121	84	is	be	AUX
ejpam-4610	121	85	a	a	DET
ejpam-4610	121	86	thd	thd	NOUN
ejpam-4610	121	87	-	-	PUNCT
ejpam-4610	121	88	set	set	NOUN
ejpam-4610	121	89	of	of	ADP
ejpam-4610	121	90	g	g	NOUN
ejpam-4610	121	91	as	as	ADP
ejpam-4610	121	92	{	{	PUNCT
ejpam-4610	121	93	w	w	PROPN
ejpam-4610	121	94	,	,	PUNCT
ejpam-4610	121	95	y	y	PROPN
ejpam-4610	121	96	}	}	PUNCT
ejpam-4610	121	97	does	do	AUX
ejpam-4610	121	98	not	not	PART
ejpam-4610	121	99	hop	hop	AUX
ejpam-4610	121	100	-	-	PUNCT
ejpam-4610	121	101	dominate	dominate	VERB
ejpam-4610	121	102	x.	x.	NOUN
ejpam-4610	121	103	accordingly	accordingly	ADV
ejpam-4610	121	104	,	,	PUNCT
ejpam-4610	121	105	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	121	106	)	)	PUNCT
ejpam-4610	121	107	≤	≤	NUM
ejpam-4610	121	108	|s|	|s|	PROPN
ejpam-4610	121	109	=	=	SYM
ejpam-4610	121	110	n−	n−	NOUN
ejpam-4610	121	111	2	2	NUM
ejpam-4610	121	112	,	,	PUNCT
ejpam-4610	121	113	a	a	DET
ejpam-4610	121	114	contradiction	contradiction	NOUN
ejpam-4610	121	115	.	.	PUNCT
ejpam-4610	122	1	therefore	therefore	ADV
ejpam-4610	122	2	,	,	PUNCT
ejpam-4610	122	3	ux	ux	PROPN
ejpam-4610	122	4	∈	∈	PROPN
ejpam-4610	122	5	e(g	e(g	PROPN
ejpam-4610	122	6	)	)	PUNCT
ejpam-4610	123	1	for	for	ADP
ejpam-4610	123	2	all	all	PRON
ejpam-4610	123	3	x	x	SYM
ejpam-4610	123	4	∈	∈	PROPN
ejpam-4610	123	5	v	v	NOUN
ejpam-4610	123	6	(	(	PUNCT
ejpam-4610	123	7	g	g	NOUN
ejpam-4610	123	8	)	)	PUNCT
ejpam-4610	123	9	\	\	NOUN
ejpam-4610	123	10	{	{	PUNCT
ejpam-4610	123	11	u	u	NOUN
ejpam-4610	123	12	,	,	PUNCT
ejpam-4610	123	13	v	v	NOUN
ejpam-4610	123	14	}	}	PUNCT
ejpam-4610	123	15	.	.	PUNCT
ejpam-4610	124	1	similarly	similarly	ADV
ejpam-4610	124	2	,	,	PUNCT
ejpam-4610	124	3	vx	vx	PROPN
ejpam-4610	124	4	∈	∈	PROPN
ejpam-4610	124	5	e(g	e(g	PROPN
ejpam-4610	124	6	)	)	PUNCT
ejpam-4610	125	1	for	for	ADP
ejpam-4610	125	2	all	all	PRON
ejpam-4610	125	3	x	x	SYM
ejpam-4610	125	4	∈	∈	PROPN
ejpam-4610	125	5	v	v	NOUN
ejpam-4610	125	6	(	(	PUNCT
ejpam-4610	125	7	g	g	NOUN
ejpam-4610	125	8	)	)	PUNCT
ejpam-4610	125	9	\	\	NOUN
ejpam-4610	125	10	{	{	PUNCT
ejpam-4610	125	11	u	u	NOUN
ejpam-4610	125	12	,	,	PUNCT
ejpam-4610	125	13	v	v	NOUN
ejpam-4610	125	14	}	}	PUNCT
ejpam-4610	125	15	.	.	PUNCT
ejpam-4610	126	1	next	next	ADV
ejpam-4610	126	2	,	,	PUNCT
ejpam-4610	126	3	we	we	PRON
ejpam-4610	126	4	claim	claim	VERB
ejpam-4610	126	5	that	that	SCONJ
ejpam-4610	126	6	h	h	NOUN
ejpam-4610	126	7	=	=	SYM
ejpam-4610	126	8	⟨v	⟨v	NUM
ejpam-4610	126	9	(	(	PUNCT
ejpam-4610	126	10	g)\{u	g)\{u	PROPN
ejpam-4610	126	11	,	,	PUNCT
ejpam-4610	126	12	v}⟩	v}⟩	PROPN
ejpam-4610	126	13	is	be	AUX
ejpam-4610	126	14	complete	complete	ADJ
ejpam-4610	126	15	.	.	PUNCT
ejpam-4610	127	1	suppose	suppose	VERB
ejpam-4610	127	2	not	not	PART
ejpam-4610	127	3	,	,	PUNCT
ejpam-4610	127	4	and	and	CCONJ
ejpam-4610	127	5	let	let	VERB
ejpam-4610	127	6	x	x	PRON
ejpam-4610	127	7	,	,	PUNCT
ejpam-4610	127	8	y	y	PROPN
ejpam-4610	127	9	∈	∈	PROPN
ejpam-4610	127	10	v	v	ADP
ejpam-4610	127	11	(	(	PUNCT
ejpam-4610	127	12	h	h	NOUN
ejpam-4610	127	13	)	)	PUNCT
ejpam-4610	127	14	with	with	ADP
ejpam-4610	127	15	dh(x	dh(x	PROPN
ejpam-4610	127	16	,	,	PUNCT
ejpam-4610	127	17	y	y	NOUN
ejpam-4610	127	18	)	)	PUNCT
ejpam-4610	127	19	=	=	SYM
ejpam-4610	128	1	2	2	X
ejpam-4610	128	2	.	.	X
ejpam-4610	128	3	let	let	VERB
ejpam-4610	128	4	[	[	X
ejpam-4610	128	5	x	x	X
ejpam-4610	128	6	,	,	PUNCT
ejpam-4610	128	7	z	z	PROPN
ejpam-4610	128	8	,	,	PUNCT
ejpam-4610	128	9	y	y	PROPN
ejpam-4610	128	10	]	]	PUNCT
ejpam-4610	128	11	be	be	AUX
ejpam-4610	128	12	a	a	DET
ejpam-4610	128	13	geodesic	geodesic	NOUN
ejpam-4610	128	14	in	in	ADP
ejpam-4610	128	15	h.	h.	PROPN
ejpam-4610	128	16	in	in	ADP
ejpam-4610	128	17	particular	particular	ADJ
ejpam-4610	128	18	,	,	PUNCT
ejpam-4610	128	19	[	[	X
ejpam-4610	128	20	u	u	NOUN
ejpam-4610	128	21	,	,	PUNCT
ejpam-4610	128	22	x	x	X
ejpam-4610	128	23	,	,	PUNCT
ejpam-4610	128	24	v	v	NOUN
ejpam-4610	128	25	]	]	PUNCT
ejpam-4610	128	26	is	be	AUX
ejpam-4610	128	27	a	a	DET
ejpam-4610	128	28	geodesic	geodesic	NOUN
ejpam-4610	128	29	in	in	ADP
ejpam-4610	128	30	g	g	NOUN
ejpam-4610	128	31	by	by	ADP
ejpam-4610	128	32	the	the	DET
ejpam-4610	128	33	above	above	ADJ
ejpam-4610	128	34	claim	claim	NOUN
ejpam-4610	128	35	.	.	PUNCT
ejpam-4610	129	1	observe	observe	VERB
ejpam-4610	129	2	also	also	ADV
ejpam-4610	129	3	that	that	PRON
ejpam-4610	129	4	s	s	VERB
ejpam-4610	129	5	=	=	X
ejpam-4610	129	6	v	v	X
ejpam-4610	129	7	(	(	PUNCT
ejpam-4610	129	8	g	g	NOUN
ejpam-4610	129	9	)	)	PUNCT
ejpam-4610	129	10	\	\	NOUN
ejpam-4610	129	11	{	{	PUNCT
ejpam-4610	129	12	u	u	NOUN
ejpam-4610	129	13	,	,	PUNCT
ejpam-4610	129	14	y	y	PROPN
ejpam-4610	129	15	}	}	PUNCT
ejpam-4610	129	16	is	be	AUX
ejpam-4610	129	17	a	a	DET
ejpam-4610	129	18	hd	hd	NOUN
ejpam-4610	129	19	-	-	PUNCT
ejpam-4610	129	20	set	set	NOUN
ejpam-4610	129	21	of	of	ADP
ejpam-4610	129	22	g.	g.	PROPN
ejpam-4610	129	23	by	by	ADP
ejpam-4610	129	24	the	the	DET
ejpam-4610	129	25	first	first	ADJ
ejpam-4610	129	26	claim	claim	NOUN
ejpam-4610	129	27	,	,	PUNCT
ejpam-4610	129	28	uz	uz	PROPN
ejpam-4610	129	29	∈	∈	PROPN
ejpam-4610	129	30	e(g	e(g	PROPN
ejpam-4610	129	31	)	)	PUNCT
ejpam-4610	129	32	.	.	PUNCT
ejpam-4610	130	1	thus	thus	ADV
ejpam-4610	130	2	,	,	PUNCT
ejpam-4610	130	3	{	{	PUNCT
ejpam-4610	130	4	u	u	NOUN
ejpam-4610	130	5	,	,	PUNCT
ejpam-4610	130	6	y	y	PROPN
ejpam-4610	130	7	}	}	PUNCT
ejpam-4610	130	8	does	do	AUX
ejpam-4610	130	9	not	not	PART
ejpam-4610	130	10	hop	hop	NOUN
ejpam-4610	130	11	-	-	PUNCT
ejpam-4610	130	12	dominate	dominate	VERB
ejpam-4610	130	13	z.	z.	PROPN
ejpam-4610	131	1	this	this	PRON
ejpam-4610	131	2	means	mean	VERB
ejpam-4610	131	3	that	that	SCONJ
ejpam-4610	131	4	s	s	VERB
ejpam-4610	131	5	is	be	AUX
ejpam-4610	131	6	a	a	DET
ejpam-4610	131	7	thd	thd	NOUN
ejpam-4610	131	8	-	-	PUNCT
ejpam-4610	131	9	set	set	NOUN
ejpam-4610	131	10	of	of	ADP
ejpam-4610	131	11	g.	g.	PROPN
ejpam-4610	131	12	consequently	consequently	ADV
ejpam-4610	131	13	,	,	PUNCT
ejpam-4610	131	14	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	131	15	)	)	PUNCT
ejpam-4610	131	16	≤	≤	NUM
ejpam-4610	131	17	|s|	|s|	PROPN
ejpam-4610	131	18	=	=	PUNCT
ejpam-4610	131	19	n	n	CCONJ
ejpam-4610	131	20	−	−	PROPN
ejpam-4610	131	21	2	2	NUM
ejpam-4610	131	22	,	,	PUNCT
ejpam-4610	131	23	a	a	DET
ejpam-4610	131	24	contradiction	contradiction	NOUN
ejpam-4610	131	25	.	.	PUNCT
ejpam-4610	132	1	therefore	therefore	ADV
ejpam-4610	132	2	,	,	PUNCT
ejpam-4610	132	3	h	h	NOUN
ejpam-4610	132	4	is	be	AUX
ejpam-4610	132	5	complete	complete	ADJ
ejpam-4610	132	6	.	.	PUNCT
ejpam-4610	133	1	accordingly	accordingly	ADV
ejpam-4610	133	2	,	,	PUNCT
ejpam-4610	133	3	g	g	PROPN
ejpam-4610	133	4	=	=	SYM
ejpam-4610	133	5	⟨{u	⟨{u	PROPN
ejpam-4610	133	6	,	,	PUNCT
ejpam-4610	133	7	v}⟩+h	v}⟩+h	NOUN
ejpam-4610	133	8	=	=	PROPN
ejpam-4610	133	9	k2	k2	PROPN
ejpam-4610	133	10	+	+	PROPN
ejpam-4610	133	11	kn−2	kn−2	PROPN
ejpam-4610	133	12	.	.	PUNCT
ejpam-4610	134	1	theorem	theorem	NOUN
ejpam-4610	134	2	1	1	NUM
ejpam-4610	134	3	.	.	PUNCT
ejpam-4610	135	1	if	if	SCONJ
ejpam-4610	135	2	g	g	PROPN
ejpam-4610	135	3	is	be	AUX
ejpam-4610	135	4	a	a	DET
ejpam-4610	135	5	disconnected	disconnected	ADJ
ejpam-4610	135	6	graph	graph	NOUN
ejpam-4610	135	7	with	with	ADP
ejpam-4610	135	8	components	component	NOUN
ejpam-4610	135	9	g1	g1	PROPN
ejpam-4610	135	10	,	,	PUNCT
ejpam-4610	135	11	g2	g2	PROPN
ejpam-4610	135	12	,	,	PUNCT
ejpam-4610	135	13	.	.	PUNCT
ejpam-4610	135	14	.	.	PUNCT
ejpam-4610	136	1	.	.	PUNCT
ejpam-4610	137	1	,	,	PUNCT
ejpam-4610	137	2	gm	gm	PROPN
ejpam-4610	137	3	then	then	ADV
ejpam-4610	137	4	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	137	5	)	)	PUNCT
ejpam-4610	138	1	=	=	SYM
ejpam-4610	138	2	min	min	PROPN
ejpam-4610	138	3	1≤k≤m	1≤k≤m	NUM
ejpam-4610	138	4	{	{	PUNCT
ejpam-4610	138	5	γ̂h(gk	γ̂h(gk	NOUN
ejpam-4610	138	6	)	)	PUNCT
ejpam-4610	138	7	+	+	CCONJ
ejpam-4610	138	8	m∑	m∑	ADV
ejpam-4610	138	9	j=1,j	j=1,j	VERB
ejpam-4610	138	10	̸=k	̸=k	PROPN
ejpam-4610	138	11	γh(gj	γh(gj	PROPN
ejpam-4610	138	12	)	)	PUNCT
ejpam-4610	138	13	}	}	PUNCT
ejpam-4610	138	14	.	.	PUNCT
ejpam-4610	139	1	in	in	ADP
ejpam-4610	139	2	particular	particular	ADJ
ejpam-4610	139	3	,	,	PUNCT
ejpam-4610	139	4	γ̂h(kn	γ̂h(kn	PROPN
ejpam-4610	139	5	)	)	PUNCT
ejpam-4610	139	6	=	=	SYM
ejpam-4610	140	1	n.	n.	NOUN
ejpam-4610	140	2	proof	proof	NOUN
ejpam-4610	140	3	.	.	PUNCT
ejpam-4610	141	1	for	for	ADP
ejpam-4610	141	2	each	each	DET
ejpam-4610	141	3	k	k	PROPN
ejpam-4610	141	4	∈	∈	PROPN
ejpam-4610	141	5	{	{	PUNCT
ejpam-4610	141	6	1	1	NUM
ejpam-4610	141	7	,	,	PUNCT
ejpam-4610	141	8	2	2	NUM
ejpam-4610	141	9	,	,	PUNCT
ejpam-4610	141	10	.	.	PUNCT
ejpam-4610	141	11	.	.	PUNCT
ejpam-4610	141	12	.	.	PUNCT
ejpam-4610	142	1	,	,	PUNCT
ejpam-4610	142	2	m	m	VERB
ejpam-4610	142	3	}	}	PUNCT
ejpam-4610	142	4	,	,	PUNCT
ejpam-4610	142	5	let	let	VERB
ejpam-4610	142	6	dk	dk	PRON
ejpam-4610	142	7	and	and	CCONJ
ejpam-4610	142	8	sk	sk	AUX
ejpam-4610	142	9	be	be	AUX
ejpam-4610	142	10	a	a	DET
ejpam-4610	142	11	γ̂h	γ̂h	NOUN
ejpam-4610	142	12	-	-	PUNCT
ejpam-4610	142	13	set	set	VERB
ejpam-4610	142	14	and	and	CCONJ
ejpam-4610	142	15	a	a	DET
ejpam-4610	142	16	γh	γh	ADV
ejpam-4610	142	17	-	-	PUNCT
ejpam-4610	142	18	set	set	NOUN
ejpam-4610	142	19	,	,	PUNCT
ejpam-4610	142	20	respectively	respectively	ADV
ejpam-4610	142	21	,	,	PUNCT
ejpam-4610	142	22	of	of	ADP
ejpam-4610	142	23	gk	gk	PROPN
ejpam-4610	142	24	.	.	PUNCT
ejpam-4610	143	1	then	then	ADV
ejpam-4610	143	2	dk	dk	PROPN
ejpam-4610	143	3	∪	∪	X
ejpam-4610	143	4	(	(	PUNCT
ejpam-4610	143	5	∪m	∪m	NUM
ejpam-4610	143	6	j=1,j	j=1,j	NOUN
ejpam-4610	143	7	̸=ksj	̸=ksj	ADJ
ejpam-4610	143	8	)	)	PUNCT
ejpam-4610	143	9	is	be	AUX
ejpam-4610	143	10	a	a	DET
ejpam-4610	143	11	thd	thd	NOUN
ejpam-4610	143	12	-	-	PUNCT
ejpam-4610	143	13	set	set	NOUN
ejpam-4610	143	14	of	of	ADP
ejpam-4610	143	15	g	g	NOUN
ejpam-4610	143	16	for	for	ADP
ejpam-4610	143	17	all	all	DET
ejpam-4610	143	18	k	k	PROPN
ejpam-4610	143	19	∈	∈	PROPN
ejpam-4610	143	20	{	{	PUNCT
ejpam-4610	143	21	1	1	NUM
ejpam-4610	143	22	,	,	PUNCT
ejpam-4610	143	23	2	2	NUM
ejpam-4610	143	24	,	,	PUNCT
ejpam-4610	143	25	.	.	PUNCT
ejpam-4610	143	26	.	.	PUNCT
ejpam-4610	144	1	.	.	PUNCT
ejpam-4610	145	1	,	,	PUNCT
ejpam-4610	145	2	m	m	VERB
ejpam-4610	145	3	}	}	PUNCT
ejpam-4610	145	4	.	.	PUNCT
ejpam-4610	146	1	thus	thus	ADV
ejpam-4610	146	2	,	,	PUNCT
ejpam-4610	146	3	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	146	4	)	)	PUNCT
ejpam-4610	146	5	≤	≤	NUM
ejpam-4610	146	6	min1≤k≤m{γ̂h(gk	min1≤k≤m{γ̂h(gk	NOUN
ejpam-4610	146	7	)	)	PUNCT
ejpam-4610	147	1	+	+	CCONJ
ejpam-4610	147	2	∑m	∑m	ADJ
ejpam-4610	147	3	j=1,j	j=1,j	PROPN
ejpam-4610	147	4	̸=k	̸=k	PROPN
ejpam-4610	147	5	γh(gj	γh(gj	PROPN
ejpam-4610	147	6	)	)	PUNCT
ejpam-4610	147	7	}	}	PUNCT
ejpam-4610	147	8	.	.	PUNCT
ejpam-4610	148	1	m.a	m.a	PROPN
ejpam-4610	148	2	.	.	PROPN
ejpam-4610	148	3	bonsocan	bonsocan	PROPN
ejpam-4610	148	4	,	,	PUNCT
ejpam-4610	148	5	f.	f.	PROPN
ejpam-4610	148	6	jamil	jamil	PROPN
ejpam-4610	148	7	/	/	SYM
ejpam-4610	148	8	eur	eur	PROPN
ejpam-4610	148	9	.	.	PUNCT
ejpam-4610	149	1	j.	j.	PROPN
ejpam-4610	149	2	pure	pure	PROPN
ejpam-4610	149	3	appl	appl	PROPN
ejpam-4610	149	4	.	.	PROPN
ejpam-4610	149	5	math	math	PROPN
ejpam-4610	149	6	,	,	PUNCT
ejpam-4610	149	7	16	16	NUM
ejpam-4610	149	8	(	(	PUNCT
ejpam-4610	149	9	1	1	NUM
ejpam-4610	149	10	)	)	PUNCT
ejpam-4610	149	11	(	(	PUNCT
ejpam-4610	149	12	2023	2023	NUM
ejpam-4610	149	13	)	)	PUNCT
ejpam-4610	149	14	,	,	PUNCT
ejpam-4610	149	15	192	192	NUM
ejpam-4610	149	16	-	-	SYM
ejpam-4610	149	17	206	206	NUM
ejpam-4610	149	18	196	196	NUM
ejpam-4610	149	19	to	to	PART
ejpam-4610	149	20	get	get	VERB
ejpam-4610	149	21	the	the	DET
ejpam-4610	149	22	other	other	ADJ
ejpam-4610	149	23	inequality	inequality	NOUN
ejpam-4610	149	24	,	,	PUNCT
ejpam-4610	149	25	let	let	VERB
ejpam-4610	149	26	s	s	PRON
ejpam-4610	149	27	be	be	AUX
ejpam-4610	149	28	any	any	DET
ejpam-4610	149	29	thd	thd	NOUN
ejpam-4610	149	30	-	-	PUNCT
ejpam-4610	149	31	set	set	NOUN
ejpam-4610	149	32	of	of	ADP
ejpam-4610	149	33	g.	g.	PROPN
ejpam-4610	150	1	then	then	ADV
ejpam-4610	150	2	tk	tk	PROPN
ejpam-4610	151	1	=	=	PROPN
ejpam-4610	151	2	s	s	PROPN
ejpam-4610	151	3	∩	∩	ADJ
ejpam-4610	151	4	v	v	X
ejpam-4610	151	5	(	(	PUNCT
ejpam-4610	151	6	gk	gk	NOUN
ejpam-4610	151	7	)	)	PUNCT
ejpam-4610	151	8	is	be	AUX
ejpam-4610	151	9	a	a	DET
ejpam-4610	151	10	hd	hd	NOUN
ejpam-4610	151	11	-	-	NOUN
ejpam-4610	151	12	set	set	NOUN
ejpam-4610	151	13	for	for	ADP
ejpam-4610	151	14	all	all	DET
ejpam-4610	151	15	k	k	PROPN
ejpam-4610	151	16	∈	∈	PROPN
ejpam-4610	151	17	{	{	PUNCT
ejpam-4610	151	18	1	1	NUM
ejpam-4610	151	19	,	,	PUNCT
ejpam-4610	151	20	2	2	NUM
ejpam-4610	151	21	,	,	PUNCT
ejpam-4610	151	22	.	.	PUNCT
ejpam-4610	151	23	.	.	PUNCT
ejpam-4610	152	1	.	.	PUNCT
ejpam-4610	153	1	,	,	PUNCT
ejpam-4610	153	2	m	m	VERB
ejpam-4610	153	3	}	}	PUNCT
ejpam-4610	153	4	.	.	PUNCT
ejpam-4610	154	1	we	we	PRON
ejpam-4610	154	2	claim	claim	VERB
ejpam-4610	154	3	that	that	SCONJ
ejpam-4610	154	4	tk	tk	PROPN
ejpam-4610	154	5	is	be	AUX
ejpam-4610	154	6	a	a	DET
ejpam-4610	154	7	thd	thd	NOUN
ejpam-4610	154	8	-	-	PUNCT
ejpam-4610	154	9	set	set	NOUN
ejpam-4610	154	10	of	of	ADP
ejpam-4610	154	11	gk	gk	PROPN
ejpam-4610	154	12	for	for	ADP
ejpam-4610	154	13	at	at	ADV
ejpam-4610	154	14	least	least	ADV
ejpam-4610	154	15	one	one	NUM
ejpam-4610	154	16	k	k	NOUN
ejpam-4610	154	17	∈	∈	PROPN
ejpam-4610	154	18	{	{	PUNCT
ejpam-4610	154	19	1	1	NUM
ejpam-4610	154	20	,	,	PUNCT
ejpam-4610	154	21	2	2	NUM
ejpam-4610	154	22	,	,	PUNCT
ejpam-4610	154	23	.	.	PUNCT
ejpam-4610	154	24	.	.	PUNCT
ejpam-4610	154	25	.	.	PUNCT
ejpam-4610	155	1	,	,	PUNCT
ejpam-4610	155	2	m	m	VERB
ejpam-4610	155	3	}	}	PUNCT
ejpam-4610	155	4	.	.	PUNCT
ejpam-4610	156	1	suppose	suppose	VERB
ejpam-4610	156	2	not	not	PART
ejpam-4610	156	3	,	,	PUNCT
ejpam-4610	156	4	and	and	CCONJ
ejpam-4610	156	5	let	let	VERB
ejpam-4610	156	6	,	,	PUNCT
ejpam-4610	156	7	for	for	ADP
ejpam-4610	156	8	each	each	DET
ejpam-4610	156	9	k	k	PROPN
ejpam-4610	156	10	∈	∈	PROPN
ejpam-4610	156	11	{	{	PUNCT
ejpam-4610	156	12	1	1	NUM
ejpam-4610	156	13	,	,	PUNCT
ejpam-4610	156	14	2	2	NUM
ejpam-4610	156	15	,	,	PUNCT
ejpam-4610	156	16	.	.	PUNCT
ejpam-4610	156	17	.	.	PUNCT
ejpam-4610	157	1	.	.	PUNCT
ejpam-4610	158	1	,	,	PUNCT
ejpam-4610	158	2	m	m	PROPN
ejpam-4610	158	3	}	}	PUNCT
ejpam-4610	158	4	,	,	PUNCT
ejpam-4610	158	5	sk	sk	X
ejpam-4610	158	6	be	be	AUX
ejpam-4610	158	7	a	a	DET
ejpam-4610	158	8	γhset	γhset	NOUN
ejpam-4610	158	9	of	of	ADP
ejpam-4610	158	10	gk	gk	PROPN
ejpam-4610	158	11	for	for	ADP
ejpam-4610	158	12	which	which	PRON
ejpam-4610	158	13	tk	tk	PROPN
ejpam-4610	158	14	∩	∩	NOUN
ejpam-4610	158	15	sk	sk	VERB
ejpam-4610	158	16	=	=	PUNCT
ejpam-4610	158	17	∅.	∅.	NOUN
ejpam-4610	158	18	since	since	SCONJ
ejpam-4610	158	19	∪m	∪m	NUM
ejpam-4610	158	20	k=1sk	k=1sk	X
ejpam-4610	158	21	is	be	AUX
ejpam-4610	158	22	a	a	DET
ejpam-4610	158	23	γh	γh	ADV
ejpam-4610	158	24	-	-	PUNCT
ejpam-4610	158	25	set	set	NOUN
ejpam-4610	158	26	of	of	ADP
ejpam-4610	158	27	g	g	NOUN
ejpam-4610	158	28	,	,	PUNCT
ejpam-4610	158	29	s	s	PART
ejpam-4610	158	30	∩	∩	X
ejpam-4610	158	31	(	(	PUNCT
ejpam-4610	158	32	∪m	∪m	NUM
ejpam-4610	158	33	k=1)sk	k=1)sk	X
ejpam-4610	158	34	̸=	̸=	PROPN
ejpam-4610	158	35	∅.	∅.	ADV
ejpam-4610	158	36	since	since	SCONJ
ejpam-4610	158	37	s	s	NOUN
ejpam-4610	158	38	=	=	SYM
ejpam-4610	158	39	∪m	∪m	NUM
ejpam-4610	158	40	k=1tk	k=1tk	PROPN
ejpam-4610	158	41	,	,	PUNCT
ejpam-4610	158	42	this	this	PRON
ejpam-4610	158	43	is	be	AUX
ejpam-4610	158	44	impossible	impossible	ADJ
ejpam-4610	158	45	and	and	CCONJ
ejpam-4610	158	46	our	our	PRON
ejpam-4610	158	47	claim	claim	NOUN
ejpam-4610	158	48	holds	hold	VERB
ejpam-4610	158	49	.	.	PUNCT
ejpam-4610	159	1	hence	hence	ADV
ejpam-4610	159	2	,	,	PUNCT
ejpam-4610	159	3	|s|	|s|	PROPN
ejpam-4610	159	4	=	=	SYM
ejpam-4610	159	5	∑m	∑m	PROPN
ejpam-4610	159	6	k=1	k=1	X
ejpam-4610	159	7	|tk|	|tk|	PROPN
ejpam-4610	159	8	≥	≥	NUM
ejpam-4610	159	9	min1≤k≤m{γ̂h(gk	min1≤k≤m{γ̂h(gk	NOUN
ejpam-4610	159	10	)	)	PUNCT
ejpam-4610	160	1	+	+	CCONJ
ejpam-4610	160	2	∑m	∑m	ADJ
ejpam-4610	160	3	j=1,j	j=1,j	PROPN
ejpam-4610	160	4	̸=k	̸=k	PROPN
ejpam-4610	160	5	γh(gj	γh(gj	PROPN
ejpam-4610	160	6	)	)	PUNCT
ejpam-4610	160	7	}	}	PUNCT
ejpam-4610	160	8	.	.	PUNCT
ejpam-4610	161	1	theorem	theorem	NOUN
ejpam-4610	161	2	2	2	NUM
ejpam-4610	161	3	.	.	PUNCT
ejpam-4610	162	1	let	let	VERB
ejpam-4610	162	2	g	g	NOUN
ejpam-4610	162	3	be	be	AUX
ejpam-4610	162	4	any	any	DET
ejpam-4610	162	5	nontrivial	nontrivial	ADJ
ejpam-4610	162	6	graph	graph	NOUN
ejpam-4610	162	7	.	.	PUNCT
ejpam-4610	163	1	then	then	ADV
ejpam-4610	163	2	4	4	NUM
ejpam-4610	163	3	≤	≤	NUM
ejpam-4610	163	4	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	163	5	)	)	PUNCT
ejpam-4610	164	1	+	+	NUM
ejpam-4610	164	2	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	164	3	)	)	PUNCT
ejpam-4610	164	4	≤	≤	NUM
ejpam-4610	164	5	2n	2n	NUM
ejpam-4610	164	6	,	,	PUNCT
ejpam-4610	164	7	and	and	CCONJ
ejpam-4610	164	8	these	these	DET
ejpam-4610	164	9	bounds	bound	NOUN
ejpam-4610	164	10	are	be	AUX
ejpam-4610	164	11	sharp	sharp	ADJ
ejpam-4610	164	12	.	.	PUNCT
ejpam-4610	165	1	proof	proof	NOUN
ejpam-4610	165	2	.	.	PUNCT
ejpam-4610	166	1	let	let	VERB
ejpam-4610	166	2	g	g	NOUN
ejpam-4610	166	3	be	be	AUX
ejpam-4610	166	4	any	any	DET
ejpam-4610	166	5	nontrivial	nontrivial	ADJ
ejpam-4610	166	6	graph	graph	NOUN
ejpam-4610	166	7	.	.	PUNCT
ejpam-4610	167	1	then	then	ADV
ejpam-4610	167	2	,	,	PUNCT
ejpam-4610	167	3	we	we	PRON
ejpam-4610	167	4	have	have	VERB
ejpam-4610	167	5	2	2	NUM
ejpam-4610	167	6	≤	≤	NUM
ejpam-4610	167	7	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	167	8	)	)	PUNCT
ejpam-4610	167	9	≤	≤	NUM
ejpam-4610	167	10	n.	n.	NOUN
ejpam-4610	167	11	similarly	similarly	ADV
ejpam-4610	167	12	,	,	PUNCT
ejpam-4610	167	13	2	2	NUM
ejpam-4610	167	14	≤	≤	NUM
ejpam-4610	167	15	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	167	16	)	)	PUNCT
ejpam-4610	167	17	≤	≤	NUM
ejpam-4610	167	18	n.	n.	NOUN
ejpam-4610	167	19	therefore	therefore	ADV
ejpam-4610	167	20	,	,	PUNCT
ejpam-4610	167	21	4	4	NUM
ejpam-4610	167	22	≤	≤	NUM
ejpam-4610	167	23	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	167	24	)	)	PUNCT
ejpam-4610	168	1	+	+	NUM
ejpam-4610	168	2	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	168	3	)	)	PUNCT
ejpam-4610	168	4	≤	≤	NOUN
ejpam-4610	168	5	2n	2n	NUM
ejpam-4610	168	6	.	.	PUNCT
ejpam-4610	169	1	to	to	PART
ejpam-4610	169	2	show	show	VERB
ejpam-4610	169	3	sharpness	sharpness	NOUN
ejpam-4610	169	4	of	of	ADP
ejpam-4610	169	5	the	the	DET
ejpam-4610	169	6	bounds	bound	NOUN
ejpam-4610	169	7	,	,	PUNCT
ejpam-4610	169	8	consider	consider	VERB
ejpam-4610	169	9	g	g	NOUN
ejpam-4610	169	10	=	=	SYM
ejpam-4610	169	11	k2	k2	PROPN
ejpam-4610	169	12	for	for	ADP
ejpam-4610	169	13	the	the	DET
ejpam-4610	169	14	lower	lower	ADV
ejpam-4610	169	15	bound	bind	VERB
ejpam-4610	169	16	and	and	CCONJ
ejpam-4610	169	17	g	g	NOUN
ejpam-4610	169	18	=	=	PROPN
ejpam-4610	169	19	kn	kn	PROPN
ejpam-4610	169	20	for	for	ADP
ejpam-4610	169	21	the	the	DET
ejpam-4610	169	22	upper	upper	ADJ
ejpam-4610	169	23	bound	bind	VERB
ejpam-4610	169	24	.	.	PUNCT
ejpam-4610	170	1	3	3	X
ejpam-4610	170	2	.	.	X
ejpam-4610	170	3	on	on	ADP
ejpam-4610	170	4	some	some	DET
ejpam-4610	170	5	specific	specific	ADJ
ejpam-4610	170	6	graphs	graph	NOUN
ejpam-4610	170	7	proposition	proposition	NOUN
ejpam-4610	170	8	2	2	NUM
ejpam-4610	170	9	.	.	PUNCT
ejpam-4610	170	10	let	let	VERB
ejpam-4610	170	11	g	g	PROPN
ejpam-4610	170	12	=	=	PUNCT
ejpam-4610	170	13	km1,m2,	km1,m2,	PROPN
ejpam-4610	170	14	...	...	PUNCT
ejpam-4610	170	15	,mk	,mk	PUNCT
ejpam-4610	170	16	be	be	AUX
ejpam-4610	170	17	a	a	DET
ejpam-4610	170	18	complete	complete	ADJ
ejpam-4610	170	19	multipartite	multipartite	ADJ
ejpam-4610	170	20	graph	graph	NOUN
ejpam-4610	170	21	such	such	ADJ
ejpam-4610	170	22	that	that	SCONJ
ejpam-4610	170	23	1	1	NUM
ejpam-4610	170	24	≤	≤	NUM
ejpam-4610	170	25	m1	m1	NOUN
ejpam-4610	170	26	≤	≤	NUM
ejpam-4610	170	27	m2	m2	PROPN
ejpam-4610	170	28	≤	≤	PROPN
ejpam-4610	170	29	.	.	PUNCT
ejpam-4610	170	30	.	.	PUNCT
ejpam-4610	170	31	.	.	PUNCT
ejpam-4610	171	1	≤	≤	NUM
ejpam-4610	171	2	mk	mk	PROPN
ejpam-4610	171	3	,	,	PUNCT
ejpam-4610	171	4	and	and	CCONJ
ejpam-4610	171	5	k	k	PROPN
ejpam-4610	171	6	≥	≥	NUM
ejpam-4610	171	7	2	2	NUM
ejpam-4610	171	8	.	.	PUNCT
ejpam-4610	171	9	then	then	ADV
ejpam-4610	171	10	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	171	11	)	)	PUNCT
ejpam-4610	172	1	=	=	SYM
ejpam-4610	172	2	m1	m1	PROPN
ejpam-4610	172	3	+	+	CCONJ
ejpam-4610	172	4	k	k	PROPN
ejpam-4610	173	1	−	−	PROPN
ejpam-4610	173	2	1	1	X
ejpam-4610	173	3	.	.	PUNCT
ejpam-4610	174	1	in	in	ADP
ejpam-4610	174	2	particular	particular	ADJ
ejpam-4610	174	3	,	,	PUNCT
ejpam-4610	174	4	for	for	ADP
ejpam-4610	174	5	m	m	PROPN
ejpam-4610	174	6	,	,	PUNCT
ejpam-4610	174	7	n	n	PRON
ejpam-4610	174	8	≥	≥	NOUN
ejpam-4610	174	9	1	1	NUM
ejpam-4610	174	10	,	,	PUNCT
ejpam-4610	174	11	γ̂h(km	γ̂h(km	PROPN
ejpam-4610	174	12	,	,	PUNCT
ejpam-4610	174	13	n	n	CCONJ
ejpam-4610	174	14	)	)	PUNCT
ejpam-4610	174	15	=	=	SYM
ejpam-4610	174	16	1	1	NUM
ejpam-4610	174	17	+	+	NOUN
ejpam-4610	174	18	min{m	min{m	NOUN
ejpam-4610	174	19	,	,	PUNCT
ejpam-4610	174	20	n	n	CCONJ
ejpam-4610	174	21	}	}	PUNCT
ejpam-4610	174	22	.	.	PUNCT
ejpam-4610	175	1	proof	proof	NOUN
ejpam-4610	175	2	.	.	PUNCT
ejpam-4610	176	1	let	let	VERB
ejpam-4610	176	2	u1	u1	NOUN
ejpam-4610	176	3	,	,	PUNCT
ejpam-4610	176	4	u2	u2	NOUN
ejpam-4610	176	5	,	,	PUNCT
ejpam-4610	176	6	.	.	PUNCT
ejpam-4610	176	7	.	.	PUNCT
ejpam-4610	176	8	.	.	PUNCT
ejpam-4610	177	1	uk	uk	PROPN
ejpam-4610	177	2	be	be	VERB
ejpam-4610	177	3	the	the	DET
ejpam-4610	177	4	partite	partite	ADJ
ejpam-4610	177	5	sets	set	NOUN
ejpam-4610	177	6	ofg	ofg	PROPN
ejpam-4610	177	7	with	with	ADP
ejpam-4610	177	8	|ui|	|ui|	PROPN
ejpam-4610	177	9	=	=	SYM
ejpam-4610	177	10	mi	mi	PROPN
ejpam-4610	177	11	for	for	ADP
ejpam-4610	177	12	each	each	DET
ejpam-4610	177	13	i	i	PRON
ejpam-4610	177	14	∈	∈	PROPN
ejpam-4610	177	15	{	{	PUNCT
ejpam-4610	177	16	1	1	NUM
ejpam-4610	177	17	,	,	PUNCT
ejpam-4610	177	18	2	2	NUM
ejpam-4610	177	19	,	,	PUNCT
ejpam-4610	177	20	.	.	PUNCT
ejpam-4610	177	21	.	.	PUNCT
ejpam-4610	178	1	.	.	PUNCT
ejpam-4610	179	1	,	,	PUNCT
ejpam-4610	179	2	k	k	X
ejpam-4610	179	3	}	}	PUNCT
ejpam-4610	179	4	.	.	PUNCT
ejpam-4610	180	1	then	then	ADV
ejpam-4610	180	2	γh(g	γh(g	NOUN
ejpam-4610	180	3	)	)	PUNCT
ejpam-4610	180	4	=	=	SYM
ejpam-4610	180	5	k	k	NOUN
ejpam-4610	180	6	,	,	PUNCT
ejpam-4610	180	7	and	and	CCONJ
ejpam-4610	180	8	s	s	VERB
ejpam-4610	180	9	⊆	⊆	NUM
ejpam-4610	180	10	v	v	NOUN
ejpam-4610	180	11	(	(	PUNCT
ejpam-4610	180	12	g	g	NOUN
ejpam-4610	180	13	)	)	PUNCT
ejpam-4610	180	14	is	be	AUX
ejpam-4610	180	15	a	a	DET
ejpam-4610	180	16	γh	γh	ADV
ejpam-4610	180	17	-	-	PUNCT
ejpam-4610	180	18	set	set	NOUN
ejpam-4610	180	19	of	of	ADP
ejpam-4610	180	20	g	g	PROPN
ejpam-4610	180	21	if	if	SCONJ
ejpam-4610	181	1	and	and	CCONJ
ejpam-4610	181	2	only	only	ADV
ejpam-4610	181	3	if	if	SCONJ
ejpam-4610	181	4	|s	|s	PROPN
ejpam-4610	181	5	∩	∩	NOUN
ejpam-4610	181	6	ui|	ui|	PROPN
ejpam-4610	181	7	=	=	NOUN
ejpam-4610	181	8	1	1	NUM
ejpam-4610	181	9	for	for	ADP
ejpam-4610	181	10	each	each	DET
ejpam-4610	181	11	i	i	PRON
ejpam-4610	181	12	∈	∈	PROPN
ejpam-4610	181	13	{	{	PUNCT
ejpam-4610	181	14	1	1	NUM
ejpam-4610	181	15	,	,	PUNCT
ejpam-4610	181	16	2	2	NUM
ejpam-4610	181	17	,	,	PUNCT
ejpam-4610	181	18	.	.	PUNCT
ejpam-4610	181	19	.	.	PUNCT
ejpam-4610	182	1	.	.	PUNCT
ejpam-4610	183	1	,	,	PUNCT
ejpam-4610	183	2	k	k	X
ejpam-4610	183	3	}	}	PUNCT
ejpam-4610	183	4	.	.	PUNCT
ejpam-4610	184	1	thus	thus	ADV
ejpam-4610	184	2	,	,	PUNCT
ejpam-4610	184	3	t	t	PROPN
ejpam-4610	184	4	⊆	⊆	NUM
ejpam-4610	184	5	v	v	NOUN
ejpam-4610	184	6	(	(	PUNCT
ejpam-4610	184	7	g	g	NOUN
ejpam-4610	184	8	)	)	PUNCT
ejpam-4610	184	9	is	be	AUX
ejpam-4610	184	10	a	a	DET
ejpam-4610	184	11	thd	thd	NOUN
ejpam-4610	184	12	-	-	PUNCT
ejpam-4610	184	13	set	set	NOUN
ejpam-4610	184	14	of	of	ADP
ejpam-4610	184	15	g	g	PROPN
ejpam-4610	184	16	if	if	SCONJ
ejpam-4610	185	1	and	and	CCONJ
ejpam-4610	185	2	only	only	ADV
ejpam-4610	185	3	if	if	SCONJ
ejpam-4610	185	4	t	t	NOUN
ejpam-4610	185	5	=	=	SYM
ejpam-4610	185	6	ui	ui	NOUN
ejpam-4610	185	7	∪	∪	X
ejpam-4610	185	8	(	(	PUNCT
ejpam-4610	185	9	∪k	∪k	PROPN
ejpam-4610	185	10	j=1;j	j=1;j	PROPN
ejpam-4610	185	11	̸=isj	̸=isj	PROPN
ejpam-4610	185	12	)	)	PUNCT
ejpam-4610	185	13	for	for	ADP
ejpam-4610	185	14	some	some	DET
ejpam-4610	185	15	i	i	PRON
ejpam-4610	185	16	∈	∈	PROPN
ejpam-4610	185	17	{	{	PUNCT
ejpam-4610	185	18	1	1	NUM
ejpam-4610	185	19	,	,	PUNCT
ejpam-4610	185	20	2	2	NUM
ejpam-4610	185	21	,	,	PUNCT
ejpam-4610	185	22	.	.	PUNCT
ejpam-4610	185	23	.	.	PUNCT
ejpam-4610	185	24	.	.	PUNCT
ejpam-4610	186	1	,	,	PUNCT
ejpam-4610	186	2	k	k	X
ejpam-4610	186	3	}	}	PUNCT
ejpam-4610	186	4	and	and	CCONJ
ejpam-4610	186	5	∅	∅	NOUN
ejpam-4610	186	6	̸=	̸=	PROPN
ejpam-4610	186	7	sj	sj	VERB
ejpam-4610	186	8	⊆	⊆	NUM
ejpam-4610	186	9	uj	uj	PROPN
ejpam-4610	186	10	for	for	ADP
ejpam-4610	186	11	all	all	DET
ejpam-4610	186	12	j	j	PROPN
ejpam-4610	186	13	̸=	̸=	PROPN
ejpam-4610	186	14	i.	i.	NOUN
ejpam-4610	186	15	consequently	consequently	ADV
ejpam-4610	186	16	,	,	PUNCT
ejpam-4610	186	17	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	186	18	)	)	PUNCT
ejpam-4610	186	19	=	=	SYM
ejpam-4610	186	20	m1+k−1	m1+k−1	PROPN
ejpam-4610	186	21	.	.	PUNCT
ejpam-4610	187	1	proposition	proposition	NOUN
ejpam-4610	187	2	3	3	NUM
ejpam-4610	187	3	.	.	X
ejpam-4610	188	1	for	for	ADP
ejpam-4610	188	2	a	a	DET
ejpam-4610	188	3	path	path	NOUN
ejpam-4610	188	4	pn	pn	NOUN
ejpam-4610	188	5	on	on	ADP
ejpam-4610	188	6	n	n	PRON
ejpam-4610	188	7	vertices	vertex	NOUN
ejpam-4610	188	8	,	,	PUNCT
ejpam-4610	188	9	γ̂h(pn	γ̂h(pn	NOUN
ejpam-4610	188	10	)	)	PUNCT
ejpam-4610	188	11	=	=	SYM
ejpam-4610	188	12			NUM
ejpam-4610	188	13	2	2	NUM
ejpam-4610	188	14	,	,	PUNCT
ejpam-4610	188	15	if	if	SCONJ
ejpam-4610	188	16	n	n	NOUN
ejpam-4610	188	17	=	=	SYM
ejpam-4610	188	18	3	3	NUM
ejpam-4610	188	19	,	,	PUNCT
ejpam-4610	188	20	5	5	NUM
ejpam-4610	188	21	3	3	NUM
ejpam-4610	188	22	,	,	PUNCT
ejpam-4610	188	23	if	if	SCONJ
ejpam-4610	188	24	n	n	NOUN
ejpam-4610	188	25	=	=	SYM
ejpam-4610	188	26	4	4	NUM
ejpam-4610	188	27	2r	2r	NUM
ejpam-4610	188	28	,	,	PUNCT
ejpam-4610	188	29	if	if	SCONJ
ejpam-4610	188	30	n	n	NOUN
ejpam-4610	188	31	=	=	SYM
ejpam-4610	188	32	6r	6r	NUM
ejpam-4610	188	33	2r	2r	NUM
ejpam-4610	189	1	+	+	CCONJ
ejpam-4610	189	2	1	1	NUM
ejpam-4610	189	3	,	,	PUNCT
ejpam-4610	189	4	if	if	SCONJ
ejpam-4610	189	5	n	n	NOUN
ejpam-4610	189	6	=	=	SYM
ejpam-4610	189	7	6r	6r	NUM
ejpam-4610	189	8	+	+	CCONJ
ejpam-4610	189	9	1	1	NUM
ejpam-4610	189	10	2r	2r	NUM
ejpam-4610	189	11	+	+	CCONJ
ejpam-4610	189	12	2	2	NUM
ejpam-4610	189	13	,	,	PUNCT
ejpam-4610	189	14	if	if	SCONJ
ejpam-4610	189	15	n	n	NOUN
ejpam-4610	189	16	=	=	SYM
ejpam-4610	189	17	6r	6r	NUM
ejpam-4610	190	1	+	+	CCONJ
ejpam-4610	190	2	s	s	NOUN
ejpam-4610	190	3	,	,	PUNCT
ejpam-4610	190	4	s	s	PART
ejpam-4610	190	5	=	=	SYM
ejpam-4610	190	6	2	2	NUM
ejpam-4610	190	7	,	,	PUNCT
ejpam-4610	190	8	3	3	NUM
ejpam-4610	190	9	,	,	PUNCT
ejpam-4610	190	10	4	4	NUM
ejpam-4610	190	11	,	,	PUNCT
ejpam-4610	190	12	5	5	NUM
ejpam-4610	190	13	proof	proof	NOUN
ejpam-4610	190	14	.	.	PUNCT
ejpam-4610	191	1	let	let	VERB
ejpam-4610	191	2	pn	pn	VERB
ejpam-4610	191	3	=	=	PUNCT
ejpam-4610	192	1	[	[	X
ejpam-4610	192	2	v1	v1	NOUN
ejpam-4610	192	3	,	,	PUNCT
ejpam-4610	192	4	v2	v2	NOUN
ejpam-4610	192	5	,	,	PUNCT
ejpam-4610	192	6	.	.	PUNCT
ejpam-4610	192	7	.	.	PUNCT
ejpam-4610	192	8	.	.	PUNCT
ejpam-4610	193	1	,	,	PUNCT
ejpam-4610	193	2	vn	vn	X
ejpam-4610	193	3	]	]	PUNCT
ejpam-4610	193	4	.	.	PUNCT
ejpam-4610	194	1	the	the	DET
ejpam-4610	194	2	case	case	NOUN
ejpam-4610	194	3	where	where	SCONJ
ejpam-4610	194	4	n	n	PROPN
ejpam-4610	194	5	=	=	SYM
ejpam-4610	194	6	3	3	NUM
ejpam-4610	194	7	,	,	PUNCT
ejpam-4610	194	8	4	4	NUM
ejpam-4610	194	9	,	,	PUNCT
ejpam-4610	194	10	5	5	NUM
ejpam-4610	194	11	can	can	AUX
ejpam-4610	194	12	easily	easily	ADV
ejpam-4610	194	13	be	be	AUX
ejpam-4610	194	14	verified	verify	VERB
ejpam-4610	194	15	.	.	PUNCT
ejpam-4610	195	1	let	let	VERB
ejpam-4610	195	2	n	n	PRON
ejpam-4610	195	3	≥	≥	X
ejpam-4610	195	4	6	6	NUM
ejpam-4610	195	5	and	and	CCONJ
ejpam-4610	195	6	let	let	VERB
ejpam-4610	195	7	r	r	NOUN
ejpam-4610	195	8	and	and	CCONJ
ejpam-4610	195	9	s	s	AUX
ejpam-4610	195	10	be	be	AUX
ejpam-4610	195	11	integers	integer	NOUN
ejpam-4610	195	12	for	for	ADP
ejpam-4610	195	13	which	which	PRON
ejpam-4610	195	14	n	n	NOUN
ejpam-4610	195	15	=	=	SYM
ejpam-4610	195	16	6r	6r	NUM
ejpam-4610	196	1	+	+	CCONJ
ejpam-4610	196	2	s	s	VERB
ejpam-4610	196	3	with	with	ADP
ejpam-4610	196	4	0	0	NUM
ejpam-4610	196	5	≤	≤	NUM
ejpam-4610	196	6	s	s	PART
ejpam-4610	196	7	≤	≤	NUM
ejpam-4610	196	8	5	5	NUM
ejpam-4610	196	9	.	.	PUNCT
ejpam-4610	197	1	let	let	VERB
ejpam-4610	197	2	s	s	PRON
ejpam-4610	197	3	=	=	PUNCT
ejpam-4610	197	4	{	{	PUNCT
ejpam-4610	197	5	v3	v3	PROPN
ejpam-4610	197	6	,	,	PUNCT
ejpam-4610	197	7	v4	v4	PROPN
ejpam-4610	197	8	,	,	PUNCT
ejpam-4610	197	9	v9	v9	PROPN
ejpam-4610	197	10	,	,	PUNCT
ejpam-4610	197	11	v10	v10	NOUN
ejpam-4610	197	12	,	,	PUNCT
ejpam-4610	197	13	.	.	PUNCT
ejpam-4610	197	14	.	.	PUNCT
ejpam-4610	198	1	.	.	PUNCT
ejpam-4610	199	1	,	,	PUNCT
ejpam-4610	199	2	v6r−3	v6r−3	PROPN
ejpam-4610	199	3	,	,	PUNCT
ejpam-4610	199	4	v6r−2	v6r−2	PROPN
ejpam-4610	199	5	}	}	PUNCT
ejpam-4610	199	6	.	.	PUNCT
ejpam-4610	200	1	if	if	SCONJ
ejpam-4610	200	2	s	s	NOUN
ejpam-4610	200	3	=	=	NOUN
ejpam-4610	200	4	0	0	NUM
ejpam-4610	200	5	,	,	PUNCT
ejpam-4610	200	6	then	then	ADV
ejpam-4610	200	7	s	s	VERB
ejpam-4610	200	8	is	be	AUX
ejpam-4610	200	9	the	the	DET
ejpam-4610	200	10	unique	unique	ADJ
ejpam-4610	200	11	γ̂h	γ̂h	NOUN
ejpam-4610	200	12	-	-	PUNCT
ejpam-4610	200	13	set	set	NOUN
ejpam-4610	200	14	of	of	ADP
ejpam-4610	200	15	pn	pn	PROPN
ejpam-4610	200	16	.	.	PUNCT
ejpam-4610	201	1	in	in	ADP
ejpam-4610	201	2	this	this	DET
ejpam-4610	201	3	case	case	NOUN
ejpam-4610	201	4	,	,	PUNCT
ejpam-4610	201	5	γ̂h(pn	γ̂h(pn	NOUN
ejpam-4610	201	6	)	)	PUNCT
ejpam-4610	201	7	=	=	SYM
ejpam-4610	201	8	γh(pn	γh(pn	X
ejpam-4610	201	9	)	)	PUNCT
ejpam-4610	201	10	=	=	SYM
ejpam-4610	201	11	2r	2r	NUM
ejpam-4610	201	12	.	.	PUNCT
ejpam-4610	202	1	if	if	SCONJ
ejpam-4610	202	2	s	s	NOUN
ejpam-4610	202	3	=	=	SYM
ejpam-4610	202	4	1	1	NUM
ejpam-4610	202	5	,	,	PUNCT
ejpam-4610	202	6	then	then	ADV
ejpam-4610	202	7	every	every	DET
ejpam-4610	202	8	γh	γh	ADV
ejpam-4610	202	9	-	-	PUNCT
ejpam-4610	202	10	set	set	NOUN
ejpam-4610	202	11	contains	contain	VERB
ejpam-4610	202	12	the	the	DET
ejpam-4610	202	13	vertex	vertex	NOUN
ejpam-4610	202	14	v4	v4	NOUN
ejpam-4610	202	15	.	.	PUNCT
ejpam-4610	203	1	thus	thus	ADV
ejpam-4610	203	2	,	,	PUNCT
ejpam-4610	203	3	γ̂h(pn	γ̂h(pn	NOUN
ejpam-4610	203	4	)	)	PUNCT
ejpam-4610	203	5	=	=	SYM
ejpam-4610	203	6	γh(pn	γh(pn	X
ejpam-4610	203	7	)	)	PUNCT
ejpam-4610	203	8	=	=	SYM
ejpam-4610	204	1	2r	2r	NUM
ejpam-4610	205	1	+	+	CCONJ
ejpam-4610	205	2	1	1	X
ejpam-4610	205	3	.	.	PUNCT
ejpam-4610	205	4	suppose	suppose	VERB
ejpam-4610	205	5	that	that	SCONJ
ejpam-4610	205	6	s	s	VERB
ejpam-4610	205	7	∈	∈	PROPN
ejpam-4610	205	8	{	{	PUNCT
ejpam-4610	205	9	2	2	NUM
ejpam-4610	205	10	,	,	PUNCT
ejpam-4610	205	11	3	3	NUM
ejpam-4610	205	12	,	,	PUNCT
ejpam-4610	205	13	4	4	NUM
ejpam-4610	205	14	,	,	PUNCT
ejpam-4610	205	15	5	5	NUM
ejpam-4610	205	16	}	}	PUNCT
ejpam-4610	205	17	.	.	PUNCT
ejpam-4610	206	1	then	then	ADV
ejpam-4610	206	2	t	t	PROPN
ejpam-4610	206	3	=	=	SYM
ejpam-4610	206	4	s	s	PART
ejpam-4610	206	5	∪	∪	X
ejpam-4610	206	6	{	{	PUNCT
ejpam-4610	206	7	vn−2	vn−2	PROPN
ejpam-4610	206	8	,	,	PUNCT
ejpam-4610	206	9	vn−1	vn−1	ADJ
ejpam-4610	206	10	}	}	PUNCT
ejpam-4610	206	11	is	be	AUX
ejpam-4610	206	12	a	a	DET
ejpam-4610	206	13	γ̂h	γ̂h	NOUN
ejpam-4610	206	14	-	-	PUNCT
ejpam-4610	206	15	set	set	NOUN
ejpam-4610	206	16	of	of	ADP
ejpam-4610	206	17	pn	pn	PROPN
ejpam-4610	206	18	.	.	PUNCT
ejpam-4610	207	1	thus	thus	ADV
ejpam-4610	207	2	,	,	PUNCT
ejpam-4610	207	3	γ̂h(pn	γ̂h(pn	NOUN
ejpam-4610	207	4	)	)	PUNCT
ejpam-4610	207	5	=	=	VERB
ejpam-4610	207	6	|t	|t	VERB
ejpam-4610	208	1	|	|	ADV
ejpam-4610	208	2	=	=	SYM
ejpam-4610	208	3	2r	2r	NUM
ejpam-4610	209	1	+	+	CCONJ
ejpam-4610	209	2	2	2	X
ejpam-4610	209	3	.	.	X
ejpam-4610	209	4	m.a	m.a	PROPN
ejpam-4610	209	5	.	.	PROPN
ejpam-4610	209	6	bonsocan	bonsocan	PROPN
ejpam-4610	209	7	,	,	PUNCT
ejpam-4610	209	8	f.	f.	PROPN
ejpam-4610	209	9	jamil	jamil	PROPN
ejpam-4610	209	10	/	/	SYM
ejpam-4610	209	11	eur	eur	PROPN
ejpam-4610	209	12	.	.	PUNCT
ejpam-4610	210	1	j.	j.	PROPN
ejpam-4610	210	2	pure	pure	PROPN
ejpam-4610	210	3	appl	appl	PROPN
ejpam-4610	210	4	.	.	PROPN
ejpam-4610	210	5	math	math	PROPN
ejpam-4610	210	6	,	,	PUNCT
ejpam-4610	210	7	16	16	NUM
ejpam-4610	210	8	(	(	PUNCT
ejpam-4610	210	9	1	1	NUM
ejpam-4610	210	10	)	)	PUNCT
ejpam-4610	210	11	(	(	PUNCT
ejpam-4610	210	12	2023	2023	NUM
ejpam-4610	210	13	)	)	PUNCT
ejpam-4610	210	14	,	,	PUNCT
ejpam-4610	210	15	192	192	NUM
ejpam-4610	210	16	-	-	SYM
ejpam-4610	210	17	206	206	NUM
ejpam-4610	210	18	197	197	NUM
ejpam-4610	210	19	proposition	proposition	NOUN
ejpam-4610	210	20	4	4	NUM
ejpam-4610	210	21	.	.	PUNCT
ejpam-4610	211	1	for	for	ADP
ejpam-4610	211	2	a	a	DET
ejpam-4610	211	3	cycle	cycle	NOUN
ejpam-4610	211	4	cn	cn	NOUN
ejpam-4610	211	5	of	of	ADP
ejpam-4610	211	6	length	length	NOUN
ejpam-4610	211	7	n	n	CCONJ
ejpam-4610	211	8	,	,	PUNCT
ejpam-4610	211	9	γ̂h(cn	γ̂h(cn	NOUN
ejpam-4610	211	10	)	)	PUNCT
ejpam-4610	211	11	=	=	SYM
ejpam-4610	211	12			NOUN
ejpam-4610	211	13	3	3	NUM
ejpam-4610	211	14	,	,	PUNCT
ejpam-4610	211	15	if	if	SCONJ
ejpam-4610	211	16	n	n	NOUN
ejpam-4610	211	17	=	=	SYM
ejpam-4610	211	18	4	4	NUM
ejpam-4610	211	19	,	,	PUNCT
ejpam-4610	211	20	5	5	NUM
ejpam-4610	211	21	2r	2r	NUM
ejpam-4610	211	22	+	+	CCONJ
ejpam-4610	211	23	2	2	NUM
ejpam-4610	211	24	,	,	PUNCT
ejpam-4610	211	25	if	if	SCONJ
ejpam-4610	211	26	n	n	NOUN
ejpam-4610	211	27	=	=	SYM
ejpam-4610	211	28	6r	6r	NUM
ejpam-4610	211	29	,	,	PUNCT
ejpam-4610	211	30	6r	6r	NUM
ejpam-4610	211	31	+	+	CCONJ
ejpam-4610	211	32	1	1	NUM
ejpam-4610	211	33	2r	2r	NUM
ejpam-4610	211	34	+	+	CCONJ
ejpam-4610	211	35	3	3	NUM
ejpam-4610	211	36	,	,	PUNCT
ejpam-4610	211	37	if	if	SCONJ
ejpam-4610	211	38	n	n	NOUN
ejpam-4610	211	39	=	=	SYM
ejpam-4610	211	40	6r	6r	NUM
ejpam-4610	211	41	+	+	CCONJ
ejpam-4610	211	42	s	s	NOUN
ejpam-4610	211	43	,	,	PUNCT
ejpam-4610	211	44	s	s	PART
ejpam-4610	211	45	=	=	SYM
ejpam-4610	211	46	2	2	NUM
ejpam-4610	211	47	,	,	PUNCT
ejpam-4610	211	48	3	3	NUM
ejpam-4610	211	49	,	,	PUNCT
ejpam-4610	211	50	4	4	NUM
ejpam-4610	211	51	,	,	PUNCT
ejpam-4610	211	52	5	5	NUM
ejpam-4610	211	53	proof	proof	NOUN
ejpam-4610	211	54	.	.	PUNCT
ejpam-4610	212	1	let	let	VERB
ejpam-4610	212	2	cn	cn	PROPN
ejpam-4610	212	3	=	=	PUNCT
ejpam-4610	213	1	[	[	X
ejpam-4610	213	2	v1	v1	NOUN
ejpam-4610	213	3	,	,	PUNCT
ejpam-4610	213	4	v2	v2	NOUN
ejpam-4610	213	5	,	,	PUNCT
ejpam-4610	213	6	.	.	PUNCT
ejpam-4610	213	7	.	.	PUNCT
ejpam-4610	213	8	.	.	PUNCT
ejpam-4610	214	1	,	,	PUNCT
ejpam-4610	214	2	vn	vn	X
ejpam-4610	214	3	,	,	PUNCT
ejpam-4610	214	4	v1	v1	PROPN
ejpam-4610	214	5	]	]	PUNCT
ejpam-4610	214	6	.	.	PUNCT
ejpam-4610	215	1	the	the	DET
ejpam-4610	215	2	case	case	NOUN
ejpam-4610	215	3	where	where	SCONJ
ejpam-4610	215	4	n	n	NOUN
ejpam-4610	215	5	=	=	SYM
ejpam-4610	215	6	4	4	NUM
ejpam-4610	215	7	,	,	PUNCT
ejpam-4610	215	8	5	5	NUM
ejpam-4610	215	9	can	can	AUX
ejpam-4610	215	10	easily	easily	ADV
ejpam-4610	215	11	be	be	AUX
ejpam-4610	215	12	verified	verify	VERB
ejpam-4610	215	13	.	.	PUNCT
ejpam-4610	216	1	let	let	VERB
ejpam-4610	216	2	n	n	PRON
ejpam-4610	216	3	≥	≥	X
ejpam-4610	216	4	6	6	NUM
ejpam-4610	216	5	and	and	CCONJ
ejpam-4610	216	6	write	write	VERB
ejpam-4610	216	7	n	n	PRON
ejpam-4610	216	8	=	=	NUM
ejpam-4610	217	1	6r+	6r+	NUM
ejpam-4610	217	2	s	s	NOUN
ejpam-4610	217	3	where	where	SCONJ
ejpam-4610	217	4	0	0	NUM
ejpam-4610	217	5	≤	≤	NOUN
ejpam-4610	217	6	s	s	PART
ejpam-4610	217	7	≤	≤	NOUN
ejpam-4610	217	8	5	5	NUM
ejpam-4610	217	9	.	.	PUNCT
ejpam-4610	218	1	let	let	VERB
ejpam-4610	218	2	s	s	PRON
ejpam-4610	218	3	=	=	PUNCT
ejpam-4610	218	4	{	{	PUNCT
ejpam-4610	218	5	v3	v3	PROPN
ejpam-4610	218	6	,	,	PUNCT
ejpam-4610	218	7	v4	v4	PROPN
ejpam-4610	218	8	,	,	PUNCT
ejpam-4610	218	9	.	.	PUNCT
ejpam-4610	218	10	.	.	PUNCT
ejpam-4610	219	1	.	.	PUNCT
ejpam-4610	220	1	,	,	PUNCT
ejpam-4610	220	2	v6r−3	v6r−3	PROPN
ejpam-4610	220	3	,	,	PUNCT
ejpam-4610	220	4	v6r−2	v6r−2	PROPN
ejpam-4610	220	5	}	}	PUNCT
ejpam-4610	220	6	.	.	PUNCT
ejpam-4610	221	1	then	then	ADV
ejpam-4610	221	2	s	s	VERB
ejpam-4610	221	3	∪	∪	ADJ
ejpam-4610	221	4	{	{	PUNCT
ejpam-4610	221	5	vn−4	vn−4	NOUN
ejpam-4610	221	6	,	,	PUNCT
ejpam-4610	221	7	vn	vn	NOUN
ejpam-4610	221	8	}	}	PUNCT
ejpam-4610	221	9	,	,	PUNCT
ejpam-4610	221	10	s∪{vn−2	s∪{vn−2	PROPN
ejpam-4610	221	11	,	,	PUNCT
ejpam-4610	221	12	vn	vn	NOUN
ejpam-4610	221	13	}	}	PUNCT
ejpam-4610	221	14	,	,	PUNCT
ejpam-4610	221	15	s∪{vn−2	s∪{vn−2	PROPN
ejpam-4610	221	16	,	,	PUNCT
ejpam-4610	221	17	vn−1	vn−1	ADJ
ejpam-4610	221	18	,	,	PUNCT
ejpam-4610	221	19	vn	vn	NOUN
ejpam-4610	221	20	}	}	PUNCT
ejpam-4610	221	21	,	,	PUNCT
ejpam-4610	221	22	s∪{vn−3	s∪{vn−3	ADJ
ejpam-4610	221	23	,	,	PUNCT
ejpam-4610	221	24	vn−1	vn−1	ADJ
ejpam-4610	221	25	,	,	PUNCT
ejpam-4610	221	26	vn	vn	NOUN
ejpam-4610	221	27	}	}	PUNCT
ejpam-4610	221	28	,	,	PUNCT
ejpam-4610	221	29	s∪{vn−4	s∪{vn−4	NOUN
ejpam-4610	221	30	,	,	PUNCT
ejpam-4610	221	31	vn−3	vn−3	PROPN
ejpam-4610	221	32	,	,	PUNCT
ejpam-4610	221	33	vn−2	vn−2	PROPN
ejpam-4610	221	34	}	}	PUNCT
ejpam-4610	221	35	and	and	CCONJ
ejpam-4610	221	36	s	s	VERB
ejpam-4610	221	37	∪	∪	X
ejpam-4610	221	38	{	{	PUNCT
ejpam-4610	221	39	vn−5	vn−5	NOUN
ejpam-4610	221	40	,	,	PUNCT
ejpam-4610	221	41	vn−3	vn−3	PROPN
ejpam-4610	221	42	,	,	PUNCT
ejpam-4610	221	43	vn−2	vn−2	PROPN
ejpam-4610	221	44	}	}	PUNCT
ejpam-4610	221	45	are	be	AUX
ejpam-4610	221	46	γ̂h	γ̂h	NOUN
ejpam-4610	221	47	-	-	PUNCT
ejpam-4610	221	48	sets	set	NOUN
ejpam-4610	221	49	of	of	ADP
ejpam-4610	221	50	cn	cn	PROPN
ejpam-4610	221	51	provided	provide	VERB
ejpam-4610	221	52	s	s	NOUN
ejpam-4610	221	53	=	=	SYM
ejpam-4610	221	54	0	0	NUM
ejpam-4610	221	55	,	,	PUNCT
ejpam-4610	221	56	s	s	PART
ejpam-4610	221	57	=	=	SYM
ejpam-4610	221	58	1	1	NUM
ejpam-4610	221	59	,	,	PUNCT
ejpam-4610	221	60	s	s	PART
ejpam-4610	221	61	=	=	SYM
ejpam-4610	221	62	2	2	NUM
ejpam-4610	221	63	,	,	PUNCT
ejpam-4610	221	64	s	s	PART
ejpam-4610	221	65	=	=	SYM
ejpam-4610	221	66	3	3	NUM
ejpam-4610	221	67	,	,	PUNCT
ejpam-4610	221	68	s	s	PART
ejpam-4610	221	69	=	=	SYM
ejpam-4610	221	70	4	4	NUM
ejpam-4610	221	71	and	and	CCONJ
ejpam-4610	221	72	s	s	NOUN
ejpam-4610	221	73	=	=	SYM
ejpam-4610	221	74	5	5	NUM
ejpam-4610	221	75	,	,	PUNCT
ejpam-4610	221	76	respectively	respectively	ADV
ejpam-4610	221	77	.	.	PUNCT
ejpam-4610	222	1	since	since	SCONJ
ejpam-4610	222	2	|s|	|s|	NOUN
ejpam-4610	222	3	=	=	SYM
ejpam-4610	222	4	2r	2r	NUM
ejpam-4610	222	5	,	,	PUNCT
ejpam-4610	222	6	the	the	DET
ejpam-4610	222	7	result	result	NOUN
ejpam-4610	222	8	follows	follow	VERB
ejpam-4610	222	9	.	.	PUNCT
ejpam-4610	223	1	proposition	proposition	NOUN
ejpam-4610	223	2	5	5	NUM
ejpam-4610	223	3	.	.	PUNCT
ejpam-4610	224	1	let	let	VERB
ejpam-4610	224	2	g	g	NOUN
ejpam-4610	224	3	=	=	PUNCT
ejpam-4610	224	4	km(a1	km(a1	X
ejpam-4610	224	5	,	,	PUNCT
ejpam-4610	224	6	a2	a2	PROPN
ejpam-4610	224	7	,	,	PUNCT
ejpam-4610	224	8	·	·	PUNCT
ejpam-4610	224	9	·	·	PUNCT
ejpam-4610	224	10	·	·	PUNCT
ejpam-4610	224	11	,	,	PUNCT
ejpam-4610	224	12	am	be	AUX
ejpam-4610	224	13	)	)	PUNCT
ejpam-4610	224	14	be	be	AUX
ejpam-4610	224	15	a	a	DET
ejpam-4610	224	16	multi	multi	ADJ
ejpam-4610	224	17	-	-	ADJ
ejpam-4610	224	18	star	star	ADJ
ejpam-4610	224	19	graph	graph	NOUN
ejpam-4610	224	20	.	.	PUNCT
ejpam-4610	225	1	then	then	ADV
ejpam-4610	225	2	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	225	3	)	)	PUNCT
ejpam-4610	226	1	=	=	PUNCT
ejpam-4610	226	2	m	m	VERB
ejpam-4610	226	3	for	for	ADP
ejpam-4610	226	4	m	m	PROPN
ejpam-4610	226	5	≥	≥	NOUN
ejpam-4610	226	6	2	2	NUM
ejpam-4610	226	7	.	.	PUNCT
ejpam-4610	227	1	proof	proof	NOUN
ejpam-4610	227	2	.	.	PUNCT
ejpam-4610	228	1	let	let	VERB
ejpam-4610	228	2	v	v	NOUN
ejpam-4610	228	3	(	(	PUNCT
ejpam-4610	228	4	km	km	NOUN
ejpam-4610	228	5	)	)	PUNCT
ejpam-4610	228	6	=	=	PRON
ejpam-4610	228	7	{	{	PUNCT
ejpam-4610	228	8	v1	v1	PROPN
ejpam-4610	228	9	,	,	PUNCT
ejpam-4610	228	10	v2	v2	PROPN
ejpam-4610	228	11	,	,	PUNCT
ejpam-4610	228	12	.	.	PUNCT
ejpam-4610	228	13	.	.	PUNCT
ejpam-4610	229	1	.	.	PUNCT
ejpam-4610	230	1	,	,	PUNCT
ejpam-4610	230	2	vm	vm	NOUN
ejpam-4610	230	3	}	}	PUNCT
ejpam-4610	230	4	and	and	CCONJ
ejpam-4610	230	5	for	for	ADP
ejpam-4610	230	6	each	each	DET
ejpam-4610	230	7	i	i	NOUN
ejpam-4610	230	8	=	=	NOUN
ejpam-4610	230	9	1	1	NUM
ejpam-4610	230	10	,	,	PUNCT
ejpam-4610	230	11	2	2	NUM
ejpam-4610	230	12	,	,	PUNCT
ejpam-4610	230	13	3	3	NUM
ejpam-4610	230	14	.	.	PUNCT
ejpam-4610	230	15	.	.	PUNCT
ejpam-4610	231	1	.	.	PUNCT
ejpam-4610	232	1	,	,	PUNCT
ejpam-4610	232	2	m	m	VERB
ejpam-4610	232	3	,	,	PUNCT
ejpam-4610	232	4	let	let	VERB
ejpam-4610	233	1	vix	vix	PROPN
ejpam-4610	234	1	i	i	PRON
ejpam-4610	234	2	j	j	PROPN
ejpam-4610	234	3	(	(	PUNCT
ejpam-4610	234	4	j	j	PROPN
ejpam-4610	234	5	=	=	SYM
ejpam-4610	234	6	1	1	NUM
ejpam-4610	234	7	,	,	PUNCT
ejpam-4610	234	8	2	2	NUM
ejpam-4610	234	9	,	,	PUNCT
ejpam-4610	234	10	.	.	PUNCT
ejpam-4610	234	11	.	.	PUNCT
ejpam-4610	235	1	.	.	PUNCT
ejpam-4610	236	1	,	,	PUNCT
ejpam-4610	236	2	ai	ai	AUX
ejpam-4610	236	3	)	)	PUNCT
ejpam-4610	236	4	be	be	AUX
ejpam-4610	236	5	the	the	DET
ejpam-4610	236	6	pendant	pendant	ADJ
ejpam-4610	236	7	edges	edge	NOUN
ejpam-4610	236	8	joined	join	VERB
ejpam-4610	236	9	with	with	ADP
ejpam-4610	236	10	vi	vi	PROPN
ejpam-4610	236	11	(	(	PUNCT
ejpam-4610	236	12	figure	figure	NOUN
ejpam-4610	236	13	1	1	NUM
ejpam-4610	236	14	shows	show	VERB
ejpam-4610	236	15	the	the	DET
ejpam-4610	236	16	particular	particular	ADJ
ejpam-4610	236	17	g	g	NOUN
ejpam-4610	236	18	with	with	ADP
ejpam-4610	236	19	m	m	PROPN
ejpam-4610	236	20	=	=	NOUN
ejpam-4610	236	21	4	4	NUM
ejpam-4610	236	22	)	)	PUNCT
ejpam-4610	236	23	.	.	PUNCT
ejpam-4610	237	1	then	then	ADV
ejpam-4610	237	2	the	the	DET
ejpam-4610	237	3	γh	γh	NOUN
ejpam-4610	237	4	-	-	PUNCT
ejpam-4610	237	5	sets	set	NOUN
ejpam-4610	237	6	of	of	ADP
ejpam-4610	237	7	g	g	NOUN
ejpam-4610	237	8	are	be	AUX
ejpam-4610	237	9	of	of	ADP
ejpam-4610	237	10	the	the	DET
ejpam-4610	237	11	form	form	NOUN
ejpam-4610	237	12	{	{	PUNCT
ejpam-4610	237	13	vi	vi	PROPN
ejpam-4610	237	14	,	,	PUNCT
ejpam-4610	237	15	xij	xij	NOUN
ejpam-4610	237	16	}	}	PUNCT
ejpam-4610	237	17	.	.	PUNCT
ejpam-4610	238	1	hence	hence	ADV
ejpam-4610	238	2	g	g	PROPN
ejpam-4610	238	3	has	have	VERB
ejpam-4610	238	4	a	a	DET
ejpam-4610	238	5	unique	unique	ADJ
ejpam-4610	238	6	γ̂h	γ̂h	NOUN
ejpam-4610	238	7	-	-	PUNCT
ejpam-4610	238	8	set	set	NOUN
ejpam-4610	238	9	,	,	PUNCT
ejpam-4610	238	10	....................................	....................................	PUNCT
ejpam-4610	238	11	....................................	....................................	PUNCT
ejpam-4610	238	12	....................................	....................................	PUNCT
ejpam-4610	239	1	....................................	....................................	PUNCT
ejpam-4610	239	2	....................................	....................................	PUNCT
ejpam-4610	240	1	....................................	....................................	PUNCT
ejpam-4610	240	2	....................................	....................................	PUNCT
ejpam-4610	241	1	....................................	....................................	PUNCT
ejpam-4610	241	2	....................................	....................................	PUNCT
ejpam-4610	242	1	....................................	....................................	PUNCT
ejpam-4610	242	2	....................................	....................................	PUNCT
ejpam-4610	243	1	....................................	....................................	PUNCT
ejpam-4610	243	2	....................................	....................................	PUNCT
ejpam-4610	244	1	....................................	....................................	PUNCT
ejpam-4610	244	2	....................................	....................................	PUNCT
ejpam-4610	245	1	....................................	....................................	PUNCT
ejpam-4610	245	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	246	1	.........	.........	PUNCT
ejpam-4610	246	2	........	........	PUNCT
ejpam-4610	246	3	........	........	PUNCT
ejpam-4610	246	4	........	........	PUNCT
ejpam-4610	246	5	........	........	PUNCT
ejpam-4610	246	6	........	........	PUNCT
ejpam-4610	246	7	........	........	PUNCT
ejpam-4610	246	8	........	........	PUNCT
ejpam-4610	246	9	........	........	PUNCT
ejpam-4610	246	10	........	........	PUNCT
ejpam-4610	246	11	........	........	PUNCT
ejpam-4610	246	12	........	........	PUNCT
ejpam-4610	246	13	........	........	PUNCT
ejpam-4610	246	14	........	........	PUNCT
ejpam-4610	247	1	........	........	PUNCT
ejpam-4610	247	2	........	........	PUNCT
ejpam-4610	248	1	.................................................................................................................................................................................................................	.................................................................................................................................................................................................................	PROPN
ejpam-4610	248	2	...........	...........	PUNCT
ejpam-4610	248	3	...........	...........	PUNCT
ejpam-4610	248	4	...........	...........	PUNCT
ejpam-4610	248	5	...........	...........	PUNCT
ejpam-4610	248	6	...........	...........	PUNCT
ejpam-4610	248	7	...........	...........	PUNCT
ejpam-4610	248	8	...........	...........	PUNCT
ejpam-4610	248	9	...........	...........	PUNCT
ejpam-4610	248	10	...........	...........	PUNCT
ejpam-4610	248	11	...........	...........	PUNCT
ejpam-4610	248	12	...........	...........	PUNCT
ejpam-4610	248	13	...........	...........	PUNCT
ejpam-4610	248	14	...........	...........	PUNCT
ejpam-4610	248	15	...........	...........	PUNCT
ejpam-4610	248	16	...........	...........	PUNCT
ejpam-4610	248	17	...........	...........	PUNCT
ejpam-4610	248	18	.....	.....	PUNCT
ejpam-4610	248	19	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	248	20	....	....	PUNCT
ejpam-4610	248	21	........	........	PUNCT
ejpam-4610	248	22	........	........	PUNCT
ejpam-4610	248	23	........	........	PUNCT
ejpam-4610	248	24	........	........	PUNCT
ejpam-4610	248	25	........	........	PUNCT
ejpam-4610	248	26	........	........	PUNCT
ejpam-4610	248	27	........	........	PUNCT
ejpam-4610	248	28	........	........	PUNCT
ejpam-4610	248	29	........	........	PUNCT
ejpam-4610	248	30	........	........	PUNCT
ejpam-4610	248	31	........	........	PUNCT
ejpam-4610	248	32	........	........	PUNCT
ejpam-4610	248	33	........	........	PUNCT
ejpam-4610	248	34	........	........	PUNCT
ejpam-4610	248	35	........	........	PUNCT
ejpam-4610	248	36	........	........	PUNCT
ejpam-4610	249	1	.............................................................................	.............................................................................	PUNCT
ejpam-4610	249	2	...................................................................	...................................................................	PUNCT
ejpam-4610	249	3	.......	.......	PUNCT
ejpam-4610	249	4	........	........	PUNCT
ejpam-4610	249	5	........	........	PUNCT
ejpam-4610	249	6	........	........	PUNCT
ejpam-4610	249	7	........	........	PUNCT
ejpam-4610	249	8	........	........	PUNCT
ejpam-4610	249	9	........	........	PUNCT
ejpam-4610	249	10	........	........	PUNCT
ejpam-4610	249	11	.......................................................................................	.......................................................................................	PUNCT
ejpam-4610	250	1	..........	..........	PUNCT
ejpam-4610	250	2	..........	..........	PUNCT
ejpam-4610	251	1	..........	..........	PUNCT
ejpam-4610	251	2	..........	..........	PUNCT
ejpam-4610	252	1	..........	..........	PUNCT
ejpam-4610	252	2	.	.	PUNCT
ejpam-4610	253	1	...............................................................	...............................................................	PUNCT
ejpam-4610	253	2	.....................................................................................................................................................	.....................................................................................................................................................	PUNCT
ejpam-4610	254	1	.........	.........	PUNCT
ejpam-4610	254	2	........	........	PUNCT
ejpam-4610	254	3	........	........	PUNCT
ejpam-4610	254	4	........	........	PUNCT
ejpam-4610	254	5	........	........	PUNCT
ejpam-4610	255	1	........	........	PUNCT
ejpam-4610	255	2	........	........	PUNCT
ejpam-4610	256	1	......	......	PUNCT
ejpam-4610	256	2	............................................................................	............................................................................	PUNCT
ejpam-4610	257	1	.................	.................	PUNCT
ejpam-4610	257	2	................	................	PUNCT
ejpam-4610	258	1	................	................	PUNCT
ejpam-4610	258	2	................	................	PUNCT
ejpam-4610	258	3	........	........	PUNCT
ejpam-4610	258	4	...............................................................	...............................................................	PUNCT
ejpam-4610	259	1	v1	v1	VERB
ejpam-4610	259	2	v2	v2	PROPN
ejpam-4610	260	1	v3v4	v3v4	X
ejpam-4610	260	2	x11	x11	NOUN
ejpam-4610	260	3	x12	x12	NUM
ejpam-4610	260	4	.	.	PUNCT
ejpam-4610	260	5	.	.	PUNCT
ejpam-4610	260	6	.	.	PUNCT
ejpam-4610	261	1	x1a1	x1a1	PROPN
ejpam-4610	262	1	x21	x21	NUM
ejpam-4610	262	2	x22	x22	PROPN
ejpam-4610	262	3	.	.	PUNCT
ejpam-4610	262	4	.	.	PUNCT
ejpam-4610	262	5	.	.	PUNCT
ejpam-4610	263	1	x2a2	x2a2	PROPN
ejpam-4610	263	2	x31	x31	NUM
ejpam-4610	263	3	x32	x32	PROPN
ejpam-4610	263	4	.	.	PUNCT
ejpam-4610	263	5	.	.	PUNCT
ejpam-4610	263	6	.	.	PUNCT
ejpam-4610	264	1	x3a3	x3a3	PROPN
ejpam-4610	264	2	x41	x41	PROPN
ejpam-4610	264	3	x42	x42	PROPN
ejpam-4610	264	4	.	.	PUNCT
ejpam-4610	264	5	.	.	PUNCT
ejpam-4610	264	6	.	.	PUNCT
ejpam-4610	265	1	x4a4	x4a4	PUNCT
ejpam-4610	265	2	figure	figure	VERB
ejpam-4610	265	3	1	1	NUM
ejpam-4610	265	4	:	:	PUNCT
ejpam-4610	265	5	multi	multi	ADJ
ejpam-4610	265	6	-	-	ADJ
ejpam-4610	265	7	star	star	ADJ
ejpam-4610	265	8	k4(a1	k4(a1	PROPN
ejpam-4610	265	9	,	,	PUNCT
ejpam-4610	265	10	a2	a2	PROPN
ejpam-4610	265	11	,	,	PUNCT
ejpam-4610	265	12	a3	a3	NOUN
ejpam-4610	265	13	,	,	PUNCT
ejpam-4610	265	14	a4	a4	NOUN
ejpam-4610	265	15	)	)	PUNCT
ejpam-4610	265	16	namely	namely	ADV
ejpam-4610	265	17	,	,	PUNCT
ejpam-4610	265	18	the	the	DET
ejpam-4610	265	19	v	v	NOUN
ejpam-4610	265	20	(	(	PUNCT
ejpam-4610	265	21	km	km	PROPN
ejpam-4610	265	22	)	)	PUNCT
ejpam-4610	265	23	.	.	PUNCT
ejpam-4610	266	1	thus	thus	ADV
ejpam-4610	266	2	,	,	PUNCT
ejpam-4610	266	3	γ̂h(g	γ̂h(g	X
ejpam-4610	266	4	)	)	PUNCT
ejpam-4610	266	5	=	=	SYM
ejpam-4610	266	6	m.	m.	NOUN
ejpam-4610	266	7	proposition	proposition	NOUN
ejpam-4610	266	8	6	6	NUM
ejpam-4610	266	9	.	.	PUNCT
ejpam-4610	266	10	for	for	ADP
ejpam-4610	266	11	the	the	DET
ejpam-4610	266	12	petersen	petersen	PROPN
ejpam-4610	266	13	graph	graph	NOUN
ejpam-4610	266	14	p	p	PROPN
ejpam-4610	266	15	,	,	PUNCT
ejpam-4610	266	16	γ̂h(p	γ̂h(p	PROPN
ejpam-4610	266	17	)	)	PUNCT
ejpam-4610	266	18	=	=	SYM
ejpam-4610	267	1	6	6	X
ejpam-4610	267	2	.	.	PUNCT
ejpam-4610	267	3	proof	proof	NOUN
ejpam-4610	267	4	.	.	PUNCT
ejpam-4610	268	1	let	let	VERB
ejpam-4610	268	2	v	v	X
ejpam-4610	268	3	(	(	PUNCT
ejpam-4610	268	4	p	p	NOUN
ejpam-4610	268	5	)	)	PUNCT
ejpam-4610	268	6	=	=	PUNCT
ejpam-4610	268	7	{	{	PUNCT
ejpam-4610	268	8	x1	x1	PROPN
ejpam-4610	268	9	,	,	PUNCT
ejpam-4610	268	10	x2	x2	PROPN
ejpam-4610	268	11	,	,	PUNCT
ejpam-4610	268	12	x3	x3	PROPN
ejpam-4610	268	13	,	,	PUNCT
ejpam-4610	268	14	x4	x4	PROPN
ejpam-4610	268	15	,	,	PUNCT
ejpam-4610	268	16	x5	x5	PROPN
ejpam-4610	268	17	,	,	PUNCT
ejpam-4610	268	18	y1	y1	NOUN
ejpam-4610	268	19	,	,	PUNCT
ejpam-4610	268	20	y2	y2	PROPN
ejpam-4610	268	21	,	,	PUNCT
ejpam-4610	268	22	y3	y3	PROPN
ejpam-4610	268	23	,	,	PUNCT
ejpam-4610	268	24	y4	y4	NOUN
ejpam-4610	268	25	,	,	PUNCT
ejpam-4610	268	26	y5	y5	PROPN
ejpam-4610	268	27	}	}	PUNCT
ejpam-4610	268	28	where	where	SCONJ
ejpam-4610	268	29	x1	x1	PROPN
ejpam-4610	268	30	,	,	PUNCT
ejpam-4610	268	31	x2	x2	PROPN
ejpam-4610	268	32	,	,	PUNCT
ejpam-4610	268	33	x3	x3	PROPN
ejpam-4610	268	34	,	,	PUNCT
ejpam-4610	268	35	x4	x4	PROPN
ejpam-4610	268	36	,	,	PUNCT
ejpam-4610	268	37	x5	x5	PROPN
ejpam-4610	268	38	are	be	AUX
ejpam-4610	268	39	the	the	DET
ejpam-4610	268	40	vertices	vertex	NOUN
ejpam-4610	268	41	of	of	ADP
ejpam-4610	268	42	the	the	DET
ejpam-4610	268	43	outer	outer	ADJ
ejpam-4610	268	44	cycle	cycle	NOUN
ejpam-4610	268	45	and	and	CCONJ
ejpam-4610	268	46	y1	y1	NOUN
ejpam-4610	268	47	,	,	PUNCT
ejpam-4610	268	48	y2	y2	PROPN
ejpam-4610	268	49	,	,	PUNCT
ejpam-4610	268	50	y3	y3	PROPN
ejpam-4610	268	51	,	,	PUNCT
ejpam-4610	268	52	y4	y4	PROPN
ejpam-4610	268	53	,	,	PUNCT
ejpam-4610	268	54	y5	y5	PROPN
ejpam-4610	268	55	are	be	AUX
ejpam-4610	268	56	the	the	DET
ejpam-4610	268	57	corresponding	corresponding	ADJ
ejpam-4610	268	58	vertices	vertex	NOUN
ejpam-4610	268	59	of	of	ADP
ejpam-4610	268	60	the	the	DET
ejpam-4610	268	61	inner	inner	ADJ
ejpam-4610	268	62	cycle	cycle	NOUN
ejpam-4610	268	63	.	.	PUNCT
ejpam-4610	269	1	then	then	ADV
ejpam-4610	269	2	the	the	DET
ejpam-4610	269	3	γh	γh	NOUN
ejpam-4610	269	4	-	-	PUNCT
ejpam-4610	269	5	sets	set	NOUN
ejpam-4610	269	6	of	of	ADP
ejpam-4610	269	7	p	p	NOUN
ejpam-4610	269	8	are	be	AUX
ejpam-4610	269	9	of	of	ADP
ejpam-4610	269	10	the	the	DET
ejpam-4610	269	11	form	form	NOUN
ejpam-4610	269	12	{	{	PUNCT
ejpam-4610	269	13	xi	xi	PROPN
ejpam-4610	269	14	,	,	PUNCT
ejpam-4610	269	15	yi	yi	NOUN
ejpam-4610	269	16	}	}	PUNCT
ejpam-4610	269	17	where	where	SCONJ
ejpam-4610	269	18	xiyi	xiyi	PROPN
ejpam-4610	269	19	∈	∈	PROPN
ejpam-4610	269	20	e(p	e(p	PROPN
ejpam-4610	269	21	)	)	PUNCT
ejpam-4610	269	22	,	,	PUNCT
ejpam-4610	269	23	{	{	PUNCT
ejpam-4610	269	24	xi	xi	PROPN
ejpam-4610	269	25	,	,	PUNCT
ejpam-4610	269	26	xj	xj	PROPN
ejpam-4610	269	27	}	}	PUNCT
ejpam-4610	269	28	where	where	SCONJ
ejpam-4610	269	29	xixj	xixj	PROPN
ejpam-4610	269	30	∈	∈	PROPN
ejpam-4610	269	31	e(p	e(p	PROPN
ejpam-4610	269	32	)	)	PUNCT
ejpam-4610	269	33	,	,	PUNCT
ejpam-4610	270	1	i	i	PRON
ejpam-4610	270	2	̸=	̸=	PROPN
ejpam-4610	270	3	j	j	PROPN
ejpam-4610	270	4	and	and	CCONJ
ejpam-4610	270	5	{	{	PUNCT
ejpam-4610	270	6	yi	yi	PROPN
ejpam-4610	270	7	,	,	PUNCT
ejpam-4610	270	8	yj	yj	PROPN
ejpam-4610	270	9	}	}	PUNCT
ejpam-4610	270	10	where	where	SCONJ
ejpam-4610	270	11	yiyj	yiyj	NOUN
ejpam-4610	270	12	∈	∈	PROPN
ejpam-4610	270	13	e(p	e(p	PROPN
ejpam-4610	270	14	)	)	PUNCT
ejpam-4610	270	15	,	,	PUNCT
ejpam-4610	270	16	i	i	PRON
ejpam-4610	270	17	̸=	̸=	PROPN
ejpam-4610	270	18	j	j	PROPN
ejpam-4610	270	19	for	for	ADP
ejpam-4610	270	20	all	all	DET
ejpam-4610	270	21	i	i	PROPN
ejpam-4610	270	22	,	,	PUNCT
ejpam-4610	270	23	j	j	PROPN
ejpam-4610	270	24	=	=	SYM
ejpam-4610	270	25	1	1	NUM
ejpam-4610	270	26	,	,	PUNCT
ejpam-4610	270	27	2	2	NUM
ejpam-4610	270	28	,	,	PUNCT
ejpam-4610	270	29	.	.	PUNCT
ejpam-4610	270	30	.	.	PUNCT
ejpam-4610	270	31	.	.	PUNCT
ejpam-4610	271	1	,	,	PUNCT
ejpam-4610	271	2	5	5	X
ejpam-4610	271	3	.	.	PUNCT
ejpam-4610	271	4	thus	thus	ADV
ejpam-4610	271	5	,	,	PUNCT
ejpam-4610	271	6	s	s	VERB
ejpam-4610	271	7	=	=	PUNCT
ejpam-4610	271	8	{	{	PUNCT
ejpam-4610	271	9	xi	xi	PROPN
ejpam-4610	271	10	,	,	PUNCT
ejpam-4610	271	11	xj	xj	PROPN
ejpam-4610	271	12	,	,	PUNCT
ejpam-4610	271	13	xk	xk	PROPN
ejpam-4610	271	14	,	,	PUNCT
ejpam-4610	271	15	yi	yi	PROPN
ejpam-4610	271	16	,	,	PUNCT
ejpam-4610	271	17	yj	yj	PROPN
ejpam-4610	271	18	,	,	PUNCT
ejpam-4610	271	19	yk	yk	PROPN
ejpam-4610	271	20	}	}	PUNCT
ejpam-4610	271	21	is	be	AUX
ejpam-4610	271	22	a	a	DET
ejpam-4610	271	23	γ̂h	γ̂h	NOUN
ejpam-4610	271	24	-	-	PUNCT
ejpam-4610	271	25	set	set	NOUN
ejpam-4610	271	26	of	of	ADP
ejpam-4610	271	27	p	p	NOUN
ejpam-4610	271	28	where	where	SCONJ
ejpam-4610	271	29	xi	xi	PROPN
ejpam-4610	271	30	and	and	CCONJ
ejpam-4610	271	31	xj	xj	PROPN
ejpam-4610	271	32	are	be	AUX
ejpam-4610	271	33	adjacent	adjacent	ADJ
ejpam-4610	271	34	in	in	ADP
ejpam-4610	271	35	p	p	PROPN
ejpam-4610	271	36	and	and	CCONJ
ejpam-4610	271	37	the	the	DET
ejpam-4610	271	38	vertex	vertex	NOUN
ejpam-4610	271	39	xk	xk	PROPN
ejpam-4610	271	40	/∈	/∈	PUNCT
ejpam-4610	272	1	np	np	INTJ
ejpam-4610	272	2	(	(	PUNCT
ejpam-4610	272	3	xi)∪np	xi)∪np	PROPN
ejpam-4610	272	4	(	(	PUNCT
ejpam-4610	272	5	xj	xj	PROPN
ejpam-4610	272	6	)	)	PUNCT
ejpam-4610	272	7	and	and	CCONJ
ejpam-4610	272	8	yk	yk	PROPN
ejpam-4610	272	9	is	be	AUX
ejpam-4610	272	10	adjacent	adjacent	ADJ
ejpam-4610	272	11	to	to	ADP
ejpam-4610	272	12	the	the	DET
ejpam-4610	272	13	vertex	vertex	NOUN
ejpam-4610	272	14	xk	xk	PROPN
ejpam-4610	272	15	in	in	ADP
ejpam-4610	272	16	p	p	PROPN
ejpam-4610	272	17	and	and	CCONJ
ejpam-4610	272	18	yi	yi	PROPN
ejpam-4610	272	19	,	,	PUNCT
ejpam-4610	272	20	yj	yj	PROPN
ejpam-4610	272	21	/∈	/∈	PROPN
ejpam-4610	273	1	np	np	INTJ
ejpam-4610	273	2	(	(	PUNCT
ejpam-4610	273	3	xi)∪np	xi)∪np	PROPN
ejpam-4610	273	4	(	(	PUNCT
ejpam-4610	273	5	xj	xj	PROPN
ejpam-4610	273	6	)	)	PUNCT
ejpam-4610	273	7	.	.	PUNCT
ejpam-4610	274	1	therefore	therefore	ADV
ejpam-4610	274	2	,	,	PUNCT
ejpam-4610	274	3	γ̂h(p	γ̂h(p	NOUN
ejpam-4610	274	4	)	)	PUNCT
ejpam-4610	274	5	=	=	SYM
ejpam-4610	274	6	|s|	|s|	NOUN
ejpam-4610	274	7	=	=	SYM
ejpam-4610	274	8	6	6	NUM
ejpam-4610	274	9	.	.	PUNCT
ejpam-4610	275	1	m.a	m.a	PROPN
ejpam-4610	275	2	.	.	PROPN
ejpam-4610	275	3	bonsocan	bonsocan	PROPN
ejpam-4610	275	4	,	,	PUNCT
ejpam-4610	275	5	f.	f.	PROPN
ejpam-4610	275	6	jamil	jamil	PROPN
ejpam-4610	275	7	/	/	SYM
ejpam-4610	275	8	eur	eur	PROPN
ejpam-4610	275	9	.	.	PUNCT
ejpam-4610	276	1	j.	j.	PROPN
ejpam-4610	276	2	pure	pure	PROPN
ejpam-4610	276	3	appl	appl	PROPN
ejpam-4610	276	4	.	.	PROPN
ejpam-4610	276	5	math	math	PROPN
ejpam-4610	276	6	,	,	PUNCT
ejpam-4610	276	7	16	16	NUM
ejpam-4610	276	8	(	(	PUNCT
ejpam-4610	276	9	1	1	NUM
ejpam-4610	276	10	)	)	PUNCT
ejpam-4610	276	11	(	(	PUNCT
ejpam-4610	276	12	2023	2023	NUM
ejpam-4610	276	13	)	)	PUNCT
ejpam-4610	276	14	,	,	PUNCT
ejpam-4610	276	15	192	192	NUM
ejpam-4610	276	16	-	-	SYM
ejpam-4610	276	17	206	206	NUM
ejpam-4610	276	18	198	198	NUM
ejpam-4610	276	19	proposition	proposition	NOUN
ejpam-4610	276	20	7	7	NUM
ejpam-4610	276	21	.	.	PUNCT
ejpam-4610	277	1	let	let	VERB
ejpam-4610	277	2	g	g	PRON
ejpam-4610	277	3	be	be	AUX
ejpam-4610	277	4	a	a	DET
ejpam-4610	277	5	firefly	firefly	NOUN
ejpam-4610	277	6	graph	graph	NOUN
ejpam-4610	277	7	with	with	ADP
ejpam-4610	277	8	t	t	PROPN
ejpam-4610	277	9	≥	≥	NUM
ejpam-4610	277	10	1	1	NUM
ejpam-4610	277	11	pendant	pendant	ADJ
ejpam-4610	277	12	paths	path	NOUN
ejpam-4610	277	13	,	,	PUNCT
ejpam-4610	277	14	s	s	VERB
ejpam-4610	277	15	≥	≥	NOUN
ejpam-4610	277	16	1	1	NUM
ejpam-4610	277	17	triangles	triangle	NOUN
ejpam-4610	277	18	and	and	CCONJ
ejpam-4610	277	19	n−	n−	NOUN
ejpam-4610	277	20	2s−	2s−	NUM
ejpam-4610	277	21	2t−	2t−	NUM
ejpam-4610	277	22	1	1	NUM
ejpam-4610	277	23	≥	≥	NUM
ejpam-4610	277	24	1	1	NUM
ejpam-4610	277	25	pendant	pendant	ADJ
ejpam-4610	277	26	edges	edge	NOUN
ejpam-4610	277	27	.	.	PUNCT
ejpam-4610	278	1	then	then	ADV
ejpam-4610	278	2	,	,	PUNCT
ejpam-4610	278	3	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	278	4	)	)	PUNCT
ejpam-4610	278	5	=	=	SYM
ejpam-4610	279	1	2	2	X
ejpam-4610	279	2	.	.	X
ejpam-4610	279	3	proof	proof	NOUN
ejpam-4610	279	4	.	.	PUNCT
ejpam-4610	280	1	let	let	VERB
ejpam-4610	280	2	g	g	PRON
ejpam-4610	280	3	be	be	AUX
ejpam-4610	280	4	a	a	DET
ejpam-4610	280	5	firefly	firefly	NOUN
ejpam-4610	280	6	graph	graph	NOUN
ejpam-4610	280	7	as	as	SCONJ
ejpam-4610	280	8	shown	show	VERB
ejpam-4610	280	9	in	in	ADP
ejpam-4610	280	10	figure	figure	NOUN
ejpam-4610	280	11	2	2	NUM
ejpam-4610	280	12	,	,	PUNCT
ejpam-4610	280	13	where	where	SCONJ
ejpam-4610	280	14	a	a	PRON
ejpam-4610	280	15	is	be	AUX
ejpam-4610	280	16	the	the	DET
ejpam-4610	280	17	vertex	vertex	NOUN
ejpam-4610	280	18	common	common	ADJ
ejpam-4610	280	19	to	to	ADP
ejpam-4610	280	20	the	the	DET
ejpam-4610	280	21	triangles	triangle	NOUN
ejpam-4610	281	1	[	[	X
ejpam-4610	281	2	a	a	X
ejpam-4610	281	3	,	,	PUNCT
ejpam-4610	281	4	a2k−1	a2k−1	PROPN
ejpam-4610	281	5	,	,	PUNCT
ejpam-4610	281	6	a2k	a2k	PROPN
ejpam-4610	281	7	,	,	PUNCT
ejpam-4610	281	8	a	a	PRON
ejpam-4610	281	9	]	]	X
ejpam-4610	281	10	(	(	PUNCT
ejpam-4610	281	11	k	k	NOUN
ejpam-4610	281	12	=	=	SYM
ejpam-4610	281	13	1	1	NUM
ejpam-4610	281	14	,	,	PUNCT
ejpam-4610	281	15	2	2	NUM
ejpam-4610	281	16	,	,	PUNCT
ejpam-4610	281	17	.	.	PUNCT
ejpam-4610	281	18	.	.	PUNCT
ejpam-4610	281	19	.	.	PUNCT
ejpam-4610	281	20	,	,	PUNCT
ejpam-4610	281	21	s	s	X
ejpam-4610	281	22	)	)	PUNCT
ejpam-4610	281	23	,	,	PUNCT
ejpam-4610	281	24	pendant	pendant	ADJ
ejpam-4610	281	25	edges	edge	NOUN
ejpam-4610	282	1	[	[	X
ejpam-4610	282	2	a	a	X
ejpam-4610	282	3	,	,	PUNCT
ejpam-4610	282	4	wk	wk	PROPN
ejpam-4610	282	5	]	]	PUNCT
ejpam-4610	282	6	(	(	PUNCT
ejpam-4610	282	7	k	k	NOUN
ejpam-4610	282	8	=	=	SYM
ejpam-4610	282	9	1	1	NUM
ejpam-4610	282	10	,	,	PUNCT
ejpam-4610	282	11	2	2	NUM
ejpam-4610	282	12	,	,	PUNCT
ejpam-4610	282	13	.	.	PUNCT
ejpam-4610	282	14	.	.	PUNCT
ejpam-4610	283	1	.	.	PUNCT
ejpam-4610	284	1	,	,	PUNCT
ejpam-4610	284	2	n−2s−	n−2s−	PROPN
ejpam-4610	285	1	2t−	2t−	NOUN
ejpam-4610	285	2	1	1	NUM
ejpam-4610	285	3	)	)	PUNCT
ejpam-4610	285	4	and	and	CCONJ
ejpam-4610	285	5	pendant	pendant	ADJ
ejpam-4610	285	6	paths	path	NOUN
ejpam-4610	286	1	[	[	X
ejpam-4610	286	2	a	a	X
ejpam-4610	286	3	,	,	PUNCT
ejpam-4610	286	4	uk	uk	PROPN
ejpam-4610	286	5	,	,	PUNCT
ejpam-4610	286	6	vk	vk	ADP
ejpam-4610	286	7	]	]	X
ejpam-4610	286	8	(	(	PUNCT
ejpam-4610	286	9	k	k	NOUN
ejpam-4610	286	10	=	=	SYM
ejpam-4610	286	11	1	1	NUM
ejpam-4610	286	12	,	,	PUNCT
ejpam-4610	286	13	2	2	NUM
ejpam-4610	286	14	,	,	PUNCT
ejpam-4610	286	15	.	.	PUNCT
ejpam-4610	286	16	.	.	PUNCT
ejpam-4610	287	1	.	.	PUNCT
ejpam-4610	288	1	,	,	PUNCT
ejpam-4610	288	2	t	t	X
ejpam-4610	288	3	)	)	PUNCT
ejpam-4610	288	4	in	in	ADP
ejpam-4610	288	5	g.	g.	PROPN
ejpam-4610	289	1	if	if	SCONJ
ejpam-4610	289	2	t	t	PROPN
ejpam-4610	289	3	=	=	SYM
ejpam-4610	289	4	1	1	NUM
ejpam-4610	289	5	,	,	PUNCT
ejpam-4610	289	6	then	then	ADV
ejpam-4610	289	7	the	the	DET
ejpam-4610	289	8	γh	γh	NOUN
ejpam-4610	289	9	-	-	PUNCT
ejpam-4610	289	10	sets	set	NOUN
ejpam-4610	289	11	of	of	ADP
ejpam-4610	289	12	g	g	NOUN
ejpam-4610	289	13	are	be	AUX
ejpam-4610	289	14	the	the	DET
ejpam-4610	289	15	sets	set	NOUN
ejpam-4610	289	16	{	{	PUNCT
ejpam-4610	289	17	a	a	DET
ejpam-4610	289	18	,	,	PUNCT
ejpam-4610	289	19	u1	u1	NOUN
ejpam-4610	289	20	}	}	PUNCT
ejpam-4610	289	21	,	,	PUNCT
ejpam-4610	289	22	{	{	PUNCT
ejpam-4610	289	23	u1	u1	NOUN
ejpam-4610	289	24	,	,	PUNCT
ejpam-4610	289	25	v1	v1	NOUN
ejpam-4610	289	26	}	}	PUNCT
ejpam-4610	289	27	and	and	CCONJ
ejpam-4610	289	28	the	the	DET
ejpam-4610	289	29	sets	set	NOUN
ejpam-4610	289	30	of	of	ADP
ejpam-4610	289	31	the	the	DET
ejpam-4610	289	32	form	form	NOUN
ejpam-4610	289	33	{	{	PUNCT
ejpam-4610	289	34	a	a	PRON
ejpam-4610	289	35	,	,	PUNCT
ejpam-4610	289	36	wi	wi	PROPN
ejpam-4610	289	37	}	}	PUNCT
ejpam-4610	289	38	for	for	ADP
ejpam-4610	289	39	i	i	PRON
ejpam-4610	289	40	≥	≥	NOUN
ejpam-4610	289	41	1	1	NUM
ejpam-4610	289	42	.	.	PUNCT
ejpam-4610	290	1	hence	hence	ADV
ejpam-4610	290	2	,	,	PUNCT
ejpam-4610	290	3	{	{	PUNCT
ejpam-4610	290	4	a	a	DET
ejpam-4610	290	5	,	,	PUNCT
ejpam-4610	290	6	u1	u1	NOUN
ejpam-4610	290	7	}	}	PUNCT
ejpam-4610	290	8	is	be	AUX
ejpam-4610	290	9	the	the	DET
ejpam-4610	290	10	unique	unique	ADJ
ejpam-4610	290	11	γ̂h	γ̂h	NOUN
ejpam-4610	290	12	-	-	PUNCT
ejpam-4610	290	13	set	set	NOUN
ejpam-4610	290	14	of	of	ADP
ejpam-4610	290	15	g.	g.	PROPN
ejpam-4610	290	16	therefore	therefore	ADV
ejpam-4610	290	17	,	,	PUNCT
ejpam-4610	290	18	γ̂h(g	γ̂h(g	X
ejpam-4610	290	19	)	)	PUNCT
ejpam-4610	290	20	=	=	SYM
ejpam-4610	290	21	2	2	X
ejpam-4610	290	22	.	.	X
ejpam-4610	290	23	assume	assume	VERB
ejpam-4610	290	24	t	t	PROPN
ejpam-4610	290	25	>	>	X
ejpam-4610	291	1	1	1	X
ejpam-4610	291	2	.	.	PUNCT
ejpam-4610	292	1	then	then	ADV
ejpam-4610	292	2	the	the	DET
ejpam-4610	292	3	γh	γh	NOUN
ejpam-4610	292	4	-	-	PUNCT
ejpam-4610	292	5	sets	set	NOUN
ejpam-4610	292	6	of	of	ADP
ejpam-4610	292	7	g	g	NOUN
ejpam-4610	292	8	are	be	AUX
ejpam-4610	292	9	of	of	ADP
ejpam-4610	292	10	the	the	DET
ejpam-4610	292	11	form	form	NOUN
ejpam-4610	292	12	{	{	PUNCT
ejpam-4610	292	13	a	a	PRON
ejpam-4610	292	14	,	,	PUNCT
ejpam-4610	292	15	wi	wi	PROPN
ejpam-4610	292	16	}	}	PUNCT
ejpam-4610	292	17	and	and	CCONJ
ejpam-4610	292	18	{	{	PUNCT
ejpam-4610	292	19	a	a	X
ejpam-4610	292	20	,	,	PUNCT
ejpam-4610	292	21	ui	ui	NOUN
ejpam-4610	292	22	}	}	PUNCT
ejpam-4610	292	23	for	for	ADP
ejpam-4610	292	24	i	i	PRON
ejpam-4610	292	25	≥	≥	NOUN
ejpam-4610	292	26	1	1	NUM
ejpam-4610	292	27	.	.	PUNCT
ejpam-4610	293	1	since	since	SCONJ
ejpam-4610	293	2	the	the	DET
ejpam-4610	293	3	vertex	vertex	NOUN
ejpam-4610	293	4	a	a	PRON
ejpam-4610	293	5	is	be	AUX
ejpam-4610	293	6	in	in	ADP
ejpam-4610	293	7	every	every	DET
ejpam-4610	293	8	γh	γh	ADV
ejpam-4610	293	9	-	-	PUNCT
ejpam-4610	293	10	set	set	NOUN
ejpam-4610	293	11	of	of	ADP
ejpam-4610	293	12	g.	g.	PROPN
ejpam-4610	293	13	therefore	therefore	ADV
ejpam-4610	293	14	,	,	PUNCT
ejpam-4610	293	15	γ̂h(g	γ̂h(g	X
ejpam-4610	293	16	)	)	PUNCT
ejpam-4610	293	17	=	=	SYM
ejpam-4610	293	18	2	2	X
ejpam-4610	293	19	.	.	PUNCT
ejpam-4610	293	20	....................................	....................................	PUNCT
ejpam-4610	294	1	........................................................................	........................................................................	PUNCT
ejpam-4610	294	2	....................................	....................................	PUNCT
ejpam-4610	295	1	....................................	....................................	PUNCT
ejpam-4610	295	2	....................................	....................................	PUNCT
ejpam-4610	296	1	....................................	....................................	PUNCT
ejpam-4610	296	2	....................................	....................................	PUNCT
ejpam-4610	297	1	....................................	....................................	PUNCT
ejpam-4610	297	2	....................................	....................................	PUNCT
ejpam-4610	298	1	....................................	....................................	PUNCT
ejpam-4610	298	2	....................................	....................................	PUNCT
ejpam-4610	299	1	....................................	....................................	PUNCT
ejpam-4610	299	2	....................................	....................................	PUNCT
ejpam-4610	300	1	.........................................................................................................................................................	.........................................................................................................................................................	PUNCT
ejpam-4610	300	2	........	........	PUNCT
ejpam-4610	300	3	........	........	PUNCT
ejpam-4610	300	4	........	........	PUNCT
ejpam-4610	300	5	........	........	PUNCT
ejpam-4610	300	6	........	........	PUNCT
ejpam-4610	300	7	........	........	PUNCT
ejpam-4610	300	8	........	........	PUNCT
ejpam-4610	300	9	........	........	PUNCT
ejpam-4610	300	10	........	........	PUNCT
ejpam-4610	300	11	........	........	PUNCT
ejpam-4610	300	12	........	........	PUNCT
ejpam-4610	300	13	........	........	PUNCT
ejpam-4610	300	14	........	........	PUNCT
ejpam-4610	300	15	........	........	PUNCT
ejpam-4610	300	16	........	........	PUNCT
ejpam-4610	301	1	....	....	PUNCT
ejpam-4610	301	2	..........	..........	PUNCT
ejpam-4610	302	1	.........	.........	PUNCT
ejpam-4610	302	2	.........	.........	PUNCT
ejpam-4610	303	1	.........	.........	PUNCT
ejpam-4610	303	2	.........	.........	PUNCT
ejpam-4610	304	1	.........	.........	PUNCT
ejpam-4610	304	2	.........	.........	PUNCT
ejpam-4610	305	1	.........	.........	PUNCT
ejpam-4610	305	2	.........	.........	PUNCT
ejpam-4610	306	1	.........	.........	PUNCT
ejpam-4610	306	2	.........	.........	PUNCT
ejpam-4610	307	1	.........	.........	PUNCT
ejpam-4610	307	2	.........	.........	PUNCT
ejpam-4610	308	1	.........	.........	PUNCT
ejpam-4610	308	2	.........	.........	PUNCT
ejpam-4610	309	1	........	........	PUNCT
ejpam-4610	309	2	......................................................................................................................................................	......................................................................................................................................................	NUM
ejpam-4610	309	3	...................	...................	PUNCT
ejpam-4610	309	4	..................	..................	PUNCT
ejpam-4610	309	5	..................	..................	PUNCT
ejpam-4610	309	6	..................	..................	PUNCT
ejpam-4610	309	7	..................	..................	PUNCT
ejpam-4610	309	8	..................	..................	PUNCT
ejpam-4610	310	1	..................	..................	PUNCT
ejpam-4610	310	2	..................	..................	PUNCT
ejpam-4610	311	1	.....	.....	PUNCT
ejpam-4610	311	2	.........	.........	PUNCT
ejpam-4610	311	3	........	........	PUNCT
ejpam-4610	311	4	........	........	PUNCT
ejpam-4610	311	5	........	........	PUNCT
ejpam-4610	311	6	........	........	PUNCT
ejpam-4610	311	7	........	........	PUNCT
ejpam-4610	311	8	........	........	PUNCT
ejpam-4610	311	9	........	........	PUNCT
ejpam-4610	311	10	........	........	PUNCT
ejpam-4610	311	11	........	........	PUNCT
ejpam-4610	311	12	........	........	PUNCT
ejpam-4610	311	13	........	........	PUNCT
ejpam-4610	311	14	........	........	PUNCT
ejpam-4610	311	15	........	........	PUNCT
ejpam-4610	311	16	........	........	PUNCT
ejpam-4610	311	17	........	........	PUNCT
ejpam-4610	312	1	....	....	PUNCT
ejpam-4610	312	2	.....................................................................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4610	313	1	.........	.........	PUNCT
ejpam-4610	313	2	.........	.........	PUNCT
ejpam-4610	314	1	.........	.........	PUNCT
ejpam-4610	314	2	.........	.........	PUNCT
ejpam-4610	315	1	.........	.........	PUNCT
ejpam-4610	315	2	.........	.........	PUNCT
ejpam-4610	316	1	.........	.........	PUNCT
ejpam-4610	316	2	.........	.........	PUNCT
ejpam-4610	317	1	.........	.........	PUNCT
ejpam-4610	317	2	.........	.........	PUNCT
ejpam-4610	318	1	.........	.........	PUNCT
ejpam-4610	318	2	.........	.........	PUNCT
ejpam-4610	319	1	.........	.........	PUNCT
ejpam-4610	319	2	.........	.........	PUNCT
ejpam-4610	320	1	.........	.........	PUNCT
ejpam-4610	320	2	.....	.....	PUNCT
ejpam-4610	320	3	..............	..............	PUNCT
ejpam-4610	320	4	.............	.............	PUNCT
ejpam-4610	320	5	.............	.............	PUNCT
ejpam-4610	320	6	.............	.............	PUNCT
ejpam-4610	320	7	.............	.............	PUNCT
ejpam-4610	320	8	.............	.............	PUNCT
ejpam-4610	320	9	.............	.............	PUNCT
ejpam-4610	320	10	.............	.............	PUNCT
ejpam-4610	320	11	.............	.............	PUNCT
ejpam-4610	320	12	.............	.............	PUNCT
ejpam-4610	320	13	.............	.............	PUNCT
ejpam-4610	320	14	.............	.............	PUNCT
ejpam-4610	320	15	.............	.............	PUNCT
ejpam-4610	320	16	...	...	PUNCT
ejpam-4610	320	17	..................................................................................................................................................................................................................................................................................................................	..................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4610	320	18	............................................................................	............................................................................	PUNCT
ejpam-4610	320	19	............................................................................	............................................................................	PUNCT
ejpam-4610	320	20	............................................................................	............................................................................	PUNCT
ejpam-4610	321	1	a	a	DET
ejpam-4610	321	2	w1w2w3	w1w2w3	NOUN
ejpam-4610	321	3	a1	a1	NOUN
ejpam-4610	321	4	a2	a2	PROPN
ejpam-4610	321	5	a3	a3	PROPN
ejpam-4610	321	6	a4	a4	NOUN
ejpam-4610	321	7	u1	u1	NOUN
ejpam-4610	321	8	v1	v1	NOUN
ejpam-4610	321	9	u2	u2	PROPN
ejpam-4610	321	10	v2	v2	PROPN
ejpam-4610	321	11	u3	u3	NOUN
ejpam-4610	321	12	v3	v3	PROPN
ejpam-4610	321	13	figure	figure	NOUN
ejpam-4610	321	14	2	2	NUM
ejpam-4610	321	15	:	:	PUNCT
ejpam-4610	321	16	firefly	firefly	NOUN
ejpam-4610	321	17	graph	graph	NOUN
ejpam-4610	321	18	f2,3,3	f2,3,3	PROPN
ejpam-4610	321	19	4	4	NUM
ejpam-4610	321	20	.	.	PUNCT
ejpam-4610	321	21	realization	realization	NOUN
ejpam-4610	321	22	problems	problem	NOUN
ejpam-4610	321	23	theorem	theorem	VERB
ejpam-4610	321	24	3	3	X
ejpam-4610	321	25	.	.	PUNCT
ejpam-4610	322	1	let	let	VERB
ejpam-4610	322	2	a	a	PRON
ejpam-4610	322	3	and	and	CCONJ
ejpam-4610	322	4	b	b	NOUN
ejpam-4610	322	5	be	be	AUX
ejpam-4610	322	6	two	two	NUM
ejpam-4610	322	7	positive	positive	ADJ
ejpam-4610	322	8	integers	integer	NOUN
ejpam-4610	322	9	with	with	ADP
ejpam-4610	322	10	a	a	DET
ejpam-4610	322	11	≥	≥	NUM
ejpam-4610	322	12	2	2	NUM
ejpam-4610	322	13	and	and	CCONJ
ejpam-4610	322	14	b	b	NOUN
ejpam-4610	322	15	≥	≥	X
ejpam-4610	322	16	3a	3a	NUM
ejpam-4610	322	17	.	.	PUNCT
ejpam-4610	323	1	then	then	ADV
ejpam-4610	323	2	there	there	PRON
ejpam-4610	323	3	exists	exist	VERB
ejpam-4610	323	4	a	a	DET
ejpam-4610	323	5	connected	connected	ADJ
ejpam-4610	323	6	graph	graph	NOUN
ejpam-4610	323	7	g	g	NOUN
ejpam-4610	323	8	on	on	ADP
ejpam-4610	323	9	b	b	NOUN
ejpam-4610	323	10	vertices	vertex	NOUN
ejpam-4610	323	11	such	such	ADJ
ejpam-4610	323	12	that	that	SCONJ
ejpam-4610	323	13	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	323	14	)	)	PUNCT
ejpam-4610	323	15	=	=	SYM
ejpam-4610	323	16	a.	a.	NOUN
ejpam-4610	323	17	proof	proof	NOUN
ejpam-4610	323	18	.	.	PUNCT
ejpam-4610	324	1	write	write	VERB
ejpam-4610	324	2	b	b	NOUN
ejpam-4610	324	3	=	=	SYM
ejpam-4610	324	4	3a+	3a+	NUM
ejpam-4610	324	5	r	r	NOUN
ejpam-4610	324	6	for	for	ADP
ejpam-4610	324	7	some	some	DET
ejpam-4610	324	8	integer	integer	NOUN
ejpam-4610	324	9	r	r	NOUN
ejpam-4610	324	10	≥	≥	NOUN
ejpam-4610	324	11	0	0	NUM
ejpam-4610	324	12	.	.	PUNCT
ejpam-4610	325	1	consider	consider	VERB
ejpam-4610	325	2	the	the	DET
ejpam-4610	325	3	corona	corona	PROPN
ejpam-4610	325	4	ka	ka	PROPN
ejpam-4610	325	5	◦	◦	PROPN
ejpam-4610	325	6	k2	k2	PROPN
ejpam-4610	325	7	,	,	PUNCT
ejpam-4610	325	8	and	and	CCONJ
ejpam-4610	325	9	let	let	VERB
ejpam-4610	325	10	x	x	SYM
ejpam-4610	325	11	∈	∈	PROPN
ejpam-4610	325	12	v	v	X
ejpam-4610	325	13	(	(	PUNCT
ejpam-4610	325	14	ka	ka	PROPN
ejpam-4610	325	15	)	)	PUNCT
ejpam-4610	325	16	.	.	PUNCT
ejpam-4610	326	1	obtain	obtain	VERB
ejpam-4610	326	2	g	g	NOUN
ejpam-4610	326	3	from	from	ADP
ejpam-4610	326	4	ka	ka	PROPN
ejpam-4610	326	5	◦	◦	PROPN
ejpam-4610	326	6	k2	k2	PROPN
ejpam-4610	326	7	by	by	ADP
ejpam-4610	326	8	joining	join	VERB
ejpam-4610	326	9	to	to	ADP
ejpam-4610	326	10	kx	kx	PROPN
ejpam-4610	326	11	2	2	NUM
ejpam-4610	326	12	+	+	CCONJ
ejpam-4610	326	13	x	x	SYM
ejpam-4610	326	14	,	,	PUNCT
ejpam-4610	326	15	the	the	DET
ejpam-4610	326	16	complete	complete	ADJ
ejpam-4610	326	17	graph	graph	NOUN
ejpam-4610	326	18	kr	kr	PROPN
ejpam-4610	326	19	(	(	PUNCT
ejpam-4610	326	20	see	see	VERB
ejpam-4610	326	21	g	g	PROPN
ejpam-4610	326	22	in	in	ADP
ejpam-4610	326	23	figure	figure	NOUN
ejpam-4610	326	24	3	3	NUM
ejpam-4610	326	25	where	where	SCONJ
ejpam-4610	326	26	a	a	DET
ejpam-4610	326	27	=	=	SYM
ejpam-4610	326	28	4	4	NUM
ejpam-4610	326	29	and	and	CCONJ
ejpam-4610	326	30	r	r	NOUN
ejpam-4610	326	31	=	=	SYM
ejpam-4610	326	32	3	3	NUM
ejpam-4610	326	33	)	)	PUNCT
ejpam-4610	326	34	.	.	PUNCT
ejpam-4610	327	1	then	then	ADV
ejpam-4610	327	2	g	g	PROPN
ejpam-4610	327	3	is	be	AUX
ejpam-4610	327	4	a	a	DET
ejpam-4610	327	5	connected	connected	ADJ
ejpam-4610	327	6	graph	graph	NOUN
ejpam-4610	327	7	on	on	ADP
ejpam-4610	327	8	b	b	NOUN
ejpam-4610	327	9	vertices	vertex	NOUN
ejpam-4610	327	10	.	.	PUNCT
ejpam-4610	328	1	if	if	SCONJ
ejpam-4610	328	2	........................................................................	........................................................................	PUNCT
ejpam-4610	328	3	....................................	....................................	PUNCT
ejpam-4610	328	4	....................................	....................................	PUNCT
ejpam-4610	328	5	....................................	....................................	PUNCT
ejpam-4610	328	6	....................................	....................................	PUNCT
ejpam-4610	328	7	....................................	....................................	PUNCT
ejpam-4610	328	8	....................................	....................................	PUNCT
ejpam-4610	328	9	....................................	....................................	PUNCT
ejpam-4610	328	10	....................................	....................................	PUNCT
ejpam-4610	328	11	....................................	....................................	PUNCT
ejpam-4610	328	12	....................................	....................................	PUNCT
ejpam-4610	328	13	....................................	....................................	PUNCT
ejpam-4610	328	14	....................................	....................................	PUNCT
ejpam-4610	328	15	....................................	....................................	PUNCT
ejpam-4610	328	16	............	............	PUNCT
ejpam-4610	328	17	...........	...........	PUNCT
ejpam-4610	328	18	...........	...........	PUNCT
ejpam-4610	328	19	...........	...........	PUNCT
ejpam-4610	328	20	...........	...........	PUNCT
ejpam-4610	328	21	...........	...........	PUNCT
ejpam-4610	328	22	....	....	PUNCT
ejpam-4610	328	23	.........................................	.........................................	PUNCT
ejpam-4610	328	24	......................	......................	PUNCT
ejpam-4610	328	25	.......................................................................	.......................................................................	PUNCT
ejpam-4610	328	26	...............................................................	...............................................................	PUNCT
ejpam-4610	328	27	...................................	...................................	PUNCT
ejpam-4610	328	28	..........	..........	PUNCT
ejpam-4610	328	29	.........	.........	PUNCT
ejpam-4610	328	30	.........	.........	PUNCT
ejpam-4610	328	31	..........................................	..........................................	PUNCT
ejpam-4610	328	32	.........................................	.........................................	PUNCT
ejpam-4610	328	33	......................	......................	PUNCT
ejpam-4610	328	34	............	............	PUNCT
ejpam-4610	328	35	...........	...........	PUNCT
ejpam-4610	328	36	...........	...........	PUNCT
ejpam-4610	328	37	...........	...........	PUNCT
ejpam-4610	328	38	...........	...........	PUNCT
ejpam-4610	328	39	...........	...........	PUNCT
ejpam-4610	328	40	....	....	PUNCT
ejpam-4610	328	41	............................................................................	............................................................................	PUNCT
ejpam-4610	328	42	.........	.........	PUNCT
ejpam-4610	328	43	........	........	PUNCT
ejpam-4610	328	44	........	........	PUNCT
ejpam-4610	328	45	........	........	PUNCT
ejpam-4610	328	46	........	........	PUNCT
ejpam-4610	328	47	........	........	PUNCT
ejpam-4610	328	48	........	........	PUNCT
ejpam-4610	328	49	........	........	PUNCT
ejpam-4610	328	50	........	........	PUNCT
ejpam-4610	328	51	..............................................................................................................................	..............................................................................................................................	PUNCT
ejpam-4610	328	52	...........	...........	PUNCT
ejpam-4610	328	53	...........	...........	PUNCT
ejpam-4610	328	54	...........	...........	PUNCT
ejpam-4610	328	55	...........	...........	PUNCT
ejpam-4610	328	56	...........	...........	PUNCT
ejpam-4610	328	57	...........	...........	PUNCT
ejpam-4610	328	58	...........	...........	PUNCT
ejpam-4610	328	59	...........	...........	PUNCT
ejpam-4610	328	60	...........	...........	PUNCT
ejpam-4610	328	61	............................................................................	............................................................................	PUNCT
ejpam-4610	328	62	....	....	PUNCT
ejpam-4610	328	63	........	........	PUNCT
ejpam-4610	328	64	........	........	PUNCT
ejpam-4610	328	65	........	........	PUNCT
ejpam-4610	328	66	........	........	PUNCT
ejpam-4610	328	67	........	........	PUNCT
ejpam-4610	328	68	........	........	PUNCT
ejpam-4610	328	69	........	........	PUNCT
ejpam-4610	328	70	........	........	PUNCT
ejpam-4610	328	71	........	........	PUNCT
ejpam-4610	328	72	.........	.........	PUNCT
ejpam-4610	328	73	........	........	PUNCT
ejpam-4610	328	74	........	........	PUNCT
ejpam-4610	328	75	........	........	PUNCT
ejpam-4610	328	76	........	........	PUNCT
ejpam-4610	328	77	........	........	PUNCT
ejpam-4610	328	78	........	........	PUNCT
ejpam-4610	328	79	........	........	PUNCT
ejpam-4610	328	80	........	........	PUNCT
ejpam-4610	328	81	...	...	PUNCT
ejpam-4610	328	82	............	............	PUNCT
ejpam-4610	328	83	...........	...........	PUNCT
ejpam-4610	328	84	...........	...........	PUNCT
ejpam-4610	328	85	...........	...........	PUNCT
ejpam-4610	328	86	......	......	PUNCT
ejpam-4610	328	87	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4610	328	88	......................................................................................................................................................................................................................	......................................................................................................................................................................................................................	PUNCT
ejpam-4610	328	89	...........	...........	PUNCT
ejpam-4610	328	90	...........	...........	PUNCT
ejpam-4610	328	91	...........	...........	PUNCT
ejpam-4610	328	92	...........	...........	PUNCT
ejpam-4610	328	93	...........	...........	PUNCT
ejpam-4610	328	94	...........	...........	PUNCT
ejpam-4610	328	95	...........	...........	PUNCT
ejpam-4610	328	96	...........	...........	PUNCT
ejpam-4610	328	97	...........	...........	PUNCT
ejpam-4610	328	98	..........................	..........................	PUNCT
ejpam-4610	328	99	.........................	.........................	PUNCT
ejpam-4610	328	100	.........................	.........................	PUNCT
ejpam-4610	328	101	.........................	.........................	PUNCT
ejpam-4610	328	102	.........................	.........................	PUNCT
ejpam-4610	328	103	.........	.........	PUNCT
ejpam-4610	328	104	........	........	PUNCT
ejpam-4610	328	105	........	........	PUNCT
ejpam-4610	328	106	........	........	PUNCT
ejpam-4610	328	107	........	........	PUNCT
ejpam-4610	328	108	........	........	PUNCT
ejpam-4610	328	109	........	........	PUNCT
ejpam-4610	328	110	........	........	PUNCT
ejpam-4610	328	111	........	........	PUNCT
ejpam-4610	328	112	...	...	PUNCT
ejpam-4610	329	1	...................................................	...................................................	PUNCT
ejpam-4610	329	2	..........................	..........................	PUNCT
ejpam-4610	329	3	.........................	.........................	PUNCT
ejpam-4610	329	4	.........................	.........................	PUNCT
ejpam-4610	329	5	.........................	.........................	PUNCT
ejpam-4610	329	6	.........................	.........................	PUNCT
ejpam-4610	329	7	..............................................................................................................................................................................	..............................................................................................................................................................................	PUNCT
ejpam-4610	329	8	...........	...........	PUNCT
ejpam-4610	329	9	...........	...........	PUNCT
ejpam-4610	329	10	...........	...........	PUNCT
ejpam-4610	329	11	......	......	PUNCT
ejpam-4610	330	1	..........................................................................................................................................................................................................	..........................................................................................................................................................................................................	PUNCT
ejpam-4610	330	2	.............................................................................	.............................................................................	PUNCT
ejpam-4610	330	3	.........................	.........................	PUNCT
ejpam-4610	330	4	.........................	.........................	PUNCT
ejpam-4610	330	5	.........................	.........................	PUNCT
ejpam-4610	330	6	.........................	.........................	PUNCT
ejpam-4610	331	1	x	x	PRON
ejpam-4610	331	2	figure	figure	VERB
ejpam-4610	331	3	3	3	NUM
ejpam-4610	331	4	:	:	PUNCT
ejpam-4610	331	5	graph	graph	NOUN
ejpam-4610	331	6	g	g	NOUN
ejpam-4610	331	7	where	where	SCONJ
ejpam-4610	331	8	a	a	DET
ejpam-4610	331	9	=	=	NOUN
ejpam-4610	331	10	4	4	NUM
ejpam-4610	331	11	,	,	PUNCT
ejpam-4610	331	12	r	r	NOUN
ejpam-4610	331	13	=	=	SYM
ejpam-4610	331	14	3	3	NUM
ejpam-4610	331	15	and	and	CCONJ
ejpam-4610	331	16	|v	|v	PROPN
ejpam-4610	331	17	(	(	PUNCT
ejpam-4610	331	18	g)|	g)|	NOUN
ejpam-4610	331	19	=	=	SYM
ejpam-4610	331	20	3a+	3a+	NUM
ejpam-4610	331	21	r	r	NOUN
ejpam-4610	331	22	=	=	SYM
ejpam-4610	331	23	15	15	NUM
ejpam-4610	331	24	a	a	DET
ejpam-4610	331	25	=	=	ADJ
ejpam-4610	331	26	2	2	NUM
ejpam-4610	331	27	,	,	PUNCT
ejpam-4610	331	28	then	then	ADV
ejpam-4610	331	29	γh(g	γh(g	PUNCT
ejpam-4610	331	30	)	)	PUNCT
ejpam-4610	331	31	=	=	PUNCT
ejpam-4610	331	32	a	a	PRON
ejpam-4610	331	33	and	and	CCONJ
ejpam-4610	331	34	v	v	NOUN
ejpam-4610	331	35	(	(	PUNCT
ejpam-4610	331	36	ka	ka	X
ejpam-4610	331	37	)	)	PUNCT
ejpam-4610	331	38	is	be	AUX
ejpam-4610	331	39	the	the	DET
ejpam-4610	331	40	unique	unique	ADJ
ejpam-4610	331	41	γh	γh	NOUN
ejpam-4610	331	42	-	-	PUNCT
ejpam-4610	331	43	set	set	NOUN
ejpam-4610	331	44	of	of	ADP
ejpam-4610	331	45	g.	g.	PROPN
ejpam-4610	331	46	in	in	ADP
ejpam-4610	331	47	this	this	DET
ejpam-4610	331	48	case	case	NOUN
ejpam-4610	331	49	,	,	PUNCT
ejpam-4610	331	50	v	v	NOUN
ejpam-4610	331	51	(	(	PUNCT
ejpam-4610	331	52	ka	ka	X
ejpam-4610	331	53	)	)	PUNCT
ejpam-4610	331	54	is	be	AUX
ejpam-4610	331	55	also	also	ADV
ejpam-4610	331	56	the	the	DET
ejpam-4610	331	57	unique	unique	ADJ
ejpam-4610	331	58	γ̂h	γ̂h	NOUN
ejpam-4610	331	59	-	-	PUNCT
ejpam-4610	331	60	set	set	NOUN
ejpam-4610	331	61	of	of	ADP
ejpam-4610	331	62	g	g	NOUN
ejpam-4610	331	63	so	so	SCONJ
ejpam-4610	331	64	that	that	SCONJ
ejpam-4610	331	65	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	331	66	)	)	PUNCT
ejpam-4610	332	1	=	=	PUNCT
ejpam-4610	332	2	a.	a.	NOUN
ejpam-4610	332	3	if	if	SCONJ
ejpam-4610	332	4	a	a	DET
ejpam-4610	332	5	≥	≥	NOUN
ejpam-4610	332	6	3	3	NUM
ejpam-4610	332	7	,	,	PUNCT
ejpam-4610	332	8	then	then	ADV
ejpam-4610	332	9	except	except	SCONJ
ejpam-4610	332	10	for	for	ADP
ejpam-4610	332	11	the	the	DET
ejpam-4610	332	12	case	case	NOUN
ejpam-4610	332	13	of	of	ADP
ejpam-4610	332	14	a	a	DET
ejpam-4610	332	15	=	=	SYM
ejpam-4610	332	16	3	3	NUM
ejpam-4610	332	17	m.a	m.a	PROPN
ejpam-4610	332	18	.	.	PROPN
ejpam-4610	332	19	bonsocan	bonsocan	PROPN
ejpam-4610	332	20	,	,	PUNCT
ejpam-4610	332	21	f.	f.	PROPN
ejpam-4610	332	22	jamil	jamil	PROPN
ejpam-4610	332	23	/	/	SYM
ejpam-4610	332	24	eur	eur	PROPN
ejpam-4610	332	25	.	.	PUNCT
ejpam-4610	333	1	j.	j.	PROPN
ejpam-4610	333	2	pure	pure	PROPN
ejpam-4610	333	3	appl	appl	PROPN
ejpam-4610	333	4	.	.	PROPN
ejpam-4610	333	5	math	math	PROPN
ejpam-4610	333	6	,	,	PUNCT
ejpam-4610	333	7	16	16	NUM
ejpam-4610	333	8	(	(	PUNCT
ejpam-4610	333	9	1	1	NUM
ejpam-4610	333	10	)	)	PUNCT
ejpam-4610	333	11	(	(	PUNCT
ejpam-4610	333	12	2023	2023	NUM
ejpam-4610	333	13	)	)	PUNCT
ejpam-4610	333	14	,	,	PUNCT
ejpam-4610	333	15	192	192	NUM
ejpam-4610	333	16	-	-	SYM
ejpam-4610	333	17	206	206	NUM
ejpam-4610	333	18	199	199	NUM
ejpam-4610	333	19	which	which	PRON
ejpam-4610	333	20	also	also	ADV
ejpam-4610	333	21	includes	include	VERB
ejpam-4610	333	22	v	v	NUM
ejpam-4610	333	23	(	(	PUNCT
ejpam-4610	333	24	ka	ka	NOUN
ejpam-4610	333	25	)	)	PUNCT
ejpam-4610	333	26	as	as	ADP
ejpam-4610	333	27	a	a	DET
ejpam-4610	333	28	γh	γh	ADV
ejpam-4610	333	29	-	-	PUNCT
ejpam-4610	333	30	set	set	NOUN
ejpam-4610	333	31	,	,	PUNCT
ejpam-4610	333	32	the	the	DET
ejpam-4610	333	33	γh	γh	NOUN
ejpam-4610	333	34	-	-	PUNCT
ejpam-4610	333	35	sets	set	NOUN
ejpam-4610	333	36	of	of	ADP
ejpam-4610	333	37	g	g	NOUN
ejpam-4610	333	38	are	be	AUX
ejpam-4610	333	39	all	all	PRON
ejpam-4610	333	40	sets	set	NOUN
ejpam-4610	333	41	of	of	ADP
ejpam-4610	333	42	the	the	DET
ejpam-4610	333	43	form	form	NOUN
ejpam-4610	333	44	{	{	PUNCT
ejpam-4610	333	45	u	u	NOUN
ejpam-4610	333	46	,	,	PUNCT
ejpam-4610	333	47	y	y	PROPN
ejpam-4610	333	48	,	,	PUNCT
ejpam-4610	333	49	v	v	NOUN
ejpam-4610	333	50	}	}	PUNCT
ejpam-4610	333	51	for	for	ADP
ejpam-4610	333	52	distinct	distinct	ADJ
ejpam-4610	333	53	vertices	vertex	NOUN
ejpam-4610	333	54	u	u	NOUN
ejpam-4610	333	55	,	,	PUNCT
ejpam-4610	333	56	v	v	NOUN
ejpam-4610	333	57	∈	∈	PROPN
ejpam-4610	333	58	v	v	NOUN
ejpam-4610	333	59	(	(	PUNCT
ejpam-4610	333	60	ka	ka	PROPN
ejpam-4610	333	61	)	)	PUNCT
ejpam-4610	333	62	and	and	CCONJ
ejpam-4610	333	63	y	y	PROPN
ejpam-4610	333	64	∈	∈	PROPN
ejpam-4610	333	65	v	v	PROPN
ejpam-4610	333	66	(	(	PUNCT
ejpam-4610	333	67	hu	hu	PROPN
ejpam-4610	333	68	)	)	PUNCT
ejpam-4610	333	69	∪	∪	ADP
ejpam-4610	333	70	v	v	PROPN
ejpam-4610	333	71	(	(	PUNCT
ejpam-4610	333	72	hv	hv	PROPN
ejpam-4610	333	73	)	)	PUNCT
ejpam-4610	333	74	and	and	CCONJ
ejpam-4610	333	75	{	{	PUNCT
ejpam-4610	333	76	p	p	X
ejpam-4610	333	77	,	,	PUNCT
ejpam-4610	333	78	q	q	ADJ
ejpam-4610	333	79	,	,	PUNCT
ejpam-4610	333	80	z	z	NOUN
ejpam-4610	333	81	}	}	PUNCT
ejpam-4610	333	82	where	where	SCONJ
ejpam-4610	333	83	z	z	PROPN
ejpam-4610	333	84	∈	∈	PROPN
ejpam-4610	333	85	v	v	X
ejpam-4610	333	86	(	(	PUNCT
ejpam-4610	333	87	ka	ka	PROPN
ejpam-4610	333	88	)	)	PUNCT
ejpam-4610	333	89	and	and	CCONJ
ejpam-4610	333	90	p	p	X
ejpam-4610	333	91	,	,	PUNCT
ejpam-4610	333	92	q	q	PROPN
ejpam-4610	333	93	∈	∈	PROPN
ejpam-4610	333	94	v	v	NOUN
ejpam-4610	333	95	(	(	PUNCT
ejpam-4610	333	96	kz	kz	PROPN
ejpam-4610	333	97	2	2	NUM
ejpam-4610	333	98	)	)	PUNCT
ejpam-4610	333	99	.	.	PUNCT
ejpam-4610	334	1	thus	thus	ADV
ejpam-4610	334	2	,	,	PUNCT
ejpam-4610	334	3	v	v	X
ejpam-4610	334	4	(	(	PUNCT
ejpam-4610	334	5	ka	ka	X
ejpam-4610	334	6	)	)	PUNCT
ejpam-4610	334	7	is	be	AUX
ejpam-4610	334	8	a	a	DET
ejpam-4610	334	9	γ̂h	γ̂h	NOUN
ejpam-4610	334	10	-	-	PUNCT
ejpam-4610	334	11	set	set	NOUN
ejpam-4610	334	12	of	of	ADP
ejpam-4610	334	13	g.	g.	PROPN
ejpam-4610	334	14	therefore	therefore	ADV
ejpam-4610	334	15	,	,	PUNCT
ejpam-4610	334	16	γ̂h(g	γ̂h(g	X
ejpam-4610	334	17	)	)	PUNCT
ejpam-4610	334	18	=	=	SYM
ejpam-4610	334	19	a.	a.	NOUN
ejpam-4610	334	20	theorem	theorem	NOUN
ejpam-4610	334	21	4	4	NUM
ejpam-4610	334	22	.	.	X
ejpam-4610	335	1	for	for	ADP
ejpam-4610	335	2	any	any	DET
ejpam-4610	335	3	positive	positive	ADJ
ejpam-4610	335	4	integers	integer	NOUN
ejpam-4610	335	5	a	a	PRON
ejpam-4610	335	6	and	and	CCONJ
ejpam-4610	335	7	b	b	NOUN
ejpam-4610	335	8	with	with	ADP
ejpam-4610	335	9	2	2	NUM
ejpam-4610	335	10	≤	≤	NOUN
ejpam-4610	335	11	a	a	DET
ejpam-4610	335	12	≤	≤	NUM
ejpam-4610	335	13	b	b	NOUN
ejpam-4610	335	14	,	,	PUNCT
ejpam-4610	335	15	there	there	PRON
ejpam-4610	335	16	exists	exist	VERB
ejpam-4610	335	17	a	a	DET
ejpam-4610	335	18	connected	connected	ADJ
ejpam-4610	335	19	graph	graph	NOUN
ejpam-4610	335	20	g	g	NOUN
ejpam-4610	335	21	for	for	ADP
ejpam-4610	335	22	which	which	PRON
ejpam-4610	335	23	γh(g	γh(g	NOUN
ejpam-4610	335	24	)	)	PUNCT
ejpam-4610	335	25	=	=	SYM
ejpam-4610	335	26	a	a	PRON
ejpam-4610	335	27	and	and	CCONJ
ejpam-4610	335	28	γ̂h(g	γ̂h(g	PROPN
ejpam-4610	335	29	)	)	PUNCT
ejpam-4610	335	30	=	=	SYM
ejpam-4610	335	31	b.	b.	NOUN
ejpam-4610	335	32	proof	proof	NOUN
ejpam-4610	335	33	.	.	PUNCT
ejpam-4610	336	1	if	if	SCONJ
ejpam-4610	336	2	a	a	DET
ejpam-4610	336	3	=	=	SYM
ejpam-4610	336	4	b	b	NOUN
ejpam-4610	336	5	,	,	PUNCT
ejpam-4610	336	6	then	then	ADV
ejpam-4610	336	7	we	we	PRON
ejpam-4610	336	8	consider	consider	VERB
ejpam-4610	336	9	the	the	DET
ejpam-4610	336	10	complete	complete	ADJ
ejpam-4610	336	11	graph	graph	NOUN
ejpam-4610	336	12	ka	ka	PROPN
ejpam-4610	336	13	.	.	PUNCT
ejpam-4610	337	1	by	by	ADP
ejpam-4610	337	2	proposition	proposition	NOUN
ejpam-4610	337	3	1	1	NUM
ejpam-4610	337	4	,	,	PUNCT
ejpam-4610	337	5	γh(ka	γh(ka	NOUN
ejpam-4610	337	6	)	)	PUNCT
ejpam-4610	337	7	=	=	PUNCT
ejpam-4610	337	8	a	a	DET
ejpam-4610	337	9	=	=	SYM
ejpam-4610	337	10	γ̂h(kb	γ̂h(kb	PROPN
ejpam-4610	337	11	)	)	PUNCT
ejpam-4610	337	12	.	.	PUNCT
ejpam-4610	338	1	suppose	suppose	VERB
ejpam-4610	338	2	that	that	SCONJ
ejpam-4610	338	3	a	a	DET
ejpam-4610	338	4	<	<	X
ejpam-4610	338	5	b.	b.	PROPN
ejpam-4610	338	6	then	then	ADV
ejpam-4610	338	7	b	b	X
ejpam-4610	338	8	=	=	PUNCT
ejpam-4610	338	9	a	a	DET
ejpam-4610	338	10	+	+	X
ejpam-4610	338	11	n	n	NOUN
ejpam-4610	338	12	for	for	ADP
ejpam-4610	338	13	some	some	DET
ejpam-4610	338	14	positive	positive	ADJ
ejpam-4610	338	15	integer	integer	NOUN
ejpam-4610	338	16	n.	n.	NOUN
ejpam-4610	338	17	consider	consider	VERB
ejpam-4610	338	18	the	the	DET
ejpam-4610	338	19	graph	graph	NOUN
ejpam-4610	338	20	g	g	NOUN
ejpam-4610	338	21	as	as	SCONJ
ejpam-4610	338	22	shown	show	VERB
ejpam-4610	338	23	in	in	ADP
ejpam-4610	338	24	figure	figure	NOUN
ejpam-4610	338	25	4	4	NUM
ejpam-4610	338	26	.	.	PUNCT
ejpam-4610	339	1	g	g	PROPN
ejpam-4610	339	2	is	be	AUX
ejpam-4610	339	3	obtained	obtain	VERB
ejpam-4610	339	4	from	from	ADP
ejpam-4610	339	5	the	the	DET
ejpam-4610	339	6	rectangular	rectangular	ADJ
ejpam-4610	339	7	grid	grid	NOUN
ejpam-4610	339	8	graph	graph	NOUN
ejpam-4610	339	9	l(a	l(a	PROPN
ejpam-4610	339	10	,	,	PUNCT
ejpam-4610	339	11	3	3	NUM
ejpam-4610	339	12	)	)	PUNCT
ejpam-4610	339	13	by	by	ADP
ejpam-4610	339	14	adding	add	VERB
ejpam-4610	339	15	the	the	DET
ejpam-4610	339	16	edges	edge	NOUN
ejpam-4610	339	17	wivi	wivi	NOUN
ejpam-4610	339	18	and	and	CCONJ
ejpam-4610	339	19	yizi	yizi	PROPN
ejpam-4610	339	20	and	and	CCONJ
ejpam-4610	339	21	the	the	DET
ejpam-4610	339	22	paths	path	NOUN
ejpam-4610	339	23	[	[	X
ejpam-4610	339	24	wi	wi	PROPN
ejpam-4610	339	25	,	,	PUNCT
ejpam-4610	339	26	x	x	PROPN
ejpam-4610	340	1	k	k	PROPN
ejpam-4610	340	2	i	i	PRON
ejpam-4610	340	3	,	,	PUNCT
ejpam-4610	340	4	yi	yi	PROPN
ejpam-4610	340	5	]	]	PUNCT
ejpam-4610	340	6	for	for	ADP
ejpam-4610	340	7	each	each	DET
ejpam-4610	340	8	i	i	PRON
ejpam-4610	340	9	∈	∈	PROPN
ejpam-4610	340	10	{	{	PUNCT
ejpam-4610	340	11	1	1	NUM
ejpam-4610	340	12	,	,	PUNCT
ejpam-4610	340	13	2	2	NUM
ejpam-4610	340	14	,	,	PUNCT
ejpam-4610	340	15	.	.	PUNCT
ejpam-4610	340	16	.	.	PUNCT
ejpam-4610	340	17	.	.	PUNCT
ejpam-4610	341	1	,	,	PUNCT
ejpam-4610	341	2	a	a	PRON
ejpam-4610	341	3	}	}	PUNCT
ejpam-4610	341	4	and	and	CCONJ
ejpam-4610	341	5	k	k	PROPN
ejpam-4610	341	6	∈	∈	PROPN
ejpam-4610	341	7	{	{	PUNCT
ejpam-4610	341	8	1	1	NUM
ejpam-4610	341	9	,	,	PUNCT
ejpam-4610	341	10	2	2	NUM
ejpam-4610	341	11	,	,	PUNCT
ejpam-4610	341	12	.	.	PUNCT
ejpam-4610	341	13	.	.	PUNCT
ejpam-4610	342	1	.	.	PUNCT
ejpam-4610	342	2	,	,	PUNCT
ejpam-4610	342	3	n	n	CCONJ
ejpam-4610	342	4	}	}	PUNCT
ejpam-4610	342	5	.	.	PUNCT
ejpam-4610	343	1	for	for	ADP
ejpam-4610	343	2	each	each	DET
ejpam-4610	343	3	i	i	PRON
ejpam-4610	343	4	∈	∈	PROPN
ejpam-4610	343	5	{	{	PUNCT
ejpam-4610	343	6	1	1	NUM
ejpam-4610	343	7	,	,	PUNCT
ejpam-4610	343	8	2	2	NUM
ejpam-4610	343	9	,	,	PUNCT
ejpam-4610	343	10	3	3	NUM
ejpam-4610	343	11	,	,	PUNCT
ejpam-4610	343	12	.	.	PUNCT
ejpam-4610	343	13	.	.	PUNCT
ejpam-4610	343	14	.	.	PUNCT
ejpam-4610	344	1	,	,	PUNCT
ejpam-4610	344	2	a	a	X
ejpam-4610	344	3	}	}	PUNCT
ejpam-4610	344	4	,	,	PUNCT
ejpam-4610	344	5	let	let	VERB
ejpam-4610	344	6	ui	ui	PROPN
ejpam-4610	344	7	=	=	PUNCT
ejpam-4610	344	8	{	{	PUNCT
ejpam-4610	344	9	xi	xi	PROPN
ejpam-4610	344	10	,	,	PUNCT
ejpam-4610	344	11	x1i	x1i	PROPN
ejpam-4610	344	12	,	,	PUNCT
ejpam-4610	344	13	x2i	x2i	PROPN
ejpam-4610	344	14	.	.	PUNCT
ejpam-4610	344	15	.	.	PUNCT
ejpam-4610	345	1	.	.	PUNCT
ejpam-4610	346	1	,	,	PUNCT
ejpam-4610	346	2	xni	xni	PROPN
ejpam-4610	346	3	}	}	PUNCT
ejpam-4610	346	4	.	.	PUNCT
ejpam-4610	347	1	then	then	ADV
ejpam-4610	347	2	γh(g	γh(g	NOUN
ejpam-4610	347	3	)	)	PUNCT
ejpam-4610	347	4	=	=	SYM
ejpam-4610	347	5	a	a	PRON
ejpam-4610	347	6	and	and	CCONJ
ejpam-4610	347	7	s	s	VERB
ejpam-4610	347	8	is	be	AUX
ejpam-4610	347	9	a	a	DET
ejpam-4610	347	10	γh	γh	ADV
ejpam-4610	347	11	-	-	PUNCT
ejpam-4610	347	12	set	set	NOUN
ejpam-4610	347	13	of	of	ADP
ejpam-4610	347	14	g	g	PROPN
ejpam-4610	347	15	if	if	SCONJ
ejpam-4610	348	1	and	and	CCONJ
ejpam-4610	348	2	only	only	ADV
ejpam-4610	348	3	if	if	SCONJ
ejpam-4610	348	4	|s	|s	PROPN
ejpam-4610	348	5	∩	∩	NOUN
ejpam-4610	348	6	ui|	ui|	PROPN
ejpam-4610	348	7	=	=	NOUN
ejpam-4610	348	8	1	1	NUM
ejpam-4610	348	9	for	for	ADP
ejpam-4610	348	10	all	all	DET
ejpam-4610	348	11	i	i	PRON
ejpam-4610	348	12	=	=	NOUN
ejpam-4610	348	13	1	1	NUM
ejpam-4610	348	14	,	,	PUNCT
ejpam-4610	348	15	2	2	NUM
ejpam-4610	348	16	,	,	PUNCT
ejpam-4610	348	17	3	3	NUM
ejpam-4610	348	18	,	,	PUNCT
ejpam-4610	348	19	.	.	PUNCT
ejpam-4610	348	20	.	.	PUNCT
ejpam-4610	349	1	.	.	PUNCT
ejpam-4610	350	1	,	,	PUNCT
ejpam-4610	350	2	a	a	DET
ejpam-4610	350	3	and	and	CCONJ
ejpam-4610	350	4	s	s	X
ejpam-4610	350	5	\	\	X
ejpam-4610	350	6	∪a	∪a	X
ejpam-4610	350	7	i=1ui	i=1ui	X
ejpam-4610	351	1	=	=	PUNCT
ejpam-4610	351	2	∅.	∅.	NOUN
ejpam-4610	351	3	in	in	ADP
ejpam-4610	351	4	particular	particular	ADJ
ejpam-4610	351	5	,	,	PUNCT
ejpam-4610	351	6	the	the	DET
ejpam-4610	351	7	set	set	NOUN
ejpam-4610	351	8	s∗	s∗	PROPN
ejpam-4610	351	9	=	=	SYM
ejpam-4610	351	10	{	{	PUNCT
ejpam-4610	351	11	x1	x1	PROPN
ejpam-4610	351	12	,	,	PUNCT
ejpam-4610	351	13	x2	x2	PROPN
ejpam-4610	351	14	,	,	PUNCT
ejpam-4610	351	15	x3	x3	ADJ
ejpam-4610	351	16	,	,	PUNCT
ejpam-4610	351	17	.	.	PUNCT
ejpam-4610	351	18	.	.	PUNCT
ejpam-4610	351	19	.	.	PUNCT
ejpam-4610	352	1	,	,	PUNCT
ejpam-4610	352	2	xa−1	xa−1	PROPN
ejpam-4610	352	3	,	,	PUNCT
ejpam-4610	352	4	xa	xa	PROPN
ejpam-4610	352	5	}	}	PUNCT
ejpam-4610	352	6	is	be	AUX
ejpam-4610	352	7	a	a	DET
ejpam-4610	352	8	γh	γh	ADV
ejpam-4610	352	9	-	-	PUNCT
ejpam-4610	352	10	set	set	NOUN
ejpam-4610	352	11	of	of	ADP
ejpam-4610	352	12	g.	g.	PROPN
ejpam-4610	352	13	put	put	VERB
ejpam-4610	352	14	d	d	PROPN
ejpam-4610	352	15	=	=	PUNCT
ejpam-4610	352	16	s∗	s∗	PROPN
ejpam-4610	352	17	∪	∪	PROPN
ejpam-4610	352	18	u1	u1	NOUN
ejpam-4610	352	19	.	.	PUNCT
ejpam-4610	353	1	for	for	ADP
ejpam-4610	353	2	each	each	DET
ejpam-4610	353	3	γh	γh	ADV
ejpam-4610	353	4	-	-	PUNCT
ejpam-4610	353	5	set	set	NOUN
ejpam-4610	353	6	s	s	NOUN
ejpam-4610	353	7	of	of	ADP
ejpam-4610	353	8	g	g	NOUN
ejpam-4610	353	9	,	,	PUNCT
ejpam-4610	353	10	s	s	PART
ejpam-4610	353	11	∩d	∩d	NOUN
ejpam-4610	353	12	̸=	̸=	PROPN
ejpam-4610	353	13	∅.	∅.	VERB
ejpam-4610	353	14	clearly	clearly	ADV
ejpam-4610	353	15	,	,	PUNCT
ejpam-4610	353	16	d	d	PROPN
ejpam-4610	353	17	is	be	AUX
ejpam-4610	353	18	a	a	DET
ejpam-4610	353	19	γ̂h	γ̂h	NOUN
ejpam-4610	353	20	-	-	PUNCT
ejpam-4610	353	21	set	set	NOUN
ejpam-4610	353	22	of	of	ADP
ejpam-4610	353	23	g.	g.	PROPN
ejpam-4610	353	24	therefore	therefore	ADV
ejpam-4610	353	25	,	,	PUNCT
ejpam-4610	353	26	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	353	27	)	)	PUNCT
ejpam-4610	353	28	=	=	SYM
ejpam-4610	353	29	|d|	|d|	PROPN
ejpam-4610	353	30	=	=	SYM
ejpam-4610	353	31	a+	a+	PUNCT
ejpam-4610	353	32	n	n	PROPN
ejpam-4610	353	33	=	=	PROPN
ejpam-4610	353	34	b.	b.	PROPN
ejpam-4610	353	35	....................................	....................................	PUNCT
ejpam-4610	354	1	....................................	....................................	PUNCT
ejpam-4610	354	2	....................................	....................................	PUNCT
ejpam-4610	355	1	....................................	....................................	PUNCT
ejpam-4610	355	2	....................................	....................................	PUNCT
ejpam-4610	356	1	....................................	....................................	PUNCT
ejpam-4610	356	2	....................................	....................................	PUNCT
ejpam-4610	357	1	....................................	....................................	PUNCT
ejpam-4610	357	2	....................................	....................................	PUNCT
ejpam-4610	358	1	....................................	....................................	PUNCT
ejpam-4610	358	2	........................................................................	........................................................................	PUNCT
ejpam-4610	359	1	....................................	....................................	PUNCT
ejpam-4610	359	2	....................................	....................................	PUNCT
ejpam-4610	360	1	....................................	....................................	PUNCT
ejpam-4610	360	2	....................................	....................................	PUNCT
ejpam-4610	361	1	....................................	....................................	PUNCT
ejpam-4610	361	2	....................................	....................................	PUNCT
ejpam-4610	362	1	....................................	....................................	PUNCT
ejpam-4610	362	2	....................................	....................................	PUNCT
ejpam-4610	363	1	....................................	....................................	PUNCT
ejpam-4610	363	2	....................................	....................................	PUNCT
ejpam-4610	364	1	....................................	....................................	PUNCT
ejpam-4610	364	2	....................................	....................................	PUNCT
ejpam-4610	365	1	....................................	....................................	PUNCT
ejpam-4610	365	2	....................................	....................................	PUNCT
ejpam-4610	366	1	....................................	....................................	PUNCT
ejpam-4610	366	2	....................................	....................................	PUNCT
ejpam-4610	367	1	....................................	....................................	PUNCT
ejpam-4610	367	2	....................................	....................................	PUNCT
ejpam-4610	368	1	....................................	....................................	PUNCT
ejpam-4610	368	2	....................................	....................................	PUNCT
ejpam-4610	369	1	....................................	....................................	PUNCT
ejpam-4610	369	2	....................................	....................................	PUNCT
ejpam-4610	370	1	....................................	....................................	PUNCT
ejpam-4610	370	2	....................................	....................................	PUNCT
ejpam-4610	371	1	....................................	....................................	PUNCT
ejpam-4610	371	2	....................................	....................................	PUNCT
ejpam-4610	372	1	....................................	....................................	PUNCT
ejpam-4610	372	2	....................................	....................................	PUNCT
ejpam-4610	373	1	....................................	....................................	PUNCT
ejpam-4610	373	2	....................................	....................................	PUNCT
ejpam-4610	374	1	....................................	....................................	PUNCT
ejpam-4610	374	2	....................................	....................................	PUNCT
ejpam-4610	375	1	....................................	....................................	PUNCT
ejpam-4610	375	2	....................................	....................................	PUNCT
ejpam-4610	376	1	....................................	....................................	PUNCT
ejpam-4610	376	2	....................................	....................................	PUNCT
ejpam-4610	377	1	....................................	....................................	PUNCT
ejpam-4610	377	2	....................................	....................................	PUNCT
ejpam-4610	378	1	....................................	....................................	PUNCT
ejpam-4610	378	2	....................................	....................................	PUNCT
ejpam-4610	379	1	....................................	....................................	PUNCT
ejpam-4610	379	2	....................................	....................................	PUNCT
ejpam-4610	380	1	....................................	....................................	PUNCT
ejpam-4610	380	2	....................................	....................................	PUNCT
ejpam-4610	381	1	...........	...........	PUNCT
ejpam-4610	381	2	..........	..........	PUNCT
ejpam-4610	382	1	..........	..........	PUNCT
ejpam-4610	382	2	..........	..........	PUNCT
ejpam-4610	383	1	..........	..........	PUNCT
ejpam-4610	383	2	..........	..........	PUNCT
ejpam-4610	383	3	.	.	PUNCT
ejpam-4610	384	1	.................	.................	PUNCT
ejpam-4610	385	1	................	................	PUNCT
ejpam-4610	386	1	................	................	PUNCT
ejpam-4610	387	1	................	................	PUNCT
ejpam-4610	388	1	........	........	PUNCT
ejpam-4610	389	1	.................................	.................................	PUNCT
ejpam-4610	390	1	................................	................................	PUNCT
ejpam-4610	391	1	................................	................................	PUNCT
ejpam-4610	392	1	...........	...........	PUNCT
ejpam-4610	392	2	......................................................................................	......................................................................................	PUNCT
ejpam-4610	393	1	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-4610	393	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4610	394	1	...........	...........	PUNCT
ejpam-4610	395	1	..........	..........	PUNCT
ejpam-4610	396	1	..........	..........	PUNCT
ejpam-4610	397	1	..........	..........	PUNCT
ejpam-4610	398	1	..........	..........	PUNCT
ejpam-4610	399	1	..........	..........	PUNCT
ejpam-4610	399	2	.	.	PUNCT
ejpam-4610	400	1	.................	.................	PUNCT
ejpam-4610	401	1	................	................	PUNCT
ejpam-4610	402	1	................	................	PUNCT
ejpam-4610	403	1	................	................	PUNCT
ejpam-4610	404	1	........	........	PUNCT
ejpam-4610	405	1	.................................	.................................	PUNCT
ejpam-4610	406	1	................................	................................	PUNCT
ejpam-4610	407	1	................................	................................	PUNCT
ejpam-4610	408	1	...........	...........	PUNCT
ejpam-4610	408	2	......................................................................................	......................................................................................	PUNCT
ejpam-4610	409	1	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-4610	409	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4610	410	1	...........	...........	PUNCT
ejpam-4610	411	1	..........	..........	PUNCT
ejpam-4610	412	1	..........	..........	PUNCT
ejpam-4610	413	1	..........	..........	PUNCT
ejpam-4610	414	1	..........	..........	PUNCT
ejpam-4610	415	1	..........	..........	PUNCT
ejpam-4610	415	2	.	.	PUNCT
ejpam-4610	416	1	.................	.................	PUNCT
ejpam-4610	417	1	................	................	PUNCT
ejpam-4610	418	1	................	................	PUNCT
ejpam-4610	419	1	................	................	PUNCT
ejpam-4610	420	1	........	........	PUNCT
ejpam-4610	421	1	.................................	.................................	PUNCT
ejpam-4610	422	1	................................	................................	PUNCT
ejpam-4610	423	1	................................	................................	PUNCT
ejpam-4610	424	1	...........	...........	PUNCT
ejpam-4610	424	2	......................................................................................	......................................................................................	PUNCT
ejpam-4610	425	1	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-4610	425	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4610	426	1	...........	...........	PUNCT
ejpam-4610	427	1	..........	..........	PUNCT
ejpam-4610	428	1	..........	..........	PUNCT
ejpam-4610	429	1	..........	..........	PUNCT
ejpam-4610	430	1	..........	..........	PUNCT
ejpam-4610	431	1	..........	..........	PUNCT
ejpam-4610	431	2	.	.	PUNCT
ejpam-4610	432	1	.................	.................	PUNCT
ejpam-4610	433	1	................	................	PUNCT
ejpam-4610	434	1	................	................	PUNCT
ejpam-4610	435	1	................	................	PUNCT
ejpam-4610	436	1	........	........	PUNCT
ejpam-4610	437	1	.................................	.................................	PUNCT
ejpam-4610	438	1	................................	................................	PUNCT
ejpam-4610	439	1	................................	................................	PUNCT
ejpam-4610	440	1	...........	...........	PUNCT
ejpam-4610	440	2	......................................................................................	......................................................................................	PUNCT
ejpam-4610	441	1	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-4610	441	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4610	442	1	...........	...........	PUNCT
ejpam-4610	443	1	..........	..........	PUNCT
ejpam-4610	444	1	..........	..........	PUNCT
ejpam-4610	445	1	..........	..........	PUNCT
ejpam-4610	446	1	..........	..........	PUNCT
ejpam-4610	447	1	..........	..........	PUNCT
ejpam-4610	447	2	.	.	PUNCT
ejpam-4610	448	1	.................	.................	PUNCT
ejpam-4610	449	1	................	................	PUNCT
ejpam-4610	450	1	................	................	PUNCT
ejpam-4610	451	1	................	................	PUNCT
ejpam-4610	452	1	........	........	PUNCT
ejpam-4610	453	1	.................................	.................................	PUNCT
ejpam-4610	454	1	................................	................................	PUNCT
ejpam-4610	455	1	................................	................................	PUNCT
ejpam-4610	456	1	...........	...........	PUNCT
ejpam-4610	456	2	......................................................................................	......................................................................................	PUNCT
ejpam-4610	457	1	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-4610	457	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4610	458	1	...........	...........	PUNCT
ejpam-4610	459	1	..........	..........	PUNCT
ejpam-4610	460	1	..........	..........	PUNCT
ejpam-4610	461	1	..........	..........	PUNCT
ejpam-4610	462	1	..........	..........	PUNCT
ejpam-4610	463	1	..........	..........	PUNCT
ejpam-4610	463	2	.	.	PUNCT
ejpam-4610	464	1	.................	.................	PUNCT
ejpam-4610	465	1	................	................	PUNCT
ejpam-4610	466	1	................	................	PUNCT
ejpam-4610	467	1	................	................	PUNCT
ejpam-4610	468	1	........	........	PUNCT
ejpam-4610	469	1	.................................	.................................	PUNCT
ejpam-4610	470	1	................................	................................	PUNCT
ejpam-4610	471	1	................................	................................	PUNCT
ejpam-4610	472	1	...........	...........	PUNCT
ejpam-4610	472	2	......................................................................................	......................................................................................	PUNCT
ejpam-4610	473	1	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-4610	473	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4610	474	1	...........	...........	PUNCT
ejpam-4610	475	1	..........	..........	PUNCT
ejpam-4610	476	1	..........	..........	PUNCT
ejpam-4610	477	1	..........	..........	PUNCT
ejpam-4610	478	1	..........	..........	PUNCT
ejpam-4610	479	1	..........	..........	PUNCT
ejpam-4610	479	2	.	.	PUNCT
ejpam-4610	480	1	.................	.................	PUNCT
ejpam-4610	481	1	................	................	PUNCT
ejpam-4610	482	1	................	................	PUNCT
ejpam-4610	483	1	................	................	PUNCT
ejpam-4610	484	1	........	........	PUNCT
ejpam-4610	485	1	.................................	.................................	PUNCT
ejpam-4610	486	1	................................	................................	PUNCT
ejpam-4610	487	1	................................	................................	PUNCT
ejpam-4610	488	1	...........	...........	PUNCT
ejpam-4610	488	2	......................................................................................	......................................................................................	PUNCT
ejpam-4610	489	1	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-4610	489	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4610	490	1	.........	.........	PUNCT
ejpam-4610	491	1	........	........	PUNCT
ejpam-4610	492	1	........	........	PUNCT
ejpam-4610	493	1	........	........	PUNCT
ejpam-4610	494	1	........	........	PUNCT
ejpam-4610	495	1	........	........	PUNCT
ejpam-4610	496	1	........	........	PUNCT
ejpam-4610	497	1	.....	.....	PUNCT
ejpam-4610	498	1	.........	.........	PUNCT
ejpam-4610	499	1	........	........	PUNCT
ejpam-4610	500	1	........	........	PUNCT
ejpam-4610	501	1	........	........	PUNCT
ejpam-4610	502	1	........	........	PUNCT
ejpam-4610	503	1	........	........	PUNCT
ejpam-4610	504	1	........	........	PUNCT
ejpam-4610	505	1	.....	.....	PUNCT
ejpam-4610	506	1	.........	.........	PUNCT
ejpam-4610	507	1	........	........	PUNCT
ejpam-4610	508	1	........	........	PUNCT
ejpam-4610	509	1	........	........	PUNCT
ejpam-4610	510	1	........	........	PUNCT
ejpam-4610	511	1	........	........	PUNCT
ejpam-4610	512	1	........	........	PUNCT
ejpam-4610	513	1	.....	.....	PUNCT
ejpam-4610	514	1	.........	.........	PUNCT
ejpam-4610	515	1	........	........	PUNCT
ejpam-4610	516	1	........	........	PUNCT
ejpam-4610	517	1	........	........	PUNCT
ejpam-4610	518	1	........	........	PUNCT
ejpam-4610	519	1	........	........	PUNCT
ejpam-4610	520	1	........	........	PUNCT
ejpam-4610	521	1	.....	.....	PUNCT
ejpam-4610	522	1	.........	.........	PUNCT
ejpam-4610	523	1	........	........	PUNCT
ejpam-4610	524	1	........	........	PUNCT
ejpam-4610	525	1	........	........	PUNCT
ejpam-4610	526	1	........	........	PUNCT
ejpam-4610	527	1	........	........	PUNCT
ejpam-4610	528	1	........	........	PUNCT
ejpam-4610	529	1	.....	.....	PUNCT
ejpam-4610	530	1	.........	.........	PUNCT
ejpam-4610	531	1	........	........	PUNCT
ejpam-4610	532	1	........	........	PUNCT
ejpam-4610	533	1	........	........	PUNCT
ejpam-4610	534	1	........	........	PUNCT
ejpam-4610	535	1	........	........	PUNCT
ejpam-4610	536	1	........	........	PUNCT
ejpam-4610	537	1	.....	.....	PUNCT
ejpam-4610	538	1	.........	.........	PUNCT
ejpam-4610	539	1	........	........	PUNCT
ejpam-4610	540	1	........	........	PUNCT
ejpam-4610	541	1	........	........	PUNCT
ejpam-4610	542	1	........	........	PUNCT
ejpam-4610	543	1	........	........	PUNCT
ejpam-4610	544	1	........	........	PUNCT
ejpam-4610	545	1	.....	.....	PUNCT
ejpam-4610	546	1	.........	.........	PUNCT
ejpam-4610	547	1	........	........	PUNCT
ejpam-4610	548	1	........	........	PUNCT
ejpam-4610	549	1	........	........	PUNCT
ejpam-4610	550	1	........	........	PUNCT
ejpam-4610	551	1	........	........	PUNCT
ejpam-4610	552	1	........	........	PUNCT
ejpam-4610	553	1	.....	.....	PUNCT
ejpam-4610	554	1	.........	.........	PUNCT
ejpam-4610	555	1	........	........	PUNCT
ejpam-4610	556	1	........	........	PUNCT
ejpam-4610	557	1	........	........	PUNCT
ejpam-4610	558	1	........	........	PUNCT
ejpam-4610	559	1	........	........	PUNCT
ejpam-4610	560	1	........	........	PUNCT
ejpam-4610	561	1	.....	.....	PUNCT
ejpam-4610	562	1	.........	.........	PUNCT
ejpam-4610	563	1	........	........	PUNCT
ejpam-4610	564	1	........	........	PUNCT
ejpam-4610	565	1	........	........	PUNCT
ejpam-4610	566	1	........	........	PUNCT
ejpam-4610	567	1	........	........	PUNCT
ejpam-4610	568	1	........	........	PUNCT
ejpam-4610	569	1	.....	.....	PUNCT
ejpam-4610	570	1	.........	.........	PUNCT
ejpam-4610	571	1	........	........	PUNCT
ejpam-4610	572	1	........	........	PUNCT
ejpam-4610	573	1	........	........	PUNCT
ejpam-4610	574	1	........	........	PUNCT
ejpam-4610	575	1	........	........	PUNCT
ejpam-4610	576	1	........	........	PUNCT
ejpam-4610	577	1	.....	.....	PUNCT
ejpam-4610	578	1	.........	.........	PUNCT
ejpam-4610	579	1	........	........	PUNCT
ejpam-4610	580	1	........	........	PUNCT
ejpam-4610	581	1	........	........	PUNCT
ejpam-4610	582	1	........	........	PUNCT
ejpam-4610	583	1	........	........	PUNCT
ejpam-4610	584	1	........	........	PUNCT
ejpam-4610	585	1	.....	.....	PUNCT
ejpam-4610	586	1	.........	.........	PUNCT
ejpam-4610	587	1	........	........	PUNCT
ejpam-4610	588	1	........	........	PUNCT
ejpam-4610	589	1	........	........	PUNCT
ejpam-4610	590	1	........	........	PUNCT
ejpam-4610	591	1	........	........	PUNCT
ejpam-4610	592	1	........	........	PUNCT
ejpam-4610	593	1	.....	.....	PUNCT
ejpam-4610	594	1	.........	.........	PUNCT
ejpam-4610	595	1	........	........	PUNCT
ejpam-4610	596	1	........	........	PUNCT
ejpam-4610	597	1	........	........	PUNCT
ejpam-4610	598	1	........	........	PUNCT
ejpam-4610	599	1	........	........	PUNCT
ejpam-4610	600	1	........	........	PUNCT
ejpam-4610	601	1	.....	.....	PUNCT
ejpam-4610	602	1	.........	.........	PUNCT
ejpam-4610	603	1	........	........	PUNCT
ejpam-4610	604	1	........	........	PUNCT
ejpam-4610	605	1	........	........	PUNCT
ejpam-4610	606	1	........	........	PUNCT
ejpam-4610	607	1	........	........	PUNCT
ejpam-4610	608	1	........	........	PUNCT
ejpam-4610	609	1	.....	.....	PUNCT
ejpam-4610	610	1	.........	.........	PUNCT
ejpam-4610	611	1	........	........	PUNCT
ejpam-4610	612	1	........	........	PUNCT
ejpam-4610	613	1	........	........	PUNCT
ejpam-4610	614	1	........	........	PUNCT
ejpam-4610	615	1	........	........	PUNCT
ejpam-4610	616	1	........	........	PUNCT
ejpam-4610	617	1	.....	.....	PUNCT
ejpam-4610	618	1	.........	.........	PUNCT
ejpam-4610	619	1	........	........	PUNCT
ejpam-4610	620	1	........	........	PUNCT
ejpam-4610	621	1	........	........	PUNCT
ejpam-4610	622	1	........	........	PUNCT
ejpam-4610	623	1	........	........	PUNCT
ejpam-4610	624	1	........	........	PUNCT
ejpam-4610	625	1	.....	.....	PUNCT
ejpam-4610	626	1	.........	.........	PUNCT
ejpam-4610	627	1	........	........	PUNCT
ejpam-4610	628	1	........	........	PUNCT
ejpam-4610	629	1	........	........	PUNCT
ejpam-4610	630	1	........	........	PUNCT
ejpam-4610	631	1	........	........	PUNCT
ejpam-4610	632	1	........	........	PUNCT
ejpam-4610	633	1	.....	.....	PUNCT
ejpam-4610	634	1	.........	.........	PUNCT
ejpam-4610	635	1	........	........	PUNCT
ejpam-4610	636	1	........	........	PUNCT
ejpam-4610	637	1	........	........	PUNCT
ejpam-4610	638	1	........	........	PUNCT
ejpam-4610	639	1	........	........	PUNCT
ejpam-4610	640	1	........	........	PUNCT
ejpam-4610	641	1	.....	.....	PUNCT
ejpam-4610	642	1	.........	.........	PUNCT
ejpam-4610	643	1	........	........	PUNCT
ejpam-4610	644	1	........	........	PUNCT
ejpam-4610	645	1	........	........	PUNCT
ejpam-4610	646	1	........	........	PUNCT
ejpam-4610	647	1	........	........	PUNCT
ejpam-4610	648	1	........	........	PUNCT
ejpam-4610	649	1	.....	.....	PUNCT
ejpam-4610	650	1	.........	.........	PUNCT
ejpam-4610	651	1	........	........	PUNCT
ejpam-4610	652	1	........	........	PUNCT
ejpam-4610	653	1	........	........	PUNCT
ejpam-4610	654	1	........	........	PUNCT
ejpam-4610	655	1	........	........	PUNCT
ejpam-4610	656	1	........	........	PUNCT
ejpam-4610	657	1	.....	.....	PUNCT
ejpam-4610	658	1	.........	.........	PUNCT
ejpam-4610	659	1	........	........	PUNCT
ejpam-4610	660	1	........	........	PUNCT
ejpam-4610	661	1	........	........	PUNCT
ejpam-4610	662	1	........	........	PUNCT
ejpam-4610	663	1	........	........	PUNCT
ejpam-4610	664	1	........	........	PUNCT
ejpam-4610	665	1	.....	.....	PUNCT
ejpam-4610	666	1	.........	.........	PUNCT
ejpam-4610	667	1	........	........	PUNCT
ejpam-4610	668	1	........	........	PUNCT
ejpam-4610	669	1	........	........	PUNCT
ejpam-4610	670	1	........	........	PUNCT
ejpam-4610	671	1	........	........	PUNCT
ejpam-4610	672	1	........	........	PUNCT
ejpam-4610	673	1	.....	.....	PUNCT
ejpam-4610	674	1	.........	.........	PUNCT
ejpam-4610	675	1	........	........	PUNCT
ejpam-4610	676	1	........	........	PUNCT
ejpam-4610	677	1	........	........	PUNCT
ejpam-4610	678	1	........	........	PUNCT
ejpam-4610	679	1	........	........	PUNCT
ejpam-4610	680	1	........	........	PUNCT
ejpam-4610	681	1	.....	.....	PUNCT
ejpam-4610	682	1	.........	.........	PUNCT
ejpam-4610	683	1	........	........	PUNCT
ejpam-4610	684	1	........	........	PUNCT
ejpam-4610	685	1	........	........	PUNCT
ejpam-4610	686	1	........	........	PUNCT
ejpam-4610	687	1	........	........	PUNCT
ejpam-4610	688	1	........	........	PUNCT
ejpam-4610	689	1	.....	.....	PUNCT
ejpam-4610	690	1	.........	.........	PUNCT
ejpam-4610	691	1	........	........	PUNCT
ejpam-4610	692	1	........	........	PUNCT
ejpam-4610	693	1	........	........	PUNCT
ejpam-4610	694	1	........	........	PUNCT
ejpam-4610	695	1	........	........	PUNCT
ejpam-4610	696	1	........	........	PUNCT
ejpam-4610	697	1	.....	.....	PUNCT
ejpam-4610	698	1	.........	.........	PUNCT
ejpam-4610	699	1	........	........	PUNCT
ejpam-4610	700	1	........	........	PUNCT
ejpam-4610	701	1	........	........	PUNCT
ejpam-4610	702	1	........	........	PUNCT
ejpam-4610	703	1	........	........	PUNCT
ejpam-4610	704	1	........	........	PUNCT
ejpam-4610	705	1	.....	.....	PUNCT
ejpam-4610	706	1	.........	.........	PUNCT
ejpam-4610	707	1	........	........	PUNCT
ejpam-4610	708	1	........	........	PUNCT
ejpam-4610	709	1	........	........	PUNCT
ejpam-4610	710	1	........	........	PUNCT
ejpam-4610	711	1	........	........	PUNCT
ejpam-4610	712	1	........	........	PUNCT
ejpam-4610	713	1	.....	.....	PUNCT
ejpam-4610	714	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	715	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	716	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	717	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	718	1	............................................................................	............................................................................	PUNCT
ejpam-4610	719	1	............................................................................	............................................................................	PUNCT
ejpam-4610	720	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	721	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	722	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	723	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	724	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	725	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	726	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	727	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	728	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	729	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	730	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4610	731	1	x1	x1	NUM
ejpam-4610	732	1	x2	x2	NOUN
ejpam-4610	732	2	x3	x3	PROPN
ejpam-4610	732	3	x4	x4	PROPN
ejpam-4610	732	4	x5	x5	PROPN
ejpam-4610	732	5	.	.	PUNCT
ejpam-4610	732	6	.	.	PUNCT
ejpam-4610	732	7	.	.	PUNCT
ejpam-4610	733	1	xa−1	xa−1	PROPN
ejpam-4610	733	2	xa	xa	PROPN
ejpam-4610	734	1	y1	y1	INTJ
ejpam-4610	734	2	y2	y2	PROPN
ejpam-4610	734	3	y3	y3	PROPN
ejpam-4610	734	4	y4	y4	NOUN
ejpam-4610	734	5	y5	y5	PROPN
ejpam-4610	734	6	ya−1	ya−1	NOUN
ejpam-4610	734	7	ya	ya	PROPN
ejpam-4610	734	8	z1	z1	PROPN
ejpam-4610	734	9	z2	z2	PROPN
ejpam-4610	734	10	z3	z3	PROPN
ejpam-4610	734	11	z4	z4	PROPN
ejpam-4610	734	12	z5	z5	PROPN
ejpam-4610	734	13	za−1	za−1	PROPN
ejpam-4610	734	14	za	za	PROPN
ejpam-4610	734	15	v1	v1	PROPN
ejpam-4610	734	16	v2	v2	PROPN
ejpam-4610	734	17	v3	v3	PROPN
ejpam-4610	734	18	v4	v4	PROPN
ejpam-4610	734	19	v5	v5	PROPN
ejpam-4610	734	20	va−1	va−1	PROPN
ejpam-4610	734	21	va	va	PROPN
ejpam-4610	734	22	w1	w1	PROPN
ejpam-4610	734	23	w2	w2	PROPN
ejpam-4610	734	24	w3	w3	PROPN
ejpam-4610	734	25	w4	w4	PROPN
ejpam-4610	734	26	w5	w5	PROPN
ejpam-4610	734	27	wa−1	wa−1	PROPN
ejpam-4610	734	28	wa	wa	PROPN
ejpam-4610	735	1	x1	x1	PROPN
ejpam-4610	735	2	1	1	NUM
ejpam-4610	735	3	x2	x2	NOUN
ejpam-4610	735	4	1	1	NUM
ejpam-4610	735	5	.	.	PUNCT
ejpam-4610	735	6	.	.	PUNCT
ejpam-4610	735	7	.	.	PUNCT
ejpam-4610	736	1	xn	xn	PROPN
ejpam-4610	737	1	1	1	NUM
ejpam-4610	737	2	x1	x1	NUM
ejpam-4610	737	3	2	2	NUM
ejpam-4610	737	4	x2	x2	NOUN
ejpam-4610	737	5	2	2	NUM
ejpam-4610	737	6	.	.	PUNCT
ejpam-4610	737	7	.	.	PUNCT
ejpam-4610	737	8	.	.	PUNCT
ejpam-4610	738	1	xn	xn	PROPN
ejpam-4610	739	1	2	2	NUM
ejpam-4610	739	2	x1	x1	PROPN
ejpam-4610	739	3	3	3	NUM
ejpam-4610	739	4	x2	x2	NOUN
ejpam-4610	739	5	3	3	NUM
ejpam-4610	739	6	.	.	PUNCT
ejpam-4610	739	7	.	.	PUNCT
ejpam-4610	739	8	.	.	PUNCT
ejpam-4610	740	1	xn	xn	PROPN
ejpam-4610	741	1	3	3	NUM
ejpam-4610	741	2	x1	x1	PROPN
ejpam-4610	741	3	4	4	NUM
ejpam-4610	741	4	x2	x2	NOUN
ejpam-4610	741	5	4	4	NUM
ejpam-4610	741	6	.	.	PUNCT
ejpam-4610	741	7	.	.	PUNCT
ejpam-4610	741	8	.	.	PUNCT
ejpam-4610	742	1	xn	xn	PROPN
ejpam-4610	743	1	4	4	NUM
ejpam-4610	744	1	x1	x1	PROPN
ejpam-4610	744	2	5	5	NUM
ejpam-4610	744	3	x2	x2	NOUN
ejpam-4610	744	4	5	5	NUM
ejpam-4610	744	5	.	.	PUNCT
ejpam-4610	744	6	.	.	PUNCT
ejpam-4610	744	7	.	.	PUNCT
ejpam-4610	745	1	xn	xn	PROPN
ejpam-4610	746	1	5	5	NUM
ejpam-4610	747	1	x1	x1	NOUN
ejpam-4610	747	2	5	5	NUM
ejpam-4610	747	3	x2	x2	NOUN
ejpam-4610	747	4	5	5	NUM
ejpam-4610	747	5	.	.	PUNCT
ejpam-4610	747	6	.	.	PUNCT
ejpam-4610	747	7	.	.	PUNCT
ejpam-4610	748	1	xn	xn	PROPN
ejpam-4610	748	2	5	5	NUM
ejpam-4610	749	1	x1	x1	NUM
ejpam-4610	749	2	a−1	a−1	PROPN
ejpam-4610	749	3	x2	x2	PROPN
ejpam-4610	749	4	a−1	a−1	PROPN
ejpam-4610	749	5	.	.	PUNCT
ejpam-4610	749	6	.	.	PUNCT
ejpam-4610	749	7	.	.	PUNCT
ejpam-4610	750	1	xn	xn	PROPN
ejpam-4610	751	1	a−1	a−1	PROPN
ejpam-4610	751	2	x1	x1	PROPN
ejpam-4610	751	3	a	a	DET
ejpam-4610	751	4	x2	x2	NOUN
ejpam-4610	751	5	a	a	X
ejpam-4610	751	6	.	.	PUNCT
ejpam-4610	751	7	.	.	PUNCT
ejpam-4610	751	8	.	.	PUNCT
ejpam-4610	752	1	xn	xn	PROPN
ejpam-4610	753	1	a	a	DET
ejpam-4610	753	2	figure	figure	NOUN
ejpam-4610	753	3	4	4	NUM
ejpam-4610	753	4	:	:	PUNCT
ejpam-4610	753	5	graph	graph	VERB
ejpam-4610	753	6	g	g	NOUN
ejpam-4610	753	7	with	with	ADP
ejpam-4610	753	8	γh(g	γh(g	NOUN
ejpam-4610	753	9	)	)	PUNCT
ejpam-4610	753	10	=	=	SYM
ejpam-4610	753	11	a	a	PRON
ejpam-4610	753	12	and	and	CCONJ
ejpam-4610	753	13	γ̂h(g	γ̂h(g	PROPN
ejpam-4610	753	14	)	)	PUNCT
ejpam-4610	754	1	=	=	SYM
ejpam-4610	754	2	b	b	X
ejpam-4610	754	3	corollary	corollary	ADJ
ejpam-4610	754	4	1	1	NUM
ejpam-4610	754	5	.	.	PUNCT
ejpam-4610	755	1	for	for	ADP
ejpam-4610	755	2	each	each	DET
ejpam-4610	755	3	positive	positive	ADJ
ejpam-4610	755	4	integer	integer	NOUN
ejpam-4610	755	5	n	n	CCONJ
ejpam-4610	755	6	,	,	PUNCT
ejpam-4610	755	7	there	there	PRON
ejpam-4610	755	8	exists	exist	VERB
ejpam-4610	755	9	a	a	DET
ejpam-4610	755	10	connected	connected	ADJ
ejpam-4610	755	11	graph	graph	NOUN
ejpam-4610	755	12	g	g	ADP
ejpam-4610	755	13	such	such	ADJ
ejpam-4610	755	14	that	that	DET
ejpam-4610	755	15	γ̂h(g)−	γ̂h(g)−	NOUN
ejpam-4610	755	16	γh(g	γh(g	NOUN
ejpam-4610	755	17	)	)	PUNCT
ejpam-4610	756	1	=	=	VERB
ejpam-4610	756	2	n.	n.	NOUN
ejpam-4610	756	3	that	that	PRON
ejpam-4610	756	4	is	be	AUX
ejpam-4610	756	5	,	,	PUNCT
ejpam-4610	756	6	the	the	DET
ejpam-4610	756	7	difference	difference	NOUN
ejpam-4610	756	8	γ̂h	γ̂h	NOUN
ejpam-4610	756	9	−	−	NOUN
ejpam-4610	756	10	γh	γh	INTJ
ejpam-4610	756	11	can	can	AUX
ejpam-4610	756	12	be	be	AUX
ejpam-4610	756	13	made	make	VERB
ejpam-4610	756	14	arbitrarily	arbitrarily	ADV
ejpam-4610	756	15	large	large	ADJ
ejpam-4610	756	16	.	.	PUNCT
ejpam-4610	757	1	5	5	X
ejpam-4610	757	2	.	.	X
ejpam-4610	757	3	in	in	ADP
ejpam-4610	757	4	the	the	DET
ejpam-4610	757	5	join	join	NOUN
ejpam-4610	757	6	of	of	ADP
ejpam-4610	757	7	graphs	graph	NOUN
ejpam-4610	757	8	to	to	PART
ejpam-4610	757	9	attain	attain	VERB
ejpam-4610	757	10	a	a	DET
ejpam-4610	757	11	precise	precise	ADJ
ejpam-4610	757	12	characterization	characterization	NOUN
ejpam-4610	757	13	of	of	ADP
ejpam-4610	757	14	transversal	transversal	ADJ
ejpam-4610	757	15	hop	hop	NOUN
ejpam-4610	757	16	dominating	dominating	NOUN
ejpam-4610	757	17	sets	set	NOUN
ejpam-4610	757	18	in	in	ADP
ejpam-4610	757	19	the	the	DET
ejpam-4610	757	20	join	join	NOUN
ejpam-4610	757	21	of	of	ADP
ejpam-4610	757	22	graphs	graph	NOUN
ejpam-4610	757	23	,	,	PUNCT
ejpam-4610	757	24	we	we	PRON
ejpam-4610	757	25	give	give	VERB
ejpam-4610	757	26	the	the	DET
ejpam-4610	757	27	following	follow	VERB
ejpam-4610	757	28	definition	definition	NOUN
ejpam-4610	757	29	.	.	PUNCT
ejpam-4610	758	1	a	a	DET
ejpam-4610	758	2	set	set	NOUN
ejpam-4610	758	3	s	s	NOUN
ejpam-4610	758	4	⊆	⊆	NUM
ejpam-4610	758	5	v	v	NOUN
ejpam-4610	758	6	(	(	PUNCT
ejpam-4610	758	7	g	g	NOUN
ejpam-4610	758	8	)	)	PUNCT
ejpam-4610	758	9	is	be	AUX
ejpam-4610	758	10	a	a	DET
ejpam-4610	758	11	transversal	transversal	ADJ
ejpam-4610	758	12	point	point	NOUN
ejpam-4610	758	13	-	-	PUNCT
ejpam-4610	758	14	wise	wise	ADJ
ejpam-4610	758	15	non	non	ADJ
ejpam-4610	758	16	-	-	ADJ
ejpam-4610	758	17	dominating	dominating	ADJ
ejpam-4610	758	18	set	set	NOUN
ejpam-4610	758	19	(	(	PUNCT
ejpam-4610	758	20	or	or	CCONJ
ejpam-4610	758	21	trpnd	trpnd	ADV
ejpam-4610	758	22	-	-	PUNCT
ejpam-4610	758	23	set	set	NOUN
ejpam-4610	758	24	)	)	PUNCT
ejpam-4610	758	25	of	of	ADP
ejpam-4610	758	26	g	g	PROPN
ejpam-4610	758	27	if	if	SCONJ
ejpam-4610	758	28	s	s	VERB
ejpam-4610	758	29	is	be	AUX
ejpam-4610	758	30	a	a	DET
ejpam-4610	758	31	pnd	pnd	NOUN
ejpam-4610	758	32	-	-	PUNCT
ejpam-4610	758	33	set	set	NOUN
ejpam-4610	758	34	of	of	ADP
ejpam-4610	758	35	g	g	NOUN
ejpam-4610	758	36	that	that	PRON
ejpam-4610	758	37	intersects	intersect	VERB
ejpam-4610	758	38	every	every	DET
ejpam-4610	758	39	pnd	pnd	NOUN
ejpam-4610	758	40	-	-	PUNCT
ejpam-4610	758	41	set	set	NOUN
ejpam-4610	758	42	of	of	ADP
ejpam-4610	758	43	g.	g.	PROPN
ejpam-4610	758	44	the	the	DET
ejpam-4610	758	45	minimum	minimum	ADJ
ejpam-4610	758	46	cardinality	cardinality	NOUN
ejpam-4610	758	47	of	of	ADP
ejpam-4610	758	48	a	a	DET
ejpam-4610	758	49	trpnd	trpnd	NOUN
ejpam-4610	758	50	-	-	PUNCT
ejpam-4610	758	51	set	set	NOUN
ejpam-4610	758	52	of	of	ADP
ejpam-4610	758	53	g	g	NOUN
ejpam-4610	758	54	,	,	PUNCT
ejpam-4610	758	55	denoted	denote	VERB
ejpam-4610	758	56	trpnd(g	trpnd(g	PROPN
ejpam-4610	758	57	)	)	PUNCT
ejpam-4610	758	58	,	,	PUNCT
ejpam-4610	758	59	is	be	AUX
ejpam-4610	758	60	the	the	DET
ejpam-4610	758	61	transversal	transversal	ADJ
ejpam-4610	758	62	point	point	NOUN
ejpam-4610	758	63	-	-	PUNCT
ejpam-4610	758	64	wise	wise	ADJ
ejpam-4610	758	65	non	non	ADJ
ejpam-4610	758	66	-	-	ADJ
ejpam-4610	758	67	domination	domination	ADJ
ejpam-4610	758	68	number	number	NOUN
ejpam-4610	758	69	of	of	ADP
ejpam-4610	758	70	g.	g.	PROPN
ejpam-4610	758	71	any	any	DET
ejpam-4610	758	72	transversal	transversal	ADJ
ejpam-4610	758	73	point	point	NOUN
ejpam-4610	758	74	-	-	PUNCT
ejpam-4610	758	75	wise	wise	ADV
ejpam-4610	758	76	nondominating	nondominate	VERB
ejpam-4610	758	77	set	set	NOUN
ejpam-4610	758	78	of	of	ADP
ejpam-4610	758	79	g	g	NOUN
ejpam-4610	758	80	of	of	ADP
ejpam-4610	758	81	cardinality	cardinality	PROPN
ejpam-4610	758	82	trpnd(g	trpnd(g	PROPN
ejpam-4610	758	83	)	)	PUNCT
ejpam-4610	758	84	is	be	AUX
ejpam-4610	758	85	referred	refer	VERB
ejpam-4610	758	86	to	to	ADP
ejpam-4610	758	87	as	as	ADP
ejpam-4610	758	88	a	a	DET
ejpam-4610	758	89	trpnd	trpnd	NOUN
ejpam-4610	758	90	-	-	PUNCT
ejpam-4610	758	91	set	set	NOUN
ejpam-4610	758	92	.	.	PUNCT
ejpam-4610	759	1	for	for	ADP
ejpam-4610	759	2	complete	complete	ADJ
ejpam-4610	759	3	graphs	graph	NOUN
ejpam-4610	759	4	,	,	PUNCT
ejpam-4610	759	5	complete	complete	ADJ
ejpam-4610	759	6	bipartite	bipartite	NOUN
ejpam-4610	759	7	graphs	graph	NOUN
ejpam-4610	759	8	,	,	PUNCT
ejpam-4610	759	9	paths	path	NOUN
ejpam-4610	759	10	and	and	CCONJ
ejpam-4610	759	11	cycles	cycle	NOUN
ejpam-4610	759	12	,	,	PUNCT
ejpam-4610	759	13	we	we	PRON
ejpam-4610	759	14	have	have	VERB
ejpam-4610	759	15	trpnd(kn	trpnd(kn	NOUN
ejpam-4610	759	16	)	)	PUNCT
ejpam-4610	759	17	=	=	SYM
ejpam-4610	759	18	n	n	PROPN
ejpam-4610	759	19	for	for	ADP
ejpam-4610	759	20	all	all	DET
ejpam-4610	759	21	n	n	PRON
ejpam-4610	759	22	≥	≥	NOUN
ejpam-4610	759	23	1	1	NUM
ejpam-4610	759	24	;	;	PUNCT
ejpam-4610	759	25	m.a	m.a	PROPN
ejpam-4610	759	26	.	.	PROPN
ejpam-4610	759	27	bonsocan	bonsocan	PROPN
ejpam-4610	759	28	,	,	PUNCT
ejpam-4610	759	29	f.	f.	PROPN
ejpam-4610	759	30	jamil	jamil	PROPN
ejpam-4610	759	31	/	/	SYM
ejpam-4610	759	32	eur	eur	PROPN
ejpam-4610	759	33	.	.	PUNCT
ejpam-4610	760	1	j.	j.	PROPN
ejpam-4610	760	2	pure	pure	PROPN
ejpam-4610	760	3	appl	appl	PROPN
ejpam-4610	760	4	.	.	PROPN
ejpam-4610	760	5	math	math	PROPN
ejpam-4610	760	6	,	,	PUNCT
ejpam-4610	760	7	16	16	NUM
ejpam-4610	760	8	(	(	PUNCT
ejpam-4610	760	9	1	1	NUM
ejpam-4610	760	10	)	)	PUNCT
ejpam-4610	760	11	(	(	PUNCT
ejpam-4610	760	12	2023	2023	NUM
ejpam-4610	760	13	)	)	PUNCT
ejpam-4610	760	14	,	,	PUNCT
ejpam-4610	760	15	192	192	NUM
ejpam-4610	760	16	-	-	SYM
ejpam-4610	760	17	206	206	NUM
ejpam-4610	760	18	200	200	NUM
ejpam-4610	760	19	trpnd(km	trpnd(km	PROPN
ejpam-4610	760	20	,	,	PUNCT
ejpam-4610	760	21	n	n	CCONJ
ejpam-4610	760	22	)	)	PUNCT
ejpam-4610	760	23	=	=	SYM
ejpam-4610	761	1	1	1	NUM
ejpam-4610	761	2	+	+	NOUN
ejpam-4610	761	3	min{m	min{m	NOUN
ejpam-4610	761	4	,	,	PUNCT
ejpam-4610	761	5	n	n	CCONJ
ejpam-4610	761	6	}	}	PUNCT
ejpam-4610	761	7	for	for	ADP
ejpam-4610	761	8	all	all	DET
ejpam-4610	761	9	m	m	PROPN
ejpam-4610	761	10	,	,	PUNCT
ejpam-4610	761	11	n	n	CCONJ
ejpam-4610	761	12	not	not	PART
ejpam-4610	761	13	both	both	ADV
ejpam-4610	761	14	equal	equal	ADJ
ejpam-4610	761	15	to	to	ADP
ejpam-4610	761	16	1	1	NUM
ejpam-4610	761	17	;	;	PUNCT
ejpam-4610	761	18	trpnd(pn	trpnd(pn	NUM
ejpam-4610	761	19	)	)	PUNCT
ejpam-4610	761	20	=	=	PRON
ejpam-4610	761	21	{	{	PUNCT
ejpam-4610	761	22	n−	n−	NOUN
ejpam-4610	761	23	1	1	NUM
ejpam-4610	761	24	,	,	PUNCT
ejpam-4610	761	25	if	if	SCONJ
ejpam-4610	761	26	n	n	NOUN
ejpam-4610	761	27	=	=	SYM
ejpam-4610	761	28	3	3	NUM
ejpam-4610	761	29	,	,	PUNCT
ejpam-4610	761	30	4	4	NUM
ejpam-4610	761	31	n−	n−	NOUN
ejpam-4610	761	32	2	2	NUM
ejpam-4610	761	33	,	,	PUNCT
ejpam-4610	761	34	if	if	SCONJ
ejpam-4610	761	35	n	n	PRON
ejpam-4610	761	36	≥	≥	NOUN
ejpam-4610	761	37	5	5	NUM
ejpam-4610	761	38	;	;	PUNCT
ejpam-4610	761	39	and	and	CCONJ
ejpam-4610	761	40	trpnd(cn	trpnd(cn	X
ejpam-4610	761	41	)	)	PUNCT
ejpam-4610	761	42	=	=	PUNCT
ejpam-4610	762	1			PRON
ejpam-4610	762	2	n−	n−	NOUN
ejpam-4610	762	3	1	1	NUM
ejpam-4610	762	4	,	,	PUNCT
ejpam-4610	762	5	if	if	SCONJ
ejpam-4610	762	6	n	n	NOUN
ejpam-4610	762	7	=	=	SYM
ejpam-4610	762	8	4	4	NUM
ejpam-4610	762	9	,	,	PUNCT
ejpam-4610	762	10	n−	n−	NOUN
ejpam-4610	762	11	3	3	NUM
ejpam-4610	762	12	,	,	PUNCT
ejpam-4610	762	13	if	if	SCONJ
ejpam-4610	762	14	n	n	NOUN
ejpam-4610	762	15	=	=	SYM
ejpam-4610	762	16	6	6	NUM
ejpam-4610	762	17	,	,	PUNCT
ejpam-4610	762	18	n−	n−	NOUN
ejpam-4610	762	19	2	2	NUM
ejpam-4610	762	20	,	,	PUNCT
ejpam-4610	762	21	if	if	SCONJ
ejpam-4610	762	22	n	n	NOUN
ejpam-4610	762	23	=	=	SYM
ejpam-4610	762	24	5	5	NUM
ejpam-4610	762	25	and	and	CCONJ
ejpam-4610	762	26	n	n	PRON
ejpam-4610	762	27	≥	≥	NOUN
ejpam-4610	762	28	7	7	NUM
ejpam-4610	762	29	.	.	PUNCT
ejpam-4610	763	1	the	the	DET
ejpam-4610	763	2	following	follow	VERB
ejpam-4610	763	3	theorem	theorem	NOUN
ejpam-4610	763	4	is	be	AUX
ejpam-4610	763	5	due	due	ADJ
ejpam-4610	763	6	to	to	PART
ejpam-4610	763	7	canoy	canoy	VERB
ejpam-4610	763	8	et	et	PROPN
ejpam-4610	763	9	al	al	PROPN
ejpam-4610	763	10	.	.	PUNCT
ejpam-4610	764	1	[	[	X
ejpam-4610	764	2	13	13	NUM
ejpam-4610	764	3	]	]	PUNCT
ejpam-4610	764	4	from	from	ADP
ejpam-4610	764	5	which	which	PRON
ejpam-4610	764	6	we	we	PRON
ejpam-4610	764	7	draw	draw	VERB
ejpam-4610	764	8	the	the	DET
ejpam-4610	764	9	succeeding	succeed	VERB
ejpam-4610	764	10	lemma	lemma	PROPN
ejpam-4610	764	11	.	.	PUNCT
ejpam-4610	764	12	theorem	theorem	VERB
ejpam-4610	764	13	5	5	NUM
ejpam-4610	764	14	.	.	PUNCT
ejpam-4610	765	1	[	[	X
ejpam-4610	765	2	13	13	NUM
ejpam-4610	765	3	]	]	PUNCT
ejpam-4610	765	4	let	let	VERB
ejpam-4610	765	5	g	g	NOUN
ejpam-4610	765	6	and	and	CCONJ
ejpam-4610	765	7	h	h	NOUN
ejpam-4610	765	8	be	be	VERB
ejpam-4610	765	9	any	any	DET
ejpam-4610	765	10	two	two	NUM
ejpam-4610	765	11	graphs	graph	NOUN
ejpam-4610	765	12	.	.	PUNCT
ejpam-4610	766	1	a	a	DET
ejpam-4610	766	2	set	set	NOUN
ejpam-4610	766	3	s	s	NOUN
ejpam-4610	766	4	⊆	⊆	NUM
ejpam-4610	766	5	v	v	NOUN
ejpam-4610	766	6	(	(	PUNCT
ejpam-4610	766	7	g+h	g+h	PROPN
ejpam-4610	766	8	)	)	PUNCT
ejpam-4610	766	9	is	be	AUX
ejpam-4610	766	10	hop	hop	NOUN
ejpam-4610	766	11	dominating	dominate	VERB
ejpam-4610	766	12	set	set	NOUN
ejpam-4610	766	13	of	of	ADP
ejpam-4610	766	14	g	g	PROPN
ejpam-4610	766	15	+	+	PROPN
ejpam-4610	766	16	h	h	NOUN
ejpam-4610	766	17	if	if	SCONJ
ejpam-4610	767	1	and	and	CCONJ
ejpam-4610	767	2	only	only	ADV
ejpam-4610	767	3	if	if	SCONJ
ejpam-4610	767	4	s	s	VERB
ejpam-4610	767	5	=	=	PUNCT
ejpam-4610	767	6	sg	sg	X
ejpam-4610	767	7	∪	∪	ADJ
ejpam-4610	768	1	sh	sh	PROPN
ejpam-4610	768	2	,	,	PUNCT
ejpam-4610	768	3	where	where	SCONJ
ejpam-4610	768	4	sg	sg	PROPN
ejpam-4610	768	5	and	and	CCONJ
ejpam-4610	768	6	sh	sh	PROPN
ejpam-4610	768	7	are	be	AUX
ejpam-4610	768	8	pnd	pnd	NOUN
ejpam-4610	768	9	-	-	PUNCT
ejpam-4610	768	10	sets	set	NOUN
ejpam-4610	768	11	of	of	ADP
ejpam-4610	768	12	g	g	PROPN
ejpam-4610	768	13	and	and	CCONJ
ejpam-4610	768	14	h	h	NOUN
ejpam-4610	768	15	,	,	PUNCT
ejpam-4610	768	16	respectively	respectively	ADV
ejpam-4610	768	17	.	.	PUNCT
ejpam-4610	769	1	lemma	lemma	PROPN
ejpam-4610	769	2	1	1	X
ejpam-4610	769	3	.	.	PUNCT
ejpam-4610	770	1	let	let	VERB
ejpam-4610	770	2	g	g	NOUN
ejpam-4610	770	3	and	and	CCONJ
ejpam-4610	770	4	h	h	NOUN
ejpam-4610	770	5	be	be	VERB
ejpam-4610	770	6	any	any	DET
ejpam-4610	770	7	two	two	NUM
ejpam-4610	770	8	graphs	graph	NOUN
ejpam-4610	770	9	.	.	PUNCT
ejpam-4610	771	1	then	then	ADV
ejpam-4610	771	2	s	s	VERB
ejpam-4610	771	3	is	be	AUX
ejpam-4610	771	4	a	a	DET
ejpam-4610	771	5	γh	γh	ADV
ejpam-4610	771	6	-	-	PUNCT
ejpam-4610	771	7	set	set	NOUN
ejpam-4610	771	8	of	of	ADP
ejpam-4610	771	9	g+h	g+h	PROPN
ejpam-4610	771	10	if	if	SCONJ
ejpam-4610	771	11	and	and	CCONJ
ejpam-4610	771	12	only	only	ADV
ejpam-4610	771	13	if	if	SCONJ
ejpam-4610	771	14	s	s	VERB
ejpam-4610	771	15	=	=	PUNCT
ejpam-4610	771	16	sg	sg	X
ejpam-4610	771	17	∪	∪	ADJ
ejpam-4610	771	18	sh	sh	PROPN
ejpam-4610	771	19	,	,	PUNCT
ejpam-4610	771	20	where	where	SCONJ
ejpam-4610	771	21	sg	sg	ADP
ejpam-4610	771	22	⊆	⊆	NUM
ejpam-4610	771	23	v	v	NOUN
ejpam-4610	771	24	(	(	PUNCT
ejpam-4610	771	25	g	g	NOUN
ejpam-4610	771	26	)	)	PUNCT
ejpam-4610	771	27	and	and	CCONJ
ejpam-4610	771	28	sh	sh	PROPN
ejpam-4610	771	29	⊆	⊆	NUM
ejpam-4610	771	30	v	v	NOUN
ejpam-4610	771	31	(	(	PUNCT
ejpam-4610	771	32	h	h	NOUN
ejpam-4610	771	33	)	)	PUNCT
ejpam-4610	771	34	are	be	AUX
ejpam-4610	771	35	pnd	pnd	NOUN
ejpam-4610	771	36	-	-	PUNCT
ejpam-4610	771	37	sets	set	NOUN
ejpam-4610	771	38	of	of	ADP
ejpam-4610	771	39	g	g	PROPN
ejpam-4610	771	40	and	and	CCONJ
ejpam-4610	771	41	h	h	NOUN
ejpam-4610	771	42	,	,	PUNCT
ejpam-4610	771	43	respectively	respectively	ADV
ejpam-4610	771	44	.	.	PUNCT
ejpam-4610	772	1	theorem	theorem	VERB
ejpam-4610	772	2	6	6	NUM
ejpam-4610	772	3	.	.	PUNCT
ejpam-4610	773	1	let	let	VERB
ejpam-4610	773	2	g	g	NOUN
ejpam-4610	773	3	and	and	CCONJ
ejpam-4610	773	4	h	h	NOUN
ejpam-4610	773	5	be	be	VERB
ejpam-4610	773	6	any	any	DET
ejpam-4610	773	7	two	two	NUM
ejpam-4610	773	8	graphs	graph	NOUN
ejpam-4610	773	9	.	.	PUNCT
ejpam-4610	774	1	then	then	ADV
ejpam-4610	774	2	s	s	VERB
ejpam-4610	774	3	⊆	⊆	NUM
ejpam-4610	774	4	v	v	NOUN
ejpam-4610	774	5	(	(	PUNCT
ejpam-4610	774	6	g	g	PROPN
ejpam-4610	774	7	+	+	NOUN
ejpam-4610	774	8	h	h	NOUN
ejpam-4610	774	9	)	)	PUNCT
ejpam-4610	774	10	is	be	AUX
ejpam-4610	774	11	a	a	DET
ejpam-4610	774	12	thd	thd	NOUN
ejpam-4610	774	13	-	-	PUNCT
ejpam-4610	774	14	set	set	NOUN
ejpam-4610	774	15	of	of	ADP
ejpam-4610	774	16	g	g	PROPN
ejpam-4610	774	17	+	+	PROPN
ejpam-4610	774	18	h	h	NOUN
ejpam-4610	774	19	if	if	SCONJ
ejpam-4610	774	20	and	and	CCONJ
ejpam-4610	774	21	only	only	ADV
ejpam-4610	774	22	if	if	SCONJ
ejpam-4610	774	23	s	s	VERB
ejpam-4610	774	24	=	=	PUNCT
ejpam-4610	774	25	sg	sg	X
ejpam-4610	774	26	∪	∪	NOUN
ejpam-4610	774	27	sh	sh	PROPN
ejpam-4610	774	28	where	where	SCONJ
ejpam-4610	774	29	sg	sg	PROPN
ejpam-4610	774	30	⊆	⊆	NUM
ejpam-4610	774	31	v	v	NOUN
ejpam-4610	774	32	(	(	PUNCT
ejpam-4610	774	33	g	g	NOUN
ejpam-4610	774	34	)	)	PUNCT
ejpam-4610	774	35	and	and	CCONJ
ejpam-4610	774	36	sh	sh	PROPN
ejpam-4610	774	37	⊆	⊆	NUM
ejpam-4610	774	38	v	v	NOUN
ejpam-4610	774	39	(	(	PUNCT
ejpam-4610	774	40	h	h	NOUN
ejpam-4610	774	41	)	)	PUNCT
ejpam-4610	774	42	for	for	ADP
ejpam-4610	774	43	which	which	PRON
ejpam-4610	774	44	one	one	NUM
ejpam-4610	774	45	of	of	ADP
ejpam-4610	774	46	the	the	DET
ejpam-4610	774	47	following	follow	VERB
ejpam-4610	774	48	holds	hold	VERB
ejpam-4610	774	49	:	:	PUNCT
ejpam-4610	774	50	(	(	PUNCT
ejpam-4610	774	51	i	i	NOUN
ejpam-4610	774	52	)	)	PUNCT
ejpam-4610	774	53	sg	sg	PROPN
ejpam-4610	774	54	is	be	AUX
ejpam-4610	774	55	a	a	DET
ejpam-4610	774	56	trpnd	trpnd	NOUN
ejpam-4610	774	57	-	-	PUNCT
ejpam-4610	774	58	set	set	NOUN
ejpam-4610	774	59	of	of	ADP
ejpam-4610	774	60	g	g	PROPN
ejpam-4610	774	61	and	and	CCONJ
ejpam-4610	774	62	sh	sh	PROPN
ejpam-4610	774	63	is	be	AUX
ejpam-4610	774	64	a	a	DET
ejpam-4610	774	65	pnd	pnd	NOUN
ejpam-4610	774	66	-	-	PUNCT
ejpam-4610	774	67	set	set	NOUN
ejpam-4610	774	68	of	of	ADP
ejpam-4610	774	69	h.	h.	PROPN
ejpam-4610	774	70	(	(	PUNCT
ejpam-4610	774	71	ii	ii	PROPN
ejpam-4610	774	72	)	)	PUNCT
ejpam-4610	774	73	sh	sh	PROPN
ejpam-4610	774	74	is	be	AUX
ejpam-4610	774	75	a	a	DET
ejpam-4610	774	76	trpnd	trpnd	NOUN
ejpam-4610	774	77	-	-	PUNCT
ejpam-4610	774	78	set	set	NOUN
ejpam-4610	774	79	of	of	ADP
ejpam-4610	774	80	h	h	NOUN
ejpam-4610	774	81	and	and	CCONJ
ejpam-4610	774	82	sg	sg	PROPN
ejpam-4610	774	83	is	be	AUX
ejpam-4610	774	84	a	a	DET
ejpam-4610	774	85	pnd	pnd	NOUN
ejpam-4610	774	86	-	-	PUNCT
ejpam-4610	774	87	set	set	NOUN
ejpam-4610	774	88	of	of	ADP
ejpam-4610	774	89	g.	g.	PROPN
ejpam-4610	774	90	proof	proof	PROPN
ejpam-4610	774	91	.	.	PUNCT
ejpam-4610	775	1	suppose	suppose	VERB
ejpam-4610	775	2	that	that	SCONJ
ejpam-4610	775	3	s	s	VERB
ejpam-4610	775	4	is	be	AUX
ejpam-4610	775	5	a	a	DET
ejpam-4610	775	6	thd	thd	NOUN
ejpam-4610	775	7	-	-	PUNCT
ejpam-4610	775	8	set	set	NOUN
ejpam-4610	775	9	of	of	ADP
ejpam-4610	775	10	g+h	g+h	PROPN
ejpam-4610	775	11	.	.	PUNCT
ejpam-4610	776	1	put	put	VERB
ejpam-4610	776	2	sg	sg	NOUN
ejpam-4610	776	3	=	=	PUNCT
ejpam-4610	776	4	s∩v	s∩v	PROPN
ejpam-4610	776	5	(	(	PUNCT
ejpam-4610	776	6	g	g	NOUN
ejpam-4610	776	7	)	)	PUNCT
ejpam-4610	776	8	and	and	CCONJ
ejpam-4610	776	9	sh	sh	INTJ
ejpam-4610	776	10	=	=	SYM
ejpam-4610	776	11	s∩v	s∩v	PROPN
ejpam-4610	776	12	(	(	PUNCT
ejpam-4610	776	13	h	h	NOUN
ejpam-4610	776	14	)	)	PUNCT
ejpam-4610	776	15	.	.	PUNCT
ejpam-4610	777	1	since	since	SCONJ
ejpam-4610	777	2	s	s	PART
ejpam-4610	777	3	=	=	PUNCT
ejpam-4610	777	4	sg	sg	PROPN
ejpam-4610	777	5	∪	∪	NOUN
ejpam-4610	777	6	sh	sh	PROPN
ejpam-4610	777	7	is	be	AUX
ejpam-4610	777	8	a	a	DET
ejpam-4610	777	9	hop	hop	NOUN
ejpam-4610	777	10	dominating	dominating	NOUN
ejpam-4610	777	11	set	set	NOUN
ejpam-4610	777	12	of	of	ADP
ejpam-4610	777	13	g	g	PROPN
ejpam-4610	777	14	+	+	PROPN
ejpam-4610	777	15	h	h	NOUN
ejpam-4610	777	16	,	,	PUNCT
ejpam-4610	777	17	sg	sg	ADP
ejpam-4610	777	18	̸=	̸=	PROPN
ejpam-4610	777	19	∅	∅	NOUN
ejpam-4610	777	20	and	and	CCONJ
ejpam-4610	777	21	sh	sh	PROPN
ejpam-4610	777	22	̸=	̸=	PROPN
ejpam-4610	777	23	∅.	∅.	ADP
ejpam-4610	777	24	moreover	moreover	ADV
ejpam-4610	777	25	,	,	PUNCT
ejpam-4610	777	26	by	by	ADP
ejpam-4610	777	27	theorem	theorem	NOUN
ejpam-4610	777	28	5	5	NUM
ejpam-4610	777	29	,	,	PUNCT
ejpam-4610	777	30	sg	sg	PROPN
ejpam-4610	777	31	and	and	CCONJ
ejpam-4610	777	32	sh	sh	PROPN
ejpam-4610	777	33	are	be	AUX
ejpam-4610	777	34	pnd	pnd	NOUN
ejpam-4610	777	35	-	-	PUNCT
ejpam-4610	777	36	sets	set	NOUN
ejpam-4610	777	37	of	of	ADP
ejpam-4610	777	38	g	g	PROPN
ejpam-4610	777	39	and	and	CCONJ
ejpam-4610	777	40	h	h	NOUN
ejpam-4610	777	41	,	,	PUNCT
ejpam-4610	777	42	respectively	respectively	ADV
ejpam-4610	777	43	.	.	PUNCT
ejpam-4610	778	1	suppose	suppose	VERB
ejpam-4610	778	2	that	that	SCONJ
ejpam-4610	778	3	sg	sg	PROPN
ejpam-4610	778	4	and	and	CCONJ
ejpam-4610	778	5	sh	sh	PROPN
ejpam-4610	778	6	are	be	AUX
ejpam-4610	778	7	,	,	PUNCT
ejpam-4610	778	8	respectively	respectively	ADV
ejpam-4610	778	9	,	,	PUNCT
ejpam-4610	778	10	not	not	PART
ejpam-4610	778	11	trpnd	trpnd	NOUN
ejpam-4610	778	12	-	-	PUNCT
ejpam-4610	778	13	sets	set	NOUN
ejpam-4610	778	14	of	of	ADP
ejpam-4610	778	15	g	g	PROPN
ejpam-4610	778	16	and	and	CCONJ
ejpam-4610	778	17	h.	h.	PROPN
ejpam-4610	778	18	there	there	PRON
ejpam-4610	778	19	exist	exist	VERB
ejpam-4610	778	20	pnd	pnd	NOUN
ejpam-4610	778	21	-	-	PUNCT
ejpam-4610	778	22	sets	set	NOUN
ejpam-4610	778	23	a	a	PRON
ejpam-4610	778	24	and	and	CCONJ
ejpam-4610	778	25	b	b	NOUN
ejpam-4610	778	26	of	of	ADP
ejpam-4610	778	27	g	g	PROPN
ejpam-4610	778	28	and	and	CCONJ
ejpam-4610	778	29	h	h	NOUN
ejpam-4610	778	30	,	,	PUNCT
ejpam-4610	778	31	respectively	respectively	ADV
ejpam-4610	778	32	,	,	PUNCT
ejpam-4610	778	33	for	for	ADP
ejpam-4610	778	34	which	which	PRON
ejpam-4610	778	35	a	a	DET
ejpam-4610	778	36	∩	∩	ADJ
ejpam-4610	778	37	sg	sg	NOUN
ejpam-4610	778	38	=	=	PUNCT
ejpam-4610	778	39	∅	∅	NOUN
ejpam-4610	778	40	and	and	CCONJ
ejpam-4610	778	41	b	b	NOUN
ejpam-4610	778	42	∩	∩	NOUN
ejpam-4610	779	1	sh	sh	NOUN
ejpam-4610	779	2	=	=	PUNCT
ejpam-4610	779	3	∅.	∅.	X
ejpam-4610	779	4	by	by	ADP
ejpam-4610	779	5	lemma	lemma	PROPN
ejpam-4610	779	6	1	1	NUM
ejpam-4610	779	7	,	,	PUNCT
ejpam-4610	779	8	a	a	DET
ejpam-4610	779	9	∪	∪	X
ejpam-4610	779	10	b	b	NOUN
ejpam-4610	779	11	is	be	AUX
ejpam-4610	779	12	a	a	DET
ejpam-4610	779	13	pnd	pnd	NOUN
ejpam-4610	779	14	-	-	PUNCT
ejpam-4610	779	15	set	set	NOUN
ejpam-4610	779	16	of	of	ADP
ejpam-4610	779	17	g+h	g+h	PROPN
ejpam-4610	779	18	.	.	PUNCT
ejpam-4610	780	1	being	be	AUX
ejpam-4610	780	2	a	a	DET
ejpam-4610	780	3	trpnd	trpnd	NOUN
ejpam-4610	780	4	-	-	PUNCT
ejpam-4610	780	5	set	set	ADJ
ejpam-4610	780	6	,	,	PUNCT
ejpam-4610	780	7	s	s	NOUN
ejpam-4610	780	8	∩	∩	X
ejpam-4610	780	9	(	(	PUNCT
ejpam-4610	780	10	a	a	DET
ejpam-4610	780	11	∪b	∪b	NOUN
ejpam-4610	780	12	)	)	PUNCT
ejpam-4610	780	13	̸=	̸=	NOUN
ejpam-4610	780	14	∅	∅	NOUN
ejpam-4610	780	15	,	,	PUNCT
ejpam-4610	780	16	which	which	PRON
ejpam-4610	780	17	is	be	AUX
ejpam-4610	780	18	impossible	impossible	ADJ
ejpam-4610	780	19	.	.	PUNCT
ejpam-4610	781	1	thus	thus	ADV
ejpam-4610	781	2	,	,	PUNCT
ejpam-4610	781	3	the	the	DET
ejpam-4610	781	4	conclusion	conclusion	NOUN
ejpam-4610	781	5	follows	follow	VERB
ejpam-4610	781	6	.	.	PUNCT
ejpam-4610	782	1	conversely	conversely	ADV
ejpam-4610	782	2	,	,	PUNCT
ejpam-4610	782	3	suppose	suppose	VERB
ejpam-4610	782	4	s	s	VERB
ejpam-4610	782	5	=	=	PUNCT
ejpam-4610	782	6	sg	sg	X
ejpam-4610	782	7	∪	∪	NOUN
ejpam-4610	782	8	sh	sh	PROPN
ejpam-4610	782	9	where	where	SCONJ
ejpam-4610	782	10	sg	sg	PROPN
ejpam-4610	782	11	and	and	CCONJ
ejpam-4610	782	12	sh	sh	PROPN
ejpam-4610	782	13	are	be	AUX
ejpam-4610	782	14	as	as	ADP
ejpam-4610	782	15	described	describe	VERB
ejpam-4610	782	16	in	in	ADP
ejpam-4610	782	17	(	(	PUNCT
ejpam-4610	782	18	i	i	NOUN
ejpam-4610	782	19	)	)	PUNCT
ejpam-4610	782	20	.	.	PUNCT
ejpam-4610	783	1	let	let	VERB
ejpam-4610	783	2	t	t	PROPN
ejpam-4610	783	3	=	=	PUNCT
ejpam-4610	783	4	tg∪th	tg∪th	PRON
ejpam-4610	783	5	be	be	AUX
ejpam-4610	783	6	a	a	DET
ejpam-4610	783	7	γh	γh	ADV
ejpam-4610	783	8	-	-	PUNCT
ejpam-4610	783	9	set	set	NOUN
ejpam-4610	783	10	of	of	ADP
ejpam-4610	783	11	g+h	g+h	PROPN
ejpam-4610	783	12	.	.	PUNCT
ejpam-4610	784	1	write	write	VERB
ejpam-4610	784	2	tg	tg	PROPN
ejpam-4610	784	3	=	=	PUNCT
ejpam-4610	784	4	t	t	PROPN
ejpam-4610	785	1	∩v	∩v	NOUN
ejpam-4610	785	2	(	(	PUNCT
ejpam-4610	785	3	g	g	NOUN
ejpam-4610	785	4	)	)	PUNCT
ejpam-4610	785	5	and	and	CCONJ
ejpam-4610	785	6	th	th	X
ejpam-4610	785	7	=	=	SYM
ejpam-4610	785	8	t	t	PROPN
ejpam-4610	786	1	∩v	∩v	NOUN
ejpam-4610	786	2	(	(	PUNCT
ejpam-4610	786	3	h	h	NOUN
ejpam-4610	786	4	)	)	PUNCT
ejpam-4610	786	5	.	.	PUNCT
ejpam-4610	787	1	by	by	ADP
ejpam-4610	787	2	lemma	lemma	PROPN
ejpam-4610	787	3	1	1	NUM
ejpam-4610	787	4	,	,	PUNCT
ejpam-4610	787	5	tg	tg	PROPN
ejpam-4610	787	6	is	be	AUX
ejpam-4610	787	7	a	a	DET
ejpam-4610	787	8	pnd	pnd	NOUN
ejpam-4610	787	9	-	-	PUNCT
ejpam-4610	787	10	set	set	NOUN
ejpam-4610	787	11	of	of	ADP
ejpam-4610	787	12	g.	g.	PROPN
ejpam-4610	787	13	thus	thus	ADV
ejpam-4610	787	14	,	,	PUNCT
ejpam-4610	787	15	sg	sg	ADP
ejpam-4610	787	16	∩	∩	NOUN
ejpam-4610	787	17	tg	tg	PROPN
ejpam-4610	787	18	̸=	̸=	PROPN
ejpam-4610	787	19	∅.	∅.	ADP
ejpam-4610	787	20	this	this	PRON
ejpam-4610	787	21	means	mean	VERB
ejpam-4610	787	22	that	that	SCONJ
ejpam-4610	787	23	s	s	VERB
ejpam-4610	787	24	∩	∩	NOUN
ejpam-4610	787	25	t	t	PROPN
ejpam-4610	787	26	̸=	̸=	PROPN
ejpam-4610	787	27	∅.	∅.	VERB
ejpam-4610	787	28	therefore	therefore	ADV
ejpam-4610	787	29	,	,	PUNCT
ejpam-4610	787	30	s	s	PART
ejpam-4610	787	31	is	be	AUX
ejpam-4610	787	32	a	a	DET
ejpam-4610	787	33	thd	thd	NOUN
ejpam-4610	787	34	-	-	PUNCT
ejpam-4610	787	35	set	set	NOUN
ejpam-4610	787	36	of	of	ADP
ejpam-4610	787	37	g	g	PROPN
ejpam-4610	787	38	+	+	PROPN
ejpam-4610	787	39	h.	h.	PROPN
ejpam-4610	787	40	similarly	similarly	ADV
ejpam-4610	787	41	,	,	PUNCT
ejpam-4610	787	42	if	if	SCONJ
ejpam-4610	787	43	(	(	PUNCT
ejpam-4610	787	44	ii	ii	NOUN
ejpam-4610	787	45	)	)	PUNCT
ejpam-4610	787	46	holds	hold	VERB
ejpam-4610	787	47	for	for	ADP
ejpam-4610	787	48	sg	sg	NOUN
ejpam-4610	787	49	and	and	CCONJ
ejpam-4610	787	50	sh	sh	INTJ
ejpam-4610	787	51	,	,	PUNCT
ejpam-4610	787	52	then	then	ADV
ejpam-4610	787	53	s	s	VERB
ejpam-4610	787	54	is	be	AUX
ejpam-4610	787	55	a	a	DET
ejpam-4610	787	56	thd	thd	NOUN
ejpam-4610	787	57	-	-	PUNCT
ejpam-4610	787	58	set	set	NOUN
ejpam-4610	787	59	of	of	ADP
ejpam-4610	787	60	g+h	g+h	PROPN
ejpam-4610	787	61	.	.	PUNCT
ejpam-4610	788	1	corollary	corollary	ADJ
ejpam-4610	788	2	2	2	NUM
ejpam-4610	788	3	.	.	PUNCT
ejpam-4610	789	1	let	let	VERB
ejpam-4610	789	2	g	g	NOUN
ejpam-4610	789	3	and	and	CCONJ
ejpam-4610	789	4	h	h	NOUN
ejpam-4610	789	5	be	be	VERB
ejpam-4610	789	6	any	any	DET
ejpam-4610	789	7	two	two	NUM
ejpam-4610	789	8	graphs	graph	NOUN
ejpam-4610	789	9	.	.	PUNCT
ejpam-4610	790	1	then	then	ADV
ejpam-4610	790	2	γ̂h(g+h	γ̂h(g+h	PUNCT
ejpam-4610	790	3	)	)	PUNCT
ejpam-4610	791	1	=	=	SYM
ejpam-4610	791	2	min{trpnd(g	min{trpnd(g	PROPN
ejpam-4610	791	3	)	)	PUNCT
ejpam-4610	791	4	+	+	NUM
ejpam-4610	791	5	pnd(h	pnd(h	NUM
ejpam-4610	791	6	)	)	PUNCT
ejpam-4610	791	7	,	,	PUNCT
ejpam-4610	791	8	trpnd(h	trpnd(h	NOUN
ejpam-4610	791	9	)	)	PUNCT
ejpam-4610	791	10	+	+	CCONJ
ejpam-4610	791	11	pnd(g	pnd(g	ADP
ejpam-4610	791	12	)	)	PUNCT
ejpam-4610	791	13	}	}	PUNCT
ejpam-4610	791	14	.	.	PUNCT
ejpam-4610	792	1	m.a	m.a	PROPN
ejpam-4610	792	2	.	.	PROPN
ejpam-4610	792	3	bonsocan	bonsocan	PROPN
ejpam-4610	792	4	,	,	PUNCT
ejpam-4610	792	5	f.	f.	PROPN
ejpam-4610	792	6	jamil	jamil	PROPN
ejpam-4610	792	7	/	/	SYM
ejpam-4610	792	8	eur	eur	PROPN
ejpam-4610	792	9	.	.	PUNCT
ejpam-4610	793	1	j.	j.	PROPN
ejpam-4610	793	2	pure	pure	PROPN
ejpam-4610	793	3	appl	appl	PROPN
ejpam-4610	793	4	.	.	PROPN
ejpam-4610	793	5	math	math	PROPN
ejpam-4610	793	6	,	,	PUNCT
ejpam-4610	793	7	16	16	NUM
ejpam-4610	793	8	(	(	PUNCT
ejpam-4610	793	9	1	1	NUM
ejpam-4610	793	10	)	)	PUNCT
ejpam-4610	793	11	(	(	PUNCT
ejpam-4610	793	12	2023	2023	NUM
ejpam-4610	793	13	)	)	PUNCT
ejpam-4610	793	14	,	,	PUNCT
ejpam-4610	793	15	192	192	NUM
ejpam-4610	793	16	-	-	SYM
ejpam-4610	793	17	206	206	NUM
ejpam-4610	793	18	201	201	NUM
ejpam-4610	793	19	6	6	NUM
ejpam-4610	793	20	.	.	PUNCT
ejpam-4610	794	1	in	in	ADP
ejpam-4610	794	2	the	the	DET
ejpam-4610	794	3	corona	corona	NOUN
ejpam-4610	794	4	of	of	ADP
ejpam-4610	794	5	graphs	graph	NOUN
ejpam-4610	794	6	(	(	PUNCT
ejpam-4610	794	7	i	i	NOUN
ejpam-4610	794	8	)	)	PUNCT
ejpam-4610	794	9	if	if	SCONJ
ejpam-4610	794	10	h	h	NOUN
ejpam-4610	794	11	has	have	VERB
ejpam-4610	794	12	no	no	DET
ejpam-4610	794	13	isolated	isolated	ADJ
ejpam-4610	794	14	vertex	vertex	NOUN
ejpam-4610	794	15	,	,	PUNCT
ejpam-4610	794	16	then	then	ADV
ejpam-4610	794	17	γ̂h(k2	γ̂h(k2	VERB
ejpam-4610	794	18	◦	◦	NOUN
ejpam-4610	794	19	h	h	NOUN
ejpam-4610	794	20	)	)	PUNCT
ejpam-4610	794	21	=	=	SYM
ejpam-4610	794	22	2	2	X
ejpam-4610	794	23	.	.	PUNCT
ejpam-4610	794	24	(	(	PUNCT
ejpam-4610	794	25	ii	ii	NOUN
ejpam-4610	794	26	)	)	PUNCT
ejpam-4610	794	27	if	if	SCONJ
ejpam-4610	794	28	h	h	NOUN
ejpam-4610	794	29	has	have	VERB
ejpam-4610	794	30	k	k	PROPN
ejpam-4610	794	31	≥	≥	NUM
ejpam-4610	794	32	1	1	NUM
ejpam-4610	794	33	isolated	isolated	ADJ
ejpam-4610	794	34	vertices	vertex	NOUN
ejpam-4610	794	35	,	,	PUNCT
ejpam-4610	794	36	then	then	ADV
ejpam-4610	794	37	γ̂h(k2	γ̂h(k2	VERB
ejpam-4610	794	38	◦	◦	NOUN
ejpam-4610	794	39	h	h	NOUN
ejpam-4610	794	40	)	)	PUNCT
ejpam-4610	795	1	=	=	SYM
ejpam-4610	796	1	k	k	PROPN
ejpam-4610	797	1	+	+	NOUN
ejpam-4610	797	2	2	2	X
ejpam-4610	797	3	.	.	X
ejpam-4610	797	4	proposition	proposition	NOUN
ejpam-4610	797	5	8	8	NUM
ejpam-4610	797	6	.	.	PUNCT
ejpam-4610	798	1	let	let	VERB
ejpam-4610	798	2	g	g	PRON
ejpam-4610	798	3	be	be	AUX
ejpam-4610	798	4	a	a	DET
ejpam-4610	798	5	connected	connected	ADJ
ejpam-4610	798	6	graph	graph	NOUN
ejpam-4610	798	7	of	of	ADP
ejpam-4610	798	8	order	order	NOUN
ejpam-4610	798	9	n	n	PRON
ejpam-4610	798	10	≥	≥	NOUN
ejpam-4610	798	11	3	3	NUM
ejpam-4610	798	12	,	,	PUNCT
ejpam-4610	798	13	and	and	CCONJ
ejpam-4610	798	14	let	let	VERB
ejpam-4610	798	15	h	h	NOUN
ejpam-4610	798	16	be	be	AUX
ejpam-4610	798	17	any	any	DET
ejpam-4610	798	18	graph	graph	NOUN
ejpam-4610	798	19	.	.	PUNCT
ejpam-4610	799	1	then	then	ADV
ejpam-4610	799	2	γ̂h(g	γ̂h(g	VERB
ejpam-4610	799	3	◦	◦	NOUN
ejpam-4610	799	4	h	h	NOUN
ejpam-4610	799	5	)	)	PUNCT
ejpam-4610	799	6	≤	≤	NOUN
ejpam-4610	799	7	n	n	CCONJ
ejpam-4610	799	8	,	,	PUNCT
ejpam-4610	799	9	and	and	CCONJ
ejpam-4610	799	10	equality	equality	NOUN
ejpam-4610	799	11	is	be	AUX
ejpam-4610	799	12	attained	attain	VERB
ejpam-4610	800	1	if	if	SCONJ
ejpam-4610	800	2	g	g	PROPN
ejpam-4610	800	3	=	=	PROPN
ejpam-4610	800	4	kn	kn	PROPN
ejpam-4610	800	5	.	.	PUNCT
ejpam-4610	800	6	proof	proof	NOUN
ejpam-4610	800	7	.	.	PUNCT
ejpam-4610	801	1	it	it	PRON
ejpam-4610	801	2	is	be	AUX
ejpam-4610	801	3	easy	easy	ADJ
ejpam-4610	801	4	to	to	PART
ejpam-4610	801	5	verify	verify	VERB
ejpam-4610	801	6	that	that	PRON
ejpam-4610	801	7	v	v	NOUN
ejpam-4610	801	8	(	(	PUNCT
ejpam-4610	801	9	g	g	NOUN
ejpam-4610	801	10	)	)	PUNCT
ejpam-4610	801	11	is	be	AUX
ejpam-4610	801	12	a	a	DET
ejpam-4610	801	13	hop	hop	NOUN
ejpam-4610	801	14	dominating	dominating	NOUN
ejpam-4610	801	15	set	set	NOUN
ejpam-4610	801	16	of	of	ADP
ejpam-4610	801	17	g	g	PROPN
ejpam-4610	801	18	◦	◦	PROPN
ejpam-4610	801	19	h.	h.	PROPN
ejpam-4610	801	20	let	let	VERB
ejpam-4610	801	21	s	s	PRON
ejpam-4610	801	22	be	be	AUX
ejpam-4610	801	23	a	a	DET
ejpam-4610	801	24	γh	γh	ADV
ejpam-4610	801	25	-	-	PUNCT
ejpam-4610	801	26	set	set	NOUN
ejpam-4610	801	27	of	of	ADP
ejpam-4610	801	28	g	g	PROPN
ejpam-4610	801	29	◦	◦	NOUN
ejpam-4610	801	30	h.	h.	PROPN
ejpam-4610	801	31	suppose	suppose	VERB
ejpam-4610	801	32	that	that	SCONJ
ejpam-4610	801	33	s	s	VERB
ejpam-4610	801	34	∩v	∩v	NOUN
ejpam-4610	801	35	(	(	PUNCT
ejpam-4610	801	36	g	g	NOUN
ejpam-4610	801	37	)	)	PUNCT
ejpam-4610	801	38	=	=	PUNCT
ejpam-4610	801	39	∅.	∅.	VERB
ejpam-4610	801	40	then	then	ADV
ejpam-4610	801	41	|s	|s	PROPN
ejpam-4610	801	42	∩v	∩v	NOUN
ejpam-4610	801	43	(	(	PUNCT
ejpam-4610	801	44	hv)|	hv)|	X
ejpam-4610	801	45	≥	≥	NOUN
ejpam-4610	801	46	1	1	NUM
ejpam-4610	801	47	,	,	PUNCT
ejpam-4610	801	48	say	say	VERB
ejpam-4610	801	49	uv	uv	NOUN
ejpam-4610	801	50	∈	∈	PROPN
ejpam-4610	801	51	s	s	PART
ejpam-4610	801	52	∩v	∩v	NOUN
ejpam-4610	801	53	(	(	PUNCT
ejpam-4610	801	54	hv	hv	PROPN
ejpam-4610	801	55	)	)	PUNCT
ejpam-4610	801	56	,	,	PUNCT
ejpam-4610	801	57	for	for	ADP
ejpam-4610	801	58	each	each	DET
ejpam-4610	801	59	v	v	NUM
ejpam-4610	801	60	∈	∈	PROPN
ejpam-4610	801	61	v	v	NOUN
ejpam-4610	801	62	(	(	PUNCT
ejpam-4610	801	63	g	g	NOUN
ejpam-4610	801	64	)	)	PUNCT
ejpam-4610	801	65	.	.	PUNCT
ejpam-4610	802	1	let	let	VERB
ejpam-4610	802	2	[	[	X
ejpam-4610	802	3	z	z	NOUN
ejpam-4610	802	4	,	,	PUNCT
ejpam-4610	802	5	v	v	NOUN
ejpam-4610	802	6	,	,	PUNCT
ejpam-4610	802	7	w	w	PROPN
ejpam-4610	802	8	]	]	PUNCT
ejpam-4610	802	9	be	be	AUX
ejpam-4610	802	10	a	a	DET
ejpam-4610	802	11	path	path	NOUN
ejpam-4610	802	12	in	in	ADP
ejpam-4610	802	13	g.	g.	PROPN
ejpam-4610	802	14	define	define	VERB
ejpam-4610	802	15	s∗	s∗	PROPN
ejpam-4610	802	16	=	=	SYM
ejpam-4610	802	17	(	(	PUNCT
ejpam-4610	802	18	s	s	NOUN
ejpam-4610	802	19	\	\	X
ejpam-4610	802	20	{	{	PUNCT
ejpam-4610	802	21	uz	uz	PROPN
ejpam-4610	802	22	,	,	PUNCT
ejpam-4610	802	23	uw	uw	PROPN
ejpam-4610	802	24	}	}	PUNCT
ejpam-4610	802	25	)	)	PUNCT
ejpam-4610	802	26	∪	∪	ADP
ejpam-4610	802	27	{	{	PUNCT
ejpam-4610	802	28	v	v	NOUN
ejpam-4610	802	29	}	}	PUNCT
ejpam-4610	802	30	.	.	PUNCT
ejpam-4610	803	1	to	to	PART
ejpam-4610	803	2	show	show	VERB
ejpam-4610	803	3	that	that	SCONJ
ejpam-4610	803	4	s∗	s∗	PROPN
ejpam-4610	803	5	is	be	AUX
ejpam-4610	803	6	a	a	DET
ejpam-4610	803	7	hop	hop	NOUN
ejpam-4610	803	8	dominating	dominating	NOUN
ejpam-4610	803	9	set	set	NOUN
ejpam-4610	803	10	of	of	ADP
ejpam-4610	803	11	g	g	PROPN
ejpam-4610	803	12	◦	◦	NOUN
ejpam-4610	803	13	h	h	NOUN
ejpam-4610	803	14	,	,	PUNCT
ejpam-4610	803	15	it	it	PRON
ejpam-4610	803	16	is	be	AUX
ejpam-4610	803	17	enough	enough	ADJ
ejpam-4610	803	18	to	to	PART
ejpam-4610	803	19	consider	consider	VERB
ejpam-4610	803	20	only	only	ADV
ejpam-4610	803	21	the	the	DET
ejpam-4610	803	22	vertices	vertex	NOUN
ejpam-4610	803	23	in	in	ADP
ejpam-4610	803	24	v	v	ADP
ejpam-4610	803	25	(	(	PUNCT
ejpam-4610	803	26	g	g	NOUN
ejpam-4610	803	27	)	)	PUNCT
ejpam-4610	803	28	∩	∩	NOUN
ejpam-4610	803	29	(	(	PUNCT
ejpam-4610	803	30	ng(z	ng(z	PROPN
ejpam-4610	803	31	)	)	PUNCT
ejpam-4610	803	32	∪ng(w	∪ng(w	PROPN
ejpam-4610	803	33	)	)	PUNCT
ejpam-4610	803	34	)	)	PUNCT
ejpam-4610	803	35	.	.	PUNCT
ejpam-4610	804	1	let	let	VERB
ejpam-4610	804	2	a	a	DET
ejpam-4610	804	3	∈	∈	PROPN
ejpam-4610	804	4	v	v	NOUN
ejpam-4610	804	5	(	(	PUNCT
ejpam-4610	804	6	g	g	NOUN
ejpam-4610	804	7	)	)	PUNCT
ejpam-4610	804	8	∩	∩	NOUN
ejpam-4610	804	9	ng(z	ng(z	PROPN
ejpam-4610	804	10	)	)	PUNCT
ejpam-4610	804	11	with	with	ADP
ejpam-4610	804	12	a	a	DET
ejpam-4610	804	13	̸=	̸=	PROPN
ejpam-4610	804	14	v.	v.	ADV
ejpam-4610	804	15	if	if	SCONJ
ejpam-4610	804	16	av	av	PROPN
ejpam-4610	804	17	∈	∈	PROPN
ejpam-4610	804	18	e(g	e(g	PROPN
ejpam-4610	804	19	)	)	PUNCT
ejpam-4610	804	20	,	,	PUNCT
ejpam-4610	804	21	then	then	ADV
ejpam-4610	804	22	dg	dg	VERB
ejpam-4610	804	23	◦	◦	PROPN
ejpam-4610	804	24	h(a	h(a	PROPN
ejpam-4610	804	25	,	,	PUNCT
ejpam-4610	804	26	uv	uv	NOUN
ejpam-4610	804	27	)	)	PUNCT
ejpam-4610	804	28	=	=	SYM
ejpam-4610	805	1	2	2	X
ejpam-4610	805	2	.	.	X
ejpam-4610	806	1	on	on	ADP
ejpam-4610	806	2	the	the	DET
ejpam-4610	806	3	other	other	ADJ
ejpam-4610	806	4	hand	hand	NOUN
ejpam-4610	806	5	,	,	PUNCT
ejpam-4610	806	6	if	if	SCONJ
ejpam-4610	806	7	av	av	PROPN
ejpam-4610	806	8	/∈	/∈	PUNCT
ejpam-4610	806	9	e(g	e(g	PROPN
ejpam-4610	806	10	)	)	PUNCT
ejpam-4610	806	11	,	,	PUNCT
ejpam-4610	806	12	then	then	ADV
ejpam-4610	806	13	dg	dg	VERB
ejpam-4610	806	14	◦	◦	PROPN
ejpam-4610	806	15	h(a	h(a	PROPN
ejpam-4610	806	16	,	,	PUNCT
ejpam-4610	806	17	v	v	NOUN
ejpam-4610	806	18	)	)	PUNCT
ejpam-4610	806	19	=	=	SYM
ejpam-4610	806	20	2	2	X
ejpam-4610	806	21	.	.	PUNCT
ejpam-4610	807	1	thus	thus	ADV
ejpam-4610	807	2	,	,	PUNCT
ejpam-4610	807	3	s∗	s∗	PROPN
ejpam-4610	807	4	hop	hop	PROPN
ejpam-4610	807	5	dominates	dominate	VERB
ejpam-4610	807	6	v	v	NOUN
ejpam-4610	807	7	(	(	PUNCT
ejpam-4610	807	8	g)∩ng(z	g)∩ng(z	PROPN
ejpam-4610	807	9	)	)	PUNCT
ejpam-4610	807	10	.	.	PUNCT
ejpam-4610	808	1	similarly	similarly	ADV
ejpam-4610	808	2	,	,	PUNCT
ejpam-4610	808	3	s∗	s∗	PROPN
ejpam-4610	808	4	hop	hop	PROPN
ejpam-4610	808	5	dominates	dominate	VERB
ejpam-4610	808	6	v	v	NOUN
ejpam-4610	808	7	(	(	PUNCT
ejpam-4610	808	8	g)∩ng(w	g)∩ng(w	PROPN
ejpam-4610	808	9	)	)	PUNCT
ejpam-4610	808	10	.	.	PUNCT
ejpam-4610	809	1	this	this	PRON
ejpam-4610	809	2	means	mean	VERB
ejpam-4610	809	3	that	that	SCONJ
ejpam-4610	809	4	s∗	s∗	PROPN
ejpam-4610	809	5	is	be	AUX
ejpam-4610	809	6	a	a	DET
ejpam-4610	809	7	hop	hop	NOUN
ejpam-4610	809	8	dominating	dominating	NOUN
ejpam-4610	809	9	set	set	NOUN
ejpam-4610	809	10	of	of	ADP
ejpam-4610	809	11	g	g	NOUN
ejpam-4610	809	12	◦	◦	NOUN
ejpam-4610	809	13	h	h	NOUN
ejpam-4610	809	14	with	with	ADP
ejpam-4610	809	15	|s∗|	|s∗|	NOUN
ejpam-4610	809	16	<	<	X
ejpam-4610	809	17	|s|	|s|	NOUN
ejpam-4610	809	18	,	,	PUNCT
ejpam-4610	809	19	a	a	DET
ejpam-4610	809	20	contradiction	contradiction	NOUN
ejpam-4610	809	21	.	.	PUNCT
ejpam-4610	810	1	therefore	therefore	ADV
ejpam-4610	810	2	,	,	PUNCT
ejpam-4610	810	3	s∩v	s∩v	PROPN
ejpam-4610	810	4	(	(	PUNCT
ejpam-4610	810	5	g	g	NOUN
ejpam-4610	810	6	)	)	PUNCT
ejpam-4610	810	7	̸=	̸=	NOUN
ejpam-4610	810	8	∅	∅	NOUN
ejpam-4610	810	9	for	for	ADP
ejpam-4610	810	10	all	all	DET
ejpam-4610	810	11	γh	γh	NOUN
ejpam-4610	810	12	-	-	PUNCT
ejpam-4610	810	13	sets	set	NOUN
ejpam-4610	810	14	s	s	NOUN
ejpam-4610	810	15	of	of	ADP
ejpam-4610	810	16	g	g	NOUN
ejpam-4610	810	17	◦	◦	NOUN
ejpam-4610	810	18	h	h	NOUN
ejpam-4610	810	19	so	so	SCONJ
ejpam-4610	810	20	that	that	SCONJ
ejpam-4610	810	21	v	v	NOUN
ejpam-4610	810	22	(	(	PUNCT
ejpam-4610	810	23	g	g	NOUN
ejpam-4610	810	24	)	)	PUNCT
ejpam-4610	810	25	is	be	AUX
ejpam-4610	810	26	a	a	DET
ejpam-4610	810	27	thd	thd	NOUN
ejpam-4610	810	28	-	-	PUNCT
ejpam-4610	810	29	set	set	NOUN
ejpam-4610	810	30	of	of	ADP
ejpam-4610	810	31	g	g	PROPN
ejpam-4610	810	32	◦	◦	NOUN
ejpam-4610	810	33	h.	h.	NOUN
ejpam-4610	810	34	consequently	consequently	ADV
ejpam-4610	810	35	,	,	PUNCT
ejpam-4610	810	36	γ̂h(g	γ̂h(g	NOUN
ejpam-4610	810	37	◦	◦	NOUN
ejpam-4610	810	38	h	h	NOUN
ejpam-4610	810	39	)	)	PUNCT
ejpam-4610	810	40	≤	≤	NOUN
ejpam-4610	810	41	n.	n.	NOUN
ejpam-4610	810	42	now	now	ADV
ejpam-4610	810	43	,	,	PUNCT
ejpam-4610	810	44	consider	consider	VERB
ejpam-4610	810	45	g	g	PROPN
ejpam-4610	810	46	=	=	PROPN
ejpam-4610	810	47	kn	kn	PROPN
ejpam-4610	810	48	.	.	PUNCT
ejpam-4610	811	1	if	if	SCONJ
ejpam-4610	811	2	h	h	NOUN
ejpam-4610	811	3	has	have	VERB
ejpam-4610	811	4	an	an	DET
ejpam-4610	811	5	isolated	isolated	ADJ
ejpam-4610	811	6	vertex	vertex	NOUN
ejpam-4610	811	7	,	,	PUNCT
ejpam-4610	811	8	then	then	ADV
ejpam-4610	811	9	s	s	VERB
ejpam-4610	811	10	is	be	AUX
ejpam-4610	811	11	a	a	DET
ejpam-4610	811	12	γh	γh	ADV
ejpam-4610	811	13	-	-	PUNCT
ejpam-4610	811	14	set	set	NOUN
ejpam-4610	811	15	of	of	ADP
ejpam-4610	811	16	g	g	PROPN
ejpam-4610	811	17	◦	◦	NOUN
ejpam-4610	811	18	h	h	NOUN
ejpam-4610	811	19	if	if	SCONJ
ejpam-4610	812	1	and	and	CCONJ
ejpam-4610	812	2	only	only	ADV
ejpam-4610	812	3	if	if	SCONJ
ejpam-4610	812	4	s	s	VERB
ejpam-4610	812	5	=	=	SYM
ejpam-4610	812	6	{	{	PUNCT
ejpam-4610	812	7	u	u	NOUN
ejpam-4610	812	8	,	,	PUNCT
ejpam-4610	812	9	v	v	NOUN
ejpam-4610	812	10	}	}	PUNCT
ejpam-4610	812	11	where	where	SCONJ
ejpam-4610	812	12	v	v	X
ejpam-4610	812	13	∈	∈	PROPN
ejpam-4610	812	14	v	v	NOUN
ejpam-4610	812	15	(	(	PUNCT
ejpam-4610	812	16	g	g	NOUN
ejpam-4610	812	17	)	)	PUNCT
ejpam-4610	812	18	and	and	CCONJ
ejpam-4610	812	19	u	u	NOUN
ejpam-4610	812	20	is	be	AUX
ejpam-4610	812	21	an	an	DET
ejpam-4610	812	22	isolated	isolated	ADJ
ejpam-4610	812	23	vertex	vertex	NOUN
ejpam-4610	812	24	of	of	ADP
ejpam-4610	812	25	hv	hv	PROPN
ejpam-4610	812	26	.	.	PUNCT
ejpam-4610	813	1	in	in	ADP
ejpam-4610	813	2	this	this	DET
ejpam-4610	813	3	case	case	NOUN
ejpam-4610	813	4	,	,	PUNCT
ejpam-4610	813	5	v	v	NOUN
ejpam-4610	813	6	(	(	PUNCT
ejpam-4610	813	7	g	g	NOUN
ejpam-4610	813	8	)	)	PUNCT
ejpam-4610	813	9	is	be	AUX
ejpam-4610	813	10	a	a	DET
ejpam-4610	813	11	γ̂h	γ̂h	NOUN
ejpam-4610	813	12	-	-	PUNCT
ejpam-4610	813	13	set	set	NOUN
ejpam-4610	813	14	of	of	ADP
ejpam-4610	813	15	g	g	PROPN
ejpam-4610	813	16	◦	◦	NOUN
ejpam-4610	813	17	h.	h.	PROPN
ejpam-4610	813	18	suppose	suppose	VERB
ejpam-4610	813	19	that	that	SCONJ
ejpam-4610	813	20	h	h	NOUN
ejpam-4610	813	21	has	have	VERB
ejpam-4610	813	22	no	no	DET
ejpam-4610	813	23	isolated	isolated	ADJ
ejpam-4610	813	24	vertices	vertex	NOUN
ejpam-4610	813	25	.	.	PUNCT
ejpam-4610	814	1	then	then	ADV
ejpam-4610	814	2	s	s	VERB
ejpam-4610	814	3	is	be	AUX
ejpam-4610	814	4	a	a	DET
ejpam-4610	814	5	γh	γh	ADV
ejpam-4610	814	6	-	-	PUNCT
ejpam-4610	814	7	set	set	NOUN
ejpam-4610	814	8	of	of	ADP
ejpam-4610	814	9	g	g	PROPN
ejpam-4610	814	10	◦	◦	NOUN
ejpam-4610	814	11	h	h	NOUN
ejpam-4610	814	12	if	if	SCONJ
ejpam-4610	815	1	and	and	CCONJ
ejpam-4610	815	2	only	only	ADV
ejpam-4610	815	3	if	if	SCONJ
ejpam-4610	815	4	one	one	NUM
ejpam-4610	815	5	of	of	ADP
ejpam-4610	815	6	the	the	DET
ejpam-4610	815	7	following	following	NOUN
ejpam-4610	815	8	holds	hold	VERB
ejpam-4610	815	9	for	for	ADP
ejpam-4610	815	10	s	s	PRON
ejpam-4610	815	11	:	:	PUNCT
ejpam-4610	815	12	(	(	PUNCT
ejpam-4610	815	13	i	i	NOUN
ejpam-4610	815	14	)	)	PUNCT
ejpam-4610	815	15	s	s	PART
ejpam-4610	815	16	=	=	SYM
ejpam-4610	815	17	v	v	X
ejpam-4610	815	18	(	(	PUNCT
ejpam-4610	815	19	g	g	NOUN
ejpam-4610	815	20	)	)	PUNCT
ejpam-4610	815	21	(	(	PUNCT
ejpam-4610	815	22	whenever	whenever	SCONJ
ejpam-4610	815	23	n	n	X
ejpam-4610	815	24	=	=	SYM
ejpam-4610	815	25	3	3	NUM
ejpam-4610	815	26	)	)	PUNCT
ejpam-4610	815	27	;	;	PUNCT
ejpam-4610	815	28	(	(	PUNCT
ejpam-4610	815	29	ii	ii	NOUN
ejpam-4610	815	30	)	)	PUNCT
ejpam-4610	815	31	s	s	PART
ejpam-4610	815	32	=	=	SYM
ejpam-4610	815	33	v	v	PROPN
ejpam-4610	815	34	(	(	PUNCT
ejpam-4610	815	35	hv	hv	PROPN
ejpam-4610	815	36	+	+	PROPN
ejpam-4610	815	37	v	v	NOUN
ejpam-4610	815	38	)	)	PUNCT
ejpam-4610	815	39	(	(	PUNCT
ejpam-4610	815	40	whenever	whenever	SCONJ
ejpam-4610	815	41	h	h	PROPN
ejpam-4610	815	42	=	=	SYM
ejpam-4610	815	43	k2	k2	PROPN
ejpam-4610	815	44	)	)	PUNCT
ejpam-4610	815	45	;	;	PUNCT
ejpam-4610	815	46	(	(	PUNCT
ejpam-4610	815	47	iii	iii	X
ejpam-4610	815	48	)	)	PUNCT
ejpam-4610	815	49	s	s	PART
ejpam-4610	815	50	=	=	PUNCT
ejpam-4610	815	51	{	{	PUNCT
ejpam-4610	815	52	v	v	NOUN
ejpam-4610	815	53	,	,	PUNCT
ejpam-4610	815	54	u	u	NOUN
ejpam-4610	815	55	,	,	PUNCT
ejpam-4610	815	56	w	w	NOUN
ejpam-4610	815	57	}	}	PUNCT
ejpam-4610	815	58	where	where	SCONJ
ejpam-4610	815	59	v	v	X
ejpam-4610	815	60	∈	∈	PROPN
ejpam-4610	815	61	v	v	NOUN
ejpam-4610	815	62	(	(	PUNCT
ejpam-4610	815	63	g	g	NOUN
ejpam-4610	815	64	)	)	PUNCT
ejpam-4610	815	65	and	and	CCONJ
ejpam-4610	815	66	u	u	PROPN
ejpam-4610	815	67	and	and	CCONJ
ejpam-4610	815	68	w	w	NOUN
ejpam-4610	815	69	belong	belong	VERB
ejpam-4610	815	70	to	to	ADP
ejpam-4610	815	71	distinct	distinct	ADJ
ejpam-4610	815	72	components	component	NOUN
ejpam-4610	815	73	of	of	ADP
ejpam-4610	815	74	hv	hv	PROPN
ejpam-4610	815	75	(	(	PUNCT
ejpam-4610	815	76	whenever	whenever	SCONJ
ejpam-4610	815	77	h	h	NOUN
ejpam-4610	815	78	has	have	AUX
ejpam-4610	815	79	at	at	ADV
ejpam-4610	815	80	least	least	ADJ
ejpam-4610	815	81	2	2	NUM
ejpam-4610	815	82	components	component	NOUN
ejpam-4610	815	83	)	)	PUNCT
ejpam-4610	815	84	;	;	PUNCT
ejpam-4610	815	85	(	(	PUNCT
ejpam-4610	815	86	iv	iv	X
ejpam-4610	815	87	)	)	PUNCT
ejpam-4610	815	88	s	s	PART
ejpam-4610	815	89	=	=	PUNCT
ejpam-4610	815	90	{	{	PUNCT
ejpam-4610	815	91	v	v	NOUN
ejpam-4610	815	92	,	,	PUNCT
ejpam-4610	815	93	u	u	NOUN
ejpam-4610	815	94	,	,	PUNCT
ejpam-4610	815	95	w	w	NOUN
ejpam-4610	815	96	}	}	PUNCT
ejpam-4610	815	97	where	where	SCONJ
ejpam-4610	815	98	v	v	X
ejpam-4610	815	99	∈	∈	PROPN
ejpam-4610	815	100	v	v	NOUN
ejpam-4610	815	101	(	(	PUNCT
ejpam-4610	815	102	g	g	NOUN
ejpam-4610	815	103	)	)	PUNCT
ejpam-4610	815	104	and	and	CCONJ
ejpam-4610	815	105	both	both	DET
ejpam-4610	815	106	u	u	NOUN
ejpam-4610	815	107	and	and	CCONJ
ejpam-4610	815	108	w	w	AUX
ejpam-4610	815	109	belong	belong	VERB
ejpam-4610	815	110	the	the	DET
ejpam-4610	815	111	same	same	ADJ
ejpam-4610	815	112	component	component	NOUN
ejpam-4610	815	113	of	of	ADP
ejpam-4610	815	114	hv	hv	NOUN
ejpam-4610	815	115	such	such	ADJ
ejpam-4610	815	116	that	that	PRON
ejpam-4610	815	117	for	for	ADP
ejpam-4610	815	118	each	each	DET
ejpam-4610	815	119	z	z	NOUN
ejpam-4610	815	120	∈	∈	PROPN
ejpam-4610	815	121	v	v	ADP
ejpam-4610	815	122	(	(	PUNCT
ejpam-4610	815	123	hv	hv	PROPN
ejpam-4610	815	124	)	)	PUNCT
ejpam-4610	815	125	\	\	NOUN
ejpam-4610	815	126	{	{	PUNCT
ejpam-4610	815	127	u	u	NOUN
ejpam-4610	815	128	,	,	PUNCT
ejpam-4610	815	129	w	w	PROPN
ejpam-4610	815	130	}	}	PUNCT
ejpam-4610	815	131	we	we	PRON
ejpam-4610	815	132	have	have	VERB
ejpam-4610	815	133	uz	uz	PROPN
ejpam-4610	815	134	/∈	/∈	PUNCT
ejpam-4610	815	135	e(hv	e(hv	PROPN
ejpam-4610	815	136	)	)	PUNCT
ejpam-4610	815	137	or	or	CCONJ
ejpam-4610	815	138	wz	wz	ADP
ejpam-4610	815	139	/∈	/∈	PUNCT
ejpam-4610	815	140	e(hv	e(hv	PROPN
ejpam-4610	815	141	)	)	PUNCT
ejpam-4610	815	142	;	;	PUNCT
ejpam-4610	815	143	(	(	PUNCT
ejpam-4610	815	144	v	v	NOUN
ejpam-4610	815	145	)	)	PUNCT
ejpam-4610	815	146	s	s	PART
ejpam-4610	815	147	=	=	PUNCT
ejpam-4610	815	148	{	{	PUNCT
ejpam-4610	815	149	v	v	NOUN
ejpam-4610	815	150	,	,	PUNCT
ejpam-4610	815	151	u	u	NOUN
ejpam-4610	815	152	,	,	PUNCT
ejpam-4610	815	153	w	w	NOUN
ejpam-4610	815	154	}	}	PUNCT
ejpam-4610	815	155	where	where	SCONJ
ejpam-4610	815	156	u	u	NOUN
ejpam-4610	815	157	,	,	PUNCT
ejpam-4610	815	158	v	v	PROPN
ejpam-4610	815	159	∈	∈	PROPN
ejpam-4610	815	160	v	v	NOUN
ejpam-4610	815	161	(	(	PUNCT
ejpam-4610	815	162	g	g	NOUN
ejpam-4610	815	163	)	)	PUNCT
ejpam-4610	815	164	and	and	CCONJ
ejpam-4610	815	165	w	w	PROPN
ejpam-4610	815	166	∈	∈	PROPN
ejpam-4610	815	167	v	v	ADP
ejpam-4610	815	168	(	(	PUNCT
ejpam-4610	815	169	hv	hv	NOUN
ejpam-4610	815	170	)	)	PUNCT
ejpam-4610	815	171	∪	∪	NOUN
ejpam-4610	815	172	v	v	PROPN
ejpam-4610	815	173	(	(	PUNCT
ejpam-4610	815	174	hu	hu	PROPN
ejpam-4610	815	175	)	)	PUNCT
ejpam-4610	815	176	.	.	PUNCT
ejpam-4610	816	1	therefore	therefore	ADV
ejpam-4610	816	2	,	,	PUNCT
ejpam-4610	816	3	v	v	X
ejpam-4610	816	4	(	(	PUNCT
ejpam-4610	816	5	g	g	NOUN
ejpam-4610	816	6	)	)	PUNCT
ejpam-4610	816	7	is	be	AUX
ejpam-4610	816	8	a	a	DET
ejpam-4610	816	9	γ̂h	γ̂h	NOUN
ejpam-4610	816	10	-	-	PUNCT
ejpam-4610	816	11	set	set	VERB
ejpam-4610	816	12	so	so	SCONJ
ejpam-4610	816	13	that	that	SCONJ
ejpam-4610	816	14	γ̂h(g	γ̂h(g	VERB
ejpam-4610	816	15	◦	◦	NOUN
ejpam-4610	816	16	h	h	NOUN
ejpam-4610	816	17	)	)	PUNCT
ejpam-4610	816	18	=	=	VERB
ejpam-4610	816	19	n.	n.	VERB
ejpam-4610	816	20	the	the	DET
ejpam-4610	816	21	inequality	inequality	NOUN
ejpam-4610	816	22	in	in	ADP
ejpam-4610	816	23	proposition	proposition	NOUN
ejpam-4610	816	24	8	8	NUM
ejpam-4610	816	25	can	can	AUX
ejpam-4610	816	26	be	be	AUX
ejpam-4610	816	27	strict	strict	ADJ
ejpam-4610	816	28	.	.	PUNCT
ejpam-4610	817	1	if	if	SCONJ
ejpam-4610	817	2	g	g	PROPN
ejpam-4610	817	3	=	=	SYM
ejpam-4610	817	4	k1,4	k1,4	PROPN
ejpam-4610	817	5	and	and	CCONJ
ejpam-4610	817	6	h	h	NOUN
ejpam-4610	817	7	=	=	SYM
ejpam-4610	817	8	k2	k2	PROPN
ejpam-4610	817	9	,	,	PUNCT
ejpam-4610	817	10	then	then	ADV
ejpam-4610	817	11	γ̂h(g	γ̂h(g	VERB
ejpam-4610	817	12	◦	◦	NOUN
ejpam-4610	817	13	h	h	NOUN
ejpam-4610	817	14	)	)	PUNCT
ejpam-4610	817	15	=	=	SYM
ejpam-4610	817	16	2	2	NUM
ejpam-4610	817	17	<	<	X
ejpam-4610	817	18	n.	n.	NOUN
ejpam-4610	817	19	proposition	proposition	NOUN
ejpam-4610	817	20	9	9	NUM
ejpam-4610	817	21	.	.	PUNCT
ejpam-4610	818	1	[	[	X
ejpam-4610	818	2	1	1	X
ejpam-4610	818	3	]	]	PUNCT
ejpam-4610	818	4	let	let	VERB
ejpam-4610	818	5	g	g	PRON
ejpam-4610	818	6	be	be	AUX
ejpam-4610	818	7	a	a	DET
ejpam-4610	818	8	graph	graph	NOUN
ejpam-4610	818	9	.	.	PUNCT
ejpam-4610	819	1	then	then	ADV
ejpam-4610	819	2	1	1	NUM
ejpam-4610	819	3	≤	≤	NUM
ejpam-4610	819	4	pnd(g	pnd(g	ADP
ejpam-4610	819	5	)	)	PUNCT
ejpam-4610	819	6	≤	≤	NOUN
ejpam-4610	819	7	|v	|v	X
ejpam-4610	819	8	(	(	PUNCT
ejpam-4610	819	9	g)|	g)|	PROPN
ejpam-4610	819	10	.	.	PUNCT
ejpam-4610	820	1	moreover	moreover	ADV
ejpam-4610	820	2	,	,	PUNCT
ejpam-4610	820	3	(	(	PUNCT
ejpam-4610	820	4	i	i	NOUN
ejpam-4610	820	5	)	)	PUNCT
ejpam-4610	820	6	pnd(g	pnd(g	PROPN
ejpam-4610	820	7	)	)	PUNCT
ejpam-4610	820	8	=	=	SYM
ejpam-4610	820	9	|v	|v	PROPN
ejpam-4610	820	10	(	(	PUNCT
ejpam-4610	820	11	g)|	g)|	VERB
ejpam-4610	820	12	if	if	SCONJ
ejpam-4610	820	13	and	and	CCONJ
ejpam-4610	820	14	only	only	ADV
ejpam-4610	820	15	if	if	SCONJ
ejpam-4610	820	16	g	g	PROPN
ejpam-4610	820	17	is	be	AUX
ejpam-4610	820	18	a	a	DET
ejpam-4610	820	19	complete	complete	ADJ
ejpam-4610	820	20	graph	graph	NOUN
ejpam-4610	820	21	;	;	PUNCT
ejpam-4610	820	22	(	(	PUNCT
ejpam-4610	820	23	ii	ii	NOUN
ejpam-4610	820	24	)	)	PUNCT
ejpam-4610	820	25	pnd(g	pnd(g	PROPN
ejpam-4610	820	26	)	)	PUNCT
ejpam-4610	820	27	=	=	SYM
ejpam-4610	820	28	1	1	NUM
ejpam-4610	820	29	if	if	SCONJ
ejpam-4610	820	30	and	and	CCONJ
ejpam-4610	820	31	only	only	ADV
ejpam-4610	820	32	if	if	SCONJ
ejpam-4610	820	33	g	g	PROPN
ejpam-4610	820	34	has	have	VERB
ejpam-4610	820	35	an	an	DET
ejpam-4610	820	36	isolated	isolated	ADJ
ejpam-4610	820	37	vertex	vertex	NOUN
ejpam-4610	820	38	;	;	PUNCT
ejpam-4610	820	39	and	and	CCONJ
ejpam-4610	820	40	m.a	m.a	PROPN
ejpam-4610	820	41	.	.	PROPN
ejpam-4610	820	42	bonsocan	bonsocan	PROPN
ejpam-4610	820	43	,	,	PUNCT
ejpam-4610	820	44	f.	f.	PROPN
ejpam-4610	820	45	jamil	jamil	PROPN
ejpam-4610	820	46	/	/	SYM
ejpam-4610	820	47	eur	eur	PROPN
ejpam-4610	820	48	.	.	PUNCT
ejpam-4610	821	1	j.	j.	PROPN
ejpam-4610	821	2	pure	pure	PROPN
ejpam-4610	821	3	appl	appl	PROPN
ejpam-4610	821	4	.	.	PROPN
ejpam-4610	821	5	math	math	PROPN
ejpam-4610	821	6	,	,	PUNCT
ejpam-4610	821	7	16	16	NUM
ejpam-4610	821	8	(	(	PUNCT
ejpam-4610	821	9	1	1	NUM
ejpam-4610	821	10	)	)	PUNCT
ejpam-4610	821	11	(	(	PUNCT
ejpam-4610	821	12	2023	2023	NUM
ejpam-4610	821	13	)	)	PUNCT
ejpam-4610	821	14	,	,	PUNCT
ejpam-4610	821	15	192	192	NUM
ejpam-4610	821	16	-	-	SYM
ejpam-4610	821	17	206	206	NUM
ejpam-4610	821	18	202	202	NUM
ejpam-4610	821	19	(	(	PUNCT
ejpam-4610	821	20	iii	iii	NOUN
ejpam-4610	821	21	)	)	PUNCT
ejpam-4610	821	22	pnd(g	pnd(g	PROPN
ejpam-4610	821	23	)	)	PUNCT
ejpam-4610	821	24	=	=	SYM
ejpam-4610	821	25	2	2	NUM
ejpam-4610	821	26	if	if	SCONJ
ejpam-4610	821	27	and	and	CCONJ
ejpam-4610	821	28	only	only	ADV
ejpam-4610	821	29	if	if	SCONJ
ejpam-4610	821	30	g	g	PROPN
ejpam-4610	821	31	has	have	VERB
ejpam-4610	821	32	no	no	DET
ejpam-4610	821	33	isolated	isolated	ADJ
ejpam-4610	821	34	vertex	vertex	NOUN
ejpam-4610	821	35	and	and	CCONJ
ejpam-4610	821	36	there	there	PRON
ejpam-4610	821	37	exist	exist	VERB
ejpam-4610	821	38	distinct	distinct	ADJ
ejpam-4610	821	39	vertices	vertex	NOUN
ejpam-4610	821	40	a	a	PRON
ejpam-4610	821	41	and	and	CCONJ
ejpam-4610	821	42	b	b	NOUN
ejpam-4610	821	43	of	of	ADP
ejpam-4610	821	44	g	g	NOUN
ejpam-4610	821	45	such	such	ADJ
ejpam-4610	821	46	that	that	DET
ejpam-4610	821	47	ng(a	ng(a	NOUN
ejpam-4610	821	48	)	)	PUNCT
ejpam-4610	822	1	∩ng(b	∩ng(b	NOUN
ejpam-4610	822	2	)	)	PUNCT
ejpam-4610	822	3	=	=	PUNCT
ejpam-4610	822	4	∅.	∅.	NOUN
ejpam-4610	822	5	theorem	theorem	VERB
ejpam-4610	822	6	7	7	NUM
ejpam-4610	822	7	.	.	PUNCT
ejpam-4610	823	1	[	[	X
ejpam-4610	823	2	13	13	NUM
ejpam-4610	823	3	]	]	PUNCT
ejpam-4610	823	4	let	let	VERB
ejpam-4610	823	5	g	g	NOUN
ejpam-4610	823	6	and	and	CCONJ
ejpam-4610	823	7	h	h	NOUN
ejpam-4610	823	8	be	be	VERB
ejpam-4610	823	9	any	any	DET
ejpam-4610	823	10	two	two	NUM
ejpam-4610	823	11	graphs	graph	NOUN
ejpam-4610	823	12	.	.	PUNCT
ejpam-4610	824	1	a	a	DET
ejpam-4610	824	2	set	set	NOUN
ejpam-4610	824	3	c	c	NOUN
ejpam-4610	824	4	⊆	⊆	NUM
ejpam-4610	824	5	v	v	NOUN
ejpam-4610	824	6	(	(	PUNCT
ejpam-4610	824	7	g	g	PROPN
ejpam-4610	824	8	◦	◦	NOUN
ejpam-4610	824	9	h	h	NOUN
ejpam-4610	824	10	)	)	PUNCT
ejpam-4610	824	11	is	be	AUX
ejpam-4610	824	12	a	a	DET
ejpam-4610	824	13	hop	hop	NOUN
ejpam-4610	824	14	dominating	dominating	NOUN
ejpam-4610	824	15	set	set	NOUN
ejpam-4610	824	16	of	of	ADP
ejpam-4610	824	17	g	g	PROPN
ejpam-4610	824	18	◦	◦	NOUN
ejpam-4610	824	19	h	h	NOUN
ejpam-4610	824	20	if	if	SCONJ
ejpam-4610	825	1	and	and	CCONJ
ejpam-4610	825	2	only	only	ADV
ejpam-4610	825	3	if	if	SCONJ
ejpam-4610	825	4	c	c	X
ejpam-4610	825	5	=	=	PUNCT
ejpam-4610	825	6	a	a	DET
ejpam-4610	825	7	∪	∪	X
ejpam-4610	825	8	(	(	PUNCT
ejpam-4610	825	9	∪v∈v	∪v∈v	X
ejpam-4610	825	10	(	(	PUNCT
ejpam-4610	825	11	g)∩ng(a)sv	g)∩ng(a)sv	PROPN
ejpam-4610	825	12	)	)	PUNCT
ejpam-4610	825	13	∪	∪	NOUN
ejpam-4610	825	14	(	(	PUNCT
ejpam-4610	825	15	∪w∈v	∪w∈v	PROPN
ejpam-4610	825	16	(	(	PUNCT
ejpam-4610	825	17	g)\ng(a)ew	g)\ng(a)ew	PROPN
ejpam-4610	825	18	)	)	PUNCT
ejpam-4610	825	19	,	,	PUNCT
ejpam-4610	825	20	where	where	SCONJ
ejpam-4610	825	21	(	(	PUNCT
ejpam-4610	825	22	i	i	NOUN
ejpam-4610	825	23	)	)	PUNCT
ejpam-4610	825	24	a	a	DET
ejpam-4610	825	25	⊆	⊆	NUM
ejpam-4610	825	26	v	v	NOUN
ejpam-4610	825	27	(	(	PUNCT
ejpam-4610	825	28	g	g	NOUN
ejpam-4610	825	29	)	)	PUNCT
ejpam-4610	825	30	such	such	ADJ
ejpam-4610	825	31	that	that	PRON
ejpam-4610	825	32	for	for	ADP
ejpam-4610	825	33	each	each	DET
ejpam-4610	825	34	w	w	PROPN
ejpam-4610	825	35	∈	∈	PROPN
ejpam-4610	825	36	v	v	ADP
ejpam-4610	825	37	(	(	PUNCT
ejpam-4610	825	38	g	g	NOUN
ejpam-4610	825	39	)	)	PUNCT
ejpam-4610	825	40	\a	\a	ADJ
ejpam-4610	825	41	,	,	PUNCT
ejpam-4610	825	42	there	there	PRON
ejpam-4610	825	43	exists	exist	VERB
ejpam-4610	825	44	x	x	X
ejpam-4610	825	45	∈	∈	PROPN
ejpam-4610	825	46	a	a	PRON
ejpam-4610	825	47	with	with	ADP
ejpam-4610	825	48	dg(w	dg(w	NOUN
ejpam-4610	825	49	,	,	PUNCT
ejpam-4610	825	50	x	x	X
ejpam-4610	825	51	)	)	PUNCT
ejpam-4610	825	52	=	=	SYM
ejpam-4610	825	53	2	2	NUM
ejpam-4610	825	54	or	or	CCONJ
ejpam-4610	825	55	there	there	PRON
ejpam-4610	825	56	exists	exist	VERB
ejpam-4610	825	57	y	y	PROPN
ejpam-4610	825	58	∈	∈	PROPN
ejpam-4610	825	59	v	v	ADP
ejpam-4610	825	60	(	(	PUNCT
ejpam-4610	825	61	g	g	NOUN
ejpam-4610	825	62	)	)	PUNCT
ejpam-4610	825	63	∩ng(w	∩ng(w	PROPN
ejpam-4610	825	64	)	)	PUNCT
ejpam-4610	825	65	with	with	ADP
ejpam-4610	825	66	v	v	NUM
ejpam-4610	825	67	(	(	PUNCT
ejpam-4610	825	68	hy	hy	NOUN
ejpam-4610	825	69	)	)	PUNCT
ejpam-4610	825	70	∩	∩	NOUN
ejpam-4610	825	71	c	c	PROPN
ejpam-4610	825	72	̸=	̸=	PROPN
ejpam-4610	825	73	∅	∅	NOUN
ejpam-4610	825	74	,	,	PUNCT
ejpam-4610	825	75	(	(	PUNCT
ejpam-4610	825	76	ii	ii	NOUN
ejpam-4610	825	77	)	)	PUNCT
ejpam-4610	825	78	sv	sv	VERB
ejpam-4610	826	1	⊆	⊆	NUM
ejpam-4610	826	2	v	v	X
ejpam-4610	826	3	(	(	PUNCT
ejpam-4610	826	4	hv	hv	PROPN
ejpam-4610	826	5	)	)	PUNCT
ejpam-4610	826	6	for	for	ADP
ejpam-4610	826	7	each	each	DET
ejpam-4610	826	8	v	v	NUM
ejpam-4610	826	9	∈	∈	PROPN
ejpam-4610	826	10	v	v	NOUN
ejpam-4610	826	11	(	(	PUNCT
ejpam-4610	826	12	g	g	NOUN
ejpam-4610	826	13	)	)	PUNCT
ejpam-4610	826	14	∩ng(a	∩ng(a	NOUN
ejpam-4610	826	15	)	)	PUNCT
ejpam-4610	826	16	,	,	PUNCT
ejpam-4610	826	17	and	and	CCONJ
ejpam-4610	826	18	(	(	PUNCT
ejpam-4610	826	19	iii	iii	NOUN
ejpam-4610	826	20	)	)	PUNCT
ejpam-4610	826	21	ew	ew	NOUN
ejpam-4610	826	22	⊆	⊆	NUM
ejpam-4610	826	23	v	v	NOUN
ejpam-4610	826	24	(	(	PUNCT
ejpam-4610	826	25	hw	hw	NOUN
ejpam-4610	826	26	)	)	PUNCT
ejpam-4610	826	27	is	be	AUX
ejpam-4610	826	28	a	a	DET
ejpam-4610	826	29	point	point	NOUN
ejpam-4610	826	30	-	-	PUNCT
ejpam-4610	826	31	wise	wise	ADJ
ejpam-4610	826	32	non	non	ADJ
ejpam-4610	826	33	-	-	ADJ
ejpam-4610	826	34	dominating	dominating	ADJ
ejpam-4610	826	35	set	set	NOUN
ejpam-4610	826	36	of	of	ADP
ejpam-4610	826	37	hw	hw	PRON
ejpam-4610	826	38	for	for	ADP
ejpam-4610	826	39	each	each	DET
ejpam-4610	826	40	w	w	PROPN
ejpam-4610	826	41	∈	∈	PROPN
ejpam-4610	826	42	v	v	NOUN
ejpam-4610	826	43	(	(	PUNCT
ejpam-4610	826	44	g)\ng(a	g)\ng(a	NOUN
ejpam-4610	826	45	)	)	PUNCT
ejpam-4610	826	46	.	.	PUNCT
ejpam-4610	827	1	lemma	lemma	PROPN
ejpam-4610	827	2	2	2	X
ejpam-4610	827	3	.	.	PUNCT
ejpam-4610	828	1	let	let	VERB
ejpam-4610	828	2	g	g	PRON
ejpam-4610	828	3	be	be	AUX
ejpam-4610	828	4	a	a	DET
ejpam-4610	828	5	connected	connect	VERB
ejpam-4610	828	6	k3	k3	VERB
ejpam-4610	828	7	-	-	PUNCT
ejpam-4610	828	8	free	free	ADJ
ejpam-4610	828	9	graph	graph	NOUN
ejpam-4610	828	10	and	and	CCONJ
ejpam-4610	828	11	h	h	NOUN
ejpam-4610	828	12	be	be	AUX
ejpam-4610	828	13	a	a	DET
ejpam-4610	828	14	nontrivial	nontrivial	ADJ
ejpam-4610	828	15	connected	connect	VERB
ejpam-4610	828	16	graph	graph	NOUN
ejpam-4610	828	17	,	,	PUNCT
ejpam-4610	828	18	and	and	CCONJ
ejpam-4610	828	19	let	let	VERB
ejpam-4610	828	20	s	s	PRON
ejpam-4610	828	21	⊆	⊆	NUM
ejpam-4610	828	22	v	v	NOUN
ejpam-4610	828	23	(	(	PUNCT
ejpam-4610	828	24	g	g	PROPN
ejpam-4610	828	25	◦	◦	NOUN
ejpam-4610	828	26	h	h	NOUN
ejpam-4610	828	27	)	)	PUNCT
ejpam-4610	828	28	.	.	PUNCT
ejpam-4610	829	1	then	then	ADV
ejpam-4610	829	2	s	s	VERB
ejpam-4610	829	3	is	be	AUX
ejpam-4610	829	4	a	a	DET
ejpam-4610	829	5	γh	γh	ADV
ejpam-4610	829	6	-	-	PUNCT
ejpam-4610	829	7	set	set	NOUN
ejpam-4610	829	8	of	of	ADP
ejpam-4610	829	9	g	g	PROPN
ejpam-4610	829	10	◦	◦	NOUN
ejpam-4610	829	11	h	h	NOUN
ejpam-4610	829	12	if	if	SCONJ
ejpam-4610	830	1	and	and	CCONJ
ejpam-4610	830	2	only	only	ADV
ejpam-4610	830	3	if	if	SCONJ
ejpam-4610	830	4	s	s	VERB
ejpam-4610	830	5	⊆	⊆	NUM
ejpam-4610	830	6	v	v	NOUN
ejpam-4610	830	7	(	(	PUNCT
ejpam-4610	830	8	g	g	NOUN
ejpam-4610	830	9	)	)	PUNCT
ejpam-4610	830	10	and	and	CCONJ
ejpam-4610	830	11	is	be	AUX
ejpam-4610	830	12	a	a	DET
ejpam-4610	830	13	γ∗t1,2	γ∗t1,2	NOUN
ejpam-4610	830	14	-	-	PUNCT
ejpam-4610	830	15	set	set	NOUN
ejpam-4610	830	16	of	of	ADP
ejpam-4610	830	17	g.	g.	PROPN
ejpam-4610	830	18	proof	proof	PROPN
ejpam-4610	830	19	.	.	PUNCT
ejpam-4610	831	1	let	let	VERB
ejpam-4610	831	2	s	s	PRON
ejpam-4610	831	3	⊆	⊆	NUM
ejpam-4610	831	4	v	v	NOUN
ejpam-4610	831	5	(	(	PUNCT
ejpam-4610	831	6	g	g	PROPN
ejpam-4610	831	7	◦	◦	NOUN
ejpam-4610	831	8	h	h	NOUN
ejpam-4610	831	9	)	)	PUNCT
ejpam-4610	831	10	be	be	VERB
ejpam-4610	831	11	a	a	DET
ejpam-4610	831	12	γh	γh	ADV
ejpam-4610	831	13	-	-	PUNCT
ejpam-4610	831	14	set	set	NOUN
ejpam-4610	831	15	of	of	ADP
ejpam-4610	831	16	g	g	PROPN
ejpam-4610	831	17	◦	◦	PROPN
ejpam-4610	831	18	h.	h.	PROPN
ejpam-4610	832	1	first	first	ADV
ejpam-4610	832	2	,	,	PUNCT
ejpam-4610	832	3	we	we	PRON
ejpam-4610	832	4	claim	claim	VERB
ejpam-4610	832	5	that	that	SCONJ
ejpam-4610	832	6	s	s	VERB
ejpam-4610	832	7	⊆	⊆	NUM
ejpam-4610	832	8	v	v	NOUN
ejpam-4610	832	9	(	(	PUNCT
ejpam-4610	832	10	g	g	NOUN
ejpam-4610	832	11	)	)	PUNCT
ejpam-4610	832	12	.	.	PUNCT
ejpam-4610	833	1	assume	assume	VERB
ejpam-4610	833	2	,	,	PUNCT
ejpam-4610	833	3	to	to	ADP
ejpam-4610	833	4	the	the	DET
ejpam-4610	833	5	contrary	contrary	NOUN
ejpam-4610	833	6	,	,	PUNCT
ejpam-4610	833	7	that	that	SCONJ
ejpam-4610	833	8	sv	sv	VERB
ejpam-4610	833	9	=	=	SYM
ejpam-4610	833	10	s	s	PROPN
ejpam-4610	833	11	∩	∩	ADJ
ejpam-4610	833	12	v	v	X
ejpam-4610	833	13	(	(	PUNCT
ejpam-4610	833	14	hv	hv	NOUN
ejpam-4610	833	15	)	)	PUNCT
ejpam-4610	833	16	̸=	̸=	PROPN
ejpam-4610	833	17	∅	∅	NOUN
ejpam-4610	833	18	for	for	ADP
ejpam-4610	833	19	some	some	DET
ejpam-4610	833	20	v	v	ADP
ejpam-4610	833	21	∈	∈	NOUN
ejpam-4610	833	22	v	v	NOUN
ejpam-4610	833	23	(	(	PUNCT
ejpam-4610	833	24	g	g	NOUN
ejpam-4610	833	25	)	)	PUNCT
ejpam-4610	833	26	.	.	PUNCT
ejpam-4610	834	1	suppose	suppose	VERB
ejpam-4610	834	2	that	that	SCONJ
ejpam-4610	834	3	s	s	VERB
ejpam-4610	834	4	∩	∩	NOUN
ejpam-4610	834	5	ng(v	ng(v	X
ejpam-4610	834	6	)	)	PUNCT
ejpam-4610	834	7	=	=	VERB
ejpam-4610	834	8	∅.	∅.	X
ejpam-4610	834	9	by	by	ADP
ejpam-4610	834	10	theorem	theorem	NOUN
ejpam-4610	834	11	7	7	NUM
ejpam-4610	834	12	,	,	PUNCT
ejpam-4610	834	13	sv	sv	X
ejpam-4610	834	14	is	be	AUX
ejpam-4610	834	15	a	a	DET
ejpam-4610	834	16	pnd	pnd	NOUN
ejpam-4610	834	17	-	-	PUNCT
ejpam-4610	834	18	set	set	NOUN
ejpam-4610	834	19	of	of	ADP
ejpam-4610	834	20	hv	hv	PROPN
ejpam-4610	834	21	.	.	PUNCT
ejpam-4610	835	1	by	by	ADP
ejpam-4610	835	2	proposition	proposition	NOUN
ejpam-4610	835	3	9	9	NUM
ejpam-4610	835	4	,	,	PUNCT
ejpam-4610	835	5	|sv|	|sv|	PROPN
ejpam-4610	835	6	≥	≥	NOUN
ejpam-4610	835	7	2	2	NUM
ejpam-4610	835	8	.	.	PUNCT
ejpam-4610	835	9	choose	choose	VERB
ejpam-4610	835	10	w	w	PROPN
ejpam-4610	835	11	∈	∈	PROPN
ejpam-4610	835	12	ng(v	ng(v	NOUN
ejpam-4610	835	13	)	)	PUNCT
ejpam-4610	835	14	,	,	PUNCT
ejpam-4610	835	15	and	and	CCONJ
ejpam-4610	835	16	define	define	VERB
ejpam-4610	835	17	s∗	s∗	PROPN
ejpam-4610	835	18	=	=	SYM
ejpam-4610	835	19	(	(	PUNCT
ejpam-4610	835	20	s	s	X
ejpam-4610	835	21	\sv)∪	\sv)∪	NOUN
ejpam-4610	835	22	{	{	PUNCT
ejpam-4610	835	23	w	w	NOUN
ejpam-4610	835	24	}	}	PUNCT
ejpam-4610	835	25	.	.	PUNCT
ejpam-4610	836	1	let	let	VERB
ejpam-4610	836	2	x	x	SYM
ejpam-4610	836	3	∈	∈	PROPN
ejpam-4610	836	4	v	v	X
ejpam-4610	836	5	(	(	PUNCT
ejpam-4610	836	6	g	g	PROPN
ejpam-4610	836	7	◦	◦	NOUN
ejpam-4610	836	8	h	h	NOUN
ejpam-4610	836	9	)	)	PUNCT
ejpam-4610	836	10	\s∗.	\s∗.	ADJ
ejpam-4610	836	11	if	if	SCONJ
ejpam-4610	836	12	x	x	SYM
ejpam-4610	836	13	∈	∈	PROPN
ejpam-4610	836	14	v	v	ADP
ejpam-4610	836	15	(	(	PUNCT
ejpam-4610	836	16	hy	hy	NOUN
ejpam-4610	836	17	)	)	PUNCT
ejpam-4610	836	18	for	for	ADP
ejpam-4610	836	19	y	y	PROPN
ejpam-4610	836	20	̸=	̸=	PROPN
ejpam-4610	836	21	v	v	PROPN
ejpam-4610	836	22	and	and	CCONJ
ejpam-4610	836	23	z	z	NOUN
ejpam-4610	836	24	∈	∈	PROPN
ejpam-4610	836	25	s	s	VERB
ejpam-4610	836	26	is	be	AUX
ejpam-4610	836	27	such	such	ADJ
ejpam-4610	836	28	that	that	SCONJ
ejpam-4610	836	29	dg	dg	AUX
ejpam-4610	836	30	◦	◦	NOUN
ejpam-4610	836	31	h(x	h(x	PROPN
ejpam-4610	836	32	,	,	PUNCT
ejpam-4610	836	33	z	z	NOUN
ejpam-4610	836	34	)	)	PUNCT
ejpam-4610	837	1	=	=	SYM
ejpam-4610	837	2	2	2	NUM
ejpam-4610	837	3	,	,	PUNCT
ejpam-4610	837	4	then	then	ADV
ejpam-4610	837	5	z	z	NOUN
ejpam-4610	837	6	∈	∈	PROPN
ejpam-4610	837	7	s∗.	s∗.	ADJ
ejpam-4610	837	8	if	if	SCONJ
ejpam-4610	837	9	x	x	SYM
ejpam-4610	837	10	∈	∈	PROPN
ejpam-4610	837	11	v	v	X
ejpam-4610	837	12	(	(	PUNCT
ejpam-4610	837	13	hv	hv	PROPN
ejpam-4610	837	14	)	)	PUNCT
ejpam-4610	837	15	,	,	PUNCT
ejpam-4610	837	16	then	then	ADV
ejpam-4610	837	17	dg	dg	VERB
ejpam-4610	837	18	◦	◦	NOUN
ejpam-4610	837	19	h(w	h(w	PROPN
ejpam-4610	837	20	,	,	PUNCT
ejpam-4610	837	21	x	x	X
ejpam-4610	837	22	)	)	PUNCT
ejpam-4610	837	23	=	=	SYM
ejpam-4610	837	24	2	2	X
ejpam-4610	837	25	.	.	PUNCT
ejpam-4610	837	26	suppose	suppose	VERB
ejpam-4610	837	27	that	that	SCONJ
ejpam-4610	837	28	x	x	SYM
ejpam-4610	837	29	∈	∈	NOUN
ejpam-4610	837	30	v	v	X
ejpam-4610	837	31	(	(	PUNCT
ejpam-4610	837	32	g	g	NOUN
ejpam-4610	837	33	)	)	PUNCT
ejpam-4610	837	34	.	.	PUNCT
ejpam-4610	838	1	then	then	ADV
ejpam-4610	838	2	x	x	SYM
ejpam-4610	838	3	∈	∈	PROPN
ejpam-4610	838	4	v	v	ADP
ejpam-4610	838	5	(	(	PUNCT
ejpam-4610	838	6	g	g	NOUN
ejpam-4610	838	7	)	)	PUNCT
ejpam-4610	838	8	\	\	PROPN
ejpam-4610	838	9	s	s	PART
ejpam-4610	838	10	and	and	CCONJ
ejpam-4610	838	11	x	x	SYM
ejpam-4610	838	12	̸=	̸=	PROPN
ejpam-4610	838	13	w.	w.	NOUN
ejpam-4610	838	14	there	there	PRON
ejpam-4610	838	15	exists	exist	VERB
ejpam-4610	838	16	z	z	PROPN
ejpam-4610	838	17	∈	∈	PROPN
ejpam-4610	838	18	s	s	VERB
ejpam-4610	838	19	such	such	ADJ
ejpam-4610	838	20	that	that	SCONJ
ejpam-4610	839	1	dg	dg	AUX
ejpam-4610	839	2	◦	◦	NOUN
ejpam-4610	839	3	h(x	h(x	PROPN
ejpam-4610	839	4	,	,	PUNCT
ejpam-4610	839	5	z	z	NOUN
ejpam-4610	839	6	)	)	PUNCT
ejpam-4610	840	1	=	=	SYM
ejpam-4610	840	2	2	2	X
ejpam-4610	840	3	.	.	PUNCT
ejpam-4610	841	1	if	if	SCONJ
ejpam-4610	841	2	z	z	PROPN
ejpam-4610	841	3	∈	∈	PROPN
ejpam-4610	841	4	sv	sv	PROPN
ejpam-4610	841	5	,	,	PUNCT
ejpam-4610	841	6	then	then	ADV
ejpam-4610	841	7	dg	dg	VERB
ejpam-4610	841	8	◦	◦	NOUN
ejpam-4610	841	9	h(x	h(x	PROPN
ejpam-4610	841	10	,	,	PUNCT
ejpam-4610	841	11	w	w	NOUN
ejpam-4610	841	12	)	)	PUNCT
ejpam-4610	841	13	=	=	SYM
ejpam-4610	841	14	2	2	NUM
ejpam-4610	841	15	since	since	SCONJ
ejpam-4610	841	16	g	g	PROPN
ejpam-4610	841	17	is	be	AUX
ejpam-4610	841	18	k3	k3	ADJ
ejpam-4610	841	19	-	-	PUNCT
ejpam-4610	841	20	free	free	ADJ
ejpam-4610	841	21	.	.	PUNCT
ejpam-4610	842	1	if	if	SCONJ
ejpam-4610	842	2	z	z	PROPN
ejpam-4610	842	3	/∈	/∈	PUNCT
ejpam-4610	843	1	sv	sv	INTJ
ejpam-4610	843	2	,	,	PUNCT
ejpam-4610	843	3	then	then	ADV
ejpam-4610	843	4	z	z	PROPN
ejpam-4610	843	5	∈	∈	PROPN
ejpam-4610	843	6	s\sv	s\sv	PROPN
ejpam-4610	843	7	so	so	SCONJ
ejpam-4610	843	8	that	that	SCONJ
ejpam-4610	843	9	z	z	NOUN
ejpam-4610	843	10	∈	∈	PROPN
ejpam-4610	843	11	s∗.	s∗.	ADJ
ejpam-4610	843	12	this	this	PRON
ejpam-4610	843	13	shows	show	VERB
ejpam-4610	843	14	that	that	SCONJ
ejpam-4610	843	15	s∗	s∗	PROPN
ejpam-4610	843	16	is	be	AUX
ejpam-4610	843	17	a	a	DET
ejpam-4610	843	18	hop	hop	NOUN
ejpam-4610	843	19	dominating	dominating	NOUN
ejpam-4610	843	20	set	set	NOUN
ejpam-4610	843	21	of	of	ADP
ejpam-4610	843	22	g	g	PROPN
ejpam-4610	843	23	◦	◦	NOUN
ejpam-4610	843	24	h.	h.	NOUN
ejpam-4610	843	25	since	since	SCONJ
ejpam-4610	843	26	|s∗|	|s∗|	NUM
ejpam-4610	843	27	<	<	X
ejpam-4610	843	28	|s|	|s|	NOUN
ejpam-4610	843	29	,	,	PUNCT
ejpam-4610	843	30	this	this	PRON
ejpam-4610	843	31	is	be	AUX
ejpam-4610	843	32	a	a	DET
ejpam-4610	843	33	contradiction	contradiction	NOUN
ejpam-4610	843	34	.	.	PUNCT
ejpam-4610	844	1	suppose	suppose	VERB
ejpam-4610	844	2	,	,	PUNCT
ejpam-4610	844	3	s	s	PART
ejpam-4610	844	4	∩	∩	NOUN
ejpam-4610	844	5	ng(v	ng(v	PRON
ejpam-4610	844	6	)	)	PUNCT
ejpam-4610	844	7	̸=	̸=	PROPN
ejpam-4610	844	8	∅.	∅.	ADV
ejpam-4610	844	9	let	let	VERB
ejpam-4610	844	10	w	w	PROPN
ejpam-4610	844	11	∈	∈	NOUN
ejpam-4610	844	12	s	s	PART
ejpam-4610	844	13	∩	∩	NOUN
ejpam-4610	844	14	ng(v	ng(v	NUM
ejpam-4610	844	15	)	)	PUNCT
ejpam-4610	844	16	.	.	PUNCT
ejpam-4610	845	1	define	define	VERB
ejpam-4610	845	2	t	t	PROPN
ejpam-4610	845	3	=	=	SYM
ejpam-4610	845	4	s	s	PROPN
ejpam-4610	845	5	\sv	\sv	PROPN
ejpam-4610	845	6	.	.	PUNCT
ejpam-4610	846	1	following	follow	VERB
ejpam-4610	846	2	similar	similar	ADJ
ejpam-4610	846	3	argument	argument	NOUN
ejpam-4610	846	4	,	,	PUNCT
ejpam-4610	846	5	t	t	PROPN
ejpam-4610	846	6	is	be	AUX
ejpam-4610	846	7	a	a	DET
ejpam-4610	846	8	hop	hop	NOUN
ejpam-4610	846	9	dominating	dominating	NOUN
ejpam-4610	846	10	set	set	NOUN
ejpam-4610	846	11	of	of	ADP
ejpam-4610	846	12	g	g	PROPN
ejpam-4610	846	13	◦	◦	NOUN
ejpam-4610	846	14	h.	h.	PROPN
ejpam-4610	846	15	since	since	SCONJ
ejpam-4610	846	16	|t	|t	PROPN
ejpam-4610	847	1	|	|	ADV
ejpam-4610	847	2	<	<	X
ejpam-4610	847	3	|s|	|s|	PROPN
ejpam-4610	847	4	,	,	PUNCT
ejpam-4610	847	5	this	this	PRON
ejpam-4610	847	6	is	be	AUX
ejpam-4610	847	7	a	a	DET
ejpam-4610	847	8	contradiction	contradiction	NOUN
ejpam-4610	847	9	.	.	PUNCT
ejpam-4610	848	1	therefore	therefore	ADV
ejpam-4610	848	2	,	,	PUNCT
ejpam-4610	848	3	s	s	VERB
ejpam-4610	848	4	⊆	⊆	NUM
ejpam-4610	848	5	v	v	NOUN
ejpam-4610	848	6	(	(	PUNCT
ejpam-4610	848	7	g	g	NOUN
ejpam-4610	848	8	)	)	PUNCT
ejpam-4610	848	9	.	.	PUNCT
ejpam-4610	849	1	now	now	ADV
ejpam-4610	849	2	,	,	PUNCT
ejpam-4610	849	3	let	let	VERB
ejpam-4610	849	4	x	x	PUNCT
ejpam-4610	849	5	∈	∈	PROPN
ejpam-4610	849	6	v	v	X
ejpam-4610	849	7	(	(	PUNCT
ejpam-4610	849	8	g	g	NOUN
ejpam-4610	849	9	)	)	PUNCT
ejpam-4610	849	10	.	.	PUNCT
ejpam-4610	850	1	pick	pick	VERB
ejpam-4610	850	2	u	u	PRON
ejpam-4610	850	3	∈	∈	PROPN
ejpam-4610	850	4	v	v	NOUN
ejpam-4610	850	5	(	(	PUNCT
ejpam-4610	850	6	hx	hx	PROPN
ejpam-4610	850	7	)	)	PUNCT
ejpam-4610	850	8	.	.	PUNCT
ejpam-4610	851	1	then	then	ADV
ejpam-4610	851	2	u	u	X
ejpam-4610	851	3	/∈	/∈	PROPN
ejpam-4610	851	4	s	s	PART
ejpam-4610	851	5	and	and	CCONJ
ejpam-4610	851	6	there	there	PRON
ejpam-4610	851	7	exists	exist	VERB
ejpam-4610	851	8	v	v	ADP
ejpam-4610	851	9	∈	∈	PROPN
ejpam-4610	851	10	s	s	NOUN
ejpam-4610	851	11	for	for	ADP
ejpam-4610	851	12	which	which	PRON
ejpam-4610	851	13	dg	dg	VERB
ejpam-4610	851	14	◦	◦	PROPN
ejpam-4610	851	15	h(u	h(u	PROPN
ejpam-4610	851	16	,	,	PUNCT
ejpam-4610	851	17	v	v	NOUN
ejpam-4610	851	18	)	)	PUNCT
ejpam-4610	851	19	=	=	SYM
ejpam-4610	851	20	2	2	X
ejpam-4610	851	21	.	.	X
ejpam-4610	851	22	necessarily	necessarily	ADV
ejpam-4610	851	23	,	,	PUNCT
ejpam-4610	851	24	dg(x	dg(x	X
ejpam-4610	851	25	,	,	PUNCT
ejpam-4610	851	26	v	v	NOUN
ejpam-4610	851	27	)	)	PUNCT
ejpam-4610	851	28	=	=	SYM
ejpam-4610	852	1	1	1	X
ejpam-4610	852	2	.	.	PUNCT
ejpam-4610	852	3	therefore	therefore	ADV
ejpam-4610	852	4	,	,	PUNCT
ejpam-4610	852	5	s	s	VERB
ejpam-4610	852	6	is	be	AUX
ejpam-4610	852	7	a	a	DET
ejpam-4610	852	8	(	(	PUNCT
ejpam-4610	852	9	1	1	NUM
ejpam-4610	852	10	,	,	PUNCT
ejpam-4610	852	11	2)∗-total	2)∗-total	ADJ
ejpam-4610	852	12	dominating	dominating	NOUN
ejpam-4610	852	13	set	set	NOUN
ejpam-4610	852	14	of	of	ADP
ejpam-4610	852	15	g.	g.	PROPN
ejpam-4610	852	16	hence	hence	ADV
ejpam-4610	852	17	,	,	PUNCT
ejpam-4610	852	18	|s|	|s|	NOUN
ejpam-4610	852	19	≥	≥	NOUN
ejpam-4610	852	20	γ∗t1,2(g	γ∗t1,2(g	NUM
ejpam-4610	852	21	)	)	PUNCT
ejpam-4610	852	22	.	.	PUNCT
ejpam-4610	853	1	suppose	suppose	VERB
ejpam-4610	853	2	that	that	SCONJ
ejpam-4610	853	3	a	a	DET
ejpam-4610	853	4	⊆	⊆	NUM
ejpam-4610	853	5	v	v	NOUN
ejpam-4610	853	6	(	(	PUNCT
ejpam-4610	853	7	g	g	NOUN
ejpam-4610	853	8	)	)	PUNCT
ejpam-4610	853	9	is	be	AUX
ejpam-4610	853	10	a	a	DET
ejpam-4610	853	11	γ∗t1,2	γ∗t1,2	NOUN
ejpam-4610	853	12	-	-	PUNCT
ejpam-4610	853	13	set	set	NOUN
ejpam-4610	853	14	of	of	ADP
ejpam-4610	853	15	g.	g.	PROPN
ejpam-4610	853	16	then	then	ADV
ejpam-4610	853	17	a	a	PRON
ejpam-4610	853	18	is	be	AUX
ejpam-4610	853	19	a	a	DET
ejpam-4610	853	20	hop	hop	NOUN
ejpam-4610	853	21	dominating	dominating	NOUN
ejpam-4610	853	22	set	set	NOUN
ejpam-4610	853	23	of	of	ADP
ejpam-4610	853	24	g	g	PROPN
ejpam-4610	853	25	◦	◦	NOUN
ejpam-4610	853	26	h	h	NOUN
ejpam-4610	853	27	so	so	SCONJ
ejpam-4610	853	28	that	that	PRON
ejpam-4610	853	29	|s|	|s|	VERB
ejpam-4610	853	30	≤	≤	PROPN
ejpam-4610	853	31	|a|	|a|	PROPN
ejpam-4610	853	32	=	=	PUNCT
ejpam-4610	853	33	γ∗t1,2(g	γ∗t1,2(g	PROPN
ejpam-4610	853	34	)	)	PUNCT
ejpam-4610	853	35	.	.	PUNCT
ejpam-4610	854	1	therefore	therefore	ADV
ejpam-4610	854	2	,	,	PUNCT
ejpam-4610	854	3	s	s	VERB
ejpam-4610	854	4	is	be	AUX
ejpam-4610	854	5	a	a	DET
ejpam-4610	854	6	γ∗t1,2	γ∗t1,2	NOUN
ejpam-4610	854	7	-	-	PUNCT
ejpam-4610	854	8	set	set	NOUN
ejpam-4610	854	9	of	of	ADP
ejpam-4610	854	10	g.	g.	NOUN
ejpam-4610	854	11	conversely	conversely	ADV
ejpam-4610	854	12	,	,	PUNCT
ejpam-4610	854	13	suppose	suppose	VERB
ejpam-4610	854	14	that	that	SCONJ
ejpam-4610	854	15	s	s	VERB
ejpam-4610	854	16	⊆	⊆	NUM
ejpam-4610	854	17	v	v	NOUN
ejpam-4610	854	18	(	(	PUNCT
ejpam-4610	854	19	g	g	NOUN
ejpam-4610	854	20	)	)	PUNCT
ejpam-4610	854	21	is	be	AUX
ejpam-4610	854	22	a	a	DET
ejpam-4610	854	23	γ∗t1,2	γ∗t1,2	NOUN
ejpam-4610	854	24	-	-	PUNCT
ejpam-4610	854	25	set	set	NOUN
ejpam-4610	854	26	of	of	ADP
ejpam-4610	854	27	g.	g.	PROPN
ejpam-4610	854	28	then	then	ADV
ejpam-4610	854	29	s	s	VERB
ejpam-4610	854	30	is	be	AUX
ejpam-4610	854	31	a	a	DET
ejpam-4610	854	32	hop	hop	NOUN
ejpam-4610	854	33	dominating	dominating	NOUN
ejpam-4610	854	34	set	set	NOUN
ejpam-4610	854	35	of	of	ADP
ejpam-4610	854	36	g.	g.	PROPN
ejpam-4610	854	37	let	let	VERB
ejpam-4610	854	38	v	v	NUM
ejpam-4610	854	39	∈	∈	PROPN
ejpam-4610	854	40	v	v	NOUN
ejpam-4610	854	41	(	(	PUNCT
ejpam-4610	854	42	g	g	NOUN
ejpam-4610	854	43	)	)	PUNCT
ejpam-4610	854	44	and	and	CCONJ
ejpam-4610	854	45	x	x	PUNCT
ejpam-4610	854	46	∈	∈	NOUN
ejpam-4610	854	47	v	v	ADP
ejpam-4610	854	48	(	(	PUNCT
ejpam-4610	854	49	hv	hv	PROPN
ejpam-4610	854	50	)	)	PUNCT
ejpam-4610	854	51	.	.	PUNCT
ejpam-4610	855	1	since	since	SCONJ
ejpam-4610	855	2	s	s	PROPN
ejpam-4610	855	3	is	be	AUX
ejpam-4610	855	4	a	a	DET
ejpam-4610	855	5	total	total	ADJ
ejpam-4610	855	6	dominating	dominating	NOUN
ejpam-4610	855	7	set	set	NOUN
ejpam-4610	855	8	of	of	ADP
ejpam-4610	855	9	g	g	NOUN
ejpam-4610	855	10	,	,	PUNCT
ejpam-4610	855	11	uv	uv	PROPN
ejpam-4610	855	12	∈	∈	PROPN
ejpam-4610	855	13	e(g	e(g	PROPN
ejpam-4610	855	14	)	)	PUNCT
ejpam-4610	855	15	for	for	ADP
ejpam-4610	855	16	some	some	DET
ejpam-4610	855	17	u	u	NOUN
ejpam-4610	855	18	∈	∈	PROPN
ejpam-4610	855	19	s.	s.	PROPN
ejpam-4610	855	20	then	then	ADV
ejpam-4610	855	21	dg	dg	VERB
ejpam-4610	855	22	◦	◦	NOUN
ejpam-4610	855	23	h(x	h(x	PROPN
ejpam-4610	855	24	,	,	PUNCT
ejpam-4610	855	25	u	u	NOUN
ejpam-4610	855	26	)	)	PUNCT
ejpam-4610	855	27	=	=	SYM
ejpam-4610	856	1	2	2	X
ejpam-4610	856	2	.	.	PUNCT
ejpam-4610	856	3	since	since	SCONJ
ejpam-4610	856	4	x	x	PROPN
ejpam-4610	856	5	and	and	CCONJ
ejpam-4610	856	6	v	v	NOUN
ejpam-4610	856	7	are	be	AUX
ejpam-4610	856	8	arbitrary	arbitrary	ADJ
ejpam-4610	856	9	,	,	PUNCT
ejpam-4610	856	10	s	s	PART
ejpam-4610	856	11	hop	hop	NOUN
ejpam-4610	856	12	dominates	dominate	VERB
ejpam-4610	856	13	v	v	NUM
ejpam-4610	856	14	(	(	PUNCT
ejpam-4610	856	15	hv	hv	PROPN
ejpam-4610	856	16	)	)	PUNCT
ejpam-4610	856	17	for	for	ADP
ejpam-4610	856	18	all	all	PRON
ejpam-4610	856	19	v	v	ADP
ejpam-4610	856	20	∈	∈	NOUN
ejpam-4610	856	21	v	v	NOUN
ejpam-4610	856	22	(	(	PUNCT
ejpam-4610	856	23	g	g	NOUN
ejpam-4610	856	24	)	)	PUNCT
ejpam-4610	856	25	.	.	PUNCT
ejpam-4610	857	1	thus	thus	ADV
ejpam-4610	857	2	s	s	X
ejpam-4610	857	3	is	be	AUX
ejpam-4610	857	4	a	a	DET
ejpam-4610	857	5	hop	hop	NOUN
ejpam-4610	857	6	dominating	dominating	NOUN
ejpam-4610	857	7	set	set	NOUN
ejpam-4610	857	8	of	of	ADP
ejpam-4610	857	9	g	g	PROPN
ejpam-4610	857	10	◦	◦	NOUN
ejpam-4610	857	11	h.	h.	PROPN
ejpam-4610	857	12	let	let	VERB
ejpam-4610	857	13	s∗	s∗	PROPN
ejpam-4610	857	14	be	be	AUX
ejpam-4610	857	15	a	a	DET
ejpam-4610	857	16	γh	γh	ADV
ejpam-4610	857	17	-	-	PUNCT
ejpam-4610	857	18	set	set	NOUN
ejpam-4610	857	19	of	of	ADP
ejpam-4610	857	20	g.	g.	PROPN
ejpam-4610	857	21	by	by	ADP
ejpam-4610	857	22	the	the	DET
ejpam-4610	857	23	above	above	ADJ
ejpam-4610	857	24	result	result	NOUN
ejpam-4610	857	25	,	,	PUNCT
ejpam-4610	857	26	s∗	s∗	VERB
ejpam-4610	857	27	⊆	⊆	NUM
ejpam-4610	857	28	v	v	NOUN
ejpam-4610	857	29	(	(	PUNCT
ejpam-4610	857	30	g	g	NOUN
ejpam-4610	857	31	)	)	PUNCT
ejpam-4610	857	32	and	and	CCONJ
ejpam-4610	857	33	is	be	AUX
ejpam-4610	857	34	a	a	DET
ejpam-4610	857	35	γ∗t1,2	γ∗t1,2	NOUN
ejpam-4610	857	36	-	-	PUNCT
ejpam-4610	857	37	set	set	NOUN
ejpam-4610	857	38	of	of	ADP
ejpam-4610	857	39	g.	g.	PROPN
ejpam-4610	857	40	therefore	therefore	ADV
ejpam-4610	857	41	,	,	PUNCT
ejpam-4610	857	42	|s|	|s|	PROPN
ejpam-4610	857	43	=	=	NOUN
ejpam-4610	857	44	|s∗|	|s∗|	NUM
ejpam-4610	857	45	and	and	CCONJ
ejpam-4610	857	46	s	s	VERB
ejpam-4610	857	47	is	be	AUX
ejpam-4610	857	48	a	a	DET
ejpam-4610	857	49	γh	γh	ADV
ejpam-4610	857	50	-	-	PUNCT
ejpam-4610	857	51	set	set	NOUN
ejpam-4610	857	52	of	of	ADP
ejpam-4610	857	53	g	g	PROPN
ejpam-4610	857	54	◦	◦	NOUN
ejpam-4610	857	55	h.	h.	PROPN
ejpam-4610	857	56	corollary	corollary	ADJ
ejpam-4610	857	57	3	3	PROPN
ejpam-4610	857	58	.	.	PUNCT
ejpam-4610	857	59	for	for	ADP
ejpam-4610	857	60	all	all	DET
ejpam-4610	857	61	connected	connect	VERB
ejpam-4610	857	62	k3	k3	VERB
ejpam-4610	857	63	-	-	PUNCT
ejpam-4610	857	64	free	free	ADJ
ejpam-4610	857	65	graphs	graph	NOUN
ejpam-4610	857	66	g	g	NOUN
ejpam-4610	857	67	and	and	CCONJ
ejpam-4610	857	68	nontrivial	nontrivial	ADJ
ejpam-4610	857	69	connected	connect	VERB
ejpam-4610	857	70	graphs	graph	NOUN
ejpam-4610	857	71	h	h	NOUN
ejpam-4610	857	72	,	,	PUNCT
ejpam-4610	857	73	γh(g	γh(g	PUNCT
ejpam-4610	857	74	◦	◦	NOUN
ejpam-4610	857	75	h	h	NOUN
ejpam-4610	857	76	)	)	PUNCT
ejpam-4610	857	77	=	=	SYM
ejpam-4610	857	78	γ∗t1,2(g	γ∗t1,2(g	PROPN
ejpam-4610	857	79	)	)	PUNCT
ejpam-4610	857	80	.	.	PUNCT
ejpam-4610	858	1	m.a	m.a	PROPN
ejpam-4610	858	2	.	.	PROPN
ejpam-4610	858	3	bonsocan	bonsocan	PROPN
ejpam-4610	858	4	,	,	PUNCT
ejpam-4610	858	5	f.	f.	PROPN
ejpam-4610	858	6	jamil	jamil	PROPN
ejpam-4610	858	7	/	/	SYM
ejpam-4610	858	8	eur	eur	PROPN
ejpam-4610	858	9	.	.	PUNCT
ejpam-4610	859	1	j.	j.	PROPN
ejpam-4610	859	2	pure	pure	PROPN
ejpam-4610	859	3	appl	appl	PROPN
ejpam-4610	859	4	.	.	PROPN
ejpam-4610	859	5	math	math	PROPN
ejpam-4610	859	6	,	,	PUNCT
ejpam-4610	859	7	16	16	NUM
ejpam-4610	859	8	(	(	PUNCT
ejpam-4610	859	9	1	1	NUM
ejpam-4610	859	10	)	)	PUNCT
ejpam-4610	859	11	(	(	PUNCT
ejpam-4610	859	12	2023	2023	NUM
ejpam-4610	859	13	)	)	PUNCT
ejpam-4610	859	14	,	,	PUNCT
ejpam-4610	859	15	192	192	NUM
ejpam-4610	859	16	-	-	SYM
ejpam-4610	859	17	206	206	NUM
ejpam-4610	859	18	203	203	NUM
ejpam-4610	859	19	...............	...............	PUNCT
ejpam-4610	859	20	..............	..............	PUNCT
ejpam-4610	859	21	..............	..............	PUNCT
ejpam-4610	859	22	..............	..............	PUNCT
ejpam-4610	859	23	..............	..............	PUNCT
ejpam-4610	859	24	..............	..............	PUNCT
ejpam-4610	859	25	........	........	PUNCT
ejpam-4610	860	1	....................................	....................................	PUNCT
ejpam-4610	860	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4610	861	1	....................................	....................................	PUNCT
ejpam-4610	861	2	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4610	861	3	........................................................................	........................................................................	PUNCT
ejpam-4610	862	1	....................................	....................................	PUNCT
ejpam-4610	862	2	....................................	....................................	PUNCT
ejpam-4610	863	1	....................................	....................................	PUNCT
ejpam-4610	863	2	....................................	....................................	PUNCT
ejpam-4610	864	1	....................................	....................................	PUNCT
ejpam-4610	864	2	....................................	....................................	PUNCT
ejpam-4610	865	1	................................................................	................................................................	PUNCT
ejpam-4610	865	2	.........	.........	PUNCT
ejpam-4610	866	1	.........	.........	PUNCT
ejpam-4610	866	2	.........	.........	PUNCT
ejpam-4610	866	3	.........	.........	PUNCT
ejpam-4610	866	4	........	........	PUNCT
ejpam-4610	866	5	...............................................	...............................................	PUNCT
ejpam-4610	866	6	................................................................	................................................................	PUNCT
ejpam-4610	867	1	.........	.........	PUNCT
ejpam-4610	867	2	.........	.........	PUNCT
ejpam-4610	868	1	.........	.........	PUNCT
ejpam-4610	868	2	.........	.........	PUNCT
ejpam-4610	868	3	........	........	PUNCT
ejpam-4610	868	4	...............................................	...............................................	PUNCT
ejpam-4610	868	5	................................................................	................................................................	PUNCT
ejpam-4610	869	1	.........	.........	PUNCT
ejpam-4610	869	2	.........	.........	PUNCT
ejpam-4610	870	1	.........	.........	PUNCT
ejpam-4610	870	2	.........	.........	PUNCT
ejpam-4610	871	1	........	........	PUNCT
ejpam-4610	871	2	...............................................	...............................................	PUNCT
ejpam-4610	872	1	•	•	NUM
ejpam-4610	872	2	•	•	NOUN
ejpam-4610	872	3	•	•	NUM
ejpam-4610	872	4	figure	figure	NOUN
ejpam-4610	872	5	5	5	NUM
ejpam-4610	872	6	:	:	PUNCT
ejpam-4610	872	7	the	the	DET
ejpam-4610	872	8	corona	corona	NOUN
ejpam-4610	872	9	k3	k3	VERB
ejpam-4610	872	10	◦	◦	NOUN
ejpam-4610	872	11	k2	k2	ADJ
ejpam-4610	872	12	it	it	PRON
ejpam-4610	872	13	is	be	AUX
ejpam-4610	872	14	worth	worth	ADJ
ejpam-4610	872	15	noting	note	VERB
ejpam-4610	872	16	that	that	SCONJ
ejpam-4610	872	17	the	the	DET
ejpam-4610	872	18	necessity	necessity	NOUN
ejpam-4610	872	19	part	part	NOUN
ejpam-4610	872	20	of	of	ADP
ejpam-4610	872	21	lemma	lemma	PROPN
ejpam-4610	872	22	2	2	NUM
ejpam-4610	872	23	need	need	AUX
ejpam-4610	872	24	not	not	PART
ejpam-4610	872	25	be	be	AUX
ejpam-4610	872	26	true	true	ADJ
ejpam-4610	872	27	if	if	SCONJ
ejpam-4610	872	28	g	g	PROPN
ejpam-4610	872	29	contains	contain	VERB
ejpam-4610	872	30	a	a	DET
ejpam-4610	872	31	k3	k3	NOUN
ejpam-4610	872	32	.	.	PUNCT
ejpam-4610	873	1	consider	consider	VERB
ejpam-4610	873	2	,	,	PUNCT
ejpam-4610	873	3	for	for	ADP
ejpam-4610	873	4	example	example	NOUN
ejpam-4610	873	5	,	,	PUNCT
ejpam-4610	873	6	the	the	DET
ejpam-4610	873	7	corona	corona	NOUN
ejpam-4610	873	8	k3	k3	VERB
ejpam-4610	873	9	◦	◦	NOUN
ejpam-4610	873	10	k2	k2	NOUN
ejpam-4610	873	11	as	as	SCONJ
ejpam-4610	873	12	shown	show	VERB
ejpam-4610	873	13	in	in	ADP
ejpam-4610	873	14	figure	figure	NOUN
ejpam-4610	873	15	5	5	NUM
ejpam-4610	873	16	.	.	PUNCT
ejpam-4610	873	17	observe	observe	VERB
ejpam-4610	873	18	that	that	SCONJ
ejpam-4610	873	19	the	the	DET
ejpam-4610	873	20	blackened	blacken	VERB
ejpam-4610	873	21	vertices	vertex	NOUN
ejpam-4610	873	22	constitute	constitute	VERB
ejpam-4610	873	23	a	a	DET
ejpam-4610	873	24	γh	γh	ADV
ejpam-4610	873	25	-	-	PUNCT
ejpam-4610	873	26	set	set	NOUN
ejpam-4610	873	27	of	of	ADP
ejpam-4610	873	28	k3	k3	ADJ
ejpam-4610	873	29	◦	◦	NOUN
ejpam-4610	873	30	k2	k2	ADJ
ejpam-4610	873	31	.	.	PUNCT
ejpam-4610	874	1	for	for	ADP
ejpam-4610	874	2	what	what	PRON
ejpam-4610	874	3	follows	follow	VERB
ejpam-4610	874	4	,	,	PUNCT
ejpam-4610	874	5	we	we	PRON
ejpam-4610	874	6	give	give	VERB
ejpam-4610	874	7	the	the	DET
ejpam-4610	874	8	following	follow	VERB
ejpam-4610	874	9	definition	definition	NOUN
ejpam-4610	874	10	.	.	PUNCT
ejpam-4610	875	1	a	a	DET
ejpam-4610	875	2	subset	subset	NOUN
ejpam-4610	875	3	s	s	VERB
ejpam-4610	875	4	⊆	⊆	NUM
ejpam-4610	875	5	v	v	NOUN
ejpam-4610	875	6	(	(	PUNCT
ejpam-4610	875	7	g	g	NOUN
ejpam-4610	875	8	)	)	PUNCT
ejpam-4610	875	9	is	be	AUX
ejpam-4610	875	10	said	say	VERB
ejpam-4610	875	11	to	to	PART
ejpam-4610	875	12	be	be	AUX
ejpam-4610	875	13	a	a	DET
ejpam-4610	875	14	transversal	transversal	NOUN
ejpam-4610	875	15	(	(	PUNCT
ejpam-4610	875	16	1	1	NUM
ejpam-4610	875	17	,	,	PUNCT
ejpam-4610	875	18	2)∗-total	2)∗-total	ADJ
ejpam-4610	875	19	dominating	dominating	NOUN
ejpam-4610	875	20	set	set	NOUN
ejpam-4610	875	21	of	of	ADP
ejpam-4610	875	22	g	g	PROPN
ejpam-4610	875	23	if	if	SCONJ
ejpam-4610	875	24	s	s	VERB
ejpam-4610	875	25	is	be	AUX
ejpam-4610	875	26	a	a	DET
ejpam-4610	875	27	(	(	PUNCT
ejpam-4610	875	28	1	1	NUM
ejpam-4610	875	29	,	,	PUNCT
ejpam-4610	875	30	2)∗-total	2)∗-total	ADJ
ejpam-4610	875	31	dominating	dominating	NOUN
ejpam-4610	875	32	set	set	NOUN
ejpam-4610	875	33	of	of	ADP
ejpam-4610	875	34	g	g	PROPN
ejpam-4610	875	35	which	which	PRON
ejpam-4610	875	36	intersects	intersect	VERB
ejpam-4610	875	37	every	every	DET
ejpam-4610	875	38	γ∗t1,2	γ∗t1,2	NOUN
ejpam-4610	875	39	-	-	PUNCT
ejpam-4610	875	40	set	set	NOUN
ejpam-4610	875	41	of	of	ADP
ejpam-4610	875	42	g.	g.	PROPN
ejpam-4610	875	43	the	the	DET
ejpam-4610	875	44	minimum	minimum	ADJ
ejpam-4610	875	45	cardinality	cardinality	NOUN
ejpam-4610	875	46	of	of	ADP
ejpam-4610	875	47	a	a	DET
ejpam-4610	875	48	transversal	transversal	NOUN
ejpam-4610	875	49	(	(	PUNCT
ejpam-4610	875	50	1	1	NUM
ejpam-4610	875	51	,	,	PUNCT
ejpam-4610	875	52	2)∗-total	2)∗-total	ADJ
ejpam-4610	875	53	dominating	dominating	NOUN
ejpam-4610	875	54	set	set	NOUN
ejpam-4610	875	55	,	,	PUNCT
ejpam-4610	875	56	denoted	denote	VERB
ejpam-4610	875	57	γ̂∗t1,2(g	γ̂∗t1,2(g	NOUN
ejpam-4610	875	58	)	)	PUNCT
ejpam-4610	875	59	,	,	PUNCT
ejpam-4610	875	60	is	be	AUX
ejpam-4610	875	61	the	the	DET
ejpam-4610	875	62	transversal	transversal	NOUN
ejpam-4610	875	63	(	(	PUNCT
ejpam-4610	875	64	1	1	NUM
ejpam-4610	875	65	,	,	PUNCT
ejpam-4610	875	66	2)∗-total	2)∗-total	ADJ
ejpam-4610	875	67	domination	domination	NOUN
ejpam-4610	875	68	number	number	NOUN
ejpam-4610	875	69	of	of	ADP
ejpam-4610	875	70	g.	g.	PROPN
ejpam-4610	875	71	any	any	DET
ejpam-4610	875	72	transversal	transversal	NOUN
ejpam-4610	875	73	(	(	PUNCT
ejpam-4610	875	74	1	1	NUM
ejpam-4610	875	75	,	,	PUNCT
ejpam-4610	875	76	2)∗-total	2)∗-total	ADJ
ejpam-4610	875	77	dominating	dominating	NOUN
ejpam-4610	875	78	set	set	NOUN
ejpam-4610	875	79	of	of	ADP
ejpam-4610	875	80	g	g	PROPN
ejpam-4610	875	81	of	of	ADP
ejpam-4610	875	82	cardinality	cardinality	NOUN
ejpam-4610	875	83	γ̂∗t1,2(g	γ̂∗t1,2(g	PROPN
ejpam-4610	875	84	)	)	PUNCT
ejpam-4610	875	85	is	be	AUX
ejpam-4610	875	86	referred	refer	VERB
ejpam-4610	875	87	to	to	ADP
ejpam-4610	875	88	as	as	ADP
ejpam-4610	875	89	a	a	DET
ejpam-4610	875	90	γ̂∗t1,2	γ̂∗t1,2	ADJ
ejpam-4610	875	91	-	-	PUNCT
ejpam-4610	875	92	set	set	NOUN
ejpam-4610	875	93	.	.	PUNCT
ejpam-4610	876	1	theorem	theorem	VERB
ejpam-4610	876	2	8	8	NUM
ejpam-4610	876	3	.	.	PUNCT
ejpam-4610	877	1	if	if	SCONJ
ejpam-4610	877	2	g	g	PROPN
ejpam-4610	877	3	is	be	AUX
ejpam-4610	877	4	a	a	DET
ejpam-4610	877	5	connected	connect	VERB
ejpam-4610	877	6	k3	k3	VERB
ejpam-4610	877	7	-	-	PUNCT
ejpam-4610	877	8	free	free	ADJ
ejpam-4610	877	9	graph	graph	NOUN
ejpam-4610	877	10	of	of	ADP
ejpam-4610	877	11	order	order	NOUN
ejpam-4610	877	12	n	n	PRON
ejpam-4610	877	13	≥	≥	NOUN
ejpam-4610	877	14	2	2	NUM
ejpam-4610	877	15	,	,	PUNCT
ejpam-4610	877	16	then	then	ADV
ejpam-4610	877	17	γ̂h(g	γ̂h(g	VERB
ejpam-4610	877	18	◦	◦	NOUN
ejpam-4610	877	19	h	h	NOUN
ejpam-4610	877	20	)	)	PUNCT
ejpam-4610	877	21	=	=	SYM
ejpam-4610	877	22	γ̂∗t1,2(g	γ̂∗t1,2(g	X
ejpam-4610	877	23	)	)	PUNCT
ejpam-4610	877	24	for	for	ADP
ejpam-4610	877	25	all	all	DET
ejpam-4610	877	26	nontrivial	nontrivial	ADJ
ejpam-4610	877	27	connected	connect	VERB
ejpam-4610	877	28	graphs	graph	NOUN
ejpam-4610	877	29	h.	h.	NOUN
ejpam-4610	877	30	proof	proof	NOUN
ejpam-4610	877	31	.	.	PUNCT
ejpam-4610	878	1	this	this	PRON
ejpam-4610	878	2	is	be	AUX
ejpam-4610	878	3	clear	clear	ADJ
ejpam-4610	878	4	if	if	SCONJ
ejpam-4610	878	5	n	n	NOUN
ejpam-4610	878	6	=	=	SYM
ejpam-4610	878	7	2	2	X
ejpam-4610	878	8	.	.	PUNCT
ejpam-4610	878	9	suppose	suppose	VERB
ejpam-4610	879	1	that	that	SCONJ
ejpam-4610	879	2	n	n	PROPN
ejpam-4610	879	3	≥	≥	NOUN
ejpam-4610	879	4	3	3	NUM
ejpam-4610	879	5	.	.	PUNCT
ejpam-4610	880	1	first	first	ADV
ejpam-4610	880	2	,	,	PUNCT
ejpam-4610	880	3	let	let	VERB
ejpam-4610	880	4	s	s	PRON
ejpam-4610	880	5	⊆	⊆	NUM
ejpam-4610	880	6	v	v	NOUN
ejpam-4610	880	7	(	(	PUNCT
ejpam-4610	880	8	g	g	NOUN
ejpam-4610	880	9	)	)	PUNCT
ejpam-4610	880	10	be	be	AUX
ejpam-4610	880	11	a	a	DET
ejpam-4610	880	12	γ̂∗1,2	γ̂∗1,2	ADV
ejpam-4610	880	13	-	-	PUNCT
ejpam-4610	880	14	set	set	NOUN
ejpam-4610	880	15	of	of	ADP
ejpam-4610	880	16	g.	g.	PROPN
ejpam-4610	880	17	following	follow	VERB
ejpam-4610	880	18	the	the	DET
ejpam-4610	880	19	sufficiency	sufficiency	NOUN
ejpam-4610	880	20	proof	proof	NOUN
ejpam-4610	880	21	of	of	ADP
ejpam-4610	880	22	lemma	lemma	PROPN
ejpam-4610	880	23	2	2	NUM
ejpam-4610	880	24	,	,	PUNCT
ejpam-4610	880	25	s	s	VERB
ejpam-4610	880	26	is	be	AUX
ejpam-4610	880	27	a	a	DET
ejpam-4610	880	28	hop	hop	NOUN
ejpam-4610	880	29	dominating	dominating	NOUN
ejpam-4610	880	30	set	set	NOUN
ejpam-4610	880	31	of	of	ADP
ejpam-4610	880	32	g	g	PROPN
ejpam-4610	880	33	◦	◦	NOUN
ejpam-4610	880	34	h.	h.	NOUN
ejpam-4610	880	35	by	by	ADP
ejpam-4610	880	36	lemma	lemma	PROPN
ejpam-4610	880	37	2	2	NUM
ejpam-4610	880	38	,	,	PUNCT
ejpam-4610	880	39	s	s	VERB
ejpam-4610	880	40	is	be	AUX
ejpam-4610	880	41	a	a	DET
ejpam-4610	880	42	thd	thd	NOUN
ejpam-4610	880	43	-	-	PUNCT
ejpam-4610	880	44	set	set	NOUN
ejpam-4610	880	45	of	of	ADP
ejpam-4610	880	46	g	g	PROPN
ejpam-4610	880	47	◦	◦	NOUN
ejpam-4610	880	48	h.	h.	PROPN
ejpam-4610	880	49	consequently	consequently	ADV
ejpam-4610	880	50	,	,	PUNCT
ejpam-4610	880	51	γ̂h(g	γ̂h(g	PROPN
ejpam-4610	880	52	◦	◦	NOUN
ejpam-4610	880	53	h	h	NOUN
ejpam-4610	880	54	)	)	PUNCT
ejpam-4610	880	55	≤	≤	NUM
ejpam-4610	880	56	|s|	|s|	PROPN
ejpam-4610	880	57	=	=	PUNCT
ejpam-4610	880	58	γ̂∗t1,2(g	γ̂∗t1,2(g	PROPN
ejpam-4610	880	59	)	)	PUNCT
ejpam-4610	880	60	.	.	PUNCT
ejpam-4610	881	1	now	now	ADV
ejpam-4610	881	2	,	,	PUNCT
ejpam-4610	881	3	let	let	VERB
ejpam-4610	881	4	s	s	PRON
ejpam-4610	881	5	⊆	⊆	NUM
ejpam-4610	881	6	v	v	NOUN
ejpam-4610	881	7	(	(	PUNCT
ejpam-4610	881	8	g	g	PROPN
ejpam-4610	881	9	◦	◦	NOUN
ejpam-4610	881	10	h	h	NOUN
ejpam-4610	881	11	)	)	PUNCT
ejpam-4610	881	12	be	be	VERB
ejpam-4610	881	13	a	a	DET
ejpam-4610	881	14	γ̂h	γ̂h	NOUN
ejpam-4610	881	15	-	-	PUNCT
ejpam-4610	881	16	set	set	NOUN
ejpam-4610	881	17	of	of	ADP
ejpam-4610	881	18	g	g	PROPN
ejpam-4610	881	19	◦	◦	NOUN
ejpam-4610	881	20	h.	h.	NOUN
ejpam-4610	881	21	let	let	VERB
ejpam-4610	881	22	a	a	DET
ejpam-4610	881	23	=	=	PUNCT
ejpam-4610	881	24	s∩v	s∩v	NOUN
ejpam-4610	881	25	(	(	PUNCT
ejpam-4610	881	26	g	g	NOUN
ejpam-4610	881	27	)	)	PUNCT
ejpam-4610	881	28	and	and	CCONJ
ejpam-4610	882	1	sv	sv	X
ejpam-4610	882	2	=	=	SYM
ejpam-4610	882	3	s∩v	s∩v	PROPN
ejpam-4610	882	4	(	(	PUNCT
ejpam-4610	882	5	hv	hv	PROPN
ejpam-4610	882	6	)	)	PUNCT
ejpam-4610	882	7	for	for	ADP
ejpam-4610	882	8	each	each	DET
ejpam-4610	882	9	v	v	NUM
ejpam-4610	882	10	∈	∈	PROPN
ejpam-4610	882	11	v	v	NOUN
ejpam-4610	882	12	(	(	PUNCT
ejpam-4610	882	13	g	g	NOUN
ejpam-4610	882	14	)	)	PUNCT
ejpam-4610	882	15	.	.	PUNCT
ejpam-4610	883	1	by	by	ADP
ejpam-4610	883	2	theorem	theorem	NOUN
ejpam-4610	883	3	7	7	NUM
ejpam-4610	883	4	and	and	CCONJ
ejpam-4610	883	5	proposition	proposition	NOUN
ejpam-4610	883	6	9	9	NUM
ejpam-4610	883	7	,	,	PUNCT
ejpam-4610	883	8	sv	sv	PROPN
ejpam-4610	883	9	is	be	AUX
ejpam-4610	883	10	a	a	DET
ejpam-4610	883	11	pnd	pnd	NOUN
ejpam-4610	883	12	-	-	PUNCT
ejpam-4610	883	13	set	set	NOUN
ejpam-4610	883	14	of	of	ADP
ejpam-4610	883	15	hv	hv	PROPN
ejpam-4610	883	16	,	,	PUNCT
ejpam-4610	883	17	hence	hence	ADV
ejpam-4610	883	18	|sv|	|sv|	PROPN
ejpam-4610	883	19	≥	≥	NUM
ejpam-4610	883	20	2	2	NUM
ejpam-4610	883	21	,	,	PUNCT
ejpam-4610	883	22	for	for	ADP
ejpam-4610	883	23	all	all	PRON
ejpam-4610	883	24	v	v	ADP
ejpam-4610	883	25	∈	∈	NUM
ejpam-4610	883	26	v	v	NOUN
ejpam-4610	883	27	(	(	PUNCT
ejpam-4610	883	28	g	g	NOUN
ejpam-4610	883	29	)	)	PUNCT
ejpam-4610	883	30	\ng(a	\ng(a	PROPN
ejpam-4610	883	31	)	)	PUNCT
ejpam-4610	883	32	.	.	PUNCT
ejpam-4610	884	1	for	for	ADP
ejpam-4610	884	2	each	each	PRON
ejpam-4610	884	3	v	v	NUM
ejpam-4610	884	4	∈	∈	PROPN
ejpam-4610	884	5	v	v	NOUN
ejpam-4610	884	6	(	(	PUNCT
ejpam-4610	884	7	g	g	NOUN
ejpam-4610	884	8	)	)	PUNCT
ejpam-4610	884	9	\ng(a	\ng(a	PROPN
ejpam-4610	884	10	)	)	PUNCT
ejpam-4610	884	11	,	,	PUNCT
ejpam-4610	884	12	choose	choose	VERB
ejpam-4610	884	13	uv	uv	NOUN
ejpam-4610	884	14	∈	∈	PROPN
ejpam-4610	884	15	ng(v	ng(v	NOUN
ejpam-4610	884	16	)	)	PUNCT
ejpam-4610	884	17	.	.	PUNCT
ejpam-4610	885	1	define	define	VERB
ejpam-4610	885	2	c	c	NOUN
ejpam-4610	885	3	=	=	PUNCT
ejpam-4610	885	4	a	a	DET
ejpam-4610	885	5	∪	∪	ADJ
ejpam-4610	885	6	{	{	PUNCT
ejpam-4610	885	7	v	v	NOUN
ejpam-4610	885	8	,	,	PUNCT
ejpam-4610	885	9	uv	uv	NOUN
ejpam-4610	885	10	:	:	PUNCT
ejpam-4610	885	11	v	v	NUM
ejpam-4610	885	12	∈	∈	PROPN
ejpam-4610	885	13	v	v	NOUN
ejpam-4610	885	14	(	(	PUNCT
ejpam-4610	885	15	g	g	NOUN
ejpam-4610	885	16	)	)	PUNCT
ejpam-4610	885	17	\ng(a	\ng(a	NOUN
ejpam-4610	885	18	)	)	PUNCT
ejpam-4610	885	19	}	}	PUNCT
ejpam-4610	885	20	.	.	PUNCT
ejpam-4610	886	1	clearly	clearly	ADV
ejpam-4610	886	2	,	,	PUNCT
ejpam-4610	886	3	|c|	|c|	PROPN
ejpam-4610	886	4	≤	≤	PROPN
ejpam-4610	886	5	|s|	|s|	PROPN
ejpam-4610	886	6	.	.	PUNCT
ejpam-4610	887	1	claim	claim	NOUN
ejpam-4610	887	2	1	1	NUM
ejpam-4610	887	3	:	:	PUNCT
ejpam-4610	887	4	c	c	NOUN
ejpam-4610	887	5	is	be	AUX
ejpam-4610	887	6	a	a	DET
ejpam-4610	887	7	hop	hop	NOUN
ejpam-4610	887	8	dominating	dominating	NOUN
ejpam-4610	887	9	set	set	NOUN
ejpam-4610	887	10	of	of	ADP
ejpam-4610	887	11	g.	g.	PROPN
ejpam-4610	887	12	let	let	VERB
ejpam-4610	887	13	x	x	SYM
ejpam-4610	887	14	∈	∈	PROPN
ejpam-4610	887	15	v	v	X
ejpam-4610	887	16	(	(	PUNCT
ejpam-4610	887	17	g	g	NOUN
ejpam-4610	887	18	)	)	PUNCT
ejpam-4610	887	19	\	\	PROPN
ejpam-4610	887	20	c.	c.	NOUN
ejpam-4610	887	21	since	since	SCONJ
ejpam-4610	887	22	s	s	PROPN
ejpam-4610	887	23	is	be	AUX
ejpam-4610	887	24	a	a	DET
ejpam-4610	887	25	hop	hop	NOUN
ejpam-4610	887	26	dominating	dominating	NOUN
ejpam-4610	887	27	set	set	NOUN
ejpam-4610	887	28	of	of	ADP
ejpam-4610	887	29	g	g	PROPN
ejpam-4610	887	30	◦	◦	NOUN
ejpam-4610	887	31	h	h	NOUN
ejpam-4610	887	32	and	and	CCONJ
ejpam-4610	887	33	x	x	SYM
ejpam-4610	887	34	/∈	/∈	PROPN
ejpam-4610	888	1	s	s	X
ejpam-4610	888	2	,	,	PUNCT
ejpam-4610	888	3	there	there	PRON
ejpam-4610	888	4	exists	exist	VERB
ejpam-4610	888	5	y	y	PROPN
ejpam-4610	888	6	∈	∈	PROPN
ejpam-4610	888	7	s	s	X
ejpam-4610	888	8	for	for	ADP
ejpam-4610	888	9	which	which	PRON
ejpam-4610	888	10	dg	dg	VERB
ejpam-4610	888	11	◦	◦	NOUN
ejpam-4610	888	12	h(x	h(x	PROPN
ejpam-4610	888	13	,	,	PUNCT
ejpam-4610	888	14	y	y	PROPN
ejpam-4610	888	15	)	)	PUNCT
ejpam-4610	888	16	=	=	SYM
ejpam-4610	889	1	2	2	X
ejpam-4610	889	2	.	.	X
ejpam-4610	890	1	if	if	SCONJ
ejpam-4610	890	2	y	y	PROPN
ejpam-4610	890	3	∈	∈	PROPN
ejpam-4610	890	4	a	a	PRON
ejpam-4610	890	5	,	,	PUNCT
ejpam-4610	890	6	then	then	ADV
ejpam-4610	890	7	y	y	PROPN
ejpam-4610	890	8	∈	∈	PROPN
ejpam-4610	890	9	c.	c.	PROPN
ejpam-4610	890	10	suppose	suppose	VERB
ejpam-4610	890	11	that	that	SCONJ
ejpam-4610	890	12	y	y	PROPN
ejpam-4610	890	13	/∈	/∈	PUNCT
ejpam-4610	890	14	a	a	PRON
ejpam-4610	890	15	and	and	CCONJ
ejpam-4610	890	16	a	a	DET
ejpam-4610	890	17	∩	∩	NOUN
ejpam-4610	890	18	ng(x	ng(x	NUM
ejpam-4610	890	19	,	,	PUNCT
ejpam-4610	890	20	2	2	X
ejpam-4610	890	21	)	)	PUNCT
ejpam-4610	890	22	=	=	VERB
ejpam-4610	890	23	∅.	∅.	NOUN
ejpam-4610	890	24	then	then	ADV
ejpam-4610	890	25	there	there	PRON
ejpam-4610	890	26	exists	exist	VERB
ejpam-4610	890	27	v	v	ADP
ejpam-4610	890	28	∈	∈	PROPN
ejpam-4610	890	29	v	v	NOUN
ejpam-4610	890	30	(	(	PUNCT
ejpam-4610	890	31	g	g	NOUN
ejpam-4610	890	32	)	)	PUNCT
ejpam-4610	890	33	such	such	ADJ
ejpam-4610	890	34	that	that	SCONJ
ejpam-4610	890	35	xv	xv	PROPN
ejpam-4610	890	36	∈	∈	PROPN
ejpam-4610	890	37	e(g	e(g	PROPN
ejpam-4610	890	38	)	)	PUNCT
ejpam-4610	890	39	and	and	CCONJ
ejpam-4610	890	40	y	y	PROPN
ejpam-4610	890	41	∈	∈	PROPN
ejpam-4610	890	42	v	v	PROPN
ejpam-4610	890	43	(	(	PUNCT
ejpam-4610	890	44	hv	hv	PROPN
ejpam-4610	890	45	)	)	PUNCT
ejpam-4610	890	46	.	.	PUNCT
ejpam-4610	891	1	since	since	SCONJ
ejpam-4610	891	2	g	g	PROPN
ejpam-4610	891	3	is	be	AUX
ejpam-4610	891	4	k3	k3	ADJ
ejpam-4610	891	5	-	-	PUNCT
ejpam-4610	891	6	free	free	ADJ
ejpam-4610	891	7	,	,	PUNCT
ejpam-4610	891	8	v	v	NOUN
ejpam-4610	891	9	∈	∈	PROPN
ejpam-4610	891	10	v	v	NOUN
ejpam-4610	891	11	(	(	PUNCT
ejpam-4610	891	12	g	g	NOUN
ejpam-4610	891	13	)	)	PUNCT
ejpam-4610	891	14	\ng(a	\ng(a	PROPN
ejpam-4610	891	15	)	)	PUNCT
ejpam-4610	891	16	.	.	PUNCT
ejpam-4610	892	1	thus	thus	ADV
ejpam-4610	892	2	,	,	PUNCT
ejpam-4610	892	3	there	there	PRON
ejpam-4610	892	4	exists	exist	VERB
ejpam-4610	892	5	uv	uv	NOUN
ejpam-4610	892	6	∈	∈	PROPN
ejpam-4610	892	7	ng(v	ng(v	PUNCT
ejpam-4610	892	8	)	)	PUNCT
ejpam-4610	892	9	such	such	ADJ
ejpam-4610	892	10	that	that	DET
ejpam-4610	892	11	v	v	NOUN
ejpam-4610	892	12	,	,	PUNCT
ejpam-4610	892	13	uv	uv	PROPN
ejpam-4610	892	14	∈	∈	PROPN
ejpam-4610	892	15	c.	c.	NOUN
ejpam-4610	892	16	since	since	SCONJ
ejpam-4610	892	17	g	g	PROPN
ejpam-4610	892	18	is	be	AUX
ejpam-4610	892	19	k3	k3	ADJ
ejpam-4610	892	20	-	-	PUNCT
ejpam-4610	892	21	free	free	ADJ
ejpam-4610	892	22	,	,	PUNCT
ejpam-4610	892	23	dg(x	dg(x	NUM
ejpam-4610	892	24	,	,	PUNCT
ejpam-4610	892	25	uv	uv	NOUN
ejpam-4610	892	26	)	)	PUNCT
ejpam-4610	892	27	=	=	SYM
ejpam-4610	893	1	2	2	X
ejpam-4610	893	2	.	.	PUNCT
ejpam-4610	893	3	this	this	PRON
ejpam-4610	893	4	shows	show	VERB
ejpam-4610	893	5	that	that	SCONJ
ejpam-4610	893	6	c	c	PROPN
ejpam-4610	893	7	is	be	AUX
ejpam-4610	893	8	a	a	DET
ejpam-4610	893	9	hop	hop	NOUN
ejpam-4610	893	10	dominating	dominating	NOUN
ejpam-4610	893	11	set	set	NOUN
ejpam-4610	893	12	of	of	ADP
ejpam-4610	893	13	g.	g.	PROPN
ejpam-4610	893	14	claim	claim	VERB
ejpam-4610	893	15	2	2	NUM
ejpam-4610	893	16	:	:	PUNCT
ejpam-4610	893	17	c	c	NOUN
ejpam-4610	893	18	is	be	AUX
ejpam-4610	893	19	a	a	DET
ejpam-4610	893	20	total	total	ADJ
ejpam-4610	893	21	dominating	dominating	NOUN
ejpam-4610	893	22	set	set	NOUN
ejpam-4610	893	23	of	of	ADP
ejpam-4610	893	24	g.	g.	PROPN
ejpam-4610	893	25	let	let	VERB
ejpam-4610	893	26	v	v	NUM
ejpam-4610	893	27	∈	∈	PROPN
ejpam-4610	893	28	v	v	NOUN
ejpam-4610	893	29	(	(	PUNCT
ejpam-4610	893	30	g	g	NOUN
ejpam-4610	893	31	)	)	PUNCT
ejpam-4610	893	32	.	.	PUNCT
ejpam-4610	894	1	if	if	SCONJ
ejpam-4610	894	2	v	v	NUM
ejpam-4610	894	3	∈	∈	PROPN
ejpam-4610	894	4	ng(a	ng(a	NOUN
ejpam-4610	894	5	)	)	PUNCT
ejpam-4610	895	1	,	,	PUNCT
ejpam-4610	895	2	then	then	ADV
ejpam-4610	895	3	there	there	PRON
ejpam-4610	895	4	exists	exist	VERB
ejpam-4610	895	5	u	u	PROPN
ejpam-4610	895	6	∈	∈	PROPN
ejpam-4610	895	7	c	c	NOUN
ejpam-4610	895	8	such	such	ADJ
ejpam-4610	895	9	that	that	DET
ejpam-4610	895	10	uv	uv	PROPN
ejpam-4610	895	11	∈	∈	PROPN
ejpam-4610	895	12	e(g	e(g	PROPN
ejpam-4610	895	13	)	)	PUNCT
ejpam-4610	895	14	.	.	PUNCT
ejpam-4610	896	1	suppose	suppose	VERB
ejpam-4610	896	2	that	that	SCONJ
ejpam-4610	896	3	v	v	NOUN
ejpam-4610	896	4	/∈	/∈	PUNCT
ejpam-4610	896	5	ng(a	ng(a	NUM
ejpam-4610	896	6	)	)	PUNCT
ejpam-4610	896	7	.	.	PUNCT
ejpam-4610	897	1	then	then	ADV
ejpam-4610	897	2	there	there	PRON
ejpam-4610	897	3	exists	exist	VERB
ejpam-4610	897	4	uv	uv	NOUN
ejpam-4610	897	5	∈	∈	PROPN
ejpam-4610	897	6	ng(v	ng(v	PUNCT
ejpam-4610	897	7	)	)	PUNCT
ejpam-4610	897	8	such	such	ADJ
ejpam-4610	897	9	that	that	DET
ejpam-4610	897	10	v	v	NOUN
ejpam-4610	897	11	,	,	PUNCT
ejpam-4610	897	12	uv	uv	PROPN
ejpam-4610	897	13	∈	∈	PROPN
ejpam-4610	897	14	c.	c.	NOUN
ejpam-4610	897	15	in	in	ADP
ejpam-4610	897	16	this	this	DET
ejpam-4610	897	17	case	case	NOUN
ejpam-4610	897	18	,	,	PUNCT
ejpam-4610	897	19	uv	uv	NOUN
ejpam-4610	897	20	is	be	AUX
ejpam-4610	897	21	the	the	DET
ejpam-4610	897	22	desired	desire	VERB
ejpam-4610	897	23	vertex	vertex	NOUN
ejpam-4610	897	24	in	in	ADP
ejpam-4610	897	25	c	c	NOUN
ejpam-4610	897	26	for	for	ADP
ejpam-4610	897	27	which	which	PRON
ejpam-4610	897	28	vuv	vuv	PROPN
ejpam-4610	897	29	∈	∈	PROPN
ejpam-4610	897	30	e(g	e(g	PROPN
ejpam-4610	897	31	)	)	PUNCT
ejpam-4610	897	32	.	.	PUNCT
ejpam-4610	898	1	accordingly	accordingly	ADV
ejpam-4610	898	2	,	,	PUNCT
ejpam-4610	898	3	c	c	PROPN
ejpam-4610	898	4	is	be	AUX
ejpam-4610	898	5	a	a	DET
ejpam-4610	898	6	total	total	ADJ
ejpam-4610	898	7	dominating	dominating	NOUN
ejpam-4610	898	8	set	set	NOUN
ejpam-4610	898	9	of	of	ADP
ejpam-4610	898	10	g.	g.	PROPN
ejpam-4610	898	11	references	reference	NOUN
ejpam-4610	898	12	204	204	NUM
ejpam-4610	898	13	claim	claim	NOUN
ejpam-4610	898	14	1	1	NUM
ejpam-4610	898	15	and	and	CCONJ
ejpam-4610	898	16	claim	claim	VERB
ejpam-4610	898	17	2	2	NUM
ejpam-4610	898	18	all	all	PRON
ejpam-4610	898	19	show	show	VERB
ejpam-4610	898	20	that	that	SCONJ
ejpam-4610	898	21	c	c	PROPN
ejpam-4610	898	22	is	be	AUX
ejpam-4610	898	23	a	a	DET
ejpam-4610	898	24	(	(	PUNCT
ejpam-4610	898	25	1	1	NUM
ejpam-4610	898	26	,	,	PUNCT
ejpam-4610	898	27	2)∗-total	2)∗-total	ADJ
ejpam-4610	898	28	dominating	dominating	NOUN
ejpam-4610	898	29	set	set	NOUN
ejpam-4610	898	30	of	of	ADP
ejpam-4610	898	31	g.	g.	PROPN
ejpam-4610	898	32	let	let	VERB
ejpam-4610	898	33	t	t	PROPN
ejpam-4610	898	34	⊆	⊆	NUM
ejpam-4610	898	35	v	v	NOUN
ejpam-4610	898	36	(	(	PUNCT
ejpam-4610	898	37	g	g	NOUN
ejpam-4610	898	38	)	)	PUNCT
ejpam-4610	898	39	be	be	AUX
ejpam-4610	898	40	a	a	DET
ejpam-4610	898	41	γ∗t1,2	γ∗t1,2	NOUN
ejpam-4610	898	42	-	-	PUNCT
ejpam-4610	898	43	set	set	NOUN
ejpam-4610	898	44	of	of	ADP
ejpam-4610	898	45	g.	g.	PROPN
ejpam-4610	898	46	by	by	ADP
ejpam-4610	898	47	corollary	corollary	ADJ
ejpam-4610	898	48	3	3	NUM
ejpam-4610	898	49	,	,	PUNCT
ejpam-4610	898	50	t	t	PROPN
ejpam-4610	898	51	is	be	AUX
ejpam-4610	898	52	a	a	DET
ejpam-4610	898	53	γh	γh	ADV
ejpam-4610	898	54	-	-	PUNCT
ejpam-4610	898	55	set	set	NOUN
ejpam-4610	898	56	of	of	ADP
ejpam-4610	898	57	g	g	PROPN
ejpam-4610	898	58	◦	◦	NOUN
ejpam-4610	898	59	h.	h.	PROPN
ejpam-4610	898	60	thus	thus	ADV
ejpam-4610	898	61	,	,	PUNCT
ejpam-4610	898	62	s	s	PART
ejpam-4610	898	63	∩	∩	NOUN
ejpam-4610	898	64	t	t	PROPN
ejpam-4610	898	65	̸=	̸=	PROPN
ejpam-4610	898	66	∅.	∅.	ADP
ejpam-4610	898	67	this	this	PRON
ejpam-4610	898	68	means	mean	VERB
ejpam-4610	898	69	that	that	SCONJ
ejpam-4610	898	70	a	a	DET
ejpam-4610	898	71	∩	∩	NOUN
ejpam-4610	898	72	t	t	X
ejpam-4610	898	73	̸=	̸=	PROPN
ejpam-4610	898	74	∅.	∅.	PRON
ejpam-4610	898	75	therefore	therefore	ADV
ejpam-4610	898	76	,	,	PUNCT
ejpam-4610	898	77	c	c	PROPN
ejpam-4610	898	78	∩	∩	PROPN
ejpam-4610	898	79	t	t	PROPN
ejpam-4610	898	80	̸=	̸=	PROPN
ejpam-4610	898	81	∅	∅	NOUN
ejpam-4610	898	82	and	and	CCONJ
ejpam-4610	898	83	c	c	NOUN
ejpam-4610	898	84	is	be	AUX
ejpam-4610	898	85	a	a	DET
ejpam-4610	898	86	transversal	transversal	NOUN
ejpam-4610	898	87	(	(	PUNCT
ejpam-4610	898	88	1	1	NUM
ejpam-4610	898	89	,	,	PUNCT
ejpam-4610	898	90	2)∗-total	2)∗-total	ADJ
ejpam-4610	898	91	dominating	dominating	NOUN
ejpam-4610	898	92	set	set	NOUN
ejpam-4610	898	93	of	of	ADP
ejpam-4610	898	94	g.	g.	PROPN
ejpam-4610	898	95	consequently	consequently	ADV
ejpam-4610	898	96	,	,	PUNCT
ejpam-4610	898	97	γ̂∗t1,2(g	γ̂∗t1,2(g	NUM
ejpam-4610	898	98	)	)	PUNCT
ejpam-4610	898	99	≤	≤	NUM
ejpam-4610	898	100	|c|	|c|	PROPN
ejpam-4610	898	101	≤	≤	NUM
ejpam-4610	898	102	|s|	|s|	PROPN
ejpam-4610	898	103	=	=	PUNCT
ejpam-4610	898	104	γ̂h(g	γ̂h(g	PROPN
ejpam-4610	898	105	◦	◦	NOUN
ejpam-4610	898	106	h	h	NOUN
ejpam-4610	898	107	)	)	PUNCT
ejpam-4610	898	108	.	.	PUNCT
ejpam-4610	899	1	example	example	NOUN
ejpam-4610	900	1	1	1	NUM
ejpam-4610	900	2	.	.	PUNCT
ejpam-4610	900	3	let	let	VERB
ejpam-4610	900	4	h	h	PRON
ejpam-4610	900	5	be	be	AUX
ejpam-4610	900	6	a	a	DET
ejpam-4610	900	7	nontrivial	nontrivial	ADJ
ejpam-4610	900	8	connected	connect	VERB
ejpam-4610	900	9	graph	graph	NOUN
ejpam-4610	900	10	.	.	PUNCT
ejpam-4610	901	1	1	1	X
ejpam-4610	901	2	.	.	X
ejpam-4610	901	3	for	for	ADP
ejpam-4610	901	4	a	a	DET
ejpam-4610	901	5	path	path	NOUN
ejpam-4610	901	6	pn	pn	NOUN
ejpam-4610	901	7	on	on	ADP
ejpam-4610	901	8	n	n	PRON
ejpam-4610	901	9	vertices	vertex	NOUN
ejpam-4610	901	10	,	,	PUNCT
ejpam-4610	901	11	γ̂h(pn	γ̂h(pn	ADJ
ejpam-4610	901	12	◦	◦	NOUN
ejpam-4610	901	13	h	h	NOUN
ejpam-4610	901	14	)	)	PUNCT
ejpam-4610	901	15	=	=	SYM
ejpam-4610	901	16	γ̂∗t1,2(pn	γ̂∗t1,2(pn	PROPN
ejpam-4610	901	17	)	)	PUNCT
ejpam-4610	901	18	=	=	PUNCT
ejpam-4610	902	1			NOUN
ejpam-4610	902	2	2	2	NUM
ejpam-4610	902	3	,	,	PUNCT
ejpam-4610	902	4	if	if	SCONJ
ejpam-4610	902	5	n	n	NOUN
ejpam-4610	902	6	=	=	SYM
ejpam-4610	902	7	2	2	NUM
ejpam-4610	902	8	,	,	PUNCT
ejpam-4610	902	9	3	3	NUM
ejpam-4610	902	10	;	;	PUNCT
ejpam-4610	902	11	2r	2r	NUM
ejpam-4610	902	12	,	,	PUNCT
ejpam-4610	902	13	if	if	SCONJ
ejpam-4610	902	14	n	n	NOUN
ejpam-4610	902	15	=	=	NOUN
ejpam-4610	902	16	4r	4r	NOUN
ejpam-4610	902	17	;	;	PUNCT
ejpam-4610	902	18	2r	2r	NUM
ejpam-4610	903	1	+	+	CCONJ
ejpam-4610	903	2	1	1	NUM
ejpam-4610	903	3	,	,	PUNCT
ejpam-4610	903	4	if	if	SCONJ
ejpam-4610	903	5	n	n	NOUN
ejpam-4610	903	6	=	=	NOUN
ejpam-4610	903	7	4r	4r	NOUN
ejpam-4610	903	8	+	+	CCONJ
ejpam-4610	903	9	1	1	NUM
ejpam-4610	903	10	;	;	PUNCT
ejpam-4610	903	11	2r	2r	NUM
ejpam-4610	903	12	+	+	CCONJ
ejpam-4610	904	1	2	2	NUM
ejpam-4610	904	2	,	,	PUNCT
ejpam-4610	904	3	if	if	SCONJ
ejpam-4610	904	4	n	n	NOUN
ejpam-4610	904	5	=	=	NOUN
ejpam-4610	904	6	4r	4r	NOUN
ejpam-4610	904	7	+	+	SYM
ejpam-4610	904	8	s	s	X
ejpam-4610	904	9	,	,	PUNCT
ejpam-4610	904	10	s	s	PART
ejpam-4610	904	11	=	=	SYM
ejpam-4610	904	12	2	2	NUM
ejpam-4610	904	13	,	,	PUNCT
ejpam-4610	904	14	3	3	NUM
ejpam-4610	904	15	.	.	NOUN
ejpam-4610	904	16	2	2	NUM
ejpam-4610	904	17	.	.	X
ejpam-4610	905	1	for	for	ADP
ejpam-4610	905	2	a	a	DET
ejpam-4610	905	3	cycle	cycle	NOUN
ejpam-4610	905	4	cn	cn	NOUN
ejpam-4610	905	5	of	of	ADP
ejpam-4610	905	6	order	order	NOUN
ejpam-4610	905	7	n	n	PRON
ejpam-4610	905	8	≥	≥	NOUN
ejpam-4610	905	9	4	4	NUM
ejpam-4610	905	10	,	,	PUNCT
ejpam-4610	905	11	γ̂h(cn	γ̂h(cn	NOUN
ejpam-4610	905	12	◦	◦	NOUN
ejpam-4610	905	13	h	h	NOUN
ejpam-4610	905	14	)	)	PUNCT
ejpam-4610	905	15	=	=	SYM
ejpam-4610	905	16	γ̂∗t1,2(cn	γ̂∗t1,2(cn	NOUN
ejpam-4610	905	17	)	)	PUNCT
ejpam-4610	905	18	=	=	PRON
ejpam-4610	906	1	{	{	PUNCT
ejpam-4610	906	2	2r	2r	NUM
ejpam-4610	907	1	+	+	CCONJ
ejpam-4610	907	2	1	1	NUM
ejpam-4610	907	3	,	,	PUNCT
ejpam-4610	907	4	if	if	SCONJ
ejpam-4610	907	5	n	n	NOUN
ejpam-4610	907	6	=	=	NOUN
ejpam-4610	907	7	4r	4r	NOUN
ejpam-4610	907	8	,	,	PUNCT
ejpam-4610	907	9	4r	4r	NUM
ejpam-4610	907	10	+	+	CCONJ
ejpam-4610	907	11	1	1	NUM
ejpam-4610	907	12	2r	2r	NUM
ejpam-4610	907	13	+	+	CCONJ
ejpam-4610	907	14	2	2	NUM
ejpam-4610	907	15	,	,	PUNCT
ejpam-4610	907	16	if	if	SCONJ
ejpam-4610	907	17	n	n	NOUN
ejpam-4610	907	18	=	=	NOUN
ejpam-4610	907	19	4r	4r	NOUN
ejpam-4610	907	20	+	+	CCONJ
ejpam-4610	907	21	2	2	NUM
ejpam-4610	907	22	,	,	PUNCT
ejpam-4610	907	23	4r	4r	NUM
ejpam-4610	907	24	+	+	CCONJ
ejpam-4610	907	25	3	3	NUM
ejpam-4610	907	26	3	3	NUM
ejpam-4610	907	27	.	.	PUNCT
ejpam-4610	908	1	for	for	ADP
ejpam-4610	908	2	the	the	DET
ejpam-4610	908	3	complete	complete	ADJ
ejpam-4610	908	4	bipartite	bipartite	PROPN
ejpam-4610	908	5	graph	graph	NOUN
ejpam-4610	908	6	km	km	PROPN
ejpam-4610	908	7	,	,	PUNCT
ejpam-4610	908	8	n	n	CCONJ
ejpam-4610	908	9	with	with	ADP
ejpam-4610	908	10	m	m	PROPN
ejpam-4610	908	11	,	,	PUNCT
ejpam-4610	908	12	n	n	PRON
ejpam-4610	908	13	≥	≥	NOUN
ejpam-4610	908	14	2	2	NUM
ejpam-4610	908	15	,	,	PUNCT
ejpam-4610	908	16	γ̂h(km	γ̂h(km	PROPN
ejpam-4610	908	17	,	,	PUNCT
ejpam-4610	908	18	n	n	PRON
ejpam-4610	908	19	◦	◦	NOUN
ejpam-4610	908	20	h	h	NOUN
ejpam-4610	908	21	)	)	PUNCT
ejpam-4610	908	22	=	=	SYM
ejpam-4610	908	23	γ̂∗t1,2(km	γ̂∗t1,2(km	PROPN
ejpam-4610	908	24	,	,	PUNCT
ejpam-4610	908	25	n	n	CCONJ
ejpam-4610	908	26	)	)	PUNCT
ejpam-4610	908	27	=	=	SYM
ejpam-4610	908	28	1	1	NUM
ejpam-4610	908	29	+	+	NOUN
ejpam-4610	908	30	min{m	min{m	NOUN
ejpam-4610	908	31	,	,	PUNCT
ejpam-4610	908	32	n	n	CCONJ
ejpam-4610	908	33	}	}	PUNCT
ejpam-4610	908	34	.	.	PUNCT
ejpam-4610	909	1	acknowledgements	acknowledgement	NOUN
ejpam-4610	909	2	the	the	DET
ejpam-4610	909	3	authors	author	NOUN
ejpam-4610	909	4	would	would	AUX
ejpam-4610	909	5	like	like	VERB
ejpam-4610	909	6	to	to	PART
ejpam-4610	909	7	thank	thank	VERB
ejpam-4610	909	8	the	the	DET
ejpam-4610	909	9	department	department	NOUN
ejpam-4610	909	10	of	of	ADP
ejpam-4610	909	11	science	science	NOUN
ejpam-4610	909	12	and	and	CCONJ
ejpam-4610	909	13	technology	technology	NOUN
ejpam-4610	909	14	accelerated	accelerate	VERB
ejpam-4610	909	15	science	science	NOUN
ejpam-4610	909	16	and	and	CCONJ
ejpam-4610	909	17	technology	technology	NOUN
ejpam-4610	909	18	human	human	ADJ
ejpam-4610	909	19	resource	resource	NOUN
ejpam-4610	909	20	development	development	NOUN
ejpam-4610	909	21	program	program	NOUN
ejpam-4610	909	22	(	(	PUNCT
ejpam-4610	909	23	dost	dost	NOUN
ejpam-4610	909	24	-	-	PUNCT
ejpam-4610	909	25	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4610	909	26	,	,	PUNCT
ejpam-4610	909	27	msu	msu	PROPN
ejpam-4610	909	28	-	-	PUNCT
ejpam-4610	909	29	iligan	iligan	PROPN
ejpam-4610	909	30	institute	institute	PROPN
ejpam-4610	909	31	of	of	ADP
ejpam-4610	909	32	technology	technology	PROPN
ejpam-4610	909	33	.	.	PUNCT
ejpam-4610	910	1	references	reference	NOUN
ejpam-4610	910	2	[	[	X
ejpam-4610	910	3	1	1	X
ejpam-4610	910	4	]	]	PUNCT
ejpam-4610	910	5	s.	s.	PROPN
ejpam-4610	910	6	arriola	arriola	PROPN
ejpam-4610	910	7	and	and	CCONJ
ejpam-4610	910	8	jr	jr	PROPN
ejpam-4610	910	9	.	.	PROPN
ejpam-4610	910	10	s.	s.	PROPN
ejpam-4610	910	11	canoy	canoy	PROPN
ejpam-4610	910	12	.	.	PUNCT
ejpam-4610	911	1	(	(	PUNCT
ejpam-4610	911	2	1	1	NUM
ejpam-4610	911	3	,	,	PUNCT
ejpam-4610	911	4	2)∗-domination	2)∗-domination	NOUN
ejpam-4610	911	5	in	in	ADP
ejpam-4610	911	6	graphs	graph	NOUN
ejpam-4610	911	7	.	.	PUNCT
ejpam-4610	912	1	advances	advance	NOUN
ejpam-4610	912	2	and	and	CCONJ
ejpam-4610	912	3	applications	application	NOUN
ejpam-4610	912	4	in	in	ADP
ejpam-4610	912	5	discrete	discrete	ADJ
ejpam-4610	912	6	mathematics	mathematic	NOUN
ejpam-4610	912	7	,	,	PUNCT
ejpam-4610	912	8	18(2):179–190	18(2):179–190	NUM
ejpam-4610	912	9	,	,	PUNCT
ejpam-4610	912	10	2017	2017	NUM
ejpam-4610	912	11	.	.	PUNCT
ejpam-4610	913	1	[	[	X
ejpam-4610	913	2	2	2	NUM
ejpam-4610	913	3	]	]	PUNCT
ejpam-4610	913	4	c.	c.	PROPN
ejpam-4610	913	5	berge	berge	PROPN
ejpam-4610	913	6	.	.	PUNCT
ejpam-4610	914	1	theory	theory	NOUN
ejpam-4610	914	2	of	of	ADP
ejpam-4610	914	3	graphs	graph	NOUN
ejpam-4610	914	4	and	and	CCONJ
ejpam-4610	914	5	its	its	PRON
ejpam-4610	914	6	applications	application	NOUN
ejpam-4610	914	7	.	.	PUNCT
ejpam-4610	915	1	methuen	methuen	PROPN
ejpam-4610	915	2	,	,	PUNCT
ejpam-4610	915	3	london	london	PROPN
ejpam-4610	915	4	,	,	PUNCT
ejpam-4610	915	5	1962	1962	NUM
ejpam-4610	915	6	.	.	PUNCT
ejpam-4610	916	1	[	[	X
ejpam-4610	916	2	3	3	NUM
ejpam-4610	916	3	]	]	X
ejpam-4610	916	4	f.	f.	PROPN
ejpam-4610	916	5	buckley	buckley	PROPN
ejpam-4610	916	6	and	and	CCONJ
ejpam-4610	916	7	f.	f.	PROPN
ejpam-4610	916	8	harary	harary	PROPN
ejpam-4610	916	9	.	.	PUNCT
ejpam-4610	917	1	distance	distance	NOUN
ejpam-4610	917	2	in	in	ADP
ejpam-4610	917	3	graphs	graph	NOUN
ejpam-4610	917	4	.	.	PUNCT
ejpam-4610	918	1	addison	addison	PROPN
ejpam-4610	918	2	-	-	PUNCT
ejpam-4610	918	3	wesley	wesley	PROPN
ejpam-4610	918	4	,	,	PUNCT
ejpam-4610	918	5	redwood	redwood	NOUN
ejpam-4610	918	6	city	city	NOUN
ejpam-4610	918	7	,	,	PUNCT
ejpam-4610	918	8	ca	ca	NOUN
ejpam-4610	918	9	,	,	PUNCT
ejpam-4610	918	10	1990	1990	NUM
ejpam-4610	918	11	.	.	PUNCT
ejpam-4610	919	1	[	[	X
ejpam-4610	919	2	4	4	X
ejpam-4610	919	3	]	]	X
ejpam-4610	919	4	e.	e.	PROPN
ejpam-4610	919	5	cockayne	cockayne	PROPN
ejpam-4610	919	6	and	and	CCONJ
ejpam-4610	919	7	s.	s.	PROPN
ejpam-4610	919	8	hedetniemi	hedetniemi	PROPN
ejpam-4610	919	9	.	.	PUNCT
ejpam-4610	920	1	towards	towards	ADP
ejpam-4610	920	2	a	a	DET
ejpam-4610	920	3	theory	theory	NOUN
ejpam-4610	920	4	of	of	ADP
ejpam-4610	920	5	domination	domination	NOUN
ejpam-4610	920	6	in	in	ADP
ejpam-4610	920	7	graphs	graph	NOUN
ejpam-4610	920	8	.	.	PUNCT
ejpam-4610	921	1	networks	network	NOUN
ejpam-4610	921	2	,	,	PUNCT
ejpam-4610	921	3	7(3):247–261	7(3):247–261	NUM
ejpam-4610	921	4	,	,	PUNCT
ejpam-4610	921	5	1977	1977	NUM
ejpam-4610	921	6	.	.	PUNCT
ejpam-4610	922	1	references	reference	NOUN
ejpam-4610	922	2	205	205	NUM
ejpam-4610	922	3	[	[	X
ejpam-4610	922	4	5	5	NUM
ejpam-4610	922	5	]	]	X
ejpam-4610	922	6	n.	n.	PROPN
ejpam-4610	922	7	alon	alon	PROPN
ejpam-4610	922	8	m.r	m.r	PROPN
ejpam-4610	922	9	.	.	PROPN
ejpam-4610	922	10	fellows	fellows	PROPN
ejpam-4610	922	11	and	and	CCONJ
ejpam-4610	922	12	d.r	d.r	PROPN
ejpam-4610	922	13	.	.	PROPN
ejpam-4610	922	14	hare	hare	PROPN
ejpam-4610	922	15	.	.	PUNCT
ejpam-4610	923	1	vertex	vertex	NOUN
ejpam-4610	923	2	transversals	transversal	NOUN
ejpam-4610	923	3	that	that	PRON
ejpam-4610	923	4	dominate	dominate	VERB
ejpam-4610	923	5	.	.	PUNCT
ejpam-4610	924	1	journal	journal	NOUN
ejpam-4610	924	2	of	of	ADP
ejpam-4610	924	3	graph	graph	NOUN
ejpam-4610	924	4	theory	theory	NOUN
ejpam-4610	924	5	,	,	PUNCT
ejpam-4610	924	6	21(1):21–31	21(1):21–31	NUM
ejpam-4610	924	7	,	,	PUNCT
ejpam-4610	924	8	1996	1996	NUM
ejpam-4610	924	9	.	.	PUNCT
ejpam-4610	925	1	[	[	X
ejpam-4610	925	2	6	6	NUM
ejpam-4610	925	3	]	]	X
ejpam-4610	925	4	i.s	i.s	PROPN
ejpam-4610	925	5	.	.	PROPN
ejpam-4610	925	6	hamid	hamid	PROPN
ejpam-4610	925	7	.	.	PUNCT
ejpam-4610	925	8	independent	independent	ADJ
ejpam-4610	925	9	transversal	transversal	ADJ
ejpam-4610	925	10	domination	domination	NOUN
ejpam-4610	925	11	in	in	ADP
ejpam-4610	925	12	graphs	graph	NOUN
ejpam-4610	925	13	.	.	PUNCT
ejpam-4610	926	1	discussiones	discussione	NOUN
ejpam-4610	926	2	mathematicae	mathematicae	PROPN
ejpam-4610	926	3	graph	graph	NOUN
ejpam-4610	926	4	theory	theory	NOUN
ejpam-4610	926	5	,	,	PUNCT
ejpam-4610	926	6	32:5–7	32:5–7	NUM
ejpam-4610	926	7	,	,	PUNCT
ejpam-4610	926	8	2012	2012	NUM
ejpam-4610	926	9	.	.	PUNCT
ejpam-4610	927	1	[	[	X
ejpam-4610	927	2	7	7	X
ejpam-4610	927	3	]	]	X
ejpam-4610	927	4	jw.j	jw.j	NOUN
ejpam-4610	927	5	.	.	PUNCT
ejpam-4610	928	1	desormeaux	desormeaux	PROPN
ejpam-4610	928	2	t.w	t.w	PROPN
ejpam-4610	928	3	.	.	PROPN
ejpam-4610	928	4	haynes	haynes	PROPN
ejpam-4610	928	5	and	and	CCONJ
ejpam-4610	928	6	m.a	m.a	PROPN
ejpam-4610	928	7	.	.	PROPN
ejpam-4610	928	8	henning	henning	PROPN
ejpam-4610	928	9	.	.	PUNCT
ejpam-4610	929	1	an	an	DET
ejpam-4610	929	2	extremal	extremal	ADJ
ejpam-4610	929	3	problem	problem	NOUN
ejpam-4610	929	4	for	for	ADP
ejpam-4610	929	5	total	total	ADJ
ejpam-4610	929	6	domination	domination	NOUN
ejpam-4610	929	7	stable	stable	ADJ
ejpam-4610	929	8	graphs	graph	NOUN
ejpam-4610	929	9	upon	upon	SCONJ
ejpam-4610	929	10	edge	edge	NOUN
ejpam-4610	929	11	removal	removal	NOUN
ejpam-4610	929	12	.	.	PUNCT
ejpam-4610	930	1	discrete	discrete	ADJ
ejpam-4610	930	2	appl	appl	PROPN
ejpam-4610	930	3	.	.	PUNCT
ejpam-4610	930	4	math	math	PROPN
ejpam-4610	930	5	,	,	PUNCT
ejpam-4610	930	6	159:1048–1052	159:1048–1052	NUM
ejpam-4610	930	7	,	,	PUNCT
ejpam-4610	930	8	2011	2011	NUM
ejpam-4610	930	9	.	.	PUNCT
ejpam-4610	931	1	[	[	X
ejpam-4610	931	2	8	8	X
ejpam-4610	931	3	]	]	X
ejpam-4610	931	4	t.w	t.w	PROPN
ejpam-4610	931	5	.	.	PROPN
ejpam-4610	931	6	haynes	haynes	PROPN
ejpam-4610	931	7	s.t	s.t	PROPN
ejpam-4610	931	8	.	.	PROPN
ejpam-4610	931	9	hedetniemi	hedetniemi	PROPN
ejpam-4610	931	10	and	and	CCONJ
ejpam-4610	931	11	p.j	p.j	PROPN
ejpam-4610	931	12	.	.	PROPN
ejpam-4610	931	13	slater	slater	PROPN
ejpam-4610	931	14	.	.	PUNCT
ejpam-4610	932	1	fundamentals	fundamental	NOUN
ejpam-4610	932	2	of	of	ADP
ejpam-4610	932	3	domination	domination	NOUN
ejpam-4610	932	4	in	in	ADP
ejpam-4610	932	5	graphs	graph	NOUN
ejpam-4610	932	6	.	.	PUNCT
ejpam-4610	933	1	marcel	marcel	PROPN
ejpam-4610	933	2	dekker	dekker	PROPN
ejpam-4610	933	3	,	,	PUNCT
ejpam-4610	933	4	inc	inc	PROPN
ejpam-4610	933	5	.	.	PROPN
ejpam-4610	933	6	,	,	PUNCT
ejpam-4610	933	7	new	new	PROPN
ejpam-4610	933	8	york	york	PROPN
ejpam-4610	933	9	,	,	PUNCT
ejpam-4610	933	10	1990	1990	NUM
ejpam-4610	933	11	.	.	PUNCT
ejpam-4610	934	1	[	[	X
ejpam-4610	934	2	9	9	NUM
ejpam-4610	934	3	]	]	X
ejpam-4610	934	4	m.	m.	NOUN
ejpam-4610	934	5	henning	henning	PROPN
ejpam-4610	934	6	and	and	CCONJ
ejpam-4610	934	7	a.	a.	PROPN
ejpam-4610	934	8	yeo	yeo	PROPN
ejpam-4610	934	9	.	.	PROPN
ejpam-4610	935	1	total	total	ADJ
ejpam-4610	935	2	domination	domination	NOUN
ejpam-4610	935	3	in	in	ADP
ejpam-4610	935	4	graphs	graph	NOUN
ejpam-4610	935	5	.	.	PUNCT
ejpam-4610	936	1	springer	springer	NOUN
ejpam-4610	936	2	,	,	PUNCT
ejpam-4610	936	3	2013	2013	NUM
ejpam-4610	936	4	.	.	PUNCT
ejpam-4610	937	1	[	[	X
ejpam-4610	937	2	10	10	NUM
ejpam-4610	937	3	]	]	X
ejpam-4610	937	4	f.p	f.p	PROPN
ejpam-4610	937	5	.	.	PROPN
ejpam-4610	937	6	jamil	jamil	PROPN
ejpam-4610	937	7	and	and	CCONJ
ejpam-4610	937	8	h.n	h.n	PROPN
ejpam-4610	937	9	.	.	PROPN
ejpam-4610	937	10	maglanque	maglanque	PROPN
ejpam-4610	937	11	.	.	PUNCT
ejpam-4610	938	1	cost	cost	NOUN
ejpam-4610	938	2	effective	effective	ADJ
ejpam-4610	938	3	domination	domination	NOUN
ejpam-4610	938	4	in	in	ADP
ejpam-4610	938	5	the	the	DET
ejpam-4610	938	6	join	join	NOUN
ejpam-4610	938	7	,	,	PUNCT
ejpam-4610	938	8	corona	corona	NOUN
ejpam-4610	938	9	and	and	CCONJ
ejpam-4610	938	10	composition	composition	NOUN
ejpam-4610	938	11	of	of	ADP
ejpam-4610	938	12	graphs	graph	NOUN
ejpam-4610	938	13	.	.	PUNCT
ejpam-4610	939	1	european	european	ADJ
ejpam-4610	939	2	journal	journal	PROPN
ejpam-4610	939	3	of	of	ADP
ejpam-4610	939	4	pure	pure	ADJ
ejpam-4610	939	5	and	and	CCONJ
ejpam-4610	939	6	applied	applied	ADJ
ejpam-4610	939	7	mathematics	mathematic	NOUN
ejpam-4610	939	8	,	,	PUNCT
ejpam-4610	939	9	12(3):978–998	12(3):978–998	NUM
ejpam-4610	939	10	,	,	PUNCT
ejpam-4610	939	11	2019	2019	NUM
ejpam-4610	939	12	.	.	PUNCT
ejpam-4610	940	1	[	[	X
ejpam-4610	940	2	11	11	NUM
ejpam-4610	940	3	]	]	X
ejpam-4610	940	4	f.p	f.p	PROPN
ejpam-4610	940	5	.	.	PROPN
ejpam-4610	940	6	jamil	jamil	PROPN
ejpam-4610	940	7	and	and	CCONJ
ejpam-4610	940	8	r.p	r.p	PROPN
ejpam-4610	940	9	.	.	PROPN
ejpam-4610	940	10	malalay	malalay	PROPN
ejpam-4610	940	11	.	.	PUNCT
ejpam-4610	941	1	on	on	ADP
ejpam-4610	941	2	disjunctive	disjunctive	ADJ
ejpam-4610	941	3	domination	domination	NOUN
ejpam-4610	941	4	in	in	ADP
ejpam-4610	941	5	graphs	graph	NOUN
ejpam-4610	941	6	.	.	PUNCT
ejpam-4610	942	1	quaestiones	quaestione	NOUN
ejpam-4610	942	2	mathematicae	mathematicae	PROPN
ejpam-4610	942	3	,	,	PUNCT
ejpam-4610	942	4	43(2):149–168	43(2):149–168	PROPN
ejpam-4610	942	5	,	,	PUNCT
ejpam-4610	942	6	2020	2020	NUM
ejpam-4610	942	7	.	.	PUNCT
ejpam-4610	943	1	[	[	X
ejpam-4610	943	2	12	12	NUM
ejpam-4610	943	3	]	]	X
ejpam-4610	943	4	r.g	r.g	PROPN
ejpam-4610	943	5	.	.	PROPN
ejpam-4610	943	6	eballe	eballe	PROPN
ejpam-4610	943	7	r.	r.	PROPN
ejpam-4610	943	8	aldema	aldema	PROPN
ejpam-4610	943	9	e.m	e.m	PROPN
ejpam-4610	943	10	.	.	PROPN
ejpam-4610	943	11	paluga	paluga	PROPN
ejpam-4610	943	12	r.f	r.f	PROPN
ejpam-4610	943	13	.	.	PROPN
ejpam-4610	943	14	rulete	rulete	PROPN
ejpam-4610	943	15	f.p	f.p	PROPN
ejpam-4610	943	16	.	.	PROPN
ejpam-4610	943	17	jamil	jamil	PROPN
ejpam-4610	943	18	.	.	PUNCT
ejpam-4610	944	1	global	global	ADJ
ejpam-4610	944	2	defensive	defensive	ADJ
ejpam-4610	944	3	alliances	alliance	NOUN
ejpam-4610	944	4	in	in	ADP
ejpam-4610	944	5	the	the	DET
ejpam-4610	944	6	join	join	NOUN
ejpam-4610	944	7	,	,	PUNCT
ejpam-4610	944	8	corona	corona	NOUN
ejpam-4610	944	9	and	and	CCONJ
ejpam-4610	944	10	composition	composition	NOUN
ejpam-4610	944	11	of	of	ADP
ejpam-4610	944	12	graphs	graph	NOUN
ejpam-4610	944	13	.	.	PUNCT
ejpam-4610	945	1	ars	ars	PROPN
ejpam-4610	945	2	combinatoria	combinatoria	PROPN
ejpam-4610	945	3	,	,	PUNCT
ejpam-4610	945	4	107:225–245	107:225–245	NUM
ejpam-4610	945	5	,	,	PUNCT
ejpam-4610	945	6	2012	2012	NUM
ejpam-4610	945	7	.	.	PUNCT
ejpam-4610	946	1	[	[	X
ejpam-4610	946	2	13	13	NUM
ejpam-4610	946	3	]	]	PUNCT
ejpam-4610	946	4	j.g.canoy	j.g.canoy	PROPN
ejpam-4610	946	5	r.	r.	PROPN
ejpam-4610	946	6	mollejon	mollejon	NOUN
ejpam-4610	946	7	and	and	CCONJ
ejpam-4610	946	8	s.	s.	PROPN
ejpam-4610	946	9	canoy	canoy	PROPN
ejpam-4610	946	10	jr	jr	PROPN
ejpam-4610	946	11	.	.	PROPN
ejpam-4610	946	12	hop	hop	PROPN
ejpam-4610	946	13	dominating	dominating	NOUN
ejpam-4610	946	14	sets	set	NOUN
ejpam-4610	946	15	in	in	ADP
ejpam-4610	946	16	graphs	graph	NOUN
ejpam-4610	946	17	under	under	ADP
ejpam-4610	946	18	binary	binary	ADJ
ejpam-4610	946	19	operations	operation	NOUN
ejpam-4610	946	20	.	.	PUNCT
ejpam-4610	947	1	european	european	ADJ
ejpam-4610	947	2	journal	journal	PROPN
ejpam-4610	947	3	of	of	ADP
ejpam-4610	947	4	pure	pure	ADJ
ejpam-4610	947	5	and	and	CCONJ
ejpam-4610	947	6	applied	applied	ADJ
ejpam-4610	947	7	mathematics	mathematic	NOUN
ejpam-4610	947	8	,	,	PUNCT
ejpam-4610	947	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4610	947	10	,	,	PUNCT
ejpam-4610	947	11	2019	2019	NUM
ejpam-4610	947	12	.	.	PUNCT
ejpam-4610	948	1	[	[	X
ejpam-4610	948	2	14	14	NUM
ejpam-4610	948	3	]	]	PUNCT
ejpam-4610	948	4	p.	p.	NOUN
ejpam-4610	948	5	dankelmann	dankelmann	PROPN
ejpam-4610	948	6	d.	d.	PROPN
ejpam-4610	948	7	day	day	PROPN
ejpam-4610	948	8	d.	d.	PROPN
ejpam-4610	948	9	erwin	erwin	PROPN
ejpam-4610	948	10	s.	s.	PROPN
ejpam-4610	948	11	mukwembi	mukwembi	PROPN
ejpam-4610	948	12	and	and	CCONJ
ejpam-4610	948	13	h.	h.	PROPN
ejpam-4610	948	14	swart	swart	PROPN
ejpam-4610	948	15	.	.	PUNCT
ejpam-4610	949	1	domination	domination	NOUN
ejpam-4610	949	2	with	with	ADP
ejpam-4610	949	3	exponential	exponential	ADJ
ejpam-4610	949	4	decay	decay	NOUN
ejpam-4610	949	5	.	.	PUNCT
ejpam-4610	950	1	discrete	discrete	ADJ
ejpam-4610	950	2	math	math	NOUN
ejpam-4610	950	3	,	,	PUNCT
ejpam-4610	950	4	309(19):5877	309(19):5877	NUM
ejpam-4610	950	5	–	–	PUNCT
ejpam-4610	950	6	5883	5883	NUM
ejpam-4610	950	7	,	,	PUNCT
ejpam-4610	950	8	2009	2009	NUM
ejpam-4610	950	9	.	.	PUNCT
ejpam-4610	951	1	[	[	X
ejpam-4610	951	2	15	15	NUM
ejpam-4610	951	3	]	]	X
ejpam-4610	951	4	c.	c.	PROPN
ejpam-4610	951	5	natarajan	natarajan	PROPN
ejpam-4610	951	6	and	and	CCONJ
ejpam-4610	951	7	s.k	s.k	PROPN
ejpam-4610	951	8	.	.	PROPN
ejpam-4610	951	9	ayyaswamy	ayyaswamy	PROPN
ejpam-4610	951	10	.	.	PUNCT
ejpam-4610	952	1	hop	hop	PROPN
ejpam-4610	952	2	domination	domination	NOUN
ejpam-4610	952	3	in	in	ADP
ejpam-4610	952	4	graphs	graph	NOUN
ejpam-4610	952	5	-	-	PUNCT
ejpam-4610	952	6	ii	ii	NOUN
ejpam-4610	952	7	.	.	PUNCT
ejpam-4610	952	8	versita	versita	PROPN
ejpam-4610	952	9	,	,	PUNCT
ejpam-4610	952	10	23(2):187	23(2):187	NUM
ejpam-4610	952	11	–	–	PUNCT
ejpam-4610	952	12	199	199	NUM
ejpam-4610	952	13	,	,	PUNCT
ejpam-4610	952	14	2015	2015	NUM
ejpam-4610	952	15	.	.	PUNCT
ejpam-4610	953	1	[	[	X
ejpam-4610	953	2	16	16	NUM
ejpam-4610	953	3	]	]	X
ejpam-4610	953	4	o.	o.	PROPN
ejpam-4610	953	5	ore	ore	PROPN
ejpam-4610	953	6	.	.	PUNCT
ejpam-4610	954	1	theory	theory	NOUN
ejpam-4610	954	2	of	of	ADP
ejpam-4610	954	3	graphs	graph	NOUN
ejpam-4610	954	4	,	,	PUNCT
ejpam-4610	954	5	volume	volume	NOUN
ejpam-4610	954	6	38	38	NUM
ejpam-4610	954	7	.	.	PUNCT
ejpam-4610	955	1	1962	1962	NUM
ejpam-4610	955	2	.	.	PUNCT
ejpam-4610	956	1	[	[	X
ejpam-4610	956	2	17	17	NUM
ejpam-4610	956	3	]	]	X
ejpam-4610	956	4	y.	y.	PROPN
ejpam-4610	956	5	pabilona	pabilona	PROPN
ejpam-4610	956	6	and	and	CCONJ
ejpam-4610	956	7	h.	h.	PROPN
ejpam-4610	956	8	rara	rara	PROPN
ejpam-4610	956	9	.	.	PUNCT
ejpam-4610	957	1	total	total	ADJ
ejpam-4610	957	2	hop	hop	NOUN
ejpam-4610	957	3	dominating	dominating	NOUN
ejpam-4610	957	4	sets	set	NOUN
ejpam-4610	957	5	in	in	ADP
ejpam-4610	957	6	the	the	DET
ejpam-4610	957	7	join	join	NOUN
ejpam-4610	957	8	,	,	PUNCT
ejpam-4610	957	9	corona	corona	PROPN
ejpam-4610	957	10	,	,	PUNCT
ejpam-4610	957	11	and	and	CCONJ
ejpam-4610	957	12	lexicographic	lexicographic	ADJ
ejpam-4610	957	13	product	product	NOUN
ejpam-4610	957	14	of	of	ADP
ejpam-4610	957	15	graphs	graph	NOUN
ejpam-4610	957	16	.	.	PUNCT
ejpam-4610	958	1	ournal	ournal	ADJ
ejpam-4610	958	2	of	of	ADP
ejpam-4610	958	3	algebra	algebra	PROPN
ejpam-4610	958	4	and	and	CCONJ
ejpam-4610	958	5	applied	apply	VERB
ejpam-4610	958	6	mathematics	mathematic	NOUN
ejpam-4610	958	7	,	,	PUNCT
ejpam-4610	958	8	2017	2017	NUM
ejpam-4610	958	9	.	.	PUNCT
ejpam-4610	959	1	[	[	X
ejpam-4610	959	2	18	18	NUM
ejpam-4610	959	3	]	]	PUNCT
ejpam-4610	959	4	a.	a.	NOUN
ejpam-4610	959	5	alwardi	alwardi	PROPN
ejpam-4610	959	6	n.	n.	PROPN
ejpam-4610	959	7	abhi	abhi	PROPN
ejpam-4610	959	8	r.	r.	PROPN
ejpam-4610	959	9	puttaswamy	puttaswamy	PROPN
ejpam-4610	959	10	.	.	PUNCT
ejpam-4610	959	11	transversal	transversal	PROPN
ejpam-4610	959	12	domination	domination	NOUN
ejpam-4610	959	13	in	in	ADP
ejpam-4610	959	14	graphs	graph	NOUN
ejpam-4610	959	15	.	.	PUNCT
ejpam-4610	960	1	gulf	gulf	PROPN
ejpam-4610	960	2	journal	journal	PROPN
ejpam-4610	960	3	of	of	ADP
ejpam-4610	960	4	mathematics	mathematic	NOUN
ejpam-4610	960	5	,	,	PUNCT
ejpam-4610	960	6	6:41–49	6:41–49	NUM
ejpam-4610	960	7	,	,	PUNCT
ejpam-4610	960	8	2018	2018	NUM
ejpam-4610	960	9	.	.	PUNCT
ejpam-4610	961	1	[	[	X
ejpam-4610	961	2	19	19	NUM
ejpam-4610	961	3	]	]	PUNCT
ejpam-4610	961	4	a.	a.	NOUN
ejpam-4610	961	5	alwardi	alwardi	PROPN
ejpam-4610	961	6	n.	n.	PROPN
ejpam-4610	961	7	abhi	abhi	PROPN
ejpam-4610	961	8	r.	r.	PROPN
ejpam-4610	961	9	puttaswamy	puttaswamy	PROPN
ejpam-4610	961	10	.	.	PUNCT
ejpam-4610	962	1	transversal	transversal	PROPN
ejpam-4610	962	2	total	total	ADJ
ejpam-4610	962	3	domination	domination	NOUN
ejpam-4610	962	4	in	in	ADP
ejpam-4610	962	5	graphs	graph	NOUN
ejpam-4610	962	6	.	.	PUNCT
ejpam-4610	963	1	preprint	preprint	NOUN
ejpam-4610	963	2	at	at	ADP
ejpam-4610	963	3	https://www.researchgate.net/publication/325063470	https://www.researchgate.net/publication/325063470	PROPN
ejpam-4610	963	4	,	,	PUNCT
ejpam-4610	963	5	2018	2018	NUM
ejpam-4610	963	6	.	.	PUNCT
ejpam-4610	964	1	[	[	X
ejpam-4610	964	2	20	20	NUM
ejpam-4610	964	3	]	]	X
ejpam-4610	964	4	h.a	h.a	PROPN
ejpam-4610	964	5	.	.	PROPN
ejpam-4610	964	6	ahangar	ahangar	PROPN
ejpam-4610	964	7	v.	v.	ADP
ejpam-4610	964	8	samodivkin	samodivkin	PROPN
ejpam-4610	964	9	and	and	CCONJ
ejpam-4610	964	10	i.	i.	PROPN
ejpam-4610	964	11	yero	yero	PROPN
ejpam-4610	964	12	.	.	PUNCT
ejpam-4610	965	1	independent	independent	ADJ
ejpam-4610	965	2	transversal	transversal	ADJ
ejpam-4610	965	3	dominating	dominating	NOUN
ejpam-4610	965	4	sets	set	NOUN
ejpam-4610	965	5	in	in	ADP
ejpam-4610	965	6	graphs	graph	NOUN
ejpam-4610	965	7	:	:	PUNCT
ejpam-4610	965	8	complexity	complexity	NOUN
ejpam-4610	965	9	and	and	CCONJ
ejpam-4610	965	10	structural	structural	ADJ
ejpam-4610	965	11	properties	property	NOUN
ejpam-4610	965	12	.	.	PUNCT
ejpam-4610	966	1	filomat	filomat	PROPN
ejpam-4610	966	2	,	,	PUNCT
ejpam-4610	966	3	30(2):293–303	30(2):293–303	PROPN
ejpam-4610	966	4	,	,	PUNCT
ejpam-4610	966	5	2016	2016	NUM
ejpam-4610	966	6	.	.	PUNCT
ejpam-4610	967	1	references	reference	NOUN
ejpam-4610	967	2	206	206	NUM
ejpam-4610	968	1	[	[	X
ejpam-4610	968	2	21	21	NUM
ejpam-4610	968	3	]	]	X
ejpam-4610	968	4	t.	t.	NOUN
ejpam-4610	968	5	andreae	andreae	ADP
ejpam-4610	968	6	m.	m.	PROPN
ejpam-4610	968	7	schughart	schughart	PROPN
ejpam-4610	968	8	and	and	CCONJ
ejpam-4610	968	9	z.	z.	PROPN
ejpam-4610	968	10	tuza	tuza	PROPN
ejpam-4610	968	11	.	.	PUNCT
ejpam-4610	969	1	clique	clique	ADJ
ejpam-4610	969	2	-	-	PUNCT
ejpam-4610	969	3	transversal	transversal	ADJ
ejpam-4610	969	4	sets	set	NOUN
ejpam-4610	969	5	of	of	ADP
ejpam-4610	969	6	line	line	NOUN
ejpam-4610	969	7	graphs	graph	NOUN
ejpam-4610	969	8	and	and	CCONJ
ejpam-4610	969	9	complements	complement	NOUN
ejpam-4610	969	10	of	of	ADP
ejpam-4610	969	11	line	line	NOUN
ejpam-4610	969	12	graphs	graph	NOUN
ejpam-4610	969	13	.	.	PUNCT
ejpam-4610	970	1	discrete	discrete	ADJ
ejpam-4610	970	2	mathematics	mathematic	NOUN
ejpam-4610	970	3	,	,	PUNCT
ejpam-4610	970	4	88(1):11–20	88(1):11–20	NUM
ejpam-4610	970	5	,	,	PUNCT
ejpam-4610	970	6	1991	1991	NUM
ejpam-4610	970	7	.	.	PUNCT
ejpam-4610	971	1	[	[	X
ejpam-4610	971	2	22	22	NUM
ejpam-4610	971	3	]	]	X
ejpam-4610	971	4	d.s	d.s	PROPN
ejpam-4610	971	5	.	.	PROPN
ejpam-4610	971	6	sevilleno	sevilleno	PROPN
ejpam-4610	971	7	and	and	CCONJ
ejpam-4610	971	8	f.p	f.p	PROPN
ejpam-4610	971	9	.	.	PROPN
ejpam-4610	971	10	jamil	jamil	PROPN
ejpam-4610	971	11	.	.	PUNCT
ejpam-4610	972	1	on	on	ADP
ejpam-4610	972	2	independent	independent	ADJ
ejpam-4610	972	3	transversal	transversal	ADJ
ejpam-4610	972	4	dominating	dominating	NOUN
ejpam-4610	972	5	sets	set	NOUN
ejpam-4610	972	6	in	in	ADP
ejpam-4610	972	7	graphs	graph	NOUN
ejpam-4610	972	8	.	.	PUNCT
ejpam-4610	973	1	european	european	ADJ
ejpam-4610	973	2	journal	journal	PROPN
ejpam-4610	973	3	of	of	ADP
ejpam-4610	973	4	pure	pure	ADJ
ejpam-4610	973	5	and	and	CCONJ
ejpam-4610	973	6	applied	applied	ADJ
ejpam-4610	973	7	mathematics	mathematic	NOUN
ejpam-4610	973	8	,	,	PUNCT
ejpam-4610	973	9	14(1):140–163	14(1):140–163	NUM
ejpam-4610	973	10	,	,	PUNCT
ejpam-4610	973	11	2021	2021	NUM
ejpam-4610	973	12	.	.	PUNCT