id	sid	tid	token	lemma	pos
ejpam-6124	1	1	european	european	PROPN
ejpam-6124	1	2	journal	journal	PROPN
ejpam-6124	1	3	of	of	ADP
ejpam-6124	1	4	pure	pure	ADJ
ejpam-6124	1	5	and	and	CCONJ
ejpam-6124	1	6	applied	applied	ADJ
ejpam-6124	1	7	mathematics	mathematic	NOUN
ejpam-6124	1	8	2025	2025	NUM
ejpam-6124	1	9	,	,	PUNCT
ejpam-6124	1	10	vol	vol	NOUN
ejpam-6124	1	11	.	.	PROPN
ejpam-6124	1	12	18	18	NUM
ejpam-6124	1	13	,	,	PUNCT
ejpam-6124	1	14	issue	issue	NOUN
ejpam-6124	1	15	2	2	NUM
ejpam-6124	1	16	,	,	PUNCT
ejpam-6124	1	17	article	article	NOUN
ejpam-6124	1	18	number	number	NOUN
ejpam-6124	1	19	6124	6124	NUM
ejpam-6124	1	20	issn	issn	PROPN
ejpam-6124	1	21	1307	1307	NUM
ejpam-6124	1	22	-	-	SYM
ejpam-6124	1	23	5543	5543	NUM
ejpam-6124	1	24	–	–	PUNCT
ejpam-6124	1	25	ejpam.com	ejpam.com	X
ejpam-6124	1	26	published	publish	VERB
ejpam-6124	1	27	by	by	ADP
ejpam-6124	1	28	new	new	PROPN
ejpam-6124	1	29	york	york	PROPN
ejpam-6124	1	30	business	business	PROPN
ejpam-6124	1	31	global	global	ADJ
ejpam-6124	1	32	total	total	ADJ
ejpam-6124	1	33	exact	exact	ADJ
ejpam-6124	1	34	domination	domination	NOUN
ejpam-6124	1	35	in	in	ADP
ejpam-6124	1	36	graphs	graph	NOUN
ejpam-6124	1	37	ritchie	ritchie	PROPN
ejpam-6124	1	38	g.	g.	PROPN
ejpam-6124	1	39	aguinod1	aguinod1	PROPN
ejpam-6124	1	40	,	,	PUNCT
ejpam-6124	1	41	edward	edward	PROPN
ejpam-6124	1	42	m.	m.	PROPN
ejpam-6124	1	43	kiunisala2	kiunisala2	PROPN
ejpam-6124	1	44	,	,	PUNCT
ejpam-6124	1	45	cris	cris	PROPN
ejpam-6124	1	46	l.	l.	PROPN
ejpam-6124	1	47	armada3,4	armada3,4	PROPN
ejpam-6124	1	48	1	1	NUM
ejpam-6124	1	49	college	college	NOUN
ejpam-6124	1	50	of	of	ADP
ejpam-6124	1	51	computing	computing	NOUN
ejpam-6124	1	52	,	,	PUNCT
ejpam-6124	1	53	artificial	artificial	ADJ
ejpam-6124	1	54	intelligence	intelligence	NOUN
ejpam-6124	1	55	and	and	CCONJ
ejpam-6124	1	56	sciences	science	NOUN
ejpam-6124	1	57	,	,	PUNCT
ejpam-6124	1	58	cebu	cebu	NOUN
ejpam-6124	1	59	normal	normal	ADJ
ejpam-6124	1	60	university	university	NOUN
ejpam-6124	1	61	,	,	PUNCT
ejpam-6124	1	62	6000	6000	NUM
ejpam-6124	1	63	cebu	cebu	NOUN
ejpam-6124	1	64	city	city	NOUN
ejpam-6124	1	65	,	,	PUNCT
ejpam-6124	1	66	philippines	philippine	NOUN
ejpam-6124	1	67	2	2	NUM
ejpam-6124	1	68	mathematics	mathematics	NOUN
ejpam-6124	1	69	department	department	NOUN
ejpam-6124	1	70	,	,	PUNCT
ejpam-6124	1	71	college	college	NOUN
ejpam-6124	1	72	of	of	ADP
ejpam-6124	1	73	computing	computing	NOUN
ejpam-6124	1	74	,	,	PUNCT
ejpam-6124	1	75	artificial	artificial	ADJ
ejpam-6124	1	76	intelligence	intelligence	NOUN
ejpam-6124	1	77	and	and	CCONJ
ejpam-6124	1	78	sciences	science	NOUN
ejpam-6124	1	79	,	,	PUNCT
ejpam-6124	1	80	cebu	cebu	NOUN
ejpam-6124	1	81	normal	normal	ADJ
ejpam-6124	1	82	university	university	NOUN
ejpam-6124	1	83	,	,	PUNCT
ejpam-6124	1	84	6000	6000	NUM
ejpam-6124	1	85	cebu	cebu	NOUN
ejpam-6124	1	86	city	city	NOUN
ejpam-6124	1	87	,	,	PUNCT
ejpam-6124	1	88	philippines	philippines	PROPN
ejpam-6124	1	89	3	3	NUM
ejpam-6124	1	90	vietnam	vietnam	PROPN
ejpam-6124	1	91	national	national	PROPN
ejpam-6124	1	92	university	university	PROPN
ejpam-6124	1	93	ho	ho	PROPN
ejpam-6124	1	94	chi	chi	PROPN
ejpam-6124	1	95	minh	minh	PROPN
ejpam-6124	1	96	city	city	PROPN
ejpam-6124	1	97	,	,	PUNCT
ejpam-6124	1	98	linh	linh	NOUN
ejpam-6124	1	99	trung	trung	VERB
ejpam-6124	1	100	ward	ward	NOUN
ejpam-6124	1	101	,	,	PUNCT
ejpam-6124	1	102	thu	thu	PROPN
ejpam-6124	1	103	duc	duc	PROPN
ejpam-6124	1	104	city	city	PROPN
ejpam-6124	1	105	,	,	PUNCT
ejpam-6124	1	106	ho	ho	PROPN
ejpam-6124	1	107	chi	chi	PROPN
ejpam-6124	1	108	minh	minh	PROPN
ejpam-6124	1	109	city	city	PROPN
ejpam-6124	1	110	,	,	PUNCT
ejpam-6124	1	111	vietnam	vietnam	PROPN
ejpam-6124	1	112	4	4	NUM
ejpam-6124	1	113	department	department	NOUN
ejpam-6124	1	114	of	of	ADP
ejpam-6124	1	115	applied	apply	VERB
ejpam-6124	1	116	mathematics	mathematic	NOUN
ejpam-6124	1	117	,	,	PUNCT
ejpam-6124	1	118	faculty	faculty	NOUN
ejpam-6124	1	119	of	of	ADP
ejpam-6124	1	120	applied	apply	VERB
ejpam-6124	1	121	science	science	NOUN
ejpam-6124	1	122	,	,	PUNCT
ejpam-6124	1	123	ho	ho	PROPN
ejpam-6124	1	124	chi	chi	PROPN
ejpam-6124	1	125	minh	minh	PROPN
ejpam-6124	1	126	city	city	PROPN
ejpam-6124	1	127	university	university	PROPN
ejpam-6124	1	128	of	of	ADP
ejpam-6124	1	129	technology	technology	NOUN
ejpam-6124	1	130	(	(	PUNCT
ejpam-6124	1	131	hcmut	hcmut	ADJ
ejpam-6124	1	132	)	)	PUNCT
ejpam-6124	1	133	,	,	PUNCT
ejpam-6124	1	134	268	268	NUM
ejpam-6124	1	135	ly	ly	ADP
ejpam-6124	1	136	thuong	thuong	NOUN
ejpam-6124	1	137	kiet	kiet	PROPN
ejpam-6124	1	138	,	,	PUNCT
ejpam-6124	1	139	district	district	NOUN
ejpam-6124	1	140	10	10	NUM
ejpam-6124	1	141	,	,	PUNCT
ejpam-6124	1	142	ward	ward	NOUN
ejpam-6124	1	143	14	14	NUM
ejpam-6124	1	144	,	,	PUNCT
ejpam-6124	1	145	ho	ho	PROPN
ejpam-6124	1	146	chi	chi	PROPN
ejpam-6124	1	147	minh	minh	PROPN
ejpam-6124	1	148	city	city	PROPN
ejpam-6124	1	149	,	,	PUNCT
ejpam-6124	1	150	vietnam	vietnam	PROPN
ejpam-6124	1	151	abstract	abstract	NOUN
ejpam-6124	1	152	.	.	PUNCT
ejpam-6124	2	1	let	let	VERB
ejpam-6124	2	2	g	g	PROPN
ejpam-6124	2	3	=	=	SYM
ejpam-6124	2	4	(	(	PUNCT
ejpam-6124	2	5	v	v	NOUN
ejpam-6124	2	6	(	(	PUNCT
ejpam-6124	2	7	g	g	NOUN
ejpam-6124	2	8	)	)	PUNCT
ejpam-6124	2	9	,	,	PUNCT
ejpam-6124	2	10	e(g	e(g	PROPN
ejpam-6124	2	11	)	)	PUNCT
ejpam-6124	2	12	)	)	PUNCT
ejpam-6124	3	1	be	be	AUX
ejpam-6124	3	2	a	a	DET
ejpam-6124	3	3	simple	simple	ADJ
ejpam-6124	3	4	nontrivial	nontrivial	ADJ
ejpam-6124	3	5	undirected	undirected	ADJ
ejpam-6124	3	6	graph	graph	NOUN
ejpam-6124	3	7	.	.	PUNCT
ejpam-6124	4	1	a	a	DET
ejpam-6124	4	2	set	set	NOUN
ejpam-6124	4	3	t	t	PROPN
ejpam-6124	4	4	⊆	⊆	NUM
ejpam-6124	4	5	v	v	NOUN
ejpam-6124	4	6	(	(	PUNCT
ejpam-6124	4	7	g	g	NOUN
ejpam-6124	4	8	)	)	PUNCT
ejpam-6124	4	9	is	be	AUX
ejpam-6124	4	10	said	say	VERB
ejpam-6124	4	11	to	to	PART
ejpam-6124	4	12	be	be	AUX
ejpam-6124	4	13	a	a	DET
ejpam-6124	4	14	total	total	ADJ
ejpam-6124	4	15	exact	exact	ADJ
ejpam-6124	4	16	dominating	dominating	NOUN
ejpam-6124	4	17	set	set	NOUN
ejpam-6124	4	18	if	if	SCONJ
ejpam-6124	4	19	t	t	PROPN
ejpam-6124	4	20	is	be	AUX
ejpam-6124	4	21	both	both	CCONJ
ejpam-6124	4	22	a	a	DET
ejpam-6124	4	23	total	total	ADJ
ejpam-6124	4	24	dominating	dominating	NOUN
ejpam-6124	4	25	set	set	NOUN
ejpam-6124	4	26	and	and	CCONJ
ejpam-6124	4	27	an	an	DET
ejpam-6124	4	28	exact	exact	ADJ
ejpam-6124	4	29	dominating	dominating	NOUN
ejpam-6124	4	30	set	set	NOUN
ejpam-6124	4	31	of	of	ADP
ejpam-6124	4	32	g.	g.	PROPN
ejpam-6124	4	33	the	the	DET
ejpam-6124	4	34	cardinality	cardinality	NOUN
ejpam-6124	4	35	of	of	ADP
ejpam-6124	4	36	a	a	DET
ejpam-6124	4	37	minimum	minimum	ADJ
ejpam-6124	4	38	total	total	ADJ
ejpam-6124	4	39	exact	exact	ADJ
ejpam-6124	4	40	dominating	dominating	NOUN
ejpam-6124	4	41	set	set	NOUN
ejpam-6124	4	42	is	be	AUX
ejpam-6124	4	43	called	call	VERB
ejpam-6124	4	44	the	the	DET
ejpam-6124	4	45	total	total	ADJ
ejpam-6124	4	46	exact	exact	ADJ
ejpam-6124	4	47	domination	domination	NOUN
ejpam-6124	4	48	number	number	NOUN
ejpam-6124	4	49	and	and	CCONJ
ejpam-6124	4	50	is	be	AUX
ejpam-6124	4	51	denoted	denote	VERB
ejpam-6124	4	52	by	by	ADP
ejpam-6124	4	53	γte(g	γte(g	PROPN
ejpam-6124	4	54	)	)	PUNCT
ejpam-6124	4	55	.	.	PUNCT
ejpam-6124	5	1	the	the	DET
ejpam-6124	5	2	total	total	ADJ
ejpam-6124	5	3	exact	exact	ADJ
ejpam-6124	5	4	domination	domination	NOUN
ejpam-6124	5	5	numbers	number	NOUN
ejpam-6124	5	6	of	of	ADP
ejpam-6124	5	7	various	various	ADJ
ejpam-6124	5	8	types	type	NOUN
ejpam-6124	5	9	of	of	ADP
ejpam-6124	5	10	special	special	ADJ
ejpam-6124	5	11	graphs	graph	NOUN
ejpam-6124	5	12	,	,	PUNCT
ejpam-6124	5	13	such	such	ADJ
ejpam-6124	5	14	as	as	ADP
ejpam-6124	5	15	path	path	NOUN
ejpam-6124	5	16	,	,	PUNCT
ejpam-6124	5	17	cycle	cycle	NOUN
ejpam-6124	5	18	,	,	PUNCT
ejpam-6124	5	19	star	star	NOUN
ejpam-6124	5	20	,	,	PUNCT
ejpam-6124	5	21	complete	complete	ADJ
ejpam-6124	5	22	bipartite	bipartite	NOUN
ejpam-6124	5	23	,	,	PUNCT
ejpam-6124	5	24	and	and	CCONJ
ejpam-6124	5	25	graphs	graph	NOUN
ejpam-6124	5	26	resulting	result	VERB
ejpam-6124	5	27	from	from	ADP
ejpam-6124	5	28	binary	binary	ADJ
ejpam-6124	5	29	operations	operation	NOUN
ejpam-6124	5	30	such	such	ADJ
ejpam-6124	5	31	as	as	ADP
ejpam-6124	5	32	join	join	NOUN
ejpam-6124	5	33	,	,	PUNCT
ejpam-6124	5	34	corona	corona	NOUN
ejpam-6124	5	35	,	,	PUNCT
ejpam-6124	5	36	and	and	CCONJ
ejpam-6124	5	37	lexicographic	lexicographic	ADJ
ejpam-6124	5	38	product	product	NOUN
ejpam-6124	5	39	are	be	AUX
ejpam-6124	5	40	obtained	obtain	VERB
ejpam-6124	5	41	in	in	ADP
ejpam-6124	5	42	this	this	DET
ejpam-6124	5	43	study	study	NOUN
ejpam-6124	5	44	.	.	PUNCT
ejpam-6124	6	1	furthermore	furthermore	ADV
ejpam-6124	6	2	,	,	PUNCT
ejpam-6124	6	3	if	if	SCONJ
ejpam-6124	6	4	g	g	PROPN
ejpam-6124	6	5	does	do	AUX
ejpam-6124	6	6	not	not	PART
ejpam-6124	6	7	have	have	VERB
ejpam-6124	6	8	a	a	DET
ejpam-6124	6	9	total	total	ADJ
ejpam-6124	6	10	exact	exact	ADJ
ejpam-6124	6	11	dominating	dominating	NOUN
ejpam-6124	6	12	set	set	NOUN
ejpam-6124	6	13	,	,	PUNCT
ejpam-6124	6	14	then	then	ADV
ejpam-6124	6	15	g	g	PROPN
ejpam-6124	6	16	is	be	AUX
ejpam-6124	6	17	called	call	VERB
ejpam-6124	6	18	a	a	DET
ejpam-6124	6	19	non−	non−	PROPN
ejpam-6124	6	20	γte	γte	NOUN
ejpam-6124	6	21	-	-	PUNCT
ejpam-6124	6	22	graph	graph	NOUN
ejpam-6124	6	23	.	.	PUNCT
ejpam-6124	7	1	examples	example	NOUN
ejpam-6124	7	2	include	include	VERB
ejpam-6124	7	3	complete	complete	ADJ
ejpam-6124	7	4	graphs	graph	NOUN
ejpam-6124	7	5	,	,	PUNCT
ejpam-6124	7	6	fan	fan	NOUN
ejpam-6124	7	7	graphs	graph	NOUN
ejpam-6124	7	8	,	,	PUNCT
ejpam-6124	7	9	and	and	CCONJ
ejpam-6124	7	10	wheel	wheel	NOUN
ejpam-6124	7	11	graphs	graph	NOUN
ejpam-6124	7	12	with	with	ADP
ejpam-6124	7	13	more	more	ADJ
ejpam-6124	7	14	than	than	ADP
ejpam-6124	7	15	two	two	NUM
ejpam-6124	7	16	vertices	vertex	NOUN
ejpam-6124	7	17	.	.	PUNCT
ejpam-6124	8	1	we	we	PRON
ejpam-6124	8	2	also	also	ADV
ejpam-6124	8	3	consider	consider	VERB
ejpam-6124	8	4	some	some	DET
ejpam-6124	8	5	disconnected	disconnected	ADJ
ejpam-6124	8	6	graphs	graph	NOUN
ejpam-6124	8	7	in	in	ADP
ejpam-6124	8	8	the	the	DET
ejpam-6124	8	9	corona	corona	NOUN
ejpam-6124	8	10	and	and	CCONJ
ejpam-6124	8	11	lexicographic	lexicographic	ADJ
ejpam-6124	8	12	product	product	NOUN
ejpam-6124	8	13	,	,	PUNCT
ejpam-6124	8	14	making	make	VERB
ejpam-6124	8	15	the	the	DET
ejpam-6124	8	16	study	study	NOUN
ejpam-6124	8	17	more	more	ADV
ejpam-6124	8	18	interesting	interesting	ADJ
ejpam-6124	8	19	.	.	PUNCT
ejpam-6124	9	1	in	in	ADP
ejpam-6124	9	2	defining	define	VERB
ejpam-6124	9	3	total	total	ADJ
ejpam-6124	9	4	exact	exact	ADJ
ejpam-6124	9	5	domination	domination	NOUN
ejpam-6124	9	6	,	,	PUNCT
ejpam-6124	9	7	a	a	DET
ejpam-6124	9	8	condition	condition	NOUN
ejpam-6124	9	9	of	of	ADP
ejpam-6124	9	10	exact	exact	ADJ
ejpam-6124	9	11	domination	domination	NOUN
ejpam-6124	9	12	was	be	AUX
ejpam-6124	9	13	modified	modify	VERB
ejpam-6124	9	14	because	because	SCONJ
ejpam-6124	9	15	it	it	PRON
ejpam-6124	9	16	contradicted	contradict	VERB
ejpam-6124	9	17	the	the	DET
ejpam-6124	9	18	definition	definition	NOUN
ejpam-6124	9	19	of	of	ADP
ejpam-6124	9	20	total	total	ADJ
ejpam-6124	9	21	domination	domination	NOUN
ejpam-6124	9	22	.	.	PUNCT
ejpam-6124	10	1	2020	2020	NUM
ejpam-6124	10	2	mathematics	mathematic	NOUN
ejpam-6124	10	3	subject	subject	NOUN
ejpam-6124	10	4	classifications	classification	NOUN
ejpam-6124	10	5	:	:	PUNCT
ejpam-6124	10	6	05c69,05c38	05c69,05c38	NUM
ejpam-6124	10	7	,	,	PUNCT
ejpam-6124	10	8	05c76	05c76	PRON
ejpam-6124	10	9	key	key	ADJ
ejpam-6124	10	10	words	word	NOUN
ejpam-6124	10	11	and	and	CCONJ
ejpam-6124	10	12	phrases	phrase	NOUN
ejpam-6124	10	13	:	:	PUNCT
ejpam-6124	10	14	total	total	ADJ
ejpam-6124	10	15	domination	domination	NOUN
ejpam-6124	10	16	,	,	PUNCT
ejpam-6124	10	17	exact	exact	ADJ
ejpam-6124	10	18	domination	domination	NOUN
ejpam-6124	10	19	,	,	PUNCT
ejpam-6124	10	20	total	total	ADJ
ejpam-6124	10	21	exact	exact	ADJ
ejpam-6124	10	22	domination	domination	NOUN
ejpam-6124	10	23	1	1	NUM
ejpam-6124	10	24	.	.	PUNCT
ejpam-6124	11	1	introduction	introduction	NOUN
ejpam-6124	11	2	graph	graph	NOUN
ejpam-6124	11	3	domination	domination	NOUN
ejpam-6124	11	4	is	be	AUX
ejpam-6124	11	5	a	a	DET
ejpam-6124	11	6	thoroughly	thoroughly	ADV
ejpam-6124	11	7	researched	research	VERB
ejpam-6124	11	8	area	area	NOUN
ejpam-6124	11	9	in	in	ADP
ejpam-6124	11	10	graph	graph	NOUN
ejpam-6124	11	11	theory	theory	NOUN
ejpam-6124	11	12	,	,	PUNCT
ejpam-6124	11	13	which	which	PRON
ejpam-6124	11	14	is	be	AUX
ejpam-6124	11	15	essential	essential	ADJ
ejpam-6124	11	16	for	for	ADP
ejpam-6124	11	17	optimizing	optimize	VERB
ejpam-6124	11	18	networks	network	NOUN
ejpam-6124	11	19	,	,	PUNCT
ejpam-6124	11	20	managing	manage	VERB
ejpam-6124	11	21	resources	resource	NOUN
ejpam-6124	11	22	,	,	PUNCT
ejpam-6124	11	23	and	and	CCONJ
ejpam-6124	11	24	modeling	model	VERB
ejpam-6124	11	25	social	social	ADJ
ejpam-6124	11	26	networks	network	NOUN
ejpam-6124	11	27	.	.	PUNCT
ejpam-6124	12	1	the	the	DET
ejpam-6124	12	2	basic	basic	ADJ
ejpam-6124	12	3	concept	concept	NOUN
ejpam-6124	12	4	of	of	ADP
ejpam-6124	12	5	a	a	DET
ejpam-6124	12	6	dominating	dominating	NOUN
ejpam-6124	12	7	set	set	NOUN
ejpam-6124	12	8	and	and	CCONJ
ejpam-6124	12	9	its	its	PRON
ejpam-6124	12	10	associated	associated	ADJ
ejpam-6124	12	11	domination	domination	NOUN
ejpam-6124	12	12	number	number	NOUN
ejpam-6124	12	13	was	be	AUX
ejpam-6124	12	14	initially	initially	ADV
ejpam-6124	12	15	presented	present	VERB
ejpam-6124	12	16	by	by	ADP
ejpam-6124	12	17	o.	o.	PROPN
ejpam-6124	12	18	ore	ore	NOUN
ejpam-6124	12	19	in	in	ADP
ejpam-6124	12	20	1962	1962	NUM
ejpam-6124	12	21	in	in	ADP
ejpam-6124	12	22	his	his	PRON
ejpam-6124	12	23	foundational	foundational	ADJ
ejpam-6124	12	24	paper	paper	NOUN
ejpam-6124	12	25	on	on	ADP
ejpam-6124	12	26	graph	graph	NOUN
ejpam-6124	12	27	theory	theory	NOUN
ejpam-6124	12	28	[	[	X
ejpam-6124	12	29	1	1	NUM
ejpam-6124	12	30	]	]	PUNCT
ejpam-6124	12	31	.	.	PUNCT
ejpam-6124	13	1	since	since	SCONJ
ejpam-6124	13	2	then	then	ADV
ejpam-6124	13	3	,	,	PUNCT
ejpam-6124	13	4	various	various	ADJ
ejpam-6124	13	5	forms	form	NOUN
ejpam-6124	13	6	of	of	ADP
ejpam-6124	13	7	domination	domination	NOUN
ejpam-6124	13	8	have	have	AUX
ejpam-6124	13	9	been	be	AUX
ejpam-6124	13	10	studied	study	VERB
ejpam-6124	13	11	,	,	PUNCT
ejpam-6124	13	12	each	each	PRON
ejpam-6124	13	13	offering	offer	VERB
ejpam-6124	13	14	unique	unique	ADJ
ejpam-6124	13	15	insights	insight	NOUN
ejpam-6124	13	16	into	into	ADP
ejpam-6124	13	17	the	the	DET
ejpam-6124	13	18	structural	structural	ADJ
ejpam-6124	13	19	doi	doi	NOUN
ejpam-6124	13	20	:	:	PUNCT
ejpam-6124	13	21	https://doi.org/10.29020/nybg.ejpam.v18i2.6124	https://doi.org/10.29020/nybg.ejpam.v18i2.6124	ADJ
ejpam-6124	13	22	email	email	NOUN
ejpam-6124	13	23	addresses	address	VERB
ejpam-6124	13	24	:	:	PUNCT
ejpam-6124	13	25	aguinodr@cnu.edu.ph	aguinodr@cnu.edu.ph	PROPN
ejpam-6124	13	26	(	(	PUNCT
ejpam-6124	13	27	r.	r.	PROPN
ejpam-6124	13	28	g.	g.	PROPN
ejpam-6124	13	29	aguinod	aguinod	PROPN
ejpam-6124	13	30	)	)	PUNCT
ejpam-6124	13	31	,	,	PUNCT
ejpam-6124	13	32	kiunisalae@cnu.edu.ph	kiunisalae@cnu.edu.ph	PROPN
ejpam-6124	13	33	(	(	PUNCT
ejpam-6124	13	34	e.	e.	PROPN
ejpam-6124	13	35	m.	m.	PROPN
ejpam-6124	13	36	kiunisala	kiunisala	PROPN
ejpam-6124	13	37	)	)	PUNCT
ejpam-6124	13	38	,	,	PUNCT
ejpam-6124	13	39	cris.armada@hcmut.edu.vn	cris.armada@hcmut.edu.vn	X
ejpam-6124	13	40	(	(	PUNCT
ejpam-6124	13	41	c.	c.	PROPN
ejpam-6124	13	42	l.	l.	PROPN
ejpam-6124	13	43	armada	armada	PROPN
ejpam-6124	13	44	)	)	PUNCT
ejpam-6124	13	45	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6124	14	1	1	1	NUM
ejpam-6124	14	2	copyright	copyright	NOUN
ejpam-6124	14	3	:	:	PUNCT
ejpam-6124	14	4	©	©	PROPN
ejpam-6124	14	5	2025	2025	NUM
ejpam-6124	14	6	the	the	DET
ejpam-6124	14	7	author(s	author(s	NOUN
ejpam-6124	14	8	)	)	PUNCT
ejpam-6124	14	9	.	.	PUNCT
ejpam-6124	15	1	(	(	PUNCT
ejpam-6124	15	2	cc	cc	NOUN
ejpam-6124	15	3	by	by	ADP
ejpam-6124	15	4	-	-	PUNCT
ejpam-6124	15	5	nc	nc	PROPN
ejpam-6124	15	6	4.0	4.0	NUM
ejpam-6124	15	7	)	)	PUNCT
ejpam-6124	15	8	r.	r.	PROPN
ejpam-6124	15	9	g.	g.	PROPN
ejpam-6124	15	10	aguinod	aguinod	PROPN
ejpam-6124	15	11	,	,	PUNCT
ejpam-6124	15	12	e.	e.	PROPN
ejpam-6124	15	13	m.	m.	PROPN
ejpam-6124	15	14	kiunisala	kiunisala	PROPN
ejpam-6124	15	15	,	,	PUNCT
ejpam-6124	15	16	c.	c.	PROPN
ejpam-6124	15	17	l.	l.	PROPN
ejpam-6124	15	18	armada	armada	PROPN
ejpam-6124	15	19	/	/	SYM
ejpam-6124	15	20	eur	eur	PROPN
ejpam-6124	15	21	.	.	PUNCT
ejpam-6124	16	1	j.	j.	PROPN
ejpam-6124	16	2	pure	pure	PROPN
ejpam-6124	16	3	appl	appl	PROPN
ejpam-6124	16	4	.	.	PROPN
ejpam-6124	16	5	math	math	PROPN
ejpam-6124	16	6	,	,	PUNCT
ejpam-6124	16	7	18	18	NUM
ejpam-6124	16	8	(	(	PUNCT
ejpam-6124	16	9	2	2	NUM
ejpam-6124	16	10	)	)	PUNCT
ejpam-6124	16	11	(	(	PUNCT
ejpam-6124	16	12	2025	2025	NUM
ejpam-6124	16	13	)	)	PUNCT
ejpam-6124	16	14	,	,	PUNCT
ejpam-6124	16	15	6124	6124	NUM
ejpam-6124	16	16	2	2	NUM
ejpam-6124	16	17	of	of	ADP
ejpam-6124	16	18	26	26	NUM
ejpam-6124	16	19	properties	property	NOUN
ejpam-6124	16	20	of	of	ADP
ejpam-6124	16	21	graphs	graph	NOUN
ejpam-6124	16	22	.	.	PUNCT
ejpam-6124	17	1	graph	graph	NOUN
ejpam-6124	17	2	domination	domination	NOUN
ejpam-6124	17	3	is	be	AUX
ejpam-6124	17	4	a	a	DET
ejpam-6124	17	5	well	well	ADV
ejpam-6124	17	6	-	-	PUNCT
ejpam-6124	17	7	explored	explore	VERB
ejpam-6124	17	8	topic	topic	NOUN
ejpam-6124	17	9	within	within	ADP
ejpam-6124	17	10	graph	graph	NOUN
ejpam-6124	17	11	theory	theory	NOUN
ejpam-6124	17	12	,	,	PUNCT
ejpam-6124	17	13	playing	play	VERB
ejpam-6124	17	14	a	a	DET
ejpam-6124	17	15	crucial	crucial	ADJ
ejpam-6124	17	16	role	role	NOUN
ejpam-6124	17	17	in	in	ADP
ejpam-6124	17	18	fields	field	NOUN
ejpam-6124	17	19	such	such	ADJ
ejpam-6124	17	20	as	as	ADP
ejpam-6124	17	21	network	network	NOUN
ejpam-6124	17	22	optimization	optimization	NOUN
ejpam-6124	17	23	,	,	PUNCT
ejpam-6124	17	24	resource	resource	NOUN
ejpam-6124	17	25	management	management	NOUN
ejpam-6124	17	26	,	,	PUNCT
ejpam-6124	17	27	and	and	CCONJ
ejpam-6124	17	28	social	social	ADJ
ejpam-6124	17	29	network	network	NOUN
ejpam-6124	17	30	modeling	modeling	NOUN
ejpam-6124	17	31	.	.	PUNCT
ejpam-6124	18	1	cockayne	cockayne	NOUN
ejpam-6124	18	2	,	,	PUNCT
ejpam-6124	18	3	dawes	dawe	NOUN
ejpam-6124	18	4	,	,	PUNCT
ejpam-6124	18	5	and	and	CCONJ
ejpam-6124	18	6	hedetniemi	hedetniemi	ADV
ejpam-6124	18	7	[	[	X
ejpam-6124	18	8	2	2	NUM
ejpam-6124	18	9	]	]	PUNCT
ejpam-6124	18	10	were	be	AUX
ejpam-6124	18	11	among	among	ADP
ejpam-6124	18	12	the	the	DET
ejpam-6124	18	13	first	first	ADJ
ejpam-6124	18	14	to	to	PART
ejpam-6124	18	15	formally	formally	ADV
ejpam-6124	18	16	define	define	VERB
ejpam-6124	18	17	total	total	ADJ
ejpam-6124	18	18	domination	domination	NOUN
ejpam-6124	18	19	in	in	ADP
ejpam-6124	18	20	graphs	graph	NOUN
ejpam-6124	18	21	in	in	ADP
ejpam-6124	18	22	1980	1980	NUM
ejpam-6124	18	23	.	.	PUNCT
ejpam-6124	19	1	in	in	ADP
ejpam-6124	19	2	their	their	PRON
ejpam-6124	19	3	study	study	NOUN
ejpam-6124	19	4	,	,	PUNCT
ejpam-6124	19	5	a	a	DET
ejpam-6124	19	6	set	set	NOUN
ejpam-6124	19	7	t	t	PROPN
ejpam-6124	19	8	⊆	⊆	NUM
ejpam-6124	19	9	v	v	NOUN
ejpam-6124	19	10	(	(	PUNCT
ejpam-6124	19	11	g	g	NOUN
ejpam-6124	19	12	)	)	PUNCT
ejpam-6124	19	13	,	,	PUNCT
ejpam-6124	19	14	where	where	SCONJ
ejpam-6124	19	15	v	v	X
ejpam-6124	19	16	(	(	PUNCT
ejpam-6124	19	17	g	g	NOUN
ejpam-6124	19	18	)	)	PUNCT
ejpam-6124	19	19	is	be	AUX
ejpam-6124	19	20	the	the	DET
ejpam-6124	19	21	vertex	vertex	NOUN
ejpam-6124	19	22	set	set	NOUN
ejpam-6124	19	23	of	of	ADP
ejpam-6124	19	24	g	g	NOUN
ejpam-6124	19	25	,	,	PUNCT
ejpam-6124	19	26	was	be	AUX
ejpam-6124	19	27	defined	define	VERB
ejpam-6124	19	28	as	as	ADP
ejpam-6124	19	29	a	a	DET
ejpam-6124	19	30	total	total	ADJ
ejpam-6124	19	31	dominating	dominating	NOUN
ejpam-6124	19	32	set	set	NOUN
ejpam-6124	19	33	if	if	SCONJ
ejpam-6124	19	34	every	every	DET
ejpam-6124	19	35	vertex	vertex	NOUN
ejpam-6124	19	36	in	in	ADP
ejpam-6124	19	37	v	v	NOUN
ejpam-6124	19	38	(	(	PUNCT
ejpam-6124	19	39	g	g	NOUN
ejpam-6124	19	40	)	)	PUNCT
ejpam-6124	19	41	is	be	AUX
ejpam-6124	19	42	adjacent	adjacent	ADJ
ejpam-6124	19	43	to	to	ADP
ejpam-6124	19	44	at	at	ADV
ejpam-6124	19	45	least	least	ADV
ejpam-6124	19	46	one	one	NUM
ejpam-6124	19	47	vertex	vertex	NOUN
ejpam-6124	19	48	in	in	ADP
ejpam-6124	19	49	t	t	PROPN
ejpam-6124	19	50	.	.	PUNCT
ejpam-6124	20	1	building	build	VERB
ejpam-6124	20	2	upon	upon	SCONJ
ejpam-6124	20	3	this	this	DET
ejpam-6124	20	4	definition	definition	NOUN
ejpam-6124	20	5	,	,	PUNCT
ejpam-6124	20	6	we	we	PRON
ejpam-6124	20	7	explore	explore	VERB
ejpam-6124	20	8	its	its	PRON
ejpam-6124	20	9	intersection	intersection	NOUN
ejpam-6124	20	10	with	with	ADP
ejpam-6124	20	11	exact	exact	ADJ
ejpam-6124	20	12	domination	domination	NOUN
ejpam-6124	20	13	in	in	ADP
ejpam-6124	20	14	this	this	DET
ejpam-6124	20	15	paper	paper	NOUN
ejpam-6124	20	16	.	.	PUNCT
ejpam-6124	21	1	the	the	DET
ejpam-6124	21	2	idea	idea	NOUN
ejpam-6124	21	3	of	of	ADP
ejpam-6124	21	4	exact	exact	ADJ
ejpam-6124	21	5	domination	domination	NOUN
ejpam-6124	21	6	in	in	ADP
ejpam-6124	21	7	graphs	graph	NOUN
ejpam-6124	21	8	was	be	AUX
ejpam-6124	21	9	formally	formally	ADV
ejpam-6124	21	10	put	put	VERB
ejpam-6124	21	11	forth	forth	ADP
ejpam-6124	21	12	by	by	ADP
ejpam-6124	21	13	kinsley	kinsley	PROPN
ejpam-6124	21	14	and	and	CCONJ
ejpam-6124	21	15	joeshi	joeshi	NOUN
ejpam-6124	21	16	in	in	ADP
ejpam-6124	21	17	2020	2020	NUM
ejpam-6124	21	18	,	,	PUNCT
ejpam-6124	21	19	building	build	VERB
ejpam-6124	21	20	upon	upon	SCONJ
ejpam-6124	21	21	earlier	early	ADJ
ejpam-6124	21	22	work	work	NOUN
ejpam-6124	21	23	in	in	ADP
ejpam-6124	21	24	domination	domination	NOUN
ejpam-6124	21	25	theory	theory	NOUN
ejpam-6124	21	26	[	[	X
ejpam-6124	21	27	3	3	NUM
ejpam-6124	21	28	]	]	PUNCT
ejpam-6124	21	29	.	.	PUNCT
ejpam-6124	22	1	where	where	SCONJ
ejpam-6124	22	2	n(v	n(v	PROPN
ejpam-6124	22	3	)	)	PUNCT
ejpam-6124	22	4	denotes	denote	VERB
ejpam-6124	22	5	the	the	DET
ejpam-6124	22	6	set	set	NOUN
ejpam-6124	22	7	of	of	ADP
ejpam-6124	22	8	all	all	DET
ejpam-6124	22	9	vertices	vertex	NOUN
ejpam-6124	22	10	adjacent	adjacent	ADJ
ejpam-6124	22	11	to	to	ADP
ejpam-6124	22	12	v	v	NOUN
ejpam-6124	22	13	,	,	PUNCT
ejpam-6124	22	14	a	a	DET
ejpam-6124	22	15	set	set	NOUN
ejpam-6124	22	16	t	t	NOUN
ejpam-6124	22	17	⊆	⊆	NUM
ejpam-6124	22	18	v	v	NOUN
ejpam-6124	22	19	(	(	PUNCT
ejpam-6124	22	20	g	g	NOUN
ejpam-6124	22	21	)	)	PUNCT
ejpam-6124	22	22	is	be	AUX
ejpam-6124	22	23	called	call	VERB
ejpam-6124	22	24	an	an	DET
ejpam-6124	22	25	exact	exact	ADJ
ejpam-6124	22	26	dominating	dominating	NOUN
ejpam-6124	22	27	set	set	NOUN
ejpam-6124	22	28	if	if	SCONJ
ejpam-6124	22	29	it	it	PRON
ejpam-6124	22	30	satisfies	satisfy	VERB
ejpam-6124	22	31	the	the	DET
ejpam-6124	22	32	following	follow	VERB
ejpam-6124	22	33	conditions	condition	NOUN
ejpam-6124	22	34	:	:	PUNCT
ejpam-6124	22	35	i	i	PROPN
ejpam-6124	22	36	|n(v	|n(v	PROPN
ejpam-6124	22	37	)	)	PUNCT
ejpam-6124	22	38	∩	∩	NOUN
ejpam-6124	22	39	t	t	NOUN
ejpam-6124	23	1	|	|	NOUN
ejpam-6124	23	2	=	=	SYM
ejpam-6124	23	3	1	1	NUM
ejpam-6124	23	4	for	for	ADP
ejpam-6124	23	5	all	all	PRON
ejpam-6124	23	6	v	v	ADP
ejpam-6124	23	7	∈	∈	NUM
ejpam-6124	23	8	v	v	NOUN
ejpam-6124	23	9	(	(	PUNCT
ejpam-6124	23	10	g	g	NOUN
ejpam-6124	23	11	)	)	PUNCT
ejpam-6124	23	12	\	\	PROPN
ejpam-6124	23	13	t	t	PROPN
ejpam-6124	23	14	and	and	CCONJ
ejpam-6124	23	15	ii	ii	PROPN
ejpam-6124	23	16	|n(u	|n(u	PROPN
ejpam-6124	23	17	)	)	PUNCT
ejpam-6124	23	18	∩	∩	PROPN
ejpam-6124	23	19	t	t	NOUN
ejpam-6124	23	20	|	|	ADV
ejpam-6124	23	21	≤	≤	NUM
ejpam-6124	23	22	1	1	NUM
ejpam-6124	23	23	for	for	ADP
ejpam-6124	23	24	all	all	PRON
ejpam-6124	23	25	u	u	PROPN
ejpam-6124	23	26	∈	∈	PROPN
ejpam-6124	23	27	t	t	NOUN
ejpam-6124	23	28	.	.	PUNCT
ejpam-6124	24	1	in	in	ADP
ejpam-6124	24	2	this	this	DET
ejpam-6124	24	3	paper	paper	NOUN
ejpam-6124	24	4	,	,	PUNCT
ejpam-6124	24	5	we	we	PRON
ejpam-6124	24	6	introduce	introduce	VERB
ejpam-6124	24	7	an	an	DET
ejpam-6124	24	8	integration	integration	NOUN
ejpam-6124	24	9	of	of	ADP
ejpam-6124	24	10	total	total	ADJ
ejpam-6124	24	11	and	and	CCONJ
ejpam-6124	24	12	exact	exact	ADJ
ejpam-6124	24	13	domination	domination	NOUN
ejpam-6124	24	14	.	.	PUNCT
ejpam-6124	25	1	combining	combine	VERB
ejpam-6124	25	2	the	the	DET
ejpam-6124	25	3	two	two	NUM
ejpam-6124	25	4	domination	domination	NOUN
ejpam-6124	25	5	conditions	condition	NOUN
ejpam-6124	25	6	will	will	AUX
ejpam-6124	25	7	modify	modify	VERB
ejpam-6124	25	8	the	the	DET
ejpam-6124	25	9	second	second	ADJ
ejpam-6124	25	10	condition	condition	NOUN
ejpam-6124	25	11	for	for	ADP
ejpam-6124	25	12	an	an	DET
ejpam-6124	25	13	exact	exact	ADJ
ejpam-6124	25	14	dominating	dominating	NOUN
ejpam-6124	25	15	set	set	NOUN
ejpam-6124	25	16	,	,	PUNCT
ejpam-6124	25	17	changing	change	VERB
ejpam-6124	25	18	|n(u	|n(u	NOUN
ejpam-6124	25	19	)	)	PUNCT
ejpam-6124	25	20	∩	∩	NOUN
ejpam-6124	25	21	t	t	NOUN
ejpam-6124	25	22	|	|	ADV
ejpam-6124	25	23	≤	≤	NUM
ejpam-6124	25	24	1	1	NUM
ejpam-6124	25	25	to	to	ADP
ejpam-6124	25	26	|n(u	|n(u	NOUN
ejpam-6124	25	27	)	)	PUNCT
ejpam-6124	25	28	∩	∩	PROPN
ejpam-6124	25	29	t	t	NOUN
ejpam-6124	26	1	|	|	NOUN
ejpam-6124	26	2	=	=	NOUN
ejpam-6124	26	3	1	1	NUM
ejpam-6124	26	4	,	,	PUNCT
ejpam-6124	26	5	since	since	SCONJ
ejpam-6124	26	6	|n(u	|n(u	NOUN
ejpam-6124	26	7	)	)	PUNCT
ejpam-6124	26	8	∩	∩	PROPN
ejpam-6124	26	9	t	t	NOUN
ejpam-6124	26	10	|	|	ADV
ejpam-6124	26	11	<	<	X
ejpam-6124	26	12	1	1	NUM
ejpam-6124	26	13	for	for	ADP
ejpam-6124	26	14	all	all	DET
ejpam-6124	26	15	u	u	PROPN
ejpam-6124	26	16	∈	∈	PROPN
ejpam-6124	26	17	t	t	NOUN
ejpam-6124	26	18	contradicts	contradict	VERB
ejpam-6124	26	19	the	the	DET
ejpam-6124	26	20	definition	definition	NOUN
ejpam-6124	26	21	of	of	ADP
ejpam-6124	26	22	a	a	DET
ejpam-6124	26	23	total	total	ADJ
ejpam-6124	26	24	dominating	dominating	NOUN
ejpam-6124	26	25	set	set	NOUN
ejpam-6124	26	26	.	.	PUNCT
ejpam-6124	27	1	furthermore	furthermore	ADV
ejpam-6124	27	2	,	,	PUNCT
ejpam-6124	27	3	not	not	PART
ejpam-6124	27	4	all	all	DET
ejpam-6124	27	5	graphs	graph	NOUN
ejpam-6124	27	6	have	have	VERB
ejpam-6124	27	7	a	a	DET
ejpam-6124	27	8	total	total	ADJ
ejpam-6124	27	9	exact	exact	ADJ
ejpam-6124	27	10	dominating	dominating	NOUN
ejpam-6124	27	11	set	set	NOUN
ejpam-6124	27	12	;	;	PUNCT
ejpam-6124	27	13	we	we	PRON
ejpam-6124	27	14	denote	denote	VERB
ejpam-6124	27	15	them	they	PRON
ejpam-6124	27	16	as	as	ADP
ejpam-6124	27	17	non	non	ADJ
ejpam-6124	27	18	-	-	ADJ
ejpam-6124	27	19	γte	γte	PRON
ejpam-6124	27	20	-	-	PUNCT
ejpam-6124	27	21	graphs	graph	NOUN
ejpam-6124	27	22	.	.	PUNCT
ejpam-6124	28	1	2	2	X
ejpam-6124	28	2	.	.	X
ejpam-6124	28	3	terminology	terminology	NOUN
ejpam-6124	28	4	and	and	CCONJ
ejpam-6124	28	5	notation	notation	NOUN
ejpam-6124	28	6	let	let	VERB
ejpam-6124	28	7	g	g	NOUN
ejpam-6124	28	8	=	=	SYM
ejpam-6124	28	9	(	(	PUNCT
ejpam-6124	28	10	v	v	NOUN
ejpam-6124	28	11	(	(	PUNCT
ejpam-6124	28	12	g	g	NOUN
ejpam-6124	28	13	)	)	PUNCT
ejpam-6124	28	14	,	,	PUNCT
ejpam-6124	28	15	e(g	e(g	PROPN
ejpam-6124	28	16	)	)	PUNCT
ejpam-6124	28	17	)	)	PUNCT
ejpam-6124	28	18	be	be	AUX
ejpam-6124	28	19	a	a	DET
ejpam-6124	28	20	simple	simple	ADJ
ejpam-6124	28	21	nontrivial	nontrivial	ADJ
ejpam-6124	28	22	undirected	undirected	ADJ
ejpam-6124	28	23	graph	graph	NOUN
ejpam-6124	28	24	where	where	SCONJ
ejpam-6124	28	25	v	v	X
ejpam-6124	28	26	(	(	PUNCT
ejpam-6124	28	27	g	g	NOUN
ejpam-6124	28	28	)	)	PUNCT
ejpam-6124	28	29	is	be	AUX
ejpam-6124	28	30	the	the	DET
ejpam-6124	28	31	vertex	vertex	NOUN
ejpam-6124	28	32	set	set	NOUN
ejpam-6124	28	33	and	and	CCONJ
ejpam-6124	28	34	e(g	e(g	PROPN
ejpam-6124	28	35	)	)	PUNCT
ejpam-6124	28	36	is	be	AUX
ejpam-6124	28	37	the	the	DET
ejpam-6124	28	38	edge	edge	NOUN
ejpam-6124	28	39	set	set	NOUN
ejpam-6124	28	40	of	of	ADP
ejpam-6124	28	41	g.	g.	PROPN
ejpam-6124	28	42	the	the	DET
ejpam-6124	28	43	set	set	NOUN
ejpam-6124	28	44	of	of	ADP
ejpam-6124	28	45	neighbors	neighbor	NOUN
ejpam-6124	28	46	of	of	ADP
ejpam-6124	28	47	a	a	DET
ejpam-6124	28	48	vertex	vertex	NOUN
ejpam-6124	28	49	u	u	NOUN
ejpam-6124	28	50	in	in	ADP
ejpam-6124	28	51	g	g	PROPN
ejpam-6124	28	52	is	be	AUX
ejpam-6124	28	53	called	call	VERB
ejpam-6124	28	54	the	the	DET
ejpam-6124	28	55	open	open	ADJ
ejpam-6124	28	56	neighborhood	neighborhood	NOUN
ejpam-6124	28	57	of	of	ADP
ejpam-6124	28	58	u	u	NOUN
ejpam-6124	28	59	in	in	ADP
ejpam-6124	28	60	g	g	PROPN
ejpam-6124	28	61	and	and	CCONJ
ejpam-6124	28	62	is	be	AUX
ejpam-6124	28	63	denoted	denote	VERB
ejpam-6124	28	64	by	by	ADP
ejpam-6124	28	65	ng(u	ng(u	NOUN
ejpam-6124	28	66	)	)	PUNCT
ejpam-6124	28	67	=	=	SYM
ejpam-6124	28	68	n(u	n(u	PROPN
ejpam-6124	28	69	)	)	PUNCT
ejpam-6124	29	1	=	=	PRON
ejpam-6124	29	2	{	{	PUNCT
ejpam-6124	29	3	v	v	NUM
ejpam-6124	29	4	∈	∈	NOUN
ejpam-6124	29	5	v	v	NOUN
ejpam-6124	29	6	(	(	PUNCT
ejpam-6124	29	7	g	g	NOUN
ejpam-6124	29	8	)	)	PUNCT
ejpam-6124	29	9	:	:	PUNCT
ejpam-6124	29	10	uv	uv	PROPN
ejpam-6124	29	11	∈	∈	PROPN
ejpam-6124	29	12	e(g	e(g	PROPN
ejpam-6124	29	13	)	)	PUNCT
ejpam-6124	29	14	}	}	PUNCT
ejpam-6124	29	15	and	and	CCONJ
ejpam-6124	29	16	the	the	DET
ejpam-6124	29	17	closed	closed	ADJ
ejpam-6124	29	18	neighborhood	neighborhood	NOUN
ejpam-6124	29	19	of	of	ADP
ejpam-6124	29	20	u	u	NOUN
ejpam-6124	29	21	is	be	AUX
ejpam-6124	29	22	the	the	DET
ejpam-6124	29	23	set	set	ADJ
ejpam-6124	29	24	n	n	NOUN
ejpam-6124	29	25	[	[	X
ejpam-6124	29	26	u	u	X
ejpam-6124	29	27	]	]	X
ejpam-6124	29	28	=	=	SYM
ejpam-6124	29	29	n(u)∪{u	n(u)∪{u	PROPN
ejpam-6124	29	30	}	}	PUNCT
ejpam-6124	29	31	.	.	PUNCT
ejpam-6124	30	1	the	the	DET
ejpam-6124	30	2	open	open	ADJ
ejpam-6124	30	3	neighborhood	neighborhood	NOUN
ejpam-6124	30	4	of	of	ADP
ejpam-6124	30	5	a	a	DET
ejpam-6124	30	6	subset	subset	NOUN
ejpam-6124	30	7	t	t	NOUN
ejpam-6124	30	8	of	of	ADP
ejpam-6124	30	9	v	v	PROPN
ejpam-6124	30	10	(	(	PUNCT
ejpam-6124	30	11	g	g	NOUN
ejpam-6124	30	12	)	)	PUNCT
ejpam-6124	30	13	is	be	AUX
ejpam-6124	30	14	the	the	DET
ejpam-6124	30	15	set	set	NOUN
ejpam-6124	30	16	ng(t	ng(t	PUNCT
ejpam-6124	30	17	)	)	PUNCT
ejpam-6124	31	1	=	=	SYM
ejpam-6124	31	2	n(t	n(t	PROPN
ejpam-6124	31	3	)	)	PUNCT
ejpam-6124	31	4	=	=	SYM
ejpam-6124	31	5	∪v∈tng(v	∪v∈tng(v	PROPN
ejpam-6124	31	6	)	)	PUNCT
ejpam-6124	31	7	and	and	CCONJ
ejpam-6124	31	8	its	its	PRON
ejpam-6124	31	9	closed	closed	ADJ
ejpam-6124	31	10	neighborhood	neighborhood	NOUN
ejpam-6124	31	11	is	be	AUX
ejpam-6124	31	12	the	the	DET
ejpam-6124	31	13	set	set	VERB
ejpam-6124	31	14	ng[t	ng[t	NOUN
ejpam-6124	31	15	]	]	PUNCT
ejpam-6124	32	1	=	=	PUNCT
ejpam-6124	32	2	n	n	PRON
ejpam-6124	33	1	[	[	X
ejpam-6124	33	2	t	t	X
ejpam-6124	33	3	]	]	PUNCT
ejpam-6124	33	4	=	=	SYM
ejpam-6124	33	5	n(t	n(t	PROPN
ejpam-6124	33	6	)	)	PUNCT
ejpam-6124	33	7	∪	∪	ADP
ejpam-6124	33	8	t	t	PROPN
ejpam-6124	34	1	[	[	X
ejpam-6124	34	2	4	4	NUM
ejpam-6124	34	3	]	]	PUNCT
ejpam-6124	34	4	.	.	PUNCT
ejpam-6124	35	1	a	a	DET
ejpam-6124	35	2	set	set	NOUN
ejpam-6124	35	3	t	t	PROPN
ejpam-6124	35	4	⊆	⊆	NUM
ejpam-6124	35	5	v	v	NOUN
ejpam-6124	35	6	(	(	PUNCT
ejpam-6124	35	7	g	g	NOUN
ejpam-6124	35	8	)	)	PUNCT
ejpam-6124	35	9	is	be	AUX
ejpam-6124	35	10	a	a	DET
ejpam-6124	35	11	dominating	dominating	NOUN
ejpam-6124	35	12	set	set	NOUN
ejpam-6124	35	13	(	(	PUNCT
ejpam-6124	35	14	resp	resp	NOUN
ejpam-6124	35	15	.	.	PUNCT
ejpam-6124	36	1	total	total	ADJ
ejpam-6124	36	2	dominating	dominating	NOUN
ejpam-6124	36	3	set	set	NOUN
ejpam-6124	36	4	)	)	PUNCT
ejpam-6124	36	5	of	of	ADP
ejpam-6124	36	6	g	g	PROPN
ejpam-6124	36	7	if	if	SCONJ
ejpam-6124	36	8	n	n	PROPN
ejpam-6124	36	9	[	[	X
ejpam-6124	36	10	t	t	X
ejpam-6124	36	11	]	]	X
ejpam-6124	36	12	=	=	SYM
ejpam-6124	36	13	v	v	X
ejpam-6124	36	14	(	(	PUNCT
ejpam-6124	36	15	g	g	NOUN
ejpam-6124	36	16	)	)	PUNCT
ejpam-6124	36	17	(	(	PUNCT
ejpam-6124	36	18	resp	resp	NOUN
ejpam-6124	36	19	.	.	PUNCT
ejpam-6124	37	1	n(t	n(t	X
ejpam-6124	37	2	)	)	PUNCT
ejpam-6124	38	1	=	=	SYM
ejpam-6124	38	2	v	v	X
ejpam-6124	38	3	(	(	PUNCT
ejpam-6124	38	4	g	g	NOUN
ejpam-6124	38	5	)	)	PUNCT
ejpam-6124	38	6	)	)	PUNCT
ejpam-6124	38	7	.	.	PUNCT
ejpam-6124	39	1	the	the	DET
ejpam-6124	39	2	domination	domination	NOUN
ejpam-6124	39	3	number	number	NOUN
ejpam-6124	39	4	γ(g	γ(g	PROPN
ejpam-6124	39	5	)	)	PUNCT
ejpam-6124	39	6	(	(	PUNCT
ejpam-6124	39	7	resp	resp	NOUN
ejpam-6124	39	8	.	.	PUNCT
ejpam-6124	40	1	total	total	ADJ
ejpam-6124	40	2	domination	domination	NOUN
ejpam-6124	40	3	number	number	NOUN
ejpam-6124	40	4	γt(g	γt(g	NUM
ejpam-6124	40	5	)	)	PUNCT
ejpam-6124	40	6	)	)	PUNCT
ejpam-6124	40	7	of	of	ADP
ejpam-6124	40	8	g	g	PROPN
ejpam-6124	40	9	is	be	AUX
ejpam-6124	40	10	the	the	DET
ejpam-6124	40	11	minimum	minimum	ADJ
ejpam-6124	40	12	cardinality	cardinality	NOUN
ejpam-6124	40	13	of	of	ADP
ejpam-6124	40	14	a	a	DET
ejpam-6124	40	15	dominating	dominating	NOUN
ejpam-6124	40	16	set	set	NOUN
ejpam-6124	40	17	(	(	PUNCT
ejpam-6124	40	18	resp	resp	NOUN
ejpam-6124	40	19	.	.	PUNCT
ejpam-6124	41	1	total	total	ADJ
ejpam-6124	41	2	dominating	dominating	NOUN
ejpam-6124	41	3	set	set	NOUN
ejpam-6124	41	4	)	)	PUNCT
ejpam-6124	42	1	[	[	X
ejpam-6124	42	2	4	4	NUM
ejpam-6124	42	3	]	]	PUNCT
ejpam-6124	42	4	.	.	PUNCT
ejpam-6124	43	1	a	a	DET
ejpam-6124	43	2	set	set	NOUN
ejpam-6124	43	3	that	that	PRON
ejpam-6124	43	4	has	have	VERB
ejpam-6124	43	5	a	a	DET
ejpam-6124	43	6	cardinality	cardinality	NOUN
ejpam-6124	43	7	of	of	ADP
ejpam-6124	43	8	γt(g	γt(g	NOUN
ejpam-6124	43	9	)	)	PUNCT
ejpam-6124	43	10	is	be	AUX
ejpam-6124	43	11	a	a	DET
ejpam-6124	43	12	γt	γt	NOUN
ejpam-6124	43	13	-	-	NOUN
ejpam-6124	43	14	set	set	NOUN
ejpam-6124	43	15	.	.	PUNCT
ejpam-6124	44	1	a	a	DET
ejpam-6124	44	2	set	set	NOUN
ejpam-6124	44	3	t	t	PROPN
ejpam-6124	44	4	⊆	⊆	NUM
ejpam-6124	44	5	v	v	NOUN
ejpam-6124	44	6	(	(	PUNCT
ejpam-6124	44	7	g	g	NOUN
ejpam-6124	44	8	)	)	PUNCT
ejpam-6124	44	9	is	be	AUX
ejpam-6124	44	10	said	say	VERB
ejpam-6124	44	11	to	to	PART
ejpam-6124	44	12	be	be	AUX
ejpam-6124	44	13	an	an	DET
ejpam-6124	44	14	exact	exact	ADJ
ejpam-6124	44	15	dominating	dominating	NOUN
ejpam-6124	44	16	set	set	NOUN
ejpam-6124	45	1	if	if	SCONJ
ejpam-6124	45	2	(	(	PUNCT
ejpam-6124	45	3	i	i	NOUN
ejpam-6124	45	4	)	)	PUNCT
ejpam-6124	45	5	|n(v	|n(v	PROPN
ejpam-6124	45	6	)	)	PUNCT
ejpam-6124	45	7	∩	∩	NOUN
ejpam-6124	45	8	t	t	NOUN
ejpam-6124	45	9	|	|	NOUN
ejpam-6124	45	10	=	=	SYM
ejpam-6124	45	11	1	1	NUM
ejpam-6124	45	12	∀	∀	NOUN
ejpam-6124	45	13	v	v	ADP
ejpam-6124	45	14	∈	∈	PROPN
ejpam-6124	45	15	v	v	NOUN
ejpam-6124	45	16	(	(	PUNCT
ejpam-6124	45	17	g	g	NOUN
ejpam-6124	45	18	)	)	PUNCT
ejpam-6124	45	19	\	\	PROPN
ejpam-6124	45	20	t	t	PROPN
ejpam-6124	45	21	and	and	CCONJ
ejpam-6124	45	22	(	(	PUNCT
ejpam-6124	45	23	ii	ii	PROPN
ejpam-6124	45	24	)	)	PUNCT
ejpam-6124	45	25	|n(u	|n(u	PROPN
ejpam-6124	45	26	)	)	PUNCT
ejpam-6124	45	27	∩	∩	NOUN
ejpam-6124	45	28	t	t	NOUN
ejpam-6124	45	29	|	|	ADV
ejpam-6124	45	30	≤	≤	NUM
ejpam-6124	45	31	1	1	NUM
ejpam-6124	45	32	∀	∀	NOUN
ejpam-6124	45	33	u	u	NOUN
ejpam-6124	45	34	∈	∈	PROPN
ejpam-6124	45	35	t	t	NOUN
ejpam-6124	45	36	.	.	PUNCT
ejpam-6124	46	1	the	the	DET
ejpam-6124	46	2	minimum	minimum	ADJ
ejpam-6124	46	3	cardinality	cardinality	NOUN
ejpam-6124	46	4	of	of	ADP
ejpam-6124	46	5	an	an	DET
ejpam-6124	46	6	exact	exact	ADJ
ejpam-6124	46	7	dominating	dominating	NOUN
ejpam-6124	46	8	set	set	NOUN
ejpam-6124	46	9	is	be	AUX
ejpam-6124	46	10	the	the	DET
ejpam-6124	46	11	exact	exact	ADJ
ejpam-6124	46	12	domination	domination	NOUN
ejpam-6124	46	13	number	number	NOUN
ejpam-6124	46	14	of	of	ADP
ejpam-6124	46	15	the	the	DET
ejpam-6124	46	16	graph	graph	NOUN
ejpam-6124	46	17	denoted	denote	VERB
ejpam-6124	46	18	by	by	ADP
ejpam-6124	46	19	γe(g	γe(g	NUM
ejpam-6124	46	20	)	)	PUNCT
ejpam-6124	46	21	.	.	PUNCT
ejpam-6124	47	1	a	a	DET
ejpam-6124	47	2	set	set	NOUN
ejpam-6124	47	3	that	that	PRON
ejpam-6124	47	4	has	have	VERB
ejpam-6124	47	5	a	a	DET
ejpam-6124	47	6	cardinality	cardinality	NOUN
ejpam-6124	47	7	of	of	ADP
ejpam-6124	47	8	γe(g	γe(g	NUM
ejpam-6124	47	9	)	)	PUNCT
ejpam-6124	47	10	is	be	AUX
ejpam-6124	47	11	a	a	DET
ejpam-6124	47	12	γe	γe	NOUN
ejpam-6124	47	13	-	-	NOUN
ejpam-6124	47	14	set	set	VERB
ejpam-6124	47	15	[	[	X
ejpam-6124	47	16	3	3	NUM
ejpam-6124	47	17	]	]	PUNCT
ejpam-6124	47	18	.	.	PUNCT
ejpam-6124	48	1	a	a	DET
ejpam-6124	48	2	set	set	NOUN
ejpam-6124	48	3	t	t	PROPN
ejpam-6124	48	4	⊆	⊆	NUM
ejpam-6124	48	5	v	v	NOUN
ejpam-6124	48	6	(	(	PUNCT
ejpam-6124	48	7	g	g	NOUN
ejpam-6124	48	8	)	)	PUNCT
ejpam-6124	48	9	is	be	AUX
ejpam-6124	48	10	said	say	VERB
ejpam-6124	48	11	to	to	PART
ejpam-6124	48	12	be	be	AUX
ejpam-6124	48	13	the	the	DET
ejpam-6124	48	14	total	total	ADJ
ejpam-6124	48	15	exact	exact	ADJ
ejpam-6124	48	16	dominating	dominating	NOUN
ejpam-6124	48	17	set	set	NOUN
ejpam-6124	48	18	if	if	SCONJ
ejpam-6124	48	19	it	it	PRON
ejpam-6124	48	20	satisfies	satisfy	VERB
ejpam-6124	48	21	(	(	PUNCT
ejpam-6124	48	22	i	i	NOUN
ejpam-6124	48	23	)	)	PUNCT
ejpam-6124	48	24	|n(v	|n(v	PROPN
ejpam-6124	48	25	)	)	PUNCT
ejpam-6124	48	26	∩	∩	NOUN
ejpam-6124	48	27	t	t	NOUN
ejpam-6124	49	1	|	|	NOUN
ejpam-6124	49	2	=	=	SYM
ejpam-6124	49	3	1	1	NUM
ejpam-6124	49	4	∀	∀	NOUN
ejpam-6124	49	5	v	v	ADP
ejpam-6124	49	6	∈	∈	PROPN
ejpam-6124	49	7	v	v	NOUN
ejpam-6124	49	8	(	(	PUNCT
ejpam-6124	49	9	g	g	NOUN
ejpam-6124	49	10	)	)	PUNCT
ejpam-6124	49	11	\	\	PROPN
ejpam-6124	49	12	t	t	PROPN
ejpam-6124	49	13	and	and	CCONJ
ejpam-6124	49	14	(	(	PUNCT
ejpam-6124	49	15	ii	ii	PROPN
ejpam-6124	49	16	)	)	PUNCT
ejpam-6124	49	17	|n(u	|n(u	PROPN
ejpam-6124	49	18	)	)	PUNCT
ejpam-6124	49	19	∩	∩	PROPN
ejpam-6124	49	20	t	t	NOUN
ejpam-6124	50	1	|	|	NOUN
ejpam-6124	50	2	=	=	SYM
ejpam-6124	50	3	1	1	NUM
ejpam-6124	50	4	∀	∀	NOUN
ejpam-6124	50	5	u	u	NOUN
ejpam-6124	50	6	∈	∈	PROPN
ejpam-6124	50	7	t	t	NOUN
ejpam-6124	50	8	.	.	PUNCT
ejpam-6124	51	1	combining	combine	VERB
ejpam-6124	51	2	the	the	DET
ejpam-6124	51	3	two	two	NUM
ejpam-6124	51	4	conditions	condition	NOUN
ejpam-6124	51	5	,	,	PUNCT
ejpam-6124	51	6	we	we	PRON
ejpam-6124	51	7	can	can	AUX
ejpam-6124	51	8	express	express	VERB
ejpam-6124	51	9	it	it	PRON
ejpam-6124	51	10	concisely	concisely	ADV
ejpam-6124	51	11	as	as	ADP
ejpam-6124	51	12	:	:	PUNCT
ejpam-6124	51	13	|n(u)∩t	|n(u)∩t	PROPN
ejpam-6124	51	14	|	|	NOUN
ejpam-6124	51	15	=	=	SYM
ejpam-6124	51	16	1	1	NUM
ejpam-6124	51	17	∀	∀	NOUN
ejpam-6124	51	18	u	u	NOUN
ejpam-6124	51	19	∈	∈	PROPN
ejpam-6124	51	20	v	v	NOUN
ejpam-6124	51	21	(	(	PUNCT
ejpam-6124	51	22	g	g	NOUN
ejpam-6124	51	23	)	)	PUNCT
ejpam-6124	51	24	.	.	PUNCT
ejpam-6124	52	1	the	the	DET
ejpam-6124	52	2	cardinality	cardinality	NOUN
ejpam-6124	52	3	of	of	ADP
ejpam-6124	52	4	a	a	DET
ejpam-6124	52	5	minimum	minimum	ADJ
ejpam-6124	52	6	total	total	ADJ
ejpam-6124	52	7	exact	exact	ADJ
ejpam-6124	52	8	dominating	dominating	NOUN
ejpam-6124	52	9	set	set	NOUN
ejpam-6124	52	10	is	be	AUX
ejpam-6124	52	11	the	the	DET
ejpam-6124	52	12	total	total	ADJ
ejpam-6124	52	13	exact	exact	ADJ
ejpam-6124	52	14	domination	domination	NOUN
ejpam-6124	52	15	number	number	NOUN
ejpam-6124	52	16	,	,	PUNCT
ejpam-6124	52	17	denoted	denote	VERB
ejpam-6124	52	18	by	by	ADP
ejpam-6124	52	19	γte(g	γte(g	PROPN
ejpam-6124	52	20	)	)	PUNCT
ejpam-6124	52	21	.	.	PUNCT
ejpam-6124	53	1	a	a	DET
ejpam-6124	53	2	set	set	NOUN
ejpam-6124	53	3	that	that	PRON
ejpam-6124	53	4	has	have	VERB
ejpam-6124	53	5	a	a	DET
ejpam-6124	53	6	cardinality	cardinality	NOUN
ejpam-6124	53	7	of	of	ADP
ejpam-6124	53	8	γte(g	γte(g	PROPN
ejpam-6124	53	9	)	)	PUNCT
ejpam-6124	53	10	is	be	AUX
ejpam-6124	53	11	a	a	DET
ejpam-6124	53	12	γte	γte	NOUN
ejpam-6124	53	13	-	-	PUNCT
ejpam-6124	53	14	set	set	NOUN
ejpam-6124	53	15	.	.	PUNCT
ejpam-6124	54	1	graph	graph	NOUN
ejpam-6124	54	2	g	g	NOUN
ejpam-6124	54	3	is	be	AUX
ejpam-6124	54	4	considered	consider	VERB
ejpam-6124	54	5	a	a	DET
ejpam-6124	54	6	non−γte−graph	non−γte−graph	NOUN
ejpam-6124	54	7	if	if	SCONJ
ejpam-6124	54	8	it	it	PRON
ejpam-6124	54	9	does	do	AUX
ejpam-6124	54	10	not	not	PART
ejpam-6124	54	11	contain	contain	VERB
ejpam-6124	54	12	a	a	DET
ejpam-6124	54	13	total	total	ADJ
ejpam-6124	54	14	exact	exact	ADJ
ejpam-6124	54	15	dominating	dominating	NOUN
ejpam-6124	54	16	set	set	NOUN
ejpam-6124	54	17	,	,	PUNCT
ejpam-6124	54	18	following	follow	VERB
ejpam-6124	54	19	r.	r.	PROPN
ejpam-6124	54	20	g.	g.	PROPN
ejpam-6124	54	21	aguinod	aguinod	PROPN
ejpam-6124	54	22	,	,	PUNCT
ejpam-6124	54	23	e.	e.	PROPN
ejpam-6124	54	24	m.	m.	PROPN
ejpam-6124	54	25	kiunisala	kiunisala	PROPN
ejpam-6124	54	26	,	,	PUNCT
ejpam-6124	54	27	c.	c.	PROPN
ejpam-6124	54	28	l.	l.	PROPN
ejpam-6124	54	29	armada	armada	PROPN
ejpam-6124	54	30	/	/	SYM
ejpam-6124	54	31	eur	eur	PROPN
ejpam-6124	54	32	.	.	PUNCT
ejpam-6124	55	1	j.	j.	PROPN
ejpam-6124	55	2	pure	pure	PROPN
ejpam-6124	55	3	appl	appl	PROPN
ejpam-6124	55	4	.	.	PROPN
ejpam-6124	55	5	math	math	PROPN
ejpam-6124	55	6	,	,	PUNCT
ejpam-6124	55	7	18	18	NUM
ejpam-6124	55	8	(	(	PUNCT
ejpam-6124	55	9	2	2	NUM
ejpam-6124	55	10	)	)	PUNCT
ejpam-6124	55	11	(	(	PUNCT
ejpam-6124	55	12	2025	2025	NUM
ejpam-6124	55	13	)	)	PUNCT
ejpam-6124	55	14	,	,	PUNCT
ejpam-6124	55	15	6124	6124	NUM
ejpam-6124	55	16	3	3	NUM
ejpam-6124	55	17	of	of	ADP
ejpam-6124	55	18	26	26	NUM
ejpam-6124	55	19	a	a	DET
ejpam-6124	55	20	definition	definition	NOUN
ejpam-6124	55	21	analogous	analogous	ADJ
ejpam-6124	55	22	to	to	ADP
ejpam-6124	55	23	that	that	PRON
ejpam-6124	55	24	of	of	ADP
ejpam-6124	55	25	a	a	DET
ejpam-6124	55	26	non	non	ADJ
ejpam-6124	55	27	-	-	ADJ
ejpam-6124	55	28	γp0	γp0	NOUN
ejpam-6124	55	29	-	-	PUNCT
ejpam-6124	55	30	graph	graph	NOUN
ejpam-6124	55	31	as	as	SCONJ
ejpam-6124	55	32	presented	present	VERB
ejpam-6124	55	33	in	in	ADP
ejpam-6124	55	34	[	[	X
ejpam-6124	55	35	5	5	NUM
ejpam-6124	55	36	]	]	PUNCT
ejpam-6124	55	37	.	.	PUNCT
ejpam-6124	56	1	the	the	DET
ejpam-6124	56	2	join	join	NOUN
ejpam-6124	56	3	of	of	ADP
ejpam-6124	56	4	two	two	NUM
ejpam-6124	56	5	graphs	graph	NOUN
ejpam-6124	56	6	,	,	PUNCT
ejpam-6124	56	7	g	g	PROPN
ejpam-6124	56	8	and	and	CCONJ
ejpam-6124	56	9	h	h	NOUN
ejpam-6124	56	10	,	,	PUNCT
ejpam-6124	56	11	denoted	denote	VERB
ejpam-6124	56	12	by	by	ADP
ejpam-6124	56	13	g	g	PROPN
ejpam-6124	56	14	+	+	PROPN
ejpam-6124	56	15	h	h	NOUN
ejpam-6124	56	16	,	,	PUNCT
ejpam-6124	56	17	is	be	AUX
ejpam-6124	56	18	the	the	DET
ejpam-6124	56	19	graph	graph	NOUN
ejpam-6124	56	20	with	with	ADP
ejpam-6124	56	21	vertex	vertex	NOUN
ejpam-6124	56	22	set	set	VERB
ejpam-6124	56	23	v	v	NOUN
ejpam-6124	56	24	(	(	PUNCT
ejpam-6124	56	25	g+h	g+h	NOUN
ejpam-6124	56	26	)	)	PUNCT
ejpam-6124	56	27	=	=	SYM
ejpam-6124	56	28	v	v	X
ejpam-6124	56	29	(	(	PUNCT
ejpam-6124	56	30	g	g	NOUN
ejpam-6124	56	31	)	)	PUNCT
ejpam-6124	56	32	∪	∪	NOUN
ejpam-6124	56	33	v	v	NOUN
ejpam-6124	56	34	(	(	PUNCT
ejpam-6124	56	35	h	h	NOUN
ejpam-6124	56	36	)	)	PUNCT
ejpam-6124	56	37	and	and	CCONJ
ejpam-6124	56	38	edge	edge	NOUN
ejpam-6124	56	39	set	set	VERB
ejpam-6124	56	40	e(g+h	e(g+h	NUM
ejpam-6124	56	41	)	)	PUNCT
ejpam-6124	56	42	=	=	SYM
ejpam-6124	56	43	e(g	e(g	NOUN
ejpam-6124	56	44	)	)	PUNCT
ejpam-6124	56	45	∪	∪	ADP
ejpam-6124	56	46	e(h	e(h	PROPN
ejpam-6124	56	47	)	)	PUNCT
ejpam-6124	56	48	∪	∪	NOUN
ejpam-6124	56	49	{	{	PUNCT
ejpam-6124	56	50	uv	uv	NOUN
ejpam-6124	56	51	:	:	PUNCT
ejpam-6124	56	52	u	u	PROPN
ejpam-6124	56	53	∈	∈	PROPN
ejpam-6124	56	54	v	v	ADP
ejpam-6124	56	55	(	(	PUNCT
ejpam-6124	56	56	g	g	NOUN
ejpam-6124	56	57	)	)	PUNCT
ejpam-6124	56	58	,	,	PUNCT
ejpam-6124	56	59	v	v	X
ejpam-6124	56	60	∈	∈	PROPN
ejpam-6124	56	61	v	v	NOUN
ejpam-6124	56	62	(	(	PUNCT
ejpam-6124	56	63	h	h	NOUN
ejpam-6124	56	64	)	)	PUNCT
ejpam-6124	56	65	}	}	PUNCT
ejpam-6124	57	1	[	[	X
ejpam-6124	57	2	6	6	NUM
ejpam-6124	57	3	]	]	PUNCT
ejpam-6124	57	4	.	.	PUNCT
ejpam-6124	58	1	the	the	DET
ejpam-6124	58	2	corona	corona	NOUN
ejpam-6124	58	3	g	g	PROPN
ejpam-6124	58	4	◦	◦	NOUN
ejpam-6124	58	5	h	h	NOUN
ejpam-6124	58	6	of	of	ADP
ejpam-6124	58	7	two	two	NUM
ejpam-6124	58	8	graphs	graph	NOUN
ejpam-6124	58	9	g	g	NOUN
ejpam-6124	58	10	and	and	CCONJ
ejpam-6124	58	11	h	h	NOUN
ejpam-6124	58	12	is	be	AUX
ejpam-6124	58	13	the	the	DET
ejpam-6124	58	14	graph	graph	NOUN
ejpam-6124	58	15	obtained	obtain	VERB
ejpam-6124	58	16	by	by	ADP
ejpam-6124	58	17	taking	take	VERB
ejpam-6124	58	18	one	one	NUM
ejpam-6124	58	19	copy	copy	NOUN
ejpam-6124	58	20	of	of	ADP
ejpam-6124	58	21	g	g	PROPN
ejpam-6124	58	22	and	and	CCONJ
ejpam-6124	58	23	|v	|v	PROPN
ejpam-6124	58	24	(	(	PUNCT
ejpam-6124	58	25	g)|	g)|	NOUN
ejpam-6124	58	26	copies	copy	NOUN
ejpam-6124	58	27	of	of	ADP
ejpam-6124	58	28	h	h	NOUN
ejpam-6124	58	29	and	and	CCONJ
ejpam-6124	58	30	then	then	ADV
ejpam-6124	58	31	forming	form	VERB
ejpam-6124	58	32	the	the	DET
ejpam-6124	58	33	join	join	NOUN
ejpam-6124	58	34	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-6124	58	35	=	=	PUNCT
ejpam-6124	58	36	v	v	PROPN
ejpam-6124	58	37	+	+	PROPN
ejpam-6124	58	38	hv	hv	PROPN
ejpam-6124	58	39	,	,	PUNCT
ejpam-6124	58	40	where	where	SCONJ
ejpam-6124	58	41	hv	hv	PROPN
ejpam-6124	58	42	is	be	AUX
ejpam-6124	58	43	a	a	DET
ejpam-6124	58	44	copy	copy	NOUN
ejpam-6124	58	45	of	of	ADP
ejpam-6124	58	46	h	h	NOUN
ejpam-6124	58	47	,	,	PUNCT
ejpam-6124	58	48	for	for	ADP
ejpam-6124	58	49	each	each	DET
ejpam-6124	58	50	v	v	NUM
ejpam-6124	58	51	∈	∈	PROPN
ejpam-6124	58	52	v	v	NOUN
ejpam-6124	58	53	(	(	PUNCT
ejpam-6124	58	54	g	g	NOUN
ejpam-6124	58	55	)	)	PUNCT
ejpam-6124	59	1	[	[	X
ejpam-6124	59	2	6	6	NUM
ejpam-6124	59	3	]	]	PUNCT
ejpam-6124	59	4	.	.	PUNCT
ejpam-6124	60	1	the	the	DET
ejpam-6124	60	2	lexicographic	lexicographic	ADJ
ejpam-6124	60	3	product	product	NOUN
ejpam-6124	60	4	or	or	CCONJ
ejpam-6124	60	5	composition	composition	NOUN
ejpam-6124	60	6	of	of	ADP
ejpam-6124	60	7	two	two	NUM
ejpam-6124	60	8	graphs	graph	NOUN
ejpam-6124	60	9	g	g	NOUN
ejpam-6124	60	10	and	and	CCONJ
ejpam-6124	60	11	h	h	NOUN
ejpam-6124	60	12	is	be	AUX
ejpam-6124	60	13	the	the	DET
ejpam-6124	60	14	graph	graph	NOUN
ejpam-6124	60	15	g[h	g[h	PROPN
ejpam-6124	60	16	]	]	PUNCT
ejpam-6124	60	17	with	with	ADP
ejpam-6124	60	18	vertex	vertex	NOUN
ejpam-6124	60	19	set	set	VERB
ejpam-6124	60	20	v	v	NOUN
ejpam-6124	60	21	(	(	PUNCT
ejpam-6124	60	22	g[h	g[h	PROPN
ejpam-6124	60	23	]	]	PUNCT
ejpam-6124	60	24	)	)	PUNCT
ejpam-6124	60	25	=	=	SYM
ejpam-6124	60	26	v	v	X
ejpam-6124	60	27	(	(	PUNCT
ejpam-6124	60	28	g	g	NOUN
ejpam-6124	60	29	)	)	PUNCT
ejpam-6124	60	30	×	×	NOUN
ejpam-6124	60	31	v	v	NOUN
ejpam-6124	60	32	(	(	PUNCT
ejpam-6124	60	33	h	h	NOUN
ejpam-6124	60	34	)	)	PUNCT
ejpam-6124	60	35	and	and	CCONJ
ejpam-6124	60	36	edge	edge	VERB
ejpam-6124	60	37	set	set	VERB
ejpam-6124	60	38	e(g[h	e(g[h	NOUN
ejpam-6124	60	39	]	]	PUNCT
ejpam-6124	60	40	)	)	PUNCT
ejpam-6124	60	41	=	=	SYM
ejpam-6124	60	42	{	{	PUNCT
ejpam-6124	60	43	(	(	PUNCT
ejpam-6124	60	44	x	x	NOUN
ejpam-6124	60	45	,	,	PUNCT
ejpam-6124	60	46	u)(y	u)(y	PROPN
ejpam-6124	60	47	,	,	PUNCT
ejpam-6124	60	48	v	v	NOUN
ejpam-6124	60	49	)	)	PUNCT
ejpam-6124	60	50	|	|	ADV
ejpam-6124	60	51	xy	xy	PROPN
ejpam-6124	60	52	∈	∈	PROPN
ejpam-6124	60	53	e(g	e(g	PROPN
ejpam-6124	60	54	)	)	PUNCT
ejpam-6124	60	55	or	or	CCONJ
ejpam-6124	60	56	x	x	X
ejpam-6124	60	57	=	=	SYM
ejpam-6124	60	58	y	y	PROPN
ejpam-6124	60	59	and	and	CCONJ
ejpam-6124	60	60	uv	uv	PROPN
ejpam-6124	60	61	∈	∈	PROPN
ejpam-6124	60	62	e(h	e(h	PROPN
ejpam-6124	60	63	)	)	PUNCT
ejpam-6124	60	64	}	}	PUNCT
ejpam-6124	60	65	.	.	PUNCT
ejpam-6124	61	1	any	any	DET
ejpam-6124	61	2	subset	subset	NOUN
ejpam-6124	61	3	(	(	PUNCT
ejpam-6124	61	4	c	c	NOUN
ejpam-6124	61	5	)	)	PUNCT
ejpam-6124	61	6	of	of	ADP
ejpam-6124	61	7	(	(	PUNCT
ejpam-6124	61	8	v	v	NOUN
ejpam-6124	61	9	(	(	PUNCT
ejpam-6124	61	10	g[h	g[h	PROPN
ejpam-6124	61	11	]	]	PUNCT
ejpam-6124	61	12	)	)	PUNCT
ejpam-6124	61	13	)	)	PUNCT
ejpam-6124	61	14	can	can	AUX
ejpam-6124	61	15	be	be	AUX
ejpam-6124	61	16	expressed	express	VERB
ejpam-6124	61	17	as	as	ADP
ejpam-6124	61	18	c	c	NOUN
ejpam-6124	61	19	=	=	PUNCT
ejpam-6124	61	20	⋃	⋃	NOUN
ejpam-6124	61	21	x∈s({x	x∈s({x	NOUN
ejpam-6124	61	22	}	}	PUNCT
ejpam-6124	61	23	×	×	PROPN
ejpam-6124	61	24	tx	tx	PROPN
ejpam-6124	61	25	)	)	PUNCT
ejpam-6124	61	26	,	,	PUNCT
ejpam-6124	61	27	where	where	SCONJ
ejpam-6124	61	28	s	s	VERB
ejpam-6124	61	29	⊆	⊆	NUM
ejpam-6124	61	30	v	v	NOUN
ejpam-6124	61	31	(	(	PUNCT
ejpam-6124	61	32	g	g	NOUN
ejpam-6124	61	33	)	)	PUNCT
ejpam-6124	61	34	and	and	CCONJ
ejpam-6124	61	35	tx	tx	VERB
ejpam-6124	61	36	⊆	⊆	NUM
ejpam-6124	61	37	v	v	NOUN
ejpam-6124	61	38	(	(	PUNCT
ejpam-6124	61	39	h	h	NOUN
ejpam-6124	61	40	)	)	PUNCT
ejpam-6124	61	41	for	for	ADP
ejpam-6124	61	42	each	each	DET
ejpam-6124	61	43	x	x	PROPN
ejpam-6124	61	44	∈	∈	PROPN
ejpam-6124	61	45	s.	s.	PROPN
ejpam-6124	61	46	the	the	DET
ejpam-6124	61	47	set	set	PROPN
ejpam-6124	61	48	s	s	PART
ejpam-6124	61	49	is	be	AUX
ejpam-6124	61	50	called	call	VERB
ejpam-6124	61	51	the	the	DET
ejpam-6124	61	52	g	g	NOUN
ejpam-6124	61	53	-	-	PUNCT
ejpam-6124	61	54	projection	projection	NOUN
ejpam-6124	61	55	of	of	ADP
ejpam-6124	61	56	c	c	NOUN
ejpam-6124	61	57	,	,	PUNCT
ejpam-6124	61	58	and	and	CCONJ
ejpam-6124	61	59	⋃	⋃	PROPN
ejpam-6124	61	60	x∈s	x∈s	PROPN
ejpam-6124	61	61	tx	tx	PROPN
ejpam-6124	61	62	is	be	AUX
ejpam-6124	61	63	called	call	VERB
ejpam-6124	61	64	the	the	DET
ejpam-6124	61	65	h	h	NOUN
ejpam-6124	61	66	-	-	PUNCT
ejpam-6124	61	67	projection	projection	NOUN
ejpam-6124	61	68	of	of	ADP
ejpam-6124	61	69	c	c	NOUN
ejpam-6124	62	1	[	[	X
ejpam-6124	62	2	7	7	NUM
ejpam-6124	62	3	]	]	PUNCT
ejpam-6124	62	4	.	.	PUNCT
ejpam-6124	63	1	the	the	DET
ejpam-6124	63	2	path	path	NOUN
ejpam-6124	63	3	graph	graph	NOUN
ejpam-6124	63	4	pn	pn	PROPN
ejpam-6124	63	5	is	be	AUX
ejpam-6124	63	6	a	a	DET
ejpam-6124	63	7	tree	tree	NOUN
ejpam-6124	63	8	with	with	ADP
ejpam-6124	63	9	two	two	NUM
ejpam-6124	63	10	nodes	node	NOUN
ejpam-6124	63	11	of	of	ADP
ejpam-6124	63	12	vertex	vertex	NOUN
ejpam-6124	63	13	degree	degree	NOUN
ejpam-6124	63	14	1	1	NUM
ejpam-6124	63	15	,	,	PUNCT
ejpam-6124	63	16	and	and	CCONJ
ejpam-6124	63	17	the	the	DET
ejpam-6124	63	18	other	other	ADJ
ejpam-6124	63	19	n	n	CCONJ
ejpam-6124	63	20	−	−	NUM
ejpam-6124	63	21	2	2	NUM
ejpam-6124	63	22	nodes	node	NOUN
ejpam-6124	63	23	of	of	ADP
ejpam-6124	63	24	vertex	vertex	NOUN
ejpam-6124	63	25	degree	degree	NOUN
ejpam-6124	63	26	2	2	NUM
ejpam-6124	63	27	[	[	NOUN
ejpam-6124	63	28	8	8	NUM
ejpam-6124	63	29	]	]	PUNCT
ejpam-6124	63	30	.	.	PUNCT
ejpam-6124	64	1	a	a	DET
ejpam-6124	64	2	cycle	cycle	NOUN
ejpam-6124	64	3	graph	graph	NOUN
ejpam-6124	64	4	cn	cn	PROPN
ejpam-6124	64	5	are	be	AUX
ejpam-6124	64	6	defined	define	VERB
ejpam-6124	64	7	as	as	ADP
ejpam-6124	64	8	simple	simple	ADJ
ejpam-6124	64	9	,	,	PUNCT
ejpam-6124	64	10	connected	connect	VERB
ejpam-6124	64	11	,	,	PUNCT
ejpam-6124	64	12	undirected	undirected	ADJ
ejpam-6124	64	13	graphs	graph	NOUN
ejpam-6124	64	14	consisting	consist	VERB
ejpam-6124	64	15	of	of	ADP
ejpam-6124	64	16	a	a	DET
ejpam-6124	64	17	single	single	ADJ
ejpam-6124	64	18	cycle	cycle	NOUN
ejpam-6124	64	19	passing	pass	VERB
ejpam-6124	64	20	through	through	ADP
ejpam-6124	64	21	all	all	DET
ejpam-6124	64	22	n	n	PRON
ejpam-6124	64	23	vertices	vertex	NOUN
ejpam-6124	64	24	,	,	PUNCT
ejpam-6124	64	25	with	with	ADP
ejpam-6124	64	26	each	each	DET
ejpam-6124	64	27	vertex	vertex	NOUN
ejpam-6124	64	28	having	have	VERB
ejpam-6124	64	29	degree	degree	NOUN
ejpam-6124	64	30	2	2	NUM
ejpam-6124	64	31	and	and	CCONJ
ejpam-6124	64	32	the	the	DET
ejpam-6124	64	33	graph	graph	NOUN
ejpam-6124	64	34	forming	form	VERB
ejpam-6124	64	35	a	a	DET
ejpam-6124	64	36	closed	closed	ADJ
ejpam-6124	64	37	loop	loop	NOUN
ejpam-6124	64	38	[	[	X
ejpam-6124	64	39	9	9	NUM
ejpam-6124	64	40	]	]	PUNCT
ejpam-6124	64	41	.	.	PUNCT
ejpam-6124	65	1	the	the	DET
ejpam-6124	65	2	complete	complete	ADJ
ejpam-6124	65	3	graph	graph	NOUN
ejpam-6124	65	4	km	km	NOUN
ejpam-6124	65	5	has	have	VERB
ejpam-6124	65	6	every	every	DET
ejpam-6124	65	7	pair	pair	NOUN
ejpam-6124	65	8	of	of	ADP
ejpam-6124	65	9	its	its	PRON
ejpam-6124	65	10	m	m	NOUN
ejpam-6124	65	11	points	point	NOUN
ejpam-6124	65	12	adjacent	adjacent	ADJ
ejpam-6124	65	13	[	[	X
ejpam-6124	65	14	7	7	NUM
ejpam-6124	65	15	]	]	PUNCT
ejpam-6124	65	16	.	.	PUNCT
ejpam-6124	66	1	the	the	DET
ejpam-6124	66	2	complement	complement	NOUN
ejpam-6124	66	3	of	of	ADP
ejpam-6124	66	4	complete	complete	ADJ
ejpam-6124	66	5	graphs	graph	NOUN
ejpam-6124	66	6	km	km	NOUN
ejpam-6124	66	7	are	be	AUX
ejpam-6124	66	8	totally	totally	ADV
ejpam-6124	66	9	disconnected	disconnected	ADJ
ejpam-6124	66	10	graphs	graph	NOUN
ejpam-6124	66	11	and	and	CCONJ
ejpam-6124	66	12	are	be	AUX
ejpam-6124	66	13	regular	regular	ADJ
ejpam-6124	66	14	of	of	ADP
ejpam-6124	66	15	degree	degree	NOUN
ejpam-6124	66	16	0	0	PUNCT
ejpam-6124	67	1	[	[	X
ejpam-6124	67	2	7	7	NUM
ejpam-6124	67	3	]	]	PUNCT
ejpam-6124	67	4	.	.	PUNCT
ejpam-6124	68	1	a	a	DET
ejpam-6124	68	2	complete	complete	ADJ
ejpam-6124	68	3	bipartite	bipartite	NOUN
ejpam-6124	68	4	graph	graph	NOUN
ejpam-6124	68	5	km	km	PROPN
ejpam-6124	68	6	,	,	PUNCT
ejpam-6124	68	7	n	n	PRON
ejpam-6124	68	8	is	be	AUX
ejpam-6124	68	9	a	a	DET
ejpam-6124	68	10	graph	graph	NOUN
ejpam-6124	68	11	equivalent	equivalent	ADJ
ejpam-6124	68	12	to	to	AUX
ejpam-6124	68	13	km	km	VERB
ejpam-6124	68	14	+	+	PROPN
ejpam-6124	68	15	kn	kn	PROPN
ejpam-6124	68	16	such	such	ADJ
ejpam-6124	68	17	that	that	DET
ejpam-6124	68	18	n	n	CCONJ
ejpam-6124	68	19	,	,	PUNCT
ejpam-6124	68	20	m	m	VERB
ejpam-6124	68	21	≥	≥	NOUN
ejpam-6124	68	22	1	1	NUM
ejpam-6124	69	1	[	[	X
ejpam-6124	69	2	6	6	NUM
ejpam-6124	69	3	]	]	PUNCT
ejpam-6124	69	4	.	.	PUNCT
ejpam-6124	70	1	the	the	DET
ejpam-6124	70	2	star	star	NOUN
ejpam-6124	70	3	graph	graph	PROPN
ejpam-6124	70	4	sn	sn	PROPN
ejpam-6124	70	5	,	,	PUNCT
ejpam-6124	70	6	of	of	ADP
ejpam-6124	70	7	order	order	NOUN
ejpam-6124	70	8	n	n	CCONJ
ejpam-6124	70	9	,	,	PUNCT
ejpam-6124	70	10	is	be	AUX
ejpam-6124	70	11	a	a	DET
ejpam-6124	70	12	tree	tree	NOUN
ejpam-6124	70	13	on	on	ADP
ejpam-6124	70	14	n	n	PRON
ejpam-6124	70	15	vertices	vertex	NOUN
ejpam-6124	70	16	with	with	ADP
ejpam-6124	70	17	one	one	NUM
ejpam-6124	70	18	vertex	vertex	NOUN
ejpam-6124	70	19	of	of	ADP
ejpam-6124	70	20	degree	degree	NOUN
ejpam-6124	70	21	n−	n−	NOUN
ejpam-6124	70	22	1	1	NUM
ejpam-6124	70	23	and	and	CCONJ
ejpam-6124	70	24	the	the	DET
ejpam-6124	70	25	remaining	remain	VERB
ejpam-6124	70	26	n−	n−	NOUN
ejpam-6124	70	27	1	1	NUM
ejpam-6124	70	28	vertices	vertex	NOUN
ejpam-6124	70	29	of	of	ADP
ejpam-6124	70	30	degree	degree	NOUN
ejpam-6124	70	31	1	1	NUM
ejpam-6124	70	32	[	[	X
ejpam-6124	70	33	7	7	NUM
ejpam-6124	70	34	]	]	PUNCT
ejpam-6124	70	35	.	.	PUNCT
ejpam-6124	71	1	a	a	DET
ejpam-6124	71	2	wheel	wheel	NOUN
ejpam-6124	71	3	graph	graph	NOUN
ejpam-6124	71	4	wn	wn	PROPN
ejpam-6124	71	5	,	,	PUNCT
ejpam-6124	71	6	of	of	ADP
ejpam-6124	71	7	order	order	NOUN
ejpam-6124	71	8	n	n	CCONJ
ejpam-6124	71	9	,	,	PUNCT
ejpam-6124	71	10	is	be	AUX
ejpam-6124	71	11	formed	form	VERB
ejpam-6124	71	12	by	by	ADP
ejpam-6124	71	13	adding	add	VERB
ejpam-6124	71	14	a	a	DET
ejpam-6124	71	15	vertex	vertex	NOUN
ejpam-6124	71	16	adjacent	adjacent	ADJ
ejpam-6124	71	17	to	to	ADP
ejpam-6124	71	18	all	all	DET
ejpam-6124	71	19	vertices	vertex	NOUN
ejpam-6124	71	20	of	of	ADP
ejpam-6124	71	21	a	a	DET
ejpam-6124	71	22	cycle	cycle	NOUN
ejpam-6124	71	23	[	[	X
ejpam-6124	71	24	7	7	NUM
ejpam-6124	71	25	]	]	PUNCT
ejpam-6124	71	26	.	.	PUNCT
ejpam-6124	72	1	a	a	DET
ejpam-6124	72	2	fan	fan	NOUN
ejpam-6124	72	3	graph	graph	NOUN
ejpam-6124	72	4	fn	fn	NOUN
ejpam-6124	72	5	is	be	AUX
ejpam-6124	72	6	formed	form	VERB
ejpam-6124	72	7	by	by	ADP
ejpam-6124	72	8	joining	join	VERB
ejpam-6124	72	9	a	a	DET
ejpam-6124	72	10	path	path	NOUN
ejpam-6124	72	11	to	to	ADP
ejpam-6124	72	12	a	a	DET
ejpam-6124	72	13	single	single	ADJ
ejpam-6124	72	14	vertex	vertex	NOUN
ejpam-6124	72	15	[	[	X
ejpam-6124	72	16	7	7	NUM
ejpam-6124	72	17	]	]	PUNCT
ejpam-6124	72	18	.	.	PUNCT
ejpam-6124	73	1	the	the	DET
ejpam-6124	73	2	generalized	generalized	ADJ
ejpam-6124	73	3	fan	fan	PROPN
ejpam-6124	73	4	graph	graph	PROPN
ejpam-6124	73	5	fm	fm	PROPN
ejpam-6124	73	6	,	,	PUNCT
ejpam-6124	73	7	n	n	PRON
ejpam-6124	73	8	is	be	AUX
ejpam-6124	73	9	defined	define	VERB
ejpam-6124	73	10	as	as	SCONJ
ejpam-6124	73	11	the	the	DET
ejpam-6124	73	12	graph	graph	NOUN
ejpam-6124	73	13	join	join	VERB
ejpam-6124	73	14	km	km	PROPN
ejpam-6124	73	15	+	+	CCONJ
ejpam-6124	73	16	pn	pn	PROPN
ejpam-6124	73	17	,	,	PUNCT
ejpam-6124	73	18	where	where	SCONJ
ejpam-6124	73	19	km	km	NOUN
ejpam-6124	73	20	is	be	AUX
ejpam-6124	73	21	the	the	DET
ejpam-6124	73	22	empty	empty	ADJ
ejpam-6124	73	23	graph	graph	NOUN
ejpam-6124	73	24	on	on	ADP
ejpam-6124	73	25	m	m	NOUN
ejpam-6124	73	26	vertices	vertex	NOUN
ejpam-6124	73	27	and	and	CCONJ
ejpam-6124	73	28	pn	pn	PROPN
ejpam-6124	73	29	is	be	AUX
ejpam-6124	73	30	the	the	DET
ejpam-6124	73	31	path	path	NOUN
ejpam-6124	73	32	graph	graph	NOUN
ejpam-6124	73	33	on	on	ADP
ejpam-6124	73	34	n	n	DET
ejpam-6124	73	35	vertices	vertex	NOUN
ejpam-6124	73	36	[	[	X
ejpam-6124	73	37	10	10	NUM
ejpam-6124	73	38	]	]	PUNCT
ejpam-6124	73	39	.	.	PUNCT
ejpam-6124	74	1	the	the	DET
ejpam-6124	74	2	generalized	generalize	VERB
ejpam-6124	74	3	wheel	wheel	NOUN
ejpam-6124	74	4	graph	graph	NOUN
ejpam-6124	74	5	wm	wm	PROPN
ejpam-6124	74	6	,	,	PUNCT
ejpam-6124	74	7	n	n	PROPN
ejpam-6124	74	8	is	be	AUX
ejpam-6124	74	9	a	a	DET
ejpam-6124	74	10	graph	graph	NOUN
ejpam-6124	74	11	obtained	obtain	VERB
ejpam-6124	74	12	by	by	ADP
ejpam-6124	74	13	joining	join	VERB
ejpam-6124	74	14	the	the	DET
ejpam-6124	74	15	vertices	vertex	NOUN
ejpam-6124	74	16	of	of	ADP
ejpam-6124	74	17	km	km	NOUN
ejpam-6124	74	18	to	to	ADP
ejpam-6124	74	19	every	every	DET
ejpam-6124	74	20	vertex	vertex	NOUN
ejpam-6124	74	21	of	of	ADP
ejpam-6124	74	22	a	a	DET
ejpam-6124	74	23	cycle	cycle	NOUN
ejpam-6124	74	24	cn	cn	PROPN
ejpam-6124	74	25	.	.	PUNCT
ejpam-6124	75	1	that	that	PRON
ejpam-6124	75	2	is	be	AUX
ejpam-6124	75	3	,	,	PUNCT
ejpam-6124	75	4	wm	wm	PROPN
ejpam-6124	75	5	,	,	PUNCT
ejpam-6124	75	6	n	n	NOUN
ejpam-6124	75	7	=	=	PUNCT
ejpam-6124	75	8	cn+km	cn+km	NOUN
ejpam-6124	76	1	[	[	X
ejpam-6124	76	2	11	11	NUM
ejpam-6124	76	3	]	]	PUNCT
ejpam-6124	76	4	.	.	PUNCT
ejpam-6124	77	1	a	a	DET
ejpam-6124	77	2	windmill	windmill	NOUN
ejpam-6124	77	3	graph	graph	NOUN
ejpam-6124	77	4	wm	wm	PROPN
ejpam-6124	77	5	n	n	PROPN
ejpam-6124	77	6	is	be	AUX
ejpam-6124	77	7	a	a	DET
ejpam-6124	77	8	graph	graph	NOUN
ejpam-6124	77	9	formed	form	VERB
ejpam-6124	77	10	by	by	ADP
ejpam-6124	77	11	connecting	connect	VERB
ejpam-6124	77	12	m	m	PROPN
ejpam-6124	77	13	copies	copy	NOUN
ejpam-6124	77	14	of	of	ADP
ejpam-6124	77	15	a	a	DET
ejpam-6124	77	16	complete	complete	ADJ
ejpam-6124	77	17	graph	graph	NOUN
ejpam-6124	77	18	kn−1	kn−1	PROPN
ejpam-6124	77	19	to	to	ADP
ejpam-6124	77	20	a	a	DET
ejpam-6124	77	21	single	single	ADJ
ejpam-6124	77	22	common	common	ADJ
ejpam-6124	77	23	vertex	vertex	NOUN
ejpam-6124	77	24	[	[	X
ejpam-6124	77	25	9	9	NUM
ejpam-6124	77	26	]	]	PUNCT
ejpam-6124	77	27	.	.	PUNCT
ejpam-6124	78	1	the	the	DET
ejpam-6124	78	2	friendship	friendship	NOUN
ejpam-6124	78	3	graph	graph	NOUN
ejpam-6124	78	4	fn	fn	NOUN
ejpam-6124	78	5	is	be	AUX
ejpam-6124	78	6	a	a	DET
ejpam-6124	78	7	graph	graph	NOUN
ejpam-6124	78	8	consisting	consist	VERB
ejpam-6124	78	9	of	of	ADP
ejpam-6124	78	10	n	n	PRON
ejpam-6124	78	11	triangles	triangle	NOUN
ejpam-6124	78	12	that	that	PRON
ejpam-6124	78	13	share	share	VERB
ejpam-6124	78	14	a	a	DET
ejpam-6124	78	15	common	common	ADJ
ejpam-6124	78	16	central	central	ADJ
ejpam-6124	78	17	vertex	vertex	NOUN
ejpam-6124	78	18	.	.	PUNCT
ejpam-6124	79	1	it	it	PRON
ejpam-6124	79	2	is	be	AUX
ejpam-6124	79	3	also	also	ADV
ejpam-6124	79	4	called	call	VERB
ejpam-6124	79	5	the	the	DET
ejpam-6124	79	6	dutch	dutch	ADJ
ejpam-6124	79	7	windmill	windmill	NOUN
ejpam-6124	79	8	graph	graph	NOUN
ejpam-6124	80	1	[	[	X
ejpam-6124	80	2	12	12	NUM
ejpam-6124	80	3	]	]	PUNCT
ejpam-6124	80	4	.	.	PUNCT
ejpam-6124	81	1	example	example	NOUN
ejpam-6124	82	1	1	1	NUM
ejpam-6124	82	2	.	.	PUNCT
ejpam-6124	82	3	let	let	VERB
ejpam-6124	82	4	g	g	NOUN
ejpam-6124	82	5	be	be	AUX
ejpam-6124	82	6	the	the	DET
ejpam-6124	82	7	graph	graph	NOUN
ejpam-6124	82	8	in	in	ADP
ejpam-6124	82	9	figure	figure	NOUN
ejpam-6124	82	10	1	1	NUM
ejpam-6124	82	11	and	and	CCONJ
ejpam-6124	82	12	let	let	VERB
ejpam-6124	82	13	t	t	NOUN
ejpam-6124	82	14	=	=	SYM
ejpam-6124	82	15	{	{	PUNCT
ejpam-6124	82	16	t4	t4	PROPN
ejpam-6124	82	17	,	,	PUNCT
ejpam-6124	82	18	u1	u1	PROPN
ejpam-6124	82	19	,	,	PUNCT
ejpam-6124	82	20	u4	u4	PROPN
ejpam-6124	82	21	,	,	PUNCT
ejpam-6124	82	22	u5	u5	PROPN
ejpam-6124	82	23	,	,	PUNCT
ejpam-6124	82	24	u8	u8	PROPN
ejpam-6124	82	25	,	,	PUNCT
ejpam-6124	82	26	u9	u9	PROPN
ejpam-6124	82	27	,	,	PUNCT
ejpam-6124	82	28	r3	r3	PROPN
ejpam-6124	82	29	,	,	PUNCT
ejpam-6124	82	30	r4	r4	NOUN
ejpam-6124	82	31	,	,	PUNCT
ejpam-6124	82	32	w3	w3	PROPN
ejpam-6124	82	33	,	,	PUNCT
ejpam-6124	82	34	w4	w4	NOUN
ejpam-6124	82	35	,	,	PUNCT
ejpam-6124	82	36	z1	z1	PROPN
ejpam-6124	82	37	,	,	PUNCT
ejpam-6124	82	38	x1	x1	PROPN
ejpam-6124	82	39	}	}	PUNCT
ejpam-6124	82	40	.	.	PUNCT
ejpam-6124	83	1	the	the	DET
ejpam-6124	83	2	vertices	vertex	NOUN
ejpam-6124	83	3	in	in	ADP
ejpam-6124	83	4	t	t	PROPN
ejpam-6124	83	5	are	be	AUX
ejpam-6124	83	6	colored	color	VERB
ejpam-6124	83	7	red	red	ADJ
ejpam-6124	83	8	,	,	PUNCT
ejpam-6124	83	9	and	and	CCONJ
ejpam-6124	83	10	the	the	DET
ejpam-6124	83	11	vertices	vertex	NOUN
ejpam-6124	83	12	in	in	ADP
ejpam-6124	83	13	v	v	ADP
ejpam-6124	83	14	(	(	PUNCT
ejpam-6124	83	15	g	g	NOUN
ejpam-6124	83	16	)	)	PUNCT
ejpam-6124	83	17	\	\	PROPN
ejpam-6124	83	18	t	t	PROPN
ejpam-6124	83	19	are	be	AUX
ejpam-6124	83	20	colored	color	VERB
ejpam-6124	83	21	blue	blue	ADJ
ejpam-6124	83	22	.	.	PUNCT
ejpam-6124	84	1	clearly	clearly	ADV
ejpam-6124	84	2	,	,	PUNCT
ejpam-6124	84	3	each	each	DET
ejpam-6124	84	4	blue	blue	ADJ
ejpam-6124	84	5	vertex	vertex	NOUN
ejpam-6124	84	6	is	be	AUX
ejpam-6124	84	7	adjacent	adjacent	ADJ
ejpam-6124	84	8	to	to	ADP
ejpam-6124	84	9	exactly	exactly	ADV
ejpam-6124	84	10	one	one	NUM
ejpam-6124	84	11	red	red	ADJ
ejpam-6124	84	12	vertex	vertex	NOUN
ejpam-6124	84	13	in	in	ADP
ejpam-6124	84	14	t	t	PROPN
ejpam-6124	84	15	,	,	PUNCT
ejpam-6124	84	16	that	that	ADV
ejpam-6124	84	17	is	is	ADV
ejpam-6124	84	18	,	,	PUNCT
ejpam-6124	84	19	each	each	DET
ejpam-6124	84	20	vertex	vertex	NOUN
ejpam-6124	84	21	in	in	ADP
ejpam-6124	84	22	v	v	NOUN
ejpam-6124	84	23	(	(	PUNCT
ejpam-6124	84	24	g	g	NOUN
ejpam-6124	84	25	)	)	PUNCT
ejpam-6124	84	26	\	\	PROPN
ejpam-6124	84	27	t	t	PROPN
ejpam-6124	84	28	is	be	AUX
ejpam-6124	84	29	adjacent	adjacent	ADJ
ejpam-6124	84	30	to	to	ADP
ejpam-6124	84	31	exactly	exactly	ADV
ejpam-6124	84	32	one	one	NUM
ejpam-6124	84	33	vertex	vertex	NOUN
ejpam-6124	84	34	in	in	ADP
ejpam-6124	84	35	t	t	PROPN
ejpam-6124	84	36	or	or	CCONJ
ejpam-6124	84	37	|n(v	|n(v	ADJ
ejpam-6124	84	38	)	)	PUNCT
ejpam-6124	85	1	∩	∩	NOUN
ejpam-6124	85	2	t	t	NOUN
ejpam-6124	86	1	|	|	NOUN
ejpam-6124	86	2	=	=	SYM
ejpam-6124	86	3	1	1	NUM
ejpam-6124	86	4	∀v	∀v	NOUN
ejpam-6124	86	5	∈	∈	NOUN
ejpam-6124	86	6	v	v	NOUN
ejpam-6124	86	7	(	(	PUNCT
ejpam-6124	86	8	g	g	NOUN
ejpam-6124	86	9	)	)	PUNCT
ejpam-6124	86	10	\	\	PROPN
ejpam-6124	86	11	t	t	PROPN
ejpam-6124	86	12	.	.	PUNCT
ejpam-6124	87	1	observe	observe	VERB
ejpam-6124	87	2	further	far	ADV
ejpam-6124	87	3	that	that	SCONJ
ejpam-6124	87	4	each	each	DET
ejpam-6124	87	5	red	red	ADJ
ejpam-6124	87	6	vertex	vertex	NOUN
ejpam-6124	87	7	is	be	AUX
ejpam-6124	87	8	adjacent	adjacent	ADJ
ejpam-6124	87	9	to	to	ADP
ejpam-6124	87	10	exactly	exactly	ADV
ejpam-6124	87	11	one	one	NUM
ejpam-6124	87	12	red	red	ADJ
ejpam-6124	87	13	vertex	vertex	NOUN
ejpam-6124	87	14	in	in	ADP
ejpam-6124	87	15	t	t	PROPN
ejpam-6124	87	16	,	,	PUNCT
ejpam-6124	87	17	that	that	ADV
ejpam-6124	87	18	is	is	ADV
ejpam-6124	87	19	,	,	PUNCT
ejpam-6124	87	20	each	each	DET
ejpam-6124	87	21	vertex	vertex	NOUN
ejpam-6124	87	22	in	in	ADP
ejpam-6124	87	23	t	t	PROPN
ejpam-6124	87	24	are	be	AUX
ejpam-6124	87	25	adjacent	adjacent	ADJ
ejpam-6124	87	26	to	to	ADP
ejpam-6124	87	27	exactly	exactly	ADV
ejpam-6124	87	28	one	one	NUM
ejpam-6124	87	29	vertex	vertex	NOUN
ejpam-6124	87	30	in	in	ADP
ejpam-6124	87	31	t	t	PROPN
ejpam-6124	87	32	or	or	CCONJ
ejpam-6124	87	33	|n(u	|n(u	PROPN
ejpam-6124	88	1	)	)	PUNCT
ejpam-6124	88	2	∩	∩	PROPN
ejpam-6124	88	3	t	t	NOUN
ejpam-6124	89	1	|	|	NOUN
ejpam-6124	89	2	=	=	SYM
ejpam-6124	89	3	1	1	NUM
ejpam-6124	89	4	∀u	∀u	PROPN
ejpam-6124	89	5	∈	∈	PROPN
ejpam-6124	89	6	t	t	NOUN
ejpam-6124	89	7	.	.	PUNCT
ejpam-6124	90	1	r.	r.	PROPN
ejpam-6124	90	2	g.	g.	PROPN
ejpam-6124	90	3	aguinod	aguinod	PROPN
ejpam-6124	90	4	,	,	PUNCT
ejpam-6124	90	5	e.	e.	PROPN
ejpam-6124	90	6	m.	m.	PROPN
ejpam-6124	90	7	kiunisala	kiunisala	PROPN
ejpam-6124	90	8	,	,	PUNCT
ejpam-6124	90	9	c.	c.	PROPN
ejpam-6124	90	10	l.	l.	PROPN
ejpam-6124	90	11	armada	armada	PROPN
ejpam-6124	90	12	/	/	SYM
ejpam-6124	90	13	eur	eur	PROPN
ejpam-6124	90	14	.	.	PUNCT
ejpam-6124	91	1	j.	j.	PROPN
ejpam-6124	91	2	pure	pure	PROPN
ejpam-6124	91	3	appl	appl	PROPN
ejpam-6124	91	4	.	.	PROPN
ejpam-6124	91	5	math	math	PROPN
ejpam-6124	91	6	,	,	PUNCT
ejpam-6124	91	7	18	18	NUM
ejpam-6124	91	8	(	(	PUNCT
ejpam-6124	91	9	2	2	NUM
ejpam-6124	91	10	)	)	PUNCT
ejpam-6124	91	11	(	(	PUNCT
ejpam-6124	91	12	2025	2025	NUM
ejpam-6124	91	13	)	)	PUNCT
ejpam-6124	91	14	,	,	PUNCT
ejpam-6124	91	15	6124	6124	NUM
ejpam-6124	91	16	4	4	NUM
ejpam-6124	91	17	of	of	ADP
ejpam-6124	91	18	26	26	NUM
ejpam-6124	91	19	thus	thus	ADV
ejpam-6124	91	20	,	,	PUNCT
ejpam-6124	91	21	t	t	PROPN
ejpam-6124	91	22	is	be	AUX
ejpam-6124	91	23	a	a	DET
ejpam-6124	91	24	total	total	ADJ
ejpam-6124	91	25	exact	exact	ADJ
ejpam-6124	91	26	dominating	dominating	NOUN
ejpam-6124	91	27	set	set	NOUN
ejpam-6124	91	28	of	of	ADP
ejpam-6124	91	29	g	g	PROPN
ejpam-6124	91	30	and	and	CCONJ
ejpam-6124	91	31	γte(g	γte(g	NOUN
ejpam-6124	91	32	)	)	PUNCT
ejpam-6124	92	1	=	=	PRON
ejpam-6124	92	2	|t	|t	VERB
ejpam-6124	93	1	|	|	ADV
ejpam-6124	93	2	=	=	NOUN
ejpam-6124	93	3	12	12	NUM
ejpam-6124	93	4	.	.	PUNCT
ejpam-6124	94	1	in	in	ADP
ejpam-6124	94	2	figure	figure	NOUN
ejpam-6124	94	3	2	2	NUM
ejpam-6124	94	4	,	,	PUNCT
ejpam-6124	94	5	clearly	clearly	ADV
ejpam-6124	94	6	,	,	PUNCT
ejpam-6124	94	7	s	s	PART
ejpam-6124	94	8	=	=	PUNCT
ejpam-6124	94	9	{	{	PUNCT
ejpam-6124	94	10	u1	u1	PROPN
ejpam-6124	94	11	,	,	PUNCT
ejpam-6124	94	12	u4	u4	PROPN
ejpam-6124	94	13	,	,	PUNCT
ejpam-6124	94	14	u5	u5	PROPN
ejpam-6124	94	15	,	,	PUNCT
ejpam-6124	94	16	u8	u8	PROPN
ejpam-6124	94	17	,	,	PUNCT
ejpam-6124	94	18	u9	u9	PROPN
ejpam-6124	94	19	,	,	PUNCT
ejpam-6124	94	20	r3	r3	PROPN
ejpam-6124	94	21	,	,	PUNCT
ejpam-6124	94	22	w3	w3	PROPN
ejpam-6124	94	23	,	,	PUNCT
ejpam-6124	94	24	z1	z1	PROPN
ejpam-6124	94	25	,	,	PUNCT
ejpam-6124	94	26	x1	x1	PROPN
ejpam-6124	94	27	}	}	PUNCT
ejpam-6124	94	28	is	be	AUX
ejpam-6124	94	29	a	a	DET
ejpam-6124	94	30	γe	γe	NOUN
ejpam-6124	94	31	-	-	PUNCT
ejpam-6124	94	32	set	set	NOUN
ejpam-6124	94	33	of	of	ADP
ejpam-6124	94	34	g	g	PROPN
ejpam-6124	94	35	since	since	SCONJ
ejpam-6124	94	36	|n(u	|n(u	NOUN
ejpam-6124	94	37	)	)	PUNCT
ejpam-6124	94	38	∩	∩	NOUN
ejpam-6124	94	39	s|	s|	VERB
ejpam-6124	94	40	=	=	SYM
ejpam-6124	94	41	1	1	NUM
ejpam-6124	94	42	∀v	∀v	NOUN
ejpam-6124	94	43	∈	∈	NOUN
ejpam-6124	94	44	v	v	NOUN
ejpam-6124	94	45	(	(	PUNCT
ejpam-6124	94	46	g	g	NOUN
ejpam-6124	94	47	)	)	PUNCT
ejpam-6124	94	48	\	\	PROPN
ejpam-6124	94	49	s	s	PROPN
ejpam-6124	94	50	and	and	CCONJ
ejpam-6124	94	51	|n(v	|n(v	ADJ
ejpam-6124	94	52	)	)	PUNCT
ejpam-6124	94	53	∩	∩	NOUN
ejpam-6124	94	54	s|	s|	VERB
ejpam-6124	94	55	≤	≤	NUM
ejpam-6124	94	56	1	1	NUM
ejpam-6124	94	57	∀v	∀v	NOUN
ejpam-6124	94	58	∈	∈	NOUN
ejpam-6124	94	59	s	s	NOUN
ejpam-6124	94	60	with	with	ADP
ejpam-6124	94	61	|n(u1	|n(u1	ADJ
ejpam-6124	94	62	)	)	PUNCT
ejpam-6124	95	1	∩	∩	NOUN
ejpam-6124	95	2	s|	s|	NOUN
ejpam-6124	95	3	=	=	SYM
ejpam-6124	95	4	|n(r3	|n(r3	NOUN
ejpam-6124	95	5	)	)	PUNCT
ejpam-6124	95	6	∩	∩	NOUN
ejpam-6124	95	7	s|	s|	NOUN
ejpam-6124	95	8	=	=	SYM
ejpam-6124	95	9	|n(w3	|n(w3	NUM
ejpam-6124	95	10	)	)	PUNCT
ejpam-6124	95	11	∩	∩	NOUN
ejpam-6124	95	12	s|	s|	VERB
ejpam-6124	95	13	=	=	SYM
ejpam-6124	95	14	0	0	X
ejpam-6124	95	15	.	.	PUNCT
ejpam-6124	96	1	thus	thus	ADV
ejpam-6124	96	2	,	,	PUNCT
ejpam-6124	96	3	γe(g	γe(g	NUM
ejpam-6124	96	4	)	)	PUNCT
ejpam-6124	97	1	=	=	SYM
ejpam-6124	97	2	|s|	|s|	NOUN
ejpam-6124	97	3	=	=	SYM
ejpam-6124	97	4	9	9	X
ejpam-6124	97	5	.	.	X
ejpam-6124	97	6	figure	figure	NOUN
ejpam-6124	97	7	1	1	NUM
ejpam-6124	97	8	:	:	PUNCT
ejpam-6124	97	9	graph	graph	VERB
ejpam-6124	97	10	g	g	NOUN
ejpam-6124	97	11	with	with	ADP
ejpam-6124	97	12	γte(g	γte(g	PROPN
ejpam-6124	97	13	)	)	PUNCT
ejpam-6124	97	14	=	=	SYM
ejpam-6124	98	1	12	12	NUM
ejpam-6124	98	2	.	.	PUNCT
ejpam-6124	98	3	figure	figure	NOUN
ejpam-6124	98	4	2	2	NUM
ejpam-6124	98	5	:	:	PUNCT
ejpam-6124	98	6	graph	graph	VERB
ejpam-6124	98	7	g	g	NOUN
ejpam-6124	98	8	with	with	ADP
ejpam-6124	98	9	γe(g	γe(g	NUM
ejpam-6124	98	10	)	)	PUNCT
ejpam-6124	98	11	=	=	SYM
ejpam-6124	99	1	9	9	X
ejpam-6124	99	2	.	.	X
ejpam-6124	99	3	r.	r.	PROPN
ejpam-6124	99	4	g.	g.	PROPN
ejpam-6124	99	5	aguinod	aguinod	PROPN
ejpam-6124	99	6	,	,	PUNCT
ejpam-6124	99	7	e.	e.	PROPN
ejpam-6124	99	8	m.	m.	PROPN
ejpam-6124	99	9	kiunisala	kiunisala	PROPN
ejpam-6124	99	10	,	,	PUNCT
ejpam-6124	99	11	c.	c.	PROPN
ejpam-6124	99	12	l.	l.	PROPN
ejpam-6124	99	13	armada	armada	PROPN
ejpam-6124	99	14	/	/	SYM
ejpam-6124	99	15	eur	eur	PROPN
ejpam-6124	99	16	.	.	PUNCT
ejpam-6124	100	1	j.	j.	PROPN
ejpam-6124	100	2	pure	pure	PROPN
ejpam-6124	100	3	appl	appl	PROPN
ejpam-6124	100	4	.	.	PROPN
ejpam-6124	100	5	math	math	PROPN
ejpam-6124	100	6	,	,	PUNCT
ejpam-6124	100	7	18	18	NUM
ejpam-6124	100	8	(	(	PUNCT
ejpam-6124	100	9	2	2	NUM
ejpam-6124	100	10	)	)	PUNCT
ejpam-6124	100	11	(	(	PUNCT
ejpam-6124	100	12	2025	2025	NUM
ejpam-6124	100	13	)	)	PUNCT
ejpam-6124	100	14	,	,	PUNCT
ejpam-6124	100	15	6124	6124	NUM
ejpam-6124	100	16	5	5	NUM
ejpam-6124	100	17	of	of	ADP
ejpam-6124	100	18	26	26	NUM
ejpam-6124	100	19	3	3	NUM
ejpam-6124	100	20	.	.	PUNCT
ejpam-6124	101	1	known	know	VERB
ejpam-6124	101	2	results	result	VERB
ejpam-6124	101	3	the	the	DET
ejpam-6124	101	4	following	follow	VERB
ejpam-6124	101	5	results	result	NOUN
ejpam-6124	101	6	will	will	AUX
ejpam-6124	101	7	be	be	AUX
ejpam-6124	101	8	used	use	VERB
ejpam-6124	101	9	to	to	PART
ejpam-6124	101	10	prove	prove	VERB
ejpam-6124	101	11	the	the	DET
ejpam-6124	101	12	main	main	ADJ
ejpam-6124	101	13	results	result	NOUN
ejpam-6124	101	14	.	.	PUNCT
ejpam-6124	102	1	theorem	theorem	NOUN
ejpam-6124	102	2	1	1	NUM
ejpam-6124	102	3	.	.	PUNCT
ejpam-6124	103	1	[	[	X
ejpam-6124	103	2	2	2	NUM
ejpam-6124	103	3	]	]	PUNCT
ejpam-6124	103	4	.	.	PUNCT
ejpam-6124	104	1	for	for	ADP
ejpam-6124	104	2	any	any	DET
ejpam-6124	104	3	connected	connected	ADJ
ejpam-6124	104	4	graph	graph	NOUN
ejpam-6124	104	5	g	g	NOUN
ejpam-6124	104	6	with	with	ADP
ejpam-6124	104	7	p	p	PROPN
ejpam-6124	104	8	≥	≥	NUM
ejpam-6124	104	9	3	3	NUM
ejpam-6124	104	10	vertices	vertex	NOUN
ejpam-6124	104	11	,	,	PUNCT
ejpam-6124	104	12	then	then	ADV
ejpam-6124	104	13	γt(g	γt(g	PUNCT
ejpam-6124	104	14	)	)	PUNCT
ejpam-6124	104	15	≤	≤	NUM
ejpam-6124	104	16	2p	2p	NUM
ejpam-6124	104	17	3	3	NUM
ejpam-6124	104	18	.	.	PUNCT
ejpam-6124	105	1	proposition	proposition	NOUN
ejpam-6124	105	2	1	1	NUM
ejpam-6124	105	3	.	.	PUNCT
ejpam-6124	106	1	[	[	X
ejpam-6124	106	2	6	6	NUM
ejpam-6124	106	3	]	]	PUNCT
ejpam-6124	106	4	the	the	DET
ejpam-6124	106	5	total	total	ADJ
ejpam-6124	106	6	domination	domination	NOUN
ejpam-6124	106	7	number	number	NOUN
ejpam-6124	106	8	of	of	ADP
ejpam-6124	106	9	a	a	DET
ejpam-6124	106	10	cycle	cycle	NOUN
ejpam-6124	106	11	cn	cn	NOUN
ejpam-6124	106	12	or	or	CCONJ
ejpam-6124	106	13	a	a	DET
ejpam-6124	106	14	path	path	NOUN
ejpam-6124	106	15	pn	pn	NOUN
ejpam-6124	106	16	on	on	ADP
ejpam-6124	106	17	n	n	PRON
ejpam-6124	106	18	≥	≥	NUM
ejpam-6124	106	19	3	3	NUM
ejpam-6124	106	20	vertices	vertex	NOUN
ejpam-6124	106	21	are	be	AUX
ejpam-6124	106	22	given	give	VERB
ejpam-6124	106	23	by	by	ADP
ejpam-6124	106	24	γt(cn	γt(cn	PROPN
ejpam-6124	106	25	)	)	PUNCT
ejpam-6124	107	1	=	=	SYM
ejpam-6124	107	2	γt(pn	γt(pn	NOUN
ejpam-6124	107	3	)	)	PUNCT
ejpam-6124	108	1	=	=	PUNCT
ejpam-6124	109	1			PROPN
ejpam-6124	109	2	n	n	PRON
ejpam-6124	109	3	2	2	NUM
ejpam-6124	109	4	,	,	PUNCT
ejpam-6124	109	5	if	if	SCONJ
ejpam-6124	109	6	n	n	PRON
ejpam-6124	109	7	≡	≡	PROPN
ejpam-6124	109	8	0	0	PUNCT
ejpam-6124	110	1	(	(	PUNCT
ejpam-6124	110	2	mod	mod	PROPN
ejpam-6124	110	3	4	4	NUM
ejpam-6124	110	4	)	)	PUNCT
ejpam-6124	110	5	,	,	PUNCT
ejpam-6124	110	6	n+2	n+2	PRON
ejpam-6124	110	7	2	2	NUM
ejpam-6124	110	8	,	,	PUNCT
ejpam-6124	110	9	if	if	SCONJ
ejpam-6124	110	10	n	n	PRON
ejpam-6124	110	11	≡	≡	PROPN
ejpam-6124	110	12	2	2	NUM
ejpam-6124	110	13	(	(	PUNCT
ejpam-6124	110	14	mod	mod	NOUN
ejpam-6124	110	15	4	4	NUM
ejpam-6124	110	16	)	)	PUNCT
ejpam-6124	110	17	,	,	PUNCT
ejpam-6124	110	18	n+1	n+1	PROPN
ejpam-6124	110	19	2	2	NUM
ejpam-6124	110	20	,	,	PUNCT
ejpam-6124	110	21	otherwise	otherwise	ADV
ejpam-6124	110	22	.	.	PUNCT
ejpam-6124	111	1	theorem	theorem	NOUN
ejpam-6124	111	2	2	2	NUM
ejpam-6124	111	3	.	.	PUNCT
ejpam-6124	112	1	[	[	X
ejpam-6124	112	2	13	13	NUM
ejpam-6124	112	3	]	]	PUNCT
ejpam-6124	112	4	let	let	VERB
ejpam-6124	112	5	g	g	PROPN
ejpam-6124	112	6	and	and	CCONJ
ejpam-6124	112	7	h	h	NOUN
ejpam-6124	112	8	be	be	AUX
ejpam-6124	112	9	connected	connect	VERB
ejpam-6124	112	10	graphs	graph	NOUN
ejpam-6124	112	11	.	.	PUNCT
ejpam-6124	113	1	then	then	ADV
ejpam-6124	113	2	c	c	PROPN
ejpam-6124	113	3	⊆	⊆	NUM
ejpam-6124	113	4	v	v	NOUN
ejpam-6124	113	5	(	(	PUNCT
ejpam-6124	113	6	g	g	PROPN
ejpam-6124	113	7	+	+	NOUN
ejpam-6124	113	8	h	h	NOUN
ejpam-6124	113	9	)	)	PUNCT
ejpam-6124	113	10	is	be	AUX
ejpam-6124	113	11	a	a	DET
ejpam-6124	113	12	total	total	ADJ
ejpam-6124	113	13	dominating	dominating	NOUN
ejpam-6124	113	14	set	set	NOUN
ejpam-6124	113	15	of	of	ADP
ejpam-6124	113	16	g+h	g+h	PROPN
ejpam-6124	114	1	if	if	SCONJ
ejpam-6124	114	2	and	and	CCONJ
ejpam-6124	114	3	only	only	ADV
ejpam-6124	114	4	if	if	SCONJ
ejpam-6124	114	5	it	it	PRON
ejpam-6124	114	6	satisfies	satisfy	VERB
ejpam-6124	114	7	at	at	ADP
ejpam-6124	114	8	least	least	ADJ
ejpam-6124	114	9	one	one	NUM
ejpam-6124	114	10	of	of	ADP
ejpam-6124	114	11	the	the	DET
ejpam-6124	114	12	following	following	NOUN
ejpam-6124	114	13	:	:	PUNCT
ejpam-6124	114	14	(	(	PUNCT
ejpam-6124	114	15	i	i	NOUN
ejpam-6124	114	16	)	)	PUNCT
ejpam-6124	114	17	c	c	PROPN
ejpam-6124	114	18	∩	∩	PROPN
ejpam-6124	114	19	v	v	X
ejpam-6124	114	20	(	(	PUNCT
ejpam-6124	114	21	g	g	NOUN
ejpam-6124	114	22	)	)	PUNCT
ejpam-6124	114	23	is	be	AUX
ejpam-6124	114	24	a	a	DET
ejpam-6124	114	25	total	total	ADJ
ejpam-6124	114	26	dominating	dominating	NOUN
ejpam-6124	114	27	set	set	NOUN
ejpam-6124	114	28	of	of	ADP
ejpam-6124	114	29	g.	g.	PROPN
ejpam-6124	114	30	(	(	PUNCT
ejpam-6124	114	31	ii	ii	PROPN
ejpam-6124	114	32	)	)	PUNCT
ejpam-6124	114	33	c	c	NOUN
ejpam-6124	114	34	∩	∩	PROPN
ejpam-6124	114	35	v	v	X
ejpam-6124	114	36	(	(	PUNCT
ejpam-6124	114	37	h	h	NOUN
ejpam-6124	114	38	)	)	PUNCT
ejpam-6124	114	39	is	be	AUX
ejpam-6124	114	40	a	a	DET
ejpam-6124	114	41	total	total	ADJ
ejpam-6124	114	42	dominating	dominating	NOUN
ejpam-6124	114	43	set	set	NOUN
ejpam-6124	114	44	of	of	ADP
ejpam-6124	114	45	h.	h.	PROPN
ejpam-6124	114	46	(	(	PUNCT
ejpam-6124	114	47	iii	iii	NOUN
ejpam-6124	114	48	)	)	PUNCT
ejpam-6124	114	49	c	c	NOUN
ejpam-6124	114	50	∩	∩	X
ejpam-6124	114	51	v	v	X
ejpam-6124	114	52	(	(	PUNCT
ejpam-6124	114	53	g	g	NOUN
ejpam-6124	114	54	)	)	PUNCT
ejpam-6124	114	55	̸=	̸=	PROPN
ejpam-6124	114	56	∅	∅	NOUN
ejpam-6124	114	57	and	and	CCONJ
ejpam-6124	114	58	c	c	NOUN
ejpam-6124	114	59	∩	∩	ADJ
ejpam-6124	114	60	v	v	X
ejpam-6124	114	61	(	(	PUNCT
ejpam-6124	114	62	h	h	NOUN
ejpam-6124	114	63	)	)	PUNCT
ejpam-6124	114	64	̸=	̸=	PROPN
ejpam-6124	114	65	∅.	∅.	ADP
ejpam-6124	114	66	corollary	corollary	ADJ
ejpam-6124	114	67	1	1	NUM
ejpam-6124	114	68	.	.	PUNCT
ejpam-6124	115	1	[	[	X
ejpam-6124	115	2	13	13	NUM
ejpam-6124	115	3	]	]	PUNCT
ejpam-6124	115	4	let	let	VERB
ejpam-6124	115	5	g	g	PROPN
ejpam-6124	115	6	and	and	CCONJ
ejpam-6124	115	7	h	h	NOUN
ejpam-6124	115	8	be	be	AUX
ejpam-6124	115	9	connected	connect	VERB
ejpam-6124	115	10	graphs	graph	NOUN
ejpam-6124	115	11	.	.	PUNCT
ejpam-6124	116	1	then	then	ADV
ejpam-6124	116	2	c	c	X
ejpam-6124	116	3	=	=	SYM
ejpam-6124	116	4	{	{	PUNCT
ejpam-6124	116	5	x	x	PROPN
ejpam-6124	116	6	,	,	PUNCT
ejpam-6124	116	7	y	y	PROPN
ejpam-6124	116	8	}	}	PUNCT
ejpam-6124	116	9	,	,	PUNCT
ejpam-6124	116	10	where	where	SCONJ
ejpam-6124	116	11	x	x	PUNCT
ejpam-6124	116	12	∈	∈	PROPN
ejpam-6124	116	13	v	v	X
ejpam-6124	116	14	(	(	PUNCT
ejpam-6124	116	15	g	g	NOUN
ejpam-6124	116	16	)	)	PUNCT
ejpam-6124	116	17	and	and	CCONJ
ejpam-6124	116	18	y	y	PROPN
ejpam-6124	116	19	∈	∈	PROPN
ejpam-6124	116	20	v	v	ADP
ejpam-6124	116	21	(	(	PUNCT
ejpam-6124	116	22	h	h	NOUN
ejpam-6124	116	23	)	)	PUNCT
ejpam-6124	116	24	,	,	PUNCT
ejpam-6124	116	25	is	be	AUX
ejpam-6124	116	26	a	a	DET
ejpam-6124	116	27	minimum	minimum	ADJ
ejpam-6124	116	28	total	total	ADJ
ejpam-6124	116	29	dominating	dominating	NOUN
ejpam-6124	116	30	set	set	NOUN
ejpam-6124	116	31	of	of	ADP
ejpam-6124	116	32	g+h	g+h	PROPN
ejpam-6124	116	33	and	and	CCONJ
ejpam-6124	116	34	γt(g+h	γt(g+h	NUM
ejpam-6124	116	35	)	)	PUNCT
ejpam-6124	116	36	=	=	SYM
ejpam-6124	116	37	2	2	X
ejpam-6124	116	38	.	.	PUNCT
ejpam-6124	116	39	corollary	corollary	ADJ
ejpam-6124	116	40	2	2	NUM
ejpam-6124	116	41	.	.	PUNCT
ejpam-6124	117	1	[	[	X
ejpam-6124	117	2	14	14	NUM
ejpam-6124	117	3	]	]	PUNCT
ejpam-6124	117	4	let	let	VERB
ejpam-6124	117	5	g	g	PRON
ejpam-6124	117	6	be	be	AUX
ejpam-6124	117	7	a	a	DET
ejpam-6124	117	8	connected	connected	ADJ
ejpam-6124	117	9	graph	graph	NOUN
ejpam-6124	117	10	of	of	ADP
ejpam-6124	117	11	order	order	NOUN
ejpam-6124	117	12	m	m	VERB
ejpam-6124	117	13	and	and	CCONJ
ejpam-6124	117	14	let	let	VERB
ejpam-6124	117	15	h	h	NOUN
ejpam-6124	117	16	be	be	AUX
ejpam-6124	117	17	any	any	DET
ejpam-6124	117	18	graph	graph	NOUN
ejpam-6124	117	19	of	of	ADP
ejpam-6124	117	20	order	order	NOUN
ejpam-6124	117	21	n.	n.	NOUN
ejpam-6124	117	22	then	then	ADV
ejpam-6124	117	23	γt(g	γt(g	PUNCT
ejpam-6124	117	24	◦	◦	NOUN
ejpam-6124	117	25	h	h	NOUN
ejpam-6124	117	26	)	)	PUNCT
ejpam-6124	117	27	=	=	SYM
ejpam-6124	117	28	m.	m.	NOUN
ejpam-6124	117	29	4	4	NUM
ejpam-6124	117	30	.	.	PUNCT
ejpam-6124	117	31	main	main	ADJ
ejpam-6124	117	32	results	result	NOUN
ejpam-6124	117	33	this	this	DET
ejpam-6124	117	34	section	section	NOUN
ejpam-6124	117	35	contains	contain	VERB
ejpam-6124	117	36	results	result	NOUN
ejpam-6124	117	37	corresponding	correspond	VERB
ejpam-6124	117	38	to	to	ADP
ejpam-6124	117	39	the	the	DET
ejpam-6124	117	40	total	total	ADJ
ejpam-6124	117	41	exact	exact	ADJ
ejpam-6124	117	42	domination	domination	NOUN
ejpam-6124	117	43	number	number	NOUN
ejpam-6124	117	44	of	of	ADP
ejpam-6124	117	45	paths	path	NOUN
ejpam-6124	117	46	,	,	PUNCT
ejpam-6124	117	47	cycles	cycle	NOUN
ejpam-6124	117	48	,	,	PUNCT
ejpam-6124	117	49	complete	complete	ADJ
ejpam-6124	117	50	bipartite	bipartite	NOUN
ejpam-6124	117	51	graphs	graph	NOUN
ejpam-6124	117	52	and	and	CCONJ
ejpam-6124	117	53	graphs	graph	NOUN
ejpam-6124	117	54	resulting	result	VERB
ejpam-6124	117	55	from	from	ADP
ejpam-6124	117	56	some	some	DET
ejpam-6124	117	57	binary	binary	ADJ
ejpam-6124	117	58	operations	operation	NOUN
ejpam-6124	117	59	.	.	PUNCT
ejpam-6124	118	1	furthermore	furthermore	ADV
ejpam-6124	118	2	,	,	PUNCT
ejpam-6124	118	3	some	some	DET
ejpam-6124	118	4	non−	non−	PROPN
ejpam-6124	118	5	γte	γte	VERB
ejpam-6124	118	6	−	−	NOUN
ejpam-6124	118	7	graphs	graph	NOUN
ejpam-6124	118	8	are	be	AUX
ejpam-6124	118	9	shown	show	VERB
ejpam-6124	118	10	.	.	PUNCT
ejpam-6124	119	1	clearly	clearly	ADV
ejpam-6124	119	2	,	,	PUNCT
ejpam-6124	119	3	every	every	DET
ejpam-6124	119	4	total	total	ADJ
ejpam-6124	119	5	exact	exact	ADJ
ejpam-6124	119	6	dominating	dominating	NOUN
ejpam-6124	119	7	set	set	NOUN
ejpam-6124	119	8	of	of	ADP
ejpam-6124	119	9	g	g	PROPN
ejpam-6124	119	10	is	be	AUX
ejpam-6124	119	11	an	an	DET
ejpam-6124	119	12	exact	exact	ADJ
ejpam-6124	119	13	dominating	dominating	NOUN
ejpam-6124	119	14	set	set	NOUN
ejpam-6124	119	15	and	and	CCONJ
ejpam-6124	119	16	a	a	DET
ejpam-6124	119	17	total	total	ADJ
ejpam-6124	119	18	dominating	dominating	NOUN
ejpam-6124	119	19	set	set	NOUN
ejpam-6124	119	20	.	.	PUNCT
ejpam-6124	120	1	thus	thus	ADV
ejpam-6124	120	2	,	,	PUNCT
ejpam-6124	120	3	the	the	DET
ejpam-6124	120	4	next	next	ADJ
ejpam-6124	120	5	statement	statement	NOUN
ejpam-6124	120	6	is	be	AUX
ejpam-6124	120	7	immediate	immediate	ADJ
ejpam-6124	120	8	from	from	ADP
ejpam-6124	120	9	this	this	DET
ejpam-6124	120	10	observation	observation	NOUN
ejpam-6124	120	11	,	,	PUNCT
ejpam-6124	120	12	definition	definition	NOUN
ejpam-6124	120	13	of	of	ADP
ejpam-6124	120	14	total	total	ADJ
ejpam-6124	120	15	exact	exact	ADJ
ejpam-6124	120	16	dominating	dominating	NOUN
ejpam-6124	120	17	set	set	NOUN
ejpam-6124	120	18	and	and	CCONJ
ejpam-6124	120	19	theorem	theorem	VERB
ejpam-6124	120	20	1	1	NUM
ejpam-6124	120	21	.	.	NOUN
ejpam-6124	120	22	remark	remark	NOUN
ejpam-6124	120	23	1	1	NUM
ejpam-6124	120	24	.	.	PUNCT
ejpam-6124	121	1	let	let	VERB
ejpam-6124	121	2	g	g	NOUN
ejpam-6124	121	3	be	be	AUX
ejpam-6124	121	4	any	any	DET
ejpam-6124	121	5	graph	graph	NOUN
ejpam-6124	121	6	such	such	ADJ
ejpam-6124	121	7	that	that	SCONJ
ejpam-6124	121	8	g	g	PROPN
ejpam-6124	121	9	has	have	VERB
ejpam-6124	121	10	a	a	DET
ejpam-6124	121	11	total	total	ADJ
ejpam-6124	121	12	exact	exact	ADJ
ejpam-6124	121	13	dominating	dominating	NOUN
ejpam-6124	121	14	set	set	VERB
ejpam-6124	121	15	with	with	ADP
ejpam-6124	121	16	p	p	PROPN
ejpam-6124	121	17	≥	≥	NUM
ejpam-6124	121	18	3	3	NUM
ejpam-6124	121	19	vertices	vertex	NOUN
ejpam-6124	121	20	.	.	PUNCT
ejpam-6124	122	1	then	then	ADV
ejpam-6124	122	2	γe(g	γe(g	NUM
ejpam-6124	122	3	)	)	PUNCT
ejpam-6124	122	4	≤	≤	NUM
ejpam-6124	122	5	γte(g	γte(g	PROPN
ejpam-6124	122	6	)	)	PUNCT
ejpam-6124	122	7	and	and	CCONJ
ejpam-6124	122	8	2	2	NUM
ejpam-6124	122	9	≤	≤	NUM
ejpam-6124	122	10	γte(g	γte(g	PROPN
ejpam-6124	122	11	)	)	PUNCT
ejpam-6124	122	12	≤	≤	NUM
ejpam-6124	122	13	2p	2p	NUM
ejpam-6124	122	14	3	3	NUM
ejpam-6124	122	15	.	.	PUNCT
ejpam-6124	123	1	r.	r.	PROPN
ejpam-6124	123	2	g.	g.	PROPN
ejpam-6124	123	3	aguinod	aguinod	PROPN
ejpam-6124	123	4	,	,	PUNCT
ejpam-6124	123	5	e.	e.	PROPN
ejpam-6124	123	6	m.	m.	PROPN
ejpam-6124	123	7	kiunisala	kiunisala	PROPN
ejpam-6124	123	8	,	,	PUNCT
ejpam-6124	123	9	c.	c.	PROPN
ejpam-6124	123	10	l.	l.	PROPN
ejpam-6124	123	11	armada	armada	PROPN
ejpam-6124	123	12	/	/	SYM
ejpam-6124	123	13	eur	eur	PROPN
ejpam-6124	123	14	.	.	PUNCT
ejpam-6124	124	1	j.	j.	PROPN
ejpam-6124	124	2	pure	pure	PROPN
ejpam-6124	124	3	appl	appl	PROPN
ejpam-6124	124	4	.	.	PROPN
ejpam-6124	124	5	math	math	PROPN
ejpam-6124	124	6	,	,	PUNCT
ejpam-6124	124	7	18	18	NUM
ejpam-6124	124	8	(	(	PUNCT
ejpam-6124	124	9	2	2	NUM
ejpam-6124	124	10	)	)	PUNCT
ejpam-6124	124	11	(	(	PUNCT
ejpam-6124	124	12	2025	2025	NUM
ejpam-6124	124	13	)	)	PUNCT
ejpam-6124	124	14	,	,	PUNCT
ejpam-6124	124	15	6124	6124	NUM
ejpam-6124	124	16	6	6	NUM
ejpam-6124	124	17	of	of	ADP
ejpam-6124	124	18	26	26	NUM
ejpam-6124	124	19	theorem	theorem	NOUN
ejpam-6124	124	20	3	3	NUM
ejpam-6124	124	21	.	.	X
ejpam-6124	125	1	for	for	ADP
ejpam-6124	125	2	any	any	DET
ejpam-6124	125	3	positive	positive	ADJ
ejpam-6124	125	4	integers	integer	NOUN
ejpam-6124	125	5	p	p	NOUN
ejpam-6124	125	6	and	and	CCONJ
ejpam-6124	125	7	q	q	NOUN
ejpam-6124	125	8	with	with	ADP
ejpam-6124	125	9	1	1	NUM
ejpam-6124	125	10	≤	≤	NOUN
ejpam-6124	125	11	p	p	NOUN
ejpam-6124	125	12	≤	≤	NUM
ejpam-6124	125	13	q	q	NOUN
ejpam-6124	125	14	,	,	PUNCT
ejpam-6124	125	15	there	there	PRON
ejpam-6124	125	16	exists	exist	VERB
ejpam-6124	125	17	a	a	DET
ejpam-6124	125	18	simple	simple	ADJ
ejpam-6124	125	19	graph	graph	NOUN
ejpam-6124	125	20	g	g	ADP
ejpam-6124	125	21	such	such	ADJ
ejpam-6124	125	22	that	that	PRON
ejpam-6124	125	23	γe(g	γe(g	NUM
ejpam-6124	125	24	)	)	PUNCT
ejpam-6124	126	1	=	=	SYM
ejpam-6124	126	2	p	p	NOUN
ejpam-6124	126	3	and	and	CCONJ
ejpam-6124	126	4	γte(g	γte(g	NOUN
ejpam-6124	126	5	)	)	PUNCT
ejpam-6124	127	1	=	=	SYM
ejpam-6124	127	2	q.	q.	NOUN
ejpam-6124	127	3	proof	proof	NOUN
ejpam-6124	127	4	.	.	PUNCT
ejpam-6124	128	1	consider	consider	VERB
ejpam-6124	128	2	the	the	DET
ejpam-6124	128	3	following	follow	VERB
ejpam-6124	128	4	cases	case	NOUN
ejpam-6124	128	5	:	:	PUNCT
ejpam-6124	128	6	case	case	NOUN
ejpam-6124	128	7	1	1	NUM
ejpam-6124	128	8	:	:	PUNCT
ejpam-6124	128	9	p	p	X
ejpam-6124	128	10	=	=	X
ejpam-6124	128	11	q	q	PART
ejpam-6124	128	12	let	let	VERB
ejpam-6124	128	13	g	g	PRON
ejpam-6124	128	14	be	be	AUX
ejpam-6124	128	15	the	the	DET
ejpam-6124	128	16	graph	graph	NOUN
ejpam-6124	128	17	shown	show	VERB
ejpam-6124	128	18	in	in	ADP
ejpam-6124	128	19	figure	figure	NOUN
ejpam-6124	128	20	3	3	NUM
ejpam-6124	128	21	.	.	PUNCT
ejpam-6124	129	1	clearly	clearly	ADV
ejpam-6124	129	2	,	,	PUNCT
ejpam-6124	129	3	the	the	DET
ejpam-6124	129	4	set	set	NOUN
ejpam-6124	129	5	t	t	NOUN
ejpam-6124	129	6	=	=	SYM
ejpam-6124	129	7	{	{	PUNCT
ejpam-6124	129	8	u1	u1	NOUN
ejpam-6124	129	9	,	,	PUNCT
ejpam-6124	129	10	u2	u2	NOUN
ejpam-6124	129	11	,	,	PUNCT
ejpam-6124	129	12	u3	u3	PROPN
ejpam-6124	129	13	,	,	PUNCT
ejpam-6124	129	14	u4	u4	PROPN
ejpam-6124	129	15	,	,	PUNCT
ejpam-6124	129	16	u5	u5	PROPN
ejpam-6124	129	17	,	,	PUNCT
ejpam-6124	129	18	u6	u6	NOUN
ejpam-6124	129	19	,	,	PUNCT
ejpam-6124	129	20	.	.	PUNCT
ejpam-6124	129	21	.	.	PUNCT
ejpam-6124	129	22	.	.	PUNCT
ejpam-6124	130	1	,	,	PUNCT
ejpam-6124	130	2	up−1	up−1	PROPN
ejpam-6124	130	3	,	,	PUNCT
ejpam-6124	130	4	up	up	ADV
ejpam-6124	130	5	}	}	PUNCT
ejpam-6124	130	6	is	be	AUX
ejpam-6124	130	7	both	both	PRON
ejpam-6124	130	8	a	a	DET
ejpam-6124	130	9	γe	γe	NOUN
ejpam-6124	130	10	-	-	PUNCT
ejpam-6124	130	11	set	set	VERB
ejpam-6124	130	12	and	and	CCONJ
ejpam-6124	130	13	a	a	DET
ejpam-6124	130	14	γte	γte	NOUN
ejpam-6124	130	15	-	-	PUNCT
ejpam-6124	130	16	set	set	NOUN
ejpam-6124	130	17	of	of	ADP
ejpam-6124	130	18	g.	g.	PROPN
ejpam-6124	130	19	therefore	therefore	ADV
ejpam-6124	130	20	,	,	PUNCT
ejpam-6124	130	21	γe(g	γe(g	NUM
ejpam-6124	130	22	)	)	PUNCT
ejpam-6124	131	1	=	=	SYM
ejpam-6124	131	2	p	p	NOUN
ejpam-6124	131	3	=	=	X
ejpam-6124	131	4	q	q	X
ejpam-6124	131	5	=	=	SYM
ejpam-6124	131	6	γte(g	γte(g	PROPN
ejpam-6124	131	7	)	)	PUNCT
ejpam-6124	131	8	.	.	PUNCT
ejpam-6124	132	1	figure	figure	VERB
ejpam-6124	132	2	3	3	NUM
ejpam-6124	132	3	:	:	PUNCT
ejpam-6124	132	4	graph	graph	VERB
ejpam-6124	132	5	g	g	NOUN
ejpam-6124	132	6	with	with	ADP
ejpam-6124	132	7	γte(g	γte(g	PROPN
ejpam-6124	132	8	)	)	PUNCT
ejpam-6124	132	9	=	=	SYM
ejpam-6124	132	10	γe(g	γe(g	NUM
ejpam-6124	132	11	)	)	PUNCT
ejpam-6124	133	1	=	=	PUNCT
ejpam-6124	134	1	p.	p.	NOUN
ejpam-6124	134	2	case	case	NOUN
ejpam-6124	134	3	2	2	NUM
ejpam-6124	134	4	:	:	PUNCT
ejpam-6124	134	5	p	p	X
ejpam-6124	134	6	<	<	X
ejpam-6124	134	7	q	q	PUNCT
ejpam-6124	134	8	let	let	VERB
ejpam-6124	134	9	g	g	PRON
ejpam-6124	134	10	be	be	AUX
ejpam-6124	134	11	the	the	DET
ejpam-6124	134	12	graph	graph	NOUN
ejpam-6124	134	13	shown	show	VERB
ejpam-6124	134	14	in	in	ADP
ejpam-6124	134	15	figure	figure	NOUN
ejpam-6124	134	16	4	4	NUM
ejpam-6124	134	17	or	or	CCONJ
ejpam-6124	134	18	figure	figure	VERB
ejpam-6124	134	19	5	5	NUM
ejpam-6124	134	20	.	.	PUNCT
ejpam-6124	135	1	let	let	AUX
ejpam-6124	135	2	m	m	VERB
ejpam-6124	135	3	=	=	VERB
ejpam-6124	135	4	q	q	X
ejpam-6124	135	5	−	−	PROPN
ejpam-6124	135	6	p	p	NOUN
ejpam-6124	135	7	and	and	CCONJ
ejpam-6124	135	8	m	m	PROPN
ejpam-6124	135	9	∈	∈	NOUN
ejpam-6124	135	10	z+	z+	PUNCT
ejpam-6124	135	11	.	.	PUNCT
ejpam-6124	135	12	observe	observe	VERB
ejpam-6124	135	13	that	that	SCONJ
ejpam-6124	135	14	s1	s1	NOUN
ejpam-6124	135	15	=	=	PUNCT
ejpam-6124	135	16	{	{	PUNCT
ejpam-6124	135	17	u1	u1	NOUN
ejpam-6124	135	18	,	,	PUNCT
ejpam-6124	135	19	u2	u2	NOUN
ejpam-6124	135	20	,	,	PUNCT
ejpam-6124	135	21	u3	u3	NOUN
ejpam-6124	135	22	,	,	PUNCT
ejpam-6124	135	23	.	.	PUNCT
ejpam-6124	135	24	.	.	PUNCT
ejpam-6124	136	1	.	.	PUNCT
ejpam-6124	137	1	,	,	PUNCT
ejpam-6124	137	2	up−m	up−m	ADJ
ejpam-6124	137	3	}	}	PUNCT
ejpam-6124	137	4	∪	∪	X
ejpam-6124	137	5	{	{	PUNCT
ejpam-6124	137	6	vi	vi	NOUN
ejpam-6124	137	7	:	:	PUNCT
ejpam-6124	137	8	i	i	NOUN
ejpam-6124	137	9	=	=	NOUN
ejpam-6124	137	10	1	1	NUM
ejpam-6124	137	11	,	,	PUNCT
ejpam-6124	137	12	2	2	NUM
ejpam-6124	137	13	,	,	PUNCT
ejpam-6124	137	14	.	.	PUNCT
ejpam-6124	137	15	.	.	PUNCT
ejpam-6124	137	16	.	.	PUNCT
ejpam-6124	138	1	,	,	PUNCT
ejpam-6124	138	2	m	m	AUX
ejpam-6124	138	3	}	}	PUNCT
ejpam-6124	138	4	is	be	AUX
ejpam-6124	138	5	a	a	DET
ejpam-6124	138	6	γe	γe	NOUN
ejpam-6124	138	7	-	-	PUNCT
ejpam-6124	138	8	set	set	NOUN
ejpam-6124	138	9	of	of	ADP
ejpam-6124	138	10	g	g	NOUN
ejpam-6124	138	11	,	,	PUNCT
ejpam-6124	138	12	and	and	CCONJ
ejpam-6124	138	13	s2	s2	VERB
ejpam-6124	138	14	=	=	SYM
ejpam-6124	138	15	{	{	PUNCT
ejpam-6124	138	16	u1	u1	NOUN
ejpam-6124	138	17	,	,	PUNCT
ejpam-6124	138	18	u2	u2	NOUN
ejpam-6124	138	19	,	,	PUNCT
ejpam-6124	138	20	u3	u3	NOUN
ejpam-6124	138	21	,	,	PUNCT
ejpam-6124	138	22	.	.	PUNCT
ejpam-6124	138	23	.	.	PUNCT
ejpam-6124	139	1	.	.	PUNCT
ejpam-6124	140	1	,	,	PUNCT
ejpam-6124	140	2	up−m	up−m	ADJ
ejpam-6124	140	3	}	}	PUNCT
ejpam-6124	140	4	∪	∪	X
ejpam-6124	140	5	{	{	PUNCT
ejpam-6124	140	6	vi	vi	NOUN
ejpam-6124	140	7	:	:	PUNCT
ejpam-6124	140	8	i	i	NOUN
ejpam-6124	140	9	=	=	NOUN
ejpam-6124	140	10	1	1	NUM
ejpam-6124	140	11	,	,	PUNCT
ejpam-6124	140	12	2	2	NUM
ejpam-6124	140	13	,	,	PUNCT
ejpam-6124	140	14	.	.	PUNCT
ejpam-6124	140	15	.	.	PUNCT
ejpam-6124	140	16	.	.	PUNCT
ejpam-6124	141	1	,	,	PUNCT
ejpam-6124	141	2	m	m	VERB
ejpam-6124	141	3	}	}	PUNCT
ejpam-6124	141	4	∪	∪	ADJ
ejpam-6124	141	5	{	{	PUNCT
ejpam-6124	141	6	wi	wi	PROPN
ejpam-6124	141	7	:	:	PUNCT
ejpam-6124	141	8	i	i	NOUN
ejpam-6124	141	9	=	=	NOUN
ejpam-6124	141	10	1	1	NUM
ejpam-6124	141	11	,	,	PUNCT
ejpam-6124	141	12	2	2	NUM
ejpam-6124	141	13	,	,	PUNCT
ejpam-6124	141	14	.	.	PUNCT
ejpam-6124	141	15	.	.	PUNCT
ejpam-6124	142	1	.	.	PUNCT
ejpam-6124	143	1	,	,	PUNCT
ejpam-6124	143	2	m	m	AUX
ejpam-6124	143	3	}	}	PUNCT
ejpam-6124	143	4	is	be	AUX
ejpam-6124	143	5	a	a	DET
ejpam-6124	143	6	γte	γte	NOUN
ejpam-6124	143	7	-	-	PUNCT
ejpam-6124	143	8	set	set	NOUN
ejpam-6124	143	9	of	of	ADP
ejpam-6124	143	10	g.	g.	PROPN
ejpam-6124	144	1	it	it	PRON
ejpam-6124	144	2	follows	follow	VERB
ejpam-6124	144	3	that	that	PRON
ejpam-6124	144	4	γe(g	γe(g	NUM
ejpam-6124	144	5	)	)	PUNCT
ejpam-6124	145	1	=	=	SYM
ejpam-6124	145	2	|s1|	|s1|	NOUN
ejpam-6124	145	3	=	=	PUNCT
ejpam-6124	145	4	p−m+m	p−m+m	X
ejpam-6124	145	5	=	=	PUNCT
ejpam-6124	145	6	p	p	PROPN
ejpam-6124	145	7	and	and	CCONJ
ejpam-6124	145	8	γte(g	γte(g	NOUN
ejpam-6124	145	9	)	)	PUNCT
ejpam-6124	146	1	=	=	SYM
ejpam-6124	146	2	|s2|	|s2|	NOUN
ejpam-6124	146	3	=	=	SYM
ejpam-6124	146	4	(	(	PUNCT
ejpam-6124	146	5	p−m	p−m	X
ejpam-6124	146	6	)	)	PUNCT
ejpam-6124	146	7	+	+	NOUN
ejpam-6124	146	8	m+m	m+m	NOUN
ejpam-6124	146	9	=	=	SYM
ejpam-6124	146	10	p+m	p+m	X
ejpam-6124	146	11	=	=	SYM
ejpam-6124	146	12	p+	p+	X
ejpam-6124	146	13	(	(	PUNCT
ejpam-6124	146	14	q	q	NOUN
ejpam-6124	146	15	−	−	X
ejpam-6124	146	16	p	p	NOUN
ejpam-6124	146	17	)	)	PUNCT
ejpam-6124	146	18	=	=	SYM
ejpam-6124	146	19	q.	q.	PROPN
ejpam-6124	146	20	therefore	therefore	ADV
ejpam-6124	146	21	,	,	PUNCT
ejpam-6124	146	22	γe(g	γe(g	NUM
ejpam-6124	146	23	)	)	PUNCT
ejpam-6124	147	1	=	=	PUNCT
ejpam-6124	148	1	p	p	X
ejpam-6124	148	2	<	<	X
ejpam-6124	148	3	q	q	X
ejpam-6124	148	4	=	=	SYM
ejpam-6124	148	5	γte(g	γte(g	PROPN
ejpam-6124	148	6	)	)	PUNCT
ejpam-6124	148	7	.	.	PUNCT
ejpam-6124	149	1	r.	r.	PROPN
ejpam-6124	149	2	g.	g.	PROPN
ejpam-6124	149	3	aguinod	aguinod	PROPN
ejpam-6124	149	4	,	,	PUNCT
ejpam-6124	149	5	e.	e.	PROPN
ejpam-6124	149	6	m.	m.	PROPN
ejpam-6124	149	7	kiunisala	kiunisala	PROPN
ejpam-6124	149	8	,	,	PUNCT
ejpam-6124	149	9	c.	c.	PROPN
ejpam-6124	149	10	l.	l.	PROPN
ejpam-6124	149	11	armada	armada	PROPN
ejpam-6124	149	12	/	/	SYM
ejpam-6124	149	13	eur	eur	PROPN
ejpam-6124	149	14	.	.	PUNCT
ejpam-6124	150	1	j.	j.	PROPN
ejpam-6124	150	2	pure	pure	PROPN
ejpam-6124	150	3	appl	appl	PROPN
ejpam-6124	150	4	.	.	PROPN
ejpam-6124	150	5	math	math	PROPN
ejpam-6124	150	6	,	,	PUNCT
ejpam-6124	150	7	18	18	NUM
ejpam-6124	150	8	(	(	PUNCT
ejpam-6124	150	9	2	2	NUM
ejpam-6124	150	10	)	)	PUNCT
ejpam-6124	150	11	(	(	PUNCT
ejpam-6124	150	12	2025	2025	NUM
ejpam-6124	150	13	)	)	PUNCT
ejpam-6124	150	14	,	,	PUNCT
ejpam-6124	150	15	6124	6124	NUM
ejpam-6124	150	16	7	7	NUM
ejpam-6124	150	17	of	of	ADP
ejpam-6124	150	18	26	26	NUM
ejpam-6124	150	19	figure	figure	NOUN
ejpam-6124	150	20	4	4	NUM
ejpam-6124	150	21	:	:	PUNCT
ejpam-6124	150	22	graph	graph	VERB
ejpam-6124	150	23	g	g	NOUN
ejpam-6124	150	24	with	with	ADP
ejpam-6124	150	25	γe(g	γe(g	NUM
ejpam-6124	150	26	)	)	PUNCT
ejpam-6124	150	27	=	=	PUNCT
ejpam-6124	151	1	p.	p.	NOUN
ejpam-6124	151	2	figure	figure	NOUN
ejpam-6124	151	3	5	5	NUM
ejpam-6124	151	4	:	:	PUNCT
ejpam-6124	151	5	graph	graph	VERB
ejpam-6124	151	6	g	g	NOUN
ejpam-6124	151	7	with	with	ADP
ejpam-6124	151	8	γte(g	γte(g	PROPN
ejpam-6124	151	9	)	)	PUNCT
ejpam-6124	152	1	=	=	VERB
ejpam-6124	152	2	q.	q.	NOUN
ejpam-6124	152	3	this	this	PRON
ejpam-6124	152	4	confirms	confirm	VERB
ejpam-6124	152	5	the	the	DET
ejpam-6124	152	6	claim	claim	NOUN
ejpam-6124	152	7	.	.	PUNCT
ejpam-6124	153	1	r.	r.	PROPN
ejpam-6124	153	2	g.	g.	PROPN
ejpam-6124	153	3	aguinod	aguinod	PROPN
ejpam-6124	153	4	,	,	PUNCT
ejpam-6124	153	5	e.	e.	PROPN
ejpam-6124	153	6	m.	m.	PROPN
ejpam-6124	153	7	kiunisala	kiunisala	PROPN
ejpam-6124	153	8	,	,	PUNCT
ejpam-6124	153	9	c.	c.	PROPN
ejpam-6124	153	10	l.	l.	PROPN
ejpam-6124	153	11	armada	armada	PROPN
ejpam-6124	153	12	/	/	SYM
ejpam-6124	153	13	eur	eur	PROPN
ejpam-6124	153	14	.	.	PUNCT
ejpam-6124	154	1	j.	j.	PROPN
ejpam-6124	154	2	pure	pure	PROPN
ejpam-6124	154	3	appl	appl	PROPN
ejpam-6124	154	4	.	.	PROPN
ejpam-6124	154	5	math	math	PROPN
ejpam-6124	154	6	,	,	PUNCT
ejpam-6124	154	7	18	18	NUM
ejpam-6124	154	8	(	(	PUNCT
ejpam-6124	154	9	2	2	NUM
ejpam-6124	154	10	)	)	PUNCT
ejpam-6124	154	11	(	(	PUNCT
ejpam-6124	154	12	2025	2025	NUM
ejpam-6124	154	13	)	)	PUNCT
ejpam-6124	154	14	,	,	PUNCT
ejpam-6124	154	15	6124	6124	NUM
ejpam-6124	154	16	8	8	NUM
ejpam-6124	154	17	of	of	ADP
ejpam-6124	154	18	26	26	NUM
ejpam-6124	154	19	the	the	DET
ejpam-6124	154	20	next	next	ADJ
ejpam-6124	154	21	result	result	NOUN
ejpam-6124	154	22	follows	follow	VERB
ejpam-6124	154	23	from	from	ADP
ejpam-6124	154	24	theorem	theorem	ADJ
ejpam-6124	154	25	3	3	NUM
ejpam-6124	154	26	.	.	PUNCT
ejpam-6124	154	27	corollary	corollary	ADJ
ejpam-6124	154	28	3	3	NUM
ejpam-6124	154	29	.	.	PUNCT
ejpam-6124	155	1	the	the	DET
ejpam-6124	155	2	difference	difference	NOUN
ejpam-6124	155	3	γte	γte	CCONJ
ejpam-6124	155	4	−	−	PROPN
ejpam-6124	155	5	γe	γe	PRON
ejpam-6124	155	6	can	can	AUX
ejpam-6124	155	7	be	be	AUX
ejpam-6124	155	8	made	make	VERB
ejpam-6124	155	9	arbitrarily	arbitrarily	ADV
ejpam-6124	155	10	large	large	ADJ
ejpam-6124	155	11	.	.	PUNCT
ejpam-6124	156	1	theorem	theorem	NOUN
ejpam-6124	156	2	4	4	NUM
ejpam-6124	156	3	.	.	PUNCT
ejpam-6124	157	1	if	if	SCONJ
ejpam-6124	157	2	t	t	PROPN
ejpam-6124	157	3	is	be	AUX
ejpam-6124	157	4	a	a	DET
ejpam-6124	157	5	total	total	ADJ
ejpam-6124	157	6	exact	exact	ADJ
ejpam-6124	157	7	dominating	dominating	NOUN
ejpam-6124	157	8	set	set	NOUN
ejpam-6124	157	9	of	of	ADP
ejpam-6124	157	10	a	a	DET
ejpam-6124	157	11	graph	graph	NOUN
ejpam-6124	157	12	g	g	NOUN
ejpam-6124	157	13	,	,	PUNCT
ejpam-6124	157	14	then	then	ADV
ejpam-6124	157	15	|t	|t	VERB
ejpam-6124	157	16	|	|	ADV
ejpam-6124	157	17	is	be	AUX
ejpam-6124	157	18	even	even	ADV
ejpam-6124	157	19	.	.	PUNCT
ejpam-6124	158	1	proof	proof	NOUN
ejpam-6124	158	2	.	.	PUNCT
ejpam-6124	159	1	let	let	VERB
ejpam-6124	159	2	t	t	NOUN
ejpam-6124	159	3	be	be	AUX
ejpam-6124	159	4	a	a	DET
ejpam-6124	159	5	total	total	ADJ
ejpam-6124	159	6	exact	exact	ADJ
ejpam-6124	159	7	dominating	dominating	NOUN
ejpam-6124	159	8	set	set	VERB
ejpam-6124	159	9	with	with	ADP
ejpam-6124	159	10	n	n	ADP
ejpam-6124	159	11	vertices	vertex	NOUN
ejpam-6124	159	12	.	.	PUNCT
ejpam-6124	160	1	by	by	ADP
ejpam-6124	160	2	definition	definition	NOUN
ejpam-6124	160	3	,	,	PUNCT
ejpam-6124	160	4	|n(v	|n(v	PROPN
ejpam-6124	160	5	)	)	PUNCT
ejpam-6124	160	6	∩	∩	NOUN
ejpam-6124	160	7	t	t	NOUN
ejpam-6124	160	8	|	|	NOUN
ejpam-6124	160	9	=	=	SYM
ejpam-6124	160	10	1	1	NUM
ejpam-6124	160	11	∀	∀	NOUN
ejpam-6124	160	12	v	v	ADP
ejpam-6124	160	13	∈	∈	PROPN
ejpam-6124	160	14	t	t	NOUN
ejpam-6124	160	15	.	.	PUNCT
ejpam-6124	161	1	thus	thus	ADV
ejpam-6124	161	2	,	,	PUNCT
ejpam-6124	161	3	for	for	ADP
ejpam-6124	161	4	every	every	DET
ejpam-6124	161	5	vertex	vertex	NOUN
ejpam-6124	161	6	v	v	ADP
ejpam-6124	161	7	∈	∈	PROPN
ejpam-6124	161	8	t	t	NOUN
ejpam-6124	161	9	,	,	PUNCT
ejpam-6124	161	10	there	there	PRON
ejpam-6124	161	11	exists	exist	VERB
ejpam-6124	161	12	exactly	exactly	ADV
ejpam-6124	161	13	one	one	NUM
ejpam-6124	161	14	other	other	ADJ
ejpam-6124	161	15	vertex	vertex	NOUN
ejpam-6124	161	16	x	x	SYM
ejpam-6124	161	17	∈	∈	PROPN
ejpam-6124	161	18	t	t	NOUN
ejpam-6124	161	19	such	such	ADJ
ejpam-6124	161	20	that	that	SCONJ
ejpam-6124	161	21	n(v	n(v	PROPN
ejpam-6124	161	22	)	)	PUNCT
ejpam-6124	161	23	∩	∩	NOUN
ejpam-6124	161	24	t	t	NOUN
ejpam-6124	161	25	=	=	SYM
ejpam-6124	161	26	{	{	PUNCT
ejpam-6124	161	27	x	x	NOUN
ejpam-6124	161	28	}	}	PUNCT
ejpam-6124	161	29	and	and	CCONJ
ejpam-6124	161	30	n(x	n(x	ADJ
ejpam-6124	161	31	)	)	PUNCT
ejpam-6124	161	32	∩	∩	NOUN
ejpam-6124	161	33	t	t	NOUN
ejpam-6124	161	34	=	=	SYM
ejpam-6124	161	35	{	{	PUNCT
ejpam-6124	161	36	v}.thus	v}.thus	X
ejpam-6124	161	37	the	the	DET
ejpam-6124	161	38	vertices	vertex	NOUN
ejpam-6124	161	39	of	of	ADP
ejpam-6124	161	40	t	t	NOUN
ejpam-6124	161	41	can	can	AUX
ejpam-6124	161	42	be	be	AUX
ejpam-6124	161	43	paired	pair	VERB
ejpam-6124	161	44	uniquely	uniquely	ADV
ejpam-6124	161	45	into	into	ADP
ejpam-6124	161	46	disjoint	disjoint	NOUN
ejpam-6124	161	47	sets	set	NOUN
ejpam-6124	161	48	of	of	ADP
ejpam-6124	161	49	two	two	NUM
ejpam-6124	161	50	.	.	PUNCT
ejpam-6124	162	1	therefore	therefore	ADV
ejpam-6124	162	2	,	,	PUNCT
ejpam-6124	162	3	|t	|t	PROPN
ejpam-6124	162	4	|	|	ADV
ejpam-6124	162	5	must	must	AUX
ejpam-6124	162	6	be	be	AUX
ejpam-6124	162	7	even	even	ADV
ejpam-6124	162	8	.	.	PUNCT
ejpam-6124	163	1	theorem	theorem	ADJ
ejpam-6124	163	2	5	5	NUM
ejpam-6124	163	3	.	.	PUNCT
ejpam-6124	164	1	if	if	SCONJ
ejpam-6124	164	2	t	t	PROPN
ejpam-6124	164	3	is	be	AUX
ejpam-6124	164	4	a	a	DET
ejpam-6124	164	5	γt	γt	NOUN
ejpam-6124	164	6	-	-	NOUN
ejpam-6124	164	7	set	set	NOUN
ejpam-6124	164	8	of	of	ADP
ejpam-6124	164	9	a	a	DET
ejpam-6124	164	10	graph	graph	NOUN
ejpam-6124	164	11	g	g	NOUN
ejpam-6124	164	12	and	and	CCONJ
ejpam-6124	164	13	|t	|t	PROPN
ejpam-6124	164	14	|	|	INTJ
ejpam-6124	164	15	is	be	AUX
ejpam-6124	164	16	odd	odd	ADJ
ejpam-6124	164	17	,	,	PUNCT
ejpam-6124	164	18	then	then	ADV
ejpam-6124	164	19	t	t	PROPN
ejpam-6124	164	20	is	be	AUX
ejpam-6124	164	21	not	not	PART
ejpam-6124	164	22	a	a	DET
ejpam-6124	164	23	γte	γte	NOUN
ejpam-6124	164	24	-	-	PUNCT
ejpam-6124	164	25	set	set	NOUN
ejpam-6124	164	26	of	of	ADP
ejpam-6124	164	27	g.	g.	PROPN
ejpam-6124	164	28	proof	proof	PROPN
ejpam-6124	164	29	.	.	PUNCT
ejpam-6124	165	1	let	let	VERB
ejpam-6124	165	2	t	t	NOUN
ejpam-6124	165	3	be	be	AUX
ejpam-6124	165	4	a	a	DET
ejpam-6124	165	5	γt	γt	NOUN
ejpam-6124	165	6	-	-	NOUN
ejpam-6124	165	7	set	set	NOUN
ejpam-6124	165	8	of	of	ADP
ejpam-6124	165	9	a	a	DET
ejpam-6124	165	10	graph	graph	NOUN
ejpam-6124	165	11	g	g	NOUN
ejpam-6124	165	12	and	and	CCONJ
ejpam-6124	165	13	|t	|t	PROPN
ejpam-6124	165	14	|	|	INTJ
ejpam-6124	165	15	is	be	AUX
ejpam-6124	165	16	odd	odd	ADJ
ejpam-6124	165	17	.	.	PUNCT
ejpam-6124	166	1	then	then	ADV
ejpam-6124	166	2	there	there	PRON
ejpam-6124	166	3	exists	exist	VERB
ejpam-6124	166	4	three	three	NUM
ejpam-6124	166	5	vertices	vertex	NOUN
ejpam-6124	166	6	,	,	PUNCT
ejpam-6124	166	7	say	say	VERB
ejpam-6124	166	8	ui	ui	PROPN
ejpam-6124	166	9	,	,	PUNCT
ejpam-6124	166	10	uj	uj	PROPN
ejpam-6124	166	11	,	,	PUNCT
ejpam-6124	166	12	uk	uk	PROPN
ejpam-6124	166	13	such	such	ADJ
ejpam-6124	166	14	that	that	SCONJ
ejpam-6124	166	15	the	the	DET
ejpam-6124	166	16	vertex	vertex	NOUN
ejpam-6124	166	17	uj	uj	PROPN
ejpam-6124	166	18	is	be	AUX
ejpam-6124	166	19	adjacent	adjacent	ADJ
ejpam-6124	166	20	to	to	ADP
ejpam-6124	166	21	ui	ui	PROPN
ejpam-6124	166	22	and	and	CCONJ
ejpam-6124	166	23	uk	uk	PROPN
ejpam-6124	166	24	by	by	ADP
ejpam-6124	166	25	definition	definition	NOUN
ejpam-6124	166	26	of	of	ADP
ejpam-6124	166	27	total	total	ADJ
ejpam-6124	166	28	dominating	dominating	NOUN
ejpam-6124	166	29	set	set	NOUN
ejpam-6124	166	30	.	.	PUNCT
ejpam-6124	167	1	hence	hence	ADV
ejpam-6124	167	2	,	,	PUNCT
ejpam-6124	167	3	|n(uj	|n(uj	PROPN
ejpam-6124	167	4	)	)	PUNCT
ejpam-6124	167	5	∩	∩	PROPN
ejpam-6124	167	6	t	t	NOUN
ejpam-6124	168	1	|	|	NOUN
ejpam-6124	168	2	=	=	SYM
ejpam-6124	168	3	2	2	NUM
ejpam-6124	168	4	,	,	PUNCT
ejpam-6124	168	5	a	a	DET
ejpam-6124	168	6	contradiction	contradiction	NOUN
ejpam-6124	168	7	to	to	ADP
ejpam-6124	168	8	the	the	DET
ejpam-6124	168	9	definition	definition	NOUN
ejpam-6124	168	10	of	of	ADP
ejpam-6124	168	11	exact	exact	ADJ
ejpam-6124	168	12	dominating	dominating	NOUN
ejpam-6124	168	13	set	set	NOUN
ejpam-6124	168	14	.	.	PUNCT
ejpam-6124	169	1	therefore	therefore	ADV
ejpam-6124	169	2	,	,	PUNCT
ejpam-6124	169	3	t	t	PROPN
ejpam-6124	169	4	is	be	AUX
ejpam-6124	169	5	not	not	PART
ejpam-6124	169	6	a	a	DET
ejpam-6124	169	7	γte	γte	NOUN
ejpam-6124	169	8	-	-	PUNCT
ejpam-6124	169	9	set	set	NOUN
ejpam-6124	169	10	of	of	ADP
ejpam-6124	169	11	g.	g.	PROPN
ejpam-6124	169	12	theorem	theorem	VERB
ejpam-6124	169	13	6	6	NUM
ejpam-6124	169	14	.	.	PUNCT
ejpam-6124	170	1	let	let	VERB
ejpam-6124	170	2	n	n	PRON
ejpam-6124	170	3	be	be	AUX
ejpam-6124	170	4	a	a	DET
ejpam-6124	170	5	positive	positive	ADJ
ejpam-6124	170	6	integer	integer	NOUN
ejpam-6124	170	7	such	such	ADJ
ejpam-6124	170	8	that	that	SCONJ
ejpam-6124	170	9	n	n	NUM
ejpam-6124	170	10	≥	≥	NOUN
ejpam-6124	170	11	5	5	NUM
ejpam-6124	170	12	.	.	PUNCT
ejpam-6124	171	1	if	if	SCONJ
ejpam-6124	171	2	n	n	NUM
ejpam-6124	171	3	≡	≡	PROPN
ejpam-6124	171	4	1	1	NUM
ejpam-6124	171	5	(	(	PUNCT
ejpam-6124	171	6	mod	mod	NOUN
ejpam-6124	171	7	4	4	NUM
ejpam-6124	171	8	)	)	PUNCT
ejpam-6124	171	9	,	,	PUNCT
ejpam-6124	171	10	then	then	ADV
ejpam-6124	171	11	the	the	DET
ejpam-6124	171	12	path	path	NOUN
ejpam-6124	171	13	graph	graph	NOUN
ejpam-6124	171	14	pn	pn	PROPN
ejpam-6124	171	15	is	be	AUX
ejpam-6124	171	16	non−	non−	PROPN
ejpam-6124	171	17	γte	γte	NOUN
ejpam-6124	171	18	−	−	NOUN
ejpam-6124	171	19	graph	graph	NOUN
ejpam-6124	171	20	.	.	PUNCT
ejpam-6124	172	1	proof	proof	NOUN
ejpam-6124	172	2	.	.	PUNCT
ejpam-6124	173	1	let	let	VERB
ejpam-6124	173	2	n	n	NOUN
ejpam-6124	173	3	=	=	SYM
ejpam-6124	173	4	5	5	X
ejpam-6124	173	5	.	.	PUNCT
ejpam-6124	173	6	by	by	ADP
ejpam-6124	173	7	proposition	proposition	NOUN
ejpam-6124	173	8	1	1	NUM
ejpam-6124	173	9	,	,	PUNCT
ejpam-6124	173	10	γt(p5	γt(p5	NOUN
ejpam-6124	173	11	)	)	PUNCT
ejpam-6124	173	12	=	=	PUNCT
ejpam-6124	174	1	5	5	NUM
ejpam-6124	174	2	+	+	SYM
ejpam-6124	174	3	1	1	NUM
ejpam-6124	174	4	2	2	NUM
ejpam-6124	174	5	=	=	SYM
ejpam-6124	174	6	3	3	X
ejpam-6124	174	7	.	.	PUNCT
ejpam-6124	174	8	let	let	VERB
ejpam-6124	174	9	t1	t1	NOUN
ejpam-6124	174	10	=	=	PUNCT
ejpam-6124	174	11	{	{	PUNCT
ejpam-6124	174	12	u2	u2	PROPN
ejpam-6124	174	13	,	,	PUNCT
ejpam-6124	174	14	u5	u5	PROPN
ejpam-6124	174	15	}	}	PUNCT
ejpam-6124	174	16	and	and	CCONJ
ejpam-6124	174	17	t2	t2	PROPN
ejpam-6124	174	18	=	=	SYM
ejpam-6124	174	19	{	{	PUNCT
ejpam-6124	174	20	u2	u2	PROPN
ejpam-6124	174	21	,	,	PUNCT
ejpam-6124	174	22	u4	u4	PROPN
ejpam-6124	174	23	}	}	PUNCT
ejpam-6124	174	24	.	.	PUNCT
ejpam-6124	175	1	clearly	clearly	ADV
ejpam-6124	175	2	,	,	PUNCT
ejpam-6124	175	3	t1	t1	NOUN
ejpam-6124	175	4	and	and	CCONJ
ejpam-6124	175	5	t2	t2	NOUN
ejpam-6124	175	6	are	be	AUX
ejpam-6124	175	7	not	not	PART
ejpam-6124	175	8	total	total	ADJ
ejpam-6124	175	9	dominating	dominating	NOUN
ejpam-6124	175	10	sets	set	NOUN
ejpam-6124	175	11	since	since	SCONJ
ejpam-6124	175	12	γt(p5	γt(p5	NOUN
ejpam-6124	175	13	)	)	PUNCT
ejpam-6124	175	14	=	=	SYM
ejpam-6124	176	1	3	3	X
ejpam-6124	176	2	.	.	X
ejpam-6124	176	3	therefore	therefore	ADV
ejpam-6124	176	4	,	,	PUNCT
ejpam-6124	176	5	they	they	PRON
ejpam-6124	176	6	are	be	AUX
ejpam-6124	176	7	not	not	PART
ejpam-6124	176	8	γte	γte	NOUN
ejpam-6124	176	9	-	-	PUNCT
ejpam-6124	176	10	sets	set	NOUN
ejpam-6124	176	11	.	.	PUNCT
ejpam-6124	177	1	it	it	PRON
ejpam-6124	177	2	is	be	AUX
ejpam-6124	177	3	also	also	ADV
ejpam-6124	177	4	clear	clear	ADJ
ejpam-6124	177	5	that	that	SCONJ
ejpam-6124	177	6	t3	t3	NOUN
ejpam-6124	177	7	=	=	PUNCT
ejpam-6124	177	8	{	{	PUNCT
ejpam-6124	177	9	u2	u2	PROPN
ejpam-6124	177	10	,	,	PUNCT
ejpam-6124	177	11	u3	u3	PROPN
ejpam-6124	177	12	,	,	PUNCT
ejpam-6124	177	13	u4	u4	PROPN
ejpam-6124	177	14	}	}	PUNCT
ejpam-6124	177	15	is	be	AUX
ejpam-6124	177	16	the	the	DET
ejpam-6124	177	17	only	only	ADJ
ejpam-6124	177	18	γt	γt	NOUN
ejpam-6124	177	19	-	-	NOUN
ejpam-6124	177	20	set	set	NOUN
ejpam-6124	177	21	of	of	ADP
ejpam-6124	177	22	p5	p5	ADJ
ejpam-6124	177	23	and	and	CCONJ
ejpam-6124	177	24	|t3|	|t3|	NOUN
ejpam-6124	177	25	is	be	AUX
ejpam-6124	177	26	odd	odd	ADJ
ejpam-6124	177	27	.	.	PUNCT
ejpam-6124	178	1	by	by	ADP
ejpam-6124	178	2	theorem	theorem	NOUN
ejpam-6124	178	3	5	5	NUM
ejpam-6124	178	4	,	,	PUNCT
ejpam-6124	178	5	t3	t3	PROPN
ejpam-6124	178	6	is	be	AUX
ejpam-6124	178	7	not	not	PART
ejpam-6124	178	8	a	a	DET
ejpam-6124	178	9	γte	γte	NOUN
ejpam-6124	178	10	−	−	PROPN
ejpam-6124	178	11	set	set	NOUN
ejpam-6124	178	12	of	of	ADP
ejpam-6124	178	13	p5	p5	PROPN
ejpam-6124	178	14	.	.	PUNCT
ejpam-6124	179	1	let	let	VERB
ejpam-6124	179	2	t4	t4	PROPN
ejpam-6124	179	3	=	=	PROPN
ejpam-6124	179	4	{	{	PUNCT
ejpam-6124	179	5	u1	u1	PROPN
ejpam-6124	179	6	,	,	PUNCT
ejpam-6124	179	7	u2	u2	PROPN
ejpam-6124	179	8	,	,	PUNCT
ejpam-6124	179	9	u4	u4	PROPN
ejpam-6124	179	10	,	,	PUNCT
ejpam-6124	179	11	u5	u5	PROPN
ejpam-6124	179	12	}	}	PUNCT
ejpam-6124	179	13	.	.	PUNCT
ejpam-6124	180	1	clearly	clearly	ADV
ejpam-6124	180	2	,	,	PUNCT
ejpam-6124	180	3	|n(ui	|n(ui	PROPN
ejpam-6124	180	4	)	)	PUNCT
ejpam-6124	180	5	∩	∩	NOUN
ejpam-6124	180	6	t4|	t4|	PROPN
ejpam-6124	180	7	=	=	NOUN
ejpam-6124	180	8	1	1	NUM
ejpam-6124	180	9	for	for	ADP
ejpam-6124	180	10	ui	ui	PROPN
ejpam-6124	180	11	∈	∈	PROPN
ejpam-6124	180	12	v	v	ADP
ejpam-6124	180	13	(	(	PUNCT
ejpam-6124	180	14	p5	p5	ADJ
ejpam-6124	180	15	)	)	PUNCT
ejpam-6124	180	16	\	\	NOUN
ejpam-6124	180	17	{	{	PUNCT
ejpam-6124	180	18	u3	u3	PROPN
ejpam-6124	180	19	}	}	PUNCT
ejpam-6124	180	20	and	and	CCONJ
ejpam-6124	180	21	|n(u3	|n(u3	NOUN
ejpam-6124	180	22	)	)	PUNCT
ejpam-6124	180	23	∩	∩	NOUN
ejpam-6124	180	24	t4|	t4|	NOUN
ejpam-6124	180	25	=	=	SYM
ejpam-6124	180	26	2	2	X
ejpam-6124	180	27	.	.	PUNCT
ejpam-6124	180	28	thus	thus	ADV
ejpam-6124	180	29	,	,	PUNCT
ejpam-6124	180	30	t4	t4	PROPN
ejpam-6124	180	31	is	be	AUX
ejpam-6124	180	32	not	not	PART
ejpam-6124	180	33	a	a	DET
ejpam-6124	180	34	γte	γte	NOUN
ejpam-6124	180	35	−	−	PROPN
ejpam-6124	180	36	set	set	NOUN
ejpam-6124	180	37	of	of	ADP
ejpam-6124	180	38	p5	p5	PROPN
ejpam-6124	180	39	.	.	PUNCT
ejpam-6124	181	1	since	since	SCONJ
ejpam-6124	181	2	there	there	PRON
ejpam-6124	181	3	is	be	VERB
ejpam-6124	181	4	no	no	DET
ejpam-6124	181	5	possible	possible	ADJ
ejpam-6124	181	6	way	way	NOUN
ejpam-6124	181	7	to	to	PART
ejpam-6124	181	8	create	create	VERB
ejpam-6124	181	9	a	a	DET
ejpam-6124	181	10	set	set	NOUN
ejpam-6124	181	11	that	that	PRON
ejpam-6124	181	12	is	be	AUX
ejpam-6124	181	13	both	both	PRON
ejpam-6124	181	14	total	total	ADJ
ejpam-6124	181	15	and	and	CCONJ
ejpam-6124	181	16	exact	exact	ADJ
ejpam-6124	181	17	dominating	dominating	NOUN
ejpam-6124	181	18	set	set	NOUN
ejpam-6124	181	19	,	,	PUNCT
ejpam-6124	181	20	p5	p5	ADJ
ejpam-6124	181	21	is	be	AUX
ejpam-6124	181	22	a	a	DET
ejpam-6124	181	23	non−	non−	PROPN
ejpam-6124	181	24	γte	γte	NOUN
ejpam-6124	181	25	−	−	NOUN
ejpam-6124	181	26	graph	graph	NOUN
ejpam-6124	181	27	.	.	PUNCT
ejpam-6124	182	1	now	now	ADV
ejpam-6124	182	2	,	,	PUNCT
ejpam-6124	182	3	suppose	suppose	VERB
ejpam-6124	182	4	that	that	SCONJ
ejpam-6124	182	5	n	n	PROPN
ejpam-6124	182	6	>	>	X
ejpam-6124	182	7	5	5	X
ejpam-6124	182	8	.	.	PUNCT
ejpam-6124	182	9	let	let	VERB
ejpam-6124	182	10	p	p	NOUN
ejpam-6124	182	11	=	=	PUNCT
ejpam-6124	182	12	n−1	n−1	PROPN
ejpam-6124	182	13	4	4	NUM
ejpam-6124	182	14	and	and	CCONJ
ejpam-6124	182	15	j	j	NOUN
ejpam-6124	182	16	=	=	SYM
ejpam-6124	182	17	1	1	NUM
ejpam-6124	182	18	,	,	PUNCT
ejpam-6124	182	19	2	2	NUM
ejpam-6124	182	20	,	,	PUNCT
ejpam-6124	182	21	.	.	PUNCT
ejpam-6124	182	22	.	.	PUNCT
ejpam-6124	182	23	.	.	PUNCT
ejpam-6124	183	1	,	,	PUNCT
ejpam-6124	183	2	p.	p.	NOUN
ejpam-6124	183	3	group	group	NOUN
ejpam-6124	183	4	the	the	DET
ejpam-6124	183	5	vertices	vertex	NOUN
ejpam-6124	183	6	of	of	ADP
ejpam-6124	183	7	pn	pn	NOUN
ejpam-6124	183	8	into	into	ADP
ejpam-6124	183	9	p	p	PROPN
ejpam-6124	183	10	disjoint	disjoint	PROPN
ejpam-6124	183	11	subsets	subset	NOUN
ejpam-6124	183	12	rj	rj	PROPN
ejpam-6124	183	13	,	,	PUNCT
ejpam-6124	183	14	such	such	ADJ
ejpam-6124	183	15	that	that	SCONJ
ejpam-6124	183	16	r1	r1	NOUN
ejpam-6124	183	17	=	=	SYM
ejpam-6124	183	18	{	{	PUNCT
ejpam-6124	183	19	u1	u1	NOUN
ejpam-6124	183	20	,	,	PUNCT
ejpam-6124	183	21	u2	u2	NOUN
ejpam-6124	183	22	,	,	PUNCT
ejpam-6124	183	23	u3	u3	NOUN
ejpam-6124	183	24	,	,	PUNCT
ejpam-6124	183	25	u4	u4	PROPN
ejpam-6124	183	26	}	}	PUNCT
ejpam-6124	183	27	,	,	PUNCT
ejpam-6124	183	28	r2	r2	PROPN
ejpam-6124	183	29	=	=	SYM
ejpam-6124	183	30	{	{	PUNCT
ejpam-6124	183	31	u5	u5	PROPN
ejpam-6124	183	32	,	,	PUNCT
ejpam-6124	183	33	u6	u6	PROPN
ejpam-6124	183	34	,	,	PUNCT
ejpam-6124	183	35	u7	u7	PROPN
ejpam-6124	183	36	,	,	PUNCT
ejpam-6124	183	37	u8	u8	PROPN
ejpam-6124	183	38	}	}	PUNCT
ejpam-6124	183	39	,	,	PUNCT
ejpam-6124	183	40	r3	r3	PROPN
ejpam-6124	183	41	=	=	SYM
ejpam-6124	183	42	{	{	PUNCT
ejpam-6124	183	43	u9	u9	PROPN
ejpam-6124	183	44	,	,	PUNCT
ejpam-6124	183	45	u10	u10	PROPN
ejpam-6124	183	46	,	,	PUNCT
ejpam-6124	183	47	u11	u11	PROPN
ejpam-6124	183	48	,	,	PUNCT
ejpam-6124	183	49	u12	u12	PROPN
ejpam-6124	183	50	}	}	PUNCT
ejpam-6124	183	51	,	,	PUNCT
ejpam-6124	183	52	...	...	PUNCT
ejpam-6124	184	1	rp−1	rp−1	NOUN
ejpam-6124	184	2	=	=	PUNCT
ejpam-6124	184	3	{	{	PUNCT
ejpam-6124	184	4	un−8	un−8	ADJ
ejpam-6124	184	5	,	,	PUNCT
ejpam-6124	184	6	un−7	un−7	PROPN
ejpam-6124	184	7	,	,	PUNCT
ejpam-6124	184	8	un−6	un−6	PROPN
ejpam-6124	184	9	,	,	PUNCT
ejpam-6124	184	10	un−5	un−5	PROPN
ejpam-6124	184	11	}	}	PUNCT
ejpam-6124	184	12	,	,	PUNCT
ejpam-6124	184	13	and	and	CCONJ
ejpam-6124	184	14	rp	rp	NOUN
ejpam-6124	184	15	=	=	SYM
ejpam-6124	184	16	{	{	PUNCT
ejpam-6124	184	17	un−4	un−4	NOUN
ejpam-6124	184	18	,	,	PUNCT
ejpam-6124	184	19	un−3	un−3	ADJ
ejpam-6124	184	20	,	,	PUNCT
ejpam-6124	184	21	un−2	un−2	PROPN
ejpam-6124	184	22	,	,	PUNCT
ejpam-6124	184	23	un−1	un−1	PROPN
ejpam-6124	184	24	,	,	PUNCT
ejpam-6124	184	25	un	un	ADJ
ejpam-6124	184	26	}	}	PUNCT
ejpam-6124	184	27	where	where	SCONJ
ejpam-6124	184	28	|rj	|rj	PART
ejpam-6124	184	29	|	|	ADV
ejpam-6124	184	30	=	=	SYM
ejpam-6124	184	31	4	4	NUM
ejpam-6124	184	32	for	for	ADP
ejpam-6124	184	33	j	j	PROPN
ejpam-6124	184	34	=	=	SYM
ejpam-6124	184	35	1	1	NUM
ejpam-6124	184	36	,	,	PUNCT
ejpam-6124	184	37	2	2	NUM
ejpam-6124	184	38	,	,	PUNCT
ejpam-6124	184	39	.	.	PUNCT
ejpam-6124	184	40	.	.	PUNCT
ejpam-6124	184	41	.	.	PUNCT
ejpam-6124	185	1	,	,	PUNCT
ejpam-6124	185	2	p−	p−	NOUN
ejpam-6124	185	3	1	1	NUM
ejpam-6124	185	4	and	and	CCONJ
ejpam-6124	185	5	|rp|	|rp|	NUM
ejpam-6124	185	6	=	=	SYM
ejpam-6124	185	7	5	5	X
ejpam-6124	185	8	.	.	PUNCT
ejpam-6124	185	9	case	case	NOUN
ejpam-6124	185	10	1	1	NUM
ejpam-6124	185	11	:	:	PUNCT
ejpam-6124	185	12	suppose	suppose	VERB
ejpam-6124	185	13	that	that	SCONJ
ejpam-6124	185	14	we	we	PRON
ejpam-6124	185	15	pick	pick	VERB
ejpam-6124	185	16	u2	u2	NOUN
ejpam-6124	185	17	and	and	CCONJ
ejpam-6124	185	18	u3	u3	NOUN
ejpam-6124	185	19	first	first	ADV
ejpam-6124	185	20	to	to	PART
ejpam-6124	185	21	form	form	VERB
ejpam-6124	185	22	t	t	PROPN
ejpam-6124	185	23	.	.	PUNCT
ejpam-6124	186	1	let	let	VERB
ejpam-6124	186	2	t	t	NOUN
ejpam-6124	186	3	=	=	SYM
ejpam-6124	186	4	{	{	PUNCT
ejpam-6124	186	5	u2	u2	PROPN
ejpam-6124	186	6	,	,	PUNCT
ejpam-6124	186	7	u3	u3	NOUN
ejpam-6124	186	8	,	,	PUNCT
ejpam-6124	186	9	u6	u6	PROPN
ejpam-6124	186	10	,	,	PUNCT
ejpam-6124	186	11	u7	u7	PROPN
ejpam-6124	186	12	,	,	PUNCT
ejpam-6124	186	13	u10	u10	PROPN
ejpam-6124	186	14	,	,	PUNCT
ejpam-6124	186	15	u11	u11	PROPN
ejpam-6124	186	16	,	,	PUNCT
ejpam-6124	186	17	.	.	PUNCT
ejpam-6124	186	18	.	.	PUNCT
ejpam-6124	187	1	.	.	PUNCT
ejpam-6124	188	1	,	,	PUNCT
ejpam-6124	188	2	un−7	un−7	PROPN
ejpam-6124	188	3	,	,	PUNCT
ejpam-6124	188	4	un−6	un−6	PROPN
ejpam-6124	188	5	,	,	PUNCT
ejpam-6124	188	6	un−3	un−3	NOUN
ejpam-6124	188	7	,	,	PUNCT
ejpam-6124	188	8	un−2	un−2	PROPN
ejpam-6124	188	9	,	,	PUNCT
ejpam-6124	188	10	un−1	un−1	PROPN
ejpam-6124	188	11	}	}	PUNCT
ejpam-6124	188	12	,	,	PUNCT
ejpam-6124	188	13	r.	r.	PROPN
ejpam-6124	188	14	g.	g.	PROPN
ejpam-6124	188	15	aguinod	aguinod	PROPN
ejpam-6124	188	16	,	,	PUNCT
ejpam-6124	188	17	e.	e.	PROPN
ejpam-6124	188	18	m.	m.	PROPN
ejpam-6124	188	19	kiunisala	kiunisala	PROPN
ejpam-6124	188	20	,	,	PUNCT
ejpam-6124	188	21	c.	c.	PROPN
ejpam-6124	188	22	l.	l.	PROPN
ejpam-6124	188	23	armada	armada	PROPN
ejpam-6124	188	24	/	/	SYM
ejpam-6124	188	25	eur	eur	PROPN
ejpam-6124	188	26	.	.	PUNCT
ejpam-6124	189	1	j.	j.	PROPN
ejpam-6124	189	2	pure	pure	PROPN
ejpam-6124	189	3	appl	appl	PROPN
ejpam-6124	189	4	.	.	PROPN
ejpam-6124	189	5	math	math	PROPN
ejpam-6124	189	6	,	,	PUNCT
ejpam-6124	189	7	18	18	NUM
ejpam-6124	189	8	(	(	PUNCT
ejpam-6124	189	9	2	2	NUM
ejpam-6124	189	10	)	)	PUNCT
ejpam-6124	189	11	(	(	PUNCT
ejpam-6124	189	12	2025	2025	NUM
ejpam-6124	189	13	)	)	PUNCT
ejpam-6124	189	14	,	,	PUNCT
ejpam-6124	189	15	6124	6124	NUM
ejpam-6124	189	16	9	9	NUM
ejpam-6124	189	17	of	of	ADP
ejpam-6124	189	18	26	26	NUM
ejpam-6124	189	19	where	where	SCONJ
ejpam-6124	189	20	t	t	PROPN
ejpam-6124	189	21	is	be	AUX
ejpam-6124	189	22	formed	form	VERB
ejpam-6124	189	23	by	by	ADP
ejpam-6124	189	24	getting	get	VERB
ejpam-6124	189	25	2	2	NUM
ejpam-6124	189	26	vertices	vertex	NOUN
ejpam-6124	189	27	in	in	ADP
ejpam-6124	189	28	each	each	DET
ejpam-6124	189	29	rj	rj	PROPN
ejpam-6124	189	30	for	for	ADP
ejpam-6124	189	31	j	j	PROPN
ejpam-6124	189	32	=	=	SYM
ejpam-6124	189	33	1	1	NUM
ejpam-6124	189	34	,	,	PUNCT
ejpam-6124	189	35	2	2	NUM
ejpam-6124	189	36	,	,	PUNCT
ejpam-6124	189	37	.	.	PUNCT
ejpam-6124	189	38	.	.	PUNCT
ejpam-6124	190	1	.	.	PUNCT
ejpam-6124	191	1	,	,	PUNCT
ejpam-6124	191	2	p−	p−	NOUN
ejpam-6124	191	3	1	1	NUM
ejpam-6124	191	4	and	and	CCONJ
ejpam-6124	191	5	3	3	NUM
ejpam-6124	191	6	vertices	vertex	NOUN
ejpam-6124	191	7	in	in	ADP
ejpam-6124	191	8	rp	rp	NOUN
ejpam-6124	191	9	.	.	PUNCT
ejpam-6124	192	1	thus	thus	ADV
ejpam-6124	192	2	,	,	PUNCT
ejpam-6124	192	3	|t	|t	PROPN
ejpam-6124	192	4	|	|	ADV
ejpam-6124	192	5	=	=	SYM
ejpam-6124	192	6	2(p−	2(p−	NUM
ejpam-6124	192	7	1	1	NUM
ejpam-6124	192	8	)	)	PUNCT
ejpam-6124	192	9	+	+	CCONJ
ejpam-6124	192	10	3	3	NUM
ejpam-6124	192	11	=	=	SYM
ejpam-6124	192	12	2p+	2p+	NUM
ejpam-6124	192	13	1	1	NUM
ejpam-6124	192	14	=	=	SYM
ejpam-6124	192	15	2	2	NUM
ejpam-6124	192	16	(	(	PUNCT
ejpam-6124	192	17	n−1	n−1	PROPN
ejpam-6124	192	18	4	4	NUM
ejpam-6124	192	19	)	)	PUNCT
ejpam-6124	193	1	+	+	CCONJ
ejpam-6124	193	2	1	1	NUM
ejpam-6124	193	3	=	=	SYM
ejpam-6124	193	4	n+1	n+1	NUM
ejpam-6124	193	5	2	2	NUM
ejpam-6124	193	6	,	,	PUNCT
ejpam-6124	193	7	and	and	CCONJ
ejpam-6124	193	8	clearly	clearly	ADV
ejpam-6124	193	9	,	,	PUNCT
ejpam-6124	193	10	n(t	n(t	PROPN
ejpam-6124	193	11	)	)	PUNCT
ejpam-6124	194	1	=	=	SYM
ejpam-6124	194	2	v	v	X
ejpam-6124	194	3	(	(	PUNCT
ejpam-6124	194	4	pn	pn	NOUN
ejpam-6124	194	5	)	)	PUNCT
ejpam-6124	194	6	.	.	PUNCT
ejpam-6124	195	1	by	by	ADP
ejpam-6124	195	2	proposition	proposition	NOUN
ejpam-6124	195	3	1	1	NUM
ejpam-6124	195	4	,	,	PUNCT
ejpam-6124	195	5	t	t	PROPN
ejpam-6124	195	6	is	be	AUX
ejpam-6124	195	7	a	a	DET
ejpam-6124	195	8	γt	γt	NOUN
ejpam-6124	195	9	-	-	NOUN
ejpam-6124	195	10	set	set	NOUN
ejpam-6124	195	11	of	of	ADP
ejpam-6124	195	12	pn	pn	PROPN
ejpam-6124	195	13	.	.	PUNCT
ejpam-6124	196	1	also	also	ADV
ejpam-6124	196	2	,	,	PUNCT
ejpam-6124	196	3	since	since	SCONJ
ejpam-6124	196	4	|t	|t	PROPN
ejpam-6124	196	5	|	|	INTJ
ejpam-6124	196	6	is	be	AUX
ejpam-6124	196	7	odd	odd	ADJ
ejpam-6124	196	8	,	,	PUNCT
ejpam-6124	196	9	by	by	ADP
ejpam-6124	196	10	theorem	theorem	NOUN
ejpam-6124	196	11	5	5	NUM
ejpam-6124	196	12	,	,	PUNCT
ejpam-6124	196	13	t	t	PROPN
ejpam-6124	196	14	is	be	AUX
ejpam-6124	196	15	not	not	PART
ejpam-6124	196	16	a	a	DET
ejpam-6124	196	17	γte	γte	NOUN
ejpam-6124	196	18	-	-	PUNCT
ejpam-6124	196	19	set	set	NOUN
ejpam-6124	196	20	of	of	ADP
ejpam-6124	196	21	pn	pn	PROPN
ejpam-6124	196	22	,	,	PUNCT
ejpam-6124	196	23	and	and	CCONJ
ejpam-6124	196	24	un−1	un−1	PROPN
ejpam-6124	196	25	must	must	AUX
ejpam-6124	196	26	not	not	PART
ejpam-6124	196	27	be	be	AUX
ejpam-6124	196	28	in	in	ADP
ejpam-6124	196	29	t	t	PROPN
ejpam-6124	196	30	.	.	PUNCT
ejpam-6124	197	1	removing	remove	VERB
ejpam-6124	197	2	un−1	un−1	PROPN
ejpam-6124	197	3	from	from	ADP
ejpam-6124	197	4	t	t	NOUN
ejpam-6124	197	5	or	or	CCONJ
ejpam-6124	197	6	replacing	replace	VERB
ejpam-6124	197	7	un−1	un−1	PROPN
ejpam-6124	197	8	by	by	ADP
ejpam-6124	197	9	un	un	PROPN
ejpam-6124	197	10	in	in	ADP
ejpam-6124	197	11	t	t	PROPN
ejpam-6124	197	12	means	mean	VERB
ejpam-6124	197	13	that	that	SCONJ
ejpam-6124	197	14	un	un	PROPN
ejpam-6124	197	15	is	be	AUX
ejpam-6124	197	16	not	not	PART
ejpam-6124	197	17	adjacent	adjacent	ADJ
ejpam-6124	197	18	to	to	ADP
ejpam-6124	197	19	a	a	DET
ejpam-6124	197	20	vertex	vertex	NOUN
ejpam-6124	197	21	in	in	ADP
ejpam-6124	197	22	t	t	PROPN
ejpam-6124	197	23	,	,	PUNCT
ejpam-6124	197	24	that	that	ADV
ejpam-6124	197	25	is	is	ADV
ejpam-6124	197	26	,	,	PUNCT
ejpam-6124	197	27	|n(un	|n(un	PROPN
ejpam-6124	197	28	)	)	PUNCT
ejpam-6124	197	29	∩	∩	NOUN
ejpam-6124	197	30	t	t	NOUN
ejpam-6124	198	1	|	|	NOUN
ejpam-6124	198	2	=	=	SYM
ejpam-6124	198	3	0	0	NUM
ejpam-6124	198	4	and	and	CCONJ
ejpam-6124	198	5	|n(ui	|n(ui	NUM
ejpam-6124	198	6	)	)	PUNCT
ejpam-6124	198	7	∩	∩	NOUN
ejpam-6124	198	8	t	t	NOUN
ejpam-6124	199	1	|	|	NOUN
ejpam-6124	199	2	=	=	SYM
ejpam-6124	199	3	1	1	NUM
ejpam-6124	199	4	for	for	ADP
ejpam-6124	199	5	all	all	DET
ejpam-6124	199	6	ui	ui	NOUN
ejpam-6124	199	7	∈	∈	PROPN
ejpam-6124	199	8	v	v	NOUN
ejpam-6124	199	9	(	(	PUNCT
ejpam-6124	199	10	pn	pn	NOUN
ejpam-6124	199	11	)	)	PUNCT
ejpam-6124	199	12	\	\	PROPN
ejpam-6124	199	13	{	{	PUNCT
ejpam-6124	199	14	un	un	PROPN
ejpam-6124	199	15	}	}	PUNCT
ejpam-6124	199	16	.	.	PUNCT
ejpam-6124	200	1	thus	thus	ADV
ejpam-6124	200	2	,	,	PUNCT
ejpam-6124	200	3	t	t	PROPN
ejpam-6124	200	4	is	be	AUX
ejpam-6124	200	5	not	not	PART
ejpam-6124	200	6	a	a	DET
ejpam-6124	200	7	total	total	ADJ
ejpam-6124	200	8	exact	exact	ADJ
ejpam-6124	200	9	dominating	dominating	NOUN
ejpam-6124	200	10	set	set	NOUN
ejpam-6124	200	11	.	.	PUNCT
ejpam-6124	201	1	hence	hence	ADV
ejpam-6124	201	2	,	,	PUNCT
ejpam-6124	201	3	it	it	PRON
ejpam-6124	201	4	is	be	AUX
ejpam-6124	201	5	not	not	PART
ejpam-6124	201	6	possible	possible	ADJ
ejpam-6124	201	7	to	to	PART
ejpam-6124	201	8	form	form	VERB
ejpam-6124	201	9	a	a	DET
ejpam-6124	201	10	γte	γte	NOUN
ejpam-6124	201	11	-	-	PUNCT
ejpam-6124	201	12	set	set	VERB
ejpam-6124	201	13	t	t	NOUN
ejpam-6124	201	14	of	of	ADP
ejpam-6124	201	15	pn	pn	PROPN
ejpam-6124	201	16	.	.	PROPN
ejpam-6124	201	17	case	case	NOUN
ejpam-6124	201	18	2	2	NUM
ejpam-6124	201	19	:	:	PUNCT
ejpam-6124	201	20	suppose	suppose	VERB
ejpam-6124	201	21	that	that	SCONJ
ejpam-6124	201	22	we	we	PRON
ejpam-6124	201	23	pick	pick	VERB
ejpam-6124	201	24	u1	u1	NOUN
ejpam-6124	201	25	and	and	CCONJ
ejpam-6124	201	26	u2	u2	PROPN
ejpam-6124	201	27	first	first	ADV
ejpam-6124	201	28	to	to	PART
ejpam-6124	201	29	form	form	VERB
ejpam-6124	201	30	t	t	PROPN
ejpam-6124	201	31	.	.	PUNCT
ejpam-6124	202	1	let	let	VERB
ejpam-6124	202	2	t	t	NOUN
ejpam-6124	202	3	=	=	SYM
ejpam-6124	202	4	{	{	PUNCT
ejpam-6124	202	5	u1	u1	NOUN
ejpam-6124	202	6	,	,	PUNCT
ejpam-6124	202	7	u2	u2	PROPN
ejpam-6124	202	8	,	,	PUNCT
ejpam-6124	202	9	u5	u5	PROPN
ejpam-6124	202	10	,	,	PUNCT
ejpam-6124	202	11	u6	u6	PROPN
ejpam-6124	202	12	,	,	PUNCT
ejpam-6124	202	13	u9	u9	PROPN
ejpam-6124	202	14	,	,	PUNCT
ejpam-6124	202	15	u10	u10	PROPN
ejpam-6124	202	16	,	,	PUNCT
ejpam-6124	202	17	.	.	PUNCT
ejpam-6124	202	18	.	.	PUNCT
ejpam-6124	203	1	.	.	PUNCT
ejpam-6124	204	1	,	,	PUNCT
ejpam-6124	204	2	un−8	un−8	ADJ
ejpam-6124	204	3	,	,	PUNCT
ejpam-6124	204	4	un−7	un−7	NOUN
ejpam-6124	204	5	,	,	PUNCT
ejpam-6124	204	6	un−4	un−4	NOUN
ejpam-6124	204	7	,	,	PUNCT
ejpam-6124	204	8	un−3	un−3	ADJ
ejpam-6124	204	9	,	,	PUNCT
ejpam-6124	204	10	un−1	un−1	PROPN
ejpam-6124	204	11	,	,	PUNCT
ejpam-6124	204	12	un	un	ADJ
ejpam-6124	204	13	}	}	PUNCT
ejpam-6124	204	14	,	,	PUNCT
ejpam-6124	204	15	where	where	SCONJ
ejpam-6124	204	16	t	t	PROPN
ejpam-6124	204	17	is	be	AUX
ejpam-6124	204	18	formed	form	VERB
ejpam-6124	204	19	by	by	ADP
ejpam-6124	204	20	getting	get	VERB
ejpam-6124	204	21	2	2	NUM
ejpam-6124	204	22	vertices	vertex	NOUN
ejpam-6124	204	23	in	in	ADP
ejpam-6124	204	24	each	each	DET
ejpam-6124	204	25	rj	rj	PROPN
ejpam-6124	204	26	for	for	ADP
ejpam-6124	204	27	j	j	PROPN
ejpam-6124	204	28	=	=	SYM
ejpam-6124	204	29	1	1	NUM
ejpam-6124	204	30	,	,	PUNCT
ejpam-6124	204	31	2	2	NUM
ejpam-6124	204	32	,	,	PUNCT
ejpam-6124	204	33	.	.	PUNCT
ejpam-6124	204	34	.	.	PUNCT
ejpam-6124	205	1	.	.	PUNCT
ejpam-6124	206	1	,	,	PUNCT
ejpam-6124	206	2	p	p	NOUN
ejpam-6124	206	3	−	−	PROPN
ejpam-6124	206	4	1	1	NUM
ejpam-6124	206	5	and	and	CCONJ
ejpam-6124	206	6	4	4	NUM
ejpam-6124	206	7	vertices	vertex	NOUN
ejpam-6124	206	8	in	in	ADP
ejpam-6124	206	9	rp	rp	NOUN
ejpam-6124	206	10	.	.	PUNCT
ejpam-6124	207	1	clearly	clearly	ADV
ejpam-6124	207	2	,	,	PUNCT
ejpam-6124	207	3	|t	|t	PROPN
ejpam-6124	207	4	|	|	ADV
ejpam-6124	207	5	is	be	AUX
ejpam-6124	207	6	even	even	ADV
ejpam-6124	207	7	and	and	CCONJ
ejpam-6124	207	8	n(t	n(t	PROPN
ejpam-6124	207	9	)	)	PUNCT
ejpam-6124	208	1	=	=	SYM
ejpam-6124	208	2	v	v	X
ejpam-6124	208	3	(	(	PUNCT
ejpam-6124	208	4	pn	pn	NOUN
ejpam-6124	208	5	)	)	PUNCT
ejpam-6124	208	6	.	.	PUNCT
ejpam-6124	209	1	thus	thus	ADV
ejpam-6124	209	2	,	,	PUNCT
ejpam-6124	209	3	t	t	PROPN
ejpam-6124	209	4	is	be	AUX
ejpam-6124	209	5	a	a	DET
ejpam-6124	209	6	total	total	ADJ
ejpam-6124	209	7	dominating	dominating	NOUN
ejpam-6124	209	8	set	set	NOUN
ejpam-6124	209	9	of	of	ADP
ejpam-6124	209	10	pn	pn	PROPN
ejpam-6124	209	11	.	.	PUNCT
ejpam-6124	210	1	it	it	PRON
ejpam-6124	210	2	is	be	AUX
ejpam-6124	210	3	also	also	ADV
ejpam-6124	210	4	clear	clear	ADJ
ejpam-6124	210	5	that	that	SCONJ
ejpam-6124	210	6	|n(ui	|n(ui	NOUN
ejpam-6124	210	7	)	)	PUNCT
ejpam-6124	210	8	∩	∩	NOUN
ejpam-6124	210	9	t	t	NOUN
ejpam-6124	211	1	|	|	NOUN
ejpam-6124	211	2	=	=	SYM
ejpam-6124	211	3	1	1	NUM
ejpam-6124	211	4	for	for	ADP
ejpam-6124	211	5	all	all	DET
ejpam-6124	211	6	ui	ui	NOUN
ejpam-6124	211	7	∈	∈	PROPN
ejpam-6124	211	8	v	v	NOUN
ejpam-6124	211	9	(	(	PUNCT
ejpam-6124	211	10	pn	pn	NOUN
ejpam-6124	211	11	)	)	PUNCT
ejpam-6124	211	12	\	\	PROPN
ejpam-6124	211	13	{	{	PUNCT
ejpam-6124	211	14	un−2	un−2	PROPN
ejpam-6124	211	15	}	}	PUNCT
ejpam-6124	211	16	since	since	SCONJ
ejpam-6124	211	17	un−2	un−2	NOUN
ejpam-6124	211	18	is	be	AUX
ejpam-6124	211	19	adjacent	adjacent	ADJ
ejpam-6124	211	20	to	to	ADP
ejpam-6124	211	21	un−3	un−3	ADJ
ejpam-6124	211	22	and	and	CCONJ
ejpam-6124	211	23	un−1	un−1	ADJ
ejpam-6124	211	24	in	in	ADP
ejpam-6124	211	25	t	t	PROPN
ejpam-6124	211	26	,	,	PUNCT
ejpam-6124	211	27	that	that	ADV
ejpam-6124	211	28	is	is	ADV
ejpam-6124	211	29	,	,	PUNCT
ejpam-6124	211	30	|n(un−2	|n(un−2	ADJ
ejpam-6124	211	31	)	)	PUNCT
ejpam-6124	211	32	∩	∩	NOUN
ejpam-6124	211	33	t	t	NOUN
ejpam-6124	212	1	|	|	NOUN
ejpam-6124	212	2	=	=	SYM
ejpam-6124	212	3	2	2	NUM
ejpam-6124	212	4	and	and	CCONJ
ejpam-6124	212	5	so	so	ADV
ejpam-6124	212	6	,	,	PUNCT
ejpam-6124	212	7	t	t	PROPN
ejpam-6124	212	8	is	be	AUX
ejpam-6124	212	9	not	not	PART
ejpam-6124	212	10	an	an	DET
ejpam-6124	212	11	exact	exact	ADJ
ejpam-6124	212	12	dominating	dominating	NOUN
ejpam-6124	212	13	set	set	NOUN
ejpam-6124	212	14	.	.	PUNCT
ejpam-6124	213	1	therefore	therefore	ADV
ejpam-6124	213	2	,	,	PUNCT
ejpam-6124	213	3	t	t	PROPN
ejpam-6124	213	4	is	be	AUX
ejpam-6124	213	5	not	not	PART
ejpam-6124	213	6	a	a	DET
ejpam-6124	213	7	γte	γte	NOUN
ejpam-6124	213	8	-	-	PUNCT
ejpam-6124	213	9	set	set	VERB
ejpam-6124	213	10	and	and	CCONJ
ejpam-6124	213	11	un−1	un−1	ADJ
ejpam-6124	213	12	must	must	AUX
ejpam-6124	213	13	not	not	PART
ejpam-6124	213	14	be	be	AUX
ejpam-6124	213	15	in	in	ADP
ejpam-6124	213	16	t	t	PROPN
ejpam-6124	213	17	.	.	PUNCT
ejpam-6124	214	1	removing	remove	VERB
ejpam-6124	214	2	un−1	un−1	PROPN
ejpam-6124	214	3	from	from	ADP
ejpam-6124	214	4	t	t	PROPN
ejpam-6124	214	5	means	mean	VERB
ejpam-6124	214	6	that	that	SCONJ
ejpam-6124	214	7	un	un	PROPN
ejpam-6124	214	8	is	be	AUX
ejpam-6124	214	9	not	not	PART
ejpam-6124	214	10	adjacent	adjacent	ADJ
ejpam-6124	214	11	to	to	ADP
ejpam-6124	214	12	a	a	DET
ejpam-6124	214	13	vertex	vertex	NOUN
ejpam-6124	214	14	in	in	ADP
ejpam-6124	214	15	t	t	PROPN
ejpam-6124	214	16	,	,	PUNCT
ejpam-6124	214	17	that	that	ADV
ejpam-6124	214	18	is	is	ADV
ejpam-6124	214	19	,	,	PUNCT
ejpam-6124	214	20	|n(un	|n(un	PROPN
ejpam-6124	214	21	)	)	PUNCT
ejpam-6124	214	22	∩	∩	NOUN
ejpam-6124	214	23	t	t	NOUN
ejpam-6124	215	1	|	|	NOUN
ejpam-6124	215	2	=	=	SYM
ejpam-6124	215	3	0	0	NUM
ejpam-6124	215	4	and	and	CCONJ
ejpam-6124	215	5	|n(ui	|n(ui	NUM
ejpam-6124	215	6	)	)	PUNCT
ejpam-6124	215	7	∩	∩	NOUN
ejpam-6124	215	8	t	t	NOUN
ejpam-6124	216	1	|	|	NOUN
ejpam-6124	216	2	=	=	SYM
ejpam-6124	216	3	1	1	NUM
ejpam-6124	216	4	for	for	ADP
ejpam-6124	216	5	all	all	DET
ejpam-6124	216	6	ui	ui	NOUN
ejpam-6124	216	7	∈	∈	PROPN
ejpam-6124	216	8	v	v	NOUN
ejpam-6124	216	9	(	(	PUNCT
ejpam-6124	216	10	pn	pn	NOUN
ejpam-6124	216	11	)	)	PUNCT
ejpam-6124	216	12	\	\	PROPN
ejpam-6124	216	13	{	{	PUNCT
ejpam-6124	216	14	un	un	PROPN
ejpam-6124	216	15	}	}	PUNCT
ejpam-6124	216	16	.	.	PUNCT
ejpam-6124	217	1	thus	thus	ADV
ejpam-6124	217	2	,	,	PUNCT
ejpam-6124	217	3	t	t	PROPN
ejpam-6124	217	4	is	be	AUX
ejpam-6124	217	5	not	not	PART
ejpam-6124	217	6	a	a	DET
ejpam-6124	217	7	total	total	ADJ
ejpam-6124	217	8	exact	exact	ADJ
ejpam-6124	217	9	dominating	dominating	NOUN
ejpam-6124	217	10	set	set	NOUN
ejpam-6124	217	11	.	.	PUNCT
ejpam-6124	218	1	hence	hence	ADV
ejpam-6124	218	2	,	,	PUNCT
ejpam-6124	218	3	it	it	PRON
ejpam-6124	218	4	is	be	AUX
ejpam-6124	218	5	not	not	PART
ejpam-6124	218	6	possible	possible	ADJ
ejpam-6124	218	7	to	to	PART
ejpam-6124	218	8	form	form	VERB
ejpam-6124	218	9	a	a	DET
ejpam-6124	218	10	γte	γte	NOUN
ejpam-6124	218	11	-	-	PUNCT
ejpam-6124	218	12	set	set	VERB
ejpam-6124	218	13	t	t	NOUN
ejpam-6124	218	14	of	of	ADP
ejpam-6124	218	15	pn	pn	PROPN
ejpam-6124	218	16	.	.	PROPN
ejpam-6124	219	1	in	in	ADP
ejpam-6124	219	2	both	both	DET
ejpam-6124	219	3	cases	case	NOUN
ejpam-6124	219	4	,	,	PUNCT
ejpam-6124	219	5	it	it	PRON
ejpam-6124	219	6	is	be	AUX
ejpam-6124	219	7	not	not	PART
ejpam-6124	219	8	possible	possible	ADJ
ejpam-6124	219	9	to	to	PART
ejpam-6124	219	10	create	create	VERB
ejpam-6124	219	11	a	a	DET
ejpam-6124	219	12	set	set	NOUN
ejpam-6124	219	13	that	that	PRON
ejpam-6124	219	14	is	be	AUX
ejpam-6124	219	15	both	both	CCONJ
ejpam-6124	219	16	a	a	DET
ejpam-6124	219	17	total	total	ADJ
ejpam-6124	219	18	and	and	CCONJ
ejpam-6124	219	19	exact	exact	ADJ
ejpam-6124	219	20	dominating	dominating	NOUN
ejpam-6124	219	21	set	set	NOUN
ejpam-6124	219	22	of	of	ADP
ejpam-6124	219	23	pn	pn	PROPN
ejpam-6124	219	24	.	.	PUNCT
ejpam-6124	220	1	therefore	therefore	ADV
ejpam-6124	220	2	,	,	PUNCT
ejpam-6124	220	3	pn	pn	PROPN
ejpam-6124	220	4	is	be	AUX
ejpam-6124	220	5	a	a	DET
ejpam-6124	220	6	non	non	ADJ
ejpam-6124	220	7	-	-	ADJ
ejpam-6124	220	8	γte	γte	PRON
ejpam-6124	220	9	-	-	PUNCT
ejpam-6124	220	10	graph	graph	NOUN
ejpam-6124	220	11	if	if	SCONJ
ejpam-6124	220	12	n	n	PRON
ejpam-6124	220	13	≡	≡	PROPN
ejpam-6124	220	14	1	1	NUM
ejpam-6124	220	15	(	(	PUNCT
ejpam-6124	220	16	mod	mod	NOUN
ejpam-6124	220	17	4	4	NUM
ejpam-6124	220	18	)	)	PUNCT
ejpam-6124	220	19	.	.	PUNCT
ejpam-6124	221	1	theorem	theorem	ADJ
ejpam-6124	221	2	7	7	NUM
ejpam-6124	221	3	.	.	PUNCT
ejpam-6124	222	1	let	let	VERB
ejpam-6124	222	2	n	n	PRON
ejpam-6124	222	3	be	be	AUX
ejpam-6124	222	4	a	a	DET
ejpam-6124	222	5	positive	positive	ADJ
ejpam-6124	222	6	integer	integer	NOUN
ejpam-6124	223	1	such	such	ADJ
ejpam-6124	223	2	that	that	SCONJ
ejpam-6124	223	3	n	n	CCONJ
ejpam-6124	223	4	≥	≥	NOUN
ejpam-6124	223	5	2	2	NUM
ejpam-6124	223	6	.	.	PUNCT
ejpam-6124	224	1	then	then	ADV
ejpam-6124	224	2	the	the	DET
ejpam-6124	224	3	total	total	ADJ
ejpam-6124	224	4	exact	exact	ADJ
ejpam-6124	224	5	domination	domination	NOUN
ejpam-6124	224	6	number	number	NOUN
ejpam-6124	224	7	of	of	ADP
ejpam-6124	224	8	a	a	DET
ejpam-6124	224	9	path	path	NOUN
ejpam-6124	224	10	pn	pn	NOUN
ejpam-6124	224	11	of	of	ADP
ejpam-6124	224	12	order	order	NOUN
ejpam-6124	224	13	n	n	CCONJ
ejpam-6124	224	14	,	,	PUNCT
ejpam-6124	224	15	where	where	SCONJ
ejpam-6124	224	16	n	n	X
ejpam-6124	224	17	̸≡	̸≡	X
ejpam-6124	224	18	1	1	NUM
ejpam-6124	224	19	(	(	PUNCT
ejpam-6124	224	20	mod	mod	NOUN
ejpam-6124	224	21	4	4	NUM
ejpam-6124	224	22	)	)	PUNCT
ejpam-6124	224	23	,	,	PUNCT
ejpam-6124	224	24	is	be	AUX
ejpam-6124	224	25	given	give	VERB
ejpam-6124	224	26	by	by	ADP
ejpam-6124	224	27	γte(pn	γte(pn	ADJ
ejpam-6124	224	28	)	)	PUNCT
ejpam-6124	224	29	=	=	SYM
ejpam-6124	225	1			PROPN
ejpam-6124	225	2	n	n	PRON
ejpam-6124	225	3	2	2	NUM
ejpam-6124	225	4	,	,	PUNCT
ejpam-6124	225	5	if	if	SCONJ
ejpam-6124	225	6	n	n	PRON
ejpam-6124	225	7	≡	≡	PROPN
ejpam-6124	225	8	0	0	PUNCT
ejpam-6124	226	1	(	(	PUNCT
ejpam-6124	226	2	mod	mod	PROPN
ejpam-6124	226	3	4	4	NUM
ejpam-6124	226	4	)	)	PUNCT
ejpam-6124	226	5	n+2	n+2	ADV
ejpam-6124	226	6	2	2	NUM
ejpam-6124	226	7	,	,	PUNCT
ejpam-6124	226	8	if	if	SCONJ
ejpam-6124	226	9	n	n	PRON
ejpam-6124	226	10	≡	≡	PROPN
ejpam-6124	226	11	2	2	NUM
ejpam-6124	226	12	(	(	PUNCT
ejpam-6124	226	13	mod	mod	NOUN
ejpam-6124	226	14	4	4	NUM
ejpam-6124	226	15	)	)	PUNCT
ejpam-6124	226	16	n+1	n+1	NUM
ejpam-6124	226	17	2	2	NUM
ejpam-6124	226	18	,	,	PUNCT
ejpam-6124	226	19	if	if	SCONJ
ejpam-6124	226	20	n	n	PRON
ejpam-6124	226	21	≡	≡	PROPN
ejpam-6124	226	22	3	3	NUM
ejpam-6124	226	23	(	(	PUNCT
ejpam-6124	226	24	mod	mod	NOUN
ejpam-6124	226	25	4	4	NUM
ejpam-6124	226	26	)	)	PUNCT
ejpam-6124	226	27	.	.	PUNCT
ejpam-6124	227	1	proof	proof	NOUN
ejpam-6124	227	2	.	.	PUNCT
ejpam-6124	228	1	let	let	VERB
ejpam-6124	228	2	v	v	X
ejpam-6124	228	3	(	(	PUNCT
ejpam-6124	228	4	pn	pn	NOUN
ejpam-6124	228	5	)	)	PUNCT
ejpam-6124	228	6	=	=	SYM
ejpam-6124	228	7	{	{	PUNCT
ejpam-6124	228	8	u1	u1	NOUN
ejpam-6124	228	9	,	,	PUNCT
ejpam-6124	228	10	u2	u2	NOUN
ejpam-6124	228	11	,	,	PUNCT
ejpam-6124	228	12	u3	u3	NOUN
ejpam-6124	228	13	,	,	PUNCT
ejpam-6124	228	14	.	.	PUNCT
ejpam-6124	228	15	.	.	PUNCT
ejpam-6124	229	1	.	.	PUNCT
ejpam-6124	230	1	,	,	PUNCT
ejpam-6124	230	2	un−1	un−1	PROPN
ejpam-6124	230	3	,	,	PUNCT
ejpam-6124	230	4	un	un	ADJ
ejpam-6124	230	5	}	}	PUNCT
ejpam-6124	230	6	.	.	PUNCT
ejpam-6124	231	1	consider	consider	VERB
ejpam-6124	231	2	the	the	DET
ejpam-6124	231	3	following	follow	VERB
ejpam-6124	231	4	cases	case	NOUN
ejpam-6124	231	5	:	:	PUNCT
ejpam-6124	231	6	case	case	NOUN
ejpam-6124	231	7	1	1	NUM
ejpam-6124	231	8	:	:	PUNCT
ejpam-6124	231	9	suppose	suppose	VERB
ejpam-6124	231	10	that	that	SCONJ
ejpam-6124	231	11	n	n	PROPN
ejpam-6124	231	12	≡	≡	PROPN
ejpam-6124	231	13	0	0	PUNCT
ejpam-6124	232	1	(	(	PUNCT
ejpam-6124	232	2	mod	mod	PROPN
ejpam-6124	232	3	4	4	NUM
ejpam-6124	232	4	)	)	PUNCT
ejpam-6124	232	5	.	.	PUNCT
ejpam-6124	233	1	let	let	VERB
ejpam-6124	233	2	n	n	NOUN
ejpam-6124	233	3	=	=	SYM
ejpam-6124	233	4	4	4	X
ejpam-6124	233	5	.	.	PUNCT
ejpam-6124	233	6	by	by	ADP
ejpam-6124	233	7	proposition	proposition	NOUN
ejpam-6124	233	8	1	1	NUM
ejpam-6124	233	9	,	,	PUNCT
ejpam-6124	233	10	γt(p4	γt(p4	NOUN
ejpam-6124	233	11	)	)	PUNCT
ejpam-6124	233	12	=	=	SYM
ejpam-6124	233	13	4	4	NUM
ejpam-6124	233	14	2	2	NUM
ejpam-6124	233	15	=	=	SYM
ejpam-6124	233	16	2	2	X
ejpam-6124	233	17	.	.	PUNCT
ejpam-6124	234	1	let	let	VERB
ejpam-6124	234	2	t	t	NOUN
ejpam-6124	234	3	=	=	SYM
ejpam-6124	234	4	{	{	PUNCT
ejpam-6124	234	5	u2	u2	NOUN
ejpam-6124	234	6	,	,	PUNCT
ejpam-6124	234	7	u3	u3	NOUN
ejpam-6124	234	8	}	}	PUNCT
ejpam-6124	234	9	.	.	PUNCT
ejpam-6124	235	1	clearly	clearly	ADV
ejpam-6124	235	2	,	,	PUNCT
ejpam-6124	235	3	|n(ui	|n(ui	PROPN
ejpam-6124	235	4	)	)	PUNCT
ejpam-6124	235	5	∩	∩	NOUN
ejpam-6124	235	6	t	t	NOUN
ejpam-6124	236	1	|	|	NOUN
ejpam-6124	236	2	=	=	SYM
ejpam-6124	236	3	1	1	NUM
ejpam-6124	236	4	for	for	ADP
ejpam-6124	236	5	all	all	DET
ejpam-6124	236	6	ui	ui	NOUN
ejpam-6124	236	7	∈	∈	PROPN
ejpam-6124	236	8	v	v	NOUN
ejpam-6124	236	9	(	(	PUNCT
ejpam-6124	236	10	p4	p4	ADJ
ejpam-6124	236	11	)	)	PUNCT
ejpam-6124	236	12	.	.	PUNCT
ejpam-6124	237	1	thus	thus	ADV
ejpam-6124	237	2	,	,	PUNCT
ejpam-6124	237	3	t	t	PROPN
ejpam-6124	237	4	is	be	AUX
ejpam-6124	237	5	a	a	DET
ejpam-6124	237	6	γte	γte	NOUN
ejpam-6124	237	7	-	-	PUNCT
ejpam-6124	237	8	set	set	NOUN
ejpam-6124	237	9	of	of	ADP
ejpam-6124	237	10	p4	p4	ADJ
ejpam-6124	237	11	,	,	PUNCT
ejpam-6124	237	12	and	and	CCONJ
ejpam-6124	237	13	γte(p4	γte(p4	NOUN
ejpam-6124	237	14	)	)	PUNCT
ejpam-6124	238	1	=	=	VERB
ejpam-6124	238	2	|t	|t	VERB
ejpam-6124	239	1	|	|	ADV
ejpam-6124	239	2	=	=	NOUN
ejpam-6124	239	3	2	2	X
ejpam-6124	239	4	.	.	PUNCT
ejpam-6124	240	1	now	now	ADV
ejpam-6124	240	2	,	,	PUNCT
ejpam-6124	240	3	suppose	suppose	VERB
ejpam-6124	240	4	that	that	SCONJ
ejpam-6124	240	5	n	n	PROPN
ejpam-6124	240	6	>	>	X
ejpam-6124	240	7	4	4	X
ejpam-6124	240	8	.	.	PUNCT
ejpam-6124	240	9	let	let	VERB
ejpam-6124	240	10	p	p	NOUN
ejpam-6124	240	11	=	=	PUNCT
ejpam-6124	240	12	n	n	PRON
ejpam-6124	240	13	4	4	NUM
ejpam-6124	240	14	and	and	CCONJ
ejpam-6124	240	15	j	j	PROPN
ejpam-6124	240	16	=	=	SYM
ejpam-6124	240	17	1	1	NUM
ejpam-6124	240	18	,	,	PUNCT
ejpam-6124	240	19	2	2	NUM
ejpam-6124	240	20	,	,	PUNCT
ejpam-6124	240	21	.	.	PUNCT
ejpam-6124	240	22	.	.	PUNCT
ejpam-6124	241	1	.	.	PUNCT
ejpam-6124	242	1	,	,	PUNCT
ejpam-6124	243	1	p	p	X
ejpam-6124	243	2	−	−	PROPN
ejpam-6124	243	3	1	1	NUM
ejpam-6124	243	4	,	,	PUNCT
ejpam-6124	243	5	p.	p.	NOUN
ejpam-6124	243	6	group	group	NOUN
ejpam-6124	243	7	the	the	DET
ejpam-6124	243	8	vertices	vertex	NOUN
ejpam-6124	243	9	of	of	ADP
ejpam-6124	243	10	pn	pn	NOUN
ejpam-6124	243	11	into	into	ADP
ejpam-6124	243	12	p	p	PROPN
ejpam-6124	243	13	disjoint	disjoint	PROPN
ejpam-6124	243	14	subsets	subset	NOUN
ejpam-6124	243	15	rj	rj	PROPN
ejpam-6124	243	16	,	,	PUNCT
ejpam-6124	243	17	such	such	ADJ
ejpam-6124	243	18	that	that	SCONJ
ejpam-6124	243	19	r.	r.	PROPN
ejpam-6124	243	20	g.	g.	PROPN
ejpam-6124	243	21	aguinod	aguinod	PROPN
ejpam-6124	243	22	,	,	PUNCT
ejpam-6124	243	23	e.	e.	PROPN
ejpam-6124	243	24	m.	m.	PROPN
ejpam-6124	243	25	kiunisala	kiunisala	PROPN
ejpam-6124	243	26	,	,	PUNCT
ejpam-6124	243	27	c.	c.	PROPN
ejpam-6124	243	28	l.	l.	PROPN
ejpam-6124	243	29	armada	armada	PROPN
ejpam-6124	243	30	/	/	SYM
ejpam-6124	243	31	eur	eur	PROPN
ejpam-6124	243	32	.	.	PUNCT
ejpam-6124	244	1	j.	j.	PROPN
ejpam-6124	244	2	pure	pure	PROPN
ejpam-6124	244	3	appl	appl	PROPN
ejpam-6124	244	4	.	.	PROPN
ejpam-6124	244	5	math	math	PROPN
ejpam-6124	244	6	,	,	PUNCT
ejpam-6124	244	7	18	18	NUM
ejpam-6124	244	8	(	(	PUNCT
ejpam-6124	244	9	2	2	NUM
ejpam-6124	244	10	)	)	PUNCT
ejpam-6124	244	11	(	(	PUNCT
ejpam-6124	244	12	2025	2025	NUM
ejpam-6124	244	13	)	)	PUNCT
ejpam-6124	244	14	,	,	PUNCT
ejpam-6124	244	15	6124	6124	NUM
ejpam-6124	244	16	10	10	NUM
ejpam-6124	244	17	of	of	ADP
ejpam-6124	244	18	26	26	NUM
ejpam-6124	244	19	r1	r1	NOUN
ejpam-6124	244	20	=	=	SYM
ejpam-6124	244	21	{	{	PUNCT
ejpam-6124	244	22	u1	u1	NOUN
ejpam-6124	244	23	,	,	PUNCT
ejpam-6124	244	24	u2	u2	NOUN
ejpam-6124	244	25	,	,	PUNCT
ejpam-6124	244	26	u3	u3	NOUN
ejpam-6124	244	27	,	,	PUNCT
ejpam-6124	244	28	u4	u4	PROPN
ejpam-6124	244	29	}	}	PUNCT
ejpam-6124	244	30	,	,	PUNCT
ejpam-6124	244	31	r2	r2	PROPN
ejpam-6124	244	32	=	=	SYM
ejpam-6124	244	33	{	{	PUNCT
ejpam-6124	244	34	u5	u5	PROPN
ejpam-6124	244	35	,	,	PUNCT
ejpam-6124	244	36	u6	u6	PROPN
ejpam-6124	244	37	,	,	PUNCT
ejpam-6124	244	38	u7	u7	PROPN
ejpam-6124	244	39	,	,	PUNCT
ejpam-6124	244	40	u8	u8	PROPN
ejpam-6124	244	41	}	}	PUNCT
ejpam-6124	244	42	,	,	PUNCT
ejpam-6124	244	43	r3	r3	PROPN
ejpam-6124	244	44	=	=	SYM
ejpam-6124	244	45	{	{	PUNCT
ejpam-6124	244	46	u9	u9	PROPN
ejpam-6124	244	47	,	,	PUNCT
ejpam-6124	244	48	u10	u10	PROPN
ejpam-6124	244	49	,	,	PUNCT
ejpam-6124	244	50	u11	u11	PROPN
ejpam-6124	244	51	,	,	PUNCT
ejpam-6124	244	52	u12	u12	PROPN
ejpam-6124	244	53	}	}	PUNCT
ejpam-6124	244	54	,	,	PUNCT
ejpam-6124	244	55	...	...	PUNCT
ejpam-6124	245	1	rp−1	rp−1	NOUN
ejpam-6124	245	2	=	=	SYM
ejpam-6124	245	3	{	{	PUNCT
ejpam-6124	245	4	un−7	un−7	PROPN
ejpam-6124	245	5	,	,	PUNCT
ejpam-6124	245	6	un−6	un−6	PROPN
ejpam-6124	245	7	,	,	PUNCT
ejpam-6124	245	8	un−5	un−5	PROPN
ejpam-6124	245	9	,	,	PUNCT
ejpam-6124	245	10	un−4	un−4	NOUN
ejpam-6124	245	11	}	}	PUNCT
ejpam-6124	245	12	,	,	PUNCT
ejpam-6124	245	13	and	and	CCONJ
ejpam-6124	245	14	rp	rp	NOUN
ejpam-6124	245	15	=	=	PUNCT
ejpam-6124	245	16	{	{	PUNCT
ejpam-6124	245	17	un−3	un−3	PROPN
ejpam-6124	245	18	,	,	PUNCT
ejpam-6124	245	19	un−2	un−2	PROPN
ejpam-6124	245	20	,	,	PUNCT
ejpam-6124	245	21	un−1	un−1	PROPN
ejpam-6124	245	22	,	,	PUNCT
ejpam-6124	245	23	un	un	ADJ
ejpam-6124	245	24	}	}	PUNCT
ejpam-6124	245	25	where	where	SCONJ
ejpam-6124	245	26	|rj	|rj	PART
ejpam-6124	245	27	|	|	ADV
ejpam-6124	245	28	=	=	SYM
ejpam-6124	245	29	4	4	NUM
ejpam-6124	245	30	for	for	ADP
ejpam-6124	245	31	j	j	PROPN
ejpam-6124	245	32	=	=	SYM
ejpam-6124	245	33	1	1	NUM
ejpam-6124	245	34	,	,	PUNCT
ejpam-6124	245	35	2	2	NUM
ejpam-6124	245	36	,	,	PUNCT
ejpam-6124	245	37	.	.	PUNCT
ejpam-6124	245	38	.	.	PUNCT
ejpam-6124	245	39	.	.	PUNCT
ejpam-6124	246	1	,	,	PUNCT
ejpam-6124	246	2	p−	p−	NOUN
ejpam-6124	246	3	1	1	NUM
ejpam-6124	246	4	,	,	PUNCT
ejpam-6124	246	5	p.	p.	NOUN
ejpam-6124	246	6	let	let	VERB
ejpam-6124	246	7	t	t	NOUN
ejpam-6124	246	8	=	=	SYM
ejpam-6124	246	9	{	{	PUNCT
ejpam-6124	246	10	u2	u2	PROPN
ejpam-6124	246	11	,	,	PUNCT
ejpam-6124	246	12	u3	u3	NOUN
ejpam-6124	246	13	,	,	PUNCT
ejpam-6124	246	14	u6	u6	PROPN
ejpam-6124	246	15	,	,	PUNCT
ejpam-6124	246	16	u7	u7	PROPN
ejpam-6124	246	17	,	,	PUNCT
ejpam-6124	246	18	u10	u10	PROPN
ejpam-6124	246	19	,	,	PUNCT
ejpam-6124	246	20	u11	u11	PROPN
ejpam-6124	246	21	,	,	PUNCT
ejpam-6124	246	22	.	.	PUNCT
ejpam-6124	246	23	.	.	PUNCT
ejpam-6124	247	1	.	.	PUNCT
ejpam-6124	248	1	,	,	PUNCT
ejpam-6124	248	2	un−6	un−6	PROPN
ejpam-6124	248	3	,	,	PUNCT
ejpam-6124	248	4	un−5	un−5	PROPN
ejpam-6124	248	5	,	,	PUNCT
ejpam-6124	248	6	un−2	un−2	PROPN
ejpam-6124	248	7	,	,	PUNCT
ejpam-6124	248	8	un−1	un−1	PROPN
ejpam-6124	248	9	}	}	PUNCT
ejpam-6124	248	10	,	,	PUNCT
ejpam-6124	248	11	where	where	SCONJ
ejpam-6124	248	12	t	t	PROPN
ejpam-6124	248	13	is	be	AUX
ejpam-6124	248	14	formed	form	VERB
ejpam-6124	248	15	by	by	ADP
ejpam-6124	248	16	getting	get	VERB
ejpam-6124	248	17	2	2	NUM
ejpam-6124	248	18	vertices	vertex	NOUN
ejpam-6124	248	19	in	in	ADP
ejpam-6124	248	20	each	each	DET
ejpam-6124	248	21	rj	rj	PROPN
ejpam-6124	248	22	for	for	ADP
ejpam-6124	248	23	j	j	PROPN
ejpam-6124	248	24	=	=	SYM
ejpam-6124	248	25	1	1	NUM
ejpam-6124	248	26	,	,	PUNCT
ejpam-6124	248	27	2	2	NUM
ejpam-6124	248	28	,	,	PUNCT
ejpam-6124	248	29	.	.	PUNCT
ejpam-6124	248	30	.	.	PUNCT
ejpam-6124	249	1	.	.	PUNCT
ejpam-6124	250	1	,	,	PUNCT
ejpam-6124	250	2	p−	p−	NOUN
ejpam-6124	250	3	1	1	NUM
ejpam-6124	250	4	,	,	PUNCT
ejpam-6124	250	5	p.	p.	NOUN
ejpam-6124	250	6	it	it	PRON
ejpam-6124	250	7	follows	follow	VERB
ejpam-6124	250	8	that	that	PRON
ejpam-6124	250	9	|t	|t	VERB
ejpam-6124	251	1	|	|	ADV
ejpam-6124	251	2	=	=	SYM
ejpam-6124	251	3	2p	2p	NUM
ejpam-6124	251	4	=	=	SYM
ejpam-6124	251	5	2	2	NUM
ejpam-6124	251	6	(	(	PUNCT
ejpam-6124	251	7	n	n	ADV
ejpam-6124	251	8	4	4	NUM
ejpam-6124	251	9	)	)	PUNCT
ejpam-6124	252	1	=	=	SYM
ejpam-6124	252	2	n	n	PRON
ejpam-6124	252	3	2	2	NUM
ejpam-6124	252	4	.	.	PUNCT
ejpam-6124	253	1	also	also	ADV
ejpam-6124	253	2	,	,	PUNCT
ejpam-6124	253	3	note	note	VERB
ejpam-6124	253	4	that	that	SCONJ
ejpam-6124	253	5	n(t	n(t	PROPN
ejpam-6124	253	6	)	)	PUNCT
ejpam-6124	254	1	=	=	SYM
ejpam-6124	254	2	v	v	X
ejpam-6124	254	3	(	(	PUNCT
ejpam-6124	254	4	pn	pn	NOUN
ejpam-6124	254	5	)	)	PUNCT
ejpam-6124	254	6	.	.	PUNCT
ejpam-6124	255	1	thus	thus	ADV
ejpam-6124	255	2	,	,	PUNCT
ejpam-6124	255	3	t	t	PROPN
ejpam-6124	255	4	is	be	AUX
ejpam-6124	255	5	a	a	DET
ejpam-6124	255	6	γt	γt	NOUN
ejpam-6124	255	7	-	-	NOUN
ejpam-6124	255	8	set	set	NOUN
ejpam-6124	255	9	of	of	ADP
ejpam-6124	255	10	pn	pn	PROPN
ejpam-6124	255	11	by	by	ADP
ejpam-6124	255	12	proposition	proposition	NOUN
ejpam-6124	255	13	1	1	NUM
ejpam-6124	255	14	.	.	PUNCT
ejpam-6124	256	1	it	it	PRON
ejpam-6124	256	2	is	be	AUX
ejpam-6124	256	3	also	also	ADV
ejpam-6124	256	4	clear	clear	ADJ
ejpam-6124	256	5	that	that	SCONJ
ejpam-6124	256	6	|n(ui	|n(ui	NOUN
ejpam-6124	256	7	)	)	PUNCT
ejpam-6124	256	8	∩	∩	NOUN
ejpam-6124	256	9	t	t	NOUN
ejpam-6124	257	1	|	|	NOUN
ejpam-6124	257	2	=	=	SYM
ejpam-6124	257	3	1	1	NUM
ejpam-6124	257	4	for	for	ADP
ejpam-6124	257	5	all	all	DET
ejpam-6124	257	6	ui	ui	NOUN
ejpam-6124	257	7	∈	∈	PROPN
ejpam-6124	257	8	v	v	NOUN
ejpam-6124	257	9	(	(	PUNCT
ejpam-6124	257	10	pn	pn	NOUN
ejpam-6124	257	11	)	)	PUNCT
ejpam-6124	257	12	.	.	PUNCT
ejpam-6124	258	1	therefore	therefore	ADV
ejpam-6124	258	2	,	,	PUNCT
ejpam-6124	258	3	t	t	PROPN
ejpam-6124	258	4	is	be	AUX
ejpam-6124	258	5	a	a	DET
ejpam-6124	258	6	γte	γte	NOUN
ejpam-6124	258	7	-	-	PUNCT
ejpam-6124	258	8	set	set	NOUN
ejpam-6124	258	9	.	.	PUNCT
ejpam-6124	259	1	this	this	PRON
ejpam-6124	259	2	implies	imply	VERB
ejpam-6124	259	3	that	that	SCONJ
ejpam-6124	259	4	γte(pn	γte(pn	ADV
ejpam-6124	259	5	)	)	PUNCT
ejpam-6124	259	6	=	=	VERB
ejpam-6124	259	7	|t	|t	VERB
ejpam-6124	260	1	|	|	ADV
ejpam-6124	260	2	=	=	SYM
ejpam-6124	260	3	n	n	PRON
ejpam-6124	260	4	2	2	NUM
ejpam-6124	260	5	.	.	PUNCT
ejpam-6124	261	1	case	case	NOUN
ejpam-6124	261	2	2	2	NUM
ejpam-6124	261	3	:	:	PUNCT
ejpam-6124	261	4	suppose	suppose	VERB
ejpam-6124	261	5	that	that	SCONJ
ejpam-6124	261	6	n	n	NUM
ejpam-6124	261	7	≡	≡	PROPN
ejpam-6124	261	8	2	2	NUM
ejpam-6124	261	9	(	(	PUNCT
ejpam-6124	261	10	mod	mod	NOUN
ejpam-6124	261	11	4	4	NUM
ejpam-6124	261	12	)	)	PUNCT
ejpam-6124	261	13	.	.	PUNCT
ejpam-6124	262	1	when	when	SCONJ
ejpam-6124	262	2	n	n	X
ejpam-6124	262	3	=	=	SYM
ejpam-6124	262	4	2	2	NUM
ejpam-6124	262	5	,	,	PUNCT
ejpam-6124	262	6	s	s	PART
ejpam-6124	262	7	=	=	PUNCT
ejpam-6124	262	8	{	{	PUNCT
ejpam-6124	262	9	u1	u1	NOUN
ejpam-6124	262	10	,	,	PUNCT
ejpam-6124	262	11	u2	u2	PROPN
ejpam-6124	262	12	}	}	PUNCT
ejpam-6124	262	13	is	be	AUX
ejpam-6124	262	14	a	a	DET
ejpam-6124	262	15	γte	γte	NOUN
ejpam-6124	262	16	-	-	PUNCT
ejpam-6124	262	17	set	set	NOUN
ejpam-6124	262	18	of	of	ADP
ejpam-6124	262	19	p2	p2	PROPN
ejpam-6124	262	20	since	since	SCONJ
ejpam-6124	262	21	|n(u1)∩s|	|n(u1)∩s|	NOUN
ejpam-6124	262	22	=	=	SYM
ejpam-6124	262	23	1	1	NUM
ejpam-6124	262	24	and	and	CCONJ
ejpam-6124	262	25	|n(u2)∩s|	|n(u2)∩s|	PROPN
ejpam-6124	262	26	=	=	SYM
ejpam-6124	262	27	1	1	X
ejpam-6124	262	28	.	.	PUNCT
ejpam-6124	263	1	thus	thus	ADV
ejpam-6124	263	2	,	,	PUNCT
ejpam-6124	263	3	γte(p2	γte(p2	ADJ
ejpam-6124	263	4	)	)	PUNCT
ejpam-6124	263	5	=	=	PUNCT
ejpam-6124	263	6	|s|	|s|	NOUN
ejpam-6124	263	7	=	=	SYM
ejpam-6124	263	8	2	2	X
ejpam-6124	263	9	.	.	PUNCT
ejpam-6124	263	10	let	let	VERB
ejpam-6124	263	11	n	n	NOUN
ejpam-6124	263	12	=	=	SYM
ejpam-6124	263	13	6	6	NUM
ejpam-6124	263	14	.	.	PUNCT
ejpam-6124	263	15	by	by	ADP
ejpam-6124	263	16	proposition	proposition	NOUN
ejpam-6124	263	17	1	1	NUM
ejpam-6124	263	18	,	,	PUNCT
ejpam-6124	263	19	γt(p6	γt(p6	NUM
ejpam-6124	263	20	)	)	PUNCT
ejpam-6124	263	21	=	=	PUNCT
ejpam-6124	264	1	6	6	NUM
ejpam-6124	264	2	+	+	SYM
ejpam-6124	264	3	2	2	NUM
ejpam-6124	264	4	2	2	NUM
ejpam-6124	264	5	=	=	SYM
ejpam-6124	264	6	2	2	X
ejpam-6124	264	7	.	.	PUNCT
ejpam-6124	265	1	let	let	VERB
ejpam-6124	265	2	t	t	NOUN
ejpam-6124	265	3	=	=	SYM
ejpam-6124	265	4	{	{	PUNCT
ejpam-6124	265	5	u1	u1	NOUN
ejpam-6124	265	6	,	,	PUNCT
ejpam-6124	265	7	u2	u2	PROPN
ejpam-6124	265	8	,	,	PUNCT
ejpam-6124	265	9	u5	u5	PROPN
ejpam-6124	265	10	,	,	PUNCT
ejpam-6124	265	11	u6	u6	NOUN
ejpam-6124	265	12	}	}	PUNCT
ejpam-6124	265	13	.	.	PUNCT
ejpam-6124	266	1	clearly	clearly	ADV
ejpam-6124	266	2	,	,	PUNCT
ejpam-6124	266	3	|n(ui	|n(ui	PROPN
ejpam-6124	266	4	)	)	PUNCT
ejpam-6124	266	5	∩	∩	NOUN
ejpam-6124	266	6	t	t	NOUN
ejpam-6124	267	1	|	|	NOUN
ejpam-6124	267	2	=	=	SYM
ejpam-6124	267	3	1	1	NUM
ejpam-6124	267	4	for	for	ADP
ejpam-6124	267	5	all	all	DET
ejpam-6124	267	6	ui	ui	NOUN
ejpam-6124	267	7	∈	∈	PROPN
ejpam-6124	267	8	v	v	NOUN
ejpam-6124	267	9	(	(	PUNCT
ejpam-6124	267	10	p6	p6	PROPN
ejpam-6124	267	11	)	)	PUNCT
ejpam-6124	267	12	.	.	PUNCT
ejpam-6124	268	1	thus	thus	ADV
ejpam-6124	268	2	,	,	PUNCT
ejpam-6124	268	3	t	t	PROPN
ejpam-6124	268	4	is	be	AUX
ejpam-6124	268	5	a	a	DET
ejpam-6124	268	6	γte	γte	NOUN
ejpam-6124	268	7	-	-	PUNCT
ejpam-6124	268	8	set	set	NOUN
ejpam-6124	268	9	of	of	ADP
ejpam-6124	268	10	p6	p6	PROPN
ejpam-6124	268	11	,	,	PUNCT
ejpam-6124	268	12	and	and	CCONJ
ejpam-6124	268	13	γte(p6	γte(p6	NOUN
ejpam-6124	268	14	)	)	PUNCT
ejpam-6124	268	15	=	=	VERB
ejpam-6124	268	16	|t	|t	VERB
ejpam-6124	269	1	|	|	ADV
ejpam-6124	269	2	=	=	NOUN
ejpam-6124	269	3	4	4	X
ejpam-6124	269	4	.	.	PUNCT
ejpam-6124	269	5	now	now	ADV
ejpam-6124	269	6	,	,	PUNCT
ejpam-6124	269	7	suppose	suppose	VERB
ejpam-6124	269	8	that	that	SCONJ
ejpam-6124	269	9	n	n	PROPN
ejpam-6124	269	10	>	>	X
ejpam-6124	269	11	6	6	NUM
ejpam-6124	269	12	,	,	PUNCT
ejpam-6124	269	13	let	let	VERB
ejpam-6124	269	14	p	p	NOUN
ejpam-6124	269	15	=	=	PUNCT
ejpam-6124	269	16	n−2	n−2	PROPN
ejpam-6124	269	17	4	4	NUM
ejpam-6124	269	18	and	and	CCONJ
ejpam-6124	269	19	j	j	NOUN
ejpam-6124	269	20	=	=	SYM
ejpam-6124	269	21	1	1	NUM
ejpam-6124	269	22	,	,	PUNCT
ejpam-6124	269	23	2	2	NUM
ejpam-6124	269	24	,	,	PUNCT
ejpam-6124	269	25	.	.	PUNCT
ejpam-6124	269	26	.	.	PUNCT
ejpam-6124	270	1	.	.	PUNCT
ejpam-6124	271	1	,	,	PUNCT
ejpam-6124	271	2	p−	p−	NOUN
ejpam-6124	271	3	1	1	NUM
ejpam-6124	271	4	,	,	PUNCT
ejpam-6124	271	5	p.	p.	NOUN
ejpam-6124	271	6	group	group	NOUN
ejpam-6124	271	7	the	the	DET
ejpam-6124	271	8	vertices	vertex	NOUN
ejpam-6124	271	9	of	of	ADP
ejpam-6124	271	10	pn	pn	NOUN
ejpam-6124	271	11	into	into	ADP
ejpam-6124	271	12	p	p	PROPN
ejpam-6124	271	13	disjoint	disjoint	PROPN
ejpam-6124	271	14	subsets	subset	NOUN
ejpam-6124	271	15	rj	rj	PROPN
ejpam-6124	271	16	,	,	PUNCT
ejpam-6124	271	17	such	such	ADJ
ejpam-6124	271	18	that	that	SCONJ
ejpam-6124	271	19	r1	r1	NOUN
ejpam-6124	271	20	=	=	SYM
ejpam-6124	271	21	{	{	PUNCT
ejpam-6124	271	22	u1	u1	NOUN
ejpam-6124	271	23	,	,	PUNCT
ejpam-6124	271	24	u2	u2	NOUN
ejpam-6124	271	25	,	,	PUNCT
ejpam-6124	271	26	u3	u3	NOUN
ejpam-6124	271	27	,	,	PUNCT
ejpam-6124	271	28	u4	u4	PROPN
ejpam-6124	271	29	}	}	PUNCT
ejpam-6124	271	30	,	,	PUNCT
ejpam-6124	271	31	r2	r2	PROPN
ejpam-6124	271	32	=	=	SYM
ejpam-6124	271	33	{	{	PUNCT
ejpam-6124	271	34	u5	u5	PROPN
ejpam-6124	271	35	,	,	PUNCT
ejpam-6124	271	36	u6	u6	PROPN
ejpam-6124	271	37	,	,	PUNCT
ejpam-6124	271	38	u7	u7	PROPN
ejpam-6124	271	39	,	,	PUNCT
ejpam-6124	271	40	u8	u8	PROPN
ejpam-6124	271	41	}	}	PUNCT
ejpam-6124	271	42	,	,	PUNCT
ejpam-6124	271	43	r3	r3	PROPN
ejpam-6124	271	44	=	=	SYM
ejpam-6124	271	45	{	{	PUNCT
ejpam-6124	271	46	u9	u9	PROPN
ejpam-6124	271	47	,	,	PUNCT
ejpam-6124	271	48	u10	u10	PROPN
ejpam-6124	271	49	,	,	PUNCT
ejpam-6124	271	50	u11	u11	PROPN
ejpam-6124	271	51	,	,	PUNCT
ejpam-6124	271	52	u12	u12	PROPN
ejpam-6124	271	53	}	}	PUNCT
ejpam-6124	271	54	,	,	PUNCT
ejpam-6124	271	55	...	...	PUNCT
ejpam-6124	272	1	rp−1	rp−1	NOUN
ejpam-6124	272	2	=	=	SYM
ejpam-6124	272	3	{	{	PUNCT
ejpam-6124	272	4	un−9	un−9	PROPN
ejpam-6124	272	5	,	,	PUNCT
ejpam-6124	272	6	un−8	un−8	ADJ
ejpam-6124	272	7	,	,	PUNCT
ejpam-6124	272	8	un−7	un−7	PROPN
ejpam-6124	272	9	,	,	PUNCT
ejpam-6124	272	10	un−6	un−6	PROPN
ejpam-6124	272	11	}	}	PUNCT
ejpam-6124	272	12	,	,	PUNCT
ejpam-6124	272	13	and	and	CCONJ
ejpam-6124	272	14	rp	rp	NOUN
ejpam-6124	272	15	=	=	SYM
ejpam-6124	272	16	{	{	PUNCT
ejpam-6124	272	17	un−5	un−5	PROPN
ejpam-6124	272	18	,	,	PUNCT
ejpam-6124	272	19	un−4	un−4	NOUN
ejpam-6124	272	20	,	,	PUNCT
ejpam-6124	272	21	un−3	un−3	ADJ
ejpam-6124	272	22	,	,	PUNCT
ejpam-6124	272	23	un−2	un−2	PROPN
ejpam-6124	272	24	,	,	PUNCT
ejpam-6124	272	25	un−1	un−1	PROPN
ejpam-6124	272	26	,	,	PUNCT
ejpam-6124	272	27	un	un	ADJ
ejpam-6124	272	28	}	}	PUNCT
ejpam-6124	272	29	where	where	SCONJ
ejpam-6124	272	30	|rj	|rj	PART
ejpam-6124	272	31	|	|	ADV
ejpam-6124	272	32	=	=	SYM
ejpam-6124	272	33	4	4	NUM
ejpam-6124	272	34	for	for	ADP
ejpam-6124	272	35	j	j	PROPN
ejpam-6124	272	36	=	=	SYM
ejpam-6124	272	37	1	1	NUM
ejpam-6124	272	38	,	,	PUNCT
ejpam-6124	272	39	2	2	NUM
ejpam-6124	272	40	,	,	PUNCT
ejpam-6124	272	41	.	.	PUNCT
ejpam-6124	272	42	.	.	PUNCT
ejpam-6124	272	43	.	.	PUNCT
ejpam-6124	273	1	,	,	PUNCT
ejpam-6124	273	2	p−	p−	NOUN
ejpam-6124	273	3	1	1	NUM
ejpam-6124	273	4	and	and	CCONJ
ejpam-6124	273	5	|rp|	|rp|	NUM
ejpam-6124	273	6	=	=	SYM
ejpam-6124	273	7	6	6	X
ejpam-6124	273	8	.	.	PUNCT
ejpam-6124	273	9	let	let	VERB
ejpam-6124	273	10	t	t	NOUN
ejpam-6124	273	11	=	=	SYM
ejpam-6124	273	12	{	{	PUNCT
ejpam-6124	273	13	u1	u1	NOUN
ejpam-6124	273	14	,	,	PUNCT
ejpam-6124	273	15	u2	u2	PROPN
ejpam-6124	273	16	,	,	PUNCT
ejpam-6124	273	17	u5	u5	PROPN
ejpam-6124	273	18	,	,	PUNCT
ejpam-6124	273	19	u6	u6	PROPN
ejpam-6124	273	20	,	,	PUNCT
ejpam-6124	273	21	u9	u9	PROPN
ejpam-6124	273	22	,	,	PUNCT
ejpam-6124	273	23	u10	u10	PROPN
ejpam-6124	273	24	,	,	PUNCT
ejpam-6124	273	25	.	.	PUNCT
ejpam-6124	273	26	.	.	PUNCT
ejpam-6124	274	1	.	.	PUNCT
ejpam-6124	275	1	,	,	PUNCT
ejpam-6124	275	2	un−9	un−9	PROPN
ejpam-6124	275	3	,	,	PUNCT
ejpam-6124	275	4	un−8	un−8	ADJ
ejpam-6124	275	5	,	,	PUNCT
ejpam-6124	275	6	un−5	un−5	PROPN
ejpam-6124	275	7	,	,	PUNCT
ejpam-6124	275	8	un−4	un−4	NOUN
ejpam-6124	275	9	,	,	PUNCT
ejpam-6124	275	10	un−1	un−1	PROPN
ejpam-6124	275	11	,	,	PUNCT
ejpam-6124	275	12	un	un	ADJ
ejpam-6124	275	13	}	}	PUNCT
ejpam-6124	275	14	,	,	PUNCT
ejpam-6124	275	15	r.	r.	PROPN
ejpam-6124	275	16	g.	g.	PROPN
ejpam-6124	275	17	aguinod	aguinod	PROPN
ejpam-6124	275	18	,	,	PUNCT
ejpam-6124	275	19	e.	e.	PROPN
ejpam-6124	275	20	m.	m.	PROPN
ejpam-6124	275	21	kiunisala	kiunisala	PROPN
ejpam-6124	275	22	,	,	PUNCT
ejpam-6124	275	23	c.	c.	PROPN
ejpam-6124	275	24	l.	l.	PROPN
ejpam-6124	275	25	armada	armada	PROPN
ejpam-6124	275	26	/	/	SYM
ejpam-6124	275	27	eur	eur	PROPN
ejpam-6124	275	28	.	.	PUNCT
ejpam-6124	276	1	j.	j.	PROPN
ejpam-6124	276	2	pure	pure	PROPN
ejpam-6124	276	3	appl	appl	PROPN
ejpam-6124	276	4	.	.	PROPN
ejpam-6124	276	5	math	math	PROPN
ejpam-6124	276	6	,	,	PUNCT
ejpam-6124	276	7	18	18	NUM
ejpam-6124	276	8	(	(	PUNCT
ejpam-6124	276	9	2	2	NUM
ejpam-6124	276	10	)	)	PUNCT
ejpam-6124	276	11	(	(	PUNCT
ejpam-6124	276	12	2025	2025	NUM
ejpam-6124	276	13	)	)	PUNCT
ejpam-6124	276	14	,	,	PUNCT
ejpam-6124	276	15	6124	6124	NUM
ejpam-6124	276	16	11	11	NUM
ejpam-6124	276	17	of	of	ADP
ejpam-6124	276	18	26	26	NUM
ejpam-6124	276	19	where	where	SCONJ
ejpam-6124	276	20	t	t	PROPN
ejpam-6124	276	21	is	be	AUX
ejpam-6124	276	22	formed	form	VERB
ejpam-6124	276	23	by	by	ADP
ejpam-6124	276	24	getting	get	VERB
ejpam-6124	276	25	2	2	NUM
ejpam-6124	276	26	vertices	vertex	NOUN
ejpam-6124	276	27	in	in	ADP
ejpam-6124	276	28	each	each	DET
ejpam-6124	276	29	rj	rj	PROPN
ejpam-6124	276	30	for	for	ADP
ejpam-6124	276	31	j	j	PROPN
ejpam-6124	276	32	=	=	SYM
ejpam-6124	276	33	1	1	NUM
ejpam-6124	276	34	,	,	PUNCT
ejpam-6124	276	35	2	2	NUM
ejpam-6124	276	36	,	,	PUNCT
ejpam-6124	276	37	.	.	PUNCT
ejpam-6124	276	38	.	.	PUNCT
ejpam-6124	277	1	.	.	PUNCT
ejpam-6124	278	1	,	,	PUNCT
ejpam-6124	278	2	p−	p−	NOUN
ejpam-6124	278	3	1	1	NUM
ejpam-6124	278	4	and	and	CCONJ
ejpam-6124	278	5	4	4	NUM
ejpam-6124	278	6	vertices	vertex	NOUN
ejpam-6124	278	7	in	in	ADP
ejpam-6124	278	8	rp	rp	NOUN
ejpam-6124	278	9	.	.	PUNCT
ejpam-6124	279	1	it	it	PRON
ejpam-6124	279	2	follows	follow	VERB
ejpam-6124	279	3	that	that	PRON
ejpam-6124	279	4	|t	|t	VERB
ejpam-6124	280	1	|	|	ADV
ejpam-6124	281	1	=	=	SYM
ejpam-6124	281	2	2(p−	2(p−	NUM
ejpam-6124	281	3	1	1	NUM
ejpam-6124	281	4	)	)	PUNCT
ejpam-6124	281	5	+	+	CCONJ
ejpam-6124	281	6	4	4	NUM
ejpam-6124	281	7	=	=	SYM
ejpam-6124	281	8	2p+	2p+	NUM
ejpam-6124	281	9	2	2	NUM
ejpam-6124	281	10	=	=	SYM
ejpam-6124	281	11	2	2	NUM
ejpam-6124	281	12	(	(	PUNCT
ejpam-6124	281	13	n−	n−	NOUN
ejpam-6124	281	14	2	2	NUM
ejpam-6124	281	15	4	4	NUM
ejpam-6124	281	16	)	)	PUNCT
ejpam-6124	281	17	+	+	CCONJ
ejpam-6124	281	18	2	2	X
ejpam-6124	281	19	=	=	SYM
ejpam-6124	281	20	n+	n+	X
ejpam-6124	281	21	2	2	NUM
ejpam-6124	281	22	2	2	NUM
ejpam-6124	281	23	.	.	PUNCT
ejpam-6124	282	1	also	also	ADV
ejpam-6124	282	2	,	,	PUNCT
ejpam-6124	282	3	note	note	VERB
ejpam-6124	282	4	that	that	SCONJ
ejpam-6124	282	5	n(t	n(t	PROPN
ejpam-6124	282	6	)	)	PUNCT
ejpam-6124	283	1	=	=	SYM
ejpam-6124	283	2	v	v	X
ejpam-6124	283	3	(	(	PUNCT
ejpam-6124	283	4	pn	pn	NOUN
ejpam-6124	283	5	)	)	PUNCT
ejpam-6124	283	6	.	.	PUNCT
ejpam-6124	284	1	thus	thus	ADV
ejpam-6124	284	2	,	,	PUNCT
ejpam-6124	284	3	t	t	PROPN
ejpam-6124	284	4	is	be	AUX
ejpam-6124	284	5	a	a	DET
ejpam-6124	284	6	γt	γt	NOUN
ejpam-6124	284	7	-	-	NOUN
ejpam-6124	284	8	set	set	NOUN
ejpam-6124	284	9	of	of	ADP
ejpam-6124	284	10	pn	pn	PROPN
ejpam-6124	284	11	by	by	ADP
ejpam-6124	284	12	proposition	proposition	NOUN
ejpam-6124	284	13	1	1	NUM
ejpam-6124	284	14	.	.	PUNCT
ejpam-6124	285	1	it	it	PRON
ejpam-6124	285	2	is	be	AUX
ejpam-6124	285	3	also	also	ADV
ejpam-6124	285	4	clear	clear	ADJ
ejpam-6124	285	5	that	that	SCONJ
ejpam-6124	285	6	|n(ui	|n(ui	NOUN
ejpam-6124	285	7	)	)	PUNCT
ejpam-6124	285	8	∩	∩	NOUN
ejpam-6124	285	9	t	t	NOUN
ejpam-6124	286	1	|	|	NOUN
ejpam-6124	286	2	=	=	SYM
ejpam-6124	286	3	1	1	NUM
ejpam-6124	286	4	for	for	ADP
ejpam-6124	286	5	all	all	DET
ejpam-6124	286	6	ui	ui	NOUN
ejpam-6124	286	7	∈	∈	PROPN
ejpam-6124	286	8	v	v	NOUN
ejpam-6124	286	9	(	(	PUNCT
ejpam-6124	286	10	pn	pn	NOUN
ejpam-6124	286	11	)	)	PUNCT
ejpam-6124	286	12	.	.	PUNCT
ejpam-6124	287	1	therefore	therefore	ADV
ejpam-6124	287	2	,	,	PUNCT
ejpam-6124	287	3	t	t	PROPN
ejpam-6124	287	4	is	be	AUX
ejpam-6124	287	5	a	a	DET
ejpam-6124	287	6	γte	γte	NOUN
ejpam-6124	287	7	-	-	PUNCT
ejpam-6124	287	8	set	set	VERB
ejpam-6124	287	9	and	and	CCONJ
ejpam-6124	287	10	γte(pn	γte(pn	NUM
ejpam-6124	287	11	)	)	PUNCT
ejpam-6124	287	12	=	=	VERB
ejpam-6124	287	13	|t	|t	PROPN
ejpam-6124	288	1	|	|	ADV
ejpam-6124	288	2	=	=	SYM
ejpam-6124	288	3	n+	n+	PUNCT
ejpam-6124	288	4	2	2	NUM
ejpam-6124	288	5	2	2	NUM
ejpam-6124	288	6	.	.	PUNCT
ejpam-6124	289	1	case	case	NOUN
ejpam-6124	289	2	3	3	X
ejpam-6124	289	3	:	:	PUNCT
ejpam-6124	289	4	suppose	suppose	VERB
ejpam-6124	289	5	that	that	SCONJ
ejpam-6124	289	6	n	n	NUM
ejpam-6124	289	7	≡	≡	PROPN
ejpam-6124	289	8	3	3	NUM
ejpam-6124	289	9	(	(	PUNCT
ejpam-6124	289	10	mod	mod	NOUN
ejpam-6124	289	11	4	4	NUM
ejpam-6124	289	12	)	)	PUNCT
ejpam-6124	289	13	.	.	PUNCT
ejpam-6124	290	1	when	when	SCONJ
ejpam-6124	290	2	n	n	X
ejpam-6124	290	3	=	=	SYM
ejpam-6124	290	4	3	3	NUM
ejpam-6124	290	5	,	,	PUNCT
ejpam-6124	290	6	s	s	PART
ejpam-6124	290	7	=	=	PUNCT
ejpam-6124	290	8	{	{	PUNCT
ejpam-6124	290	9	u1	u1	NOUN
ejpam-6124	290	10	,	,	PUNCT
ejpam-6124	290	11	u2	u2	PROPN
ejpam-6124	290	12	}	}	PUNCT
ejpam-6124	290	13	is	be	AUX
ejpam-6124	290	14	a	a	DET
ejpam-6124	290	15	γte	γte	NOUN
ejpam-6124	290	16	-	-	PUNCT
ejpam-6124	290	17	set	set	NOUN
ejpam-6124	290	18	of	of	ADP
ejpam-6124	290	19	p3	p3	PROPN
ejpam-6124	290	20	since	since	SCONJ
ejpam-6124	290	21	|n(u1	|n(u1	ADJ
ejpam-6124	290	22	)	)	PUNCT
ejpam-6124	290	23	∩	∩	NOUN
ejpam-6124	290	24	s|	s|	VERB
ejpam-6124	290	25	=	=	SYM
ejpam-6124	290	26	1	1	NUM
ejpam-6124	290	27	,	,	PUNCT
ejpam-6124	290	28	|n(u2	|n(u2	NOUN
ejpam-6124	290	29	)	)	PUNCT
ejpam-6124	290	30	∩	∩	NOUN
ejpam-6124	290	31	s|	s|	VERB
ejpam-6124	290	32	=	=	SYM
ejpam-6124	290	33	1	1	NUM
ejpam-6124	290	34	and	and	CCONJ
ejpam-6124	290	35	|n(u3)∩s|	|n(u3)∩s|	PROPN
ejpam-6124	290	36	=	=	SYM
ejpam-6124	290	37	1	1	NUM
ejpam-6124	290	38	.	.	PUNCT
ejpam-6124	291	1	thus	thus	ADV
ejpam-6124	291	2	,	,	PUNCT
ejpam-6124	291	3	γte(p3	γte(p3	PROPN
ejpam-6124	291	4	)	)	PUNCT
ejpam-6124	291	5	=	=	SYM
ejpam-6124	291	6	|s|	|s|	NOUN
ejpam-6124	291	7	=	=	SYM
ejpam-6124	291	8	2	2	X
ejpam-6124	291	9	.	.	PUNCT
ejpam-6124	291	10	let	let	VERB
ejpam-6124	291	11	n	n	NOUN
ejpam-6124	291	12	=	=	SYM
ejpam-6124	291	13	7	7	X
ejpam-6124	291	14	.	.	PUNCT
ejpam-6124	291	15	by	by	ADP
ejpam-6124	291	16	proposition	proposition	NOUN
ejpam-6124	291	17	1	1	NUM
ejpam-6124	291	18	,	,	PUNCT
ejpam-6124	291	19	γt(p7	γt(p7	NUM
ejpam-6124	291	20	)	)	PUNCT
ejpam-6124	291	21	=	=	PUNCT
ejpam-6124	292	1	7	7	NUM
ejpam-6124	292	2	+	+	SYM
ejpam-6124	292	3	1	1	NUM
ejpam-6124	292	4	2	2	NUM
ejpam-6124	292	5	=	=	SYM
ejpam-6124	292	6	4	4	X
ejpam-6124	292	7	.	.	PUNCT
ejpam-6124	292	8	let	let	VERB
ejpam-6124	292	9	t	t	NOUN
ejpam-6124	292	10	=	=	SYM
ejpam-6124	292	11	{	{	PUNCT
ejpam-6124	292	12	u1	u1	NOUN
ejpam-6124	292	13	,	,	PUNCT
ejpam-6124	292	14	u2	u2	PROPN
ejpam-6124	292	15	,	,	PUNCT
ejpam-6124	292	16	u5	u5	PROPN
ejpam-6124	292	17	,	,	PUNCT
ejpam-6124	292	18	u6	u6	NOUN
ejpam-6124	292	19	}	}	PUNCT
ejpam-6124	292	20	.	.	PUNCT
ejpam-6124	293	1	clearly	clearly	ADV
ejpam-6124	293	2	,	,	PUNCT
ejpam-6124	293	3	|n(ui	|n(ui	PROPN
ejpam-6124	293	4	)	)	PUNCT
ejpam-6124	293	5	∩	∩	NOUN
ejpam-6124	293	6	t	t	NOUN
ejpam-6124	294	1	|	|	NOUN
ejpam-6124	294	2	=	=	SYM
ejpam-6124	294	3	1	1	NUM
ejpam-6124	294	4	for	for	ADP
ejpam-6124	294	5	all	all	DET
ejpam-6124	294	6	ui	ui	NOUN
ejpam-6124	294	7	∈	∈	PROPN
ejpam-6124	294	8	v	v	NOUN
ejpam-6124	294	9	(	(	PUNCT
ejpam-6124	294	10	p7	p7	PROPN
ejpam-6124	294	11	)	)	PUNCT
ejpam-6124	294	12	.	.	PUNCT
ejpam-6124	295	1	thus	thus	ADV
ejpam-6124	295	2	,	,	PUNCT
ejpam-6124	295	3	t	t	PROPN
ejpam-6124	295	4	is	be	AUX
ejpam-6124	295	5	a	a	DET
ejpam-6124	295	6	γte	γte	NOUN
ejpam-6124	295	7	-	-	PUNCT
ejpam-6124	295	8	set	set	NOUN
ejpam-6124	295	9	of	of	ADP
ejpam-6124	295	10	p7	p7	NOUN
ejpam-6124	295	11	,	,	PUNCT
ejpam-6124	295	12	and	and	CCONJ
ejpam-6124	295	13	γte(p7	γte(p7	PROPN
ejpam-6124	295	14	)	)	PUNCT
ejpam-6124	295	15	=	=	VERB
ejpam-6124	295	16	|t	|t	PROPN
ejpam-6124	296	1	|	|	ADV
ejpam-6124	296	2	=	=	NOUN
ejpam-6124	296	3	4	4	X
ejpam-6124	296	4	.	.	PUNCT
ejpam-6124	296	5	also	also	ADV
ejpam-6124	296	6	,	,	PUNCT
ejpam-6124	296	7	r	r	NOUN
ejpam-6124	296	8	=	=	SYM
ejpam-6124	296	9	{	{	PUNCT
ejpam-6124	296	10	u2	u2	NOUN
ejpam-6124	296	11	,	,	PUNCT
ejpam-6124	296	12	u3	u3	NOUN
ejpam-6124	296	13	,	,	PUNCT
ejpam-6124	296	14	u6	u6	PROPN
ejpam-6124	296	15	,	,	PUNCT
ejpam-6124	296	16	u7	u7	PROPN
ejpam-6124	296	17	}	}	PUNCT
ejpam-6124	296	18	is	be	AUX
ejpam-6124	296	19	another	another	DET
ejpam-6124	296	20	γte	γte	NOUN
ejpam-6124	296	21	-	-	PUNCT
ejpam-6124	296	22	set	set	NOUN
ejpam-6124	296	23	of	of	ADP
ejpam-6124	296	24	p7	p7	NOUN
ejpam-6124	296	25	since	since	SCONJ
ejpam-6124	296	26	|n(ui	|n(ui	PROPN
ejpam-6124	296	27	)	)	PUNCT
ejpam-6124	297	1	∩r|	∩r|	PROPN
ejpam-6124	297	2	=	=	PUNCT
ejpam-6124	297	3	1	1	NUM
ejpam-6124	297	4	for	for	ADP
ejpam-6124	297	5	all	all	DET
ejpam-6124	297	6	ui	ui	NOUN
ejpam-6124	297	7	∈	∈	PROPN
ejpam-6124	297	8	v	v	NOUN
ejpam-6124	297	9	(	(	PUNCT
ejpam-6124	297	10	p7	p7	PROPN
ejpam-6124	297	11	)	)	PUNCT
ejpam-6124	297	12	.	.	PUNCT
ejpam-6124	298	1	now	now	ADV
ejpam-6124	298	2	,	,	PUNCT
ejpam-6124	298	3	suppose	suppose	VERB
ejpam-6124	298	4	that	that	SCONJ
ejpam-6124	298	5	n	n	PROPN
ejpam-6124	298	6	>	>	X
ejpam-6124	298	7	7	7	NUM
ejpam-6124	298	8	,	,	PUNCT
ejpam-6124	298	9	let	let	VERB
ejpam-6124	298	10	p	p	NOUN
ejpam-6124	298	11	=	=	PUNCT
ejpam-6124	298	12	n−3	n−3	PROPN
ejpam-6124	298	13	4	4	NUM
ejpam-6124	298	14	and	and	CCONJ
ejpam-6124	298	15	j	j	NOUN
ejpam-6124	298	16	=	=	SYM
ejpam-6124	298	17	1	1	NUM
ejpam-6124	298	18	,	,	PUNCT
ejpam-6124	298	19	2	2	NUM
ejpam-6124	298	20	,	,	PUNCT
ejpam-6124	298	21	.	.	PUNCT
ejpam-6124	298	22	.	.	PUNCT
ejpam-6124	298	23	.	.	PUNCT
ejpam-6124	299	1	,	,	PUNCT
ejpam-6124	299	2	p−	p−	NOUN
ejpam-6124	299	3	1	1	NUM
ejpam-6124	299	4	,	,	PUNCT
ejpam-6124	299	5	p.	p.	NOUN
ejpam-6124	299	6	group	group	NOUN
ejpam-6124	299	7	the	the	DET
ejpam-6124	299	8	vertices	vertex	NOUN
ejpam-6124	299	9	of	of	ADP
ejpam-6124	299	10	pn	pn	NOUN
ejpam-6124	299	11	into	into	ADP
ejpam-6124	299	12	p	p	PROPN
ejpam-6124	299	13	disjoint	disjoint	PROPN
ejpam-6124	299	14	subsets	subset	NOUN
ejpam-6124	299	15	rj	rj	PROPN
ejpam-6124	299	16	,	,	PUNCT
ejpam-6124	299	17	such	such	ADJ
ejpam-6124	299	18	that	that	SCONJ
ejpam-6124	299	19	r1	r1	NOUN
ejpam-6124	299	20	=	=	SYM
ejpam-6124	299	21	{	{	PUNCT
ejpam-6124	299	22	u1	u1	NOUN
ejpam-6124	299	23	,	,	PUNCT
ejpam-6124	299	24	u2	u2	NOUN
ejpam-6124	299	25	,	,	PUNCT
ejpam-6124	299	26	u3	u3	NOUN
ejpam-6124	299	27	,	,	PUNCT
ejpam-6124	299	28	u4	u4	PROPN
ejpam-6124	299	29	}	}	PUNCT
ejpam-6124	299	30	,	,	PUNCT
ejpam-6124	299	31	r2	r2	PROPN
ejpam-6124	299	32	=	=	SYM
ejpam-6124	299	33	{	{	PUNCT
ejpam-6124	299	34	u5	u5	PROPN
ejpam-6124	299	35	,	,	PUNCT
ejpam-6124	299	36	u6	u6	PROPN
ejpam-6124	299	37	,	,	PUNCT
ejpam-6124	299	38	u7	u7	PROPN
ejpam-6124	299	39	,	,	PUNCT
ejpam-6124	299	40	u8	u8	PROPN
ejpam-6124	299	41	}	}	PUNCT
ejpam-6124	299	42	,	,	PUNCT
ejpam-6124	299	43	r3	r3	PROPN
ejpam-6124	299	44	=	=	SYM
ejpam-6124	299	45	{	{	PUNCT
ejpam-6124	299	46	u9	u9	PROPN
ejpam-6124	299	47	,	,	PUNCT
ejpam-6124	299	48	u10	u10	PROPN
ejpam-6124	299	49	,	,	PUNCT
ejpam-6124	299	50	u11	u11	PROPN
ejpam-6124	299	51	,	,	PUNCT
ejpam-6124	299	52	u12	u12	PROPN
ejpam-6124	299	53	}	}	PUNCT
ejpam-6124	299	54	,	,	PUNCT
ejpam-6124	299	55	...	...	PUNCT
ejpam-6124	300	1	rp−1	rp−1	NOUN
ejpam-6124	300	2	=	=	SYM
ejpam-6124	300	3	{	{	PUNCT
ejpam-6124	300	4	un−10	un−10	PROPN
ejpam-6124	300	5	,	,	PUNCT
ejpam-6124	300	6	un−9	un−9	PROPN
ejpam-6124	300	7	,	,	PUNCT
ejpam-6124	300	8	un−8	un−8	ADJ
ejpam-6124	300	9	,	,	PUNCT
ejpam-6124	300	10	un−7	un−7	NOUN
ejpam-6124	300	11	}	}	PUNCT
ejpam-6124	300	12	,	,	PUNCT
ejpam-6124	300	13	and	and	CCONJ
ejpam-6124	300	14	rp	rp	NOUN
ejpam-6124	300	15	=	=	SYM
ejpam-6124	300	16	{	{	PUNCT
ejpam-6124	300	17	un−6	un−6	PROPN
ejpam-6124	300	18	,	,	PUNCT
ejpam-6124	300	19	un−5	un−5	PROPN
ejpam-6124	300	20	,	,	PUNCT
ejpam-6124	300	21	un−4	un−4	NOUN
ejpam-6124	300	22	,	,	PUNCT
ejpam-6124	300	23	un−3	un−3	ADJ
ejpam-6124	300	24	,	,	PUNCT
ejpam-6124	300	25	un−2	un−2	PROPN
ejpam-6124	300	26	,	,	PUNCT
ejpam-6124	300	27	un−1	un−1	PROPN
ejpam-6124	300	28	,	,	PUNCT
ejpam-6124	300	29	un	un	ADJ
ejpam-6124	300	30	}	}	PUNCT
ejpam-6124	300	31	where	where	SCONJ
ejpam-6124	300	32	|rj	|rj	PART
ejpam-6124	300	33	|	|	ADV
ejpam-6124	300	34	=	=	SYM
ejpam-6124	300	35	4	4	NUM
ejpam-6124	300	36	for	for	ADP
ejpam-6124	300	37	j	j	PROPN
ejpam-6124	300	38	=	=	SYM
ejpam-6124	300	39	1	1	NUM
ejpam-6124	300	40	,	,	PUNCT
ejpam-6124	300	41	2	2	NUM
ejpam-6124	300	42	,	,	PUNCT
ejpam-6124	300	43	.	.	PUNCT
ejpam-6124	300	44	.	.	PUNCT
ejpam-6124	300	45	.	.	PUNCT
ejpam-6124	301	1	,	,	PUNCT
ejpam-6124	301	2	p−	p−	NOUN
ejpam-6124	301	3	1	1	NUM
ejpam-6124	301	4	and	and	CCONJ
ejpam-6124	301	5	|rp|	|rp|	NUM
ejpam-6124	301	6	=	=	PUNCT
ejpam-6124	301	7	7	7	X
ejpam-6124	301	8	.	.	PUNCT
ejpam-6124	302	1	let	let	VERB
ejpam-6124	302	2	t	t	NOUN
ejpam-6124	302	3	=	=	SYM
ejpam-6124	302	4	{	{	PUNCT
ejpam-6124	302	5	u1	u1	NOUN
ejpam-6124	302	6	,	,	PUNCT
ejpam-6124	302	7	u2	u2	PROPN
ejpam-6124	302	8	,	,	PUNCT
ejpam-6124	302	9	u5	u5	PROPN
ejpam-6124	302	10	,	,	PUNCT
ejpam-6124	302	11	u6	u6	PROPN
ejpam-6124	302	12	,	,	PUNCT
ejpam-6124	302	13	u9	u9	PROPN
ejpam-6124	302	14	,	,	PUNCT
ejpam-6124	302	15	u10	u10	PROPN
ejpam-6124	302	16	,	,	PUNCT
ejpam-6124	302	17	.	.	PUNCT
ejpam-6124	302	18	.	.	PUNCT
ejpam-6124	303	1	.	.	PUNCT
ejpam-6124	304	1	,	,	PUNCT
ejpam-6124	304	2	un−10	un−10	PROPN
ejpam-6124	304	3	,	,	PUNCT
ejpam-6124	304	4	un−9	un−9	PROPN
ejpam-6124	304	5	,	,	PUNCT
ejpam-6124	304	6	un−6	un−6	PROPN
ejpam-6124	304	7	,	,	PUNCT
ejpam-6124	304	8	un−5	un−5	PROPN
ejpam-6124	304	9	,	,	PUNCT
ejpam-6124	304	10	un−2	un−2	PROPN
ejpam-6124	304	11	,	,	PUNCT
ejpam-6124	304	12	un−1	un−1	PROPN
ejpam-6124	304	13	}	}	PUNCT
ejpam-6124	304	14	,	,	PUNCT
ejpam-6124	304	15	where	where	SCONJ
ejpam-6124	304	16	t	t	PROPN
ejpam-6124	304	17	is	be	AUX
ejpam-6124	304	18	formed	form	VERB
ejpam-6124	304	19	by	by	ADP
ejpam-6124	304	20	getting	get	VERB
ejpam-6124	304	21	2	2	NUM
ejpam-6124	304	22	vertices	vertex	NOUN
ejpam-6124	304	23	in	in	ADP
ejpam-6124	304	24	each	each	DET
ejpam-6124	304	25	rj	rj	PROPN
ejpam-6124	304	26	for	for	ADP
ejpam-6124	304	27	j	j	PROPN
ejpam-6124	304	28	=	=	SYM
ejpam-6124	304	29	1	1	NUM
ejpam-6124	304	30	,	,	PUNCT
ejpam-6124	304	31	2	2	NUM
ejpam-6124	304	32	,	,	PUNCT
ejpam-6124	304	33	.	.	PUNCT
ejpam-6124	304	34	.	.	PUNCT
ejpam-6124	305	1	.	.	PUNCT
ejpam-6124	306	1	,	,	PUNCT
ejpam-6124	306	2	p−	p−	NOUN
ejpam-6124	306	3	1	1	NUM
ejpam-6124	306	4	and	and	CCONJ
ejpam-6124	306	5	4	4	NUM
ejpam-6124	306	6	vertices	vertex	NOUN
ejpam-6124	306	7	in	in	ADP
ejpam-6124	306	8	rp	rp	NOUN
ejpam-6124	306	9	.	.	PUNCT
ejpam-6124	307	1	it	it	PRON
ejpam-6124	307	2	follows	follow	VERB
ejpam-6124	307	3	that	that	PRON
ejpam-6124	307	4	|t	|t	VERB
ejpam-6124	308	1	|	|	ADV
ejpam-6124	309	1	=	=	SYM
ejpam-6124	309	2	2(p−	2(p−	NUM
ejpam-6124	309	3	1	1	NUM
ejpam-6124	309	4	)	)	PUNCT
ejpam-6124	309	5	+	+	CCONJ
ejpam-6124	309	6	4	4	NUM
ejpam-6124	309	7	=	=	SYM
ejpam-6124	309	8	2p+	2p+	NUM
ejpam-6124	309	9	2	2	NUM
ejpam-6124	309	10	=	=	SYM
ejpam-6124	309	11	2	2	NUM
ejpam-6124	309	12	(	(	PUNCT
ejpam-6124	309	13	n−	n−	NOUN
ejpam-6124	309	14	3	3	NUM
ejpam-6124	309	15	4	4	NUM
ejpam-6124	309	16	)	)	PUNCT
ejpam-6124	309	17	+	+	CCONJ
ejpam-6124	309	18	2	2	X
ejpam-6124	309	19	=	=	SYM
ejpam-6124	309	20	n+	n+	NUM
ejpam-6124	309	21	1	1	NUM
ejpam-6124	309	22	2	2	NUM
ejpam-6124	309	23	.	.	PUNCT
ejpam-6124	310	1	also	also	ADV
ejpam-6124	310	2	,	,	PUNCT
ejpam-6124	310	3	note	note	VERB
ejpam-6124	310	4	that	that	SCONJ
ejpam-6124	310	5	n(t	n(t	PROPN
ejpam-6124	310	6	)	)	PUNCT
ejpam-6124	311	1	=	=	SYM
ejpam-6124	311	2	v	v	X
ejpam-6124	311	3	(	(	PUNCT
ejpam-6124	311	4	pn	pn	NOUN
ejpam-6124	311	5	)	)	PUNCT
ejpam-6124	311	6	.	.	PUNCT
ejpam-6124	312	1	thus	thus	ADV
ejpam-6124	312	2	,	,	PUNCT
ejpam-6124	312	3	t	t	PROPN
ejpam-6124	312	4	is	be	AUX
ejpam-6124	312	5	a	a	DET
ejpam-6124	312	6	γt	γt	NOUN
ejpam-6124	312	7	-	-	NOUN
ejpam-6124	312	8	set	set	NOUN
ejpam-6124	312	9	of	of	ADP
ejpam-6124	312	10	pn	pn	PROPN
ejpam-6124	312	11	by	by	ADP
ejpam-6124	312	12	proposition	proposition	NOUN
ejpam-6124	312	13	1	1	NUM
ejpam-6124	312	14	.	.	PUNCT
ejpam-6124	313	1	it	it	PRON
ejpam-6124	313	2	is	be	AUX
ejpam-6124	313	3	also	also	ADV
ejpam-6124	313	4	clear	clear	ADJ
ejpam-6124	313	5	that	that	SCONJ
ejpam-6124	313	6	|n(ui	|n(ui	NOUN
ejpam-6124	313	7	)	)	PUNCT
ejpam-6124	313	8	∩	∩	NOUN
ejpam-6124	313	9	t	t	NOUN
ejpam-6124	314	1	|	|	NOUN
ejpam-6124	314	2	=	=	SYM
ejpam-6124	314	3	1	1	NUM
ejpam-6124	314	4	for	for	ADP
ejpam-6124	314	5	all	all	DET
ejpam-6124	314	6	ui	ui	NOUN
ejpam-6124	314	7	∈	∈	PROPN
ejpam-6124	314	8	v	v	NOUN
ejpam-6124	314	9	(	(	PUNCT
ejpam-6124	314	10	pn	pn	NOUN
ejpam-6124	314	11	)	)	PUNCT
ejpam-6124	314	12	.	.	PUNCT
ejpam-6124	315	1	therefore	therefore	ADV
ejpam-6124	315	2	,	,	PUNCT
ejpam-6124	315	3	t	t	PROPN
ejpam-6124	315	4	is	be	AUX
ejpam-6124	315	5	a	a	DET
ejpam-6124	315	6	γte	γte	NOUN
ejpam-6124	315	7	-	-	PUNCT
ejpam-6124	315	8	set	set	NOUN
ejpam-6124	315	9	.	.	PUNCT
ejpam-6124	316	1	this	this	PRON
ejpam-6124	316	2	implies	imply	VERB
ejpam-6124	316	3	that	that	SCONJ
ejpam-6124	316	4	γte(pn	γte(pn	ADV
ejpam-6124	316	5	)	)	PUNCT
ejpam-6124	316	6	=	=	SYM
ejpam-6124	316	7	|t	|t	VERB
ejpam-6124	317	1	|	|	ADV
ejpam-6124	317	2	=	=	SYM
ejpam-6124	317	3	n+	n+	PUNCT
ejpam-6124	317	4	1	1	NUM
ejpam-6124	317	5	2	2	NUM
ejpam-6124	317	6	.	.	PUNCT
ejpam-6124	318	1	r.	r.	PROPN
ejpam-6124	318	2	g.	g.	PROPN
ejpam-6124	318	3	aguinod	aguinod	PROPN
ejpam-6124	318	4	,	,	PUNCT
ejpam-6124	318	5	e.	e.	PROPN
ejpam-6124	318	6	m.	m.	PROPN
ejpam-6124	318	7	kiunisala	kiunisala	PROPN
ejpam-6124	318	8	,	,	PUNCT
ejpam-6124	318	9	c.	c.	PROPN
ejpam-6124	318	10	l.	l.	PROPN
ejpam-6124	318	11	armada	armada	PROPN
ejpam-6124	318	12	/	/	SYM
ejpam-6124	318	13	eur	eur	PROPN
ejpam-6124	318	14	.	.	PUNCT
ejpam-6124	319	1	j.	j.	PROPN
ejpam-6124	319	2	pure	pure	PROPN
ejpam-6124	319	3	appl	appl	PROPN
ejpam-6124	319	4	.	.	PROPN
ejpam-6124	319	5	math	math	PROPN
ejpam-6124	319	6	,	,	PUNCT
ejpam-6124	319	7	18	18	NUM
ejpam-6124	319	8	(	(	PUNCT
ejpam-6124	319	9	2	2	NUM
ejpam-6124	319	10	)	)	PUNCT
ejpam-6124	319	11	(	(	PUNCT
ejpam-6124	319	12	2025	2025	NUM
ejpam-6124	319	13	)	)	PUNCT
ejpam-6124	319	14	,	,	PUNCT
ejpam-6124	319	15	6124	6124	NUM
ejpam-6124	319	16	12	12	NUM
ejpam-6124	319	17	of	of	ADP
ejpam-6124	319	18	26	26	NUM
ejpam-6124	319	19	theorem	theorem	NOUN
ejpam-6124	319	20	8	8	NUM
ejpam-6124	319	21	.	.	PUNCT
ejpam-6124	320	1	let	let	VERB
ejpam-6124	320	2	n	n	PRON
ejpam-6124	320	3	be	be	AUX
ejpam-6124	320	4	a	a	DET
ejpam-6124	320	5	positive	positive	ADJ
ejpam-6124	320	6	integer	integer	NOUN
ejpam-6124	320	7	such	such	ADJ
ejpam-6124	320	8	that	that	SCONJ
ejpam-6124	320	9	n	n	NUM
ejpam-6124	320	10	≥	≥	NOUN
ejpam-6124	320	11	3	3	NUM
ejpam-6124	320	12	.	.	PUNCT
ejpam-6124	321	1	if	if	SCONJ
ejpam-6124	321	2	n	n	X
ejpam-6124	321	3	̸≡	̸≡	VERB
ejpam-6124	321	4	0	0	PUNCT
ejpam-6124	321	5	(	(	PUNCT
ejpam-6124	321	6	mod	mod	PROPN
ejpam-6124	321	7	4	4	NUM
ejpam-6124	321	8	)	)	PUNCT
ejpam-6124	321	9	,	,	PUNCT
ejpam-6124	321	10	then	then	ADV
ejpam-6124	321	11	the	the	DET
ejpam-6124	321	12	cycle	cycle	NOUN
ejpam-6124	321	13	graph	graph	NOUN
ejpam-6124	321	14	cn	cn	PROPN
ejpam-6124	321	15	is	be	AUX
ejpam-6124	321	16	a	a	DET
ejpam-6124	321	17	non−	non−	PROPN
ejpam-6124	321	18	γte	γte	NOUN
ejpam-6124	321	19	−	−	NOUN
ejpam-6124	321	20	graph	graph	NOUN
ejpam-6124	321	21	.	.	PUNCT
ejpam-6124	322	1	proof	proof	NOUN
ejpam-6124	322	2	.	.	PUNCT
ejpam-6124	323	1	let	let	VERB
ejpam-6124	323	2	v	v	X
ejpam-6124	323	3	(	(	PUNCT
ejpam-6124	323	4	cn	cn	PROPN
ejpam-6124	323	5	)	)	PUNCT
ejpam-6124	323	6	=	=	SYM
ejpam-6124	323	7	{	{	PUNCT
ejpam-6124	323	8	u1	u1	NOUN
ejpam-6124	323	9	,	,	PUNCT
ejpam-6124	323	10	u2	u2	NOUN
ejpam-6124	323	11	,	,	PUNCT
ejpam-6124	323	12	u3	u3	NOUN
ejpam-6124	323	13	,	,	PUNCT
ejpam-6124	323	14	.	.	PUNCT
ejpam-6124	323	15	.	.	PUNCT
ejpam-6124	324	1	.	.	PUNCT
ejpam-6124	325	1	,	,	PUNCT
ejpam-6124	325	2	un−1	un−1	PROPN
ejpam-6124	325	3	,	,	PUNCT
ejpam-6124	325	4	un	un	ADJ
ejpam-6124	325	5	}	}	PUNCT
ejpam-6124	325	6	with	with	ADP
ejpam-6124	325	7	deg(ui	deg(ui	NOUN
ejpam-6124	325	8	)	)	PUNCT
ejpam-6124	325	9	=	=	SYM
ejpam-6124	325	10	2	2	NUM
ejpam-6124	325	11	for	for	ADP
ejpam-6124	325	12	all	all	PRON
ejpam-6124	325	13	ui	ui	NOUN
ejpam-6124	325	14	∈	∈	PROPN
ejpam-6124	325	15	v	v	NOUN
ejpam-6124	325	16	(	(	PUNCT
ejpam-6124	325	17	cn	cn	PROPN
ejpam-6124	325	18	)	)	PUNCT
ejpam-6124	325	19	.	.	PUNCT
ejpam-6124	326	1	consider	consider	VERB
ejpam-6124	326	2	the	the	DET
ejpam-6124	326	3	following	follow	VERB
ejpam-6124	326	4	cases	case	NOUN
ejpam-6124	326	5	:	:	PUNCT
ejpam-6124	326	6	case	case	NOUN
ejpam-6124	326	7	1	1	NUM
ejpam-6124	326	8	:	:	PUNCT
ejpam-6124	326	9	n	n	NUM
ejpam-6124	326	10	≡	≡	PROPN
ejpam-6124	326	11	1	1	NUM
ejpam-6124	326	12	(	(	PUNCT
ejpam-6124	326	13	mod	mod	NOUN
ejpam-6124	326	14	4	4	X
ejpam-6124	326	15	)	)	PUNCT
ejpam-6124	326	16	let	let	VERB
ejpam-6124	326	17	n	n	NOUN
ejpam-6124	326	18	=	=	SYM
ejpam-6124	326	19	5	5	X
ejpam-6124	326	20	.	.	PUNCT
ejpam-6124	326	21	by	by	ADP
ejpam-6124	326	22	proposition	proposition	NOUN
ejpam-6124	326	23	1	1	NUM
ejpam-6124	326	24	,	,	PUNCT
ejpam-6124	326	25	γt(c5	γt(c5	NOUN
ejpam-6124	326	26	)	)	PUNCT
ejpam-6124	326	27	=	=	SYM
ejpam-6124	327	1	3	3	X
ejpam-6124	327	2	.	.	PUNCT
ejpam-6124	327	3	clearly	clearly	ADV
ejpam-6124	327	4	,	,	PUNCT
ejpam-6124	327	5	t1	t1	NOUN
ejpam-6124	327	6	=	=	PUNCT
ejpam-6124	327	7	{	{	PUNCT
ejpam-6124	327	8	u1	u1	NOUN
ejpam-6124	327	9	,	,	PUNCT
ejpam-6124	327	10	u2	u2	NOUN
ejpam-6124	327	11	,	,	PUNCT
ejpam-6124	327	12	u3	u3	NOUN
ejpam-6124	327	13	}	}	PUNCT
ejpam-6124	327	14	,	,	PUNCT
ejpam-6124	327	15	t2	t2	NOUN
ejpam-6124	327	16	=	=	SYM
ejpam-6124	327	17	{	{	PUNCT
ejpam-6124	327	18	u2	u2	PROPN
ejpam-6124	327	19	,	,	PUNCT
ejpam-6124	327	20	u3	u3	NOUN
ejpam-6124	327	21	,	,	PUNCT
ejpam-6124	327	22	u4	u4	PROPN
ejpam-6124	327	23	}	}	PUNCT
ejpam-6124	327	24	,	,	PUNCT
ejpam-6124	327	25	t3	t3	PROPN
ejpam-6124	327	26	=	=	SYM
ejpam-6124	327	27	{	{	PUNCT
ejpam-6124	327	28	u3	u3	PROPN
ejpam-6124	327	29	,	,	PUNCT
ejpam-6124	327	30	u4	u4	PROPN
ejpam-6124	327	31	,	,	PUNCT
ejpam-6124	327	32	u5	u5	PROPN
ejpam-6124	327	33	}	}	PUNCT
ejpam-6124	327	34	,	,	PUNCT
ejpam-6124	327	35	t4	t4	PROPN
ejpam-6124	327	36	=	=	PROPN
ejpam-6124	327	37	{	{	PUNCT
ejpam-6124	327	38	u4	u4	PROPN
ejpam-6124	327	39	,	,	PUNCT
ejpam-6124	327	40	u5	u5	PROPN
ejpam-6124	327	41	,	,	PUNCT
ejpam-6124	327	42	u1	u1	NOUN
ejpam-6124	327	43	}	}	PUNCT
ejpam-6124	327	44	,	,	PUNCT
ejpam-6124	327	45	and	and	CCONJ
ejpam-6124	327	46	t5	t5	PROPN
ejpam-6124	327	47	=	=	SYM
ejpam-6124	327	48	{	{	PUNCT
ejpam-6124	327	49	u5	u5	PROPN
ejpam-6124	327	50	,	,	PUNCT
ejpam-6124	327	51	u1	u1	NOUN
ejpam-6124	327	52	,	,	PUNCT
ejpam-6124	327	53	u2	u2	PROPN
ejpam-6124	327	54	}	}	PUNCT
ejpam-6124	327	55	are	be	AUX
ejpam-6124	327	56	the	the	DET
ejpam-6124	327	57	only	only	ADJ
ejpam-6124	327	58	γt	γt	NOUN
ejpam-6124	327	59	-	-	NOUN
ejpam-6124	327	60	sets	set	NOUN
ejpam-6124	327	61	of	of	ADP
ejpam-6124	327	62	c5	c5	PROPN
ejpam-6124	327	63	.	.	PUNCT
ejpam-6124	328	1	for	for	ADP
ejpam-6124	328	2	i	i	PRON
ejpam-6124	328	3	=	=	NOUN
ejpam-6124	328	4	1	1	NUM
ejpam-6124	328	5	,	,	PUNCT
ejpam-6124	328	6	2	2	NUM
ejpam-6124	328	7	,	,	PUNCT
ejpam-6124	328	8	3	3	NUM
ejpam-6124	328	9	,	,	PUNCT
ejpam-6124	328	10	...	...	PUNCT
ejpam-6124	328	11	,	,	PUNCT
ejpam-6124	328	12	5	5	NUM
ejpam-6124	328	13	,	,	PUNCT
ejpam-6124	328	14	|ti|	|ti|	PROPN
ejpam-6124	328	15	is	be	AUX
ejpam-6124	328	16	odd	odd	ADJ
ejpam-6124	328	17	and	and	CCONJ
ejpam-6124	328	18	so	so	ADV
ejpam-6124	328	19	,	,	PUNCT
ejpam-6124	328	20	by	by	ADP
ejpam-6124	328	21	theorem	theorem	NOUN
ejpam-6124	328	22	5	5	NUM
ejpam-6124	328	23	,	,	PUNCT
ejpam-6124	328	24	ti	ti	PROPN
ejpam-6124	328	25	is	be	AUX
ejpam-6124	328	26	not	not	PART
ejpam-6124	328	27	a	a	DET
ejpam-6124	328	28	γte	γte	NOUN
ejpam-6124	328	29	−	−	PROPN
ejpam-6124	328	30	set	set	NOUN
ejpam-6124	328	31	.	.	PUNCT
ejpam-6124	329	1	suppose	suppose	VERB
ejpam-6124	329	2	that	that	SCONJ
ejpam-6124	329	3	t	t	PROPN
ejpam-6124	329	4	has	have	VERB
ejpam-6124	329	5	4	4	NUM
ejpam-6124	329	6	vertices	vertex	NOUN
ejpam-6124	329	7	.	.	PUNCT
ejpam-6124	330	1	then	then	ADV
ejpam-6124	330	2	there	there	PRON
ejpam-6124	330	3	exists	exist	VERB
ejpam-6124	330	4	one	one	NUM
ejpam-6124	330	5	vertex	vertex	NOUN
ejpam-6124	330	6	,	,	PUNCT
ejpam-6124	330	7	say	say	VERB
ejpam-6124	330	8	ui	ui	PROPN
ejpam-6124	330	9	,	,	PUNCT
ejpam-6124	330	10	such	such	ADJ
ejpam-6124	330	11	that	that	SCONJ
ejpam-6124	330	12	ui	ui	PROPN
ejpam-6124	330	13	is	be	AUX
ejpam-6124	330	14	adjacent	adjacent	ADJ
ejpam-6124	330	15	to	to	ADP
ejpam-6124	330	16	2	2	NUM
ejpam-6124	330	17	vertices	vertex	NOUN
ejpam-6124	330	18	of	of	ADP
ejpam-6124	330	19	c5	c5	PROPN
ejpam-6124	330	20	,	,	PUNCT
ejpam-6124	330	21	that	that	ADV
ejpam-6124	330	22	is	is	ADV
ejpam-6124	330	23	,	,	PUNCT
ejpam-6124	330	24	|n(ui	|n(ui	PROPN
ejpam-6124	330	25	)	)	PUNCT
ejpam-6124	331	1	∩	∩	NOUN
ejpam-6124	331	2	t	t	NOUN
ejpam-6124	332	1	|	|	NOUN
ejpam-6124	332	2	=	=	NOUN
ejpam-6124	332	3	2	2	NUM
ejpam-6124	332	4	.	.	PUNCT
ejpam-6124	332	5	thus	thus	ADV
ejpam-6124	332	6	,	,	PUNCT
ejpam-6124	332	7	t	t	PROPN
ejpam-6124	332	8	is	be	AUX
ejpam-6124	332	9	not	not	PART
ejpam-6124	332	10	a	a	DET
ejpam-6124	332	11	γte	γte	NOUN
ejpam-6124	332	12	−	−	PROPN
ejpam-6124	332	13	set	set	NOUN
ejpam-6124	332	14	.	.	PUNCT
ejpam-6124	333	1	since	since	SCONJ
ejpam-6124	333	2	there	there	PRON
ejpam-6124	333	3	is	be	VERB
ejpam-6124	333	4	no	no	DET
ejpam-6124	333	5	possible	possible	ADJ
ejpam-6124	333	6	way	way	NOUN
ejpam-6124	333	7	to	to	PART
ejpam-6124	333	8	create	create	VERB
ejpam-6124	333	9	a	a	DET
ejpam-6124	333	10	set	set	NOUN
ejpam-6124	333	11	that	that	PRON
ejpam-6124	333	12	is	be	AUX
ejpam-6124	333	13	both	both	PRON
ejpam-6124	333	14	total	total	ADJ
ejpam-6124	333	15	and	and	CCONJ
ejpam-6124	333	16	exact	exact	ADJ
ejpam-6124	333	17	dominating	dominating	NOUN
ejpam-6124	333	18	set	set	NOUN
ejpam-6124	333	19	,	,	PUNCT
ejpam-6124	333	20	c5	c5	PROPN
ejpam-6124	333	21	is	be	AUX
ejpam-6124	333	22	a	a	DET
ejpam-6124	333	23	non−	non−	PROPN
ejpam-6124	333	24	γte	γte	NOUN
ejpam-6124	333	25	−	−	NOUN
ejpam-6124	333	26	graph	graph	NOUN
ejpam-6124	333	27	.	.	PUNCT
ejpam-6124	334	1	now	now	ADV
ejpam-6124	334	2	,	,	PUNCT
ejpam-6124	334	3	suppose	suppose	VERB
ejpam-6124	334	4	that	that	SCONJ
ejpam-6124	334	5	n	n	PROPN
ejpam-6124	334	6	>	>	X
ejpam-6124	334	7	5	5	X
ejpam-6124	334	8	.	.	PUNCT
ejpam-6124	334	9	let	let	VERB
ejpam-6124	334	10	p	p	NOUN
ejpam-6124	334	11	=	=	PUNCT
ejpam-6124	334	12	n−1	n−1	PROPN
ejpam-6124	334	13	4	4	NUM
ejpam-6124	334	14	and	and	CCONJ
ejpam-6124	334	15	j	j	NOUN
ejpam-6124	334	16	=	=	SYM
ejpam-6124	334	17	1	1	NUM
ejpam-6124	334	18	,	,	PUNCT
ejpam-6124	334	19	2	2	NUM
ejpam-6124	334	20	,	,	PUNCT
ejpam-6124	334	21	.	.	PUNCT
ejpam-6124	334	22	.	.	PUNCT
ejpam-6124	335	1	.	.	PUNCT
ejpam-6124	336	1	,	,	PUNCT
ejpam-6124	336	2	p−	p−	NOUN
ejpam-6124	336	3	1	1	NUM
ejpam-6124	336	4	,	,	PUNCT
ejpam-6124	336	5	p.	p.	NOUN
ejpam-6124	336	6	group	group	NOUN
ejpam-6124	336	7	the	the	DET
ejpam-6124	336	8	vertices	vertex	NOUN
ejpam-6124	336	9	of	of	ADP
ejpam-6124	336	10	cn	cn	PROPN
ejpam-6124	336	11	into	into	ADP
ejpam-6124	336	12	p	p	PROPN
ejpam-6124	336	13	disjoint	disjoint	PROPN
ejpam-6124	336	14	subsets	subset	NOUN
ejpam-6124	336	15	rj	rj	PROPN
ejpam-6124	336	16	,	,	PUNCT
ejpam-6124	336	17	such	such	ADJ
ejpam-6124	336	18	that	that	SCONJ
ejpam-6124	336	19	r1	r1	NOUN
ejpam-6124	336	20	=	=	SYM
ejpam-6124	336	21	{	{	PUNCT
ejpam-6124	336	22	u1	u1	NOUN
ejpam-6124	336	23	,	,	PUNCT
ejpam-6124	336	24	u2	u2	NOUN
ejpam-6124	336	25	,	,	PUNCT
ejpam-6124	336	26	u3	u3	NOUN
ejpam-6124	336	27	,	,	PUNCT
ejpam-6124	336	28	u4	u4	PROPN
ejpam-6124	336	29	}	}	PUNCT
ejpam-6124	336	30	,	,	PUNCT
ejpam-6124	336	31	r2	r2	PROPN
ejpam-6124	336	32	=	=	SYM
ejpam-6124	336	33	{	{	PUNCT
ejpam-6124	336	34	u5	u5	PROPN
ejpam-6124	336	35	,	,	PUNCT
ejpam-6124	336	36	u6	u6	PROPN
ejpam-6124	336	37	,	,	PUNCT
ejpam-6124	336	38	u7	u7	PROPN
ejpam-6124	336	39	,	,	PUNCT
ejpam-6124	336	40	u8	u8	PROPN
ejpam-6124	336	41	}	}	PUNCT
ejpam-6124	336	42	,	,	PUNCT
ejpam-6124	336	43	r3	r3	PROPN
ejpam-6124	336	44	=	=	SYM
ejpam-6124	336	45	{	{	PUNCT
ejpam-6124	336	46	u9	u9	PROPN
ejpam-6124	336	47	,	,	PUNCT
ejpam-6124	336	48	u10	u10	PROPN
ejpam-6124	336	49	,	,	PUNCT
ejpam-6124	336	50	u11	u11	PROPN
ejpam-6124	336	51	,	,	PUNCT
ejpam-6124	336	52	u12	u12	PROPN
ejpam-6124	336	53	}	}	PUNCT
ejpam-6124	336	54	,	,	PUNCT
ejpam-6124	336	55	...	...	PUNCT
ejpam-6124	337	1	rp−1	rp−1	NOUN
ejpam-6124	337	2	=	=	PUNCT
ejpam-6124	337	3	{	{	PUNCT
ejpam-6124	337	4	un−8	un−8	ADJ
ejpam-6124	337	5	,	,	PUNCT
ejpam-6124	337	6	un−7	un−7	PROPN
ejpam-6124	337	7	,	,	PUNCT
ejpam-6124	337	8	un−6	un−6	PROPN
ejpam-6124	337	9	,	,	PUNCT
ejpam-6124	337	10	un−5	un−5	PROPN
ejpam-6124	337	11	}	}	PUNCT
ejpam-6124	337	12	,	,	PUNCT
ejpam-6124	337	13	and	and	CCONJ
ejpam-6124	337	14	rp	rp	NOUN
ejpam-6124	337	15	=	=	SYM
ejpam-6124	337	16	{	{	PUNCT
ejpam-6124	337	17	un−4	un−4	NOUN
ejpam-6124	337	18	,	,	PUNCT
ejpam-6124	337	19	un−3	un−3	ADJ
ejpam-6124	337	20	,	,	PUNCT
ejpam-6124	337	21	un−2	un−2	PROPN
ejpam-6124	337	22	,	,	PUNCT
ejpam-6124	337	23	un−1	un−1	PROPN
ejpam-6124	337	24	,	,	PUNCT
ejpam-6124	337	25	un	un	ADJ
ejpam-6124	337	26	}	}	PUNCT
ejpam-6124	337	27	where	where	SCONJ
ejpam-6124	337	28	|rj	|rj	PART
ejpam-6124	337	29	|	|	ADV
ejpam-6124	337	30	=	=	SYM
ejpam-6124	337	31	4	4	NUM
ejpam-6124	337	32	for	for	ADP
ejpam-6124	337	33	j	j	PROPN
ejpam-6124	337	34	=	=	SYM
ejpam-6124	337	35	1	1	NUM
ejpam-6124	337	36	,	,	PUNCT
ejpam-6124	337	37	2	2	NUM
ejpam-6124	337	38	,	,	PUNCT
ejpam-6124	337	39	.	.	PUNCT
ejpam-6124	337	40	.	.	PUNCT
ejpam-6124	337	41	.	.	PUNCT
ejpam-6124	338	1	,	,	PUNCT
ejpam-6124	338	2	p−	p−	NOUN
ejpam-6124	338	3	1	1	NUM
ejpam-6124	338	4	and	and	CCONJ
ejpam-6124	338	5	|rp|	|rp|	NUM
ejpam-6124	338	6	=	=	SYM
ejpam-6124	338	7	5	5	X
ejpam-6124	338	8	.	.	PUNCT
ejpam-6124	338	9	let	let	VERB
ejpam-6124	338	10	t	t	NOUN
ejpam-6124	338	11	=	=	SYM
ejpam-6124	338	12	{	{	PUNCT
ejpam-6124	338	13	u2	u2	PROPN
ejpam-6124	338	14	,	,	PUNCT
ejpam-6124	338	15	u3	u3	NOUN
ejpam-6124	338	16	,	,	PUNCT
ejpam-6124	338	17	u6	u6	PROPN
ejpam-6124	338	18	,	,	PUNCT
ejpam-6124	338	19	u7	u7	PROPN
ejpam-6124	338	20	,	,	PUNCT
ejpam-6124	338	21	u10	u10	PROPN
ejpam-6124	338	22	,	,	PUNCT
ejpam-6124	338	23	u11	u11	PROPN
ejpam-6124	338	24	,	,	PUNCT
ejpam-6124	338	25	.	.	PUNCT
ejpam-6124	338	26	.	.	PUNCT
ejpam-6124	339	1	.	.	PUNCT
ejpam-6124	340	1	,	,	PUNCT
ejpam-6124	340	2	un−7	un−7	PROPN
ejpam-6124	340	3	,	,	PUNCT
ejpam-6124	340	4	un−6	un−6	PROPN
ejpam-6124	340	5	,	,	PUNCT
ejpam-6124	340	6	un−3	un−3	NOUN
ejpam-6124	340	7	,	,	PUNCT
ejpam-6124	340	8	un−2	un−2	PROPN
ejpam-6124	340	9	,	,	PUNCT
ejpam-6124	340	10	un−1	un−1	PROPN
ejpam-6124	340	11	}	}	PUNCT
ejpam-6124	340	12	,	,	PUNCT
ejpam-6124	340	13	where	where	SCONJ
ejpam-6124	340	14	t	t	PROPN
ejpam-6124	340	15	is	be	AUX
ejpam-6124	340	16	formed	form	VERB
ejpam-6124	340	17	by	by	ADP
ejpam-6124	340	18	getting	get	VERB
ejpam-6124	340	19	2	2	NUM
ejpam-6124	340	20	vertices	vertex	NOUN
ejpam-6124	340	21	in	in	ADP
ejpam-6124	340	22	each	each	DET
ejpam-6124	340	23	rj	rj	PROPN
ejpam-6124	340	24	for	for	ADP
ejpam-6124	340	25	j	j	PROPN
ejpam-6124	340	26	=	=	SYM
ejpam-6124	340	27	1	1	NUM
ejpam-6124	340	28	,	,	PUNCT
ejpam-6124	340	29	2	2	NUM
ejpam-6124	340	30	,	,	PUNCT
ejpam-6124	340	31	.	.	PUNCT
ejpam-6124	340	32	.	.	PUNCT
ejpam-6124	341	1	.	.	PUNCT
ejpam-6124	342	1	,	,	PUNCT
ejpam-6124	342	2	p−	p−	NOUN
ejpam-6124	342	3	1	1	NUM
ejpam-6124	342	4	and	and	CCONJ
ejpam-6124	342	5	3	3	NUM
ejpam-6124	342	6	vertices	vertex	NOUN
ejpam-6124	342	7	in	in	ADP
ejpam-6124	342	8	rp	rp	NOUN
ejpam-6124	342	9	.	.	PUNCT
ejpam-6124	343	1	it	it	PRON
ejpam-6124	343	2	follows	follow	VERB
ejpam-6124	343	3	that	that	PRON
ejpam-6124	343	4	|t	|t	VERB
ejpam-6124	344	1	|	|	ADV
ejpam-6124	345	1	=	=	SYM
ejpam-6124	345	2	2(p−	2(p−	NUM
ejpam-6124	345	3	1	1	NUM
ejpam-6124	345	4	)	)	PUNCT
ejpam-6124	345	5	+	+	CCONJ
ejpam-6124	346	1	3	3	NUM
ejpam-6124	346	2	=	=	SYM
ejpam-6124	346	3	2p+	2p+	NUM
ejpam-6124	346	4	1	1	NUM
ejpam-6124	346	5	=	=	SYM
ejpam-6124	346	6	2	2	NUM
ejpam-6124	346	7	(	(	PUNCT
ejpam-6124	346	8	n−	n−	NOUN
ejpam-6124	346	9	1	1	NUM
ejpam-6124	346	10	4	4	NUM
ejpam-6124	346	11	)	)	PUNCT
ejpam-6124	346	12	+	+	CCONJ
ejpam-6124	346	13	1	1	X
ejpam-6124	346	14	=	=	SYM
ejpam-6124	346	15	n+	n+	NUM
ejpam-6124	346	16	1	1	NUM
ejpam-6124	346	17	2	2	NUM
ejpam-6124	346	18	.	.	PUNCT
ejpam-6124	347	1	also	also	ADV
ejpam-6124	347	2	,	,	PUNCT
ejpam-6124	347	3	it	it	PRON
ejpam-6124	347	4	is	be	AUX
ejpam-6124	347	5	clear	clear	ADJ
ejpam-6124	347	6	that	that	SCONJ
ejpam-6124	347	7	n(t	n(t	PROPN
ejpam-6124	347	8	)	)	PUNCT
ejpam-6124	347	9	=	=	SYM
ejpam-6124	347	10	v	v	X
ejpam-6124	347	11	(	(	PUNCT
ejpam-6124	347	12	cn	cn	PROPN
ejpam-6124	347	13	)	)	PUNCT
ejpam-6124	347	14	and	and	CCONJ
ejpam-6124	347	15	so	so	ADV
ejpam-6124	347	16	,	,	PUNCT
ejpam-6124	347	17	t	t	PROPN
ejpam-6124	347	18	is	be	AUX
ejpam-6124	347	19	a	a	DET
ejpam-6124	347	20	γt	γt	NOUN
ejpam-6124	347	21	-	-	ADJ
ejpam-6124	347	22	set	set	VERB
ejpam-6124	347	23	by	by	ADP
ejpam-6124	347	24	proposition	proposition	NOUN
ejpam-6124	347	25	1	1	NUM
ejpam-6124	347	26	.	.	PUNCT
ejpam-6124	347	27	note	note	VERB
ejpam-6124	348	1	that	that	SCONJ
ejpam-6124	348	2	|t	|t	VERB
ejpam-6124	349	1	|	|	INTJ
ejpam-6124	349	2	is	be	AUX
ejpam-6124	349	3	odd	odd	ADJ
ejpam-6124	349	4	.	.	PUNCT
ejpam-6124	350	1	by	by	ADP
ejpam-6124	350	2	theorem	theorem	NOUN
ejpam-6124	350	3	5	5	NUM
ejpam-6124	350	4	,	,	PUNCT
ejpam-6124	350	5	t	t	PROPN
ejpam-6124	350	6	is	be	AUX
ejpam-6124	350	7	not	not	PART
ejpam-6124	350	8	a	a	DET
ejpam-6124	350	9	γte	γte	NOUN
ejpam-6124	350	10	-	-	PUNCT
ejpam-6124	350	11	set	set	NOUN
ejpam-6124	350	12	.	.	PUNCT
ejpam-6124	351	1	clearly	clearly	ADV
ejpam-6124	351	2	,	,	PUNCT
ejpam-6124	351	3	|n(ui)∩t	|n(ui)∩t	PROPN
ejpam-6124	351	4	|	|	ADV
ejpam-6124	351	5	=	=	NOUN
ejpam-6124	351	6	1	1	NUM
ejpam-6124	351	7	for	for	ADP
ejpam-6124	351	8	all	all	PRON
ejpam-6124	351	9	ui	ui	NOUN
ejpam-6124	351	10	∈	∈	PROPN
ejpam-6124	351	11	v	v	NOUN
ejpam-6124	351	12	(	(	PUNCT
ejpam-6124	351	13	cn)\{un−2	cn)\{un−2	ADV
ejpam-6124	351	14	}	}	PUNCT
ejpam-6124	351	15	and	and	CCONJ
ejpam-6124	351	16	|n(un−2)∩t	|n(un−2)∩t	NOUN
ejpam-6124	351	17	|	|	NOUN
ejpam-6124	351	18	=	=	SYM
ejpam-6124	351	19	2	2	NUM
ejpam-6124	351	20	and	and	CCONJ
ejpam-6124	351	21	so	so	ADV
ejpam-6124	351	22	,	,	PUNCT
ejpam-6124	351	23	un−1	un−1	PROPN
ejpam-6124	351	24	must	must	AUX
ejpam-6124	351	25	not	not	PART
ejpam-6124	351	26	be	be	AUX
ejpam-6124	351	27	in	in	ADP
ejpam-6124	351	28	t	t	PROPN
ejpam-6124	351	29	.	.	PUNCT
ejpam-6124	352	1	note	note	VERB
ejpam-6124	352	2	that	that	SCONJ
ejpam-6124	352	3	u1	u1	NOUN
ejpam-6124	352	4	must	must	AUX
ejpam-6124	352	5	not	not	PART
ejpam-6124	352	6	be	be	AUX
ejpam-6124	352	7	in	in	ADP
ejpam-6124	352	8	t	t	PROPN
ejpam-6124	352	9	also	also	ADV
ejpam-6124	352	10	since	since	SCONJ
ejpam-6124	352	11	otherwise	otherwise	ADV
ejpam-6124	352	12	,	,	PUNCT
ejpam-6124	352	13	|n(u2)∩t	|n(u2)∩t	NOUN
ejpam-6124	352	14	|	|	ADV
ejpam-6124	352	15	would	would	AUX
ejpam-6124	352	16	become	become	VERB
ejpam-6124	352	17	2	2	NUM
ejpam-6124	352	18	.	.	PUNCT
ejpam-6124	353	1	thus	thus	ADV
ejpam-6124	353	2	,	,	PUNCT
ejpam-6124	353	3	the	the	DET
ejpam-6124	353	4	only	only	ADJ
ejpam-6124	353	5	option	option	NOUN
ejpam-6124	353	6	left	leave	VERB
ejpam-6124	353	7	is	be	AUX
ejpam-6124	353	8	to	to	PART
ejpam-6124	353	9	replace	replace	VERB
ejpam-6124	353	10	un−1	un−1	ADJ
ejpam-6124	353	11	with	with	ADP
ejpam-6124	353	12	un	un	PROPN
ejpam-6124	353	13	;	;	PUNCT
ejpam-6124	353	14	however	however	ADV
ejpam-6124	353	15	,	,	PUNCT
ejpam-6124	353	16	|t	|t	PROPN
ejpam-6124	353	17	|	|	ADV
ejpam-6124	353	18	remains	remain	VERB
ejpam-6124	353	19	odd	odd	ADJ
ejpam-6124	353	20	and	and	CCONJ
ejpam-6124	353	21	so	so	ADV
ejpam-6124	353	22	t	t	PROPN
ejpam-6124	353	23	is	be	AUX
ejpam-6124	353	24	not	not	PART
ejpam-6124	353	25	a	a	DET
ejpam-6124	353	26	γte	γte	NOUN
ejpam-6124	353	27	-	-	PUNCT
ejpam-6124	353	28	set	set	NOUN
ejpam-6124	353	29	.	.	PUNCT
ejpam-6124	354	1	since	since	SCONJ
ejpam-6124	354	2	t	t	PROPN
ejpam-6124	354	3	is	be	AUX
ejpam-6124	354	4	arbitrarily	arbitrarily	ADV
ejpam-6124	354	5	chosen	choose	VERB
ejpam-6124	354	6	,	,	PUNCT
ejpam-6124	354	7	there	there	PRON
ejpam-6124	354	8	is	be	VERB
ejpam-6124	354	9	no	no	DET
ejpam-6124	354	10	possible	possible	ADJ
ejpam-6124	354	11	way	way	NOUN
ejpam-6124	354	12	to	to	PART
ejpam-6124	354	13	create	create	VERB
ejpam-6124	354	14	a	a	DET
ejpam-6124	354	15	set	set	NOUN
ejpam-6124	354	16	that	that	PRON
ejpam-6124	354	17	is	be	AUX
ejpam-6124	354	18	both	both	CCONJ
ejpam-6124	354	19	a	a	DET
ejpam-6124	354	20	total	total	ADJ
ejpam-6124	354	21	and	and	CCONJ
ejpam-6124	354	22	exact	exact	ADJ
ejpam-6124	354	23	dominating	dominating	NOUN
ejpam-6124	354	24	set	set	NOUN
ejpam-6124	354	25	of	of	ADP
ejpam-6124	354	26	cn	cn	PROPN
ejpam-6124	354	27	.	.	PUNCT
ejpam-6124	355	1	thus	thus	ADV
ejpam-6124	355	2	,	,	PUNCT
ejpam-6124	355	3	cn	cn	PROPN
ejpam-6124	355	4	is	be	AUX
ejpam-6124	355	5	a	a	DET
ejpam-6124	355	6	non	non	ADJ
ejpam-6124	355	7	-	-	ADJ
ejpam-6124	355	8	γte	γte	PRON
ejpam-6124	355	9	-	-	PUNCT
ejpam-6124	355	10	graph	graph	NOUN
ejpam-6124	355	11	if	if	SCONJ
ejpam-6124	355	12	n	n	PRON
ejpam-6124	355	13	≡	≡	PROPN
ejpam-6124	355	14	1	1	NUM
ejpam-6124	355	15	(	(	PUNCT
ejpam-6124	355	16	mod	mod	NOUN
ejpam-6124	355	17	4	4	NUM
ejpam-6124	355	18	)	)	PUNCT
ejpam-6124	355	19	.	.	PUNCT
ejpam-6124	356	1	case	case	NOUN
ejpam-6124	356	2	2	2	NUM
ejpam-6124	356	3	:	:	PUNCT
ejpam-6124	356	4	n	n	NUM
ejpam-6124	356	5	≡	≡	PROPN
ejpam-6124	356	6	2	2	NUM
ejpam-6124	356	7	(	(	PUNCT
ejpam-6124	356	8	mod	mod	NOUN
ejpam-6124	356	9	4	4	X
ejpam-6124	356	10	)	)	PUNCT
ejpam-6124	356	11	let	let	VERB
ejpam-6124	356	12	n	n	NOUN
ejpam-6124	356	13	=	=	SYM
ejpam-6124	356	14	6	6	NUM
ejpam-6124	356	15	.	.	PUNCT
ejpam-6124	356	16	by	by	ADP
ejpam-6124	356	17	proposition	proposition	NOUN
ejpam-6124	356	18	1	1	NUM
ejpam-6124	356	19	,	,	PUNCT
ejpam-6124	356	20	γt(c6	γt(c6	ADJ
ejpam-6124	356	21	)	)	PUNCT
ejpam-6124	356	22	=	=	PUNCT
ejpam-6124	357	1	6	6	NUM
ejpam-6124	357	2	+	+	SYM
ejpam-6124	357	3	2	2	NUM
ejpam-6124	357	4	2	2	NUM
ejpam-6124	357	5	=	=	SYM
ejpam-6124	357	6	4	4	NUM
ejpam-6124	357	7	.	.	PUNCT
ejpam-6124	357	8	clearly	clearly	ADV
ejpam-6124	357	9	,	,	PUNCT
ejpam-6124	357	10	t1	t1	NOUN
ejpam-6124	357	11	=	=	PUNCT
ejpam-6124	357	12	{	{	PUNCT
ejpam-6124	357	13	u1	u1	NOUN
ejpam-6124	357	14	,	,	PUNCT
ejpam-6124	357	15	u2	u2	NOUN
ejpam-6124	357	16	,	,	PUNCT
ejpam-6124	357	17	u3	u3	NOUN
ejpam-6124	357	18	,	,	PUNCT
ejpam-6124	357	19	u4	u4	PROPN
ejpam-6124	357	20	}	}	PUNCT
ejpam-6124	357	21	,	,	PUNCT
ejpam-6124	357	22	t2	t2	NOUN
ejpam-6124	357	23	=	=	SYM
ejpam-6124	357	24	{	{	PUNCT
ejpam-6124	357	25	u1	u1	NOUN
ejpam-6124	357	26	,	,	PUNCT
ejpam-6124	357	27	u2	u2	PROPN
ejpam-6124	357	28	,	,	PUNCT
ejpam-6124	357	29	u4	u4	PROPN
ejpam-6124	357	30	,	,	PUNCT
ejpam-6124	357	31	u5	u5	PROPN
ejpam-6124	357	32	}	}	PUNCT
ejpam-6124	357	33	,	,	PUNCT
ejpam-6124	357	34	t3	t3	PROPN
ejpam-6124	357	35	=	=	PUNCT
ejpam-6124	357	36	{	{	PUNCT
ejpam-6124	357	37	u1	u1	NOUN
ejpam-6124	357	38	,	,	PUNCT
ejpam-6124	357	39	u2	u2	PROPN
ejpam-6124	357	40	,	,	PUNCT
ejpam-6124	357	41	u5	u5	PROPN
ejpam-6124	357	42	,	,	PUNCT
ejpam-6124	357	43	u6	u6	NOUN
ejpam-6124	357	44	}	}	PUNCT
ejpam-6124	357	45	,	,	PUNCT
ejpam-6124	357	46	t4	t4	PROPN
ejpam-6124	357	47	=	=	PROPN
ejpam-6124	357	48	{	{	PUNCT
ejpam-6124	357	49	u2	u2	PROPN
ejpam-6124	357	50	,	,	PUNCT
ejpam-6124	357	51	u3	u3	PROPN
ejpam-6124	357	52	,	,	PUNCT
ejpam-6124	357	53	u4	u4	PROPN
ejpam-6124	357	54	,	,	PUNCT
ejpam-6124	357	55	u5	u5	PROPN
ejpam-6124	357	56	}	}	PUNCT
ejpam-6124	357	57	,	,	PUNCT
ejpam-6124	357	58	t5	t5	PROPN
ejpam-6124	357	59	=	=	SYM
ejpam-6124	357	60	{	{	PUNCT
ejpam-6124	357	61	u2	u2	PROPN
ejpam-6124	357	62	,	,	PUNCT
ejpam-6124	357	63	u3	u3	PROPN
ejpam-6124	357	64	,	,	PUNCT
ejpam-6124	357	65	u5	u5	PROPN
ejpam-6124	357	66	,	,	PUNCT
ejpam-6124	357	67	u6	u6	PROPN
ejpam-6124	357	68	}	}	PUNCT
ejpam-6124	357	69	,	,	PUNCT
ejpam-6124	357	70	r.	r.	PROPN
ejpam-6124	357	71	g.	g.	PROPN
ejpam-6124	357	72	aguinod	aguinod	PROPN
ejpam-6124	357	73	,	,	PUNCT
ejpam-6124	357	74	e.	e.	PROPN
ejpam-6124	357	75	m.	m.	PROPN
ejpam-6124	357	76	kiunisala	kiunisala	PROPN
ejpam-6124	357	77	,	,	PUNCT
ejpam-6124	357	78	c.	c.	PROPN
ejpam-6124	357	79	l.	l.	PROPN
ejpam-6124	357	80	armada	armada	PROPN
ejpam-6124	357	81	/	/	SYM
ejpam-6124	357	82	eur	eur	PROPN
ejpam-6124	357	83	.	.	PUNCT
ejpam-6124	358	1	j.	j.	PROPN
ejpam-6124	358	2	pure	pure	PROPN
ejpam-6124	358	3	appl	appl	PROPN
ejpam-6124	358	4	.	.	PROPN
ejpam-6124	358	5	math	math	PROPN
ejpam-6124	358	6	,	,	PUNCT
ejpam-6124	358	7	18	18	NUM
ejpam-6124	358	8	(	(	PUNCT
ejpam-6124	358	9	2	2	NUM
ejpam-6124	358	10	)	)	PUNCT
ejpam-6124	358	11	(	(	PUNCT
ejpam-6124	358	12	2025	2025	NUM
ejpam-6124	358	13	)	)	PUNCT
ejpam-6124	358	14	,	,	PUNCT
ejpam-6124	358	15	6124	6124	NUM
ejpam-6124	358	16	13	13	NUM
ejpam-6124	358	17	of	of	ADP
ejpam-6124	358	18	26	26	NUM
ejpam-6124	358	19	t6	t6	PROPN
ejpam-6124	358	20	=	=	SYM
ejpam-6124	358	21	{	{	PUNCT
ejpam-6124	358	22	u2	u2	PROPN
ejpam-6124	358	23	,	,	PUNCT
ejpam-6124	358	24	u3	u3	NOUN
ejpam-6124	358	25	,	,	PUNCT
ejpam-6124	358	26	u6	u6	NOUN
ejpam-6124	358	27	,	,	PUNCT
ejpam-6124	358	28	u1	u1	NOUN
ejpam-6124	358	29	}	}	PUNCT
ejpam-6124	358	30	,	,	PUNCT
ejpam-6124	358	31	t7	t7	PROPN
ejpam-6124	358	32	=	=	SYM
ejpam-6124	358	33	{	{	PUNCT
ejpam-6124	358	34	u3	u3	PROPN
ejpam-6124	358	35	,	,	PUNCT
ejpam-6124	358	36	u4	u4	PROPN
ejpam-6124	358	37	,	,	PUNCT
ejpam-6124	358	38	u5	u5	PROPN
ejpam-6124	358	39	,	,	PUNCT
ejpam-6124	358	40	u6	u6	NOUN
ejpam-6124	358	41	}	}	PUNCT
ejpam-6124	358	42	,	,	PUNCT
ejpam-6124	358	43	t8	t8	NOUN
ejpam-6124	358	44	=	=	SYM
ejpam-6124	358	45	{	{	PUNCT
ejpam-6124	358	46	u3	u3	PROPN
ejpam-6124	358	47	,	,	PUNCT
ejpam-6124	358	48	u4	u4	PROPN
ejpam-6124	358	49	,	,	PUNCT
ejpam-6124	358	50	u6	u6	PROPN
ejpam-6124	358	51	,	,	PUNCT
ejpam-6124	358	52	u1	u1	NOUN
ejpam-6124	358	53	}	}	PUNCT
ejpam-6124	358	54	,	,	PUNCT
ejpam-6124	358	55	and	and	CCONJ
ejpam-6124	358	56	t9	t9	PROPN
ejpam-6124	358	57	=	=	SYM
ejpam-6124	358	58	{	{	PUNCT
ejpam-6124	358	59	u4	u4	PROPN
ejpam-6124	358	60	,	,	PUNCT
ejpam-6124	358	61	u5	u5	PROPN
ejpam-6124	358	62	,	,	PUNCT
ejpam-6124	358	63	u6	u6	NOUN
ejpam-6124	358	64	,	,	PUNCT
ejpam-6124	358	65	u1	u1	NOUN
ejpam-6124	358	66	}	}	PUNCT
ejpam-6124	358	67	are	be	AUX
ejpam-6124	358	68	the	the	DET
ejpam-6124	358	69	only	only	ADJ
ejpam-6124	358	70	γt	γt	NOUN
ejpam-6124	358	71	-	-	NOUN
ejpam-6124	358	72	sets	set	NOUN
ejpam-6124	358	73	of	of	ADP
ejpam-6124	358	74	c6	c6	PROPN
ejpam-6124	358	75	.	.	PUNCT
ejpam-6124	359	1	it	it	PRON
ejpam-6124	359	2	is	be	AUX
ejpam-6124	359	3	also	also	ADV
ejpam-6124	359	4	clear	clear	ADJ
ejpam-6124	359	5	that	that	SCONJ
ejpam-6124	359	6	for	for	ADP
ejpam-6124	359	7	i	i	PROPN
ejpam-6124	359	8	=	=	NOUN
ejpam-6124	359	9	1	1	NUM
ejpam-6124	359	10	,	,	PUNCT
ejpam-6124	359	11	2	2	NUM
ejpam-6124	359	12	,	,	PUNCT
ejpam-6124	359	13	3	3	NUM
ejpam-6124	359	14	,	,	PUNCT
ejpam-6124	359	15	...	...	PUNCT
ejpam-6124	359	16	,	,	PUNCT
ejpam-6124	359	17	9	9	NUM
ejpam-6124	359	18	,	,	PUNCT
ejpam-6124	359	19	there	there	PRON
ejpam-6124	359	20	always	always	ADV
ejpam-6124	359	21	exists	exist	VERB
ejpam-6124	359	22	a	a	DET
ejpam-6124	359	23	vertex	vertex	NOUN
ejpam-6124	359	24	uk	uk	PROPN
ejpam-6124	359	25	in	in	ADP
ejpam-6124	359	26	v	v	PROPN
ejpam-6124	359	27	(	(	PUNCT
ejpam-6124	359	28	c6	c6	PROPN
ejpam-6124	359	29	)	)	PUNCT
ejpam-6124	359	30	such	such	ADJ
ejpam-6124	359	31	that	that	SCONJ
ejpam-6124	359	32	|n(uk	|n(uk	PROPN
ejpam-6124	359	33	)	)	PUNCT
ejpam-6124	359	34	∩	∩	ADJ
ejpam-6124	359	35	ti|	ti|	NOUN
ejpam-6124	359	36	=	=	SYM
ejpam-6124	359	37	2	2	NUM
ejpam-6124	359	38	;	;	PUNCT
ejpam-6124	359	39	that	that	PRON
ejpam-6124	359	40	is	is	ADV
ejpam-6124	359	41	,	,	PUNCT
ejpam-6124	359	42	u2	u2	PROPN
ejpam-6124	359	43	is	be	AUX
ejpam-6124	359	44	associated	associate	VERB
ejpam-6124	359	45	with	with	ADP
ejpam-6124	359	46	t1	t1	PROPN
ejpam-6124	359	47	,	,	PUNCT
ejpam-6124	359	48	u3	u3	NOUN
ejpam-6124	359	49	with	with	ADP
ejpam-6124	359	50	t2	t2	NOUN
ejpam-6124	359	51	,	,	PUNCT
ejpam-6124	359	52	u1	u1	NOUN
ejpam-6124	359	53	with	with	ADP
ejpam-6124	359	54	t3	t3	PROPN
ejpam-6124	359	55	,	,	PUNCT
ejpam-6124	359	56	u3	u3	NOUN
ejpam-6124	359	57	with	with	ADP
ejpam-6124	359	58	t4	t4	PROPN
ejpam-6124	359	59	,	,	PUNCT
ejpam-6124	359	60	u4	u4	PROPN
ejpam-6124	359	61	with	with	ADP
ejpam-6124	359	62	t5	t5	PROPN
ejpam-6124	359	63	,	,	PUNCT
ejpam-6124	359	64	u2	u2	PROPN
ejpam-6124	359	65	with	with	ADP
ejpam-6124	359	66	t6	t6	PROPN
ejpam-6124	359	67	,	,	PUNCT
ejpam-6124	359	68	u4	u4	PROPN
ejpam-6124	359	69	with	with	ADP
ejpam-6124	359	70	t7	t7	PROPN
ejpam-6124	359	71	,	,	PUNCT
ejpam-6124	359	72	u2	u2	PROPN
ejpam-6124	359	73	with	with	ADP
ejpam-6124	359	74	t8	t8	NOUN
ejpam-6124	359	75	,	,	PUNCT
ejpam-6124	359	76	and	and	CCONJ
ejpam-6124	359	77	u5	u5	PROPN
ejpam-6124	359	78	with	with	ADP
ejpam-6124	359	79	t9	t9	PROPN
ejpam-6124	359	80	.	.	PUNCT
ejpam-6124	360	1	it	it	PRON
ejpam-6124	360	2	follows	follow	VERB
ejpam-6124	360	3	that	that	SCONJ
ejpam-6124	360	4	for	for	ADP
ejpam-6124	360	5	i	i	PROPN
ejpam-6124	360	6	=	=	NOUN
ejpam-6124	360	7	1	1	NUM
ejpam-6124	360	8	,	,	PUNCT
ejpam-6124	360	9	2	2	NUM
ejpam-6124	360	10	,	,	PUNCT
ejpam-6124	360	11	3	3	NUM
ejpam-6124	360	12	,	,	PUNCT
ejpam-6124	360	13	...	...	PUNCT
ejpam-6124	360	14	,	,	PUNCT
ejpam-6124	360	15	9	9	NUM
ejpam-6124	360	16	,	,	PUNCT
ejpam-6124	360	17	ti	ti	NOUN
ejpam-6124	360	18	is	be	AUX
ejpam-6124	360	19	not	not	PART
ejpam-6124	360	20	a	a	DET
ejpam-6124	360	21	γte	γte	NOUN
ejpam-6124	360	22	-	-	PUNCT
ejpam-6124	360	23	set	set	NOUN
ejpam-6124	360	24	of	of	ADP
ejpam-6124	360	25	c6	c6	PROPN
ejpam-6124	360	26	.	.	PUNCT
ejpam-6124	361	1	hence	hence	ADV
ejpam-6124	361	2	,	,	PUNCT
ejpam-6124	361	3	there	there	PRON
ejpam-6124	361	4	is	be	VERB
ejpam-6124	361	5	no	no	DET
ejpam-6124	361	6	possible	possible	ADJ
ejpam-6124	361	7	way	way	NOUN
ejpam-6124	361	8	to	to	PART
ejpam-6124	361	9	create	create	VERB
ejpam-6124	361	10	a	a	DET
ejpam-6124	361	11	set	set	NOUN
ejpam-6124	361	12	that	that	PRON
ejpam-6124	361	13	is	be	AUX
ejpam-6124	361	14	both	both	CCONJ
ejpam-6124	361	15	a	a	DET
ejpam-6124	361	16	total	total	ADJ
ejpam-6124	361	17	and	and	CCONJ
ejpam-6124	361	18	exact	exact	ADJ
ejpam-6124	361	19	dominating	dominating	NOUN
ejpam-6124	361	20	set	set	NOUN
ejpam-6124	361	21	of	of	ADP
ejpam-6124	361	22	c6	c6	PROPN
ejpam-6124	361	23	and	and	CCONJ
ejpam-6124	361	24	so	so	ADV
ejpam-6124	361	25	,	,	PUNCT
ejpam-6124	361	26	c6	c6	PROPN
ejpam-6124	361	27	is	be	AUX
ejpam-6124	361	28	a	a	DET
ejpam-6124	361	29	non	non	ADJ
ejpam-6124	361	30	-	-	ADJ
ejpam-6124	361	31	γte	γte	PRON
ejpam-6124	361	32	-	-	PUNCT
ejpam-6124	361	33	graph	graph	NOUN
ejpam-6124	361	34	.	.	PUNCT
ejpam-6124	362	1	now	now	ADV
ejpam-6124	362	2	,	,	PUNCT
ejpam-6124	362	3	suppose	suppose	VERB
ejpam-6124	362	4	that	that	SCONJ
ejpam-6124	362	5	n	n	PROPN
ejpam-6124	362	6	>	>	X
ejpam-6124	362	7	6	6	NUM
ejpam-6124	362	8	.	.	PUNCT
ejpam-6124	363	1	let	let	VERB
ejpam-6124	363	2	p	p	NOUN
ejpam-6124	363	3	=	=	PUNCT
ejpam-6124	363	4	n−2	n−2	PROPN
ejpam-6124	363	5	4	4	NUM
ejpam-6124	363	6	and	and	CCONJ
ejpam-6124	363	7	j	j	NOUN
ejpam-6124	363	8	=	=	SYM
ejpam-6124	363	9	1	1	NUM
ejpam-6124	363	10	,	,	PUNCT
ejpam-6124	363	11	2	2	NUM
ejpam-6124	363	12	,	,	PUNCT
ejpam-6124	363	13	.	.	PUNCT
ejpam-6124	363	14	.	.	PUNCT
ejpam-6124	364	1	.	.	PUNCT
ejpam-6124	365	1	,	,	PUNCT
ejpam-6124	365	2	p.	p.	NOUN
ejpam-6124	365	3	group	group	NOUN
ejpam-6124	365	4	the	the	DET
ejpam-6124	365	5	vertices	vertex	NOUN
ejpam-6124	365	6	of	of	ADP
ejpam-6124	365	7	cn	cn	PROPN
ejpam-6124	365	8	into	into	ADP
ejpam-6124	365	9	p	p	PROPN
ejpam-6124	365	10	disjoint	disjoint	PROPN
ejpam-6124	365	11	subsets	subset	NOUN
ejpam-6124	365	12	rj	rj	PROPN
ejpam-6124	365	13	,	,	PUNCT
ejpam-6124	365	14	such	such	ADJ
ejpam-6124	365	15	that	that	SCONJ
ejpam-6124	365	16	r1	r1	NOUN
ejpam-6124	365	17	=	=	SYM
ejpam-6124	365	18	{	{	PUNCT
ejpam-6124	365	19	u1	u1	NOUN
ejpam-6124	365	20	,	,	PUNCT
ejpam-6124	365	21	u2	u2	NOUN
ejpam-6124	365	22	,	,	PUNCT
ejpam-6124	365	23	u3	u3	NOUN
ejpam-6124	365	24	,	,	PUNCT
ejpam-6124	365	25	u4	u4	PROPN
ejpam-6124	365	26	}	}	PUNCT
ejpam-6124	365	27	,	,	PUNCT
ejpam-6124	365	28	r2	r2	PROPN
ejpam-6124	365	29	=	=	SYM
ejpam-6124	365	30	{	{	PUNCT
ejpam-6124	365	31	u5	u5	PROPN
ejpam-6124	365	32	,	,	PUNCT
ejpam-6124	365	33	u6	u6	PROPN
ejpam-6124	365	34	,	,	PUNCT
ejpam-6124	365	35	u7	u7	PROPN
ejpam-6124	365	36	,	,	PUNCT
ejpam-6124	365	37	u8	u8	PROPN
ejpam-6124	365	38	}	}	PUNCT
ejpam-6124	365	39	,	,	PUNCT
ejpam-6124	365	40	r3	r3	PROPN
ejpam-6124	365	41	=	=	SYM
ejpam-6124	365	42	{	{	PUNCT
ejpam-6124	365	43	u9	u9	PROPN
ejpam-6124	365	44	,	,	PUNCT
ejpam-6124	365	45	u10	u10	PROPN
ejpam-6124	365	46	,	,	PUNCT
ejpam-6124	365	47	u11	u11	PROPN
ejpam-6124	365	48	,	,	PUNCT
ejpam-6124	365	49	u12	u12	PROPN
ejpam-6124	365	50	}	}	PUNCT
ejpam-6124	365	51	,	,	PUNCT
ejpam-6124	365	52	...	...	PUNCT
ejpam-6124	366	1	rp−1	rp−1	NOUN
ejpam-6124	366	2	=	=	SYM
ejpam-6124	366	3	{	{	PUNCT
ejpam-6124	366	4	un−9	un−9	PROPN
ejpam-6124	366	5	,	,	PUNCT
ejpam-6124	366	6	un−8	un−8	ADJ
ejpam-6124	366	7	,	,	PUNCT
ejpam-6124	366	8	un−7	un−7	PROPN
ejpam-6124	366	9	,	,	PUNCT
ejpam-6124	366	10	un−6	un−6	PROPN
ejpam-6124	366	11	}	}	PUNCT
ejpam-6124	366	12	,	,	PUNCT
ejpam-6124	366	13	and	and	CCONJ
ejpam-6124	366	14	rp	rp	NOUN
ejpam-6124	366	15	=	=	SYM
ejpam-6124	366	16	{	{	PUNCT
ejpam-6124	366	17	un−5	un−5	PROPN
ejpam-6124	366	18	,	,	PUNCT
ejpam-6124	366	19	un−4	un−4	NOUN
ejpam-6124	366	20	,	,	PUNCT
ejpam-6124	366	21	un−3	un−3	ADJ
ejpam-6124	366	22	,	,	PUNCT
ejpam-6124	366	23	un−2	un−2	PROPN
ejpam-6124	366	24	,	,	PUNCT
ejpam-6124	366	25	un−1	un−1	PROPN
ejpam-6124	366	26	,	,	PUNCT
ejpam-6124	366	27	un	un	ADJ
ejpam-6124	366	28	}	}	PUNCT
ejpam-6124	366	29	where	where	SCONJ
ejpam-6124	366	30	|rj	|rj	PART
ejpam-6124	366	31	|	|	ADV
ejpam-6124	366	32	=	=	SYM
ejpam-6124	366	33	4	4	NUM
ejpam-6124	366	34	for	for	ADP
ejpam-6124	366	35	j	j	PROPN
ejpam-6124	366	36	=	=	SYM
ejpam-6124	366	37	1	1	NUM
ejpam-6124	366	38	,	,	PUNCT
ejpam-6124	366	39	2	2	NUM
ejpam-6124	366	40	,	,	PUNCT
ejpam-6124	366	41	.	.	PUNCT
ejpam-6124	366	42	.	.	PUNCT
ejpam-6124	366	43	.	.	PUNCT
ejpam-6124	367	1	,	,	PUNCT
ejpam-6124	367	2	p−	p−	NOUN
ejpam-6124	367	3	1	1	NUM
ejpam-6124	367	4	and	and	CCONJ
ejpam-6124	367	5	|rp|	|rp|	NUM
ejpam-6124	367	6	=	=	SYM
ejpam-6124	367	7	6	6	X
ejpam-6124	367	8	.	.	PUNCT
ejpam-6124	367	9	let	let	VERB
ejpam-6124	367	10	t	t	NOUN
ejpam-6124	367	11	=	=	SYM
ejpam-6124	367	12	{	{	PUNCT
ejpam-6124	367	13	u2	u2	PROPN
ejpam-6124	367	14	,	,	PUNCT
ejpam-6124	367	15	u3	u3	NOUN
ejpam-6124	367	16	,	,	PUNCT
ejpam-6124	367	17	u6	u6	PROPN
ejpam-6124	367	18	,	,	PUNCT
ejpam-6124	367	19	u7	u7	PROPN
ejpam-6124	367	20	,	,	PUNCT
ejpam-6124	367	21	u10	u10	PROPN
ejpam-6124	367	22	,	,	PUNCT
ejpam-6124	367	23	u11	u11	PROPN
ejpam-6124	367	24	,	,	PUNCT
ejpam-6124	367	25	.	.	PUNCT
ejpam-6124	367	26	.	.	PUNCT
ejpam-6124	368	1	.	.	PUNCT
ejpam-6124	369	1	,	,	PUNCT
ejpam-6124	369	2	un−8	un−8	ADJ
ejpam-6124	369	3	,	,	PUNCT
ejpam-6124	369	4	un−7	un−7	NOUN
ejpam-6124	369	5	,	,	PUNCT
ejpam-6124	369	6	un−4	un−4	NOUN
ejpam-6124	369	7	,	,	PUNCT
ejpam-6124	369	8	un−3	un−3	ADJ
ejpam-6124	369	9	,	,	PUNCT
ejpam-6124	369	10	un−1	un−1	PROPN
ejpam-6124	369	11	,	,	PUNCT
ejpam-6124	369	12	un	un	ADJ
ejpam-6124	369	13	}	}	PUNCT
ejpam-6124	369	14	,	,	PUNCT
ejpam-6124	369	15	where	where	SCONJ
ejpam-6124	369	16	t	t	PROPN
ejpam-6124	369	17	is	be	AUX
ejpam-6124	369	18	formed	form	VERB
ejpam-6124	369	19	by	by	ADP
ejpam-6124	369	20	getting	get	VERB
ejpam-6124	369	21	2	2	NUM
ejpam-6124	369	22	vertices	vertex	NOUN
ejpam-6124	369	23	in	in	ADP
ejpam-6124	369	24	each	each	DET
ejpam-6124	369	25	rj	rj	PROPN
ejpam-6124	369	26	for	for	ADP
ejpam-6124	369	27	j	j	PROPN
ejpam-6124	369	28	=	=	SYM
ejpam-6124	369	29	1	1	NUM
ejpam-6124	369	30	,	,	PUNCT
ejpam-6124	369	31	2	2	NUM
ejpam-6124	369	32	,	,	PUNCT
ejpam-6124	369	33	.	.	PUNCT
ejpam-6124	369	34	.	.	PUNCT
ejpam-6124	370	1	.	.	PUNCT
ejpam-6124	371	1	,	,	PUNCT
ejpam-6124	371	2	p−	p−	NOUN
ejpam-6124	371	3	1	1	NUM
ejpam-6124	371	4	and	and	CCONJ
ejpam-6124	371	5	4	4	NUM
ejpam-6124	371	6	vertices	vertex	NOUN
ejpam-6124	371	7	in	in	ADP
ejpam-6124	371	8	rp	rp	NOUN
ejpam-6124	371	9	.	.	PUNCT
ejpam-6124	372	1	it	it	PRON
ejpam-6124	372	2	follows	follow	VERB
ejpam-6124	372	3	that	that	PRON
ejpam-6124	372	4	|t	|t	VERB
ejpam-6124	373	1	|	|	ADV
ejpam-6124	374	1	=	=	SYM
ejpam-6124	374	2	2(p−	2(p−	NUM
ejpam-6124	374	3	1	1	NUM
ejpam-6124	374	4	)	)	PUNCT
ejpam-6124	374	5	+	+	CCONJ
ejpam-6124	374	6	4	4	NUM
ejpam-6124	374	7	=	=	SYM
ejpam-6124	374	8	2p+	2p+	NUM
ejpam-6124	374	9	2	2	NUM
ejpam-6124	374	10	=	=	SYM
ejpam-6124	374	11	2	2	NUM
ejpam-6124	374	12	(	(	PUNCT
ejpam-6124	374	13	n−	n−	NOUN
ejpam-6124	374	14	2	2	NUM
ejpam-6124	374	15	4	4	NUM
ejpam-6124	374	16	)	)	PUNCT
ejpam-6124	374	17	+	+	CCONJ
ejpam-6124	374	18	2	2	X
ejpam-6124	374	19	=	=	SYM
ejpam-6124	374	20	n+	n+	X
ejpam-6124	374	21	2	2	NUM
ejpam-6124	374	22	2	2	NUM
ejpam-6124	374	23	.	.	PUNCT
ejpam-6124	375	1	also	also	ADV
ejpam-6124	375	2	,	,	PUNCT
ejpam-6124	375	3	it	it	PRON
ejpam-6124	375	4	is	be	AUX
ejpam-6124	375	5	clear	clear	ADJ
ejpam-6124	375	6	that	that	SCONJ
ejpam-6124	375	7	n(t	n(t	PROPN
ejpam-6124	375	8	)	)	PUNCT
ejpam-6124	375	9	=	=	SYM
ejpam-6124	375	10	v	v	X
ejpam-6124	375	11	(	(	PUNCT
ejpam-6124	375	12	cn	cn	PROPN
ejpam-6124	375	13	)	)	PUNCT
ejpam-6124	375	14	and	and	CCONJ
ejpam-6124	375	15	so	so	ADV
ejpam-6124	375	16	,	,	PUNCT
ejpam-6124	375	17	t	t	PROPN
ejpam-6124	375	18	is	be	AUX
ejpam-6124	375	19	a	a	DET
ejpam-6124	375	20	γt	γt	NOUN
ejpam-6124	375	21	-	-	ADJ
ejpam-6124	375	22	set	set	VERB
ejpam-6124	375	23	by	by	ADP
ejpam-6124	375	24	proposition	proposition	NOUN
ejpam-6124	375	25	1	1	NUM
ejpam-6124	375	26	.	.	PUNCT
ejpam-6124	375	27	clearly	clearly	ADV
ejpam-6124	375	28	,	,	PUNCT
ejpam-6124	375	29	|n(ui	|n(ui	PROPN
ejpam-6124	375	30	)	)	PUNCT
ejpam-6124	375	31	∩	∩	NOUN
ejpam-6124	375	32	t	t	NOUN
ejpam-6124	376	1	|	|	NOUN
ejpam-6124	376	2	=	=	SYM
ejpam-6124	376	3	1	1	NUM
ejpam-6124	376	4	for	for	ADP
ejpam-6124	376	5	all	all	DET
ejpam-6124	376	6	ui	ui	NOUN
ejpam-6124	376	7	∈	∈	PROPN
ejpam-6124	376	8	v	v	NOUN
ejpam-6124	376	9	(	(	PUNCT
ejpam-6124	376	10	cn	cn	PROPN
ejpam-6124	376	11	)	)	PUNCT
ejpam-6124	376	12	\	\	PROPN
ejpam-6124	376	13	{	{	PUNCT
ejpam-6124	376	14	un−2	un−2	PROPN
ejpam-6124	376	15	,	,	PUNCT
ejpam-6124	376	16	u1	u1	NOUN
ejpam-6124	376	17	}	}	PUNCT
ejpam-6124	376	18	,	,	PUNCT
ejpam-6124	376	19	|n(un−2	|n(un−2	PROPN
ejpam-6124	376	20	)	)	PUNCT
ejpam-6124	376	21	∩	∩	NOUN
ejpam-6124	376	22	t	t	NOUN
ejpam-6124	377	1	|	|	NOUN
ejpam-6124	377	2	=	=	SYM
ejpam-6124	377	3	2	2	NUM
ejpam-6124	377	4	and	and	CCONJ
ejpam-6124	377	5	|n(u1	|n(u1	ADJ
ejpam-6124	377	6	)	)	PUNCT
ejpam-6124	377	7	∩	∩	NOUN
ejpam-6124	377	8	t	t	NOUN
ejpam-6124	378	1	|	|	NOUN
ejpam-6124	378	2	=	=	NOUN
ejpam-6124	378	3	2	2	X
ejpam-6124	378	4	.	.	PUNCT
ejpam-6124	378	5	therefore	therefore	ADV
ejpam-6124	378	6	,	,	PUNCT
ejpam-6124	378	7	t	t	PROPN
ejpam-6124	378	8	is	be	AUX
ejpam-6124	378	9	not	not	PART
ejpam-6124	378	10	a	a	DET
ejpam-6124	378	11	γte	γte	NOUN
ejpam-6124	378	12	-	-	PUNCT
ejpam-6124	378	13	set	set	NOUN
ejpam-6124	378	14	,	,	PUNCT
ejpam-6124	378	15	and	and	CCONJ
ejpam-6124	378	16	both	both	CCONJ
ejpam-6124	378	17	un−1	un−1	PROPN
ejpam-6124	378	18	and	and	CCONJ
ejpam-6124	378	19	un	un	PROPN
ejpam-6124	378	20	must	must	AUX
ejpam-6124	378	21	not	not	PART
ejpam-6124	378	22	be	be	AUX
ejpam-6124	378	23	in	in	ADP
ejpam-6124	378	24	t	t	NOUN
ejpam-6124	378	25	so	so	SCONJ
ejpam-6124	378	26	that	that	SCONJ
ejpam-6124	378	27	|n(un−2	|n(un−2	ADJ
ejpam-6124	378	28	)	)	PUNCT
ejpam-6124	378	29	∩	∩	NOUN
ejpam-6124	378	30	t	t	NOUN
ejpam-6124	378	31	|	|	NOUN
ejpam-6124	378	32	=	=	SYM
ejpam-6124	378	33	1	1	NUM
ejpam-6124	378	34	and	and	CCONJ
ejpam-6124	378	35	|n(u1	|n(u1	ADJ
ejpam-6124	378	36	)	)	PUNCT
ejpam-6124	378	37	∩	∩	NOUN
ejpam-6124	378	38	t	t	NOUN
ejpam-6124	379	1	|	|	NOUN
ejpam-6124	379	2	=	=	SYM
ejpam-6124	379	3	1	1	X
ejpam-6124	379	4	.	.	X
ejpam-6124	379	5	note	note	NOUN
ejpam-6124	379	6	also	also	ADV
ejpam-6124	379	7	that	that	SCONJ
ejpam-6124	379	8	un−2	un−2	VERB
ejpam-6124	379	9	and	and	CCONJ
ejpam-6124	379	10	u1	u1	NOUN
ejpam-6124	379	11	must	must	AUX
ejpam-6124	379	12	not	not	PART
ejpam-6124	379	13	be	be	AUX
ejpam-6124	379	14	in	in	ADP
ejpam-6124	379	15	t	t	PROPN
ejpam-6124	379	16	since	since	SCONJ
ejpam-6124	379	17	otherwise	otherwise	ADV
ejpam-6124	379	18	,	,	PUNCT
ejpam-6124	379	19	|n(un−3	|n(un−3	PROPN
ejpam-6124	379	20	)	)	PUNCT
ejpam-6124	379	21	∩	∩	NOUN
ejpam-6124	379	22	t	t	NOUN
ejpam-6124	379	23	|	|	ADV
ejpam-6124	379	24	and	and	CCONJ
ejpam-6124	379	25	|n(u2	|n(u2	NOUN
ejpam-6124	379	26	)	)	PUNCT
ejpam-6124	380	1	∩	∩	PROPN
ejpam-6124	380	2	t	t	PROPN
ejpam-6124	380	3	|	|	ADV
ejpam-6124	380	4	would	would	AUX
ejpam-6124	380	5	become	become	VERB
ejpam-6124	380	6	2	2	NUM
ejpam-6124	380	7	.	.	PUNCT
ejpam-6124	381	1	thus	thus	ADV
ejpam-6124	381	2	,	,	PUNCT
ejpam-6124	381	3	no	no	DET
ejpam-6124	381	4	two	two	NUM
ejpam-6124	381	5	vertices	vertex	NOUN
ejpam-6124	381	6	can	can	AUX
ejpam-6124	381	7	replace	replace	VERB
ejpam-6124	381	8	both	both	CCONJ
ejpam-6124	381	9	un−1	un−1	ADJ
ejpam-6124	381	10	and	and	CCONJ
ejpam-6124	381	11	un	un	PROPN
ejpam-6124	381	12	in	in	ADP
ejpam-6124	381	13	t	t	PROPN
ejpam-6124	381	14	.	.	PUNCT
ejpam-6124	382	1	since	since	SCONJ
ejpam-6124	382	2	t	t	PROPN
ejpam-6124	382	3	is	be	AUX
ejpam-6124	382	4	arbitrarily	arbitrarily	ADV
ejpam-6124	382	5	chosen	choose	VERB
ejpam-6124	382	6	,	,	PUNCT
ejpam-6124	382	7	there	there	PRON
ejpam-6124	382	8	is	be	VERB
ejpam-6124	382	9	no	no	DET
ejpam-6124	382	10	possible	possible	ADJ
ejpam-6124	382	11	way	way	NOUN
ejpam-6124	382	12	to	to	PART
ejpam-6124	382	13	create	create	VERB
ejpam-6124	382	14	a	a	DET
ejpam-6124	382	15	set	set	NOUN
ejpam-6124	382	16	that	that	PRON
ejpam-6124	382	17	is	be	AUX
ejpam-6124	382	18	both	both	CCONJ
ejpam-6124	382	19	a	a	DET
ejpam-6124	382	20	total	total	ADJ
ejpam-6124	382	21	and	and	CCONJ
ejpam-6124	382	22	exact	exact	ADJ
ejpam-6124	382	23	dominating	dominating	NOUN
ejpam-6124	382	24	set	set	NOUN
ejpam-6124	382	25	of	of	ADP
ejpam-6124	382	26	cn	cn	PROPN
ejpam-6124	382	27	.	.	PUNCT
ejpam-6124	383	1	thus	thus	ADV
ejpam-6124	383	2	,	,	PUNCT
ejpam-6124	383	3	cn	cn	PROPN
ejpam-6124	383	4	is	be	AUX
ejpam-6124	383	5	a	a	DET
ejpam-6124	383	6	non	non	ADJ
ejpam-6124	383	7	-	-	ADJ
ejpam-6124	383	8	γte	γte	PRON
ejpam-6124	383	9	-	-	PUNCT
ejpam-6124	383	10	graph	graph	NOUN
ejpam-6124	383	11	if	if	SCONJ
ejpam-6124	383	12	n	n	PRON
ejpam-6124	383	13	≡	≡	PROPN
ejpam-6124	383	14	2	2	NUM
ejpam-6124	383	15	(	(	PUNCT
ejpam-6124	383	16	mod	mod	NOUN
ejpam-6124	383	17	4	4	NUM
ejpam-6124	383	18	)	)	PUNCT
ejpam-6124	383	19	.	.	PUNCT
ejpam-6124	384	1	case	case	NOUN
ejpam-6124	384	2	3	3	NUM
ejpam-6124	384	3	:	:	PUNCT
ejpam-6124	384	4	n	n	NUM
ejpam-6124	384	5	≡	≡	PROPN
ejpam-6124	384	6	3	3	NUM
ejpam-6124	384	7	(	(	PUNCT
ejpam-6124	384	8	mod	mod	NOUN
ejpam-6124	384	9	4	4	X
ejpam-6124	384	10	)	)	PUNCT
ejpam-6124	384	11	let	let	VERB
ejpam-6124	384	12	n	n	NOUN
ejpam-6124	384	13	=	=	SYM
ejpam-6124	384	14	7	7	X
ejpam-6124	384	15	.	.	PUNCT
ejpam-6124	384	16	by	by	ADP
ejpam-6124	384	17	proposition	proposition	NOUN
ejpam-6124	384	18	1	1	NUM
ejpam-6124	384	19	,	,	PUNCT
ejpam-6124	384	20	γt(c7	γt(c7	ADJ
ejpam-6124	384	21	)	)	PUNCT
ejpam-6124	384	22	=	=	SYM
ejpam-6124	384	23	4	4	X
ejpam-6124	384	24	.	.	PUNCT
ejpam-6124	384	25	clearly	clearly	ADV
ejpam-6124	384	26	,	,	PUNCT
ejpam-6124	384	27	t1	t1	NOUN
ejpam-6124	384	28	=	=	PUNCT
ejpam-6124	384	29	{	{	PUNCT
ejpam-6124	384	30	u1	u1	NOUN
ejpam-6124	384	31	,	,	PUNCT
ejpam-6124	384	32	u2	u2	PROPN
ejpam-6124	384	33	,	,	PUNCT
ejpam-6124	384	34	u4	u4	PROPN
ejpam-6124	384	35	,	,	PUNCT
ejpam-6124	384	36	u5	u5	PROPN
ejpam-6124	384	37	}	}	PUNCT
ejpam-6124	384	38	,	,	PUNCT
ejpam-6124	384	39	t2	t2	NOUN
ejpam-6124	384	40	=	=	SYM
ejpam-6124	384	41	{	{	PUNCT
ejpam-6124	384	42	u1	u1	NOUN
ejpam-6124	384	43	,	,	PUNCT
ejpam-6124	384	44	u2	u2	PROPN
ejpam-6124	384	45	,	,	PUNCT
ejpam-6124	384	46	u5	u5	PROPN
ejpam-6124	384	47	,	,	PUNCT
ejpam-6124	384	48	u6	u6	NOUN
ejpam-6124	384	49	}	}	PUNCT
ejpam-6124	384	50	,	,	PUNCT
ejpam-6124	384	51	t3	t3	PROPN
ejpam-6124	384	52	=	=	PUNCT
ejpam-6124	384	53	{	{	PUNCT
ejpam-6124	384	54	u2	u2	PROPN
ejpam-6124	384	55	,	,	PUNCT
ejpam-6124	384	56	u3	u3	PROPN
ejpam-6124	384	57	,	,	PUNCT
ejpam-6124	384	58	u5	u5	PROPN
ejpam-6124	384	59	,	,	PUNCT
ejpam-6124	384	60	u6	u6	PROPN
ejpam-6124	384	61	}	}	PUNCT
ejpam-6124	384	62	,	,	PUNCT
ejpam-6124	384	63	t4	t4	PROPN
ejpam-6124	384	64	=	=	PROPN
ejpam-6124	384	65	{	{	PUNCT
ejpam-6124	384	66	u2	u2	PROPN
ejpam-6124	384	67	,	,	PUNCT
ejpam-6124	384	68	u3	u3	NOUN
ejpam-6124	384	69	,	,	PUNCT
ejpam-6124	384	70	u6	u6	PROPN
ejpam-6124	384	71	,	,	PUNCT
ejpam-6124	384	72	u7	u7	PROPN
ejpam-6124	384	73	}	}	PUNCT
ejpam-6124	384	74	,	,	PUNCT
ejpam-6124	384	75	t5	t5	PROPN
ejpam-6124	384	76	=	=	SYM
ejpam-6124	384	77	{	{	PUNCT
ejpam-6124	384	78	u3	u3	PROPN
ejpam-6124	384	79	,	,	PUNCT
ejpam-6124	384	80	u4	u4	PROPN
ejpam-6124	384	81	,	,	PUNCT
ejpam-6124	384	82	u6	u6	PROPN
ejpam-6124	384	83	,	,	PUNCT
ejpam-6124	384	84	u7	u7	PROPN
ejpam-6124	384	85	}	}	PUNCT
ejpam-6124	384	86	,	,	PUNCT
ejpam-6124	384	87	t6	t6	PROPN
ejpam-6124	384	88	=	=	SYM
ejpam-6124	384	89	{	{	PUNCT
ejpam-6124	384	90	u3	u3	PROPN
ejpam-6124	384	91	,	,	PUNCT
ejpam-6124	384	92	u4	u4	PROPN
ejpam-6124	384	93	,	,	PUNCT
ejpam-6124	384	94	u7	u7	PROPN
ejpam-6124	384	95	,	,	PUNCT
ejpam-6124	384	96	u1	u1	NOUN
ejpam-6124	384	97	}	}	PUNCT
ejpam-6124	384	98	,	,	PUNCT
ejpam-6124	384	99	and	and	CCONJ
ejpam-6124	384	100	t7	t7	PROPN
ejpam-6124	384	101	=	=	PROPN
ejpam-6124	384	102	{	{	PUNCT
ejpam-6124	384	103	u4	u4	PROPN
ejpam-6124	384	104	,	,	PUNCT
ejpam-6124	384	105	u5	u5	PROPN
ejpam-6124	384	106	,	,	PUNCT
ejpam-6124	384	107	u7	u7	PROPN
ejpam-6124	384	108	,	,	PUNCT
ejpam-6124	384	109	u1	u1	PROPN
ejpam-6124	384	110	}	}	PUNCT
ejpam-6124	384	111	are	be	AUX
ejpam-6124	384	112	the	the	DET
ejpam-6124	384	113	only	only	ADJ
ejpam-6124	384	114	γt	γt	NOUN
ejpam-6124	384	115	-	-	NOUN
ejpam-6124	384	116	sets	set	NOUN
ejpam-6124	384	117	of	of	ADP
ejpam-6124	384	118	c7	c7	PROPN
ejpam-6124	384	119	.	.	PUNCT
ejpam-6124	385	1	it	it	PRON
ejpam-6124	385	2	is	be	AUX
ejpam-6124	385	3	also	also	ADV
ejpam-6124	385	4	clear	clear	ADJ
ejpam-6124	385	5	that	that	SCONJ
ejpam-6124	385	6	for	for	ADP
ejpam-6124	385	7	i	i	PROPN
ejpam-6124	385	8	=	=	NOUN
ejpam-6124	385	9	1	1	NUM
ejpam-6124	385	10	,	,	PUNCT
ejpam-6124	385	11	2	2	NUM
ejpam-6124	385	12	,	,	PUNCT
ejpam-6124	385	13	3	3	NUM
ejpam-6124	385	14	,	,	PUNCT
ejpam-6124	385	15	...	...	PUNCT
ejpam-6124	385	16	,	,	PUNCT
ejpam-6124	385	17	7	7	NUM
ejpam-6124	385	18	,	,	PUNCT
ejpam-6124	385	19	there	there	PRON
ejpam-6124	385	20	always	always	ADV
ejpam-6124	385	21	exists	exist	VERB
ejpam-6124	385	22	a	a	DET
ejpam-6124	385	23	vertex	vertex	NOUN
ejpam-6124	385	24	uk	uk	PROPN
ejpam-6124	385	25	in	in	ADP
ejpam-6124	385	26	v	v	PROPN
ejpam-6124	385	27	(	(	PUNCT
ejpam-6124	385	28	c7	c7	PROPN
ejpam-6124	385	29	)	)	PUNCT
ejpam-6124	385	30	such	such	ADJ
ejpam-6124	385	31	that	that	DET
ejpam-6124	385	32	|n(uk)∩ti|	|n(uk)∩ti|	NOUN
ejpam-6124	385	33	=	=	SYM
ejpam-6124	385	34	2	2	NUM
ejpam-6124	385	35	;	;	PUNCT
ejpam-6124	385	36	that	that	PRON
ejpam-6124	385	37	is	is	ADV
ejpam-6124	385	38	,	,	PUNCT
ejpam-6124	385	39	u3	u3	PROPN
ejpam-6124	385	40	is	be	AUX
ejpam-6124	385	41	associated	associate	VERB
ejpam-6124	385	42	with	with	ADP
ejpam-6124	385	43	t1	t1	PROPN
ejpam-6124	385	44	,	,	PUNCT
ejpam-6124	385	45	u7	u7	PROPN
ejpam-6124	385	46	with	with	ADP
ejpam-6124	385	47	t2	t2	PROPN
ejpam-6124	385	48	,	,	PUNCT
ejpam-6124	385	49	u4	u4	PROPN
ejpam-6124	385	50	with	with	ADP
ejpam-6124	385	51	t3	t3	PROPN
ejpam-6124	385	52	,	,	PUNCT
ejpam-6124	385	53	u1	u1	NOUN
ejpam-6124	385	54	with	with	ADP
ejpam-6124	385	55	t4	t4	PROPN
ejpam-6124	385	56	,	,	PUNCT
ejpam-6124	385	57	u5	u5	PROPN
ejpam-6124	385	58	with	with	ADP
ejpam-6124	385	59	t5	t5	PROPN
ejpam-6124	385	60	,	,	PUNCT
ejpam-6124	385	61	u2	u2	PROPN
ejpam-6124	385	62	with	with	ADP
ejpam-6124	385	63	r.	r.	PROPN
ejpam-6124	385	64	g.	g.	PROPN
ejpam-6124	385	65	aguinod	aguinod	PROPN
ejpam-6124	385	66	,	,	PUNCT
ejpam-6124	385	67	e.	e.	PROPN
ejpam-6124	385	68	m.	m.	PROPN
ejpam-6124	385	69	kiunisala	kiunisala	PROPN
ejpam-6124	385	70	,	,	PUNCT
ejpam-6124	385	71	c.	c.	PROPN
ejpam-6124	385	72	l.	l.	PROPN
ejpam-6124	385	73	armada	armada	PROPN
ejpam-6124	385	74	/	/	SYM
ejpam-6124	385	75	eur	eur	PROPN
ejpam-6124	385	76	.	.	PUNCT
ejpam-6124	386	1	j.	j.	PROPN
ejpam-6124	386	2	pure	pure	PROPN
ejpam-6124	386	3	appl	appl	PROPN
ejpam-6124	386	4	.	.	PROPN
ejpam-6124	386	5	math	math	PROPN
ejpam-6124	386	6	,	,	PUNCT
ejpam-6124	386	7	18	18	NUM
ejpam-6124	386	8	(	(	PUNCT
ejpam-6124	386	9	2	2	NUM
ejpam-6124	386	10	)	)	PUNCT
ejpam-6124	386	11	(	(	PUNCT
ejpam-6124	386	12	2025	2025	NUM
ejpam-6124	386	13	)	)	PUNCT
ejpam-6124	386	14	,	,	PUNCT
ejpam-6124	386	15	6124	6124	NUM
ejpam-6124	386	16	14	14	NUM
ejpam-6124	386	17	of	of	ADP
ejpam-6124	386	18	26	26	NUM
ejpam-6124	386	19	t6	t6	PROPN
ejpam-6124	386	20	,	,	PUNCT
ejpam-6124	386	21	and	and	CCONJ
ejpam-6124	386	22	u6	u6	PROPN
ejpam-6124	386	23	with	with	ADP
ejpam-6124	386	24	t7	t7	PROPN
ejpam-6124	386	25	.	.	PUNCT
ejpam-6124	387	1	it	it	PRON
ejpam-6124	387	2	follows	follow	VERB
ejpam-6124	387	3	that	that	SCONJ
ejpam-6124	387	4	for	for	ADP
ejpam-6124	387	5	i	i	PROPN
ejpam-6124	387	6	=	=	NOUN
ejpam-6124	387	7	1	1	NUM
ejpam-6124	387	8	,	,	PUNCT
ejpam-6124	387	9	2	2	NUM
ejpam-6124	387	10	,	,	PUNCT
ejpam-6124	387	11	3	3	NUM
ejpam-6124	387	12	,	,	PUNCT
ejpam-6124	387	13	...	...	PUNCT
ejpam-6124	387	14	,	,	PUNCT
ejpam-6124	387	15	7	7	NUM
ejpam-6124	387	16	,	,	PUNCT
ejpam-6124	387	17	ti	ti	NOUN
ejpam-6124	387	18	is	be	AUX
ejpam-6124	387	19	not	not	PART
ejpam-6124	387	20	a	a	DET
ejpam-6124	387	21	γte	γte	NOUN
ejpam-6124	387	22	-	-	PUNCT
ejpam-6124	387	23	set	set	NOUN
ejpam-6124	387	24	of	of	ADP
ejpam-6124	387	25	c7	c7	PROPN
ejpam-6124	387	26	.	.	PUNCT
ejpam-6124	388	1	hence	hence	ADV
ejpam-6124	388	2	,	,	PUNCT
ejpam-6124	388	3	there	there	PRON
ejpam-6124	388	4	is	be	VERB
ejpam-6124	388	5	no	no	DET
ejpam-6124	388	6	possible	possible	ADJ
ejpam-6124	388	7	way	way	NOUN
ejpam-6124	388	8	to	to	PART
ejpam-6124	388	9	create	create	VERB
ejpam-6124	388	10	a	a	DET
ejpam-6124	388	11	set	set	NOUN
ejpam-6124	388	12	that	that	PRON
ejpam-6124	388	13	is	be	AUX
ejpam-6124	388	14	both	both	CCONJ
ejpam-6124	388	15	a	a	DET
ejpam-6124	388	16	total	total	ADJ
ejpam-6124	388	17	and	and	CCONJ
ejpam-6124	388	18	exact	exact	ADJ
ejpam-6124	388	19	dominating	dominating	NOUN
ejpam-6124	388	20	set	set	NOUN
ejpam-6124	388	21	of	of	ADP
ejpam-6124	388	22	c7	c7	PROPN
ejpam-6124	388	23	and	and	CCONJ
ejpam-6124	388	24	so	so	ADV
ejpam-6124	388	25	,	,	PUNCT
ejpam-6124	388	26	c7	c7	PROPN
ejpam-6124	388	27	is	be	AUX
ejpam-6124	388	28	a	a	DET
ejpam-6124	388	29	non	non	ADJ
ejpam-6124	388	30	-	-	ADJ
ejpam-6124	388	31	γte	γte	PRON
ejpam-6124	388	32	-	-	PUNCT
ejpam-6124	388	33	graph	graph	NOUN
ejpam-6124	388	34	.	.	PUNCT
ejpam-6124	389	1	now	now	ADV
ejpam-6124	389	2	,	,	PUNCT
ejpam-6124	389	3	suppose	suppose	VERB
ejpam-6124	389	4	that	that	SCONJ
ejpam-6124	389	5	n	n	PROPN
ejpam-6124	389	6	>	>	X
ejpam-6124	389	7	7	7	X
ejpam-6124	389	8	.	.	PUNCT
ejpam-6124	390	1	let	let	VERB
ejpam-6124	390	2	p	p	NOUN
ejpam-6124	390	3	=	=	PUNCT
ejpam-6124	390	4	n−3	n−3	PROPN
ejpam-6124	390	5	4	4	NUM
ejpam-6124	390	6	and	and	CCONJ
ejpam-6124	390	7	j	j	NOUN
ejpam-6124	391	1	=	=	SYM
ejpam-6124	391	2	1	1	NUM
ejpam-6124	391	3	,	,	PUNCT
ejpam-6124	391	4	2	2	NUM
ejpam-6124	391	5	,	,	PUNCT
ejpam-6124	391	6	.	.	PUNCT
ejpam-6124	391	7	.	.	PUNCT
ejpam-6124	392	1	.	.	PUNCT
ejpam-6124	393	1	,	,	PUNCT
ejpam-6124	393	2	p.	p.	NOUN
ejpam-6124	393	3	group	group	NOUN
ejpam-6124	393	4	the	the	DET
ejpam-6124	393	5	vertices	vertex	NOUN
ejpam-6124	393	6	of	of	ADP
ejpam-6124	393	7	cn	cn	PROPN
ejpam-6124	393	8	into	into	ADP
ejpam-6124	393	9	p	p	PROPN
ejpam-6124	393	10	disjoint	disjoint	PROPN
ejpam-6124	393	11	subsets	subset	NOUN
ejpam-6124	393	12	rj	rj	PROPN
ejpam-6124	393	13	,	,	PUNCT
ejpam-6124	393	14	such	such	ADJ
ejpam-6124	393	15	that	that	SCONJ
ejpam-6124	393	16	r1	r1	NOUN
ejpam-6124	393	17	=	=	SYM
ejpam-6124	393	18	{	{	PUNCT
ejpam-6124	393	19	u1	u1	NOUN
ejpam-6124	393	20	,	,	PUNCT
ejpam-6124	393	21	u2	u2	NOUN
ejpam-6124	393	22	,	,	PUNCT
ejpam-6124	393	23	u3	u3	NOUN
ejpam-6124	393	24	,	,	PUNCT
ejpam-6124	393	25	u4	u4	PROPN
ejpam-6124	393	26	}	}	PUNCT
ejpam-6124	393	27	,	,	PUNCT
ejpam-6124	393	28	r2	r2	PROPN
ejpam-6124	393	29	=	=	SYM
ejpam-6124	393	30	{	{	PUNCT
ejpam-6124	393	31	u5	u5	PROPN
ejpam-6124	393	32	,	,	PUNCT
ejpam-6124	393	33	u6	u6	PROPN
ejpam-6124	393	34	,	,	PUNCT
ejpam-6124	393	35	u7	u7	PROPN
ejpam-6124	393	36	,	,	PUNCT
ejpam-6124	393	37	u8	u8	PROPN
ejpam-6124	393	38	}	}	PUNCT
ejpam-6124	393	39	,	,	PUNCT
ejpam-6124	393	40	r3	r3	PROPN
ejpam-6124	393	41	=	=	SYM
ejpam-6124	393	42	{	{	PUNCT
ejpam-6124	393	43	u9	u9	PROPN
ejpam-6124	393	44	,	,	PUNCT
ejpam-6124	393	45	u10	u10	PROPN
ejpam-6124	393	46	,	,	PUNCT
ejpam-6124	393	47	u11	u11	PROPN
ejpam-6124	393	48	,	,	PUNCT
ejpam-6124	393	49	u12	u12	PROPN
ejpam-6124	393	50	}	}	PUNCT
ejpam-6124	393	51	,	,	PUNCT
ejpam-6124	393	52	...	...	PUNCT
ejpam-6124	394	1	rp−1	rp−1	NOUN
ejpam-6124	394	2	=	=	SYM
ejpam-6124	394	3	{	{	PUNCT
ejpam-6124	394	4	un−10	un−10	PROPN
ejpam-6124	394	5	,	,	PUNCT
ejpam-6124	394	6	un−9	un−9	PROPN
ejpam-6124	394	7	,	,	PUNCT
ejpam-6124	394	8	un−8	un−8	ADJ
ejpam-6124	394	9	,	,	PUNCT
ejpam-6124	394	10	un−7	un−7	NOUN
ejpam-6124	394	11	}	}	PUNCT
ejpam-6124	394	12	,	,	PUNCT
ejpam-6124	394	13	and	and	CCONJ
ejpam-6124	394	14	rp	rp	NOUN
ejpam-6124	394	15	=	=	SYM
ejpam-6124	394	16	{	{	PUNCT
ejpam-6124	394	17	un−6	un−6	PROPN
ejpam-6124	394	18	,	,	PUNCT
ejpam-6124	394	19	un−5	un−5	PROPN
ejpam-6124	394	20	,	,	PUNCT
ejpam-6124	394	21	un−4	un−4	NOUN
ejpam-6124	394	22	,	,	PUNCT
ejpam-6124	394	23	un−3	un−3	ADJ
ejpam-6124	394	24	,	,	PUNCT
ejpam-6124	394	25	un−2	un−2	PROPN
ejpam-6124	394	26	,	,	PUNCT
ejpam-6124	394	27	un−1	un−1	PROPN
ejpam-6124	394	28	,	,	PUNCT
ejpam-6124	394	29	un	un	ADJ
ejpam-6124	394	30	}	}	PUNCT
ejpam-6124	394	31	,	,	PUNCT
ejpam-6124	394	32	where	where	SCONJ
ejpam-6124	394	33	|rj	|rj	PART
ejpam-6124	394	34	|	|	ADV
ejpam-6124	394	35	=	=	SYM
ejpam-6124	394	36	4	4	NUM
ejpam-6124	394	37	for	for	ADP
ejpam-6124	394	38	j	j	PROPN
ejpam-6124	394	39	=	=	SYM
ejpam-6124	394	40	1	1	NUM
ejpam-6124	394	41	,	,	PUNCT
ejpam-6124	394	42	2	2	NUM
ejpam-6124	394	43	,	,	PUNCT
ejpam-6124	394	44	.	.	PUNCT
ejpam-6124	394	45	.	.	PUNCT
ejpam-6124	394	46	.	.	PUNCT
ejpam-6124	395	1	,	,	PUNCT
ejpam-6124	395	2	p−	p−	NOUN
ejpam-6124	395	3	1	1	NUM
ejpam-6124	395	4	and	and	CCONJ
ejpam-6124	395	5	|rp|	|rp|	NUM
ejpam-6124	395	6	=	=	PUNCT
ejpam-6124	395	7	7	7	X
ejpam-6124	395	8	.	.	PUNCT
ejpam-6124	396	1	let	let	VERB
ejpam-6124	396	2	t	t	NOUN
ejpam-6124	396	3	=	=	SYM
ejpam-6124	396	4	{	{	PUNCT
ejpam-6124	396	5	u2	u2	PROPN
ejpam-6124	396	6	,	,	PUNCT
ejpam-6124	396	7	u3	u3	NOUN
ejpam-6124	396	8	,	,	PUNCT
ejpam-6124	396	9	u6	u6	PROPN
ejpam-6124	396	10	,	,	PUNCT
ejpam-6124	396	11	u7	u7	PROPN
ejpam-6124	396	12	,	,	PUNCT
ejpam-6124	396	13	u10	u10	PROPN
ejpam-6124	396	14	,	,	PUNCT
ejpam-6124	396	15	u11	u11	PROPN
ejpam-6124	396	16	,	,	PUNCT
ejpam-6124	396	17	.	.	PUNCT
ejpam-6124	396	18	.	.	PUNCT
ejpam-6124	396	19	.	.	PUNCT
ejpam-6124	397	1	un−9	un−9	PROPN
ejpam-6124	397	2	,	,	PUNCT
ejpam-6124	397	3	un−8	un−8	PROPN
ejpam-6124	397	4	,	,	PUNCT
ejpam-6124	397	5	un−5	un−5	PROPN
ejpam-6124	397	6	,	,	PUNCT
ejpam-6124	397	7	un−4	un−4	NOUN
ejpam-6124	397	8	,	,	PUNCT
ejpam-6124	397	9	un−1	un−1	PROPN
ejpam-6124	397	10	,	,	PUNCT
ejpam-6124	397	11	un	un	ADJ
ejpam-6124	397	12	}	}	PUNCT
ejpam-6124	397	13	,	,	PUNCT
ejpam-6124	397	14	where	where	SCONJ
ejpam-6124	397	15	t	t	PROPN
ejpam-6124	397	16	is	be	AUX
ejpam-6124	397	17	formed	form	VERB
ejpam-6124	397	18	by	by	ADP
ejpam-6124	397	19	getting	get	VERB
ejpam-6124	397	20	2	2	NUM
ejpam-6124	397	21	vertices	vertex	NOUN
ejpam-6124	397	22	in	in	ADP
ejpam-6124	397	23	each	each	DET
ejpam-6124	397	24	rj	rj	PROPN
ejpam-6124	397	25	for	for	ADP
ejpam-6124	397	26	j	j	PROPN
ejpam-6124	397	27	=	=	SYM
ejpam-6124	397	28	1	1	NUM
ejpam-6124	397	29	,	,	PUNCT
ejpam-6124	397	30	2	2	NUM
ejpam-6124	397	31	,	,	PUNCT
ejpam-6124	397	32	.	.	PUNCT
ejpam-6124	397	33	.	.	PUNCT
ejpam-6124	397	34	.	.	PUNCT
ejpam-6124	398	1	,	,	PUNCT
ejpam-6124	398	2	p−	p−	NOUN
ejpam-6124	398	3	1	1	NUM
ejpam-6124	398	4	and	and	CCONJ
ejpam-6124	398	5	4	4	NUM
ejpam-6124	398	6	vertices	vertex	NOUN
ejpam-6124	398	7	in	in	ADP
ejpam-6124	398	8	rp	rp	NOUN
ejpam-6124	398	9	.	.	PUNCT
ejpam-6124	399	1	it	it	PRON
ejpam-6124	399	2	follows	follow	VERB
ejpam-6124	399	3	that	that	PRON
ejpam-6124	399	4	|t	|t	VERB
ejpam-6124	400	1	|	|	ADV
ejpam-6124	401	1	=	=	SYM
ejpam-6124	401	2	2(p−	2(p−	NUM
ejpam-6124	401	3	1	1	NUM
ejpam-6124	401	4	)	)	PUNCT
ejpam-6124	401	5	+	+	CCONJ
ejpam-6124	401	6	4	4	NUM
ejpam-6124	401	7	=	=	SYM
ejpam-6124	401	8	2p+	2p+	NUM
ejpam-6124	401	9	2	2	NUM
ejpam-6124	401	10	=	=	SYM
ejpam-6124	401	11	2	2	NUM
ejpam-6124	401	12	(	(	PUNCT
ejpam-6124	401	13	n−	n−	NOUN
ejpam-6124	401	14	3	3	NUM
ejpam-6124	401	15	4	4	NUM
ejpam-6124	401	16	)	)	PUNCT
ejpam-6124	401	17	+	+	CCONJ
ejpam-6124	401	18	2	2	X
ejpam-6124	401	19	=	=	SYM
ejpam-6124	401	20	n+	n+	NUM
ejpam-6124	401	21	1	1	NUM
ejpam-6124	401	22	2	2	NUM
ejpam-6124	401	23	.	.	PUNCT
ejpam-6124	402	1	also	also	ADV
ejpam-6124	402	2	,	,	PUNCT
ejpam-6124	402	3	it	it	PRON
ejpam-6124	402	4	is	be	AUX
ejpam-6124	402	5	clear	clear	ADJ
ejpam-6124	402	6	that	that	SCONJ
ejpam-6124	402	7	n(t	n(t	PROPN
ejpam-6124	402	8	)	)	PUNCT
ejpam-6124	402	9	=	=	SYM
ejpam-6124	402	10	v	v	X
ejpam-6124	402	11	(	(	PUNCT
ejpam-6124	402	12	cn	cn	PROPN
ejpam-6124	402	13	)	)	PUNCT
ejpam-6124	402	14	and	and	CCONJ
ejpam-6124	402	15	so	so	ADV
ejpam-6124	402	16	,	,	PUNCT
ejpam-6124	402	17	t	t	PROPN
ejpam-6124	402	18	is	be	AUX
ejpam-6124	402	19	a	a	DET
ejpam-6124	402	20	γt	γt	NOUN
ejpam-6124	402	21	-	-	ADJ
ejpam-6124	402	22	set	set	VERB
ejpam-6124	402	23	by	by	ADP
ejpam-6124	402	24	proposition	proposition	NOUN
ejpam-6124	402	25	1	1	NUM
ejpam-6124	402	26	.	.	PUNCT
ejpam-6124	402	27	clearly	clearly	ADV
ejpam-6124	402	28	,	,	PUNCT
ejpam-6124	402	29	|n(ui	|n(ui	PROPN
ejpam-6124	402	30	)	)	PUNCT
ejpam-6124	402	31	∩	∩	NOUN
ejpam-6124	402	32	t	t	NOUN
ejpam-6124	403	1	|	|	NOUN
ejpam-6124	403	2	=	=	SYM
ejpam-6124	403	3	1	1	NUM
ejpam-6124	403	4	for	for	ADP
ejpam-6124	403	5	all	all	PRON
ejpam-6124	403	6	ui	ui	NOUN
ejpam-6124	403	7	∈	∈	PROPN
ejpam-6124	403	8	v	v	NOUN
ejpam-6124	403	9	(	(	PUNCT
ejpam-6124	403	10	cn	cn	PROPN
ejpam-6124	403	11	)	)	PUNCT
ejpam-6124	403	12	\	\	NOUN
ejpam-6124	403	13	{	{	PUNCT
ejpam-6124	403	14	u1	u1	NOUN
ejpam-6124	403	15	}	}	PUNCT
ejpam-6124	403	16	and	and	CCONJ
ejpam-6124	403	17	|n(u1	|n(u1	ADJ
ejpam-6124	403	18	)	)	PUNCT
ejpam-6124	403	19	∩	∩	NOUN
ejpam-6124	403	20	t	t	NOUN
ejpam-6124	404	1	|	|	NOUN
ejpam-6124	404	2	=	=	NOUN
ejpam-6124	404	3	2	2	X
ejpam-6124	404	4	.	.	PUNCT
ejpam-6124	404	5	therefore	therefore	ADV
ejpam-6124	404	6	,	,	PUNCT
ejpam-6124	404	7	t	t	PROPN
ejpam-6124	404	8	is	be	AUX
ejpam-6124	404	9	not	not	PART
ejpam-6124	404	10	a	a	DET
ejpam-6124	404	11	γte	γte	NOUN
ejpam-6124	404	12	-	-	PUNCT
ejpam-6124	404	13	set	set	NOUN
ejpam-6124	404	14	.	.	PUNCT
ejpam-6124	405	1	note	note	VERB
ejpam-6124	405	2	that	that	PRON
ejpam-6124	405	3	|n(u1	|n(u1	NOUN
ejpam-6124	405	4	)	)	PUNCT
ejpam-6124	405	5	∩	∩	NOUN
ejpam-6124	405	6	t	t	NOUN
ejpam-6124	406	1	|	|	NOUN
ejpam-6124	406	2	=	=	SYM
ejpam-6124	406	3	1	1	NUM
ejpam-6124	406	4	if	if	SCONJ
ejpam-6124	406	5	either	either	CCONJ
ejpam-6124	406	6	u2	u2	NOUN
ejpam-6124	406	7	or	or	CCONJ
ejpam-6124	406	8	un	un	ADJ
ejpam-6124	406	9	,	,	PUNCT
ejpam-6124	406	10	but	but	CCONJ
ejpam-6124	406	11	not	not	PART
ejpam-6124	406	12	both	both	PRON
ejpam-6124	406	13	,	,	PUNCT
ejpam-6124	406	14	is	be	AUX
ejpam-6124	406	15	not	not	PART
ejpam-6124	406	16	in	in	ADP
ejpam-6124	406	17	t	t	PROPN
ejpam-6124	406	18	.	.	PUNCT
ejpam-6124	407	1	if	if	SCONJ
ejpam-6124	407	2	u2	u2	PROPN
ejpam-6124	407	3	/∈	/∈	PROPN
ejpam-6124	407	4	t	t	PROPN
ejpam-6124	407	5	and	and	CCONJ
ejpam-6124	407	6	un	un	PROPN
ejpam-6124	407	7	∈	∈	PROPN
ejpam-6124	407	8	t	t	PROPN
ejpam-6124	407	9	,	,	PUNCT
ejpam-6124	407	10	|n(u3	|n(u3	NOUN
ejpam-6124	407	11	)	)	PUNCT
ejpam-6124	407	12	∩	∩	NOUN
ejpam-6124	407	13	t	t	NOUN
ejpam-6124	407	14	|	|	NOUN
ejpam-6124	407	15	=	=	NOUN
ejpam-6124	407	16	0	0	X
ejpam-6124	407	17	.	.	PUNCT
ejpam-6124	408	1	if	if	SCONJ
ejpam-6124	408	2	un	un	PROPN
ejpam-6124	408	3	/∈	/∈	PROPN
ejpam-6124	408	4	t	t	PROPN
ejpam-6124	408	5	and	and	CCONJ
ejpam-6124	408	6	u2	u2	PROPN
ejpam-6124	408	7	∈	∈	PROPN
ejpam-6124	408	8	t	t	PROPN
ejpam-6124	408	9	,	,	PUNCT
ejpam-6124	408	10	|n(un−1	|n(un−1	NOUN
ejpam-6124	408	11	)	)	PUNCT
ejpam-6124	408	12	∩	∩	NOUN
ejpam-6124	408	13	t	t	NOUN
ejpam-6124	409	1	|	|	NOUN
ejpam-6124	409	2	=	=	NOUN
ejpam-6124	409	3	0	0	X
ejpam-6124	409	4	.	.	PUNCT
ejpam-6124	410	1	in	in	ADP
ejpam-6124	410	2	either	either	DET
ejpam-6124	410	3	case	case	NOUN
ejpam-6124	410	4	,	,	PUNCT
ejpam-6124	410	5	t	t	PROPN
ejpam-6124	410	6	is	be	AUX
ejpam-6124	410	7	not	not	PART
ejpam-6124	410	8	a	a	DET
ejpam-6124	410	9	γte	γte	NOUN
ejpam-6124	410	10	-	-	PUNCT
ejpam-6124	410	11	set	set	NOUN
ejpam-6124	410	12	.	.	PUNCT
ejpam-6124	411	1	since	since	SCONJ
ejpam-6124	411	2	t	t	PROPN
ejpam-6124	411	3	is	be	AUX
ejpam-6124	411	4	arbitrarily	arbitrarily	ADV
ejpam-6124	411	5	chosen	choose	VERB
ejpam-6124	411	6	,	,	PUNCT
ejpam-6124	411	7	there	there	PRON
ejpam-6124	411	8	is	be	VERB
ejpam-6124	411	9	no	no	DET
ejpam-6124	411	10	possible	possible	ADJ
ejpam-6124	411	11	way	way	NOUN
ejpam-6124	411	12	to	to	PART
ejpam-6124	411	13	create	create	VERB
ejpam-6124	411	14	a	a	DET
ejpam-6124	411	15	set	set	NOUN
ejpam-6124	411	16	that	that	PRON
ejpam-6124	411	17	is	be	AUX
ejpam-6124	411	18	both	both	CCONJ
ejpam-6124	411	19	a	a	DET
ejpam-6124	411	20	total	total	ADJ
ejpam-6124	411	21	and	and	CCONJ
ejpam-6124	411	22	exact	exact	ADJ
ejpam-6124	411	23	dominating	dominating	NOUN
ejpam-6124	411	24	set	set	NOUN
ejpam-6124	411	25	of	of	ADP
ejpam-6124	411	26	cn	cn	PROPN
ejpam-6124	411	27	.	.	PUNCT
ejpam-6124	412	1	thus	thus	ADV
ejpam-6124	412	2	,	,	PUNCT
ejpam-6124	412	3	cn	cn	PROPN
ejpam-6124	412	4	is	be	AUX
ejpam-6124	412	5	a	a	DET
ejpam-6124	412	6	non	non	ADJ
ejpam-6124	412	7	-	-	ADJ
ejpam-6124	412	8	γte	γte	PRON
ejpam-6124	412	9	-	-	PUNCT
ejpam-6124	412	10	graph	graph	NOUN
ejpam-6124	412	11	if	if	SCONJ
ejpam-6124	412	12	n	n	PRON
ejpam-6124	412	13	≡	≡	PROPN
ejpam-6124	412	14	3	3	NUM
ejpam-6124	412	15	(	(	PUNCT
ejpam-6124	412	16	mod	mod	NOUN
ejpam-6124	412	17	4	4	NUM
ejpam-6124	412	18	)	)	PUNCT
ejpam-6124	412	19	.	.	PUNCT
ejpam-6124	413	1	therefore	therefore	ADV
ejpam-6124	413	2	,	,	PUNCT
ejpam-6124	413	3	in	in	ADP
ejpam-6124	413	4	any	any	DET
ejpam-6124	413	5	case	case	NOUN
ejpam-6124	413	6	,	,	PUNCT
ejpam-6124	413	7	cn	cn	PROPN
ejpam-6124	413	8	is	be	AUX
ejpam-6124	413	9	a	a	DET
ejpam-6124	413	10	non	non	ADJ
ejpam-6124	413	11	-	-	ADJ
ejpam-6124	413	12	γte	γte	PRON
ejpam-6124	413	13	-	-	PUNCT
ejpam-6124	413	14	graph	graph	NOUN
ejpam-6124	413	15	if	if	SCONJ
ejpam-6124	413	16	n	n	NOUN
ejpam-6124	413	17	̸≡	̸≡	VERB
ejpam-6124	413	18	0	0	PUNCT
ejpam-6124	414	1	(	(	PUNCT
ejpam-6124	414	2	mod	mod	PROPN
ejpam-6124	414	3	4	4	NUM
ejpam-6124	414	4	)	)	PUNCT
ejpam-6124	414	5	.	.	PUNCT
ejpam-6124	415	1	theorem	theorem	VERB
ejpam-6124	415	2	9	9	NUM
ejpam-6124	415	3	.	.	PUNCT
ejpam-6124	416	1	let	let	VERB
ejpam-6124	416	2	n	n	PRON
ejpam-6124	416	3	be	be	AUX
ejpam-6124	416	4	a	a	DET
ejpam-6124	416	5	positive	positive	ADJ
ejpam-6124	416	6	integer	integer	NOUN
ejpam-6124	416	7	such	such	ADJ
ejpam-6124	416	8	that	that	SCONJ
ejpam-6124	416	9	n	n	CCONJ
ejpam-6124	416	10	≥	≥	NOUN
ejpam-6124	416	11	4	4	NUM
ejpam-6124	416	12	.	.	PUNCT
ejpam-6124	417	1	then	then	ADV
ejpam-6124	417	2	the	the	DET
ejpam-6124	417	3	total	total	ADJ
ejpam-6124	417	4	exact	exact	ADJ
ejpam-6124	417	5	domination	domination	NOUN
ejpam-6124	417	6	number	number	NOUN
ejpam-6124	417	7	of	of	ADP
ejpam-6124	417	8	a	a	DET
ejpam-6124	417	9	cycle	cycle	NOUN
ejpam-6124	417	10	cn	cn	NOUN
ejpam-6124	417	11	of	of	ADP
ejpam-6124	417	12	order	order	NOUN
ejpam-6124	417	13	n	n	CCONJ
ejpam-6124	417	14	,	,	PUNCT
ejpam-6124	417	15	where	where	SCONJ
ejpam-6124	417	16	n	n	PRON
ejpam-6124	417	17	≡	≡	PROPN
ejpam-6124	417	18	0	0	PUNCT
ejpam-6124	417	19	(	(	PUNCT
ejpam-6124	417	20	mod	mod	PROPN
ejpam-6124	417	21	4	4	NUM
ejpam-6124	417	22	)	)	PUNCT
ejpam-6124	417	23	,	,	PUNCT
ejpam-6124	417	24	is	be	AUX
ejpam-6124	417	25	given	give	VERB
ejpam-6124	417	26	by	by	ADP
ejpam-6124	417	27	γte(cn	γte(cn	PROPN
ejpam-6124	417	28	)	)	PUNCT
ejpam-6124	417	29	=	=	SYM
ejpam-6124	417	30	n	n	PRON
ejpam-6124	417	31	2	2	NUM
ejpam-6124	417	32	.	.	PUNCT
ejpam-6124	418	1	proof	proof	NOUN
ejpam-6124	418	2	.	.	PUNCT
ejpam-6124	419	1	suppose	suppose	VERB
ejpam-6124	419	2	that	that	SCONJ
ejpam-6124	419	3	n	n	PROPN
ejpam-6124	419	4	≡	≡	PROPN
ejpam-6124	419	5	0	0	PUNCT
ejpam-6124	419	6	(	(	PUNCT
ejpam-6124	419	7	mod	mod	PROPN
ejpam-6124	419	8	4	4	NUM
ejpam-6124	419	9	)	)	PUNCT
ejpam-6124	419	10	.	.	PUNCT
ejpam-6124	420	1	let	let	VERB
ejpam-6124	420	2	n	n	NOUN
ejpam-6124	420	3	=	=	SYM
ejpam-6124	420	4	4	4	X
ejpam-6124	420	5	.	.	PUNCT
ejpam-6124	420	6	by	by	ADP
ejpam-6124	420	7	proposition	proposition	NOUN
ejpam-6124	420	8	1	1	NUM
ejpam-6124	420	9	,	,	PUNCT
ejpam-6124	420	10	γt(c4	γt(c4	NOUN
ejpam-6124	420	11	)	)	PUNCT
ejpam-6124	420	12	=	=	SYM
ejpam-6124	421	1	4	4	NUM
ejpam-6124	421	2	2	2	NUM
ejpam-6124	421	3	=	=	SYM
ejpam-6124	421	4	2	2	NUM
ejpam-6124	421	5	.	.	PUNCT
ejpam-6124	421	6	clearly	clearly	ADV
ejpam-6124	421	7	,	,	PUNCT
ejpam-6124	421	8	t1	t1	NOUN
ejpam-6124	421	9	=	=	PUNCT
ejpam-6124	421	10	{	{	PUNCT
ejpam-6124	421	11	u1	u1	NOUN
ejpam-6124	421	12	,	,	PUNCT
ejpam-6124	421	13	u2	u2	PROPN
ejpam-6124	421	14	}	}	PUNCT
ejpam-6124	421	15	,	,	PUNCT
ejpam-6124	421	16	t2	t2	NOUN
ejpam-6124	421	17	=	=	SYM
ejpam-6124	421	18	{	{	PUNCT
ejpam-6124	421	19	u2	u2	NOUN
ejpam-6124	421	20	,	,	PUNCT
ejpam-6124	421	21	u3	u3	NOUN
ejpam-6124	421	22	}	}	PUNCT
ejpam-6124	421	23	,	,	PUNCT
ejpam-6124	421	24	t3	t3	PROPN
ejpam-6124	421	25	=	=	SYM
ejpam-6124	421	26	{	{	PUNCT
ejpam-6124	421	27	u3	u3	PROPN
ejpam-6124	421	28	,	,	PUNCT
ejpam-6124	421	29	u4	u4	PROPN
ejpam-6124	421	30	}	}	PUNCT
ejpam-6124	421	31	,	,	PUNCT
ejpam-6124	421	32	and	and	CCONJ
ejpam-6124	421	33	t4	t4	PROPN
ejpam-6124	421	34	=	=	PROPN
ejpam-6124	421	35	{	{	PUNCT
ejpam-6124	421	36	u4	u4	PROPN
ejpam-6124	421	37	,	,	PUNCT
ejpam-6124	421	38	u1	u1	PROPN
ejpam-6124	421	39	}	}	PUNCT
ejpam-6124	421	40	are	be	AUX
ejpam-6124	421	41	the	the	DET
ejpam-6124	421	42	only	only	ADJ
ejpam-6124	421	43	γt	γt	NOUN
ejpam-6124	421	44	-	-	NOUN
ejpam-6124	421	45	sets	set	NOUN
ejpam-6124	421	46	of	of	ADP
ejpam-6124	421	47	c4	c4	NOUN
ejpam-6124	421	48	.	.	PUNCT
ejpam-6124	422	1	it	it	PRON
ejpam-6124	422	2	is	be	AUX
ejpam-6124	422	3	also	also	ADV
ejpam-6124	422	4	clear	clear	ADJ
ejpam-6124	422	5	that	that	SCONJ
ejpam-6124	422	6	for	for	ADP
ejpam-6124	422	7	i	i	PROPN
ejpam-6124	422	8	=	=	NOUN
ejpam-6124	422	9	1	1	NUM
ejpam-6124	422	10	,	,	PUNCT
ejpam-6124	422	11	2	2	NUM
ejpam-6124	422	12	,	,	PUNCT
ejpam-6124	422	13	3	3	NUM
ejpam-6124	422	14	,	,	PUNCT
ejpam-6124	422	15	4	4	NUM
ejpam-6124	422	16	,	,	PUNCT
ejpam-6124	422	17	|n(uk	|n(uk	ADJ
ejpam-6124	422	18	)	)	PUNCT
ejpam-6124	422	19	∩	∩	ADJ
ejpam-6124	422	20	ti|	ti|	NOUN
ejpam-6124	422	21	=	=	NOUN
ejpam-6124	422	22	1	1	NUM
ejpam-6124	422	23	for	for	ADP
ejpam-6124	422	24	all	all	DET
ejpam-6124	422	25	vertices	vertex	NOUN
ejpam-6124	422	26	uk	uk	PROPN
ejpam-6124	422	27	in	in	ADP
ejpam-6124	422	28	v	v	PROPN
ejpam-6124	422	29	(	(	PUNCT
ejpam-6124	422	30	c4	c4	NOUN
ejpam-6124	422	31	)	)	PUNCT
ejpam-6124	422	32	.	.	PUNCT
ejpam-6124	423	1	thus	thus	ADV
ejpam-6124	423	2	,	,	PUNCT
ejpam-6124	423	3	for	for	ADP
ejpam-6124	423	4	i	i	PROPN
ejpam-6124	423	5	=	=	SYM
ejpam-6124	423	6	1	1	NUM
ejpam-6124	423	7	,	,	PUNCT
ejpam-6124	423	8	2	2	NUM
ejpam-6124	423	9	,	,	PUNCT
ejpam-6124	423	10	3	3	NUM
ejpam-6124	423	11	,	,	PUNCT
ejpam-6124	423	12	4	4	NUM
ejpam-6124	423	13	,	,	PUNCT
ejpam-6124	423	14	ti	ti	X
ejpam-6124	423	15	is	be	AUX
ejpam-6124	423	16	a	a	DET
ejpam-6124	423	17	γte	γte	NOUN
ejpam-6124	423	18	-	-	PUNCT
ejpam-6124	423	19	set	set	NOUN
ejpam-6124	423	20	of	of	ADP
ejpam-6124	423	21	c4	c4	NOUN
ejpam-6124	423	22	and	and	CCONJ
ejpam-6124	423	23	so	so	ADV
ejpam-6124	423	24	,	,	PUNCT
ejpam-6124	423	25	γte(c4	γte(c4	ADJ
ejpam-6124	423	26	)	)	PUNCT
ejpam-6124	423	27	=	=	SYM
ejpam-6124	423	28	|ti|	|ti|	NOUN
ejpam-6124	424	1	=	=	NOUN
ejpam-6124	424	2	2	2	X
ejpam-6124	424	3	.	.	PUNCT
ejpam-6124	424	4	r.	r.	PROPN
ejpam-6124	424	5	g.	g.	PROPN
ejpam-6124	424	6	aguinod	aguinod	PROPN
ejpam-6124	424	7	,	,	PUNCT
ejpam-6124	424	8	e.	e.	PROPN
ejpam-6124	424	9	m.	m.	PROPN
ejpam-6124	424	10	kiunisala	kiunisala	PROPN
ejpam-6124	424	11	,	,	PUNCT
ejpam-6124	424	12	c.	c.	PROPN
ejpam-6124	424	13	l.	l.	PROPN
ejpam-6124	424	14	armada	armada	PROPN
ejpam-6124	424	15	/	/	SYM
ejpam-6124	424	16	eur	eur	PROPN
ejpam-6124	424	17	.	.	PUNCT
ejpam-6124	425	1	j.	j.	PROPN
ejpam-6124	425	2	pure	pure	PROPN
ejpam-6124	425	3	appl	appl	PROPN
ejpam-6124	425	4	.	.	PROPN
ejpam-6124	425	5	math	math	PROPN
ejpam-6124	425	6	,	,	PUNCT
ejpam-6124	425	7	18	18	NUM
ejpam-6124	425	8	(	(	PUNCT
ejpam-6124	425	9	2	2	NUM
ejpam-6124	425	10	)	)	PUNCT
ejpam-6124	425	11	(	(	PUNCT
ejpam-6124	425	12	2025	2025	NUM
ejpam-6124	425	13	)	)	PUNCT
ejpam-6124	425	14	,	,	PUNCT
ejpam-6124	425	15	6124	6124	NUM
ejpam-6124	425	16	15	15	NUM
ejpam-6124	425	17	of	of	ADP
ejpam-6124	425	18	26	26	NUM
ejpam-6124	425	19	now	now	ADV
ejpam-6124	425	20	,	,	PUNCT
ejpam-6124	425	21	suppose	suppose	VERB
ejpam-6124	425	22	that	that	SCONJ
ejpam-6124	425	23	n	n	PROPN
ejpam-6124	425	24	>	>	X
ejpam-6124	425	25	4	4	X
ejpam-6124	425	26	.	.	PUNCT
ejpam-6124	425	27	let	let	VERB
ejpam-6124	425	28	p	p	NOUN
ejpam-6124	425	29	=	=	VERB
ejpam-6124	425	30	n/4	n/4	PROPN
ejpam-6124	425	31	and	and	CCONJ
ejpam-6124	425	32	j	j	PROPN
ejpam-6124	425	33	=	=	SYM
ejpam-6124	425	34	1	1	NUM
ejpam-6124	425	35	,	,	PUNCT
ejpam-6124	425	36	2	2	NUM
ejpam-6124	425	37	,	,	PUNCT
ejpam-6124	425	38	.	.	PUNCT
ejpam-6124	425	39	.	.	PUNCT
ejpam-6124	425	40	.	.	PUNCT
ejpam-6124	426	1	,	,	PUNCT
ejpam-6124	426	2	p.	p.	NOUN
ejpam-6124	426	3	group	group	NOUN
ejpam-6124	426	4	the	the	DET
ejpam-6124	426	5	vertices	vertex	NOUN
ejpam-6124	426	6	of	of	ADP
ejpam-6124	426	7	cn	cn	PROPN
ejpam-6124	426	8	into	into	ADP
ejpam-6124	426	9	p	p	PROPN
ejpam-6124	426	10	disjoint	disjoint	PROPN
ejpam-6124	426	11	subsets	subset	NOUN
ejpam-6124	426	12	rj	rj	PROPN
ejpam-6124	426	13	,	,	PUNCT
ejpam-6124	426	14	such	such	ADJ
ejpam-6124	426	15	that	that	SCONJ
ejpam-6124	426	16	r1	r1	NOUN
ejpam-6124	426	17	=	=	SYM
ejpam-6124	426	18	{	{	PUNCT
ejpam-6124	426	19	u1	u1	NOUN
ejpam-6124	426	20	,	,	PUNCT
ejpam-6124	426	21	u2	u2	NOUN
ejpam-6124	426	22	,	,	PUNCT
ejpam-6124	426	23	u3	u3	NOUN
ejpam-6124	426	24	,	,	PUNCT
ejpam-6124	426	25	u4	u4	PROPN
ejpam-6124	426	26	}	}	PUNCT
ejpam-6124	426	27	,	,	PUNCT
ejpam-6124	426	28	r2	r2	PROPN
ejpam-6124	426	29	=	=	SYM
ejpam-6124	426	30	{	{	PUNCT
ejpam-6124	426	31	u5	u5	PROPN
ejpam-6124	426	32	,	,	PUNCT
ejpam-6124	426	33	u6	u6	PROPN
ejpam-6124	426	34	,	,	PUNCT
ejpam-6124	426	35	u7	u7	PROPN
ejpam-6124	426	36	,	,	PUNCT
ejpam-6124	426	37	u8	u8	PROPN
ejpam-6124	426	38	}	}	PUNCT
ejpam-6124	426	39	,	,	PUNCT
ejpam-6124	426	40	r3	r3	PROPN
ejpam-6124	426	41	=	=	SYM
ejpam-6124	426	42	{	{	PUNCT
ejpam-6124	426	43	u9	u9	PROPN
ejpam-6124	426	44	,	,	PUNCT
ejpam-6124	426	45	u10	u10	PROPN
ejpam-6124	426	46	,	,	PUNCT
ejpam-6124	426	47	u11	u11	PROPN
ejpam-6124	426	48	,	,	PUNCT
ejpam-6124	426	49	u12	u12	PROPN
ejpam-6124	426	50	}	}	PUNCT
ejpam-6124	426	51	,	,	PUNCT
ejpam-6124	426	52	...	...	PUNCT
ejpam-6124	427	1	rp−1	rp−1	NOUN
ejpam-6124	427	2	=	=	SYM
ejpam-6124	427	3	{	{	PUNCT
ejpam-6124	427	4	un−7	un−7	PROPN
ejpam-6124	427	5	,	,	PUNCT
ejpam-6124	427	6	un−6	un−6	PROPN
ejpam-6124	427	7	,	,	PUNCT
ejpam-6124	427	8	un−5	un−5	PROPN
ejpam-6124	427	9	,	,	PUNCT
ejpam-6124	427	10	un−4	un−4	NOUN
ejpam-6124	427	11	}	}	PUNCT
ejpam-6124	427	12	,	,	PUNCT
ejpam-6124	427	13	and	and	CCONJ
ejpam-6124	427	14	rp	rp	NOUN
ejpam-6124	427	15	=	=	PUNCT
ejpam-6124	427	16	{	{	PUNCT
ejpam-6124	427	17	un−3	un−3	PROPN
ejpam-6124	427	18	,	,	PUNCT
ejpam-6124	427	19	un−2	un−2	PROPN
ejpam-6124	427	20	,	,	PUNCT
ejpam-6124	427	21	un−1	un−1	PROPN
ejpam-6124	427	22	,	,	PUNCT
ejpam-6124	427	23	un	un	ADJ
ejpam-6124	427	24	}	}	PUNCT
ejpam-6124	427	25	.	.	PUNCT
ejpam-6124	428	1	where	where	SCONJ
ejpam-6124	428	2	|rj	|rj	PART
ejpam-6124	428	3	|	|	ADV
ejpam-6124	428	4	=	=	SYM
ejpam-6124	428	5	4	4	NUM
ejpam-6124	428	6	for	for	ADP
ejpam-6124	428	7	j	j	PROPN
ejpam-6124	428	8	=	=	SYM
ejpam-6124	428	9	1	1	NUM
ejpam-6124	428	10	,	,	PUNCT
ejpam-6124	428	11	2	2	NUM
ejpam-6124	428	12	,	,	PUNCT
ejpam-6124	428	13	.	.	PUNCT
ejpam-6124	428	14	.	.	PUNCT
ejpam-6124	429	1	.	.	PUNCT
ejpam-6124	430	1	,	,	PUNCT
ejpam-6124	430	2	p−	p−	NOUN
ejpam-6124	430	3	1	1	NUM
ejpam-6124	430	4	,	,	PUNCT
ejpam-6124	430	5	p.	p.	NOUN
ejpam-6124	430	6	let	let	VERB
ejpam-6124	430	7	t	t	NOUN
ejpam-6124	430	8	=	=	SYM
ejpam-6124	430	9	{	{	PUNCT
ejpam-6124	430	10	u2	u2	PROPN
ejpam-6124	430	11	,	,	PUNCT
ejpam-6124	430	12	u3	u3	NOUN
ejpam-6124	430	13	,	,	PUNCT
ejpam-6124	430	14	u6	u6	PROPN
ejpam-6124	430	15	,	,	PUNCT
ejpam-6124	430	16	u7	u7	PROPN
ejpam-6124	430	17	,	,	PUNCT
ejpam-6124	430	18	u10	u10	PROPN
ejpam-6124	430	19	,	,	PUNCT
ejpam-6124	430	20	u11	u11	PROPN
ejpam-6124	430	21	,	,	PUNCT
ejpam-6124	430	22	.	.	PUNCT
ejpam-6124	430	23	.	.	PUNCT
ejpam-6124	431	1	.	.	PUNCT
ejpam-6124	432	1	,	,	PUNCT
ejpam-6124	432	2	un−6	un−6	PROPN
ejpam-6124	432	3	,	,	PUNCT
ejpam-6124	432	4	un−5	un−5	PROPN
ejpam-6124	432	5	,	,	PUNCT
ejpam-6124	432	6	un−2	un−2	PROPN
ejpam-6124	432	7	,	,	PUNCT
ejpam-6124	432	8	un−1	un−1	PROPN
ejpam-6124	432	9	}	}	PUNCT
ejpam-6124	432	10	where	where	SCONJ
ejpam-6124	432	11	t	t	PROPN
ejpam-6124	432	12	is	be	AUX
ejpam-6124	432	13	formed	form	VERB
ejpam-6124	432	14	by	by	ADP
ejpam-6124	432	15	getting	get	VERB
ejpam-6124	432	16	2	2	NUM
ejpam-6124	432	17	vertices	vertex	NOUN
ejpam-6124	432	18	in	in	ADP
ejpam-6124	432	19	each	each	DET
ejpam-6124	432	20	rj	rj	PROPN
ejpam-6124	432	21	for	for	ADP
ejpam-6124	432	22	j	j	PROPN
ejpam-6124	432	23	=	=	SYM
ejpam-6124	432	24	1	1	NUM
ejpam-6124	432	25	,	,	PUNCT
ejpam-6124	432	26	2	2	NUM
ejpam-6124	432	27	,	,	PUNCT
ejpam-6124	432	28	.	.	PUNCT
ejpam-6124	432	29	.	.	PUNCT
ejpam-6124	433	1	.	.	PUNCT
ejpam-6124	434	1	,	,	PUNCT
ejpam-6124	434	2	p−	p−	NOUN
ejpam-6124	434	3	1	1	NUM
ejpam-6124	434	4	,	,	PUNCT
ejpam-6124	434	5	p.	p.	NOUN
ejpam-6124	434	6	it	it	PRON
ejpam-6124	434	7	follows	follow	VERB
ejpam-6124	434	8	that	that	PRON
ejpam-6124	434	9	|t	|t	VERB
ejpam-6124	435	1	|	|	ADV
ejpam-6124	435	2	=	=	SYM
ejpam-6124	435	3	2p	2p	NUM
ejpam-6124	435	4	=	=	SYM
ejpam-6124	435	5	2	2	NUM
ejpam-6124	435	6	(	(	PUNCT
ejpam-6124	435	7	n	n	ADV
ejpam-6124	435	8	4	4	NUM
ejpam-6124	435	9	)	)	PUNCT
ejpam-6124	436	1	=	=	SYM
ejpam-6124	436	2	n	n	PRON
ejpam-6124	436	3	2	2	NUM
ejpam-6124	436	4	.	.	PUNCT
ejpam-6124	437	1	also	also	ADV
ejpam-6124	437	2	,	,	PUNCT
ejpam-6124	437	3	it	it	PRON
ejpam-6124	437	4	is	be	AUX
ejpam-6124	437	5	clear	clear	ADJ
ejpam-6124	437	6	that	that	SCONJ
ejpam-6124	437	7	n(t	n(t	PROPN
ejpam-6124	437	8	)	)	PUNCT
ejpam-6124	437	9	=	=	SYM
ejpam-6124	437	10	v	v	X
ejpam-6124	437	11	(	(	PUNCT
ejpam-6124	437	12	cn	cn	PROPN
ejpam-6124	437	13	)	)	PUNCT
ejpam-6124	437	14	and	and	CCONJ
ejpam-6124	437	15	so	so	ADV
ejpam-6124	437	16	,	,	PUNCT
ejpam-6124	437	17	t	t	PROPN
ejpam-6124	437	18	is	be	AUX
ejpam-6124	437	19	a	a	DET
ejpam-6124	437	20	γt	γt	NOUN
ejpam-6124	437	21	-	-	ADJ
ejpam-6124	437	22	set	set	VERB
ejpam-6124	437	23	by	by	ADP
ejpam-6124	437	24	proposition	proposition	NOUN
ejpam-6124	437	25	1	1	NUM
ejpam-6124	437	26	.	.	PUNCT
ejpam-6124	437	27	clearly	clearly	ADV
ejpam-6124	437	28	,	,	PUNCT
ejpam-6124	437	29	|n(ui	|n(ui	PROPN
ejpam-6124	437	30	)	)	PUNCT
ejpam-6124	437	31	∩	∩	NOUN
ejpam-6124	437	32	t	t	NOUN
ejpam-6124	438	1	|	|	NOUN
ejpam-6124	438	2	=	=	SYM
ejpam-6124	438	3	1	1	NUM
ejpam-6124	438	4	for	for	ADP
ejpam-6124	438	5	all	all	DET
ejpam-6124	438	6	ui	ui	NOUN
ejpam-6124	438	7	∈	∈	PROPN
ejpam-6124	438	8	v	v	NOUN
ejpam-6124	438	9	(	(	PUNCT
ejpam-6124	438	10	cn	cn	PROPN
ejpam-6124	438	11	)	)	PUNCT
ejpam-6124	438	12	.	.	PUNCT
ejpam-6124	439	1	therefore	therefore	ADV
ejpam-6124	439	2	,	,	PUNCT
ejpam-6124	439	3	t	t	PROPN
ejpam-6124	439	4	is	be	AUX
ejpam-6124	439	5	a	a	DET
ejpam-6124	439	6	γte	γte	NOUN
ejpam-6124	439	7	-	-	PUNCT
ejpam-6124	439	8	set	set	NOUN
ejpam-6124	439	9	.	.	PUNCT
ejpam-6124	440	1	this	this	PRON
ejpam-6124	440	2	implies	imply	VERB
ejpam-6124	440	3	that	that	SCONJ
ejpam-6124	440	4	γte(cn	γte(cn	NOUN
ejpam-6124	440	5	)	)	PUNCT
ejpam-6124	441	1	=	=	VERB
ejpam-6124	441	2	|t	|t	VERB
ejpam-6124	442	1	|	|	ADV
ejpam-6124	442	2	=	=	SYM
ejpam-6124	442	3	n	n	PRON
ejpam-6124	442	4	2	2	NUM
ejpam-6124	442	5	.	.	PUNCT
ejpam-6124	442	6	theorem	theorem	VERB
ejpam-6124	442	7	10	10	NUM
ejpam-6124	442	8	.	.	PUNCT
ejpam-6124	443	1	the	the	DET
ejpam-6124	443	2	total	total	ADJ
ejpam-6124	443	3	exact	exact	ADJ
ejpam-6124	443	4	domination	domination	NOUN
ejpam-6124	443	5	number	number	NOUN
ejpam-6124	443	6	of	of	ADP
ejpam-6124	443	7	a	a	DET
ejpam-6124	443	8	complete	complete	ADJ
ejpam-6124	443	9	bipartite	bipartite	NOUN
ejpam-6124	443	10	graph	graph	NOUN
ejpam-6124	443	11	km	km	PROPN
ejpam-6124	443	12	,	,	PUNCT
ejpam-6124	443	13	n	n	PUNCT
ejpam-6124	443	14	is	be	AUX
ejpam-6124	443	15	given	give	VERB
ejpam-6124	443	16	by	by	ADP
ejpam-6124	443	17	γte(km	γte(km	PROPN
ejpam-6124	443	18	,	,	PUNCT
ejpam-6124	443	19	n	n	CCONJ
ejpam-6124	443	20	)	)	PUNCT
ejpam-6124	443	21	=	=	SYM
ejpam-6124	443	22	2	2	X
ejpam-6124	443	23	.	.	PUNCT
ejpam-6124	444	1	proof	proof	NOUN
ejpam-6124	444	2	.	.	PUNCT
ejpam-6124	445	1	the	the	DET
ejpam-6124	445	2	vertex	vertex	NOUN
ejpam-6124	445	3	set	set	NOUN
ejpam-6124	445	4	of	of	ADP
ejpam-6124	445	5	km	km	PROPN
ejpam-6124	445	6	,	,	PUNCT
ejpam-6124	445	7	n	n	PRON
ejpam-6124	445	8	can	can	AUX
ejpam-6124	445	9	be	be	AUX
ejpam-6124	445	10	partitioned	partition	VERB
ejpam-6124	445	11	into	into	ADP
ejpam-6124	445	12	two	two	NUM
ejpam-6124	445	13	disjoint	disjoint	NOUN
ejpam-6124	445	14	sets	set	NOUN
ejpam-6124	445	15	,	,	PUNCT
ejpam-6124	445	16	u	u	NOUN
ejpam-6124	445	17	and	and	CCONJ
ejpam-6124	445	18	v	v	NOUN
ejpam-6124	445	19	,	,	PUNCT
ejpam-6124	445	20	where	where	SCONJ
ejpam-6124	445	21	each	each	DET
ejpam-6124	445	22	vertex	vertex	NOUN
ejpam-6124	445	23	in	in	ADP
ejpam-6124	445	24	u	u	NOUN
ejpam-6124	445	25	is	be	AUX
ejpam-6124	445	26	adjacent	adjacent	ADJ
ejpam-6124	445	27	to	to	ADP
ejpam-6124	445	28	every	every	DET
ejpam-6124	445	29	vertex	vertex	NOUN
ejpam-6124	445	30	in	in	ADP
ejpam-6124	445	31	v	v	NOUN
ejpam-6124	445	32	and	and	CCONJ
ejpam-6124	445	33	and	and	CCONJ
ejpam-6124	445	34	there	there	PRON
ejpam-6124	445	35	are	be	VERB
ejpam-6124	445	36	no	no	DET
ejpam-6124	445	37	edges	edge	NOUN
ejpam-6124	445	38	within	within	ADP
ejpam-6124	445	39	u	u	NOUN
ejpam-6124	445	40	and	and	CCONJ
ejpam-6124	445	41	within	within	ADP
ejpam-6124	445	42	v	v	NOUN
ejpam-6124	445	43	.	.	PUNCT
ejpam-6124	446	1	let	let	VERB
ejpam-6124	446	2	u	u	PRON
ejpam-6124	446	3	=	=	NOUN
ejpam-6124	446	4	{	{	PUNCT
ejpam-6124	446	5	u1	u1	NOUN
ejpam-6124	446	6	,	,	PUNCT
ejpam-6124	446	7	u2	u2	NOUN
ejpam-6124	446	8	,	,	PUNCT
ejpam-6124	446	9	.	.	PUNCT
ejpam-6124	446	10	.	.	PUNCT
ejpam-6124	447	1	.	.	PUNCT
ejpam-6124	448	1	,	,	PUNCT
ejpam-6124	448	2	um	um	INTJ
ejpam-6124	448	3	}	}	PUNCT
ejpam-6124	448	4	and	and	CCONJ
ejpam-6124	448	5	v	v	NOUN
ejpam-6124	448	6	=	=	SYM
ejpam-6124	448	7	{	{	PUNCT
ejpam-6124	448	8	v1	v1	PROPN
ejpam-6124	448	9	,	,	PUNCT
ejpam-6124	448	10	v2	v2	PROPN
ejpam-6124	448	11	,	,	PUNCT
ejpam-6124	448	12	.	.	PUNCT
ejpam-6124	448	13	.	.	PUNCT
ejpam-6124	449	1	.	.	PUNCT
ejpam-6124	450	1	,	,	PUNCT
ejpam-6124	450	2	vn	vn	PROPN
ejpam-6124	450	3	}	}	PUNCT
ejpam-6124	450	4	.	.	PUNCT
ejpam-6124	451	1	consider	consider	VERB
ejpam-6124	451	2	t	t	PROPN
ejpam-6124	451	3	⊆	⊆	NUM
ejpam-6124	451	4	v	v	NOUN
ejpam-6124	451	5	(	(	PUNCT
ejpam-6124	451	6	km	km	PROPN
ejpam-6124	451	7	,	,	PUNCT
ejpam-6124	451	8	n	n	CCONJ
ejpam-6124	451	9	)	)	PUNCT
ejpam-6124	451	10	containing	contain	VERB
ejpam-6124	451	11	exactly	exactly	ADV
ejpam-6124	451	12	one	one	NUM
ejpam-6124	451	13	vertex	vertex	NOUN
ejpam-6124	451	14	up	up	ADP
ejpam-6124	451	15	∈	∈	PROPN
ejpam-6124	451	16	u	u	NOUN
ejpam-6124	451	17	and	and	CCONJ
ejpam-6124	451	18	one	one	NUM
ejpam-6124	451	19	vertex	vertex	NOUN
ejpam-6124	451	20	vq	vq	PROPN
ejpam-6124	451	21	∈	∈	PROPN
ejpam-6124	451	22	v	v	NOUN
ejpam-6124	451	23	,	,	PUNCT
ejpam-6124	451	24	that	that	ADV
ejpam-6124	451	25	is	is	ADV
ejpam-6124	451	26	,	,	PUNCT
ejpam-6124	451	27	t	t	PROPN
ejpam-6124	451	28	=	=	PUNCT
ejpam-6124	451	29	{	{	PUNCT
ejpam-6124	451	30	up	up	ADP
ejpam-6124	451	31	,	,	PUNCT
ejpam-6124	451	32	vq	vq	NOUN
ejpam-6124	451	33	}	}	PUNCT
ejpam-6124	451	34	.	.	PUNCT
ejpam-6124	452	1	clearly	clearly	ADV
ejpam-6124	452	2	,	,	PUNCT
ejpam-6124	452	3	|n(ui)∩t	|n(ui)∩t	PROPN
ejpam-6124	452	4	|	|	ADV
ejpam-6124	452	5	=	=	SYM
ejpam-6124	452	6	|{vq}|	|{vq}|	PROPN
ejpam-6124	452	7	=	=	NOUN
ejpam-6124	452	8	1	1	NUM
ejpam-6124	452	9	for	for	ADP
ejpam-6124	452	10	all	all	DET
ejpam-6124	452	11	ui	ui	NOUN
ejpam-6124	452	12	∈	∈	PROPN
ejpam-6124	452	13	u	u	NOUN
ejpam-6124	452	14	and	and	CCONJ
ejpam-6124	452	15	|n(vj)∩t	|n(vj)∩t	NOUN
ejpam-6124	452	16	|	|	ADV
ejpam-6124	452	17	=	=	PUNCT
ejpam-6124	452	18	|{up}|	|{up}|	NOUN
ejpam-6124	452	19	=	=	SYM
ejpam-6124	452	20	1	1	NUM
ejpam-6124	452	21	for	for	ADP
ejpam-6124	452	22	all	all	PRON
ejpam-6124	452	23	vj	vj	PRON
ejpam-6124	452	24	∈	∈	PROPN
ejpam-6124	452	25	v	v	NOUN
ejpam-6124	452	26	.	.	PUNCT
ejpam-6124	453	1	hence	hence	ADV
ejpam-6124	453	2	,	,	PUNCT
ejpam-6124	453	3	t	t	PROPN
ejpam-6124	453	4	is	be	AUX
ejpam-6124	453	5	a	a	DET
ejpam-6124	453	6	γte	γte	NOUN
ejpam-6124	453	7	-	-	PUNCT
ejpam-6124	453	8	set	set	NOUN
ejpam-6124	453	9	of	of	ADP
ejpam-6124	453	10	km	km	PROPN
ejpam-6124	453	11	,	,	PUNCT
ejpam-6124	453	12	n	n	PROPN
ejpam-6124	453	13	and	and	CCONJ
ejpam-6124	453	14	so	so	ADV
ejpam-6124	453	15	,	,	PUNCT
ejpam-6124	453	16	γte(km	γte(km	PROPN
ejpam-6124	453	17	,	,	PUNCT
ejpam-6124	453	18	n	n	CCONJ
ejpam-6124	453	19	)	)	PUNCT
ejpam-6124	453	20	=	=	VERB
ejpam-6124	453	21	|t	|t	PROPN
ejpam-6124	454	1	|	|	ADV
ejpam-6124	454	2	=	=	SYM
ejpam-6124	454	3	2	2	X
ejpam-6124	454	4	.	.	PUNCT
ejpam-6124	454	5	r.	r.	PROPN
ejpam-6124	454	6	g.	g.	PROPN
ejpam-6124	454	7	aguinod	aguinod	PROPN
ejpam-6124	454	8	,	,	PUNCT
ejpam-6124	454	9	e.	e.	PROPN
ejpam-6124	454	10	m.	m.	PROPN
ejpam-6124	454	11	kiunisala	kiunisala	PROPN
ejpam-6124	454	12	,	,	PUNCT
ejpam-6124	454	13	c.	c.	PROPN
ejpam-6124	454	14	l.	l.	PROPN
ejpam-6124	454	15	armada	armada	PROPN
ejpam-6124	454	16	/	/	SYM
ejpam-6124	454	17	eur	eur	PROPN
ejpam-6124	454	18	.	.	PUNCT
ejpam-6124	455	1	j.	j.	PROPN
ejpam-6124	455	2	pure	pure	PROPN
ejpam-6124	455	3	appl	appl	PROPN
ejpam-6124	455	4	.	.	PROPN
ejpam-6124	455	5	math	math	PROPN
ejpam-6124	455	6	,	,	PUNCT
ejpam-6124	455	7	18	18	NUM
ejpam-6124	455	8	(	(	PUNCT
ejpam-6124	455	9	2	2	NUM
ejpam-6124	455	10	)	)	PUNCT
ejpam-6124	455	11	(	(	PUNCT
ejpam-6124	455	12	2025	2025	NUM
ejpam-6124	455	13	)	)	PUNCT
ejpam-6124	455	14	,	,	PUNCT
ejpam-6124	455	15	6124	6124	NUM
ejpam-6124	455	16	16	16	NUM
ejpam-6124	455	17	of	of	ADP
ejpam-6124	455	18	26	26	NUM
ejpam-6124	455	19	4.1	4.1	NUM
ejpam-6124	455	20	.	.	PUNCT
ejpam-6124	456	1	total	total	ADJ
ejpam-6124	456	2	exact	exact	ADJ
ejpam-6124	456	3	dominating	dominating	NOUN
ejpam-6124	456	4	sets	set	NOUN
ejpam-6124	456	5	in	in	ADP
ejpam-6124	456	6	the	the	DET
ejpam-6124	456	7	join	join	NOUN
ejpam-6124	456	8	of	of	ADP
ejpam-6124	456	9	graphs	graph	NOUN
ejpam-6124	456	10	this	this	DET
ejpam-6124	456	11	section	section	NOUN
ejpam-6124	456	12	contains	contain	VERB
ejpam-6124	456	13	results	result	NOUN
ejpam-6124	456	14	when	when	SCONJ
ejpam-6124	456	15	the	the	DET
ejpam-6124	456	16	join	join	NOUN
ejpam-6124	456	17	g	g	PROPN
ejpam-6124	457	1	+	+	PROPN
ejpam-6124	457	2	h	h	NOUN
ejpam-6124	457	3	has	have	AUX
ejpam-6124	457	4	either	either	CCONJ
ejpam-6124	457	5	a	a	DET
ejpam-6124	457	6	γte	γte	NOUN
ejpam-6124	457	7	−	−	PROPN
ejpam-6124	457	8	set	set	NOUN
ejpam-6124	457	9	or	or	CCONJ
ejpam-6124	457	10	has	have	VERB
ejpam-6124	457	11	no	no	DET
ejpam-6124	457	12	γte	γte	NOUN
ejpam-6124	457	13	−	−	PROPN
ejpam-6124	457	14	set	set	NOUN
ejpam-6124	457	15	and	and	CCONJ
ejpam-6124	457	16	its	its	PRON
ejpam-6124	457	17	total	total	ADJ
ejpam-6124	457	18	exact	exact	ADJ
ejpam-6124	457	19	domination	domination	NOUN
ejpam-6124	457	20	number	number	NOUN
ejpam-6124	457	21	.	.	PUNCT
ejpam-6124	458	1	theorem	theorem	NOUN
ejpam-6124	458	2	11	11	NUM
ejpam-6124	458	3	.	.	PUNCT
ejpam-6124	459	1	let	let	VERB
ejpam-6124	459	2	g	g	NOUN
ejpam-6124	460	1	and	and	CCONJ
ejpam-6124	460	2	h	h	NOUN
ejpam-6124	460	3	be	be	VERB
ejpam-6124	460	4	any	any	DET
ejpam-6124	460	5	graphs	graph	NOUN
ejpam-6124	460	6	.	.	PUNCT
ejpam-6124	461	1	then	then	ADV
ejpam-6124	461	2	g+h	g+h	PROPN
ejpam-6124	461	3	is	be	AUX
ejpam-6124	461	4	a	a	DET
ejpam-6124	461	5	non	non	ADJ
ejpam-6124	461	6	-	-	ADJ
ejpam-6124	461	7	γte	γte	PRON
ejpam-6124	461	8	-	-	PUNCT
ejpam-6124	461	9	graph	graph	NOUN
ejpam-6124	461	10	if	if	SCONJ
ejpam-6124	462	1	and	and	CCONJ
ejpam-6124	462	2	only	only	ADV
ejpam-6124	462	3	if	if	SCONJ
ejpam-6124	462	4	it	it	PRON
ejpam-6124	462	5	satisfies	satisfy	VERB
ejpam-6124	462	6	one	one	NUM
ejpam-6124	462	7	of	of	ADP
ejpam-6124	462	8	the	the	DET
ejpam-6124	462	9	following	following	NOUN
ejpam-6124	462	10	:	:	PUNCT
ejpam-6124	462	11	(	(	PUNCT
ejpam-6124	462	12	i	i	NOUN
ejpam-6124	462	13	)	)	PUNCT
ejpam-6124	462	14	both	both	CCONJ
ejpam-6124	462	15	g	g	PROPN
ejpam-6124	462	16	and	and	CCONJ
ejpam-6124	462	17	h	h	NOUN
ejpam-6124	462	18	have	have	VERB
ejpam-6124	462	19	no	no	DET
ejpam-6124	462	20	isolated	isolated	ADJ
ejpam-6124	462	21	vertices	vertex	NOUN
ejpam-6124	462	22	;	;	PUNCT
ejpam-6124	462	23	or	or	CCONJ
ejpam-6124	462	24	(	(	PUNCT
ejpam-6124	462	25	ii	ii	NOUN
ejpam-6124	462	26	)	)	PUNCT
ejpam-6124	462	27	exactly	exactly	ADV
ejpam-6124	462	28	one	one	NUM
ejpam-6124	462	29	of	of	ADP
ejpam-6124	462	30	the	the	DET
ejpam-6124	462	31	graphs	graph	NOUN
ejpam-6124	462	32	g	g	NOUN
ejpam-6124	462	33	and	and	CCONJ
ejpam-6124	462	34	h	h	NOUN
ejpam-6124	462	35	has	have	VERB
ejpam-6124	462	36	at	at	ADV
ejpam-6124	462	37	least	least	ADJ
ejpam-6124	462	38	one	one	NUM
ejpam-6124	462	39	isolated	isolated	ADJ
ejpam-6124	462	40	vertex	vertex	NOUN
ejpam-6124	462	41	,	,	PUNCT
ejpam-6124	462	42	while	while	SCONJ
ejpam-6124	462	43	the	the	DET
ejpam-6124	462	44	other	other	ADJ
ejpam-6124	462	45	has	have	VERB
ejpam-6124	462	46	none	none	NOUN
ejpam-6124	462	47	.	.	PUNCT
ejpam-6124	463	1	proof	proof	NOUN
ejpam-6124	463	2	.	.	PUNCT
ejpam-6124	464	1	suppose	suppose	VERB
ejpam-6124	464	2	that	that	SCONJ
ejpam-6124	464	3	both	both	PRON
ejpam-6124	464	4	g	g	PROPN
ejpam-6124	464	5	and	and	CCONJ
ejpam-6124	464	6	h	h	NOUN
ejpam-6124	464	7	have	have	VERB
ejpam-6124	464	8	at	at	ADV
ejpam-6124	464	9	least	least	ADV
ejpam-6124	464	10	one	one	NUM
ejpam-6124	464	11	isolated	isolated	ADJ
ejpam-6124	464	12	vertex	vertex	NOUN
ejpam-6124	464	13	.	.	PUNCT
ejpam-6124	465	1	let	let	VERB
ejpam-6124	465	2	u	u	PRON
ejpam-6124	465	3	and	and	CCONJ
ejpam-6124	465	4	v	v	NOUN
ejpam-6124	465	5	be	be	AUX
ejpam-6124	465	6	isolated	isolate	VERB
ejpam-6124	465	7	vertices	vertex	NOUN
ejpam-6124	465	8	in	in	ADP
ejpam-6124	465	9	g	g	PROPN
ejpam-6124	465	10	and	and	CCONJ
ejpam-6124	465	11	h	h	NOUN
ejpam-6124	465	12	,	,	PUNCT
ejpam-6124	465	13	respectively	respectively	ADV
ejpam-6124	465	14	.	.	PUNCT
ejpam-6124	466	1	clearly	clearly	ADV
ejpam-6124	466	2	,	,	PUNCT
ejpam-6124	466	3	t	t	PROPN
ejpam-6124	466	4	=	=	SYM
ejpam-6124	466	5	{	{	PUNCT
ejpam-6124	466	6	u	u	NOUN
ejpam-6124	466	7	,	,	PUNCT
ejpam-6124	466	8	v	v	NOUN
ejpam-6124	466	9	}	}	PUNCT
ejpam-6124	466	10	is	be	AUX
ejpam-6124	466	11	a	a	DET
ejpam-6124	466	12	total	total	ADJ
ejpam-6124	466	13	dominating	dominating	NOUN
ejpam-6124	466	14	set	set	NOUN
ejpam-6124	466	15	of	of	ADP
ejpam-6124	466	16	g	g	PROPN
ejpam-6124	466	17	+	+	CCONJ
ejpam-6124	466	18	h	h	NOUN
ejpam-6124	466	19	by	by	ADP
ejpam-6124	466	20	theorem	theorem	ADJ
ejpam-6124	466	21	2(iii	2(iii	NUM
ejpam-6124	466	22	)	)	PUNCT
ejpam-6124	466	23	.	.	PUNCT
ejpam-6124	467	1	clearly	clearly	ADV
ejpam-6124	467	2	,	,	PUNCT
ejpam-6124	467	3	|n(u	|n(u	PROPN
ejpam-6124	467	4	)	)	PUNCT
ejpam-6124	467	5	∩	∩	PROPN
ejpam-6124	467	6	t	t	NOUN
ejpam-6124	467	7	|	|	ADV
ejpam-6124	467	8	=	=	PUNCT
ejpam-6124	467	9	|{v}|	|{v}|	PUNCT
ejpam-6124	467	10	=	=	SYM
ejpam-6124	467	11	1	1	NUM
ejpam-6124	467	12	and	and	CCONJ
ejpam-6124	467	13	|n(v	|n(v	ADJ
ejpam-6124	467	14	)	)	PUNCT
ejpam-6124	467	15	∩	∩	NOUN
ejpam-6124	467	16	t	t	NOUN
ejpam-6124	467	17	|	|	NOUN
ejpam-6124	467	18	=	=	SYM
ejpam-6124	467	19	|{u}|	|{u}|	PUNCT
ejpam-6124	467	20	=	=	SYM
ejpam-6124	467	21	1	1	X
ejpam-6124	467	22	.	.	PUNCT
ejpam-6124	467	23	since	since	SCONJ
ejpam-6124	467	24	u	u	NOUN
ejpam-6124	467	25	is	be	AUX
ejpam-6124	467	26	an	an	DET
ejpam-6124	467	27	isolated	isolated	ADJ
ejpam-6124	467	28	vertex	vertex	NOUN
ejpam-6124	467	29	in	in	ADP
ejpam-6124	467	30	g	g	NOUN
ejpam-6124	467	31	,	,	PUNCT
ejpam-6124	467	32	any	any	DET
ejpam-6124	467	33	vertex	vertex	NOUN
ejpam-6124	467	34	p	p	X
ejpam-6124	467	35	̸=	̸=	PROPN
ejpam-6124	467	36	u	u	NOUN
ejpam-6124	467	37	in	in	ADP
ejpam-6124	467	38	g	g	PROPN
ejpam-6124	467	39	is	be	AUX
ejpam-6124	467	40	adjacent	adjacent	ADJ
ejpam-6124	467	41	to	to	ADP
ejpam-6124	467	42	the	the	DET
ejpam-6124	467	43	vertex	vertex	NOUN
ejpam-6124	467	44	v	v	NOUN
ejpam-6124	467	45	in	in	ADP
ejpam-6124	467	46	g	g	PROPN
ejpam-6124	467	47	+	+	PROPN
ejpam-6124	467	48	h.	h.	NOUN
ejpam-6124	467	49	that	that	PRON
ejpam-6124	467	50	is	be	AUX
ejpam-6124	467	51	,	,	PUNCT
ejpam-6124	467	52	in	in	ADP
ejpam-6124	467	53	g	g	PROPN
ejpam-6124	467	54	+	+	NOUN
ejpam-6124	467	55	h	h	NOUN
ejpam-6124	467	56	,	,	PUNCT
ejpam-6124	467	57	|n(p	|n(p	ADJ
ejpam-6124	467	58	)	)	PUNCT
ejpam-6124	467	59	∩	∩	NOUN
ejpam-6124	468	1	t	t	NOUN
ejpam-6124	468	2	|	|	ADV
ejpam-6124	468	3	=	=	PUNCT
ejpam-6124	468	4	|{v}|	|{v}|	PUNCT
ejpam-6124	468	5	=	=	SYM
ejpam-6124	468	6	1	1	NUM
ejpam-6124	468	7	for	for	ADP
ejpam-6124	468	8	all	all	PRON
ejpam-6124	468	9	p	p	NOUN
ejpam-6124	468	10	∈	∈	PROPN
ejpam-6124	468	11	v	v	NOUN
ejpam-6124	468	12	(	(	PUNCT
ejpam-6124	468	13	g	g	NOUN
ejpam-6124	468	14	)	)	PUNCT
ejpam-6124	468	15	.	.	PUNCT
ejpam-6124	469	1	also	also	ADV
ejpam-6124	469	2	,	,	PUNCT
ejpam-6124	469	3	since	since	SCONJ
ejpam-6124	469	4	v	v	NOUN
ejpam-6124	469	5	is	be	AUX
ejpam-6124	469	6	an	an	DET
ejpam-6124	469	7	isolated	isolated	ADJ
ejpam-6124	469	8	vertex	vertex	NOUN
ejpam-6124	469	9	in	in	ADP
ejpam-6124	469	10	h	h	NOUN
ejpam-6124	469	11	,	,	PUNCT
ejpam-6124	469	12	any	any	DET
ejpam-6124	469	13	vertex	vertex	NOUN
ejpam-6124	469	14	q	q	X
ejpam-6124	469	15	̸=	̸=	PROPN
ejpam-6124	469	16	v	v	NOUN
ejpam-6124	469	17	in	in	ADP
ejpam-6124	469	18	h	h	NOUN
ejpam-6124	469	19	is	be	AUX
ejpam-6124	469	20	adjacent	adjacent	ADJ
ejpam-6124	469	21	to	to	ADP
ejpam-6124	469	22	the	the	DET
ejpam-6124	469	23	vertex	vertex	NOUN
ejpam-6124	469	24	u	u	NOUN
ejpam-6124	469	25	in	in	ADP
ejpam-6124	469	26	g	g	PROPN
ejpam-6124	469	27	+	+	PROPN
ejpam-6124	469	28	h.	h.	NOUN
ejpam-6124	469	29	that	that	PRON
ejpam-6124	469	30	is	be	AUX
ejpam-6124	469	31	,	,	PUNCT
ejpam-6124	469	32	in	in	ADP
ejpam-6124	469	33	g+h	g+h	PROPN
ejpam-6124	469	34	,	,	PUNCT
ejpam-6124	469	35	|n(q	|n(q	PROPN
ejpam-6124	469	36	)	)	PUNCT
ejpam-6124	469	37	∩	∩	NOUN
ejpam-6124	469	38	t	t	NOUN
ejpam-6124	469	39	|	|	NOUN
ejpam-6124	469	40	=	=	SYM
ejpam-6124	469	41	|{u}|	|{u}|	PUNCT
ejpam-6124	469	42	=	=	SYM
ejpam-6124	469	43	1	1	NUM
ejpam-6124	469	44	for	for	ADP
ejpam-6124	469	45	all	all	DET
ejpam-6124	469	46	q	q	PROPN
ejpam-6124	469	47	∈	∈	PROPN
ejpam-6124	469	48	v	v	NOUN
ejpam-6124	469	49	(	(	PUNCT
ejpam-6124	469	50	h	h	NOUN
ejpam-6124	469	51	)	)	PUNCT
ejpam-6124	469	52	.	.	PUNCT
ejpam-6124	470	1	therefore	therefore	ADV
ejpam-6124	470	2	,	,	PUNCT
ejpam-6124	470	3	t	t	PROPN
ejpam-6124	470	4	is	be	AUX
ejpam-6124	470	5	a	a	DET
ejpam-6124	470	6	γte	γte	NOUN
ejpam-6124	470	7	−	−	ADP
ejpam-6124	470	8	set	set	NOUN
ejpam-6124	470	9	and	and	CCONJ
ejpam-6124	470	10	so	so	ADV
ejpam-6124	470	11	,	,	PUNCT
ejpam-6124	470	12	g+h	g+h	PROPN
ejpam-6124	470	13	is	be	AUX
ejpam-6124	470	14	not	not	PART
ejpam-6124	470	15	a	a	DET
ejpam-6124	470	16	non	non	ADJ
ejpam-6124	470	17	-	-	ADJ
ejpam-6124	470	18	γte	γte	PRON
ejpam-6124	470	19	-	-	PUNCT
ejpam-6124	470	20	graph	graph	NOUN
ejpam-6124	470	21	.	.	PUNCT
ejpam-6124	471	1	suppose	suppose	VERB
ejpam-6124	471	2	that	that	SCONJ
ejpam-6124	471	3	(	(	PUNCT
ejpam-6124	471	4	i	i	NOUN
ejpam-6124	471	5	)	)	PUNCT
ejpam-6124	471	6	holds	hold	VERB
ejpam-6124	471	7	,	,	PUNCT
ejpam-6124	471	8	that	that	ADV
ejpam-6124	471	9	is	is	ADV
ejpam-6124	471	10	,	,	PUNCT
ejpam-6124	471	11	both	both	PRON
ejpam-6124	471	12	g	g	PROPN
ejpam-6124	471	13	and	and	CCONJ
ejpam-6124	471	14	h	h	NOUN
ejpam-6124	471	15	have	have	VERB
ejpam-6124	471	16	no	no	DET
ejpam-6124	471	17	isolated	isolated	ADJ
ejpam-6124	471	18	vertices	vertex	NOUN
ejpam-6124	471	19	.	.	PUNCT
ejpam-6124	472	1	by	by	ADP
ejpam-6124	472	2	corollary	corollary	ADJ
ejpam-6124	472	3	1	1	NUM
ejpam-6124	472	4	,	,	PUNCT
ejpam-6124	472	5	γt(g+h	γt(g+h	PROPN
ejpam-6124	472	6	)	)	PUNCT
ejpam-6124	472	7	=	=	SYM
ejpam-6124	472	8	2	2	X
ejpam-6124	472	9	.	.	X
ejpam-6124	472	10	consider	consider	VERB
ejpam-6124	472	11	the	the	DET
ejpam-6124	472	12	following	follow	VERB
ejpam-6124	472	13	cases	case	NOUN
ejpam-6124	472	14	:	:	PUNCT
ejpam-6124	472	15	case	case	NOUN
ejpam-6124	472	16	1	1	NUM
ejpam-6124	472	17	:	:	PUNCT
ejpam-6124	472	18	t	t	PROPN
ejpam-6124	472	19	is	be	AUX
ejpam-6124	472	20	a	a	DET
ejpam-6124	472	21	total	total	ADJ
ejpam-6124	472	22	dominating	dominating	NOUN
ejpam-6124	472	23	set	set	NOUN
ejpam-6124	472	24	that	that	PRON
ejpam-6124	472	25	contains	contain	VERB
ejpam-6124	472	26	two	two	NUM
ejpam-6124	472	27	vertices	vertex	NOUN
ejpam-6124	472	28	in	in	ADP
ejpam-6124	472	29	v	v	ADP
ejpam-6124	472	30	(	(	PUNCT
ejpam-6124	472	31	g	g	NOUN
ejpam-6124	472	32	)	)	PUNCT
ejpam-6124	472	33	or	or	CCONJ
ejpam-6124	472	34	v	v	NOUN
ejpam-6124	472	35	(	(	PUNCT
ejpam-6124	472	36	h	h	NOUN
ejpam-6124	472	37	)	)	PUNCT
ejpam-6124	472	38	.	.	PUNCT
ejpam-6124	473	1	without	without	ADP
ejpam-6124	473	2	loss	loss	NOUN
ejpam-6124	473	3	of	of	ADP
ejpam-6124	473	4	generality	generality	NOUN
ejpam-6124	473	5	,	,	PUNCT
ejpam-6124	473	6	let	let	VERB
ejpam-6124	473	7	t	t	NOUN
ejpam-6124	473	8	=	=	PUNCT
ejpam-6124	473	9	{	{	PUNCT
ejpam-6124	473	10	p	p	X
ejpam-6124	473	11	,	,	PUNCT
ejpam-6124	473	12	q	q	NOUN
ejpam-6124	473	13	}	}	PUNCT
ejpam-6124	473	14	where	where	SCONJ
ejpam-6124	473	15	p	p	X
ejpam-6124	473	16	,	,	PUNCT
ejpam-6124	473	17	q	q	PROPN
ejpam-6124	473	18	∈	∈	PROPN
ejpam-6124	473	19	v	v	NOUN
ejpam-6124	473	20	(	(	PUNCT
ejpam-6124	473	21	g	g	NOUN
ejpam-6124	473	22	)	)	PUNCT
ejpam-6124	473	23	.	.	PUNCT
ejpam-6124	474	1	note	note	VERB
ejpam-6124	474	2	that	that	SCONJ
ejpam-6124	474	3	for	for	ADP
ejpam-6124	474	4	any	any	DET
ejpam-6124	474	5	vertex	vertex	NOUN
ejpam-6124	474	6	r	r	NOUN
ejpam-6124	474	7	∈	∈	NOUN
ejpam-6124	474	8	v	v	NOUN
ejpam-6124	474	9	(	(	PUNCT
ejpam-6124	474	10	h	h	NOUN
ejpam-6124	474	11	)	)	PUNCT
ejpam-6124	474	12	,	,	PUNCT
ejpam-6124	474	13	r	r	NOUN
ejpam-6124	474	14	is	be	AUX
ejpam-6124	474	15	adjacent	adjacent	ADJ
ejpam-6124	474	16	to	to	ADP
ejpam-6124	474	17	both	both	DET
ejpam-6124	474	18	p	p	NOUN
ejpam-6124	474	19	and	and	CCONJ
ejpam-6124	474	20	q	q	NOUN
ejpam-6124	474	21	in	in	ADP
ejpam-6124	474	22	g+h	g+h	PROPN
ejpam-6124	474	23	,	,	PUNCT
ejpam-6124	474	24	that	that	ADV
ejpam-6124	474	25	is	is	ADV
ejpam-6124	474	26	,	,	PUNCT
ejpam-6124	474	27	|n(r)∩t	|n(r)∩t	PROPN
ejpam-6124	474	28	|	|	ADV
ejpam-6124	474	29	=	=	SYM
ejpam-6124	474	30	2	2	NUM
ejpam-6124	474	31	for	for	ADP
ejpam-6124	474	32	all	all	DET
ejpam-6124	474	33	r	r	NOUN
ejpam-6124	474	34	∈	∈	NOUN
ejpam-6124	474	35	v	v	NOUN
ejpam-6124	474	36	(	(	PUNCT
ejpam-6124	474	37	h	h	NOUN
ejpam-6124	474	38	)	)	PUNCT
ejpam-6124	474	39	.	.	PUNCT
ejpam-6124	475	1	thus	thus	ADV
ejpam-6124	475	2	,	,	PUNCT
ejpam-6124	475	3	t	t	PROPN
ejpam-6124	475	4	is	be	AUX
ejpam-6124	475	5	not	not	PART
ejpam-6124	475	6	a	a	DET
ejpam-6124	475	7	total	total	ADJ
ejpam-6124	475	8	exact	exact	ADJ
ejpam-6124	475	9	dominating	dominating	NOUN
ejpam-6124	475	10	set	set	NOUN
ejpam-6124	475	11	.	.	PUNCT
ejpam-6124	476	1	similarly	similarly	ADV
ejpam-6124	476	2	,	,	PUNCT
ejpam-6124	476	3	if	if	SCONJ
ejpam-6124	476	4	t	t	PROPN
ejpam-6124	476	5	is	be	AUX
ejpam-6124	476	6	a	a	DET
ejpam-6124	476	7	total	total	ADJ
ejpam-6124	476	8	dominating	dominating	NOUN
ejpam-6124	476	9	set	set	NOUN
ejpam-6124	476	10	that	that	PRON
ejpam-6124	476	11	contains	contain	VERB
ejpam-6124	476	12	two	two	NUM
ejpam-6124	476	13	vertices	vertex	NOUN
ejpam-6124	476	14	in	in	ADP
ejpam-6124	476	15	v	v	NOUN
ejpam-6124	476	16	(	(	PUNCT
ejpam-6124	476	17	h	h	NOUN
ejpam-6124	476	18	)	)	PUNCT
ejpam-6124	476	19	,	,	PUNCT
ejpam-6124	476	20	then	then	ADV
ejpam-6124	476	21	t	t	PROPN
ejpam-6124	476	22	is	be	AUX
ejpam-6124	476	23	not	not	PART
ejpam-6124	476	24	a	a	DET
ejpam-6124	476	25	total	total	ADJ
ejpam-6124	476	26	exact	exact	ADJ
ejpam-6124	476	27	dominating	dominating	NOUN
ejpam-6124	476	28	set	set	NOUN
ejpam-6124	476	29	.	.	PUNCT
ejpam-6124	477	1	case	case	NOUN
ejpam-6124	477	2	2	2	NUM
ejpam-6124	477	3	:	:	PUNCT
ejpam-6124	477	4	t	t	PROPN
ejpam-6124	477	5	is	be	AUX
ejpam-6124	477	6	a	a	DET
ejpam-6124	477	7	total	total	ADJ
ejpam-6124	477	8	dominating	dominating	NOUN
ejpam-6124	477	9	set	set	NOUN
ejpam-6124	477	10	that	that	PRON
ejpam-6124	477	11	contains	contain	VERB
ejpam-6124	477	12	one	one	NUM
ejpam-6124	477	13	vertex	vertex	NOUN
ejpam-6124	477	14	in	in	ADP
ejpam-6124	477	15	v	v	NOUN
ejpam-6124	477	16	(	(	PUNCT
ejpam-6124	477	17	g	g	NOUN
ejpam-6124	477	18	)	)	PUNCT
ejpam-6124	477	19	and	and	CCONJ
ejpam-6124	477	20	one	one	NUM
ejpam-6124	477	21	vertex	vertex	NOUN
ejpam-6124	477	22	in	in	ADP
ejpam-6124	477	23	v	v	NOUN
ejpam-6124	477	24	(	(	PUNCT
ejpam-6124	477	25	h	h	NOUN
ejpam-6124	477	26	)	)	PUNCT
ejpam-6124	477	27	.	.	PUNCT
ejpam-6124	478	1	let	let	VERB
ejpam-6124	478	2	t	t	NOUN
ejpam-6124	478	3	=	=	PUNCT
ejpam-6124	478	4	{	{	PUNCT
ejpam-6124	478	5	s	s	PROPN
ejpam-6124	478	6	,	,	PUNCT
ejpam-6124	478	7	t	t	PROPN
ejpam-6124	478	8	}	}	PUNCT
ejpam-6124	478	9	where	where	SCONJ
ejpam-6124	478	10	s	s	VERB
ejpam-6124	478	11	∈	∈	PROPN
ejpam-6124	478	12	v	v	ADP
ejpam-6124	478	13	(	(	PUNCT
ejpam-6124	478	14	g	g	NOUN
ejpam-6124	478	15	)	)	PUNCT
ejpam-6124	478	16	and	and	CCONJ
ejpam-6124	478	17	t	t	PROPN
ejpam-6124	478	18	∈	∈	PROPN
ejpam-6124	478	19	v	v	ADP
ejpam-6124	478	20	(	(	PUNCT
ejpam-6124	478	21	h	h	NOUN
ejpam-6124	478	22	)	)	PUNCT
ejpam-6124	478	23	.	.	PUNCT
ejpam-6124	479	1	note	note	VERB
ejpam-6124	479	2	that	that	SCONJ
ejpam-6124	479	3	s	s	VERB
ejpam-6124	479	4	and	and	CCONJ
ejpam-6124	479	5	t	t	PROPN
ejpam-6124	479	6	are	be	AUX
ejpam-6124	479	7	adjacent	adjacent	ADJ
ejpam-6124	479	8	in	in	ADP
ejpam-6124	479	9	g+h	g+h	PROPN
ejpam-6124	479	10	.	.	PUNCT
ejpam-6124	480	1	since	since	SCONJ
ejpam-6124	480	2	g	g	PROPN
ejpam-6124	480	3	has	have	VERB
ejpam-6124	480	4	no	no	DET
ejpam-6124	480	5	isolated	isolated	ADJ
ejpam-6124	480	6	vertices	vertex	NOUN
ejpam-6124	480	7	,	,	PUNCT
ejpam-6124	480	8	there	there	PRON
ejpam-6124	480	9	exists	exist	VERB
ejpam-6124	480	10	at	at	ADV
ejpam-6124	480	11	least	least	ADV
ejpam-6124	480	12	one	one	NUM
ejpam-6124	480	13	vertex	vertex	NOUN
ejpam-6124	480	14	w	w	NOUN
ejpam-6124	480	15	∈	∈	PROPN
ejpam-6124	480	16	v	v	ADP
ejpam-6124	480	17	(	(	PUNCT
ejpam-6124	480	18	g	g	NOUN
ejpam-6124	480	19	)	)	PUNCT
ejpam-6124	480	20	that	that	PRON
ejpam-6124	480	21	is	be	AUX
ejpam-6124	480	22	adjacent	adjacent	ADJ
ejpam-6124	480	23	to	to	ADP
ejpam-6124	480	24	the	the	DET
ejpam-6124	480	25	vertex	vertex	NOUN
ejpam-6124	480	26	s	s	VERB
ejpam-6124	480	27	also	also	ADV
ejpam-6124	480	28	.	.	PUNCT
ejpam-6124	481	1	note	note	VERB
ejpam-6124	481	2	that	that	SCONJ
ejpam-6124	481	3	w	w	NOUN
ejpam-6124	481	4	is	be	AUX
ejpam-6124	481	5	also	also	ADV
ejpam-6124	481	6	adjacent	adjacent	ADJ
ejpam-6124	481	7	to	to	ADP
ejpam-6124	481	8	the	the	DET
ejpam-6124	481	9	vertex	vertex	NOUN
ejpam-6124	481	10	t	t	PROPN
ejpam-6124	481	11	in	in	ADP
ejpam-6124	481	12	g+h	g+h	PROPN
ejpam-6124	481	13	.	.	PUNCT
ejpam-6124	482	1	thus	thus	ADV
ejpam-6124	482	2	,	,	PUNCT
ejpam-6124	482	3	|n(w	|n(w	NOUN
ejpam-6124	482	4	)	)	PUNCT
ejpam-6124	482	5	∩	∩	NOUN
ejpam-6124	482	6	t	t	NOUN
ejpam-6124	483	1	|	|	NOUN
ejpam-6124	483	2	=	=	NOUN
ejpam-6124	483	3	2	2	X
ejpam-6124	483	4	.	.	PUNCT
ejpam-6124	484	1	hence	hence	ADV
ejpam-6124	484	2	,	,	PUNCT
ejpam-6124	484	3	t	t	PROPN
ejpam-6124	484	4	is	be	AUX
ejpam-6124	484	5	also	also	ADV
ejpam-6124	484	6	not	not	PART
ejpam-6124	484	7	a	a	DET
ejpam-6124	484	8	total	total	ADJ
ejpam-6124	484	9	exact	exact	ADJ
ejpam-6124	484	10	dominating	dominating	NOUN
ejpam-6124	484	11	set	set	NOUN
ejpam-6124	484	12	.	.	PUNCT
ejpam-6124	485	1	suppose	suppose	VERB
ejpam-6124	485	2	that	that	SCONJ
ejpam-6124	485	3	(	(	PUNCT
ejpam-6124	485	4	ii	ii	NOUN
ejpam-6124	485	5	)	)	PUNCT
ejpam-6124	485	6	holds	hold	VERB
ejpam-6124	485	7	.	.	PUNCT
ejpam-6124	486	1	without	without	ADP
ejpam-6124	486	2	loss	loss	NOUN
ejpam-6124	486	3	of	of	ADP
ejpam-6124	486	4	generality	generality	NOUN
ejpam-6124	486	5	,	,	PUNCT
ejpam-6124	486	6	suppose	suppose	VERB
ejpam-6124	486	7	that	that	SCONJ
ejpam-6124	486	8	g	g	PROPN
ejpam-6124	486	9	has	have	VERB
ejpam-6124	486	10	no	no	DET
ejpam-6124	486	11	isolated	isolated	ADJ
ejpam-6124	486	12	vertices	vertex	NOUN
ejpam-6124	486	13	,	,	PUNCT
ejpam-6124	486	14	and	and	CCONJ
ejpam-6124	486	15	h	h	NOUN
ejpam-6124	486	16	has	have	VERB
ejpam-6124	486	17	at	at	ADV
ejpam-6124	486	18	least	least	ADJ
ejpam-6124	486	19	one	one	NUM
ejpam-6124	486	20	isolated	isolated	ADJ
ejpam-6124	486	21	vertex	vertex	NOUN
ejpam-6124	486	22	.	.	PUNCT
ejpam-6124	487	1	let	let	VERB
ejpam-6124	487	2	u	u	PRON
ejpam-6124	487	3	be	be	AUX
ejpam-6124	487	4	an	an	DET
ejpam-6124	487	5	isolated	isolated	ADJ
ejpam-6124	487	6	vertex	vertex	NOUN
ejpam-6124	487	7	in	in	ADP
ejpam-6124	487	8	h	h	NOUN
ejpam-6124	487	9	,	,	PUNCT
ejpam-6124	487	10	and	and	CCONJ
ejpam-6124	487	11	let	let	VERB
ejpam-6124	487	12	v	v	NUM
ejpam-6124	487	13	∈	∈	PROPN
ejpam-6124	487	14	v	v	NOUN
ejpam-6124	487	15	(	(	PUNCT
ejpam-6124	487	16	g	g	NOUN
ejpam-6124	487	17	)	)	PUNCT
ejpam-6124	487	18	.	.	PUNCT
ejpam-6124	488	1	pick	pick	VERB
ejpam-6124	488	2	t	t	PROPN
ejpam-6124	488	3	=	=	SYM
ejpam-6124	488	4	{	{	PUNCT
ejpam-6124	488	5	u	u	NOUN
ejpam-6124	488	6	,	,	PUNCT
ejpam-6124	488	7	v	v	NOUN
ejpam-6124	488	8	}	}	PUNCT
ejpam-6124	488	9	.	.	PUNCT
ejpam-6124	489	1	then	then	ADV
ejpam-6124	489	2	there	there	PRON
ejpam-6124	489	3	exists	exist	VERB
ejpam-6124	489	4	at	at	ADV
ejpam-6124	489	5	least	least	ADV
ejpam-6124	489	6	one	one	NUM
ejpam-6124	489	7	vertex	vertex	NOUN
ejpam-6124	489	8	z	z	NOUN
ejpam-6124	489	9	∈	∈	PROPN
ejpam-6124	489	10	v	v	ADP
ejpam-6124	489	11	(	(	PUNCT
ejpam-6124	489	12	g	g	NOUN
ejpam-6124	489	13	)	)	PUNCT
ejpam-6124	489	14	such	such	ADJ
ejpam-6124	489	15	that	that	SCONJ
ejpam-6124	489	16	z	z	NOUN
ejpam-6124	489	17	is	be	AUX
ejpam-6124	489	18	adjacent	adjacent	ADJ
ejpam-6124	489	19	to	to	ADP
ejpam-6124	489	20	v	v	NOUN
ejpam-6124	489	21	since	since	SCONJ
ejpam-6124	489	22	g	g	PROPN
ejpam-6124	489	23	has	have	VERB
ejpam-6124	489	24	no	no	DET
ejpam-6124	489	25	isolated	isolated	ADJ
ejpam-6124	489	26	vertices	vertex	NOUN
ejpam-6124	489	27	.	.	PUNCT
ejpam-6124	490	1	note	note	VERB
ejpam-6124	490	2	that	that	SCONJ
ejpam-6124	490	3	z	z	NOUN
ejpam-6124	490	4	is	be	AUX
ejpam-6124	490	5	also	also	ADV
ejpam-6124	490	6	adjacent	adjacent	ADJ
ejpam-6124	490	7	to	to	ADP
ejpam-6124	490	8	u	u	NOUN
ejpam-6124	490	9	in	in	ADP
ejpam-6124	490	10	g+h	g+h	PROPN
ejpam-6124	490	11	,	,	PUNCT
ejpam-6124	490	12	that	that	ADV
ejpam-6124	490	13	is	is	ADV
ejpam-6124	490	14	,	,	PUNCT
ejpam-6124	490	15	|n(z	|n(z	PROPN
ejpam-6124	490	16	)	)	PUNCT
ejpam-6124	490	17	∩	∩	NOUN
ejpam-6124	490	18	t	t	NOUN
ejpam-6124	491	1	|	|	NOUN
ejpam-6124	491	2	=	=	NOUN
ejpam-6124	491	3	2	2	X
ejpam-6124	491	4	.	.	PUNCT
ejpam-6124	492	1	hence	hence	ADV
ejpam-6124	492	2	,	,	PUNCT
ejpam-6124	492	3	t	t	PROPN
ejpam-6124	492	4	is	be	AUX
ejpam-6124	492	5	also	also	ADV
ejpam-6124	492	6	not	not	PART
ejpam-6124	492	7	a	a	DET
ejpam-6124	492	8	total	total	ADJ
ejpam-6124	492	9	exact	exact	ADJ
ejpam-6124	492	10	dominating	dominating	NOUN
ejpam-6124	492	11	set	set	NOUN
ejpam-6124	492	12	.	.	PUNCT
ejpam-6124	493	1	thus	thus	ADV
ejpam-6124	493	2	,	,	PUNCT
ejpam-6124	493	3	a	a	DET
ejpam-6124	493	4	total	total	ADJ
ejpam-6124	493	5	exact	exact	ADJ
ejpam-6124	493	6	dominating	dominating	NOUN
ejpam-6124	493	7	set	set	NOUN
ejpam-6124	493	8	can	can	AUX
ejpam-6124	493	9	not	not	PART
ejpam-6124	493	10	exist	exist	VERB
ejpam-6124	493	11	.	.	PUNCT
ejpam-6124	494	1	therefore	therefore	ADV
ejpam-6124	494	2	,	,	PUNCT
ejpam-6124	494	3	under	under	ADP
ejpam-6124	494	4	conditions	condition	NOUN
ejpam-6124	494	5	(	(	PUNCT
ejpam-6124	494	6	i	i	NOUN
ejpam-6124	494	7	)	)	PUNCT
ejpam-6124	494	8	and	and	CCONJ
ejpam-6124	494	9	(	(	PUNCT
ejpam-6124	494	10	ii	ii	NOUN
ejpam-6124	494	11	)	)	PUNCT
ejpam-6124	494	12	,	,	PUNCT
ejpam-6124	494	13	g+h	g+h	PROPN
ejpam-6124	494	14	is	be	AUX
ejpam-6124	494	15	a	a	DET
ejpam-6124	494	16	non	non	ADJ
ejpam-6124	494	17	-	-	ADJ
ejpam-6124	494	18	γte	γte	PRON
ejpam-6124	494	19	-	-	PUNCT
ejpam-6124	494	20	graph	graph	NOUN
ejpam-6124	494	21	.	.	PUNCT
ejpam-6124	495	1	r.	r.	PROPN
ejpam-6124	495	2	g.	g.	PROPN
ejpam-6124	495	3	aguinod	aguinod	PROPN
ejpam-6124	495	4	,	,	PUNCT
ejpam-6124	495	5	e.	e.	PROPN
ejpam-6124	495	6	m.	m.	PROPN
ejpam-6124	495	7	kiunisala	kiunisala	PROPN
ejpam-6124	495	8	,	,	PUNCT
ejpam-6124	495	9	c.	c.	PROPN
ejpam-6124	495	10	l.	l.	PROPN
ejpam-6124	495	11	armada	armada	PROPN
ejpam-6124	495	12	/	/	SYM
ejpam-6124	495	13	eur	eur	PROPN
ejpam-6124	495	14	.	.	PUNCT
ejpam-6124	496	1	j.	j.	PROPN
ejpam-6124	496	2	pure	pure	PROPN
ejpam-6124	496	3	appl	appl	PROPN
ejpam-6124	496	4	.	.	PROPN
ejpam-6124	496	5	math	math	PROPN
ejpam-6124	496	6	,	,	PUNCT
ejpam-6124	496	7	18	18	NUM
ejpam-6124	496	8	(	(	PUNCT
ejpam-6124	496	9	2	2	NUM
ejpam-6124	496	10	)	)	PUNCT
ejpam-6124	496	11	(	(	PUNCT
ejpam-6124	496	12	2025	2025	NUM
ejpam-6124	496	13	)	)	PUNCT
ejpam-6124	496	14	,	,	PUNCT
ejpam-6124	496	15	6124	6124	NUM
ejpam-6124	496	16	17	17	NUM
ejpam-6124	496	17	of	of	ADP
ejpam-6124	496	18	26	26	NUM
ejpam-6124	496	19	theorem	theorem	NOUN
ejpam-6124	496	20	12	12	NUM
ejpam-6124	496	21	.	.	PUNCT
ejpam-6124	497	1	let	let	VERB
ejpam-6124	497	2	g	g	NOUN
ejpam-6124	498	1	and	and	CCONJ
ejpam-6124	498	2	h	h	NOUN
ejpam-6124	498	3	be	be	VERB
ejpam-6124	498	4	any	any	DET
ejpam-6124	498	5	graphs	graph	NOUN
ejpam-6124	498	6	.	.	PUNCT
ejpam-6124	499	1	then	then	ADV
ejpam-6124	499	2	a	a	DET
ejpam-6124	499	3	subset	subset	ADJ
ejpam-6124	499	4	t	t	NOUN
ejpam-6124	499	5	of	of	ADP
ejpam-6124	499	6	v	v	PROPN
ejpam-6124	499	7	(	(	PUNCT
ejpam-6124	499	8	g+h	g+h	PROPN
ejpam-6124	499	9	)	)	PUNCT
ejpam-6124	499	10	is	be	AUX
ejpam-6124	499	11	a	a	DET
ejpam-6124	499	12	γte	γte	NOUN
ejpam-6124	499	13	-	-	PUNCT
ejpam-6124	499	14	set	set	NOUN
ejpam-6124	499	15	of	of	ADP
ejpam-6124	499	16	g+h	g+h	PROPN
ejpam-6124	499	17	if	if	SCONJ
ejpam-6124	499	18	and	and	CCONJ
ejpam-6124	499	19	only	only	ADV
ejpam-6124	499	20	if	if	SCONJ
ejpam-6124	499	21	t	t	NOUN
ejpam-6124	499	22	=	=	SYM
ejpam-6124	499	23	{	{	PUNCT
ejpam-6124	499	24	u	u	NOUN
ejpam-6124	499	25	,	,	PUNCT
ejpam-6124	499	26	v	v	NOUN
ejpam-6124	499	27	}	}	PUNCT
ejpam-6124	499	28	,	,	PUNCT
ejpam-6124	499	29	where	where	SCONJ
ejpam-6124	499	30	u	u	NOUN
ejpam-6124	499	31	is	be	AUX
ejpam-6124	499	32	an	an	DET
ejpam-6124	499	33	isolated	isolated	ADJ
ejpam-6124	499	34	vertex	vertex	NOUN
ejpam-6124	499	35	in	in	ADP
ejpam-6124	499	36	v	v	NOUN
ejpam-6124	499	37	(	(	PUNCT
ejpam-6124	499	38	g	g	NOUN
ejpam-6124	499	39	)	)	PUNCT
ejpam-6124	499	40	and	and	CCONJ
ejpam-6124	499	41	v	v	NOUN
ejpam-6124	499	42	is	be	AUX
ejpam-6124	499	43	an	an	DET
ejpam-6124	499	44	isolated	isolated	ADJ
ejpam-6124	499	45	vertex	vertex	NOUN
ejpam-6124	499	46	in	in	ADP
ejpam-6124	499	47	v	v	PROPN
ejpam-6124	499	48	(	(	PUNCT
ejpam-6124	499	49	h	h	NOUN
ejpam-6124	499	50	)	)	PUNCT
ejpam-6124	499	51	.	.	PUNCT
ejpam-6124	500	1	proof	proof	NOUN
ejpam-6124	500	2	.	.	PUNCT
ejpam-6124	501	1	let	let	AUX
ejpam-6124	501	2	t	t	PROPN
ejpam-6124	501	3	⊆	⊆	NUM
ejpam-6124	501	4	v	v	NOUN
ejpam-6124	501	5	(	(	PUNCT
ejpam-6124	501	6	g+h	g+h	NOUN
ejpam-6124	501	7	)	)	PUNCT
ejpam-6124	501	8	be	be	AUX
ejpam-6124	501	9	a	a	DET
ejpam-6124	501	10	γte	γte	NOUN
ejpam-6124	501	11	-	-	PUNCT
ejpam-6124	501	12	set	set	NOUN
ejpam-6124	501	13	of	of	ADP
ejpam-6124	501	14	g+h	g+h	PROPN
ejpam-6124	501	15	.	.	PUNCT
ejpam-6124	502	1	by	by	ADP
ejpam-6124	502	2	the	the	DET
ejpam-6124	502	3	proof	proof	NOUN
ejpam-6124	502	4	of	of	ADP
ejpam-6124	502	5	theorem	theorem	NOUN
ejpam-6124	502	6	11	11	NUM
ejpam-6124	502	7	,	,	PUNCT
ejpam-6124	502	8	g+h	g+h	PROPN
ejpam-6124	502	9	has	have	VERB
ejpam-6124	502	10	a	a	DET
ejpam-6124	502	11	total	total	ADJ
ejpam-6124	502	12	exact	exact	ADJ
ejpam-6124	502	13	dominating	dominating	NOUN
ejpam-6124	502	14	set	set	NOUN
ejpam-6124	502	15	if	if	SCONJ
ejpam-6124	502	16	both	both	DET
ejpam-6124	502	17	g	g	PROPN
ejpam-6124	502	18	and	and	CCONJ
ejpam-6124	502	19	h	h	NOUN
ejpam-6124	502	20	have	have	VERB
ejpam-6124	502	21	at	at	ADV
ejpam-6124	502	22	least	least	ADV
ejpam-6124	502	23	one	one	NUM
ejpam-6124	502	24	isolated	isolated	ADJ
ejpam-6124	502	25	vertex	vertex	NOUN
ejpam-6124	502	26	,	,	PUNCT
ejpam-6124	502	27	say	say	VERB
ejpam-6124	502	28	u	u	NOUN
ejpam-6124	502	29	and	and	CCONJ
ejpam-6124	502	30	v	v	NOUN
ejpam-6124	502	31	,	,	PUNCT
ejpam-6124	502	32	respectively	respectively	ADV
ejpam-6124	502	33	.	.	PUNCT
ejpam-6124	503	1	clearly	clearly	ADV
ejpam-6124	503	2	,	,	PUNCT
ejpam-6124	503	3	the	the	DET
ejpam-6124	503	4	vertices	vertex	NOUN
ejpam-6124	503	5	u	u	NOUN
ejpam-6124	503	6	and	and	CCONJ
ejpam-6124	503	7	v	v	NOUN
ejpam-6124	503	8	are	be	AUX
ejpam-6124	503	9	adjacent	adjacent	ADJ
ejpam-6124	503	10	in	in	ADP
ejpam-6124	503	11	g+h	g+h	PROPN
ejpam-6124	503	12	and	and	CCONJ
ejpam-6124	503	13	set	set	VERB
ejpam-6124	503	14	{	{	PUNCT
ejpam-6124	503	15	u	u	NOUN
ejpam-6124	503	16	,	,	PUNCT
ejpam-6124	503	17	v	v	NOUN
ejpam-6124	503	18	}	}	PUNCT
ejpam-6124	503	19	is	be	AUX
ejpam-6124	503	20	a	a	DET
ejpam-6124	503	21	total	total	ADJ
ejpam-6124	503	22	dominating	dominating	NOUN
ejpam-6124	503	23	set	set	NOUN
ejpam-6124	503	24	of	of	ADP
ejpam-6124	503	25	g	g	PROPN
ejpam-6124	503	26	+	+	PROPN
ejpam-6124	503	27	h	h	NOUN
ejpam-6124	503	28	by	by	ADP
ejpam-6124	503	29	theorem	theorem	ADJ
ejpam-6124	503	30	2	2	NUM
ejpam-6124	503	31	(	(	PUNCT
ejpam-6124	503	32	iii	iii	NOUN
ejpam-6124	503	33	)	)	PUNCT
ejpam-6124	503	34	.	.	PUNCT
ejpam-6124	504	1	note	note	VERB
ejpam-6124	504	2	that	that	SCONJ
ejpam-6124	504	3	in	in	ADP
ejpam-6124	504	4	the	the	DET
ejpam-6124	504	5	graph	graph	NOUN
ejpam-6124	504	6	g	g	PROPN
ejpam-6124	504	7	+	+	PROPN
ejpam-6124	504	8	h	h	NOUN
ejpam-6124	504	9	,	,	PUNCT
ejpam-6124	504	10	all	all	DET
ejpam-6124	504	11	vertices	vertice	VERB
ejpam-6124	504	12	in	in	ADP
ejpam-6124	504	13	v	v	ADP
ejpam-6124	504	14	(	(	PUNCT
ejpam-6124	504	15	g	g	NOUN
ejpam-6124	504	16	)	)	PUNCT
ejpam-6124	504	17	\	\	NOUN
ejpam-6124	504	18	{	{	PUNCT
ejpam-6124	504	19	u	u	NOUN
ejpam-6124	504	20	}	}	PUNCT
ejpam-6124	504	21	is	be	AUX
ejpam-6124	504	22	adjacent	adjacent	ADJ
ejpam-6124	504	23	to	to	ADP
ejpam-6124	504	24	the	the	DET
ejpam-6124	504	25	vertex	vertex	NOUN
ejpam-6124	504	26	v	v	NOUN
ejpam-6124	504	27	but	but	CCONJ
ejpam-6124	504	28	not	not	PART
ejpam-6124	504	29	in	in	ADP
ejpam-6124	504	30	u	u	PRON
ejpam-6124	504	31	while	while	SCONJ
ejpam-6124	504	32	all	all	PRON
ejpam-6124	504	33	vertices	vertice	VERB
ejpam-6124	504	34	in	in	ADP
ejpam-6124	504	35	v	v	ADP
ejpam-6124	504	36	(	(	PUNCT
ejpam-6124	504	37	h	h	NOUN
ejpam-6124	504	38	)	)	PUNCT
ejpam-6124	504	39	\	\	NOUN
ejpam-6124	504	40	{	{	PUNCT
ejpam-6124	504	41	v	v	NOUN
ejpam-6124	504	42	}	}	PUNCT
ejpam-6124	504	43	is	be	AUX
ejpam-6124	504	44	adjacent	adjacent	ADJ
ejpam-6124	504	45	to	to	ADP
ejpam-6124	504	46	the	the	DET
ejpam-6124	504	47	vertex	vertex	NOUN
ejpam-6124	504	48	u	u	NOUN
ejpam-6124	504	49	but	but	CCONJ
ejpam-6124	504	50	not	not	PART
ejpam-6124	504	51	in	in	ADP
ejpam-6124	504	52	v.	v.	ADP
ejpam-6124	504	53	thus	thus	ADV
ejpam-6124	504	54	,	,	PUNCT
ejpam-6124	504	55	|n(r	|n(r	NOUN
ejpam-6124	504	56	)	)	PUNCT
ejpam-6124	504	57	∩	∩	NOUN
ejpam-6124	504	58	{	{	PUNCT
ejpam-6124	504	59	u	u	NOUN
ejpam-6124	504	60	,	,	PUNCT
ejpam-6124	504	61	v}|	v}|	NOUN
ejpam-6124	504	62	=	=	SYM
ejpam-6124	504	63	1	1	NUM
ejpam-6124	504	64	for	for	ADP
ejpam-6124	504	65	all	all	DET
ejpam-6124	504	66	r	r	NOUN
ejpam-6124	504	67	∈	∈	NOUN
ejpam-6124	504	68	v	v	NOUN
ejpam-6124	504	69	(	(	PUNCT
ejpam-6124	504	70	g	g	PROPN
ejpam-6124	504	71	+	+	NOUN
ejpam-6124	504	72	h	h	NOUN
ejpam-6124	504	73	)	)	PUNCT
ejpam-6124	504	74	.	.	PUNCT
ejpam-6124	505	1	therefore	therefore	ADV
ejpam-6124	505	2	,	,	PUNCT
ejpam-6124	505	3	t	t	PROPN
ejpam-6124	505	4	=	=	SYM
ejpam-6124	505	5	{	{	PUNCT
ejpam-6124	505	6	u	u	NOUN
ejpam-6124	505	7	,	,	PUNCT
ejpam-6124	505	8	v	v	NOUN
ejpam-6124	505	9	}	}	PUNCT
ejpam-6124	505	10	.	.	PUNCT
ejpam-6124	506	1	the	the	DET
ejpam-6124	506	2	converse	converse	NOUN
ejpam-6124	506	3	is	be	AUX
ejpam-6124	506	4	clear	clear	ADJ
ejpam-6124	506	5	.	.	PUNCT
ejpam-6124	507	1	the	the	DET
ejpam-6124	507	2	next	next	ADJ
ejpam-6124	507	3	results	result	NOUN
ejpam-6124	507	4	follow	follow	VERB
ejpam-6124	507	5	directly	directly	ADV
ejpam-6124	507	6	from	from	ADP
ejpam-6124	507	7	theorems	theorem	NOUN
ejpam-6124	507	8	11	11	NUM
ejpam-6124	507	9	and	and	CCONJ
ejpam-6124	507	10	12	12	NUM
ejpam-6124	507	11	.	.	PUNCT
ejpam-6124	508	1	corollary	corollary	ADJ
ejpam-6124	508	2	4	4	NUM
ejpam-6124	508	3	.	.	PUNCT
ejpam-6124	509	1	if	if	SCONJ
ejpam-6124	509	2	both	both	PRON
ejpam-6124	509	3	graphs	graph	VERB
ejpam-6124	509	4	g	g	NOUN
ejpam-6124	509	5	and	and	CCONJ
ejpam-6124	509	6	h	h	NOUN
ejpam-6124	509	7	have	have	VERB
ejpam-6124	509	8	at	at	ADV
ejpam-6124	509	9	least	least	ADV
ejpam-6124	509	10	one	one	NUM
ejpam-6124	509	11	isolated	isolated	ADJ
ejpam-6124	509	12	vertex	vertex	NOUN
ejpam-6124	509	13	,	,	PUNCT
ejpam-6124	509	14	then	then	ADV
ejpam-6124	509	15	γte(g+h	γte(g+h	ADJ
ejpam-6124	509	16	)	)	PUNCT
ejpam-6124	510	1	=	=	SYM
ejpam-6124	510	2	2	2	X
ejpam-6124	510	3	.	.	NOUN
ejpam-6124	510	4	example	example	NOUN
ejpam-6124	511	1	2	2	NUM
ejpam-6124	511	2	.	.	PUNCT
ejpam-6124	511	3	the	the	DET
ejpam-6124	511	4	following	follow	VERB
ejpam-6124	511	5	example	example	NOUN
ejpam-6124	511	6	illustrates	illustrate	VERB
ejpam-6124	511	7	the	the	DET
ejpam-6124	511	8	validity	validity	NOUN
ejpam-6124	511	9	of	of	ADP
ejpam-6124	511	10	corollary	corollary	ADJ
ejpam-6124	511	11	4	4	NUM
ejpam-6124	511	12	.	.	PUNCT
ejpam-6124	511	13	figure	figure	VERB
ejpam-6124	511	14	6	6	NUM
ejpam-6124	511	15	:	:	PUNCT
ejpam-6124	511	16	join	join	VERB
ejpam-6124	511	17	of	of	ADP
ejpam-6124	511	18	graphs	graph	NOUN
ejpam-6124	511	19	g	g	NOUN
ejpam-6124	511	20	and	and	CCONJ
ejpam-6124	511	21	h	h	NOUN
ejpam-6124	511	22	with	with	ADP
ejpam-6124	511	23	γte(g+h	γte(g+h	ADJ
ejpam-6124	511	24	)	)	PUNCT
ejpam-6124	511	25	=	=	SYM
ejpam-6124	511	26	2	2	X
ejpam-6124	511	27	.	.	PUNCT
ejpam-6124	511	28	corollary	corollary	ADJ
ejpam-6124	511	29	5	5	NUM
ejpam-6124	511	30	.	.	PUNCT
ejpam-6124	512	1	let	let	VERB
ejpam-6124	512	2	g	g	NOUN
ejpam-6124	512	3	and	and	CCONJ
ejpam-6124	512	4	h	h	NOUN
ejpam-6124	512	5	be	be	AUX
ejpam-6124	512	6	nontrivial	nontrivial	ADJ
ejpam-6124	512	7	connected	connected	ADJ
ejpam-6124	512	8	graphs	graph	NOUN
ejpam-6124	512	9	,	,	PUNCT
ejpam-6124	512	10	and	and	CCONJ
ejpam-6124	512	11	let	let	VERB
ejpam-6124	512	12	u	u	PRON
ejpam-6124	512	13	and	and	CCONJ
ejpam-6124	512	14	v	v	NOUN
ejpam-6124	512	15	be	be	AUX
ejpam-6124	512	16	isolated	isolate	VERB
ejpam-6124	512	17	vertices	vertex	NOUN
ejpam-6124	512	18	,	,	PUNCT
ejpam-6124	512	19	then	then	ADV
ejpam-6124	512	20	(	(	PUNCT
ejpam-6124	512	21	(	(	PUNCT
ejpam-6124	512	22	g∪h)+{u	g∪h)+{u	ADJ
ejpam-6124	512	23	,	,	PUNCT
ejpam-6124	512	24	v	v	NOUN
ejpam-6124	512	25	}	}	PUNCT
ejpam-6124	512	26	)	)	PUNCT
ejpam-6124	513	1	is	be	AUX
ejpam-6124	513	2	a	a	DET
ejpam-6124	513	3	non−γte−graph	non−γte−graph	PROPN
ejpam-6124	513	4	and	and	CCONJ
ejpam-6124	513	5	γte((g∪{u})+(h	γte((g∪{u})+(h	NOUN
ejpam-6124	513	6	∪{v	∪{v	PROPN
ejpam-6124	513	7	}	}	PUNCT
ejpam-6124	513	8	)	)	PUNCT
ejpam-6124	513	9	)	)	PUNCT
ejpam-6124	514	1	=	=	SYM
ejpam-6124	514	2	2	2	X
ejpam-6124	514	3	.	.	X
ejpam-6124	514	4	corollary	corollary	ADJ
ejpam-6124	514	5	6	6	NUM
ejpam-6124	514	6	.	.	PUNCT
ejpam-6124	515	1	if	if	SCONJ
ejpam-6124	515	2	either	either	CCONJ
ejpam-6124	515	3	g	g	PROPN
ejpam-6124	515	4	or	or	CCONJ
ejpam-6124	515	5	h	h	NOUN
ejpam-6124	515	6	or	or	CCONJ
ejpam-6124	515	7	both	both	PRON
ejpam-6124	515	8	have	have	VERB
ejpam-6124	515	9	no	no	DET
ejpam-6124	515	10	isolated	isolate	VERB
ejpam-6124	515	11	vertex	vertex	NOUN
ejpam-6124	515	12	,	,	PUNCT
ejpam-6124	515	13	then	then	ADV
ejpam-6124	515	14	g	g	PROPN
ejpam-6124	515	15	+	+	CCONJ
ejpam-6124	515	16	h	h	NOUN
ejpam-6124	515	17	is	be	AUX
ejpam-6124	515	18	a	a	DET
ejpam-6124	515	19	non	non	ADJ
ejpam-6124	515	20	-	-	ADJ
ejpam-6124	515	21	γte	γte	ADJ
ejpam-6124	515	22	graph	graph	NOUN
ejpam-6124	515	23	.	.	PUNCT
ejpam-6124	516	1	corollary	corollary	ADJ
ejpam-6124	516	2	7	7	NUM
ejpam-6124	516	3	.	.	PUNCT
ejpam-6124	517	1	the	the	DET
ejpam-6124	517	2	following	follow	VERB
ejpam-6124	517	3	are	be	AUX
ejpam-6124	517	4	graphs	graph	NOUN
ejpam-6124	517	5	having	have	VERB
ejpam-6124	517	6	γte(g	γte(g	NOUN
ejpam-6124	517	7	)	)	PUNCT
ejpam-6124	517	8	=	=	SYM
ejpam-6124	518	1	2	2	X
ejpam-6124	518	2	.	.	PUNCT
ejpam-6124	518	3	(	(	PUNCT
ejpam-6124	518	4	i	i	NOUN
ejpam-6124	518	5	)	)	PUNCT
ejpam-6124	518	6	star	star	NOUN
ejpam-6124	518	7	graph	graph	NOUN
ejpam-6124	518	8	sn	sn	PROPN
ejpam-6124	518	9	=	=	SYM
ejpam-6124	518	10	k1	k1	PROPN
ejpam-6124	519	1	+	+	PROPN
ejpam-6124	519	2	kn	kn	PROPN
ejpam-6124	519	3	,	,	PUNCT
ejpam-6124	519	4	n	n	PRON
ejpam-6124	519	5	≥	≥	NUM
ejpam-6124	519	6	1	1	NUM
ejpam-6124	519	7	(	(	PUNCT
ejpam-6124	519	8	ii	ii	NOUN
ejpam-6124	519	9	)	)	PUNCT
ejpam-6124	519	10	complete	complete	ADJ
ejpam-6124	519	11	bipartite	bipartite	PROPN
ejpam-6124	519	12	graph	graph	NOUN
ejpam-6124	519	13	km	km	PROPN
ejpam-6124	519	14	,	,	PUNCT
ejpam-6124	519	15	n	n	NOUN
ejpam-6124	520	1	=	=	SYM
ejpam-6124	520	2	km	km	NOUN
ejpam-6124	520	3	+	+	PROPN
ejpam-6124	520	4	kn	kn	PROPN
ejpam-6124	520	5	m	m	PROPN
ejpam-6124	520	6	≥	≥	NUM
ejpam-6124	520	7	2	2	NUM
ejpam-6124	520	8	and	and	CCONJ
ejpam-6124	520	9	n	n	PRON
ejpam-6124	520	10	≥	≥	NOUN
ejpam-6124	520	11	1	1	NUM
ejpam-6124	520	12	.	.	PUNCT
ejpam-6124	520	13	r.	r.	PROPN
ejpam-6124	520	14	g.	g.	PROPN
ejpam-6124	520	15	aguinod	aguinod	PROPN
ejpam-6124	520	16	,	,	PUNCT
ejpam-6124	521	1	e.	e.	PROPN
ejpam-6124	521	2	m.	m.	PROPN
ejpam-6124	521	3	kiunisala	kiunisala	PROPN
ejpam-6124	521	4	,	,	PUNCT
ejpam-6124	521	5	c.	c.	PROPN
ejpam-6124	521	6	l.	l.	PROPN
ejpam-6124	521	7	armada	armada	PROPN
ejpam-6124	521	8	/	/	SYM
ejpam-6124	521	9	eur	eur	PROPN
ejpam-6124	521	10	.	.	PUNCT
ejpam-6124	522	1	j.	j.	PROPN
ejpam-6124	522	2	pure	pure	PROPN
ejpam-6124	522	3	appl	appl	PROPN
ejpam-6124	522	4	.	.	PROPN
ejpam-6124	522	5	math	math	PROPN
ejpam-6124	522	6	,	,	PUNCT
ejpam-6124	522	7	18	18	NUM
ejpam-6124	522	8	(	(	PUNCT
ejpam-6124	522	9	2	2	NUM
ejpam-6124	522	10	)	)	PUNCT
ejpam-6124	522	11	(	(	PUNCT
ejpam-6124	522	12	2025	2025	NUM
ejpam-6124	522	13	)	)	PUNCT
ejpam-6124	522	14	,	,	PUNCT
ejpam-6124	522	15	6124	6124	NUM
ejpam-6124	522	16	18	18	NUM
ejpam-6124	522	17	of	of	ADP
ejpam-6124	522	18	26	26	NUM
ejpam-6124	522	19	example	example	NOUN
ejpam-6124	522	20	3	3	NUM
ejpam-6124	522	21	.	.	PUNCT
ejpam-6124	523	1	the	the	DET
ejpam-6124	523	2	following	follow	VERB
ejpam-6124	523	3	examples	example	NOUN
ejpam-6124	523	4	verify	verify	VERB
ejpam-6124	523	5	the	the	DET
ejpam-6124	523	6	results	result	NOUN
ejpam-6124	523	7	of	of	ADP
ejpam-6124	523	8	corollary	corollary	ADJ
ejpam-6124	523	9	7	7	NUM
ejpam-6124	523	10	.	.	PUNCT
ejpam-6124	523	11	figure	figure	NOUN
ejpam-6124	523	12	7	7	NUM
ejpam-6124	523	13	:	:	PUNCT
ejpam-6124	523	14	graph	graph	NOUN
ejpam-6124	523	15	s6	s6	PROPN
ejpam-6124	523	16	with	with	ADP
ejpam-6124	523	17	γte(s6	γte(s6	PROPN
ejpam-6124	523	18	)	)	PUNCT
ejpam-6124	523	19	=	=	SYM
ejpam-6124	523	20	2	2	NUM
ejpam-6124	523	21	and	and	CCONJ
ejpam-6124	523	22	graph	graph	NOUN
ejpam-6124	523	23	k3,4	k3,4	ADJ
ejpam-6124	523	24	with	with	ADP
ejpam-6124	523	25	γte(k3,4	γte(k3,4	NOUN
ejpam-6124	523	26	)	)	PUNCT
ejpam-6124	523	27	=	=	SYM
ejpam-6124	523	28	2	2	X
ejpam-6124	523	29	.	.	PUNCT
ejpam-6124	523	30	corollary	corollary	ADJ
ejpam-6124	523	31	8	8	NUM
ejpam-6124	523	32	.	.	PUNCT
ejpam-6124	524	1	the	the	DET
ejpam-6124	524	2	following	follow	VERB
ejpam-6124	524	3	are	be	AUX
ejpam-6124	524	4	non	non	ADJ
ejpam-6124	524	5	-	-	ADJ
ejpam-6124	524	6	γte	γte	PRON
ejpam-6124	524	7	-	-	PUNCT
ejpam-6124	524	8	graphs	graph	NOUN
ejpam-6124	524	9	.	.	PUNCT
ejpam-6124	525	1	(	(	PUNCT
ejpam-6124	525	2	i	i	NOUN
ejpam-6124	525	3	)	)	PUNCT
ejpam-6124	525	4	fan	fan	NOUN
ejpam-6124	525	5	graph	graph	NOUN
ejpam-6124	525	6	fn	fn	NOUN
ejpam-6124	525	7	=	=	SYM
ejpam-6124	525	8	k1	k1	PROPN
ejpam-6124	525	9	+	+	CCONJ
ejpam-6124	525	10	pn	pn	PROPN
ejpam-6124	525	11	,	,	PUNCT
ejpam-6124	525	12	n	n	PRON
ejpam-6124	525	13	≥	≥	NOUN
ejpam-6124	525	14	2	2	NUM
ejpam-6124	525	15	(	(	PUNCT
ejpam-6124	525	16	ii	ii	NOUN
ejpam-6124	525	17	)	)	PUNCT
ejpam-6124	525	18	wheel	wheel	NOUN
ejpam-6124	525	19	graph	graph	NOUN
ejpam-6124	525	20	wn	wn	PROPN
ejpam-6124	525	21	=	=	PROPN
ejpam-6124	525	22	k1	k1	PROPN
ejpam-6124	525	23	+	+	CCONJ
ejpam-6124	525	24	cn	cn	PROPN
ejpam-6124	525	25	,	,	PUNCT
ejpam-6124	525	26	n	n	PRON
ejpam-6124	525	27	≥	≥	NOUN
ejpam-6124	525	28	3	3	NUM
ejpam-6124	525	29	(	(	PUNCT
ejpam-6124	525	30	iii	iii	NOUN
ejpam-6124	525	31	)	)	PUNCT
ejpam-6124	525	32	friendship	friendship	NOUN
ejpam-6124	525	33	graph	graph	NOUN
ejpam-6124	525	34	fn	fn	NOUN
ejpam-6124	525	35	=	=	NOUN
ejpam-6124	525	36	k1	k1	PROPN
ejpam-6124	525	37	+	+	CCONJ
ejpam-6124	525	38	np2	np2	PROPN
ejpam-6124	525	39	,	,	PUNCT
ejpam-6124	525	40	n	n	PRON
ejpam-6124	525	41	≥	≥	NUM
ejpam-6124	525	42	2	2	NUM
ejpam-6124	525	43	(	(	PUNCT
ejpam-6124	525	44	iv	iv	X
ejpam-6124	525	45	)	)	PUNCT
ejpam-6124	525	46	windmill	windmill	NOUN
ejpam-6124	525	47	graph	graph	NOUN
ejpam-6124	525	48	wm	wm	PROPN
ejpam-6124	525	49	n	n	PROPN
ejpam-6124	525	50	=	=	PROPN
ejpam-6124	525	51	k1	k1	PROPN
ejpam-6124	526	1	+	+	PROPN
ejpam-6124	526	2	mkn−1	mkn−1	PROPN
ejpam-6124	526	3	,	,	PUNCT
ejpam-6124	526	4	n	n	PRON
ejpam-6124	526	5	≥	≥	NOUN
ejpam-6124	526	6	3	3	NUM
ejpam-6124	526	7	and	and	CCONJ
ejpam-6124	526	8	m	m	PROPN
ejpam-6124	526	9	≥	≥	NOUN
ejpam-6124	526	10	2	2	NUM
ejpam-6124	526	11	.	.	PUNCT
ejpam-6124	526	12	(	(	PUNCT
ejpam-6124	526	13	v	v	NOUN
ejpam-6124	526	14	)	)	PUNCT
ejpam-6124	526	15	generalized	generalize	VERB
ejpam-6124	526	16	fan	fan	NOUN
ejpam-6124	526	17	graph	graph	PROPN
ejpam-6124	526	18	fm	fm	PROPN
ejpam-6124	526	19	,	,	PUNCT
ejpam-6124	526	20	n	n	NOUN
ejpam-6124	526	21	=	=	SYM
ejpam-6124	526	22	km	km	PROPN
ejpam-6124	526	23	+	+	CCONJ
ejpam-6124	526	24	pn	pn	PROPN
ejpam-6124	526	25	,	,	PUNCT
ejpam-6124	526	26	m	m	VERB
ejpam-6124	526	27	≥	≥	NOUN
ejpam-6124	526	28	2	2	NUM
ejpam-6124	526	29	and	and	CCONJ
ejpam-6124	526	30	n	n	PRON
ejpam-6124	526	31	≥	≥	NOUN
ejpam-6124	526	32	2	2	NUM
ejpam-6124	527	1	.	.	PUNCT
ejpam-6124	527	2	(	(	PUNCT
ejpam-6124	527	3	vi	vi	NOUN
ejpam-6124	527	4	)	)	PUNCT
ejpam-6124	527	5	generalized	generalized	ADJ
ejpam-6124	527	6	wheel	wheel	NOUN
ejpam-6124	527	7	graph	graph	NOUN
ejpam-6124	527	8	wm	wm	PROPN
ejpam-6124	527	9	,	,	PUNCT
ejpam-6124	527	10	n	n	NOUN
ejpam-6124	527	11	=	=	SYM
ejpam-6124	527	12	km	km	PROPN
ejpam-6124	528	1	+	+	CCONJ
ejpam-6124	528	2	cn	cn	PROPN
ejpam-6124	528	3	,	,	PUNCT
ejpam-6124	528	4	m	m	PROPN
ejpam-6124	528	5	≥	≥	NOUN
ejpam-6124	528	6	2	2	NUM
ejpam-6124	528	7	and	and	CCONJ
ejpam-6124	528	8	n	n	PRON
ejpam-6124	528	9	≥	≥	NOUN
ejpam-6124	528	10	3	3	NUM
ejpam-6124	528	11	.	.	NOUN
ejpam-6124	528	12	4.2	4.2	NUM
ejpam-6124	528	13	.	.	PUNCT
ejpam-6124	529	1	total	total	ADJ
ejpam-6124	529	2	exact	exact	ADJ
ejpam-6124	529	3	dominating	dominating	NOUN
ejpam-6124	529	4	set	set	VERB
ejpam-6124	529	5	in	in	ADP
ejpam-6124	529	6	the	the	DET
ejpam-6124	529	7	corona	corona	NOUN
ejpam-6124	529	8	of	of	ADP
ejpam-6124	529	9	graphs	graph	NOUN
ejpam-6124	529	10	this	this	DET
ejpam-6124	529	11	section	section	NOUN
ejpam-6124	529	12	contains	contain	VERB
ejpam-6124	529	13	results	result	NOUN
ejpam-6124	529	14	when	when	SCONJ
ejpam-6124	529	15	the	the	DET
ejpam-6124	529	16	corona	corona	NOUN
ejpam-6124	529	17	g	g	PROPN
ejpam-6124	529	18	◦	◦	NOUN
ejpam-6124	529	19	h	h	NOUN
ejpam-6124	529	20	has	have	AUX
ejpam-6124	529	21	either	either	CCONJ
ejpam-6124	529	22	a	a	DET
ejpam-6124	529	23	γte	γte	NOUN
ejpam-6124	529	24	−	−	PROPN
ejpam-6124	529	25	set	set	NOUN
ejpam-6124	529	26	or	or	CCONJ
ejpam-6124	529	27	has	have	VERB
ejpam-6124	529	28	no	no	DET
ejpam-6124	529	29	γte	γte	NOUN
ejpam-6124	529	30	−	−	PROPN
ejpam-6124	529	31	set	set	NOUN
ejpam-6124	529	32	and	and	CCONJ
ejpam-6124	529	33	its	its	PRON
ejpam-6124	529	34	total	total	ADJ
ejpam-6124	529	35	exact	exact	ADJ
ejpam-6124	529	36	domination	domination	NOUN
ejpam-6124	529	37	number	number	NOUN
ejpam-6124	529	38	.	.	PUNCT
ejpam-6124	530	1	theorem	theorem	VERB
ejpam-6124	530	2	13	13	NUM
ejpam-6124	530	3	.	.	PUNCT
ejpam-6124	531	1	let	let	VERB
ejpam-6124	531	2	g	g	PRON
ejpam-6124	531	3	be	be	AUX
ejpam-6124	531	4	a	a	DET
ejpam-6124	531	5	connected	connected	ADJ
ejpam-6124	531	6	graph	graph	NOUN
ejpam-6124	531	7	,	,	PUNCT
ejpam-6124	531	8	and	and	CCONJ
ejpam-6124	531	9	h	h	NOUN
ejpam-6124	531	10	be	be	VERB
ejpam-6124	531	11	any	any	DET
ejpam-6124	531	12	graph	graph	NOUN
ejpam-6124	531	13	.	.	PUNCT
ejpam-6124	532	1	then	then	ADV
ejpam-6124	532	2	g	g	PROPN
ejpam-6124	532	3	◦	◦	NOUN
ejpam-6124	532	4	h	h	NOUN
ejpam-6124	532	5	is	be	AUX
ejpam-6124	532	6	a	a	DET
ejpam-6124	532	7	non	non	ADJ
ejpam-6124	532	8	-	-	ADJ
ejpam-6124	532	9	γte	γte	PRON
ejpam-6124	532	10	-	-	PUNCT
ejpam-6124	532	11	graph	graph	NOUN
ejpam-6124	532	12	if	if	SCONJ
ejpam-6124	533	1	and	and	CCONJ
ejpam-6124	533	2	only	only	ADV
ejpam-6124	533	3	if	if	SCONJ
ejpam-6124	533	4	either	either	PRON
ejpam-6124	533	5	of	of	ADP
ejpam-6124	533	6	the	the	DET
ejpam-6124	533	7	following	follow	VERB
ejpam-6124	533	8	is	be	AUX
ejpam-6124	533	9	satisfied	satisfied	ADJ
ejpam-6124	533	10	:	:	PUNCT
ejpam-6124	533	11	(	(	PUNCT
ejpam-6124	533	12	i	i	NOUN
ejpam-6124	533	13	)	)	PUNCT
ejpam-6124	533	14	|v	|v	PROPN
ejpam-6124	533	15	(	(	PUNCT
ejpam-6124	533	16	g)|	g)|	X
ejpam-6124	533	17	≥	≥	NOUN
ejpam-6124	533	18	3	3	NUM
ejpam-6124	533	19	,	,	PUNCT
ejpam-6124	533	20	(	(	PUNCT
ejpam-6124	533	21	ii	ii	NOUN
ejpam-6124	533	22	)	)	PUNCT
ejpam-6124	533	23	|v	|v	PROPN
ejpam-6124	533	24	(	(	PUNCT
ejpam-6124	533	25	g)|	g)|	NOUN
ejpam-6124	533	26	=	=	SYM
ejpam-6124	533	27	1	1	NUM
ejpam-6124	533	28	and	and	CCONJ
ejpam-6124	533	29	h	h	NOUN
ejpam-6124	533	30	has	have	VERB
ejpam-6124	533	31	no	no	DET
ejpam-6124	533	32	isolated	isolated	ADJ
ejpam-6124	533	33	vertices	vertex	NOUN
ejpam-6124	533	34	.	.	PUNCT
ejpam-6124	534	1	proof	proof	NOUN
ejpam-6124	534	2	.	.	PUNCT
ejpam-6124	535	1	suppose	suppose	VERB
ejpam-6124	535	2	that	that	SCONJ
ejpam-6124	535	3	|v	|v	PROPN
ejpam-6124	535	4	(	(	PUNCT
ejpam-6124	535	5	g)|	g)|	NOUN
ejpam-6124	535	6	=	=	SYM
ejpam-6124	535	7	2	2	NUM
ejpam-6124	535	8	.	.	PUNCT
ejpam-6124	535	9	by	by	ADP
ejpam-6124	535	10	corollary	corollary	ADJ
ejpam-6124	535	11	2	2	NUM
ejpam-6124	535	12	,	,	PUNCT
ejpam-6124	535	13	γt(g	γt(g	PUNCT
ejpam-6124	535	14	◦	◦	NOUN
ejpam-6124	535	15	h	h	NOUN
ejpam-6124	535	16	)	)	PUNCT
ejpam-6124	535	17	=	=	SYM
ejpam-6124	535	18	2	2	X
ejpam-6124	535	19	.	.	PUNCT
ejpam-6124	535	20	thus	thus	ADV
ejpam-6124	535	21	,	,	PUNCT
ejpam-6124	535	22	v	v	INTJ
ejpam-6124	535	23	(	(	PUNCT
ejpam-6124	535	24	g	g	NOUN
ejpam-6124	535	25	)	)	PUNCT
ejpam-6124	535	26	=	=	SYM
ejpam-6124	535	27	{	{	PUNCT
ejpam-6124	535	28	u	u	NOUN
ejpam-6124	535	29	,	,	PUNCT
ejpam-6124	535	30	v	v	NOUN
ejpam-6124	535	31	}	}	PUNCT
ejpam-6124	535	32	is	be	AUX
ejpam-6124	535	33	a	a	DET
ejpam-6124	535	34	γt	γt	NOUN
ejpam-6124	535	35	-	-	NOUN
ejpam-6124	535	36	set	set	NOUN
ejpam-6124	535	37	of	of	ADP
ejpam-6124	535	38	g	g	PROPN
ejpam-6124	535	39	◦	◦	PROPN
ejpam-6124	535	40	h.	h.	PROPN
ejpam-6124	535	41	take	take	VERB
ejpam-6124	535	42	t	t	PROPN
ejpam-6124	535	43	=	=	SYM
ejpam-6124	535	44	v	v	PROPN
ejpam-6124	535	45	(	(	PUNCT
ejpam-6124	535	46	g	g	NOUN
ejpam-6124	535	47	)	)	PUNCT
ejpam-6124	535	48	.	.	PUNCT
ejpam-6124	536	1	clearly	clearly	ADV
ejpam-6124	536	2	,	,	PUNCT
ejpam-6124	536	3	in	in	ADP
ejpam-6124	536	4	g	g	PROPN
ejpam-6124	536	5	◦	◦	NOUN
ejpam-6124	536	6	h	h	NOUN
ejpam-6124	536	7	,	,	PUNCT
ejpam-6124	536	8	|n(u	|n(u	PROPN
ejpam-6124	536	9	)	)	PUNCT
ejpam-6124	536	10	∩	∩	PROPN
ejpam-6124	536	11	t	t	NOUN
ejpam-6124	536	12	|	|	NOUN
ejpam-6124	536	13	=	=	SYM
ejpam-6124	536	14	|n(v	|n(v	ADJ
ejpam-6124	536	15	)	)	PUNCT
ejpam-6124	536	16	∩	∩	NOUN
ejpam-6124	536	17	t	t	NOUN
ejpam-6124	537	1	|	|	NOUN
ejpam-6124	537	2	=	=	SYM
ejpam-6124	537	3	1	1	NUM
ejpam-6124	537	4	,	,	PUNCT
ejpam-6124	537	5	|n(au	|n(au	NOUN
ejpam-6124	537	6	)	)	PUNCT
ejpam-6124	537	7	∩	∩	NOUN
ejpam-6124	537	8	t	t	NOUN
ejpam-6124	537	9	|	|	NOUN
ejpam-6124	537	10	=	=	SYM
ejpam-6124	537	11	|{u}|	|{u}|	PUNCT
ejpam-6124	537	12	=	=	SYM
ejpam-6124	537	13	1	1	NUM
ejpam-6124	537	14	for	for	ADP
ejpam-6124	537	15	all	all	DET
ejpam-6124	537	16	vertices	vertex	NOUN
ejpam-6124	537	17	au	au	ADP
ejpam-6124	537	18	∈	∈	PROPN
ejpam-6124	537	19	v	v	NOUN
ejpam-6124	537	20	(	(	PUNCT
ejpam-6124	537	21	hu	hu	PROPN
ejpam-6124	537	22	)	)	PUNCT
ejpam-6124	537	23	and	and	CCONJ
ejpam-6124	537	24	|n(av	|n(av	PROPN
ejpam-6124	537	25	)	)	PUNCT
ejpam-6124	537	26	∩	∩	PROPN
ejpam-6124	537	27	t	t	NOUN
ejpam-6124	537	28	|	|	ADV
ejpam-6124	537	29	=	=	PUNCT
ejpam-6124	537	30	|{v}|	|{v}|	PUNCT
ejpam-6124	537	31	=	=	SYM
ejpam-6124	537	32	1	1	NUM
ejpam-6124	537	33	for	for	ADP
ejpam-6124	537	34	all	all	DET
ejpam-6124	537	35	vertices	vertex	NOUN
ejpam-6124	537	36	av	av	PROPN
ejpam-6124	537	37	∈	∈	PROPN
ejpam-6124	537	38	v	v	PROPN
ejpam-6124	537	39	(	(	PUNCT
ejpam-6124	537	40	hv	hv	PROPN
ejpam-6124	537	41	)	)	PUNCT
ejpam-6124	537	42	.	.	PUNCT
ejpam-6124	538	1	hence	hence	ADV
ejpam-6124	538	2	,	,	PUNCT
ejpam-6124	538	3	t	t	PROPN
ejpam-6124	538	4	is	be	AUX
ejpam-6124	538	5	a	a	DET
ejpam-6124	538	6	γte	γte	NOUN
ejpam-6124	538	7	-	-	PUNCT
ejpam-6124	538	8	set	set	NOUN
ejpam-6124	538	9	of	of	ADP
ejpam-6124	538	10	g	g	PROPN
ejpam-6124	538	11	◦	◦	NOUN
ejpam-6124	538	12	h.	h.	NOUN
ejpam-6124	538	13	therefore	therefore	ADV
ejpam-6124	538	14	,	,	PUNCT
ejpam-6124	538	15	g	g	ADP
ejpam-6124	538	16	◦	◦	NOUN
ejpam-6124	538	17	h	h	NOUN
ejpam-6124	538	18	is	be	AUX
ejpam-6124	538	19	not	not	PART
ejpam-6124	538	20	a	a	DET
ejpam-6124	538	21	non	non	ADJ
ejpam-6124	538	22	-	-	ADJ
ejpam-6124	538	23	γte	γte	PRON
ejpam-6124	538	24	-	-	PUNCT
ejpam-6124	538	25	graph	graph	NOUN
ejpam-6124	538	26	.	.	PUNCT
ejpam-6124	539	1	suppose	suppose	VERB
ejpam-6124	539	2	that	that	SCONJ
ejpam-6124	539	3	|v	|v	PROPN
ejpam-6124	539	4	(	(	PUNCT
ejpam-6124	539	5	g)|	g)|	NOUN
ejpam-6124	539	6	=	=	SYM
ejpam-6124	539	7	1	1	NUM
ejpam-6124	539	8	and	and	CCONJ
ejpam-6124	539	9	h	h	NOUN
ejpam-6124	539	10	has	have	VERB
ejpam-6124	539	11	at	at	ADV
ejpam-6124	539	12	least	least	ADJ
ejpam-6124	539	13	one	one	NUM
ejpam-6124	539	14	isolated	isolated	ADJ
ejpam-6124	539	15	vertex	vertex	NOUN
ejpam-6124	539	16	,	,	PUNCT
ejpam-6124	539	17	say	say	VERB
ejpam-6124	539	18	r.	r.	PROPN
ejpam-6124	539	19	let	let	VERB
ejpam-6124	539	20	v	v	NOUN
ejpam-6124	539	21	(	(	PUNCT
ejpam-6124	539	22	g	g	NOUN
ejpam-6124	539	23	)	)	PUNCT
ejpam-6124	539	24	=	=	PUNCT
ejpam-6124	539	25	{	{	PUNCT
ejpam-6124	539	26	s	s	NOUN
ejpam-6124	539	27	}	}	PUNCT
ejpam-6124	539	28	and	and	CCONJ
ejpam-6124	539	29	so	so	ADV
ejpam-6124	539	30	,	,	PUNCT
ejpam-6124	539	31	rs	rs	X
ejpam-6124	539	32	is	be	AUX
ejpam-6124	539	33	an	an	DET
ejpam-6124	539	34	isolated	isolated	ADJ
ejpam-6124	539	35	vertex	vertex	NOUN
ejpam-6124	539	36	in	in	ADP
ejpam-6124	539	37	hs	hs	PROPN
ejpam-6124	539	38	.	.	PROPN
ejpam-6124	540	1	take	take	VERB
ejpam-6124	540	2	t	t	NOUN
ejpam-6124	540	3	=	=	PUNCT
ejpam-6124	540	4	{	{	PUNCT
ejpam-6124	540	5	s	s	PROPN
ejpam-6124	540	6	,	,	PUNCT
ejpam-6124	540	7	rs	rs	NOUN
ejpam-6124	540	8	}	}	PUNCT
ejpam-6124	540	9	.	.	PUNCT
ejpam-6124	541	1	since	since	SCONJ
ejpam-6124	541	2	rs	rs	NOUN
ejpam-6124	541	3	and	and	CCONJ
ejpam-6124	541	4	s	s	VERB
ejpam-6124	541	5	are	be	AUX
ejpam-6124	541	6	adjacent	adjacent	ADJ
ejpam-6124	541	7	in	in	ADP
ejpam-6124	541	8	g	g	ADP
ejpam-6124	541	9	◦	◦	NOUN
ejpam-6124	541	10	h	h	NOUN
ejpam-6124	541	11	,	,	PUNCT
ejpam-6124	541	12	|n(s)∩t	|n(s)∩t	AUX
ejpam-6124	541	13	|	|	ADV
ejpam-6124	541	14	=	=	PUNCT
ejpam-6124	541	15	|n(rs)∩t	|n(rs)∩t	X
ejpam-6124	541	16	|	|	ADV
ejpam-6124	541	17	=	=	NOUN
ejpam-6124	541	18	1	1	X
ejpam-6124	541	19	.	.	PUNCT
ejpam-6124	542	1	also	also	ADV
ejpam-6124	542	2	,	,	PUNCT
ejpam-6124	542	3	in	in	ADP
ejpam-6124	542	4	g	g	PROPN
ejpam-6124	542	5	◦	◦	NOUN
ejpam-6124	542	6	h	h	NOUN
ejpam-6124	542	7	,	,	PUNCT
ejpam-6124	542	8	it	it	PRON
ejpam-6124	542	9	is	be	AUX
ejpam-6124	542	10	clear	clear	ADJ
ejpam-6124	542	11	that	that	SCONJ
ejpam-6124	542	12	|n(ts)∩t	|n(ts)∩t	X
ejpam-6124	542	13	|	|	ADV
ejpam-6124	542	14	=	=	SYM
ejpam-6124	542	15	|{s}|	|{s}|	PUNCT
ejpam-6124	542	16	=	=	NOUN
ejpam-6124	542	17	1	1	NUM
ejpam-6124	542	18	for	for	ADP
ejpam-6124	542	19	all	all	DET
ejpam-6124	542	20	r.	r.	PROPN
ejpam-6124	542	21	g.	g.	PROPN
ejpam-6124	542	22	aguinod	aguinod	PROPN
ejpam-6124	542	23	,	,	PUNCT
ejpam-6124	542	24	e.	e.	PROPN
ejpam-6124	542	25	m.	m.	PROPN
ejpam-6124	542	26	kiunisala	kiunisala	PROPN
ejpam-6124	542	27	,	,	PUNCT
ejpam-6124	542	28	c.	c.	PROPN
ejpam-6124	542	29	l.	l.	PROPN
ejpam-6124	542	30	armada	armada	PROPN
ejpam-6124	542	31	/	/	SYM
ejpam-6124	542	32	eur	eur	PROPN
ejpam-6124	542	33	.	.	PUNCT
ejpam-6124	543	1	j.	j.	PROPN
ejpam-6124	543	2	pure	pure	PROPN
ejpam-6124	543	3	appl	appl	PROPN
ejpam-6124	543	4	.	.	PROPN
ejpam-6124	543	5	math	math	PROPN
ejpam-6124	543	6	,	,	PUNCT
ejpam-6124	543	7	18	18	NUM
ejpam-6124	543	8	(	(	PUNCT
ejpam-6124	543	9	2	2	NUM
ejpam-6124	543	10	)	)	PUNCT
ejpam-6124	543	11	(	(	PUNCT
ejpam-6124	543	12	2025	2025	NUM
ejpam-6124	543	13	)	)	PUNCT
ejpam-6124	543	14	,	,	PUNCT
ejpam-6124	543	15	6124	6124	NUM
ejpam-6124	543	16	19	19	NUM
ejpam-6124	543	17	of	of	ADP
ejpam-6124	543	18	26	26	NUM
ejpam-6124	543	19	vertices	vertex	NOUN
ejpam-6124	543	20	ts	ts	ADP
ejpam-6124	543	21	∈	∈	PROPN
ejpam-6124	543	22	v	v	PROPN
ejpam-6124	543	23	(	(	PUNCT
ejpam-6124	543	24	hs	hs	X
ejpam-6124	543	25	)	)	PUNCT
ejpam-6124	543	26	.	.	PUNCT
ejpam-6124	544	1	hence	hence	ADV
ejpam-6124	544	2	,	,	PUNCT
ejpam-6124	544	3	t	t	PROPN
ejpam-6124	544	4	is	be	AUX
ejpam-6124	544	5	a	a	DET
ejpam-6124	544	6	γte	γte	NOUN
ejpam-6124	544	7	-	-	PUNCT
ejpam-6124	544	8	set	set	NOUN
ejpam-6124	544	9	of	of	ADP
ejpam-6124	544	10	g	g	PROPN
ejpam-6124	544	11	◦	◦	NOUN
ejpam-6124	544	12	h.	h.	NOUN
ejpam-6124	544	13	therefore	therefore	ADV
ejpam-6124	544	14	,	,	PUNCT
ejpam-6124	544	15	g	g	ADP
ejpam-6124	544	16	◦	◦	NOUN
ejpam-6124	544	17	h	h	NOUN
ejpam-6124	544	18	is	be	AUX
ejpam-6124	544	19	not	not	PART
ejpam-6124	544	20	a	a	DET
ejpam-6124	544	21	non	non	ADJ
ejpam-6124	544	22	-	-	ADJ
ejpam-6124	544	23	γte	γte	PRON
ejpam-6124	544	24	-	-	PUNCT
ejpam-6124	544	25	graph	graph	NOUN
ejpam-6124	544	26	.	.	PUNCT
ejpam-6124	545	1	suppose	suppose	VERB
ejpam-6124	545	2	that	that	SCONJ
ejpam-6124	545	3	(	(	PUNCT
ejpam-6124	545	4	i	i	NOUN
ejpam-6124	545	5	)	)	PUNCT
ejpam-6124	545	6	holds	hold	VERB
ejpam-6124	545	7	,	,	PUNCT
ejpam-6124	545	8	that	that	ADV
ejpam-6124	545	9	is	is	ADV
ejpam-6124	545	10	,	,	PUNCT
ejpam-6124	545	11	g	g	PROPN
ejpam-6124	545	12	is	be	AUX
ejpam-6124	545	13	of	of	ADP
ejpam-6124	545	14	order	order	NOUN
ejpam-6124	545	15	m	m	VERB
ejpam-6124	545	16	≥	≥	NOUN
ejpam-6124	545	17	3	3	NUM
ejpam-6124	545	18	.	.	PUNCT
ejpam-6124	545	19	by	by	ADP
ejpam-6124	545	20	corollary	corollary	ADJ
ejpam-6124	545	21	2	2	NUM
ejpam-6124	545	22	,	,	PUNCT
ejpam-6124	545	23	γt(g	γt(g	PUNCT
ejpam-6124	545	24	◦	◦	NOUN
ejpam-6124	545	25	h	h	NOUN
ejpam-6124	545	26	)	)	PUNCT
ejpam-6124	545	27	=	=	SYM
ejpam-6124	545	28	m.	m.	NOUN
ejpam-6124	545	29	note	note	VERB
ejpam-6124	545	30	that	that	SCONJ
ejpam-6124	545	31	v	v	X
ejpam-6124	545	32	(	(	PUNCT
ejpam-6124	545	33	g	g	NOUN
ejpam-6124	545	34	)	)	PUNCT
ejpam-6124	545	35	is	be	AUX
ejpam-6124	545	36	a	a	DET
ejpam-6124	545	37	γt	γt	NOUN
ejpam-6124	545	38	-	-	NOUN
ejpam-6124	545	39	set	set	NOUN
ejpam-6124	545	40	of	of	ADP
ejpam-6124	545	41	g	g	PROPN
ejpam-6124	545	42	◦	◦	NOUN
ejpam-6124	545	43	h	h	NOUN
ejpam-6124	545	44	since	since	SCONJ
ejpam-6124	545	45	n(v	n(v	PROPN
ejpam-6124	545	46	(	(	PUNCT
ejpam-6124	545	47	g	g	NOUN
ejpam-6124	545	48	)	)	PUNCT
ejpam-6124	545	49	)	)	PUNCT
ejpam-6124	546	1	=	=	SYM
ejpam-6124	546	2	v	v	X
ejpam-6124	546	3	(	(	PUNCT
ejpam-6124	546	4	g	g	PROPN
ejpam-6124	546	5	◦	◦	NOUN
ejpam-6124	546	6	h	h	NOUN
ejpam-6124	546	7	)	)	PUNCT
ejpam-6124	546	8	and	and	CCONJ
ejpam-6124	546	9	|v	|v	PROPN
ejpam-6124	546	10	(	(	PUNCT
ejpam-6124	546	11	g)|	g)|	NOUN
ejpam-6124	546	12	=	=	NOUN
ejpam-6124	546	13	m.	m.	NOUN
ejpam-6124	546	14	let	let	VERB
ejpam-6124	546	15	t	t	PROPN
ejpam-6124	546	16	be	be	AUX
ejpam-6124	546	17	a	a	DET
ejpam-6124	546	18	total	total	ADJ
ejpam-6124	546	19	exact	exact	ADJ
ejpam-6124	546	20	dominating	dominating	NOUN
ejpam-6124	546	21	set	set	NOUN
ejpam-6124	546	22	of	of	ADP
ejpam-6124	546	23	g	g	PROPN
ejpam-6124	546	24	◦	◦	PROPN
ejpam-6124	546	25	h.	h.	PROPN
ejpam-6124	546	26	suppose	suppose	VERB
ejpam-6124	546	27	that	that	SCONJ
ejpam-6124	546	28	t	t	PROPN
ejpam-6124	546	29	̸=	̸=	PROPN
ejpam-6124	546	30	v	v	NOUN
ejpam-6124	546	31	(	(	PUNCT
ejpam-6124	546	32	g	g	NOUN
ejpam-6124	546	33	)	)	PUNCT
ejpam-6124	546	34	,	,	PUNCT
ejpam-6124	546	35	that	that	ADV
ejpam-6124	546	36	is	is	ADV
ejpam-6124	546	37	,	,	PUNCT
ejpam-6124	546	38	not	not	PART
ejpam-6124	546	39	all	all	DET
ejpam-6124	546	40	vertices	vertex	NOUN
ejpam-6124	546	41	in	in	ADP
ejpam-6124	546	42	v	v	ADP
ejpam-6124	546	43	(	(	PUNCT
ejpam-6124	546	44	g	g	NOUN
ejpam-6124	546	45	)	)	PUNCT
ejpam-6124	546	46	are	be	AUX
ejpam-6124	546	47	in	in	ADP
ejpam-6124	546	48	t	t	PROPN
ejpam-6124	546	49	,	,	PUNCT
ejpam-6124	546	50	say	say	VERB
ejpam-6124	546	51	z	z	PROPN
ejpam-6124	546	52	∈	∈	PROPN
ejpam-6124	546	53	v	v	ADP
ejpam-6124	546	54	(	(	PUNCT
ejpam-6124	546	55	g	g	NOUN
ejpam-6124	546	56	)	)	PUNCT
ejpam-6124	546	57	\	\	PROPN
ejpam-6124	546	58	t	t	PROPN
ejpam-6124	546	59	.	.	PUNCT
ejpam-6124	547	1	then	then	ADV
ejpam-6124	547	2	there	there	PRON
ejpam-6124	547	3	exist	exist	VERB
ejpam-6124	547	4	at	at	ADV
ejpam-6124	547	5	least	least	ADV
ejpam-6124	547	6	two	two	NUM
ejpam-6124	547	7	adjacent	adjacent	ADJ
ejpam-6124	547	8	vertices	vertex	NOUN
ejpam-6124	547	9	in	in	ADP
ejpam-6124	547	10	v	v	NOUN
ejpam-6124	547	11	(	(	PUNCT
ejpam-6124	547	12	hz	hz	PROPN
ejpam-6124	547	13	)	)	PUNCT
ejpam-6124	547	14	,	,	PUNCT
ejpam-6124	547	15	say	say	VERB
ejpam-6124	547	16	az	az	PROPN
ejpam-6124	547	17	and	and	CCONJ
ejpam-6124	547	18	bz	bz	PROPN
ejpam-6124	547	19	such	such	ADJ
ejpam-6124	547	20	that	that	SCONJ
ejpam-6124	547	21	the	the	DET
ejpam-6124	547	22	vertices	vertex	NOUN
ejpam-6124	547	23	az	az	PROPN
ejpam-6124	547	24	and	and	CCONJ
ejpam-6124	547	25	bz	bz	PROPN
ejpam-6124	547	26	must	must	AUX
ejpam-6124	547	27	be	be	AUX
ejpam-6124	547	28	in	in	ADP
ejpam-6124	547	29	t	t	PROPN
ejpam-6124	547	30	and	and	CCONJ
ejpam-6124	547	31	|n(az)∩t	|n(az)∩t	X
ejpam-6124	547	32	|	|	ADV
ejpam-6124	547	33	=	=	SYM
ejpam-6124	547	34	|n(bz)∩t	|n(bz)∩t	X
ejpam-6124	547	35	|	|	ADV
ejpam-6124	547	36	=	=	SYM
ejpam-6124	547	37	1	1	X
ejpam-6124	547	38	.	.	X
ejpam-6124	547	39	note	note	VERB
ejpam-6124	547	40	that	that	SCONJ
ejpam-6124	547	41	z	z	NOUN
ejpam-6124	547	42	is	be	AUX
ejpam-6124	547	43	adjacent	adjacent	ADJ
ejpam-6124	547	44	to	to	ADP
ejpam-6124	547	45	both	both	DET
ejpam-6124	547	46	az	az	PROPN
ejpam-6124	547	47	and	and	CCONJ
ejpam-6124	547	48	bz	bz	PROPN
ejpam-6124	547	49	in	in	ADP
ejpam-6124	547	50	g	g	PROPN
ejpam-6124	547	51	◦	◦	NOUN
ejpam-6124	547	52	h	h	NOUN
ejpam-6124	547	53	,	,	PUNCT
ejpam-6124	547	54	that	that	ADV
ejpam-6124	547	55	is	is	ADV
ejpam-6124	547	56	,	,	PUNCT
ejpam-6124	547	57	|n(z	|n(z	PROPN
ejpam-6124	547	58	)	)	PUNCT
ejpam-6124	547	59	∩	∩	NOUN
ejpam-6124	548	1	t	t	NOUN
ejpam-6124	549	1	|	|	NOUN
ejpam-6124	549	2	=	=	SYM
ejpam-6124	549	3	|{az	|{az	PROPN
ejpam-6124	549	4	,	,	PUNCT
ejpam-6124	549	5	bz}|	bz}|	PROPN
ejpam-6124	549	6	=	=	SYM
ejpam-6124	549	7	2	2	X
ejpam-6124	549	8	.	.	PUNCT
ejpam-6124	550	1	this	this	PRON
ejpam-6124	550	2	is	be	AUX
ejpam-6124	550	3	a	a	DET
ejpam-6124	550	4	contradiction	contradiction	NOUN
ejpam-6124	550	5	to	to	ADP
ejpam-6124	550	6	the	the	DET
ejpam-6124	550	7	definition	definition	NOUN
ejpam-6124	550	8	of	of	ADP
ejpam-6124	550	9	a	a	DET
ejpam-6124	550	10	total	total	ADJ
ejpam-6124	550	11	exact	exact	ADJ
ejpam-6124	550	12	dominating	dominating	NOUN
ejpam-6124	550	13	set	set	NOUN
ejpam-6124	550	14	.	.	PUNCT
ejpam-6124	551	1	thus	thus	ADV
ejpam-6124	551	2	,	,	PUNCT
ejpam-6124	551	3	for	for	ADP
ejpam-6124	551	4	all	all	DET
ejpam-6124	551	5	z	z	NOUN
ejpam-6124	551	6	∈	∈	PROPN
ejpam-6124	551	7	v	v	NOUN
ejpam-6124	551	8	(	(	PUNCT
ejpam-6124	551	9	g	g	NOUN
ejpam-6124	551	10	)	)	PUNCT
ejpam-6124	551	11	,	,	PUNCT
ejpam-6124	551	12	no	no	DET
ejpam-6124	551	13	two	two	NUM
ejpam-6124	551	14	vertices	vertex	NOUN
ejpam-6124	551	15	in	in	ADP
ejpam-6124	551	16	v	v	NOUN
ejpam-6124	551	17	(	(	PUNCT
ejpam-6124	551	18	hz	hz	NOUN
ejpam-6124	551	19	)	)	PUNCT
ejpam-6124	551	20	can	can	AUX
ejpam-6124	551	21	be	be	AUX
ejpam-6124	551	22	chosen	choose	VERB
ejpam-6124	551	23	to	to	PART
ejpam-6124	551	24	form	form	VERB
ejpam-6124	551	25	a	a	DET
ejpam-6124	551	26	total	total	ADJ
ejpam-6124	551	27	exact	exact	ADJ
ejpam-6124	551	28	dominating	dominating	NOUN
ejpam-6124	551	29	set	set	NOUN
ejpam-6124	551	30	of	of	ADP
ejpam-6124	551	31	g	g	PROPN
ejpam-6124	551	32	◦	◦	NOUN
ejpam-6124	551	33	h	h	NOUN
ejpam-6124	551	34	and	and	CCONJ
ejpam-6124	551	35	t	t	NOUN
ejpam-6124	551	36	=	=	SYM
ejpam-6124	551	37	v	v	PROPN
ejpam-6124	551	38	(	(	PUNCT
ejpam-6124	551	39	g	g	NOUN
ejpam-6124	551	40	)	)	PUNCT
ejpam-6124	551	41	.	.	PUNCT
ejpam-6124	552	1	now	now	ADV
ejpam-6124	552	2	,	,	PUNCT
ejpam-6124	552	3	suppose	suppose	VERB
ejpam-6124	552	4	that	that	SCONJ
ejpam-6124	552	5	t	t	NOUN
ejpam-6124	552	6	=	=	SYM
ejpam-6124	552	7	v	v	PROPN
ejpam-6124	552	8	(	(	PUNCT
ejpam-6124	552	9	g	g	NOUN
ejpam-6124	552	10	)	)	PUNCT
ejpam-6124	552	11	,	,	PUNCT
ejpam-6124	552	12	that	that	ADV
ejpam-6124	552	13	is	is	ADV
ejpam-6124	552	14	,	,	PUNCT
ejpam-6124	552	15	all	all	DET
ejpam-6124	552	16	vertices	vertex	NOUN
ejpam-6124	552	17	in	in	ADP
ejpam-6124	552	18	g	g	PROPN
ejpam-6124	552	19	are	be	AUX
ejpam-6124	552	20	in	in	ADP
ejpam-6124	552	21	t	t	PROPN
ejpam-6124	552	22	.	.	PUNCT
ejpam-6124	553	1	since	since	SCONJ
ejpam-6124	553	2	g	g	PROPN
ejpam-6124	553	3	is	be	AUX
ejpam-6124	553	4	connected	connect	VERB
ejpam-6124	553	5	and	and	CCONJ
ejpam-6124	553	6	|v	|v	PROPN
ejpam-6124	553	7	(	(	PUNCT
ejpam-6124	553	8	g)|	g)|	X
ejpam-6124	553	9	≥	≥	NOUN
ejpam-6124	553	10	3	3	NUM
ejpam-6124	553	11	,	,	PUNCT
ejpam-6124	553	12	there	there	PRON
ejpam-6124	553	13	exists	exist	VERB
ejpam-6124	553	14	at	at	ADV
ejpam-6124	553	15	least	least	ADV
ejpam-6124	553	16	one	one	NUM
ejpam-6124	553	17	vertex	vertex	NOUN
ejpam-6124	553	18	u	u	NOUN
ejpam-6124	553	19	∈	∈	PROPN
ejpam-6124	553	20	v	v	ADP
ejpam-6124	553	21	(	(	PUNCT
ejpam-6124	553	22	g	g	NOUN
ejpam-6124	553	23	)	)	PUNCT
ejpam-6124	553	24	that	that	PRON
ejpam-6124	553	25	is	be	AUX
ejpam-6124	553	26	adjacent	adjacent	ADJ
ejpam-6124	553	27	to	to	ADP
ejpam-6124	553	28	two	two	NUM
ejpam-6124	553	29	vertices	vertex	NOUN
ejpam-6124	553	30	in	in	ADP
ejpam-6124	553	31	g	g	NOUN
ejpam-6124	553	32	,	,	PUNCT
ejpam-6124	553	33	and	and	CCONJ
ejpam-6124	553	34	so	so	ADV
ejpam-6124	553	35	,	,	PUNCT
ejpam-6124	553	36	|n(u	|n(u	PROPN
ejpam-6124	553	37	)	)	PUNCT
ejpam-6124	553	38	∩	∩	PROPN
ejpam-6124	553	39	t	t	NOUN
ejpam-6124	554	1	|	|	NOUN
ejpam-6124	554	2	=	=	SYM
ejpam-6124	554	3	2	2	NUM
ejpam-6124	554	4	for	for	ADP
ejpam-6124	554	5	some	some	DET
ejpam-6124	554	6	u	u	NOUN
ejpam-6124	554	7	∈	∈	PROPN
ejpam-6124	554	8	v	v	NOUN
ejpam-6124	554	9	(	(	PUNCT
ejpam-6124	554	10	g	g	NOUN
ejpam-6124	554	11	)	)	PUNCT
ejpam-6124	554	12	,	,	PUNCT
ejpam-6124	554	13	a	a	DET
ejpam-6124	554	14	contradiction	contradiction	NOUN
ejpam-6124	554	15	.	.	PUNCT
ejpam-6124	555	1	hence	hence	ADV
ejpam-6124	555	2	,	,	PUNCT
ejpam-6124	555	3	t	t	PROPN
ejpam-6124	555	4	̸=	̸=	PROPN
ejpam-6124	555	5	v	v	NOUN
ejpam-6124	555	6	(	(	PUNCT
ejpam-6124	555	7	g	g	NOUN
ejpam-6124	555	8	)	)	PUNCT
ejpam-6124	555	9	and	and	CCONJ
ejpam-6124	555	10	t	t	PROPN
ejpam-6124	555	11	is	be	AUX
ejpam-6124	555	12	not	not	PART
ejpam-6124	555	13	a	a	DET
ejpam-6124	555	14	total	total	ADJ
ejpam-6124	555	15	exact	exact	ADJ
ejpam-6124	555	16	dominating	dominating	NOUN
ejpam-6124	555	17	set	set	NOUN
ejpam-6124	555	18	of	of	ADP
ejpam-6124	555	19	g	g	PROPN
ejpam-6124	555	20	◦	◦	PROPN
ejpam-6124	555	21	h.	h.	PROPN
ejpam-6124	555	22	suppose	suppose	VERB
ejpam-6124	555	23	that	that	SCONJ
ejpam-6124	555	24	(	(	PUNCT
ejpam-6124	555	25	ii	ii	NOUN
ejpam-6124	555	26	)	)	PUNCT
ejpam-6124	555	27	holds	hold	VERB
ejpam-6124	555	28	,	,	PUNCT
ejpam-6124	555	29	that	that	ADV
ejpam-6124	555	30	is	is	ADV
ejpam-6124	555	31	,	,	PUNCT
ejpam-6124	555	32	|v	|v	PROPN
ejpam-6124	555	33	(	(	PUNCT
ejpam-6124	555	34	g)|	g)|	NOUN
ejpam-6124	555	35	=	=	SYM
ejpam-6124	555	36	1	1	NUM
ejpam-6124	555	37	and	and	CCONJ
ejpam-6124	555	38	h	h	NOUN
ejpam-6124	555	39	has	have	VERB
ejpam-6124	555	40	no	no	DET
ejpam-6124	555	41	isolated	isolated	ADJ
ejpam-6124	555	42	vertices	vertex	NOUN
ejpam-6124	555	43	.	.	PUNCT
ejpam-6124	556	1	let	let	VERB
ejpam-6124	556	2	v	v	X
ejpam-6124	556	3	(	(	PUNCT
ejpam-6124	556	4	g	g	NOUN
ejpam-6124	556	5	)	)	PUNCT
ejpam-6124	556	6	=	=	PUNCT
ejpam-6124	556	7	{	{	PUNCT
ejpam-6124	556	8	p	p	X
ejpam-6124	556	9	}	}	PUNCT
ejpam-6124	556	10	.	.	PUNCT
ejpam-6124	557	1	by	by	ADP
ejpam-6124	557	2	the	the	DET
ejpam-6124	557	3	previous	previous	ADJ
ejpam-6124	557	4	argument	argument	NOUN
ejpam-6124	557	5	,	,	PUNCT
ejpam-6124	557	6	no	no	DET
ejpam-6124	557	7	two	two	NUM
ejpam-6124	557	8	vertices	vertex	NOUN
ejpam-6124	557	9	in	in	ADP
ejpam-6124	557	10	v	v	NOUN
ejpam-6124	557	11	(	(	PUNCT
ejpam-6124	557	12	hp	hp	NOUN
ejpam-6124	557	13	)	)	PUNCT
ejpam-6124	557	14	can	can	AUX
ejpam-6124	557	15	be	be	AUX
ejpam-6124	557	16	chosen	choose	VERB
ejpam-6124	557	17	to	to	PART
ejpam-6124	557	18	form	form	VERB
ejpam-6124	557	19	a	a	DET
ejpam-6124	557	20	total	total	ADJ
ejpam-6124	557	21	exact	exact	ADJ
ejpam-6124	557	22	dominating	dominating	NOUN
ejpam-6124	557	23	set	set	NOUN
ejpam-6124	557	24	of	of	ADP
ejpam-6124	557	25	g	g	PROPN
ejpam-6124	557	26	◦	◦	PROPN
ejpam-6124	557	27	h.	h.	PROPN
ejpam-6124	557	28	take	take	VERB
ejpam-6124	557	29	t	t	PROPN
ejpam-6124	557	30	=	=	PUNCT
ejpam-6124	557	31	{	{	PUNCT
ejpam-6124	557	32	p	p	X
ejpam-6124	557	33	,	,	PUNCT
ejpam-6124	557	34	qp	qp	ADP
ejpam-6124	557	35	}	}	PUNCT
ejpam-6124	557	36	where	where	SCONJ
ejpam-6124	557	37	qp	qp	ADV
ejpam-6124	557	38	is	be	AUX
ejpam-6124	557	39	a	a	DET
ejpam-6124	557	40	vertex	vertex	NOUN
ejpam-6124	557	41	in	in	ADP
ejpam-6124	557	42	v	v	NOUN
ejpam-6124	557	43	(	(	PUNCT
ejpam-6124	557	44	hp	hp	PROPN
ejpam-6124	557	45	)	)	PUNCT
ejpam-6124	557	46	.	.	PUNCT
ejpam-6124	558	1	clearly	clearly	ADV
ejpam-6124	558	2	,	,	PUNCT
ejpam-6124	558	3	t	t	PROPN
ejpam-6124	558	4	is	be	AUX
ejpam-6124	558	5	a	a	DET
ejpam-6124	558	6	total	total	ADJ
ejpam-6124	558	7	dominating	dominating	NOUN
ejpam-6124	558	8	set	set	NOUN
ejpam-6124	558	9	of	of	ADP
ejpam-6124	558	10	g	g	PROPN
ejpam-6124	558	11	◦	◦	NOUN
ejpam-6124	558	12	h	h	NOUN
ejpam-6124	558	13	since	since	SCONJ
ejpam-6124	558	14	n(t	n(t	PROPN
ejpam-6124	558	15	)	)	PUNCT
ejpam-6124	559	1	=	=	SYM
ejpam-6124	559	2	v	v	NOUN
ejpam-6124	559	3	(	(	PUNCT
ejpam-6124	559	4	g	g	PROPN
ejpam-6124	559	5	◦	◦	NOUN
ejpam-6124	559	6	h	h	NOUN
ejpam-6124	559	7	)	)	PUNCT
ejpam-6124	559	8	.	.	PUNCT
ejpam-6124	560	1	since	since	SCONJ
ejpam-6124	560	2	h	h	NOUN
ejpam-6124	560	3	has	have	VERB
ejpam-6124	560	4	no	no	DET
ejpam-6124	560	5	isolated	isolated	ADJ
ejpam-6124	560	6	vertices	vertex	NOUN
ejpam-6124	560	7	,	,	PUNCT
ejpam-6124	560	8	there	there	PRON
ejpam-6124	560	9	exists	exist	VERB
ejpam-6124	560	10	at	at	ADV
ejpam-6124	560	11	least	least	ADV
ejpam-6124	560	12	one	one	NUM
ejpam-6124	560	13	vertex	vertex	NOUN
ejpam-6124	560	14	cp	cp	INTJ
ejpam-6124	560	15	that	that	PRON
ejpam-6124	560	16	is	be	AUX
ejpam-6124	560	17	adjacent	adjacent	ADJ
ejpam-6124	560	18	to	to	ADP
ejpam-6124	560	19	qp	qp	PROPN
ejpam-6124	560	20	.	.	PROPN
ejpam-6124	561	1	note	note	NOUN
ejpam-6124	561	2	that	that	SCONJ
ejpam-6124	561	3	cp	cp	PROPN
ejpam-6124	561	4	is	be	AUX
ejpam-6124	561	5	also	also	ADV
ejpam-6124	561	6	adjacent	adjacent	ADJ
ejpam-6124	561	7	to	to	ADP
ejpam-6124	561	8	p	p	NOUN
ejpam-6124	561	9	in	in	ADP
ejpam-6124	561	10	g	g	PROPN
ejpam-6124	561	11	◦	◦	NOUN
ejpam-6124	561	12	h	h	NOUN
ejpam-6124	561	13	,	,	PUNCT
ejpam-6124	561	14	that	that	ADV
ejpam-6124	561	15	is	is	ADV
ejpam-6124	561	16	,	,	PUNCT
ejpam-6124	561	17	|n(cp)∩	|n(cp)∩	PROPN
ejpam-6124	561	18	t	t	NOUN
ejpam-6124	561	19	|	|	ADV
ejpam-6124	561	20	=	=	PUNCT
ejpam-6124	562	1	|{p	|{p	X
ejpam-6124	562	2	,	,	PUNCT
ejpam-6124	562	3	qp}|	qp}|	NUM
ejpam-6124	562	4	=	=	SYM
ejpam-6124	562	5	2	2	NUM
ejpam-6124	562	6	,	,	PUNCT
ejpam-6124	562	7	a	a	DET
ejpam-6124	562	8	contradiction	contradiction	NOUN
ejpam-6124	562	9	.	.	PUNCT
ejpam-6124	563	1	hence	hence	ADV
ejpam-6124	563	2	,	,	PUNCT
ejpam-6124	563	3	t	t	PROPN
ejpam-6124	563	4	is	be	AUX
ejpam-6124	563	5	not	not	PART
ejpam-6124	563	6	a	a	DET
ejpam-6124	563	7	total	total	ADJ
ejpam-6124	563	8	exact	exact	ADJ
ejpam-6124	563	9	dominating	dominating	NOUN
ejpam-6124	563	10	set	set	NOUN
ejpam-6124	563	11	of	of	ADP
ejpam-6124	563	12	g	g	PROPN
ejpam-6124	563	13	◦	◦	NOUN
ejpam-6124	563	14	h.	h.	PROPN
ejpam-6124	563	15	thus	thus	ADV
ejpam-6124	563	16	,	,	PUNCT
ejpam-6124	563	17	it	it	PRON
ejpam-6124	563	18	is	be	AUX
ejpam-6124	563	19	not	not	PART
ejpam-6124	563	20	possible	possible	ADJ
ejpam-6124	563	21	to	to	PART
ejpam-6124	563	22	create	create	VERB
ejpam-6124	563	23	a	a	DET
ejpam-6124	563	24	total	total	ADJ
ejpam-6124	563	25	exact	exact	ADJ
ejpam-6124	563	26	dominating	dominating	NOUN
ejpam-6124	563	27	set	set	NOUN
ejpam-6124	563	28	of	of	ADP
ejpam-6124	563	29	g	g	PROPN
ejpam-6124	563	30	◦	◦	PROPN
ejpam-6124	563	31	h.	h.	PROPN
ejpam-6124	563	32	therefore	therefore	ADV
ejpam-6124	563	33	,	,	PUNCT
ejpam-6124	563	34	g	g	PROPN
ejpam-6124	563	35	◦	◦	NOUN
ejpam-6124	563	36	h	h	NOUN
ejpam-6124	563	37	is	be	AUX
ejpam-6124	563	38	a	a	DET
ejpam-6124	563	39	non	non	ADJ
ejpam-6124	563	40	-	-	ADJ
ejpam-6124	563	41	γte	γte	PRON
ejpam-6124	563	42	-	-	PUNCT
ejpam-6124	563	43	graph	graph	NOUN
ejpam-6124	563	44	.	.	PUNCT
ejpam-6124	564	1	theorem	theorem	NOUN
ejpam-6124	564	2	14	14	NUM
ejpam-6124	564	3	.	.	PUNCT
ejpam-6124	565	1	let	let	VERB
ejpam-6124	565	2	g	g	PRON
ejpam-6124	565	3	be	be	AUX
ejpam-6124	565	4	a	a	DET
ejpam-6124	565	5	connected	connected	ADJ
ejpam-6124	565	6	graph	graph	NOUN
ejpam-6124	565	7	,	,	PUNCT
ejpam-6124	565	8	and	and	CCONJ
ejpam-6124	565	9	h	h	NOUN
ejpam-6124	565	10	be	be	VERB
ejpam-6124	565	11	any	any	DET
ejpam-6124	565	12	graph	graph	NOUN
ejpam-6124	565	13	.	.	PUNCT
ejpam-6124	566	1	then	then	ADV
ejpam-6124	566	2	the	the	DET
ejpam-6124	566	3	set	set	NOUN
ejpam-6124	566	4	t	t	PROPN
ejpam-6124	566	5	⊆	⊆	NUM
ejpam-6124	566	6	v	v	NOUN
ejpam-6124	566	7	(	(	PUNCT
ejpam-6124	566	8	g	g	PROPN
ejpam-6124	566	9	◦	◦	NOUN
ejpam-6124	566	10	h	h	NOUN
ejpam-6124	566	11	)	)	PUNCT
ejpam-6124	566	12	is	be	AUX
ejpam-6124	566	13	a	a	DET
ejpam-6124	566	14	γte	γte	NOUN
ejpam-6124	566	15	-	-	PUNCT
ejpam-6124	566	16	set	set	NOUN
ejpam-6124	566	17	of	of	ADP
ejpam-6124	566	18	g	g	PROPN
ejpam-6124	566	19	◦	◦	NOUN
ejpam-6124	566	20	h	h	NOUN
ejpam-6124	566	21	if	if	SCONJ
ejpam-6124	567	1	and	and	CCONJ
ejpam-6124	567	2	only	only	ADV
ejpam-6124	567	3	if	if	SCONJ
ejpam-6124	567	4	either	either	PRON
ejpam-6124	567	5	of	of	ADP
ejpam-6124	567	6	the	the	DET
ejpam-6124	567	7	following	follow	VERB
ejpam-6124	567	8	conditions	condition	NOUN
ejpam-6124	567	9	is	be	AUX
ejpam-6124	567	10	satisfied	satisfied	ADJ
ejpam-6124	567	11	:	:	PUNCT
ejpam-6124	567	12	(	(	PUNCT
ejpam-6124	567	13	i	i	NOUN
ejpam-6124	567	14	)	)	PUNCT
ejpam-6124	567	15	g	g	PROPN
ejpam-6124	567	16	∼=	∼=	PROPN
ejpam-6124	567	17	p1	p1	NOUN
ejpam-6124	567	18	and	and	CCONJ
ejpam-6124	567	19	t	t	NOUN
ejpam-6124	567	20	=	=	SYM
ejpam-6124	567	21	v	v	PROPN
ejpam-6124	567	22	(	(	PUNCT
ejpam-6124	567	23	p1	p1	NOUN
ejpam-6124	567	24	)	)	PUNCT
ejpam-6124	567	25	∪	∪	NOUN
ejpam-6124	567	26	{	{	PUNCT
ejpam-6124	567	27	u	u	NOUN
ejpam-6124	567	28	}	}	PUNCT
ejpam-6124	567	29	,	,	PUNCT
ejpam-6124	567	30	where	where	SCONJ
ejpam-6124	567	31	u	u	NOUN
ejpam-6124	567	32	is	be	AUX
ejpam-6124	567	33	an	an	DET
ejpam-6124	567	34	isolated	isolated	ADJ
ejpam-6124	567	35	vertex	vertex	NOUN
ejpam-6124	567	36	in	in	ADP
ejpam-6124	567	37	h	h	NOUN
ejpam-6124	567	38	or	or	CCONJ
ejpam-6124	567	39	(	(	PUNCT
ejpam-6124	567	40	ii	ii	NOUN
ejpam-6124	567	41	)	)	PUNCT
ejpam-6124	567	42	g	g	PROPN
ejpam-6124	567	43	∼=	∼=	NOUN
ejpam-6124	567	44	p2	p2	NOUN
ejpam-6124	567	45	and	and	CCONJ
ejpam-6124	567	46	t	t	NOUN
ejpam-6124	567	47	=	=	SYM
ejpam-6124	567	48	v	v	PROPN
ejpam-6124	567	49	(	(	PUNCT
ejpam-6124	567	50	p2	p2	PROPN
ejpam-6124	567	51	)	)	PUNCT
ejpam-6124	567	52	.	.	PUNCT
ejpam-6124	568	1	proof	proof	NOUN
ejpam-6124	568	2	.	.	PUNCT
ejpam-6124	569	1	suppose	suppose	VERB
ejpam-6124	569	2	that	that	SCONJ
ejpam-6124	569	3	t	t	PROPN
ejpam-6124	569	4	⊆	⊆	NUM
ejpam-6124	569	5	v	v	NOUN
ejpam-6124	569	6	(	(	PUNCT
ejpam-6124	569	7	g	g	PROPN
ejpam-6124	569	8	◦	◦	NOUN
ejpam-6124	569	9	h	h	NOUN
ejpam-6124	569	10	)	)	PUNCT
ejpam-6124	569	11	is	be	AUX
ejpam-6124	569	12	a	a	DET
ejpam-6124	569	13	γte	γte	NOUN
ejpam-6124	569	14	-	-	PUNCT
ejpam-6124	569	15	set	set	NOUN
ejpam-6124	569	16	of	of	ADP
ejpam-6124	569	17	g	g	PROPN
ejpam-6124	569	18	◦	◦	PROPN
ejpam-6124	569	19	h.	h.	NOUN
ejpam-6124	569	20	then	then	ADV
ejpam-6124	569	21	by	by	ADP
ejpam-6124	569	22	using	use	VERB
ejpam-6124	569	23	the	the	DET
ejpam-6124	569	24	same	same	ADJ
ejpam-6124	569	25	argument	argument	NOUN
ejpam-6124	569	26	from	from	ADP
ejpam-6124	569	27	theorem	theorem	ADJ
ejpam-6124	569	28	13	13	NUM
ejpam-6124	569	29	,	,	PUNCT
ejpam-6124	569	30	the	the	DET
ejpam-6124	569	31	graph	graph	NOUN
ejpam-6124	569	32	g	g	PROPN
ejpam-6124	569	33	◦	◦	NOUN
ejpam-6124	569	34	h	h	NOUN
ejpam-6124	569	35	will	will	AUX
ejpam-6124	569	36	have	have	VERB
ejpam-6124	569	37	a	a	DET
ejpam-6124	569	38	γte	γte	NOUN
ejpam-6124	569	39	-	-	PUNCT
ejpam-6124	569	40	set	set	VERB
ejpam-6124	569	41	if	if	SCONJ
ejpam-6124	569	42	and	and	CCONJ
ejpam-6124	569	43	only	only	ADV
ejpam-6124	569	44	if	if	SCONJ
ejpam-6124	569	45	either	either	CCONJ
ejpam-6124	569	46	(	(	PUNCT
ejpam-6124	569	47	i	i	NOUN
ejpam-6124	569	48	)	)	PUNCT
ejpam-6124	569	49	|v	|v	PROPN
ejpam-6124	569	50	(	(	PUNCT
ejpam-6124	569	51	g)|	g)|	NOUN
ejpam-6124	569	52	=	=	SYM
ejpam-6124	569	53	1	1	NUM
ejpam-6124	569	54	and	and	CCONJ
ejpam-6124	569	55	h	h	NOUN
ejpam-6124	569	56	has	have	VERB
ejpam-6124	569	57	at	at	ADV
ejpam-6124	569	58	least	least	ADJ
ejpam-6124	569	59	one	one	NUM
ejpam-6124	569	60	isolated	isolated	ADJ
ejpam-6124	569	61	vertex	vertex	NOUN
ejpam-6124	569	62	,	,	PUNCT
ejpam-6124	569	63	or	or	CCONJ
ejpam-6124	569	64	(	(	PUNCT
ejpam-6124	569	65	ii	ii	NOUN
ejpam-6124	569	66	)	)	PUNCT
ejpam-6124	569	67	|v	|v	PROPN
ejpam-6124	569	68	(	(	PUNCT
ejpam-6124	569	69	g)|	g)|	NOUN
ejpam-6124	569	70	=	=	SYM
ejpam-6124	569	71	2	2	X
ejpam-6124	569	72	.	.	PUNCT
ejpam-6124	569	73	suppose	suppose	VERB
ejpam-6124	569	74	that	that	SCONJ
ejpam-6124	569	75	|v	|v	PROPN
ejpam-6124	569	76	(	(	PUNCT
ejpam-6124	569	77	g)|	g)|	NOUN
ejpam-6124	569	78	=	=	SYM
ejpam-6124	569	79	1	1	NUM
ejpam-6124	569	80	and	and	CCONJ
ejpam-6124	569	81	h	h	NOUN
ejpam-6124	569	82	has	have	VERB
ejpam-6124	569	83	at	at	ADV
ejpam-6124	569	84	least	least	ADJ
ejpam-6124	569	85	one	one	NUM
ejpam-6124	569	86	isolated	isolated	ADJ
ejpam-6124	569	87	vertex	vertex	NOUN
ejpam-6124	569	88	,	,	PUNCT
ejpam-6124	569	89	say	say	VERB
ejpam-6124	569	90	u.	u.	NOUN
ejpam-6124	569	91	clearly	clearly	ADV
ejpam-6124	569	92	,	,	PUNCT
ejpam-6124	569	93	g	g	PROPN
ejpam-6124	569	94	∼=	∼=	PROPN
ejpam-6124	569	95	p1	p1	NOUN
ejpam-6124	569	96	.	.	PUNCT
ejpam-6124	570	1	since	since	SCONJ
ejpam-6124	570	2	both	both	DET
ejpam-6124	570	3	g	g	PROPN
ejpam-6124	570	4	and	and	CCONJ
ejpam-6124	570	5	h	h	NOUN
ejpam-6124	570	6	have	have	AUX
ejpam-6124	570	7	isolated	isolate	VERB
ejpam-6124	570	8	vertices	vertex	NOUN
ejpam-6124	570	9	and	and	CCONJ
ejpam-6124	570	10	p1	p1	NOUN
ejpam-6124	570	11	◦	◦	NOUN
ejpam-6124	570	12	h	h	NOUN
ejpam-6124	570	13	=	=	SYM
ejpam-6124	570	14	p1+h	p1+h	PROPN
ejpam-6124	570	15	,	,	PUNCT
ejpam-6124	570	16	by	by	ADP
ejpam-6124	570	17	theorem	theorem	NOUN
ejpam-6124	570	18	12	12	NUM
ejpam-6124	570	19	,	,	PUNCT
ejpam-6124	570	20	t	t	NOUN
ejpam-6124	570	21	=	=	SYM
ejpam-6124	570	22	{	{	PUNCT
ejpam-6124	570	23	x	x	NOUN
ejpam-6124	570	24	,	,	PUNCT
ejpam-6124	570	25	u	u	NOUN
ejpam-6124	570	26	}	}	PUNCT
ejpam-6124	570	27	where	where	SCONJ
ejpam-6124	570	28	x	x	SYM
ejpam-6124	570	29	∈	∈	PROPN
ejpam-6124	570	30	v	v	NOUN
ejpam-6124	570	31	(	(	PUNCT
ejpam-6124	570	32	p1	p1	NOUN
ejpam-6124	570	33	)	)	PUNCT
ejpam-6124	570	34	and	and	CCONJ
ejpam-6124	570	35	u	u	NOUN
ejpam-6124	570	36	is	be	AUX
ejpam-6124	570	37	an	an	DET
ejpam-6124	570	38	isolated	isolated	ADJ
ejpam-6124	570	39	vertex	vertex	NOUN
ejpam-6124	570	40	in	in	ADP
ejpam-6124	570	41	v	v	PROPN
ejpam-6124	570	42	(	(	PUNCT
ejpam-6124	570	43	h	h	NOUN
ejpam-6124	570	44	)	)	PUNCT
ejpam-6124	570	45	.	.	PUNCT
ejpam-6124	571	1	therefore	therefore	ADV
ejpam-6124	571	2	,	,	PUNCT
ejpam-6124	571	3	t	t	PROPN
ejpam-6124	571	4	=	=	SYM
ejpam-6124	571	5	v	v	PROPN
ejpam-6124	571	6	(	(	PUNCT
ejpam-6124	571	7	p1	p1	NOUN
ejpam-6124	571	8	)	)	PUNCT
ejpam-6124	571	9	∪	∪	ADP
ejpam-6124	571	10	{	{	PUNCT
ejpam-6124	571	11	u	u	NOUN
ejpam-6124	571	12	}	}	PUNCT
ejpam-6124	571	13	where	where	SCONJ
ejpam-6124	571	14	u	u	NOUN
ejpam-6124	571	15	is	be	AUX
ejpam-6124	571	16	an	an	DET
ejpam-6124	571	17	isolated	isolated	ADJ
ejpam-6124	571	18	vertex	vertex	NOUN
ejpam-6124	571	19	in	in	ADP
ejpam-6124	571	20	v	v	PROPN
ejpam-6124	571	21	(	(	PUNCT
ejpam-6124	571	22	h	h	NOUN
ejpam-6124	571	23	)	)	PUNCT
ejpam-6124	571	24	.	.	PUNCT
ejpam-6124	572	1	r.	r.	PROPN
ejpam-6124	572	2	g.	g.	PROPN
ejpam-6124	572	3	aguinod	aguinod	PROPN
ejpam-6124	572	4	,	,	PUNCT
ejpam-6124	572	5	e.	e.	PROPN
ejpam-6124	572	6	m.	m.	PROPN
ejpam-6124	572	7	kiunisala	kiunisala	PROPN
ejpam-6124	572	8	,	,	PUNCT
ejpam-6124	572	9	c.	c.	PROPN
ejpam-6124	572	10	l.	l.	PROPN
ejpam-6124	572	11	armada	armada	PROPN
ejpam-6124	572	12	/	/	SYM
ejpam-6124	572	13	eur	eur	PROPN
ejpam-6124	572	14	.	.	PUNCT
ejpam-6124	573	1	j.	j.	PROPN
ejpam-6124	573	2	pure	pure	PROPN
ejpam-6124	573	3	appl	appl	PROPN
ejpam-6124	573	4	.	.	PROPN
ejpam-6124	573	5	math	math	PROPN
ejpam-6124	573	6	,	,	PUNCT
ejpam-6124	573	7	18	18	NUM
ejpam-6124	573	8	(	(	PUNCT
ejpam-6124	573	9	2	2	NUM
ejpam-6124	573	10	)	)	PUNCT
ejpam-6124	573	11	(	(	PUNCT
ejpam-6124	573	12	2025	2025	NUM
ejpam-6124	573	13	)	)	PUNCT
ejpam-6124	573	14	,	,	PUNCT
ejpam-6124	573	15	6124	6124	NUM
ejpam-6124	573	16	20	20	NUM
ejpam-6124	573	17	of	of	ADP
ejpam-6124	573	18	26	26	NUM
ejpam-6124	573	19	suppose	suppose	VERB
ejpam-6124	573	20	that	that	SCONJ
ejpam-6124	573	21	|v	|v	PROPN
ejpam-6124	573	22	(	(	PUNCT
ejpam-6124	573	23	g)|	g)|	NOUN
ejpam-6124	573	24	=	=	SYM
ejpam-6124	573	25	2	2	NUM
ejpam-6124	573	26	.	.	PUNCT
ejpam-6124	573	27	then	then	ADV
ejpam-6124	573	28	g	g	PROPN
ejpam-6124	573	29	∼=	∼=	PROPN
ejpam-6124	573	30	p2	p2	NOUN
ejpam-6124	573	31	.	.	PUNCT
ejpam-6124	573	32	by	by	ADP
ejpam-6124	573	33	corollary	corollary	ADJ
ejpam-6124	573	34	2	2	NUM
ejpam-6124	573	35	,	,	PUNCT
ejpam-6124	573	36	γt(g	γt(g	PUNCT
ejpam-6124	573	37	◦	◦	NOUN
ejpam-6124	573	38	h	h	NOUN
ejpam-6124	573	39	)	)	PUNCT
ejpam-6124	573	40	=	=	SYM
ejpam-6124	573	41	2	2	X
ejpam-6124	573	42	.	.	PUNCT
ejpam-6124	573	43	clearly	clearly	ADV
ejpam-6124	573	44	,	,	PUNCT
ejpam-6124	573	45	v	v	INTJ
ejpam-6124	573	46	(	(	PUNCT
ejpam-6124	573	47	p2	p2	PROPN
ejpam-6124	573	48	)	)	PUNCT
ejpam-6124	573	49	is	be	AUX
ejpam-6124	573	50	a	a	DET
ejpam-6124	573	51	γte	γte	NOUN
ejpam-6124	573	52	-	-	PUNCT
ejpam-6124	573	53	set	set	NOUN
ejpam-6124	573	54	of	of	ADP
ejpam-6124	573	55	g	g	PROPN
ejpam-6124	573	56	◦	◦	NOUN
ejpam-6124	573	57	h	h	NOUN
ejpam-6124	573	58	since	since	SCONJ
ejpam-6124	573	59	|n(v	|n(v	PROPN
ejpam-6124	573	60	)	)	PUNCT
ejpam-6124	573	61	∩	∩	NOUN
ejpam-6124	573	62	v	v	X
ejpam-6124	573	63	(	(	PUNCT
ejpam-6124	573	64	p2)|	p2)|	NOUN
ejpam-6124	573	65	=	=	NOUN
ejpam-6124	573	66	1	1	NUM
ejpam-6124	573	67	for	for	ADP
ejpam-6124	573	68	all	all	PRON
ejpam-6124	573	69	v	v	ADP
ejpam-6124	573	70	∈	∈	PRON
ejpam-6124	573	71	g	g	PROPN
ejpam-6124	573	72	◦	◦	NOUN
ejpam-6124	573	73	h.	h.	PROPN
ejpam-6124	573	74	thus	thus	ADV
ejpam-6124	573	75	,	,	PUNCT
ejpam-6124	573	76	t	t	PROPN
ejpam-6124	573	77	=	=	SYM
ejpam-6124	573	78	v	v	PROPN
ejpam-6124	573	79	(	(	PUNCT
ejpam-6124	573	80	p2	p2	PROPN
ejpam-6124	573	81	)	)	PUNCT
ejpam-6124	573	82	.	.	PUNCT
ejpam-6124	574	1	the	the	DET
ejpam-6124	574	2	converse	converse	NOUN
ejpam-6124	574	3	is	be	AUX
ejpam-6124	574	4	easy	easy	ADJ
ejpam-6124	574	5	.	.	PUNCT
ejpam-6124	575	1	the	the	DET
ejpam-6124	575	2	next	next	ADJ
ejpam-6124	575	3	results	result	NOUN
ejpam-6124	575	4	follow	follow	VERB
ejpam-6124	575	5	directly	directly	ADV
ejpam-6124	575	6	from	from	ADP
ejpam-6124	575	7	theorems	theorem	NOUN
ejpam-6124	575	8	13	13	NUM
ejpam-6124	575	9	and	and	CCONJ
ejpam-6124	575	10	14	14	NUM
ejpam-6124	575	11	:	:	PUNCT
ejpam-6124	575	12	corollary	corollary	ADJ
ejpam-6124	575	13	9	9	NUM
ejpam-6124	575	14	.	.	PUNCT
ejpam-6124	576	1	let	let	VERB
ejpam-6124	576	2	g	g	PRON
ejpam-6124	576	3	∼=	∼=	PROPN
ejpam-6124	576	4	p1	p1	NOUN
ejpam-6124	576	5	graph	graph	NOUN
ejpam-6124	576	6	and	and	CCONJ
ejpam-6124	576	7	h	h	NOUN
ejpam-6124	576	8	be	be	AUX
ejpam-6124	576	9	any	any	DET
ejpam-6124	576	10	graph	graph	NOUN
ejpam-6124	576	11	with	with	ADP
ejpam-6124	576	12	an	an	DET
ejpam-6124	576	13	isolated	isolated	ADJ
ejpam-6124	576	14	vertex	vertex	NOUN
ejpam-6124	576	15	.	.	PUNCT
ejpam-6124	577	1	then	then	ADV
ejpam-6124	577	2	γte(g	γte(g	PRON
ejpam-6124	578	1	◦	◦	NOUN
ejpam-6124	578	2	h	h	NOUN
ejpam-6124	578	3	)	)	PUNCT
ejpam-6124	579	1	=	=	SYM
ejpam-6124	579	2	2	2	X
ejpam-6124	579	3	.	.	PUNCT
ejpam-6124	579	4	corollary	corollary	ADJ
ejpam-6124	579	5	10	10	NUM
ejpam-6124	579	6	.	.	PUNCT
ejpam-6124	580	1	let	let	VERB
ejpam-6124	580	2	g	g	PRON
ejpam-6124	580	3	∼=	∼=	NOUN
ejpam-6124	580	4	p2	p2	NOUN
ejpam-6124	580	5	graph	graph	NOUN
ejpam-6124	580	6	and	and	CCONJ
ejpam-6124	580	7	h	h	NOUN
ejpam-6124	580	8	be	be	AUX
ejpam-6124	580	9	any	any	DET
ejpam-6124	580	10	graph	graph	NOUN
ejpam-6124	580	11	.	.	PUNCT
ejpam-6124	581	1	then	then	ADV
ejpam-6124	581	2	γte(g	γte(g	PRON
ejpam-6124	582	1	◦	◦	NOUN
ejpam-6124	582	2	h	h	NOUN
ejpam-6124	582	3	)	)	PUNCT
ejpam-6124	582	4	=	=	SYM
ejpam-6124	582	5	2	2	X
ejpam-6124	582	6	.	.	NOUN
ejpam-6124	582	7	example	example	NOUN
ejpam-6124	582	8	4	4	NUM
ejpam-6124	582	9	.	.	PUNCT
ejpam-6124	582	10	consider	consider	VERB
ejpam-6124	582	11	the	the	DET
ejpam-6124	582	12	graphs	graph	NOUN
ejpam-6124	582	13	g1	g1	VERB
ejpam-6124	582	14	◦	◦	VERB
ejpam-6124	582	15	h1	h1	PROPN
ejpam-6124	582	16	and	and	CCONJ
ejpam-6124	582	17	g2	g2	PROPN
ejpam-6124	582	18	◦	◦	PROPN
ejpam-6124	582	19	h2	h2	PROPN
ejpam-6124	582	20	in	in	ADP
ejpam-6124	582	21	figure	figure	NOUN
ejpam-6124	582	22	8	8	NUM
ejpam-6124	582	23	.	.	PUNCT
ejpam-6124	583	1	let	let	VERB
ejpam-6124	583	2	t1	t1	NOUN
ejpam-6124	583	3	=	=	PUNCT
ejpam-6124	583	4	{	{	PUNCT
ejpam-6124	583	5	a	a	PROPN
ejpam-6124	583	6	,	,	PUNCT
ejpam-6124	583	7	ua	ua	NOUN
ejpam-6124	583	8	}	}	PUNCT
ejpam-6124	583	9	and	and	CCONJ
ejpam-6124	583	10	t2	t2	PROPN
ejpam-6124	583	11	=	=	PUNCT
ejpam-6124	583	12	{	{	PUNCT
ejpam-6124	583	13	a	a	DET
ejpam-6124	583	14	,	,	PUNCT
ejpam-6124	583	15	b	b	NOUN
ejpam-6124	583	16	}	}	PUNCT
ejpam-6124	583	17	.	.	PUNCT
ejpam-6124	584	1	it	it	PRON
ejpam-6124	584	2	is	be	AUX
ejpam-6124	584	3	clear	clear	ADJ
ejpam-6124	584	4	that	that	SCONJ
ejpam-6124	584	5	|n(ra	|n(ra	PROPN
ejpam-6124	584	6	)	)	PUNCT
ejpam-6124	584	7	∩	∩	NOUN
ejpam-6124	584	8	t1|	t1|	NOUN
ejpam-6124	585	1	=	=	SYM
ejpam-6124	586	1	1	1	NUM
ejpam-6124	586	2	for	for	ADP
ejpam-6124	586	3	all	all	DET
ejpam-6124	586	4	vertices	vertex	NOUN
ejpam-6124	586	5	ra	ra	PROPN
ejpam-6124	586	6	∈	∈	PROPN
ejpam-6124	586	7	v	v	NOUN
ejpam-6124	586	8	(	(	PUNCT
ejpam-6124	586	9	g1	g1	VERB
ejpam-6124	586	10	◦	◦	PROPN
ejpam-6124	586	11	h1	h1	PROPN
ejpam-6124	586	12	)	)	PUNCT
ejpam-6124	586	13	and	and	CCONJ
ejpam-6124	586	14	|n(sa	|n(sa	NOUN
ejpam-6124	586	15	)	)	PUNCT
ejpam-6124	586	16	∩	∩	NOUN
ejpam-6124	586	17	t1|	t1|	NOUN
ejpam-6124	586	18	=	=	SYM
ejpam-6124	586	19	|n(sb	|n(sb	PROPN
ejpam-6124	586	20	)	)	PUNCT
ejpam-6124	586	21	∩	∩	NOUN
ejpam-6124	586	22	t1|	t1|	NOUN
ejpam-6124	586	23	=	=	SYM
ejpam-6124	586	24	1	1	NUM
ejpam-6124	586	25	for	for	ADP
ejpam-6124	586	26	all	all	DET
ejpam-6124	586	27	vertices	vertex	NOUN
ejpam-6124	586	28	sa	sa	PROPN
ejpam-6124	586	29	,	,	PUNCT
ejpam-6124	586	30	sb	sb	PROPN
ejpam-6124	586	31	∈	∈	PROPN
ejpam-6124	586	32	v	v	PROPN
ejpam-6124	586	33	(	(	PUNCT
ejpam-6124	586	34	g2	g2	PROPN
ejpam-6124	586	35	◦	◦	PROPN
ejpam-6124	586	36	h2	h2	PROPN
ejpam-6124	586	37	)	)	PUNCT
ejpam-6124	586	38	.	.	PUNCT
ejpam-6124	587	1	hence	hence	ADV
ejpam-6124	587	2	,	,	PUNCT
ejpam-6124	587	3	t1	t1	NOUN
ejpam-6124	587	4	and	and	CCONJ
ejpam-6124	587	5	t2	t2	NOUN
ejpam-6124	587	6	are	be	AUX
ejpam-6124	587	7	γte	γte	NOUN
ejpam-6124	587	8	-	-	PUNCT
ejpam-6124	587	9	sets	set	NOUN
ejpam-6124	587	10	of	of	ADP
ejpam-6124	587	11	g1	g1	PROPN
ejpam-6124	587	12	◦	◦	VERB
ejpam-6124	587	13	h1	h1	PROPN
ejpam-6124	587	14	and	and	CCONJ
ejpam-6124	587	15	g2	g2	PROPN
ejpam-6124	587	16	◦	◦	PROPN
ejpam-6124	587	17	h2	h2	PROPN
ejpam-6124	587	18	,	,	PUNCT
ejpam-6124	587	19	respectively	respectively	ADV
ejpam-6124	587	20	.	.	PUNCT
ejpam-6124	588	1	it	it	PRON
ejpam-6124	588	2	follows	follow	VERB
ejpam-6124	588	3	that	that	SCONJ
ejpam-6124	588	4	γte(g1	γte(g1	PROPN
ejpam-6124	588	5	◦	◦	PROPN
ejpam-6124	588	6	h1	h1	NOUN
ejpam-6124	588	7	)	)	PUNCT
ejpam-6124	588	8	=	=	SYM
ejpam-6124	588	9	2	2	NUM
ejpam-6124	588	10	and	and	CCONJ
ejpam-6124	588	11	γte(g2	γte(g2	PROPN
ejpam-6124	588	12	◦	◦	PROPN
ejpam-6124	588	13	h2	h2	NOUN
ejpam-6124	588	14	)	)	PUNCT
ejpam-6124	588	15	=	=	SYM
ejpam-6124	588	16	2	2	X
ejpam-6124	588	17	.	.	X
ejpam-6124	588	18	figure	figure	NOUN
ejpam-6124	588	19	8	8	NUM
ejpam-6124	588	20	:	:	PUNCT
ejpam-6124	588	21	graphs	graph	NOUN
ejpam-6124	588	22	g1	g1	PROPN
ejpam-6124	588	23	◦	◦	VERB
ejpam-6124	588	24	h1	h1	PROPN
ejpam-6124	588	25	and	and	CCONJ
ejpam-6124	588	26	g2	g2	PROPN
ejpam-6124	588	27	◦	◦	NOUN
ejpam-6124	588	28	h2	h2	PROPN
ejpam-6124	588	29	with	with	ADP
ejpam-6124	588	30	γte(g1	γte(g1	PROPN
ejpam-6124	588	31	◦	◦	PROPN
ejpam-6124	588	32	h1	h1	NOUN
ejpam-6124	588	33	)	)	PUNCT
ejpam-6124	589	1	=	=	SYM
ejpam-6124	589	2	γte(g2	γte(g2	PROPN
ejpam-6124	589	3	◦	◦	PROPN
ejpam-6124	589	4	h2	h2	NOUN
ejpam-6124	589	5	)	)	PUNCT
ejpam-6124	589	6	=	=	SYM
ejpam-6124	590	1	2	2	X
ejpam-6124	590	2	.	.	PUNCT
ejpam-6124	590	3	corollary	corollary	ADJ
ejpam-6124	590	4	11	11	NUM
ejpam-6124	590	5	.	.	PUNCT
ejpam-6124	591	1	if	if	SCONJ
ejpam-6124	591	2	g	g	PROPN
ejpam-6124	591	3	≇	≇	PROPN
ejpam-6124	591	4	p1	p1	PROPN
ejpam-6124	591	5	or	or	CCONJ
ejpam-6124	591	6	g	g	PROPN
ejpam-6124	591	7	≇	≇	PROPN
ejpam-6124	591	8	p2	p2	PROPN
ejpam-6124	591	9	,	,	PUNCT
ejpam-6124	591	10	then	then	ADV
ejpam-6124	591	11	for	for	ADP
ejpam-6124	591	12	any	any	DET
ejpam-6124	591	13	graph	graph	NOUN
ejpam-6124	591	14	h	h	NOUN
ejpam-6124	591	15	,	,	PUNCT
ejpam-6124	591	16	g	g	PROPN
ejpam-6124	591	17	◦	◦	NOUN
ejpam-6124	591	18	h	h	NOUN
ejpam-6124	591	19	is	be	AUX
ejpam-6124	591	20	a	a	DET
ejpam-6124	591	21	non	non	ADJ
ejpam-6124	591	22	-	-	ADJ
ejpam-6124	591	23	γte	γte	PRON
ejpam-6124	591	24	-	-	PUNCT
ejpam-6124	591	25	graph	graph	NOUN
ejpam-6124	591	26	.	.	PUNCT
ejpam-6124	592	1	corollary	corollary	ADJ
ejpam-6124	592	2	12	12	NUM
ejpam-6124	592	3	.	.	PUNCT
ejpam-6124	593	1	let	let	VERB
ejpam-6124	593	2	g	g	PRON
ejpam-6124	593	3	be	be	AUX
ejpam-6124	593	4	a	a	DET
ejpam-6124	593	5	disconnected	disconnected	ADJ
ejpam-6124	593	6	graph	graph	NOUN
ejpam-6124	593	7	with	with	ADP
ejpam-6124	593	8	k	k	PROPN
ejpam-6124	593	9	components	component	NOUN
ejpam-6124	593	10	such	such	ADJ
ejpam-6124	593	11	that	that	SCONJ
ejpam-6124	593	12	each	each	DET
ejpam-6124	593	13	component	component	NOUN
ejpam-6124	593	14	is	be	AUX
ejpam-6124	593	15	isomorphic	isomorphic	ADJ
ejpam-6124	593	16	to	to	ADP
ejpam-6124	593	17	either	either	CCONJ
ejpam-6124	593	18	p1	p1	PROPN
ejpam-6124	593	19	or	or	CCONJ
ejpam-6124	593	20	p2	p2	PROPN
ejpam-6124	593	21	and	and	CCONJ
ejpam-6124	593	22	h	h	NOUN
ejpam-6124	593	23	be	be	VERB
ejpam-6124	593	24	any	any	DET
ejpam-6124	593	25	graph	graph	NOUN
ejpam-6124	593	26	with	with	ADP
ejpam-6124	593	27	an	an	DET
ejpam-6124	593	28	isolated	isolated	ADJ
ejpam-6124	593	29	vertex	vertex	NOUN
ejpam-6124	593	30	.	.	PUNCT
ejpam-6124	594	1	then	then	ADV
ejpam-6124	594	2	γte(g	γte(g	PRON
ejpam-6124	595	1	◦	◦	NOUN
ejpam-6124	595	2	h	h	NOUN
ejpam-6124	595	3	)	)	PUNCT
ejpam-6124	595	4	=	=	SYM
ejpam-6124	595	5	2k	2k	NUM
ejpam-6124	595	6	.	.	PUNCT
ejpam-6124	596	1	r.	r.	PROPN
ejpam-6124	596	2	g.	g.	PROPN
ejpam-6124	596	3	aguinod	aguinod	PROPN
ejpam-6124	596	4	,	,	PUNCT
ejpam-6124	596	5	e.	e.	PROPN
ejpam-6124	596	6	m.	m.	PROPN
ejpam-6124	596	7	kiunisala	kiunisala	PROPN
ejpam-6124	596	8	,	,	PUNCT
ejpam-6124	596	9	c.	c.	PROPN
ejpam-6124	596	10	l.	l.	PROPN
ejpam-6124	596	11	armada	armada	PROPN
ejpam-6124	596	12	/	/	SYM
ejpam-6124	596	13	eur	eur	PROPN
ejpam-6124	596	14	.	.	PUNCT
ejpam-6124	597	1	j.	j.	PROPN
ejpam-6124	597	2	pure	pure	PROPN
ejpam-6124	597	3	appl	appl	PROPN
ejpam-6124	597	4	.	.	PROPN
ejpam-6124	597	5	math	math	PROPN
ejpam-6124	597	6	,	,	PUNCT
ejpam-6124	597	7	18	18	NUM
ejpam-6124	597	8	(	(	PUNCT
ejpam-6124	597	9	2	2	NUM
ejpam-6124	597	10	)	)	PUNCT
ejpam-6124	597	11	(	(	PUNCT
ejpam-6124	597	12	2025	2025	NUM
ejpam-6124	597	13	)	)	PUNCT
ejpam-6124	597	14	,	,	PUNCT
ejpam-6124	597	15	6124	6124	NUM
ejpam-6124	597	16	21	21	NUM
ejpam-6124	597	17	of	of	ADP
ejpam-6124	597	18	26	26	NUM
ejpam-6124	597	19	example	example	NOUN
ejpam-6124	597	20	5	5	NUM
ejpam-6124	597	21	.	.	PUNCT
ejpam-6124	598	1	the	the	DET
ejpam-6124	598	2	following	follow	VERB
ejpam-6124	598	3	example	example	NOUN
ejpam-6124	598	4	verifies	verifie	NOUN
ejpam-6124	598	5	the	the	DET
ejpam-6124	598	6	result	result	NOUN
ejpam-6124	598	7	of	of	ADP
ejpam-6124	598	8	corollary	corollary	ADJ
ejpam-6124	598	9	12	12	NUM
ejpam-6124	598	10	.	.	PUNCT
ejpam-6124	599	1	figure	figure	NOUN
ejpam-6124	599	2	9	9	NUM
ejpam-6124	599	3	:	:	PUNCT
ejpam-6124	599	4	graph	graph	NOUN
ejpam-6124	599	5	g	g	PROPN
ejpam-6124	599	6	◦	◦	NOUN
ejpam-6124	599	7	h	h	NOUN
ejpam-6124	599	8	with	with	ADP
ejpam-6124	599	9	γte(g	γte(g	PROPN
ejpam-6124	599	10	◦	◦	NOUN
ejpam-6124	599	11	h	h	NOUN
ejpam-6124	599	12	)	)	PUNCT
ejpam-6124	599	13	=	=	SYM
ejpam-6124	599	14	2(5	2(5	NOUN
ejpam-6124	599	15	)	)	PUNCT
ejpam-6124	599	16	=	=	SYM
ejpam-6124	600	1	10	10	NUM
ejpam-6124	600	2	.	.	PUNCT
ejpam-6124	600	3	corollary	corollary	ADJ
ejpam-6124	600	4	13	13	NUM
ejpam-6124	600	5	.	.	PUNCT
ejpam-6124	601	1	let	let	VERB
ejpam-6124	601	2	g	g	PRON
ejpam-6124	601	3	be	be	AUX
ejpam-6124	601	4	a	a	DET
ejpam-6124	601	5	disconnected	disconnected	ADJ
ejpam-6124	601	6	graph	graph	NOUN
ejpam-6124	601	7	with	with	ADP
ejpam-6124	601	8	k	k	PROPN
ejpam-6124	601	9	components	component	NOUN
ejpam-6124	601	10	such	such	ADJ
ejpam-6124	601	11	that	that	SCONJ
ejpam-6124	601	12	each	each	DET
ejpam-6124	601	13	component	component	NOUN
ejpam-6124	601	14	is	be	AUX
ejpam-6124	601	15	isomorphic	isomorphic	ADJ
ejpam-6124	601	16	to	to	ADP
ejpam-6124	601	17	p2	p2	PROPN
ejpam-6124	601	18	and	and	CCONJ
ejpam-6124	601	19	h	h	NOUN
ejpam-6124	601	20	be	be	AUX
ejpam-6124	601	21	any	any	DET
ejpam-6124	601	22	graph	graph	NOUN
ejpam-6124	601	23	.	.	PUNCT
ejpam-6124	602	1	then	then	ADV
ejpam-6124	602	2	γte(g	γte(g	PRON
ejpam-6124	603	1	◦	◦	NOUN
ejpam-6124	603	2	h	h	NOUN
ejpam-6124	603	3	)	)	PUNCT
ejpam-6124	603	4	=	=	SYM
ejpam-6124	603	5	2k	2k	NUM
ejpam-6124	603	6	.	.	PUNCT
ejpam-6124	604	1	4.3	4.3	NUM
ejpam-6124	604	2	.	.	PUNCT
ejpam-6124	605	1	total	total	ADJ
ejpam-6124	605	2	exact	exact	ADJ
ejpam-6124	605	3	dominating	dominating	NOUN
ejpam-6124	605	4	set	set	VERB
ejpam-6124	605	5	in	in	ADP
ejpam-6124	605	6	the	the	DET
ejpam-6124	605	7	lexicographic	lexicographic	ADJ
ejpam-6124	605	8	product	product	NOUN
ejpam-6124	605	9	of	of	ADP
ejpam-6124	605	10	graphs	graph	NOUN
ejpam-6124	605	11	this	this	DET
ejpam-6124	605	12	section	section	NOUN
ejpam-6124	605	13	contains	contain	VERB
ejpam-6124	605	14	results	result	NOUN
ejpam-6124	605	15	when	when	SCONJ
ejpam-6124	605	16	the	the	DET
ejpam-6124	605	17	lexicographic	lexicographic	ADJ
ejpam-6124	605	18	product	product	NOUN
ejpam-6124	605	19	g[h	g[h	PROPN
ejpam-6124	605	20	]	]	PUNCT
ejpam-6124	605	21	has	have	VERB
ejpam-6124	605	22	either	either	CCONJ
ejpam-6124	605	23	a	a	DET
ejpam-6124	605	24	γte−set	γte−set	NOUN
ejpam-6124	605	25	or	or	CCONJ
ejpam-6124	605	26	has	have	VERB
ejpam-6124	605	27	no	no	DET
ejpam-6124	605	28	γte	γte	NOUN
ejpam-6124	605	29	−	−	PROPN
ejpam-6124	605	30	set	set	NOUN
ejpam-6124	605	31	and	and	CCONJ
ejpam-6124	605	32	its	its	PRON
ejpam-6124	605	33	total	total	ADJ
ejpam-6124	605	34	exact	exact	ADJ
ejpam-6124	605	35	domination	domination	NOUN
ejpam-6124	605	36	number	number	NOUN
ejpam-6124	605	37	.	.	PUNCT
ejpam-6124	606	1	theorem	theorem	VERB
ejpam-6124	606	2	15	15	NUM
ejpam-6124	606	3	.	.	PUNCT
ejpam-6124	607	1	let	let	VERB
ejpam-6124	607	2	g	g	NOUN
ejpam-6124	608	1	and	and	CCONJ
ejpam-6124	608	2	h	h	NOUN
ejpam-6124	608	3	be	be	AUX
ejpam-6124	608	4	graphs	graph	NOUN
ejpam-6124	608	5	such	such	ADJ
ejpam-6124	608	6	that	that	SCONJ
ejpam-6124	608	7	at	at	ADV
ejpam-6124	608	8	least	least	ADJ
ejpam-6124	608	9	one	one	NUM
ejpam-6124	608	10	of	of	ADP
ejpam-6124	608	11	them	they	PRON
ejpam-6124	608	12	is	be	AUX
ejpam-6124	608	13	connected	connect	VERB
ejpam-6124	608	14	,	,	PUNCT
ejpam-6124	608	15	and	and	CCONJ
ejpam-6124	608	16	at	at	ADP
ejpam-6124	608	17	most	most	ADJ
ejpam-6124	608	18	one	one	NOUN
ejpam-6124	608	19	is	be	AUX
ejpam-6124	608	20	an	an	DET
ejpam-6124	608	21	empty	empty	ADJ
ejpam-6124	608	22	graph	graph	NOUN
ejpam-6124	608	23	.	.	PUNCT
ejpam-6124	609	1	then	then	ADV
ejpam-6124	609	2	g[h	g[h	VERB
ejpam-6124	609	3	]	]	PUNCT
ejpam-6124	609	4	is	be	AUX
ejpam-6124	609	5	a	a	DET
ejpam-6124	609	6	non	non	ADJ
ejpam-6124	609	7	-	-	ADJ
ejpam-6124	609	8	γte	γte	PRON
ejpam-6124	609	9	-	-	PUNCT
ejpam-6124	609	10	graph	graph	NOUN
ejpam-6124	609	11	if	if	SCONJ
ejpam-6124	610	1	and	and	CCONJ
ejpam-6124	610	2	only	only	ADV
ejpam-6124	610	3	if	if	SCONJ
ejpam-6124	610	4	one	one	NUM
ejpam-6124	610	5	of	of	ADP
ejpam-6124	610	6	the	the	DET
ejpam-6124	610	7	following	follow	VERB
ejpam-6124	610	8	is	be	AUX
ejpam-6124	610	9	satisfied	satisfied	ADJ
ejpam-6124	610	10	:	:	PUNCT
ejpam-6124	610	11	(	(	PUNCT
ejpam-6124	610	12	i	i	NOUN
ejpam-6124	610	13	)	)	PUNCT
ejpam-6124	610	14	both	both	CCONJ
ejpam-6124	610	15	g	g	PROPN
ejpam-6124	610	16	and	and	CCONJ
ejpam-6124	610	17	h	h	NOUN
ejpam-6124	610	18	are	be	AUX
ejpam-6124	610	19	nontrivial	nontrivial	ADJ
ejpam-6124	610	20	connected	connect	VERB
ejpam-6124	610	21	graphs	graph	NOUN
ejpam-6124	610	22	,	,	PUNCT
ejpam-6124	610	23	(	(	PUNCT
ejpam-6124	610	24	ii	ii	NOUN
ejpam-6124	610	25	)	)	PUNCT
ejpam-6124	610	26	g	g	NOUN
ejpam-6124	610	27	is	be	AUX
ejpam-6124	610	28	an	an	DET
ejpam-6124	610	29	empty	empty	ADJ
ejpam-6124	610	30	graph	graph	NOUN
ejpam-6124	610	31	and	and	CCONJ
ejpam-6124	610	32	h	h	NOUN
ejpam-6124	610	33	is	be	AUX
ejpam-6124	610	34	a	a	DET
ejpam-6124	610	35	connected	connected	ADJ
ejpam-6124	610	36	nonγte	nonγte	NOUN
ejpam-6124	610	37	-	-	PUNCT
ejpam-6124	610	38	graph	graph	NOUN
ejpam-6124	610	39	,	,	PUNCT
ejpam-6124	610	40	or	or	CCONJ
ejpam-6124	610	41	(	(	PUNCT
ejpam-6124	610	42	iii	iii	X
ejpam-6124	610	43	)	)	PUNCT
ejpam-6124	610	44	h	h	NOUN
ejpam-6124	610	45	is	be	AUX
ejpam-6124	610	46	an	an	DET
ejpam-6124	610	47	empty	empty	ADJ
ejpam-6124	610	48	graph	graph	NOUN
ejpam-6124	610	49	and	and	CCONJ
ejpam-6124	610	50	g	g	NOUN
ejpam-6124	610	51	is	be	AUX
ejpam-6124	610	52	a	a	DET
ejpam-6124	610	53	connected	connected	ADJ
ejpam-6124	610	54	nonγte	nonγte	NOUN
ejpam-6124	610	55	-	-	PUNCT
ejpam-6124	610	56	graph	graph	NOUN
ejpam-6124	610	57	.	.	PUNCT
ejpam-6124	611	1	proof	proof	NOUN
ejpam-6124	611	2	.	.	PUNCT
ejpam-6124	612	1	suppose	suppose	VERB
ejpam-6124	612	2	that	that	SCONJ
ejpam-6124	612	3	g	g	PROPN
ejpam-6124	612	4	is	be	AUX
ejpam-6124	612	5	an	an	DET
ejpam-6124	612	6	empty	empty	ADJ
ejpam-6124	612	7	graph	graph	NOUN
ejpam-6124	612	8	and	and	CCONJ
ejpam-6124	612	9	h	h	NOUN
ejpam-6124	612	10	is	be	AUX
ejpam-6124	612	11	a	a	DET
ejpam-6124	612	12	connected	connected	ADJ
ejpam-6124	612	13	graph	graph	NOUN
ejpam-6124	612	14	,	,	PUNCT
ejpam-6124	612	15	and	and	CCONJ
ejpam-6124	612	16	let	let	VERB
ejpam-6124	612	17	t	t	PROPN
ejpam-6124	612	18	be	be	AUX
ejpam-6124	612	19	a	a	DET
ejpam-6124	612	20	γte	γte	NOUN
ejpam-6124	612	21	-	-	PUNCT
ejpam-6124	612	22	set	set	NOUN
ejpam-6124	612	23	of	of	ADP
ejpam-6124	612	24	h.	h.	NOUN
ejpam-6124	612	25	since	since	SCONJ
ejpam-6124	612	26	g	g	PROPN
ejpam-6124	612	27	is	be	AUX
ejpam-6124	612	28	an	an	DET
ejpam-6124	612	29	empty	empty	ADJ
ejpam-6124	612	30	graph	graph	NOUN
ejpam-6124	612	31	,	,	PUNCT
ejpam-6124	612	32	g[h	g[h	PROPN
ejpam-6124	612	33	]	]	PUNCT
ejpam-6124	612	34	is	be	AUX
ejpam-6124	612	35	a	a	DET
ejpam-6124	612	36	disjoint	disjoint	ADJ
ejpam-6124	612	37	union	union	NOUN
ejpam-6124	612	38	of	of	ADP
ejpam-6124	612	39	|v	|v	PROPN
ejpam-6124	612	40	(	(	PUNCT
ejpam-6124	612	41	g)|	g)|	NOUN
ejpam-6124	612	42	copies	copy	NOUN
ejpam-6124	612	43	of	of	ADP
ejpam-6124	612	44	h.	h.	PROPN
ejpam-6124	612	45	clearly	clearly	ADV
ejpam-6124	612	46	,	,	PUNCT
ejpam-6124	612	47	|c|	|c|	PROPN
ejpam-6124	612	48	=	=	SYM
ejpam-6124	612	49	|v	|v	PROPN
ejpam-6124	612	50	(	(	PUNCT
ejpam-6124	612	51	g)||t	g)||t	NOUN
ejpam-6124	612	52	|	|	ADV
ejpam-6124	612	53	and	and	CCONJ
ejpam-6124	612	54	c	c	PROPN
ejpam-6124	612	55	is	be	AUX
ejpam-6124	612	56	a	a	DET
ejpam-6124	612	57	γte	γte	NOUN
ejpam-6124	612	58	-	-	PUNCT
ejpam-6124	612	59	set	set	NOUN
ejpam-6124	612	60	of	of	ADP
ejpam-6124	612	61	g[h	g[h	NOUN
ejpam-6124	612	62	]	]	PUNCT
ejpam-6124	612	63	.	.	PUNCT
ejpam-6124	613	1	hence	hence	ADV
ejpam-6124	613	2	,	,	PUNCT
ejpam-6124	613	3	g[h	g[h	PROPN
ejpam-6124	613	4	]	]	PUNCT
ejpam-6124	613	5	is	be	AUX
ejpam-6124	613	6	not	not	PART
ejpam-6124	613	7	a	a	DET
ejpam-6124	613	8	non	non	ADJ
ejpam-6124	613	9	-	-	ADJ
ejpam-6124	613	10	γte	γte	PRON
ejpam-6124	613	11	-	-	PUNCT
ejpam-6124	613	12	graph	graph	NOUN
ejpam-6124	613	13	.	.	PUNCT
ejpam-6124	614	1	suppose	suppose	VERB
ejpam-6124	614	2	that	that	SCONJ
ejpam-6124	614	3	h	h	NOUN
ejpam-6124	614	4	is	be	AUX
ejpam-6124	614	5	an	an	DET
ejpam-6124	614	6	empty	empty	ADJ
ejpam-6124	614	7	graph	graph	NOUN
ejpam-6124	614	8	and	and	CCONJ
ejpam-6124	614	9	g	g	NOUN
ejpam-6124	614	10	is	be	AUX
ejpam-6124	614	11	a	a	DET
ejpam-6124	614	12	connected	connected	ADJ
ejpam-6124	614	13	graph	graph	NOUN
ejpam-6124	614	14	,	,	PUNCT
ejpam-6124	614	15	and	and	CCONJ
ejpam-6124	614	16	s	s	VERB
ejpam-6124	614	17	is	be	AUX
ejpam-6124	614	18	a	a	DET
ejpam-6124	614	19	γte	γte	NOUN
ejpam-6124	614	20	-	-	PUNCT
ejpam-6124	614	21	set	set	NOUN
ejpam-6124	614	22	of	of	ADP
ejpam-6124	614	23	g.	g.	PROPN
ejpam-6124	614	24	let	let	VERB
ejpam-6124	614	25	c	c	NOUN
ejpam-6124	614	26	=	=	PUNCT
ejpam-6124	614	27	⋃	⋃	PROPN
ejpam-6124	614	28	x∈s({x	x∈s({x	NOUN
ejpam-6124	614	29	}	}	SYM
ejpam-6124	614	30	×	×	PROPN
ejpam-6124	614	31	y	y	PROPN
ejpam-6124	614	32	)	)	PUNCT
ejpam-6124	614	33	where	where	SCONJ
ejpam-6124	614	34	y	y	PROPN
ejpam-6124	614	35	∈	∈	PROPN
ejpam-6124	614	36	v	v	ADP
ejpam-6124	614	37	(	(	PUNCT
ejpam-6124	614	38	h	h	NOUN
ejpam-6124	614	39	)	)	PUNCT
ejpam-6124	614	40	.	.	PUNCT
ejpam-6124	615	1	since	since	SCONJ
ejpam-6124	615	2	h	h	NOUN
ejpam-6124	615	3	is	be	AUX
ejpam-6124	615	4	an	an	DET
ejpam-6124	615	5	empty	empty	ADJ
ejpam-6124	615	6	graph	graph	NOUN
ejpam-6124	615	7	,	,	PUNCT
ejpam-6124	615	8	all	all	DET
ejpam-6124	615	9	vertices	vertex	NOUN
ejpam-6124	615	10	of	of	ADP
ejpam-6124	615	11	the	the	DET
ejpam-6124	615	12	|v	|v	NOUN
ejpam-6124	615	13	(	(	PUNCT
ejpam-6124	615	14	h)|	h)|	NOUN
ejpam-6124	615	15	copies	copy	NOUN
ejpam-6124	615	16	of	of	ADP
ejpam-6124	615	17	g	g	PROPN
ejpam-6124	615	18	is	be	AUX
ejpam-6124	615	19	adjacent	adjacent	ADJ
ejpam-6124	615	20	to	to	ADP
ejpam-6124	615	21	the	the	DET
ejpam-6124	615	22	exactly	exactly	ADV
ejpam-6124	615	23	one	one	NUM
ejpam-6124	615	24	vertex	vertex	NOUN
ejpam-6124	615	25	in	in	ADP
ejpam-6124	615	26	c.	c.	PROPN
ejpam-6124	615	27	thus	thus	ADV
ejpam-6124	615	28	,	,	PUNCT
ejpam-6124	615	29	|n(u	|n(u	PROPN
ejpam-6124	615	30	,	,	PUNCT
ejpam-6124	615	31	v)∩c|	v)∩c|	X
ejpam-6124	615	32	=	=	SYM
ejpam-6124	615	33	1	1	NUM
ejpam-6124	615	34	for	for	ADP
ejpam-6124	615	35	all	all	DET
ejpam-6124	615	36	vertices	vertex	NOUN
ejpam-6124	615	37	(	(	PUNCT
ejpam-6124	615	38	u	u	NOUN
ejpam-6124	615	39	,	,	PUNCT
ejpam-6124	615	40	v	v	NOUN
ejpam-6124	615	41	)	)	PUNCT
ejpam-6124	615	42	∈	∈	NOUN
ejpam-6124	615	43	v	v	NOUN
ejpam-6124	615	44	(	(	PUNCT
ejpam-6124	615	45	g[h	g[h	PROPN
ejpam-6124	615	46	]	]	PUNCT
ejpam-6124	615	47	)	)	PUNCT
ejpam-6124	615	48	.	.	PUNCT
ejpam-6124	616	1	therefore	therefore	ADV
ejpam-6124	616	2	,	,	PUNCT
ejpam-6124	616	3	c	c	PROPN
ejpam-6124	616	4	is	be	AUX
ejpam-6124	616	5	a	a	DET
ejpam-6124	616	6	γte	γte	NOUN
ejpam-6124	616	7	-	-	PUNCT
ejpam-6124	616	8	set	set	NOUN
ejpam-6124	616	9	of	of	ADP
ejpam-6124	616	10	g[h	g[h	NOUN
ejpam-6124	616	11	]	]	PUNCT
ejpam-6124	616	12	.	.	PUNCT
ejpam-6124	617	1	hence	hence	ADV
ejpam-6124	617	2	,	,	PUNCT
ejpam-6124	617	3	g[h	g[h	PROPN
ejpam-6124	617	4	]	]	PUNCT
ejpam-6124	617	5	is	be	AUX
ejpam-6124	617	6	not	not	PART
ejpam-6124	617	7	a	a	DET
ejpam-6124	617	8	r.	r.	PROPN
ejpam-6124	617	9	g.	g.	PROPN
ejpam-6124	617	10	aguinod	aguinod	PROPN
ejpam-6124	617	11	,	,	PUNCT
ejpam-6124	617	12	e.	e.	PROPN
ejpam-6124	617	13	m.	m.	PROPN
ejpam-6124	617	14	kiunisala	kiunisala	PROPN
ejpam-6124	617	15	,	,	PUNCT
ejpam-6124	617	16	c.	c.	PROPN
ejpam-6124	617	17	l.	l.	PROPN
ejpam-6124	617	18	armada	armada	PROPN
ejpam-6124	617	19	/	/	SYM
ejpam-6124	617	20	eur	eur	PROPN
ejpam-6124	617	21	.	.	PUNCT
ejpam-6124	618	1	j.	j.	PROPN
ejpam-6124	618	2	pure	pure	PROPN
ejpam-6124	618	3	appl	appl	PROPN
ejpam-6124	618	4	.	.	PROPN
ejpam-6124	618	5	math	math	PROPN
ejpam-6124	618	6	,	,	PUNCT
ejpam-6124	618	7	18	18	NUM
ejpam-6124	618	8	(	(	PUNCT
ejpam-6124	618	9	2	2	NUM
ejpam-6124	618	10	)	)	PUNCT
ejpam-6124	618	11	(	(	PUNCT
ejpam-6124	618	12	2025	2025	NUM
ejpam-6124	618	13	)	)	PUNCT
ejpam-6124	618	14	,	,	PUNCT
ejpam-6124	618	15	6124	6124	NUM
ejpam-6124	618	16	22	22	NUM
ejpam-6124	618	17	of	of	ADP
ejpam-6124	618	18	26	26	NUM
ejpam-6124	618	19	non	non	ADJ
ejpam-6124	618	20	-	-	ADJ
ejpam-6124	618	21	γte	γte	PRON
ejpam-6124	618	22	-	-	PUNCT
ejpam-6124	618	23	graph	graph	NOUN
ejpam-6124	618	24	.	.	PUNCT
ejpam-6124	618	25	suppose	suppose	VERB
ejpam-6124	618	26	that	that	SCONJ
ejpam-6124	618	27	(	(	PUNCT
ejpam-6124	618	28	i	i	NOUN
ejpam-6124	618	29	)	)	PUNCT
ejpam-6124	618	30	holds	hold	VERB
ejpam-6124	618	31	,	,	PUNCT
ejpam-6124	618	32	that	that	ADV
ejpam-6124	618	33	is	is	ADV
ejpam-6124	618	34	,	,	PUNCT
ejpam-6124	618	35	both	both	PRON
ejpam-6124	618	36	g	g	PROPN
ejpam-6124	618	37	and	and	CCONJ
ejpam-6124	618	38	h	h	NOUN
ejpam-6124	618	39	are	be	AUX
ejpam-6124	618	40	nontrivial	nontrivial	ADJ
ejpam-6124	618	41	connected	connected	ADJ
ejpam-6124	618	42	graphs	graph	NOUN
ejpam-6124	618	43	.	.	PUNCT
ejpam-6124	619	1	let	let	VERB
ejpam-6124	619	2	c	c	PRON
ejpam-6124	619	3	be	be	AUX
ejpam-6124	619	4	a	a	DET
ejpam-6124	619	5	γte	γte	NOUN
ejpam-6124	619	6	-	-	PUNCT
ejpam-6124	619	7	set	set	NOUN
ejpam-6124	619	8	of	of	ADP
ejpam-6124	619	9	g[h	g[h	NOUN
ejpam-6124	619	10	]	]	PUNCT
ejpam-6124	619	11	.	.	PUNCT
ejpam-6124	620	1	note	note	VERB
ejpam-6124	620	2	that	that	SCONJ
ejpam-6124	620	3	for	for	ADP
ejpam-6124	620	4	any	any	DET
ejpam-6124	620	5	two	two	NUM
ejpam-6124	620	6	adjacent	adjacent	ADJ
ejpam-6124	620	7	vertices	vertex	NOUN
ejpam-6124	620	8	u	u	NOUN
ejpam-6124	620	9	,	,	PUNCT
ejpam-6124	620	10	v	v	NOUN
ejpam-6124	620	11	∈	∈	PROPN
ejpam-6124	620	12	v	v	NOUN
ejpam-6124	620	13	(	(	PUNCT
ejpam-6124	620	14	g	g	NOUN
ejpam-6124	620	15	)	)	PUNCT
ejpam-6124	620	16	and	and	CCONJ
ejpam-6124	620	17	any	any	DET
ejpam-6124	620	18	two	two	NUM
ejpam-6124	620	19	adjacent	adjacent	ADJ
ejpam-6124	620	20	vertices	vertex	NOUN
ejpam-6124	620	21	p	p	NOUN
ejpam-6124	620	22	,	,	PUNCT
ejpam-6124	620	23	q	q	PROPN
ejpam-6124	620	24	∈	∈	PROPN
ejpam-6124	620	25	v	v	ADP
ejpam-6124	620	26	(	(	PUNCT
ejpam-6124	620	27	h	h	NOUN
ejpam-6124	620	28	)	)	PUNCT
ejpam-6124	620	29	,	,	PUNCT
ejpam-6124	620	30	the	the	DET
ejpam-6124	620	31	vertices	vertex	NOUN
ejpam-6124	620	32	formed	form	VERB
ejpam-6124	620	33	in	in	ADP
ejpam-6124	620	34	g[h	g[h	PROPN
ejpam-6124	620	35	]	]	PUNCT
ejpam-6124	620	36	are	be	AUX
ejpam-6124	620	37	(	(	PUNCT
ejpam-6124	620	38	u	u	NOUN
ejpam-6124	620	39	,	,	PUNCT
ejpam-6124	620	40	p	p	NOUN
ejpam-6124	620	41	)	)	PUNCT
ejpam-6124	620	42	,	,	PUNCT
ejpam-6124	620	43	(	(	PUNCT
ejpam-6124	620	44	v	v	NOUN
ejpam-6124	620	45	,	,	PUNCT
ejpam-6124	620	46	p	p	NOUN
ejpam-6124	620	47	)	)	PUNCT
ejpam-6124	620	48	,	,	PUNCT
ejpam-6124	620	49	(	(	PUNCT
ejpam-6124	620	50	u	u	NOUN
ejpam-6124	620	51	,	,	PUNCT
ejpam-6124	620	52	q	q	NOUN
ejpam-6124	620	53	)	)	PUNCT
ejpam-6124	620	54	,	,	PUNCT
ejpam-6124	620	55	and	and	CCONJ
ejpam-6124	620	56	(	(	PUNCT
ejpam-6124	620	57	v	v	NOUN
ejpam-6124	620	58	,	,	PUNCT
ejpam-6124	620	59	q	q	NOUN
ejpam-6124	620	60	)	)	PUNCT
ejpam-6124	620	61	.	.	PUNCT
ejpam-6124	621	1	these	these	DET
ejpam-6124	621	2	vertices	vertex	NOUN
ejpam-6124	621	3	are	be	AUX
ejpam-6124	621	4	all	all	ADV
ejpam-6124	621	5	adjacent	adjacent	ADJ
ejpam-6124	621	6	to	to	ADP
ejpam-6124	621	7	each	each	DET
ejpam-6124	621	8	other	other	ADJ
ejpam-6124	621	9	,	,	PUNCT
ejpam-6124	621	10	forming	form	VERB
ejpam-6124	621	11	a	a	DET
ejpam-6124	621	12	complete	complete	ADJ
ejpam-6124	621	13	subgraph	subgraph	NOUN
ejpam-6124	621	14	k4	k4	NOUN
ejpam-6124	621	15	.	.	PUNCT
ejpam-6124	622	1	this	this	PRON
ejpam-6124	622	2	holds	hold	VERB
ejpam-6124	622	3	for	for	ADP
ejpam-6124	622	4	every	every	DET
ejpam-6124	622	5	pair	pair	NOUN
ejpam-6124	622	6	of	of	ADP
ejpam-6124	622	7	adjacent	adjacent	ADJ
ejpam-6124	622	8	vertices	vertex	NOUN
ejpam-6124	622	9	in	in	ADP
ejpam-6124	622	10	v	v	ADP
ejpam-6124	622	11	(	(	PUNCT
ejpam-6124	622	12	g	g	NOUN
ejpam-6124	622	13	)	)	PUNCT
ejpam-6124	622	14	and	and	CCONJ
ejpam-6124	622	15	v	v	NOUN
ejpam-6124	622	16	(	(	PUNCT
ejpam-6124	622	17	h	h	NOUN
ejpam-6124	622	18	)	)	PUNCT
ejpam-6124	622	19	when	when	SCONJ
ejpam-6124	622	20	constructing	construct	VERB
ejpam-6124	622	21	the	the	DET
ejpam-6124	622	22	vertices	vertex	NOUN
ejpam-6124	622	23	of	of	ADP
ejpam-6124	622	24	g[h	g[h	NOUN
ejpam-6124	622	25	]	]	PUNCT
ejpam-6124	622	26	.	.	PUNCT
ejpam-6124	623	1	moreover	moreover	ADV
ejpam-6124	623	2	,	,	PUNCT
ejpam-6124	623	3	note	note	VERB
ejpam-6124	623	4	that	that	SCONJ
ejpam-6124	623	5	two	two	NUM
ejpam-6124	623	6	vertices	vertex	NOUN
ejpam-6124	623	7	in	in	ADP
ejpam-6124	623	8	c	c	PROPN
ejpam-6124	623	9	must	must	AUX
ejpam-6124	623	10	be	be	AUX
ejpam-6124	623	11	adjacent	adjacent	ADJ
ejpam-6124	623	12	.	.	PUNCT
ejpam-6124	624	1	thus	thus	ADV
ejpam-6124	624	2	,	,	PUNCT
ejpam-6124	624	3	there	there	PRON
ejpam-6124	624	4	exists	exist	VERB
ejpam-6124	624	5	a	a	DET
ejpam-6124	624	6	vertex	vertex	NOUN
ejpam-6124	624	7	in	in	ADP
ejpam-6124	624	8	v	v	NOUN
ejpam-6124	624	9	(	(	PUNCT
ejpam-6124	624	10	g[h	g[h	PROPN
ejpam-6124	624	11	]	]	PUNCT
ejpam-6124	624	12	)	)	PUNCT
ejpam-6124	624	13	\	\	PUNCT
ejpam-6124	625	1	c	c	NOUN
ejpam-6124	625	2	such	such	ADJ
ejpam-6124	625	3	that	that	DET
ejpam-6124	625	4	|n(s	|n(s	PROPN
ejpam-6124	625	5	,	,	PUNCT
ejpam-6124	625	6	t	t	PROPN
ejpam-6124	625	7	)	)	PUNCT
ejpam-6124	625	8	∩	∩	NOUN
ejpam-6124	625	9	c|	c|	PROPN
ejpam-6124	625	10	=	=	SYM
ejpam-6124	625	11	2	2	X
ejpam-6124	625	12	.	.	PUNCT
ejpam-6124	625	13	this	this	PRON
ejpam-6124	625	14	contradicts	contradict	VERB
ejpam-6124	625	15	the	the	DET
ejpam-6124	625	16	definition	definition	NOUN
ejpam-6124	625	17	of	of	ADP
ejpam-6124	625	18	c.	c.	PROPN
ejpam-6124	625	19	hence	hence	ADV
ejpam-6124	625	20	,	,	PUNCT
ejpam-6124	625	21	g[h	g[h	PROPN
ejpam-6124	625	22	]	]	PUNCT
ejpam-6124	625	23	is	be	AUX
ejpam-6124	625	24	non	non	ADJ
ejpam-6124	625	25	-	-	ADJ
ejpam-6124	625	26	γte	γte	PRON
ejpam-6124	625	27	-	-	PUNCT
ejpam-6124	625	28	graph	graph	NOUN
ejpam-6124	625	29	.	.	PUNCT
ejpam-6124	626	1	suppose	suppose	VERB
ejpam-6124	626	2	that	that	SCONJ
ejpam-6124	626	3	(	(	PUNCT
ejpam-6124	626	4	ii	ii	NOUN
ejpam-6124	626	5	)	)	PUNCT
ejpam-6124	626	6	holds	hold	VERB
ejpam-6124	626	7	,	,	PUNCT
ejpam-6124	626	8	that	that	ADV
ejpam-6124	626	9	is	is	ADV
ejpam-6124	626	10	,	,	PUNCT
ejpam-6124	626	11	g	g	PROPN
ejpam-6124	626	12	is	be	AUX
ejpam-6124	626	13	an	an	DET
ejpam-6124	626	14	empty	empty	ADJ
ejpam-6124	626	15	graph	graph	NOUN
ejpam-6124	626	16	and	and	CCONJ
ejpam-6124	626	17	h	h	NOUN
ejpam-6124	626	18	is	be	AUX
ejpam-6124	626	19	a	a	DET
ejpam-6124	626	20	connected	connected	ADJ
ejpam-6124	626	21	nonγte	nonγte	NOUN
ejpam-6124	626	22	-	-	PUNCT
ejpam-6124	626	23	graph	graph	NOUN
ejpam-6124	626	24	.	.	PUNCT
ejpam-6124	627	1	let	let	VERB
ejpam-6124	627	2	c	c	PRON
ejpam-6124	627	3	be	be	AUX
ejpam-6124	627	4	a	a	DET
ejpam-6124	627	5	γte	γte	NOUN
ejpam-6124	627	6	-	-	PUNCT
ejpam-6124	627	7	set	set	NOUN
ejpam-6124	627	8	of	of	ADP
ejpam-6124	627	9	g[h	g[h	NOUN
ejpam-6124	627	10	]	]	PUNCT
ejpam-6124	627	11	.	.	PUNCT
ejpam-6124	628	1	since	since	SCONJ
ejpam-6124	628	2	g	g	PROPN
ejpam-6124	628	3	is	be	AUX
ejpam-6124	628	4	an	an	DET
ejpam-6124	628	5	empty	empty	ADJ
ejpam-6124	628	6	graph	graph	NOUN
ejpam-6124	628	7	,	,	PUNCT
ejpam-6124	628	8	g[h	g[h	PROPN
ejpam-6124	628	9	]	]	PUNCT
ejpam-6124	628	10	is	be	AUX
ejpam-6124	628	11	a	a	DET
ejpam-6124	628	12	disjoint	disjoint	ADJ
ejpam-6124	628	13	union	union	NOUN
ejpam-6124	628	14	of	of	ADP
ejpam-6124	628	15	|v	|v	PROPN
ejpam-6124	628	16	(	(	PUNCT
ejpam-6124	628	17	g)|	g)|	NOUN
ejpam-6124	628	18	copies	copy	NOUN
ejpam-6124	628	19	of	of	ADP
ejpam-6124	628	20	h	h	NOUN
ejpam-6124	628	21	and	and	CCONJ
ejpam-6124	628	22	so	so	ADV
ejpam-6124	628	23	,	,	PUNCT
ejpam-6124	628	24	the	the	DET
ejpam-6124	628	25	set	set	NOUN
ejpam-6124	628	26	c	c	PROPN
ejpam-6124	628	27	must	must	AUX
ejpam-6124	628	28	be	be	AUX
ejpam-6124	628	29	the	the	DET
ejpam-6124	628	30	union	union	NOUN
ejpam-6124	628	31	of	of	ADP
ejpam-6124	628	32	γte	γte	NOUN
ejpam-6124	628	33	-	-	PUNCT
ejpam-6124	628	34	sets	set	NOUN
ejpam-6124	628	35	from	from	ADP
ejpam-6124	628	36	each	each	DET
ejpam-6124	628	37	copy	copy	NOUN
ejpam-6124	628	38	of	of	ADP
ejpam-6124	628	39	h.	h.	PROPN
ejpam-6124	628	40	however	however	ADV
ejpam-6124	628	41	,	,	PUNCT
ejpam-6124	628	42	since	since	SCONJ
ejpam-6124	628	43	h	h	NOUN
ejpam-6124	628	44	is	be	AUX
ejpam-6124	628	45	a	a	DET
ejpam-6124	628	46	non	non	ADJ
ejpam-6124	628	47	-	-	ADJ
ejpam-6124	628	48	γte	γte	PRON
ejpam-6124	628	49	-	-	PUNCT
ejpam-6124	628	50	graph	graph	NOUN
ejpam-6124	628	51	,	,	PUNCT
ejpam-6124	628	52	no	no	DET
ejpam-6124	628	53	such	such	ADJ
ejpam-6124	628	54	γte	γte	NOUN
ejpam-6124	628	55	-	-	PUNCT
ejpam-6124	628	56	set	set	NOUN
ejpam-6124	628	57	can	can	AUX
ejpam-6124	628	58	exist	exist	VERB
ejpam-6124	628	59	in	in	ADP
ejpam-6124	628	60	any	any	DET
ejpam-6124	628	61	copy	copy	NOUN
ejpam-6124	628	62	of	of	ADP
ejpam-6124	628	63	h	h	NOUN
ejpam-6124	628	64	,	,	PUNCT
ejpam-6124	628	65	making	make	VERB
ejpam-6124	628	66	it	it	PRON
ejpam-6124	628	67	impossible	impossible	ADJ
ejpam-6124	628	68	to	to	PART
ejpam-6124	628	69	form	form	VERB
ejpam-6124	628	70	c.	c.	NOUN
ejpam-6124	628	71	hence	hence	ADV
ejpam-6124	628	72	,	,	PUNCT
ejpam-6124	628	73	g[h	g[h	PROPN
ejpam-6124	628	74	]	]	PUNCT
ejpam-6124	628	75	is	be	AUX
ejpam-6124	628	76	non	non	ADJ
ejpam-6124	628	77	-	-	ADJ
ejpam-6124	628	78	γte	γte	PRON
ejpam-6124	628	79	-	-	PUNCT
ejpam-6124	628	80	graph	graph	NOUN
ejpam-6124	628	81	.	.	PUNCT
ejpam-6124	629	1	suppose	suppose	VERB
ejpam-6124	629	2	that	that	SCONJ
ejpam-6124	629	3	(	(	PUNCT
ejpam-6124	629	4	iii	iii	NOUN
ejpam-6124	629	5	)	)	PUNCT
ejpam-6124	629	6	holds	hold	VERB
ejpam-6124	629	7	,	,	PUNCT
ejpam-6124	629	8	that	that	ADV
ejpam-6124	629	9	is	is	ADV
ejpam-6124	629	10	,	,	PUNCT
ejpam-6124	629	11	h	h	NOUN
ejpam-6124	629	12	is	be	AUX
ejpam-6124	629	13	an	an	DET
ejpam-6124	629	14	empty	empty	ADJ
ejpam-6124	629	15	graph	graph	NOUN
ejpam-6124	629	16	and	and	CCONJ
ejpam-6124	629	17	g	g	NOUN
ejpam-6124	629	18	is	be	AUX
ejpam-6124	629	19	a	a	DET
ejpam-6124	629	20	connected	connected	ADJ
ejpam-6124	629	21	nonγte	nonγte	NOUN
ejpam-6124	629	22	-	-	PUNCT
ejpam-6124	629	23	graph	graph	NOUN
ejpam-6124	629	24	.	.	PUNCT
ejpam-6124	630	1	let	let	VERB
ejpam-6124	630	2	c	c	PRON
ejpam-6124	630	3	be	be	AUX
ejpam-6124	630	4	a	a	DET
ejpam-6124	630	5	γte	γte	NOUN
ejpam-6124	630	6	-	-	PUNCT
ejpam-6124	630	7	set	set	NOUN
ejpam-6124	630	8	of	of	ADP
ejpam-6124	630	9	g[h	g[h	NOUN
ejpam-6124	630	10	]	]	PUNCT
ejpam-6124	630	11	.	.	PUNCT
ejpam-6124	631	1	since	since	SCONJ
ejpam-6124	631	2	h	h	PROPN
ejpam-6124	631	3	is	be	AUX
ejpam-6124	631	4	an	an	DET
ejpam-6124	631	5	empty	empty	ADJ
ejpam-6124	631	6	graph	graph	NOUN
ejpam-6124	631	7	and	and	CCONJ
ejpam-6124	631	8	g	g	NOUN
ejpam-6124	631	9	is	be	AUX
ejpam-6124	631	10	a	a	DET
ejpam-6124	631	11	connected	connected	ADJ
ejpam-6124	631	12	graph	graph	NOUN
ejpam-6124	631	13	,	,	PUNCT
ejpam-6124	631	14	g[h	g[h	PROPN
ejpam-6124	631	15	]	]	PUNCT
ejpam-6124	631	16	is	be	AUX
ejpam-6124	631	17	a	a	DET
ejpam-6124	631	18	connected	connected	ADJ
ejpam-6124	631	19	graph	graph	NOUN
ejpam-6124	631	20	such	such	ADJ
ejpam-6124	631	21	that	that	SCONJ
ejpam-6124	631	22	the	the	DET
ejpam-6124	631	23	neighbors	neighbor	NOUN
ejpam-6124	631	24	of	of	ADP
ejpam-6124	631	25	(	(	PUNCT
ejpam-6124	631	26	u	u	NOUN
ejpam-6124	631	27	,	,	PUNCT
ejpam-6124	631	28	p	p	NOUN
ejpam-6124	631	29	)	)	PUNCT
ejpam-6124	631	30	∈	∈	PROPN
ejpam-6124	631	31	v	v	NOUN
ejpam-6124	631	32	(	(	PUNCT
ejpam-6124	631	33	g[h	g[h	PROPN
ejpam-6124	631	34	]	]	PUNCT
ejpam-6124	631	35	)	)	PUNCT
ejpam-6124	631	36	come	come	VERB
ejpam-6124	631	37	only	only	ADV
ejpam-6124	631	38	from	from	ADP
ejpam-6124	631	39	adjacent	adjacent	ADJ
ejpam-6124	631	40	copies	copy	NOUN
ejpam-6124	631	41	of	of	ADP
ejpam-6124	631	42	h	h	NOUN
ejpam-6124	631	43	in	in	ADP
ejpam-6124	631	44	g[h	g[h	PROPN
ejpam-6124	631	45	]	]	PUNCT
ejpam-6124	631	46	.	.	PUNCT
ejpam-6124	632	1	that	that	PRON
ejpam-6124	632	2	is	be	AUX
ejpam-6124	632	3	,	,	PUNCT
ejpam-6124	632	4	n(u	n(u	PROPN
ejpam-6124	632	5	,	,	PUNCT
ejpam-6124	632	6	p	p	NOUN
ejpam-6124	632	7	)	)	PUNCT
ejpam-6124	632	8	contains	contain	VERB
ejpam-6124	632	9	all	all	DET
ejpam-6124	632	10	vertices	vertex	NOUN
ejpam-6124	632	11	from	from	ADP
ejpam-6124	632	12	independent	independent	ADJ
ejpam-6124	632	13	sets	set	NOUN
ejpam-6124	632	14	corresponding	correspond	VERB
ejpam-6124	632	15	to	to	ADP
ejpam-6124	632	16	neighbors	neighbor	NOUN
ejpam-6124	632	17	of	of	ADP
ejpam-6124	632	18	u	u	PROPN
ejpam-6124	632	19	in	in	ADP
ejpam-6124	632	20	g.	g.	PROPN
ejpam-6124	632	21	since	since	SCONJ
ejpam-6124	632	22	the	the	DET
ejpam-6124	632	23	independent	independent	ADJ
ejpam-6124	632	24	sets	set	NOUN
ejpam-6124	632	25	are	be	AUX
ejpam-6124	632	26	fully	fully	ADV
ejpam-6124	632	27	connected	connect	VERB
ejpam-6124	632	28	through	through	ADP
ejpam-6124	632	29	the	the	DET
ejpam-6124	632	30	edges	edge	NOUN
ejpam-6124	632	31	of	of	ADP
ejpam-6124	632	32	g	g	NOUN
ejpam-6124	632	33	and	and	CCONJ
ejpam-6124	632	34	g	g	PROPN
ejpam-6124	632	35	is	be	AUX
ejpam-6124	632	36	a	a	DET
ejpam-6124	632	37	nonγte	nonγte	NOUN
ejpam-6124	632	38	-	-	PUNCT
ejpam-6124	632	39	graph	graph	NOUN
ejpam-6124	632	40	,	,	PUNCT
ejpam-6124	632	41	it	it	PRON
ejpam-6124	632	42	is	be	AUX
ejpam-6124	632	43	impossible	impossible	ADJ
ejpam-6124	632	44	to	to	PART
ejpam-6124	632	45	pick	pick	VERB
ejpam-6124	632	46	a	a	DET
ejpam-6124	632	47	set	set	NOUN
ejpam-6124	632	48	c	c	NOUN
ejpam-6124	632	49	such	such	ADJ
ejpam-6124	632	50	that	that	SCONJ
ejpam-6124	632	51	every	every	DET
ejpam-6124	632	52	vertex	vertex	NOUN
ejpam-6124	632	53	has	have	VERB
ejpam-6124	632	54	exactly	exactly	ADV
ejpam-6124	632	55	one	one	NUM
ejpam-6124	632	56	neighbor	neighbor	NOUN
ejpam-6124	632	57	in	in	ADP
ejpam-6124	632	58	c.	c.	PROPN
ejpam-6124	632	59	thus	thus	ADV
ejpam-6124	632	60	,	,	PUNCT
ejpam-6124	632	61	g[h	g[h	PROPN
ejpam-6124	632	62	]	]	PUNCT
ejpam-6124	632	63	is	be	AUX
ejpam-6124	632	64	non	non	ADJ
ejpam-6124	632	65	-	-	ADJ
ejpam-6124	632	66	γte	γte	PRON
ejpam-6124	632	67	-	-	PUNCT
ejpam-6124	632	68	graph	graph	NOUN
ejpam-6124	632	69	.	.	PUNCT
ejpam-6124	633	1	theorem	theorem	NOUN
ejpam-6124	633	2	16	16	NUM
ejpam-6124	633	3	.	.	PUNCT
ejpam-6124	634	1	let	let	VERB
ejpam-6124	634	2	g	g	PRON
ejpam-6124	634	3	be	be	AUX
ejpam-6124	634	4	a	a	DET
ejpam-6124	634	5	connected	connected	ADJ
ejpam-6124	634	6	graph	graph	NOUN
ejpam-6124	634	7	,	,	PUNCT
ejpam-6124	634	8	and	and	CCONJ
ejpam-6124	634	9	h	h	NOUN
ejpam-6124	634	10	be	be	VERB
ejpam-6124	634	11	any	any	DET
ejpam-6124	634	12	graph	graph	NOUN
ejpam-6124	634	13	of	of	ADP
ejpam-6124	634	14	order	order	NOUN
ejpam-6124	634	15	m.	m.	NOUN
ejpam-6124	635	1	then	then	ADV
ejpam-6124	635	2	c	c	NOUN
ejpam-6124	635	3	=	=	PUNCT
ejpam-6124	636	1	⋃	⋃	PROPN
ejpam-6124	636	2	x∈s	x∈s	NOUN
ejpam-6124	636	3	(	(	PUNCT
ejpam-6124	636	4	{	{	PUNCT
ejpam-6124	636	5	x	x	NOUN
ejpam-6124	636	6	}	}	PUNCT
ejpam-6124	636	7	×	×	PROPN
ejpam-6124	636	8	tx	tx	PROPN
ejpam-6124	636	9	)	)	PUNCT
ejpam-6124	636	10	⊆	⊆	NUM
ejpam-6124	636	11	v	v	NOUN
ejpam-6124	636	12	(	(	PUNCT
ejpam-6124	636	13	g[h	g[h	PROPN
ejpam-6124	636	14	]	]	PUNCT
ejpam-6124	636	15	)	)	PUNCT
ejpam-6124	636	16	is	be	AUX
ejpam-6124	636	17	a	a	DET
ejpam-6124	636	18	γte	γte	NOUN
ejpam-6124	636	19	-	-	PUNCT
ejpam-6124	636	20	set	set	NOUN
ejpam-6124	636	21	of	of	ADP
ejpam-6124	636	22	g[h	g[h	NOUN
ejpam-6124	636	23	]	]	PUNCT
ejpam-6124	636	24	if	if	SCONJ
ejpam-6124	636	25	and	and	CCONJ
ejpam-6124	636	26	only	only	ADV
ejpam-6124	636	27	if	if	SCONJ
ejpam-6124	636	28	either	either	DET
ejpam-6124	636	29	one	one	NUM
ejpam-6124	636	30	of	of	ADP
ejpam-6124	636	31	the	the	DET
ejpam-6124	636	32	following	follow	VERB
ejpam-6124	636	33	is	be	AUX
ejpam-6124	636	34	satisfied	satisfied	ADJ
ejpam-6124	636	35	:	:	PUNCT
ejpam-6124	636	36	(	(	PUNCT
ejpam-6124	636	37	i	i	NOUN
ejpam-6124	636	38	)	)	PUNCT
ejpam-6124	636	39	s	s	VERB
ejpam-6124	636	40	is	be	AUX
ejpam-6124	636	41	a	a	DET
ejpam-6124	636	42	γte	γte	NOUN
ejpam-6124	636	43	-	-	PUNCT
ejpam-6124	636	44	set	set	NOUN
ejpam-6124	636	45	of	of	ADP
ejpam-6124	636	46	g	g	PROPN
ejpam-6124	636	47	and	and	CCONJ
ejpam-6124	636	48	h	h	NOUN
ejpam-6124	636	49	is	be	AUX
ejpam-6124	636	50	an	an	DET
ejpam-6124	636	51	empty	empty	ADJ
ejpam-6124	636	52	graph	graph	NOUN
ejpam-6124	636	53	or	or	CCONJ
ejpam-6124	636	54	(	(	PUNCT
ejpam-6124	636	55	ii	ii	NOUN
ejpam-6124	636	56	)	)	PUNCT
ejpam-6124	636	57	tx	tx	PROPN
ejpam-6124	636	58	is	be	AUX
ejpam-6124	636	59	a	a	DET
ejpam-6124	636	60	γte	γte	NOUN
ejpam-6124	636	61	-	-	PUNCT
ejpam-6124	636	62	set	set	NOUN
ejpam-6124	636	63	of	of	ADP
ejpam-6124	636	64	h	h	NOUN
ejpam-6124	636	65	for	for	ADP
ejpam-6124	636	66	every	every	DET
ejpam-6124	636	67	x	x	SYM
ejpam-6124	636	68	∈	∈	PROPN
ejpam-6124	636	69	v	v	ADP
ejpam-6124	636	70	(	(	PUNCT
ejpam-6124	636	71	g	g	NOUN
ejpam-6124	636	72	)	)	PUNCT
ejpam-6124	636	73	and	and	CCONJ
ejpam-6124	636	74	g	g	PROPN
ejpam-6124	636	75	is	be	AUX
ejpam-6124	636	76	an	an	DET
ejpam-6124	636	77	empty	empty	ADJ
ejpam-6124	636	78	graph	graph	NOUN
ejpam-6124	636	79	.	.	PUNCT
ejpam-6124	637	1	proof	proof	NOUN
ejpam-6124	637	2	.	.	PUNCT
ejpam-6124	638	1	let	let	VERB
ejpam-6124	638	2	c	c	PRON
ejpam-6124	638	3	be	be	AUX
ejpam-6124	638	4	a	a	DET
ejpam-6124	638	5	γte	γte	NOUN
ejpam-6124	638	6	-	-	PUNCT
ejpam-6124	638	7	set	set	NOUN
ejpam-6124	638	8	of	of	ADP
ejpam-6124	638	9	g[h	g[h	NOUN
ejpam-6124	638	10	]	]	PUNCT
ejpam-6124	638	11	.	.	PUNCT
ejpam-6124	639	1	by	by	ADP
ejpam-6124	639	2	theorem	theorem	NOUN
ejpam-6124	639	3	15	15	NUM
ejpam-6124	639	4	,	,	PUNCT
ejpam-6124	639	5	either	either	CCONJ
ejpam-6124	639	6	(	(	PUNCT
ejpam-6124	639	7	i	i	NOUN
ejpam-6124	639	8	)	)	PUNCT
ejpam-6124	639	9	h	h	PROPN
ejpam-6124	639	10	is	be	AUX
ejpam-6124	639	11	an	an	DET
ejpam-6124	639	12	empty	empty	ADJ
ejpam-6124	639	13	graph	graph	NOUN
ejpam-6124	639	14	and	and	CCONJ
ejpam-6124	639	15	g	g	NOUN
ejpam-6124	639	16	is	be	AUX
ejpam-6124	639	17	a	a	DET
ejpam-6124	639	18	connected	connected	ADJ
ejpam-6124	639	19	graph	graph	NOUN
ejpam-6124	639	20	and	and	CCONJ
ejpam-6124	639	21	not	not	PART
ejpam-6124	639	22	a	a	DET
ejpam-6124	639	23	non	non	ADJ
ejpam-6124	639	24	-	-	ADJ
ejpam-6124	639	25	γte	γte	PRON
ejpam-6124	639	26	-	-	PUNCT
ejpam-6124	639	27	graph	graph	NOUN
ejpam-6124	639	28	or	or	CCONJ
ejpam-6124	639	29	(	(	PUNCT
ejpam-6124	639	30	ii	ii	NOUN
ejpam-6124	639	31	)	)	PUNCT
ejpam-6124	639	32	g	g	NOUN
ejpam-6124	639	33	is	be	AUX
ejpam-6124	639	34	an	an	DET
ejpam-6124	639	35	empty	empty	ADJ
ejpam-6124	639	36	graph	graph	NOUN
ejpam-6124	639	37	and	and	CCONJ
ejpam-6124	639	38	h	h	NOUN
ejpam-6124	639	39	is	be	AUX
ejpam-6124	639	40	a	a	DET
ejpam-6124	639	41	connected	connected	ADJ
ejpam-6124	639	42	graph	graph	NOUN
ejpam-6124	639	43	and	and	CCONJ
ejpam-6124	639	44	not	not	PART
ejpam-6124	639	45	a	a	DET
ejpam-6124	639	46	non	non	ADJ
ejpam-6124	639	47	-	-	ADJ
ejpam-6124	639	48	γte	γte	PRON
ejpam-6124	639	49	-	-	PUNCT
ejpam-6124	639	50	graph	graph	NOUN
ejpam-6124	639	51	.	.	PUNCT
ejpam-6124	640	1	consider	consider	VERB
ejpam-6124	640	2	the	the	DET
ejpam-6124	640	3	following	follow	VERB
ejpam-6124	640	4	cases	case	NOUN
ejpam-6124	640	5	:	:	PUNCT
ejpam-6124	640	6	(	(	PUNCT
ejpam-6124	640	7	i	i	NOUN
ejpam-6124	640	8	)	)	PUNCT
ejpam-6124	640	9	suppose	suppose	VERB
ejpam-6124	640	10	that	that	SCONJ
ejpam-6124	640	11	h	h	NOUN
ejpam-6124	640	12	is	be	AUX
ejpam-6124	640	13	an	an	DET
ejpam-6124	640	14	empty	empty	ADJ
ejpam-6124	640	15	graph	graph	NOUN
ejpam-6124	640	16	and	and	CCONJ
ejpam-6124	640	17	g	g	NOUN
ejpam-6124	640	18	is	be	AUX
ejpam-6124	640	19	a	a	DET
ejpam-6124	640	20	connected	connected	ADJ
ejpam-6124	640	21	graph	graph	NOUN
ejpam-6124	640	22	and	and	CCONJ
ejpam-6124	640	23	not	not	PART
ejpam-6124	640	24	a	a	DET
ejpam-6124	640	25	non	non	ADJ
ejpam-6124	640	26	-	-	ADJ
ejpam-6124	640	27	γte	γte	PRON
ejpam-6124	640	28	-	-	PUNCT
ejpam-6124	640	29	graph	graph	NOUN
ejpam-6124	640	30	.	.	PUNCT
ejpam-6124	641	1	let	let	VERB
ejpam-6124	641	2	u	u	PRON
ejpam-6124	641	3	∈	∈	PROPN
ejpam-6124	641	4	v	v	ADP
ejpam-6124	641	5	(	(	PUNCT
ejpam-6124	641	6	g	g	NOUN
ejpam-6124	641	7	)	)	PUNCT
ejpam-6124	641	8	.	.	PUNCT
ejpam-6124	642	1	pick	pick	VERB
ejpam-6124	642	2	any	any	DET
ejpam-6124	642	3	v	v	NOUN
ejpam-6124	642	4	∈	∈	PROPN
ejpam-6124	642	5	v	v	NOUN
ejpam-6124	642	6	(	(	PUNCT
ejpam-6124	642	7	h	h	NOUN
ejpam-6124	642	8	)	)	PUNCT
ejpam-6124	642	9	.	.	PUNCT
ejpam-6124	643	1	since	since	SCONJ
ejpam-6124	643	2	c	c	PROPN
ejpam-6124	643	3	is	be	AUX
ejpam-6124	643	4	a	a	DET
ejpam-6124	643	5	γte	γte	NOUN
ejpam-6124	643	6	-	-	PUNCT
ejpam-6124	643	7	set	set	ADJ
ejpam-6124	643	8	,	,	PUNCT
ejpam-6124	643	9	there	there	PRON
ejpam-6124	643	10	exists	exist	VERB
ejpam-6124	643	11	(	(	PUNCT
ejpam-6124	643	12	y	y	NOUN
ejpam-6124	643	13	,	,	PUNCT
ejpam-6124	643	14	z	z	NOUN
ejpam-6124	643	15	)	)	PUNCT
ejpam-6124	643	16	∈	∈	PROPN
ejpam-6124	643	17	c	c	NOUN
ejpam-6124	643	18	such	such	ADJ
ejpam-6124	643	19	that	that	SCONJ
ejpam-6124	643	20	ng[h](u	ng[h](u	PROPN
ejpam-6124	643	21	,	,	PUNCT
ejpam-6124	643	22	v	v	NOUN
ejpam-6124	643	23	)	)	PUNCT
ejpam-6124	643	24	∩	∩	NOUN
ejpam-6124	643	25	c	c	NOUN
ejpam-6124	643	26	=	=	SYM
ejpam-6124	643	27	{	{	PUNCT
ejpam-6124	643	28	(	(	PUNCT
ejpam-6124	643	29	y	y	PROPN
ejpam-6124	643	30	,	,	PUNCT
ejpam-6124	643	31	z	z	NOUN
ejpam-6124	643	32	)	)	PUNCT
ejpam-6124	643	33	}	}	PUNCT
ejpam-6124	643	34	.	.	PUNCT
ejpam-6124	644	1	this	this	PRON
ejpam-6124	644	2	implies	imply	VERB
ejpam-6124	644	3	that	that	SCONJ
ejpam-6124	644	4	ng(u)∩	ng(u)∩	PRON
ejpam-6124	644	5	s	s	X
ejpam-6124	644	6	=	=	PUNCT
ejpam-6124	644	7	{	{	PUNCT
ejpam-6124	644	8	y	y	NOUN
ejpam-6124	644	9	}	}	PUNCT
ejpam-6124	644	10	.	.	PUNCT
ejpam-6124	645	1	hence	hence	ADV
ejpam-6124	645	2	,	,	PUNCT
ejpam-6124	645	3	every	every	DET
ejpam-6124	645	4	u	u	PROPN
ejpam-6124	645	5	∈	∈	PROPN
ejpam-6124	645	6	v	v	NOUN
ejpam-6124	645	7	(	(	PUNCT
ejpam-6124	645	8	g	g	NOUN
ejpam-6124	645	9	)	)	PUNCT
ejpam-6124	645	10	is	be	AUX
ejpam-6124	645	11	dominated	dominate	VERB
ejpam-6124	645	12	by	by	ADP
ejpam-6124	645	13	exactly	exactly	ADV
ejpam-6124	645	14	one	one	NUM
ejpam-6124	645	15	vertex	vertex	NOUN
ejpam-6124	645	16	in	in	ADP
ejpam-6124	645	17	s	s	PROPN
ejpam-6124	645	18	,	,	PUNCT
ejpam-6124	645	19	and	and	CCONJ
ejpam-6124	645	20	so	so	ADV
ejpam-6124	645	21	,	,	PUNCT
ejpam-6124	645	22	s	s	VERB
ejpam-6124	645	23	is	be	AUX
ejpam-6124	645	24	a	a	DET
ejpam-6124	645	25	γte	γte	NOUN
ejpam-6124	645	26	-	-	PUNCT
ejpam-6124	645	27	set	set	NOUN
ejpam-6124	645	28	of	of	ADP
ejpam-6124	645	29	g.	g.	PROPN
ejpam-6124	645	30	r.	r.	PROPN
ejpam-6124	645	31	g.	g.	PROPN
ejpam-6124	645	32	aguinod	aguinod	PROPN
ejpam-6124	645	33	,	,	PUNCT
ejpam-6124	645	34	e.	e.	PROPN
ejpam-6124	645	35	m.	m.	PROPN
ejpam-6124	645	36	kiunisala	kiunisala	PROPN
ejpam-6124	645	37	,	,	PUNCT
ejpam-6124	645	38	c.	c.	PROPN
ejpam-6124	645	39	l.	l.	PROPN
ejpam-6124	645	40	armada	armada	PROPN
ejpam-6124	645	41	/	/	SYM
ejpam-6124	645	42	eur	eur	PROPN
ejpam-6124	645	43	.	.	PUNCT
ejpam-6124	646	1	j.	j.	PROPN
ejpam-6124	646	2	pure	pure	PROPN
ejpam-6124	646	3	appl	appl	PROPN
ejpam-6124	646	4	.	.	PROPN
ejpam-6124	646	5	math	math	PROPN
ejpam-6124	646	6	,	,	PUNCT
ejpam-6124	646	7	18	18	NUM
ejpam-6124	646	8	(	(	PUNCT
ejpam-6124	646	9	2	2	NUM
ejpam-6124	646	10	)	)	PUNCT
ejpam-6124	646	11	(	(	PUNCT
ejpam-6124	646	12	2025	2025	NUM
ejpam-6124	646	13	)	)	PUNCT
ejpam-6124	646	14	,	,	PUNCT
ejpam-6124	646	15	6124	6124	NUM
ejpam-6124	646	16	23	23	NUM
ejpam-6124	646	17	of	of	ADP
ejpam-6124	646	18	26	26	NUM
ejpam-6124	646	19	(	(	PUNCT
ejpam-6124	646	20	ii	ii	NOUN
ejpam-6124	646	21	)	)	PUNCT
ejpam-6124	646	22	suppose	suppose	VERB
ejpam-6124	646	23	that	that	SCONJ
ejpam-6124	646	24	g	g	PROPN
ejpam-6124	646	25	is	be	AUX
ejpam-6124	646	26	an	an	DET
ejpam-6124	646	27	empty	empty	ADJ
ejpam-6124	646	28	graph	graph	NOUN
ejpam-6124	646	29	and	and	CCONJ
ejpam-6124	646	30	h	h	NOUN
ejpam-6124	646	31	is	be	AUX
ejpam-6124	646	32	a	a	DET
ejpam-6124	646	33	connected	connected	ADJ
ejpam-6124	646	34	graph	graph	NOUN
ejpam-6124	646	35	and	and	CCONJ
ejpam-6124	646	36	not	not	PART
ejpam-6124	646	37	a	a	DET
ejpam-6124	646	38	non	non	ADJ
ejpam-6124	646	39	-	-	ADJ
ejpam-6124	646	40	γte	γte	PRON
ejpam-6124	646	41	-	-	PUNCT
ejpam-6124	646	42	graph	graph	NOUN
ejpam-6124	646	43	.	.	PUNCT
ejpam-6124	646	44	suppose	suppose	VERB
ejpam-6124	646	45	that	that	SCONJ
ejpam-6124	646	46	tx	tx	PROPN
ejpam-6124	646	47	is	be	AUX
ejpam-6124	646	48	not	not	PART
ejpam-6124	646	49	a	a	DET
ejpam-6124	646	50	γte	γte	NOUN
ejpam-6124	646	51	-	-	PUNCT
ejpam-6124	646	52	set	set	NOUN
ejpam-6124	646	53	of	of	ADP
ejpam-6124	646	54	h	h	NOUN
ejpam-6124	646	55	for	for	ADP
ejpam-6124	646	56	every	every	DET
ejpam-6124	646	57	x	x	SYM
ejpam-6124	646	58	∈	∈	PROPN
ejpam-6124	646	59	v	v	NOUN
ejpam-6124	646	60	(	(	PUNCT
ejpam-6124	646	61	g	g	NOUN
ejpam-6124	646	62	)	)	PUNCT
ejpam-6124	646	63	.	.	PUNCT
ejpam-6124	647	1	then	then	ADV
ejpam-6124	647	2	,	,	PUNCT
ejpam-6124	647	3	since	since	SCONJ
ejpam-6124	647	4	g	g	PROPN
ejpam-6124	647	5	is	be	AUX
ejpam-6124	647	6	an	an	DET
ejpam-6124	647	7	empty	empty	ADJ
ejpam-6124	647	8	graph	graph	NOUN
ejpam-6124	647	9	,	,	PUNCT
ejpam-6124	647	10	g[h	g[h	PROPN
ejpam-6124	647	11	]	]	PUNCT
ejpam-6124	647	12	is	be	AUX
ejpam-6124	647	13	a	a	DET
ejpam-6124	647	14	disjoint	disjoint	ADJ
ejpam-6124	647	15	union	union	NOUN
ejpam-6124	647	16	of	of	ADP
ejpam-6124	647	17	|v	|v	PROPN
ejpam-6124	647	18	(	(	PUNCT
ejpam-6124	647	19	g)|	g)|	NOUN
ejpam-6124	647	20	copies	copy	NOUN
ejpam-6124	647	21	of	of	ADP
ejpam-6124	647	22	h.	h.	PROPN
ejpam-6124	647	23	thus	thus	ADV
ejpam-6124	647	24	,	,	PUNCT
ejpam-6124	647	25	c	c	PROPN
ejpam-6124	647	26	=	=	PUNCT
ejpam-6124	647	27	⋃	⋃	PROPN
ejpam-6124	647	28	x∈s	x∈s	NOUN
ejpam-6124	647	29	(	(	PUNCT
ejpam-6124	647	30	{	{	PUNCT
ejpam-6124	647	31	x	x	NOUN
ejpam-6124	647	32	}	}	PUNCT
ejpam-6124	647	33	×	×	PROPN
ejpam-6124	647	34	tx	tx	PROPN
ejpam-6124	647	35	)	)	PUNCT
ejpam-6124	647	36	is	be	AUX
ejpam-6124	647	37	not	not	PART
ejpam-6124	647	38	a	a	DET
ejpam-6124	647	39	γte	γte	NOUN
ejpam-6124	647	40	-	-	PUNCT
ejpam-6124	647	41	set	set	NOUN
ejpam-6124	647	42	of	of	ADP
ejpam-6124	647	43	g[h	g[h	NOUN
ejpam-6124	647	44	]	]	PUNCT
ejpam-6124	647	45	since	since	SCONJ
ejpam-6124	647	46	tx	tx	PROPN
ejpam-6124	647	47	is	be	AUX
ejpam-6124	647	48	not	not	PART
ejpam-6124	647	49	a	a	DET
ejpam-6124	647	50	γte	γte	NOUN
ejpam-6124	647	51	-	-	PUNCT
ejpam-6124	647	52	set	set	NOUN
ejpam-6124	647	53	of	of	ADP
ejpam-6124	647	54	h	h	NOUN
ejpam-6124	647	55	for	for	ADP
ejpam-6124	647	56	every	every	DET
ejpam-6124	647	57	x	x	SYM
ejpam-6124	647	58	∈	∈	PROPN
ejpam-6124	647	59	v	v	NOUN
ejpam-6124	647	60	(	(	PUNCT
ejpam-6124	647	61	g	g	NOUN
ejpam-6124	647	62	)	)	PUNCT
ejpam-6124	647	63	.	.	PUNCT
ejpam-6124	648	1	this	this	PRON
ejpam-6124	648	2	is	be	AUX
ejpam-6124	648	3	a	a	DET
ejpam-6124	648	4	contradiction	contradiction	NOUN
ejpam-6124	648	5	.	.	PUNCT
ejpam-6124	649	1	therefore	therefore	ADV
ejpam-6124	649	2	,	,	PUNCT
ejpam-6124	649	3	tx	tx	PROPN
ejpam-6124	649	4	is	be	AUX
ejpam-6124	649	5	a	a	DET
ejpam-6124	649	6	γte	γte	NOUN
ejpam-6124	649	7	-	-	PUNCT
ejpam-6124	649	8	set	set	NOUN
ejpam-6124	649	9	of	of	ADP
ejpam-6124	649	10	h	h	NOUN
ejpam-6124	649	11	for	for	ADP
ejpam-6124	649	12	every	every	DET
ejpam-6124	649	13	x	x	SYM
ejpam-6124	649	14	∈	∈	PROPN
ejpam-6124	649	15	v	v	NOUN
ejpam-6124	649	16	(	(	PUNCT
ejpam-6124	649	17	g	g	NOUN
ejpam-6124	649	18	)	)	PUNCT
ejpam-6124	649	19	.	.	PUNCT
ejpam-6124	650	1	the	the	DET
ejpam-6124	650	2	converse	converse	NOUN
ejpam-6124	650	3	is	be	AUX
ejpam-6124	650	4	easy	easy	ADJ
ejpam-6124	650	5	.	.	PUNCT
ejpam-6124	651	1	corollary	corollary	ADJ
ejpam-6124	651	2	14	14	NUM
ejpam-6124	651	3	.	.	PUNCT
ejpam-6124	652	1	let	let	VERB
ejpam-6124	652	2	g	g	PRON
ejpam-6124	652	3	be	be	AUX
ejpam-6124	652	4	a	a	DET
ejpam-6124	652	5	connected	connected	ADJ
ejpam-6124	652	6	graph	graph	NOUN
ejpam-6124	652	7	such	such	ADJ
ejpam-6124	652	8	that	that	SCONJ
ejpam-6124	652	9	g	g	PROPN
ejpam-6124	652	10	has	have	VERB
ejpam-6124	652	11	a	a	DET
ejpam-6124	652	12	total	total	ADJ
ejpam-6124	652	13	exact	exact	ADJ
ejpam-6124	652	14	dominating	dominating	NOUN
ejpam-6124	652	15	set	set	NOUN
ejpam-6124	652	16	and	and	CCONJ
ejpam-6124	652	17	h	h	NOUN
ejpam-6124	652	18	be	be	AUX
ejpam-6124	652	19	an	an	DET
ejpam-6124	652	20	empty	empty	ADJ
ejpam-6124	652	21	graph	graph	NOUN
ejpam-6124	652	22	.	.	PUNCT
ejpam-6124	653	1	then	then	ADV
ejpam-6124	653	2	γte(g[h	γte(g[h	NUM
ejpam-6124	653	3	]	]	PUNCT
ejpam-6124	653	4	)	)	PUNCT
ejpam-6124	653	5	=	=	SYM
ejpam-6124	653	6	γte(g	γte(g	PROPN
ejpam-6124	653	7	)	)	PUNCT
ejpam-6124	653	8	.	.	PUNCT
ejpam-6124	654	1	proof	proof	NOUN
ejpam-6124	654	2	.	.	PUNCT
ejpam-6124	655	1	since	since	SCONJ
ejpam-6124	655	2	h	h	NOUN
ejpam-6124	655	3	is	be	AUX
ejpam-6124	655	4	an	an	DET
ejpam-6124	655	5	empty	empty	ADJ
ejpam-6124	655	6	graph	graph	NOUN
ejpam-6124	655	7	,	,	PUNCT
ejpam-6124	655	8	by	by	ADP
ejpam-6124	655	9	theorem	theorem	NOUN
ejpam-6124	655	10	16	16	NUM
ejpam-6124	655	11	(	(	PUNCT
ejpam-6124	655	12	i	i	NOUN
ejpam-6124	655	13	)	)	PUNCT
ejpam-6124	655	14	,	,	PUNCT
ejpam-6124	655	15	γte(g[h	γte(g[h	NUM
ejpam-6124	655	16	]	]	PUNCT
ejpam-6124	655	17	)	)	PUNCT
ejpam-6124	655	18	=	=	SYM
ejpam-6124	655	19	γte(g	γte(g	PROPN
ejpam-6124	655	20	)	)	PUNCT
ejpam-6124	655	21	.	.	PUNCT
ejpam-6124	656	1	corollary	corollary	ADJ
ejpam-6124	656	2	15	15	NUM
ejpam-6124	656	3	.	.	PUNCT
ejpam-6124	657	1	let	let	VERB
ejpam-6124	657	2	h	h	PRON
ejpam-6124	657	3	be	be	AUX
ejpam-6124	657	4	a	a	DET
ejpam-6124	657	5	connected	connected	ADJ
ejpam-6124	657	6	graph	graph	NOUN
ejpam-6124	657	7	such	such	ADJ
ejpam-6124	657	8	that	that	SCONJ
ejpam-6124	657	9	h	h	NOUN
ejpam-6124	657	10	has	have	VERB
ejpam-6124	657	11	a	a	DET
ejpam-6124	657	12	total	total	ADJ
ejpam-6124	657	13	exact	exact	ADJ
ejpam-6124	657	14	dominating	dominating	NOUN
ejpam-6124	657	15	set	set	NOUN
ejpam-6124	657	16	and	and	CCONJ
ejpam-6124	657	17	g	g	NOUN
ejpam-6124	657	18	be	be	AUX
ejpam-6124	657	19	an	an	DET
ejpam-6124	657	20	empty	empty	ADJ
ejpam-6124	657	21	graph	graph	NOUN
ejpam-6124	657	22	of	of	ADP
ejpam-6124	657	23	order	order	NOUN
ejpam-6124	657	24	n.	n.	NOUN
ejpam-6124	657	25	then	then	ADV
ejpam-6124	657	26	γte(g[h	γte(g[h	NUM
ejpam-6124	657	27	]	]	PUNCT
ejpam-6124	657	28	)	)	PUNCT
ejpam-6124	657	29	=	=	SYM
ejpam-6124	657	30	nγte(h	nγte(h	PROPN
ejpam-6124	657	31	)	)	PUNCT
ejpam-6124	657	32	.	.	PUNCT
ejpam-6124	658	1	proof	proof	NOUN
ejpam-6124	658	2	.	.	PUNCT
ejpam-6124	659	1	since	since	SCONJ
ejpam-6124	659	2	g	g	PROPN
ejpam-6124	659	3	is	be	AUX
ejpam-6124	659	4	an	an	DET
ejpam-6124	659	5	empty	empty	ADJ
ejpam-6124	659	6	graph	graph	NOUN
ejpam-6124	659	7	of	of	ADP
ejpam-6124	659	8	order	order	NOUN
ejpam-6124	659	9	n	n	NOUN
ejpam-6124	660	1	and	and	CCONJ
ejpam-6124	660	2	h	h	NOUN
ejpam-6124	660	3	has	have	VERB
ejpam-6124	660	4	a	a	DET
ejpam-6124	660	5	total	total	ADJ
ejpam-6124	660	6	exact	exact	ADJ
ejpam-6124	660	7	dominating	dominating	NOUN
ejpam-6124	660	8	set	set	NOUN
ejpam-6124	660	9	,	,	PUNCT
ejpam-6124	660	10	by	by	ADP
ejpam-6124	660	11	theorem	theorem	VERB
ejpam-6124	660	12	16	16	NUM
ejpam-6124	660	13	(	(	PUNCT
ejpam-6124	660	14	ii	ii	NOUN
ejpam-6124	660	15	)	)	PUNCT
ejpam-6124	660	16	,	,	PUNCT
ejpam-6124	660	17	γte(g[h	γte(g[h	NUM
ejpam-6124	660	18	]	]	PUNCT
ejpam-6124	660	19	)	)	PUNCT
ejpam-6124	660	20	=	=	SYM
ejpam-6124	660	21	nγte(h	nγte(h	PROPN
ejpam-6124	660	22	)	)	PUNCT
ejpam-6124	660	23	.	.	PUNCT
ejpam-6124	661	1	example	example	NOUN
ejpam-6124	662	1	6	6	NUM
ejpam-6124	662	2	.	.	PUNCT
ejpam-6124	663	1	the	the	DET
ejpam-6124	663	2	following	follow	VERB
ejpam-6124	663	3	examples	example	NOUN
ejpam-6124	663	4	verify	verify	VERB
ejpam-6124	663	5	the	the	DET
ejpam-6124	663	6	results	result	NOUN
ejpam-6124	663	7	of	of	ADP
ejpam-6124	663	8	corollaries	corollary	NOUN
ejpam-6124	663	9	14	14	NUM
ejpam-6124	663	10	and	and	CCONJ
ejpam-6124	663	11	15	15	NUM
ejpam-6124	663	12	.	.	PUNCT
ejpam-6124	664	1	figure	figure	NOUN
ejpam-6124	664	2	10	10	NUM
ejpam-6124	664	3	:	:	PUNCT
ejpam-6124	664	4	graph	graph	NOUN
ejpam-6124	664	5	g1[h1	g1[h1	X
ejpam-6124	664	6	]	]	X
ejpam-6124	664	7	with	with	ADP
ejpam-6124	664	8	γte(g1[h1	γte(g1[h1	NUM
ejpam-6124	664	9	]	]	PUNCT
ejpam-6124	664	10	)	)	PUNCT
ejpam-6124	664	11	=	=	SYM
ejpam-6124	665	1	γte(g1	γte(g1	X
ejpam-6124	665	2	)	)	PUNCT
ejpam-6124	665	3	=	=	SYM
ejpam-6124	665	4	4	4	X
ejpam-6124	665	5	.	.	X
ejpam-6124	665	6	r.	r.	PROPN
ejpam-6124	665	7	g.	g.	PROPN
ejpam-6124	665	8	aguinod	aguinod	PROPN
ejpam-6124	665	9	,	,	PUNCT
ejpam-6124	665	10	e.	e.	PROPN
ejpam-6124	665	11	m.	m.	PROPN
ejpam-6124	665	12	kiunisala	kiunisala	PROPN
ejpam-6124	665	13	,	,	PUNCT
ejpam-6124	665	14	c.	c.	PROPN
ejpam-6124	665	15	l.	l.	PROPN
ejpam-6124	665	16	armada	armada	PROPN
ejpam-6124	665	17	/	/	SYM
ejpam-6124	665	18	eur	eur	PROPN
ejpam-6124	665	19	.	.	PUNCT
ejpam-6124	666	1	j.	j.	PROPN
ejpam-6124	666	2	pure	pure	PROPN
ejpam-6124	666	3	appl	appl	PROPN
ejpam-6124	666	4	.	.	PROPN
ejpam-6124	666	5	math	math	PROPN
ejpam-6124	666	6	,	,	PUNCT
ejpam-6124	666	7	18	18	NUM
ejpam-6124	666	8	(	(	PUNCT
ejpam-6124	666	9	2	2	NUM
ejpam-6124	666	10	)	)	PUNCT
ejpam-6124	666	11	(	(	PUNCT
ejpam-6124	666	12	2025	2025	NUM
ejpam-6124	666	13	)	)	PUNCT
ejpam-6124	666	14	,	,	PUNCT
ejpam-6124	666	15	6124	6124	NUM
ejpam-6124	666	16	24	24	NUM
ejpam-6124	666	17	of	of	ADP
ejpam-6124	666	18	26	26	NUM
ejpam-6124	666	19	figure	figure	NOUN
ejpam-6124	666	20	11	11	NUM
ejpam-6124	666	21	:	:	PUNCT
ejpam-6124	666	22	graph	graph	VERB
ejpam-6124	666	23	g2[h2	g2[h2	PROPN
ejpam-6124	666	24	]	]	PUNCT
ejpam-6124	666	25	with	with	ADP
ejpam-6124	666	26	γte(g2[h2	γte(g2[h2	NOUN
ejpam-6124	666	27	]	]	X
ejpam-6124	666	28	)	)	PUNCT
ejpam-6124	667	1	=	=	SYM
ejpam-6124	667	2	3(γte(h2	3(γte(h2	NOUN
ejpam-6124	667	3	)	)	PUNCT
ejpam-6124	667	4	)	)	PUNCT
ejpam-6124	668	1	=	=	PUNCT
ejpam-6124	668	2	3(4	3(4	X
ejpam-6124	668	3	)	)	PUNCT
ejpam-6124	668	4	=	=	SYM
ejpam-6124	669	1	12	12	NUM
ejpam-6124	669	2	.	.	PUNCT
ejpam-6124	670	1	the	the	DET
ejpam-6124	670	2	next	next	ADJ
ejpam-6124	670	3	results	result	NOUN
ejpam-6124	670	4	follow	follow	VERB
ejpam-6124	670	5	directly	directly	ADV
ejpam-6124	670	6	from	from	ADP
ejpam-6124	670	7	corollaries	corollary	NOUN
ejpam-6124	670	8	14	14	NUM
ejpam-6124	670	9	and	and	CCONJ
ejpam-6124	670	10	15	15	NUM
ejpam-6124	670	11	.	.	PUNCT
ejpam-6124	671	1	corollary	corollary	ADJ
ejpam-6124	671	2	16	16	NUM
ejpam-6124	671	3	.	.	PUNCT
ejpam-6124	672	1	let	let	VERB
ejpam-6124	672	2	m	m	PRON
ejpam-6124	672	3	and	and	CCONJ
ejpam-6124	672	4	n	n	ADV
ejpam-6124	672	5	be	be	AUX
ejpam-6124	672	6	positive	positive	ADJ
ejpam-6124	672	7	integers	integer	NOUN
ejpam-6124	672	8	where	where	SCONJ
ejpam-6124	672	9	m	m	VERB
ejpam-6124	672	10	,	,	PUNCT
ejpam-6124	672	11	n	n	PRON
ejpam-6124	672	12	≥	≥	NOUN
ejpam-6124	672	13	2	2	NUM
ejpam-6124	672	14	.	.	PUNCT
ejpam-6124	673	1	then	then	ADV
ejpam-6124	673	2	γte(km[pn	γte(km[pn	NOUN
ejpam-6124	673	3	]	]	PUNCT
ejpam-6124	673	4	)	)	PUNCT
ejpam-6124	674	1	=	=	SYM
ejpam-6124	675	1			NOUN
ejpam-6124	675	2	mn	mn	PROPN
ejpam-6124	675	3	2	2	NUM
ejpam-6124	675	4	,	,	PUNCT
ejpam-6124	675	5	if	if	SCONJ
ejpam-6124	675	6	n	n	PRON
ejpam-6124	675	7	≡	≡	PROPN
ejpam-6124	675	8	0	0	PUNCT
ejpam-6124	675	9	(	(	PUNCT
ejpam-6124	675	10	mod	mod	PROPN
ejpam-6124	675	11	4	4	NUM
ejpam-6124	675	12	)	)	PUNCT
ejpam-6124	675	13	m	m	VERB
ejpam-6124	675	14	(	(	PUNCT
ejpam-6124	675	15	n+2	n+2	NOUN
ejpam-6124	675	16	2	2	NUM
ejpam-6124	675	17	)	)	PUNCT
ejpam-6124	675	18	,	,	PUNCT
ejpam-6124	675	19	if	if	SCONJ
ejpam-6124	675	20	n	n	PRON
ejpam-6124	675	21	≡	≡	PROPN
ejpam-6124	675	22	2	2	NUM
ejpam-6124	675	23	(	(	PUNCT
ejpam-6124	675	24	mod	mod	NOUN
ejpam-6124	675	25	4	4	NUM
ejpam-6124	675	26	)	)	PUNCT
ejpam-6124	675	27	m	m	VERB
ejpam-6124	675	28	(	(	PUNCT
ejpam-6124	675	29	n+1	n+1	PROPN
ejpam-6124	675	30	2	2	NUM
ejpam-6124	675	31	)	)	PUNCT
ejpam-6124	675	32	,	,	PUNCT
ejpam-6124	675	33	if	if	SCONJ
ejpam-6124	675	34	n	n	PRON
ejpam-6124	675	35	≡	≡	PROPN
ejpam-6124	675	36	3	3	NUM
ejpam-6124	675	37	(	(	PUNCT
ejpam-6124	675	38	mod	mod	NOUN
ejpam-6124	675	39	4	4	NUM
ejpam-6124	675	40	)	)	PUNCT
ejpam-6124	675	41	and	and	CCONJ
ejpam-6124	675	42	γte(pn[km	γte(pn[km	NOUN
ejpam-6124	675	43	]	]	X
ejpam-6124	675	44	)	)	PUNCT
ejpam-6124	675	45	=	=	SYM
ejpam-6124	676	1	γte(pn	γte(pn	X
ejpam-6124	676	2	)	)	PUNCT
ejpam-6124	676	3	=	=	SYM
ejpam-6124	677	1			PROPN
ejpam-6124	677	2	n	n	PRON
ejpam-6124	677	3	2	2	NUM
ejpam-6124	677	4	,	,	PUNCT
ejpam-6124	677	5	if	if	SCONJ
ejpam-6124	677	6	n	n	PRON
ejpam-6124	677	7	≡	≡	PROPN
ejpam-6124	677	8	0	0	PUNCT
ejpam-6124	678	1	(	(	PUNCT
ejpam-6124	678	2	mod	mod	PROPN
ejpam-6124	678	3	4	4	NUM
ejpam-6124	678	4	)	)	PUNCT
ejpam-6124	678	5	n+2	n+2	ADV
ejpam-6124	678	6	2	2	NUM
ejpam-6124	678	7	,	,	PUNCT
ejpam-6124	678	8	if	if	SCONJ
ejpam-6124	678	9	n	n	PRON
ejpam-6124	678	10	≡	≡	PROPN
ejpam-6124	678	11	2	2	NUM
ejpam-6124	678	12	(	(	PUNCT
ejpam-6124	678	13	mod	mod	NOUN
ejpam-6124	678	14	4	4	NUM
ejpam-6124	678	15	)	)	PUNCT
ejpam-6124	678	16	n+1	n+1	NUM
ejpam-6124	678	17	2	2	NUM
ejpam-6124	678	18	,	,	PUNCT
ejpam-6124	678	19	if	if	SCONJ
ejpam-6124	678	20	n	n	PRON
ejpam-6124	678	21	≡	≡	PROPN
ejpam-6124	678	22	3	3	NUM
ejpam-6124	678	23	(	(	PUNCT
ejpam-6124	678	24	mod	mod	NOUN
ejpam-6124	678	25	4	4	NUM
ejpam-6124	678	26	)	)	PUNCT
ejpam-6124	678	27	.	.	PUNCT
ejpam-6124	679	1	corollary	corollary	ADJ
ejpam-6124	679	2	17	17	NUM
ejpam-6124	679	3	.	.	PUNCT
ejpam-6124	680	1	the	the	DET
ejpam-6124	680	2	total	total	ADJ
ejpam-6124	680	3	exact	exact	ADJ
ejpam-6124	680	4	domination	domination	NOUN
ejpam-6124	680	5	number	number	NOUN
ejpam-6124	680	6	of	of	ADP
ejpam-6124	680	7	the	the	DET
ejpam-6124	680	8	lexicographic	lexicographic	ADJ
ejpam-6124	680	9	product	product	NOUN
ejpam-6124	680	10	of	of	ADP
ejpam-6124	680	11	km	km	PROPN
ejpam-6124	680	12	and	and	CCONJ
ejpam-6124	680	13	cn	cn	PROPN
ejpam-6124	680	14	is	be	AUX
ejpam-6124	680	15	given	give	VERB
ejpam-6124	680	16	by	by	ADP
ejpam-6124	680	17	γte(km[cn	γte(km[cn	NOUN
ejpam-6124	680	18	]	]	PUNCT
ejpam-6124	680	19	)	)	PUNCT
ejpam-6124	680	20	=	=	SYM
ejpam-6124	680	21	mn	mn	PROPN
ejpam-6124	680	22	2	2	NUM
ejpam-6124	680	23	,	,	PUNCT
ejpam-6124	680	24	∀	∀	X
ejpam-6124	680	25	n	n	PRON
ejpam-6124	680	26	≡	≡	PROPN
ejpam-6124	680	27	0	0	PUNCT
ejpam-6124	680	28	(	(	PUNCT
ejpam-6124	680	29	mod	mod	NOUN
ejpam-6124	680	30	4	4	NUM
ejpam-6124	680	31	)	)	PUNCT
ejpam-6124	680	32	and	and	CCONJ
ejpam-6124	680	33	γte(cn[km	γte(cn[km	ADP
ejpam-6124	680	34	]	]	X
ejpam-6124	680	35	)	)	PUNCT
ejpam-6124	680	36	=	=	SYM
ejpam-6124	680	37	n	n	PRON
ejpam-6124	680	38	2	2	NUM
ejpam-6124	680	39	,	,	PUNCT
ejpam-6124	680	40	∀	∀	NOUN
ejpam-6124	680	41	n	n	PRON
ejpam-6124	680	42	≡	≡	PROPN
ejpam-6124	680	43	0	0	PUNCT
ejpam-6124	680	44	(	(	PUNCT
ejpam-6124	680	45	mod	mod	PROPN
ejpam-6124	680	46	4	4	NUM
ejpam-6124	680	47	)	)	PUNCT
ejpam-6124	680	48	.	.	PUNCT
ejpam-6124	681	1	the	the	DET
ejpam-6124	681	2	next	next	ADJ
ejpam-6124	681	3	result	result	NOUN
ejpam-6124	681	4	follows	follow	VERB
ejpam-6124	681	5	directly	directly	ADV
ejpam-6124	681	6	from	from	ADP
ejpam-6124	681	7	theorems	theorem	NOUN
ejpam-6124	681	8	6	6	NUM
ejpam-6124	681	9	,	,	PUNCT
ejpam-6124	681	10	8	8	NUM
ejpam-6124	681	11	and	and	CCONJ
ejpam-6124	681	12	15	15	NUM
ejpam-6124	681	13	.	.	PUNCT
ejpam-6124	682	1	corollary	corollary	ADJ
ejpam-6124	682	2	18	18	NUM
ejpam-6124	682	3	.	.	PUNCT
ejpam-6124	683	1	the	the	DET
ejpam-6124	683	2	following	follow	VERB
ejpam-6124	683	3	lexicographic	lexicographic	ADJ
ejpam-6124	683	4	products	product	NOUN
ejpam-6124	683	5	are	be	AUX
ejpam-6124	683	6	non	non	ADJ
ejpam-6124	683	7	-	-	ADJ
ejpam-6124	683	8	γte	γte	PRON
ejpam-6124	683	9	-	-	PUNCT
ejpam-6124	683	10	graphs	graph	NOUN
ejpam-6124	683	11	:	:	PUNCT
ejpam-6124	683	12	i.	i.	PROPN
ejpam-6124	683	13	pn[km	pn[km	PROPN
ejpam-6124	683	14	]	]	X
ejpam-6124	683	15	∀	∀	X
ejpam-6124	683	16	n	n	CCONJ
ejpam-6124	683	17	≡	≡	PROPN
ejpam-6124	683	18	1	1	NUM
ejpam-6124	683	19	(	(	PUNCT
ejpam-6124	683	20	mod	mod	NOUN
ejpam-6124	683	21	4	4	NUM
ejpam-6124	683	22	)	)	PUNCT
ejpam-6124	683	23	,	,	PUNCT
ejpam-6124	683	24	ii	ii	PROPN
ejpam-6124	683	25	.	.	PUNCT
ejpam-6124	684	1	km[pn	km[pn	PROPN
ejpam-6124	684	2	]	]	X
ejpam-6124	684	3	∀	∀	X
ejpam-6124	684	4	n	n	CCONJ
ejpam-6124	684	5	≡	≡	PROPN
ejpam-6124	684	6	1	1	NUM
ejpam-6124	684	7	(	(	PUNCT
ejpam-6124	684	8	mod	mod	NOUN
ejpam-6124	684	9	4	4	NUM
ejpam-6124	684	10	)	)	PUNCT
ejpam-6124	684	11	,	,	PUNCT
ejpam-6124	684	12	iii	iii	X
ejpam-6124	684	13	.	.	PUNCT
ejpam-6124	684	14	cn[km	cn[km	PROPN
ejpam-6124	684	15	]	]	PUNCT
ejpam-6124	684	16	∀	∀	X
ejpam-6124	685	1	n	n	X
ejpam-6124	685	2	̸≡	̸≡	X
ejpam-6124	685	3	0	0	PUNCT
ejpam-6124	686	1	(	(	PUNCT
ejpam-6124	686	2	mod	mod	PROPN
ejpam-6124	686	3	4	4	NUM
ejpam-6124	686	4	)	)	PUNCT
ejpam-6124	686	5	,	,	PUNCT
ejpam-6124	686	6	iv	iv	X
ejpam-6124	686	7	.	.	PUNCT
ejpam-6124	687	1	km[cn	km[cn	NOUN
ejpam-6124	687	2	]	]	X
ejpam-6124	687	3	∀	∀	X
ejpam-6124	687	4	n	n	X
ejpam-6124	687	5	̸≡	̸≡	X
ejpam-6124	687	6	0	0	PUNCT
ejpam-6124	688	1	(	(	PUNCT
ejpam-6124	688	2	mod	mod	PROPN
ejpam-6124	688	3	4	4	NUM
ejpam-6124	688	4	)	)	PUNCT
ejpam-6124	688	5	.	.	PUNCT
ejpam-6124	689	1	r.	r.	PROPN
ejpam-6124	689	2	g.	g.	PROPN
ejpam-6124	689	3	aguinod	aguinod	PROPN
ejpam-6124	689	4	,	,	PUNCT
ejpam-6124	689	5	e.	e.	PROPN
ejpam-6124	689	6	m.	m.	PROPN
ejpam-6124	689	7	kiunisala	kiunisala	PROPN
ejpam-6124	689	8	,	,	PUNCT
ejpam-6124	689	9	c.	c.	PROPN
ejpam-6124	689	10	l.	l.	PROPN
ejpam-6124	689	11	armada	armada	PROPN
ejpam-6124	689	12	/	/	SYM
ejpam-6124	689	13	eur	eur	PROPN
ejpam-6124	689	14	.	.	PUNCT
ejpam-6124	690	1	j.	j.	PROPN
ejpam-6124	690	2	pure	pure	PROPN
ejpam-6124	690	3	appl	appl	PROPN
ejpam-6124	690	4	.	.	PROPN
ejpam-6124	690	5	math	math	PROPN
ejpam-6124	690	6	,	,	PUNCT
ejpam-6124	690	7	18	18	NUM
ejpam-6124	690	8	(	(	PUNCT
ejpam-6124	690	9	2	2	NUM
ejpam-6124	690	10	)	)	PUNCT
ejpam-6124	690	11	(	(	PUNCT
ejpam-6124	690	12	2025	2025	NUM
ejpam-6124	690	13	)	)	PUNCT
ejpam-6124	690	14	,	,	PUNCT
ejpam-6124	690	15	6124	6124	NUM
ejpam-6124	690	16	25	25	NUM
ejpam-6124	690	17	of	of	ADP
ejpam-6124	690	18	26	26	NUM
ejpam-6124	690	19	5	5	NUM
ejpam-6124	690	20	.	.	PUNCT
ejpam-6124	691	1	conclusion	conclusion	NOUN
ejpam-6124	691	2	in	in	ADP
ejpam-6124	691	3	this	this	DET
ejpam-6124	691	4	study	study	NOUN
ejpam-6124	691	5	,	,	PUNCT
ejpam-6124	691	6	we	we	PRON
ejpam-6124	691	7	explored	explore	VERB
ejpam-6124	691	8	and	and	CCONJ
ejpam-6124	691	9	introduced	introduce	VERB
ejpam-6124	691	10	the	the	DET
ejpam-6124	691	11	concept	concept	NOUN
ejpam-6124	691	12	of	of	ADP
ejpam-6124	691	13	total	total	ADJ
ejpam-6124	691	14	exact	exact	ADJ
ejpam-6124	691	15	domination	domination	NOUN
ejpam-6124	691	16	in	in	ADP
ejpam-6124	691	17	graphs	graph	NOUN
ejpam-6124	691	18	.	.	PUNCT
ejpam-6124	692	1	we	we	PRON
ejpam-6124	692	2	computed	compute	VERB
ejpam-6124	692	3	γte(g	γte(g	PROPN
ejpam-6124	692	4	)	)	PUNCT
ejpam-6124	692	5	for	for	ADP
ejpam-6124	692	6	several	several	ADJ
ejpam-6124	692	7	families	family	NOUN
ejpam-6124	692	8	of	of	ADP
ejpam-6124	692	9	special	special	ADJ
ejpam-6124	692	10	graphs	graph	NOUN
ejpam-6124	692	11	such	such	ADJ
ejpam-6124	692	12	as	as	ADP
ejpam-6124	692	13	paths	path	NOUN
ejpam-6124	692	14	,	,	PUNCT
ejpam-6124	692	15	cycles	cycle	NOUN
ejpam-6124	692	16	,	,	PUNCT
ejpam-6124	692	17	stars	star	NOUN
ejpam-6124	692	18	,	,	PUNCT
ejpam-6124	692	19	and	and	CCONJ
ejpam-6124	692	20	complete	complete	ADJ
ejpam-6124	692	21	bipartite	bipartite	NOUN
ejpam-6124	692	22	graphs	graph	NOUN
ejpam-6124	692	23	,	,	PUNCT
ejpam-6124	692	24	as	as	ADV
ejpam-6124	692	25	well	well	ADV
ejpam-6124	692	26	as	as	ADP
ejpam-6124	692	27	for	for	ADP
ejpam-6124	692	28	graphs	graph	NOUN
ejpam-6124	692	29	resulting	result	VERB
ejpam-6124	692	30	from	from	ADP
ejpam-6124	692	31	some	some	DET
ejpam-6124	692	32	binary	binary	ADJ
ejpam-6124	692	33	operations	operation	NOUN
ejpam-6124	692	34	including	include	VERB
ejpam-6124	692	35	the	the	DET
ejpam-6124	692	36	join	join	NOUN
ejpam-6124	692	37	,	,	PUNCT
ejpam-6124	692	38	corona	corona	PROPN
ejpam-6124	692	39	,	,	PUNCT
ejpam-6124	692	40	and	and	CCONJ
ejpam-6124	692	41	lexicographic	lexicographic	ADJ
ejpam-6124	692	42	product	product	NOUN
ejpam-6124	692	43	.	.	PUNCT
ejpam-6124	693	1	graphs	graph	NOUN
ejpam-6124	693	2	that	that	PRON
ejpam-6124	693	3	do	do	AUX
ejpam-6124	693	4	not	not	PART
ejpam-6124	693	5	have	have	VERB
ejpam-6124	693	6	total	total	ADJ
ejpam-6124	693	7	exact	exact	ADJ
ejpam-6124	693	8	dominating	dominating	NOUN
ejpam-6124	693	9	sets	set	NOUN
ejpam-6124	693	10	were	be	AUX
ejpam-6124	693	11	identified	identify	VERB
ejpam-6124	693	12	as	as	ADP
ejpam-6124	693	13	non	non	ADJ
ejpam-6124	693	14	-	-	ADJ
ejpam-6124	693	15	γte	γte	PRON
ejpam-6124	693	16	-	-	PUNCT
ejpam-6124	693	17	graphs	graph	NOUN
ejpam-6124	693	18	,	,	PUNCT
ejpam-6124	693	19	examples	example	NOUN
ejpam-6124	693	20	of	of	ADP
ejpam-6124	693	21	which	which	PRON
ejpam-6124	693	22	include	include	VERB
ejpam-6124	693	23	complete	complete	ADJ
ejpam-6124	693	24	graphs	graph	NOUN
ejpam-6124	693	25	,	,	PUNCT
ejpam-6124	693	26	fan	fan	NOUN
ejpam-6124	693	27	graphs	graph	NOUN
ejpam-6124	693	28	,	,	PUNCT
ejpam-6124	693	29	and	and	CCONJ
ejpam-6124	693	30	wheel	wheel	NOUN
ejpam-6124	693	31	graphs	graph	NOUN
ejpam-6124	693	32	with	with	ADP
ejpam-6124	693	33	more	more	ADJ
ejpam-6124	693	34	than	than	ADP
ejpam-6124	693	35	two	two	NUM
ejpam-6124	693	36	vertices	vertex	NOUN
ejpam-6124	693	37	.	.	PUNCT
ejpam-6124	694	1	in	in	ADP
ejpam-6124	694	2	addition	addition	NOUN
ejpam-6124	694	3	,	,	PUNCT
ejpam-6124	694	4	we	we	PRON
ejpam-6124	694	5	considered	consider	VERB
ejpam-6124	694	6	some	some	DET
ejpam-6124	694	7	disconnected	disconnected	ADJ
ejpam-6124	694	8	graphs	graph	NOUN
ejpam-6124	694	9	in	in	ADP
ejpam-6124	694	10	the	the	DET
ejpam-6124	694	11	binary	binary	ADJ
ejpam-6124	694	12	operations	operation	NOUN
ejpam-6124	694	13	,	,	PUNCT
ejpam-6124	694	14	enriching	enrich	VERB
ejpam-6124	694	15	the	the	DET
ejpam-6124	694	16	scope	scope	NOUN
ejpam-6124	694	17	of	of	ADP
ejpam-6124	694	18	the	the	DET
ejpam-6124	694	19	investigation	investigation	NOUN
ejpam-6124	694	20	.	.	PUNCT
ejpam-6124	695	1	the	the	DET
ejpam-6124	695	2	total	total	ADJ
ejpam-6124	695	3	exact	exact	ADJ
ejpam-6124	695	4	domination	domination	NOUN
ejpam-6124	695	5	has	have	VERB
ejpam-6124	695	6	applications	application	NOUN
ejpam-6124	695	7	in	in	ADP
ejpam-6124	695	8	communication	communication	NOUN
ejpam-6124	695	9	and	and	CCONJ
ejpam-6124	695	10	sensor	sensor	NOUN
ejpam-6124	695	11	networks	network	NOUN
ejpam-6124	695	12	,	,	PUNCT
ejpam-6124	695	13	where	where	SCONJ
ejpam-6124	695	14	nodes	node	NOUN
ejpam-6124	695	15	must	must	AUX
ejpam-6124	695	16	be	be	AUX
ejpam-6124	695	17	fully	fully	ADV
ejpam-6124	695	18	covered	cover	VERB
ejpam-6124	695	19	(	(	PUNCT
ejpam-6124	695	20	total	total	ADJ
ejpam-6124	695	21	domination	domination	NOUN
ejpam-6124	695	22	)	)	PUNCT
ejpam-6124	695	23	with	with	ADP
ejpam-6124	695	24	minimal	minimal	ADJ
ejpam-6124	695	25	overlapping	overlap	VERB
ejpam-6124	695	26	influence	influence	NOUN
ejpam-6124	695	27	(	(	PUNCT
ejpam-6124	695	28	exact	exact	ADJ
ejpam-6124	695	29	domination	domination	NOUN
ejpam-6124	695	30	)	)	PUNCT
ejpam-6124	695	31	,	,	PUNCT
ejpam-6124	695	32	similar	similar	ADJ
ejpam-6124	695	33	to	to	ADP
ejpam-6124	695	34	applications	application	NOUN
ejpam-6124	695	35	discussed	discuss	VERB
ejpam-6124	695	36	in	in	ADP
ejpam-6124	695	37	network	network	NOUN
ejpam-6124	695	38	design	design	NOUN
ejpam-6124	695	39	scenarios	scenario	NOUN
ejpam-6124	695	40	[	[	X
ejpam-6124	695	41	15	15	NUM
ejpam-6124	695	42	]	]	PUNCT
ejpam-6124	695	43	.	.	PUNCT
ejpam-6124	696	1	the	the	DET
ejpam-6124	696	2	total	total	ADJ
ejpam-6124	696	3	exact	exact	ADJ
ejpam-6124	696	4	domination	domination	NOUN
ejpam-6124	696	5	model	model	NOUN
ejpam-6124	696	6	ensures	ensure	VERB
ejpam-6124	696	7	efficient	efficient	ADJ
ejpam-6124	696	8	placement	placement	NOUN
ejpam-6124	696	9	of	of	ADP
ejpam-6124	696	10	resources	resource	NOUN
ejpam-6124	696	11	or	or	CCONJ
ejpam-6124	696	12	control	control	NOUN
ejpam-6124	696	13	centers	center	NOUN
ejpam-6124	696	14	with	with	ADP
ejpam-6124	696	15	distinct	distinct	ADJ
ejpam-6124	696	16	coverage	coverage	NOUN
ejpam-6124	696	17	,	,	PUNCT
ejpam-6124	696	18	reducing	reduce	VERB
ejpam-6124	696	19	redundancy	redundancy	NOUN
ejpam-6124	696	20	.	.	PUNCT
ejpam-6124	697	1	for	for	ADP
ejpam-6124	697	2	future	future	ADJ
ejpam-6124	697	3	research	research	NOUN
ejpam-6124	697	4	,	,	PUNCT
ejpam-6124	697	5	we	we	PRON
ejpam-6124	697	6	recommend	recommend	VERB
ejpam-6124	697	7	studying	study	VERB
ejpam-6124	697	8	the	the	DET
ejpam-6124	697	9	total	total	ADJ
ejpam-6124	697	10	exact	exact	ADJ
ejpam-6124	697	11	domination	domination	NOUN
ejpam-6124	697	12	number	number	NOUN
ejpam-6124	697	13	under	under	ADP
ejpam-6124	697	14	other	other	ADJ
ejpam-6124	697	15	binary	binary	ADJ
ejpam-6124	697	16	operations	operation	NOUN
ejpam-6124	697	17	not	not	PART
ejpam-6124	697	18	mentioned	mention	VERB
ejpam-6124	697	19	in	in	ADP
ejpam-6124	697	20	this	this	DET
ejpam-6124	697	21	study	study	NOUN
ejpam-6124	697	22	,	,	PUNCT
ejpam-6124	697	23	such	such	ADJ
ejpam-6124	697	24	as	as	ADP
ejpam-6124	697	25	the	the	DET
ejpam-6124	697	26	strong	strong	ADJ
ejpam-6124	697	27	product	product	NOUN
ejpam-6124	697	28	,	,	PUNCT
ejpam-6124	697	29	cartesian	cartesian	ADJ
ejpam-6124	697	30	product	product	NOUN
ejpam-6124	697	31	,	,	PUNCT
ejpam-6124	697	32	and	and	CCONJ
ejpam-6124	697	33	tensor	tensor	NOUN
ejpam-6124	697	34	product	product	NOUN
ejpam-6124	697	35	of	of	ADP
ejpam-6124	697	36	graphs	graph	NOUN
ejpam-6124	697	37	.	.	PUNCT
ejpam-6124	698	1	additionally	additionally	ADV
ejpam-6124	698	2	,	,	PUNCT
ejpam-6124	698	3	extending	extend	VERB
ejpam-6124	698	4	the	the	DET
ejpam-6124	698	5	study	study	NOUN
ejpam-6124	698	6	to	to	ADP
ejpam-6124	698	7	weighted	weighted	ADJ
ejpam-6124	698	8	graphs	graph	NOUN
ejpam-6124	698	9	,	,	PUNCT
ejpam-6124	698	10	directed	direct	VERB
ejpam-6124	698	11	graphs	graph	NOUN
ejpam-6124	698	12	,	,	PUNCT
ejpam-6124	698	13	or	or	CCONJ
ejpam-6124	698	14	random	random	ADJ
ejpam-6124	698	15	graphs	graph	NOUN
ejpam-6124	698	16	could	could	AUX
ejpam-6124	698	17	broaden	broaden	VERB
ejpam-6124	698	18	its	its	PRON
ejpam-6124	698	19	computational	computational	ADJ
ejpam-6124	698	20	relevance	relevance	NOUN
ejpam-6124	698	21	and	and	CCONJ
ejpam-6124	698	22	applicability	applicability	NOUN
ejpam-6124	698	23	.	.	PUNCT
ejpam-6124	699	1	acknowledgements	acknowledgement	NOUN
ejpam-6124	699	2	the	the	DET
ejpam-6124	699	3	authors	author	NOUN
ejpam-6124	699	4	would	would	AUX
ejpam-6124	699	5	like	like	VERB
ejpam-6124	699	6	to	to	PART
ejpam-6124	699	7	thank	thank	VERB
ejpam-6124	699	8	the	the	DET
ejpam-6124	699	9	anonymous	anonymous	ADJ
ejpam-6124	699	10	referees	referee	NOUN
ejpam-6124	699	11	for	for	ADP
ejpam-6124	699	12	their	their	PRON
ejpam-6124	699	13	notable	notable	ADJ
ejpam-6124	699	14	and	and	CCONJ
ejpam-6124	699	15	valuable	valuable	ADJ
ejpam-6124	699	16	suggestions	suggestion	NOUN
ejpam-6124	699	17	and	and	CCONJ
ejpam-6124	699	18	comments	comment	NOUN
ejpam-6124	699	19	that	that	PRON
ejpam-6124	699	20	helped	help	VERB
ejpam-6124	699	21	shape	shape	VERB
ejpam-6124	699	22	the	the	DET
ejpam-6124	699	23	quality	quality	NOUN
ejpam-6124	699	24	of	of	ADP
ejpam-6124	699	25	this	this	DET
ejpam-6124	699	26	study	study	NOUN
ejpam-6124	699	27	.	.	PUNCT
ejpam-6124	700	1	they	they	PRON
ejpam-6124	700	2	also	also	ADV
ejpam-6124	700	3	express	express	VERB
ejpam-6124	700	4	their	their	PRON
ejpam-6124	700	5	heartfelt	heartfelt	ADJ
ejpam-6124	700	6	gratitude	gratitude	NOUN
ejpam-6124	700	7	to	to	ADP
ejpam-6124	700	8	the	the	DET
ejpam-6124	700	9	department	department	PROPN
ejpam-6124	700	10	of	of	ADP
ejpam-6124	700	11	science	science	NOUN
ejpam-6124	700	12	and	and	CCONJ
ejpam-6124	700	13	technology	technology	NOUN
ejpam-6124	700	14	–	–	PUNCT
ejpam-6124	700	15	science	science	NOUN
ejpam-6124	700	16	and	and	CCONJ
ejpam-6124	700	17	technology	technology	NOUN
ejpam-6124	700	18	regional	regional	ADJ
ejpam-6124	700	19	alliance	alliance	NOUN
ejpam-6124	700	20	of	of	ADP
ejpam-6124	700	21	universities	university	NOUN
ejpam-6124	700	22	for	for	ADP
ejpam-6124	700	23	national	national	ADJ
ejpam-6124	700	24	development	development	NOUN
ejpam-6124	700	25	(	(	PUNCT
ejpam-6124	700	26	doststrand	doststrand	NOUN
ejpam-6124	700	27	)	)	PUNCT
ejpam-6124	700	28	for	for	ADP
ejpam-6124	700	29	the	the	DET
ejpam-6124	700	30	financial	financial	ADJ
ejpam-6124	700	31	support	support	NOUN
ejpam-6124	700	32	,	,	PUNCT
ejpam-6124	700	33	which	which	PRON
ejpam-6124	700	34	is	be	AUX
ejpam-6124	700	35	vital	vital	ADJ
ejpam-6124	700	36	in	in	ADP
ejpam-6124	700	37	the	the	DET
ejpam-6124	700	38	actualization	actualization	NOUN
ejpam-6124	700	39	of	of	ADP
ejpam-6124	700	40	this	this	DET
ejpam-6124	700	41	study	study	NOUN
ejpam-6124	700	42	,	,	PUNCT
ejpam-6124	700	43	cebu	cebu	NOUN
ejpam-6124	700	44	normal	normal	ADJ
ejpam-6124	700	45	university	university	PROPN
ejpam-6124	700	46	college	college	NOUN
ejpam-6124	700	47	of	of	ADP
ejpam-6124	700	48	computing	computing	NOUN
ejpam-6124	700	49	,	,	PUNCT
ejpam-6124	700	50	artificial	artificial	ADJ
ejpam-6124	700	51	intelligence	intelligence	NOUN
ejpam-6124	700	52	and	and	CCONJ
ejpam-6124	700	53	sciences	science	NOUN
ejpam-6124	700	54	,	,	PUNCT
ejpam-6124	700	55	which	which	PRON
ejpam-6124	700	56	also	also	ADV
ejpam-6124	700	57	provided	provide	VERB
ejpam-6124	700	58	guidance	guidance	NOUN
ejpam-6124	700	59	and	and	CCONJ
ejpam-6124	700	60	made	make	VERB
ejpam-6124	700	61	the	the	DET
ejpam-6124	700	62	publication	publication	NOUN
ejpam-6124	700	63	of	of	ADP
ejpam-6124	700	64	this	this	DET
ejpam-6124	700	65	work	work	NOUN
ejpam-6124	700	66	possible	possible	ADJ
ejpam-6124	700	67	.	.	PUNCT
ejpam-6124	701	1	we	we	PRON
ejpam-6124	701	2	acknowledge	acknowledge	VERB
ejpam-6124	701	3	ho	ho	PROPN
ejpam-6124	701	4	chi	chi	PROPN
ejpam-6124	701	5	minh	minh	PROPN
ejpam-6124	701	6	city	city	PROPN
ejpam-6124	701	7	university	university	PROPN
ejpam-6124	701	8	of	of	ADP
ejpam-6124	701	9	technology	technology	NOUN
ejpam-6124	701	10	(	(	PUNCT
ejpam-6124	701	11	hcmut	hcmut	NOUN
ejpam-6124	701	12	)	)	PUNCT
ejpam-6124	701	13	,	,	PUNCT
ejpam-6124	701	14	vnu	vnu	PROPN
ejpam-6124	701	15	-	-	PUNCT
ejpam-6124	701	16	hcm	hcm	PROPN
ejpam-6124	701	17	for	for	ADP
ejpam-6124	701	18	supporting	support	VERB
ejpam-6124	701	19	this	this	DET
ejpam-6124	701	20	study	study	NOUN
ejpam-6124	701	21	.	.	PUNCT
ejpam-6124	702	1	references	reference	NOUN
ejpam-6124	702	2	[	[	X
ejpam-6124	702	3	1	1	NUM
ejpam-6124	702	4	]	]	X
ejpam-6124	702	5	o.	o.	PROPN
ejpam-6124	702	6	ore	ore	PROPN
ejpam-6124	702	7	.	.	PUNCT
ejpam-6124	703	1	theory	theory	NOUN
ejpam-6124	703	2	of	of	ADP
ejpam-6124	703	3	graphs	graph	NOUN
ejpam-6124	703	4	.	.	PUNCT
ejpam-6124	704	1	american	american	PROPN
ejpam-6124	704	2	mathematical	mathematical	PROPN
ejpam-6124	704	3	society	society	NOUN
ejpam-6124	704	4	,	,	PUNCT
ejpam-6124	704	5	1962	1962	NUM
ejpam-6124	704	6	.	.	PUNCT
ejpam-6124	705	1	[	[	X
ejpam-6124	705	2	2	2	NUM
ejpam-6124	705	3	]	]	SYM
ejpam-6124	705	4	e.j	e.j	PROPN
ejpam-6124	705	5	.	.	PROPN
ejpam-6124	705	6	cockayne	cockayne	PROPN
ejpam-6124	705	7	,	,	PUNCT
ejpam-6124	705	8	r.m	r.m	PROPN
ejpam-6124	705	9	.	.	PROPN
ejpam-6124	705	10	dawes	dawes	PROPN
ejpam-6124	705	11	,	,	PUNCT
ejpam-6124	705	12	s.t	s.t	PROPN
ejpam-6124	705	13	.	.	PROPN
ejpam-6124	705	14	hedetniemi	hedetniemi	PROPN
ejpam-6124	705	15	.	.	PUNCT
ejpam-6124	706	1	total	total	ADJ
ejpam-6124	706	2	domination	domination	NOUN
ejpam-6124	706	3	in	in	ADP
ejpam-6124	706	4	graphs	graph	NOUN
ejpam-6124	706	5	.	.	PUNCT
ejpam-6124	707	1	networks	network	NOUN
ejpam-6124	707	2	,	,	PUNCT
ejpam-6124	707	3	10(3):211–219	10(3):211–219	NUM
ejpam-6124	707	4	,	,	PUNCT
ejpam-6124	707	5	1980	1980	NUM
ejpam-6124	707	6	.	.	PUNCT
ejpam-6124	708	1	[	[	X
ejpam-6124	708	2	3	3	NUM
ejpam-6124	708	3	]	]	PUNCT
ejpam-6124	708	4	a.	a.	NOUN
ejpam-6124	708	5	kinsley	kinsley	PROPN
ejpam-6124	708	6	,	,	PUNCT
ejpam-6124	708	7	a.	a.	PROPN
ejpam-6124	708	8	vetha	vetha	PROPN
ejpam-6124	708	9	.	.	PUNCT
ejpam-6124	709	1	exact	exact	ADJ
ejpam-6124	709	2	domination	domination	NOUN
ejpam-6124	709	3	in	in	ADP
ejpam-6124	709	4	graphs	graph	NOUN
ejpam-6124	709	5	.	.	PUNCT
ejpam-6124	710	1	malaya	malaya	PROPN
ejpam-6124	710	2	journal	journal	PROPN
ejpam-6124	710	3	of	of	ADP
ejpam-6124	710	4	matematik	matematik	PROPN
ejpam-6124	710	5	,	,	PUNCT
ejpam-6124	710	6	s(1):236–242	s(1):236–242	PROPN
ejpam-6124	710	7	,	,	PUNCT
ejpam-6124	710	8	2020	2020	NUM
ejpam-6124	710	9	.	.	PUNCT
ejpam-6124	711	1	r.	r.	PROPN
ejpam-6124	711	2	g.	g.	PROPN
ejpam-6124	711	3	aguinod	aguinod	PROPN
ejpam-6124	711	4	,	,	PUNCT
ejpam-6124	711	5	e.	e.	PROPN
ejpam-6124	711	6	m.	m.	PROPN
ejpam-6124	711	7	kiunisala	kiunisala	PROPN
ejpam-6124	711	8	,	,	PUNCT
ejpam-6124	711	9	c.	c.	PROPN
ejpam-6124	711	10	l.	l.	PROPN
ejpam-6124	711	11	armada	armada	PROPN
ejpam-6124	711	12	/	/	SYM
ejpam-6124	711	13	eur	eur	PROPN
ejpam-6124	711	14	.	.	PUNCT
ejpam-6124	712	1	j.	j.	PROPN
ejpam-6124	712	2	pure	pure	PROPN
ejpam-6124	712	3	appl	appl	PROPN
ejpam-6124	712	4	.	.	PROPN
ejpam-6124	712	5	math	math	PROPN
ejpam-6124	712	6	,	,	PUNCT
ejpam-6124	712	7	18	18	NUM
ejpam-6124	712	8	(	(	PUNCT
ejpam-6124	712	9	2	2	NUM
ejpam-6124	712	10	)	)	PUNCT
ejpam-6124	712	11	(	(	PUNCT
ejpam-6124	712	12	2025	2025	NUM
ejpam-6124	712	13	)	)	PUNCT
ejpam-6124	712	14	,	,	PUNCT
ejpam-6124	712	15	6124	6124	NUM
ejpam-6124	712	16	26	26	NUM
ejpam-6124	712	17	of	of	ADP
ejpam-6124	712	18	26	26	NUM
ejpam-6124	712	19	[	[	SYM
ejpam-6124	712	20	4	4	NUM
ejpam-6124	712	21	]	]	X
ejpam-6124	712	22	c.	c.	PROPN
ejpam-6124	712	23	armada	armada	PROPN
ejpam-6124	712	24	.	.	PUNCT
ejpam-6124	713	1	forcing	force	VERB
ejpam-6124	713	2	subsets	subset	NOUN
ejpam-6124	713	3	for	for	ADP
ejpam-6124	713	4	γ∗tpw	γ∗tpw	NOUN
ejpam-6124	713	5	-	-	PUNCT
ejpam-6124	713	6	sets	set	NOUN
ejpam-6124	713	7	in	in	ADP
ejpam-6124	713	8	graphs	graph	NOUN
ejpam-6124	713	9	.	.	PUNCT
ejpam-6124	714	1	european	european	ADJ
ejpam-6124	714	2	journal	journal	PROPN
ejpam-6124	714	3	of	of	ADP
ejpam-6124	714	4	pure	pure	ADJ
ejpam-6124	714	5	and	and	CCONJ
ejpam-6124	714	6	applied	applied	ADJ
ejpam-6124	714	7	mathematics	mathematic	NOUN
ejpam-6124	714	8	,	,	PUNCT
ejpam-6124	714	9	14(2):451–470	14(2):451–470	PROPN
ejpam-6124	714	10	,	,	PUNCT
ejpam-6124	714	11	2021	2021	NUM
ejpam-6124	714	12	.	.	PUNCT
ejpam-6124	715	1	[	[	X
ejpam-6124	715	2	5	5	NUM
ejpam-6124	715	3	]	]	X
ejpam-6124	715	4	c.	c.	PROPN
ejpam-6124	715	5	armada	armada	PROPN
ejpam-6124	715	6	,	,	PUNCT
ejpam-6124	715	7	j.	j.	PROPN
ejpam-6124	715	8	hamja	hamja	PROPN
ejpam-6124	715	9	.	.	PUNCT
ejpam-6124	716	1	perfect	perfect	PROPN
ejpam-6124	716	2	isolate	isolate	NOUN
ejpam-6124	716	3	domination	domination	NOUN
ejpam-6124	716	4	in	in	ADP
ejpam-6124	716	5	graphs	graph	NOUN
ejpam-6124	716	6	.	.	PUNCT
ejpam-6124	717	1	european	european	ADJ
ejpam-6124	717	2	journal	journal	PROPN
ejpam-6124	717	3	of	of	ADP
ejpam-6124	717	4	pure	pure	ADJ
ejpam-6124	717	5	and	and	CCONJ
ejpam-6124	717	6	applied	applied	ADJ
ejpam-6124	717	7	mathematics	mathematic	NOUN
ejpam-6124	717	8	,	,	PUNCT
ejpam-6124	717	9	16(2):1326–1341	16(2):1326–1341	NUM
ejpam-6124	717	10	,	,	PUNCT
ejpam-6124	717	11	2023	2023	NUM
ejpam-6124	717	12	.	.	PUNCT
ejpam-6124	718	1	[	[	X
ejpam-6124	718	2	6	6	NUM
ejpam-6124	718	3	]	]	X
ejpam-6124	718	4	c.	c.	PROPN
ejpam-6124	718	5	armada	armada	PROPN
ejpam-6124	718	6	.	.	PUNCT
ejpam-6124	719	1	forcing	force	VERB
ejpam-6124	719	2	total	total	ADJ
ejpam-6124	719	3	dr	dr	PROPN
ejpam-6124	719	4	-	-	PUNCT
ejpam-6124	719	5	power	power	NOUN
ejpam-6124	719	6	domination	domination	NOUN
ejpam-6124	719	7	number	number	NOUN
ejpam-6124	719	8	of	of	ADP
ejpam-6124	719	9	graphs	graph	NOUN
ejpam-6124	719	10	under	under	ADP
ejpam-6124	719	11	some	some	DET
ejpam-6124	719	12	binary	binary	ADJ
ejpam-6124	719	13	operations	operation	NOUN
ejpam-6124	719	14	.	.	PUNCT
ejpam-6124	720	1	european	european	ADJ
ejpam-6124	720	2	journal	journal	PROPN
ejpam-6124	720	3	of	of	ADP
ejpam-6124	720	4	pure	pure	ADJ
ejpam-6124	720	5	and	and	CCONJ
ejpam-6124	720	6	applied	applied	ADJ
ejpam-6124	720	7	mathematics	mathematic	NOUN
ejpam-6124	720	8	,	,	PUNCT
ejpam-6124	720	9	14(3):1098–1107	14(3):1098–1107	NUM
ejpam-6124	720	10	,	,	PUNCT
ejpam-6124	720	11	2021	2021	NUM
ejpam-6124	720	12	.	.	PUNCT
ejpam-6124	721	1	[	[	X
ejpam-6124	721	2	7	7	X
ejpam-6124	721	3	]	]	X
ejpam-6124	721	4	f.	f.	PROPN
ejpam-6124	721	5	harary	harary	PROPN
ejpam-6124	721	6	.	.	PUNCT
ejpam-6124	722	1	graph	graph	NOUN
ejpam-6124	722	2	theory	theory	NOUN
ejpam-6124	722	3	.	.	PUNCT
ejpam-6124	723	1	addison	addison	PROPN
ejpam-6124	723	2	-	-	PUNCT
ejpam-6124	723	3	wesley	wesley	PROPN
ejpam-6124	723	4	publication	publication	PROPN
ejpam-6124	723	5	company	company	PROPN
ejpam-6124	723	6	,	,	PUNCT
ejpam-6124	723	7	inc	inc	PROPN
ejpam-6124	723	8	.	.	PROPN
ejpam-6124	723	9	,	,	PUNCT
ejpam-6124	723	10	massachusetts	massachusetts	PROPN
ejpam-6124	723	11	,	,	PUNCT
ejpam-6124	723	12	1969	1969	NUM
ejpam-6124	723	13	.	.	PUNCT
ejpam-6124	724	1	[	[	X
ejpam-6124	724	2	8	8	NUM
ejpam-6124	724	3	]	]	X
ejpam-6124	724	4	j.l	j.l	PROPN
ejpam-6124	724	5	.	.	PROPN
ejpam-6124	724	6	gross	gross	PROPN
ejpam-6124	724	7	,	,	PUNCT
ejpam-6124	724	8	j.	j.	PROPN
ejpam-6124	724	9	yellen	yellen	PROPN
ejpam-6124	724	10	.	.	PUNCT
ejpam-6124	725	1	handbook	handbook	NOUN
ejpam-6124	725	2	of	of	ADP
ejpam-6124	725	3	graph	graph	NOUN
ejpam-6124	725	4	theory	theory	NOUN
ejpam-6124	725	5	,	,	PUNCT
ejpam-6124	725	6	1st	1st	ADJ
ejpam-6124	725	7	edition	edition	NOUN
ejpam-6124	725	8	.	.	PUNCT
ejpam-6124	726	1	crc	crc	PROPN
ejpam-6124	726	2	press	press	PROPN
ejpam-6124	726	3	,	,	PUNCT
ejpam-6124	726	4	boca	boca	PROPN
ejpam-6124	726	5	raton	raton	PROPN
ejpam-6124	726	6	,	,	PUNCT
ejpam-6124	726	7	florida	florida	PROPN
ejpam-6124	726	8	,	,	PUNCT
ejpam-6124	726	9	2003	2003	NUM
ejpam-6124	726	10	.	.	PUNCT
ejpam-6124	727	1	[	[	X
ejpam-6124	727	2	9	9	NUM
ejpam-6124	727	3	]	]	X
ejpam-6124	727	4	r.	r.	PROPN
ejpam-6124	727	5	diestel	diestel	PROPN
ejpam-6124	727	6	.	.	PUNCT
ejpam-6124	728	1	graph	graph	NOUN
ejpam-6124	728	2	theory	theory	NOUN
ejpam-6124	728	3	,	,	PUNCT
ejpam-6124	728	4	4th	4th	ADJ
ejpam-6124	728	5	edition	edition	NOUN
ejpam-6124	728	6	.	.	PUNCT
ejpam-6124	729	1	springer	springer	NOUN
ejpam-6124	729	2	-	-	PUNCT
ejpam-6124	729	3	verlag	verlag	PROPN
ejpam-6124	729	4	,	,	PUNCT
ejpam-6124	729	5	2017	2017	NUM
ejpam-6124	729	6	.	.	PUNCT
ejpam-6124	730	1	[	[	X
ejpam-6124	730	2	10	10	NUM
ejpam-6124	730	3	]	]	PUNCT
ejpam-6124	730	4	m.	m.	NOUN
ejpam-6124	730	5	subbulakshmi	subbulakshmi	PROPN
ejpam-6124	730	6	,	,	PUNCT
ejpam-6124	730	7	i.	i.	NOUN
ejpam-6124	730	8	valliammal	valliammal	NOUN
ejpam-6124	730	9	.	.	PUNCT
ejpam-6124	731	1	decomposition	decomposition	NOUN
ejpam-6124	731	2	of	of	ADP
ejpam-6124	731	3	generalized	generalized	ADJ
ejpam-6124	731	4	fan	fan	NOUN
ejpam-6124	731	5	graphs	graph	NOUN
ejpam-6124	731	6	.	.	PUNCT
ejpam-6124	732	1	advances	advance	NOUN
ejpam-6124	732	2	in	in	ADP
ejpam-6124	732	3	mathematics	mathematic	NOUN
ejpam-6124	732	4	:	:	PUNCT
ejpam-6124	732	5	scientific	scientific	ADJ
ejpam-6124	732	6	journal	journal	NOUN
ejpam-6124	732	7	,	,	PUNCT
ejpam-6124	732	8	10(5):2381–2392	10(5):2381–2392	NUM
ejpam-6124	732	9	,	,	PUNCT
ejpam-6124	732	10	2021	2021	NUM
ejpam-6124	732	11	.	.	PUNCT
ejpam-6124	733	1	[	[	X
ejpam-6124	733	2	11	11	NUM
ejpam-6124	733	3	]	]	PUNCT
ejpam-6124	733	4	b.	b.	PROPN
ejpam-6124	733	5	sooryanarayana	sooryanarayana	PROPN
ejpam-6124	733	6	,	,	PUNCT
ejpam-6124	733	7	s.	s.	PROPN
ejpam-6124	733	8	kunikullaya	kunikullaya	PROPN
ejpam-6124	733	9	,	,	PUNCT
ejpam-6124	733	10	n.n	n.n	PROPN
ejpam-6124	733	11	.	.	PROPN
ejpam-6124	733	12	swamy	swamy	PROPN
ejpam-6124	733	13	.	.	PUNCT
ejpam-6124	734	1	metric	metric	ADJ
ejpam-6124	734	2	dimension	dimension	NOUN
ejpam-6124	734	3	of	of	ADP
ejpam-6124	734	4	generalized	generalized	ADJ
ejpam-6124	734	5	wheels	wheel	NOUN
ejpam-6124	734	6	.	.	PUNCT
ejpam-6124	735	1	asian	asian	ADJ
ejpam-6124	735	2	journal	journal	PROPN
ejpam-6124	735	3	of	of	ADP
ejpam-6124	735	4	mathematics	mathematics	PROPN
ejpam-6124	735	5	and	and	CCONJ
ejpam-6124	735	6	computer	computer	NOUN
ejpam-6124	735	7	science	science	NOUN
ejpam-6124	735	8	,	,	PUNCT
ejpam-6124	735	9	7(3):167–178	7(3):167–178	NUM
ejpam-6124	735	10	,	,	PUNCT
ejpam-6124	735	11	2017	2017	NUM
ejpam-6124	735	12	.	.	PUNCT
ejpam-6124	736	1	[	[	X
ejpam-6124	736	2	12	12	NUM
ejpam-6124	736	3	]	]	X
ejpam-6124	736	4	d.b	d.b	PROPN
ejpam-6124	736	5	.	.	PROPN
ejpam-6124	736	6	west	west	PROPN
ejpam-6124	736	7	.	.	PUNCT
ejpam-6124	737	1	introduction	introduction	NOUN
ejpam-6124	737	2	to	to	AUX
ejpam-6124	737	3	graph	graph	NOUN
ejpam-6124	737	4	theory	theory	NOUN
ejpam-6124	737	5	,	,	PUNCT
ejpam-6124	737	6	2nd	2nd	PROPN
ejpam-6124	737	7	edition	edition	NOUN
ejpam-6124	737	8	.	.	PUNCT
ejpam-6124	738	1	prentice	prentice	PROPN
ejpam-6124	738	2	hall	hall	PROPN
ejpam-6124	738	3	,	,	PUNCT
ejpam-6124	738	4	2001	2001	NUM
ejpam-6124	738	5	.	.	PUNCT
ejpam-6124	739	1	[	[	X
ejpam-6124	739	2	13	13	NUM
ejpam-6124	739	3	]	]	X
ejpam-6124	739	4	c.	c.	NOUN
ejpam-6124	739	5	go	go	VERB
ejpam-6124	739	6	.	.	PUNCT
ejpam-6124	740	1	domination	domination	NOUN
ejpam-6124	740	2	in	in	ADP
ejpam-6124	740	3	the	the	DET
ejpam-6124	740	4	kr	kr	PROPN
ejpam-6124	740	5	-	-	PUNCT
ejpam-6124	740	6	gluing	gluing	NOUN
ejpam-6124	740	7	of	of	ADP
ejpam-6124	740	8	complete	complete	ADJ
ejpam-6124	740	9	graphs	graph	NOUN
ejpam-6124	740	10	and	and	CCONJ
ejpam-6124	740	11	join	join	VERB
ejpam-6124	740	12	of	of	ADP
ejpam-6124	740	13	graphs	graph	NOUN
ejpam-6124	740	14	.	.	PUNCT
ejpam-6124	741	1	the	the	DET
ejpam-6124	741	2	mindanawan	mindanawan	PROPN
ejpam-6124	741	3	journal	journal	PROPN
ejpam-6124	741	4	of	of	ADP
ejpam-6124	741	5	mathematics	mathematic	NOUN
ejpam-6124	741	6	,	,	PUNCT
ejpam-6124	741	7	2(1):38–42	2(1):38–42	NUM
ejpam-6124	741	8	,	,	PUNCT
ejpam-6124	741	9	2011	2011	NUM
ejpam-6124	741	10	.	.	PUNCT
ejpam-6124	742	1	[	[	X
ejpam-6124	742	2	14	14	NUM
ejpam-6124	742	3	]	]	X
ejpam-6124	742	4	c.	c.	PROPN
ejpam-6124	742	5	go	go	PROPN
ejpam-6124	742	6	,	,	PUNCT
ejpam-6124	742	7	s.	s.	PROPN
ejpam-6124	742	8	canoy	canoy	PROPN
ejpam-6124	742	9	,	,	PUNCT
ejpam-6124	742	10	jr	jr	PROPN
ejpam-6124	742	11	.	.	PROPN
ejpam-6124	742	12	domination	domination	NOUN
ejpam-6124	742	13	in	in	ADP
ejpam-6124	742	14	the	the	DET
ejpam-6124	742	15	corona	corona	NOUN
ejpam-6124	742	16	and	and	CCONJ
ejpam-6124	742	17	join	join	VERB
ejpam-6124	742	18	of	of	ADP
ejpam-6124	742	19	graphs	graph	NOUN
ejpam-6124	742	20	.	.	PUNCT
ejpam-6124	743	1	international	international	ADJ
ejpam-6124	743	2	mathematical	mathematical	PROPN
ejpam-6124	743	3	forum	forum	PROPN
ejpam-6124	743	4	,	,	PUNCT
ejpam-6124	743	5	6(16):763–771	6(16):763–771	NUM
ejpam-6124	743	6	,	,	PUNCT
ejpam-6124	743	7	2011	2011	NUM
ejpam-6124	743	8	.	.	PUNCT
ejpam-6124	744	1	[	[	X
ejpam-6124	744	2	15	15	NUM
ejpam-6124	744	3	]	]	X
ejpam-6124	744	4	p.j	p.j	PROPN
ejpam-6124	744	5	.	.	PROPN
ejpam-6124	744	6	slater	slater	PROPN
ejpam-6124	744	7	t.w	t.w	PROPN
ejpam-6124	744	8	.	.	PROPN
ejpam-6124	744	9	haynes	haynes	PROPN
ejpam-6124	744	10	,	,	PUNCT
ejpam-6124	744	11	s.t	s.t	PROPN
ejpam-6124	744	12	.	.	PROPN
ejpam-6124	744	13	hedetniemi	hedetniemi	PROPN
ejpam-6124	744	14	.	.	PUNCT
ejpam-6124	745	1	domination	domination	NOUN
ejpam-6124	745	2	in	in	ADP
ejpam-6124	745	3	graphs	graph	NOUN
ejpam-6124	745	4	:	:	PUNCT
ejpam-6124	745	5	advanced	advanced	ADJ
ejpam-6124	745	6	topics	topic	NOUN
ejpam-6124	745	7	.	.	PUNCT
ejpam-6124	746	1	marcel	marcel	PROPN
ejpam-6124	746	2	dekker	dekker	PROPN
ejpam-6124	746	3	,	,	PUNCT
ejpam-6124	746	4	1998	1998	NUM
ejpam-6124	746	5	.	.	PUNCT