id	sid	tid	token	lemma	pos
ejpam-3967	1	1	european	european	PROPN
ejpam-3967	1	2	journal	journal	PROPN
ejpam-3967	1	3	of	of	ADP
ejpam-3967	1	4	pure	pure	ADJ
ejpam-3967	1	5	and	and	CCONJ
ejpam-3967	1	6	applied	apply	VERB
ejpam-3967	1	7	mathematics	mathematic	NOUN
ejpam-3967	1	8	vol	vol	NOUN
ejpam-3967	1	9	.	.	PUNCT
ejpam-3967	2	1	14	14	NUM
ejpam-3967	2	2	,	,	PUNCT
ejpam-3967	2	3	no	no	INTJ
ejpam-3967	2	4	.	.	NOUN
ejpam-3967	2	5	2	2	NUM
ejpam-3967	2	6	,	,	PUNCT
ejpam-3967	2	7	2021	2021	NUM
ejpam-3967	2	8	,	,	PUNCT
ejpam-3967	2	9	578	578	NUM
ejpam-3967	2	10	-	-	SYM
ejpam-3967	2	11	589	589	NUM
ejpam-3967	2	12	issn	issn	PROPN
ejpam-3967	2	13	1307	1307	NUM
ejpam-3967	2	14	-	-	SYM
ejpam-3967	2	15	5543	5543	NUM
ejpam-3967	2	16	–	–	PUNCT
ejpam-3967	3	1	ejpam.com	ejpam.com	X
ejpam-3967	3	2	published	publish	VERB
ejpam-3967	3	3	by	by	ADP
ejpam-3967	3	4	new	new	PROPN
ejpam-3967	3	5	york	york	PROPN
ejpam-3967	3	6	business	business	PROPN
ejpam-3967	3	7	global	global	PROPN
ejpam-3967	3	8	on	on	ADP
ejpam-3967	3	9	k	k	ADJ
ejpam-3967	3	10	-	-	ADJ
ejpam-3967	3	11	fair	fair	ADJ
ejpam-3967	3	12	total	total	ADJ
ejpam-3967	3	13	domination	domination	NOUN
ejpam-3967	3	14	in	in	ADP
ejpam-3967	3	15	graphs	graph	NOUN
ejpam-3967	3	16	wardah	wardah	PROPN
ejpam-3967	3	17	m.	m.	NOUN
ejpam-3967	3	18	bent	bent	NOUN
ejpam-3967	3	19	-	-	PUNCT
ejpam-3967	3	20	usman1,∗	usman1,∗	NOUN
ejpam-3967	3	21	,	,	PUNCT
ejpam-3967	3	22	rowena	rowena	PROPN
ejpam-3967	3	23	t.	t.	PROPN
ejpam-3967	3	24	isla2	isla2	PROPN
ejpam-3967	3	25	1	1	NUM
ejpam-3967	3	26	mathematics	mathematics	PROPN
ejpam-3967	3	27	department	department	NOUN
ejpam-3967	3	28	,	,	PUNCT
ejpam-3967	3	29	college	college	NOUN
ejpam-3967	3	30	of	of	ADP
ejpam-3967	3	31	natural	natural	ADJ
ejpam-3967	3	32	sciences	science	NOUN
ejpam-3967	3	33	and	and	CCONJ
ejpam-3967	3	34	mathematics	mathematic	NOUN
ejpam-3967	3	35	,	,	PUNCT
ejpam-3967	3	36	mindanao	mindanao	PROPN
ejpam-3967	3	37	state	state	PROPN
ejpam-3967	3	38	university	university	NOUN
ejpam-3967	3	39	-	-	PUNCT
ejpam-3967	3	40	main	main	ADJ
ejpam-3967	3	41	campus	campus	NOUN
ejpam-3967	3	42	,	,	PUNCT
ejpam-3967	3	43	9700	9700	NUM
ejpam-3967	3	44	marawi	marawi	PROPN
ejpam-3967	3	45	city	city	PROPN
ejpam-3967	3	46	,	,	PUNCT
ejpam-3967	3	47	philippines	philippines	PROPN
ejpam-3967	3	48	2	2	NUM
ejpam-3967	3	49	department	department	NOUN
ejpam-3967	3	50	of	of	ADP
ejpam-3967	3	51	mathematics	mathematic	NOUN
ejpam-3967	3	52	and	and	CCONJ
ejpam-3967	3	53	statistics	statistic	NOUN
ejpam-3967	3	54	,	,	PUNCT
ejpam-3967	3	55	college	college	NOUN
ejpam-3967	3	56	of	of	ADP
ejpam-3967	3	57	science	science	NOUN
ejpam-3967	3	58	and	and	CCONJ
ejpam-3967	3	59	mathematics	mathematic	NOUN
ejpam-3967	3	60	,	,	PUNCT
ejpam-3967	3	61	center	center	NOUN
ejpam-3967	3	62	for	for	ADP
ejpam-3967	3	63	graph	graph	NOUN
ejpam-3967	3	64	theory	theory	NOUN
ejpam-3967	3	65	,	,	PUNCT
ejpam-3967	3	66	algebra	algebra	NOUN
ejpam-3967	3	67	,	,	PUNCT
ejpam-3967	3	68	and	and	CCONJ
ejpam-3967	3	69	analysis	analysis	NOUN
ejpam-3967	3	70	,	,	PUNCT
ejpam-3967	3	71	premier	premier	PROPN
ejpam-3967	3	72	research	research	PROPN
ejpam-3967	3	73	institute	institute	PROPN
ejpam-3967	3	74	of	of	ADP
ejpam-3967	3	75	science	science	NOUN
ejpam-3967	3	76	and	and	CCONJ
ejpam-3967	3	77	mathematics	mathematic	NOUN
ejpam-3967	3	78	,	,	PUNCT
ejpam-3967	3	79	mindanao	mindanao	PROPN
ejpam-3967	3	80	state	state	PROPN
ejpam-3967	3	81	university	university	PROPN
ejpam-3967	3	82	-	-	PUNCT
ejpam-3967	3	83	iligan	iligan	PROPN
ejpam-3967	3	84	institute	institute	PROPN
ejpam-3967	3	85	of	of	ADP
ejpam-3967	3	86	technology	technology	PROPN
ejpam-3967	3	87	,	,	PUNCT
ejpam-3967	3	88	9200	9200	NUM
ejpam-3967	3	89	iligan	iligan	ADJ
ejpam-3967	3	90	city	city	NOUN
ejpam-3967	3	91	,	,	PUNCT
ejpam-3967	3	92	philippines	philippine	NOUN
ejpam-3967	3	93	abstract	abstract	ADJ
ejpam-3967	3	94	.	.	PUNCT
ejpam-3967	4	1	let	let	VERB
ejpam-3967	4	2	g	g	PROPN
ejpam-3967	4	3	=	=	SYM
ejpam-3967	4	4	(	(	PUNCT
ejpam-3967	4	5	v	v	NOUN
ejpam-3967	4	6	(	(	PUNCT
ejpam-3967	4	7	g	g	NOUN
ejpam-3967	4	8	)	)	PUNCT
ejpam-3967	4	9	,	,	PUNCT
ejpam-3967	4	10	e(g	e(g	PROPN
ejpam-3967	4	11	)	)	PUNCT
ejpam-3967	4	12	)	)	PUNCT
ejpam-3967	5	1	be	be	AUX
ejpam-3967	5	2	a	a	DET
ejpam-3967	5	3	simple	simple	ADJ
ejpam-3967	5	4	non	non	ADJ
ejpam-3967	5	5	-	-	ADJ
ejpam-3967	5	6	empty	empty	ADJ
ejpam-3967	5	7	graph	graph	NOUN
ejpam-3967	5	8	.	.	PUNCT
ejpam-3967	6	1	for	for	ADP
ejpam-3967	6	2	an	an	DET
ejpam-3967	6	3	integer	integer	NOUN
ejpam-3967	6	4	k	k	PROPN
ejpam-3967	6	5	≥	≥	NUM
ejpam-3967	6	6	1	1	NUM
ejpam-3967	6	7	,	,	PUNCT
ejpam-3967	6	8	a	a	DET
ejpam-3967	6	9	k	k	ADJ
ejpam-3967	6	10	-	-	PUNCT
ejpam-3967	6	11	fair	fair	ADJ
ejpam-3967	6	12	total	total	ADJ
ejpam-3967	6	13	dominating	dominating	NOUN
ejpam-3967	6	14	set	set	NOUN
ejpam-3967	6	15	(	(	PUNCT
ejpam-3967	6	16	kftd	kftd	NOUN
ejpam-3967	6	17	-	-	PUNCT
ejpam-3967	6	18	set	set	NOUN
ejpam-3967	6	19	)	)	PUNCT
ejpam-3967	6	20	is	be	AUX
ejpam-3967	6	21	a	a	DET
ejpam-3967	6	22	total	total	ADJ
ejpam-3967	6	23	dominating	dominating	NOUN
ejpam-3967	6	24	set	set	NOUN
ejpam-3967	6	25	s	s	PROPN
ejpam-3967	6	26	⊆	⊆	NUM
ejpam-3967	6	27	v	v	NOUN
ejpam-3967	6	28	(	(	PUNCT
ejpam-3967	6	29	g	g	NOUN
ejpam-3967	6	30	)	)	PUNCT
ejpam-3967	6	31	such	such	ADJ
ejpam-3967	6	32	that	that	SCONJ
ejpam-3967	6	33	|ng(u	|ng(u	X
ejpam-3967	6	34	)	)	PUNCT
ejpam-3967	6	35	∩	∩	NOUN
ejpam-3967	6	36	s|	s|	VERB
ejpam-3967	6	37	=	=	SYM
ejpam-3967	6	38	k	k	NOUN
ejpam-3967	6	39	for	for	ADP
ejpam-3967	6	40	every	every	DET
ejpam-3967	6	41	u	u	PROPN
ejpam-3967	6	42	∈	∈	PROPN
ejpam-3967	6	43	v	v	NOUN
ejpam-3967	6	44	(	(	PUNCT
ejpam-3967	6	45	g)\s	g)\s	NOUN
ejpam-3967	6	46	.	.	PUNCT
ejpam-3967	7	1	the	the	DET
ejpam-3967	7	2	k	k	ADJ
ejpam-3967	7	3	-	-	PUNCT
ejpam-3967	7	4	fair	fair	ADJ
ejpam-3967	7	5	total	total	ADJ
ejpam-3967	7	6	domination	domination	NOUN
ejpam-3967	7	7	number	number	NOUN
ejpam-3967	7	8	of	of	ADP
ejpam-3967	7	9	g	g	NOUN
ejpam-3967	7	10	,	,	PUNCT
ejpam-3967	7	11	denoted	denote	VERB
ejpam-3967	7	12	by	by	ADP
ejpam-3967	7	13	γkftd(g	γkftd(g	PROPN
ejpam-3967	7	14	)	)	PUNCT
ejpam-3967	7	15	,	,	PUNCT
ejpam-3967	7	16	is	be	AUX
ejpam-3967	7	17	the	the	DET
ejpam-3967	7	18	minimum	minimum	ADJ
ejpam-3967	7	19	cardinality	cardinality	NOUN
ejpam-3967	7	20	of	of	ADP
ejpam-3967	7	21	a	a	DET
ejpam-3967	7	22	kftd	kftd	NOUN
ejpam-3967	7	23	-	-	PUNCT
ejpam-3967	7	24	set	set	NOUN
ejpam-3967	7	25	.	.	PUNCT
ejpam-3967	8	1	a	a	DET
ejpam-3967	8	2	k	k	ADJ
ejpam-3967	8	3	-	-	ADJ
ejpam-3967	8	4	fair	fair	ADJ
ejpam-3967	8	5	total	total	ADJ
ejpam-3967	8	6	dominating	dominating	NOUN
ejpam-3967	8	7	set	set	NOUN
ejpam-3967	8	8	of	of	ADP
ejpam-3967	8	9	cardinality	cardinality	PROPN
ejpam-3967	8	10	γkftd(g	γkftd(g	PROPN
ejpam-3967	8	11	)	)	PUNCT
ejpam-3967	8	12	is	be	AUX
ejpam-3967	8	13	called	call	VERB
ejpam-3967	8	14	a	a	DET
ejpam-3967	8	15	minimum	minimum	ADJ
ejpam-3967	8	16	k	k	ADJ
ejpam-3967	8	17	-	-	ADJ
ejpam-3967	8	18	fair	fair	ADJ
ejpam-3967	8	19	total	total	ADJ
ejpam-3967	8	20	dominating	dominating	NOUN
ejpam-3967	8	21	set	set	NOUN
ejpam-3967	8	22	or	or	CCONJ
ejpam-3967	8	23	a	a	DET
ejpam-3967	8	24	γkftd	γkftd	NOUN
ejpam-3967	8	25	-	-	PUNCT
ejpam-3967	8	26	set	set	NOUN
ejpam-3967	8	27	.	.	PUNCT
ejpam-3967	9	1	we	we	PRON
ejpam-3967	9	2	investigate	investigate	VERB
ejpam-3967	9	3	the	the	DET
ejpam-3967	9	4	notion	notion	NOUN
ejpam-3967	9	5	of	of	ADP
ejpam-3967	9	6	k	k	ADJ
ejpam-3967	9	7	-	-	PUNCT
ejpam-3967	9	8	fair	fair	ADJ
ejpam-3967	9	9	total	total	ADJ
ejpam-3967	9	10	domination	domination	NOUN
ejpam-3967	9	11	in	in	ADP
ejpam-3967	9	12	this	this	DET
ejpam-3967	9	13	paper	paper	NOUN
ejpam-3967	9	14	.	.	PUNCT
ejpam-3967	10	1	we	we	PRON
ejpam-3967	10	2	also	also	ADV
ejpam-3967	10	3	characterize	characterize	VERB
ejpam-3967	10	4	the	the	DET
ejpam-3967	10	5	k	k	ADJ
ejpam-3967	10	6	-	-	PUNCT
ejpam-3967	10	7	fair	fair	ADJ
ejpam-3967	10	8	total	total	ADJ
ejpam-3967	10	9	dominating	dominating	NOUN
ejpam-3967	10	10	sets	set	NOUN
ejpam-3967	10	11	in	in	ADP
ejpam-3967	10	12	the	the	DET
ejpam-3967	10	13	join	join	NOUN
ejpam-3967	10	14	,	,	PUNCT
ejpam-3967	10	15	corona	corona	PROPN
ejpam-3967	10	16	,	,	PUNCT
ejpam-3967	10	17	lexicographic	lexicographic	ADJ
ejpam-3967	10	18	product	product	NOUN
ejpam-3967	10	19	and	and	CCONJ
ejpam-3967	10	20	cartesian	cartesian	ADJ
ejpam-3967	10	21	product	product	NOUN
ejpam-3967	10	22	of	of	ADP
ejpam-3967	10	23	graphs	graph	NOUN
ejpam-3967	10	24	and	and	CCONJ
ejpam-3967	10	25	determine	determine	VERB
ejpam-3967	10	26	the	the	DET
ejpam-3967	10	27	exact	exact	ADJ
ejpam-3967	10	28	values	value	NOUN
ejpam-3967	10	29	or	or	CCONJ
ejpam-3967	10	30	sharp	sharp	ADJ
ejpam-3967	10	31	bounds	bound	NOUN
ejpam-3967	10	32	of	of	ADP
ejpam-3967	10	33	their	their	PRON
ejpam-3967	10	34	corresponding	corresponding	ADJ
ejpam-3967	10	35	k	k	ADJ
ejpam-3967	10	36	-	-	PUNCT
ejpam-3967	10	37	fair	fair	ADJ
ejpam-3967	10	38	total	total	ADJ
ejpam-3967	10	39	domination	domination	NOUN
ejpam-3967	10	40	number	number	NOUN
ejpam-3967	10	41	.	.	PUNCT
ejpam-3967	11	1	2020	2020	NUM
ejpam-3967	11	2	mathematics	mathematic	NOUN
ejpam-3967	11	3	subject	subject	NOUN
ejpam-3967	11	4	classifications	classification	NOUN
ejpam-3967	11	5	:	:	PUNCT
ejpam-3967	11	6	05c69	05c69	NUM
ejpam-3967	11	7	,	,	PUNCT
ejpam-3967	11	8	05c76	05c76	DET
ejpam-3967	11	9	key	key	ADJ
ejpam-3967	11	10	words	word	NOUN
ejpam-3967	11	11	and	and	CCONJ
ejpam-3967	11	12	phrases	phrase	NOUN
ejpam-3967	11	13	:	:	PUNCT
ejpam-3967	11	14	k	k	ADJ
ejpam-3967	11	15	-	-	PUNCT
ejpam-3967	11	16	fair	fair	ADJ
ejpam-3967	11	17	domination	domination	NOUN
ejpam-3967	11	18	,	,	PUNCT
ejpam-3967	11	19	k	k	ADJ
ejpam-3967	11	20	-	-	PUNCT
ejpam-3967	11	21	fair	fair	ADJ
ejpam-3967	11	22	total	total	ADJ
ejpam-3967	11	23	domination	domination	NOUN
ejpam-3967	11	24	,	,	PUNCT
ejpam-3967	11	25	join	join	NOUN
ejpam-3967	11	26	,	,	PUNCT
ejpam-3967	11	27	corona	corona	PROPN
ejpam-3967	11	28	,	,	PUNCT
ejpam-3967	11	29	lexicographic	lexicographic	ADJ
ejpam-3967	11	30	product	product	NOUN
ejpam-3967	11	31	,	,	PUNCT
ejpam-3967	11	32	cartesian	cartesian	ADJ
ejpam-3967	11	33	product	product	NOUN
ejpam-3967	11	34	1	1	NUM
ejpam-3967	11	35	.	.	PUNCT
ejpam-3967	12	1	introduction	introduction	NOUN
ejpam-3967	12	2	let	let	VERB
ejpam-3967	12	3	g	g	NOUN
ejpam-3967	12	4	=	=	SYM
ejpam-3967	12	5	(	(	PUNCT
ejpam-3967	12	6	v	v	NOUN
ejpam-3967	12	7	(	(	PUNCT
ejpam-3967	12	8	g	g	NOUN
ejpam-3967	12	9	)	)	PUNCT
ejpam-3967	12	10	,	,	PUNCT
ejpam-3967	12	11	e(g	e(g	PROPN
ejpam-3967	12	12	)	)	PUNCT
ejpam-3967	12	13	)	)	PUNCT
ejpam-3967	12	14	be	be	AUX
ejpam-3967	12	15	a	a	DET
ejpam-3967	12	16	simple	simple	ADJ
ejpam-3967	12	17	graph	graph	NOUN
ejpam-3967	12	18	and	and	CCONJ
ejpam-3967	12	19	v	v	ADP
ejpam-3967	12	20	∈	∈	PROPN
ejpam-3967	12	21	v	v	NOUN
ejpam-3967	12	22	(	(	PUNCT
ejpam-3967	12	23	g	g	NOUN
ejpam-3967	12	24	)	)	PUNCT
ejpam-3967	12	25	.	.	PUNCT
ejpam-3967	13	1	the	the	DET
ejpam-3967	13	2	open	open	ADJ
ejpam-3967	13	3	neighborhood	neighborhood	NOUN
ejpam-3967	13	4	of	of	ADP
ejpam-3967	13	5	v	v	NOUN
ejpam-3967	13	6	in	in	ADP
ejpam-3967	13	7	g	g	PROPN
ejpam-3967	13	8	is	be	AUX
ejpam-3967	13	9	the	the	DET
ejpam-3967	13	10	set	set	NOUN
ejpam-3967	13	11	ng(v	ng(v	PUNCT
ejpam-3967	13	12	)	)	PUNCT
ejpam-3967	13	13	=	=	SYM
ejpam-3967	14	1	{	{	PUNCT
ejpam-3967	14	2	u	u	NOUN
ejpam-3967	14	3	∈	∈	PROPN
ejpam-3967	14	4	v	v	NOUN
ejpam-3967	14	5	(	(	PUNCT
ejpam-3967	14	6	g	g	NOUN
ejpam-3967	14	7	)	)	PUNCT
ejpam-3967	14	8	:	:	PUNCT
ejpam-3967	14	9	uv	uv	PROPN
ejpam-3967	14	10	∈	∈	PROPN
ejpam-3967	14	11	e(g	e(g	PROPN
ejpam-3967	14	12	)	)	PUNCT
ejpam-3967	14	13	}	}	PUNCT
ejpam-3967	14	14	and	and	CCONJ
ejpam-3967	14	15	the	the	DET
ejpam-3967	14	16	closed	closed	ADJ
ejpam-3967	14	17	neighborhood	neighborhood	NOUN
ejpam-3967	14	18	of	of	ADP
ejpam-3967	14	19	v	v	NOUN
ejpam-3967	14	20	is	be	AUX
ejpam-3967	14	21	the	the	DET
ejpam-3967	14	22	set	set	NOUN
ejpam-3967	14	23	ng[v	ng[v	NOUN
ejpam-3967	14	24	]	]	X
ejpam-3967	14	25	=	=	SYM
ejpam-3967	14	26	ng(v	ng(v	X
ejpam-3967	14	27	)	)	PUNCT
ejpam-3967	14	28	∪	∪	ADP
ejpam-3967	14	29	{	{	PUNCT
ejpam-3967	14	30	v	v	NOUN
ejpam-3967	14	31	}	}	PUNCT
ejpam-3967	14	32	.	.	PUNCT
ejpam-3967	15	1	for	for	ADP
ejpam-3967	15	2	x	x	SYM
ejpam-3967	15	3	⊆	⊆	NUM
ejpam-3967	15	4	v	v	ADP
ejpam-3967	15	5	(	(	PUNCT
ejpam-3967	15	6	g	g	NOUN
ejpam-3967	15	7	)	)	PUNCT
ejpam-3967	15	8	,	,	PUNCT
ejpam-3967	15	9	the	the	DET
ejpam-3967	15	10	open	open	ADJ
ejpam-3967	15	11	neighborhood	neighborhood	NOUN
ejpam-3967	15	12	of	of	ADP
ejpam-3967	15	13	x	x	PUNCT
ejpam-3967	15	14	in	in	ADP
ejpam-3967	15	15	g	g	PROPN
ejpam-3967	15	16	is	be	AUX
ejpam-3967	15	17	the	the	DET
ejpam-3967	15	18	set	set	NOUN
ejpam-3967	15	19	ng(x	ng(x	NUM
ejpam-3967	15	20	)	)	PUNCT
ejpam-3967	16	1	=	=	SYM
ejpam-3967	16	2	⋃	⋃	NOUN
ejpam-3967	16	3	v∈x	v∈x	NOUN
ejpam-3967	16	4	ng(v	ng(v	PUNCT
ejpam-3967	16	5	)	)	PUNCT
ejpam-3967	16	6	and	and	CCONJ
ejpam-3967	16	7	its	its	PRON
ejpam-3967	16	8	closed	closed	ADJ
ejpam-3967	16	9	neighborhood	neighborhood	NOUN
ejpam-3967	16	10	is	be	AUX
ejpam-3967	16	11	the	the	DET
ejpam-3967	16	12	set	set	NOUN
ejpam-3967	16	13	ng[x	ng[x	PROPN
ejpam-3967	16	14	]	]	X
ejpam-3967	16	15	=	=	PUNCT
ejpam-3967	16	16	ng(x	ng(x	X
ejpam-3967	16	17	)	)	PUNCT
ejpam-3967	16	18	∪x	∪x	X
ejpam-3967	16	19	.	.	PUNCT
ejpam-3967	17	1	a	a	DET
ejpam-3967	17	2	set	set	NOUN
ejpam-3967	17	3	s	s	NOUN
ejpam-3967	17	4	⊆	⊆	NUM
ejpam-3967	17	5	v	v	NOUN
ejpam-3967	17	6	(	(	PUNCT
ejpam-3967	17	7	g	g	NOUN
ejpam-3967	17	8	)	)	PUNCT
ejpam-3967	17	9	is	be	AUX
ejpam-3967	17	10	a	a	DET
ejpam-3967	17	11	dominating	dominating	NOUN
ejpam-3967	17	12	set	set	VERB
ejpam-3967	17	13	in	in	ADP
ejpam-3967	17	14	g	g	PROPN
ejpam-3967	17	15	if	if	SCONJ
ejpam-3967	17	16	for	for	ADP
ejpam-3967	17	17	every	every	DET
ejpam-3967	17	18	v	v	NUM
ejpam-3967	17	19	∈	∈	NOUN
ejpam-3967	17	20	v	v	NOUN
ejpam-3967	17	21	(	(	PUNCT
ejpam-3967	17	22	g)\s	g)\s	NOUN
ejpam-3967	17	23	,	,	PUNCT
ejpam-3967	17	24	there	there	PRON
ejpam-3967	17	25	exists	exist	VERB
ejpam-3967	17	26	u	u	PROPN
ejpam-3967	17	27	∈	∈	PROPN
ejpam-3967	17	28	s	s	VERB
ejpam-3967	17	29	such	such	ADJ
ejpam-3967	17	30	that	that	DET
ejpam-3967	17	31	uv	uv	PROPN
ejpam-3967	17	32	∈	∈	PROPN
ejpam-3967	17	33	e(g	e(g	PROPN
ejpam-3967	17	34	)	)	PUNCT
ejpam-3967	17	35	,	,	PUNCT
ejpam-3967	17	36	that	that	ADV
ejpam-3967	17	37	is	is	ADV
ejpam-3967	17	38	,	,	PUNCT
ejpam-3967	17	39	ng[s	ng[s	PROPN
ejpam-3967	17	40	]	]	PUNCT
ejpam-3967	17	41	=	=	SYM
ejpam-3967	17	42	v	v	X
ejpam-3967	17	43	(	(	PUNCT
ejpam-3967	17	44	g	g	NOUN
ejpam-3967	17	45	)	)	PUNCT
ejpam-3967	17	46	.	.	PUNCT
ejpam-3967	18	1	the	the	DET
ejpam-3967	18	2	minimum	minimum	ADJ
ejpam-3967	18	3	cardinality	cardinality	NOUN
ejpam-3967	18	4	of	of	ADP
ejpam-3967	18	5	a	a	DET
ejpam-3967	18	6	dominating	dominating	NOUN
ejpam-3967	18	7	set	set	NOUN
ejpam-3967	18	8	in	in	ADP
ejpam-3967	18	9	g	g	NOUN
ejpam-3967	18	10	,	,	PUNCT
ejpam-3967	18	11	denoted	denote	VERB
ejpam-3967	18	12	by	by	ADP
ejpam-3967	18	13	γ(g	γ(g	PROPN
ejpam-3967	18	14	)	)	PUNCT
ejpam-3967	18	15	,	,	PUNCT
ejpam-3967	18	16	is	be	AUX
ejpam-3967	18	17	the	the	DET
ejpam-3967	18	18	domination	domination	NOUN
ejpam-3967	18	19	number	number	NOUN
ejpam-3967	18	20	of	of	ADP
ejpam-3967	18	21	g.	g.	PROPN
ejpam-3967	18	22	any	any	DET
ejpam-3967	18	23	dominating	dominating	NOUN
ejpam-3967	18	24	set	set	VERB
ejpam-3967	18	25	in	in	ADP
ejpam-3967	18	26	g	g	PROPN
ejpam-3967	18	27	of	of	ADP
ejpam-3967	18	28	cardinality	cardinality	PROPN
ejpam-3967	18	29	γ(g	γ(g	PROPN
ejpam-3967	18	30	)	)	PUNCT
ejpam-3967	18	31	is	be	AUX
ejpam-3967	18	32	referred	refer	VERB
ejpam-3967	18	33	to	to	ADP
ejpam-3967	18	34	as	as	ADP
ejpam-3967	18	35	a	a	DET
ejpam-3967	18	36	γ	γ	NOUN
ejpam-3967	18	37	-	-	PUNCT
ejpam-3967	18	38	set	set	VERB
ejpam-3967	18	39	in	in	ADP
ejpam-3967	18	40	g.	g.	PROPN
ejpam-3967	18	41	for	for	ADP
ejpam-3967	18	42	a	a	DET
ejpam-3967	18	43	connected	connected	ADJ
ejpam-3967	18	44	graph	graph	NOUN
ejpam-3967	18	45	g	g	NOUN
ejpam-3967	18	46	,	,	PUNCT
ejpam-3967	18	47	a	a	DET
ejpam-3967	18	48	set	set	NOUN
ejpam-3967	18	49	s	s	NOUN
ejpam-3967	18	50	⊆	⊆	NUM
ejpam-3967	18	51	v	v	NOUN
ejpam-3967	18	52	(	(	PUNCT
ejpam-3967	18	53	g	g	NOUN
ejpam-3967	18	54	)	)	PUNCT
ejpam-3967	18	55	is	be	AUX
ejpam-3967	18	56	a	a	DET
ejpam-3967	18	57	total	total	ADJ
ejpam-3967	18	58	∗corresponding	∗corresponde	VERB
ejpam-3967	18	59	author	author	NOUN
ejpam-3967	18	60	.	.	PUNCT
ejpam-3967	19	1	doi	doi	NOUN
ejpam-3967	19	2	:	:	PUNCT
ejpam-3967	19	3	https://doi.org/10.29020/nybg.ejpam.v14i2.3967	https://doi.org/10.29020/nybg.ejpam.v14i2.3967	PROPN
ejpam-3967	19	4	email	email	NOUN
ejpam-3967	19	5	addresses	address	VERB
ejpam-3967	19	6	:	:	PUNCT
ejpam-3967	19	7	wardah.bentusman@msumain.edu.ph	wardah.bentusman@msumain.edu.ph	X
ejpam-3967	19	8	(	(	PUNCT
ejpam-3967	19	9	w.	w.	PROPN
ejpam-3967	19	10	bent	bent	PROPN
ejpam-3967	19	11	-	-	PUNCT
ejpam-3967	19	12	usman	usman	PROPN
ejpam-3967	19	13	)	)	PUNCT
ejpam-3967	19	14	,	,	PUNCT
ejpam-3967	19	15	rowena.isla@g.msuiit.edu.ph	rowena.isla@g.msuiit.edu.ph	PROPN
ejpam-3967	19	16	(	(	PUNCT
ejpam-3967	19	17	r.	r.	PROPN
ejpam-3967	19	18	isla	isla	PROPN
ejpam-3967	19	19	)	)	PUNCT
ejpam-3967	19	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3967	20	1	578	578	NUM
ejpam-3967	20	2	c	c	X
ejpam-3967	20	3	©	©	PROPN
ejpam-3967	20	4	2021	2021	NUM
ejpam-3967	20	5	ejpam	ejpam	VERB
ejpam-3967	20	6	all	all	DET
ejpam-3967	20	7	rights	right	NOUN
ejpam-3967	20	8	reserved	reserve	VERB
ejpam-3967	20	9	.	.	PUNCT
ejpam-3967	21	1	w.	w.	PROPN
ejpam-3967	21	2	bent	bent	PROPN
ejpam-3967	21	3	-	-	PUNCT
ejpam-3967	21	4	usman	usman	PROPN
ejpam-3967	21	5	,	,	PUNCT
ejpam-3967	21	6	r.	r.	PROPN
ejpam-3967	21	7	isla	isla	PROPN
ejpam-3967	21	8	/	/	SYM
ejpam-3967	21	9	eur	eur	PROPN
ejpam-3967	21	10	.	.	PUNCT
ejpam-3967	22	1	j.	j.	PROPN
ejpam-3967	22	2	pure	pure	PROPN
ejpam-3967	22	3	appl	appl	PROPN
ejpam-3967	22	4	.	.	PROPN
ejpam-3967	22	5	math	math	PROPN
ejpam-3967	22	6	,	,	PUNCT
ejpam-3967	22	7	14	14	NUM
ejpam-3967	22	8	(	(	PUNCT
ejpam-3967	22	9	2	2	NUM
ejpam-3967	22	10	)	)	PUNCT
ejpam-3967	22	11	(	(	PUNCT
ejpam-3967	22	12	2021	2021	NUM
ejpam-3967	22	13	)	)	PUNCT
ejpam-3967	22	14	,	,	PUNCT
ejpam-3967	22	15	578	578	NUM
ejpam-3967	22	16	-	-	SYM
ejpam-3967	22	17	589	589	NUM
ejpam-3967	22	18	579	579	NUM
ejpam-3967	22	19	dominating	dominating	NOUN
ejpam-3967	22	20	set	set	VERB
ejpam-3967	22	21	in	in	ADP
ejpam-3967	22	22	g	g	PROPN
ejpam-3967	22	23	if	if	SCONJ
ejpam-3967	22	24	ng(s	ng(s	NUM
ejpam-3967	22	25	)	)	PUNCT
ejpam-3967	23	1	=	=	SYM
ejpam-3967	23	2	v	v	X
ejpam-3967	23	3	(	(	PUNCT
ejpam-3967	23	4	g	g	NOUN
ejpam-3967	23	5	)	)	PUNCT
ejpam-3967	23	6	.	.	PUNCT
ejpam-3967	24	1	a	a	DET
ejpam-3967	24	2	domination	domination	NOUN
ejpam-3967	24	3	variant	variant	NOUN
ejpam-3967	24	4	called	call	VERB
ejpam-3967	24	5	fair	fair	ADJ
ejpam-3967	24	6	domination	domination	NOUN
ejpam-3967	24	7	was	be	AUX
ejpam-3967	24	8	introduced	introduce	VERB
ejpam-3967	24	9	by	by	ADP
ejpam-3967	24	10	caro	caro	PROPN
ejpam-3967	24	11	,	,	PUNCT
ejpam-3967	24	12	hansberg	hansberg	PROPN
ejpam-3967	24	13	and	and	CCONJ
ejpam-3967	24	14	henning	henne	VERB
ejpam-3967	25	1	[	[	X
ejpam-3967	25	2	2	2	NUM
ejpam-3967	25	3	]	]	PUNCT
ejpam-3967	25	4	in	in	ADP
ejpam-3967	25	5	2012	2012	NUM
ejpam-3967	25	6	.	.	PUNCT
ejpam-3967	26	1	for	for	ADP
ejpam-3967	26	2	an	an	DET
ejpam-3967	26	3	integer	integer	NOUN
ejpam-3967	26	4	k	k	PROPN
ejpam-3967	26	5	≥	≥	NUM
ejpam-3967	26	6	1	1	NUM
ejpam-3967	26	7	,	,	PUNCT
ejpam-3967	26	8	a	a	DET
ejpam-3967	26	9	k	k	ADJ
ejpam-3967	26	10	-	-	ADJ
ejpam-3967	26	11	fair	fair	ADJ
ejpam-3967	26	12	dominating	dominating	NOUN
ejpam-3967	26	13	set	set	NOUN
ejpam-3967	26	14	(	(	PUNCT
ejpam-3967	26	15	kfd	kfd	NOUN
ejpam-3967	26	16	-	-	PUNCT
ejpam-3967	26	17	set	set	NOUN
ejpam-3967	26	18	)	)	PUNCT
ejpam-3967	26	19	is	be	AUX
ejpam-3967	26	20	a	a	DET
ejpam-3967	26	21	dominating	dominating	NOUN
ejpam-3967	26	22	set	set	NOUN
ejpam-3967	26	23	s	s	PROPN
ejpam-3967	26	24	⊆	⊆	NUM
ejpam-3967	26	25	v	v	NOUN
ejpam-3967	26	26	(	(	PUNCT
ejpam-3967	26	27	g	g	NOUN
ejpam-3967	26	28	)	)	PUNCT
ejpam-3967	26	29	such	such	ADJ
ejpam-3967	26	30	that	that	SCONJ
ejpam-3967	26	31	|ng(u)∩s|	|ng(u)∩s|	NUM
ejpam-3967	26	32	=	=	SYM
ejpam-3967	26	33	k	k	PROPN
ejpam-3967	26	34	for	for	ADP
ejpam-3967	26	35	every	every	DET
ejpam-3967	26	36	u	u	PROPN
ejpam-3967	26	37	∈	∈	PROPN
ejpam-3967	26	38	v	v	NOUN
ejpam-3967	26	39	(	(	PUNCT
ejpam-3967	26	40	g)\s	g)\s	NOUN
ejpam-3967	26	41	.	.	PUNCT
ejpam-3967	27	1	the	the	DET
ejpam-3967	27	2	k	k	ADJ
ejpam-3967	27	3	-	-	PUNCT
ejpam-3967	27	4	fair	fair	ADJ
ejpam-3967	27	5	domination	domination	NOUN
ejpam-3967	27	6	number	number	NOUN
ejpam-3967	27	7	of	of	ADP
ejpam-3967	27	8	g	g	NOUN
ejpam-3967	27	9	,	,	PUNCT
ejpam-3967	27	10	denoted	denote	VERB
ejpam-3967	27	11	by	by	ADP
ejpam-3967	27	12	γkfd(g	γkfd(g	PROPN
ejpam-3967	27	13	)	)	PUNCT
ejpam-3967	27	14	,	,	PUNCT
ejpam-3967	27	15	is	be	AUX
ejpam-3967	27	16	the	the	DET
ejpam-3967	27	17	minimum	minimum	ADJ
ejpam-3967	27	18	cardinality	cardinality	NOUN
ejpam-3967	27	19	of	of	ADP
ejpam-3967	27	20	a	a	DET
ejpam-3967	27	21	kfd	kfd	NOUN
ejpam-3967	27	22	-	-	PUNCT
ejpam-3967	27	23	set	set	NOUN
ejpam-3967	27	24	.	.	PUNCT
ejpam-3967	28	1	in	in	ADP
ejpam-3967	28	2	2014	2014	NUM
ejpam-3967	28	3	,	,	PUNCT
ejpam-3967	28	4	maravilla	maravilla	PROPN
ejpam-3967	28	5	et	et	PROPN
ejpam-3967	28	6	al.[5	al.[5	PROPN
ejpam-3967	28	7	]	]	PUNCT
ejpam-3967	28	8	characterized	characterize	VERB
ejpam-3967	28	9	the	the	DET
ejpam-3967	28	10	k	k	ADJ
ejpam-3967	28	11	-	-	ADJ
ejpam-3967	28	12	fair	fair	ADJ
ejpam-3967	28	13	dominating	dominating	NOUN
ejpam-3967	28	14	sets	set	NOUN
ejpam-3967	28	15	in	in	ADP
ejpam-3967	28	16	the	the	DET
ejpam-3967	28	17	join	join	NOUN
ejpam-3967	28	18	,	,	PUNCT
ejpam-3967	28	19	corona	corona	PROPN
ejpam-3967	28	20	,	,	PUNCT
ejpam-3967	28	21	lexicographic	lexicographic	ADJ
ejpam-3967	28	22	product	product	NOUN
ejpam-3967	28	23	,	,	PUNCT
ejpam-3967	28	24	and	and	CCONJ
ejpam-3967	28	25	cartesian	cartesian	ADJ
ejpam-3967	28	26	product	product	NOUN
ejpam-3967	28	27	of	of	ADP
ejpam-3967	28	28	graphs	graph	NOUN
ejpam-3967	28	29	and	and	CCONJ
ejpam-3967	28	30	determined	determine	VERB
ejpam-3967	28	31	the	the	DET
ejpam-3967	28	32	bounds	bound	NOUN
ejpam-3967	28	33	or	or	CCONJ
ejpam-3967	28	34	exact	exact	ADJ
ejpam-3967	28	35	values	value	NOUN
ejpam-3967	28	36	of	of	ADP
ejpam-3967	28	37	the	the	DET
ejpam-3967	28	38	k	k	ADJ
ejpam-3967	28	39	-	-	PUNCT
ejpam-3967	28	40	fair	fair	ADJ
ejpam-3967	28	41	domination	domination	NOUN
ejpam-3967	28	42	numbers	number	NOUN
ejpam-3967	28	43	of	of	ADP
ejpam-3967	28	44	these	these	DET
ejpam-3967	28	45	graphs	graph	NOUN
ejpam-3967	28	46	.	.	PUNCT
ejpam-3967	29	1	two	two	NUM
ejpam-3967	29	2	variants	variant	NOUN
ejpam-3967	29	3	of	of	ADP
ejpam-3967	29	4	k	k	ADJ
ejpam-3967	29	5	-	-	PUNCT
ejpam-3967	29	6	fair	fair	ADJ
ejpam-3967	29	7	domination	domination	NOUN
ejpam-3967	29	8	,	,	PUNCT
ejpam-3967	29	9	namely	namely	ADV
ejpam-3967	29	10	connected	connected	ADJ
ejpam-3967	29	11	k	k	ADJ
ejpam-3967	29	12	-	-	PUNCT
ejpam-3967	29	13	fair	fair	ADJ
ejpam-3967	29	14	domination	domination	NOUN
ejpam-3967	29	15	and	and	CCONJ
ejpam-3967	29	16	neighborhood	neighborhood	NOUN
ejpam-3967	29	17	connected	connect	VERB
ejpam-3967	29	18	k	k	ADJ
ejpam-3967	29	19	-	-	PUNCT
ejpam-3967	29	20	fair	fair	ADJ
ejpam-3967	29	21	domination	domination	NOUN
ejpam-3967	29	22	,	,	PUNCT
ejpam-3967	29	23	were	be	AUX
ejpam-3967	29	24	studied	study	VERB
ejpam-3967	29	25	by	by	ADP
ejpam-3967	29	26	bent	bent	ADJ
ejpam-3967	29	27	-	-	PUNCT
ejpam-3967	29	28	usman	usman	PROPN
ejpam-3967	29	29	et	et	PROPN
ejpam-3967	29	30	al	al	PROPN
ejpam-3967	29	31	.	.	PUNCT
ejpam-3967	30	1	[	[	X
ejpam-3967	30	2	1	1	NUM
ejpam-3967	30	3	,	,	PUNCT
ejpam-3967	30	4	6	6	NUM
ejpam-3967	30	5	]	]	PUNCT
ejpam-3967	30	6	in	in	ADP
ejpam-3967	30	7	2018	2018	NUM
ejpam-3967	30	8	and	and	CCONJ
ejpam-3967	30	9	2019	2019	NUM
ejpam-3967	30	10	,	,	PUNCT
ejpam-3967	30	11	respectively	respectively	ADV
ejpam-3967	30	12	.	.	PUNCT
ejpam-3967	31	1	recently	recently	ADV
ejpam-3967	31	2	,	,	PUNCT
ejpam-3967	31	3	ortega	ortega	PROPN
ejpam-3967	31	4	and	and	CCONJ
ejpam-3967	31	5	isla	isla	PROPN
ejpam-3967	32	1	[	[	X
ejpam-3967	32	2	7	7	X
ejpam-3967	32	3	]	]	PUNCT
ejpam-3967	32	4	introduced	introduce	VERB
ejpam-3967	32	5	and	and	CCONJ
ejpam-3967	32	6	investigated	investigate	VERB
ejpam-3967	32	7	the	the	DET
ejpam-3967	32	8	concepts	concept	NOUN
ejpam-3967	32	9	of	of	ADP
ejpam-3967	32	10	semitotal	semitotal	ADJ
ejpam-3967	32	11	k	k	ADJ
ejpam-3967	32	12	-	-	PUNCT
ejpam-3967	32	13	fair	fair	ADJ
ejpam-3967	32	14	domination	domination	NOUN
ejpam-3967	32	15	and	and	CCONJ
ejpam-3967	32	16	independent	independent	ADJ
ejpam-3967	32	17	k	k	ADJ
ejpam-3967	32	18	-	-	PUNCT
ejpam-3967	32	19	fair	fair	ADJ
ejpam-3967	32	20	domination	domination	NOUN
ejpam-3967	32	21	in	in	ADP
ejpam-3967	32	22	graphs	graph	NOUN
ejpam-3967	32	23	.	.	PUNCT
ejpam-3967	33	1	maravilla	maravilla	PROPN
ejpam-3967	33	2	et	et	PROPN
ejpam-3967	33	3	al	al	PROPN
ejpam-3967	33	4	.	.	PUNCT
ejpam-3967	34	1	[	[	X
ejpam-3967	34	2	4	4	X
ejpam-3967	34	3	]	]	PUNCT
ejpam-3967	34	4	introduced	introduce	VERB
ejpam-3967	34	5	the	the	DET
ejpam-3967	34	6	notion	notion	NOUN
ejpam-3967	34	7	of	of	ADP
ejpam-3967	34	8	k	k	ADJ
ejpam-3967	34	9	-	-	PUNCT
ejpam-3967	34	10	fair	fair	ADJ
ejpam-3967	34	11	total	total	ADJ
ejpam-3967	34	12	domination	domination	NOUN
ejpam-3967	34	13	in	in	ADP
ejpam-3967	34	14	graphs	graph	NOUN
ejpam-3967	34	15	.	.	PUNCT
ejpam-3967	35	1	for	for	ADP
ejpam-3967	35	2	a	a	DET
ejpam-3967	35	3	non	non	ADJ
ejpam-3967	35	4	-	-	ADJ
ejpam-3967	35	5	empty	empty	ADJ
ejpam-3967	35	6	graph	graph	NOUN
ejpam-3967	35	7	g	g	NOUN
ejpam-3967	35	8	and	and	CCONJ
ejpam-3967	35	9	an	an	DET
ejpam-3967	35	10	integer	integer	NOUN
ejpam-3967	35	11	k	k	PROPN
ejpam-3967	35	12	≥	≥	NUM
ejpam-3967	35	13	1	1	NUM
ejpam-3967	35	14	,	,	PUNCT
ejpam-3967	35	15	a	a	DET
ejpam-3967	35	16	k	k	ADJ
ejpam-3967	35	17	-	-	PUNCT
ejpam-3967	35	18	fair	fair	ADJ
ejpam-3967	35	19	total	total	ADJ
ejpam-3967	35	20	dominating	dominating	NOUN
ejpam-3967	35	21	set	set	NOUN
ejpam-3967	35	22	(	(	PUNCT
ejpam-3967	35	23	kftd	kftd	NOUN
ejpam-3967	35	24	-	-	PUNCT
ejpam-3967	35	25	set	set	NOUN
ejpam-3967	35	26	)	)	PUNCT
ejpam-3967	35	27	is	be	AUX
ejpam-3967	35	28	a	a	DET
ejpam-3967	35	29	total	total	ADJ
ejpam-3967	35	30	dominating	dominating	NOUN
ejpam-3967	35	31	set	set	NOUN
ejpam-3967	35	32	s	s	PROPN
ejpam-3967	35	33	⊆	⊆	NUM
ejpam-3967	35	34	v	v	NOUN
ejpam-3967	35	35	(	(	PUNCT
ejpam-3967	35	36	g	g	NOUN
ejpam-3967	35	37	)	)	PUNCT
ejpam-3967	35	38	such	such	ADJ
ejpam-3967	35	39	that	that	SCONJ
ejpam-3967	35	40	|ng(u	|ng(u	X
ejpam-3967	35	41	)	)	PUNCT
ejpam-3967	35	42	∩	∩	NOUN
ejpam-3967	35	43	s|	s|	VERB
ejpam-3967	35	44	=	=	SYM
ejpam-3967	35	45	k	k	NOUN
ejpam-3967	35	46	for	for	ADP
ejpam-3967	35	47	every	every	DET
ejpam-3967	35	48	u	u	PROPN
ejpam-3967	35	49	∈	∈	PROPN
ejpam-3967	35	50	v	v	NOUN
ejpam-3967	35	51	(	(	PUNCT
ejpam-3967	35	52	g)\s	g)\s	NOUN
ejpam-3967	35	53	.	.	PUNCT
ejpam-3967	36	1	the	the	DET
ejpam-3967	36	2	k	k	ADJ
ejpam-3967	36	3	-	-	PUNCT
ejpam-3967	36	4	fair	fair	ADJ
ejpam-3967	36	5	total	total	ADJ
ejpam-3967	36	6	domination	domination	NOUN
ejpam-3967	36	7	number	number	NOUN
ejpam-3967	36	8	of	of	ADP
ejpam-3967	36	9	g	g	NOUN
ejpam-3967	36	10	,	,	PUNCT
ejpam-3967	36	11	denoted	denote	VERB
ejpam-3967	36	12	by	by	ADP
ejpam-3967	36	13	γkftd(g	γkftd(g	PROPN
ejpam-3967	36	14	)	)	PUNCT
ejpam-3967	36	15	,	,	PUNCT
ejpam-3967	36	16	is	be	AUX
ejpam-3967	36	17	the	the	DET
ejpam-3967	36	18	minimum	minimum	ADJ
ejpam-3967	36	19	cardinality	cardinality	NOUN
ejpam-3967	36	20	of	of	ADP
ejpam-3967	36	21	a	a	DET
ejpam-3967	36	22	kftd	kftd	NOUN
ejpam-3967	36	23	-	-	PUNCT
ejpam-3967	36	24	set	set	NOUN
ejpam-3967	36	25	.	.	PUNCT
ejpam-3967	37	1	a	a	DET
ejpam-3967	37	2	k	k	ADJ
ejpam-3967	37	3	-	-	ADJ
ejpam-3967	37	4	fair	fair	ADJ
ejpam-3967	37	5	total	total	ADJ
ejpam-3967	37	6	dominating	dominating	NOUN
ejpam-3967	37	7	set	set	NOUN
ejpam-3967	37	8	of	of	ADP
ejpam-3967	37	9	cardinality	cardinality	PROPN
ejpam-3967	37	10	γkftd(g	γkftd(g	PROPN
ejpam-3967	37	11	)	)	PUNCT
ejpam-3967	37	12	is	be	AUX
ejpam-3967	37	13	called	call	VERB
ejpam-3967	37	14	a	a	DET
ejpam-3967	37	15	minimum	minimum	ADJ
ejpam-3967	37	16	k	k	ADJ
ejpam-3967	37	17	-	-	ADJ
ejpam-3967	37	18	fair	fair	ADJ
ejpam-3967	37	19	total	total	ADJ
ejpam-3967	37	20	dominating	dominating	NOUN
ejpam-3967	37	21	set	set	NOUN
ejpam-3967	37	22	or	or	CCONJ
ejpam-3967	37	23	a	a	DET
ejpam-3967	37	24	γkftd	γkftd	NOUN
ejpam-3967	37	25	-	-	PUNCT
ejpam-3967	37	26	set	set	NOUN
ejpam-3967	37	27	.	.	PUNCT
ejpam-3967	38	1	in	in	ADP
ejpam-3967	38	2	this	this	DET
ejpam-3967	38	3	paper	paper	NOUN
ejpam-3967	38	4	,	,	PUNCT
ejpam-3967	38	5	we	we	PRON
ejpam-3967	38	6	investigate	investigate	VERB
ejpam-3967	38	7	the	the	DET
ejpam-3967	38	8	concept	concept	NOUN
ejpam-3967	38	9	of	of	ADP
ejpam-3967	38	10	k	k	ADJ
ejpam-3967	38	11	-	-	PUNCT
ejpam-3967	38	12	fair	fair	ADJ
ejpam-3967	38	13	total	total	ADJ
ejpam-3967	38	14	domination	domination	NOUN
ejpam-3967	38	15	and	and	CCONJ
ejpam-3967	38	16	characterize	characterize	VERB
ejpam-3967	38	17	the	the	DET
ejpam-3967	38	18	k	k	ADJ
ejpam-3967	38	19	-	-	PUNCT
ejpam-3967	38	20	fair	fair	ADJ
ejpam-3967	38	21	total	total	ADJ
ejpam-3967	38	22	dominating	dominating	NOUN
ejpam-3967	38	23	sets	set	NOUN
ejpam-3967	38	24	in	in	ADP
ejpam-3967	38	25	graphs	graph	NOUN
ejpam-3967	38	26	under	under	ADP
ejpam-3967	38	27	some	some	DET
ejpam-3967	38	28	binary	binary	ADJ
ejpam-3967	38	29	operations	operation	NOUN
ejpam-3967	38	30	.	.	PUNCT
ejpam-3967	39	1	we	we	PRON
ejpam-3967	39	2	also	also	ADV
ejpam-3967	39	3	determine	determine	VERB
ejpam-3967	39	4	the	the	DET
ejpam-3967	39	5	exact	exact	ADJ
ejpam-3967	39	6	values	value	NOUN
ejpam-3967	39	7	or	or	CCONJ
ejpam-3967	39	8	sharp	sharp	ADJ
ejpam-3967	39	9	bounds	bound	NOUN
ejpam-3967	39	10	of	of	ADP
ejpam-3967	39	11	their	their	PRON
ejpam-3967	39	12	corresponding	corresponding	ADJ
ejpam-3967	39	13	k	k	ADJ
ejpam-3967	39	14	-	-	PUNCT
ejpam-3967	39	15	fair	fair	ADJ
ejpam-3967	39	16	total	total	ADJ
ejpam-3967	39	17	domination	domination	NOUN
ejpam-3967	39	18	number	number	NOUN
ejpam-3967	39	19	.	.	PUNCT
ejpam-3967	40	1	a	a	DET
ejpam-3967	40	2	comprehensive	comprehensive	ADJ
ejpam-3967	40	3	treatment	treatment	NOUN
ejpam-3967	40	4	of	of	ADP
ejpam-3967	40	5	the	the	DET
ejpam-3967	40	6	theoretical	theoretical	ADJ
ejpam-3967	40	7	,	,	PUNCT
ejpam-3967	40	8	algorithmic	algorithmic	ADJ
ejpam-3967	40	9	,	,	PUNCT
ejpam-3967	40	10	and	and	CCONJ
ejpam-3967	40	11	application	application	NOUN
ejpam-3967	40	12	(	(	PUNCT
ejpam-3967	40	13	e.g.	e.g.	ADV
ejpam-3967	40	14	,	,	PUNCT
ejpam-3967	40	15	facility	facility	NOUN
ejpam-3967	40	16	location	location	NOUN
ejpam-3967	40	17	)	)	PUNCT
ejpam-3967	40	18	aspects	aspect	NOUN
ejpam-3967	40	19	of	of	ADP
ejpam-3967	40	20	domination	domination	NOUN
ejpam-3967	40	21	in	in	ADP
ejpam-3967	40	22	graphs	graph	NOUN
ejpam-3967	40	23	was	be	AUX
ejpam-3967	40	24	provided	provide	VERB
ejpam-3967	40	25	by	by	ADP
ejpam-3967	40	26	haynes	hayne	NOUN
ejpam-3967	40	27	et	et	PROPN
ejpam-3967	40	28	al.[3	al.[3	PROPN
ejpam-3967	40	29	]	]	PUNCT
ejpam-3967	40	30	in	in	ADP
ejpam-3967	40	31	1998	1998	NUM
ejpam-3967	40	32	.	.	PUNCT
ejpam-3967	41	1	the	the	DET
ejpam-3967	41	2	join	join	NOUN
ejpam-3967	41	3	g	g	PROPN
ejpam-3967	41	4	+	+	CCONJ
ejpam-3967	41	5	h	h	NOUN
ejpam-3967	41	6	of	of	ADP
ejpam-3967	41	7	two	two	NUM
ejpam-3967	41	8	graphs	graph	NOUN
ejpam-3967	41	9	g	g	NOUN
ejpam-3967	41	10	and	and	CCONJ
ejpam-3967	41	11	h	h	NOUN
ejpam-3967	41	12	is	be	AUX
ejpam-3967	41	13	the	the	DET
ejpam-3967	41	14	graph	graph	NOUN
ejpam-3967	41	15	with	with	ADP
ejpam-3967	41	16	vertex	vertex	NOUN
ejpam-3967	41	17	set	set	VERB
ejpam-3967	41	18	v	v	NOUN
ejpam-3967	41	19	(	(	PUNCT
ejpam-3967	41	20	g	g	PROPN
ejpam-3967	41	21	+	+	NOUN
ejpam-3967	41	22	h	h	NOUN
ejpam-3967	41	23	)	)	PUNCT
ejpam-3967	42	1	=	=	NOUN
ejpam-3967	42	2	v	v	X
ejpam-3967	42	3	(	(	PUNCT
ejpam-3967	42	4	g	g	NOUN
ejpam-3967	42	5	)	)	PUNCT
ejpam-3967	42	6	∪	∪	NOUN
ejpam-3967	42	7	v	v	NOUN
ejpam-3967	42	8	(	(	PUNCT
ejpam-3967	42	9	h	h	NOUN
ejpam-3967	42	10	)	)	PUNCT
ejpam-3967	42	11	and	and	CCONJ
ejpam-3967	42	12	edge	edge	NOUN
ejpam-3967	42	13	set	set	VERB
ejpam-3967	42	14	e(g	e(g	PROPN
ejpam-3967	42	15	+	+	CCONJ
ejpam-3967	42	16	h	h	NOUN
ejpam-3967	42	17	)	)	PUNCT
ejpam-3967	42	18	=	=	SYM
ejpam-3967	42	19	e(g	e(g	PROPN
ejpam-3967	42	20	)	)	PUNCT
ejpam-3967	42	21	∪	∪	ADP
ejpam-3967	42	22	e(h	e(h	PROPN
ejpam-3967	42	23	)	)	PUNCT
ejpam-3967	42	24	∪	∪	NOUN
ejpam-3967	42	25	{	{	PUNCT
ejpam-3967	42	26	uv	uv	NOUN
ejpam-3967	42	27	:	:	PUNCT
ejpam-3967	42	28	u	u	PROPN
ejpam-3967	42	29	∈	∈	PROPN
ejpam-3967	42	30	v	v	ADP
ejpam-3967	42	31	(	(	PUNCT
ejpam-3967	42	32	g	g	NOUN
ejpam-3967	42	33	)	)	PUNCT
ejpam-3967	42	34	,	,	PUNCT
ejpam-3967	42	35	v	v	X
ejpam-3967	42	36	∈	∈	PROPN
ejpam-3967	42	37	v	v	NOUN
ejpam-3967	42	38	(	(	PUNCT
ejpam-3967	42	39	h	h	NOUN
ejpam-3967	42	40	)	)	PUNCT
ejpam-3967	42	41	}	}	PUNCT
ejpam-3967	42	42	.	.	PUNCT
ejpam-3967	43	1	the	the	DET
ejpam-3967	43	2	corona	corona	NOUN
ejpam-3967	43	3	of	of	ADP
ejpam-3967	43	4	two	two	NUM
ejpam-3967	43	5	graphs	graph	NOUN
ejpam-3967	43	6	g	g	NOUN
ejpam-3967	43	7	and	and	CCONJ
ejpam-3967	43	8	h	h	NOUN
ejpam-3967	43	9	,	,	PUNCT
ejpam-3967	43	10	denoted	denote	VERB
ejpam-3967	43	11	by	by	ADP
ejpam-3967	43	12	g	g	PROPN
ejpam-3967	43	13	◦	◦	NOUN
ejpam-3967	43	14	h	h	NOUN
ejpam-3967	43	15	,	,	PUNCT
ejpam-3967	43	16	is	be	AUX
ejpam-3967	43	17	the	the	DET
ejpam-3967	43	18	graph	graph	NOUN
ejpam-3967	43	19	obtained	obtain	VERB
ejpam-3967	43	20	by	by	ADP
ejpam-3967	43	21	taking	take	VERB
ejpam-3967	43	22	one	one	NUM
ejpam-3967	43	23	copy	copy	NOUN
ejpam-3967	43	24	of	of	ADP
ejpam-3967	43	25	g	g	NOUN
ejpam-3967	43	26	of	of	ADP
ejpam-3967	43	27	order	order	NOUN
ejpam-3967	43	28	n	n	NOUN
ejpam-3967	43	29	and	and	CCONJ
ejpam-3967	43	30	n	n	PRON
ejpam-3967	43	31	copies	copy	NOUN
ejpam-3967	43	32	of	of	ADP
ejpam-3967	43	33	h	h	NOUN
ejpam-3967	43	34	,	,	PUNCT
ejpam-3967	43	35	and	and	CCONJ
ejpam-3967	43	36	then	then	ADV
ejpam-3967	43	37	joining	join	VERB
ejpam-3967	43	38	the	the	DET
ejpam-3967	43	39	i	i	PROPN
ejpam-3967	43	40	-	-	PUNCT
ejpam-3967	43	41	th	th	X
ejpam-3967	43	42	vertex	vertex	NOUN
ejpam-3967	43	43	of	of	ADP
ejpam-3967	43	44	g	g	NOUN
ejpam-3967	43	45	to	to	ADP
ejpam-3967	43	46	every	every	DET
ejpam-3967	43	47	vertex	vertex	NOUN
ejpam-3967	43	48	in	in	ADP
ejpam-3967	43	49	the	the	DET
ejpam-3967	43	50	i	i	PROPN
ejpam-3967	43	51	-	-	PUNCT
ejpam-3967	43	52	th	th	PROPN
ejpam-3967	43	53	copy	copy	NOUN
ejpam-3967	43	54	of	of	ADP
ejpam-3967	43	55	h.	h.	PROPN
ejpam-3967	43	56	for	for	ADP
ejpam-3967	43	57	every	every	DET
ejpam-3967	43	58	v	v	NUM
ejpam-3967	43	59	∈	∈	PROPN
ejpam-3967	43	60	v	v	NOUN
ejpam-3967	43	61	(	(	PUNCT
ejpam-3967	43	62	g	g	NOUN
ejpam-3967	43	63	)	)	PUNCT
ejpam-3967	43	64	,	,	PUNCT
ejpam-3967	43	65	we	we	PRON
ejpam-3967	43	66	denote	denote	VERB
ejpam-3967	43	67	by	by	ADP
ejpam-3967	43	68	hv	hv	PROPN
ejpam-3967	43	69	the	the	DET
ejpam-3967	43	70	copy	copy	NOUN
ejpam-3967	43	71	of	of	ADP
ejpam-3967	43	72	h	h	NOUN
ejpam-3967	43	73	whose	whose	DET
ejpam-3967	43	74	vertices	vertex	NOUN
ejpam-3967	43	75	are	be	AUX
ejpam-3967	43	76	joined	join	VERB
ejpam-3967	43	77	or	or	CCONJ
ejpam-3967	43	78	attached	attach	VERB
ejpam-3967	43	79	to	to	ADP
ejpam-3967	43	80	the	the	DET
ejpam-3967	43	81	vertex	vertex	NOUN
ejpam-3967	43	82	v.	v.	CCONJ
ejpam-3967	43	83	for	for	ADP
ejpam-3967	43	84	each	each	DET
ejpam-3967	43	85	v	v	NUM
ejpam-3967	43	86	∈	∈	PROPN
ejpam-3967	43	87	v	v	NOUN
ejpam-3967	43	88	(	(	PUNCT
ejpam-3967	43	89	g	g	NOUN
ejpam-3967	43	90	)	)	PUNCT
ejpam-3967	43	91	,	,	PUNCT
ejpam-3967	44	1	the	the	DET
ejpam-3967	44	2	subgraph	subgraph	NOUN
ejpam-3967	44	3	〈	〈	PROPN
ejpam-3967	44	4	v	v	NOUN
ejpam-3967	44	5	〉	〉	PROPN
ejpam-3967	44	6	+	+	CCONJ
ejpam-3967	44	7	hv	hv	NOUN
ejpam-3967	44	8	of	of	ADP
ejpam-3967	44	9	g	g	PROPN
ejpam-3967	44	10	◦	◦	NOUN
ejpam-3967	44	11	h	h	NOUN
ejpam-3967	44	12	will	will	AUX
ejpam-3967	44	13	be	be	AUX
ejpam-3967	44	14	denoted	denote	VERB
ejpam-3967	44	15	by	by	ADP
ejpam-3967	44	16	v+hv	v+hv	PROPN
ejpam-3967	44	17	.	.	PUNCT
ejpam-3967	45	1	the	the	DET
ejpam-3967	45	2	lexicographic	lexicographic	ADJ
ejpam-3967	45	3	product	product	NOUN
ejpam-3967	45	4	of	of	ADP
ejpam-3967	45	5	two	two	NUM
ejpam-3967	45	6	graphs	graph	NOUN
ejpam-3967	45	7	g	g	NOUN
ejpam-3967	45	8	and	and	CCONJ
ejpam-3967	45	9	h	h	NOUN
ejpam-3967	45	10	,	,	PUNCT
ejpam-3967	45	11	denoted	denote	VERB
ejpam-3967	45	12	by	by	ADP
ejpam-3967	45	13	g[h	g[h	NOUN
ejpam-3967	45	14	]	]	PUNCT
ejpam-3967	45	15	,	,	PUNCT
ejpam-3967	45	16	is	be	AUX
ejpam-3967	45	17	the	the	DET
ejpam-3967	45	18	graph	graph	NOUN
ejpam-3967	45	19	with	with	ADP
ejpam-3967	45	20	vertex	vertex	NOUN
ejpam-3967	45	21	set	set	VERB
ejpam-3967	45	22	v	v	NOUN
ejpam-3967	45	23	(	(	PUNCT
ejpam-3967	45	24	g[h	g[h	PROPN
ejpam-3967	45	25	]	]	PUNCT
ejpam-3967	45	26	)	)	PUNCT
ejpam-3967	45	27	=	=	SYM
ejpam-3967	45	28	v	v	X
ejpam-3967	45	29	(	(	PUNCT
ejpam-3967	45	30	g	g	NOUN
ejpam-3967	45	31	)	)	PUNCT
ejpam-3967	45	32	×	×	NOUN
ejpam-3967	45	33	v	v	NOUN
ejpam-3967	45	34	(	(	PUNCT
ejpam-3967	45	35	h	h	NOUN
ejpam-3967	45	36	)	)	PUNCT
ejpam-3967	45	37	and	and	CCONJ
ejpam-3967	45	38	edge	edge	VERB
ejpam-3967	45	39	set	set	VERB
ejpam-3967	45	40	e(g[h	e(g[h	NOUN
ejpam-3967	45	41	]	]	PUNCT
ejpam-3967	45	42	)	)	PUNCT
ejpam-3967	45	43	satisfying	satisfy	VERB
ejpam-3967	45	44	the	the	DET
ejpam-3967	45	45	following	follow	VERB
ejpam-3967	45	46	conditions	condition	NOUN
ejpam-3967	45	47	:	:	PUNCT
ejpam-3967	45	48	(	(	PUNCT
ejpam-3967	45	49	u1	u1	PROPN
ejpam-3967	45	50	,	,	PUNCT
ejpam-3967	45	51	v1)(u2	v1)(u2	PROPN
ejpam-3967	45	52	,	,	PUNCT
ejpam-3967	45	53	v2	v2	PROPN
ejpam-3967	45	54	)	)	PUNCT
ejpam-3967	45	55	∈	∈	NOUN
ejpam-3967	45	56	e(g[h	e(g[h	NOUN
ejpam-3967	45	57	]	]	PUNCT
ejpam-3967	45	58	)	)	PUNCT
ejpam-3967	45	59	if	if	SCONJ
ejpam-3967	45	60	and	and	CCONJ
ejpam-3967	45	61	only	only	ADV
ejpam-3967	45	62	if	if	SCONJ
ejpam-3967	45	63	either	either	PRON
ejpam-3967	45	64	u1u2	u1u2	PROPN
ejpam-3967	45	65	∈	∈	PROPN
ejpam-3967	45	66	e(g	e(g	PROPN
ejpam-3967	45	67	)	)	PUNCT
ejpam-3967	45	68	or	or	CCONJ
ejpam-3967	45	69	u1	u1	NOUN
ejpam-3967	45	70	=	=	SYM
ejpam-3967	45	71	u2	u2	PROPN
ejpam-3967	45	72	and	and	CCONJ
ejpam-3967	45	73	v1v2	v1v2	PUNCT
ejpam-3967	45	74	∈	∈	PROPN
ejpam-3967	45	75	e(h	e(h	PROPN
ejpam-3967	45	76	)	)	PUNCT
ejpam-3967	45	77	.	.	PUNCT
ejpam-3967	46	1	the	the	DET
ejpam-3967	46	2	cartesian	cartesian	ADJ
ejpam-3967	46	3	product	product	NOUN
ejpam-3967	46	4	of	of	ADP
ejpam-3967	46	5	two	two	NUM
ejpam-3967	46	6	graphs	graph	NOUN
ejpam-3967	46	7	g	g	NOUN
ejpam-3967	46	8	and	and	CCONJ
ejpam-3967	46	9	h	h	NOUN
ejpam-3967	46	10	,	,	PUNCT
ejpam-3967	46	11	denoted	denote	VERB
ejpam-3967	46	12	by	by	ADP
ejpam-3967	46	13	g	g	PROPN
ejpam-3967	46	14	�	�	PROPN
ejpam-3967	46	15	h	h	NOUN
ejpam-3967	46	16	,	,	PUNCT
ejpam-3967	46	17	is	be	AUX
ejpam-3967	46	18	the	the	DET
ejpam-3967	46	19	graph	graph	NOUN
ejpam-3967	46	20	with	with	ADP
ejpam-3967	46	21	vertex	vertex	NOUN
ejpam-3967	46	22	-	-	PUNCT
ejpam-3967	46	23	set	set	VERB
ejpam-3967	46	24	v	v	NOUN
ejpam-3967	46	25	(	(	PUNCT
ejpam-3967	46	26	g	g	PROPN
ejpam-3967	46	27	�	�	NOUN
ejpam-3967	46	28	h	h	NOUN
ejpam-3967	46	29	)	)	PUNCT
ejpam-3967	47	1	=	=	NOUN
ejpam-3967	47	2	v	v	X
ejpam-3967	47	3	(	(	PUNCT
ejpam-3967	47	4	g	g	NOUN
ejpam-3967	47	5	)	)	PUNCT
ejpam-3967	47	6	×	×	NOUN
ejpam-3967	47	7	v	v	NOUN
ejpam-3967	47	8	(	(	PUNCT
ejpam-3967	47	9	h	h	NOUN
ejpam-3967	47	10	)	)	PUNCT
ejpam-3967	47	11	and	and	CCONJ
ejpam-3967	47	12	edge	edge	NOUN
ejpam-3967	47	13	-	-	PUNCT
ejpam-3967	47	14	set	set	VERB
ejpam-3967	47	15	e(g	e(g	PROPN
ejpam-3967	47	16	�	�	PROPN
ejpam-3967	47	17	h	h	NOUN
ejpam-3967	47	18	)	)	PUNCT
ejpam-3967	47	19	satisfying	satisfy	VERB
ejpam-3967	47	20	the	the	DET
ejpam-3967	47	21	following	follow	VERB
ejpam-3967	47	22	conditions	condition	NOUN
ejpam-3967	47	23	:	:	PUNCT
ejpam-3967	47	24	(	(	PUNCT
ejpam-3967	47	25	u1	u1	PROPN
ejpam-3967	47	26	,	,	PUNCT
ejpam-3967	47	27	v1)(u2	v1)(u2	PROPN
ejpam-3967	47	28	,	,	PUNCT
ejpam-3967	47	29	v2	v2	PROPN
ejpam-3967	47	30	)	)	PUNCT
ejpam-3967	47	31	∈	∈	PROPN
ejpam-3967	47	32	e(g	e(g	PROPN
ejpam-3967	47	33	�	�	PROPN
ejpam-3967	47	34	h	h	PROPN
ejpam-3967	47	35	)	)	PUNCT
ejpam-3967	47	36	if	if	SCONJ
ejpam-3967	47	37	and	and	CCONJ
ejpam-3967	47	38	only	only	ADV
ejpam-3967	47	39	if	if	SCONJ
ejpam-3967	47	40	either	either	PRON
ejpam-3967	47	41	u1u2	u1u2	PROPN
ejpam-3967	47	42	∈	∈	PROPN
ejpam-3967	47	43	e(g	e(g	PROPN
ejpam-3967	47	44	)	)	PUNCT
ejpam-3967	47	45	and	and	CCONJ
ejpam-3967	47	46	v1	v1	NOUN
ejpam-3967	47	47	=	=	SYM
ejpam-3967	47	48	v2	v2	NOUN
ejpam-3967	47	49	or	or	CCONJ
ejpam-3967	47	50	u1	u1	NOUN
ejpam-3967	47	51	=	=	SYM
ejpam-3967	47	52	u2	u2	PROPN
ejpam-3967	47	53	and	and	CCONJ
ejpam-3967	47	54	v1v2	v1v2	PUNCT
ejpam-3967	47	55	∈	∈	PROPN
ejpam-3967	47	56	e(h	e(h	PROPN
ejpam-3967	47	57	)	)	PUNCT
ejpam-3967	47	58	.	.	PUNCT
ejpam-3967	48	1	w.	w.	PROPN
ejpam-3967	48	2	bent	bent	PROPN
ejpam-3967	48	3	-	-	PUNCT
ejpam-3967	48	4	usman	usman	PROPN
ejpam-3967	48	5	,	,	PUNCT
ejpam-3967	48	6	r.	r.	PROPN
ejpam-3967	48	7	isla	isla	PROPN
ejpam-3967	48	8	/	/	SYM
ejpam-3967	48	9	eur	eur	PROPN
ejpam-3967	48	10	.	.	PUNCT
ejpam-3967	49	1	j.	j.	PROPN
ejpam-3967	49	2	pure	pure	PROPN
ejpam-3967	49	3	appl	appl	PROPN
ejpam-3967	49	4	.	.	PROPN
ejpam-3967	49	5	math	math	PROPN
ejpam-3967	49	6	,	,	PUNCT
ejpam-3967	49	7	14	14	NUM
ejpam-3967	49	8	(	(	PUNCT
ejpam-3967	49	9	2	2	NUM
ejpam-3967	49	10	)	)	PUNCT
ejpam-3967	49	11	(	(	PUNCT
ejpam-3967	49	12	2021	2021	NUM
ejpam-3967	49	13	)	)	PUNCT
ejpam-3967	49	14	,	,	PUNCT
ejpam-3967	49	15	578	578	NUM
ejpam-3967	49	16	-	-	SYM
ejpam-3967	49	17	589	589	NUM
ejpam-3967	49	18	580	580	NUM
ejpam-3967	49	19	2	2	NUM
ejpam-3967	49	20	.	.	PUNCT
ejpam-3967	49	21	preliminary	preliminary	ADJ
ejpam-3967	49	22	results	result	NOUN
ejpam-3967	49	23	remark	remark	VERB
ejpam-3967	49	24	1	1	NUM
ejpam-3967	49	25	.	.	PUNCT
ejpam-3967	50	1	for	for	ADP
ejpam-3967	50	2	any	any	DET
ejpam-3967	50	3	connected	connected	ADJ
ejpam-3967	50	4	graph	graph	NOUN
ejpam-3967	50	5	g	g	NOUN
ejpam-3967	50	6	of	of	ADP
ejpam-3967	50	7	order	order	NOUN
ejpam-3967	50	8	n	n	PRON
ejpam-3967	50	9	≥	≥	NOUN
ejpam-3967	50	10	2	2	NUM
ejpam-3967	50	11	and	and	CCONJ
ejpam-3967	50	12	a	a	DET
ejpam-3967	50	13	positive	positive	ADJ
ejpam-3967	50	14	integer	integer	NOUN
ejpam-3967	50	15	k	k	PROPN
ejpam-3967	50	16	,	,	PUNCT
ejpam-3967	50	17	γkfd(g	γkfd(g	PROPN
ejpam-3967	50	18	)	)	PUNCT
ejpam-3967	50	19	≤	≤	NUM
ejpam-3967	50	20	γkftd(g	γkftd(g	PROPN
ejpam-3967	50	21	)	)	PUNCT
ejpam-3967	50	22	and	and	CCONJ
ejpam-3967	50	23	γkftd(g	γkftd(g	PROPN
ejpam-3967	50	24	)	)	PUNCT
ejpam-3967	50	25	≥	≥	NOUN
ejpam-3967	50	26	2	2	NUM
ejpam-3967	50	27	.	.	PUNCT
ejpam-3967	50	28	remark	remark	NOUN
ejpam-3967	50	29	2	2	NUM
ejpam-3967	50	30	.	.	PUNCT
ejpam-3967	51	1	any	any	DET
ejpam-3967	51	2	kftd	kftd	NOUN
ejpam-3967	51	3	-	-	PUNCT
ejpam-3967	51	4	set	set	NOUN
ejpam-3967	51	5	is	be	AUX
ejpam-3967	51	6	a	a	DET
ejpam-3967	51	7	kfd	kfd	NOUN
ejpam-3967	51	8	-	-	PUNCT
ejpam-3967	51	9	set	set	NOUN
ejpam-3967	51	10	,	,	PUNCT
ejpam-3967	51	11	where	where	SCONJ
ejpam-3967	51	12	k	k	PROPN
ejpam-3967	51	13	is	be	AUX
ejpam-3967	51	14	a	a	DET
ejpam-3967	51	15	positive	positive	ADJ
ejpam-3967	51	16	integer	integer	NOUN
ejpam-3967	51	17	.	.	PUNCT
ejpam-3967	52	1	theorem	theorem	NOUN
ejpam-3967	52	2	1	1	NUM
ejpam-3967	52	3	.	.	PUNCT
ejpam-3967	53	1	let	let	VERB
ejpam-3967	53	2	n	n	NOUN
ejpam-3967	53	3	and	and	CCONJ
ejpam-3967	53	4	r	r	NOUN
ejpam-3967	53	5	be	be	VERB
ejpam-3967	53	6	positive	positive	ADJ
ejpam-3967	53	7	integers	integer	NOUN
ejpam-3967	53	8	where	where	SCONJ
ejpam-3967	53	9	n	n	NUM
ejpam-3967	53	10	≥	≥	X
ejpam-3967	53	11	2	2	NUM
ejpam-3967	53	12	and	and	CCONJ
ejpam-3967	53	13	r	r	NOUN
ejpam-3967	53	14	≥	≥	NUM
ejpam-3967	53	15	1	1	NUM
ejpam-3967	53	16	.	.	PUNCT
ejpam-3967	54	1	then	then	ADV
ejpam-3967	54	2	γ1ftd(pn	γ1ftd(pn	NUM
ejpam-3967	54	3	)	)	PUNCT
ejpam-3967	55	1	=	=	PUNCT
ejpam-3967	55	2			NOUN
ejpam-3967	55	3	2	2	NUM
ejpam-3967	55	4	,	,	PUNCT
ejpam-3967	55	5	n	n	NOUN
ejpam-3967	55	6	=	=	SYM
ejpam-3967	55	7	2	2	NUM
ejpam-3967	55	8	,	,	PUNCT
ejpam-3967	55	9	3	3	NUM
ejpam-3967	55	10	2r	2r	NUM
ejpam-3967	55	11	,	,	PUNCT
ejpam-3967	55	12	n	n	NOUN
ejpam-3967	55	13	=	=	NOUN
ejpam-3967	55	14	4r	4r	NUM
ejpam-3967	55	15	2r	2r	NUM
ejpam-3967	56	1	+	+	CCONJ
ejpam-3967	56	2	1	1	NUM
ejpam-3967	56	3	,	,	PUNCT
ejpam-3967	56	4	n	n	NOUN
ejpam-3967	56	5	=	=	NOUN
ejpam-3967	56	6	4r	4r	NOUN
ejpam-3967	56	7	+	+	CCONJ
ejpam-3967	56	8	1	1	NUM
ejpam-3967	56	9	2r	2r	NUM
ejpam-3967	56	10	+	+	CCONJ
ejpam-3967	56	11	2	2	NUM
ejpam-3967	56	12	,	,	PUNCT
ejpam-3967	56	13	otherwise	otherwise	ADV
ejpam-3967	56	14	.	.	PUNCT
ejpam-3967	57	1	proof	proof	NOUN
ejpam-3967	57	2	.	.	PUNCT
ejpam-3967	58	1	let	let	VERB
ejpam-3967	58	2	g	g	NOUN
ejpam-3967	58	3	=	=	PUNCT
ejpam-3967	58	4	pn	pn	PROPN
ejpam-3967	58	5	=	=	PUNCT
ejpam-3967	58	6	{	{	PUNCT
ejpam-3967	58	7	v1	v1	PROPN
ejpam-3967	58	8	,	,	PUNCT
ejpam-3967	58	9	v2	v2	PROPN
ejpam-3967	58	10	,	,	PUNCT
ejpam-3967	58	11	v3	v3	PROPN
ejpam-3967	58	12	,	,	PUNCT
ejpam-3967	58	13	...	...	PUNCT
ejpam-3967	58	14	,	,	PUNCT
ejpam-3967	58	15	vn	vn	PROPN
ejpam-3967	58	16	}	}	PUNCT
ejpam-3967	58	17	.	.	PUNCT
ejpam-3967	59	1	if	if	SCONJ
ejpam-3967	59	2	n	n	NOUN
ejpam-3967	59	3	=	=	SYM
ejpam-3967	59	4	2	2	NUM
ejpam-3967	59	5	or	or	CCONJ
ejpam-3967	59	6	n	n	NOUN
ejpam-3967	59	7	=	=	SYM
ejpam-3967	59	8	3	3	NUM
ejpam-3967	59	9	,	,	PUNCT
ejpam-3967	59	10	then	then	ADV
ejpam-3967	59	11	clearly	clearly	ADV
ejpam-3967	59	12	,	,	PUNCT
ejpam-3967	59	13	γ1ftd(pn	γ1ftd(pn	NUM
ejpam-3967	59	14	)	)	PUNCT
ejpam-3967	59	15	=	=	SYM
ejpam-3967	59	16	2	2	X
ejpam-3967	59	17	.	.	PUNCT
ejpam-3967	60	1	let	let	VERB
ejpam-3967	60	2	n	n	PRON
ejpam-3967	60	3	≥	≥	X
ejpam-3967	60	4	4	4	NUM
ejpam-3967	60	5	and	and	CCONJ
ejpam-3967	60	6	consider	consider	VERB
ejpam-3967	60	7	the	the	DET
ejpam-3967	60	8	following	follow	VERB
ejpam-3967	60	9	cases	case	NOUN
ejpam-3967	60	10	:	:	PUNCT
ejpam-3967	60	11	case	case	NOUN
ejpam-3967	60	12	1	1	NUM
ejpam-3967	60	13	:	:	PUNCT
ejpam-3967	60	14	n	n	NOUN
ejpam-3967	60	15	=	=	SYM
ejpam-3967	60	16	4r	4r	NUM
ejpam-3967	60	17	group	group	NOUN
ejpam-3967	60	18	the	the	DET
ejpam-3967	60	19	first	first	ADJ
ejpam-3967	60	20	4r	4r	ADJ
ejpam-3967	60	21	vertices	vertex	NOUN
ejpam-3967	60	22	of	of	ADP
ejpam-3967	60	23	pn	pn	NOUN
ejpam-3967	60	24	into	into	ADP
ejpam-3967	60	25	r	r	NOUN
ejpam-3967	60	26	disjoint	disjoint	NOUN
ejpam-3967	60	27	subsets	subset	NOUN
ejpam-3967	60	28	.	.	PUNCT
ejpam-3967	61	1	s1	s1	NOUN
ejpam-3967	61	2	=	=	PUNCT
ejpam-3967	61	3	{	{	PUNCT
ejpam-3967	61	4	v1	v1	PROPN
ejpam-3967	61	5	,	,	PUNCT
ejpam-3967	61	6	v2	v2	PROPN
ejpam-3967	61	7	,	,	PUNCT
ejpam-3967	61	8	v3	v3	PROPN
ejpam-3967	61	9	,	,	PUNCT
ejpam-3967	61	10	v4	v4	PROPN
ejpam-3967	61	11	}	}	PUNCT
ejpam-3967	61	12	s2	s2	NOUN
ejpam-3967	61	13	=	=	SYM
ejpam-3967	61	14	{	{	PUNCT
ejpam-3967	61	15	v5	v5	PROPN
ejpam-3967	61	16	,	,	PUNCT
ejpam-3967	61	17	v6	v6	NOUN
ejpam-3967	61	18	,	,	PUNCT
ejpam-3967	61	19	v7	v7	NUM
ejpam-3967	61	20	,	,	PUNCT
ejpam-3967	61	21	v8	v8	PROPN
ejpam-3967	61	22	}	}	PUNCT
ejpam-3967	61	23	s3	s3	NOUN
ejpam-3967	61	24	=	=	SYM
ejpam-3967	61	25	{	{	PUNCT
ejpam-3967	61	26	v9	v9	PROPN
ejpam-3967	61	27	,	,	PUNCT
ejpam-3967	61	28	v10	v10	NOUN
ejpam-3967	61	29	,	,	PUNCT
ejpam-3967	61	30	v11	v11	NOUN
ejpam-3967	61	31	,	,	PUNCT
ejpam-3967	61	32	v12	v12	VERB
ejpam-3967	61	33	}	}	PUNCT
ejpam-3967	61	34	...	...	PUNCT
ejpam-3967	62	1	sr−1	sr−1	PROPN
ejpam-3967	62	2	=	=	SYM
ejpam-3967	62	3	{	{	PUNCT
ejpam-3967	62	4	v4r−7	v4r−7	PROPN
ejpam-3967	62	5	,	,	PUNCT
ejpam-3967	62	6	v4r−6	v4r−6	PROPN
ejpam-3967	62	7	,	,	PUNCT
ejpam-3967	62	8	v4r−5	v4r−5	PROPN
ejpam-3967	62	9	,	,	PUNCT
ejpam-3967	62	10	v4r−4	v4r−4	PROPN
ejpam-3967	62	11	}	}	PUNCT
ejpam-3967	62	12	sr	sr	NOUN
ejpam-3967	62	13	=	=	SYM
ejpam-3967	62	14	{	{	PUNCT
ejpam-3967	62	15	v4r−3	v4r−3	NOUN
ejpam-3967	62	16	,	,	PUNCT
ejpam-3967	62	17	v4r−2	v4r−2	PROPN
ejpam-3967	62	18	,	,	PUNCT
ejpam-3967	62	19	v4r−1	v4r−1	PROPN
ejpam-3967	62	20	,	,	PUNCT
ejpam-3967	62	21	v4r	v4r	ADJ
ejpam-3967	62	22	}	}	PUNCT
ejpam-3967	62	23	for	for	ADP
ejpam-3967	62	24	every	every	DET
ejpam-3967	62	25	induced	induce	VERB
ejpam-3967	62	26	subgraph	subgraph	NOUN
ejpam-3967	62	27	〈	〈	PROPN
ejpam-3967	62	28	vi	vi	PROPN
ejpam-3967	62	29	,	,	PUNCT
ejpam-3967	62	30	vi+1	vi+1	NOUN
ejpam-3967	62	31	,	,	PUNCT
ejpam-3967	62	32	vi+2	vi+2	NUM
ejpam-3967	62	33	,	,	PUNCT
ejpam-3967	62	34	vi+3	vi+3	VERB
ejpam-3967	62	35	〉	〉	NOUN
ejpam-3967	62	36	of	of	ADP
ejpam-3967	62	37	pn	pn	PROPN
ejpam-3967	62	38	,	,	PUNCT
ejpam-3967	62	39	where	where	SCONJ
ejpam-3967	62	40	i	i	PRON
ejpam-3967	62	41	=	=	NOUN
ejpam-3967	62	42	1	1	NUM
ejpam-3967	62	43	,	,	PUNCT
ejpam-3967	62	44	5	5	NUM
ejpam-3967	62	45	,	,	PUNCT
ejpam-3967	62	46	9	9	NUM
ejpam-3967	62	47	,	,	PUNCT
ejpam-3967	62	48	...	...	PUNCT
ejpam-3967	62	49	,	,	PUNCT
ejpam-3967	62	50	4r	4r	NUM
ejpam-3967	62	51	−	−	PROPN
ejpam-3967	62	52	3	3	NUM
ejpam-3967	62	53	,	,	PUNCT
ejpam-3967	62	54	the	the	DET
ejpam-3967	62	55	vertices	vertex	NOUN
ejpam-3967	62	56	vi+1	vi+1	ADV
ejpam-3967	62	57	and	and	CCONJ
ejpam-3967	62	58	vi+2	vi+2	NUM
ejpam-3967	62	59	are	be	AUX
ejpam-3967	62	60	in	in	ADP
ejpam-3967	62	61	a	a	DET
ejpam-3967	62	62	1	1	NUM
ejpam-3967	62	63	-	-	PUNCT
ejpam-3967	62	64	fair	fair	ADJ
ejpam-3967	62	65	total	total	ADJ
ejpam-3967	62	66	dominating	dominating	NOUN
ejpam-3967	62	67	set	set	NOUN
ejpam-3967	62	68	of	of	ADP
ejpam-3967	62	69	pn	pn	PROPN
ejpam-3967	62	70	.	.	PUNCT
ejpam-3967	63	1	thus	thus	ADV
ejpam-3967	63	2	,	,	PUNCT
ejpam-3967	63	3	the	the	DET
ejpam-3967	63	4	set	set	NOUN
ejpam-3967	63	5	t	t	NOUN
ejpam-3967	63	6	=	=	SYM
ejpam-3967	63	7	{	{	PUNCT
ejpam-3967	63	8	v2	v2	PROPN
ejpam-3967	63	9	,	,	PUNCT
ejpam-3967	63	10	v3	v3	PROPN
ejpam-3967	63	11	,	,	PUNCT
ejpam-3967	63	12	v6	v6	NOUN
ejpam-3967	63	13	,	,	PUNCT
ejpam-3967	63	14	v7	v7	VERB
ejpam-3967	63	15	,	,	PUNCT
ejpam-3967	63	16	...	...	PUNCT
ejpam-3967	63	17	,	,	PUNCT
ejpam-3967	63	18	v4r−2	v4r−2	ADV
ejpam-3967	63	19	,	,	PUNCT
ejpam-3967	63	20	v4r−1	v4r−1	PROPN
ejpam-3967	63	21	}	}	PUNCT
ejpam-3967	63	22	is	be	AUX
ejpam-3967	63	23	a	a	DET
ejpam-3967	63	24	1	1	NUM
ejpam-3967	63	25	-	-	PUNCT
ejpam-3967	63	26	fair	fair	ADJ
ejpam-3967	63	27	total	total	ADJ
ejpam-3967	63	28	dominating	dominating	NOUN
ejpam-3967	63	29	set	set	NOUN
ejpam-3967	63	30	of	of	ADP
ejpam-3967	63	31	pn	pn	PROPN
ejpam-3967	63	32	.	.	PUNCT
ejpam-3967	64	1	since	since	SCONJ
ejpam-3967	64	2	|t	|t	PROPN
ejpam-3967	64	3	|	|	ADV
ejpam-3967	64	4	=	=	SYM
ejpam-3967	64	5	2r	2r	NUM
ejpam-3967	64	6	,	,	PUNCT
ejpam-3967	64	7	γ1ftd(pn	γ1ftd(pn	NUM
ejpam-3967	64	8	)	)	PUNCT
ejpam-3967	64	9	≤	≤	NOUN
ejpam-3967	64	10	2r	2r	NUM
ejpam-3967	64	11	.	.	PUNCT
ejpam-3967	65	1	note	note	VERB
ejpam-3967	65	2	that	that	SCONJ
ejpam-3967	65	3	every	every	DET
ejpam-3967	65	4	pair	pair	NOUN
ejpam-3967	65	5	of	of	ADP
ejpam-3967	65	6	adjacent	adjacent	ADJ
ejpam-3967	65	7	vertices	vertex	NOUN
ejpam-3967	65	8	in	in	ADP
ejpam-3967	65	9	pn	pn	PROPN
ejpam-3967	65	10	can	can	AUX
ejpam-3967	65	11	dominate	dominate	VERB
ejpam-3967	65	12	at	at	ADP
ejpam-3967	65	13	most	most	ADJ
ejpam-3967	65	14	2	2	NUM
ejpam-3967	65	15	vertices	vertex	NOUN
ejpam-3967	65	16	.	.	PUNCT
ejpam-3967	66	1	thus	thus	ADV
ejpam-3967	66	2	,	,	PUNCT
ejpam-3967	66	3	every	every	DET
ejpam-3967	66	4	1	1	NUM
ejpam-3967	66	5	-	-	PUNCT
ejpam-3967	66	6	fair	fair	ADJ
ejpam-3967	66	7	total	total	ADJ
ejpam-3967	66	8	dominating	dominating	NOUN
ejpam-3967	66	9	set	set	NOUN
ejpam-3967	66	10	of	of	ADP
ejpam-3967	66	11	pn	pn	PROPN
ejpam-3967	66	12	contains	contain	VERB
ejpam-3967	66	13	at	at	ADP
ejpam-3967	66	14	least	least	ADJ
ejpam-3967	66	15	dn2	dn2	NOUN
ejpam-3967	66	16	e	e	NOUN
ejpam-3967	66	17	vertices	vertex	NOUN
ejpam-3967	66	18	.	.	PUNCT
ejpam-3967	67	1	hence	hence	ADV
ejpam-3967	67	2	,	,	PUNCT
ejpam-3967	67	3	γ1ftd(pn	γ1ftd(pn	NUM
ejpam-3967	67	4	)	)	PUNCT
ejpam-3967	67	5	≥	≥	NOUN
ejpam-3967	67	6	dn2	dn2	NOUN
ejpam-3967	67	7	e	e	NOUN
ejpam-3967	67	8	=	=	SYM
ejpam-3967	67	9	2r	2r	NUM
ejpam-3967	67	10	since	since	SCONJ
ejpam-3967	67	11	n	n	NOUN
ejpam-3967	67	12	=	=	NOUN
ejpam-3967	67	13	4r	4r	NOUN
ejpam-3967	67	14	.	.	PUNCT
ejpam-3967	68	1	thus	thus	ADV
ejpam-3967	68	2	,	,	PUNCT
ejpam-3967	68	3	γ1ftd(pn	γ1ftd(pn	NUM
ejpam-3967	68	4	)	)	PUNCT
ejpam-3967	68	5	=	=	SYM
ejpam-3967	68	6	2r	2r	NUM
ejpam-3967	68	7	.	.	PUNCT
ejpam-3967	69	1	case	case	NOUN
ejpam-3967	69	2	2	2	NUM
ejpam-3967	69	3	:	:	PUNCT
ejpam-3967	69	4	n	n	NOUN
ejpam-3967	69	5	=	=	SYM
ejpam-3967	69	6	4r	4r	NOUN
ejpam-3967	69	7	+	+	CCONJ
ejpam-3967	69	8	1	1	NUM
ejpam-3967	69	9	the	the	DET
ejpam-3967	69	10	set	set	ADJ
ejpam-3967	69	11	t	t	NOUN
ejpam-3967	69	12	in	in	ADP
ejpam-3967	69	13	case	case	NOUN
ejpam-3967	69	14	1	1	NUM
ejpam-3967	69	15	is	be	AUX
ejpam-3967	69	16	no	no	PRON
ejpam-3967	69	17	longer	long	ADV
ejpam-3967	69	18	a	a	DET
ejpam-3967	69	19	γ1ftd	γ1ftd	PROPN
ejpam-3967	69	20	-	-	PUNCT
ejpam-3967	69	21	set	set	NOUN
ejpam-3967	69	22	of	of	ADP
ejpam-3967	69	23	tn	tn	NOUN
ejpam-3967	69	24	here	here	ADV
ejpam-3967	69	25	since	since	SCONJ
ejpam-3967	69	26	v4r+1	v4r+1	NOUN
ejpam-3967	69	27	is	be	AUX
ejpam-3967	69	28	not	not	PART
ejpam-3967	69	29	adjacent	adjacent	ADJ
ejpam-3967	69	30	to	to	ADP
ejpam-3967	69	31	any	any	DET
ejpam-3967	69	32	vertex	vertex	NOUN
ejpam-3967	69	33	in	in	ADP
ejpam-3967	69	34	t	t	PROPN
ejpam-3967	69	35	,	,	PUNCT
ejpam-3967	69	36	but	but	CCONJ
ejpam-3967	69	37	clearly	clearly	ADV
ejpam-3967	69	38	,	,	PUNCT
ejpam-3967	69	39	t	t	PROPN
ejpam-3967	69	40	∪	∪	X
ejpam-3967	69	41	{	{	PUNCT
ejpam-3967	69	42	v4r	v4r	NOUN
ejpam-3967	69	43	}	}	PUNCT
ejpam-3967	69	44	is	be	AUX
ejpam-3967	69	45	a	a	DET
ejpam-3967	69	46	γ1ftd	γ1ftd	NOUN
ejpam-3967	69	47	-	-	PUNCT
ejpam-3967	69	48	set	set	NOUN
ejpam-3967	69	49	.	.	PUNCT
ejpam-3967	70	1	thus	thus	ADV
ejpam-3967	70	2	,	,	PUNCT
ejpam-3967	70	3	γ1ftd(pn	γ1ftd(pn	NUM
ejpam-3967	70	4	)	)	PUNCT
ejpam-3967	70	5	=	=	SYM
ejpam-3967	70	6	2r	2r	NUM
ejpam-3967	71	1	+	+	CCONJ
ejpam-3967	71	2	1	1	X
ejpam-3967	71	3	.	.	X
ejpam-3967	71	4	case	case	NOUN
ejpam-3967	71	5	3	3	NUM
ejpam-3967	71	6	.	.	PUNCT
ejpam-3967	72	1	n	n	NOUN
ejpam-3967	72	2	=	=	NOUN
ejpam-3967	72	3	4r	4r	NOUN
ejpam-3967	72	4	+	+	CCONJ
ejpam-3967	72	5	2	2	NUM
ejpam-3967	72	6	the	the	DET
ejpam-3967	72	7	set	set	NOUN
ejpam-3967	72	8	s	s	PART
ejpam-3967	72	9	=	=	X
ejpam-3967	72	10	t	t	X
ejpam-3967	72	11	∪	∪	X
ejpam-3967	72	12	{	{	PUNCT
ejpam-3967	72	13	v4r	v4r	NOUN
ejpam-3967	72	14	}	}	PUNCT
ejpam-3967	72	15	is	be	AUX
ejpam-3967	72	16	not	not	PART
ejpam-3967	72	17	a	a	DET
ejpam-3967	72	18	γ1ftd	γ1ftd	NOUN
ejpam-3967	72	19	-	-	PUNCT
ejpam-3967	72	20	set	set	NOUN
ejpam-3967	72	21	of	of	ADP
ejpam-3967	72	22	pn	pn	PROPN
ejpam-3967	72	23	here	here	ADV
ejpam-3967	72	24	since	since	SCONJ
ejpam-3967	72	25	v4r+2	v4r+2	NOUN
ejpam-3967	72	26	is	be	AUX
ejpam-3967	72	27	not	not	PART
ejpam-3967	72	28	adjacent	adjacent	ADJ
ejpam-3967	72	29	to	to	ADP
ejpam-3967	72	30	any	any	DET
ejpam-3967	72	31	vertex	vertex	NOUN
ejpam-3967	72	32	in	in	ADP
ejpam-3967	72	33	s	s	PROPN
ejpam-3967	72	34	,	,	PUNCT
ejpam-3967	72	35	but	but	CCONJ
ejpam-3967	72	36	t	t	PROPN
ejpam-3967	72	37	∪	∪	X
ejpam-3967	72	38	{	{	PUNCT
ejpam-3967	72	39	v4r	v4r	ADJ
ejpam-3967	72	40	,	,	PUNCT
ejpam-3967	72	41	v4r+1	v4r+1	PRON
ejpam-3967	72	42	}	}	PUNCT
ejpam-3967	72	43	is	be	AUX
ejpam-3967	72	44	clearly	clearly	ADV
ejpam-3967	72	45	a	a	DET
ejpam-3967	72	46	γ1ftd	γ1ftd	NOUN
ejpam-3967	72	47	-	-	PUNCT
ejpam-3967	72	48	set	set	NOUN
ejpam-3967	72	49	.	.	PUNCT
ejpam-3967	73	1	hence	hence	ADV
ejpam-3967	73	2	,	,	PUNCT
ejpam-3967	73	3	γ1ftd(pn	γ1ftd(pn	NUM
ejpam-3967	73	4	)	)	PUNCT
ejpam-3967	73	5	=	=	SYM
ejpam-3967	74	1	2r	2r	NUM
ejpam-3967	75	1	+	+	CCONJ
ejpam-3967	75	2	2	2	X
ejpam-3967	75	3	.	.	X
ejpam-3967	75	4	case	case	NOUN
ejpam-3967	75	5	4	4	NUM
ejpam-3967	75	6	.	.	PUNCT
ejpam-3967	76	1	n	n	NOUN
ejpam-3967	76	2	=	=	SYM
ejpam-3967	76	3	4r	4r	NOUN
ejpam-3967	76	4	+	+	CCONJ
ejpam-3967	76	5	3	3	NUM
ejpam-3967	76	6	consider	consider	VERB
ejpam-3967	76	7	the	the	DET
ejpam-3967	76	8	1	1	NUM
ejpam-3967	76	9	-	-	PUNCT
ejpam-3967	76	10	fair	fair	ADJ
ejpam-3967	76	11	total	total	ADJ
ejpam-3967	76	12	dominating	dominating	NOUN
ejpam-3967	76	13	set	set	VERB
ejpam-3967	76	14	t	t	NOUN
ejpam-3967	76	15	in	in	ADP
ejpam-3967	76	16	case	case	NOUN
ejpam-3967	76	17	1	1	X
ejpam-3967	76	18	.	.	PUNCT
ejpam-3967	76	19	add	add	VERB
ejpam-3967	76	20	v4r+2	v4r+2	NOUN
ejpam-3967	76	21	and	and	CCONJ
ejpam-3967	76	22	v4r+3	v4r+3	VERB
ejpam-3967	76	23	to	to	ADP
ejpam-3967	76	24	the	the	DET
ejpam-3967	76	25	vertices	vertex	NOUN
ejpam-3967	76	26	in	in	ADP
ejpam-3967	76	27	t	t	PROPN
ejpam-3967	76	28	so	so	SCONJ
ejpam-3967	76	29	that	that	SCONJ
ejpam-3967	76	30	t	t	PROPN
ejpam-3967	76	31	∪	∪	X
ejpam-3967	76	32	{	{	PUNCT
ejpam-3967	76	33	v4r+2	v4r+2	NOUN
ejpam-3967	76	34	,	,	PUNCT
ejpam-3967	76	35	v4r+3	v4r+3	PROPN
ejpam-3967	76	36	}	}	PUNCT
ejpam-3967	76	37	is	be	AUX
ejpam-3967	76	38	a	a	DET
ejpam-3967	76	39	γ1ftd	γ1ftd	NOUN
ejpam-3967	76	40	-	-	PUNCT
ejpam-3967	76	41	set	set	NOUN
ejpam-3967	76	42	of	of	ADP
ejpam-3967	76	43	pn	pn	PROPN
ejpam-3967	76	44	.	.	PROPN
ejpam-3967	76	45	hence	hence	ADV
ejpam-3967	76	46	,	,	PUNCT
ejpam-3967	76	47	γ1ftd(pn	γ1ftd(pn	NUM
ejpam-3967	76	48	)	)	PUNCT
ejpam-3967	76	49	=	=	SYM
ejpam-3967	77	1	2r	2r	NUM
ejpam-3967	78	1	+	+	CCONJ
ejpam-3967	78	2	2	2	X
ejpam-3967	78	3	.	.	X
ejpam-3967	78	4	�	�	PROPN
ejpam-3967	78	5	w.	w.	PROPN
ejpam-3967	78	6	bent	bent	PROPN
ejpam-3967	78	7	-	-	PUNCT
ejpam-3967	78	8	usman	usman	PROPN
ejpam-3967	78	9	,	,	PUNCT
ejpam-3967	78	10	r.	r.	PROPN
ejpam-3967	78	11	isla	isla	PROPN
ejpam-3967	78	12	/	/	SYM
ejpam-3967	78	13	eur	eur	PROPN
ejpam-3967	78	14	.	.	PUNCT
ejpam-3967	79	1	j.	j.	PROPN
ejpam-3967	79	2	pure	pure	PROPN
ejpam-3967	79	3	appl	appl	PROPN
ejpam-3967	79	4	.	.	PROPN
ejpam-3967	79	5	math	math	PROPN
ejpam-3967	79	6	,	,	PUNCT
ejpam-3967	79	7	14	14	NUM
ejpam-3967	79	8	(	(	PUNCT
ejpam-3967	79	9	2	2	NUM
ejpam-3967	79	10	)	)	PUNCT
ejpam-3967	79	11	(	(	PUNCT
ejpam-3967	79	12	2021	2021	NUM
ejpam-3967	79	13	)	)	PUNCT
ejpam-3967	79	14	,	,	PUNCT
ejpam-3967	79	15	578	578	NUM
ejpam-3967	79	16	-	-	SYM
ejpam-3967	79	17	589	589	NUM
ejpam-3967	79	18	581	581	NUM
ejpam-3967	79	19	theorem	theorem	NOUN
ejpam-3967	79	20	2	2	NUM
ejpam-3967	79	21	.	.	PUNCT
ejpam-3967	80	1	let	let	VERB
ejpam-3967	80	2	n	n	NOUN
ejpam-3967	80	3	and	and	CCONJ
ejpam-3967	80	4	r	r	NOUN
ejpam-3967	80	5	be	be	VERB
ejpam-3967	80	6	positive	positive	ADJ
ejpam-3967	80	7	integers	integer	NOUN
ejpam-3967	80	8	where	where	SCONJ
ejpam-3967	80	9	n	n	NUM
ejpam-3967	80	10	≥	≥	NOUN
ejpam-3967	80	11	3	3	NUM
ejpam-3967	80	12	and	and	CCONJ
ejpam-3967	80	13	r	r	NOUN
ejpam-3967	80	14	≥	≥	NUM
ejpam-3967	80	15	1	1	NUM
ejpam-3967	80	16	.	.	PUNCT
ejpam-3967	81	1	then	then	ADV
ejpam-3967	81	2	γ1ftd(cn	γ1ftd(cn	NUM
ejpam-3967	81	3	)	)	PUNCT
ejpam-3967	82	1	=	=	PUNCT
ejpam-3967	83	1			NUM
ejpam-3967	83	2	3	3	NUM
ejpam-3967	83	3	,	,	PUNCT
ejpam-3967	83	4	n	n	NOUN
ejpam-3967	83	5	=	=	SYM
ejpam-3967	83	6	3	3	NUM
ejpam-3967	83	7	2r	2r	NUM
ejpam-3967	83	8	,	,	PUNCT
ejpam-3967	83	9	n	n	NOUN
ejpam-3967	83	10	=	=	NOUN
ejpam-3967	83	11	4r	4r	NUM
ejpam-3967	83	12	2r	2r	NUM
ejpam-3967	84	1	+	+	CCONJ
ejpam-3967	84	2	1	1	NUM
ejpam-3967	84	3	,	,	PUNCT
ejpam-3967	84	4	n	n	NOUN
ejpam-3967	84	5	=	=	NOUN
ejpam-3967	84	6	4r	4r	NOUN
ejpam-3967	84	7	+	+	CCONJ
ejpam-3967	84	8	1	1	NUM
ejpam-3967	84	9	2r	2r	NUM
ejpam-3967	84	10	+	+	CCONJ
ejpam-3967	84	11	2	2	NUM
ejpam-3967	84	12	,	,	PUNCT
ejpam-3967	84	13	n	n	NOUN
ejpam-3967	84	14	=	=	NOUN
ejpam-3967	84	15	4r	4r	NOUN
ejpam-3967	84	16	+	+	CCONJ
ejpam-3967	84	17	2	2	NUM
ejpam-3967	84	18	2r	2r	NUM
ejpam-3967	84	19	+	+	CCONJ
ejpam-3967	84	20	3	3	NUM
ejpam-3967	84	21	,	,	PUNCT
ejpam-3967	84	22	n	n	NOUN
ejpam-3967	84	23	=	=	NOUN
ejpam-3967	84	24	4r	4r	NOUN
ejpam-3967	84	25	+	+	CCONJ
ejpam-3967	84	26	3	3	X
ejpam-3967	84	27	.	.	X
ejpam-3967	84	28	proof	proof	NOUN
ejpam-3967	84	29	.	.	PUNCT
ejpam-3967	85	1	suppose	suppose	VERB
ejpam-3967	85	2	that	that	SCONJ
ejpam-3967	85	3	cn	cn	PROPN
ejpam-3967	85	4	=	=	PUNCT
ejpam-3967	85	5	[	[	X
ejpam-3967	85	6	v1	v1	NOUN
ejpam-3967	85	7	,	,	PUNCT
ejpam-3967	85	8	v2	v2	PROPN
ejpam-3967	85	9	,	,	PUNCT
ejpam-3967	85	10	...	...	PUNCT
ejpam-3967	85	11	,	,	PUNCT
ejpam-3967	85	12	vn	vn	X
ejpam-3967	85	13	,	,	PUNCT
ejpam-3967	85	14	v1	v1	PROPN
ejpam-3967	85	15	]	]	PUNCT
ejpam-3967	85	16	.	.	PUNCT
ejpam-3967	86	1	if	if	SCONJ
ejpam-3967	86	2	n	n	NUM
ejpam-3967	86	3	=	=	SYM
ejpam-3967	86	4	3	3	NUM
ejpam-3967	86	5	,	,	PUNCT
ejpam-3967	86	6	then	then	ADV
ejpam-3967	86	7	clearly	clearly	ADV
ejpam-3967	86	8	,	,	PUNCT
ejpam-3967	86	9	γ1ftd(c3	γ1ftd(c3	NOUN
ejpam-3967	86	10	)	)	PUNCT
ejpam-3967	86	11	=	=	SYM
ejpam-3967	87	1	3	3	X
ejpam-3967	87	2	.	.	PUNCT
ejpam-3967	87	3	the	the	DET
ejpam-3967	87	4	proof	proof	NOUN
ejpam-3967	87	5	for	for	ADP
ejpam-3967	87	6	n	n	NOUN
ejpam-3967	87	7	=	=	NOUN
ejpam-3967	87	8	4r	4r	NOUN
ejpam-3967	87	9	,	,	PUNCT
ejpam-3967	87	10	n	n	NOUN
ejpam-3967	87	11	=	=	NOUN
ejpam-3967	87	12	4r	4r	NOUN
ejpam-3967	87	13	+	+	CCONJ
ejpam-3967	87	14	1	1	NUM
ejpam-3967	87	15	,	,	PUNCT
ejpam-3967	87	16	and	and	CCONJ
ejpam-3967	87	17	n	n	CCONJ
ejpam-3967	87	18	=	=	NOUN
ejpam-3967	87	19	4r	4r	NOUN
ejpam-3967	87	20	+	+	CCONJ
ejpam-3967	87	21	2	2	NUM
ejpam-3967	87	22	is	be	AUX
ejpam-3967	87	23	similar	similar	ADJ
ejpam-3967	87	24	to	to	ADP
ejpam-3967	87	25	the	the	DET
ejpam-3967	87	26	proof	proof	NOUN
ejpam-3967	87	27	of	of	ADP
ejpam-3967	87	28	cases	case	NOUN
ejpam-3967	87	29	1	1	NUM
ejpam-3967	87	30	to	to	PART
ejpam-3967	87	31	3	3	NUM
ejpam-3967	87	32	of	of	ADP
ejpam-3967	87	33	theorem	theorem	NOUN
ejpam-3967	87	34	1	1	NUM
ejpam-3967	87	35	.	.	PUNCT
ejpam-3967	87	36	when	when	SCONJ
ejpam-3967	87	37	n	n	NOUN
ejpam-3967	87	38	=	=	SYM
ejpam-3967	87	39	4r	4r	NOUN
ejpam-3967	87	40	+	+	CCONJ
ejpam-3967	87	41	3	3	NUM
ejpam-3967	87	42	,	,	PUNCT
ejpam-3967	87	43	let	let	VERB
ejpam-3967	87	44	t	t	NOUN
ejpam-3967	87	45	=	=	SYM
ejpam-3967	87	46	{	{	PUNCT
ejpam-3967	87	47	v2	v2	PROPN
ejpam-3967	87	48	,	,	PUNCT
ejpam-3967	87	49	v3	v3	PROPN
ejpam-3967	87	50	,	,	PUNCT
ejpam-3967	87	51	v6	v6	NOUN
ejpam-3967	87	52	,	,	PUNCT
ejpam-3967	87	53	v7	v7	VERB
ejpam-3967	87	54	,	,	PUNCT
ejpam-3967	87	55	....	....	PUNCT
ejpam-3967	87	56	,	,	PUNCT
ejpam-3967	87	57	v4r−2	v4r−2	ADV
ejpam-3967	87	58	,	,	PUNCT
ejpam-3967	87	59	v4r−1	v4r−1	PROPN
ejpam-3967	87	60	}	}	PUNCT
ejpam-3967	87	61	.	.	PUNCT
ejpam-3967	88	1	it	it	PRON
ejpam-3967	88	2	can	can	AUX
ejpam-3967	88	3	be	be	AUX
ejpam-3967	88	4	verified	verify	VERB
ejpam-3967	88	5	that	that	SCONJ
ejpam-3967	88	6	t	t	PROPN
ejpam-3967	88	7	∪	∪	X
ejpam-3967	88	8	{	{	PUNCT
ejpam-3967	88	9	v4r	v4r	ADJ
ejpam-3967	88	10	,	,	PUNCT
ejpam-3967	88	11	v4r+1	v4r+1	NOUN
ejpam-3967	88	12	,	,	PUNCT
ejpam-3967	88	13	v4r+2	v4r+2	NOUN
ejpam-3967	88	14	}	}	PUNCT
ejpam-3967	88	15	is	be	AUX
ejpam-3967	88	16	a	a	DET
ejpam-3967	88	17	γ1ftd	γ1ftd	NOUN
ejpam-3967	88	18	-	-	PUNCT
ejpam-3967	88	19	set	set	NOUN
ejpam-3967	88	20	of	of	ADP
ejpam-3967	88	21	cn	cn	PROPN
ejpam-3967	88	22	.	.	PUNCT
ejpam-3967	88	23	thus	thus	ADV
ejpam-3967	88	24	,	,	PUNCT
ejpam-3967	88	25	γ1ftd(cn	γ1ftd(cn	NUM
ejpam-3967	88	26	)	)	PUNCT
ejpam-3967	89	1	=	=	SYM
ejpam-3967	89	2	2r	2r	NUM
ejpam-3967	90	1	+	+	CCONJ
ejpam-3967	90	2	3	3	X
ejpam-3967	90	3	.	.	X
ejpam-3967	90	4	�	�	PROPN
ejpam-3967	90	5	lemma	lemma	PROPN
ejpam-3967	90	6	1	1	X
ejpam-3967	90	7	.	.	PUNCT
ejpam-3967	91	1	[	[	X
ejpam-3967	91	2	5	5	NUM
ejpam-3967	91	3	]	]	PUNCT
ejpam-3967	91	4	let	let	VERB
ejpam-3967	91	5	kn	kn	PROPN
ejpam-3967	91	6	be	be	AUX
ejpam-3967	91	7	the	the	DET
ejpam-3967	91	8	complete	complete	ADJ
ejpam-3967	91	9	graph	graph	NOUN
ejpam-3967	91	10	of	of	ADP
ejpam-3967	91	11	order	order	NOUN
ejpam-3967	91	12	n	n	NOUN
ejpam-3967	91	13	and	and	CCONJ
ejpam-3967	91	14	k	k	PROPN
ejpam-3967	91	15	a	a	DET
ejpam-3967	91	16	positive	positive	ADJ
ejpam-3967	91	17	integer	integer	NOUN
ejpam-3967	91	18	with	with	ADP
ejpam-3967	91	19	k	k	PROPN
ejpam-3967	91	20	≤	≤	PROPN
ejpam-3967	91	21	n.	n.	NOUN
ejpam-3967	91	22	then	then	ADV
ejpam-3967	91	23	γkfd(kn	γkfd(kn	VERB
ejpam-3967	91	24	)	)	PUNCT
ejpam-3967	91	25	=	=	SYM
ejpam-3967	91	26	k.	k.	PROPN
ejpam-3967	91	27	theorem	theorem	VERB
ejpam-3967	91	28	3	3	X
ejpam-3967	91	29	.	.	PUNCT
ejpam-3967	92	1	let	let	VERB
ejpam-3967	92	2	n	n	PRON
ejpam-3967	93	1	and	and	CCONJ
ejpam-3967	93	2	k	k	PROPN
ejpam-3967	93	3	be	be	AUX
ejpam-3967	93	4	positive	positive	ADJ
ejpam-3967	93	5	integers	integer	NOUN
ejpam-3967	93	6	,	,	PUNCT
ejpam-3967	93	7	2	2	NUM
ejpam-3967	93	8	≤	≤	NUM
ejpam-3967	93	9	k	k	PROPN
ejpam-3967	93	10	≤	≤	PROPN
ejpam-3967	93	11	n.	n.	NOUN
ejpam-3967	93	12	then	then	ADV
ejpam-3967	93	13	,	,	PUNCT
ejpam-3967	93	14	γkftd(kn	γkftd(kn	NOUN
ejpam-3967	93	15	)	)	PUNCT
ejpam-3967	93	16	=	=	PUNCT
ejpam-3967	94	1	k.	k.	NOUN
ejpam-3967	94	2	proof	proof	NOUN
ejpam-3967	94	3	.	.	PUNCT
ejpam-3967	95	1	clearly	clearly	ADV
ejpam-3967	95	2	,	,	PUNCT
ejpam-3967	95	3	γ2ftd(k2	γ2ftd(k2	X
ejpam-3967	95	4	)	)	PUNCT
ejpam-3967	95	5	=	=	SYM
ejpam-3967	95	6	2	2	NUM
ejpam-3967	95	7	,	,	PUNCT
ejpam-3967	95	8	γ2ftd(k3	γ2ftd(k3	NOUN
ejpam-3967	95	9	)	)	PUNCT
ejpam-3967	95	10	=	=	SYM
ejpam-3967	95	11	2	2	NUM
ejpam-3967	95	12	,	,	PUNCT
ejpam-3967	95	13	and	and	CCONJ
ejpam-3967	95	14	γ3ftd(k3	γ3ftd(k3	PROPN
ejpam-3967	95	15	)	)	PUNCT
ejpam-3967	95	16	=	=	SYM
ejpam-3967	96	1	3	3	X
ejpam-3967	96	2	.	.	X
ejpam-3967	96	3	let	let	VERB
ejpam-3967	96	4	n	n	PRON
ejpam-3967	96	5	>	>	X
ejpam-3967	96	6	3	3	X
ejpam-3967	96	7	.	.	PUNCT
ejpam-3967	97	1	let	let	VERB
ejpam-3967	97	2	v	v	X
ejpam-3967	97	3	(	(	PUNCT
ejpam-3967	97	4	kn	kn	PROPN
ejpam-3967	97	5	)	)	PUNCT
ejpam-3967	97	6	=	=	SYM
ejpam-3967	97	7	{	{	PUNCT
ejpam-3967	97	8	v1	v1	PROPN
ejpam-3967	97	9	,	,	PUNCT
ejpam-3967	97	10	v2	v2	PROPN
ejpam-3967	97	11	,	,	PUNCT
ejpam-3967	97	12	...	...	PUNCT
ejpam-3967	97	13	,	,	PUNCT
ejpam-3967	97	14	vn	vn	PROPN
ejpam-3967	97	15	}	}	PUNCT
ejpam-3967	97	16	,	,	PUNCT
ejpam-3967	97	17	and	and	CCONJ
ejpam-3967	97	18	s	s	VERB
ejpam-3967	97	19	=	=	NOUN
ejpam-3967	97	20	{	{	PUNCT
ejpam-3967	97	21	v1	v1	PROPN
ejpam-3967	97	22	,	,	PUNCT
ejpam-3967	97	23	v2	v2	PROPN
ejpam-3967	97	24	,	,	PUNCT
ejpam-3967	97	25	...	...	PUNCT
ejpam-3967	97	26	,	,	PUNCT
ejpam-3967	97	27	vk	vk	ADP
ejpam-3967	97	28	}	}	PUNCT
ejpam-3967	97	29	.	.	PUNCT
ejpam-3967	98	1	note	note	VERB
ejpam-3967	98	2	that	that	SCONJ
ejpam-3967	98	3	each	each	DET
ejpam-3967	98	4	vertex	vertex	NOUN
ejpam-3967	98	5	in	in	ADP
ejpam-3967	98	6	s	s	PROPN
ejpam-3967	98	7	is	be	AUX
ejpam-3967	98	8	adjacent	adjacent	ADJ
ejpam-3967	98	9	to	to	ADP
ejpam-3967	98	10	the	the	DET
ejpam-3967	98	11	remaining	remain	VERB
ejpam-3967	98	12	k	k	NOUN
ejpam-3967	98	13	−	−	NOUN
ejpam-3967	98	14	1	1	NUM
ejpam-3967	98	15	vertices	vertex	NOUN
ejpam-3967	98	16	in	in	ADP
ejpam-3967	98	17	s.	s.	PROPN
ejpam-3967	98	18	moreover	moreover	ADV
ejpam-3967	98	19	,	,	PUNCT
ejpam-3967	98	20	for	for	ADP
ejpam-3967	98	21	each	each	DET
ejpam-3967	98	22	vi	vi	PROPN
ejpam-3967	98	23	∈	∈	PROPN
ejpam-3967	98	24	v	v	NOUN
ejpam-3967	98	25	(	(	PUNCT
ejpam-3967	98	26	kn)\s	kn)\s	NOUN
ejpam-3967	98	27	,	,	PUNCT
ejpam-3967	98	28	that	that	ADV
ejpam-3967	98	29	is	is	ADV
ejpam-3967	98	30	,	,	PUNCT
ejpam-3967	98	31	for	for	ADP
ejpam-3967	98	32	each	each	DET
ejpam-3967	98	33	vi	vi	NOUN
ejpam-3967	98	34	,	,	PUNCT
ejpam-3967	98	35	k+	k+	NOUN
ejpam-3967	98	36	1	1	NUM
ejpam-3967	98	37	≤	≤	NUM
ejpam-3967	98	38	i	i	PRON
ejpam-3967	98	39	≤	≤	PROPN
ejpam-3967	98	40	n	n	CCONJ
ejpam-3967	98	41	,	,	PUNCT
ejpam-3967	98	42	|n(vi	|n(vi	NOUN
ejpam-3967	98	43	)	)	PUNCT
ejpam-3967	98	44	∩	∩	NOUN
ejpam-3967	98	45	s|	s|	NOUN
ejpam-3967	98	46	=	=	PUNCT
ejpam-3967	98	47	k.	k.	PROPN
ejpam-3967	99	1	thus	thus	ADV
ejpam-3967	99	2	,	,	PUNCT
ejpam-3967	99	3	s	s	VERB
ejpam-3967	99	4	is	be	AUX
ejpam-3967	99	5	a	a	DET
ejpam-3967	99	6	kftd	kftd	NOUN
ejpam-3967	99	7	-	-	PUNCT
ejpam-3967	99	8	set	set	NOUN
ejpam-3967	99	9	in	in	ADP
ejpam-3967	99	10	kn	kn	PROPN
ejpam-3967	99	11	and	and	CCONJ
ejpam-3967	99	12	γkftd(kn	γkftd(kn	NOUN
ejpam-3967	99	13	)	)	PUNCT
ejpam-3967	99	14	≤	≤	NOUN
ejpam-3967	99	15	k.	k.	PROPN
ejpam-3967	100	1	however	however	ADV
ejpam-3967	100	2	,	,	PUNCT
ejpam-3967	100	3	γkftd(kn	γkftd(kn	NOUN
ejpam-3967	100	4	)	)	PUNCT
ejpam-3967	100	5	≥	≥	NOUN
ejpam-3967	100	6	γkfd(kn	γkfd(kn	VERB
ejpam-3967	100	7	)	)	PUNCT
ejpam-3967	100	8	=	=	SYM
ejpam-3967	101	1	k	k	X
ejpam-3967	101	2	by	by	ADP
ejpam-3967	101	3	remark	remark	NOUN
ejpam-3967	101	4	1	1	NUM
ejpam-3967	101	5	and	and	CCONJ
ejpam-3967	101	6	lemma	lemma	PROPN
ejpam-3967	101	7	1	1	NUM
ejpam-3967	101	8	.	.	PUNCT
ejpam-3967	102	1	thus	thus	ADV
ejpam-3967	102	2	,	,	PUNCT
ejpam-3967	102	3	γkftd(kn	γkftd(kn	NOUN
ejpam-3967	102	4	)	)	PUNCT
ejpam-3967	102	5	=	=	PUNCT
ejpam-3967	102	6	k.	k.	PROPN
ejpam-3967	102	7	�	�	PROPN
ejpam-3967	102	8	theorem	theorem	VERB
ejpam-3967	102	9	4	4	NUM
ejpam-3967	102	10	.	.	PUNCT
ejpam-3967	103	1	let	let	VERB
ejpam-3967	103	2	a	a	PRON
ejpam-3967	103	3	and	and	CCONJ
ejpam-3967	103	4	b	b	NOUN
ejpam-3967	103	5	be	be	AUX
ejpam-3967	103	6	positive	positive	ADJ
ejpam-3967	103	7	integers	integer	NOUN
ejpam-3967	103	8	such	such	ADJ
ejpam-3967	103	9	that	that	SCONJ
ejpam-3967	103	10	a	a	DET
ejpam-3967	103	11	≤	≤	PROPN
ejpam-3967	103	12	b.	b.	NOUN
ejpam-3967	103	13	then	then	ADV
ejpam-3967	103	14	there	there	PRON
ejpam-3967	103	15	exists	exist	VERB
ejpam-3967	103	16	a	a	DET
ejpam-3967	103	17	connected	connected	ADJ
ejpam-3967	103	18	graph	graph	NOUN
ejpam-3967	103	19	g	g	ADP
ejpam-3967	103	20	such	such	ADJ
ejpam-3967	103	21	that	that	DET
ejpam-3967	103	22	γ1fd(g	γ1fd(g	PROPN
ejpam-3967	103	23	)	)	PUNCT
ejpam-3967	104	1	=	=	SYM
ejpam-3967	104	2	a	a	PRON
ejpam-3967	104	3	and	and	CCONJ
ejpam-3967	104	4	γ1ftd(g	γ1ftd(g	NUM
ejpam-3967	104	5	)	)	PUNCT
ejpam-3967	104	6	=	=	SYM
ejpam-3967	104	7	b.	b.	PROPN
ejpam-3967	104	8	proof	proof	NOUN
ejpam-3967	104	9	.	.	PUNCT
ejpam-3967	105	1	consider	consider	VERB
ejpam-3967	105	2	the	the	DET
ejpam-3967	105	3	following	follow	VERB
ejpam-3967	105	4	cases	case	NOUN
ejpam-3967	105	5	:	:	PUNCT
ejpam-3967	105	6	case	case	NOUN
ejpam-3967	105	7	1	1	NUM
ejpam-3967	105	8	.	.	PUNCT
ejpam-3967	106	1	a	a	DET
ejpam-3967	106	2	=	=	X
ejpam-3967	106	3	b	b	NOUN
ejpam-3967	106	4	let	let	VERB
ejpam-3967	106	5	g	g	NOUN
ejpam-3967	106	6	=	=	PUNCT
ejpam-3967	106	7	g1	g1	PROPN
ejpam-3967	106	8	be	be	VERB
ejpam-3967	106	9	the	the	DET
ejpam-3967	106	10	graph	graph	NOUN
ejpam-3967	106	11	shown	show	VERB
ejpam-3967	106	12	in	in	ADP
ejpam-3967	106	13	figure	figure	NOUN
ejpam-3967	106	14	1	1	NUM
ejpam-3967	106	15	.	.	PUNCT
ejpam-3967	107	1	it	it	PRON
ejpam-3967	107	2	is	be	AUX
ejpam-3967	107	3	clear	clear	ADJ
ejpam-3967	107	4	that	that	SCONJ
ejpam-3967	107	5	the	the	DET
ejpam-3967	107	6	set	set	NOUN
ejpam-3967	107	7	a	a	X
ejpam-3967	107	8	=	=	X
ejpam-3967	107	9	{	{	PUNCT
ejpam-3967	107	10	xi	xi	X
ejpam-3967	107	11	:	:	PUNCT
ejpam-3967	107	12	i	i	NOUN
ejpam-3967	107	13	=	=	NOUN
ejpam-3967	107	14	1	1	NUM
ejpam-3967	107	15	,	,	PUNCT
ejpam-3967	107	16	2	2	NUM
ejpam-3967	107	17	,	,	PUNCT
ejpam-3967	107	18	...	...	PUNCT
ejpam-3967	107	19	a	a	X
ejpam-3967	107	20	}	}	PUNCT
ejpam-3967	107	21	is	be	AUX
ejpam-3967	107	22	both	both	PRON
ejpam-3967	107	23	a	a	DET
ejpam-3967	107	24	γ1fd	γ1fd	NOUN
ejpam-3967	107	25	-	-	PUNCT
ejpam-3967	107	26	set	set	VERB
ejpam-3967	107	27	and	and	CCONJ
ejpam-3967	107	28	a	a	DET
ejpam-3967	107	29	γ1ftd	γ1ftd	NOUN
ejpam-3967	107	30	-	-	PUNCT
ejpam-3967	107	31	set	set	NOUN
ejpam-3967	107	32	in	in	ADP
ejpam-3967	107	33	g1	g1	PROPN
ejpam-3967	107	34	.	.	PUNCT
ejpam-3967	108	1	it	it	PRON
ejpam-3967	108	2	follows	follow	VERB
ejpam-3967	108	3	that	that	SCONJ
ejpam-3967	108	4	γ1fd(g1	γ1fd(g1	NUM
ejpam-3967	108	5	)	)	PUNCT
ejpam-3967	109	1	=	=	SYM
ejpam-3967	109	2	γ1ftd(g1	γ1ftd(g1	X
ejpam-3967	109	3	)	)	PUNCT
ejpam-3967	109	4	=	=	SYM
ejpam-3967	109	5	a.	a.	NOUN
ejpam-3967	109	6	w.	w.	PROPN
ejpam-3967	109	7	bent	bent	PROPN
ejpam-3967	109	8	-	-	PUNCT
ejpam-3967	109	9	usman	usman	PROPN
ejpam-3967	109	10	,	,	PUNCT
ejpam-3967	109	11	r.	r.	PROPN
ejpam-3967	109	12	isla	isla	PROPN
ejpam-3967	109	13	/	/	SYM
ejpam-3967	109	14	eur	eur	PROPN
ejpam-3967	109	15	.	.	PUNCT
ejpam-3967	110	1	j.	j.	PROPN
ejpam-3967	110	2	pure	pure	PROPN
ejpam-3967	110	3	appl	appl	PROPN
ejpam-3967	110	4	.	.	PROPN
ejpam-3967	110	5	math	math	PROPN
ejpam-3967	110	6	,	,	PUNCT
ejpam-3967	110	7	14	14	NUM
ejpam-3967	110	8	(	(	PUNCT
ejpam-3967	110	9	2	2	NUM
ejpam-3967	110	10	)	)	PUNCT
ejpam-3967	110	11	(	(	PUNCT
ejpam-3967	110	12	2021	2021	NUM
ejpam-3967	110	13	)	)	PUNCT
ejpam-3967	110	14	,	,	PUNCT
ejpam-3967	110	15	578	578	NUM
ejpam-3967	110	16	-	-	SYM
ejpam-3967	110	17	589	589	NUM
ejpam-3967	110	18	582	582	NUM
ejpam-3967	110	19	case	case	NOUN
ejpam-3967	110	20	2	2	NUM
ejpam-3967	110	21	.	.	PUNCT
ejpam-3967	111	1	a	a	DET
ejpam-3967	111	2	<	<	X
ejpam-3967	111	3	b	b	X
ejpam-3967	111	4	let	let	VERB
ejpam-3967	111	5	g	g	PROPN
ejpam-3967	111	6	=	=	PUNCT
ejpam-3967	111	7	g2	g2	PROPN
ejpam-3967	111	8	be	be	VERB
ejpam-3967	111	9	the	the	DET
ejpam-3967	111	10	graph	graph	NOUN
ejpam-3967	111	11	shown	show	VERB
ejpam-3967	111	12	in	in	ADP
ejpam-3967	111	13	figure	figure	NOUN
ejpam-3967	111	14	2	2	NUM
ejpam-3967	111	15	.	.	PUNCT
ejpam-3967	111	16	let	let	VERB
ejpam-3967	111	17	a	a	PRON
ejpam-3967	111	18	=	=	SYM
ejpam-3967	111	19	{	{	PUNCT
ejpam-3967	111	20	x1	x1	PROPN
ejpam-3967	111	21	,	,	PUNCT
ejpam-3967	111	22	x2	x2	PROPN
ejpam-3967	111	23	,	,	PUNCT
ejpam-3967	111	24	...	...	PUNCT
ejpam-3967	111	25	,	,	PUNCT
ejpam-3967	111	26	xa−1	xa−1	PROPN
ejpam-3967	111	27	}	}	PUNCT
ejpam-3967	111	28	.	.	PUNCT
ejpam-3967	112	1	it	it	PRON
ejpam-3967	112	2	is	be	AUX
ejpam-3967	112	3	clear	clear	ADJ
ejpam-3967	112	4	that	that	SCONJ
ejpam-3967	112	5	the	the	DET
ejpam-3967	112	6	set	set	NOUN
ejpam-3967	112	7	b	b	PROPN
ejpam-3967	112	8	=	=	NOUN
ejpam-3967	112	9	a	a	DET
ejpam-3967	112	10	∪	∪	X
ejpam-3967	112	11	{	{	PUNCT
ejpam-3967	112	12	za	za	NOUN
ejpam-3967	112	13	}	}	PUNCT
ejpam-3967	112	14	is	be	AUX
ejpam-3967	112	15	a	a	DET
ejpam-3967	112	16	γ1fd	γ1fd	NOUN
ejpam-3967	112	17	-	-	PUNCT
ejpam-3967	112	18	set	set	VERB
ejpam-3967	112	19	and	and	CCONJ
ejpam-3967	113	1	the	the	DET
ejpam-3967	113	2	set	set	NOUN
ejpam-3967	113	3	c	c	NOUN
ejpam-3967	113	4	=	=	SYM
ejpam-3967	113	5	a∪{xa}∪{y1	a∪{xa}∪{y1	PROPN
ejpam-3967	113	6	,	,	PUNCT
ejpam-3967	113	7	y2	y2	PROPN
ejpam-3967	113	8	,	,	PUNCT
ejpam-3967	113	9	...	...	PUNCT
ejpam-3967	113	10	,	,	PUNCT
ejpam-3967	113	11	yb−a	yb−a	PRON
ejpam-3967	113	12	}	}	PUNCT
ejpam-3967	113	13	is	be	AUX
ejpam-3967	113	14	a	a	DET
ejpam-3967	113	15	γ1ftd	γ1ftd	NOUN
ejpam-3967	113	16	-	-	PUNCT
ejpam-3967	113	17	set	set	NOUN
ejpam-3967	113	18	in	in	ADP
ejpam-3967	113	19	g2	g2	PROPN
ejpam-3967	113	20	.	.	PUNCT
ejpam-3967	114	1	it	it	PRON
ejpam-3967	114	2	follows	follow	VERB
ejpam-3967	114	3	that	that	SCONJ
ejpam-3967	114	4	γ1fd(g2	γ1fd(g2	PUNCT
ejpam-3967	114	5	)	)	PUNCT
ejpam-3967	115	1	=	=	PRON
ejpam-3967	115	2	|b|	|b|	X
ejpam-3967	115	3	=	=	PUNCT
ejpam-3967	115	4	a	a	PRON
ejpam-3967	115	5	and	and	CCONJ
ejpam-3967	115	6	γ1ftd(g2	γ1ftd(g2	PROPN
ejpam-3967	115	7	)	)	PUNCT
ejpam-3967	115	8	=	=	SYM
ejpam-3967	115	9	|c|	|c|	PROPN
ejpam-3967	115	10	=	=	SYM
ejpam-3967	115	11	b.	b.	PROPN
ejpam-3967	115	12	�	�	PROPN
ejpam-3967	115	13	corollary	corollary	NOUN
ejpam-3967	115	14	1	1	NUM
ejpam-3967	115	15	.	.	PUNCT
ejpam-3967	116	1	γ1ftd	γ1ftd	PROPN
ejpam-3967	116	2	−	−	PROPN
ejpam-3967	116	3	γ1fd	γ1fd	PUNCT
ejpam-3967	116	4	can	can	AUX
ejpam-3967	116	5	be	be	AUX
ejpam-3967	116	6	made	make	VERB
ejpam-3967	116	7	arbitrarily	arbitrarily	ADV
ejpam-3967	116	8	large	large	ADJ
ejpam-3967	116	9	.	.	PUNCT
ejpam-3967	117	1	3	3	X
ejpam-3967	117	2	.	.	X
ejpam-3967	117	3	known	know	VERB
ejpam-3967	117	4	results	result	VERB
ejpam-3967	117	5	the	the	DET
ejpam-3967	117	6	following	follow	VERB
ejpam-3967	117	7	characterizations	characterization	NOUN
ejpam-3967	117	8	of	of	ADP
ejpam-3967	117	9	k	k	ADJ
ejpam-3967	117	10	-	-	ADJ
ejpam-3967	117	11	fair	fair	ADJ
ejpam-3967	117	12	dominating	dominating	NOUN
ejpam-3967	117	13	sets	set	NOUN
ejpam-3967	117	14	in	in	ADP
ejpam-3967	117	15	the	the	DET
ejpam-3967	117	16	join	join	NOUN
ejpam-3967	117	17	,	,	PUNCT
ejpam-3967	117	18	corona	corona	PROPN
ejpam-3967	117	19	,	,	PUNCT
ejpam-3967	117	20	and	and	CCONJ
ejpam-3967	117	21	lexicographic	lexicographic	ADJ
ejpam-3967	117	22	product	product	NOUN
ejpam-3967	117	23	of	of	ADP
ejpam-3967	117	24	two	two	NUM
ejpam-3967	117	25	nontrivial	nontrivial	NOUN
ejpam-3967	117	26	,	,	PUNCT
ejpam-3967	117	27	connected	connected	ADJ
ejpam-3967	117	28	graphs	graph	NOUN
ejpam-3967	117	29	are	be	AUX
ejpam-3967	117	30	found	find	VERB
ejpam-3967	117	31	in	in	ADP
ejpam-3967	117	32	maravilla	maravilla	PROPN
ejpam-3967	117	33	et	et	PROPN
ejpam-3967	117	34	al	al	PROPN
ejpam-3967	117	35	.	.	PUNCT
ejpam-3967	118	1	[	[	X
ejpam-3967	118	2	5	5	NUM
ejpam-3967	118	3	]	]	PUNCT
ejpam-3967	118	4	.	.	PUNCT
ejpam-3967	119	1	theorem	theorem	ADJ
ejpam-3967	119	2	5	5	NUM
ejpam-3967	119	3	.	.	PUNCT
ejpam-3967	120	1	[	[	X
ejpam-3967	120	2	5	5	NUM
ejpam-3967	120	3	]	]	PUNCT
ejpam-3967	120	4	let	let	VERB
ejpam-3967	120	5	g	g	NOUN
ejpam-3967	120	6	and	and	CCONJ
ejpam-3967	120	7	h	h	NOUN
ejpam-3967	120	8	be	be	AUX
ejpam-3967	120	9	nontrivial	nontrivial	ADJ
ejpam-3967	120	10	connected	connect	VERB
ejpam-3967	120	11	graphs	graph	NOUN
ejpam-3967	120	12	of	of	ADP
ejpam-3967	120	13	orders	order	NOUN
ejpam-3967	120	14	m	m	VERB
ejpam-3967	120	15	and	and	CCONJ
ejpam-3967	120	16	n	n	CCONJ
ejpam-3967	120	17	,	,	PUNCT
ejpam-3967	120	18	respectively	respectively	ADV
ejpam-3967	120	19	,	,	PUNCT
ejpam-3967	120	20	and	and	CCONJ
ejpam-3967	120	21	k	k	X
ejpam-3967	120	22	a	a	DET
ejpam-3967	120	23	positive	positive	ADJ
ejpam-3967	120	24	integer	integer	NOUN
ejpam-3967	120	25	with	with	ADP
ejpam-3967	120	26	1	1	NUM
ejpam-3967	120	27	≤	≤	NUM
ejpam-3967	120	28	k	k	NOUN
ejpam-3967	120	29	≤	≤	ADJ
ejpam-3967	120	30	max{m	max{m	NOUN
ejpam-3967	120	31	,	,	PUNCT
ejpam-3967	120	32	n	n	CCONJ
ejpam-3967	120	33	}	}	PUNCT
ejpam-3967	120	34	.	.	PUNCT
ejpam-3967	121	1	then	then	ADV
ejpam-3967	121	2	s	s	VERB
ejpam-3967	121	3	⊆	⊆	NUM
ejpam-3967	121	4	v	v	NOUN
ejpam-3967	121	5	(	(	PUNCT
ejpam-3967	121	6	g+h	g+h	PROPN
ejpam-3967	121	7	)	)	PUNCT
ejpam-3967	121	8	is	be	AUX
ejpam-3967	121	9	a	a	DET
ejpam-3967	121	10	kfd	kfd	NOUN
ejpam-3967	121	11	-	-	PUNCT
ejpam-3967	121	12	set	set	NOUN
ejpam-3967	121	13	in	in	ADP
ejpam-3967	121	14	g+h	g+h	PROPN
ejpam-3967	121	15	if	if	SCONJ
ejpam-3967	121	16	and	and	CCONJ
ejpam-3967	121	17	only	only	ADV
ejpam-3967	121	18	if	if	SCONJ
ejpam-3967	121	19	one	one	NUM
ejpam-3967	121	20	of	of	ADP
ejpam-3967	121	21	the	the	DET
ejpam-3967	121	22	following	following	NOUN
ejpam-3967	121	23	holds	hold	VERB
ejpam-3967	121	24	:	:	PUNCT
ejpam-3967	121	25	(	(	PUNCT
ejpam-3967	121	26	a	a	X
ejpam-3967	121	27	)	)	PUNCT
ejpam-3967	121	28	s	s	PART
ejpam-3967	121	29	=	=	SYM
ejpam-3967	121	30	v	v	PROPN
ejpam-3967	121	31	(	(	PUNCT
ejpam-3967	121	32	g+h	g+h	PROPN
ejpam-3967	121	33	)	)	PUNCT
ejpam-3967	121	34	.	.	PUNCT
ejpam-3967	122	1	(	(	PUNCT
ejpam-3967	122	2	b	b	X
ejpam-3967	122	3	)	)	PUNCT
ejpam-3967	122	4	s	s	PART
ejpam-3967	122	5	⊆	⊆	NUM
ejpam-3967	122	6	v	v	NOUN
ejpam-3967	122	7	(	(	PUNCT
ejpam-3967	122	8	g	g	NOUN
ejpam-3967	122	9	)	)	PUNCT
ejpam-3967	122	10	,	,	PUNCT
ejpam-3967	122	11	|s|	|s|	PROPN
ejpam-3967	122	12	=	=	SYM
ejpam-3967	122	13	k	k	PROPN
ejpam-3967	122	14	and	and	CCONJ
ejpam-3967	122	15	s	s	PROPN
ejpam-3967	122	16	is	be	AUX
ejpam-3967	122	17	a	a	DET
ejpam-3967	122	18	kfd	kfd	NOUN
ejpam-3967	122	19	-	-	PUNCT
ejpam-3967	122	20	set	set	NOUN
ejpam-3967	122	21	in	in	ADP
ejpam-3967	122	22	g.	g.	PROPN
ejpam-3967	122	23	(	(	PUNCT
ejpam-3967	122	24	c	c	X
ejpam-3967	122	25	)	)	PUNCT
ejpam-3967	122	26	s	s	PART
ejpam-3967	122	27	⊆	⊆	NUM
ejpam-3967	122	28	v	v	NOUN
ejpam-3967	122	29	(	(	PUNCT
ejpam-3967	122	30	h	h	NOUN
ejpam-3967	122	31	)	)	PUNCT
ejpam-3967	122	32	,	,	PUNCT
ejpam-3967	122	33	|s|	|s|	PROPN
ejpam-3967	122	34	=	=	SYM
ejpam-3967	122	35	k	k	PROPN
ejpam-3967	122	36	and	and	CCONJ
ejpam-3967	122	37	s	s	PROPN
ejpam-3967	122	38	is	be	AUX
ejpam-3967	122	39	a	a	DET
ejpam-3967	122	40	kfd	kfd	NOUN
ejpam-3967	122	41	-	-	PUNCT
ejpam-3967	122	42	set	set	NOUN
ejpam-3967	122	43	in	in	ADP
ejpam-3967	122	44	h.	h.	PROPN
ejpam-3967	122	45	(	(	PUNCT
ejpam-3967	122	46	d	d	X
ejpam-3967	122	47	)	)	PUNCT
ejpam-3967	122	48	s	s	PART
ejpam-3967	122	49	=	=	PUNCT
ejpam-3967	122	50	sg	sg	X
ejpam-3967	122	51	∪	∪	ADJ
ejpam-3967	122	52	sh	sh	PROPN
ejpam-3967	122	53	,	,	PUNCT
ejpam-3967	122	54	where	where	SCONJ
ejpam-3967	122	55	sg	sg	PROPN
ejpam-3967	122	56	is	be	AUX
ejpam-3967	122	57	a	a	DET
ejpam-3967	122	58	(	(	PUNCT
ejpam-3967	122	59	k	k	PROPN
ejpam-3967	122	60	−	−	PROPN
ejpam-3967	122	61	|sh	|sh	ADP
ejpam-3967	122	62	|)fd	|)fd	PROPN
ejpam-3967	122	63	-	-	PUNCT
ejpam-3967	122	64	set	set	VERB
ejpam-3967	122	65	in	in	ADP
ejpam-3967	122	66	g	g	PROPN
ejpam-3967	122	67	and	and	CCONJ
ejpam-3967	122	68	sh	sh	PROPN
ejpam-3967	122	69	is	be	AUX
ejpam-3967	122	70	a	a	DET
ejpam-3967	122	71	(	(	PUNCT
ejpam-3967	122	72	k	k	PROPN
ejpam-3967	122	73	−	−	PROPN
ejpam-3967	122	74	|sg|)fd	|sg|)fd	NOUN
ejpam-3967	122	75	-	-	PUNCT
ejpam-3967	122	76	set	set	NOUN
ejpam-3967	122	77	in	in	ADP
ejpam-3967	122	78	h.	h.	PROPN
ejpam-3967	122	79	(	(	PUNCT
ejpam-3967	122	80	e	e	X
ejpam-3967	122	81	)	)	PUNCT
ejpam-3967	122	82	s	s	PART
ejpam-3967	122	83	=	=	SYM
ejpam-3967	122	84	v	v	X
ejpam-3967	122	85	(	(	PUNCT
ejpam-3967	122	86	g	g	NOUN
ejpam-3967	122	87	)	)	PUNCT
ejpam-3967	122	88	∪	∪	ADP
ejpam-3967	122	89	t	t	PROPN
ejpam-3967	122	90	,	,	PUNCT
ejpam-3967	122	91	where	where	SCONJ
ejpam-3967	122	92	|v	|v	PROPN
ejpam-3967	122	93	(	(	PUNCT
ejpam-3967	122	94	g)|	g)|	NOUN
ejpam-3967	122	95	=	=	NOUN
ejpam-3967	122	96	m	m	PROPN
ejpam-3967	122	97	<	<	X
ejpam-3967	122	98	k	k	X
ejpam-3967	122	99	and	and	CCONJ
ejpam-3967	122	100	t	t	PROPN
ejpam-3967	122	101	is	be	AUX
ejpam-3967	122	102	a	a	DET
ejpam-3967	122	103	(	(	PUNCT
ejpam-3967	122	104	k	k	X
ejpam-3967	122	105	−m)fd	−m)fd	X
ejpam-3967	122	106	-	-	PUNCT
ejpam-3967	122	107	set	set	NOUN
ejpam-3967	122	108	in	in	ADP
ejpam-3967	122	109	h.	h.	PROPN
ejpam-3967	122	110	(	(	PUNCT
ejpam-3967	122	111	f	f	X
ejpam-3967	122	112	)	)	PUNCT
ejpam-3967	122	113	s	s	PART
ejpam-3967	123	1	=	=	X
ejpam-3967	123	2	d	d	X
ejpam-3967	123	3	∪	∪	X
ejpam-3967	123	4	v	v	NOUN
ejpam-3967	123	5	(	(	PUNCT
ejpam-3967	123	6	h	h	NOUN
ejpam-3967	123	7	)	)	PUNCT
ejpam-3967	123	8	,	,	PUNCT
ejpam-3967	124	1	where	where	SCONJ
ejpam-3967	124	2	|v	|v	PROPN
ejpam-3967	124	3	(	(	PUNCT
ejpam-3967	124	4	h)|	h)|	NOUN
ejpam-3967	124	5	=	=	SYM
ejpam-3967	124	6	n	n	CCONJ
ejpam-3967	124	7	<	<	X
ejpam-3967	124	8	k	k	PROPN
ejpam-3967	124	9	and	and	CCONJ
ejpam-3967	124	10	d	d	PROPN
ejpam-3967	124	11	is	be	AUX
ejpam-3967	124	12	a	a	DET
ejpam-3967	124	13	(	(	PUNCT
ejpam-3967	124	14	k	k	PROPN
ejpam-3967	124	15	−	−	PROPN
ejpam-3967	124	16	n)fd	n)fd	PROPN
ejpam-3967	124	17	-	-	PUNCT
ejpam-3967	124	18	set	set	NOUN
ejpam-3967	124	19	in	in	ADP
ejpam-3967	124	20	g.	g.	PROPN
ejpam-3967	124	21	theorem	theorem	VERB
ejpam-3967	124	22	6	6	NUM
ejpam-3967	124	23	.	.	PUNCT
ejpam-3967	125	1	[	[	X
ejpam-3967	125	2	5	5	NUM
ejpam-3967	125	3	]	]	PUNCT
ejpam-3967	125	4	let	let	VERB
ejpam-3967	125	5	g	g	NOUN
ejpam-3967	125	6	and	and	CCONJ
ejpam-3967	125	7	h	h	NOUN
ejpam-3967	125	8	be	be	AUX
ejpam-3967	125	9	nontrivial	nontrivial	ADJ
ejpam-3967	125	10	connected	connect	VERB
ejpam-3967	125	11	graphs	graph	NOUN
ejpam-3967	125	12	and	and	CCONJ
ejpam-3967	125	13	let	let	VERB
ejpam-3967	125	14	k	k	PRON
ejpam-3967	125	15	be	be	AUX
ejpam-3967	125	16	a	a	DET
ejpam-3967	125	17	positive	positive	ADJ
ejpam-3967	125	18	integer	integer	NOUN
ejpam-3967	125	19	with	with	ADP
ejpam-3967	125	20	k	k	PROPN
ejpam-3967	125	21	≤	≤	PROPN
ejpam-3967	125	22	|v	|v	PROPN
ejpam-3967	125	23	(	(	PUNCT
ejpam-3967	125	24	h)|	h)|	PROPN
ejpam-3967	125	25	.	.	PUNCT
ejpam-3967	126	1	then	then	ADV
ejpam-3967	126	2	c	c	PROPN
ejpam-3967	126	3	⊆	⊆	NUM
ejpam-3967	126	4	v	v	NOUN
ejpam-3967	126	5	(	(	PUNCT
ejpam-3967	126	6	g	g	PROPN
ejpam-3967	126	7	◦	◦	NOUN
ejpam-3967	126	8	h	h	NOUN
ejpam-3967	126	9	)	)	PUNCT
ejpam-3967	126	10	is	be	AUX
ejpam-3967	126	11	a	a	DET
ejpam-3967	126	12	kfd	kfd	NOUN
ejpam-3967	126	13	-	-	PUNCT
ejpam-3967	126	14	set	set	NOUN
ejpam-3967	126	15	in	in	ADP
ejpam-3967	126	16	g	g	PROPN
ejpam-3967	126	17	◦	◦	NOUN
ejpam-3967	126	18	h	h	NOUN
ejpam-3967	127	1	if	if	SCONJ
ejpam-3967	128	1	and	and	CCONJ
ejpam-3967	128	2	only	only	ADV
ejpam-3967	128	3	if	if	SCONJ
ejpam-3967	128	4	one	one	NUM
ejpam-3967	128	5	of	of	ADP
ejpam-3967	128	6	the	the	DET
ejpam-3967	128	7	following	follow	VERB
ejpam-3967	128	8	holds	hold	NOUN
ejpam-3967	128	9	:	:	PUNCT
ejpam-3967	128	10	w.	w.	PROPN
ejpam-3967	128	11	bent	bent	PROPN
ejpam-3967	128	12	-	-	PUNCT
ejpam-3967	128	13	usman	usman	PROPN
ejpam-3967	128	14	,	,	PUNCT
ejpam-3967	128	15	r.	r.	PROPN
ejpam-3967	128	16	isla	isla	PROPN
ejpam-3967	128	17	/	/	SYM
ejpam-3967	128	18	eur	eur	PROPN
ejpam-3967	128	19	.	.	PUNCT
ejpam-3967	129	1	j.	j.	PROPN
ejpam-3967	129	2	pure	pure	PROPN
ejpam-3967	129	3	appl	appl	PROPN
ejpam-3967	129	4	.	.	PROPN
ejpam-3967	129	5	math	math	PROPN
ejpam-3967	129	6	,	,	PUNCT
ejpam-3967	129	7	14	14	NUM
ejpam-3967	129	8	(	(	PUNCT
ejpam-3967	129	9	2	2	NUM
ejpam-3967	129	10	)	)	PUNCT
ejpam-3967	129	11	(	(	PUNCT
ejpam-3967	129	12	2021	2021	NUM
ejpam-3967	129	13	)	)	PUNCT
ejpam-3967	129	14	,	,	PUNCT
ejpam-3967	129	15	578	578	NUM
ejpam-3967	129	16	-	-	SYM
ejpam-3967	129	17	589	589	NUM
ejpam-3967	129	18	583	583	NUM
ejpam-3967	129	19	(	(	PUNCT
ejpam-3967	129	20	a	a	X
ejpam-3967	129	21	)	)	PUNCT
ejpam-3967	129	22	c	c	NOUN
ejpam-3967	129	23	=	=	SYM
ejpam-3967	129	24	v	v	PROPN
ejpam-3967	129	25	(	(	PUNCT
ejpam-3967	129	26	g	g	NOUN
ejpam-3967	129	27	)	)	PUNCT
ejpam-3967	129	28	∪b	∪b	VERB
ejpam-3967	129	29	,	,	PUNCT
ejpam-3967	129	30	where	where	SCONJ
ejpam-3967	129	31	b	b	NOUN
ejpam-3967	129	32	=	=	NOUN
ejpam-3967	129	33	∅	∅	NOUN
ejpam-3967	129	34	or	or	CCONJ
ejpam-3967	129	35	b	b	NOUN
ejpam-3967	129	36	=	=	SYM
ejpam-3967	129	37	⋃	⋃	NOUN
ejpam-3967	129	38	v∈v	v∈v	NOUN
ejpam-3967	129	39	(	(	PUNCT
ejpam-3967	129	40	g	g	NOUN
ejpam-3967	129	41	)	)	PUNCT
ejpam-3967	129	42	sv	sv	NOUN
ejpam-3967	129	43	,	,	PUNCT
ejpam-3967	129	44	where	where	SCONJ
ejpam-3967	129	45	each	each	PRON
ejpam-3967	129	46	sv	sv	PROPN
ejpam-3967	129	47	is	be	AUX
ejpam-3967	129	48	a	a	DET
ejpam-3967	129	49	(	(	PUNCT
ejpam-3967	129	50	k	k	PROPN
ejpam-3967	129	51	−	−	PROPN
ejpam-3967	129	52	1)fd	1)fd	PROPN
ejpam-3967	129	53	-	-	PUNCT
ejpam-3967	129	54	set	set	NOUN
ejpam-3967	129	55	in	in	ADP
ejpam-3967	129	56	hv	hv	PROPN
ejpam-3967	129	57	.	.	PUNCT
ejpam-3967	130	1	(	(	PUNCT
ejpam-3967	130	2	b	b	X
ejpam-3967	130	3	)	)	PUNCT
ejpam-3967	130	4	c	c	NOUN
ejpam-3967	131	1	=	=	PUNCT
ejpam-3967	131	2	⋃	⋃	NOUN
ejpam-3967	131	3	v∈v	v∈v	NOUN
ejpam-3967	131	4	(	(	PUNCT
ejpam-3967	131	5	g	g	NOUN
ejpam-3967	131	6	)	)	PUNCT
ejpam-3967	131	7	sv	sv	NOUN
ejpam-3967	131	8	,	,	PUNCT
ejpam-3967	131	9	where	where	SCONJ
ejpam-3967	131	10	each	each	PRON
ejpam-3967	131	11	sv	sv	PROPN
ejpam-3967	131	12	is	be	AUX
ejpam-3967	131	13	a	a	DET
ejpam-3967	131	14	kfd	kfd	NOUN
ejpam-3967	131	15	-	-	PUNCT
ejpam-3967	131	16	set	set	NOUN
ejpam-3967	131	17	in	in	ADP
ejpam-3967	131	18	hv	hv	PROPN
ejpam-3967	131	19	and	and	CCONJ
ejpam-3967	131	20	|sv|	|sv|	PROPN
ejpam-3967	131	21	=	=	SYM
ejpam-3967	131	22	k.	k.	PROPN
ejpam-3967	131	23	theorem	theorem	VERB
ejpam-3967	131	24	7	7	NUM
ejpam-3967	131	25	.	.	PUNCT
ejpam-3967	132	1	[	[	X
ejpam-3967	132	2	5	5	NUM
ejpam-3967	132	3	]	]	PUNCT
ejpam-3967	132	4	let	let	VERB
ejpam-3967	132	5	g	g	NOUN
ejpam-3967	132	6	and	and	CCONJ
ejpam-3967	132	7	h	h	NOUN
ejpam-3967	132	8	be	be	AUX
ejpam-3967	132	9	nontrivial	nontrivial	ADJ
ejpam-3967	132	10	connected	connected	ADJ
ejpam-3967	132	11	graphs	graph	NOUN
ejpam-3967	132	12	.	.	PUNCT
ejpam-3967	133	1	then	then	ADV
ejpam-3967	133	2	c	c	X
ejpam-3967	133	3	=	=	PUNCT
ejpam-3967	133	4	⋃	⋃	PROPN
ejpam-3967	133	5	x∈s	x∈s	NOUN
ejpam-3967	133	6	(	(	PUNCT
ejpam-3967	133	7	{	{	PUNCT
ejpam-3967	133	8	x}×tx	x}×tx	NUM
ejpam-3967	133	9	)	)	PUNCT
ejpam-3967	133	10	⊆	⊆	NUM
ejpam-3967	133	11	v	v	NOUN
ejpam-3967	133	12	(	(	PUNCT
ejpam-3967	133	13	g[h	g[h	PROPN
ejpam-3967	133	14	]	]	PUNCT
ejpam-3967	133	15	)	)	PUNCT
ejpam-3967	133	16	is	be	AUX
ejpam-3967	133	17	a	a	DET
ejpam-3967	133	18	kfd	kfd	NOUN
ejpam-3967	133	19	-	-	PUNCT
ejpam-3967	133	20	set	set	NOUN
ejpam-3967	133	21	in	in	ADP
ejpam-3967	133	22	g[h	g[h	PROPN
ejpam-3967	133	23	]	]	PUNCT
ejpam-3967	133	24	if	if	SCONJ
ejpam-3967	134	1	and	and	CCONJ
ejpam-3967	134	2	only	only	ADV
ejpam-3967	134	3	if	if	SCONJ
ejpam-3967	134	4	the	the	DET
ejpam-3967	134	5	following	follow	VERB
ejpam-3967	134	6	hold	hold	NOUN
ejpam-3967	134	7	:	:	PUNCT
ejpam-3967	134	8	(	(	PUNCT
ejpam-3967	134	9	i	i	NOUN
ejpam-3967	134	10	)	)	PUNCT
ejpam-3967	134	11	s	s	VERB
ejpam-3967	134	12	is	be	AUX
ejpam-3967	134	13	a	a	DET
ejpam-3967	134	14	dominating	dominating	NOUN
ejpam-3967	134	15	set	set	VERB
ejpam-3967	134	16	in	in	ADP
ejpam-3967	134	17	g.	g.	PROPN
ejpam-3967	134	18	(	(	PUNCT
ejpam-3967	134	19	ii	ii	PROPN
ejpam-3967	134	20	)	)	PUNCT
ejpam-3967	134	21	for	for	ADP
ejpam-3967	134	22	each	each	DET
ejpam-3967	134	23	x	x	SYM
ejpam-3967	134	24	∈	∈	PROPN
ejpam-3967	134	25	s	s	NOUN
ejpam-3967	134	26	∩ng(s	∩ng(s	NOUN
ejpam-3967	134	27	)	)	PUNCT
ejpam-3967	134	28	,	,	PUNCT
ejpam-3967	134	29	tx	tx	PROPN
ejpam-3967	134	30	=	=	SYM
ejpam-3967	134	31	v	v	PROPN
ejpam-3967	134	32	(	(	PUNCT
ejpam-3967	134	33	h	h	NOUN
ejpam-3967	134	34	)	)	PUNCT
ejpam-3967	134	35	and	and	CCONJ
ejpam-3967	134	36	|v	|v	PROPN
ejpam-3967	134	37	(	(	PUNCT
ejpam-3967	134	38	h)|	h)|	NOUN
ejpam-3967	134	39	=	=	NOUN
ejpam-3967	134	40	r	r	NOUN
ejpam-3967	134	41	≤	≤	NOUN
ejpam-3967	135	1	k	k	NOUN
ejpam-3967	135	2	whenever	whenever	SCONJ
ejpam-3967	135	3	c	c	PROPN
ejpam-3967	135	4	6=	6=	PROPN
ejpam-3967	135	5	v	v	PROPN
ejpam-3967	135	6	(	(	PUNCT
ejpam-3967	135	7	g[h	g[h	PROPN
ejpam-3967	135	8	]	]	PUNCT
ejpam-3967	135	9	)	)	PUNCT
ejpam-3967	135	10	or	or	CCONJ
ejpam-3967	135	11	tx	tx	PROPN
ejpam-3967	135	12	is	be	AUX
ejpam-3967	135	13	an	an	DET
ejpam-3967	135	14	rfd	rfd	NOUN
ejpam-3967	135	15	-	-	PUNCT
ejpam-3967	135	16	set	set	VERB
ejpam-3967	135	17	and	and	CCONJ
ejpam-3967	135	18	∑	∑	ADP
ejpam-3967	135	19	z∈ng(x)∩s	z∈ng(x)∩s	NUM
ejpam-3967	135	20	|tz|	|tz|	NOUN
ejpam-3967	136	1	=	=	SYM
ejpam-3967	136	2	k	k	PROPN
ejpam-3967	136	3	−	−	PROPN
ejpam-3967	136	4	r.	r.	PROPN
ejpam-3967	136	5	(	(	PUNCT
ejpam-3967	136	6	iii	iii	NOUN
ejpam-3967	136	7	)	)	PUNCT
ejpam-3967	136	8	for	for	ADP
ejpam-3967	136	9	each	each	DET
ejpam-3967	136	10	x	x	SYM
ejpam-3967	136	11	∈	∈	PROPN
ejpam-3967	136	12	s\ng(s	s\ng(s	NOUN
ejpam-3967	136	13	)	)	PUNCT
ejpam-3967	136	14	,	,	PUNCT
ejpam-3967	136	15	tx	tx	PROPN
ejpam-3967	136	16	=	=	SYM
ejpam-3967	136	17	v	v	PROPN
ejpam-3967	136	18	(	(	PUNCT
ejpam-3967	136	19	h	h	NOUN
ejpam-3967	136	20	)	)	PUNCT
ejpam-3967	136	21	and	and	CCONJ
ejpam-3967	136	22	|v	|v	PROPN
ejpam-3967	136	23	(	(	PUNCT
ejpam-3967	136	24	h)|	h)|	NOUN
ejpam-3967	136	25	≤	≤	PROPN
ejpam-3967	136	26	k	k	NOUN
ejpam-3967	136	27	or	or	CCONJ
ejpam-3967	136	28	|tx|	|tx|	NUM
ejpam-3967	136	29	=	=	SYM
ejpam-3967	136	30	k	k	PROPN
ejpam-3967	136	31	and	and	CCONJ
ejpam-3967	136	32	tx	tx	PROPN
ejpam-3967	136	33	is	be	AUX
ejpam-3967	136	34	a	a	DET
ejpam-3967	136	35	kfd	kfd	NOUN
ejpam-3967	136	36	-	-	PUNCT
ejpam-3967	136	37	set	set	NOUN
ejpam-3967	136	38	in	in	ADP
ejpam-3967	136	39	h.	h.	PROPN
ejpam-3967	136	40	(	(	PUNCT
ejpam-3967	136	41	iv	iv	X
ejpam-3967	136	42	)	)	PUNCT
ejpam-3967	136	43	for	for	ADP
ejpam-3967	136	44	each	each	DET
ejpam-3967	136	45	y	y	PROPN
ejpam-3967	136	46	∈	∈	PROPN
ejpam-3967	136	47	v	v	NOUN
ejpam-3967	136	48	(	(	PUNCT
ejpam-3967	136	49	g)\s	g)\s	NOUN
ejpam-3967	136	50	,	,	PUNCT
ejpam-3967	136	51	∑	∑	PUNCT
ejpam-3967	136	52	v∈ng(y)∩s	v∈ng(y)∩s	ADJ
ejpam-3967	136	53	|tv|	|tv|	PROPN
ejpam-3967	137	1	=	=	SYM
ejpam-3967	137	2	k.	k.	PROPN
ejpam-3967	137	3	4	4	X
ejpam-3967	137	4	.	.	PUNCT
ejpam-3967	137	5	main	main	ADJ
ejpam-3967	137	6	results	result	NOUN
ejpam-3967	137	7	we	we	PRON
ejpam-3967	137	8	characterize	characterize	VERB
ejpam-3967	137	9	the	the	DET
ejpam-3967	137	10	k	k	ADJ
ejpam-3967	137	11	-	-	PUNCT
ejpam-3967	137	12	fair	fair	ADJ
ejpam-3967	137	13	total	total	ADJ
ejpam-3967	137	14	dominating	dominating	NOUN
ejpam-3967	137	15	sets	set	NOUN
ejpam-3967	137	16	in	in	ADP
ejpam-3967	137	17	the	the	DET
ejpam-3967	137	18	join	join	NOUN
ejpam-3967	137	19	,	,	PUNCT
ejpam-3967	137	20	corona	corona	PROPN
ejpam-3967	137	21	,	,	PUNCT
ejpam-3967	137	22	and	and	CCONJ
ejpam-3967	137	23	lexicographic	lexicographic	ADJ
ejpam-3967	137	24	product	product	NOUN
ejpam-3967	137	25	of	of	ADP
ejpam-3967	137	26	graphs	graph	NOUN
ejpam-3967	137	27	in	in	ADP
ejpam-3967	137	28	this	this	DET
ejpam-3967	137	29	section	section	NOUN
ejpam-3967	137	30	,	,	PUNCT
ejpam-3967	137	31	as	as	ADV
ejpam-3967	137	32	well	well	ADV
ejpam-3967	137	33	as	as	ADP
ejpam-3967	137	34	some	some	DET
ejpam-3967	137	35	such	such	ADJ
ejpam-3967	137	36	sets	set	NOUN
ejpam-3967	137	37	in	in	ADP
ejpam-3967	137	38	the	the	DET
ejpam-3967	137	39	cartesian	cartesian	ADJ
ejpam-3967	137	40	product	product	NOUN
ejpam-3967	137	41	of	of	ADP
ejpam-3967	137	42	graphs	graph	NOUN
ejpam-3967	137	43	.	.	PUNCT
ejpam-3967	138	1	we	we	PRON
ejpam-3967	138	2	also	also	ADV
ejpam-3967	138	3	determine	determine	VERB
ejpam-3967	138	4	the	the	DET
ejpam-3967	138	5	k	k	ADJ
ejpam-3967	138	6	-	-	PUNCT
ejpam-3967	138	7	fair	fair	ADJ
ejpam-3967	138	8	total	total	ADJ
ejpam-3967	138	9	domination	domination	NOUN
ejpam-3967	138	10	number	number	NOUN
ejpam-3967	138	11	of	of	ADP
ejpam-3967	138	12	the	the	DET
ejpam-3967	138	13	join	join	NOUN
ejpam-3967	138	14	and	and	CCONJ
ejpam-3967	138	15	corona	corona	NOUN
ejpam-3967	138	16	of	of	ADP
ejpam-3967	138	17	any	any	DET
ejpam-3967	138	18	two	two	NUM
ejpam-3967	138	19	connected	connected	ADJ
ejpam-3967	138	20	graphs	graph	NOUN
ejpam-3967	138	21	and	and	CCONJ
ejpam-3967	138	22	establish	establish	VERB
ejpam-3967	138	23	sharp	sharp	ADJ
ejpam-3967	138	24	bounds	bound	NOUN
ejpam-3967	138	25	of	of	ADP
ejpam-3967	138	26	the	the	DET
ejpam-3967	138	27	k	k	ADJ
ejpam-3967	138	28	-	-	PUNCT
ejpam-3967	138	29	fair	fair	ADJ
ejpam-3967	138	30	total	total	ADJ
ejpam-3967	138	31	domination	domination	NOUN
ejpam-3967	138	32	number	number	NOUN
ejpam-3967	138	33	of	of	ADP
ejpam-3967	138	34	the	the	DET
ejpam-3967	138	35	lexicographic	lexicographic	ADJ
ejpam-3967	138	36	and	and	CCONJ
ejpam-3967	138	37	cartesian	cartesian	ADJ
ejpam-3967	138	38	products	product	NOUN
ejpam-3967	138	39	of	of	ADP
ejpam-3967	138	40	graphs	graph	NOUN
ejpam-3967	138	41	.	.	PUNCT
ejpam-3967	139	1	theorem	theorem	ADJ
ejpam-3967	139	2	8	8	NUM
ejpam-3967	139	3	.	.	PUNCT
ejpam-3967	140	1	let	let	VERB
ejpam-3967	140	2	g	g	NOUN
ejpam-3967	140	3	and	and	CCONJ
ejpam-3967	140	4	h	h	NOUN
ejpam-3967	140	5	be	be	AUX
ejpam-3967	140	6	nontrivial	nontrivial	ADJ
ejpam-3967	140	7	connected	connect	VERB
ejpam-3967	140	8	graphs	graph	NOUN
ejpam-3967	140	9	of	of	ADP
ejpam-3967	140	10	orders	order	NOUN
ejpam-3967	140	11	m	m	VERB
ejpam-3967	140	12	and	and	CCONJ
ejpam-3967	140	13	n	n	CCONJ
ejpam-3967	140	14	,	,	PUNCT
ejpam-3967	140	15	respectively	respectively	ADV
ejpam-3967	140	16	,	,	PUNCT
ejpam-3967	140	17	and	and	CCONJ
ejpam-3967	140	18	k	k	X
ejpam-3967	140	19	a	a	DET
ejpam-3967	140	20	positive	positive	ADJ
ejpam-3967	140	21	integer	integer	NOUN
ejpam-3967	140	22	with	with	ADP
ejpam-3967	140	23	2	2	NUM
ejpam-3967	140	24	≤	≤	NOUN
ejpam-3967	140	25	k	k	NOUN
ejpam-3967	140	26	≤	≤	ADJ
ejpam-3967	140	27	max{m	max{m	NOUN
ejpam-3967	140	28	,	,	PUNCT
ejpam-3967	140	29	n	n	CCONJ
ejpam-3967	140	30	}	}	PUNCT
ejpam-3967	140	31	.	.	PUNCT
ejpam-3967	141	1	then	then	ADV
ejpam-3967	141	2	s	s	VERB
ejpam-3967	141	3	⊆	⊆	NUM
ejpam-3967	141	4	v	v	NOUN
ejpam-3967	141	5	(	(	PUNCT
ejpam-3967	141	6	g	g	PROPN
ejpam-3967	141	7	+	+	NOUN
ejpam-3967	141	8	h	h	NOUN
ejpam-3967	141	9	)	)	PUNCT
ejpam-3967	141	10	is	be	AUX
ejpam-3967	141	11	a	a	DET
ejpam-3967	141	12	kftd	kftd	NOUN
ejpam-3967	141	13	-	-	PUNCT
ejpam-3967	141	14	set	set	NOUN
ejpam-3967	141	15	in	in	ADP
ejpam-3967	141	16	g+h	g+h	PROPN
ejpam-3967	141	17	if	if	SCONJ
ejpam-3967	141	18	and	and	CCONJ
ejpam-3967	141	19	only	only	ADV
ejpam-3967	141	20	if	if	SCONJ
ejpam-3967	141	21	one	one	NUM
ejpam-3967	141	22	of	of	ADP
ejpam-3967	141	23	the	the	DET
ejpam-3967	141	24	following	following	NOUN
ejpam-3967	141	25	holds	hold	VERB
ejpam-3967	141	26	:	:	PUNCT
ejpam-3967	141	27	(	(	PUNCT
ejpam-3967	141	28	a	a	X
ejpam-3967	141	29	)	)	PUNCT
ejpam-3967	141	30	s	s	PART
ejpam-3967	141	31	=	=	SYM
ejpam-3967	141	32	v	v	PROPN
ejpam-3967	141	33	(	(	PUNCT
ejpam-3967	141	34	g+h	g+h	PROPN
ejpam-3967	141	35	)	)	PUNCT
ejpam-3967	141	36	.	.	PUNCT
ejpam-3967	142	1	(	(	PUNCT
ejpam-3967	142	2	b	b	X
ejpam-3967	142	3	)	)	PUNCT
ejpam-3967	142	4	s	s	PART
ejpam-3967	142	5	⊆	⊆	NUM
ejpam-3967	142	6	v	v	NOUN
ejpam-3967	142	7	(	(	PUNCT
ejpam-3967	142	8	g	g	NOUN
ejpam-3967	142	9	)	)	PUNCT
ejpam-3967	142	10	,	,	PUNCT
ejpam-3967	142	11	|s|	|s|	PROPN
ejpam-3967	142	12	=	=	SYM
ejpam-3967	142	13	k	k	PROPN
ejpam-3967	142	14	and	and	CCONJ
ejpam-3967	142	15	s	s	PROPN
ejpam-3967	142	16	is	be	AUX
ejpam-3967	142	17	a	a	DET
ejpam-3967	142	18	kftd	kftd	NOUN
ejpam-3967	142	19	-	-	PUNCT
ejpam-3967	142	20	set	set	NOUN
ejpam-3967	142	21	in	in	ADP
ejpam-3967	142	22	g.	g.	PROPN
ejpam-3967	142	23	(	(	PUNCT
ejpam-3967	142	24	c	c	X
ejpam-3967	142	25	)	)	PUNCT
ejpam-3967	142	26	s	s	PART
ejpam-3967	142	27	⊆	⊆	NUM
ejpam-3967	142	28	v	v	NOUN
ejpam-3967	142	29	(	(	PUNCT
ejpam-3967	142	30	h	h	NOUN
ejpam-3967	142	31	)	)	PUNCT
ejpam-3967	142	32	,	,	PUNCT
ejpam-3967	142	33	|s|	|s|	PROPN
ejpam-3967	142	34	=	=	SYM
ejpam-3967	142	35	k	k	PROPN
ejpam-3967	142	36	and	and	CCONJ
ejpam-3967	142	37	s	s	PROPN
ejpam-3967	142	38	is	be	AUX
ejpam-3967	142	39	a	a	DET
ejpam-3967	142	40	kftd	kftd	NOUN
ejpam-3967	142	41	-	-	PUNCT
ejpam-3967	142	42	set	set	NOUN
ejpam-3967	142	43	in	in	ADP
ejpam-3967	142	44	h.	h.	PROPN
ejpam-3967	142	45	(	(	PUNCT
ejpam-3967	142	46	d	d	X
ejpam-3967	142	47	)	)	PUNCT
ejpam-3967	142	48	s	s	PART
ejpam-3967	142	49	=	=	PUNCT
ejpam-3967	142	50	sg	sg	X
ejpam-3967	142	51	∪	∪	ADJ
ejpam-3967	142	52	sh	sh	PROPN
ejpam-3967	142	53	,	,	PUNCT
ejpam-3967	142	54	where	where	SCONJ
ejpam-3967	142	55	sg	sg	PROPN
ejpam-3967	142	56	is	be	AUX
ejpam-3967	142	57	a	a	DET
ejpam-3967	142	58	(	(	PUNCT
ejpam-3967	142	59	k	k	PROPN
ejpam-3967	142	60	−	−	PROPN
ejpam-3967	142	61	|sh	|sh	ADP
ejpam-3967	142	62	|)fd	|)fd	PROPN
ejpam-3967	142	63	-	-	PUNCT
ejpam-3967	142	64	set	set	VERB
ejpam-3967	142	65	in	in	ADP
ejpam-3967	142	66	g	g	PROPN
ejpam-3967	142	67	and	and	CCONJ
ejpam-3967	142	68	sh	sh	PROPN
ejpam-3967	142	69	is	be	AUX
ejpam-3967	142	70	a	a	DET
ejpam-3967	142	71	(	(	PUNCT
ejpam-3967	142	72	k	k	PROPN
ejpam-3967	142	73	−	−	PROPN
ejpam-3967	142	74	|sg|)fd	|sg|)fd	NOUN
ejpam-3967	142	75	-	-	PUNCT
ejpam-3967	142	76	set	set	NOUN
ejpam-3967	142	77	in	in	ADP
ejpam-3967	142	78	h.	h.	PROPN
ejpam-3967	142	79	(	(	PUNCT
ejpam-3967	142	80	e	e	X
ejpam-3967	142	81	)	)	PUNCT
ejpam-3967	142	82	s	s	PART
ejpam-3967	142	83	=	=	SYM
ejpam-3967	142	84	v	v	X
ejpam-3967	142	85	(	(	PUNCT
ejpam-3967	142	86	g	g	NOUN
ejpam-3967	142	87	)	)	PUNCT
ejpam-3967	142	88	∪	∪	ADP
ejpam-3967	142	89	t	t	PROPN
ejpam-3967	142	90	,	,	PUNCT
ejpam-3967	142	91	where	where	SCONJ
ejpam-3967	142	92	|v	|v	PROPN
ejpam-3967	142	93	(	(	PUNCT
ejpam-3967	142	94	g)|	g)|	NOUN
ejpam-3967	142	95	=	=	NOUN
ejpam-3967	142	96	m	m	PROPN
ejpam-3967	142	97	<	<	X
ejpam-3967	142	98	k	k	X
ejpam-3967	142	99	and	and	CCONJ
ejpam-3967	142	100	t	t	PROPN
ejpam-3967	142	101	is	be	AUX
ejpam-3967	142	102	a	a	DET
ejpam-3967	142	103	(	(	PUNCT
ejpam-3967	142	104	k	k	X
ejpam-3967	142	105	−m)fd	−m)fd	X
ejpam-3967	142	106	-	-	PUNCT
ejpam-3967	142	107	set	set	NOUN
ejpam-3967	142	108	in	in	ADP
ejpam-3967	142	109	h.	h.	PROPN
ejpam-3967	142	110	(	(	PUNCT
ejpam-3967	142	111	f	f	X
ejpam-3967	142	112	)	)	PUNCT
ejpam-3967	142	113	s	s	PART
ejpam-3967	143	1	=	=	X
ejpam-3967	143	2	d	d	X
ejpam-3967	143	3	∪	∪	X
ejpam-3967	143	4	v	v	NOUN
ejpam-3967	143	5	(	(	PUNCT
ejpam-3967	143	6	h	h	NOUN
ejpam-3967	143	7	)	)	PUNCT
ejpam-3967	143	8	,	,	PUNCT
ejpam-3967	144	1	where	where	SCONJ
ejpam-3967	144	2	|v	|v	PROPN
ejpam-3967	144	3	(	(	PUNCT
ejpam-3967	144	4	h)|	h)|	NOUN
ejpam-3967	144	5	=	=	SYM
ejpam-3967	144	6	n	n	CCONJ
ejpam-3967	144	7	<	<	X
ejpam-3967	144	8	k	k	PROPN
ejpam-3967	144	9	and	and	CCONJ
ejpam-3967	144	10	d	d	PROPN
ejpam-3967	144	11	is	be	AUX
ejpam-3967	144	12	a	a	DET
ejpam-3967	144	13	(	(	PUNCT
ejpam-3967	144	14	k	k	PROPN
ejpam-3967	144	15	−	−	PROPN
ejpam-3967	144	16	n)fd	n)fd	PROPN
ejpam-3967	144	17	-	-	PUNCT
ejpam-3967	144	18	set	set	NOUN
ejpam-3967	144	19	in	in	ADP
ejpam-3967	144	20	g.	g.	PROPN
ejpam-3967	144	21	w.	w.	PROPN
ejpam-3967	144	22	bent	bent	PROPN
ejpam-3967	144	23	-	-	PUNCT
ejpam-3967	144	24	usman	usman	PROPN
ejpam-3967	144	25	,	,	PUNCT
ejpam-3967	144	26	r.	r.	PROPN
ejpam-3967	144	27	isla	isla	PROPN
ejpam-3967	144	28	/	/	SYM
ejpam-3967	144	29	eur	eur	PROPN
ejpam-3967	144	30	.	.	PUNCT
ejpam-3967	145	1	j.	j.	PROPN
ejpam-3967	145	2	pure	pure	PROPN
ejpam-3967	145	3	appl	appl	PROPN
ejpam-3967	145	4	.	.	PROPN
ejpam-3967	145	5	math	math	PROPN
ejpam-3967	145	6	,	,	PUNCT
ejpam-3967	145	7	14	14	NUM
ejpam-3967	145	8	(	(	PUNCT
ejpam-3967	145	9	2	2	NUM
ejpam-3967	145	10	)	)	PUNCT
ejpam-3967	145	11	(	(	PUNCT
ejpam-3967	145	12	2021	2021	NUM
ejpam-3967	145	13	)	)	PUNCT
ejpam-3967	145	14	,	,	PUNCT
ejpam-3967	145	15	578	578	NUM
ejpam-3967	145	16	-	-	SYM
ejpam-3967	145	17	589	589	NUM
ejpam-3967	145	18	584	584	NUM
ejpam-3967	145	19	proof	proof	NOUN
ejpam-3967	145	20	.	.	PUNCT
ejpam-3967	145	21	suppose	suppose	VERB
ejpam-3967	145	22	that	that	SCONJ
ejpam-3967	145	23	s	s	VERB
ejpam-3967	145	24	⊆	⊆	NUM
ejpam-3967	145	25	v	v	NOUN
ejpam-3967	145	26	(	(	PUNCT
ejpam-3967	145	27	g	g	PROPN
ejpam-3967	145	28	+	+	NOUN
ejpam-3967	145	29	h	h	NOUN
ejpam-3967	145	30	)	)	PUNCT
ejpam-3967	145	31	is	be	AUX
ejpam-3967	145	32	a	a	DET
ejpam-3967	145	33	kftd	kftd	NOUN
ejpam-3967	145	34	-	-	PUNCT
ejpam-3967	145	35	set	set	NOUN
ejpam-3967	145	36	in	in	ADP
ejpam-3967	145	37	g	g	PROPN
ejpam-3967	146	1	+	+	CCONJ
ejpam-3967	146	2	h	h	NOUN
ejpam-3967	146	3	,	,	PUNCT
ejpam-3967	146	4	where	where	SCONJ
ejpam-3967	146	5	k	k	PROPN
ejpam-3967	146	6	≥	≥	NUM
ejpam-3967	146	7	2	2	NUM
ejpam-3967	146	8	.	.	PUNCT
ejpam-3967	147	1	then	then	ADV
ejpam-3967	147	2	s	s	VERB
ejpam-3967	147	3	is	be	AUX
ejpam-3967	147	4	a	a	DET
ejpam-3967	147	5	kfd	kfd	NOUN
ejpam-3967	147	6	-	-	PUNCT
ejpam-3967	147	7	set	set	NOUN
ejpam-3967	147	8	in	in	ADP
ejpam-3967	147	9	g	g	PROPN
ejpam-3967	147	10	+	+	CCONJ
ejpam-3967	147	11	h.	h.	PROPN
ejpam-3967	147	12	suppose	suppose	VERB
ejpam-3967	147	13	further	far	ADV
ejpam-3967	147	14	that	that	PRON
ejpam-3967	147	15	s	s	PROPN
ejpam-3967	147	16	6=	6=	NUM
ejpam-3967	147	17	v	v	NOUN
ejpam-3967	147	18	(	(	PUNCT
ejpam-3967	147	19	g	g	PROPN
ejpam-3967	147	20	+	+	NOUN
ejpam-3967	147	21	h	h	NOUN
ejpam-3967	147	22	)	)	PUNCT
ejpam-3967	147	23	.	.	PUNCT
ejpam-3967	148	1	if	if	SCONJ
ejpam-3967	148	2	s	s	VERB
ejpam-3967	148	3	⊆	⊆	NUM
ejpam-3967	148	4	v	v	NOUN
ejpam-3967	148	5	(	(	PUNCT
ejpam-3967	148	6	g	g	NOUN
ejpam-3967	148	7	)	)	PUNCT
ejpam-3967	148	8	,	,	PUNCT
ejpam-3967	148	9	then	then	ADV
ejpam-3967	148	10	|s|	|s|	PROPN
ejpam-3967	148	11	=	=	SYM
ejpam-3967	148	12	k	k	PROPN
ejpam-3967	148	13	and	and	CCONJ
ejpam-3967	148	14	s	s	PROPN
ejpam-3967	148	15	is	be	AUX
ejpam-3967	148	16	a	a	DET
ejpam-3967	148	17	kfd	kfd	NOUN
ejpam-3967	148	18	-	-	PUNCT
ejpam-3967	148	19	set	set	NOUN
ejpam-3967	148	20	in	in	ADP
ejpam-3967	148	21	g	g	NOUN
ejpam-3967	148	22	by	by	ADP
ejpam-3967	148	23	theorem	theorem	NOUN
ejpam-3967	148	24	5	5	NUM
ejpam-3967	148	25	.	.	PUNCT
ejpam-3967	149	1	since	since	SCONJ
ejpam-3967	149	2	s	s	PROPN
ejpam-3967	149	3	is	be	AUX
ejpam-3967	149	4	a	a	DET
ejpam-3967	149	5	total	total	ADJ
ejpam-3967	149	6	dominating	dominating	NOUN
ejpam-3967	149	7	set	set	VERB
ejpam-3967	149	8	in	in	ADP
ejpam-3967	149	9	g	g	PROPN
ejpam-3967	149	10	+	+	CCONJ
ejpam-3967	149	11	h	h	NOUN
ejpam-3967	149	12	,	,	PUNCT
ejpam-3967	149	13	it	it	PRON
ejpam-3967	149	14	is	be	AUX
ejpam-3967	149	15	a	a	DET
ejpam-3967	149	16	total	total	ADJ
ejpam-3967	149	17	dominating	dominating	NOUN
ejpam-3967	149	18	set	set	VERB
ejpam-3967	149	19	in	in	ADP
ejpam-3967	149	20	g.	g.	PROPN
ejpam-3967	149	21	hence	hence	ADV
ejpam-3967	149	22	,	,	PUNCT
ejpam-3967	149	23	s	s	VERB
ejpam-3967	149	24	must	must	AUX
ejpam-3967	149	25	be	be	AUX
ejpam-3967	149	26	a	a	DET
ejpam-3967	149	27	kftd	kftd	NOUN
ejpam-3967	149	28	-	-	PUNCT
ejpam-3967	149	29	set	set	NOUN
ejpam-3967	149	30	in	in	ADP
ejpam-3967	149	31	g.	g.	NOUN
ejpam-3967	149	32	similarly	similarly	ADV
ejpam-3967	149	33	,	,	PUNCT
ejpam-3967	149	34	if	if	SCONJ
ejpam-3967	149	35	s	s	VERB
ejpam-3967	149	36	⊆	⊆	NUM
ejpam-3967	149	37	v	v	NOUN
ejpam-3967	149	38	(	(	PUNCT
ejpam-3967	149	39	h	h	NOUN
ejpam-3967	149	40	)	)	PUNCT
ejpam-3967	149	41	,	,	PUNCT
ejpam-3967	149	42	then	then	ADV
ejpam-3967	149	43	|s|	|s|	PROPN
ejpam-3967	149	44	=	=	SYM
ejpam-3967	149	45	k	k	PROPN
ejpam-3967	149	46	and	and	CCONJ
ejpam-3967	149	47	s	s	PROPN
ejpam-3967	149	48	is	be	AUX
ejpam-3967	149	49	a	a	DET
ejpam-3967	149	50	kftd	kftd	NOUN
ejpam-3967	149	51	-	-	PUNCT
ejpam-3967	149	52	set	set	NOUN
ejpam-3967	149	53	in	in	ADP
ejpam-3967	149	54	h.	h.	PROPN
ejpam-3967	149	55	suppose	suppose	VERB
ejpam-3967	149	56	s	s	VERB
ejpam-3967	149	57	∩	∩	ADJ
ejpam-3967	149	58	v	v	X
ejpam-3967	149	59	(	(	PUNCT
ejpam-3967	149	60	g	g	NOUN
ejpam-3967	149	61	)	)	PUNCT
ejpam-3967	149	62	6=	6=	ADP
ejpam-3967	149	63	∅	∅	NOUN
ejpam-3967	149	64	and	and	CCONJ
ejpam-3967	149	65	s	s	X
ejpam-3967	149	66	∩	∩	ADJ
ejpam-3967	149	67	v	v	ADJ
ejpam-3967	149	68	(	(	PUNCT
ejpam-3967	149	69	h	h	NOUN
ejpam-3967	149	70	)	)	PUNCT
ejpam-3967	149	71	6=	6=	ADP
ejpam-3967	149	72	∅.	∅.	VERB
ejpam-3967	149	73	then	then	ADV
ejpam-3967	149	74	by	by	ADP
ejpam-3967	149	75	theorem	theorem	NOUN
ejpam-3967	149	76	5	5	NUM
ejpam-3967	149	77	,	,	PUNCT
ejpam-3967	149	78	s	s	PART
ejpam-3967	149	79	=	=	PUNCT
ejpam-3967	149	80	sg	sg	X
ejpam-3967	149	81	∪	∪	ADJ
ejpam-3967	149	82	sh	sh	PROPN
ejpam-3967	149	83	,	,	PUNCT
ejpam-3967	149	84	where	where	SCONJ
ejpam-3967	149	85	sg	sg	PROPN
ejpam-3967	149	86	is	be	AUX
ejpam-3967	149	87	a	a	DET
ejpam-3967	149	88	(	(	PUNCT
ejpam-3967	149	89	k	k	PROPN
ejpam-3967	149	90	−	−	PROPN
ejpam-3967	149	91	|sh	|sh	ADP
ejpam-3967	149	92	|)fd	|)fd	PROPN
ejpam-3967	149	93	-	-	PUNCT
ejpam-3967	149	94	set	set	VERB
ejpam-3967	149	95	in	in	ADP
ejpam-3967	149	96	g	g	PROPN
ejpam-3967	149	97	and	and	CCONJ
ejpam-3967	149	98	sh	sh	PROPN
ejpam-3967	149	99	is	be	AUX
ejpam-3967	149	100	a	a	DET
ejpam-3967	149	101	(	(	PUNCT
ejpam-3967	149	102	k−	k−	NOUN
ejpam-3967	149	103	|sg|)fd	|sg|)fd	PROPN
ejpam-3967	149	104	-	-	PUNCT
ejpam-3967	149	105	set	set	NOUN
ejpam-3967	149	106	in	in	ADP
ejpam-3967	149	107	h	h	NOUN
ejpam-3967	149	108	,	,	PUNCT
ejpam-3967	149	109	or	or	CCONJ
ejpam-3967	149	110	s	s	X
ejpam-3967	149	111	=	=	SYM
ejpam-3967	149	112	v	v	NOUN
ejpam-3967	149	113	(	(	PUNCT
ejpam-3967	149	114	g)∪	g)∪	VERB
ejpam-3967	149	115	t	t	NOUN
ejpam-3967	149	116	,	,	PUNCT
ejpam-3967	149	117	where	where	SCONJ
ejpam-3967	149	118	|v	|v	PROPN
ejpam-3967	149	119	(	(	PUNCT
ejpam-3967	149	120	g)|	g)|	NOUN
ejpam-3967	149	121	=	=	NOUN
ejpam-3967	149	122	m	m	PROPN
ejpam-3967	149	123	<	<	X
ejpam-3967	149	124	k	k	X
ejpam-3967	149	125	and	and	CCONJ
ejpam-3967	149	126	t	t	PROPN
ejpam-3967	149	127	is	be	AUX
ejpam-3967	149	128	a	a	DET
ejpam-3967	149	129	(	(	PUNCT
ejpam-3967	149	130	k−m)fd	k−m)fd	PROPN
ejpam-3967	149	131	-	-	PUNCT
ejpam-3967	149	132	set	set	NOUN
ejpam-3967	149	133	in	in	ADP
ejpam-3967	149	134	h	h	NOUN
ejpam-3967	149	135	,	,	PUNCT
ejpam-3967	149	136	or	or	CCONJ
ejpam-3967	149	137	s	s	VERB
ejpam-3967	150	1	=	=	SYM
ejpam-3967	150	2	d	d	X
ejpam-3967	150	3	∪	∪	X
ejpam-3967	150	4	v	v	NOUN
ejpam-3967	150	5	(	(	PUNCT
ejpam-3967	150	6	h	h	NOUN
ejpam-3967	150	7	)	)	PUNCT
ejpam-3967	150	8	,	,	PUNCT
ejpam-3967	151	1	where	where	SCONJ
ejpam-3967	151	2	|v	|v	PROPN
ejpam-3967	151	3	(	(	PUNCT
ejpam-3967	151	4	h)|	h)|	NOUN
ejpam-3967	151	5	=	=	SYM
ejpam-3967	151	6	n	n	CCONJ
ejpam-3967	151	7	<	<	X
ejpam-3967	151	8	k	k	PROPN
ejpam-3967	151	9	and	and	CCONJ
ejpam-3967	151	10	d	d	PROPN
ejpam-3967	151	11	is	be	AUX
ejpam-3967	151	12	a	a	DET
ejpam-3967	151	13	(	(	PUNCT
ejpam-3967	151	14	k	k	PROPN
ejpam-3967	151	15	−	−	PROPN
ejpam-3967	151	16	n)fd	n)fd	PROPN
ejpam-3967	151	17	-	-	PUNCT
ejpam-3967	151	18	set	set	NOUN
ejpam-3967	151	19	in	in	ADP
ejpam-3967	151	20	g.	g.	NOUN
ejpam-3967	151	21	conversely	conversely	ADV
ejpam-3967	151	22	,	,	PUNCT
ejpam-3967	151	23	suppose	suppose	VERB
ejpam-3967	151	24	one	one	NUM
ejpam-3967	151	25	of	of	ADP
ejpam-3967	151	26	statements	statement	NOUN
ejpam-3967	151	27	(	(	PUNCT
ejpam-3967	151	28	a	a	NOUN
ejpam-3967	151	29	)	)	PUNCT
ejpam-3967	151	30	to	to	ADP
ejpam-3967	151	31	(	(	PUNCT
ejpam-3967	151	32	f	f	X
ejpam-3967	151	33	)	)	PUNCT
ejpam-3967	151	34	holds	hold	VERB
ejpam-3967	151	35	.	.	PUNCT
ejpam-3967	152	1	then	then	ADV
ejpam-3967	152	2	s	s	VERB
ejpam-3967	152	3	is	be	AUX
ejpam-3967	152	4	a	a	DET
ejpam-3967	152	5	kfd	kfd	NOUN
ejpam-3967	152	6	-	-	PUNCT
ejpam-3967	152	7	set	set	NOUN
ejpam-3967	152	8	in	in	ADP
ejpam-3967	152	9	g+h	g+h	PROPN
ejpam-3967	152	10	by	by	ADP
ejpam-3967	152	11	theorem	theorem	NOUN
ejpam-3967	152	12	5	5	NUM
ejpam-3967	152	13	.	.	PUNCT
ejpam-3967	153	1	if	if	SCONJ
ejpam-3967	153	2	statement	statement	NOUN
ejpam-3967	153	3	(	(	PUNCT
ejpam-3967	153	4	a	a	NOUN
ejpam-3967	153	5	)	)	PUNCT
ejpam-3967	153	6	holds	hold	NOUN
ejpam-3967	153	7	,	,	PUNCT
ejpam-3967	153	8	then	then	ADV
ejpam-3967	153	9	s	s	VERB
ejpam-3967	153	10	is	be	AUX
ejpam-3967	153	11	clearly	clearly	ADV
ejpam-3967	153	12	a	a	DET
ejpam-3967	153	13	kftd	kftd	NOUN
ejpam-3967	153	14	-	-	PUNCT
ejpam-3967	153	15	set	set	NOUN
ejpam-3967	153	16	in	in	ADP
ejpam-3967	153	17	g	g	PROPN
ejpam-3967	153	18	+	+	PROPN
ejpam-3967	153	19	h.	h.	PROPN
ejpam-3967	153	20	suppose	suppose	VERB
ejpam-3967	153	21	statement	statement	NOUN
ejpam-3967	153	22	(	(	PUNCT
ejpam-3967	153	23	b	b	NOUN
ejpam-3967	153	24	)	)	PUNCT
ejpam-3967	153	25	holds	hold	VERB
ejpam-3967	153	26	.	.	PUNCT
ejpam-3967	154	1	since	since	SCONJ
ejpam-3967	154	2	s	s	PROPN
ejpam-3967	154	3	is	be	AUX
ejpam-3967	154	4	a	a	DET
ejpam-3967	154	5	kftd	kftd	NOUN
ejpam-3967	154	6	-	-	PUNCT
ejpam-3967	154	7	set	set	NOUN
ejpam-3967	154	8	in	in	ADP
ejpam-3967	154	9	g	g	NOUN
ejpam-3967	154	10	,	,	PUNCT
ejpam-3967	154	11	s	s	PART
ejpam-3967	154	12	is	be	AUX
ejpam-3967	154	13	a	a	DET
ejpam-3967	154	14	kftd	kftd	NOUN
ejpam-3967	154	15	-	-	PUNCT
ejpam-3967	154	16	set	set	NOUN
ejpam-3967	154	17	in	in	ADP
ejpam-3967	154	18	g	g	PROPN
ejpam-3967	154	19	+	+	CCONJ
ejpam-3967	154	20	h.	h.	PROPN
ejpam-3967	154	21	similarly	similarly	ADV
ejpam-3967	154	22	,	,	PUNCT
ejpam-3967	154	23	if	if	SCONJ
ejpam-3967	154	24	statement	statement	NOUN
ejpam-3967	154	25	(	(	PUNCT
ejpam-3967	154	26	c	c	NOUN
ejpam-3967	154	27	)	)	PUNCT
ejpam-3967	154	28	holds	hold	NOUN
ejpam-3967	154	29	,	,	PUNCT
ejpam-3967	154	30	then	then	ADV
ejpam-3967	154	31	the	the	DET
ejpam-3967	154	32	same	same	ADJ
ejpam-3967	154	33	conclusion	conclusion	NOUN
ejpam-3967	154	34	follows	follow	VERB
ejpam-3967	154	35	.	.	PUNCT
ejpam-3967	155	1	if	if	SCONJ
ejpam-3967	155	2	statement	statement	NOUN
ejpam-3967	155	3	(	(	PUNCT
ejpam-3967	155	4	d	d	X
ejpam-3967	155	5	)	)	PUNCT
ejpam-3967	155	6	is	be	AUX
ejpam-3967	155	7	satisfied	satisfied	ADJ
ejpam-3967	155	8	,	,	PUNCT
ejpam-3967	155	9	then	then	ADV
ejpam-3967	155	10	every	every	DET
ejpam-3967	155	11	vertex	vertex	NOUN
ejpam-3967	155	12	in	in	ADP
ejpam-3967	155	13	sg	sg	PROPN
ejpam-3967	155	14	is	be	AUX
ejpam-3967	155	15	adjacent	adjacent	ADJ
ejpam-3967	155	16	to	to	ADP
ejpam-3967	155	17	each	each	DET
ejpam-3967	155	18	vertex	vertex	NOUN
ejpam-3967	155	19	in	in	ADP
ejpam-3967	155	20	sh	sh	PROPN
ejpam-3967	155	21	and	and	CCONJ
ejpam-3967	155	22	vice	vice	ADV
ejpam-3967	155	23	versa	versa	ADV
ejpam-3967	155	24	,	,	PUNCT
ejpam-3967	155	25	hence	hence	ADV
ejpam-3967	155	26	s	s	PART
ejpam-3967	155	27	=	=	PUNCT
ejpam-3967	155	28	sg	sg	PROPN
ejpam-3967	155	29	∪	∪	NOUN
ejpam-3967	155	30	sh	sh	PROPN
ejpam-3967	155	31	is	be	AUX
ejpam-3967	155	32	a	a	DET
ejpam-3967	155	33	kftd	kftd	NOUN
ejpam-3967	155	34	-	-	PUNCT
ejpam-3967	155	35	set	set	NOUN
ejpam-3967	155	36	in	in	ADP
ejpam-3967	155	37	g	g	PROPN
ejpam-3967	155	38	+	+	CCONJ
ejpam-3967	155	39	h.	h.	NOUN
ejpam-3967	155	40	if	if	SCONJ
ejpam-3967	155	41	statement	statement	NOUN
ejpam-3967	155	42	(	(	PUNCT
ejpam-3967	155	43	e	e	NOUN
ejpam-3967	155	44	)	)	PUNCT
ejpam-3967	155	45	holds	hold	VERB
ejpam-3967	155	46	,	,	PUNCT
ejpam-3967	155	47	then	then	ADV
ejpam-3967	155	48	every	every	DET
ejpam-3967	155	49	vertex	vertex	NOUN
ejpam-3967	155	50	in	in	ADP
ejpam-3967	155	51	t	t	PROPN
ejpam-3967	155	52	is	be	AUX
ejpam-3967	155	53	adjacent	adjacent	ADJ
ejpam-3967	155	54	to	to	ADP
ejpam-3967	155	55	each	each	PRON
ejpam-3967	155	56	of	of	ADP
ejpam-3967	155	57	the	the	DET
ejpam-3967	155	58	vertices	vertex	NOUN
ejpam-3967	155	59	in	in	ADP
ejpam-3967	155	60	g	g	PROPN
ejpam-3967	155	61	and	and	CCONJ
ejpam-3967	155	62	each	each	DET
ejpam-3967	155	63	vertex	vertex	NOUN
ejpam-3967	155	64	in	in	ADP
ejpam-3967	155	65	g	g	PROPN
ejpam-3967	155	66	is	be	AUX
ejpam-3967	155	67	adjacent	adjacent	ADJ
ejpam-3967	155	68	to	to	ADP
ejpam-3967	155	69	some	some	DET
ejpam-3967	155	70	vertex	vertex	NOUN
ejpam-3967	155	71	in	in	ADP
ejpam-3967	155	72	g	g	PROPN
ejpam-3967	155	73	and	and	CCONJ
ejpam-3967	155	74	to	to	ADP
ejpam-3967	155	75	each	each	PRON
ejpam-3967	155	76	of	of	ADP
ejpam-3967	155	77	the	the	DET
ejpam-3967	155	78	vertices	vertex	NOUN
ejpam-3967	155	79	in	in	ADP
ejpam-3967	155	80	t	t	PROPN
ejpam-3967	155	81	,	,	PUNCT
ejpam-3967	155	82	hence	hence	ADV
ejpam-3967	155	83	s	s	PART
ejpam-3967	155	84	=	=	SYM
ejpam-3967	155	85	v	v	NOUN
ejpam-3967	155	86	(	(	PUNCT
ejpam-3967	155	87	g)∪	g)∪	VERB
ejpam-3967	155	88	t	t	NOUN
ejpam-3967	155	89	is	be	AUX
ejpam-3967	155	90	a	a	DET
ejpam-3967	155	91	kftd	kftd	NOUN
ejpam-3967	155	92	-	-	PUNCT
ejpam-3967	155	93	set	set	NOUN
ejpam-3967	155	94	in	in	ADP
ejpam-3967	155	95	g+h	g+h	PROPN
ejpam-3967	155	96	.	.	PUNCT
ejpam-3967	156	1	similarly	similarly	ADV
ejpam-3967	156	2	,	,	PUNCT
ejpam-3967	156	3	if	if	SCONJ
ejpam-3967	156	4	statement	statement	NOUN
ejpam-3967	156	5	(	(	PUNCT
ejpam-3967	156	6	f	f	X
ejpam-3967	156	7	)	)	PUNCT
ejpam-3967	156	8	holds	hold	VERB
ejpam-3967	156	9	,	,	PUNCT
ejpam-3967	156	10	then	then	ADV
ejpam-3967	156	11	s	s	VERB
ejpam-3967	156	12	=	=	X
ejpam-3967	156	13	d	d	X
ejpam-3967	156	14	∪	∪	X
ejpam-3967	156	15	v	v	NOUN
ejpam-3967	156	16	(	(	PUNCT
ejpam-3967	156	17	h	h	NOUN
ejpam-3967	156	18	)	)	PUNCT
ejpam-3967	156	19	is	be	AUX
ejpam-3967	156	20	a	a	DET
ejpam-3967	156	21	kftd	kftd	NOUN
ejpam-3967	156	22	-	-	PUNCT
ejpam-3967	156	23	set	set	NOUN
ejpam-3967	156	24	in	in	ADP
ejpam-3967	156	25	g+h	g+h	PROPN
ejpam-3967	156	26	.	.	PUNCT
ejpam-3967	157	1	this	this	PRON
ejpam-3967	157	2	proves	prove	VERB
ejpam-3967	157	3	the	the	DET
ejpam-3967	157	4	assertion	assertion	NOUN
ejpam-3967	157	5	.	.	PUNCT
ejpam-3967	158	1	�	�	PROPN
ejpam-3967	158	2	corollary	corollary	NOUN
ejpam-3967	158	3	2	2	PROPN
ejpam-3967	158	4	.	.	PUNCT
ejpam-3967	159	1	let	let	VERB
ejpam-3967	159	2	g	g	NOUN
ejpam-3967	159	3	and	and	CCONJ
ejpam-3967	159	4	h	h	NOUN
ejpam-3967	159	5	be	be	AUX
ejpam-3967	159	6	connected	connect	VERB
ejpam-3967	159	7	nontrivial	nontrivial	ADJ
ejpam-3967	159	8	graphs	graph	NOUN
ejpam-3967	159	9	of	of	ADP
ejpam-3967	159	10	orders	order	NOUN
ejpam-3967	159	11	m	m	VERB
ejpam-3967	159	12	and	and	CCONJ
ejpam-3967	159	13	n	n	CCONJ
ejpam-3967	159	14	,	,	PUNCT
ejpam-3967	159	15	respectively	respectively	ADV
ejpam-3967	159	16	,	,	PUNCT
ejpam-3967	159	17	and	and	CCONJ
ejpam-3967	159	18	k	k	X
ejpam-3967	159	19	a	a	DET
ejpam-3967	159	20	positive	positive	ADJ
ejpam-3967	159	21	integer	integer	NOUN
ejpam-3967	159	22	with	with	ADP
ejpam-3967	159	23	2	2	NUM
ejpam-3967	159	24	≤	≤	NOUN
ejpam-3967	159	25	k	k	NOUN
ejpam-3967	159	26	≤	≤	ADJ
ejpam-3967	159	27	max{m	max{m	NOUN
ejpam-3967	159	28	,	,	PUNCT
ejpam-3967	159	29	n	n	CCONJ
ejpam-3967	159	30	}	}	PUNCT
ejpam-3967	159	31	.	.	PUNCT
ejpam-3967	160	1	if	if	SCONJ
ejpam-3967	160	2	g	g	PROPN
ejpam-3967	160	3	or	or	CCONJ
ejpam-3967	160	4	h	h	NOUN
ejpam-3967	160	5	has	have	VERB
ejpam-3967	160	6	a	a	DET
ejpam-3967	160	7	kftd	kftd	NOUN
ejpam-3967	160	8	-	-	PUNCT
ejpam-3967	160	9	set	set	PROPN
ejpam-3967	160	10	s	s	NOUN
ejpam-3967	160	11	with	with	ADP
ejpam-3967	160	12	|s|	|s|	PROPN
ejpam-3967	160	13	=	=	SYM
ejpam-3967	160	14	k	k	PROPN
ejpam-3967	160	15	,	,	PUNCT
ejpam-3967	160	16	then	then	ADV
ejpam-3967	160	17	γkftd(g+h	γkftd(g+h	PROPN
ejpam-3967	160	18	)	)	PUNCT
ejpam-3967	161	1	=	=	PUNCT
ejpam-3967	161	2	k.	k.	PROPN
ejpam-3967	161	3	theorem	theorem	VERB
ejpam-3967	161	4	9	9	NUM
ejpam-3967	161	5	.	.	PUNCT
ejpam-3967	162	1	let	let	VERB
ejpam-3967	162	2	g	g	PRON
ejpam-3967	162	3	be	be	AUX
ejpam-3967	162	4	a	a	DET
ejpam-3967	162	5	nontrivial	nontrivial	ADJ
ejpam-3967	162	6	connected	connect	VERB
ejpam-3967	162	7	graph	graph	NOUN
ejpam-3967	162	8	and	and	CCONJ
ejpam-3967	162	9	h	h	NOUN
ejpam-3967	162	10	a	a	DET
ejpam-3967	162	11	nontrivial	nontrivial	ADJ
ejpam-3967	162	12	graph	graph	NOUN
ejpam-3967	162	13	,	,	PUNCT
ejpam-3967	162	14	and	and	CCONJ
ejpam-3967	162	15	let	let	VERB
ejpam-3967	162	16	k	k	PRON
ejpam-3967	162	17	be	be	AUX
ejpam-3967	162	18	a	a	DET
ejpam-3967	162	19	positive	positive	ADJ
ejpam-3967	162	20	integer	integer	NOUN
ejpam-3967	162	21	with	with	ADP
ejpam-3967	162	22	k	k	PROPN
ejpam-3967	162	23	≤	≤	PROPN
ejpam-3967	162	24	|v	|v	PROPN
ejpam-3967	162	25	(	(	PUNCT
ejpam-3967	162	26	h)|	h)|	PROPN
ejpam-3967	162	27	.	.	PUNCT
ejpam-3967	163	1	then	then	ADV
ejpam-3967	163	2	c	c	PROPN
ejpam-3967	163	3	⊆	⊆	NUM
ejpam-3967	163	4	v	v	NOUN
ejpam-3967	163	5	(	(	PUNCT
ejpam-3967	163	6	g	g	PROPN
ejpam-3967	163	7	◦	◦	NOUN
ejpam-3967	163	8	h	h	NOUN
ejpam-3967	163	9	)	)	PUNCT
ejpam-3967	163	10	is	be	AUX
ejpam-3967	163	11	a	a	DET
ejpam-3967	163	12	kftd	kftd	NOUN
ejpam-3967	163	13	-	-	PUNCT
ejpam-3967	163	14	set	set	NOUN
ejpam-3967	163	15	in	in	ADP
ejpam-3967	163	16	g	g	PROPN
ejpam-3967	163	17	◦	◦	NOUN
ejpam-3967	163	18	h	h	NOUN
ejpam-3967	163	19	if	if	SCONJ
ejpam-3967	164	1	and	and	CCONJ
ejpam-3967	164	2	only	only	ADV
ejpam-3967	164	3	if	if	SCONJ
ejpam-3967	164	4	one	one	NUM
ejpam-3967	164	5	of	of	ADP
ejpam-3967	164	6	the	the	DET
ejpam-3967	164	7	following	following	NOUN
ejpam-3967	164	8	holds	hold	VERB
ejpam-3967	164	9	:	:	PUNCT
ejpam-3967	164	10	(	(	PUNCT
ejpam-3967	164	11	a	a	X
ejpam-3967	164	12	)	)	PUNCT
ejpam-3967	164	13	c	c	NOUN
ejpam-3967	164	14	=	=	SYM
ejpam-3967	164	15	v	v	PROPN
ejpam-3967	164	16	(	(	PUNCT
ejpam-3967	164	17	g	g	NOUN
ejpam-3967	164	18	)	)	PUNCT
ejpam-3967	164	19	∪	∪	ADP
ejpam-3967	164	20	b	b	NOUN
ejpam-3967	164	21	,	,	PUNCT
ejpam-3967	164	22	where	where	SCONJ
ejpam-3967	164	23	b	b	NOUN
ejpam-3967	164	24	=	=	NOUN
ejpam-3967	164	25	∅	∅	NOUN
ejpam-3967	165	1	when	when	SCONJ
ejpam-3967	165	2	k	k	PROPN
ejpam-3967	165	3	=	=	SYM
ejpam-3967	165	4	1	1	NUM
ejpam-3967	165	5	and	and	CCONJ
ejpam-3967	165	6	b	b	NOUN
ejpam-3967	165	7	=	=	PUNCT
ejpam-3967	165	8	⋃	⋃	NOUN
ejpam-3967	165	9	v∈v	v∈v	NOUN
ejpam-3967	165	10	(	(	PUNCT
ejpam-3967	165	11	g	g	NOUN
ejpam-3967	165	12	)	)	PUNCT
ejpam-3967	165	13	sv	sv	NOUN
ejpam-3967	165	14	,	,	PUNCT
ejpam-3967	165	15	where	where	SCONJ
ejpam-3967	165	16	each	each	PRON
ejpam-3967	165	17	sv	sv	PROPN
ejpam-3967	165	18	is	be	AUX
ejpam-3967	165	19	a	a	DET
ejpam-3967	165	20	(	(	PUNCT
ejpam-3967	165	21	k	k	PROPN
ejpam-3967	165	22	−	−	PROPN
ejpam-3967	165	23	1)fd	1)fd	PROPN
ejpam-3967	165	24	-	-	PUNCT
ejpam-3967	165	25	set	set	NOUN
ejpam-3967	165	26	in	in	ADP
ejpam-3967	165	27	hv	hv	PROPN
ejpam-3967	165	28	when	when	SCONJ
ejpam-3967	165	29	k	k	PROPN
ejpam-3967	165	30	≥	≥	PROPN
ejpam-3967	165	31	2	2	NUM
ejpam-3967	165	32	.	.	PUNCT
ejpam-3967	165	33	(	(	PUNCT
ejpam-3967	165	34	b	b	X
ejpam-3967	165	35	)	)	PUNCT
ejpam-3967	165	36	c	c	NOUN
ejpam-3967	166	1	=	=	PUNCT
ejpam-3967	166	2	⋃	⋃	NOUN
ejpam-3967	166	3	v∈v	v∈v	NOUN
ejpam-3967	166	4	(	(	PUNCT
ejpam-3967	166	5	g	g	NOUN
ejpam-3967	166	6	)	)	PUNCT
ejpam-3967	166	7	sv	sv	NOUN
ejpam-3967	166	8	,	,	PUNCT
ejpam-3967	166	9	where	where	SCONJ
ejpam-3967	166	10	each	each	DET
ejpam-3967	166	11	sv	sv	PROPN
ejpam-3967	166	12	is	be	AUX
ejpam-3967	166	13	a	a	DET
ejpam-3967	166	14	kftd	kftd	NOUN
ejpam-3967	166	15	-	-	PUNCT
ejpam-3967	166	16	set	set	NOUN
ejpam-3967	166	17	in	in	ADP
ejpam-3967	166	18	hv	hv	PROPN
ejpam-3967	166	19	and	and	CCONJ
ejpam-3967	166	20	|sv|	|sv|	PROPN
ejpam-3967	166	21	=	=	SYM
ejpam-3967	166	22	k.	k.	PROPN
ejpam-3967	166	23	proof	proof	NOUN
ejpam-3967	166	24	.	.	PUNCT
ejpam-3967	167	1	suppose	suppose	VERB
ejpam-3967	167	2	that	that	SCONJ
ejpam-3967	167	3	statement	statement	NOUN
ejpam-3967	167	4	(	(	PUNCT
ejpam-3967	167	5	a	a	NOUN
ejpam-3967	167	6	)	)	PUNCT
ejpam-3967	167	7	holds	hold	NOUN
ejpam-3967	167	8	.	.	PUNCT
ejpam-3967	168	1	then	then	ADV
ejpam-3967	168	2	by	by	ADP
ejpam-3967	168	3	theorem	theorem	NOUN
ejpam-3967	168	4	6	6	NUM
ejpam-3967	168	5	,	,	PUNCT
ejpam-3967	168	6	c	c	PROPN
ejpam-3967	168	7	is	be	AUX
ejpam-3967	168	8	a	a	DET
ejpam-3967	168	9	kfd	kfd	NOUN
ejpam-3967	168	10	-	-	PUNCT
ejpam-3967	168	11	set	set	NOUN
ejpam-3967	168	12	in	in	ADP
ejpam-3967	168	13	g	g	NOUN
ejpam-3967	168	14	◦	◦	NOUN
ejpam-3967	168	15	h	h	NOUN
ejpam-3967	169	1	when	when	SCONJ
ejpam-3967	169	2	k	k	PROPN
ejpam-3967	169	3	=	=	NOUN
ejpam-3967	169	4	1	1	X
ejpam-3967	169	5	.	.	PUNCT
ejpam-3967	170	1	if	if	SCONJ
ejpam-3967	170	2	b	b	NOUN
ejpam-3967	170	3	=	=	SYM
ejpam-3967	170	4	∅	∅	NOUN
ejpam-3967	170	5	,	,	PUNCT
ejpam-3967	170	6	then	then	ADV
ejpam-3967	170	7	c	c	PROPN
ejpam-3967	170	8	=	=	SYM
ejpam-3967	170	9	v	v	PROPN
ejpam-3967	170	10	(	(	PUNCT
ejpam-3967	170	11	g	g	NOUN
ejpam-3967	170	12	)	)	PUNCT
ejpam-3967	170	13	is	be	AUX
ejpam-3967	170	14	clearly	clearly	ADV
ejpam-3967	170	15	a	a	DET
ejpam-3967	170	16	kftd	kftd	NOUN
ejpam-3967	170	17	-	-	PUNCT
ejpam-3967	170	18	set	set	NOUN
ejpam-3967	170	19	in	in	ADP
ejpam-3967	170	20	g	g	NOUN
ejpam-3967	170	21	◦	◦	NOUN
ejpam-3967	170	22	h	h	NOUN
ejpam-3967	170	23	when	when	SCONJ
ejpam-3967	170	24	k	k	PROPN
ejpam-3967	170	25	=	=	SYM
ejpam-3967	170	26	1	1	X
ejpam-3967	170	27	.	.	PUNCT
ejpam-3967	170	28	suppose	suppose	VERB
ejpam-3967	170	29	b	b	PROPN
ejpam-3967	170	30	=	=	PUNCT
ejpam-3967	170	31	⋃	⋃	NOUN
ejpam-3967	170	32	v∈v	v∈v	NOUN
ejpam-3967	170	33	(	(	PUNCT
ejpam-3967	170	34	g	g	NOUN
ejpam-3967	170	35	)	)	PUNCT
ejpam-3967	170	36	sv	sv	NOUN
ejpam-3967	170	37	,	,	PUNCT
ejpam-3967	170	38	where	where	SCONJ
ejpam-3967	170	39	each	each	PRON
ejpam-3967	170	40	sv	sv	PROPN
ejpam-3967	170	41	is	be	AUX
ejpam-3967	170	42	a	a	DET
ejpam-3967	170	43	(	(	PUNCT
ejpam-3967	170	44	k−	k−	PROPN
ejpam-3967	170	45	1)fd	1)fd	PROPN
ejpam-3967	170	46	-	-	PUNCT
ejpam-3967	170	47	set	set	NOUN
ejpam-3967	170	48	in	in	ADP
ejpam-3967	170	49	hv	hv	PROPN
ejpam-3967	170	50	.	.	PUNCT
ejpam-3967	171	1	each	each	DET
ejpam-3967	171	2	vertex	vertex	NOUN
ejpam-3967	171	3	v	v	NOUN
ejpam-3967	171	4	in	in	ADP
ejpam-3967	171	5	v	v	NOUN
ejpam-3967	171	6	(	(	PUNCT
ejpam-3967	171	7	g	g	NOUN
ejpam-3967	171	8	)	)	PUNCT
ejpam-3967	171	9	is	be	AUX
ejpam-3967	171	10	adjacent	adjacent	ADJ
ejpam-3967	171	11	to	to	ADP
ejpam-3967	171	12	some	some	DET
ejpam-3967	171	13	vertex	vertex	NOUN
ejpam-3967	171	14	u	u	NOUN
ejpam-3967	171	15	in	in	ADP
ejpam-3967	171	16	v	v	NOUN
ejpam-3967	171	17	(	(	PUNCT
ejpam-3967	171	18	g	g	NOUN
ejpam-3967	171	19	)	)	PUNCT
ejpam-3967	171	20	,	,	PUNCT
ejpam-3967	171	21	and	and	CCONJ
ejpam-3967	171	22	each	each	DET
ejpam-3967	171	23	x	x	SYM
ejpam-3967	171	24	∈	∈	PROPN
ejpam-3967	171	25	sv	sv	NOUN
ejpam-3967	171	26	is	be	AUX
ejpam-3967	171	27	adjacent	adjacent	ADJ
ejpam-3967	171	28	to	to	ADP
ejpam-3967	171	29	v.	v.	ADP
ejpam-3967	171	30	thus	thus	ADV
ejpam-3967	171	31	,	,	PUNCT
ejpam-3967	171	32	c	c	PROPN
ejpam-3967	171	33	=	=	SYM
ejpam-3967	171	34	v	v	PROPN
ejpam-3967	171	35	(	(	PUNCT
ejpam-3967	171	36	g	g	NOUN
ejpam-3967	171	37	)	)	PUNCT
ejpam-3967	171	38	∪	∪	ADP
ejpam-3967	171	39	b	b	PROPN
ejpam-3967	171	40	is	be	AUX
ejpam-3967	171	41	a	a	DET
ejpam-3967	171	42	kftd	kftd	NOUN
ejpam-3967	171	43	-	-	PUNCT
ejpam-3967	171	44	set	set	NOUN
ejpam-3967	171	45	in	in	ADP
ejpam-3967	171	46	hv	hv	PROPN
ejpam-3967	171	47	.	.	PUNCT
ejpam-3967	172	1	suppose	suppose	VERB
ejpam-3967	172	2	statement	statement	NOUN
ejpam-3967	172	3	(	(	PUNCT
ejpam-3967	172	4	b	b	NOUN
ejpam-3967	172	5	)	)	PUNCT
ejpam-3967	172	6	holds	hold	VERB
ejpam-3967	172	7	.	.	PUNCT
ejpam-3967	173	1	since	since	SCONJ
ejpam-3967	173	2	each	each	PRON
ejpam-3967	173	3	sv	sv	PROPN
ejpam-3967	173	4	is	be	AUX
ejpam-3967	173	5	a	a	DET
ejpam-3967	173	6	kfd	kfd	NOUN
ejpam-3967	173	7	-	-	PUNCT
ejpam-3967	173	8	set	set	NOUN
ejpam-3967	173	9	in	in	ADP
ejpam-3967	173	10	hv	hv	PROPN
ejpam-3967	173	11	and	and	CCONJ
ejpam-3967	173	12	|sv|	|sv|	PROPN
ejpam-3967	173	13	=	=	SYM
ejpam-3967	173	14	k	k	PROPN
ejpam-3967	173	15	,	,	PUNCT
ejpam-3967	173	16	c	c	X
ejpam-3967	173	17	=	=	PUNCT
ejpam-3967	173	18	⋃	⋃	NOUN
ejpam-3967	173	19	v∈v	v∈v	NOUN
ejpam-3967	173	20	(	(	PUNCT
ejpam-3967	173	21	g	g	NOUN
ejpam-3967	173	22	)	)	PUNCT
ejpam-3967	173	23	sv	sv	PROPN
ejpam-3967	173	24	is	be	AUX
ejpam-3967	173	25	a	a	DET
ejpam-3967	173	26	kfd	kfd	NOUN
ejpam-3967	173	27	-	-	PUNCT
ejpam-3967	173	28	set	set	NOUN
ejpam-3967	173	29	in	in	ADP
ejpam-3967	173	30	g	g	PROPN
ejpam-3967	173	31	◦	◦	NOUN
ejpam-3967	173	32	h	h	NOUN
ejpam-3967	173	33	by	by	ADP
ejpam-3967	173	34	theorem	theorem	NOUN
ejpam-3967	173	35	6	6	NUM
ejpam-3967	173	36	.	.	PUNCT
ejpam-3967	174	1	moreover	moreover	ADV
ejpam-3967	174	2	,	,	PUNCT
ejpam-3967	174	3	since	since	SCONJ
ejpam-3967	174	4	each	each	PRON
ejpam-3967	174	5	sv	sv	NOUN
ejpam-3967	174	6	is	be	AUX
ejpam-3967	174	7	a	a	DET
ejpam-3967	174	8	kftd	kftd	NOUN
ejpam-3967	174	9	-	-	PUNCT
ejpam-3967	174	10	set	set	NOUN
ejpam-3967	174	11	in	in	ADP
ejpam-3967	174	12	hv	hv	PROPN
ejpam-3967	174	13	,	,	PUNCT
ejpam-3967	174	14	it	it	PRON
ejpam-3967	174	15	follows	follow	VERB
ejpam-3967	174	16	that	that	SCONJ
ejpam-3967	174	17	c	c	PROPN
ejpam-3967	174	18	is	be	AUX
ejpam-3967	174	19	a	a	DET
ejpam-3967	174	20	kftd	kftd	NOUN
ejpam-3967	174	21	-	-	PUNCT
ejpam-3967	174	22	set	set	NOUN
ejpam-3967	174	23	in	in	ADP
ejpam-3967	174	24	g	g	PROPN
ejpam-3967	174	25	◦	◦	NOUN
ejpam-3967	174	26	h.	h.	NOUN
ejpam-3967	174	27	conversely	conversely	ADV
ejpam-3967	174	28	,	,	PUNCT
ejpam-3967	174	29	suppose	suppose	VERB
ejpam-3967	174	30	c	c	SYM
ejpam-3967	174	31	⊆	⊆	NUM
ejpam-3967	174	32	v	v	NOUN
ejpam-3967	174	33	(	(	PUNCT
ejpam-3967	174	34	g	g	PROPN
ejpam-3967	174	35	◦	◦	NOUN
ejpam-3967	174	36	h	h	NOUN
ejpam-3967	174	37	)	)	PUNCT
ejpam-3967	174	38	is	be	AUX
ejpam-3967	174	39	a	a	DET
ejpam-3967	174	40	kftd	kftd	NOUN
ejpam-3967	174	41	-	-	PUNCT
ejpam-3967	174	42	set	set	NOUN
ejpam-3967	174	43	in	in	ADP
ejpam-3967	174	44	g	g	PROPN
ejpam-3967	174	45	◦	◦	NOUN
ejpam-3967	174	46	h.	h.	NOUN
ejpam-3967	175	1	then	then	ADV
ejpam-3967	175	2	c	c	PROPN
ejpam-3967	175	3	is	be	AUX
ejpam-3967	175	4	a	a	DET
ejpam-3967	175	5	kfd	kfd	NOUN
ejpam-3967	175	6	-	-	PUNCT
ejpam-3967	175	7	set	set	NOUN
ejpam-3967	175	8	in	in	ADP
ejpam-3967	175	9	g	g	PROPN
ejpam-3967	175	10	◦	◦	NOUN
ejpam-3967	175	11	h	h	NOUN
ejpam-3967	175	12	and	and	CCONJ
ejpam-3967	175	13	by	by	ADP
ejpam-3967	175	14	theorem	theorem	NOUN
ejpam-3967	175	15	6	6	NUM
ejpam-3967	175	16	,	,	PUNCT
ejpam-3967	175	17	either	either	CCONJ
ejpam-3967	175	18	statement	statement	NOUN
ejpam-3967	175	19	(	(	PUNCT
ejpam-3967	175	20	a	a	NOUN
ejpam-3967	175	21	)	)	PUNCT
ejpam-3967	175	22	holds	hold	NOUN
ejpam-3967	175	23	,	,	PUNCT
ejpam-3967	175	24	or	or	CCONJ
ejpam-3967	175	25	c	c	NOUN
ejpam-3967	175	26	=	=	SYM
ejpam-3967	175	27	⋃	⋃	NOUN
ejpam-3967	175	28	v∈v	v∈v	NOUN
ejpam-3967	175	29	(	(	PUNCT
ejpam-3967	175	30	g	g	NOUN
ejpam-3967	175	31	)	)	PUNCT
ejpam-3967	175	32	sv	sv	NOUN
ejpam-3967	175	33	,	,	PUNCT
ejpam-3967	175	34	where	where	SCONJ
ejpam-3967	175	35	each	each	DET
ejpam-3967	175	36	sv	sv	PROPN
ejpam-3967	175	37	is	be	AUX
ejpam-3967	175	38	w.	w.	PROPN
ejpam-3967	175	39	bent	bent	PROPN
ejpam-3967	175	40	-	-	PUNCT
ejpam-3967	175	41	usman	usman	PROPN
ejpam-3967	175	42	,	,	PUNCT
ejpam-3967	175	43	r.	r.	PROPN
ejpam-3967	175	44	isla	isla	PROPN
ejpam-3967	175	45	/	/	SYM
ejpam-3967	175	46	eur	eur	PROPN
ejpam-3967	175	47	.	.	PUNCT
ejpam-3967	176	1	j.	j.	PROPN
ejpam-3967	176	2	pure	pure	PROPN
ejpam-3967	176	3	appl	appl	PROPN
ejpam-3967	176	4	.	.	PROPN
ejpam-3967	176	5	math	math	PROPN
ejpam-3967	176	6	,	,	PUNCT
ejpam-3967	176	7	14	14	NUM
ejpam-3967	176	8	(	(	PUNCT
ejpam-3967	176	9	2	2	NUM
ejpam-3967	176	10	)	)	PUNCT
ejpam-3967	176	11	(	(	PUNCT
ejpam-3967	176	12	2021	2021	NUM
ejpam-3967	176	13	)	)	PUNCT
ejpam-3967	176	14	,	,	PUNCT
ejpam-3967	176	15	578	578	NUM
ejpam-3967	176	16	-	-	SYM
ejpam-3967	176	17	589	589	NUM
ejpam-3967	176	18	585	585	NUM
ejpam-3967	176	19	a	a	DET
ejpam-3967	176	20	kfd	kfd	NOUN
ejpam-3967	176	21	-	-	PUNCT
ejpam-3967	176	22	set	set	NOUN
ejpam-3967	176	23	in	in	ADP
ejpam-3967	176	24	hv	hv	PROPN
ejpam-3967	176	25	and	and	CCONJ
ejpam-3967	176	26	|sv|	|sv|	PROPN
ejpam-3967	176	27	=	=	PUNCT
ejpam-3967	176	28	k.	k.	PROPN
ejpam-3967	176	29	suppose	suppose	VERB
ejpam-3967	176	30	that	that	SCONJ
ejpam-3967	176	31	there	there	PRON
ejpam-3967	176	32	is	be	VERB
ejpam-3967	176	33	a	a	DET
ejpam-3967	176	34	vertex	vertex	NOUN
ejpam-3967	176	35	x	x	INTJ
ejpam-3967	176	36	in	in	ADP
ejpam-3967	176	37	sv	sv	PROPN
ejpam-3967	176	38	that	that	PRON
ejpam-3967	176	39	is	be	AUX
ejpam-3967	176	40	not	not	PART
ejpam-3967	176	41	adjacent	adjacent	ADJ
ejpam-3967	176	42	to	to	ADP
ejpam-3967	176	43	another	another	DET
ejpam-3967	176	44	vertex	vertex	NOUN
ejpam-3967	176	45	in	in	ADP
ejpam-3967	176	46	sv	sv	PROPN
ejpam-3967	176	47	.	.	PUNCT
ejpam-3967	177	1	then	then	ADV
ejpam-3967	177	2	c	c	PROPN
ejpam-3967	177	3	is	be	AUX
ejpam-3967	177	4	not	not	PART
ejpam-3967	177	5	a	a	DET
ejpam-3967	177	6	kftd	kftd	NOUN
ejpam-3967	177	7	-	-	PUNCT
ejpam-3967	177	8	set	set	NOUN
ejpam-3967	177	9	in	in	ADP
ejpam-3967	177	10	v	v	NOUN
ejpam-3967	177	11	(	(	PUNCT
ejpam-3967	177	12	g	g	PROPN
ejpam-3967	177	13	◦	◦	NOUN
ejpam-3967	177	14	h	h	NOUN
ejpam-3967	177	15	)	)	PUNCT
ejpam-3967	177	16	,	,	PUNCT
ejpam-3967	177	17	contrary	contrary	ADV
ejpam-3967	177	18	to	to	ADP
ejpam-3967	177	19	assumption	assumption	NOUN
ejpam-3967	177	20	.	.	PUNCT
ejpam-3967	178	1	thus	thus	ADV
ejpam-3967	178	2	,	,	PUNCT
ejpam-3967	178	3	each	each	PRON
ejpam-3967	178	4	sv	sv	VERB
ejpam-3967	178	5	must	must	AUX
ejpam-3967	178	6	be	be	AUX
ejpam-3967	178	7	a	a	DET
ejpam-3967	178	8	kftd	kftd	NOUN
ejpam-3967	178	9	-	-	PUNCT
ejpam-3967	178	10	set	set	NOUN
ejpam-3967	178	11	in	in	ADP
ejpam-3967	178	12	hv	hv	PROPN
ejpam-3967	178	13	and	and	CCONJ
ejpam-3967	178	14	statement	statement	NOUN
ejpam-3967	178	15	(	(	PUNCT
ejpam-3967	178	16	b	b	NOUN
ejpam-3967	178	17	)	)	PUNCT
ejpam-3967	178	18	holds	hold	NOUN
ejpam-3967	178	19	.	.	PUNCT
ejpam-3967	179	1	�	�	PROPN
ejpam-3967	179	2	the	the	DET
ejpam-3967	179	3	next	next	ADJ
ejpam-3967	179	4	result	result	NOUN
ejpam-3967	179	5	is	be	AUX
ejpam-3967	179	6	an	an	DET
ejpam-3967	179	7	immediate	immediate	ADJ
ejpam-3967	179	8	consequence	consequence	NOUN
ejpam-3967	179	9	of	of	ADP
ejpam-3967	179	10	theorem	theorem	ADJ
ejpam-3967	179	11	9	9	NUM
ejpam-3967	179	12	.	.	PUNCT
ejpam-3967	179	13	corollary	corollary	ADJ
ejpam-3967	179	14	3	3	X
ejpam-3967	179	15	.	.	PUNCT
ejpam-3967	180	1	let	let	VERB
ejpam-3967	180	2	g	g	PRON
ejpam-3967	180	3	be	be	AUX
ejpam-3967	180	4	a	a	DET
ejpam-3967	180	5	nontrivial	nontrivial	ADJ
ejpam-3967	180	6	connected	connect	VERB
ejpam-3967	180	7	graph	graph	NOUN
ejpam-3967	180	8	of	of	ADP
ejpam-3967	180	9	order	order	NOUN
ejpam-3967	180	10	m	m	VERB
ejpam-3967	180	11	and	and	CCONJ
ejpam-3967	180	12	let	let	VERB
ejpam-3967	180	13	h	h	NOUN
ejpam-3967	180	14	be	be	AUX
ejpam-3967	180	15	a	a	DET
ejpam-3967	180	16	nontrivial	nontrivial	ADJ
ejpam-3967	180	17	graph	graph	NOUN
ejpam-3967	180	18	of	of	ADP
ejpam-3967	180	19	order	order	NOUN
ejpam-3967	180	20	n	n	CCONJ
ejpam-3967	180	21	,	,	PUNCT
ejpam-3967	180	22	and	and	CCONJ
ejpam-3967	180	23	let	let	VERB
ejpam-3967	180	24	k	k	PRON
ejpam-3967	180	25	be	be	AUX
ejpam-3967	180	26	a	a	DET
ejpam-3967	180	27	positive	positive	ADJ
ejpam-3967	180	28	integer	integer	NOUN
ejpam-3967	180	29	with	with	ADP
ejpam-3967	180	30	1	1	NUM
ejpam-3967	180	31	≤	≤	NUM
ejpam-3967	180	32	k	k	PROPN
ejpam-3967	180	33	≤	≤	PROPN
ejpam-3967	180	34	n.	n.	NOUN
ejpam-3967	180	35	then	then	ADV
ejpam-3967	180	36	γkftd(g	γkftd(g	PROPN
ejpam-3967	180	37	◦	◦	NOUN
ejpam-3967	180	38	h	h	NOUN
ejpam-3967	180	39	)	)	PUNCT
ejpam-3967	181	1	=	=	PUNCT
ejpam-3967	182	1			NOUN
ejpam-3967	182	2	m	m	ADV
ejpam-3967	182	3	,	,	PUNCT
ejpam-3967	182	4	if	if	SCONJ
ejpam-3967	182	5	k	k	PROPN
ejpam-3967	182	6	=	=	SYM
ejpam-3967	182	7	1	1	NUM
ejpam-3967	182	8	mk	mk	NOUN
ejpam-3967	182	9	,	,	PUNCT
ejpam-3967	182	10	if	if	SCONJ
ejpam-3967	182	11	k	k	PROPN
ejpam-3967	182	12	≥	≥	NUM
ejpam-3967	182	13	2	2	NUM
ejpam-3967	182	14	and	and	CCONJ
ejpam-3967	182	15	h	h	NOUN
ejpam-3967	182	16	has	have	VERB
ejpam-3967	182	17	a	a	DET
ejpam-3967	182	18	kftd	kftd	NOUN
ejpam-3967	182	19	-	-	PUNCT
ejpam-3967	182	20	set	set	PROPN
ejpam-3967	182	21	s	s	NOUN
ejpam-3967	182	22	with	with	ADP
ejpam-3967	182	23	|s|	|s|	PROPN
ejpam-3967	182	24	=	=	SYM
ejpam-3967	182	25	k	k	NOUN
ejpam-3967	182	26	m(1	m(1	PROPN
ejpam-3967	182	27	+	+	PROPN
ejpam-3967	182	28	γ(k−1)fd(h	γ(k−1)fd(h	NOUN
ejpam-3967	182	29	)	)	PUNCT
ejpam-3967	182	30	)	)	PUNCT
ejpam-3967	182	31	,	,	PUNCT
ejpam-3967	182	32	if	if	SCONJ
ejpam-3967	182	33	k	k	PROPN
ejpam-3967	182	34	≥	≥	NUM
ejpam-3967	182	35	2	2	NUM
ejpam-3967	182	36	and	and	CCONJ
ejpam-3967	182	37	h	h	NOUN
ejpam-3967	182	38	has	have	VERB
ejpam-3967	182	39	no	no	DET
ejpam-3967	182	40	kftd	kftd	NOUN
ejpam-3967	182	41	-	-	PUNCT
ejpam-3967	182	42	set	set	PROPN
ejpam-3967	182	43	s	s	NOUN
ejpam-3967	182	44	with	with	ADP
ejpam-3967	182	45	|s|	|s|	PROPN
ejpam-3967	182	46	=	=	SYM
ejpam-3967	182	47	k	k	PROPN
ejpam-3967	182	48	.	.	PUNCT
ejpam-3967	183	1	theorem	theorem	ADJ
ejpam-3967	183	2	10	10	NUM
ejpam-3967	183	3	.	.	PUNCT
ejpam-3967	184	1	let	let	VERB
ejpam-3967	184	2	g	g	NOUN
ejpam-3967	184	3	and	and	CCONJ
ejpam-3967	184	4	h	h	NOUN
ejpam-3967	184	5	be	be	AUX
ejpam-3967	184	6	nontrivial	nontrivial	ADJ
ejpam-3967	184	7	connected	connect	VERB
ejpam-3967	184	8	graphs	graph	NOUN
ejpam-3967	184	9	and	and	CCONJ
ejpam-3967	184	10	let	let	VERB
ejpam-3967	184	11	k	k	PROPN
ejpam-3967	184	12	≥	≥	NUM
ejpam-3967	184	13	2	2	NUM
ejpam-3967	184	14	.	.	PUNCT
ejpam-3967	185	1	then	then	ADV
ejpam-3967	185	2	c	c	NOUN
ejpam-3967	185	3	=	=	PUNCT
ejpam-3967	185	4	⋃	⋃	PROPN
ejpam-3967	185	5	x∈s	x∈s	NOUN
ejpam-3967	185	6	(	(	PUNCT
ejpam-3967	185	7	{	{	PUNCT
ejpam-3967	185	8	x	x	NOUN
ejpam-3967	185	9	}	}	PUNCT
ejpam-3967	185	10	×	×	PROPN
ejpam-3967	185	11	tx	tx	PROPN
ejpam-3967	185	12	)	)	PUNCT
ejpam-3967	185	13	⊆	⊆	NUM
ejpam-3967	185	14	v	v	NOUN
ejpam-3967	185	15	(	(	PUNCT
ejpam-3967	185	16	g[h	g[h	PROPN
ejpam-3967	185	17	]	]	PUNCT
ejpam-3967	185	18	)	)	PUNCT
ejpam-3967	185	19	is	be	AUX
ejpam-3967	185	20	a	a	DET
ejpam-3967	185	21	kftd	kftd	NOUN
ejpam-3967	185	22	-	-	PUNCT
ejpam-3967	185	23	set	set	NOUN
ejpam-3967	185	24	in	in	ADP
ejpam-3967	185	25	g[h	g[h	PROPN
ejpam-3967	185	26	]	]	PUNCT
ejpam-3967	185	27	if	if	SCONJ
ejpam-3967	186	1	and	and	CCONJ
ejpam-3967	186	2	only	only	ADV
ejpam-3967	186	3	if	if	SCONJ
ejpam-3967	186	4	the	the	DET
ejpam-3967	186	5	following	follow	VERB
ejpam-3967	186	6	hold	hold	NOUN
ejpam-3967	186	7	:	:	PUNCT
ejpam-3967	186	8	(	(	PUNCT
ejpam-3967	186	9	i	i	NOUN
ejpam-3967	186	10	)	)	PUNCT
ejpam-3967	186	11	s	s	VERB
ejpam-3967	186	12	is	be	AUX
ejpam-3967	186	13	a	a	DET
ejpam-3967	186	14	dominating	dominating	NOUN
ejpam-3967	186	15	set	set	NOUN
ejpam-3967	186	16	in	in	ADP
ejpam-3967	186	17	g	g	PROPN
ejpam-3967	186	18	,	,	PUNCT
ejpam-3967	186	19	(	(	PUNCT
ejpam-3967	186	20	ii	ii	NOUN
ejpam-3967	186	21	)	)	PUNCT
ejpam-3967	186	22	for	for	ADP
ejpam-3967	186	23	each	each	DET
ejpam-3967	186	24	x	x	SYM
ejpam-3967	186	25	∈	∈	PROPN
ejpam-3967	186	26	s	s	PART
ejpam-3967	186	27	∩	∩	NOUN
ejpam-3967	186	28	ng(s	ng(s	CCONJ
ejpam-3967	186	29	)	)	PUNCT
ejpam-3967	186	30	such	such	ADJ
ejpam-3967	186	31	that	that	PRON
ejpam-3967	186	32	tx	tx	PROPN
ejpam-3967	186	33	6=	6=	PROPN
ejpam-3967	186	34	v	v	ADP
ejpam-3967	186	35	(	(	PUNCT
ejpam-3967	186	36	h	h	NOUN
ejpam-3967	186	37	)	)	PUNCT
ejpam-3967	186	38	,	,	PUNCT
ejpam-3967	186	39	tx	tx	PROPN
ejpam-3967	186	40	is	be	AUX
ejpam-3967	186	41	an	an	DET
ejpam-3967	186	42	rfd	rfd	NOUN
ejpam-3967	186	43	-	-	PUNCT
ejpam-3967	186	44	set	set	VERB
ejpam-3967	186	45	and∑	and∑	NOUN
ejpam-3967	186	46	z∈ng(x)∩s	z∈ng(x)∩s	ADJ
ejpam-3967	186	47	|tz|	|tz|	NOUN
ejpam-3967	187	1	=	=	PUNCT
ejpam-3967	187	2	k	k	NOUN
ejpam-3967	187	3	−	−	NOUN
ejpam-3967	187	4	r	r	NOUN
ejpam-3967	187	5	,	,	PUNCT
ejpam-3967	187	6	(	(	PUNCT
ejpam-3967	187	7	iii	iii	NOUN
ejpam-3967	187	8	)	)	PUNCT
ejpam-3967	187	9	for	for	ADP
ejpam-3967	187	10	each	each	DET
ejpam-3967	187	11	x	x	SYM
ejpam-3967	187	12	∈	∈	PROPN
ejpam-3967	187	13	s\ng(s	s\ng(s	NOUN
ejpam-3967	187	14	)	)	PUNCT
ejpam-3967	187	15	with	with	ADP
ejpam-3967	187	16	tx	tx	PROPN
ejpam-3967	187	17	6=	6=	PROPN
ejpam-3967	187	18	v	v	ADP
ejpam-3967	187	19	(	(	PUNCT
ejpam-3967	187	20	h	h	NOUN
ejpam-3967	187	21	)	)	PUNCT
ejpam-3967	187	22	,	,	PUNCT
ejpam-3967	187	23	|tx|	|tx|	X
ejpam-3967	187	24	=	=	SYM
ejpam-3967	187	25	k	k	PROPN
ejpam-3967	187	26	and	and	CCONJ
ejpam-3967	187	27	tx	tx	PROPN
ejpam-3967	187	28	is	be	AUX
ejpam-3967	187	29	a	a	DET
ejpam-3967	187	30	kftd	kftd	NOUN
ejpam-3967	187	31	-	-	PUNCT
ejpam-3967	187	32	set	set	NOUN
ejpam-3967	187	33	in	in	ADP
ejpam-3967	187	34	h	h	NOUN
ejpam-3967	187	35	,	,	PUNCT
ejpam-3967	187	36	and	and	CCONJ
ejpam-3967	187	37	(	(	PUNCT
ejpam-3967	187	38	iv	iv	X
ejpam-3967	187	39	)	)	PUNCT
ejpam-3967	187	40	for	for	ADP
ejpam-3967	187	41	each	each	DET
ejpam-3967	187	42	y	y	PROPN
ejpam-3967	187	43	∈	∈	PROPN
ejpam-3967	187	44	v	v	NOUN
ejpam-3967	187	45	(	(	PUNCT
ejpam-3967	187	46	g)\s	g)\s	NOUN
ejpam-3967	187	47	,	,	PUNCT
ejpam-3967	187	48	∑	∑	PUNCT
ejpam-3967	187	49	v∈ng(y)∩s	v∈ng(y)∩s	ADJ
ejpam-3967	187	50	|tv|	|tv|	PROPN
ejpam-3967	187	51	=	=	SYM
ejpam-3967	187	52	k.	k.	PROPN
ejpam-3967	187	53	proof	proof	NOUN
ejpam-3967	187	54	.	.	PUNCT
ejpam-3967	188	1	suppose	suppose	VERB
ejpam-3967	188	2	c	c	NOUN
ejpam-3967	188	3	=	=	SYM
ejpam-3967	188	4	⋃	⋃	PROPN
ejpam-3967	188	5	x∈s	x∈s	NOUN
ejpam-3967	188	6	(	(	PUNCT
ejpam-3967	188	7	{	{	PUNCT
ejpam-3967	188	8	x	x	NOUN
ejpam-3967	188	9	}	}	PUNCT
ejpam-3967	188	10	×	×	PROPN
ejpam-3967	188	11	tx	tx	PROPN
ejpam-3967	188	12	)	)	PUNCT
ejpam-3967	188	13	⊆	⊆	NUM
ejpam-3967	188	14	v	v	NOUN
ejpam-3967	188	15	(	(	PUNCT
ejpam-3967	188	16	g[h	g[h	PROPN
ejpam-3967	188	17	]	]	PUNCT
ejpam-3967	188	18	)	)	PUNCT
ejpam-3967	188	19	is	be	AUX
ejpam-3967	188	20	a	a	DET
ejpam-3967	188	21	kftd	kftd	NOUN
ejpam-3967	188	22	-	-	PUNCT
ejpam-3967	188	23	set	set	NOUN
ejpam-3967	188	24	in	in	ADP
ejpam-3967	188	25	g[h	g[h	NOUN
ejpam-3967	188	26	]	]	PUNCT
ejpam-3967	188	27	.	.	PUNCT
ejpam-3967	189	1	then	then	ADV
ejpam-3967	189	2	c	c	PROPN
ejpam-3967	189	3	is	be	AUX
ejpam-3967	189	4	a	a	DET
ejpam-3967	189	5	kfd	kfd	NOUN
ejpam-3967	189	6	-	-	PUNCT
ejpam-3967	189	7	set	set	NOUN
ejpam-3967	189	8	in	in	ADP
ejpam-3967	189	9	g[h	g[h	NOUN
ejpam-3967	189	10	]	]	PUNCT
ejpam-3967	189	11	and	and	CCONJ
ejpam-3967	189	12	by	by	ADP
ejpam-3967	189	13	theorem	theorem	ADJ
ejpam-3967	189	14	7	7	NUM
ejpam-3967	189	15	,	,	PUNCT
ejpam-3967	189	16	statements	statement	NOUN
ejpam-3967	189	17	(	(	PUNCT
ejpam-3967	189	18	i	i	NOUN
ejpam-3967	189	19	)	)	PUNCT
ejpam-3967	189	20	,	,	PUNCT
ejpam-3967	189	21	(	(	PUNCT
ejpam-3967	189	22	ii	ii	NOUN
ejpam-3967	189	23	)	)	PUNCT
ejpam-3967	189	24	,	,	PUNCT
ejpam-3967	189	25	and	and	CCONJ
ejpam-3967	189	26	(	(	PUNCT
ejpam-3967	189	27	iv	iv	X
ejpam-3967	189	28	)	)	PUNCT
ejpam-3967	189	29	hold	hold	NOUN
ejpam-3967	189	30	.	.	PUNCT
ejpam-3967	190	1	moreover	moreover	ADV
ejpam-3967	190	2	,	,	PUNCT
ejpam-3967	190	3	for	for	ADP
ejpam-3967	190	4	each	each	DET
ejpam-3967	190	5	x	x	SYM
ejpam-3967	190	6	∈	∈	PROPN
ejpam-3967	190	7	s\ng(s	s\ng(s	NOUN
ejpam-3967	190	8	)	)	PUNCT
ejpam-3967	190	9	,	,	PUNCT
ejpam-3967	190	10	tx	tx	PROPN
ejpam-3967	190	11	=	=	SYM
ejpam-3967	190	12	v	v	PROPN
ejpam-3967	190	13	(	(	PUNCT
ejpam-3967	190	14	h	h	NOUN
ejpam-3967	190	15	)	)	PUNCT
ejpam-3967	190	16	and	and	CCONJ
ejpam-3967	190	17	|v	|v	PROPN
ejpam-3967	190	18	(	(	PUNCT
ejpam-3967	190	19	h)|	h)|	NOUN
ejpam-3967	190	20	≤	≤	PROPN
ejpam-3967	190	21	k	k	NOUN
ejpam-3967	190	22	or	or	CCONJ
ejpam-3967	190	23	|tx|	|tx|	NUM
ejpam-3967	190	24	=	=	SYM
ejpam-3967	190	25	k	k	PROPN
ejpam-3967	190	26	and	and	CCONJ
ejpam-3967	190	27	tx	tx	PROPN
ejpam-3967	190	28	is	be	AUX
ejpam-3967	190	29	a	a	DET
ejpam-3967	190	30	kfd	kfd	NOUN
ejpam-3967	190	31	-	-	PUNCT
ejpam-3967	190	32	set	set	NOUN
ejpam-3967	190	33	in	in	ADP
ejpam-3967	190	34	h.	h.	PROPN
ejpam-3967	190	35	suppose	suppose	VERB
ejpam-3967	190	36	there	there	PRON
ejpam-3967	190	37	is	be	VERB
ejpam-3967	190	38	a	a	DET
ejpam-3967	190	39	vertex	vertex	NOUN
ejpam-3967	190	40	a	a	DET
ejpam-3967	190	41	∈	∈	PROPN
ejpam-3967	190	42	tx	tx	PROPN
ejpam-3967	190	43	which	which	PRON
ejpam-3967	190	44	is	be	AUX
ejpam-3967	190	45	not	not	PART
ejpam-3967	190	46	adjacent	adjacent	ADJ
ejpam-3967	190	47	to	to	ADP
ejpam-3967	190	48	any	any	DET
ejpam-3967	190	49	other	other	ADJ
ejpam-3967	190	50	vertex	vertex	NOUN
ejpam-3967	190	51	in	in	ADP
ejpam-3967	190	52	tx	tx	PROPN
ejpam-3967	190	53	.	.	PUNCT
ejpam-3967	191	1	then	then	ADV
ejpam-3967	191	2	(	(	PUNCT
ejpam-3967	191	3	x	x	X
ejpam-3967	191	4	,	,	PUNCT
ejpam-3967	191	5	a	a	PRON
ejpam-3967	191	6	)	)	PUNCT
ejpam-3967	191	7	is	be	AUX
ejpam-3967	191	8	not	not	PART
ejpam-3967	191	9	adjacent	adjacent	ADJ
ejpam-3967	191	10	to	to	ADP
ejpam-3967	191	11	any	any	DET
ejpam-3967	191	12	vertex	vertex	NOUN
ejpam-3967	191	13	in	in	ADP
ejpam-3967	191	14	c	c	PROPN
ejpam-3967	191	15	,	,	PUNCT
ejpam-3967	191	16	contrary	contrary	ADJ
ejpam-3967	191	17	to	to	ADP
ejpam-3967	191	18	assumption	assumption	NOUN
ejpam-3967	191	19	.	.	PUNCT
ejpam-3967	192	1	hence	hence	ADV
ejpam-3967	192	2	,	,	PUNCT
ejpam-3967	192	3	tx	tx	PROPN
ejpam-3967	192	4	is	be	AUX
ejpam-3967	192	5	a	a	DET
ejpam-3967	192	6	kftd	kftd	NOUN
ejpam-3967	192	7	-	-	PUNCT
ejpam-3967	192	8	set	set	NOUN
ejpam-3967	192	9	in	in	ADP
ejpam-3967	192	10	h	h	NOUN
ejpam-3967	192	11	and	and	CCONJ
ejpam-3967	192	12	statement	statement	NOUN
ejpam-3967	192	13	(	(	PUNCT
ejpam-3967	192	14	iii	iii	NOUN
ejpam-3967	192	15	)	)	PUNCT
ejpam-3967	192	16	holds	hold	VERB
ejpam-3967	192	17	.	.	PUNCT
ejpam-3967	193	1	conversely	conversely	ADV
ejpam-3967	193	2	,	,	PUNCT
ejpam-3967	193	3	suppose	suppose	VERB
ejpam-3967	193	4	statements	statement	NOUN
ejpam-3967	193	5	(	(	PUNCT
ejpam-3967	193	6	i	i	NOUN
ejpam-3967	193	7	)	)	PUNCT
ejpam-3967	193	8	to	to	PART
ejpam-3967	193	9	(	(	PUNCT
ejpam-3967	193	10	iv	iv	X
ejpam-3967	193	11	)	)	PUNCT
ejpam-3967	193	12	hold	hold	NOUN
ejpam-3967	193	13	.	.	PUNCT
ejpam-3967	194	1	then	then	ADV
ejpam-3967	194	2	tx	tx	PROPN
ejpam-3967	194	3	is	be	AUX
ejpam-3967	194	4	a	a	DET
ejpam-3967	194	5	kfd	kfd	NOUN
ejpam-3967	194	6	-	-	PUNCT
ejpam-3967	194	7	set	set	NOUN
ejpam-3967	194	8	in	in	ADP
ejpam-3967	194	9	h.	h.	PROPN
ejpam-3967	194	10	thus	thus	ADV
ejpam-3967	194	11	,	,	PUNCT
ejpam-3967	194	12	c	c	PROPN
ejpam-3967	194	13	is	be	AUX
ejpam-3967	194	14	a	a	DET
ejpam-3967	194	15	kfd	kfd	NOUN
ejpam-3967	194	16	-	-	PUNCT
ejpam-3967	194	17	set	set	NOUN
ejpam-3967	194	18	in	in	ADP
ejpam-3967	194	19	g[h	g[h	NOUN
ejpam-3967	194	20	]	]	PUNCT
ejpam-3967	194	21	by	by	ADP
ejpam-3967	194	22	theorem	theorem	NOUN
ejpam-3967	194	23	7	7	NUM
ejpam-3967	194	24	.	.	PUNCT
ejpam-3967	194	25	suppose	suppose	VERB
ejpam-3967	194	26	c	c	PROPN
ejpam-3967	194	27	6=	6=	ADP
ejpam-3967	194	28	v	v	PROPN
ejpam-3967	194	29	(	(	PUNCT
ejpam-3967	194	30	g[h	g[h	PROPN
ejpam-3967	194	31	]	]	PUNCT
ejpam-3967	194	32	)	)	PUNCT
ejpam-3967	194	33	.	.	PUNCT
ejpam-3967	195	1	let	let	VERB
ejpam-3967	195	2	(	(	PUNCT
ejpam-3967	195	3	x	x	NOUN
ejpam-3967	195	4	,	,	PUNCT
ejpam-3967	195	5	a	a	DET
ejpam-3967	195	6	)	)	PUNCT
ejpam-3967	195	7	∈	∈	PROPN
ejpam-3967	195	8	c.	c.	NOUN
ejpam-3967	195	9	consider	consider	VERB
ejpam-3967	195	10	the	the	DET
ejpam-3967	195	11	following	follow	VERB
ejpam-3967	195	12	cases	case	NOUN
ejpam-3967	195	13	.	.	PUNCT
ejpam-3967	196	1	case	case	NOUN
ejpam-3967	196	2	1	1	NUM
ejpam-3967	196	3	:	:	PUNCT
ejpam-3967	196	4	x	x	SYM
ejpam-3967	196	5	∈	∈	NOUN
ejpam-3967	196	6	s	s	NOUN
ejpam-3967	196	7	∩ng(s	∩ng(s	NOUN
ejpam-3967	196	8	)	)	PUNCT
ejpam-3967	196	9	if	if	SCONJ
ejpam-3967	196	10	tx	tx	PROPN
ejpam-3967	196	11	=	=	SYM
ejpam-3967	196	12	v	v	PROPN
ejpam-3967	196	13	(	(	PUNCT
ejpam-3967	196	14	h	h	NOUN
ejpam-3967	196	15	)	)	PUNCT
ejpam-3967	197	1	where	where	SCONJ
ejpam-3967	197	2	|v	|v	PROPN
ejpam-3967	197	3	(	(	PUNCT
ejpam-3967	197	4	h)|	h)|	NOUN
ejpam-3967	197	5	=	=	NOUN
ejpam-3967	197	6	r	r	NOUN
ejpam-3967	197	7	≤	≤	NUM
ejpam-3967	197	8	k	k	NOUN
ejpam-3967	197	9	,	,	PUNCT
ejpam-3967	197	10	then	then	ADV
ejpam-3967	197	11	there	there	PRON
ejpam-3967	197	12	exists	exist	VERB
ejpam-3967	197	13	a	a	DET
ejpam-3967	197	14	b	b	PROPN
ejpam-3967	197	15	∈	∈	NOUN
ejpam-3967	197	16	tx	tx	ADP
ejpam-3967	197	17	such	such	ADJ
ejpam-3967	197	18	that	that	SCONJ
ejpam-3967	197	19	ab	ab	PROPN
ejpam-3967	197	20	∈	∈	PROPN
ejpam-3967	197	21	e(h	e(h	PROPN
ejpam-3967	197	22	)	)	PUNCT
ejpam-3967	197	23	since	since	SCONJ
ejpam-3967	197	24	h	h	NOUN
ejpam-3967	197	25	is	be	AUX
ejpam-3967	197	26	a	a	DET
ejpam-3967	197	27	nontrivial	nontrivial	ADJ
ejpam-3967	197	28	connected	connect	VERB
ejpam-3967	197	29	graph	graph	NOUN
ejpam-3967	197	30	.	.	PUNCT
ejpam-3967	198	1	it	it	PRON
ejpam-3967	198	2	follows	follow	VERB
ejpam-3967	198	3	that	that	SCONJ
ejpam-3967	198	4	(	(	PUNCT
ejpam-3967	198	5	x	x	NOUN
ejpam-3967	198	6	,	,	PUNCT
ejpam-3967	198	7	b	b	NOUN
ejpam-3967	198	8	)	)	PUNCT
ejpam-3967	198	9	∈	∈	PROPN
ejpam-3967	198	10	c	c	NOUN
ejpam-3967	198	11	and	and	CCONJ
ejpam-3967	198	12	(	(	PUNCT
ejpam-3967	198	13	x	x	NOUN
ejpam-3967	198	14	,	,	PUNCT
ejpam-3967	198	15	a)(x	a)(x	PROPN
ejpam-3967	198	16	,	,	PUNCT
ejpam-3967	198	17	b	b	X
ejpam-3967	198	18	)	)	PUNCT
ejpam-3967	198	19	∈	∈	NOUN
ejpam-3967	198	20	e(g[h	e(g[h	NOUN
ejpam-3967	198	21	]	]	PUNCT
ejpam-3967	198	22	)	)	PUNCT
ejpam-3967	198	23	.	.	PUNCT
ejpam-3967	199	1	if	if	SCONJ
ejpam-3967	199	2	tx	tx	PROPN
ejpam-3967	199	3	is	be	AUX
ejpam-3967	199	4	an	an	DET
ejpam-3967	199	5	rfd	rfd	NOUN
ejpam-3967	199	6	-	-	PUNCT
ejpam-3967	199	7	set	set	VERB
ejpam-3967	199	8	and	and	CCONJ
ejpam-3967	199	9	∑	∑	ADP
ejpam-3967	199	10	z∈ng(x)∩s	z∈ng(x)∩s	NUM
ejpam-3967	199	11	|tz|	|tz|	NOUN
ejpam-3967	200	1	=	=	PUNCT
ejpam-3967	200	2	k	k	NOUN
ejpam-3967	201	1	−	−	NOUN
ejpam-3967	201	2	r	r	NOUN
ejpam-3967	201	3	,	,	PUNCT
ejpam-3967	201	4	then	then	ADV
ejpam-3967	201	5	there	there	PRON
ejpam-3967	201	6	is	be	VERB
ejpam-3967	201	7	a	a	DET
ejpam-3967	201	8	z	z	NOUN
ejpam-3967	201	9	∈	∈	PROPN
ejpam-3967	201	10	ng(x	ng(x	NUM
ejpam-3967	201	11	)	)	PUNCT
ejpam-3967	201	12	∩	∩	NOUN
ejpam-3967	201	13	s	s	PART
ejpam-3967	201	14	and	and	CCONJ
ejpam-3967	201	15	there	there	PRON
ejpam-3967	201	16	is	be	VERB
ejpam-3967	201	17	a	a	DET
ejpam-3967	201	18	d	d	PROPN
ejpam-3967	201	19	∈	∈	PROPN
ejpam-3967	201	20	tz	tz	NOUN
ejpam-3967	201	21	such	such	ADJ
ejpam-3967	201	22	that	that	SCONJ
ejpam-3967	201	23	(	(	PUNCT
ejpam-3967	201	24	z	z	NOUN
ejpam-3967	201	25	,	,	PUNCT
ejpam-3967	201	26	d	d	NOUN
ejpam-3967	201	27	)	)	PUNCT
ejpam-3967	201	28	∈	∈	PROPN
ejpam-3967	201	29	c.	c.	NOUN
ejpam-3967	201	30	clearly	clearly	ADV
ejpam-3967	201	31	,	,	PUNCT
ejpam-3967	201	32	(	(	PUNCT
ejpam-3967	201	33	x	x	X
ejpam-3967	201	34	,	,	PUNCT
ejpam-3967	201	35	a)(z	a)(z	NOUN
ejpam-3967	201	36	,	,	PUNCT
ejpam-3967	201	37	d	d	X
ejpam-3967	201	38	)	)	PUNCT
ejpam-3967	201	39	∈	∈	NOUN
ejpam-3967	201	40	e(g[h	e(g[h	NOUN
ejpam-3967	201	41	]	]	PUNCT
ejpam-3967	201	42	)	)	PUNCT
ejpam-3967	201	43	.	.	PUNCT
ejpam-3967	202	1	case	case	NOUN
ejpam-3967	202	2	2	2	NUM
ejpam-3967	202	3	:	:	PUNCT
ejpam-3967	202	4	x	x	SYM
ejpam-3967	202	5	∈	∈	PROPN
ejpam-3967	202	6	s\ng(s	s\ng(s	NOUN
ejpam-3967	202	7	)	)	PUNCT
ejpam-3967	202	8	if	if	SCONJ
ejpam-3967	202	9	tx	tx	PROPN
ejpam-3967	202	10	=	=	SYM
ejpam-3967	202	11	v	v	PROPN
ejpam-3967	202	12	(	(	PUNCT
ejpam-3967	202	13	h	h	NOUN
ejpam-3967	202	14	)	)	PUNCT
ejpam-3967	202	15	where	where	SCONJ
ejpam-3967	202	16	|v	|v	PROPN
ejpam-3967	202	17	(	(	PUNCT
ejpam-3967	202	18	h)|	h)|	PROPN
ejpam-3967	202	19	≤	≤	PROPN
ejpam-3967	202	20	k	k	PROPN
ejpam-3967	202	21	,	,	PUNCT
ejpam-3967	202	22	then	then	ADV
ejpam-3967	202	23	similar	similar	ADJ
ejpam-3967	202	24	to	to	ADP
ejpam-3967	202	25	case	case	NOUN
ejpam-3967	202	26	1	1	NUM
ejpam-3967	202	27	,	,	PUNCT
ejpam-3967	202	28	there	there	PRON
ejpam-3967	202	29	exists	exist	VERB
ejpam-3967	202	30	a	a	DET
ejpam-3967	202	31	b	b	PROPN
ejpam-3967	202	32	∈	∈	NOUN
ejpam-3967	202	33	tx	tx	ADP
ejpam-3967	202	34	such	such	ADJ
ejpam-3967	202	35	that	that	SCONJ
ejpam-3967	202	36	ab	ab	PROPN
ejpam-3967	202	37	∈	∈	PROPN
ejpam-3967	202	38	e(h	e(h	PROPN
ejpam-3967	202	39	)	)	PUNCT
ejpam-3967	202	40	,	,	PUNCT
ejpam-3967	202	41	(	(	PUNCT
ejpam-3967	202	42	x	x	NOUN
ejpam-3967	202	43	,	,	PUNCT
ejpam-3967	202	44	b	b	NOUN
ejpam-3967	202	45	)	)	PUNCT
ejpam-3967	202	46	∈	∈	PROPN
ejpam-3967	202	47	c	c	NOUN
ejpam-3967	202	48	,	,	PUNCT
ejpam-3967	202	49	and	and	CCONJ
ejpam-3967	202	50	(	(	PUNCT
ejpam-3967	202	51	x	x	NOUN
ejpam-3967	202	52	,	,	PUNCT
ejpam-3967	202	53	a)(x	a)(x	PROPN
ejpam-3967	202	54	,	,	PUNCT
ejpam-3967	202	55	b	b	X
ejpam-3967	202	56	)	)	PUNCT
ejpam-3967	202	57	∈	∈	NOUN
ejpam-3967	202	58	e(g[h	e(g[h	NOUN
ejpam-3967	202	59	]	]	PUNCT
ejpam-3967	202	60	)	)	PUNCT
ejpam-3967	202	61	.	.	PUNCT
ejpam-3967	203	1	if	if	SCONJ
ejpam-3967	203	2	|tx|	|tx|	NOUN
ejpam-3967	203	3	=	=	SYM
ejpam-3967	203	4	k	k	PROPN
ejpam-3967	203	5	and	and	CCONJ
ejpam-3967	203	6	tx	tx	PROPN
ejpam-3967	203	7	is	be	AUX
ejpam-3967	203	8	a	a	DET
ejpam-3967	203	9	kftd	kftd	NOUN
ejpam-3967	203	10	-	-	PUNCT
ejpam-3967	203	11	set	set	NOUN
ejpam-3967	203	12	in	in	ADP
ejpam-3967	203	13	h	h	PROPN
ejpam-3967	203	14	,	,	PUNCT
ejpam-3967	203	15	w.	w.	PROPN
ejpam-3967	203	16	bent	bent	PROPN
ejpam-3967	203	17	-	-	PUNCT
ejpam-3967	203	18	usman	usman	PROPN
ejpam-3967	203	19	,	,	PUNCT
ejpam-3967	203	20	r.	r.	PROPN
ejpam-3967	203	21	isla	isla	PROPN
ejpam-3967	203	22	/	/	SYM
ejpam-3967	203	23	eur	eur	PROPN
ejpam-3967	203	24	.	.	PUNCT
ejpam-3967	204	1	j.	j.	PROPN
ejpam-3967	204	2	pure	pure	PROPN
ejpam-3967	204	3	appl	appl	PROPN
ejpam-3967	204	4	.	.	PROPN
ejpam-3967	204	5	math	math	PROPN
ejpam-3967	204	6	,	,	PUNCT
ejpam-3967	204	7	14	14	NUM
ejpam-3967	204	8	(	(	PUNCT
ejpam-3967	204	9	2	2	NUM
ejpam-3967	204	10	)	)	PUNCT
ejpam-3967	204	11	(	(	PUNCT
ejpam-3967	204	12	2021	2021	NUM
ejpam-3967	204	13	)	)	PUNCT
ejpam-3967	204	14	,	,	PUNCT
ejpam-3967	204	15	578	578	NUM
ejpam-3967	204	16	-	-	SYM
ejpam-3967	204	17	589	589	NUM
ejpam-3967	204	18	586	586	NUM
ejpam-3967	204	19	then	then	ADV
ejpam-3967	204	20	there	there	PRON
ejpam-3967	204	21	exists	exist	VERB
ejpam-3967	204	22	a	a	DET
ejpam-3967	204	23	d	d	PROPN
ejpam-3967	204	24	∈	∈	PROPN
ejpam-3967	204	25	tx	tx	ADP
ejpam-3967	204	26	such	such	ADJ
ejpam-3967	204	27	that	that	SCONJ
ejpam-3967	204	28	ad	ad	NOUN
ejpam-3967	204	29	∈	∈	PROPN
ejpam-3967	204	30	e(h	e(h	PROPN
ejpam-3967	204	31	)	)	PUNCT
ejpam-3967	204	32	,	,	PUNCT
ejpam-3967	204	33	(	(	PUNCT
ejpam-3967	204	34	x	x	X
ejpam-3967	204	35	,	,	PUNCT
ejpam-3967	204	36	d	d	NOUN
ejpam-3967	204	37	)	)	PUNCT
ejpam-3967	204	38	∈	∈	PROPN
ejpam-3967	204	39	c	c	NOUN
ejpam-3967	204	40	,	,	PUNCT
ejpam-3967	204	41	and	and	CCONJ
ejpam-3967	204	42	(	(	PUNCT
ejpam-3967	204	43	x	x	NOUN
ejpam-3967	204	44	,	,	PUNCT
ejpam-3967	204	45	a)(x	a)(x	NOUN
ejpam-3967	204	46	,	,	PUNCT
ejpam-3967	204	47	d	d	X
ejpam-3967	204	48	)	)	PUNCT
ejpam-3967	204	49	∈	∈	NOUN
ejpam-3967	204	50	e(g[h	e(g[h	NOUN
ejpam-3967	204	51	]	]	PUNCT
ejpam-3967	204	52	)	)	PUNCT
ejpam-3967	204	53	.	.	PUNCT
ejpam-3967	205	1	therefore	therefore	ADV
ejpam-3967	205	2	,	,	PUNCT
ejpam-3967	205	3	in	in	ADP
ejpam-3967	205	4	both	both	DET
ejpam-3967	205	5	cases	case	NOUN
ejpam-3967	205	6	,	,	PUNCT
ejpam-3967	205	7	c	c	PROPN
ejpam-3967	205	8	is	be	AUX
ejpam-3967	205	9	a	a	DET
ejpam-3967	205	10	kftd	kftd	NOUN
ejpam-3967	205	11	-	-	PUNCT
ejpam-3967	205	12	set	set	NOUN
ejpam-3967	205	13	in	in	ADP
ejpam-3967	205	14	g[h	g[h	NOUN
ejpam-3967	205	15	]	]	PUNCT
ejpam-3967	205	16	.	.	PUNCT
ejpam-3967	206	1	�	�	PROPN
ejpam-3967	206	2	corollary	corollary	ADJ
ejpam-3967	206	3	4	4	NUM
ejpam-3967	206	4	.	.	PUNCT
ejpam-3967	207	1	let	let	VERB
ejpam-3967	207	2	g	g	NOUN
ejpam-3967	207	3	and	and	CCONJ
ejpam-3967	207	4	h	h	NOUN
ejpam-3967	207	5	be	be	AUX
ejpam-3967	207	6	nontrivial	nontrivial	ADJ
ejpam-3967	207	7	connected	connect	VERB
ejpam-3967	207	8	graphs	graph	NOUN
ejpam-3967	207	9	with	with	ADP
ejpam-3967	207	10	γ1fd(h	γ1fd(h	PROPN
ejpam-3967	207	11	)	)	PUNCT
ejpam-3967	207	12	=	=	SYM
ejpam-3967	208	1	1	1	X
ejpam-3967	208	2	.	.	PUNCT
ejpam-3967	209	1	if	if	SCONJ
ejpam-3967	209	2	g	g	PROPN
ejpam-3967	209	3	has	have	VERB
ejpam-3967	209	4	a	a	DET
ejpam-3967	209	5	γ2ftd	γ2ftd	ADV
ejpam-3967	209	6	-	-	PUNCT
ejpam-3967	209	7	set	set	NOUN
ejpam-3967	209	8	s	s	NOUN
ejpam-3967	209	9	with	with	ADP
ejpam-3967	209	10	|ng(x	|ng(x	ADJ
ejpam-3967	209	11	)	)	PUNCT
ejpam-3967	209	12	∩	∩	NOUN
ejpam-3967	209	13	s|	s|	NOUN
ejpam-3967	209	14	=	=	SYM
ejpam-3967	209	15	1	1	NUM
ejpam-3967	209	16	for	for	ADP
ejpam-3967	209	17	all	all	DET
ejpam-3967	209	18	x	x	SYM
ejpam-3967	209	19	∈	∈	PROPN
ejpam-3967	209	20	s	s	NOUN
ejpam-3967	209	21	,	,	PUNCT
ejpam-3967	209	22	then	then	ADV
ejpam-3967	209	23	γ2ftd(g[h	γ2ftd(g[h	NOUN
ejpam-3967	209	24	]	]	PUNCT
ejpam-3967	209	25	)	)	PUNCT
ejpam-3967	209	26	≤	≤	NUM
ejpam-3967	209	27	γ2ftd(g	γ2ftd(g	NUM
ejpam-3967	209	28	)	)	PUNCT
ejpam-3967	209	29	.	.	PUNCT
ejpam-3967	210	1	proof	proof	NOUN
ejpam-3967	210	2	.	.	PUNCT
ejpam-3967	211	1	for	for	ADP
ejpam-3967	211	2	each	each	DET
ejpam-3967	211	3	x	x	SYM
ejpam-3967	211	4	∈	∈	PROPN
ejpam-3967	211	5	s	s	NOUN
ejpam-3967	211	6	,	,	PUNCT
ejpam-3967	211	7	let	let	VERB
ejpam-3967	211	8	tx	tx	VERB
ejpam-3967	211	9	=	=	PUNCT
ejpam-3967	211	10	{	{	PUNCT
ejpam-3967	211	11	a	a	NOUN
ejpam-3967	211	12	}	}	PUNCT
ejpam-3967	211	13	,	,	PUNCT
ejpam-3967	211	14	where	where	SCONJ
ejpam-3967	211	15	{	{	PUNCT
ejpam-3967	211	16	a	a	PRON
ejpam-3967	211	17	}	}	PUNCT
ejpam-3967	211	18	is	be	AUX
ejpam-3967	211	19	a	a	DET
ejpam-3967	211	20	γ1fd	γ1fd	NOUN
ejpam-3967	211	21	-	-	PUNCT
ejpam-3967	211	22	set	set	NOUN
ejpam-3967	211	23	of	of	ADP
ejpam-3967	211	24	h	h	NOUN
ejpam-3967	211	25	,	,	PUNCT
ejpam-3967	211	26	and	and	CCONJ
ejpam-3967	211	27	let	let	VERB
ejpam-3967	211	28	c	c	NOUN
ejpam-3967	211	29	=	=	PUNCT
ejpam-3967	212	1	⋃	⋃	PROPN
ejpam-3967	212	2	x∈s	x∈s	NOUN
ejpam-3967	213	1	[	[	X
ejpam-3967	213	2	{	{	PUNCT
ejpam-3967	213	3	x	x	NOUN
ejpam-3967	213	4	}	}	PUNCT
ejpam-3967	213	5	×	×	PROPN
ejpam-3967	213	6	tx	tx	PROPN
ejpam-3967	213	7	]	]	PUNCT
ejpam-3967	213	8	.	.	PUNCT
ejpam-3967	214	1	since	since	SCONJ
ejpam-3967	214	2	s	s	PROPN
ejpam-3967	214	3	is	be	AUX
ejpam-3967	214	4	a	a	DET
ejpam-3967	214	5	total	total	ADJ
ejpam-3967	214	6	dominating	dominating	NOUN
ejpam-3967	214	7	set	set	NOUN
ejpam-3967	214	8	,	,	PUNCT
ejpam-3967	214	9	|ng(x	|ng(x	NUM
ejpam-3967	214	10	)	)	PUNCT
ejpam-3967	214	11	∩	∩	NOUN
ejpam-3967	214	12	s|	s|	NOUN
ejpam-3967	214	13	=	=	SYM
ejpam-3967	214	14	1	1	NUM
ejpam-3967	214	15	and	and	CCONJ
ejpam-3967	214	16	|tx|	|tx|	NUM
ejpam-3967	214	17	=	=	SYM
ejpam-3967	214	18	1	1	NUM
ejpam-3967	214	19	for	for	ADP
ejpam-3967	214	20	all	all	DET
ejpam-3967	214	21	x	x	SYM
ejpam-3967	214	22	∈	∈	PROPN
ejpam-3967	214	23	s	s	NOUN
ejpam-3967	214	24	,	,	PUNCT
ejpam-3967	214	25	conditions	condition	NOUN
ejpam-3967	214	26	(	(	PUNCT
ejpam-3967	214	27	i	i	NOUN
ejpam-3967	214	28	)	)	PUNCT
ejpam-3967	214	29	,	,	PUNCT
ejpam-3967	214	30	(	(	PUNCT
ejpam-3967	214	31	ii	ii	NOUN
ejpam-3967	214	32	)	)	PUNCT
ejpam-3967	214	33	,	,	PUNCT
ejpam-3967	214	34	and	and	CCONJ
ejpam-3967	214	35	(	(	PUNCT
ejpam-3967	214	36	iii	iii	NOUN
ejpam-3967	214	37	)	)	PUNCT
ejpam-3967	214	38	of	of	ADP
ejpam-3967	214	39	theorem	theorem	NOUN
ejpam-3967	214	40	10	10	NUM
ejpam-3967	214	41	are	be	AUX
ejpam-3967	214	42	satisfied	satisfied	ADJ
ejpam-3967	214	43	.	.	PUNCT
ejpam-3967	215	1	moreover	moreover	ADV
ejpam-3967	215	2	,	,	PUNCT
ejpam-3967	215	3	since	since	SCONJ
ejpam-3967	215	4	s	s	NOUN
ejpam-3967	215	5	is	be	AUX
ejpam-3967	215	6	a	a	DET
ejpam-3967	215	7	γ2fd	γ2fd	NOUN
ejpam-3967	215	8	-	-	PUNCT
ejpam-3967	215	9	set	set	ADJ
ejpam-3967	215	10	,	,	PUNCT
ejpam-3967	215	11	|ng(y	|ng(y	NUM
ejpam-3967	215	12	)	)	PUNCT
ejpam-3967	215	13	∩	∩	NOUN
ejpam-3967	215	14	s|	s|	VERB
ejpam-3967	215	15	=	=	SYM
ejpam-3967	215	16	2	2	NUM
ejpam-3967	215	17	for	for	ADP
ejpam-3967	215	18	each	each	DET
ejpam-3967	215	19	y	y	PROPN
ejpam-3967	215	20	∈	∈	PROPN
ejpam-3967	215	21	v	v	NOUN
ejpam-3967	215	22	(	(	PUNCT
ejpam-3967	215	23	g)\s	g)\s	NOUN
ejpam-3967	215	24	.	.	PUNCT
ejpam-3967	216	1	hence	hence	ADV
ejpam-3967	216	2	,	,	PUNCT
ejpam-3967	216	3	condition	condition	NOUN
ejpam-3967	216	4	(	(	PUNCT
ejpam-3967	216	5	iv	iv	X
ejpam-3967	216	6	)	)	PUNCT
ejpam-3967	216	7	of	of	ADP
ejpam-3967	216	8	theorem	theorem	NOUN
ejpam-3967	216	9	10	10	NUM
ejpam-3967	216	10	is	be	AUX
ejpam-3967	216	11	also	also	ADV
ejpam-3967	216	12	satisfied	satisfied	ADJ
ejpam-3967	216	13	.	.	PUNCT
ejpam-3967	217	1	therefore	therefore	ADV
ejpam-3967	217	2	,	,	PUNCT
ejpam-3967	217	3	by	by	ADP
ejpam-3967	217	4	theorem	theorem	NOUN
ejpam-3967	217	5	10	10	NUM
ejpam-3967	217	6	,	,	PUNCT
ejpam-3967	217	7	c	c	PROPN
ejpam-3967	217	8	is	be	AUX
ejpam-3967	217	9	a	a	DET
ejpam-3967	217	10	2ftd	2ftd	NOUN
ejpam-3967	217	11	-	-	PUNCT
ejpam-3967	217	12	set	set	NOUN
ejpam-3967	217	13	of	of	ADP
ejpam-3967	217	14	g[h	g[h	NOUN
ejpam-3967	217	15	]	]	PUNCT
ejpam-3967	217	16	.	.	PUNCT
ejpam-3967	218	1	accordingly	accordingly	ADV
ejpam-3967	218	2	,	,	PUNCT
ejpam-3967	218	3	γ2ftd(g[h	γ2ftd(g[h	PROPN
ejpam-3967	218	4	]	]	PUNCT
ejpam-3967	218	5	)	)	PUNCT
ejpam-3967	218	6	≤	≤	NOUN
ejpam-3967	218	7	|c|	|c|	PROPN
ejpam-3967	218	8	=	=	PUNCT
ejpam-3967	218	9	∑	∑	PROPN
ejpam-3967	218	10	x∈s	x∈s	PROPN
ejpam-3967	218	11	|tx|	|tx|	PROPN
ejpam-3967	218	12	=	=	SYM
ejpam-3967	218	13	|s|	|s|	PROPN
ejpam-3967	218	14	=	=	SYM
ejpam-3967	218	15	γ2ftd(g	γ2ftd(g	NUM
ejpam-3967	218	16	)	)	PUNCT
ejpam-3967	218	17	.	.	PUNCT
ejpam-3967	219	1	�	�	PROPN
ejpam-3967	219	2	remark	remark	VERB
ejpam-3967	219	3	3	3	NUM
ejpam-3967	219	4	.	.	PUNCT
ejpam-3967	220	1	the	the	DET
ejpam-3967	220	2	bound	bind	VERB
ejpam-3967	220	3	given	give	VERB
ejpam-3967	220	4	in	in	ADP
ejpam-3967	220	5	corollary	corollary	ADJ
ejpam-3967	220	6	4	4	NUM
ejpam-3967	220	7	is	be	AUX
ejpam-3967	220	8	sharp	sharp	ADJ
ejpam-3967	220	9	.	.	PUNCT
ejpam-3967	221	1	to	to	PART
ejpam-3967	221	2	see	see	VERB
ejpam-3967	221	3	this	this	PRON
ejpam-3967	221	4	,	,	PUNCT
ejpam-3967	221	5	consider	consider	VERB
ejpam-3967	221	6	the	the	DET
ejpam-3967	221	7	graph	graph	NOUN
ejpam-3967	221	8	p5[p3	p5[p3	PRON
ejpam-3967	221	9	]	]	PUNCT
ejpam-3967	221	10	shown	show	VERB
ejpam-3967	221	11	in	in	ADP
ejpam-3967	221	12	figure	figure	NOUN
ejpam-3967	221	13	3	3	NUM
ejpam-3967	221	14	.	.	PUNCT
ejpam-3967	222	1	the	the	DET
ejpam-3967	222	2	shaded	shade	VERB
ejpam-3967	222	3	vertices	vertex	NOUN
ejpam-3967	222	4	in	in	ADP
ejpam-3967	222	5	p5[p3	p5[p3	NUM
ejpam-3967	222	6	]	]	PUNCT
ejpam-3967	222	7	form	form	NOUN
ejpam-3967	222	8	a	a	DET
ejpam-3967	222	9	γ2ftd	γ2ftd	NOUN
ejpam-3967	222	10	-	-	PUNCT
ejpam-3967	222	11	set	set	NOUN
ejpam-3967	222	12	.	.	PUNCT
ejpam-3967	223	1	thus	thus	ADV
ejpam-3967	223	2	,	,	PUNCT
ejpam-3967	223	3	γ2ftd(p5[p3	γ2ftd(p5[p3	PROPN
ejpam-3967	223	4	]	]	PUNCT
ejpam-3967	223	5	)	)	PUNCT
ejpam-3967	223	6	=	=	SYM
ejpam-3967	224	1	4	4	NUM
ejpam-3967	224	2	=	=	SYM
ejpam-3967	224	3	γ2ftd(p5	γ2ftd(p5	NOUN
ejpam-3967	224	4	)	)	PUNCT
ejpam-3967	224	5	.	.	PUNCT
ejpam-3967	225	1	corollary	corollary	ADJ
ejpam-3967	225	2	5	5	NUM
ejpam-3967	225	3	.	.	PUNCT
ejpam-3967	226	1	let	let	VERB
ejpam-3967	226	2	g	g	NOUN
ejpam-3967	226	3	and	and	CCONJ
ejpam-3967	226	4	h	h	NOUN
ejpam-3967	226	5	be	be	AUX
ejpam-3967	226	6	nontrivial	nontrivial	ADJ
ejpam-3967	226	7	connected	connect	VERB
ejpam-3967	226	8	graphs	graph	NOUN
ejpam-3967	226	9	such	such	ADJ
ejpam-3967	226	10	that	that	SCONJ
ejpam-3967	226	11	|v	|v	PROPN
ejpam-3967	226	12	(	(	PUNCT
ejpam-3967	226	13	h)|	h)|	PROPN
ejpam-3967	226	14	≥	≥	NUM
ejpam-3967	226	15	3	3	NUM
ejpam-3967	226	16	and	and	CCONJ
ejpam-3967	226	17	γ2ftd(h	γ2ftd(h	NUM
ejpam-3967	226	18	)	)	PUNCT
ejpam-3967	227	1	=	=	SYM
ejpam-3967	227	2	2	2	X
ejpam-3967	227	3	.	.	X
ejpam-3967	227	4	if	if	SCONJ
ejpam-3967	227	5	g	g	PROPN
ejpam-3967	227	6	has	have	VERB
ejpam-3967	227	7	a	a	DET
ejpam-3967	227	8	γ	γ	X
ejpam-3967	227	9	-	-	PUNCT
ejpam-3967	227	10	set	set	VERB
ejpam-3967	227	11	s	s	NOUN
ejpam-3967	227	12	such	such	ADJ
ejpam-3967	227	13	that	that	DET
ejpam-3967	227	14	ng(s	ng(s	NOUN
ejpam-3967	227	15	)	)	PUNCT
ejpam-3967	227	16	∩	∩	PROPN
ejpam-3967	227	17	s	s	PART
ejpam-3967	227	18	=	=	NOUN
ejpam-3967	227	19	∅	∅	NOUN
ejpam-3967	227	20	and	and	CCONJ
ejpam-3967	227	21	|ng(y	|ng(y	NUM
ejpam-3967	227	22	)	)	PUNCT
ejpam-3967	227	23	∩	∩	NOUN
ejpam-3967	227	24	s|	s|	VERB
ejpam-3967	227	25	=	=	SYM
ejpam-3967	227	26	1	1	NUM
ejpam-3967	227	27	for	for	ADP
ejpam-3967	227	28	all	all	DET
ejpam-3967	227	29	y	y	PROPN
ejpam-3967	227	30	∈	∈	PROPN
ejpam-3967	227	31	v	v	NOUN
ejpam-3967	227	32	(	(	PUNCT
ejpam-3967	227	33	g)\s	g)\s	NOUN
ejpam-3967	227	34	,	,	PUNCT
ejpam-3967	227	35	then	then	ADV
ejpam-3967	227	36	γ2ftd(g[h	γ2ftd(g[h	ADV
ejpam-3967	227	37	]	]	PUNCT
ejpam-3967	227	38	)	)	PUNCT
ejpam-3967	227	39	≤	≤	NUM
ejpam-3967	227	40	2γ(g	2γ(g	NUM
ejpam-3967	227	41	)	)	PUNCT
ejpam-3967	227	42	.	.	PUNCT
ejpam-3967	228	1	proof	proof	NOUN
ejpam-3967	228	2	.	.	PUNCT
ejpam-3967	229	1	let	let	VERB
ejpam-3967	229	2	{	{	PUNCT
ejpam-3967	229	3	a	a	PRON
ejpam-3967	229	4	,	,	PUNCT
ejpam-3967	229	5	b	b	AUX
ejpam-3967	229	6	}	}	PUNCT
ejpam-3967	229	7	be	be	AUX
ejpam-3967	229	8	a	a	DET
ejpam-3967	229	9	γ2ftd	γ2ftd	NOUN
ejpam-3967	229	10	-	-	PUNCT
ejpam-3967	229	11	set	set	NOUN
ejpam-3967	229	12	of	of	ADP
ejpam-3967	229	13	h	h	NOUN
ejpam-3967	229	14	and	and	CCONJ
ejpam-3967	229	15	let	let	VERB
ejpam-3967	229	16	tx	tx	VERB
ejpam-3967	229	17	=	=	PUNCT
ejpam-3967	229	18	{	{	PUNCT
ejpam-3967	229	19	a	a	DET
ejpam-3967	229	20	,	,	PUNCT
ejpam-3967	229	21	b	b	NOUN
ejpam-3967	229	22	}	}	PUNCT
ejpam-3967	229	23	for	for	SCONJ
ejpam-3967	229	24	each	each	DET
ejpam-3967	229	25	x	x	SYM
ejpam-3967	229	26	∈	∈	PROPN
ejpam-3967	229	27	s.	s.	PROPN
ejpam-3967	229	28	let	let	VERB
ejpam-3967	229	29	c	c	NOUN
ejpam-3967	229	30	=	=	PUNCT
ejpam-3967	230	1	⋃	⋃	PROPN
ejpam-3967	230	2	x∈s	x∈s	NOUN
ejpam-3967	231	1	[	[	X
ejpam-3967	231	2	{	{	PUNCT
ejpam-3967	231	3	x	x	NOUN
ejpam-3967	231	4	}	}	PUNCT
ejpam-3967	231	5	×	×	PROPN
ejpam-3967	231	6	tx	tx	PROPN
ejpam-3967	231	7	]	]	PUNCT
ejpam-3967	231	8	.	.	PUNCT
ejpam-3967	232	1	since	since	SCONJ
ejpam-3967	232	2	ng(s	ng(s	NUM
ejpam-3967	232	3	)	)	PUNCT
ejpam-3967	232	4	∩	∩	PROPN
ejpam-3967	232	5	s	s	PART
ejpam-3967	232	6	=	=	SYM
ejpam-3967	232	7	∅	∅	NOUN
ejpam-3967	232	8	,	,	PUNCT
ejpam-3967	232	9	s\ng(s	s\ng(s	NUM
ejpam-3967	232	10	)	)	PUNCT
ejpam-3967	232	11	=	=	SYM
ejpam-3967	232	12	s	s	PROPN
ejpam-3967	232	13	,	,	PUNCT
ejpam-3967	232	14	|tx|	|tx|	NOUN
ejpam-3967	232	15	=	=	SYM
ejpam-3967	232	16	2	2	NUM
ejpam-3967	232	17	and	and	CCONJ
ejpam-3967	232	18	tx	tx	PROPN
ejpam-3967	232	19	is	be	AUX
ejpam-3967	232	20	a	a	DET
ejpam-3967	232	21	2ftd	2ftd	NOUN
ejpam-3967	232	22	-	-	PUNCT
ejpam-3967	232	23	set	set	NOUN
ejpam-3967	232	24	of	of	ADP
ejpam-3967	232	25	h	h	NOUN
ejpam-3967	232	26	for	for	ADP
ejpam-3967	232	27	each	each	DET
ejpam-3967	232	28	x	x	SYM
ejpam-3967	232	29	∈	∈	PROPN
ejpam-3967	232	30	s	s	NOUN
ejpam-3967	232	31	,	,	PUNCT
ejpam-3967	232	32	conditions	condition	NOUN
ejpam-3967	232	33	(	(	PUNCT
ejpam-3967	232	34	i	i	NOUN
ejpam-3967	232	35	)	)	PUNCT
ejpam-3967	232	36	,	,	PUNCT
ejpam-3967	232	37	(	(	PUNCT
ejpam-3967	232	38	ii	ii	NOUN
ejpam-3967	232	39	)	)	PUNCT
ejpam-3967	232	40	,	,	PUNCT
ejpam-3967	232	41	and	and	CCONJ
ejpam-3967	232	42	(	(	PUNCT
ejpam-3967	232	43	iii	iii	NOUN
ejpam-3967	232	44	)	)	PUNCT
ejpam-3967	232	45	of	of	ADP
ejpam-3967	232	46	theorem	theorem	NOUN
ejpam-3967	232	47	10	10	NUM
ejpam-3967	232	48	are	be	AUX
ejpam-3967	232	49	satisfied	satisfied	ADJ
ejpam-3967	232	50	.	.	PUNCT
ejpam-3967	233	1	also	also	ADV
ejpam-3967	233	2	,	,	PUNCT
ejpam-3967	233	3	since	since	SCONJ
ejpam-3967	233	4	|ng(y	|ng(y	NUM
ejpam-3967	233	5	)	)	PUNCT
ejpam-3967	233	6	∩	∩	NOUN
ejpam-3967	233	7	s|	s|	VERB
ejpam-3967	233	8	=	=	SYM
ejpam-3967	233	9	1	1	NUM
ejpam-3967	233	10	for	for	ADP
ejpam-3967	233	11	each	each	DET
ejpam-3967	233	12	y	y	PROPN
ejpam-3967	233	13	∈	∈	PROPN
ejpam-3967	233	14	v	v	NOUN
ejpam-3967	233	15	(	(	PUNCT
ejpam-3967	233	16	g)\s	g)\s	NOUN
ejpam-3967	233	17	,	,	PUNCT
ejpam-3967	233	18	condition	condition	NOUN
ejpam-3967	233	19	(	(	PUNCT
ejpam-3967	233	20	iv	iv	X
ejpam-3967	233	21	)	)	PUNCT
ejpam-3967	233	22	of	of	ADP
ejpam-3967	233	23	theorem	theorem	NOUN
ejpam-3967	233	24	10	10	NUM
ejpam-3967	233	25	is	be	AUX
ejpam-3967	233	26	also	also	ADV
ejpam-3967	233	27	satisfied	satisfied	ADJ
ejpam-3967	233	28	.	.	PUNCT
ejpam-3967	234	1	thus	thus	ADV
ejpam-3967	234	2	,	,	PUNCT
ejpam-3967	234	3	by	by	ADP
ejpam-3967	234	4	theorem	theorem	NOUN
ejpam-3967	234	5	10	10	NUM
ejpam-3967	234	6	,	,	PUNCT
ejpam-3967	234	7	c	c	PROPN
ejpam-3967	234	8	is	be	AUX
ejpam-3967	234	9	a	a	DET
ejpam-3967	234	10	2ftd	2ftd	NOUN
ejpam-3967	234	11	-	-	PUNCT
ejpam-3967	234	12	set	set	NOUN
ejpam-3967	234	13	of	of	ADP
ejpam-3967	234	14	g[h	g[h	NOUN
ejpam-3967	234	15	]	]	PUNCT
ejpam-3967	234	16	.	.	PUNCT
ejpam-3967	235	1	therefore	therefore	ADV
ejpam-3967	235	2	,	,	PUNCT
ejpam-3967	235	3	γ2ftd(g[h	γ2ftd(g[h	PROPN
ejpam-3967	235	4	]	]	PUNCT
ejpam-3967	235	5	)	)	PUNCT
ejpam-3967	235	6	≤	≤	NOUN
ejpam-3967	235	7	|c|	|c|	PROPN
ejpam-3967	235	8	=	=	PUNCT
ejpam-3967	235	9	∑	∑	PROPN
ejpam-3967	235	10	x∈s	x∈s	PROPN
ejpam-3967	235	11	|tx|	|tx|	PROPN
ejpam-3967	235	12	=	=	SYM
ejpam-3967	235	13	2|s|	2|s|	NUM
ejpam-3967	235	14	=	=	SYM
ejpam-3967	235	15	2γ(g	2γ(g	NUM
ejpam-3967	235	16	)	)	PUNCT
ejpam-3967	235	17	.	.	PUNCT
ejpam-3967	236	1	�	�	PROPN
ejpam-3967	236	2	remark	remark	VERB
ejpam-3967	236	3	4	4	NUM
ejpam-3967	236	4	.	.	PUNCT
ejpam-3967	237	1	the	the	DET
ejpam-3967	237	2	bound	bind	VERB
ejpam-3967	237	3	given	give	VERB
ejpam-3967	237	4	in	in	ADP
ejpam-3967	237	5	corollary	corollary	ADJ
ejpam-3967	237	6	5	5	NUM
ejpam-3967	237	7	is	be	AUX
ejpam-3967	237	8	sharp	sharp	ADJ
ejpam-3967	237	9	.	.	PUNCT
ejpam-3967	238	1	to	to	PART
ejpam-3967	238	2	see	see	VERB
ejpam-3967	238	3	this	this	PRON
ejpam-3967	238	4	,	,	PUNCT
ejpam-3967	238	5	consider	consider	VERB
ejpam-3967	238	6	the	the	DET
ejpam-3967	238	7	graph	graph	NOUN
ejpam-3967	238	8	p6[c3	p6[c3	PROPN
ejpam-3967	238	9	]	]	PUNCT
ejpam-3967	238	10	shown	show	VERB
ejpam-3967	238	11	in	in	ADP
ejpam-3967	238	12	figure	figure	NOUN
ejpam-3967	238	13	3	3	NUM
ejpam-3967	238	14	.	.	PUNCT
ejpam-3967	239	1	the	the	DET
ejpam-3967	239	2	shaded	shade	VERB
ejpam-3967	239	3	vertices	vertex	NOUN
ejpam-3967	239	4	in	in	ADP
ejpam-3967	239	5	p6[c3	p6[c3	PROPN
ejpam-3967	239	6	]	]	PUNCT
ejpam-3967	239	7	form	form	NOUN
ejpam-3967	239	8	a	a	DET
ejpam-3967	239	9	γ2ftd	γ2ftd	NOUN
ejpam-3967	239	10	-	-	PUNCT
ejpam-3967	239	11	set	set	NOUN
ejpam-3967	239	12	.	.	PUNCT
ejpam-3967	240	1	thus	thus	ADV
ejpam-3967	240	2	,	,	PUNCT
ejpam-3967	240	3	γ2ftd(p6[c3	γ2ftd(p6[c3	PROPN
ejpam-3967	240	4	]	]	PUNCT
ejpam-3967	240	5	)	)	PUNCT
ejpam-3967	241	1	=	=	SYM
ejpam-3967	241	2	4	4	NUM
ejpam-3967	241	3	=	=	SYM
ejpam-3967	241	4	2γ(p6	2γ(p6	NUM
ejpam-3967	241	5	)	)	PUNCT
ejpam-3967	241	6	.	.	PUNCT
ejpam-3967	242	1	w.	w.	PROPN
ejpam-3967	242	2	bent	bent	PROPN
ejpam-3967	242	3	-	-	PUNCT
ejpam-3967	242	4	usman	usman	PROPN
ejpam-3967	242	5	,	,	PUNCT
ejpam-3967	242	6	r.	r.	PROPN
ejpam-3967	242	7	isla	isla	PROPN
ejpam-3967	242	8	/	/	SYM
ejpam-3967	242	9	eur	eur	PROPN
ejpam-3967	242	10	.	.	PUNCT
ejpam-3967	243	1	j.	j.	PROPN
ejpam-3967	243	2	pure	pure	PROPN
ejpam-3967	243	3	appl	appl	PROPN
ejpam-3967	243	4	.	.	PROPN
ejpam-3967	243	5	math	math	PROPN
ejpam-3967	243	6	,	,	PUNCT
ejpam-3967	243	7	14	14	NUM
ejpam-3967	243	8	(	(	PUNCT
ejpam-3967	243	9	2	2	NUM
ejpam-3967	243	10	)	)	PUNCT
ejpam-3967	243	11	(	(	PUNCT
ejpam-3967	243	12	2021	2021	NUM
ejpam-3967	243	13	)	)	PUNCT
ejpam-3967	243	14	,	,	PUNCT
ejpam-3967	243	15	578	578	NUM
ejpam-3967	243	16	-	-	SYM
ejpam-3967	243	17	589	589	NUM
ejpam-3967	243	18	587	587	NUM
ejpam-3967	243	19	theorem	theorem	NOUN
ejpam-3967	243	20	11	11	NUM
ejpam-3967	243	21	.	.	PUNCT
ejpam-3967	244	1	let	let	VERB
ejpam-3967	244	2	g	g	NOUN
ejpam-3967	244	3	and	and	CCONJ
ejpam-3967	244	4	h	h	NOUN
ejpam-3967	244	5	be	be	AUX
ejpam-3967	244	6	nontrivial	nontrivial	ADJ
ejpam-3967	244	7	connected	connect	VERB
ejpam-3967	244	8	graphs	graph	NOUN
ejpam-3967	244	9	of	of	ADP
ejpam-3967	244	10	orders	order	NOUN
ejpam-3967	244	11	m	m	VERB
ejpam-3967	244	12	and	and	CCONJ
ejpam-3967	244	13	n	n	CCONJ
ejpam-3967	244	14	,	,	PUNCT
ejpam-3967	244	15	respectively	respectively	ADV
ejpam-3967	244	16	.	.	PUNCT
ejpam-3967	245	1	then	then	ADV
ejpam-3967	245	2	c1	c1	PROPN
ejpam-3967	245	3	=	=	PROPN
ejpam-3967	245	4	s1	s1	PROPN
ejpam-3967	245	5	×	×	PROPN
ejpam-3967	245	6	v	v	NOUN
ejpam-3967	245	7	(	(	PUNCT
ejpam-3967	245	8	h	h	NOUN
ejpam-3967	245	9	)	)	PUNCT
ejpam-3967	245	10	and	and	CCONJ
ejpam-3967	245	11	c2	c2	PROPN
ejpam-3967	245	12	=	=	SYM
ejpam-3967	245	13	v	v	PROPN
ejpam-3967	245	14	(	(	PUNCT
ejpam-3967	245	15	g)×	g)×	NOUN
ejpam-3967	245	16	s2	s2	NOUN
ejpam-3967	245	17	are	be	AUX
ejpam-3967	245	18	kftd	kftd	NOUN
ejpam-3967	245	19	-	-	PUNCT
ejpam-3967	245	20	sets	set	NOUN
ejpam-3967	245	21	in	in	ADP
ejpam-3967	245	22	g	g	PROPN
ejpam-3967	245	23	�	�	NOUN
ejpam-3967	245	24	h	h	NOUN
ejpam-3967	245	25	if	if	SCONJ
ejpam-3967	246	1	and	and	CCONJ
ejpam-3967	246	2	only	only	ADV
ejpam-3967	246	3	if	if	SCONJ
ejpam-3967	246	4	s1	s1	PROPN
ejpam-3967	246	5	and	and	CCONJ
ejpam-3967	246	6	s2	s2	PROPN
ejpam-3967	246	7	are	be	AUX
ejpam-3967	246	8	kfd	kfd	ADJ
ejpam-3967	246	9	-	-	PUNCT
ejpam-3967	246	10	sets	set	NOUN
ejpam-3967	246	11	in	in	ADP
ejpam-3967	246	12	g	g	PROPN
ejpam-3967	246	13	and	and	CCONJ
ejpam-3967	246	14	h	h	NOUN
ejpam-3967	246	15	,	,	PUNCT
ejpam-3967	246	16	respectively	respectively	ADV
ejpam-3967	246	17	.	.	PUNCT
ejpam-3967	247	1	proof	proof	NOUN
ejpam-3967	247	2	.	.	PUNCT
ejpam-3967	248	1	suppose	suppose	VERB
ejpam-3967	248	2	s1	s1	NOUN
ejpam-3967	248	3	is	be	AUX
ejpam-3967	248	4	a	a	DET
ejpam-3967	248	5	kfd	kfd	NOUN
ejpam-3967	248	6	-	-	PUNCT
ejpam-3967	248	7	set	set	NOUN
ejpam-3967	248	8	in	in	ADP
ejpam-3967	248	9	g	g	PROPN
ejpam-3967	248	10	and	and	CCONJ
ejpam-3967	248	11	c1	c1	PROPN
ejpam-3967	248	12	=	=	PROPN
ejpam-3967	249	1	s1	s1	PROPN
ejpam-3967	249	2	×	×	PROPN
ejpam-3967	249	3	v	v	NOUN
ejpam-3967	249	4	(	(	PUNCT
ejpam-3967	249	5	h	h	NOUN
ejpam-3967	249	6	)	)	PUNCT
ejpam-3967	249	7	.	.	PUNCT
ejpam-3967	250	1	let	let	VERB
ejpam-3967	250	2	(	(	PUNCT
ejpam-3967	250	3	x	x	NOUN
ejpam-3967	250	4	,	,	PUNCT
ejpam-3967	250	5	a	a	PRON
ejpam-3967	250	6	)	)	PUNCT
ejpam-3967	250	7	∈	∈	PROPN
ejpam-3967	250	8	(	(	PUNCT
ejpam-3967	250	9	g	g	PROPN
ejpam-3967	250	10	�	�	PROPN
ejpam-3967	250	11	h)\c1	h)\c1	PROPN
ejpam-3967	250	12	.	.	PUNCT
ejpam-3967	251	1	then	then	ADV
ejpam-3967	251	2	x	x	X
ejpam-3967	251	3	/∈	/∈	PUNCT
ejpam-3967	251	4	s1	s1	PROPN
ejpam-3967	251	5	.	.	PUNCT
ejpam-3967	252	1	since	since	SCONJ
ejpam-3967	252	2	s1	s1	PROPN
ejpam-3967	252	3	is	be	AUX
ejpam-3967	252	4	a	a	DET
ejpam-3967	252	5	kfd	kfd	NOUN
ejpam-3967	252	6	-	-	PUNCT
ejpam-3967	252	7	set	set	NOUN
ejpam-3967	252	8	in	in	ADP
ejpam-3967	252	9	g	g	PROPN
ejpam-3967	252	10	,	,	PUNCT
ejpam-3967	252	11	|ng(x	|ng(x	NOUN
ejpam-3967	252	12	)	)	PUNCT
ejpam-3967	252	13	∩	∩	NOUN
ejpam-3967	252	14	s1|	s1|	PROPN
ejpam-3967	252	15	=	=	SYM
ejpam-3967	252	16	k.	k.	PROPN
ejpam-3967	252	17	since	since	SCONJ
ejpam-3967	252	18	ng	ng	PROPN
ejpam-3967	252	19	�	�	PROPN
ejpam-3967	252	20	h((x	h((x	NOUN
ejpam-3967	252	21	,	,	PUNCT
ejpam-3967	252	22	a	a	PRON
ejpam-3967	252	23	)	)	PUNCT
ejpam-3967	252	24	)	)	PUNCT
ejpam-3967	253	1	∩	∩	NOUN
ejpam-3967	253	2	c	c	NOUN
ejpam-3967	254	1	=	=	SYM
ejpam-3967	254	2	⋃	⋃	NOUN
ejpam-3967	254	3	y∈ng(x)∩s	y∈ng(x)∩s	NOUN
ejpam-3967	254	4	[	[	X
ejpam-3967	254	5	{	{	PUNCT
ejpam-3967	254	6	y	y	NOUN
ejpam-3967	254	7	}	}	PUNCT
ejpam-3967	254	8	×	×	NOUN
ejpam-3967	254	9	{	{	PUNCT
ejpam-3967	254	10	a	a	NOUN
ejpam-3967	254	11	}	}	PUNCT
ejpam-3967	254	12	]	]	PUNCT
ejpam-3967	254	13	,	,	PUNCT
ejpam-3967	254	14	it	it	PRON
ejpam-3967	254	15	follows	follow	VERB
ejpam-3967	254	16	that	that	SCONJ
ejpam-3967	254	17	|ng	|ng	VERB
ejpam-3967	254	18	�	�	PROPN
ejpam-3967	254	19	h(x	h(x	PROPN
ejpam-3967	254	20	,	,	PUNCT
ejpam-3967	254	21	a	a	PRON
ejpam-3967	254	22	)	)	PUNCT
ejpam-3967	254	23	∩	∩	NOUN
ejpam-3967	254	24	c1|	c1|	NOUN
ejpam-3967	254	25	=	=	SYM
ejpam-3967	254	26	|ng(x	|ng(x	NUM
ejpam-3967	254	27	)	)	PUNCT
ejpam-3967	254	28	∩	∩	NOUN
ejpam-3967	254	29	s|	s|	NOUN
ejpam-3967	254	30	=	=	SYM
ejpam-3967	254	31	k	k	NOUN
ejpam-3967	254	32	,	,	PUNCT
ejpam-3967	254	33	showing	show	VERB
ejpam-3967	254	34	that	that	DET
ejpam-3967	254	35	c1	c1	PROPN
ejpam-3967	254	36	is	be	AUX
ejpam-3967	254	37	a	a	DET
ejpam-3967	254	38	k	k	ADJ
ejpam-3967	254	39	-	-	ADJ
ejpam-3967	254	40	fair	fair	ADJ
ejpam-3967	254	41	dominating	dominating	NOUN
ejpam-3967	254	42	set	set	NOUN
ejpam-3967	254	43	in	in	ADP
ejpam-3967	254	44	g	g	PROPN
ejpam-3967	254	45	�	�	PROPN
ejpam-3967	254	46	h.	h.	PROPN
ejpam-3967	254	47	let	let	NOUN
ejpam-3967	254	48	(	(	PUNCT
ejpam-3967	254	49	z	z	NOUN
ejpam-3967	254	50	,	,	PUNCT
ejpam-3967	254	51	c	c	NOUN
ejpam-3967	254	52	)	)	PUNCT
ejpam-3967	254	53	∈	∈	PROPN
ejpam-3967	254	54	c1	c1	NOUN
ejpam-3967	254	55	.	.	PUNCT
ejpam-3967	255	1	since	since	SCONJ
ejpam-3967	255	2	h	h	NOUN
ejpam-3967	255	3	is	be	AUX
ejpam-3967	255	4	a	a	DET
ejpam-3967	255	5	nontrivial	nontrivial	ADJ
ejpam-3967	255	6	connected	connect	VERB
ejpam-3967	255	7	graph	graph	NOUN
ejpam-3967	255	8	,	,	PUNCT
ejpam-3967	255	9	there	there	PRON
ejpam-3967	255	10	exists	exist	VERB
ejpam-3967	255	11	d	d	X
ejpam-3967	255	12	∈	∈	PROPN
ejpam-3967	255	13	v	v	ADP
ejpam-3967	255	14	(	(	PUNCT
ejpam-3967	255	15	h	h	NOUN
ejpam-3967	255	16	)	)	PUNCT
ejpam-3967	255	17	such	such	ADJ
ejpam-3967	255	18	that	that	SCONJ
ejpam-3967	255	19	cd	cd	PROPN
ejpam-3967	255	20	∈	∈	PROPN
ejpam-3967	255	21	e(h	e(h	PROPN
ejpam-3967	255	22	)	)	PUNCT
ejpam-3967	255	23	.	.	PUNCT
ejpam-3967	256	1	thus	thus	ADV
ejpam-3967	256	2	,	,	PUNCT
ejpam-3967	256	3	(	(	PUNCT
ejpam-3967	256	4	z	z	X
ejpam-3967	256	5	,	,	PUNCT
ejpam-3967	256	6	d	d	NOUN
ejpam-3967	256	7	)	)	PUNCT
ejpam-3967	256	8	∈	∈	PROPN
ejpam-3967	256	9	c1	c1	PROPN
ejpam-3967	256	10	and	and	CCONJ
ejpam-3967	256	11	(	(	PUNCT
ejpam-3967	256	12	z	z	NOUN
ejpam-3967	256	13	,	,	PUNCT
ejpam-3967	256	14	c)(z	c)(z	PROPN
ejpam-3967	256	15	,	,	PUNCT
ejpam-3967	256	16	d	d	X
ejpam-3967	256	17	)	)	PUNCT
ejpam-3967	256	18	∈	∈	PROPN
ejpam-3967	256	19	e〈c1	e〈c1	NOUN
ejpam-3967	256	20	〉	〉	NOUN
ejpam-3967	256	21	.	.	PUNCT
ejpam-3967	257	1	hence	hence	ADV
ejpam-3967	257	2	,	,	PUNCT
ejpam-3967	257	3	c1	c1	PROPN
ejpam-3967	257	4	is	be	AUX
ejpam-3967	257	5	a	a	DET
ejpam-3967	257	6	kftd	kftd	NOUN
ejpam-3967	257	7	-	-	PUNCT
ejpam-3967	257	8	set	set	NOUN
ejpam-3967	257	9	in	in	ADP
ejpam-3967	257	10	g	g	PROPN
ejpam-3967	257	11	�	�	PROPN
ejpam-3967	257	12	h.	h.	PROPN
ejpam-3967	257	13	similarly	similarly	ADV
ejpam-3967	257	14	,	,	PUNCT
ejpam-3967	257	15	c2	c2	PROPN
ejpam-3967	257	16	=	=	SYM
ejpam-3967	257	17	v	v	PROPN
ejpam-3967	257	18	(	(	PUNCT
ejpam-3967	257	19	g)×	g)×	NOUN
ejpam-3967	257	20	s2	s2	PROPN
ejpam-3967	257	21	,	,	PUNCT
ejpam-3967	257	22	where	where	SCONJ
ejpam-3967	257	23	s2	s2	PROPN
ejpam-3967	257	24	is	be	AUX
ejpam-3967	257	25	a	a	DET
ejpam-3967	257	26	kfd	kfd	NOUN
ejpam-3967	257	27	-	-	PUNCT
ejpam-3967	257	28	set	set	NOUN
ejpam-3967	257	29	in	in	ADP
ejpam-3967	257	30	h	h	NOUN
ejpam-3967	257	31	,	,	PUNCT
ejpam-3967	257	32	is	be	AUX
ejpam-3967	257	33	a	a	DET
ejpam-3967	257	34	kftd	kftd	NOUN
ejpam-3967	257	35	-	-	PUNCT
ejpam-3967	257	36	set	set	NOUN
ejpam-3967	257	37	in	in	ADP
ejpam-3967	257	38	g	g	PROPN
ejpam-3967	257	39	�	�	PROPN
ejpam-3967	257	40	h.	h.	PROPN
ejpam-3967	257	41	for	for	ADP
ejpam-3967	257	42	the	the	DET
ejpam-3967	257	43	converse	converse	NOUN
ejpam-3967	257	44	,	,	PUNCT
ejpam-3967	257	45	suppose	suppose	VERB
ejpam-3967	257	46	that	that	SCONJ
ejpam-3967	257	47	c1	c1	PROPN
ejpam-3967	257	48	=	=	PROPN
ejpam-3967	257	49	s1	s1	PROPN
ejpam-3967	257	50	×	×	PROPN
ejpam-3967	257	51	v	v	NOUN
ejpam-3967	257	52	(	(	PUNCT
ejpam-3967	257	53	h	h	NOUN
ejpam-3967	257	54	)	)	PUNCT
ejpam-3967	257	55	is	be	AUX
ejpam-3967	257	56	a	a	DET
ejpam-3967	257	57	kftd	kftd	NOUN
ejpam-3967	257	58	-	-	PUNCT
ejpam-3967	257	59	set	set	NOUN
ejpam-3967	257	60	in	in	ADP
ejpam-3967	257	61	g	g	PROPN
ejpam-3967	257	62	�	�	PROPN
ejpam-3967	257	63	h.	h.	PROPN
ejpam-3967	257	64	suppose	suppose	VERB
ejpam-3967	257	65	further	far	ADV
ejpam-3967	257	66	that	that	SCONJ
ejpam-3967	257	67	s1	s1	PROPN
ejpam-3967	257	68	is	be	AUX
ejpam-3967	257	69	not	not	PART
ejpam-3967	257	70	a	a	DET
ejpam-3967	257	71	kfd	kfd	NOUN
ejpam-3967	257	72	-	-	PUNCT
ejpam-3967	257	73	set	set	NOUN
ejpam-3967	257	74	in	in	ADP
ejpam-3967	257	75	g.	g.	PROPN
ejpam-3967	257	76	if	if	SCONJ
ejpam-3967	257	77	s1	s1	NOUN
ejpam-3967	257	78	is	be	AUX
ejpam-3967	257	79	not	not	PART
ejpam-3967	257	80	a	a	DET
ejpam-3967	257	81	dominating	dominating	NOUN
ejpam-3967	257	82	set	set	NOUN
ejpam-3967	257	83	in	in	ADP
ejpam-3967	257	84	g	g	NOUN
ejpam-3967	257	85	,	,	PUNCT
ejpam-3967	257	86	then	then	ADV
ejpam-3967	257	87	there	there	PRON
ejpam-3967	257	88	exists	exist	VERB
ejpam-3967	257	89	an	an	DET
ejpam-3967	257	90	x	x	SYM
ejpam-3967	257	91	∈	∈	PROPN
ejpam-3967	257	92	v	v	NOUN
ejpam-3967	257	93	(	(	PUNCT
ejpam-3967	257	94	g)\s1	g)\s1	PROPN
ejpam-3967	257	95	such	such	ADJ
ejpam-3967	257	96	that	that	PRON
ejpam-3967	257	97	xy	xy	PROPN
ejpam-3967	257	98	/∈	/∈	PUNCT
ejpam-3967	258	1	e(g	e(g	PROPN
ejpam-3967	258	2	)	)	PUNCT
ejpam-3967	259	1	for	for	ADP
ejpam-3967	259	2	every	every	DET
ejpam-3967	259	3	y	y	PROPN
ejpam-3967	259	4	∈	∈	PROPN
ejpam-3967	259	5	s1	s1	PROPN
ejpam-3967	259	6	.	.	PUNCT
ejpam-3967	260	1	let	let	VERB
ejpam-3967	260	2	a	a	DET
ejpam-3967	260	3	∈	∈	PROPN
ejpam-3967	260	4	v	v	NOUN
ejpam-3967	260	5	(	(	PUNCT
ejpam-3967	260	6	h	h	NOUN
ejpam-3967	260	7	)	)	PUNCT
ejpam-3967	260	8	.	.	PUNCT
ejpam-3967	261	1	then	then	ADV
ejpam-3967	261	2	(	(	PUNCT
ejpam-3967	261	3	x	x	X
ejpam-3967	261	4	,	,	PUNCT
ejpam-3967	261	5	a	a	PRON
ejpam-3967	261	6	)	)	PUNCT
ejpam-3967	261	7	∈	∈	NOUN
ejpam-3967	261	8	v	v	NOUN
ejpam-3967	261	9	(	(	PUNCT
ejpam-3967	261	10	g	g	PROPN
ejpam-3967	261	11	�	�	NOUN
ejpam-3967	261	12	h)\c1	h)\c1	PROPN
ejpam-3967	261	13	and	and	CCONJ
ejpam-3967	261	14	(	(	PUNCT
ejpam-3967	261	15	x	x	NOUN
ejpam-3967	261	16	,	,	PUNCT
ejpam-3967	261	17	a)(y	a)(y	PROPN
ejpam-3967	261	18	,	,	PUNCT
ejpam-3967	261	19	a	a	PRON
ejpam-3967	261	20	)	)	PUNCT
ejpam-3967	261	21	/∈	/∈	PUNCT
ejpam-3967	262	1	e(g	e(g	PROPN
ejpam-3967	262	2	�	�	PROPN
ejpam-3967	262	3	h	h	PROPN
ejpam-3967	262	4	)	)	PUNCT
ejpam-3967	263	1	for	for	ADP
ejpam-3967	263	2	any	any	DET
ejpam-3967	263	3	(	(	PUNCT
ejpam-3967	263	4	y	y	PROPN
ejpam-3967	263	5	,	,	PUNCT
ejpam-3967	263	6	a	a	PRON
ejpam-3967	263	7	)	)	PUNCT
ejpam-3967	263	8	∈	∈	PROPN
ejpam-3967	263	9	c1	c1	NOUN
ejpam-3967	263	10	,	,	PUNCT
ejpam-3967	263	11	contrary	contrary	ADV
ejpam-3967	263	12	to	to	ADP
ejpam-3967	263	13	the	the	DET
ejpam-3967	263	14	assumption	assumption	NOUN
ejpam-3967	263	15	that	that	SCONJ
ejpam-3967	263	16	c1	c1	PROPN
ejpam-3967	263	17	is	be	AUX
ejpam-3967	263	18	a	a	DET
ejpam-3967	263	19	kftd	kftd	NOUN
ejpam-3967	263	20	-	-	PUNCT
ejpam-3967	263	21	set	set	NOUN
ejpam-3967	263	22	,	,	PUNCT
ejpam-3967	263	23	hence	hence	ADV
ejpam-3967	263	24	a	a	DET
ejpam-3967	263	25	dominating	dominating	NOUN
ejpam-3967	263	26	set	set	NOUN
ejpam-3967	263	27	.	.	PUNCT
ejpam-3967	264	1	thus	thus	ADV
ejpam-3967	264	2	,	,	PUNCT
ejpam-3967	264	3	s1	s1	PROPN
ejpam-3967	264	4	is	be	AUX
ejpam-3967	264	5	a	a	DET
ejpam-3967	264	6	dominating	dominating	NOUN
ejpam-3967	264	7	set	set	NOUN
ejpam-3967	264	8	.	.	PUNCT
ejpam-3967	265	1	if	if	SCONJ
ejpam-3967	265	2	s1	s1	PROPN
ejpam-3967	265	3	is	be	AUX
ejpam-3967	265	4	not	not	PART
ejpam-3967	265	5	a	a	DET
ejpam-3967	265	6	kfd	kfd	NOUN
ejpam-3967	265	7	-	-	PUNCT
ejpam-3967	265	8	set	set	NOUN
ejpam-3967	265	9	,	,	PUNCT
ejpam-3967	265	10	then	then	ADV
ejpam-3967	265	11	there	there	PRON
ejpam-3967	265	12	exists	exist	VERB
ejpam-3967	265	13	a	a	DET
ejpam-3967	265	14	u	u	NOUN
ejpam-3967	265	15	∈	∈	PROPN
ejpam-3967	265	16	v	v	NOUN
ejpam-3967	265	17	(	(	PUNCT
ejpam-3967	265	18	g)\s1	g)\s1	PROPN
ejpam-3967	265	19	such	such	ADJ
ejpam-3967	265	20	that	that	SCONJ
ejpam-3967	265	21	|ng(u	|ng(u	X
ejpam-3967	265	22	)	)	PUNCT
ejpam-3967	265	23	∩	∩	NOUN
ejpam-3967	265	24	s1|	s1|	NOUN
ejpam-3967	265	25	=	=	SYM
ejpam-3967	265	26	r	r	PROPN
ejpam-3967	265	27	6=	6=	PROPN
ejpam-3967	265	28	k.	k.	PROPN
ejpam-3967	265	29	let	let	VERB
ejpam-3967	265	30	a	a	DET
ejpam-3967	265	31	∈	∈	PROPN
ejpam-3967	265	32	v	v	NOUN
ejpam-3967	265	33	(	(	PUNCT
ejpam-3967	265	34	h	h	NOUN
ejpam-3967	265	35	)	)	PUNCT
ejpam-3967	265	36	.	.	PUNCT
ejpam-3967	266	1	then	then	ADV
ejpam-3967	266	2	(	(	PUNCT
ejpam-3967	266	3	u	u	NOUN
ejpam-3967	266	4	,	,	PUNCT
ejpam-3967	266	5	a	a	PRON
ejpam-3967	266	6	)	)	PUNCT
ejpam-3967	266	7	∈	∈	NOUN
ejpam-3967	266	8	v	v	NOUN
ejpam-3967	266	9	(	(	PUNCT
ejpam-3967	266	10	g	g	PROPN
ejpam-3967	266	11	�	�	NOUN
ejpam-3967	266	12	h)\c1	h)\c1	PROPN
ejpam-3967	266	13	and	and	CCONJ
ejpam-3967	266	14	|ng	|ng	NOUN
ejpam-3967	266	15	�	�	PROPN
ejpam-3967	266	16	h(u	h(u	PROPN
ejpam-3967	266	17	,	,	PUNCT
ejpam-3967	266	18	a	a	PRON
ejpam-3967	266	19	)	)	PUNCT
ejpam-3967	266	20	∩	∩	NOUN
ejpam-3967	266	21	c1|	c1|	NOUN
ejpam-3967	266	22	=	=	SYM
ejpam-3967	266	23	r	r	NOUN
ejpam-3967	266	24	6=	6=	PROPN
ejpam-3967	266	25	k	k	PROPN
ejpam-3967	266	26	,	,	PUNCT
ejpam-3967	266	27	contrary	contrary	ADV
ejpam-3967	266	28	to	to	ADP
ejpam-3967	266	29	the	the	DET
ejpam-3967	266	30	assumption	assumption	NOUN
ejpam-3967	266	31	that	that	SCONJ
ejpam-3967	266	32	c1	c1	PROPN
ejpam-3967	266	33	is	be	AUX
ejpam-3967	266	34	a	a	DET
ejpam-3967	266	35	kftd	kftd	NOUN
ejpam-3967	266	36	-	-	PUNCT
ejpam-3967	266	37	set	set	NOUN
ejpam-3967	266	38	.	.	PUNCT
ejpam-3967	267	1	therefore	therefore	ADV
ejpam-3967	267	2	,	,	PUNCT
ejpam-3967	267	3	s1	s1	PROPN
ejpam-3967	267	4	is	be	AUX
ejpam-3967	267	5	a	a	DET
ejpam-3967	267	6	kfd	kfd	NOUN
ejpam-3967	267	7	-	-	PUNCT
ejpam-3967	267	8	set	set	NOUN
ejpam-3967	267	9	in	in	ADP
ejpam-3967	267	10	g.	g.	NOUN
ejpam-3967	267	11	similarly	similarly	ADV
ejpam-3967	267	12	,	,	PUNCT
ejpam-3967	267	13	if	if	SCONJ
ejpam-3967	267	14	c2	c2	PROPN
ejpam-3967	267	15	=	=	SYM
ejpam-3967	267	16	v	v	PROPN
ejpam-3967	267	17	(	(	PUNCT
ejpam-3967	267	18	g)×	g)×	NOUN
ejpam-3967	267	19	s2	s2	NOUN
ejpam-3967	267	20	is	be	AUX
ejpam-3967	267	21	a	a	DET
ejpam-3967	267	22	kftd	kftd	NOUN
ejpam-3967	267	23	-	-	PUNCT
ejpam-3967	267	24	set	set	NOUN
ejpam-3967	267	25	in	in	ADP
ejpam-3967	267	26	g	g	PROPN
ejpam-3967	267	27	�	�	PROPN
ejpam-3967	267	28	h	h	NOUN
ejpam-3967	267	29	,	,	PUNCT
ejpam-3967	267	30	then	then	ADV
ejpam-3967	267	31	s2	s2	PROPN
ejpam-3967	267	32	is	be	AUX
ejpam-3967	267	33	a	a	DET
ejpam-3967	267	34	kfd	kfd	NOUN
ejpam-3967	267	35	-	-	PUNCT
ejpam-3967	267	36	set	set	NOUN
ejpam-3967	267	37	in	in	ADP
ejpam-3967	267	38	h.	h.	PROPN
ejpam-3967	267	39	�	�	PROPN
ejpam-3967	267	40	corollary	corollary	PROPN
ejpam-3967	267	41	6	6	NUM
ejpam-3967	267	42	.	.	PUNCT
ejpam-3967	268	1	let	let	VERB
ejpam-3967	268	2	g	g	NOUN
ejpam-3967	268	3	and	and	CCONJ
ejpam-3967	268	4	h	h	NOUN
ejpam-3967	268	5	be	be	AUX
ejpam-3967	268	6	nontrivial	nontrivial	ADJ
ejpam-3967	268	7	connected	connect	VERB
ejpam-3967	268	8	graphs	graph	NOUN
ejpam-3967	268	9	of	of	ADP
ejpam-3967	268	10	orders	order	NOUN
ejpam-3967	268	11	m	m	VERB
ejpam-3967	268	12	and	and	CCONJ
ejpam-3967	268	13	n	n	CCONJ
ejpam-3967	268	14	,	,	PUNCT
ejpam-3967	268	15	respectively	respectively	ADV
ejpam-3967	268	16	,	,	PUNCT
ejpam-3967	268	17	and	and	CCONJ
ejpam-3967	268	18	k	k	X
ejpam-3967	268	19	a	a	DET
ejpam-3967	268	20	positive	positive	ADJ
ejpam-3967	268	21	integer	integer	NOUN
ejpam-3967	268	22	with	with	ADP
ejpam-3967	268	23	k	k	PROPN
ejpam-3967	268	24	≤	≤	X
ejpam-3967	268	25	min{m	min{m	PROPN
ejpam-3967	268	26	,	,	PUNCT
ejpam-3967	268	27	n	n	CCONJ
ejpam-3967	268	28	}	}	PUNCT
ejpam-3967	268	29	.	.	PUNCT
ejpam-3967	269	1	then	then	ADV
ejpam-3967	269	2	γkftd(g	γkftd(g	PROPN
ejpam-3967	269	3	�	�	PROPN
ejpam-3967	269	4	h	h	NOUN
ejpam-3967	269	5	)	)	PUNCT
ejpam-3967	269	6	≤	≤	NOUN
ejpam-3967	269	7	min{m	min{m	PROPN
ejpam-3967	269	8	·	·	SYM
ejpam-3967	269	9	γkfd(h	γkfd(h	PROPN
ejpam-3967	269	10	)	)	PUNCT
ejpam-3967	269	11	,	,	PUNCT
ejpam-3967	269	12	n	n	PROPN
ejpam-3967	269	13	·	·	PUNCT
ejpam-3967	269	14	γkfd(g	γkfd(g	NOUN
ejpam-3967	269	15	)	)	PUNCT
ejpam-3967	269	16	}	}	PUNCT
ejpam-3967	269	17	.	.	PUNCT
ejpam-3967	270	1	remark	remark	NOUN
ejpam-3967	270	2	5	5	NUM
ejpam-3967	270	3	.	.	PUNCT
ejpam-3967	271	1	the	the	DET
ejpam-3967	271	2	bound	bind	VERB
ejpam-3967	271	3	given	give	VERB
ejpam-3967	271	4	in	in	ADP
ejpam-3967	271	5	corollary	corollary	ADJ
ejpam-3967	271	6	6	6	NUM
ejpam-3967	271	7	is	be	AUX
ejpam-3967	271	8	sharp	sharp	ADJ
ejpam-3967	271	9	.	.	PUNCT
ejpam-3967	272	1	to	to	PART
ejpam-3967	272	2	see	see	VERB
ejpam-3967	272	3	this	this	PRON
ejpam-3967	272	4	,	,	PUNCT
ejpam-3967	272	5	consider	consider	VERB
ejpam-3967	272	6	the	the	DET
ejpam-3967	272	7	graphs	graph	NOUN
ejpam-3967	272	8	shown	show	VERB
ejpam-3967	272	9	in	in	ADP
ejpam-3967	272	10	figure	figure	NOUN
ejpam-3967	272	11	4	4	NUM
ejpam-3967	272	12	.	.	PUNCT
ejpam-3967	273	1	the	the	DET
ejpam-3967	273	2	shaded	shade	VERB
ejpam-3967	273	3	vertices	vertex	NOUN
ejpam-3967	273	4	in	in	ADP
ejpam-3967	273	5	each	each	DET
ejpam-3967	273	6	graph	graph	NOUN
ejpam-3967	273	7	form	form	VERB
ejpam-3967	273	8	a	a	DET
ejpam-3967	273	9	γkftd	γkftd	NOUN
ejpam-3967	273	10	-	-	PUNCT
ejpam-3967	273	11	set	set	NOUN
ejpam-3967	273	12	.	.	PUNCT
ejpam-3967	274	1	thus	thus	ADV
ejpam-3967	274	2	,	,	PUNCT
ejpam-3967	274	3	γ1ftd(p4	γ1ftd(p4	PROPN
ejpam-3967	274	4	�	�	NOUN
ejpam-3967	274	5	c3	c3	NOUN
ejpam-3967	274	6	)	)	PUNCT
ejpam-3967	274	7	=	=	SYM
ejpam-3967	274	8	4	4	NUM
ejpam-3967	274	9	=	=	SYM
ejpam-3967	274	10	min{4	min{4	PROPN
ejpam-3967	274	11	,	,	PUNCT
ejpam-3967	274	12	6	6	NUM
ejpam-3967	274	13	}	}	PUNCT
ejpam-3967	274	14	=	=	SYM
ejpam-3967	274	15	{	{	PUNCT
ejpam-3967	274	16	4	4	NUM
ejpam-3967	274	17	·	·	SYM
ejpam-3967	274	18	1	1	NUM
ejpam-3967	274	19	,	,	PUNCT
ejpam-3967	274	20	3	3	NUM
ejpam-3967	274	21	·	·	SYM
ejpam-3967	274	22	2	2	NUM
ejpam-3967	274	23	}	}	PUNCT
ejpam-3967	274	24	=	=	SYM
ejpam-3967	274	25	min{m	min{m	PROPN
ejpam-3967	274	26	·	·	PUNCT
ejpam-3967	274	27	γ1fd(c3	γ1fd(c3	NUM
ejpam-3967	274	28	)	)	PUNCT
ejpam-3967	274	29	,	,	PUNCT
ejpam-3967	274	30	n	n	PROPN
ejpam-3967	274	31	·	·	PUNCT
ejpam-3967	274	32	γ1fd(p4	γ1fd(p4	NUM
ejpam-3967	274	33	)	)	PUNCT
ejpam-3967	274	34	}	}	PUNCT
ejpam-3967	274	35	=	=	PUNCT
ejpam-3967	274	36	m	m	PUNCT
ejpam-3967	274	37	·	·	PUNCT
ejpam-3967	274	38	γ1fd(c3	γ1fd(c3	NUM
ejpam-3967	274	39	)	)	PUNCT
ejpam-3967	274	40	,	,	PUNCT
ejpam-3967	274	41	and	and	CCONJ
ejpam-3967	274	42	γ2ftd(p5	γ2ftd(p5	PROPN
ejpam-3967	274	43	�	�	NOUN
ejpam-3967	274	44	p3	p3	NOUN
ejpam-3967	274	45	)	)	PUNCT
ejpam-3967	275	1	=	=	SYM
ejpam-3967	275	2	9	9	NUM
ejpam-3967	275	3	=	=	SYM
ejpam-3967	275	4	min{10	min{10	PROPN
ejpam-3967	275	5	,	,	PUNCT
ejpam-3967	275	6	9	9	NUM
ejpam-3967	275	7	}	}	PUNCT
ejpam-3967	275	8	=	=	SYM
ejpam-3967	275	9	{	{	PUNCT
ejpam-3967	275	10	5	5	NUM
ejpam-3967	275	11	·	·	SYM
ejpam-3967	275	12	2	2	NUM
ejpam-3967	275	13	,	,	PUNCT
ejpam-3967	275	14	3	3	NUM
ejpam-3967	275	15	·	·	SYM
ejpam-3967	275	16	3	3	X
ejpam-3967	275	17	}	}	PUNCT
ejpam-3967	275	18	=	=	SYM
ejpam-3967	275	19	min{m	min{m	PROPN
ejpam-3967	275	20	·	·	PUNCT
ejpam-3967	275	21	γ2fd(p3	γ2fd(p3	PROPN
ejpam-3967	275	22	)	)	PUNCT
ejpam-3967	275	23	,	,	PUNCT
ejpam-3967	275	24	n	n	PROPN
ejpam-3967	275	25	·	·	PUNCT
ejpam-3967	275	26	γ2fd(p5	γ2fd(p5	NUM
ejpam-3967	275	27	)	)	PUNCT
ejpam-3967	275	28	}	}	PUNCT
ejpam-3967	275	29	=	=	SYM
ejpam-3967	275	30	n	n	PROPN
ejpam-3967	275	31	·	·	PUNCT
ejpam-3967	275	32	γ2fd(p5	γ2fd(p5	NUM
ejpam-3967	275	33	)	)	PUNCT
ejpam-3967	275	34	.	.	PUNCT
ejpam-3967	276	1	references	reference	NOUN
ejpam-3967	276	2	588	588	NUM
ejpam-3967	276	3	acknowledgements	acknowledgement	NOUN
ejpam-3967	276	4	this	this	DET
ejpam-3967	276	5	research	research	NOUN
ejpam-3967	276	6	is	be	AUX
ejpam-3967	276	7	funded	fund	VERB
ejpam-3967	276	8	by	by	ADP
ejpam-3967	276	9	the	the	DET
ejpam-3967	276	10	philippine	philippine	ADJ
ejpam-3967	276	11	commission	commission	NOUN
ejpam-3967	276	12	on	on	ADP
ejpam-3967	276	13	higher	high	ADJ
ejpam-3967	276	14	education	education	NOUN
ejpam-3967	276	15	-	-	PUNCT
ejpam-3967	276	16	faculty	faculty	NOUN
ejpam-3967	276	17	development	development	NOUN
ejpam-3967	276	18	program	program	NOUN
ejpam-3967	276	19	phase	phase	PROPN
ejpam-3967	276	20	ii	ii	PROPN
ejpam-3967	276	21	,	,	PUNCT
ejpam-3967	276	22	the	the	DET
ejpam-3967	276	23	mindanao	mindanao	PROPN
ejpam-3967	276	24	state	state	PROPN
ejpam-3967	276	25	university	university	NOUN
ejpam-3967	276	26	-	-	PUNCT
ejpam-3967	276	27	main	main	ADJ
ejpam-3967	276	28	campus	campus	NOUN
ejpam-3967	276	29	,	,	PUNCT
ejpam-3967	276	30	and	and	CCONJ
ejpam-3967	276	31	the	the	DET
ejpam-3967	276	32	mindanao	mindanao	PROPN
ejpam-3967	276	33	state	state	PROPN
ejpam-3967	276	34	university	university	PROPN
ejpam-3967	276	35	-	-	PUNCT
ejpam-3967	276	36	iligan	iligan	PROPN
ejpam-3967	276	37	institute	institute	PROPN
ejpam-3967	276	38	of	of	ADP
ejpam-3967	276	39	technology	technology	PROPN
ejpam-3967	276	40	.	.	PUNCT
ejpam-3967	277	1	the	the	DET
ejpam-3967	277	2	authors	author	NOUN
ejpam-3967	277	3	wish	wish	VERB
ejpam-3967	277	4	to	to	PART
ejpam-3967	277	5	express	express	VERB
ejpam-3967	277	6	their	their	PRON
ejpam-3967	277	7	sincere	sincere	ADJ
ejpam-3967	277	8	thanks	thank	NOUN
ejpam-3967	277	9	to	to	ADP
ejpam-3967	277	10	the	the	DET
ejpam-3967	277	11	reviewers	reviewer	NOUN
ejpam-3967	277	12	for	for	ADP
ejpam-3967	277	13	their	their	PRON
ejpam-3967	277	14	valuable	valuable	ADJ
ejpam-3967	277	15	suggestions	suggestion	NOUN
ejpam-3967	277	16	for	for	ADP
ejpam-3967	277	17	the	the	DET
ejpam-3967	277	18	improvement	improvement	NOUN
ejpam-3967	277	19	of	of	ADP
ejpam-3967	277	20	this	this	DET
ejpam-3967	277	21	paper	paper	NOUN
ejpam-3967	277	22	.	.	PUNCT
ejpam-3967	278	1	references	reference	NOUN
ejpam-3967	278	2	[	[	X
ejpam-3967	278	3	1	1	NUM
ejpam-3967	278	4	]	]	PUNCT
ejpam-3967	278	5	w.	w.	PROPN
ejpam-3967	278	6	bent	bent	PROPN
ejpam-3967	278	7	-	-	PUNCT
ejpam-3967	278	8	usman	usman	PROPN
ejpam-3967	278	9	d.	d.	PROPN
ejpam-3967	278	10	gomisong	gomisong	PROPN
ejpam-3967	278	11	and	and	CCONJ
ejpam-3967	278	12	r.	r.	PROPN
ejpam-3967	278	13	isla	isla	PROPN
ejpam-3967	278	14	.	.	PUNCT
ejpam-3967	279	1	connected	connect	VERB
ejpam-3967	279	2	k	k	ADJ
ejpam-3967	279	3	-	-	PUNCT
ejpam-3967	279	4	fair	fair	ADJ
ejpam-3967	279	5	domination	domination	NOUN
ejpam-3967	279	6	in	in	ADP
ejpam-3967	279	7	the	the	DET
ejpam-3967	279	8	join	join	NOUN
ejpam-3967	279	9	,	,	PUNCT
ejpam-3967	279	10	corona	corona	PROPN
ejpam-3967	279	11	,	,	PUNCT
ejpam-3967	279	12	lexicographic	lexicographic	ADJ
ejpam-3967	279	13	and	and	CCONJ
ejpam-3967	279	14	cartesian	cartesian	ADJ
ejpam-3967	279	15	products	product	NOUN
ejpam-3967	279	16	of	of	ADP
ejpam-3967	279	17	graphs	graph	NOUN
ejpam-3967	279	18	.	.	PUNCT
ejpam-3967	280	1	applied	apply	VERB
ejpam-3967	280	2	mathematical	mathematical	ADJ
ejpam-3967	280	3	sciences	science	NOUN
ejpam-3967	280	4	,	,	PUNCT
ejpam-3967	280	5	12:1341–1355	12:1341–1355	NUM
ejpam-3967	280	6	,	,	PUNCT
ejpam-3967	280	7	2018	2018	NUM
ejpam-3967	280	8	.	.	PUNCT
ejpam-3967	281	1	[	[	X
ejpam-3967	281	2	2	2	X
ejpam-3967	281	3	]	]	X
ejpam-3967	281	4	y.	y.	PROPN
ejpam-3967	281	5	caro	caro	PROPN
ejpam-3967	281	6	a.	a.	PROPN
ejpam-3967	281	7	hansberg	hansberg	PROPN
ejpam-3967	281	8	and	and	CCONJ
ejpam-3967	281	9	m.	m.	PROPN
ejpam-3967	281	10	henning	henning	PROPN
ejpam-3967	281	11	.	.	PUNCT
ejpam-3967	282	1	fair	fair	ADJ
ejpam-3967	282	2	domination	domination	NOUN
ejpam-3967	282	3	in	in	ADP
ejpam-3967	282	4	graphs	graph	NOUN
ejpam-3967	282	5	.	.	PUNCT
ejpam-3967	283	1	discrete	discrete	ADJ
ejpam-3967	283	2	mathematics	mathematic	NOUN
ejpam-3967	283	3	,	,	PUNCT
ejpam-3967	283	4	19:1–18	19:1–18	NUM
ejpam-3967	283	5	,	,	PUNCT
ejpam-3967	283	6	2012	2012	NUM
ejpam-3967	283	7	.	.	PUNCT
ejpam-3967	284	1	[	[	X
ejpam-3967	284	2	3	3	X
ejpam-3967	284	3	]	]	PUNCT
ejpam-3967	284	4	t.	t.	PROPN
ejpam-3967	284	5	haynes	haynes	PROPN
ejpam-3967	284	6	s.	s.	PROPN
ejpam-3967	284	7	hedetniemi	hedetniemi	PROPN
ejpam-3967	284	8	and	and	CCONJ
ejpam-3967	284	9	p.	p.	PROPN
ejpam-3967	284	10	slater	slater	PROPN
ejpam-3967	284	11	.	.	PUNCT
ejpam-3967	285	1	fundamentals	fundamental	NOUN
ejpam-3967	285	2	of	of	ADP
ejpam-3967	285	3	domination	domination	NOUN
ejpam-3967	285	4	in	in	ADP
ejpam-3967	285	5	graphs	graph	NOUN
ejpam-3967	285	6	.	.	PUNCT
ejpam-3967	286	1	marcel	marcel	PROPN
ejpam-3967	286	2	dekker	dekker	PROPN
ejpam-3967	286	3	,	,	PUNCT
ejpam-3967	286	4	new	new	PROPN
ejpam-3967	286	5	york	york	PROPN
ejpam-3967	286	6	,	,	PUNCT
ejpam-3967	286	7	1998	1998	NUM
ejpam-3967	286	8	.	.	PUNCT
ejpam-3967	287	1	[	[	X
ejpam-3967	287	2	4	4	X
ejpam-3967	287	3	]	]	PUNCT
ejpam-3967	287	4	e.	e.	PROPN
ejpam-3967	287	5	maravilla	maravilla	PROPN
ejpam-3967	287	6	r.	r.	PROPN
ejpam-3967	287	7	isla	isla	PROPN
ejpam-3967	287	8	and	and	CCONJ
ejpam-3967	287	9	s.	s.	PROPN
ejpam-3967	287	10	canoy	canoy	PROPN
ejpam-3967	287	11	jr	jr	PROPN
ejpam-3967	287	12	.	.	PROPN
ejpam-3967	287	13	fair	fair	ADJ
ejpam-3967	287	14	total	total	ADJ
ejpam-3967	287	15	domination	domination	NOUN
ejpam-3967	287	16	in	in	ADP
ejpam-3967	287	17	the	the	DET
ejpam-3967	287	18	join	join	NOUN
ejpam-3967	287	19	,	,	PUNCT
ejpam-3967	287	20	corona	corona	NOUN
ejpam-3967	287	21	and	and	CCONJ
ejpam-3967	287	22	composition	composition	NOUN
ejpam-3967	287	23	of	of	ADP
ejpam-3967	287	24	graphs	graph	NOUN
ejpam-3967	287	25	.	.	PUNCT
ejpam-3967	288	1	international	international	ADJ
ejpam-3967	288	2	journal	journal	PROPN
ejpam-3967	288	3	of	of	ADP
ejpam-3967	288	4	mathematical	mathematical	ADJ
ejpam-3967	288	5	analysis	analysis	NOUN
ejpam-3967	288	6	,	,	PUNCT
ejpam-3967	288	7	8(54):2677	8(54):2677	NUM
ejpam-3967	288	8	–	–	PUNCT
ejpam-3967	288	9	2685	2685	NUM
ejpam-3967	288	10	,	,	PUNCT
ejpam-3967	288	11	2014	2014	NUM
ejpam-3967	288	12	.	.	PUNCT
ejpam-3967	289	1	[	[	X
ejpam-3967	289	2	5	5	X
ejpam-3967	289	3	]	]	PUNCT
ejpam-3967	289	4	e.	e.	PROPN
ejpam-3967	289	5	maravilla	maravilla	PROPN
ejpam-3967	289	6	r.	r.	PROPN
ejpam-3967	289	7	isla	isla	PROPN
ejpam-3967	289	8	and	and	CCONJ
ejpam-3967	289	9	s.	s.	PROPN
ejpam-3967	289	10	canoy	canoy	PROPN
ejpam-3967	289	11	jr	jr	PROPN
ejpam-3967	289	12	.	.	PUNCT
ejpam-3967	290	1	k	k	ADJ
ejpam-3967	290	2	-	-	PUNCT
ejpam-3967	290	3	fair	fair	ADJ
ejpam-3967	290	4	domination	domination	NOUN
ejpam-3967	290	5	in	in	ADP
ejpam-3967	290	6	the	the	DET
ejpam-3967	290	7	join	join	NOUN
ejpam-3967	290	8	,	,	PUNCT
ejpam-3967	290	9	corona	corona	NOUN
ejpam-3967	290	10	,	,	PUNCT
ejpam-3967	290	11	composition	composition	NOUN
ejpam-3967	290	12	and	and	CCONJ
ejpam-3967	290	13	cartesian	cartesian	ADJ
ejpam-3967	290	14	product	product	NOUN
ejpam-3967	290	15	of	of	ADP
ejpam-3967	290	16	graphs	graph	NOUN
ejpam-3967	290	17	.	.	PUNCT
ejpam-3967	291	1	applied	apply	VERB
ejpam-3967	291	2	mathematical	mathematical	ADJ
ejpam-3967	291	3	sciences	science	NOUN
ejpam-3967	291	4	,	,	PUNCT
ejpam-3967	291	5	8(178):8863	8(178):8863	NUM
ejpam-3967	291	6	–	–	PUNCT
ejpam-3967	291	7	8874	8874	NUM
ejpam-3967	291	8	,	,	PUNCT
ejpam-3967	291	9	2014	2014	NUM
ejpam-3967	291	10	.	.	PUNCT
ejpam-3967	292	1	[	[	X
ejpam-3967	292	2	6	6	NUM
ejpam-3967	292	3	]	]	PUNCT
ejpam-3967	292	4	w.	w.	PROPN
ejpam-3967	292	5	bent	bent	PROPN
ejpam-3967	292	6	-	-	PUNCT
ejpam-3967	292	7	usman	usman	PROPN
ejpam-3967	292	8	r.	r.	PROPN
ejpam-3967	292	9	isla	isla	PROPN
ejpam-3967	292	10	and	and	CCONJ
ejpam-3967	292	11	s.	s.	PROPN
ejpam-3967	292	12	canoy	canoy	PROPN
ejpam-3967	292	13	jr	jr	PROPN
ejpam-3967	292	14	.	.	PROPN
ejpam-3967	292	15	neighborhood	neighborhood	PROPN
ejpam-3967	292	16	connected	connect	VERB
ejpam-3967	292	17	k	k	ADJ
ejpam-3967	292	18	-	-	PUNCT
ejpam-3967	292	19	fair	fair	ADJ
ejpam-3967	292	20	domination	domination	NOUN
ejpam-3967	292	21	under	under	ADP
ejpam-3967	292	22	some	some	DET
ejpam-3967	292	23	binary	binary	ADJ
ejpam-3967	292	24	operations	operation	NOUN
ejpam-3967	292	25	.	.	PUNCT
ejpam-3967	293	1	european	european	ADJ
ejpam-3967	293	2	journal	journal	PROPN
ejpam-3967	293	3	of	of	ADP
ejpam-3967	293	4	pure	pure	ADJ
ejpam-3967	293	5	and	and	CCONJ
ejpam-3967	293	6	applied	applied	ADJ
ejpam-3967	293	7	mathematics	mathematic	NOUN
ejpam-3967	293	8	,	,	PUNCT
ejpam-3967	293	9	12:1337–1349	12:1337–1349	NUM
ejpam-3967	293	10	,	,	PUNCT
ejpam-3967	293	11	2019	2019	NUM
ejpam-3967	293	12	.	.	PUNCT
ejpam-3967	294	1	references	reference	NOUN
ejpam-3967	294	2	589	589	NUM
ejpam-3967	294	3	[	[	X
ejpam-3967	294	4	7	7	NUM
ejpam-3967	294	5	]	]	PUNCT
ejpam-3967	294	6	m.	m.	NOUN
ejpam-3967	294	7	ortega	ortega	PROPN
ejpam-3967	294	8	and	and	CCONJ
ejpam-3967	294	9	r.isla	r.isla	PROPN
ejpam-3967	294	10	.	.	PUNCT
ejpam-3967	295	1	semitotal	semitotal	ADJ
ejpam-3967	295	2	k	k	ADJ
ejpam-3967	295	3	-	-	PUNCT
ejpam-3967	295	4	fair	fair	ADJ
ejpam-3967	295	5	and	and	CCONJ
ejpam-3967	295	6	independent	independent	ADJ
ejpam-3967	295	7	k	k	ADJ
ejpam-3967	295	8	-	-	PUNCT
ejpam-3967	295	9	fair	fair	ADJ
ejpam-3967	295	10	domination	domination	NOUN
ejpam-3967	295	11	in	in	ADP
ejpam-3967	295	12	graphs	graph	NOUN
ejpam-3967	295	13	.	.	PUNCT
ejpam-3967	296	1	european	european	ADJ
ejpam-3967	296	2	journal	journal	PROPN
ejpam-3967	296	3	of	of	ADP
ejpam-3967	296	4	pure	pure	ADJ
ejpam-3967	296	5	and	and	CCONJ
ejpam-3967	296	6	applied	applied	ADJ
ejpam-3967	296	7	mathematics	mathematic	NOUN
ejpam-3967	296	8	,	,	PUNCT
ejpam-3967	296	9	13(4):779–793	13(4):779–793	NUM
ejpam-3967	296	10	,	,	PUNCT
ejpam-3967	296	11	2020	2020	NUM
ejpam-3967	296	12	.	.	PUNCT