id	sid	tid	token	lemma	pos
ejpam-5313	1	1	european	european	PROPN
ejpam-5313	1	2	journal	journal	PROPN
ejpam-5313	1	3	of	of	ADP
ejpam-5313	1	4	pure	pure	ADJ
ejpam-5313	1	5	and	and	CCONJ
ejpam-5313	1	6	applied	apply	VERB
ejpam-5313	1	7	mathematics	mathematic	NOUN
ejpam-5313	1	8	vol	vol	NOUN
ejpam-5313	1	9	.	.	PROPN
ejpam-5313	2	1	17	17	NUM
ejpam-5313	2	2	,	,	PUNCT
ejpam-5313	2	3	no	no	INTJ
ejpam-5313	2	4	.	.	NOUN
ejpam-5313	2	5	3	3	NUM
ejpam-5313	2	6	,	,	PUNCT
ejpam-5313	2	7	2024	2024	NUM
ejpam-5313	2	8	,	,	PUNCT
ejpam-5313	2	9	2084	2084	NUM
ejpam-5313	2	10	-	-	SYM
ejpam-5313	2	11	2091	2091	NUM
ejpam-5313	2	12	issn	issn	PROPN
ejpam-5313	2	13	1307	1307	NUM
ejpam-5313	2	14	-	-	SYM
ejpam-5313	2	15	5543	5543	NUM
ejpam-5313	2	16	–	–	PUNCT
ejpam-5313	2	17	ejpam.com	ejpam.com	X
ejpam-5313	2	18	published	publish	VERB
ejpam-5313	2	19	by	by	ADP
ejpam-5313	2	20	new	new	PROPN
ejpam-5313	2	21	york	york	PROPN
ejpam-5313	2	22	business	business	PROPN
ejpam-5313	2	23	global	global	ADJ
ejpam-5313	2	24	study	study	NOUN
ejpam-5313	2	25	on	on	ADP
ejpam-5313	2	26	even	even	ADV
ejpam-5313	2	27	sum	sum	VERB
ejpam-5313	2	28	domination	domination	NOUN
ejpam-5313	2	29	number	number	NOUN
ejpam-5313	2	30	of	of	ADP
ejpam-5313	2	31	some	some	DET
ejpam-5313	2	32	graphs	graph	NOUN
ejpam-5313	2	33	sejal	sejal	ADJ
ejpam-5313	2	34	h	h	NOUN
ejpam-5313	2	35	karkar1,∗	karkar1,∗	NOUN
ejpam-5313	2	36	,	,	PUNCT
ejpam-5313	2	37	d	d	PROPN
ejpam-5313	2	38	d	d	PROPN
ejpam-5313	2	39	pandya2	pandya2	PROPN
ejpam-5313	2	40	,	,	PUNCT
ejpam-5313	2	41	s	s	PART
ejpam-5313	2	42	g	g	NOUN
ejpam-5313	2	43	sonchhatra2	sonchhatra2	NOUN
ejpam-5313	2	44	,	,	PUNCT
ejpam-5313	2	45	p	p	PROPN
ejpam-5313	2	46	dmaheta3	dmaheta3	PROPN
ejpam-5313	2	47	,	,	PUNCT
ejpam-5313	2	48	h	h	PROPN
ejpam-5313	2	49	m	m	VERB
ejpam-5313	2	50	rathod3	rathod3	PROPN
ejpam-5313	2	51	,	,	PUNCT
ejpam-5313	2	52	s	s	PART
ejpam-5313	2	53	d	d	NOUN
ejpam-5313	2	54	bhanderi3	bhanderi3	NOUN
ejpam-5313	2	55	1	1	NUM
ejpam-5313	2	56	department	department	NOUN
ejpam-5313	2	57	of	of	ADP
ejpam-5313	2	58	humanities	humanity	NOUN
ejpam-5313	2	59	and	and	CCONJ
ejpam-5313	2	60	science	science	NOUN
ejpam-5313	2	61	,	,	PUNCT
ejpam-5313	2	62	lukhdhirji	lukhdhirji	PROPN
ejpam-5313	2	63	engineering	engineering	NOUN
ejpam-5313	2	64	college	college	PROPN
ejpam-5313	2	65	,	,	PUNCT
ejpam-5313	2	66	morbi	morbi	NOUN
ejpam-5313	2	67	,	,	PUNCT
ejpam-5313	2	68	gujarat	gujarat	NOUN
ejpam-5313	2	69	,	,	PUNCT
ejpam-5313	2	70	india	india	PROPN
ejpam-5313	2	71	.	.	PROPN
ejpam-5313	2	72	2	2	NUM
ejpam-5313	2	73	department	department	NOUN
ejpam-5313	2	74	of	of	ADP
ejpam-5313	2	75	humanities	humanity	NOUN
ejpam-5313	2	76	and	and	CCONJ
ejpam-5313	2	77	science	science	NOUN
ejpam-5313	2	78	,	,	PUNCT
ejpam-5313	2	79	government	government	NOUN
ejpam-5313	2	80	engineering	engineering	NOUN
ejpam-5313	2	81	college	college	PROPN
ejpam-5313	2	82	,	,	PUNCT
ejpam-5313	2	83	rajkot	rajkot	NOUN
ejpam-5313	2	84	,	,	PUNCT
ejpam-5313	2	85	gujarat	gujarat	PROPN
ejpam-5313	2	86	,	,	PUNCT
ejpam-5313	2	87	india	india	PROPN
ejpam-5313	2	88	.	.	PROPN
ejpam-5313	2	89	3	3	NUM
ejpam-5313	2	90	department	department	NOUN
ejpam-5313	2	91	of	of	ADP
ejpam-5313	2	92	computer	computer	NOUN
ejpam-5313	2	93	engineering	engineering	NOUN
ejpam-5313	2	94	,	,	PUNCT
ejpam-5313	2	95	government	government	NOUN
ejpam-5313	2	96	engineering	engineering	NOUN
ejpam-5313	2	97	college	college	PROPN
ejpam-5313	2	98	,	,	PUNCT
ejpam-5313	2	99	rajkot	rajkot	NOUN
ejpam-5313	2	100	,	,	PUNCT
ejpam-5313	2	101	gujarat	gujarat	PROPN
ejpam-5313	2	102	,	,	PUNCT
ejpam-5313	2	103	india	india	PROPN
ejpam-5313	2	104	.	.	PUNCT
ejpam-5313	3	1	abstract	abstract	PROPN
ejpam-5313	3	2	.	.	PUNCT
ejpam-5313	4	1	let	let	VERB
ejpam-5313	4	2	g	g	PRON
ejpam-5313	4	3	be	be	AUX
ejpam-5313	4	4	a	a	DET
ejpam-5313	4	5	connected	connected	ADJ
ejpam-5313	4	6	graph	graph	NOUN
ejpam-5313	4	7	and	and	CCONJ
ejpam-5313	4	8	uv	uv	NOUN
ejpam-5313	4	9	∈	∈	PROPN
ejpam-5313	4	10	e(g	e(g	PROPN
ejpam-5313	4	11	)	)	PUNCT
ejpam-5313	4	12	.	.	PUNCT
ejpam-5313	5	1	we	we	PRON
ejpam-5313	5	2	say	say	VERB
ejpam-5313	5	3	,	,	PUNCT
ejpam-5313	5	4	the	the	DET
ejpam-5313	5	5	vertex	vertex	NOUN
ejpam-5313	5	6	v	v	PART
ejpam-5313	5	7	even	even	ADV
ejpam-5313	5	8	sum	sum	VERB
ejpam-5313	5	9	dominates	dominate	VERB
ejpam-5313	5	10	u	u	NOUN
ejpam-5313	5	11	(	(	PUNCT
ejpam-5313	5	12	u	u	NOUN
ejpam-5313	5	13	even	even	ADV
ejpam-5313	5	14	sum	sum	VERB
ejpam-5313	5	15	dominates	dominate	VERB
ejpam-5313	5	16	v	v	NOUN
ejpam-5313	5	17	)	)	PUNCT
ejpam-5313	5	18	if	if	SCONJ
ejpam-5313	5	19	deg(v)+deg(u	deg(v)+deg(u	PROPN
ejpam-5313	5	20	)	)	PUNCT
ejpam-5313	5	21	is	be	AUX
ejpam-5313	5	22	an	an	DET
ejpam-5313	5	23	even	even	ADJ
ejpam-5313	5	24	number	number	NOUN
ejpam-5313	5	25	.	.	PUNCT
ejpam-5313	6	1	a	a	DET
ejpam-5313	6	2	set	set	NOUN
ejpam-5313	6	3	s	s	PART
ejpam-5313	6	4	is	be	AUX
ejpam-5313	6	5	an	an	DET
ejpam-5313	6	6	even	even	ADV
ejpam-5313	6	7	sum	sum	NOUN
ejpam-5313	6	8	dominating	dominating	NOUN
ejpam-5313	6	9	set	set	NOUN
ejpam-5313	6	10	(	(	PUNCT
ejpam-5313	6	11	esds	esds	NOUN
ejpam-5313	6	12	)	)	PUNCT
ejpam-5313	6	13	if	if	SCONJ
ejpam-5313	6	14	every	every	DET
ejpam-5313	6	15	vertex	vertex	NOUN
ejpam-5313	6	16	v	v	ADP
ejpam-5313	6	17	∈	∈	NOUN
ejpam-5313	6	18	v	v	NOUN
ejpam-5313	6	19	is	be	AUX
ejpam-5313	6	20	either	either	CCONJ
ejpam-5313	6	21	in	in	ADP
ejpam-5313	6	22	s	s	PRON
ejpam-5313	6	23	or	or	CCONJ
ejpam-5313	6	24	even	even	ADV
ejpam-5313	6	25	sum	sum	NOUN
ejpam-5313	6	26	dominated	dominate	VERB
ejpam-5313	6	27	by	by	ADP
ejpam-5313	6	28	a	a	DET
ejpam-5313	6	29	vertex	vertex	NOUN
ejpam-5313	6	30	in	in	ADP
ejpam-5313	6	31	s.	s.	PROPN
ejpam-5313	6	32	an	an	DET
ejpam-5313	6	33	even	even	ADV
ejpam-5313	6	34	sum	sum	NOUN
ejpam-5313	6	35	dominating	dominating	NOUN
ejpam-5313	6	36	set	set	NOUN
ejpam-5313	6	37	s	s	VERB
ejpam-5313	6	38	is	be	AUX
ejpam-5313	6	39	a	a	DET
ejpam-5313	6	40	mimimal	mimimal	NOUN
ejpam-5313	6	41	even	even	ADV
ejpam-5313	6	42	sum	sum	NOUN
ejpam-5313	6	43	dominating	dominating	NOUN
ejpam-5313	6	44	set	set	VERB
ejpam-5313	6	45	if	if	SCONJ
ejpam-5313	6	46	no	no	DET
ejpam-5313	6	47	proper	proper	ADJ
ejpam-5313	6	48	subset	subset	NOUN
ejpam-5313	6	49	s	s	PART
ejpam-5313	6	50	′	′	NUM
ejpam-5313	7	1	⊂	⊂	ADJ
ejpam-5313	7	2	s	s	VERB
ejpam-5313	7	3	is	be	AUX
ejpam-5313	7	4	an	an	DET
ejpam-5313	7	5	even	even	ADV
ejpam-5313	7	6	sum	sum	NOUN
ejpam-5313	7	7	dominating	dominating	NOUN
ejpam-5313	7	8	set	set	NOUN
ejpam-5313	7	9	.	.	PUNCT
ejpam-5313	8	1	the	the	DET
ejpam-5313	8	2	even	even	ADJ
ejpam-5313	8	3	sum	sum	NOUN
ejpam-5313	8	4	domination	domination	NOUN
ejpam-5313	8	5	number	number	NOUN
ejpam-5313	8	6	γes(g	γes(g	NUM
ejpam-5313	8	7	)	)	PUNCT
ejpam-5313	8	8	of	of	ADP
ejpam-5313	8	9	a	a	DET
ejpam-5313	8	10	graph	graph	NOUN
ejpam-5313	8	11	g	g	NOUN
ejpam-5313	8	12	is	be	AUX
ejpam-5313	8	13	the	the	DET
ejpam-5313	8	14	minimum	minimum	ADJ
ejpam-5313	8	15	cardinality	cardinality	NOUN
ejpam-5313	8	16	of	of	ADP
ejpam-5313	8	17	an	an	DET
ejpam-5313	8	18	even	even	ADV
ejpam-5313	8	19	sum	sum	NOUN
ejpam-5313	8	20	dominating	dominating	NOUN
ejpam-5313	8	21	set	set	NOUN
ejpam-5313	8	22	of	of	ADP
ejpam-5313	8	23	g.	g.	PROPN
ejpam-5313	8	24	in	in	ADP
ejpam-5313	8	25	this	this	DET
ejpam-5313	8	26	paper	paper	NOUN
ejpam-5313	8	27	,	,	PUNCT
ejpam-5313	8	28	we	we	PRON
ejpam-5313	8	29	discuss	discuss	VERB
ejpam-5313	8	30	some	some	DET
ejpam-5313	8	31	properties	property	NOUN
ejpam-5313	8	32	and	and	CCONJ
ejpam-5313	8	33	bounds	bound	NOUN
ejpam-5313	8	34	for	for	ADP
ejpam-5313	8	35	this	this	DET
ejpam-5313	8	36	concept	concept	NOUN
ejpam-5313	8	37	.	.	PUNCT
ejpam-5313	9	1	we	we	PRON
ejpam-5313	9	2	also	also	ADV
ejpam-5313	9	3	derive	derive	VERB
ejpam-5313	9	4	even	even	ADV
ejpam-5313	9	5	sum	sum	NOUN
ejpam-5313	9	6	domination	domination	NOUN
ejpam-5313	9	7	number	number	NOUN
ejpam-5313	9	8	for	for	ADP
ejpam-5313	9	9	some	some	DET
ejpam-5313	9	10	standard	standard	ADJ
ejpam-5313	9	11	graphs	graph	NOUN
ejpam-5313	9	12	.	.	PUNCT
ejpam-5313	10	1	2020	2020	NUM
ejpam-5313	10	2	mathematics	mathematic	NOUN
ejpam-5313	10	3	subject	subject	NOUN
ejpam-5313	10	4	classifications	classification	NOUN
ejpam-5313	10	5	:	:	PUNCT
ejpam-5313	10	6	05c45	05c45	NUM
ejpam-5313	10	7	,	,	PUNCT
ejpam-5313	10	8	05c69	05c69	X
ejpam-5313	10	9	key	key	ADJ
ejpam-5313	10	10	words	word	NOUN
ejpam-5313	10	11	and	and	CCONJ
ejpam-5313	10	12	phrases	phrase	NOUN
ejpam-5313	10	13	:	:	PUNCT
ejpam-5313	10	14	degree	degree	NOUN
ejpam-5313	10	15	of	of	ADP
ejpam-5313	10	16	a	a	DET
ejpam-5313	10	17	vertex	vertex	NOUN
ejpam-5313	10	18	,	,	PUNCT
ejpam-5313	10	19	domination	domination	NOUN
ejpam-5313	10	20	number	number	NOUN
ejpam-5313	10	21	,	,	PUNCT
ejpam-5313	10	22	even	even	ADV
ejpam-5313	10	23	sum	sum	VERB
ejpam-5313	10	24	domination	domination	NOUN
ejpam-5313	10	25	number	number	NOUN
ejpam-5313	10	26	1	1	NUM
ejpam-5313	10	27	.	.	PUNCT
ejpam-5313	11	1	introduction	introduction	NOUN
ejpam-5313	11	2	we	we	PRON
ejpam-5313	11	3	consider	consider	VERB
ejpam-5313	11	4	simple	simple	ADJ
ejpam-5313	11	5	,	,	PUNCT
ejpam-5313	11	6	finite	finite	NOUN
ejpam-5313	11	7	,	,	PUNCT
ejpam-5313	11	8	connected	connected	ADJ
ejpam-5313	11	9	and	and	CCONJ
ejpam-5313	11	10	undirected	undirected	ADJ
ejpam-5313	11	11	graph	graph	NOUN
ejpam-5313	11	12	g	g	NOUN
ejpam-5313	11	13	with	with	ADP
ejpam-5313	11	14	vertex	vertex	NOUN
ejpam-5313	11	15	set	set	VERB
ejpam-5313	11	16	v	v	NOUN
ejpam-5313	11	17	(	(	PUNCT
ejpam-5313	11	18	g	g	NOUN
ejpam-5313	11	19	)	)	PUNCT
ejpam-5313	11	20	and	and	CCONJ
ejpam-5313	11	21	edge	edge	VERB
ejpam-5313	11	22	set	set	VERB
ejpam-5313	11	23	e(g	e(g	PROPN
ejpam-5313	11	24	)	)	PUNCT
ejpam-5313	11	25	.	.	PUNCT
ejpam-5313	12	1	we	we	PRON
ejpam-5313	12	2	follow	follow	VERB
ejpam-5313	12	3	west	west	NOUN
ejpam-5313	13	1	[	[	X
ejpam-5313	13	2	9	9	X
ejpam-5313	13	3	]	]	PUNCT
ejpam-5313	13	4	for	for	ADP
ejpam-5313	13	5	all	all	DET
ejpam-5313	13	6	standard	standard	ADJ
ejpam-5313	13	7	terminology	terminology	NOUN
ejpam-5313	13	8	and	and	CCONJ
ejpam-5313	13	9	notations	notation	NOUN
ejpam-5313	13	10	while	while	SCONJ
ejpam-5313	13	11	the	the	DET
ejpam-5313	13	12	terms	term	NOUN
ejpam-5313	13	13	related	relate	VERB
ejpam-5313	13	14	to	to	ADP
ejpam-5313	13	15	the	the	DET
ejpam-5313	13	16	theory	theory	NOUN
ejpam-5313	13	17	of	of	ADP
ejpam-5313	13	18	domination	domination	NOUN
ejpam-5313	13	19	in	in	ADP
ejpam-5313	13	20	graphs	graph	NOUN
ejpam-5313	13	21	are	be	AUX
ejpam-5313	13	22	used	use	VERB
ejpam-5313	13	23	in	in	ADP
ejpam-5313	13	24	the	the	DET
ejpam-5313	13	25	sense	sense	NOUN
ejpam-5313	13	26	of	of	ADP
ejpam-5313	13	27	haynes	hayne	NOUN
ejpam-5313	13	28	et	et	PROPN
ejpam-5313	13	29	al	al	PROPN
ejpam-5313	13	30	.	.	PUNCT
ejpam-5313	14	1	[	[	X
ejpam-5313	14	2	4	4	NUM
ejpam-5313	14	3	]	]	PUNCT
ejpam-5313	14	4	.	.	PUNCT
ejpam-5313	15	1	we	we	PRON
ejpam-5313	15	2	shall	shall	AUX
ejpam-5313	15	3	give	give	VERB
ejpam-5313	15	4	brief	brief	ADJ
ejpam-5313	15	5	summary	summary	NOUN
ejpam-5313	15	6	of	of	ADP
ejpam-5313	15	7	definitions	definition	NOUN
ejpam-5313	15	8	which	which	PRON
ejpam-5313	15	9	are	be	AUX
ejpam-5313	15	10	useful	useful	ADJ
ejpam-5313	15	11	for	for	ADP
ejpam-5313	15	12	the	the	DET
ejpam-5313	15	13	present	present	ADJ
ejpam-5313	15	14	investigations	investigation	NOUN
ejpam-5313	15	15	.	.	PUNCT
ejpam-5313	16	1	the	the	DET
ejpam-5313	16	2	domination	domination	NOUN
ejpam-5313	16	3	number	number	NOUN
ejpam-5313	16	4	is	be	AUX
ejpam-5313	16	5	a	a	DET
ejpam-5313	16	6	well	well	ADV
ejpam-5313	16	7	studied	study	VERB
ejpam-5313	16	8	parameter	parameter	NOUN
ejpam-5313	16	9	as	as	SCONJ
ejpam-5313	16	10	observed	observe	VERB
ejpam-5313	16	11	by	by	ADP
ejpam-5313	16	12	hedetniemi	hedetniemi	ADV
ejpam-5313	16	13	and	and	CCONJ
ejpam-5313	16	14	laskar	laskar	PROPN
ejpam-5313	17	1	[	[	X
ejpam-5313	17	2	5	5	NUM
ejpam-5313	17	3	]	]	PUNCT
ejpam-5313	17	4	.	.	PUNCT
ejpam-5313	18	1	a	a	DET
ejpam-5313	18	2	set	set	NOUN
ejpam-5313	18	3	s	s	NOUN
ejpam-5313	18	4	⊆	⊆	NUM
ejpam-5313	18	5	v	v	NOUN
ejpam-5313	18	6	(	(	PUNCT
ejpam-5313	18	7	g	g	NOUN
ejpam-5313	18	8	)	)	PUNCT
ejpam-5313	18	9	of	of	ADP
ejpam-5313	18	10	vertices	vertex	NOUN
ejpam-5313	18	11	in	in	ADP
ejpam-5313	18	12	a	a	DET
ejpam-5313	18	13	graph	graph	NOUN
ejpam-5313	18	14	g	g	NOUN
ejpam-5313	18	15	=	=	PUNCT
ejpam-5313	18	16	(	(	PUNCT
ejpam-5313	18	17	v	v	NOUN
ejpam-5313	18	18	(	(	PUNCT
ejpam-5313	18	19	g	g	NOUN
ejpam-5313	18	20	)	)	PUNCT
ejpam-5313	18	21	,	,	PUNCT
ejpam-5313	18	22	e(g	e(g	PROPN
ejpam-5313	18	23	)	)	PUNCT
ejpam-5313	18	24	)	)	PUNCT
ejpam-5313	18	25	is	be	AUX
ejpam-5313	18	26	called	call	VERB
ejpam-5313	18	27	a	a	DET
ejpam-5313	18	28	dominating	dominating	NOUN
ejpam-5313	18	29	set	set	NOUN
ejpam-5313	18	30	if	if	SCONJ
ejpam-5313	18	31	every	every	DET
ejpam-5313	18	32	vertex	vertex	NOUN
ejpam-5313	18	33	v	v	ADP
ejpam-5313	18	34	∈	∈	PROPN
ejpam-5313	18	35	v	v	NOUN
ejpam-5313	18	36	(	(	PUNCT
ejpam-5313	18	37	g	g	NOUN
ejpam-5313	18	38	)	)	PUNCT
ejpam-5313	18	39	is	be	AUX
ejpam-5313	18	40	either	either	CCONJ
ejpam-5313	18	41	an	an	DET
ejpam-5313	18	42	element	element	NOUN
ejpam-5313	18	43	of	of	ADP
ejpam-5313	18	44	s	s	PRON
ejpam-5313	18	45	or	or	CCONJ
ejpam-5313	18	46	is	be	AUX
ejpam-5313	18	47	adjacent	adjacent	ADJ
ejpam-5313	18	48	to	to	ADP
ejpam-5313	18	49	an	an	DET
ejpam-5313	18	50	∗corresponding	∗corresponding	NOUN
ejpam-5313	18	51	author	author	NOUN
ejpam-5313	18	52	.	.	PUNCT
ejpam-5313	19	1	doi	doi	NOUN
ejpam-5313	19	2	:	:	PUNCT
ejpam-5313	19	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5313	https://doi.org/10.29020/nybg.ejpam.v17i3.5313	PROPN
ejpam-5313	19	4	email	email	NOUN
ejpam-5313	19	5	addresses	address	NOUN
ejpam-5313	19	6	:	:	PUNCT
ejpam-5313	19	7	sdpansuria@gmail.com	sdpansuria@gmail.com	X
ejpam-5313	19	8	(	(	PUNCT
ejpam-5313	19	9	sejal	sejal	PROPN
ejpam-5313	19	10	h.	h.	PROPN
ejpam-5313	19	11	karkar	karkar	PROPN
ejpam-5313	19	12	)	)	PUNCT
ejpam-5313	19	13	,	,	PUNCT
ejpam-5313	19	14	ddpandya@gecrajkot.ac.in	ddpandya@gecrajkot.ac.in	ADV
ejpam-5313	19	15	(	(	PUNCT
ejpam-5313	19	16	d	d	X
ejpam-5313	19	17	d	d	X
ejpam-5313	19	18	pandya	pandya	PROPN
ejpam-5313	19	19	)	)	PUNCT
ejpam-5313	19	20	,	,	PUNCT
ejpam-5313	19	21	sgsonchhatra@gecrajkot.ac.in	sgsonchhatra@gecrajkot.ac.in	PROPN
ejpam-5313	19	22	(	(	PUNCT
ejpam-5313	19	23	s	s	VERB
ejpam-5313	19	24	g	g	PROPN
ejpam-5313	19	25	sonchhatra	sonchhatra	PROPN
ejpam-5313	19	26	)	)	PUNCT
ejpam-5313	19	27	,	,	PUNCT
ejpam-5313	19	28	pdmaheta@gecrajkot.ac.in	pdmaheta@gecrajkot.ac.in	PROPN
ejpam-5313	19	29	(	(	PUNCT
ejpam-5313	19	30	p	p	NOUN
ejpam-5313	19	31	d	d	X
ejpam-5313	19	32	maheta	maheta	NOUN
ejpam-5313	19	33	)	)	PUNCT
ejpam-5313	19	34	,	,	PUNCT
ejpam-5313	19	35	hmrathod@gecrajkot.ac.in	hmrathod@gecrajkot.ac.in	X
ejpam-5313	19	36	(	(	PUNCT
ejpam-5313	19	37	h	h	NOUN
ejpam-5313	19	38	m	m	PROPN
ejpam-5313	19	39	rathod	rathod	PROPN
ejpam-5313	19	40	)	)	PUNCT
ejpam-5313	19	41	,	,	PUNCT
ejpam-5313	19	42	sdbhanderi@gecrajkot.ac.in	sdbhanderi@gecrajkot.ac.in	PROPN
ejpam-5313	19	43	(	(	PUNCT
ejpam-5313	19	44	s	s	NOUN
ejpam-5313	19	45	d	d	X
ejpam-5313	19	46	bhanderi	bhanderi	ADJ
ejpam-5313	19	47	)	)	PUNCT
ejpam-5313	19	48	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5313	19	49	2084	2084	NUM
ejpam-5313	19	50	©	©	ADP
ejpam-5313	19	51	2024	2024	NUM
ejpam-5313	19	52	ejpam	ejpam	NOUN
ejpam-5313	19	53	all	all	DET
ejpam-5313	19	54	rights	right	NOUN
ejpam-5313	19	55	reserved	reserve	VERB
ejpam-5313	19	56	.	.	PUNCT
ejpam-5313	20	1	s.	s.	PROPN
ejpam-5313	20	2	h	h	PROPN
ejpam-5313	20	3	karkar	karkar	PROPN
ejpam-5313	20	4	et	et	PROPN
ejpam-5313	20	5	al	al	PROPN
ejpam-5313	20	6	.	.	PUNCT
ejpam-5313	20	7	/	/	SYM
ejpam-5313	20	8	eur	eur	PROPN
ejpam-5313	20	9	.	.	PUNCT
ejpam-5313	21	1	j.	j.	PROPN
ejpam-5313	21	2	pure	pure	PROPN
ejpam-5313	21	3	appl	appl	PROPN
ejpam-5313	21	4	.	.	PROPN
ejpam-5313	21	5	math	math	PROPN
ejpam-5313	21	6	,	,	PUNCT
ejpam-5313	21	7	17	17	NUM
ejpam-5313	21	8	(	(	PUNCT
ejpam-5313	21	9	3	3	NUM
ejpam-5313	21	10	)	)	PUNCT
ejpam-5313	21	11	(	(	PUNCT
ejpam-5313	21	12	2024	2024	NUM
ejpam-5313	21	13	)	)	PUNCT
ejpam-5313	21	14	,	,	PUNCT
ejpam-5313	21	15	2084	2084	NUM
ejpam-5313	21	16	-	-	SYM
ejpam-5313	21	17	2091	2091	NUM
ejpam-5313	21	18	2085	2085	NUM
ejpam-5313	21	19	element	element	NOUN
ejpam-5313	21	20	of	of	ADP
ejpam-5313	21	21	s.	s.	PROPN
ejpam-5313	21	22	a	a	DET
ejpam-5313	21	23	dominating	dominating	NOUN
ejpam-5313	21	24	set	set	NOUN
ejpam-5313	21	25	s	s	VERB
ejpam-5313	21	26	is	be	AUX
ejpam-5313	21	27	a	a	DET
ejpam-5313	21	28	minimal	minimal	ADJ
ejpam-5313	21	29	dominating	dominating	NOUN
ejpam-5313	21	30	set	set	NOUN
ejpam-5313	21	31	if	if	SCONJ
ejpam-5313	21	32	no	no	DET
ejpam-5313	21	33	proper	proper	ADJ
ejpam-5313	21	34	subset	subset	NOUN
ejpam-5313	21	35	s	s	PART
ejpam-5313	21	36	′	′	NUM
ejpam-5313	22	1	⊂	⊂	ADJ
ejpam-5313	22	2	s	s	VERB
ejpam-5313	22	3	is	be	AUX
ejpam-5313	22	4	a	a	DET
ejpam-5313	22	5	dominating	dominating	NOUN
ejpam-5313	22	6	set	set	NOUN
ejpam-5313	22	7	.	.	PUNCT
ejpam-5313	23	1	the	the	DET
ejpam-5313	23	2	domination	domination	NOUN
ejpam-5313	23	3	number	number	PROPN
ejpam-5313	23	4	γ(g	γ(g	PROPN
ejpam-5313	23	5	)	)	PUNCT
ejpam-5313	23	6	of	of	ADP
ejpam-5313	23	7	a	a	DET
ejpam-5313	23	8	graph	graph	NOUN
ejpam-5313	23	9	g	g	NOUN
ejpam-5313	23	10	is	be	AUX
ejpam-5313	23	11	the	the	DET
ejpam-5313	23	12	minimum	minimum	ADJ
ejpam-5313	23	13	cardinality	cardinality	NOUN
ejpam-5313	23	14	of	of	ADP
ejpam-5313	23	15	a	a	DET
ejpam-5313	23	16	dominating	dominating	NOUN
ejpam-5313	23	17	set	set	VERB
ejpam-5313	23	18	in	in	ADP
ejpam-5313	23	19	graph	graph	NOUN
ejpam-5313	23	20	g.	g.	NOUN
ejpam-5313	23	21	this	this	DET
ejpam-5313	23	22	concept	concept	NOUN
ejpam-5313	23	23	is	be	AUX
ejpam-5313	23	24	explored	explore	VERB
ejpam-5313	23	25	and	and	CCONJ
ejpam-5313	23	26	reformed	reform	VERB
ejpam-5313	23	27	in	in	ADP
ejpam-5313	23	28	various	various	ADJ
ejpam-5313	23	29	fields	field	NOUN
ejpam-5313	23	30	to	to	PART
ejpam-5313	23	31	solved	solved	VERB
ejpam-5313	23	32	many	many	ADJ
ejpam-5313	23	33	real	real	ADJ
ejpam-5313	23	34	life	life	NOUN
ejpam-5313	23	35	problems	problem	NOUN
ejpam-5313	23	36	.	.	PUNCT
ejpam-5313	24	1	furthermore	furthermore	ADV
ejpam-5313	24	2	,	,	PUNCT
ejpam-5313	24	3	a	a	DET
ejpam-5313	24	4	number	number	NOUN
ejpam-5313	24	5	of	of	ADP
ejpam-5313	24	6	broad	broad	ADJ
ejpam-5313	24	7	formulations	formulation	NOUN
ejpam-5313	24	8	of	of	ADP
ejpam-5313	24	9	this	this	DET
ejpam-5313	24	10	idea	idea	NOUN
ejpam-5313	24	11	have	have	AUX
ejpam-5313	24	12	emerged	emerge	VERB
ejpam-5313	24	13	recently	recently	ADV
ejpam-5313	24	14	;	;	PUNCT
ejpam-5313	24	15	these	these	DET
ejpam-5313	24	16	definitions	definition	NOUN
ejpam-5313	24	17	,	,	PUNCT
ejpam-5313	24	18	however	however	ADV
ejpam-5313	24	19	,	,	PUNCT
ejpam-5313	24	20	rely	rely	VERB
ejpam-5313	24	21	on	on	ADP
ejpam-5313	24	22	certain	certain	ADJ
ejpam-5313	24	23	requirements	requirement	NOUN
ejpam-5313	24	24	that	that	PRON
ejpam-5313	24	25	can	can	AUX
ejpam-5313	24	26	be	be	AUX
ejpam-5313	24	27	applied	apply	VERB
ejpam-5313	24	28	to	to	ADP
ejpam-5313	24	29	the	the	DET
ejpam-5313	24	30	dominating	dominating	NOUN
ejpam-5313	24	31	set	set	NOUN
ejpam-5313	24	32	,	,	PUNCT
ejpam-5313	24	33	outside	outside	ADP
ejpam-5313	24	34	of	of	ADP
ejpam-5313	24	35	it	it	PRON
ejpam-5313	24	36	,	,	PUNCT
ejpam-5313	24	37	or	or	CCONJ
ejpam-5313	24	38	both[1	both[1	NOUN
ejpam-5313	24	39	,	,	PUNCT
ejpam-5313	24	40	2	2	NUM
ejpam-5313	24	41	,	,	PUNCT
ejpam-5313	24	42	8	8	NUM
ejpam-5313	24	43	]	]	PUNCT
ejpam-5313	24	44	.	.	PUNCT
ejpam-5313	25	1	this	this	DET
ejpam-5313	25	2	paper	paper	NOUN
ejpam-5313	25	3	is	be	AUX
ejpam-5313	25	4	worked	work	VERB
ejpam-5313	25	5	on	on	ADP
ejpam-5313	25	6	one	one	NUM
ejpam-5313	25	7	of	of	ADP
ejpam-5313	25	8	the	the	DET
ejpam-5313	25	9	recently	recently	ADV
ejpam-5313	25	10	introduced	introduce	VERB
ejpam-5313	25	11	parameter	parameter	NOUN
ejpam-5313	25	12	known	know	VERB
ejpam-5313	25	13	as	as	ADP
ejpam-5313	25	14	even	even	ADV
ejpam-5313	25	15	sum	sum	NOUN
ejpam-5313	25	16	domination	domination	NOUN
ejpam-5313	25	17	[	[	X
ejpam-5313	25	18	7	7	NUM
ejpam-5313	25	19	]	]	PUNCT
ejpam-5313	25	20	.	.	PUNCT
ejpam-5313	26	1	this	this	DET
ejpam-5313	26	2	definition	definition	NOUN
ejpam-5313	26	3	is	be	AUX
ejpam-5313	26	4	dependent	dependent	ADJ
ejpam-5313	26	5	on	on	ADP
ejpam-5313	26	6	the	the	DET
ejpam-5313	26	7	real	real	ADJ
ejpam-5313	26	8	-	-	PUNCT
ejpam-5313	26	9	world	world	NOUN
ejpam-5313	26	10	situations	situation	NOUN
ejpam-5313	26	11	when	when	SCONJ
ejpam-5313	26	12	it	it	PRON
ejpam-5313	26	13	is	be	AUX
ejpam-5313	26	14	feasible	feasible	ADJ
ejpam-5313	26	15	to	to	PART
ejpam-5313	26	16	divide	divide	VERB
ejpam-5313	26	17	the	the	DET
ejpam-5313	26	18	set	set	NOUN
ejpam-5313	26	19	’s	’s	PART
ejpam-5313	26	20	elements	element	NOUN
ejpam-5313	26	21	into	into	ADP
ejpam-5313	26	22	two	two	NUM
ejpam-5313	26	23	partitions	partition	NOUN
ejpam-5313	26	24	,	,	PUNCT
ejpam-5313	26	25	with	with	ADP
ejpam-5313	26	26	each	each	DET
ejpam-5313	26	27	partition	partition	NOUN
ejpam-5313	26	28	being	be	AUX
ejpam-5313	26	29	dominated	dominate	VERB
ejpam-5313	26	30	by	by	ADP
ejpam-5313	26	31	a	a	DET
ejpam-5313	26	32	same	same	ADJ
ejpam-5313	26	33	type	type	NOUN
ejpam-5313	26	34	of	of	ADP
ejpam-5313	26	35	that	that	DET
ejpam-5313	26	36	partition	partition	NOUN
ejpam-5313	26	37	.	.	PUNCT
ejpam-5313	27	1	the	the	DET
ejpam-5313	27	2	degree	degree	NOUN
ejpam-5313	27	3	of	of	ADP
ejpam-5313	27	4	a	a	DET
ejpam-5313	27	5	vertex	vertex	NOUN
ejpam-5313	27	6	v	v	NOUN
ejpam-5313	27	7	in	in	ADP
ejpam-5313	27	8	graph	graph	NOUN
ejpam-5313	27	9	g	g	NOUN
ejpam-5313	27	10	,	,	PUNCT
ejpam-5313	27	11	denoted	denote	VERB
ejpam-5313	27	12	as	as	ADP
ejpam-5313	27	13	d(v	d(v	PROPN
ejpam-5313	27	14	)	)	PUNCT
ejpam-5313	27	15	or	or	CCONJ
ejpam-5313	27	16	deg(v	deg(v	PROPN
ejpam-5313	27	17	)	)	PUNCT
ejpam-5313	27	18	,	,	PUNCT
ejpam-5313	27	19	is	be	AUX
ejpam-5313	27	20	the	the	DET
ejpam-5313	27	21	number	number	NOUN
ejpam-5313	27	22	of	of	ADP
ejpam-5313	27	23	edges	edge	NOUN
ejpam-5313	27	24	incident	incident	NOUN
ejpam-5313	27	25	to	to	ADP
ejpam-5313	27	26	v	v	NOUN
ejpam-5313	27	27	,	,	PUNCT
ejpam-5313	27	28	counting	count	VERB
ejpam-5313	27	29	each	each	DET
ejpam-5313	27	30	loop	loop	NOUN
ejpam-5313	27	31	twice	twice	ADV
ejpam-5313	27	32	.	.	PUNCT
ejpam-5313	28	1	for	for	ADP
ejpam-5313	28	2	any	any	DET
ejpam-5313	28	3	connected	connected	ADJ
ejpam-5313	28	4	graph	graph	NOUN
ejpam-5313	28	5	g	g	NOUN
ejpam-5313	28	6	and	and	CCONJ
ejpam-5313	28	7	uv	uv	NOUN
ejpam-5313	28	8	∈	∈	PROPN
ejpam-5313	28	9	e(g	e(g	PROPN
ejpam-5313	28	10	)	)	PUNCT
ejpam-5313	28	11	,	,	PUNCT
ejpam-5313	28	12	the	the	DET
ejpam-5313	28	13	vertex	vertex	NOUN
ejpam-5313	28	14	v	v	PART
ejpam-5313	28	15	even	even	ADV
ejpam-5313	28	16	sum	sum	VERB
ejpam-5313	28	17	dominates	dominate	VERB
ejpam-5313	28	18	u	u	NOUN
ejpam-5313	28	19	(	(	PUNCT
ejpam-5313	28	20	u	u	NOUN
ejpam-5313	28	21	even	even	ADV
ejpam-5313	28	22	sum	sum	VERB
ejpam-5313	28	23	dominates	dominate	VERB
ejpam-5313	28	24	v	v	NOUN
ejpam-5313	28	25	)	)	PUNCT
ejpam-5313	28	26	if	if	SCONJ
ejpam-5313	28	27	deg(v	deg(v	X
ejpam-5313	28	28	)	)	PUNCT
ejpam-5313	29	1	+	+	X
ejpam-5313	29	2	deg(u	deg(u	PROPN
ejpam-5313	29	3	)	)	PUNCT
ejpam-5313	29	4	is	be	AUX
ejpam-5313	29	5	an	an	DET
ejpam-5313	29	6	even	even	ADJ
ejpam-5313	29	7	number	number	NOUN
ejpam-5313	29	8	.	.	PUNCT
ejpam-5313	30	1	precisely	precisely	ADV
ejpam-5313	30	2	,	,	PUNCT
ejpam-5313	30	3	two	two	NUM
ejpam-5313	30	4	adjacent	adjacent	ADJ
ejpam-5313	30	5	vertices	vertex	NOUN
ejpam-5313	30	6	of	of	ADP
ejpam-5313	30	7	odd	odd	ADJ
ejpam-5313	30	8	degree	degree	NOUN
ejpam-5313	30	9	as	as	ADV
ejpam-5313	30	10	well	well	ADV
ejpam-5313	30	11	as	as	ADP
ejpam-5313	30	12	two	two	NUM
ejpam-5313	30	13	adjacent	adjacent	ADJ
ejpam-5313	30	14	vertices	vertex	NOUN
ejpam-5313	30	15	of	of	ADP
ejpam-5313	30	16	even	even	ADJ
ejpam-5313	30	17	degree	degree	NOUN
ejpam-5313	30	18	can	can	AUX
ejpam-5313	30	19	even	even	ADV
ejpam-5313	30	20	sum	sum	VERB
ejpam-5313	30	21	dominate	dominate	VERB
ejpam-5313	30	22	each	each	DET
ejpam-5313	30	23	other	other	ADJ
ejpam-5313	30	24	.	.	PUNCT
ejpam-5313	31	1	a	a	DET
ejpam-5313	31	2	set	set	NOUN
ejpam-5313	31	3	s	s	PART
ejpam-5313	31	4	is	be	AUX
ejpam-5313	31	5	called	call	VERB
ejpam-5313	31	6	even	even	ADV
ejpam-5313	31	7	sum	sum	NOUN
ejpam-5313	31	8	dominating	dominating	NOUN
ejpam-5313	31	9	set(esds	set(esds	CCONJ
ejpam-5313	31	10	)	)	PUNCT
ejpam-5313	31	11	if	if	SCONJ
ejpam-5313	31	12	every	every	DET
ejpam-5313	31	13	vertex	vertex	NOUN
ejpam-5313	31	14	v	v	ADP
ejpam-5313	31	15	∈	∈	NOUN
ejpam-5313	31	16	v	v	NOUN
ejpam-5313	31	17	is	be	AUX
ejpam-5313	31	18	either	either	CCONJ
ejpam-5313	31	19	an	an	DET
ejpam-5313	31	20	element	element	NOUN
ejpam-5313	31	21	of	of	ADP
ejpam-5313	31	22	s	s	PRON
ejpam-5313	31	23	or	or	CCONJ
ejpam-5313	31	24	it	it	PRON
ejpam-5313	31	25	is	be	AUX
ejpam-5313	31	26	even	even	ADV
ejpam-5313	31	27	sum	sum	NOUN
ejpam-5313	31	28	dominated	dominate	VERB
ejpam-5313	31	29	by	by	ADP
ejpam-5313	31	30	some	some	DET
ejpam-5313	31	31	vertex	vertex	NOUN
ejpam-5313	31	32	of	of	ADP
ejpam-5313	31	33	s.	s.	PROPN
ejpam-5313	31	34	an	an	DET
ejpam-5313	31	35	even	even	ADV
ejpam-5313	31	36	sum	sum	NOUN
ejpam-5313	31	37	dominating	dominating	NOUN
ejpam-5313	31	38	set	set	NOUN
ejpam-5313	31	39	s	s	VERB
ejpam-5313	31	40	is	be	AUX
ejpam-5313	31	41	a	a	DET
ejpam-5313	31	42	mimimal	mimimal	NOUN
ejpam-5313	31	43	even	even	ADV
ejpam-5313	31	44	sum	sum	NOUN
ejpam-5313	31	45	dominating	dominating	NOUN
ejpam-5313	31	46	set	set	VERB
ejpam-5313	31	47	if	if	SCONJ
ejpam-5313	31	48	no	no	DET
ejpam-5313	31	49	proper	proper	ADJ
ejpam-5313	31	50	subset	subset	NOUN
ejpam-5313	31	51	s	s	PART
ejpam-5313	31	52	′	′	NUM
ejpam-5313	32	1	⊂	⊂	ADJ
ejpam-5313	32	2	s	s	VERB
ejpam-5313	32	3	is	be	AUX
ejpam-5313	32	4	an	an	DET
ejpam-5313	32	5	even	even	ADV
ejpam-5313	32	6	sum	sum	NOUN
ejpam-5313	32	7	dominating	dominating	NOUN
ejpam-5313	32	8	set	set	NOUN
ejpam-5313	32	9	.	.	PUNCT
ejpam-5313	33	1	the	the	DET
ejpam-5313	33	2	even	even	ADJ
ejpam-5313	33	3	sum	sum	NOUN
ejpam-5313	33	4	domination	domination	NOUN
ejpam-5313	33	5	number	number	NOUN
ejpam-5313	33	6	γes(g	γes(g	NUM
ejpam-5313	33	7	)	)	PUNCT
ejpam-5313	33	8	of	of	ADP
ejpam-5313	33	9	a	a	DET
ejpam-5313	33	10	graph	graph	NOUN
ejpam-5313	33	11	g	g	NOUN
ejpam-5313	33	12	is	be	AUX
ejpam-5313	33	13	the	the	DET
ejpam-5313	33	14	minimum	minimum	ADJ
ejpam-5313	33	15	cardinality	cardinality	NOUN
ejpam-5313	33	16	of	of	ADP
ejpam-5313	33	17	an	an	DET
ejpam-5313	33	18	even	even	ADV
ejpam-5313	33	19	sum	sum	NOUN
ejpam-5313	33	20	dominating	dominating	NOUN
ejpam-5313	33	21	set	set	NOUN
ejpam-5313	33	22	of	of	ADP
ejpam-5313	33	23	g.	g.	PROPN
ejpam-5313	33	24	v	v	ADP
ejpam-5313	33	25	1	1	NUM
ejpam-5313	33	26	v	v	NUM
ejpam-5313	33	27	2	2	NUM
ejpam-5313	33	28	v7	v7	NOUN
ejpam-5313	33	29	v	v	NOUN
ejpam-5313	33	30	3	3	NUM
ejpam-5313	33	31	v4	v4	NOUN
ejpam-5313	33	32	v	v	ADP
ejpam-5313	33	33	6	6	NUM
ejpam-5313	33	34	v5	v5	PROPN
ejpam-5313	33	35	figure	figure	NOUN
ejpam-5313	33	36	1	1	NUM
ejpam-5313	33	37	g	g	NOUN
ejpam-5313	33	38	for	for	ADP
ejpam-5313	33	39	the	the	DET
ejpam-5313	33	40	graph	graph	NOUN
ejpam-5313	33	41	g	g	NOUN
ejpam-5313	33	42	given	give	VERB
ejpam-5313	33	43	in	in	ADP
ejpam-5313	33	44	figure	figure	NOUN
ejpam-5313	33	45	1	1	NUM
ejpam-5313	33	46	,	,	PUNCT
ejpam-5313	33	47	the	the	DET
ejpam-5313	33	48	even	even	ADV
ejpam-5313	33	49	sum	sum	NOUN
ejpam-5313	33	50	dominating	dominating	NOUN
ejpam-5313	33	51	set	set	NOUN
ejpam-5313	33	52	s	s	PART
ejpam-5313	33	53	=	=	PUNCT
ejpam-5313	33	54	{	{	PUNCT
ejpam-5313	33	55	v1	v1	PROPN
ejpam-5313	33	56	,	,	PUNCT
ejpam-5313	33	57	v3	v3	PROPN
ejpam-5313	33	58	,	,	PUNCT
ejpam-5313	33	59	v4	v4	PROPN
ejpam-5313	33	60	,	,	PUNCT
ejpam-5313	33	61	v6	v6	NOUN
ejpam-5313	33	62	}	}	PUNCT
ejpam-5313	33	63	.	.	PUNCT
ejpam-5313	34	1	2	2	X
ejpam-5313	34	2	.	.	X
ejpam-5313	34	3	main	main	ADJ
ejpam-5313	34	4	results	result	NOUN
ejpam-5313	34	5	let	let	VERB
ejpam-5313	34	6	g	g	NOUN
ejpam-5313	34	7	=	=	SYM
ejpam-5313	34	8	(	(	PUNCT
ejpam-5313	34	9	v	v	NOUN
ejpam-5313	34	10	,	,	PUNCT
ejpam-5313	34	11	e	e	NOUN
ejpam-5313	34	12	)	)	PUNCT
ejpam-5313	34	13	be	be	AUX
ejpam-5313	34	14	a	a	DET
ejpam-5313	34	15	connected	connected	ADJ
ejpam-5313	34	16	graph	graph	NOUN
ejpam-5313	34	17	and	and	CCONJ
ejpam-5313	34	18	u	u	NOUN
ejpam-5313	34	19	,	,	PUNCT
ejpam-5313	34	20	v	v	PROPN
ejpam-5313	34	21	∈	∈	PROPN
ejpam-5313	34	22	v	v	NOUN
ejpam-5313	34	23	,	,	PUNCT
ejpam-5313	34	24	then	then	ADV
ejpam-5313	34	25	we	we	PRON
ejpam-5313	34	26	say	say	VERB
ejpam-5313	34	27	that	that	SCONJ
ejpam-5313	34	28	u	u	NOUN
ejpam-5313	34	29	is	be	AUX
ejpam-5313	34	30	even	even	ADV
ejpam-5313	34	31	sum	sum	NOUN
ejpam-5313	34	32	neighbor	neighbor	NOUN
ejpam-5313	34	33	of	of	ADP
ejpam-5313	34	34	v	v	NOUN
ejpam-5313	34	35	if	if	SCONJ
ejpam-5313	34	36	uv	uv	NOUN
ejpam-5313	34	37	∈	∈	PROPN
ejpam-5313	34	38	e	e	NOUN
ejpam-5313	34	39	and	and	CCONJ
ejpam-5313	34	40	deg(u	deg(u	PROPN
ejpam-5313	34	41	)	)	PUNCT
ejpam-5313	34	42	+	+	NUM
ejpam-5313	34	43	deg(v	deg(v	PROPN
ejpam-5313	34	44	)	)	PUNCT
ejpam-5313	34	45	is	be	AUX
ejpam-5313	34	46	an	an	DET
ejpam-5313	34	47	even	even	ADJ
ejpam-5313	34	48	number	number	NOUN
ejpam-5313	34	49	.	.	PUNCT
ejpam-5313	35	1	the	the	DET
ejpam-5313	35	2	even	even	ADJ
ejpam-5313	35	3	sum	sum	VERB
ejpam-5313	35	4	open	open	ADJ
ejpam-5313	35	5	neighborhood	neighborhood	NOUN
ejpam-5313	35	6	nes(v	nes(v	NOUN
ejpam-5313	35	7	)	)	PUNCT
ejpam-5313	35	8	of	of	ADP
ejpam-5313	35	9	the	the	DET
ejpam-5313	35	10	vertex	vertex	NOUN
ejpam-5313	35	11	v	v	NOUN
ejpam-5313	35	12	is	be	AUX
ejpam-5313	35	13	the	the	DET
ejpam-5313	35	14	set	set	NOUN
ejpam-5313	35	15	of	of	ADP
ejpam-5313	35	16	vertices	vertex	NOUN
ejpam-5313	35	17	which	which	PRON
ejpam-5313	35	18	are	be	AUX
ejpam-5313	35	19	even	even	ADV
ejpam-5313	35	20	sum	sum	NOUN
ejpam-5313	35	21	neighbors	neighbor	NOUN
ejpam-5313	35	22	of	of	ADP
ejpam-5313	35	23	v	v	NOUN
ejpam-5313	35	24	,	,	PUNCT
ejpam-5313	35	25	that	that	PRON
ejpam-5313	35	26	is	be	AUX
ejpam-5313	35	27	nes(v)=	nes(v)=	X
ejpam-5313	35	28	{	{	PUNCT
ejpam-5313	35	29	u	u	NOUN
ejpam-5313	35	30	∈	∈	PROPN
ejpam-5313	35	31	v	v	NOUN
ejpam-5313	35	32	(	(	PUNCT
ejpam-5313	35	33	g):uv	g):uv	X
ejpam-5313	35	34	∈	∈	PROPN
ejpam-5313	35	35	e	e	X
ejpam-5313	35	36	and	and	CCONJ
ejpam-5313	35	37	(	(	PUNCT
ejpam-5313	35	38	deg(u	deg(u	PROPN
ejpam-5313	35	39	)	)	PUNCT
ejpam-5313	35	40	+	+	NUM
ejpam-5313	35	41	deg(v	deg(v	PROPN
ejpam-5313	35	42	)	)	PUNCT
ejpam-5313	35	43	)	)	PUNCT
ejpam-5313	35	44	is	be	AUX
ejpam-5313	35	45	an	an	DET
ejpam-5313	35	46	even	even	ADJ
ejpam-5313	35	47	number	number	NOUN
ejpam-5313	35	48	}	}	PUNCT
ejpam-5313	35	49	.	.	PUNCT
ejpam-5313	36	1	we	we	PRON
ejpam-5313	36	2	say	say	VERB
ejpam-5313	36	3	a	a	DET
ejpam-5313	36	4	vertex	vertex	NOUN
ejpam-5313	36	5	v	v	ADP
ejpam-5313	36	6	∈	∈	NOUN
ejpam-5313	36	7	v	v	NOUN
ejpam-5313	36	8	is	be	AUX
ejpam-5313	36	9	an	an	DET
ejpam-5313	36	10	even	even	ADJ
ejpam-5313	36	11	sum	sum	NOUN
ejpam-5313	36	12	isolate	isolate	NOUN
ejpam-5313	36	13	of	of	ADP
ejpam-5313	36	14	s	s	PRON
ejpam-5313	36	15	if	if	SCONJ
ejpam-5313	36	16	nes(v	nes(v	NOUN
ejpam-5313	36	17	)	)	PUNCT
ejpam-5313	36	18	⊆	⊆	NUM
ejpam-5313	36	19	v	v	ADP
ejpam-5313	36	20	−	−	PROPN
ejpam-5313	36	21	s.	s.	PROPN
ejpam-5313	36	22	the	the	DET
ejpam-5313	36	23	vertex	vertex	NOUN
ejpam-5313	36	24	v	v	NOUN
ejpam-5313	36	25	is	be	AUX
ejpam-5313	36	26	said	say	VERB
ejpam-5313	36	27	to	to	PART
ejpam-5313	36	28	be	be	AUX
ejpam-5313	36	29	an	an	DET
ejpam-5313	36	30	even	even	ADJ
ejpam-5313	36	31	sum	sum	NOUN
ejpam-5313	36	32	isolate	isolate	NOUN
ejpam-5313	36	33	of	of	ADP
ejpam-5313	36	34	v	v	NOUN
ejpam-5313	36	35	if	if	SCONJ
ejpam-5313	36	36	v	v	NOUN
ejpam-5313	36	37	has	have	VERB
ejpam-5313	36	38	no	no	DET
ejpam-5313	36	39	even	even	ADV
ejpam-5313	36	40	sum	sum	NOUN
ejpam-5313	36	41	neighbors	neighbor	NOUN
ejpam-5313	36	42	in	in	ADP
ejpam-5313	36	43	v	v	NUM
ejpam-5313	36	44	,	,	PUNCT
ejpam-5313	36	45	that	that	ADV
ejpam-5313	36	46	is	is	ADV
ejpam-5313	36	47	,	,	PUNCT
ejpam-5313	36	48	there	there	PRON
ejpam-5313	36	49	does	do	AUX
ejpam-5313	36	50	not	not	PART
ejpam-5313	36	51	exist	exist	VERB
ejpam-5313	36	52	the	the	DET
ejpam-5313	36	53	vertex	vertex	NOUN
ejpam-5313	36	54	u	u	NOUN
ejpam-5313	36	55	∈	∈	PROPN
ejpam-5313	36	56	v	v	NOUN
ejpam-5313	36	57	which	which	PRON
ejpam-5313	36	58	is	be	AUX
ejpam-5313	36	59	adjacent	adjacent	ADJ
ejpam-5313	36	60	to	to	ADP
ejpam-5313	36	61	v	v	NOUN
ejpam-5313	36	62	in	in	ADP
ejpam-5313	36	63	such	such	DET
ejpam-5313	36	64	a	a	DET
ejpam-5313	36	65	way	way	NOUN
ejpam-5313	36	66	that	that	PRON
ejpam-5313	36	67	deg(u	deg(u	X
ejpam-5313	36	68	)	)	PUNCT
ejpam-5313	36	69	+	+	NUM
ejpam-5313	36	70	deg(v	deg(v	PROPN
ejpam-5313	36	71	)	)	PUNCT
ejpam-5313	36	72	will	will	AUX
ejpam-5313	36	73	be	be	AUX
ejpam-5313	36	74	s.	s.	PROPN
ejpam-5313	36	75	h	h	PROPN
ejpam-5313	36	76	karkar	karkar	PROPN
ejpam-5313	36	77	et	et	PROPN
ejpam-5313	36	78	al	al	PROPN
ejpam-5313	36	79	.	.	PUNCT
ejpam-5313	36	80	/	/	SYM
ejpam-5313	36	81	eur	eur	PROPN
ejpam-5313	36	82	.	.	PUNCT
ejpam-5313	37	1	j.	j.	PROPN
ejpam-5313	37	2	pure	pure	PROPN
ejpam-5313	37	3	appl	appl	PROPN
ejpam-5313	37	4	.	.	PROPN
ejpam-5313	37	5	math	math	PROPN
ejpam-5313	37	6	,	,	PUNCT
ejpam-5313	37	7	17	17	NUM
ejpam-5313	37	8	(	(	PUNCT
ejpam-5313	37	9	3	3	NUM
ejpam-5313	37	10	)	)	PUNCT
ejpam-5313	37	11	(	(	PUNCT
ejpam-5313	37	12	2024	2024	NUM
ejpam-5313	37	13	)	)	PUNCT
ejpam-5313	37	14	,	,	PUNCT
ejpam-5313	37	15	2084	2084	NUM
ejpam-5313	37	16	-	-	SYM
ejpam-5313	37	17	2091	2091	NUM
ejpam-5313	37	18	2086	2086	NUM
ejpam-5313	37	19	an	an	DET
ejpam-5313	37	20	even	even	ADJ
ejpam-5313	37	21	number	number	NOUN
ejpam-5313	37	22	.	.	PUNCT
ejpam-5313	38	1	for	for	ADP
ejpam-5313	38	2	the	the	DET
ejpam-5313	38	3	graph	graph	NOUN
ejpam-5313	38	4	g	g	NOUN
ejpam-5313	38	5	given	give	VERB
ejpam-5313	38	6	in	in	ADP
ejpam-5313	38	7	figure	figure	NOUN
ejpam-5313	38	8	1	1	NUM
ejpam-5313	38	9	,	,	PUNCT
ejpam-5313	38	10	the	the	DET
ejpam-5313	38	11	vertices	vertex	NOUN
ejpam-5313	38	12	v1	v1	NOUN
ejpam-5313	38	13	,	,	PUNCT
ejpam-5313	38	14	v3	v3	PROPN
ejpam-5313	38	15	and	and	CCONJ
ejpam-5313	38	16	v6	v6	NOUN
ejpam-5313	38	17	are	be	AUX
ejpam-5313	38	18	even	even	ADV
ejpam-5313	38	19	sum	sum	NOUN
ejpam-5313	38	20	isolates	isolate	NOUN
ejpam-5313	38	21	of	of	ADP
ejpam-5313	38	22	s	s	PRON
ejpam-5313	38	23	while	while	SCONJ
ejpam-5313	38	24	the	the	DET
ejpam-5313	38	25	vertex	vertex	NOUN
ejpam-5313	38	26	v4	v4	NOUN
ejpam-5313	38	27	is	be	AUX
ejpam-5313	38	28	an	an	DET
ejpam-5313	38	29	even	even	ADJ
ejpam-5313	38	30	sum	sum	NOUN
ejpam-5313	38	31	isolate	isolate	NOUN
ejpam-5313	38	32	of	of	ADP
ejpam-5313	38	33	v	v	NOUN
ejpam-5313	38	34	.	.	PUNCT
ejpam-5313	39	1	theorem	theorem	NOUN
ejpam-5313	39	2	1	1	NUM
ejpam-5313	39	3	.	.	PUNCT
ejpam-5313	40	1	an	an	DET
ejpam-5313	40	2	even	even	ADV
ejpam-5313	40	3	sum	sum	NOUN
ejpam-5313	40	4	dominating	dominating	NOUN
ejpam-5313	40	5	set	set	NOUN
ejpam-5313	40	6	s	s	VERB
ejpam-5313	40	7	is	be	AUX
ejpam-5313	40	8	a	a	DET
ejpam-5313	40	9	minimal	minimal	ADJ
ejpam-5313	40	10	even	even	ADV
ejpam-5313	40	11	sum	sum	NOUN
ejpam-5313	40	12	dominating	dominating	NOUN
ejpam-5313	40	13	set	set	VERB
ejpam-5313	40	14	if	if	SCONJ
ejpam-5313	40	15	and	and	CCONJ
ejpam-5313	40	16	only	only	ADV
ejpam-5313	40	17	if	if	SCONJ
ejpam-5313	40	18	for	for	ADP
ejpam-5313	40	19	every	every	DET
ejpam-5313	40	20	u	u	PROPN
ejpam-5313	40	21	∈	∈	PROPN
ejpam-5313	40	22	s	s	PROPN
ejpam-5313	40	23	,	,	PUNCT
ejpam-5313	40	24	one	one	NUM
ejpam-5313	40	25	of	of	ADP
ejpam-5313	40	26	the	the	DET
ejpam-5313	40	27	following	follow	VERB
ejpam-5313	40	28	condition	condition	NOUN
ejpam-5313	40	29	holds	hold	VERB
ejpam-5313	40	30	.	.	PUNCT
ejpam-5313	41	1	(	(	PUNCT
ejpam-5313	41	2	a	a	X
ejpam-5313	41	3	)	)	PUNCT
ejpam-5313	41	4	no	no	DET
ejpam-5313	41	5	vertex	vertex	NOUN
ejpam-5313	41	6	in	in	ADP
ejpam-5313	41	7	s	s	PRON
ejpam-5313	41	8	even	even	ADV
ejpam-5313	41	9	sum	sum	NOUN
ejpam-5313	41	10	dominates	dominate	VERB
ejpam-5313	41	11	u.	u.	NOUN
ejpam-5313	41	12	(	(	PUNCT
ejpam-5313	41	13	b	b	X
ejpam-5313	41	14	)	)	PUNCT
ejpam-5313	41	15	there	there	PRON
ejpam-5313	41	16	exists	exist	VERB
ejpam-5313	41	17	a	a	DET
ejpam-5313	41	18	vertex	vertex	NOUN
ejpam-5313	41	19	v	v	ADP
ejpam-5313	41	20	∈	∈	NOUN
ejpam-5313	41	21	v	v	ADP
ejpam-5313	41	22	−	−	PROPN
ejpam-5313	41	23	s	s	NOUN
ejpam-5313	41	24	for	for	ADP
ejpam-5313	41	25	which	which	PRON
ejpam-5313	41	26	nes(v	nes(v	PROPN
ejpam-5313	41	27	)	)	PUNCT
ejpam-5313	41	28	∩	∩	NOUN
ejpam-5313	41	29	s	s	PART
ejpam-5313	41	30	=	=	PUNCT
ejpam-5313	41	31	{	{	PUNCT
ejpam-5313	41	32	u	u	NOUN
ejpam-5313	41	33	}	}	PUNCT
ejpam-5313	41	34	.	.	PUNCT
ejpam-5313	42	1	proof	proof	NOUN
ejpam-5313	42	2	.	.	PUNCT
ejpam-5313	43	1	assume	assume	VERB
ejpam-5313	43	2	that	that	SCONJ
ejpam-5313	43	3	s	s	VERB
ejpam-5313	43	4	is	be	AUX
ejpam-5313	43	5	a	a	DET
ejpam-5313	43	6	minimal	minimal	ADJ
ejpam-5313	43	7	even	even	ADV
ejpam-5313	43	8	sum	sum	NOUN
ejpam-5313	43	9	dominating	dominating	NOUN
ejpam-5313	43	10	set	set	NOUN
ejpam-5313	43	11	of	of	ADP
ejpam-5313	43	12	g.	g.	PROPN
ejpam-5313	43	13	then	then	ADV
ejpam-5313	43	14	for	for	ADP
ejpam-5313	43	15	every	every	DET
ejpam-5313	43	16	vertex	vertex	NOUN
ejpam-5313	43	17	u	u	NOUN
ejpam-5313	43	18	∈	∈	PROPN
ejpam-5313	43	19	s	s	PROPN
ejpam-5313	43	20	,	,	PUNCT
ejpam-5313	43	21	s	s	PART
ejpam-5313	43	22	−	−	PROPN
ejpam-5313	43	23	{	{	PUNCT
ejpam-5313	43	24	u	u	NOUN
ejpam-5313	43	25	}	}	PUNCT
ejpam-5313	43	26	is	be	AUX
ejpam-5313	43	27	not	not	PART
ejpam-5313	43	28	an	an	DET
ejpam-5313	43	29	even	even	ADV
ejpam-5313	43	30	sum	sum	NOUN
ejpam-5313	43	31	dominating	dominating	NOUN
ejpam-5313	43	32	set	set	NOUN
ejpam-5313	43	33	.	.	PUNCT
ejpam-5313	44	1	this	this	PRON
ejpam-5313	44	2	means	mean	VERB
ejpam-5313	44	3	there	there	PRON
ejpam-5313	44	4	is	be	VERB
ejpam-5313	44	5	a	a	DET
ejpam-5313	44	6	vertex	vertex	NOUN
ejpam-5313	44	7	v	v	NOUN
ejpam-5313	44	8	in	in	ADP
ejpam-5313	44	9	v	v	ADP
ejpam-5313	44	10	−	−	PROPN
ejpam-5313	44	11	s	s	NOUN
ejpam-5313	44	12	∪	∪	X
ejpam-5313	44	13	{	{	PUNCT
ejpam-5313	44	14	u	u	NOUN
ejpam-5313	44	15	}	}	PUNCT
ejpam-5313	44	16	is	be	AUX
ejpam-5313	44	17	not	not	PART
ejpam-5313	44	18	even	even	ADV
ejpam-5313	44	19	sum	sum	NOUN
ejpam-5313	44	20	dominated	dominate	VERB
ejpam-5313	44	21	by	by	ADP
ejpam-5313	44	22	any	any	DET
ejpam-5313	44	23	vertex	vertex	NOUN
ejpam-5313	44	24	of	of	ADP
ejpam-5313	44	25	s	s	PRON
ejpam-5313	44	26	−	−	PROPN
ejpam-5313	44	27	{	{	PUNCT
ejpam-5313	44	28	u	u	NOUN
ejpam-5313	44	29	}	}	PUNCT
ejpam-5313	44	30	.	.	PUNCT
ejpam-5313	45	1	now	now	ADV
ejpam-5313	45	2	either	either	CCONJ
ejpam-5313	45	3	u	u	PROPN
ejpam-5313	45	4	=	=	PROPN
ejpam-5313	45	5	v	v	NOUN
ejpam-5313	45	6	,	,	PUNCT
ejpam-5313	45	7	in	in	ADP
ejpam-5313	45	8	which	which	DET
ejpam-5313	45	9	case	case	NOUN
ejpam-5313	45	10	u	u	NOUN
ejpam-5313	45	11	is	be	AUX
ejpam-5313	45	12	not	not	PART
ejpam-5313	45	13	even	even	ADV
ejpam-5313	45	14	sum	sum	NOUN
ejpam-5313	45	15	dominated	dominate	VERB
ejpam-5313	45	16	by	by	ADP
ejpam-5313	45	17	any	any	DET
ejpam-5313	45	18	vertex	vertex	NOUN
ejpam-5313	45	19	of	of	ADP
ejpam-5313	45	20	s	s	PRON
ejpam-5313	45	21	other	other	ADJ
ejpam-5313	45	22	than	than	ADP
ejpam-5313	45	23	u	u	PROPN
ejpam-5313	45	24	,	,	PUNCT
ejpam-5313	45	25	or	or	CCONJ
ejpam-5313	45	26	v	v	ADP
ejpam-5313	45	27	∈	∈	NOUN
ejpam-5313	45	28	v	v	ADP
ejpam-5313	45	29	−	−	PROPN
ejpam-5313	45	30	s.	s.	PROPN
ejpam-5313	45	31	if	if	SCONJ
ejpam-5313	45	32	v	v	NOUN
ejpam-5313	45	33	is	be	AUX
ejpam-5313	45	34	not	not	PART
ejpam-5313	45	35	even	even	ADV
ejpam-5313	45	36	sum	sum	NOUN
ejpam-5313	45	37	dominated	dominate	VERB
ejpam-5313	45	38	by	by	ADP
ejpam-5313	45	39	any	any	DET
ejpam-5313	45	40	vertex	vertex	NOUN
ejpam-5313	45	41	of	of	ADP
ejpam-5313	45	42	s	s	PRON
ejpam-5313	45	43	−{u	−{u	NOUN
ejpam-5313	45	44	}	}	PUNCT
ejpam-5313	45	45	but	but	CCONJ
ejpam-5313	45	46	even	even	ADV
ejpam-5313	45	47	sum	sum	NOUN
ejpam-5313	45	48	dominated	dominate	VERB
ejpam-5313	45	49	by	by	ADP
ejpam-5313	45	50	any	any	DET
ejpam-5313	45	51	vertex	vertex	NOUN
ejpam-5313	45	52	of	of	ADP
ejpam-5313	45	53	s	s	PROPN
ejpam-5313	45	54	,	,	PUNCT
ejpam-5313	45	55	then	then	ADV
ejpam-5313	45	56	vertex	vertex	NOUN
ejpam-5313	45	57	v	v	NOUN
ejpam-5313	45	58	has	have	VERB
ejpam-5313	45	59	only	only	ADV
ejpam-5313	45	60	one	one	NUM
ejpam-5313	45	61	even	even	ADV
ejpam-5313	45	62	sum	sum	VERB
ejpam-5313	45	63	neighbor	neighbor	NOUN
ejpam-5313	45	64	u	u	PROPN
ejpam-5313	45	65	in	in	ADP
ejpam-5313	45	66	s	s	PROPN
ejpam-5313	45	67	,	,	PUNCT
ejpam-5313	45	68	that	that	PRON
ejpam-5313	45	69	is	be	AUX
ejpam-5313	45	70	nes(v)∩s	nes(v)∩s	NOUN
ejpam-5313	45	71	=	=	SYM
ejpam-5313	45	72	{	{	PUNCT
ejpam-5313	45	73	u	u	NOUN
ejpam-5313	45	74	}	}	PUNCT
ejpam-5313	45	75	.	.	PUNCT
ejpam-5313	46	1	conversely	conversely	ADV
ejpam-5313	46	2	,	,	PUNCT
ejpam-5313	46	3	suppose	suppose	VERB
ejpam-5313	46	4	that	that	SCONJ
ejpam-5313	46	5	s	s	VERB
ejpam-5313	46	6	is	be	AUX
ejpam-5313	46	7	an	an	DET
ejpam-5313	46	8	even	even	ADV
ejpam-5313	46	9	sum	sum	NOUN
ejpam-5313	46	10	dominating	dominating	NOUN
ejpam-5313	46	11	set	set	NOUN
ejpam-5313	46	12	and	and	CCONJ
ejpam-5313	46	13	for	for	ADP
ejpam-5313	46	14	every	every	DET
ejpam-5313	46	15	u	u	PROPN
ejpam-5313	46	16	∈	∈	PROPN
ejpam-5313	46	17	s	s	PROPN
ejpam-5313	46	18	,	,	PUNCT
ejpam-5313	46	19	one	one	NUM
ejpam-5313	46	20	of	of	ADP
ejpam-5313	46	21	the	the	DET
ejpam-5313	46	22	two	two	NUM
ejpam-5313	46	23	axioms	axiom	NOUN
ejpam-5313	46	24	holds	hold	VERB
ejpam-5313	46	25	.	.	PUNCT
ejpam-5313	47	1	we	we	PRON
ejpam-5313	47	2	will	will	AUX
ejpam-5313	47	3	try	try	VERB
ejpam-5313	47	4	to	to	PART
ejpam-5313	47	5	prove	prove	VERB
ejpam-5313	47	6	that	that	SCONJ
ejpam-5313	47	7	s	s	VERB
ejpam-5313	47	8	is	be	AUX
ejpam-5313	47	9	an	an	DET
ejpam-5313	47	10	minimal	minimal	ADJ
ejpam-5313	47	11	even	even	ADV
ejpam-5313	47	12	sum	sum	NOUN
ejpam-5313	47	13	dominating	dominating	NOUN
ejpam-5313	47	14	set	set	NOUN
ejpam-5313	47	15	.	.	PUNCT
ejpam-5313	48	1	suppose	suppose	VERB
ejpam-5313	48	2	that	that	SCONJ
ejpam-5313	48	3	s	s	VERB
ejpam-5313	48	4	is	be	AUX
ejpam-5313	48	5	not	not	PART
ejpam-5313	48	6	a	a	DET
ejpam-5313	48	7	minimal	minimal	ADJ
ejpam-5313	48	8	even	even	ADV
ejpam-5313	48	9	sum	sum	NOUN
ejpam-5313	48	10	dominating	dominating	NOUN
ejpam-5313	48	11	set	set	NOUN
ejpam-5313	48	12	,	,	PUNCT
ejpam-5313	48	13	that	that	ADV
ejpam-5313	48	14	is	is	ADV
ejpam-5313	48	15	,	,	PUNCT
ejpam-5313	48	16	there	there	PRON
ejpam-5313	48	17	is	be	VERB
ejpam-5313	48	18	at	at	ADV
ejpam-5313	48	19	least	least	ADJ
ejpam-5313	48	20	one	one	NUM
ejpam-5313	48	21	vertex	vertex	NOUN
ejpam-5313	48	22	u	u	NOUN
ejpam-5313	48	23	∈	∈	NOUN
ejpam-5313	48	24	s	s	VERB
ejpam-5313	48	25	such	such	ADJ
ejpam-5313	48	26	that	that	PRON
ejpam-5313	48	27	s	s	PART
ejpam-5313	48	28	−	−	PROPN
ejpam-5313	48	29	{	{	PUNCT
ejpam-5313	48	30	u	u	NOUN
ejpam-5313	48	31	}	}	PUNCT
ejpam-5313	48	32	is	be	AUX
ejpam-5313	48	33	an	an	DET
ejpam-5313	48	34	even	even	ADV
ejpam-5313	48	35	sum	sum	NOUN
ejpam-5313	48	36	dominating	dominating	NOUN
ejpam-5313	48	37	set	set	NOUN
ejpam-5313	48	38	.	.	PUNCT
ejpam-5313	49	1	hence	hence	ADV
ejpam-5313	49	2	,	,	PUNCT
ejpam-5313	49	3	u	u	PROPN
ejpam-5313	49	4	is	be	AUX
ejpam-5313	49	5	even	even	ADV
ejpam-5313	49	6	sum	sum	NOUN
ejpam-5313	49	7	dominated	dominate	VERB
ejpam-5313	49	8	by	by	ADP
ejpam-5313	49	9	at	at	ADV
ejpam-5313	49	10	least	least	ADV
ejpam-5313	49	11	one	one	NUM
ejpam-5313	49	12	vertex	vertex	NOUN
ejpam-5313	49	13	in	in	ADP
ejpam-5313	49	14	s−{u	s−{u	PROPN
ejpam-5313	49	15	}	}	PUNCT
ejpam-5313	49	16	,	,	PUNCT
ejpam-5313	49	17	that	that	ADV
ejpam-5313	49	18	is	is	ADV
ejpam-5313	49	19	,	,	PUNCT
ejpam-5313	49	20	there	there	PRON
ejpam-5313	49	21	exists	exist	VERB
ejpam-5313	49	22	a	a	DET
ejpam-5313	49	23	vertex	vertex	NOUN
ejpam-5313	49	24	w	w	PROPN
ejpam-5313	49	25	∈	∈	PROPN
ejpam-5313	49	26	s−{u	s−{u	PROPN
ejpam-5313	49	27	}	}	PUNCT
ejpam-5313	49	28	which	which	DET
ejpam-5313	49	29	even	even	ADV
ejpam-5313	49	30	sum	sum	NOUN
ejpam-5313	49	31	dominates	dominate	VERB
ejpam-5313	49	32	u.	u.	NOUN
ejpam-5313	49	33	hence	hence	ADV
ejpam-5313	49	34	,	,	PUNCT
ejpam-5313	49	35	axiom	axiom	NOUN
ejpam-5313	49	36	(	(	PUNCT
ejpam-5313	49	37	a	a	X
ejpam-5313	49	38	)	)	PUNCT
ejpam-5313	49	39	does	do	AUX
ejpam-5313	49	40	not	not	PART
ejpam-5313	49	41	hold	hold	VERB
ejpam-5313	49	42	.	.	PUNCT
ejpam-5313	50	1	also	also	ADV
ejpam-5313	50	2	if	if	SCONJ
ejpam-5313	50	3	s	s	PRON
ejpam-5313	50	4	−	−	PROPN
ejpam-5313	50	5	{	{	PUNCT
ejpam-5313	50	6	u	u	NOUN
ejpam-5313	50	7	}	}	PUNCT
ejpam-5313	50	8	is	be	AUX
ejpam-5313	50	9	a	a	DET
ejpam-5313	50	10	dominating	dominating	NOUN
ejpam-5313	50	11	set	set	NOUN
ejpam-5313	50	12	then	then	ADV
ejpam-5313	50	13	every	every	DET
ejpam-5313	50	14	vertex	vertex	NOUN
ejpam-5313	50	15	in	in	ADP
ejpam-5313	50	16	v	v	NOUN
ejpam-5313	50	17	−	−	PROPN
ejpam-5313	50	18	s	s	PART
ejpam-5313	50	19	is	be	AUX
ejpam-5313	50	20	even	even	ADV
ejpam-5313	50	21	sum	sum	NOUN
ejpam-5313	50	22	dominated	dominate	VERB
ejpam-5313	50	23	by	by	ADP
ejpam-5313	50	24	some	some	DET
ejpam-5313	50	25	vertex	vertex	NOUN
ejpam-5313	50	26	of	of	ADP
ejpam-5313	50	27	s	s	PRON
ejpam-5313	50	28	−	−	PROPN
ejpam-5313	50	29	{	{	PUNCT
ejpam-5313	50	30	u	u	NOUN
ejpam-5313	50	31	}	}	PUNCT
ejpam-5313	50	32	,	,	PUNCT
ejpam-5313	50	33	that	that	ADV
ejpam-5313	50	34	is	is	ADV
ejpam-5313	50	35	,	,	PUNCT
ejpam-5313	50	36	there	there	PRON
ejpam-5313	50	37	exists	exist	VERB
ejpam-5313	50	38	an	an	DET
ejpam-5313	50	39	another	another	DET
ejpam-5313	50	40	vertex	vertex	NOUN
ejpam-5313	50	41	x	x	PUNCT
ejpam-5313	50	42	in	in	ADP
ejpam-5313	50	43	s	s	PRON
ejpam-5313	50	44	such	such	ADJ
ejpam-5313	50	45	that	that	SCONJ
ejpam-5313	50	46	x	x	SYM
ejpam-5313	50	47	∈	∈	PROPN
ejpam-5313	50	48	nes(v	nes(v	PROPN
ejpam-5313	50	49	)	)	PUNCT
ejpam-5313	50	50	for	for	ADP
ejpam-5313	50	51	some	some	DET
ejpam-5313	50	52	v	v	NUM
ejpam-5313	50	53	∈	∈	PROPN
ejpam-5313	50	54	v	v	NOUN
ejpam-5313	50	55	−s	−s	NOUN
ejpam-5313	50	56	and	and	CCONJ
ejpam-5313	50	57	x	x	PUNCT
ejpam-5313	50	58	̸=	̸=	PROPN
ejpam-5313	50	59	u.	u.	NOUN
ejpam-5313	50	60	hence	hence	ADV
ejpam-5313	50	61	,	,	PUNCT
ejpam-5313	50	62	axiom	axiom	NOUN
ejpam-5313	50	63	(	(	PUNCT
ejpam-5313	50	64	b	b	NOUN
ejpam-5313	50	65	)	)	PUNCT
ejpam-5313	50	66	does	do	AUX
ejpam-5313	50	67	not	not	PART
ejpam-5313	50	68	hold	hold	VERB
ejpam-5313	50	69	.	.	PUNCT
ejpam-5313	51	1	so	so	ADV
ejpam-5313	51	2	neither	neither	DET
ejpam-5313	51	3	axiom	axiom	NOUN
ejpam-5313	51	4	(	(	PUNCT
ejpam-5313	51	5	a	a	NOUN
ejpam-5313	51	6	)	)	PUNCT
ejpam-5313	51	7	nor	nor	CCONJ
ejpam-5313	51	8	(	(	PUNCT
ejpam-5313	51	9	b	b	X
ejpam-5313	51	10	)	)	PUNCT
ejpam-5313	51	11	holds	hold	VERB
ejpam-5313	51	12	that	that	PRON
ejpam-5313	51	13	contradicts	contradict	VERB
ejpam-5313	51	14	our	our	PRON
ejpam-5313	51	15	assumption	assumption	NOUN
ejpam-5313	51	16	that	that	SCONJ
ejpam-5313	51	17	one	one	NUM
ejpam-5313	51	18	of	of	ADP
ejpam-5313	51	19	these	these	DET
ejpam-5313	51	20	two	two	NUM
ejpam-5313	51	21	axioms	axiom	NOUN
ejpam-5313	51	22	holds	hold	NOUN
ejpam-5313	51	23	.	.	PUNCT
ejpam-5313	52	1	theorem	theorem	NOUN
ejpam-5313	52	2	2	2	NUM
ejpam-5313	52	3	.	.	PUNCT
ejpam-5313	53	1	if	if	SCONJ
ejpam-5313	53	2	there	there	PRON
ejpam-5313	53	3	exists	exist	VERB
ejpam-5313	53	4	any	any	DET
ejpam-5313	53	5	isolate	isolate	NOUN
ejpam-5313	53	6	of	of	ADP
ejpam-5313	53	7	v	v	NOUN
ejpam-5313	53	8	in	in	ADP
ejpam-5313	53	9	g	g	PROPN
ejpam-5313	53	10	then	then	ADV
ejpam-5313	53	11	it	it	PRON
ejpam-5313	53	12	must	must	AUX
ejpam-5313	53	13	be	be	AUX
ejpam-5313	53	14	in	in	ADP
ejpam-5313	53	15	every	every	DET
ejpam-5313	53	16	minimal	minimal	ADJ
ejpam-5313	53	17	even	even	ADV
ejpam-5313	53	18	sum	sum	NOUN
ejpam-5313	53	19	dominating	dominating	NOUN
ejpam-5313	53	20	set	set	NOUN
ejpam-5313	53	21	of	of	ADP
ejpam-5313	53	22	g.	g.	PROPN
ejpam-5313	53	23	proof	proof	PROPN
ejpam-5313	53	24	.	.	PUNCT
ejpam-5313	54	1	as	as	ADP
ejpam-5313	54	2	per	per	ADP
ejpam-5313	54	3	the	the	DET
ejpam-5313	54	4	definition	definition	NOUN
ejpam-5313	54	5	an	an	DET
ejpam-5313	54	6	even	even	ADJ
ejpam-5313	54	7	sum	sum	NOUN
ejpam-5313	54	8	isolate	isolate	NOUN
ejpam-5313	54	9	of	of	ADP
ejpam-5313	54	10	v	v	NOUN
ejpam-5313	54	11	,	,	PUNCT
ejpam-5313	54	12	the	the	DET
ejpam-5313	54	13	vertex	vertex	NOUN
ejpam-5313	54	14	v	v	NOUN
ejpam-5313	54	15	is	be	AUX
ejpam-5313	54	16	not	not	PART
ejpam-5313	54	17	even	even	ADV
ejpam-5313	54	18	sum	sum	NOUN
ejpam-5313	54	19	dominated	dominate	VERB
ejpam-5313	54	20	by	by	ADP
ejpam-5313	54	21	any	any	DET
ejpam-5313	54	22	vertex	vertex	NOUN
ejpam-5313	54	23	of	of	ADP
ejpam-5313	54	24	v	v	NOUN
ejpam-5313	54	25	other	other	ADJ
ejpam-5313	54	26	than	than	ADP
ejpam-5313	54	27	itself	itself	PRON
ejpam-5313	54	28	.	.	PUNCT
ejpam-5313	55	1	hence	hence	ADV
ejpam-5313	55	2	,	,	PUNCT
ejpam-5313	55	3	it	it	PRON
ejpam-5313	55	4	must	must	AUX
ejpam-5313	55	5	be	be	AUX
ejpam-5313	55	6	in	in	ADP
ejpam-5313	55	7	every	every	DET
ejpam-5313	55	8	minimal	minimal	ADJ
ejpam-5313	55	9	even	even	ADV
ejpam-5313	55	10	sum	sum	NOUN
ejpam-5313	55	11	dominating	dominating	NOUN
ejpam-5313	55	12	set	set	NOUN
ejpam-5313	55	13	of	of	ADP
ejpam-5313	55	14	g.	g.	PROPN
ejpam-5313	55	15	theorem	theorem	VERB
ejpam-5313	55	16	3.([6	3.([6	NUM
ejpam-5313	55	17	]	]	PUNCT
ejpam-5313	55	18	)	)	PUNCT
ejpam-5313	55	19	.	.	PUNCT
ejpam-5313	56	1	every	every	DET
ejpam-5313	56	2	connected	connect	VERB
ejpam-5313	56	3	graph	graph	NOUN
ejpam-5313	56	4	g	g	NOUN
ejpam-5313	56	5	of	of	ADP
ejpam-5313	56	6	order	order	NOUN
ejpam-5313	56	7	n	n	PRON
ejpam-5313	56	8	≥	≥	NOUN
ejpam-5313	56	9	2	2	NUM
ejpam-5313	56	10	has	have	VERB
ejpam-5313	56	11	a	a	DET
ejpam-5313	56	12	dominating	dominating	NOUN
ejpam-5313	56	13	set	set	NOUN
ejpam-5313	56	14	s	s	VERB
ejpam-5313	56	15	whose	whose	DET
ejpam-5313	56	16	complement	complement	NOUN
ejpam-5313	56	17	v	v	ADP
ejpam-5313	56	18	−	−	PROPN
ejpam-5313	56	19	s	s	PART
ejpam-5313	56	20	is	be	AUX
ejpam-5313	56	21	also	also	ADV
ejpam-5313	56	22	a	a	DET
ejpam-5313	56	23	dominating	dominating	NOUN
ejpam-5313	56	24	set	set	NOUN
ejpam-5313	56	25	.	.	PUNCT
ejpam-5313	57	1	for	for	ADP
ejpam-5313	57	2	even	even	ADV
ejpam-5313	57	3	sum	sum	NOUN
ejpam-5313	57	4	dominating	dominating	NOUN
ejpam-5313	57	5	set	set	NOUN
ejpam-5313	57	6	there	there	PRON
ejpam-5313	57	7	may	may	AUX
ejpam-5313	57	8	not	not	PART
ejpam-5313	57	9	exist	exist	VERB
ejpam-5313	57	10	an	an	DET
ejpam-5313	57	11	even	even	ADJ
ejpam-5313	57	12	sum	sum	NOUN
ejpam-5313	57	13	dominating	dominating	NOUN
ejpam-5313	57	14	set	set	NOUN
ejpam-5313	57	15	s	s	VERB
ejpam-5313	57	16	whose	whose	DET
ejpam-5313	57	17	complement	complement	NOUN
ejpam-5313	57	18	v	v	ADP
ejpam-5313	57	19	−	−	PROPN
ejpam-5313	57	20	s	s	PART
ejpam-5313	57	21	is	be	AUX
ejpam-5313	57	22	an	an	DET
ejpam-5313	57	23	even	even	ADV
ejpam-5313	57	24	sum	sum	NOUN
ejpam-5313	57	25	dominating	dominating	NOUN
ejpam-5313	57	26	set	set	NOUN
ejpam-5313	57	27	.	.	PUNCT
ejpam-5313	58	1	for	for	ADP
ejpam-5313	58	2	graph	graph	NOUN
ejpam-5313	58	3	g	g	NOUN
ejpam-5313	58	4	,	,	PUNCT
ejpam-5313	58	5	given	give	VERB
ejpam-5313	58	6	in	in	ADP
ejpam-5313	58	7	figure	figure	NOUN
ejpam-5313	58	8	1	1	NUM
ejpam-5313	58	9	,	,	PUNCT
ejpam-5313	58	10	s	s	PART
ejpam-5313	58	11	=	=	NOUN
ejpam-5313	58	12	{	{	PUNCT
ejpam-5313	58	13	v1	v1	PROPN
ejpam-5313	58	14	,	,	PUNCT
ejpam-5313	58	15	v3	v3	PROPN
ejpam-5313	58	16	,	,	PUNCT
ejpam-5313	58	17	v4	v4	PROPN
ejpam-5313	58	18	,	,	PUNCT
ejpam-5313	58	19	v6	v6	NOUN
ejpam-5313	58	20	}	}	PUNCT
ejpam-5313	58	21	while	while	SCONJ
ejpam-5313	58	22	v	v	ADP
ejpam-5313	58	23	−	−	PROPN
ejpam-5313	58	24	s	s	PART
ejpam-5313	58	25	=	=	PUNCT
ejpam-5313	58	26	{	{	PUNCT
ejpam-5313	58	27	v2	v2	PROPN
ejpam-5313	58	28	,	,	PUNCT
ejpam-5313	58	29	v5	v5	NOUN
ejpam-5313	58	30	,	,	PUNCT
ejpam-5313	58	31	v7	v7	NOUN
ejpam-5313	58	32	}	}	PUNCT
ejpam-5313	58	33	is	be	AUX
ejpam-5313	58	34	not	not	PART
ejpam-5313	58	35	an	an	DET
ejpam-5313	58	36	even	even	ADV
ejpam-5313	58	37	sum	sum	NOUN
ejpam-5313	58	38	dominating	dominating	NOUN
ejpam-5313	58	39	set	set	NOUN
ejpam-5313	58	40	.	.	PUNCT
ejpam-5313	59	1	theorem	theorem	VERB
ejpam-5313	59	2	4	4	NUM
ejpam-5313	59	3	.	.	PUNCT
ejpam-5313	60	1	let	let	VERB
ejpam-5313	60	2	g	g	PRON
ejpam-5313	60	3	be	be	AUX
ejpam-5313	60	4	a	a	DET
ejpam-5313	60	5	connected	connected	ADJ
ejpam-5313	60	6	graph	graph	NOUN
ejpam-5313	60	7	with	with	ADP
ejpam-5313	60	8	even	even	ADV
ejpam-5313	60	9	sum	sum	VERB
ejpam-5313	60	10	dominating	dominating	NOUN
ejpam-5313	60	11	set	set	VERB
ejpam-5313	60	12	s.	s.	PROPN
ejpam-5313	60	13	if	if	SCONJ
ejpam-5313	60	14	g	g	PROPN
ejpam-5313	60	15	has	have	VERB
ejpam-5313	60	16	no	no	DET
ejpam-5313	60	17	isolate	isolate	NOUN
ejpam-5313	60	18	of	of	ADP
ejpam-5313	60	19	s	s	NOUN
ejpam-5313	60	20	and	and	CCONJ
ejpam-5313	60	21	v	v	NOUN
ejpam-5313	60	22	then	then	ADV
ejpam-5313	60	23	v	v	ADP
ejpam-5313	60	24	−	−	PROPN
ejpam-5313	60	25	s	s	NOUN
ejpam-5313	60	26	of	of	ADP
ejpam-5313	60	27	every	every	DET
ejpam-5313	60	28	minimal	minimal	ADJ
ejpam-5313	60	29	even	even	ADV
ejpam-5313	60	30	sum	sum	NOUN
ejpam-5313	60	31	dominating	dominating	NOUN
ejpam-5313	60	32	set	set	NOUN
ejpam-5313	60	33	s	s	VERB
ejpam-5313	60	34	is	be	AUX
ejpam-5313	60	35	an	an	DET
ejpam-5313	60	36	even	even	ADV
ejpam-5313	60	37	sum	sum	NOUN
ejpam-5313	60	38	dominating	dominating	NOUN
ejpam-5313	60	39	set	set	NOUN
ejpam-5313	60	40	.	.	PUNCT
ejpam-5313	61	1	proof	proof	NOUN
ejpam-5313	61	2	.	.	PUNCT
ejpam-5313	62	1	as	as	SCONJ
ejpam-5313	62	2	s	s	AUX
ejpam-5313	62	3	being	be	AUX
ejpam-5313	62	4	any	any	DET
ejpam-5313	62	5	minimal	minimal	ADJ
ejpam-5313	62	6	even	even	ADV
ejpam-5313	62	7	sum	sum	NOUN
ejpam-5313	62	8	dominating	dominating	NOUN
ejpam-5313	62	9	set	set	NOUN
ejpam-5313	62	10	of	of	ADP
ejpam-5313	62	11	g	g	NOUN
ejpam-5313	62	12	,	,	PUNCT
ejpam-5313	62	13	every	every	DET
ejpam-5313	62	14	vertex	vertex	NOUN
ejpam-5313	62	15	v	v	ADP
ejpam-5313	62	16	∈	∈	NOUN
ejpam-5313	62	17	v	v	ADP
ejpam-5313	62	18	−	−	PROPN
ejpam-5313	62	19	s	s	PART
ejpam-5313	62	20	is	be	AUX
ejpam-5313	62	21	even	even	ADV
ejpam-5313	62	22	sum	sum	NOUN
ejpam-5313	62	23	dominated	dominate	VERB
ejpam-5313	62	24	by	by	ADP
ejpam-5313	62	25	atleast	atleast	ADJ
ejpam-5313	62	26	one	one	NUM
ejpam-5313	62	27	vertex	vertex	NOUN
ejpam-5313	62	28	of	of	ADP
ejpam-5313	62	29	s.	s.	PROPN
ejpam-5313	62	30	so	so	ADV
ejpam-5313	62	31	,	,	PUNCT
ejpam-5313	62	32	by	by	ADP
ejpam-5313	62	33	the	the	DET
ejpam-5313	62	34	definition	definition	NOUN
ejpam-5313	62	35	of	of	ADP
ejpam-5313	62	36	even	even	ADV
ejpam-5313	62	37	sum	sum	PROPN
ejpam-5313	62	38	domination	domination	NOUN
ejpam-5313	62	39	,	,	PUNCT
ejpam-5313	62	40	∀v	∀v	PROPN
ejpam-5313	62	41	∈	∈	PROPN
ejpam-5313	62	42	v	v	ADP
ejpam-5313	62	43	−	−	PROPN
ejpam-5313	62	44	s	s	NOUN
ejpam-5313	62	45	can	can	AUX
ejpam-5313	62	46	also	also	ADV
ejpam-5313	62	47	even	even	ADV
ejpam-5313	62	48	sum	sum	VERB
ejpam-5313	62	49	dominate	dominate	VERB
ejpam-5313	62	50	some	some	DET
ejpam-5313	62	51	u	u	NOUN
ejpam-5313	62	52	∈	∈	PROPN
ejpam-5313	62	53	s.	s.	PROPN
ejpam-5313	62	54	assume	assume	VERB
ejpam-5313	62	55	that	that	SCONJ
ejpam-5313	62	56	v	v	ADP
ejpam-5313	62	57	−	−	PROPN
ejpam-5313	62	58	s	s	PART
ejpam-5313	62	59	is	be	AUX
ejpam-5313	62	60	not	not	PART
ejpam-5313	62	61	an	an	DET
ejpam-5313	62	62	even	even	ADV
ejpam-5313	62	63	sum	sum	NOUN
ejpam-5313	62	64	dominating	dominating	NOUN
ejpam-5313	62	65	set	set	NOUN
ejpam-5313	62	66	.	.	PUNCT
ejpam-5313	63	1	therefore	therefore	ADV
ejpam-5313	63	2	,	,	PUNCT
ejpam-5313	63	3	there	there	PRON
ejpam-5313	63	4	exists	exist	VERB
ejpam-5313	63	5	at	at	ADV
ejpam-5313	63	6	least	least	ADV
ejpam-5313	63	7	one	one	NUM
ejpam-5313	63	8	vertex	vertex	NOUN
ejpam-5313	63	9	w	w	NOUN
ejpam-5313	63	10	∈	∈	NOUN
ejpam-5313	63	11	s	s	PART
ejpam-5313	63	12	which	which	PRON
ejpam-5313	63	13	is	be	AUX
ejpam-5313	63	14	not	not	PART
ejpam-5313	63	15	even	even	ADV
ejpam-5313	63	16	sum	sum	NOUN
ejpam-5313	63	17	dominated	dominate	VERB
ejpam-5313	63	18	by	by	ADP
ejpam-5313	63	19	any	any	DET
ejpam-5313	63	20	vertex	vertex	NOUN
ejpam-5313	63	21	of	of	ADP
ejpam-5313	63	22	v	v	NOUN
ejpam-5313	63	23	−	−	PROPN
ejpam-5313	63	24	s.	s.	PROPN
ejpam-5313	64	1	so	so	ADV
ejpam-5313	64	2	,	,	PUNCT
ejpam-5313	64	3	w	w	NOUN
ejpam-5313	64	4	is	be	AUX
ejpam-5313	64	5	even	even	ADV
ejpam-5313	64	6	sum	sum	NOUN
ejpam-5313	64	7	dominated	dominate	VERB
ejpam-5313	64	8	by	by	ADP
ejpam-5313	64	9	only	only	ADV
ejpam-5313	64	10	some	some	DET
ejpam-5313	64	11	vertex	vertex	NOUN
ejpam-5313	64	12	of	of	ADP
ejpam-5313	64	13	s	s	PRON
ejpam-5313	64	14	that	that	PRON
ejpam-5313	64	15	is	be	AUX
ejpam-5313	64	16	,	,	PUNCT
ejpam-5313	64	17	s	s	PART
ejpam-5313	64	18	−	−	PROPN
ejpam-5313	64	19	{	{	PUNCT
ejpam-5313	64	20	w	w	NOUN
ejpam-5313	64	21	}	}	PUNCT
ejpam-5313	64	22	is	be	AUX
ejpam-5313	64	23	also	also	ADV
ejpam-5313	64	24	an	an	DET
ejpam-5313	64	25	even	even	ADV
ejpam-5313	64	26	sum	sum	NOUN
ejpam-5313	64	27	dominating	dominating	NOUN
ejpam-5313	64	28	set	set	NOUN
ejpam-5313	64	29	.	.	PUNCT
ejpam-5313	65	1	in	in	ADP
ejpam-5313	65	2	this	this	DET
ejpam-5313	65	3	case	case	NOUN
ejpam-5313	65	4	s	s	VERB
ejpam-5313	65	5	is	be	AUX
ejpam-5313	65	6	not	not	PART
ejpam-5313	65	7	minimal	minimal	ADJ
ejpam-5313	65	8	even	even	ADV
ejpam-5313	65	9	sum	sum	NOUN
ejpam-5313	65	10	dominating	dominating	NOUN
ejpam-5313	65	11	set	set	NOUN
ejpam-5313	65	12	of	of	ADP
ejpam-5313	65	13	g	g	PROPN
ejpam-5313	65	14	which	which	PRON
ejpam-5313	65	15	contradicts	contradict	VERB
ejpam-5313	65	16	to	to	ADP
ejpam-5313	65	17	our	our	PRON
ejpam-5313	65	18	assumption	assumption	NOUN
ejpam-5313	65	19	that	that	SCONJ
ejpam-5313	65	20	s	s	VERB
ejpam-5313	65	21	is	be	AUX
ejpam-5313	65	22	a	a	DET
ejpam-5313	65	23	minimal	minimal	ADJ
ejpam-5313	65	24	even	even	ADV
ejpam-5313	65	25	sum	sum	NOUN
ejpam-5313	65	26	dominating	dominating	NOUN
ejpam-5313	65	27	set	set	NOUN
ejpam-5313	65	28	of	of	ADP
ejpam-5313	65	29	g.	g.	PROPN
ejpam-5313	65	30	hence	hence	ADV
ejpam-5313	65	31	,	,	PUNCT
ejpam-5313	65	32	v	v	ADP
ejpam-5313	65	33	−	−	PROPN
ejpam-5313	65	34	s	s	NOUN
ejpam-5313	65	35	of	of	ADP
ejpam-5313	65	36	every	every	DET
ejpam-5313	65	37	minimal	minimal	ADJ
ejpam-5313	66	1	even	even	ADV
ejpam-5313	66	2	sum	sum	PROPN
ejpam-5313	66	3	s.	s.	PROPN
ejpam-5313	66	4	h	h	PROPN
ejpam-5313	66	5	karkar	karkar	PROPN
ejpam-5313	66	6	et	et	PROPN
ejpam-5313	66	7	al	al	PROPN
ejpam-5313	66	8	.	.	PUNCT
ejpam-5313	66	9	/	/	SYM
ejpam-5313	66	10	eur	eur	PROPN
ejpam-5313	66	11	.	.	PUNCT
ejpam-5313	67	1	j.	j.	PROPN
ejpam-5313	67	2	pure	pure	PROPN
ejpam-5313	67	3	appl	appl	PROPN
ejpam-5313	67	4	.	.	PROPN
ejpam-5313	67	5	math	math	PROPN
ejpam-5313	67	6	,	,	PUNCT
ejpam-5313	67	7	17	17	NUM
ejpam-5313	67	8	(	(	PUNCT
ejpam-5313	67	9	3	3	NUM
ejpam-5313	67	10	)	)	PUNCT
ejpam-5313	67	11	(	(	PUNCT
ejpam-5313	67	12	2024	2024	NUM
ejpam-5313	67	13	)	)	PUNCT
ejpam-5313	67	14	,	,	PUNCT
ejpam-5313	67	15	2084	2084	NUM
ejpam-5313	67	16	-	-	SYM
ejpam-5313	67	17	2091	2091	NUM
ejpam-5313	67	18	2087	2087	NUM
ejpam-5313	67	19	dominating	dominating	NOUN
ejpam-5313	67	20	set	set	NOUN
ejpam-5313	67	21	s	s	VERB
ejpam-5313	67	22	is	be	AUX
ejpam-5313	67	23	an	an	DET
ejpam-5313	67	24	even	even	ADV
ejpam-5313	67	25	sum	sum	NOUN
ejpam-5313	67	26	dominating	dominating	NOUN
ejpam-5313	67	27	set	set	NOUN
ejpam-5313	67	28	.	.	PUNCT
ejpam-5313	68	1	theorem	theorem	VERB
ejpam-5313	68	2	5	5	NUM
ejpam-5313	68	3	.	.	NOUN
ejpam-5313	68	4	1	1	NUM
ejpam-5313	68	5	≤	≤	NUM
ejpam-5313	68	6	γes(g	γes(g	PART
ejpam-5313	68	7	)	)	PUNCT
ejpam-5313	68	8	≤	≤	NOUN
ejpam-5313	69	1	n	n	DET
ejpam-5313	69	2	proof	proof	NOUN
ejpam-5313	69	3	.	.	PUNCT
ejpam-5313	70	1	let	let	VERB
ejpam-5313	70	2	g	g	PRON
ejpam-5313	70	3	be	be	AUX
ejpam-5313	70	4	a	a	DET
ejpam-5313	70	5	simple	simple	ADJ
ejpam-5313	70	6	graph	graph	NOUN
ejpam-5313	70	7	and	and	CCONJ
ejpam-5313	70	8	|g|	|g|	PROPN
ejpam-5313	70	9	is	be	AUX
ejpam-5313	70	10	an	an	DET
ejpam-5313	70	11	odd	odd	ADJ
ejpam-5313	70	12	number	number	NOUN
ejpam-5313	70	13	.	.	PUNCT
ejpam-5313	71	1	as	as	ADP
ejpam-5313	71	2	per	per	ADP
ejpam-5313	71	3	the	the	DET
ejpam-5313	71	4	definition	definition	NOUN
ejpam-5313	71	5	of	of	ADP
ejpam-5313	71	6	an	an	DET
ejpam-5313	71	7	even	even	ADV
ejpam-5313	71	8	sum	sum	NOUN
ejpam-5313	71	9	dominating	dominating	NOUN
ejpam-5313	71	10	set	set	VERB
ejpam-5313	71	11	if	if	SCONJ
ejpam-5313	71	12	g	g	PROPN
ejpam-5313	71	13	has	have	AUX
ejpam-5313	71	14	atleast	atleast	VERB
ejpam-5313	71	15	one	one	NUM
ejpam-5313	71	16	vertex	vertex	NOUN
ejpam-5313	71	17	of	of	ADP
ejpam-5313	71	18	n−	n−	NOUN
ejpam-5313	71	19	1	1	NUM
ejpam-5313	71	20	degree	degree	NOUN
ejpam-5313	71	21	then	then	ADV
ejpam-5313	71	22	γes(g	γes(g	NUM
ejpam-5313	71	23	)	)	PUNCT
ejpam-5313	71	24	=	=	SYM
ejpam-5313	71	25	1	1	NUM
ejpam-5313	71	26	and	and	CCONJ
ejpam-5313	71	27	if	if	SCONJ
ejpam-5313	71	28	the	the	DET
ejpam-5313	71	29	graph	graph	NOUN
ejpam-5313	71	30	has	have	VERB
ejpam-5313	71	31	all	all	DET
ejpam-5313	71	32	the	the	DET
ejpam-5313	71	33	vertices	vertex	NOUN
ejpam-5313	71	34	of	of	ADP
ejpam-5313	71	35	odd	odd	ADJ
ejpam-5313	71	36	degree	degree	NOUN
ejpam-5313	71	37	than	than	ADP
ejpam-5313	71	38	γes(g	γes(g	ADV
ejpam-5313	71	39	)	)	PUNCT
ejpam-5313	71	40	=	=	VERB
ejpam-5313	72	1	n.	n.	NOUN
ejpam-5313	72	2	here	here	ADV
ejpam-5313	72	3	,	,	PUNCT
ejpam-5313	72	4	star	star	NOUN
ejpam-5313	72	5	graph	graph	NOUN
ejpam-5313	72	6	k1	k1	PROPN
ejpam-5313	72	7	,	,	PUNCT
ejpam-5313	72	8	n	n	PRON
ejpam-5313	72	9	achieves	achieve	VERB
ejpam-5313	72	10	lower	lower	ADV
ejpam-5313	72	11	bound	bind	VERB
ejpam-5313	72	12	for	for	ADP
ejpam-5313	72	13	any	any	DET
ejpam-5313	72	14	odd	odd	ADJ
ejpam-5313	72	15	number	number	NOUN
ejpam-5313	72	16	n	n	NUM
ejpam-5313	72	17	while	while	SCONJ
ejpam-5313	72	18	it	it	PRON
ejpam-5313	72	19	achieves	achieve	VERB
ejpam-5313	72	20	the	the	DET
ejpam-5313	72	21	upper	upper	ADJ
ejpam-5313	72	22	bounds	bound	NOUN
ejpam-5313	72	23	for	for	ADP
ejpam-5313	72	24	even	even	ADV
ejpam-5313	72	25	number	number	NOUN
ejpam-5313	72	26	n.	n.	NOUN
ejpam-5313	72	27	the	the	DET
ejpam-5313	72	28	graph	graph	NOUN
ejpam-5313	72	29	containing	contain	VERB
ejpam-5313	72	30	the	the	DET
ejpam-5313	72	31	property	property	NOUN
ejpam-5313	72	32	given	give	VERB
ejpam-5313	72	33	in	in	ADP
ejpam-5313	72	34	below	below	ADP
ejpam-5313	72	35	theorem	theorem	NOUN
ejpam-5313	72	36	also	also	ADV
ejpam-5313	72	37	achieves	achieve	VERB
ejpam-5313	72	38	the	the	DET
ejpam-5313	72	39	upper	upper	ADJ
ejpam-5313	72	40	bound	bind	VERB
ejpam-5313	72	41	.	.	PUNCT
ejpam-5313	73	1	theorem	theorem	VERB
ejpam-5313	73	2	6	6	NUM
ejpam-5313	73	3	.	.	PUNCT
ejpam-5313	74	1	let	let	VERB
ejpam-5313	74	2	g	g	NOUN
ejpam-5313	74	3	be	be	AUX
ejpam-5313	74	4	the	the	DET
ejpam-5313	74	5	graph	graph	NOUN
ejpam-5313	74	6	in	in	ADP
ejpam-5313	74	7	which	which	PRON
ejpam-5313	74	8	every	every	DET
ejpam-5313	74	9	vertex	vertex	NOUN
ejpam-5313	74	10	of	of	ADP
ejpam-5313	74	11	even	even	ADJ
ejpam-5313	74	12	degree	degree	NOUN
ejpam-5313	74	13	is	be	AUX
ejpam-5313	74	14	adjacent	adjacent	ADJ
ejpam-5313	74	15	to	to	ADP
ejpam-5313	74	16	the	the	DET
ejpam-5313	74	17	vertices	vertex	NOUN
ejpam-5313	74	18	of	of	ADP
ejpam-5313	74	19	odd	odd	ADJ
ejpam-5313	74	20	degree	degree	NOUN
ejpam-5313	74	21	only	only	ADV
ejpam-5313	74	22	and	and	CCONJ
ejpam-5313	74	23	every	every	DET
ejpam-5313	74	24	vertex	vertex	NOUN
ejpam-5313	74	25	of	of	ADP
ejpam-5313	74	26	odd	odd	ADJ
ejpam-5313	74	27	degree	degree	NOUN
ejpam-5313	74	28	is	be	AUX
ejpam-5313	74	29	adjacent	adjacent	ADJ
ejpam-5313	74	30	to	to	ADP
ejpam-5313	74	31	the	the	DET
ejpam-5313	74	32	vertices	vertex	NOUN
ejpam-5313	74	33	of	of	ADP
ejpam-5313	74	34	even	even	ADJ
ejpam-5313	74	35	degree	degree	NOUN
ejpam-5313	74	36	only	only	ADV
ejpam-5313	74	37	then	then	ADV
ejpam-5313	74	38	γes(g	γes(g	NUM
ejpam-5313	74	39	)	)	PUNCT
ejpam-5313	75	1	=	=	SYM
ejpam-5313	75	2	|v	|v	PROPN
ejpam-5313	75	3	(	(	PUNCT
ejpam-5313	75	4	g)|	g)|	NOUN
ejpam-5313	75	5	.	.	PUNCT
ejpam-5313	76	1	proof	proof	NOUN
ejpam-5313	76	2	.	.	PUNCT
ejpam-5313	77	1	here	here	ADV
ejpam-5313	77	2	sum	sum	NOUN
ejpam-5313	77	3	of	of	ADP
ejpam-5313	77	4	degree	degree	NOUN
ejpam-5313	77	5	of	of	ADP
ejpam-5313	77	6	any	any	DET
ejpam-5313	77	7	two	two	NUM
ejpam-5313	77	8	adjacent	adjacent	ADJ
ejpam-5313	77	9	vertices	vertex	NOUN
ejpam-5313	77	10	of	of	ADP
ejpam-5313	77	11	g	g	NOUN
ejpam-5313	77	12	will	will	AUX
ejpam-5313	77	13	be	be	AUX
ejpam-5313	77	14	an	an	DET
ejpam-5313	77	15	odd	odd	ADJ
ejpam-5313	77	16	number	number	NOUN
ejpam-5313	77	17	.	.	PUNCT
ejpam-5313	78	1	so	so	ADV
ejpam-5313	78	2	any	any	DET
ejpam-5313	78	3	vertex	vertex	NOUN
ejpam-5313	78	4	of	of	ADP
ejpam-5313	78	5	g	g	NOUN
ejpam-5313	78	6	can	can	AUX
ejpam-5313	78	7	not	not	PART
ejpam-5313	78	8	even	even	ADV
ejpam-5313	78	9	sum	sum	VERB
ejpam-5313	78	10	dominate	dominate	VERB
ejpam-5313	78	11	any	any	DET
ejpam-5313	78	12	other	other	ADJ
ejpam-5313	78	13	vertex	vertex	NOUN
ejpam-5313	78	14	of	of	ADP
ejpam-5313	78	15	g.	g.	PROPN
ejpam-5313	78	16	therefore	therefore	ADV
ejpam-5313	78	17	to	to	PART
ejpam-5313	78	18	construct	construct	VERB
ejpam-5313	78	19	an	an	DET
ejpam-5313	78	20	even	even	ADV
ejpam-5313	78	21	sum	sum	NOUN
ejpam-5313	78	22	dominating	dominating	NOUN
ejpam-5313	78	23	set	set	NOUN
ejpam-5313	78	24	of	of	ADP
ejpam-5313	78	25	minimum	minimum	ADJ
ejpam-5313	78	26	cardinality	cardinality	NOUN
ejpam-5313	78	27	we	we	PRON
ejpam-5313	78	28	include	include	VERB
ejpam-5313	78	29	all	all	DET
ejpam-5313	78	30	the	the	DET
ejpam-5313	78	31	vertices	vertex	NOUN
ejpam-5313	78	32	of	of	ADP
ejpam-5313	78	33	g.	g.	PROPN
ejpam-5313	78	34	hence	hence	ADV
ejpam-5313	78	35	,	,	PUNCT
ejpam-5313	78	36	γes(g	γes(g	PRON
ejpam-5313	78	37	)	)	PUNCT
ejpam-5313	78	38	=	=	SYM
ejpam-5313	78	39	|v	|v	PROPN
ejpam-5313	78	40	(	(	PUNCT
ejpam-5313	78	41	g)|	g)|	PROPN
ejpam-5313	78	42	.	.	PUNCT
ejpam-5313	79	1	theorem	theorem	VERB
ejpam-5313	79	2	7	7	NUM
ejpam-5313	79	3	(	(	PUNCT
ejpam-5313	79	4	[	[	X
ejpam-5313	79	5	3	3	NUM
ejpam-5313	79	6	]	]	NUM
ejpam-5313	79	7	)	)	PUNCT
ejpam-5313	79	8	.	.	PUNCT
ejpam-5313	80	1	a	a	DET
ejpam-5313	80	2	connected	connected	ADJ
ejpam-5313	80	3	graph	graph	NOUN
ejpam-5313	80	4	g	g	PROPN
ejpam-5313	80	5	is	be	AUX
ejpam-5313	80	6	euler	euler	NOUN
ejpam-5313	80	7	if	if	SCONJ
ejpam-5313	81	1	and	and	CCONJ
ejpam-5313	81	2	only	only	ADV
ejpam-5313	81	3	if	if	SCONJ
ejpam-5313	81	4	the	the	DET
ejpam-5313	81	5	degree	degree	NOUN
ejpam-5313	81	6	of	of	ADP
ejpam-5313	81	7	each	each	DET
ejpam-5313	81	8	vertex	vertex	NOUN
ejpam-5313	81	9	is	be	AUX
ejpam-5313	81	10	even	even	ADV
ejpam-5313	81	11	.	.	PUNCT
ejpam-5313	82	1	theorem	theorem	ADJ
ejpam-5313	82	2	8	8	NUM
ejpam-5313	82	3	.	.	PUNCT
ejpam-5313	83	1	if	if	SCONJ
ejpam-5313	83	2	g	g	PROPN
ejpam-5313	83	3	is	be	AUX
ejpam-5313	83	4	an	an	DET
ejpam-5313	83	5	euler	euler	NOUN
ejpam-5313	83	6	graph	graph	NOUN
ejpam-5313	83	7	then	then	ADV
ejpam-5313	83	8	γes(g	γes(g	PRON
ejpam-5313	83	9	)	)	PUNCT
ejpam-5313	83	10	=	=	PUNCT
ejpam-5313	83	11	γ(g	γ(g	PROPN
ejpam-5313	83	12	)	)	PUNCT
ejpam-5313	83	13	.	.	PUNCT
ejpam-5313	84	1	proof	proof	NOUN
ejpam-5313	84	2	.	.	PUNCT
ejpam-5313	85	1	let	let	VERB
ejpam-5313	85	2	g	g	PROPN
ejpam-5313	85	3	is	be	AUX
ejpam-5313	85	4	an	an	DET
ejpam-5313	85	5	euler	euler	NOUN
ejpam-5313	85	6	graph	graph	NOUN
ejpam-5313	85	7	then	then	ADV
ejpam-5313	85	8	by	by	ADP
ejpam-5313	85	9	theorem	theorem	NOUN
ejpam-5313	85	10	7	7	NUM
ejpam-5313	85	11	,	,	PUNCT
ejpam-5313	85	12	the	the	DET
ejpam-5313	85	13	degree	degree	NOUN
ejpam-5313	85	14	of	of	ADP
ejpam-5313	85	15	each	each	DET
ejpam-5313	85	16	vertex	vertex	NOUN
ejpam-5313	85	17	is	be	AUX
ejpam-5313	85	18	even	even	ADV
ejpam-5313	85	19	.	.	PUNCT
ejpam-5313	86	1	so	so	ADV
ejpam-5313	86	2	,	,	PUNCT
ejpam-5313	86	3	any	any	DET
ejpam-5313	86	4	two	two	NUM
ejpam-5313	86	5	vertices	vertex	NOUN
ejpam-5313	86	6	of	of	ADP
ejpam-5313	86	7	g	g	NOUN
ejpam-5313	86	8	can	can	AUX
ejpam-5313	86	9	even	even	ADV
ejpam-5313	86	10	sum	sum	VERB
ejpam-5313	86	11	dominate	dominate	VERB
ejpam-5313	86	12	each	each	DET
ejpam-5313	86	13	other	other	ADJ
ejpam-5313	86	14	if	if	SCONJ
ejpam-5313	86	15	they	they	PRON
ejpam-5313	86	16	are	be	AUX
ejpam-5313	86	17	adjacent	adjacent	ADJ
ejpam-5313	86	18	to	to	ADP
ejpam-5313	86	19	each	each	DET
ejpam-5313	86	20	other	other	ADJ
ejpam-5313	86	21	.	.	PUNCT
ejpam-5313	87	1	hence	hence	ADV
ejpam-5313	87	2	,	,	PUNCT
ejpam-5313	87	3	γes(g	γes(g	X
ejpam-5313	87	4	)	)	PUNCT
ejpam-5313	87	5	=	=	PUNCT
ejpam-5313	87	6	γ(g	γ(g	PROPN
ejpam-5313	87	7	)	)	PUNCT
ejpam-5313	87	8	.	.	PUNCT
ejpam-5313	88	1	corollary	corollary	ADJ
ejpam-5313	88	2	1	1	NUM
ejpam-5313	88	3	.	.	PUNCT
ejpam-5313	88	4	γes(cn	γes(cn	NOUN
ejpam-5313	88	5	)	)	PUNCT
ejpam-5313	89	1	=	=	PUNCT
ejpam-5313	89	2	⌈n	⌈n	NOUN
ejpam-5313	89	3	3	3	NUM
ejpam-5313	89	4	⌉	⌉	X
ejpam-5313	89	5	.	.	PUNCT
ejpam-5313	90	1	proof	proof	NOUN
ejpam-5313	90	2	.	.	PUNCT
ejpam-5313	91	1	as	as	SCONJ
ejpam-5313	91	2	the	the	DET
ejpam-5313	91	3	cycle	cycle	NOUN
ejpam-5313	91	4	cn	cn	PROPN
ejpam-5313	91	5	is	be	AUX
ejpam-5313	91	6	an	an	DET
ejpam-5313	91	7	euler	euler	NOUN
ejpam-5313	91	8	graph	graph	NOUN
ejpam-5313	91	9	,	,	PUNCT
ejpam-5313	91	10	according	accord	VERB
ejpam-5313	91	11	to	to	ADP
ejpam-5313	91	12	theorem	theorem	ADJ
ejpam-5313	91	13	8	8	NUM
ejpam-5313	91	14	,	,	PUNCT
ejpam-5313	91	15	γes(cn	γes(cn	NOUN
ejpam-5313	91	16	)	)	PUNCT
ejpam-5313	91	17	=	=	SYM
ejpam-5313	91	18	γ(cn	γ(cn	PROPN
ejpam-5313	91	19	)	)	PUNCT
ejpam-5313	91	20	=	=	PUNCT
ejpam-5313	91	21	⌈n	⌈n	NOUN
ejpam-5313	91	22	3	3	NUM
ejpam-5313	91	23	⌉	⌉	X
ejpam-5313	91	24	.	.	PUNCT
ejpam-5313	92	1	3	3	X
ejpam-5313	92	2	.	.	X
ejpam-5313	92	3	even	even	ADV
ejpam-5313	92	4	sum	sum	VERB
ejpam-5313	92	5	domination	domination	NOUN
ejpam-5313	92	6	number	number	NOUN
ejpam-5313	92	7	of	of	ADP
ejpam-5313	92	8	some	some	DET
ejpam-5313	92	9	standard	standard	ADJ
ejpam-5313	92	10	graphs	graph	NOUN
ejpam-5313	92	11	theorem	theorem	VERB
ejpam-5313	92	12	1	1	NUM
ejpam-5313	92	13	.	.	PUNCT
ejpam-5313	92	14	γes(pn	γes(pn	NOUN
ejpam-5313	92	15	)	)	PUNCT
ejpam-5313	92	16	=	=	SYM
ejpam-5313	93	1	2	2	NUM
ejpam-5313	93	2	+	+	CCONJ
ejpam-5313	93	3	⌈	⌈	NOUN
ejpam-5313	93	4	n−	n−	NOUN
ejpam-5313	93	5	2	2	NUM
ejpam-5313	93	6	3	3	NUM
ejpam-5313	93	7	⌉	⌉	NOUN
ejpam-5313	93	8	.	.	PUNCT
ejpam-5313	94	1	proof	proof	NOUN
ejpam-5313	94	2	.	.	PUNCT
ejpam-5313	95	1	let	let	VERB
ejpam-5313	95	2	v1	v1	NOUN
ejpam-5313	95	3	,	,	PUNCT
ejpam-5313	95	4	v2	v2	PROPN
ejpam-5313	95	5	,	,	PUNCT
ejpam-5313	95	6	v3	v3	PROPN
ejpam-5313	95	7	,	,	PUNCT
ejpam-5313	95	8	.	.	PUNCT
ejpam-5313	95	9	.	.	PUNCT
ejpam-5313	96	1	.	.	PUNCT
ejpam-5313	97	1	,	,	PUNCT
ejpam-5313	97	2	vn	vn	INTJ
ejpam-5313	97	3	be	be	AUX
ejpam-5313	97	4	the	the	DET
ejpam-5313	97	5	n	n	DET
ejpam-5313	97	6	vertices	vertex	NOUN
ejpam-5313	97	7	of	of	ADP
ejpam-5313	97	8	pn	pn	PROPN
ejpam-5313	97	9	where	where	SCONJ
ejpam-5313	97	10	v1	v1	VERB
ejpam-5313	97	11	and	and	CCONJ
ejpam-5313	97	12	vn	vn	PROPN
ejpam-5313	97	13	are	be	AUX
ejpam-5313	97	14	pendant	pendant	ADJ
ejpam-5313	97	15	vertices	vertex	NOUN
ejpam-5313	97	16	.	.	PUNCT
ejpam-5313	98	1	so	so	ADV
ejpam-5313	98	2	degree	degree	NOUN
ejpam-5313	98	3	of	of	ADP
ejpam-5313	98	4	v1	v1	NOUN
ejpam-5313	98	5	and	and	CCONJ
ejpam-5313	98	6	vn	vn	PROPN
ejpam-5313	98	7	is	be	AUX
ejpam-5313	98	8	1	1	NUM
ejpam-5313	98	9	while	while	SCONJ
ejpam-5313	98	10	degree	degree	NOUN
ejpam-5313	98	11	of	of	ADP
ejpam-5313	98	12	v2,	v2,	NOUN
ejpam-5313	98	13	...	...	PUNCT
ejpam-5313	98	14	,vn−1	,vn−1	PUNCT
ejpam-5313	98	15	is	be	AUX
ejpam-5313	98	16	2	2	NUM
ejpam-5313	98	17	.	.	PUNCT
ejpam-5313	98	18	therefore	therefore	ADV
ejpam-5313	98	19	v1	v1	VERB
ejpam-5313	98	20	and	and	CCONJ
ejpam-5313	98	21	vn	vn	PROPN
ejpam-5313	98	22	can	can	AUX
ejpam-5313	98	23	even	even	ADV
ejpam-5313	98	24	sum	sum	VERB
ejpam-5313	98	25	dominate	dominate	VERB
ejpam-5313	98	26	themselves	themselves	PRON
ejpam-5313	98	27	only	only	ADV
ejpam-5313	98	28	and	and	CCONJ
ejpam-5313	98	29	they	they	PRON
ejpam-5313	98	30	are	be	AUX
ejpam-5313	98	31	not	not	PART
ejpam-5313	98	32	even	even	ADV
ejpam-5313	98	33	sum	sum	NOUN
ejpam-5313	98	34	dominated	dominate	VERB
ejpam-5313	98	35	by	by	ADP
ejpam-5313	98	36	their	their	PRON
ejpam-5313	98	37	neighbors	neighbor	NOUN
ejpam-5313	98	38	.	.	PUNCT
ejpam-5313	99	1	so	so	ADV
ejpam-5313	99	2	,	,	PUNCT
ejpam-5313	99	3	they	they	PRON
ejpam-5313	99	4	must	must	AUX
ejpam-5313	99	5	be	be	AUX
ejpam-5313	99	6	in	in	ADP
ejpam-5313	99	7	even	even	ADV
ejpam-5313	99	8	sum	sum	NOUN
ejpam-5313	99	9	dominating	dominating	NOUN
ejpam-5313	99	10	set	set	VERB
ejpam-5313	99	11	s.	s.	PROPN
ejpam-5313	99	12	now	now	ADV
ejpam-5313	99	13	as	as	ADP
ejpam-5313	99	14	remaining	remaining	ADJ
ejpam-5313	99	15	vertices	vertex	NOUN
ejpam-5313	99	16	v2,	v2,	NOUN
ejpam-5313	99	17	...	...	PUNCT
ejpam-5313	99	18	,vn−1	,vn−1	PUNCT
ejpam-5313	99	19	having	having	AUX
ejpam-5313	99	20	even	even	ADV
ejpam-5313	99	21	degree	degree	VERB
ejpam-5313	99	22	they	they	PRON
ejpam-5313	99	23	even	even	ADV
ejpam-5313	99	24	sum	sum	VERB
ejpam-5313	99	25	dominate	dominate	VERB
ejpam-5313	99	26	their	their	PRON
ejpam-5313	99	27	selves	self	NOUN
ejpam-5313	99	28	and	and	CCONJ
ejpam-5313	99	29	their	their	PRON
ejpam-5313	99	30	neighbors	neighbor	NOUN
ejpam-5313	99	31	.	.	PUNCT
ejpam-5313	100	1	so	so	ADV
ejpam-5313	100	2	to	to	PART
ejpam-5313	100	3	even	even	ADV
ejpam-5313	100	4	sum	sum	VERB
ejpam-5313	100	5	dominate	dominate	VERB
ejpam-5313	100	6	remaining	remain	VERB
ejpam-5313	100	7	n	n	CCONJ
ejpam-5313	100	8	−	−	NUM
ejpam-5313	100	9	2	2	NUM
ejpam-5313	100	10	vertices	vertex	NOUN
ejpam-5313	100	11	we	we	PRON
ejpam-5313	100	12	need	need	VERB
ejpam-5313	100	13	⌈	⌈	SYM
ejpam-5313	100	14	n−	n−	NOUN
ejpam-5313	100	15	2	2	NUM
ejpam-5313	100	16	3	3	NUM
ejpam-5313	100	17	⌉	⌉	NOUN
ejpam-5313	100	18	vertices	vertex	NOUN
ejpam-5313	100	19	.	.	PUNCT
ejpam-5313	101	1	therefore	therefore	ADV
ejpam-5313	101	2	,	,	PUNCT
ejpam-5313	101	3	we	we	PRON
ejpam-5313	101	4	require	require	VERB
ejpam-5313	101	5	2	2	NUM
ejpam-5313	101	6	+	+	CCONJ
ejpam-5313	101	7	⌈	⌈	ADJ
ejpam-5313	101	8	n−	n−	NOUN
ejpam-5313	101	9	2	2	NUM
ejpam-5313	101	10	3	3	NUM
ejpam-5313	101	11	⌉	⌉	ADP
ejpam-5313	101	12	vertices	vertice	VERB
ejpam-5313	101	13	to	to	PART
ejpam-5313	101	14	even	even	ADV
ejpam-5313	101	15	sum	sum	AUX
ejpam-5313	101	16	dominate	dominate	VERB
ejpam-5313	101	17	all	all	DET
ejpam-5313	101	18	the	the	DET
ejpam-5313	101	19	vertices	vertex	NOUN
ejpam-5313	101	20	of	of	ADP
ejpam-5313	101	21	pn	pn	PROPN
ejpam-5313	101	22	.	.	PROPN
ejpam-5313	101	23	theorem	theorem	PROPN
ejpam-5313	101	24	2	2	NUM
ejpam-5313	101	25	.	.	NOUN
ejpam-5313	101	26	γes(km	γes(km	NOUN
ejpam-5313	101	27	,	,	PUNCT
ejpam-5313	101	28	n	n	CCONJ
ejpam-5313	101	29	)	)	PUNCT
ejpam-5313	101	30	=	=	SYM
ejpam-5313	101	31			NUM
ejpam-5313	101	32	2	2	NUM
ejpam-5313	101	33	,	,	PUNCT
ejpam-5313	101	34	if	if	SCONJ
ejpam-5313	101	35	m+	m+	PRON
ejpam-5313	101	36	n	n	PROPN
ejpam-5313	101	37	is	be	AUX
ejpam-5313	101	38	an	an	DET
ejpam-5313	101	39	even	even	ADJ
ejpam-5313	101	40	number	number	NOUN
ejpam-5313	101	41	,	,	PUNCT
ejpam-5313	101	42	where	where	SCONJ
ejpam-5313	101	43	m	m	VERB
ejpam-5313	101	44	,	,	PUNCT
ejpam-5313	101	45	n	n	PROPN
ejpam-5313	101	46	>	>	X
ejpam-5313	101	47	1	1	NUM
ejpam-5313	101	48	.	.	PUNCT
ejpam-5313	102	1	|v	|v	PROPN
ejpam-5313	102	2	(	(	PUNCT
ejpam-5313	102	3	km	km	PROPN
ejpam-5313	102	4	,	,	PUNCT
ejpam-5313	102	5	n)|	n)|	PROPN
ejpam-5313	102	6	,	,	PUNCT
ejpam-5313	102	7	if	if	SCONJ
ejpam-5313	102	8	m+	m+	PRON
ejpam-5313	102	9	n	n	PROPN
ejpam-5313	102	10	is	be	AUX
ejpam-5313	102	11	an	an	DET
ejpam-5313	102	12	odd	odd	ADJ
ejpam-5313	102	13	number	number	NOUN
ejpam-5313	102	14	.	.	PUNCT
ejpam-5313	103	1	s.	s.	PROPN
ejpam-5313	103	2	h	h	PROPN
ejpam-5313	103	3	karkar	karkar	PROPN
ejpam-5313	103	4	et	et	PROPN
ejpam-5313	103	5	al	al	PROPN
ejpam-5313	103	6	.	.	PUNCT
ejpam-5313	103	7	/	/	SYM
ejpam-5313	103	8	eur	eur	PROPN
ejpam-5313	103	9	.	.	PUNCT
ejpam-5313	104	1	j.	j.	PROPN
ejpam-5313	104	2	pure	pure	PROPN
ejpam-5313	104	3	appl	appl	PROPN
ejpam-5313	104	4	.	.	PROPN
ejpam-5313	104	5	math	math	PROPN
ejpam-5313	104	6	,	,	PUNCT
ejpam-5313	104	7	17	17	NUM
ejpam-5313	104	8	(	(	PUNCT
ejpam-5313	104	9	3	3	NUM
ejpam-5313	104	10	)	)	PUNCT
ejpam-5313	104	11	(	(	PUNCT
ejpam-5313	104	12	2024	2024	NUM
ejpam-5313	104	13	)	)	PUNCT
ejpam-5313	104	14	,	,	PUNCT
ejpam-5313	104	15	2084	2084	NUM
ejpam-5313	104	16	-	-	SYM
ejpam-5313	104	17	2091	2091	NUM
ejpam-5313	104	18	2088	2088	NUM
ejpam-5313	104	19	proof	proof	NOUN
ejpam-5313	104	20	.	.	PUNCT
ejpam-5313	105	1	let	let	VERB
ejpam-5313	105	2	v1	v1	VERB
ejpam-5313	105	3	and	and	CCONJ
ejpam-5313	105	4	v2	v2	NOUN
ejpam-5313	105	5	be	be	AUX
ejpam-5313	105	6	two	two	NUM
ejpam-5313	105	7	subsets	subset	NOUN
ejpam-5313	105	8	of	of	ADP
ejpam-5313	105	9	km	km	PROPN
ejpam-5313	105	10	,	,	PUNCT
ejpam-5313	105	11	n	n	PRON
ejpam-5313	105	12	such	such	ADJ
ejpam-5313	105	13	that	that	DET
ejpam-5313	105	14	v1	v1	NOUN
ejpam-5313	105	15	∪	∪	VERB
ejpam-5313	105	16	v2	v2	PROPN
ejpam-5313	105	17	=	=	SYM
ejpam-5313	105	18	v	v	NOUN
ejpam-5313	105	19	(	(	PUNCT
ejpam-5313	105	20	km	km	PROPN
ejpam-5313	105	21	,	,	PUNCT
ejpam-5313	105	22	n	n	CCONJ
ejpam-5313	105	23	)	)	PUNCT
ejpam-5313	106	1	where	where	SCONJ
ejpam-5313	106	2	|v1|	|v1|	NOUN
ejpam-5313	106	3	=	=	NOUN
ejpam-5313	106	4	m	m	NOUN
ejpam-5313	106	5	and	and	CCONJ
ejpam-5313	106	6	|v2|	|v2|	NOUN
ejpam-5313	106	7	=	=	SYM
ejpam-5313	106	8	n	n	NOUN
ejpam-5313	106	9	and	and	CCONJ
ejpam-5313	106	10	v1,v2,	v1,v2,	NOUN
ejpam-5313	106	11	...	...	PUNCT
ejpam-5313	106	12	,vm	,vm	PUNCT
ejpam-5313	106	13	are	be	AUX
ejpam-5313	106	14	vertices	vertex	NOUN
ejpam-5313	106	15	of	of	ADP
ejpam-5313	106	16	v1	v1	NOUN
ejpam-5313	106	17	and	and	CCONJ
ejpam-5313	106	18	u1,u2,	u1,u2,	NUM
ejpam-5313	106	19	...	...	PUNCT
ejpam-5313	106	20	,un	,un	PUNCT
ejpam-5313	106	21	are	be	AUX
ejpam-5313	106	22	vertices	vertex	NOUN
ejpam-5313	106	23	of	of	ADP
ejpam-5313	106	24	v2	v2	NOUN
ejpam-5313	106	25	.	.	PUNCT
ejpam-5313	107	1	now	now	ADV
ejpam-5313	107	2	according	accord	VERB
ejpam-5313	107	3	to	to	ADP
ejpam-5313	107	4	the	the	DET
ejpam-5313	107	5	values	value	NOUN
ejpam-5313	107	6	of	of	ADP
ejpam-5313	107	7	m	m	PROPN
ejpam-5313	107	8	and	and	CCONJ
ejpam-5313	107	9	n	n	PRON
ejpam-5313	107	10	we	we	PRON
ejpam-5313	107	11	consider	consider	VERB
ejpam-5313	107	12	two	two	NUM
ejpam-5313	107	13	cases	case	NOUN
ejpam-5313	107	14	as	as	ADP
ejpam-5313	107	15	below	below	ADV
ejpam-5313	107	16	.	.	PUNCT
ejpam-5313	108	1	case	case	NOUN
ejpam-5313	108	2	1	1	NUM
ejpam-5313	108	3	:	:	PUNCT
ejpam-5313	108	4	m+	m+	NUM
ejpam-5313	109	1	n	n	PROPN
ejpam-5313	109	2	is	be	AUX
ejpam-5313	109	3	an	an	DET
ejpam-5313	109	4	even	even	ADJ
ejpam-5313	109	5	number	number	NOUN
ejpam-5313	109	6	.	.	PUNCT
ejpam-5313	110	1	that	that	PRON
ejpam-5313	110	2	is	be	AUX
ejpam-5313	110	3	either	either	DET
ejpam-5313	110	4	m	m	PROPN
ejpam-5313	110	5	and	and	CCONJ
ejpam-5313	110	6	n	n	PRON
ejpam-5313	110	7	both	both	PRON
ejpam-5313	110	8	are	be	AUX
ejpam-5313	110	9	even	even	ADV
ejpam-5313	110	10	number	number	NOUN
ejpam-5313	110	11	or	or	CCONJ
ejpam-5313	110	12	both	both	PRON
ejpam-5313	110	13	are	be	AUX
ejpam-5313	110	14	odd	odd	ADJ
ejpam-5313	110	15	number	number	NOUN
ejpam-5313	110	16	.	.	PUNCT
ejpam-5313	111	1	according	accord	VERB
ejpam-5313	111	2	to	to	ADP
ejpam-5313	111	3	that	that	SCONJ
ejpam-5313	111	4	we	we	PRON
ejpam-5313	111	5	consider	consider	VERB
ejpam-5313	111	6	two	two	NUM
ejpam-5313	111	7	subcases	subcase	NOUN
ejpam-5313	111	8	as	as	SCONJ
ejpam-5313	111	9	given	give	VERB
ejpam-5313	111	10	below	below	ADV
ejpam-5313	111	11	.	.	PUNCT
ejpam-5313	112	1	subcase	subcase	PROPN
ejpam-5313	112	2	1.1	1.1	NUM
ejpam-5313	112	3	:	:	PUNCT
ejpam-5313	112	4	if	if	SCONJ
ejpam-5313	112	5	m	m	VERB
ejpam-5313	112	6	and	and	CCONJ
ejpam-5313	112	7	n	n	PRON
ejpam-5313	112	8	both	both	PRON
ejpam-5313	112	9	are	be	AUX
ejpam-5313	112	10	even	even	ADV
ejpam-5313	112	11	number	number	NOUN
ejpam-5313	112	12	.	.	PUNCT
ejpam-5313	113	1	if	if	SCONJ
ejpam-5313	113	2	m	m	PROPN
ejpam-5313	113	3	and	and	CCONJ
ejpam-5313	113	4	n	n	PRON
ejpam-5313	113	5	both	both	PRON
ejpam-5313	113	6	are	be	AUX
ejpam-5313	113	7	even	even	ADV
ejpam-5313	113	8	number	number	NOUN
ejpam-5313	113	9	then	then	ADV
ejpam-5313	113	10	v1,v2,	v1,v2,	NOUN
ejpam-5313	113	11	...	...	PUNCT
ejpam-5313	113	12	,vm	,vm	PUNCT
ejpam-5313	113	13	,	,	PUNCT
ejpam-5313	113	14	u1,u2,	u1,u2,	NOUN
ejpam-5313	113	15	...	...	PUNCT
ejpam-5313	113	16	,un	,un	PUNCT
ejpam-5313	113	17	are	be	AUX
ejpam-5313	113	18	vertices	vertex	NOUN
ejpam-5313	113	19	of	of	ADP
ejpam-5313	113	20	even	even	ADJ
ejpam-5313	113	21	degree	degree	NOUN
ejpam-5313	113	22	.	.	PUNCT
ejpam-5313	114	1	according	accord	VERB
ejpam-5313	114	2	to	to	ADP
ejpam-5313	114	3	the	the	DET
ejpam-5313	114	4	definition	definition	NOUN
ejpam-5313	114	5	of	of	ADP
ejpam-5313	114	6	even	even	ADV
ejpam-5313	114	7	sum	sum	NOUN
ejpam-5313	114	8	domination	domination	NOUN
ejpam-5313	114	9	every	every	DET
ejpam-5313	114	10	vi	vi	NOUN
ejpam-5313	114	11	,	,	PUNCT
ejpam-5313	114	12	i	i	PRON
ejpam-5313	114	13	=	=	NOUN
ejpam-5313	114	14	1	1	NUM
ejpam-5313	114	15	,	,	PUNCT
ejpam-5313	114	16	2	2	NUM
ejpam-5313	114	17	,	,	PUNCT
ejpam-5313	114	18	...	...	PUNCT
ejpam-5313	114	19	,	,	PUNCT
ejpam-5313	114	20	m	m	NOUN
ejpam-5313	114	21	can	can	AUX
ejpam-5313	114	22	even	even	ADV
ejpam-5313	114	23	sum	sum	VERB
ejpam-5313	114	24	dominate	dominate	VERB
ejpam-5313	114	25	itself	itself	PRON
ejpam-5313	114	26	and	and	CCONJ
ejpam-5313	114	27	all	all	DET
ejpam-5313	114	28	the	the	DET
ejpam-5313	114	29	vertices	vertex	NOUN
ejpam-5313	114	30	of	of	ADP
ejpam-5313	114	31	v2	v2	NOUN
ejpam-5313	114	32	.	.	PUNCT
ejpam-5313	115	1	similarly	similarly	ADV
ejpam-5313	115	2	every	every	DET
ejpam-5313	115	3	uj	uj	NOUN
ejpam-5313	115	4	,	,	PUNCT
ejpam-5313	115	5	j	j	PROPN
ejpam-5313	115	6	=	=	SYM
ejpam-5313	115	7	1	1	NUM
ejpam-5313	115	8	,	,	PUNCT
ejpam-5313	115	9	2	2	NUM
ejpam-5313	115	10	,	,	PUNCT
ejpam-5313	115	11	...	...	PUNCT
ejpam-5313	115	12	,	,	PUNCT
ejpam-5313	115	13	n	n	PRON
ejpam-5313	115	14	can	can	AUX
ejpam-5313	115	15	even	even	ADV
ejpam-5313	115	16	sum	sum	VERB
ejpam-5313	115	17	dominate	dominate	VERB
ejpam-5313	115	18	itself	itself	PRON
ejpam-5313	115	19	and	and	CCONJ
ejpam-5313	115	20	all	all	DET
ejpam-5313	115	21	the	the	DET
ejpam-5313	115	22	vertices	vertex	NOUN
ejpam-5313	115	23	of	of	ADP
ejpam-5313	115	24	v1	v1	NOUN
ejpam-5313	115	25	.	.	PUNCT
ejpam-5313	116	1	therefore	therefore	ADV
ejpam-5313	116	2	,	,	PUNCT
ejpam-5313	116	3	it	it	PRON
ejpam-5313	116	4	is	be	AUX
ejpam-5313	116	5	enough	enough	ADJ
ejpam-5313	116	6	to	to	PART
ejpam-5313	116	7	consider	consider	VERB
ejpam-5313	116	8	one	one	NUM
ejpam-5313	116	9	vertex	vertex	NOUN
ejpam-5313	116	10	from	from	ADP
ejpam-5313	116	11	v1	v1	NOUN
ejpam-5313	116	12	and	and	CCONJ
ejpam-5313	116	13	one	one	NUM
ejpam-5313	116	14	vertex	vertex	NOUN
ejpam-5313	116	15	from	from	ADP
ejpam-5313	116	16	v2	v2	PROPN
ejpam-5313	116	17	to	to	PART
ejpam-5313	116	18	even	even	ADV
ejpam-5313	116	19	sum	sum	AUX
ejpam-5313	116	20	dominate	dominate	VERB
ejpam-5313	116	21	all	all	DET
ejpam-5313	116	22	the	the	DET
ejpam-5313	116	23	vertices	vertex	NOUN
ejpam-5313	116	24	of	of	ADP
ejpam-5313	116	25	km	km	PROPN
ejpam-5313	116	26	,	,	PUNCT
ejpam-5313	116	27	n.	n.	PROPN
ejpam-5313	116	28	subcase	subcase	PROPN
ejpam-5313	116	29	1.2	1.2	NUM
ejpam-5313	116	30	:	:	PUNCT
ejpam-5313	116	31	if	if	SCONJ
ejpam-5313	116	32	m	m	VERB
ejpam-5313	116	33	and	and	CCONJ
ejpam-5313	116	34	n	n	PRON
ejpam-5313	116	35	both	both	PRON
ejpam-5313	116	36	are	be	AUX
ejpam-5313	116	37	odd	odd	ADJ
ejpam-5313	116	38	number	number	NOUN
ejpam-5313	116	39	.	.	PUNCT
ejpam-5313	117	1	if	if	SCONJ
ejpam-5313	117	2	m	m	PROPN
ejpam-5313	117	3	and	and	CCONJ
ejpam-5313	117	4	n	n	PRON
ejpam-5313	117	5	both	both	PRON
ejpam-5313	117	6	are	be	AUX
ejpam-5313	117	7	odd	odd	ADJ
ejpam-5313	117	8	number	number	NOUN
ejpam-5313	117	9	then	then	ADV
ejpam-5313	117	10	deg(vi)+deg(uj	deg(vi)+deg(uj	PROPN
ejpam-5313	117	11	)	)	PUNCT
ejpam-5313	117	12	is	be	AUX
ejpam-5313	117	13	even	even	ADV
ejpam-5313	117	14	number	number	NOUN
ejpam-5313	117	15	for	for	ADP
ejpam-5313	117	16	1	1	NUM
ejpam-5313	117	17	≤	≤	NUM
ejpam-5313	117	18	i	i	PRON
ejpam-5313	117	19	,	,	PUNCT
ejpam-5313	117	20	j	j	PROPN
ejpam-5313	117	21	≤	≤	PROPN
ejpam-5313	117	22	m	m	PROPN
ejpam-5313	117	23	,	,	PUNCT
ejpam-5313	117	24	n.	n.	PROPN
ejpam-5313	118	1	so	so	ADV
ejpam-5313	118	2	from	from	ADP
ejpam-5313	118	3	the	the	DET
ejpam-5313	118	4	definition	definition	NOUN
ejpam-5313	118	5	of	of	ADP
ejpam-5313	118	6	even	even	ADV
ejpam-5313	118	7	sum	sum	NOUN
ejpam-5313	118	8	domination	domination	NOUN
ejpam-5313	118	9	every	every	DET
ejpam-5313	118	10	vi	vi	NOUN
ejpam-5313	118	11	,	,	PUNCT
ejpam-5313	118	12	i	i	PRON
ejpam-5313	118	13	=	=	NOUN
ejpam-5313	118	14	1	1	NUM
ejpam-5313	118	15	,	,	PUNCT
ejpam-5313	118	16	2	2	NUM
ejpam-5313	118	17	,	,	PUNCT
ejpam-5313	118	18	...	...	PUNCT
ejpam-5313	118	19	,	,	PUNCT
ejpam-5313	118	20	m	m	NOUN
ejpam-5313	118	21	can	can	AUX
ejpam-5313	118	22	even	even	ADV
ejpam-5313	118	23	sum	sum	VERB
ejpam-5313	118	24	dominate	dominate	VERB
ejpam-5313	118	25	itself	itself	PRON
ejpam-5313	118	26	and	and	CCONJ
ejpam-5313	118	27	all	all	DET
ejpam-5313	118	28	the	the	DET
ejpam-5313	118	29	vertices	vertex	NOUN
ejpam-5313	118	30	of	of	ADP
ejpam-5313	118	31	v2	v2	NOUN
ejpam-5313	118	32	.	.	PUNCT
ejpam-5313	119	1	similarly	similarly	ADV
ejpam-5313	119	2	every	every	DET
ejpam-5313	119	3	uj	uj	NOUN
ejpam-5313	119	4	,	,	PUNCT
ejpam-5313	119	5	j	j	PROPN
ejpam-5313	119	6	=	=	SYM
ejpam-5313	119	7	1	1	NUM
ejpam-5313	119	8	,	,	PUNCT
ejpam-5313	119	9	2	2	NUM
ejpam-5313	119	10	,	,	PUNCT
ejpam-5313	119	11	...	...	PUNCT
ejpam-5313	119	12	,	,	PUNCT
ejpam-5313	119	13	n	n	PRON
ejpam-5313	119	14	can	can	AUX
ejpam-5313	119	15	even	even	ADV
ejpam-5313	119	16	sum	sum	VERB
ejpam-5313	119	17	dominate	dominate	VERB
ejpam-5313	119	18	itself	itself	PRON
ejpam-5313	119	19	and	and	CCONJ
ejpam-5313	119	20	all	all	DET
ejpam-5313	119	21	the	the	DET
ejpam-5313	119	22	vertices	vertex	NOUN
ejpam-5313	119	23	of	of	ADP
ejpam-5313	119	24	v1	v1	NOUN
ejpam-5313	119	25	.	.	PUNCT
ejpam-5313	120	1	therefore	therefore	ADV
ejpam-5313	120	2	,	,	PUNCT
ejpam-5313	120	3	it	it	PRON
ejpam-5313	120	4	is	be	AUX
ejpam-5313	120	5	enough	enough	ADJ
ejpam-5313	120	6	to	to	PART
ejpam-5313	120	7	consider	consider	VERB
ejpam-5313	120	8	one	one	NUM
ejpam-5313	120	9	vertex	vertex	NOUN
ejpam-5313	120	10	from	from	ADP
ejpam-5313	120	11	v1	v1	NOUN
ejpam-5313	120	12	and	and	CCONJ
ejpam-5313	120	13	one	one	NUM
ejpam-5313	120	14	vertex	vertex	NOUN
ejpam-5313	120	15	from	from	ADP
ejpam-5313	120	16	v2	v2	PROPN
ejpam-5313	120	17	to	to	PART
ejpam-5313	120	18	even	even	ADV
ejpam-5313	120	19	sum	sum	AUX
ejpam-5313	120	20	dominate	dominate	VERB
ejpam-5313	120	21	all	all	DET
ejpam-5313	120	22	the	the	DET
ejpam-5313	120	23	vertices	vertex	NOUN
ejpam-5313	120	24	of	of	ADP
ejpam-5313	120	25	km	km	PROPN
ejpam-5313	120	26	,	,	PUNCT
ejpam-5313	120	27	n.	n.	PROPN
ejpam-5313	120	28	hence	hence	ADV
ejpam-5313	120	29	,	,	PUNCT
ejpam-5313	120	30	from	from	ADP
ejpam-5313	120	31	the	the	DET
ejpam-5313	120	32	above	above	ADJ
ejpam-5313	120	33	both	both	DET
ejpam-5313	120	34	subcases	subcase	NOUN
ejpam-5313	120	35	γes(km	γes(km	NOUN
ejpam-5313	120	36	,	,	PUNCT
ejpam-5313	120	37	n	n	CCONJ
ejpam-5313	120	38	)	)	PUNCT
ejpam-5313	120	39	=	=	SYM
ejpam-5313	120	40	2	2	X
ejpam-5313	120	41	.	.	X
ejpam-5313	120	42	case	case	NOUN
ejpam-5313	120	43	2	2	NUM
ejpam-5313	120	44	:	:	PUNCT
ejpam-5313	120	45	m+	m+	NUM
ejpam-5313	120	46	n	n	PROPN
ejpam-5313	120	47	is	be	AUX
ejpam-5313	120	48	an	an	DET
ejpam-5313	120	49	odd	odd	ADJ
ejpam-5313	120	50	number	number	NOUN
ejpam-5313	120	51	.	.	PUNCT
ejpam-5313	121	1	if	if	SCONJ
ejpam-5313	121	2	m+n	m+n	PROPN
ejpam-5313	121	3	is	be	AUX
ejpam-5313	121	4	an	an	DET
ejpam-5313	121	5	odd	odd	ADJ
ejpam-5313	121	6	number	number	NOUN
ejpam-5313	121	7	then	then	ADV
ejpam-5313	121	8	either	either	CCONJ
ejpam-5313	121	9	m	m	VERB
ejpam-5313	121	10	is	be	AUX
ejpam-5313	121	11	an	an	DET
ejpam-5313	121	12	odd	odd	ADJ
ejpam-5313	121	13	number	number	NOUN
ejpam-5313	121	14	and	and	CCONJ
ejpam-5313	121	15	n	n	NOUN
ejpam-5313	121	16	is	be	AUX
ejpam-5313	121	17	an	an	DET
ejpam-5313	121	18	even	even	ADJ
ejpam-5313	121	19	number	number	NOUN
ejpam-5313	121	20	or	or	CCONJ
ejpam-5313	121	21	n	n	NOUN
ejpam-5313	121	22	is	be	AUX
ejpam-5313	121	23	an	an	DET
ejpam-5313	121	24	odd	odd	ADJ
ejpam-5313	121	25	number	number	NOUN
ejpam-5313	121	26	andm	andm	NOUN
ejpam-5313	121	27	is	be	AUX
ejpam-5313	121	28	an	an	DET
ejpam-5313	121	29	even	even	ADJ
ejpam-5313	121	30	number	number	NOUN
ejpam-5313	121	31	.	.	PUNCT
ejpam-5313	122	1	therefore	therefore	ADV
ejpam-5313	122	2	,	,	PUNCT
ejpam-5313	122	3	in	in	ADP
ejpam-5313	122	4	both	both	CCONJ
ejpam-5313	122	5	the	the	DET
ejpam-5313	122	6	cases	case	NOUN
ejpam-5313	122	7	deg(vi)+deg(uj	deg(vi)+deg(uj	PROPN
ejpam-5313	122	8	)	)	PUNCT
ejpam-5313	122	9	will	will	AUX
ejpam-5313	122	10	be	be	AUX
ejpam-5313	122	11	an	an	DET
ejpam-5313	122	12	odd	odd	ADJ
ejpam-5313	122	13	number	number	NOUN
ejpam-5313	122	14	for	for	ADP
ejpam-5313	122	15	1	1	NUM
ejpam-5313	122	16	≤	≤	NUM
ejpam-5313	122	17	i	i	PRON
ejpam-5313	122	18	,	,	PUNCT
ejpam-5313	122	19	j	j	PROPN
ejpam-5313	122	20	≤	≤	PROPN
ejpam-5313	122	21	m	m	PROPN
ejpam-5313	122	22	,	,	PUNCT
ejpam-5313	122	23	n.	n.	PROPN
ejpam-5313	123	1	so	so	ADV
ejpam-5313	123	2	from	from	ADP
ejpam-5313	123	3	the	the	DET
ejpam-5313	123	4	definition	definition	NOUN
ejpam-5313	123	5	of	of	ADP
ejpam-5313	123	6	even	even	ADV
ejpam-5313	123	7	sum	sum	NOUN
ejpam-5313	123	8	domination	domination	NOUN
ejpam-5313	123	9	every	every	DET
ejpam-5313	123	10	vi	vi	NOUN
ejpam-5313	123	11	,	,	PUNCT
ejpam-5313	123	12	i	i	PRON
ejpam-5313	123	13	=	=	NOUN
ejpam-5313	123	14	1	1	NUM
ejpam-5313	123	15	,	,	PUNCT
ejpam-5313	123	16	2	2	NUM
ejpam-5313	123	17	,	,	PUNCT
ejpam-5313	123	18	...	...	PUNCT
ejpam-5313	123	19	,	,	PUNCT
ejpam-5313	123	20	m	m	NOUN
ejpam-5313	123	21	can	can	AUX
ejpam-5313	123	22	even	even	ADV
ejpam-5313	123	23	sum	sum	VERB
ejpam-5313	123	24	dominate	dominate	VERB
ejpam-5313	123	25	itself	itself	PRON
ejpam-5313	123	26	only	only	ADV
ejpam-5313	123	27	and	and	CCONJ
ejpam-5313	123	28	similarly	similarly	ADV
ejpam-5313	123	29	for	for	ADP
ejpam-5313	123	30	every	every	DET
ejpam-5313	123	31	uj	uj	PROPN
ejpam-5313	123	32	,	,	PUNCT
ejpam-5313	123	33	j	j	PROPN
ejpam-5313	123	34	=	=	SYM
ejpam-5313	123	35	1	1	NUM
ejpam-5313	123	36	,	,	PUNCT
ejpam-5313	123	37	2	2	NUM
ejpam-5313	123	38	,	,	PUNCT
ejpam-5313	123	39	...	...	PUNCT
ejpam-5313	123	40	,	,	PUNCT
ejpam-5313	123	41	n	n	PRON
ejpam-5313	123	42	can	can	AUX
ejpam-5313	123	43	even	even	ADV
ejpam-5313	123	44	sum	sum	AUX
ejpam-5313	123	45	dominate	dominate	VERB
ejpam-5313	123	46	itself	itself	PRON
ejpam-5313	123	47	only	only	ADV
ejpam-5313	123	48	.	.	PUNCT
ejpam-5313	124	1	therefore	therefore	ADV
ejpam-5313	124	2	to	to	PART
ejpam-5313	124	3	even	even	ADV
ejpam-5313	124	4	sum	sum	AUX
ejpam-5313	124	5	dominate	dominate	VERB
ejpam-5313	124	6	all	all	DET
ejpam-5313	124	7	the	the	DET
ejpam-5313	124	8	vertices	vertex	NOUN
ejpam-5313	124	9	ofkm	ofkm	PROPN
ejpam-5313	124	10	,	,	PUNCT
ejpam-5313	124	11	n	n	CCONJ
ejpam-5313	124	12	we	we	PRON
ejpam-5313	124	13	must	must	AUX
ejpam-5313	124	14	include	include	VERB
ejpam-5313	124	15	all	all	DET
ejpam-5313	124	16	the	the	DET
ejpam-5313	124	17	vertices	vertex	NOUN
ejpam-5313	124	18	of	of	ADP
ejpam-5313	124	19	km	km	PROPN
ejpam-5313	124	20	,	,	PUNCT
ejpam-5313	124	21	n.	n.	NOUN
ejpam-5313	124	22	hence	hence	ADV
ejpam-5313	124	23	,	,	PUNCT
ejpam-5313	124	24	γes(km	γes(km	NOUN
ejpam-5313	124	25	,	,	PUNCT
ejpam-5313	124	26	n	n	CCONJ
ejpam-5313	124	27	)	)	PUNCT
ejpam-5313	125	1	=	=	SYM
ejpam-5313	125	2	m+	m+	NUM
ejpam-5313	126	1	n	n	PROPN
ejpam-5313	126	2	=	=	X
ejpam-5313	126	3	|v	|v	X
ejpam-5313	126	4	(	(	PUNCT
ejpam-5313	126	5	km	km	PROPN
ejpam-5313	126	6	,	,	PUNCT
ejpam-5313	126	7	n)|	n)|	PROPN
ejpam-5313	126	8	.	.	PUNCT
ejpam-5313	127	1	definition	definition	NOUN
ejpam-5313	127	2	1	1	NUM
ejpam-5313	127	3	.	.	PUNCT
ejpam-5313	128	1	the	the	DET
ejpam-5313	128	2	middle	middle	ADJ
ejpam-5313	128	3	graph	graph	NOUN
ejpam-5313	128	4	m(g	m(g	PROPN
ejpam-5313	128	5	)	)	PUNCT
ejpam-5313	128	6	of	of	ADP
ejpam-5313	128	7	a	a	DET
ejpam-5313	128	8	graph	graph	NOUN
ejpam-5313	128	9	g	g	NOUN
ejpam-5313	128	10	is	be	AUX
ejpam-5313	128	11	the	the	DET
ejpam-5313	128	12	graph	graph	NOUN
ejpam-5313	128	13	whose	whose	DET
ejpam-5313	128	14	vertex	vertex	NOUN
ejpam-5313	128	15	set	set	NOUN
ejpam-5313	128	16	is	be	AUX
ejpam-5313	128	17	v	v	NOUN
ejpam-5313	128	18	(	(	PUNCT
ejpam-5313	128	19	g	g	NOUN
ejpam-5313	128	20	)	)	PUNCT
ejpam-5313	128	21	∪	∪	ADP
ejpam-5313	128	22	e(g	e(g	PROPN
ejpam-5313	128	23	)	)	PUNCT
ejpam-5313	128	24	and	and	CCONJ
ejpam-5313	128	25	in	in	ADP
ejpam-5313	128	26	which	which	PRON
ejpam-5313	128	27	two	two	NUM
ejpam-5313	128	28	vertices	vertex	NOUN
ejpam-5313	128	29	are	be	AUX
ejpam-5313	128	30	adjacent	adjacent	ADJ
ejpam-5313	128	31	whenever	whenever	SCONJ
ejpam-5313	128	32	either	either	CCONJ
ejpam-5313	128	33	they	they	PRON
ejpam-5313	128	34	are	be	AUX
ejpam-5313	128	35	adjacent	adjacent	ADJ
ejpam-5313	128	36	edges	edge	NOUN
ejpam-5313	128	37	of	of	ADP
ejpam-5313	128	38	g	g	NOUN
ejpam-5313	128	39	or	or	CCONJ
ejpam-5313	128	40	one	one	NUM
ejpam-5313	128	41	is	be	AUX
ejpam-5313	128	42	a	a	DET
ejpam-5313	128	43	vertex	vertex	NOUN
ejpam-5313	128	44	of	of	ADP
ejpam-5313	128	45	g	g	PROPN
ejpam-5313	128	46	and	and	CCONJ
ejpam-5313	128	47	the	the	DET
ejpam-5313	128	48	other	other	ADJ
ejpam-5313	128	49	is	be	AUX
ejpam-5313	128	50	an	an	DET
ejpam-5313	128	51	edge	edge	NOUN
ejpam-5313	128	52	incident	incident	NOUN
ejpam-5313	128	53	with	with	ADP
ejpam-5313	128	54	it	it	PRON
ejpam-5313	128	55	.	.	PUNCT
ejpam-5313	129	1	theorem	theorem	VERB
ejpam-5313	129	2	3	3	NUM
ejpam-5313	129	3	.	.	PUNCT
ejpam-5313	129	4	γes(m(pn	γes(m(pn	PROPN
ejpam-5313	129	5	)	)	PUNCT
ejpam-5313	129	6	)	)	PUNCT
ejpam-5313	130	1	=	=	SYM
ejpam-5313	130	2	4	4	NUM
ejpam-5313	130	3	+	+	NUM
ejpam-5313	130	4	⌈	⌈	NOUN
ejpam-5313	130	5	n−	n−	NOUN
ejpam-5313	130	6	6	6	NUM
ejpam-5313	130	7	2	2	NUM
ejpam-5313	130	8	⌉	⌉	X
ejpam-5313	130	9	.	.	PUNCT
ejpam-5313	131	1	proof	proof	NOUN
ejpam-5313	131	2	.	.	PUNCT
ejpam-5313	132	1	let	let	VERB
ejpam-5313	132	2	v1	v1	NOUN
ejpam-5313	132	3	,	,	PUNCT
ejpam-5313	132	4	v2	v2	NOUN
ejpam-5313	132	5	,	,	PUNCT
ejpam-5313	132	6	.	.	PUNCT
ejpam-5313	132	7	.	.	PUNCT
ejpam-5313	133	1	.	.	PUNCT
ejpam-5313	134	1	,	,	PUNCT
ejpam-5313	134	2	vn	vn	INTJ
ejpam-5313	134	3	be	be	AUX
ejpam-5313	134	4	the	the	DET
ejpam-5313	134	5	vertices	vertex	NOUN
ejpam-5313	134	6	and	and	CCONJ
ejpam-5313	134	7	e1	e1	NOUN
ejpam-5313	134	8	,	,	PUNCT
ejpam-5313	134	9	e2	e2	PROPN
ejpam-5313	134	10	,	,	PUNCT
ejpam-5313	134	11	.	.	PUNCT
ejpam-5313	134	12	.	.	PUNCT
ejpam-5313	135	1	.	.	PUNCT
ejpam-5313	136	1	,	,	PUNCT
ejpam-5313	136	2	en−1	en−1	PROPN
ejpam-5313	136	3	be	be	VERB
ejpam-5313	136	4	the	the	DET
ejpam-5313	136	5	edges	edge	NOUN
ejpam-5313	136	6	of	of	ADP
ejpam-5313	136	7	path	path	NOUN
ejpam-5313	137	1	pn	pn	PROPN
ejpam-5313	137	2	.	.	PROPN
ejpam-5313	138	1	then	then	ADV
ejpam-5313	138	2	v	v	X
ejpam-5313	138	3	(	(	PUNCT
ejpam-5313	138	4	m(pn	m(pn	NOUN
ejpam-5313	138	5	)	)	PUNCT
ejpam-5313	138	6	)	)	PUNCT
ejpam-5313	139	1	=	=	PRON
ejpam-5313	139	2	{	{	PUNCT
ejpam-5313	139	3	v1	v1	PROPN
ejpam-5313	139	4	,	,	PUNCT
ejpam-5313	139	5	v2	v2	PROPN
ejpam-5313	139	6	,	,	PUNCT
ejpam-5313	139	7	.	.	PUNCT
ejpam-5313	139	8	.	.	PUNCT
ejpam-5313	140	1	.	.	PUNCT
ejpam-5313	141	1	,	,	PUNCT
ejpam-5313	141	2	vn	vn	PROPN
ejpam-5313	141	3	,	,	PUNCT
ejpam-5313	141	4	e1	e1	PROPN
ejpam-5313	141	5	,	,	PUNCT
ejpam-5313	141	6	e2	e2	PROPN
ejpam-5313	141	7	,	,	PUNCT
ejpam-5313	141	8	.	.	PUNCT
ejpam-5313	141	9	.	.	PUNCT
ejpam-5313	141	10	.	.	PUNCT
ejpam-5313	142	1	,	,	PUNCT
ejpam-5313	142	2	en−1	en−1	PROPN
ejpam-5313	142	3	}	}	PUNCT
ejpam-5313	142	4	and	and	CCONJ
ejpam-5313	142	5	let	let	VERB
ejpam-5313	142	6	v	v	NOUN
ejpam-5313	142	7	(	(	PUNCT
ejpam-5313	142	8	m(pn	m(pn	NOUN
ejpam-5313	142	9	)	)	PUNCT
ejpam-5313	142	10	)	)	PUNCT
ejpam-5313	143	1	=	=	SYM
ejpam-5313	143	2	v1	v1	VERB
ejpam-5313	143	3	∪	∪	NOUN
ejpam-5313	143	4	v2	v2	PROPN
ejpam-5313	143	5	where	where	SCONJ
ejpam-5313	143	6	v1	v1	NOUN
ejpam-5313	143	7	=	=	SYM
ejpam-5313	143	8	{	{	PUNCT
ejpam-5313	143	9	v1	v1	PROPN
ejpam-5313	143	10	,	,	PUNCT
ejpam-5313	143	11	v2	v2	PROPN
ejpam-5313	143	12	,	,	PUNCT
ejpam-5313	143	13	.	.	PUNCT
ejpam-5313	143	14	.	.	PUNCT
ejpam-5313	143	15	.	.	PUNCT
ejpam-5313	144	1	,	,	PUNCT
ejpam-5313	144	2	vn	vn	NOUN
ejpam-5313	144	3	}	}	PUNCT
ejpam-5313	144	4	and	and	CCONJ
ejpam-5313	144	5	v2	v2	NOUN
ejpam-5313	144	6	=	=	SYM
ejpam-5313	144	7	{	{	PUNCT
ejpam-5313	144	8	e1	e1	PROPN
ejpam-5313	144	9	,	,	PUNCT
ejpam-5313	144	10	e2	e2	PROPN
ejpam-5313	144	11	,	,	PUNCT
ejpam-5313	144	12	.	.	PUNCT
ejpam-5313	144	13	.	.	PUNCT
ejpam-5313	145	1	.	.	PUNCT
ejpam-5313	146	1	,	,	PUNCT
ejpam-5313	146	2	en−1	en−1	PROPN
ejpam-5313	146	3	}	}	PUNCT
ejpam-5313	146	4	.	.	PUNCT
ejpam-5313	147	1	here	here	ADV
ejpam-5313	147	2	,	,	PUNCT
ejpam-5313	147	3	d(v1	d(v1	X
ejpam-5313	147	4	)	)	PUNCT
ejpam-5313	147	5	=	=	SYM
ejpam-5313	147	6	d(vn	d(vn	PROPN
ejpam-5313	147	7	)	)	PUNCT
ejpam-5313	147	8	=	=	SYM
ejpam-5313	148	1	1	1	NUM
ejpam-5313	148	2	,	,	PUNCT
ejpam-5313	148	3	d(vi	d(vi	PROPN
ejpam-5313	148	4	)	)	PUNCT
ejpam-5313	148	5	=	=	SYM
ejpam-5313	148	6	2	2	NUM
ejpam-5313	148	7	for	for	ADP
ejpam-5313	148	8	i	i	PRON
ejpam-5313	148	9	=	=	SYM
ejpam-5313	148	10	2	2	NUM
ejpam-5313	148	11	,	,	PUNCT
ejpam-5313	148	12	3	3	NUM
ejpam-5313	148	13	,	,	PUNCT
ejpam-5313	148	14	.	.	PUNCT
ejpam-5313	148	15	.	.	PUNCT
ejpam-5313	148	16	.	.	PUNCT
ejpam-5313	149	1	,	,	PUNCT
ejpam-5313	149	2	n	n	CCONJ
ejpam-5313	149	3	−	−	PROPN
ejpam-5313	149	4	1	1	NUM
ejpam-5313	149	5	,	,	PUNCT
ejpam-5313	149	6	d(e1	d(e1	NOUN
ejpam-5313	149	7	)	)	PUNCT
ejpam-5313	149	8	=	=	SYM
ejpam-5313	149	9	2	2	NUM
ejpam-5313	149	10	for	for	ADP
ejpam-5313	149	11	n	n	NOUN
ejpam-5313	149	12	=	=	SYM
ejpam-5313	149	13	2	2	NUM
ejpam-5313	149	14	,	,	PUNCT
ejpam-5313	149	15	d(e1	d(e1	NOUN
ejpam-5313	149	16	)	)	PUNCT
ejpam-5313	149	17	=	=	SYM
ejpam-5313	149	18	d(e2	d(e2	PROPN
ejpam-5313	149	19	)	)	PUNCT
ejpam-5313	149	20	=	=	SYM
ejpam-5313	149	21	3	3	NUM
ejpam-5313	149	22	for	for	ADP
ejpam-5313	149	23	n	n	NOUN
ejpam-5313	149	24	=	=	SYM
ejpam-5313	149	25	3	3	NUM
ejpam-5313	149	26	,	,	PUNCT
ejpam-5313	149	27	d(e1	d(e1	NOUN
ejpam-5313	149	28	)	)	PUNCT
ejpam-5313	149	29	=	=	SYM
ejpam-5313	150	1	d(en−1	d(en−1	PROPN
ejpam-5313	150	2	)	)	PUNCT
ejpam-5313	150	3	=	=	SYM
ejpam-5313	150	4	3	3	NUM
ejpam-5313	150	5	for	for	ADP
ejpam-5313	150	6	i	i	PRON
ejpam-5313	150	7	=	=	SYM
ejpam-5313	150	8	3	3	NUM
ejpam-5313	150	9	,	,	PUNCT
ejpam-5313	150	10	4	4	NUM
ejpam-5313	150	11	,	,	PUNCT
ejpam-5313	150	12	.	.	PUNCT
ejpam-5313	150	13	.	.	PUNCT
ejpam-5313	151	1	.	.	PUNCT
ejpam-5313	152	1	,	,	PUNCT
ejpam-5313	152	2	n	n	PROPN
ejpam-5313	152	3	and	and	CCONJ
ejpam-5313	152	4	d(ei	d(ei	PROPN
ejpam-5313	152	5	)	)	PUNCT
ejpam-5313	152	6	=	=	SYM
ejpam-5313	152	7	4	4	NUM
ejpam-5313	153	1	for	for	ADP
ejpam-5313	153	2	i	i	PRON
ejpam-5313	153	3	=	=	SYM
ejpam-5313	153	4	2	2	NUM
ejpam-5313	153	5	,	,	PUNCT
ejpam-5313	153	6	3	3	NUM
ejpam-5313	153	7	,	,	PUNCT
ejpam-5313	153	8	.	.	PUNCT
ejpam-5313	153	9	.	.	PUNCT
ejpam-5313	153	10	.	.	PUNCT
ejpam-5313	154	1	,	,	PUNCT
ejpam-5313	155	1	n	n	CCONJ
ejpam-5313	155	2	−	−	PROPN
ejpam-5313	155	3	2	2	NUM
ejpam-5313	155	4	.	.	PUNCT
ejpam-5313	156	1	as	as	ADP
ejpam-5313	156	2	per	per	ADP
ejpam-5313	156	3	the	the	DET
ejpam-5313	156	4	definition	definition	NOUN
ejpam-5313	156	5	of	of	ADP
ejpam-5313	156	6	even	even	ADV
ejpam-5313	156	7	sum	sum	NOUN
ejpam-5313	156	8	domination	domination	NOUN
ejpam-5313	156	9	the	the	DET
ejpam-5313	156	10	vertex	vertex	NOUN
ejpam-5313	156	11	v1	v1	NOUN
ejpam-5313	156	12	and	and	CCONJ
ejpam-5313	156	13	the	the	DET
ejpam-5313	156	14	vertex	vertex	NOUN
ejpam-5313	156	15	e1	e1	NOUN
ejpam-5313	156	16	can	can	AUX
ejpam-5313	156	17	even	even	ADV
ejpam-5313	156	18	sum	sum	VERB
ejpam-5313	156	19	dominate	dominate	VERB
ejpam-5313	156	20	each	each	DET
ejpam-5313	156	21	other	other	ADJ
ejpam-5313	156	22	and	and	CCONJ
ejpam-5313	156	23	the	the	DET
ejpam-5313	156	24	vertex	vertex	NOUN
ejpam-5313	156	25	vn	vn	NOUN
ejpam-5313	156	26	and	and	CCONJ
ejpam-5313	156	27	the	the	DET
ejpam-5313	156	28	vertex	vertex	NOUN
ejpam-5313	156	29	en−1	en−1	PROPN
ejpam-5313	156	30	can	can	AUX
ejpam-5313	156	31	even	even	ADV
ejpam-5313	156	32	sum	sum	VERB
ejpam-5313	156	33	dominate	dominate	VERB
ejpam-5313	156	34	each	each	DET
ejpam-5313	156	35	other	other	ADJ
ejpam-5313	156	36	.	.	PUNCT
ejpam-5313	157	1	so	so	ADV
ejpam-5313	157	2	,	,	PUNCT
ejpam-5313	157	3	let	let	VERB
ejpam-5313	157	4	’s	’s	NOUN
ejpam-5313	157	5	consider	consider	VERB
ejpam-5313	157	6	e1	e1	NOUN
ejpam-5313	157	7	and	and	CCONJ
ejpam-5313	157	8	en−1	en−1	PROPN
ejpam-5313	157	9	in	in	ADP
ejpam-5313	157	10	even	even	ADV
ejpam-5313	157	11	sum	sum	NOUN
ejpam-5313	157	12	dominating	dominating	NOUN
ejpam-5313	157	13	set	set	VERB
ejpam-5313	157	14	s.	s.	PROPN
ejpam-5313	157	15	now	now	ADV
ejpam-5313	157	16	v2	v2	VERB
ejpam-5313	157	17	and	and	CCONJ
ejpam-5313	157	18	vn−1	vn−1	PROPN
ejpam-5313	157	19	can	can	AUX
ejpam-5313	157	20	even	even	ADV
ejpam-5313	157	21	sum	sum	VERB
ejpam-5313	157	22	dominate	dominate	VERB
ejpam-5313	157	23	e2	e2	PROPN
ejpam-5313	157	24	and	and	CCONJ
ejpam-5313	157	25	en−2	en−2	PROPN
ejpam-5313	157	26	respectively	respectively	ADV
ejpam-5313	157	27	other	other	ADJ
ejpam-5313	157	28	than	than	ADP
ejpam-5313	157	29	themselves	themselves	PRON
ejpam-5313	157	30	while	while	SCONJ
ejpam-5313	157	31	e2	e2	PROPN
ejpam-5313	157	32	and	and	CCONJ
ejpam-5313	157	33	en−2	en−2	PROPN
ejpam-5313	157	34	can	can	AUX
ejpam-5313	157	35	even	even	ADV
ejpam-5313	157	36	sum	sum	VERB
ejpam-5313	157	37	dominate	dominate	VERB
ejpam-5313	157	38	their	their	PRON
ejpam-5313	157	39	three	three	NUM
ejpam-5313	157	40	neighbor	neighbor	NOUN
ejpam-5313	157	41	vertices	vertice	VERB
ejpam-5313	157	42	other	other	ADJ
ejpam-5313	157	43	than	than	ADP
ejpam-5313	157	44	themselves	themselves	PRON
ejpam-5313	157	45	.	.	PUNCT
ejpam-5313	158	1	therefore	therefore	ADV
ejpam-5313	158	2	e2	e2	PROPN
ejpam-5313	158	3	,	,	PUNCT
ejpam-5313	158	4	en−2	en−2	PROPN
ejpam-5313	158	5	∈	∈	PROPN
ejpam-5313	158	6	s.	s.	PROPN
ejpam-5313	158	7	so	so	ADV
ejpam-5313	158	8	after	after	ADP
ejpam-5313	158	9	considering	consider	VERB
ejpam-5313	158	10	e1	e1	NOUN
ejpam-5313	158	11	,	,	PUNCT
ejpam-5313	158	12	en−1	en−1	PROPN
ejpam-5313	158	13	,	,	PUNCT
ejpam-5313	158	14	e2	e2	PROPN
ejpam-5313	158	15	and	and	CCONJ
ejpam-5313	158	16	en−2	en−2	NOUN
ejpam-5313	158	17	in	in	ADP
ejpam-5313	158	18	s	s	PROPN
ejpam-5313	158	19	,	,	PUNCT
ejpam-5313	158	20	in	in	ADP
ejpam-5313	158	21	total	total	ADJ
ejpam-5313	158	22	six	six	NUM
ejpam-5313	158	23	vertices	vertex	NOUN
ejpam-5313	158	24	v1	v1	NOUN
ejpam-5313	158	25	,	,	PUNCT
ejpam-5313	158	26	v2	v2	PROPN
ejpam-5313	158	27	,	,	PUNCT
ejpam-5313	158	28	v3	v3	PROPN
ejpam-5313	158	29	,	,	PUNCT
ejpam-5313	158	30	vn	vn	INTJ
ejpam-5313	158	31	,	,	PUNCT
ejpam-5313	158	32	vn−1	vn−1	PROPN
ejpam-5313	158	33	,	,	PUNCT
ejpam-5313	158	34	vn−2	vn−2	PROPN
ejpam-5313	158	35	from	from	ADP
ejpam-5313	158	36	v1	v1	PROPN
ejpam-5313	158	37	and	and	CCONJ
ejpam-5313	158	38	six	six	NUM
ejpam-5313	158	39	vertices	vertex	NOUN
ejpam-5313	158	40	e1	e1	PROPN
ejpam-5313	158	41	,	,	PUNCT
ejpam-5313	158	42	e2	e2	PROPN
ejpam-5313	158	43	,	,	PUNCT
ejpam-5313	158	44	e3	e3	NOUN
ejpam-5313	158	45	,	,	PUNCT
ejpam-5313	158	46	en−1	en−1	PROPN
ejpam-5313	158	47	,	,	PUNCT
ejpam-5313	158	48	en−2	en−2	PROPN
ejpam-5313	158	49	,	,	PUNCT
ejpam-5313	158	50	en−3	en−3	ADJ
ejpam-5313	158	51	from	from	ADP
ejpam-5313	158	52	v2	v2	PROPN
ejpam-5313	158	53	will	will	AUX
ejpam-5313	158	54	be	be	AUX
ejpam-5313	158	55	even	even	ADV
ejpam-5313	158	56	sum	sum	NOUN
ejpam-5313	158	57	dominated	dominate	VERB
ejpam-5313	158	58	.	.	PUNCT
ejpam-5313	159	1	now	now	ADV
ejpam-5313	159	2	to	to	PART
ejpam-5313	159	3	even	even	ADV
ejpam-5313	159	4	sum	sum	VERB
ejpam-5313	159	5	s.	s.	PROPN
ejpam-5313	159	6	h	h	PROPN
ejpam-5313	159	7	karkar	karkar	PROPN
ejpam-5313	160	1	et	et	PROPN
ejpam-5313	160	2	al	al	PROPN
ejpam-5313	160	3	.	.	PUNCT
ejpam-5313	160	4	/	/	SYM
ejpam-5313	160	5	eur	eur	PROPN
ejpam-5313	160	6	.	.	PUNCT
ejpam-5313	161	1	j.	j.	PROPN
ejpam-5313	161	2	pure	pure	PROPN
ejpam-5313	161	3	appl	appl	PROPN
ejpam-5313	161	4	.	.	PROPN
ejpam-5313	161	5	math	math	PROPN
ejpam-5313	161	6	,	,	PUNCT
ejpam-5313	161	7	17	17	NUM
ejpam-5313	161	8	(	(	PUNCT
ejpam-5313	161	9	3	3	NUM
ejpam-5313	161	10	)	)	PUNCT
ejpam-5313	161	11	(	(	PUNCT
ejpam-5313	161	12	2024	2024	NUM
ejpam-5313	161	13	)	)	PUNCT
ejpam-5313	161	14	,	,	PUNCT
ejpam-5313	161	15	2084	2084	NUM
ejpam-5313	161	16	-	-	SYM
ejpam-5313	161	17	2091	2091	NUM
ejpam-5313	161	18	2089	2089	NUM
ejpam-5313	161	19	dominate	dominate	VERB
ejpam-5313	161	20	remaining	remain	VERB
ejpam-5313	161	21	n	n	CCONJ
ejpam-5313	161	22	−	−	NUM
ejpam-5313	161	23	6	6	NUM
ejpam-5313	161	24	vertices	vertex	NOUN
ejpam-5313	161	25	from	from	ADP
ejpam-5313	161	26	v1	v1	NOUN
ejpam-5313	161	27	and	and	CCONJ
ejpam-5313	161	28	n	n	CCONJ
ejpam-5313	161	29	−	−	NOUN
ejpam-5313	161	30	7	7	NUM
ejpam-5313	161	31	vertices	vertex	NOUN
ejpam-5313	161	32	from	from	ADP
ejpam-5313	161	33	v2	v2	PROPN
ejpam-5313	161	34	it	it	PRON
ejpam-5313	161	35	is	be	AUX
ejpam-5313	161	36	enough	enough	ADJ
ejpam-5313	161	37	to	to	PART
ejpam-5313	161	38	consider	consider	VERB
ejpam-5313	161	39	⌈	⌈	SYM
ejpam-5313	161	40	n−	n−	NOUN
ejpam-5313	161	41	6	6	NUM
ejpam-5313	161	42	2	2	NUM
ejpam-5313	161	43	⌉	⌉	X
ejpam-5313	161	44	from	from	ADP
ejpam-5313	161	45	v2	v2	PROPN
ejpam-5313	161	46	.	.	PUNCT
ejpam-5313	162	1	thus	thus	ADV
ejpam-5313	162	2	,	,	PUNCT
ejpam-5313	162	3	e1	e1	PROPN
ejpam-5313	162	4	,	,	PUNCT
ejpam-5313	162	5	en−1	en−1	PROPN
ejpam-5313	162	6	,	,	PUNCT
ejpam-5313	162	7	e2	e2	PROPN
ejpam-5313	162	8	,	,	PUNCT
ejpam-5313	162	9	en−2	en−2	PROPN
ejpam-5313	162	10	and	and	CCONJ
ejpam-5313	162	11	⌈	⌈	NUM
ejpam-5313	162	12	n−	n−	NOUN
ejpam-5313	162	13	6	6	NUM
ejpam-5313	162	14	2	2	NUM
ejpam-5313	162	15	⌉	⌉	ADP
ejpam-5313	162	16	vertices	vertice	VERB
ejpam-5313	162	17	from	from	ADP
ejpam-5313	162	18	v2	v2	PROPN
ejpam-5313	162	19	even	even	ADV
ejpam-5313	162	20	sum	sum	NOUN
ejpam-5313	162	21	dominate	dominate	VERB
ejpam-5313	162	22	all	all	DET
ejpam-5313	162	23	the	the	DET
ejpam-5313	162	24	vertices	vertex	NOUN
ejpam-5313	162	25	of	of	ADP
ejpam-5313	162	26	m(pn	m(pn	NOUN
ejpam-5313	162	27	)	)	PUNCT
ejpam-5313	162	28	.	.	PUNCT
ejpam-5313	163	1	theorem	theorem	VERB
ejpam-5313	163	2	4	4	NUM
ejpam-5313	163	3	.	.	PUNCT
ejpam-5313	163	4	γes(m(cn	γes(m(cn	NOUN
ejpam-5313	163	5	)	)	PUNCT
ejpam-5313	163	6	)	)	PUNCT
ejpam-5313	164	1	=	=	PUNCT
ejpam-5313	164	2			PROPN
ejpam-5313	164	3	n	n	ADV
ejpam-5313	164	4	2	2	NUM
ejpam-5313	164	5	,	,	PUNCT
ejpam-5313	164	6	if	if	SCONJ
ejpam-5313	164	7	n	n	PRON
ejpam-5313	164	8	is	be	AUX
ejpam-5313	164	9	an	an	DET
ejpam-5313	164	10	even	even	ADJ
ejpam-5313	164	11	number	number	NOUN
ejpam-5313	164	12	,	,	PUNCT
ejpam-5313	164	13	n+	n+	PUNCT
ejpam-5313	164	14	1	1	NUM
ejpam-5313	164	15	2	2	NUM
ejpam-5313	164	16	,	,	PUNCT
ejpam-5313	164	17	if	if	SCONJ
ejpam-5313	164	18	n	n	PRON
ejpam-5313	164	19	is	be	AUX
ejpam-5313	164	20	an	an	DET
ejpam-5313	164	21	odd	odd	ADJ
ejpam-5313	164	22	number	number	NOUN
ejpam-5313	164	23	.	.	PUNCT
ejpam-5313	165	1	proof	proof	NOUN
ejpam-5313	165	2	.	.	PUNCT
ejpam-5313	166	1	let	let	VERB
ejpam-5313	166	2	v1	v1	NOUN
ejpam-5313	166	3	,	,	PUNCT
ejpam-5313	166	4	v2	v2	PROPN
ejpam-5313	166	5	,	,	PUNCT
ejpam-5313	166	6	v3	v3	PROPN
ejpam-5313	166	7	,	,	PUNCT
ejpam-5313	166	8	.	.	PUNCT
ejpam-5313	166	9	.	.	PUNCT
ejpam-5313	167	1	.	.	PUNCT
ejpam-5313	168	1	,	,	PUNCT
ejpam-5313	168	2	vn	vn	INTJ
ejpam-5313	168	3	be	be	AUX
ejpam-5313	168	4	the	the	DET
ejpam-5313	168	5	vertices	vertex	NOUN
ejpam-5313	168	6	and	and	CCONJ
ejpam-5313	168	7	e1	e1	NOUN
ejpam-5313	168	8	,	,	PUNCT
ejpam-5313	168	9	e2	e2	PROPN
ejpam-5313	168	10	,	,	PUNCT
ejpam-5313	168	11	e3	e3	NOUN
ejpam-5313	168	12	,	,	PUNCT
ejpam-5313	168	13	.	.	PUNCT
ejpam-5313	168	14	.	.	PUNCT
ejpam-5313	169	1	.	.	PUNCT
ejpam-5313	170	1	,	,	PUNCT
ejpam-5313	170	2	en	en	X
ejpam-5313	170	3	be	be	AUX
ejpam-5313	170	4	the	the	DET
ejpam-5313	170	5	edges	edge	NOUN
ejpam-5313	170	6	of	of	ADP
ejpam-5313	170	7	cycle	cycle	NOUN
ejpam-5313	170	8	cn	cn	PROPN
ejpam-5313	170	9	.	.	PUNCT
ejpam-5313	171	1	then	then	ADV
ejpam-5313	171	2	v	v	X
ejpam-5313	171	3	(	(	PUNCT
ejpam-5313	171	4	m(cn	m(cn	NUM
ejpam-5313	171	5	)	)	PUNCT
ejpam-5313	171	6	)	)	PUNCT
ejpam-5313	172	1	=	=	PRON
ejpam-5313	172	2	{	{	PUNCT
ejpam-5313	172	3	v1	v1	PROPN
ejpam-5313	172	4	,	,	PUNCT
ejpam-5313	172	5	v2	v2	PROPN
ejpam-5313	172	6	,	,	PUNCT
ejpam-5313	172	7	.	.	PUNCT
ejpam-5313	172	8	.	.	PUNCT
ejpam-5313	173	1	.	.	PUNCT
ejpam-5313	174	1	,	,	PUNCT
ejpam-5313	174	2	vn	vn	PROPN
ejpam-5313	174	3	,	,	PUNCT
ejpam-5313	174	4	e1	e1	PROPN
ejpam-5313	174	5	,	,	PUNCT
ejpam-5313	174	6	e2	e2	PROPN
ejpam-5313	174	7	,	,	PUNCT
ejpam-5313	174	8	.	.	PUNCT
ejpam-5313	174	9	.	.	PUNCT
ejpam-5313	174	10	.	.	PUNCT
ejpam-5313	175	1	,	,	PUNCT
ejpam-5313	175	2	en	en	ADP
ejpam-5313	175	3	}	}	PUNCT
ejpam-5313	175	4	.	.	PUNCT
ejpam-5313	176	1	here	here	ADV
ejpam-5313	176	2	,	,	PUNCT
ejpam-5313	176	3	d(vi	d(vi	PROPN
ejpam-5313	176	4	)	)	PUNCT
ejpam-5313	176	5	=	=	SYM
ejpam-5313	176	6	4	4	NUM
ejpam-5313	176	7	for	for	ADP
ejpam-5313	176	8	1	1	NUM
ejpam-5313	176	9	≤	≤	NUM
ejpam-5313	176	10	i	i	PRON
ejpam-5313	176	11	≤	≤	PROPN
ejpam-5313	176	12	n	n	CCONJ
ejpam-5313	176	13	,	,	PUNCT
ejpam-5313	176	14	d(ei	d(ei	PROPN
ejpam-5313	176	15	)	)	PUNCT
ejpam-5313	176	16	=	=	SYM
ejpam-5313	176	17	2	2	NUM
ejpam-5313	176	18	for	for	ADP
ejpam-5313	176	19	1	1	NUM
ejpam-5313	176	20	≤	≤	NUM
ejpam-5313	176	21	i	i	PRON
ejpam-5313	176	22	≤	≤	PROPN
ejpam-5313	176	23	n.	n.	NOUN
ejpam-5313	176	24	therefore	therefore	ADV
ejpam-5313	176	25	,	,	PUNCT
ejpam-5313	176	26	every	every	DET
ejpam-5313	176	27	vi	vi	NOUN
ejpam-5313	176	28	even	even	ADV
ejpam-5313	176	29	sum	sum	NOUN
ejpam-5313	176	30	dominates	dominate	VERB
ejpam-5313	176	31	four	four	NUM
ejpam-5313	176	32	vertices	vertex	NOUN
ejpam-5313	176	33	other	other	ADJ
ejpam-5313	176	34	than	than	ADP
ejpam-5313	176	35	itself	itself	PRON
ejpam-5313	176	36	while	while	SCONJ
ejpam-5313	176	37	every	every	DET
ejpam-5313	176	38	ei	ei	NOUN
ejpam-5313	176	39	even	even	ADV
ejpam-5313	176	40	sum	sum	NOUN
ejpam-5313	176	41	dominates	dominate	VERB
ejpam-5313	176	42	two	two	NUM
ejpam-5313	176	43	vertices	vertex	NOUN
ejpam-5313	176	44	other	other	ADJ
ejpam-5313	176	45	than	than	ADP
ejpam-5313	176	46	itself	itself	PRON
ejpam-5313	176	47	.	.	PUNCT
ejpam-5313	177	1	if	if	SCONJ
ejpam-5313	177	2	n	n	PRON
ejpam-5313	177	3	is	be	AUX
ejpam-5313	177	4	an	an	DET
ejpam-5313	177	5	even	even	ADJ
ejpam-5313	177	6	number	number	NOUN
ejpam-5313	177	7	then	then	ADV
ejpam-5313	177	8	in	in	ADP
ejpam-5313	177	9	order	order	NOUN
ejpam-5313	177	10	to	to	PART
ejpam-5313	177	11	form	form	VERB
ejpam-5313	177	12	an	an	DET
ejpam-5313	177	13	even	even	ADV
ejpam-5313	177	14	sum	sum	NOUN
ejpam-5313	177	15	dominating	dominating	NOUN
ejpam-5313	177	16	set	set	NOUN
ejpam-5313	177	17	of	of	ADP
ejpam-5313	177	18	minimum	minimum	ADJ
ejpam-5313	177	19	cardinality	cardinality	NOUN
ejpam-5313	177	20	it	it	PRON
ejpam-5313	177	21	is	be	AUX
ejpam-5313	177	22	enough	enough	ADJ
ejpam-5313	177	23	to	to	PART
ejpam-5313	177	24	consider	consider	VERB
ejpam-5313	177	25	either	either	CCONJ
ejpam-5313	177	26	n	n	PRON
ejpam-5313	177	27	2	2	NUM
ejpam-5313	177	28	vertices	vertex	NOUN
ejpam-5313	177	29	,	,	PUNCT
ejpam-5313	177	30	either	either	CCONJ
ejpam-5313	177	31	v1	v1	NOUN
ejpam-5313	177	32	,	,	PUNCT
ejpam-5313	177	33	v3	v3	PROPN
ejpam-5313	177	34	,	,	PUNCT
ejpam-5313	177	35	v5	v5	PROPN
ejpam-5313	177	36	,	,	PUNCT
ejpam-5313	177	37	...	...	PUNCT
ejpam-5313	177	38	,	,	PUNCT
ejpam-5313	177	39	vn−1	vn−1	ADJ
ejpam-5313	177	40	or	or	CCONJ
ejpam-5313	177	41	v2	v2	PROPN
ejpam-5313	177	42	,	,	PUNCT
ejpam-5313	177	43	v4	v4	PROPN
ejpam-5313	177	44	,	,	PUNCT
ejpam-5313	177	45	v6	v6	NOUN
ejpam-5313	177	46	,	,	PUNCT
ejpam-5313	177	47	...	...	PUNCT
ejpam-5313	177	48	,	,	PUNCT
ejpam-5313	177	49	vn	vn	VERB
ejpam-5313	177	50	from	from	ADP
ejpam-5313	177	51	m(cn	m(cn	NUM
ejpam-5313	177	52	)	)	PUNCT
ejpam-5313	177	53	.	.	PUNCT
ejpam-5313	178	1	now	now	ADV
ejpam-5313	178	2	if	if	SCONJ
ejpam-5313	178	3	n	n	PRON
ejpam-5313	178	4	is	be	AUX
ejpam-5313	178	5	an	an	DET
ejpam-5313	178	6	odd	odd	ADJ
ejpam-5313	178	7	number	number	NOUN
ejpam-5313	178	8	then	then	ADV
ejpam-5313	178	9	to	to	PART
ejpam-5313	178	10	form	form	VERB
ejpam-5313	178	11	an	an	DET
ejpam-5313	178	12	even	even	ADV
ejpam-5313	178	13	sum	sum	NOUN
ejpam-5313	178	14	dominating	dominating	NOUN
ejpam-5313	178	15	set	set	NOUN
ejpam-5313	178	16	of	of	ADP
ejpam-5313	178	17	minimum	minimum	ADJ
ejpam-5313	178	18	cardinality	cardinality	NOUN
ejpam-5313	178	19	it	it	PRON
ejpam-5313	178	20	is	be	AUX
ejpam-5313	178	21	enough	enough	ADJ
ejpam-5313	178	22	to	to	PART
ejpam-5313	178	23	consider	consider	VERB
ejpam-5313	178	24	n+	n+	ADP
ejpam-5313	178	25	1	1	NUM
ejpam-5313	178	26	2	2	NUM
ejpam-5313	178	27	vertices	vertex	NOUN
ejpam-5313	178	28	,	,	PUNCT
ejpam-5313	178	29	which	which	PRON
ejpam-5313	178	30	may	may	AUX
ejpam-5313	178	31	be	be	AUX
ejpam-5313	178	32	v1	v1	NOUN
ejpam-5313	178	33	,	,	PUNCT
ejpam-5313	178	34	v3	v3	PROPN
ejpam-5313	178	35	,	,	PUNCT
ejpam-5313	178	36	...	...	PUNCT
ejpam-5313	178	37	,	,	PUNCT
ejpam-5313	178	38	vn	vn	NOUN
ejpam-5313	178	39	or	or	CCONJ
ejpam-5313	178	40	v2	v2	PROPN
ejpam-5313	178	41	,	,	PUNCT
ejpam-5313	178	42	v4	v4	NOUN
ejpam-5313	178	43	,	,	PUNCT
ejpam-5313	178	44	...	...	PUNCT
ejpam-5313	178	45	,	,	PUNCT
ejpam-5313	178	46	vn−1	vn−1	PROPN
ejpam-5313	178	47	,	,	PUNCT
ejpam-5313	178	48	vn	vn	VERB
ejpam-5313	178	49	from	from	ADP
ejpam-5313	178	50	m(cn	m(cn	NUM
ejpam-5313	178	51	)	)	PUNCT
ejpam-5313	178	52	.	.	PUNCT
ejpam-5313	179	1	definition	definition	NOUN
ejpam-5313	179	2	2	2	NUM
ejpam-5313	179	3	.	.	PUNCT
ejpam-5313	180	1	let	let	VERB
ejpam-5313	180	2	g	g	PRON
ejpam-5313	180	3	be	be	AUX
ejpam-5313	180	4	a	a	DET
ejpam-5313	180	5	graph	graph	NOUN
ejpam-5313	180	6	with	with	ADP
ejpam-5313	180	7	v	v	NOUN
ejpam-5313	180	8	(	(	PUNCT
ejpam-5313	180	9	g	g	NOUN
ejpam-5313	180	10	)	)	PUNCT
ejpam-5313	180	11	=	=	PUNCT
ejpam-5313	180	12	s1∪s2∪	s1∪s2∪	PROPN
ejpam-5313	180	13	.	.	PUNCT
ejpam-5313	180	14	.	.	PUNCT
ejpam-5313	181	1	.	.	PUNCT
ejpam-5313	182	1	st∪t	st∪t	NOUN
ejpam-5313	182	2	where	where	SCONJ
ejpam-5313	182	3	si	si	PROPN
ejpam-5313	182	4	is	be	AUX
ejpam-5313	182	5	the	the	DET
ejpam-5313	182	6	set	set	NOUN
ejpam-5313	182	7	having	have	VERB
ejpam-5313	182	8	at	at	ADV
ejpam-5313	182	9	least	least	ADV
ejpam-5313	182	10	two	two	NUM
ejpam-5313	182	11	vertices	vertex	NOUN
ejpam-5313	182	12	of	of	ADP
ejpam-5313	182	13	same	same	ADJ
ejpam-5313	182	14	degree	degree	NOUN
ejpam-5313	182	15	and	and	CCONJ
ejpam-5313	182	16	t	t	NOUN
ejpam-5313	182	17	=	=	SYM
ejpam-5313	182	18	v	v	PROPN
ejpam-5313	182	19	(	(	PUNCT
ejpam-5313	182	20	g)−∪si	g)−∪si	NOUN
ejpam-5313	182	21	where	where	SCONJ
ejpam-5313	182	22	i	i	PRON
ejpam-5313	182	23	=	=	NOUN
ejpam-5313	182	24	1	1	NUM
ejpam-5313	182	25	,	,	PUNCT
ejpam-5313	182	26	2	2	NUM
ejpam-5313	182	27	,	,	PUNCT
ejpam-5313	182	28	.	.	PUNCT
ejpam-5313	182	29	.	.	PUNCT
ejpam-5313	183	1	.	.	PUNCT
ejpam-5313	184	1	,	,	PUNCT
ejpam-5313	184	2	t.	t.	NOUN
ejpam-5313	184	3	the	the	DET
ejpam-5313	184	4	degree	degree	NOUN
ejpam-5313	184	5	splitting	splitting	NOUN
ejpam-5313	184	6	graph	graph	NOUN
ejpam-5313	184	7	ds(g	ds(g	NOUN
ejpam-5313	184	8	)	)	PUNCT
ejpam-5313	184	9	is	be	AUX
ejpam-5313	184	10	obtained	obtain	VERB
ejpam-5313	184	11	from	from	ADP
ejpam-5313	184	12	g	g	NOUN
ejpam-5313	184	13	by	by	ADP
ejpam-5313	184	14	adding	add	VERB
ejpam-5313	184	15	vertices	vertex	NOUN
ejpam-5313	184	16	w1	w1	NOUN
ejpam-5313	184	17	,	,	PUNCT
ejpam-5313	184	18	w2	w2	NOUN
ejpam-5313	184	19	,	,	PUNCT
ejpam-5313	184	20	.	.	PUNCT
ejpam-5313	184	21	.	.	PUNCT
ejpam-5313	185	1	.	.	PUNCT
ejpam-5313	186	1	,	,	PUNCT
ejpam-5313	186	2	wt	wt	INTJ
ejpam-5313	186	3	and	and	CCONJ
ejpam-5313	186	4	joining	join	VERB
ejpam-5313	186	5	wi	wi	PROPN
ejpam-5313	186	6	to	to	ADP
ejpam-5313	186	7	each	each	DET
ejpam-5313	186	8	vertex	vertex	NOUN
ejpam-5313	186	9	of	of	ADP
ejpam-5313	186	10	si	si	X
ejpam-5313	186	11	for	for	ADP
ejpam-5313	186	12	1	1	NUM
ejpam-5313	186	13	≤	≤	NUM
ejpam-5313	187	1	i	i	PRON
ejpam-5313	187	2	≤	≤	ADJ
ejpam-5313	187	3	t.	t.	NOUN
ejpam-5313	187	4	theorem	theorem	NOUN
ejpam-5313	187	5	5	5	NUM
ejpam-5313	187	6	.	.	PUNCT
ejpam-5313	187	7	γes(ds(pn	γes(ds(pn	NOUN
ejpam-5313	187	8	)	)	PUNCT
ejpam-5313	187	9	)	)	PUNCT
ejpam-5313	188	1	=	=	PUNCT
ejpam-5313	188	2			NUM
ejpam-5313	188	3	2	2	NUM
ejpam-5313	188	4	,	,	PUNCT
ejpam-5313	188	5	if	if	SCONJ
ejpam-5313	188	6	n	n	PRON
ejpam-5313	188	7	is	be	AUX
ejpam-5313	188	8	an	an	DET
ejpam-5313	188	9	odd	odd	ADJ
ejpam-5313	188	10	number	number	NOUN
ejpam-5313	188	11	,	,	PUNCT
ejpam-5313	188	12	2	2	NUM
ejpam-5313	188	13	+	+	CCONJ
ejpam-5313	188	14	⌈	⌈	ADJ
ejpam-5313	188	15	n−	n−	NOUN
ejpam-5313	188	16	2	2	NUM
ejpam-5313	188	17	3	3	NUM
ejpam-5313	188	18	⌉	⌉	NOUN
ejpam-5313	188	19	,	,	PUNCT
ejpam-5313	188	20	if	if	SCONJ
ejpam-5313	188	21	n	n	PRON
ejpam-5313	188	22	is	be	AUX
ejpam-5313	188	23	an	an	DET
ejpam-5313	188	24	even	even	ADJ
ejpam-5313	188	25	number	number	NOUN
ejpam-5313	188	26	.	.	PUNCT
ejpam-5313	189	1	proof	proof	NOUN
ejpam-5313	189	2	.	.	PUNCT
ejpam-5313	190	1	the	the	DET
ejpam-5313	190	2	path	path	NOUN
ejpam-5313	190	3	pn	pn	PROPN
ejpam-5313	190	4	has	have	VERB
ejpam-5313	190	5	two	two	NUM
ejpam-5313	190	6	pendant	pendant	ADJ
ejpam-5313	190	7	vertices	vertex	NOUN
ejpam-5313	190	8	and	and	CCONJ
ejpam-5313	190	9	the	the	DET
ejpam-5313	190	10	remaining	remain	VERB
ejpam-5313	190	11	n	n	CCONJ
ejpam-5313	190	12	−	−	PRON
ejpam-5313	190	13	2	2	NUM
ejpam-5313	190	14	vertices	vertex	NOUN
ejpam-5313	190	15	are	be	AUX
ejpam-5313	190	16	of	of	ADP
ejpam-5313	190	17	degree	degree	NOUN
ejpam-5313	190	18	2	2	NUM
ejpam-5313	190	19	.	.	PUNCT
ejpam-5313	191	1	thus	thus	ADV
ejpam-5313	191	2	,	,	PUNCT
ejpam-5313	191	3	v	v	INTJ
ejpam-5313	191	4	(	(	PUNCT
ejpam-5313	191	5	pn	pn	NOUN
ejpam-5313	191	6	)	)	PUNCT
ejpam-5313	191	7	=	=	PRON
ejpam-5313	191	8	{	{	PUNCT
ejpam-5313	191	9	vi	vi	PROPN
ejpam-5313	191	10	;	;	PUNCT
ejpam-5313	191	11	1	1	NUM
ejpam-5313	191	12	≤	≤	NUM
ejpam-5313	191	13	i	i	PRON
ejpam-5313	191	14	≤	≤	NOUN
ejpam-5313	191	15	n	n	CCONJ
ejpam-5313	191	16	}	}	PUNCT
ejpam-5313	191	17	=	=	SYM
ejpam-5313	191	18	s1	s1	NOUN
ejpam-5313	191	19	∪	∪	X
ejpam-5313	191	20	s2	s2	VERB
ejpam-5313	191	21	where	where	SCONJ
ejpam-5313	191	22	s1	s1	NOUN
ejpam-5313	191	23	=	=	PUNCT
ejpam-5313	191	24	{	{	PUNCT
ejpam-5313	191	25	v1	v1	PROPN
ejpam-5313	191	26	,	,	PUNCT
ejpam-5313	191	27	vn	vn	NOUN
ejpam-5313	191	28	}	}	PUNCT
ejpam-5313	191	29	and	and	CCONJ
ejpam-5313	191	30	s2	s2	VERB
ejpam-5313	191	31	=	=	SYM
ejpam-5313	191	32	{	{	PUNCT
ejpam-5313	191	33	vi	vi	PROPN
ejpam-5313	191	34	;	;	PUNCT
ejpam-5313	191	35	2	2	NUM
ejpam-5313	191	36	≤	≤	NUM
ejpam-5313	191	37	i	i	PRON
ejpam-5313	191	38	≤	≤	ADJ
ejpam-5313	191	39	n−	n−	NOUN
ejpam-5313	191	40	1	1	NUM
ejpam-5313	191	41	}	}	PUNCT
ejpam-5313	191	42	.	.	PUNCT
ejpam-5313	192	1	to	to	PART
ejpam-5313	192	2	obtain	obtain	VERB
ejpam-5313	192	3	ds(pn	ds(pn	NOUN
ejpam-5313	192	4	)	)	PUNCT
ejpam-5313	192	5	from	from	ADP
ejpam-5313	192	6	pn	pn	PROPN
ejpam-5313	192	7	,	,	PUNCT
ejpam-5313	192	8	add	add	VERB
ejpam-5313	192	9	two	two	NUM
ejpam-5313	192	10	vertices	vertex	NOUN
ejpam-5313	192	11	w1	w1	NOUN
ejpam-5313	192	12	and	and	CCONJ
ejpam-5313	192	13	w2	w2	NOUN
ejpam-5313	192	14	corresponding	correspond	VERB
ejpam-5313	192	15	to	to	ADP
ejpam-5313	192	16	s1	s1	NOUN
ejpam-5313	192	17	and	and	CCONJ
ejpam-5313	192	18	s2	s2	VERB
ejpam-5313	192	19	respectively	respectively	ADV
ejpam-5313	192	20	.	.	PUNCT
ejpam-5313	193	1	thus	thus	ADV
ejpam-5313	193	2	,	,	PUNCT
ejpam-5313	193	3	v	v	INTJ
ejpam-5313	193	4	(	(	PUNCT
ejpam-5313	193	5	ds(pn	ds(pn	PROPN
ejpam-5313	193	6	)	)	PUNCT
ejpam-5313	193	7	)	)	PUNCT
ejpam-5313	194	1	=	=	SYM
ejpam-5313	194	2	v	v	X
ejpam-5313	194	3	(	(	PUNCT
ejpam-5313	194	4	pn)∪{w1	pn)∪{w1	PROPN
ejpam-5313	194	5	,	,	PUNCT
ejpam-5313	194	6	w2	w2	NOUN
ejpam-5313	194	7	}	}	PUNCT
ejpam-5313	194	8	and	and	CCONJ
ejpam-5313	194	9	|v	|v	PROPN
ejpam-5313	194	10	(	(	PUNCT
ejpam-5313	194	11	ds(pn))|	ds(pn))|	NOUN
ejpam-5313	194	12	=	=	SYM
ejpam-5313	194	13	n+2	n+2	X
ejpam-5313	194	14	.	.	PUNCT
ejpam-5313	195	1	we	we	PRON
ejpam-5313	195	2	shall	shall	AUX
ejpam-5313	195	3	consider	consider	VERB
ejpam-5313	195	4	two	two	NUM
ejpam-5313	195	5	cases	case	NOUN
ejpam-5313	195	6	according	accord	VERB
ejpam-5313	195	7	to	to	ADP
ejpam-5313	195	8	values	value	NOUN
ejpam-5313	195	9	of	of	ADP
ejpam-5313	195	10	n.	n.	NOUN
ejpam-5313	195	11	case	case	NOUN
ejpam-5313	195	12	1	1	NUM
ejpam-5313	195	13	:	:	PUNCT
ejpam-5313	195	14	n	n	PRON
ejpam-5313	195	15	is	be	AUX
ejpam-5313	195	16	an	an	DET
ejpam-5313	195	17	odd	odd	ADJ
ejpam-5313	195	18	number	number	NOUN
ejpam-5313	195	19	.	.	PUNCT
ejpam-5313	196	1	according	accord	VERB
ejpam-5313	196	2	to	to	ADP
ejpam-5313	196	3	the	the	DET
ejpam-5313	196	4	definition	definition	NOUN
ejpam-5313	196	5	of	of	ADP
ejpam-5313	196	6	even	even	ADV
ejpam-5313	196	7	sum	sum	NOUN
ejpam-5313	196	8	domination	domination	NOUN
ejpam-5313	196	9	the	the	DET
ejpam-5313	196	10	vertex	vertex	NOUN
ejpam-5313	196	11	w1	w1	NOUN
ejpam-5313	196	12	even	even	ADV
ejpam-5313	196	13	sum	sum	NOUN
ejpam-5313	196	14	dominates	dominate	VERB
ejpam-5313	196	15	both	both	CCONJ
ejpam-5313	196	16	the	the	DET
ejpam-5313	196	17	vertices	vertex	NOUN
ejpam-5313	196	18	v1	v1	NOUN
ejpam-5313	196	19	,	,	PUNCT
ejpam-5313	196	20	vn	vn	NOUN
ejpam-5313	196	21	and	and	CCONJ
ejpam-5313	196	22	itself	itself	PRON
ejpam-5313	196	23	also	also	ADV
ejpam-5313	196	24	.	.	PUNCT
ejpam-5313	197	1	therefore	therefore	ADV
ejpam-5313	197	2	,	,	PUNCT
ejpam-5313	197	3	by	by	ADP
ejpam-5313	197	4	considering	consider	VERB
ejpam-5313	197	5	w1	w1	NOUN
ejpam-5313	197	6	in	in	ADP
ejpam-5313	197	7	s	s	PROPN
ejpam-5313	197	8	,	,	PUNCT
ejpam-5313	197	9	all	all	DET
ejpam-5313	197	10	the	the	DET
ejpam-5313	197	11	vertices	vertex	NOUN
ejpam-5313	197	12	of	of	ADP
ejpam-5313	197	13	s1	s1	NOUN
ejpam-5313	197	14	will	will	AUX
ejpam-5313	197	15	be	be	AUX
ejpam-5313	197	16	even	even	ADV
ejpam-5313	197	17	sum	sum	NOUN
ejpam-5313	197	18	dominated	dominate	VERB
ejpam-5313	197	19	.	.	PUNCT
ejpam-5313	198	1	so	so	ADV
ejpam-5313	198	2	,	,	PUNCT
ejpam-5313	198	3	w1	w1	PROPN
ejpam-5313	198	4	∈	∈	PROPN
ejpam-5313	198	5	s.	s.	PROPN
ejpam-5313	198	6	now	now	ADV
ejpam-5313	198	7	w2	w2	PROPN
ejpam-5313	198	8	can	can	AUX
ejpam-5313	198	9	even	even	ADV
ejpam-5313	198	10	sum	sum	VERB
ejpam-5313	198	11	dominate	dominate	VERB
ejpam-5313	198	12	every	every	DET
ejpam-5313	198	13	vi	vi	NOUN
ejpam-5313	198	14	from	from	ADP
ejpam-5313	198	15	s2	s2	PROPN
ejpam-5313	198	16	while	while	SCONJ
ejpam-5313	198	17	every	every	DET
ejpam-5313	198	18	vi	vi	NOUN
ejpam-5313	198	19	from	from	ADP
ejpam-5313	198	20	s2	s2	NOUN
ejpam-5313	198	21	can	can	AUX
ejpam-5313	198	22	even	even	ADV
ejpam-5313	198	23	sum	sum	VERB
ejpam-5313	198	24	dominate	dominate	VERB
ejpam-5313	198	25	only	only	ADV
ejpam-5313	198	26	its	its	PRON
ejpam-5313	198	27	three	three	NUM
ejpam-5313	198	28	neighbors	neighbor	NOUN
ejpam-5313	198	29	other	other	ADJ
ejpam-5313	198	30	than	than	ADP
ejpam-5313	198	31	itself	itself	PRON
ejpam-5313	198	32	.	.	PUNCT
ejpam-5313	199	1	therefore	therefore	ADV
ejpam-5313	199	2	,	,	PUNCT
ejpam-5313	199	3	we	we	PRON
ejpam-5313	199	4	also	also	ADV
ejpam-5313	199	5	consider	consider	VERB
ejpam-5313	199	6	w2	w2	NOUN
ejpam-5313	199	7	in	in	ADP
ejpam-5313	199	8	s.	s.	PROPN
ejpam-5313	199	9	hence	hence	ADV
ejpam-5313	199	10	s	s	PART
ejpam-5313	199	11	=	=	SYM
ejpam-5313	199	12	{	{	PUNCT
ejpam-5313	199	13	w1	w1	NOUN
ejpam-5313	199	14	,	,	PUNCT
ejpam-5313	199	15	w2	w2	NOUN
ejpam-5313	199	16	}	}	PUNCT
ejpam-5313	199	17	will	will	AUX
ejpam-5313	199	18	be	be	AUX
ejpam-5313	199	19	an	an	DET
ejpam-5313	199	20	even	even	ADV
ejpam-5313	199	21	sum	sum	NOUN
ejpam-5313	199	22	dominating	dominating	NOUN
ejpam-5313	199	23	set	set	NOUN
ejpam-5313	199	24	of	of	ADP
ejpam-5313	199	25	minimum	minimum	ADJ
ejpam-5313	199	26	cardinality	cardinality	NOUN
ejpam-5313	199	27	.	.	PUNCT
ejpam-5313	200	1	therefore	therefore	ADV
ejpam-5313	200	2	,	,	PUNCT
ejpam-5313	200	3	γes(ds(pn	γes(ds(pn	PROPN
ejpam-5313	200	4	)	)	PUNCT
ejpam-5313	200	5	)	)	PUNCT
ejpam-5313	201	1	=	=	SYM
ejpam-5313	201	2	2	2	X
ejpam-5313	201	3	.	.	X
ejpam-5313	201	4	case	case	NOUN
ejpam-5313	201	5	2	2	NUM
ejpam-5313	201	6	:	:	PUNCT
ejpam-5313	201	7	n	n	PRON
ejpam-5313	201	8	is	be	AUX
ejpam-5313	201	9	an	an	DET
ejpam-5313	201	10	even	even	ADJ
ejpam-5313	201	11	number	number	NOUN
ejpam-5313	201	12	.	.	PUNCT
ejpam-5313	202	1	according	accord	VERB
ejpam-5313	202	2	to	to	ADP
ejpam-5313	202	3	the	the	DET
ejpam-5313	202	4	definition	definition	NOUN
ejpam-5313	202	5	of	of	ADP
ejpam-5313	202	6	even	even	ADV
ejpam-5313	202	7	sum	sum	NOUN
ejpam-5313	202	8	domination	domination	NOUN
ejpam-5313	202	9	the	the	DET
ejpam-5313	202	10	vertex	vertex	NOUN
ejpam-5313	202	11	w1	w1	NOUN
ejpam-5313	202	12	even	even	ADV
ejpam-5313	202	13	sum	sum	NOUN
ejpam-5313	202	14	dominates	dominate	VERB
ejpam-5313	202	15	both	both	CCONJ
ejpam-5313	202	16	the	the	DET
ejpam-5313	202	17	vertices	vertex	NOUN
ejpam-5313	202	18	v1	v1	NOUN
ejpam-5313	202	19	,	,	PUNCT
ejpam-5313	202	20	vn	vn	NOUN
ejpam-5313	202	21	and	and	CCONJ
ejpam-5313	202	22	itself	itself	PRON
ejpam-5313	202	23	also	also	ADV
ejpam-5313	202	24	.	.	PUNCT
ejpam-5313	203	1	therefore	therefore	ADV
ejpam-5313	203	2	,	,	PUNCT
ejpam-5313	203	3	if	if	SCONJ
ejpam-5313	203	4	we	we	PRON
ejpam-5313	203	5	consider	consider	VERB
ejpam-5313	203	6	w1	w1	NOUN
ejpam-5313	203	7	in	in	ADP
ejpam-5313	203	8	s	s	PRON
ejpam-5313	203	9	then	then	ADV
ejpam-5313	203	10	all	all	DET
ejpam-5313	203	11	the	the	DET
ejpam-5313	203	12	vertices	vertex	NOUN
ejpam-5313	203	13	of	of	ADP
ejpam-5313	203	14	s1	s1	NOUN
ejpam-5313	203	15	are	be	AUX
ejpam-5313	203	16	even	even	ADV
ejpam-5313	203	17	sum	sum	NOUN
ejpam-5313	203	18	dominated	dominate	VERB
ejpam-5313	203	19	.	.	PUNCT
ejpam-5313	204	1	in	in	ADP
ejpam-5313	204	2	s2	s2	PROPN
ejpam-5313	204	3	,	,	PUNCT
ejpam-5313	204	4	deg(vi	deg(vi	NOUN
ejpam-5313	204	5	)	)	PUNCT
ejpam-5313	205	1	=	=	SYM
ejpam-5313	205	2	3	3	NUM
ejpam-5313	205	3	which	which	PRON
ejpam-5313	205	4	is	be	AUX
ejpam-5313	205	5	odd	odd	ADJ
ejpam-5313	205	6	number	number	NOUN
ejpam-5313	205	7	while	while	SCONJ
ejpam-5313	205	8	deg(w2	deg(w2	NOUN
ejpam-5313	205	9	)	)	PUNCT
ejpam-5313	205	10	=	=	SYM
ejpam-5313	205	11	n	n	CCONJ
ejpam-5313	205	12	−	−	PROPN
ejpam-5313	205	13	2	2	NUM
ejpam-5313	205	14	which	which	PRON
ejpam-5313	205	15	is	be	AUX
ejpam-5313	205	16	even	even	ADV
ejpam-5313	205	17	number	number	NOUN
ejpam-5313	205	18	w2	w2	NOUN
ejpam-5313	205	19	even	even	ADV
ejpam-5313	205	20	sum	sum	NOUN
ejpam-5313	205	21	dominates	dominate	VERB
ejpam-5313	205	22	itself	itself	PRON
ejpam-5313	205	23	only	only	ADV
ejpam-5313	205	24	and	and	CCONJ
ejpam-5313	205	25	every	every	DET
ejpam-5313	205	26	vi	vi	NOUN
ejpam-5313	205	27	can	can	AUX
ejpam-5313	205	28	even	even	ADV
ejpam-5313	205	29	sum	sum	AUX
ejpam-5313	205	30	dominates	dominate	VERB
ejpam-5313	205	31	only	only	ADV
ejpam-5313	205	32	its	its	PRON
ejpam-5313	205	33	neighbor	neighbor	NOUN
ejpam-5313	205	34	from	from	ADP
ejpam-5313	205	35	s2	s2	PROPN
ejpam-5313	205	36	and	and	CCONJ
ejpam-5313	205	37	itself	itself	PRON
ejpam-5313	205	38	.	.	PUNCT
ejpam-5313	206	1	so	so	ADV
ejpam-5313	206	2	,	,	PUNCT
ejpam-5313	206	3	from	from	ADP
ejpam-5313	206	4	n	n	CCONJ
ejpam-5313	206	5	−	−	NUM
ejpam-5313	206	6	2	2	NUM
ejpam-5313	206	7	vertices	vertex	NOUN
ejpam-5313	206	8	of	of	ADP
ejpam-5313	206	9	s.	s.	PROPN
ejpam-5313	206	10	h	h	PROPN
ejpam-5313	206	11	karkar	karkar	PROPN
ejpam-5313	206	12	et	et	PROPN
ejpam-5313	206	13	al	al	PROPN
ejpam-5313	206	14	.	.	PUNCT
ejpam-5313	206	15	/	/	SYM
ejpam-5313	206	16	eur	eur	PROPN
ejpam-5313	206	17	.	.	PUNCT
ejpam-5313	207	1	j.	j.	PROPN
ejpam-5313	207	2	pure	pure	PROPN
ejpam-5313	207	3	appl	appl	PROPN
ejpam-5313	207	4	.	.	PROPN
ejpam-5313	207	5	math	math	PROPN
ejpam-5313	207	6	,	,	PUNCT
ejpam-5313	207	7	17	17	NUM
ejpam-5313	207	8	(	(	PUNCT
ejpam-5313	207	9	3	3	NUM
ejpam-5313	207	10	)	)	PUNCT
ejpam-5313	207	11	(	(	PUNCT
ejpam-5313	207	12	2024	2024	NUM
ejpam-5313	207	13	)	)	PUNCT
ejpam-5313	207	14	,	,	PUNCT
ejpam-5313	207	15	2084	2084	NUM
ejpam-5313	207	16	-	-	SYM
ejpam-5313	207	17	2091	2091	NUM
ejpam-5313	207	18	2090	2090	NUM
ejpam-5313	207	19	s2	s2	NOUN
ejpam-5313	207	20	it	it	PRON
ejpam-5313	207	21	is	be	AUX
ejpam-5313	207	22	enough	enough	ADJ
ejpam-5313	207	23	to	to	PART
ejpam-5313	207	24	consider	consider	VERB
ejpam-5313	207	25	⌈	⌈	SYM
ejpam-5313	207	26	n−	n−	NOUN
ejpam-5313	207	27	2	2	NUM
ejpam-5313	207	28	3	3	NUM
ejpam-5313	207	29	⌉	⌉	ADP
ejpam-5313	207	30	vertices	vertex	NOUN
ejpam-5313	207	31	from	from	ADP
ejpam-5313	207	32	s2	s2	PROPN
ejpam-5313	207	33	.	.	PUNCT
ejpam-5313	208	1	therefore	therefore	ADV
ejpam-5313	208	2	,	,	PUNCT
ejpam-5313	208	3	s	s	VERB
ejpam-5313	208	4	forms	form	NOUN
ejpam-5313	208	5	an	an	DET
ejpam-5313	208	6	even	even	ADV
ejpam-5313	208	7	sum	sum	NOUN
ejpam-5313	208	8	dominating	dominating	NOUN
ejpam-5313	208	9	set	set	NOUN
ejpam-5313	208	10	of	of	ADP
ejpam-5313	208	11	minimum	minimum	ADJ
ejpam-5313	208	12	cardinality	cardinality	NOUN
ejpam-5313	208	13	.	.	PUNCT
ejpam-5313	209	1	hence	hence	ADV
ejpam-5313	209	2	,	,	PUNCT
ejpam-5313	209	3	γes(ds(pn	γes(ds(pn	PROPN
ejpam-5313	209	4	)	)	PUNCT
ejpam-5313	209	5	)	)	PUNCT
ejpam-5313	210	1	=	=	SYM
ejpam-5313	210	2	2	2	NUM
ejpam-5313	210	3	+	+	NUM
ejpam-5313	210	4	⌈	⌈	NOUN
ejpam-5313	210	5	n−	n−	NOUN
ejpam-5313	210	6	2	2	NUM
ejpam-5313	210	7	3	3	NUM
ejpam-5313	210	8	⌉	⌉	X
ejpam-5313	210	9	.	.	PUNCT
ejpam-5313	211	1	definition	definition	NOUN
ejpam-5313	211	2	3	3	NUM
ejpam-5313	211	3	.	.	PUNCT
ejpam-5313	212	1	the	the	DET
ejpam-5313	212	2	wheel	wheel	NOUN
ejpam-5313	212	3	wn	wn	PROPN
ejpam-5313	212	4	is	be	AUX
ejpam-5313	212	5	defined	define	VERB
ejpam-5313	212	6	to	to	PART
ejpam-5313	212	7	be	be	AUX
ejpam-5313	212	8	the	the	DET
ejpam-5313	212	9	join	join	NOUN
ejpam-5313	212	10	k1	k1	NOUN
ejpam-5313	213	1	+	+	CCONJ
ejpam-5313	213	2	cn	cn	PROPN
ejpam-5313	213	3	.	.	PUNCT
ejpam-5313	214	1	the	the	DET
ejpam-5313	214	2	vertex	vertex	NOUN
ejpam-5313	214	3	corresponding	correspond	VERB
ejpam-5313	214	4	to	to	ADP
ejpam-5313	214	5	k1	k1	PROPN
ejpam-5313	214	6	is	be	AUX
ejpam-5313	214	7	known	know	VERB
ejpam-5313	214	8	as	as	ADP
ejpam-5313	214	9	the	the	DET
ejpam-5313	214	10	apex	apex	NOUN
ejpam-5313	214	11	and	and	CCONJ
ejpam-5313	214	12	the	the	DET
ejpam-5313	214	13	vertices	vertex	NOUN
ejpam-5313	214	14	corresponding	correspond	VERB
ejpam-5313	214	15	to	to	ADP
ejpam-5313	214	16	cycle	cycle	NOUN
ejpam-5313	214	17	are	be	AUX
ejpam-5313	214	18	known	know	VERB
ejpam-5313	214	19	as	as	ADP
ejpam-5313	214	20	rim	rim	NOUN
ejpam-5313	214	21	vertices	vertex	NOUN
ejpam-5313	214	22	while	while	SCONJ
ejpam-5313	214	23	the	the	DET
ejpam-5313	214	24	edges	edge	NOUN
ejpam-5313	214	25	corresponding	correspond	VERB
ejpam-5313	214	26	to	to	ADP
ejpam-5313	214	27	cycle	cycle	NOUN
ejpam-5313	214	28	are	be	AUX
ejpam-5313	214	29	known	know	VERB
ejpam-5313	214	30	as	as	ADP
ejpam-5313	214	31	rim	rim	NOUN
ejpam-5313	214	32	edges	edge	NOUN
ejpam-5313	214	33	.	.	PUNCT
ejpam-5313	215	1	theorem	theorem	VERB
ejpam-5313	215	2	6	6	NUM
ejpam-5313	215	3	.	.	PUNCT
ejpam-5313	215	4	γes(wn	γes(wn	NOUN
ejpam-5313	215	5	)	)	PUNCT
ejpam-5313	215	6	=	=	PUNCT
ejpam-5313	216	1			PROPN
ejpam-5313	216	2	1	1	NUM
ejpam-5313	216	3	,	,	PUNCT
ejpam-5313	216	4	if	if	SCONJ
ejpam-5313	216	5	n	n	PRON
ejpam-5313	216	6	is	be	AUX
ejpam-5313	216	7	an	an	DET
ejpam-5313	216	8	odd	odd	ADJ
ejpam-5313	216	9	number	number	NOUN
ejpam-5313	216	10	,	,	PUNCT
ejpam-5313	216	11	γes(cn	γes(cn	NOUN
ejpam-5313	216	12	)	)	PUNCT
ejpam-5313	217	1	+	+	NUM
ejpam-5313	217	2	1	1	NUM
ejpam-5313	217	3	,	,	PUNCT
ejpam-5313	217	4	if	if	SCONJ
ejpam-5313	217	5	n	n	PRON
ejpam-5313	217	6	is	be	AUX
ejpam-5313	217	7	an	an	DET
ejpam-5313	217	8	even	even	ADJ
ejpam-5313	217	9	number	number	NOUN
ejpam-5313	217	10	.	.	PUNCT
ejpam-5313	218	1	proof	proof	NOUN
ejpam-5313	218	2	.	.	PUNCT
ejpam-5313	219	1	consider	consider	VERB
ejpam-5313	219	2	the	the	DET
ejpam-5313	219	3	wheel	wheel	NOUN
ejpam-5313	219	4	wn	wn	NOUN
ejpam-5313	219	5	with	with	ADP
ejpam-5313	219	6	the	the	DET
ejpam-5313	219	7	vertices	vertex	NOUN
ejpam-5313	219	8	v1	v1	NOUN
ejpam-5313	219	9	,	,	PUNCT
ejpam-5313	219	10	v2	v2	NOUN
ejpam-5313	219	11	,	,	PUNCT
ejpam-5313	219	12	.	.	PUNCT
ejpam-5313	219	13	.	.	PUNCT
ejpam-5313	220	1	.	.	PUNCT
ejpam-5313	221	1	,	,	PUNCT
ejpam-5313	221	2	vn	vn	INTJ
ejpam-5313	221	3	as	as	ADP
ejpam-5313	221	4	its	its	PRON
ejpam-5313	221	5	rim	rim	NOUN
ejpam-5313	221	6	vertices	vertex	NOUN
ejpam-5313	221	7	and	and	CCONJ
ejpam-5313	221	8	v0	v0	NOUN
ejpam-5313	221	9	as	as	ADP
ejpam-5313	221	10	its	its	PRON
ejpam-5313	221	11	apex	apex	NOUN
ejpam-5313	221	12	vertex	vertex	NOUN
ejpam-5313	221	13	.	.	PUNCT
ejpam-5313	222	1	according	accord	VERB
ejpam-5313	222	2	to	to	ADP
ejpam-5313	222	3	value	value	NOUN
ejpam-5313	222	4	of	of	ADP
ejpam-5313	222	5	n	n	PRON
ejpam-5313	222	6	we	we	PRON
ejpam-5313	222	7	consider	consider	VERB
ejpam-5313	222	8	following	follow	VERB
ejpam-5313	222	9	two	two	NUM
ejpam-5313	222	10	cases	case	NOUN
ejpam-5313	222	11	.	.	PUNCT
ejpam-5313	223	1	case	case	NOUN
ejpam-5313	223	2	1	1	NUM
ejpam-5313	223	3	:	:	PUNCT
ejpam-5313	223	4	n	n	PRON
ejpam-5313	223	5	is	be	AUX
ejpam-5313	223	6	an	an	DET
ejpam-5313	223	7	odd	odd	ADJ
ejpam-5313	223	8	number	number	NOUN
ejpam-5313	223	9	.	.	PUNCT
ejpam-5313	224	1	in	in	ADP
ejpam-5313	224	2	this	this	DET
ejpam-5313	224	3	case	case	NOUN
ejpam-5313	224	4	,	,	PUNCT
ejpam-5313	224	5	deg(vi	deg(vi	X
ejpam-5313	224	6	)	)	PUNCT
ejpam-5313	224	7	=	=	SYM
ejpam-5313	224	8	3	3	NUM
ejpam-5313	224	9	,	,	PUNCT
ejpam-5313	224	10	1	1	NUM
ejpam-5313	224	11	≤	≤	NUM
ejpam-5313	224	12	i	i	PRON
ejpam-5313	224	13	≤	≤	ADJ
ejpam-5313	224	14	n	n	CCONJ
ejpam-5313	224	15	and	and	CCONJ
ejpam-5313	224	16	deg(v0	deg(v0	ADJ
ejpam-5313	224	17	)	)	PUNCT
ejpam-5313	224	18	=	=	SYM
ejpam-5313	224	19	n	n	CCONJ
ejpam-5313	224	20	,	,	PUNCT
ejpam-5313	224	21	which	which	PRON
ejpam-5313	224	22	is	be	AUX
ejpam-5313	224	23	an	an	DET
ejpam-5313	224	24	odd	odd	ADJ
ejpam-5313	224	25	number	number	NOUN
ejpam-5313	224	26	.	.	PUNCT
ejpam-5313	225	1	so	so	ADV
ejpam-5313	225	2	,	,	PUNCT
ejpam-5313	225	3	deg(vi	deg(vi	NOUN
ejpam-5313	225	4	)	)	PUNCT
ejpam-5313	226	1	+	+	CCONJ
ejpam-5313	226	2	deg(v0	deg(v0	PROPN
ejpam-5313	226	3	)	)	PUNCT
ejpam-5313	226	4	will	will	AUX
ejpam-5313	226	5	be	be	AUX
ejpam-5313	226	6	an	an	DET
ejpam-5313	226	7	even	even	ADJ
ejpam-5313	226	8	number	number	NOUN
ejpam-5313	226	9	.	.	PUNCT
ejpam-5313	227	1	therefore	therefore	ADV
ejpam-5313	227	2	,	,	PUNCT
ejpam-5313	227	3	the	the	DET
ejpam-5313	227	4	vertex	vertex	NOUN
ejpam-5313	227	5	v0	v0	NOUN
ejpam-5313	227	6	even	even	ADV
ejpam-5313	227	7	sum	sum	NOUN
ejpam-5313	227	8	dominates	dominate	VERB
ejpam-5313	227	9	every	every	DET
ejpam-5313	227	10	rim	rim	NOUN
ejpam-5313	227	11	vertex	vertex	NOUN
ejpam-5313	227	12	.	.	PUNCT
ejpam-5313	228	1	thus	thus	ADV
ejpam-5313	228	2	it	it	PRON
ejpam-5313	228	3	is	be	AUX
ejpam-5313	228	4	enough	enough	ADJ
ejpam-5313	228	5	to	to	PART
ejpam-5313	228	6	consider	consider	VERB
ejpam-5313	228	7	an	an	DET
ejpam-5313	228	8	apex	apex	NOUN
ejpam-5313	228	9	vertex	vertex	NOUN
ejpam-5313	228	10	v0	v0	NOUN
ejpam-5313	228	11	in	in	ADP
ejpam-5313	228	12	even	even	ADV
ejpam-5313	228	13	sum	sum	NOUN
ejpam-5313	228	14	dominating	dominating	NOUN
ejpam-5313	228	15	set	set	VERB
ejpam-5313	228	16	s.	s.	PROPN
ejpam-5313	228	17	hence	hence	PROPN
ejpam-5313	228	18	,	,	PUNCT
ejpam-5313	228	19	γes(wn	γes(wn	NOUN
ejpam-5313	228	20	)	)	PUNCT
ejpam-5313	228	21	=	=	SYM
ejpam-5313	228	22	1	1	X
ejpam-5313	228	23	.	.	X
ejpam-5313	228	24	case	case	NOUN
ejpam-5313	228	25	2	2	NUM
ejpam-5313	228	26	:	:	PUNCT
ejpam-5313	228	27	n	n	PRON
ejpam-5313	228	28	is	be	AUX
ejpam-5313	228	29	an	an	DET
ejpam-5313	228	30	even	even	ADJ
ejpam-5313	228	31	number	number	NOUN
ejpam-5313	228	32	.	.	PUNCT
ejpam-5313	229	1	in	in	ADP
ejpam-5313	229	2	this	this	DET
ejpam-5313	229	3	case	case	NOUN
ejpam-5313	229	4	,	,	PUNCT
ejpam-5313	229	5	deg(vi	deg(vi	X
ejpam-5313	229	6	)	)	PUNCT
ejpam-5313	229	7	=	=	SYM
ejpam-5313	229	8	3	3	NUM
ejpam-5313	229	9	,	,	PUNCT
ejpam-5313	229	10	1	1	NUM
ejpam-5313	229	11	≤	≤	NUM
ejpam-5313	229	12	i	i	PRON
ejpam-5313	229	13	≤	≤	ADJ
ejpam-5313	229	14	n	n	CCONJ
ejpam-5313	229	15	and	and	CCONJ
ejpam-5313	229	16	deg(v0	deg(v0	ADJ
ejpam-5313	229	17	)	)	PUNCT
ejpam-5313	229	18	=	=	SYM
ejpam-5313	229	19	n	n	CCONJ
ejpam-5313	229	20	,	,	PUNCT
ejpam-5313	229	21	which	which	PRON
ejpam-5313	229	22	is	be	AUX
ejpam-5313	229	23	an	an	DET
ejpam-5313	229	24	even	even	ADJ
ejpam-5313	229	25	number	number	NOUN
ejpam-5313	229	26	.	.	PUNCT
ejpam-5313	230	1	the	the	DET
ejpam-5313	230	2	apex	apex	PROPN
ejpam-5313	230	3	vertex	vertex	NOUN
ejpam-5313	230	4	v0	v0	NOUN
ejpam-5313	230	5	does	do	AUX
ejpam-5313	230	6	not	not	PART
ejpam-5313	230	7	even	even	ADV
ejpam-5313	230	8	sum	sum	VERB
ejpam-5313	230	9	dominate	dominate	VERB
ejpam-5313	230	10	any	any	DET
ejpam-5313	230	11	rim	rim	NOUN
ejpam-5313	230	12	vertex	vertex	NOUN
ejpam-5313	230	13	and	and	CCONJ
ejpam-5313	230	14	it	it	PRON
ejpam-5313	230	15	is	be	AUX
ejpam-5313	230	16	not	not	PART
ejpam-5313	230	17	even	even	ADV
ejpam-5313	230	18	sum	sum	NOUN
ejpam-5313	230	19	dominated	dominate	VERB
ejpam-5313	230	20	by	by	ADP
ejpam-5313	230	21	any	any	DET
ejpam-5313	230	22	rim	rim	NOUN
ejpam-5313	230	23	vertex	vertex	NOUN
ejpam-5313	230	24	also	also	ADV
ejpam-5313	230	25	.	.	PUNCT
ejpam-5313	231	1	so	so	ADV
ejpam-5313	231	2	the	the	DET
ejpam-5313	231	3	vertex	vertex	NOUN
ejpam-5313	231	4	v0	v0	NOUN
ejpam-5313	231	5	must	must	AUX
ejpam-5313	231	6	be	be	AUX
ejpam-5313	231	7	in	in	ADP
ejpam-5313	231	8	even	even	ADV
ejpam-5313	231	9	sum	sum	NOUN
ejpam-5313	231	10	dominating	dominating	NOUN
ejpam-5313	231	11	set	set	NOUN
ejpam-5313	231	12	s	s	PART
ejpam-5313	231	13	while	while	SCONJ
ejpam-5313	231	14	each	each	DET
ejpam-5313	231	15	rim	rim	NOUN
ejpam-5313	231	16	vertex	vertex	NOUN
ejpam-5313	231	17	can	can	AUX
ejpam-5313	231	18	even	even	ADV
ejpam-5313	231	19	sum	sum	VERB
ejpam-5313	231	20	dominate	dominate	VERB
ejpam-5313	231	21	its	its	PRON
ejpam-5313	231	22	both	both	DET
ejpam-5313	231	23	neighbors	neighbor	NOUN
ejpam-5313	231	24	likewise	likewise	ADV
ejpam-5313	231	25	cycle	cycle	NOUN
ejpam-5313	231	26	.	.	PUNCT
ejpam-5313	232	1	thus	thus	ADV
ejpam-5313	232	2	we	we	PRON
ejpam-5313	232	3	need	need	VERB
ejpam-5313	232	4	⌈n	⌈n	NOUN
ejpam-5313	232	5	3	3	NUM
ejpam-5313	232	6	⌉	⌉	ADP
ejpam-5313	232	7	vertices	vertice	VERB
ejpam-5313	232	8	to	to	PART
ejpam-5313	232	9	even	even	ADV
ejpam-5313	232	10	sum	sum	VERB
ejpam-5313	232	11	dominate	dominate	VERB
ejpam-5313	232	12	all	all	DET
ejpam-5313	232	13	the	the	DET
ejpam-5313	232	14	rim	rim	NOUN
ejpam-5313	232	15	vertices	vertex	NOUN
ejpam-5313	232	16	.	.	PUNCT
ejpam-5313	233	1	therefore	therefore	ADV
ejpam-5313	233	2	,	,	PUNCT
ejpam-5313	233	3	it	it	PRON
ejpam-5313	233	4	is	be	AUX
ejpam-5313	233	5	enough	enough	ADJ
ejpam-5313	233	6	to	to	PART
ejpam-5313	233	7	consider⌈n	consider⌈n	VERB
ejpam-5313	233	8	3	3	NUM
ejpam-5313	233	9	⌉	⌉	PRON
ejpam-5313	233	10	+1	+1	PROPN
ejpam-5313	233	11	vertices	vertice	VERB
ejpam-5313	233	12	to	to	PART
ejpam-5313	233	13	construct	construct	VERB
ejpam-5313	233	14	the	the	DET
ejpam-5313	233	15	even	even	ADJ
ejpam-5313	233	16	sum	sum	NOUN
ejpam-5313	233	17	dominating	dominating	NOUN
ejpam-5313	233	18	set	set	NOUN
ejpam-5313	233	19	of	of	ADP
ejpam-5313	233	20	minimum	minimum	ADJ
ejpam-5313	233	21	cardinality	cardinality	NOUN
ejpam-5313	233	22	.	.	PUNCT
ejpam-5313	234	1	hence	hence	ADV
ejpam-5313	234	2	,	,	PUNCT
ejpam-5313	234	3	γes(wn	γes(wn	NOUN
ejpam-5313	234	4	)	)	PUNCT
ejpam-5313	234	5	=	=	SYM
ejpam-5313	234	6	γes(cn	γes(cn	NOUN
ejpam-5313	234	7	)	)	PUNCT
ejpam-5313	235	1	+	+	CCONJ
ejpam-5313	235	2	1	1	NUM
ejpam-5313	235	3	.	.	X
ejpam-5313	235	4	4	4	NUM
ejpam-5313	235	5	.	.	X
ejpam-5313	235	6	concluding	conclude	VERB
ejpam-5313	235	7	remarks	remark	NOUN
ejpam-5313	235	8	we	we	PRON
ejpam-5313	235	9	have	have	AUX
ejpam-5313	235	10	derived	derive	VERB
ejpam-5313	235	11	some	some	DET
ejpam-5313	235	12	basic	basic	ADJ
ejpam-5313	235	13	results	result	NOUN
ejpam-5313	235	14	on	on	ADP
ejpam-5313	235	15	even	even	ADV
ejpam-5313	235	16	sum	sum	VERB
ejpam-5313	235	17	domination	domination	NOUN
ejpam-5313	235	18	number	number	NOUN
ejpam-5313	235	19	.	.	PUNCT
ejpam-5313	236	1	in	in	ADP
ejpam-5313	236	2	different	different	ADJ
ejpam-5313	236	3	sport	sport	NOUN
ejpam-5313	236	4	centers	center	NOUN
ejpam-5313	236	5	of	of	ADP
ejpam-5313	236	6	any	any	DET
ejpam-5313	236	7	sport	sport	NOUN
ejpam-5313	236	8	academy	academy	NOUN
ejpam-5313	236	9	even	even	ADV
ejpam-5313	236	10	sum	sum	NOUN
ejpam-5313	236	11	domination	domination	NOUN
ejpam-5313	236	12	can	can	AUX
ejpam-5313	236	13	be	be	AUX
ejpam-5313	236	14	used	use	VERB
ejpam-5313	236	15	to	to	PART
ejpam-5313	236	16	schedule	schedule	VERB
ejpam-5313	236	17	match	match	NOUN
ejpam-5313	236	18	without	without	ADP
ejpam-5313	236	19	wasting	waste	VERB
ejpam-5313	236	20	time	time	NOUN
ejpam-5313	236	21	of	of	ADP
ejpam-5313	236	22	players	player	NOUN
ejpam-5313	236	23	and	and	CCONJ
ejpam-5313	236	24	using	use	VERB
ejpam-5313	236	25	minimum	minimum	ADJ
ejpam-5313	236	26	resources	resource	NOUN
ejpam-5313	236	27	for	for	ADP
ejpam-5313	236	28	some	some	DET
ejpam-5313	236	29	particular	particular	ADJ
ejpam-5313	236	30	game	game	NOUN
ejpam-5313	236	31	like	like	ADP
ejpam-5313	236	32	carrom	carrom	NOUN
ejpam-5313	236	33	,	,	PUNCT
ejpam-5313	236	34	tennis	tennis	NOUN
ejpam-5313	236	35	,	,	PUNCT
ejpam-5313	236	36	badminton	badminton	NOUN
ejpam-5313	236	37	in	in	ADP
ejpam-5313	236	38	which	which	PRON
ejpam-5313	236	39	we	we	PRON
ejpam-5313	236	40	need	need	VERB
ejpam-5313	236	41	even	even	ADV
ejpam-5313	236	42	number	number	NOUN
ejpam-5313	236	43	of	of	ADP
ejpam-5313	236	44	players	player	NOUN
ejpam-5313	236	45	.	.	PUNCT
ejpam-5313	237	1	we	we	PRON
ejpam-5313	237	2	have	have	AUX
ejpam-5313	237	3	discussed	discuss	VERB
ejpam-5313	237	4	some	some	DET
ejpam-5313	237	5	properties	property	NOUN
ejpam-5313	237	6	and	and	CCONJ
ejpam-5313	237	7	boundaries	boundary	NOUN
ejpam-5313	237	8	for	for	ADP
ejpam-5313	237	9	this	this	DET
ejpam-5313	237	10	concept	concept	NOUN
ejpam-5313	237	11	.	.	PUNCT
ejpam-5313	238	1	we	we	PRON
ejpam-5313	238	2	have	have	AUX
ejpam-5313	238	3	also	also	ADV
ejpam-5313	238	4	discussed	discuss	VERB
ejpam-5313	238	5	even	even	ADV
ejpam-5313	238	6	sum	sum	NOUN
ejpam-5313	238	7	domination	domination	NOUN
ejpam-5313	238	8	number	number	NOUN
ejpam-5313	238	9	for	for	ADP
ejpam-5313	238	10	some	some	DET
ejpam-5313	238	11	standard	standard	ADJ
ejpam-5313	238	12	graphs	graph	NOUN
ejpam-5313	238	13	.	.	PUNCT
ejpam-5313	239	1	in	in	ADP
ejpam-5313	239	2	future	future	ADJ
ejpam-5313	239	3	research	research	NOUN
ejpam-5313	239	4	,	,	PUNCT
ejpam-5313	239	5	it	it	PRON
ejpam-5313	239	6	may	may	AUX
ejpam-5313	239	7	be	be	AUX
ejpam-5313	239	8	fascinating	fascinating	ADJ
ejpam-5313	239	9	to	to	PART
ejpam-5313	239	10	find	find	VERB
ejpam-5313	239	11	even	even	ADV
ejpam-5313	239	12	sum	sum	VERB
ejpam-5313	239	13	domination	domination	NOUN
ejpam-5313	239	14	number	number	NOUN
ejpam-5313	239	15	of	of	ADP
ejpam-5313	239	16	some	some	DET
ejpam-5313	239	17	graphs	graph	NOUN
ejpam-5313	239	18	obtain	obtain	VERB
ejpam-5313	239	19	by	by	ADP
ejpam-5313	239	20	binary	binary	ADJ
ejpam-5313	239	21	operations	operation	NOUN
ejpam-5313	239	22	and	and	CCONJ
ejpam-5313	239	23	compare	compare	VERB
ejpam-5313	239	24	various	various	ADJ
ejpam-5313	239	25	domination	domination	NOUN
ejpam-5313	239	26	models	model	NOUN
ejpam-5313	239	27	with	with	ADP
ejpam-5313	239	28	even	even	ADV
ejpam-5313	239	29	sum	sum	NOUN
ejpam-5313	239	30	domination	domination	NOUN
ejpam-5313	239	31	.	.	PUNCT
ejpam-5313	240	1	acknowledgements	acknowledgement	NOUN
ejpam-5313	240	2	the	the	DET
ejpam-5313	240	3	authors	author	NOUN
ejpam-5313	240	4	thank	thank	VERB
ejpam-5313	240	5	the	the	DET
ejpam-5313	240	6	reviewers	reviewer	NOUN
ejpam-5313	240	7	and	and	CCONJ
ejpam-5313	240	8	editors	editor	NOUN
ejpam-5313	240	9	of	of	ADP
ejpam-5313	240	10	european	european	ADJ
ejpam-5313	240	11	journal	journal	PROPN
ejpam-5313	240	12	of	of	ADP
ejpam-5313	240	13	pure	pure	ADJ
ejpam-5313	240	14	and	and	CCONJ
ejpam-5313	240	15	applied	applied	ADJ
ejpam-5313	240	16	mathematics	mathematic	NOUN
ejpam-5313	240	17	,	,	PUNCT
ejpam-5313	240	18	for	for	ADP
ejpam-5313	240	19	reviewing	review	VERB
ejpam-5313	240	20	the	the	DET
ejpam-5313	240	21	paper	paper	NOUN
ejpam-5313	240	22	and	and	CCONJ
ejpam-5313	240	23	for	for	ADP
ejpam-5313	240	24	the	the	DET
ejpam-5313	240	25	comments	comment	NOUN
ejpam-5313	240	26	and	and	CCONJ
ejpam-5313	240	27	suggestions	suggestion	NOUN
ejpam-5313	240	28	they	they	PRON
ejpam-5313	240	29	provided	provide	VERB
ejpam-5313	240	30	.	.	PUNCT
ejpam-5313	241	1	references	reference	NOUN
ejpam-5313	241	2	2091	2091	NUM
ejpam-5313	241	3	references	reference	NOUN
ejpam-5313	241	4	[	[	X
ejpam-5313	241	5	1	1	NUM
ejpam-5313	241	6	]	]	PUNCT
ejpam-5313	241	7	s.	s.	PROPN
ejpam-5313	241	8	r.	r.	PROPN
ejpam-5313	241	9	canoy	canoy	PROPN
ejpam-5313	241	10	and	and	CCONJ
ejpam-5313	241	11	a.	a.	PROPN
ejpam-5313	241	12	e.	e.	PROPN
ejpam-5313	241	13	gamorez	gamorez	PROPN
ejpam-5313	241	14	.	.	PUNCT
ejpam-5313	242	1	monophonic	monophonic	ADJ
ejpam-5313	242	2	eccentric	eccentric	ADJ
ejpam-5313	242	3	domination	domination	NOUN
ejpam-5313	242	4	numbers	number	NOUN
ejpam-5313	242	5	of	of	ADP
ejpam-5313	242	6	graphs	graph	NOUN
ejpam-5313	242	7	.	.	PUNCT
ejpam-5313	243	1	european	european	ADJ
ejpam-5313	243	2	journal	journal	PROPN
ejpam-5313	243	3	of	of	ADP
ejpam-5313	243	4	pure	pure	ADJ
ejpam-5313	243	5	and	and	CCONJ
ejpam-5313	243	6	applied	applied	ADJ
ejpam-5313	243	7	mathematics	mathematic	NOUN
ejpam-5313	243	8	,	,	PUNCT
ejpam-5313	243	9	15:635–645	15:635–645	NUM
ejpam-5313	243	10	,	,	PUNCT
ejpam-5313	243	11	2022	2022	NUM
ejpam-5313	243	12	.	.	PUNCT
ejpam-5313	244	1	[	[	X
ejpam-5313	244	2	2	2	X
ejpam-5313	244	3	]	]	X
ejpam-5313	244	4	g.	g.	PROPN
ejpam-5313	244	5	chartrand	chartrand	PROPN
ejpam-5313	244	6	and	and	CCONJ
ejpam-5313	244	7	p.	p.	PROPN
ejpam-5313	244	8	zhang	zhang	PROPN
ejpam-5313	244	9	.	.	PUNCT
ejpam-5313	245	1	the	the	DET
ejpam-5313	245	2	steiner	steiner	ADJ
ejpam-5313	245	3	number	number	NOUN
ejpam-5313	245	4	of	of	ADP
ejpam-5313	245	5	a	a	DET
ejpam-5313	245	6	graph	graph	NOUN
ejpam-5313	245	7	.	.	PUNCT
ejpam-5313	245	8	discrete	discrete	ADJ
ejpam-5313	245	9	mathematics	mathematic	NOUN
ejpam-5313	245	10	,	,	PUNCT
ejpam-5313	245	11	242:41–54	242:41–54	NUM
ejpam-5313	245	12	,	,	PUNCT
ejpam-5313	245	13	2002	2002	NUM
ejpam-5313	245	14	.	.	PUNCT
ejpam-5313	246	1	[	[	X
ejpam-5313	246	2	3	3	X
ejpam-5313	246	3	]	]	PUNCT
ejpam-5313	246	4	j.	j.	PROPN
ejpam-5313	246	5	clark	clark	PROPN
ejpam-5313	246	6	and	and	CCONJ
ejpam-5313	246	7	d.	d.	PROPN
ejpam-5313	246	8	a.	a.	PROPN
ejpam-5313	246	9	holton	holton	PROPN
ejpam-5313	246	10	.	.	PUNCT
ejpam-5313	247	1	a	a	DET
ejpam-5313	247	2	first	first	ADJ
ejpam-5313	247	3	look	look	NOUN
ejpam-5313	247	4	at	at	ADP
ejpam-5313	247	5	graph	graph	NOUN
ejpam-5313	247	6	theory	theory	NOUN
ejpam-5313	247	7	.	.	PUNCT
ejpam-5313	248	1	world	world	PROPN
ejpam-5313	248	2	scientific	scientific	ADJ
ejpam-5313	248	3	,	,	PUNCT
ejpam-5313	248	4	1995	1995	NUM
ejpam-5313	248	5	.	.	PUNCT
ejpam-5313	249	1	[	[	X
ejpam-5313	249	2	4	4	X
ejpam-5313	249	3	]	]	PUNCT
ejpam-5313	249	4	t.	t.	PROPN
ejpam-5313	249	5	w.	w.	PROPN
ejpam-5313	249	6	haynes	haynes	PROPN
ejpam-5313	249	7	,	,	PUNCT
ejpam-5313	249	8	s.	s.	PROPN
ejpam-5313	249	9	t.	t.	PROPN
ejpam-5313	249	10	hedetniemi	hedetniemi	PROPN
ejpam-5313	249	11	,	,	PUNCT
ejpam-5313	249	12	and	and	CCONJ
ejpam-5313	249	13	p.	p.	PROPN
ejpam-5313	249	14	j.	j.	PROPN
ejpam-5313	249	15	slater	slater	PROPN
ejpam-5313	249	16	.	.	PUNCT
ejpam-5313	250	1	fundamentals	fundamental	NOUN
ejpam-5313	250	2	of	of	ADP
ejpam-5313	250	3	domination	domination	NOUN
ejpam-5313	250	4	in	in	ADP
ejpam-5313	250	5	graphs	graph	NOUN
ejpam-5313	250	6	.	.	PUNCT
ejpam-5313	251	1	marcel	marcel	PROPN
ejpam-5313	251	2	dekker	dekker	PROPN
ejpam-5313	251	3	,	,	PUNCT
ejpam-5313	251	4	new	new	PROPN
ejpam-5313	251	5	york	york	PROPN
ejpam-5313	251	6	,	,	PUNCT
ejpam-5313	251	7	1998	1998	NUM
ejpam-5313	251	8	.	.	PUNCT
ejpam-5313	252	1	[	[	X
ejpam-5313	252	2	5	5	X
ejpam-5313	252	3	]	]	PUNCT
ejpam-5313	252	4	s.	s.	PROPN
ejpam-5313	252	5	t.	t.	PROPN
ejpam-5313	252	6	hedetniemi	hedetniemi	PROPN
ejpam-5313	252	7	and	and	CCONJ
ejpam-5313	252	8	r.	r.	PROPN
ejpam-5313	252	9	c.	c.	PROPN
ejpam-5313	252	10	laskar	laskar	PROPN
ejpam-5313	252	11	.	.	PUNCT
ejpam-5313	253	1	bibliography	bibliography	NOUN
ejpam-5313	253	2	on	on	ADP
ejpam-5313	253	3	domination	domination	NOUN
ejpam-5313	253	4	in	in	ADP
ejpam-5313	253	5	graphs	graph	NOUN
ejpam-5313	253	6	and	and	CCONJ
ejpam-5313	253	7	some	some	DET
ejpam-5313	253	8	basic	basic	ADJ
ejpam-5313	253	9	definitions	definition	NOUN
ejpam-5313	253	10	of	of	ADP
ejpam-5313	253	11	domination	domination	NOUN
ejpam-5313	253	12	parameters	parameter	NOUN
ejpam-5313	253	13	.	.	PUNCT
ejpam-5313	254	1	discrete	discrete	ADJ
ejpam-5313	254	2	math	math	NOUN
ejpam-5313	254	3	.	.	PUNCT
ejpam-5313	254	4	,	,	PUNCT
ejpam-5313	254	5	86:257–277	86:257–277	NUM
ejpam-5313	254	6	,	,	PUNCT
ejpam-5313	254	7	1990	1990	NUM
ejpam-5313	254	8	.	.	PUNCT
ejpam-5313	255	1	[	[	X
ejpam-5313	255	2	6	6	NUM
ejpam-5313	255	3	]	]	PUNCT
ejpam-5313	255	4	o.	o.	PROPN
ejpam-5313	255	5	ore	ore	PROPN
ejpam-5313	255	6	.	.	PUNCT
ejpam-5313	256	1	theory	theory	NOUN
ejpam-5313	256	2	of	of	ADP
ejpam-5313	256	3	graphs	graph	NOUN
ejpam-5313	256	4	.	.	PUNCT
ejpam-5313	257	1	amer	amer	PROPN
ejpam-5313	257	2	.	.	PUNCT
ejpam-5313	257	3	math	math	PROPN
ejpam-5313	257	4	.	.	PUNCT
ejpam-5313	258	1	soc	soc	PROPN
ejpam-5313	258	2	.	.	PUNCT
ejpam-5313	259	1	transl	transl	PROPN
ejpam-5313	259	2	.	.	PUNCT
ejpam-5313	259	3	,	,	PUNCT
ejpam-5313	260	1	38:206–212	38:206–212	NUM
ejpam-5313	260	2	,	,	PUNCT
ejpam-5313	260	3	1962	1962	NUM
ejpam-5313	260	4	.	.	PUNCT
ejpam-5313	261	1	[	[	X
ejpam-5313	261	2	7	7	NUM
ejpam-5313	261	3	]	]	X
ejpam-5313	261	4	i.	i.	PROPN
ejpam-5313	261	5	m.	m.	PROPN
ejpam-5313	261	6	rasheed	rasheed	PROPN
ejpam-5313	261	7	and	and	CCONJ
ejpam-5313	261	8	a.	a.	NOUN
ejpam-5313	261	9	a.	a.	NOUN
ejpam-5313	261	10	omran	omran	PROPN
ejpam-5313	261	11	.	.	PUNCT
ejpam-5313	262	1	even	even	ADV
ejpam-5313	262	2	sum	sum	VERB
ejpam-5313	262	3	domination	domination	NOUN
ejpam-5313	262	4	in	in	ADP
ejpam-5313	262	5	graphs	graph	NOUN
ejpam-5313	262	6	with	with	ADP
ejpam-5313	262	7	algorithm	algorithm	NOUN
ejpam-5313	262	8	.	.	PUNCT
ejpam-5313	263	1	in	in	ADP
ejpam-5313	263	2	aip	aip	PROPN
ejpam-5313	263	3	conference	conference	NOUN
ejpam-5313	263	4	proceedings	proceeding	NOUN
ejpam-5313	263	5	,	,	PUNCT
ejpam-5313	263	6	volume	volume	NOUN
ejpam-5313	263	7	2368	2368	NUM
ejpam-5313	263	8	,	,	PUNCT
ejpam-5313	263	9	2022	2022	NUM
ejpam-5313	263	10	.	.	PUNCT
ejpam-5313	264	1	[	[	X
ejpam-5313	264	2	8	8	NUM
ejpam-5313	264	3	]	]	X
ejpam-5313	264	4	e.	e.	PROPN
ejpam-5313	264	5	sampathkumar	sampathkumar	PROPN
ejpam-5313	264	6	and	and	CCONJ
ejpam-5313	264	7	l.	l.	PROPN
ejpam-5313	264	8	pushpa	pushpa	PROPN
ejpam-5313	264	9	latha	latha	PROPN
ejpam-5313	264	10	.	.	PUNCT
ejpam-5313	265	1	strong	strong	ADJ
ejpam-5313	265	2	weak	weak	ADJ
ejpam-5313	265	3	domination	domination	NOUN
ejpam-5313	265	4	and	and	CCONJ
ejpam-5313	265	5	domination	domination	NOUN
ejpam-5313	265	6	balance	balance	NOUN
ejpam-5313	265	7	in	in	ADP
ejpam-5313	265	8	graph	graph	NOUN
ejpam-5313	265	9	.	.	PUNCT
ejpam-5313	266	1	discrete	discrete	ADJ
ejpam-5313	266	2	mathematics	mathematic	NOUN
ejpam-5313	266	3	,	,	PUNCT
ejpam-5313	266	4	161:235–242	161:235–242	NUM
ejpam-5313	266	5	,	,	PUNCT
ejpam-5313	266	6	1996	1996	NUM
ejpam-5313	266	7	.	.	PUNCT
ejpam-5313	267	1	[	[	X
ejpam-5313	267	2	9	9	NUM
ejpam-5313	267	3	]	]	X
ejpam-5313	267	4	d.	d.	PROPN
ejpam-5313	267	5	b.	b.	PROPN
ejpam-5313	267	6	west	west	PROPN
ejpam-5313	267	7	.	.	PUNCT
ejpam-5313	268	1	introduction	introduction	NOUN
ejpam-5313	268	2	to	to	AUX
ejpam-5313	268	3	graph	graph	NOUN
ejpam-5313	268	4	theory	theory	NOUN
ejpam-5313	268	5	,	,	PUNCT
ejpam-5313	268	6	2	2	NUM
ejpam-5313	268	7	/	/	SYM
ejpam-5313	268	8	e.	e.	PROPN
ejpam-5313	268	9	prentice	prentice	PROPN
ejpam-5313	268	10	-	-	PUNCT
ejpam-5313	268	11	hall	hall	NOUN
ejpam-5313	268	12	of	of	ADP
ejpam-5313	268	13	india	india	PROPN
ejpam-5313	268	14	,	,	PUNCT
ejpam-5313	268	15	new	new	PROPN
ejpam-5313	268	16	delhi	delhi	PROPN
ejpam-5313	268	17	,	,	PUNCT
ejpam-5313	268	18	2003	2003	NUM
ejpam-5313	268	19	.	.	PUNCT