id	sid	tid	token	lemma	pos
ejpam-3975	1	1	european	european	PROPN
ejpam-3975	1	2	journal	journal	PROPN
ejpam-3975	1	3	of	of	ADP
ejpam-3975	1	4	pure	pure	ADJ
ejpam-3975	1	5	and	and	CCONJ
ejpam-3975	1	6	applied	apply	VERB
ejpam-3975	1	7	mathematics	mathematic	NOUN
ejpam-3975	1	8	vol	vol	NOUN
ejpam-3975	1	9	.	.	PUNCT
ejpam-3975	2	1	14	14	NUM
ejpam-3975	2	2	,	,	PUNCT
ejpam-3975	2	3	no	no	INTJ
ejpam-3975	2	4	.	.	NOUN
ejpam-3975	2	5	3	3	NUM
ejpam-3975	2	6	,	,	PUNCT
ejpam-3975	2	7	2021	2021	NUM
ejpam-3975	2	8	,	,	PUNCT
ejpam-3975	2	9	803	803	NUM
ejpam-3975	2	10	-	-	SYM
ejpam-3975	2	11	815	815	NUM
ejpam-3975	2	12	issn	issn	PROPN
ejpam-3975	2	13	1307	1307	NUM
ejpam-3975	2	14	-	-	SYM
ejpam-3975	2	15	5543	5543	NUM
ejpam-3975	2	16	–	–	PUNCT
ejpam-3975	2	17	ejpam.com	ejpam.com	X
ejpam-3975	2	18	published	publish	VERB
ejpam-3975	2	19	by	by	ADP
ejpam-3975	2	20	new	new	PROPN
ejpam-3975	2	21	york	york	PROPN
ejpam-3975	2	22	business	business	PROPN
ejpam-3975	2	23	global	global	ADJ
ejpam-3975	2	24	total	total	NOUN
ejpam-3975	2	25	perfect	perfect	ADJ
ejpam-3975	2	26	hop	hop	NOUN
ejpam-3975	2	27	domination	domination	NOUN
ejpam-3975	2	28	in	in	ADP
ejpam-3975	2	29	graphs	graph	NOUN
ejpam-3975	2	30	under	under	ADP
ejpam-3975	2	31	some	some	DET
ejpam-3975	2	32	binary	binary	ADJ
ejpam-3975	2	33	operations	operation	NOUN
ejpam-3975	2	34	raicah	raicah	VERB
ejpam-3975	2	35	c.	c.	PROPN
ejpam-3975	2	36	rakim1,∗	rakim1,∗	PROPN
ejpam-3975	2	37	,	,	PUNCT
ejpam-3975	2	38	helen	helen	PROPN
ejpam-3975	2	39	m.	m.	PROPN
ejpam-3975	2	40	rara1	rara1	PROPN
ejpam-3975	3	1	1	1	NUM
ejpam-3975	3	2	mathematics	mathematics	PROPN
ejpam-3975	3	3	department	department	NOUN
ejpam-3975	3	4	,	,	PUNCT
ejpam-3975	3	5	college	college	NOUN
ejpam-3975	3	6	of	of	ADP
ejpam-3975	3	7	natural	natural	ADJ
ejpam-3975	3	8	sciences	science	NOUN
ejpam-3975	3	9	and	and	CCONJ
ejpam-3975	3	10	mathematics	mathematic	NOUN
ejpam-3975	3	11	,	,	PUNCT
ejpam-3975	3	12	mindanao	mindanao	PROPN
ejpam-3975	3	13	state	state	PROPN
ejpam-3975	3	14	university	university	NOUN
ejpam-3975	3	15	-	-	PUNCT
ejpam-3975	3	16	main	main	ADJ
ejpam-3975	3	17	campus	campus	NOUN
ejpam-3975	3	18	,	,	PUNCT
ejpam-3975	3	19	9700	9700	NUM
ejpam-3975	3	20	marawi	marawi	PROPN
ejpam-3975	3	21	city	city	PROPN
ejpam-3975	3	22	,	,	PUNCT
ejpam-3975	3	23	philippines	philippines	PROPN
ejpam-3975	3	24	2	2	NUM
ejpam-3975	3	25	department	department	NOUN
ejpam-3975	3	26	of	of	ADP
ejpam-3975	3	27	mathematics	mathematic	NOUN
ejpam-3975	3	28	and	and	CCONJ
ejpam-3975	3	29	statistics	statistic	NOUN
ejpam-3975	3	30	,	,	PUNCT
ejpam-3975	3	31	college	college	NOUN
ejpam-3975	3	32	of	of	ADP
ejpam-3975	3	33	science	science	NOUN
ejpam-3975	3	34	and	and	CCONJ
ejpam-3975	3	35	mathematics	mathematic	NOUN
ejpam-3975	3	36	,	,	PUNCT
ejpam-3975	3	37	center	center	NOUN
ejpam-3975	3	38	for	for	ADP
ejpam-3975	3	39	graph	graph	NOUN
ejpam-3975	3	40	theory	theory	NOUN
ejpam-3975	3	41	,	,	PUNCT
ejpam-3975	3	42	algebra	algebra	NOUN
ejpam-3975	3	43	,	,	PUNCT
ejpam-3975	3	44	and	and	CCONJ
ejpam-3975	3	45	analysis	analysis	NOUN
ejpam-3975	3	46	,	,	PUNCT
ejpam-3975	3	47	premier	premier	PROPN
ejpam-3975	3	48	research	research	PROPN
ejpam-3975	3	49	institute	institute	PROPN
ejpam-3975	3	50	of	of	ADP
ejpam-3975	3	51	science	science	NOUN
ejpam-3975	3	52	and	and	CCONJ
ejpam-3975	3	53	mathematics	mathematic	NOUN
ejpam-3975	3	54	,	,	PUNCT
ejpam-3975	3	55	mindanao	mindanao	PROPN
ejpam-3975	3	56	state	state	PROPN
ejpam-3975	3	57	university	university	PROPN
ejpam-3975	3	58	-	-	PUNCT
ejpam-3975	3	59	iligan	iligan	PROPN
ejpam-3975	3	60	institute	institute	PROPN
ejpam-3975	3	61	of	of	ADP
ejpam-3975	3	62	technology	technology	PROPN
ejpam-3975	3	63	,	,	PUNCT
ejpam-3975	3	64	9200	9200	NUM
ejpam-3975	3	65	iligan	iligan	ADJ
ejpam-3975	3	66	city	city	NOUN
ejpam-3975	3	67	,	,	PUNCT
ejpam-3975	3	68	philippines	philippine	NOUN
ejpam-3975	3	69	abstract	abstract	ADJ
ejpam-3975	3	70	.	.	PUNCT
ejpam-3975	4	1	let	let	VERB
ejpam-3975	4	2	g	g	PROPN
ejpam-3975	4	3	=	=	SYM
ejpam-3975	4	4	(	(	PUNCT
ejpam-3975	4	5	v	v	NOUN
ejpam-3975	4	6	(	(	PUNCT
ejpam-3975	4	7	g	g	NOUN
ejpam-3975	4	8	)	)	PUNCT
ejpam-3975	4	9	,	,	PUNCT
ejpam-3975	4	10	e(g	e(g	PROPN
ejpam-3975	4	11	)	)	PUNCT
ejpam-3975	4	12	)	)	PUNCT
ejpam-3975	5	1	be	be	AUX
ejpam-3975	5	2	a	a	DET
ejpam-3975	5	3	simple	simple	ADJ
ejpam-3975	5	4	graph	graph	NOUN
ejpam-3975	5	5	.	.	PUNCT
ejpam-3975	6	1	a	a	DET
ejpam-3975	6	2	set	set	NOUN
ejpam-3975	6	3	s	s	NOUN
ejpam-3975	6	4	⊆	⊆	NUM
ejpam-3975	6	5	v	v	NOUN
ejpam-3975	6	6	(	(	PUNCT
ejpam-3975	6	7	g	g	NOUN
ejpam-3975	6	8	)	)	PUNCT
ejpam-3975	6	9	is	be	AUX
ejpam-3975	6	10	a	a	DET
ejpam-3975	6	11	perfect	perfect	ADJ
ejpam-3975	6	12	hop	hop	NOUN
ejpam-3975	6	13	dominating	dominating	NOUN
ejpam-3975	6	14	set	set	NOUN
ejpam-3975	6	15	of	of	ADP
ejpam-3975	6	16	g	g	PROPN
ejpam-3975	6	17	if	if	SCONJ
ejpam-3975	6	18	for	for	ADP
ejpam-3975	6	19	every	every	PRON
ejpam-3975	6	20	v	v	NUM
ejpam-3975	6	21	∈	∈	NOUN
ejpam-3975	6	22	v	v	NOUN
ejpam-3975	6	23	(	(	PUNCT
ejpam-3975	6	24	g	g	NOUN
ejpam-3975	6	25	)	)	PUNCT
ejpam-3975	6	26	\	\	PROPN
ejpam-3975	7	1	s	s	X
ejpam-3975	7	2	,	,	PUNCT
ejpam-3975	7	3	there	there	PRON
ejpam-3975	7	4	is	be	VERB
ejpam-3975	7	5	exactly	exactly	ADV
ejpam-3975	7	6	one	one	NUM
ejpam-3975	7	7	vertex	vertex	NOUN
ejpam-3975	7	8	u	u	NOUN
ejpam-3975	7	9	∈	∈	NOUN
ejpam-3975	7	10	s	s	VERB
ejpam-3975	7	11	such	such	ADJ
ejpam-3975	7	12	that	that	DET
ejpam-3975	7	13	dg(u	dg(u	ADJ
ejpam-3975	7	14	,	,	PUNCT
ejpam-3975	7	15	v	v	NOUN
ejpam-3975	7	16	)	)	PUNCT
ejpam-3975	7	17	=	=	SYM
ejpam-3975	7	18	2	2	X
ejpam-3975	7	19	.	.	X
ejpam-3975	7	20	the	the	DET
ejpam-3975	7	21	smallest	small	ADJ
ejpam-3975	7	22	cardinality	cardinality	NOUN
ejpam-3975	7	23	of	of	ADP
ejpam-3975	7	24	a	a	DET
ejpam-3975	7	25	perfect	perfect	ADJ
ejpam-3975	7	26	hop	hop	NOUN
ejpam-3975	7	27	dominating	dominating	NOUN
ejpam-3975	7	28	set	set	NOUN
ejpam-3975	7	29	of	of	ADP
ejpam-3975	7	30	g	g	PROPN
ejpam-3975	7	31	is	be	AUX
ejpam-3975	7	32	called	call	VERB
ejpam-3975	7	33	the	the	DET
ejpam-3975	7	34	perfect	perfect	ADJ
ejpam-3975	7	35	hop	hop	NOUN
ejpam-3975	7	36	domination	domination	NOUN
ejpam-3975	7	37	number	number	NOUN
ejpam-3975	7	38	of	of	ADP
ejpam-3975	7	39	g	g	NOUN
ejpam-3975	7	40	,	,	PUNCT
ejpam-3975	7	41	denoted	denote	VERB
ejpam-3975	7	42	by	by	ADP
ejpam-3975	7	43	γph(g	γph(g	NOUN
ejpam-3975	7	44	)	)	PUNCT
ejpam-3975	7	45	.	.	PUNCT
ejpam-3975	8	1	a	a	DET
ejpam-3975	8	2	perfect	perfect	ADJ
ejpam-3975	8	3	hop	hop	NOUN
ejpam-3975	8	4	dominating	dominating	NOUN
ejpam-3975	8	5	set	set	NOUN
ejpam-3975	8	6	s	s	PROPN
ejpam-3975	8	7	⊆	⊆	NUM
ejpam-3975	8	8	v	v	NOUN
ejpam-3975	8	9	(	(	PUNCT
ejpam-3975	8	10	g	g	NOUN
ejpam-3975	8	11	)	)	PUNCT
ejpam-3975	8	12	is	be	AUX
ejpam-3975	8	13	called	call	VERB
ejpam-3975	8	14	a	a	DET
ejpam-3975	8	15	total	total	ADJ
ejpam-3975	8	16	perfect	perfect	ADJ
ejpam-3975	8	17	hop	hop	NOUN
ejpam-3975	8	18	dominating	dominating	NOUN
ejpam-3975	8	19	set	set	NOUN
ejpam-3975	8	20	of	of	ADP
ejpam-3975	8	21	g	g	PROPN
ejpam-3975	8	22	if	if	SCONJ
ejpam-3975	8	23	for	for	ADP
ejpam-3975	8	24	every	every	DET
ejpam-3975	8	25	v	v	NUM
ejpam-3975	8	26	∈	∈	NOUN
ejpam-3975	8	27	v	v	NOUN
ejpam-3975	8	28	(	(	PUNCT
ejpam-3975	8	29	g	g	NOUN
ejpam-3975	8	30	)	)	PUNCT
ejpam-3975	8	31	,	,	PUNCT
ejpam-3975	8	32	there	there	PRON
ejpam-3975	8	33	is	be	VERB
ejpam-3975	8	34	exactly	exactly	ADV
ejpam-3975	8	35	one	one	NUM
ejpam-3975	8	36	vertex	vertex	NOUN
ejpam-3975	8	37	u	u	NOUN
ejpam-3975	8	38	∈	∈	NOUN
ejpam-3975	8	39	s	s	VERB
ejpam-3975	8	40	such	such	ADJ
ejpam-3975	8	41	that	that	DET
ejpam-3975	8	42	dg(u	dg(u	ADJ
ejpam-3975	8	43	,	,	PUNCT
ejpam-3975	8	44	v	v	NOUN
ejpam-3975	8	45	)	)	PUNCT
ejpam-3975	9	1	=	=	SYM
ejpam-3975	9	2	2	2	X
ejpam-3975	9	3	.	.	PUNCT
ejpam-3975	10	1	the	the	DET
ejpam-3975	10	2	total	total	ADJ
ejpam-3975	10	3	perfect	perfect	ADJ
ejpam-3975	10	4	hop	hop	NOUN
ejpam-3975	10	5	domination	domination	NOUN
ejpam-3975	10	6	number	number	NOUN
ejpam-3975	10	7	of	of	ADP
ejpam-3975	10	8	g	g	NOUN
ejpam-3975	10	9	,	,	PUNCT
ejpam-3975	10	10	denoted	denote	VERB
ejpam-3975	10	11	by	by	ADP
ejpam-3975	10	12	γtph(g	γtph(g	NOUN
ejpam-3975	10	13	)	)	PUNCT
ejpam-3975	10	14	,	,	PUNCT
ejpam-3975	10	15	is	be	AUX
ejpam-3975	10	16	the	the	DET
ejpam-3975	10	17	smallest	small	ADJ
ejpam-3975	10	18	cardinality	cardinality	NOUN
ejpam-3975	10	19	of	of	ADP
ejpam-3975	10	20	a	a	DET
ejpam-3975	10	21	total	total	ADJ
ejpam-3975	10	22	perfect	perfect	ADJ
ejpam-3975	10	23	hop	hop	NOUN
ejpam-3975	10	24	dominating	dominating	NOUN
ejpam-3975	10	25	set	set	NOUN
ejpam-3975	10	26	of	of	ADP
ejpam-3975	10	27	g.	g.	PROPN
ejpam-3975	10	28	any	any	DET
ejpam-3975	10	29	total	total	ADJ
ejpam-3975	10	30	perfect	perfect	ADJ
ejpam-3975	10	31	hop	hop	NOUN
ejpam-3975	10	32	dominating	dominating	NOUN
ejpam-3975	10	33	set	set	NOUN
ejpam-3975	10	34	of	of	ADP
ejpam-3975	10	35	g	g	NOUN
ejpam-3975	10	36	of	of	ADP
ejpam-3975	10	37	cardinality	cardinality	NOUN
ejpam-3975	10	38	γtph(g	γtph(g	PROPN
ejpam-3975	10	39	)	)	PUNCT
ejpam-3975	10	40	is	be	AUX
ejpam-3975	10	41	referred	refer	VERB
ejpam-3975	10	42	to	to	ADP
ejpam-3975	10	43	as	as	ADP
ejpam-3975	10	44	a	a	DET
ejpam-3975	10	45	γtph	γtph	NOUN
ejpam-3975	10	46	-	-	PUNCT
ejpam-3975	10	47	set	set	NOUN
ejpam-3975	10	48	of	of	ADP
ejpam-3975	10	49	g.	g.	PROPN
ejpam-3975	10	50	in	in	ADP
ejpam-3975	10	51	this	this	DET
ejpam-3975	10	52	paper	paper	NOUN
ejpam-3975	10	53	,	,	PUNCT
ejpam-3975	10	54	we	we	PRON
ejpam-3975	10	55	characterize	characterize	VERB
ejpam-3975	10	56	the	the	DET
ejpam-3975	10	57	total	total	ADJ
ejpam-3975	10	58	perfect	perfect	ADJ
ejpam-3975	10	59	hop	hop	NOUN
ejpam-3975	10	60	dominating	dominating	NOUN
ejpam-3975	10	61	sets	set	NOUN
ejpam-3975	10	62	in	in	ADP
ejpam-3975	10	63	the	the	DET
ejpam-3975	10	64	join	join	NOUN
ejpam-3975	10	65	,	,	PUNCT
ejpam-3975	10	66	corona	corona	NOUN
ejpam-3975	10	67	and	and	CCONJ
ejpam-3975	10	68	lexicographic	lexicographic	ADJ
ejpam-3975	10	69	product	product	NOUN
ejpam-3975	10	70	of	of	ADP
ejpam-3975	10	71	graphs	graph	NOUN
ejpam-3975	10	72	and	and	CCONJ
ejpam-3975	10	73	determine	determine	VERB
ejpam-3975	10	74	their	their	PRON
ejpam-3975	10	75	corresponding	correspond	VERB
ejpam-3975	10	76	total	total	ADJ
ejpam-3975	10	77	perfect	perfect	ADJ
ejpam-3975	10	78	hop	hop	NOUN
ejpam-3975	10	79	domination	domination	NOUN
ejpam-3975	10	80	number	number	NOUN
ejpam-3975	10	81	.	.	PUNCT
ejpam-3975	11	1	2020	2020	NUM
ejpam-3975	11	2	mathematics	mathematic	NOUN
ejpam-3975	11	3	subject	subject	NOUN
ejpam-3975	11	4	classifications	classification	NOUN
ejpam-3975	11	5	:	:	PUNCT
ejpam-3975	11	6	05c76	05c76	NUM
ejpam-3975	11	7	key	key	ADJ
ejpam-3975	11	8	words	word	NOUN
ejpam-3975	11	9	and	and	CCONJ
ejpam-3975	11	10	phrases	phrase	NOUN
ejpam-3975	11	11	:	:	PUNCT
ejpam-3975	11	12	total	total	ADJ
ejpam-3975	11	13	perfect	perfect	ADJ
ejpam-3975	11	14	hop	hop	NOUN
ejpam-3975	11	15	domination	domination	NOUN
ejpam-3975	11	16	,	,	PUNCT
ejpam-3975	11	17	total	total	ADJ
ejpam-3975	11	18	perfect	perfect	ADJ
ejpam-3975	11	19	point	point	NOUN
ejpam-3975	11	20	-	-	PUNCT
ejpam-3975	11	21	wise	wise	ADJ
ejpam-3975	11	22	non	non	ADJ
ejpam-3975	11	23	-	-	NOUN
ejpam-3975	11	24	domination	domination	ADJ
ejpam-3975	11	25	,	,	PUNCT
ejpam-3975	11	26	perfect	perfect	ADJ
ejpam-3975	11	27	total	total	NOUN
ejpam-3975	11	28	(	(	PUNCT
ejpam-3975	11	29	1	1	NUM
ejpam-3975	11	30	,	,	PUNCT
ejpam-3975	11	31	2)∗-domination	2)∗-domination	NOUN
ejpam-3975	11	32	,	,	PUNCT
ejpam-3975	11	33	join	join	NOUN
ejpam-3975	11	34	,	,	PUNCT
ejpam-3975	11	35	corona	corona	PROPN
ejpam-3975	11	36	,	,	PUNCT
ejpam-3975	11	37	lexicographic	lexicographic	ADJ
ejpam-3975	11	38	product	product	NOUN
ejpam-3975	11	39	1	1	NUM
ejpam-3975	11	40	.	.	PUNCT
ejpam-3975	12	1	introduction	introduction	NOUN
ejpam-3975	12	2	let	let	VERB
ejpam-3975	12	3	g	g	NOUN
ejpam-3975	12	4	=	=	SYM
ejpam-3975	12	5	(	(	PUNCT
ejpam-3975	12	6	v	v	NOUN
ejpam-3975	12	7	(	(	PUNCT
ejpam-3975	12	8	g	g	NOUN
ejpam-3975	12	9	)	)	PUNCT
ejpam-3975	12	10	,	,	PUNCT
ejpam-3975	12	11	e(g	e(g	PROPN
ejpam-3975	12	12	)	)	PUNCT
ejpam-3975	12	13	)	)	PUNCT
ejpam-3975	12	14	be	be	AUX
ejpam-3975	12	15	a	a	DET
ejpam-3975	12	16	simple	simple	ADJ
ejpam-3975	12	17	graph	graph	NOUN
ejpam-3975	12	18	.	.	PUNCT
ejpam-3975	13	1	the	the	DET
ejpam-3975	13	2	open	open	ADJ
ejpam-3975	13	3	neighborhood	neighborhood	NOUN
ejpam-3975	13	4	of	of	ADP
ejpam-3975	13	5	a	a	DET
ejpam-3975	13	6	vertex	vertex	NOUN
ejpam-3975	13	7	v	v	NOUN
ejpam-3975	13	8	of	of	ADP
ejpam-3975	13	9	g	g	PROPN
ejpam-3975	13	10	is	be	AUX
ejpam-3975	13	11	the	the	DET
ejpam-3975	13	12	set	set	NOUN
ejpam-3975	13	13	ng(v	ng(v	PUNCT
ejpam-3975	13	14	)	)	PUNCT
ejpam-3975	13	15	=	=	SYM
ejpam-3975	14	1	{	{	PUNCT
ejpam-3975	14	2	u	u	NOUN
ejpam-3975	14	3	∈	∈	PROPN
ejpam-3975	14	4	v	v	NOUN
ejpam-3975	14	5	(	(	PUNCT
ejpam-3975	14	6	g	g	NOUN
ejpam-3975	14	7	)	)	PUNCT
ejpam-3975	14	8	:	:	PUNCT
ejpam-3975	14	9	uv	uv	PROPN
ejpam-3975	14	10	∈	∈	PROPN
ejpam-3975	14	11	e(g	e(g	PROPN
ejpam-3975	14	12	)	)	PUNCT
ejpam-3975	14	13	}	}	PUNCT
ejpam-3975	14	14	and	and	CCONJ
ejpam-3975	14	15	its	its	PRON
ejpam-3975	14	16	closed	closed	ADJ
ejpam-3975	14	17	neighborhood	neighborhood	NOUN
ejpam-3975	14	18	is	be	AUX
ejpam-3975	14	19	the	the	DET
ejpam-3975	14	20	set	set	NOUN
ejpam-3975	14	21	ng[v	ng[v	NOUN
ejpam-3975	14	22	]	]	X
ejpam-3975	14	23	=	=	SYM
ejpam-3975	14	24	ng(v	ng(v	X
ejpam-3975	14	25	)	)	PUNCT
ejpam-3975	14	26	∪	∪	ADP
ejpam-3975	14	27	{	{	PUNCT
ejpam-3975	14	28	v	v	NOUN
ejpam-3975	14	29	}	}	PUNCT
ejpam-3975	14	30	.	.	PUNCT
ejpam-3975	15	1	the	the	DET
ejpam-3975	15	2	degree	degree	NOUN
ejpam-3975	15	3	of	of	ADP
ejpam-3975	15	4	v	v	NOUN
ejpam-3975	15	5	,	,	PUNCT
ejpam-3975	15	6	denoted	denote	VERB
ejpam-3975	15	7	by	by	ADP
ejpam-3975	15	8	degg(v	degg(v	PROPN
ejpam-3975	15	9	)	)	PUNCT
ejpam-3975	15	10	,	,	PUNCT
ejpam-3975	15	11	is	be	AUX
ejpam-3975	15	12	equal	equal	ADJ
ejpam-3975	15	13	to	to	ADP
ejpam-3975	15	14	|ng(v)|	|ng(v)|	NOUN
ejpam-3975	15	15	.	.	PUNCT
ejpam-3975	16	1	the	the	DET
ejpam-3975	16	2	maximum	maximum	ADJ
ejpam-3975	16	3	degree	degree	NOUN
ejpam-3975	16	4	of	of	ADP
ejpam-3975	16	5	a	a	DET
ejpam-3975	16	6	graph	graph	NOUN
ejpam-3975	16	7	g	g	NOUN
ejpam-3975	16	8	,	,	PUNCT
ejpam-3975	16	9	denoted	denote	VERB
ejpam-3975	16	10	by	by	ADP
ejpam-3975	16	11	∆(g	∆(g	PROPN
ejpam-3975	16	12	)	)	PUNCT
ejpam-3975	16	13	,	,	PUNCT
ejpam-3975	16	14	is	be	AUX
ejpam-3975	16	15	the	the	DET
ejpam-3975	16	16	maximum	maximum	ADJ
ejpam-3975	16	17	degg(u	degg(u	PROPN
ejpam-3975	16	18	)	)	PUNCT
ejpam-3975	16	19	,	,	PUNCT
ejpam-3975	16	20	for	for	ADP
ejpam-3975	16	21	all	all	DET
ejpam-3975	16	22	u	u	PROPN
ejpam-3975	16	23	∈	∈	PROPN
ejpam-3975	16	24	v	v	NOUN
ejpam-3975	16	25	(	(	PUNCT
ejpam-3975	16	26	g	g	NOUN
ejpam-3975	16	27	)	)	PUNCT
ejpam-3975	16	28	.	.	PUNCT
ejpam-3975	17	1	similarly	similarly	ADV
ejpam-3975	17	2	,	,	PUNCT
ejpam-3975	17	3	the	the	DET
ejpam-3975	17	4	minimum	minimum	NOUN
ejpam-3975	17	5	degree	degree	NOUN
ejpam-3975	17	6	of	of	ADP
ejpam-3975	17	7	a	a	DET
ejpam-3975	17	8	graph	graph	NOUN
ejpam-3975	17	9	g	g	NOUN
ejpam-3975	17	10	,	,	PUNCT
ejpam-3975	17	11	denoted	denote	VERB
ejpam-3975	17	12	by	by	ADP
ejpam-3975	17	13	δ(g	δ(g	PROPN
ejpam-3975	17	14	)	)	PUNCT
ejpam-3975	17	15	,	,	PUNCT
ejpam-3975	17	16	is	be	AUX
ejpam-3975	17	17	the	the	DET
ejpam-3975	17	18	minimum	minimum	ADJ
ejpam-3975	17	19	degg(u	degg(u	PROPN
ejpam-3975	17	20	)	)	PUNCT
ejpam-3975	17	21	,	,	PUNCT
ejpam-3975	17	22	for	for	ADP
ejpam-3975	17	23	all	all	DET
ejpam-3975	17	24	u	u	PROPN
ejpam-3975	17	25	∈	∈	PROPN
ejpam-3975	17	26	v	v	NOUN
ejpam-3975	17	27	(	(	PUNCT
ejpam-3975	17	28	g	g	NOUN
ejpam-3975	17	29	)	)	PUNCT
ejpam-3975	17	30	.	.	PUNCT
ejpam-3975	18	1	if	if	SCONJ
ejpam-3975	18	2	x	x	PROPN
ejpam-3975	18	3	⊆	⊆	NUM
ejpam-3975	18	4	v	v	X
ejpam-3975	18	5	(	(	PUNCT
ejpam-3975	18	6	g	g	NOUN
ejpam-3975	18	7	)	)	PUNCT
ejpam-3975	18	8	,	,	PUNCT
ejpam-3975	18	9	the	the	DET
ejpam-3975	18	10	open	open	ADJ
ejpam-3975	18	11	neighborhood	neighborhood	NOUN
ejpam-3975	18	12	of	of	ADP
ejpam-3975	18	13	x	x	PUNCT
ejpam-3975	18	14	in	in	ADP
ejpam-3975	18	15	g	g	PROPN
ejpam-3975	18	16	is	be	AUX
ejpam-3975	18	17	the	the	DET
ejpam-3975	18	18	set	set	NOUN
ejpam-3975	18	19	ng(x	ng(x	NUM
ejpam-3975	18	20	)	)	PUNCT
ejpam-3975	19	1	=	=	SYM
ejpam-3975	19	2	⋃	⋃	NOUN
ejpam-3975	19	3	u∈x	u∈x	NOUN
ejpam-3975	19	4	ng(u	ng(u	NOUN
ejpam-3975	19	5	)	)	PUNCT
ejpam-3975	19	6	.	.	PUNCT
ejpam-3975	20	1	the	the	DET
ejpam-3975	20	2	closed	closed	ADJ
ejpam-3975	20	3	neighborhood	neighborhood	NOUN
ejpam-3975	20	4	of	of	ADP
ejpam-3975	20	5	x	x	PUNCT
ejpam-3975	20	6	in	in	ADP
ejpam-3975	20	7	g	g	PROPN
ejpam-3975	20	8	is	be	AUX
ejpam-3975	20	9	the	the	DET
ejpam-3975	20	10	set	set	NOUN
ejpam-3975	20	11	ng[x	ng[x	PROPN
ejpam-3975	20	12	]	]	X
ejpam-3975	20	13	=	=	SYM
ejpam-3975	20	14	ng(x)∪x	ng(x)∪x	PROPN
ejpam-3975	20	15	.	.	PUNCT
ejpam-3975	20	16	∗corresponding	∗corresponde	VERB
ejpam-3975	20	17	author	author	NOUN
ejpam-3975	20	18	.	.	PUNCT
ejpam-3975	21	1	doi	doi	NOUN
ejpam-3975	21	2	:	:	PUNCT
ejpam-3975	21	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3975	https://doi.org/10.29020/nybg.ejpam.v14i3.3975	NOUN
ejpam-3975	21	4	email	email	NOUN
ejpam-3975	21	5	addresses	address	NOUN
ejpam-3975	21	6	:	:	PUNCT
ejpam-3975	21	7	raicah.rakim@gmail.com	raicah.rakim@gmail.com	X
ejpam-3975	21	8	(	(	PUNCT
ejpam-3975	21	9	r.	r.	PROPN
ejpam-3975	21	10	rakim	rakim	PROPN
ejpam-3975	21	11	)	)	PUNCT
ejpam-3975	21	12	,	,	PUNCT
ejpam-3975	21	13	helenrara@yahoo.com	helenrara@yahoo.com	X
ejpam-3975	22	1	(	(	PUNCT
ejpam-3975	22	2	h.	h.	PROPN
ejpam-3975	22	3	rara	rara	PROPN
ejpam-3975	22	4	)	)	PUNCT
ejpam-3975	22	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3975	22	6	803	803	NUM
ejpam-3975	23	1	©	©	PROPN
ejpam-3975	23	2	2021	2021	NUM
ejpam-3975	23	3	ejpam	ejpam	VERB
ejpam-3975	23	4	all	all	DET
ejpam-3975	23	5	rights	right	NOUN
ejpam-3975	23	6	reserved	reserve	VERB
ejpam-3975	23	7	.	.	PUNCT
ejpam-3975	24	1	r.	r.	PROPN
ejpam-3975	24	2	rakim	rakim	PROPN
ejpam-3975	24	3	,	,	PUNCT
ejpam-3975	24	4	h.	h.	PROPN
ejpam-3975	24	5	rara	rara	PROPN
ejpam-3975	24	6	/	/	SYM
ejpam-3975	24	7	eur	eur	PROPN
ejpam-3975	24	8	.	.	PUNCT
ejpam-3975	25	1	j.	j.	PROPN
ejpam-3975	25	2	pure	pure	PROPN
ejpam-3975	25	3	appl	appl	PROPN
ejpam-3975	25	4	.	.	PROPN
ejpam-3975	25	5	math	math	PROPN
ejpam-3975	25	6	,	,	PUNCT
ejpam-3975	25	7	14	14	NUM
ejpam-3975	25	8	(	(	PUNCT
ejpam-3975	25	9	3	3	NUM
ejpam-3975	25	10	)	)	PUNCT
ejpam-3975	25	11	(	(	PUNCT
ejpam-3975	25	12	2021	2021	NUM
ejpam-3975	25	13	)	)	PUNCT
ejpam-3975	25	14	,	,	PUNCT
ejpam-3975	25	15	803	803	NUM
ejpam-3975	25	16	-	-	SYM
ejpam-3975	25	17	815	815	NUM
ejpam-3975	25	18	804	804	NUM
ejpam-3975	25	19	a	a	DET
ejpam-3975	25	20	graph	graph	NOUN
ejpam-3975	25	21	h	h	NOUN
ejpam-3975	25	22	=	=	PUNCT
ejpam-3975	25	23	(	(	PUNCT
ejpam-3975	25	24	v	v	NOUN
ejpam-3975	25	25	(	(	PUNCT
ejpam-3975	25	26	h	h	NOUN
ejpam-3975	25	27	)	)	PUNCT
ejpam-3975	25	28	,	,	PUNCT
ejpam-3975	25	29	e(h	e(h	PROPN
ejpam-3975	25	30	)	)	PUNCT
ejpam-3975	25	31	)	)	PUNCT
ejpam-3975	25	32	is	be	AUX
ejpam-3975	25	33	a	a	DET
ejpam-3975	25	34	subgraph	subgraph	NOUN
ejpam-3975	25	35	of	of	ADP
ejpam-3975	25	36	a	a	DET
ejpam-3975	25	37	graph	graph	NOUN
ejpam-3975	25	38	g	g	NOUN
ejpam-3975	25	39	=	=	PUNCT
ejpam-3975	25	40	(	(	PUNCT
ejpam-3975	25	41	v	v	NOUN
ejpam-3975	25	42	(	(	PUNCT
ejpam-3975	25	43	g	g	NOUN
ejpam-3975	25	44	)	)	PUNCT
ejpam-3975	25	45	,	,	PUNCT
ejpam-3975	25	46	e(g	e(g	PROPN
ejpam-3975	25	47	)	)	PUNCT
ejpam-3975	25	48	)	)	PUNCT
ejpam-3975	26	1	if	if	SCONJ
ejpam-3975	26	2	v	v	X
ejpam-3975	26	3	(	(	PUNCT
ejpam-3975	26	4	h	h	NOUN
ejpam-3975	26	5	)	)	PUNCT
ejpam-3975	26	6	⊆	⊆	NUM
ejpam-3975	26	7	v	v	NOUN
ejpam-3975	26	8	(	(	PUNCT
ejpam-3975	26	9	g	g	NOUN
ejpam-3975	26	10	)	)	PUNCT
ejpam-3975	26	11	and	and	CCONJ
ejpam-3975	26	12	e(h	e(h	NOUN
ejpam-3975	26	13	)	)	PUNCT
ejpam-3975	26	14	⊆	⊆	NUM
ejpam-3975	26	15	e(g	e(g	PROPN
ejpam-3975	26	16	)	)	PUNCT
ejpam-3975	26	17	.	.	PUNCT
ejpam-3975	27	1	if	if	SCONJ
ejpam-3975	27	2	c	c	PROPN
ejpam-3975	27	3	⊆	⊆	NUM
ejpam-3975	27	4	v	v	NOUN
ejpam-3975	27	5	(	(	PUNCT
ejpam-3975	27	6	g	g	NOUN
ejpam-3975	27	7	)	)	PUNCT
ejpam-3975	27	8	,	,	PUNCT
ejpam-3975	27	9	then	then	ADV
ejpam-3975	27	10	the	the	DET
ejpam-3975	27	11	induced	induced	ADJ
ejpam-3975	27	12	subgraph	subgraph	NOUN
ejpam-3975	27	13	〈	〈	PROPN
ejpam-3975	27	14	c	c	NOUN
ejpam-3975	27	15	〉	〉	NUM
ejpam-3975	27	16	of	of	ADP
ejpam-3975	27	17	g	g	PROPN
ejpam-3975	27	18	is	be	AUX
ejpam-3975	27	19	the	the	DET
ejpam-3975	27	20	graph	graph	NOUN
ejpam-3975	27	21	with	with	ADP
ejpam-3975	27	22	vertex	vertex	NOUN
ejpam-3975	27	23	set	set	VERB
ejpam-3975	27	24	c	c	PROPN
ejpam-3975	27	25	and	and	CCONJ
ejpam-3975	27	26	such	such	ADJ
ejpam-3975	28	1	that	that	SCONJ
ejpam-3975	28	2	uv	uv	PROPN
ejpam-3975	28	3	∈	∈	PROPN
ejpam-3975	28	4	e(〈c	e(〈c	PROPN
ejpam-3975	28	5	〉	〉	PROPN
ejpam-3975	28	6	)	)	PUNCT
ejpam-3975	28	7	whenever	whenever	SCONJ
ejpam-3975	28	8	u	u	NOUN
ejpam-3975	28	9	,	,	PUNCT
ejpam-3975	28	10	v	v	ADP
ejpam-3975	28	11	∈	∈	NOUN
ejpam-3975	28	12	c	c	NOUN
ejpam-3975	28	13	and	and	CCONJ
ejpam-3975	28	14	uv	uv	PROPN
ejpam-3975	28	15	∈	∈	PROPN
ejpam-3975	28	16	e(g	e(g	PROPN
ejpam-3975	28	17	)	)	PUNCT
ejpam-3975	28	18	.	.	PUNCT
ejpam-3975	29	1	domination	domination	NOUN
ejpam-3975	29	2	in	in	ADP
ejpam-3975	29	3	graphs	graph	NOUN
ejpam-3975	29	4	is	be	AUX
ejpam-3975	29	5	one	one	NUM
ejpam-3975	29	6	of	of	ADP
ejpam-3975	29	7	the	the	DET
ejpam-3975	29	8	fastest	fast	ADJ
ejpam-3975	29	9	growing	grow	VERB
ejpam-3975	29	10	research	research	NOUN
ejpam-3975	29	11	areas	area	NOUN
ejpam-3975	29	12	in	in	ADP
ejpam-3975	29	13	graph	graph	NOUN
ejpam-3975	29	14	theory	theory	NOUN
ejpam-3975	29	15	.	.	PUNCT
ejpam-3975	30	1	since	since	SCONJ
ejpam-3975	30	2	then	then	ADV
ejpam-3975	30	3	it	it	PRON
ejpam-3975	30	4	has	have	AUX
ejpam-3975	30	5	been	be	AUX
ejpam-3975	30	6	an	an	DET
ejpam-3975	30	7	extensively	extensively	ADV
ejpam-3975	30	8	investigated	investigate	VERB
ejpam-3975	30	9	branch	branch	NOUN
ejpam-3975	30	10	of	of	ADP
ejpam-3975	30	11	graph	graph	NOUN
ejpam-3975	30	12	theory	theory	NOUN
ejpam-3975	30	13	.	.	PUNCT
ejpam-3975	31	1	this	this	PRON
ejpam-3975	31	2	is	be	AUX
ejpam-3975	31	3	largely	largely	ADV
ejpam-3975	31	4	due	due	ADJ
ejpam-3975	31	5	to	to	ADP
ejpam-3975	31	6	a	a	DET
ejpam-3975	31	7	variety	variety	NOUN
ejpam-3975	31	8	of	of	ADP
ejpam-3975	31	9	new	new	ADJ
ejpam-3975	31	10	parameters	parameter	NOUN
ejpam-3975	31	11	that	that	PRON
ejpam-3975	31	12	can	can	AUX
ejpam-3975	31	13	be	be	AUX
ejpam-3975	31	14	developed	develop	VERB
ejpam-3975	31	15	from	from	ADP
ejpam-3975	31	16	the	the	DET
ejpam-3975	31	17	basic	basic	ADJ
ejpam-3975	31	18	definition	definition	NOUN
ejpam-3975	31	19	of	of	ADP
ejpam-3975	31	20	domination	domination	NOUN
ejpam-3975	31	21	and	and	CCONJ
ejpam-3975	31	22	its	its	PRON
ejpam-3975	31	23	wide	wide	ADJ
ejpam-3975	31	24	range	range	NOUN
ejpam-3975	31	25	of	of	ADP
ejpam-3975	31	26	applications	application	NOUN
ejpam-3975	31	27	to	to	ADP
ejpam-3975	31	28	other	other	ADJ
ejpam-3975	31	29	fields	field	NOUN
ejpam-3975	31	30	of	of	ADP
ejpam-3975	31	31	study	study	NOUN
ejpam-3975	31	32	.	.	PUNCT
ejpam-3975	32	1	many	many	ADJ
ejpam-3975	32	2	authors	author	NOUN
ejpam-3975	32	3	contribute	contribute	VERB
ejpam-3975	32	4	several	several	ADJ
ejpam-3975	32	5	interesting	interesting	ADJ
ejpam-3975	32	6	domination	domination	NOUN
ejpam-3975	32	7	parameters	parameter	NOUN
ejpam-3975	32	8	to	to	PART
ejpam-3975	32	9	nurture	nurture	VERB
ejpam-3975	32	10	the	the	DET
ejpam-3975	32	11	growth	growth	NOUN
ejpam-3975	32	12	of	of	ADP
ejpam-3975	32	13	this	this	DET
ejpam-3975	32	14	research	research	NOUN
ejpam-3975	32	15	area	area	NOUN
ejpam-3975	32	16	.	.	PUNCT
ejpam-3975	33	1	in	in	ADP
ejpam-3975	33	2	2015	2015	NUM
ejpam-3975	33	3	,	,	PUNCT
ejpam-3975	33	4	natarajan	natarajan	PROPN
ejpam-3975	33	5	and	and	CCONJ
ejpam-3975	33	6	ayyaswamy	ayyaswamy	PROPN
ejpam-3975	33	7	[	[	X
ejpam-3975	33	8	3	3	NUM
ejpam-3975	33	9	]	]	PUNCT
ejpam-3975	33	10	introduced	introduce	VERB
ejpam-3975	33	11	a	a	DET
ejpam-3975	33	12	new	new	ADJ
ejpam-3975	33	13	domination	domination	NOUN
ejpam-3975	33	14	parameter	parameter	NOUN
ejpam-3975	33	15	called	call	VERB
ejpam-3975	33	16	the	the	DET
ejpam-3975	33	17	hop	hop	NOUN
ejpam-3975	33	18	domination	domination	NOUN
ejpam-3975	33	19	number	number	NOUN
ejpam-3975	33	20	of	of	ADP
ejpam-3975	33	21	a	a	DET
ejpam-3975	33	22	graph	graph	NOUN
ejpam-3975	33	23	.	.	PUNCT
ejpam-3975	34	1	in	in	ADP
ejpam-3975	34	2	2016	2016	NUM
ejpam-3975	34	3	,	,	PUNCT
ejpam-3975	34	4	some	some	DET
ejpam-3975	34	5	variations	variation	NOUN
ejpam-3975	34	6	of	of	ADP
ejpam-3975	34	7	hop	hop	NOUN
ejpam-3975	34	8	domination	domination	NOUN
ejpam-3975	34	9	was	be	AUX
ejpam-3975	34	10	studied	study	VERB
ejpam-3975	34	11	by	by	ADP
ejpam-3975	34	12	pabilona	pabilona	NOUN
ejpam-3975	34	13	and	and	CCONJ
ejpam-3975	34	14	rara	rara	NOUN
ejpam-3975	35	1	[	[	X
ejpam-3975	35	2	4	4	NUM
ejpam-3975	35	3	]	]	PUNCT
ejpam-3975	35	4	.	.	PUNCT
ejpam-3975	36	1	a	a	DET
ejpam-3975	36	2	subset	subset	NOUN
ejpam-3975	36	3	s	s	X
ejpam-3975	36	4	of	of	ADP
ejpam-3975	36	5	v	v	NOUN
ejpam-3975	36	6	(	(	PUNCT
ejpam-3975	36	7	g	g	NOUN
ejpam-3975	36	8	)	)	PUNCT
ejpam-3975	36	9	is	be	AUX
ejpam-3975	36	10	a	a	DET
ejpam-3975	36	11	hop	hop	NOUN
ejpam-3975	36	12	dominating	dominating	NOUN
ejpam-3975	36	13	set	set	NOUN
ejpam-3975	36	14	of	of	ADP
ejpam-3975	36	15	g	g	PROPN
ejpam-3975	36	16	if	if	SCONJ
ejpam-3975	36	17	for	for	ADP
ejpam-3975	36	18	every	every	PRON
ejpam-3975	36	19	v	v	NUM
ejpam-3975	36	20	∈	∈	NOUN
ejpam-3975	36	21	v	v	NOUN
ejpam-3975	36	22	(	(	PUNCT
ejpam-3975	36	23	g	g	NOUN
ejpam-3975	36	24	)	)	PUNCT
ejpam-3975	36	25	\	\	PROPN
ejpam-3975	37	1	s	s	X
ejpam-3975	37	2	,	,	PUNCT
ejpam-3975	37	3	there	there	PRON
ejpam-3975	37	4	exists	exist	VERB
ejpam-3975	37	5	u	u	PROPN
ejpam-3975	37	6	∈	∈	PROPN
ejpam-3975	37	7	s	s	VERB
ejpam-3975	37	8	such	such	ADJ
ejpam-3975	37	9	that	that	DET
ejpam-3975	37	10	dg(u	dg(u	ADJ
ejpam-3975	37	11	,	,	PUNCT
ejpam-3975	37	12	v	v	NOUN
ejpam-3975	37	13	)	)	PUNCT
ejpam-3975	37	14	=	=	SYM
ejpam-3975	37	15	2	2	X
ejpam-3975	37	16	.	.	X
ejpam-3975	37	17	the	the	DET
ejpam-3975	37	18	smallest	small	ADJ
ejpam-3975	37	19	cardinality	cardinality	NOUN
ejpam-3975	37	20	of	of	ADP
ejpam-3975	37	21	a	a	DET
ejpam-3975	37	22	hop	hop	NOUN
ejpam-3975	37	23	dominating	dominating	NOUN
ejpam-3975	37	24	set	set	NOUN
ejpam-3975	37	25	of	of	ADP
ejpam-3975	37	26	g	g	NOUN
ejpam-3975	37	27	,	,	PUNCT
ejpam-3975	37	28	denoted	denote	VERB
ejpam-3975	37	29	by	by	ADP
ejpam-3975	37	30	γh(g	γh(g	NOUN
ejpam-3975	37	31	)	)	PUNCT
ejpam-3975	37	32	is	be	AUX
ejpam-3975	37	33	the	the	DET
ejpam-3975	37	34	hop	hop	NOUN
ejpam-3975	37	35	domination	domination	NOUN
ejpam-3975	37	36	number	number	NOUN
ejpam-3975	37	37	of	of	ADP
ejpam-3975	37	38	g.	g.	PROPN
ejpam-3975	37	39	a	a	DET
ejpam-3975	37	40	hop	hop	NOUN
ejpam-3975	37	41	dominating	dominating	NOUN
ejpam-3975	37	42	set	set	NOUN
ejpam-3975	37	43	s	s	NOUN
ejpam-3975	37	44	of	of	ADP
ejpam-3975	37	45	g	g	NOUN
ejpam-3975	37	46	with	with	ADP
ejpam-3975	37	47	cardinality	cardinality	NOUN
ejpam-3975	37	48	γh(g	γh(g	NOUN
ejpam-3975	37	49	)	)	PUNCT
ejpam-3975	37	50	is	be	AUX
ejpam-3975	37	51	called	call	VERB
ejpam-3975	37	52	a	a	DET
ejpam-3975	37	53	γh	γh	ADV
ejpam-3975	37	54	-	-	PUNCT
ejpam-3975	37	55	set	set	NOUN
ejpam-3975	37	56	of	of	ADP
ejpam-3975	37	57	g.	g.	PROPN
ejpam-3975	37	58	at	at	ADP
ejpam-3975	37	59	the	the	DET
ejpam-3975	37	60	same	same	ADJ
ejpam-3975	37	61	time	time	NOUN
ejpam-3975	37	62	of	of	ADP
ejpam-3975	37	63	this	this	DET
ejpam-3975	37	64	year	year	NOUN
ejpam-3975	37	65	,	,	PUNCT
ejpam-3975	37	66	saromines	saromine	NOUN
ejpam-3975	37	67	and	and	CCONJ
ejpam-3975	37	68	rara	rara	NOUN
ejpam-3975	38	1	[	[	X
ejpam-3975	38	2	5	5	NUM
ejpam-3975	38	3	]	]	PUNCT
ejpam-3975	38	4	introduced	introduce	VERB
ejpam-3975	38	5	a	a	DET
ejpam-3975	38	6	new	new	ADJ
ejpam-3975	38	7	hop	hop	NOUN
ejpam-3975	38	8	domination	domination	NOUN
ejpam-3975	38	9	parameter	parameter	NOUN
ejpam-3975	38	10	called	call	VERB
ejpam-3975	38	11	the	the	DET
ejpam-3975	38	12	perfect	perfect	ADJ
ejpam-3975	38	13	hop	hop	NOUN
ejpam-3975	38	14	domination	domination	NOUN
ejpam-3975	38	15	in	in	ADP
ejpam-3975	38	16	graphs	graph	NOUN
ejpam-3975	38	17	in	in	ADP
ejpam-3975	38	18	which	which	PRON
ejpam-3975	38	19	they	they	PRON
ejpam-3975	38	20	characterized	characterize	VERB
ejpam-3975	38	21	the	the	DET
ejpam-3975	38	22	perfect	perfect	ADJ
ejpam-3975	38	23	hop	hop	NOUN
ejpam-3975	38	24	dominating	dominating	NOUN
ejpam-3975	38	25	set	set	NOUN
ejpam-3975	38	26	of	of	ADP
ejpam-3975	38	27	the	the	DET
ejpam-3975	38	28	join	join	NOUN
ejpam-3975	38	29	and	and	CCONJ
ejpam-3975	38	30	corona	corona	NOUN
ejpam-3975	38	31	of	of	ADP
ejpam-3975	38	32	graphs	graph	NOUN
ejpam-3975	38	33	.	.	PUNCT
ejpam-3975	39	1	a	a	DET
ejpam-3975	39	2	subset	subset	NOUN
ejpam-3975	39	3	s	s	X
ejpam-3975	39	4	of	of	ADP
ejpam-3975	39	5	v	v	NOUN
ejpam-3975	39	6	(	(	PUNCT
ejpam-3975	39	7	g	g	NOUN
ejpam-3975	39	8	)	)	PUNCT
ejpam-3975	39	9	is	be	AUX
ejpam-3975	39	10	a	a	DET
ejpam-3975	39	11	perfect	perfect	ADJ
ejpam-3975	39	12	hop	hop	NOUN
ejpam-3975	39	13	dominating	dominating	NOUN
ejpam-3975	39	14	set	set	NOUN
ejpam-3975	39	15	of	of	ADP
ejpam-3975	39	16	g	g	PROPN
ejpam-3975	39	17	if	if	SCONJ
ejpam-3975	39	18	for	for	ADP
ejpam-3975	39	19	every	every	PRON
ejpam-3975	39	20	v	v	NUM
ejpam-3975	39	21	∈	∈	NOUN
ejpam-3975	39	22	v	v	NOUN
ejpam-3975	39	23	(	(	PUNCT
ejpam-3975	39	24	g	g	NOUN
ejpam-3975	39	25	)	)	PUNCT
ejpam-3975	39	26	\	\	PROPN
ejpam-3975	40	1	s	s	X
ejpam-3975	40	2	,	,	PUNCT
ejpam-3975	40	3	there	there	PRON
ejpam-3975	40	4	is	be	VERB
ejpam-3975	40	5	exactly	exactly	ADV
ejpam-3975	40	6	one	one	NUM
ejpam-3975	40	7	vertex	vertex	NOUN
ejpam-3975	40	8	u	u	NOUN
ejpam-3975	40	9	∈	∈	NOUN
ejpam-3975	40	10	s	s	VERB
ejpam-3975	40	11	such	such	ADJ
ejpam-3975	40	12	that	that	DET
ejpam-3975	40	13	dg(u	dg(u	ADJ
ejpam-3975	40	14	,	,	PUNCT
ejpam-3975	40	15	v	v	NOUN
ejpam-3975	40	16	)	)	PUNCT
ejpam-3975	40	17	=	=	SYM
ejpam-3975	40	18	2	2	X
ejpam-3975	40	19	.	.	X
ejpam-3975	40	20	the	the	DET
ejpam-3975	40	21	smallest	small	ADJ
ejpam-3975	40	22	cardinality	cardinality	NOUN
ejpam-3975	40	23	of	of	ADP
ejpam-3975	40	24	a	a	DET
ejpam-3975	40	25	perfect	perfect	ADJ
ejpam-3975	40	26	hop	hop	NOUN
ejpam-3975	40	27	dominating	dominating	NOUN
ejpam-3975	40	28	set	set	NOUN
ejpam-3975	40	29	of	of	ADP
ejpam-3975	40	30	g	g	NOUN
ejpam-3975	40	31	,	,	PUNCT
ejpam-3975	40	32	denoted	denote	VERB
ejpam-3975	40	33	by	by	ADP
ejpam-3975	40	34	γph(g	γph(g	NOUN
ejpam-3975	40	35	)	)	PUNCT
ejpam-3975	40	36	)	)	PUNCT
ejpam-3975	41	1	is	be	AUX
ejpam-3975	41	2	the	the	DET
ejpam-3975	41	3	perfect	perfect	ADJ
ejpam-3975	41	4	hop	hop	NOUN
ejpam-3975	41	5	domination	domination	NOUN
ejpam-3975	41	6	number	number	NOUN
ejpam-3975	41	7	of	of	ADP
ejpam-3975	41	8	g.	g.	PROPN
ejpam-3975	41	9	a	a	DET
ejpam-3975	41	10	perfect	perfect	ADJ
ejpam-3975	41	11	hop	hop	NOUN
ejpam-3975	41	12	dominating	dominating	NOUN
ejpam-3975	41	13	set	set	NOUN
ejpam-3975	41	14	)	)	PUNCT
ejpam-3975	41	15	s	s	PROPN
ejpam-3975	41	16	of	of	ADP
ejpam-3975	41	17	g	g	NOUN
ejpam-3975	41	18	with	with	ADP
ejpam-3975	41	19	cardinality	cardinality	PROPN
ejpam-3975	41	20	γph(g	γph(g	NOUN
ejpam-3975	41	21	)	)	PUNCT
ejpam-3975	41	22	)	)	PUNCT
ejpam-3975	42	1	is	be	AUX
ejpam-3975	42	2	called	call	VERB
ejpam-3975	42	3	a	a	DET
ejpam-3975	42	4	γph	γph	NOUN
ejpam-3975	42	5	-	-	PUNCT
ejpam-3975	42	6	set	set	NOUN
ejpam-3975	42	7	)	)	PUNCT
ejpam-3975	42	8	of	of	ADP
ejpam-3975	42	9	g.	g.	PROPN
ejpam-3975	42	10	in	in	ADP
ejpam-3975	42	11	2018	2018	NUM
ejpam-3975	42	12	,	,	PUNCT
ejpam-3975	42	13	rara	rara	NOUN
ejpam-3975	42	14	and	and	CCONJ
ejpam-3975	42	15	rakim	rakim	PROPN
ejpam-3975	42	16	present	present	VERB
ejpam-3975	42	17	a	a	DET
ejpam-3975	42	18	further	further	ADJ
ejpam-3975	42	19	study	study	NOUN
ejpam-3975	42	20	on	on	ADP
ejpam-3975	42	21	perfect	perfect	ADJ
ejpam-3975	42	22	hop	hop	NOUN
ejpam-3975	42	23	dominaton	dominaton	NOUN
ejpam-3975	42	24	in	in	ADP
ejpam-3975	42	25	graphs	graph	NOUN
ejpam-3975	42	26	[	[	X
ejpam-3975	42	27	5	5	NUM
ejpam-3975	42	28	]	]	PUNCT
ejpam-3975	42	29	and	and	CCONJ
ejpam-3975	42	30	in	in	ADP
ejpam-3975	42	31	the	the	DET
ejpam-3975	42	32	following	following	ADJ
ejpam-3975	42	33	year	year	NOUN
ejpam-3975	42	34	we	we	PRON
ejpam-3975	42	35	also	also	ADV
ejpam-3975	42	36	introduce	introduce	VERB
ejpam-3975	42	37	connected	connected	ADJ
ejpam-3975	42	38	perfect	perfect	ADJ
ejpam-3975	42	39	hop	hop	NOUN
ejpam-3975	42	40	domination	domination	NOUN
ejpam-3975	42	41	in	in	ADP
ejpam-3975	42	42	graphs	graph	NOUN
ejpam-3975	42	43	under	under	ADP
ejpam-3975	42	44	some	some	DET
ejpam-3975	42	45	binary	binary	ADJ
ejpam-3975	42	46	operations	operation	NOUN
ejpam-3975	43	1	[	[	X
ejpam-3975	43	2	6	6	NUM
ejpam-3975	43	3	]	]	PUNCT
ejpam-3975	43	4	.	.	PUNCT
ejpam-3975	44	1	a	a	DET
ejpam-3975	44	2	subset	subset	NOUN
ejpam-3975	44	3	s	s	X
ejpam-3975	44	4	of	of	ADP
ejpam-3975	44	5	v	v	NOUN
ejpam-3975	44	6	(	(	PUNCT
ejpam-3975	44	7	g	g	NOUN
ejpam-3975	44	8	)	)	PUNCT
ejpam-3975	44	9	is	be	AUX
ejpam-3975	44	10	a	a	DET
ejpam-3975	44	11	total	total	ADJ
ejpam-3975	44	12	hop	hop	NOUN
ejpam-3975	44	13	dominating	dominating	NOUN
ejpam-3975	44	14	set	set	NOUN
ejpam-3975	44	15	[	[	X
ejpam-3975	44	16	4	4	NUM
ejpam-3975	44	17	]	]	PUNCT
ejpam-3975	44	18	of	of	ADP
ejpam-3975	44	19	g	g	PROPN
ejpam-3975	44	20	if	if	SCONJ
ejpam-3975	44	21	for	for	ADP
ejpam-3975	44	22	every	every	DET
ejpam-3975	44	23	v	v	NUM
ejpam-3975	44	24	∈	∈	NOUN
ejpam-3975	44	25	v	v	NOUN
ejpam-3975	44	26	(	(	PUNCT
ejpam-3975	44	27	g	g	NOUN
ejpam-3975	44	28	)	)	PUNCT
ejpam-3975	44	29	,	,	PUNCT
ejpam-3975	44	30	there	there	PRON
ejpam-3975	44	31	exists	exist	VERB
ejpam-3975	44	32	u	u	PROPN
ejpam-3975	44	33	∈	∈	PROPN
ejpam-3975	44	34	s	s	VERB
ejpam-3975	44	35	such	such	ADJ
ejpam-3975	44	36	that	that	DET
ejpam-3975	44	37	dg(u	dg(u	ADJ
ejpam-3975	44	38	,	,	PUNCT
ejpam-3975	44	39	v	v	NOUN
ejpam-3975	44	40	)	)	PUNCT
ejpam-3975	44	41	=	=	SYM
ejpam-3975	45	1	2	2	X
ejpam-3975	45	2	.	.	X
ejpam-3975	45	3	the	the	DET
ejpam-3975	45	4	smallest	small	ADJ
ejpam-3975	45	5	cardinality	cardinality	NOUN
ejpam-3975	45	6	of	of	ADP
ejpam-3975	45	7	a	a	DET
ejpam-3975	45	8	total	total	ADJ
ejpam-3975	45	9	hop	hop	NOUN
ejpam-3975	45	10	dominating	dominating	NOUN
ejpam-3975	45	11	set	set	NOUN
ejpam-3975	45	12	of	of	ADP
ejpam-3975	45	13	g	g	NOUN
ejpam-3975	45	14	,	,	PUNCT
ejpam-3975	45	15	denoted	denote	VERB
ejpam-3975	45	16	by	by	ADP
ejpam-3975	45	17	γth(g	γth(g	NOUN
ejpam-3975	45	18	)	)	PUNCT
ejpam-3975	45	19	is	be	AUX
ejpam-3975	45	20	called	call	VERB
ejpam-3975	45	21	the	the	DET
ejpam-3975	45	22	total	total	ADJ
ejpam-3975	45	23	hop	hop	NOUN
ejpam-3975	45	24	domination	domination	NOUN
ejpam-3975	45	25	number	number	NOUN
ejpam-3975	45	26	of	of	ADP
ejpam-3975	45	27	g.	g.	PROPN
ejpam-3975	45	28	any	any	DET
ejpam-3975	45	29	total	total	ADJ
ejpam-3975	45	30	hop	hop	NOUN
ejpam-3975	45	31	dominating	dominating	NOUN
ejpam-3975	45	32	set	set	NOUN
ejpam-3975	45	33	of	of	ADP
ejpam-3975	45	34	g	g	PROPN
ejpam-3975	45	35	with	with	ADP
ejpam-3975	45	36	cardinality	cardinality	PROPN
ejpam-3975	45	37	γth(g	γth(g	NOUN
ejpam-3975	45	38	)	)	PUNCT
ejpam-3975	45	39	is	be	AUX
ejpam-3975	45	40	called	call	VERB
ejpam-3975	45	41	a	a	DET
ejpam-3975	45	42	γth	γth	NOUN
ejpam-3975	45	43	-	-	PUNCT
ejpam-3975	45	44	set	set	NOUN
ejpam-3975	45	45	.	.	PUNCT
ejpam-3975	46	1	a	a	DET
ejpam-3975	46	2	set	set	NOUN
ejpam-3975	46	3	s	s	NOUN
ejpam-3975	46	4	⊆	⊆	NUM
ejpam-3975	46	5	v	v	NOUN
ejpam-3975	46	6	(	(	PUNCT
ejpam-3975	46	7	g	g	NOUN
ejpam-3975	46	8	)	)	PUNCT
ejpam-3975	46	9	is	be	AUX
ejpam-3975	46	10	a	a	DET
ejpam-3975	46	11	total	total	ADJ
ejpam-3975	46	12	point	point	ADV
ejpam-3975	46	13	-	-	PUNCT
ejpam-3975	46	14	wise	wise	ADJ
ejpam-3975	46	15	non	non	ADJ
ejpam-3975	46	16	-	-	ADJ
ejpam-3975	46	17	dominating	dominating	ADJ
ejpam-3975	46	18	set	set	NOUN
ejpam-3975	46	19	[	[	X
ejpam-3975	46	20	4	4	NUM
ejpam-3975	46	21	]	]	PUNCT
ejpam-3975	46	22	of	of	ADP
ejpam-3975	46	23	g	g	PROPN
ejpam-3975	46	24	if	if	SCONJ
ejpam-3975	46	25	for	for	ADP
ejpam-3975	46	26	every	every	DET
ejpam-3975	46	27	v	v	NUM
ejpam-3975	46	28	∈	∈	NOUN
ejpam-3975	46	29	v	v	NOUN
ejpam-3975	46	30	(	(	PUNCT
ejpam-3975	46	31	g	g	NOUN
ejpam-3975	46	32	)	)	PUNCT
ejpam-3975	46	33	,	,	PUNCT
ejpam-3975	46	34	there	there	PRON
ejpam-3975	46	35	is	be	VERB
ejpam-3975	46	36	a	a	DET
ejpam-3975	46	37	vertex	vertex	NOUN
ejpam-3975	46	38	u	u	NOUN
ejpam-3975	46	39	∈	∈	NOUN
ejpam-3975	46	40	s	s	VERB
ejpam-3975	46	41	such	such	ADJ
ejpam-3975	46	42	that	that	DET
ejpam-3975	46	43	v	v	NOUN
ejpam-3975	46	44	/∈	/∈	PUNCT
ejpam-3975	46	45	ng(u	ng(u	NOUN
ejpam-3975	46	46	)	)	PUNCT
ejpam-3975	46	47	.	.	PUNCT
ejpam-3975	47	1	the	the	DET
ejpam-3975	47	2	smallest	small	ADJ
ejpam-3975	47	3	cardinality	cardinality	NOUN
ejpam-3975	47	4	of	of	ADP
ejpam-3975	47	5	a	a	DET
ejpam-3975	47	6	total	total	ADJ
ejpam-3975	47	7	point	point	ADV
ejpam-3975	47	8	-	-	PUNCT
ejpam-3975	47	9	wise	wise	ADJ
ejpam-3975	47	10	non	non	ADJ
ejpam-3975	47	11	-	-	ADJ
ejpam-3975	47	12	dominating	dominating	ADJ
ejpam-3975	47	13	set	set	NOUN
ejpam-3975	47	14	of	of	ADP
ejpam-3975	47	15	g	g	NOUN
ejpam-3975	47	16	,	,	PUNCT
ejpam-3975	47	17	denoted	denote	VERB
ejpam-3975	47	18	by	by	ADP
ejpam-3975	47	19	tpnd(g	tpnd(g	NOUN
ejpam-3975	47	20	)	)	PUNCT
ejpam-3975	47	21	is	be	AUX
ejpam-3975	47	22	called	call	VERB
ejpam-3975	47	23	the	the	DET
ejpam-3975	47	24	total	total	ADJ
ejpam-3975	47	25	point	point	ADV
ejpam-3975	47	26	-	-	PUNCT
ejpam-3975	47	27	wise	wise	ADJ
ejpam-3975	47	28	non	non	ADJ
ejpam-3975	47	29	-	-	ADJ
ejpam-3975	47	30	domination	domination	ADJ
ejpam-3975	47	31	number	number	NOUN
ejpam-3975	47	32	of	of	ADP
ejpam-3975	47	33	g.	g.	PROPN
ejpam-3975	47	34	any	any	DET
ejpam-3975	47	35	total	total	ADJ
ejpam-3975	47	36	point	point	ADV
ejpam-3975	47	37	-	-	PUNCT
ejpam-3975	47	38	wise	wise	ADJ
ejpam-3975	47	39	non	non	ADJ
ejpam-3975	47	40	-	-	ADJ
ejpam-3975	47	41	dominating	dominating	ADJ
ejpam-3975	47	42	set	set	NOUN
ejpam-3975	47	43	s	s	NOUN
ejpam-3975	47	44	of	of	ADP
ejpam-3975	47	45	g	g	NOUN
ejpam-3975	47	46	with	with	ADP
ejpam-3975	47	47	|s|	|s|	NOUN
ejpam-3975	47	48	=	=	PUNCT
ejpam-3975	47	49	tppnd(g	tppnd(g	PROPN
ejpam-3975	47	50	)	)	PUNCT
ejpam-3975	47	51	is	be	AUX
ejpam-3975	47	52	called	call	VERB
ejpam-3975	47	53	a	a	DET
ejpam-3975	47	54	tpnd	tpnd	NOUN
ejpam-3975	47	55	-	-	PUNCT
ejpam-3975	47	56	set	set	NOUN
ejpam-3975	47	57	.	.	PUNCT
ejpam-3975	48	1	a	a	DET
ejpam-3975	48	2	set	set	NOUN
ejpam-3975	48	3	s	s	NOUN
ejpam-3975	48	4	⊆	⊆	NUM
ejpam-3975	48	5	v	v	NOUN
ejpam-3975	48	6	(	(	PUNCT
ejpam-3975	48	7	g	g	NOUN
ejpam-3975	48	8	)	)	PUNCT
ejpam-3975	48	9	is	be	AUX
ejpam-3975	48	10	a	a	DET
ejpam-3975	48	11	(	(	PUNCT
ejpam-3975	48	12	1	1	NUM
ejpam-3975	48	13	,	,	PUNCT
ejpam-3975	48	14	2)∗-dominating	2)∗-dominate	VERB
ejpam-3975	48	15	set	set	NOUN
ejpam-3975	48	16	[	[	X
ejpam-3975	48	17	1	1	NUM
ejpam-3975	48	18	]	]	PUNCT
ejpam-3975	48	19	of	of	ADP
ejpam-3975	48	20	g	g	PROPN
ejpam-3975	48	21	if	if	SCONJ
ejpam-3975	48	22	for	for	ADP
ejpam-3975	48	23	every	every	PRON
ejpam-3975	48	24	w	w	PROPN
ejpam-3975	48	25	∈	∈	PROPN
ejpam-3975	48	26	v	v	ADP
ejpam-3975	48	27	(	(	PUNCT
ejpam-3975	48	28	g	g	NOUN
ejpam-3975	48	29	)	)	PUNCT
ejpam-3975	48	30	\	\	PROPN
ejpam-3975	49	1	s	s	X
ejpam-3975	49	2	,	,	PUNCT
ejpam-3975	49	3	there	there	PRON
ejpam-3975	49	4	exists	exist	VERB
ejpam-3975	49	5	vertex	vertex	NOUN
ejpam-3975	49	6	x	x	X
ejpam-3975	49	7	∈	∈	NOUN
ejpam-3975	49	8	s	s	VERB
ejpam-3975	49	9	such	such	ADJ
ejpam-3975	49	10	that	that	SCONJ
ejpam-3975	49	11	wx	wx	PROPN
ejpam-3975	49	12	∈	∈	PROPN
ejpam-3975	49	13	e(g	e(g	PROPN
ejpam-3975	49	14	)	)	PUNCT
ejpam-3975	49	15	and	and	CCONJ
ejpam-3975	49	16	for	for	ADP
ejpam-3975	49	17	every	every	DET
ejpam-3975	49	18	u	u	PROPN
ejpam-3975	49	19	∈	∈	PROPN
ejpam-3975	49	20	v	v	NOUN
ejpam-3975	49	21	(	(	PUNCT
ejpam-3975	49	22	g)\s	g)\s	NOUN
ejpam-3975	49	23	,	,	PUNCT
ejpam-3975	49	24	there	there	PRON
ejpam-3975	49	25	is	be	VERB
ejpam-3975	49	26	vertex	vertex	NOUN
ejpam-3975	49	27	v	v	ADP
ejpam-3975	49	28	∈	∈	NOUN
ejpam-3975	49	29	s	s	VERB
ejpam-3975	49	30	such	such	ADJ
ejpam-3975	49	31	that	that	DET
ejpam-3975	49	32	dg(u	dg(u	ADJ
ejpam-3975	49	33	,	,	PUNCT
ejpam-3975	49	34	v	v	NOUN
ejpam-3975	49	35	)	)	PUNCT
ejpam-3975	49	36	=	=	SYM
ejpam-3975	50	1	2	2	X
ejpam-3975	50	2	.	.	X
ejpam-3975	50	3	the	the	DET
ejpam-3975	50	4	smallest	small	ADJ
ejpam-3975	50	5	cardinality	cardinality	NOUN
ejpam-3975	50	6	of	of	ADP
ejpam-3975	50	7	a	a	PRON
ejpam-3975	50	8	(	(	PUNCT
ejpam-3975	50	9	1	1	NUM
ejpam-3975	50	10	,	,	PUNCT
ejpam-3975	50	11	2)∗-dominating	2)∗-dominate	VERB
ejpam-3975	50	12	set	set	NOUN
ejpam-3975	50	13	of	of	ADP
ejpam-3975	50	14	g	g	PROPN
ejpam-3975	50	15	is	be	AUX
ejpam-3975	50	16	called	call	VERB
ejpam-3975	50	17	the	the	DET
ejpam-3975	50	18	(	(	PUNCT
ejpam-3975	50	19	1	1	NUM
ejpam-3975	50	20	,	,	PUNCT
ejpam-3975	50	21	2)∗-domination	2)∗-domination	NOUN
ejpam-3975	50	22	number	number	NOUN
ejpam-3975	50	23	of	of	ADP
ejpam-3975	50	24	g	g	NOUN
ejpam-3975	50	25	,	,	PUNCT
ejpam-3975	50	26	denoted	denote	VERB
ejpam-3975	50	27	by	by	ADP
ejpam-3975	50	28	γ∗1,2(g	γ∗1,2(g	NOUN
ejpam-3975	50	29	)	)	PUNCT
ejpam-3975	50	30	.	.	PUNCT
ejpam-3975	51	1	a	a	DET
ejpam-3975	51	2	(	(	PUNCT
ejpam-3975	51	3	1	1	NUM
ejpam-3975	51	4	,	,	PUNCT
ejpam-3975	51	5	2)∗-dominating	2)∗-dominate	VERB
ejpam-3975	51	6	set	set	NOUN
ejpam-3975	51	7	s	s	NOUN
ejpam-3975	51	8	of	of	ADP
ejpam-3975	51	9	g	g	NOUN
ejpam-3975	51	10	with	with	ADP
ejpam-3975	51	11	cardinality	cardinality	NOUN
ejpam-3975	51	12	γ∗1,2(g	γ∗1,2(g	NOUN
ejpam-3975	51	13	)	)	PUNCT
ejpam-3975	51	14	is	be	AUX
ejpam-3975	51	15	called	call	VERB
ejpam-3975	51	16	a	a	DET
ejpam-3975	51	17	γ∗1,2	γ∗1,2	NOUN
ejpam-3975	51	18	-	-	PUNCT
ejpam-3975	51	19	set	set	NOUN
ejpam-3975	51	20	of	of	ADP
ejpam-3975	51	21	g.	g.	PROPN
ejpam-3975	51	22	for	for	ADP
ejpam-3975	51	23	other	other	ADJ
ejpam-3975	51	24	terms	term	NOUN
ejpam-3975	51	25	not	not	PART
ejpam-3975	51	26	define	define	VERB
ejpam-3975	51	27	here	here	ADV
ejpam-3975	51	28	,	,	PUNCT
ejpam-3975	51	29	refer	refer	VERB
ejpam-3975	51	30	to	to	ADP
ejpam-3975	51	31	[	[	X
ejpam-3975	51	32	2	2	NUM
ejpam-3975	51	33	]	]	PUNCT
ejpam-3975	51	34	.	.	PUNCT
ejpam-3975	52	1	in	in	ADP
ejpam-3975	52	2	the	the	DET
ejpam-3975	52	3	next	next	ADJ
ejpam-3975	52	4	section	section	NOUN
ejpam-3975	52	5	,	,	PUNCT
ejpam-3975	52	6	we	we	PRON
ejpam-3975	52	7	introduce	introduce	VERB
ejpam-3975	52	8	total	total	ADJ
ejpam-3975	52	9	perfect	perfect	ADJ
ejpam-3975	52	10	hop	hop	NOUN
ejpam-3975	52	11	dominating	dominating	NOUN
ejpam-3975	52	12	set	set	NOUN
ejpam-3975	52	13	and	and	CCONJ
ejpam-3975	52	14	explore	explore	VERB
ejpam-3975	52	15	some	some	PRON
ejpam-3975	52	16	of	of	ADP
ejpam-3975	52	17	its	its	PRON
ejpam-3975	52	18	properties	property	NOUN
ejpam-3975	52	19	.	.	PUNCT
ejpam-3975	53	1	r.	r.	PROPN
ejpam-3975	53	2	rakim	rakim	PROPN
ejpam-3975	53	3	,	,	PUNCT
ejpam-3975	53	4	h.	h.	PROPN
ejpam-3975	53	5	rara	rara	PROPN
ejpam-3975	53	6	/	/	SYM
ejpam-3975	53	7	eur	eur	PROPN
ejpam-3975	53	8	.	.	PUNCT
ejpam-3975	54	1	j.	j.	PROPN
ejpam-3975	54	2	pure	pure	PROPN
ejpam-3975	54	3	appl	appl	PROPN
ejpam-3975	54	4	.	.	PROPN
ejpam-3975	54	5	math	math	PROPN
ejpam-3975	54	6	,	,	PUNCT
ejpam-3975	54	7	14	14	NUM
ejpam-3975	54	8	(	(	PUNCT
ejpam-3975	54	9	3	3	NUM
ejpam-3975	54	10	)	)	PUNCT
ejpam-3975	54	11	(	(	PUNCT
ejpam-3975	54	12	2021	2021	NUM
ejpam-3975	54	13	)	)	PUNCT
ejpam-3975	54	14	,	,	PUNCT
ejpam-3975	54	15	803	803	NUM
ejpam-3975	54	16	-	-	SYM
ejpam-3975	54	17	815	815	NUM
ejpam-3975	54	18	805	805	NUM
ejpam-3975	54	19	2	2	NUM
ejpam-3975	54	20	.	.	PUNCT
ejpam-3975	54	21	total	total	ADJ
ejpam-3975	54	22	perfect	perfect	ADJ
ejpam-3975	54	23	hop	hop	NOUN
ejpam-3975	54	24	dominating	dominating	NOUN
ejpam-3975	54	25	set	set	NOUN
ejpam-3975	54	26	definition	definition	NOUN
ejpam-3975	54	27	2.1	2.1	NUM
ejpam-3975	54	28	.	.	PUNCT
ejpam-3975	55	1	a	a	DET
ejpam-3975	55	2	perfect	perfect	ADJ
ejpam-3975	55	3	hop	hop	NOUN
ejpam-3975	55	4	dominating	dominating	NOUN
ejpam-3975	55	5	set	set	NOUN
ejpam-3975	55	6	s	s	PROPN
ejpam-3975	55	7	of	of	ADP
ejpam-3975	55	8	v	v	NOUN
ejpam-3975	55	9	(	(	PUNCT
ejpam-3975	55	10	g	g	NOUN
ejpam-3975	55	11	)	)	PUNCT
ejpam-3975	55	12	is	be	AUX
ejpam-3975	55	13	a	a	DET
ejpam-3975	55	14	total	total	ADJ
ejpam-3975	55	15	perfect	perfect	ADJ
ejpam-3975	55	16	hop	hop	NOUN
ejpam-3975	55	17	dominating	dominating	NOUN
ejpam-3975	55	18	set	set	NOUN
ejpam-3975	55	19	of	of	ADP
ejpam-3975	55	20	g	g	PROPN
ejpam-3975	55	21	if	if	SCONJ
ejpam-3975	55	22	for	for	ADP
ejpam-3975	55	23	every	every	DET
ejpam-3975	55	24	v	v	NUM
ejpam-3975	55	25	∈	∈	NOUN
ejpam-3975	55	26	v	v	NOUN
ejpam-3975	55	27	(	(	PUNCT
ejpam-3975	55	28	g	g	NOUN
ejpam-3975	55	29	)	)	PUNCT
ejpam-3975	55	30	,	,	PUNCT
ejpam-3975	55	31	there	there	PRON
ejpam-3975	55	32	is	be	VERB
ejpam-3975	55	33	exactly	exactly	ADV
ejpam-3975	55	34	one	one	NUM
ejpam-3975	55	35	vertex	vertex	NOUN
ejpam-3975	55	36	u	u	NOUN
ejpam-3975	55	37	∈	∈	NOUN
ejpam-3975	55	38	s	s	VERB
ejpam-3975	55	39	such	such	ADJ
ejpam-3975	55	40	that	that	DET
ejpam-3975	55	41	dg(u	dg(u	ADJ
ejpam-3975	55	42	,	,	PUNCT
ejpam-3975	55	43	v	v	NOUN
ejpam-3975	55	44	)	)	PUNCT
ejpam-3975	55	45	=	=	SYM
ejpam-3975	55	46	2	2	X
ejpam-3975	55	47	.	.	X
ejpam-3975	55	48	the	the	DET
ejpam-3975	55	49	smallest	small	ADJ
ejpam-3975	55	50	cardinality	cardinality	NOUN
ejpam-3975	55	51	of	of	ADP
ejpam-3975	55	52	a	a	DET
ejpam-3975	55	53	total	total	ADJ
ejpam-3975	55	54	perfect	perfect	ADJ
ejpam-3975	55	55	hop	hop	NOUN
ejpam-3975	55	56	dominating	dominating	NOUN
ejpam-3975	55	57	set	set	NOUN
ejpam-3975	55	58	of	of	ADP
ejpam-3975	55	59	g	g	NOUN
ejpam-3975	55	60	,	,	PUNCT
ejpam-3975	55	61	denoted	denote	VERB
ejpam-3975	55	62	by	by	ADP
ejpam-3975	55	63	γtph(g	γtph(g	NOUN
ejpam-3975	55	64	)	)	PUNCT
ejpam-3975	55	65	is	be	AUX
ejpam-3975	55	66	called	call	VERB
ejpam-3975	55	67	the	the	DET
ejpam-3975	55	68	total	total	ADJ
ejpam-3975	55	69	perfect	perfect	ADJ
ejpam-3975	55	70	hop	hop	NOUN
ejpam-3975	55	71	domination	domination	NOUN
ejpam-3975	55	72	number	number	NOUN
ejpam-3975	55	73	of	of	ADP
ejpam-3975	55	74	g.	g.	PROPN
ejpam-3975	55	75	any	any	DET
ejpam-3975	55	76	total	total	ADJ
ejpam-3975	55	77	perfect	perfect	ADJ
ejpam-3975	55	78	hop	hop	NOUN
ejpam-3975	55	79	dominating	dominating	NOUN
ejpam-3975	55	80	set	set	NOUN
ejpam-3975	55	81	of	of	ADP
ejpam-3975	55	82	g	g	NOUN
ejpam-3975	55	83	with	with	ADP
ejpam-3975	55	84	cardinality	cardinality	NOUN
ejpam-3975	55	85	γtph(g	γtph(g	PROPN
ejpam-3975	55	86	)	)	PUNCT
ejpam-3975	55	87	)	)	PUNCT
ejpam-3975	55	88	is	be	AUX
ejpam-3975	55	89	called	call	VERB
ejpam-3975	55	90	a	a	DET
ejpam-3975	55	91	γtph	γtph	NOUN
ejpam-3975	55	92	-	-	PUNCT
ejpam-3975	55	93	set	set	NOUN
ejpam-3975	55	94	.	.	PUNCT
ejpam-3975	56	1	remark	remark	PROPN
ejpam-3975	56	2	2.2	2.2	NUM
ejpam-3975	56	3	.	.	PUNCT
ejpam-3975	57	1	let	let	VERB
ejpam-3975	57	2	g	g	PRON
ejpam-3975	57	3	be	be	AUX
ejpam-3975	57	4	a	a	DET
ejpam-3975	57	5	connected	connected	ADJ
ejpam-3975	57	6	graph	graph	NOUN
ejpam-3975	57	7	of	of	ADP
ejpam-3975	57	8	order	order	NOUN
ejpam-3975	57	9	n	n	PRON
ejpam-3975	57	10	≥	≥	NOUN
ejpam-3975	57	11	4	4	NUM
ejpam-3975	57	12	.	.	PUNCT
ejpam-3975	57	13	then	then	ADV
ejpam-3975	57	14	γtph(g	γtph(g	NOUN
ejpam-3975	57	15	)	)	PUNCT
ejpam-3975	57	16	≥	≥	NOUN
ejpam-3975	57	17	4	4	NUM
ejpam-3975	57	18	.	.	PUNCT
ejpam-3975	58	1	moreover	moreover	ADV
ejpam-3975	58	2	,	,	PUNCT
ejpam-3975	58	3	for	for	ADP
ejpam-3975	58	4	g	g	NOUN
ejpam-3975	58	5	=	=	SYM
ejpam-3975	58	6	p4	p4	ADJ
ejpam-3975	58	7	or	or	CCONJ
ejpam-3975	58	8	c4	c4	NOUN
ejpam-3975	58	9	,	,	PUNCT
ejpam-3975	58	10	v	v	NOUN
ejpam-3975	58	11	(	(	PUNCT
ejpam-3975	58	12	g	g	NOUN
ejpam-3975	58	13	)	)	PUNCT
ejpam-3975	58	14	is	be	AUX
ejpam-3975	58	15	a	a	DET
ejpam-3975	58	16	total	total	ADJ
ejpam-3975	58	17	perfect	perfect	ADJ
ejpam-3975	58	18	hop	hop	NOUN
ejpam-3975	58	19	dominating	dominating	NOUN
ejpam-3975	58	20	set	set	NOUN
ejpam-3975	58	21	of	of	ADP
ejpam-3975	58	22	g.	g.	PROPN
ejpam-3975	58	23	for	for	ADP
ejpam-3975	58	24	n	n	PROPN
ejpam-3975	58	25	≥	≥	NUM
ejpam-3975	58	26	6	6	NUM
ejpam-3975	58	27	,	,	PUNCT
ejpam-3975	58	28	v	v	NOUN
ejpam-3975	58	29	(	(	PUNCT
ejpam-3975	58	30	g	g	NOUN
ejpam-3975	58	31	)	)	PUNCT
ejpam-3975	58	32	is	be	AUX
ejpam-3975	58	33	a	a	DET
ejpam-3975	58	34	total	total	ADJ
ejpam-3975	58	35	perfect	perfect	ADJ
ejpam-3975	58	36	hop	hop	NOUN
ejpam-3975	58	37	dominating	dominating	NOUN
ejpam-3975	58	38	set	set	NOUN
ejpam-3975	58	39	of	of	ADP
ejpam-3975	58	40	g	g	PROPN
ejpam-3975	58	41	if	if	SCONJ
ejpam-3975	59	1	and	and	CCONJ
ejpam-3975	59	2	only	only	ADV
ejpam-3975	59	3	if	if	SCONJ
ejpam-3975	59	4	|v	|v	PROPN
ejpam-3975	59	5	(	(	PUNCT
ejpam-3975	59	6	g)|	g)|	NOUN
ejpam-3975	59	7	is	be	AUX
ejpam-3975	59	8	even	even	ADV
ejpam-3975	59	9	and	and	CCONJ
ejpam-3975	59	10	the	the	DET
ejpam-3975	59	11	vertices	vertex	NOUN
ejpam-3975	59	12	of	of	ADP
ejpam-3975	59	13	g	g	NOUN
ejpam-3975	59	14	can	can	AUX
ejpam-3975	59	15	be	be	AUX
ejpam-3975	59	16	labeled	label	VERB
ejpam-3975	59	17	u1	u1	NOUN
ejpam-3975	59	18	,	,	PUNCT
ejpam-3975	59	19	u2	u2	NOUN
ejpam-3975	59	20	,	,	PUNCT
ejpam-3975	59	21	...	...	PUNCT
ejpam-3975	59	22	,	,	PUNCT
ejpam-3975	60	1	uv	uv	INTJ
ejpam-3975	60	2	(	(	PUNCT
ejpam-3975	60	3	g	g	NOUN
ejpam-3975	60	4	)	)	PUNCT
ejpam-3975	60	5	2	2	NUM
ejpam-3975	60	6	,	,	PUNCT
ejpam-3975	60	7	v1	v1	NOUN
ejpam-3975	60	8	,	,	PUNCT
ejpam-3975	60	9	v2	v2	PROPN
ejpam-3975	60	10	,	,	PUNCT
ejpam-3975	60	11	...	...	PUNCT
ejpam-3975	60	12	,	,	PUNCT
ejpam-3975	60	13	vv	vv	X
ejpam-3975	60	14	(	(	PUNCT
ejpam-3975	60	15	g	g	NOUN
ejpam-3975	60	16	)	)	PUNCT
ejpam-3975	60	17	2	2	NUM
ejpam-3975	60	18	such	such	ADJ
ejpam-3975	60	19	that	that	DET
ejpam-3975	60	20	dg(ui	dg(ui	NOUN
ejpam-3975	60	21	,	,	PUNCT
ejpam-3975	60	22	vi	vi	NOUN
ejpam-3975	60	23	)	)	PUNCT
ejpam-3975	60	24	=	=	SYM
ejpam-3975	60	25	2	2	NUM
ejpam-3975	60	26	,	,	PUNCT
ejpam-3975	60	27	dg(ui	dg(ui	NOUN
ejpam-3975	60	28	,	,	PUNCT
ejpam-3975	60	29	uj	uj	PROPN
ejpam-3975	60	30	)	)	PUNCT
ejpam-3975	60	31	=	=	SYM
ejpam-3975	60	32	dg(vi	dg(vi	PROPN
ejpam-3975	60	33	,	,	PUNCT
ejpam-3975	60	34	vj	vj	INTJ
ejpam-3975	60	35	)	)	PUNCT
ejpam-3975	60	36	=	=	SYM
ejpam-3975	60	37	dg(ui	dg(ui	PROPN
ejpam-3975	60	38	,	,	PUNCT
ejpam-3975	60	39	vj	vj	PROPN
ejpam-3975	60	40	)	)	PUNCT
ejpam-3975	60	41	=	=	SYM
ejpam-3975	60	42	1	1	NUM
ejpam-3975	60	43	,	,	PUNCT
ejpam-3975	60	44	whenever	whenever	SCONJ
ejpam-3975	60	45	i	i	PRON
ejpam-3975	60	46	6=	6=	PROPN
ejpam-3975	60	47	j.	j.	PROPN
ejpam-3975	60	48	remark	remark	PROPN
ejpam-3975	60	49	2.3	2.3	NUM
ejpam-3975	60	50	.	.	PUNCT
ejpam-3975	61	1	let	let	VERB
ejpam-3975	61	2	g	g	PRON
ejpam-3975	61	3	be	be	AUX
ejpam-3975	61	4	a	a	DET
ejpam-3975	61	5	graph	graph	NOUN
ejpam-3975	61	6	of	of	ADP
ejpam-3975	61	7	order	order	NOUN
ejpam-3975	61	8	n.	n.	NOUN
ejpam-3975	61	9	then	then	ADV
ejpam-3975	61	10	the	the	DET
ejpam-3975	61	11	total	total	ADJ
ejpam-3975	61	12	perfect	perfect	ADJ
ejpam-3975	61	13	hop	hop	NOUN
ejpam-3975	61	14	dominating	dominating	NOUN
ejpam-3975	61	15	set	set	NOUN
ejpam-3975	61	16	of	of	ADP
ejpam-3975	61	17	g	g	PROPN
ejpam-3975	61	18	does	do	AUX
ejpam-3975	61	19	not	not	PART
ejpam-3975	61	20	exist	exist	VERB
ejpam-3975	61	21	if	if	SCONJ
ejpam-3975	61	22	γ(h	γ(h	NOUN
ejpam-3975	61	23	)	)	PUNCT
ejpam-3975	61	24	=	=	SYM
ejpam-3975	62	1	1	1	X
ejpam-3975	62	2	.	.	PUNCT
ejpam-3975	62	3	lemma	lemma	PROPN
ejpam-3975	62	4	2.4	2.4	NUM
ejpam-3975	62	5	.	.	PUNCT
ejpam-3975	63	1	let	let	VERB
ejpam-3975	63	2	g	g	PRON
ejpam-3975	63	3	be	be	AUX
ejpam-3975	63	4	a	a	DET
ejpam-3975	63	5	connected	connected	ADJ
ejpam-3975	63	6	graph	graph	NOUN
ejpam-3975	63	7	of	of	ADP
ejpam-3975	63	8	order	order	NOUN
ejpam-3975	63	9	n	n	PRON
ejpam-3975	63	10	≥	≥	NOUN
ejpam-3975	63	11	4	4	NUM
ejpam-3975	63	12	.	.	PUNCT
ejpam-3975	64	1	then	then	ADV
ejpam-3975	64	2	s	s	VERB
ejpam-3975	64	3	=	=	PUNCT
ejpam-3975	64	4	{	{	PUNCT
ejpam-3975	64	5	x1	x1	PROPN
ejpam-3975	64	6	,	,	PUNCT
ejpam-3975	64	7	x2	x2	PROPN
ejpam-3975	64	8	,	,	PUNCT
ejpam-3975	64	9	x3	x3	PROPN
ejpam-3975	64	10	,	,	PUNCT
ejpam-3975	64	11	x4	x4	PROPN
ejpam-3975	64	12	}	}	PUNCT
ejpam-3975	64	13	is	be	AUX
ejpam-3975	64	14	a	a	DET
ejpam-3975	64	15	total	total	ADJ
ejpam-3975	64	16	perfect	perfect	ADJ
ejpam-3975	64	17	hop	hop	NOUN
ejpam-3975	64	18	dominating	dominating	NOUN
ejpam-3975	64	19	set	set	NOUN
ejpam-3975	64	20	of	of	ADP
ejpam-3975	64	21	g	g	PROPN
ejpam-3975	64	22	if	if	SCONJ
ejpam-3975	64	23	〈	〈	PROPN
ejpam-3975	64	24	s	s	PART
ejpam-3975	64	25	〉	〉	NOUN
ejpam-3975	64	26	∼=	∼=	NOUN
ejpam-3975	64	27	p4	p4	ADJ
ejpam-3975	64	28	=	=	PUNCT
ejpam-3975	65	1	[	[	X
ejpam-3975	65	2	x1	x1	PROPN
ejpam-3975	65	3	,	,	PUNCT
ejpam-3975	65	4	x2	x2	PROPN
ejpam-3975	65	5	,	,	PUNCT
ejpam-3975	65	6	x3	x3	PROPN
ejpam-3975	65	7	,	,	PUNCT
ejpam-3975	65	8	x4	x4	PROPN
ejpam-3975	65	9	]	]	PUNCT
ejpam-3975	65	10	and	and	CCONJ
ejpam-3975	65	11	for	for	ADP
ejpam-3975	65	12	every	every	DET
ejpam-3975	65	13	v	v	NUM
ejpam-3975	65	14	∈	∈	PROPN
ejpam-3975	65	15	v	v	NOUN
ejpam-3975	65	16	(	(	PUNCT
ejpam-3975	65	17	g	g	NOUN
ejpam-3975	65	18	)	)	PUNCT
ejpam-3975	65	19	at	at	ADP
ejpam-3975	65	20	least	least	ADJ
ejpam-3975	65	21	one	one	NUM
ejpam-3975	65	22	of	of	ADP
ejpam-3975	65	23	the	the	DET
ejpam-3975	65	24	following	follow	VERB
ejpam-3975	65	25	holds	hold	NOUN
ejpam-3975	65	26	.	.	PUNCT
ejpam-3975	66	1	(	(	PUNCT
ejpam-3975	66	2	i	i	NOUN
ejpam-3975	66	3	)	)	PUNCT
ejpam-3975	66	4	v	v	ADP
ejpam-3975	66	5	∈	∈	NOUN
ejpam-3975	66	6	ng(x1)\	ng(x1)\	PUNCT
ejpam-3975	67	1	⋃	⋃	PROPN
ejpam-3975	67	2	i	i	PROPN
ejpam-3975	67	3	6=1	6=1	NUM
ejpam-3975	67	4	ng(xi	ng(xi	X
ejpam-3975	67	5	)	)	PUNCT
ejpam-3975	67	6	and	and	CCONJ
ejpam-3975	67	7	v	v	NOUN
ejpam-3975	67	8	/∈	/∈	PUNCT
ejpam-3975	67	9	ng(u	ng(u	NOUN
ejpam-3975	67	10	)	)	PUNCT
ejpam-3975	67	11	for	for	ADP
ejpam-3975	67	12	each	each	DET
ejpam-3975	67	13	u	u	NOUN
ejpam-3975	67	14	∈	∈	PROPN
ejpam-3975	67	15	ng(xj	ng(xj	NOUN
ejpam-3975	67	16	)	)	PUNCT
ejpam-3975	67	17	where	where	SCONJ
ejpam-3975	67	18	j	j	PROPN
ejpam-3975	67	19	=	=	SYM
ejpam-3975	67	20	3	3	NUM
ejpam-3975	67	21	or	or	CCONJ
ejpam-3975	67	22	4	4	NUM
ejpam-3975	67	23	,	,	PUNCT
ejpam-3975	67	24	or	or	CCONJ
ejpam-3975	67	25	(	(	PUNCT
ejpam-3975	67	26	ii	ii	NOUN
ejpam-3975	67	27	)	)	PUNCT
ejpam-3975	67	28	v	v	ADP
ejpam-3975	67	29	∈	∈	NOUN
ejpam-3975	67	30	ng(x4)\	ng(x4)\	PUNCT
ejpam-3975	67	31	⋃	⋃	PROPN
ejpam-3975	67	32	i	i	PROPN
ejpam-3975	67	33	6=4	6=4	NUM
ejpam-3975	67	34	ng(xi	ng(xi	PUNCT
ejpam-3975	67	35	)	)	PUNCT
ejpam-3975	67	36	and	and	CCONJ
ejpam-3975	67	37	v	v	NOUN
ejpam-3975	67	38	/∈	/∈	PUNCT
ejpam-3975	67	39	ng(u	ng(u	NOUN
ejpam-3975	67	40	)	)	PUNCT
ejpam-3975	67	41	for	for	ADP
ejpam-3975	67	42	each	each	DET
ejpam-3975	67	43	u	u	NOUN
ejpam-3975	67	44	∈	∈	PROPN
ejpam-3975	67	45	ng(xj	ng(xj	NOUN
ejpam-3975	67	46	)	)	PUNCT
ejpam-3975	67	47	where	where	SCONJ
ejpam-3975	67	48	j	j	PROPN
ejpam-3975	67	49	=	=	SYM
ejpam-3975	67	50	1	1	NUM
ejpam-3975	67	51	or	or	CCONJ
ejpam-3975	67	52	2	2	NUM
ejpam-3975	67	53	,	,	PUNCT
ejpam-3975	67	54	or	or	CCONJ
ejpam-3975	67	55	(	(	PUNCT
ejpam-3975	67	56	iii	iii	NOUN
ejpam-3975	67	57	)	)	PUNCT
ejpam-3975	67	58	v	v	NOUN
ejpam-3975	67	59	∈	∈	PROPN
ejpam-3975	67	60	[	[	X
ejpam-3975	67	61	ng(x1	ng(x1	NOUN
ejpam-3975	67	62	)	)	PUNCT
ejpam-3975	67	63	∩ng(x2)]\	∩ng(x2)]\	PROPN
ejpam-3975	67	64	⋃	⋃	NOUN
ejpam-3975	67	65	i=3,4	i=3,4	NOUN
ejpam-3975	67	66	ng(xi	ng(xi	PROPN
ejpam-3975	67	67	)	)	PUNCT
ejpam-3975	67	68	and	and	CCONJ
ejpam-3975	67	69	v	v	NOUN
ejpam-3975	67	70	/∈	/∈	PUNCT
ejpam-3975	67	71	ng(u	ng(u	NOUN
ejpam-3975	67	72	)	)	PUNCT
ejpam-3975	67	73	for	for	ADP
ejpam-3975	67	74	each	each	DET
ejpam-3975	67	75	u	u	PROPN
ejpam-3975	67	76	∈	∈	PROPN
ejpam-3975	67	77	ng(x4	ng(x4	NOUN
ejpam-3975	67	78	)	)	PUNCT
ejpam-3975	67	79	,	,	PUNCT
ejpam-3975	67	80	or	or	CCONJ
ejpam-3975	67	81	(	(	PUNCT
ejpam-3975	67	82	iv	iv	X
ejpam-3975	67	83	)	)	PUNCT
ejpam-3975	67	84	v	v	NOUN
ejpam-3975	67	85	∈	∈	PROPN
ejpam-3975	67	86	[	[	X
ejpam-3975	67	87	ng(x3	ng(x3	NUM
ejpam-3975	67	88	)	)	PUNCT
ejpam-3975	67	89	∩ng(x4)]\	∩ng(x4)]\	NOUN
ejpam-3975	67	90	⋃	⋃	NOUN
ejpam-3975	67	91	i=1,2	i=1,2	NOUN
ejpam-3975	67	92	ng(xi	ng(xi	PROPN
ejpam-3975	67	93	)	)	PUNCT
ejpam-3975	67	94	and	and	CCONJ
ejpam-3975	67	95	v	v	NOUN
ejpam-3975	67	96	/∈	/∈	PUNCT
ejpam-3975	67	97	ng(u	ng(u	NOUN
ejpam-3975	67	98	)	)	PUNCT
ejpam-3975	67	99	for	for	ADP
ejpam-3975	67	100	each	each	DET
ejpam-3975	67	101	u	u	PROPN
ejpam-3975	67	102	∈	∈	PROPN
ejpam-3975	67	103	ng(x1	ng(x1	NOUN
ejpam-3975	67	104	)	)	PUNCT
ejpam-3975	67	105	,	,	PUNCT
ejpam-3975	67	106	or	or	CCONJ
ejpam-3975	67	107	(	(	PUNCT
ejpam-3975	67	108	v	v	NOUN
ejpam-3975	67	109	)	)	PUNCT
ejpam-3975	67	110	v	v	NOUN
ejpam-3975	67	111	∈	∈	NOUN
ejpam-3975	67	112	⋂	⋂	PROPN
ejpam-3975	67	113	j	j	PROPN
ejpam-3975	67	114	ng(xj	ng(xj	ADV
ejpam-3975	67	115	)	)	PUNCT
ejpam-3975	67	116	for	for	ADP
ejpam-3975	67	117	exactly	exactly	ADV
ejpam-3975	67	118	three	three	NUM
ejpam-3975	67	119	xj	xj	NOUN
ejpam-3975	67	120	’s	’s	PART
ejpam-3975	67	121	,	,	PUNCT
ejpam-3975	67	122	or	or	CCONJ
ejpam-3975	67	123	(	(	PUNCT
ejpam-3975	67	124	vi	vi	NOUN
ejpam-3975	67	125	)	)	PUNCT
ejpam-3975	67	126	v	v	NOUN
ejpam-3975	67	127	∈	∈	PROPN
ejpam-3975	67	128	ng(xk	ng(xk	NOUN
ejpam-3975	67	129	,	,	PUNCT
ejpam-3975	67	130	2)\	2)\	NUM
ejpam-3975	67	131	⋃	⋃	PUNCT
ejpam-3975	67	132	i	i	PRON
ejpam-3975	67	133	6	6	NUM
ejpam-3975	67	134	=	=	SYM
ejpam-3975	67	135	k	k	X
ejpam-3975	67	136	ng(xi	ng(xi	PROPN
ejpam-3975	67	137	)	)	PUNCT
ejpam-3975	67	138	for	for	ADP
ejpam-3975	67	139	k	k	PROPN
ejpam-3975	67	140	=	=	SYM
ejpam-3975	67	141	1	1	NUM
ejpam-3975	67	142	or	or	CCONJ
ejpam-3975	67	143	4	4	NUM
ejpam-3975	67	144	and	and	CCONJ
ejpam-3975	67	145	degg(v	degg(v	PROPN
ejpam-3975	67	146	)	)	PUNCT
ejpam-3975	67	147	=	=	SYM
ejpam-3975	67	148	1	1	NUM
ejpam-3975	67	149	,	,	PUNCT
ejpam-3975	67	150	or	or	CCONJ
ejpam-3975	67	151	(	(	PUNCT
ejpam-3975	67	152	vii	vii	PROPN
ejpam-3975	67	153	)	)	PUNCT
ejpam-3975	67	154	v	v	ADP
ejpam-3975	67	155	∈	∈	PROPN
ejpam-3975	67	156	ng(x1	ng(x1	NOUN
ejpam-3975	67	157	,	,	PUNCT
ejpam-3975	67	158	2)\	2)\	NUM
ejpam-3975	67	159	⋃	⋃	PUNCT
ejpam-3975	67	160	i	i	PROPN
ejpam-3975	67	161	6=1	6=1	NUM
ejpam-3975	67	162	ng(xi	ng(xi	X
ejpam-3975	67	163	)	)	PUNCT
ejpam-3975	67	164	and	and	CCONJ
ejpam-3975	67	165	v	v	ADP
ejpam-3975	67	166	∈	∈	PROPN
ejpam-3975	67	167	ng(u	ng(u	NOUN
ejpam-3975	67	168	)	)	PUNCT
ejpam-3975	67	169	for	for	ADP
ejpam-3975	67	170	each	each	DET
ejpam-3975	67	171	u	u	PROPN
ejpam-3975	67	172	∈	∈	PROPN
ejpam-3975	67	173	ng(x4	ng(x4	NOUN
ejpam-3975	67	174	,	,	PUNCT
ejpam-3975	67	175	2)\	2)\	NUM
ejpam-3975	67	176	⋃	⋃	NOUN
ejpam-3975	67	177	j	j	PROPN
ejpam-3975	67	178	6=4	6=4	NUM
ejpam-3975	67	179	ng(xj	ng(xj	ADV
ejpam-3975	67	180	)	)	PUNCT
ejpam-3975	67	181	.	.	PUNCT
ejpam-3975	68	1	proof	proof	NOUN
ejpam-3975	68	2	.	.	PUNCT
ejpam-3975	69	1	suppose	suppose	VERB
ejpam-3975	69	2	s	s	VERB
ejpam-3975	69	3	=	=	PUNCT
ejpam-3975	69	4	{	{	PUNCT
ejpam-3975	69	5	x1	x1	PROPN
ejpam-3975	69	6	,	,	PUNCT
ejpam-3975	69	7	x2	x2	PROPN
ejpam-3975	69	8	,	,	PUNCT
ejpam-3975	69	9	x3	x3	ADJ
ejpam-3975	69	10	,	,	PUNCT
ejpam-3975	69	11	x4	x4	PROPN
ejpam-3975	69	12	}	}	PUNCT
ejpam-3975	69	13	and	and	CCONJ
ejpam-3975	70	1	〈	〈	PROPN
ejpam-3975	70	2	s	s	PROPN
ejpam-3975	70	3	〉	〉	NOUN
ejpam-3975	70	4	∼=	∼=	NOUN
ejpam-3975	70	5	p4	p4	ADJ
ejpam-3975	70	6	=	=	PUNCT
ejpam-3975	71	1	[	[	X
ejpam-3975	71	2	x1	x1	PROPN
ejpam-3975	71	3	,	,	PUNCT
ejpam-3975	71	4	x2	x2	PROPN
ejpam-3975	71	5	,	,	PUNCT
ejpam-3975	71	6	x3	x3	PROPN
ejpam-3975	71	7	,	,	PUNCT
ejpam-3975	71	8	x4	x4	PROPN
ejpam-3975	71	9	]	]	PUNCT
ejpam-3975	71	10	.	.	PUNCT
ejpam-3975	72	1	let	let	VERB
ejpam-3975	72	2	v	v	NUM
ejpam-3975	72	3	∈	∈	PROPN
ejpam-3975	72	4	v	v	NOUN
ejpam-3975	72	5	(	(	PUNCT
ejpam-3975	72	6	g	g	NOUN
ejpam-3975	72	7	)	)	PUNCT
ejpam-3975	72	8	.	.	PUNCT
ejpam-3975	73	1	if	if	SCONJ
ejpam-3975	73	2	v	v	NUM
ejpam-3975	73	3	∈	∈	PROPN
ejpam-3975	73	4	s	s	NOUN
ejpam-3975	73	5	,	,	PUNCT
ejpam-3975	73	6	then	then	ADV
ejpam-3975	73	7	by	by	ADP
ejpam-3975	73	8	remark	remark	NOUN
ejpam-3975	73	9	2.2	2.2	NUM
ejpam-3975	73	10	,	,	PUNCT
ejpam-3975	73	11	|ng(v	|ng(v	PROPN
ejpam-3975	73	12	,	,	PUNCT
ejpam-3975	73	13	2	2	X
ejpam-3975	73	14	)	)	PUNCT
ejpam-3975	73	15	∩	∩	NOUN
ejpam-3975	73	16	s|	s|	NOUN
ejpam-3975	73	17	=	=	SYM
ejpam-3975	73	18	1	1	X
ejpam-3975	73	19	.	.	PUNCT
ejpam-3975	73	20	suppose	suppose	VERB
ejpam-3975	73	21	that	that	SCONJ
ejpam-3975	73	22	v	v	NOUN
ejpam-3975	73	23	/∈	/∈	PUNCT
ejpam-3975	73	24	s.	s.	PROPN
ejpam-3975	74	1	if	if	SCONJ
ejpam-3975	74	2	(	(	PUNCT
ejpam-3975	74	3	i	i	NOUN
ejpam-3975	74	4	)	)	PUNCT
ejpam-3975	74	5	and	and	CCONJ
ejpam-3975	74	6	(	(	PUNCT
ejpam-3975	74	7	ii	ii	NOUN
ejpam-3975	74	8	)	)	PUNCT
ejpam-3975	74	9	hold	hold	VERB
ejpam-3975	74	10	,	,	PUNCT
ejpam-3975	74	11	then	then	ADV
ejpam-3975	74	12	ng(v	ng(v	PUNCT
ejpam-3975	74	13	,	,	PUNCT
ejpam-3975	74	14	2	2	X
ejpam-3975	74	15	)	)	PUNCT
ejpam-3975	74	16	∩	∩	NOUN
ejpam-3975	74	17	s	s	PART
ejpam-3975	74	18	=	=	SYM
ejpam-3975	74	19	{	{	PUNCT
ejpam-3975	74	20	xj	xj	PROPN
ejpam-3975	74	21	}	}	PUNCT
ejpam-3975	74	22	for	for	ADP
ejpam-3975	74	23	j	j	PROPN
ejpam-3975	74	24	=	=	SYM
ejpam-3975	74	25	2	2	NUM
ejpam-3975	74	26	and	and	CCONJ
ejpam-3975	74	27	j	j	NOUN
ejpam-3975	74	28	=	=	SYM
ejpam-3975	74	29	3	3	NUM
ejpam-3975	74	30	,	,	PUNCT
ejpam-3975	74	31	respectively	respectively	ADV
ejpam-3975	74	32	.	.	PUNCT
ejpam-3975	75	1	if	if	SCONJ
ejpam-3975	75	2	(	(	PUNCT
ejpam-3975	75	3	iii	iii	NOUN
ejpam-3975	75	4	)	)	PUNCT
ejpam-3975	75	5	and	and	CCONJ
ejpam-3975	75	6	(	(	PUNCT
ejpam-3975	75	7	iv	iv	X
ejpam-3975	75	8	)	)	PUNCT
ejpam-3975	75	9	hold	hold	NOUN
ejpam-3975	75	10	,	,	PUNCT
ejpam-3975	75	11	then	then	ADV
ejpam-3975	75	12	ng(v	ng(v	PUNCT
ejpam-3975	75	13	,	,	PUNCT
ejpam-3975	75	14	2	2	X
ejpam-3975	75	15	)	)	PUNCT
ejpam-3975	75	16	∩	∩	NOUN
ejpam-3975	75	17	s	s	PART
ejpam-3975	75	18	=	=	PUNCT
ejpam-3975	75	19	{	{	PUNCT
ejpam-3975	75	20	xk	xk	NOUN
ejpam-3975	75	21	}	}	PUNCT
ejpam-3975	75	22	for	for	ADP
ejpam-3975	75	23	k	k	PROPN
ejpam-3975	75	24	=	=	SYM
ejpam-3975	75	25	3	3	NUM
ejpam-3975	75	26	and	and	CCONJ
ejpam-3975	75	27	k	k	NOUN
ejpam-3975	75	28	=	=	SYM
ejpam-3975	75	29	2	2	NUM
ejpam-3975	75	30	,	,	PUNCT
ejpam-3975	75	31	respectively	respectively	ADV
ejpam-3975	75	32	.	.	PUNCT
ejpam-3975	76	1	for	for	ADP
ejpam-3975	76	2	condition	condition	NOUN
ejpam-3975	76	3	r.	r.	PROPN
ejpam-3975	76	4	rakim	rakim	PROPN
ejpam-3975	76	5	,	,	PUNCT
ejpam-3975	76	6	h.	h.	PROPN
ejpam-3975	76	7	rara	rara	PROPN
ejpam-3975	76	8	/	/	SYM
ejpam-3975	76	9	eur	eur	PROPN
ejpam-3975	76	10	.	.	PUNCT
ejpam-3975	77	1	j.	j.	PROPN
ejpam-3975	77	2	pure	pure	PROPN
ejpam-3975	77	3	appl	appl	PROPN
ejpam-3975	77	4	.	.	PROPN
ejpam-3975	77	5	math	math	PROPN
ejpam-3975	77	6	,	,	PUNCT
ejpam-3975	77	7	14	14	NUM
ejpam-3975	77	8	(	(	PUNCT
ejpam-3975	77	9	3	3	NUM
ejpam-3975	77	10	)	)	PUNCT
ejpam-3975	77	11	(	(	PUNCT
ejpam-3975	77	12	2021	2021	NUM
ejpam-3975	77	13	)	)	PUNCT
ejpam-3975	77	14	,	,	PUNCT
ejpam-3975	77	15	803	803	NUM
ejpam-3975	77	16	-	-	SYM
ejpam-3975	77	17	815	815	NUM
ejpam-3975	77	18	806	806	NUM
ejpam-3975	77	19	(	(	PUNCT
ejpam-3975	77	20	v	v	NOUN
ejpam-3975	77	21	)	)	PUNCT
ejpam-3975	78	1	,	,	PUNCT
ejpam-3975	78	2	it	it	PRON
ejpam-3975	78	3	can	can	AUX
ejpam-3975	78	4	easily	easily	ADV
ejpam-3975	78	5	be	be	AUX
ejpam-3975	78	6	verified	verify	VERB
ejpam-3975	78	7	that	that	SCONJ
ejpam-3975	78	8	ng(v	ng(v	NOUN
ejpam-3975	78	9	,	,	PUNCT
ejpam-3975	78	10	2	2	X
ejpam-3975	78	11	)	)	PUNCT
ejpam-3975	78	12	∩	∩	NOUN
ejpam-3975	78	13	s	s	PART
ejpam-3975	78	14	=	=	X
ejpam-3975	78	15	{	{	PUNCT
ejpam-3975	78	16	xp	xp	INTJ
ejpam-3975	78	17	}	}	PUNCT
ejpam-3975	78	18	where	where	SCONJ
ejpam-3975	78	19	p	p	PROPN
ejpam-3975	78	20	∈	∈	PROPN
ejpam-3975	78	21	{	{	PUNCT
ejpam-3975	78	22	1	1	NUM
ejpam-3975	78	23	,	,	PUNCT
ejpam-3975	78	24	2	2	NUM
ejpam-3975	78	25	,	,	PUNCT
ejpam-3975	78	26	3	3	NUM
ejpam-3975	78	27	,	,	PUNCT
ejpam-3975	78	28	4	4	NUM
ejpam-3975	78	29	}	}	PUNCT
ejpam-3975	78	30	.	.	PUNCT
ejpam-3975	79	1	if	if	SCONJ
ejpam-3975	79	2	(	(	PUNCT
ejpam-3975	79	3	vi	vi	NOUN
ejpam-3975	79	4	)	)	PUNCT
ejpam-3975	79	5	and	and	CCONJ
ejpam-3975	79	6	(	(	PUNCT
ejpam-3975	79	7	vii	vii	PROPN
ejpam-3975	79	8	)	)	PUNCT
ejpam-3975	79	9	hold	hold	NOUN
ejpam-3975	79	10	,	,	PUNCT
ejpam-3975	79	11	then	then	ADV
ejpam-3975	79	12	ng(v	ng(v	PUNCT
ejpam-3975	79	13	,	,	PUNCT
ejpam-3975	79	14	2	2	X
ejpam-3975	79	15	)	)	PUNCT
ejpam-3975	80	1	∩	∩	NOUN
ejpam-3975	80	2	s	s	PART
ejpam-3975	80	3	=	=	SYM
ejpam-3975	80	4	{	{	PUNCT
ejpam-3975	80	5	xs	xs	PROPN
ejpam-3975	80	6	}	}	PUNCT
ejpam-3975	80	7	where	where	SCONJ
ejpam-3975	80	8	s	s	VERB
ejpam-3975	80	9	∈	∈	NOUN
ejpam-3975	80	10	{	{	PUNCT
ejpam-3975	80	11	1	1	NUM
ejpam-3975	80	12	,	,	PUNCT
ejpam-3975	80	13	4	4	NUM
ejpam-3975	80	14	}	}	PUNCT
ejpam-3975	80	15	.	.	PUNCT
ejpam-3975	81	1	therefore	therefore	ADV
ejpam-3975	81	2	s	s	VERB
ejpam-3975	81	3	is	be	AUX
ejpam-3975	81	4	a	a	DET
ejpam-3975	81	5	total	total	ADJ
ejpam-3975	81	6	perfect	perfect	ADJ
ejpam-3975	81	7	hop	hop	NOUN
ejpam-3975	81	8	dominating	dominating	NOUN
ejpam-3975	81	9	set	set	NOUN
ejpam-3975	81	10	of	of	ADP
ejpam-3975	81	11	g.	g.	PROPN
ejpam-3975	81	12	�	�	PROPN
ejpam-3975	81	13	lemma	lemma	PROPN
ejpam-3975	81	14	2.5	2.5	NUM
ejpam-3975	81	15	.	.	PUNCT
ejpam-3975	82	1	let	let	VERB
ejpam-3975	82	2	g	g	PRON
ejpam-3975	82	3	be	be	AUX
ejpam-3975	82	4	a	a	DET
ejpam-3975	82	5	connected	connected	ADJ
ejpam-3975	82	6	graph	graph	NOUN
ejpam-3975	82	7	of	of	ADP
ejpam-3975	82	8	order	order	NOUN
ejpam-3975	82	9	n	n	PRON
ejpam-3975	82	10	≥	≥	NUM
ejpam-3975	82	11	6	6	NUM
ejpam-3975	82	12	.	.	PUNCT
ejpam-3975	83	1	then	then	ADV
ejpam-3975	83	2	s	s	VERB
ejpam-3975	83	3	=	=	PUNCT
ejpam-3975	83	4	{	{	PUNCT
ejpam-3975	83	5	x1	x1	PROPN
ejpam-3975	83	6	,	,	PUNCT
ejpam-3975	83	7	x2	x2	PROPN
ejpam-3975	83	8	,	,	PUNCT
ejpam-3975	83	9	x3	x3	PROPN
ejpam-3975	83	10	,	,	PUNCT
ejpam-3975	83	11	x4	x4	PROPN
ejpam-3975	83	12	}	}	PUNCT
ejpam-3975	83	13	is	be	AUX
ejpam-3975	83	14	a	a	DET
ejpam-3975	83	15	total	total	ADJ
ejpam-3975	83	16	perfect	perfect	ADJ
ejpam-3975	83	17	hop	hop	NOUN
ejpam-3975	83	18	dominating	dominating	NOUN
ejpam-3975	83	19	set	set	NOUN
ejpam-3975	83	20	of	of	ADP
ejpam-3975	83	21	g	g	PROPN
ejpam-3975	83	22	if	if	SCONJ
ejpam-3975	83	23	〈	〈	PROPN
ejpam-3975	83	24	s	s	PART
ejpam-3975	83	25	〉	〉	NOUN
ejpam-3975	83	26	∼=	∼=	NOUN
ejpam-3975	83	27	p2	p2	NOUN
ejpam-3975	83	28	∪	∪	X
ejpam-3975	83	29	k2	k2	PROPN
ejpam-3975	83	30	where	where	SCONJ
ejpam-3975	83	31	p2	p2	PROPN
ejpam-3975	83	32	=	=	PUNCT
ejpam-3975	84	1	[	[	X
ejpam-3975	84	2	x2	x2	X
ejpam-3975	84	3	,	,	PUNCT
ejpam-3975	84	4	x3	x3	ADJ
ejpam-3975	84	5	]	]	PUNCT
ejpam-3975	84	6	and	and	CCONJ
ejpam-3975	84	7	v	v	NOUN
ejpam-3975	84	8	(	(	PUNCT
ejpam-3975	84	9	k2	k2	NOUN
ejpam-3975	84	10	)	)	PUNCT
ejpam-3975	84	11	=	=	PRON
ejpam-3975	84	12	{	{	PUNCT
ejpam-3975	84	13	x1	x1	PROPN
ejpam-3975	84	14	,	,	PUNCT
ejpam-3975	84	15	x4	x4	PROPN
ejpam-3975	84	16	}	}	PUNCT
ejpam-3975	84	17	and	and	CCONJ
ejpam-3975	84	18	the	the	DET
ejpam-3975	84	19	following	follow	VERB
ejpam-3975	84	20	hold	hold	NOUN
ejpam-3975	84	21	.	.	PUNCT
ejpam-3975	85	1	(	(	PUNCT
ejpam-3975	85	2	i	i	NOUN
ejpam-3975	85	3	)	)	PUNCT
ejpam-3975	85	4	|ng(x2	|ng(x2	NOUN
ejpam-3975	85	5	)	)	PUNCT
ejpam-3975	85	6	∩ng(x4)|	∩ng(x4)|	NOUN
ejpam-3975	86	1	=	=	SYM
ejpam-3975	86	2	0	0	NUM
ejpam-3975	86	3	and	and	CCONJ
ejpam-3975	86	4	|ng(x1	|ng(x1	ADJ
ejpam-3975	86	5	)	)	PUNCT
ejpam-3975	86	6	∩ng(x2)|	∩ng(x2)|	NOUN
ejpam-3975	87	1	6=	6=	ADP
ejpam-3975	87	2	0	0	NUM
ejpam-3975	87	3	(	(	PUNCT
ejpam-3975	87	4	ii	ii	NOUN
ejpam-3975	87	5	)	)	PUNCT
ejpam-3975	87	6	|ng(x1	|ng(x1	NOUN
ejpam-3975	87	7	)	)	PUNCT
ejpam-3975	87	8	∩ng(x3)|	∩ng(x3)|	NOUN
ejpam-3975	88	1	=	=	NOUN
ejpam-3975	88	2	0	0	NUM
ejpam-3975	88	3	and	and	CCONJ
ejpam-3975	88	4	|ng(x3	|ng(x3	NUM
ejpam-3975	88	5	)	)	PUNCT
ejpam-3975	88	6	∩ng(x4)|	∩ng(x4)|	NOUN
ejpam-3975	88	7	6=	6=	ADP
ejpam-3975	88	8	0	0	NUM
ejpam-3975	88	9	(	(	PUNCT
ejpam-3975	88	10	iii	iii	NOUN
ejpam-3975	88	11	)	)	PUNCT
ejpam-3975	88	12	for	for	ADP
ejpam-3975	88	13	every	every	DET
ejpam-3975	88	14	v	v	NUM
ejpam-3975	88	15	∈	∈	PROPN
ejpam-3975	88	16	v	v	NOUN
ejpam-3975	88	17	(	(	PUNCT
ejpam-3975	88	18	g	g	NOUN
ejpam-3975	88	19	)	)	PUNCT
ejpam-3975	88	20	,	,	PUNCT
ejpam-3975	88	21	at	at	ADP
ejpam-3975	88	22	least	least	ADJ
ejpam-3975	88	23	one	one	NUM
ejpam-3975	88	24	of	of	ADP
ejpam-3975	88	25	the	the	DET
ejpam-3975	88	26	following	follow	VERB
ejpam-3975	88	27	holds	hold	NOUN
ejpam-3975	88	28	.	.	PUNCT
ejpam-3975	89	1	(	(	PUNCT
ejpam-3975	89	2	a	a	X
ejpam-3975	89	3	)	)	PUNCT
ejpam-3975	89	4	v	v	NOUN
ejpam-3975	89	5	∈	∈	PROPN
ejpam-3975	89	6	[	[	X
ejpam-3975	89	7	ng(x1	ng(x1	NOUN
ejpam-3975	89	8	)	)	PUNCT
ejpam-3975	89	9	∩ng(u)]\	∩ng(u)]\	PROPN
ejpam-3975	89	10	⋃	⋃	PROPN
ejpam-3975	89	11	k	k	PROPN
ejpam-3975	89	12	6=1	6=1	NUM
ejpam-3975	89	13	ng[xk	ng[xk	NOUN
ejpam-3975	89	14	]	]	PUNCT
ejpam-3975	89	15	for	for	ADP
ejpam-3975	89	16	each	each	DET
ejpam-3975	89	17	u	u	NOUN
ejpam-3975	89	18	∈	∈	PROPN
ejpam-3975	89	19	ng(x4)\	ng(x4)\	PUNCT
ejpam-3975	89	20	⋃	⋃	PROPN
ejpam-3975	89	21	j	j	PROPN
ejpam-3975	89	22	6=4	6=4	NUM
ejpam-3975	89	23	ng[xj	ng[xj	NOUN
ejpam-3975	89	24	]	]	PUNCT
ejpam-3975	89	25	,	,	PUNCT
ejpam-3975	89	26	or	or	CCONJ
ejpam-3975	89	27	(	(	PUNCT
ejpam-3975	89	28	b	b	NOUN
ejpam-3975	89	29	)	)	PUNCT
ejpam-3975	89	30	v	v	NOUN
ejpam-3975	89	31	∈	∈	PROPN
ejpam-3975	89	32	ng(x2)\(ng[x3	ng(x2)\(ng[x3	NOUN
ejpam-3975	89	33	]	]	SYM
ejpam-3975	89	34	∪	∪	ADP
ejpam-3975	89	35	ng[u	ng[u	PROPN
ejpam-3975	89	36	]	]	PUNCT
ejpam-3975	89	37	)	)	PUNCT
ejpam-3975	89	38	or	or	CCONJ
ejpam-3975	89	39	v	v	ADP
ejpam-3975	89	40	∈	∈	PROPN
ejpam-3975	89	41	ng(x3)\(ng[x2	ng(x3)\(ng[x2	NOUN
ejpam-3975	89	42	]	]	PUNCT
ejpam-3975	89	43	∪	∪	ADP
ejpam-3975	89	44	ng[u	ng[u	PROPN
ejpam-3975	89	45	]	]	PUNCT
ejpam-3975	89	46	)	)	PUNCT
ejpam-3975	89	47	for	for	ADP
ejpam-3975	89	48	each	each	DET
ejpam-3975	89	49	u	u	PROPN
ejpam-3975	89	50	∈	∈	PROPN
ejpam-3975	89	51	(	(	PUNCT
ejpam-3975	89	52	ng(xi	ng(xi	PROPN
ejpam-3975	89	53	)	)	PUNCT
ejpam-3975	89	54	∩ng(xi+1	∩ng(xi+1	NOUN
ejpam-3975	89	55	)	)	PUNCT
ejpam-3975	89	56	)	)	PUNCT
ejpam-3975	89	57	where	where	SCONJ
ejpam-3975	89	58	i	i	PRON
ejpam-3975	89	59	∈	∈	PROPN
ejpam-3975	89	60	{	{	PUNCT
ejpam-3975	89	61	1	1	NUM
ejpam-3975	89	62	,	,	PUNCT
ejpam-3975	89	63	3	3	NUM
ejpam-3975	89	64	}	}	PUNCT
ejpam-3975	89	65	,	,	PUNCT
ejpam-3975	89	66	or	or	CCONJ
ejpam-3975	89	67	(	(	PUNCT
ejpam-3975	89	68	c	c	NOUN
ejpam-3975	89	69	)	)	PUNCT
ejpam-3975	89	70	v	v	NOUN
ejpam-3975	89	71	∈	∈	PROPN
ejpam-3975	90	1	[	[	X
ejpam-3975	90	2	ng(x2	ng(x2	NOUN
ejpam-3975	90	3	)	)	PUNCT
ejpam-3975	90	4	∩ng(u)]\	∩ng(u)]\	PROPN
ejpam-3975	90	5	⋃	⋃	PROPN
ejpam-3975	90	6	k	k	PROPN
ejpam-3975	90	7	6=2	6=2	NUM
ejpam-3975	90	8	ng(xk	ng(xk	NOUN
ejpam-3975	90	9	)	)	PUNCT
ejpam-3975	90	10	for	for	ADP
ejpam-3975	90	11	each	each	DET
ejpam-3975	90	12	u	u	NOUN
ejpam-3975	90	13	∈	∈	NOUN
ejpam-3975	90	14	ng(x3)\	ng(x3)\	PUNCT
ejpam-3975	91	1	⋃	⋃	PROPN
ejpam-3975	91	2	j	j	PROPN
ejpam-3975	91	3	6=3	6=3	NUM
ejpam-3975	91	4	ng(xj	ng(xj	NOUN
ejpam-3975	91	5	)	)	PUNCT
ejpam-3975	91	6	,	,	PUNCT
ejpam-3975	91	7	or	or	CCONJ
ejpam-3975	91	8	(	(	PUNCT
ejpam-3975	91	9	d	d	NOUN
ejpam-3975	91	10	)	)	PUNCT
ejpam-3975	91	11	v	v	NOUN
ejpam-3975	91	12	∈	∈	PROPN
ejpam-3975	92	1	[	[	X
ejpam-3975	92	2	ng(x2	ng(x2	NOUN
ejpam-3975	92	3	)	)	PUNCT
ejpam-3975	92	4	∩ng(x4)]\ng[x3	∩ng(x4)]\ng[x3	PROPN
ejpam-3975	92	5	]	]	X
ejpam-3975	92	6	,	,	PUNCT
ejpam-3975	92	7	or	or	CCONJ
ejpam-3975	92	8	(	(	PUNCT
ejpam-3975	92	9	e	e	NOUN
ejpam-3975	92	10	)	)	PUNCT
ejpam-3975	92	11	v	v	ADP
ejpam-3975	92	12	∈	∈	PROPN
ejpam-3975	92	13	[	[	X
ejpam-3975	92	14	ng(x1	ng(x1	NOUN
ejpam-3975	92	15	)	)	PUNCT
ejpam-3975	92	16	∩ng(x3)]\ng[x2	∩ng(x3)]\ng[x2	PROPN
ejpam-3975	92	17	]	]	X
ejpam-3975	92	18	,	,	PUNCT
ejpam-3975	92	19	or	or	CCONJ
ejpam-3975	92	20	(	(	PUNCT
ejpam-3975	92	21	f	f	X
ejpam-3975	92	22	)	)	PUNCT
ejpam-3975	92	23	v	v	NOUN
ejpam-3975	92	24	∈	∈	PROPN
ejpam-3975	93	1	[	[	X
ejpam-3975	93	2	ng(x2)∩ng(x3)∩ng(u)]\ng[xk	ng(x2)∩ng(x3)∩ng(u)]\ng[xk	X
ejpam-3975	93	3	]	]	X
ejpam-3975	93	4	for	for	ADP
ejpam-3975	93	5	each	each	DET
ejpam-3975	93	6	u	u	NOUN
ejpam-3975	93	7	∈	∈	PROPN
ejpam-3975	93	8	[	[	X
ejpam-3975	93	9	ng(xk)∩ng(xk+1)]\ng[x4	ng(xk)∩ng(xk+1)]\ng[x4	X
ejpam-3975	93	10	]	]	X
ejpam-3975	93	11	if	if	SCONJ
ejpam-3975	93	12	k	k	PROPN
ejpam-3975	93	13	=	=	SYM
ejpam-3975	93	14	1	1	NUM
ejpam-3975	93	15	or	or	CCONJ
ejpam-3975	93	16	u	u	NOUN
ejpam-3975	93	17	∈	∈	PROPN
ejpam-3975	94	1	[	[	X
ejpam-3975	94	2	ng(xk	ng(xk	X
ejpam-3975	94	3	)	)	PUNCT
ejpam-3975	94	4	∩ng(xk−1)]\ng[x1	∩ng(xk−1)]\ng[x1	NOUN
ejpam-3975	94	5	]	]	X
ejpam-3975	94	6	if	if	SCONJ
ejpam-3975	94	7	k	k	PROPN
ejpam-3975	94	8	=	=	SYM
ejpam-3975	94	9	4	4	NUM
ejpam-3975	94	10	,	,	PUNCT
ejpam-3975	94	11	or	or	CCONJ
ejpam-3975	94	12	(	(	PUNCT
ejpam-3975	94	13	g	g	NOUN
ejpam-3975	94	14	)	)	PUNCT
ejpam-3975	94	15	v	v	NOUN
ejpam-3975	94	16	∈	∈	PROPN
ejpam-3975	94	17	[	[	X
ejpam-3975	94	18	ng(x1	ng(x1	NOUN
ejpam-3975	94	19	)	)	PUNCT
ejpam-3975	94	20	∩	∩	ADJ
ejpam-3975	94	21	ng(x2	ng(x2	NOUN
ejpam-3975	94	22	)	)	PUNCT
ejpam-3975	94	23	∩	∩	ADJ
ejpam-3975	94	24	ng(u)]\[ng[x3	ng(u)]\[ng[x3	PROPN
ejpam-3975	94	25	]	]	PUNCT
ejpam-3975	94	26	∪	∪	ADP
ejpam-3975	94	27	ng(w	ng(w	NOUN
ejpam-3975	94	28	)	)	PUNCT
ejpam-3975	94	29	]	]	PUNCT
ejpam-3975	94	30	for	for	ADP
ejpam-3975	94	31	each	each	DET
ejpam-3975	94	32	u	u	PROPN
ejpam-3975	94	33	∈	∈	PROPN
ejpam-3975	94	34	[	[	X
ejpam-3975	94	35	ng(x1	ng(x1	NOUN
ejpam-3975	94	36	)	)	PUNCT
ejpam-3975	94	37	∩	∩	NOUN
ejpam-3975	94	38	ng(x2)]\ng[x4	ng(x2)]\ng[x4	PROPN
ejpam-3975	94	39	]	]	PUNCT
ejpam-3975	94	40	and	and	CCONJ
ejpam-3975	94	41	for	for	ADP
ejpam-3975	94	42	each	each	DET
ejpam-3975	94	43	w	w	PROPN
ejpam-3975	94	44	∈	∈	PROPN
ejpam-3975	94	45	[	[	X
ejpam-3975	94	46	ng(x3	ng(x3	NUM
ejpam-3975	94	47	)	)	PUNCT
ejpam-3975	94	48	∩ng(x4)]\ng[x4	∩ng(x4)]\ng[x4	PROPN
ejpam-3975	94	49	]	]	X
ejpam-3975	94	50	,	,	PUNCT
ejpam-3975	94	51	or	or	CCONJ
ejpam-3975	94	52	(	(	PUNCT
ejpam-3975	94	53	h	h	NOUN
ejpam-3975	94	54	)	)	PUNCT
ejpam-3975	94	55	v	v	NOUN
ejpam-3975	94	56	∈	∈	PROPN
ejpam-3975	94	57	[	[	X
ejpam-3975	94	58	ng(x3	ng(x3	NUM
ejpam-3975	94	59	)	)	PUNCT
ejpam-3975	94	60	∩	∩	NOUN
ejpam-3975	94	61	ng(x4	ng(x4	NOUN
ejpam-3975	94	62	)	)	PUNCT
ejpam-3975	94	63	∩	∩	NOUN
ejpam-3975	94	64	ng(u)]\(ng[x2	ng(u)]\(ng[x2	NOUN
ejpam-3975	94	65	]	]	PUNCT
ejpam-3975	94	66	∪	∪	X
ejpam-3975	94	67	ng[w	ng[w	PROPN
ejpam-3975	94	68	]	]	PUNCT
ejpam-3975	94	69	)	)	PUNCT
ejpam-3975	94	70	for	for	ADP
ejpam-3975	94	71	each	each	DET
ejpam-3975	94	72	u	u	PROPN
ejpam-3975	94	73	∈	∈	PROPN
ejpam-3975	94	74	[	[	X
ejpam-3975	94	75	ng(x3	ng(x3	NUM
ejpam-3975	94	76	)	)	PUNCT
ejpam-3975	94	77	∩	∩	NOUN
ejpam-3975	94	78	ng(x4)]\ng[x1	ng(x4)]\ng[x1	VERB
ejpam-3975	94	79	]	]	PUNCT
ejpam-3975	94	80	and	and	CCONJ
ejpam-3975	94	81	for	for	ADP
ejpam-3975	94	82	each	each	DET
ejpam-3975	94	83	w	w	PROPN
ejpam-3975	94	84	∈	∈	PROPN
ejpam-3975	94	85	ng(x1	ng(x1	NOUN
ejpam-3975	94	86	)	)	PUNCT
ejpam-3975	94	87	∩ng(x2	∩ng(x2	NOUN
ejpam-3975	94	88	)	)	PUNCT
ejpam-3975	94	89	,	,	PUNCT
ejpam-3975	94	90	or	or	CCONJ
ejpam-3975	94	91	(	(	PUNCT
ejpam-3975	94	92	i	i	NOUN
ejpam-3975	94	93	)	)	PUNCT
ejpam-3975	94	94	v	v	ADP
ejpam-3975	94	95	∈	∈	PROPN
ejpam-3975	95	1	[	[	X
ejpam-3975	95	2	ng(x1)∩ng(u)]\	ng(x1)∩ng(u)]\	X
ejpam-3975	95	3	[	[	X
ejpam-3975	95	4	(	(	PUNCT
ejpam-3975	95	5	⋃	⋃	PROPN
ejpam-3975	95	6	k	k	PROPN
ejpam-3975	95	7	6=1ng(xk))∪ng(w	6=1ng(xk))∪ng(w	NUM
ejpam-3975	95	8	)	)	PUNCT
ejpam-3975	95	9	]	]	PUNCT
ejpam-3975	95	10	for	for	ADP
ejpam-3975	95	11	each	each	DET
ejpam-3975	95	12	u	u	PROPN
ejpam-3975	95	13	∈	∈	PROPN
ejpam-3975	95	14	ng(x1)∩ng(x2	ng(x1)∩ng(x2	NUM
ejpam-3975	95	15	)	)	PUNCT
ejpam-3975	95	16	and	and	CCONJ
ejpam-3975	95	17	for	for	ADP
ejpam-3975	95	18	each	each	DET
ejpam-3975	95	19	w	w	PROPN
ejpam-3975	95	20	∈	∈	PROPN
ejpam-3975	95	21	ng(x4	ng(x4	NOUN
ejpam-3975	95	22	)	)	PUNCT
ejpam-3975	95	23	,	,	PUNCT
ejpam-3975	95	24	or	or	CCONJ
ejpam-3975	95	25	(	(	PUNCT
ejpam-3975	95	26	j	j	NOUN
ejpam-3975	95	27	)	)	PUNCT
ejpam-3975	95	28	v	v	ADP
ejpam-3975	95	29	∈	∈	PROPN
ejpam-3975	95	30	[	[	X
ejpam-3975	95	31	ng(x4)∩ng(u)]\	ng(x4)∩ng(u)]\	NUM
ejpam-3975	95	32	[	[	X
ejpam-3975	95	33	(	(	PUNCT
ejpam-3975	95	34	⋃	⋃	PROPN
ejpam-3975	95	35	k	k	NOUN
ejpam-3975	95	36	6=4ng(xk))∪ng(w	6=4ng(xk))∪ng(w	NOUN
ejpam-3975	95	37	)	)	PUNCT
ejpam-3975	95	38	]	]	PUNCT
ejpam-3975	95	39	for	for	ADP
ejpam-3975	95	40	each	each	DET
ejpam-3975	95	41	u	u	PROPN
ejpam-3975	95	42	∈	∈	PROPN
ejpam-3975	95	43	ng(x3)∩ng(x4	ng(x3)∩ng(x4	NUM
ejpam-3975	95	44	)	)	PUNCT
ejpam-3975	95	45	,	,	PUNCT
ejpam-3975	95	46	and	and	CCONJ
ejpam-3975	95	47	for	for	ADP
ejpam-3975	95	48	each	each	DET
ejpam-3975	95	49	w	w	PROPN
ejpam-3975	95	50	∈	∈	PROPN
ejpam-3975	95	51	ng(x1	ng(x1	NOUN
ejpam-3975	95	52	)	)	PUNCT
ejpam-3975	95	53	,	,	PUNCT
ejpam-3975	95	54	or	or	CCONJ
ejpam-3975	95	55	(	(	PUNCT
ejpam-3975	95	56	k	k	NOUN
ejpam-3975	95	57	)	)	PUNCT
ejpam-3975	95	58	v	v	NOUN
ejpam-3975	95	59	satisfies	satisfie	NOUN
ejpam-3975	95	60	condition	condition	NOUN
ejpam-3975	95	61	(	(	PUNCT
ejpam-3975	95	62	f	f	X
ejpam-3975	95	63	)	)	PUNCT
ejpam-3975	95	64	and	and	CCONJ
ejpam-3975	95	65	v	v	ADP
ejpam-3975	95	66	∈	∈	NOUN
ejpam-3975	95	67	ng(w	ng(w	NOUN
ejpam-3975	95	68	)	)	PUNCT
ejpam-3975	95	69	for	for	ADP
ejpam-3975	95	70	w	w	PROPN
ejpam-3975	95	71	∈	∈	PROPN
ejpam-3975	95	72	ng(x2)\	ng(x2)\	PUNCT
ejpam-3975	95	73	⋃	⋃	PROPN
ejpam-3975	95	74	k	k	PROPN
ejpam-3975	95	75	6=2	6=2	NUM
ejpam-3975	95	76	ng(xk	ng(xk	NOUN
ejpam-3975	95	77	)	)	PUNCT
ejpam-3975	95	78	,	,	PUNCT
ejpam-3975	95	79	or	or	CCONJ
ejpam-3975	95	80	(	(	PUNCT
ejpam-3975	95	81	l	l	NOUN
ejpam-3975	95	82	)	)	PUNCT
ejpam-3975	95	83	v	v	NOUN
ejpam-3975	95	84	satisfies	satisfie	NOUN
ejpam-3975	95	85	condition	condition	NOUN
ejpam-3975	95	86	(	(	PUNCT
ejpam-3975	95	87	i	i	NOUN
ejpam-3975	95	88	)	)	PUNCT
ejpam-3975	95	89	and	and	CCONJ
ejpam-3975	95	90	v	v	ADP
ejpam-3975	95	91	∈	∈	PROPN
ejpam-3975	95	92	ng(w	ng(w	NOUN
ejpam-3975	95	93	)	)	PUNCT
ejpam-3975	95	94	where	where	SCONJ
ejpam-3975	95	95	degg(w	degg(w	ADJ
ejpam-3975	95	96	)	)	PUNCT
ejpam-3975	95	97	=	=	SYM
ejpam-3975	95	98	1	1	NUM
ejpam-3975	95	99	,	,	PUNCT
ejpam-3975	95	100	or	or	CCONJ
ejpam-3975	95	101	r.	r.	PROPN
ejpam-3975	95	102	rakim	rakim	PROPN
ejpam-3975	95	103	,	,	PUNCT
ejpam-3975	95	104	h.	h.	PROPN
ejpam-3975	95	105	rara	rara	PROPN
ejpam-3975	95	106	/	/	SYM
ejpam-3975	95	107	eur	eur	PROPN
ejpam-3975	95	108	.	.	PUNCT
ejpam-3975	96	1	j.	j.	PROPN
ejpam-3975	96	2	pure	pure	PROPN
ejpam-3975	96	3	appl	appl	PROPN
ejpam-3975	96	4	.	.	PROPN
ejpam-3975	96	5	math	math	PROPN
ejpam-3975	96	6	,	,	PUNCT
ejpam-3975	96	7	14	14	NUM
ejpam-3975	96	8	(	(	PUNCT
ejpam-3975	96	9	3	3	NUM
ejpam-3975	96	10	)	)	PUNCT
ejpam-3975	96	11	(	(	PUNCT
ejpam-3975	96	12	2021	2021	NUM
ejpam-3975	96	13	)	)	PUNCT
ejpam-3975	96	14	,	,	PUNCT
ejpam-3975	96	15	803	803	NUM
ejpam-3975	96	16	-	-	SYM
ejpam-3975	96	17	815	815	NUM
ejpam-3975	96	18	807	807	NUM
ejpam-3975	96	19	(	(	PUNCT
ejpam-3975	96	20	m	m	NOUN
ejpam-3975	96	21	)	)	PUNCT
ejpam-3975	96	22	v	v	NOUN
ejpam-3975	96	23	satisfies	satisfie	NOUN
ejpam-3975	96	24	condition	condition	NOUN
ejpam-3975	96	25	(	(	PUNCT
ejpam-3975	96	26	j	j	NOUN
ejpam-3975	96	27	)	)	PUNCT
ejpam-3975	96	28	and	and	CCONJ
ejpam-3975	96	29	v	v	ADP
ejpam-3975	96	30	∈	∈	PROPN
ejpam-3975	96	31	ng(w	ng(w	NOUN
ejpam-3975	96	32	)	)	PUNCT
ejpam-3975	96	33	where	where	SCONJ
ejpam-3975	96	34	degg(w	degg(w	ADJ
ejpam-3975	96	35	)	)	PUNCT
ejpam-3975	96	36	=	=	SYM
ejpam-3975	96	37	1	1	NUM
ejpam-3975	96	38	,	,	PUNCT
ejpam-3975	96	39	or	or	CCONJ
ejpam-3975	96	40	(	(	PUNCT
ejpam-3975	96	41	n	n	CCONJ
ejpam-3975	96	42	)	)	PUNCT
ejpam-3975	97	1	v	v	NOUN
ejpam-3975	97	2	satisfies	satisfie	NOUN
ejpam-3975	97	3	condition	condition	NOUN
ejpam-3975	97	4	(	(	PUNCT
ejpam-3975	97	5	c	c	NOUN
ejpam-3975	97	6	)	)	PUNCT
ejpam-3975	97	7	and	and	CCONJ
ejpam-3975	97	8	v	v	ADP
ejpam-3975	97	9	∈	∈	NOUN
ejpam-3975	97	10	ng(w	ng(w	NOUN
ejpam-3975	97	11	)	)	PUNCT
ejpam-3975	97	12	and	and	CCONJ
ejpam-3975	97	13	u	u	PROPN
ejpam-3975	97	14	∈	∈	PROPN
ejpam-3975	97	15	ng(y	ng(y	NOUN
ejpam-3975	97	16	)	)	PUNCT
ejpam-3975	97	17	where	where	SCONJ
ejpam-3975	97	18	degg(w	degg(w	ADJ
ejpam-3975	97	19	)	)	PUNCT
ejpam-3975	97	20	=	=	SYM
ejpam-3975	97	21	degg(y	degg(y	PROPN
ejpam-3975	97	22	)	)	PUNCT
ejpam-3975	97	23	=	=	SYM
ejpam-3975	97	24	1	1	X
ejpam-3975	97	25	.	.	PUNCT
ejpam-3975	97	26	proof	proof	NOUN
ejpam-3975	97	27	.	.	PUNCT
ejpam-3975	98	1	suppoose	suppoose	VERB
ejpam-3975	98	2	s	s	PART
ejpam-3975	98	3	=	=	PUNCT
ejpam-3975	98	4	{	{	PUNCT
ejpam-3975	98	5	x1	x1	PROPN
ejpam-3975	98	6	,	,	PUNCT
ejpam-3975	98	7	x2	x2	PROPN
ejpam-3975	98	8	,	,	PUNCT
ejpam-3975	98	9	x3	x3	ADJ
ejpam-3975	98	10	,	,	PUNCT
ejpam-3975	98	11	x4	x4	PROPN
ejpam-3975	98	12	}	}	PUNCT
ejpam-3975	98	13	and	and	CCONJ
ejpam-3975	98	14	〈	〈	PROPN
ejpam-3975	98	15	s	s	PROPN
ejpam-3975	98	16	〉	〉	NOUN
ejpam-3975	98	17	∼=	∼=	NOUN
ejpam-3975	98	18	p2∪k2	p2∪k2	NUM
ejpam-3975	98	19	where	where	SCONJ
ejpam-3975	98	20	p2	p2	X
ejpam-3975	98	21	=	=	PUNCT
ejpam-3975	99	1	[	[	X
ejpam-3975	99	2	x2	x2	X
ejpam-3975	99	3	,	,	PUNCT
ejpam-3975	99	4	x3	x3	ADJ
ejpam-3975	99	5	]	]	PUNCT
ejpam-3975	99	6	and	and	CCONJ
ejpam-3975	99	7	v	v	NOUN
ejpam-3975	99	8	(	(	PUNCT
ejpam-3975	99	9	k2	k2	NOUN
ejpam-3975	99	10	)	)	PUNCT
ejpam-3975	99	11	=	=	PRON
ejpam-3975	99	12	{	{	PUNCT
ejpam-3975	99	13	x1	x1	PROPN
ejpam-3975	99	14	,	,	PUNCT
ejpam-3975	99	15	x4	x4	PROPN
ejpam-3975	99	16	}	}	PUNCT
ejpam-3975	99	17	.	.	PUNCT
ejpam-3975	100	1	let	let	VERB
ejpam-3975	100	2	v	v	NUM
ejpam-3975	100	3	∈	∈	PROPN
ejpam-3975	100	4	v	v	NOUN
ejpam-3975	100	5	(	(	PUNCT
ejpam-3975	100	6	g	g	NOUN
ejpam-3975	100	7	)	)	PUNCT
ejpam-3975	100	8	.	.	PUNCT
ejpam-3975	101	1	if	if	SCONJ
ejpam-3975	101	2	v	v	NUM
ejpam-3975	101	3	∈	∈	PROPN
ejpam-3975	101	4	s	s	NOUN
ejpam-3975	101	5	,	,	PUNCT
ejpam-3975	101	6	then	then	ADV
ejpam-3975	101	7	by	by	ADP
ejpam-3975	101	8	(	(	PUNCT
ejpam-3975	101	9	i	i	NOUN
ejpam-3975	101	10	)	)	PUNCT
ejpam-3975	101	11	and	and	CCONJ
ejpam-3975	101	12	(	(	PUNCT
ejpam-3975	101	13	ii	ii	NOUN
ejpam-3975	101	14	)	)	PUNCT
ejpam-3975	101	15	,	,	PUNCT
ejpam-3975	101	16	|ng(v	|ng(v	ADP
ejpam-3975	101	17	,	,	PUNCT
ejpam-3975	101	18	2	2	X
ejpam-3975	101	19	)	)	PUNCT
ejpam-3975	101	20	∩	∩	NOUN
ejpam-3975	101	21	s|	s|	NOUN
ejpam-3975	101	22	=	=	SYM
ejpam-3975	101	23	1	1	X
ejpam-3975	101	24	.	.	PUNCT
ejpam-3975	101	25	suppose	suppose	VERB
ejpam-3975	101	26	that	that	SCONJ
ejpam-3975	101	27	v	v	NOUN
ejpam-3975	101	28	/∈	/∈	PUNCT
ejpam-3975	101	29	s.	s.	PROPN
ejpam-3975	102	1	if	if	SCONJ
ejpam-3975	102	2	(	(	PUNCT
ejpam-3975	102	3	iii)(a	iii)(a	NOUN
ejpam-3975	102	4	)	)	PUNCT
ejpam-3975	102	5	holds	hold	VERB
ejpam-3975	102	6	,	,	PUNCT
ejpam-3975	102	7	then	then	ADV
ejpam-3975	102	8	ng(v	ng(v	PUNCT
ejpam-3975	102	9	,	,	PUNCT
ejpam-3975	102	10	2	2	X
ejpam-3975	102	11	)	)	PUNCT
ejpam-3975	102	12	∩	∩	NOUN
ejpam-3975	102	13	s	s	PART
ejpam-3975	102	14	=	=	PUNCT
ejpam-3975	102	15	{	{	PUNCT
ejpam-3975	102	16	x4	x4	PROPN
ejpam-3975	102	17	}	}	PUNCT
ejpam-3975	102	18	.	.	PUNCT
ejpam-3975	103	1	if	if	SCONJ
ejpam-3975	103	2	(	(	PUNCT
ejpam-3975	103	3	iii)(b	iii)(b	ADJ
ejpam-3975	103	4	)	)	PUNCT
ejpam-3975	103	5	holds	hold	VERB
ejpam-3975	103	6	,	,	PUNCT
ejpam-3975	103	7	then	then	ADV
ejpam-3975	103	8	ng(v	ng(v	PUNCT
ejpam-3975	103	9	,	,	PUNCT
ejpam-3975	103	10	2	2	X
ejpam-3975	103	11	)	)	PUNCT
ejpam-3975	103	12	∩	∩	NOUN
ejpam-3975	103	13	s	s	PART
ejpam-3975	103	14	=	=	X
ejpam-3975	103	15	{	{	PUNCT
ejpam-3975	103	16	x3	x3	ADJ
ejpam-3975	103	17	}	}	PUNCT
ejpam-3975	103	18	for	for	ADP
ejpam-3975	103	19	v	v	PROPN
ejpam-3975	103	20	∈	∈	PROPN
ejpam-3975	103	21	ng(x2	ng(x2	NOUN
ejpam-3975	103	22	)	)	PUNCT
ejpam-3975	103	23	and	and	CCONJ
ejpam-3975	103	24	ng(v	ng(v	PROPN
ejpam-3975	103	25	,	,	PUNCT
ejpam-3975	103	26	2	2	X
ejpam-3975	103	27	)	)	PUNCT
ejpam-3975	103	28	∩	∩	NOUN
ejpam-3975	103	29	s	s	PART
ejpam-3975	103	30	=	=	X
ejpam-3975	103	31	{	{	PUNCT
ejpam-3975	103	32	x2	x2	NOUN
ejpam-3975	103	33	}	}	PUNCT
ejpam-3975	103	34	for	for	ADP
ejpam-3975	103	35	v	v	NUM
ejpam-3975	103	36	∈	∈	NOUN
ejpam-3975	103	37	ng(x3	ng(x3	NUM
ejpam-3975	103	38	)	)	PUNCT
ejpam-3975	103	39	.	.	PUNCT
ejpam-3975	104	1	if	if	SCONJ
ejpam-3975	104	2	(	(	PUNCT
ejpam-3975	104	3	iii)(c	iii)(c	NOUN
ejpam-3975	104	4	)	)	PUNCT
ejpam-3975	104	5	holds	hold	VERB
ejpam-3975	104	6	,	,	PUNCT
ejpam-3975	104	7	then	then	ADV
ejpam-3975	104	8	ng(v	ng(v	PUNCT
ejpam-3975	104	9	,	,	PUNCT
ejpam-3975	104	10	2	2	X
ejpam-3975	104	11	)	)	PUNCT
ejpam-3975	104	12	∩	∩	NOUN
ejpam-3975	104	13	s	s	PART
ejpam-3975	104	14	=	=	X
ejpam-3975	104	15	{	{	PUNCT
ejpam-3975	104	16	x3	x3	ADJ
ejpam-3975	104	17	}	}	PUNCT
ejpam-3975	104	18	.	.	PUNCT
ejpam-3975	105	1	if	if	SCONJ
ejpam-3975	105	2	(	(	PUNCT
ejpam-3975	105	3	iii)(d	iii)(d	ADV
ejpam-3975	105	4	)	)	PUNCT
ejpam-3975	105	5	and	and	CCONJ
ejpam-3975	105	6	(	(	PUNCT
ejpam-3975	105	7	iii)(e	iii)(e	NOUN
ejpam-3975	105	8	)	)	PUNCT
ejpam-3975	105	9	hold	hold	VERB
ejpam-3975	105	10	,	,	PUNCT
ejpam-3975	105	11	then	then	ADV
ejpam-3975	105	12	ng(v	ng(v	PUNCT
ejpam-3975	105	13	,	,	PUNCT
ejpam-3975	105	14	2	2	X
ejpam-3975	105	15	)	)	PUNCT
ejpam-3975	105	16	∩	∩	NOUN
ejpam-3975	105	17	s	s	PART
ejpam-3975	105	18	=	=	X
ejpam-3975	105	19	{	{	PUNCT
ejpam-3975	105	20	x3	x3	ADJ
ejpam-3975	105	21	}	}	PUNCT
ejpam-3975	105	22	for	for	ADP
ejpam-3975	105	23	v	v	PROPN
ejpam-3975	105	24	∈	∈	PROPN
ejpam-3975	105	25	ng(x2	ng(x2	NOUN
ejpam-3975	105	26	)	)	PUNCT
ejpam-3975	105	27	∩	∩	NOUN
ejpam-3975	105	28	ng(x4	ng(x4	NOUN
ejpam-3975	105	29	)	)	PUNCT
ejpam-3975	105	30	or	or	CCONJ
ejpam-3975	105	31	ng(v	ng(v	PUNCT
ejpam-3975	105	32	,	,	PUNCT
ejpam-3975	105	33	2	2	X
ejpam-3975	105	34	)	)	PUNCT
ejpam-3975	105	35	∩	∩	NOUN
ejpam-3975	105	36	s	s	PART
ejpam-3975	105	37	=	=	X
ejpam-3975	105	38	{	{	PUNCT
ejpam-3975	105	39	x2	x2	NOUN
ejpam-3975	105	40	}	}	PUNCT
ejpam-3975	105	41	for	for	ADP
ejpam-3975	105	42	v	v	PROPN
ejpam-3975	105	43	∈	∈	PROPN
ejpam-3975	105	44	ng(x1	ng(x1	NOUN
ejpam-3975	105	45	)	)	PUNCT
ejpam-3975	105	46	∩	∩	NOUN
ejpam-3975	105	47	ng(x3	ng(x3	NUM
ejpam-3975	105	48	)	)	PUNCT
ejpam-3975	105	49	.	.	PUNCT
ejpam-3975	106	1	if	if	SCONJ
ejpam-3975	106	2	(	(	PUNCT
ejpam-3975	106	3	iii)(f	iii)(f	ADJ
ejpam-3975	106	4	)	)	PUNCT
ejpam-3975	106	5	holds	hold	NOUN
ejpam-3975	106	6	,	,	PUNCT
ejpam-3975	106	7	then	then	ADV
ejpam-3975	106	8	ng(v	ng(v	PUNCT
ejpam-3975	106	9	,	,	PUNCT
ejpam-3975	106	10	2	2	X
ejpam-3975	106	11	)	)	PUNCT
ejpam-3975	106	12	∩	∩	NOUN
ejpam-3975	106	13	s	s	PART
ejpam-3975	106	14	=	=	PUNCT
ejpam-3975	106	15	{	{	PUNCT
ejpam-3975	106	16	x1	x1	PROPN
ejpam-3975	106	17	}	}	PUNCT
ejpam-3975	106	18	for	for	ADP
ejpam-3975	106	19	v	v	PROPN
ejpam-3975	106	20	∈	∈	PROPN
ejpam-3975	106	21	ng(x2	ng(x2	NOUN
ejpam-3975	106	22	)	)	PUNCT
ejpam-3975	106	23	∩	∩	NOUN
ejpam-3975	106	24	ng(x3	ng(x3	NUM
ejpam-3975	106	25	)	)	PUNCT
ejpam-3975	106	26	∩	∩	NOUN
ejpam-3975	106	27	ng(u	ng(u	NOUN
ejpam-3975	106	28	)	)	PUNCT
ejpam-3975	106	29	and	and	CCONJ
ejpam-3975	106	30	u	u	PROPN
ejpam-3975	106	31	∈	∈	PROPN
ejpam-3975	106	32	ng(x1	ng(x1	NOUN
ejpam-3975	106	33	)	)	PUNCT
ejpam-3975	106	34	∩	∩	ADJ
ejpam-3975	106	35	ng(x2	ng(x2	NOUN
ejpam-3975	106	36	)	)	PUNCT
ejpam-3975	106	37	or	or	CCONJ
ejpam-3975	106	38	ng(v	ng(v	NUM
ejpam-3975	106	39	,	,	PUNCT
ejpam-3975	106	40	2	2	X
ejpam-3975	106	41	)	)	PUNCT
ejpam-3975	106	42	∩	∩	NOUN
ejpam-3975	106	43	s	s	PART
ejpam-3975	106	44	=	=	PUNCT
ejpam-3975	106	45	{	{	PUNCT
ejpam-3975	106	46	x4	x4	PROPN
ejpam-3975	106	47	}	}	PUNCT
ejpam-3975	106	48	for	for	ADP
ejpam-3975	106	49	v	v	PROPN
ejpam-3975	106	50	∈	∈	PROPN
ejpam-3975	106	51	ng(x2	ng(x2	NOUN
ejpam-3975	106	52	)	)	PUNCT
ejpam-3975	106	53	∩	∩	NOUN
ejpam-3975	106	54	ng(x3	ng(x3	NUM
ejpam-3975	106	55	)	)	PUNCT
ejpam-3975	106	56	∩	∩	NOUN
ejpam-3975	106	57	ng(u	ng(u	NOUN
ejpam-3975	106	58	)	)	PUNCT
ejpam-3975	106	59	and	and	CCONJ
ejpam-3975	106	60	u	u	PROPN
ejpam-3975	106	61	∈	∈	PROPN
ejpam-3975	106	62	ng(x3	ng(x3	NUM
ejpam-3975	106	63	)	)	PUNCT
ejpam-3975	106	64	∩	∩	NOUN
ejpam-3975	106	65	ng(x4	ng(x4	NOUN
ejpam-3975	106	66	)	)	PUNCT
ejpam-3975	106	67	.	.	PUNCT
ejpam-3975	107	1	if	if	SCONJ
ejpam-3975	107	2	(	(	PUNCT
ejpam-3975	107	3	iii)(g	iii)(g	NOUN
ejpam-3975	107	4	)	)	PUNCT
ejpam-3975	107	5	and	and	CCONJ
ejpam-3975	107	6	(	(	PUNCT
ejpam-3975	107	7	iii)(h	iii)(h	NOUN
ejpam-3975	107	8	)	)	PUNCT
ejpam-3975	107	9	hold	hold	VERB
ejpam-3975	107	10	,	,	PUNCT
ejpam-3975	107	11	then	then	ADV
ejpam-3975	107	12	ng(v	ng(v	PUNCT
ejpam-3975	107	13	,	,	PUNCT
ejpam-3975	107	14	2	2	X
ejpam-3975	107	15	)	)	PUNCT
ejpam-3975	107	16	∩	∩	NOUN
ejpam-3975	107	17	s	s	PART
ejpam-3975	107	18	=	=	X
ejpam-3975	107	19	{	{	PUNCT
ejpam-3975	107	20	x3	x3	ADJ
ejpam-3975	107	21	}	}	PUNCT
ejpam-3975	107	22	for	for	ADP
ejpam-3975	107	23	v	v	PROPN
ejpam-3975	107	24	∈	∈	PROPN
ejpam-3975	107	25	ng(x1	ng(x1	NOUN
ejpam-3975	107	26	)	)	PUNCT
ejpam-3975	107	27	∩	∩	ADJ
ejpam-3975	107	28	ng(x2	ng(x2	NOUN
ejpam-3975	107	29	)	)	PUNCT
ejpam-3975	107	30	∩	∩	NOUN
ejpam-3975	107	31	ng(u	ng(u	NOUN
ejpam-3975	107	32	)	)	PUNCT
ejpam-3975	107	33	or	or	CCONJ
ejpam-3975	107	34	ng(v	ng(v	NUM
ejpam-3975	107	35	,	,	PUNCT
ejpam-3975	107	36	2	2	X
ejpam-3975	107	37	)	)	PUNCT
ejpam-3975	107	38	∩	∩	NOUN
ejpam-3975	107	39	s	s	PART
ejpam-3975	107	40	=	=	X
ejpam-3975	107	41	{	{	PUNCT
ejpam-3975	107	42	x2	x2	NOUN
ejpam-3975	107	43	}	}	PUNCT
ejpam-3975	107	44	for	for	ADP
ejpam-3975	107	45	v	v	NOUN
ejpam-3975	107	46	∈	∈	PROPN
ejpam-3975	107	47	ng(x3	ng(x3	NUM
ejpam-3975	107	48	)	)	PUNCT
ejpam-3975	107	49	∩	∩	NOUN
ejpam-3975	107	50	ng(x4	ng(x4	NOUN
ejpam-3975	107	51	)	)	PUNCT
ejpam-3975	107	52	∩	∩	NOUN
ejpam-3975	107	53	ng(u	ng(u	NOUN
ejpam-3975	107	54	)	)	PUNCT
ejpam-3975	107	55	.	.	PUNCT
ejpam-3975	108	1	if	if	SCONJ
ejpam-3975	108	2	(	(	PUNCT
ejpam-3975	108	3	iii)((i	iii)((i	ADV
ejpam-3975	108	4	)	)	PUNCT
ejpam-3975	108	5	and	and	CCONJ
ejpam-3975	108	6	(	(	PUNCT
ejpam-3975	108	7	j	j	NOUN
ejpam-3975	108	8	)	)	PUNCT
ejpam-3975	108	9	)	)	PUNCT
ejpam-3975	109	1	hold	hold	VERB
ejpam-3975	109	2	,	,	PUNCT
ejpam-3975	109	3	then	then	ADV
ejpam-3975	109	4	ng(v	ng(v	PUNCT
ejpam-3975	109	5	,	,	PUNCT
ejpam-3975	109	6	2)∩s	2)∩s	PROPN
ejpam-3975	109	7	=	=	SYM
ejpam-3975	109	8	{	{	PUNCT
ejpam-3975	109	9	x2	x2	PROPN
ejpam-3975	109	10	}	}	PUNCT
ejpam-3975	109	11	for	for	ADP
ejpam-3975	109	12	v	v	NOUN
ejpam-3975	109	13	∈	∈	PROPN
ejpam-3975	109	14	ng(x1)∩ng(u	ng(x1)∩ng(u	NOUN
ejpam-3975	109	15	)	)	PUNCT
ejpam-3975	109	16	or	or	CCONJ
ejpam-3975	109	17	ng(v	ng(v	NUM
ejpam-3975	109	18	,	,	PUNCT
ejpam-3975	109	19	2)∩s	2)∩s	PROPN
ejpam-3975	109	20	=	=	SYM
ejpam-3975	109	21	{	{	PUNCT
ejpam-3975	109	22	x3	x3	PROPN
ejpam-3975	109	23	}	}	PUNCT
ejpam-3975	109	24	for	for	ADP
ejpam-3975	109	25	v	v	PROPN
ejpam-3975	109	26	∈	∈	PROPN
ejpam-3975	109	27	ng(x4)∩ng(u	ng(x4)∩ng(u	PROPN
ejpam-3975	109	28	)	)	PUNCT
ejpam-3975	109	29	.	.	PUNCT
ejpam-3975	110	1	if	if	SCONJ
ejpam-3975	110	2	(	(	PUNCT
ejpam-3975	110	3	k	k	NOUN
ejpam-3975	110	4	)	)	PUNCT
ejpam-3975	110	5	holds	hold	NOUN
ejpam-3975	110	6	,	,	PUNCT
ejpam-3975	110	7	then	then	ADV
ejpam-3975	110	8	ng(w	ng(w	NOUN
ejpam-3975	110	9	,	,	PUNCT
ejpam-3975	110	10	2	2	X
ejpam-3975	110	11	)	)	PUNCT
ejpam-3975	110	12	∩	∩	NOUN
ejpam-3975	110	13	s	s	PART
ejpam-3975	110	14	=	=	X
ejpam-3975	110	15	{	{	PUNCT
ejpam-3975	110	16	x2	x2	NOUN
ejpam-3975	110	17	}	}	PUNCT
ejpam-3975	110	18	for	for	ADP
ejpam-3975	110	19	w	w	PROPN
ejpam-3975	110	20	∈	∈	PROPN
ejpam-3975	110	21	ng(v	ng(v	PRON
ejpam-3975	110	22	)	)	PUNCT
ejpam-3975	110	23	∩ng(x3	∩ng(x3	SYM
ejpam-3975	110	24	)	)	PUNCT
ejpam-3975	110	25	or	or	CCONJ
ejpam-3975	110	26	ng(w	ng(w	NOUN
ejpam-3975	110	27	,	,	PUNCT
ejpam-3975	110	28	2	2	X
ejpam-3975	110	29	)	)	PUNCT
ejpam-3975	110	30	∩	∩	NOUN
ejpam-3975	110	31	s	s	PART
ejpam-3975	110	32	=	=	X
ejpam-3975	110	33	{	{	PUNCT
ejpam-3975	110	34	x3	x3	ADJ
ejpam-3975	110	35	}	}	PUNCT
ejpam-3975	110	36	for	for	ADP
ejpam-3975	110	37	w	w	PROPN
ejpam-3975	110	38	∈	∈	PROPN
ejpam-3975	110	39	ng(v	ng(v	NOUN
ejpam-3975	110	40	)	)	PUNCT
ejpam-3975	110	41	∩	∩	ADJ
ejpam-3975	110	42	ng(x2	ng(x2	NOUN
ejpam-3975	110	43	)	)	PUNCT
ejpam-3975	110	44	.	.	PUNCT
ejpam-3975	111	1	if	if	SCONJ
ejpam-3975	111	2	(	(	PUNCT
ejpam-3975	111	3	l	l	NOUN
ejpam-3975	111	4	)	)	PUNCT
ejpam-3975	111	5	holds	hold	NOUN
ejpam-3975	111	6	,	,	PUNCT
ejpam-3975	111	7	then	then	ADV
ejpam-3975	111	8	ng(w	ng(w	NOUN
ejpam-3975	111	9	,	,	PUNCT
ejpam-3975	111	10	2	2	X
ejpam-3975	111	11	)	)	PUNCT
ejpam-3975	111	12	∩	∩	NOUN
ejpam-3975	111	13	s	s	PART
ejpam-3975	111	14	=	=	PUNCT
ejpam-3975	111	15	{	{	PUNCT
ejpam-3975	111	16	x1	x1	PROPN
ejpam-3975	111	17	}	}	PUNCT
ejpam-3975	111	18	.	.	PUNCT
ejpam-3975	112	1	if	if	SCONJ
ejpam-3975	112	2	(	(	PUNCT
ejpam-3975	112	3	m	m	NOUN
ejpam-3975	112	4	)	)	PUNCT
ejpam-3975	112	5	holds	hold	NOUN
ejpam-3975	112	6	,	,	PUNCT
ejpam-3975	112	7	then	then	ADV
ejpam-3975	112	8	ng(w	ng(w	NOUN
ejpam-3975	112	9	,	,	PUNCT
ejpam-3975	112	10	2	2	X
ejpam-3975	112	11	)	)	PUNCT
ejpam-3975	112	12	∩	∩	NOUN
ejpam-3975	112	13	s	s	PART
ejpam-3975	112	14	=	=	PUNCT
ejpam-3975	112	15	{	{	PUNCT
ejpam-3975	112	16	x4	x4	PROPN
ejpam-3975	112	17	}	}	PUNCT
ejpam-3975	112	18	.	.	PUNCT
ejpam-3975	113	1	if	if	SCONJ
ejpam-3975	113	2	(	(	PUNCT
ejpam-3975	113	3	n	n	CCONJ
ejpam-3975	113	4	)	)	PUNCT
ejpam-3975	113	5	holds	hold	NOUN
ejpam-3975	113	6	,	,	PUNCT
ejpam-3975	113	7	then	then	ADV
ejpam-3975	113	8	ng(w	ng(w	NOUN
ejpam-3975	113	9	,	,	PUNCT
ejpam-3975	113	10	2	2	X
ejpam-3975	113	11	)	)	PUNCT
ejpam-3975	113	12	∩	∩	NOUN
ejpam-3975	113	13	s	s	PART
ejpam-3975	113	14	=	=	X
ejpam-3975	113	15	{	{	PUNCT
ejpam-3975	113	16	x2	x2	PROPN
ejpam-3975	113	17	}	}	PUNCT
ejpam-3975	113	18	.	.	PUNCT
ejpam-3975	114	1	therefore	therefore	ADV
ejpam-3975	114	2	,	,	PUNCT
ejpam-3975	114	3	s	s	VERB
ejpam-3975	114	4	is	be	AUX
ejpam-3975	114	5	a	a	DET
ejpam-3975	114	6	total	total	ADJ
ejpam-3975	114	7	perfect	perfect	ADJ
ejpam-3975	114	8	hop	hop	NOUN
ejpam-3975	114	9	dominating	dominating	NOUN
ejpam-3975	114	10	set	set	NOUN
ejpam-3975	114	11	of	of	ADP
ejpam-3975	114	12	g.	g.	PROPN
ejpam-3975	114	13	�	�	PROPN
ejpam-3975	114	14	lemma	lemma	PROPN
ejpam-3975	114	15	2.6	2.6	NUM
ejpam-3975	114	16	.	.	PUNCT
ejpam-3975	115	1	let	let	VERB
ejpam-3975	115	2	g	g	PRON
ejpam-3975	115	3	be	be	AUX
ejpam-3975	115	4	a	a	DET
ejpam-3975	115	5	graph	graph	NOUN
ejpam-3975	115	6	of	of	ADP
ejpam-3975	115	7	order	order	NOUN
ejpam-3975	115	8	n	n	PRON
ejpam-3975	115	9	≥	≥	NOUN
ejpam-3975	115	10	4	4	NUM
ejpam-3975	115	11	.	.	PUNCT
ejpam-3975	116	1	then	then	ADV
ejpam-3975	116	2	s	s	VERB
ejpam-3975	116	3	=	=	PUNCT
ejpam-3975	116	4	{	{	PUNCT
ejpam-3975	116	5	x1	x1	PROPN
ejpam-3975	116	6	,	,	PUNCT
ejpam-3975	116	7	x2	x2	PROPN
ejpam-3975	116	8	,	,	PUNCT
ejpam-3975	116	9	x3	x3	PROPN
ejpam-3975	116	10	,	,	PUNCT
ejpam-3975	116	11	x4	x4	PROPN
ejpam-3975	116	12	}	}	PUNCT
ejpam-3975	116	13	is	be	AUX
ejpam-3975	116	14	not	not	PART
ejpam-3975	116	15	a	a	DET
ejpam-3975	116	16	total	total	ADJ
ejpam-3975	116	17	perfect	perfect	ADJ
ejpam-3975	116	18	hop	hop	NOUN
ejpam-3975	116	19	dominating	dominating	NOUN
ejpam-3975	116	20	set	set	NOUN
ejpam-3975	116	21	of	of	ADP
ejpam-3975	116	22	g	g	PROPN
ejpam-3975	116	23	if	if	SCONJ
ejpam-3975	116	24	the	the	DET
ejpam-3975	116	25	following	follow	VERB
ejpam-3975	116	26	hold	hold	NOUN
ejpam-3975	116	27	.	.	PUNCT
ejpam-3975	117	1	(	(	PUNCT
ejpam-3975	117	2	i	i	NOUN
ejpam-3975	117	3	)	)	PUNCT
ejpam-3975	118	1	〈	〈	PROPN
ejpam-3975	118	2	s	s	PROPN
ejpam-3975	118	3	〉	〉	NOUN
ejpam-3975	118	4	∼=	∼=	PROPN
ejpam-3975	118	5	k2	k2	NOUN
ejpam-3975	118	6	∪k2	∪k2	X
ejpam-3975	118	7	where	where	SCONJ
ejpam-3975	118	8	x1x2	x1x2	X
ejpam-3975	118	9	,	,	PUNCT
ejpam-3975	118	10	x3x4	x3x4	PROPN
ejpam-3975	118	11	∈	∈	PROPN
ejpam-3975	118	12	e(g	e(g	PROPN
ejpam-3975	118	13	)	)	PUNCT
ejpam-3975	118	14	.	.	PUNCT
ejpam-3975	119	1	(	(	PUNCT
ejpam-3975	119	2	ii	ii	X
ejpam-3975	119	3	)	)	PUNCT
ejpam-3975	120	1	〈	〈	PROPN
ejpam-3975	120	2	s	s	PART
ejpam-3975	120	3	〉	〉	NOUN
ejpam-3975	120	4	∼=	∼=	PROPN
ejpam-3975	120	5	p3	p3	NOUN
ejpam-3975	120	6	∪k1	∪k1	ADJ
ejpam-3975	120	7	.	.	PUNCT
ejpam-3975	121	1	(	(	PUNCT
ejpam-3975	121	2	iii	iii	X
ejpam-3975	121	3	)	)	PUNCT
ejpam-3975	121	4	〈	〈	PROPN
ejpam-3975	121	5	s	s	PART
ejpam-3975	121	6	〉	〉	NOUN
ejpam-3975	121	7	∼=	∼=	NOUN
ejpam-3975	121	8	k4	k4	NOUN
ejpam-3975	121	9	.	.	PUNCT
ejpam-3975	122	1	proof	proof	NOUN
ejpam-3975	122	2	.	.	PUNCT
ejpam-3975	123	1	if	if	SCONJ
ejpam-3975	123	2	(	(	PUNCT
ejpam-3975	123	3	i	i	NOUN
ejpam-3975	123	4	)	)	PUNCT
ejpam-3975	123	5	holds	hold	VERB
ejpam-3975	123	6	and	and	CCONJ
ejpam-3975	123	7	s	s	VERB
ejpam-3975	123	8	=	=	X
ejpam-3975	123	9	{	{	PUNCT
ejpam-3975	123	10	x1	x1	PROPN
ejpam-3975	123	11	,	,	PUNCT
ejpam-3975	123	12	x2	x2	PROPN
ejpam-3975	123	13	,	,	PUNCT
ejpam-3975	123	14	x3	x3	PROPN
ejpam-3975	123	15	,	,	PUNCT
ejpam-3975	123	16	x4	x4	PROPN
ejpam-3975	123	17	}	}	PUNCT
ejpam-3975	123	18	is	be	AUX
ejpam-3975	123	19	a	a	DET
ejpam-3975	123	20	total	total	ADJ
ejpam-3975	123	21	perfect	perfect	ADJ
ejpam-3975	123	22	hop	hop	NOUN
ejpam-3975	123	23	dominating	dominating	NOUN
ejpam-3975	123	24	set	set	NOUN
ejpam-3975	123	25	of	of	ADP
ejpam-3975	123	26	g	g	NOUN
ejpam-3975	123	27	,	,	PUNCT
ejpam-3975	123	28	then	then	ADV
ejpam-3975	123	29	there	there	PRON
ejpam-3975	123	30	exists	exist	VERB
ejpam-3975	123	31	v	v	ADP
ejpam-3975	123	32	∈	∈	PROPN
ejpam-3975	123	33	⋂	⋂	PROPN
ejpam-3975	123	34	j	j	PROPN
ejpam-3975	123	35	ng(xj	ng(xj	ADV
ejpam-3975	123	36	)	)	PUNCT
ejpam-3975	123	37	for	for	ADP
ejpam-3975	123	38	j	j	PROPN
ejpam-3975	123	39	=	=	SYM
ejpam-3975	123	40	1	1	NUM
ejpam-3975	123	41	,	,	PUNCT
ejpam-3975	123	42	2	2	NUM
ejpam-3975	123	43	,	,	PUNCT
ejpam-3975	123	44	3	3	NUM
ejpam-3975	123	45	since	since	SCONJ
ejpam-3975	123	46	ng(x1	ng(x1	NUM
ejpam-3975	123	47	,	,	PUNCT
ejpam-3975	123	48	2)∩	2)∩	PROPN
ejpam-3975	123	49	s	s	PART
ejpam-3975	123	50	6=	6=	NOUN
ejpam-3975	123	51	∅	∅	NOUN
ejpam-3975	123	52	and	and	CCONJ
ejpam-3975	123	53	ng(x2	ng(x2	NOUN
ejpam-3975	123	54	,	,	PUNCT
ejpam-3975	123	55	2)∩	2)∩	PROPN
ejpam-3975	123	56	s	s	PART
ejpam-3975	123	57	6=	6=	X
ejpam-3975	123	58	∅.	∅.	ADP
ejpam-3975	123	59	hence	hence	ADV
ejpam-3975	123	60	,	,	PUNCT
ejpam-3975	123	61	dg(x3	dg(x3	PROPN
ejpam-3975	123	62	,	,	PUNCT
ejpam-3975	123	63	x1	x1	PROPN
ejpam-3975	123	64	)	)	PUNCT
ejpam-3975	123	65	=	=	SYM
ejpam-3975	124	1	dg(x3	dg(x3	PROPN
ejpam-3975	124	2	,	,	PUNCT
ejpam-3975	124	3	x2	x2	PROPN
ejpam-3975	124	4	)	)	PUNCT
ejpam-3975	124	5	=	=	SYM
ejpam-3975	124	6	2	2	NUM
ejpam-3975	124	7	contrary	contrary	ADV
ejpam-3975	124	8	to	to	ADP
ejpam-3975	124	9	our	our	PRON
ejpam-3975	124	10	assumption	assumption	NOUN
ejpam-3975	124	11	that	that	SCONJ
ejpam-3975	124	12	s	s	VERB
ejpam-3975	124	13	is	be	AUX
ejpam-3975	124	14	a	a	DET
ejpam-3975	124	15	total	total	ADJ
ejpam-3975	124	16	perfect	perfect	ADJ
ejpam-3975	124	17	hop	hop	NOUN
ejpam-3975	124	18	dominating	dominating	NOUN
ejpam-3975	124	19	set	set	NOUN
ejpam-3975	124	20	of	of	ADP
ejpam-3975	124	21	g.	g.	PROPN
ejpam-3975	124	22	similarly	similarly	ADV
ejpam-3975	124	23	,	,	PUNCT
ejpam-3975	124	24	there	there	PRON
ejpam-3975	124	25	exists	exist	VERB
ejpam-3975	124	26	u	u	PROPN
ejpam-3975	124	27	∈	∈	PROPN
ejpam-3975	124	28	⋂	⋂	PROPN
ejpam-3975	124	29	kng(xk	kng(xk	NOUN
ejpam-3975	124	30	)	)	PUNCT
ejpam-3975	124	31	for	for	ADP
ejpam-3975	124	32	k	k	PROPN
ejpam-3975	124	33	=	=	SYM
ejpam-3975	124	34	2	2	NUM
ejpam-3975	124	35	,	,	PUNCT
ejpam-3975	124	36	3	3	NUM
ejpam-3975	124	37	,	,	PUNCT
ejpam-3975	124	38	4	4	NUM
ejpam-3975	124	39	since	since	SCONJ
ejpam-3975	124	40	ng(x3	ng(x3	NUM
ejpam-3975	124	41	,	,	PUNCT
ejpam-3975	124	42	2	2	X
ejpam-3975	124	43	)	)	PUNCT
ejpam-3975	124	44	∩	∩	X
ejpam-3975	124	45	s	s	PART
ejpam-3975	124	46	6=	6=	NOUN
ejpam-3975	124	47	∅	∅	NOUN
ejpam-3975	124	48	and	and	CCONJ
ejpam-3975	124	49	ng(x4	ng(x4	ADJ
ejpam-3975	124	50	,	,	PUNCT
ejpam-3975	124	51	2	2	X
ejpam-3975	124	52	)	)	PUNCT
ejpam-3975	124	53	∩	∩	X
ejpam-3975	124	54	s	s	PART
ejpam-3975	124	55	6=	6=	NUM
ejpam-3975	124	56	∅.	∅.	ADP
ejpam-3975	124	57	hence	hence	ADV
ejpam-3975	124	58	,	,	PUNCT
ejpam-3975	124	59	dg(x2	dg(x2	NOUN
ejpam-3975	124	60	,	,	PUNCT
ejpam-3975	124	61	x3	x3	ADJ
ejpam-3975	124	62	)	)	PUNCT
ejpam-3975	124	63	=	=	SYM
ejpam-3975	124	64	dg(x2	dg(x2	NOUN
ejpam-3975	124	65	,	,	PUNCT
ejpam-3975	124	66	x4	x4	PROPN
ejpam-3975	124	67	)	)	PUNCT
ejpam-3975	124	68	=	=	SYM
ejpam-3975	124	69	2	2	NUM
ejpam-3975	124	70	is	be	AUX
ejpam-3975	124	71	a	a	DET
ejpam-3975	124	72	contradiction	contradiction	NOUN
ejpam-3975	124	73	to	to	ADP
ejpam-3975	124	74	our	our	PRON
ejpam-3975	124	75	assumption	assumption	NOUN
ejpam-3975	124	76	that	that	SCONJ
ejpam-3975	124	77	s	s	VERB
ejpam-3975	124	78	is	be	AUX
ejpam-3975	124	79	a	a	DET
ejpam-3975	124	80	total	total	ADJ
ejpam-3975	124	81	perfect	perfect	ADJ
ejpam-3975	124	82	hop	hop	NOUN
ejpam-3975	124	83	dominating	dominating	NOUN
ejpam-3975	124	84	set	set	NOUN
ejpam-3975	124	85	of	of	ADP
ejpam-3975	124	86	g.	g.	PROPN
ejpam-3975	124	87	similarly	similarly	ADV
ejpam-3975	124	88	,	,	PUNCT
ejpam-3975	124	89	if	if	SCONJ
ejpam-3975	124	90	(	(	PUNCT
ejpam-3975	124	91	ii	ii	NOUN
ejpam-3975	124	92	)	)	PUNCT
ejpam-3975	124	93	and	and	CCONJ
ejpam-3975	124	94	(	(	PUNCT
ejpam-3975	124	95	iii	iii	NOUN
ejpam-3975	124	96	)	)	PUNCT
ejpam-3975	124	97	hold	hold	NOUN
ejpam-3975	124	98	,	,	PUNCT
ejpam-3975	124	99	then	then	ADV
ejpam-3975	124	100	s	s	VERB
ejpam-3975	124	101	is	be	AUX
ejpam-3975	124	102	not	not	PART
ejpam-3975	124	103	a	a	DET
ejpam-3975	124	104	perfect	perfect	ADJ
ejpam-3975	124	105	hop	hop	NOUN
ejpam-3975	124	106	dominating	dominating	NOUN
ejpam-3975	124	107	set	set	NOUN
ejpam-3975	124	108	of	of	ADP
ejpam-3975	124	109	g.	g.	PROPN
ejpam-3975	124	110	�	�	PROPN
ejpam-3975	124	111	theorem	theorem	VERB
ejpam-3975	124	112	2.7	2.7	NUM
ejpam-3975	124	113	.	.	PUNCT
ejpam-3975	125	1	let	let	VERB
ejpam-3975	125	2	g	g	PRON
ejpam-3975	125	3	be	be	AUX
ejpam-3975	125	4	a	a	DET
ejpam-3975	125	5	connected	connected	ADJ
ejpam-3975	125	6	graph	graph	NOUN
ejpam-3975	125	7	of	of	ADP
ejpam-3975	125	8	order	order	NOUN
ejpam-3975	125	9	greater	great	ADJ
ejpam-3975	125	10	than	than	ADP
ejpam-3975	125	11	3	3	NUM
ejpam-3975	125	12	.	.	PUNCT
ejpam-3975	125	13	then	then	ADV
ejpam-3975	125	14	γtph(g	γtph(g	NOUN
ejpam-3975	125	15	)	)	PUNCT
ejpam-3975	125	16	=	=	SYM
ejpam-3975	125	17	4	4	NUM
ejpam-3975	125	18	if	if	SCONJ
ejpam-3975	125	19	and	and	CCONJ
ejpam-3975	125	20	only	only	ADV
ejpam-3975	125	21	if	if	SCONJ
ejpam-3975	125	22	g	g	PROPN
ejpam-3975	125	23	=	=	SYM
ejpam-3975	125	24	p4	p4	ADJ
ejpam-3975	125	25	or	or	CCONJ
ejpam-3975	125	26	g	g	NOUN
ejpam-3975	125	27	=	=	SYM
ejpam-3975	125	28	c4	c4	NOUN
ejpam-3975	125	29	or	or	CCONJ
ejpam-3975	125	30	|v	|v	PROPN
ejpam-3975	125	31	(	(	PUNCT
ejpam-3975	125	32	g)|	g)|	X
ejpam-3975	125	33	≥	≥	NUM
ejpam-3975	125	34	5	5	NUM
ejpam-3975	125	35	and	and	CCONJ
ejpam-3975	125	36	there	there	PRON
ejpam-3975	125	37	exist	exist	VERB
ejpam-3975	125	38	vertices	vertex	NOUN
ejpam-3975	125	39	x1	x1	PROPN
ejpam-3975	125	40	,	,	PUNCT
ejpam-3975	125	41	x2	x2	PROPN
ejpam-3975	125	42	,	,	PUNCT
ejpam-3975	125	43	x3	x3	ADJ
ejpam-3975	125	44	,	,	PUNCT
ejpam-3975	125	45	x4	x4	PROPN
ejpam-3975	125	46	of	of	ADP
ejpam-3975	125	47	g	g	PROPN
ejpam-3975	125	48	such	such	ADJ
ejpam-3975	125	49	that	that	SCONJ
ejpam-3975	125	50	〈	〈	PROPN
ejpam-3975	125	51	{	{	PUNCT
ejpam-3975	125	52	x1	x1	PROPN
ejpam-3975	125	53	,	,	PUNCT
ejpam-3975	125	54	x2	x2	PROPN
ejpam-3975	125	55	,	,	PUNCT
ejpam-3975	125	56	x3	x3	ADJ
ejpam-3975	125	57	,	,	PUNCT
ejpam-3975	125	58	x4	x4	ADJ
ejpam-3975	125	59	}	}	PUNCT
ejpam-3975	125	60	〉	〉	NOUN
ejpam-3975	125	61	∼=	∼=	PROPN
ejpam-3975	125	62	p4	p4	ADJ
ejpam-3975	125	63	or	or	CCONJ
ejpam-3975	125	64	〈	〈	PROPN
ejpam-3975	125	65	{	{	PUNCT
ejpam-3975	125	66	x1	x1	PROPN
ejpam-3975	125	67	,	,	PUNCT
ejpam-3975	125	68	x2	x2	PROPN
ejpam-3975	125	69	,	,	PUNCT
ejpam-3975	125	70	x3	x3	ADJ
ejpam-3975	125	71	,	,	PUNCT
ejpam-3975	125	72	x4	x4	ADJ
ejpam-3975	125	73	}	}	PUNCT
ejpam-3975	125	74	〉	〉	NOUN
ejpam-3975	125	75	∼=	∼=	PROPN
ejpam-3975	125	76	p2	p2	NOUN
ejpam-3975	125	77	∪k2	∪k2	NOUN
ejpam-3975	125	78	and	and	CCONJ
ejpam-3975	125	79	the	the	DET
ejpam-3975	125	80	conditions	condition	NOUN
ejpam-3975	125	81	given	give	VERB
ejpam-3975	125	82	in	in	ADP
ejpam-3975	125	83	lemma	lemma	PROPN
ejpam-3975	125	84	2.4	2.4	NUM
ejpam-3975	125	85	and	and	CCONJ
ejpam-3975	125	86	lemma	lemma	PROPN
ejpam-3975	125	87	2.5	2.5	NUM
ejpam-3975	125	88	are	be	AUX
ejpam-3975	125	89	satisfied	satisfied	ADJ
ejpam-3975	125	90	.	.	PUNCT
ejpam-3975	126	1	proof	proof	NOUN
ejpam-3975	126	2	.	.	PUNCT
ejpam-3975	127	1	let	let	VERB
ejpam-3975	127	2	γtph(g	γtph(g	PRON
ejpam-3975	127	3	)	)	PUNCT
ejpam-3975	127	4	=	=	SYM
ejpam-3975	128	1	4	4	X
ejpam-3975	128	2	.	.	X
ejpam-3975	129	1	if	if	SCONJ
ejpam-3975	129	2	|v	|v	PROPN
ejpam-3975	129	3	(	(	PUNCT
ejpam-3975	129	4	g)|	g)|	NOUN
ejpam-3975	129	5	=	=	SYM
ejpam-3975	129	6	4	4	NUM
ejpam-3975	129	7	,	,	PUNCT
ejpam-3975	129	8	then	then	ADV
ejpam-3975	129	9	g4	g4	NOUN
ejpam-3975	129	10	or	or	CCONJ
ejpam-3975	129	11	c4	c4	NOUN
ejpam-3975	129	12	.	.	PUNCT
ejpam-3975	129	13	suppose	suppose	VERB
ejpam-3975	129	14	that	that	SCONJ
ejpam-3975	129	15	|v	|v	PROPN
ejpam-3975	129	16	(	(	PUNCT
ejpam-3975	129	17	g)|	g)|	X
ejpam-3975	129	18	≥	≥	NUM
ejpam-3975	129	19	6	6	NUM
ejpam-3975	129	20	and	and	CCONJ
ejpam-3975	129	21	s	s	NOUN
ejpam-3975	129	22	=	=	PUNCT
ejpam-3975	129	23	{	{	PUNCT
ejpam-3975	129	24	x1	x1	PROPN
ejpam-3975	129	25	,	,	PUNCT
ejpam-3975	129	26	x2	x2	PROPN
ejpam-3975	129	27	,	,	PUNCT
ejpam-3975	129	28	x3	x3	PROPN
ejpam-3975	129	29	,	,	PUNCT
ejpam-3975	129	30	x4	x4	PROPN
ejpam-3975	129	31	}	}	PUNCT
ejpam-3975	129	32	be	be	AUX
ejpam-3975	129	33	a	a	DET
ejpam-3975	129	34	γtph	γtph	NOUN
ejpam-3975	129	35	-	-	PUNCT
ejpam-3975	129	36	set	set	NOUN
ejpam-3975	129	37	.	.	PUNCT
ejpam-3975	129	38	suppose	suppose	VERB
ejpam-3975	129	39	that	that	SCONJ
ejpam-3975	129	40	〈	〈	PROPN
ejpam-3975	129	41	{	{	PUNCT
ejpam-3975	129	42	x1	x1	PROPN
ejpam-3975	129	43	,	,	PUNCT
ejpam-3975	129	44	x2	x2	PROPN
ejpam-3975	129	45	,	,	PUNCT
ejpam-3975	129	46	x3	x3	ADJ
ejpam-3975	129	47	,	,	PUNCT
ejpam-3975	129	48	x4	x4	ADJ
ejpam-3975	129	49	}	}	PUNCT
ejpam-3975	129	50	〉	〉	PROPN
ejpam-3975	129	51	�	�	PROPN
ejpam-3975	129	52	p4	p4	ADJ
ejpam-3975	129	53	or	or	CCONJ
ejpam-3975	129	54	〈	〈	PROPN
ejpam-3975	129	55	{	{	PUNCT
ejpam-3975	129	56	x1	x1	PROPN
ejpam-3975	129	57	,	,	PUNCT
ejpam-3975	129	58	x2	x2	PROPN
ejpam-3975	129	59	,	,	PUNCT
ejpam-3975	129	60	x3	x3	ADJ
ejpam-3975	129	61	,	,	PUNCT
ejpam-3975	129	62	x4	x4	ADJ
ejpam-3975	129	63	}	}	PUNCT
ejpam-3975	129	64	〉	〉	PROPN
ejpam-3975	129	65	�	�	PROPN
ejpam-3975	129	66	p2	p2	PROPN
ejpam-3975	129	67	∪k2	∪k2	X
ejpam-3975	129	68	.	.	PUNCT
ejpam-3975	130	1	then	then	ADV
ejpam-3975	130	2	either	either	CCONJ
ejpam-3975	130	3	〈	〈	PROPN
ejpam-3975	130	4	s	s	PROPN
ejpam-3975	130	5	〉	〉	NOUN
ejpam-3975	130	6	∼=	∼=	PROPN
ejpam-3975	130	7	[	[	X
ejpam-3975	130	8	x1	x1	ADJ
ejpam-3975	130	9	,	,	PUNCT
ejpam-3975	130	10	x2]∪	x2]∪	PUNCT
ejpam-3975	131	1	[	[	X
ejpam-3975	131	2	x3	x3	ADJ
ejpam-3975	131	3	,	,	PUNCT
ejpam-3975	131	4	x4	x4	PROPN
ejpam-3975	131	5	]	]	PUNCT
ejpam-3975	131	6	or	or	CCONJ
ejpam-3975	131	7	〈	〈	PROPN
ejpam-3975	131	8	s	s	PROPN
ejpam-3975	131	9	〉	〉	NOUN
ejpam-3975	131	10	∼=	∼=	PROPN
ejpam-3975	132	1	[	[	X
ejpam-3975	132	2	x1	x1	PROPN
ejpam-3975	132	3	,	,	PUNCT
ejpam-3975	132	4	x2	x2	PROPN
ejpam-3975	132	5	,	,	PUNCT
ejpam-3975	132	6	x3]∪k1	x3]∪k1	PROPN
ejpam-3975	132	7	r.	r.	PROPN
ejpam-3975	132	8	rakim	rakim	PROPN
ejpam-3975	132	9	,	,	PUNCT
ejpam-3975	132	10	h.	h.	PROPN
ejpam-3975	132	11	rara	rara	PROPN
ejpam-3975	132	12	/	/	SYM
ejpam-3975	132	13	eur	eur	PROPN
ejpam-3975	132	14	.	.	PUNCT
ejpam-3975	133	1	j.	j.	PROPN
ejpam-3975	133	2	pure	pure	PROPN
ejpam-3975	133	3	appl	appl	PROPN
ejpam-3975	133	4	.	.	PROPN
ejpam-3975	133	5	math	math	PROPN
ejpam-3975	133	6	,	,	PUNCT
ejpam-3975	133	7	14	14	NUM
ejpam-3975	133	8	(	(	PUNCT
ejpam-3975	133	9	3	3	NUM
ejpam-3975	133	10	)	)	PUNCT
ejpam-3975	133	11	(	(	PUNCT
ejpam-3975	133	12	2021	2021	NUM
ejpam-3975	133	13	)	)	PUNCT
ejpam-3975	133	14	,	,	PUNCT
ejpam-3975	133	15	803	803	NUM
ejpam-3975	133	16	-	-	SYM
ejpam-3975	133	17	815	815	NUM
ejpam-3975	133	18	808	808	NUM
ejpam-3975	133	19	where	where	SCONJ
ejpam-3975	133	20	v	v	NOUN
ejpam-3975	133	21	(	(	PUNCT
ejpam-3975	133	22	k1	k1	NOUN
ejpam-3975	133	23	)	)	PUNCT
ejpam-3975	133	24	=	=	SYM
ejpam-3975	133	25	{	{	PUNCT
ejpam-3975	133	26	x4	x4	PROPN
ejpam-3975	133	27	}	}	PUNCT
ejpam-3975	133	28	or	or	CCONJ
ejpam-3975	133	29	〈	〈	PROPN
ejpam-3975	133	30	s	s	PROPN
ejpam-3975	133	31	〉	〉	NOUN
ejpam-3975	133	32	∼=	∼=	NOUN
ejpam-3975	133	33	k4	k4	NOUN
ejpam-3975	133	34	where	where	SCONJ
ejpam-3975	133	35	v	v	NOUN
ejpam-3975	133	36	(	(	PUNCT
ejpam-3975	133	37	k4	k4	NOUN
ejpam-3975	133	38	)	)	PUNCT
ejpam-3975	133	39	=	=	PUNCT
ejpam-3975	133	40	{	{	PUNCT
ejpam-3975	133	41	x1	x1	PROPN
ejpam-3975	133	42	,	,	PUNCT
ejpam-3975	133	43	x2	x2	PROPN
ejpam-3975	133	44	,	,	PUNCT
ejpam-3975	133	45	x3	x3	ADJ
ejpam-3975	133	46	,	,	PUNCT
ejpam-3975	133	47	x4	x4	PROPN
ejpam-3975	133	48	}	}	PUNCT
ejpam-3975	133	49	.	.	PUNCT
ejpam-3975	134	1	thus	thus	ADV
ejpam-3975	134	2	,	,	PUNCT
ejpam-3975	134	3	by	by	ADP
ejpam-3975	134	4	lemma	lemma	PROPN
ejpam-3975	134	5	2.6	2.6	NUM
ejpam-3975	134	6	,	,	PUNCT
ejpam-3975	134	7	s	s	VERB
ejpam-3975	134	8	is	be	AUX
ejpam-3975	134	9	not	not	PART
ejpam-3975	134	10	a	a	DET
ejpam-3975	134	11	total	total	ADJ
ejpam-3975	134	12	perfect	perfect	ADJ
ejpam-3975	134	13	hop	hop	NOUN
ejpam-3975	134	14	dominating	dominating	NOUN
ejpam-3975	134	15	set	set	NOUN
ejpam-3975	134	16	of	of	ADP
ejpam-3975	134	17	g	g	PROPN
ejpam-3975	134	18	contrary	contrary	ADV
ejpam-3975	134	19	to	to	ADP
ejpam-3975	134	20	our	our	PRON
ejpam-3975	134	21	assumption	assumption	NOUN
ejpam-3975	134	22	.	.	PUNCT
ejpam-3975	135	1	the	the	DET
ejpam-3975	135	2	converse	converse	NOUN
ejpam-3975	135	3	follows	follow	VERB
ejpam-3975	135	4	immediately	immediately	ADV
ejpam-3975	135	5	from	from	ADP
ejpam-3975	135	6	lemmas	lemmas	PROPN
ejpam-3975	135	7	2.4	2.4	NUM
ejpam-3975	135	8	and	and	CCONJ
ejpam-3975	135	9	2.5	2.5	NUM
ejpam-3975	135	10	.	.	PUNCT
ejpam-3975	136	1	�	�	PROPN
ejpam-3975	136	2	corollary	corollary	ADJ
ejpam-3975	136	3	2.8	2.8	NUM
ejpam-3975	136	4	.	.	PUNCT
ejpam-3975	137	1	let	let	VERB
ejpam-3975	137	2	n	n	CCONJ
ejpam-3975	137	3	,	,	PUNCT
ejpam-3975	137	4	s	s	X
ejpam-3975	137	5	,	,	PUNCT
ejpam-3975	137	6	and	and	CCONJ
ejpam-3975	137	7	r	r	NOUN
ejpam-3975	137	8	be	be	VERB
ejpam-3975	137	9	positive	positive	ADJ
ejpam-3975	137	10	integers	integer	NOUN
ejpam-3975	137	11	with	with	ADP
ejpam-3975	137	12	r	r	NOUN
ejpam-3975	137	13	≥	≥	NOUN
ejpam-3975	137	14	0	0	NUM
ejpam-3975	137	15	.	.	PUNCT
ejpam-3975	138	1	(	(	PUNCT
ejpam-3975	138	2	i	i	NOUN
ejpam-3975	138	3	)	)	PUNCT
ejpam-3975	138	4	γtph(pn	γtph(pn	NOUN
ejpam-3975	138	5	)	)	PUNCT
ejpam-3975	138	6	=	=	SYM
ejpam-3975	138	7	4r	4r	NOUN
ejpam-3975	138	8	+	+	CCONJ
ejpam-3975	138	9	4	4	NUM
ejpam-3975	138	10	if	if	SCONJ
ejpam-3975	138	11	n	n	NOUN
ejpam-3975	138	12	=	=	SYM
ejpam-3975	138	13	8r	8r	X
ejpam-3975	139	1	+	+	SYM
ejpam-3975	139	2	s	s	X
ejpam-3975	139	3	;	;	PUNCT
ejpam-3975	139	4	4	4	NUM
ejpam-3975	139	5	≤	≤	NOUN
ejpam-3975	139	6	s	s	PART
ejpam-3975	139	7	≤	≤	NUM
ejpam-3975	139	8	8	8	NUM
ejpam-3975	139	9	(	(	PUNCT
ejpam-3975	139	10	ii	ii	NOUN
ejpam-3975	139	11	)	)	PUNCT
ejpam-3975	139	12	γtph(cn	γtph(cn	NOUN
ejpam-3975	139	13	)	)	PUNCT
ejpam-3975	139	14	=	=	PUNCT
ejpam-3975	139	15	{	{	PUNCT
ejpam-3975	139	16	4	4	NUM
ejpam-3975	139	17	,	,	PUNCT
ejpam-3975	139	18	if	if	SCONJ
ejpam-3975	139	19	n	n	NOUN
ejpam-3975	139	20	=	=	SYM
ejpam-3975	139	21	4	4	NUM
ejpam-3975	139	22	4r	4r	NOUN
ejpam-3975	139	23	+	+	CCONJ
ejpam-3975	139	24	4	4	NUM
ejpam-3975	139	25	,	,	PUNCT
ejpam-3975	139	26	if	if	SCONJ
ejpam-3975	139	27	n	n	NOUN
ejpam-3975	139	28	=	=	SYM
ejpam-3975	139	29	8r	8r	NUM
ejpam-3975	140	1	+	+	CCONJ
ejpam-3975	140	2	8	8	X
ejpam-3975	140	3	.	.	PUNCT
ejpam-3975	141	1	definition	definition	NOUN
ejpam-3975	141	2	2.9	2.9	NUM
ejpam-3975	141	3	.	.	PUNCT
ejpam-3975	142	1	a	a	DET
ejpam-3975	142	2	set	set	NOUN
ejpam-3975	142	3	s	s	NOUN
ejpam-3975	142	4	⊆	⊆	NUM
ejpam-3975	142	5	v	v	NOUN
ejpam-3975	142	6	(	(	PUNCT
ejpam-3975	142	7	g	g	NOUN
ejpam-3975	142	8	)	)	PUNCT
ejpam-3975	142	9	is	be	AUX
ejpam-3975	142	10	a	a	DET
ejpam-3975	142	11	total	total	ADJ
ejpam-3975	142	12	perfect	perfect	ADJ
ejpam-3975	142	13	point	point	NOUN
ejpam-3975	142	14	-	-	PUNCT
ejpam-3975	142	15	wise	wise	ADJ
ejpam-3975	142	16	non	non	ADJ
ejpam-3975	142	17	-	-	ADJ
ejpam-3975	142	18	dominating	dominating	ADJ
ejpam-3975	142	19	set	set	NOUN
ejpam-3975	142	20	of	of	ADP
ejpam-3975	142	21	g	g	PROPN
ejpam-3975	142	22	if	if	SCONJ
ejpam-3975	142	23	for	for	ADP
ejpam-3975	142	24	every	every	DET
ejpam-3975	142	25	v	v	NUM
ejpam-3975	142	26	∈	∈	NOUN
ejpam-3975	142	27	v	v	NOUN
ejpam-3975	142	28	(	(	PUNCT
ejpam-3975	142	29	g	g	NOUN
ejpam-3975	142	30	)	)	PUNCT
ejpam-3975	142	31	,	,	PUNCT
ejpam-3975	142	32	there	there	PRON
ejpam-3975	142	33	is	be	VERB
ejpam-3975	142	34	exactly	exactly	ADV
ejpam-3975	142	35	one	one	NUM
ejpam-3975	142	36	vertex	vertex	NOUN
ejpam-3975	142	37	u	u	NOUN
ejpam-3975	142	38	∈	∈	NOUN
ejpam-3975	142	39	s	s	VERB
ejpam-3975	142	40	such	such	ADJ
ejpam-3975	142	41	that	that	DET
ejpam-3975	142	42	v	v	NOUN
ejpam-3975	142	43	/∈	/∈	PUNCT
ejpam-3975	142	44	ng(u	ng(u	NOUN
ejpam-3975	142	45	)	)	PUNCT
ejpam-3975	142	46	.	.	PUNCT
ejpam-3975	143	1	the	the	DET
ejpam-3975	143	2	smallest	small	ADJ
ejpam-3975	143	3	cardinality	cardinality	NOUN
ejpam-3975	143	4	of	of	ADP
ejpam-3975	143	5	a	a	DET
ejpam-3975	143	6	total	total	ADJ
ejpam-3975	143	7	perfect	perfect	ADJ
ejpam-3975	143	8	point	point	NOUN
ejpam-3975	143	9	-	-	PUNCT
ejpam-3975	143	10	wise	wise	ADJ
ejpam-3975	143	11	non	non	ADJ
ejpam-3975	143	12	-	-	ADJ
ejpam-3975	143	13	dominating	dominating	ADJ
ejpam-3975	143	14	set	set	NOUN
ejpam-3975	143	15	of	of	ADP
ejpam-3975	143	16	g	g	NOUN
ejpam-3975	143	17	,	,	PUNCT
ejpam-3975	143	18	denoted	denote	VERB
ejpam-3975	143	19	by	by	ADP
ejpam-3975	143	20	tppnd(g	tppnd(g	NOUN
ejpam-3975	143	21	)	)	PUNCT
ejpam-3975	143	22	is	be	AUX
ejpam-3975	143	23	called	call	VERB
ejpam-3975	143	24	the	the	DET
ejpam-3975	143	25	total	total	ADJ
ejpam-3975	143	26	perfect	perfect	ADJ
ejpam-3975	143	27	point	point	NOUN
ejpam-3975	143	28	-	-	PUNCT
ejpam-3975	143	29	wise	wise	ADJ
ejpam-3975	143	30	non	non	ADJ
ejpam-3975	143	31	-	-	ADJ
ejpam-3975	143	32	domination	domination	ADJ
ejpam-3975	143	33	number	number	NOUN
ejpam-3975	143	34	of	of	ADP
ejpam-3975	143	35	g.	g.	PROPN
ejpam-3975	143	36	any	any	DET
ejpam-3975	143	37	total	total	ADJ
ejpam-3975	143	38	perfect	perfect	ADJ
ejpam-3975	143	39	point	point	NOUN
ejpam-3975	143	40	-	-	PUNCT
ejpam-3975	143	41	wise	wise	ADJ
ejpam-3975	143	42	non	non	ADJ
ejpam-3975	143	43	-	-	ADJ
ejpam-3975	143	44	dominating	dominating	ADJ
ejpam-3975	143	45	set	set	NOUN
ejpam-3975	143	46	s	s	NOUN
ejpam-3975	143	47	of	of	ADP
ejpam-3975	143	48	g	g	NOUN
ejpam-3975	143	49	with	with	ADP
ejpam-3975	143	50	|s|	|s|	NOUN
ejpam-3975	143	51	=	=	PUNCT
ejpam-3975	143	52	tppnd(g	tppnd(g	PROPN
ejpam-3975	143	53	)	)	PUNCT
ejpam-3975	143	54	is	be	AUX
ejpam-3975	143	55	called	call	VERB
ejpam-3975	143	56	a	a	DET
ejpam-3975	143	57	tppnd	tppnd	NOUN
ejpam-3975	143	58	-	-	PUNCT
ejpam-3975	143	59	set	set	NOUN
ejpam-3975	143	60	.	.	PUNCT
ejpam-3975	144	1	remark	remark	PROPN
ejpam-3975	144	2	2.10	2.10	NUM
ejpam-3975	144	3	.	.	PUNCT
ejpam-3975	145	1	let	let	VERB
ejpam-3975	145	2	g	g	PRON
ejpam-3975	145	3	be	be	AUX
ejpam-3975	145	4	a	a	DET
ejpam-3975	145	5	graph	graph	NOUN
ejpam-3975	145	6	of	of	ADP
ejpam-3975	145	7	order	order	NOUN
ejpam-3975	145	8	n.	n.	NOUN
ejpam-3975	145	9	then	then	ADV
ejpam-3975	145	10	the	the	DET
ejpam-3975	145	11	total	total	ADJ
ejpam-3975	145	12	perfect	perfect	ADJ
ejpam-3975	145	13	point	point	NOUN
ejpam-3975	145	14	-	-	PUNCT
ejpam-3975	145	15	wise	wise	ADJ
ejpam-3975	145	16	non	non	ADJ
ejpam-3975	145	17	-	-	ADJ
ejpam-3975	145	18	dominating	dominating	ADJ
ejpam-3975	145	19	set	set	NOUN
ejpam-3975	145	20	of	of	ADP
ejpam-3975	145	21	g	g	PROPN
ejpam-3975	145	22	does	do	AUX
ejpam-3975	145	23	not	not	PART
ejpam-3975	145	24	exist	exist	VERB
ejpam-3975	145	25	if	if	SCONJ
ejpam-3975	145	26	γ(h	γ(h	NOUN
ejpam-3975	145	27	)	)	PUNCT
ejpam-3975	145	28	=	=	SYM
ejpam-3975	146	1	1	1	X
ejpam-3975	146	2	.	.	PUNCT
ejpam-3975	146	3	remark	remark	PROPN
ejpam-3975	146	4	2.11	2.11	NUM
ejpam-3975	146	5	.	.	PUNCT
ejpam-3975	147	1	let	let	VERB
ejpam-3975	147	2	g	g	PRON
ejpam-3975	147	3	be	be	AUX
ejpam-3975	147	4	a	a	DET
ejpam-3975	147	5	graph	graph	NOUN
ejpam-3975	147	6	of	of	ADP
ejpam-3975	147	7	order	order	NOUN
ejpam-3975	147	8	n	n	PRON
ejpam-3975	147	9	≥	≥	NOUN
ejpam-3975	147	10	4	4	NUM
ejpam-3975	147	11	.	.	PUNCT
ejpam-3975	147	12	then	then	ADV
ejpam-3975	147	13	tppnd(g	tppnd(g	PROPN
ejpam-3975	147	14	)	)	PUNCT
ejpam-3975	147	15	≥	≥	NOUN
ejpam-3975	147	16	2	2	NUM
ejpam-3975	147	17	.	.	PUNCT
ejpam-3975	147	18	theorem	theorem	VERB
ejpam-3975	147	19	2.12	2.12	NUM
ejpam-3975	147	20	.	.	PUNCT
ejpam-3975	148	1	let	let	VERB
ejpam-3975	148	2	g	g	PRON
ejpam-3975	148	3	be	be	AUX
ejpam-3975	148	4	a	a	DET
ejpam-3975	148	5	connected	connected	ADJ
ejpam-3975	148	6	graph	graph	NOUN
ejpam-3975	148	7	of	of	ADP
ejpam-3975	148	8	order	order	NOUN
ejpam-3975	148	9	n	n	PRON
ejpam-3975	148	10	≥	≥	NOUN
ejpam-3975	148	11	4	4	NUM
ejpam-3975	148	12	.	.	PUNCT
ejpam-3975	148	13	then	then	ADV
ejpam-3975	148	14	tppnd(g	tppnd(g	ADP
ejpam-3975	148	15	)	)	PUNCT
ejpam-3975	148	16	=	=	SYM
ejpam-3975	148	17	2	2	NUM
ejpam-3975	148	18	if	if	SCONJ
ejpam-3975	148	19	only	only	ADV
ejpam-3975	148	20	if	if	SCONJ
ejpam-3975	148	21	there	there	PRON
ejpam-3975	148	22	exist	exist	VERB
ejpam-3975	148	23	non	non	ADJ
ejpam-3975	148	24	-	-	ADJ
ejpam-3975	148	25	adjacent	adjacent	ADJ
ejpam-3975	148	26	vertices	vertex	NOUN
ejpam-3975	148	27	x	x	X
ejpam-3975	148	28	,	,	PUNCT
ejpam-3975	148	29	y	y	PROPN
ejpam-3975	148	30	∈	∈	PROPN
ejpam-3975	148	31	v	v	ADP
ejpam-3975	148	32	(	(	PUNCT
ejpam-3975	148	33	g	g	NOUN
ejpam-3975	148	34	)	)	PUNCT
ejpam-3975	148	35	such	such	ADJ
ejpam-3975	148	36	that	that	PRON
ejpam-3975	148	37	v	v	NOUN
ejpam-3975	148	38	(	(	PUNCT
ejpam-3975	148	39	g)\{x	g)\{x	PROPN
ejpam-3975	148	40	,	,	PUNCT
ejpam-3975	148	41	y	y	NOUN
ejpam-3975	148	42	}	}	PUNCT
ejpam-3975	148	43	=	=	SYM
ejpam-3975	148	44	ng(x	ng(x	NUM
ejpam-3975	148	45	)	)	PUNCT
ejpam-3975	148	46	∪ng(y	∪ng(y	PROPN
ejpam-3975	148	47	)	)	PUNCT
ejpam-3975	148	48	and	and	CCONJ
ejpam-3975	148	49	ng(y	ng(y	NOUN
ejpam-3975	148	50	)	)	PUNCT
ejpam-3975	148	51	∩ng(x	∩ng(x	NOUN
ejpam-3975	148	52	)	)	PUNCT
ejpam-3975	148	53	=	=	SYM
ejpam-3975	148	54	∅.	∅.	NOUN
ejpam-3975	148	55	proof	proof	NOUN
ejpam-3975	148	56	.	.	PUNCT
ejpam-3975	149	1	suppose	suppose	VERB
ejpam-3975	149	2	tppnd(g	tppnd(g	ADP
ejpam-3975	149	3	)	)	PUNCT
ejpam-3975	149	4	=	=	SYM
ejpam-3975	150	1	2	2	X
ejpam-3975	150	2	.	.	X
ejpam-3975	150	3	let	let	VERB
ejpam-3975	150	4	s	s	VERB
ejpam-3975	150	5	=	=	PUNCT
ejpam-3975	150	6	{	{	PUNCT
ejpam-3975	150	7	x	x	PROPN
ejpam-3975	150	8	,	,	PUNCT
ejpam-3975	150	9	y	y	PROPN
ejpam-3975	150	10	}	}	PUNCT
ejpam-3975	150	11	be	be	AUX
ejpam-3975	150	12	a	a	DET
ejpam-3975	150	13	tppnd	tppnd	NOUN
ejpam-3975	150	14	-	-	PUNCT
ejpam-3975	150	15	set	set	NOUN
ejpam-3975	150	16	of	of	ADP
ejpam-3975	150	17	g.	g.	PROPN
ejpam-3975	150	18	let	let	VERB
ejpam-3975	150	19	z	z	PROPN
ejpam-3975	150	20	∈	∈	PROPN
ejpam-3975	150	21	v	v	PROPN
ejpam-3975	150	22	(	(	PUNCT
ejpam-3975	150	23	g)\{x	g)\{x	PROPN
ejpam-3975	150	24	,	,	PUNCT
ejpam-3975	150	25	y	y	NOUN
ejpam-3975	150	26	}	}	PUNCT
ejpam-3975	150	27	.	.	PUNCT
ejpam-3975	151	1	since	since	SCONJ
ejpam-3975	151	2	s	s	PROPN
ejpam-3975	151	3	is	be	AUX
ejpam-3975	151	4	a	a	DET
ejpam-3975	151	5	total	total	ADJ
ejpam-3975	151	6	perfect	perfect	ADJ
ejpam-3975	151	7	point	point	NOUN
ejpam-3975	151	8	-	-	PUNCT
ejpam-3975	151	9	wise	wise	ADJ
ejpam-3975	151	10	non	non	ADJ
ejpam-3975	151	11	-	-	ADJ
ejpam-3975	151	12	dominating	dominating	ADJ
ejpam-3975	151	13	set	set	NOUN
ejpam-3975	151	14	of	of	ADP
ejpam-3975	151	15	g	g	PROPN
ejpam-3975	151	16	,	,	PUNCT
ejpam-3975	151	17	z	z	NOUN
ejpam-3975	151	18	/∈	/∈	PUNCT
ejpam-3975	151	19	ng(x	ng(x	NUM
ejpam-3975	151	20	)	)	PUNCT
ejpam-3975	151	21	or	or	CCONJ
ejpam-3975	151	22	z	z	NOUN
ejpam-3975	151	23	/∈	/∈	PUNCT
ejpam-3975	151	24	ng(y	ng(y	NOUN
ejpam-3975	151	25	)	)	PUNCT
ejpam-3975	151	26	but	but	CCONJ
ejpam-3975	151	27	not	not	PART
ejpam-3975	151	28	both	both	PRON
ejpam-3975	151	29	.	.	PUNCT
ejpam-3975	152	1	hence	hence	ADV
ejpam-3975	152	2	,	,	PUNCT
ejpam-3975	152	3	ng(x	ng(x	NUM
ejpam-3975	152	4	)	)	PUNCT
ejpam-3975	152	5	∪ng(y	∪ng(y	PROPN
ejpam-3975	152	6	)	)	PUNCT
ejpam-3975	152	7	and	and	CCONJ
ejpam-3975	152	8	ng(y	ng(y	NOUN
ejpam-3975	152	9	)	)	PUNCT
ejpam-3975	152	10	∩ng(x	∩ng(x	NOUN
ejpam-3975	152	11	)	)	PUNCT
ejpam-3975	153	1	=	=	VERB
ejpam-3975	153	2	∅.	∅.	VERB
ejpam-3975	153	3	conversely	conversely	ADV
ejpam-3975	153	4	,	,	PUNCT
ejpam-3975	153	5	suppose	suppose	VERB
ejpam-3975	153	6	that	that	SCONJ
ejpam-3975	153	7	there	there	PRON
ejpam-3975	153	8	exist	exist	VERB
ejpam-3975	153	9	non	non	ADJ
ejpam-3975	153	10	-	-	ADJ
ejpam-3975	153	11	adjacent	adjacent	ADJ
ejpam-3975	153	12	vertices	vertex	NOUN
ejpam-3975	153	13	x	x	X
ejpam-3975	153	14	,	,	PUNCT
ejpam-3975	153	15	y	y	PROPN
ejpam-3975	153	16	∈	∈	PROPN
ejpam-3975	153	17	v	v	ADP
ejpam-3975	153	18	(	(	PUNCT
ejpam-3975	153	19	g	g	NOUN
ejpam-3975	153	20	)	)	PUNCT
ejpam-3975	153	21	satisfying	satisfy	VERB
ejpam-3975	153	22	the	the	DET
ejpam-3975	153	23	given	give	VERB
ejpam-3975	153	24	condition	condition	NOUN
ejpam-3975	153	25	.	.	PUNCT
ejpam-3975	154	1	let	let	VERB
ejpam-3975	154	2	s	s	PRON
ejpam-3975	154	3	=	=	PUNCT
ejpam-3975	154	4	{	{	PUNCT
ejpam-3975	154	5	x	x	PROPN
ejpam-3975	154	6	,	,	PUNCT
ejpam-3975	154	7	y	y	NOUN
ejpam-3975	154	8	}	}	PUNCT
ejpam-3975	154	9	and	and	CCONJ
ejpam-3975	154	10	let	let	VERB
ejpam-3975	154	11	u	u	PRON
ejpam-3975	154	12	∈	∈	PROPN
ejpam-3975	154	13	v	v	ADP
ejpam-3975	154	14	(	(	PUNCT
ejpam-3975	154	15	g	g	NOUN
ejpam-3975	154	16	)	)	PUNCT
ejpam-3975	154	17	.	.	PUNCT
ejpam-3975	155	1	then	then	ADV
ejpam-3975	155	2	either	either	CCONJ
ejpam-3975	155	3	u	u	PROPN
ejpam-3975	155	4	∈	∈	PROPN
ejpam-3975	155	5	ng(x)\ng(y	ng(x)\ng(y	NOUN
ejpam-3975	155	6	)	)	PUNCT
ejpam-3975	155	7	or	or	CCONJ
ejpam-3975	155	8	u	u	PROPN
ejpam-3975	155	9	∈	∈	PROPN
ejpam-3975	155	10	ng(y)\ng(x	ng(y)\ng(x	NOUN
ejpam-3975	155	11	)	)	PUNCT
ejpam-3975	155	12	.	.	PUNCT
ejpam-3975	156	1	it	it	PRON
ejpam-3975	156	2	follows	follow	VERB
ejpam-3975	156	3	that	that	SCONJ
ejpam-3975	156	4	s	s	VERB
ejpam-3975	156	5	is	be	AUX
ejpam-3975	156	6	a	a	DET
ejpam-3975	156	7	total	total	ADJ
ejpam-3975	156	8	perfect	perfect	ADJ
ejpam-3975	156	9	point	point	NOUN
ejpam-3975	156	10	-	-	PUNCT
ejpam-3975	156	11	wise	wise	ADJ
ejpam-3975	156	12	non	non	ADJ
ejpam-3975	156	13	-	-	ADJ
ejpam-3975	156	14	dominating	dominating	ADJ
ejpam-3975	156	15	set	set	NOUN
ejpam-3975	156	16	of	of	ADP
ejpam-3975	156	17	g.	g.	PROPN
ejpam-3975	156	18	by	by	ADP
ejpam-3975	156	19	remark	remark	NOUN
ejpam-3975	156	20	2.11	2.11	NUM
ejpam-3975	156	21	,	,	PUNCT
ejpam-3975	156	22	tppnd(g	tppnd(g	ADP
ejpam-3975	156	23	)	)	PUNCT
ejpam-3975	156	24	=	=	SYM
ejpam-3975	156	25	2	2	X
ejpam-3975	156	26	.	.	X
ejpam-3975	156	27	�	�	PROPN
ejpam-3975	156	28	corollary	corollary	PROPN
ejpam-3975	156	29	2.13	2.13	NUM
ejpam-3975	156	30	.	.	PUNCT
ejpam-3975	157	1	let	let	VERB
ejpam-3975	157	2	n	n	PRON
ejpam-3975	157	3	≥	≥	X
ejpam-3975	157	4	4	4	NUM
ejpam-3975	157	5	be	be	AUX
ejpam-3975	157	6	a	a	DET
ejpam-3975	157	7	positive	positive	ADJ
ejpam-3975	157	8	integer	integer	NOUN
ejpam-3975	157	9	.	.	PUNCT
ejpam-3975	158	1	(	(	PUNCT
ejpam-3975	158	2	i	i	NOUN
ejpam-3975	158	3	)	)	PUNCT
ejpam-3975	158	4	tppnd(pn	tppnd(pn	PROPN
ejpam-3975	158	5	)	)	PUNCT
ejpam-3975	158	6	=	=	SYM
ejpam-3975	158	7	2	2	NUM
ejpam-3975	158	8	if	if	SCONJ
ejpam-3975	158	9	4	4	NUM
ejpam-3975	158	10	≤	≤	NUM
ejpam-3975	158	11	n	n	PRON
ejpam-3975	158	12	≤	≤	NUM
ejpam-3975	158	13	6	6	NUM
ejpam-3975	158	14	(	(	PUNCT
ejpam-3975	158	15	ii	ii	NOUN
ejpam-3975	158	16	)	)	PUNCT
ejpam-3975	158	17	tppnd(cn	tppnd(cn	PROPN
ejpam-3975	158	18	)	)	PUNCT
ejpam-3975	158	19	=	=	SYM
ejpam-3975	158	20	2	2	NUM
ejpam-3975	158	21	if	if	SCONJ
ejpam-3975	158	22	n	n	X
ejpam-3975	158	23	=	=	SYM
ejpam-3975	158	24	4	4	NUM
ejpam-3975	158	25	,	,	PUNCT
ejpam-3975	158	26	6	6	NUM
ejpam-3975	158	27	.	.	PUNCT
ejpam-3975	158	28	remark	remark	PROPN
ejpam-3975	158	29	2.14	2.14	NUM
ejpam-3975	158	30	.	.	PUNCT
ejpam-3975	159	1	let	let	VERB
ejpam-3975	159	2	g	g	PRON
ejpam-3975	159	3	be	be	AUX
ejpam-3975	159	4	a	a	DET
ejpam-3975	159	5	graph	graph	NOUN
ejpam-3975	159	6	of	of	ADP
ejpam-3975	159	7	order	order	NOUN
ejpam-3975	159	8	n	n	PRON
ejpam-3975	159	9	≥	≥	NOUN
ejpam-3975	159	10	4	4	NUM
ejpam-3975	159	11	.	.	PUNCT
ejpam-3975	160	1	if	if	SCONJ
ejpam-3975	160	2	s	s	PROPN
ejpam-3975	160	3	is	be	AUX
ejpam-3975	160	4	a	a	DET
ejpam-3975	160	5	tppnd	tppnd	NOUN
ejpam-3975	160	6	-	-	PUNCT
ejpam-3975	160	7	set	set	NOUN
ejpam-3975	160	8	of	of	ADP
ejpam-3975	160	9	g	g	NOUN
ejpam-3975	160	10	,	,	PUNCT
ejpam-3975	160	11	then	then	ADV
ejpam-3975	160	12	|s|	|s|	PROPN
ejpam-3975	160	13	is	be	AUX
ejpam-3975	160	14	even	even	ADV
ejpam-3975	160	15	.	.	PUNCT
ejpam-3975	161	1	r.	r.	PROPN
ejpam-3975	161	2	rakim	rakim	PROPN
ejpam-3975	161	3	,	,	PUNCT
ejpam-3975	161	4	h.	h.	PROPN
ejpam-3975	161	5	rara	rara	PROPN
ejpam-3975	161	6	/	/	SYM
ejpam-3975	161	7	eur	eur	PROPN
ejpam-3975	161	8	.	.	PUNCT
ejpam-3975	162	1	j.	j.	PROPN
ejpam-3975	162	2	pure	pure	PROPN
ejpam-3975	162	3	appl	appl	PROPN
ejpam-3975	162	4	.	.	PROPN
ejpam-3975	162	5	math	math	PROPN
ejpam-3975	162	6	,	,	PUNCT
ejpam-3975	162	7	14	14	NUM
ejpam-3975	162	8	(	(	PUNCT
ejpam-3975	162	9	3	3	NUM
ejpam-3975	162	10	)	)	PUNCT
ejpam-3975	162	11	(	(	PUNCT
ejpam-3975	162	12	2021	2021	NUM
ejpam-3975	162	13	)	)	PUNCT
ejpam-3975	162	14	,	,	PUNCT
ejpam-3975	162	15	803	803	NUM
ejpam-3975	162	16	-	-	SYM
ejpam-3975	162	17	815	815	NUM
ejpam-3975	162	18	809	809	NUM
ejpam-3975	162	19	3	3	NUM
ejpam-3975	162	20	.	.	X
ejpam-3975	162	21	join	join	VERB
ejpam-3975	162	22	of	of	ADP
ejpam-3975	162	23	graphs	graph	NOUN
ejpam-3975	162	24	the	the	DET
ejpam-3975	162	25	join	join	NOUN
ejpam-3975	162	26	g	g	PROPN
ejpam-3975	163	1	+	+	CCONJ
ejpam-3975	163	2	h	h	NOUN
ejpam-3975	163	3	of	of	ADP
ejpam-3975	163	4	two	two	NUM
ejpam-3975	163	5	graphs	graph	NOUN
ejpam-3975	163	6	g	g	NOUN
ejpam-3975	163	7	and	and	CCONJ
ejpam-3975	163	8	h	h	NOUN
ejpam-3975	163	9	is	be	AUX
ejpam-3975	163	10	the	the	DET
ejpam-3975	163	11	graph	graph	NOUN
ejpam-3975	163	12	with	with	ADP
ejpam-3975	163	13	vertex	vertex	NOUN
ejpam-3975	163	14	set	set	VERB
ejpam-3975	163	15	v	v	NOUN
ejpam-3975	163	16	(	(	PUNCT
ejpam-3975	163	17	g	g	PROPN
ejpam-3975	163	18	+	+	NOUN
ejpam-3975	163	19	h	h	NOUN
ejpam-3975	163	20	)	)	PUNCT
ejpam-3975	163	21	=	=	NOUN
ejpam-3975	163	22	v	v	X
ejpam-3975	163	23	(	(	PUNCT
ejpam-3975	163	24	g	g	NOUN
ejpam-3975	163	25	)	)	PUNCT
ejpam-3975	163	26	∪	∪	NOUN
ejpam-3975	163	27	v	v	NOUN
ejpam-3975	163	28	(	(	PUNCT
ejpam-3975	163	29	h	h	NOUN
ejpam-3975	163	30	)	)	PUNCT
ejpam-3975	163	31	and	and	CCONJ
ejpam-3975	163	32	edge	edge	NOUN
ejpam-3975	163	33	-	-	PUNCT
ejpam-3975	163	34	set	set	VERB
ejpam-3975	163	35	e(g+h	e(g+h	NUM
ejpam-3975	163	36	)	)	PUNCT
ejpam-3975	163	37	=	=	SYM
ejpam-3975	163	38	e(g	e(g	NOUN
ejpam-3975	163	39	)	)	PUNCT
ejpam-3975	163	40	∪	∪	ADP
ejpam-3975	163	41	e(h	e(h	PROPN
ejpam-3975	163	42	)	)	PUNCT
ejpam-3975	163	43	∪	∪	NOUN
ejpam-3975	163	44	{	{	PUNCT
ejpam-3975	163	45	uv	uv	NOUN
ejpam-3975	163	46	:	:	PUNCT
ejpam-3975	163	47	u	u	PROPN
ejpam-3975	163	48	∈	∈	PROPN
ejpam-3975	163	49	v	v	ADP
ejpam-3975	163	50	(	(	PUNCT
ejpam-3975	163	51	g	g	NOUN
ejpam-3975	163	52	)	)	PUNCT
ejpam-3975	163	53	and	and	CCONJ
ejpam-3975	163	54	v	v	ADP
ejpam-3975	163	55	∈	∈	PROPN
ejpam-3975	163	56	v	v	NOUN
ejpam-3975	163	57	(	(	PUNCT
ejpam-3975	163	58	h	h	NOUN
ejpam-3975	163	59	)	)	PUNCT
ejpam-3975	163	60	}	}	PUNCT
ejpam-3975	163	61	.	.	PUNCT
ejpam-3975	164	1	theorem	theorem	VERB
ejpam-3975	164	2	3.1	3.1	NUM
ejpam-3975	164	3	.	.	PUNCT
ejpam-3975	165	1	let	let	VERB
ejpam-3975	165	2	g	g	NOUN
ejpam-3975	166	1	and	and	CCONJ
ejpam-3975	166	2	h	h	NOUN
ejpam-3975	166	3	be	be	AUX
ejpam-3975	166	4	graphs	graph	NOUN
ejpam-3975	166	5	with	with	ADP
ejpam-3975	166	6	∆(g	∆(g	NOUN
ejpam-3975	166	7	)	)	PUNCT
ejpam-3975	167	1	6=	6=	ADP
ejpam-3975	167	2	|v	|v	PROPN
ejpam-3975	167	3	(	(	PUNCT
ejpam-3975	167	4	g)|	g)|	INTJ
ejpam-3975	167	5	−	−	PROPN
ejpam-3975	167	6	1	1	NUM
ejpam-3975	167	7	and	and	CCONJ
ejpam-3975	167	8	∆(h	∆(h	NOUN
ejpam-3975	167	9	)	)	PUNCT
ejpam-3975	167	10	6=	6=	NUM
ejpam-3975	167	11	|v	|v	PROPN
ejpam-3975	167	12	(	(	PUNCT
ejpam-3975	167	13	h)|	h)|	NOUN
ejpam-3975	167	14	−	−	PROPN
ejpam-3975	167	15	1	1	NUM
ejpam-3975	167	16	.	.	PUNCT
ejpam-3975	168	1	a	a	DET
ejpam-3975	168	2	subset	subset	NOUN
ejpam-3975	168	3	s	s	X
ejpam-3975	168	4	of	of	ADP
ejpam-3975	168	5	v	v	NOUN
ejpam-3975	168	6	(	(	PUNCT
ejpam-3975	168	7	g	g	PROPN
ejpam-3975	168	8	+	+	NOUN
ejpam-3975	168	9	h	h	NOUN
ejpam-3975	168	10	)	)	PUNCT
ejpam-3975	168	11	is	be	AUX
ejpam-3975	168	12	a	a	DET
ejpam-3975	168	13	total	total	ADJ
ejpam-3975	168	14	perfect	perfect	ADJ
ejpam-3975	168	15	hop	hop	NOUN
ejpam-3975	168	16	dominating	dominating	NOUN
ejpam-3975	168	17	set	set	NOUN
ejpam-3975	168	18	of	of	ADP
ejpam-3975	168	19	g	g	PROPN
ejpam-3975	169	1	+	+	CCONJ
ejpam-3975	169	2	h	h	NOUN
ejpam-3975	169	3	if	if	SCONJ
ejpam-3975	169	4	and	and	CCONJ
ejpam-3975	169	5	only	only	ADV
ejpam-3975	169	6	if	if	SCONJ
ejpam-3975	169	7	s	s	VERB
ejpam-3975	169	8	=	=	PUNCT
ejpam-3975	169	9	sg	sg	X
ejpam-3975	169	10	∪	∪	ADJ
ejpam-3975	169	11	sh	sh	PROPN
ejpam-3975	169	12	,	,	PUNCT
ejpam-3975	169	13	where	where	SCONJ
ejpam-3975	169	14	sg	sg	PROPN
ejpam-3975	169	15	and	and	CCONJ
ejpam-3975	169	16	sh	sh	PROPN
ejpam-3975	169	17	are	be	AUX
ejpam-3975	169	18	total	total	ADJ
ejpam-3975	169	19	perfect	perfect	ADJ
ejpam-3975	169	20	point	point	NOUN
ejpam-3975	169	21	-	-	PUNCT
ejpam-3975	169	22	wise	wise	ADJ
ejpam-3975	169	23	non	non	ADJ
ejpam-3975	169	24	-	-	ADJ
ejpam-3975	169	25	dominating	dominating	ADJ
ejpam-3975	169	26	sets	set	NOUN
ejpam-3975	169	27	of	of	ADP
ejpam-3975	169	28	g	g	PROPN
ejpam-3975	169	29	and	and	CCONJ
ejpam-3975	169	30	h	h	NOUN
ejpam-3975	169	31	,	,	PUNCT
ejpam-3975	169	32	respectively	respectively	ADV
ejpam-3975	169	33	.	.	PUNCT
ejpam-3975	170	1	proof	proof	NOUN
ejpam-3975	170	2	.	.	PUNCT
ejpam-3975	171	1	suppose	suppose	VERB
ejpam-3975	171	2	that	that	SCONJ
ejpam-3975	171	3	s	s	VERB
ejpam-3975	171	4	⊆	⊆	NUM
ejpam-3975	171	5	v	v	NOUN
ejpam-3975	171	6	(	(	PUNCT
ejpam-3975	171	7	g+h	g+h	PROPN
ejpam-3975	171	8	)	)	PUNCT
ejpam-3975	171	9	is	be	AUX
ejpam-3975	171	10	a	a	DET
ejpam-3975	171	11	total	total	ADJ
ejpam-3975	171	12	perfect	perfect	ADJ
ejpam-3975	171	13	hop	hop	NOUN
ejpam-3975	171	14	dominating	dominating	NOUN
ejpam-3975	171	15	set	set	NOUN
ejpam-3975	171	16	of	of	ADP
ejpam-3975	171	17	g+h	g+h	PROPN
ejpam-3975	171	18	.	.	PUNCT
ejpam-3975	172	1	let	let	VERB
ejpam-3975	172	2	sg	sg	VERB
ejpam-3975	172	3	=	=	SYM
ejpam-3975	172	4	s	s	PART
ejpam-3975	172	5	∩	∩	ADJ
ejpam-3975	172	6	v	v	X
ejpam-3975	172	7	(	(	PUNCT
ejpam-3975	172	8	g	g	NOUN
ejpam-3975	172	9	)	)	PUNCT
ejpam-3975	172	10	and	and	CCONJ
ejpam-3975	172	11	sh	sh	INTJ
ejpam-3975	172	12	=	=	SYM
ejpam-3975	172	13	s	s	PROPN
ejpam-3975	172	14	∩	∩	ADJ
ejpam-3975	172	15	v	v	ADJ
ejpam-3975	172	16	(	(	PUNCT
ejpam-3975	172	17	h	h	NOUN
ejpam-3975	172	18	)	)	PUNCT
ejpam-3975	172	19	.	.	PUNCT
ejpam-3975	173	1	if	if	SCONJ
ejpam-3975	173	2	sg	sg	NOUN
ejpam-3975	173	3	=	=	NOUN
ejpam-3975	173	4	∅	∅	NOUN
ejpam-3975	173	5	,	,	PUNCT
ejpam-3975	173	6	then	then	ADV
ejpam-3975	173	7	s	s	VERB
ejpam-3975	173	8	=	=	ADJ
ejpam-3975	173	9	sh	sh	INTJ
ejpam-3975	173	10	.	.	PUNCT
ejpam-3975	174	1	since	since	SCONJ
ejpam-3975	174	2	v	v	NOUN
ejpam-3975	174	3	(	(	PUNCT
ejpam-3975	174	4	g	g	NOUN
ejpam-3975	174	5	)	)	PUNCT
ejpam-3975	174	6	⊆	⊆	NUM
ejpam-3975	174	7	ng+h(s	ng+h(s	NUM
ejpam-3975	174	8	)	)	PUNCT
ejpam-3975	174	9	,	,	PUNCT
ejpam-3975	174	10	s	s	VERB
ejpam-3975	174	11	is	be	AUX
ejpam-3975	174	12	not	not	PART
ejpam-3975	174	13	a	a	DET
ejpam-3975	174	14	total	total	ADJ
ejpam-3975	174	15	perfect	perfect	ADJ
ejpam-3975	174	16	hop	hop	NOUN
ejpam-3975	174	17	dominating	dominating	NOUN
ejpam-3975	174	18	set	set	NOUN
ejpam-3975	174	19	of	of	ADP
ejpam-3975	174	20	g+h	g+h	PROPN
ejpam-3975	174	21	,	,	PUNCT
ejpam-3975	174	22	a	a	DET
ejpam-3975	174	23	contradiction	contradiction	NOUN
ejpam-3975	174	24	to	to	ADP
ejpam-3975	174	25	our	our	PRON
ejpam-3975	174	26	assumption	assumption	NOUN
ejpam-3975	174	27	.	.	PUNCT
ejpam-3975	175	1	thus	thus	ADV
ejpam-3975	175	2	,	,	PUNCT
ejpam-3975	175	3	sg	sg	PROPN
ejpam-3975	175	4	6=	6=	X
ejpam-3975	175	5	∅.	∅.	ADP
ejpam-3975	175	6	similarly	similarly	ADV
ejpam-3975	175	7	,	,	PUNCT
ejpam-3975	175	8	sh	sh	PROPN
ejpam-3975	175	9	6=	6=	NOUN
ejpam-3975	175	10	∅.	∅.	ADV
ejpam-3975	175	11	let	let	VERB
ejpam-3975	175	12	v	v	ADP
ejpam-3975	175	13	∈	∈	PROPN
ejpam-3975	175	14	v	v	NOUN
ejpam-3975	175	15	(	(	PUNCT
ejpam-3975	175	16	g	g	NOUN
ejpam-3975	175	17	)	)	PUNCT
ejpam-3975	175	18	.	.	PUNCT
ejpam-3975	176	1	then	then	ADV
ejpam-3975	176	2	there	there	PRON
ejpam-3975	176	3	exists	exist	VERB
ejpam-3975	176	4	a	a	DET
ejpam-3975	176	5	unique	unique	ADJ
ejpam-3975	176	6	vertex	vertex	NOUN
ejpam-3975	176	7	y	y	PROPN
ejpam-3975	176	8	∈	∈	PROPN
ejpam-3975	176	9	s	s	VERB
ejpam-3975	177	1	such	such	ADJ
ejpam-3975	177	2	that	that	SCONJ
ejpam-3975	177	3	dg+h(y	dg+h(y	PROPN
ejpam-3975	177	4	,	,	PUNCT
ejpam-3975	177	5	v	v	NOUN
ejpam-3975	177	6	)	)	PUNCT
ejpam-3975	177	7	=	=	SYM
ejpam-3975	177	8	2	2	X
ejpam-3975	177	9	.	.	PUNCT
ejpam-3975	178	1	so	so	SCONJ
ejpam-3975	178	2	that	that	SCONJ
ejpam-3975	178	3	y	y	PROPN
ejpam-3975	178	4	∈	∈	PROPN
ejpam-3975	178	5	sg	sg	NOUN
ejpam-3975	178	6	and	and	CCONJ
ejpam-3975	178	7	v	v	NOUN
ejpam-3975	178	8	/∈	/∈	PUNCT
ejpam-3975	178	9	ng(y	ng(y	NOUN
ejpam-3975	178	10	)	)	PUNCT
ejpam-3975	178	11	.	.	PUNCT
ejpam-3975	179	1	hence	hence	ADV
ejpam-3975	179	2	,	,	PUNCT
ejpam-3975	179	3	sg	sg	PROPN
ejpam-3975	179	4	is	be	AUX
ejpam-3975	179	5	a	a	DET
ejpam-3975	179	6	total	total	ADJ
ejpam-3975	179	7	perfect	perfect	ADJ
ejpam-3975	179	8	point	point	NOUN
ejpam-3975	179	9	-	-	PUNCT
ejpam-3975	179	10	wise	wise	ADJ
ejpam-3975	179	11	non	non	ADJ
ejpam-3975	179	12	-	-	ADJ
ejpam-3975	179	13	dominating	dominating	ADJ
ejpam-3975	179	14	set	set	NOUN
ejpam-3975	179	15	of	of	ADP
ejpam-3975	179	16	g.	g.	PROPN
ejpam-3975	179	17	similarly	similarly	ADV
ejpam-3975	179	18	,	,	PUNCT
ejpam-3975	179	19	sh	sh	PROPN
ejpam-3975	179	20	is	be	AUX
ejpam-3975	179	21	a	a	DET
ejpam-3975	179	22	total	total	ADJ
ejpam-3975	179	23	perfect	perfect	ADJ
ejpam-3975	179	24	point	point	NOUN
ejpam-3975	179	25	-	-	PUNCT
ejpam-3975	179	26	wise	wise	ADJ
ejpam-3975	179	27	non	non	ADJ
ejpam-3975	179	28	-	-	ADJ
ejpam-3975	179	29	dominating	dominating	ADJ
ejpam-3975	179	30	set	set	NOUN
ejpam-3975	179	31	of	of	ADP
ejpam-3975	179	32	h.	h.	NOUN
ejpam-3975	179	33	conversely	conversely	ADV
ejpam-3975	179	34	,	,	PUNCT
ejpam-3975	179	35	suppose	suppose	VERB
ejpam-3975	179	36	s	s	VERB
ejpam-3975	179	37	=	=	PUNCT
ejpam-3975	179	38	sg	sg	X
ejpam-3975	179	39	∪	∪	ADJ
ejpam-3975	179	40	sh	sh	PROPN
ejpam-3975	179	41	,	,	PUNCT
ejpam-3975	179	42	where	where	SCONJ
ejpam-3975	179	43	sg	sg	PROPN
ejpam-3975	179	44	and	and	CCONJ
ejpam-3975	179	45	sh	sh	PROPN
ejpam-3975	179	46	are	be	AUX
ejpam-3975	179	47	total	total	ADJ
ejpam-3975	179	48	perfect	perfect	ADJ
ejpam-3975	179	49	point	point	NOUN
ejpam-3975	179	50	-	-	PUNCT
ejpam-3975	179	51	wise	wise	ADJ
ejpam-3975	179	52	non	non	ADJ
ejpam-3975	179	53	-	-	ADJ
ejpam-3975	179	54	dominating	dominating	ADJ
ejpam-3975	179	55	sets	set	NOUN
ejpam-3975	179	56	of	of	ADP
ejpam-3975	179	57	g	g	PROPN
ejpam-3975	179	58	and	and	CCONJ
ejpam-3975	179	59	h	h	NOUN
ejpam-3975	179	60	,	,	PUNCT
ejpam-3975	179	61	respectively	respectively	ADV
ejpam-3975	179	62	.	.	PUNCT
ejpam-3975	180	1	let	let	VERB
ejpam-3975	180	2	v	v	NUM
ejpam-3975	180	3	∈	∈	PROPN
ejpam-3975	180	4	v	v	NOUN
ejpam-3975	180	5	(	(	PUNCT
ejpam-3975	180	6	g	g	PROPN
ejpam-3975	180	7	+	+	NOUN
ejpam-3975	180	8	h	h	NOUN
ejpam-3975	180	9	)	)	PUNCT
ejpam-3975	180	10	.	.	PUNCT
ejpam-3975	181	1	if	if	SCONJ
ejpam-3975	181	2	v	v	NUM
ejpam-3975	181	3	∈	∈	PROPN
ejpam-3975	181	4	v	v	NOUN
ejpam-3975	181	5	(	(	PUNCT
ejpam-3975	181	6	g	g	NOUN
ejpam-3975	181	7	)	)	PUNCT
ejpam-3975	181	8	,	,	PUNCT
ejpam-3975	181	9	then	then	ADV
ejpam-3975	181	10	there	there	PRON
ejpam-3975	181	11	exists	exist	VERB
ejpam-3975	181	12	a	a	DET
ejpam-3975	181	13	unique	unique	ADJ
ejpam-3975	181	14	vertex	vertex	NOUN
ejpam-3975	181	15	z	z	NOUN
ejpam-3975	181	16	∈	∈	PROPN
ejpam-3975	181	17	sg	sg	ADP
ejpam-3975	181	18	such	such	ADJ
ejpam-3975	181	19	that	that	DET
ejpam-3975	181	20	v	v	NOUN
ejpam-3975	181	21	/∈	/∈	PUNCT
ejpam-3975	181	22	ng(z	ng(z	NUM
ejpam-3975	181	23	)	)	PUNCT
ejpam-3975	181	24	.	.	PUNCT
ejpam-3975	182	1	hence	hence	ADV
ejpam-3975	182	2	,	,	PUNCT
ejpam-3975	182	3	by	by	ADP
ejpam-3975	182	4	definition	definition	NOUN
ejpam-3975	182	5	of	of	ADP
ejpam-3975	182	6	g+h	g+h	PROPN
ejpam-3975	182	7	,	,	PUNCT
ejpam-3975	182	8	dg+h(z	dg+h(z	PROPN
ejpam-3975	182	9	,	,	PUNCT
ejpam-3975	182	10	v	v	NOUN
ejpam-3975	182	11	)	)	PUNCT
ejpam-3975	182	12	=	=	SYM
ejpam-3975	182	13	2	2	X
ejpam-3975	182	14	.	.	X
ejpam-3975	182	15	similarly	similarly	ADV
ejpam-3975	182	16	,	,	PUNCT
ejpam-3975	182	17	if	if	SCONJ
ejpam-3975	182	18	v	v	NUM
ejpam-3975	182	19	∈	∈	PROPN
ejpam-3975	182	20	v	v	NOUN
ejpam-3975	182	21	(	(	PUNCT
ejpam-3975	182	22	h	h	NOUN
ejpam-3975	182	23	)	)	PUNCT
ejpam-3975	182	24	,	,	PUNCT
ejpam-3975	182	25	then	then	ADV
ejpam-3975	182	26	there	there	PRON
ejpam-3975	182	27	exists	exist	VERB
ejpam-3975	182	28	a	a	DET
ejpam-3975	182	29	unique	unique	ADJ
ejpam-3975	182	30	vertex	vertex	NOUN
ejpam-3975	182	31	z∗	z∗	NOUN
ejpam-3975	182	32	∈	∈	PROPN
ejpam-3975	183	1	sh	sh	INTJ
ejpam-3975	183	2	such	such	ADJ
ejpam-3975	183	3	that	that	DET
ejpam-3975	183	4	dg+h(z∗	dg+h(z∗	NOUN
ejpam-3975	183	5	,	,	PUNCT
ejpam-3975	183	6	v	v	NOUN
ejpam-3975	183	7	)	)	PUNCT
ejpam-3975	183	8	=	=	SYM
ejpam-3975	183	9	2	2	X
ejpam-3975	183	10	.	.	X
ejpam-3975	183	11	therefore	therefore	ADV
ejpam-3975	183	12	,	,	PUNCT
ejpam-3975	183	13	s	s	VERB
ejpam-3975	183	14	is	be	AUX
ejpam-3975	183	15	a	a	DET
ejpam-3975	183	16	total	total	ADJ
ejpam-3975	183	17	perfect	perfect	ADJ
ejpam-3975	183	18	hop	hop	NOUN
ejpam-3975	183	19	dominating	dominating	NOUN
ejpam-3975	183	20	set	set	NOUN
ejpam-3975	183	21	of	of	ADP
ejpam-3975	183	22	g+h	g+h	PROPN
ejpam-3975	183	23	.	.	PUNCT
ejpam-3975	184	1	�	�	PROPN
ejpam-3975	184	2	the	the	DET
ejpam-3975	184	3	next	next	ADJ
ejpam-3975	184	4	result	result	NOUN
ejpam-3975	184	5	follows	follow	VERB
ejpam-3975	184	6	immediately	immediately	ADV
ejpam-3975	184	7	from	from	ADP
ejpam-3975	184	8	theorem	theorem	ADJ
ejpam-3975	184	9	3.1	3.1	NUM
ejpam-3975	184	10	corollary	corollary	ADJ
ejpam-3975	184	11	3.2	3.2	NUM
ejpam-3975	184	12	.	.	PUNCT
ejpam-3975	185	1	let	let	VERB
ejpam-3975	185	2	g	g	NOUN
ejpam-3975	186	1	and	and	CCONJ
ejpam-3975	186	2	h	h	NOUN
ejpam-3975	186	3	be	be	AUX
ejpam-3975	186	4	graphs	graph	NOUN
ejpam-3975	186	5	with	with	ADP
ejpam-3975	186	6	∆(g	∆(g	NOUN
ejpam-3975	186	7	)	)	PUNCT
ejpam-3975	187	1	6=	6=	ADP
ejpam-3975	187	2	|v	|v	PROPN
ejpam-3975	187	3	(	(	PUNCT
ejpam-3975	187	4	g)|	g)|	INTJ
ejpam-3975	187	5	−	−	PROPN
ejpam-3975	187	6	1	1	NUM
ejpam-3975	187	7	and	and	CCONJ
ejpam-3975	187	8	∆(h	∆(h	NOUN
ejpam-3975	187	9	)	)	PUNCT
ejpam-3975	187	10	6=	6=	NUM
ejpam-3975	187	11	|v	|v	PROPN
ejpam-3975	187	12	(	(	PUNCT
ejpam-3975	187	13	h)|	h)|	NOUN
ejpam-3975	187	14	−	−	PROPN
ejpam-3975	187	15	1	1	NUM
ejpam-3975	187	16	.	.	PUNCT
ejpam-3975	188	1	then	then	ADV
ejpam-3975	188	2	,	,	PUNCT
ejpam-3975	188	3	γtph(g+h	γtph(g+h	NOUN
ejpam-3975	188	4	)	)	PUNCT
ejpam-3975	188	5	=	=	SYM
ejpam-3975	188	6	tppnd(g	tppnd(g	PROPN
ejpam-3975	188	7	)	)	PUNCT
ejpam-3975	188	8	+	+	NUM
ejpam-3975	188	9	tppnd(h	tppnd(h	NOUN
ejpam-3975	188	10	)	)	PUNCT
ejpam-3975	188	11	.	.	PUNCT
ejpam-3975	189	1	in	in	ADP
ejpam-3975	189	2	particular	particular	ADJ
ejpam-3975	189	3	,	,	PUNCT
ejpam-3975	189	4	(	(	PUNCT
ejpam-3975	189	5	i	i	NOUN
ejpam-3975	189	6	)	)	PUNCT
ejpam-3975	189	7	γtph(pn	γtph(pn	PROPN
ejpam-3975	189	8	+	+	CCONJ
ejpam-3975	189	9	pm	pm	NOUN
ejpam-3975	189	10	)	)	PUNCT
ejpam-3975	190	1	=	=	SYM
ejpam-3975	190	2	4	4	NUM
ejpam-3975	190	3	if	if	SCONJ
ejpam-3975	190	4	4	4	NUM
ejpam-3975	190	5	≤	≤	NUM
ejpam-3975	190	6	m	m	NOUN
ejpam-3975	190	7	,	,	PUNCT
ejpam-3975	190	8	n	n	PROPN
ejpam-3975	190	9	≤	≤	NUM
ejpam-3975	190	10	6	6	NUM
ejpam-3975	190	11	(	(	PUNCT
ejpam-3975	190	12	ii	ii	NOUN
ejpam-3975	190	13	)	)	PUNCT
ejpam-3975	190	14	γtph(cn	γtph(cn	PROPN
ejpam-3975	190	15	+	+	CCONJ
ejpam-3975	190	16	cm	cm	NOUN
ejpam-3975	190	17	)	)	PUNCT
ejpam-3975	190	18	=	=	SYM
ejpam-3975	190	19	4	4	NUM
ejpam-3975	190	20	if	if	SCONJ
ejpam-3975	190	21	n	n	CCONJ
ejpam-3975	190	22	,	,	PUNCT
ejpam-3975	190	23	m	m	VERB
ejpam-3975	190	24	=	=	NOUN
ejpam-3975	190	25	4	4	NUM
ejpam-3975	190	26	,	,	PUNCT
ejpam-3975	190	27	6	6	NUM
ejpam-3975	190	28	.	.	NOUN
ejpam-3975	190	29	4	4	NUM
ejpam-3975	190	30	.	.	X
ejpam-3975	190	31	corona	corona	NOUN
ejpam-3975	190	32	of	of	ADP
ejpam-3975	190	33	graphs	graph	NOUN
ejpam-3975	190	34	the	the	DET
ejpam-3975	190	35	corona	corona	NOUN
ejpam-3975	190	36	g	g	PROPN
ejpam-3975	190	37	◦	◦	NOUN
ejpam-3975	190	38	h	h	NOUN
ejpam-3975	190	39	of	of	ADP
ejpam-3975	190	40	two	two	NUM
ejpam-3975	190	41	graphs	graph	NOUN
ejpam-3975	190	42	g	g	NOUN
ejpam-3975	190	43	and	and	CCONJ
ejpam-3975	190	44	h	h	NOUN
ejpam-3975	190	45	is	be	AUX
ejpam-3975	190	46	the	the	DET
ejpam-3975	190	47	graph	graph	NOUN
ejpam-3975	190	48	obtained	obtain	VERB
ejpam-3975	190	49	by	by	ADP
ejpam-3975	190	50	taking	take	VERB
ejpam-3975	190	51	one	one	NUM
ejpam-3975	190	52	copy	copy	NOUN
ejpam-3975	190	53	of	of	ADP
ejpam-3975	190	54	g	g	NOUN
ejpam-3975	190	55	of	of	ADP
ejpam-3975	190	56	order	order	NOUN
ejpam-3975	190	57	n	n	NOUN
ejpam-3975	190	58	and	and	CCONJ
ejpam-3975	190	59	n	n	PRON
ejpam-3975	190	60	copies	copy	NOUN
ejpam-3975	190	61	of	of	ADP
ejpam-3975	190	62	h	h	NOUN
ejpam-3975	190	63	,	,	PUNCT
ejpam-3975	190	64	and	and	CCONJ
ejpam-3975	190	65	then	then	ADV
ejpam-3975	190	66	joining	join	VERB
ejpam-3975	190	67	the	the	DET
ejpam-3975	190	68	ith	ith	PROPN
ejpam-3975	190	69	vertex	vertex	NOUN
ejpam-3975	190	70	of	of	ADP
ejpam-3975	190	71	g	g	NOUN
ejpam-3975	190	72	to	to	ADP
ejpam-3975	190	73	every	every	DET
ejpam-3975	190	74	vertex	vertex	NOUN
ejpam-3975	190	75	in	in	ADP
ejpam-3975	190	76	the	the	DET
ejpam-3975	190	77	ith	ith	PROPN
ejpam-3975	190	78	copy	copy	NOUN
ejpam-3975	190	79	of	of	ADP
ejpam-3975	190	80	h.	h.	PROPN
ejpam-3975	190	81	for	for	ADP
ejpam-3975	190	82	every	every	DET
ejpam-3975	190	83	v	v	NUM
ejpam-3975	190	84	∈	∈	PROPN
ejpam-3975	190	85	v	v	NOUN
ejpam-3975	190	86	(	(	PUNCT
ejpam-3975	190	87	g	g	NOUN
ejpam-3975	190	88	)	)	PUNCT
ejpam-3975	190	89	,	,	PUNCT
ejpam-3975	190	90	denote	denote	VERB
ejpam-3975	190	91	by	by	ADP
ejpam-3975	190	92	hv	hv	PROPN
ejpam-3975	190	93	the	the	DET
ejpam-3975	190	94	copy	copy	NOUN
ejpam-3975	190	95	of	of	ADP
ejpam-3975	190	96	h	h	NOUN
ejpam-3975	190	97	whose	whose	DET
ejpam-3975	190	98	vertices	vertex	NOUN
ejpam-3975	190	99	are	be	AUX
ejpam-3975	190	100	attached	attach	VERB
ejpam-3975	190	101	one	one	NUM
ejpam-3975	190	102	by	by	ADP
ejpam-3975	190	103	one	one	NUM
ejpam-3975	190	104	to	to	ADP
ejpam-3975	190	105	the	the	DET
ejpam-3975	190	106	vertex	vertex	NOUN
ejpam-3975	190	107	v.	v.	ADP
ejpam-3975	190	108	subsequently	subsequently	ADV
ejpam-3975	190	109	,	,	PUNCT
ejpam-3975	190	110	denote	denote	VERB
ejpam-3975	190	111	by	by	ADP
ejpam-3975	190	112	v+hv	v+hv	NOUN
ejpam-3975	190	113	the	the	DET
ejpam-3975	190	114	subgraph	subgraph	NOUN
ejpam-3975	190	115	of	of	ADP
ejpam-3975	190	116	the	the	DET
ejpam-3975	190	117	corona	corona	NOUN
ejpam-3975	190	118	g	g	PROPN
ejpam-3975	190	119	◦	◦	NOUN
ejpam-3975	190	120	h	h	NOUN
ejpam-3975	190	121	corresponding	correspond	VERB
ejpam-3975	190	122	to	to	ADP
ejpam-3975	190	123	the	the	DET
ejpam-3975	190	124	join	join	NOUN
ejpam-3975	190	125	〈	〈	PROPN
ejpam-3975	190	126	v〉+hv	v〉+hv	NOUN
ejpam-3975	190	127	=	=	SYM
ejpam-3975	190	128	v	v	ADP
ejpam-3975	190	129	+	+	NOUN
ejpam-3975	190	130	hv	hv	PROPN
ejpam-3975	190	131	.	.	PUNCT
ejpam-3975	190	132	definition	definition	NOUN
ejpam-3975	190	133	4.1	4.1	NUM
ejpam-3975	190	134	.	.	PUNCT
ejpam-3975	191	1	a	a	DET
ejpam-3975	191	2	set	set	NOUN
ejpam-3975	191	3	s	s	NOUN
ejpam-3975	191	4	⊆	⊆	NUM
ejpam-3975	191	5	v	v	NOUN
ejpam-3975	191	6	(	(	PUNCT
ejpam-3975	191	7	g	g	NOUN
ejpam-3975	191	8	)	)	PUNCT
ejpam-3975	191	9	is	be	AUX
ejpam-3975	191	10	a	a	DET
ejpam-3975	191	11	perfect	perfect	ADJ
ejpam-3975	191	12	total	total	NOUN
ejpam-3975	191	13	(	(	PUNCT
ejpam-3975	191	14	1	1	NUM
ejpam-3975	191	15	,	,	PUNCT
ejpam-3975	191	16	2)∗-dominating	2)∗-dominate	VERB
ejpam-3975	191	17	set	set	NOUN
ejpam-3975	191	18	of	of	ADP
ejpam-3975	191	19	g	g	PROPN
ejpam-3975	191	20	if	if	SCONJ
ejpam-3975	191	21	for	for	ADP
ejpam-3975	191	22	every	every	DET
ejpam-3975	191	23	w	w	PROPN
ejpam-3975	191	24	∈	∈	PROPN
ejpam-3975	191	25	v	v	ADP
ejpam-3975	191	26	(	(	PUNCT
ejpam-3975	191	27	g	g	NOUN
ejpam-3975	191	28	)	)	PUNCT
ejpam-3975	191	29	,	,	PUNCT
ejpam-3975	191	30	there	there	PRON
ejpam-3975	191	31	is	be	VERB
ejpam-3975	191	32	exactly	exactly	ADV
ejpam-3975	191	33	one	one	NUM
ejpam-3975	191	34	vertex	vertex	NOUN
ejpam-3975	191	35	x	x	X
ejpam-3975	191	36	∈	∈	NOUN
ejpam-3975	191	37	s	s	VERB
ejpam-3975	191	38	such	such	ADJ
ejpam-3975	191	39	that	that	SCONJ
ejpam-3975	191	40	wx	wx	PROPN
ejpam-3975	191	41	∈	∈	PROPN
ejpam-3975	191	42	e(g	e(g	PROPN
ejpam-3975	191	43	)	)	PUNCT
ejpam-3975	191	44	and	and	CCONJ
ejpam-3975	191	45	for	for	ADP
ejpam-3975	191	46	every	every	DET
ejpam-3975	191	47	u	u	PROPN
ejpam-3975	191	48	∈	∈	PROPN
ejpam-3975	191	49	v	v	NOUN
ejpam-3975	191	50	(	(	PUNCT
ejpam-3975	191	51	g)\s	g)\s	NOUN
ejpam-3975	191	52	,	,	PUNCT
ejpam-3975	191	53	there	there	PRON
ejpam-3975	191	54	is	be	VERB
ejpam-3975	191	55	exactly	exactly	ADV
ejpam-3975	191	56	one	one	NUM
ejpam-3975	191	57	vertex	vertex	NOUN
ejpam-3975	191	58	v	v	ADP
ejpam-3975	191	59	∈	∈	NOUN
ejpam-3975	191	60	s	s	VERB
ejpam-3975	191	61	such	such	ADJ
ejpam-3975	191	62	that	that	DET
ejpam-3975	191	63	dg(u	dg(u	ADJ
ejpam-3975	191	64	,	,	PUNCT
ejpam-3975	191	65	v	v	NOUN
ejpam-3975	191	66	)	)	PUNCT
ejpam-3975	191	67	=	=	SYM
ejpam-3975	191	68	2	2	X
ejpam-3975	191	69	.	.	X
ejpam-3975	191	70	the	the	DET
ejpam-3975	191	71	smallest	small	ADJ
ejpam-3975	191	72	cardinality	cardinality	NOUN
ejpam-3975	191	73	of	of	ADP
ejpam-3975	191	74	a	a	DET
ejpam-3975	191	75	perfect	perfect	ADJ
ejpam-3975	191	76	total	total	NOUN
ejpam-3975	191	77	(	(	PUNCT
ejpam-3975	191	78	1	1	NUM
ejpam-3975	191	79	,	,	PUNCT
ejpam-3975	191	80	2)∗-dominating	2)∗-dominate	VERB
ejpam-3975	191	81	set	set	NOUN
ejpam-3975	191	82	of	of	ADP
ejpam-3975	191	83	g	g	PROPN
ejpam-3975	191	84	is	be	AUX
ejpam-3975	191	85	called	call	VERB
ejpam-3975	191	86	the	the	DET
ejpam-3975	191	87	perfect	perfect	ADJ
ejpam-3975	191	88	total	total	NOUN
ejpam-3975	191	89	(	(	PUNCT
ejpam-3975	191	90	1	1	NUM
ejpam-3975	191	91	,	,	PUNCT
ejpam-3975	191	92	2)∗-domination	2)∗-domination	NOUN
ejpam-3975	191	93	number	number	NOUN
ejpam-3975	191	94	of	of	ADP
ejpam-3975	191	95	g	g	NOUN
ejpam-3975	191	96	,	,	PUNCT
ejpam-3975	191	97	denoted	denote	VERB
ejpam-3975	191	98	by	by	ADP
ejpam-3975	191	99	γ∗pt1,2	γ∗pt1,2	PROPN
ejpam-3975	191	100	(	(	PUNCT
ejpam-3975	191	101	g	g	NOUN
ejpam-3975	191	102	)	)	PUNCT
ejpam-3975	191	103	.	.	PUNCT
ejpam-3975	192	1	a	a	DET
ejpam-3975	192	2	perfect	perfect	ADJ
ejpam-3975	192	3	total	total	NOUN
ejpam-3975	192	4	(	(	PUNCT
ejpam-3975	192	5	1	1	NUM
ejpam-3975	192	6	,	,	PUNCT
ejpam-3975	192	7	2)∗-dominating	2)∗-dominate	VERB
ejpam-3975	192	8	set	set	NOUN
ejpam-3975	192	9	s	s	NOUN
ejpam-3975	192	10	of	of	ADP
ejpam-3975	192	11	g	g	NOUN
ejpam-3975	192	12	with	with	ADP
ejpam-3975	192	13	cardinality	cardinality	PROPN
ejpam-3975	192	14	γ∗pt1,2	γ∗pt1,2	PROPN
ejpam-3975	192	15	(	(	PUNCT
ejpam-3975	192	16	g	g	NOUN
ejpam-3975	192	17	)	)	PUNCT
ejpam-3975	192	18	is	be	AUX
ejpam-3975	192	19	called	call	VERB
ejpam-3975	192	20	a	a	DET
ejpam-3975	192	21	γ∗pt1,2	γ∗pt1,2	PROPN
ejpam-3975	192	22	-set	-set	PUNCT
ejpam-3975	192	23	of	of	ADP
ejpam-3975	192	24	g.	g.	PROPN
ejpam-3975	192	25	r.	r.	PROPN
ejpam-3975	192	26	rakim	rakim	PROPN
ejpam-3975	192	27	,	,	PUNCT
ejpam-3975	192	28	h.	h.	PROPN
ejpam-3975	192	29	rara	rara	PROPN
ejpam-3975	192	30	/	/	SYM
ejpam-3975	192	31	eur	eur	PROPN
ejpam-3975	192	32	.	.	PUNCT
ejpam-3975	193	1	j.	j.	PROPN
ejpam-3975	193	2	pure	pure	PROPN
ejpam-3975	193	3	appl	appl	PROPN
ejpam-3975	193	4	.	.	PROPN
ejpam-3975	193	5	math	math	PROPN
ejpam-3975	193	6	,	,	PUNCT
ejpam-3975	193	7	14	14	NUM
ejpam-3975	193	8	(	(	PUNCT
ejpam-3975	193	9	3	3	NUM
ejpam-3975	193	10	)	)	PUNCT
ejpam-3975	193	11	(	(	PUNCT
ejpam-3975	193	12	2021	2021	NUM
ejpam-3975	193	13	)	)	PUNCT
ejpam-3975	193	14	,	,	PUNCT
ejpam-3975	193	15	803	803	NUM
ejpam-3975	193	16	-	-	SYM
ejpam-3975	193	17	815	815	NUM
ejpam-3975	193	18	810	810	NUM
ejpam-3975	193	19	theorem	theorem	VERB
ejpam-3975	193	20	4.2	4.2	NUM
ejpam-3975	193	21	.	.	PUNCT
ejpam-3975	194	1	let	let	VERB
ejpam-3975	194	2	g	g	PRON
ejpam-3975	194	3	be	be	AUX
ejpam-3975	194	4	a	a	DET
ejpam-3975	194	5	connected	connected	ADJ
ejpam-3975	194	6	nontrivial	nontrivial	NOUN
ejpam-3975	194	7	graph	graph	NOUN
ejpam-3975	194	8	whose	whose	DET
ejpam-3975	194	9	perfect	perfect	ADJ
ejpam-3975	194	10	total	total	NOUN
ejpam-3975	194	11	(	(	PUNCT
ejpam-3975	194	12	1	1	NUM
ejpam-3975	194	13	,	,	PUNCT
ejpam-3975	194	14	2)∗-dominating	2)∗-dominating	NUM
ejpam-3975	194	15	set	set	NOUN
ejpam-3975	194	16	exists	exist	VERB
ejpam-3975	194	17	and	and	CCONJ
ejpam-3975	194	18	h	h	DET
ejpam-3975	194	19	a	a	DET
ejpam-3975	194	20	graph	graph	NOUN
ejpam-3975	194	21	with	with	ADP
ejpam-3975	194	22	γ(h	γ(h	NOUN
ejpam-3975	194	23	)	)	PUNCT
ejpam-3975	194	24	=	=	SYM
ejpam-3975	195	1	1	1	X
ejpam-3975	195	2	.	.	PUNCT
ejpam-3975	195	3	then	then	ADV
ejpam-3975	195	4	g	g	PROPN
ejpam-3975	195	5	◦	◦	NOUN
ejpam-3975	195	6	h	h	NOUN
ejpam-3975	195	7	has	have	VERB
ejpam-3975	195	8	a	a	DET
ejpam-3975	195	9	total	total	ADJ
ejpam-3975	195	10	perfect	perfect	ADJ
ejpam-3975	195	11	hop	hop	NOUN
ejpam-3975	195	12	dominating	dominating	NOUN
ejpam-3975	195	13	set	set	NOUN
ejpam-3975	195	14	s	s	VERB
ejpam-3975	195	15	if	if	SCONJ
ejpam-3975	196	1	and	and	CCONJ
ejpam-3975	196	2	only	only	ADV
ejpam-3975	196	3	if	if	SCONJ
ejpam-3975	196	4	s	s	VERB
ejpam-3975	196	5	=	=	NOUN
ejpam-3975	196	6	a	a	PRON
ejpam-3975	196	7	∪	∪	X
ejpam-3975	196	8	(	(	PUNCT
ejpam-3975	196	9	⋃	⋃	NOUN
ejpam-3975	196	10	v∈v	v∈v	NOUN
ejpam-3975	196	11	(	(	PUNCT
ejpam-3975	196	12	g	g	NOUN
ejpam-3975	196	13	)	)	PUNCT
ejpam-3975	196	14	sv	sv	NOUN
ejpam-3975	196	15	)	)	PUNCT
ejpam-3975	196	16	where	where	SCONJ
ejpam-3975	196	17	sv	sv	PROPN
ejpam-3975	196	18	⊆	⊆	NUM
ejpam-3975	196	19	v	v	X
ejpam-3975	196	20	(	(	PUNCT
ejpam-3975	196	21	hv	hv	NOUN
ejpam-3975	196	22	)	)	PUNCT
ejpam-3975	196	23	for	for	ADP
ejpam-3975	196	24	every	every	DET
ejpam-3975	196	25	v	v	NUM
ejpam-3975	196	26	∈	∈	PROPN
ejpam-3975	196	27	v	v	NOUN
ejpam-3975	196	28	(	(	PUNCT
ejpam-3975	196	29	g	g	NOUN
ejpam-3975	196	30	)	)	PUNCT
ejpam-3975	196	31	and	and	CCONJ
ejpam-3975	196	32	the	the	DET
ejpam-3975	196	33	following	follow	VERB
ejpam-3975	196	34	conditions	condition	NOUN
ejpam-3975	196	35	are	be	AUX
ejpam-3975	196	36	satisfied	satisfied	ADJ
ejpam-3975	196	37	.	.	PUNCT
ejpam-3975	197	1	(	(	PUNCT
ejpam-3975	197	2	i	i	NOUN
ejpam-3975	197	3	)	)	PUNCT
ejpam-3975	197	4	a	a	DET
ejpam-3975	197	5	⊆	⊆	NUM
ejpam-3975	197	6	v	v	NOUN
ejpam-3975	197	7	(	(	PUNCT
ejpam-3975	197	8	g	g	NOUN
ejpam-3975	197	9	)	)	PUNCT
ejpam-3975	197	10	is	be	AUX
ejpam-3975	197	11	a	a	DET
ejpam-3975	197	12	perfect	perfect	ADJ
ejpam-3975	197	13	total	total	NOUN
ejpam-3975	197	14	(	(	PUNCT
ejpam-3975	197	15	1	1	NUM
ejpam-3975	197	16	,	,	PUNCT
ejpam-3975	197	17	2)∗-dominating	2)∗-dominate	VERB
ejpam-3975	197	18	set	set	NOUN
ejpam-3975	197	19	of	of	ADP
ejpam-3975	197	20	g.	g.	PROPN
ejpam-3975	197	21	(	(	PUNCT
ejpam-3975	197	22	ii	ii	PROPN
ejpam-3975	197	23	)	)	PUNCT
ejpam-3975	197	24	for	for	ADP
ejpam-3975	197	25	each	each	DET
ejpam-3975	197	26	v	v	NUM
ejpam-3975	197	27	∈	∈	PROPN
ejpam-3975	197	28	v	v	NOUN
ejpam-3975	197	29	(	(	PUNCT
ejpam-3975	197	30	g)\a	g)\a	NOUN
ejpam-3975	197	31	,	,	PUNCT
ejpam-3975	197	32	su	su	NOUN
ejpam-3975	197	33	=	=	NOUN
ejpam-3975	197	34	∅	∅	NOUN
ejpam-3975	197	35	for	for	ADP
ejpam-3975	197	36	all	all	DET
ejpam-3975	197	37	u	u	NOUN
ejpam-3975	197	38	∈	∈	NOUN
ejpam-3975	197	39	ng(v	ng(v	NUM
ejpam-3975	197	40	)	)	PUNCT
ejpam-3975	197	41	.	.	PUNCT
ejpam-3975	198	1	(	(	PUNCT
ejpam-3975	198	2	iii	iii	X
ejpam-3975	198	3	)	)	PUNCT
ejpam-3975	198	4	for	for	ADP
ejpam-3975	198	5	each	each	DET
ejpam-3975	198	6	v	v	ADP
ejpam-3975	198	7	∈	∈	PROPN
ejpam-3975	198	8	a	a	PRON
ejpam-3975	198	9	,	,	PUNCT
ejpam-3975	198	10	ng(v	ng(v	PUNCT
ejpam-3975	198	11	,	,	PUNCT
ejpam-3975	198	12	2	2	X
ejpam-3975	198	13	)	)	PUNCT
ejpam-3975	198	14	∩	∩	NOUN
ejpam-3975	198	15	s	s	PART
ejpam-3975	198	16	=	=	SYM
ejpam-3975	198	17	∅	∅	NOUN
ejpam-3975	198	18	and	and	CCONJ
ejpam-3975	198	19	sw	sw	PROPN
ejpam-3975	198	20	is	be	AUX
ejpam-3975	198	21	a	a	DET
ejpam-3975	198	22	γ	γ	NOUN
ejpam-3975	198	23	-	-	PUNCT
ejpam-3975	198	24	set	set	NOUN
ejpam-3975	198	25	of	of	ADP
ejpam-3975	198	26	h	h	NOUN
ejpam-3975	198	27	for	for	ADP
ejpam-3975	198	28	a	a	DET
ejpam-3975	198	29	unique	unique	ADJ
ejpam-3975	198	30	w	w	NOUN
ejpam-3975	198	31	∈	∈	PROPN
ejpam-3975	198	32	v	v	ADP
ejpam-3975	198	33	(	(	PUNCT
ejpam-3975	198	34	g	g	NOUN
ejpam-3975	198	35	)	)	PUNCT
ejpam-3975	198	36	∩ng(v	∩ng(v	PROPN
ejpam-3975	198	37	)	)	PUNCT
ejpam-3975	198	38	.	.	PUNCT
ejpam-3975	199	1	proof	proof	NOUN
ejpam-3975	199	2	.	.	PUNCT
ejpam-3975	200	1	suppose	suppose	VERB
ejpam-3975	200	2	s	s	PRON
ejpam-3975	200	3	is	be	AUX
ejpam-3975	200	4	a	a	DET
ejpam-3975	200	5	total	total	ADJ
ejpam-3975	200	6	perfect	perfect	ADJ
ejpam-3975	200	7	hop	hop	NOUN
ejpam-3975	200	8	dominating	dominating	NOUN
ejpam-3975	200	9	set	set	NOUN
ejpam-3975	200	10	of	of	ADP
ejpam-3975	200	11	g	g	NOUN
ejpam-3975	200	12	◦	◦	NOUN
ejpam-3975	200	13	h	h	NOUN
ejpam-3975	200	14	and	and	CCONJ
ejpam-3975	200	15	a	a	DET
ejpam-3975	200	16	=	=	NOUN
ejpam-3975	200	17	v	v	NOUN
ejpam-3975	200	18	(	(	PUNCT
ejpam-3975	200	19	g)∩s	g)∩s	PROPN
ejpam-3975	200	20	.	.	PUNCT
ejpam-3975	201	1	then	then	ADV
ejpam-3975	201	2	a	a	DET
ejpam-3975	201	3	⊆	⊆	NUM
ejpam-3975	201	4	v	v	NOUN
ejpam-3975	201	5	(	(	PUNCT
ejpam-3975	201	6	g	g	NOUN
ejpam-3975	201	7	)	)	PUNCT
ejpam-3975	201	8	.	.	PUNCT
ejpam-3975	202	1	also	also	ADV
ejpam-3975	202	2	,	,	PUNCT
ejpam-3975	202	3	s	s	VERB
ejpam-3975	202	4	is	be	AUX
ejpam-3975	202	5	a	a	DET
ejpam-3975	202	6	perfect	perfect	ADJ
ejpam-3975	202	7	hop	hop	NOUN
ejpam-3975	202	8	dominating	dominating	NOUN
ejpam-3975	202	9	set	set	NOUN
ejpam-3975	202	10	of	of	ADP
ejpam-3975	202	11	g	g	PROPN
ejpam-3975	202	12	◦	◦	PROPN
ejpam-3975	202	13	h.	h.	PROPN
ejpam-3975	202	14	let	let	VERB
ejpam-3975	202	15	x	x	SYM
ejpam-3975	202	16	∈	∈	PROPN
ejpam-3975	202	17	v	v	X
ejpam-3975	202	18	(	(	PUNCT
ejpam-3975	202	19	g	g	NOUN
ejpam-3975	202	20	)	)	PUNCT
ejpam-3975	202	21	.	.	PUNCT
ejpam-3975	203	1	if	if	SCONJ
ejpam-3975	203	2	x	x	X
ejpam-3975	203	3	/∈	/∈	NOUN
ejpam-3975	204	1	a	a	X
ejpam-3975	204	2	,	,	PUNCT
ejpam-3975	204	3	then	then	ADV
ejpam-3975	204	4	x	x	PROPN
ejpam-3975	204	5	/∈	/∈	PROPN
ejpam-3975	205	1	c.	c.	PROPN
ejpam-3975	205	2	hence	hence	ADV
ejpam-3975	205	3	,	,	PUNCT
ejpam-3975	205	4	there	there	PRON
ejpam-3975	205	5	exists	exist	VERB
ejpam-3975	205	6	a	a	DET
ejpam-3975	205	7	unique	unique	ADJ
ejpam-3975	205	8	vertex	vertex	NOUN
ejpam-3975	205	9	v	v	ADP
ejpam-3975	205	10	∈	∈	NOUN
ejpam-3975	205	11	c	c	NOUN
ejpam-3975	205	12	such	such	ADJ
ejpam-3975	205	13	that	that	SCONJ
ejpam-3975	205	14	dg	dg	VERB
ejpam-3975	205	15	◦	◦	NOUN
ejpam-3975	205	16	h(x	h(x	PROPN
ejpam-3975	205	17	,	,	PUNCT
ejpam-3975	205	18	v	v	NOUN
ejpam-3975	205	19	)	)	PUNCT
ejpam-3975	205	20	=	=	SYM
ejpam-3975	206	1	2	2	X
ejpam-3975	206	2	.	.	X
ejpam-3975	206	3	we	we	PRON
ejpam-3975	206	4	claim	claim	VERB
ejpam-3975	206	5	that	that	SCONJ
ejpam-3975	206	6	v	v	NUM
ejpam-3975	206	7	∈	∈	PROPN
ejpam-3975	206	8	a.	a.	NOUN
ejpam-3975	206	9	suppose	suppose	VERB
ejpam-3975	206	10	that	that	SCONJ
ejpam-3975	206	11	v	v	X
ejpam-3975	206	12	/∈	/∈	PUNCT
ejpam-3975	206	13	a.	a.	NOUN
ejpam-3975	207	1	then	then	ADV
ejpam-3975	207	2	there	there	PRON
ejpam-3975	207	3	exists	exist	VERB
ejpam-3975	207	4	a	a	DET
ejpam-3975	207	5	vertex	vertex	NOUN
ejpam-3975	207	6	w	w	NOUN
ejpam-3975	207	7	∈	∈	PROPN
ejpam-3975	207	8	v	v	ADP
ejpam-3975	207	9	(	(	PUNCT
ejpam-3975	207	10	g	g	NOUN
ejpam-3975	207	11	)	)	PUNCT
ejpam-3975	207	12	such	such	ADJ
ejpam-3975	207	13	that	that	DET
ejpam-3975	207	14	v	v	NUM
ejpam-3975	207	15	∈	∈	PROPN
ejpam-3975	207	16	v	v	NOUN
ejpam-3975	207	17	(	(	PUNCT
ejpam-3975	207	18	hw	hw	NOUN
ejpam-3975	207	19	)	)	PUNCT
ejpam-3975	207	20	and	and	CCONJ
ejpam-3975	207	21	xw	xw	PROPN
ejpam-3975	207	22	∈	∈	PROPN
ejpam-3975	207	23	e(g	e(g	PROPN
ejpam-3975	207	24	)	)	PUNCT
ejpam-3975	207	25	.	.	PUNCT
ejpam-3975	208	1	if	if	SCONJ
ejpam-3975	208	2	|v	|v	PROPN
ejpam-3975	208	3	(	(	PUNCT
ejpam-3975	208	4	g)|	g)|	NOUN
ejpam-3975	208	5	=	=	SYM
ejpam-3975	208	6	2	2	NUM
ejpam-3975	208	7	,	,	PUNCT
ejpam-3975	208	8	then	then	ADV
ejpam-3975	208	9	h	h	PROPN
ejpam-3975	208	10	is	be	AUX
ejpam-3975	208	11	a	a	DET
ejpam-3975	208	12	trivial	trivial	ADJ
ejpam-3975	208	13	graph	graph	NOUN
ejpam-3975	208	14	or	or	CCONJ
ejpam-3975	208	15	v	v	NOUN
ejpam-3975	208	16	is	be	AUX
ejpam-3975	208	17	an	an	DET
ejpam-3975	208	18	isolated	isolated	ADJ
ejpam-3975	208	19	vertex	vertex	NOUN
ejpam-3975	208	20	of	of	ADP
ejpam-3975	208	21	h	h	NOUN
ejpam-3975	208	22	,	,	PUNCT
ejpam-3975	208	23	which	which	PRON
ejpam-3975	208	24	is	be	AUX
ejpam-3975	208	25	a	a	DET
ejpam-3975	208	26	contradiction	contradiction	NOUN
ejpam-3975	208	27	to	to	ADP
ejpam-3975	208	28	the	the	DET
ejpam-3975	208	29	hypothesis	hypothesis	NOUN
ejpam-3975	208	30	.	.	PUNCT
ejpam-3975	209	1	if	if	SCONJ
ejpam-3975	209	2	|v	|v	PROPN
ejpam-3975	209	3	(	(	PUNCT
ejpam-3975	209	4	g)|	g)|	X
ejpam-3975	209	5	>	>	X
ejpam-3975	209	6	2	2	NUM
ejpam-3975	209	7	,	,	PUNCT
ejpam-3975	209	8	then	then	ADV
ejpam-3975	209	9	there	there	PRON
ejpam-3975	209	10	exist	exist	VERB
ejpam-3975	209	11	vertices	vertex	NOUN
ejpam-3975	209	12	a	a	DET
ejpam-3975	209	13	∈	∈	PROPN
ejpam-3975	209	14	nhw(v	nhw(v	PROPN
ejpam-3975	209	15	)	)	PUNCT
ejpam-3975	209	16	\	\	PROPN
ejpam-3975	210	1	c	c	NOUN
ejpam-3975	210	2	and	and	CCONJ
ejpam-3975	210	3	b	b	PROPN
ejpam-3975	210	4	∈	∈	PROPN
ejpam-3975	210	5	a	a	DET
ejpam-3975	210	6	such	such	ADJ
ejpam-3975	210	7	that	that	SCONJ
ejpam-3975	210	8	dg	dg	PROPN
ejpam-3975	210	9	◦	◦	PROPN
ejpam-3975	210	10	h(a	h(a	PROPN
ejpam-3975	210	11	,	,	PUNCT
ejpam-3975	210	12	b	b	NOUN
ejpam-3975	210	13	)	)	PUNCT
ejpam-3975	210	14	=	=	SYM
ejpam-3975	210	15	2	2	X
ejpam-3975	210	16	.	.	PUNCT
ejpam-3975	211	1	thus	thus	ADV
ejpam-3975	211	2	,	,	PUNCT
ejpam-3975	211	3	wb	wb	PROPN
ejpam-3975	211	4	∈	∈	PROPN
ejpam-3975	211	5	e(g	e(g	PROPN
ejpam-3975	211	6	)	)	PUNCT
ejpam-3975	212	1	implying	imply	VERB
ejpam-3975	212	2	that	that	SCONJ
ejpam-3975	212	3	dg	dg	AUX
ejpam-3975	212	4	◦	◦	NOUN
ejpam-3975	212	5	h(x	h(x	PROPN
ejpam-3975	212	6	,	,	PUNCT
ejpam-3975	212	7	b	b	NOUN
ejpam-3975	212	8	)	)	PUNCT
ejpam-3975	212	9	=	=	SYM
ejpam-3975	212	10	2	2	X
ejpam-3975	212	11	.	.	PUNCT
ejpam-3975	213	1	this	this	PRON
ejpam-3975	213	2	is	be	AUX
ejpam-3975	213	3	a	a	DET
ejpam-3975	213	4	contradiction	contradiction	NOUN
ejpam-3975	213	5	since	since	SCONJ
ejpam-3975	213	6	c	c	PROPN
ejpam-3975	213	7	is	be	AUX
ejpam-3975	213	8	a	a	DET
ejpam-3975	213	9	perfect	perfect	ADJ
ejpam-3975	213	10	hop	hop	NOUN
ejpam-3975	213	11	dominating	dominating	NOUN
ejpam-3975	213	12	set	set	NOUN
ejpam-3975	213	13	of	of	ADP
ejpam-3975	213	14	g	g	PROPN
ejpam-3975	213	15	◦	◦	NOUN
ejpam-3975	213	16	h	h	NOUN
ejpam-3975	213	17	and	and	CCONJ
ejpam-3975	213	18	dg	dg	NOUN
ejpam-3975	213	19	◦	◦	NOUN
ejpam-3975	213	20	h(x	h(x	PROPN
ejpam-3975	213	21	,	,	PUNCT
ejpam-3975	213	22	v	v	NOUN
ejpam-3975	213	23	)	)	PUNCT
ejpam-3975	213	24	=	=	SYM
ejpam-3975	213	25	2	2	NUM
ejpam-3975	213	26	=	=	SYM
ejpam-3975	213	27	dg	dg	NOUN
ejpam-3975	213	28	◦	◦	NOUN
ejpam-3975	213	29	h(x	h(x	PROPN
ejpam-3975	213	30	,	,	PUNCT
ejpam-3975	213	31	b	b	NOUN
ejpam-3975	213	32	)	)	PUNCT
ejpam-3975	213	33	where	where	SCONJ
ejpam-3975	213	34	v	v	NOUN
ejpam-3975	213	35	,	,	PUNCT
ejpam-3975	213	36	b	b	PROPN
ejpam-3975	213	37	∈	∈	PROPN
ejpam-3975	213	38	c.	c.	NOUN
ejpam-3975	213	39	hence	hence	ADV
ejpam-3975	213	40	,	,	PUNCT
ejpam-3975	213	41	v	v	PROPN
ejpam-3975	213	42	∈	∈	PROPN
ejpam-3975	213	43	a.	a.	NOUN
ejpam-3975	213	44	this	this	PRON
ejpam-3975	213	45	implies	imply	VERB
ejpam-3975	213	46	that	that	SCONJ
ejpam-3975	213	47	a	a	PRON
ejpam-3975	213	48	is	be	AUX
ejpam-3975	213	49	a	a	DET
ejpam-3975	213	50	perfect	perfect	ADJ
ejpam-3975	213	51	hop	hop	NOUN
ejpam-3975	213	52	dominating	dominating	NOUN
ejpam-3975	213	53	set	set	NOUN
ejpam-3975	213	54	of	of	ADP
ejpam-3975	213	55	g.	g.	PROPN
ejpam-3975	213	56	we	we	PRON
ejpam-3975	213	57	claim	claim	VERB
ejpam-3975	213	58	that	that	SCONJ
ejpam-3975	213	59	a	a	PRON
ejpam-3975	213	60	is	be	AUX
ejpam-3975	213	61	a	a	DET
ejpam-3975	213	62	perfect	perfect	ADJ
ejpam-3975	213	63	total	total	ADJ
ejpam-3975	213	64	dominating	dominating	NOUN
ejpam-3975	213	65	set	set	NOUN
ejpam-3975	213	66	of	of	ADP
ejpam-3975	213	67	g.	g.	PROPN
ejpam-3975	213	68	let	let	VERB
ejpam-3975	213	69	v	v	NUM
ejpam-3975	213	70	∈	∈	PROPN
ejpam-3975	213	71	v	v	NOUN
ejpam-3975	213	72	(	(	PUNCT
ejpam-3975	213	73	g	g	NOUN
ejpam-3975	213	74	)	)	PUNCT
ejpam-3975	213	75	and	and	CCONJ
ejpam-3975	213	76	a	a	DET
ejpam-3975	213	77	∈	∈	PROPN
ejpam-3975	213	78	v	v	ADP
ejpam-3975	213	79	(	(	PUNCT
ejpam-3975	213	80	hv	hv	X
ejpam-3975	213	81	)	)	PUNCT
ejpam-3975	213	82	such	such	ADJ
ejpam-3975	213	83	that	that	DET
ejpam-3975	213	84	deghv(a	deghv(a	NOUN
ejpam-3975	213	85	)	)	PUNCT
ejpam-3975	214	1	=	=	SYM
ejpam-3975	214	2	|v	|v	PROPN
ejpam-3975	214	3	(	(	PUNCT
ejpam-3975	214	4	h)|	h)|	NOUN
ejpam-3975	214	5	−	−	PROPN
ejpam-3975	214	6	1	1	NUM
ejpam-3975	214	7	.	.	PUNCT
ejpam-3975	215	1	since	since	SCONJ
ejpam-3975	215	2	s	s	PROPN
ejpam-3975	215	3	is	be	AUX
ejpam-3975	215	4	a	a	DET
ejpam-3975	215	5	total	total	ADJ
ejpam-3975	215	6	perfect	perfect	ADJ
ejpam-3975	215	7	hop	hop	NOUN
ejpam-3975	215	8	dominating	dominating	NOUN
ejpam-3975	215	9	set	set	NOUN
ejpam-3975	215	10	of	of	ADP
ejpam-3975	215	11	g	g	PROPN
ejpam-3975	215	12	◦	◦	NOUN
ejpam-3975	215	13	h	h	NOUN
ejpam-3975	215	14	,	,	PUNCT
ejpam-3975	215	15	a	a	DET
ejpam-3975	215	16	unique	unique	ADJ
ejpam-3975	215	17	vertex	vertex	NOUN
ejpam-3975	215	18	u	u	NOUN
ejpam-3975	215	19	∈	∈	PROPN
ejpam-3975	215	20	ng(v	ng(v	PUNCT
ejpam-3975	215	21	)	)	PUNCT
ejpam-3975	215	22	∩	∩	NOUN
ejpam-3975	215	23	s	s	PART
ejpam-3975	215	24	exists	exist	NOUN
ejpam-3975	215	25	.	.	PUNCT
ejpam-3975	216	1	thus	thus	ADV
ejpam-3975	216	2	,	,	PUNCT
ejpam-3975	216	3	u	u	PROPN
ejpam-3975	216	4	∈	∈	PROPN
ejpam-3975	216	5	a	a	DET
ejpam-3975	216	6	implying	implying	NOUN
ejpam-3975	216	7	that	that	SCONJ
ejpam-3975	216	8	a	a	PRON
ejpam-3975	216	9	is	be	AUX
ejpam-3975	216	10	a	a	DET
ejpam-3975	216	11	perfect	perfect	ADJ
ejpam-3975	216	12	total	total	ADJ
ejpam-3975	216	13	dominating	dominating	NOUN
ejpam-3975	216	14	set	set	NOUN
ejpam-3975	216	15	of	of	ADP
ejpam-3975	216	16	g.	g.	PROPN
ejpam-3975	216	17	hence	hence	ADV
ejpam-3975	216	18	,	,	PUNCT
ejpam-3975	216	19	(	(	PUNCT
ejpam-3975	216	20	i	i	NOUN
ejpam-3975	216	21	)	)	PUNCT
ejpam-3975	216	22	holds	hold	VERB
ejpam-3975	216	23	.	.	PUNCT
ejpam-3975	217	1	let	let	VERB
ejpam-3975	217	2	v	v	NUM
ejpam-3975	217	3	∈	∈	PROPN
ejpam-3975	217	4	v	v	NOUN
ejpam-3975	217	5	(	(	PUNCT
ejpam-3975	217	6	g)\a	g)\a	NOUN
ejpam-3975	217	7	.	.	PUNCT
ejpam-3975	218	1	by	by	ADP
ejpam-3975	218	2	(	(	PUNCT
ejpam-3975	218	3	i	i	NOUN
ejpam-3975	218	4	)	)	PUNCT
ejpam-3975	218	5	,	,	PUNCT
ejpam-3975	218	6	there	there	PRON
ejpam-3975	218	7	exists	exist	VERB
ejpam-3975	218	8	a	a	DET
ejpam-3975	218	9	unique	unique	ADJ
ejpam-3975	218	10	vertex	vertex	NOUN
ejpam-3975	218	11	w	w	NOUN
ejpam-3975	218	12	∈	∈	PROPN
ejpam-3975	218	13	ng(v	ng(v	NOUN
ejpam-3975	218	14	,	,	PUNCT
ejpam-3975	218	15	2	2	X
ejpam-3975	218	16	)	)	PUNCT
ejpam-3975	218	17	∩	∩	NOUN
ejpam-3975	218	18	a.	a.	NOUN
ejpam-3975	218	19	suppose	suppose	VERB
ejpam-3975	218	20	that	that	SCONJ
ejpam-3975	218	21	su	su	PROPN
ejpam-3975	218	22	6=	6=	PROPN
ejpam-3975	218	23	∅	∅	NOUN
ejpam-3975	218	24	for	for	ADP
ejpam-3975	218	25	some	some	DET
ejpam-3975	218	26	u	u	NOUN
ejpam-3975	218	27	∈	∈	PROPN
ejpam-3975	218	28	ng(v	ng(v	PUNCT
ejpam-3975	218	29	)	)	PUNCT
ejpam-3975	218	30	.	.	PUNCT
ejpam-3975	219	1	then	then	ADV
ejpam-3975	219	2	there	there	PRON
ejpam-3975	219	3	exists	exist	VERB
ejpam-3975	219	4	a	a	DET
ejpam-3975	219	5	∈	∈	PROPN
ejpam-3975	219	6	su	su	NOUN
ejpam-3975	219	7	and	and	CCONJ
ejpam-3975	219	8	a	a	DET
ejpam-3975	219	9	∈	∈	PROPN
ejpam-3975	219	10	ng	ng	PROPN
ejpam-3975	219	11	◦	◦	NOUN
ejpam-3975	219	12	h(v	h(v	PROPN
ejpam-3975	219	13	,	,	PUNCT
ejpam-3975	219	14	2)∩	2)∩	PROPN
ejpam-3975	219	15	s	s	PART
ejpam-3975	219	16	,	,	PUNCT
ejpam-3975	219	17	contrary	contrary	ADJ
ejpam-3975	219	18	to	to	ADP
ejpam-3975	219	19	our	our	PRON
ejpam-3975	219	20	assumption	assumption	NOUN
ejpam-3975	219	21	that	that	SCONJ
ejpam-3975	219	22	s	s	VERB
ejpam-3975	219	23	is	be	AUX
ejpam-3975	219	24	a	a	DET
ejpam-3975	219	25	total	total	ADJ
ejpam-3975	219	26	perfect	perfect	ADJ
ejpam-3975	219	27	hop	hop	NOUN
ejpam-3975	219	28	dominating	dominating	NOUN
ejpam-3975	219	29	set	set	NOUN
ejpam-3975	219	30	of	of	ADP
ejpam-3975	219	31	g	g	PROPN
ejpam-3975	219	32	◦	◦	NOUN
ejpam-3975	219	33	h.	h.	PROPN
ejpam-3975	219	34	thus	thus	ADV
ejpam-3975	219	35	,	,	PUNCT
ejpam-3975	219	36	su	su	NOUN
ejpam-3975	219	37	=	=	NOUN
ejpam-3975	219	38	∅	∅	NOUN
ejpam-3975	219	39	and	and	CCONJ
ejpam-3975	219	40	(	(	PUNCT
ejpam-3975	219	41	ii	ii	NOUN
ejpam-3975	219	42	)	)	PUNCT
ejpam-3975	219	43	holds	hold	VERB
ejpam-3975	219	44	.	.	PUNCT
ejpam-3975	220	1	for	for	ADP
ejpam-3975	220	2	(	(	PUNCT
ejpam-3975	220	3	iii	iii	NOUN
ejpam-3975	220	4	)	)	PUNCT
ejpam-3975	220	5	,	,	PUNCT
ejpam-3975	220	6	let	let	VERB
ejpam-3975	220	7	v	v	NUM
ejpam-3975	220	8	∈	∈	VERB
ejpam-3975	220	9	a.	a.	NOUN
ejpam-3975	220	10	if	if	SCONJ
ejpam-3975	220	11	a	a	DET
ejpam-3975	220	12	∈	∈	PROPN
ejpam-3975	220	13	ng(v	ng(v	PUNCT
ejpam-3975	220	14	,	,	PUNCT
ejpam-3975	220	15	2	2	X
ejpam-3975	220	16	)	)	PUNCT
ejpam-3975	220	17	∩	∩	NOUN
ejpam-3975	220	18	s	s	X
ejpam-3975	220	19	,	,	PUNCT
ejpam-3975	220	20	then	then	ADV
ejpam-3975	220	21	there	there	PRON
ejpam-3975	220	22	exists	exist	VERB
ejpam-3975	220	23	b	b	PROPN
ejpam-3975	220	24	∈	∈	PROPN
ejpam-3975	220	25	ng(v	ng(v	NOUN
ejpam-3975	220	26	)	)	PUNCT
ejpam-3975	220	27	∩	∩	NOUN
ejpam-3975	220	28	ng(a	ng(a	NOUN
ejpam-3975	220	29	)	)	PUNCT
ejpam-3975	220	30	.	.	PUNCT
ejpam-3975	221	1	this	this	PRON
ejpam-3975	221	2	implies	imply	VERB
ejpam-3975	221	3	that	that	SCONJ
ejpam-3975	221	4	for	for	ADP
ejpam-3975	221	5	all	all	PRON
ejpam-3975	221	6	x	x	SYM
ejpam-3975	221	7	∈	∈	NOUN
ejpam-3975	221	8	v	v	NOUN
ejpam-3975	221	9	(	(	PUNCT
ejpam-3975	221	10	hb	hb	PROPN
ejpam-3975	221	11	)	)	PUNCT
ejpam-3975	221	12	,	,	PUNCT
ejpam-3975	221	13	x	x	PUNCT
ejpam-3975	221	14	∈	∈	NOUN
ejpam-3975	221	15	ng(v	ng(v	NOUN
ejpam-3975	221	16	,	,	PUNCT
ejpam-3975	221	17	2	2	X
ejpam-3975	221	18	)	)	PUNCT
ejpam-3975	221	19	∩ng(a	∩ng(a	NOUN
ejpam-3975	221	20	,	,	PUNCT
ejpam-3975	221	21	2	2	NUM
ejpam-3975	221	22	)	)	PUNCT
ejpam-3975	221	23	,	,	PUNCT
ejpam-3975	221	24	a	a	DET
ejpam-3975	221	25	contradiction	contradiction	NOUN
ejpam-3975	221	26	to	to	ADP
ejpam-3975	221	27	our	our	PRON
ejpam-3975	221	28	assumption	assumption	NOUN
ejpam-3975	221	29	for	for	ADP
ejpam-3975	221	30	s.	s.	PROPN
ejpam-3975	221	31	thus	thus	ADV
ejpam-3975	221	32	,	,	PUNCT
ejpam-3975	221	33	ng(v	ng(v	NOUN
ejpam-3975	221	34	,	,	PUNCT
ejpam-3975	221	35	2	2	X
ejpam-3975	221	36	)	)	PUNCT
ejpam-3975	221	37	∩	∩	NOUN
ejpam-3975	221	38	s	s	PART
ejpam-3975	221	39	=	=	X
ejpam-3975	221	40	∅.	∅.	NOUN
ejpam-3975	221	41	since	since	SCONJ
ejpam-3975	221	42	s	s	PROPN
ejpam-3975	221	43	is	be	AUX
ejpam-3975	221	44	a	a	DET
ejpam-3975	221	45	total	total	ADJ
ejpam-3975	221	46	perfect	perfect	ADJ
ejpam-3975	221	47	hop	hop	NOUN
ejpam-3975	221	48	dominating	dominating	NOUN
ejpam-3975	221	49	set	set	NOUN
ejpam-3975	221	50	of	of	ADP
ejpam-3975	221	51	g	g	PROPN
ejpam-3975	221	52	◦	◦	NOUN
ejpam-3975	221	53	h	h	NOUN
ejpam-3975	221	54	,	,	PUNCT
ejpam-3975	221	55	there	there	PRON
ejpam-3975	221	56	exists	exist	VERB
ejpam-3975	221	57	a	a	DET
ejpam-3975	221	58	unique	unique	ADJ
ejpam-3975	221	59	vertex	vertex	NOUN
ejpam-3975	221	60	u	u	NOUN
ejpam-3975	221	61	∈	∈	PROPN
ejpam-3975	221	62	s	s	AUX
ejpam-3975	221	63	∩ng	∩ng	NOUN
ejpam-3975	221	64	◦	◦	NOUN
ejpam-3975	221	65	h(v	h(v	NOUN
ejpam-3975	221	66	,	,	PUNCT
ejpam-3975	221	67	2	2	NUM
ejpam-3975	221	68	)	)	PUNCT
ejpam-3975	221	69	.	.	PUNCT
ejpam-3975	222	1	since	since	SCONJ
ejpam-3975	222	2	ng(v	ng(v	NOUN
ejpam-3975	222	3	,	,	PUNCT
ejpam-3975	222	4	2	2	X
ejpam-3975	222	5	)	)	PUNCT
ejpam-3975	222	6	∩	∩	NOUN
ejpam-3975	222	7	s	s	PART
ejpam-3975	222	8	=	=	SYM
ejpam-3975	222	9	∅	∅	NOUN
ejpam-3975	222	10	,	,	PUNCT
ejpam-3975	222	11	u	u	PROPN
ejpam-3975	222	12	∈	∈	PROPN
ejpam-3975	222	13	v	v	NOUN
ejpam-3975	222	14	(	(	PUNCT
ejpam-3975	222	15	hw	hw	NOUN
ejpam-3975	222	16	)	)	PUNCT
ejpam-3975	222	17	∩	∩	NOUN
ejpam-3975	222	18	s	s	PART
ejpam-3975	222	19	=	=	SYM
ejpam-3975	222	20	sw	sw	PROPN
ejpam-3975	222	21	for	for	ADP
ejpam-3975	222	22	a	a	DET
ejpam-3975	222	23	unique	unique	ADJ
ejpam-3975	222	24	w	w	NOUN
ejpam-3975	222	25	∈	∈	PROPN
ejpam-3975	222	26	v	v	ADP
ejpam-3975	222	27	(	(	PUNCT
ejpam-3975	222	28	g	g	NOUN
ejpam-3975	222	29	)	)	PUNCT
ejpam-3975	222	30	∩ng(v	∩ng(v	PROPN
ejpam-3975	222	31	)	)	PUNCT
ejpam-3975	222	32	.	.	PUNCT
ejpam-3975	223	1	since	since	SCONJ
ejpam-3975	223	2	γ(h	γ(h	NOUN
ejpam-3975	223	3	)	)	PUNCT
ejpam-3975	223	4	=	=	SYM
ejpam-3975	223	5	1	1	NUM
ejpam-3975	223	6	,	,	PUNCT
ejpam-3975	223	7	sw	sw	PROPN
ejpam-3975	223	8	is	be	AUX
ejpam-3975	223	9	γ	γ	X
ejpam-3975	223	10	-	-	PUNCT
ejpam-3975	223	11	set	set	NOUN
ejpam-3975	223	12	of	of	ADP
ejpam-3975	223	13	h.	h.	NOUN
ejpam-3975	223	14	conversely	conversely	ADV
ejpam-3975	223	15	,	,	PUNCT
ejpam-3975	223	16	suppose	suppose	VERB
ejpam-3975	223	17	that	that	SCONJ
ejpam-3975	223	18	s	s	VERB
ejpam-3975	223	19	=	=	PUNCT
ejpam-3975	223	20	a	a	PRON
ejpam-3975	223	21	∪	∪	X
ejpam-3975	223	22	(	(	PUNCT
ejpam-3975	223	23	⋃	⋃	NOUN
ejpam-3975	223	24	v∈v	v∈v	NOUN
ejpam-3975	223	25	(	(	PUNCT
ejpam-3975	223	26	g)\a	g)\a	NOUN
ejpam-3975	223	27	sv	sv	NOUN
ejpam-3975	223	28	)	)	PUNCT
ejpam-3975	223	29	satisfying	satisfy	VERB
ejpam-3975	223	30	conditions	condition	NOUN
ejpam-3975	223	31	(	(	PUNCT
ejpam-3975	223	32	i),(ii	i),(ii	PROPN
ejpam-3975	223	33	)	)	PUNCT
ejpam-3975	223	34	and	and	CCONJ
ejpam-3975	223	35	(	(	PUNCT
ejpam-3975	223	36	iii	iii	NOUN
ejpam-3975	223	37	)	)	PUNCT
ejpam-3975	223	38	.	.	PUNCT
ejpam-3975	224	1	let	let	VERB
ejpam-3975	224	2	v	v	NUM
ejpam-3975	224	3	∈	∈	PROPN
ejpam-3975	224	4	v	v	NOUN
ejpam-3975	224	5	(	(	PUNCT
ejpam-3975	224	6	g	g	PROPN
ejpam-3975	224	7	◦	◦	NOUN
ejpam-3975	224	8	h	h	NOUN
ejpam-3975	224	9	)	)	PUNCT
ejpam-3975	224	10	.	.	PUNCT
ejpam-3975	225	1	suppose	suppose	VERB
ejpam-3975	225	2	that	that	SCONJ
ejpam-3975	225	3	v	v	NUM
ejpam-3975	225	4	∈	∈	PROPN
ejpam-3975	225	5	v	v	NOUN
ejpam-3975	225	6	(	(	PUNCT
ejpam-3975	225	7	g)\a	g)\a	NOUN
ejpam-3975	225	8	.	.	PUNCT
ejpam-3975	225	9	then	then	ADV
ejpam-3975	225	10	by	by	ADP
ejpam-3975	225	11	(	(	PUNCT
ejpam-3975	225	12	i	i	NOUN
ejpam-3975	225	13	)	)	PUNCT
ejpam-3975	225	14	and	and	CCONJ
ejpam-3975	225	15	(	(	PUNCT
ejpam-3975	225	16	ii	ii	NOUN
ejpam-3975	225	17	)	)	PUNCT
ejpam-3975	225	18	,	,	PUNCT
ejpam-3975	225	19	we	we	PRON
ejpam-3975	225	20	are	be	AUX
ejpam-3975	225	21	done	do	VERB
ejpam-3975	225	22	.	.	PUNCT
ejpam-3975	226	1	if	if	SCONJ
ejpam-3975	226	2	v	v	NUM
ejpam-3975	226	3	∈	∈	PROPN
ejpam-3975	226	4	a	a	PRON
ejpam-3975	226	5	,	,	PUNCT
ejpam-3975	226	6	then	then	ADV
ejpam-3975	226	7	by	by	ADP
ejpam-3975	226	8	(	(	PUNCT
ejpam-3975	226	9	iii	iii	X
ejpam-3975	226	10	)	)	PUNCT
ejpam-3975	226	11	there	there	PRON
ejpam-3975	226	12	exists	exist	VERB
ejpam-3975	226	13	a	a	DET
ejpam-3975	226	14	unique	unique	ADJ
ejpam-3975	226	15	w	w	NOUN
ejpam-3975	226	16	∈	∈	PROPN
ejpam-3975	226	17	ng(v)∩v	ng(v)∩v	PROPN
ejpam-3975	226	18	(	(	PUNCT
ejpam-3975	226	19	g	g	NOUN
ejpam-3975	226	20	)	)	PUNCT
ejpam-3975	226	21	such	such	ADJ
ejpam-3975	226	22	that	that	SCONJ
ejpam-3975	226	23	sw	sw	PROPN
ejpam-3975	226	24	is	be	AUX
ejpam-3975	226	25	a	a	DET
ejpam-3975	226	26	γ	γ	NOUN
ejpam-3975	226	27	-	-	PUNCT
ejpam-3975	226	28	set	set	NOUN
ejpam-3975	226	29	of	of	ADP
ejpam-3975	226	30	h.	h.	PROPN
ejpam-3975	226	31	hence	hence	ADV
ejpam-3975	226	32	,	,	PUNCT
ejpam-3975	226	33	there	there	PRON
ejpam-3975	226	34	exists	exist	VERB
ejpam-3975	226	35	a	a	DET
ejpam-3975	226	36	vertex	vertex	NOUN
ejpam-3975	226	37	a	a	DET
ejpam-3975	226	38	∈	∈	PROPN
ejpam-3975	226	39	sw	sw	PROPN
ejpam-3975	226	40	∩ng(v	∩ng(v	PROPN
ejpam-3975	226	41	,	,	PUNCT
ejpam-3975	226	42	2	2	NUM
ejpam-3975	226	43	)	)	PUNCT
ejpam-3975	226	44	.	.	PUNCT
ejpam-3975	227	1	suppose	suppose	VERB
ejpam-3975	227	2	v	v	ADP
ejpam-3975	227	3	∈	∈	PROPN
ejpam-3975	227	4	v	v	NOUN
ejpam-3975	227	5	(	(	PUNCT
ejpam-3975	227	6	hw	hw	NOUN
ejpam-3975	227	7	)	)	PUNCT
ejpam-3975	227	8	for	for	ADP
ejpam-3975	227	9	w	w	PROPN
ejpam-3975	227	10	∈	∈	PROPN
ejpam-3975	227	11	v	v	ADP
ejpam-3975	227	12	(	(	PUNCT
ejpam-3975	227	13	g	g	NOUN
ejpam-3975	227	14	)	)	PUNCT
ejpam-3975	227	15	.	.	PUNCT
ejpam-3975	228	1	by	by	ADP
ejpam-3975	228	2	(	(	PUNCT
ejpam-3975	228	3	i	i	NOUN
ejpam-3975	228	4	)	)	PUNCT
ejpam-3975	228	5	,	,	PUNCT
ejpam-3975	228	6	there	there	PRON
ejpam-3975	228	7	exists	exist	VERB
ejpam-3975	228	8	a	a	DET
ejpam-3975	228	9	unique	unique	ADJ
ejpam-3975	228	10	vertex	vertex	NOUN
ejpam-3975	228	11	u	u	NOUN
ejpam-3975	228	12	∈	∈	PROPN
ejpam-3975	228	13	ng(w	ng(w	NOUN
ejpam-3975	228	14	)	)	PUNCT
ejpam-3975	228	15	∩	∩	ADJ
ejpam-3975	228	16	a.	a.	NOUN
ejpam-3975	228	17	hence	hence	ADV
ejpam-3975	228	18	,	,	PUNCT
ejpam-3975	228	19	u	u	PROPN
ejpam-3975	228	20	∈	∈	PROPN
ejpam-3975	228	21	ng	ng	PROPN
ejpam-3975	228	22	◦	◦	NOUN
ejpam-3975	228	23	h(v	h(v	PROPN
ejpam-3975	228	24	,	,	PUNCT
ejpam-3975	228	25	2	2	NUM
ejpam-3975	228	26	)	)	PUNCT
ejpam-3975	228	27	.	.	PUNCT
ejpam-3975	229	1	therefore	therefore	ADV
ejpam-3975	229	2	s	s	VERB
ejpam-3975	229	3	is	be	AUX
ejpam-3975	229	4	a	a	DET
ejpam-3975	229	5	total	total	ADJ
ejpam-3975	229	6	perfect	perfect	ADJ
ejpam-3975	229	7	hop	hop	NOUN
ejpam-3975	229	8	dominating	dominating	NOUN
ejpam-3975	229	9	set	set	NOUN
ejpam-3975	229	10	of	of	ADP
ejpam-3975	229	11	g	g	PROPN
ejpam-3975	229	12	◦	◦	PROPN
ejpam-3975	229	13	h.	h.	PROPN
ejpam-3975	229	14	�	�	PROPN
ejpam-3975	229	15	corollary	corollary	PROPN
ejpam-3975	229	16	4.3	4.3	NUM
ejpam-3975	229	17	.	.	PUNCT
ejpam-3975	230	1	let	let	VERB
ejpam-3975	230	2	g	g	PRON
ejpam-3975	230	3	be	be	AUX
ejpam-3975	230	4	a	a	DET
ejpam-3975	230	5	connected	connected	ADJ
ejpam-3975	230	6	graph	graph	NOUN
ejpam-3975	230	7	of	of	ADP
ejpam-3975	230	8	order	order	NOUN
ejpam-3975	230	9	n	n	PRON
ejpam-3975	230	10	≥	≥	NOUN
ejpam-3975	230	11	4	4	NUM
ejpam-3975	230	12	whose	whose	DET
ejpam-3975	230	13	perfect	perfect	ADJ
ejpam-3975	230	14	total	total	NOUN
ejpam-3975	230	15	(	(	PUNCT
ejpam-3975	230	16	1	1	NUM
ejpam-3975	230	17	,	,	PUNCT
ejpam-3975	230	18	2)∗-dominating	2)∗-dominating	NUM
ejpam-3975	230	19	set	set	NOUN
ejpam-3975	230	20	exists	exist	VERB
ejpam-3975	230	21	and	and	CCONJ
ejpam-3975	230	22	h	h	DET
ejpam-3975	230	23	a	a	DET
ejpam-3975	230	24	graph	graph	NOUN
ejpam-3975	230	25	with	with	ADP
ejpam-3975	230	26	γ(h	γ(h	NOUN
ejpam-3975	230	27	)	)	PUNCT
ejpam-3975	230	28	=	=	SYM
ejpam-3975	231	1	1	1	X
ejpam-3975	231	2	.	.	PUNCT
ejpam-3975	231	3	then	then	ADV
ejpam-3975	231	4	γtph(g	γtph(g	ADP
ejpam-3975	231	5	◦	◦	NOUN
ejpam-3975	231	6	h	h	NOUN
ejpam-3975	231	7	)	)	PUNCT
ejpam-3975	231	8	≤	≤	NUM
ejpam-3975	231	9	γ∗pt1,2	γ∗pt1,2	PROPN
ejpam-3975	231	10	(	(	PUNCT
ejpam-3975	231	11	g)+n	g)+n	PROPN
ejpam-3975	231	12	.	.	PUNCT
ejpam-3975	232	1	r.	r.	PROPN
ejpam-3975	232	2	rakim	rakim	PROPN
ejpam-3975	232	3	,	,	PUNCT
ejpam-3975	232	4	h.	h.	PROPN
ejpam-3975	232	5	rara	rara	PROPN
ejpam-3975	232	6	/	/	SYM
ejpam-3975	232	7	eur	eur	PROPN
ejpam-3975	232	8	.	.	PUNCT
ejpam-3975	233	1	j.	j.	PROPN
ejpam-3975	233	2	pure	pure	PROPN
ejpam-3975	233	3	appl	appl	PROPN
ejpam-3975	233	4	.	.	PROPN
ejpam-3975	233	5	math	math	PROPN
ejpam-3975	233	6	,	,	PUNCT
ejpam-3975	233	7	14	14	NUM
ejpam-3975	233	8	(	(	PUNCT
ejpam-3975	233	9	3	3	NUM
ejpam-3975	233	10	)	)	PUNCT
ejpam-3975	233	11	(	(	PUNCT
ejpam-3975	233	12	2021	2021	NUM
ejpam-3975	233	13	)	)	PUNCT
ejpam-3975	233	14	,	,	PUNCT
ejpam-3975	233	15	803	803	NUM
ejpam-3975	233	16	-	-	SYM
ejpam-3975	233	17	815	815	NUM
ejpam-3975	233	18	811	811	NUM
ejpam-3975	233	19	proof	proof	NOUN
ejpam-3975	233	20	.	.	PUNCT
ejpam-3975	234	1	let	let	VERB
ejpam-3975	234	2	s	s	PRON
ejpam-3975	234	3	=	=	X
ejpam-3975	234	4	a∪	a∪	X
ejpam-3975	234	5	(	(	PUNCT
ejpam-3975	234	6	⋃	⋃	NOUN
ejpam-3975	234	7	v∈v	v∈v	NOUN
ejpam-3975	234	8	(	(	PUNCT
ejpam-3975	234	9	g	g	NOUN
ejpam-3975	234	10	)	)	PUNCT
ejpam-3975	234	11	sv	sv	NOUN
ejpam-3975	234	12	)	)	PUNCT
ejpam-3975	234	13	be	be	AUX
ejpam-3975	234	14	a	a	DET
ejpam-3975	234	15	minimum	minimum	ADJ
ejpam-3975	234	16	total	total	NOUN
ejpam-3975	234	17	perfect	perfect	ADJ
ejpam-3975	234	18	hop	hop	NOUN
ejpam-3975	234	19	dominating	dominating	NOUN
ejpam-3975	234	20	set	set	NOUN
ejpam-3975	234	21	of	of	ADP
ejpam-3975	234	22	g	g	PROPN
ejpam-3975	234	23	◦	◦	NOUN
ejpam-3975	234	24	h.	h.	NOUN
ejpam-3975	234	25	by	by	ADP
ejpam-3975	234	26	theorem	theorem	ADJ
ejpam-3975	234	27	4.2	4.2	NUM
ejpam-3975	234	28	,	,	PUNCT
ejpam-3975	234	29	a	a	PRON
ejpam-3975	234	30	is	be	AUX
ejpam-3975	234	31	a	a	DET
ejpam-3975	234	32	γ∗pt1,2	γ∗pt1,2	NOUN
ejpam-3975	234	33	-set	-set	PUNCT
ejpam-3975	234	34	of	of	ADP
ejpam-3975	234	35	g	g	PROPN
ejpam-3975	234	36	and	and	CCONJ
ejpam-3975	234	37	(	(	PUNCT
ejpam-3975	234	38	ii	ii	NOUN
ejpam-3975	234	39	)	)	PUNCT
ejpam-3975	234	40	and	and	CCONJ
ejpam-3975	234	41	(	(	PUNCT
ejpam-3975	234	42	iii	iii	NOUN
ejpam-3975	234	43	)	)	PUNCT
ejpam-3975	234	44	hold	hold	NOUN
ejpam-3975	234	45	.	.	PUNCT
ejpam-3975	235	1	then	then	ADV
ejpam-3975	235	2	γtph(g	γtph(g	ADP
ejpam-3975	235	3	◦	◦	NOUN
ejpam-3975	235	4	h	h	NOUN
ejpam-3975	235	5	)	)	PUNCT
ejpam-3975	235	6	=	=	SYM
ejpam-3975	235	7	|c|	|c|	PROPN
ejpam-3975	235	8	=	=	PUNCT
ejpam-3975	235	9	|a|+	|a|+	VERB
ejpam-3975	235	10	∑	∑	PUNCT
ejpam-3975	235	11	v∈v	v∈v	NOUN
ejpam-3975	235	12	(	(	PUNCT
ejpam-3975	235	13	g	g	NOUN
ejpam-3975	235	14	)	)	PUNCT
ejpam-3975	235	15	|sv|	|sv|	PROPN
ejpam-3975	235	16	≤	≤	NUM
ejpam-3975	235	17	|a|+	|a|+	NOUN
ejpam-3975	235	18	v	v	ADP
ejpam-3975	235	19	(	(	PUNCT
ejpam-3975	235	20	g	g	NOUN
ejpam-3975	235	21	)	)	PUNCT
ejpam-3975	235	22	=	=	SYM
ejpam-3975	235	23	γ∗pt1,2	γ∗pt1,2	PROPN
ejpam-3975	235	24	(	(	PUNCT
ejpam-3975	235	25	g	g	NOUN
ejpam-3975	235	26	)	)	PUNCT
ejpam-3975	236	1	+	+	CCONJ
ejpam-3975	236	2	n.	n.	PROPN
ejpam-3975	236	3	�	�	PROPN
ejpam-3975	236	4	the	the	DET
ejpam-3975	236	5	next	next	ADJ
ejpam-3975	236	6	result	result	NOUN
ejpam-3975	236	7	shows	show	VERB
ejpam-3975	236	8	that	that	SCONJ
ejpam-3975	236	9	the	the	DET
ejpam-3975	236	10	bound	bind	VERB
ejpam-3975	236	11	given	give	VERB
ejpam-3975	236	12	in	in	ADP
ejpam-3975	236	13	corollary	corollary	ADJ
ejpam-3975	236	14	4.3	4.3	NUM
ejpam-3975	236	15	is	be	AUX
ejpam-3975	236	16	sharp	sharp	ADJ
ejpam-3975	236	17	.	.	PUNCT
ejpam-3975	237	1	corollary	corollary	ADJ
ejpam-3975	237	2	4.4	4.4	NUM
ejpam-3975	237	3	.	.	PUNCT
ejpam-3975	238	1	let	let	VERB
ejpam-3975	238	2	h	h	PRON
ejpam-3975	238	3	be	be	AUX
ejpam-3975	238	4	a	a	DET
ejpam-3975	238	5	graph	graph	NOUN
ejpam-3975	238	6	with	with	ADP
ejpam-3975	238	7	γ(h	γ(h	NOUN
ejpam-3975	238	8	)	)	PUNCT
ejpam-3975	238	9	=	=	SYM
ejpam-3975	239	1	1	1	X
ejpam-3975	239	2	.	.	PUNCT
ejpam-3975	240	1	then	then	ADV
ejpam-3975	240	2	the	the	DET
ejpam-3975	240	3	total	total	ADJ
ejpam-3975	240	4	perfect	perfect	ADJ
ejpam-3975	240	5	hop	hop	NOUN
ejpam-3975	240	6	dominating	dominating	NOUN
ejpam-3975	240	7	set	set	NOUN
ejpam-3975	240	8	of	of	ADP
ejpam-3975	240	9	p2	p2	PROPN
ejpam-3975	240	10	◦	◦	NOUN
ejpam-3975	240	11	h	h	NOUN
ejpam-3975	240	12	exists	exist	VERB
ejpam-3975	240	13	and	and	CCONJ
ejpam-3975	240	14	γtph(p2	γtph(p2	ADP
ejpam-3975	240	15	◦	◦	NOUN
ejpam-3975	240	16	h	h	NOUN
ejpam-3975	240	17	)	)	PUNCT
ejpam-3975	240	18	=	=	SYM
ejpam-3975	241	1	4	4	X
ejpam-3975	241	2	.	.	X
ejpam-3975	242	1	proof	proof	NOUN
ejpam-3975	242	2	.	.	PUNCT
ejpam-3975	243	1	let	let	VERB
ejpam-3975	243	2	p2	p2	PROPN
ejpam-3975	243	3	=	=	PUNCT
ejpam-3975	244	1	[	[	X
ejpam-3975	244	2	x1	x1	PROPN
ejpam-3975	244	3	,	,	PUNCT
ejpam-3975	244	4	x2	x2	PROPN
ejpam-3975	244	5	]	]	PUNCT
ejpam-3975	244	6	.	.	PUNCT
ejpam-3975	245	1	by	by	ADP
ejpam-3975	245	2	theorem	theorem	NOUN
ejpam-3975	245	3	4.2	4.2	NUM
ejpam-3975	245	4	,	,	PUNCT
ejpam-3975	245	5	s	s	PART
ejpam-3975	245	6	=	=	PUNCT
ejpam-3975	245	7	{	{	PUNCT
ejpam-3975	245	8	x1	x1	PROPN
ejpam-3975	245	9	,	,	PUNCT
ejpam-3975	245	10	x2	x2	PROPN
ejpam-3975	245	11	,	,	PUNCT
ejpam-3975	245	12	a	a	PRON
ejpam-3975	245	13	,	,	PUNCT
ejpam-3975	245	14	b	b	NOUN
ejpam-3975	245	15	}	}	PUNCT
ejpam-3975	245	16	,	,	PUNCT
ejpam-3975	245	17	where	where	SCONJ
ejpam-3975	245	18	a	a	DET
ejpam-3975	245	19	∈	∈	PROPN
ejpam-3975	245	20	v	v	NOUN
ejpam-3975	245	21	(	(	PUNCT
ejpam-3975	245	22	hx1	hx1	PROPN
ejpam-3975	245	23	)	)	PUNCT
ejpam-3975	245	24	,	,	PUNCT
ejpam-3975	245	25	b	b	X
ejpam-3975	245	26	∈	∈	PROPN
ejpam-3975	245	27	v	v	NOUN
ejpam-3975	245	28	(	(	PUNCT
ejpam-3975	245	29	hx2	hx2	NOUN
ejpam-3975	245	30	)	)	PUNCT
ejpam-3975	245	31	and	and	CCONJ
ejpam-3975	245	32	degh(a	degh(a	NOUN
ejpam-3975	245	33	)	)	PUNCT
ejpam-3975	245	34	=	=	SYM
ejpam-3975	245	35	degh(b	degh(b	NOUN
ejpam-3975	245	36	)	)	PUNCT
ejpam-3975	245	37	=	=	SYM
ejpam-3975	245	38	|v	|v	PROPN
ejpam-3975	245	39	(	(	PUNCT
ejpam-3975	245	40	h)|	h)|	NOUN
ejpam-3975	245	41	−	−	PROPN
ejpam-3975	245	42	1	1	NUM
ejpam-3975	245	43	is	be	AUX
ejpam-3975	245	44	a	a	DET
ejpam-3975	245	45	total	total	ADJ
ejpam-3975	245	46	perfect	perfect	ADJ
ejpam-3975	245	47	hop	hop	NOUN
ejpam-3975	245	48	dominating	dominating	NOUN
ejpam-3975	245	49	set	set	NOUN
ejpam-3975	245	50	of	of	ADP
ejpam-3975	245	51	p2	p2	PROPN
ejpam-3975	245	52	◦	◦	PROPN
ejpam-3975	245	53	h.	h.	PROPN
ejpam-3975	245	54	thus	thus	ADV
ejpam-3975	245	55	,	,	PUNCT
ejpam-3975	245	56	by	by	ADP
ejpam-3975	245	57	remark	remark	NOUN
ejpam-3975	245	58	2.2	2.2	NUM
ejpam-3975	245	59	,	,	PUNCT
ejpam-3975	245	60	γtph(p2	γtph(p2	ADP
ejpam-3975	245	61	◦	◦	NOUN
ejpam-3975	245	62	h	h	NOUN
ejpam-3975	245	63	)	)	PUNCT
ejpam-3975	245	64	=	=	PUNCT
ejpam-3975	246	1	|s|	|s|	NOUN
ejpam-3975	246	2	=	=	SYM
ejpam-3975	246	3	4	4	PROPN
ejpam-3975	246	4	.	.	X
ejpam-3975	246	5	�	�	PROPN
ejpam-3975	246	6	remark	remark	VERB
ejpam-3975	246	7	4.5	4.5	NUM
ejpam-3975	246	8	.	.	PUNCT
ejpam-3975	247	1	the	the	DET
ejpam-3975	247	2	strict	strict	ADJ
ejpam-3975	247	3	inequality	inequality	NOUN
ejpam-3975	247	4	in	in	ADP
ejpam-3975	247	5	corollary	corollary	ADJ
ejpam-3975	247	6	4.3	4.3	NUM
ejpam-3975	247	7	can	can	AUX
ejpam-3975	247	8	be	be	AUX
ejpam-3975	247	9	attained	attain	VERB
ejpam-3975	247	10	.	.	PUNCT
ejpam-3975	248	1	to	to	PART
ejpam-3975	248	2	illustrate	illustrate	VERB
ejpam-3975	248	3	remark	remark	NOUN
ejpam-3975	248	4	4.5	4.5	NUM
ejpam-3975	248	5	,	,	PUNCT
ejpam-3975	248	6	consider	consider	VERB
ejpam-3975	248	7	the	the	DET
ejpam-3975	248	8	graph	graph	NOUN
ejpam-3975	248	9	p4	p4	ADJ
ejpam-3975	248	10	◦	◦	NOUN
ejpam-3975	248	11	p3	p3	PROPN
ejpam-3975	248	12	.	.	PUNCT
ejpam-3975	249	1	it	it	PRON
ejpam-3975	249	2	can	can	AUX
ejpam-3975	249	3	be	be	AUX
ejpam-3975	249	4	verified	verify	VERB
ejpam-3975	249	5	that	that	SCONJ
ejpam-3975	249	6	γtph(p4	γtph(p4	NOUN
ejpam-3975	249	7	◦	◦	PROPN
ejpam-3975	249	8	p3	p3	PROPN
ejpam-3975	249	9	)	)	PUNCT
ejpam-3975	249	10	=	=	SYM
ejpam-3975	250	1	4	4	X
ejpam-3975	250	2	.	.	PUNCT
ejpam-3975	250	3	however	however	ADV
ejpam-3975	250	4	,	,	PUNCT
ejpam-3975	250	5	γ∗pt1,2	γ∗pt1,2	PROPN
ejpam-3975	250	6	(	(	PUNCT
ejpam-3975	250	7	g	g	NOUN
ejpam-3975	250	8	)	)	PUNCT
ejpam-3975	250	9	+	+	CCONJ
ejpam-3975	250	10	|v	|v	X
ejpam-3975	250	11	(	(	PUNCT
ejpam-3975	250	12	g)|	g)|	NOUN
ejpam-3975	250	13	=	=	SYM
ejpam-3975	250	14	2	2	NUM
ejpam-3975	250	15	+	+	CCONJ
ejpam-3975	250	16	4	4	NUM
ejpam-3975	250	17	=	=	SYM
ejpam-3975	250	18	6	6	NUM
ejpam-3975	250	19	.	.	PUNCT
ejpam-3975	250	20	hence	hence	ADV
ejpam-3975	250	21	,	,	PUNCT
ejpam-3975	250	22	strict	strict	ADJ
ejpam-3975	250	23	inequality	inequality	NOUN
ejpam-3975	250	24	is	be	AUX
ejpam-3975	250	25	attained	attain	VERB
ejpam-3975	250	26	.	.	PUNCT
ejpam-3975	251	1	corollary	corollary	ADJ
ejpam-3975	251	2	4.6	4.6	NUM
ejpam-3975	251	3	.	.	PUNCT
ejpam-3975	252	1	let	let	VERB
ejpam-3975	252	2	g	g	PRON
ejpam-3975	252	3	be	be	AUX
ejpam-3975	252	4	a	a	DET
ejpam-3975	252	5	connected	connected	ADJ
ejpam-3975	252	6	graph	graph	NOUN
ejpam-3975	252	7	of	of	ADP
ejpam-3975	252	8	order	order	NOUN
ejpam-3975	252	9	3	3	NUM
ejpam-3975	252	10	and	and	CCONJ
ejpam-3975	252	11	h	h	NOUN
ejpam-3975	252	12	be	be	AUX
ejpam-3975	252	13	a	a	DET
ejpam-3975	252	14	graph	graph	NOUN
ejpam-3975	252	15	with	with	ADP
ejpam-3975	252	16	γ(h	γ(h	NOUN
ejpam-3975	252	17	)	)	PUNCT
ejpam-3975	252	18	=	=	SYM
ejpam-3975	253	1	1	1	X
ejpam-3975	253	2	.	.	PUNCT
ejpam-3975	254	1	then	then	ADV
ejpam-3975	254	2	the	the	DET
ejpam-3975	254	3	total	total	ADJ
ejpam-3975	254	4	perfect	perfect	ADJ
ejpam-3975	254	5	hop	hop	NOUN
ejpam-3975	254	6	dominating	dominating	NOUN
ejpam-3975	254	7	set	set	NOUN
ejpam-3975	254	8	of	of	ADP
ejpam-3975	254	9	g	g	PROPN
ejpam-3975	254	10	◦	◦	NOUN
ejpam-3975	254	11	h	h	NOUN
ejpam-3975	254	12	does	do	AUX
ejpam-3975	254	13	not	not	PART
ejpam-3975	254	14	exist	exist	VERB
ejpam-3975	254	15	.	.	PUNCT
ejpam-3975	255	1	proof	proof	NOUN
ejpam-3975	255	2	.	.	PUNCT
ejpam-3975	256	1	if	if	SCONJ
ejpam-3975	256	2	|v	|v	PROPN
ejpam-3975	256	3	(	(	PUNCT
ejpam-3975	256	4	g)|	g)|	NOUN
ejpam-3975	256	5	=	=	SYM
ejpam-3975	256	6	3	3	NUM
ejpam-3975	256	7	,	,	PUNCT
ejpam-3975	256	8	then	then	ADV
ejpam-3975	256	9	g	g	PROPN
ejpam-3975	256	10	∼=	∼=	PROPN
ejpam-3975	256	11	p3	p3	NOUN
ejpam-3975	256	12	or	or	CCONJ
ejpam-3975	256	13	g	g	NOUN
ejpam-3975	256	14	∼=	∼=	PROPN
ejpam-3975	256	15	k3	k3	VERB
ejpam-3975	256	16	.	.	PUNCT
ejpam-3975	257	1	hence	hence	ADV
ejpam-3975	257	2	,	,	PUNCT
ejpam-3975	257	3	theorem	theorem	VERB
ejpam-3975	257	4	4.2	4.2	NUM
ejpam-3975	257	5	is	be	AUX
ejpam-3975	257	6	not	not	PART
ejpam-3975	257	7	satisfied	satisfied	ADJ
ejpam-3975	257	8	.	.	PUNCT
ejpam-3975	258	1	therefore	therefore	ADV
ejpam-3975	258	2	,	,	PUNCT
ejpam-3975	258	3	the	the	DET
ejpam-3975	258	4	total	total	ADJ
ejpam-3975	258	5	perfect	perfect	ADJ
ejpam-3975	258	6	hop	hop	NOUN
ejpam-3975	258	7	dominating	dominating	NOUN
ejpam-3975	258	8	set	set	NOUN
ejpam-3975	258	9	of	of	ADP
ejpam-3975	258	10	g	g	PROPN
ejpam-3975	258	11	◦	◦	NOUN
ejpam-3975	258	12	h	h	NOUN
ejpam-3975	258	13	does	do	AUX
ejpam-3975	258	14	not	not	PART
ejpam-3975	258	15	exist	exist	VERB
ejpam-3975	258	16	.	.	PUNCT
ejpam-3975	259	1	�	�	PROPN
ejpam-3975	259	2	if	if	SCONJ
ejpam-3975	259	3	g	g	PROPN
ejpam-3975	259	4	is	be	AUX
ejpam-3975	259	5	a	a	DET
ejpam-3975	259	6	complete	complete	ADJ
ejpam-3975	259	7	graph	graph	NOUN
ejpam-3975	259	8	kn	kn	PROPN
ejpam-3975	259	9	,	,	PUNCT
ejpam-3975	259	10	then	then	ADV
ejpam-3975	259	11	g	g	PROPN
ejpam-3975	259	12	has	have	VERB
ejpam-3975	259	13	no	no	DET
ejpam-3975	259	14	total	total	ADJ
ejpam-3975	259	15	perfect	perfect	ADJ
ejpam-3975	259	16	hop	hop	NOUN
ejpam-3975	259	17	dominating	dominating	NOUN
ejpam-3975	259	18	set	set	NOUN
ejpam-3975	259	19	.	.	PUNCT
ejpam-3975	260	1	thus	thus	ADV
ejpam-3975	260	2	,	,	PUNCT
ejpam-3975	260	3	the	the	DET
ejpam-3975	260	4	next	next	ADJ
ejpam-3975	260	5	result	result	NOUN
ejpam-3975	260	6	follows	follow	VERB
ejpam-3975	260	7	immediately	immediately	ADV
ejpam-3975	260	8	from	from	ADP
ejpam-3975	260	9	theorem	theorem	ADJ
ejpam-3975	260	10	4.2	4.2	NUM
ejpam-3975	260	11	.	.	PUNCT
ejpam-3975	261	1	corollary	corollary	ADJ
ejpam-3975	261	2	4.7	4.7	NUM
ejpam-3975	261	3	.	.	PUNCT
ejpam-3975	262	1	let	let	VERB
ejpam-3975	262	2	n	n	PRON
ejpam-3975	262	3	≥	≥	X
ejpam-3975	262	4	3	3	NUM
ejpam-3975	262	5	and	and	CCONJ
ejpam-3975	262	6	h	h	DET
ejpam-3975	262	7	a	a	DET
ejpam-3975	262	8	graph	graph	NOUN
ejpam-3975	262	9	with	with	ADP
ejpam-3975	262	10	γ(h	γ(h	NOUN
ejpam-3975	262	11	)	)	PUNCT
ejpam-3975	262	12	=	=	SYM
ejpam-3975	263	1	1	1	X
ejpam-3975	263	2	.	.	PUNCT
ejpam-3975	264	1	then	then	ADV
ejpam-3975	264	2	the	the	DET
ejpam-3975	264	3	total	total	ADJ
ejpam-3975	264	4	perfect	perfect	ADJ
ejpam-3975	264	5	hop	hop	NOUN
ejpam-3975	264	6	dominating	dominating	NOUN
ejpam-3975	264	7	set	set	NOUN
ejpam-3975	264	8	of	of	ADP
ejpam-3975	264	9	kn	kn	PROPN
ejpam-3975	264	10	◦	◦	PROPN
ejpam-3975	264	11	h	h	NOUN
ejpam-3975	264	12	does	do	AUX
ejpam-3975	264	13	not	not	PART
ejpam-3975	264	14	exist	exist	VERB
ejpam-3975	264	15	.	.	PUNCT
ejpam-3975	265	1	corollary	corollary	ADJ
ejpam-3975	265	2	4.8	4.8	NUM
ejpam-3975	265	3	.	.	PUNCT
ejpam-3975	266	1	let	let	VERB
ejpam-3975	266	2	h	h	PRON
ejpam-3975	266	3	be	be	AUX
ejpam-3975	266	4	a	a	DET
ejpam-3975	266	5	connected	connected	ADJ
ejpam-3975	266	6	graph	graph	NOUN
ejpam-3975	266	7	with	with	ADP
ejpam-3975	266	8	γ(h	γ(h	NOUN
ejpam-3975	266	9	)	)	PUNCT
ejpam-3975	266	10	=	=	SYM
ejpam-3975	267	1	1	1	X
ejpam-3975	267	2	.	.	PUNCT
ejpam-3975	268	1	then	then	ADV
ejpam-3975	268	2	the	the	DET
ejpam-3975	268	3	total	total	ADJ
ejpam-3975	268	4	perfect	perfect	ADJ
ejpam-3975	268	5	hop	hop	NOUN
ejpam-3975	268	6	dominating	dominating	NOUN
ejpam-3975	268	7	set	set	NOUN
ejpam-3975	268	8	of	of	ADP
ejpam-3975	268	9	cn	cn	PROPN
ejpam-3975	268	10	◦	◦	PROPN
ejpam-3975	268	11	h	h	NOUN
ejpam-3975	268	12	for	for	ADP
ejpam-3975	268	13	n	n	X
ejpam-3975	268	14	≥	≥	NOUN
ejpam-3975	268	15	3	3	NUM
ejpam-3975	268	16	does	do	AUX
ejpam-3975	268	17	not	not	PART
ejpam-3975	268	18	exist	exist	VERB
ejpam-3975	268	19	.	.	PUNCT
ejpam-3975	269	1	proof	proof	NOUN
ejpam-3975	269	2	.	.	PUNCT
ejpam-3975	270	1	note	note	VERB
ejpam-3975	270	2	that	that	SCONJ
ejpam-3975	270	3	if	if	SCONJ
ejpam-3975	270	4	n	n	ADV
ejpam-3975	270	5	6≡	6≡	NUM
ejpam-3975	270	6	0	0	X
ejpam-3975	270	7	(	(	PUNCT
ejpam-3975	270	8	mod	mod	PROPN
ejpam-3975	270	9	4	4	NUM
ejpam-3975	270	10	)	)	PUNCT
ejpam-3975	270	11	,	,	PUNCT
ejpam-3975	270	12	then	then	ADV
ejpam-3975	270	13	cn	cn	PROPN
ejpam-3975	270	14	does	do	AUX
ejpam-3975	270	15	not	not	PART
ejpam-3975	270	16	have	have	VERB
ejpam-3975	270	17	a	a	DET
ejpam-3975	270	18	total	total	ADJ
ejpam-3975	270	19	perfect	perfect	ADJ
ejpam-3975	270	20	hop	hop	NOUN
ejpam-3975	270	21	dominating	dominating	NOUN
ejpam-3975	270	22	set	set	NOUN
ejpam-3975	270	23	.	.	PUNCT
ejpam-3975	271	1	if	if	SCONJ
ejpam-3975	271	2	cn	cn	PROPN
ejpam-3975	271	3	has	have	VERB
ejpam-3975	271	4	a	a	DET
ejpam-3975	271	5	total	total	ADJ
ejpam-3975	271	6	perfect	perfect	ADJ
ejpam-3975	271	7	hop	hop	NOUN
ejpam-3975	271	8	dominating	dominating	NOUN
ejpam-3975	271	9	set	set	NOUN
ejpam-3975	271	10	a	a	PRON
ejpam-3975	271	11	,	,	PUNCT
ejpam-3975	271	12	then	then	ADV
ejpam-3975	271	13	every	every	DET
ejpam-3975	271	14	vertex	vertex	NOUN
ejpam-3975	271	15	outside	outside	ADP
ejpam-3975	271	16	a	a	DET
ejpam-3975	271	17	hops	hop	NOUN
ejpam-3975	271	18	in	in	ADP
ejpam-3975	271	19	a	a	PRON
ejpam-3975	271	20	and	and	CCONJ
ejpam-3975	271	21	so	so	ADV
ejpam-3975	271	22	none	none	NOUN
ejpam-3975	271	23	of	of	ADP
ejpam-3975	271	24	the	the	DET
ejpam-3975	271	25	element	element	NOUN
ejpam-3975	271	26	in	in	ADP
ejpam-3975	271	27	a	a	DET
ejpam-3975	271	28	hops	hop	NOUN
ejpam-3975	271	29	in	in	ADP
ejpam-3975	271	30	a.	a.	NOUN
ejpam-3975	271	31	thus	thus	ADV
ejpam-3975	271	32	,	,	PUNCT
ejpam-3975	271	33	(	(	PUNCT
ejpam-3975	271	34	iii	iii	NOUN
ejpam-3975	271	35	)	)	PUNCT
ejpam-3975	271	36	in	in	ADP
ejpam-3975	271	37	theorem	theorem	ADJ
ejpam-3975	271	38	4.2	4.2	NUM
ejpam-3975	271	39	is	be	AUX
ejpam-3975	271	40	never	never	ADV
ejpam-3975	271	41	satisfied	satisfied	ADJ
ejpam-3975	271	42	.	.	PUNCT
ejpam-3975	272	1	�	�	PROPN
ejpam-3975	272	2	corollary	corollary	NOUN
ejpam-3975	272	3	4.9	4.9	NUM
ejpam-3975	272	4	.	.	PUNCT
ejpam-3975	273	1	let	let	VERB
ejpam-3975	273	2	g	g	PRON
ejpam-3975	273	3	be	be	AUX
ejpam-3975	273	4	a	a	DET
ejpam-3975	273	5	connected	connected	ADJ
ejpam-3975	273	6	graph	graph	NOUN
ejpam-3975	273	7	of	of	ADP
ejpam-3975	273	8	order	order	NOUN
ejpam-3975	273	9	4	4	NUM
ejpam-3975	273	10	and	and	CCONJ
ejpam-3975	273	11	h	h	NOUN
ejpam-3975	273	12	be	be	VERB
ejpam-3975	273	13	any	any	DET
ejpam-3975	273	14	graph	graph	NOUN
ejpam-3975	273	15	with	with	ADP
ejpam-3975	273	16	γ(h	γ(h	NOUN
ejpam-3975	273	17	)	)	PUNCT
ejpam-3975	273	18	=	=	SYM
ejpam-3975	274	1	1	1	X
ejpam-3975	274	2	.	.	PUNCT
ejpam-3975	275	1	then	then	ADV
ejpam-3975	275	2	the	the	DET
ejpam-3975	275	3	total	total	ADJ
ejpam-3975	275	4	perfect	perfect	ADJ
ejpam-3975	275	5	hop	hop	NOUN
ejpam-3975	275	6	dominating	dominating	NOUN
ejpam-3975	275	7	set	set	NOUN
ejpam-3975	275	8	of	of	ADP
ejpam-3975	275	9	g	g	PROPN
ejpam-3975	275	10	◦	◦	NOUN
ejpam-3975	275	11	h	h	NOUN
ejpam-3975	275	12	exists	exist	VERB
ejpam-3975	275	13	if	if	SCONJ
ejpam-3975	275	14	and	and	CCONJ
ejpam-3975	275	15	only	only	ADV
ejpam-3975	275	16	if	if	SCONJ
ejpam-3975	275	17	g	g	PROPN
ejpam-3975	275	18	∼=	∼=	PROPN
ejpam-3975	275	19	p4	p4	ADJ
ejpam-3975	275	20	.	.	PUNCT
ejpam-3975	276	1	proof	proof	NOUN
ejpam-3975	276	2	.	.	PUNCT
ejpam-3975	277	1	if	if	SCONJ
ejpam-3975	277	2	g	g	PROPN
ejpam-3975	277	3	∼=	∼=	VERB
ejpam-3975	277	4	p4	p4	ADJ
ejpam-3975	277	5	=	=	PUNCT
ejpam-3975	278	1	[	[	X
ejpam-3975	278	2	x1	x1	PROPN
ejpam-3975	278	3	,	,	PUNCT
ejpam-3975	278	4	x2	x2	PROPN
ejpam-3975	278	5	,	,	PUNCT
ejpam-3975	278	6	x3	x3	PROPN
ejpam-3975	278	7	,	,	PUNCT
ejpam-3975	278	8	x4	x4	PROPN
ejpam-3975	278	9	]	]	PUNCT
ejpam-3975	278	10	,	,	PUNCT
ejpam-3975	278	11	then	then	ADV
ejpam-3975	278	12	s	s	VERB
ejpam-3975	278	13	=	=	SYM
ejpam-3975	278	14	{	{	PUNCT
ejpam-3975	278	15	x2	x2	PROPN
ejpam-3975	278	16	,	,	PUNCT
ejpam-3975	278	17	x3	x3	PROPN
ejpam-3975	278	18	,	,	PUNCT
ejpam-3975	278	19	a	a	DET
ejpam-3975	278	20	,	,	PUNCT
ejpam-3975	278	21	b	b	NOUN
ejpam-3975	278	22	}	}	PUNCT
ejpam-3975	278	23	where	where	SCONJ
ejpam-3975	278	24	a	a	DET
ejpam-3975	278	25	∈	∈	PROPN
ejpam-3975	278	26	v	v	NOUN
ejpam-3975	278	27	(	(	PUNCT
ejpam-3975	278	28	hx1	hx1	PROPN
ejpam-3975	278	29	)	)	PUNCT
ejpam-3975	278	30	,	,	PUNCT
ejpam-3975	278	31	b	b	X
ejpam-3975	278	32	∈	∈	PROPN
ejpam-3975	278	33	v	v	NOUN
ejpam-3975	278	34	(	(	PUNCT
ejpam-3975	278	35	hx4	hx4	NOUN
ejpam-3975	278	36	)	)	PUNCT
ejpam-3975	278	37	and	and	CCONJ
ejpam-3975	278	38	degh(a	degh(a	NOUN
ejpam-3975	278	39	)	)	PUNCT
ejpam-3975	278	40	=	=	SYM
ejpam-3975	278	41	degh(b	degh(b	NOUN
ejpam-3975	278	42	)	)	PUNCT
ejpam-3975	278	43	=	=	SYM
ejpam-3975	279	1	|v	|v	PROPN
ejpam-3975	279	2	(	(	PUNCT
ejpam-3975	279	3	h)|	h)|	NOUN
ejpam-3975	279	4	−	−	PROPN
ejpam-3975	279	5	1	1	NUM
ejpam-3975	279	6	is	be	AUX
ejpam-3975	279	7	a	a	DET
ejpam-3975	279	8	total	total	ADJ
ejpam-3975	279	9	perfect	perfect	ADJ
ejpam-3975	279	10	hop	hop	NOUN
ejpam-3975	279	11	dominating	dominating	NOUN
ejpam-3975	279	12	set	set	NOUN
ejpam-3975	279	13	of	of	ADP
ejpam-3975	279	14	g	g	PROPN
ejpam-3975	279	15	◦	◦	PROPN
ejpam-3975	279	16	h.	h.	NOUN
ejpam-3975	279	17	if	if	SCONJ
ejpam-3975	279	18	g	g	PROPN
ejpam-3975	279	19	∼=	∼=	PROPN
ejpam-3975	279	20	c4	c4	NOUN
ejpam-3975	279	21	or	or	CCONJ
ejpam-3975	279	22	g	g	NOUN
ejpam-3975	279	23	∼=	∼=	PROPN
ejpam-3975	279	24	k4	k4	NOUN
ejpam-3975	279	25	,	,	PUNCT
ejpam-3975	279	26	then	then	ADV
ejpam-3975	279	27	by	by	ADP
ejpam-3975	279	28	corollary	corollary	ADJ
ejpam-3975	279	29	4.8	4.8	NUM
ejpam-3975	279	30	or	or	CCONJ
ejpam-3975	279	31	corollary	corollary	ADJ
ejpam-3975	279	32	4.7	4.7	NUM
ejpam-3975	279	33	,	,	PUNCT
ejpam-3975	279	34	respectively	respectively	ADV
ejpam-3975	279	35	,	,	PUNCT
ejpam-3975	279	36	the	the	DET
ejpam-3975	279	37	total	total	ADJ
ejpam-3975	279	38	perfect	perfect	ADJ
ejpam-3975	279	39	hop	hop	NOUN
ejpam-3975	279	40	dominating	dominating	NOUN
ejpam-3975	279	41	set	set	NOUN
ejpam-3975	279	42	of	of	ADP
ejpam-3975	279	43	g	g	PROPN
ejpam-3975	279	44	◦	◦	NOUN
ejpam-3975	279	45	h	h	NOUN
ejpam-3975	279	46	does	do	AUX
ejpam-3975	279	47	not	not	PART
ejpam-3975	279	48	exist	exist	VERB
ejpam-3975	279	49	.	.	PUNCT
ejpam-3975	280	1	suppose	suppose	VERB
ejpam-3975	280	2	g	g	PROPN
ejpam-3975	280	3	/∈	/∈	PUNCT
ejpam-3975	280	4	{	{	PUNCT
ejpam-3975	280	5	p4	p4	ADJ
ejpam-3975	280	6	,	,	PUNCT
ejpam-3975	280	7	c4,k4	c4,k4	PROPN
ejpam-3975	280	8	}	}	PUNCT
ejpam-3975	280	9	.	.	PUNCT
ejpam-3975	281	1	then	then	ADV
ejpam-3975	281	2	g	g	PROPN
ejpam-3975	281	3	is	be	AUX
ejpam-3975	281	4	isomorphic	isomorphic	ADJ
ejpam-3975	281	5	to	to	ADP
ejpam-3975	281	6	one	one	NUM
ejpam-3975	281	7	of	of	ADP
ejpam-3975	281	8	the	the	DET
ejpam-3975	281	9	graphs	graph	NOUN
ejpam-3975	281	10	shown	show	VERB
ejpam-3975	281	11	in	in	ADP
ejpam-3975	281	12	figure	figure	NOUN
ejpam-3975	281	13	below	below	ADV
ejpam-3975	281	14	.	.	PUNCT
ejpam-3975	282	1	by	by	ADP
ejpam-3975	282	2	theorem	theorem	NOUN
ejpam-3975	282	3	4.2	4.2	NUM
ejpam-3975	282	4	below	below	ADV
ejpam-3975	282	5	,	,	PUNCT
ejpam-3975	282	6	it	it	PRON
ejpam-3975	282	7	can	can	AUX
ejpam-3975	282	8	be	be	AUX
ejpam-3975	282	9	verified	verify	VERB
ejpam-3975	282	10	that	that	SCONJ
ejpam-3975	282	11	the	the	DET
ejpam-3975	282	12	total	total	ADJ
ejpam-3975	282	13	perfect	perfect	ADJ
ejpam-3975	282	14	hop	hop	NOUN
ejpam-3975	282	15	dominating	dominating	NOUN
ejpam-3975	282	16	set	set	NOUN
ejpam-3975	282	17	of	of	ADP
ejpam-3975	282	18	g	g	PROPN
ejpam-3975	282	19	◦	◦	NOUN
ejpam-3975	282	20	h	h	NOUN
ejpam-3975	282	21	where	where	SCONJ
ejpam-3975	282	22	g	g	PROPN
ejpam-3975	282	23	is	be	AUX
ejpam-3975	282	24	one	one	NUM
ejpam-3975	282	25	of	of	ADP
ejpam-3975	282	26	the	the	DET
ejpam-3975	282	27	graphs	graph	NOUN
ejpam-3975	282	28	shown	show	VERB
ejpam-3975	282	29	below	below	ADP
ejpam-3975	282	30	does	do	AUX
ejpam-3975	282	31	not	not	PART
ejpam-3975	282	32	exist	exist	VERB
ejpam-3975	282	33	.	.	PUNCT
ejpam-3975	283	1	r.	r.	PROPN
ejpam-3975	283	2	rakim	rakim	PROPN
ejpam-3975	283	3	,	,	PUNCT
ejpam-3975	283	4	h.	h.	PROPN
ejpam-3975	283	5	rara	rara	PROPN
ejpam-3975	283	6	/	/	SYM
ejpam-3975	283	7	eur	eur	PROPN
ejpam-3975	283	8	.	.	PUNCT
ejpam-3975	284	1	j.	j.	PROPN
ejpam-3975	284	2	pure	pure	PROPN
ejpam-3975	284	3	appl	appl	PROPN
ejpam-3975	284	4	.	.	PROPN
ejpam-3975	284	5	math	math	PROPN
ejpam-3975	284	6	,	,	PUNCT
ejpam-3975	284	7	14	14	NUM
ejpam-3975	284	8	(	(	PUNCT
ejpam-3975	284	9	3	3	NUM
ejpam-3975	284	10	)	)	PUNCT
ejpam-3975	284	11	(	(	PUNCT
ejpam-3975	284	12	2021	2021	NUM
ejpam-3975	284	13	)	)	PUNCT
ejpam-3975	284	14	,	,	PUNCT
ejpam-3975	284	15	803	803	NUM
ejpam-3975	284	16	-	-	SYM
ejpam-3975	284	17	815	815	NUM
ejpam-3975	284	18	812	812	NUM
ejpam-3975	284	19	therefore	therefore	ADV
ejpam-3975	284	20	the	the	DET
ejpam-3975	284	21	corollary	corollary	NOUN
ejpam-3975	284	22	follows	follow	VERB
ejpam-3975	284	23	.	.	PUNCT
ejpam-3975	285	1	�	�	PROPN
ejpam-3975	285	2	theorem	theorem	VERB
ejpam-3975	285	3	4.10	4.10	NUM
ejpam-3975	285	4	.	.	PUNCT
ejpam-3975	286	1	let	let	VERB
ejpam-3975	286	2	h	h	PRON
ejpam-3975	286	3	be	be	AUX
ejpam-3975	286	4	a	a	DET
ejpam-3975	286	5	graph	graph	NOUN
ejpam-3975	286	6	with	with	ADP
ejpam-3975	286	7	γ(h	γ(h	NOUN
ejpam-3975	286	8	)	)	PUNCT
ejpam-3975	286	9	=	=	SYM
ejpam-3975	287	1	1	1	X
ejpam-3975	287	2	.	.	PUNCT
ejpam-3975	288	1	then	then	ADV
ejpam-3975	288	2	the	the	DET
ejpam-3975	288	3	total	total	ADJ
ejpam-3975	288	4	perfect	perfect	ADJ
ejpam-3975	288	5	hop	hop	NOUN
ejpam-3975	288	6	dominating	dominating	NOUN
ejpam-3975	288	7	set	set	NOUN
ejpam-3975	288	8	of	of	ADP
ejpam-3975	288	9	pn	pn	PROPN
ejpam-3975	288	10	◦	◦	NOUN
ejpam-3975	288	11	h	h	NOUN
ejpam-3975	288	12	exists	exist	VERB
ejpam-3975	288	13	if	if	SCONJ
ejpam-3975	288	14	and	and	CCONJ
ejpam-3975	288	15	only	only	ADV
ejpam-3975	288	16	if	if	SCONJ
ejpam-3975	288	17	n	n	PROPN
ejpam-3975	288	18	=	=	SYM
ejpam-3975	288	19	2	2	NUM
ejpam-3975	288	20	and	and	CCONJ
ejpam-3975	288	21	n	n	NOUN
ejpam-3975	288	22	=	=	NOUN
ejpam-3975	288	23	4	4	NUM
ejpam-3975	288	24	.	.	PUNCT
ejpam-3975	289	1	moreover	moreover	ADV
ejpam-3975	289	2	,	,	PUNCT
ejpam-3975	289	3	γtph(pn	γtph(pn	ADJ
ejpam-3975	289	4	◦	◦	NOUN
ejpam-3975	289	5	h	h	NOUN
ejpam-3975	289	6	)	)	PUNCT
ejpam-3975	289	7	=	=	SYM
ejpam-3975	290	1	4	4	X
ejpam-3975	290	2	.	.	PUNCT
ejpam-3975	290	3	proof	proof	NOUN
ejpam-3975	290	4	.	.	PUNCT
ejpam-3975	291	1	by	by	ADP
ejpam-3975	291	2	corollary	corollary	ADJ
ejpam-3975	291	3	4.4	4.4	NUM
ejpam-3975	291	4	and	and	CCONJ
ejpam-3975	291	5	corollary	corollary	ADJ
ejpam-3975	291	6	4.9	4.9	NUM
ejpam-3975	291	7	,	,	PUNCT
ejpam-3975	291	8	p2	p2	PROPN
ejpam-3975	291	9	◦	◦	NOUN
ejpam-3975	291	10	h	h	NOUN
ejpam-3975	291	11	and	and	CCONJ
ejpam-3975	291	12	p4	p4	ADJ
ejpam-3975	291	13	◦	◦	NOUN
ejpam-3975	291	14	h	h	NOUN
ejpam-3975	291	15	both	both	PRON
ejpam-3975	291	16	have	have	VERB
ejpam-3975	291	17	total	total	ADJ
ejpam-3975	291	18	perfect	perfect	ADJ
ejpam-3975	291	19	hop	hop	NOUN
ejpam-3975	291	20	dominating	dominating	NOUN
ejpam-3975	291	21	set	set	NOUN
ejpam-3975	291	22	.	.	PUNCT
ejpam-3975	292	1	let	let	VERB
ejpam-3975	292	2	pn	pn	NOUN
ejpam-3975	292	3	=	=	PUNCT
ejpam-3975	293	1	[	[	X
ejpam-3975	293	2	x1	x1	PROPN
ejpam-3975	293	3	,	,	PUNCT
ejpam-3975	293	4	x2	x2	PROPN
ejpam-3975	293	5	,	,	PUNCT
ejpam-3975	293	6	...	...	PUNCT
ejpam-3975	293	7	,	,	PUNCT
ejpam-3975	293	8	xn	xn	PROPN
ejpam-3975	293	9	]	]	PUNCT
ejpam-3975	293	10	.	.	PUNCT
ejpam-3975	294	1	suppose	suppose	VERB
ejpam-3975	294	2	n	n	PROPN
ejpam-3975	294	3	6=	6=	ADP
ejpam-3975	294	4	2	2	NUM
ejpam-3975	294	5	and	and	CCONJ
ejpam-3975	294	6	n	n	NOUN
ejpam-3975	294	7	6=	6=	NUM
ejpam-3975	294	8	4	4	NUM
ejpam-3975	294	9	.	.	PUNCT
ejpam-3975	294	10	by	by	ADP
ejpam-3975	294	11	corollary	corollary	ADJ
ejpam-3975	294	12	4.6	4.6	NUM
ejpam-3975	294	13	,	,	PUNCT
ejpam-3975	294	14	p3	p3	PROPN
ejpam-3975	294	15	◦	◦	NOUN
ejpam-3975	294	16	h	h	NOUN
ejpam-3975	294	17	does	do	AUX
ejpam-3975	294	18	not	not	PART
ejpam-3975	294	19	exist	exist	VERB
ejpam-3975	294	20	.	.	PUNCT
ejpam-3975	295	1	let	let	VERB
ejpam-3975	295	2	n	n	PRON
ejpam-3975	295	3	>	>	X
ejpam-3975	295	4	4	4	NUM
ejpam-3975	295	5	and	and	CCONJ
ejpam-3975	295	6	assume	assume	VERB
ejpam-3975	295	7	that	that	SCONJ
ejpam-3975	295	8	pn	pn	PROPN
ejpam-3975	295	9	◦	◦	NOUN
ejpam-3975	295	10	h	h	NOUN
ejpam-3975	295	11	has	have	VERB
ejpam-3975	295	12	a	a	DET
ejpam-3975	295	13	total	total	ADJ
ejpam-3975	295	14	perfect	perfect	ADJ
ejpam-3975	295	15	hop	hop	NOUN
ejpam-3975	295	16	dominating	dominating	NOUN
ejpam-3975	295	17	set	set	NOUN
ejpam-3975	295	18	s.	s.	PROPN
ejpam-3975	295	19	by	by	ADP
ejpam-3975	295	20	theorem	theorem	NOUN
ejpam-3975	295	21	4.2(i	4.2(i	NUM
ejpam-3975	295	22	)	)	PUNCT
ejpam-3975	295	23	,	,	PUNCT
ejpam-3975	296	1	x2	x2	PROPN
ejpam-3975	296	2	∈	∈	PROPN
ejpam-3975	296	3	s	s	PART
ejpam-3975	296	4	and	and	CCONJ
ejpam-3975	296	5	x1	x1	PROPN
ejpam-3975	296	6	∈	∈	PROPN
ejpam-3975	296	7	s	s	PART
ejpam-3975	296	8	or	or	CCONJ
ejpam-3975	296	9	x3	x3	PROPN
ejpam-3975	296	10	∈	∈	PROPN
ejpam-3975	296	11	s	s	PART
ejpam-3975	296	12	but	but	CCONJ
ejpam-3975	296	13	not	not	PART
ejpam-3975	296	14	both	both	PRON
ejpam-3975	296	15	.	.	PUNCT
ejpam-3975	297	1	suppose	suppose	VERB
ejpam-3975	297	2	x1	x1	PROPN
ejpam-3975	297	3	∈	∈	PROPN
ejpam-3975	297	4	s.	s.	PROPN
ejpam-3975	297	5	since	since	SCONJ
ejpam-3975	297	6	x3	x3	PROPN
ejpam-3975	297	7	/∈	/∈	PUNCT
ejpam-3975	298	1	s	s	X
ejpam-3975	298	2	,	,	PUNCT
ejpam-3975	298	3	by	by	ADP
ejpam-3975	298	4	theorem	theorem	NOUN
ejpam-3975	298	5	4.2(iii	4.2(iii	NUM
ejpam-3975	298	6	)	)	PUNCT
ejpam-3975	298	7	,	,	PUNCT
ejpam-3975	298	8	v	v	X
ejpam-3975	298	9	(	(	PUNCT
ejpam-3975	298	10	hx1	hx1	NOUN
ejpam-3975	298	11	)	)	PUNCT
ejpam-3975	298	12	∩	∩	X
ejpam-3975	298	13	s	s	PART
ejpam-3975	298	14	6=	6=	NUM
ejpam-3975	298	15	∅.	∅.	ADV
ejpam-3975	298	16	let	let	VERB
ejpam-3975	298	17	y	y	PROPN
ejpam-3975	298	18	∈	∈	PROPN
ejpam-3975	298	19	v	v	PROPN
ejpam-3975	298	20	(	(	PUNCT
ejpam-3975	298	21	hx2	hx2	NOUN
ejpam-3975	298	22	)	)	PUNCT
ejpam-3975	298	23	∩	∩	PROPN
ejpam-3975	298	24	s.	s.	PROPN
ejpam-3975	298	25	then	then	ADV
ejpam-3975	298	26	y	y	PROPN
ejpam-3975	298	27	∈	∈	PROPN
ejpam-3975	298	28	npn	npn	PROPN
ejpam-3975	298	29	◦	◦	NOUN
ejpam-3975	298	30	h(x3	h(x3	NOUN
ejpam-3975	298	31	,	,	PUNCT
ejpam-3975	298	32	2	2	X
ejpam-3975	298	33	)	)	PUNCT
ejpam-3975	298	34	∩	∩	NOUN
ejpam-3975	298	35	s	s	PART
ejpam-3975	298	36	and	and	CCONJ
ejpam-3975	298	37	x1	x1	PROPN
ejpam-3975	298	38	∈	∈	PROPN
ejpam-3975	298	39	npn	npn	PROPN
ejpam-3975	298	40	◦	◦	NOUN
ejpam-3975	298	41	h(x3	h(x3	NOUN
ejpam-3975	298	42	,	,	PUNCT
ejpam-3975	298	43	2	2	X
ejpam-3975	298	44	)	)	PUNCT
ejpam-3975	298	45	∩	∩	NOUN
ejpam-3975	298	46	s	s	SYM
ejpam-3975	298	47	,	,	PUNCT
ejpam-3975	298	48	contrary	contrary	ADJ
ejpam-3975	298	49	to	to	ADP
ejpam-3975	298	50	our	our	PRON
ejpam-3975	298	51	assumption	assumption	NOUN
ejpam-3975	298	52	that	that	SCONJ
ejpam-3975	298	53	s	s	VERB
ejpam-3975	298	54	is	be	AUX
ejpam-3975	298	55	a	a	DET
ejpam-3975	298	56	total	total	ADJ
ejpam-3975	298	57	perfect	perfect	ADJ
ejpam-3975	298	58	hop	hop	NOUN
ejpam-3975	298	59	dominating	dominating	NOUN
ejpam-3975	298	60	set	set	NOUN
ejpam-3975	298	61	of	of	ADP
ejpam-3975	298	62	pn	pn	PROPN
ejpam-3975	298	63	◦	◦	PROPN
ejpam-3975	298	64	h.	h.	PROPN
ejpam-3975	298	65	suppose	suppose	VERB
ejpam-3975	298	66	x3	x3	PROPN
ejpam-3975	298	67	∈	∈	PROPN
ejpam-3975	298	68	s	s	PART
ejpam-3975	298	69	and	and	CCONJ
ejpam-3975	298	70	x1	x1	PROPN
ejpam-3975	298	71	/∈	/∈	PUNCT
ejpam-3975	299	1	s.	s.	PROPN
ejpam-3975	299	2	by	by	ADP
ejpam-3975	299	3	theorem	theorem	NOUN
ejpam-3975	299	4	4.2(i	4.2(i	NUM
ejpam-3975	299	5	)	)	PUNCT
ejpam-3975	299	6	,	,	PUNCT
ejpam-3975	299	7	x4	x4	PROPN
ejpam-3975	299	8	/∈	/∈	PUNCT
ejpam-3975	300	1	s.	s.	PROPN
ejpam-3975	300	2	this	this	PRON
ejpam-3975	300	3	implies	imply	VERB
ejpam-3975	300	4	that	that	SCONJ
ejpam-3975	300	5	e	e	PROPN
ejpam-3975	300	6	/∈	/∈	PUNCT
ejpam-3975	300	7	s	s	X
ejpam-3975	300	8	for	for	ADP
ejpam-3975	300	9	all	all	DET
ejpam-3975	300	10	e	e	PROPN
ejpam-3975	300	11	∈	∈	PROPN
ejpam-3975	300	12	v	v	NOUN
ejpam-3975	300	13	(	(	PUNCT
ejpam-3975	300	14	hx3	hx3	NOUN
ejpam-3975	300	15	)	)	PUNCT
ejpam-3975	300	16	.	.	PUNCT
ejpam-3975	301	1	thus	thus	ADV
ejpam-3975	301	2	,	,	PUNCT
ejpam-3975	301	3	c	c	PROPN
ejpam-3975	301	4	∈	∈	PROPN
ejpam-3975	301	5	s	s	VERB
ejpam-3975	301	6	for	for	ADP
ejpam-3975	301	7	a	a	DET
ejpam-3975	301	8	unique	unique	ADJ
ejpam-3975	301	9	vertex	vertex	NOUN
ejpam-3975	301	10	c	c	NOUN
ejpam-3975	301	11	∈	∈	PROPN
ejpam-3975	301	12	v	v	PROPN
ejpam-3975	301	13	(	(	PUNCT
ejpam-3975	301	14	hx1	hx1	PROPN
ejpam-3975	301	15	)	)	PUNCT
ejpam-3975	301	16	where	where	SCONJ
ejpam-3975	301	17	degh(c	degh(c	NOUN
ejpam-3975	301	18	)	)	PUNCT
ejpam-3975	301	19	=	=	SYM
ejpam-3975	301	20	|v	|v	PROPN
ejpam-3975	301	21	(	(	PUNCT
ejpam-3975	301	22	h)|	h)|	NOUN
ejpam-3975	301	23	−	−	PROPN
ejpam-3975	301	24	1	1	NUM
ejpam-3975	301	25	.	.	PUNCT
ejpam-3975	301	26	again	again	ADV
ejpam-3975	301	27	by	by	ADP
ejpam-3975	301	28	theorem	theorem	NOUN
ejpam-3975	301	29	4.2(i	4.2(i	NUM
ejpam-3975	301	30	)	)	PUNCT
ejpam-3975	301	31	,	,	PUNCT
ejpam-3975	301	32	x1	x1	PROPN
ejpam-3975	301	33	/∈	/∈	PUNCT
ejpam-3975	301	34	s	s	NOUN
ejpam-3975	301	35	and	and	CCONJ
ejpam-3975	301	36	x5	x5	PROPN
ejpam-3975	301	37	/∈	/∈	PROPN
ejpam-3975	301	38	s.	s.	PROPN
ejpam-3975	301	39	hence	hence	ADV
ejpam-3975	301	40	,	,	PUNCT
ejpam-3975	301	41	by	by	ADP
ejpam-3975	301	42	theorem	theorem	NOUN
ejpam-3975	301	43	4.2(ii	4.2(ii	NUM
ejpam-3975	301	44	)	)	PUNCT
ejpam-3975	301	45	,	,	PUNCT
ejpam-3975	301	46	|v	|v	PROPN
ejpam-3975	301	47	(	(	PUNCT
ejpam-3975	301	48	hx4	hx4	NOUN
ejpam-3975	301	49	∩	∩	ADJ
ejpam-3975	301	50	s)|	s)|	NOUN
ejpam-3975	301	51	=	=	NOUN
ejpam-3975	301	52	1	1	X
ejpam-3975	301	53	.	.	PUNCT
ejpam-3975	302	1	let	let	VERB
ejpam-3975	302	2	y	y	PROPN
ejpam-3975	302	3	∈	∈	PROPN
ejpam-3975	302	4	v	v	NOUN
ejpam-3975	302	5	(	(	PUNCT
ejpam-3975	302	6	hx4	hx4	NOUN
ejpam-3975	302	7	)	)	PUNCT
ejpam-3975	302	8	∩	∩	PROPN
ejpam-3975	302	9	s.	s.	PROPN
ejpam-3975	302	10	then	then	ADV
ejpam-3975	302	11	dpn	dpn	PROPN
ejpam-3975	302	12	◦	◦	PROPN
ejpam-3975	302	13	h(x5	h(x5	PROPN
ejpam-3975	302	14	,	,	PUNCT
ejpam-3975	302	15	x3	x3	ADJ
ejpam-3975	302	16	)	)	PUNCT
ejpam-3975	302	17	=	=	SYM
ejpam-3975	302	18	dpn	dpn	PROPN
ejpam-3975	302	19	◦	◦	NOUN
ejpam-3975	302	20	h(x5	h(x5	PROPN
ejpam-3975	302	21	,	,	PUNCT
ejpam-3975	302	22	y	y	NOUN
ejpam-3975	302	23	)	)	PUNCT
ejpam-3975	302	24	=	=	SYM
ejpam-3975	302	25	2	2	NUM
ejpam-3975	302	26	,	,	PUNCT
ejpam-3975	302	27	contrary	contrary	ADJ
ejpam-3975	302	28	to	to	ADP
ejpam-3975	302	29	our	our	PRON
ejpam-3975	302	30	assumption	assumption	NOUN
ejpam-3975	302	31	that	that	SCONJ
ejpam-3975	302	32	s	s	VERB
ejpam-3975	302	33	is	be	AUX
ejpam-3975	302	34	a	a	DET
ejpam-3975	302	35	total	total	ADJ
ejpam-3975	302	36	perfect	perfect	ADJ
ejpam-3975	302	37	hop	hop	NOUN
ejpam-3975	302	38	dominating	dominating	NOUN
ejpam-3975	302	39	set	set	NOUN
ejpam-3975	302	40	of	of	ADP
ejpam-3975	302	41	pn	pn	PROPN
ejpam-3975	302	42	◦	◦	PROPN
ejpam-3975	302	43	h.	h.	PROPN
ejpam-3975	302	44	thus	thus	ADV
ejpam-3975	302	45	,	,	PUNCT
ejpam-3975	302	46	the	the	DET
ejpam-3975	302	47	total	total	ADJ
ejpam-3975	302	48	perfect	perfect	ADJ
ejpam-3975	302	49	hop	hop	NOUN
ejpam-3975	302	50	dominating	dominating	NOUN
ejpam-3975	302	51	set	set	NOUN
ejpam-3975	302	52	of	of	ADP
ejpam-3975	302	53	pn	pn	PROPN
ejpam-3975	302	54	◦	◦	PROPN
ejpam-3975	302	55	h	h	PROPN
ejpam-3975	302	56	for	for	ADP
ejpam-3975	302	57	n	n	PROPN
ejpam-3975	302	58	>	>	SYM
ejpam-3975	302	59	4	4	NUM
ejpam-3975	302	60	does	do	AUX
ejpam-3975	302	61	not	not	PART
ejpam-3975	302	62	exist	exist	VERB
ejpam-3975	302	63	.	.	PUNCT
ejpam-3975	303	1	therefore	therefore	ADV
ejpam-3975	303	2	,	,	PUNCT
ejpam-3975	303	3	the	the	DET
ejpam-3975	303	4	total	total	ADJ
ejpam-3975	303	5	perfect	perfect	ADJ
ejpam-3975	303	6	hop	hop	NOUN
ejpam-3975	303	7	dominating	dominating	NOUN
ejpam-3975	303	8	set	set	NOUN
ejpam-3975	303	9	of	of	ADP
ejpam-3975	303	10	pn	pn	PROPN
ejpam-3975	303	11	◦	◦	NOUN
ejpam-3975	303	12	h	h	NOUN
ejpam-3975	303	13	exists	exist	VERB
ejpam-3975	303	14	if	if	SCONJ
ejpam-3975	303	15	and	and	CCONJ
ejpam-3975	303	16	only	only	ADV
ejpam-3975	303	17	if	if	SCONJ
ejpam-3975	303	18	n	n	PROPN
ejpam-3975	303	19	=	=	SYM
ejpam-3975	303	20	2	2	NUM
ejpam-3975	303	21	and	and	CCONJ
ejpam-3975	303	22	n	n	NOUN
ejpam-3975	303	23	=	=	NOUN
ejpam-3975	303	24	4	4	X
ejpam-3975	303	25	.	.	PUNCT
ejpam-3975	303	26	clearly	clearly	ADV
ejpam-3975	303	27	,	,	PUNCT
ejpam-3975	303	28	γtph(pn	γtph(pn	PROPN
ejpam-3975	303	29	◦	◦	NOUN
ejpam-3975	303	30	h	h	NOUN
ejpam-3975	303	31	)	)	PUNCT
ejpam-3975	303	32	=	=	SYM
ejpam-3975	303	33	4	4	NUM
ejpam-3975	303	34	for	for	ADP
ejpam-3975	303	35	n	n	NOUN
ejpam-3975	303	36	=	=	SYM
ejpam-3975	303	37	2	2	NUM
ejpam-3975	303	38	and	and	CCONJ
ejpam-3975	303	39	n	n	NOUN
ejpam-3975	303	40	=	=	SYM
ejpam-3975	303	41	4	4	X
ejpam-3975	303	42	.	.	X
ejpam-3975	303	43	�	�	PROPN
ejpam-3975	303	44	theorem	theorem	VERB
ejpam-3975	303	45	4.11	4.11	NUM
ejpam-3975	303	46	.	.	PUNCT
ejpam-3975	304	1	let	let	VERB
ejpam-3975	304	2	g	g	PRON
ejpam-3975	304	3	be	be	AUX
ejpam-3975	304	4	a	a	DET
ejpam-3975	304	5	non	non	ADJ
ejpam-3975	304	6	-	-	ADJ
ejpam-3975	304	7	complete	complete	ADJ
ejpam-3975	304	8	graph	graph	NOUN
ejpam-3975	304	9	with	with	ADP
ejpam-3975	304	10	|v	|v	PROPN
ejpam-3975	304	11	(	(	PUNCT
ejpam-3975	304	12	g)|	g)|	X
ejpam-3975	304	13	≥	≥	NUM
ejpam-3975	304	14	3	3	NUM
ejpam-3975	304	15	and	and	CCONJ
ejpam-3975	304	16	γ(g	γ(g	PROPN
ejpam-3975	304	17	)	)	PUNCT
ejpam-3975	304	18	=	=	SYM
ejpam-3975	304	19	1	1	NUM
ejpam-3975	304	20	and	and	CCONJ
ejpam-3975	304	21	h	h	DET
ejpam-3975	304	22	a	a	DET
ejpam-3975	304	23	graph	graph	NOUN
ejpam-3975	304	24	with	with	ADP
ejpam-3975	304	25	γ(h	γ(h	NOUN
ejpam-3975	304	26	)	)	PUNCT
ejpam-3975	304	27	=	=	SYM
ejpam-3975	305	1	1	1	X
ejpam-3975	305	2	.	.	PUNCT
ejpam-3975	306	1	then	then	ADV
ejpam-3975	306	2	the	the	DET
ejpam-3975	306	3	total	total	ADJ
ejpam-3975	306	4	perfect	perfect	ADJ
ejpam-3975	306	5	hop	hop	NOUN
ejpam-3975	306	6	dominating	dominating	NOUN
ejpam-3975	306	7	set	set	NOUN
ejpam-3975	306	8	of	of	ADP
ejpam-3975	306	9	g	g	PROPN
ejpam-3975	306	10	◦	◦	NOUN
ejpam-3975	306	11	h	h	NOUN
ejpam-3975	306	12	does	do	AUX
ejpam-3975	306	13	not	not	PART
ejpam-3975	306	14	exist	exist	VERB
ejpam-3975	306	15	.	.	PUNCT
ejpam-3975	307	1	proof	proof	NOUN
ejpam-3975	307	2	.	.	PUNCT
ejpam-3975	308	1	suppose	suppose	VERB
ejpam-3975	308	2	that	that	SCONJ
ejpam-3975	308	3	g	g	PROPN
ejpam-3975	308	4	◦	◦	NOUN
ejpam-3975	308	5	h	h	NOUN
ejpam-3975	308	6	has	have	VERB
ejpam-3975	308	7	a	a	DET
ejpam-3975	308	8	total	total	ADJ
ejpam-3975	308	9	perfect	perfect	ADJ
ejpam-3975	308	10	hop	hop	NOUN
ejpam-3975	308	11	dominating	dominating	NOUN
ejpam-3975	308	12	set	set	NOUN
ejpam-3975	308	13	s.	s.	PROPN
ejpam-3975	308	14	let	let	VERB
ejpam-3975	308	15	y	y	PROPN
ejpam-3975	308	16	∈	∈	PROPN
ejpam-3975	308	17	v	v	ADP
ejpam-3975	308	18	(	(	PUNCT
ejpam-3975	308	19	g	g	NOUN
ejpam-3975	308	20	)	)	PUNCT
ejpam-3975	308	21	with	with	ADP
ejpam-3975	308	22	degg(y	degg(y	NOUN
ejpam-3975	308	23	)	)	PUNCT
ejpam-3975	308	24	=	=	SYM
ejpam-3975	308	25	|v	|v	PROPN
ejpam-3975	308	26	(	(	PUNCT
ejpam-3975	308	27	g)|	g)|	INTJ
ejpam-3975	308	28	−	−	NOUN
ejpam-3975	308	29	1	1	NUM
ejpam-3975	308	30	.	.	PUNCT
ejpam-3975	308	31	by	by	ADP
ejpam-3975	308	32	theorem	theorem	NOUN
ejpam-3975	308	33	4.2(i	4.2(i	NUM
ejpam-3975	308	34	)	)	PUNCT
ejpam-3975	308	35	,	,	PUNCT
ejpam-3975	308	36	there	there	PRON
ejpam-3975	308	37	exists	exist	VERB
ejpam-3975	308	38	a	a	DET
ejpam-3975	308	39	unique	unique	ADJ
ejpam-3975	308	40	vertex	vertex	NOUN
ejpam-3975	308	41	x	x	SYM
ejpam-3975	308	42	∈	∈	NOUN
ejpam-3975	308	43	v	v	AUX
ejpam-3975	308	44	(	(	PUNCT
ejpam-3975	308	45	g	g	NOUN
ejpam-3975	308	46	)	)	PUNCT
ejpam-3975	308	47	∩	∩	PROPN
ejpam-3975	308	48	s.	s.	PROPN
ejpam-3975	308	49	if	if	SCONJ
ejpam-3975	308	50	degg(z	degg(z	PROPN
ejpam-3975	308	51	)	)	PUNCT
ejpam-3975	309	1	=	=	SYM
ejpam-3975	309	2	|v	|v	PROPN
ejpam-3975	309	3	(	(	PUNCT
ejpam-3975	309	4	h)|	h)|	NOUN
ejpam-3975	309	5	−	−	PROPN
ejpam-3975	309	6	1	1	NUM
ejpam-3975	309	7	,	,	PUNCT
ejpam-3975	309	8	y	y	PROPN
ejpam-3975	309	9	∈	∈	PROPN
ejpam-3975	309	10	s.	s.	PROPN
ejpam-3975	309	11	if	if	SCONJ
ejpam-3975	309	12	there	there	PRON
ejpam-3975	309	13	exists	exist	VERB
ejpam-3975	309	14	a	a	DET
ejpam-3975	309	15	unique	unique	ADJ
ejpam-3975	309	16	vertex	vertex	NOUN
ejpam-3975	309	17	z	z	NOUN
ejpam-3975	309	18	∈	∈	PROPN
ejpam-3975	309	19	ng(x	ng(x	NUM
ejpam-3975	309	20	,	,	PUNCT
ejpam-3975	309	21	2)∩s	2)∩s	PROPN
ejpam-3975	309	22	,	,	PUNCT
ejpam-3975	309	23	then	then	ADV
ejpam-3975	309	24	dg	dg	VERB
ejpam-3975	309	25	◦	◦	PROPN
ejpam-3975	309	26	h(a	h(a	PROPN
ejpam-3975	309	27	,	,	PUNCT
ejpam-3975	309	28	z	z	NOUN
ejpam-3975	309	29	)	)	PUNCT
ejpam-3975	309	30	=	=	SYM
ejpam-3975	309	31	dg	dg	PROPN
ejpam-3975	309	32	◦	◦	PROPN
ejpam-3975	309	33	h(a	h(a	PROPN
ejpam-3975	309	34	,	,	PUNCT
ejpam-3975	309	35	x	x	NOUN
ejpam-3975	309	36	)	)	PUNCT
ejpam-3975	309	37	=	=	SYM
ejpam-3975	309	38	2	2	NUM
ejpam-3975	309	39	for	for	ADP
ejpam-3975	309	40	a	a	DET
ejpam-3975	309	41	∈	∈	PROPN
ejpam-3975	309	42	v	v	ADP
ejpam-3975	309	43	(	(	PUNCT
ejpam-3975	309	44	hy	hy	NOUN
ejpam-3975	309	45	)	)	PUNCT
ejpam-3975	309	46	.	.	PUNCT
ejpam-3975	310	1	if	if	SCONJ
ejpam-3975	310	2	there	there	PRON
ejpam-3975	310	3	exists	exist	VERB
ejpam-3975	310	4	a	a	DET
ejpam-3975	310	5	unique	unique	ADJ
ejpam-3975	310	6	a	a	DET
ejpam-3975	310	7	∈	∈	NOUN
ejpam-3975	310	8	v	v	NOUN
ejpam-3975	310	9	(	(	PUNCT
ejpam-3975	310	10	hy)∩s	hy)∩s	PROPN
ejpam-3975	310	11	.	.	PUNCT
ejpam-3975	311	1	then	then	ADV
ejpam-3975	311	2	dg	dg	VERB
ejpam-3975	311	3	◦	◦	NOUN
ejpam-3975	311	4	h(z	h(z	NOUN
ejpam-3975	311	5	,	,	PUNCT
ejpam-3975	311	6	a	a	PRON
ejpam-3975	311	7	)	)	PUNCT
ejpam-3975	311	8	=	=	SYM
ejpam-3975	311	9	dg	dg	NOUN
ejpam-3975	311	10	◦	◦	NOUN
ejpam-3975	311	11	h(z	h(z	NOUN
ejpam-3975	311	12	,	,	PUNCT
ejpam-3975	311	13	x	x	NOUN
ejpam-3975	311	14	)	)	PUNCT
ejpam-3975	311	15	=	=	SYM
ejpam-3975	311	16	2	2	NUM
ejpam-3975	311	17	where	where	SCONJ
ejpam-3975	311	18	z	z	PROPN
ejpam-3975	311	19	∈	∈	PROPN
ejpam-3975	311	20	v	v	X
ejpam-3975	311	21	(	(	PUNCT
ejpam-3975	311	22	g)\{x	g)\{x	PROPN
ejpam-3975	311	23	}	}	PUNCT
ejpam-3975	311	24	.	.	PUNCT
ejpam-3975	312	1	suppose	suppose	VERB
ejpam-3975	312	2	degg(x	degg(x	X
ejpam-3975	312	3	)	)	PUNCT
ejpam-3975	312	4	≥	≥	NOUN
ejpam-3975	312	5	2	2	NUM
ejpam-3975	312	6	.	.	PUNCT
ejpam-3975	313	1	let	let	VERB
ejpam-3975	313	2	u	u	NOUN
ejpam-3975	313	3	,	,	PUNCT
ejpam-3975	313	4	v	v	PROPN
ejpam-3975	313	5	∈	∈	PROPN
ejpam-3975	313	6	ng(x	ng(x	NUM
ejpam-3975	313	7	)	)	PUNCT
ejpam-3975	313	8	with	with	ADP
ejpam-3975	313	9	u	u	PROPN
ejpam-3975	313	10	6=	6=	ADP
ejpam-3975	313	11	v.	v.	ADP
ejpam-3975	313	12	by	by	ADP
ejpam-3975	313	13	theorem	theorem	NOUN
ejpam-3975	313	14	4.2(i	4.2(i	NUM
ejpam-3975	313	15	)	)	PUNCT
ejpam-3975	313	16	,	,	PUNCT
ejpam-3975	313	17	there	there	PRON
ejpam-3975	313	18	exists	exist	VERB
ejpam-3975	313	19	a	a	DET
ejpam-3975	313	20	unique	unique	ADJ
ejpam-3975	313	21	vertex	vertex	NOUN
ejpam-3975	313	22	z	z	NOUN
ejpam-3975	313	23	∈	∈	PROPN
ejpam-3975	313	24	v	v	ADP
ejpam-3975	313	25	(	(	PUNCT
ejpam-3975	313	26	g	g	NOUN
ejpam-3975	313	27	)	)	PUNCT
ejpam-3975	313	28	∩ng(x	∩ng(x	NOUN
ejpam-3975	313	29	)	)	PUNCT
ejpam-3975	313	30	∩	∩	NOUN
ejpam-3975	313	31	s.	s.	PROPN
ejpam-3975	313	32	if	if	SCONJ
ejpam-3975	313	33	z	z	NOUN
ejpam-3975	313	34	=	=	SYM
ejpam-3975	313	35	y	y	PROPN
ejpam-3975	313	36	=	=	SYM
ejpam-3975	313	37	u	u	PROPN
ejpam-3975	313	38	6=	6=	PROPN
ejpam-3975	313	39	v	v	PROPN
ejpam-3975	313	40	,	,	PUNCT
ejpam-3975	313	41	then	then	ADV
ejpam-3975	313	42	dg	dg	VERB
ejpam-3975	313	43	◦	◦	NOUN
ejpam-3975	313	44	h(b	h(b	PROPN
ejpam-3975	313	45	,	,	PUNCT
ejpam-3975	313	46	y	y	NOUN
ejpam-3975	313	47	)	)	PUNCT
ejpam-3975	313	48	=	=	SYM
ejpam-3975	313	49	dg	dg	NOUN
ejpam-3975	313	50	◦	◦	NOUN
ejpam-3975	313	51	h(b	h(b	PROPN
ejpam-3975	313	52	,	,	PUNCT
ejpam-3975	313	53	x	x	NOUN
ejpam-3975	313	54	)	)	PUNCT
ejpam-3975	313	55	=	=	SYM
ejpam-3975	313	56	2	2	NUM
ejpam-3975	313	57	for	for	ADP
ejpam-3975	313	58	all	all	DET
ejpam-3975	313	59	b	b	PROPN
ejpam-3975	313	60	∈	∈	ADP
ejpam-3975	313	61	v	v	NOUN
ejpam-3975	313	62	(	(	PUNCT
ejpam-3975	313	63	hv	hv	PROPN
ejpam-3975	313	64	)	)	PUNCT
ejpam-3975	313	65	.	.	PUNCT
ejpam-3975	314	1	if	if	SCONJ
ejpam-3975	314	2	z	z	NOUN
ejpam-3975	314	3	=	=	SYM
ejpam-3975	314	4	v	v	PROPN
ejpam-3975	314	5	6=	6=	PROPN
ejpam-3975	314	6	y	y	PROPN
ejpam-3975	314	7	,	,	PUNCT
ejpam-3975	314	8	then	then	ADV
ejpam-3975	314	9	dg	dg	VERB
ejpam-3975	314	10	◦	◦	NOUN
ejpam-3975	314	11	h(b	h(b	PROPN
ejpam-3975	314	12	,	,	PUNCT
ejpam-3975	314	13	v	v	NOUN
ejpam-3975	314	14	)	)	PUNCT
ejpam-3975	314	15	=	=	SYM
ejpam-3975	314	16	dg	dg	NOUN
ejpam-3975	314	17	◦	◦	NOUN
ejpam-3975	314	18	h(b	h(b	PROPN
ejpam-3975	314	19	,	,	PUNCT
ejpam-3975	314	20	x	x	NOUN
ejpam-3975	314	21	)	)	PUNCT
ejpam-3975	314	22	=	=	SYM
ejpam-3975	314	23	2	2	NUM
ejpam-3975	314	24	for	for	ADP
ejpam-3975	314	25	all	all	DET
ejpam-3975	314	26	b	b	PROPN
ejpam-3975	314	27	∈	∈	ADP
ejpam-3975	314	28	v	v	ADP
ejpam-3975	314	29	(	(	PUNCT
ejpam-3975	314	30	hy	hy	NOUN
ejpam-3975	314	31	)	)	PUNCT
ejpam-3975	314	32	.	.	PUNCT
ejpam-3975	315	1	this	this	PRON
ejpam-3975	315	2	implies	imply	VERB
ejpam-3975	315	3	that	that	SCONJ
ejpam-3975	315	4	s	s	VERB
ejpam-3975	315	5	is	be	AUX
ejpam-3975	315	6	not	not	PART
ejpam-3975	315	7	a	a	DET
ejpam-3975	315	8	total	total	ADJ
ejpam-3975	315	9	perfect	perfect	ADJ
ejpam-3975	315	10	hop	hop	NOUN
ejpam-3975	315	11	dominating	dominating	NOUN
ejpam-3975	315	12	set	set	NOUN
ejpam-3975	315	13	of	of	ADP
ejpam-3975	315	14	g	g	PROPN
ejpam-3975	315	15	◦	◦	PROPN
ejpam-3975	315	16	h.	h.	PROPN
ejpam-3975	315	17	therefore	therefore	ADV
ejpam-3975	315	18	,	,	PUNCT
ejpam-3975	315	19	the	the	DET
ejpam-3975	315	20	total	total	ADJ
ejpam-3975	315	21	perfect	perfect	ADJ
ejpam-3975	315	22	hop	hop	NOUN
ejpam-3975	315	23	dominating	dominating	NOUN
ejpam-3975	315	24	set	set	NOUN
ejpam-3975	315	25	of	of	ADP
ejpam-3975	315	26	g	g	PROPN
ejpam-3975	315	27	◦	◦	NOUN
ejpam-3975	315	28	h	h	NOUN
ejpam-3975	315	29	does	do	AUX
ejpam-3975	315	30	not	not	PART
ejpam-3975	315	31	exist	exist	VERB
ejpam-3975	315	32	.	.	PUNCT
ejpam-3975	316	1	�	�	PROPN
ejpam-3975	316	2	5	5	NUM
ejpam-3975	316	3	.	.	PUNCT
ejpam-3975	316	4	lexicographic	lexicographic	ADJ
ejpam-3975	316	5	product	product	NOUN
ejpam-3975	316	6	the	the	DET
ejpam-3975	316	7	lexicographic	lexicographic	ADJ
ejpam-3975	316	8	product	product	NOUN
ejpam-3975	316	9	of	of	ADP
ejpam-3975	316	10	two	two	NUM
ejpam-3975	316	11	graphs	graph	NOUN
ejpam-3975	316	12	g	g	NOUN
ejpam-3975	316	13	and	and	CCONJ
ejpam-3975	316	14	h	h	NOUN
ejpam-3975	316	15	,	,	PUNCT
ejpam-3975	316	16	denoted	denote	VERB
ejpam-3975	316	17	by	by	ADP
ejpam-3975	316	18	g[h	g[h	NOUN
ejpam-3975	316	19	]	]	PUNCT
ejpam-3975	316	20	,	,	PUNCT
ejpam-3975	316	21	is	be	AUX
ejpam-3975	316	22	the	the	DET
ejpam-3975	316	23	graph	graph	NOUN
ejpam-3975	316	24	with	with	ADP
ejpam-3975	316	25	v	v	NOUN
ejpam-3975	316	26	(	(	PUNCT
ejpam-3975	316	27	g[h	g[h	PROPN
ejpam-3975	316	28	]	]	PUNCT
ejpam-3975	316	29	)	)	PUNCT
ejpam-3975	316	30	=	=	SYM
ejpam-3975	316	31	v	v	X
ejpam-3975	316	32	(	(	PUNCT
ejpam-3975	316	33	g)×v	g)×v	PROPN
ejpam-3975	316	34	(	(	PUNCT
ejpam-3975	316	35	h	h	NOUN
ejpam-3975	316	36	)	)	PUNCT
ejpam-3975	316	37	and	and	CCONJ
ejpam-3975	316	38	(	(	PUNCT
ejpam-3975	316	39	u1	u1	NOUN
ejpam-3975	316	40	,	,	PUNCT
ejpam-3975	316	41	u2)(v1	u2)(v1	NOUN
ejpam-3975	316	42	,	,	PUNCT
ejpam-3975	316	43	v2	v2	NOUN
ejpam-3975	316	44	)	)	PUNCT
ejpam-3975	316	45	∈	∈	NOUN
ejpam-3975	316	46	e(g[h	e(g[h	NOUN
ejpam-3975	316	47	]	]	PUNCT
ejpam-3975	316	48	)	)	PUNCT
ejpam-3975	316	49	if	if	SCONJ
ejpam-3975	316	50	either	either	CCONJ
ejpam-3975	316	51	u1v1	u1v1	PROPN
ejpam-3975	316	52	∈	∈	PROPN
ejpam-3975	316	53	e(g	e(g	PROPN
ejpam-3975	316	54	)	)	PUNCT
ejpam-3975	316	55	or	or	CCONJ
ejpam-3975	316	56	u1	u1	NOUN
ejpam-3975	316	57	=	=	SYM
ejpam-3975	316	58	v1	v1	NOUN
ejpam-3975	316	59	and	and	CCONJ
ejpam-3975	316	60	u2v2	u2v2	ADJ
ejpam-3975	316	61	∈	∈	PROPN
ejpam-3975	316	62	e(h	e(h	PROPN
ejpam-3975	316	63	)	)	PUNCT
ejpam-3975	316	64	.	.	PUNCT
ejpam-3975	317	1	r.	r.	PROPN
ejpam-3975	317	2	rakim	rakim	PROPN
ejpam-3975	317	3	,	,	PUNCT
ejpam-3975	317	4	h.	h.	PROPN
ejpam-3975	317	5	rara	rara	PROPN
ejpam-3975	317	6	/	/	SYM
ejpam-3975	317	7	eur	eur	PROPN
ejpam-3975	317	8	.	.	PUNCT
ejpam-3975	318	1	j.	j.	PROPN
ejpam-3975	318	2	pure	pure	PROPN
ejpam-3975	318	3	appl	appl	PROPN
ejpam-3975	318	4	.	.	PROPN
ejpam-3975	318	5	math	math	PROPN
ejpam-3975	318	6	,	,	PUNCT
ejpam-3975	318	7	14	14	NUM
ejpam-3975	318	8	(	(	PUNCT
ejpam-3975	318	9	3	3	NUM
ejpam-3975	318	10	)	)	PUNCT
ejpam-3975	318	11	(	(	PUNCT
ejpam-3975	318	12	2021	2021	NUM
ejpam-3975	318	13	)	)	PUNCT
ejpam-3975	318	14	,	,	PUNCT
ejpam-3975	318	15	803	803	NUM
ejpam-3975	318	16	-	-	SYM
ejpam-3975	318	17	815	815	NUM
ejpam-3975	318	18	813	813	NUM
ejpam-3975	318	19	theorem	theorem	NOUN
ejpam-3975	318	20	5.1	5.1	NUM
ejpam-3975	318	21	.	.	PUNCT
ejpam-3975	319	1	let	let	VERB
ejpam-3975	319	2	g	g	PRON
ejpam-3975	319	3	be	be	AUX
ejpam-3975	319	4	a	a	DET
ejpam-3975	319	5	nontrivial	nontrivial	ADJ
ejpam-3975	319	6	complete	complete	ADJ
ejpam-3975	319	7	graph	graph	NOUN
ejpam-3975	319	8	and	and	CCONJ
ejpam-3975	319	9	h	h	NOUN
ejpam-3975	319	10	a	a	DET
ejpam-3975	319	11	nontrivial	nontrivial	ADJ
ejpam-3975	319	12	connected	connect	VERB
ejpam-3975	319	13	non	non	ADJ
ejpam-3975	319	14	-	-	ADJ
ejpam-3975	319	15	complete	complete	ADJ
ejpam-3975	319	16	graph	graph	NOUN
ejpam-3975	319	17	whose	whose	DET
ejpam-3975	319	18	total	total	ADJ
ejpam-3975	319	19	perfect	perfect	ADJ
ejpam-3975	319	20	point	point	NOUN
ejpam-3975	319	21	-	-	PUNCT
ejpam-3975	319	22	wise	wise	ADJ
ejpam-3975	319	23	non	non	ADJ
ejpam-3975	319	24	-	-	ADJ
ejpam-3975	319	25	dominating	dominating	ADJ
ejpam-3975	319	26	set	set	NOUN
ejpam-3975	319	27	exists	exist	VERB
ejpam-3975	319	28	.	.	PUNCT
ejpam-3975	320	1	a	a	DET
ejpam-3975	320	2	subset	subset	NOUN
ejpam-3975	320	3	c	c	NOUN
ejpam-3975	320	4	=	=	PUNCT
ejpam-3975	320	5	⋃	⋃	PROPN
ejpam-3975	320	6	x∈s	x∈s	NOUN
ejpam-3975	321	1	[	[	X
ejpam-3975	321	2	{	{	PUNCT
ejpam-3975	321	3	x}×tx	x}×tx	X
ejpam-3975	321	4	]	]	X
ejpam-3975	321	5	of	of	ADP
ejpam-3975	321	6	v	v	NOUN
ejpam-3975	321	7	(	(	PUNCT
ejpam-3975	321	8	g[h	g[h	PROPN
ejpam-3975	321	9	]	]	PUNCT
ejpam-3975	321	10	)	)	PUNCT
ejpam-3975	321	11	where	where	SCONJ
ejpam-3975	321	12	s	s	VERB
ejpam-3975	321	13	⊆	⊆	NUM
ejpam-3975	321	14	v	v	NOUN
ejpam-3975	321	15	(	(	PUNCT
ejpam-3975	321	16	g	g	NOUN
ejpam-3975	321	17	)	)	PUNCT
ejpam-3975	321	18	and	and	CCONJ
ejpam-3975	321	19	tx	tx	VERB
ejpam-3975	321	20	⊆	⊆	NUM
ejpam-3975	321	21	v	v	NOUN
ejpam-3975	321	22	(	(	PUNCT
ejpam-3975	321	23	h	h	NOUN
ejpam-3975	321	24	)	)	PUNCT
ejpam-3975	321	25	for	for	ADP
ejpam-3975	321	26	each	each	DET
ejpam-3975	321	27	x	x	SYM
ejpam-3975	321	28	∈	∈	PROPN
ejpam-3975	321	29	s	s	NOUN
ejpam-3975	321	30	,	,	PUNCT
ejpam-3975	321	31	is	be	AUX
ejpam-3975	321	32	a	a	DET
ejpam-3975	321	33	total	total	ADJ
ejpam-3975	321	34	perfect	perfect	ADJ
ejpam-3975	321	35	hop	hop	NOUN
ejpam-3975	321	36	dominating	dominating	NOUN
ejpam-3975	321	37	set	set	NOUN
ejpam-3975	321	38	of	of	ADP
ejpam-3975	321	39	g[h	g[h	PROPN
ejpam-3975	321	40	]	]	PUNCT
ejpam-3975	321	41	if	if	SCONJ
ejpam-3975	321	42	and	and	CCONJ
ejpam-3975	321	43	only	only	ADV
ejpam-3975	321	44	if	if	SCONJ
ejpam-3975	321	45	s	s	VERB
ejpam-3975	321	46	=	=	SYM
ejpam-3975	321	47	v	v	X
ejpam-3975	321	48	(	(	PUNCT
ejpam-3975	321	49	g	g	NOUN
ejpam-3975	321	50	)	)	PUNCT
ejpam-3975	321	51	and	and	CCONJ
ejpam-3975	321	52	tx	tx	PROPN
ejpam-3975	321	53	is	be	AUX
ejpam-3975	321	54	a	a	DET
ejpam-3975	321	55	total	total	ADJ
ejpam-3975	321	56	perfect	perfect	ADJ
ejpam-3975	321	57	point	point	NOUN
ejpam-3975	321	58	-	-	PUNCT
ejpam-3975	321	59	wise	wise	ADJ
ejpam-3975	321	60	non	non	ADJ
ejpam-3975	321	61	-	-	ADJ
ejpam-3975	321	62	dominating	dominating	ADJ
ejpam-3975	321	63	set	set	NOUN
ejpam-3975	321	64	of	of	ADP
ejpam-3975	321	65	h	h	NOUN
ejpam-3975	321	66	for	for	ADP
ejpam-3975	321	67	each	each	DET
ejpam-3975	321	68	x	x	SYM
ejpam-3975	321	69	∈	∈	PROPN
ejpam-3975	321	70	s.	s.	PROPN
ejpam-3975	321	71	proof	proof	PROPN
ejpam-3975	321	72	.	.	PUNCT
ejpam-3975	322	1	let	let	VERB
ejpam-3975	322	2	c	c	NOUN
ejpam-3975	322	3	=	=	PUNCT
ejpam-3975	323	1	⋃	⋃	PROPN
ejpam-3975	323	2	x∈s	x∈s	NOUN
ejpam-3975	324	1	[	[	X
ejpam-3975	324	2	{	{	PUNCT
ejpam-3975	324	3	x	x	NOUN
ejpam-3975	324	4	}	}	PUNCT
ejpam-3975	324	5	×	×	PROPN
ejpam-3975	324	6	tx	tx	PROPN
ejpam-3975	324	7	]	]	PUNCT
ejpam-3975	324	8	where	where	SCONJ
ejpam-3975	324	9	s	s	VERB
ejpam-3975	324	10	⊆	⊆	NUM
ejpam-3975	324	11	v	v	NOUN
ejpam-3975	324	12	(	(	PUNCT
ejpam-3975	324	13	g	g	NOUN
ejpam-3975	324	14	)	)	PUNCT
ejpam-3975	324	15	and	and	CCONJ
ejpam-3975	324	16	tx	tx	VERB
ejpam-3975	324	17	⊆	⊆	NUM
ejpam-3975	324	18	v	v	NOUN
ejpam-3975	324	19	(	(	PUNCT
ejpam-3975	324	20	h	h	NOUN
ejpam-3975	324	21	)	)	PUNCT
ejpam-3975	324	22	for	for	ADP
ejpam-3975	324	23	each	each	DET
ejpam-3975	324	24	x	x	SYM
ejpam-3975	324	25	∈	∈	PROPN
ejpam-3975	324	26	s	s	AUX
ejpam-3975	324	27	be	be	AUX
ejpam-3975	324	28	a	a	DET
ejpam-3975	324	29	total	total	ADJ
ejpam-3975	324	30	perfect	perfect	ADJ
ejpam-3975	324	31	hop	hop	NOUN
ejpam-3975	324	32	dominating	dominating	NOUN
ejpam-3975	324	33	set	set	NOUN
ejpam-3975	324	34	of	of	ADP
ejpam-3975	324	35	g[h	g[h	PROPN
ejpam-3975	324	36	]	]	PUNCT
ejpam-3975	324	37	.	.	PUNCT
ejpam-3975	325	1	then	then	ADV
ejpam-3975	325	2	c	c	PROPN
ejpam-3975	325	3	is	be	AUX
ejpam-3975	325	4	a	a	DET
ejpam-3975	325	5	perfect	perfect	ADJ
ejpam-3975	325	6	hop	hop	NOUN
ejpam-3975	325	7	dominating	dominating	NOUN
ejpam-3975	325	8	set	set	NOUN
ejpam-3975	325	9	of	of	ADP
ejpam-3975	325	10	g[h	g[h	PROPN
ejpam-3975	325	11	]	]	PUNCT
ejpam-3975	325	12	.	.	PUNCT
ejpam-3975	326	1	suppose	suppose	VERB
ejpam-3975	326	2	s	s	PROPN
ejpam-3975	326	3	6=	6=	NUM
ejpam-3975	326	4	v	v	ADP
ejpam-3975	326	5	(	(	PUNCT
ejpam-3975	326	6	g	g	NOUN
ejpam-3975	326	7	)	)	PUNCT
ejpam-3975	326	8	.	.	PUNCT
ejpam-3975	327	1	let	let	VERB
ejpam-3975	327	2	u	u	PRON
ejpam-3975	327	3	∈	∈	PROPN
ejpam-3975	327	4	v	v	NOUN
ejpam-3975	327	5	(	(	PUNCT
ejpam-3975	327	6	g)\s	g)\s	NOUN
ejpam-3975	327	7	.	.	PUNCT
ejpam-3975	328	1	then	then	ADV
ejpam-3975	328	2	(	(	PUNCT
ejpam-3975	328	3	u	u	NOUN
ejpam-3975	328	4	,	,	PUNCT
ejpam-3975	328	5	a	a	PRON
ejpam-3975	328	6	)	)	PUNCT
ejpam-3975	328	7	/∈	/∈	PUNCT
ejpam-3975	329	1	c	c	NOUN
ejpam-3975	329	2	for	for	ADP
ejpam-3975	329	3	any	any	DET
ejpam-3975	329	4	a	a	DET
ejpam-3975	329	5	∈	∈	PROPN
ejpam-3975	329	6	v	v	NOUN
ejpam-3975	329	7	(	(	PUNCT
ejpam-3975	329	8	h	h	NOUN
ejpam-3975	329	9	)	)	PUNCT
ejpam-3975	329	10	.	.	PUNCT
ejpam-3975	330	1	thus	thus	ADV
ejpam-3975	330	2	,	,	PUNCT
ejpam-3975	330	3	there	there	PRON
ejpam-3975	330	4	exists	exist	VERB
ejpam-3975	330	5	a	a	DET
ejpam-3975	330	6	unique	unique	ADJ
ejpam-3975	330	7	vertex	vertex	NOUN
ejpam-3975	330	8	(	(	PUNCT
ejpam-3975	330	9	y	y	PROPN
ejpam-3975	330	10	,	,	PUNCT
ejpam-3975	330	11	b	b	NOUN
ejpam-3975	330	12	)	)	PUNCT
ejpam-3975	330	13	∈	∈	PROPN
ejpam-3975	330	14	c	c	NOUN
ejpam-3975	330	15	such	such	ADJ
ejpam-3975	330	16	that	that	SCONJ
ejpam-3975	330	17	dg[h]((u	dg[h]((u	NOUN
ejpam-3975	330	18	,	,	PUNCT
ejpam-3975	330	19	a	a	PRON
ejpam-3975	330	20	)	)	PUNCT
ejpam-3975	330	21	,	,	PUNCT
ejpam-3975	330	22	(	(	PUNCT
ejpam-3975	330	23	y	y	PROPN
ejpam-3975	330	24	,	,	PUNCT
ejpam-3975	330	25	b	b	NOUN
ejpam-3975	330	26	)	)	PUNCT
ejpam-3975	330	27	)	)	PUNCT
ejpam-3975	331	1	=	=	SYM
ejpam-3975	331	2	2	2	X
ejpam-3975	331	3	.	.	PUNCT
ejpam-3975	331	4	since	since	SCONJ
ejpam-3975	331	5	u	u	PROPN
ejpam-3975	331	6	/∈	/∈	PROPN
ejpam-3975	331	7	s	s	PART
ejpam-3975	331	8	and	and	CCONJ
ejpam-3975	331	9	y	y	PROPN
ejpam-3975	331	10	∈	∈	PROPN
ejpam-3975	331	11	s	s	PROPN
ejpam-3975	331	12	,	,	PUNCT
ejpam-3975	331	13	u	u	PROPN
ejpam-3975	331	14	6=	6=	PROPN
ejpam-3975	331	15	y	y	PROPN
ejpam-3975	331	16	and	and	CCONJ
ejpam-3975	331	17	dg(u	dg(u	PROPN
ejpam-3975	331	18	,	,	PUNCT
ejpam-3975	331	19	y	y	NOUN
ejpam-3975	331	20	)	)	PUNCT
ejpam-3975	331	21	=	=	SYM
ejpam-3975	332	1	2	2	X
ejpam-3975	332	2	.	.	PUNCT
ejpam-3975	332	3	this	this	PRON
ejpam-3975	332	4	implies	imply	VERB
ejpam-3975	332	5	that	that	SCONJ
ejpam-3975	332	6	(	(	PUNCT
ejpam-3975	332	7	y	y	NOUN
ejpam-3975	332	8	,	,	PUNCT
ejpam-3975	332	9	p	p	NOUN
ejpam-3975	332	10	)	)	PUNCT
ejpam-3975	332	11	/∈	/∈	PUNCT
ejpam-3975	333	1	c	c	NOUN
ejpam-3975	333	2	for	for	ADP
ejpam-3975	333	3	all	all	DET
ejpam-3975	333	4	p	p	PROPN
ejpam-3975	333	5	∈	∈	PROPN
ejpam-3975	333	6	v	v	NOUN
ejpam-3975	333	7	(	(	PUNCT
ejpam-3975	333	8	h)\{b	h)\{b	PROPN
ejpam-3975	333	9	}	}	PUNCT
ejpam-3975	333	10	.	.	PUNCT
ejpam-3975	334	1	since	since	SCONJ
ejpam-3975	334	2	γ(h	γ(h	PROPN
ejpam-3975	334	3	)	)	PUNCT
ejpam-3975	334	4	6=	6=	ADP
ejpam-3975	334	5	1	1	NUM
ejpam-3975	334	6	,	,	PUNCT
ejpam-3975	334	7	choose	choose	VERB
ejpam-3975	334	8	q	q	PROPN
ejpam-3975	334	9	∈	∈	PROPN
ejpam-3975	334	10	v	v	NOUN
ejpam-3975	334	11	(	(	PUNCT
ejpam-3975	334	12	h)\{b	h)\{b	NOUN
ejpam-3975	334	13	}	}	PUNCT
ejpam-3975	334	14	such	such	ADJ
ejpam-3975	334	15	that	that	PRON
ejpam-3975	334	16	q	q	NOUN
ejpam-3975	334	17	/∈	/∈	PUNCT
ejpam-3975	334	18	nh(b	nh(b	NUM
ejpam-3975	334	19	)	)	PUNCT
ejpam-3975	334	20	.	.	PUNCT
ejpam-3975	335	1	then	then	ADV
ejpam-3975	335	2	dg[h]((y	dg[h]((y	VERB
ejpam-3975	335	3	,	,	PUNCT
ejpam-3975	335	4	q	q	NOUN
ejpam-3975	335	5	)	)	PUNCT
ejpam-3975	335	6	,	,	PUNCT
ejpam-3975	335	7	(	(	PUNCT
ejpam-3975	335	8	y	y	PROPN
ejpam-3975	335	9	,	,	PUNCT
ejpam-3975	335	10	b	b	NOUN
ejpam-3975	335	11	)	)	PUNCT
ejpam-3975	335	12	)	)	PUNCT
ejpam-3975	336	1	=	=	SYM
ejpam-3975	336	2	2	2	X
ejpam-3975	336	3	.	.	X
ejpam-3975	336	4	pick	pick	VERB
ejpam-3975	336	5	any	any	DET
ejpam-3975	336	6	t	t	NOUN
ejpam-3975	336	7	∈	∈	PROPN
ejpam-3975	336	8	nh(b	nh(b	PROPN
ejpam-3975	336	9	)	)	PUNCT
ejpam-3975	336	10	.	.	PUNCT
ejpam-3975	337	1	then	then	ADV
ejpam-3975	337	2	there	there	PRON
ejpam-3975	337	3	exists	exist	VERB
ejpam-3975	337	4	z	z	PROPN
ejpam-3975	337	5	∈	∈	PROPN
ejpam-3975	337	6	s\{y	s\{y	X
ejpam-3975	337	7	}	}	PUNCT
ejpam-3975	337	8	such	such	ADJ
ejpam-3975	337	9	that	that	PRON
ejpam-3975	337	10	dg(y	dg(y	ADJ
ejpam-3975	337	11	,	,	PUNCT
ejpam-3975	337	12	z	z	NOUN
ejpam-3975	337	13	)	)	PUNCT
ejpam-3975	337	14	=	=	SYM
ejpam-3975	337	15	2	2	X
ejpam-3975	337	16	.	.	X
ejpam-3975	337	17	let	let	VERB
ejpam-3975	337	18	r	r	NOUN
ejpam-3975	337	19	∈	∈	PROPN
ejpam-3975	337	20	tz	tz	NOUN
ejpam-3975	337	21	.	.	PUNCT
ejpam-3975	338	1	then	then	ADV
ejpam-3975	338	2	dg[h]((y	dg[h]((y	VERB
ejpam-3975	338	3	,	,	PUNCT
ejpam-3975	338	4	q	q	NOUN
ejpam-3975	338	5	)	)	PUNCT
ejpam-3975	338	6	,	,	PUNCT
ejpam-3975	338	7	(	(	PUNCT
ejpam-3975	338	8	z	z	X
ejpam-3975	338	9	,	,	PUNCT
ejpam-3975	338	10	r	r	NOUN
ejpam-3975	338	11	)	)	PUNCT
ejpam-3975	338	12	)	)	PUNCT
ejpam-3975	339	1	=	=	SYM
ejpam-3975	339	2	2	2	NUM
ejpam-3975	339	3	,	,	PUNCT
ejpam-3975	339	4	a	a	DET
ejpam-3975	339	5	contradiction	contradiction	NOUN
ejpam-3975	339	6	to	to	ADP
ejpam-3975	339	7	the	the	DET
ejpam-3975	339	8	fact	fact	NOUN
ejpam-3975	339	9	that	that	SCONJ
ejpam-3975	339	10	c	c	PROPN
ejpam-3975	339	11	is	be	AUX
ejpam-3975	339	12	a	a	DET
ejpam-3975	339	13	perfect	perfect	ADJ
ejpam-3975	339	14	hop	hop	NOUN
ejpam-3975	339	15	dominating	dominating	NOUN
ejpam-3975	339	16	set	set	NOUN
ejpam-3975	339	17	of	of	ADP
ejpam-3975	339	18	g[h	g[h	PROPN
ejpam-3975	339	19	]	]	PUNCT
ejpam-3975	339	20	.	.	PUNCT
ejpam-3975	340	1	therefore	therefore	ADV
ejpam-3975	340	2	s	s	VERB
ejpam-3975	340	3	=	=	SYM
ejpam-3975	340	4	v	v	ADJ
ejpam-3975	340	5	(	(	PUNCT
ejpam-3975	340	6	g	g	NOUN
ejpam-3975	340	7	)	)	PUNCT
ejpam-3975	340	8	.	.	PUNCT
ejpam-3975	341	1	let	let	VERB
ejpam-3975	341	2	x	x	SYM
ejpam-3975	341	3	∈	∈	PROPN
ejpam-3975	341	4	s.	s.	PROPN
ejpam-3975	341	5	suppose	suppose	VERB
ejpam-3975	341	6	that	that	SCONJ
ejpam-3975	341	7	ng(x	ng(x	NUM
ejpam-3975	341	8	,	,	PUNCT
ejpam-3975	341	9	2	2	NUM
ejpam-3975	341	10	)	)	PUNCT
ejpam-3975	341	11	6=	6=	NOUN
ejpam-3975	341	12	∅	∅	NOUN
ejpam-3975	341	13	and	and	CCONJ
ejpam-3975	341	14	tx	tx	VERB
ejpam-3975	341	15	6=	6=	PROPN
ejpam-3975	341	16	v	v	PROPN
ejpam-3975	341	17	(	(	PUNCT
ejpam-3975	341	18	h	h	NOUN
ejpam-3975	341	19	)	)	PUNCT
ejpam-3975	341	20	.	.	PUNCT
ejpam-3975	342	1	let	let	VERB
ejpam-3975	342	2	z	z	PROPN
ejpam-3975	342	3	∈	∈	PROPN
ejpam-3975	342	4	ng(x	ng(x	NUM
ejpam-3975	342	5	,	,	PUNCT
ejpam-3975	342	6	2	2	NUM
ejpam-3975	342	7	)	)	PUNCT
ejpam-3975	342	8	,	,	PUNCT
ejpam-3975	342	9	p	p	PROPN
ejpam-3975	342	10	∈	∈	PROPN
ejpam-3975	342	11	tz	tz	NOUN
ejpam-3975	342	12	and	and	CCONJ
ejpam-3975	342	13	a	a	DET
ejpam-3975	342	14	∈	∈	NOUN
ejpam-3975	342	15	v	v	NOUN
ejpam-3975	342	16	(	(	PUNCT
ejpam-3975	342	17	h)\tx	h)\tx	PROPN
ejpam-3975	342	18	.	.	NOUN
ejpam-3975	343	1	since	since	SCONJ
ejpam-3975	343	2	(	(	PUNCT
ejpam-3975	343	3	x	x	X
ejpam-3975	343	4	,	,	PUNCT
ejpam-3975	343	5	a	a	PRON
ejpam-3975	343	6	)	)	PUNCT
ejpam-3975	343	7	/∈	/∈	PUNCT
ejpam-3975	344	1	c	c	X
ejpam-3975	344	2	,	,	PUNCT
ejpam-3975	344	3	there	there	PRON
ejpam-3975	344	4	is	be	VERB
ejpam-3975	344	5	exactly	exactly	ADV
ejpam-3975	344	6	one	one	NUM
ejpam-3975	344	7	vertex	vertex	NOUN
ejpam-3975	344	8	(	(	PUNCT
ejpam-3975	344	9	y	y	PROPN
ejpam-3975	344	10	,	,	PUNCT
ejpam-3975	344	11	b	b	NOUN
ejpam-3975	344	12	)	)	PUNCT
ejpam-3975	344	13	∈	∈	PROPN
ejpam-3975	344	14	c	c	NOUN
ejpam-3975	344	15	such	such	ADJ
ejpam-3975	344	16	that	that	DET
ejpam-3975	344	17	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	344	18	,	,	PUNCT
ejpam-3975	344	19	a	a	PRON
ejpam-3975	344	20	)	)	PUNCT
ejpam-3975	344	21	,	,	PUNCT
ejpam-3975	344	22	(	(	PUNCT
ejpam-3975	344	23	y	y	PROPN
ejpam-3975	344	24	,	,	PUNCT
ejpam-3975	344	25	b	b	NOUN
ejpam-3975	344	26	)	)	PUNCT
ejpam-3975	344	27	)	)	PUNCT
ejpam-3975	345	1	=	=	SYM
ejpam-3975	345	2	2	2	X
ejpam-3975	345	3	.	.	PUNCT
ejpam-3975	346	1	this	this	PRON
ejpam-3975	346	2	implies	imply	VERB
ejpam-3975	346	3	that	that	SCONJ
ejpam-3975	346	4	x	x	X
ejpam-3975	346	5	=	=	SYM
ejpam-3975	346	6	y	y	PROPN
ejpam-3975	346	7	and	and	CCONJ
ejpam-3975	346	8	ab	ab	PROPN
ejpam-3975	346	9	/∈	/∈	PUNCT
ejpam-3975	347	1	e(h	e(h	PROPN
ejpam-3975	347	2	)	)	PUNCT
ejpam-3975	347	3	or	or	CCONJ
ejpam-3975	347	4	dg(x	dg(x	NUM
ejpam-3975	347	5	,	,	PUNCT
ejpam-3975	347	6	y	y	NOUN
ejpam-3975	347	7	)	)	PUNCT
ejpam-3975	347	8	=	=	SYM
ejpam-3975	348	1	2	2	X
ejpam-3975	348	2	.	.	PUNCT
ejpam-3975	348	3	suppose	suppose	VERB
ejpam-3975	348	4	x	x	SYM
ejpam-3975	348	5	=	=	SYM
ejpam-3975	348	6	y	y	PROPN
ejpam-3975	348	7	and	and	CCONJ
ejpam-3975	348	8	ab	ab	PROPN
ejpam-3975	348	9	/∈	/∈	PUNCT
ejpam-3975	348	10	e(g	e(g	PROPN
ejpam-3975	348	11	)	)	PUNCT
ejpam-3975	348	12	.	.	PUNCT
ejpam-3975	349	1	then	then	ADV
ejpam-3975	349	2	dg[h]((x	dg[h]((x	VERB
ejpam-3975	349	3	,	,	PUNCT
ejpam-3975	349	4	a	a	PRON
ejpam-3975	349	5	)	)	PUNCT
ejpam-3975	349	6	,	,	PUNCT
ejpam-3975	349	7	(	(	PUNCT
ejpam-3975	349	8	y	y	PROPN
ejpam-3975	349	9	,	,	PUNCT
ejpam-3975	349	10	b	b	NOUN
ejpam-3975	349	11	)	)	PUNCT
ejpam-3975	349	12	)	)	PUNCT
ejpam-3975	350	1	=	=	PUNCT
ejpam-3975	350	2	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	350	3	,	,	PUNCT
ejpam-3975	350	4	a	a	PRON
ejpam-3975	350	5	)	)	PUNCT
ejpam-3975	350	6	,	,	PUNCT
ejpam-3975	350	7	(	(	PUNCT
ejpam-3975	350	8	z	z	X
ejpam-3975	350	9	,	,	PUNCT
ejpam-3975	350	10	p	p	NOUN
ejpam-3975	350	11	)	)	PUNCT
ejpam-3975	350	12	)	)	PUNCT
ejpam-3975	351	1	=	=	SYM
ejpam-3975	351	2	2	2	NUM
ejpam-3975	351	3	contrary	contrary	ADV
ejpam-3975	351	4	to	to	ADP
ejpam-3975	351	5	our	our	PRON
ejpam-3975	351	6	assumption	assumption	NOUN
ejpam-3975	351	7	that	that	SCONJ
ejpam-3975	351	8	c	c	PROPN
ejpam-3975	351	9	is	be	AUX
ejpam-3975	351	10	a	a	DET
ejpam-3975	351	11	perfect	perfect	ADJ
ejpam-3975	351	12	hop	hop	NOUN
ejpam-3975	351	13	dominating	dominating	NOUN
ejpam-3975	351	14	set	set	NOUN
ejpam-3975	351	15	of	of	ADP
ejpam-3975	351	16	g[h	g[h	NOUN
ejpam-3975	351	17	]	]	PUNCT
ejpam-3975	351	18	.	.	PUNCT
ejpam-3975	352	1	on	on	ADP
ejpam-3975	352	2	the	the	DET
ejpam-3975	352	3	other	other	ADJ
ejpam-3975	352	4	hand	hand	NOUN
ejpam-3975	352	5	,	,	PUNCT
ejpam-3975	352	6	suppose	suppose	VERB
ejpam-3975	352	7	that	that	SCONJ
ejpam-3975	352	8	dg(x	dg(x	PROPN
ejpam-3975	352	9	,	,	PUNCT
ejpam-3975	352	10	y	y	NOUN
ejpam-3975	352	11	)	)	PUNCT
ejpam-3975	352	12	=	=	SYM
ejpam-3975	353	1	2	2	X
ejpam-3975	353	2	.	.	X
ejpam-3975	354	1	if	if	SCONJ
ejpam-3975	354	2	y	y	PROPN
ejpam-3975	354	3	6=	6=	PROPN
ejpam-3975	354	4	z	z	PROPN
ejpam-3975	354	5	,	,	PUNCT
ejpam-3975	354	6	then	then	ADV
ejpam-3975	354	7	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	354	8	,	,	PUNCT
ejpam-3975	354	9	a	a	PRON
ejpam-3975	354	10	)	)	PUNCT
ejpam-3975	354	11	,	,	PUNCT
ejpam-3975	354	12	(	(	PUNCT
ejpam-3975	354	13	y	y	PROPN
ejpam-3975	354	14	,	,	PUNCT
ejpam-3975	354	15	b	b	NOUN
ejpam-3975	354	16	)	)	PUNCT
ejpam-3975	354	17	)	)	PUNCT
ejpam-3975	355	1	=	=	PUNCT
ejpam-3975	355	2	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	355	3	,	,	PUNCT
ejpam-3975	355	4	a	a	PRON
ejpam-3975	355	5	)	)	PUNCT
ejpam-3975	355	6	,	,	PUNCT
ejpam-3975	355	7	(	(	PUNCT
ejpam-3975	355	8	z	z	X
ejpam-3975	355	9	,	,	PUNCT
ejpam-3975	355	10	p	p	NOUN
ejpam-3975	355	11	)	)	PUNCT
ejpam-3975	355	12	)	)	PUNCT
ejpam-3975	356	1	=	=	SYM
ejpam-3975	356	2	2	2	X
ejpam-3975	356	3	.	.	X
ejpam-3975	357	1	if	if	SCONJ
ejpam-3975	357	2	y	y	PROPN
ejpam-3975	357	3	=	=	SYM
ejpam-3975	357	4	z	z	PROPN
ejpam-3975	357	5	,	,	PUNCT
ejpam-3975	357	6	then	then	ADV
ejpam-3975	357	7	b	b	X
ejpam-3975	357	8	=	=	SYM
ejpam-3975	357	9	p.	p.	NOUN
ejpam-3975	357	10	since	since	SCONJ
ejpam-3975	357	11	γ(h	γ(h	PROPN
ejpam-3975	357	12	)	)	PUNCT
ejpam-3975	357	13	6=	6=	ADP
ejpam-3975	357	14	1	1	NUM
ejpam-3975	357	15	,	,	PUNCT
ejpam-3975	357	16	there	there	PRON
ejpam-3975	357	17	exists	exist	VERB
ejpam-3975	357	18	q	q	PROPN
ejpam-3975	357	19	∈	∈	PROPN
ejpam-3975	357	20	v	v	NOUN
ejpam-3975	357	21	(	(	PUNCT
ejpam-3975	357	22	h)\nh	h)\nh	PROPN
ejpam-3975	358	1	[	[	X
ejpam-3975	358	2	p	p	X
ejpam-3975	358	3	]	]	X
ejpam-3975	358	4	.	.	PUNCT
ejpam-3975	359	1	let	let	VERB
ejpam-3975	359	2	w	w	PROPN
ejpam-3975	359	3	∈	∈	PROPN
ejpam-3975	359	4	tx	tx	PROPN
ejpam-3975	359	5	.	.	PUNCT
ejpam-3975	360	1	then	then	ADV
ejpam-3975	360	2	dg[h]((z	dg[h]((z	VERB
ejpam-3975	360	3	,	,	PUNCT
ejpam-3975	360	4	q	q	NOUN
ejpam-3975	360	5	)	)	PUNCT
ejpam-3975	360	6	,	,	PUNCT
ejpam-3975	360	7	(	(	PUNCT
ejpam-3975	360	8	z	z	X
ejpam-3975	360	9	,	,	PUNCT
ejpam-3975	360	10	p	p	NOUN
ejpam-3975	360	11	)	)	PUNCT
ejpam-3975	360	12	)	)	PUNCT
ejpam-3975	361	1	=	=	SYM
ejpam-3975	361	2	dg[h]((z	dg[h]((z	X
ejpam-3975	361	3	,	,	PUNCT
ejpam-3975	361	4	q	q	NOUN
ejpam-3975	361	5	)	)	PUNCT
ejpam-3975	361	6	,	,	PUNCT
ejpam-3975	361	7	(	(	PUNCT
ejpam-3975	361	8	x	x	NOUN
ejpam-3975	361	9	,	,	PUNCT
ejpam-3975	361	10	w	w	NOUN
ejpam-3975	361	11	)	)	PUNCT
ejpam-3975	361	12	)	)	PUNCT
ejpam-3975	361	13	=	=	SYM
ejpam-3975	362	1	2	2	X
ejpam-3975	362	2	.	.	PUNCT
ejpam-3975	362	3	since	since	SCONJ
ejpam-3975	362	4	(	(	PUNCT
ejpam-3975	362	5	z	z	NOUN
ejpam-3975	362	6	,	,	PUNCT
ejpam-3975	362	7	q	q	NOUN
ejpam-3975	362	8	)	)	PUNCT
ejpam-3975	362	9	/∈	/∈	PUNCT
ejpam-3975	362	10	c	c	NOUN
ejpam-3975	362	11	because	because	SCONJ
ejpam-3975	362	12	|tx|	|tx|	NOUN
ejpam-3975	362	13	=	=	SYM
ejpam-3975	362	14	1	1	NUM
ejpam-3975	362	15	,	,	PUNCT
ejpam-3975	362	16	it	it	PRON
ejpam-3975	362	17	follows	follow	VERB
ejpam-3975	362	18	that	that	SCONJ
ejpam-3975	362	19	c	c	PROPN
ejpam-3975	362	20	is	be	AUX
ejpam-3975	362	21	not	not	PART
ejpam-3975	362	22	a	a	DET
ejpam-3975	362	23	perfect	perfect	ADJ
ejpam-3975	362	24	hop	hop	NOUN
ejpam-3975	362	25	dominating	dominating	NOUN
ejpam-3975	362	26	set	set	NOUN
ejpam-3975	362	27	of	of	ADP
ejpam-3975	362	28	g[h	g[h	PROPN
ejpam-3975	362	29	]	]	X
ejpam-3975	362	30	a	a	DET
ejpam-3975	362	31	contradiction	contradiction	NOUN
ejpam-3975	362	32	to	to	ADP
ejpam-3975	362	33	our	our	PRON
ejpam-3975	362	34	assumption	assumption	NOUN
ejpam-3975	362	35	for	for	ADP
ejpam-3975	362	36	c.	c.	PROPN
ejpam-3975	362	37	therefore	therefore	ADV
ejpam-3975	362	38	tx	tx	PROPN
ejpam-3975	362	39	=	=	SYM
ejpam-3975	362	40	v	v	PROPN
ejpam-3975	362	41	(	(	PUNCT
ejpam-3975	362	42	h	h	NOUN
ejpam-3975	362	43	)	)	PUNCT
ejpam-3975	362	44	.	.	PUNCT
ejpam-3975	363	1	now	now	ADV
ejpam-3975	363	2	,	,	PUNCT
ejpam-3975	363	3	let	let	VERB
ejpam-3975	363	4	ng(x	ng(x	NUM
ejpam-3975	363	5	,	,	PUNCT
ejpam-3975	363	6	2	2	X
ejpam-3975	363	7	)	)	PUNCT
ejpam-3975	363	8	=	=	NOUN
ejpam-3975	363	9	∅	∅	NOUN
ejpam-3975	363	10	and	and	CCONJ
ejpam-3975	363	11	a	a	DET
ejpam-3975	363	12	∈	∈	NOUN
ejpam-3975	363	13	v	v	NOUN
ejpam-3975	363	14	(	(	PUNCT
ejpam-3975	363	15	h)\tx	h)\tx	PROPN
ejpam-3975	363	16	.	.	NOUN
ejpam-3975	364	1	then	then	ADV
ejpam-3975	364	2	(	(	PUNCT
ejpam-3975	364	3	x	x	X
ejpam-3975	364	4	,	,	PUNCT
ejpam-3975	364	5	a	a	PRON
ejpam-3975	364	6	)	)	PUNCT
ejpam-3975	364	7	/∈	/∈	PUNCT
ejpam-3975	365	1	c	c	NOUN
ejpam-3975	366	1	and	and	CCONJ
ejpam-3975	366	2	it	it	PRON
ejpam-3975	366	3	follows	follow	VERB
ejpam-3975	366	4	that	that	SCONJ
ejpam-3975	366	5	there	there	PRON
ejpam-3975	366	6	is	be	VERB
ejpam-3975	366	7	a	a	DET
ejpam-3975	366	8	unique	unique	ADJ
ejpam-3975	366	9	vertex	vertex	NOUN
ejpam-3975	366	10	(	(	PUNCT
ejpam-3975	366	11	y	y	PROPN
ejpam-3975	366	12	,	,	PUNCT
ejpam-3975	366	13	b	b	NOUN
ejpam-3975	366	14	)	)	PUNCT
ejpam-3975	366	15	∈	∈	PROPN
ejpam-3975	366	16	c	c	NOUN
ejpam-3975	366	17	such	such	ADJ
ejpam-3975	366	18	that	that	DET
ejpam-3975	366	19	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	366	20	,	,	PUNCT
ejpam-3975	366	21	a	a	PRON
ejpam-3975	366	22	)	)	PUNCT
ejpam-3975	366	23	,	,	PUNCT
ejpam-3975	366	24	(	(	PUNCT
ejpam-3975	366	25	y	y	PROPN
ejpam-3975	366	26	,	,	PUNCT
ejpam-3975	366	27	b	b	NOUN
ejpam-3975	366	28	)	)	PUNCT
ejpam-3975	366	29	)	)	PUNCT
ejpam-3975	367	1	=	=	SYM
ejpam-3975	367	2	2	2	X
ejpam-3975	367	3	.	.	PUNCT
ejpam-3975	367	4	since	since	SCONJ
ejpam-3975	367	5	ng(x	ng(x	NUM
ejpam-3975	367	6	,	,	PUNCT
ejpam-3975	367	7	2	2	X
ejpam-3975	367	8	)	)	PUNCT
ejpam-3975	367	9	=	=	NOUN
ejpam-3975	367	10	∅	∅	NOUN
ejpam-3975	367	11	,	,	PUNCT
ejpam-3975	367	12	x	x	PROPN
ejpam-3975	367	13	=	=	SYM
ejpam-3975	367	14	y	y	PROPN
ejpam-3975	367	15	and	and	CCONJ
ejpam-3975	367	16	ab	ab	PROPN
ejpam-3975	367	17	/∈	/∈	PUNCT
ejpam-3975	367	18	e(h	e(h	PROPN
ejpam-3975	367	19	)	)	PUNCT
ejpam-3975	367	20	.	.	PUNCT
ejpam-3975	368	1	this	this	PRON
ejpam-3975	368	2	implies	imply	VERB
ejpam-3975	368	3	that	that	SCONJ
ejpam-3975	368	4	tx	tx	PROPN
ejpam-3975	368	5	is	be	AUX
ejpam-3975	368	6	a	a	DET
ejpam-3975	368	7	perfect	perfect	ADJ
ejpam-3975	368	8	point	point	NOUN
ejpam-3975	368	9	-	-	PUNCT
ejpam-3975	368	10	wise	wise	ADJ
ejpam-3975	368	11	non	non	ADJ
ejpam-3975	368	12	-	-	ADJ
ejpam-3975	368	13	dominating	dominating	ADJ
ejpam-3975	368	14	set	set	NOUN
ejpam-3975	368	15	of	of	ADP
ejpam-3975	368	16	h.	h.	PROPN
ejpam-3975	368	17	therefore	therefore	ADV
ejpam-3975	368	18	tx	tx	PROPN
ejpam-3975	368	19	is	be	AUX
ejpam-3975	368	20	a	a	DET
ejpam-3975	368	21	perfect	perfect	ADJ
ejpam-3975	368	22	point	point	NOUN
ejpam-3975	368	23	-	-	PUNCT
ejpam-3975	368	24	wise	wise	ADJ
ejpam-3975	368	25	non	non	ADJ
ejpam-3975	368	26	-	-	ADJ
ejpam-3975	368	27	dominating	dominating	ADJ
ejpam-3975	368	28	set	set	NOUN
ejpam-3975	368	29	of	of	ADP
ejpam-3975	368	30	h	h	NOUN
ejpam-3975	368	31	for	for	ADP
ejpam-3975	368	32	all	all	DET
ejpam-3975	368	33	x	x	SYM
ejpam-3975	368	34	∈	∈	PROPN
ejpam-3975	368	35	s.	s.	PROPN
ejpam-3975	368	36	we	we	PRON
ejpam-3975	368	37	claim	claim	VERB
ejpam-3975	368	38	that	that	SCONJ
ejpam-3975	368	39	tx	tx	PROPN
ejpam-3975	368	40	is	be	AUX
ejpam-3975	368	41	a	a	DET
ejpam-3975	368	42	total	total	ADJ
ejpam-3975	368	43	perfect	perfect	ADJ
ejpam-3975	368	44	point	point	NOUN
ejpam-3975	368	45	-	-	PUNCT
ejpam-3975	368	46	wise	wise	ADJ
ejpam-3975	368	47	non	non	ADJ
ejpam-3975	368	48	-	-	ADJ
ejpam-3975	368	49	dominating	dominating	ADJ
ejpam-3975	368	50	set	set	NOUN
ejpam-3975	368	51	of	of	ADP
ejpam-3975	368	52	h	h	NOUN
ejpam-3975	368	53	for	for	ADP
ejpam-3975	368	54	all	all	DET
ejpam-3975	368	55	x	x	SYM
ejpam-3975	368	56	∈	∈	PROPN
ejpam-3975	368	57	s.	s.	PROPN
ejpam-3975	368	58	let	let	VERB
ejpam-3975	368	59	x	x	PUNCT
ejpam-3975	368	60	∈	∈	PROPN
ejpam-3975	368	61	s	s	X
ejpam-3975	368	62	and	and	CCONJ
ejpam-3975	368	63	c	c	PROPN
ejpam-3975	368	64	∈	∈	PROPN
ejpam-3975	368	65	tx	tx	PROPN
ejpam-3975	368	66	.	.	PUNCT
ejpam-3975	369	1	then	then	ADV
ejpam-3975	369	2	(	(	PUNCT
ejpam-3975	369	3	x	x	X
ejpam-3975	369	4	,	,	PUNCT
ejpam-3975	369	5	c	c	NOUN
ejpam-3975	369	6	)	)	PUNCT
ejpam-3975	369	7	∈	∈	PROPN
ejpam-3975	369	8	c.	c.	NOUN
ejpam-3975	369	9	since	since	SCONJ
ejpam-3975	369	10	c	c	PROPN
ejpam-3975	369	11	is	be	AUX
ejpam-3975	369	12	a	a	DET
ejpam-3975	369	13	total	total	ADJ
ejpam-3975	369	14	perfect	perfect	ADJ
ejpam-3975	369	15	hop	hop	NOUN
ejpam-3975	369	16	dominating	dominating	NOUN
ejpam-3975	369	17	set	set	NOUN
ejpam-3975	369	18	of	of	ADP
ejpam-3975	369	19	g[h	g[h	PROPN
ejpam-3975	369	20	]	]	PUNCT
ejpam-3975	369	21	,	,	PUNCT
ejpam-3975	369	22	there	there	PRON
ejpam-3975	369	23	is	be	VERB
ejpam-3975	369	24	a	a	DET
ejpam-3975	369	25	unique	unique	ADJ
ejpam-3975	369	26	vertex	vertex	NOUN
ejpam-3975	369	27	(	(	PUNCT
ejpam-3975	369	28	y	y	NOUN
ejpam-3975	369	29	,	,	PUNCT
ejpam-3975	369	30	d	d	NOUN
ejpam-3975	369	31	)	)	PUNCT
ejpam-3975	369	32	∈	∈	PROPN
ejpam-3975	369	33	c	c	NOUN
ejpam-3975	369	34	such	such	ADJ
ejpam-3975	369	35	that	that	DET
ejpam-3975	369	36	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	369	37	,	,	PUNCT
ejpam-3975	369	38	c	c	NOUN
ejpam-3975	369	39	)	)	PUNCT
ejpam-3975	369	40	,	,	PUNCT
ejpam-3975	369	41	(	(	PUNCT
ejpam-3975	369	42	y	y	NOUN
ejpam-3975	369	43	,	,	PUNCT
ejpam-3975	369	44	d	d	NOUN
ejpam-3975	369	45	)	)	PUNCT
ejpam-3975	369	46	)	)	PUNCT
ejpam-3975	370	1	=	=	SYM
ejpam-3975	370	2	2	2	X
ejpam-3975	370	3	.	.	PUNCT
ejpam-3975	370	4	since	since	SCONJ
ejpam-3975	370	5	g	g	PROPN
ejpam-3975	370	6	is	be	AUX
ejpam-3975	370	7	complete	complete	ADJ
ejpam-3975	370	8	,	,	PUNCT
ejpam-3975	370	9	x	x	SYM
ejpam-3975	370	10	=	=	PUNCT
ejpam-3975	370	11	y	y	PROPN
ejpam-3975	370	12	and	and	CCONJ
ejpam-3975	370	13	cd	cd	PROPN
ejpam-3975	370	14	/∈	/∈	PUNCT
ejpam-3975	371	1	e(g	e(g	PROPN
ejpam-3975	371	2	)	)	PUNCT
ejpam-3975	372	1	this	this	PRON
ejpam-3975	372	2	implies	imply	VERB
ejpam-3975	372	3	that	that	SCONJ
ejpam-3975	372	4	d	d	PROPN
ejpam-3975	372	5	∈	∈	PROPN
ejpam-3975	372	6	tx	tx	PROPN
ejpam-3975	372	7	and	and	CCONJ
ejpam-3975	372	8	cd	cd	PROPN
ejpam-3975	372	9	/∈	/∈	PUNCT
ejpam-3975	372	10	e(h	e(h	PROPN
ejpam-3975	372	11	)	)	PUNCT
ejpam-3975	372	12	.	.	PUNCT
ejpam-3975	373	1	therefore	therefore	ADV
ejpam-3975	373	2	,	,	PUNCT
ejpam-3975	373	3	tx	tx	PROPN
ejpam-3975	373	4	is	be	AUX
ejpam-3975	373	5	a	a	DET
ejpam-3975	373	6	total	total	ADJ
ejpam-3975	373	7	perfect	perfect	ADJ
ejpam-3975	373	8	point	point	NOUN
ejpam-3975	373	9	-	-	PUNCT
ejpam-3975	373	10	wise	wise	ADJ
ejpam-3975	373	11	non	non	ADJ
ejpam-3975	373	12	-	-	ADJ
ejpam-3975	373	13	dominating	dominating	ADJ
ejpam-3975	373	14	set	set	NOUN
ejpam-3975	373	15	of	of	ADP
ejpam-3975	373	16	h.	h.	NOUN
ejpam-3975	373	17	conversely	conversely	ADV
ejpam-3975	373	18	,	,	PUNCT
ejpam-3975	373	19	let	let	VERB
ejpam-3975	373	20	s	s	PRON
ejpam-3975	373	21	=	=	VERB
ejpam-3975	373	22	v	v	ADJ
ejpam-3975	373	23	(	(	PUNCT
ejpam-3975	373	24	g	g	NOUN
ejpam-3975	373	25	)	)	PUNCT
ejpam-3975	373	26	and	and	CCONJ
ejpam-3975	373	27	tx	tx	AUX
ejpam-3975	373	28	be	be	AUX
ejpam-3975	373	29	a	a	DET
ejpam-3975	373	30	total	total	ADJ
ejpam-3975	373	31	perfect	perfect	ADJ
ejpam-3975	373	32	point	point	NOUN
ejpam-3975	373	33	-	-	PUNCT
ejpam-3975	373	34	wise	wise	ADJ
ejpam-3975	373	35	non	non	ADJ
ejpam-3975	373	36	-	-	ADJ
ejpam-3975	373	37	dominating	dominating	ADJ
ejpam-3975	373	38	set	set	NOUN
ejpam-3975	373	39	of	of	ADP
ejpam-3975	373	40	h	h	NOUN
ejpam-3975	373	41	for	for	ADP
ejpam-3975	373	42	all	all	DET
ejpam-3975	373	43	x	x	SYM
ejpam-3975	373	44	∈	∈	PROPN
ejpam-3975	373	45	s.	s.	PROPN
ejpam-3975	373	46	since	since	SCONJ
ejpam-3975	373	47	every	every	DET
ejpam-3975	373	48	total	total	ADJ
ejpam-3975	373	49	perfect	perfect	ADJ
ejpam-3975	373	50	point	point	NOUN
ejpam-3975	373	51	-	-	PUNCT
ejpam-3975	373	52	wise	wise	ADJ
ejpam-3975	373	53	non	non	ADJ
ejpam-3975	373	54	-	-	ADJ
ejpam-3975	373	55	dominating	dominating	ADJ
ejpam-3975	373	56	set	set	NOUN
ejpam-3975	373	57	is	be	AUX
ejpam-3975	373	58	a	a	DET
ejpam-3975	373	59	perfect	perfect	ADJ
ejpam-3975	373	60	point	point	NOUN
ejpam-3975	373	61	-	-	PUNCT
ejpam-3975	373	62	wise	wise	ADJ
ejpam-3975	373	63	non	non	ADJ
ejpam-3975	373	64	-	-	ADJ
ejpam-3975	373	65	dominating	dominating	ADJ
ejpam-3975	373	66	set	set	NOUN
ejpam-3975	373	67	,	,	PUNCT
ejpam-3975	373	68	tx	tx	PROPN
ejpam-3975	373	69	is	be	AUX
ejpam-3975	373	70	a	a	DET
ejpam-3975	373	71	perfect	perfect	ADJ
ejpam-3975	373	72	point	point	NOUN
ejpam-3975	373	73	-	-	PUNCT
ejpam-3975	373	74	wise	wise	ADJ
ejpam-3975	373	75	non	non	ADJ
ejpam-3975	373	76	-	-	ADJ
ejpam-3975	373	77	dominating	dominating	ADJ
ejpam-3975	373	78	set	set	NOUN
ejpam-3975	373	79	of	of	ADP
ejpam-3975	373	80	h	h	NOUN
ejpam-3975	373	81	for	for	ADP
ejpam-3975	373	82	all	all	DET
ejpam-3975	373	83	x	x	SYM
ejpam-3975	373	84	∈	∈	PROPN
ejpam-3975	373	85	s.	s.	PROPN
ejpam-3975	373	86	let	let	VERB
ejpam-3975	373	87	(	(	PUNCT
ejpam-3975	373	88	x	x	NOUN
ejpam-3975	373	89	,	,	PUNCT
ejpam-3975	373	90	a	a	PRON
ejpam-3975	373	91	)	)	PUNCT
ejpam-3975	373	92	/∈	/∈	PUNCT
ejpam-3975	374	1	c.	c.	NOUN
ejpam-3975	374	2	since	since	SCONJ
ejpam-3975	374	3	s	s	PROPN
ejpam-3975	374	4	=	=	SYM
ejpam-3975	374	5	v	v	PROPN
ejpam-3975	374	6	(	(	PUNCT
ejpam-3975	374	7	g	g	NOUN
ejpam-3975	374	8	)	)	PUNCT
ejpam-3975	374	9	,	,	PUNCT
ejpam-3975	374	10	a	a	PRON
ejpam-3975	374	11	/∈	/∈	X
ejpam-3975	375	1	tx	tx	INTJ
ejpam-3975	375	2	.	.	PUNCT
ejpam-3975	376	1	if	if	SCONJ
ejpam-3975	376	2	ng(x	ng(x	NUM
ejpam-3975	376	3	,	,	PUNCT
ejpam-3975	376	4	2	2	NUM
ejpam-3975	376	5	)	)	PUNCT
ejpam-3975	376	6	6=	6=	ADP
ejpam-3975	376	7	∅	∅	NOUN
ejpam-3975	376	8	,	,	PUNCT
ejpam-3975	376	9	then	then	ADV
ejpam-3975	376	10	we	we	PRON
ejpam-3975	376	11	are	be	AUX
ejpam-3975	376	12	done	do	VERB
ejpam-3975	376	13	since	since	SCONJ
ejpam-3975	376	14	tx	tx	PROPN
ejpam-3975	376	15	=	=	SYM
ejpam-3975	376	16	v	v	PROPN
ejpam-3975	376	17	(	(	PUNCT
ejpam-3975	376	18	h	h	NOUN
ejpam-3975	376	19	)	)	PUNCT
ejpam-3975	376	20	.	.	PUNCT
ejpam-3975	377	1	if	if	SCONJ
ejpam-3975	377	2	ng(x	ng(x	NUM
ejpam-3975	377	3	,	,	PUNCT
ejpam-3975	377	4	2	2	X
ejpam-3975	377	5	)	)	PUNCT
ejpam-3975	377	6	=	=	NOUN
ejpam-3975	377	7	∅	∅	NOUN
ejpam-3975	377	8	,	,	PUNCT
ejpam-3975	377	9	then	then	ADV
ejpam-3975	377	10	there	there	PRON
ejpam-3975	377	11	exists	exist	VERB
ejpam-3975	377	12	a	a	DET
ejpam-3975	377	13	unique	unique	ADJ
ejpam-3975	377	14	vertex	vertex	NOUN
ejpam-3975	377	15	b	b	NOUN
ejpam-3975	377	16	∈	∈	PROPN
ejpam-3975	377	17	tx	tx	VERB
ejpam-3975	377	18	such	such	ADJ
ejpam-3975	377	19	that	that	SCONJ
ejpam-3975	377	20	ab	ab	PROPN
ejpam-3975	377	21	/∈	/∈	PUNCT
ejpam-3975	377	22	e(h	e(h	PROPN
ejpam-3975	377	23	)	)	PUNCT
ejpam-3975	377	24	.	.	PUNCT
ejpam-3975	378	1	thus	thus	ADV
ejpam-3975	378	2	,	,	PUNCT
ejpam-3975	378	3	(	(	PUNCT
ejpam-3975	378	4	x	x	X
ejpam-3975	378	5	,	,	PUNCT
ejpam-3975	378	6	b	b	NOUN
ejpam-3975	378	7	)	)	PUNCT
ejpam-3975	378	8	∈	∈	PROPN
ejpam-3975	378	9	c	c	PROPN
ejpam-3975	378	10	and	and	CCONJ
ejpam-3975	378	11	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	378	12	,	,	PUNCT
ejpam-3975	378	13	a	a	PRON
ejpam-3975	378	14	)	)	PUNCT
ejpam-3975	378	15	,	,	PUNCT
ejpam-3975	378	16	(	(	PUNCT
ejpam-3975	378	17	x	x	NOUN
ejpam-3975	378	18	,	,	PUNCT
ejpam-3975	378	19	b	b	NOUN
ejpam-3975	378	20	)	)	PUNCT
ejpam-3975	378	21	)	)	PUNCT
ejpam-3975	379	1	=	=	SYM
ejpam-3975	379	2	2	2	X
ejpam-3975	379	3	.	.	PUNCT
ejpam-3975	379	4	accordingly	accordingly	ADV
ejpam-3975	379	5	,	,	PUNCT
ejpam-3975	379	6	c	c	PROPN
ejpam-3975	379	7	is	be	AUX
ejpam-3975	379	8	a	a	DET
ejpam-3975	379	9	perfect	perfect	ADJ
ejpam-3975	379	10	hop	hop	NOUN
ejpam-3975	379	11	dominating	dominating	NOUN
ejpam-3975	379	12	set	set	NOUN
ejpam-3975	379	13	of	of	ADP
ejpam-3975	379	14	g[h	g[h	PROPN
ejpam-3975	379	15	]	]	PUNCT
ejpam-3975	379	16	.	.	PUNCT
ejpam-3975	380	1	let	let	VERB
ejpam-3975	380	2	(	(	PUNCT
ejpam-3975	380	3	x	x	NOUN
ejpam-3975	380	4	,	,	PUNCT
ejpam-3975	380	5	a	a	DET
ejpam-3975	380	6	)	)	PUNCT
ejpam-3975	380	7	∈	∈	PROPN
ejpam-3975	380	8	c.	c.	NOUN
ejpam-3975	380	9	then	then	ADV
ejpam-3975	380	10	x	x	SYM
ejpam-3975	380	11	∈	∈	PROPN
ejpam-3975	380	12	s	s	X
ejpam-3975	380	13	and	and	CCONJ
ejpam-3975	380	14	a	a	DET
ejpam-3975	380	15	∈	∈	PROPN
ejpam-3975	380	16	tx	tx	PROPN
ejpam-3975	380	17	.	.	PUNCT
ejpam-3975	381	1	since	since	SCONJ
ejpam-3975	381	2	tx	tx	PROPN
ejpam-3975	381	3	is	be	AUX
ejpam-3975	381	4	a	a	DET
ejpam-3975	381	5	total	total	ADJ
ejpam-3975	381	6	perfect	perfect	ADJ
ejpam-3975	381	7	point	point	NOUN
ejpam-3975	381	8	-	-	PUNCT
ejpam-3975	381	9	wise	wise	ADJ
ejpam-3975	381	10	non	non	ADJ
ejpam-3975	381	11	-	-	ADJ
ejpam-3975	381	12	dominating	dominating	ADJ
ejpam-3975	381	13	set	set	NOUN
ejpam-3975	381	14	of	of	ADP
ejpam-3975	381	15	h	h	NOUN
ejpam-3975	381	16	,	,	PUNCT
ejpam-3975	381	17	there	there	PRON
ejpam-3975	381	18	is	be	VERB
ejpam-3975	381	19	a	a	DET
ejpam-3975	381	20	unique	unique	ADJ
ejpam-3975	381	21	vertex	vertex	NOUN
ejpam-3975	381	22	b	b	NOUN
ejpam-3975	381	23	∈	∈	PROPN
ejpam-3975	381	24	tx	tx	VERB
ejpam-3975	381	25	such	such	ADJ
ejpam-3975	381	26	that	that	SCONJ
ejpam-3975	381	27	ab	ab	PROPN
ejpam-3975	381	28	/∈	/∈	PUNCT
ejpam-3975	381	29	e(h	e(h	PROPN
ejpam-3975	381	30	)	)	PUNCT
ejpam-3975	381	31	.	.	PUNCT
ejpam-3975	382	1	since	since	SCONJ
ejpam-3975	382	2	g	g	PROPN
ejpam-3975	382	3	is	be	AUX
ejpam-3975	382	4	a	a	DET
ejpam-3975	382	5	nontrivial	nontrivial	ADJ
ejpam-3975	382	6	complete	complete	ADJ
ejpam-3975	382	7	graph	graph	NOUN
ejpam-3975	382	8	,	,	PUNCT
ejpam-3975	382	9	there	there	PRON
ejpam-3975	382	10	exists	exist	VERB
ejpam-3975	382	11	y	y	PROPN
ejpam-3975	382	12	∈	∈	PROPN
ejpam-3975	382	13	v	v	PROPN
ejpam-3975	382	14	(	(	PUNCT
ejpam-3975	382	15	g)∩ng(x	g)∩ng(x	PROPN
ejpam-3975	382	16	)	)	PUNCT
ejpam-3975	382	17	.	.	PUNCT
ejpam-3975	383	1	thus	thus	ADV
ejpam-3975	383	2	,	,	PUNCT
ejpam-3975	383	3	r.	r.	PROPN
ejpam-3975	383	4	rakim	rakim	PROPN
ejpam-3975	383	5	,	,	PUNCT
ejpam-3975	383	6	h.	h.	PROPN
ejpam-3975	383	7	rara	rara	PROPN
ejpam-3975	383	8	/	/	SYM
ejpam-3975	383	9	eur	eur	PROPN
ejpam-3975	383	10	.	.	PUNCT
ejpam-3975	384	1	j.	j.	PROPN
ejpam-3975	384	2	pure	pure	PROPN
ejpam-3975	384	3	appl	appl	PROPN
ejpam-3975	384	4	.	.	PROPN
ejpam-3975	384	5	math	math	PROPN
ejpam-3975	384	6	,	,	PUNCT
ejpam-3975	384	7	14	14	NUM
ejpam-3975	384	8	(	(	PUNCT
ejpam-3975	384	9	3	3	NUM
ejpam-3975	384	10	)	)	PUNCT
ejpam-3975	384	11	(	(	PUNCT
ejpam-3975	384	12	2021	2021	NUM
ejpam-3975	384	13	)	)	PUNCT
ejpam-3975	384	14	,	,	PUNCT
ejpam-3975	384	15	803	803	NUM
ejpam-3975	384	16	-	-	SYM
ejpam-3975	384	17	815	815	NUM
ejpam-3975	384	18	814	814	NUM
ejpam-3975	384	19	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	384	20	,	,	PUNCT
ejpam-3975	384	21	a	a	NOUN
ejpam-3975	384	22	)	)	PUNCT
ejpam-3975	384	23	,	,	PUNCT
ejpam-3975	384	24	(	(	PUNCT
ejpam-3975	384	25	x	x	NOUN
ejpam-3975	384	26	,	,	PUNCT
ejpam-3975	384	27	b	b	NOUN
ejpam-3975	384	28	)	)	PUNCT
ejpam-3975	384	29	)	)	PUNCT
ejpam-3975	385	1	=	=	PUNCT
ejpam-3975	385	2	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	385	3	,	,	PUNCT
ejpam-3975	385	4	a	a	PRON
ejpam-3975	385	5	)	)	PUNCT
ejpam-3975	385	6	,	,	PUNCT
ejpam-3975	385	7	(	(	PUNCT
ejpam-3975	385	8	y	y	NOUN
ejpam-3975	385	9	,	,	PUNCT
ejpam-3975	385	10	a	a	PRON
ejpam-3975	385	11	)	)	PUNCT
ejpam-3975	385	12	)	)	PUNCT
ejpam-3975	386	1	+	+	CCONJ
ejpam-3975	386	2	dg[h]((y	dg[h]((y	NOUN
ejpam-3975	386	3	,	,	PUNCT
ejpam-3975	386	4	a	a	PRON
ejpam-3975	386	5	)	)	PUNCT
ejpam-3975	386	6	,	,	PUNCT
ejpam-3975	386	7	(	(	PUNCT
ejpam-3975	386	8	x	x	NOUN
ejpam-3975	386	9	,	,	PUNCT
ejpam-3975	386	10	b	b	NOUN
ejpam-3975	386	11	)	)	PUNCT
ejpam-3975	386	12	)	)	PUNCT
ejpam-3975	387	1	=	=	SYM
ejpam-3975	387	2	1	1	NUM
ejpam-3975	388	1	+	+	SYM
ejpam-3975	388	2	1	1	NUM
ejpam-3975	388	3	=	=	SYM
ejpam-3975	388	4	2	2	NUM
ejpam-3975	388	5	.	.	PUNCT
ejpam-3975	389	1	since	since	SCONJ
ejpam-3975	389	2	b	b	NOUN
ejpam-3975	389	3	is	be	AUX
ejpam-3975	389	4	unique	unique	ADJ
ejpam-3975	389	5	,	,	PUNCT
ejpam-3975	389	6	(	(	PUNCT
ejpam-3975	389	7	x	x	NOUN
ejpam-3975	389	8	,	,	PUNCT
ejpam-3975	389	9	b	b	NOUN
ejpam-3975	389	10	)	)	PUNCT
ejpam-3975	389	11	is	be	AUX
ejpam-3975	389	12	a	a	DET
ejpam-3975	389	13	unique	unique	ADJ
ejpam-3975	389	14	vertex	vertex	NOUN
ejpam-3975	389	15	in	in	ADP
ejpam-3975	389	16	c.	c.	PROPN
ejpam-3975	389	17	therefore	therefore	ADV
ejpam-3975	389	18	c	c	PROPN
ejpam-3975	389	19	is	be	AUX
ejpam-3975	389	20	a	a	DET
ejpam-3975	389	21	total	total	ADJ
ejpam-3975	389	22	perfect	perfect	ADJ
ejpam-3975	389	23	hop	hop	NOUN
ejpam-3975	389	24	dominating	dominating	NOUN
ejpam-3975	389	25	set	set	NOUN
ejpam-3975	389	26	of	of	ADP
ejpam-3975	389	27	g[h	g[h	PROPN
ejpam-3975	389	28	]	]	PUNCT
ejpam-3975	389	29	.	.	PUNCT
ejpam-3975	390	1	�	�	PROPN
ejpam-3975	390	2	corollary	corollary	ADJ
ejpam-3975	390	3	5.2	5.2	NUM
ejpam-3975	390	4	.	.	PUNCT
ejpam-3975	391	1	let	let	VERB
ejpam-3975	391	2	g	g	PRON
ejpam-3975	391	3	be	be	AUX
ejpam-3975	391	4	a	a	DET
ejpam-3975	391	5	nontrivial	nontrivial	ADJ
ejpam-3975	391	6	complete	complete	ADJ
ejpam-3975	391	7	graph	graph	NOUN
ejpam-3975	391	8	and	and	CCONJ
ejpam-3975	391	9	h	h	NOUN
ejpam-3975	391	10	a	a	DET
ejpam-3975	391	11	nontrivial	nontrivial	ADJ
ejpam-3975	391	12	connected	connect	VERB
ejpam-3975	391	13	non	non	ADJ
ejpam-3975	391	14	-	-	ADJ
ejpam-3975	391	15	complete	complete	ADJ
ejpam-3975	391	16	graph	graph	NOUN
ejpam-3975	391	17	whose	whose	DET
ejpam-3975	391	18	total	total	ADJ
ejpam-3975	391	19	perfect	perfect	ADJ
ejpam-3975	391	20	point	point	NOUN
ejpam-3975	391	21	-	-	PUNCT
ejpam-3975	391	22	wise	wise	ADJ
ejpam-3975	391	23	non	non	ADJ
ejpam-3975	391	24	-	-	ADJ
ejpam-3975	391	25	dominating	dominating	ADJ
ejpam-3975	391	26	set	set	NOUN
ejpam-3975	391	27	exists	exist	VERB
ejpam-3975	391	28	.	.	PUNCT
ejpam-3975	392	1	then	then	ADV
ejpam-3975	392	2	γtph(g[h	γtph(g[h	ADJ
ejpam-3975	392	3	]	]	X
ejpam-3975	392	4	)	)	PUNCT
ejpam-3975	392	5	=	=	SYM
ejpam-3975	392	6	|v	|v	PROPN
ejpam-3975	392	7	(	(	PUNCT
ejpam-3975	392	8	g)|	g)|	PROPN
ejpam-3975	392	9	·	·	PUNCT
ejpam-3975	392	10	tppnd(h	tppnd(h	PROPN
ejpam-3975	392	11	)	)	PUNCT
ejpam-3975	392	12	.	.	PUNCT
ejpam-3975	393	1	proof	proof	NOUN
ejpam-3975	393	2	.	.	PUNCT
ejpam-3975	394	1	let	let	VERB
ejpam-3975	394	2	c	c	NOUN
ejpam-3975	394	3	=	=	PUNCT
ejpam-3975	395	1	⋃	⋃	PROPN
ejpam-3975	395	2	x∈s	x∈s	NOUN
ejpam-3975	396	1	[	[	X
ejpam-3975	396	2	{	{	PUNCT
ejpam-3975	396	3	x	x	NOUN
ejpam-3975	396	4	}	}	PUNCT
ejpam-3975	396	5	×	×	PROPN
ejpam-3975	396	6	tx	tx	PROPN
ejpam-3975	396	7	]	]	PUNCT
ejpam-3975	396	8	be	be	AUX
ejpam-3975	396	9	a	a	DET
ejpam-3975	396	10	minimum	minimum	ADJ
ejpam-3975	396	11	total	total	NOUN
ejpam-3975	396	12	perfect	perfect	ADJ
ejpam-3975	396	13	hop	hop	NOUN
ejpam-3975	396	14	dominating	dominating	NOUN
ejpam-3975	396	15	set	set	NOUN
ejpam-3975	396	16	of	of	ADP
ejpam-3975	396	17	g[h	g[h	NOUN
ejpam-3975	396	18	]	]	PUNCT
ejpam-3975	396	19	.	.	PUNCT
ejpam-3975	397	1	by	by	ADP
ejpam-3975	397	2	theorem	theorem	NOUN
ejpam-3975	397	3	5.1	5.1	NUM
ejpam-3975	397	4	,	,	PUNCT
ejpam-3975	397	5	s	s	PART
ejpam-3975	397	6	=	=	SYM
ejpam-3975	397	7	v	v	X
ejpam-3975	397	8	(	(	PUNCT
ejpam-3975	397	9	g	g	NOUN
ejpam-3975	397	10	)	)	PUNCT
ejpam-3975	397	11	and	and	CCONJ
ejpam-3975	397	12	tx	tx	PROPN
ejpam-3975	397	13	is	be	AUX
ejpam-3975	397	14	a	a	DET
ejpam-3975	397	15	minimum	minimum	ADJ
ejpam-3975	397	16	total	total	NOUN
ejpam-3975	397	17	perfect	perfect	ADJ
ejpam-3975	397	18	point	point	NOUN
ejpam-3975	397	19	-	-	PUNCT
ejpam-3975	397	20	wise	wise	ADJ
ejpam-3975	397	21	non	non	ADJ
ejpam-3975	397	22	-	-	ADJ
ejpam-3975	397	23	dominating	dominating	ADJ
ejpam-3975	397	24	set	set	NOUN
ejpam-3975	397	25	of	of	ADP
ejpam-3975	397	26	h	h	NOUN
ejpam-3975	397	27	for	for	ADP
ejpam-3975	397	28	all	all	DET
ejpam-3975	397	29	x	x	SYM
ejpam-3975	397	30	∈	∈	PROPN
ejpam-3975	397	31	s.	s.	PROPN
ejpam-3975	397	32	therefore	therefore	ADV
ejpam-3975	397	33	γtph(g[h	γtph(g[h	PROPN
ejpam-3975	397	34	]	]	X
ejpam-3975	397	35	)	)	PUNCT
ejpam-3975	398	1	=	=	SYM
ejpam-3975	398	2	|c|	|c|	PROPN
ejpam-3975	398	3	=	=	PUNCT
ejpam-3975	398	4	∑	∑	PUNCT
ejpam-3975	398	5	x∈v	x∈v	PROPN
ejpam-3975	398	6	(	(	PUNCT
ejpam-3975	398	7	g	g	NOUN
ejpam-3975	398	8	)	)	PUNCT
ejpam-3975	398	9	|tx|	|tx|	NOUN
ejpam-3975	398	10	=	=	SYM
ejpam-3975	398	11	|v	|v	PROPN
ejpam-3975	398	12	(	(	PUNCT
ejpam-3975	398	13	g)|	g)|	PROPN
ejpam-3975	398	14	·	·	SYM
ejpam-3975	398	15	tppnd(h	tppnd(h	PROPN
ejpam-3975	398	16	)	)	PUNCT
ejpam-3975	398	17	�	�	PROPN
ejpam-3975	398	18	theorem	theorem	VERB
ejpam-3975	398	19	5.3	5.3	NUM
ejpam-3975	398	20	.	.	PUNCT
ejpam-3975	399	1	let	let	VERB
ejpam-3975	399	2	g	g	PRON
ejpam-3975	399	3	be	be	AUX
ejpam-3975	399	4	a	a	DET
ejpam-3975	399	5	nontrivial	nontrivial	ADJ
ejpam-3975	399	6	connected	connect	VERB
ejpam-3975	399	7	graph	graph	NOUN
ejpam-3975	399	8	whose	whose	DET
ejpam-3975	399	9	total	total	ADJ
ejpam-3975	399	10	perfect	perfect	ADJ
ejpam-3975	399	11	hop	hop	NOUN
ejpam-3975	399	12	dominating	dominating	NOUN
ejpam-3975	399	13	set	set	NOUN
ejpam-3975	399	14	exists	exist	VERB
ejpam-3975	399	15	and	and	CCONJ
ejpam-3975	399	16	h	h	DET
ejpam-3975	399	17	a	a	DET
ejpam-3975	399	18	nontrivial	nontrivial	ADJ
ejpam-3975	399	19	connected	connect	VERB
ejpam-3975	399	20	graph	graph	NOUN
ejpam-3975	399	21	with	with	ADP
ejpam-3975	399	22	γ(h	γ(h	NOUN
ejpam-3975	399	23	)	)	PUNCT
ejpam-3975	399	24	=	=	SYM
ejpam-3975	400	1	1	1	X
ejpam-3975	400	2	.	.	PUNCT
ejpam-3975	400	3	then	then	ADV
ejpam-3975	400	4	a	a	DET
ejpam-3975	400	5	nonempty	nonempty	NOUN
ejpam-3975	400	6	subset	subset	VERB
ejpam-3975	400	7	c	c	NOUN
ejpam-3975	400	8	=	=	PUNCT
ejpam-3975	400	9	⋃	⋃	PROPN
ejpam-3975	400	10	x∈s	x∈s	NOUN
ejpam-3975	401	1	[	[	X
ejpam-3975	401	2	{	{	PUNCT
ejpam-3975	401	3	x	x	NOUN
ejpam-3975	401	4	}	}	PUNCT
ejpam-3975	401	5	×	×	PROPN
ejpam-3975	401	6	tx	tx	PROPN
ejpam-3975	401	7	]	]	PUNCT
ejpam-3975	401	8	of	of	ADP
ejpam-3975	401	9	v	v	NOUN
ejpam-3975	401	10	(	(	PUNCT
ejpam-3975	401	11	g[h	g[h	PROPN
ejpam-3975	401	12	]	]	PUNCT
ejpam-3975	401	13	)	)	PUNCT
ejpam-3975	401	14	where	where	SCONJ
ejpam-3975	401	15	s	s	VERB
ejpam-3975	401	16	⊆	⊆	NUM
ejpam-3975	401	17	v	v	NOUN
ejpam-3975	401	18	(	(	PUNCT
ejpam-3975	401	19	g	g	NOUN
ejpam-3975	401	20	)	)	PUNCT
ejpam-3975	401	21	and	and	CCONJ
ejpam-3975	401	22	tx	tx	VERB
ejpam-3975	401	23	⊆	⊆	NUM
ejpam-3975	401	24	v	v	NOUN
ejpam-3975	401	25	(	(	PUNCT
ejpam-3975	401	26	h	h	NOUN
ejpam-3975	401	27	)	)	PUNCT
ejpam-3975	401	28	for	for	ADP
ejpam-3975	401	29	all	all	PRON
ejpam-3975	401	30	x	x	SYM
ejpam-3975	401	31	∈	∈	PROPN
ejpam-3975	401	32	s	s	NOUN
ejpam-3975	401	33	,	,	PUNCT
ejpam-3975	401	34	is	be	AUX
ejpam-3975	401	35	a	a	DET
ejpam-3975	401	36	total	total	ADJ
ejpam-3975	401	37	perfect	perfect	ADJ
ejpam-3975	401	38	hop	hop	NOUN
ejpam-3975	401	39	dominating	dominating	NOUN
ejpam-3975	401	40	set	set	NOUN
ejpam-3975	401	41	of	of	ADP
ejpam-3975	401	42	g[h	g[h	PROPN
ejpam-3975	401	43	]	]	PUNCT
ejpam-3975	401	44	if	if	SCONJ
ejpam-3975	402	1	and	and	CCONJ
ejpam-3975	402	2	only	only	ADV
ejpam-3975	402	3	if	if	SCONJ
ejpam-3975	402	4	s	s	NOUN
ejpam-3975	402	5	is	be	AUX
ejpam-3975	402	6	a	a	DET
ejpam-3975	402	7	total	total	ADJ
ejpam-3975	402	8	perfect	perfect	ADJ
ejpam-3975	402	9	hop	hop	NOUN
ejpam-3975	402	10	dominating	dominating	NOUN
ejpam-3975	402	11	set	set	NOUN
ejpam-3975	402	12	of	of	ADP
ejpam-3975	402	13	g	g	PROPN
ejpam-3975	402	14	and	and	CCONJ
ejpam-3975	402	15	tx	tx	PROPN
ejpam-3975	402	16	is	be	AUX
ejpam-3975	402	17	a	a	DET
ejpam-3975	402	18	γ	γ	NOUN
ejpam-3975	402	19	-	-	PUNCT
ejpam-3975	402	20	set	set	NOUN
ejpam-3975	402	21	of	of	ADP
ejpam-3975	402	22	h.	h.	NOUN
ejpam-3975	402	23	proof	proof	NOUN
ejpam-3975	402	24	.	.	PUNCT
ejpam-3975	403	1	let	let	VERB
ejpam-3975	403	2	c	c	NOUN
ejpam-3975	403	3	=	=	PUNCT
ejpam-3975	404	1	⋃	⋃	PROPN
ejpam-3975	404	2	x∈s	x∈s	NOUN
ejpam-3975	405	1	[	[	X
ejpam-3975	405	2	{	{	PUNCT
ejpam-3975	405	3	x	x	NOUN
ejpam-3975	405	4	}	}	PUNCT
ejpam-3975	405	5	×	×	PROPN
ejpam-3975	405	6	tx	tx	PROPN
ejpam-3975	405	7	]	]	X
ejpam-3975	405	8	,	,	PUNCT
ejpam-3975	405	9	where	where	SCONJ
ejpam-3975	405	10	s	s	VERB
ejpam-3975	405	11	⊆	⊆	NUM
ejpam-3975	405	12	v	v	NOUN
ejpam-3975	405	13	(	(	PUNCT
ejpam-3975	405	14	g	g	NOUN
ejpam-3975	405	15	)	)	PUNCT
ejpam-3975	405	16	and	and	CCONJ
ejpam-3975	405	17	tx	tx	VERB
ejpam-3975	405	18	⊆	⊆	NUM
ejpam-3975	405	19	v	v	NOUN
ejpam-3975	405	20	(	(	PUNCT
ejpam-3975	405	21	h	h	NOUN
ejpam-3975	405	22	)	)	PUNCT
ejpam-3975	405	23	for	for	ADP
ejpam-3975	405	24	all	all	PRON
ejpam-3975	405	25	x	x	SYM
ejpam-3975	405	26	∈	∈	PROPN
ejpam-3975	405	27	s	s	AUX
ejpam-3975	405	28	,	,	PUNCT
ejpam-3975	405	29	be	be	AUX
ejpam-3975	405	30	a	a	DET
ejpam-3975	405	31	total	total	ADJ
ejpam-3975	405	32	perfect	perfect	ADJ
ejpam-3975	405	33	hop	hop	NOUN
ejpam-3975	405	34	dominating	dominating	NOUN
ejpam-3975	405	35	set	set	NOUN
ejpam-3975	405	36	of	of	ADP
ejpam-3975	405	37	g[h	g[h	PROPN
ejpam-3975	405	38	]	]	PUNCT
ejpam-3975	405	39	.	.	PUNCT
ejpam-3975	406	1	then	then	ADV
ejpam-3975	406	2	c	c	PROPN
ejpam-3975	406	3	is	be	AUX
ejpam-3975	406	4	a	a	DET
ejpam-3975	406	5	perfect	perfect	ADJ
ejpam-3975	406	6	hop	hop	NOUN
ejpam-3975	406	7	dominating	dominating	NOUN
ejpam-3975	406	8	set	set	NOUN
ejpam-3975	406	9	of	of	ADP
ejpam-3975	406	10	g[h	g[h	NOUN
ejpam-3975	406	11	]	]	PUNCT
ejpam-3975	406	12	.	.	PUNCT
ejpam-3975	407	1	we	we	PRON
ejpam-3975	407	2	claim	claim	VERB
ejpam-3975	407	3	that	that	SCONJ
ejpam-3975	407	4	s	s	VERB
ejpam-3975	407	5	is	be	AUX
ejpam-3975	407	6	a	a	DET
ejpam-3975	407	7	total	total	ADJ
ejpam-3975	407	8	perfect	perfect	ADJ
ejpam-3975	407	9	hop	hop	NOUN
ejpam-3975	407	10	dominating	dominating	NOUN
ejpam-3975	407	11	set	set	NOUN
ejpam-3975	407	12	of	of	ADP
ejpam-3975	407	13	g.	g.	PROPN
ejpam-3975	407	14	let	let	VERB
ejpam-3975	407	15	u	u	PRON
ejpam-3975	407	16	∈	∈	PROPN
ejpam-3975	407	17	v	v	ADP
ejpam-3975	407	18	(	(	PUNCT
ejpam-3975	407	19	g	g	NOUN
ejpam-3975	407	20	)	)	PUNCT
ejpam-3975	407	21	.	.	PUNCT
ejpam-3975	408	1	if	if	SCONJ
ejpam-3975	408	2	u	u	PROPN
ejpam-3975	408	3	/∈	/∈	PUNCT
ejpam-3975	408	4	s	s	PART
ejpam-3975	408	5	,	,	PUNCT
ejpam-3975	408	6	then	then	ADV
ejpam-3975	408	7	(	(	PUNCT
ejpam-3975	408	8	u	u	NOUN
ejpam-3975	408	9	,	,	PUNCT
ejpam-3975	408	10	a	a	PRON
ejpam-3975	408	11	)	)	PUNCT
ejpam-3975	408	12	/∈	/∈	PUNCT
ejpam-3975	409	1	c	c	NOUN
ejpam-3975	409	2	for	for	ADP
ejpam-3975	409	3	any	any	DET
ejpam-3975	409	4	a	a	DET
ejpam-3975	409	5	∈	∈	PROPN
ejpam-3975	409	6	v	v	NOUN
ejpam-3975	409	7	(	(	PUNCT
ejpam-3975	409	8	h	h	NOUN
ejpam-3975	409	9	)	)	PUNCT
ejpam-3975	409	10	.	.	PUNCT
ejpam-3975	410	1	thus	thus	ADV
ejpam-3975	410	2	,	,	PUNCT
ejpam-3975	410	3	there	there	PRON
ejpam-3975	410	4	is	be	VERB
ejpam-3975	410	5	exactly	exactly	ADV
ejpam-3975	410	6	one	one	NUM
ejpam-3975	410	7	vertex	vertex	NOUN
ejpam-3975	410	8	(	(	PUNCT
ejpam-3975	410	9	v	v	NOUN
ejpam-3975	410	10	,	,	PUNCT
ejpam-3975	410	11	b	b	NOUN
ejpam-3975	410	12	)	)	PUNCT
ejpam-3975	410	13	∈	∈	PROPN
ejpam-3975	410	14	c	c	NOUN
ejpam-3975	410	15	such	such	ADJ
ejpam-3975	410	16	that	that	SCONJ
ejpam-3975	410	17	dg[h]((u	dg[h]((u	NOUN
ejpam-3975	410	18	,	,	PUNCT
ejpam-3975	410	19	a	a	PRON
ejpam-3975	410	20	)	)	PUNCT
ejpam-3975	410	21	,	,	PUNCT
ejpam-3975	410	22	(	(	PUNCT
ejpam-3975	410	23	v	v	NOUN
ejpam-3975	410	24	,	,	PUNCT
ejpam-3975	410	25	b	b	NOUN
ejpam-3975	410	26	)	)	PUNCT
ejpam-3975	410	27	)	)	PUNCT
ejpam-3975	411	1	=	=	SYM
ejpam-3975	411	2	2	2	X
ejpam-3975	411	3	.	.	PUNCT
ejpam-3975	411	4	since	since	SCONJ
ejpam-3975	411	5	u	u	PROPN
ejpam-3975	411	6	/∈	/∈	PROPN
ejpam-3975	411	7	s	s	PART
ejpam-3975	411	8	and	and	CCONJ
ejpam-3975	411	9	v	v	ADP
ejpam-3975	411	10	∈	∈	PROPN
ejpam-3975	411	11	s	s	PROPN
ejpam-3975	411	12	,	,	PUNCT
ejpam-3975	411	13	u	u	PROPN
ejpam-3975	411	14	6=	6=	PROPN
ejpam-3975	411	15	v	v	ADP
ejpam-3975	411	16	and	and	CCONJ
ejpam-3975	411	17	dg(u	dg(u	NOUN
ejpam-3975	411	18	,	,	PUNCT
ejpam-3975	411	19	v	v	NOUN
ejpam-3975	411	20	)	)	PUNCT
ejpam-3975	411	21	=	=	SYM
ejpam-3975	411	22	2	2	X
ejpam-3975	411	23	.	.	PUNCT
ejpam-3975	411	24	suppose	suppose	VERB
ejpam-3975	411	25	u	u	PROPN
ejpam-3975	411	26	∈	∈	PROPN
ejpam-3975	411	27	s.	s.	PROPN
ejpam-3975	411	28	since	since	SCONJ
ejpam-3975	411	29	g	g	PROPN
ejpam-3975	411	30	has	have	VERB
ejpam-3975	411	31	a	a	DET
ejpam-3975	411	32	total	total	ADJ
ejpam-3975	411	33	perfect	perfect	ADJ
ejpam-3975	411	34	hop	hop	NOUN
ejpam-3975	411	35	dominating	dominating	NOUN
ejpam-3975	411	36	set	set	NOUN
ejpam-3975	411	37	,	,	PUNCT
ejpam-3975	411	38	ng(u	ng(u	NOUN
ejpam-3975	411	39	,	,	PUNCT
ejpam-3975	411	40	2	2	NUM
ejpam-3975	411	41	)	)	PUNCT
ejpam-3975	411	42	6=	6=	ADP
ejpam-3975	411	43	∅.	∅.	AUX
ejpam-3975	411	44	let	let	VERB
ejpam-3975	411	45	z	z	PROPN
ejpam-3975	411	46	∈	∈	PROPN
ejpam-3975	411	47	ng(u	ng(u	NOUN
ejpam-3975	411	48	,	,	PUNCT
ejpam-3975	411	49	2	2	NUM
ejpam-3975	411	50	)	)	PUNCT
ejpam-3975	411	51	.	.	PUNCT
ejpam-3975	412	1	if	if	SCONJ
ejpam-3975	412	2	z	z	PROPN
ejpam-3975	412	3	∈	∈	PROPN
ejpam-3975	412	4	s	s	PART
ejpam-3975	412	5	,	,	PUNCT
ejpam-3975	412	6	then	then	ADV
ejpam-3975	412	7	we	we	PRON
ejpam-3975	412	8	are	be	AUX
ejpam-3975	412	9	done	do	VERB
ejpam-3975	412	10	.	.	PUNCT
ejpam-3975	413	1	so	so	ADV
ejpam-3975	413	2	suppose	suppose	VERB
ejpam-3975	413	3	that	that	SCONJ
ejpam-3975	413	4	z	z	PROPN
ejpam-3975	413	5	/∈	/∈	PUNCT
ejpam-3975	413	6	s.	s.	PROPN
ejpam-3975	413	7	then	then	ADV
ejpam-3975	413	8	|tu|	|tu|	NOUN
ejpam-3975	413	9	=	=	SYM
ejpam-3975	413	10	1	1	NUM
ejpam-3975	413	11	,	,	PUNCT
ejpam-3975	413	12	say	say	VERB
ejpam-3975	413	13	tu	tu	PROPN
ejpam-3975	413	14	=	=	PUNCT
ejpam-3975	413	15	{	{	PUNCT
ejpam-3975	413	16	p	p	X
ejpam-3975	413	17	}	}	PUNCT
ejpam-3975	413	18	for	for	ADP
ejpam-3975	413	19	some	some	DET
ejpam-3975	413	20	p	p	NOUN
ejpam-3975	413	21	∈	∈	PROPN
ejpam-3975	413	22	v	v	ADP
ejpam-3975	413	23	(	(	PUNCT
ejpam-3975	413	24	h	h	NOUN
ejpam-3975	413	25	)	)	PUNCT
ejpam-3975	413	26	because	because	SCONJ
ejpam-3975	413	27	c	c	PROPN
ejpam-3975	413	28	is	be	AUX
ejpam-3975	413	29	a	a	DET
ejpam-3975	413	30	perfect	perfect	ADJ
ejpam-3975	413	31	hop	hop	NOUN
ejpam-3975	413	32	dominating	dominating	NOUN
ejpam-3975	413	33	set	set	NOUN
ejpam-3975	413	34	of	of	ADP
ejpam-3975	413	35	g[h	g[h	PROPN
ejpam-3975	413	36	]	]	PUNCT
ejpam-3975	413	37	.	.	PUNCT
ejpam-3975	414	1	let	let	VERB
ejpam-3975	414	2	a	a	DET
ejpam-3975	414	3	∈	∈	PROPN
ejpam-3975	414	4	nh(p	nh(p	NUM
ejpam-3975	414	5	)	)	PUNCT
ejpam-3975	414	6	.	.	PUNCT
ejpam-3975	415	1	then	then	ADV
ejpam-3975	415	2	there	there	PRON
ejpam-3975	415	3	exists	exist	VERB
ejpam-3975	415	4	a	a	DET
ejpam-3975	415	5	unique	unique	ADJ
ejpam-3975	415	6	(	(	PUNCT
ejpam-3975	415	7	w	w	PROPN
ejpam-3975	415	8	,	,	PUNCT
ejpam-3975	415	9	b	b	NOUN
ejpam-3975	415	10	)	)	PUNCT
ejpam-3975	415	11	∈	∈	PROPN
ejpam-3975	415	12	c	c	NOUN
ejpam-3975	415	13	∩	∩	ADJ
ejpam-3975	415	14	ng[h]((u	ng[h]((u	NOUN
ejpam-3975	415	15	,	,	PUNCT
ejpam-3975	415	16	a	a	PRON
ejpam-3975	415	17	)	)	PUNCT
ejpam-3975	415	18	,	,	PUNCT
ejpam-3975	415	19	2	2	NUM
ejpam-3975	415	20	)	)	PUNCT
ejpam-3975	415	21	.	.	PUNCT
ejpam-3975	416	1	since	since	SCONJ
ejpam-3975	416	2	b	b	PROPN
ejpam-3975	416	3	6=	6=	PROPN
ejpam-3975	416	4	p	p	X
ejpam-3975	416	5	,	,	PUNCT
ejpam-3975	416	6	u	u	PROPN
ejpam-3975	416	7	6=	6=	PROPN
ejpam-3975	416	8	w.	w.	PROPN
ejpam-3975	416	9	thus	thus	ADV
ejpam-3975	416	10	,	,	PUNCT
ejpam-3975	416	11	w	w	PROPN
ejpam-3975	416	12	∈	∈	PROPN
ejpam-3975	416	13	s	s	PART
ejpam-3975	416	14	∩	∩	NOUN
ejpam-3975	416	15	ng(u	ng(u	NOUN
ejpam-3975	416	16	,	,	PUNCT
ejpam-3975	416	17	2	2	NUM
ejpam-3975	416	18	)	)	PUNCT
ejpam-3975	416	19	.	.	PUNCT
ejpam-3975	417	1	hence	hence	ADV
ejpam-3975	417	2	,	,	PUNCT
ejpam-3975	417	3	ng(u	ng(u	NOUN
ejpam-3975	417	4	,	,	PUNCT
ejpam-3975	417	5	2	2	X
ejpam-3975	417	6	)	)	PUNCT
ejpam-3975	417	7	∩	∩	X
ejpam-3975	417	8	s	s	PART
ejpam-3975	417	9	6=	6=	NUM
ejpam-3975	417	10	∅.	∅.	NOUN
ejpam-3975	417	11	therefore	therefore	ADV
ejpam-3975	417	12	s	s	VERB
ejpam-3975	417	13	is	be	AUX
ejpam-3975	417	14	a	a	DET
ejpam-3975	417	15	total	total	ADJ
ejpam-3975	417	16	perfect	perfect	ADJ
ejpam-3975	417	17	hop	hop	NOUN
ejpam-3975	417	18	dominating	dominating	NOUN
ejpam-3975	417	19	set	set	NOUN
ejpam-3975	417	20	of	of	ADP
ejpam-3975	417	21	g.	g.	PROPN
ejpam-3975	417	22	now	now	ADV
ejpam-3975	417	23	,	,	PUNCT
ejpam-3975	417	24	let	let	VERB
ejpam-3975	417	25	x	x	PROPN
ejpam-3975	417	26	∈	∈	PROPN
ejpam-3975	417	27	s.	s.	PROPN
ejpam-3975	417	28	since	since	SCONJ
ejpam-3975	417	29	s	s	PROPN
ejpam-3975	417	30	is	be	AUX
ejpam-3975	417	31	a	a	DET
ejpam-3975	417	32	total	total	ADJ
ejpam-3975	417	33	perfect	perfect	ADJ
ejpam-3975	417	34	hop	hop	NOUN
ejpam-3975	417	35	dominating	dominating	NOUN
ejpam-3975	417	36	set	set	NOUN
ejpam-3975	417	37	of	of	ADP
ejpam-3975	417	38	g	g	NOUN
ejpam-3975	417	39	,	,	PUNCT
ejpam-3975	417	40	|tx|	|tx|	X
ejpam-3975	417	41	=	=	SYM
ejpam-3975	417	42	1	1	NUM
ejpam-3975	417	43	,	,	PUNCT
ejpam-3975	417	44	say	say	VERB
ejpam-3975	417	45	tx	tx	ADV
ejpam-3975	417	46	=	=	PUNCT
ejpam-3975	417	47	{	{	PUNCT
ejpam-3975	417	48	a	a	X
ejpam-3975	417	49	}	}	PUNCT
ejpam-3975	417	50	.	.	PUNCT
ejpam-3975	418	1	let	let	VERB
ejpam-3975	418	2	p	p	PRON
ejpam-3975	418	3	∈	∈	PROPN
ejpam-3975	418	4	v	v	NOUN
ejpam-3975	418	5	(	(	PUNCT
ejpam-3975	418	6	h)\tx	h)\tx	PROPN
ejpam-3975	418	7	.	.	PROPN
ejpam-3975	418	8	suppose	suppose	VERB
ejpam-3975	418	9	p	p	PROPN
ejpam-3975	418	10	/∈	/∈	PUNCT
ejpam-3975	418	11	nh(a	nh(a	NUM
ejpam-3975	418	12	)	)	PUNCT
ejpam-3975	418	13	.	.	PUNCT
ejpam-3975	419	1	then	then	ADV
ejpam-3975	419	2	dg[h]((x	dg[h]((x	VERB
ejpam-3975	419	3	,	,	PUNCT
ejpam-3975	419	4	p	p	NOUN
ejpam-3975	419	5	)	)	PUNCT
ejpam-3975	419	6	,	,	PUNCT
ejpam-3975	419	7	(	(	PUNCT
ejpam-3975	419	8	x	x	X
ejpam-3975	419	9	,	,	PUNCT
ejpam-3975	419	10	a	a	NOUN
ejpam-3975	419	11	)	)	PUNCT
ejpam-3975	419	12	)	)	PUNCT
ejpam-3975	419	13	=	=	SYM
ejpam-3975	420	1	2	2	X
ejpam-3975	420	2	.	.	PUNCT
ejpam-3975	420	3	since	since	SCONJ
ejpam-3975	420	4	s	s	PROPN
ejpam-3975	420	5	is	be	AUX
ejpam-3975	420	6	a	a	DET
ejpam-3975	420	7	total	total	ADJ
ejpam-3975	420	8	perfect	perfect	ADJ
ejpam-3975	420	9	hop	hop	NOUN
ejpam-3975	420	10	dominating	dominating	NOUN
ejpam-3975	420	11	set	set	NOUN
ejpam-3975	420	12	of	of	ADP
ejpam-3975	420	13	g	g	NOUN
ejpam-3975	420	14	,	,	PUNCT
ejpam-3975	420	15	there	there	PRON
ejpam-3975	420	16	exists	exist	VERB
ejpam-3975	420	17	a	a	DET
ejpam-3975	420	18	unique	unique	ADJ
ejpam-3975	420	19	y	y	PROPN
ejpam-3975	420	20	∈	∈	PROPN
ejpam-3975	420	21	ng(x	ng(x	NUM
ejpam-3975	420	22	,	,	PUNCT
ejpam-3975	420	23	2)∩	2)∩	ADJ
ejpam-3975	420	24	s.	s.	PROPN
ejpam-3975	420	25	pick	pick	VERB
ejpam-3975	420	26	any	any	DET
ejpam-3975	420	27	c	c	PROPN
ejpam-3975	420	28	∈	∈	PROPN
ejpam-3975	420	29	ty	ty	INTJ
ejpam-3975	420	30	.	.	PUNCT
ejpam-3975	421	1	then	then	ADV
ejpam-3975	421	2	(	(	PUNCT
ejpam-3975	421	3	y	y	NOUN
ejpam-3975	421	4	,	,	PUNCT
ejpam-3975	421	5	c	c	NOUN
ejpam-3975	421	6	)	)	PUNCT
ejpam-3975	421	7	6=	6=	PUNCT
ejpam-3975	421	8	(	(	PUNCT
ejpam-3975	421	9	x	x	X
ejpam-3975	421	10	,	,	PUNCT
ejpam-3975	421	11	a	a	NOUN
ejpam-3975	421	12	)	)	PUNCT
ejpam-3975	421	13	but	but	CCONJ
ejpam-3975	421	14	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	421	15	,	,	PUNCT
ejpam-3975	421	16	p	p	NOUN
ejpam-3975	421	17	)	)	PUNCT
ejpam-3975	421	18	,	,	PUNCT
ejpam-3975	421	19	(	(	PUNCT
ejpam-3975	421	20	y	y	NOUN
ejpam-3975	421	21	,	,	PUNCT
ejpam-3975	421	22	c	c	NOUN
ejpam-3975	421	23	)	)	PUNCT
ejpam-3975	421	24	)	)	PUNCT
ejpam-3975	422	1	=	=	SYM
ejpam-3975	422	2	2	2	X
ejpam-3975	422	3	.	.	PUNCT
ejpam-3975	423	1	this	this	PRON
ejpam-3975	423	2	implies	imply	VERB
ejpam-3975	423	3	that	that	SCONJ
ejpam-3975	423	4	c	c	PROPN
ejpam-3975	423	5	is	be	AUX
ejpam-3975	423	6	not	not	PART
ejpam-3975	423	7	a	a	DET
ejpam-3975	423	8	perfect	perfect	ADJ
ejpam-3975	423	9	hop	hop	NOUN
ejpam-3975	423	10	dominating	dominating	NOUN
ejpam-3975	423	11	set	set	NOUN
ejpam-3975	423	12	of	of	ADP
ejpam-3975	423	13	g[h	g[h	PROPN
ejpam-3975	423	14	]	]	PUNCT
ejpam-3975	423	15	,	,	PUNCT
ejpam-3975	423	16	a	a	DET
ejpam-3975	423	17	contradiction	contradiction	NOUN
ejpam-3975	423	18	.	.	PUNCT
ejpam-3975	424	1	therefore	therefore	ADV
ejpam-3975	424	2	,	,	PUNCT
ejpam-3975	424	3	tx	tx	PROPN
ejpam-3975	424	4	is	be	AUX
ejpam-3975	424	5	a	a	DET
ejpam-3975	424	6	γ	γ	NOUN
ejpam-3975	424	7	-	-	PUNCT
ejpam-3975	424	8	set	set	NOUN
ejpam-3975	424	9	of	of	ADP
ejpam-3975	424	10	h.	h.	NOUN
ejpam-3975	424	11	conversely	conversely	ADV
ejpam-3975	424	12	,	,	PUNCT
ejpam-3975	424	13	let	let	VERB
ejpam-3975	424	14	s	s	PRON
ejpam-3975	424	15	be	be	AUX
ejpam-3975	424	16	a	a	DET
ejpam-3975	424	17	total	total	ADJ
ejpam-3975	424	18	perfect	perfect	ADJ
ejpam-3975	424	19	hop	hop	NOUN
ejpam-3975	424	20	dominating	dominating	NOUN
ejpam-3975	424	21	set	set	NOUN
ejpam-3975	424	22	of	of	ADP
ejpam-3975	424	23	g	g	PROPN
ejpam-3975	424	24	and	and	CCONJ
ejpam-3975	424	25	tx	tx	PROPN
ejpam-3975	424	26	is	be	AUX
ejpam-3975	424	27	a	a	DET
ejpam-3975	424	28	γ	γ	NOUN
ejpam-3975	424	29	-	-	PUNCT
ejpam-3975	424	30	set	set	NOUN
ejpam-3975	424	31	of	of	ADP
ejpam-3975	424	32	h	h	NOUN
ejpam-3975	424	33	for	for	SCONJ
ejpam-3975	424	34	every	every	DET
ejpam-3975	424	35	x	x	PROPN
ejpam-3975	424	36	∈	∈	PROPN
ejpam-3975	424	37	s.	s.	PROPN
ejpam-3975	424	38	let	let	VERB
ejpam-3975	424	39	(	(	PUNCT
ejpam-3975	424	40	x	x	NOUN
ejpam-3975	424	41	,	,	PUNCT
ejpam-3975	424	42	a	a	PRON
ejpam-3975	424	43	)	)	PUNCT
ejpam-3975	424	44	/∈	/∈	PUNCT
ejpam-3975	425	1	c.	c.	NOUN
ejpam-3975	425	2	then	then	ADV
ejpam-3975	425	3	either	either	CCONJ
ejpam-3975	425	4	x	x	X
ejpam-3975	425	5	/∈	/∈	PROPN
ejpam-3975	425	6	s	s	PART
ejpam-3975	425	7	or	or	CCONJ
ejpam-3975	425	8	x	x	SYM
ejpam-3975	425	9	∈	∈	NOUN
ejpam-3975	425	10	s	s	X
ejpam-3975	425	11	and	and	CCONJ
ejpam-3975	425	12	a	a	PRON
ejpam-3975	425	13	/∈	/∈	INTJ
ejpam-3975	426	1	tx	tx	INTJ
ejpam-3975	426	2	.	.	PUNCT
ejpam-3975	427	1	if	if	SCONJ
ejpam-3975	427	2	x	x	PROPN
ejpam-3975	427	3	/∈	/∈	PROPN
ejpam-3975	428	1	s	s	X
ejpam-3975	428	2	,	,	PUNCT
ejpam-3975	428	3	then	then	ADV
ejpam-3975	428	4	a	a	DET
ejpam-3975	428	5	unique	unique	ADJ
ejpam-3975	428	6	vertex	vertex	NOUN
ejpam-3975	428	7	y	y	PROPN
ejpam-3975	428	8	∈	∈	PROPN
ejpam-3975	428	9	s	s	PART
ejpam-3975	428	10	exists	exist	VERB
ejpam-3975	428	11	such	such	ADJ
ejpam-3975	428	12	that	that	PRON
ejpam-3975	428	13	dg(x	dg(x	PROPN
ejpam-3975	428	14	,	,	PUNCT
ejpam-3975	428	15	y	y	NOUN
ejpam-3975	428	16	)	)	PUNCT
ejpam-3975	428	17	=	=	SYM
ejpam-3975	429	1	2	2	X
ejpam-3975	429	2	.	.	PUNCT
ejpam-3975	429	3	since	since	SCONJ
ejpam-3975	429	4	ty	ty	PRON
ejpam-3975	429	5	is	be	AUX
ejpam-3975	429	6	a	a	DET
ejpam-3975	429	7	γ	γ	NOUN
ejpam-3975	429	8	-	-	PUNCT
ejpam-3975	429	9	set	set	NOUN
ejpam-3975	429	10	of	of	ADP
ejpam-3975	429	11	h	h	NOUN
ejpam-3975	429	12	for	for	ADP
ejpam-3975	429	13	every	every	DET
ejpam-3975	429	14	y	y	PROPN
ejpam-3975	429	15	∈	∈	PROPN
ejpam-3975	429	16	s	s	PROPN
ejpam-3975	429	17	,	,	PUNCT
ejpam-3975	429	18	a	a	DET
ejpam-3975	429	19	unique	unique	ADJ
ejpam-3975	429	20	vertex	vertex	NOUN
ejpam-3975	429	21	b	b	NOUN
ejpam-3975	429	22	∈	∈	NOUN
ejpam-3975	429	23	ty	ty	NOUN
ejpam-3975	429	24	exists	exist	VERB
ejpam-3975	429	25	such	such	ADJ
ejpam-3975	429	26	that	that	SCONJ
ejpam-3975	429	27	for	for	ADP
ejpam-3975	429	28	all	all	DET
ejpam-3975	429	29	p	p	NOUN
ejpam-3975	429	30	∈	∈	PROPN
ejpam-3975	429	31	v	v	NOUN
ejpam-3975	429	32	(	(	PUNCT
ejpam-3975	429	33	h)\{b	h)\{b	PROPN
ejpam-3975	429	34	}	}	PUNCT
ejpam-3975	429	35	,	,	PUNCT
ejpam-3975	429	36	p	p	PROPN
ejpam-3975	429	37	∈	∈	PROPN
ejpam-3975	429	38	nh(b	nh(b	NUM
ejpam-3975	429	39	)	)	PUNCT
ejpam-3975	429	40	.	.	PUNCT
ejpam-3975	430	1	then	then	ADV
ejpam-3975	430	2	(	(	PUNCT
ejpam-3975	430	3	y	y	PROPN
ejpam-3975	430	4	,	,	PUNCT
ejpam-3975	430	5	b	b	NOUN
ejpam-3975	430	6	)	)	PUNCT
ejpam-3975	430	7	∈	∈	PROPN
ejpam-3975	430	8	c	c	PROPN
ejpam-3975	430	9	and	and	CCONJ
ejpam-3975	430	10	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	430	11	,	,	PUNCT
ejpam-3975	430	12	a	a	PRON
ejpam-3975	430	13	)	)	PUNCT
ejpam-3975	430	14	,	,	PUNCT
ejpam-3975	430	15	(	(	PUNCT
ejpam-3975	430	16	y	y	PROPN
ejpam-3975	430	17	,	,	PUNCT
ejpam-3975	430	18	b	b	NOUN
ejpam-3975	430	19	)	)	PUNCT
ejpam-3975	430	20	)	)	PUNCT
ejpam-3975	431	1	=	=	SYM
ejpam-3975	431	2	2	2	X
ejpam-3975	431	3	.	.	X
ejpam-3975	431	4	suppose	suppose	VERB
ejpam-3975	431	5	x	x	X
ejpam-3975	431	6	∈	∈	PROPN
ejpam-3975	431	7	s	s	X
ejpam-3975	431	8	and	and	CCONJ
ejpam-3975	431	9	a	a	DET
ejpam-3975	431	10	/∈	/∈	INTJ
ejpam-3975	431	11	tx	tx	PROPN
ejpam-3975	431	12	.	.	PUNCT
ejpam-3975	432	1	then	then	ADV
ejpam-3975	432	2	there	there	PRON
ejpam-3975	432	3	is	be	VERB
ejpam-3975	432	4	exactly	exactly	ADV
ejpam-3975	432	5	one	one	NUM
ejpam-3975	432	6	vertex	vertex	NOUN
ejpam-3975	432	7	z	z	NOUN
ejpam-3975	432	8	∈	∈	NOUN
ejpam-3975	432	9	s	s	VERB
ejpam-3975	432	10	such	such	ADJ
ejpam-3975	432	11	that	that	PRON
ejpam-3975	432	12	dg(x	dg(x	NOUN
ejpam-3975	432	13	,	,	PUNCT
ejpam-3975	432	14	z	z	NOUN
ejpam-3975	432	15	)	)	PUNCT
ejpam-3975	432	16	=	=	SYM
ejpam-3975	432	17	2	2	X
ejpam-3975	432	18	.	.	PUNCT
ejpam-3975	433	1	since	since	SCONJ
ejpam-3975	433	2	tz	tz	PROPN
ejpam-3975	433	3	is	be	AUX
ejpam-3975	433	4	a	a	DET
ejpam-3975	433	5	γ	γ	NOUN
ejpam-3975	433	6	-	-	PUNCT
ejpam-3975	433	7	set	set	NOUN
ejpam-3975	433	8	of	of	ADP
ejpam-3975	433	9	h	h	NOUN
ejpam-3975	433	10	for	for	ADP
ejpam-3975	433	11	every	every	DET
ejpam-3975	433	12	z	z	PROPN
ejpam-3975	433	13	∈	∈	PROPN
ejpam-3975	433	14	s	s	PROPN
ejpam-3975	433	15	,	,	PUNCT
ejpam-3975	433	16	a	a	DET
ejpam-3975	433	17	unique	unique	ADJ
ejpam-3975	433	18	vertex	vertex	NOUN
ejpam-3975	433	19	c	c	NOUN
ejpam-3975	433	20	∈	∈	NOUN
ejpam-3975	433	21	tz	tz	NOUN
ejpam-3975	433	22	exists	exist	VERB
ejpam-3975	433	23	.	.	PUNCT
ejpam-3975	434	1	hence	hence	ADV
ejpam-3975	434	2	,	,	PUNCT
ejpam-3975	434	3	(	(	PUNCT
ejpam-3975	434	4	z	z	X
ejpam-3975	434	5	,	,	PUNCT
ejpam-3975	434	6	c	c	NOUN
ejpam-3975	434	7	)	)	PUNCT
ejpam-3975	434	8	∈	∈	PROPN
ejpam-3975	434	9	c	c	PROPN
ejpam-3975	434	10	and	and	CCONJ
ejpam-3975	434	11	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	434	12	,	,	PUNCT
ejpam-3975	434	13	a	a	PRON
ejpam-3975	434	14	)	)	PUNCT
ejpam-3975	434	15	,	,	PUNCT
ejpam-3975	434	16	(	(	PUNCT
ejpam-3975	434	17	z	z	X
ejpam-3975	434	18	,	,	PUNCT
ejpam-3975	434	19	c	c	NOUN
ejpam-3975	434	20	)	)	PUNCT
ejpam-3975	434	21	)	)	PUNCT
ejpam-3975	435	1	=	=	SYM
ejpam-3975	435	2	2	2	X
ejpam-3975	435	3	.	.	X
ejpam-3975	435	4	therefore	therefore	ADV
ejpam-3975	435	5	c	c	PROPN
ejpam-3975	435	6	is	be	AUX
ejpam-3975	435	7	a	a	DET
ejpam-3975	435	8	perfect	perfect	ADJ
ejpam-3975	435	9	hop	hop	NOUN
ejpam-3975	435	10	dominating	dominating	NOUN
ejpam-3975	435	11	set	set	NOUN
ejpam-3975	435	12	of	of	ADP
ejpam-3975	435	13	g[h	g[h	PROPN
ejpam-3975	435	14	]	]	PUNCT
ejpam-3975	435	15	.	.	PUNCT
ejpam-3975	436	1	let	let	VERB
ejpam-3975	436	2	(	(	PUNCT
ejpam-3975	436	3	x	x	NOUN
ejpam-3975	436	4	,	,	PUNCT
ejpam-3975	436	5	a	a	DET
ejpam-3975	436	6	)	)	PUNCT
ejpam-3975	436	7	∈	∈	PROPN
ejpam-3975	436	8	c.	c.	NOUN
ejpam-3975	436	9	since	since	SCONJ
ejpam-3975	436	10	x	x	PROPN
ejpam-3975	436	11	∈	∈	PROPN
ejpam-3975	436	12	s	s	X
ejpam-3975	436	13	and	and	CCONJ
ejpam-3975	436	14	s	s	NOUN
ejpam-3975	436	15	references	reference	NOUN
ejpam-3975	436	16	815	815	NUM
ejpam-3975	436	17	is	be	AUX
ejpam-3975	436	18	a	a	DET
ejpam-3975	436	19	total	total	ADJ
ejpam-3975	436	20	perfect	perfect	ADJ
ejpam-3975	436	21	hop	hop	NOUN
ejpam-3975	436	22	dominating	dominating	NOUN
ejpam-3975	436	23	set	set	NOUN
ejpam-3975	436	24	of	of	ADP
ejpam-3975	436	25	g	g	NOUN
ejpam-3975	436	26	,	,	PUNCT
ejpam-3975	436	27	there	there	PRON
ejpam-3975	436	28	exists	exist	VERB
ejpam-3975	436	29	a	a	DET
ejpam-3975	436	30	unique	unique	ADJ
ejpam-3975	436	31	vertex	vertex	NOUN
ejpam-3975	436	32	y	y	PROPN
ejpam-3975	436	33	∈	∈	PROPN
ejpam-3975	436	34	s	s	VERB
ejpam-3975	436	35	such	such	ADJ
ejpam-3975	436	36	that	that	DET
ejpam-3975	436	37	dg(x	dg(x	NOUN
ejpam-3975	436	38	,	,	PUNCT
ejpam-3975	436	39	y	y	NOUN
ejpam-3975	436	40	)	)	PUNCT
ejpam-3975	436	41	=	=	SYM
ejpam-3975	437	1	2	2	X
ejpam-3975	437	2	.	.	PUNCT
ejpam-3975	437	3	since	since	SCONJ
ejpam-3975	437	4	ty	ty	PRON
ejpam-3975	437	5	is	be	AUX
ejpam-3975	437	6	a	a	DET
ejpam-3975	437	7	γ	γ	NOUN
ejpam-3975	437	8	-	-	PUNCT
ejpam-3975	437	9	set	set	NOUN
ejpam-3975	437	10	of	of	ADP
ejpam-3975	437	11	h	h	NOUN
ejpam-3975	437	12	and	and	CCONJ
ejpam-3975	437	13	γ(h	γ(h	NOUN
ejpam-3975	437	14	)	)	PUNCT
ejpam-3975	437	15	=	=	SYM
ejpam-3975	438	1	1	1	NUM
ejpam-3975	438	2	,	,	PUNCT
ejpam-3975	438	3	there	there	PRON
ejpam-3975	438	4	exists	exist	VERB
ejpam-3975	438	5	b	b	PROPN
ejpam-3975	438	6	∈	∈	PROPN
ejpam-3975	438	7	ty	ty	PRON
ejpam-3975	438	8	.	.	PUNCT
ejpam-3975	439	1	hence	hence	ADV
ejpam-3975	439	2	,	,	PUNCT
ejpam-3975	439	3	(	(	PUNCT
ejpam-3975	439	4	y	y	PROPN
ejpam-3975	439	5	,	,	PUNCT
ejpam-3975	439	6	b	b	NOUN
ejpam-3975	439	7	)	)	PUNCT
ejpam-3975	439	8	∈	∈	PROPN
ejpam-3975	439	9	c	c	PROPN
ejpam-3975	439	10	and	and	CCONJ
ejpam-3975	439	11	dg[h]((x	dg[h]((x	NOUN
ejpam-3975	439	12	,	,	PUNCT
ejpam-3975	439	13	a	a	PRON
ejpam-3975	439	14	)	)	PUNCT
ejpam-3975	439	15	,	,	PUNCT
ejpam-3975	439	16	(	(	PUNCT
ejpam-3975	439	17	y	y	PROPN
ejpam-3975	439	18	,	,	PUNCT
ejpam-3975	439	19	b	b	NOUN
ejpam-3975	439	20	)	)	PUNCT
ejpam-3975	439	21	)	)	PUNCT
ejpam-3975	440	1	=	=	SYM
ejpam-3975	440	2	2	2	X
ejpam-3975	440	3	.	.	X
ejpam-3975	440	4	therefore	therefore	ADV
ejpam-3975	440	5	c	c	PROPN
ejpam-3975	440	6	is	be	AUX
ejpam-3975	440	7	a	a	DET
ejpam-3975	440	8	total	total	ADJ
ejpam-3975	440	9	perfect	perfect	ADJ
ejpam-3975	440	10	hop	hop	NOUN
ejpam-3975	440	11	dominating	dominating	NOUN
ejpam-3975	440	12	set	set	NOUN
ejpam-3975	440	13	of	of	ADP
ejpam-3975	440	14	g[h	g[h	PROPN
ejpam-3975	440	15	]	]	PUNCT
ejpam-3975	440	16	.	.	PUNCT
ejpam-3975	441	1	�	�	PROPN
ejpam-3975	441	2	corollary	corollary	ADJ
ejpam-3975	441	3	5.4	5.4	NUM
ejpam-3975	441	4	.	.	PUNCT
ejpam-3975	442	1	let	let	VERB
ejpam-3975	442	2	g	g	PRON
ejpam-3975	442	3	be	be	AUX
ejpam-3975	442	4	a	a	DET
ejpam-3975	442	5	nontrivial	nontrivial	ADJ
ejpam-3975	442	6	connected	connect	VERB
ejpam-3975	442	7	graph	graph	NOUN
ejpam-3975	442	8	whose	whose	DET
ejpam-3975	442	9	total	total	ADJ
ejpam-3975	442	10	perfect	perfect	ADJ
ejpam-3975	442	11	hop	hop	NOUN
ejpam-3975	442	12	dominating	dominating	NOUN
ejpam-3975	442	13	set	set	NOUN
ejpam-3975	442	14	exists	exist	VERB
ejpam-3975	442	15	and	and	CCONJ
ejpam-3975	442	16	h	h	DET
ejpam-3975	442	17	a	a	DET
ejpam-3975	442	18	nontrivial	nontrivial	ADJ
ejpam-3975	442	19	connected	connect	VERB
ejpam-3975	442	20	graphs	graph	NOUN
ejpam-3975	442	21	with	with	ADP
ejpam-3975	442	22	γ(h	γ(h	NOUN
ejpam-3975	442	23	)	)	PUNCT
ejpam-3975	442	24	=	=	SYM
ejpam-3975	443	1	1	1	X
ejpam-3975	443	2	.	.	PUNCT
ejpam-3975	443	3	then	then	ADV
ejpam-3975	443	4	γtph(g[h	γtph(g[h	ADJ
ejpam-3975	443	5	]	]	X
ejpam-3975	443	6	)	)	PUNCT
ejpam-3975	443	7	=	=	SYM
ejpam-3975	443	8	γtph(g	γtph(g	NOUN
ejpam-3975	443	9	)	)	PUNCT
ejpam-3975	443	10	.	.	PUNCT
ejpam-3975	444	1	proof	proof	NOUN
ejpam-3975	444	2	.	.	PUNCT
ejpam-3975	445	1	let	let	VERB
ejpam-3975	445	2	c	c	NOUN
ejpam-3975	445	3	=	=	PUNCT
ejpam-3975	446	1	⋃	⋃	PROPN
ejpam-3975	446	2	x∈s	x∈s	NOUN
ejpam-3975	447	1	[	[	X
ejpam-3975	447	2	{	{	PUNCT
ejpam-3975	447	3	x	x	NOUN
ejpam-3975	447	4	}	}	PUNCT
ejpam-3975	447	5	×	×	PROPN
ejpam-3975	447	6	tx	tx	PROPN
ejpam-3975	447	7	]	]	PUNCT
ejpam-3975	447	8	be	be	AUX
ejpam-3975	447	9	a	a	DET
ejpam-3975	447	10	minimum	minimum	NOUN
ejpam-3975	447	11	connected	connect	VERB
ejpam-3975	447	12	perfect	perfect	ADJ
ejpam-3975	447	13	hop	hop	NOUN
ejpam-3975	447	14	dominating	dominating	NOUN
ejpam-3975	447	15	set	set	NOUN
ejpam-3975	447	16	of	of	ADP
ejpam-3975	447	17	g[h	g[h	PROPN
ejpam-3975	447	18	]	]	PUNCT
ejpam-3975	447	19	.	.	PUNCT
ejpam-3975	448	1	then	then	ADV
ejpam-3975	448	2	by	by	ADP
ejpam-3975	448	3	theorem	theorem	NOUN
ejpam-3975	448	4	5.3	5.3	NUM
ejpam-3975	448	5	,	,	PUNCT
ejpam-3975	448	6	s	s	PART
ejpam-3975	448	7	is	be	AUX
ejpam-3975	448	8	a	a	DET
ejpam-3975	448	9	minimum	minimum	ADJ
ejpam-3975	448	10	total	total	NOUN
ejpam-3975	448	11	perfect	perfect	ADJ
ejpam-3975	448	12	hop	hop	NOUN
ejpam-3975	448	13	dominating	dominating	NOUN
ejpam-3975	448	14	set	set	NOUN
ejpam-3975	448	15	of	of	ADP
ejpam-3975	448	16	g	g	PROPN
ejpam-3975	448	17	and	and	CCONJ
ejpam-3975	448	18	tx	tx	PROPN
ejpam-3975	448	19	=	=	PUNCT
ejpam-3975	448	20	{	{	PUNCT
ejpam-3975	448	21	a	a	NOUN
ejpam-3975	448	22	}	}	PUNCT
ejpam-3975	448	23	where	where	SCONJ
ejpam-3975	448	24	a	a	DET
ejpam-3975	448	25	∈	∈	PROPN
ejpam-3975	448	26	v	v	ADP
ejpam-3975	448	27	(	(	PUNCT
ejpam-3975	448	28	h	h	NOUN
ejpam-3975	448	29	)	)	PUNCT
ejpam-3975	448	30	such	such	ADJ
ejpam-3975	448	31	that	that	DET
ejpam-3975	448	32	degh(a	degh(a	NOUN
ejpam-3975	448	33	)	)	PUNCT
ejpam-3975	448	34	=	=	SYM
ejpam-3975	448	35	|v	|v	PROPN
ejpam-3975	448	36	(	(	PUNCT
ejpam-3975	448	37	h)|−1	h)|−1	NOUN
ejpam-3975	448	38	.	.	PUNCT
ejpam-3975	449	1	therefore	therefore	ADV
ejpam-3975	449	2	γtph(g[h	γtph(g[h	ADJ
ejpam-3975	449	3	]	]	X
ejpam-3975	449	4	)	)	PUNCT
ejpam-3975	449	5	=	=	SYM
ejpam-3975	449	6	|c|	|c|	PROPN
ejpam-3975	449	7	=	=	SYM
ejpam-3975	449	8	|s|	|s|	PROPN
ejpam-3975	449	9	=	=	PUNCT
ejpam-3975	449	10	γtph(g	γtph(g	PROPN
ejpam-3975	449	11	)	)	PUNCT
ejpam-3975	449	12	.	.	PUNCT
ejpam-3975	450	1	�	�	PROPN
ejpam-3975	450	2	references	reference	NOUN
ejpam-3975	450	3	[	[	X
ejpam-3975	450	4	1	1	NUM
ejpam-3975	450	5	]	]	X
ejpam-3975	450	6	s	s	VERB
ejpam-3975	450	7	arriola	arriola	PROPN
ejpam-3975	450	8	and	and	CCONJ
ejpam-3975	450	9	s	s	NOUN
ejpam-3975	450	10	canoy	canoy	NOUN
ejpam-3975	450	11	.	.	PUNCT
ejpam-3975	451	1	(	(	PUNCT
ejpam-3975	451	2	1	1	NUM
ejpam-3975	451	3	;	;	PUNCT
ejpam-3975	451	4	2)∗	2)∗	NOUN
ejpam-3975	451	5	-domination	-domination	NOUN
ejpam-3975	451	6	in	in	ADP
ejpam-3975	451	7	graphs	graph	NOUN
ejpam-3975	451	8	.	.	PUNCT
ejpam-3975	452	1	the	the	DET
ejpam-3975	452	2	asian	asian	PROPN
ejpam-3975	452	3	mathematical	mathematical	PROPN
ejpam-3975	452	4	conference	conference	NOUN
ejpam-3975	452	5	,	,	PUNCT
ejpam-3975	452	6	2016	2016	NUM
ejpam-3975	452	7	.	.	PUNCT
ejpam-3975	453	1	[	[	X
ejpam-3975	453	2	2	2	NUM
ejpam-3975	453	3	]	]	PUNCT
ejpam-3975	453	4	f	f	PROPN
ejpam-3975	453	5	harary	harary	NOUN
ejpam-3975	453	6	.	.	PUNCT
ejpam-3975	454	1	graph	graph	NOUN
ejpam-3975	454	2	theory	theory	NOUN
ejpam-3975	454	3	.	.	PUNCT
ejpam-3975	455	1	addisson	addisson	NOUN
ejpam-3975	455	2	-	-	PUNCT
ejpam-3975	455	3	wesley	wesley	PROPN
ejpam-3975	455	4	publishing	publishing	PROPN
ejpam-3975	455	5	company	company	NOUN
ejpam-3975	455	6	,	,	PUNCT
ejpam-3975	455	7	1969	1969	NUM
ejpam-3975	455	8	.	.	PUNCT
ejpam-3975	456	1	[	[	X
ejpam-3975	456	2	3	3	X
ejpam-3975	456	3	]	]	X
ejpam-3975	456	4	c	c	PROPN
ejpam-3975	456	5	natarajan	natarajan	PROPN
ejpam-3975	456	6	and	and	CCONJ
ejpam-3975	456	7	s	s	PROPN
ejpam-3975	456	8	k	k	X
ejpam-3975	456	9	ayyaswamy	ayyaswamy	PROPN
ejpam-3975	456	10	.	.	PUNCT
ejpam-3975	457	1	hop	hop	PROPN
ejpam-3975	457	2	domination	domination	NOUN
ejpam-3975	457	3	in	in	ADP
ejpam-3975	457	4	graphs	graphs	PROPN
ejpam-3975	457	5	ii	ii	PROPN
ejpam-3975	457	6	.	.	PUNCT
ejpam-3975	457	7	versita	versita	PROPN
ejpam-3975	457	8	,	,	PUNCT
ejpam-3975	457	9	23(2):187–199	23(2):187–199	PROPN
ejpam-3975	457	10	,	,	PUNCT
ejpam-3975	457	11	2015	2015	NUM
ejpam-3975	457	12	.	.	PUNCT
ejpam-3975	458	1	[	[	X
ejpam-3975	458	2	4	4	NUM
ejpam-3975	458	3	]	]	X
ejpam-3975	458	4	y	y	PROPN
ejpam-3975	458	5	pabilona	pabilona	PROPN
ejpam-3975	458	6	and	and	CCONJ
ejpam-3975	458	7	h	h	PROPN
ejpam-3975	458	8	rara	rara	PROPN
ejpam-3975	458	9	.	.	PUNCT
ejpam-3975	459	1	total	total	ADJ
ejpam-3975	459	2	hop	hop	NOUN
ejpam-3975	459	3	dominating	dominating	NOUN
ejpam-3975	459	4	set	set	VERB
ejpam-3975	459	5	in	in	ADP
ejpam-3975	459	6	the	the	DET
ejpam-3975	459	7	join	join	NOUN
ejpam-3975	459	8	,	,	PUNCT
ejpam-3975	459	9	corona	corona	PROPN
ejpam-3975	459	10	,	,	PUNCT
ejpam-3975	459	11	and	and	CCONJ
ejpam-3975	459	12	lexicographic	lexicographic	ADJ
ejpam-3975	459	13	product	product	NOUN
ejpam-3975	459	14	of	of	ADP
ejpam-3975	459	15	graphs	graph	NOUN
ejpam-3975	459	16	.	.	PUNCT
ejpam-3975	460	1	journal	journal	NOUN
ejpam-3975	460	2	of	of	ADP
ejpam-3975	460	3	algebra	algebra	PROPN
ejpam-3975	460	4	and	and	CCONJ
ejpam-3975	460	5	applied	apply	VERB
ejpam-3975	460	6	mathematics	mathematic	NOUN
ejpam-3975	460	7	,	,	PUNCT
ejpam-3975	460	8	2017	2017	NUM
ejpam-3975	460	9	.	.	PUNCT
ejpam-3975	461	1	[	[	X
ejpam-3975	461	2	5	5	NUM
ejpam-3975	461	3	]	]	SYM
ejpam-3975	461	4	c	c	NOUN
ejpam-3975	461	5	saromines	saromine	VERB
ejpam-3975	461	6	r	r	NOUN
ejpam-3975	461	7	rakim	rakim	NOUN
ejpam-3975	461	8	and	and	CCONJ
ejpam-3975	461	9	h	h	PROPN
ejpam-3975	461	10	rara	rara	PROPN
ejpam-3975	461	11	.	.	PUNCT
ejpam-3975	462	1	perfect	perfect	ADJ
ejpam-3975	462	2	hop	hop	NOUN
ejpam-3975	462	3	domination	domination	NOUN
ejpam-3975	462	4	in	in	ADP
ejpam-3975	462	5	graphs	graph	NOUN
ejpam-3975	462	6	.	.	PUNCT
ejpam-3975	463	1	applied	apply	VERB
ejpam-3975	463	2	mathematical	mathematical	ADJ
ejpam-3975	463	3	sciences	science	NOUN
ejpam-3975	463	4	,	,	PUNCT
ejpam-3975	463	5	12:635–649	12:635–649	NUM
ejpam-3975	463	6	,	,	PUNCT
ejpam-3975	463	7	2018	2018	NUM
ejpam-3975	463	8	.	.	PUNCT
ejpam-3975	464	1	[	[	X
ejpam-3975	464	2	6	6	NUM
ejpam-3975	464	3	]	]	PUNCT
ejpam-3975	464	4	y	y	PROPN
ejpam-3975	464	5	pabilona	pabilona	PROPN
ejpam-3975	464	6	r	r	PROPN
ejpam-3975	464	7	rakim	rakim	PROPN
ejpam-3975	464	8	and	and	CCONJ
ejpam-3975	464	9	h	h	PROPN
ejpam-3975	464	10	rara	rara	PROPN
ejpam-3975	464	11	.	.	PUNCT
ejpam-3975	465	1	connected	connect	VERB
ejpam-3975	465	2	perfect	perfect	ADJ
ejpam-3975	465	3	hop	hop	NOUN
ejpam-3975	465	4	domination	domination	NOUN
ejpam-3975	465	5	in	in	ADP
ejpam-3975	465	6	graphs	graph	NOUN
ejpam-3975	465	7	under	under	ADP
ejpam-3975	465	8	some	some	DET
ejpam-3975	465	9	binary	binary	ADJ
ejpam-3975	465	10	operations	operation	NOUN
ejpam-3975	465	11	.	.	PUNCT
ejpam-3975	466	1	advances	advance	NOUN
ejpam-3975	466	2	and	and	CCONJ
ejpam-3975	466	3	applications	application	NOUN
ejpam-3975	466	4	in	in	ADP
ejpam-3975	466	5	discrete	discrete	ADJ
ejpam-3975	466	6	mathematics	mathematic	NOUN
ejpam-3975	466	7	,	,	PUNCT
ejpam-3975	466	8	20	20	NUM
ejpam-3975	466	9	,	,	PUNCT
ejpam-3975	466	10	2019	2019	NUM
ejpam-3975	466	11	.	.	PUNCT