id	sid	tid	token	lemma	pos
ejpam-3554	1	1	european	european	PROPN
ejpam-3554	1	2	journal	journal	PROPN
ejpam-3554	1	3	of	of	ADP
ejpam-3554	1	4	pure	pure	ADJ
ejpam-3554	1	5	and	and	CCONJ
ejpam-3554	1	6	applied	apply	VERB
ejpam-3554	1	7	mathematics	mathematic	NOUN
ejpam-3554	1	8	vol	vol	NOUN
ejpam-3554	1	9	.	.	PROPN
ejpam-3554	2	1	12	12	NUM
ejpam-3554	2	2	,	,	PUNCT
ejpam-3554	2	3	no	no	INTJ
ejpam-3554	2	4	.	.	NOUN
ejpam-3554	2	5	4	4	NUM
ejpam-3554	2	6	,	,	PUNCT
ejpam-3554	2	7	2019	2019	NUM
ejpam-3554	2	8	,	,	PUNCT
ejpam-3554	2	9	1643	1643	NUM
ejpam-3554	2	10	-	-	SYM
ejpam-3554	2	11	1655	1655	NUM
ejpam-3554	2	12	issn	issn	PROPN
ejpam-3554	2	13	1307	1307	NUM
ejpam-3554	2	14	-	-	SYM
ejpam-3554	2	15	5543	5543	NUM
ejpam-3554	2	16	–	–	PUNCT
ejpam-3554	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3554	2	18	published	publish	VERB
ejpam-3554	2	19	by	by	ADP
ejpam-3554	2	20	new	new	PROPN
ejpam-3554	2	21	york	york	PROPN
ejpam-3554	2	22	business	business	PROPN
ejpam-3554	2	23	global	global	ADJ
ejpam-3554	2	24	total	total	ADJ
ejpam-3554	2	25	partial	partial	ADJ
ejpam-3554	2	26	domination	domination	NOUN
ejpam-3554	2	27	in	in	ADP
ejpam-3554	2	28	graphs	graph	NOUN
ejpam-3554	2	29	under	under	ADP
ejpam-3554	2	30	some	some	DET
ejpam-3554	2	31	binary	binary	ADJ
ejpam-3554	2	32	operations	operation	NOUN
ejpam-3554	2	33	roselainie	roselainie	PROPN
ejpam-3554	2	34	d.	d.	PROPN
ejpam-3554	2	35	macapodi1,∗	macapodi1,∗	PROPN
ejpam-3554	2	36	,	,	PUNCT
ejpam-3554	2	37	rowena	rowena	PROPN
ejpam-3554	2	38	t.	t.	PROPN
ejpam-3554	2	39	isla2,3	isla2,3	PROPN
ejpam-3554	2	40	1	1	NUM
ejpam-3554	2	41	mathematics	mathematics	PROPN
ejpam-3554	2	42	department	department	NOUN
ejpam-3554	2	43	,	,	PUNCT
ejpam-3554	2	44	college	college	NOUN
ejpam-3554	2	45	of	of	ADP
ejpam-3554	2	46	natural	natural	ADJ
ejpam-3554	2	47	sciences	science	NOUN
ejpam-3554	2	48	and	and	CCONJ
ejpam-3554	2	49	mathematics	mathematic	NOUN
ejpam-3554	2	50	,	,	PUNCT
ejpam-3554	2	51	mindanao	mindanao	PROPN
ejpam-3554	2	52	state	state	PROPN
ejpam-3554	2	53	university	university	NOUN
ejpam-3554	2	54	-	-	PUNCT
ejpam-3554	2	55	main	main	ADJ
ejpam-3554	2	56	campus	campus	NOUN
ejpam-3554	2	57	,	,	PUNCT
ejpam-3554	2	58	9700	9700	NUM
ejpam-3554	2	59	marawi	marawi	PROPN
ejpam-3554	2	60	city	city	PROPN
ejpam-3554	2	61	,	,	PUNCT
ejpam-3554	2	62	philippines	philippines	PROPN
ejpam-3554	2	63	2	2	NUM
ejpam-3554	2	64	department	department	NOUN
ejpam-3554	2	65	of	of	ADP
ejpam-3554	2	66	mathematics	mathematic	NOUN
ejpam-3554	2	67	and	and	CCONJ
ejpam-3554	2	68	statistics	statistic	NOUN
ejpam-3554	2	69	,	,	PUNCT
ejpam-3554	2	70	college	college	NOUN
ejpam-3554	2	71	of	of	ADP
ejpam-3554	2	72	science	science	NOUN
ejpam-3554	2	73	and	and	CCONJ
ejpam-3554	2	74	mathematics	mathematic	NOUN
ejpam-3554	2	75	,	,	PUNCT
ejpam-3554	2	76	mindanao	mindanao	PROPN
ejpam-3554	2	77	state	state	PROPN
ejpam-3554	2	78	university	university	PROPN
ejpam-3554	2	79	-	-	PUNCT
ejpam-3554	2	80	iligan	iligan	PROPN
ejpam-3554	2	81	institute	institute	PROPN
ejpam-3554	2	82	of	of	ADP
ejpam-3554	2	83	technology	technology	PROPN
ejpam-3554	2	84	,	,	PUNCT
ejpam-3554	2	85	9200	9200	NUM
ejpam-3554	2	86	iligan	iligan	ADJ
ejpam-3554	2	87	city	city	NOUN
ejpam-3554	2	88	,	,	PUNCT
ejpam-3554	2	89	philippines	philippine	NOUN
ejpam-3554	2	90	3	3	NUM
ejpam-3554	2	91	center	center	NOUN
ejpam-3554	2	92	for	for	ADP
ejpam-3554	2	93	graph	graph	NOUN
ejpam-3554	2	94	theory	theory	NOUN
ejpam-3554	2	95	,	,	PUNCT
ejpam-3554	2	96	algebra	algebra	NOUN
ejpam-3554	2	97	,	,	PUNCT
ejpam-3554	2	98	and	and	CCONJ
ejpam-3554	2	99	analysis	analysis	NOUN
ejpam-3554	2	100	,	,	PUNCT
ejpam-3554	2	101	premier	premier	PROPN
ejpam-3554	2	102	research	research	PROPN
ejpam-3554	2	103	institute	institute	PROPN
ejpam-3554	2	104	of	of	ADP
ejpam-3554	2	105	science	science	NOUN
ejpam-3554	2	106	and	and	CCONJ
ejpam-3554	2	107	mathematics	mathematic	NOUN
ejpam-3554	2	108	,	,	PUNCT
ejpam-3554	2	109	mindanao	mindanao	PROPN
ejpam-3554	2	110	state	state	PROPN
ejpam-3554	2	111	university	university	PROPN
ejpam-3554	2	112	-	-	PUNCT
ejpam-3554	2	113	iligan	iligan	PROPN
ejpam-3554	2	114	institute	institute	PROPN
ejpam-3554	2	115	of	of	ADP
ejpam-3554	2	116	technology	technology	PROPN
ejpam-3554	2	117	,	,	PUNCT
ejpam-3554	2	118	9200	9200	NUM
ejpam-3554	2	119	iligan	iligan	ADJ
ejpam-3554	2	120	city	city	NOUN
ejpam-3554	2	121	,	,	PUNCT
ejpam-3554	3	1	philippines	philippine	NOUN
ejpam-3554	3	2	abstract	abstract	ADJ
ejpam-3554	3	3	.	.	PUNCT
ejpam-3554	4	1	let	let	VERB
ejpam-3554	4	2	g	g	PROPN
ejpam-3554	4	3	=	=	SYM
ejpam-3554	4	4	(	(	PUNCT
ejpam-3554	4	5	v	v	NOUN
ejpam-3554	4	6	(	(	PUNCT
ejpam-3554	4	7	g	g	NOUN
ejpam-3554	4	8	)	)	PUNCT
ejpam-3554	4	9	,	,	PUNCT
ejpam-3554	4	10	e(g	e(g	PROPN
ejpam-3554	4	11	)	)	PUNCT
ejpam-3554	4	12	)	)	PUNCT
ejpam-3554	5	1	be	be	AUX
ejpam-3554	5	2	a	a	DET
ejpam-3554	5	3	simple	simple	ADJ
ejpam-3554	5	4	graph	graph	NOUN
ejpam-3554	5	5	without	without	ADP
ejpam-3554	5	6	isolated	isolated	ADJ
ejpam-3554	5	7	vertices	vertex	NOUN
ejpam-3554	5	8	and	and	CCONJ
ejpam-3554	5	9	let	let	VERB
ejpam-3554	5	10	α	α	PRON
ejpam-3554	5	11	∈	∈	PROPN
ejpam-3554	5	12	(	(	PUNCT
ejpam-3554	5	13	0	0	NUM
ejpam-3554	5	14	,	,	PUNCT
ejpam-3554	5	15	1	1	NUM
ejpam-3554	5	16	]	]	PUNCT
ejpam-3554	5	17	.	.	PUNCT
ejpam-3554	6	1	a	a	DET
ejpam-3554	6	2	set	set	NOUN
ejpam-3554	6	3	s	s	NOUN
ejpam-3554	6	4	⊆	⊆	NUM
ejpam-3554	6	5	v	v	NOUN
ejpam-3554	6	6	(	(	PUNCT
ejpam-3554	6	7	g	g	NOUN
ejpam-3554	6	8	)	)	PUNCT
ejpam-3554	6	9	is	be	AUX
ejpam-3554	6	10	an	an	DET
ejpam-3554	6	11	α	α	NOUN
ejpam-3554	6	12	-	-	ADJ
ejpam-3554	6	13	partial	partial	ADJ
ejpam-3554	6	14	dominating	dominating	NOUN
ejpam-3554	6	15	set	set	VERB
ejpam-3554	6	16	in	in	ADP
ejpam-3554	6	17	g	g	PROPN
ejpam-3554	6	18	if	if	SCONJ
ejpam-3554	6	19	|n	|n	PRON
ejpam-3554	6	20	[	[	X
ejpam-3554	6	21	s]|	s]|	PROPN
ejpam-3554	6	22	≥	≥	NUM
ejpam-3554	6	23	α	α	PROPN
ejpam-3554	6	24	|v	|v	PROPN
ejpam-3554	6	25	(	(	PUNCT
ejpam-3554	6	26	g)|	g)|	PROPN
ejpam-3554	6	27	.	.	PUNCT
ejpam-3554	7	1	the	the	DET
ejpam-3554	7	2	smallest	small	ADJ
ejpam-3554	7	3	cardinality	cardinality	NOUN
ejpam-3554	7	4	of	of	ADP
ejpam-3554	7	5	an	an	DET
ejpam-3554	7	6	α	α	NOUN
ejpam-3554	7	7	-	-	ADJ
ejpam-3554	7	8	partial	partial	ADJ
ejpam-3554	7	9	dominating	dominating	NOUN
ejpam-3554	7	10	set	set	VERB
ejpam-3554	7	11	in	in	ADP
ejpam-3554	7	12	g	g	PROPN
ejpam-3554	7	13	is	be	AUX
ejpam-3554	7	14	called	call	VERB
ejpam-3554	7	15	the	the	DET
ejpam-3554	7	16	α	α	ADJ
ejpam-3554	7	17	-	-	ADJ
ejpam-3554	7	18	partial	partial	ADJ
ejpam-3554	7	19	domination	domination	NOUN
ejpam-3554	7	20	number	number	NOUN
ejpam-3554	7	21	of	of	ADP
ejpam-3554	7	22	g	g	NOUN
ejpam-3554	7	23	,	,	PUNCT
ejpam-3554	7	24	denoted	denote	VERB
ejpam-3554	7	25	by	by	ADP
ejpam-3554	7	26	∂α(g	∂α(g	PROPN
ejpam-3554	7	27	)	)	PUNCT
ejpam-3554	7	28	.	.	PUNCT
ejpam-3554	8	1	an	an	DET
ejpam-3554	8	2	α	α	NUM
ejpam-3554	8	3	-	-	ADJ
ejpam-3554	8	4	partial	partial	ADJ
ejpam-3554	8	5	dominating	dominating	NOUN
ejpam-3554	8	6	set	set	NOUN
ejpam-3554	8	7	s	s	PROPN
ejpam-3554	8	8	⊆	⊆	NUM
ejpam-3554	8	9	v	v	NOUN
ejpam-3554	8	10	(	(	PUNCT
ejpam-3554	8	11	g	g	NOUN
ejpam-3554	8	12	)	)	PUNCT
ejpam-3554	8	13	is	be	AUX
ejpam-3554	8	14	a	a	DET
ejpam-3554	8	15	total	total	ADJ
ejpam-3554	8	16	α	α	PRON
ejpam-3554	8	17	-	-	ADJ
ejpam-3554	8	18	partial	partial	ADJ
ejpam-3554	8	19	dominating	dominating	NOUN
ejpam-3554	8	20	set	set	VERB
ejpam-3554	8	21	in	in	ADP
ejpam-3554	8	22	g	g	PROPN
ejpam-3554	8	23	if	if	SCONJ
ejpam-3554	8	24	every	every	DET
ejpam-3554	8	25	vertex	vertex	NOUN
ejpam-3554	8	26	in	in	ADP
ejpam-3554	8	27	s	s	PROPN
ejpam-3554	8	28	is	be	AUX
ejpam-3554	8	29	adjacent	adjacent	ADJ
ejpam-3554	8	30	to	to	ADP
ejpam-3554	8	31	some	some	DET
ejpam-3554	8	32	vertex	vertex	NOUN
ejpam-3554	8	33	in	in	ADP
ejpam-3554	8	34	s.	s.	PROPN
ejpam-3554	8	35	the	the	DET
ejpam-3554	8	36	total	total	ADJ
ejpam-3554	8	37	α	α	ADJ
ejpam-3554	8	38	-	-	ADJ
ejpam-3554	8	39	partial	partial	ADJ
ejpam-3554	8	40	domination	domination	NOUN
ejpam-3554	8	41	number	number	NOUN
ejpam-3554	8	42	of	of	ADP
ejpam-3554	8	43	g	g	NOUN
ejpam-3554	8	44	,	,	PUNCT
ejpam-3554	8	45	denoted	denote	VERB
ejpam-3554	8	46	by	by	ADP
ejpam-3554	8	47	∂tα(g	∂tα(g	PROPN
ejpam-3554	8	48	)	)	PUNCT
ejpam-3554	8	49	,	,	PUNCT
ejpam-3554	8	50	is	be	AUX
ejpam-3554	8	51	the	the	DET
ejpam-3554	8	52	smallest	small	ADJ
ejpam-3554	8	53	cardinality	cardinality	NOUN
ejpam-3554	8	54	of	of	ADP
ejpam-3554	8	55	a	a	DET
ejpam-3554	8	56	total	total	ADJ
ejpam-3554	8	57	α	α	PRON
ejpam-3554	8	58	-	-	ADJ
ejpam-3554	8	59	partial	partial	ADJ
ejpam-3554	8	60	dominating	dominating	NOUN
ejpam-3554	8	61	set	set	VERB
ejpam-3554	8	62	in	in	ADP
ejpam-3554	8	63	g.	g.	PROPN
ejpam-3554	8	64	in	in	ADP
ejpam-3554	8	65	this	this	DET
ejpam-3554	8	66	paper	paper	NOUN
ejpam-3554	8	67	,	,	PUNCT
ejpam-3554	8	68	we	we	PRON
ejpam-3554	8	69	characterize	characterize	VERB
ejpam-3554	8	70	the	the	DET
ejpam-3554	8	71	total	total	ADJ
ejpam-3554	8	72	partial	partial	ADJ
ejpam-3554	8	73	dominating	dominating	NOUN
ejpam-3554	8	74	sets	set	NOUN
ejpam-3554	8	75	in	in	ADP
ejpam-3554	8	76	the	the	DET
ejpam-3554	8	77	join	join	NOUN
ejpam-3554	8	78	,	,	PUNCT
ejpam-3554	8	79	corona	corona	PROPN
ejpam-3554	8	80	,	,	PUNCT
ejpam-3554	8	81	lexicographic	lexicographic	ADJ
ejpam-3554	8	82	product	product	NOUN
ejpam-3554	8	83	and	and	CCONJ
ejpam-3554	8	84	cartesian	cartesian	ADJ
ejpam-3554	8	85	product	product	NOUN
ejpam-3554	8	86	of	of	ADP
ejpam-3554	8	87	graphs	graph	NOUN
ejpam-3554	8	88	and	and	CCONJ
ejpam-3554	8	89	determine	determine	VERB
ejpam-3554	8	90	the	the	DET
ejpam-3554	8	91	exact	exact	ADJ
ejpam-3554	8	92	values	value	NOUN
ejpam-3554	8	93	or	or	CCONJ
ejpam-3554	8	94	sharp	sharp	ADJ
ejpam-3554	8	95	bounds	bound	NOUN
ejpam-3554	8	96	of	of	ADP
ejpam-3554	8	97	the	the	DET
ejpam-3554	8	98	corresponding	corresponding	ADJ
ejpam-3554	8	99	total	total	ADJ
ejpam-3554	8	100	partial	partial	ADJ
ejpam-3554	8	101	domination	domination	NOUN
ejpam-3554	8	102	number	number	NOUN
ejpam-3554	8	103	of	of	ADP
ejpam-3554	8	104	these	these	DET
ejpam-3554	8	105	graphs	graph	NOUN
ejpam-3554	8	106	.	.	PUNCT
ejpam-3554	9	1	2010	2010	NUM
ejpam-3554	9	2	mathematics	mathematic	NOUN
ejpam-3554	9	3	subject	subject	NOUN
ejpam-3554	9	4	classifications	classification	NOUN
ejpam-3554	9	5	:	:	PUNCT
ejpam-3554	9	6	05c69	05c69	NUM
ejpam-3554	9	7	,	,	PUNCT
ejpam-3554	9	8	05c76	05c76	DET
ejpam-3554	9	9	key	key	ADJ
ejpam-3554	9	10	words	word	NOUN
ejpam-3554	9	11	and	and	CCONJ
ejpam-3554	9	12	phrases	phrase	NOUN
ejpam-3554	9	13	:	:	PUNCT
ejpam-3554	9	14	partial	partial	ADJ
ejpam-3554	9	15	domination	domination	NOUN
ejpam-3554	9	16	,	,	PUNCT
ejpam-3554	9	17	total	total	ADJ
ejpam-3554	9	18	partial	partial	ADJ
ejpam-3554	9	19	domination	domination	NOUN
ejpam-3554	9	20	,	,	PUNCT
ejpam-3554	9	21	join	join	NOUN
ejpam-3554	9	22	,	,	PUNCT
ejpam-3554	9	23	corona	corona	PROPN
ejpam-3554	9	24	,	,	PUNCT
ejpam-3554	9	25	lexicographic	lexicographic	ADJ
ejpam-3554	9	26	product	product	NOUN
ejpam-3554	9	27	,	,	PUNCT
ejpam-3554	9	28	cartesian	cartesian	ADJ
ejpam-3554	9	29	product	product	NOUN
ejpam-3554	9	30	1	1	NUM
ejpam-3554	9	31	.	.	PUNCT
ejpam-3554	10	1	introduction	introduction	NOUN
ejpam-3554	10	2	let	let	VERB
ejpam-3554	10	3	g	g	NOUN
ejpam-3554	10	4	=	=	SYM
ejpam-3554	10	5	(	(	PUNCT
ejpam-3554	10	6	v	v	NOUN
ejpam-3554	10	7	(	(	PUNCT
ejpam-3554	10	8	g	g	NOUN
ejpam-3554	10	9	)	)	PUNCT
ejpam-3554	10	10	,	,	PUNCT
ejpam-3554	10	11	e(g	e(g	PROPN
ejpam-3554	10	12	)	)	PUNCT
ejpam-3554	10	13	)	)	PUNCT
ejpam-3554	10	14	be	be	AUX
ejpam-3554	10	15	a	a	DET
ejpam-3554	10	16	simple	simple	ADJ
ejpam-3554	10	17	graph	graph	NOUN
ejpam-3554	10	18	and	and	CCONJ
ejpam-3554	10	19	v	v	ADP
ejpam-3554	10	20	∈	∈	PROPN
ejpam-3554	10	21	v	v	NOUN
ejpam-3554	10	22	(	(	PUNCT
ejpam-3554	10	23	g	g	NOUN
ejpam-3554	10	24	)	)	PUNCT
ejpam-3554	10	25	.	.	PUNCT
ejpam-3554	11	1	the	the	DET
ejpam-3554	11	2	open	open	ADJ
ejpam-3554	11	3	neighborhood	neighborhood	NOUN
ejpam-3554	11	4	of	of	ADP
ejpam-3554	11	5	v	v	NOUN
ejpam-3554	11	6	in	in	ADP
ejpam-3554	11	7	g	g	PROPN
ejpam-3554	11	8	is	be	AUX
ejpam-3554	11	9	the	the	DET
ejpam-3554	11	10	set	set	NOUN
ejpam-3554	11	11	ng(v	ng(v	PUNCT
ejpam-3554	11	12	)	)	PUNCT
ejpam-3554	11	13	=	=	SYM
ejpam-3554	12	1	{	{	PUNCT
ejpam-3554	12	2	u	u	NOUN
ejpam-3554	12	3	∈	∈	PROPN
ejpam-3554	12	4	v	v	NOUN
ejpam-3554	12	5	(	(	PUNCT
ejpam-3554	12	6	g	g	NOUN
ejpam-3554	12	7	)	)	PUNCT
ejpam-3554	12	8	:	:	PUNCT
ejpam-3554	12	9	uv	uv	PROPN
ejpam-3554	12	10	∈	∈	PROPN
ejpam-3554	12	11	e(g	e(g	PROPN
ejpam-3554	12	12	)	)	PUNCT
ejpam-3554	12	13	}	}	PUNCT
ejpam-3554	12	14	and	and	CCONJ
ejpam-3554	12	15	the	the	DET
ejpam-3554	12	16	closed	closed	ADJ
ejpam-3554	12	17	neighborhood	neighborhood	NOUN
ejpam-3554	12	18	of	of	ADP
ejpam-3554	12	19	v	v	NOUN
ejpam-3554	12	20	is	be	AUX
ejpam-3554	12	21	the	the	DET
ejpam-3554	12	22	set	set	NOUN
ejpam-3554	12	23	ng[v	ng[v	NOUN
ejpam-3554	12	24	]	]	X
ejpam-3554	12	25	=	=	SYM
ejpam-3554	12	26	ng(v	ng(v	X
ejpam-3554	12	27	)	)	PUNCT
ejpam-3554	12	28	∪	∪	ADP
ejpam-3554	12	29	{	{	PUNCT
ejpam-3554	12	30	v	v	NOUN
ejpam-3554	12	31	}	}	PUNCT
ejpam-3554	12	32	.	.	PUNCT
ejpam-3554	13	1	for	for	ADP
ejpam-3554	13	2	x	x	SYM
ejpam-3554	13	3	⊆	⊆	NUM
ejpam-3554	13	4	v	v	ADP
ejpam-3554	13	5	(	(	PUNCT
ejpam-3554	13	6	g	g	NOUN
ejpam-3554	13	7	)	)	PUNCT
ejpam-3554	13	8	,	,	PUNCT
ejpam-3554	13	9	the	the	DET
ejpam-3554	13	10	open	open	ADJ
ejpam-3554	13	11	neighborhood	neighborhood	NOUN
ejpam-3554	13	12	of	of	ADP
ejpam-3554	13	13	x	x	PUNCT
ejpam-3554	13	14	in	in	ADP
ejpam-3554	13	15	g	g	PROPN
ejpam-3554	13	16	is	be	AUX
ejpam-3554	13	17	the	the	DET
ejpam-3554	13	18	set	set	NOUN
ejpam-3554	13	19	ng(x	ng(x	NUM
ejpam-3554	13	20	)	)	PUNCT
ejpam-3554	13	21	=	=	SYM
ejpam-3554	13	22	n(x	n(x	X
ejpam-3554	13	23	)	)	PUNCT
ejpam-3554	13	24	=	=	SYM
ejpam-3554	14	1	⋃	⋃	NOUN
ejpam-3554	14	2	v∈x	v∈x	NOUN
ejpam-3554	14	3	ng(v	ng(v	PUNCT
ejpam-3554	14	4	)	)	PUNCT
ejpam-3554	14	5	and	and	CCONJ
ejpam-3554	14	6	its	its	PRON
ejpam-3554	14	7	closed	closed	ADJ
ejpam-3554	14	8	neighborhood	neighborhood	NOUN
ejpam-3554	14	9	is	be	AUX
ejpam-3554	14	10	the	the	DET
ejpam-3554	14	11	set	set	NOUN
ejpam-3554	14	12	ng[x	ng[x	PROPN
ejpam-3554	14	13	]	]	X
ejpam-3554	14	14	=	=	SYM
ejpam-3554	15	1	n	n	PROPN
ejpam-3554	15	2	[	[	X
ejpam-3554	15	3	x	x	X
ejpam-3554	15	4	]	]	X
ejpam-3554	15	5	=	=	SYM
ejpam-3554	15	6	n(x	n(x	X
ejpam-3554	15	7	)	)	PUNCT
ejpam-3554	15	8	∪	∪	ADP
ejpam-3554	15	9	x.	x.	NOUN
ejpam-3554	15	10	a	a	DET
ejpam-3554	15	11	set	set	NOUN
ejpam-3554	16	1	d	d	NOUN
ejpam-3554	16	2	⊆	⊆	NUM
ejpam-3554	16	3	v	v	ADP
ejpam-3554	16	4	(	(	PUNCT
ejpam-3554	16	5	g	g	NOUN
ejpam-3554	16	6	)	)	PUNCT
ejpam-3554	16	7	is	be	AUX
ejpam-3554	16	8	a	a	DET
ejpam-3554	16	9	dominating	dominating	NOUN
ejpam-3554	16	10	set	set	VERB
ejpam-3554	16	11	in	in	ADP
ejpam-3554	16	12	g	g	PROPN
ejpam-3554	16	13	if	if	SCONJ
ejpam-3554	16	14	for	for	ADP
ejpam-3554	16	15	every	every	DET
ejpam-3554	16	16	v	v	NUM
ejpam-3554	16	17	∈	∈	NOUN
ejpam-3554	16	18	v	v	NOUN
ejpam-3554	16	19	(	(	PUNCT
ejpam-3554	16	20	g)\d	g)\d	NOUN
ejpam-3554	16	21	,	,	PUNCT
ejpam-3554	16	22	there	there	PRON
ejpam-3554	16	23	exists	exist	VERB
ejpam-3554	16	24	u	u	NOUN
ejpam-3554	16	25	∈	∈	PROPN
ejpam-3554	16	26	d	d	ADP
ejpam-3554	16	27	such	such	ADJ
ejpam-3554	16	28	that	that	DET
ejpam-3554	16	29	uv	uv	PROPN
ejpam-3554	16	30	∈	∈	PROPN
ejpam-3554	16	31	e(g	e(g	PROPN
ejpam-3554	16	32	)	)	PUNCT
ejpam-3554	16	33	,	,	PUNCT
ejpam-3554	16	34	that	that	ADV
ejpam-3554	16	35	is	is	ADV
ejpam-3554	16	36	,	,	PUNCT
ejpam-3554	16	37	n	n	PROPN
ejpam-3554	16	38	[	[	X
ejpam-3554	16	39	d]=	d]=	PROPN
ejpam-3554	16	40	v	v	X
ejpam-3554	16	41	(	(	PUNCT
ejpam-3554	16	42	g	g	NOUN
ejpam-3554	16	43	)	)	PUNCT
ejpam-3554	16	44	.	.	PUNCT
ejpam-3554	17	1	the	the	DET
ejpam-3554	17	2	minimum	minimum	ADJ
ejpam-3554	17	3	cardinality	cardinality	NOUN
ejpam-3554	17	4	of	of	ADP
ejpam-3554	17	5	a	a	DET
ejpam-3554	17	6	dominating	dominating	NOUN
ejpam-3554	17	7	set	set	NOUN
ejpam-3554	17	8	in	in	ADP
ejpam-3554	17	9	g	g	NOUN
ejpam-3554	17	10	,	,	PUNCT
ejpam-3554	17	11	denoted	denote	VERB
ejpam-3554	17	12	by	by	ADP
ejpam-3554	17	13	γ(g	γ(g	PROPN
ejpam-3554	17	14	)	)	PUNCT
ejpam-3554	17	15	,	,	PUNCT
ejpam-3554	17	16	is	be	AUX
ejpam-3554	17	17	the	the	DET
ejpam-3554	17	18	domination	domination	NOUN
ejpam-3554	17	19	number	number	NOUN
ejpam-3554	17	20	of	of	ADP
ejpam-3554	17	21	∗corresponding	∗corresponde	VERB
ejpam-3554	17	22	author	author	NOUN
ejpam-3554	17	23	.	.	PUNCT
ejpam-3554	18	1	doi	doi	NOUN
ejpam-3554	18	2	:	:	PUNCT
ejpam-3554	18	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3554	https://doi.org/10.29020/nybg.ejpam.v12i4.3554	PROPN
ejpam-3554	18	4	email	email	NOUN
ejpam-3554	18	5	addresses	address	NOUN
ejpam-3554	18	6	:	:	PUNCT
ejpam-3554	19	1	macapodiroselainie@gmail.com	macapodiroselainie@gmail.com	X
ejpam-3554	19	2	(	(	PUNCT
ejpam-3554	19	3	r.	r.	PROPN
ejpam-3554	19	4	macapodi	macapodi	PROPN
ejpam-3554	19	5	)	)	PUNCT
ejpam-3554	19	6	rowena.isla@g.msuiit.edu.ph	rowena.isla@g.msuiit.edu.ph	PROPN
ejpam-3554	19	7	(	(	PUNCT
ejpam-3554	19	8	r.	r.	PROPN
ejpam-3554	19	9	isla	isla	PROPN
ejpam-3554	19	10	)	)	PUNCT
ejpam-3554	19	11	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3554	20	1	1643	1643	NUM
ejpam-3554	21	1	c	c	NOUN
ejpam-3554	21	2	©	©	PROPN
ejpam-3554	21	3	2019	2019	NUM
ejpam-3554	21	4	ejpam	ejpam	NOUN
ejpam-3554	21	5	all	all	DET
ejpam-3554	21	6	rights	right	NOUN
ejpam-3554	21	7	reserved	reserve	VERB
ejpam-3554	21	8	.	.	PUNCT
ejpam-3554	22	1	r.	r.	PROPN
ejpam-3554	22	2	macapodi	macapodi	PROPN
ejpam-3554	22	3	,	,	PUNCT
ejpam-3554	22	4	r.	r.	PROPN
ejpam-3554	22	5	isla	isla	PROPN
ejpam-3554	22	6	/	/	SYM
ejpam-3554	22	7	eur	eur	PROPN
ejpam-3554	22	8	.	.	PUNCT
ejpam-3554	23	1	j.	j.	PROPN
ejpam-3554	23	2	pure	pure	PROPN
ejpam-3554	23	3	appl	appl	PROPN
ejpam-3554	23	4	.	.	PROPN
ejpam-3554	23	5	math	math	PROPN
ejpam-3554	23	6	,	,	PUNCT
ejpam-3554	23	7	12	12	NUM
ejpam-3554	23	8	(	(	PUNCT
ejpam-3554	23	9	4	4	NUM
ejpam-3554	23	10	)	)	PUNCT
ejpam-3554	23	11	(	(	PUNCT
ejpam-3554	23	12	2019	2019	NUM
ejpam-3554	23	13	)	)	PUNCT
ejpam-3554	23	14	,	,	PUNCT
ejpam-3554	23	15	1643	1643	NUM
ejpam-3554	23	16	-	-	SYM
ejpam-3554	23	17	1655	1655	NUM
ejpam-3554	23	18	1644	1644	NUM
ejpam-3554	23	19	g.	g.	NOUN
ejpam-3554	24	1	any	any	DET
ejpam-3554	24	2	dominating	dominating	NOUN
ejpam-3554	24	3	set	set	VERB
ejpam-3554	24	4	in	in	ADP
ejpam-3554	24	5	g	g	PROPN
ejpam-3554	24	6	of	of	ADP
ejpam-3554	24	7	cardinality	cardinality	PROPN
ejpam-3554	24	8	γ(g	γ(g	PROPN
ejpam-3554	24	9	)	)	PUNCT
ejpam-3554	24	10	is	be	AUX
ejpam-3554	24	11	referred	refer	VERB
ejpam-3554	24	12	to	to	ADP
ejpam-3554	24	13	as	as	ADP
ejpam-3554	24	14	a	a	DET
ejpam-3554	24	15	γ	γ	NOUN
ejpam-3554	24	16	-	-	PUNCT
ejpam-3554	24	17	set	set	VERB
ejpam-3554	24	18	in	in	ADP
ejpam-3554	24	19	g.	g.	PROPN
ejpam-3554	24	20	let	let	VERB
ejpam-3554	24	21	g	g	NOUN
ejpam-3554	24	22	be	be	AUX
ejpam-3554	24	23	a	a	DET
ejpam-3554	24	24	graph	graph	NOUN
ejpam-3554	24	25	without	without	ADP
ejpam-3554	24	26	isolated	isolated	ADJ
ejpam-3554	24	27	vertices	vertex	NOUN
ejpam-3554	24	28	.	.	PUNCT
ejpam-3554	25	1	a	a	DET
ejpam-3554	25	2	set	set	NOUN
ejpam-3554	25	3	t	t	PROPN
ejpam-3554	25	4	⊆	⊆	NUM
ejpam-3554	25	5	v	v	NOUN
ejpam-3554	25	6	(	(	PUNCT
ejpam-3554	25	7	g	g	NOUN
ejpam-3554	25	8	)	)	PUNCT
ejpam-3554	25	9	is	be	AUX
ejpam-3554	25	10	a	a	DET
ejpam-3554	25	11	total	total	ADJ
ejpam-3554	25	12	dominating	dominating	NOUN
ejpam-3554	25	13	set	set	VERB
ejpam-3554	25	14	in	in	ADP
ejpam-3554	25	15	g	g	PROPN
ejpam-3554	25	16	if	if	SCONJ
ejpam-3554	25	17	n(t	n(t	PROPN
ejpam-3554	25	18	)	)	PUNCT
ejpam-3554	26	1	=	=	SYM
ejpam-3554	26	2	v	v	X
ejpam-3554	26	3	(	(	PUNCT
ejpam-3554	26	4	g	g	NOUN
ejpam-3554	26	5	)	)	PUNCT
ejpam-3554	26	6	.	.	PUNCT
ejpam-3554	27	1	the	the	DET
ejpam-3554	27	2	total	total	ADJ
ejpam-3554	27	3	domination	domination	NOUN
ejpam-3554	27	4	number	number	NOUN
ejpam-3554	27	5	γt(g	γt(g	PUNCT
ejpam-3554	27	6	)	)	PUNCT
ejpam-3554	27	7	of	of	ADP
ejpam-3554	27	8	g	g	PROPN
ejpam-3554	27	9	is	be	AUX
ejpam-3554	27	10	the	the	DET
ejpam-3554	27	11	minimum	minimum	ADJ
ejpam-3554	27	12	cardinality	cardinality	NOUN
ejpam-3554	27	13	of	of	ADP
ejpam-3554	27	14	a	a	DET
ejpam-3554	27	15	total	total	ADJ
ejpam-3554	27	16	dominating	dominating	NOUN
ejpam-3554	27	17	set	set	VERB
ejpam-3554	27	18	in	in	ADP
ejpam-3554	27	19	g.	g.	PROPN
ejpam-3554	27	20	dominating	dominating	NOUN
ejpam-3554	27	21	sets	set	NOUN
ejpam-3554	27	22	are	be	AUX
ejpam-3554	27	23	important	important	ADJ
ejpam-3554	27	24	in	in	ADP
ejpam-3554	27	25	a	a	DET
ejpam-3554	27	26	wide	wide	ADJ
ejpam-3554	27	27	range	range	NOUN
ejpam-3554	27	28	of	of	ADP
ejpam-3554	27	29	applications	application	NOUN
ejpam-3554	27	30	where	where	SCONJ
ejpam-3554	27	31	some	some	DET
ejpam-3554	27	32	level	level	NOUN
ejpam-3554	27	33	of	of	ADP
ejpam-3554	27	34	service	service	NOUN
ejpam-3554	27	35	or	or	CCONJ
ejpam-3554	27	36	resource	resource	NOUN
ejpam-3554	27	37	must	must	AUX
ejpam-3554	27	38	be	be	AUX
ejpam-3554	27	39	provided	provide	VERB
ejpam-3554	27	40	to	to	ADP
ejpam-3554	27	41	each	each	DET
ejpam-3554	27	42	member	member	NOUN
ejpam-3554	27	43	of	of	ADP
ejpam-3554	27	44	a	a	DET
ejpam-3554	27	45	network	network	NOUN
ejpam-3554	27	46	.	.	PUNCT
ejpam-3554	28	1	however	however	ADV
ejpam-3554	28	2	,	,	PUNCT
ejpam-3554	28	3	considerations	consideration	NOUN
ejpam-3554	28	4	of	of	ADP
ejpam-3554	28	5	scarcity	scarcity	NOUN
ejpam-3554	28	6	of	of	ADP
ejpam-3554	28	7	resources	resource	NOUN
ejpam-3554	28	8	,	,	PUNCT
ejpam-3554	28	9	practicality	practicality	NOUN
ejpam-3554	28	10	,	,	PUNCT
ejpam-3554	28	11	or	or	CCONJ
ejpam-3554	28	12	profitability	profitability	NOUN
ejpam-3554	28	13	may	may	AUX
ejpam-3554	28	14	lead	lead	VERB
ejpam-3554	28	15	to	to	ADP
ejpam-3554	28	16	a	a	DET
ejpam-3554	28	17	necessity	necessity	NOUN
ejpam-3554	28	18	for	for	ADP
ejpam-3554	28	19	less	less	ADJ
ejpam-3554	28	20	than	than	ADP
ejpam-3554	28	21	complete	complete	ADJ
ejpam-3554	28	22	coverage	coverage	NOUN
ejpam-3554	28	23	of	of	ADP
ejpam-3554	28	24	the	the	DET
ejpam-3554	28	25	nodes	node	NOUN
ejpam-3554	28	26	in	in	ADP
ejpam-3554	28	27	a	a	DET
ejpam-3554	28	28	network	network	NOUN
ejpam-3554	28	29	.	.	PUNCT
ejpam-3554	29	1	this	this	PRON
ejpam-3554	29	2	gives	give	VERB
ejpam-3554	29	3	rise	rise	NOUN
ejpam-3554	29	4	to	to	ADP
ejpam-3554	29	5	the	the	DET
ejpam-3554	29	6	notion	notion	NOUN
ejpam-3554	29	7	of	of	ADP
ejpam-3554	29	8	partial	partial	ADJ
ejpam-3554	29	9	domination	domination	NOUN
ejpam-3554	29	10	in	in	ADP
ejpam-3554	29	11	graphs	graph	NOUN
ejpam-3554	29	12	[	[	X
ejpam-3554	29	13	1	1	NUM
ejpam-3554	29	14	]	]	PUNCT
ejpam-3554	29	15	.	.	PUNCT
ejpam-3554	30	1	for	for	ADP
ejpam-3554	30	2	any	any	DET
ejpam-3554	30	3	simple	simple	ADJ
ejpam-3554	30	4	graph	graph	NOUN
ejpam-3554	30	5	g	g	NOUN
ejpam-3554	30	6	and	and	CCONJ
ejpam-3554	30	7	an	an	DET
ejpam-3554	30	8	α	α	NOUN
ejpam-3554	30	9	∈	∈	PROPN
ejpam-3554	30	10	(	(	PUNCT
ejpam-3554	30	11	0	0	NUM
ejpam-3554	30	12	,	,	PUNCT
ejpam-3554	30	13	1	1	NUM
ejpam-3554	30	14	]	]	PUNCT
ejpam-3554	30	15	,	,	PUNCT
ejpam-3554	30	16	a	a	DET
ejpam-3554	30	17	set	set	NOUN
ejpam-3554	30	18	s	s	NOUN
ejpam-3554	30	19	⊆	⊆	NUM
ejpam-3554	30	20	v	v	NOUN
ejpam-3554	30	21	(	(	PUNCT
ejpam-3554	30	22	g	g	NOUN
ejpam-3554	30	23	)	)	PUNCT
ejpam-3554	30	24	is	be	AUX
ejpam-3554	30	25	an	an	DET
ejpam-3554	30	26	α	α	NOUN
ejpam-3554	30	27	-	-	ADJ
ejpam-3554	30	28	partial	partial	ADJ
ejpam-3554	30	29	dominating	dominating	NOUN
ejpam-3554	30	30	set	set	VERB
ejpam-3554	30	31	in	in	ADP
ejpam-3554	30	32	g	g	PROPN
ejpam-3554	30	33	if	if	SCONJ
ejpam-3554	30	34	|n	|n	PRON
ejpam-3554	30	35	[	[	X
ejpam-3554	30	36	s]|	s]|	PROPN
ejpam-3554	30	37	≥	≥	NUM
ejpam-3554	30	38	α	α	PROPN
ejpam-3554	30	39	|v	|v	PROPN
ejpam-3554	30	40	(	(	PUNCT
ejpam-3554	30	41	g)|	g)|	NOUN
ejpam-3554	30	42	.	.	PUNCT
ejpam-3554	31	1	case	case	NOUN
ejpam-3554	31	2	et	et	PROPN
ejpam-3554	31	3	al	al	PROPN
ejpam-3554	31	4	.	.	PUNCT
ejpam-3554	32	1	[	[	X
ejpam-3554	32	2	1	1	X
ejpam-3554	32	3	]	]	PUNCT
ejpam-3554	32	4	and	and	CCONJ
ejpam-3554	32	5	das	das	PROPN
ejpam-3554	32	6	[	[	X
ejpam-3554	32	7	2	2	NUM
ejpam-3554	32	8	]	]	PUNCT
ejpam-3554	32	9	independently	independently	ADV
ejpam-3554	32	10	worked	work	VERB
ejpam-3554	32	11	on	on	ADP
ejpam-3554	32	12	α	α	ADJ
ejpam-3554	32	13	-	-	ADJ
ejpam-3554	32	14	partial	partial	ADJ
ejpam-3554	32	15	domination	domination	NOUN
ejpam-3554	32	16	in	in	ADP
ejpam-3554	32	17	graphs	graph	NOUN
ejpam-3554	32	18	in	in	ADP
ejpam-3554	32	19	2017	2017	NUM
ejpam-3554	32	20	.	.	PUNCT
ejpam-3554	33	1	case	case	NOUN
ejpam-3554	33	2	et	et	PROPN
ejpam-3554	33	3	al	al	PROPN
ejpam-3554	33	4	.	.	PROPN
ejpam-3554	33	5	focused	focus	VERB
ejpam-3554	33	6	on	on	ADP
ejpam-3554	33	7	α	α	NOUN
ejpam-3554	33	8	=	=	SYM
ejpam-3554	33	9	1	1	NUM
ejpam-3554	33	10	2	2	NUM
ejpam-3554	33	11	while	while	SCONJ
ejpam-3554	33	12	das	das	PROPN
ejpam-3554	33	13	dealt	deal	VERB
ejpam-3554	33	14	with	with	ADP
ejpam-3554	33	15	general	general	ADJ
ejpam-3554	33	16	values	value	NOUN
ejpam-3554	33	17	of	of	ADP
ejpam-3554	33	18	α	α	PRON
ejpam-3554	33	19	∈	∈	PROPN
ejpam-3554	33	20	(	(	PUNCT
ejpam-3554	33	21	0	0	NUM
ejpam-3554	33	22	,	,	PUNCT
ejpam-3554	33	23	1	1	NUM
ejpam-3554	33	24	]	]	PUNCT
ejpam-3554	33	25	.	.	PUNCT
ejpam-3554	34	1	the	the	DET
ejpam-3554	34	2	α	α	NOUN
ejpam-3554	34	3	-	-	ADJ
ejpam-3554	34	4	partial	partial	ADJ
ejpam-3554	34	5	domination	domination	NOUN
ejpam-3554	34	6	number	number	NOUN
ejpam-3554	34	7	∂α(g	∂α(g	PROPN
ejpam-3554	34	8	)	)	PUNCT
ejpam-3554	34	9	is	be	AUX
ejpam-3554	34	10	the	the	DET
ejpam-3554	34	11	minimum	minimum	ADJ
ejpam-3554	34	12	cardinality	cardinality	NOUN
ejpam-3554	34	13	of	of	ADP
ejpam-3554	34	14	an	an	DET
ejpam-3554	34	15	α	α	NOUN
ejpam-3554	34	16	-	-	ADJ
ejpam-3554	34	17	partial	partial	ADJ
ejpam-3554	34	18	dominating	dominating	NOUN
ejpam-3554	34	19	set	set	VERB
ejpam-3554	34	20	in	in	ADP
ejpam-3554	34	21	g.	g.	PROPN
ejpam-3554	34	22	∂α(g	∂α(g	PROPN
ejpam-3554	34	23	)	)	PUNCT
ejpam-3554	34	24	is	be	AUX
ejpam-3554	34	25	denoted	denote	VERB
ejpam-3554	34	26	by	by	ADP
ejpam-3554	34	27	pdα(g	pdα(g	PROPN
ejpam-3554	34	28	)	)	PUNCT
ejpam-3554	34	29	in	in	ADP
ejpam-3554	34	30	das	das	PROPN
ejpam-3554	35	1	[	[	X
ejpam-3554	35	2	2	2	NUM
ejpam-3554	35	3	]	]	PUNCT
ejpam-3554	35	4	and	and	CCONJ
ejpam-3554	35	5	by	by	ADP
ejpam-3554	35	6	γ	γ	PROPN
ejpam-3554	35	7	1	1	NUM
ejpam-3554	35	8	2	2	NUM
ejpam-3554	35	9	(	(	PUNCT
ejpam-3554	35	10	g	g	NOUN
ejpam-3554	35	11	)	)	PUNCT
ejpam-3554	35	12	in	in	ADP
ejpam-3554	35	13	case	case	NOUN
ejpam-3554	35	14	et	et	NOUN
ejpam-3554	35	15	al	al	PROPN
ejpam-3554	35	16	.	.	PUNCT
ejpam-3554	36	1	[	[	X
ejpam-3554	36	2	1	1	X
ejpam-3554	36	3	]	]	PUNCT
ejpam-3554	36	4	when	when	SCONJ
ejpam-3554	36	5	α	α	PROPN
ejpam-3554	36	6	=	=	NOUN
ejpam-3554	36	7	1	1	NUM
ejpam-3554	36	8	2	2	NUM
ejpam-3554	36	9	.	.	PUNCT
ejpam-3554	37	1	an	an	DET
ejpam-3554	37	2	α	α	NOUN
ejpam-3554	37	3	-	-	ADJ
ejpam-3554	37	4	partial	partial	ADJ
ejpam-3554	37	5	dominating	dominating	NOUN
ejpam-3554	37	6	set	set	NOUN
ejpam-3554	37	7	s	s	VERB
ejpam-3554	37	8	in	in	ADP
ejpam-3554	37	9	g	g	NOUN
ejpam-3554	37	10	with	with	ADP
ejpam-3554	37	11	|s|	|s|	NOUN
ejpam-3554	37	12	=	=	SYM
ejpam-3554	37	13	∂α(g	∂α(g	PROPN
ejpam-3554	37	14	)	)	PUNCT
ejpam-3554	37	15	is	be	AUX
ejpam-3554	37	16	referred	refer	VERB
ejpam-3554	37	17	to	to	ADP
ejpam-3554	37	18	as	as	ADP
ejpam-3554	37	19	an	an	DET
ejpam-3554	37	20	∂α	∂α	PROPN
ejpam-3554	37	21	-	-	PUNCT
ejpam-3554	37	22	set	set	VERB
ejpam-3554	37	23	in	in	ADP
ejpam-3554	37	24	g.	g.	PROPN
ejpam-3554	37	25	case	case	NOUN
ejpam-3554	37	26	et	et	PROPN
ejpam-3554	37	27	al	al	PROPN
ejpam-3554	37	28	.	.	PUNCT
ejpam-3554	38	1	[	[	X
ejpam-3554	38	2	1	1	X
ejpam-3554	38	3	]	]	PUNCT
ejpam-3554	38	4	investigated	investigate	VERB
ejpam-3554	38	5	the	the	DET
ejpam-3554	38	6	partial	partial	ADJ
ejpam-3554	38	7	domination	domination	NOUN
ejpam-3554	38	8	number	number	NOUN
ejpam-3554	38	9	of	of	ADP
ejpam-3554	38	10	some	some	DET
ejpam-3554	38	11	special	special	ADJ
ejpam-3554	38	12	graphs	graph	NOUN
ejpam-3554	38	13	and	and	CCONJ
ejpam-3554	38	14	presented	present	VERB
ejpam-3554	38	15	some	some	DET
ejpam-3554	38	16	bounds	bound	NOUN
ejpam-3554	38	17	of	of	ADP
ejpam-3554	38	18	the	the	DET
ejpam-3554	38	19	said	say	VERB
ejpam-3554	38	20	parameter	parameter	NOUN
ejpam-3554	38	21	.	.	PUNCT
ejpam-3554	39	1	das	das	PROPN
ejpam-3554	40	1	[	[	X
ejpam-3554	40	2	2	2	NUM
ejpam-3554	40	3	]	]	PUNCT
ejpam-3554	40	4	also	also	ADV
ejpam-3554	40	5	studied	study	VERB
ejpam-3554	40	6	different	different	ADJ
ejpam-3554	40	7	bounds	bound	NOUN
ejpam-3554	40	8	on	on	ADP
ejpam-3554	40	9	the	the	DET
ejpam-3554	40	10	partial	partial	ADJ
ejpam-3554	40	11	domination	domination	NOUN
ejpam-3554	40	12	number	number	NOUN
ejpam-3554	40	13	of	of	ADP
ejpam-3554	40	14	a	a	DET
ejpam-3554	40	15	graph	graph	NOUN
ejpam-3554	40	16	with	with	ADP
ejpam-3554	40	17	respect	respect	NOUN
ejpam-3554	40	18	to	to	ADP
ejpam-3554	40	19	several	several	ADJ
ejpam-3554	40	20	parameters	parameter	NOUN
ejpam-3554	40	21	like	like	ADP
ejpam-3554	40	22	its	its	PRON
ejpam-3554	40	23	order	order	NOUN
ejpam-3554	40	24	,	,	PUNCT
ejpam-3554	40	25	maximum	maximum	ADJ
ejpam-3554	40	26	degree	degree	NOUN
ejpam-3554	40	27	,	,	PUNCT
ejpam-3554	40	28	and	and	CCONJ
ejpam-3554	40	29	domination	domination	NOUN
ejpam-3554	40	30	number	number	NOUN
ejpam-3554	40	31	.	.	PUNCT
ejpam-3554	41	1	macapodi	macapodi	PROPN
ejpam-3554	41	2	,	,	PUNCT
ejpam-3554	41	3	isla	isla	PROPN
ejpam-3554	41	4	and	and	CCONJ
ejpam-3554	41	5	canoy	canoy	ADJ
ejpam-3554	41	6	[	[	X
ejpam-3554	41	7	3	3	X
ejpam-3554	41	8	]	]	PUNCT
ejpam-3554	41	9	characterized	characterize	VERB
ejpam-3554	41	10	the	the	DET
ejpam-3554	41	11	partial	partial	ADJ
ejpam-3554	41	12	dominating	dominating	NOUN
ejpam-3554	41	13	sets	set	NOUN
ejpam-3554	41	14	in	in	ADP
ejpam-3554	41	15	the	the	DET
ejpam-3554	41	16	join	join	NOUN
ejpam-3554	41	17	,	,	PUNCT
ejpam-3554	41	18	corona	corona	PROPN
ejpam-3554	41	19	,	,	PUNCT
ejpam-3554	41	20	lexicographic	lexicographic	ADJ
ejpam-3554	41	21	product	product	NOUN
ejpam-3554	41	22	and	and	CCONJ
ejpam-3554	41	23	cartesian	cartesian	ADJ
ejpam-3554	41	24	product	product	NOUN
ejpam-3554	41	25	of	of	ADP
ejpam-3554	41	26	graphs	graph	NOUN
ejpam-3554	41	27	and	and	CCONJ
ejpam-3554	41	28	determined	determine	VERB
ejpam-3554	41	29	the	the	DET
ejpam-3554	41	30	exact	exact	ADJ
ejpam-3554	41	31	values	value	NOUN
ejpam-3554	41	32	or	or	CCONJ
ejpam-3554	41	33	sharp	sharp	ADJ
ejpam-3554	41	34	bounds	bound	NOUN
ejpam-3554	41	35	of	of	ADP
ejpam-3554	41	36	the	the	DET
ejpam-3554	41	37	corresponding	corresponding	ADJ
ejpam-3554	41	38	partial	partial	ADJ
ejpam-3554	41	39	domination	domination	NOUN
ejpam-3554	41	40	number	number	NOUN
ejpam-3554	41	41	of	of	ADP
ejpam-3554	41	42	these	these	DET
ejpam-3554	41	43	graphs	graph	NOUN
ejpam-3554	41	44	.	.	PUNCT
ejpam-3554	42	1	they	they	PRON
ejpam-3554	42	2	also	also	ADV
ejpam-3554	42	3	introduced	introduce	VERB
ejpam-3554	42	4	and	and	CCONJ
ejpam-3554	42	5	examined	examine	VERB
ejpam-3554	42	6	the	the	DET
ejpam-3554	42	7	concepts	concept	NOUN
ejpam-3554	42	8	of	of	ADP
ejpam-3554	42	9	total	total	ADJ
ejpam-3554	42	10	partial	partial	ADJ
ejpam-3554	42	11	domination	domination	NOUN
ejpam-3554	42	12	and	and	CCONJ
ejpam-3554	42	13	(	(	PUNCT
ejpam-3554	42	14	α	α	PROPN
ejpam-3554	42	15	,	,	PUNCT
ejpam-3554	42	16	k)-partial	k)-partial	ADJ
ejpam-3554	42	17	domination	domination	NOUN
ejpam-3554	42	18	,	,	PUNCT
ejpam-3554	42	19	where	where	SCONJ
ejpam-3554	42	20	α	α	PRON
ejpam-3554	42	21	∈	∈	PROPN
ejpam-3554	42	22	(	(	PUNCT
ejpam-3554	42	23	0	0	NUM
ejpam-3554	42	24	,	,	PUNCT
ejpam-3554	42	25	1	1	NUM
ejpam-3554	42	26	]	]	PUNCT
ejpam-3554	42	27	and	and	CCONJ
ejpam-3554	42	28	k	k	PROPN
ejpam-3554	42	29	∈	∈	PROPN
ejpam-3554	42	30	(	(	PUNCT
ejpam-3554	42	31	−∞	−∞	NOUN
ejpam-3554	42	32	,	,	PUNCT
ejpam-3554	42	33	0	0	NUM
ejpam-3554	42	34	]	]	PUNCT
ejpam-3554	42	35	.	.	PUNCT
ejpam-3554	43	1	let	let	VERB
ejpam-3554	43	2	g	g	PRON
ejpam-3554	43	3	be	be	AUX
ejpam-3554	43	4	a	a	DET
ejpam-3554	43	5	simple	simple	ADJ
ejpam-3554	43	6	graph	graph	NOUN
ejpam-3554	43	7	.	.	PUNCT
ejpam-3554	44	1	a	a	DET
ejpam-3554	44	2	nonempty	nonempty	ADV
ejpam-3554	44	3	set	set	VERB
ejpam-3554	44	4	s	s	PROPN
ejpam-3554	44	5	⊆	⊆	NUM
ejpam-3554	44	6	v	v	NOUN
ejpam-3554	44	7	(	(	PUNCT
ejpam-3554	44	8	g	g	NOUN
ejpam-3554	44	9	)	)	PUNCT
ejpam-3554	44	10	is	be	AUX
ejpam-3554	44	11	an	an	DET
ejpam-3554	44	12	(	(	PUNCT
ejpam-3554	44	13	α	α	NOUN
ejpam-3554	44	14	,	,	PUNCT
ejpam-3554	44	15	k)-partial	k)-partial	ADJ
ejpam-3554	44	16	dominating	dominating	NOUN
ejpam-3554	44	17	set	set	VERB
ejpam-3554	44	18	in	in	ADP
ejpam-3554	44	19	g	g	PROPN
ejpam-3554	44	20	if	if	SCONJ
ejpam-3554	44	21	|n	|n	PRON
ejpam-3554	44	22	[	[	X
ejpam-3554	44	23	s]|	s]|	PROPN
ejpam-3554	44	24	≥	≥	NUM
ejpam-3554	44	25	α	α	PROPN
ejpam-3554	44	26	|v	|v	PROPN
ejpam-3554	44	27	(	(	PUNCT
ejpam-3554	44	28	g)|+	g)|+	PROPN
ejpam-3554	44	29	k.	k.	PROPN
ejpam-3554	44	30	let	let	VERB
ejpam-3554	44	31	g	g	NOUN
ejpam-3554	44	32	be	be	AUX
ejpam-3554	44	33	a	a	DET
ejpam-3554	44	34	graph	graph	NOUN
ejpam-3554	44	35	without	without	ADP
ejpam-3554	44	36	isolated	isolated	ADJ
ejpam-3554	44	37	vertices	vertex	NOUN
ejpam-3554	44	38	.	.	PUNCT
ejpam-3554	45	1	an	an	DET
ejpam-3554	45	2	α	α	NUM
ejpam-3554	45	3	-	-	ADJ
ejpam-3554	45	4	partial	partial	ADJ
ejpam-3554	45	5	dominating	dominating	NOUN
ejpam-3554	45	6	set	set	NOUN
ejpam-3554	45	7	s	s	PROPN
ejpam-3554	45	8	⊆	⊆	NUM
ejpam-3554	45	9	v	v	NOUN
ejpam-3554	45	10	(	(	PUNCT
ejpam-3554	45	11	g	g	NOUN
ejpam-3554	45	12	)	)	PUNCT
ejpam-3554	45	13	is	be	AUX
ejpam-3554	45	14	a	a	DET
ejpam-3554	45	15	total	total	ADJ
ejpam-3554	45	16	α	α	PRON
ejpam-3554	45	17	-	-	ADJ
ejpam-3554	45	18	partial	partial	ADJ
ejpam-3554	45	19	dominating	dominating	NOUN
ejpam-3554	45	20	set	set	VERB
ejpam-3554	45	21	in	in	ADP
ejpam-3554	45	22	g	g	PROPN
ejpam-3554	45	23	if	if	SCONJ
ejpam-3554	45	24	every	every	DET
ejpam-3554	45	25	vertex	vertex	NOUN
ejpam-3554	45	26	in	in	ADP
ejpam-3554	45	27	s	s	PROPN
ejpam-3554	45	28	is	be	AUX
ejpam-3554	45	29	adjacent	adjacent	ADJ
ejpam-3554	45	30	to	to	ADP
ejpam-3554	45	31	some	some	DET
ejpam-3554	45	32	vertex	vertex	NOUN
ejpam-3554	45	33	in	in	ADP
ejpam-3554	45	34	s.	s.	PROPN
ejpam-3554	45	35	in	in	ADP
ejpam-3554	45	36	this	this	DET
ejpam-3554	45	37	case	case	NOUN
ejpam-3554	45	38	,	,	PUNCT
ejpam-3554	45	39	we	we	PRON
ejpam-3554	45	40	also	also	ADV
ejpam-3554	45	41	say	say	VERB
ejpam-3554	45	42	that	that	SCONJ
ejpam-3554	45	43	g	g	PROPN
ejpam-3554	45	44	is	be	AUX
ejpam-3554	45	45	totally	totally	ADV
ejpam-3554	45	46	α	α	ADJ
ejpam-3554	45	47	-	-	ADJ
ejpam-3554	45	48	partial	partial	ADJ
ejpam-3554	45	49	dominated	dominate	VERB
ejpam-3554	45	50	by	by	ADP
ejpam-3554	45	51	the	the	DET
ejpam-3554	45	52	vertices	vertex	NOUN
ejpam-3554	45	53	in	in	ADP
ejpam-3554	45	54	s.	s.	PROPN
ejpam-3554	45	55	the	the	DET
ejpam-3554	45	56	total	total	ADJ
ejpam-3554	45	57	α	α	ADJ
ejpam-3554	45	58	-	-	ADJ
ejpam-3554	45	59	partial	partial	ADJ
ejpam-3554	45	60	domination	domination	NOUN
ejpam-3554	45	61	number	number	NOUN
ejpam-3554	45	62	of	of	ADP
ejpam-3554	45	63	g	g	NOUN
ejpam-3554	45	64	,	,	PUNCT
ejpam-3554	45	65	denoted	denote	VERB
ejpam-3554	45	66	by	by	ADP
ejpam-3554	45	67	∂tα(g	∂tα(g	PROPN
ejpam-3554	45	68	)	)	PUNCT
ejpam-3554	45	69	,	,	PUNCT
ejpam-3554	45	70	is	be	AUX
ejpam-3554	45	71	the	the	DET
ejpam-3554	45	72	minimum	minimum	ADJ
ejpam-3554	45	73	cardinality	cardinality	NOUN
ejpam-3554	45	74	of	of	ADP
ejpam-3554	45	75	a	a	DET
ejpam-3554	45	76	total	total	ADJ
ejpam-3554	45	77	α	α	PRON
ejpam-3554	45	78	-	-	ADJ
ejpam-3554	45	79	partial	partial	ADJ
ejpam-3554	45	80	dominating	dominating	NOUN
ejpam-3554	45	81	set	set	VERB
ejpam-3554	45	82	in	in	ADP
ejpam-3554	45	83	g.	g.	PROPN
ejpam-3554	45	84	a	a	DET
ejpam-3554	45	85	total	total	ADJ
ejpam-3554	45	86	α	α	PRON
ejpam-3554	45	87	-	-	ADJ
ejpam-3554	45	88	partial	partial	ADJ
ejpam-3554	45	89	dominating	dominating	NOUN
ejpam-3554	45	90	set	set	NOUN
ejpam-3554	45	91	s	s	NOUN
ejpam-3554	45	92	with	with	ADP
ejpam-3554	45	93	|s|	|s|	NOUN
ejpam-3554	45	94	=	=	PUNCT
ejpam-3554	45	95	∂tα(g	∂tα(g	NOUN
ejpam-3554	45	96	)	)	PUNCT
ejpam-3554	45	97	is	be	AUX
ejpam-3554	45	98	referred	refer	VERB
ejpam-3554	45	99	to	to	ADP
ejpam-3554	45	100	as	as	ADP
ejpam-3554	45	101	a	a	DET
ejpam-3554	45	102	∂tα	∂tα	NOUN
ejpam-3554	45	103	-	-	PUNCT
ejpam-3554	45	104	set	set	NOUN
ejpam-3554	45	105	in	in	ADP
ejpam-3554	45	106	g.	g.	PROPN
ejpam-3554	45	107	letg	letg	PROPN
ejpam-3554	45	108	be	be	AUX
ejpam-3554	45	109	a	a	DET
ejpam-3554	45	110	connected	connected	ADJ
ejpam-3554	45	111	graph	graph	NOUN
ejpam-3554	45	112	.	.	PUNCT
ejpam-3554	46	1	let	let	VERB
ejpam-3554	46	2	α	α	PRON
ejpam-3554	46	3	∈	∈	PROPN
ejpam-3554	46	4	(	(	PUNCT
ejpam-3554	46	5	0	0	NUM
ejpam-3554	46	6	,	,	PUNCT
ejpam-3554	46	7	1	1	NUM
ejpam-3554	46	8	]	]	PUNCT
ejpam-3554	46	9	and	and	CCONJ
ejpam-3554	46	10	k	k	PROPN
ejpam-3554	46	11	∈	∈	PROPN
ejpam-3554	46	12	(	(	PUNCT
ejpam-3554	46	13	−∞	−∞	NOUN
ejpam-3554	46	14	,	,	PUNCT
ejpam-3554	46	15	0	0	NUM
ejpam-3554	46	16	]	]	PUNCT
ejpam-3554	46	17	.	.	PUNCT
ejpam-3554	47	1	a	a	DET
ejpam-3554	47	2	nonempty	nonempty	ADV
ejpam-3554	47	3	set	set	VERB
ejpam-3554	47	4	s	s	PROPN
ejpam-3554	47	5	⊆	⊆	NUM
ejpam-3554	47	6	v	v	NOUN
ejpam-3554	47	7	(	(	PUNCT
ejpam-3554	47	8	g	g	NOUN
ejpam-3554	47	9	)	)	PUNCT
ejpam-3554	47	10	is	be	AUX
ejpam-3554	47	11	a	a	DET
ejpam-3554	47	12	total	total	ADJ
ejpam-3554	47	13	(	(	PUNCT
ejpam-3554	47	14	α	α	NOUN
ejpam-3554	47	15	,	,	PUNCT
ejpam-3554	47	16	k)-partial	k)-partial	ADJ
ejpam-3554	47	17	dominating	dominating	NOUN
ejpam-3554	47	18	set	set	VERB
ejpam-3554	47	19	in	in	ADP
ejpam-3554	47	20	g	g	PROPN
ejpam-3554	47	21	if	if	SCONJ
ejpam-3554	47	22	|n	|n	PRON
ejpam-3554	47	23	[	[	X
ejpam-3554	47	24	s]|	s]|	PROPN
ejpam-3554	47	25	≥	≥	NUM
ejpam-3554	47	26	α	α	PROPN
ejpam-3554	47	27	|v	|v	PROPN
ejpam-3554	47	28	(	(	PUNCT
ejpam-3554	47	29	g)|+k	g)|+k	PROPN
ejpam-3554	47	30	and	and	CCONJ
ejpam-3554	47	31	every	every	DET
ejpam-3554	47	32	element	element	NOUN
ejpam-3554	47	33	in	in	ADP
ejpam-3554	47	34	s	s	PROPN
ejpam-3554	47	35	is	be	AUX
ejpam-3554	47	36	adjacent	adjacent	ADJ
ejpam-3554	47	37	to	to	ADP
ejpam-3554	47	38	an	an	DET
ejpam-3554	47	39	element	element	NOUN
ejpam-3554	47	40	in	in	ADP
ejpam-3554	47	41	s.	s.	PROPN
ejpam-3554	47	42	the	the	DET
ejpam-3554	47	43	total	total	ADJ
ejpam-3554	47	44	(	(	PUNCT
ejpam-3554	47	45	α	α	X
ejpam-3554	47	46	,	,	PUNCT
ejpam-3554	47	47	k)-partial	k)-partial	ADJ
ejpam-3554	47	48	domination	domination	NOUN
ejpam-3554	47	49	number	number	NOUN
ejpam-3554	47	50	of	of	ADP
ejpam-3554	47	51	g	g	NOUN
ejpam-3554	47	52	,	,	PUNCT
ejpam-3554	47	53	denoted	denote	VERB
ejpam-3554	47	54	by	by	ADP
ejpam-3554	47	55	∂tα	∂tα	PROPN
ejpam-3554	47	56	,	,	PUNCT
ejpam-3554	47	57	k(g	k(g	PROPN
ejpam-3554	47	58	)	)	PUNCT
ejpam-3554	47	59	,	,	PUNCT
ejpam-3554	47	60	is	be	AUX
ejpam-3554	47	61	given	give	VERB
ejpam-3554	47	62	by	by	ADP
ejpam-3554	47	63	∂tα	∂tα	PROPN
ejpam-3554	47	64	,	,	PUNCT
ejpam-3554	47	65	k(g	k(g	PROPN
ejpam-3554	47	66	)	)	PUNCT
ejpam-3554	47	67	=	=	SYM
ejpam-3554	47	68	min{|s|	min{|s|	NOUN
ejpam-3554	47	69	:	:	PUNCT
ejpam-3554	47	70	s	s	VERB
ejpam-3554	47	71	is	be	AUX
ejpam-3554	47	72	a	a	DET
ejpam-3554	47	73	total	total	ADJ
ejpam-3554	47	74	(	(	PUNCT
ejpam-3554	47	75	α	α	NOUN
ejpam-3554	47	76	,	,	PUNCT
ejpam-3554	47	77	k)-partial	k)-partial	ADJ
ejpam-3554	47	78	dominating	dominating	NOUN
ejpam-3554	47	79	set	set	VERB
ejpam-3554	47	80	in	in	ADP
ejpam-3554	47	81	g	g	NOUN
ejpam-3554	47	82	}	}	PUNCT
ejpam-3554	47	83	.	.	PUNCT
ejpam-3554	48	1	any	any	DET
ejpam-3554	48	2	partial	partial	ADJ
ejpam-3554	48	3	dominating	dominating	NOUN
ejpam-3554	48	4	set	set	VERB
ejpam-3554	48	5	in	in	ADP
ejpam-3554	48	6	g	g	PROPN
ejpam-3554	48	7	with	with	ADP
ejpam-3554	48	8	cardinality	cardinality	PROPN
ejpam-3554	48	9	∂tα	∂tα	PROPN
ejpam-3554	48	10	,	,	PUNCT
ejpam-3554	48	11	k(g	k(g	PROPN
ejpam-3554	48	12	)	)	PUNCT
ejpam-3554	48	13	is	be	AUX
ejpam-3554	48	14	referred	refer	VERB
ejpam-3554	48	15	to	to	ADP
ejpam-3554	48	16	as	as	ADP
ejpam-3554	48	17	a	a	DET
ejpam-3554	48	18	∂tα	∂tα	PROPN
ejpam-3554	48	19	,	,	PUNCT
ejpam-3554	48	20	k	k	NOUN
ejpam-3554	48	21	-	-	PUNCT
ejpam-3554	48	22	set	set	NOUN
ejpam-3554	48	23	in	in	ADP
ejpam-3554	48	24	g.	g.	PROPN
ejpam-3554	48	25	the	the	DET
ejpam-3554	48	26	join	join	PROPN
ejpam-3554	48	27	g+h	g+h	PROPN
ejpam-3554	48	28	of	of	ADP
ejpam-3554	48	29	two	two	NUM
ejpam-3554	48	30	graphs	graph	NOUN
ejpam-3554	48	31	g	g	NOUN
ejpam-3554	49	1	and	and	CCONJ
ejpam-3554	49	2	h	h	NOUN
ejpam-3554	49	3	is	be	AUX
ejpam-3554	49	4	the	the	DET
ejpam-3554	49	5	graph	graph	NOUN
ejpam-3554	49	6	with	with	ADP
ejpam-3554	49	7	vertex	vertex	NOUN
ejpam-3554	49	8	set	set	VERB
ejpam-3554	49	9	v	v	NOUN
ejpam-3554	49	10	(	(	PUNCT
ejpam-3554	49	11	g+h	g+h	NOUN
ejpam-3554	49	12	)	)	PUNCT
ejpam-3554	50	1	=	=	SYM
ejpam-3554	50	2	v	v	X
ejpam-3554	50	3	(	(	PUNCT
ejpam-3554	50	4	g	g	NOUN
ejpam-3554	50	5	)	)	PUNCT
ejpam-3554	50	6	∪	∪	NOUN
ejpam-3554	50	7	v	v	NOUN
ejpam-3554	50	8	(	(	PUNCT
ejpam-3554	50	9	h	h	NOUN
ejpam-3554	50	10	)	)	PUNCT
ejpam-3554	50	11	and	and	CCONJ
ejpam-3554	50	12	edge	edge	NOUN
ejpam-3554	50	13	set	set	VERB
ejpam-3554	50	14	e(g+h	e(g+h	NUM
ejpam-3554	50	15	)	)	PUNCT
ejpam-3554	50	16	=	=	SYM
ejpam-3554	50	17	e(g	e(g	NOUN
ejpam-3554	50	18	)	)	PUNCT
ejpam-3554	50	19	∪	∪	ADP
ejpam-3554	50	20	e(h	e(h	PROPN
ejpam-3554	50	21	)	)	PUNCT
ejpam-3554	50	22	∪	∪	NOUN
ejpam-3554	50	23	{	{	PUNCT
ejpam-3554	50	24	uv	uv	NOUN
ejpam-3554	50	25	:	:	PUNCT
ejpam-3554	50	26	u	u	PROPN
ejpam-3554	50	27	∈	∈	PROPN
ejpam-3554	50	28	v	v	ADP
ejpam-3554	50	29	(	(	PUNCT
ejpam-3554	50	30	g	g	NOUN
ejpam-3554	50	31	)	)	PUNCT
ejpam-3554	50	32	,	,	PUNCT
ejpam-3554	50	33	v	v	X
ejpam-3554	50	34	∈	∈	PROPN
ejpam-3554	50	35	v	v	NOUN
ejpam-3554	50	36	(	(	PUNCT
ejpam-3554	50	37	h	h	NOUN
ejpam-3554	50	38	)	)	PUNCT
ejpam-3554	50	39	}	}	PUNCT
ejpam-3554	50	40	.	.	PUNCT
ejpam-3554	51	1	r.	r.	PROPN
ejpam-3554	51	2	macapodi	macapodi	PROPN
ejpam-3554	51	3	,	,	PUNCT
ejpam-3554	51	4	r.	r.	PROPN
ejpam-3554	51	5	isla	isla	PROPN
ejpam-3554	51	6	/	/	SYM
ejpam-3554	51	7	eur	eur	PROPN
ejpam-3554	51	8	.	.	PUNCT
ejpam-3554	52	1	j.	j.	PROPN
ejpam-3554	52	2	pure	pure	PROPN
ejpam-3554	52	3	appl	appl	PROPN
ejpam-3554	52	4	.	.	PROPN
ejpam-3554	52	5	math	math	PROPN
ejpam-3554	52	6	,	,	PUNCT
ejpam-3554	52	7	12	12	NUM
ejpam-3554	52	8	(	(	PUNCT
ejpam-3554	52	9	4	4	NUM
ejpam-3554	52	10	)	)	PUNCT
ejpam-3554	52	11	(	(	PUNCT
ejpam-3554	52	12	2019	2019	NUM
ejpam-3554	52	13	)	)	PUNCT
ejpam-3554	52	14	,	,	PUNCT
ejpam-3554	52	15	1643	1643	NUM
ejpam-3554	52	16	-	-	SYM
ejpam-3554	52	17	1655	1655	NUM
ejpam-3554	52	18	1645	1645	NUM
ejpam-3554	52	19	the	the	DET
ejpam-3554	52	20	corona	corona	NOUN
ejpam-3554	52	21	of	of	ADP
ejpam-3554	52	22	two	two	NUM
ejpam-3554	52	23	graphs	graph	NOUN
ejpam-3554	52	24	g	g	NOUN
ejpam-3554	52	25	and	and	CCONJ
ejpam-3554	52	26	h	h	NOUN
ejpam-3554	52	27	,	,	PUNCT
ejpam-3554	52	28	denoted	denote	VERB
ejpam-3554	52	29	by	by	ADP
ejpam-3554	52	30	g	g	PROPN
ejpam-3554	52	31	◦	◦	NOUN
ejpam-3554	52	32	h	h	NOUN
ejpam-3554	52	33	,	,	PUNCT
ejpam-3554	52	34	is	be	AUX
ejpam-3554	52	35	the	the	DET
ejpam-3554	52	36	graph	graph	NOUN
ejpam-3554	52	37	obtained	obtain	VERB
ejpam-3554	52	38	by	by	ADP
ejpam-3554	52	39	taking	take	VERB
ejpam-3554	52	40	one	one	NUM
ejpam-3554	52	41	copy	copy	NOUN
ejpam-3554	52	42	of	of	ADP
ejpam-3554	52	43	g	g	NOUN
ejpam-3554	52	44	of	of	ADP
ejpam-3554	52	45	order	order	NOUN
ejpam-3554	52	46	n	n	NOUN
ejpam-3554	52	47	and	and	CCONJ
ejpam-3554	52	48	n	n	PRON
ejpam-3554	52	49	copies	copy	NOUN
ejpam-3554	52	50	of	of	ADP
ejpam-3554	52	51	h	h	NOUN
ejpam-3554	52	52	,	,	PUNCT
ejpam-3554	52	53	and	and	CCONJ
ejpam-3554	52	54	then	then	ADV
ejpam-3554	52	55	joining	join	VERB
ejpam-3554	52	56	the	the	DET
ejpam-3554	52	57	i	i	PROPN
ejpam-3554	52	58	-	-	PUNCT
ejpam-3554	52	59	th	th	X
ejpam-3554	52	60	vertex	vertex	NOUN
ejpam-3554	52	61	of	of	ADP
ejpam-3554	52	62	g	g	NOUN
ejpam-3554	52	63	to	to	ADP
ejpam-3554	52	64	every	every	DET
ejpam-3554	52	65	vertex	vertex	NOUN
ejpam-3554	52	66	in	in	ADP
ejpam-3554	52	67	the	the	DET
ejpam-3554	52	68	i	i	PROPN
ejpam-3554	52	69	-	-	PUNCT
ejpam-3554	52	70	th	th	PROPN
ejpam-3554	52	71	copy	copy	NOUN
ejpam-3554	52	72	of	of	ADP
ejpam-3554	52	73	h.	h.	PROPN
ejpam-3554	52	74	for	for	ADP
ejpam-3554	52	75	every	every	DET
ejpam-3554	52	76	v	v	NUM
ejpam-3554	52	77	∈	∈	PROPN
ejpam-3554	52	78	v	v	NOUN
ejpam-3554	52	79	(	(	PUNCT
ejpam-3554	52	80	g	g	NOUN
ejpam-3554	52	81	)	)	PUNCT
ejpam-3554	52	82	,	,	PUNCT
ejpam-3554	52	83	we	we	PRON
ejpam-3554	52	84	denote	denote	VERB
ejpam-3554	52	85	by	by	ADP
ejpam-3554	52	86	hv	hv	PROPN
ejpam-3554	52	87	the	the	DET
ejpam-3554	52	88	copy	copy	NOUN
ejpam-3554	52	89	of	of	ADP
ejpam-3554	52	90	h	h	NOUN
ejpam-3554	52	91	whose	whose	DET
ejpam-3554	52	92	vertices	vertex	NOUN
ejpam-3554	52	93	are	be	AUX
ejpam-3554	52	94	joined	join	VERB
ejpam-3554	52	95	or	or	CCONJ
ejpam-3554	52	96	attached	attach	VERB
ejpam-3554	52	97	to	to	ADP
ejpam-3554	52	98	the	the	DET
ejpam-3554	52	99	vertex	vertex	NOUN
ejpam-3554	52	100	v.	v.	CCONJ
ejpam-3554	52	101	for	for	ADP
ejpam-3554	52	102	each	each	DET
ejpam-3554	52	103	v	v	NUM
ejpam-3554	52	104	∈	∈	PROPN
ejpam-3554	52	105	v	v	NOUN
ejpam-3554	52	106	(	(	PUNCT
ejpam-3554	52	107	g	g	NOUN
ejpam-3554	52	108	)	)	PUNCT
ejpam-3554	52	109	,	,	PUNCT
ejpam-3554	52	110	the	the	DET
ejpam-3554	52	111	subgraph	subgraph	PROPN
ejpam-3554	52	112	〈	〈	PROPN
ejpam-3554	52	113	v〉+hv	v〉+hv	NOUN
ejpam-3554	52	114	of	of	ADP
ejpam-3554	52	115	g	g	PROPN
ejpam-3554	52	116	◦	◦	NOUN
ejpam-3554	52	117	h	h	NOUN
ejpam-3554	52	118	will	will	AUX
ejpam-3554	52	119	be	be	AUX
ejpam-3554	52	120	denoted	denote	VERB
ejpam-3554	52	121	by	by	ADP
ejpam-3554	52	122	v	v	DET
ejpam-3554	52	123	+	+	PROPN
ejpam-3554	52	124	hv	hv	PROPN
ejpam-3554	52	125	.	.	PUNCT
ejpam-3554	53	1	the	the	DET
ejpam-3554	53	2	lexicographic	lexicographic	ADJ
ejpam-3554	53	3	product	product	NOUN
ejpam-3554	53	4	of	of	ADP
ejpam-3554	53	5	two	two	NUM
ejpam-3554	53	6	graphs	graph	NOUN
ejpam-3554	53	7	g	g	NOUN
ejpam-3554	53	8	and	and	CCONJ
ejpam-3554	53	9	h	h	NOUN
ejpam-3554	53	10	,	,	PUNCT
ejpam-3554	53	11	denoted	denote	VERB
ejpam-3554	53	12	by	by	ADP
ejpam-3554	53	13	g[h	g[h	NOUN
ejpam-3554	53	14	]	]	PUNCT
ejpam-3554	53	15	,	,	PUNCT
ejpam-3554	53	16	is	be	AUX
ejpam-3554	53	17	the	the	DET
ejpam-3554	53	18	graph	graph	NOUN
ejpam-3554	53	19	with	with	ADP
ejpam-3554	53	20	vertex	vertex	NOUN
ejpam-3554	53	21	set	set	VERB
ejpam-3554	53	22	v	v	NOUN
ejpam-3554	53	23	(	(	PUNCT
ejpam-3554	53	24	g[h	g[h	PROPN
ejpam-3554	53	25	]	]	PUNCT
ejpam-3554	53	26	)	)	PUNCT
ejpam-3554	53	27	=	=	SYM
ejpam-3554	53	28	v	v	X
ejpam-3554	53	29	(	(	PUNCT
ejpam-3554	53	30	g)×v	g)×v	PROPN
ejpam-3554	53	31	(	(	PUNCT
ejpam-3554	53	32	h	h	NOUN
ejpam-3554	53	33	)	)	PUNCT
ejpam-3554	53	34	and	and	CCONJ
ejpam-3554	53	35	edge	edge	VERB
ejpam-3554	53	36	set	set	VERB
ejpam-3554	53	37	e(g[h	e(g[h	NOUN
ejpam-3554	53	38	]	]	PUNCT
ejpam-3554	53	39	)	)	PUNCT
ejpam-3554	53	40	satisfying	satisfy	VERB
ejpam-3554	53	41	the	the	DET
ejpam-3554	53	42	following	follow	VERB
ejpam-3554	53	43	conditions	condition	NOUN
ejpam-3554	53	44	:	:	PUNCT
ejpam-3554	53	45	(	(	PUNCT
ejpam-3554	53	46	u1	u1	PROPN
ejpam-3554	53	47	,	,	PUNCT
ejpam-3554	53	48	v1)(u2	v1)(u2	PROPN
ejpam-3554	53	49	,	,	PUNCT
ejpam-3554	53	50	v2	v2	PROPN
ejpam-3554	53	51	)	)	PUNCT
ejpam-3554	53	52	∈	∈	NOUN
ejpam-3554	53	53	e(g[h	e(g[h	NOUN
ejpam-3554	53	54	]	]	PUNCT
ejpam-3554	53	55	)	)	PUNCT
ejpam-3554	53	56	if	if	SCONJ
ejpam-3554	53	57	and	and	CCONJ
ejpam-3554	53	58	only	only	ADV
ejpam-3554	53	59	if	if	SCONJ
ejpam-3554	53	60	either	either	PRON
ejpam-3554	53	61	u1u2	u1u2	PROPN
ejpam-3554	53	62	∈	∈	PROPN
ejpam-3554	53	63	e(g	e(g	PROPN
ejpam-3554	53	64	)	)	PUNCT
ejpam-3554	53	65	or	or	CCONJ
ejpam-3554	53	66	u1	u1	NOUN
ejpam-3554	53	67	=	=	SYM
ejpam-3554	53	68	u2	u2	PROPN
ejpam-3554	53	69	and	and	CCONJ
ejpam-3554	53	70	v1v2	v1v2	PUNCT
ejpam-3554	53	71	∈	∈	PROPN
ejpam-3554	53	72	e(h	e(h	PROPN
ejpam-3554	53	73	)	)	PUNCT
ejpam-3554	53	74	.	.	PUNCT
ejpam-3554	54	1	the	the	DET
ejpam-3554	54	2	cartesian	cartesian	ADJ
ejpam-3554	54	3	product	product	NOUN
ejpam-3554	54	4	of	of	ADP
ejpam-3554	54	5	two	two	NUM
ejpam-3554	54	6	graphs	graph	NOUN
ejpam-3554	54	7	g	g	NOUN
ejpam-3554	54	8	and	and	CCONJ
ejpam-3554	54	9	h	h	NOUN
ejpam-3554	54	10	,	,	PUNCT
ejpam-3554	54	11	denoted	denote	VERB
ejpam-3554	54	12	by	by	ADP
ejpam-3554	54	13	g	g	PROPN
ejpam-3554	54	14	�	�	PROPN
ejpam-3554	54	15	h	h	NOUN
ejpam-3554	54	16	,	,	PUNCT
ejpam-3554	54	17	is	be	AUX
ejpam-3554	54	18	the	the	DET
ejpam-3554	54	19	graph	graph	NOUN
ejpam-3554	54	20	with	with	ADP
ejpam-3554	54	21	vertex	vertex	NOUN
ejpam-3554	54	22	set	set	VERB
ejpam-3554	54	23	v	v	NOUN
ejpam-3554	54	24	(	(	PUNCT
ejpam-3554	54	25	g	g	PROPN
ejpam-3554	54	26	�	�	NOUN
ejpam-3554	54	27	h	h	NOUN
ejpam-3554	54	28	)	)	PUNCT
ejpam-3554	54	29	=	=	NOUN
ejpam-3554	54	30	v	v	X
ejpam-3554	54	31	(	(	PUNCT
ejpam-3554	54	32	g)×	g)×	NOUN
ejpam-3554	54	33	v	v	NOUN
ejpam-3554	54	34	(	(	PUNCT
ejpam-3554	54	35	h	h	NOUN
ejpam-3554	54	36	)	)	PUNCT
ejpam-3554	54	37	and	and	CCONJ
ejpam-3554	54	38	edge	edge	VERB
ejpam-3554	54	39	set	set	VERB
ejpam-3554	54	40	e(g	e(g	PROPN
ejpam-3554	54	41	�	�	PROPN
ejpam-3554	54	42	h	h	NOUN
ejpam-3554	54	43	)	)	PUNCT
ejpam-3554	54	44	satisfying	satisfy	VERB
ejpam-3554	54	45	the	the	DET
ejpam-3554	54	46	following	follow	VERB
ejpam-3554	54	47	conditions	condition	NOUN
ejpam-3554	54	48	:	:	PUNCT
ejpam-3554	54	49	(	(	PUNCT
ejpam-3554	54	50	u1	u1	PROPN
ejpam-3554	54	51	,	,	PUNCT
ejpam-3554	54	52	v1)(u2	v1)(u2	PROPN
ejpam-3554	54	53	,	,	PUNCT
ejpam-3554	54	54	v2	v2	PROPN
ejpam-3554	54	55	)	)	PUNCT
ejpam-3554	54	56	∈	∈	PROPN
ejpam-3554	54	57	e(g	e(g	PROPN
ejpam-3554	54	58	�	�	PROPN
ejpam-3554	54	59	h	h	PROPN
ejpam-3554	54	60	)	)	PUNCT
ejpam-3554	54	61	if	if	SCONJ
ejpam-3554	54	62	and	and	CCONJ
ejpam-3554	54	63	only	only	ADV
ejpam-3554	54	64	if	if	SCONJ
ejpam-3554	54	65	either	either	DET
ejpam-3554	54	66	u1u2	u1u2	PROPN
ejpam-3554	54	67	∈	∈	PROPN
ejpam-3554	54	68	e(g	e(g	PROPN
ejpam-3554	54	69	)	)	PUNCT
ejpam-3554	54	70	and	and	CCONJ
ejpam-3554	54	71	v1	v1	NOUN
ejpam-3554	54	72	=	=	SYM
ejpam-3554	54	73	v2	v2	NOUN
ejpam-3554	54	74	or	or	CCONJ
ejpam-3554	54	75	u1	u1	NOUN
ejpam-3554	54	76	=	=	SYM
ejpam-3554	54	77	u2	u2	PROPN
ejpam-3554	54	78	and	and	CCONJ
ejpam-3554	54	79	v1v2	v1v2	PUNCT
ejpam-3554	54	80	∈	∈	PROPN
ejpam-3554	54	81	e(h	e(h	PROPN
ejpam-3554	54	82	)	)	PUNCT
ejpam-3554	54	83	.	.	PUNCT
ejpam-3554	55	1	2	2	X
ejpam-3554	55	2	.	.	X
ejpam-3554	55	3	preliminary	preliminary	ADJ
ejpam-3554	55	4	results	result	NOUN
ejpam-3554	55	5	remark	remark	VERB
ejpam-3554	55	6	1	1	NUM
ejpam-3554	55	7	.	.	PUNCT
ejpam-3554	56	1	let	let	VERB
ejpam-3554	56	2	m	m	PRON
ejpam-3554	56	3	,	,	PUNCT
ejpam-3554	56	4	n	n	PROPN
ejpam-3554	56	5	and	and	CCONJ
ejpam-3554	56	6	p	p	NOUN
ejpam-3554	56	7	be	be	AUX
ejpam-3554	56	8	positive	positive	ADJ
ejpam-3554	56	9	integers	integer	NOUN
ejpam-3554	56	10	and	and	CCONJ
ejpam-3554	56	11	let	let	VERB
ejpam-3554	56	12	α	α	PRON
ejpam-3554	56	13	∈	∈	PROPN
ejpam-3554	56	14	(	(	PUNCT
ejpam-3554	56	15	0	0	NUM
ejpam-3554	56	16	,	,	PUNCT
ejpam-3554	56	17	1	1	NUM
ejpam-3554	56	18	]	]	PUNCT
ejpam-3554	56	19	.	.	PUNCT
ejpam-3554	57	1	let	let	VERB
ejpam-3554	57	2	g	g	PRON
ejpam-3554	57	3	be	be	AUX
ejpam-3554	57	4	a	a	DET
ejpam-3554	57	5	complete	complete	ADJ
ejpam-3554	57	6	graph	graph	NOUN
ejpam-3554	57	7	km	km	PROPN
ejpam-3554	57	8	,	,	PUNCT
ejpam-3554	57	9	a	a	DET
ejpam-3554	57	10	fan	fan	NOUN
ejpam-3554	57	11	graph	graph	NOUN
ejpam-3554	57	12	fm	fm	PROPN
ejpam-3554	57	13	,	,	PUNCT
ejpam-3554	57	14	a	a	DET
ejpam-3554	57	15	star	star	NOUN
ejpam-3554	57	16	graph	graph	NOUN
ejpam-3554	57	17	k1,n	k1,n	PROPN
ejpam-3554	57	18	or	or	CCONJ
ejpam-3554	57	19	a	a	DET
ejpam-3554	57	20	wheel	wheel	NOUN
ejpam-3554	57	21	graph	graph	NOUN
ejpam-3554	57	22	wp	wp	PROPN
ejpam-3554	57	23	.	.	PUNCT
ejpam-3554	58	1	then	then	ADV
ejpam-3554	58	2	∂tα(g	∂tα(g	PROPN
ejpam-3554	58	3	)	)	PUNCT
ejpam-3554	59	1	=	=	SYM
ejpam-3554	59	2	2	2	NUM
ejpam-3554	59	3	for	for	ADP
ejpam-3554	59	4	m	m	PROPN
ejpam-3554	59	5	≥	≥	NOUN
ejpam-3554	59	6	2	2	NUM
ejpam-3554	59	7	,	,	PUNCT
ejpam-3554	59	8	n	n	PRON
ejpam-3554	59	9	≥	≥	NOUN
ejpam-3554	59	10	1	1	NUM
ejpam-3554	59	11	and	and	CCONJ
ejpam-3554	59	12	p	p	PRON
ejpam-3554	59	13	≥	≥	NUM
ejpam-3554	59	14	3	3	NUM
ejpam-3554	59	15	.	.	PUNCT
ejpam-3554	59	16	remark	remark	NOUN
ejpam-3554	59	17	2	2	NUM
ejpam-3554	59	18	.	.	X
ejpam-3554	60	1	for	for	ADP
ejpam-3554	60	2	any	any	DET
ejpam-3554	60	3	α	α	NOUN
ejpam-3554	60	4	∈	∈	PROPN
ejpam-3554	60	5	(	(	PUNCT
ejpam-3554	60	6	0	0	NUM
ejpam-3554	60	7	,	,	PUNCT
ejpam-3554	60	8	1	1	NUM
ejpam-3554	60	9	]	]	PUNCT
ejpam-3554	60	10	and	and	CCONJ
ejpam-3554	60	11	a	a	DET
ejpam-3554	60	12	complete	complete	ADJ
ejpam-3554	60	13	bipartite	bipartite	NOUN
ejpam-3554	60	14	graph	graph	NOUN
ejpam-3554	60	15	km	km	PROPN
ejpam-3554	60	16	,	,	PUNCT
ejpam-3554	60	17	n	n	CCONJ
ejpam-3554	60	18	,	,	PUNCT
ejpam-3554	60	19	with	with	ADP
ejpam-3554	60	20	m	m	PROPN
ejpam-3554	60	21	,	,	PUNCT
ejpam-3554	60	22	n	n	PRON
ejpam-3554	60	23	≥	≥	NOUN
ejpam-3554	60	24	2	2	NUM
ejpam-3554	60	25	,	,	PUNCT
ejpam-3554	60	26	∂tα(km	∂tα(km	ADJ
ejpam-3554	60	27	,	,	PUNCT
ejpam-3554	60	28	n	n	CCONJ
ejpam-3554	60	29	)	)	PUNCT
ejpam-3554	60	30	=	=	SYM
ejpam-3554	60	31	2	2	X
ejpam-3554	60	32	.	.	NOUN
ejpam-3554	60	33	remark	remark	NOUN
ejpam-3554	60	34	3	3	NUM
ejpam-3554	60	35	.	.	PUNCT
ejpam-3554	61	1	let	let	VERB
ejpam-3554	61	2	g	g	PRON
ejpam-3554	61	3	be	be	AUX
ejpam-3554	61	4	a	a	DET
ejpam-3554	61	5	graph	graph	NOUN
ejpam-3554	61	6	without	without	ADP
ejpam-3554	61	7	isolated	isolated	ADJ
ejpam-3554	61	8	vertices	vertex	NOUN
ejpam-3554	61	9	.	.	PUNCT
ejpam-3554	62	1	if	if	SCONJ
ejpam-3554	62	2	γt(g	γt(g	NUM
ejpam-3554	62	3	)	)	PUNCT
ejpam-3554	62	4	=	=	SYM
ejpam-3554	62	5	2	2	NUM
ejpam-3554	62	6	,	,	PUNCT
ejpam-3554	62	7	then	then	ADV
ejpam-3554	62	8	∂tα(g	∂tα(g	NOUN
ejpam-3554	62	9	)	)	PUNCT
ejpam-3554	63	1	=	=	SYM
ejpam-3554	63	2	2	2	NUM
ejpam-3554	63	3	for	for	ADP
ejpam-3554	63	4	all	all	DET
ejpam-3554	63	5	α	α	PRON
ejpam-3554	63	6	∈	∈	NOUN
ejpam-3554	63	7	(	(	PUNCT
ejpam-3554	63	8	0	0	NUM
ejpam-3554	63	9	,	,	PUNCT
ejpam-3554	63	10	1	1	NUM
ejpam-3554	63	11	]	]	PUNCT
ejpam-3554	63	12	.	.	PUNCT
ejpam-3554	64	1	remark	remark	PROPN
ejpam-3554	64	2	4	4	NUM
ejpam-3554	64	3	.	.	PUNCT
ejpam-3554	65	1	let	let	VERB
ejpam-3554	65	2	g	g	PRON
ejpam-3554	65	3	be	be	AUX
ejpam-3554	65	4	a	a	DET
ejpam-3554	65	5	nontrivial	nontrivial	ADJ
ejpam-3554	65	6	graph	graph	NOUN
ejpam-3554	65	7	.	.	PUNCT
ejpam-3554	66	1	then	then	ADV
ejpam-3554	66	2	∂α(g	∂α(g	PROPN
ejpam-3554	66	3	)	)	PUNCT
ejpam-3554	66	4	≤	≤	NOUN
ejpam-3554	66	5	∂tα(g	∂tα(g	NOUN
ejpam-3554	66	6	)	)	PUNCT
ejpam-3554	66	7	≤	≤	NOUN
ejpam-3554	66	8	γt(g	γt(g	PUNCT
ejpam-3554	66	9	)	)	PUNCT
ejpam-3554	66	10	.	.	PUNCT
ejpam-3554	67	1	theorem	theorem	NOUN
ejpam-3554	67	2	1	1	X
ejpam-3554	67	3	.	.	PUNCT
ejpam-3554	68	1	let	let	VERB
ejpam-3554	68	2	n	n	PRON
ejpam-3554	68	3	be	be	AUX
ejpam-3554	68	4	a	a	DET
ejpam-3554	68	5	positive	positive	ADJ
ejpam-3554	68	6	integer	integer	NOUN
ejpam-3554	68	7	and	and	CCONJ
ejpam-3554	68	8	α	α	NOUN
ejpam-3554	68	9	=	=	NOUN
ejpam-3554	68	10	1	1	NUM
ejpam-3554	68	11	2	2	NUM
ejpam-3554	68	12	.	.	PUNCT
ejpam-3554	69	1	then	then	ADV
ejpam-3554	69	2	∂tα(pn	∂tα(pn	ADJ
ejpam-3554	69	3	)	)	PUNCT
ejpam-3554	69	4	=	=	SYM
ejpam-3554	69	5	∂tα(cn	∂tα(cn	NOUN
ejpam-3554	69	6	)	)	PUNCT
ejpam-3554	69	7	=	=	PUNCT
ejpam-3554	69	8			NOUN
ejpam-3554	69	9	2	2	NUM
ejpam-3554	69	10	,	,	PUNCT
ejpam-3554	69	11	2	2	NUM
ejpam-3554	69	12	≤	≤	NOUN
ejpam-3554	69	13	n	n	PRON
ejpam-3554	69	14	≤	≤	NUM
ejpam-3554	69	15	7	7	NUM
ejpam-3554	69	16	2r	2r	NUM
ejpam-3554	69	17	,	,	PUNCT
ejpam-3554	69	18	n	n	PROPN
ejpam-3554	69	19	=	=	SYM
ejpam-3554	69	20	8r	8r	NUM
ejpam-3554	69	21	2r	2r	NUM
ejpam-3554	70	1	+	+	CCONJ
ejpam-3554	70	2	1	1	NUM
ejpam-3554	70	3	,	,	PUNCT
ejpam-3554	70	4	n	n	NOUN
ejpam-3554	70	5	=	=	SYM
ejpam-3554	70	6	8r	8r	X
ejpam-3554	71	1	+	+	SYM
ejpam-3554	71	2	s	s	X
ejpam-3554	71	3	,	,	PUNCT
ejpam-3554	71	4	s	s	PART
ejpam-3554	71	5	=	=	SYM
ejpam-3554	71	6	1	1	NUM
ejpam-3554	71	7	,	,	PUNCT
ejpam-3554	71	8	2	2	NUM
ejpam-3554	71	9	2r	2r	NUM
ejpam-3554	71	10	+	+	CCONJ
ejpam-3554	71	11	2	2	NUM
ejpam-3554	71	12	,	,	PUNCT
ejpam-3554	71	13	n	n	NOUN
ejpam-3554	71	14	=	=	SYM
ejpam-3554	71	15	8r	8r	X
ejpam-3554	72	1	+	+	SYM
ejpam-3554	72	2	s	s	X
ejpam-3554	72	3	,	,	PUNCT
ejpam-3554	72	4	s	s	PART
ejpam-3554	72	5	=	=	SYM
ejpam-3554	72	6	3	3	NUM
ejpam-3554	72	7	,	,	PUNCT
ejpam-3554	72	8	4	4	NUM
ejpam-3554	72	9	,	,	PUNCT
ejpam-3554	72	10	5	5	NUM
ejpam-3554	72	11	,	,	PUNCT
ejpam-3554	72	12	6	6	NUM
ejpam-3554	72	13	,	,	PUNCT
ejpam-3554	72	14	7	7	NUM
ejpam-3554	72	15	where	where	SCONJ
ejpam-3554	72	16	r	r	NOUN
ejpam-3554	72	17	and	and	CCONJ
ejpam-3554	72	18	s	s	NOUN
ejpam-3554	72	19	are	be	AUX
ejpam-3554	72	20	integers	integer	NOUN
ejpam-3554	72	21	such	such	ADJ
ejpam-3554	72	22	that	that	SCONJ
ejpam-3554	72	23	n	n	NOUN
ejpam-3554	72	24	=	=	SYM
ejpam-3554	72	25	8r	8r	PROPN
ejpam-3554	73	1	+	+	SYM
ejpam-3554	73	2	s	s	X
ejpam-3554	73	3	,	,	PUNCT
ejpam-3554	73	4	1	1	NUM
ejpam-3554	73	5	≤	≤	NUM
ejpam-3554	73	6	s	s	PART
ejpam-3554	73	7	≤	≤	NUM
ejpam-3554	73	8	7	7	NUM
ejpam-3554	73	9	.	.	PUNCT
ejpam-3554	74	1	proof	proof	NOUN
ejpam-3554	74	2	.	.	PUNCT
ejpam-3554	75	1	let	let	VERB
ejpam-3554	75	2	pn	pn	VERB
ejpam-3554	75	3	=	=	PUNCT
ejpam-3554	76	1	[	[	X
ejpam-3554	76	2	v1	v1	NOUN
ejpam-3554	76	3	,	,	PUNCT
ejpam-3554	76	4	v2	v2	PROPN
ejpam-3554	76	5	,	,	PUNCT
ejpam-3554	76	6	...	...	PUNCT
ejpam-3554	76	7	,	,	PUNCT
ejpam-3554	76	8	vn	vn	X
ejpam-3554	76	9	]	]	PUNCT
ejpam-3554	76	10	.	.	PUNCT
ejpam-3554	77	1	if	if	SCONJ
ejpam-3554	77	2	2	2	NUM
ejpam-3554	77	3	≤	≤	NOUN
ejpam-3554	77	4	n	n	CCONJ
ejpam-3554	77	5	≤	≤	NOUN
ejpam-3554	77	6	7	7	NUM
ejpam-3554	77	7	,	,	PUNCT
ejpam-3554	77	8	then	then	ADV
ejpam-3554	77	9	clearly	clearly	ADV
ejpam-3554	77	10	,	,	PUNCT
ejpam-3554	77	11	∂tα(pn	∂tα(pn	ADJ
ejpam-3554	77	12	)	)	PUNCT
ejpam-3554	77	13	=	=	SYM
ejpam-3554	77	14	2	2	X
ejpam-3554	77	15	.	.	X
ejpam-3554	77	16	let	let	VERB
ejpam-3554	77	17	n	n	PRON
ejpam-3554	77	18	≥	≥	X
ejpam-3554	77	19	8	8	NUM
ejpam-3554	77	20	and	and	CCONJ
ejpam-3554	77	21	consider	consider	VERB
ejpam-3554	77	22	the	the	DET
ejpam-3554	77	23	following	follow	VERB
ejpam-3554	77	24	cases	case	NOUN
ejpam-3554	77	25	:	:	PUNCT
ejpam-3554	77	26	case	case	NOUN
ejpam-3554	77	27	1	1	NUM
ejpam-3554	77	28	:	:	PUNCT
ejpam-3554	77	29	n	n	PROPN
ejpam-3554	77	30	=	=	SYM
ejpam-3554	77	31	8r	8r	PROPN
ejpam-3554	77	32	group	group	NOUN
ejpam-3554	77	33	the	the	DET
ejpam-3554	77	34	vertices	vertex	NOUN
ejpam-3554	77	35	of	of	ADP
ejpam-3554	77	36	pn	pn	NOUN
ejpam-3554	77	37	into	into	ADP
ejpam-3554	77	38	r	r	NOUN
ejpam-3554	77	39	disjoint	disjoint	NOUN
ejpam-3554	77	40	subsets	subset	NOUN
ejpam-3554	77	41	.	.	PUNCT
ejpam-3554	78	1	s1	s1	NOUN
ejpam-3554	78	2	=	=	PUNCT
ejpam-3554	78	3	{	{	PUNCT
ejpam-3554	78	4	v1	v1	PROPN
ejpam-3554	78	5	,	,	PUNCT
ejpam-3554	78	6	v2	v2	PROPN
ejpam-3554	78	7	,	,	PUNCT
ejpam-3554	78	8	v3	v3	PROPN
ejpam-3554	78	9	,	,	PUNCT
ejpam-3554	78	10	v4	v4	PROPN
ejpam-3554	78	11	,	,	PUNCT
ejpam-3554	78	12	v5	v5	PROPN
ejpam-3554	78	13	,	,	PUNCT
ejpam-3554	78	14	v6	v6	NOUN
ejpam-3554	78	15	,	,	PUNCT
ejpam-3554	78	16	v7	v7	NUM
ejpam-3554	78	17	,	,	PUNCT
ejpam-3554	78	18	v8	v8	PROPN
ejpam-3554	78	19	}	}	PUNCT
ejpam-3554	78	20	s2	s2	NOUN
ejpam-3554	78	21	=	=	SYM
ejpam-3554	78	22	{	{	PUNCT
ejpam-3554	78	23	v9	v9	PROPN
ejpam-3554	78	24	,	,	PUNCT
ejpam-3554	78	25	v10	v10	NOUN
ejpam-3554	78	26	,	,	PUNCT
ejpam-3554	78	27	v11	v11	NOUN
ejpam-3554	78	28	,	,	PUNCT
ejpam-3554	78	29	v12	v12	VERB
ejpam-3554	78	30	,	,	PUNCT
ejpam-3554	78	31	v13	v13	PROPN
ejpam-3554	78	32	,	,	PUNCT
ejpam-3554	78	33	v14	v14	PROPN
ejpam-3554	78	34	,	,	PUNCT
ejpam-3554	78	35	v15	v15	NOUN
ejpam-3554	78	36	,	,	PUNCT
ejpam-3554	78	37	v16	v16	NOUN
ejpam-3554	78	38	}	}	PUNCT
ejpam-3554	78	39	...	...	PUNCT
ejpam-3554	79	1	sr−1	sr−1	PROPN
ejpam-3554	79	2	=	=	SYM
ejpam-3554	79	3	{	{	PUNCT
ejpam-3554	79	4	v8r−15	v8r−15	PROPN
ejpam-3554	79	5	,	,	PUNCT
ejpam-3554	79	6	v8r−14	v8r−14	PRON
ejpam-3554	79	7	,	,	PUNCT
ejpam-3554	79	8	v8r−13	v8r−13	NOUN
ejpam-3554	79	9	,	,	PUNCT
ejpam-3554	79	10	v8r−12	v8r−12	NOUN
ejpam-3554	79	11	,	,	PUNCT
ejpam-3554	79	12	v8r−11	v8r−11	VERB
ejpam-3554	79	13	,	,	PUNCT
ejpam-3554	79	14	v8r−10	v8r−10	PROPN
ejpam-3554	79	15	,	,	PUNCT
ejpam-3554	79	16	v8r−9	v8r−9	NOUN
ejpam-3554	79	17	,	,	PUNCT
ejpam-3554	79	18	v8r−8	v8r−8	PROPN
ejpam-3554	79	19	}	}	PUNCT
ejpam-3554	79	20	r.	r.	PROPN
ejpam-3554	79	21	macapodi	macapodi	PROPN
ejpam-3554	79	22	,	,	PUNCT
ejpam-3554	79	23	r.	r.	PROPN
ejpam-3554	79	24	isla	isla	PROPN
ejpam-3554	79	25	/	/	SYM
ejpam-3554	79	26	eur	eur	PROPN
ejpam-3554	79	27	.	.	PUNCT
ejpam-3554	80	1	j.	j.	PROPN
ejpam-3554	80	2	pure	pure	PROPN
ejpam-3554	80	3	appl	appl	PROPN
ejpam-3554	80	4	.	.	PROPN
ejpam-3554	80	5	math	math	PROPN
ejpam-3554	80	6	,	,	PUNCT
ejpam-3554	80	7	12	12	NUM
ejpam-3554	80	8	(	(	PUNCT
ejpam-3554	80	9	4	4	NUM
ejpam-3554	80	10	)	)	PUNCT
ejpam-3554	80	11	(	(	PUNCT
ejpam-3554	80	12	2019	2019	NUM
ejpam-3554	80	13	)	)	PUNCT
ejpam-3554	80	14	,	,	PUNCT
ejpam-3554	80	15	1643	1643	NUM
ejpam-3554	80	16	-	-	SYM
ejpam-3554	80	17	1655	1655	NUM
ejpam-3554	80	18	1646	1646	NUM
ejpam-3554	80	19	sr	sr	PROPN
ejpam-3554	80	20	=	=	PRON
ejpam-3554	80	21	{	{	PUNCT
ejpam-3554	80	22	v8r−7	v8r−7	NOUN
ejpam-3554	80	23	,	,	PUNCT
ejpam-3554	80	24	v8r−6	v8r−6	PROPN
ejpam-3554	80	25	,	,	PUNCT
ejpam-3554	80	26	v8r−5	v8r−5	PROPN
ejpam-3554	80	27	,	,	PUNCT
ejpam-3554	80	28	v8r−4	v8r−4	PROPN
ejpam-3554	80	29	,	,	PUNCT
ejpam-3554	80	30	v8r−3	v8r−3	NOUN
ejpam-3554	80	31	,	,	PUNCT
ejpam-3554	80	32	v8r−2	v8r−2	PROPN
ejpam-3554	80	33	,	,	PUNCT
ejpam-3554	80	34	v8r−1	v8r−1	PROPN
ejpam-3554	80	35	,	,	PUNCT
ejpam-3554	80	36	v8r	v8r	NOUN
ejpam-3554	80	37	}	}	PUNCT
ejpam-3554	80	38	for	for	ADP
ejpam-3554	80	39	every	every	DET
ejpam-3554	80	40	induced	induce	VERB
ejpam-3554	80	41	subgraph	subgraph	NOUN
ejpam-3554	80	42	〈	〈	PROPN
ejpam-3554	80	43	vi	vi	PROPN
ejpam-3554	80	44	,	,	PUNCT
ejpam-3554	80	45	vi+1	vi+1	NOUN
ejpam-3554	80	46	,	,	PUNCT
ejpam-3554	80	47	vi+2	vi+2	NUM
ejpam-3554	80	48	,	,	PUNCT
ejpam-3554	80	49	vi+3	vi+3	X
ejpam-3554	80	50	,	,	PUNCT
ejpam-3554	80	51	vi+4	vi+4	X
ejpam-3554	80	52	,	,	PUNCT
ejpam-3554	80	53	vi+5	vi+5	PROPN
ejpam-3554	80	54	,	,	PUNCT
ejpam-3554	80	55	vi+6	vi+6	NOUN
ejpam-3554	80	56	,	,	PUNCT
ejpam-3554	80	57	vi+7	vi+7	NOUN
ejpam-3554	80	58	〉	〉	NUM
ejpam-3554	80	59	of	of	ADP
ejpam-3554	80	60	pn	pn	PROPN
ejpam-3554	80	61	,	,	PUNCT
ejpam-3554	80	62	where	where	SCONJ
ejpam-3554	80	63	i	i	PRON
ejpam-3554	80	64	=	=	NOUN
ejpam-3554	80	65	1	1	NUM
ejpam-3554	80	66	,	,	PUNCT
ejpam-3554	80	67	9	9	NUM
ejpam-3554	80	68	,	,	PUNCT
ejpam-3554	80	69	...	...	PUNCT
ejpam-3554	80	70	,	,	PUNCT
ejpam-3554	80	71	8r	8r	NUM
ejpam-3554	80	72	−	−	PROPN
ejpam-3554	80	73	7	7	NUM
ejpam-3554	80	74	,	,	PUNCT
ejpam-3554	80	75	the	the	DET
ejpam-3554	80	76	vertices	vertex	NOUN
ejpam-3554	80	77	vi+1	vi+1	NOUN
ejpam-3554	80	78	and	and	CCONJ
ejpam-3554	80	79	vi+2	vi+2	NUM
ejpam-3554	80	80	form	form	VERB
ejpam-3554	80	81	a	a	DET
ejpam-3554	80	82	total	total	ADJ
ejpam-3554	80	83	α	α	PRON
ejpam-3554	80	84	-	-	ADJ
ejpam-3554	80	85	partial	partial	ADJ
ejpam-3554	80	86	dominating	dominating	NOUN
ejpam-3554	80	87	set	set	NOUN
ejpam-3554	80	88	of	of	ADP
ejpam-3554	80	89	pn	pn	PROPN
ejpam-3554	80	90	.	.	PUNCT
ejpam-3554	81	1	thus	thus	ADV
ejpam-3554	81	2	,	,	PUNCT
ejpam-3554	81	3	the	the	DET
ejpam-3554	81	4	set	set	NOUN
ejpam-3554	81	5	t	t	NOUN
ejpam-3554	81	6	=	=	SYM
ejpam-3554	81	7	{	{	PUNCT
ejpam-3554	81	8	v2	v2	PROPN
ejpam-3554	81	9	,	,	PUNCT
ejpam-3554	81	10	v3	v3	PROPN
ejpam-3554	81	11	,	,	PUNCT
ejpam-3554	81	12	v10	v10	NOUN
ejpam-3554	81	13	,	,	PUNCT
ejpam-3554	81	14	v11	v11	NOUN
ejpam-3554	81	15	,	,	PUNCT
ejpam-3554	81	16	.	.	PUNCT
ejpam-3554	81	17	.	.	PUNCT
ejpam-3554	81	18	.	.	PUNCT
ejpam-3554	82	1	,	,	PUNCT
ejpam-3554	82	2	v8r−6	v8r−6	PROPN
ejpam-3554	82	3	,	,	PUNCT
ejpam-3554	82	4	v8r−5	v8r−5	PROPN
ejpam-3554	82	5	}	}	PUNCT
ejpam-3554	82	6	is	be	AUX
ejpam-3554	82	7	a	a	DET
ejpam-3554	82	8	total	total	ADJ
ejpam-3554	82	9	α	α	PRON
ejpam-3554	82	10	-	-	ADJ
ejpam-3554	82	11	partial	partial	ADJ
ejpam-3554	82	12	dominating	dominating	NOUN
ejpam-3554	82	13	set	set	NOUN
ejpam-3554	82	14	of	of	ADP
ejpam-3554	82	15	pn	pn	PROPN
ejpam-3554	82	16	.	.	PUNCT
ejpam-3554	83	1	since	since	SCONJ
ejpam-3554	83	2	|t	|t	PROPN
ejpam-3554	83	3	|	|	ADV
ejpam-3554	83	4	=	=	SYM
ejpam-3554	83	5	2r	2r	NUM
ejpam-3554	83	6	,	,	PUNCT
ejpam-3554	83	7	∂tα(pn	∂tα(pn	NOUN
ejpam-3554	83	8	)	)	PUNCT
ejpam-3554	83	9	≤	≤	NOUN
ejpam-3554	83	10	2r	2r	NUM
ejpam-3554	83	11	.	.	PUNCT
ejpam-3554	84	1	note	note	VERB
ejpam-3554	84	2	that	that	SCONJ
ejpam-3554	84	3	every	every	DET
ejpam-3554	84	4	pair	pair	NOUN
ejpam-3554	84	5	of	of	ADP
ejpam-3554	84	6	adjacent	adjacent	ADJ
ejpam-3554	84	7	vertices	vertex	NOUN
ejpam-3554	84	8	in	in	ADP
ejpam-3554	84	9	pn	pn	PROPN
ejpam-3554	84	10	can	can	AUX
ejpam-3554	84	11	dominate	dominate	VERB
ejpam-3554	84	12	at	at	ADP
ejpam-3554	84	13	most	most	ADV
ejpam-3554	84	14	4	4	NUM
ejpam-3554	84	15	vertices	vertex	NOUN
ejpam-3554	84	16	.	.	PUNCT
ejpam-3554	85	1	thus	thus	ADV
ejpam-3554	85	2	,	,	PUNCT
ejpam-3554	85	3	every	every	DET
ejpam-3554	85	4	total	total	ADJ
ejpam-3554	85	5	α	α	ADJ
ejpam-3554	85	6	-	-	ADJ
ejpam-3554	85	7	partial	partial	ADJ
ejpam-3554	85	8	dominating	dominating	NOUN
ejpam-3554	85	9	set	set	VERB
ejpam-3554	85	10	in	in	ADP
ejpam-3554	85	11	pn	pn	PROPN
ejpam-3554	85	12	contains	contain	VERB
ejpam-3554	85	13	at	at	ADP
ejpam-3554	85	14	least	least	ADJ
ejpam-3554	85	15	dn4	dn4	NOUN
ejpam-3554	85	16	e	e	NOUN
ejpam-3554	85	17	vertices	vertex	NOUN
ejpam-3554	85	18	.	.	PUNCT
ejpam-3554	86	1	hence	hence	ADV
ejpam-3554	86	2	,	,	PUNCT
ejpam-3554	86	3	∂tα(pn	∂tα(pn	ADJ
ejpam-3554	86	4	)	)	PUNCT
ejpam-3554	86	5	≥	≥	NOUN
ejpam-3554	86	6	dn4	dn4	NOUN
ejpam-3554	86	7	e	e	NOUN
ejpam-3554	86	8	=	=	SYM
ejpam-3554	86	9	2r	2r	NUM
ejpam-3554	86	10	since	since	SCONJ
ejpam-3554	86	11	n	n	NOUN
ejpam-3554	86	12	=	=	SYM
ejpam-3554	86	13	8r	8r	NUM
ejpam-3554	86	14	.	.	PUNCT
ejpam-3554	87	1	thus	thus	ADV
ejpam-3554	87	2	,	,	PUNCT
ejpam-3554	87	3	∂tα(pn	∂tα(pn	ADJ
ejpam-3554	87	4	)	)	PUNCT
ejpam-3554	87	5	=	=	SYM
ejpam-3554	87	6	2r	2r	NUM
ejpam-3554	87	7	.	.	PUNCT
ejpam-3554	88	1	case	case	NOUN
ejpam-3554	88	2	2	2	NUM
ejpam-3554	88	3	:	:	PUNCT
ejpam-3554	88	4	n	n	PROPN
ejpam-3554	88	5	=	=	SYM
ejpam-3554	88	6	8r	8r	PROPN
ejpam-3554	89	1	+	+	SYM
ejpam-3554	89	2	s	s	X
ejpam-3554	89	3	,	,	PUNCT
ejpam-3554	89	4	s	s	PART
ejpam-3554	89	5	=	=	SYM
ejpam-3554	89	6	1	1	NUM
ejpam-3554	89	7	,	,	PUNCT
ejpam-3554	89	8	2	2	NUM
ejpam-3554	89	9	in	in	ADP
ejpam-3554	89	10	case	case	NOUN
ejpam-3554	89	11	1	1	NUM
ejpam-3554	89	12	,	,	PUNCT
ejpam-3554	89	13	the	the	DET
ejpam-3554	89	14	first	first	ADJ
ejpam-3554	89	15	8r	8r	NUM
ejpam-3554	89	16	vertices	vertex	NOUN
ejpam-3554	89	17	of	of	ADP
ejpam-3554	89	18	pn	pn	PROPN
ejpam-3554	89	19	are	be	AUX
ejpam-3554	89	20	totally	totally	ADV
ejpam-3554	89	21	α	α	ADJ
ejpam-3554	89	22	-	-	ADJ
ejpam-3554	89	23	partial	partial	ADJ
ejpam-3554	89	24	dominated	dominate	VERB
ejpam-3554	89	25	by	by	ADP
ejpam-3554	89	26	2r	2r	NUM
ejpam-3554	89	27	vertices	vertex	NOUN
ejpam-3554	89	28	in	in	ADP
ejpam-3554	89	29	t	t	PROPN
ejpam-3554	89	30	.	.	PUNCT
ejpam-3554	90	1	since	since	SCONJ
ejpam-3554	90	2	n	n	NOUN
ejpam-3554	90	3	=	=	SYM
ejpam-3554	90	4	8r	8r	NUM
ejpam-3554	91	1	+	+	CCONJ
ejpam-3554	91	2	1	1	NUM
ejpam-3554	91	3	or	or	CCONJ
ejpam-3554	91	4	8r	8r	NUM
ejpam-3554	91	5	+	+	CCONJ
ejpam-3554	91	6	2	2	NUM
ejpam-3554	91	7	,	,	PUNCT
ejpam-3554	91	8	vertices	vertice	VERB
ejpam-3554	91	9	v8r+1	v8r+1	NOUN
ejpam-3554	91	10	and	and	CCONJ
ejpam-3554	91	11	v8r+2	v8r+2	NOUN
ejpam-3554	91	12	of	of	ADP
ejpam-3554	91	13	pn	pn	PROPN
ejpam-3554	91	14	are	be	AUX
ejpam-3554	91	15	not	not	PART
ejpam-3554	91	16	totally	totally	ADV
ejpam-3554	91	17	α	α	ADJ
ejpam-3554	91	18	-	-	ADJ
ejpam-3554	91	19	partial	partial	ADJ
ejpam-3554	91	20	dominated	dominate	VERB
ejpam-3554	91	21	by	by	ADP
ejpam-3554	91	22	t	t	PROPN
ejpam-3554	91	23	.	.	PUNCT
ejpam-3554	92	1	hence	hence	ADV
ejpam-3554	92	2	,	,	PUNCT
ejpam-3554	92	3	∂tα(pn	∂tα(pn	NOUN
ejpam-3554	92	4	)	)	PUNCT
ejpam-3554	92	5	>	>	X
ejpam-3554	93	1	2r	2r	NUM
ejpam-3554	93	2	.	.	PUNCT
ejpam-3554	94	1	now	now	ADV
ejpam-3554	94	2	,	,	PUNCT
ejpam-3554	94	3	add	add	VERB
ejpam-3554	94	4	v8r−4	v8r−4	PROPN
ejpam-3554	94	5	to	to	ADP
ejpam-3554	94	6	t	t	PROPN
ejpam-3554	94	7	so	so	SCONJ
ejpam-3554	94	8	that	that	SCONJ
ejpam-3554	94	9	t	t	PROPN
ejpam-3554	94	10	∪	∪	X
ejpam-3554	94	11	{	{	PUNCT
ejpam-3554	94	12	v8r−4	v8r−4	PROPN
ejpam-3554	94	13	}	}	PUNCT
ejpam-3554	94	14	is	be	AUX
ejpam-3554	94	15	a	a	DET
ejpam-3554	94	16	∂tα	∂tα	NOUN
ejpam-3554	94	17	-	-	PUNCT
ejpam-3554	94	18	set	set	NOUN
ejpam-3554	94	19	in	in	ADP
ejpam-3554	94	20	pn	pn	PROPN
ejpam-3554	94	21	.	.	PUNCT
ejpam-3554	95	1	thus	thus	ADV
ejpam-3554	95	2	,	,	PUNCT
ejpam-3554	95	3	∂tα(pn	∂tα(pn	ADJ
ejpam-3554	95	4	)	)	PUNCT
ejpam-3554	95	5	=	=	SYM
ejpam-3554	96	1	2r	2r	NUM
ejpam-3554	97	1	+	+	CCONJ
ejpam-3554	97	2	1	1	X
ejpam-3554	97	3	.	.	X
ejpam-3554	97	4	case	case	NOUN
ejpam-3554	97	5	3	3	NUM
ejpam-3554	97	6	:	:	SYM
ejpam-3554	97	7	n	n	PROPN
ejpam-3554	97	8	=	=	SYM
ejpam-3554	97	9	8r	8r	PROPN
ejpam-3554	98	1	+	+	SYM
ejpam-3554	98	2	s	s	X
ejpam-3554	98	3	,	,	PUNCT
ejpam-3554	98	4	s	s	PART
ejpam-3554	98	5	=	=	SYM
ejpam-3554	98	6	3	3	NUM
ejpam-3554	98	7	,	,	PUNCT
ejpam-3554	98	8	4	4	NUM
ejpam-3554	98	9	,	,	PUNCT
ejpam-3554	98	10	5	5	NUM
ejpam-3554	98	11	,	,	PUNCT
ejpam-3554	98	12	6	6	NUM
ejpam-3554	98	13	,	,	PUNCT
ejpam-3554	98	14	7	7	NUM
ejpam-3554	98	15	consider	consider	VERB
ejpam-3554	98	16	the	the	DET
ejpam-3554	98	17	total	total	ADJ
ejpam-3554	98	18	α	α	ADJ
ejpam-3554	98	19	-	-	ADJ
ejpam-3554	98	20	partial	partial	ADJ
ejpam-3554	98	21	dominating	dominating	NOUN
ejpam-3554	98	22	set	set	VERB
ejpam-3554	98	23	t	t	NOUN
ejpam-3554	98	24	in	in	ADP
ejpam-3554	98	25	case	case	NOUN
ejpam-3554	98	26	1	1	NUM
ejpam-3554	98	27	.	.	PUNCT
ejpam-3554	99	1	since	since	SCONJ
ejpam-3554	99	2	{	{	PUNCT
ejpam-3554	99	3	v8r+s|s	v8r+s|s	NOUN
ejpam-3554	99	4	=	=	SYM
ejpam-3554	99	5	3	3	NUM
ejpam-3554	99	6	,	,	PUNCT
ejpam-3554	99	7	4	4	NUM
ejpam-3554	99	8	,	,	PUNCT
ejpam-3554	99	9	5	5	NUM
ejpam-3554	99	10	,	,	PUNCT
ejpam-3554	99	11	6	6	NUM
ejpam-3554	99	12	,	,	PUNCT
ejpam-3554	99	13	7	7	NUM
ejpam-3554	99	14	}	}	PUNCT
ejpam-3554	99	15	are	be	AUX
ejpam-3554	99	16	not	not	PART
ejpam-3554	99	17	totally	totally	ADV
ejpam-3554	99	18	α	α	ADJ
ejpam-3554	99	19	-	-	ADJ
ejpam-3554	99	20	partial	partial	ADJ
ejpam-3554	99	21	dominated	dominate	VERB
ejpam-3554	99	22	by	by	ADP
ejpam-3554	99	23	vertices	vertex	NOUN
ejpam-3554	99	24	in	in	ADP
ejpam-3554	99	25	t	t	PROPN
ejpam-3554	99	26	∪	∪	X
ejpam-3554	99	27	{	{	PUNCT
ejpam-3554	99	28	v8r−4	v8r−4	PROPN
ejpam-3554	99	29	}	}	PUNCT
ejpam-3554	99	30	,	,	PUNCT
ejpam-3554	99	31	∂tα(pn	∂tα(pn	NOUN
ejpam-3554	99	32	)	)	PUNCT
ejpam-3554	99	33	>	>	X
ejpam-3554	100	1	2r	2r	NUM
ejpam-3554	101	1	+	+	CCONJ
ejpam-3554	101	2	1	1	X
ejpam-3554	101	3	.	.	PUNCT
ejpam-3554	101	4	now	now	ADV
ejpam-3554	101	5	,	,	PUNCT
ejpam-3554	101	6	add	add	VERB
ejpam-3554	101	7	vertices	vertex	NOUN
ejpam-3554	101	8	v8r+2	v8r+2	ADV
ejpam-3554	101	9	and	and	CCONJ
ejpam-3554	101	10	v8r+3	v8r+3	VERB
ejpam-3554	101	11	to	to	ADP
ejpam-3554	101	12	t	t	PROPN
ejpam-3554	101	13	so	so	SCONJ
ejpam-3554	101	14	that	that	SCONJ
ejpam-3554	101	15	t	t	PROPN
ejpam-3554	101	16	∪	∪	X
ejpam-3554	101	17	{	{	PUNCT
ejpam-3554	101	18	v8r+2	v8r+2	ADJ
ejpam-3554	101	19	,	,	PUNCT
ejpam-3554	101	20	v8r+3	v8r+3	NOUN
ejpam-3554	101	21	}	}	PUNCT
ejpam-3554	101	22	is	be	AUX
ejpam-3554	101	23	a	a	DET
ejpam-3554	101	24	∂tα	∂tα	NOUN
ejpam-3554	101	25	-	-	PUNCT
ejpam-3554	101	26	set	set	NOUN
ejpam-3554	101	27	in	in	ADP
ejpam-3554	101	28	pn	pn	PROPN
ejpam-3554	101	29	.	.	PUNCT
ejpam-3554	102	1	thus	thus	ADV
ejpam-3554	102	2	,	,	PUNCT
ejpam-3554	102	3	∂tα(pn	∂tα(pn	ADJ
ejpam-3554	102	4	)	)	PUNCT
ejpam-3554	102	5	=	=	SYM
ejpam-3554	102	6	2r	2r	NUM
ejpam-3554	103	1	+	+	CCONJ
ejpam-3554	103	2	2	2	X
ejpam-3554	103	3	.	.	PUNCT
ejpam-3554	103	4	finally	finally	ADV
ejpam-3554	103	5	,	,	PUNCT
ejpam-3554	103	6	it	it	PRON
ejpam-3554	103	7	can	can	AUX
ejpam-3554	103	8	be	be	AUX
ejpam-3554	103	9	verified	verify	VERB
ejpam-3554	103	10	that	that	SCONJ
ejpam-3554	103	11	the	the	DET
ejpam-3554	103	12	total	total	ADJ
ejpam-3554	103	13	α	α	ADJ
ejpam-3554	103	14	-	-	ADJ
ejpam-3554	103	15	partial	partial	ADJ
ejpam-3554	103	16	domination	domination	NOUN
ejpam-3554	103	17	number	number	NOUN
ejpam-3554	103	18	of	of	ADP
ejpam-3554	103	19	pn	pn	PROPN
ejpam-3554	103	20	still	still	ADV
ejpam-3554	103	21	holds	hold	VERB
ejpam-3554	103	22	for	for	ADP
ejpam-3554	103	23	g	g	NOUN
ejpam-3554	103	24	=	=	SYM
ejpam-3554	103	25	cn	cn	PROPN
ejpam-3554	103	26	for	for	ADP
ejpam-3554	103	27	n	n	X
ejpam-3554	103	28	≥	≥	NUM
ejpam-3554	103	29	3	3	NUM
ejpam-3554	103	30	.	.	X
ejpam-3554	103	31	�	�	PROPN
ejpam-3554	103	32	we	we	PRON
ejpam-3554	103	33	now	now	ADV
ejpam-3554	103	34	present	present	VERB
ejpam-3554	103	35	a	a	DET
ejpam-3554	103	36	realization	realization	NOUN
ejpam-3554	103	37	problem	problem	NOUN
ejpam-3554	103	38	.	.	PUNCT
ejpam-3554	104	1	theorem	theorem	NOUN
ejpam-3554	104	2	2	2	NUM
ejpam-3554	104	3	.	.	PUNCT
ejpam-3554	104	4	let	let	VERB
ejpam-3554	104	5	a	a	PRON
ejpam-3554	104	6	and	and	CCONJ
ejpam-3554	104	7	b	b	NOUN
ejpam-3554	104	8	be	be	AUX
ejpam-3554	104	9	positive	positive	ADJ
ejpam-3554	104	10	integers	integer	NOUN
ejpam-3554	104	11	such	such	ADJ
ejpam-3554	104	12	that	that	SCONJ
ejpam-3554	104	13	a	a	DET
ejpam-3554	104	14	=	=	SYM
ejpam-3554	104	15	b	b	PROPN
ejpam-3554	104	16	or	or	CCONJ
ejpam-3554	104	17	b	b	NOUN
ejpam-3554	104	18	=	=	SYM
ejpam-3554	104	19	2a	2a	NUM
ejpam-3554	104	20	and	and	CCONJ
ejpam-3554	104	21	let	let	VERB
ejpam-3554	104	22	α	α	NOUN
ejpam-3554	104	23	=	=	SYM
ejpam-3554	104	24	1	1	NUM
ejpam-3554	104	25	2	2	NUM
ejpam-3554	104	26	.	.	PUNCT
ejpam-3554	105	1	then	then	ADV
ejpam-3554	105	2	there	there	PRON
ejpam-3554	105	3	exists	exist	VERB
ejpam-3554	105	4	a	a	DET
ejpam-3554	105	5	connected	connected	ADJ
ejpam-3554	105	6	graph	graph	NOUN
ejpam-3554	105	7	g	g	ADP
ejpam-3554	105	8	such	such	ADJ
ejpam-3554	105	9	that	that	DET
ejpam-3554	105	10	∂α(g	∂α(g	PROPN
ejpam-3554	105	11	)	)	PUNCT
ejpam-3554	105	12	=	=	SYM
ejpam-3554	105	13	a	a	PRON
ejpam-3554	105	14	and	and	CCONJ
ejpam-3554	105	15	∂tα(g	∂tα(g	NOUN
ejpam-3554	105	16	)	)	PUNCT
ejpam-3554	106	1	=	=	SYM
ejpam-3554	106	2	b.	b.	NOUN
ejpam-3554	106	3	proof	proof	NOUN
ejpam-3554	106	4	.	.	PUNCT
ejpam-3554	107	1	consider	consider	VERB
ejpam-3554	107	2	the	the	DET
ejpam-3554	107	3	following	follow	VERB
ejpam-3554	107	4	cases	case	NOUN
ejpam-3554	107	5	:	:	PUNCT
ejpam-3554	107	6	case	case	NOUN
ejpam-3554	107	7	1	1	NUM
ejpam-3554	107	8	:	:	PUNCT
ejpam-3554	107	9	a	a	DET
ejpam-3554	107	10	=	=	SYM
ejpam-3554	107	11	b	b	X
ejpam-3554	107	12	subcase	subcase	NOUN
ejpam-3554	107	13	(	(	PUNCT
ejpam-3554	107	14	i	i	NOUN
ejpam-3554	107	15	)	)	PUNCT
ejpam-3554	107	16	.	.	PUNCT
ejpam-3554	108	1	a	a	PRON
ejpam-3554	108	2	is	be	AUX
ejpam-3554	108	3	even	even	ADV
ejpam-3554	108	4	.	.	PUNCT
ejpam-3554	109	1	let	let	VERB
ejpam-3554	109	2	g	g	PROPN
ejpam-3554	109	3	=	=	PUNCT
ejpam-3554	109	4	g1	g1	PROPN
ejpam-3554	109	5	be	be	VERB
ejpam-3554	109	6	the	the	DET
ejpam-3554	109	7	graph	graph	NOUN
ejpam-3554	109	8	shown	show	VERB
ejpam-3554	109	9	in	in	ADP
ejpam-3554	109	10	figure	figure	NOUN
ejpam-3554	109	11	1	1	NUM
ejpam-3554	109	12	.	.	PUNCT
ejpam-3554	110	1	it	it	PRON
ejpam-3554	110	2	is	be	AUX
ejpam-3554	110	3	clear	clear	ADJ
ejpam-3554	110	4	that	that	SCONJ
ejpam-3554	110	5	the	the	DET
ejpam-3554	110	6	set	set	NOUN
ejpam-3554	110	7	a	a	X
ejpam-3554	110	8	=	=	X
ejpam-3554	110	9	{	{	PUNCT
ejpam-3554	110	10	xi	xi	X
ejpam-3554	110	11	:	:	PUNCT
ejpam-3554	110	12	i	i	NOUN
ejpam-3554	110	13	=	=	NOUN
ejpam-3554	110	14	1	1	NUM
ejpam-3554	110	15	,	,	PUNCT
ejpam-3554	110	16	2	2	NUM
ejpam-3554	110	17	,	,	PUNCT
ejpam-3554	110	18	...	...	PUNCT
ejpam-3554	110	19	,	,	PUNCT
ejpam-3554	110	20	a	a	PRON
ejpam-3554	110	21	}	}	PUNCT
ejpam-3554	110	22	is	be	AUX
ejpam-3554	110	23	both	both	PRON
ejpam-3554	110	24	an	an	DET
ejpam-3554	110	25	∂α	∂α	PROPN
ejpam-3554	110	26	-	-	PUNCT
ejpam-3554	110	27	set	set	VERB
ejpam-3554	110	28	and	and	CCONJ
ejpam-3554	110	29	a	a	DET
ejpam-3554	110	30	∂tα	∂tα	NOUN
ejpam-3554	110	31	-	-	PUNCT
ejpam-3554	110	32	set	set	NOUN
ejpam-3554	110	33	in	in	ADP
ejpam-3554	110	34	g1	g1	PROPN
ejpam-3554	110	35	.	.	PUNCT
ejpam-3554	111	1	it	it	PRON
ejpam-3554	111	2	follows	follow	VERB
ejpam-3554	111	3	that	that	SCONJ
ejpam-3554	111	4	∂α(g1	∂α(g1	NOUN
ejpam-3554	111	5	)	)	PUNCT
ejpam-3554	111	6	=	=	SYM
ejpam-3554	111	7	∂tα(g1	∂tα(g1	X
ejpam-3554	111	8	)	)	PUNCT
ejpam-3554	112	1	=	=	SYM
ejpam-3554	112	2	|a|	|a|	PROPN
ejpam-3554	112	3	=	=	NOUN
ejpam-3554	112	4	a	a	PROPN
ejpam-3554	112	5	=	=	X
ejpam-3554	112	6	b.	b.	PROPN
ejpam-3554	112	7	subcase	subcase	PROPN
ejpam-3554	112	8	(	(	PUNCT
ejpam-3554	112	9	ii	ii	PROPN
ejpam-3554	112	10	)	)	PUNCT
ejpam-3554	112	11	.	.	PUNCT
ejpam-3554	113	1	a	a	PRON
ejpam-3554	113	2	is	be	AUX
ejpam-3554	113	3	odd	odd	ADJ
ejpam-3554	113	4	.	.	PUNCT
ejpam-3554	114	1	let	let	VERB
ejpam-3554	114	2	g	g	PROPN
ejpam-3554	114	3	=	=	PUNCT
ejpam-3554	114	4	g2	g2	PROPN
ejpam-3554	114	5	be	be	VERB
ejpam-3554	114	6	the	the	DET
ejpam-3554	114	7	graph	graph	NOUN
ejpam-3554	114	8	shown	show	VERB
ejpam-3554	114	9	in	in	ADP
ejpam-3554	114	10	figure	figure	NOUN
ejpam-3554	114	11	2	2	NUM
ejpam-3554	114	12	.	.	PUNCT
ejpam-3554	115	1	it	it	PRON
ejpam-3554	115	2	is	be	AUX
ejpam-3554	115	3	clear	clear	ADJ
ejpam-3554	115	4	that	that	SCONJ
ejpam-3554	115	5	the	the	DET
ejpam-3554	115	6	set	set	NOUN
ejpam-3554	115	7	a	a	X
ejpam-3554	115	8	=	=	X
ejpam-3554	115	9	{	{	PUNCT
ejpam-3554	115	10	xi	xi	X
ejpam-3554	115	11	:	:	PUNCT
ejpam-3554	115	12	i	i	NOUN
ejpam-3554	115	13	=	=	NOUN
ejpam-3554	115	14	1	1	NUM
ejpam-3554	115	15	,	,	PUNCT
ejpam-3554	115	16	2	2	NUM
ejpam-3554	115	17	,	,	PUNCT
ejpam-3554	115	18	...	...	PUNCT
ejpam-3554	115	19	,	,	PUNCT
ejpam-3554	115	20	a	a	PRON
ejpam-3554	115	21	}	}	PUNCT
ejpam-3554	115	22	is	be	AUX
ejpam-3554	115	23	both	both	PRON
ejpam-3554	115	24	an	an	DET
ejpam-3554	115	25	∂α	∂α	PROPN
ejpam-3554	115	26	-	-	PUNCT
ejpam-3554	115	27	set	set	VERB
ejpam-3554	115	28	and	and	CCONJ
ejpam-3554	115	29	a	a	DET
ejpam-3554	115	30	∂tα	∂tα	NOUN
ejpam-3554	115	31	-	-	PUNCT
ejpam-3554	115	32	set	set	NOUN
ejpam-3554	115	33	in	in	ADP
ejpam-3554	115	34	g2	g2	PROPN
ejpam-3554	115	35	.	.	PUNCT
ejpam-3554	116	1	it	it	PRON
ejpam-3554	116	2	follows	follow	VERB
ejpam-3554	116	3	that	that	PRON
ejpam-3554	116	4	∂α(g2	∂α(g2	NUM
ejpam-3554	116	5	)	)	PUNCT
ejpam-3554	116	6	=	=	SYM
ejpam-3554	116	7	∂tα(g2	∂tα(g2	NOUN
ejpam-3554	116	8	)	)	PUNCT
ejpam-3554	117	1	=	=	PUNCT
ejpam-3554	117	2	|a|	|a|	PROPN
ejpam-3554	117	3	=	=	PROPN
ejpam-3554	117	4	a	a	PROPN
ejpam-3554	117	5	=	=	PROPN
ejpam-3554	117	6	b.	b.	PROPN
ejpam-3554	117	7	r.	r.	PROPN
ejpam-3554	117	8	macapodi	macapodi	PROPN
ejpam-3554	117	9	,	,	PUNCT
ejpam-3554	117	10	r.	r.	PROPN
ejpam-3554	117	11	isla	isla	PROPN
ejpam-3554	117	12	/	/	SYM
ejpam-3554	117	13	eur	eur	PROPN
ejpam-3554	117	14	.	.	PUNCT
ejpam-3554	118	1	j.	j.	PROPN
ejpam-3554	118	2	pure	pure	PROPN
ejpam-3554	118	3	appl	appl	PROPN
ejpam-3554	118	4	.	.	PROPN
ejpam-3554	118	5	math	math	PROPN
ejpam-3554	118	6	,	,	PUNCT
ejpam-3554	118	7	12	12	NUM
ejpam-3554	118	8	(	(	PUNCT
ejpam-3554	118	9	4	4	NUM
ejpam-3554	118	10	)	)	PUNCT
ejpam-3554	118	11	(	(	PUNCT
ejpam-3554	118	12	2019	2019	NUM
ejpam-3554	118	13	)	)	PUNCT
ejpam-3554	118	14	,	,	PUNCT
ejpam-3554	118	15	1643	1643	NUM
ejpam-3554	118	16	-	-	SYM
ejpam-3554	118	17	1655	1655	NUM
ejpam-3554	118	18	1647	1647	NUM
ejpam-3554	118	19	case	case	NOUN
ejpam-3554	118	20	2	2	NUM
ejpam-3554	118	21	:	:	SYM
ejpam-3554	118	22	b	b	X
ejpam-3554	118	23	=	=	SYM
ejpam-3554	118	24	2a	2a	NUM
ejpam-3554	118	25	let	let	VERB
ejpam-3554	118	26	g	g	PROPN
ejpam-3554	118	27	=	=	PROPN
ejpam-3554	118	28	g3	g3	PROPN
ejpam-3554	118	29	be	be	AUX
ejpam-3554	118	30	the	the	DET
ejpam-3554	118	31	graph	graph	NOUN
ejpam-3554	118	32	shown	show	VERB
ejpam-3554	118	33	in	in	ADP
ejpam-3554	118	34	figure	figure	NOUN
ejpam-3554	118	35	3	3	NUM
ejpam-3554	118	36	.	.	X
ejpam-3554	118	37	observe	observe	VERB
ejpam-3554	118	38	that	that	SCONJ
ejpam-3554	118	39	the	the	DET
ejpam-3554	118	40	set	set	NOUN
ejpam-3554	118	41	a	a	X
ejpam-3554	118	42	=	=	X
ejpam-3554	118	43	{	{	PUNCT
ejpam-3554	118	44	xi	xi	X
ejpam-3554	118	45	:	:	PUNCT
ejpam-3554	118	46	i	i	NOUN
ejpam-3554	118	47	=	=	NOUN
ejpam-3554	118	48	1	1	NUM
ejpam-3554	118	49	,	,	PUNCT
ejpam-3554	118	50	2	2	NUM
ejpam-3554	118	51	,	,	PUNCT
ejpam-3554	118	52	...	...	PUNCT
ejpam-3554	118	53	,	,	PUNCT
ejpam-3554	118	54	a	a	PRON
ejpam-3554	118	55	}	}	PUNCT
ejpam-3554	118	56	is	be	AUX
ejpam-3554	118	57	an	an	DET
ejpam-3554	118	58	∂α	∂α	PROPN
ejpam-3554	118	59	-	-	PUNCT
ejpam-3554	118	60	set	set	VERB
ejpam-3554	118	61	and	and	CCONJ
ejpam-3554	118	62	the	the	DET
ejpam-3554	118	63	set	set	NOUN
ejpam-3554	118	64	b	b	PROPN
ejpam-3554	118	65	=	=	NOUN
ejpam-3554	118	66	a	a	DET
ejpam-3554	118	67	∪	∪	X
ejpam-3554	118	68	{	{	PUNCT
ejpam-3554	118	69	zj	zj	NOUN
ejpam-3554	118	70	:	:	PUNCT
ejpam-3554	118	71	j	j	PROPN
ejpam-3554	118	72	=	=	SYM
ejpam-3554	118	73	1	1	NUM
ejpam-3554	118	74	,	,	PUNCT
ejpam-3554	118	75	2	2	NUM
ejpam-3554	118	76	,	,	PUNCT
ejpam-3554	118	77	...	...	PUNCT
ejpam-3554	118	78	,	,	PUNCT
ejpam-3554	118	79	a	a	PRON
ejpam-3554	118	80	}	}	PUNCT
ejpam-3554	118	81	is	be	AUX
ejpam-3554	118	82	a	a	DET
ejpam-3554	118	83	∂tα	∂tα	NOUN
ejpam-3554	118	84	-	-	PUNCT
ejpam-3554	118	85	set	set	NOUN
ejpam-3554	118	86	in	in	ADP
ejpam-3554	118	87	g3	g3	PROPN
ejpam-3554	118	88	.	.	PUNCT
ejpam-3554	119	1	it	it	PRON
ejpam-3554	119	2	follows	follow	VERB
ejpam-3554	119	3	that	that	SCONJ
ejpam-3554	119	4	∂α(g3	∂α(g3	NOUN
ejpam-3554	119	5	)	)	PUNCT
ejpam-3554	119	6	=	=	PUNCT
ejpam-3554	119	7	|a|	|a|	PROPN
ejpam-3554	119	8	=	=	PROPN
ejpam-3554	119	9	a	a	PROPN
ejpam-3554	119	10	and	and	CCONJ
ejpam-3554	119	11	∂tα(g3	∂tα(g3	NUM
ejpam-3554	119	12	)	)	PUNCT
ejpam-3554	120	1	=	=	PRON
ejpam-3554	120	2	|b|	|b|	X
ejpam-3554	120	3	=	=	SYM
ejpam-3554	120	4	2a	2a	NUM
ejpam-3554	120	5	=	=	SYM
ejpam-3554	120	6	b.	b.	PROPN
ejpam-3554	120	7	this	this	PRON
ejpam-3554	120	8	proves	prove	VERB
ejpam-3554	120	9	the	the	DET
ejpam-3554	120	10	assertion	assertion	NOUN
ejpam-3554	120	11	.	.	PUNCT
ejpam-3554	121	1	�	�	PROPN
ejpam-3554	121	2	corollary	corollary	NOUN
ejpam-3554	121	3	1	1	NUM
ejpam-3554	121	4	.	.	PUNCT
ejpam-3554	122	1	given	give	VERB
ejpam-3554	122	2	a	a	DET
ejpam-3554	122	3	positive	positive	ADJ
ejpam-3554	122	4	integer	integer	NOUN
ejpam-3554	122	5	m	m	NOUN
ejpam-3554	122	6	and	and	CCONJ
ejpam-3554	122	7	α	α	NOUN
ejpam-3554	122	8	=	=	SYM
ejpam-3554	122	9	1	1	NUM
ejpam-3554	122	10	2	2	NUM
ejpam-3554	122	11	,	,	PUNCT
ejpam-3554	122	12	there	there	PRON
ejpam-3554	122	13	exists	exist	VERB
ejpam-3554	122	14	a	a	DET
ejpam-3554	122	15	connected	connected	ADJ
ejpam-3554	122	16	graph	graph	NOUN
ejpam-3554	122	17	g	g	ADP
ejpam-3554	122	18	such	such	ADJ
ejpam-3554	122	19	that	that	DET
ejpam-3554	122	20	∂tα(g	∂tα(g	NOUN
ejpam-3554	122	21	)	)	PUNCT
ejpam-3554	122	22	−	−	PROPN
ejpam-3554	122	23	∂α(g	∂α(g	PROPN
ejpam-3554	122	24	)	)	PUNCT
ejpam-3554	122	25	=	=	PUNCT
ejpam-3554	122	26	m	m	PROPN
ejpam-3554	122	27	,	,	PUNCT
ejpam-3554	122	28	that	that	ADV
ejpam-3554	122	29	is	is	ADV
ejpam-3554	122	30	,	,	PUNCT
ejpam-3554	122	31	the	the	DET
ejpam-3554	122	32	difference	difference	NOUN
ejpam-3554	122	33	∂tα	∂tα	PROPN
ejpam-3554	122	34	−	−	PROPN
ejpam-3554	123	1	∂α	∂α	PROPN
ejpam-3554	123	2	can	can	AUX
ejpam-3554	123	3	be	be	AUX
ejpam-3554	123	4	made	make	VERB
ejpam-3554	123	5	arbitrarily	arbitrarily	ADV
ejpam-3554	123	6	large	large	ADJ
ejpam-3554	123	7	.	.	PUNCT
ejpam-3554	124	1	proof	proof	NOUN
ejpam-3554	124	2	.	.	PUNCT
ejpam-3554	125	1	let	let	VERB
ejpam-3554	125	2	a	a	DET
ejpam-3554	125	3	=	=	NOUN
ejpam-3554	125	4	m	m	PROPN
ejpam-3554	125	5	and	and	CCONJ
ejpam-3554	125	6	b	b	X
ejpam-3554	125	7	=	=	SYM
ejpam-3554	125	8	2	2	NUM
ejpam-3554	125	9	m.	m.	NOUN
ejpam-3554	125	10	by	by	ADP
ejpam-3554	125	11	theorem	theorem	NOUN
ejpam-3554	125	12	2	2	NUM
ejpam-3554	125	13	,	,	PUNCT
ejpam-3554	125	14	there	there	PRON
ejpam-3554	125	15	exists	exist	VERB
ejpam-3554	125	16	a	a	DET
ejpam-3554	125	17	connected	connected	ADJ
ejpam-3554	125	18	graph	graph	NOUN
ejpam-3554	125	19	g	g	NOUN
ejpam-3554	125	20	with	with	ADP
ejpam-3554	125	21	∂tα(g)−	∂tα(g)−	ADJ
ejpam-3554	125	22	∂α(g	∂α(g	PROPN
ejpam-3554	125	23	)	)	PUNCT
ejpam-3554	125	24	=	=	SYM
ejpam-3554	126	1	2m−m	2m−m	NUM
ejpam-3554	126	2	=	=	PUNCT
ejpam-3554	126	3	m.	m.	NOUN
ejpam-3554	126	4	�	�	PROPN
ejpam-3554	126	5	the	the	DET
ejpam-3554	126	6	following	follow	VERB
ejpam-3554	126	7	characterizations	characterization	NOUN
ejpam-3554	126	8	of	of	ADP
ejpam-3554	126	9	partial	partial	ADJ
ejpam-3554	126	10	dominating	dominating	NOUN
ejpam-3554	126	11	sets	set	NOUN
ejpam-3554	126	12	in	in	ADP
ejpam-3554	126	13	the	the	DET
ejpam-3554	126	14	join	join	NOUN
ejpam-3554	126	15	,	,	PUNCT
ejpam-3554	126	16	corona	corona	PROPN
ejpam-3554	126	17	,	,	PUNCT
ejpam-3554	126	18	lexicographic	lexicographic	ADJ
ejpam-3554	126	19	product	product	NOUN
ejpam-3554	126	20	and	and	CCONJ
ejpam-3554	126	21	cartesian	cartesian	ADJ
ejpam-3554	126	22	product	product	NOUN
ejpam-3554	126	23	of	of	ADP
ejpam-3554	126	24	graphs	graph	NOUN
ejpam-3554	126	25	are	be	AUX
ejpam-3554	126	26	found	find	VERB
ejpam-3554	126	27	in	in	ADP
ejpam-3554	126	28	macapodi	macapodi	NOUN
ejpam-3554	126	29	et	et	PROPN
ejpam-3554	126	30	al	al	PROPN
ejpam-3554	126	31	.	.	PUNCT
ejpam-3554	127	1	[	[	X
ejpam-3554	127	2	3	3	NUM
ejpam-3554	127	3	]	]	PUNCT
ejpam-3554	127	4	.	.	PUNCT
ejpam-3554	128	1	theorem	theorem	NOUN
ejpam-3554	128	2	3	3	X
ejpam-3554	128	3	.	.	PUNCT
ejpam-3554	129	1	let	let	VERB
ejpam-3554	129	2	g	g	NOUN
ejpam-3554	130	1	and	and	CCONJ
ejpam-3554	130	2	h	h	NOUN
ejpam-3554	130	3	be	be	AUX
ejpam-3554	130	4	connected	connect	VERB
ejpam-3554	130	5	graphs	graph	NOUN
ejpam-3554	130	6	of	of	ADP
ejpam-3554	130	7	orders	order	NOUN
ejpam-3554	130	8	m	m	VERB
ejpam-3554	130	9	and	and	CCONJ
ejpam-3554	130	10	n	n	CCONJ
ejpam-3554	130	11	,	,	PUNCT
ejpam-3554	130	12	respectively	respectively	ADV
ejpam-3554	130	13	,	,	PUNCT
ejpam-3554	130	14	and	and	CCONJ
ejpam-3554	130	15	let	let	VERB
ejpam-3554	130	16	α	α	PRON
ejpam-3554	130	17	∈	∈	PROPN
ejpam-3554	130	18	(	(	PUNCT
ejpam-3554	130	19	0	0	NUM
ejpam-3554	130	20	,	,	PUNCT
ejpam-3554	130	21	1	1	NUM
ejpam-3554	130	22	]	]	PUNCT
ejpam-3554	130	23	.	.	PUNCT
ejpam-3554	131	1	then	then	ADV
ejpam-3554	131	2	c	c	PROPN
ejpam-3554	131	3	⊆	⊆	NUM
ejpam-3554	131	4	v	v	NOUN
ejpam-3554	131	5	(	(	PUNCT
ejpam-3554	131	6	g+h	g+h	PROPN
ejpam-3554	131	7	)	)	PUNCT
ejpam-3554	131	8	is	be	AUX
ejpam-3554	131	9	an	an	DET
ejpam-3554	131	10	α	α	NOUN
ejpam-3554	131	11	-	-	ADJ
ejpam-3554	131	12	partial	partial	ADJ
ejpam-3554	131	13	dominating	dominating	NOUN
ejpam-3554	131	14	set	set	VERB
ejpam-3554	131	15	in	in	ADP
ejpam-3554	131	16	g+h	g+h	PROPN
ejpam-3554	131	17	if	if	SCONJ
ejpam-3554	131	18	and	and	CCONJ
ejpam-3554	131	19	only	only	ADV
ejpam-3554	131	20	if	if	SCONJ
ejpam-3554	131	21	at	at	ADV
ejpam-3554	131	22	least	least	ADJ
ejpam-3554	131	23	one	one	NUM
ejpam-3554	131	24	of	of	ADP
ejpam-3554	131	25	the	the	DET
ejpam-3554	131	26	following	follow	VERB
ejpam-3554	131	27	is	be	AUX
ejpam-3554	131	28	true	true	ADJ
ejpam-3554	131	29	:	:	PUNCT
ejpam-3554	131	30	(	(	PUNCT
ejpam-3554	131	31	i	i	NOUN
ejpam-3554	131	32	)	)	PUNCT
ejpam-3554	131	33	c	c	PROPN
ejpam-3554	132	1	⊆	⊆	NUM
ejpam-3554	132	2	v	v	NOUN
ejpam-3554	132	3	(	(	PUNCT
ejpam-3554	132	4	g	g	NOUN
ejpam-3554	132	5	)	)	PUNCT
ejpam-3554	132	6	and	and	CCONJ
ejpam-3554	132	7	c	c	PROPN
ejpam-3554	132	8	is	be	AUX
ejpam-3554	132	9	an	an	DET
ejpam-3554	132	10	(	(	PUNCT
ejpam-3554	132	11	α	α	NOUN
ejpam-3554	132	12	,	,	PUNCT
ejpam-3554	132	13	(	(	PUNCT
ejpam-3554	132	14	α−	α−	ADP
ejpam-3554	132	15	1)n)-partial	1)n)-partial	ADJ
ejpam-3554	132	16	dominating	dominating	NOUN
ejpam-3554	132	17	set	set	VERB
ejpam-3554	132	18	in	in	ADP
ejpam-3554	132	19	g.	g.	PROPN
ejpam-3554	132	20	(	(	PUNCT
ejpam-3554	132	21	ii	ii	PROPN
ejpam-3554	132	22	)	)	PUNCT
ejpam-3554	132	23	c	c	PROPN
ejpam-3554	133	1	⊆	⊆	NUM
ejpam-3554	133	2	v	v	NOUN
ejpam-3554	133	3	(	(	PUNCT
ejpam-3554	133	4	h	h	NOUN
ejpam-3554	133	5	)	)	PUNCT
ejpam-3554	133	6	and	and	CCONJ
ejpam-3554	133	7	c	c	PROPN
ejpam-3554	133	8	is	be	AUX
ejpam-3554	133	9	an	an	DET
ejpam-3554	133	10	(	(	PUNCT
ejpam-3554	133	11	α	α	NOUN
ejpam-3554	133	12	,	,	PUNCT
ejpam-3554	133	13	(	(	PUNCT
ejpam-3554	133	14	α−	α−	ADP
ejpam-3554	133	15	1)m)-partial	1)m)-partial	ADJ
ejpam-3554	133	16	dominating	dominating	NOUN
ejpam-3554	133	17	set	set	VERB
ejpam-3554	133	18	in	in	ADP
ejpam-3554	133	19	h.	h.	PROPN
ejpam-3554	133	20	(	(	PUNCT
ejpam-3554	133	21	iii	iii	NOUN
ejpam-3554	133	22	)	)	PUNCT
ejpam-3554	133	23	c	c	NOUN
ejpam-3554	133	24	∩	∩	X
ejpam-3554	133	25	v	v	X
ejpam-3554	133	26	(	(	PUNCT
ejpam-3554	133	27	g	g	NOUN
ejpam-3554	133	28	)	)	PUNCT
ejpam-3554	133	29	6=	6=	ADP
ejpam-3554	133	30	∅	∅	NOUN
ejpam-3554	133	31	and	and	CCONJ
ejpam-3554	133	32	c	c	NOUN
ejpam-3554	133	33	∩	∩	ADJ
ejpam-3554	133	34	v	v	X
ejpam-3554	133	35	(	(	PUNCT
ejpam-3554	133	36	h	h	NOUN
ejpam-3554	133	37	)	)	PUNCT
ejpam-3554	133	38	6=	6=	ADP
ejpam-3554	133	39	∅.	∅.	NOUN
ejpam-3554	133	40	theorem	theorem	VERB
ejpam-3554	133	41	4	4	NUM
ejpam-3554	133	42	.	.	PUNCT
ejpam-3554	134	1	let	let	VERB
ejpam-3554	134	2	g	g	PRON
ejpam-3554	134	3	be	be	AUX
ejpam-3554	134	4	a	a	DET
ejpam-3554	134	5	non	non	ADJ
ejpam-3554	134	6	-	-	ADJ
ejpam-3554	134	7	trivial	trivial	ADJ
ejpam-3554	134	8	connected	connected	ADJ
ejpam-3554	134	9	graph	graph	NOUN
ejpam-3554	134	10	of	of	ADP
ejpam-3554	134	11	order	order	NOUN
ejpam-3554	134	12	m	m	VERB
ejpam-3554	134	13	and	and	CCONJ
ejpam-3554	134	14	h	h	NOUN
ejpam-3554	134	15	be	be	VERB
ejpam-3554	134	16	any	any	DET
ejpam-3554	134	17	graph	graph	NOUN
ejpam-3554	134	18	of	of	ADP
ejpam-3554	134	19	order	order	NOUN
ejpam-3554	134	20	n.	n.	NOUN
ejpam-3554	134	21	let	let	VERB
ejpam-3554	134	22	α	α	PRON
ejpam-3554	134	23	∈	∈	PROPN
ejpam-3554	134	24	(	(	PUNCT
ejpam-3554	134	25	0	0	NUM
ejpam-3554	134	26	,	,	PUNCT
ejpam-3554	134	27	1	1	NUM
ejpam-3554	134	28	]	]	PUNCT
ejpam-3554	134	29	and	and	CCONJ
ejpam-3554	134	30	c	c	PROPN
ejpam-3554	134	31	⊆	⊆	NUM
ejpam-3554	134	32	v	v	NOUN
ejpam-3554	134	33	(	(	PUNCT
ejpam-3554	134	34	g	g	PROPN
ejpam-3554	134	35	◦	◦	NOUN
ejpam-3554	134	36	h	h	NOUN
ejpam-3554	134	37	)	)	PUNCT
ejpam-3554	134	38	.	.	PUNCT
ejpam-3554	135	1	if	if	SCONJ
ejpam-3554	135	2	at	at	ADV
ejpam-3554	135	3	least	least	ADJ
ejpam-3554	135	4	one	one	NUM
ejpam-3554	135	5	of	of	ADP
ejpam-3554	135	6	the	the	DET
ejpam-3554	135	7	following	follow	VERB
ejpam-3554	135	8	holds	hold	VERB
ejpam-3554	135	9	:	:	PUNCT
ejpam-3554	135	10	(	(	PUNCT
ejpam-3554	135	11	i	i	NOUN
ejpam-3554	135	12	)	)	PUNCT
ejpam-3554	135	13	c	c	PROPN
ejpam-3554	135	14	=	=	PUNCT
ejpam-3554	135	15	⋃	⋃	NOUN
ejpam-3554	135	16	v∈v	v∈v	NOUN
ejpam-3554	135	17	(	(	PUNCT
ejpam-3554	135	18	g	g	NOUN
ejpam-3554	135	19	)	)	PUNCT
ejpam-3554	135	20	sv	sv	NOUN
ejpam-3554	135	21	,	,	PUNCT
ejpam-3554	135	22	where	where	SCONJ
ejpam-3554	135	23	sv	sv	PROPN
ejpam-3554	135	24	is	be	AUX
ejpam-3554	135	25	an	an	DET
ejpam-3554	135	26	α	α	NOUN
ejpam-3554	135	27	-	-	ADJ
ejpam-3554	135	28	partial	partial	ADJ
ejpam-3554	135	29	dominating	dominating	NOUN
ejpam-3554	135	30	set	set	VERB
ejpam-3554	135	31	in	in	ADP
ejpam-3554	135	32	hv	hv	PROPN
ejpam-3554	135	33	for	for	ADP
ejpam-3554	135	34	each	each	PRON
ejpam-3554	135	35	v	v	NUM
ejpam-3554	135	36	∈	∈	PROPN
ejpam-3554	135	37	v	v	NOUN
ejpam-3554	135	38	(	(	PUNCT
ejpam-3554	135	39	g	g	NOUN
ejpam-3554	135	40	)	)	PUNCT
ejpam-3554	135	41	,	,	PUNCT
ejpam-3554	135	42	r.	r.	PROPN
ejpam-3554	135	43	macapodi	macapodi	PROPN
ejpam-3554	135	44	,	,	PUNCT
ejpam-3554	135	45	r.	r.	PROPN
ejpam-3554	135	46	isla	isla	PROPN
ejpam-3554	135	47	/	/	SYM
ejpam-3554	135	48	eur	eur	PROPN
ejpam-3554	135	49	.	.	PUNCT
ejpam-3554	136	1	j.	j.	PROPN
ejpam-3554	136	2	pure	pure	PROPN
ejpam-3554	136	3	appl	appl	PROPN
ejpam-3554	136	4	.	.	PROPN
ejpam-3554	136	5	math	math	PROPN
ejpam-3554	136	6	,	,	PUNCT
ejpam-3554	136	7	12	12	NUM
ejpam-3554	136	8	(	(	PUNCT
ejpam-3554	136	9	4	4	NUM
ejpam-3554	136	10	)	)	PUNCT
ejpam-3554	136	11	(	(	PUNCT
ejpam-3554	136	12	2019	2019	NUM
ejpam-3554	136	13	)	)	PUNCT
ejpam-3554	136	14	,	,	PUNCT
ejpam-3554	136	15	1643	1643	NUM
ejpam-3554	136	16	-	-	SYM
ejpam-3554	136	17	1655	1655	NUM
ejpam-3554	136	18	1648	1648	NUM
ejpam-3554	136	19	(	(	PUNCT
ejpam-3554	136	20	ii	ii	NOUN
ejpam-3554	136	21	)	)	PUNCT
ejpam-3554	136	22	c	c	PROPN
ejpam-3554	136	23	⊆	⊆	NUM
ejpam-3554	136	24	v	v	NOUN
ejpam-3554	136	25	(	(	PUNCT
ejpam-3554	136	26	g	g	NOUN
ejpam-3554	136	27	)	)	PUNCT
ejpam-3554	136	28	where	where	SCONJ
ejpam-3554	136	29	either	either	CCONJ
ejpam-3554	136	30	c	c	PROPN
ejpam-3554	136	31	is	be	AUX
ejpam-3554	136	32	a	a	DET
ejpam-3554	136	33	dominating	dominating	NOUN
ejpam-3554	136	34	set	set	NOUN
ejpam-3554	136	35	in	in	ADP
ejpam-3554	136	36	g	g	PROPN
ejpam-3554	136	37	and	and	CCONJ
ejpam-3554	136	38	|c|	|c|	PROPN
ejpam-3554	136	39	≥	≥	NOUN
ejpam-3554	136	40	αm(n+	αm(n+	PROPN
ejpam-3554	136	41	1)−m	1)−m	NUM
ejpam-3554	136	42	n	n	ADP
ejpam-3554	136	43	or	or	CCONJ
ejpam-3554	136	44	|c|	|c|	PROPN
ejpam-3554	136	45	≥	≥	NUM
ejpam-3554	136	46	αm	αm	ADV
ejpam-3554	136	47	,	,	PUNCT
ejpam-3554	136	48	then	then	ADV
ejpam-3554	136	49	c	c	PROPN
ejpam-3554	136	50	is	be	AUX
ejpam-3554	136	51	an	an	DET
ejpam-3554	136	52	α	α	NOUN
ejpam-3554	136	53	-	-	ADJ
ejpam-3554	136	54	partial	partial	ADJ
ejpam-3554	136	55	dominating	dominating	NOUN
ejpam-3554	136	56	set	set	VERB
ejpam-3554	136	57	in	in	ADP
ejpam-3554	136	58	g	g	PROPN
ejpam-3554	136	59	◦	◦	PROPN
ejpam-3554	136	60	h.	h.	NOUN
ejpam-3554	136	61	theorem	theorem	NOUN
ejpam-3554	136	62	5	5	X
ejpam-3554	136	63	.	.	PUNCT
ejpam-3554	137	1	let	let	VERB
ejpam-3554	137	2	g	g	NOUN
ejpam-3554	137	3	and	and	CCONJ
ejpam-3554	137	4	h	h	NOUN
ejpam-3554	137	5	be	be	AUX
ejpam-3554	137	6	connected	connect	VERB
ejpam-3554	137	7	graphs	graph	NOUN
ejpam-3554	137	8	.	.	PUNCT
ejpam-3554	138	1	let	let	VERB
ejpam-3554	138	2	α	α	PRON
ejpam-3554	138	3	∈	∈	PROPN
ejpam-3554	138	4	(	(	PUNCT
ejpam-3554	138	5	0	0	NUM
ejpam-3554	138	6	,	,	PUNCT
ejpam-3554	138	7	1	1	NUM
ejpam-3554	138	8	]	]	PUNCT
ejpam-3554	138	9	and	and	CCONJ
ejpam-3554	138	10	c	c	NOUN
ejpam-3554	138	11	=	=	SYM
ejpam-3554	138	12	⋃	⋃	PROPN
ejpam-3554	138	13	x∈s	x∈s	NOUN
ejpam-3554	138	14	(	(	PUNCT
ejpam-3554	138	15	{	{	PUNCT
ejpam-3554	138	16	x	x	NOUN
ejpam-3554	138	17	}	}	PUNCT
ejpam-3554	138	18	×	×	PROPN
ejpam-3554	138	19	tx	tx	PROPN
ejpam-3554	138	20	)	)	PUNCT
ejpam-3554	138	21	⊆	⊆	NUM
ejpam-3554	138	22	v	v	NOUN
ejpam-3554	138	23	(	(	PUNCT
ejpam-3554	138	24	g[h	g[h	PROPN
ejpam-3554	138	25	]	]	PUNCT
ejpam-3554	138	26	)	)	PUNCT
ejpam-3554	138	27	.	.	PUNCT
ejpam-3554	139	1	if	if	SCONJ
ejpam-3554	139	2	either	either	DET
ejpam-3554	139	3	one	one	NUM
ejpam-3554	139	4	of	of	ADP
ejpam-3554	139	5	the	the	DET
ejpam-3554	139	6	following	follow	VERB
ejpam-3554	139	7	holds	hold	VERB
ejpam-3554	139	8	:	:	PUNCT
ejpam-3554	139	9	(	(	PUNCT
ejpam-3554	139	10	i	i	NOUN
ejpam-3554	139	11	)	)	PUNCT
ejpam-3554	139	12	s	s	VERB
ejpam-3554	139	13	is	be	AUX
ejpam-3554	139	14	a	a	DET
ejpam-3554	139	15	total	total	ADJ
ejpam-3554	139	16	α	α	PRON
ejpam-3554	139	17	-	-	ADJ
ejpam-3554	139	18	partial	partial	ADJ
ejpam-3554	139	19	dominating	dominating	NOUN
ejpam-3554	139	20	set	set	VERB
ejpam-3554	139	21	in	in	ADP
ejpam-3554	139	22	g	g	PROPN
ejpam-3554	139	23	,	,	PUNCT
ejpam-3554	139	24	or	or	CCONJ
ejpam-3554	139	25	(	(	PUNCT
ejpam-3554	139	26	ii	ii	NOUN
ejpam-3554	139	27	)	)	PUNCT
ejpam-3554	139	28	s	s	VERB
ejpam-3554	139	29	is	be	AUX
ejpam-3554	139	30	an	an	DET
ejpam-3554	139	31	α	α	NOUN
ejpam-3554	139	32	-	-	ADJ
ejpam-3554	139	33	partial	partial	ADJ
ejpam-3554	139	34	dominating	dominating	NOUN
ejpam-3554	139	35	set	set	VERB
ejpam-3554	139	36	in	in	ADP
ejpam-3554	139	37	g	g	PROPN
ejpam-3554	139	38	and	and	CCONJ
ejpam-3554	139	39	tx	tx	PROPN
ejpam-3554	139	40	is	be	AUX
ejpam-3554	139	41	a	a	DET
ejpam-3554	139	42	dominating	dominating	NOUN
ejpam-3554	139	43	set	set	VERB
ejpam-3554	139	44	in	in	ADP
ejpam-3554	139	45	h	h	NOUN
ejpam-3554	139	46	for	for	ADP
ejpam-3554	139	47	every	every	DET
ejpam-3554	139	48	x	x	SYM
ejpam-3554	139	49	∈	∈	PROPN
ejpam-3554	139	50	s\ng(s	s\ng(s	NOUN
ejpam-3554	139	51	)	)	PUNCT
ejpam-3554	139	52	,	,	PUNCT
ejpam-3554	139	53	then	then	ADV
ejpam-3554	139	54	c	c	PROPN
ejpam-3554	139	55	is	be	AUX
ejpam-3554	139	56	an	an	DET
ejpam-3554	139	57	α	α	NOUN
ejpam-3554	139	58	-	-	ADJ
ejpam-3554	139	59	partial	partial	ADJ
ejpam-3554	139	60	dominating	dominating	NOUN
ejpam-3554	139	61	set	set	VERB
ejpam-3554	139	62	in	in	ADP
ejpam-3554	139	63	g[h	g[h	PROPN
ejpam-3554	139	64	]	]	PUNCT
ejpam-3554	139	65	.	.	PUNCT
ejpam-3554	140	1	theorem	theorem	ADJ
ejpam-3554	140	2	6	6	NUM
ejpam-3554	140	3	.	.	PUNCT
ejpam-3554	141	1	let	let	VERB
ejpam-3554	141	2	g	g	NOUN
ejpam-3554	141	3	and	and	CCONJ
ejpam-3554	141	4	h	h	NOUN
ejpam-3554	141	5	be	be	AUX
ejpam-3554	141	6	nontrivial	nontrivial	ADJ
ejpam-3554	141	7	connected	connect	VERB
ejpam-3554	141	8	graphs	graph	NOUN
ejpam-3554	141	9	and	and	CCONJ
ejpam-3554	141	10	α	α	PRON
ejpam-3554	141	11	∈	∈	PROPN
ejpam-3554	141	12	(	(	PUNCT
ejpam-3554	141	13	0	0	NUM
ejpam-3554	141	14	,	,	PUNCT
ejpam-3554	141	15	1	1	NUM
ejpam-3554	141	16	]	]	PUNCT
ejpam-3554	141	17	.	.	PUNCT
ejpam-3554	142	1	then	then	ADV
ejpam-3554	142	2	c1	c1	PROPN
ejpam-3554	142	3	=	=	PROPN
ejpam-3554	143	1	s1	s1	PROPN
ejpam-3554	143	2	×	×	PROPN
ejpam-3554	143	3	v	v	NOUN
ejpam-3554	143	4	(	(	PUNCT
ejpam-3554	143	5	h	h	NOUN
ejpam-3554	143	6	)	)	PUNCT
ejpam-3554	143	7	and	and	CCONJ
ejpam-3554	143	8	c2	c2	PROPN
ejpam-3554	143	9	=	=	SYM
ejpam-3554	143	10	v	v	PROPN
ejpam-3554	143	11	(	(	PUNCT
ejpam-3554	143	12	g	g	NOUN
ejpam-3554	143	13	)	)	PUNCT
ejpam-3554	143	14	×	×	NOUN
ejpam-3554	143	15	s2	s2	NOUN
ejpam-3554	143	16	are	be	AUX
ejpam-3554	143	17	α	α	DET
ejpam-3554	143	18	-	-	ADJ
ejpam-3554	143	19	partial	partial	ADJ
ejpam-3554	143	20	dominating	dominating	NOUN
ejpam-3554	143	21	sets	set	NOUN
ejpam-3554	143	22	in	in	ADP
ejpam-3554	143	23	g	g	PROPN
ejpam-3554	143	24	�	�	NOUN
ejpam-3554	143	25	h	h	NOUN
ejpam-3554	143	26	if	if	SCONJ
ejpam-3554	144	1	and	and	CCONJ
ejpam-3554	144	2	only	only	ADV
ejpam-3554	144	3	if	if	SCONJ
ejpam-3554	144	4	s1	s1	PROPN
ejpam-3554	144	5	and	and	CCONJ
ejpam-3554	144	6	s2	s2	PROPN
ejpam-3554	144	7	are	be	AUX
ejpam-3554	144	8	α	α	DET
ejpam-3554	144	9	-	-	ADJ
ejpam-3554	144	10	partial	partial	ADJ
ejpam-3554	144	11	dominating	dominating	NOUN
ejpam-3554	144	12	sets	set	NOUN
ejpam-3554	144	13	in	in	ADP
ejpam-3554	144	14	g	g	PROPN
ejpam-3554	144	15	and	and	CCONJ
ejpam-3554	144	16	h	h	NOUN
ejpam-3554	144	17	,	,	PUNCT
ejpam-3554	144	18	respectively	respectively	ADV
ejpam-3554	144	19	.	.	PUNCT
ejpam-3554	145	1	3	3	X
ejpam-3554	145	2	.	.	X
ejpam-3554	145	3	main	main	ADJ
ejpam-3554	145	4	results	result	NOUN
ejpam-3554	145	5	we	we	PRON
ejpam-3554	145	6	characterize	characterize	VERB
ejpam-3554	145	7	the	the	DET
ejpam-3554	145	8	total	total	ADJ
ejpam-3554	145	9	partial	partial	ADJ
ejpam-3554	145	10	dominating	dominating	NOUN
ejpam-3554	145	11	sets	set	NOUN
ejpam-3554	145	12	in	in	ADP
ejpam-3554	145	13	the	the	DET
ejpam-3554	145	14	join	join	NOUN
ejpam-3554	145	15	,	,	PUNCT
ejpam-3554	145	16	corona	corona	PROPN
ejpam-3554	145	17	,	,	PUNCT
ejpam-3554	145	18	lexicographic	lexicographic	ADJ
ejpam-3554	145	19	product	product	NOUN
ejpam-3554	145	20	and	and	CCONJ
ejpam-3554	145	21	cartesian	cartesian	ADJ
ejpam-3554	145	22	product	product	NOUN
ejpam-3554	145	23	of	of	ADP
ejpam-3554	145	24	graphs	graph	NOUN
ejpam-3554	145	25	in	in	ADP
ejpam-3554	145	26	this	this	DET
ejpam-3554	145	27	section	section	NOUN
ejpam-3554	145	28	.	.	PUNCT
ejpam-3554	146	1	remark	remark	PROPN
ejpam-3554	146	2	5	5	NUM
ejpam-3554	146	3	.	.	PUNCT
ejpam-3554	147	1	every	every	DET
ejpam-3554	147	2	total	total	NOUN
ejpam-3554	147	3	(	(	PUNCT
ejpam-3554	147	4	α	α	NOUN
ejpam-3554	147	5	,	,	PUNCT
ejpam-3554	147	6	(	(	PUNCT
ejpam-3554	147	7	α	α	NOUN
ejpam-3554	147	8	−	−	PROPN
ejpam-3554	147	9	1)n)-partial	1)n)-partial	ADJ
ejpam-3554	147	10	dominating	dominating	NOUN
ejpam-3554	147	11	set	set	NOUN
ejpam-3554	147	12	is	be	AUX
ejpam-3554	147	13	an	an	DET
ejpam-3554	147	14	(	(	PUNCT
ejpam-3554	147	15	α	α	NOUN
ejpam-3554	147	16	,	,	PUNCT
ejpam-3554	147	17	(	(	PUNCT
ejpam-3554	147	18	α	α	NOUN
ejpam-3554	147	19	−	−	PROPN
ejpam-3554	147	20	1)n)-partial	1)n)-partial	ADJ
ejpam-3554	147	21	dominating	dominating	NOUN
ejpam-3554	147	22	set	set	NOUN
ejpam-3554	147	23	.	.	PUNCT
ejpam-3554	148	1	remark	remark	PROPN
ejpam-3554	148	2	6	6	NUM
ejpam-3554	148	3	.	.	PUNCT
ejpam-3554	149	1	every	every	DET
ejpam-3554	149	2	total	total	ADJ
ejpam-3554	149	3	α	α	ADJ
ejpam-3554	149	4	-	-	ADJ
ejpam-3554	149	5	partial	partial	ADJ
ejpam-3554	149	6	dominating	dominating	NOUN
ejpam-3554	149	7	set	set	NOUN
ejpam-3554	149	8	is	be	AUX
ejpam-3554	149	9	an	an	DET
ejpam-3554	149	10	α	α	NOUN
ejpam-3554	149	11	-	-	ADJ
ejpam-3554	149	12	partial	partial	ADJ
ejpam-3554	149	13	dominating	dominating	NOUN
ejpam-3554	149	14	set	set	NOUN
ejpam-3554	149	15	.	.	PUNCT
ejpam-3554	150	1	theorem	theorem	VERB
ejpam-3554	150	2	7	7	NUM
ejpam-3554	150	3	.	.	PUNCT
ejpam-3554	151	1	let	let	VERB
ejpam-3554	151	2	g	g	NOUN
ejpam-3554	152	1	and	and	CCONJ
ejpam-3554	152	2	h	h	NOUN
ejpam-3554	152	3	be	be	AUX
ejpam-3554	152	4	connected	connect	VERB
ejpam-3554	152	5	graphs	graph	NOUN
ejpam-3554	152	6	of	of	ADP
ejpam-3554	152	7	orders	order	NOUN
ejpam-3554	152	8	m	m	VERB
ejpam-3554	152	9	and	and	CCONJ
ejpam-3554	152	10	n	n	CCONJ
ejpam-3554	152	11	,	,	PUNCT
ejpam-3554	152	12	respectively	respectively	ADV
ejpam-3554	152	13	,	,	PUNCT
ejpam-3554	152	14	and	and	CCONJ
ejpam-3554	152	15	let	let	VERB
ejpam-3554	152	16	α	α	PRON
ejpam-3554	152	17	∈	∈	PROPN
ejpam-3554	152	18	(	(	PUNCT
ejpam-3554	152	19	0	0	NUM
ejpam-3554	152	20	,	,	PUNCT
ejpam-3554	152	21	1	1	NUM
ejpam-3554	152	22	]	]	PUNCT
ejpam-3554	152	23	.	.	PUNCT
ejpam-3554	153	1	then	then	ADV
ejpam-3554	153	2	c	c	PROPN
ejpam-3554	153	3	⊆	⊆	NUM
ejpam-3554	153	4	v	v	NOUN
ejpam-3554	153	5	(	(	PUNCT
ejpam-3554	153	6	g+h	g+h	PROPN
ejpam-3554	153	7	)	)	PUNCT
ejpam-3554	153	8	is	be	AUX
ejpam-3554	153	9	a	a	DET
ejpam-3554	153	10	total	total	ADJ
ejpam-3554	153	11	α	α	PRON
ejpam-3554	153	12	-	-	ADJ
ejpam-3554	153	13	partial	partial	ADJ
ejpam-3554	153	14	dominating	dominating	NOUN
ejpam-3554	153	15	set	set	VERB
ejpam-3554	153	16	in	in	ADP
ejpam-3554	153	17	g+h	g+h	PROPN
ejpam-3554	153	18	if	if	SCONJ
ejpam-3554	153	19	and	and	CCONJ
ejpam-3554	153	20	only	only	ADV
ejpam-3554	153	21	if	if	SCONJ
ejpam-3554	153	22	at	at	ADV
ejpam-3554	153	23	least	least	ADJ
ejpam-3554	153	24	one	one	NUM
ejpam-3554	153	25	of	of	ADP
ejpam-3554	153	26	the	the	DET
ejpam-3554	153	27	following	follow	VERB
ejpam-3554	153	28	is	be	AUX
ejpam-3554	153	29	true	true	ADJ
ejpam-3554	153	30	:	:	PUNCT
ejpam-3554	153	31	(	(	PUNCT
ejpam-3554	153	32	a	a	X
ejpam-3554	153	33	)	)	PUNCT
ejpam-3554	153	34	c	c	NOUN
ejpam-3554	153	35	⊆	⊆	NUM
ejpam-3554	153	36	v	v	NOUN
ejpam-3554	153	37	(	(	PUNCT
ejpam-3554	153	38	g	g	NOUN
ejpam-3554	153	39	)	)	PUNCT
ejpam-3554	153	40	and	and	CCONJ
ejpam-3554	153	41	c	c	PROPN
ejpam-3554	153	42	is	be	AUX
ejpam-3554	153	43	a	a	DET
ejpam-3554	153	44	total	total	ADJ
ejpam-3554	153	45	(	(	PUNCT
ejpam-3554	153	46	α	α	X
ejpam-3554	153	47	,	,	PUNCT
ejpam-3554	153	48	(	(	PUNCT
ejpam-3554	153	49	α−	α−	ADP
ejpam-3554	153	50	1)n)-partial	1)n)-partial	ADJ
ejpam-3554	153	51	dominating	dominating	NOUN
ejpam-3554	153	52	set	set	VERB
ejpam-3554	153	53	in	in	ADP
ejpam-3554	153	54	g.	g.	PROPN
ejpam-3554	153	55	(	(	PUNCT
ejpam-3554	153	56	b	b	X
ejpam-3554	153	57	)	)	PUNCT
ejpam-3554	153	58	c	c	NOUN
ejpam-3554	153	59	⊆	⊆	NUM
ejpam-3554	153	60	v	v	NOUN
ejpam-3554	153	61	(	(	PUNCT
ejpam-3554	153	62	h	h	NOUN
ejpam-3554	153	63	)	)	PUNCT
ejpam-3554	153	64	and	and	CCONJ
ejpam-3554	153	65	c	c	PROPN
ejpam-3554	153	66	is	be	AUX
ejpam-3554	153	67	a	a	DET
ejpam-3554	153	68	total	total	ADJ
ejpam-3554	153	69	(	(	PUNCT
ejpam-3554	153	70	α	α	X
ejpam-3554	153	71	,	,	PUNCT
ejpam-3554	153	72	(	(	PUNCT
ejpam-3554	153	73	α−	α−	ADP
ejpam-3554	153	74	1)m)-partial	1)m)-partial	ADJ
ejpam-3554	153	75	dominating	dominating	NOUN
ejpam-3554	153	76	set	set	VERB
ejpam-3554	153	77	in	in	ADP
ejpam-3554	153	78	h.	h.	PROPN
ejpam-3554	153	79	(	(	PUNCT
ejpam-3554	153	80	c	c	X
ejpam-3554	153	81	)	)	PUNCT
ejpam-3554	153	82	c	c	NOUN
ejpam-3554	153	83	∩	∩	X
ejpam-3554	153	84	v	v	X
ejpam-3554	153	85	(	(	PUNCT
ejpam-3554	153	86	g	g	NOUN
ejpam-3554	153	87	)	)	PUNCT
ejpam-3554	153	88	6=	6=	ADP
ejpam-3554	153	89	∅	∅	NOUN
ejpam-3554	153	90	and	and	CCONJ
ejpam-3554	153	91	c	c	NOUN
ejpam-3554	153	92	∩	∩	ADJ
ejpam-3554	153	93	v	v	X
ejpam-3554	153	94	(	(	PUNCT
ejpam-3554	153	95	h	h	NOUN
ejpam-3554	153	96	)	)	PUNCT
ejpam-3554	153	97	6=	6=	ADP
ejpam-3554	153	98	∅.	∅.	PRON
ejpam-3554	153	99	proof	proof	NOUN
ejpam-3554	153	100	.	.	PUNCT
ejpam-3554	154	1	suppose	suppose	VERB
ejpam-3554	154	2	c	c	SYM
ejpam-3554	154	3	⊆	⊆	NUM
ejpam-3554	154	4	v	v	NOUN
ejpam-3554	154	5	(	(	PUNCT
ejpam-3554	154	6	g	g	PROPN
ejpam-3554	154	7	+	+	NOUN
ejpam-3554	154	8	h	h	NOUN
ejpam-3554	154	9	)	)	PUNCT
ejpam-3554	154	10	is	be	AUX
ejpam-3554	154	11	a	a	DET
ejpam-3554	154	12	total	total	ADJ
ejpam-3554	154	13	α	α	PRON
ejpam-3554	154	14	-	-	ADJ
ejpam-3554	154	15	partial	partial	ADJ
ejpam-3554	154	16	dominating	dominating	NOUN
ejpam-3554	154	17	set	set	VERB
ejpam-3554	154	18	in	in	ADP
ejpam-3554	154	19	g	g	PROPN
ejpam-3554	154	20	+	+	CCONJ
ejpam-3554	154	21	h.	h.	PROPN
ejpam-3554	154	22	then	then	ADV
ejpam-3554	154	23	by	by	ADP
ejpam-3554	154	24	remark	remark	NOUN
ejpam-3554	154	25	6	6	NUM
ejpam-3554	154	26	,	,	PUNCT
ejpam-3554	154	27	c	c	PROPN
ejpam-3554	154	28	is	be	AUX
ejpam-3554	154	29	an	an	DET
ejpam-3554	154	30	α	α	NOUN
ejpam-3554	154	31	-	-	ADJ
ejpam-3554	154	32	partial	partial	ADJ
ejpam-3554	154	33	dominating	dominating	NOUN
ejpam-3554	154	34	set	set	VERB
ejpam-3554	154	35	in	in	ADP
ejpam-3554	154	36	g+h	g+h	PROPN
ejpam-3554	154	37	.	.	PUNCT
ejpam-3554	155	1	by	by	ADP
ejpam-3554	155	2	theorem	theorem	NOUN
ejpam-3554	155	3	3	3	NUM
ejpam-3554	155	4	,	,	PUNCT
ejpam-3554	155	5	at	at	ADV
ejpam-3554	155	6	least	least	ADJ
ejpam-3554	155	7	one	one	NUM
ejpam-3554	155	8	of	of	ADP
ejpam-3554	155	9	the	the	DET
ejpam-3554	155	10	following	follow	VERB
ejpam-3554	155	11	is	be	AUX
ejpam-3554	155	12	true	true	ADJ
ejpam-3554	155	13	:	:	PUNCT
ejpam-3554	155	14	(	(	PUNCT
ejpam-3554	155	15	i	i	NOUN
ejpam-3554	155	16	)	)	PUNCT
ejpam-3554	155	17	c	c	PROPN
ejpam-3554	156	1	⊆	⊆	NUM
ejpam-3554	156	2	v	v	NOUN
ejpam-3554	156	3	(	(	PUNCT
ejpam-3554	156	4	g	g	NOUN
ejpam-3554	156	5	)	)	PUNCT
ejpam-3554	156	6	and	and	CCONJ
ejpam-3554	156	7	c	c	PROPN
ejpam-3554	156	8	is	be	AUX
ejpam-3554	156	9	an	an	DET
ejpam-3554	156	10	(	(	PUNCT
ejpam-3554	156	11	α	α	NOUN
ejpam-3554	156	12	,	,	PUNCT
ejpam-3554	156	13	(	(	PUNCT
ejpam-3554	156	14	α−	α−	ADP
ejpam-3554	156	15	1)n)-partial	1)n)-partial	ADJ
ejpam-3554	156	16	dominating	dominating	NOUN
ejpam-3554	156	17	set	set	NOUN
ejpam-3554	156	18	in	in	ADP
ejpam-3554	156	19	g	g	PROPN
ejpam-3554	156	20	,	,	PUNCT
ejpam-3554	156	21	(	(	PUNCT
ejpam-3554	156	22	ii	ii	NOUN
ejpam-3554	156	23	)	)	PUNCT
ejpam-3554	156	24	c	c	PROPN
ejpam-3554	157	1	⊆	⊆	NUM
ejpam-3554	157	2	v	v	NOUN
ejpam-3554	157	3	(	(	PUNCT
ejpam-3554	157	4	h	h	NOUN
ejpam-3554	157	5	)	)	PUNCT
ejpam-3554	157	6	and	and	CCONJ
ejpam-3554	157	7	c	c	PROPN
ejpam-3554	157	8	is	be	AUX
ejpam-3554	157	9	an	an	DET
ejpam-3554	157	10	(	(	PUNCT
ejpam-3554	157	11	α	α	NOUN
ejpam-3554	157	12	,	,	PUNCT
ejpam-3554	157	13	(	(	PUNCT
ejpam-3554	157	14	α−	α−	ADP
ejpam-3554	157	15	1)m)-partial	1)m)-partial	ADJ
ejpam-3554	157	16	dominating	dominating	NOUN
ejpam-3554	157	17	set	set	VERB
ejpam-3554	157	18	in	in	ADP
ejpam-3554	157	19	h	h	NOUN
ejpam-3554	157	20	,	,	PUNCT
ejpam-3554	157	21	or	or	CCONJ
ejpam-3554	157	22	(	(	PUNCT
ejpam-3554	157	23	iii	iii	X
ejpam-3554	157	24	)	)	PUNCT
ejpam-3554	157	25	c	c	NOUN
ejpam-3554	157	26	∩	∩	X
ejpam-3554	157	27	v	v	X
ejpam-3554	157	28	(	(	PUNCT
ejpam-3554	157	29	g	g	NOUN
ejpam-3554	157	30	)	)	PUNCT
ejpam-3554	157	31	6=	6=	ADP
ejpam-3554	157	32	∅	∅	NOUN
ejpam-3554	157	33	and	and	CCONJ
ejpam-3554	157	34	c	c	NOUN
ejpam-3554	157	35	∩	∩	ADJ
ejpam-3554	157	36	v	v	X
ejpam-3554	157	37	(	(	PUNCT
ejpam-3554	157	38	h	h	NOUN
ejpam-3554	157	39	)	)	PUNCT
ejpam-3554	157	40	6=	6=	ADP
ejpam-3554	157	41	∅.	∅.	AUX
ejpam-3554	157	42	suppose	suppose	VERB
ejpam-3554	157	43	(	(	PUNCT
ejpam-3554	157	44	i	i	NOUN
ejpam-3554	157	45	)	)	PUNCT
ejpam-3554	157	46	holds	hold	VERB
ejpam-3554	157	47	.	.	PUNCT
ejpam-3554	158	1	since	since	SCONJ
ejpam-3554	158	2	c	c	PROPN
ejpam-3554	158	3	is	be	AUX
ejpam-3554	158	4	a	a	DET
ejpam-3554	158	5	total	total	ADJ
ejpam-3554	158	6	α	α	PRON
ejpam-3554	158	7	-	-	ADJ
ejpam-3554	158	8	partial	partial	ADJ
ejpam-3554	158	9	dominating	dominating	NOUN
ejpam-3554	158	10	set	set	VERB
ejpam-3554	158	11	in	in	ADP
ejpam-3554	158	12	g+h	g+h	PROPN
ejpam-3554	158	13	and	and	CCONJ
ejpam-3554	158	14	c	c	PROPN
ejpam-3554	158	15	⊆	⊆	NUM
ejpam-3554	158	16	v	v	NOUN
ejpam-3554	158	17	(	(	PUNCT
ejpam-3554	158	18	g	g	NOUN
ejpam-3554	158	19	)	)	PUNCT
ejpam-3554	158	20	,	,	PUNCT
ejpam-3554	158	21	it	it	PRON
ejpam-3554	158	22	follows	follow	VERB
ejpam-3554	158	23	that	that	SCONJ
ejpam-3554	158	24	c	c	PROPN
ejpam-3554	158	25	is	be	AUX
ejpam-3554	158	26	a	a	DET
ejpam-3554	158	27	total	total	ADJ
ejpam-3554	158	28	α	α	PRON
ejpam-3554	158	29	-	-	ADJ
ejpam-3554	158	30	partial	partial	ADJ
ejpam-3554	158	31	dominating	dominating	NOUN
ejpam-3554	158	32	set	set	VERB
ejpam-3554	158	33	in	in	ADP
ejpam-3554	158	34	g.	g.	PROPN
ejpam-3554	158	35	hence	hence	ADV
ejpam-3554	158	36	,	,	PUNCT
ejpam-3554	158	37	c	c	PROPN
ejpam-3554	158	38	is	be	AUX
ejpam-3554	158	39	a	a	DET
ejpam-3554	158	40	total	total	ADJ
ejpam-3554	158	41	(	(	PUNCT
ejpam-3554	158	42	α	α	X
ejpam-3554	158	43	,	,	PUNCT
ejpam-3554	158	44	(	(	PUNCT
ejpam-3554	158	45	α	α	NOUN
ejpam-3554	158	46	−	−	PROPN
ejpam-3554	158	47	1)n)-partial	1)n)-partial	ADJ
ejpam-3554	158	48	dominating	dominating	NOUN
ejpam-3554	158	49	set	set	VERB
ejpam-3554	158	50	in	in	ADP
ejpam-3554	158	51	g	g	NOUN
ejpam-3554	158	52	,	,	PUNCT
ejpam-3554	158	53	so	so	ADV
ejpam-3554	158	54	condition	condition	NOUN
ejpam-3554	158	55	(	(	PUNCT
ejpam-3554	158	56	a	a	NOUN
ejpam-3554	158	57	)	)	PUNCT
ejpam-3554	158	58	holds	hold	NOUN
ejpam-3554	158	59	.	.	PUNCT
ejpam-3554	159	1	similarly	similarly	ADV
ejpam-3554	159	2	,	,	PUNCT
ejpam-3554	159	3	r.	r.	PROPN
ejpam-3554	159	4	macapodi	macapodi	PROPN
ejpam-3554	159	5	,	,	PUNCT
ejpam-3554	159	6	r.	r.	PROPN
ejpam-3554	159	7	isla	isla	PROPN
ejpam-3554	159	8	/	/	SYM
ejpam-3554	159	9	eur	eur	PROPN
ejpam-3554	159	10	.	.	PUNCT
ejpam-3554	160	1	j.	j.	PROPN
ejpam-3554	160	2	pure	pure	PROPN
ejpam-3554	160	3	appl	appl	PROPN
ejpam-3554	160	4	.	.	PROPN
ejpam-3554	160	5	math	math	PROPN
ejpam-3554	160	6	,	,	PUNCT
ejpam-3554	160	7	12	12	NUM
ejpam-3554	160	8	(	(	PUNCT
ejpam-3554	160	9	4	4	NUM
ejpam-3554	160	10	)	)	PUNCT
ejpam-3554	160	11	(	(	PUNCT
ejpam-3554	160	12	2019	2019	NUM
ejpam-3554	160	13	)	)	PUNCT
ejpam-3554	160	14	,	,	PUNCT
ejpam-3554	160	15	1643	1643	NUM
ejpam-3554	160	16	-	-	SYM
ejpam-3554	160	17	1655	1655	NUM
ejpam-3554	160	18	1649	1649	NUM
ejpam-3554	160	19	if	if	SCONJ
ejpam-3554	160	20	(	(	PUNCT
ejpam-3554	160	21	ii	ii	NOUN
ejpam-3554	160	22	)	)	PUNCT
ejpam-3554	160	23	holds	hold	VERB
ejpam-3554	160	24	,	,	PUNCT
ejpam-3554	160	25	then	then	ADV
ejpam-3554	160	26	condition	condition	NOUN
ejpam-3554	160	27	(	(	PUNCT
ejpam-3554	160	28	b	b	NOUN
ejpam-3554	160	29	)	)	PUNCT
ejpam-3554	160	30	is	be	AUX
ejpam-3554	160	31	true	true	ADJ
ejpam-3554	160	32	.	.	PUNCT
ejpam-3554	161	1	finally	finally	ADV
ejpam-3554	161	2	,	,	PUNCT
ejpam-3554	161	3	condition	condition	NOUN
ejpam-3554	161	4	(	(	PUNCT
ejpam-3554	161	5	iii	iii	NOUN
ejpam-3554	161	6	)	)	PUNCT
ejpam-3554	161	7	is	be	AUX
ejpam-3554	161	8	the	the	DET
ejpam-3554	161	9	same	same	ADJ
ejpam-3554	161	10	as	as	ADP
ejpam-3554	161	11	condition	condition	NOUN
ejpam-3554	161	12	(	(	PUNCT
ejpam-3554	161	13	c	c	NOUN
ejpam-3554	161	14	)	)	PUNCT
ejpam-3554	161	15	.	.	PUNCT
ejpam-3554	162	1	for	for	ADP
ejpam-3554	162	2	the	the	DET
ejpam-3554	162	3	converse	converse	NOUN
ejpam-3554	162	4	,	,	PUNCT
ejpam-3554	162	5	suppose	suppose	VERB
ejpam-3554	162	6	condition	condition	NOUN
ejpam-3554	162	7	(	(	PUNCT
ejpam-3554	162	8	a	a	NOUN
ejpam-3554	162	9	)	)	PUNCT
ejpam-3554	162	10	holds	hold	NOUN
ejpam-3554	162	11	.	.	PUNCT
ejpam-3554	163	1	then	then	ADV
ejpam-3554	163	2	c	c	PROPN
ejpam-3554	163	3	⊆	⊆	NUM
ejpam-3554	163	4	v	v	X
ejpam-3554	163	5	(	(	PUNCT
ejpam-3554	163	6	g	g	NOUN
ejpam-3554	163	7	)	)	PUNCT
ejpam-3554	163	8	and	and	CCONJ
ejpam-3554	163	9	c	c	PROPN
ejpam-3554	163	10	is	be	AUX
ejpam-3554	163	11	an	an	DET
ejpam-3554	163	12	(	(	PUNCT
ejpam-3554	163	13	α	α	NOUN
ejpam-3554	163	14	,	,	PUNCT
ejpam-3554	163	15	(	(	PUNCT
ejpam-3554	163	16	α−1)n)-partial	α−1)n)-partial	ADJ
ejpam-3554	163	17	dominating	dominating	NOUN
ejpam-3554	163	18	set	set	VERB
ejpam-3554	163	19	in	in	ADP
ejpam-3554	163	20	g	g	NOUN
ejpam-3554	163	21	by	by	ADP
ejpam-3554	163	22	remark	remark	NOUN
ejpam-3554	163	23	5	5	NUM
ejpam-3554	163	24	.	.	PUNCT
ejpam-3554	164	1	thus	thus	ADV
ejpam-3554	164	2	,	,	PUNCT
ejpam-3554	164	3	by	by	ADP
ejpam-3554	164	4	theorem	theorem	NOUN
ejpam-3554	164	5	3	3	NUM
ejpam-3554	164	6	,	,	PUNCT
ejpam-3554	164	7	c	c	PROPN
ejpam-3554	164	8	⊆	⊆	NUM
ejpam-3554	164	9	v	v	NOUN
ejpam-3554	164	10	(	(	PUNCT
ejpam-3554	164	11	g+h	g+h	PROPN
ejpam-3554	164	12	)	)	PUNCT
ejpam-3554	164	13	is	be	AUX
ejpam-3554	164	14	an	an	DET
ejpam-3554	164	15	α	α	NOUN
ejpam-3554	164	16	-	-	ADJ
ejpam-3554	164	17	partial	partial	ADJ
ejpam-3554	164	18	dominating	dominating	NOUN
ejpam-3554	164	19	set	set	VERB
ejpam-3554	164	20	in	in	ADP
ejpam-3554	164	21	g+h	g+h	PROPN
ejpam-3554	164	22	.	.	PUNCT
ejpam-3554	165	1	let	let	VERB
ejpam-3554	165	2	x	x	SYM
ejpam-3554	165	3	∈	∈	PROPN
ejpam-3554	165	4	c.	c.	NOUN
ejpam-3554	165	5	since	since	SCONJ
ejpam-3554	165	6	c	c	PROPN
ejpam-3554	165	7	is	be	AUX
ejpam-3554	165	8	a	a	DET
ejpam-3554	165	9	total	total	ADJ
ejpam-3554	165	10	(	(	PUNCT
ejpam-3554	165	11	α	α	X
ejpam-3554	165	12	,	,	PUNCT
ejpam-3554	165	13	(	(	PUNCT
ejpam-3554	165	14	α−1)n)-partial	α−1)n)-partial	ADJ
ejpam-3554	165	15	dominating	dominating	NOUN
ejpam-3554	165	16	set	set	VERB
ejpam-3554	165	17	in	in	ADP
ejpam-3554	165	18	g	g	NOUN
ejpam-3554	165	19	,	,	PUNCT
ejpam-3554	165	20	there	there	PRON
ejpam-3554	165	21	exists	exist	VERB
ejpam-3554	165	22	a	a	DET
ejpam-3554	165	23	y	y	PROPN
ejpam-3554	165	24	∈	∈	PROPN
ejpam-3554	165	25	c	c	NOUN
ejpam-3554	166	1	such	such	ADJ
ejpam-3554	166	2	that	that	SCONJ
ejpam-3554	166	3	xy	xy	PROPN
ejpam-3554	166	4	∈	∈	PROPN
ejpam-3554	166	5	e	e	X
ejpam-3554	166	6	(	(	PUNCT
ejpam-3554	166	7	〈	〈	PROPN
ejpam-3554	166	8	c	c	PROPN
ejpam-3554	166	9	〉	〉	NUM
ejpam-3554	166	10	)	)	PUNCT
ejpam-3554	166	11	.	.	PUNCT
ejpam-3554	167	1	thus	thus	ADV
ejpam-3554	167	2	,	,	PUNCT
ejpam-3554	167	3	c	c	PROPN
ejpam-3554	167	4	is	be	AUX
ejpam-3554	167	5	a	a	DET
ejpam-3554	167	6	total	total	ADJ
ejpam-3554	167	7	α	α	PRON
ejpam-3554	167	8	-	-	ADJ
ejpam-3554	167	9	partial	partial	ADJ
ejpam-3554	167	10	dominating	dominating	NOUN
ejpam-3554	167	11	set	set	VERB
ejpam-3554	167	12	in	in	ADP
ejpam-3554	167	13	g	g	PROPN
ejpam-3554	167	14	+	+	CCONJ
ejpam-3554	167	15	h.	h.	PROPN
ejpam-3554	167	16	similarly	similarly	ADV
ejpam-3554	167	17	,	,	PUNCT
ejpam-3554	167	18	if	if	SCONJ
ejpam-3554	167	19	condition	condition	NOUN
ejpam-3554	167	20	(	(	PUNCT
ejpam-3554	167	21	b	b	NOUN
ejpam-3554	167	22	)	)	PUNCT
ejpam-3554	167	23	holds	hold	VERB
ejpam-3554	167	24	,	,	PUNCT
ejpam-3554	167	25	it	it	PRON
ejpam-3554	167	26	can	can	AUX
ejpam-3554	167	27	be	be	AUX
ejpam-3554	167	28	shown	show	VERB
ejpam-3554	167	29	that	that	SCONJ
ejpam-3554	167	30	if	if	SCONJ
ejpam-3554	167	31	g	g	PROPN
ejpam-3554	167	32	∈	∈	PROPN
ejpam-3554	167	33	c	c	NOUN
ejpam-3554	167	34	⊆	⊆	NUM
ejpam-3554	167	35	v	v	X
ejpam-3554	167	36	(	(	PUNCT
ejpam-3554	167	37	h	h	NOUN
ejpam-3554	167	38	)	)	PUNCT
ejpam-3554	167	39	,	,	PUNCT
ejpam-3554	167	40	then	then	ADV
ejpam-3554	167	41	there	there	PRON
ejpam-3554	167	42	exists	exist	VERB
ejpam-3554	167	43	an	an	DET
ejpam-3554	167	44	h	h	NOUN
ejpam-3554	167	45	∈	∈	NOUN
ejpam-3554	167	46	c	c	NOUN
ejpam-3554	167	47	such	such	ADJ
ejpam-3554	167	48	that	that	SCONJ
ejpam-3554	167	49	gh	gh	PROPN
ejpam-3554	167	50	∈	∈	PROPN
ejpam-3554	167	51	e	e	PROPN
ejpam-3554	167	52	(	(	PUNCT
ejpam-3554	167	53	〈	〈	PROPN
ejpam-3554	167	54	c	c	PROPN
ejpam-3554	167	55	〉	〉	NUM
ejpam-3554	167	56	)	)	PUNCT
ejpam-3554	167	57	.	.	PUNCT
ejpam-3554	168	1	thus	thus	ADV
ejpam-3554	168	2	,	,	PUNCT
ejpam-3554	168	3	c	c	PROPN
ejpam-3554	168	4	is	be	AUX
ejpam-3554	168	5	a	a	DET
ejpam-3554	168	6	total	total	ADJ
ejpam-3554	168	7	α	α	PRON
ejpam-3554	168	8	-	-	ADJ
ejpam-3554	168	9	partial	partial	ADJ
ejpam-3554	168	10	dominating	dominating	NOUN
ejpam-3554	168	11	set	set	VERB
ejpam-3554	168	12	in	in	ADP
ejpam-3554	168	13	g	g	PROPN
ejpam-3554	168	14	+	+	CCONJ
ejpam-3554	168	15	h.	h.	NOUN
ejpam-3554	168	16	if	if	SCONJ
ejpam-3554	168	17	condition	condition	NOUN
ejpam-3554	168	18	(	(	PUNCT
ejpam-3554	168	19	c	c	NOUN
ejpam-3554	168	20	)	)	PUNCT
ejpam-3554	168	21	holds	hold	NOUN
ejpam-3554	168	22	,	,	PUNCT
ejpam-3554	168	23	then	then	ADV
ejpam-3554	168	24	by	by	ADP
ejpam-3554	168	25	theorem	theorem	NOUN
ejpam-3554	168	26	3	3	NUM
ejpam-3554	168	27	,	,	PUNCT
ejpam-3554	168	28	c	c	PROPN
ejpam-3554	168	29	⊆	⊆	NUM
ejpam-3554	168	30	v	v	NOUN
ejpam-3554	168	31	(	(	PUNCT
ejpam-3554	168	32	g	g	PROPN
ejpam-3554	168	33	+	+	NOUN
ejpam-3554	168	34	h	h	NOUN
ejpam-3554	168	35	)	)	PUNCT
ejpam-3554	168	36	is	be	AUX
ejpam-3554	168	37	an	an	DET
ejpam-3554	168	38	α	α	NOUN
ejpam-3554	168	39	-	-	ADJ
ejpam-3554	168	40	partial	partial	ADJ
ejpam-3554	168	41	dominating	dominating	NOUN
ejpam-3554	168	42	set	set	VERB
ejpam-3554	168	43	in	in	ADP
ejpam-3554	168	44	g	g	PROPN
ejpam-3554	168	45	+	+	CCONJ
ejpam-3554	168	46	h.	h.	PROPN
ejpam-3554	168	47	moreover	moreover	ADV
ejpam-3554	168	48	,	,	PUNCT
ejpam-3554	168	49	c	c	PROPN
ejpam-3554	168	50	is	be	AUX
ejpam-3554	168	51	clearly	clearly	ADV
ejpam-3554	168	52	a	a	DET
ejpam-3554	168	53	total	total	ADJ
ejpam-3554	168	54	α	α	PRON
ejpam-3554	168	55	-	-	ADJ
ejpam-3554	168	56	partial	partial	ADJ
ejpam-3554	168	57	dominating	dominating	NOUN
ejpam-3554	168	58	set	set	VERB
ejpam-3554	168	59	in	in	ADP
ejpam-3554	168	60	g+h	g+h	PROPN
ejpam-3554	168	61	.	.	PUNCT
ejpam-3554	169	1	�	�	PROPN
ejpam-3554	169	2	the	the	DET
ejpam-3554	169	3	next	next	ADJ
ejpam-3554	169	4	result	result	NOUN
ejpam-3554	169	5	immediately	immediately	ADV
ejpam-3554	169	6	follows	follow	VERB
ejpam-3554	169	7	by	by	ADP
ejpam-3554	169	8	remark	remark	NOUN
ejpam-3554	169	9	5	5	NUM
ejpam-3554	169	10	and	and	CCONJ
ejpam-3554	169	11	theorem	theorem	VERB
ejpam-3554	169	12	7	7	NUM
ejpam-3554	169	13	.	.	PUNCT
ejpam-3554	169	14	corollary	corollary	ADJ
ejpam-3554	169	15	2	2	NUM
ejpam-3554	169	16	.	.	PUNCT
ejpam-3554	170	1	let	let	VERB
ejpam-3554	170	2	g	g	NOUN
ejpam-3554	170	3	and	and	CCONJ
ejpam-3554	170	4	h	h	NOUN
ejpam-3554	170	5	be	be	AUX
ejpam-3554	170	6	connected	connect	VERB
ejpam-3554	170	7	graphs	graph	NOUN
ejpam-3554	170	8	,	,	PUNCT
ejpam-3554	170	9	α	α	PROPN
ejpam-3554	170	10	∈	∈	PROPN
ejpam-3554	170	11	(	(	PUNCT
ejpam-3554	170	12	0	0	NUM
ejpam-3554	170	13	,	,	PUNCT
ejpam-3554	170	14	1	1	NUM
ejpam-3554	170	15	]	]	PUNCT
ejpam-3554	170	16	and	and	CCONJ
ejpam-3554	170	17	let	let	VERB
ejpam-3554	170	18	c	c	PROPN
ejpam-3554	170	19	⊆	⊆	NUM
ejpam-3554	170	20	v	v	NOUN
ejpam-3554	170	21	(	(	PUNCT
ejpam-3554	170	22	g+h	g+h	NOUN
ejpam-3554	170	23	)	)	PUNCT
ejpam-3554	170	24	satisfying	satisfy	VERB
ejpam-3554	170	25	one	one	NUM
ejpam-3554	170	26	of	of	ADP
ejpam-3554	170	27	the	the	DET
ejpam-3554	170	28	following	following	ADJ
ejpam-3554	170	29	conditions	condition	NOUN
ejpam-3554	170	30	:	:	PUNCT
ejpam-3554	170	31	(	(	PUNCT
ejpam-3554	170	32	i	i	NOUN
ejpam-3554	170	33	)	)	PUNCT
ejpam-3554	170	34	c	c	PROPN
ejpam-3554	171	1	⊆	⊆	NUM
ejpam-3554	171	2	v	v	NOUN
ejpam-3554	171	3	(	(	PUNCT
ejpam-3554	171	4	g	g	NOUN
ejpam-3554	171	5	)	)	PUNCT
ejpam-3554	171	6	is	be	AUX
ejpam-3554	171	7	a	a	DET
ejpam-3554	171	8	total	total	ADJ
ejpam-3554	171	9	α	α	PRON
ejpam-3554	171	10	-	-	ADJ
ejpam-3554	171	11	partial	partial	ADJ
ejpam-3554	171	12	dominating	dominating	NOUN
ejpam-3554	171	13	set	set	VERB
ejpam-3554	171	14	in	in	ADP
ejpam-3554	171	15	g.	g.	PROPN
ejpam-3554	171	16	(	(	PUNCT
ejpam-3554	171	17	ii	ii	PROPN
ejpam-3554	171	18	)	)	PUNCT
ejpam-3554	171	19	c	c	PROPN
ejpam-3554	171	20	⊆	⊆	NUM
ejpam-3554	171	21	v	v	NOUN
ejpam-3554	171	22	(	(	PUNCT
ejpam-3554	171	23	h	h	NOUN
ejpam-3554	171	24	)	)	PUNCT
ejpam-3554	171	25	is	be	AUX
ejpam-3554	171	26	a	a	DET
ejpam-3554	171	27	total	total	ADJ
ejpam-3554	171	28	α	α	PRON
ejpam-3554	171	29	-	-	ADJ
ejpam-3554	171	30	partial	partial	ADJ
ejpam-3554	171	31	dominating	dominating	NOUN
ejpam-3554	171	32	set	set	VERB
ejpam-3554	171	33	in	in	ADP
ejpam-3554	171	34	h.	h.	PROPN
ejpam-3554	171	35	(	(	PUNCT
ejpam-3554	171	36	iii	iii	NOUN
ejpam-3554	171	37	)	)	PUNCT
ejpam-3554	171	38	|c	|c	VERB
ejpam-3554	171	39	∩	∩	ADJ
ejpam-3554	171	40	v	v	NOUN
ejpam-3554	171	41	(	(	PUNCT
ejpam-3554	171	42	g)|	g)|	VERB
ejpam-3554	171	43	≥	≥	NOUN
ejpam-3554	171	44	1	1	NUM
ejpam-3554	171	45	and	and	CCONJ
ejpam-3554	171	46	|c	|c	ADJ
ejpam-3554	171	47	∩	∩	ADJ
ejpam-3554	171	48	v	v	NOUN
ejpam-3554	171	49	(	(	PUNCT
ejpam-3554	171	50	h)|	h)|	PROPN
ejpam-3554	171	51	≥	≥	NUM
ejpam-3554	171	52	1	1	NUM
ejpam-3554	171	53	.	.	PUNCT
ejpam-3554	172	1	then	then	ADV
ejpam-3554	172	2	c	c	PROPN
ejpam-3554	172	3	is	be	AUX
ejpam-3554	172	4	a	a	DET
ejpam-3554	172	5	total	total	ADJ
ejpam-3554	172	6	α	α	PRON
ejpam-3554	172	7	-	-	ADJ
ejpam-3554	172	8	partial	partial	ADJ
ejpam-3554	172	9	dominating	dominating	NOUN
ejpam-3554	172	10	set	set	VERB
ejpam-3554	172	11	in	in	ADP
ejpam-3554	172	12	g+h	g+h	PROPN
ejpam-3554	172	13	.	.	PUNCT
ejpam-3554	173	1	corollary	corollary	ADJ
ejpam-3554	173	2	3	3	X
ejpam-3554	173	3	.	.	PUNCT
ejpam-3554	174	1	let	let	VERB
ejpam-3554	174	2	g	g	NOUN
ejpam-3554	174	3	and	and	CCONJ
ejpam-3554	174	4	h	h	NOUN
ejpam-3554	174	5	be	be	AUX
ejpam-3554	174	6	connected	connect	VERB
ejpam-3554	174	7	graphs	graph	NOUN
ejpam-3554	174	8	of	of	ADP
ejpam-3554	174	9	orders	order	NOUN
ejpam-3554	174	10	m	m	VERB
ejpam-3554	174	11	and	and	CCONJ
ejpam-3554	174	12	n	n	CCONJ
ejpam-3554	174	13	,	,	PUNCT
ejpam-3554	174	14	respectively	respectively	ADV
ejpam-3554	174	15	,	,	PUNCT
ejpam-3554	174	16	and	and	CCONJ
ejpam-3554	174	17	let	let	VERB
ejpam-3554	174	18	α	α	PRON
ejpam-3554	174	19	∈	∈	PROPN
ejpam-3554	174	20	(	(	PUNCT
ejpam-3554	174	21	0	0	NUM
ejpam-3554	174	22	,	,	PUNCT
ejpam-3554	174	23	1	1	NUM
ejpam-3554	174	24	]	]	PUNCT
ejpam-3554	174	25	.	.	PUNCT
ejpam-3554	175	1	then	then	ADV
ejpam-3554	175	2	,	,	PUNCT
ejpam-3554	175	3	∂tα(g+h	∂tα(g+h	PROPN
ejpam-3554	175	4	)	)	PUNCT
ejpam-3554	176	1	=	=	SYM
ejpam-3554	176	2	2	2	X
ejpam-3554	176	3	.	.	X
ejpam-3554	176	4	proof	proof	NOUN
ejpam-3554	176	5	.	.	PUNCT
ejpam-3554	177	1	pick	pick	VERB
ejpam-3554	177	2	x	x	SYM
ejpam-3554	177	3	∈	∈	PROPN
ejpam-3554	177	4	v	v	NOUN
ejpam-3554	177	5	(	(	PUNCT
ejpam-3554	177	6	g	g	NOUN
ejpam-3554	177	7	)	)	PUNCT
ejpam-3554	177	8	,	,	PUNCT
ejpam-3554	177	9	y	y	PROPN
ejpam-3554	177	10	∈	∈	PROPN
ejpam-3554	177	11	v	v	ADP
ejpam-3554	177	12	(	(	PUNCT
ejpam-3554	177	13	h	h	NOUN
ejpam-3554	177	14	)	)	PUNCT
ejpam-3554	177	15	.	.	PUNCT
ejpam-3554	178	1	clearly	clearly	ADV
ejpam-3554	178	2	,	,	PUNCT
ejpam-3554	178	3	s	s	VERB
ejpam-3554	178	4	=	=	PUNCT
ejpam-3554	178	5	{	{	PUNCT
ejpam-3554	178	6	x	x	PROPN
ejpam-3554	178	7	,	,	PUNCT
ejpam-3554	178	8	y	y	PRON
ejpam-3554	178	9	}	}	PUNCT
ejpam-3554	178	10	is	be	AUX
ejpam-3554	178	11	a	a	DET
ejpam-3554	178	12	γt	γt	NOUN
ejpam-3554	178	13	-	-	NOUN
ejpam-3554	178	14	set	set	ADJ
ejpam-3554	178	15	,	,	PUNCT
ejpam-3554	178	16	hence	hence	ADV
ejpam-3554	178	17	a	a	DET
ejpam-3554	178	18	∂tα	∂tα	PROPN
ejpam-3554	178	19	-	-	PUNCT
ejpam-3554	178	20	set	set	NOUN
ejpam-3554	178	21	,	,	PUNCT
ejpam-3554	178	22	in	in	ADP
ejpam-3554	178	23	g+h	g+h	PROPN
ejpam-3554	178	24	and	and	CCONJ
ejpam-3554	178	25	thus	thus	ADV
ejpam-3554	178	26	,	,	PUNCT
ejpam-3554	178	27	∂tα(g+h	∂tα(g+h	PROPN
ejpam-3554	178	28	)	)	PUNCT
ejpam-3554	179	1	=	=	SYM
ejpam-3554	179	2	2	2	X
ejpam-3554	179	3	.	.	X
ejpam-3554	179	4	�	�	PROPN
ejpam-3554	179	5	theorem	theorem	VERB
ejpam-3554	179	6	8	8	NUM
ejpam-3554	179	7	.	.	PUNCT
ejpam-3554	180	1	let	let	VERB
ejpam-3554	180	2	g	g	PRON
ejpam-3554	180	3	be	be	AUX
ejpam-3554	180	4	a	a	DET
ejpam-3554	180	5	nontrivial	nontrivial	ADJ
ejpam-3554	180	6	connected	connect	VERB
ejpam-3554	180	7	graph	graph	NOUN
ejpam-3554	180	8	of	of	ADP
ejpam-3554	180	9	order	order	NOUN
ejpam-3554	180	10	m	m	VERB
ejpam-3554	180	11	and	and	CCONJ
ejpam-3554	180	12	h	h	NOUN
ejpam-3554	180	13	be	be	VERB
ejpam-3554	180	14	any	any	DET
ejpam-3554	180	15	graph	graph	NOUN
ejpam-3554	180	16	of	of	ADP
ejpam-3554	180	17	order	order	NOUN
ejpam-3554	180	18	n.	n.	NOUN
ejpam-3554	180	19	let	let	VERB
ejpam-3554	180	20	α	α	PRON
ejpam-3554	180	21	∈	∈	PROPN
ejpam-3554	180	22	(	(	PUNCT
ejpam-3554	180	23	0	0	NUM
ejpam-3554	180	24	,	,	PUNCT
ejpam-3554	180	25	1	1	NUM
ejpam-3554	180	26	]	]	PUNCT
ejpam-3554	180	27	and	and	CCONJ
ejpam-3554	180	28	c	c	PROPN
ejpam-3554	180	29	⊆	⊆	NUM
ejpam-3554	180	30	v	v	NOUN
ejpam-3554	180	31	(	(	PUNCT
ejpam-3554	180	32	g	g	PROPN
ejpam-3554	180	33	◦	◦	NOUN
ejpam-3554	180	34	h	h	NOUN
ejpam-3554	180	35	)	)	PUNCT
ejpam-3554	180	36	.	.	PUNCT
ejpam-3554	181	1	if	if	SCONJ
ejpam-3554	181	2	at	at	ADV
ejpam-3554	181	3	least	least	ADJ
ejpam-3554	181	4	one	one	NUM
ejpam-3554	181	5	of	of	ADP
ejpam-3554	181	6	the	the	DET
ejpam-3554	181	7	following	follow	VERB
ejpam-3554	181	8	holds	hold	VERB
ejpam-3554	181	9	:	:	PUNCT
ejpam-3554	181	10	(	(	PUNCT
ejpam-3554	181	11	i	i	NOUN
ejpam-3554	181	12	)	)	PUNCT
ejpam-3554	181	13	c	c	PROPN
ejpam-3554	181	14	=	=	PUNCT
ejpam-3554	182	1	⋃	⋃	NOUN
ejpam-3554	182	2	v∈v	v∈v	NOUN
ejpam-3554	182	3	(	(	PUNCT
ejpam-3554	182	4	g	g	NOUN
ejpam-3554	182	5	)	)	PUNCT
ejpam-3554	182	6	sv	sv	NOUN
ejpam-3554	182	7	,	,	PUNCT
ejpam-3554	182	8	where	where	SCONJ
ejpam-3554	182	9	sv	sv	PROPN
ejpam-3554	182	10	is	be	AUX
ejpam-3554	182	11	a	a	DET
ejpam-3554	182	12	total	total	ADJ
ejpam-3554	182	13	α	α	PRON
ejpam-3554	182	14	-	-	ADJ
ejpam-3554	182	15	partial	partial	ADJ
ejpam-3554	182	16	dominating	dominating	NOUN
ejpam-3554	182	17	set	set	VERB
ejpam-3554	182	18	in	in	ADP
ejpam-3554	182	19	hv	hv	PROPN
ejpam-3554	182	20	for	for	ADP
ejpam-3554	182	21	each	each	DET
ejpam-3554	182	22	v	v	NUM
ejpam-3554	182	23	∈	∈	PROPN
ejpam-3554	182	24	v	v	NOUN
ejpam-3554	182	25	(	(	PUNCT
ejpam-3554	182	26	g	g	NOUN
ejpam-3554	182	27	)	)	PUNCT
ejpam-3554	182	28	,	,	PUNCT
ejpam-3554	182	29	(	(	PUNCT
ejpam-3554	182	30	ii	ii	NOUN
ejpam-3554	182	31	)	)	PUNCT
ejpam-3554	182	32	c	c	PROPN
ejpam-3554	182	33	⊆	⊆	NUM
ejpam-3554	182	34	v	v	NOUN
ejpam-3554	182	35	(	(	PUNCT
ejpam-3554	182	36	g	g	NOUN
ejpam-3554	182	37	)	)	PUNCT
ejpam-3554	182	38	where	where	SCONJ
ejpam-3554	182	39	either	either	CCONJ
ejpam-3554	182	40	c	c	PROPN
ejpam-3554	182	41	is	be	AUX
ejpam-3554	182	42	a	a	DET
ejpam-3554	182	43	total	total	ADJ
ejpam-3554	182	44	dominating	dominating	NOUN
ejpam-3554	182	45	set	set	NOUN
ejpam-3554	182	46	in	in	ADP
ejpam-3554	182	47	g	g	PROPN
ejpam-3554	182	48	and	and	CCONJ
ejpam-3554	182	49	|c|	|c|	PROPN
ejpam-3554	182	50	≥	≥	NOUN
ejpam-3554	182	51	αm(n+	αm(n+	PROPN
ejpam-3554	182	52	1)−m	1)−m	NUM
ejpam-3554	182	53	n	n	ADP
ejpam-3554	182	54	or	or	CCONJ
ejpam-3554	182	55	|c|	|c|	PROPN
ejpam-3554	182	56	≥	≥	NOUN
ejpam-3554	182	57	αm	αm	NOUN
ejpam-3554	182	58	and	and	CCONJ
ejpam-3554	182	59	c	c	NOUN
ejpam-3554	182	60	\ng(c	\ng(c	PROPN
ejpam-3554	182	61	)	)	PUNCT
ejpam-3554	182	62	=	=	SYM
ejpam-3554	182	63	∅	∅	NOUN
ejpam-3554	182	64	,	,	PUNCT
ejpam-3554	182	65	then	then	ADV
ejpam-3554	182	66	c	c	PROPN
ejpam-3554	182	67	is	be	AUX
ejpam-3554	182	68	a	a	DET
ejpam-3554	182	69	total	total	ADJ
ejpam-3554	182	70	α	α	PRON
ejpam-3554	182	71	-	-	ADJ
ejpam-3554	182	72	partial	partial	ADJ
ejpam-3554	182	73	dominating	dominating	NOUN
ejpam-3554	182	74	set	set	VERB
ejpam-3554	182	75	in	in	ADP
ejpam-3554	182	76	g	g	PROPN
ejpam-3554	182	77	◦	◦	NOUN
ejpam-3554	182	78	h.	h.	NOUN
ejpam-3554	182	79	proof	proof	NOUN
ejpam-3554	182	80	.	.	PUNCT
ejpam-3554	183	1	suppose	suppose	VERB
ejpam-3554	183	2	condition	condition	NOUN
ejpam-3554	183	3	(	(	PUNCT
ejpam-3554	183	4	i	i	NOUN
ejpam-3554	183	5	)	)	PUNCT
ejpam-3554	183	6	holds	hold	VERB
ejpam-3554	183	7	.	.	PUNCT
ejpam-3554	184	1	since	since	SCONJ
ejpam-3554	184	2	c	c	NOUN
ejpam-3554	184	3	=	=	SYM
ejpam-3554	184	4	⋃	⋃	NOUN
ejpam-3554	184	5	v∈v	v∈v	NOUN
ejpam-3554	184	6	(	(	PUNCT
ejpam-3554	184	7	g	g	NOUN
ejpam-3554	184	8	)	)	PUNCT
ejpam-3554	184	9	sv	sv	NOUN
ejpam-3554	184	10	,	,	PUNCT
ejpam-3554	184	11	where	where	SCONJ
ejpam-3554	184	12	sv	sv	PROPN
ejpam-3554	184	13	is	be	AUX
ejpam-3554	184	14	a	a	DET
ejpam-3554	184	15	total	total	ADJ
ejpam-3554	184	16	α	α	PRON
ejpam-3554	184	17	-	-	ADJ
ejpam-3554	184	18	partial	partial	ADJ
ejpam-3554	184	19	dominating	dominating	NOUN
ejpam-3554	184	20	set	set	VERB
ejpam-3554	184	21	in	in	ADP
ejpam-3554	184	22	hv	hv	PROPN
ejpam-3554	184	23	for	for	ADP
ejpam-3554	184	24	each	each	DET
ejpam-3554	184	25	v	v	NUM
ejpam-3554	184	26	∈	∈	PROPN
ejpam-3554	184	27	v	v	NOUN
ejpam-3554	184	28	(	(	PUNCT
ejpam-3554	184	29	g	g	NOUN
ejpam-3554	184	30	)	)	PUNCT
ejpam-3554	184	31	,	,	PUNCT
ejpam-3554	184	32	by	by	ADP
ejpam-3554	184	33	remark	remark	NOUN
ejpam-3554	184	34	6	6	NUM
ejpam-3554	184	35	,	,	PUNCT
ejpam-3554	184	36	sv	sv	PROPN
ejpam-3554	184	37	is	be	AUX
ejpam-3554	184	38	an	an	DET
ejpam-3554	184	39	α	α	NOUN
ejpam-3554	184	40	-	-	ADJ
ejpam-3554	184	41	partial	partial	ADJ
ejpam-3554	184	42	dominating	dominating	NOUN
ejpam-3554	184	43	set	set	VERB
ejpam-3554	184	44	in	in	ADP
ejpam-3554	184	45	hv	hv	PROPN
ejpam-3554	184	46	for	for	ADP
ejpam-3554	184	47	each	each	DET
ejpam-3554	184	48	v	v	NUM
ejpam-3554	184	49	∈	∈	PROPN
ejpam-3554	184	50	v	v	NOUN
ejpam-3554	184	51	(	(	PUNCT
ejpam-3554	184	52	g	g	NOUN
ejpam-3554	184	53	)	)	PUNCT
ejpam-3554	184	54	.	.	PUNCT
ejpam-3554	185	1	it	it	PRON
ejpam-3554	185	2	follows	follow	VERB
ejpam-3554	185	3	by	by	ADP
ejpam-3554	185	4	theorem	theorem	NOUN
ejpam-3554	185	5	4	4	NUM
ejpam-3554	185	6	that	that	SCONJ
ejpam-3554	185	7	c	c	PROPN
ejpam-3554	185	8	is	be	AUX
ejpam-3554	185	9	an	an	DET
ejpam-3554	185	10	α	α	NOUN
ejpam-3554	185	11	-	-	ADJ
ejpam-3554	185	12	partial	partial	ADJ
ejpam-3554	185	13	dominating	dominating	NOUN
ejpam-3554	185	14	set	set	VERB
ejpam-3554	185	15	r.	r.	PROPN
ejpam-3554	185	16	macapodi	macapodi	PROPN
ejpam-3554	185	17	,	,	PUNCT
ejpam-3554	185	18	r.	r.	PROPN
ejpam-3554	185	19	isla	isla	PROPN
ejpam-3554	185	20	/	/	SYM
ejpam-3554	185	21	eur	eur	PROPN
ejpam-3554	185	22	.	.	PUNCT
ejpam-3554	186	1	j.	j.	PROPN
ejpam-3554	186	2	pure	pure	PROPN
ejpam-3554	186	3	appl	appl	PROPN
ejpam-3554	186	4	.	.	PROPN
ejpam-3554	186	5	math	math	PROPN
ejpam-3554	186	6	,	,	PUNCT
ejpam-3554	186	7	12	12	NUM
ejpam-3554	186	8	(	(	PUNCT
ejpam-3554	186	9	4	4	NUM
ejpam-3554	186	10	)	)	PUNCT
ejpam-3554	186	11	(	(	PUNCT
ejpam-3554	186	12	2019	2019	NUM
ejpam-3554	186	13	)	)	PUNCT
ejpam-3554	186	14	,	,	PUNCT
ejpam-3554	186	15	1643	1643	NUM
ejpam-3554	186	16	-	-	SYM
ejpam-3554	186	17	1655	1655	NUM
ejpam-3554	186	18	1650	1650	NUM
ejpam-3554	186	19	in	in	ADP
ejpam-3554	186	20	g	g	PROPN
ejpam-3554	186	21	◦	◦	NOUN
ejpam-3554	186	22	h.	h.	NOUN
ejpam-3554	186	23	moreover	moreover	ADV
ejpam-3554	186	24	,	,	PUNCT
ejpam-3554	186	25	since	since	SCONJ
ejpam-3554	186	26	sv	sv	PROPN
ejpam-3554	186	27	is	be	AUX
ejpam-3554	186	28	a	a	DET
ejpam-3554	186	29	total	total	ADJ
ejpam-3554	186	30	α	α	PRON
ejpam-3554	186	31	-	-	ADJ
ejpam-3554	186	32	partial	partial	ADJ
ejpam-3554	186	33	dominating	dominating	NOUN
ejpam-3554	186	34	set	set	VERB
ejpam-3554	186	35	in	in	ADP
ejpam-3554	186	36	hv	hv	PROPN
ejpam-3554	186	37	for	for	ADP
ejpam-3554	186	38	each	each	DET
ejpam-3554	186	39	v	v	NUM
ejpam-3554	186	40	∈	∈	PROPN
ejpam-3554	186	41	v	v	NOUN
ejpam-3554	186	42	(	(	PUNCT
ejpam-3554	186	43	g	g	NOUN
ejpam-3554	186	44	)	)	PUNCT
ejpam-3554	186	45	,	,	PUNCT
ejpam-3554	186	46	c	c	PROPN
ejpam-3554	186	47	is	be	AUX
ejpam-3554	186	48	a	a	DET
ejpam-3554	186	49	total	total	ADJ
ejpam-3554	186	50	α	α	PRON
ejpam-3554	186	51	-	-	ADJ
ejpam-3554	186	52	partial	partial	ADJ
ejpam-3554	186	53	dominating	dominating	NOUN
ejpam-3554	186	54	set	set	VERB
ejpam-3554	186	55	in	in	ADP
ejpam-3554	186	56	g	g	PROPN
ejpam-3554	186	57	◦	◦	PROPN
ejpam-3554	186	58	h.	h.	PROPN
ejpam-3554	186	59	suppose	suppose	VERB
ejpam-3554	186	60	condition	condition	NOUN
ejpam-3554	186	61	(	(	PUNCT
ejpam-3554	186	62	ii	ii	NOUN
ejpam-3554	186	63	)	)	PUNCT
ejpam-3554	186	64	holds	hold	VERB
ejpam-3554	186	65	.	.	PUNCT
ejpam-3554	187	1	suppose	suppose	VERB
ejpam-3554	187	2	further	far	ADV
ejpam-3554	187	3	that	that	SCONJ
ejpam-3554	187	4	c	c	PROPN
ejpam-3554	187	5	is	be	AUX
ejpam-3554	187	6	a	a	DET
ejpam-3554	187	7	total	total	ADJ
ejpam-3554	187	8	dominating	dominating	NOUN
ejpam-3554	187	9	set	set	NOUN
ejpam-3554	187	10	in	in	ADP
ejpam-3554	187	11	g	g	PROPN
ejpam-3554	187	12	and	and	CCONJ
ejpam-3554	187	13	|c|	|c|	PROPN
ejpam-3554	187	14	≥	≥	NOUN
ejpam-3554	187	15	αm(n+	αm(n+	PROPN
ejpam-3554	187	16	1)−m	1)−m	NUM
ejpam-3554	187	17	n	n	NOUN
ejpam-3554	187	18	.	.	PUNCT
ejpam-3554	188	1	since	since	SCONJ
ejpam-3554	188	2	c	c	PROPN
ejpam-3554	188	3	is	be	AUX
ejpam-3554	188	4	a	a	DET
ejpam-3554	188	5	dominating	dominating	NOUN
ejpam-3554	188	6	set	set	NOUN
ejpam-3554	188	7	in	in	ADP
ejpam-3554	188	8	g	g	PROPN
ejpam-3554	188	9	,	,	PUNCT
ejpam-3554	188	10	it	it	PRON
ejpam-3554	188	11	follows	follow	VERB
ejpam-3554	188	12	by	by	ADP
ejpam-3554	188	13	theorem	theorem	NOUN
ejpam-3554	188	14	4	4	NUM
ejpam-3554	188	15	that	that	SCONJ
ejpam-3554	188	16	c	c	PROPN
ejpam-3554	188	17	is	be	AUX
ejpam-3554	188	18	an	an	DET
ejpam-3554	188	19	α	α	NOUN
ejpam-3554	188	20	-	-	ADJ
ejpam-3554	188	21	partial	partial	ADJ
ejpam-3554	188	22	dominating	dominating	NOUN
ejpam-3554	188	23	set	set	VERB
ejpam-3554	188	24	in	in	ADP
ejpam-3554	188	25	g	g	PROPN
ejpam-3554	188	26	◦	◦	NOUN
ejpam-3554	188	27	h.	h.	PROPN
ejpam-3554	189	1	moreover	moreover	ADV
ejpam-3554	189	2	,	,	PUNCT
ejpam-3554	189	3	since	since	SCONJ
ejpam-3554	189	4	c	c	PROPN
ejpam-3554	189	5	⊆	⊆	NUM
ejpam-3554	189	6	v	v	NOUN
ejpam-3554	189	7	(	(	PUNCT
ejpam-3554	189	8	g	g	NOUN
ejpam-3554	189	9	)	)	PUNCT
ejpam-3554	189	10	is	be	AUX
ejpam-3554	189	11	a	a	DET
ejpam-3554	189	12	total	total	ADJ
ejpam-3554	189	13	α	α	PRON
ejpam-3554	189	14	-	-	ADJ
ejpam-3554	189	15	partial	partial	ADJ
ejpam-3554	189	16	dominating	dominating	NOUN
ejpam-3554	189	17	set	set	VERB
ejpam-3554	189	18	in	in	ADP
ejpam-3554	189	19	g	g	PROPN
ejpam-3554	189	20	,	,	PUNCT
ejpam-3554	189	21	c	c	PROPN
ejpam-3554	189	22	is	be	AUX
ejpam-3554	189	23	a	a	DET
ejpam-3554	189	24	total	total	ADJ
ejpam-3554	189	25	α	α	PRON
ejpam-3554	189	26	-	-	ADJ
ejpam-3554	189	27	partial	partial	ADJ
ejpam-3554	189	28	dominating	dominating	NOUN
ejpam-3554	189	29	set	set	VERB
ejpam-3554	189	30	in	in	ADP
ejpam-3554	189	31	g	g	PROPN
ejpam-3554	189	32	◦	◦	PROPN
ejpam-3554	189	33	h.	h.	PROPN
ejpam-3554	190	1	next	next	ADV
ejpam-3554	190	2	,	,	PUNCT
ejpam-3554	190	3	if	if	SCONJ
ejpam-3554	190	4	|c|	|c|	PROPN
ejpam-3554	190	5	≥	≥	AUX
ejpam-3554	190	6	αm	αm	NOUN
ejpam-3554	190	7	and	and	CCONJ
ejpam-3554	190	8	every	every	DET
ejpam-3554	190	9	vertex	vertex	NOUN
ejpam-3554	190	10	in	in	ADP
ejpam-3554	190	11	c	c	PROPN
ejpam-3554	190	12	is	be	AUX
ejpam-3554	190	13	adjacent	adjacent	ADJ
ejpam-3554	190	14	to	to	ADP
ejpam-3554	190	15	some	some	DET
ejpam-3554	190	16	vertex	vertex	NOUN
ejpam-3554	190	17	in	in	ADP
ejpam-3554	190	18	c	c	NOUN
ejpam-3554	190	19	,	,	PUNCT
ejpam-3554	190	20	then	then	ADV
ejpam-3554	190	21	by	by	ADP
ejpam-3554	190	22	theorem	theorem	NOUN
ejpam-3554	190	23	4	4	NUM
ejpam-3554	190	24	,	,	PUNCT
ejpam-3554	190	25	c	c	PROPN
ejpam-3554	190	26	is	be	AUX
ejpam-3554	190	27	an	an	DET
ejpam-3554	190	28	α	α	NOUN
ejpam-3554	190	29	-	-	ADJ
ejpam-3554	190	30	partial	partial	ADJ
ejpam-3554	190	31	dominating	dominating	NOUN
ejpam-3554	190	32	set	set	VERB
ejpam-3554	190	33	in	in	ADP
ejpam-3554	190	34	g	g	PROPN
ejpam-3554	190	35	◦	◦	NOUN
ejpam-3554	190	36	h.	h.	NOUN
ejpam-3554	190	37	since	since	SCONJ
ejpam-3554	190	38	c	c	PROPN
ejpam-3554	190	39	\	\	PROPN
ejpam-3554	190	40	ng(c	ng(c	NUM
ejpam-3554	190	41	)	)	PUNCT
ejpam-3554	191	1	=	=	SYM
ejpam-3554	191	2	∅	∅	NOUN
ejpam-3554	191	3	,	,	PUNCT
ejpam-3554	191	4	c	c	PROPN
ejpam-3554	191	5	is	be	AUX
ejpam-3554	191	6	a	a	DET
ejpam-3554	191	7	total	total	ADJ
ejpam-3554	191	8	α	α	PRON
ejpam-3554	191	9	-	-	ADJ
ejpam-3554	191	10	partial	partial	ADJ
ejpam-3554	191	11	dominating	dominating	NOUN
ejpam-3554	191	12	set	set	VERB
ejpam-3554	191	13	in	in	ADP
ejpam-3554	191	14	g	g	PROPN
ejpam-3554	191	15	◦	◦	PROPN
ejpam-3554	191	16	h.	h.	PROPN
ejpam-3554	191	17	�	�	PROPN
ejpam-3554	191	18	remark	remark	VERB
ejpam-3554	191	19	7	7	NUM
ejpam-3554	191	20	.	.	PUNCT
ejpam-3554	192	1	the	the	DET
ejpam-3554	192	2	converse	converse	NOUN
ejpam-3554	192	3	of	of	ADP
ejpam-3554	192	4	theorem	theorem	NOUN
ejpam-3554	192	5	8	8	NUM
ejpam-3554	192	6	is	be	AUX
ejpam-3554	192	7	not	not	PART
ejpam-3554	192	8	true	true	ADJ
ejpam-3554	192	9	.	.	PUNCT
ejpam-3554	193	1	to	to	PART
ejpam-3554	193	2	see	see	VERB
ejpam-3554	193	3	this	this	PRON
ejpam-3554	193	4	,	,	PUNCT
ejpam-3554	193	5	consider	consider	VERB
ejpam-3554	193	6	the	the	DET
ejpam-3554	193	7	graph	graph	NOUN
ejpam-3554	193	8	p12	p12	VERB
ejpam-3554	193	9	◦	◦	NOUN
ejpam-3554	193	10	p2	p2	NOUN
ejpam-3554	193	11	in	in	ADP
ejpam-3554	193	12	figure	figure	NOUN
ejpam-3554	193	13	4	4	NUM
ejpam-3554	193	14	.	.	PUNCT
ejpam-3554	194	1	let	let	VERB
ejpam-3554	194	2	α	α	NOUN
ejpam-3554	194	3	=	=	SYM
ejpam-3554	194	4	1	1	NUM
ejpam-3554	194	5	2	2	NUM
ejpam-3554	194	6	.	.	PUNCT
ejpam-3554	195	1	the	the	DET
ejpam-3554	195	2	shaded	shade	VERB
ejpam-3554	195	3	vertices	vertex	NOUN
ejpam-3554	195	4	form	form	VERB
ejpam-3554	195	5	a	a	DET
ejpam-3554	195	6	∂tα	∂tα	PROPN
ejpam-3554	195	7	-	-	PUNCT
ejpam-3554	195	8	set	set	NOUN
ejpam-3554	195	9	but	but	CCONJ
ejpam-3554	195	10	neither	neither	PRON
ejpam-3554	195	11	of	of	ADP
ejpam-3554	195	12	condition	condition	NOUN
ejpam-3554	195	13	(	(	PUNCT
ejpam-3554	195	14	i	i	NOUN
ejpam-3554	195	15	)	)	PUNCT
ejpam-3554	195	16	nor	nor	CCONJ
ejpam-3554	195	17	(	(	PUNCT
ejpam-3554	195	18	ii	ii	NOUN
ejpam-3554	195	19	)	)	PUNCT
ejpam-3554	195	20	holds	hold	VERB
ejpam-3554	195	21	since	since	SCONJ
ejpam-3554	195	22	c	c	PROPN
ejpam-3554	195	23	=	=	PUNCT
ejpam-3554	195	24	{	{	PUNCT
ejpam-3554	195	25	2	2	NUM
ejpam-3554	195	26	,	,	PUNCT
ejpam-3554	195	27	3	3	NUM
ejpam-3554	195	28	,	,	PUNCT
ejpam-3554	195	29	6	6	NUM
ejpam-3554	195	30	,	,	PUNCT
ejpam-3554	195	31	7	7	NUM
ejpam-3554	195	32	,	,	PUNCT
ejpam-3554	195	33	8	8	NUM
ejpam-3554	195	34	}	}	PUNCT
ejpam-3554	195	35	is	be	AUX
ejpam-3554	195	36	not	not	PART
ejpam-3554	195	37	a	a	DET
ejpam-3554	195	38	total	total	ADJ
ejpam-3554	195	39	dominating	dominating	NOUN
ejpam-3554	195	40	set	set	NOUN
ejpam-3554	195	41	in	in	ADP
ejpam-3554	195	42	g	g	PROPN
ejpam-3554	195	43	and	and	CCONJ
ejpam-3554	195	44	|c|	|c|	PROPN
ejpam-3554	195	45	<	<	X
ejpam-3554	195	46	αm	αm	X
ejpam-3554	195	47	.	.	PUNCT
ejpam-3554	196	1	the	the	DET
ejpam-3554	196	2	next	next	ADJ
ejpam-3554	196	3	result	result	NOUN
ejpam-3554	196	4	is	be	AUX
ejpam-3554	196	5	an	an	DET
ejpam-3554	196	6	immediate	immediate	ADJ
ejpam-3554	196	7	consequence	consequence	NOUN
ejpam-3554	196	8	of	of	ADP
ejpam-3554	196	9	theorem	theorem	ADJ
ejpam-3554	196	10	8	8	NUM
ejpam-3554	196	11	.	.	PUNCT
ejpam-3554	196	12	corollary	corollary	ADJ
ejpam-3554	196	13	4	4	NUM
ejpam-3554	196	14	.	.	PUNCT
ejpam-3554	197	1	let	let	VERB
ejpam-3554	197	2	g	g	PRON
ejpam-3554	197	3	be	be	AUX
ejpam-3554	197	4	a	a	DET
ejpam-3554	197	5	nontrivial	nontrivial	ADJ
ejpam-3554	197	6	connected	connect	VERB
ejpam-3554	197	7	graph	graph	NOUN
ejpam-3554	197	8	of	of	ADP
ejpam-3554	197	9	order	order	NOUN
ejpam-3554	197	10	m	m	VERB
ejpam-3554	197	11	and	and	CCONJ
ejpam-3554	197	12	h	h	NOUN
ejpam-3554	197	13	be	be	VERB
ejpam-3554	197	14	any	any	DET
ejpam-3554	197	15	graph	graph	NOUN
ejpam-3554	197	16	of	of	ADP
ejpam-3554	197	17	order	order	NOUN
ejpam-3554	197	18	n	n	NOUN
ejpam-3554	197	19	and	and	CCONJ
ejpam-3554	197	20	α	α	PRON
ejpam-3554	197	21	∈	∈	PROPN
ejpam-3554	197	22	(	(	PUNCT
ejpam-3554	197	23	0	0	NUM
ejpam-3554	197	24	,	,	PUNCT
ejpam-3554	197	25	1	1	NUM
ejpam-3554	197	26	]	]	PUNCT
ejpam-3554	197	27	.	.	PUNCT
ejpam-3554	198	1	then	then	ADV
ejpam-3554	198	2	∂tα(g	∂tα(g	PROPN
ejpam-3554	198	3	◦	◦	PROPN
ejpam-3554	198	4	h	h	NOUN
ejpam-3554	198	5	)	)	PUNCT
ejpam-3554	198	6	≤	≤	NUM
ejpam-3554	198	7	min	min	NOUN
ejpam-3554	198	8	{	{	PUNCT
ejpam-3554	198	9	ηtg	ηtg	PROPN
ejpam-3554	198	10	,	,	PUNCT
ejpam-3554	198	11	µ	µ	DET
ejpam-3554	198	12	t	t	NOUN
ejpam-3554	198	13	g	g	PROPN
ejpam-3554	198	14	}	}	PUNCT
ejpam-3554	198	15	,	,	PUNCT
ejpam-3554	198	16	where	where	SCONJ
ejpam-3554	198	17	ηtg	ηtg	ADJ
ejpam-3554	198	18	=	=	SYM
ejpam-3554	198	19	min	min	PROPN
ejpam-3554	198	20	{	{	PUNCT
ejpam-3554	198	21	|c|	|c|	PROPN
ejpam-3554	198	22	:	:	PUNCT
ejpam-3554	198	23	c	c	NOUN
ejpam-3554	198	24	is	be	AUX
ejpam-3554	198	25	a	a	DET
ejpam-3554	198	26	total	total	ADJ
ejpam-3554	198	27	dominating	dominating	NOUN
ejpam-3554	198	28	set	set	NOUN
ejpam-3554	198	29	in	in	ADP
ejpam-3554	198	30	g	g	NOUN
ejpam-3554	198	31	with	with	ADP
ejpam-3554	198	32	|c|	|c|	PROPN
ejpam-3554	198	33	≥	≥	NOUN
ejpam-3554	198	34	αm(n+	αm(n+	PROPN
ejpam-3554	198	35	1)−m	1)−m	NUM
ejpam-3554	198	36	n	n	PROPN
ejpam-3554	198	37	}	}	PUNCT
ejpam-3554	198	38	and	and	CCONJ
ejpam-3554	198	39	µtg	µtg	PROPN
ejpam-3554	198	40	=	=	PUNCT
ejpam-3554	198	41	min{|c	min{|c	PROPN
ejpam-3554	198	42	′|	′|	NUM
ejpam-3554	198	43	:	:	PUNCT
ejpam-3554	198	44	c	c	NOUN
ejpam-3554	198	45	′	′	NOUN
ejpam-3554	199	1	⊆	⊆	NUM
ejpam-3554	199	2	v	v	ADP
ejpam-3554	199	3	(	(	PUNCT
ejpam-3554	199	4	g	g	NOUN
ejpam-3554	199	5	)	)	PUNCT
ejpam-3554	199	6	with	with	ADP
ejpam-3554	199	7	∣∣c	∣∣c	PROPN
ejpam-3554	199	8	′∣∣	′∣∣	NUM
ejpam-3554	199	9	≥	≥	NOUN
ejpam-3554	199	10	αm	αm	ADJ
ejpam-3554	199	11	and	and	CCONJ
ejpam-3554	199	12	c	c	NOUN
ejpam-3554	199	13	′	′	NOUN
ejpam-3554	199	14	\ng(c	\ng(c	NOUN
ejpam-3554	199	15	′	′	NUM
ejpam-3554	199	16	)	)	PUNCT
ejpam-3554	199	17	=	=	NOUN
ejpam-3554	199	18	∅	∅	NOUN
ejpam-3554	199	19	}	}	PUNCT
ejpam-3554	199	20	.	.	PUNCT
ejpam-3554	200	1	remark	remark	PROPN
ejpam-3554	200	2	8	8	NUM
ejpam-3554	200	3	.	.	PUNCT
ejpam-3554	201	1	the	the	DET
ejpam-3554	201	2	bound	bind	VERB
ejpam-3554	201	3	in	in	ADP
ejpam-3554	201	4	corollary	corollary	ADJ
ejpam-3554	201	5	4	4	NUM
ejpam-3554	201	6	is	be	AUX
ejpam-3554	201	7	sharp	sharp	ADJ
ejpam-3554	201	8	.	.	PUNCT
ejpam-3554	202	1	however	however	ADV
ejpam-3554	202	2	,	,	PUNCT
ejpam-3554	202	3	the	the	DET
ejpam-3554	202	4	strict	strict	ADJ
ejpam-3554	202	5	inequality	inequality	NOUN
ejpam-3554	202	6	can	can	AUX
ejpam-3554	202	7	be	be	AUX
ejpam-3554	202	8	attained	attain	VERB
ejpam-3554	202	9	.	.	PUNCT
ejpam-3554	203	1	to	to	PART
ejpam-3554	203	2	see	see	VERB
ejpam-3554	203	3	this	this	PRON
ejpam-3554	203	4	,	,	PUNCT
ejpam-3554	203	5	consider	consider	VERB
ejpam-3554	203	6	the	the	DET
ejpam-3554	203	7	graphs	graph	NOUN
ejpam-3554	203	8	shown	show	VERB
ejpam-3554	203	9	in	in	ADP
ejpam-3554	203	10	figures	figure	NOUN
ejpam-3554	203	11	5	5	NUM
ejpam-3554	203	12	and	and	CCONJ
ejpam-3554	203	13	6	6	NUM
ejpam-3554	203	14	.	.	PUNCT
ejpam-3554	204	1	let	let	VERB
ejpam-3554	204	2	α	α	NOUN
ejpam-3554	204	3	=	=	SYM
ejpam-3554	204	4	2	2	NUM
ejpam-3554	204	5	5	5	NUM
ejpam-3554	204	6	.	.	PUNCT
ejpam-3554	205	1	the	the	DET
ejpam-3554	205	2	shaded	shade	VERB
ejpam-3554	205	3	vertices	vertex	NOUN
ejpam-3554	205	4	in	in	ADP
ejpam-3554	205	5	figure	figure	NOUN
ejpam-3554	205	6	5	5	NUM
ejpam-3554	205	7	form	form	NOUN
ejpam-3554	205	8	a	a	DET
ejpam-3554	205	9	∂tα	∂tα	PROPN
ejpam-3554	205	10	-	-	PUNCT
ejpam-3554	205	11	set	set	NOUN
ejpam-3554	205	12	.	.	PUNCT
ejpam-3554	206	1	then	then	ADV
ejpam-3554	206	2	∂tα(p5	∂tα(p5	PUNCT
ejpam-3554	206	3	◦	◦	NOUN
ejpam-3554	206	4	p5	p5	ADJ
ejpam-3554	206	5	)	)	PUNCT
ejpam-3554	206	6	=	=	SYM
ejpam-3554	206	7	2	2	NUM
ejpam-3554	206	8	=	=	SYM
ejpam-3554	206	9	min{3	min{3	PROPN
ejpam-3554	206	10	,	,	PUNCT
ejpam-3554	206	11	2	2	NUM
ejpam-3554	206	12	}	}	PUNCT
ejpam-3554	206	13	=	=	SYM
ejpam-3554	206	14	min{ηtg	min{ηtg	X
ejpam-3554	206	15	,	,	PUNCT
ejpam-3554	206	16	µtg	µtg	ADJ
ejpam-3554	206	17	}	}	PUNCT
ejpam-3554	206	18	=	=	SYM
ejpam-3554	207	1	µtg	µtg	ADJ
ejpam-3554	207	2	.	.	PUNCT
ejpam-3554	208	1	let	let	VERB
ejpam-3554	208	2	α	α	NOUN
ejpam-3554	208	3	=	=	SYM
ejpam-3554	208	4	3	3	NUM
ejpam-3554	208	5	5	5	NUM
ejpam-3554	208	6	.	.	PUNCT
ejpam-3554	209	1	the	the	DET
ejpam-3554	209	2	shaded	shade	VERB
ejpam-3554	209	3	vertices	vertex	NOUN
ejpam-3554	209	4	in	in	ADP
ejpam-3554	209	5	figure	figure	NOUN
ejpam-3554	209	6	6	6	NUM
ejpam-3554	209	7	form	form	NOUN
ejpam-3554	209	8	a	a	DET
ejpam-3554	209	9	∂tα	∂tα	PROPN
ejpam-3554	209	10	-	-	PUNCT
ejpam-3554	209	11	set	set	NOUN
ejpam-3554	209	12	.	.	PUNCT
ejpam-3554	210	1	then	then	ADV
ejpam-3554	210	2	∂tα(p12	∂tα(p12	VERB
ejpam-3554	210	3	◦	◦	NOUN
ejpam-3554	210	4	p2	p2	NOUN
ejpam-3554	210	5	)	)	PUNCT
ejpam-3554	210	6	=	=	SYM
ejpam-3554	210	7	6	6	NUM
ejpam-3554	210	8	=	=	SYM
ejpam-3554	210	9	min{6	min{6	NOUN
ejpam-3554	210	10	,	,	PUNCT
ejpam-3554	210	11	8	8	NUM
ejpam-3554	210	12	}	}	PUNCT
ejpam-3554	210	13	=	=	PUNCT
ejpam-3554	210	14	min{ηtg	min{ηtg	X
ejpam-3554	210	15	,	,	PUNCT
ejpam-3554	210	16	µtg	µtg	ADJ
ejpam-3554	210	17	}	}	PUNCT
ejpam-3554	210	18	=	=	PUNCT
ejpam-3554	210	19	ηtg	ηtg	ADJ
ejpam-3554	210	20	while	while	SCONJ
ejpam-3554	210	21	∂tα(p5	∂tα(p5	PUNCT
ejpam-3554	210	22	◦	◦	NOUN
ejpam-3554	210	23	k1	k1	NOUN
ejpam-3554	210	24	)	)	PUNCT
ejpam-3554	210	25	=	=	SYM
ejpam-3554	210	26	2	2	NUM
ejpam-3554	210	27	<	<	SYM
ejpam-3554	210	28	3	3	NUM
ejpam-3554	210	29	=	=	SYM
ejpam-3554	210	30	min{3	min{3	PROPN
ejpam-3554	210	31	,	,	PUNCT
ejpam-3554	210	32	3	3	NUM
ejpam-3554	210	33	}	}	PUNCT
ejpam-3554	210	34	=	=	PUNCT
ejpam-3554	210	35	min{ηtg	min{ηtg	X
ejpam-3554	210	36	,	,	PUNCT
ejpam-3554	210	37	µtg	µtg	ADJ
ejpam-3554	210	38	}	}	PUNCT
ejpam-3554	210	39	.	.	PUNCT
ejpam-3554	211	1	r.	r.	PROPN
ejpam-3554	211	2	macapodi	macapodi	PROPN
ejpam-3554	211	3	,	,	PUNCT
ejpam-3554	211	4	r.	r.	PROPN
ejpam-3554	211	5	isla	isla	PROPN
ejpam-3554	211	6	/	/	SYM
ejpam-3554	211	7	eur	eur	PROPN
ejpam-3554	211	8	.	.	PUNCT
ejpam-3554	212	1	j.	j.	PROPN
ejpam-3554	212	2	pure	pure	PROPN
ejpam-3554	212	3	appl	appl	PROPN
ejpam-3554	212	4	.	.	PROPN
ejpam-3554	212	5	math	math	PROPN
ejpam-3554	212	6	,	,	PUNCT
ejpam-3554	212	7	12	12	NUM
ejpam-3554	212	8	(	(	PUNCT
ejpam-3554	212	9	4	4	NUM
ejpam-3554	212	10	)	)	PUNCT
ejpam-3554	212	11	(	(	PUNCT
ejpam-3554	212	12	2019	2019	NUM
ejpam-3554	212	13	)	)	PUNCT
ejpam-3554	212	14	,	,	PUNCT
ejpam-3554	212	15	1643	1643	NUM
ejpam-3554	212	16	-	-	SYM
ejpam-3554	212	17	1655	1655	NUM
ejpam-3554	212	18	1651	1651	NUM
ejpam-3554	212	19	theorem	theorem	NOUN
ejpam-3554	212	20	9	9	NUM
ejpam-3554	212	21	.	.	PUNCT
ejpam-3554	213	1	let	let	VERB
ejpam-3554	213	2	g	g	PRON
ejpam-3554	213	3	be	be	AUX
ejpam-3554	213	4	a	a	DET
ejpam-3554	213	5	connected	connected	ADJ
ejpam-3554	213	6	graph	graph	NOUN
ejpam-3554	213	7	and	and	CCONJ
ejpam-3554	213	8	α	α	PRON
ejpam-3554	213	9	∈	∈	PROPN
ejpam-3554	213	10	(	(	PUNCT
ejpam-3554	213	11	0	0	NUM
ejpam-3554	213	12	,	,	PUNCT
ejpam-3554	213	13	1	1	NUM
ejpam-3554	213	14	]	]	PUNCT
ejpam-3554	213	15	.	.	PUNCT
ejpam-3554	214	1	if	if	SCONJ
ejpam-3554	214	2	s	s	PROPN
ejpam-3554	214	3	is	be	AUX
ejpam-3554	214	4	an	an	DET
ejpam-3554	214	5	α	α	NOUN
ejpam-3554	214	6	-	-	ADJ
ejpam-3554	214	7	partial	partial	ADJ
ejpam-3554	214	8	dominating	dominating	NOUN
ejpam-3554	214	9	set	set	VERB
ejpam-3554	214	10	in	in	ADP
ejpam-3554	214	11	g	g	PROPN
ejpam-3554	214	12	,	,	PUNCT
ejpam-3554	214	13	then	then	ADV
ejpam-3554	214	14	∂tα(g	∂tα(g	NOUN
ejpam-3554	214	15	)	)	PUNCT
ejpam-3554	214	16	≤	≤	NUM
ejpam-3554	214	17	|s	|s	PROPN
ejpam-3554	214	18	∩ng(s)|+	∩ng(s)|+	PROPN
ejpam-3554	214	19	2|s	2|s	NUM
ejpam-3554	214	20	\ng(s)|	\ng(s)|	NOUN
ejpam-3554	214	21	.	.	PUNCT
ejpam-3554	215	1	in	in	ADP
ejpam-3554	215	2	particular	particular	ADJ
ejpam-3554	215	3	,	,	PUNCT
ejpam-3554	215	4	∂tα(g	∂tα(g	PROPN
ejpam-3554	215	5	)	)	PUNCT
ejpam-3554	215	6	≤	≤	NOUN
ejpam-3554	215	7	2∂α(g	2∂α(g	NUM
ejpam-3554	215	8	)	)	PUNCT
ejpam-3554	215	9	.	.	PUNCT
ejpam-3554	216	1	proof	proof	NOUN
ejpam-3554	216	2	.	.	PUNCT
ejpam-3554	217	1	let	let	VERB
ejpam-3554	217	2	s	s	PRON
ejpam-3554	217	3	be	be	AUX
ejpam-3554	217	4	an	an	DET
ejpam-3554	217	5	α	α	NOUN
ejpam-3554	217	6	-	-	ADJ
ejpam-3554	217	7	partial	partial	ADJ
ejpam-3554	217	8	dominating	dominating	NOUN
ejpam-3554	217	9	set	set	VERB
ejpam-3554	217	10	in	in	ADP
ejpam-3554	217	11	g.	g.	PROPN
ejpam-3554	217	12	if	if	SCONJ
ejpam-3554	217	13	s	s	X
ejpam-3554	217	14	is	be	AUX
ejpam-3554	217	15	a	a	DET
ejpam-3554	217	16	total	total	ADJ
ejpam-3554	217	17	α	α	PRON
ejpam-3554	217	18	-	-	ADJ
ejpam-3554	217	19	partial	partial	ADJ
ejpam-3554	217	20	dominating	dominating	NOUN
ejpam-3554	217	21	set	set	VERB
ejpam-3554	217	22	in	in	ADP
ejpam-3554	217	23	g	g	PROPN
ejpam-3554	217	24	,	,	PUNCT
ejpam-3554	217	25	then	then	ADV
ejpam-3554	217	26	s	s	VERB
ejpam-3554	217	27	∩ng(s	∩ng(s	NOUN
ejpam-3554	217	28	)	)	PUNCT
ejpam-3554	217	29	=	=	SYM
ejpam-3554	217	30	s	s	PROPN
ejpam-3554	217	31	and	and	CCONJ
ejpam-3554	217	32	s	s	VERB
ejpam-3554	217	33	\ng(s	\ng(s	NOUN
ejpam-3554	217	34	)	)	PUNCT
ejpam-3554	217	35	=	=	NOUN
ejpam-3554	217	36	∅.	∅.	VERB
ejpam-3554	217	37	hence	hence	ADV
ejpam-3554	217	38	,	,	PUNCT
ejpam-3554	217	39	∂tα(g	∂tα(g	PROPN
ejpam-3554	217	40	)	)	PUNCT
ejpam-3554	218	1	≤	≤	NUM
ejpam-3554	218	2	|s|	|s|	PROPN
ejpam-3554	218	3	=	=	SYM
ejpam-3554	218	4	|s	|s	PROPN
ejpam-3554	218	5	∩ng(s)|+	∩ng(s)|+	PROPN
ejpam-3554	218	6	2|s	2|s	NUM
ejpam-3554	218	7	\ng(s)|	\ng(s)|	NUM
ejpam-3554	218	8	.	.	PUNCT
ejpam-3554	219	1	so	so	ADV
ejpam-3554	219	2	suppose	suppose	VERB
ejpam-3554	219	3	that	that	SCONJ
ejpam-3554	219	4	s	s	VERB
ejpam-3554	219	5	\	\	NOUN
ejpam-3554	219	6	ng(s	ng(s	NUM
ejpam-3554	219	7	)	)	PUNCT
ejpam-3554	219	8	6=	6=	ADP
ejpam-3554	219	9	∅.	∅.	AUX
ejpam-3554	219	10	choose	choose	VERB
ejpam-3554	219	11	vx	vx	PROPN
ejpam-3554	219	12	∈	∈	PROPN
ejpam-3554	219	13	v	v	ADP
ejpam-3554	219	14	(	(	PUNCT
ejpam-3554	219	15	g	g	NOUN
ejpam-3554	219	16	)	)	PUNCT
ejpam-3554	219	17	∩	∩	NOUN
ejpam-3554	219	18	ng(x	ng(x	NUM
ejpam-3554	219	19	)	)	PUNCT
ejpam-3554	219	20	for	for	ADP
ejpam-3554	219	21	each	each	DET
ejpam-3554	219	22	x	x	SYM
ejpam-3554	219	23	∈	∈	PROPN
ejpam-3554	219	24	s	s	PART
ejpam-3554	219	25	\	\	NOUN
ejpam-3554	219	26	ng(s	ng(s	PUNCT
ejpam-3554	219	27	)	)	PUNCT
ejpam-3554	219	28	and	and	CCONJ
ejpam-3554	219	29	let	let	VERB
ejpam-3554	219	30	sg	sg	VERB
ejpam-3554	219	31	=	=	PUNCT
ejpam-3554	219	32	{	{	PUNCT
ejpam-3554	219	33	vx	vx	X
ejpam-3554	219	34	:	:	PUNCT
ejpam-3554	219	35	x	x	PUNCT
ejpam-3554	219	36	∈	∈	NOUN
ejpam-3554	219	37	s	s	PART
ejpam-3554	219	38	\ng(s	\ng(s	NOUN
ejpam-3554	219	39	)	)	PUNCT
ejpam-3554	219	40	}	}	PUNCT
ejpam-3554	219	41	.	.	PUNCT
ejpam-3554	220	1	then	then	ADV
ejpam-3554	220	2	|sg|	|sg|	PROPN
ejpam-3554	220	3	≤	≤	PROPN
ejpam-3554	220	4	|s	|s	PROPN
ejpam-3554	220	5	\ng(s)|	\ng(s)|	PROPN
ejpam-3554	220	6	and	and	CCONJ
ejpam-3554	220	7	s∗	s∗	PROPN
ejpam-3554	221	1	=	=	SYM
ejpam-3554	221	2	s	s	PART
ejpam-3554	221	3	∪	∪	NOUN
ejpam-3554	221	4	sg	sg	PROPN
ejpam-3554	221	5	is	be	AUX
ejpam-3554	221	6	a	a	DET
ejpam-3554	221	7	total	total	ADJ
ejpam-3554	221	8	α	α	PRON
ejpam-3554	221	9	-	-	ADJ
ejpam-3554	221	10	partial	partial	ADJ
ejpam-3554	221	11	dominating	dominating	NOUN
ejpam-3554	221	12	set	set	VERB
ejpam-3554	221	13	in	in	ADP
ejpam-3554	221	14	g.	g.	PROPN
ejpam-3554	221	15	thus	thus	ADV
ejpam-3554	221	16	,	,	PUNCT
ejpam-3554	221	17	∂tα(g	∂tα(g	PROPN
ejpam-3554	221	18	)	)	PUNCT
ejpam-3554	221	19	≤	≤	NOUN
ejpam-3554	221	20	|s∗|	|s∗|	NUM
ejpam-3554	222	1	=	=	SYM
ejpam-3554	222	2	|s|+	|s|+	PROPN
ejpam-3554	222	3	|sg|	|sg|	PROPN
ejpam-3554	222	4	≤	≤	PROPN
ejpam-3554	222	5	|s	|s	PROPN
ejpam-3554	222	6	∩ng(s)|+	∩ng(s)|+	NOUN
ejpam-3554	222	7	|s	|s	PROPN
ejpam-3554	222	8	\ng(s)|+	\ng(s)|+	NOUN
ejpam-3554	222	9	|s	|s	PROPN
ejpam-3554	222	10	\ng(s)|	\ng(s)|	NUM
ejpam-3554	222	11	=	=	SYM
ejpam-3554	222	12	|s	|s	PROPN
ejpam-3554	222	13	∩ng(s)|+	∩ng(s)|+	PROPN
ejpam-3554	222	14	2|s	2|s	NUM
ejpam-3554	222	15	\ng(s)|	\ng(s)|	NOUN
ejpam-3554	222	16	.	.	PUNCT
ejpam-3554	223	1	in	in	ADP
ejpam-3554	223	2	particular	particular	ADJ
ejpam-3554	223	3	,	,	PUNCT
ejpam-3554	223	4	if	if	SCONJ
ejpam-3554	223	5	s	s	VERB
ejpam-3554	223	6	is	be	AUX
ejpam-3554	223	7	an	an	DET
ejpam-3554	223	8	∂α	∂α	PROPN
ejpam-3554	223	9	-	-	PUNCT
ejpam-3554	223	10	set	set	NOUN
ejpam-3554	223	11	in	in	ADP
ejpam-3554	223	12	g	g	NOUN
ejpam-3554	223	13	,	,	PUNCT
ejpam-3554	223	14	then	then	ADV
ejpam-3554	223	15	∂tα(g	∂tα(g	NOUN
ejpam-3554	223	16	)	)	PUNCT
ejpam-3554	223	17	≤	≤	NUM
ejpam-3554	223	18	|s	|s	PROPN
ejpam-3554	223	19	∩ng(s)|+	∩ng(s)|+	NOUN
ejpam-3554	223	20	|s	|s	PROPN
ejpam-3554	223	21	\ng(s)|+	\ng(s)|+	NOUN
ejpam-3554	223	22	|s	|s	PROPN
ejpam-3554	223	23	\ng(s)|	\ng(s)|	NUM
ejpam-3554	223	24	≤	≤	ADV
ejpam-3554	223	25	2|s|	2|s|	NUM
ejpam-3554	223	26	=	=	SYM
ejpam-3554	223	27	2∂α(g	2∂α(g	NUM
ejpam-3554	223	28	)	)	PUNCT
ejpam-3554	223	29	.	.	PUNCT
ejpam-3554	224	1	�	�	PROPN
ejpam-3554	224	2	theorem	theorem	VERB
ejpam-3554	224	3	10	10	NUM
ejpam-3554	224	4	.	.	PUNCT
ejpam-3554	225	1	let	let	VERB
ejpam-3554	225	2	g	g	NOUN
ejpam-3554	225	3	and	and	CCONJ
ejpam-3554	225	4	h	h	NOUN
ejpam-3554	225	5	be	be	AUX
ejpam-3554	225	6	connected	connect	VERB
ejpam-3554	225	7	graphs	graph	NOUN
ejpam-3554	225	8	.	.	PUNCT
ejpam-3554	226	1	let	let	VERB
ejpam-3554	226	2	α	α	PRON
ejpam-3554	226	3	∈	∈	PROPN
ejpam-3554	226	4	(	(	PUNCT
ejpam-3554	226	5	0	0	NUM
ejpam-3554	226	6	,	,	PUNCT
ejpam-3554	226	7	1	1	NUM
ejpam-3554	226	8	]	]	PUNCT
ejpam-3554	226	9	and	and	CCONJ
ejpam-3554	226	10	c	c	NOUN
ejpam-3554	226	11	=	=	SYM
ejpam-3554	226	12	⋃	⋃	PROPN
ejpam-3554	226	13	x∈s	x∈s	NOUN
ejpam-3554	226	14	(	(	PUNCT
ejpam-3554	226	15	{	{	PUNCT
ejpam-3554	226	16	x	x	NOUN
ejpam-3554	226	17	}	}	PUNCT
ejpam-3554	226	18	×	×	PROPN
ejpam-3554	226	19	tx	tx	PROPN
ejpam-3554	226	20	)	)	PUNCT
ejpam-3554	226	21	⊆	⊆	NUM
ejpam-3554	226	22	v	v	NOUN
ejpam-3554	226	23	(	(	PUNCT
ejpam-3554	226	24	g[h	g[h	PROPN
ejpam-3554	226	25	]	]	PUNCT
ejpam-3554	226	26	)	)	PUNCT
ejpam-3554	226	27	.	.	PUNCT
ejpam-3554	227	1	if	if	SCONJ
ejpam-3554	227	2	either	either	DET
ejpam-3554	227	3	one	one	NUM
ejpam-3554	227	4	of	of	ADP
ejpam-3554	227	5	the	the	DET
ejpam-3554	227	6	following	follow	VERB
ejpam-3554	227	7	holds	hold	VERB
ejpam-3554	227	8	:	:	PUNCT
ejpam-3554	227	9	(	(	PUNCT
ejpam-3554	227	10	i	i	NOUN
ejpam-3554	227	11	)	)	PUNCT
ejpam-3554	227	12	s	s	VERB
ejpam-3554	227	13	is	be	AUX
ejpam-3554	227	14	a	a	DET
ejpam-3554	227	15	total	total	ADJ
ejpam-3554	227	16	α	α	PRON
ejpam-3554	227	17	-	-	ADJ
ejpam-3554	227	18	partial	partial	ADJ
ejpam-3554	227	19	dominating	dominating	NOUN
ejpam-3554	227	20	set	set	VERB
ejpam-3554	227	21	in	in	ADP
ejpam-3554	227	22	g	g	PROPN
ejpam-3554	227	23	,	,	PUNCT
ejpam-3554	227	24	or	or	CCONJ
ejpam-3554	227	25	(	(	PUNCT
ejpam-3554	227	26	ii	ii	NOUN
ejpam-3554	227	27	)	)	PUNCT
ejpam-3554	227	28	s	s	VERB
ejpam-3554	227	29	is	be	AUX
ejpam-3554	227	30	an	an	DET
ejpam-3554	227	31	α	α	NOUN
ejpam-3554	227	32	-	-	ADJ
ejpam-3554	227	33	partial	partial	ADJ
ejpam-3554	227	34	dominating	dominating	NOUN
ejpam-3554	227	35	set	set	VERB
ejpam-3554	227	36	in	in	ADP
ejpam-3554	227	37	g	g	PROPN
ejpam-3554	227	38	and	and	CCONJ
ejpam-3554	227	39	tx	tx	PROPN
ejpam-3554	227	40	is	be	AUX
ejpam-3554	227	41	a	a	DET
ejpam-3554	227	42	total	total	ADJ
ejpam-3554	227	43	dominating	dominating	NOUN
ejpam-3554	227	44	set	set	VERB
ejpam-3554	227	45	in	in	ADP
ejpam-3554	227	46	h	h	NOUN
ejpam-3554	227	47	for	for	ADP
ejpam-3554	227	48	every	every	DET
ejpam-3554	227	49	x	x	SYM
ejpam-3554	227	50	∈	∈	PROPN
ejpam-3554	227	51	s\ng(s	s\ng(s	NOUN
ejpam-3554	227	52	)	)	PUNCT
ejpam-3554	227	53	,	,	PUNCT
ejpam-3554	227	54	r.	r.	PROPN
ejpam-3554	227	55	macapodi	macapodi	PROPN
ejpam-3554	227	56	,	,	PUNCT
ejpam-3554	227	57	r.	r.	PROPN
ejpam-3554	227	58	isla	isla	PROPN
ejpam-3554	227	59	/	/	SYM
ejpam-3554	227	60	eur	eur	PROPN
ejpam-3554	227	61	.	.	PUNCT
ejpam-3554	228	1	j.	j.	PROPN
ejpam-3554	228	2	pure	pure	PROPN
ejpam-3554	228	3	appl	appl	PROPN
ejpam-3554	228	4	.	.	PROPN
ejpam-3554	228	5	math	math	PROPN
ejpam-3554	228	6	,	,	PUNCT
ejpam-3554	228	7	12	12	NUM
ejpam-3554	228	8	(	(	PUNCT
ejpam-3554	228	9	4	4	NUM
ejpam-3554	228	10	)	)	PUNCT
ejpam-3554	228	11	(	(	PUNCT
ejpam-3554	228	12	2019	2019	NUM
ejpam-3554	228	13	)	)	PUNCT
ejpam-3554	228	14	,	,	PUNCT
ejpam-3554	228	15	1643	1643	NUM
ejpam-3554	228	16	-	-	SYM
ejpam-3554	228	17	1655	1655	NUM
ejpam-3554	228	18	1652	1652	NUM
ejpam-3554	228	19	then	then	ADV
ejpam-3554	228	20	c	c	PROPN
ejpam-3554	228	21	is	be	AUX
ejpam-3554	228	22	a	a	DET
ejpam-3554	228	23	total	total	ADJ
ejpam-3554	228	24	α	α	PRON
ejpam-3554	228	25	-	-	ADJ
ejpam-3554	228	26	partial	partial	ADJ
ejpam-3554	228	27	dominating	dominating	NOUN
ejpam-3554	228	28	set	set	VERB
ejpam-3554	228	29	in	in	ADP
ejpam-3554	228	30	g[h	g[h	PROPN
ejpam-3554	228	31	]	]	PUNCT
ejpam-3554	228	32	.	.	PUNCT
ejpam-3554	229	1	proof	proof	NOUN
ejpam-3554	229	2	.	.	PUNCT
ejpam-3554	230	1	suppose	suppose	VERB
ejpam-3554	230	2	condition	condition	NOUN
ejpam-3554	230	3	(	(	PUNCT
ejpam-3554	230	4	i	i	NOUN
ejpam-3554	230	5	)	)	PUNCT
ejpam-3554	230	6	holds	hold	VERB
ejpam-3554	230	7	.	.	PUNCT
ejpam-3554	231	1	since	since	SCONJ
ejpam-3554	231	2	s	s	PROPN
ejpam-3554	231	3	is	be	AUX
ejpam-3554	231	4	a	a	DET
ejpam-3554	231	5	total	total	ADJ
ejpam-3554	231	6	α	α	PRON
ejpam-3554	231	7	-	-	ADJ
ejpam-3554	231	8	partial	partial	ADJ
ejpam-3554	231	9	dominating	dominating	NOUN
ejpam-3554	231	10	set	set	VERB
ejpam-3554	231	11	in	in	ADP
ejpam-3554	231	12	g	g	PROPN
ejpam-3554	231	13	,	,	PUNCT
ejpam-3554	231	14	c	c	PROPN
ejpam-3554	231	15	is	be	AUX
ejpam-3554	231	16	an	an	DET
ejpam-3554	231	17	α	α	NOUN
ejpam-3554	231	18	-	-	ADJ
ejpam-3554	231	19	partial	partial	ADJ
ejpam-3554	231	20	dominating	dominating	NOUN
ejpam-3554	231	21	set	set	VERB
ejpam-3554	231	22	in	in	ADP
ejpam-3554	231	23	g[h	g[h	PROPN
ejpam-3554	231	24	]	]	PUNCT
ejpam-3554	231	25	by	by	ADP
ejpam-3554	231	26	theorem	theorem	NOUN
ejpam-3554	231	27	5	5	NUM
ejpam-3554	231	28	.	.	PUNCT
ejpam-3554	232	1	let	let	VERB
ejpam-3554	232	2	(	(	PUNCT
ejpam-3554	232	3	x	x	NOUN
ejpam-3554	232	4	,	,	PUNCT
ejpam-3554	232	5	a	a	DET
ejpam-3554	232	6	)	)	PUNCT
ejpam-3554	232	7	∈	∈	PROPN
ejpam-3554	232	8	c.	c.	NOUN
ejpam-3554	232	9	then	then	ADV
ejpam-3554	232	10	x	x	PROPN
ejpam-3554	232	11	∈	∈	PROPN
ejpam-3554	232	12	s.	s.	PROPN
ejpam-3554	232	13	since	since	SCONJ
ejpam-3554	232	14	s	s	PROPN
ejpam-3554	232	15	is	be	AUX
ejpam-3554	232	16	a	a	DET
ejpam-3554	232	17	total	total	ADJ
ejpam-3554	232	18	α	α	PRON
ejpam-3554	232	19	-	-	ADJ
ejpam-3554	232	20	partial	partial	ADJ
ejpam-3554	232	21	dominating	dominating	NOUN
ejpam-3554	232	22	set	set	VERB
ejpam-3554	232	23	in	in	ADP
ejpam-3554	232	24	g	g	NOUN
ejpam-3554	232	25	,	,	PUNCT
ejpam-3554	232	26	there	there	PRON
ejpam-3554	232	27	is	be	VERB
ejpam-3554	232	28	a	a	DET
ejpam-3554	232	29	y	y	PROPN
ejpam-3554	232	30	∈	∈	PROPN
ejpam-3554	232	31	s	s	VERB
ejpam-3554	232	32	such	such	ADJ
ejpam-3554	232	33	that	that	SCONJ
ejpam-3554	232	34	xy	xy	PROPN
ejpam-3554	232	35	∈	∈	PROPN
ejpam-3554	232	36	e(g	e(g	PROPN
ejpam-3554	232	37	)	)	PUNCT
ejpam-3554	232	38	.	.	PUNCT
ejpam-3554	233	1	pick	pick	VERB
ejpam-3554	233	2	(	(	PUNCT
ejpam-3554	233	3	y	y	PROPN
ejpam-3554	233	4	,	,	PUNCT
ejpam-3554	233	5	b	b	NOUN
ejpam-3554	233	6	)	)	PUNCT
ejpam-3554	233	7	∈	∈	PROPN
ejpam-3554	233	8	c.	c.	NOUN
ejpam-3554	233	9	then	then	ADV
ejpam-3554	233	10	(	(	PUNCT
ejpam-3554	233	11	x	x	X
ejpam-3554	233	12	,	,	PUNCT
ejpam-3554	233	13	a)(y	a)(y	PROPN
ejpam-3554	233	14	,	,	PUNCT
ejpam-3554	233	15	b	b	X
ejpam-3554	233	16	)	)	PUNCT
ejpam-3554	233	17	∈	∈	NOUN
ejpam-3554	233	18	e(g[h	e(g[h	NOUN
ejpam-3554	233	19	]	]	PUNCT
ejpam-3554	233	20	)	)	PUNCT
ejpam-3554	233	21	.	.	PUNCT
ejpam-3554	234	1	hence	hence	ADV
ejpam-3554	234	2	,	,	PUNCT
ejpam-3554	234	3	c	c	PROPN
ejpam-3554	234	4	is	be	AUX
ejpam-3554	234	5	a	a	DET
ejpam-3554	234	6	total	total	ADJ
ejpam-3554	234	7	α	α	PRON
ejpam-3554	234	8	-	-	ADJ
ejpam-3554	234	9	partial	partial	ADJ
ejpam-3554	234	10	dominating	dominating	NOUN
ejpam-3554	234	11	set	set	VERB
ejpam-3554	234	12	in	in	ADP
ejpam-3554	234	13	g[h	g[h	PROPN
ejpam-3554	234	14	]	]	PUNCT
ejpam-3554	234	15	.	.	PUNCT
ejpam-3554	235	1	suppose	suppose	VERB
ejpam-3554	235	2	condition	condition	NOUN
ejpam-3554	235	3	(	(	PUNCT
ejpam-3554	235	4	ii	ii	NOUN
ejpam-3554	235	5	)	)	PUNCT
ejpam-3554	235	6	holds	hold	VERB
ejpam-3554	235	7	.	.	PUNCT
ejpam-3554	236	1	since	since	SCONJ
ejpam-3554	236	2	tx	tx	PROPN
ejpam-3554	236	3	,	,	PUNCT
ejpam-3554	236	4	being	be	AUX
ejpam-3554	236	5	a	a	DET
ejpam-3554	236	6	total	total	ADJ
ejpam-3554	236	7	dominating	dominating	NOUN
ejpam-3554	236	8	set	set	NOUN
ejpam-3554	236	9	,	,	PUNCT
ejpam-3554	236	10	is	be	AUX
ejpam-3554	236	11	a	a	DET
ejpam-3554	236	12	dominating	dominating	NOUN
ejpam-3554	236	13	set	set	VERB
ejpam-3554	236	14	in	in	ADP
ejpam-3554	236	15	h	h	NOUN
ejpam-3554	236	16	for	for	ADP
ejpam-3554	236	17	every	every	DET
ejpam-3554	236	18	x	x	SYM
ejpam-3554	236	19	∈	∈	PROPN
ejpam-3554	236	20	s	s	PART
ejpam-3554	236	21	\	\	NOUN
ejpam-3554	236	22	ng(s	ng(s	NUM
ejpam-3554	236	23	)	)	PUNCT
ejpam-3554	236	24	,	,	PUNCT
ejpam-3554	236	25	it	it	PRON
ejpam-3554	236	26	follows	follow	VERB
ejpam-3554	236	27	by	by	ADP
ejpam-3554	236	28	theorem	theorem	NOUN
ejpam-3554	236	29	5	5	NUM
ejpam-3554	236	30	that	that	SCONJ
ejpam-3554	236	31	c	c	PROPN
ejpam-3554	236	32	is	be	AUX
ejpam-3554	236	33	an	an	DET
ejpam-3554	236	34	α	α	NOUN
ejpam-3554	236	35	-	-	ADJ
ejpam-3554	236	36	partial	partial	ADJ
ejpam-3554	236	37	dominating	dominating	NOUN
ejpam-3554	236	38	set	set	VERB
ejpam-3554	236	39	in	in	ADP
ejpam-3554	236	40	g[h	g[h	PROPN
ejpam-3554	236	41	]	]	PUNCT
ejpam-3554	236	42	.	.	PUNCT
ejpam-3554	237	1	let	let	VERB
ejpam-3554	237	2	x	x	PUNCT
ejpam-3554	237	3	∈	∈	PROPN
ejpam-3554	237	4	s	s	PART
ejpam-3554	237	5	\ng(s	\ng(s	NOUN
ejpam-3554	237	6	)	)	PUNCT
ejpam-3554	237	7	.	.	PUNCT
ejpam-3554	238	1	suppose	suppose	VERB
ejpam-3554	238	2	(	(	PUNCT
ejpam-3554	238	3	x	x	X
ejpam-3554	238	4	,	,	PUNCT
ejpam-3554	238	5	a	a	DET
ejpam-3554	238	6	)	)	PUNCT
ejpam-3554	238	7	∈	∈	PROPN
ejpam-3554	238	8	c.	c.	NOUN
ejpam-3554	238	9	since	since	SCONJ
ejpam-3554	238	10	tx	tx	PROPN
ejpam-3554	238	11	is	be	AUX
ejpam-3554	238	12	a	a	DET
ejpam-3554	238	13	total	total	ADJ
ejpam-3554	238	14	dominating	dominating	NOUN
ejpam-3554	238	15	set	set	NOUN
ejpam-3554	238	16	in	in	ADP
ejpam-3554	238	17	h	h	NOUN
ejpam-3554	238	18	,	,	PUNCT
ejpam-3554	238	19	there	there	PRON
ejpam-3554	238	20	exists	exist	VERB
ejpam-3554	238	21	a	a	DET
ejpam-3554	238	22	b	b	PROPN
ejpam-3554	238	23	∈	∈	NOUN
ejpam-3554	238	24	tx	tx	ADP
ejpam-3554	238	25	such	such	ADJ
ejpam-3554	238	26	that	that	SCONJ
ejpam-3554	238	27	ab	ab	PROPN
ejpam-3554	238	28	∈	∈	PROPN
ejpam-3554	238	29	e(h	e(h	PROPN
ejpam-3554	238	30	)	)	PUNCT
ejpam-3554	238	31	,	,	PUNCT
ejpam-3554	238	32	hence	hence	ADV
ejpam-3554	238	33	(	(	PUNCT
ejpam-3554	238	34	x	x	NOUN
ejpam-3554	238	35	,	,	PUNCT
ejpam-3554	238	36	b	b	NOUN
ejpam-3554	238	37	)	)	PUNCT
ejpam-3554	238	38	∈	∈	PROPN
ejpam-3554	238	39	c	c	NOUN
ejpam-3554	238	40	and	and	CCONJ
ejpam-3554	238	41	(	(	PUNCT
ejpam-3554	238	42	x	x	NOUN
ejpam-3554	238	43	,	,	PUNCT
ejpam-3554	238	44	a)(x	a)(x	PROPN
ejpam-3554	238	45	,	,	PUNCT
ejpam-3554	238	46	b	b	X
ejpam-3554	238	47	)	)	PUNCT
ejpam-3554	238	48	∈	∈	NOUN
ejpam-3554	238	49	e(g[h	e(g[h	NOUN
ejpam-3554	238	50	]	]	PUNCT
ejpam-3554	238	51	)	)	PUNCT
ejpam-3554	238	52	.	.	PUNCT
ejpam-3554	239	1	suppose	suppose	VERB
ejpam-3554	239	2	x	x	X
ejpam-3554	239	3	∈	∈	PROPN
ejpam-3554	239	4	s	s	PART
ejpam-3554	239	5	∩	∩	NOUN
ejpam-3554	239	6	ng(s	ng(s	NUM
ejpam-3554	239	7	)	)	PUNCT
ejpam-3554	239	8	.	.	PUNCT
ejpam-3554	240	1	then	then	ADV
ejpam-3554	240	2	there	there	PRON
ejpam-3554	240	3	exists	exist	VERB
ejpam-3554	240	4	y	y	PROPN
ejpam-3554	240	5	∈	∈	PROPN
ejpam-3554	240	6	s	s	VERB
ejpam-3554	240	7	such	such	ADJ
ejpam-3554	240	8	that	that	SCONJ
ejpam-3554	240	9	xy	xy	PROPN
ejpam-3554	240	10	∈	∈	PROPN
ejpam-3554	240	11	e(g	e(g	PROPN
ejpam-3554	240	12	)	)	PUNCT
ejpam-3554	240	13	.	.	PUNCT
ejpam-3554	241	1	let	let	VERB
ejpam-3554	241	2	(	(	PUNCT
ejpam-3554	241	3	x	x	NOUN
ejpam-3554	241	4	,	,	PUNCT
ejpam-3554	241	5	a	a	PRON
ejpam-3554	241	6	)	)	PUNCT
ejpam-3554	241	7	∈	∈	PROPN
ejpam-3554	241	8	c.	c.	PROPN
ejpam-3554	241	9	pick	pick	PROPN
ejpam-3554	241	10	(	(	PUNCT
ejpam-3554	241	11	y	y	PROPN
ejpam-3554	241	12	,	,	PUNCT
ejpam-3554	241	13	b	b	NOUN
ejpam-3554	241	14	)	)	PUNCT
ejpam-3554	241	15	∈	∈	PROPN
ejpam-3554	241	16	c.	c.	NOUN
ejpam-3554	241	17	then	then	ADV
ejpam-3554	241	18	(	(	PUNCT
ejpam-3554	241	19	x	x	X
ejpam-3554	241	20	,	,	PUNCT
ejpam-3554	241	21	a)(y	a)(y	PROPN
ejpam-3554	241	22	,	,	PUNCT
ejpam-3554	241	23	b	b	X
ejpam-3554	241	24	)	)	PUNCT
ejpam-3554	241	25	∈	∈	PROPN
ejpam-3554	241	26	e	e	X
ejpam-3554	241	27	(	(	PUNCT
ejpam-3554	241	28	g[h	g[h	PROPN
ejpam-3554	241	29	]	]	PUNCT
ejpam-3554	241	30	)	)	PUNCT
ejpam-3554	241	31	.	.	PUNCT
ejpam-3554	242	1	therefore	therefore	ADV
ejpam-3554	242	2	,	,	PUNCT
ejpam-3554	242	3	c	c	PROPN
ejpam-3554	242	4	is	be	AUX
ejpam-3554	242	5	a	a	DET
ejpam-3554	242	6	total	total	ADJ
ejpam-3554	242	7	α	α	PRON
ejpam-3554	242	8	-	-	ADJ
ejpam-3554	242	9	partial	partial	ADJ
ejpam-3554	242	10	dominating	dominating	NOUN
ejpam-3554	242	11	set	set	VERB
ejpam-3554	242	12	in	in	ADP
ejpam-3554	242	13	g[h	g[h	PROPN
ejpam-3554	242	14	]	]	PUNCT
ejpam-3554	242	15	.	.	PUNCT
ejpam-3554	243	1	�	�	PROPN
ejpam-3554	243	2	remark	remark	VERB
ejpam-3554	243	3	9	9	NUM
ejpam-3554	243	4	.	.	PUNCT
ejpam-3554	244	1	the	the	DET
ejpam-3554	244	2	converse	converse	NOUN
ejpam-3554	244	3	of	of	ADP
ejpam-3554	244	4	theorem	theorem	NOUN
ejpam-3554	244	5	10	10	NUM
ejpam-3554	244	6	is	be	AUX
ejpam-3554	244	7	not	not	PART
ejpam-3554	244	8	true	true	ADJ
ejpam-3554	244	9	.	.	PUNCT
ejpam-3554	245	1	to	to	PART
ejpam-3554	245	2	see	see	VERB
ejpam-3554	245	3	this	this	PRON
ejpam-3554	245	4	,	,	PUNCT
ejpam-3554	245	5	consider	consider	VERB
ejpam-3554	245	6	the	the	DET
ejpam-3554	245	7	graph	graph	NOUN
ejpam-3554	245	8	p5[p5	p5[p5	NOUN
ejpam-3554	245	9	]	]	PUNCT
ejpam-3554	245	10	in	in	ADP
ejpam-3554	245	11	figure	figure	NOUN
ejpam-3554	245	12	7	7	NUM
ejpam-3554	245	13	.	.	PUNCT
ejpam-3554	246	1	the	the	DET
ejpam-3554	246	2	set	set	NOUN
ejpam-3554	246	3	c	c	NOUN
ejpam-3554	246	4	=	=	SYM
ejpam-3554	246	5	{	{	PUNCT
ejpam-3554	246	6	(	(	PUNCT
ejpam-3554	246	7	x	x	NOUN
ejpam-3554	246	8	,	,	PUNCT
ejpam-3554	246	9	a	a	PRON
ejpam-3554	246	10	)	)	PUNCT
ejpam-3554	246	11	,	,	PUNCT
ejpam-3554	246	12	(	(	PUNCT
ejpam-3554	246	13	x	x	NOUN
ejpam-3554	246	14	,	,	PUNCT
ejpam-3554	246	15	b	b	NOUN
ejpam-3554	246	16	)	)	PUNCT
ejpam-3554	246	17	}	}	PUNCT
ejpam-3554	246	18	form	form	VERB
ejpam-3554	246	19	a	a	DET
ejpam-3554	246	20	∂tα	∂tα	PROPN
ejpam-3554	246	21	-	-	PUNCT
ejpam-3554	246	22	set	set	NOUN
ejpam-3554	246	23	,	,	PUNCT
ejpam-3554	246	24	where	where	SCONJ
ejpam-3554	246	25	α	α	NOUN
ejpam-3554	246	26	=	=	NOUN
ejpam-3554	246	27	1	1	NUM
ejpam-3554	246	28	2	2	NUM
ejpam-3554	246	29	,	,	PUNCT
ejpam-3554	246	30	but	but	CCONJ
ejpam-3554	246	31	neither	neither	PRON
ejpam-3554	246	32	of	of	ADP
ejpam-3554	246	33	condition	condition	NOUN
ejpam-3554	246	34	(	(	PUNCT
ejpam-3554	246	35	i	i	NOUN
ejpam-3554	246	36	)	)	PUNCT
ejpam-3554	246	37	nor	nor	CCONJ
ejpam-3554	246	38	(	(	PUNCT
ejpam-3554	246	39	ii	ii	NOUN
ejpam-3554	246	40	)	)	PUNCT
ejpam-3554	246	41	holds	hold	VERB
ejpam-3554	246	42	since	since	ADV
ejpam-3554	246	43	{	{	PUNCT
ejpam-3554	246	44	x	x	X
ejpam-3554	246	45	}	}	PUNCT
ejpam-3554	246	46	is	be	AUX
ejpam-3554	246	47	not	not	PART
ejpam-3554	246	48	a	a	DET
ejpam-3554	246	49	total	total	ADJ
ejpam-3554	246	50	α	α	PRON
ejpam-3554	246	51	-	-	ADJ
ejpam-3554	246	52	partial	partial	ADJ
ejpam-3554	246	53	dominating	dominating	NOUN
ejpam-3554	246	54	set	set	VERB
ejpam-3554	246	55	in	in	ADP
ejpam-3554	246	56	g	g	NOUN
ejpam-3554	246	57	,	,	PUNCT
ejpam-3554	246	58	and	and	CCONJ
ejpam-3554	246	59	s	s	VERB
ejpam-3554	246	60	=	=	PUNCT
ejpam-3554	246	61	{	{	PUNCT
ejpam-3554	246	62	x	x	NOUN
ejpam-3554	246	63	}	}	PUNCT
ejpam-3554	246	64	is	be	AUX
ejpam-3554	246	65	an	an	DET
ejpam-3554	246	66	α	α	NOUN
ejpam-3554	246	67	-	-	ADJ
ejpam-3554	246	68	partial	partial	ADJ
ejpam-3554	246	69	dominating	dominating	NOUN
ejpam-3554	246	70	set	set	VERB
ejpam-3554	246	71	in	in	ADP
ejpam-3554	246	72	g	g	PROPN
ejpam-3554	246	73	but	but	CCONJ
ejpam-3554	246	74	tx	tx	PROPN
ejpam-3554	246	75	=	=	PUNCT
ejpam-3554	246	76	{	{	PUNCT
ejpam-3554	246	77	a	a	DET
ejpam-3554	246	78	,	,	PUNCT
ejpam-3554	246	79	b	b	NOUN
ejpam-3554	246	80	}	}	PUNCT
ejpam-3554	246	81	is	be	AUX
ejpam-3554	246	82	not	not	PART
ejpam-3554	246	83	a	a	DET
ejpam-3554	246	84	total	total	ADJ
ejpam-3554	246	85	dominating	dominating	NOUN
ejpam-3554	246	86	set	set	VERB
ejpam-3554	246	87	in	in	ADP
ejpam-3554	246	88	h.	h.	PROPN
ejpam-3554	246	89	corollary	corollary	PROPN
ejpam-3554	246	90	5	5	PROPN
ejpam-3554	246	91	.	.	PUNCT
ejpam-3554	247	1	let	let	VERB
ejpam-3554	247	2	g	g	NOUN
ejpam-3554	247	3	and	and	CCONJ
ejpam-3554	247	4	h	h	NOUN
ejpam-3554	247	5	be	be	AUX
ejpam-3554	247	6	nontrivial	nontrivial	ADJ
ejpam-3554	247	7	connected	connect	VERB
ejpam-3554	247	8	graphs	graph	NOUN
ejpam-3554	247	9	and	and	CCONJ
ejpam-3554	247	10	let	let	VERB
ejpam-3554	247	11	α	α	PRON
ejpam-3554	247	12	∈	∈	PROPN
ejpam-3554	247	13	(	(	PUNCT
ejpam-3554	247	14	0	0	NUM
ejpam-3554	247	15	,	,	PUNCT
ejpam-3554	247	16	1	1	NUM
ejpam-3554	247	17	]	]	PUNCT
ejpam-3554	247	18	.	.	PUNCT
ejpam-3554	248	1	then	then	ADV
ejpam-3554	248	2	∂tα(g[h	∂tα(g[h	VERB
ejpam-3554	248	3	]	]	PUNCT
ejpam-3554	248	4	)	)	PUNCT
ejpam-3554	248	5	=	=	SYM
ejpam-3554	248	6	∂tα(g	∂tα(g	NOUN
ejpam-3554	248	7	)	)	PUNCT
ejpam-3554	248	8	.	.	PUNCT
ejpam-3554	249	1	proof	proof	NOUN
ejpam-3554	249	2	.	.	PUNCT
ejpam-3554	250	1	by	by	ADP
ejpam-3554	250	2	theorem	theorem	NOUN
ejpam-3554	250	3	10	10	NUM
ejpam-3554	250	4	,	,	PUNCT
ejpam-3554	250	5	∂tα(g[h	∂tα(g[h	NOUN
ejpam-3554	250	6	]	]	PUNCT
ejpam-3554	250	7	)	)	PUNCT
ejpam-3554	250	8	≤	≤	NUM
ejpam-3554	250	9	min	min	NOUN
ejpam-3554	250	10	{	{	PUNCT
ejpam-3554	250	11	∂α(g	∂α(g	PROPN
ejpam-3554	250	12	)	)	PUNCT
ejpam-3554	250	13	·	·	PUNCT
ejpam-3554	250	14	γt(h	γt(h	NUM
ejpam-3554	250	15	)	)	PUNCT
ejpam-3554	250	16	,	,	PUNCT
ejpam-3554	250	17	∂tα(g	∂tα(g	NOUN
ejpam-3554	250	18	)	)	PUNCT
ejpam-3554	250	19	}	}	PUNCT
ejpam-3554	250	20	.	.	PUNCT
ejpam-3554	251	1	clearly	clearly	ADV
ejpam-3554	251	2	,	,	PUNCT
ejpam-3554	251	3	∂tα(g[h	∂tα(g[h	NOUN
ejpam-3554	251	4	]	]	PUNCT
ejpam-3554	251	5	)	)	PUNCT
ejpam-3554	251	6	≤	≤	ADJ
ejpam-3554	251	7	∂tα(g	∂tα(g	NOUN
ejpam-3554	251	8	)	)	PUNCT
ejpam-3554	251	9	.	.	PUNCT
ejpam-3554	252	1	next	next	ADV
ejpam-3554	252	2	,	,	PUNCT
ejpam-3554	252	3	let	let	VERB
ejpam-3554	252	4	c	c	NOUN
ejpam-3554	252	5	=	=	SYM
ejpam-3554	252	6	⋃	⋃	PROPN
ejpam-3554	252	7	x∈s	x∈s	NOUN
ejpam-3554	252	8	(	(	PUNCT
ejpam-3554	252	9	{	{	PUNCT
ejpam-3554	252	10	x	x	NOUN
ejpam-3554	252	11	}	}	PUNCT
ejpam-3554	252	12	×	×	PROPN
ejpam-3554	252	13	tx	tx	PROPN
ejpam-3554	252	14	)	)	PUNCT
ejpam-3554	252	15	be	be	AUX
ejpam-3554	252	16	a	a	DET
ejpam-3554	252	17	∂tα	∂tα	NOUN
ejpam-3554	252	18	-	-	PUNCT
ejpam-3554	252	19	set	set	NOUN
ejpam-3554	252	20	in	in	ADP
ejpam-3554	252	21	g[h	g[h	PROPN
ejpam-3554	252	22	]	]	PUNCT
ejpam-3554	252	23	.	.	PUNCT
ejpam-3554	253	1	suppose	suppose	VERB
ejpam-3554	253	2	that	that	SCONJ
ejpam-3554	253	3	there	there	PRON
ejpam-3554	253	4	exists	exist	VERB
ejpam-3554	253	5	y	y	PROPN
ejpam-3554	253	6	∈	∈	PROPN
ejpam-3554	253	7	s	s	PART
ejpam-3554	253	8	∩	∩	NOUN
ejpam-3554	253	9	ng(s	ng(s	CCONJ
ejpam-3554	253	10	)	)	PUNCT
ejpam-3554	253	11	such	such	ADJ
ejpam-3554	253	12	that	that	SCONJ
ejpam-3554	253	13	|ty|	|ty|	PROPN
ejpam-3554	253	14	≥	≥	NOUN
ejpam-3554	253	15	2	2	X
ejpam-3554	253	16	.	.	PUNCT
ejpam-3554	254	1	let	let	VERB
ejpam-3554	254	2	t	t	NOUN
ejpam-3554	254	3	′x	′x	PROPN
ejpam-3554	254	4	=	=	SYM
ejpam-3554	254	5	tx	tx	PROPN
ejpam-3554	254	6	for	for	ADP
ejpam-3554	254	7	all	all	DET
ejpam-3554	254	8	x	x	PART
ejpam-3554	254	9	∈	∈	PROPN
ejpam-3554	254	10	s	s	PART
ejpam-3554	254	11	\	\	X
ejpam-3554	254	12	{	{	PUNCT
ejpam-3554	254	13	y	y	NOUN
ejpam-3554	254	14	}	}	PUNCT
ejpam-3554	254	15	,	,	PUNCT
ejpam-3554	254	16	and	and	CCONJ
ejpam-3554	254	17	let	let	VERB
ejpam-3554	254	18	t	t	PROPN
ejpam-3554	254	19	′y	′y	NOUN
ejpam-3554	254	20	=	=	PUNCT
ejpam-3554	255	1	{	{	PUNCT
ejpam-3554	255	2	a	a	NOUN
ejpam-3554	255	3	}	}	PUNCT
ejpam-3554	255	4	where	where	SCONJ
ejpam-3554	255	5	a	a	DET
ejpam-3554	255	6	∈	∈	PROPN
ejpam-3554	255	7	ty	ty	INTJ
ejpam-3554	255	8	.	.	PUNCT
ejpam-3554	256	1	let	let	VERB
ejpam-3554	256	2	c	c	NOUN
ejpam-3554	256	3	′	′	VERB
ejpam-3554	257	1	=	=	PUNCT
ejpam-3554	258	1	⋃	⋃	VERB
ejpam-3554	258	2	z∈s	z∈s	NUM
ejpam-3554	258	3	(	(	PUNCT
ejpam-3554	258	4	{	{	PUNCT
ejpam-3554	258	5	z	z	NOUN
ejpam-3554	258	6	}	}	PUNCT
ejpam-3554	258	7	×	×	NOUN
ejpam-3554	258	8	t	t	NOUN
ejpam-3554	258	9	′z	′z	PROPN
ejpam-3554	258	10	)	)	PUNCT
ejpam-3554	258	11	.	.	PUNCT
ejpam-3554	259	1	since	since	SCONJ
ejpam-3554	259	2	y	y	PROPN
ejpam-3554	259	3	∈	∈	PROPN
ejpam-3554	259	4	s	s	PART
ejpam-3554	259	5	∩	∩	NOUN
ejpam-3554	259	6	ng(s	ng(s	NUM
ejpam-3554	259	7	)	)	PUNCT
ejpam-3554	259	8	,	,	PUNCT
ejpam-3554	259	9	ng[h][c	ng[h][c	PROPN
ejpam-3554	259	10	′	′	NOUN
ejpam-3554	259	11	]	]	X
ejpam-3554	259	12	=	=	PUNCT
ejpam-3554	259	13	ng[h][c	ng[h][c	PROPN
ejpam-3554	259	14	]	]	PUNCT
ejpam-3554	259	15	.	.	PUNCT
ejpam-3554	260	1	hence	hence	ADV
ejpam-3554	260	2	,	,	PUNCT
ejpam-3554	260	3	r.	r.	PROPN
ejpam-3554	260	4	macapodi	macapodi	PROPN
ejpam-3554	260	5	,	,	PUNCT
ejpam-3554	260	6	r.	r.	PROPN
ejpam-3554	260	7	isla	isla	PROPN
ejpam-3554	260	8	/	/	SYM
ejpam-3554	260	9	eur	eur	PROPN
ejpam-3554	260	10	.	.	PUNCT
ejpam-3554	261	1	j.	j.	PROPN
ejpam-3554	261	2	pure	pure	PROPN
ejpam-3554	261	3	appl	appl	PROPN
ejpam-3554	261	4	.	.	PROPN
ejpam-3554	261	5	math	math	PROPN
ejpam-3554	261	6	,	,	PUNCT
ejpam-3554	261	7	12	12	NUM
ejpam-3554	261	8	(	(	PUNCT
ejpam-3554	261	9	4	4	NUM
ejpam-3554	261	10	)	)	PUNCT
ejpam-3554	261	11	(	(	PUNCT
ejpam-3554	261	12	2019	2019	NUM
ejpam-3554	261	13	)	)	PUNCT
ejpam-3554	261	14	,	,	PUNCT
ejpam-3554	261	15	1643	1643	NUM
ejpam-3554	261	16	-	-	SYM
ejpam-3554	261	17	1655	1655	NUM
ejpam-3554	261	18	1653	1653	NUM
ejpam-3554	261	19	|ng[h][c	|ng[h][c	NOUN
ejpam-3554	261	20	′]|	′]|	NOUN
ejpam-3554	261	21	=	=	SYM
ejpam-3554	261	22	|ng[h][c]|	|ng[h][c]|	NOUN
ejpam-3554	261	23	≥	≥	NOUN
ejpam-3554	261	24	α|v	α|v	VERB
ejpam-3554	261	25	(	(	PUNCT
ejpam-3554	261	26	g[h])|	g[h])|	PROPN
ejpam-3554	261	27	,	,	PUNCT
ejpam-3554	261	28	that	that	ADV
ejpam-3554	261	29	is	is	ADV
ejpam-3554	261	30	,	,	PUNCT
ejpam-3554	261	31	c	c	NOUN
ejpam-3554	261	32	′	′	NOUN
ejpam-3554	261	33	is	be	AUX
ejpam-3554	261	34	a	a	DET
ejpam-3554	261	35	total	total	ADJ
ejpam-3554	261	36	α	α	PRON
ejpam-3554	261	37	-	-	ADJ
ejpam-3554	261	38	partial	partial	ADJ
ejpam-3554	261	39	dominating	dominating	NOUN
ejpam-3554	261	40	set	set	VERB
ejpam-3554	261	41	in	in	ADP
ejpam-3554	261	42	g[h	g[h	PROPN
ejpam-3554	261	43	]	]	PUNCT
ejpam-3554	261	44	.	.	PUNCT
ejpam-3554	262	1	further	far	ADV
ejpam-3554	262	2	,	,	PUNCT
ejpam-3554	262	3	|c	|c	ADJ
ejpam-3554	262	4	′|	′|	NUM
ejpam-3554	262	5	<	<	X
ejpam-3554	262	6	|c|	|c|	PROPN
ejpam-3554	262	7	since	since	SCONJ
ejpam-3554	262	8	|t	|t	PROPN
ejpam-3554	262	9	′y|	′y|	NOUN
ejpam-3554	262	10	=	=	SYM
ejpam-3554	262	11	1	1	NUM
ejpam-3554	262	12	<	<	X
ejpam-3554	262	13	|ty|	|ty|	PROPN
ejpam-3554	262	14	,	,	PUNCT
ejpam-3554	262	15	a	a	DET
ejpam-3554	262	16	contradiction	contradiction	NOUN
ejpam-3554	262	17	.	.	PUNCT
ejpam-3554	263	1	thus	thus	ADV
ejpam-3554	263	2	,	,	PUNCT
ejpam-3554	263	3	|tx|	|tx|	X
ejpam-3554	263	4	=	=	SYM
ejpam-3554	263	5	1	1	NUM
ejpam-3554	263	6	for	for	ADP
ejpam-3554	263	7	all	all	DET
ejpam-3554	263	8	x	x	SYM
ejpam-3554	263	9	∈	∈	NOUN
ejpam-3554	263	10	s	s	NOUN
ejpam-3554	263	11	∩ng(s	∩ng(s	NOUN
ejpam-3554	263	12	)	)	PUNCT
ejpam-3554	263	13	.	.	PUNCT
ejpam-3554	264	1	now	now	ADV
ejpam-3554	264	2	,	,	PUNCT
ejpam-3554	264	3	since	since	SCONJ
ejpam-3554	264	4	every	every	DET
ejpam-3554	264	5	element	element	NOUN
ejpam-3554	264	6	of	of	ADP
ejpam-3554	264	7	c	c	PROPN
ejpam-3554	264	8	is	be	AUX
ejpam-3554	264	9	adjacent	adjacent	ADJ
ejpam-3554	264	10	to	to	ADP
ejpam-3554	264	11	an	an	DET
ejpam-3554	264	12	element	element	NOUN
ejpam-3554	264	13	of	of	ADP
ejpam-3554	264	14	c	c	PROPN
ejpam-3554	264	15	,	,	PUNCT
ejpam-3554	264	16	it	it	PRON
ejpam-3554	264	17	follows	follow	VERB
ejpam-3554	264	18	that	that	SCONJ
ejpam-3554	264	19	|tx|	|tx|	NOUN
ejpam-3554	264	20	≥	≥	NUM
ejpam-3554	264	21	2	2	NUM
ejpam-3554	264	22	for	for	ADP
ejpam-3554	264	23	all	all	DET
ejpam-3554	264	24	x	x	PART
ejpam-3554	264	25	∈	∈	NOUN
ejpam-3554	264	26	s	s	PART
ejpam-3554	264	27	\ng(s	\ng(s	NOUN
ejpam-3554	264	28	)	)	PUNCT
ejpam-3554	264	29	.	.	PUNCT
ejpam-3554	265	1	by	by	ADP
ejpam-3554	265	2	theorem	theorem	NOUN
ejpam-3554	265	3	9	9	NUM
ejpam-3554	265	4	,	,	PUNCT
ejpam-3554	265	5	∂tα(g[h	∂tα(g[h	NOUN
ejpam-3554	265	6	]	]	PUNCT
ejpam-3554	265	7	)	)	PUNCT
ejpam-3554	265	8	=	=	SYM
ejpam-3554	265	9	|c|	|c|	PROPN
ejpam-3554	265	10	=	=	SYM
ejpam-3554	265	11	∑	∑	NOUN
ejpam-3554	265	12	x∈s∩ng(s	x∈s∩ng(s	NOUN
ejpam-3554	265	13	)	)	PUNCT
ejpam-3554	265	14	|tx|+	|tx|+	X
ejpam-3554	265	15	∑	∑	PUNCT
ejpam-3554	265	16	x∈s\ng(s	x∈s\ng(s	NUM
ejpam-3554	265	17	)	)	PUNCT
ejpam-3554	265	18	|tx|	|tx|	PROPN
ejpam-3554	265	19	≥	≥	NUM
ejpam-3554	265	20	|s	|s	PROPN
ejpam-3554	265	21	∩ng(s)|+	∩ng(s)|+	NOUN
ejpam-3554	265	22	2	2	NUM
ejpam-3554	265	23	·	·	PUNCT
ejpam-3554	265	24	|s	|s	PROPN
ejpam-3554	265	25	\ng(s)|	\ng(s)|	NUM
ejpam-3554	265	26	≥	≥	NOUN
ejpam-3554	265	27	∂tα(g	∂tα(g	PROPN
ejpam-3554	265	28	)	)	PUNCT
ejpam-3554	265	29	.	.	PUNCT
ejpam-3554	266	1	therefore	therefore	ADV
ejpam-3554	266	2	,	,	PUNCT
ejpam-3554	266	3	∂tα(g[h	∂tα(g[h	ADV
ejpam-3554	266	4	]	]	X
ejpam-3554	266	5	)	)	PUNCT
ejpam-3554	266	6	=	=	SYM
ejpam-3554	266	7	∂tα(g	∂tα(g	NOUN
ejpam-3554	266	8	)	)	PUNCT
ejpam-3554	266	9	.	.	PUNCT
ejpam-3554	267	1	�	�	PROPN
ejpam-3554	267	2	corollary	corollary	NOUN
ejpam-3554	267	3	6	6	NUM
ejpam-3554	267	4	.	.	PUNCT
ejpam-3554	268	1	if	if	SCONJ
ejpam-3554	268	2	∂α(g	∂α(g	PROPN
ejpam-3554	268	3	)	)	PUNCT
ejpam-3554	268	4	=	=	SYM
ejpam-3554	268	5	1	1	NUM
ejpam-3554	268	6	and	and	CCONJ
ejpam-3554	268	7	γt(h	γt(h	NUM
ejpam-3554	268	8	)	)	PUNCT
ejpam-3554	268	9	=	=	SYM
ejpam-3554	268	10	2	2	NUM
ejpam-3554	268	11	,	,	PUNCT
ejpam-3554	268	12	then	then	ADV
ejpam-3554	268	13	∂tα(g[h	∂tα(g[h	VERB
ejpam-3554	268	14	]	]	PUNCT
ejpam-3554	268	15	)	)	PUNCT
ejpam-3554	268	16	=	=	SYM
ejpam-3554	268	17	2	2	X
ejpam-3554	268	18	.	.	X
ejpam-3554	268	19	theorem	theorem	NOUN
ejpam-3554	268	20	11	11	NUM
ejpam-3554	268	21	.	.	PUNCT
ejpam-3554	269	1	let	let	VERB
ejpam-3554	269	2	g	g	NOUN
ejpam-3554	269	3	and	and	CCONJ
ejpam-3554	269	4	h	h	NOUN
ejpam-3554	269	5	be	be	AUX
ejpam-3554	269	6	nontrivial	nontrivial	ADJ
ejpam-3554	269	7	connected	connect	VERB
ejpam-3554	269	8	graphs	graph	NOUN
ejpam-3554	269	9	and	and	CCONJ
ejpam-3554	269	10	let	let	VERB
ejpam-3554	269	11	α	α	PRON
ejpam-3554	269	12	∈	∈	PROPN
ejpam-3554	269	13	(	(	PUNCT
ejpam-3554	269	14	0	0	NUM
ejpam-3554	269	15	,	,	PUNCT
ejpam-3554	269	16	1	1	NUM
ejpam-3554	269	17	]	]	PUNCT
ejpam-3554	269	18	.	.	PUNCT
ejpam-3554	270	1	then	then	ADV
ejpam-3554	270	2	c1	c1	PROPN
ejpam-3554	270	3	=	=	PROPN
ejpam-3554	271	1	s1	s1	PROPN
ejpam-3554	271	2	×	×	PROPN
ejpam-3554	271	3	v	v	NOUN
ejpam-3554	271	4	(	(	PUNCT
ejpam-3554	271	5	h	h	NOUN
ejpam-3554	271	6	)	)	PUNCT
ejpam-3554	271	7	and	and	CCONJ
ejpam-3554	271	8	c2	c2	PROPN
ejpam-3554	271	9	=	=	SYM
ejpam-3554	271	10	v	v	PROPN
ejpam-3554	271	11	(	(	PUNCT
ejpam-3554	271	12	g)×	g)×	NOUN
ejpam-3554	271	13	s2	s2	NOUN
ejpam-3554	271	14	are	be	AUX
ejpam-3554	271	15	total	total	ADJ
ejpam-3554	271	16	α	α	PRON
ejpam-3554	271	17	-	-	ADJ
ejpam-3554	271	18	partial	partial	ADJ
ejpam-3554	271	19	dominating	dominating	NOUN
ejpam-3554	271	20	sets	set	NOUN
ejpam-3554	271	21	in	in	ADP
ejpam-3554	271	22	g	g	PROPN
ejpam-3554	271	23	�	�	NOUN
ejpam-3554	271	24	h	h	NOUN
ejpam-3554	271	25	if	if	SCONJ
ejpam-3554	272	1	and	and	CCONJ
ejpam-3554	272	2	only	only	ADV
ejpam-3554	272	3	if	if	SCONJ
ejpam-3554	272	4	s1	s1	PROPN
ejpam-3554	272	5	and	and	CCONJ
ejpam-3554	272	6	s2	s2	PROPN
ejpam-3554	272	7	are	be	AUX
ejpam-3554	272	8	α	α	DET
ejpam-3554	272	9	-	-	ADJ
ejpam-3554	272	10	partial	partial	ADJ
ejpam-3554	272	11	dominating	dominating	NOUN
ejpam-3554	272	12	sets	set	NOUN
ejpam-3554	272	13	in	in	ADP
ejpam-3554	272	14	g	g	PROPN
ejpam-3554	272	15	and	and	CCONJ
ejpam-3554	272	16	h	h	NOUN
ejpam-3554	272	17	,	,	PUNCT
ejpam-3554	272	18	respectively	respectively	ADV
ejpam-3554	272	19	.	.	PUNCT
ejpam-3554	273	1	proof	proof	NOUN
ejpam-3554	273	2	.	.	PUNCT
ejpam-3554	274	1	suppose	suppose	VERB
ejpam-3554	274	2	c1	c1	NOUN
ejpam-3554	274	3	=	=	PROPN
ejpam-3554	274	4	s1	s1	PROPN
ejpam-3554	274	5	×	×	PROPN
ejpam-3554	274	6	v	v	NOUN
ejpam-3554	274	7	(	(	PUNCT
ejpam-3554	274	8	h	h	NOUN
ejpam-3554	274	9	)	)	PUNCT
ejpam-3554	274	10	and	and	CCONJ
ejpam-3554	274	11	c2	c2	PROPN
ejpam-3554	274	12	=	=	SYM
ejpam-3554	274	13	v	v	PROPN
ejpam-3554	274	14	(	(	PUNCT
ejpam-3554	274	15	g)×	g)×	NOUN
ejpam-3554	274	16	s2	s2	NOUN
ejpam-3554	274	17	are	be	AUX
ejpam-3554	274	18	total	total	ADJ
ejpam-3554	274	19	α	α	PRON
ejpam-3554	274	20	-	-	ADJ
ejpam-3554	274	21	partial	partial	ADJ
ejpam-3554	274	22	dominating	dominating	NOUN
ejpam-3554	274	23	sets	set	NOUN
ejpam-3554	274	24	in	in	ADP
ejpam-3554	274	25	g	g	PROPN
ejpam-3554	274	26	�	�	PROPN
ejpam-3554	274	27	h.	h.	PROPN
ejpam-3554	274	28	then	then	ADV
ejpam-3554	274	29	by	by	ADP
ejpam-3554	274	30	remark	remark	NOUN
ejpam-3554	274	31	6	6	NUM
ejpam-3554	274	32	,	,	PUNCT
ejpam-3554	274	33	c1	c1	PROPN
ejpam-3554	274	34	and	and	CCONJ
ejpam-3554	274	35	c2	c2	PROPN
ejpam-3554	274	36	are	be	AUX
ejpam-3554	274	37	α	α	DET
ejpam-3554	274	38	-	-	ADJ
ejpam-3554	274	39	partial	partial	ADJ
ejpam-3554	274	40	dominating	dominating	NOUN
ejpam-3554	274	41	sets	set	NOUN
ejpam-3554	274	42	in	in	ADP
ejpam-3554	274	43	g	g	PROPN
ejpam-3554	274	44	�	�	PROPN
ejpam-3554	274	45	h.	h.	PROPN
ejpam-3554	274	46	by	by	ADP
ejpam-3554	274	47	theorem	theorem	ADJ
ejpam-3554	274	48	6	6	NUM
ejpam-3554	274	49	,	,	PUNCT
ejpam-3554	274	50	s1	s1	NOUN
ejpam-3554	274	51	and	and	CCONJ
ejpam-3554	274	52	s2	s2	PROPN
ejpam-3554	274	53	are	be	AUX
ejpam-3554	274	54	α	α	DET
ejpam-3554	274	55	-	-	ADJ
ejpam-3554	274	56	partial	partial	ADJ
ejpam-3554	274	57	dominating	dominating	NOUN
ejpam-3554	274	58	sets	set	NOUN
ejpam-3554	274	59	in	in	ADP
ejpam-3554	274	60	g	g	PROPN
ejpam-3554	274	61	�	�	PROPN
ejpam-3554	274	62	h.	h.	PROPN
ejpam-3554	274	63	suppose	suppose	VERB
ejpam-3554	274	64	s1	s1	NOUN
ejpam-3554	274	65	and	and	CCONJ
ejpam-3554	274	66	s2	s2	PROPN
ejpam-3554	274	67	are	be	AUX
ejpam-3554	274	68	α	α	DET
ejpam-3554	274	69	-	-	ADJ
ejpam-3554	274	70	partial	partial	ADJ
ejpam-3554	274	71	dominating	dominating	NOUN
ejpam-3554	274	72	sets	set	NOUN
ejpam-3554	274	73	in	in	ADP
ejpam-3554	274	74	g	g	PROPN
ejpam-3554	274	75	and	and	CCONJ
ejpam-3554	274	76	h	h	NOUN
ejpam-3554	274	77	,	,	PUNCT
ejpam-3554	274	78	respectively	respectively	ADV
ejpam-3554	274	79	.	.	PUNCT
ejpam-3554	275	1	then	then	ADV
ejpam-3554	275	2	by	by	ADP
ejpam-3554	275	3	theorem	theorem	NOUN
ejpam-3554	275	4	6	6	NUM
ejpam-3554	275	5	,	,	PUNCT
ejpam-3554	275	6	c1	c1	NOUN
ejpam-3554	275	7	=	=	PROPN
ejpam-3554	275	8	s1	s1	PROPN
ejpam-3554	275	9	×	×	PROPN
ejpam-3554	275	10	v	v	NOUN
ejpam-3554	275	11	(	(	PUNCT
ejpam-3554	275	12	h	h	NOUN
ejpam-3554	275	13	)	)	PUNCT
ejpam-3554	275	14	and	and	CCONJ
ejpam-3554	275	15	c2	c2	PROPN
ejpam-3554	275	16	=	=	SYM
ejpam-3554	275	17	v	v	PROPN
ejpam-3554	275	18	(	(	PUNCT
ejpam-3554	275	19	g	g	NOUN
ejpam-3554	275	20	)	)	PUNCT
ejpam-3554	275	21	×	×	NOUN
ejpam-3554	275	22	s2	s2	NOUN
ejpam-3554	275	23	are	be	AUX
ejpam-3554	275	24	α	α	DET
ejpam-3554	275	25	-	-	ADJ
ejpam-3554	275	26	partial	partial	ADJ
ejpam-3554	275	27	dominating	dominating	NOUN
ejpam-3554	275	28	sets	set	NOUN
ejpam-3554	275	29	in	in	ADP
ejpam-3554	275	30	g	g	PROPN
ejpam-3554	275	31	�	�	PROPN
ejpam-3554	275	32	h.	h.	PROPN
ejpam-3554	275	33	let	let	VERB
ejpam-3554	275	34	(	(	PUNCT
ejpam-3554	275	35	x	x	NOUN
ejpam-3554	275	36	,	,	PUNCT
ejpam-3554	275	37	a	a	DET
ejpam-3554	275	38	)	)	PUNCT
ejpam-3554	275	39	∈	∈	PROPN
ejpam-3554	275	40	c1	c1	NOUN
ejpam-3554	275	41	=	=	PROPN
ejpam-3554	276	1	s1	s1	PROPN
ejpam-3554	276	2	×	×	PROPN
ejpam-3554	276	3	v	v	NOUN
ejpam-3554	276	4	(	(	PUNCT
ejpam-3554	276	5	h	h	NOUN
ejpam-3554	276	6	)	)	PUNCT
ejpam-3554	276	7	.	.	PUNCT
ejpam-3554	277	1	since	since	SCONJ
ejpam-3554	277	2	h	h	NOUN
ejpam-3554	277	3	is	be	AUX
ejpam-3554	277	4	connected	connect	VERB
ejpam-3554	277	5	,	,	PUNCT
ejpam-3554	277	6	there	there	PRON
ejpam-3554	277	7	exists	exist	VERB
ejpam-3554	277	8	a	a	DET
ejpam-3554	277	9	vertex	vertex	NOUN
ejpam-3554	277	10	b	b	PROPN
ejpam-3554	277	11	∈	∈	PROPN
ejpam-3554	277	12	v	v	ADP
ejpam-3554	277	13	(	(	PUNCT
ejpam-3554	277	14	h	h	NOUN
ejpam-3554	277	15	)	)	PUNCT
ejpam-3554	277	16	such	such	ADJ
ejpam-3554	277	17	that	that	SCONJ
ejpam-3554	277	18	ab	ab	PROPN
ejpam-3554	277	19	∈	∈	PROPN
ejpam-3554	277	20	e(h	e(h	PROPN
ejpam-3554	277	21	)	)	PUNCT
ejpam-3554	277	22	.	.	PUNCT
ejpam-3554	278	1	hence	hence	ADV
ejpam-3554	278	2	,	,	PUNCT
ejpam-3554	278	3	(	(	PUNCT
ejpam-3554	278	4	x	x	NOUN
ejpam-3554	278	5	,	,	PUNCT
ejpam-3554	278	6	b	b	NOUN
ejpam-3554	278	7	)	)	PUNCT
ejpam-3554	278	8	∈	∈	PROPN
ejpam-3554	278	9	c1	c1	NOUN
ejpam-3554	278	10	and	and	CCONJ
ejpam-3554	278	11	(	(	PUNCT
ejpam-3554	278	12	x	x	NOUN
ejpam-3554	278	13	,	,	PUNCT
ejpam-3554	278	14	a)(x	a)(x	PROPN
ejpam-3554	278	15	,	,	PUNCT
ejpam-3554	278	16	b	b	X
ejpam-3554	278	17	)	)	PUNCT
ejpam-3554	278	18	∈	∈	PROPN
ejpam-3554	278	19	e(g	e(g	PROPN
ejpam-3554	278	20	�	�	PROPN
ejpam-3554	278	21	h	h	PROPN
ejpam-3554	278	22	)	)	PUNCT
ejpam-3554	278	23	.	.	PUNCT
ejpam-3554	279	1	similarly	similarly	ADV
ejpam-3554	279	2	,	,	PUNCT
ejpam-3554	279	3	if	if	SCONJ
ejpam-3554	279	4	(	(	PUNCT
ejpam-3554	279	5	y	y	NOUN
ejpam-3554	279	6	,	,	PUNCT
ejpam-3554	279	7	c	c	NOUN
ejpam-3554	279	8	)	)	PUNCT
ejpam-3554	279	9	∈	∈	PROPN
ejpam-3554	279	10	c2	c2	PROPN
ejpam-3554	279	11	=	=	SYM
ejpam-3554	279	12	v	v	PROPN
ejpam-3554	279	13	(	(	PUNCT
ejpam-3554	279	14	g	g	NOUN
ejpam-3554	279	15	)	)	PUNCT
ejpam-3554	279	16	×	×	PROPN
ejpam-3554	279	17	s2	s2	PROPN
ejpam-3554	279	18	,	,	PUNCT
ejpam-3554	279	19	then	then	ADV
ejpam-3554	279	20	since	since	SCONJ
ejpam-3554	279	21	g	g	PROPN
ejpam-3554	279	22	is	be	AUX
ejpam-3554	279	23	connected	connect	VERB
ejpam-3554	279	24	,	,	PUNCT
ejpam-3554	279	25	there	there	PRON
ejpam-3554	279	26	exists	exist	VERB
ejpam-3554	279	27	(	(	PUNCT
ejpam-3554	279	28	z	z	NOUN
ejpam-3554	279	29	,	,	PUNCT
ejpam-3554	279	30	c	c	NOUN
ejpam-3554	279	31	)	)	PUNCT
ejpam-3554	279	32	∈	∈	PROPN
ejpam-3554	279	33	c2	c2	PROPN
ejpam-3554	279	34	such	such	ADJ
ejpam-3554	279	35	that	that	SCONJ
ejpam-3554	279	36	(	(	PUNCT
ejpam-3554	279	37	y	y	NOUN
ejpam-3554	279	38	,	,	PUNCT
ejpam-3554	279	39	c)(z	c)(z	PROPN
ejpam-3554	279	40	,	,	PUNCT
ejpam-3554	279	41	c	c	NOUN
ejpam-3554	279	42	)	)	PUNCT
ejpam-3554	279	43	∈	∈	PROPN
ejpam-3554	279	44	e(g	e(g	PROPN
ejpam-3554	279	45	�	�	PROPN
ejpam-3554	279	46	h	h	PROPN
ejpam-3554	279	47	)	)	PUNCT
ejpam-3554	279	48	.	.	PUNCT
ejpam-3554	280	1	thus	thus	ADV
ejpam-3554	280	2	,	,	PUNCT
ejpam-3554	280	3	c1	c1	PROPN
ejpam-3554	280	4	and	and	CCONJ
ejpam-3554	280	5	c2	c2	PROPN
ejpam-3554	280	6	are	be	AUX
ejpam-3554	280	7	total	total	ADJ
ejpam-3554	280	8	α	α	PRON
ejpam-3554	280	9	-	-	ADJ
ejpam-3554	280	10	partial	partial	ADJ
ejpam-3554	280	11	dominating	dominating	NOUN
ejpam-3554	280	12	sets	set	NOUN
ejpam-3554	280	13	in	in	ADP
ejpam-3554	280	14	g	g	PROPN
ejpam-3554	280	15	�	�	PROPN
ejpam-3554	280	16	h.	h.	PROPN
ejpam-3554	280	17	�	�	PROPN
ejpam-3554	280	18	corollary	corollary	PROPN
ejpam-3554	280	19	7	7	PROPN
ejpam-3554	280	20	.	.	PUNCT
ejpam-3554	281	1	let	let	VERB
ejpam-3554	281	2	g	g	NOUN
ejpam-3554	281	3	and	and	CCONJ
ejpam-3554	281	4	h	h	NOUN
ejpam-3554	281	5	be	be	AUX
ejpam-3554	281	6	nontrivial	nontrivial	ADJ
ejpam-3554	281	7	connected	connected	ADJ
ejpam-3554	281	8	graphs	graph	NOUN
ejpam-3554	281	9	.	.	PUNCT
ejpam-3554	282	1	then	then	ADV
ejpam-3554	282	2	c1	c1	PROPN
ejpam-3554	282	3	=	=	PROPN
ejpam-3554	283	1	s1	s1	PROPN
ejpam-3554	283	2	×	×	PROPN
ejpam-3554	283	3	v	v	NOUN
ejpam-3554	283	4	(	(	PUNCT
ejpam-3554	283	5	h	h	NOUN
ejpam-3554	283	6	)	)	PUNCT
ejpam-3554	283	7	and	and	CCONJ
ejpam-3554	283	8	c2	c2	PROPN
ejpam-3554	283	9	=	=	SYM
ejpam-3554	283	10	v	v	PROPN
ejpam-3554	283	11	(	(	PUNCT
ejpam-3554	283	12	g)×	g)×	NOUN
ejpam-3554	283	13	s2	s2	NOUN
ejpam-3554	283	14	are	be	AUX
ejpam-3554	283	15	α	α	DET
ejpam-3554	283	16	-	-	ADJ
ejpam-3554	283	17	partial	partial	ADJ
ejpam-3554	283	18	dominating	dominating	NOUN
ejpam-3554	283	19	sets	set	NOUN
ejpam-3554	283	20	in	in	ADP
ejpam-3554	283	21	g	g	PROPN
ejpam-3554	283	22	�	�	NOUN
ejpam-3554	283	23	h	h	NOUN
ejpam-3554	283	24	if	if	SCONJ
ejpam-3554	284	1	and	and	CCONJ
ejpam-3554	284	2	only	only	ADV
ejpam-3554	284	3	if	if	SCONJ
ejpam-3554	284	4	c1	c1	PROPN
ejpam-3554	284	5	and	and	CCONJ
ejpam-3554	284	6	c2	c2	PROPN
ejpam-3554	284	7	are	be	AUX
ejpam-3554	284	8	total	total	ADJ
ejpam-3554	284	9	α	α	PRON
ejpam-3554	284	10	-	-	ADJ
ejpam-3554	284	11	partial	partial	ADJ
ejpam-3554	284	12	dominating	dominating	NOUN
ejpam-3554	284	13	sets	set	NOUN
ejpam-3554	284	14	in	in	ADP
ejpam-3554	284	15	g	g	PROPN
ejpam-3554	284	16	�	�	PROPN
ejpam-3554	284	17	h.	h.	NOUN
ejpam-3554	284	18	proof	proof	NOUN
ejpam-3554	284	19	.	.	PUNCT
ejpam-3554	285	1	suppose	suppose	VERB
ejpam-3554	285	2	c1	c1	NOUN
ejpam-3554	285	3	=	=	PROPN
ejpam-3554	285	4	s1	s1	PROPN
ejpam-3554	285	5	×	×	PROPN
ejpam-3554	285	6	v	v	NOUN
ejpam-3554	285	7	(	(	PUNCT
ejpam-3554	285	8	h	h	NOUN
ejpam-3554	285	9	)	)	PUNCT
ejpam-3554	285	10	and	and	CCONJ
ejpam-3554	285	11	c2	c2	PROPN
ejpam-3554	285	12	=	=	SYM
ejpam-3554	285	13	v	v	PROPN
ejpam-3554	285	14	(	(	PUNCT
ejpam-3554	285	15	g	g	NOUN
ejpam-3554	285	16	)	)	PUNCT
ejpam-3554	285	17	×	×	NOUN
ejpam-3554	285	18	s2	s2	NOUN
ejpam-3554	285	19	are	be	AUX
ejpam-3554	285	20	α	α	DET
ejpam-3554	285	21	-	-	ADJ
ejpam-3554	285	22	partial	partial	ADJ
ejpam-3554	285	23	dominating	dominating	NOUN
ejpam-3554	285	24	sets	set	NOUN
ejpam-3554	285	25	in	in	ADP
ejpam-3554	285	26	g	g	PROPN
ejpam-3554	285	27	�	�	PROPN
ejpam-3554	285	28	h.	h.	PROPN
ejpam-3554	285	29	then	then	ADV
ejpam-3554	285	30	by	by	ADP
ejpam-3554	285	31	theorem	theorem	NOUN
ejpam-3554	285	32	6	6	NUM
ejpam-3554	285	33	,	,	PUNCT
ejpam-3554	285	34	s1	s1	NOUN
ejpam-3554	285	35	and	and	CCONJ
ejpam-3554	285	36	s2	s2	PROPN
ejpam-3554	285	37	are	be	AUX
ejpam-3554	285	38	α	α	DET
ejpam-3554	285	39	-	-	ADJ
ejpam-3554	285	40	partial	partial	ADJ
ejpam-3554	285	41	dominating	dominating	NOUN
ejpam-3554	285	42	sets	set	NOUN
ejpam-3554	285	43	in	in	ADP
ejpam-3554	285	44	g	g	PROPN
ejpam-3554	285	45	and	and	CCONJ
ejpam-3554	285	46	h	h	NOUN
ejpam-3554	285	47	,	,	PUNCT
ejpam-3554	285	48	respectively	respectively	ADV
ejpam-3554	285	49	.	.	PUNCT
ejpam-3554	286	1	by	by	ADP
ejpam-3554	286	2	theorem	theorem	NOUN
ejpam-3554	286	3	11	11	NUM
ejpam-3554	286	4	,	,	PUNCT
ejpam-3554	286	5	c1	c1	NOUN
ejpam-3554	286	6	=	=	PROPN
ejpam-3554	286	7	s1	s1	PROPN
ejpam-3554	286	8	×	×	PROPN
ejpam-3554	286	9	v	v	NOUN
ejpam-3554	286	10	(	(	PUNCT
ejpam-3554	286	11	h	h	NOUN
ejpam-3554	286	12	)	)	PUNCT
ejpam-3554	286	13	and	and	CCONJ
ejpam-3554	286	14	c2	c2	PROPN
ejpam-3554	286	15	=	=	SYM
ejpam-3554	286	16	v	v	PROPN
ejpam-3554	286	17	(	(	PUNCT
ejpam-3554	286	18	g	g	NOUN
ejpam-3554	286	19	)	)	PUNCT
ejpam-3554	286	20	×	×	NOUN
ejpam-3554	286	21	s2	s2	NOUN
ejpam-3554	286	22	are	be	AUX
ejpam-3554	286	23	total	total	ADJ
ejpam-3554	286	24	α	α	PRON
ejpam-3554	286	25	-	-	ADJ
ejpam-3554	286	26	partial	partial	ADJ
ejpam-3554	286	27	dominating	dominating	NOUN
ejpam-3554	286	28	sets	set	NOUN
ejpam-3554	286	29	in	in	ADP
ejpam-3554	286	30	g	g	PROPN
ejpam-3554	286	31	�	�	PROPN
ejpam-3554	286	32	h.	h.	NOUN
ejpam-3554	286	33	conversely	conversely	ADV
ejpam-3554	286	34	,	,	PUNCT
ejpam-3554	286	35	suppose	suppose	VERB
ejpam-3554	286	36	c1	c1	PROPN
ejpam-3554	286	37	=	=	PROPN
ejpam-3554	286	38	s1	s1	PROPN
ejpam-3554	286	39	×	×	PROPN
ejpam-3554	286	40	v	v	NOUN
ejpam-3554	286	41	(	(	PUNCT
ejpam-3554	286	42	h	h	NOUN
ejpam-3554	286	43	)	)	PUNCT
ejpam-3554	286	44	and	and	CCONJ
ejpam-3554	286	45	c2	c2	PROPN
ejpam-3554	286	46	=	=	SYM
ejpam-3554	286	47	v	v	PROPN
ejpam-3554	286	48	(	(	PUNCT
ejpam-3554	286	49	g	g	NOUN
ejpam-3554	286	50	)	)	PUNCT
ejpam-3554	286	51	×	×	NOUN
ejpam-3554	286	52	s2	s2	NOUN
ejpam-3554	286	53	are	be	AUX
ejpam-3554	286	54	total	total	ADJ
ejpam-3554	286	55	α	α	PRON
ejpam-3554	286	56	-	-	ADJ
ejpam-3554	286	57	partial	partial	ADJ
ejpam-3554	286	58	dominating	dominating	NOUN
ejpam-3554	286	59	sets	set	NOUN
ejpam-3554	286	60	in	in	ADP
ejpam-3554	286	61	g	g	PROPN
ejpam-3554	286	62	�	�	PROPN
ejpam-3554	286	63	h.	h.	PROPN
ejpam-3554	286	64	by	by	ADP
ejpam-3554	286	65	remark	remark	NOUN
ejpam-3554	286	66	6	6	NUM
ejpam-3554	286	67	,	,	PUNCT
ejpam-3554	286	68	c1	c1	NOUN
ejpam-3554	286	69	=	=	PROPN
ejpam-3554	286	70	s1	s1	PROPN
ejpam-3554	286	71	×	×	PROPN
ejpam-3554	286	72	v	v	NOUN
ejpam-3554	286	73	(	(	PUNCT
ejpam-3554	286	74	h	h	NOUN
ejpam-3554	286	75	)	)	PUNCT
ejpam-3554	286	76	and	and	CCONJ
ejpam-3554	286	77	c2	c2	PROPN
ejpam-3554	286	78	=	=	SYM
ejpam-3554	286	79	v	v	PROPN
ejpam-3554	286	80	(	(	PUNCT
ejpam-3554	286	81	g)×	g)×	NOUN
ejpam-3554	286	82	s2	s2	NOUN
ejpam-3554	286	83	are	be	AUX
ejpam-3554	286	84	αpartial	αpartial	ADJ
ejpam-3554	286	85	dominating	dominating	NOUN
ejpam-3554	286	86	sets	set	NOUN
ejpam-3554	286	87	in	in	ADP
ejpam-3554	286	88	g	g	PROPN
ejpam-3554	286	89	�	�	PROPN
ejpam-3554	286	90	h.	h.	PROPN
ejpam-3554	286	91	�	�	PROPN
ejpam-3554	286	92	corollary	corollary	ADJ
ejpam-3554	286	93	8	8	NUM
ejpam-3554	286	94	.	.	PUNCT
ejpam-3554	287	1	let	let	VERB
ejpam-3554	287	2	g	g	NOUN
ejpam-3554	287	3	and	and	CCONJ
ejpam-3554	287	4	h	h	NOUN
ejpam-3554	287	5	be	be	AUX
ejpam-3554	287	6	nontrivial	nontrivial	ADJ
ejpam-3554	287	7	connected	connect	VERB
ejpam-3554	287	8	graphs	graph	NOUN
ejpam-3554	287	9	of	of	ADP
ejpam-3554	287	10	orders	order	NOUN
ejpam-3554	287	11	m	m	VERB
ejpam-3554	287	12	and	and	CCONJ
ejpam-3554	287	13	n	n	CCONJ
ejpam-3554	287	14	,	,	PUNCT
ejpam-3554	287	15	respectively	respectively	ADV
ejpam-3554	287	16	,	,	PUNCT
ejpam-3554	287	17	and	and	CCONJ
ejpam-3554	287	18	α	α	PRON
ejpam-3554	287	19	∈	∈	PROPN
ejpam-3554	287	20	(	(	PUNCT
ejpam-3554	287	21	0	0	NUM
ejpam-3554	287	22	,	,	PUNCT
ejpam-3554	287	23	1	1	NUM
ejpam-3554	287	24	]	]	PUNCT
ejpam-3554	287	25	.	.	PUNCT
ejpam-3554	288	1	then	then	ADV
ejpam-3554	288	2	,	,	PUNCT
ejpam-3554	288	3	∂tα(g	∂tα(g	PROPN
ejpam-3554	288	4	�	�	PROPN
ejpam-3554	288	5	h	h	NOUN
ejpam-3554	288	6	)	)	PUNCT
ejpam-3554	288	7	≤	≤	NUM
ejpam-3554	288	8	min	min	NOUN
ejpam-3554	288	9	{	{	PUNCT
ejpam-3554	288	10	m	m	PROPN
ejpam-3554	288	11	·	·	PUNCT
ejpam-3554	288	12	∂α(h	∂α(h	NOUN
ejpam-3554	288	13	)	)	PUNCT
ejpam-3554	288	14	,	,	PUNCT
ejpam-3554	288	15	n	n	PROPN
ejpam-3554	288	16	·	·	PUNCT
ejpam-3554	288	17	∂α(g	∂α(g	PROPN
ejpam-3554	288	18	)	)	PUNCT
ejpam-3554	288	19	}	}	PUNCT
ejpam-3554	288	20	.	.	PUNCT
ejpam-3554	289	1	remark	remark	NOUN
ejpam-3554	289	2	10	10	NUM
ejpam-3554	289	3	.	.	PUNCT
ejpam-3554	290	1	the	the	DET
ejpam-3554	290	2	bound	bind	VERB
ejpam-3554	290	3	in	in	ADP
ejpam-3554	290	4	corollary	corollary	ADJ
ejpam-3554	290	5	8	8	NUM
ejpam-3554	290	6	is	be	AUX
ejpam-3554	290	7	sharp	sharp	ADJ
ejpam-3554	290	8	.	.	PUNCT
ejpam-3554	291	1	however	however	ADV
ejpam-3554	291	2	,	,	PUNCT
ejpam-3554	291	3	the	the	DET
ejpam-3554	291	4	strict	strict	ADJ
ejpam-3554	291	5	inequality	inequality	NOUN
ejpam-3554	291	6	can	can	AUX
ejpam-3554	291	7	be	be	AUX
ejpam-3554	291	8	attained	attain	VERB
ejpam-3554	291	9	.	.	PUNCT
ejpam-3554	292	1	r.	r.	PROPN
ejpam-3554	292	2	macapodi	macapodi	PROPN
ejpam-3554	292	3	,	,	PUNCT
ejpam-3554	292	4	r.	r.	PROPN
ejpam-3554	292	5	isla	isla	PROPN
ejpam-3554	292	6	/	/	SYM
ejpam-3554	292	7	eur	eur	PROPN
ejpam-3554	292	8	.	.	PUNCT
ejpam-3554	293	1	j.	j.	PROPN
ejpam-3554	293	2	pure	pure	PROPN
ejpam-3554	293	3	appl	appl	PROPN
ejpam-3554	293	4	.	.	PROPN
ejpam-3554	293	5	math	math	PROPN
ejpam-3554	293	6	,	,	PUNCT
ejpam-3554	293	7	12	12	NUM
ejpam-3554	293	8	(	(	PUNCT
ejpam-3554	293	9	4	4	NUM
ejpam-3554	293	10	)	)	PUNCT
ejpam-3554	293	11	(	(	PUNCT
ejpam-3554	293	12	2019	2019	NUM
ejpam-3554	293	13	)	)	PUNCT
ejpam-3554	293	14	,	,	PUNCT
ejpam-3554	293	15	1643	1643	NUM
ejpam-3554	293	16	-	-	SYM
ejpam-3554	293	17	1655	1655	NUM
ejpam-3554	293	18	1654	1654	NUM
ejpam-3554	293	19	to	to	PART
ejpam-3554	293	20	see	see	VERB
ejpam-3554	293	21	this	this	PRON
ejpam-3554	293	22	,	,	PUNCT
ejpam-3554	293	23	consider	consider	VERB
ejpam-3554	293	24	the	the	DET
ejpam-3554	293	25	graphs	graph	NOUN
ejpam-3554	293	26	shown	show	VERB
ejpam-3554	293	27	in	in	ADP
ejpam-3554	293	28	figure	figure	NOUN
ejpam-3554	293	29	8	8	NUM
ejpam-3554	293	30	.	.	PUNCT
ejpam-3554	294	1	let	let	VERB
ejpam-3554	294	2	α	α	NOUN
ejpam-3554	294	3	=	=	SYM
ejpam-3554	294	4	1	1	NUM
ejpam-3554	294	5	2	2	NUM
ejpam-3554	294	6	.	.	PUNCT
ejpam-3554	295	1	the	the	DET
ejpam-3554	295	2	shaded	shade	VERB
ejpam-3554	295	3	vertices	vertex	NOUN
ejpam-3554	295	4	in	in	ADP
ejpam-3554	295	5	each	each	DET
ejpam-3554	295	6	graph	graph	NOUN
ejpam-3554	295	7	form	form	VERB
ejpam-3554	295	8	a	a	DET
ejpam-3554	295	9	∂tα	∂tα	PROPN
ejpam-3554	295	10	-	-	PUNCT
ejpam-3554	295	11	set	set	NOUN
ejpam-3554	295	12	.	.	PUNCT
ejpam-3554	296	1	thus	thus	ADV
ejpam-3554	296	2	,	,	PUNCT
ejpam-3554	296	3	∂tα(p4	∂tα(p4	PROPN
ejpam-3554	296	4	�	�	NOUN
ejpam-3554	296	5	p6	p6	PROPN
ejpam-3554	296	6	)	)	PUNCT
ejpam-3554	296	7	=	=	SYM
ejpam-3554	296	8	4	4	NUM
ejpam-3554	296	9	=	=	SYM
ejpam-3554	296	10	min	min	NOUN
ejpam-3554	296	11	{	{	PUNCT
ejpam-3554	296	12	4	4	NUM
ejpam-3554	296	13	,	,	PUNCT
ejpam-3554	296	14	6	6	NUM
ejpam-3554	296	15	}	}	PUNCT
ejpam-3554	296	16	=	=	SYM
ejpam-3554	296	17	min	min	NOUN
ejpam-3554	296	18	{	{	PUNCT
ejpam-3554	296	19	4(1	4(1	NOUN
ejpam-3554	296	20	)	)	PUNCT
ejpam-3554	296	21	,	,	PUNCT
ejpam-3554	296	22	6(1	6(1	NUM
ejpam-3554	296	23	)	)	PUNCT
ejpam-3554	296	24	}	}	PUNCT
ejpam-3554	296	25	=	=	SYM
ejpam-3554	296	26	min	min	NOUN
ejpam-3554	296	27	{	{	PUNCT
ejpam-3554	296	28	4	4	NUM
ejpam-3554	296	29	·	·	PUNCT
ejpam-3554	296	30	∂α(p6	∂α(p6	NOUN
ejpam-3554	296	31	)	)	PUNCT
ejpam-3554	296	32	,	,	PUNCT
ejpam-3554	296	33	6	6	NUM
ejpam-3554	296	34	·	·	SYM
ejpam-3554	296	35	∂α(p4	∂α(p4	NOUN
ejpam-3554	296	36	)	)	PUNCT
ejpam-3554	296	37	}	}	PUNCT
ejpam-3554	296	38	=	=	SYM
ejpam-3554	296	39	4·∂α(p6	4·∂α(p6	NOUN
ejpam-3554	296	40	)	)	PUNCT
ejpam-3554	296	41	,	,	PUNCT
ejpam-3554	296	42	∂tα(p6	∂tα(p6	NUM
ejpam-3554	296	43	�	�	PROPN
ejpam-3554	296	44	p3	p3	PROPN
ejpam-3554	296	45	)	)	PUNCT
ejpam-3554	296	46	=	=	SYM
ejpam-3554	296	47	3	3	NUM
ejpam-3554	296	48	=	=	SYM
ejpam-3554	296	49	min	min	NOUN
ejpam-3554	296	50	{	{	PUNCT
ejpam-3554	296	51	6	6	NUM
ejpam-3554	296	52	,	,	PUNCT
ejpam-3554	296	53	3	3	NUM
ejpam-3554	296	54	}	}	PUNCT
ejpam-3554	296	55	=	=	SYM
ejpam-3554	296	56	min	min	NOUN
ejpam-3554	296	57	{	{	PUNCT
ejpam-3554	296	58	6(1	6(1	NUM
ejpam-3554	296	59	)	)	PUNCT
ejpam-3554	296	60	,	,	PUNCT
ejpam-3554	296	61	3(1	3(1	NUM
ejpam-3554	296	62	)	)	PUNCT
ejpam-3554	296	63	}	}	PUNCT
ejpam-3554	296	64	=	=	SYM
ejpam-3554	296	65	min	min	NOUN
ejpam-3554	296	66	{	{	PUNCT
ejpam-3554	296	67	6	6	NUM
ejpam-3554	296	68	·	·	SYM
ejpam-3554	296	69	∂α(p3	∂α(p3	PROPN
ejpam-3554	296	70	)	)	PUNCT
ejpam-3554	296	71	,	,	PUNCT
ejpam-3554	296	72	3	3	X
ejpam-3554	296	73	·	·	PUNCT
ejpam-3554	296	74	∂α(p6	∂α(p6	NOUN
ejpam-3554	296	75	)	)	PUNCT
ejpam-3554	296	76	}	}	PUNCT
ejpam-3554	296	77	=	=	SYM
ejpam-3554	296	78	3·∂α(p6	3·∂α(p6	NUM
ejpam-3554	296	79	)	)	PUNCT
ejpam-3554	296	80	,	,	PUNCT
ejpam-3554	296	81	and	and	CCONJ
ejpam-3554	296	82	∂tα(p6	∂tα(p6	NUM
ejpam-3554	296	83	�	�	NOUN
ejpam-3554	296	84	p5	p5	NOUN
ejpam-3554	296	85	)	)	PUNCT
ejpam-3554	296	86	=	=	PUNCT
ejpam-3554	296	87	4	4	NUM
ejpam-3554	296	88	<	<	SYM
ejpam-3554	296	89	5	5	NUM
ejpam-3554	296	90	=	=	SYM
ejpam-3554	296	91	min{6(1	min{6(1	NOUN
ejpam-3554	296	92	)	)	PUNCT
ejpam-3554	296	93	,	,	PUNCT
ejpam-3554	296	94	5(1	5(1	NUM
ejpam-3554	296	95	)	)	PUNCT
ejpam-3554	296	96	}	}	PUNCT
ejpam-3554	296	97	=	=	SYM
ejpam-3554	296	98	min{6	min{6	NOUN
ejpam-3554	296	99	·	·	SYM
ejpam-3554	296	100	∂α(p5	∂α(p5	PROPN
ejpam-3554	296	101	)	)	PUNCT
ejpam-3554	296	102	,	,	PUNCT
ejpam-3554	296	103	5	5	NUM
ejpam-3554	296	104	·	·	PUNCT
ejpam-3554	296	105	∂α(p6	∂α(p6	NOUN
ejpam-3554	296	106	)	)	PUNCT
ejpam-3554	296	107	}	}	PUNCT
ejpam-3554	296	108	.	.	PUNCT
ejpam-3554	297	1	corollary	corollary	ADJ
ejpam-3554	297	2	9	9	NUM
ejpam-3554	297	3	.	.	PUNCT
ejpam-3554	298	1	let	let	VERB
ejpam-3554	298	2	g	g	PRON
ejpam-3554	298	3	be	be	AUX
ejpam-3554	298	4	a	a	DET
ejpam-3554	298	5	connected	connected	ADJ
ejpam-3554	298	6	graph	graph	NOUN
ejpam-3554	298	7	of	of	ADP
ejpam-3554	298	8	order	order	NOUN
ejpam-3554	298	9	m	m	NOUN
ejpam-3554	298	10	and	and	CCONJ
ejpam-3554	298	11	kn	kn	PROPN
ejpam-3554	298	12	be	be	AUX
ejpam-3554	298	13	the	the	DET
ejpam-3554	298	14	complete	complete	ADJ
ejpam-3554	298	15	graph	graph	NOUN
ejpam-3554	298	16	of	of	ADP
ejpam-3554	298	17	order	order	NOUN
ejpam-3554	298	18	n	n	PRON
ejpam-3554	298	19	≥	≥	NOUN
ejpam-3554	298	20	2	2	NUM
ejpam-3554	298	21	.	.	PUNCT
ejpam-3554	299	1	then	then	ADV
ejpam-3554	299	2	,	,	PUNCT
ejpam-3554	299	3	∂tα(g	∂tα(g	PROPN
ejpam-3554	299	4	�	�	PROPN
ejpam-3554	299	5	kn	kn	PROPN
ejpam-3554	299	6	)	)	PUNCT
ejpam-3554	299	7	≤	≤	NOUN
ejpam-3554	299	8	min{m	min{m	PROPN
ejpam-3554	299	9	,	,	PUNCT
ejpam-3554	299	10	n	n	NOUN
ejpam-3554	299	11	·	·	PUNCT
ejpam-3554	299	12	∂α(g	∂α(g	PROPN
ejpam-3554	299	13	)	)	PUNCT
ejpam-3554	299	14	}	}	PUNCT
ejpam-3554	299	15	.	.	PUNCT
ejpam-3554	300	1	remark	remark	NOUN
ejpam-3554	300	2	11	11	NUM
ejpam-3554	300	3	.	.	PUNCT
ejpam-3554	301	1	the	the	DET
ejpam-3554	301	2	bound	bind	VERB
ejpam-3554	301	3	in	in	ADP
ejpam-3554	301	4	corollary	corollary	ADJ
ejpam-3554	301	5	9	9	NUM
ejpam-3554	301	6	is	be	AUX
ejpam-3554	301	7	sharp	sharp	ADJ
ejpam-3554	301	8	.	.	PUNCT
ejpam-3554	302	1	however	however	ADV
ejpam-3554	302	2	,	,	PUNCT
ejpam-3554	302	3	the	the	DET
ejpam-3554	302	4	strict	strict	ADJ
ejpam-3554	302	5	inequality	inequality	NOUN
ejpam-3554	302	6	can	can	AUX
ejpam-3554	302	7	be	be	AUX
ejpam-3554	302	8	attained	attain	VERB
ejpam-3554	302	9	.	.	PUNCT
ejpam-3554	303	1	to	to	PART
ejpam-3554	303	2	see	see	VERB
ejpam-3554	303	3	this	this	PRON
ejpam-3554	303	4	,	,	PUNCT
ejpam-3554	303	5	consider	consider	VERB
ejpam-3554	303	6	the	the	DET
ejpam-3554	303	7	graphs	graph	NOUN
ejpam-3554	303	8	shown	show	VERB
ejpam-3554	303	9	in	in	ADP
ejpam-3554	303	10	figure	figure	NOUN
ejpam-3554	303	11	9	9	NUM
ejpam-3554	303	12	.	.	PUNCT
ejpam-3554	304	1	let	let	VERB
ejpam-3554	304	2	α	α	NOUN
ejpam-3554	304	3	=	=	SYM
ejpam-3554	304	4	1	1	NUM
ejpam-3554	304	5	2	2	NUM
ejpam-3554	304	6	.	.	PUNCT
ejpam-3554	305	1	the	the	DET
ejpam-3554	305	2	shaded	shade	VERB
ejpam-3554	305	3	vertices	vertex	NOUN
ejpam-3554	305	4	in	in	ADP
ejpam-3554	305	5	each	each	DET
ejpam-3554	305	6	graph	graph	NOUN
ejpam-3554	305	7	form	form	VERB
ejpam-3554	305	8	a	a	DET
ejpam-3554	305	9	∂tα	∂tα	PROPN
ejpam-3554	305	10	-	-	PUNCT
ejpam-3554	305	11	set	set	NOUN
ejpam-3554	305	12	.	.	PUNCT
ejpam-3554	306	1	thus	thus	ADV
ejpam-3554	306	2	,	,	PUNCT
ejpam-3554	306	3	∂tα(p2	∂tα(p2	PROPN
ejpam-3554	306	4	�	�	NOUN
ejpam-3554	306	5	k4	k4	NOUN
ejpam-3554	306	6	)	)	PUNCT
ejpam-3554	306	7	=	=	SYM
ejpam-3554	306	8	2	2	NUM
ejpam-3554	306	9	=	=	SYM
ejpam-3554	306	10	min	min	NOUN
ejpam-3554	306	11	{	{	PUNCT
ejpam-3554	306	12	2	2	NUM
ejpam-3554	306	13	,	,	PUNCT
ejpam-3554	306	14	4(1	4(1	NOUN
ejpam-3554	306	15	)	)	PUNCT
ejpam-3554	306	16	}	}	PUNCT
ejpam-3554	306	17	=	=	SYM
ejpam-3554	306	18	min	min	NOUN
ejpam-3554	306	19	{	{	PUNCT
ejpam-3554	306	20	m	m	PROPN
ejpam-3554	306	21	,	,	PUNCT
ejpam-3554	306	22	4	4	NUM
ejpam-3554	306	23	·	·	PUNCT
ejpam-3554	306	24	∂α(p2	∂α(p2	NUM
ejpam-3554	306	25	)	)	PUNCT
ejpam-3554	306	26	}	}	PUNCT
ejpam-3554	306	27	=	=	SYM
ejpam-3554	306	28	m	m	NOUN
ejpam-3554	306	29	,	,	PUNCT
ejpam-3554	306	30	∂tα(p6	∂tα(p6	X
ejpam-3554	306	31	�	�	NOUN
ejpam-3554	306	32	k3	k3	ADJ
ejpam-3554	306	33	)	)	PUNCT
ejpam-3554	306	34	=	=	SYM
ejpam-3554	306	35	3	3	NUM
ejpam-3554	306	36	=	=	SYM
ejpam-3554	306	37	min	min	NOUN
ejpam-3554	306	38	{	{	PUNCT
ejpam-3554	306	39	6	6	NUM
ejpam-3554	306	40	,	,	PUNCT
ejpam-3554	306	41	3(1	3(1	NUM
ejpam-3554	306	42	)	)	PUNCT
ejpam-3554	306	43	}	}	PUNCT
ejpam-3554	306	44	=	=	SYM
ejpam-3554	306	45	min	min	NOUN
ejpam-3554	306	46	{	{	PUNCT
ejpam-3554	306	47	m	m	PROPN
ejpam-3554	306	48	,	,	PUNCT
ejpam-3554	306	49	3	3	NUM
ejpam-3554	306	50	·	·	SYM
ejpam-3554	306	51	∂α(k3	∂α(k3	X
ejpam-3554	306	52	)	)	PUNCT
ejpam-3554	306	53	}	}	PUNCT
ejpam-3554	306	54	=	=	SYM
ejpam-3554	306	55	3	3	X
ejpam-3554	306	56	·	·	PUNCT
ejpam-3554	306	57	∂α(k3	∂α(k3	PROPN
ejpam-3554	306	58	)	)	PUNCT
ejpam-3554	306	59	,	,	PUNCT
ejpam-3554	306	60	and	and	CCONJ
ejpam-3554	306	61	∂tα(p6	∂tα(p6	NUM
ejpam-3554	306	62	�	�	NOUN
ejpam-3554	306	63	k4	k4	NOUN
ejpam-3554	306	64	)	)	PUNCT
ejpam-3554	306	65	=	=	PUNCT
ejpam-3554	306	66	3	3	NUM
ejpam-3554	306	67	<	<	SYM
ejpam-3554	306	68	4	4	NUM
ejpam-3554	306	69	=	=	SYM
ejpam-3554	306	70	min{6	min{6	PROPN
ejpam-3554	306	71	,	,	PUNCT
ejpam-3554	306	72	4(1	4(1	NUM
ejpam-3554	306	73	)	)	PUNCT
ejpam-3554	306	74	}	}	PUNCT
ejpam-3554	306	75	=	=	SYM
ejpam-3554	306	76	min{m	min{m	NOUN
ejpam-3554	306	77	,	,	PUNCT
ejpam-3554	306	78	4	4	NUM
ejpam-3554	306	79	·	·	PUNCT
ejpam-3554	306	80	∂α(p6	∂α(p6	NOUN
ejpam-3554	306	81	)	)	PUNCT
ejpam-3554	306	82	}	}	PUNCT
ejpam-3554	306	83	.	.	PUNCT
ejpam-3554	307	1	references	reference	NOUN
ejpam-3554	307	2	1655	1655	NUM
ejpam-3554	307	3	acknowledgements	acknowledgement	NOUN
ejpam-3554	307	4	this	this	DET
ejpam-3554	307	5	research	research	NOUN
ejpam-3554	307	6	is	be	AUX
ejpam-3554	307	7	funded	fund	VERB
ejpam-3554	307	8	by	by	ADP
ejpam-3554	307	9	the	the	DET
ejpam-3554	307	10	philippine	philippine	ADJ
ejpam-3554	307	11	commission	commission	NOUN
ejpam-3554	307	12	on	on	ADP
ejpam-3554	307	13	higher	high	ADJ
ejpam-3554	307	14	education	education	NOUN
ejpam-3554	307	15	-	-	PUNCT
ejpam-3554	307	16	faculty	faculty	NOUN
ejpam-3554	307	17	development	development	NOUN
ejpam-3554	307	18	program	program	NOUN
ejpam-3554	307	19	phase	phase	NOUN
ejpam-3554	307	20	ii	ii	PROPN
ejpam-3554	307	21	(	(	PUNCT
ejpam-3554	307	22	ched	che	VERB
ejpam-3554	307	23	-	-	PUNCT
ejpam-3554	307	24	fdp	fdp	NUM
ejpam-3554	307	25	ii	ii	PROPN
ejpam-3554	307	26	)	)	PUNCT
ejpam-3554	307	27	and	and	CCONJ
ejpam-3554	307	28	the	the	DET
ejpam-3554	307	29	mindanao	mindanao	PROPN
ejpam-3554	307	30	state	state	PROPN
ejpam-3554	307	31	university	university	PROPN
ejpam-3554	307	32	-	-	PUNCT
ejpam-3554	307	33	iligan	iligan	PROPN
ejpam-3554	307	34	institute	institute	PROPN
ejpam-3554	307	35	of	of	ADP
ejpam-3554	307	36	technology	technology	PROPN
ejpam-3554	307	37	.	.	PUNCT
ejpam-3554	308	1	the	the	DET
ejpam-3554	308	2	authors	author	NOUN
ejpam-3554	308	3	thank	thank	VERB
ejpam-3554	308	4	the	the	DET
ejpam-3554	308	5	anonymous	anonymous	ADJ
ejpam-3554	308	6	reviewers	reviewer	NOUN
ejpam-3554	308	7	for	for	ADP
ejpam-3554	308	8	the	the	DET
ejpam-3554	308	9	suggestions	suggestion	NOUN
ejpam-3554	308	10	that	that	PRON
ejpam-3554	308	11	led	lead	VERB
ejpam-3554	308	12	to	to	ADP
ejpam-3554	308	13	the	the	DET
ejpam-3554	308	14	improvement	improvement	NOUN
ejpam-3554	308	15	of	of	ADP
ejpam-3554	308	16	the	the	DET
ejpam-3554	308	17	paper	paper	NOUN
ejpam-3554	308	18	.	.	PUNCT
ejpam-3554	309	1	references	reference	NOUN
ejpam-3554	309	2	[	[	X
ejpam-3554	309	3	1	1	NUM
ejpam-3554	309	4	]	]	PUNCT
ejpam-3554	309	5	b.	b.	NOUN
ejpam-3554	309	6	case	case	NOUN
ejpam-3554	309	7	,	,	PUNCT
ejpam-3554	309	8	s.	s.	PROPN
ejpam-3554	309	9	hedetniemi	hedetniemi	PROPN
ejpam-3554	309	10	,	,	PUNCT
ejpam-3554	309	11	r.	r.	PROPN
ejpam-3554	309	12	laskar	laskar	PROPN
ejpam-3554	309	13	,	,	PUNCT
ejpam-3554	309	14	and	and	CCONJ
ejpam-3554	309	15	d.	d.	PROPN
ejpam-3554	309	16	lipman	lipman	PROPN
ejpam-3554	309	17	.	.	PUNCT
ejpam-3554	310	1	partial	partial	ADJ
ejpam-3554	310	2	domination	domination	NOUN
ejpam-3554	310	3	in	in	ADP
ejpam-3554	310	4	graphs	graph	NOUN
ejpam-3554	310	5	.	.	PUNCT
ejpam-3554	311	1	eprint	eprint	NOUN
ejpam-3554	311	2	,	,	PUNCT
ejpam-3554	311	3	arxiv:1705.03096	arxiv:1705.03096	NUM
ejpam-3554	311	4	,	,	PUNCT
ejpam-3554	311	5	2017	2017	NUM
ejpam-3554	311	6	.	.	PUNCT
ejpam-3554	312	1	[	[	X
ejpam-3554	312	2	2	2	NUM
ejpam-3554	312	3	]	]	PUNCT
ejpam-3554	312	4	a.	a.	NOUN
ejpam-3554	312	5	das	das	PROPN
ejpam-3554	312	6	.	.	PUNCT
ejpam-3554	312	7	partial	partial	ADJ
ejpam-3554	312	8	domination	domination	NOUN
ejpam-3554	312	9	in	in	ADP
ejpam-3554	312	10	graphs	graph	NOUN
ejpam-3554	312	11	.	.	PUNCT
ejpam-3554	313	1	iranian	iranian	ADJ
ejpam-3554	313	2	journal	journal	PROPN
ejpam-3554	313	3	of	of	ADP
ejpam-3554	313	4	science	science	NOUN
ejpam-3554	313	5	and	and	CCONJ
ejpam-3554	313	6	technology	technology	NOUN
ejpam-3554	313	7	.	.	PUNCT
ejpam-3554	314	1	transaction	transaction	NOUN
ejpam-3554	314	2	a	a	DET
ejpam-3554	314	3	:	:	PUNCT
ejpam-3554	314	4	science	science	NOUN
ejpam-3554	314	5	,	,	PUNCT
ejpam-3554	314	6	pages	page	NOUN
ejpam-3554	314	7	1713–1718	1713–1718	NUM
ejpam-3554	314	8	,	,	PUNCT
ejpam-3554	314	9	2018	2018	NUM
ejpam-3554	314	10	doi	doi	NOUN
ejpam-3554	314	11	:	:	PUNCT
ejpam-3554	314	12	10.1007	10.1007	NUM
ejpam-3554	314	13	/	/	SYM
ejpam-3554	314	14	s40995	s40995	VERB
ejpam-3554	314	15	-	-	PUNCT
ejpam-3554	314	16	018	018	NUM
ejpam-3554	314	17	-	-	PUNCT
ejpam-3554	314	18	0618	0618	NUM
ejpam-3554	314	19	-	-	SYM
ejpam-3554	314	20	5	5	NUM
ejpam-3554	314	21	.	.	PUNCT
ejpam-3554	315	1	[	[	X
ejpam-3554	315	2	3	3	X
ejpam-3554	315	3	]	]	X
ejpam-3554	315	4	r.	r.	PROPN
ejpam-3554	315	5	macapodi	macapodi	PROPN
ejpam-3554	315	6	,	,	PUNCT
ejpam-3554	315	7	r.	r.	PROPN
ejpam-3554	315	8	isla	isla	PROPN
ejpam-3554	315	9	,	,	PUNCT
ejpam-3554	315	10	and	and	CCONJ
ejpam-3554	315	11	s.	s.	PROPN
ejpam-3554	315	12	canoy	canoy	PROPN
ejpam-3554	315	13	jr	jr	PROPN
ejpam-3554	315	14	.	.	PROPN
ejpam-3554	315	15	partial	partial	ADJ
ejpam-3554	315	16	domination	domination	NOUN
ejpam-3554	315	17	in	in	ADP
ejpam-3554	315	18	the	the	DET
ejpam-3554	315	19	join	join	NOUN
ejpam-3554	315	20	,	,	PUNCT
ejpam-3554	315	21	corona	corona	PROPN
ejpam-3554	315	22	,	,	PUNCT
ejpam-3554	315	23	lexicographic	lexicographic	ADJ
ejpam-3554	315	24	and	and	CCONJ
ejpam-3554	315	25	cartesian	cartesian	ADJ
ejpam-3554	315	26	products	product	NOUN
ejpam-3554	315	27	of	of	ADP
ejpam-3554	315	28	graphs	graph	NOUN
ejpam-3554	315	29	.	.	PUNCT
ejpam-3554	316	1	advances	advance	NOUN
ejpam-3554	316	2	and	and	CCONJ
ejpam-3554	316	3	applications	application	NOUN
ejpam-3554	316	4	in	in	ADP
ejpam-3554	316	5	discrete	discrete	ADJ
ejpam-3554	316	6	mathematics	mathematic	NOUN
ejpam-3554	316	7	,	,	PUNCT
ejpam-3554	316	8	20(2):277–293	20(2):277–293	NUM
ejpam-3554	316	9	,	,	PUNCT
ejpam-3554	316	10	2019	2019	NUM
ejpam-3554	316	11	.	.	PUNCT