id	sid	tid	token	lemma	pos
ejpam-4440	1	1	european	european	PROPN
ejpam-4440	1	2	journal	journal	PROPN
ejpam-4440	1	3	of	of	ADP
ejpam-4440	1	4	pure	pure	ADJ
ejpam-4440	1	5	and	and	CCONJ
ejpam-4440	1	6	applied	apply	VERB
ejpam-4440	1	7	mathematics	mathematic	NOUN
ejpam-4440	1	8	vol	vol	NOUN
ejpam-4440	1	9	.	.	PROPN
ejpam-4440	2	1	15	15	NUM
ejpam-4440	2	2	,	,	PUNCT
ejpam-4440	2	3	no	no	INTJ
ejpam-4440	2	4	.	.	NOUN
ejpam-4440	2	5	3	3	NUM
ejpam-4440	2	6	,	,	PUNCT
ejpam-4440	2	7	2022	2022	NUM
ejpam-4440	2	8	,	,	PUNCT
ejpam-4440	2	9	1201	1201	NUM
ejpam-4440	2	10	-	-	SYM
ejpam-4440	2	11	1210	1210	NUM
ejpam-4440	2	12	issn	issn	PROPN
ejpam-4440	2	13	1307	1307	NUM
ejpam-4440	2	14	-	-	SYM
ejpam-4440	2	15	5543	5543	NUM
ejpam-4440	2	16	–	–	PUNCT
ejpam-4440	3	1	ejpam.com	ejpam.com	X
ejpam-4440	3	2	published	publish	VERB
ejpam-4440	3	3	by	by	ADP
ejpam-4440	3	4	new	new	PROPN
ejpam-4440	3	5	york	york	PROPN
ejpam-4440	3	6	business	business	PROPN
ejpam-4440	3	7	global	global	PROPN
ejpam-4440	3	8	on	on	ADP
ejpam-4440	3	9	movable	movable	ADJ
ejpam-4440	3	10	strong	strong	ADJ
ejpam-4440	3	11	resolving	resolving	NOUN
ejpam-4440	3	12	domination	domination	NOUN
ejpam-4440	3	13	in	in	ADP
ejpam-4440	3	14	graphs	graph	NOUN
ejpam-4440	3	15	helyn	helyn	PROPN
ejpam-4440	3	16	c.	c.	PROPN
ejpam-4440	3	17	sumaoy1,∗	sumaoy1,∗	PROPN
ejpam-4440	3	18	,	,	PUNCT
ejpam-4440	3	19	helen	helen	PROPN
ejpam-4440	3	20	m.	m.	PROPN
ejpam-4440	3	21	rara1	rara1	PROPN
ejpam-4440	4	1	1	1	NUM
ejpam-4440	4	2	department	department	NOUN
ejpam-4440	4	3	of	of	ADP
ejpam-4440	4	4	mathematics	mathematic	NOUN
ejpam-4440	4	5	and	and	CCONJ
ejpam-4440	4	6	statistics	statistic	NOUN
ejpam-4440	4	7	,	,	PUNCT
ejpam-4440	4	8	college	college	NOUN
ejpam-4440	4	9	of	of	ADP
ejpam-4440	4	10	science	science	NOUN
ejpam-4440	4	11	and	and	CCONJ
ejpam-4440	4	12	mathematics	mathematic	NOUN
ejpam-4440	4	13	,	,	PUNCT
ejpam-4440	4	14	center	center	NOUN
ejpam-4440	4	15	of	of	ADP
ejpam-4440	4	16	graph	graph	NOUN
ejpam-4440	4	17	theory	theory	NOUN
ejpam-4440	4	18	,	,	PUNCT
ejpam-4440	4	19	algebra	algebra	NOUN
ejpam-4440	4	20	,	,	PUNCT
ejpam-4440	4	21	and	and	CCONJ
ejpam-4440	4	22	analysis	analysis	NOUN
ejpam-4440	4	23	-	-	PUNCT
ejpam-4440	4	24	premier	premier	NOUN
ejpam-4440	4	25	research	research	NOUN
ejpam-4440	4	26	institute	institute	PROPN
ejpam-4440	4	27	of	of	ADP
ejpam-4440	4	28	science	science	NOUN
ejpam-4440	4	29	and	and	CCONJ
ejpam-4440	4	30	mathematics	mathematic	NOUN
ejpam-4440	4	31	,	,	PUNCT
ejpam-4440	4	32	mindanao	mindanao	PROPN
ejpam-4440	4	33	state	state	PROPN
ejpam-4440	4	34	university	university	PROPN
ejpam-4440	4	35	-	-	PUNCT
ejpam-4440	4	36	iligan	iligan	PROPN
ejpam-4440	4	37	institute	institute	PROPN
ejpam-4440	4	38	of	of	ADP
ejpam-4440	4	39	technology	technology	PROPN
ejpam-4440	4	40	,	,	PUNCT
ejpam-4440	4	41	9200	9200	NUM
ejpam-4440	4	42	iligan	iligan	ADJ
ejpam-4440	4	43	city	city	NOUN
ejpam-4440	4	44	,	,	PUNCT
ejpam-4440	4	45	philippines	philippine	NOUN
ejpam-4440	4	46	abstract	abstract	ADJ
ejpam-4440	4	47	.	.	PUNCT
ejpam-4440	5	1	let	let	VERB
ejpam-4440	5	2	g	g	PRON
ejpam-4440	5	3	be	be	AUX
ejpam-4440	5	4	a	a	DET
ejpam-4440	5	5	connected	connected	ADJ
ejpam-4440	5	6	graph	graph	NOUN
ejpam-4440	5	7	.	.	PUNCT
ejpam-4440	6	1	a	a	DET
ejpam-4440	6	2	strong	strong	ADJ
ejpam-4440	6	3	resolving	resolving	NOUN
ejpam-4440	6	4	dominating	dominate	VERB
ejpam-4440	6	5	set	set	NOUN
ejpam-4440	6	6	s	s	VERB
ejpam-4440	6	7	is	be	AUX
ejpam-4440	6	8	a	a	DET
ejpam-4440	6	9	1	1	NUM
ejpam-4440	6	10	-	-	PUNCT
ejpam-4440	6	11	movable	movable	ADJ
ejpam-4440	6	12	strong	strong	ADJ
ejpam-4440	6	13	resolving	resolve	VERB
ejpam-4440	6	14	dominating	dominating	NOUN
ejpam-4440	6	15	set	set	NOUN
ejpam-4440	6	16	of	of	ADP
ejpam-4440	6	17	g	g	PROPN
ejpam-4440	6	18	if	if	SCONJ
ejpam-4440	6	19	for	for	SCONJ
ejpam-4440	6	20	every	every	DET
ejpam-4440	6	21	v	v	NUM
ejpam-4440	6	22	∈	∈	PROPN
ejpam-4440	6	23	s	s	NOUN
ejpam-4440	6	24	,	,	PUNCT
ejpam-4440	6	25	either	either	CCONJ
ejpam-4440	6	26	s	s	VERB
ejpam-4440	6	27	\	\	PROPN
ejpam-4440	6	28	{	{	PUNCT
ejpam-4440	6	29	v	v	NOUN
ejpam-4440	6	30	}	}	PUNCT
ejpam-4440	6	31	is	be	AUX
ejpam-4440	6	32	a	a	DET
ejpam-4440	6	33	strong	strong	ADJ
ejpam-4440	6	34	resolving	resolving	NOUN
ejpam-4440	6	35	dominating	dominating	NOUN
ejpam-4440	6	36	set	set	NOUN
ejpam-4440	6	37	or	or	CCONJ
ejpam-4440	6	38	there	there	PRON
ejpam-4440	6	39	exists	exist	VERB
ejpam-4440	6	40	a	a	DET
ejpam-4440	6	41	vertex	vertex	NOUN
ejpam-4440	6	42	u	u	NOUN
ejpam-4440	6	43	∈	∈	PROPN
ejpam-4440	6	44	(	(	PUNCT
ejpam-4440	6	45	v	v	NOUN
ejpam-4440	6	46	(	(	PUNCT
ejpam-4440	6	47	g	g	NOUN
ejpam-4440	6	48	)	)	PUNCT
ejpam-4440	6	49	\	\	PROPN
ejpam-4440	6	50	s	s	X
ejpam-4440	6	51	)	)	PUNCT
ejpam-4440	6	52	∩ng(v	∩ng(v	PROPN
ejpam-4440	6	53	)	)	PUNCT
ejpam-4440	6	54	such	such	ADJ
ejpam-4440	6	55	that	that	SCONJ
ejpam-4440	6	56	(	(	PUNCT
ejpam-4440	6	57	s	s	NOUN
ejpam-4440	6	58	\	\	X
ejpam-4440	6	59	{	{	PUNCT
ejpam-4440	6	60	v	v	NOUN
ejpam-4440	6	61	}	}	PUNCT
ejpam-4440	6	62	)	)	PUNCT
ejpam-4440	6	63	∪	∪	ADP
ejpam-4440	6	64	{	{	PUNCT
ejpam-4440	6	65	u	u	NOUN
ejpam-4440	6	66	}	}	PUNCT
ejpam-4440	6	67	is	be	AUX
ejpam-4440	6	68	a	a	DET
ejpam-4440	6	69	strong	strong	ADJ
ejpam-4440	6	70	resolving	resolving	NOUN
ejpam-4440	6	71	dominating	dominating	NOUN
ejpam-4440	6	72	set	set	NOUN
ejpam-4440	6	73	of	of	ADP
ejpam-4440	6	74	g.	g.	PROPN
ejpam-4440	6	75	the	the	DET
ejpam-4440	6	76	minimum	minimum	ADJ
ejpam-4440	6	77	cardinality	cardinality	NOUN
ejpam-4440	6	78	of	of	ADP
ejpam-4440	6	79	a	a	DET
ejpam-4440	6	80	1	1	NUM
ejpam-4440	6	81	-	-	PUNCT
ejpam-4440	6	82	movable	movable	ADJ
ejpam-4440	6	83	strong	strong	ADJ
ejpam-4440	6	84	resolving	resolve	VERB
ejpam-4440	6	85	dominating	dominating	NOUN
ejpam-4440	6	86	set	set	NOUN
ejpam-4440	6	87	of	of	ADP
ejpam-4440	6	88	g	g	NOUN
ejpam-4440	6	89	,	,	PUNCT
ejpam-4440	6	90	denoted	denote	VERB
ejpam-4440	6	91	by	by	ADP
ejpam-4440	6	92	γ1	γ1	PROPN
ejpam-4440	6	93	msr(g	msr(g	PROPN
ejpam-4440	6	94	)	)	PUNCT
ejpam-4440	6	95	is	be	AUX
ejpam-4440	6	96	the	the	DET
ejpam-4440	6	97	1	1	NUM
ejpam-4440	6	98	-	-	PUNCT
ejpam-4440	6	99	movable	movable	ADJ
ejpam-4440	6	100	strong	strong	ADJ
ejpam-4440	6	101	resolving	resolving	NOUN
ejpam-4440	6	102	domination	domination	NOUN
ejpam-4440	6	103	number	number	NOUN
ejpam-4440	6	104	ofg	ofg	PROPN
ejpam-4440	6	105	.	.	PUNCT
ejpam-4440	7	1	a	a	DET
ejpam-4440	7	2	1	1	NUM
ejpam-4440	7	3	-	-	PUNCT
ejpam-4440	7	4	movable	movable	ADJ
ejpam-4440	7	5	strong	strong	ADJ
ejpam-4440	7	6	resolving	resolve	VERB
ejpam-4440	7	7	dominating	dominating	NOUN
ejpam-4440	7	8	set	set	VERB
ejpam-4440	7	9	with	with	ADP
ejpam-4440	7	10	cardinality	cardinality	PROPN
ejpam-4440	7	11	γ1	γ1	PROPN
ejpam-4440	7	12	msr(g	msr(g	PROPN
ejpam-4440	7	13	)	)	PUNCT
ejpam-4440	7	14	is	be	AUX
ejpam-4440	7	15	called	call	VERB
ejpam-4440	7	16	a	a	DET
ejpam-4440	7	17	γ1	γ1	PROPN
ejpam-4440	7	18	msr	msr	NOUN
ejpam-4440	7	19	-	-	PUNCT
ejpam-4440	7	20	set	set	NOUN
ejpam-4440	7	21	of	of	ADP
ejpam-4440	7	22	g.	g.	PROPN
ejpam-4440	7	23	in	in	ADP
ejpam-4440	7	24	this	this	DET
ejpam-4440	7	25	paper	paper	NOUN
ejpam-4440	7	26	,	,	PUNCT
ejpam-4440	7	27	we	we	PRON
ejpam-4440	7	28	study	study	VERB
ejpam-4440	7	29	this	this	DET
ejpam-4440	7	30	concept	concept	NOUN
ejpam-4440	7	31	and	and	CCONJ
ejpam-4440	7	32	the	the	DET
ejpam-4440	7	33	corresponding	corresponding	ADJ
ejpam-4440	7	34	parameter	parameter	NOUN
ejpam-4440	7	35	in	in	ADP
ejpam-4440	7	36	graphs	graph	NOUN
ejpam-4440	7	37	resulting	result	VERB
ejpam-4440	7	38	from	from	ADP
ejpam-4440	7	39	the	the	DET
ejpam-4440	7	40	join	join	NOUN
ejpam-4440	7	41	,	,	PUNCT
ejpam-4440	7	42	corona	corona	NOUN
ejpam-4440	7	43	and	and	CCONJ
ejpam-4440	7	44	lexicographic	lexicographic	ADJ
ejpam-4440	7	45	product	product	NOUN
ejpam-4440	7	46	of	of	ADP
ejpam-4440	7	47	two	two	NUM
ejpam-4440	7	48	graphs	graph	NOUN
ejpam-4440	7	49	.	.	PUNCT
ejpam-4440	8	1	specifically	specifically	ADV
ejpam-4440	8	2	,	,	PUNCT
ejpam-4440	8	3	we	we	PRON
ejpam-4440	8	4	characterize	characterize	VERB
ejpam-4440	8	5	the	the	DET
ejpam-4440	8	6	1	1	NUM
ejpam-4440	8	7	-	-	PUNCT
ejpam-4440	8	8	movable	movable	ADJ
ejpam-4440	8	9	strong	strong	ADJ
ejpam-4440	8	10	resolving	resolve	VERB
ejpam-4440	8	11	dominating	dominating	NOUN
ejpam-4440	8	12	sets	set	NOUN
ejpam-4440	8	13	in	in	ADP
ejpam-4440	8	14	these	these	DET
ejpam-4440	8	15	types	type	NOUN
ejpam-4440	8	16	of	of	ADP
ejpam-4440	8	17	graphs	graph	NOUN
ejpam-4440	8	18	and	and	CCONJ
ejpam-4440	8	19	determine	determine	VERB
ejpam-4440	8	20	the	the	DET
ejpam-4440	8	21	exact	exact	ADJ
ejpam-4440	8	22	values	value	NOUN
ejpam-4440	8	23	of	of	ADP
ejpam-4440	8	24	their	their	PRON
ejpam-4440	8	25	1	1	NUM
ejpam-4440	8	26	-	-	PUNCT
ejpam-4440	8	27	movable	movable	ADJ
ejpam-4440	8	28	strong	strong	ADJ
ejpam-4440	8	29	resolving	resolve	VERB
ejpam-4440	8	30	domination	domination	NOUN
ejpam-4440	8	31	numbers	number	NOUN
ejpam-4440	8	32	.	.	PUNCT
ejpam-4440	9	1	2020	2020	NUM
ejpam-4440	9	2	mathematics	mathematic	NOUN
ejpam-4440	9	3	subject	subject	NOUN
ejpam-4440	9	4	classifications	classification	NOUN
ejpam-4440	9	5	:	:	PUNCT
ejpam-4440	9	6	05c69	05c69	X
ejpam-4440	9	7	key	key	ADJ
ejpam-4440	9	8	words	word	NOUN
ejpam-4440	9	9	and	and	CCONJ
ejpam-4440	9	10	phrases	phrase	NOUN
ejpam-4440	9	11	:	:	PUNCT
ejpam-4440	9	12	movable	movable	ADJ
ejpam-4440	9	13	strong	strong	ADJ
ejpam-4440	9	14	resolving	resolve	VERB
ejpam-4440	9	15	dominating	dominating	NOUN
ejpam-4440	9	16	set	set	NOUN
ejpam-4440	9	17	,	,	PUNCT
ejpam-4440	9	18	movable	movable	ADJ
ejpam-4440	9	19	strong	strong	ADJ
ejpam-4440	9	20	resolving	resolve	VERB
ejpam-4440	9	21	domination	domination	NOUN
ejpam-4440	9	22	number	number	NOUN
ejpam-4440	9	23	,	,	PUNCT
ejpam-4440	9	24	join	join	NOUN
ejpam-4440	9	25	,	,	PUNCT
ejpam-4440	9	26	corona	corona	PROPN
ejpam-4440	9	27	,	,	PUNCT
ejpam-4440	9	28	lexicographic	lexicographic	ADJ
ejpam-4440	9	29	product	product	NOUN
ejpam-4440	9	30	1	1	NUM
ejpam-4440	9	31	.	.	PUNCT
ejpam-4440	9	32	introduction	introduction	NOUN
ejpam-4440	9	33	domination	domination	NOUN
ejpam-4440	9	34	in	in	ADP
ejpam-4440	9	35	graphs	graph	NOUN
ejpam-4440	9	36	was	be	AUX
ejpam-4440	9	37	first	first	ADV
ejpam-4440	9	38	introduced	introduce	VERB
ejpam-4440	9	39	by	by	ADP
ejpam-4440	9	40	c.	c.	PROPN
ejpam-4440	9	41	berge	berge	PROPN
ejpam-4440	9	42	in	in	ADP
ejpam-4440	9	43	1958	1958	NUM
ejpam-4440	9	44	[	[	X
ejpam-4440	9	45	4	4	NUM
ejpam-4440	9	46	]	]	PUNCT
ejpam-4440	9	47	.	.	PUNCT
ejpam-4440	10	1	there	there	PRON
ejpam-4440	10	2	are	be	VERB
ejpam-4440	10	3	now	now	ADV
ejpam-4440	10	4	many	many	ADJ
ejpam-4440	10	5	studies	study	NOUN
ejpam-4440	10	6	involving	involve	VERB
ejpam-4440	10	7	domination	domination	NOUN
ejpam-4440	10	8	and	and	CCONJ
ejpam-4440	10	9	its	its	PRON
ejpam-4440	10	10	variations	variation	NOUN
ejpam-4440	10	11	.	.	PUNCT
ejpam-4440	11	1	domke	domke	PROPN
ejpam-4440	11	2	et	et	PROPN
ejpam-4440	11	3	.	.	PUNCT
ejpam-4440	12	1	al	al	PROPN
ejpam-4440	13	1	[	[	X
ejpam-4440	13	2	6	6	NUM
ejpam-4440	13	3	]	]	PUNCT
ejpam-4440	13	4	introduced	introduce	VERB
ejpam-4440	13	5	and	and	CCONJ
ejpam-4440	13	6	investigated	investigate	VERB
ejpam-4440	13	7	the	the	DET
ejpam-4440	13	8	concept	concept	NOUN
ejpam-4440	13	9	of	of	ADP
ejpam-4440	13	10	restrained	restrained	ADJ
ejpam-4440	13	11	domination	domination	NOUN
ejpam-4440	13	12	in	in	ADP
ejpam-4440	13	13	graphs	graph	NOUN
ejpam-4440	13	14	.	.	PUNCT
ejpam-4440	14	1	oellermann	oellermann	NOUN
ejpam-4440	14	2	,	,	PUNCT
ejpam-4440	14	3	o.	o.	NOUN
ejpam-4440	14	4	r	r	NOUN
ejpam-4440	14	5	,	,	PUNCT
ejpam-4440	14	6	and	and	CCONJ
ejpam-4440	14	7	peters	peters	PROPN
ejpam-4440	14	8	-	-	PUNCT
ejpam-4440	14	9	fransen	fransen	PROPN
ejpam-4440	14	10	,	,	PUNCT
ejpam-4440	14	11	j.	j.	PROPN
ejpam-4440	15	1	[	[	X
ejpam-4440	15	2	11	11	NUM
ejpam-4440	15	3	]	]	PUNCT
ejpam-4440	15	4	introduced	introduce	VERB
ejpam-4440	15	5	and	and	CCONJ
ejpam-4440	15	6	studied	study	VERB
ejpam-4440	15	7	the	the	DET
ejpam-4440	15	8	concept	concept	NOUN
ejpam-4440	15	9	of	of	ADP
ejpam-4440	15	10	strong	strong	ADJ
ejpam-4440	15	11	resolving	resolving	NOUN
ejpam-4440	15	12	set	set	NOUN
ejpam-4440	15	13	.	.	PUNCT
ejpam-4440	16	1	slater	slater	NOUN
ejpam-4440	17	1	[	[	X
ejpam-4440	17	2	14	14	NUM
ejpam-4440	17	3	]	]	PUNCT
ejpam-4440	17	4	introduced	introduce	VERB
ejpam-4440	17	5	and	and	CCONJ
ejpam-4440	17	6	studied	study	VERB
ejpam-4440	17	7	the	the	DET
ejpam-4440	17	8	concept	concept	NOUN
ejpam-4440	17	9	of	of	ADP
ejpam-4440	17	10	resolving	resolve	VERB
ejpam-4440	17	11	set	set	NOUN
ejpam-4440	17	12	.	.	PUNCT
ejpam-4440	18	1	resolving	resolve	VERB
ejpam-4440	18	2	sets	set	NOUN
ejpam-4440	18	3	and	and	CCONJ
ejpam-4440	18	4	resolving	resolve	VERB
ejpam-4440	18	5	dominating	dominating	NOUN
ejpam-4440	18	6	sets	set	NOUN
ejpam-4440	18	7	were	be	AUX
ejpam-4440	18	8	also	also	ADV
ejpam-4440	18	9	studied	study	VERB
ejpam-4440	18	10	in	in	ADP
ejpam-4440	18	11	[	[	X
ejpam-4440	18	12	1	1	NUM
ejpam-4440	18	13	,	,	PUNCT
ejpam-4440	18	14	10	10	NUM
ejpam-4440	18	15	]	]	PUNCT
ejpam-4440	18	16	.	.	PUNCT
ejpam-4440	19	1	the	the	DET
ejpam-4440	19	2	concept	concept	NOUN
ejpam-4440	19	3	of	of	ADP
ejpam-4440	19	4	metric	metric	ADJ
ejpam-4440	19	5	dimension	dimension	NOUN
ejpam-4440	19	6	has	have	AUX
ejpam-4440	19	7	grown	grow	VERB
ejpam-4440	19	8	to	to	PART
ejpam-4440	19	9	become	become	VERB
ejpam-4440	19	10	an	an	DET
ejpam-4440	19	11	interesting	interesting	ADJ
ejpam-4440	19	12	topic	topic	NOUN
ejpam-4440	19	13	in	in	ADP
ejpam-4440	19	14	graph	graph	NOUN
ejpam-4440	19	15	theory	theory	NOUN
ejpam-4440	19	16	.	.	PUNCT
ejpam-4440	20	1	in	in	ADP
ejpam-4440	20	2	line	line	NOUN
ejpam-4440	20	3	with	with	ADP
ejpam-4440	20	4	this	this	PRON
ejpam-4440	20	5	,	,	PUNCT
ejpam-4440	20	6	some	some	DET
ejpam-4440	20	7	researchers	researcher	NOUN
ejpam-4440	20	8	introduced	introduce	VERB
ejpam-4440	20	9	another	another	DET
ejpam-4440	20	10	variant	variant	NOUN
ejpam-4440	20	11	,	,	PUNCT
ejpam-4440	20	12	more	more	ADV
ejpam-4440	20	13	restricted	restricted	ADJ
ejpam-4440	20	14	than	than	ADP
ejpam-4440	20	15	the	the	DET
ejpam-4440	20	16	metric	metric	ADJ
ejpam-4440	20	17	dimension	dimension	NOUN
ejpam-4440	20	18	,	,	PUNCT
ejpam-4440	20	19	called	call	VERB
ejpam-4440	20	20	the	the	DET
ejpam-4440	20	21	strong	strong	ADJ
ejpam-4440	20	22	metric	metric	ADJ
ejpam-4440	20	23	dimension	dimension	NOUN
ejpam-4440	20	24	which	which	PRON
ejpam-4440	20	25	is	be	AUX
ejpam-4440	20	26	the	the	DET
ejpam-4440	20	27	cardinality	cardinality	NOUN
ejpam-4440	20	28	∗corresponding	∗corresponde	VERB
ejpam-4440	20	29	author	author	NOUN
ejpam-4440	20	30	.	.	PUNCT
ejpam-4440	21	1	doi	doi	NOUN
ejpam-4440	21	2	:	:	PUNCT
ejpam-4440	21	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4440	https://doi.org/10.29020/nybg.ejpam.v15i3.4440	PROPN
ejpam-4440	21	4	email	email	NOUN
ejpam-4440	21	5	addresses	address	VERB
ejpam-4440	21	6	:	:	PUNCT
ejpam-4440	21	7	helyn.sumaoy@g.msuiit.edu.ph	helyn.sumaoy@g.msuiit.edu.ph	PROPN
ejpam-4440	21	8	(	(	PUNCT
ejpam-4440	21	9	h.	h.	NOUN
ejpam-4440	21	10	sumaoy	sumaoy	PROPN
ejpam-4440	21	11	)	)	PUNCT
ejpam-4440	21	12	,	,	PUNCT
ejpam-4440	21	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4440	21	14	(	(	PUNCT
ejpam-4440	21	15	h.	h.	PROPN
ejpam-4440	21	16	rara	rara	PROPN
ejpam-4440	21	17	)	)	PUNCT
ejpam-4440	21	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4440	21	19	1201	1201	NUM
ejpam-4440	22	1	©	©	PROPN
ejpam-4440	22	2	2022	2022	NUM
ejpam-4440	22	3	ejpam	ejpam	VERB
ejpam-4440	22	4	all	all	DET
ejpam-4440	22	5	rights	right	NOUN
ejpam-4440	22	6	reserved	reserve	VERB
ejpam-4440	22	7	.	.	PUNCT
ejpam-4440	23	1	h.	h.	PROPN
ejpam-4440	23	2	sumaoy	sumaoy	PROPN
ejpam-4440	23	3	,	,	PUNCT
ejpam-4440	23	4	h.	h.	PROPN
ejpam-4440	23	5	rara	rara	PROPN
ejpam-4440	23	6	/	/	SYM
ejpam-4440	23	7	eur	eur	PROPN
ejpam-4440	23	8	.	.	PUNCT
ejpam-4440	24	1	j.	j.	PROPN
ejpam-4440	24	2	pure	pure	PROPN
ejpam-4440	24	3	appl	appl	PROPN
ejpam-4440	24	4	.	.	PROPN
ejpam-4440	24	5	math	math	PROPN
ejpam-4440	24	6	,	,	PUNCT
ejpam-4440	24	7	15	15	NUM
ejpam-4440	24	8	(	(	PUNCT
ejpam-4440	24	9	3	3	NUM
ejpam-4440	24	10	)	)	PUNCT
ejpam-4440	24	11	(	(	PUNCT
ejpam-4440	24	12	2022	2022	NUM
ejpam-4440	24	13	)	)	PUNCT
ejpam-4440	24	14	,	,	PUNCT
ejpam-4440	24	15	1201	1201	NUM
ejpam-4440	24	16	-	-	SYM
ejpam-4440	24	17	1210	1210	NUM
ejpam-4440	24	18	1202	1202	NUM
ejpam-4440	24	19	of	of	ADP
ejpam-4440	24	20	a	a	DET
ejpam-4440	24	21	minimum	minimum	ADJ
ejpam-4440	24	22	strong	strong	ADJ
ejpam-4440	24	23	resolving	resolving	NOUN
ejpam-4440	24	24	set	set	NOUN
ejpam-4440	24	25	.	.	PUNCT
ejpam-4440	25	1	furthermore	furthermore	ADV
ejpam-4440	25	2	,	,	PUNCT
ejpam-4440	25	3	several	several	ADJ
ejpam-4440	25	4	remarkable	remarkable	ADJ
ejpam-4440	25	5	studies	study	NOUN
ejpam-4440	25	6	are	be	AUX
ejpam-4440	25	7	continuously	continuously	ADV
ejpam-4440	25	8	appearing	appear	VERB
ejpam-4440	25	9	after	after	ADP
ejpam-4440	25	10	its	its	PRON
ejpam-4440	25	11	introduction	introduction	NOUN
ejpam-4440	25	12	by	by	ADP
ejpam-4440	25	13	p.j	p.j	PROPN
ejpam-4440	25	14	.	.	PROPN
ejpam-4440	25	15	slater	slater	PROPN
ejpam-4440	25	16	who	who	PRON
ejpam-4440	25	17	discovered	discover	VERB
ejpam-4440	25	18	its	its	PRON
ejpam-4440	25	19	usefulness	usefulness	NOUN
ejpam-4440	25	20	when	when	SCONJ
ejpam-4440	25	21	working	work	VERB
ejpam-4440	25	22	with	with	ADP
ejpam-4440	25	23	the	the	DET
ejpam-4440	25	24	united	united	PROPN
ejpam-4440	25	25	states	states	PROPN
ejpam-4440	25	26	sonar	sonar	NOUN
ejpam-4440	25	27	and	and	CCONJ
ejpam-4440	25	28	coast	coast	NOUN
ejpam-4440	25	29	guard	guard	PROPN
ejpam-4440	25	30	loran	loran	NOUN
ejpam-4440	25	31	(	(	PUNCT
ejpam-4440	25	32	long	long	ADJ
ejpam-4440	25	33	range	range	NOUN
ejpam-4440	25	34	aids	aid	NOUN
ejpam-4440	25	35	to	to	ADP
ejpam-4440	25	36	navigation	navigation	NOUN
ejpam-4440	25	37	)	)	PUNCT
ejpam-4440	25	38	stations	station	NOUN
ejpam-4440	25	39	.	.	PUNCT
ejpam-4440	26	1	its	its	PRON
ejpam-4440	26	2	applications	application	NOUN
ejpam-4440	26	3	have	have	AUX
ejpam-4440	26	4	arisen	arise	VERB
ejpam-4440	26	5	in	in	ADP
ejpam-4440	26	6	many	many	ADJ
ejpam-4440	26	7	diverse	diverse	ADJ
ejpam-4440	26	8	fields	field	NOUN
ejpam-4440	26	9	including	include	VERB
ejpam-4440	26	10	chemistry	chemistry	NOUN
ejpam-4440	26	11	,	,	PUNCT
ejpam-4440	26	12	for	for	ADP
ejpam-4440	26	13	representing	represent	VERB
ejpam-4440	26	14	chemical	chemical	NOUN
ejpam-4440	26	15	compounds	compound	NOUN
ejpam-4440	26	16	[	[	X
ejpam-4440	26	17	7	7	NUM
ejpam-4440	26	18	]	]	PUNCT
ejpam-4440	26	19	,	,	PUNCT
ejpam-4440	26	20	the	the	DET
ejpam-4440	26	21	robot	robot	NOUN
ejpam-4440	26	22	navigation	navigation	NOUN
ejpam-4440	27	1	[	[	X
ejpam-4440	27	2	12	12	NUM
ejpam-4440	27	3	]	]	PUNCT
ejpam-4440	27	4	and	and	CCONJ
ejpam-4440	27	5	geographical	geographical	ADJ
ejpam-4440	27	6	routing	routing	NOUN
ejpam-4440	27	7	protocols	protocol	NOUN
ejpam-4440	28	1	[	[	X
ejpam-4440	28	2	9	9	NUM
ejpam-4440	28	3	]	]	PUNCT
ejpam-4440	28	4	,	,	PUNCT
ejpam-4440	28	5	to	to	PART
ejpam-4440	28	6	name	name	VERB
ejpam-4440	28	7	a	a	DET
ejpam-4440	28	8	few	few	ADJ
ejpam-4440	28	9	.	.	PUNCT
ejpam-4440	29	1	in	in	ADP
ejpam-4440	29	2	[	[	X
ejpam-4440	29	3	13	13	NUM
ejpam-4440	29	4	]	]	PUNCT
ejpam-4440	29	5	,	,	PUNCT
ejpam-4440	29	6	an	an	DET
ejpam-4440	29	7	variant	variant	NOUN
ejpam-4440	29	8	called	call	VERB
ejpam-4440	29	9	the	the	DET
ejpam-4440	29	10	strong	strong	ADJ
ejpam-4440	29	11	metric	metric	ADJ
ejpam-4440	29	12	dimension	dimension	NOUN
ejpam-4440	29	13	,	,	PUNCT
ejpam-4440	29	14	was	be	AUX
ejpam-4440	29	15	presented	present	VERB
ejpam-4440	29	16	where	where	SCONJ
ejpam-4440	29	17	the	the	DET
ejpam-4440	29	18	authors	author	NOUN
ejpam-4440	29	19	illustrated	illustrate	VERB
ejpam-4440	29	20	its	its	PRON
ejpam-4440	29	21	application	application	NOUN
ejpam-4440	29	22	to	to	ADP
ejpam-4440	29	23	combinatorial	combinatorial	ADJ
ejpam-4440	29	24	search	search	NOUN
ejpam-4440	29	25	.	.	PUNCT
ejpam-4440	30	1	along	along	ADP
ejpam-4440	30	2	with	with	ADP
ejpam-4440	30	3	the	the	DET
ejpam-4440	30	4	increasing	increase	VERB
ejpam-4440	30	5	discovery	discovery	NOUN
ejpam-4440	30	6	of	of	ADP
ejpam-4440	30	7	its	its	PRON
ejpam-4440	30	8	applications	application	NOUN
ejpam-4440	30	9	,	,	PUNCT
ejpam-4440	30	10	theoretical	theoretical	ADJ
ejpam-4440	30	11	studies	study	NOUN
ejpam-4440	30	12	on	on	ADP
ejpam-4440	30	13	this	this	DET
ejpam-4440	30	14	invariant	invariant	NOUN
ejpam-4440	30	15	also	also	ADV
ejpam-4440	30	16	appear	appear	VERB
ejpam-4440	30	17	in	in	ADP
ejpam-4440	30	18	several	several	ADJ
ejpam-4440	30	19	number	number	NOUN
ejpam-4440	30	20	of	of	ADP
ejpam-4440	30	21	other	other	ADJ
ejpam-4440	30	22	papers	paper	NOUN
ejpam-4440	30	23	including	include	VERB
ejpam-4440	30	24	[	[	X
ejpam-4440	30	25	3	3	NUM
ejpam-4440	30	26	]	]	PUNCT
ejpam-4440	30	27	,	,	PUNCT
ejpam-4440	30	28	[	[	X
ejpam-4440	30	29	2	2	NUM
ejpam-4440	30	30	]	]	PUNCT
ejpam-4440	30	31	,	,	PUNCT
ejpam-4440	30	32	[	[	X
ejpam-4440	30	33	5	5	NUM
ejpam-4440	30	34	]	]	PUNCT
ejpam-4440	30	35	,	,	PUNCT
ejpam-4440	30	36	[	[	X
ejpam-4440	30	37	8	8	NUM
ejpam-4440	30	38	]	]	PUNCT
ejpam-4440	30	39	.	.	PUNCT
ejpam-4440	31	1	this	this	DET
ejpam-4440	31	2	paper	paper	NOUN
ejpam-4440	31	3	intends	intend	VERB
ejpam-4440	31	4	to	to	PART
ejpam-4440	31	5	generate	generate	VERB
ejpam-4440	31	6	additional	additional	ADJ
ejpam-4440	31	7	theoretical	theoretical	ADJ
ejpam-4440	31	8	results	result	NOUN
ejpam-4440	31	9	and	and	CCONJ
ejpam-4440	31	10	help	help	VERB
ejpam-4440	31	11	widen	widen	VERB
ejpam-4440	31	12	the	the	DET
ejpam-4440	31	13	pool	pool	NOUN
ejpam-4440	31	14	of	of	ADP
ejpam-4440	31	15	existing	exist	VERB
ejpam-4440	31	16	studies	study	NOUN
ejpam-4440	31	17	from	from	ADP
ejpam-4440	31	18	where	where	SCONJ
ejpam-4440	31	19	new	new	ADJ
ejpam-4440	31	20	researchers	researcher	NOUN
ejpam-4440	31	21	may	may	AUX
ejpam-4440	31	22	draw	draw	VERB
ejpam-4440	31	23	new	new	ADJ
ejpam-4440	31	24	insights	insight	NOUN
ejpam-4440	31	25	and	and	CCONJ
ejpam-4440	31	26	directions	direction	NOUN
ejpam-4440	31	27	for	for	ADP
ejpam-4440	31	28	further	further	ADJ
ejpam-4440	31	29	investigation	investigation	NOUN
ejpam-4440	31	30	.	.	PUNCT
ejpam-4440	32	1	let	let	VERB
ejpam-4440	32	2	g	g	NOUN
ejpam-4440	32	3	=	=	PUNCT
ejpam-4440	32	4	(	(	PUNCT
ejpam-4440	32	5	v	v	NOUN
ejpam-4440	32	6	(	(	PUNCT
ejpam-4440	32	7	g	g	NOUN
ejpam-4440	32	8	)	)	PUNCT
ejpam-4440	32	9	,	,	PUNCT
ejpam-4440	32	10	e(g	e(g	PROPN
ejpam-4440	32	11	)	)	PUNCT
ejpam-4440	32	12	)	)	PUNCT
ejpam-4440	33	1	be	be	AUX
ejpam-4440	33	2	a	a	DET
ejpam-4440	33	3	graph	graph	NOUN
ejpam-4440	33	4	.	.	PUNCT
ejpam-4440	33	5	ng(v	ng(v	PUNCT
ejpam-4440	33	6	)	)	PUNCT
ejpam-4440	34	1	=	=	PRON
ejpam-4440	34	2	{	{	PUNCT
ejpam-4440	34	3	u	u	NOUN
ejpam-4440	34	4	∈	∈	PROPN
ejpam-4440	34	5	v	v	NOUN
ejpam-4440	34	6	(	(	PUNCT
ejpam-4440	34	7	g	g	NOUN
ejpam-4440	34	8	)	)	PUNCT
ejpam-4440	34	9	:	:	PUNCT
ejpam-4440	34	10	uv	uv	PROPN
ejpam-4440	34	11	∈	∈	PROPN
ejpam-4440	34	12	e(g	e(g	PROPN
ejpam-4440	34	13	)	)	PUNCT
ejpam-4440	34	14	}	}	PUNCT
ejpam-4440	34	15	is	be	AUX
ejpam-4440	34	16	a	a	DET
ejpam-4440	34	17	neighborhood	neighborhood	NOUN
ejpam-4440	34	18	of	of	ADP
ejpam-4440	34	19	v.	v.	ADP
ejpam-4440	34	20	an	an	DET
ejpam-4440	34	21	element	element	NOUN
ejpam-4440	34	22	u	u	NOUN
ejpam-4440	34	23	∈	∈	PROPN
ejpam-4440	34	24	ng(v	ng(v	PUNCT
ejpam-4440	34	25	)	)	PUNCT
ejpam-4440	34	26	is	be	AUX
ejpam-4440	34	27	called	call	VERB
ejpam-4440	34	28	a	a	DET
ejpam-4440	34	29	neighbor	neighbor	NOUN
ejpam-4440	34	30	of	of	ADP
ejpam-4440	34	31	v.	v.	CCONJ
ejpam-4440	34	32	ng[v	ng[v	X
ejpam-4440	34	33	]	]	X
ejpam-4440	34	34	=	=	SYM
ejpam-4440	34	35	ng(v	ng(v	X
ejpam-4440	34	36	)	)	PUNCT
ejpam-4440	34	37	∪	∪	ADP
ejpam-4440	34	38	{	{	PUNCT
ejpam-4440	34	39	v	v	NOUN
ejpam-4440	34	40	}	}	PUNCT
ejpam-4440	34	41	is	be	AUX
ejpam-4440	34	42	a	a	DET
ejpam-4440	34	43	closed	closed	ADJ
ejpam-4440	34	44	neighborhood	neighborhood	NOUN
ejpam-4440	34	45	of	of	ADP
ejpam-4440	34	46	v.	v.	ADP
ejpam-4440	34	47	the	the	DET
ejpam-4440	34	48	degree	degree	NOUN
ejpam-4440	34	49	of	of	ADP
ejpam-4440	34	50	v	v	NOUN
ejpam-4440	34	51	,	,	PUNCT
ejpam-4440	34	52	denoted	denote	VERB
ejpam-4440	34	53	by	by	ADP
ejpam-4440	34	54	degg(v	degg(v	PROPN
ejpam-4440	34	55	)	)	PUNCT
ejpam-4440	34	56	,	,	PUNCT
ejpam-4440	34	57	is	be	AUX
ejpam-4440	34	58	equal	equal	ADJ
ejpam-4440	34	59	to	to	ADP
ejpam-4440	34	60	|ng(v)|	|ng(v)|	NOUN
ejpam-4440	34	61	.	.	PUNCT
ejpam-4440	35	1	for	for	ADP
ejpam-4440	35	2	s	s	PROPN
ejpam-4440	35	3	⊆	⊆	NUM
ejpam-4440	35	4	v	v	NOUN
ejpam-4440	35	5	(	(	PUNCT
ejpam-4440	35	6	g	g	NOUN
ejpam-4440	35	7	)	)	PUNCT
ejpam-4440	35	8	,	,	PUNCT
ejpam-4440	35	9	ng(s	ng(s	NUM
ejpam-4440	35	10	)	)	PUNCT
ejpam-4440	35	11	=	=	SYM
ejpam-4440	35	12	⋃	⋃	ADP
ejpam-4440	35	13	v∈s	v∈s	NOUN
ejpam-4440	35	14	ng(v	ng(v	NOUN
ejpam-4440	35	15	)	)	PUNCT
ejpam-4440	35	16	and	and	CCONJ
ejpam-4440	35	17	ng[s	ng[	NOUN
ejpam-4440	35	18	]	]	PUNCT
ejpam-4440	35	19	=	=	PUNCT
ejpam-4440	35	20	⋃	⋃	VERB
ejpam-4440	35	21	v∈s	v∈s	ADJ
ejpam-4440	35	22	ng[v	ng[v	NOUN
ejpam-4440	35	23	]	]	PUNCT
ejpam-4440	35	24	.	.	PUNCT
ejpam-4440	36	1	a	a	DET
ejpam-4440	36	2	clique	clique	NOUN
ejpam-4440	36	3	in	in	ADP
ejpam-4440	36	4	a	a	DET
ejpam-4440	36	5	graph	graph	NOUN
ejpam-4440	36	6	g	g	NOUN
ejpam-4440	36	7	is	be	AUX
ejpam-4440	36	8	a	a	DET
ejpam-4440	36	9	complete	complete	ADJ
ejpam-4440	36	10	induced	induced	ADJ
ejpam-4440	36	11	subgraph	subgraph	NOUN
ejpam-4440	36	12	.	.	PUNCT
ejpam-4440	37	1	a	a	DET
ejpam-4440	37	2	set	set	NOUN
ejpam-4440	37	3	c	c	NOUN
ejpam-4440	37	4	⊆	⊆	NUM
ejpam-4440	37	5	v	v	NOUN
ejpam-4440	37	6	(	(	PUNCT
ejpam-4440	37	7	g	g	NOUN
ejpam-4440	37	8	)	)	PUNCT
ejpam-4440	37	9	is	be	AUX
ejpam-4440	37	10	called	call	VERB
ejpam-4440	37	11	a	a	DET
ejpam-4440	37	12	superclique	superclique	NOUN
ejpam-4440	37	13	in	in	ADP
ejpam-4440	37	14	g	g	PROPN
ejpam-4440	37	15	if	if	SCONJ
ejpam-4440	37	16	⟨c⟩	⟨c⟩	PROPN
ejpam-4440	37	17	is	be	AUX
ejpam-4440	37	18	a	a	DET
ejpam-4440	37	19	clique	clique	NOUN
ejpam-4440	37	20	and	and	CCONJ
ejpam-4440	37	21	for	for	ADP
ejpam-4440	37	22	every	every	DET
ejpam-4440	37	23	pair	pair	NOUN
ejpam-4440	37	24	of	of	ADP
ejpam-4440	37	25	distinct	distinct	ADJ
ejpam-4440	37	26	vertices	vertex	NOUN
ejpam-4440	37	27	u	u	NOUN
ejpam-4440	37	28	,	,	PUNCT
ejpam-4440	37	29	v	v	NOUN
ejpam-4440	37	30	∈	∈	ADJ
ejpam-4440	37	31	c	c	NOUN
ejpam-4440	37	32	,	,	PUNCT
ejpam-4440	37	33	there	there	PRON
ejpam-4440	37	34	exists	exist	VERB
ejpam-4440	37	35	w	w	PROPN
ejpam-4440	37	36	∈	∈	PROPN
ejpam-4440	37	37	v	v	ADP
ejpam-4440	37	38	(	(	PUNCT
ejpam-4440	37	39	g	g	NOUN
ejpam-4440	37	40	)	)	PUNCT
ejpam-4440	37	41	\	\	PUNCT
ejpam-4440	38	1	c	c	NOUN
ejpam-4440	38	2	such	such	ADJ
ejpam-4440	38	3	that	that	PRON
ejpam-4440	38	4	w	w	PROPN
ejpam-4440	38	5	∈	∈	PROPN
ejpam-4440	38	6	ng(u	ng(u	NOUN
ejpam-4440	38	7	)	)	PUNCT
ejpam-4440	38	8	\	\	NOUN
ejpam-4440	38	9	ng(v	ng(v	PUNCT
ejpam-4440	38	10	)	)	PUNCT
ejpam-4440	38	11	or	or	CCONJ
ejpam-4440	38	12	w	w	PROPN
ejpam-4440	38	13	∈	∈	PROPN
ejpam-4440	38	14	ng(v	ng(v	NOUN
ejpam-4440	38	15	)	)	PUNCT
ejpam-4440	38	16	\	\	NOUN
ejpam-4440	38	17	ng(u	ng(u	NOUN
ejpam-4440	38	18	)	)	PUNCT
ejpam-4440	38	19	.	.	PUNCT
ejpam-4440	39	1	a	a	DET
ejpam-4440	39	2	superclique	superclique	NOUN
ejpam-4440	39	3	c	c	NOUN
ejpam-4440	39	4	is	be	AUX
ejpam-4440	39	5	maximum	maximum	ADJ
ejpam-4440	39	6	in	in	ADP
ejpam-4440	39	7	g	g	PROPN
ejpam-4440	39	8	if	if	SCONJ
ejpam-4440	39	9	|c|	|c|	PROPN
ejpam-4440	39	10	≥	≥	NOUN
ejpam-4440	39	11	|c∗|	|c∗|	VERB
ejpam-4440	39	12	for	for	SCONJ
ejpam-4440	39	13	all	all	DET
ejpam-4440	39	14	supercliques	superclique	NOUN
ejpam-4440	39	15	c∗	c∗	PROPN
ejpam-4440	39	16	in	in	ADP
ejpam-4440	39	17	g.	g.	PROPN
ejpam-4440	39	18	the	the	DET
ejpam-4440	39	19	superclique	superclique	ADJ
ejpam-4440	39	20	number	number	NOUN
ejpam-4440	39	21	,	,	PUNCT
ejpam-4440	39	22	ωs(g	ωs(g	NUM
ejpam-4440	39	23	)	)	PUNCT
ejpam-4440	39	24	,	,	PUNCT
ejpam-4440	39	25	of	of	ADP
ejpam-4440	39	26	g	g	PROPN
ejpam-4440	39	27	is	be	AUX
ejpam-4440	39	28	the	the	DET
ejpam-4440	39	29	cardinality	cardinality	NOUN
ejpam-4440	39	30	of	of	ADP
ejpam-4440	39	31	a	a	DET
ejpam-4440	39	32	maximum	maximum	ADJ
ejpam-4440	39	33	superclique	superclique	NOUN
ejpam-4440	39	34	in	in	ADP
ejpam-4440	39	35	g.	g.	PROPN
ejpam-4440	39	36	a	a	DET
ejpam-4440	39	37	superclique	superclique	NOUN
ejpam-4440	39	38	c	c	NOUN
ejpam-4440	39	39	is	be	AUX
ejpam-4440	39	40	called	call	VERB
ejpam-4440	39	41	a	a	DET
ejpam-4440	39	42	dominated	dominate	VERB
ejpam-4440	39	43	superclique	superclique	NOUN
ejpam-4440	39	44	if	if	SCONJ
ejpam-4440	39	45	for	for	ADP
ejpam-4440	39	46	every	every	DET
ejpam-4440	39	47	u	u	PROPN
ejpam-4440	39	48	∈	∈	PROPN
ejpam-4440	39	49	c	c	NOUN
ejpam-4440	39	50	,	,	PUNCT
ejpam-4440	39	51	there	there	PRON
ejpam-4440	39	52	exists	exist	VERB
ejpam-4440	39	53	v	v	ADP
ejpam-4440	39	54	∈	∈	PROPN
ejpam-4440	39	55	v	v	NOUN
ejpam-4440	39	56	(	(	PUNCT
ejpam-4440	39	57	g	g	NOUN
ejpam-4440	39	58	)	)	PUNCT
ejpam-4440	39	59	\	\	PUNCT
ejpam-4440	40	1	c	c	NOUN
ejpam-4440	40	2	such	such	ADJ
ejpam-4440	40	3	that	that	DET
ejpam-4440	40	4	uv	uv	PROPN
ejpam-4440	40	5	∈	∈	PROPN
ejpam-4440	40	6	e(g	e(g	PROPN
ejpam-4440	40	7	)	)	PUNCT
ejpam-4440	40	8	.	.	PUNCT
ejpam-4440	41	1	the	the	DET
ejpam-4440	41	2	dominated	dominate	VERB
ejpam-4440	41	3	superclique	superclique	ADJ
ejpam-4440	41	4	number	number	NOUN
ejpam-4440	41	5	,	,	PUNCT
ejpam-4440	41	6	ωds(g	ωds(g	PROPN
ejpam-4440	41	7	)	)	PUNCT
ejpam-4440	41	8	,	,	PUNCT
ejpam-4440	41	9	of	of	ADP
ejpam-4440	41	10	g	g	PROPN
ejpam-4440	41	11	is	be	AUX
ejpam-4440	41	12	the	the	DET
ejpam-4440	41	13	cardinality	cardinality	NOUN
ejpam-4440	41	14	of	of	ADP
ejpam-4440	41	15	a	a	DET
ejpam-4440	41	16	maximum	maximum	ADV
ejpam-4440	41	17	dominated	dominate	VERB
ejpam-4440	41	18	superclique	superclique	NOUN
ejpam-4440	41	19	in	in	ADP
ejpam-4440	41	20	g.	g.	PROPN
ejpam-4440	41	21	a	a	DET
ejpam-4440	41	22	vertex	vertex	NOUN
ejpam-4440	41	23	u	u	NOUN
ejpam-4440	41	24	of	of	ADP
ejpam-4440	41	25	g	g	PROPN
ejpam-4440	41	26	is	be	AUX
ejpam-4440	41	27	maximally	maximally	ADV
ejpam-4440	41	28	distant	distant	ADJ
ejpam-4440	41	29	from	from	ADP
ejpam-4440	41	30	vertex	vertex	NOUN
ejpam-4440	41	31	v	v	NOUN
ejpam-4440	41	32	of	of	ADP
ejpam-4440	41	33	g	g	NOUN
ejpam-4440	41	34	,	,	PUNCT
ejpam-4440	41	35	u	u	PROPN
ejpam-4440	41	36	̸=	̸=	PROPN
ejpam-4440	41	37	v	v	NOUN
ejpam-4440	41	38	,	,	PUNCT
ejpam-4440	41	39	if	if	SCONJ
ejpam-4440	41	40	for	for	ADP
ejpam-4440	41	41	every	every	DET
ejpam-4440	41	42	vertex	vertex	NOUN
ejpam-4440	41	43	w	w	PROPN
ejpam-4440	41	44	∈	∈	PROPN
ejpam-4440	41	45	ng(u	ng(u	NOUN
ejpam-4440	41	46	)	)	PUNCT
ejpam-4440	41	47	,	,	PUNCT
ejpam-4440	41	48	dg(v	dg(v	X
ejpam-4440	41	49	,	,	PUNCT
ejpam-4440	41	50	w	w	NOUN
ejpam-4440	41	51	)	)	PUNCT
ejpam-4440	41	52	≤	≤	NOUN
ejpam-4440	41	53	dg(u	dg(u	ADJ
ejpam-4440	41	54	,	,	PUNCT
ejpam-4440	41	55	v	v	NOUN
ejpam-4440	41	56	)	)	PUNCT
ejpam-4440	41	57	.	.	PUNCT
ejpam-4440	42	1	if	if	SCONJ
ejpam-4440	42	2	u	u	NOUN
ejpam-4440	42	3	is	be	AUX
ejpam-4440	42	4	maximally	maximally	ADV
ejpam-4440	42	5	distant	distant	ADJ
ejpam-4440	42	6	from	from	ADP
ejpam-4440	42	7	v	v	NOUN
ejpam-4440	42	8	and	and	CCONJ
ejpam-4440	42	9	v	v	NOUN
ejpam-4440	42	10	is	be	AUX
ejpam-4440	42	11	maximally	maximally	ADV
ejpam-4440	42	12	distant	distant	ADJ
ejpam-4440	42	13	from	from	ADP
ejpam-4440	42	14	u	u	NOUN
ejpam-4440	42	15	,	,	PUNCT
ejpam-4440	42	16	then	then	ADV
ejpam-4440	42	17	we	we	PRON
ejpam-4440	42	18	say	say	VERB
ejpam-4440	42	19	that	that	SCONJ
ejpam-4440	42	20	u	u	PROPN
ejpam-4440	42	21	and	and	CCONJ
ejpam-4440	42	22	v	v	NOUN
ejpam-4440	42	23	are	be	AUX
ejpam-4440	42	24	mutually	mutually	ADV
ejpam-4440	42	25	maximally	maximally	ADV
ejpam-4440	42	26	distant	distant	ADJ
ejpam-4440	42	27	,	,	PUNCT
ejpam-4440	42	28	denoted	denote	VERB
ejpam-4440	42	29	by	by	ADP
ejpam-4440	42	30	ummdv	ummdv	NOUN
ejpam-4440	42	31	.	.	PUNCT
ejpam-4440	43	1	a	a	DET
ejpam-4440	43	2	vertex	vertex	NOUN
ejpam-4440	43	3	x	x	X
ejpam-4440	43	4	of	of	ADP
ejpam-4440	43	5	a	a	DET
ejpam-4440	43	6	graph	graph	NOUN
ejpam-4440	43	7	g	g	NOUN
ejpam-4440	43	8	is	be	AUX
ejpam-4440	43	9	said	say	VERB
ejpam-4440	43	10	to	to	PART
ejpam-4440	43	11	resolve	resolve	VERB
ejpam-4440	43	12	two	two	NUM
ejpam-4440	43	13	vertices	vertex	NOUN
ejpam-4440	43	14	u	u	NOUN
ejpam-4440	43	15	and	and	CCONJ
ejpam-4440	43	16	v	v	NOUN
ejpam-4440	43	17	of	of	ADP
ejpam-4440	43	18	g	g	PROPN
ejpam-4440	43	19	if	if	SCONJ
ejpam-4440	43	20	dg(x	dg(x	NUM
ejpam-4440	43	21	,	,	PUNCT
ejpam-4440	43	22	u	u	NOUN
ejpam-4440	43	23	)	)	PUNCT
ejpam-4440	43	24	̸=	̸=	PROPN
ejpam-4440	43	25	dg(x	dg(x	NUM
ejpam-4440	43	26	,	,	PUNCT
ejpam-4440	43	27	v	v	NOUN
ejpam-4440	43	28	)	)	PUNCT
ejpam-4440	43	29	.	.	PUNCT
ejpam-4440	44	1	for	for	ADP
ejpam-4440	44	2	an	an	DET
ejpam-4440	44	3	ordered	order	VERB
ejpam-4440	44	4	set	set	NOUN
ejpam-4440	44	5	w	w	NOUN
ejpam-4440	44	6	=	=	PUNCT
ejpam-4440	44	7	{	{	PUNCT
ejpam-4440	44	8	x1	x1	PROPN
ejpam-4440	44	9	,	,	PUNCT
ejpam-4440	44	10	...	...	PUNCT
ejpam-4440	44	11	,	,	PUNCT
ejpam-4440	44	12	xk	xk	ADJ
ejpam-4440	44	13	}	}	PUNCT
ejpam-4440	44	14	⊆	⊆	NUM
ejpam-4440	44	15	v	v	NOUN
ejpam-4440	44	16	(	(	PUNCT
ejpam-4440	44	17	g	g	NOUN
ejpam-4440	44	18	)	)	PUNCT
ejpam-4440	44	19	and	and	CCONJ
ejpam-4440	44	20	a	a	DET
ejpam-4440	44	21	vertex	vertex	NOUN
ejpam-4440	44	22	v	v	NOUN
ejpam-4440	44	23	in	in	ADP
ejpam-4440	44	24	g	g	PROPN
ejpam-4440	44	25	,	,	PUNCT
ejpam-4440	44	26	the	the	DET
ejpam-4440	44	27	k	k	NOUN
ejpam-4440	44	28	-	-	NOUN
ejpam-4440	44	29	vector	vector	NOUN
ejpam-4440	44	30	rg(v	rg(v	NOUN
ejpam-4440	44	31	/	/	SYM
ejpam-4440	44	32	w	w	NOUN
ejpam-4440	44	33	)	)	PUNCT
ejpam-4440	44	34	=	=	SYM
ejpam-4440	44	35	(	(	PUNCT
ejpam-4440	44	36	dg(v	dg(v	X
ejpam-4440	44	37	,	,	PUNCT
ejpam-4440	44	38	x1	x1	PROPN
ejpam-4440	44	39	)	)	PUNCT
ejpam-4440	44	40	,	,	PUNCT
ejpam-4440	44	41	dg(v	dg(v	X
ejpam-4440	44	42	,	,	PUNCT
ejpam-4440	44	43	x2	x2	PROPN
ejpam-4440	44	44	)	)	PUNCT
ejpam-4440	44	45	,	,	PUNCT
ejpam-4440	44	46	...	...	PUNCT
ejpam-4440	44	47	,	,	PUNCT
ejpam-4440	44	48	dg(v	dg(v	X
ejpam-4440	44	49	,	,	PUNCT
ejpam-4440	44	50	xk	xk	NOUN
ejpam-4440	44	51	)	)	PUNCT
ejpam-4440	44	52	)	)	PUNCT
ejpam-4440	44	53	is	be	AUX
ejpam-4440	44	54	called	call	VERB
ejpam-4440	44	55	the	the	DET
ejpam-4440	44	56	representation	representation	NOUN
ejpam-4440	44	57	of	of	ADP
ejpam-4440	44	58	v	v	NOUN
ejpam-4440	44	59	with	with	ADP
ejpam-4440	44	60	respect	respect	NOUN
ejpam-4440	44	61	to	to	ADP
ejpam-4440	44	62	w	w	PROPN
ejpam-4440	44	63	.	.	PUNCT
ejpam-4440	45	1	the	the	DET
ejpam-4440	45	2	set	set	NOUN
ejpam-4440	45	3	w	w	NOUN
ejpam-4440	45	4	is	be	AUX
ejpam-4440	45	5	a	a	DET
ejpam-4440	45	6	resolving	resolving	NOUN
ejpam-4440	45	7	set	set	VERB
ejpam-4440	45	8	for	for	ADP
ejpam-4440	45	9	g	g	PROPN
ejpam-4440	45	10	if	if	SCONJ
ejpam-4440	46	1	and	and	CCONJ
ejpam-4440	46	2	only	only	ADV
ejpam-4440	46	3	if	if	SCONJ
ejpam-4440	46	4	no	no	DET
ejpam-4440	46	5	two	two	NUM
ejpam-4440	46	6	vertices	vertex	NOUN
ejpam-4440	46	7	of	of	ADP
ejpam-4440	46	8	g	g	NOUN
ejpam-4440	46	9	have	have	VERB
ejpam-4440	46	10	the	the	DET
ejpam-4440	46	11	same	same	ADJ
ejpam-4440	46	12	representation	representation	NOUN
ejpam-4440	46	13	with	with	ADP
ejpam-4440	46	14	respect	respect	NOUN
ejpam-4440	46	15	to	to	ADP
ejpam-4440	46	16	w	w	PROPN
ejpam-4440	46	17	.	.	PUNCT
ejpam-4440	47	1	the	the	DET
ejpam-4440	47	2	metric	metric	ADJ
ejpam-4440	47	3	dimension	dimension	NOUN
ejpam-4440	47	4	of	of	ADP
ejpam-4440	47	5	g	g	NOUN
ejpam-4440	47	6	,	,	PUNCT
ejpam-4440	47	7	denoted	denote	VERB
ejpam-4440	47	8	by	by	ADP
ejpam-4440	47	9	dim(g	dim(g	PROPN
ejpam-4440	47	10	)	)	PUNCT
ejpam-4440	47	11	,	,	PUNCT
ejpam-4440	47	12	is	be	AUX
ejpam-4440	47	13	the	the	DET
ejpam-4440	47	14	minimum	minimum	ADJ
ejpam-4440	47	15	cardinality	cardinality	NOUN
ejpam-4440	47	16	over	over	ADP
ejpam-4440	47	17	all	all	DET
ejpam-4440	47	18	resolving	resolve	VERB
ejpam-4440	47	19	sets	set	NOUN
ejpam-4440	47	20	of	of	ADP
ejpam-4440	47	21	g.	g.	PROPN
ejpam-4440	47	22	a	a	DET
ejpam-4440	47	23	resolving	resolve	VERB
ejpam-4440	47	24	set	set	NOUN
ejpam-4440	47	25	of	of	ADP
ejpam-4440	47	26	cardinality	cardinality	PROPN
ejpam-4440	47	27	dim(g	dim(g	PROPN
ejpam-4440	47	28	)	)	PUNCT
ejpam-4440	47	29	is	be	AUX
ejpam-4440	47	30	called	call	VERB
ejpam-4440	47	31	basis	basis	NOUN
ejpam-4440	47	32	.	.	PUNCT
ejpam-4440	48	1	a	a	DET
ejpam-4440	48	2	set	set	NOUN
ejpam-4440	48	3	s	s	NOUN
ejpam-4440	48	4	⊆	⊆	NUM
ejpam-4440	48	5	v	v	NOUN
ejpam-4440	48	6	(	(	PUNCT
ejpam-4440	48	7	g	g	NOUN
ejpam-4440	48	8	)	)	PUNCT
ejpam-4440	48	9	of	of	ADP
ejpam-4440	48	10	vertices	vertex	NOUN
ejpam-4440	48	11	of	of	ADP
ejpam-4440	48	12	g	g	PROPN
ejpam-4440	48	13	is	be	AUX
ejpam-4440	48	14	a	a	DET
ejpam-4440	48	15	dominating	dominating	NOUN
ejpam-4440	48	16	set	set	NOUN
ejpam-4440	48	17	if	if	SCONJ
ejpam-4440	48	18	every	every	DET
ejpam-4440	48	19	u	u	PROPN
ejpam-4440	48	20	∈	∈	PROPN
ejpam-4440	48	21	v	v	NOUN
ejpam-4440	48	22	(	(	PUNCT
ejpam-4440	48	23	g	g	NOUN
ejpam-4440	48	24	)	)	PUNCT
ejpam-4440	48	25	\	\	PROPN
ejpam-4440	49	1	s	s	PART
ejpam-4440	49	2	is	be	AUX
ejpam-4440	49	3	adjacent	adjacent	ADJ
ejpam-4440	49	4	to	to	ADP
ejpam-4440	49	5	at	at	ADV
ejpam-4440	49	6	least	least	ADV
ejpam-4440	49	7	one	one	NUM
ejpam-4440	49	8	vertex	vertex	NOUN
ejpam-4440	49	9	v	v	ADP
ejpam-4440	49	10	∈	∈	NOUN
ejpam-4440	49	11	s.	s.	PROPN
ejpam-4440	50	1	the	the	DET
ejpam-4440	50	2	domination	domination	NOUN
ejpam-4440	50	3	number	number	NOUN
ejpam-4440	50	4	of	of	ADP
ejpam-4440	50	5	a	a	DET
ejpam-4440	50	6	graph	graph	NOUN
ejpam-4440	50	7	g	g	NOUN
ejpam-4440	50	8	,	,	PUNCT
ejpam-4440	50	9	denoted	denote	VERB
ejpam-4440	50	10	by	by	ADP
ejpam-4440	50	11	γ(g	γ(g	PROPN
ejpam-4440	50	12	)	)	PUNCT
ejpam-4440	50	13	,	,	PUNCT
ejpam-4440	50	14	is	be	AUX
ejpam-4440	50	15	given	give	VERB
ejpam-4440	50	16	by	by	ADP
ejpam-4440	50	17	γ(g	γ(g	PROPN
ejpam-4440	50	18	)	)	PUNCT
ejpam-4440	51	1	=	=	NOUN
ejpam-4440	51	2	min{|s|	min{|s|	NOUN
ejpam-4440	51	3	:	:	PUNCT
ejpam-4440	51	4	s	s	VERB
ejpam-4440	51	5	is	be	AUX
ejpam-4440	51	6	a	a	DET
ejpam-4440	51	7	dominating	dominating	NOUN
ejpam-4440	51	8	set	set	NOUN
ejpam-4440	51	9	of	of	ADP
ejpam-4440	51	10	g	g	NOUN
ejpam-4440	51	11	}	}	PUNCT
ejpam-4440	51	12	.	.	PUNCT
ejpam-4440	52	1	a	a	DET
ejpam-4440	52	2	subset	subset	NOUN
ejpam-4440	52	3	s	s	VERB
ejpam-4440	52	4	⊆	⊆	NUM
ejpam-4440	52	5	v	v	NOUN
ejpam-4440	52	6	(	(	PUNCT
ejpam-4440	52	7	g	g	NOUN
ejpam-4440	52	8	)	)	PUNCT
ejpam-4440	52	9	is	be	AUX
ejpam-4440	52	10	a	a	DET
ejpam-4440	52	11	strong	strong	ADJ
ejpam-4440	52	12	resolving	resolving	NOUN
ejpam-4440	52	13	dominating	dominating	NOUN
ejpam-4440	52	14	set	set	NOUN
ejpam-4440	52	15	of	of	ADP
ejpam-4440	52	16	g	g	PROPN
ejpam-4440	52	17	if	if	SCONJ
ejpam-4440	52	18	s	s	VERB
ejpam-4440	52	19	is	be	AUX
ejpam-4440	52	20	a	a	DET
ejpam-4440	52	21	dominating	dominating	NOUN
ejpam-4440	52	22	set	set	NOUN
ejpam-4440	52	23	and	and	CCONJ
ejpam-4440	52	24	for	for	ADP
ejpam-4440	52	25	every	every	DET
ejpam-4440	52	26	pair	pair	NOUN
ejpam-4440	52	27	of	of	ADP
ejpam-4440	52	28	vertices	vertex	NOUN
ejpam-4440	52	29	u	u	NOUN
ejpam-4440	52	30	,	,	PUNCT
ejpam-4440	52	31	v	v	NOUN
ejpam-4440	52	32	∈	∈	PROPN
ejpam-4440	52	33	v	v	NOUN
ejpam-4440	52	34	(	(	PUNCT
ejpam-4440	52	35	g	g	NOUN
ejpam-4440	52	36	)	)	PUNCT
ejpam-4440	52	37	,	,	PUNCT
ejpam-4440	52	38	there	there	PRON
ejpam-4440	52	39	exists	exist	VERB
ejpam-4440	52	40	a	a	DET
ejpam-4440	52	41	vertex	vertex	NOUN
ejpam-4440	52	42	w	w	ADP
ejpam-4440	52	43	∈	∈	NOUN
ejpam-4440	52	44	s	s	VERB
ejpam-4440	52	45	such	such	ADJ
ejpam-4440	52	46	that	that	SCONJ
ejpam-4440	52	47	u	u	PROPN
ejpam-4440	52	48	∈	∈	PROPN
ejpam-4440	52	49	ig[v	ig[v	PROPN
ejpam-4440	52	50	,	,	PUNCT
ejpam-4440	52	51	w	w	PROPN
ejpam-4440	52	52	]	]	PUNCT
ejpam-4440	52	53	or	or	CCONJ
ejpam-4440	52	54	v	v	ADP
ejpam-4440	52	55	∈	∈	PROPN
ejpam-4440	52	56	ig[u	ig[u	NOUN
ejpam-4440	52	57	,	,	PUNCT
ejpam-4440	52	58	w	w	NOUN
ejpam-4440	52	59	]	]	X
ejpam-4440	52	60	.	.	PUNCT
ejpam-4440	53	1	the	the	DET
ejpam-4440	53	2	smallest	small	ADJ
ejpam-4440	53	3	cardinality	cardinality	NOUN
ejpam-4440	53	4	of	of	ADP
ejpam-4440	53	5	a	a	DET
ejpam-4440	53	6	strong	strong	ADJ
ejpam-4440	53	7	resolving	resolving	NOUN
ejpam-4440	53	8	dominating	dominating	NOUN
ejpam-4440	53	9	set	set	NOUN
ejpam-4440	53	10	of	of	ADP
ejpam-4440	53	11	g	g	PROPN
ejpam-4440	53	12	is	be	AUX
ejpam-4440	53	13	called	call	VERB
ejpam-4440	53	14	the	the	DET
ejpam-4440	53	15	strong	strong	ADJ
ejpam-4440	53	16	resolving	resolving	NOUN
ejpam-4440	53	17	domination	domination	NOUN
ejpam-4440	53	18	number	number	NOUN
ejpam-4440	53	19	of	of	ADP
ejpam-4440	53	20	g	g	NOUN
ejpam-4440	53	21	and	and	CCONJ
ejpam-4440	53	22	is	be	AUX
ejpam-4440	53	23	denoted	denote	VERB
ejpam-4440	53	24	by	by	ADP
ejpam-4440	53	25	γsr(g	γsr(g	PROPN
ejpam-4440	53	26	)	)	PUNCT
ejpam-4440	53	27	.	.	PUNCT
ejpam-4440	54	1	a	a	DET
ejpam-4440	54	2	strong	strong	ADJ
ejpam-4440	54	3	resolving	resolve	VERB
ejpam-4440	54	4	dominating	dominating	NOUN
ejpam-4440	54	5	set	set	NOUN
ejpam-4440	54	6	of	of	ADP
ejpam-4440	54	7	cardinality	cardinality	PROPN
ejpam-4440	54	8	γsr(g	γsr(g	NOUN
ejpam-4440	54	9	)	)	PUNCT
ejpam-4440	54	10	is	be	AUX
ejpam-4440	54	11	called	call	VERB
ejpam-4440	54	12	a	a	DET
ejpam-4440	54	13	γsr	γsr	PROPN
ejpam-4440	54	14	-	-	PUNCT
ejpam-4440	54	15	set	set	NOUN
ejpam-4440	54	16	of	of	ADP
ejpam-4440	54	17	g.	g.	PROPN
ejpam-4440	54	18	h.	h.	PROPN
ejpam-4440	54	19	sumaoy	sumaoy	PROPN
ejpam-4440	54	20	,	,	PUNCT
ejpam-4440	54	21	h.	h.	PROPN
ejpam-4440	54	22	rara	rara	PROPN
ejpam-4440	54	23	/	/	SYM
ejpam-4440	54	24	eur	eur	PROPN
ejpam-4440	54	25	.	.	PUNCT
ejpam-4440	55	1	j.	j.	PROPN
ejpam-4440	55	2	pure	pure	PROPN
ejpam-4440	55	3	appl	appl	PROPN
ejpam-4440	55	4	.	.	PROPN
ejpam-4440	55	5	math	math	PROPN
ejpam-4440	55	6	,	,	PUNCT
ejpam-4440	55	7	15	15	NUM
ejpam-4440	55	8	(	(	PUNCT
ejpam-4440	55	9	3	3	NUM
ejpam-4440	55	10	)	)	PUNCT
ejpam-4440	55	11	(	(	PUNCT
ejpam-4440	55	12	2022	2022	NUM
ejpam-4440	55	13	)	)	PUNCT
ejpam-4440	55	14	,	,	PUNCT
ejpam-4440	55	15	1201	1201	NUM
ejpam-4440	55	16	-	-	SYM
ejpam-4440	55	17	1210	1210	NUM
ejpam-4440	55	18	1203	1203	NUM
ejpam-4440	55	19	a	a	DET
ejpam-4440	55	20	non	non	ADJ
ejpam-4440	55	21	-	-	ADJ
ejpam-4440	55	22	empty	empty	ADJ
ejpam-4440	55	23	set	set	NOUN
ejpam-4440	55	24	s	s	PROPN
ejpam-4440	55	25	⊆	⊆	NUM
ejpam-4440	55	26	v	v	NOUN
ejpam-4440	55	27	(	(	PUNCT
ejpam-4440	55	28	g	g	NOUN
ejpam-4440	55	29	)	)	PUNCT
ejpam-4440	55	30	of	of	ADP
ejpam-4440	55	31	a	a	DET
ejpam-4440	55	32	connected	connected	ADJ
ejpam-4440	55	33	graph	graph	NOUN
ejpam-4440	55	34	g	g	PROPN
ejpam-4440	55	35	is	be	AUX
ejpam-4440	55	36	a	a	DET
ejpam-4440	55	37	1	1	NUM
ejpam-4440	55	38	-	-	PUNCT
ejpam-4440	55	39	movable	movable	ADJ
ejpam-4440	55	40	dominating	dominating	NOUN
ejpam-4440	55	41	set	set	NOUN
ejpam-4440	55	42	of	of	ADP
ejpam-4440	55	43	g	g	PROPN
ejpam-4440	55	44	if	if	SCONJ
ejpam-4440	55	45	s	s	VERB
ejpam-4440	55	46	is	be	AUX
ejpam-4440	55	47	a	a	DET
ejpam-4440	55	48	dominating	dominating	NOUN
ejpam-4440	55	49	set	set	NOUN
ejpam-4440	55	50	of	of	ADP
ejpam-4440	55	51	g	g	PROPN
ejpam-4440	55	52	and	and	CCONJ
ejpam-4440	55	53	for	for	ADP
ejpam-4440	55	54	every	every	DET
ejpam-4440	55	55	v	v	NUM
ejpam-4440	55	56	∈	∈	PROPN
ejpam-4440	55	57	s	s	NOUN
ejpam-4440	55	58	,	,	PUNCT
ejpam-4440	55	59	either	either	CCONJ
ejpam-4440	55	60	s	s	VERB
ejpam-4440	55	61	\	\	PROPN
ejpam-4440	55	62	{	{	PUNCT
ejpam-4440	55	63	v	v	NOUN
ejpam-4440	55	64	}	}	PUNCT
ejpam-4440	55	65	is	be	AUX
ejpam-4440	55	66	a	a	DET
ejpam-4440	55	67	dominating	dominating	NOUN
ejpam-4440	55	68	set	set	NOUN
ejpam-4440	55	69	of	of	ADP
ejpam-4440	55	70	g	g	NOUN
ejpam-4440	55	71	or	or	CCONJ
ejpam-4440	55	72	there	there	ADV
ejpam-4440	55	73	exists	exist	VERB
ejpam-4440	55	74	a	a	DET
ejpam-4440	55	75	vertex	vertex	NOUN
ejpam-4440	55	76	u	u	NOUN
ejpam-4440	55	77	∈	∈	PROPN
ejpam-4440	55	78	(	(	PUNCT
ejpam-4440	55	79	v	v	NOUN
ejpam-4440	55	80	(	(	PUNCT
ejpam-4440	55	81	g	g	NOUN
ejpam-4440	55	82	)	)	PUNCT
ejpam-4440	55	83	\	\	PROPN
ejpam-4440	55	84	s	s	X
ejpam-4440	55	85	)	)	PUNCT
ejpam-4440	55	86	∩	∩	NOUN
ejpam-4440	55	87	ng(v	ng(v	NOUN
ejpam-4440	55	88	)	)	PUNCT
ejpam-4440	55	89	such	such	ADJ
ejpam-4440	55	90	that	that	SCONJ
ejpam-4440	55	91	(	(	PUNCT
ejpam-4440	55	92	s	s	NOUN
ejpam-4440	55	93	\	\	X
ejpam-4440	55	94	{	{	PUNCT
ejpam-4440	55	95	v	v	NOUN
ejpam-4440	55	96	}	}	PUNCT
ejpam-4440	55	97	)	)	PUNCT
ejpam-4440	55	98	∪	∪	ADP
ejpam-4440	55	99	{	{	PUNCT
ejpam-4440	55	100	u	u	NOUN
ejpam-4440	55	101	}	}	PUNCT
ejpam-4440	55	102	is	be	AUX
ejpam-4440	55	103	a	a	DET
ejpam-4440	55	104	dominating	dominating	NOUN
ejpam-4440	55	105	set	set	NOUN
ejpam-4440	55	106	of	of	ADP
ejpam-4440	55	107	g.	g.	PROPN
ejpam-4440	55	108	the	the	DET
ejpam-4440	55	109	1	1	NUM
ejpam-4440	55	110	-	-	PUNCT
ejpam-4440	55	111	movable	movable	ADJ
ejpam-4440	55	112	domination	domination	NOUN
ejpam-4440	55	113	number	number	NOUN
ejpam-4440	55	114	of	of	ADP
ejpam-4440	55	115	a	a	DET
ejpam-4440	55	116	graph	graph	NOUN
ejpam-4440	55	117	g	g	NOUN
ejpam-4440	55	118	,	,	PUNCT
ejpam-4440	55	119	denoted	denote	VERB
ejpam-4440	55	120	by	by	ADP
ejpam-4440	55	121	γ1m(g	γ1m(g	PROPN
ejpam-4440	55	122	)	)	PUNCT
ejpam-4440	55	123	is	be	AUX
ejpam-4440	55	124	the	the	DET
ejpam-4440	55	125	smallest	small	ADJ
ejpam-4440	55	126	cardinality	cardinality	NOUN
ejpam-4440	55	127	of	of	ADP
ejpam-4440	55	128	a	a	DET
ejpam-4440	55	129	1	1	NUM
ejpam-4440	55	130	-	-	PUNCT
ejpam-4440	55	131	movable	movable	ADJ
ejpam-4440	55	132	dominating	dominating	NOUN
ejpam-4440	55	133	set	set	NOUN
ejpam-4440	55	134	of	of	ADP
ejpam-4440	55	135	g.	g.	PROPN
ejpam-4440	55	136	a	a	DET
ejpam-4440	55	137	1	1	NUM
ejpam-4440	55	138	-	-	PUNCT
ejpam-4440	55	139	movable	movable	ADJ
ejpam-4440	55	140	dominating	dominating	NOUN
ejpam-4440	55	141	set	set	NOUN
ejpam-4440	55	142	of	of	ADP
ejpam-4440	55	143	cardinality	cardinality	PROPN
ejpam-4440	55	144	γ1m(g	γ1m(g	PROPN
ejpam-4440	55	145	)	)	PUNCT
ejpam-4440	55	146	is	be	AUX
ejpam-4440	55	147	referred	refer	VERB
ejpam-4440	55	148	to	to	ADP
ejpam-4440	55	149	as	as	ADP
ejpam-4440	55	150	a	a	DET
ejpam-4440	55	151	γ1m	γ1m	NOUN
ejpam-4440	55	152	-	-	PUNCT
ejpam-4440	55	153	set	set	NOUN
ejpam-4440	55	154	of	of	ADP
ejpam-4440	55	155	g.	g.	PROPN
ejpam-4440	55	156	a	a	DET
ejpam-4440	55	157	resolving	resolve	VERB
ejpam-4440	55	158	dominating	dominate	VERB
ejpam-4440	55	159	set	set	NOUN
ejpam-4440	55	160	s	s	PROPN
ejpam-4440	55	161	of	of	ADP
ejpam-4440	55	162	a	a	DET
ejpam-4440	55	163	graph	graph	NOUN
ejpam-4440	55	164	g	g	NOUN
ejpam-4440	55	165	is	be	AUX
ejpam-4440	55	166	a	a	DET
ejpam-4440	55	167	1	1	NUM
ejpam-4440	55	168	-	-	PUNCT
ejpam-4440	55	169	movable	movable	ADJ
ejpam-4440	55	170	resolving	resolving	NOUN
ejpam-4440	55	171	dominating	dominating	NOUN
ejpam-4440	55	172	set	set	NOUN
ejpam-4440	55	173	of	of	ADP
ejpam-4440	55	174	g	g	PROPN
ejpam-4440	55	175	if	if	SCONJ
ejpam-4440	55	176	for	for	SCONJ
ejpam-4440	55	177	every	every	DET
ejpam-4440	55	178	v	v	NUM
ejpam-4440	55	179	∈	∈	PROPN
ejpam-4440	55	180	s	s	NOUN
ejpam-4440	55	181	,	,	PUNCT
ejpam-4440	55	182	either	either	CCONJ
ejpam-4440	55	183	s	s	VERB
ejpam-4440	55	184	\	\	PROPN
ejpam-4440	55	185	{	{	PUNCT
ejpam-4440	55	186	v	v	NOUN
ejpam-4440	55	187	}	}	PUNCT
ejpam-4440	55	188	is	be	AUX
ejpam-4440	55	189	a	a	DET
ejpam-4440	55	190	resolving	resolve	VERB
ejpam-4440	55	191	dominating	dominating	NOUN
ejpam-4440	55	192	set	set	NOUN
ejpam-4440	55	193	or	or	CCONJ
ejpam-4440	55	194	there	there	PRON
ejpam-4440	55	195	exists	exist	VERB
ejpam-4440	55	196	a	a	DET
ejpam-4440	55	197	vertex	vertex	NOUN
ejpam-4440	55	198	u	u	NOUN
ejpam-4440	55	199	∈	∈	PROPN
ejpam-4440	55	200	(	(	PUNCT
ejpam-4440	55	201	v	v	NOUN
ejpam-4440	55	202	(	(	PUNCT
ejpam-4440	55	203	g	g	NOUN
ejpam-4440	55	204	)	)	PUNCT
ejpam-4440	55	205	\	\	PROPN
ejpam-4440	55	206	s)∩ng(v	s)∩ng(v	PROPN
ejpam-4440	55	207	)	)	PUNCT
ejpam-4440	55	208	such	such	ADJ
ejpam-4440	55	209	that	that	SCONJ
ejpam-4440	55	210	(	(	PUNCT
ejpam-4440	55	211	s	s	AUX
ejpam-4440	55	212	\	\	X
ejpam-4440	55	213	{	{	PUNCT
ejpam-4440	55	214	v})∪	v})∪	PROPN
ejpam-4440	55	215	{	{	PUNCT
ejpam-4440	55	216	u	u	NOUN
ejpam-4440	55	217	}	}	PUNCT
ejpam-4440	55	218	is	be	AUX
ejpam-4440	55	219	a	a	DET
ejpam-4440	55	220	resolving	resolve	VERB
ejpam-4440	55	221	dominating	dominating	NOUN
ejpam-4440	55	222	set	set	NOUN
ejpam-4440	55	223	of	of	ADP
ejpam-4440	55	224	g.	g.	PROPN
ejpam-4440	55	225	the	the	DET
ejpam-4440	55	226	minimum	minimum	ADJ
ejpam-4440	55	227	cardinality	cardinality	NOUN
ejpam-4440	55	228	of	of	ADP
ejpam-4440	55	229	a	a	DET
ejpam-4440	55	230	1	1	NUM
ejpam-4440	55	231	-	-	PUNCT
ejpam-4440	55	232	movable	movable	ADJ
ejpam-4440	55	233	resolving	resolving	NOUN
ejpam-4440	55	234	dominating	dominating	NOUN
ejpam-4440	55	235	set	set	NOUN
ejpam-4440	55	236	of	of	ADP
ejpam-4440	55	237	g	g	NOUN
ejpam-4440	55	238	,	,	PUNCT
ejpam-4440	55	239	denoted	denote	VERB
ejpam-4440	55	240	by	by	ADP
ejpam-4440	55	241	γ1mr(g	γ1mr(g	PROPN
ejpam-4440	55	242	)	)	PUNCT
ejpam-4440	55	243	is	be	AUX
ejpam-4440	55	244	the	the	DET
ejpam-4440	55	245	1	1	NUM
ejpam-4440	55	246	-	-	PUNCT
ejpam-4440	55	247	movable	movable	ADJ
ejpam-4440	55	248	r	r	NOUN
ejpam-4440	55	249	-	-	PUNCT
ejpam-4440	55	250	domination	domination	NOUN
ejpam-4440	55	251	number	number	NOUN
ejpam-4440	55	252	of	of	ADP
ejpam-4440	55	253	g.	g.	PROPN
ejpam-4440	55	254	a	a	DET
ejpam-4440	55	255	1	1	NUM
ejpam-4440	55	256	-	-	PUNCT
ejpam-4440	55	257	movable	movable	ADJ
ejpam-4440	55	258	resolving	resolving	NOUN
ejpam-4440	55	259	dominating	dominating	NOUN
ejpam-4440	55	260	set	set	VERB
ejpam-4440	55	261	with	with	ADP
ejpam-4440	55	262	cardinality	cardinality	PROPN
ejpam-4440	55	263	γ1mr(g	γ1mr(g	PROPN
ejpam-4440	55	264	)	)	PUNCT
ejpam-4440	55	265	is	be	AUX
ejpam-4440	55	266	called	call	VERB
ejpam-4440	55	267	a	a	DET
ejpam-4440	55	268	γ1mr	γ1mr	NOUN
ejpam-4440	55	269	-	-	PUNCT
ejpam-4440	55	270	set	set	NOUN
ejpam-4440	55	271	of	of	ADP
ejpam-4440	55	272	g.	g.	PROPN
ejpam-4440	55	273	the	the	DET
ejpam-4440	55	274	join	join	NOUN
ejpam-4440	55	275	of	of	ADP
ejpam-4440	55	276	two	two	NUM
ejpam-4440	55	277	graphs	graph	NOUN
ejpam-4440	55	278	g	g	NOUN
ejpam-4440	55	279	and	and	CCONJ
ejpam-4440	55	280	h	h	NOUN
ejpam-4440	55	281	is	be	AUX
ejpam-4440	55	282	the	the	DET
ejpam-4440	55	283	graph	graph	NOUN
ejpam-4440	55	284	g	g	NOUN
ejpam-4440	55	285	+	+	CCONJ
ejpam-4440	55	286	h	h	NOUN
ejpam-4440	55	287	with	with	ADP
ejpam-4440	55	288	vertex	vertex	NOUN
ejpam-4440	55	289	set	set	VERB
ejpam-4440	55	290	v	v	NOUN
ejpam-4440	55	291	(	(	PUNCT
ejpam-4440	55	292	g	g	PROPN
ejpam-4440	55	293	+	+	NOUN
ejpam-4440	55	294	h	h	NOUN
ejpam-4440	55	295	)	)	PUNCT
ejpam-4440	56	1	=	=	NOUN
ejpam-4440	56	2	v	v	X
ejpam-4440	56	3	(	(	PUNCT
ejpam-4440	56	4	g	g	NOUN
ejpam-4440	56	5	)	)	PUNCT
ejpam-4440	56	6	•	•	ADP
ejpam-4440	56	7	∪	∪	X
ejpam-4440	56	8	v	v	NOUN
ejpam-4440	56	9	(	(	PUNCT
ejpam-4440	56	10	h	h	NOUN
ejpam-4440	56	11	)	)	PUNCT
ejpam-4440	56	12	and	and	CCONJ
ejpam-4440	56	13	edge	edge	NOUN
ejpam-4440	56	14	set	set	VERB
ejpam-4440	56	15	e(g	e(g	PROPN
ejpam-4440	57	1	+	+	CCONJ
ejpam-4440	57	2	h	h	NOUN
ejpam-4440	57	3	)	)	PUNCT
ejpam-4440	57	4	=	=	SYM
ejpam-4440	57	5	e(g	e(g	PROPN
ejpam-4440	57	6	)	)	PUNCT
ejpam-4440	58	1	•	•	ADP
ejpam-4440	58	2	∪	∪	ADP
ejpam-4440	58	3	e(h	e(h	PROPN
ejpam-4440	58	4	)	)	PUNCT
ejpam-4440	58	5	∪	∪	NOUN
ejpam-4440	58	6	{	{	PUNCT
ejpam-4440	58	7	uv	uv	NOUN
ejpam-4440	58	8	:	:	PUNCT
ejpam-4440	58	9	u	u	PROPN
ejpam-4440	58	10	∈	∈	PROPN
ejpam-4440	58	11	v	v	ADP
ejpam-4440	58	12	(	(	PUNCT
ejpam-4440	58	13	g	g	NOUN
ejpam-4440	58	14	)	)	PUNCT
ejpam-4440	58	15	,	,	PUNCT
ejpam-4440	58	16	v	v	X
ejpam-4440	58	17	∈	∈	PROPN
ejpam-4440	58	18	v	v	NOUN
ejpam-4440	58	19	(	(	PUNCT
ejpam-4440	58	20	h	h	NOUN
ejpam-4440	58	21	)	)	PUNCT
ejpam-4440	58	22	}	}	PUNCT
ejpam-4440	58	23	.	.	PUNCT
ejpam-4440	59	1	the	the	DET
ejpam-4440	59	2	corona	corona	NOUN
ejpam-4440	59	3	of	of	ADP
ejpam-4440	59	4	two	two	NUM
ejpam-4440	59	5	graphs	graph	NOUN
ejpam-4440	59	6	g	g	NOUN
ejpam-4440	59	7	and	and	CCONJ
ejpam-4440	59	8	h	h	NOUN
ejpam-4440	59	9	,	,	PUNCT
ejpam-4440	59	10	denoted	denote	VERB
ejpam-4440	59	11	by	by	ADP
ejpam-4440	59	12	g	g	PROPN
ejpam-4440	59	13	◦	◦	NOUN
ejpam-4440	59	14	h	h	NOUN
ejpam-4440	59	15	,	,	PUNCT
ejpam-4440	59	16	is	be	AUX
ejpam-4440	59	17	the	the	DET
ejpam-4440	59	18	graph	graph	NOUN
ejpam-4440	59	19	obtained	obtain	VERB
ejpam-4440	59	20	by	by	ADP
ejpam-4440	59	21	taking	take	VERB
ejpam-4440	59	22	one	one	NUM
ejpam-4440	59	23	copy	copy	NOUN
ejpam-4440	59	24	of	of	ADP
ejpam-4440	59	25	g	g	NOUN
ejpam-4440	59	26	of	of	ADP
ejpam-4440	59	27	order	order	NOUN
ejpam-4440	59	28	n	n	NOUN
ejpam-4440	59	29	and	and	CCONJ
ejpam-4440	59	30	n	n	PRON
ejpam-4440	59	31	copies	copy	NOUN
ejpam-4440	59	32	of	of	ADP
ejpam-4440	59	33	h	h	NOUN
ejpam-4440	59	34	,	,	PUNCT
ejpam-4440	59	35	and	and	CCONJ
ejpam-4440	59	36	then	then	ADV
ejpam-4440	59	37	joining	join	VERB
ejpam-4440	59	38	every	every	DET
ejpam-4440	59	39	vertex	vertex	NOUN
ejpam-4440	59	40	of	of	ADP
ejpam-4440	59	41	the	the	DET
ejpam-4440	59	42	ith	ith	PROPN
ejpam-4440	59	43	copy	copy	NOUN
ejpam-4440	59	44	of	of	ADP
ejpam-4440	59	45	h	h	NOUN
ejpam-4440	59	46	to	to	ADP
ejpam-4440	59	47	the	the	DET
ejpam-4440	59	48	ith	ith	PROPN
ejpam-4440	59	49	vertex	vertex	NOUN
ejpam-4440	59	50	of	of	ADP
ejpam-4440	59	51	g.	g.	PROPN
ejpam-4440	59	52	for	for	ADP
ejpam-4440	59	53	v	v	NOUN
ejpam-4440	59	54	∈	∈	PROPN
ejpam-4440	59	55	v	v	NOUN
ejpam-4440	59	56	(	(	PUNCT
ejpam-4440	59	57	g	g	NOUN
ejpam-4440	59	58	)	)	PUNCT
ejpam-4440	59	59	,	,	PUNCT
ejpam-4440	59	60	denote	denote	VERB
ejpam-4440	59	61	by	by	ADP
ejpam-4440	59	62	hv	hv	PROPN
ejpam-4440	59	63	the	the	DET
ejpam-4440	59	64	copy	copy	NOUN
ejpam-4440	59	65	of	of	ADP
ejpam-4440	59	66	h	h	NOUN
ejpam-4440	59	67	whose	whose	DET
ejpam-4440	59	68	vertices	vertex	NOUN
ejpam-4440	59	69	are	be	AUX
ejpam-4440	59	70	attached	attach	VERB
ejpam-4440	59	71	one	one	NUM
ejpam-4440	59	72	by	by	ADP
ejpam-4440	59	73	one	one	NUM
ejpam-4440	59	74	to	to	ADP
ejpam-4440	59	75	the	the	DET
ejpam-4440	59	76	vertex	vertex	NOUN
ejpam-4440	59	77	v.	v.	ADP
ejpam-4440	59	78	subsequently	subsequently	ADV
ejpam-4440	59	79	,	,	PUNCT
ejpam-4440	59	80	denote	denote	VERB
ejpam-4440	59	81	by	by	ADP
ejpam-4440	59	82	v+hv	v+hv	NOUN
ejpam-4440	59	83	the	the	DET
ejpam-4440	59	84	subgraph	subgraph	NOUN
ejpam-4440	59	85	of	of	ADP
ejpam-4440	59	86	the	the	DET
ejpam-4440	59	87	corona	corona	NOUN
ejpam-4440	59	88	g	g	PROPN
ejpam-4440	59	89	◦	◦	NOUN
ejpam-4440	59	90	h	h	NOUN
ejpam-4440	59	91	corresponding	correspond	VERB
ejpam-4440	59	92	to	to	ADP
ejpam-4440	59	93	the	the	DET
ejpam-4440	59	94	join	join	NOUN
ejpam-4440	59	95	⟨{v}⟩	⟨{v}⟩	AUX
ejpam-4440	59	96	+	+	CCONJ
ejpam-4440	59	97	hv	hv	PROPN
ejpam-4440	59	98	,	,	PUNCT
ejpam-4440	59	99	v	v	NOUN
ejpam-4440	59	100	∈	∈	PROPN
ejpam-4440	59	101	v	v	NOUN
ejpam-4440	59	102	(	(	PUNCT
ejpam-4440	59	103	g	g	NOUN
ejpam-4440	59	104	)	)	PUNCT
ejpam-4440	59	105	.	.	PUNCT
ejpam-4440	60	1	the	the	DET
ejpam-4440	60	2	lexicographic	lexicographic	ADJ
ejpam-4440	60	3	product	product	NOUN
ejpam-4440	60	4	of	of	ADP
ejpam-4440	60	5	two	two	NUM
ejpam-4440	60	6	graphs	graph	NOUN
ejpam-4440	60	7	g	g	NOUN
ejpam-4440	60	8	and	and	CCONJ
ejpam-4440	60	9	h	h	NOUN
ejpam-4440	60	10	,	,	PUNCT
ejpam-4440	60	11	denoted	denote	VERB
ejpam-4440	60	12	by	by	ADP
ejpam-4440	60	13	g[h	g[h	NOUN
ejpam-4440	60	14	]	]	PUNCT
ejpam-4440	60	15	,	,	PUNCT
ejpam-4440	60	16	is	be	AUX
ejpam-4440	60	17	the	the	DET
ejpam-4440	60	18	graph	graph	NOUN
ejpam-4440	60	19	with	with	ADP
ejpam-4440	60	20	vertexset	vertexset	ADJ
ejpam-4440	60	21	v	v	NOUN
ejpam-4440	60	22	(	(	PUNCT
ejpam-4440	60	23	g[h	g[h	PROPN
ejpam-4440	60	24	]	]	PUNCT
ejpam-4440	60	25	)	)	PUNCT
ejpam-4440	60	26	=	=	SYM
ejpam-4440	60	27	v	v	X
ejpam-4440	60	28	(	(	PUNCT
ejpam-4440	60	29	g	g	NOUN
ejpam-4440	60	30	)	)	PUNCT
ejpam-4440	60	31	×	×	NOUN
ejpam-4440	60	32	v	v	NOUN
ejpam-4440	60	33	(	(	PUNCT
ejpam-4440	60	34	h	h	NOUN
ejpam-4440	60	35	)	)	PUNCT
ejpam-4440	60	36	such	such	ADJ
ejpam-4440	60	37	that	that	SCONJ
ejpam-4440	60	38	(	(	PUNCT
ejpam-4440	60	39	u1	u1	NOUN
ejpam-4440	60	40	,	,	PUNCT
ejpam-4440	60	41	u2)(v1	u2)(v1	NOUN
ejpam-4440	60	42	,	,	PUNCT
ejpam-4440	60	43	v2	v2	NOUN
ejpam-4440	60	44	)	)	PUNCT
ejpam-4440	60	45	∈	∈	NOUN
ejpam-4440	60	46	e(g[h	e(g[h	NOUN
ejpam-4440	60	47	]	]	PUNCT
ejpam-4440	60	48	)	)	PUNCT
ejpam-4440	60	49	if	if	SCONJ
ejpam-4440	60	50	either	either	CCONJ
ejpam-4440	60	51	u1v1	u1v1	PROPN
ejpam-4440	60	52	∈	∈	PROPN
ejpam-4440	60	53	e(g	e(g	PROPN
ejpam-4440	60	54	)	)	PUNCT
ejpam-4440	60	55	or	or	CCONJ
ejpam-4440	60	56	u1	u1	NOUN
ejpam-4440	60	57	=	=	SYM
ejpam-4440	60	58	v1	v1	NOUN
ejpam-4440	60	59	and	and	CCONJ
ejpam-4440	60	60	u2v2	u2v2	ADJ
ejpam-4440	60	61	∈	∈	PROPN
ejpam-4440	60	62	e(h	e(h	PROPN
ejpam-4440	60	63	)	)	PUNCT
ejpam-4440	60	64	.	.	PUNCT
ejpam-4440	61	1	2	2	X
ejpam-4440	61	2	.	.	X
ejpam-4440	61	3	preliminary	preliminary	ADJ
ejpam-4440	61	4	results	result	NOUN
ejpam-4440	61	5	this	this	DET
ejpam-4440	61	6	section	section	NOUN
ejpam-4440	61	7	introduces	introduce	VERB
ejpam-4440	61	8	the	the	DET
ejpam-4440	61	9	movable	movable	ADJ
ejpam-4440	61	10	strong	strong	ADJ
ejpam-4440	61	11	resolving	resolving	NOUN
ejpam-4440	61	12	domination	domination	NOUN
ejpam-4440	61	13	in	in	ADP
ejpam-4440	61	14	some	some	DET
ejpam-4440	61	15	graphs	graph	NOUN
ejpam-4440	61	16	.	.	PUNCT
ejpam-4440	62	1	it	it	PRON
ejpam-4440	62	2	also	also	ADV
ejpam-4440	62	3	characterizes	characterize	VERB
ejpam-4440	62	4	some	some	DET
ejpam-4440	62	5	graphs	graph	NOUN
ejpam-4440	62	6	in	in	ADP
ejpam-4440	62	7	terms	term	NOUN
ejpam-4440	62	8	of	of	ADP
ejpam-4440	62	9	its	its	PRON
ejpam-4440	62	10	movable	movable	ADJ
ejpam-4440	62	11	strong	strong	ADJ
ejpam-4440	62	12	resolving	resolve	VERB
ejpam-4440	62	13	domination	domination	NOUN
ejpam-4440	62	14	number	number	NOUN
ejpam-4440	62	15	.	.	PUNCT
ejpam-4440	63	1	remark	remark	NOUN
ejpam-4440	63	2	1	1	NUM
ejpam-4440	63	3	.	.	PUNCT
ejpam-4440	64	1	[	[	X
ejpam-4440	64	2	1	1	X
ejpam-4440	64	3	]	]	PUNCT
ejpam-4440	64	4	any	any	DET
ejpam-4440	64	5	superset	superset	NOUN
ejpam-4440	64	6	of	of	ADP
ejpam-4440	64	7	a	a	DET
ejpam-4440	64	8	strong	strong	ADJ
ejpam-4440	64	9	resolving	resolving	NOUN
ejpam-4440	64	10	set	set	NOUN
ejpam-4440	64	11	is	be	AUX
ejpam-4440	64	12	a	a	DET
ejpam-4440	64	13	strong	strong	ADJ
ejpam-4440	64	14	resolving	resolving	NOUN
ejpam-4440	64	15	set	set	NOUN
ejpam-4440	64	16	.	.	PUNCT
ejpam-4440	65	1	lemma	lemma	PROPN
ejpam-4440	65	2	1	1	NUM
ejpam-4440	65	3	.	.	PUNCT
ejpam-4440	66	1	[	[	X
ejpam-4440	66	2	10	10	NUM
ejpam-4440	66	3	]	]	PUNCT
ejpam-4440	66	4	let	let	VERB
ejpam-4440	66	5	g	g	PRON
ejpam-4440	66	6	be	be	AUX
ejpam-4440	66	7	a	a	DET
ejpam-4440	66	8	nontrivial	nontrivial	ADJ
ejpam-4440	66	9	connected	connect	VERB
ejpam-4440	66	10	graph	graph	NOUN
ejpam-4440	66	11	with	with	ADP
ejpam-4440	66	12	diam(g	diam(g	NOUN
ejpam-4440	66	13	)	)	PUNCT
ejpam-4440	66	14	≤	≤	NOUN
ejpam-4440	66	15	2	2	NUM
ejpam-4440	66	16	.	.	PUNCT
ejpam-4440	67	1	then	then	ADV
ejpam-4440	67	2	s	s	VERB
ejpam-4440	67	3	=	=	SYM
ejpam-4440	67	4	v	v	PROPN
ejpam-4440	67	5	(	(	PUNCT
ejpam-4440	67	6	g	g	NOUN
ejpam-4440	67	7	)	)	PUNCT
ejpam-4440	67	8	\	\	PUNCT
ejpam-4440	68	1	c	c	NOUN
ejpam-4440	68	2	is	be	AUX
ejpam-4440	68	3	a	a	DET
ejpam-4440	68	4	strong	strong	ADJ
ejpam-4440	68	5	resolving	resolving	NOUN
ejpam-4440	68	6	dominating	dominating	NOUN
ejpam-4440	68	7	set	set	NOUN
ejpam-4440	68	8	of	of	ADP
ejpam-4440	68	9	g	g	PROPN
ejpam-4440	68	10	if	if	SCONJ
ejpam-4440	69	1	and	and	CCONJ
ejpam-4440	69	2	only	only	ADV
ejpam-4440	69	3	if	if	SCONJ
ejpam-4440	69	4	c	c	NOUN
ejpam-4440	69	5	=	=	SYM
ejpam-4440	69	6	∅	∅	NOUN
ejpam-4440	69	7	or	or	CCONJ
ejpam-4440	69	8	c	c	NOUN
ejpam-4440	69	9	is	be	AUX
ejpam-4440	69	10	a	a	DET
ejpam-4440	69	11	dominated	dominate	VERB
ejpam-4440	69	12	superclique	superclique	NOUN
ejpam-4440	69	13	in	in	ADP
ejpam-4440	69	14	g.	g.	PROPN
ejpam-4440	69	15	in	in	ADP
ejpam-4440	69	16	particular	particular	ADJ
ejpam-4440	69	17	,	,	PUNCT
ejpam-4440	69	18	γsr(g	γsr(g	NOUN
ejpam-4440	69	19	)	)	PUNCT
ejpam-4440	69	20	=	=	SYM
ejpam-4440	69	21	|v	|v	PROPN
ejpam-4440	69	22	(	(	PUNCT
ejpam-4440	69	23	g)|	g)|	PROPN
ejpam-4440	69	24	−	−	PROPN
ejpam-4440	69	25	ωds(g	ωds(g	PROPN
ejpam-4440	69	26	)	)	PUNCT
ejpam-4440	69	27	.	.	PUNCT
ejpam-4440	70	1	theorem	theorem	NOUN
ejpam-4440	70	2	1	1	NUM
ejpam-4440	70	3	.	.	PUNCT
ejpam-4440	71	1	[	[	X
ejpam-4440	71	2	1	1	X
ejpam-4440	71	3	]	]	PUNCT
ejpam-4440	71	4	let	let	VERB
ejpam-4440	71	5	g	g	PRON
ejpam-4440	71	6	be	be	AUX
ejpam-4440	71	7	a	a	DET
ejpam-4440	71	8	nontrivial	nontrivial	ADJ
ejpam-4440	71	9	connected	connect	VERB
ejpam-4440	71	10	graph	graph	NOUN
ejpam-4440	71	11	of	of	ADP
ejpam-4440	71	12	order	order	NOUN
ejpam-4440	71	13	n	n	PRON
ejpam-4440	71	14	with	with	ADP
ejpam-4440	71	15	γ(g	γ(g	PROPN
ejpam-4440	71	16	)	)	PUNCT
ejpam-4440	71	17	=	=	SYM
ejpam-4440	71	18	1	1	NUM
ejpam-4440	71	19	and	and	CCONJ
ejpam-4440	71	20	k1	k1	NOUN
ejpam-4440	72	1	=	=	SYM
ejpam-4440	72	2	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4440	72	3	then	then	ADV
ejpam-4440	72	4	s	s	VERB
ejpam-4440	72	5	⊆	⊆	NUM
ejpam-4440	72	6	v	v	NOUN
ejpam-4440	72	7	(	(	PUNCT
ejpam-4440	72	8	k1+g	k1+g	NOUN
ejpam-4440	72	9	)	)	PUNCT
ejpam-4440	72	10	is	be	AUX
ejpam-4440	72	11	a	a	DET
ejpam-4440	72	12	strong	strong	ADJ
ejpam-4440	72	13	resolving	resolving	NOUN
ejpam-4440	72	14	set	set	NOUN
ejpam-4440	72	15	of	of	ADP
ejpam-4440	72	16	k1+g	k1+g	NOUN
ejpam-4440	72	17	if	if	SCONJ
ejpam-4440	72	18	and	and	CCONJ
ejpam-4440	72	19	only	only	ADV
ejpam-4440	72	20	if	if	SCONJ
ejpam-4440	72	21	s	s	VERB
ejpam-4440	72	22	=	=	SYM
ejpam-4440	72	23	v	v	X
ejpam-4440	72	24	(	(	PUNCT
ejpam-4440	72	25	g	g	NOUN
ejpam-4440	72	26	)	)	PUNCT
ejpam-4440	72	27	,	,	PUNCT
ejpam-4440	72	28	or	or	CCONJ
ejpam-4440	72	29	s	s	VERB
ejpam-4440	72	30	=	=	SYM
ejpam-4440	72	31	v	v	PROPN
ejpam-4440	72	32	(	(	PUNCT
ejpam-4440	72	33	k1	k1	NOUN
ejpam-4440	72	34	+	+	PROPN
ejpam-4440	72	35	g	g	NOUN
ejpam-4440	72	36	)	)	PUNCT
ejpam-4440	72	37	\	\	PROPN
ejpam-4440	72	38	c∗	c∗	NOUN
ejpam-4440	72	39	or	or	CCONJ
ejpam-4440	72	40	s	s	NOUN
ejpam-4440	72	41	=	=	PUNCT
ejpam-4440	72	42	(	(	PUNCT
ejpam-4440	72	43	v	v	NOUN
ejpam-4440	72	44	(	(	PUNCT
ejpam-4440	72	45	g	g	NOUN
ejpam-4440	72	46	)	)	PUNCT
ejpam-4440	72	47	\	\	PROPN
ejpam-4440	72	48	c∗	c∗	PROPN
ejpam-4440	72	49	)	)	PUNCT
ejpam-4440	72	50	∪	∪	NOUN
ejpam-4440	72	51	{	{	PUNCT
ejpam-4440	72	52	x	x	SYM
ejpam-4440	72	53	∈	∈	PROPN
ejpam-4440	72	54	c∗	c∗	NOUN
ejpam-4440	72	55	:	:	PUNCT
ejpam-4440	72	56	degg(x	degg(x	X
ejpam-4440	72	57	)	)	PUNCT
ejpam-4440	72	58	=	=	PUNCT
ejpam-4440	72	59	n−	n−	NOUN
ejpam-4440	72	60	1	1	NUM
ejpam-4440	72	61	}	}	PUNCT
ejpam-4440	72	62	where	where	SCONJ
ejpam-4440	72	63	c∗	c∗	NOUN
ejpam-4440	72	64	is	be	AUX
ejpam-4440	72	65	a	a	DET
ejpam-4440	72	66	superclique	superclique	NOUN
ejpam-4440	72	67	in	in	ADP
ejpam-4440	72	68	g.	g.	PROPN
ejpam-4440	72	69	theorem	theorem	PROPN
ejpam-4440	72	70	2	2	NUM
ejpam-4440	72	71	.	.	PUNCT
ejpam-4440	73	1	[	[	X
ejpam-4440	73	2	1	1	X
ejpam-4440	73	3	]	]	PUNCT
ejpam-4440	73	4	let	let	VERB
ejpam-4440	73	5	g	g	PRON
ejpam-4440	73	6	be	be	AUX
ejpam-4440	73	7	a	a	DET
ejpam-4440	73	8	nontrivial	nontrivial	ADJ
ejpam-4440	73	9	connected	connect	VERB
ejpam-4440	73	10	graph	graph	NOUN
ejpam-4440	73	11	of	of	ADP
ejpam-4440	73	12	order	order	NOUN
ejpam-4440	73	13	n	n	PRON
ejpam-4440	73	14	with	with	ADP
ejpam-4440	73	15	γ(g	γ(g	PROPN
ejpam-4440	73	16	)	)	PUNCT
ejpam-4440	73	17	̸=	̸=	PROPN
ejpam-4440	73	18	1	1	NUM
ejpam-4440	73	19	and	and	CCONJ
ejpam-4440	73	20	k1	k1	NOUN
ejpam-4440	73	21	=	=	SYM
ejpam-4440	73	22	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4440	73	23	then	then	ADV
ejpam-4440	73	24	s	s	VERB
ejpam-4440	73	25	⊆	⊆	NUM
ejpam-4440	73	26	v	v	NOUN
ejpam-4440	73	27	(	(	PUNCT
ejpam-4440	73	28	k1+g	k1+g	NOUN
ejpam-4440	73	29	)	)	PUNCT
ejpam-4440	73	30	is	be	AUX
ejpam-4440	73	31	a	a	DET
ejpam-4440	73	32	strong	strong	ADJ
ejpam-4440	73	33	resolving	resolving	NOUN
ejpam-4440	73	34	set	set	NOUN
ejpam-4440	73	35	of	of	ADP
ejpam-4440	73	36	k1+g	k1+g	NOUN
ejpam-4440	73	37	if	if	SCONJ
ejpam-4440	73	38	and	and	CCONJ
ejpam-4440	73	39	only	only	ADV
ejpam-4440	73	40	if	if	SCONJ
ejpam-4440	73	41	s	s	VERB
ejpam-4440	73	42	=	=	SYM
ejpam-4440	73	43	v	v	X
ejpam-4440	73	44	(	(	PUNCT
ejpam-4440	73	45	g	g	NOUN
ejpam-4440	73	46	)	)	PUNCT
ejpam-4440	73	47	,	,	PUNCT
ejpam-4440	73	48	or	or	CCONJ
ejpam-4440	73	49	s	s	VERB
ejpam-4440	73	50	=	=	SYM
ejpam-4440	73	51	v	v	PROPN
ejpam-4440	73	52	(	(	PUNCT
ejpam-4440	73	53	g	g	NOUN
ejpam-4440	73	54	)	)	PUNCT
ejpam-4440	73	55	\	\	PUNCT
ejpam-4440	74	1	c	c	X
ejpam-4440	74	2	,	,	PUNCT
ejpam-4440	74	3	or	or	CCONJ
ejpam-4440	74	4	s	s	NOUN
ejpam-4440	74	5	=	=	SYM
ejpam-4440	74	6	v	v	PROPN
ejpam-4440	74	7	(	(	PUNCT
ejpam-4440	74	8	k1	k1	NOUN
ejpam-4440	74	9	+	+	PROPN
ejpam-4440	74	10	g	g	NOUN
ejpam-4440	74	11	)	)	PUNCT
ejpam-4440	74	12	\	\	PUNCT
ejpam-4440	75	1	c	c	NOUN
ejpam-4440	75	2	where	where	SCONJ
ejpam-4440	75	3	c	c	PROPN
ejpam-4440	75	4	is	be	AUX
ejpam-4440	75	5	a	a	DET
ejpam-4440	75	6	superclique	superclique	NOUN
ejpam-4440	75	7	in	in	ADP
ejpam-4440	75	8	g.	g.	PROPN
ejpam-4440	75	9	theorem	theorem	PROPN
ejpam-4440	75	10	3	3	NUM
ejpam-4440	75	11	.	.	PUNCT
ejpam-4440	76	1	[	[	X
ejpam-4440	76	2	1	1	X
ejpam-4440	76	3	]	]	PUNCT
ejpam-4440	76	4	let	let	VERB
ejpam-4440	76	5	k1	k1	NOUN
ejpam-4440	76	6	=	=	SYM
ejpam-4440	76	7	⟨v⟩	⟨v⟩	PROPN
ejpam-4440	76	8	and	and	CCONJ
ejpam-4440	76	9	g	g	PROPN
ejpam-4440	76	10	be	be	AUX
ejpam-4440	76	11	a	a	DET
ejpam-4440	76	12	disconnected	disconnected	ADJ
ejpam-4440	76	13	graph	graph	NOUN
ejpam-4440	76	14	whose	whose	DET
ejpam-4440	76	15	components	component	NOUN
ejpam-4440	76	16	are	be	AUX
ejpam-4440	76	17	gi	gi	ADJ
ejpam-4440	76	18	for	for	ADP
ejpam-4440	76	19	i	i	PROPN
ejpam-4440	76	20	=	=	NOUN
ejpam-4440	76	21	1	1	NUM
ejpam-4440	76	22	,	,	PUNCT
ejpam-4440	76	23	2	2	NUM
ejpam-4440	76	24	,	,	PUNCT
ejpam-4440	76	25	.	.	PUNCT
ejpam-4440	76	26	.	.	PUNCT
ejpam-4440	76	27	.	.	PUNCT
ejpam-4440	77	1	,	,	PUNCT
ejpam-4440	77	2	m.	m.	NOUN
ejpam-4440	77	3	a	a	DET
ejpam-4440	77	4	proper	proper	ADJ
ejpam-4440	77	5	subset	subset	NOUN
ejpam-4440	77	6	s	s	NOUN
ejpam-4440	77	7	of	of	ADP
ejpam-4440	77	8	v	v	NOUN
ejpam-4440	77	9	(	(	PUNCT
ejpam-4440	77	10	k1	k1	NOUN
ejpam-4440	77	11	+	+	CCONJ
ejpam-4440	77	12	g	g	NOUN
ejpam-4440	77	13	)	)	PUNCT
ejpam-4440	77	14	is	be	AUX
ejpam-4440	77	15	a	a	DET
ejpam-4440	77	16	strong	strong	ADJ
ejpam-4440	77	17	resolving	resolving	NOUN
ejpam-4440	77	18	set	set	NOUN
ejpam-4440	77	19	of	of	ADP
ejpam-4440	77	20	k1	k1	NOUN
ejpam-4440	77	21	+	+	CCONJ
ejpam-4440	77	22	g	g	PROPN
ejpam-4440	77	23	h.	h.	PROPN
ejpam-4440	77	24	sumaoy	sumaoy	NOUN
ejpam-4440	77	25	,	,	PUNCT
ejpam-4440	77	26	h.	h.	PROPN
ejpam-4440	77	27	rara	rara	PROPN
ejpam-4440	77	28	/	/	SYM
ejpam-4440	77	29	eur	eur	PROPN
ejpam-4440	77	30	.	.	PUNCT
ejpam-4440	78	1	j.	j.	PROPN
ejpam-4440	78	2	pure	pure	PROPN
ejpam-4440	78	3	appl	appl	PROPN
ejpam-4440	78	4	.	.	PROPN
ejpam-4440	78	5	math	math	PROPN
ejpam-4440	78	6	,	,	PUNCT
ejpam-4440	78	7	15	15	NUM
ejpam-4440	78	8	(	(	PUNCT
ejpam-4440	78	9	3	3	NUM
ejpam-4440	78	10	)	)	PUNCT
ejpam-4440	78	11	(	(	PUNCT
ejpam-4440	78	12	2022	2022	NUM
ejpam-4440	78	13	)	)	PUNCT
ejpam-4440	78	14	,	,	PUNCT
ejpam-4440	78	15	1201	1201	NUM
ejpam-4440	78	16	-	-	SYM
ejpam-4440	78	17	1210	1210	NUM
ejpam-4440	78	18	1204	1204	NUM
ejpam-4440	78	19	if	if	SCONJ
ejpam-4440	78	20	and	and	CCONJ
ejpam-4440	78	21	only	only	ADV
ejpam-4440	78	22	if	if	SCONJ
ejpam-4440	78	23	s	s	VERB
ejpam-4440	78	24	=	=	SYM
ejpam-4440	78	25	v	v	X
ejpam-4440	78	26	(	(	PUNCT
ejpam-4440	78	27	g	g	NOUN
ejpam-4440	78	28	)	)	PUNCT
ejpam-4440	78	29	,	,	PUNCT
ejpam-4440	78	30	or	or	CCONJ
ejpam-4440	78	31	s	s	VERB
ejpam-4440	78	32	=	=	SYM
ejpam-4440	78	33	v	v	PROPN
ejpam-4440	78	34	(	(	PUNCT
ejpam-4440	78	35	g	g	NOUN
ejpam-4440	78	36	)	)	PUNCT
ejpam-4440	78	37	\	\	PROPN
ejpam-4440	78	38	ci	ci	PROPN
ejpam-4440	78	39	,	,	PUNCT
ejpam-4440	78	40	or	or	CCONJ
ejpam-4440	78	41	s	s	NOUN
ejpam-4440	78	42	=	=	SYM
ejpam-4440	78	43	v	v	PROPN
ejpam-4440	78	44	(	(	PUNCT
ejpam-4440	78	45	k1	k1	NOUN
ejpam-4440	78	46	+	+	CCONJ
ejpam-4440	78	47	g	g	NOUN
ejpam-4440	78	48	)	)	PUNCT
ejpam-4440	78	49	\	\	PROPN
ejpam-4440	78	50	ci	ci	PROPN
ejpam-4440	78	51	,	,	PUNCT
ejpam-4440	78	52	where	where	SCONJ
ejpam-4440	78	53	ci	ci	PROPN
ejpam-4440	78	54	is	be	AUX
ejpam-4440	78	55	a	a	DET
ejpam-4440	78	56	superclique	superclique	NOUN
ejpam-4440	78	57	in	in	ADP
ejpam-4440	78	58	gi	gi	NOUN
ejpam-4440	78	59	,	,	PUNCT
ejpam-4440	78	60	for	for	ADP
ejpam-4440	78	61	some	some	DET
ejpam-4440	78	62	i	i	PRON
ejpam-4440	78	63	∈	∈	PROPN
ejpam-4440	78	64	{	{	PUNCT
ejpam-4440	78	65	1	1	NUM
ejpam-4440	78	66	,	,	PUNCT
ejpam-4440	78	67	2	2	NUM
ejpam-4440	78	68	,	,	PUNCT
ejpam-4440	78	69	.	.	PUNCT
ejpam-4440	78	70	.	.	PUNCT
ejpam-4440	78	71	.	.	PUNCT
ejpam-4440	79	1	,	,	PUNCT
ejpam-4440	79	2	m	m	VERB
ejpam-4440	79	3	}	}	PUNCT
ejpam-4440	79	4	.	.	PUNCT
ejpam-4440	80	1	remark	remark	NOUN
ejpam-4440	80	2	2	2	NUM
ejpam-4440	80	3	.	.	PUNCT
ejpam-4440	81	1	every	every	DET
ejpam-4440	81	2	movable	movable	ADJ
ejpam-4440	81	3	strong	strong	ADJ
ejpam-4440	81	4	resolving	resolve	VERB
ejpam-4440	81	5	dominating	dominating	NOUN
ejpam-4440	81	6	set	set	NOUN
ejpam-4440	81	7	of	of	ADP
ejpam-4440	81	8	a	a	DET
ejpam-4440	81	9	connected	connected	ADJ
ejpam-4440	81	10	graph	graph	NOUN
ejpam-4440	81	11	g	g	PROPN
ejpam-4440	81	12	is	be	AUX
ejpam-4440	81	13	a	a	DET
ejpam-4440	81	14	strong	strong	ADJ
ejpam-4440	81	15	resolving	resolving	NOUN
ejpam-4440	81	16	dominating	dominating	NOUN
ejpam-4440	81	17	set	set	VERB
ejpam-4440	81	18	in	in	ADP
ejpam-4440	81	19	g.	g.	PROPN
ejpam-4440	81	20	hence	hence	ADV
ejpam-4440	81	21	,	,	PUNCT
ejpam-4440	81	22	γsr(g	γsr(g	NOUN
ejpam-4440	81	23	)	)	PUNCT
ejpam-4440	81	24	≤	≤	NOUN
ejpam-4440	81	25	γ1msr(g	γ1msr(g	NUM
ejpam-4440	81	26	)	)	PUNCT
ejpam-4440	81	27	.	.	PUNCT
ejpam-4440	82	1	remark	remark	PROPN
ejpam-4440	82	2	3	3	NUM
ejpam-4440	82	3	.	.	PUNCT
ejpam-4440	83	1	the	the	DET
ejpam-4440	83	2	converse	converse	NOUN
ejpam-4440	83	3	of	of	ADP
ejpam-4440	83	4	remark	remark	NOUN
ejpam-4440	83	5	2	2	NUM
ejpam-4440	83	6	does	do	AUX
ejpam-4440	83	7	not	not	PART
ejpam-4440	83	8	hold	hold	VERB
ejpam-4440	83	9	.	.	PUNCT
ejpam-4440	84	1	to	to	PART
ejpam-4440	84	2	see	see	VERB
ejpam-4440	84	3	this	this	PRON
ejpam-4440	84	4	,	,	PUNCT
ejpam-4440	84	5	the	the	DET
ejpam-4440	84	6	set	set	NOUN
ejpam-4440	84	7	s	s	PART
ejpam-4440	84	8	=	=	NOUN
ejpam-4440	84	9	{	{	PUNCT
ejpam-4440	84	10	v1	v1	PROPN
ejpam-4440	84	11	,	,	PUNCT
ejpam-4440	84	12	v2	v2	PROPN
ejpam-4440	84	13	,	,	PUNCT
ejpam-4440	84	14	v3	v3	PROPN
ejpam-4440	84	15	}	}	PUNCT
ejpam-4440	84	16	of	of	ADP
ejpam-4440	84	17	the	the	DET
ejpam-4440	84	18	path	path	NOUN
ejpam-4440	84	19	p4	p4	NOUN
ejpam-4440	84	20	=	=	PUNCT
ejpam-4440	85	1	[	[	X
ejpam-4440	85	2	v1	v1	NOUN
ejpam-4440	85	3	,	,	PUNCT
ejpam-4440	85	4	v2	v2	PROPN
ejpam-4440	85	5	,	,	PUNCT
ejpam-4440	85	6	v3	v3	PROPN
ejpam-4440	85	7	,	,	PUNCT
ejpam-4440	85	8	v4	v4	PROPN
ejpam-4440	85	9	]	]	PUNCT
ejpam-4440	85	10	is	be	AUX
ejpam-4440	85	11	a	a	DET
ejpam-4440	85	12	strong	strong	ADJ
ejpam-4440	85	13	resolving	resolving	NOUN
ejpam-4440	85	14	dominating	dominating	NOUN
ejpam-4440	85	15	set	set	NOUN
ejpam-4440	85	16	of	of	ADP
ejpam-4440	85	17	p4	p4	ADJ
ejpam-4440	86	1	but	but	CCONJ
ejpam-4440	86	2	it	it	PRON
ejpam-4440	86	3	is	be	AUX
ejpam-4440	86	4	not	not	PART
ejpam-4440	86	5	movable	movable	ADJ
ejpam-4440	86	6	strong	strong	ADJ
ejpam-4440	86	7	resolving	resolve	VERB
ejpam-4440	86	8	dominating	dominating	NOUN
ejpam-4440	86	9	set	set	VERB
ejpam-4440	86	10	since	since	SCONJ
ejpam-4440	86	11	s	s	PROPN
ejpam-4440	86	12	\	\	PROPN
ejpam-4440	86	13	{	{	PUNCT
ejpam-4440	86	14	v1	v1	NOUN
ejpam-4440	86	15	}	}	PUNCT
ejpam-4440	86	16	is	be	AUX
ejpam-4440	86	17	not	not	PART
ejpam-4440	86	18	a	a	DET
ejpam-4440	86	19	strong	strong	ADJ
ejpam-4440	86	20	resolving	resolving	NOUN
ejpam-4440	86	21	set	set	NOUN
ejpam-4440	86	22	of	of	ADP
ejpam-4440	86	23	p4	p4	ADJ
ejpam-4440	86	24	.	.	PUNCT
ejpam-4440	87	1	proposition	proposition	NOUN
ejpam-4440	87	2	1	1	NUM
ejpam-4440	87	3	.	.	PUNCT
ejpam-4440	88	1	any	any	DET
ejpam-4440	88	2	superset	superset	NOUN
ejpam-4440	88	3	of	of	ADP
ejpam-4440	88	4	a	a	DET
ejpam-4440	88	5	movable	movable	ADJ
ejpam-4440	88	6	strong	strong	ADJ
ejpam-4440	88	7	resolving	resolving	NOUN
ejpam-4440	88	8	dominating	dominating	NOUN
ejpam-4440	88	9	set	set	NOUN
ejpam-4440	88	10	is	be	AUX
ejpam-4440	88	11	a	a	DET
ejpam-4440	88	12	movable	movable	ADJ
ejpam-4440	88	13	strong	strong	ADJ
ejpam-4440	88	14	resolving	resolve	VERB
ejpam-4440	88	15	dominating	dominating	NOUN
ejpam-4440	88	16	set	set	NOUN
ejpam-4440	88	17	.	.	PUNCT
ejpam-4440	89	1	proof	proof	NOUN
ejpam-4440	89	2	.	.	PUNCT
ejpam-4440	90	1	let	let	VERB
ejpam-4440	90	2	s	s	PRON
ejpam-4440	90	3	be	be	AUX
ejpam-4440	90	4	a	a	DET
ejpam-4440	90	5	movable	movable	ADJ
ejpam-4440	90	6	strong	strong	ADJ
ejpam-4440	90	7	resolving	resolve	VERB
ejpam-4440	90	8	dominating	dominating	NOUN
ejpam-4440	90	9	set	set	NOUN
ejpam-4440	90	10	of	of	ADP
ejpam-4440	90	11	g	g	PROPN
ejpam-4440	90	12	and	and	CCONJ
ejpam-4440	90	13	s	s	NOUN
ejpam-4440	91	1	⊆	⊆	NUM
ejpam-4440	91	2	s′.	s′.	X
ejpam-4440	91	3	then	then	ADV
ejpam-4440	91	4	by	by	ADP
ejpam-4440	91	5	remark	remark	NOUN
ejpam-4440	91	6	1	1	NUM
ejpam-4440	91	7	,	,	PUNCT
ejpam-4440	91	8	s′	s′	ADJ
ejpam-4440	91	9	is	be	AUX
ejpam-4440	91	10	a	a	DET
ejpam-4440	91	11	strong	strong	ADJ
ejpam-4440	91	12	resolving	resolving	NOUN
ejpam-4440	91	13	dominating	dominating	NOUN
ejpam-4440	91	14	set	set	NOUN
ejpam-4440	91	15	of	of	ADP
ejpam-4440	91	16	g.	g.	PROPN
ejpam-4440	91	17	we	we	PRON
ejpam-4440	91	18	show	show	VERB
ejpam-4440	91	19	that	that	SCONJ
ejpam-4440	91	20	a	a	DET
ejpam-4440	91	21	s′	s′	NOUN
ejpam-4440	91	22	is	be	AUX
ejpam-4440	91	23	movable	movable	ADJ
ejpam-4440	91	24	strong	strong	ADJ
ejpam-4440	91	25	resolving	resolve	VERB
ejpam-4440	91	26	dominating	dominating	NOUN
ejpam-4440	91	27	set	set	NOUN
ejpam-4440	91	28	of	of	ADP
ejpam-4440	91	29	g.	g.	PROPN
ejpam-4440	91	30	let	let	VERB
ejpam-4440	91	31	x	x	SYM
ejpam-4440	91	32	∈	∈	PROPN
ejpam-4440	91	33	s′.	s′.	PROPN
ejpam-4440	92	1	if	if	SCONJ
ejpam-4440	92	2	x	x	PROPN
ejpam-4440	92	3	∈	∈	PROPN
ejpam-4440	92	4	s	s	NOUN
ejpam-4440	92	5	,	,	PUNCT
ejpam-4440	92	6	then	then	ADV
ejpam-4440	92	7	s	s	VERB
ejpam-4440	92	8	\	\	X
ejpam-4440	92	9	{	{	PUNCT
ejpam-4440	92	10	x	x	NOUN
ejpam-4440	92	11	}	}	PUNCT
ejpam-4440	92	12	⊆	⊆	NUM
ejpam-4440	92	13	s′	s′	ADJ
ejpam-4440	92	14	\	\	NOUN
ejpam-4440	92	15	{	{	PUNCT
ejpam-4440	92	16	x	x	NOUN
ejpam-4440	92	17	}	}	PUNCT
ejpam-4440	92	18	.	.	PUNCT
ejpam-4440	93	1	since	since	SCONJ
ejpam-4440	93	2	s	s	PROPN
ejpam-4440	93	3	is	be	AUX
ejpam-4440	93	4	a	a	DET
ejpam-4440	93	5	movable	movable	ADJ
ejpam-4440	93	6	strong	strong	ADJ
ejpam-4440	93	7	resolving	resolve	VERB
ejpam-4440	93	8	dominating	dominating	NOUN
ejpam-4440	93	9	set	set	NOUN
ejpam-4440	93	10	of	of	ADP
ejpam-4440	93	11	g	g	NOUN
ejpam-4440	93	12	,	,	PUNCT
ejpam-4440	93	13	either	either	CCONJ
ejpam-4440	93	14	s	s	VERB
ejpam-4440	93	15	\	\	X
ejpam-4440	93	16	{	{	PUNCT
ejpam-4440	93	17	x	x	X
ejpam-4440	93	18	}	}	PUNCT
ejpam-4440	93	19	is	be	AUX
ejpam-4440	93	20	strong	strong	ADJ
ejpam-4440	93	21	resolving	resolve	VERB
ejpam-4440	93	22	dominating	dominate	VERB
ejpam-4440	93	23	set	set	NOUN
ejpam-4440	93	24	of	of	ADP
ejpam-4440	93	25	g	g	PROPN
ejpam-4440	93	26	or	or	CCONJ
ejpam-4440	93	27	∃y	∃y	PROPN
ejpam-4440	93	28	∈	∈	PROPN
ejpam-4440	93	29	(	(	PUNCT
ejpam-4440	93	30	v	v	NOUN
ejpam-4440	93	31	(	(	PUNCT
ejpam-4440	93	32	g	g	NOUN
ejpam-4440	93	33	)	)	PUNCT
ejpam-4440	93	34	\	\	PROPN
ejpam-4440	94	1	s	s	X
ejpam-4440	94	2	)	)	PUNCT
ejpam-4440	94	3	∩	∩	NOUN
ejpam-4440	94	4	ng(x	ng(x	NUM
ejpam-4440	94	5	)	)	PUNCT
ejpam-4440	94	6	such	such	ADJ
ejpam-4440	94	7	that	that	SCONJ
ejpam-4440	94	8	(	(	PUNCT
ejpam-4440	94	9	s	s	NOUN
ejpam-4440	94	10	\	\	X
ejpam-4440	94	11	{	{	PUNCT
ejpam-4440	94	12	x	x	NOUN
ejpam-4440	94	13	}	}	PUNCT
ejpam-4440	94	14	)	)	PUNCT
ejpam-4440	94	15	∪	∪	ADP
ejpam-4440	94	16	{	{	PUNCT
ejpam-4440	94	17	y	y	NOUN
ejpam-4440	94	18	}	}	PUNCT
ejpam-4440	94	19	is	be	AUX
ejpam-4440	94	20	strong	strong	ADJ
ejpam-4440	94	21	resolving	resolve	VERB
ejpam-4440	94	22	dominating	dominate	VERB
ejpam-4440	94	23	set	set	NOUN
ejpam-4440	94	24	of	of	ADP
ejpam-4440	94	25	g.	g.	PROPN
ejpam-4440	94	26	if	if	SCONJ
ejpam-4440	94	27	s	s	NOUN
ejpam-4440	94	28	\	\	X
ejpam-4440	94	29	{	{	PUNCT
ejpam-4440	94	30	x	x	NOUN
ejpam-4440	94	31	}	}	PUNCT
ejpam-4440	94	32	is	be	AUX
ejpam-4440	94	33	a	a	DET
ejpam-4440	94	34	strong	strong	ADJ
ejpam-4440	94	35	resolving	resolving	NOUN
ejpam-4440	94	36	dominating	dominating	NOUN
ejpam-4440	94	37	set	set	NOUN
ejpam-4440	94	38	of	of	ADP
ejpam-4440	94	39	g	g	NOUN
ejpam-4440	94	40	,	,	PUNCT
ejpam-4440	94	41	then	then	ADV
ejpam-4440	94	42	s′\{x	s′\{x	PRON
ejpam-4440	94	43	}	}	PUNCT
ejpam-4440	94	44	is	be	AUX
ejpam-4440	94	45	also	also	ADV
ejpam-4440	94	46	strong	strong	ADJ
ejpam-4440	94	47	resolving	resolve	VERB
ejpam-4440	94	48	dominating	dominate	VERB
ejpam-4440	94	49	set	set	VERB
ejpam-4440	94	50	ofg	ofg	PROPN
ejpam-4440	94	51	by	by	ADP
ejpam-4440	94	52	remark	remark	NOUN
ejpam-4440	94	53	1	1	NUM
ejpam-4440	94	54	.	.	PUNCT
ejpam-4440	95	1	if	if	SCONJ
ejpam-4440	95	2	∃y	∃y	PROPN
ejpam-4440	95	3	∈	∈	PROPN
ejpam-4440	95	4	(	(	PUNCT
ejpam-4440	95	5	v	v	NOUN
ejpam-4440	95	6	(	(	PUNCT
ejpam-4440	95	7	g)\s)∩ng(x	g)\s)∩ng(x	NOUN
ejpam-4440	95	8	)	)	PUNCT
ejpam-4440	95	9	such	such	ADJ
ejpam-4440	95	10	that	that	SCONJ
ejpam-4440	95	11	(	(	PUNCT
ejpam-4440	95	12	s	s	NOUN
ejpam-4440	95	13	\	\	X
ejpam-4440	95	14	{	{	PUNCT
ejpam-4440	95	15	x	x	NOUN
ejpam-4440	95	16	}	}	PUNCT
ejpam-4440	95	17	)	)	PUNCT
ejpam-4440	95	18	∪	∪	ADP
ejpam-4440	95	19	{	{	PUNCT
ejpam-4440	95	20	y	y	NOUN
ejpam-4440	95	21	}	}	PUNCT
ejpam-4440	95	22	is	be	AUX
ejpam-4440	95	23	a	a	DET
ejpam-4440	95	24	strong	strong	ADJ
ejpam-4440	95	25	resolving	resolve	VERB
ejpam-4440	95	26	dominating	dominating	NOUN
ejpam-4440	95	27	set	set	NOUN
ejpam-4440	95	28	,	,	PUNCT
ejpam-4440	95	29	then	then	ADV
ejpam-4440	95	30	(	(	PUNCT
ejpam-4440	95	31	s	s	NOUN
ejpam-4440	95	32	\	\	X
ejpam-4440	95	33	{	{	PUNCT
ejpam-4440	95	34	x	x	NOUN
ejpam-4440	95	35	}	}	PUNCT
ejpam-4440	95	36	)	)	PUNCT
ejpam-4440	95	37	∪	∪	ADP
ejpam-4440	95	38	{	{	PUNCT
ejpam-4440	95	39	y	y	NOUN
ejpam-4440	95	40	}	}	PUNCT
ejpam-4440	95	41	⊆	⊆	NUM
ejpam-4440	95	42	(	(	PUNCT
ejpam-4440	95	43	s′	s′	X
ejpam-4440	95	44	\	\	NOUN
ejpam-4440	95	45	{	{	PUNCT
ejpam-4440	95	46	x	x	NOUN
ejpam-4440	95	47	}	}	PUNCT
ejpam-4440	95	48	)	)	PUNCT
ejpam-4440	95	49	∪	∪	SCONJ
ejpam-4440	95	50	{	{	PUNCT
ejpam-4440	95	51	y	y	NOUN
ejpam-4440	95	52	}	}	PUNCT
ejpam-4440	95	53	(	(	PUNCT
ejpam-4440	95	54	s′\{x})∪{y	s′\{x})∪{y	NOUN
ejpam-4440	95	55	}	}	PUNCT
ejpam-4440	95	56	is	be	AUX
ejpam-4440	95	57	a	a	DET
ejpam-4440	95	58	strong	strong	ADJ
ejpam-4440	95	59	resolving	resolving	NOUN
ejpam-4440	95	60	dominating	dominating	NOUN
ejpam-4440	95	61	set	set	NOUN
ejpam-4440	95	62	of	of	ADP
ejpam-4440	95	63	g.	g.	PROPN
ejpam-4440	95	64	therefore	therefore	ADV
ejpam-4440	95	65	,	,	PUNCT
ejpam-4440	95	66	s′	s′	PROPN
ejpam-4440	95	67	is	be	AUX
ejpam-4440	95	68	a	a	DET
ejpam-4440	95	69	movable	movable	ADJ
ejpam-4440	95	70	strong	strong	ADJ
ejpam-4440	95	71	resolving	resolve	VERB
ejpam-4440	95	72	dominating	dominating	NOUN
ejpam-4440	95	73	set	set	NOUN
ejpam-4440	95	74	of	of	ADP
ejpam-4440	95	75	g.	g.	PROPN
ejpam-4440	95	76	proposition	proposition	PROPN
ejpam-4440	96	1	2	2	X
ejpam-4440	96	2	.	.	PUNCT
ejpam-4440	96	3	let	let	VERB
ejpam-4440	96	4	pn	pn	VERB
ejpam-4440	96	5	=	=	PUNCT
ejpam-4440	97	1	[	[	X
ejpam-4440	97	2	v1	v1	NOUN
ejpam-4440	97	3	,	,	PUNCT
ejpam-4440	97	4	v2	v2	NOUN
ejpam-4440	97	5	,	,	PUNCT
ejpam-4440	97	6	.	.	PUNCT
ejpam-4440	97	7	.	.	PUNCT
ejpam-4440	97	8	.	.	PUNCT
ejpam-4440	98	1	,	,	PUNCT
ejpam-4440	98	2	vn	vn	X
ejpam-4440	98	3	]	]	X
ejpam-4440	99	1	where	where	SCONJ
ejpam-4440	99	2	n	n	PRON
ejpam-4440	99	3	≥	≥	NOUN
ejpam-4440	99	4	1	1	NUM
ejpam-4440	99	5	.	.	PUNCT
ejpam-4440	99	6	if	if	SCONJ
ejpam-4440	99	7	a	a	DET
ejpam-4440	99	8	set	set	NOUN
ejpam-4440	99	9	s	s	VERB
ejpam-4440	99	10	⊆	⊆	NUM
ejpam-4440	99	11	v	v	NOUN
ejpam-4440	99	12	(	(	PUNCT
ejpam-4440	99	13	pn	pn	NOUN
ejpam-4440	99	14	)	)	PUNCT
ejpam-4440	99	15	is	be	AUX
ejpam-4440	99	16	a	a	DET
ejpam-4440	99	17	movable	movable	ADJ
ejpam-4440	99	18	strong	strong	ADJ
ejpam-4440	99	19	resolving	resolve	VERB
ejpam-4440	99	20	dominating	dominating	NOUN
ejpam-4440	99	21	set	set	NOUN
ejpam-4440	99	22	of	of	ADP
ejpam-4440	99	23	pn	pn	PROPN
ejpam-4440	99	24	,	,	PUNCT
ejpam-4440	99	25	then	then	ADV
ejpam-4440	99	26	s	s	VERB
ejpam-4440	99	27	is	be	AUX
ejpam-4440	99	28	a	a	DET
ejpam-4440	99	29	dominating	dominating	NOUN
ejpam-4440	99	30	set	set	NOUN
ejpam-4440	99	31	containing	contain	VERB
ejpam-4440	99	32	the	the	DET
ejpam-4440	99	33	vertices	vertex	NOUN
ejpam-4440	99	34	v1	v1	NOUN
ejpam-4440	99	35	and	and	CCONJ
ejpam-4440	99	36	vn	vn	NOUN
ejpam-4440	99	37	.	.	PUNCT
ejpam-4440	100	1	proof	proof	NOUN
ejpam-4440	100	2	.	.	PUNCT
ejpam-4440	101	1	suppose	suppose	VERB
ejpam-4440	101	2	s	s	NOUN
ejpam-4440	101	3	is	be	AUX
ejpam-4440	101	4	a	a	DET
ejpam-4440	101	5	movable	movable	ADJ
ejpam-4440	101	6	strong	strong	ADJ
ejpam-4440	101	7	resolving	resolve	VERB
ejpam-4440	101	8	dominating	dominating	NOUN
ejpam-4440	101	9	set	set	NOUN
ejpam-4440	101	10	of	of	ADP
ejpam-4440	101	11	pn	pn	PROPN
ejpam-4440	101	12	and	and	CCONJ
ejpam-4440	101	13	suppose	suppose	VERB
ejpam-4440	101	14	that	that	SCONJ
ejpam-4440	101	15	s	s	VERB
ejpam-4440	101	16	does	do	AUX
ejpam-4440	101	17	not	not	PART
ejpam-4440	101	18	contain	contain	VERB
ejpam-4440	101	19	v1	v1	NOUN
ejpam-4440	101	20	or	or	CCONJ
ejpam-4440	101	21	vn	vn	NOUN
ejpam-4440	101	22	,	,	PUNCT
ejpam-4440	101	23	say	say	VERB
ejpam-4440	101	24	v1	v1	NOUN
ejpam-4440	101	25	.	.	PUNCT
ejpam-4440	102	1	since	since	SCONJ
ejpam-4440	102	2	v1mmdvn	v1mmdvn	NOUN
ejpam-4440	102	3	,	,	PUNCT
ejpam-4440	102	4	s	s	VERB
ejpam-4440	102	5	∩	∩	NOUN
ejpam-4440	102	6	{	{	PUNCT
ejpam-4440	102	7	v1	v1	NOUN
ejpam-4440	102	8	,	,	PUNCT
ejpam-4440	102	9	vn	vn	NOUN
ejpam-4440	102	10	}	}	PUNCT
ejpam-4440	102	11	=	=	NOUN
ejpam-4440	102	12	̸	̸	X
ejpam-4440	102	13	∅.	∅.	ADV
ejpam-4440	102	14	hence	hence	ADV
ejpam-4440	102	15	vn	vn	PROPN
ejpam-4440	102	16	∈	∈	PROPN
ejpam-4440	102	17	s.	s.	PROPN
ejpam-4440	103	1	this	this	PRON
ejpam-4440	103	2	implies	imply	VERB
ejpam-4440	103	3	that	that	SCONJ
ejpam-4440	103	4	s	s	VERB
ejpam-4440	103	5	\{vn	\{vn	ADV
ejpam-4440	103	6	}	}	PUNCT
ejpam-4440	103	7	and	and	CCONJ
ejpam-4440	103	8	(	(	PUNCT
ejpam-4440	103	9	s	s	NOUN
ejpam-4440	103	10	\{vn})∪{vn−1	\{vn})∪{vn−1	NOUN
ejpam-4440	103	11	}	}	PUNCT
ejpam-4440	103	12	if	if	SCONJ
ejpam-4440	103	13	vn−1	vn−1	PROPN
ejpam-4440	103	14	/∈	/∈	PUNCT
ejpam-4440	103	15	s	s	VERB
ejpam-4440	103	16	are	be	AUX
ejpam-4440	103	17	not	not	PART
ejpam-4440	103	18	strong	strong	ADJ
ejpam-4440	103	19	resolving	resolving	NOUN
ejpam-4440	103	20	sets	set	NOUN
ejpam-4440	103	21	of	of	ADP
ejpam-4440	103	22	pn	pn	NOUN
ejpam-4440	103	23	,	,	PUNCT
ejpam-4440	103	24	a	a	DET
ejpam-4440	103	25	contradiction	contradiction	NOUN
ejpam-4440	103	26	.	.	PUNCT
ejpam-4440	104	1	therefore	therefore	ADV
ejpam-4440	104	2	,	,	PUNCT
ejpam-4440	104	3	s	s	PROPN
ejpam-4440	104	4	contains	contain	VERB
ejpam-4440	104	5	v1	v1	NOUN
ejpam-4440	104	6	and	and	CCONJ
ejpam-4440	104	7	vn	vn	NOUN
ejpam-4440	104	8	.	.	PUNCT
ejpam-4440	105	1	lemma	lemma	PROPN
ejpam-4440	105	2	2	2	X
ejpam-4440	105	3	.	.	PUNCT
ejpam-4440	106	1	let	let	VERB
ejpam-4440	106	2	g	g	PRON
ejpam-4440	106	3	be	be	AUX
ejpam-4440	106	4	a	a	DET
ejpam-4440	106	5	nontrival	nontrival	ADJ
ejpam-4440	106	6	connected	connected	ADJ
ejpam-4440	106	7	graph	graph	NOUN
ejpam-4440	106	8	with	with	ADP
ejpam-4440	106	9	diam(g	diam(g	NOUN
ejpam-4440	106	10	)	)	PUNCT
ejpam-4440	106	11	≤	≤	NOUN
ejpam-4440	106	12	2	2	NUM
ejpam-4440	106	13	.	.	PUNCT
ejpam-4440	107	1	then	then	ADV
ejpam-4440	107	2	s	s	VERB
ejpam-4440	107	3	=	=	SYM
ejpam-4440	107	4	v	v	NOUN
ejpam-4440	107	5	(	(	PUNCT
ejpam-4440	107	6	g)\c	g)\c	NOUN
ejpam-4440	107	7	is	be	AUX
ejpam-4440	107	8	a	a	DET
ejpam-4440	107	9	movable	movable	ADJ
ejpam-4440	107	10	strong	strong	ADJ
ejpam-4440	107	11	resolving	resolve	VERB
ejpam-4440	107	12	dominating	dominating	NOUN
ejpam-4440	107	13	set	set	NOUN
ejpam-4440	107	14	of	of	ADP
ejpam-4440	107	15	g	g	PROPN
ejpam-4440	107	16	if	if	SCONJ
ejpam-4440	108	1	and	and	CCONJ
ejpam-4440	108	2	only	only	ADV
ejpam-4440	108	3	if	if	SCONJ
ejpam-4440	108	4	c	c	NOUN
ejpam-4440	108	5	=	=	SYM
ejpam-4440	108	6	∅	∅	NOUN
ejpam-4440	108	7	or	or	CCONJ
ejpam-4440	108	8	c	c	NOUN
ejpam-4440	108	9	is	be	AUX
ejpam-4440	108	10	a	a	DET
ejpam-4440	108	11	dominated	dominate	VERB
ejpam-4440	108	12	superclique	superclique	NOUN
ejpam-4440	108	13	in	in	ADP
ejpam-4440	108	14	g	g	PROPN
ejpam-4440	108	15	and	and	CCONJ
ejpam-4440	108	16	either	either	ADV
ejpam-4440	108	17	for	for	ADP
ejpam-4440	108	18	each	each	DET
ejpam-4440	108	19	x	x	SYM
ejpam-4440	108	20	∈	∈	PROPN
ejpam-4440	108	21	s	s	NOUN
ejpam-4440	108	22	,	,	PUNCT
ejpam-4440	108	23	c	c	PROPN
ejpam-4440	108	24	∪	∪	X
ejpam-4440	108	25	{	{	PUNCT
ejpam-4440	108	26	x	x	NOUN
ejpam-4440	108	27	}	}	PUNCT
ejpam-4440	108	28	is	be	AUX
ejpam-4440	108	29	a	a	DET
ejpam-4440	108	30	dominated	dominate	VERB
ejpam-4440	108	31	superclique	superclique	NOUN
ejpam-4440	108	32	or	or	CCONJ
ejpam-4440	108	33	there	there	ADV
ejpam-4440	108	34	exists	exist	VERB
ejpam-4440	108	35	y	y	PROPN
ejpam-4440	108	36	∈	∈	PROPN
ejpam-4440	108	37	c	c	X
ejpam-4440	108	38	∩ng(x	∩ng(x	NOUN
ejpam-4440	108	39	)	)	PUNCT
ejpam-4440	108	40	such	such	ADJ
ejpam-4440	108	41	that	that	SCONJ
ejpam-4440	108	42	(	(	PUNCT
ejpam-4440	108	43	c	c	NOUN
ejpam-4440	108	44	\	\	PROPN
ejpam-4440	108	45	{	{	PUNCT
ejpam-4440	108	46	y	y	NOUN
ejpam-4440	108	47	}	}	PUNCT
ejpam-4440	108	48	)	)	PUNCT
ejpam-4440	108	49	∪	∪	ADP
ejpam-4440	108	50	{	{	PUNCT
ejpam-4440	108	51	x	x	NOUN
ejpam-4440	108	52	}	}	PUNCT
ejpam-4440	108	53	is	be	AUX
ejpam-4440	108	54	a	a	DET
ejpam-4440	108	55	dominated	dominate	VERB
ejpam-4440	108	56	superclique	superclique	NOUN
ejpam-4440	108	57	in	in	ADP
ejpam-4440	108	58	g.	g.	PROPN
ejpam-4440	108	59	proof	proof	PROPN
ejpam-4440	108	60	.	.	PUNCT
ejpam-4440	109	1	suppose	suppose	VERB
ejpam-4440	109	2	s	s	VERB
ejpam-4440	109	3	=	=	SYM
ejpam-4440	109	4	v	v	NOUN
ejpam-4440	109	5	(	(	PUNCT
ejpam-4440	109	6	g)\c	g)\c	NOUN
ejpam-4440	109	7	is	be	AUX
ejpam-4440	109	8	a	a	DET
ejpam-4440	109	9	movable	movable	ADJ
ejpam-4440	109	10	strong	strong	ADJ
ejpam-4440	109	11	resolving	resolve	VERB
ejpam-4440	109	12	dominating	dominating	NOUN
ejpam-4440	109	13	set	set	NOUN
ejpam-4440	109	14	of	of	ADP
ejpam-4440	109	15	g.	g.	PROPN
ejpam-4440	109	16	then	then	ADV
ejpam-4440	109	17	s	s	VERB
ejpam-4440	109	18	is	be	AUX
ejpam-4440	109	19	a	a	DET
ejpam-4440	109	20	strong	strong	ADJ
ejpam-4440	109	21	resolving	resolving	NOUN
ejpam-4440	109	22	dominating	dominating	NOUN
ejpam-4440	109	23	set	set	NOUN
ejpam-4440	109	24	of	of	ADP
ejpam-4440	109	25	g	g	PROPN
ejpam-4440	109	26	.	.	PUNCT
ejpam-4440	110	1	by	by	ADP
ejpam-4440	110	2	lemma	lemma	PROPN
ejpam-4440	110	3	1	1	NUM
ejpam-4440	110	4	,	,	PUNCT
ejpam-4440	110	5	c	c	NOUN
ejpam-4440	110	6	=	=	SYM
ejpam-4440	110	7	∅	∅	NOUN
ejpam-4440	110	8	or	or	CCONJ
ejpam-4440	110	9	c	c	NOUN
ejpam-4440	110	10	is	be	AUX
ejpam-4440	110	11	a	a	DET
ejpam-4440	110	12	dominated	dominate	VERB
ejpam-4440	110	13	superclique	superclique	NOUN
ejpam-4440	110	14	in	in	ADP
ejpam-4440	110	15	g.	g.	PROPN
ejpam-4440	110	16	let	let	VERB
ejpam-4440	110	17	x	x	PROPN
ejpam-4440	110	18	∈	∈	PROPN
ejpam-4440	110	19	s.	s.	PROPN
ejpam-4440	110	20	since	since	SCONJ
ejpam-4440	110	21	s	s	PROPN
ejpam-4440	110	22	is	be	AUX
ejpam-4440	110	23	a	a	DET
ejpam-4440	110	24	movable	movable	ADJ
ejpam-4440	110	25	strong	strong	ADJ
ejpam-4440	110	26	resolving	resolve	VERB
ejpam-4440	110	27	dominating	dominating	NOUN
ejpam-4440	110	28	set	set	NOUN
ejpam-4440	110	29	,	,	PUNCT
ejpam-4440	110	30	either	either	CCONJ
ejpam-4440	110	31	s	s	VERB
ejpam-4440	110	32	\	\	X
ejpam-4440	110	33	{	{	PUNCT
ejpam-4440	110	34	x	x	X
ejpam-4440	110	35	}	}	PUNCT
ejpam-4440	110	36	is	be	AUX
ejpam-4440	110	37	a	a	DET
ejpam-4440	110	38	strong	strong	ADJ
ejpam-4440	110	39	resolving	resolving	NOUN
ejpam-4440	110	40	dominating	dominating	NOUN
ejpam-4440	110	41	or	or	CCONJ
ejpam-4440	110	42	there	there	ADV
ejpam-4440	110	43	exists	exist	VERB
ejpam-4440	110	44	y	y	PROPN
ejpam-4440	110	45	∈	∈	PROPN
ejpam-4440	110	46	(	(	PUNCT
ejpam-4440	110	47	v	v	NOUN
ejpam-4440	110	48	(	(	PUNCT
ejpam-4440	110	49	g	g	NOUN
ejpam-4440	110	50	)	)	PUNCT
ejpam-4440	110	51	\	\	NOUN
ejpam-4440	111	1	s)∩ng(x	s)∩ng(x	X
ejpam-4440	111	2	)	)	PUNCT
ejpam-4440	111	3	such	such	ADJ
ejpam-4440	111	4	that	that	SCONJ
ejpam-4440	111	5	(	(	PUNCT
ejpam-4440	111	6	s\{x})∪{y	s\{x})∪{y	NOUN
ejpam-4440	111	7	}	}	PUNCT
ejpam-4440	111	8	is	be	AUX
ejpam-4440	111	9	a	a	DET
ejpam-4440	111	10	strong	strong	ADJ
ejpam-4440	111	11	resolving	resolving	NOUN
ejpam-4440	111	12	dominating	dominating	NOUN
ejpam-4440	111	13	set	set	NOUN
ejpam-4440	111	14	of	of	ADP
ejpam-4440	111	15	g.	g.	PROPN
ejpam-4440	111	16	since	since	SCONJ
ejpam-4440	111	17	s\{x	s\{x	X
ejpam-4440	111	18	}	}	PUNCT
ejpam-4440	111	19	=	=	SYM
ejpam-4440	111	20	v	v	NOUN
ejpam-4440	111	21	(	(	PUNCT
ejpam-4440	111	22	g)\(c∪{x	g)\(c∪{x	NOUN
ejpam-4440	111	23	}	}	PUNCT
ejpam-4440	111	24	)	)	PUNCT
ejpam-4440	111	25	h.	h.	NOUN
ejpam-4440	111	26	sumaoy	sumaoy	NOUN
ejpam-4440	111	27	,	,	PUNCT
ejpam-4440	111	28	h.	h.	PROPN
ejpam-4440	111	29	rara	rara	PROPN
ejpam-4440	111	30	/	/	SYM
ejpam-4440	111	31	eur	eur	PROPN
ejpam-4440	111	32	.	.	PUNCT
ejpam-4440	112	1	j.	j.	PROPN
ejpam-4440	112	2	pure	pure	PROPN
ejpam-4440	112	3	appl	appl	PROPN
ejpam-4440	112	4	.	.	PROPN
ejpam-4440	112	5	math	math	PROPN
ejpam-4440	112	6	,	,	PUNCT
ejpam-4440	112	7	15	15	NUM
ejpam-4440	112	8	(	(	PUNCT
ejpam-4440	112	9	3	3	NUM
ejpam-4440	112	10	)	)	PUNCT
ejpam-4440	112	11	(	(	PUNCT
ejpam-4440	112	12	2022	2022	NUM
ejpam-4440	112	13	)	)	PUNCT
ejpam-4440	112	14	,	,	PUNCT
ejpam-4440	112	15	1201	1201	NUM
ejpam-4440	112	16	-	-	SYM
ejpam-4440	112	17	1210	1210	NUM
ejpam-4440	112	18	1205	1205	NUM
ejpam-4440	112	19	and	and	CCONJ
ejpam-4440	112	20	(	(	PUNCT
ejpam-4440	112	21	s	s	NOUN
ejpam-4440	112	22	\	\	X
ejpam-4440	112	23	{	{	PUNCT
ejpam-4440	112	24	x	x	NOUN
ejpam-4440	112	25	}	}	PUNCT
ejpam-4440	112	26	)	)	PUNCT
ejpam-4440	112	27	∪	∪	ADP
ejpam-4440	112	28	{	{	PUNCT
ejpam-4440	112	29	y	y	NOUN
ejpam-4440	112	30	}	}	PUNCT
ejpam-4440	112	31	=	=	SYM
ejpam-4440	112	32	v	v	NOUN
ejpam-4440	112	33	(	(	PUNCT
ejpam-4440	112	34	g	g	NOUN
ejpam-4440	112	35	)	)	PUNCT
ejpam-4440	112	36	\	\	PUNCT
ejpam-4440	113	1	(	(	PUNCT
ejpam-4440	113	2	(	(	PUNCT
ejpam-4440	113	3	c	c	NOUN
ejpam-4440	113	4	\	\	X
ejpam-4440	113	5	{	{	PUNCT
ejpam-4440	113	6	x	x	NOUN
ejpam-4440	113	7	}	}	PUNCT
ejpam-4440	113	8	)	)	PUNCT
ejpam-4440	113	9	∪	∪	ADP
ejpam-4440	113	10	{	{	PUNCT
ejpam-4440	113	11	y	y	NOUN
ejpam-4440	113	12	}	}	PUNCT
ejpam-4440	113	13	)	)	PUNCT
ejpam-4440	113	14	,	,	PUNCT
ejpam-4440	113	15	by	by	ADP
ejpam-4440	113	16	lemma	lemma	PROPN
ejpam-4440	113	17	1	1	NUM
ejpam-4440	113	18	c	c	PROPN
ejpam-4440	113	19	∪	∪	X
ejpam-4440	113	20	{	{	PUNCT
ejpam-4440	113	21	x	x	NOUN
ejpam-4440	113	22	}	}	PUNCT
ejpam-4440	113	23	is	be	AUX
ejpam-4440	113	24	a	a	DET
ejpam-4440	113	25	dominated	dominate	VERB
ejpam-4440	113	26	superclique	superclique	NOUN
ejpam-4440	113	27	or	or	CCONJ
ejpam-4440	113	28	(	(	PUNCT
ejpam-4440	113	29	c	c	NOUN
ejpam-4440	113	30	\	\	PROPN
ejpam-4440	113	31	y	y	PROPN
ejpam-4440	113	32	)	)	PUNCT
ejpam-4440	113	33	∪	∪	NOUN
ejpam-4440	113	34	{	{	PUNCT
ejpam-4440	113	35	x	x	NOUN
ejpam-4440	113	36	}	}	PUNCT
ejpam-4440	113	37	is	be	AUX
ejpam-4440	113	38	a	a	DET
ejpam-4440	113	39	dominated	dominate	VERB
ejpam-4440	113	40	superclique	superclique	NOUN
ejpam-4440	113	41	in	in	ADP
ejpam-4440	113	42	g.	g.	PROPN
ejpam-4440	113	43	for	for	ADP
ejpam-4440	113	44	the	the	DET
ejpam-4440	113	45	converse	converse	NOUN
ejpam-4440	113	46	,	,	PUNCT
ejpam-4440	113	47	suppose	suppose	VERB
ejpam-4440	113	48	c	c	AUX
ejpam-4440	113	49	=	=	PUNCT
ejpam-4440	113	50	∅.	∅.	VERB
ejpam-4440	113	51	then	then	ADV
ejpam-4440	113	52	,	,	PUNCT
ejpam-4440	113	53	s	s	NOUN
ejpam-4440	113	54	=	=	SYM
ejpam-4440	113	55	v	v	X
ejpam-4440	113	56	(	(	PUNCT
ejpam-4440	113	57	g	g	NOUN
ejpam-4440	113	58	)	)	PUNCT
ejpam-4440	113	59	is	be	AUX
ejpam-4440	113	60	strong	strong	ADJ
ejpam-4440	113	61	resolving	resolve	VERB
ejpam-4440	113	62	dominating	dominate	VERB
ejpam-4440	113	63	set	set	NOUN
ejpam-4440	113	64	of	of	ADP
ejpam-4440	113	65	g.	g.	PROPN
ejpam-4440	113	66	thus	thus	ADV
ejpam-4440	113	67	,	,	PUNCT
ejpam-4440	113	68	s	s	VERB
ejpam-4440	113	69	\	\	X
ejpam-4440	113	70	{	{	PUNCT
ejpam-4440	113	71	x	x	NOUN
ejpam-4440	113	72	}	}	PUNCT
ejpam-4440	113	73	=	=	SYM
ejpam-4440	113	74	v	v	NOUN
ejpam-4440	113	75	(	(	PUNCT
ejpam-4440	113	76	g	g	NOUN
ejpam-4440	113	77	)	)	PUNCT
ejpam-4440	113	78	\	\	NOUN
ejpam-4440	113	79	{	{	PUNCT
ejpam-4440	113	80	x	x	NOUN
ejpam-4440	113	81	}	}	PUNCT
ejpam-4440	113	82	is	be	AUX
ejpam-4440	113	83	strong	strong	ADJ
ejpam-4440	113	84	resolving	resolve	VERB
ejpam-4440	113	85	dominating	dominating	NOUN
ejpam-4440	113	86	since	since	SCONJ
ejpam-4440	113	87	{	{	PUNCT
ejpam-4440	113	88	x	x	X
ejpam-4440	113	89	}	}	PUNCT
ejpam-4440	113	90	is	be	AUX
ejpam-4440	113	91	a	a	DET
ejpam-4440	113	92	dominated	dominate	VERB
ejpam-4440	113	93	superclique	superclique	NOUN
ejpam-4440	113	94	for	for	ADP
ejpam-4440	113	95	each	each	DET
ejpam-4440	113	96	x	x	SYM
ejpam-4440	113	97	∈	∈	PROPN
ejpam-4440	113	98	v	v	NOUN
ejpam-4440	113	99	(	(	PUNCT
ejpam-4440	113	100	g	g	NOUN
ejpam-4440	113	101	)	)	PUNCT
ejpam-4440	113	102	.	.	PUNCT
ejpam-4440	114	1	so	so	ADV
ejpam-4440	114	2	,	,	PUNCT
ejpam-4440	114	3	suppose	suppose	VERB
ejpam-4440	114	4	c	c	NOUN
ejpam-4440	114	5	is	be	AUX
ejpam-4440	114	6	a	a	DET
ejpam-4440	114	7	dominated	dominate	VERB
ejpam-4440	114	8	superclique	superclique	NOUN
ejpam-4440	114	9	in	in	ADP
ejpam-4440	114	10	g	g	PROPN
ejpam-4440	114	11	and	and	CCONJ
ejpam-4440	114	12	for	for	SCONJ
ejpam-4440	114	13	each	each	DET
ejpam-4440	114	14	x	x	SYM
ejpam-4440	114	15	∈	∈	PROPN
ejpam-4440	114	16	s	s	VERB
ejpam-4440	114	17	either	either	CCONJ
ejpam-4440	114	18	c	c	PROPN
ejpam-4440	114	19	∪	∪	X
ejpam-4440	114	20	{	{	PUNCT
ejpam-4440	114	21	x	x	NOUN
ejpam-4440	114	22	}	}	PUNCT
ejpam-4440	114	23	is	be	AUX
ejpam-4440	114	24	a	a	DET
ejpam-4440	114	25	dominated	dominate	VERB
ejpam-4440	114	26	superclique	superclique	NOUN
ejpam-4440	114	27	or	or	CCONJ
ejpam-4440	114	28	there	there	ADV
ejpam-4440	114	29	exists	exist	VERB
ejpam-4440	114	30	y	y	PROPN
ejpam-4440	114	31	∈	∈	PROPN
ejpam-4440	114	32	c	c	PROPN
ejpam-4440	114	33	∩	∩	X
ejpam-4440	114	34	ng(x	ng(x	NUM
ejpam-4440	114	35	)	)	PUNCT
ejpam-4440	114	36	such	such	ADJ
ejpam-4440	114	37	that	that	PRON
ejpam-4440	114	38	(	(	PUNCT
ejpam-4440	114	39	c	c	NOUN
ejpam-4440	114	40	\	\	PROPN
ejpam-4440	114	41	{	{	PUNCT
ejpam-4440	114	42	y	y	NOUN
ejpam-4440	114	43	}	}	PUNCT
ejpam-4440	114	44	)	)	PUNCT
ejpam-4440	114	45	∪	∪	ADP
ejpam-4440	114	46	{	{	PUNCT
ejpam-4440	114	47	x	x	NOUN
ejpam-4440	114	48	}	}	PUNCT
ejpam-4440	114	49	is	be	AUX
ejpam-4440	114	50	a	a	DET
ejpam-4440	114	51	dominated	dominate	VERB
ejpam-4440	114	52	superclique	superclique	NOUN
ejpam-4440	114	53	.	.	PUNCT
ejpam-4440	115	1	hence	hence	ADV
ejpam-4440	115	2	,	,	PUNCT
ejpam-4440	115	3	for	for	ADP
ejpam-4440	115	4	each	each	DET
ejpam-4440	115	5	x	x	SYM
ejpam-4440	115	6	∈	∈	PROPN
ejpam-4440	115	7	s	s	PART
ejpam-4440	115	8	,	,	PUNCT
ejpam-4440	115	9	(	(	PUNCT
ejpam-4440	115	10	s	s	X
ejpam-4440	115	11	\	\	X
ejpam-4440	115	12	{	{	PUNCT
ejpam-4440	115	13	x})∪	x})∪	PROPN
ejpam-4440	115	14	{	{	PUNCT
ejpam-4440	115	15	y	y	PROPN
ejpam-4440	115	16	}	}	PUNCT
ejpam-4440	115	17	=	=	SYM
ejpam-4440	115	18	v	v	NOUN
ejpam-4440	115	19	(	(	PUNCT
ejpam-4440	115	20	g	g	NOUN
ejpam-4440	115	21	)	)	PUNCT
ejpam-4440	115	22	\	\	PUNCT
ejpam-4440	115	23	(	(	PUNCT
ejpam-4440	115	24	c	c	NOUN
ejpam-4440	115	25	\	\	PROPN
ejpam-4440	115	26	{	{	PUNCT
ejpam-4440	115	27	y})∪	y})∪	PROPN
ejpam-4440	115	28	{	{	PUNCT
ejpam-4440	115	29	x	x	NOUN
ejpam-4440	115	30	}	}	PUNCT
ejpam-4440	115	31	is	be	AUX
ejpam-4440	115	32	a	a	DET
ejpam-4440	115	33	strong	strong	ADJ
ejpam-4440	115	34	resolving	resolving	NOUN
ejpam-4440	115	35	dominating	dominating	NOUN
ejpam-4440	115	36	set	set	NOUN
ejpam-4440	115	37	of	of	ADP
ejpam-4440	115	38	g.	g.	PROPN
ejpam-4440	115	39	therefore	therefore	ADV
ejpam-4440	115	40	,	,	PUNCT
ejpam-4440	115	41	s	s	VERB
ejpam-4440	115	42	is	be	AUX
ejpam-4440	115	43	a	a	DET
ejpam-4440	115	44	movable	movable	ADJ
ejpam-4440	115	45	strong	strong	ADJ
ejpam-4440	115	46	resolving	resolving	NOUN
ejpam-4440	115	47	set	set	NOUN
ejpam-4440	115	48	of	of	ADP
ejpam-4440	115	49	g.	g.	PROPN
ejpam-4440	115	50	lemma	lemma	PROPN
ejpam-4440	115	51	3	3	X
ejpam-4440	115	52	.	.	PUNCT
ejpam-4440	115	53	let	let	VERB
ejpam-4440	115	54	g	g	PRON
ejpam-4440	115	55	be	be	AUX
ejpam-4440	115	56	a	a	DET
ejpam-4440	115	57	nontrivial	nontrivial	ADJ
ejpam-4440	115	58	connected	connect	VERB
ejpam-4440	115	59	graph	graph	NOUN
ejpam-4440	115	60	.	.	PUNCT
ejpam-4440	116	1	a	a	DET
ejpam-4440	116	2	set	set	NOUN
ejpam-4440	116	3	c	c	NOUN
ejpam-4440	116	4	⊆	⊆	NUM
ejpam-4440	116	5	v	v	NOUN
ejpam-4440	116	6	(	(	PUNCT
ejpam-4440	116	7	g	g	NOUN
ejpam-4440	116	8	)	)	PUNCT
ejpam-4440	116	9	is	be	AUX
ejpam-4440	116	10	a	a	DET
ejpam-4440	116	11	superclique	superclique	NOUN
ejpam-4440	116	12	in	in	ADP
ejpam-4440	116	13	g	g	PROPN
ejpam-4440	116	14	and	and	CCONJ
ejpam-4440	116	15	for	for	ADP
ejpam-4440	116	16	each	each	DET
ejpam-4440	116	17	x	x	SYM
ejpam-4440	116	18	∈	∈	PROPN
ejpam-4440	116	19	v	v	NOUN
ejpam-4440	116	20	(	(	PUNCT
ejpam-4440	116	21	g)\c	g)\c	VERB
ejpam-4440	116	22	either	either	ADV
ejpam-4440	116	23	c∪{x	c∪{x	NOUN
ejpam-4440	116	24	}	}	PUNCT
ejpam-4440	116	25	is	be	AUX
ejpam-4440	116	26	a	a	DET
ejpam-4440	116	27	superclique	superclique	NOUN
ejpam-4440	116	28	or	or	CCONJ
ejpam-4440	116	29	there	there	ADV
ejpam-4440	116	30	exists	exist	VERB
ejpam-4440	116	31	y	y	PROPN
ejpam-4440	116	32	∈	∈	PROPN
ejpam-4440	116	33	c∩ng(x	c∩ng(x	NOUN
ejpam-4440	116	34	)	)	PUNCT
ejpam-4440	116	35	such	such	ADJ
ejpam-4440	116	36	that	that	PRON
ejpam-4440	116	37	(	(	PUNCT
ejpam-4440	116	38	c	c	NOUN
ejpam-4440	116	39	\	\	PROPN
ejpam-4440	116	40	{	{	PUNCT
ejpam-4440	116	41	y	y	NOUN
ejpam-4440	116	42	}	}	PUNCT
ejpam-4440	116	43	∪	∪	NOUN
ejpam-4440	116	44	{	{	PUNCT
ejpam-4440	116	45	x	x	NOUN
ejpam-4440	116	46	}	}	PUNCT
ejpam-4440	116	47	)	)	PUNCT
ejpam-4440	116	48	is	be	AUX
ejpam-4440	116	49	a	a	DET
ejpam-4440	116	50	superclique	superclique	NOUN
ejpam-4440	116	51	in	in	ADP
ejpam-4440	116	52	g	g	PROPN
ejpam-4440	116	53	if	if	SCONJ
ejpam-4440	117	1	and	and	CCONJ
ejpam-4440	117	2	only	only	ADV
ejpam-4440	117	3	if	if	SCONJ
ejpam-4440	117	4	|c|	|c|	PROPN
ejpam-4440	117	5	=	=	SYM
ejpam-4440	117	6	1	1	NUM
ejpam-4440	117	7	and	and	CCONJ
ejpam-4440	117	8	degg(v	degg(v	PROPN
ejpam-4440	117	9	)	)	PUNCT
ejpam-4440	117	10	=	=	SYM
ejpam-4440	117	11	|v	|v	PROPN
ejpam-4440	117	12	(	(	PUNCT
ejpam-4440	117	13	g)|	g)|	INTJ
ejpam-4440	117	14	−	−	NOUN
ejpam-4440	117	15	1	1	NUM
ejpam-4440	117	16	for	for	ADP
ejpam-4440	117	17	v	v	PROPN
ejpam-4440	117	18	∈	∈	PROPN
ejpam-4440	117	19	c.	c.	NOUN
ejpam-4440	117	20	proof	proof	NOUN
ejpam-4440	117	21	.	.	PUNCT
ejpam-4440	118	1	suppose	suppose	VERB
ejpam-4440	118	2	c	c	NOUN
ejpam-4440	118	3	is	be	AUX
ejpam-4440	118	4	a	a	DET
ejpam-4440	118	5	superclique	superclique	NOUN
ejpam-4440	118	6	in	in	ADP
ejpam-4440	118	7	g	g	NOUN
ejpam-4440	118	8	satisfying	satisfy	VERB
ejpam-4440	118	9	the	the	DET
ejpam-4440	118	10	given	give	VERB
ejpam-4440	118	11	condition	condition	NOUN
ejpam-4440	118	12	and	and	CCONJ
ejpam-4440	118	13	let	let	VERB
ejpam-4440	118	14	|c|	|c|	PROPN
ejpam-4440	118	15	>	>	X
ejpam-4440	118	16	1	1	X
ejpam-4440	118	17	.	.	PUNCT
ejpam-4440	119	1	let	let	VERB
ejpam-4440	119	2	u	u	NOUN
ejpam-4440	119	3	,	,	PUNCT
ejpam-4440	119	4	v	v	PROPN
ejpam-4440	119	5	∈	∈	PROPN
ejpam-4440	119	6	c.	c.	NOUN
ejpam-4440	119	7	then	then	ADV
ejpam-4440	119	8	uv	uv	PROPN
ejpam-4440	119	9	∈	∈	PROPN
ejpam-4440	119	10	e(g	e(g	PROPN
ejpam-4440	119	11	)	)	PUNCT
ejpam-4440	119	12	.	.	PUNCT
ejpam-4440	120	1	let	let	VERB
ejpam-4440	120	2	x	x	SYM
ejpam-4440	120	3	∈	∈	PROPN
ejpam-4440	120	4	v	v	X
ejpam-4440	120	5	(	(	PUNCT
ejpam-4440	120	6	g	g	NOUN
ejpam-4440	120	7	)	)	PUNCT
ejpam-4440	120	8	\	\	PROPN
ejpam-4440	120	9	c.	c.	NOUN
ejpam-4440	120	10	if	if	SCONJ
ejpam-4440	120	11	c	c	PROPN
ejpam-4440	120	12	∪	∪	VERB
ejpam-4440	120	13	{	{	PUNCT
ejpam-4440	120	14	x	x	NOUN
ejpam-4440	120	15	}	}	PUNCT
ejpam-4440	120	16	is	be	AUX
ejpam-4440	120	17	a	a	DET
ejpam-4440	120	18	superclique	superclique	NOUN
ejpam-4440	120	19	,	,	PUNCT
ejpam-4440	120	20	then	then	ADV
ejpam-4440	120	21	x	x	PART
ejpam-4440	120	22	∈	∈	PROPN
ejpam-4440	120	23	ng(u)∩ng(v	ng(u)∩ng(v	PROPN
ejpam-4440	120	24	)	)	PUNCT
ejpam-4440	120	25	,	,	PUNCT
ejpam-4440	120	26	a	a	DET
ejpam-4440	120	27	contradiction	contradiction	NOUN
ejpam-4440	120	28	since	since	SCONJ
ejpam-4440	120	29	c	c	PROPN
ejpam-4440	120	30	is	be	AUX
ejpam-4440	120	31	a	a	DET
ejpam-4440	120	32	superclique	superclique	NOUN
ejpam-4440	120	33	.	.	PUNCT
ejpam-4440	121	1	on	on	ADP
ejpam-4440	121	2	the	the	DET
ejpam-4440	121	3	other	other	ADJ
ejpam-4440	121	4	hand	hand	NOUN
ejpam-4440	121	5	,	,	PUNCT
ejpam-4440	121	6	suppose	suppose	VERB
ejpam-4440	121	7	there	there	PRON
ejpam-4440	121	8	exists	exist	VERB
ejpam-4440	121	9	y	y	PROPN
ejpam-4440	121	10	∈	∈	PROPN
ejpam-4440	121	11	c∩ng(x	c∩ng(x	NOUN
ejpam-4440	121	12	)	)	PUNCT
ejpam-4440	121	13	such	such	ADJ
ejpam-4440	121	14	that	that	SCONJ
ejpam-4440	121	15	(	(	PUNCT
ejpam-4440	121	16	c\{y})∪{x	c\{y})∪{x	NOUN
ejpam-4440	121	17	}	}	PUNCT
ejpam-4440	121	18	is	be	AUX
ejpam-4440	121	19	superclique	superclique	ADJ
ejpam-4440	121	20	.	.	PUNCT
ejpam-4440	122	1	if	if	SCONJ
ejpam-4440	122	2	y	y	PROPN
ejpam-4440	122	3	=	=	SYM
ejpam-4440	122	4	u	u	PROPN
ejpam-4440	122	5	,	,	PUNCT
ejpam-4440	122	6	then	then	ADV
ejpam-4440	122	7	x	x	SYM
ejpam-4440	122	8	∈	∈	NOUN
ejpam-4440	122	9	ng(v	ng(v	PUNCT
ejpam-4440	122	10	)	)	PUNCT
ejpam-4440	122	11	and	and	CCONJ
ejpam-4440	122	12	there	there	PRON
ejpam-4440	122	13	exists	exist	VERB
ejpam-4440	122	14	z	z	PROPN
ejpam-4440	122	15	∈	∈	PROPN
ejpam-4440	122	16	(	(	PUNCT
ejpam-4440	122	17	ng(x)\ng(v))∩(v	ng(x)\ng(v))∩(v	PROPN
ejpam-4440	122	18	(	(	PUNCT
ejpam-4440	122	19	g)\c	g)\c	NOUN
ejpam-4440	122	20	)	)	PUNCT
ejpam-4440	122	21	.	.	PUNCT
ejpam-4440	123	1	this	this	PRON
ejpam-4440	123	2	is	be	AUX
ejpam-4440	123	3	a	a	DET
ejpam-4440	123	4	contradiction	contradiction	NOUN
ejpam-4440	123	5	since	since	SCONJ
ejpam-4440	123	6	z	z	PROPN
ejpam-4440	123	7	∈	∈	PROPN
ejpam-4440	123	8	c∪{x	c∪{x	NOUN
ejpam-4440	123	9	}	}	PUNCT
ejpam-4440	123	10	or	or	CCONJ
ejpam-4440	123	11	z	z	NOUN
ejpam-4440	123	12	∈	∈	PROPN
ejpam-4440	123	13	(	(	PUNCT
ejpam-4440	123	14	c	c	NOUN
ejpam-4440	123	15	\{w})∪{x	\{w})∪{x	NOUN
ejpam-4440	123	16	}	}	PUNCT
ejpam-4440	123	17	for	for	ADP
ejpam-4440	123	18	some	some	DET
ejpam-4440	123	19	w	w	PROPN
ejpam-4440	123	20	∈	∈	PROPN
ejpam-4440	123	21	c∩ng(x	c∩ng(x	NOUN
ejpam-4440	123	22	)	)	PUNCT
ejpam-4440	123	23	,	,	PUNCT
ejpam-4440	123	24	that	that	PRON
ejpam-4440	123	25	is	be	AUX
ejpam-4440	123	26	z	z	PROPN
ejpam-4440	123	27	∈	∈	PROPN
ejpam-4440	123	28	ng(x)∩ng(v	ng(x)∩ng(v	PROPN
ejpam-4440	123	29	)	)	PUNCT
ejpam-4440	123	30	.	.	PUNCT
ejpam-4440	124	1	hence	hence	ADV
ejpam-4440	124	2	,	,	PUNCT
ejpam-4440	124	3	|c|	|c|	PROPN
ejpam-4440	124	4	=	=	NUM
ejpam-4440	124	5	1	1	X
ejpam-4440	124	6	.	.	PUNCT
ejpam-4440	124	7	now	now	ADV
ejpam-4440	124	8	,	,	PUNCT
ejpam-4440	124	9	suppose	suppose	VERB
ejpam-4440	124	10	degg(v	degg(v	VERB
ejpam-4440	124	11	)	)	PUNCT
ejpam-4440	124	12	<	<	X
ejpam-4440	124	13	|v	|v	PROPN
ejpam-4440	124	14	(	(	PUNCT
ejpam-4440	124	15	g)|−1	g)|−1	NOUN
ejpam-4440	124	16	where	where	SCONJ
ejpam-4440	124	17	v	v	X
ejpam-4440	124	18	∈	∈	PROPN
ejpam-4440	124	19	c.	c.	NOUN
ejpam-4440	124	20	then	then	ADV
ejpam-4440	124	21	there	there	PRON
ejpam-4440	124	22	exists	exist	VERB
ejpam-4440	124	23	y	y	PROPN
ejpam-4440	124	24	∈	∈	PROPN
ejpam-4440	124	25	v	v	PROPN
ejpam-4440	124	26	(	(	PUNCT
ejpam-4440	124	27	g)\ng(v	g)\ng(v	ADJ
ejpam-4440	124	28	)	)	PUNCT
ejpam-4440	124	29	and	and	CCONJ
ejpam-4440	124	30	c	c	PROPN
ejpam-4440	124	31	∪	∪	X
ejpam-4440	124	32	{	{	PUNCT
ejpam-4440	124	33	y	y	NOUN
ejpam-4440	124	34	}	}	PUNCT
ejpam-4440	124	35	is	be	AUX
ejpam-4440	124	36	not	not	PART
ejpam-4440	124	37	a	a	DET
ejpam-4440	124	38	superclique	superclique	NOUN
ejpam-4440	124	39	in	in	ADP
ejpam-4440	124	40	g	g	PROPN
ejpam-4440	124	41	,	,	PUNCT
ejpam-4440	124	42	a	a	DET
ejpam-4440	124	43	contradiction	contradiction	NOUN
ejpam-4440	124	44	.	.	PUNCT
ejpam-4440	125	1	thus	thus	ADV
ejpam-4440	125	2	,	,	PUNCT
ejpam-4440	125	3	degg(v	degg(v	PROPN
ejpam-4440	125	4	)	)	PUNCT
ejpam-4440	125	5	=	=	SYM
ejpam-4440	126	1	|v	|v	PROPN
ejpam-4440	126	2	(	(	PUNCT
ejpam-4440	126	3	g)|	g)|	INTJ
ejpam-4440	126	4	−	−	NOUN
ejpam-4440	126	5	1	1	NUM
ejpam-4440	126	6	,	,	PUNCT
ejpam-4440	126	7	showing	show	VERB
ejpam-4440	126	8	that	that	SCONJ
ejpam-4440	126	9	c	c	PROPN
ejpam-4440	126	10	is	be	AUX
ejpam-4440	126	11	a	a	DET
ejpam-4440	126	12	γ	γ	NOUN
ejpam-4440	126	13	-	-	PUNCT
ejpam-4440	126	14	set	set	NOUN
ejpam-4440	126	15	of	of	ADP
ejpam-4440	126	16	g.	g.	PROPN
ejpam-4440	126	17	for	for	ADP
ejpam-4440	126	18	the	the	DET
ejpam-4440	126	19	converse	converse	NOUN
ejpam-4440	126	20	,	,	PUNCT
ejpam-4440	126	21	suppose	suppose	VERB
ejpam-4440	126	22	c	c	PROPN
ejpam-4440	126	23	is	be	AUX
ejpam-4440	126	24	γ	γ	X
ejpam-4440	126	25	-	-	PUNCT
ejpam-4440	126	26	set	set	NOUN
ejpam-4440	126	27	of	of	ADP
ejpam-4440	126	28	g.	g.	PROPN
ejpam-4440	126	29	then	then	ADV
ejpam-4440	126	30	c	c	PROPN
ejpam-4440	126	31	is	be	AUX
ejpam-4440	126	32	a	a	DET
ejpam-4440	126	33	superclique	superclique	NOUN
ejpam-4440	126	34	in	in	ADP
ejpam-4440	126	35	g	g	PROPN
ejpam-4440	126	36	and	and	CCONJ
ejpam-4440	126	37	for	for	ADP
ejpam-4440	126	38	every	every	DET
ejpam-4440	126	39	x	x	SYM
ejpam-4440	126	40	∈	∈	PROPN
ejpam-4440	126	41	v	v	ADP
ejpam-4440	126	42	(	(	PUNCT
ejpam-4440	126	43	g	g	NOUN
ejpam-4440	126	44	)	)	PUNCT
ejpam-4440	126	45	\	\	PUNCT
ejpam-4440	127	1	c	c	X
ejpam-4440	127	2	,	,	PUNCT
ejpam-4440	127	3	c	c	NOUN
ejpam-4440	127	4	∪	∪	X
ejpam-4440	127	5	{	{	PUNCT
ejpam-4440	127	6	x	x	NOUN
ejpam-4440	127	7	}	}	PUNCT
ejpam-4440	127	8	is	be	AUX
ejpam-4440	127	9	a	a	DET
ejpam-4440	127	10	superclique	superclique	NOUN
ejpam-4440	127	11	in	in	ADP
ejpam-4440	127	12	g	g	NOUN
ejpam-4440	127	13	since	since	SCONJ
ejpam-4440	127	14	⟨c	⟨c	NOUN
ejpam-4440	127	15	∪	∪	ADJ
ejpam-4440	127	16	{	{	PUNCT
ejpam-4440	127	17	x}⟩	x}⟩	PROPN
ejpam-4440	127	18	is	be	AUX
ejpam-4440	127	19	a	a	DET
ejpam-4440	127	20	path	path	NOUN
ejpam-4440	127	21	in	in	ADP
ejpam-4440	127	22	g.	g.	PROPN
ejpam-4440	127	23	as	as	ADP
ejpam-4440	127	24	a	a	DET
ejpam-4440	127	25	consequence	consequence	NOUN
ejpam-4440	127	26	of	of	ADP
ejpam-4440	127	27	lemma	lemma	PROPN
ejpam-4440	127	28	2	2	PROPN
ejpam-4440	127	29	and	and	CCONJ
ejpam-4440	127	30	lemma	lemma	PROPN
ejpam-4440	127	31	3	3	NUM
ejpam-4440	127	32	,	,	PUNCT
ejpam-4440	127	33	the	the	DET
ejpam-4440	127	34	next	next	ADJ
ejpam-4440	127	35	result	result	NOUN
ejpam-4440	127	36	follows	follow	VERB
ejpam-4440	127	37	.	.	PUNCT
ejpam-4440	128	1	theorem	theorem	ADJ
ejpam-4440	128	2	4	4	NUM
ejpam-4440	128	3	.	.	PUNCT
ejpam-4440	129	1	let	let	VERB
ejpam-4440	129	2	g	g	PRON
ejpam-4440	129	3	be	be	AUX
ejpam-4440	129	4	a	a	DET
ejpam-4440	129	5	nontrivial	nontrivial	ADJ
ejpam-4440	129	6	connected	connect	VERB
ejpam-4440	129	7	graph	graph	NOUN
ejpam-4440	129	8	with	with	ADP
ejpam-4440	129	9	diam(g	diam(g	NOUN
ejpam-4440	129	10	)	)	PUNCT
ejpam-4440	129	11	≤	≤	NOUN
ejpam-4440	129	12	2	2	NUM
ejpam-4440	129	13	.	.	PUNCT
ejpam-4440	130	1	then	then	ADV
ejpam-4440	130	2	s	s	VERB
ejpam-4440	130	3	=	=	SYM
ejpam-4440	130	4	v	v	PROPN
ejpam-4440	130	5	(	(	PUNCT
ejpam-4440	130	6	g	g	NOUN
ejpam-4440	130	7	)	)	PUNCT
ejpam-4440	130	8	\	\	PUNCT
ejpam-4440	131	1	c	c	NOUN
ejpam-4440	131	2	is	be	AUX
ejpam-4440	131	3	a	a	DET
ejpam-4440	131	4	movable	movable	ADJ
ejpam-4440	131	5	strong	strong	ADJ
ejpam-4440	131	6	resolving	resolve	VERB
ejpam-4440	131	7	dominating	dominating	NOUN
ejpam-4440	131	8	set	set	NOUN
ejpam-4440	131	9	of	of	ADP
ejpam-4440	131	10	g	g	PROPN
ejpam-4440	131	11	if	if	SCONJ
ejpam-4440	132	1	and	and	CCONJ
ejpam-4440	132	2	only	only	ADV
ejpam-4440	132	3	if	if	SCONJ
ejpam-4440	132	4	c	c	NOUN
ejpam-4440	132	5	=	=	SYM
ejpam-4440	132	6	∅	∅	NOUN
ejpam-4440	132	7	or	or	CCONJ
ejpam-4440	132	8	c	c	NOUN
ejpam-4440	132	9	is	be	AUX
ejpam-4440	132	10	a	a	DET
ejpam-4440	132	11	γ	γ	NOUN
ejpam-4440	132	12	-	-	PUNCT
ejpam-4440	132	13	set	set	NOUN
ejpam-4440	132	14	of	of	ADP
ejpam-4440	132	15	g	g	PROPN
ejpam-4440	132	16	if	if	SCONJ
ejpam-4440	132	17	γ(g	γ(g	PROPN
ejpam-4440	132	18	)	)	PUNCT
ejpam-4440	133	1	=	=	PUNCT
ejpam-4440	133	2	1	1	NUM
ejpam-4440	133	3	.	.	NOUN
ejpam-4440	133	4	3	3	X
ejpam-4440	133	5	.	.	X
ejpam-4440	133	6	γ1	γ1	PROPN
ejpam-4440	133	7	msr(g+h	msr(g+h	PROPN
ejpam-4440	133	8	)	)	PUNCT
ejpam-4440	133	9	in	in	ADP
ejpam-4440	133	10	the	the	DET
ejpam-4440	133	11	join	join	NOUN
ejpam-4440	133	12	of	of	ADP
ejpam-4440	133	13	graphs	graph	NOUN
ejpam-4440	133	14	this	this	DET
ejpam-4440	133	15	section	section	NOUN
ejpam-4440	133	16	gives	give	VERB
ejpam-4440	133	17	characterization	characterization	NOUN
ejpam-4440	133	18	of	of	ADP
ejpam-4440	133	19	the	the	DET
ejpam-4440	133	20	movable	movable	ADJ
ejpam-4440	133	21	strong	strong	ADJ
ejpam-4440	133	22	resolving	resolve	VERB
ejpam-4440	133	23	dominating	dominating	NOUN
ejpam-4440	133	24	sets	set	NOUN
ejpam-4440	133	25	in	in	ADP
ejpam-4440	133	26	the	the	DET
ejpam-4440	133	27	join	join	NOUN
ejpam-4440	133	28	of	of	ADP
ejpam-4440	133	29	graphs	graph	NOUN
ejpam-4440	133	30	as	as	ADV
ejpam-4440	133	31	well	well	ADV
ejpam-4440	133	32	as	as	ADP
ejpam-4440	133	33	its	its	PRON
ejpam-4440	133	34	movable	movable	ADJ
ejpam-4440	133	35	strong	strong	ADJ
ejpam-4440	133	36	resolving	resolve	VERB
ejpam-4440	133	37	domination	domination	NOUN
ejpam-4440	133	38	number	number	NOUN
ejpam-4440	133	39	.	.	PUNCT
ejpam-4440	134	1	theorem	theorem	NOUN
ejpam-4440	134	2	5	5	NUM
ejpam-4440	134	3	.	.	PUNCT
ejpam-4440	135	1	let	let	VERB
ejpam-4440	135	2	g	g	PRON
ejpam-4440	135	3	be	be	AUX
ejpam-4440	135	4	a	a	DET
ejpam-4440	135	5	nontrivial	nontrivial	ADJ
ejpam-4440	135	6	connected	connect	VERB
ejpam-4440	135	7	graph	graph	NOUN
ejpam-4440	135	8	of	of	ADP
ejpam-4440	135	9	order	order	NOUN
ejpam-4440	135	10	n	n	PRON
ejpam-4440	135	11	with	with	ADP
ejpam-4440	135	12	γ(g	γ(g	PROPN
ejpam-4440	135	13	)	)	PUNCT
ejpam-4440	135	14	=	=	SYM
ejpam-4440	135	15	1	1	NUM
ejpam-4440	135	16	and	and	CCONJ
ejpam-4440	135	17	k1	k1	NOUN
ejpam-4440	136	1	=	=	SYM
ejpam-4440	136	2	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4440	136	3	then	then	ADV
ejpam-4440	136	4	s	s	VERB
ejpam-4440	136	5	⊆	⊆	NUM
ejpam-4440	136	6	v	v	NOUN
ejpam-4440	136	7	(	(	PUNCT
ejpam-4440	136	8	k1	k1	NOUN
ejpam-4440	136	9	+	+	NOUN
ejpam-4440	136	10	g	g	NOUN
ejpam-4440	136	11	)	)	PUNCT
ejpam-4440	136	12	is	be	AUX
ejpam-4440	136	13	a	a	DET
ejpam-4440	136	14	movable	movable	ADJ
ejpam-4440	136	15	strong	strong	ADJ
ejpam-4440	136	16	resolving	resolve	VERB
ejpam-4440	136	17	dominating	dominating	NOUN
ejpam-4440	136	18	set	set	NOUN
ejpam-4440	136	19	of	of	ADP
ejpam-4440	136	20	k1	k1	NOUN
ejpam-4440	137	1	+	+	ADP
ejpam-4440	137	2	g	g	PROPN
ejpam-4440	137	3	if	if	SCONJ
ejpam-4440	137	4	and	and	CCONJ
ejpam-4440	137	5	only	only	ADV
ejpam-4440	137	6	if	if	SCONJ
ejpam-4440	137	7	s	s	VERB
ejpam-4440	137	8	=	=	SYM
ejpam-4440	137	9	v	v	X
ejpam-4440	137	10	(	(	PUNCT
ejpam-4440	137	11	g	g	NOUN
ejpam-4440	137	12	)	)	PUNCT
ejpam-4440	137	13	,	,	PUNCT
ejpam-4440	137	14	or	or	CCONJ
ejpam-4440	137	15	s	s	VERB
ejpam-4440	137	16	=	=	SYM
ejpam-4440	137	17	v	v	PROPN
ejpam-4440	137	18	(	(	PUNCT
ejpam-4440	137	19	k1	k1	NOUN
ejpam-4440	137	20	+	+	PROPN
ejpam-4440	137	21	g	g	NOUN
ejpam-4440	137	22	)	)	PUNCT
ejpam-4440	137	23	\	\	PUNCT
ejpam-4440	138	1	c	c	NOUN
ejpam-4440	138	2	where	where	SCONJ
ejpam-4440	138	3	c	c	PROPN
ejpam-4440	138	4	is	be	AUX
ejpam-4440	138	5	a	a	DET
ejpam-4440	138	6	γ	γ	NOUN
ejpam-4440	138	7	-	-	PUNCT
ejpam-4440	138	8	set	set	NOUN
ejpam-4440	138	9	of	of	ADP
ejpam-4440	138	10	g.	g.	PROPN
ejpam-4440	138	11	proof	proof	PROPN
ejpam-4440	138	12	.	.	PUNCT
ejpam-4440	139	1	suppose	suppose	VERB
ejpam-4440	139	2	s	s	NOUN
ejpam-4440	139	3	is	be	AUX
ejpam-4440	139	4	a	a	DET
ejpam-4440	139	5	movable	movable	ADJ
ejpam-4440	139	6	strong	strong	ADJ
ejpam-4440	139	7	resolving	resolve	VERB
ejpam-4440	139	8	dominating	dominating	NOUN
ejpam-4440	139	9	set	set	NOUN
ejpam-4440	139	10	of	of	ADP
ejpam-4440	139	11	k1	k1	PROPN
ejpam-4440	139	12	+	+	PROPN
ejpam-4440	139	13	g.	g.	PROPN
ejpam-4440	139	14	then	then	ADV
ejpam-4440	139	15	,	,	PUNCT
ejpam-4440	139	16	by	by	ADP
ejpam-4440	139	17	theorem	theorem	NOUN
ejpam-4440	139	18	1	1	NUM
ejpam-4440	139	19	,	,	PUNCT
ejpam-4440	139	20	s	s	PART
ejpam-4440	139	21	=	=	SYM
ejpam-4440	139	22	v	v	X
ejpam-4440	139	23	(	(	PUNCT
ejpam-4440	139	24	g	g	NOUN
ejpam-4440	139	25	)	)	PUNCT
ejpam-4440	139	26	,	,	PUNCT
ejpam-4440	139	27	or	or	CCONJ
ejpam-4440	139	28	s	s	VERB
ejpam-4440	139	29	=	=	SYM
ejpam-4440	139	30	v	v	PROPN
ejpam-4440	139	31	(	(	PUNCT
ejpam-4440	139	32	k1	k1	NOUN
ejpam-4440	139	33	+	+	PROPN
ejpam-4440	139	34	g	g	NOUN
ejpam-4440	139	35	)	)	PUNCT
ejpam-4440	139	36	\	\	PROPN
ejpam-4440	139	37	c∗	c∗	NOUN
ejpam-4440	139	38	,	,	PUNCT
ejpam-4440	139	39	or	or	CCONJ
ejpam-4440	139	40	s	s	X
ejpam-4440	139	41	=	=	PUNCT
ejpam-4440	139	42	(	(	PUNCT
ejpam-4440	139	43	v	v	NOUN
ejpam-4440	139	44	(	(	PUNCT
ejpam-4440	139	45	g	g	NOUN
ejpam-4440	139	46	)	)	PUNCT
ejpam-4440	139	47	\	\	PUNCT
ejpam-4440	140	1	c	c	X
ejpam-4440	140	2	)	)	PUNCT
ejpam-4440	140	3	∪	∪	NOUN
ejpam-4440	140	4	{	{	PUNCT
ejpam-4440	140	5	x	x	SYM
ejpam-4440	140	6	∈	∈	PROPN
ejpam-4440	140	7	c	c	NOUN
ejpam-4440	140	8	:	:	PUNCT
ejpam-4440	140	9	degg(x	degg(x	X
ejpam-4440	140	10	)	)	PUNCT
ejpam-4440	140	11	=	=	PUNCT
ejpam-4440	140	12	n−	n−	NOUN
ejpam-4440	140	13	1	1	NUM
ejpam-4440	140	14	}	}	PUNCT
ejpam-4440	140	15	h.	h.	NOUN
ejpam-4440	140	16	sumaoy	sumaoy	NOUN
ejpam-4440	140	17	,	,	PUNCT
ejpam-4440	140	18	h.	h.	PROPN
ejpam-4440	140	19	rara	rara	PROPN
ejpam-4440	140	20	/	/	SYM
ejpam-4440	140	21	eur	eur	PROPN
ejpam-4440	140	22	.	.	PUNCT
ejpam-4440	141	1	j.	j.	PROPN
ejpam-4440	141	2	pure	pure	PROPN
ejpam-4440	141	3	appl	appl	PROPN
ejpam-4440	141	4	.	.	PROPN
ejpam-4440	141	5	math	math	PROPN
ejpam-4440	141	6	,	,	PUNCT
ejpam-4440	141	7	15	15	NUM
ejpam-4440	141	8	(	(	PUNCT
ejpam-4440	141	9	3	3	NUM
ejpam-4440	141	10	)	)	PUNCT
ejpam-4440	141	11	(	(	PUNCT
ejpam-4440	141	12	2022	2022	NUM
ejpam-4440	141	13	)	)	PUNCT
ejpam-4440	141	14	,	,	PUNCT
ejpam-4440	141	15	1201	1201	NUM
ejpam-4440	141	16	-	-	SYM
ejpam-4440	141	17	1210	1210	NUM
ejpam-4440	141	18	1206	1206	NUM
ejpam-4440	141	19	where	where	SCONJ
ejpam-4440	141	20	c	c	NOUN
ejpam-4440	141	21	is	be	AUX
ejpam-4440	141	22	a	a	DET
ejpam-4440	141	23	superclique	superclique	NOUN
ejpam-4440	141	24	in	in	ADP
ejpam-4440	141	25	g.	g.	PROPN
ejpam-4440	141	26	since	since	SCONJ
ejpam-4440	141	27	s	s	PROPN
ejpam-4440	141	28	is	be	AUX
ejpam-4440	141	29	a	a	DET
ejpam-4440	141	30	dominating	dominating	NOUN
ejpam-4440	141	31	set	set	NOUN
ejpam-4440	141	32	,	,	PUNCT
ejpam-4440	141	33	c	c	PROPN
ejpam-4440	141	34	is	be	AUX
ejpam-4440	141	35	a	a	DET
ejpam-4440	141	36	dominated	dominate	VERB
ejpam-4440	141	37	superclique	superclique	NOUN
ejpam-4440	141	38	in	in	ADP
ejpam-4440	141	39	g	g	PROPN
ejpam-4440	141	40	and	and	CCONJ
ejpam-4440	141	41	c∗	c∗	PROPN
ejpam-4440	141	42	is	be	AUX
ejpam-4440	141	43	a	a	DET
ejpam-4440	141	44	superclique	superclique	NOUN
ejpam-4440	141	45	in	in	ADP
ejpam-4440	141	46	g.	g.	PROPN
ejpam-4440	141	47	by	by	ADP
ejpam-4440	141	48	lemma	lemma	PROPN
ejpam-4440	141	49	2	2	PROPN
ejpam-4440	141	50	and	and	CCONJ
ejpam-4440	141	51	lemma	lemma	PROPN
ejpam-4440	141	52	3	3	NUM
ejpam-4440	141	53	,	,	PUNCT
ejpam-4440	141	54	c	c	PROPN
ejpam-4440	141	55	is	be	AUX
ejpam-4440	141	56	a	a	DET
ejpam-4440	141	57	γ	γ	NOUN
ejpam-4440	141	58	-	-	PUNCT
ejpam-4440	141	59	set	set	NOUN
ejpam-4440	141	60	of	of	ADP
ejpam-4440	141	61	g.	g.	PROPN
ejpam-4440	141	62	hence	hence	ADV
ejpam-4440	141	63	,	,	PUNCT
ejpam-4440	141	64	s	s	NOUN
ejpam-4440	141	65	=	=	SYM
ejpam-4440	141	66	v	v	X
ejpam-4440	141	67	(	(	PUNCT
ejpam-4440	141	68	g	g	NOUN
ejpam-4440	141	69	)	)	PUNCT
ejpam-4440	141	70	or	or	CCONJ
ejpam-4440	141	71	s	s	X
ejpam-4440	141	72	=	=	SYM
ejpam-4440	141	73	v	v	PROPN
ejpam-4440	141	74	(	(	PUNCT
ejpam-4440	141	75	k1	k1	NOUN
ejpam-4440	141	76	+	+	PROPN
ejpam-4440	141	77	g	g	NOUN
ejpam-4440	141	78	)	)	PUNCT
ejpam-4440	141	79	\	\	PUNCT
ejpam-4440	142	1	c	c	NOUN
ejpam-4440	142	2	where	where	SCONJ
ejpam-4440	142	3	c	c	PROPN
ejpam-4440	142	4	is	be	AUX
ejpam-4440	142	5	a	a	DET
ejpam-4440	142	6	γ	γ	NOUN
ejpam-4440	142	7	-	-	PUNCT
ejpam-4440	142	8	set	set	NOUN
ejpam-4440	142	9	of	of	ADP
ejpam-4440	142	10	g.	g.	NOUN
ejpam-4440	142	11	conversely	conversely	ADV
ejpam-4440	142	12	,	,	PUNCT
ejpam-4440	142	13	suppose	suppose	VERB
ejpam-4440	142	14	s	s	VERB
ejpam-4440	142	15	=	=	SYM
ejpam-4440	142	16	v	v	PROPN
ejpam-4440	142	17	(	(	PUNCT
ejpam-4440	142	18	g	g	NOUN
ejpam-4440	142	19	)	)	PUNCT
ejpam-4440	142	20	or	or	CCONJ
ejpam-4440	142	21	s	s	X
ejpam-4440	142	22	=	=	SYM
ejpam-4440	142	23	v	v	PROPN
ejpam-4440	142	24	(	(	PUNCT
ejpam-4440	142	25	k1	k1	NOUN
ejpam-4440	142	26	+	+	PROPN
ejpam-4440	142	27	g	g	NOUN
ejpam-4440	142	28	)	)	PUNCT
ejpam-4440	142	29	\	\	PUNCT
ejpam-4440	143	1	c	c	NOUN
ejpam-4440	143	2	where	where	SCONJ
ejpam-4440	143	3	c	c	PROPN
ejpam-4440	143	4	is	be	AUX
ejpam-4440	143	5	a	a	DET
ejpam-4440	143	6	γ	γ	NOUN
ejpam-4440	143	7	-	-	PUNCT
ejpam-4440	143	8	set	set	NOUN
ejpam-4440	143	9	of	of	ADP
ejpam-4440	143	10	g.	g.	PROPN
ejpam-4440	143	11	then	then	ADV
ejpam-4440	143	12	,	,	PUNCT
ejpam-4440	143	13	by	by	ADP
ejpam-4440	143	14	theorem	theorem	NOUN
ejpam-4440	143	15	1	1	NUM
ejpam-4440	143	16	,	,	PUNCT
ejpam-4440	143	17	s	s	VERB
ejpam-4440	143	18	is	be	AUX
ejpam-4440	143	19	a	a	DET
ejpam-4440	143	20	strong	strong	ADJ
ejpam-4440	143	21	resolving	resolving	NOUN
ejpam-4440	143	22	dominating	dominating	NOUN
ejpam-4440	143	23	set	set	NOUN
ejpam-4440	143	24	of	of	ADP
ejpam-4440	143	25	k1+g	k1+g	NOUN
ejpam-4440	143	26	.	.	PUNCT
ejpam-4440	144	1	if	if	SCONJ
ejpam-4440	144	2	s	s	VERB
ejpam-4440	144	3	=	=	SYM
ejpam-4440	144	4	v	v	X
ejpam-4440	144	5	(	(	PUNCT
ejpam-4440	144	6	g	g	NOUN
ejpam-4440	144	7	)	)	PUNCT
ejpam-4440	144	8	,	,	PUNCT
ejpam-4440	144	9	then	then	ADV
ejpam-4440	144	10	s	s	VERB
ejpam-4440	144	11	\{x	\{x	X
ejpam-4440	144	12	}	}	PUNCT
ejpam-4440	144	13	is	be	AUX
ejpam-4440	144	14	a	a	DET
ejpam-4440	144	15	strong	strong	ADJ
ejpam-4440	144	16	resolving	resolving	NOUN
ejpam-4440	144	17	dominating	dominating	NOUN
ejpam-4440	144	18	set	set	NOUN
ejpam-4440	144	19	of	of	ADP
ejpam-4440	144	20	k1	k1	NOUN
ejpam-4440	144	21	+	+	CCONJ
ejpam-4440	144	22	g	g	NOUN
ejpam-4440	144	23	since	since	SCONJ
ejpam-4440	144	24	{	{	PUNCT
ejpam-4440	144	25	x	x	X
ejpam-4440	144	26	}	}	PUNCT
ejpam-4440	144	27	is	be	AUX
ejpam-4440	144	28	a	a	DET
ejpam-4440	144	29	dominated	dominate	VERB
ejpam-4440	144	30	superclique	superclique	NOUN
ejpam-4440	144	31	in	in	ADP
ejpam-4440	144	32	g	g	NOUN
ejpam-4440	144	33	by	by	ADP
ejpam-4440	144	34	lemma	lemma	PROPN
ejpam-4440	144	35	2	2	PROPN
ejpam-4440	144	36	and	and	CCONJ
ejpam-4440	144	37	lemma	lemma	PROPN
ejpam-4440	144	38	3	3	NUM
ejpam-4440	144	39	and	and	CCONJ
ejpam-4440	144	40	theorem	theorem	VERB
ejpam-4440	144	41	1	1	NUM
ejpam-4440	144	42	.	.	PUNCT
ejpam-4440	145	1	hence	hence	ADV
ejpam-4440	145	2	,	,	PUNCT
ejpam-4440	145	3	s	s	VERB
ejpam-4440	145	4	is	be	AUX
ejpam-4440	145	5	a	a	DET
ejpam-4440	145	6	movable	movable	ADJ
ejpam-4440	145	7	strong	strong	ADJ
ejpam-4440	145	8	resolving	resolve	VERB
ejpam-4440	145	9	dominating	dominating	NOUN
ejpam-4440	145	10	set	set	NOUN
ejpam-4440	145	11	of	of	ADP
ejpam-4440	145	12	k1	k1	PROPN
ejpam-4440	145	13	+	+	PROPN
ejpam-4440	145	14	g.	g.	NOUN
ejpam-4440	145	15	similarly	similarly	ADV
ejpam-4440	145	16	,	,	PUNCT
ejpam-4440	145	17	if	if	SCONJ
ejpam-4440	145	18	s	s	VERB
ejpam-4440	145	19	=	=	SYM
ejpam-4440	145	20	v	v	PROPN
ejpam-4440	145	21	(	(	PUNCT
ejpam-4440	145	22	k1	k1	NOUN
ejpam-4440	145	23	+	+	PROPN
ejpam-4440	145	24	g	g	NOUN
ejpam-4440	145	25	)	)	PUNCT
ejpam-4440	145	26	\c	\c	NOUN
ejpam-4440	145	27	where	where	SCONJ
ejpam-4440	145	28	c	c	NOUN
ejpam-4440	145	29	is	be	AUX
ejpam-4440	145	30	a	a	DET
ejpam-4440	145	31	γ	γ	NOUN
ejpam-4440	145	32	-	-	PUNCT
ejpam-4440	145	33	set	set	NOUN
ejpam-4440	145	34	of	of	ADP
ejpam-4440	145	35	g	g	NOUN
ejpam-4440	145	36	,	,	PUNCT
ejpam-4440	145	37	then	then	ADV
ejpam-4440	145	38	s	s	VERB
ejpam-4440	145	39	is	be	AUX
ejpam-4440	145	40	a	a	DET
ejpam-4440	145	41	movable	movable	ADJ
ejpam-4440	145	42	strong	strong	ADJ
ejpam-4440	145	43	resolving	resolving	NOUN
ejpam-4440	145	44	set	set	NOUN
ejpam-4440	145	45	of	of	ADP
ejpam-4440	145	46	k1+g	k1+g	NOUN
ejpam-4440	145	47	by	by	ADP
ejpam-4440	145	48	lemma	lemma	PROPN
ejpam-4440	145	49	2	2	NUM
ejpam-4440	145	50	,	,	PUNCT
ejpam-4440	145	51	lemma	lemma	PROPN
ejpam-4440	145	52	3	3	NUM
ejpam-4440	145	53	and	and	CCONJ
ejpam-4440	145	54	theorem	theorem	VERB
ejpam-4440	145	55	1	1	NUM
ejpam-4440	145	56	.	.	PUNCT
ejpam-4440	145	57	theorem	theorem	NOUN
ejpam-4440	145	58	6	6	NUM
ejpam-4440	145	59	.	.	PUNCT
ejpam-4440	146	1	let	let	VERB
ejpam-4440	146	2	g	g	PRON
ejpam-4440	146	3	be	be	AUX
ejpam-4440	146	4	a	a	DET
ejpam-4440	146	5	nontrivial	nontrivial	ADJ
ejpam-4440	146	6	connected	connect	VERB
ejpam-4440	146	7	graph	graph	NOUN
ejpam-4440	146	8	with	with	ADP
ejpam-4440	146	9	γ(g	γ(g	PROPN
ejpam-4440	146	10	)	)	PUNCT
ejpam-4440	146	11	̸=	̸=	PROPN
ejpam-4440	146	12	1	1	NUM
ejpam-4440	146	13	.	.	PUNCT
ejpam-4440	147	1	then	then	ADV
ejpam-4440	147	2	,	,	PUNCT
ejpam-4440	147	3	s	s	VERB
ejpam-4440	147	4	⊆	⊆	NUM
ejpam-4440	147	5	v	v	NOUN
ejpam-4440	147	6	(	(	PUNCT
ejpam-4440	147	7	k1+g	k1+g	NOUN
ejpam-4440	147	8	)	)	PUNCT
ejpam-4440	147	9	is	be	AUX
ejpam-4440	147	10	a	a	DET
ejpam-4440	147	11	movable	movable	ADJ
ejpam-4440	147	12	strong	strong	ADJ
ejpam-4440	147	13	resolving	resolve	VERB
ejpam-4440	147	14	dominating	dominating	NOUN
ejpam-4440	147	15	set	set	NOUN
ejpam-4440	147	16	of	of	ADP
ejpam-4440	147	17	k1	k1	NOUN
ejpam-4440	148	1	+	+	ADP
ejpam-4440	148	2	g	g	PROPN
ejpam-4440	148	3	if	if	SCONJ
ejpam-4440	148	4	and	and	CCONJ
ejpam-4440	148	5	only	only	ADV
ejpam-4440	148	6	if	if	SCONJ
ejpam-4440	148	7	s	s	VERB
ejpam-4440	148	8	=	=	SYM
ejpam-4440	148	9	v	v	X
ejpam-4440	148	10	(	(	PUNCT
ejpam-4440	148	11	g	g	NOUN
ejpam-4440	148	12	)	)	PUNCT
ejpam-4440	148	13	.	.	PUNCT
ejpam-4440	149	1	proof	proof	NOUN
ejpam-4440	149	2	.	.	PUNCT
ejpam-4440	150	1	suppose	suppose	VERB
ejpam-4440	150	2	s	s	NOUN
ejpam-4440	150	3	is	be	AUX
ejpam-4440	150	4	a	a	DET
ejpam-4440	150	5	movable	movable	ADJ
ejpam-4440	150	6	strong	strong	ADJ
ejpam-4440	150	7	resolving	resolve	VERB
ejpam-4440	150	8	dominating	dominate	VERB
ejpam-4440	150	9	set	set	NOUN
ejpam-4440	150	10	of	of	ADP
ejpam-4440	150	11	k1+g	k1+g	NOUN
ejpam-4440	150	12	.	.	PUNCT
ejpam-4440	151	1	by	by	ADP
ejpam-4440	151	2	theorem	theorem	NOUN
ejpam-4440	151	3	2	2	NUM
ejpam-4440	151	4	s	s	NOUN
ejpam-4440	151	5	=	=	X
ejpam-4440	151	6	v	v	X
ejpam-4440	151	7	(	(	PUNCT
ejpam-4440	151	8	g	g	NOUN
ejpam-4440	151	9	)	)	PUNCT
ejpam-4440	151	10	or	or	CCONJ
ejpam-4440	151	11	s	s	X
ejpam-4440	151	12	=	=	SYM
ejpam-4440	151	13	v	v	PROPN
ejpam-4440	151	14	(	(	PUNCT
ejpam-4440	151	15	g	g	NOUN
ejpam-4440	151	16	)	)	PUNCT
ejpam-4440	151	17	\c	\c	NOUN
ejpam-4440	151	18	,	,	PUNCT
ejpam-4440	151	19	or	or	CCONJ
ejpam-4440	151	20	s	s	X
ejpam-4440	151	21	=	=	SYM
ejpam-4440	151	22	v	v	PROPN
ejpam-4440	151	23	(	(	PUNCT
ejpam-4440	151	24	k1+g	k1+g	NOUN
ejpam-4440	151	25	)	)	PUNCT
ejpam-4440	151	26	\c	\c	NOUN
ejpam-4440	151	27	where	where	SCONJ
ejpam-4440	151	28	c	c	NOUN
ejpam-4440	151	29	is	be	AUX
ejpam-4440	151	30	a	a	DET
ejpam-4440	151	31	superclique	superclique	NOUN
ejpam-4440	151	32	in	in	ADP
ejpam-4440	151	33	g.	g.	PROPN
ejpam-4440	151	34	since	since	SCONJ
ejpam-4440	151	35	γ(h	γ(h	NOUN
ejpam-4440	151	36	)	)	PUNCT
ejpam-4440	151	37	̸=	̸=	PROPN
ejpam-4440	151	38	1	1	NUM
ejpam-4440	151	39	,	,	PUNCT
ejpam-4440	151	40	by	by	ADP
ejpam-4440	151	41	lemma	lemma	PROPN
ejpam-4440	151	42	2	2	NUM
ejpam-4440	151	43	,	,	PUNCT
ejpam-4440	151	44	lemma	lemma	PROPN
ejpam-4440	151	45	3	3	NUM
ejpam-4440	151	46	and	and	CCONJ
ejpam-4440	151	47	theorem	theorem	VERB
ejpam-4440	151	48	2	2	NUM
ejpam-4440	151	49	,	,	PUNCT
ejpam-4440	151	50	s	s	VERB
ejpam-4440	151	51	̸=	̸=	PROPN
ejpam-4440	151	52	v	v	NOUN
ejpam-4440	151	53	(	(	PUNCT
ejpam-4440	151	54	g	g	NOUN
ejpam-4440	151	55	)	)	PUNCT
ejpam-4440	151	56	\c	\c	NOUN
ejpam-4440	151	57	and	and	CCONJ
ejpam-4440	151	58	s	s	VERB
ejpam-4440	151	59	̸=	̸=	PROPN
ejpam-4440	151	60	v	v	NOUN
ejpam-4440	151	61	(	(	PUNCT
ejpam-4440	151	62	k1+g	k1+g	NOUN
ejpam-4440	151	63	)	)	PUNCT
ejpam-4440	151	64	\c	\c	NOUN
ejpam-4440	151	65	.	.	PUNCT
ejpam-4440	152	1	hence	hence	ADV
ejpam-4440	152	2	,	,	PUNCT
ejpam-4440	152	3	s	s	NOUN
ejpam-4440	152	4	=	=	SYM
ejpam-4440	152	5	v	v	X
ejpam-4440	152	6	(	(	PUNCT
ejpam-4440	152	7	g	g	NOUN
ejpam-4440	152	8	)	)	PUNCT
ejpam-4440	152	9	.	.	PUNCT
ejpam-4440	153	1	the	the	DET
ejpam-4440	153	2	converse	converse	NOUN
ejpam-4440	153	3	is	be	AUX
ejpam-4440	153	4	clear	clear	ADJ
ejpam-4440	153	5	.	.	PUNCT
ejpam-4440	154	1	corollary	corollary	ADJ
ejpam-4440	154	2	1	1	NUM
ejpam-4440	154	3	.	.	PUNCT
ejpam-4440	155	1	let	let	VERB
ejpam-4440	155	2	g	g	PRON
ejpam-4440	155	3	be	be	AUX
ejpam-4440	155	4	a	a	DET
ejpam-4440	155	5	nontrivial	nontrivial	ADJ
ejpam-4440	155	6	connected	connect	VERB
ejpam-4440	155	7	graph	graph	NOUN
ejpam-4440	155	8	of	of	ADP
ejpam-4440	155	9	order	order	NOUN
ejpam-4440	155	10	n.	n.	NOUN
ejpam-4440	155	11	then	then	ADV
ejpam-4440	155	12	γ1msr(k1+g	γ1msr(k1+g	NOUN
ejpam-4440	155	13	)	)	PUNCT
ejpam-4440	155	14	=	=	SYM
ejpam-4440	155	15	n.	n.	NOUN
ejpam-4440	155	16	proof	proof	NOUN
ejpam-4440	155	17	.	.	PUNCT
ejpam-4440	156	1	let	let	VERB
ejpam-4440	156	2	s	s	PRON
ejpam-4440	156	3	be	be	AUX
ejpam-4440	156	4	a	a	DET
ejpam-4440	156	5	γ1msr	γ1msr	NOUN
ejpam-4440	156	6	-	-	PUNCT
ejpam-4440	156	7	set	set	VERB
ejpam-4440	156	8	ofk1+g	ofk1+g	NOUN
ejpam-4440	156	9	.	.	PUNCT
ejpam-4440	157	1	if	if	SCONJ
ejpam-4440	157	2	γ(g	γ(g	PROPN
ejpam-4440	157	3	)	)	PUNCT
ejpam-4440	157	4	=	=	SYM
ejpam-4440	157	5	1	1	NUM
ejpam-4440	157	6	,	,	PUNCT
ejpam-4440	157	7	then	then	ADV
ejpam-4440	157	8	s	s	VERB
ejpam-4440	157	9	=	=	SYM
ejpam-4440	157	10	v	v	PROPN
ejpam-4440	157	11	(	(	PUNCT
ejpam-4440	157	12	g	g	NOUN
ejpam-4440	157	13	)	)	PUNCT
ejpam-4440	157	14	or	or	CCONJ
ejpam-4440	157	15	s	s	X
ejpam-4440	157	16	=	=	SYM
ejpam-4440	157	17	v	v	PROPN
ejpam-4440	157	18	(	(	PUNCT
ejpam-4440	157	19	k1+g)\c	k1+g)\c	NOUN
ejpam-4440	157	20	where	where	SCONJ
ejpam-4440	157	21	c	c	PROPN
ejpam-4440	157	22	is	be	AUX
ejpam-4440	157	23	a	a	DET
ejpam-4440	157	24	γ	γ	NOUN
ejpam-4440	157	25	-	-	PUNCT
ejpam-4440	157	26	set	set	NOUN
ejpam-4440	157	27	of	of	ADP
ejpam-4440	157	28	g.	g.	PROPN
ejpam-4440	157	29	hence	hence	ADV
ejpam-4440	157	30	,	,	PUNCT
ejpam-4440	157	31	γ1msr(k1	γ1msr(k1	PROPN
ejpam-4440	158	1	+	+	NOUN
ejpam-4440	158	2	g	g	NOUN
ejpam-4440	158	3	)	)	PUNCT
ejpam-4440	158	4	=	=	SYM
ejpam-4440	158	5	|s|	|s|	PROPN
ejpam-4440	158	6	=	=	PUNCT
ejpam-4440	158	7	|v	|v	PROPN
ejpam-4440	158	8	(	(	PUNCT
ejpam-4440	158	9	g)|	g)|	PROPN
ejpam-4440	158	10	=	=	PUNCT
ejpam-4440	158	11	|v	|v	PROPN
ejpam-4440	158	12	(	(	PUNCT
ejpam-4440	158	13	k1	k1	NOUN
ejpam-4440	158	14	+	+	PROPN
ejpam-4440	158	15	g)|	g)|	NOUN
ejpam-4440	158	16	−	−	PROPN
ejpam-4440	158	17	|c|	|c|	PROPN
ejpam-4440	158	18	=	=	SYM
ejpam-4440	158	19	n+	n+	X
ejpam-4440	159	1	1−	1−	NUM
ejpam-4440	159	2	1	1	NUM
ejpam-4440	159	3	=	=	SYM
ejpam-4440	159	4	n.	n.	NOUN
ejpam-4440	159	5	on	on	ADP
ejpam-4440	159	6	the	the	DET
ejpam-4440	159	7	other	other	ADJ
ejpam-4440	159	8	hand	hand	NOUN
ejpam-4440	159	9	,	,	PUNCT
ejpam-4440	159	10	if	if	SCONJ
ejpam-4440	159	11	γ(g	γ(g	NOUN
ejpam-4440	159	12	)	)	PUNCT
ejpam-4440	159	13	̸=	̸=	PROPN
ejpam-4440	159	14	1	1	NUM
ejpam-4440	159	15	,	,	PUNCT
ejpam-4440	159	16	then	then	ADV
ejpam-4440	159	17	s	s	VERB
ejpam-4440	159	18	=	=	SYM
ejpam-4440	159	19	v	v	PROPN
ejpam-4440	159	20	(	(	PUNCT
ejpam-4440	159	21	g	g	NOUN
ejpam-4440	159	22	)	)	PUNCT
ejpam-4440	159	23	.	.	PUNCT
ejpam-4440	160	1	thus	thus	ADV
ejpam-4440	160	2	,	,	PUNCT
ejpam-4440	160	3	γmsr(k1	γmsr(k1	PROPN
ejpam-4440	160	4	+	+	NOUN
ejpam-4440	160	5	g	g	NOUN
ejpam-4440	160	6	)	)	PUNCT
ejpam-4440	160	7	=	=	SYM
ejpam-4440	160	8	|s|	|s|	PROPN
ejpam-4440	160	9	=	=	PUNCT
ejpam-4440	160	10	|v	|v	PROPN
ejpam-4440	160	11	(	(	PUNCT
ejpam-4440	160	12	g)|	g)|	NOUN
ejpam-4440	160	13	=	=	PUNCT
ejpam-4440	160	14	n.	n.	NOUN
ejpam-4440	160	15	theorem	theorem	VERB
ejpam-4440	160	16	7	7	NUM
ejpam-4440	160	17	.	.	PUNCT
ejpam-4440	160	18	let	let	VERB
ejpam-4440	160	19	k1	k1	NOUN
ejpam-4440	160	20	=	=	PROPN
ejpam-4440	160	21	⟨v⟩	⟨v⟩	PROPN
ejpam-4440	160	22	and	and	CCONJ
ejpam-4440	160	23	g	g	PROPN
ejpam-4440	160	24	be	be	AUX
ejpam-4440	160	25	a	a	DET
ejpam-4440	160	26	disconnected	disconnected	ADJ
ejpam-4440	160	27	graph	graph	NOUN
ejpam-4440	160	28	whose	whose	DET
ejpam-4440	160	29	components	component	NOUN
ejpam-4440	160	30	are	be	AUX
ejpam-4440	160	31	gi	gi	ADJ
ejpam-4440	160	32	for	for	ADP
ejpam-4440	160	33	i	i	PROPN
ejpam-4440	160	34	=	=	NOUN
ejpam-4440	160	35	1	1	NUM
ejpam-4440	160	36	,	,	PUNCT
ejpam-4440	160	37	2	2	NUM
ejpam-4440	160	38	,	,	PUNCT
ejpam-4440	160	39	.	.	PUNCT
ejpam-4440	160	40	.	.	PUNCT
ejpam-4440	161	1	.	.	PUNCT
ejpam-4440	162	1	,	,	PUNCT
ejpam-4440	162	2	m.	m.	NOUN
ejpam-4440	162	3	a	a	DET
ejpam-4440	162	4	proper	proper	ADJ
ejpam-4440	162	5	subset	subset	NOUN
ejpam-4440	162	6	s	s	NOUN
ejpam-4440	162	7	of	of	ADP
ejpam-4440	162	8	v	v	NOUN
ejpam-4440	162	9	(	(	PUNCT
ejpam-4440	162	10	k1+g	k1+g	NOUN
ejpam-4440	162	11	)	)	PUNCT
ejpam-4440	162	12	is	be	AUX
ejpam-4440	162	13	a	a	DET
ejpam-4440	162	14	movable	movable	ADJ
ejpam-4440	162	15	strong	strong	ADJ
ejpam-4440	162	16	resolving	resolve	VERB
ejpam-4440	162	17	dominating	dominating	NOUN
ejpam-4440	162	18	set	set	NOUN
ejpam-4440	162	19	of	of	ADP
ejpam-4440	162	20	k1	k1	NOUN
ejpam-4440	162	21	+	+	CCONJ
ejpam-4440	162	22	g	g	NOUN
ejpam-4440	162	23	if	if	SCONJ
ejpam-4440	163	1	and	and	CCONJ
ejpam-4440	163	2	only	only	ADV
ejpam-4440	163	3	if	if	SCONJ
ejpam-4440	163	4	s	s	VERB
ejpam-4440	163	5	=	=	SYM
ejpam-4440	163	6	v	v	X
ejpam-4440	163	7	(	(	PUNCT
ejpam-4440	163	8	g	g	NOUN
ejpam-4440	163	9	)	)	PUNCT
ejpam-4440	163	10	or	or	CCONJ
ejpam-4440	163	11	s	s	X
ejpam-4440	163	12	=	=	SYM
ejpam-4440	163	13	v	v	PROPN
ejpam-4440	163	14	(	(	PUNCT
ejpam-4440	163	15	k1	k1	NOUN
ejpam-4440	163	16	+	+	CCONJ
ejpam-4440	163	17	g	g	NOUN
ejpam-4440	163	18	)	)	PUNCT
ejpam-4440	163	19	\	\	PROPN
ejpam-4440	163	20	ci	ci	PROPN
ejpam-4440	163	21	where	where	SCONJ
ejpam-4440	163	22	ci	ci	PROPN
ejpam-4440	163	23	is	be	AUX
ejpam-4440	163	24	γ	γ	NOUN
ejpam-4440	163	25	-	-	PUNCT
ejpam-4440	163	26	set	set	NOUN
ejpam-4440	163	27	of	of	ADP
ejpam-4440	163	28	gi	gi	NOUN
ejpam-4440	163	29	if	if	SCONJ
ejpam-4440	163	30	γ(gi	γ(gi	PROPN
ejpam-4440	163	31	)	)	PUNCT
ejpam-4440	163	32	=	=	SYM
ejpam-4440	163	33	1	1	NUM
ejpam-4440	163	34	for	for	ADP
ejpam-4440	163	35	all	all	PRON
ejpam-4440	163	36	i	i	PRON
ejpam-4440	163	37	∈	∈	PROPN
ejpam-4440	163	38	{	{	PUNCT
ejpam-4440	163	39	1	1	NUM
ejpam-4440	163	40	,	,	PUNCT
ejpam-4440	163	41	2	2	NUM
ejpam-4440	163	42	,	,	PUNCT
ejpam-4440	163	43	.	.	PUNCT
ejpam-4440	163	44	.	.	PUNCT
ejpam-4440	163	45	.	.	PUNCT
ejpam-4440	164	1	,	,	PUNCT
ejpam-4440	164	2	m	m	VERB
ejpam-4440	164	3	}	}	PUNCT
ejpam-4440	164	4	.	.	PUNCT
ejpam-4440	165	1	proof	proof	NOUN
ejpam-4440	165	2	.	.	PUNCT
ejpam-4440	166	1	suppose	suppose	VERB
ejpam-4440	166	2	s	s	NOUN
ejpam-4440	166	3	is	be	AUX
ejpam-4440	166	4	a	a	DET
ejpam-4440	166	5	movable	movable	ADJ
ejpam-4440	166	6	strong	strong	ADJ
ejpam-4440	166	7	resolving	resolve	VERB
ejpam-4440	166	8	dominating	dominating	NOUN
ejpam-4440	166	9	set	set	NOUN
ejpam-4440	166	10	of	of	ADP
ejpam-4440	166	11	k1	k1	PROPN
ejpam-4440	166	12	+	+	CCONJ
ejpam-4440	166	13	g.	g.	PROPN
ejpam-4440	166	14	then	then	ADV
ejpam-4440	166	15	,	,	PUNCT
ejpam-4440	166	16	by	by	ADP
ejpam-4440	166	17	theorem	theorem	NOUN
ejpam-4440	166	18	3	3	NUM
ejpam-4440	166	19	,	,	PUNCT
ejpam-4440	166	20	s	s	PART
ejpam-4440	166	21	=	=	SYM
ejpam-4440	166	22	v	v	X
ejpam-4440	166	23	(	(	PUNCT
ejpam-4440	166	24	g	g	NOUN
ejpam-4440	166	25	)	)	PUNCT
ejpam-4440	166	26	or	or	CCONJ
ejpam-4440	166	27	s	s	X
ejpam-4440	166	28	=	=	SYM
ejpam-4440	166	29	v	v	PROPN
ejpam-4440	166	30	(	(	PUNCT
ejpam-4440	166	31	g	g	NOUN
ejpam-4440	166	32	)	)	PUNCT
ejpam-4440	166	33	\ci	\ci	PROPN
ejpam-4440	166	34	or	or	CCONJ
ejpam-4440	166	35	s	s	NOUN
ejpam-4440	166	36	=	=	SYM
ejpam-4440	166	37	v	v	PROPN
ejpam-4440	166	38	(	(	PUNCT
ejpam-4440	166	39	k1	k1	NOUN
ejpam-4440	166	40	+	+	PROPN
ejpam-4440	166	41	g	g	NOUN
ejpam-4440	166	42	)	)	PUNCT
ejpam-4440	166	43	\ci	\ci	PROPN
ejpam-4440	166	44	where	where	SCONJ
ejpam-4440	166	45	ci	ci	PROPN
ejpam-4440	166	46	is	be	AUX
ejpam-4440	166	47	a	a	DET
ejpam-4440	166	48	superclique	superclique	NOUN
ejpam-4440	166	49	in	in	ADP
ejpam-4440	166	50	gi	gi	NOUN
ejpam-4440	166	51	for	for	ADP
ejpam-4440	166	52	some	some	DET
ejpam-4440	166	53	i	i	PRON
ejpam-4440	166	54	∈	∈	PROPN
ejpam-4440	166	55	{	{	PUNCT
ejpam-4440	166	56	1	1	NUM
ejpam-4440	166	57	,	,	PUNCT
ejpam-4440	166	58	2	2	NUM
ejpam-4440	166	59	,	,	PUNCT
ejpam-4440	166	60	.	.	PUNCT
ejpam-4440	166	61	.	.	PUNCT
ejpam-4440	167	1	.	.	PUNCT
ejpam-4440	168	1	,	,	PUNCT
ejpam-4440	168	2	m	m	VERB
ejpam-4440	168	3	}	}	PUNCT
ejpam-4440	168	4	.	.	PUNCT
ejpam-4440	169	1	if	if	SCONJ
ejpam-4440	169	2	γ(gi	γ(gi	PROPN
ejpam-4440	169	3	)	)	PUNCT
ejpam-4440	170	1	=	=	SYM
ejpam-4440	170	2	1	1	NUM
ejpam-4440	170	3	,	,	PUNCT
ejpam-4440	170	4	then	then	ADV
ejpam-4440	170	5	by	by	ADP
ejpam-4440	170	6	lemma	lemma	PROPN
ejpam-4440	170	7	2	2	NUM
ejpam-4440	170	8	,	,	PUNCT
ejpam-4440	170	9	lemma	lemma	PROPN
ejpam-4440	170	10	3	3	NUM
ejpam-4440	170	11	and	and	CCONJ
ejpam-4440	170	12	theorem	theorem	VERB
ejpam-4440	170	13	5	5	NUM
ejpam-4440	170	14	,	,	PUNCT
ejpam-4440	170	15	ci	ci	PROPN
ejpam-4440	170	16	is	be	AUX
ejpam-4440	170	17	a	a	DET
ejpam-4440	170	18	γ	γ	NOUN
ejpam-4440	170	19	-	-	PUNCT
ejpam-4440	170	20	set	set	NOUN
ejpam-4440	170	21	of	of	ADP
ejpam-4440	170	22	gi	gi	NOUN
ejpam-4440	170	23	.	.	PUNCT
ejpam-4440	171	1	thus	thus	ADV
ejpam-4440	171	2	,	,	PUNCT
ejpam-4440	171	3	s	s	VERB
ejpam-4440	171	4	̸=	̸=	PROPN
ejpam-4440	171	5	v	v	NOUN
ejpam-4440	171	6	(	(	PUNCT
ejpam-4440	171	7	g)\ci	g)\ci	AUX
ejpam-4440	171	8	showing	show	VERB
ejpam-4440	171	9	that	that	PRON
ejpam-4440	171	10	s	s	VERB
ejpam-4440	171	11	=	=	SYM
ejpam-4440	171	12	v	v	ADJ
ejpam-4440	171	13	(	(	PUNCT
ejpam-4440	171	14	g	g	NOUN
ejpam-4440	171	15	)	)	PUNCT
ejpam-4440	171	16	or	or	CCONJ
ejpam-4440	171	17	s	s	X
ejpam-4440	171	18	=	=	SYM
ejpam-4440	171	19	v	v	PROPN
ejpam-4440	171	20	(	(	PUNCT
ejpam-4440	171	21	k1+g)\ci	k1+g)\ci	PROPN
ejpam-4440	171	22	where	where	SCONJ
ejpam-4440	171	23	ci	ci	PROPN
ejpam-4440	171	24	is	be	AUX
ejpam-4440	171	25	a	a	DET
ejpam-4440	171	26	γ	γ	NOUN
ejpam-4440	171	27	-	-	PUNCT
ejpam-4440	171	28	set	set	NOUN
ejpam-4440	171	29	of	of	ADP
ejpam-4440	171	30	gi	gi	NOUN
ejpam-4440	171	31	for	for	ADP
ejpam-4440	171	32	some	some	DET
ejpam-4440	171	33	i	i	PRON
ejpam-4440	171	34	∈	∈	PROPN
ejpam-4440	171	35	{	{	PUNCT
ejpam-4440	171	36	1	1	NUM
ejpam-4440	171	37	,	,	PUNCT
ejpam-4440	171	38	2	2	NUM
ejpam-4440	171	39	,	,	PUNCT
ejpam-4440	171	40	.	.	PUNCT
ejpam-4440	171	41	.	.	PUNCT
ejpam-4440	171	42	.	.	PUNCT
ejpam-4440	172	1	,	,	PUNCT
ejpam-4440	172	2	m	m	VERB
ejpam-4440	172	3	}	}	PUNCT
ejpam-4440	172	4	.	.	PUNCT
ejpam-4440	173	1	if	if	SCONJ
ejpam-4440	173	2	γ(gi	γ(gi	PROPN
ejpam-4440	173	3	)	)	PUNCT
ejpam-4440	173	4	̸=	̸=	PROPN
ejpam-4440	173	5	1	1	NUM
ejpam-4440	173	6	for	for	ADP
ejpam-4440	173	7	all	all	PRON
ejpam-4440	173	8	i	i	PRON
ejpam-4440	173	9	∈	∈	PROPN
ejpam-4440	173	10	{	{	PUNCT
ejpam-4440	173	11	1.2	1.2	NUM
ejpam-4440	173	12	.	.	PUNCT
ejpam-4440	173	13	.	.	PUNCT
ejpam-4440	174	1	.	.	PUNCT
ejpam-4440	174	2	.	.	PUNCT
ejpam-4440	175	1	,	,	PUNCT
ejpam-4440	175	2	m	m	PROPN
ejpam-4440	175	3	}	}	PUNCT
ejpam-4440	175	4	,	,	PUNCT
ejpam-4440	175	5	then	then	ADV
ejpam-4440	175	6	s	s	VERB
ejpam-4440	175	7	=	=	SYM
ejpam-4440	175	8	v	v	PROPN
ejpam-4440	175	9	(	(	PUNCT
ejpam-4440	175	10	g	g	NOUN
ejpam-4440	175	11	)	)	PUNCT
ejpam-4440	175	12	by	by	ADP
ejpam-4440	175	13	lemma	lemma	PROPN
ejpam-4440	175	14	2	2	NUM
ejpam-4440	175	15	,	,	PUNCT
ejpam-4440	175	16	lemma	lemma	PROPN
ejpam-4440	175	17	3	3	NUM
ejpam-4440	175	18	,	,	PUNCT
ejpam-4440	175	19	and	and	CCONJ
ejpam-4440	175	20	theorem	theorem	VERB
ejpam-4440	175	21	6	6	NUM
ejpam-4440	175	22	.	.	PUNCT
ejpam-4440	175	23	h.	h.	NOUN
ejpam-4440	175	24	sumaoy	sumaoy	NOUN
ejpam-4440	175	25	,	,	PUNCT
ejpam-4440	175	26	h.	h.	PROPN
ejpam-4440	175	27	rara	rara	PROPN
ejpam-4440	175	28	/	/	SYM
ejpam-4440	175	29	eur	eur	PROPN
ejpam-4440	175	30	.	.	PUNCT
ejpam-4440	176	1	j.	j.	PROPN
ejpam-4440	176	2	pure	pure	PROPN
ejpam-4440	176	3	appl	appl	PROPN
ejpam-4440	176	4	.	.	PROPN
ejpam-4440	176	5	math	math	PROPN
ejpam-4440	176	6	,	,	PUNCT
ejpam-4440	176	7	15	15	NUM
ejpam-4440	176	8	(	(	PUNCT
ejpam-4440	176	9	3	3	NUM
ejpam-4440	176	10	)	)	PUNCT
ejpam-4440	176	11	(	(	PUNCT
ejpam-4440	176	12	2022	2022	NUM
ejpam-4440	176	13	)	)	PUNCT
ejpam-4440	176	14	,	,	PUNCT
ejpam-4440	176	15	1201	1201	NUM
ejpam-4440	176	16	-	-	SYM
ejpam-4440	176	17	1210	1210	NUM
ejpam-4440	176	18	1207	1207	NUM
ejpam-4440	176	19	conversely	conversely	ADV
ejpam-4440	176	20	,	,	PUNCT
ejpam-4440	176	21	the	the	DET
ejpam-4440	176	22	case	case	NOUN
ejpam-4440	176	23	when	when	SCONJ
ejpam-4440	176	24	s	s	VERB
ejpam-4440	176	25	=	=	SYM
ejpam-4440	176	26	v	v	X
ejpam-4440	176	27	(	(	PUNCT
ejpam-4440	176	28	g	g	NOUN
ejpam-4440	176	29	is	be	AUX
ejpam-4440	176	30	trivial	trivial	ADJ
ejpam-4440	176	31	.	.	PUNCT
ejpam-4440	177	1	suppose	suppose	VERB
ejpam-4440	177	2	s	s	VERB
ejpam-4440	177	3	=	=	SYM
ejpam-4440	177	4	v	v	PROPN
ejpam-4440	177	5	(	(	PUNCT
ejpam-4440	177	6	k1	k1	NOUN
ejpam-4440	177	7	+	+	PROPN
ejpam-4440	177	8	g	g	NOUN
ejpam-4440	177	9	)	)	PUNCT
ejpam-4440	177	10	\ci	\ci	PROPN
ejpam-4440	177	11	where	where	SCONJ
ejpam-4440	177	12	ci	ci	PROPN
ejpam-4440	177	13	is	be	AUX
ejpam-4440	177	14	a	a	DET
ejpam-4440	177	15	γ	γ	NOUN
ejpam-4440	177	16	-	-	PUNCT
ejpam-4440	177	17	set	set	NOUN
ejpam-4440	177	18	of	of	ADP
ejpam-4440	177	19	gi	gi	NOUN
ejpam-4440	177	20	if	if	SCONJ
ejpam-4440	177	21	γ(gi	γ(gi	PROPN
ejpam-4440	177	22	)	)	PUNCT
ejpam-4440	177	23	=	=	SYM
ejpam-4440	177	24	1	1	NUM
ejpam-4440	177	25	for	for	ADP
ejpam-4440	177	26	some	some	DET
ejpam-4440	177	27	i	i	PRON
ejpam-4440	177	28	∈	∈	PROPN
ejpam-4440	177	29	{	{	PUNCT
ejpam-4440	177	30	1	1	NUM
ejpam-4440	177	31	,	,	PUNCT
ejpam-4440	177	32	2	2	NUM
ejpam-4440	177	33	,	,	PUNCT
ejpam-4440	177	34	.	.	PUNCT
ejpam-4440	177	35	.	.	PUNCT
ejpam-4440	178	1	.	.	PUNCT
ejpam-4440	179	1	,	,	PUNCT
ejpam-4440	179	2	m	m	VERB
ejpam-4440	179	3	}	}	PUNCT
ejpam-4440	179	4	.	.	PUNCT
ejpam-4440	180	1	then	then	ADV
ejpam-4440	180	2	by	by	ADP
ejpam-4440	180	3	theorem	theorem	NOUN
ejpam-4440	180	4	3	3	NUM
ejpam-4440	180	5	,	,	PUNCT
ejpam-4440	180	6	s	s	VERB
ejpam-4440	180	7	is	be	AUX
ejpam-4440	180	8	a	a	DET
ejpam-4440	180	9	strong	strong	ADJ
ejpam-4440	180	10	resolving	resolving	NOUN
ejpam-4440	180	11	dominating	dominating	NOUN
ejpam-4440	180	12	set	set	NOUN
ejpam-4440	180	13	of	of	ADP
ejpam-4440	180	14	k1	k1	PROPN
ejpam-4440	180	15	+	+	CCONJ
ejpam-4440	180	16	g.	g.	PROPN
ejpam-4440	180	17	by	by	ADP
ejpam-4440	180	18	lemma	lemma	PROPN
ejpam-4440	180	19	2	2	NUM
ejpam-4440	180	20	,	,	PUNCT
ejpam-4440	180	21	lemma	lemma	PROPN
ejpam-4440	180	22	3	3	NUM
ejpam-4440	180	23	and	and	CCONJ
ejpam-4440	180	24	theorem	theorem	VERB
ejpam-4440	180	25	5	5	NUM
ejpam-4440	180	26	,	,	PUNCT
ejpam-4440	180	27	s	s	VERB
ejpam-4440	180	28	is	be	AUX
ejpam-4440	180	29	a	a	DET
ejpam-4440	180	30	movable	movable	ADJ
ejpam-4440	180	31	strong	strong	ADJ
ejpam-4440	180	32	resolving	resolving	NOUN
ejpam-4440	180	33	set	set	NOUN
ejpam-4440	180	34	of	of	ADP
ejpam-4440	180	35	k1	k1	PROPN
ejpam-4440	180	36	+	+	PROPN
ejpam-4440	180	37	g.	g.	PROPN
ejpam-4440	180	38	corollary	corollary	NOUN
ejpam-4440	180	39	2	2	PROPN
ejpam-4440	180	40	.	.	PUNCT
ejpam-4440	181	1	let	let	VERB
ejpam-4440	181	2	gi	gi	PART
ejpam-4440	181	3	be	be	AUX
ejpam-4440	181	4	connected	connect	VERB
ejpam-4440	181	5	graphs	graph	NOUN
ejpam-4440	181	6	of	of	ADP
ejpam-4440	181	7	order	order	NOUN
ejpam-4440	181	8	ni	ni	PROPN
ejpam-4440	181	9	and	and	CCONJ
ejpam-4440	181	10	g	g	PROPN
ejpam-4440	181	11	be	be	VERB
ejpam-4440	181	12	a	a	DET
ejpam-4440	181	13	disconnected	disconnected	ADJ
ejpam-4440	181	14	graph	graph	NOUN
ejpam-4440	181	15	whose	whose	DET
ejpam-4440	181	16	components	component	NOUN
ejpam-4440	181	17	are	be	AUX
ejpam-4440	181	18	gi	gi	ADJ
ejpam-4440	181	19	for	for	ADP
ejpam-4440	181	20	i	i	PRON
ejpam-4440	181	21	∈	∈	PROPN
ejpam-4440	181	22	{	{	PUNCT
ejpam-4440	181	23	1	1	NUM
ejpam-4440	181	24	,	,	PUNCT
ejpam-4440	181	25	2	2	NUM
ejpam-4440	181	26	,	,	PUNCT
ejpam-4440	181	27	.	.	PUNCT
ejpam-4440	181	28	.	.	PUNCT
ejpam-4440	182	1	.	.	PUNCT
ejpam-4440	183	1	,	,	PUNCT
ejpam-4440	183	2	m	m	VERB
ejpam-4440	183	3	}	}	PUNCT
ejpam-4440	183	4	.	.	PUNCT
ejpam-4440	184	1	then	then	ADV
ejpam-4440	184	2	,	,	PUNCT
ejpam-4440	184	3	γ1msr(k1	γ1msr(k1	PROPN
ejpam-4440	185	1	+	+	NOUN
ejpam-4440	185	2	g	g	NOUN
ejpam-4440	185	3	)	)	PUNCT
ejpam-4440	185	4	=	=	SYM
ejpam-4440	185	5	|v	|v	PROPN
ejpam-4440	185	6	(	(	PUNCT
ejpam-4440	185	7	g)|	g)|	PROPN
ejpam-4440	185	8	.	.	PUNCT
ejpam-4440	185	9	theorem	theorem	NOUN
ejpam-4440	185	10	8	8	NUM
ejpam-4440	185	11	.	.	PUNCT
ejpam-4440	186	1	let	let	VERB
ejpam-4440	186	2	g	g	NOUN
ejpam-4440	186	3	and	and	CCONJ
ejpam-4440	186	4	h	h	NOUN
ejpam-4440	186	5	be	be	AUX
ejpam-4440	186	6	nontrivial	nontrivial	ADJ
ejpam-4440	186	7	connected	connect	VERB
ejpam-4440	186	8	graphs	graph	NOUN
ejpam-4440	186	9	of	of	ADP
ejpam-4440	186	10	orders	order	NOUN
ejpam-4440	186	11	m	m	VERB
ejpam-4440	186	12	and	and	CCONJ
ejpam-4440	186	13	n	n	CCONJ
ejpam-4440	186	14	,	,	PUNCT
ejpam-4440	186	15	respectively	respectively	ADV
ejpam-4440	186	16	.	.	PUNCT
ejpam-4440	187	1	a	a	DET
ejpam-4440	187	2	proper	proper	ADJ
ejpam-4440	187	3	subset	subset	NOUN
ejpam-4440	187	4	s	s	NOUN
ejpam-4440	187	5	of	of	ADP
ejpam-4440	187	6	v	v	NOUN
ejpam-4440	187	7	(	(	PUNCT
ejpam-4440	187	8	g	g	PROPN
ejpam-4440	187	9	+	+	NOUN
ejpam-4440	187	10	h	h	NOUN
ejpam-4440	187	11	)	)	PUNCT
ejpam-4440	187	12	is	be	AUX
ejpam-4440	187	13	a	a	DET
ejpam-4440	187	14	movable	movable	ADJ
ejpam-4440	187	15	strong	strong	ADJ
ejpam-4440	187	16	resolving	resolving	NOUN
ejpam-4440	187	17	dominatiing	dominatie	VERB
ejpam-4440	187	18	set	set	NOUN
ejpam-4440	187	19	of	of	ADP
ejpam-4440	187	20	g	g	PROPN
ejpam-4440	187	21	+	+	PROPN
ejpam-4440	187	22	h	h	NOUN
ejpam-4440	187	23	if	if	SCONJ
ejpam-4440	188	1	and	and	CCONJ
ejpam-4440	188	2	only	only	ADV
ejpam-4440	188	3	if	if	SCONJ
ejpam-4440	188	4	at	at	ADV
ejpam-4440	188	5	least	least	ADJ
ejpam-4440	188	6	one	one	NUM
ejpam-4440	188	7	of	of	ADP
ejpam-4440	188	8	the	the	DET
ejpam-4440	188	9	following	following	NOUN
ejpam-4440	188	10	is	be	AUX
ejpam-4440	188	11	satisfied	satisfied	ADJ
ejpam-4440	188	12	.	.	PUNCT
ejpam-4440	189	1	(	(	PUNCT
ejpam-4440	189	2	i	i	NOUN
ejpam-4440	189	3	)	)	PUNCT
ejpam-4440	189	4	s	s	PART
ejpam-4440	189	5	=	=	SYM
ejpam-4440	189	6	v	v	PROPN
ejpam-4440	189	7	(	(	PUNCT
ejpam-4440	189	8	g+h	g+h	NOUN
ejpam-4440	189	9	)	)	PUNCT
ejpam-4440	189	10	\	\	PROPN
ejpam-4440	190	1	cg	cg	NOUN
ejpam-4440	190	2	where	where	SCONJ
ejpam-4440	190	3	cg	cg	NOUN
ejpam-4440	190	4	is	be	AUX
ejpam-4440	190	5	a	a	DET
ejpam-4440	190	6	γ	γ	NOUN
ejpam-4440	190	7	-	-	PUNCT
ejpam-4440	190	8	set	set	NOUN
ejpam-4440	190	9	of	of	ADP
ejpam-4440	190	10	g	g	PROPN
ejpam-4440	190	11	if	if	SCONJ
ejpam-4440	190	12	γ(g	γ(g	PROPN
ejpam-4440	190	13	)	)	PUNCT
ejpam-4440	190	14	=	=	SYM
ejpam-4440	190	15	1	1	X
ejpam-4440	190	16	.	.	PUNCT
ejpam-4440	190	17	(	(	PUNCT
ejpam-4440	190	18	ii	ii	NOUN
ejpam-4440	190	19	)	)	PUNCT
ejpam-4440	190	20	s	s	PART
ejpam-4440	190	21	=	=	SYM
ejpam-4440	190	22	v	v	PROPN
ejpam-4440	190	23	(	(	PUNCT
ejpam-4440	190	24	g+h	g+h	NOUN
ejpam-4440	190	25	)	)	PUNCT
ejpam-4440	190	26	\	\	PROPN
ejpam-4440	190	27	ch	ch	NOUN
ejpam-4440	190	28	where	where	SCONJ
ejpam-4440	190	29	ch	ch	NOUN
ejpam-4440	190	30	is	be	AUX
ejpam-4440	190	31	a	a	DET
ejpam-4440	190	32	γ	γ	NOUN
ejpam-4440	190	33	-	-	PUNCT
ejpam-4440	190	34	set	set	NOUN
ejpam-4440	190	35	of	of	ADP
ejpam-4440	190	36	h	h	NOUN
ejpam-4440	190	37	if	if	SCONJ
ejpam-4440	190	38	γ(h	γ(h	NOUN
ejpam-4440	190	39	)	)	PUNCT
ejpam-4440	190	40	=	=	SYM
ejpam-4440	191	1	1	1	X
ejpam-4440	191	2	.	.	PUNCT
ejpam-4440	191	3	proof	proof	NOUN
ejpam-4440	191	4	.	.	PUNCT
ejpam-4440	192	1	suppose	suppose	VERB
ejpam-4440	192	2	s	s	NOUN
ejpam-4440	192	3	is	be	AUX
ejpam-4440	192	4	a	a	DET
ejpam-4440	192	5	movable	movable	ADJ
ejpam-4440	192	6	strong	strong	ADJ
ejpam-4440	192	7	resolving	resolve	VERB
ejpam-4440	192	8	dominating	dominating	NOUN
ejpam-4440	192	9	set	set	NOUN
ejpam-4440	192	10	of	of	ADP
ejpam-4440	192	11	g+h	g+h	PROPN
ejpam-4440	192	12	.	.	PUNCT
ejpam-4440	193	1	by	by	ADP
ejpam-4440	193	2	theorem	theorem	NOUN
ejpam-4440	193	3	[	[	X
ejpam-4440	193	4	10	10	NUM
ejpam-4440	193	5	]	]	PUNCT
ejpam-4440	193	6	,	,	PUNCT
ejpam-4440	193	7	lemma	lemma	PROPN
ejpam-4440	193	8	2	2	NUM
ejpam-4440	193	9	,	,	PUNCT
ejpam-4440	193	10	and	and	CCONJ
ejpam-4440	193	11	lemma	lemma	PROPN
ejpam-4440	193	12	3	3	NUM
ejpam-4440	193	13	,	,	PUNCT
ejpam-4440	193	14	(	(	PUNCT
ejpam-4440	193	15	i	i	NOUN
ejpam-4440	193	16	)	)	PUNCT
ejpam-4440	193	17	or	or	CCONJ
ejpam-4440	193	18	(	(	PUNCT
ejpam-4440	193	19	ii	ii	NOUN
ejpam-4440	193	20	)	)	PUNCT
ejpam-4440	193	21	holds	hold	VERB
ejpam-4440	193	22	.	.	PUNCT
ejpam-4440	194	1	the	the	DET
ejpam-4440	194	2	converse	converse	NOUN
ejpam-4440	194	3	is	be	AUX
ejpam-4440	194	4	clear	clear	ADJ
ejpam-4440	194	5	by	by	ADP
ejpam-4440	194	6	theorem	theorem	NOUN
ejpam-4440	194	7	[	[	X
ejpam-4440	194	8	10	10	NUM
ejpam-4440	194	9	]	]	PUNCT
ejpam-4440	194	10	,	,	PUNCT
ejpam-4440	194	11	lemma	lemma	PROPN
ejpam-4440	194	12	2	2	NUM
ejpam-4440	194	13	,	,	PUNCT
ejpam-4440	194	14	and	and	CCONJ
ejpam-4440	194	15	lemma	lemma	PROPN
ejpam-4440	194	16	3	3	X
ejpam-4440	194	17	.	.	PUNCT
ejpam-4440	194	18	corollary	corollary	ADJ
ejpam-4440	194	19	3	3	X
ejpam-4440	194	20	.	.	PUNCT
ejpam-4440	195	1	let	let	VERB
ejpam-4440	195	2	g	g	NOUN
ejpam-4440	195	3	andh	andh	NOUN
ejpam-4440	195	4	be	be	AUX
ejpam-4440	195	5	nontrivial	nontrivial	ADJ
ejpam-4440	195	6	connected	connect	VERB
ejpam-4440	195	7	graphs	graph	NOUN
ejpam-4440	195	8	of	of	ADP
ejpam-4440	195	9	ordersm	ordersm	NOUN
ejpam-4440	195	10	and	and	CCONJ
ejpam-4440	195	11	n	n	CCONJ
ejpam-4440	195	12	,	,	PUNCT
ejpam-4440	195	13	respectively	respectively	ADV
ejpam-4440	195	14	.	.	PUNCT
ejpam-4440	196	1	then	then	ADV
ejpam-4440	196	2	,	,	PUNCT
ejpam-4440	196	3	γ1msr(g+h	γ1msr(g+h	PROPN
ejpam-4440	196	4	)	)	PUNCT
ejpam-4440	197	1	=	=	SYM
ejpam-4440	198	1	m+	m+	NUM
ejpam-4440	198	2	n−	n−	NOUN
ejpam-4440	198	3	1	1	NUM
ejpam-4440	198	4	.	.	NOUN
ejpam-4440	198	5	4	4	NUM
ejpam-4440	198	6	.	.	X
ejpam-4440	198	7	γ1	γ1	PROPN
ejpam-4440	198	8	msr(g	msr(g	PROPN
ejpam-4440	198	9	◦	◦	PROPN
ejpam-4440	198	10	h	h	NOUN
ejpam-4440	198	11	)	)	PUNCT
ejpam-4440	198	12	in	in	ADP
ejpam-4440	198	13	the	the	DET
ejpam-4440	198	14	corona	corona	NOUN
ejpam-4440	198	15	of	of	ADP
ejpam-4440	198	16	graphs	graph	NOUN
ejpam-4440	198	17	this	this	DET
ejpam-4440	198	18	section	section	NOUN
ejpam-4440	198	19	gives	give	VERB
ejpam-4440	198	20	characterization	characterization	NOUN
ejpam-4440	198	21	of	of	ADP
ejpam-4440	198	22	the	the	DET
ejpam-4440	198	23	movable	movable	ADJ
ejpam-4440	198	24	strong	strong	ADJ
ejpam-4440	198	25	resolving	resolve	VERB
ejpam-4440	198	26	dominating	dominating	NOUN
ejpam-4440	198	27	sets	set	NOUN
ejpam-4440	198	28	in	in	ADP
ejpam-4440	198	29	the	the	DET
ejpam-4440	198	30	corona	corona	NOUN
ejpam-4440	198	31	of	of	ADP
ejpam-4440	198	32	graphs	graph	NOUN
ejpam-4440	198	33	as	as	ADV
ejpam-4440	198	34	well	well	ADV
ejpam-4440	198	35	as	as	ADP
ejpam-4440	198	36	its	its	PRON
ejpam-4440	198	37	movable	movable	ADJ
ejpam-4440	198	38	strong	strong	ADJ
ejpam-4440	198	39	resolving	resolve	VERB
ejpam-4440	198	40	domination	domination	NOUN
ejpam-4440	198	41	number	number	NOUN
ejpam-4440	198	42	.	.	PUNCT
ejpam-4440	199	1	theorem	theorem	NOUN
ejpam-4440	199	2	9	9	NUM
ejpam-4440	199	3	.	.	PUNCT
ejpam-4440	200	1	let	let	VERB
ejpam-4440	200	2	g	g	PRON
ejpam-4440	200	3	be	be	AUX
ejpam-4440	200	4	a	a	DET
ejpam-4440	200	5	nontrivial	nontrivial	ADJ
ejpam-4440	200	6	connected	connect	VERB
ejpam-4440	200	7	graph	graph	NOUN
ejpam-4440	200	8	and	and	CCONJ
ejpam-4440	200	9	h	h	NOUN
ejpam-4440	200	10	a	a	DET
ejpam-4440	200	11	connected	connected	ADJ
ejpam-4440	200	12	graph	graph	NOUN
ejpam-4440	200	13	.	.	PUNCT
ejpam-4440	201	1	a	a	DET
ejpam-4440	201	2	proper	proper	ADJ
ejpam-4440	201	3	subset	subset	NOUN
ejpam-4440	201	4	s	s	NOUN
ejpam-4440	201	5	of	of	ADP
ejpam-4440	201	6	v	v	NOUN
ejpam-4440	201	7	(	(	PUNCT
ejpam-4440	201	8	g	g	PROPN
ejpam-4440	201	9	◦	◦	NOUN
ejpam-4440	201	10	h	h	NOUN
ejpam-4440	201	11	)	)	PUNCT
ejpam-4440	201	12	is	be	AUX
ejpam-4440	201	13	a	a	DET
ejpam-4440	201	14	movable	movable	ADJ
ejpam-4440	201	15	strong	strong	ADJ
ejpam-4440	201	16	resolving	resolve	VERB
ejpam-4440	201	17	dominating	dominating	NOUN
ejpam-4440	201	18	set	set	NOUN
ejpam-4440	201	19	of	of	ADP
ejpam-4440	201	20	g	g	PROPN
ejpam-4440	201	21	◦	◦	NOUN
ejpam-4440	201	22	h	h	NOUN
ejpam-4440	201	23	if	if	SCONJ
ejpam-4440	202	1	and	and	CCONJ
ejpam-4440	202	2	only	only	ADV
ejpam-4440	202	3	if	if	SCONJ
ejpam-4440	202	4	s	s	VERB
ejpam-4440	202	5	=	=	NOUN
ejpam-4440	202	6	a	a	DET
ejpam-4440	202	7	⋃	⋃	PROPN
ejpam-4440	202	8	(	(	PUNCT
ejpam-4440	202	9	⋃	⋃	NOUN
ejpam-4440	202	10	u∈v	u∈v	NOUN
ejpam-4440	202	11	(	(	PUNCT
ejpam-4440	202	12	g	g	NOUN
ejpam-4440	202	13	)	)	PUNCT
ejpam-4440	202	14	v	v	NOUN
ejpam-4440	202	15	(	(	PUNCT
ejpam-4440	202	16	hu	hu	PROPN
ejpam-4440	202	17	)	)	PUNCT
ejpam-4440	202	18	)	)	PUNCT
ejpam-4440	202	19	where	where	SCONJ
ejpam-4440	202	20	a	a	DET
ejpam-4440	202	21	⊆	⊆	NUM
ejpam-4440	202	22	v	v	NOUN
ejpam-4440	202	23	(	(	PUNCT
ejpam-4440	202	24	g	g	NOUN
ejpam-4440	202	25	)	)	PUNCT
ejpam-4440	202	26	.	.	PUNCT
ejpam-4440	203	1	proof	proof	NOUN
ejpam-4440	203	2	.	.	PUNCT
ejpam-4440	204	1	suppose	suppose	VERB
ejpam-4440	204	2	that	that	SCONJ
ejpam-4440	204	3	a	a	DET
ejpam-4440	204	4	proper	proper	ADJ
ejpam-4440	204	5	subset	subset	NOUN
ejpam-4440	204	6	s	s	NOUN
ejpam-4440	204	7	of	of	ADP
ejpam-4440	204	8	v	v	NOUN
ejpam-4440	204	9	(	(	PUNCT
ejpam-4440	204	10	g	g	PROPN
ejpam-4440	204	11	◦	◦	NOUN
ejpam-4440	204	12	h	h	NOUN
ejpam-4440	204	13	)	)	PUNCT
ejpam-4440	204	14	is	be	AUX
ejpam-4440	204	15	a	a	DET
ejpam-4440	204	16	movable	movable	ADJ
ejpam-4440	204	17	strong	strong	ADJ
ejpam-4440	204	18	resolving	resolve	VERB
ejpam-4440	204	19	dominating	dominating	NOUN
ejpam-4440	204	20	set	set	NOUN
ejpam-4440	204	21	of	of	ADP
ejpam-4440	204	22	g	g	PROPN
ejpam-4440	204	23	◦	◦	PROPN
ejpam-4440	204	24	h.	h.	NOUN
ejpam-4440	204	25	since	since	SCONJ
ejpam-4440	204	26	s	s	PROPN
ejpam-4440	204	27	is	be	AUX
ejpam-4440	204	28	a	a	DET
ejpam-4440	204	29	strong	strong	ADJ
ejpam-4440	204	30	resolving	resolving	NOUN
ejpam-4440	204	31	dominating	dominating	NOUN
ejpam-4440	204	32	set	set	NOUN
ejpam-4440	204	33	of	of	ADP
ejpam-4440	204	34	g	g	PROPN
ejpam-4440	204	35	◦	◦	NOUN
ejpam-4440	204	36	h	h	NOUN
ejpam-4440	204	37	(	(	PUNCT
ejpam-4440	204	38	i	i	NOUN
ejpam-4440	204	39	)	)	PUNCT
ejpam-4440	204	40	or	or	CCONJ
ejpam-4440	204	41	(	(	PUNCT
ejpam-4440	204	42	ii	ii	NOUN
ejpam-4440	204	43	)	)	PUNCT
ejpam-4440	204	44	of	of	ADP
ejpam-4440	204	45	theorem	theorem	NOUN
ejpam-4440	204	46	[	[	X
ejpam-4440	204	47	10	10	NUM
ejpam-4440	204	48	]	]	PUNCT
ejpam-4440	204	49	holds	hold	VERB
ejpam-4440	204	50	.	.	PUNCT
ejpam-4440	205	1	if	if	SCONJ
ejpam-4440	205	2	(	(	PUNCT
ejpam-4440	205	3	i	i	NOUN
ejpam-4440	205	4	)	)	PUNCT
ejpam-4440	205	5	holds	hold	VERB
ejpam-4440	205	6	,	,	PUNCT
ejpam-4440	205	7	then	then	ADV
ejpam-4440	205	8	s	s	VERB
ejpam-4440	205	9	=	=	NOUN
ejpam-4440	205	10	a	a	DET
ejpam-4440	205	11	⋃	⋃	PROPN
ejpam-4440	205	12	(	(	PUNCT
ejpam-4440	205	13	⋃	⋃	NOUN
ejpam-4440	205	14	u∈v	u∈v	NOUN
ejpam-4440	205	15	(	(	PUNCT
ejpam-4440	205	16	g	g	NOUN
ejpam-4440	205	17	)	)	PUNCT
ejpam-4440	205	18	v	v	NOUN
ejpam-4440	205	19	(	(	PUNCT
ejpam-4440	205	20	hu	hu	PROPN
ejpam-4440	205	21	)	)	PUNCT
ejpam-4440	205	22	)	)	PUNCT
ejpam-4440	205	23	,	,	PUNCT
ejpam-4440	205	24	where	where	SCONJ
ejpam-4440	205	25	a	a	DET
ejpam-4440	205	26	⊆	⊆	NUM
ejpam-4440	205	27	v	v	NOUN
ejpam-4440	205	28	(	(	PUNCT
ejpam-4440	205	29	g	g	NOUN
ejpam-4440	205	30	)	)	PUNCT
ejpam-4440	205	31	.	.	PUNCT
ejpam-4440	206	1	suppose	suppose	VERB
ejpam-4440	206	2	(	(	PUNCT
ejpam-4440	206	3	ii	ii	NOUN
ejpam-4440	206	4	)	)	PUNCT
ejpam-4440	206	5	holds	hold	VERB
ejpam-4440	206	6	.	.	PUNCT
ejpam-4440	207	1	let	let	VERB
ejpam-4440	207	2	x	x	SYM
ejpam-4440	207	3	∈	∈	PROPN
ejpam-4440	207	4	v	v	NOUN
ejpam-4440	207	5	(	(	PUNCT
ejpam-4440	207	6	hw	hw	NOUN
ejpam-4440	207	7	)	)	PUNCT
ejpam-4440	207	8	for	for	ADP
ejpam-4440	207	9	some	some	DET
ejpam-4440	207	10	w	w	PROPN
ejpam-4440	207	11	∈	∈	PROPN
ejpam-4440	207	12	v	v	ADP
ejpam-4440	207	13	(	(	PUNCT
ejpam-4440	207	14	g	g	NOUN
ejpam-4440	207	15	)	)	PUNCT
ejpam-4440	207	16	.	.	PUNCT
ejpam-4440	208	1	then	then	ADV
ejpam-4440	208	2	s	s	VERB
ejpam-4440	208	3	\	\	X
ejpam-4440	208	4	{	{	PUNCT
ejpam-4440	208	5	x	x	NOUN
ejpam-4440	208	6	}	}	PUNCT
ejpam-4440	208	7	=	=	PUNCT
ejpam-4440	208	8	a	a	DET
ejpam-4440	208	9	⋃	⋃	PROPN
ejpam-4440	208	10	(	(	PUNCT
ejpam-4440	208	11	⋃	⋃	NOUN
ejpam-4440	208	12	u∈v	u∈v	NOUN
ejpam-4440	208	13	(	(	PUNCT
ejpam-4440	208	14	g)\{w	g)\{w	NOUN
ejpam-4440	208	15	,	,	PUNCT
ejpam-4440	208	16	v	v	NOUN
ejpam-4440	208	17	}	}	SYM
ejpam-4440	208	18	v	v	PROPN
ejpam-4440	208	19	(	(	PUNCT
ejpam-4440	208	20	hu	hu	PROPN
ejpam-4440	208	21	)	)	PUNCT
ejpam-4440	208	22	)	)	PUNCT
ejpam-4440	209	1	⋃	⋃	PROPN
ejpam-4440	209	2	(	(	PUNCT
ejpam-4440	209	3	v	v	NOUN
ejpam-4440	209	4	(	(	PUNCT
ejpam-4440	209	5	hw	hw	NOUN
ejpam-4440	209	6	)	)	PUNCT
ejpam-4440	209	7	\	\	AUX
ejpam-4440	209	8	{	{	PUNCT
ejpam-4440	209	9	x	x	NOUN
ejpam-4440	209	10	}	}	PUNCT
ejpam-4440	209	11	)	)	PUNCT
ejpam-4440	209	12	⋃	⋃	PUNCT
ejpam-4440	209	13	bv	bv	PROPN
ejpam-4440	209	14	is	be	AUX
ejpam-4440	209	15	not	not	PART
ejpam-4440	209	16	a	a	DET
ejpam-4440	209	17	strong	strong	ADJ
ejpam-4440	209	18	resolving	resolving	NOUN
ejpam-4440	209	19	set	set	VERB
ejpam-4440	209	20	by	by	ADP
ejpam-4440	209	21	theorem	theorem	NOUN
ejpam-4440	209	22	[	[	X
ejpam-4440	209	23	10	10	NUM
ejpam-4440	209	24	]	]	PUNCT
ejpam-4440	209	25	.	.	PUNCT
ejpam-4440	210	1	hence	hence	ADV
ejpam-4440	210	2	,	,	PUNCT
ejpam-4440	210	3	s	s	VERB
ejpam-4440	210	4	=	=	NOUN
ejpam-4440	210	5	a	a	DET
ejpam-4440	210	6	⋃	⋃	PROPN
ejpam-4440	210	7	(	(	PUNCT
ejpam-4440	210	8	⋃	⋃	NOUN
ejpam-4440	210	9	u∈v	u∈v	NOUN
ejpam-4440	210	10	(	(	PUNCT
ejpam-4440	210	11	g	g	NOUN
ejpam-4440	210	12	)	)	PUNCT
ejpam-4440	210	13	v	v	NOUN
ejpam-4440	210	14	(	(	PUNCT
ejpam-4440	210	15	hu	hu	PROPN
ejpam-4440	210	16	)	)	PUNCT
ejpam-4440	210	17	)	)	PUNCT
ejpam-4440	210	18	where	where	SCONJ
ejpam-4440	210	19	a	a	DET
ejpam-4440	210	20	⊆	⊆	NUM
ejpam-4440	210	21	v	v	NOUN
ejpam-4440	210	22	(	(	PUNCT
ejpam-4440	210	23	g	g	NOUN
ejpam-4440	210	24	)	)	PUNCT
ejpam-4440	210	25	.	.	PUNCT
ejpam-4440	211	1	h.	h.	PROPN
ejpam-4440	211	2	sumaoy	sumaoy	PROPN
ejpam-4440	211	3	,	,	PUNCT
ejpam-4440	211	4	h.	h.	PROPN
ejpam-4440	211	5	rara	rara	PROPN
ejpam-4440	211	6	/	/	SYM
ejpam-4440	211	7	eur	eur	PROPN
ejpam-4440	211	8	.	.	PUNCT
ejpam-4440	212	1	j.	j.	PROPN
ejpam-4440	212	2	pure	pure	PROPN
ejpam-4440	212	3	appl	appl	PROPN
ejpam-4440	212	4	.	.	PROPN
ejpam-4440	212	5	math	math	PROPN
ejpam-4440	212	6	,	,	PUNCT
ejpam-4440	212	7	15	15	NUM
ejpam-4440	212	8	(	(	PUNCT
ejpam-4440	212	9	3	3	NUM
ejpam-4440	212	10	)	)	PUNCT
ejpam-4440	212	11	(	(	PUNCT
ejpam-4440	212	12	2022	2022	NUM
ejpam-4440	212	13	)	)	PUNCT
ejpam-4440	212	14	,	,	PUNCT
ejpam-4440	212	15	1201	1201	NUM
ejpam-4440	212	16	-	-	SYM
ejpam-4440	212	17	1210	1210	NUM
ejpam-4440	212	18	1208	1208	NUM
ejpam-4440	212	19	for	for	ADP
ejpam-4440	212	20	the	the	DET
ejpam-4440	212	21	converse	converse	NOUN
ejpam-4440	212	22	,	,	PUNCT
ejpam-4440	212	23	suppose	suppose	VERB
ejpam-4440	212	24	s	s	VERB
ejpam-4440	212	25	=	=	NOUN
ejpam-4440	212	26	a	a	DET
ejpam-4440	212	27	⋃	⋃	PROPN
ejpam-4440	212	28	(	(	PUNCT
ejpam-4440	212	29	⋃	⋃	NOUN
ejpam-4440	212	30	u∈v	u∈v	NOUN
ejpam-4440	212	31	(	(	PUNCT
ejpam-4440	212	32	g	g	NOUN
ejpam-4440	212	33	)	)	PUNCT
ejpam-4440	212	34	v	v	NOUN
ejpam-4440	212	35	(	(	PUNCT
ejpam-4440	212	36	hu	hu	PROPN
ejpam-4440	212	37	)	)	PUNCT
ejpam-4440	212	38	)	)	PUNCT
ejpam-4440	212	39	.	.	PUNCT
ejpam-4440	213	1	by	by	ADP
ejpam-4440	213	2	theorem	theorem	NOUN
ejpam-4440	213	3	[	[	X
ejpam-4440	213	4	10	10	NUM
ejpam-4440	213	5	]	]	PUNCT
ejpam-4440	213	6	,	,	PUNCT
ejpam-4440	213	7	s	s	VERB
ejpam-4440	213	8	is	be	AUX
ejpam-4440	213	9	a	a	DET
ejpam-4440	213	10	strong	strong	ADJ
ejpam-4440	213	11	resolving	resolving	NOUN
ejpam-4440	213	12	dominating	dominating	NOUN
ejpam-4440	213	13	set	set	NOUN
ejpam-4440	213	14	.	.	PUNCT
ejpam-4440	214	1	let	let	VERB
ejpam-4440	214	2	p	p	PRON
ejpam-4440	214	3	∈	∈	PROPN
ejpam-4440	214	4	s.	s.	PROPN
ejpam-4440	214	5	if	if	SCONJ
ejpam-4440	214	6	p	p	PROPN
ejpam-4440	214	7	∈	∈	PROPN
ejpam-4440	214	8	a	a	PRON
ejpam-4440	214	9	,	,	PUNCT
ejpam-4440	214	10	then	then	ADV
ejpam-4440	214	11	s	s	VERB
ejpam-4440	214	12	\{p	\{p	NOUN
ejpam-4440	214	13	}	}	PUNCT
ejpam-4440	214	14	=	=	SYM
ejpam-4440	214	15	(	(	PUNCT
ejpam-4440	214	16	a\{p})∪	a\{p})∪	PROPN
ejpam-4440	214	17	(	(	PUNCT
ejpam-4440	214	18	⋃	⋃	ADP
ejpam-4440	214	19	u∈v	u∈v	NOUN
ejpam-4440	214	20	(	(	PUNCT
ejpam-4440	214	21	g	g	NOUN
ejpam-4440	214	22	)	)	PUNCT
ejpam-4440	214	23	v	v	NOUN
ejpam-4440	214	24	(	(	PUNCT
ejpam-4440	214	25	hu	hu	PROPN
ejpam-4440	214	26	)	)	PUNCT
ejpam-4440	214	27	)	)	PUNCT
ejpam-4440	214	28	is	be	AUX
ejpam-4440	214	29	a	a	DET
ejpam-4440	214	30	strong	strong	ADJ
ejpam-4440	214	31	resolving	resolve	VERB
ejpam-4440	214	32	dominating	dominating	NOUN
ejpam-4440	214	33	set	set	NOUN
ejpam-4440	214	34	.	.	PUNCT
ejpam-4440	215	1	if	if	SCONJ
ejpam-4440	215	2	p	p	PROPN
ejpam-4440	215	3	∈	∈	PROPN
ejpam-4440	215	4	v	v	ADP
ejpam-4440	215	5	(	(	PUNCT
ejpam-4440	215	6	hu	hu	PROPN
ejpam-4440	215	7	)	)	PUNCT
ejpam-4440	215	8	for	for	ADP
ejpam-4440	215	9	each	each	DET
ejpam-4440	215	10	u	u	PROPN
ejpam-4440	215	11	∈	∈	PROPN
ejpam-4440	215	12	v	v	NOUN
ejpam-4440	215	13	(	(	PUNCT
ejpam-4440	215	14	g	g	NOUN
ejpam-4440	215	15	)	)	PUNCT
ejpam-4440	215	16	,	,	PUNCT
ejpam-4440	215	17	then	then	ADV
ejpam-4440	215	18	s	s	VERB
ejpam-4440	215	19	\	\	X
ejpam-4440	215	20	{	{	PUNCT
ejpam-4440	215	21	p	p	X
ejpam-4440	215	22	}	}	PUNCT
ejpam-4440	215	23	=	=	PUNCT
ejpam-4440	215	24	a	a	DET
ejpam-4440	215	25	∪	∪	X
ejpam-4440	215	26	(	(	PUNCT
ejpam-4440	215	27	⋃	⋃	NOUN
ejpam-4440	215	28	u∈v	u∈v	NOUN
ejpam-4440	215	29	(	(	PUNCT
ejpam-4440	215	30	g	g	NOUN
ejpam-4440	215	31	)	)	PUNCT
ejpam-4440	215	32	v	v	NOUN
ejpam-4440	215	33	(	(	PUNCT
ejpam-4440	215	34	hu	hu	PROPN
ejpam-4440	215	35	)	)	PUNCT
ejpam-4440	215	36	\	\	NOUN
ejpam-4440	215	37	{	{	PUNCT
ejpam-4440	215	38	p	p	NOUN
ejpam-4440	215	39	}	}	PUNCT
ejpam-4440	215	40	)	)	PUNCT
ejpam-4440	215	41	is	be	AUX
ejpam-4440	215	42	a	a	DET
ejpam-4440	215	43	strong	strong	ADJ
ejpam-4440	215	44	resolving	resolving	NOUN
ejpam-4440	215	45	dominating	dominating	NOUN
ejpam-4440	215	46	set	set	VERB
ejpam-4440	215	47	since	since	SCONJ
ejpam-4440	215	48	{	{	PUNCT
ejpam-4440	215	49	p	p	X
ejpam-4440	215	50	}	}	PUNCT
ejpam-4440	215	51	is	be	AUX
ejpam-4440	215	52	a	a	DET
ejpam-4440	215	53	dominated	dominate	VERB
ejpam-4440	215	54	superclique	superclique	NOUN
ejpam-4440	215	55	in	in	ADP
ejpam-4440	215	56	hu	hu	PROPN
ejpam-4440	215	57	.	.	PUNCT
ejpam-4440	216	1	accordingly	accordingly	ADV
ejpam-4440	216	2	,	,	PUNCT
ejpam-4440	216	3	s	s	VERB
ejpam-4440	216	4	is	be	AUX
ejpam-4440	216	5	a	a	DET
ejpam-4440	216	6	movable	movable	ADJ
ejpam-4440	216	7	strong	strong	ADJ
ejpam-4440	216	8	resolving	resolve	VERB
ejpam-4440	216	9	dominating	dominating	NOUN
ejpam-4440	216	10	set	set	VERB
ejpam-4440	216	11	in	in	ADP
ejpam-4440	216	12	g	g	PROPN
ejpam-4440	216	13	◦	◦	NOUN
ejpam-4440	216	14	h.	h.	NOUN
ejpam-4440	216	15	corollary	corollary	ADJ
ejpam-4440	216	16	4	4	NUM
ejpam-4440	216	17	.	.	PUNCT
ejpam-4440	217	1	let	let	VERB
ejpam-4440	217	2	g	g	PRON
ejpam-4440	217	3	be	be	AUX
ejpam-4440	217	4	a	a	DET
ejpam-4440	217	5	connected	connected	ADJ
ejpam-4440	217	6	graph	graph	NOUN
ejpam-4440	217	7	of	of	ADP
ejpam-4440	217	8	order	order	NOUN
ejpam-4440	217	9	m	m	VERB
ejpam-4440	217	10	>	>	X
ejpam-4440	217	11	1	1	NUM
ejpam-4440	217	12	and	and	CCONJ
ejpam-4440	217	13	h	h	NOUN
ejpam-4440	217	14	be	be	VERB
ejpam-4440	217	15	any	any	DET
ejpam-4440	217	16	graph	graph	NOUN
ejpam-4440	217	17	of	of	ADP
ejpam-4440	217	18	order	order	NOUN
ejpam-4440	217	19	n.	n.	NOUN
ejpam-4440	217	20	then	then	ADV
ejpam-4440	217	21	γ1msr(g	γ1msr(g	ADP
ejpam-4440	217	22	◦	◦	NOUN
ejpam-4440	217	23	h	h	NOUN
ejpam-4440	217	24	)	)	PUNCT
ejpam-4440	217	25	=	=	SYM
ejpam-4440	217	26	mn	mn	PROPN
ejpam-4440	217	27	.	.	PUNCT
ejpam-4440	217	28	proof	proof	NOUN
ejpam-4440	217	29	.	.	PUNCT
ejpam-4440	218	1	let	let	VERB
ejpam-4440	218	2	c	c	PRON
ejpam-4440	218	3	be	be	AUX
ejpam-4440	218	4	a	a	DET
ejpam-4440	218	5	γ1msr	γ1msr	NOUN
ejpam-4440	218	6	-	-	PUNCT
ejpam-4440	218	7	set	set	NOUN
ejpam-4440	218	8	of	of	ADP
ejpam-4440	218	9	g	g	PROPN
ejpam-4440	218	10	◦	◦	NOUN
ejpam-4440	218	11	h.	h.	NOUN
ejpam-4440	218	12	then	then	ADV
ejpam-4440	218	13	by	by	ADP
ejpam-4440	218	14	theorem	theorem	NOUN
ejpam-4440	218	15	9	9	NUM
ejpam-4440	218	16	,	,	PUNCT
ejpam-4440	218	17	s	s	VERB
ejpam-4440	218	18	=	=	NOUN
ejpam-4440	218	19	a	a	DET
ejpam-4440	218	20	⋃	⋃	PROPN
ejpam-4440	218	21	(	(	PUNCT
ejpam-4440	218	22	⋃	⋃	NOUN
ejpam-4440	218	23	u∈v	u∈v	NOUN
ejpam-4440	218	24	(	(	PUNCT
ejpam-4440	218	25	g	g	NOUN
ejpam-4440	218	26	)	)	PUNCT
ejpam-4440	218	27	v	v	NOUN
ejpam-4440	218	28	(	(	PUNCT
ejpam-4440	218	29	hu	hu	PROPN
ejpam-4440	218	30	)	)	PUNCT
ejpam-4440	218	31	)	)	PUNCT
ejpam-4440	218	32	where	where	SCONJ
ejpam-4440	218	33	a	a	DET
ejpam-4440	218	34	⊆	⊆	NUM
ejpam-4440	218	35	v	v	NOUN
ejpam-4440	218	36	(	(	PUNCT
ejpam-4440	218	37	g	g	NOUN
ejpam-4440	218	38	)	)	PUNCT
ejpam-4440	218	39	.	.	PUNCT
ejpam-4440	219	1	thus	thus	ADV
ejpam-4440	219	2	,	,	PUNCT
ejpam-4440	219	3	γ1msr(g	γ1msr(g	ADP
ejpam-4440	219	4	◦	◦	NOUN
ejpam-4440	219	5	h	h	NOUN
ejpam-4440	219	6	)	)	PUNCT
ejpam-4440	220	1	=	=	SYM
ejpam-4440	220	2	|c|	|c|	PROPN
ejpam-4440	220	3	=	=	PUNCT
ejpam-4440	220	4	|a|+	|a|+	VERB
ejpam-4440	220	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4440	220	6	⋃	⋃	NOUN
ejpam-4440	220	7	u∈v	u∈v	NOUN
ejpam-4440	220	8	(	(	PUNCT
ejpam-4440	220	9	g	g	NOUN
ejpam-4440	220	10	)	)	PUNCT
ejpam-4440	220	11	v	v	NOUN
ejpam-4440	220	12	(	(	PUNCT
ejpam-4440	220	13	hu	hu	PROPN
ejpam-4440	220	14	)	)	PUNCT
ejpam-4440	220	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4440	220	16	≥	≥	NUM
ejpam-4440	220	17	|v	|v	NOUN
ejpam-4440	220	18	(	(	PUNCT
ejpam-4440	220	19	g)||v	g)||v	PROPN
ejpam-4440	220	20	(	(	PUNCT
ejpam-4440	220	21	h)|	h)|	PROPN
ejpam-4440	220	22	=	=	SYM
ejpam-4440	220	23	mn	mn	PROPN
ejpam-4440	220	24	.	.	PROPN
ejpam-4440	221	1	let	let	VERB
ejpam-4440	221	2	a	a	DET
ejpam-4440	221	3	=	=	PUNCT
ejpam-4440	221	4	∅.	∅.	NOUN
ejpam-4440	221	5	then	then	ADV
ejpam-4440	221	6	s∗	s∗	PROPN
ejpam-4440	221	7	=	=	PUNCT
ejpam-4440	221	8	a	a	DET
ejpam-4440	221	9	⋃	⋃	PROPN
ejpam-4440	221	10	(	(	PUNCT
ejpam-4440	221	11	⋃	⋃	NOUN
ejpam-4440	221	12	u∈v	u∈v	NOUN
ejpam-4440	221	13	(	(	PUNCT
ejpam-4440	221	14	g	g	NOUN
ejpam-4440	221	15	)	)	PUNCT
ejpam-4440	221	16	v	v	NOUN
ejpam-4440	221	17	(	(	PUNCT
ejpam-4440	221	18	hu	hu	PROPN
ejpam-4440	221	19	)	)	PUNCT
ejpam-4440	221	20	)	)	PUNCT
ejpam-4440	221	21	is	be	AUX
ejpam-4440	221	22	a	a	DET
ejpam-4440	221	23	movable	movable	ADJ
ejpam-4440	221	24	strong	strong	ADJ
ejpam-4440	221	25	resolving	resolve	VERB
ejpam-4440	221	26	dominating	dominating	NOUN
ejpam-4440	221	27	set	set	NOUN
ejpam-4440	221	28	of	of	ADP
ejpam-4440	221	29	g	g	PROPN
ejpam-4440	221	30	◦	◦	NOUN
ejpam-4440	221	31	h	h	NOUN
ejpam-4440	221	32	by	by	ADP
ejpam-4440	221	33	theorem	theorem	NOUN
ejpam-4440	221	34	9	9	NUM
ejpam-4440	221	35	.	.	PUNCT
ejpam-4440	222	1	hence	hence	ADV
ejpam-4440	222	2	,	,	PUNCT
ejpam-4440	222	3	γ1msr(g	γ1msr(g	ADP
ejpam-4440	222	4	◦	◦	NOUN
ejpam-4440	222	5	h	h	NOUN
ejpam-4440	222	6	)	)	PUNCT
ejpam-4440	222	7	≤	≤	NOUN
ejpam-4440	222	8	|s∗|	|s∗|	PUNCT
ejpam-4440	223	1	=	=	SYM
ejpam-4440	223	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4440	223	3	⋃	⋃	NOUN
ejpam-4440	223	4	u∈v	u∈v	NOUN
ejpam-4440	223	5	(	(	PUNCT
ejpam-4440	223	6	g	g	NOUN
ejpam-4440	223	7	)	)	PUNCT
ejpam-4440	223	8	v	v	NOUN
ejpam-4440	223	9	(	(	PUNCT
ejpam-4440	223	10	hu	hu	NOUN
ejpam-4440	223	11	)	)	PUNCT
ejpam-4440	223	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4440	223	13	=	=	SYM
ejpam-4440	223	14	mn	mn	PROPN
ejpam-4440	223	15	.	.	PROPN
ejpam-4440	223	16	therefore	therefore	ADV
ejpam-4440	223	17	,	,	PUNCT
ejpam-4440	223	18	γ1msr(g	γ1msr(g	ADP
ejpam-4440	223	19	◦	◦	NOUN
ejpam-4440	223	20	h	h	NOUN
ejpam-4440	223	21	)	)	PUNCT
ejpam-4440	223	22	=	=	SYM
ejpam-4440	223	23	mn	mn	PROPN
ejpam-4440	223	24	.	.	PROPN
ejpam-4440	223	25	5	5	NUM
ejpam-4440	223	26	.	.	X
ejpam-4440	223	27	γ1	γ1	PROPN
ejpam-4440	223	28	msr(g[h	msr(g[h	NOUN
ejpam-4440	223	29	]	]	PUNCT
ejpam-4440	223	30	)	)	PUNCT
ejpam-4440	223	31	in	in	ADP
ejpam-4440	223	32	the	the	DET
ejpam-4440	223	33	lexicographic	lexicographic	ADJ
ejpam-4440	223	34	product	product	NOUN
ejpam-4440	223	35	of	of	ADP
ejpam-4440	223	36	graphs	graph	NOUN
ejpam-4440	223	37	this	this	DET
ejpam-4440	223	38	section	section	NOUN
ejpam-4440	223	39	gives	give	VERB
ejpam-4440	223	40	characterization	characterization	NOUN
ejpam-4440	223	41	of	of	ADP
ejpam-4440	223	42	the	the	DET
ejpam-4440	223	43	movable	movable	ADJ
ejpam-4440	223	44	strong	strong	ADJ
ejpam-4440	223	45	resolving	resolve	VERB
ejpam-4440	223	46	dominating	dominating	NOUN
ejpam-4440	223	47	sets	set	NOUN
ejpam-4440	223	48	in	in	ADP
ejpam-4440	223	49	the	the	DET
ejpam-4440	223	50	lexicographic	lexicographic	ADJ
ejpam-4440	223	51	product	product	NOUN
ejpam-4440	223	52	of	of	ADP
ejpam-4440	223	53	graphs	graph	NOUN
ejpam-4440	223	54	as	as	ADV
ejpam-4440	223	55	well	well	ADV
ejpam-4440	223	56	as	as	ADP
ejpam-4440	223	57	its	its	PRON
ejpam-4440	223	58	movable	movable	ADJ
ejpam-4440	223	59	strong	strong	ADJ
ejpam-4440	223	60	resolving	resolve	VERB
ejpam-4440	223	61	domination	domination	NOUN
ejpam-4440	223	62	number	number	NOUN
ejpam-4440	223	63	.	.	PUNCT
ejpam-4440	224	1	h.	h.	PROPN
ejpam-4440	224	2	sumaoy	sumaoy	PROPN
ejpam-4440	224	3	,	,	PUNCT
ejpam-4440	224	4	h.	h.	PROPN
ejpam-4440	224	5	rara	rara	PROPN
ejpam-4440	224	6	/	/	SYM
ejpam-4440	224	7	eur	eur	PROPN
ejpam-4440	224	8	.	.	PUNCT
ejpam-4440	225	1	j.	j.	PROPN
ejpam-4440	225	2	pure	pure	PROPN
ejpam-4440	225	3	appl	appl	PROPN
ejpam-4440	225	4	.	.	PROPN
ejpam-4440	225	5	math	math	PROPN
ejpam-4440	225	6	,	,	PUNCT
ejpam-4440	225	7	15	15	NUM
ejpam-4440	225	8	(	(	PUNCT
ejpam-4440	225	9	3	3	NUM
ejpam-4440	225	10	)	)	PUNCT
ejpam-4440	225	11	(	(	PUNCT
ejpam-4440	225	12	2022	2022	NUM
ejpam-4440	225	13	)	)	PUNCT
ejpam-4440	225	14	,	,	PUNCT
ejpam-4440	225	15	1201	1201	NUM
ejpam-4440	225	16	-	-	SYM
ejpam-4440	225	17	1210	1210	NUM
ejpam-4440	225	18	1209	1209	NUM
ejpam-4440	225	19	lemma	lemma	PROPN
ejpam-4440	225	20	4	4	X
ejpam-4440	225	21	.	.	PUNCT
ejpam-4440	226	1	let	let	VERB
ejpam-4440	226	2	g	g	PROPN
ejpam-4440	226	3	=	=	PROPN
ejpam-4440	226	4	kn	kn	PROPN
ejpam-4440	226	5	for	for	ADP
ejpam-4440	226	6	n	n	PROPN
ejpam-4440	226	7	>	>	SYM
ejpam-4440	226	8	1	1	NUM
ejpam-4440	226	9	and	and	CCONJ
ejpam-4440	226	10	h	h	NOUN
ejpam-4440	226	11	be	be	VERB
ejpam-4440	226	12	a	a	DET
ejpam-4440	226	13	nontrivial	nontrivial	ADJ
ejpam-4440	226	14	connected	connect	VERB
ejpam-4440	226	15	graph	graph	NOUN
ejpam-4440	226	16	with	with	ADP
ejpam-4440	226	17	γ(h	γ(h	NOUN
ejpam-4440	226	18	)	)	PUNCT
ejpam-4440	226	19	=	=	SYM
ejpam-4440	227	1	1	1	X
ejpam-4440	227	2	.	.	PUNCT
ejpam-4440	227	3	then	then	ADV
ejpam-4440	227	4	a	a	DET
ejpam-4440	227	5	×	×	NOUN
ejpam-4440	227	6	c	c	NOUN
ejpam-4440	227	7	is	be	AUX
ejpam-4440	227	8	a	a	DET
ejpam-4440	227	9	γ	γ	NOUN
ejpam-4440	227	10	-	-	PUNCT
ejpam-4440	227	11	set	set	NOUN
ejpam-4440	227	12	of	of	ADP
ejpam-4440	227	13	g[h	g[h	NOUN
ejpam-4440	227	14	]	]	PUNCT
ejpam-4440	227	15	if	if	SCONJ
ejpam-4440	227	16	and	and	CCONJ
ejpam-4440	227	17	only	only	ADV
ejpam-4440	227	18	if	if	SCONJ
ejpam-4440	227	19	a	a	PRON
ejpam-4440	227	20	is	be	AUX
ejpam-4440	227	21	a	a	DET
ejpam-4440	227	22	singleton	singleton	NOUN
ejpam-4440	227	23	subset	subset	NOUN
ejpam-4440	227	24	of	of	ADP
ejpam-4440	227	25	v	v	PROPN
ejpam-4440	227	26	(	(	PUNCT
ejpam-4440	227	27	g	g	NOUN
ejpam-4440	227	28	)	)	PUNCT
ejpam-4440	227	29	and	and	CCONJ
ejpam-4440	227	30	c	c	PROPN
ejpam-4440	227	31	is	be	AUX
ejpam-4440	227	32	a	a	DET
ejpam-4440	227	33	γ	γ	NOUN
ejpam-4440	227	34	-	-	PUNCT
ejpam-4440	227	35	set	set	NOUN
ejpam-4440	227	36	of	of	ADP
ejpam-4440	227	37	h.	h.	NOUN
ejpam-4440	227	38	proof	proof	NOUN
ejpam-4440	227	39	.	.	PUNCT
ejpam-4440	228	1	suppose	suppose	VERB
ejpam-4440	228	2	a	a	DET
ejpam-4440	228	3	×	×	NOUN
ejpam-4440	228	4	c	c	NOUN
ejpam-4440	228	5	is	be	AUX
ejpam-4440	228	6	a	a	DET
ejpam-4440	228	7	γ	γ	NOUN
ejpam-4440	228	8	-	-	PUNCT
ejpam-4440	228	9	set	set	NOUN
ejpam-4440	228	10	of	of	ADP
ejpam-4440	228	11	g[h	g[h	NOUN
ejpam-4440	228	12	]	]	PUNCT
ejpam-4440	228	13	.	.	PUNCT
ejpam-4440	229	1	since	since	SCONJ
ejpam-4440	229	2	g	g	PROPN
ejpam-4440	229	3	=	=	PROPN
ejpam-4440	229	4	kn	kn	PROPN
ejpam-4440	229	5	for	for	ADP
ejpam-4440	229	6	n	n	PROPN
ejpam-4440	229	7	>	>	SYM
ejpam-4440	229	8	1	1	NUM
ejpam-4440	229	9	and	and	CCONJ
ejpam-4440	229	10	γ(h	γ(h	NOUN
ejpam-4440	229	11	)	)	PUNCT
ejpam-4440	229	12	=	=	SYM
ejpam-4440	229	13	1	1	NUM
ejpam-4440	229	14	,	,	PUNCT
ejpam-4440	229	15	γ(g[h	γ(g[h	NOUN
ejpam-4440	229	16	]	]	PUNCT
ejpam-4440	229	17	)	)	PUNCT
ejpam-4440	229	18	=	=	SYM
ejpam-4440	229	19	1	1	X
ejpam-4440	229	20	.	.	PUNCT
ejpam-4440	230	1	hence	hence	ADV
ejpam-4440	230	2	,	,	PUNCT
ejpam-4440	230	3	a	a	PRON
ejpam-4440	230	4	is	be	AUX
ejpam-4440	230	5	a	a	DET
ejpam-4440	230	6	singleton	singleton	NOUN
ejpam-4440	230	7	subset	subset	NOUN
ejpam-4440	230	8	of	of	ADP
ejpam-4440	230	9	v	v	PROPN
ejpam-4440	230	10	(	(	PUNCT
ejpam-4440	230	11	g	g	NOUN
ejpam-4440	230	12	)	)	PUNCT
ejpam-4440	230	13	and	and	CCONJ
ejpam-4440	230	14	c	c	PROPN
ejpam-4440	230	15	is	be	AUX
ejpam-4440	230	16	a	a	DET
ejpam-4440	230	17	singleton	singleton	NOUN
ejpam-4440	230	18	subset	subset	NOUN
ejpam-4440	230	19	of	of	ADP
ejpam-4440	230	20	h.	h.	PROPN
ejpam-4440	230	21	we	we	PRON
ejpam-4440	230	22	claim	claim	VERB
ejpam-4440	230	23	that	that	SCONJ
ejpam-4440	230	24	c	c	PROPN
ejpam-4440	230	25	is	be	AUX
ejpam-4440	230	26	a	a	DET
ejpam-4440	230	27	γ	γ	NOUN
ejpam-4440	230	28	-	-	PUNCT
ejpam-4440	230	29	set	set	NOUN
ejpam-4440	230	30	of	of	ADP
ejpam-4440	230	31	h.	h.	PROPN
ejpam-4440	230	32	suppose	suppose	VERB
ejpam-4440	230	33	c	c	NOUN
ejpam-4440	230	34	is	be	AUX
ejpam-4440	230	35	not	not	PART
ejpam-4440	230	36	a	a	DET
ejpam-4440	230	37	γ	γ	NOUN
ejpam-4440	230	38	-	-	PUNCT
ejpam-4440	230	39	set	set	NOUN
ejpam-4440	230	40	of	of	ADP
ejpam-4440	230	41	h.	h.	PROPN
ejpam-4440	230	42	then	then	ADV
ejpam-4440	230	43	there	there	PRON
ejpam-4440	230	44	exists	exist	VERB
ejpam-4440	230	45	y	y	PROPN
ejpam-4440	230	46	∈	∈	PROPN
ejpam-4440	230	47	(	(	PUNCT
ejpam-4440	230	48	v	v	NOUN
ejpam-4440	230	49	(	(	PUNCT
ejpam-4440	230	50	h	h	NOUN
ejpam-4440	230	51	)	)	PUNCT
ejpam-4440	230	52	\	\	NOUN
ejpam-4440	231	1	c	c	X
ejpam-4440	231	2	)	)	PUNCT
ejpam-4440	231	3	such	such	ADJ
ejpam-4440	231	4	that	that	SCONJ
ejpam-4440	231	5	nh(y	nh(y	ADJ
ejpam-4440	231	6	)	)	PUNCT
ejpam-4440	231	7	∩	∩	NOUN
ejpam-4440	231	8	c	c	NOUN
ejpam-4440	231	9	=	=	PUNCT
ejpam-4440	231	10	∅.	∅.	VERB
ejpam-4440	231	11	hence	hence	ADV
ejpam-4440	231	12	,	,	PUNCT
ejpam-4440	231	13	ng[h]((a	ng[h]((a	PROPN
ejpam-4440	231	14	,	,	PUNCT
ejpam-4440	231	15	y	y	NOUN
ejpam-4440	231	16	)	)	PUNCT
ejpam-4440	231	17	)	)	PUNCT
ejpam-4440	231	18	∩	∩	NOUN
ejpam-4440	231	19	(	(	PUNCT
ejpam-4440	231	20	{	{	PUNCT
ejpam-4440	231	21	a	a	PRON
ejpam-4440	231	22	}	}	PUNCT
ejpam-4440	231	23	×	×	NOUN
ejpam-4440	231	24	c	c	NOUN
ejpam-4440	231	25	)	)	PUNCT
ejpam-4440	232	1	=	=	NOUN
ejpam-4440	232	2	∅	∅	NOUN
ejpam-4440	232	3	for	for	ADP
ejpam-4440	232	4	all	all	DET
ejpam-4440	232	5	a	a	DET
ejpam-4440	232	6	∈	∈	NOUN
ejpam-4440	232	7	a.	a.	NOUN
ejpam-4440	232	8	this	this	PRON
ejpam-4440	232	9	contradicts	contradict	VERB
ejpam-4440	232	10	the	the	DET
ejpam-4440	232	11	assumption	assumption	NOUN
ejpam-4440	232	12	that	that	SCONJ
ejpam-4440	232	13	a×c	a×c	PROPN
ejpam-4440	232	14	is	be	AUX
ejpam-4440	232	15	a	a	DET
ejpam-4440	232	16	γ	γ	NOUN
ejpam-4440	232	17	-	-	PUNCT
ejpam-4440	232	18	set	set	NOUN
ejpam-4440	232	19	of	of	ADP
ejpam-4440	232	20	g[h	g[h	NOUN
ejpam-4440	232	21	]	]	PUNCT
ejpam-4440	232	22	.	.	PUNCT
ejpam-4440	233	1	thus	thus	ADV
ejpam-4440	233	2	,	,	PUNCT
ejpam-4440	233	3	c	c	PROPN
ejpam-4440	233	4	is	be	AUX
ejpam-4440	233	5	a	a	DET
ejpam-4440	233	6	γ	γ	NOUN
ejpam-4440	233	7	-	-	PUNCT
ejpam-4440	233	8	set	set	NOUN
ejpam-4440	233	9	of	of	ADP
ejpam-4440	233	10	h.	h.	NOUN
ejpam-4440	233	11	conversely	conversely	ADV
ejpam-4440	233	12	,	,	PUNCT
ejpam-4440	233	13	suppose	suppose	VERB
ejpam-4440	233	14	that	that	SCONJ
ejpam-4440	233	15	a	a	PRON
ejpam-4440	233	16	is	be	AUX
ejpam-4440	233	17	a	a	DET
ejpam-4440	233	18	singleton	singleton	NOUN
ejpam-4440	233	19	subset	subset	NOUN
ejpam-4440	233	20	of	of	ADP
ejpam-4440	233	21	v	v	PROPN
ejpam-4440	233	22	(	(	PUNCT
ejpam-4440	233	23	g	g	NOUN
ejpam-4440	233	24	)	)	PUNCT
ejpam-4440	233	25	and	and	CCONJ
ejpam-4440	233	26	c	c	PROPN
ejpam-4440	233	27	is	be	AUX
ejpam-4440	233	28	a	a	DET
ejpam-4440	233	29	γ	γ	NOUN
ejpam-4440	233	30	-	-	PUNCT
ejpam-4440	233	31	set	set	NOUN
ejpam-4440	233	32	of	of	ADP
ejpam-4440	233	33	h.	h.	NOUN
ejpam-4440	233	34	we	we	PRON
ejpam-4440	233	35	claim	claim	VERB
ejpam-4440	233	36	that	that	SCONJ
ejpam-4440	233	37	a×c	a×c	PROPN
ejpam-4440	233	38	is	be	AUX
ejpam-4440	233	39	a	a	DET
ejpam-4440	233	40	γ	γ	NOUN
ejpam-4440	233	41	-	-	PUNCT
ejpam-4440	233	42	set	set	NOUN
ejpam-4440	233	43	of	of	ADP
ejpam-4440	233	44	g[h	g[h	NOUN
ejpam-4440	233	45	]	]	PUNCT
ejpam-4440	233	46	.	.	PUNCT
ejpam-4440	234	1	let	let	VERB
ejpam-4440	234	2	(	(	PUNCT
ejpam-4440	234	3	a	a	DET
ejpam-4440	234	4	,	,	PUNCT
ejpam-4440	234	5	x	x	NOUN
ejpam-4440	234	6	)	)	PUNCT
ejpam-4440	234	7	∈	∈	NOUN
ejpam-4440	234	8	v	v	NOUN
ejpam-4440	234	9	(	(	PUNCT
ejpam-4440	234	10	g[h	g[h	PROPN
ejpam-4440	234	11	]	]	PUNCT
ejpam-4440	234	12	)	)	PUNCT
ejpam-4440	234	13	\	\	PUNCT
ejpam-4440	235	1	(	(	PUNCT
ejpam-4440	235	2	a×c	a×c	PROPN
ejpam-4440	235	3	)	)	PUNCT
ejpam-4440	235	4	.	.	PUNCT
ejpam-4440	236	1	then	then	ADV
ejpam-4440	236	2	(	(	PUNCT
ejpam-4440	236	3	a	a	DET
ejpam-4440	236	4	∈	∈	PROPN
ejpam-4440	236	5	a	a	PRON
ejpam-4440	236	6	and	and	CCONJ
ejpam-4440	236	7	x	x	ADJ
ejpam-4440	236	8	/∈	/∈	PUNCT
ejpam-4440	237	1	c	c	X
ejpam-4440	237	2	)	)	PUNCT
ejpam-4440	237	3	or	or	CCONJ
ejpam-4440	237	4	(	(	PUNCT
ejpam-4440	237	5	a	a	PRON
ejpam-4440	237	6	/∈	/∈	NOUN
ejpam-4440	237	7	a	a	NOUN
ejpam-4440	237	8	and	and	CCONJ
ejpam-4440	237	9	x	x	SYM
ejpam-4440	237	10	∈	∈	PROPN
ejpam-4440	237	11	c	c	NOUN
ejpam-4440	237	12	)	)	PUNCT
ejpam-4440	237	13	or	or	CCONJ
ejpam-4440	237	14	(	(	PUNCT
ejpam-4440	237	15	a	a	PRON
ejpam-4440	237	16	/∈	/∈	NOUN
ejpam-4440	237	17	a	a	NOUN
ejpam-4440	237	18	and	and	CCONJ
ejpam-4440	237	19	x	x	SYM
ejpam-4440	237	20	/∈	/∈	PUNCT
ejpam-4440	237	21	c	c	X
ejpam-4440	237	22	)	)	PUNCT
ejpam-4440	237	23	.	.	PUNCT
ejpam-4440	238	1	if	if	SCONJ
ejpam-4440	238	2	a	a	DET
ejpam-4440	238	3	∈	∈	PROPN
ejpam-4440	238	4	a	a	PRON
ejpam-4440	238	5	and	and	CCONJ
ejpam-4440	238	6	x	x	ADJ
ejpam-4440	238	7	/∈	/∈	PUNCT
ejpam-4440	239	1	c	c	X
ejpam-4440	239	2	,	,	PUNCT
ejpam-4440	239	3	then	then	ADV
ejpam-4440	239	4	there	there	PRON
ejpam-4440	239	5	exists	exist	VERB
ejpam-4440	239	6	y	y	PROPN
ejpam-4440	239	7	∈	∈	PROPN
ejpam-4440	239	8	c∩nh(x	c∩nh(x	PROPN
ejpam-4440	239	9	)	)	PUNCT
ejpam-4440	239	10	since	since	SCONJ
ejpam-4440	239	11	c	c	PROPN
ejpam-4440	239	12	is	be	AUX
ejpam-4440	239	13	a	a	DET
ejpam-4440	239	14	γ	γ	NOUN
ejpam-4440	239	15	-	-	PUNCT
ejpam-4440	239	16	set	set	NOUN
ejpam-4440	239	17	of	of	ADP
ejpam-4440	239	18	h.	h.	PROPN
ejpam-4440	239	19	hence	hence	PROPN
ejpam-4440	239	20	,	,	PUNCT
ejpam-4440	239	21	(	(	PUNCT
ejpam-4440	239	22	a	a	PRON
ejpam-4440	239	23	,	,	PUNCT
ejpam-4440	239	24	y	y	NOUN
ejpam-4440	239	25	)	)	PUNCT
ejpam-4440	239	26	∈	∈	PROPN
ejpam-4440	239	27	(	(	PUNCT
ejpam-4440	239	28	a×c)∩ng[h]((a	a×c)∩ng[h]((a	NOUN
ejpam-4440	239	29	,	,	PUNCT
ejpam-4440	239	30	x	x	NOUN
ejpam-4440	239	31	)	)	PUNCT
ejpam-4440	239	32	)	)	PUNCT
ejpam-4440	239	33	.	.	PUNCT
ejpam-4440	240	1	suppose	suppose	VERB
ejpam-4440	240	2	a	a	DET
ejpam-4440	240	3	/∈	/∈	NOUN
ejpam-4440	240	4	a	a	PRON
ejpam-4440	240	5	and	and	CCONJ
ejpam-4440	240	6	x	x	PROPN
ejpam-4440	240	7	∈	∈	PROPN
ejpam-4440	240	8	c.	c.	NOUN
ejpam-4440	240	9	since	since	SCONJ
ejpam-4440	240	10	a	a	PRON
ejpam-4440	240	11	is	be	AUX
ejpam-4440	240	12	a	a	DET
ejpam-4440	240	13	singleton	singleton	NOUN
ejpam-4440	240	14	subset	subset	NOUN
ejpam-4440	240	15	of	of	ADP
ejpam-4440	240	16	g	g	PROPN
ejpam-4440	240	17	=	=	PROPN
ejpam-4440	240	18	kn	kn	PROPN
ejpam-4440	240	19	for	for	ADP
ejpam-4440	240	20	n	n	PROPN
ejpam-4440	240	21	>	>	X
ejpam-4440	240	22	1	1	NUM
ejpam-4440	240	23	,	,	PUNCT
ejpam-4440	240	24	there	there	PRON
ejpam-4440	240	25	exists	exist	VERB
ejpam-4440	240	26	b	b	PROPN
ejpam-4440	240	27	∈	∈	PROPN
ejpam-4440	240	28	a	a	DET
ejpam-4440	240	29	∩	∩	NOUN
ejpam-4440	240	30	ng(a	ng(a	NOUN
ejpam-4440	240	31	)	)	PUNCT
ejpam-4440	240	32	.	.	PUNCT
ejpam-4440	241	1	hence	hence	ADV
ejpam-4440	241	2	,	,	PUNCT
ejpam-4440	241	3	(	(	PUNCT
ejpam-4440	241	4	b	b	NOUN
ejpam-4440	241	5	,	,	PUNCT
ejpam-4440	241	6	x	x	NOUN
ejpam-4440	241	7	)	)	PUNCT
ejpam-4440	241	8	∈	∈	PROPN
ejpam-4440	241	9	(	(	PUNCT
ejpam-4440	241	10	a	a	DET
ejpam-4440	241	11	×	×	NOUN
ejpam-4440	241	12	c	c	NOUN
ejpam-4440	241	13	)	)	PUNCT
ejpam-4440	241	14	∩	∩	NOUN
ejpam-4440	241	15	ng[h]((a	ng[h]((a	X
ejpam-4440	241	16	,	,	PUNCT
ejpam-4440	241	17	x	x	NOUN
ejpam-4440	241	18	)	)	PUNCT
ejpam-4440	241	19	)	)	PUNCT
ejpam-4440	241	20	.	.	PUNCT
ejpam-4440	242	1	also	also	ADV
ejpam-4440	242	2	,	,	PUNCT
ejpam-4440	242	3	if	if	SCONJ
ejpam-4440	242	4	a	a	PRON
ejpam-4440	242	5	/∈	/∈	NOUN
ejpam-4440	242	6	a	a	NOUN
ejpam-4440	242	7	and	and	CCONJ
ejpam-4440	242	8	x	x	ADJ
ejpam-4440	242	9	/∈	/∈	PUNCT
ejpam-4440	242	10	c	c	X
ejpam-4440	242	11	,	,	PUNCT
ejpam-4440	242	12	then	then	ADV
ejpam-4440	242	13	there	there	PRON
ejpam-4440	242	14	exists	exist	VERB
ejpam-4440	242	15	(	(	PUNCT
ejpam-4440	242	16	b	b	X
ejpam-4440	242	17	,	,	PUNCT
ejpam-4440	242	18	y	y	NOUN
ejpam-4440	242	19	)	)	PUNCT
ejpam-4440	242	20	∈	∈	PROPN
ejpam-4440	242	21	(	(	PUNCT
ejpam-4440	242	22	a×	a×	NOUN
ejpam-4440	242	23	c	c	NOUN
ejpam-4440	242	24	)	)	PUNCT
ejpam-4440	242	25	∩ng[h]((a	∩ng[h]((a	PROPN
ejpam-4440	242	26	,	,	PUNCT
ejpam-4440	242	27	x	x	NOUN
ejpam-4440	242	28	)	)	PUNCT
ejpam-4440	242	29	)	)	PUNCT
ejpam-4440	242	30	.	.	PUNCT
ejpam-4440	243	1	therefore	therefore	ADV
ejpam-4440	243	2	,	,	PUNCT
ejpam-4440	243	3	a×	a×	PROPN
ejpam-4440	243	4	c	c	PROPN
ejpam-4440	243	5	is	be	AUX
ejpam-4440	243	6	a	a	DET
ejpam-4440	243	7	γ	γ	NOUN
ejpam-4440	243	8	-	-	PUNCT
ejpam-4440	243	9	set	set	NOUN
ejpam-4440	243	10	of	of	ADP
ejpam-4440	243	11	g[h	g[h	NOUN
ejpam-4440	243	12	]	]	PUNCT
ejpam-4440	243	13	.	.	PUNCT
ejpam-4440	244	1	theorem	theorem	ADJ
ejpam-4440	244	2	10	10	NUM
ejpam-4440	244	3	.	.	PUNCT
ejpam-4440	245	1	let	let	VERB
ejpam-4440	245	2	g	g	PROPN
ejpam-4440	245	3	=	=	PROPN
ejpam-4440	245	4	kn	kn	PROPN
ejpam-4440	245	5	for	for	ADP
ejpam-4440	245	6	n	n	PROPN
ejpam-4440	245	7	>	>	SYM
ejpam-4440	245	8	1	1	NUM
ejpam-4440	245	9	and	and	CCONJ
ejpam-4440	245	10	h	h	DET
ejpam-4440	245	11	a	a	DET
ejpam-4440	245	12	nontrivial	nontrivial	ADJ
ejpam-4440	245	13	connected	connect	VERB
ejpam-4440	245	14	graph	graph	NOUN
ejpam-4440	245	15	.	.	PUNCT
ejpam-4440	246	1	a	a	DET
ejpam-4440	246	2	subset	subset	NOUN
ejpam-4440	246	3	s	s	NOUN
ejpam-4440	246	4	of	of	ADP
ejpam-4440	246	5	v	v	NOUN
ejpam-4440	246	6	(	(	PUNCT
ejpam-4440	246	7	g[h	g[h	PROPN
ejpam-4440	246	8	]	]	PUNCT
ejpam-4440	246	9	)	)	PUNCT
ejpam-4440	246	10	is	be	AUX
ejpam-4440	246	11	a	a	DET
ejpam-4440	246	12	movable	movable	ADJ
ejpam-4440	246	13	strong	strong	ADJ
ejpam-4440	246	14	resolving	resolve	VERB
ejpam-4440	246	15	dominating	dominating	NOUN
ejpam-4440	246	16	set	set	NOUN
ejpam-4440	246	17	of	of	ADP
ejpam-4440	246	18	g[h	g[h	PROPN
ejpam-4440	246	19	]	]	PUNCT
ejpam-4440	246	20	if	if	SCONJ
ejpam-4440	247	1	and	and	CCONJ
ejpam-4440	247	2	only	only	ADV
ejpam-4440	247	3	if	if	SCONJ
ejpam-4440	247	4	s	s	VERB
ejpam-4440	247	5	=	=	SYM
ejpam-4440	247	6	v	v	NOUN
ejpam-4440	247	7	(	(	PUNCT
ejpam-4440	247	8	g[h	g[h	PROPN
ejpam-4440	247	9	]	]	PUNCT
ejpam-4440	247	10	)	)	PUNCT
ejpam-4440	247	11	\	\	PUNCT
ejpam-4440	247	12	(	(	PUNCT
ejpam-4440	247	13	a×c	a×c	PROPN
ejpam-4440	247	14	)	)	PUNCT
ejpam-4440	247	15	,	,	PUNCT
ejpam-4440	247	16	where	where	SCONJ
ejpam-4440	247	17	a	a	PRON
ejpam-4440	247	18	is	be	AUX
ejpam-4440	247	19	a	a	DET
ejpam-4440	247	20	subset	subset	NOUN
ejpam-4440	247	21	of	of	ADP
ejpam-4440	247	22	v	v	NOUN
ejpam-4440	247	23	(	(	PUNCT
ejpam-4440	247	24	g	g	NOUN
ejpam-4440	247	25	)	)	PUNCT
ejpam-4440	247	26	and	and	CCONJ
ejpam-4440	247	27	c	c	NOUN
ejpam-4440	247	28	=	=	SYM
ejpam-4440	247	29	∅	∅	NOUN
ejpam-4440	247	30	or	or	CCONJ
ejpam-4440	247	31	a	a	PRON
ejpam-4440	247	32	is	be	AUX
ejpam-4440	247	33	a	a	DET
ejpam-4440	247	34	singleton	singleton	NOUN
ejpam-4440	247	35	subset	subset	NOUN
ejpam-4440	247	36	of	of	ADP
ejpam-4440	247	37	v	v	PROPN
ejpam-4440	247	38	(	(	PUNCT
ejpam-4440	247	39	g	g	NOUN
ejpam-4440	247	40	)	)	PUNCT
ejpam-4440	247	41	and	and	CCONJ
ejpam-4440	247	42	c	c	PROPN
ejpam-4440	247	43	is	be	AUX
ejpam-4440	247	44	a	a	DET
ejpam-4440	247	45	γ	γ	NOUN
ejpam-4440	247	46	-	-	PUNCT
ejpam-4440	247	47	set	set	NOUN
ejpam-4440	247	48	of	of	ADP
ejpam-4440	247	49	h	h	NOUN
ejpam-4440	247	50	if	if	SCONJ
ejpam-4440	247	51	γ(h	γ(h	NOUN
ejpam-4440	247	52	)	)	PUNCT
ejpam-4440	247	53	=	=	SYM
ejpam-4440	248	1	1	1	X
ejpam-4440	248	2	.	.	PUNCT
ejpam-4440	248	3	proof	proof	NOUN
ejpam-4440	248	4	.	.	PUNCT
ejpam-4440	249	1	suppose	suppose	VERB
ejpam-4440	249	2	s	s	NOUN
ejpam-4440	249	3	is	be	AUX
ejpam-4440	249	4	a	a	DET
ejpam-4440	249	5	movable	movable	ADJ
ejpam-4440	249	6	strong	strong	ADJ
ejpam-4440	249	7	resolving	resolve	VERB
ejpam-4440	249	8	dominating	dominating	NOUN
ejpam-4440	249	9	set	set	NOUN
ejpam-4440	249	10	of	of	ADP
ejpam-4440	249	11	g[h	g[h	NOUN
ejpam-4440	249	12	]	]	PUNCT
ejpam-4440	249	13	.	.	PUNCT
ejpam-4440	250	1	since	since	SCONJ
ejpam-4440	250	2	diam(g[h	diam(g[h	PROPN
ejpam-4440	250	3	]	]	PUNCT
ejpam-4440	250	4	)	)	PUNCT
ejpam-4440	250	5	=	=	SYM
ejpam-4440	250	6	2	2	X
ejpam-4440	250	7	,	,	PUNCT
ejpam-4440	250	8	by	by	ADP
ejpam-4440	250	9	theorem	theorem	NOUN
ejpam-4440	250	10	4	4	NUM
ejpam-4440	250	11	,	,	PUNCT
ejpam-4440	250	12	s	s	PART
ejpam-4440	250	13	=	=	SYM
ejpam-4440	250	14	v	v	NOUN
ejpam-4440	250	15	(	(	PUNCT
ejpam-4440	250	16	g[h	g[h	PROPN
ejpam-4440	250	17	]	]	PUNCT
ejpam-4440	250	18	)	)	PUNCT
ejpam-4440	250	19	\	\	PUNCT
ejpam-4440	251	1	(	(	PUNCT
ejpam-4440	251	2	a×	a×	NOUN
ejpam-4440	251	3	c	c	X
ejpam-4440	251	4	)	)	PUNCT
ejpam-4440	251	5	where	where	SCONJ
ejpam-4440	251	6	a×	a×	PROPN
ejpam-4440	251	7	c	c	NOUN
ejpam-4440	251	8	=	=	NOUN
ejpam-4440	251	9	∅	∅	NOUN
ejpam-4440	251	10	or	or	CCONJ
ejpam-4440	251	11	a×	a×	NOUN
ejpam-4440	251	12	c	c	NOUN
ejpam-4440	251	13	is	be	AUX
ejpam-4440	251	14	a	a	DET
ejpam-4440	251	15	γ	γ	NOUN
ejpam-4440	251	16	-	-	PUNCT
ejpam-4440	251	17	set	set	NOUN
ejpam-4440	251	18	of	of	ADP
ejpam-4440	251	19	g[h	g[h	NOUN
ejpam-4440	251	20	]	]	PUNCT
ejpam-4440	251	21	if	if	SCONJ
ejpam-4440	251	22	γ(g[h	γ(g[h	NOUN
ejpam-4440	251	23	]	]	X
ejpam-4440	251	24	)	)	PUNCT
ejpam-4440	251	25	=	=	SYM
ejpam-4440	252	1	1	1	X
ejpam-4440	252	2	.	.	PUNCT
ejpam-4440	252	3	by	by	ADP
ejpam-4440	252	4	lemma	lemma	PROPN
ejpam-4440	252	5	4	4	NUM
ejpam-4440	252	6	,	,	PUNCT
ejpam-4440	252	7	a	a	PRON
ejpam-4440	252	8	is	be	AUX
ejpam-4440	252	9	a	a	DET
ejpam-4440	252	10	singleton	singleton	NOUN
ejpam-4440	252	11	subset	subset	NOUN
ejpam-4440	252	12	of	of	ADP
ejpam-4440	252	13	v	v	PROPN
ejpam-4440	252	14	(	(	PUNCT
ejpam-4440	252	15	g	g	NOUN
ejpam-4440	252	16	)	)	PUNCT
ejpam-4440	252	17	and	and	CCONJ
ejpam-4440	252	18	c	c	PROPN
ejpam-4440	252	19	is	be	AUX
ejpam-4440	252	20	a	a	DET
ejpam-4440	252	21	γ	γ	NOUN
ejpam-4440	252	22	-	-	PUNCT
ejpam-4440	252	23	set	set	NOUN
ejpam-4440	252	24	of	of	ADP
ejpam-4440	252	25	h	h	NOUN
ejpam-4440	252	26	if	if	SCONJ
ejpam-4440	252	27	γ(h	γ(h	NOUN
ejpam-4440	252	28	)	)	PUNCT
ejpam-4440	252	29	=	=	PUNCT
ejpam-4440	253	1	1	1	X
ejpam-4440	253	2	.	.	X
ejpam-4440	253	3	for	for	ADP
ejpam-4440	253	4	the	the	DET
ejpam-4440	253	5	converse	converse	NOUN
ejpam-4440	253	6	,	,	PUNCT
ejpam-4440	253	7	suppose	suppose	VERB
ejpam-4440	253	8	s	s	VERB
ejpam-4440	253	9	=	=	SYM
ejpam-4440	253	10	v	v	PROPN
ejpam-4440	253	11	(	(	PUNCT
ejpam-4440	253	12	g[h])\(a×c	g[h])\(a×c	NOUN
ejpam-4440	253	13	)	)	PUNCT
ejpam-4440	253	14	,	,	PUNCT
ejpam-4440	253	15	where	where	SCONJ
ejpam-4440	253	16	a	a	DET
ejpam-4440	253	17	⊆	⊆	NUM
ejpam-4440	253	18	v	v	NOUN
ejpam-4440	253	19	(	(	PUNCT
ejpam-4440	253	20	g	g	NOUN
ejpam-4440	253	21	)	)	PUNCT
ejpam-4440	253	22	and	and	CCONJ
ejpam-4440	253	23	c	c	NOUN
ejpam-4440	253	24	=	=	SYM
ejpam-4440	253	25	∅	∅	NOUN
ejpam-4440	253	26	or	or	CCONJ
ejpam-4440	253	27	a	a	PRON
ejpam-4440	253	28	is	be	AUX
ejpam-4440	253	29	a	a	DET
ejpam-4440	253	30	singleton	singleton	NOUN
ejpam-4440	253	31	subset	subset	NOUN
ejpam-4440	253	32	of	of	ADP
ejpam-4440	253	33	v	v	PROPN
ejpam-4440	253	34	(	(	PUNCT
ejpam-4440	253	35	g	g	NOUN
ejpam-4440	253	36	)	)	PUNCT
ejpam-4440	253	37	and	and	CCONJ
ejpam-4440	253	38	c	c	PROPN
ejpam-4440	253	39	is	be	AUX
ejpam-4440	253	40	a	a	DET
ejpam-4440	253	41	γ	γ	NOUN
ejpam-4440	253	42	-	-	PUNCT
ejpam-4440	253	43	set	set	NOUN
ejpam-4440	253	44	of	of	ADP
ejpam-4440	253	45	h	h	NOUN
ejpam-4440	253	46	if	if	SCONJ
ejpam-4440	253	47	γ(h	γ(h	NOUN
ejpam-4440	253	48	)	)	PUNCT
ejpam-4440	253	49	=	=	PUNCT
ejpam-4440	254	1	1	1	X
ejpam-4440	254	2	.	.	PUNCT
ejpam-4440	255	1	if	if	SCONJ
ejpam-4440	255	2	a	a	DET
ejpam-4440	255	3	⊆	⊆	NUM
ejpam-4440	255	4	v	v	NOUN
ejpam-4440	255	5	(	(	PUNCT
ejpam-4440	255	6	g	g	NOUN
ejpam-4440	255	7	)	)	PUNCT
ejpam-4440	255	8	and	and	CCONJ
ejpam-4440	255	9	c	c	NOUN
ejpam-4440	255	10	=	=	SYM
ejpam-4440	255	11	∅	∅	NOUN
ejpam-4440	255	12	,	,	PUNCT
ejpam-4440	255	13	then	then	ADV
ejpam-4440	255	14	a	a	DET
ejpam-4440	255	15	×	×	NOUN
ejpam-4440	255	16	c	c	NOUN
ejpam-4440	255	17	=	=	PUNCT
ejpam-4440	255	18	∅.	∅.	ADP
ejpam-4440	255	19	hence	hence	ADV
ejpam-4440	255	20	,	,	PUNCT
ejpam-4440	255	21	s	s	NOUN
ejpam-4440	255	22	=	=	SYM
ejpam-4440	255	23	v	v	NOUN
ejpam-4440	255	24	(	(	PUNCT
ejpam-4440	255	25	g[h	g[h	PROPN
ejpam-4440	255	26	]	]	PUNCT
ejpam-4440	255	27	)	)	PUNCT
ejpam-4440	255	28	is	be	AUX
ejpam-4440	255	29	a	a	DET
ejpam-4440	255	30	movable	movable	ADJ
ejpam-4440	255	31	strong	strong	ADJ
ejpam-4440	255	32	resolving	resolve	VERB
ejpam-4440	255	33	dominating	dominating	NOUN
ejpam-4440	255	34	set	set	NOUN
ejpam-4440	255	35	of	of	ADP
ejpam-4440	255	36	g[h	g[h	NOUN
ejpam-4440	255	37	]	]	PUNCT
ejpam-4440	255	38	.	.	PUNCT
ejpam-4440	256	1	on	on	ADP
ejpam-4440	256	2	the	the	DET
ejpam-4440	256	3	other	other	ADJ
ejpam-4440	256	4	hand	hand	NOUN
ejpam-4440	256	5	,	,	PUNCT
ejpam-4440	256	6	if	if	SCONJ
ejpam-4440	256	7	a	a	PRON
ejpam-4440	256	8	is	be	AUX
ejpam-4440	256	9	a	a	DET
ejpam-4440	256	10	singleton	singleton	NOUN
ejpam-4440	256	11	subset	subset	NOUN
ejpam-4440	256	12	of	of	ADP
ejpam-4440	256	13	v	v	PROPN
ejpam-4440	256	14	(	(	PUNCT
ejpam-4440	256	15	g	g	NOUN
ejpam-4440	256	16	)	)	PUNCT
ejpam-4440	256	17	and	and	CCONJ
ejpam-4440	256	18	c	c	PROPN
ejpam-4440	256	19	is	be	AUX
ejpam-4440	256	20	γ	γ	NOUN
ejpam-4440	256	21	-	-	PUNCT
ejpam-4440	256	22	set	set	NOUN
ejpam-4440	256	23	of	of	ADP
ejpam-4440	256	24	h	h	NOUN
ejpam-4440	256	25	if	if	SCONJ
ejpam-4440	256	26	γ(h	γ(h	NOUN
ejpam-4440	256	27	)	)	PUNCT
ejpam-4440	256	28	=	=	SYM
ejpam-4440	257	1	1	1	NUM
ejpam-4440	257	2	,	,	PUNCT
ejpam-4440	257	3	then	then	ADV
ejpam-4440	257	4	a×	a×	PROPN
ejpam-4440	257	5	c	c	PROPN
ejpam-4440	257	6	is	be	AUX
ejpam-4440	257	7	a	a	DET
ejpam-4440	257	8	γ	γ	NOUN
ejpam-4440	257	9	-	-	PUNCT
ejpam-4440	257	10	set	set	NOUN
ejpam-4440	257	11	of	of	ADP
ejpam-4440	257	12	g[h	g[h	NOUN
ejpam-4440	257	13	]	]	PUNCT
ejpam-4440	257	14	if	if	SCONJ
ejpam-4440	257	15	γ(g[h	γ(g[h	NOUN
ejpam-4440	257	16	]	]	X
ejpam-4440	257	17	)	)	PUNCT
ejpam-4440	257	18	=	=	SYM
ejpam-4440	258	1	1	1	X
ejpam-4440	258	2	.	.	PUNCT
ejpam-4440	258	3	by	by	ADP
ejpam-4440	258	4	theorem	theorem	NOUN
ejpam-4440	258	5	4	4	NUM
ejpam-4440	258	6	,	,	PUNCT
ejpam-4440	258	7	s	s	PART
ejpam-4440	258	8	=	=	SYM
ejpam-4440	258	9	v	v	NOUN
ejpam-4440	258	10	(	(	PUNCT
ejpam-4440	258	11	g[h	g[h	PROPN
ejpam-4440	258	12	]	]	PUNCT
ejpam-4440	258	13	)	)	PUNCT
ejpam-4440	258	14	\	\	PUNCT
ejpam-4440	259	1	(	(	PUNCT
ejpam-4440	259	2	a×	a×	NOUN
ejpam-4440	259	3	c	c	X
ejpam-4440	259	4	)	)	PUNCT
ejpam-4440	259	5	is	be	AUX
ejpam-4440	259	6	a	a	DET
ejpam-4440	259	7	movable	movable	ADJ
ejpam-4440	259	8	strong	strong	ADJ
ejpam-4440	259	9	resolving	resolve	VERB
ejpam-4440	259	10	dominating	dominating	NOUN
ejpam-4440	259	11	set	set	NOUN
ejpam-4440	259	12	of	of	ADP
ejpam-4440	259	13	g[h	g[h	NOUN
ejpam-4440	259	14	]	]	PUNCT
ejpam-4440	259	15	.	.	PUNCT
ejpam-4440	260	1	as	as	ADP
ejpam-4440	260	2	a	a	DET
ejpam-4440	260	3	consequence	consequence	NOUN
ejpam-4440	260	4	of	of	ADP
ejpam-4440	260	5	theorem	theorem	NOUN
ejpam-4440	260	6	10	10	NUM
ejpam-4440	260	7	,	,	PUNCT
ejpam-4440	260	8	the	the	DET
ejpam-4440	260	9	next	next	ADJ
ejpam-4440	260	10	result	result	NOUN
ejpam-4440	260	11	follows	follow	VERB
ejpam-4440	260	12	.	.	PUNCT
ejpam-4440	261	1	corollary	corollary	ADJ
ejpam-4440	261	2	5	5	NUM
ejpam-4440	261	3	.	.	PUNCT
ejpam-4440	262	1	let	let	VERB
ejpam-4440	262	2	g	g	PROPN
ejpam-4440	262	3	=	=	PROPN
ejpam-4440	262	4	kn	kn	PROPN
ejpam-4440	262	5	for	for	ADP
ejpam-4440	262	6	n	n	PROPN
ejpam-4440	262	7	>	>	SYM
ejpam-4440	262	8	1	1	NUM
ejpam-4440	262	9	and	and	CCONJ
ejpam-4440	262	10	h	h	DET
ejpam-4440	262	11	a	a	DET
ejpam-4440	262	12	nontrivial	nontrivial	ADJ
ejpam-4440	262	13	connected	connect	VERB
ejpam-4440	262	14	graph	graph	NOUN
ejpam-4440	262	15	of	of	ADP
ejpam-4440	262	16	order	order	NOUN
ejpam-4440	262	17	m.	m.	NOUN
ejpam-4440	262	18	then	then	ADV
ejpam-4440	262	19	γ1msr(g[h	γ1msr(g[h	PROPN
ejpam-4440	262	20	]	]	PUNCT
ejpam-4440	262	21	)	)	PUNCT
ejpam-4440	263	1	=	=	PRON
ejpam-4440	263	2	{	{	PUNCT
ejpam-4440	263	3	mn	mn	NOUN
ejpam-4440	263	4	,	,	PUNCT
ejpam-4440	263	5	if	if	SCONJ
ejpam-4440	263	6	γ(h	γ(h	NOUN
ejpam-4440	263	7	)	)	PUNCT
ejpam-4440	263	8	̸=	̸=	PROPN
ejpam-4440	263	9	1	1	NUM
ejpam-4440	263	10	mn−	mn−	PROPN
ejpam-4440	263	11	1	1	NUM
ejpam-4440	263	12	,	,	PUNCT
ejpam-4440	263	13	if	if	SCONJ
ejpam-4440	263	14	γ(h	γ(h	NOUN
ejpam-4440	263	15	)	)	PUNCT
ejpam-4440	263	16	=	=	SYM
ejpam-4440	264	1	1	1	X
ejpam-4440	264	2	.	.	PUNCT
ejpam-4440	264	3	acknowledgements	acknowledgement	NOUN
ejpam-4440	264	4	this	this	DET
ejpam-4440	264	5	research	research	NOUN
ejpam-4440	264	6	is	be	AUX
ejpam-4440	264	7	funded	fund	VERB
ejpam-4440	264	8	by	by	ADP
ejpam-4440	264	9	the	the	DET
ejpam-4440	264	10	department	department	PROPN
ejpam-4440	264	11	of	of	ADP
ejpam-4440	264	12	science	science	NOUN
ejpam-4440	264	13	and	and	CCONJ
ejpam-4440	264	14	technology	technology	NOUN
ejpam-4440	264	15	accelerated	accelerate	VERB
ejpam-4440	264	16	science	science	NOUN
ejpam-4440	264	17	and	and	CCONJ
ejpam-4440	264	18	technology	technology	NOUN
ejpam-4440	264	19	human	human	ADJ
ejpam-4440	264	20	resource	resource	NOUN
ejpam-4440	264	21	development	development	NOUN
ejpam-4440	264	22	program	program	NOUN
ejpam-4440	264	23	(	(	PUNCT
ejpam-4440	264	24	dost	dost	NOUN
ejpam-4440	264	25	-	-	PUNCT
ejpam-4440	264	26	asthrdp	asthrdp	NOUN
ejpam-4440	264	27	)	)	PUNCT
ejpam-4440	264	28	,	,	PUNCT
ejpam-4440	264	29	philippines	philippine	NOUN
ejpam-4440	264	30	.	.	PUNCT
ejpam-4440	265	1	references	reference	NOUN
ejpam-4440	265	2	1210	1210	NUM
ejpam-4440	265	3	references	reference	NOUN
ejpam-4440	265	4	[	[	X
ejpam-4440	265	5	1	1	NUM
ejpam-4440	265	6	]	]	PUNCT
ejpam-4440	265	7	p.	p.	NOUN
ejpam-4440	265	8	acal	acal	ADJ
ejpam-4440	265	9	and	and	CCONJ
ejpam-4440	265	10	h.	h.	PROPN
ejpam-4440	265	11	rara	rara	PROPN
ejpam-4440	265	12	.	.	PUNCT
ejpam-4440	266	1	the	the	DET
ejpam-4440	266	2	strong	strong	ADJ
ejpam-4440	266	3	connected	connected	ADJ
ejpam-4440	266	4	metric	metric	ADJ
ejpam-4440	266	5	dimension	dimension	NOUN
ejpam-4440	266	6	in	in	ADP
ejpam-4440	266	7	the	the	DET
ejpam-4440	266	8	join	join	NOUN
ejpam-4440	266	9	and	and	CCONJ
ejpam-4440	266	10	corona	corona	NOUN
ejpam-4440	266	11	of	of	ADP
ejpam-4440	266	12	graphs	graph	NOUN
ejpam-4440	266	13	.	.	PUNCT
ejpam-4440	267	1	advances	advance	NOUN
ejpam-4440	267	2	and	and	CCONJ
ejpam-4440	267	3	applications	application	NOUN
ejpam-4440	267	4	in	in	ADP
ejpam-4440	267	5	discrete	discrete	ADJ
ejpam-4440	267	6	mathematics	mathematic	NOUN
ejpam-4440	267	7	,	,	PUNCT
ejpam-4440	267	8	21(1):91–101	21(1):91–101	NUM
ejpam-4440	267	9	,	,	PUNCT
ejpam-4440	267	10	2019	2019	NUM
ejpam-4440	267	11	.	.	PUNCT
ejpam-4440	268	1	[	[	X
ejpam-4440	268	2	2	2	X
ejpam-4440	268	3	]	]	X
ejpam-4440	268	4	g.	g.	PROPN
ejpam-4440	268	5	chartrand	chartrand	PROPN
ejpam-4440	268	6	andl	andl	PROPN
ejpam-4440	268	7	.	.	PUNCT
ejpam-4440	269	1	eroh	eroh	PROPN
ejpam-4440	269	2	,	,	PUNCT
ejpam-4440	269	3	m.	m.	NOUN
ejpam-4440	269	4	johnson	johnson	PROPN
ejpam-4440	269	5	,	,	PUNCT
ejpam-4440	269	6	and	and	CCONJ
ejpam-4440	269	7	o.	o.	PROPN
ejpam-4440	269	8	oellermann	oellermann	PROPN
ejpam-4440	269	9	.	.	PUNCT
ejpam-4440	270	1	resolvability	resolvability	NOUN
ejpam-4440	270	2	in	in	ADP
ejpam-4440	270	3	graphs	graph	NOUN
ejpam-4440	270	4	and	and	CCONJ
ejpam-4440	270	5	the	the	DET
ejpam-4440	270	6	metric	metric	ADJ
ejpam-4440	270	7	dimension	dimension	NOUN
ejpam-4440	270	8	of	of	ADP
ejpam-4440	270	9	a	a	DET
ejpam-4440	270	10	graph	graph	NOUN
ejpam-4440	270	11	.	.	PUNCT
ejpam-4440	271	1	discrete	discrete	ADJ
ejpam-4440	271	2	applied	apply	VERB
ejpam-4440	271	3	mathematics	mathematic	NOUN
ejpam-4440	271	4	,	,	PUNCT
ejpam-4440	271	5	105(13):99–113	105(13):99–113	NUM
ejpam-4440	271	6	.	.	PUNCT
ejpam-4440	272	1	[	[	X
ejpam-4440	272	2	3	3	X
ejpam-4440	272	3	]	]	X
ejpam-4440	272	4	r.	r.	PROPN
ejpam-4440	272	5	bailey	bailey	PROPN
ejpam-4440	272	6	and	and	CCONJ
ejpam-4440	272	7	p.	p.	PROPN
ejpam-4440	272	8	cameron	cameron	PROPN
ejpam-4440	272	9	.	.	PUNCT
ejpam-4440	273	1	base	base	PROPN
ejpam-4440	273	2	size	size	NOUN
ejpam-4440	273	3	,	,	PUNCT
ejpam-4440	273	4	metric	metric	ADJ
ejpam-4440	273	5	dimension	dimension	NOUN
ejpam-4440	273	6	and	and	CCONJ
ejpam-4440	273	7	other	other	ADJ
ejpam-4440	273	8	invariants	invariant	NOUN
ejpam-4440	273	9	of	of	ADP
ejpam-4440	273	10	groups	group	NOUN
ejpam-4440	273	11	and	and	CCONJ
ejpam-4440	273	12	graphs	graph	NOUN
ejpam-4440	273	13	,	,	PUNCT
ejpam-4440	273	14	volume	volume	NOUN
ejpam-4440	273	15	43(2	43(2	NUM
ejpam-4440	273	16	)	)	PUNCT
ejpam-4440	273	17	.	.	PUNCT
ejpam-4440	274	1	2011	2011	NUM
ejpam-4440	274	2	.	.	PUNCT
ejpam-4440	275	1	[	[	X
ejpam-4440	275	2	4	4	NUM
ejpam-4440	275	3	]	]	X
ejpam-4440	275	4	c.	c.	PROPN
ejpam-4440	275	5	berge	berge	PROPN
ejpam-4440	275	6	.	.	PUNCT
ejpam-4440	276	1	theorie	theorie	PROPN
ejpam-4440	276	2	des	des	PROPN
ejpam-4440	276	3	graphes	graphes	PROPN
ejpam-4440	276	4	et	et	PROPN
ejpam-4440	276	5	ses	ses	PROPN
ejpam-4440	276	6	applications	application	NOUN
ejpam-4440	276	7	.	.	PUNCT
ejpam-4440	277	1	metheun	metheun	NOUN
ejpam-4440	277	2	and	and	CCONJ
ejpam-4440	277	3	wiley	wiley	PROPN
ejpam-4440	277	4	,	,	PUNCT
ejpam-4440	277	5	london	london	PROPN
ejpam-4440	277	6	and	and	CCONJ
ejpam-4440	277	7	new	new	PROPN
ejpam-4440	277	8	york	york	PROPN
ejpam-4440	277	9	,	,	PUNCT
ejpam-4440	277	10	1962	1962	NUM
ejpam-4440	277	11	.	.	PUNCT
ejpam-4440	278	1	[	[	X
ejpam-4440	278	2	5	5	X
ejpam-4440	278	3	]	]	PUNCT
ejpam-4440	278	4	g.	g.	PROPN
ejpam-4440	278	5	chappell	chappell	PROPN
ejpam-4440	278	6	,	,	PUNCT
ejpam-4440	278	7	j.	j.	PROPN
ejpam-4440	278	8	gimbel	gimbel	PROPN
ejpam-4440	278	9	,	,	PUNCT
ejpam-4440	278	10	and	and	CCONJ
ejpam-4440	278	11	c.	c.	PROPN
ejpam-4440	278	12	hartman	hartman	PROPN
ejpam-4440	278	13	.	.	PUNCT
ejpam-4440	279	1	bounds	bound	VERB
ejpam-4440	279	2	on	on	ADP
ejpam-4440	279	3	the	the	DET
ejpam-4440	279	4	metric	metric	ADJ
ejpam-4440	279	5	and	and	CCONJ
ejpam-4440	279	6	partition	partition	NOUN
ejpam-4440	279	7	dimensions	dimension	NOUN
ejpam-4440	279	8	of	of	ADP
ejpam-4440	279	9	a	a	DET
ejpam-4440	279	10	graph	graph	NOUN
ejpam-4440	279	11	.	.	PUNCT
ejpam-4440	280	1	ars	ars	PROPN
ejpam-4440	280	2	combinatoria	combinatoria	PROPN
ejpam-4440	280	3	,	,	PUNCT
ejpam-4440	280	4	88:349–366	88:349–366	PROPN
ejpam-4440	280	5	.	.	PUNCT
ejpam-4440	281	1	[	[	X
ejpam-4440	281	2	6	6	NUM
ejpam-4440	281	3	]	]	PUNCT
ejpam-4440	281	4	domke	domke	PROPN
ejpam-4440	281	5	g.s	g.s	PROPN
ejpam-4440	281	6	.	.	PROPN
ejpam-4440	281	7	,	,	PUNCT
ejpam-4440	281	8	hattingh	hattingh	PROPN
ejpam-4440	281	9	j.s	j.s	PROPN
ejpam-4440	281	10	,	,	PUNCT
ejpam-4440	281	11	hedetniemi	hedetniemi	ADP
ejpam-4440	281	12	s.t	s.t	PROPN
ejpam-4440	281	13	.	.	PROPN
ejpam-4440	281	14	,	,	PUNCT
ejpam-4440	281	15	laskar	laskar	PROPN
ejpam-4440	281	16	r.c	r.c	PROPN
ejpam-4440	281	17	.	.	PROPN
ejpam-4440	281	18	,	,	PUNCT
ejpam-4440	281	19	and	and	CCONJ
ejpam-4440	281	20	markus	marku	NOUN
ejpam-4440	281	21	.	.	PUNCT
ejpam-4440	282	1	restrained	restrained	ADJ
ejpam-4440	282	2	domination	domination	NOUN
ejpam-4440	282	3	in	in	ADP
ejpam-4440	282	4	graphs	graph	NOUN
ejpam-4440	282	5	,	,	PUNCT
ejpam-4440	282	6	volume	volume	NOUN
ejpam-4440	282	7	203	203	NUM
ejpam-4440	282	8	.	.	PUNCT
ejpam-4440	283	1	discrete	discrete	ADJ
ejpam-4440	283	2	mathematics	mathematic	NOUN
ejpam-4440	283	3	,	,	PUNCT
ejpam-4440	283	4	1999	1999	NUM
ejpam-4440	283	5	.	.	PUNCT
ejpam-4440	284	1	[	[	X
ejpam-4440	284	2	7	7	X
ejpam-4440	284	3	]	]	PUNCT
ejpam-4440	284	4	m.	m.	NOUN
ejpam-4440	284	5	johnson	johnson	PROPN
ejpam-4440	284	6	.	.	PUNCT
ejpam-4440	284	7	browsable	browsable	ADJ
ejpam-4440	284	8	structure	structure	NOUN
ejpam-4440	284	9	-	-	PUNCT
ejpam-4440	284	10	activity	activity	NOUN
ejpam-4440	284	11	datasets	dataset	NOUN
ejpam-4440	284	12	.	.	PUNCT
ejpam-4440	285	1	advances	advance	NOUN
ejpam-4440	285	2	in	in	ADP
ejpam-4440	285	3	molecular	molecular	ADJ
ejpam-4440	285	4	similarity	similarity	NOUN
ejpam-4440	285	5	,	,	PUNCT
ejpam-4440	285	6	1998	1998	NUM
ejpam-4440	285	7	.	.	PUNCT
ejpam-4440	286	1	[	[	X
ejpam-4440	286	2	8	8	NUM
ejpam-4440	286	3	]	]	X
ejpam-4440	286	4	d.	d.	PROPN
ejpam-4440	286	5	kuziak	kuziak	PROPN
ejpam-4440	286	6	,	,	PUNCT
ejpam-4440	286	7	i.	i.	PROPN
ejpam-4440	286	8	yero	yero	PROPN
ejpam-4440	286	9	,	,	PUNCT
ejpam-4440	286	10	and	and	CCONJ
ejpam-4440	286	11	j.	j.	PROPN
ejpam-4440	286	12	rodriguez	rodriguez	PROPN
ejpam-4440	286	13	-	-	PUNCT
ejpam-4440	286	14	velasquez	velasquez	PROPN
ejpam-4440	286	15	.	.	PUNCT
ejpam-4440	286	16	closed	close	VERB
ejpam-4440	286	17	formuale	formuale	NOUN
ejpam-4440	286	18	for	for	ADP
ejpam-4440	286	19	the	the	DET
ejpam-4440	286	20	strong	strong	ADJ
ejpam-4440	286	21	metric	metric	ADJ
ejpam-4440	286	22	dimension	dimension	NOUN
ejpam-4440	286	23	of	of	ADP
ejpam-4440	286	24	lexicographic	lexicographic	ADJ
ejpam-4440	286	25	product	product	NOUN
ejpam-4440	286	26	graphs	graph	NOUN
ejpam-4440	286	27	,	,	PUNCT
ejpam-4440	286	28	volume	volume	NOUN
ejpam-4440	286	29	36	36	NUM
ejpam-4440	286	30	.	.	NOUN
ejpam-4440	286	31	2016	2016	NUM
ejpam-4440	286	32	.	.	PUNCT
ejpam-4440	287	1	[	[	X
ejpam-4440	287	2	9	9	NUM
ejpam-4440	287	3	]	]	PUNCT
ejpam-4440	287	4	k.	k.	PROPN
ejpam-4440	287	5	liu	liu	PROPN
ejpam-4440	287	6	and	and	CCONJ
ejpam-4440	287	7	n.	n.	PROPN
ejpam-4440	287	8	abu	abu	PROPN
ejpam-4440	287	9	-	-	PUNCT
ejpam-4440	287	10	ghazaleh	ghazaleh	PROPN
ejpam-4440	287	11	.	.	PUNCT
ejpam-4440	288	1	virtual	virtual	ADJ
ejpam-4440	288	2	coordinate	coordinate	NOUN
ejpam-4440	288	3	backtracking	backtrack	VERB
ejpam-4440	288	4	for	for	ADP
ejpam-4440	288	5	void	void	ADJ
ejpam-4440	288	6	traversal	traversal	NOUN
ejpam-4440	288	7	in	in	ADP
ejpam-4440	288	8	geographic	geographic	ADJ
ejpam-4440	288	9	routing	routing	NOUN
ejpam-4440	288	10	.	.	PUNCT
ejpam-4440	289	1	lecture	lecture	NOUN
ejpam-4440	289	2	notes	note	NOUN
ejpam-4440	289	3	in	in	ADP
ejpam-4440	289	4	comput	comput	NOUN
ejpam-4440	289	5	.	.	PUNCT
ejpam-4440	290	1	sci	sci	PROPN
ejpam-4440	290	2	.	.	PROPN
ejpam-4440	290	3	,	,	PUNCT
ejpam-4440	290	4	4104	4104	NUM
ejpam-4440	290	5	,	,	PUNCT
ejpam-4440	290	6	2006	2006	NUM
ejpam-4440	290	7	.	.	PUNCT
ejpam-4440	291	1	[	[	X
ejpam-4440	291	2	10	10	NUM
ejpam-4440	291	3	]	]	X
ejpam-4440	291	4	g.	g.	PROPN
ejpam-4440	291	5	monsanto	monsanto	PROPN
ejpam-4440	291	6	,	,	PUNCT
ejpam-4440	291	7	p.	p.	NOUN
ejpam-4440	291	8	acal	acal	ADJ
ejpam-4440	291	9	,	,	PUNCT
ejpam-4440	291	10	and	and	CCONJ
ejpam-4440	291	11	h.	h.	PROPN
ejpam-4440	291	12	rara	rara	PROPN
ejpam-4440	291	13	.	.	PUNCT
ejpam-4440	292	1	on	on	ADP
ejpam-4440	292	2	strong	strong	ADJ
ejpam-4440	292	3	resolving	resolving	NOUN
ejpam-4440	292	4	domination	domination	NOUN
ejpam-4440	292	5	in	in	ADP
ejpam-4440	292	6	the	the	DET
ejpam-4440	292	7	join	join	NOUN
ejpam-4440	292	8	and	and	CCONJ
ejpam-4440	292	9	corona	corona	NOUN
ejpam-4440	292	10	of	of	ADP
ejpam-4440	292	11	graphs	graph	NOUN
ejpam-4440	292	12	.	.	PUNCT
ejpam-4440	293	1	european	european	ADJ
ejpam-4440	293	2	journal	journal	PROPN
ejpam-4440	293	3	of	of	ADP
ejpam-4440	293	4	pure	pure	ADJ
ejpam-4440	293	5	and	and	CCONJ
ejpam-4440	293	6	applied	applied	ADJ
ejpam-4440	293	7	mathematics	mathematic	NOUN
ejpam-4440	293	8	,	,	PUNCT
ejpam-4440	293	9	13(1):170	13(1):170	NUM
ejpam-4440	293	10	–	–	PUNCT
ejpam-4440	293	11	179	179	NUM
ejpam-4440	293	12	,	,	PUNCT
ejpam-4440	293	13	2020	2020	NUM
ejpam-4440	293	14	.	.	PUNCT
ejpam-4440	294	1	[	[	X
ejpam-4440	294	2	11	11	NUM
ejpam-4440	294	3	]	]	X
ejpam-4440	294	4	o.	o.	NOUN
ejpam-4440	294	5	oellermann	oellermann	PROPN
ejpam-4440	294	6	and	and	CCONJ
ejpam-4440	294	7	j.	j.	PROPN
ejpam-4440	294	8	peters	peters	PROPN
ejpam-4440	294	9	-	-	PUNCT
ejpam-4440	294	10	fransen	fransen	PROPN
ejpam-4440	294	11	.	.	PUNCT
ejpam-4440	295	1	the	the	DET
ejpam-4440	295	2	strong	strong	ADJ
ejpam-4440	295	3	metric	metric	ADJ
ejpam-4440	295	4	dimension	dimension	NOUN
ejpam-4440	295	5	of	of	ADP
ejpam-4440	295	6	graphs	graph	NOUN
ejpam-4440	295	7	and	and	CCONJ
ejpam-4440	295	8	digraphs	digraph	NOUN
ejpam-4440	295	9	.	.	PUNCT
ejpam-4440	296	1	discrete	discrete	ADJ
ejpam-4440	296	2	mathematics	mathematic	NOUN
ejpam-4440	296	3	,	,	PUNCT
ejpam-4440	296	4	203:61–69	203:61–69	NUM
ejpam-4440	296	5	,	,	PUNCT
ejpam-4440	296	6	1999	1999	NUM
ejpam-4440	296	7	.	.	PUNCT
ejpam-4440	297	1	[	[	X
ejpam-4440	297	2	12	12	NUM
ejpam-4440	297	3	]	]	PUNCT
ejpam-4440	297	4	k.	k.	PROPN
ejpam-4440	297	5	samir	samir	PROPN
ejpam-4440	297	6	,	,	PUNCT
ejpam-4440	297	7	b.	b.	PROPN
ejpam-4440	297	8	raghavachari	raghavachari	PROPN
ejpam-4440	297	9	,	,	PUNCT
ejpam-4440	297	10	and	and	CCONJ
ejpam-4440	297	11	a.	a.	NOUN
ejpam-4440	297	12	rosenfeld	rosenfeld	PROPN
ejpam-4440	297	13	.	.	PUNCT
ejpam-4440	298	1	landmarks	landmark	NOUN
ejpam-4440	298	2	in	in	ADP
ejpam-4440	298	3	graphs	graph	NOUN
ejpam-4440	298	4	.	.	PUNCT
ejpam-4440	299	1	discrete	discrete	ADJ
ejpam-4440	299	2	applied	apply	VERB
ejpam-4440	299	3	mathematics	mathematic	NOUN
ejpam-4440	299	4	,	,	PUNCT
ejpam-4440	299	5	70.3:217–229	70.3:217–229	NUM
ejpam-4440	299	6	,	,	PUNCT
ejpam-4440	299	7	1996	1996	NUM
ejpam-4440	299	8	.	.	PUNCT
ejpam-4440	300	1	[	[	X
ejpam-4440	300	2	13	13	NUM
ejpam-4440	300	3	]	]	PUNCT
ejpam-4440	300	4	sebo	sebo	NOUN
ejpam-4440	300	5	,	,	PUNCT
ejpam-4440	300	6	andras	andra	NOUN
ejpam-4440	300	7	,	,	PUNCT
ejpam-4440	300	8	and	and	CCONJ
ejpam-4440	300	9	tannier	tannier	NOUN
ejpam-4440	300	10	.	.	PUNCT
ejpam-4440	301	1	on	on	ADP
ejpam-4440	301	2	metric	metric	ADJ
ejpam-4440	301	3	generators	generator	NOUN
ejpam-4440	301	4	of	of	ADP
ejpam-4440	301	5	graphs	graph	NOUN
ejpam-4440	301	6	.	.	PUNCT
ejpam-4440	302	1	mathematics	mathematic	NOUN
ejpam-4440	302	2	of	of	ADP
ejpam-4440	302	3	operations	operation	NOUN
ejpam-4440	302	4	research	research	NOUN
ejpam-4440	302	5	,	,	PUNCT
ejpam-4440	302	6	29(2):383–393	29(2):383–393	PROPN
ejpam-4440	302	7	.	.	PUNCT
ejpam-4440	303	1	[	[	X
ejpam-4440	303	2	14	14	NUM
ejpam-4440	303	3	]	]	X
ejpam-4440	303	4	p.	p.	PROPN
ejpam-4440	303	5	slater	slater	PROPN
ejpam-4440	303	6	.	.	PUNCT
ejpam-4440	304	1	dominating	dominating	NOUN
ejpam-4440	304	2	and	and	CCONJ
ejpam-4440	304	3	reference	reference	NOUN
ejpam-4440	304	4	sets	set	NOUN
ejpam-4440	304	5	in	in	ADP
ejpam-4440	304	6	a	a	DET
ejpam-4440	304	7	graph	graph	NOUN
ejpam-4440	304	8	.	.	PUNCT
ejpam-4440	305	1	journal	journal	NOUN
ejpam-4440	305	2	of	of	ADP
ejpam-4440	305	3	mathematics	mathematic	NOUN
ejpam-4440	305	4	and	and	CCONJ
ejpam-4440	305	5	physical	physical	ADJ
ejpam-4440	305	6	science	science	NOUN
ejpam-4440	305	7	,	,	PUNCT
ejpam-4440	305	8	22(4):445–455	22(4):445–455	PROPN
ejpam-4440	305	9	,	,	PUNCT
ejpam-4440	305	10	1988	1988	NUM
ejpam-4440	305	11	.	.	PUNCT