id	sid	tid	token	lemma	pos
ejpam-5156	1	1	european	european	PROPN
ejpam-5156	1	2	journal	journal	PROPN
ejpam-5156	1	3	of	of	ADP
ejpam-5156	1	4	pure	pure	ADJ
ejpam-5156	1	5	and	and	CCONJ
ejpam-5156	1	6	applied	apply	VERB
ejpam-5156	1	7	mathematics	mathematic	NOUN
ejpam-5156	1	8	vol	vol	NOUN
ejpam-5156	1	9	.	.	PROPN
ejpam-5156	2	1	17	17	NUM
ejpam-5156	2	2	,	,	PUNCT
ejpam-5156	2	3	no	no	INTJ
ejpam-5156	2	4	.	.	NOUN
ejpam-5156	2	5	3	3	NUM
ejpam-5156	2	6	,	,	PUNCT
ejpam-5156	2	7	2024	2024	NUM
ejpam-5156	2	8	,	,	PUNCT
ejpam-5156	2	9	2196	2196	NUM
ejpam-5156	2	10	-	-	SYM
ejpam-5156	2	11	2209	2209	NUM
ejpam-5156	2	12	issn	issn	PROPN
ejpam-5156	2	13	1307	1307	NUM
ejpam-5156	2	14	-	-	SYM
ejpam-5156	2	15	5543	5543	NUM
ejpam-5156	2	16	–	–	PUNCT
ejpam-5156	3	1	ejpam.com	ejpam.com	X
ejpam-5156	3	2	published	publish	VERB
ejpam-5156	3	3	by	by	ADP
ejpam-5156	3	4	new	new	PROPN
ejpam-5156	3	5	york	york	PROPN
ejpam-5156	3	6	business	business	PROPN
ejpam-5156	3	7	global	global	ADJ
ejpam-5156	3	8	restrained	restrained	ADJ
ejpam-5156	3	9	global	global	ADJ
ejpam-5156	3	10	defensive	defensive	ADJ
ejpam-5156	3	11	alliances	alliance	NOUN
ejpam-5156	3	12	in	in	ADP
ejpam-5156	3	13	graphs	graph	NOUN
ejpam-5156	3	14	leocint	leocint	PROPN
ejpam-5156	3	15	f.	f.	PROPN
ejpam-5156	3	16	consistente1,∗	consistente1,∗	PROPN
ejpam-5156	3	17	,	,	PUNCT
ejpam-5156	3	18	isagani	isagani	PROPN
ejpam-5156	3	19	s.	s.	PROPN
ejpam-5156	3	20	cabahug	cabahug	PROPN
ejpam-5156	3	21	,	,	PUNCT
ejpam-5156	3	22	jr.1	jr.1	PROPN
ejpam-5156	3	23	1	1	NUM
ejpam-5156	3	24	department	department	NOUN
ejpam-5156	3	25	of	of	ADP
ejpam-5156	3	26	mathematics	mathematic	NOUN
ejpam-5156	3	27	,	,	PUNCT
ejpam-5156	3	28	college	college	NOUN
ejpam-5156	3	29	of	of	ADP
ejpam-5156	3	30	arts	art	NOUN
ejpam-5156	3	31	and	and	CCONJ
ejpam-5156	3	32	sciences	science	NOUN
ejpam-5156	3	33	,	,	PUNCT
ejpam-5156	3	34	central	central	ADJ
ejpam-5156	3	35	mindanao	mindanao	PROPN
ejpam-5156	3	36	university	university	PROPN
ejpam-5156	3	37	,	,	PUNCT
ejpam-5156	3	38	musuan	musuan	PROPN
ejpam-5156	3	39	,	,	PUNCT
ejpam-5156	3	40	8710	8710	NUM
ejpam-5156	3	41	maramag	maramag	NOUN
ejpam-5156	3	42	,	,	PUNCT
ejpam-5156	3	43	bukidnon	bukidnon	NOUN
ejpam-5156	3	44	,	,	PUNCT
ejpam-5156	3	45	philippines	philippine	NOUN
ejpam-5156	3	46	abstract	abstract	ADJ
ejpam-5156	3	47	.	.	PUNCT
ejpam-5156	4	1	a	a	DET
ejpam-5156	4	2	defensive	defensive	ADJ
ejpam-5156	4	3	alliance	alliance	NOUN
ejpam-5156	4	4	in	in	ADP
ejpam-5156	4	5	a	a	DET
ejpam-5156	4	6	graph	graph	NOUN
ejpam-5156	4	7	g	g	NOUN
ejpam-5156	4	8	is	be	AUX
ejpam-5156	4	9	a	a	DET
ejpam-5156	4	10	nonempty	nonempty	ADJ
ejpam-5156	4	11	set	set	NOUN
ejpam-5156	4	12	of	of	ADP
ejpam-5156	4	13	vertices	vertex	NOUN
ejpam-5156	4	14	s	s	PART
ejpam-5156	4	15	⊆	⊆	NUM
ejpam-5156	4	16	v	v	NOUN
ejpam-5156	4	17	(	(	PUNCT
ejpam-5156	4	18	g	g	NOUN
ejpam-5156	4	19	)	)	PUNCT
ejpam-5156	4	20	such	such	ADJ
ejpam-5156	4	21	that	that	PRON
ejpam-5156	4	22	for	for	ADP
ejpam-5156	4	23	every	every	DET
ejpam-5156	4	24	vertex	vertex	NOUN
ejpam-5156	4	25	v	v	ADP
ejpam-5156	4	26	∈	∈	PROPN
ejpam-5156	4	27	s	s	NOUN
ejpam-5156	4	28	,	,	PUNCT
ejpam-5156	4	29	|n	|n	X
ejpam-5156	5	1	[	[	X
ejpam-5156	5	2	v	v	NOUN
ejpam-5156	5	3	]	]	X
ejpam-5156	5	4	∩	∩	X
ejpam-5156	5	5	s|	s|	VERB
ejpam-5156	5	6	≥	≥	NUM
ejpam-5156	5	7	|n(v	|n(v	ADJ
ejpam-5156	5	8	)	)	PUNCT
ejpam-5156	5	9	∩	∩	NOUN
ejpam-5156	5	10	(	(	PUNCT
ejpam-5156	5	11	v	v	NOUN
ejpam-5156	5	12	(	(	PUNCT
ejpam-5156	5	13	g)∖	g)∖	PROPN
ejpam-5156	5	14	s)|	s)|	PROPN
ejpam-5156	5	15	.	.	PUNCT
ejpam-5156	6	1	a	a	DET
ejpam-5156	6	2	defensive	defensive	ADJ
ejpam-5156	6	3	alliance	alliance	NOUN
ejpam-5156	6	4	s	s	PART
ejpam-5156	6	5	is	be	AUX
ejpam-5156	6	6	called	call	VERB
ejpam-5156	6	7	global	global	ADJ
ejpam-5156	6	8	if	if	SCONJ
ejpam-5156	6	9	every	every	DET
ejpam-5156	6	10	vertex	vertex	NOUN
ejpam-5156	6	11	in	in	ADP
ejpam-5156	6	12	v	v	NOUN
ejpam-5156	6	13	(	(	PUNCT
ejpam-5156	6	14	g)∖	g)∖	PROPN
ejpam-5156	6	15	s	s	PROPN
ejpam-5156	6	16	is	be	AUX
ejpam-5156	6	17	adjacent	adjacent	ADJ
ejpam-5156	6	18	to	to	ADP
ejpam-5156	6	19	at	at	ADV
ejpam-5156	6	20	least	least	ADV
ejpam-5156	6	21	one	one	NUM
ejpam-5156	6	22	member	member	NOUN
ejpam-5156	6	23	of	of	ADP
ejpam-5156	6	24	the	the	DET
ejpam-5156	6	25	alliance	alliance	NOUN
ejpam-5156	6	26	s.	s.	PROPN
ejpam-5156	6	27	in	in	ADP
ejpam-5156	6	28	this	this	DET
ejpam-5156	6	29	paper	paper	NOUN
ejpam-5156	6	30	,	,	PUNCT
ejpam-5156	6	31	the	the	DET
ejpam-5156	6	32	concept	concept	NOUN
ejpam-5156	6	33	of	of	ADP
ejpam-5156	6	34	restrained	restrained	ADJ
ejpam-5156	6	35	global	global	ADJ
ejpam-5156	6	36	defensive	defensive	ADJ
ejpam-5156	6	37	alliance	alliance	NOUN
ejpam-5156	6	38	in	in	ADP
ejpam-5156	6	39	graphs	graph	NOUN
ejpam-5156	6	40	was	be	AUX
ejpam-5156	6	41	introduced	introduce	VERB
ejpam-5156	6	42	.	.	PUNCT
ejpam-5156	7	1	in	in	ADP
ejpam-5156	7	2	particular	particular	ADJ
ejpam-5156	7	3	,	,	PUNCT
ejpam-5156	7	4	a	a	DET
ejpam-5156	7	5	global	global	ADJ
ejpam-5156	7	6	defensive	defensive	ADJ
ejpam-5156	7	7	alliance	alliance	NOUN
ejpam-5156	7	8	s	s	PART
ejpam-5156	7	9	is	be	AUX
ejpam-5156	7	10	a	a	DET
ejpam-5156	7	11	restrained	restrained	ADJ
ejpam-5156	7	12	global	global	ADJ
ejpam-5156	7	13	defensive	defensive	ADJ
ejpam-5156	7	14	alliance	alliance	NOUN
ejpam-5156	7	15	if	if	SCONJ
ejpam-5156	7	16	the	the	DET
ejpam-5156	7	17	induced	induced	ADJ
ejpam-5156	7	18	subgraph	subgraph	NOUN
ejpam-5156	7	19	of	of	ADP
ejpam-5156	7	20	v	v	NUM
ejpam-5156	7	21	∖	∖	X
ejpam-5156	7	22	s	s	PART
ejpam-5156	7	23	has	have	VERB
ejpam-5156	7	24	no	no	DET
ejpam-5156	7	25	isolated	isolated	ADJ
ejpam-5156	7	26	vertex	vertex	NOUN
ejpam-5156	7	27	.	.	PUNCT
ejpam-5156	8	1	here	here	ADV
ejpam-5156	8	2	,	,	PUNCT
ejpam-5156	8	3	some	some	DET
ejpam-5156	8	4	properties	property	NOUN
ejpam-5156	8	5	of	of	ADP
ejpam-5156	8	6	this	this	DET
ejpam-5156	8	7	alliance	alliance	NOUN
ejpam-5156	8	8	were	be	AUX
ejpam-5156	8	9	identified	identify	VERB
ejpam-5156	8	10	,	,	PUNCT
ejpam-5156	8	11	and	and	CCONJ
ejpam-5156	8	12	its	its	PRON
ejpam-5156	8	13	bounds	bound	NOUN
ejpam-5156	8	14	were	be	AUX
ejpam-5156	8	15	also	also	ADV
ejpam-5156	8	16	determined	determine	VERB
ejpam-5156	8	17	.	.	PUNCT
ejpam-5156	9	1	in	in	ADP
ejpam-5156	9	2	addition	addition	NOUN
ejpam-5156	9	3	,	,	PUNCT
ejpam-5156	9	4	the	the	DET
ejpam-5156	9	5	restrained	restrain	VERB
ejpam-5156	9	6	global	global	ADJ
ejpam-5156	9	7	defensive	defensive	ADJ
ejpam-5156	9	8	alliance	alliance	NOUN
ejpam-5156	9	9	number	number	NOUN
ejpam-5156	9	10	was	be	AUX
ejpam-5156	9	11	also	also	ADV
ejpam-5156	9	12	formulated	formulate	VERB
ejpam-5156	9	13	,	,	PUNCT
ejpam-5156	9	14	along	along	ADP
ejpam-5156	9	15	with	with	ADP
ejpam-5156	9	16	characterizations	characterization	NOUN
ejpam-5156	9	17	of	of	ADP
ejpam-5156	9	18	some	some	DET
ejpam-5156	9	19	special	special	ADJ
ejpam-5156	9	20	classes	class	NOUN
ejpam-5156	9	21	of	of	ADP
ejpam-5156	9	22	graphs	graph	NOUN
ejpam-5156	9	23	,	,	PUNCT
ejpam-5156	9	24	specifically	specifically	ADV
ejpam-5156	9	25	complete	complete	ADJ
ejpam-5156	9	26	,	,	PUNCT
ejpam-5156	9	27	complete	complete	ADJ
ejpam-5156	9	28	bipartite	bipartite	NOUN
ejpam-5156	9	29	,	,	PUNCT
ejpam-5156	9	30	and	and	CCONJ
ejpam-5156	9	31	path	path	NOUN
ejpam-5156	9	32	graphs	graph	NOUN
ejpam-5156	9	33	.	.	PUNCT
ejpam-5156	10	1	2020	2020	NUM
ejpam-5156	10	2	mathematics	mathematic	NOUN
ejpam-5156	10	3	subject	subject	NOUN
ejpam-5156	10	4	classifications	classification	NOUN
ejpam-5156	10	5	:	:	PUNCT
ejpam-5156	10	6	05c69	05c69	X
ejpam-5156	10	7	key	key	ADJ
ejpam-5156	10	8	words	word	NOUN
ejpam-5156	10	9	and	and	CCONJ
ejpam-5156	10	10	phrases	phrase	NOUN
ejpam-5156	10	11	:	:	PUNCT
ejpam-5156	10	12	restrained	restrained	ADJ
ejpam-5156	10	13	domination	domination	NOUN
ejpam-5156	10	14	,	,	PUNCT
ejpam-5156	10	15	defensive	defensive	ADJ
ejpam-5156	10	16	alliance	alliance	NOUN
ejpam-5156	10	17	,	,	PUNCT
ejpam-5156	10	18	global	global	ADJ
ejpam-5156	10	19	defensive	defensive	ADJ
ejpam-5156	10	20	alliance	alliance	NOUN
ejpam-5156	10	21	,	,	PUNCT
ejpam-5156	10	22	restrained	restrain	VERB
ejpam-5156	10	23	global	global	ADJ
ejpam-5156	10	24	defensive	defensive	ADJ
ejpam-5156	10	25	alliance	alliance	NOUN
ejpam-5156	10	26	1	1	NUM
ejpam-5156	10	27	.	.	PUNCT
ejpam-5156	11	1	introduction	introduction	NOUN
ejpam-5156	11	2	an	an	DET
ejpam-5156	11	3	alliance	alliance	NOUN
ejpam-5156	11	4	refers	refer	VERB
ejpam-5156	11	5	to	to	ADP
ejpam-5156	11	6	a	a	DET
ejpam-5156	11	7	gathering	gathering	NOUN
ejpam-5156	11	8	of	of	ADP
ejpam-5156	11	9	individuals	individual	NOUN
ejpam-5156	11	10	,	,	PUNCT
ejpam-5156	11	11	organizations	organization	NOUN
ejpam-5156	11	12	,	,	PUNCT
ejpam-5156	11	13	or	or	CCONJ
ejpam-5156	11	14	states	state	NOUN
ejpam-5156	11	15	aimed	aim	VERB
ejpam-5156	11	16	at	at	ADP
ejpam-5156	11	17	achieving	achieve	VERB
ejpam-5156	11	18	a	a	DET
ejpam-5156	11	19	common	common	ADJ
ejpam-5156	11	20	goal	goal	NOUN
ejpam-5156	11	21	,	,	PUNCT
ejpam-5156	11	22	mutual	mutual	ADJ
ejpam-5156	11	23	protection	protection	NOUN
ejpam-5156	11	24	,	,	PUNCT
ejpam-5156	11	25	or	or	CCONJ
ejpam-5156	11	26	asserting	assert	VERB
ejpam-5156	11	27	dominance	dominance	NOUN
ejpam-5156	11	28	over	over	ADP
ejpam-5156	11	29	those	those	PRON
ejpam-5156	11	30	outside	outside	ADP
ejpam-5156	11	31	the	the	DET
ejpam-5156	11	32	alliance	alliance	NOUN
ejpam-5156	11	33	.	.	PUNCT
ejpam-5156	12	1	for	for	ADP
ejpam-5156	12	2	this	this	DET
ejpam-5156	12	3	reason	reason	NOUN
ejpam-5156	12	4	,	,	PUNCT
ejpam-5156	12	5	kristiansen	kristiansen	NOUN
ejpam-5156	12	6	and	and	CCONJ
ejpam-5156	12	7	colleagues	colleague	NOUN
ejpam-5156	12	8	explored	explore	VERB
ejpam-5156	12	9	and	and	CCONJ
ejpam-5156	12	10	developed	develop	VERB
ejpam-5156	12	11	defensive	defensive	ADJ
ejpam-5156	12	12	and	and	CCONJ
ejpam-5156	12	13	offensive	offensive	ADJ
ejpam-5156	12	14	alliances	alliance	NOUN
ejpam-5156	12	15	in	in	ADP
ejpam-5156	12	16	the	the	DET
ejpam-5156	12	17	graphs	graph	NOUN
ejpam-5156	12	18	[	[	X
ejpam-5156	12	19	12	12	NUM
ejpam-5156	12	20	]	]	PUNCT
ejpam-5156	12	21	.	.	PUNCT
ejpam-5156	13	1	in	in	ADP
ejpam-5156	13	2	defensive	defensive	ADJ
ejpam-5156	13	3	alliances	alliance	NOUN
ejpam-5156	13	4	,	,	PUNCT
ejpam-5156	13	5	the	the	DET
ejpam-5156	13	6	collaboration	collaboration	NOUN
ejpam-5156	13	7	of	of	ADP
ejpam-5156	13	8	nodes	node	NOUN
ejpam-5156	13	9	or	or	CCONJ
ejpam-5156	13	10	entities	entity	NOUN
ejpam-5156	13	11	achieved	achieve	VERB
ejpam-5156	13	12	mutual	mutual	ADJ
ejpam-5156	13	13	security	security	NOUN
ejpam-5156	13	14	and	and	CCONJ
ejpam-5156	13	15	protection	protection	NOUN
ejpam-5156	13	16	.	.	PUNCT
ejpam-5156	14	1	they	they	PRON
ejpam-5156	14	2	established	establish	VERB
ejpam-5156	14	3	resilient	resilient	ADJ
ejpam-5156	14	4	networks	network	NOUN
ejpam-5156	14	5	capable	capable	ADJ
ejpam-5156	14	6	of	of	ADP
ejpam-5156	14	7	withstanding	withstand	VERB
ejpam-5156	14	8	external	external	ADJ
ejpam-5156	14	9	influences	influence	NOUN
ejpam-5156	14	10	and	and	CCONJ
ejpam-5156	14	11	pressure	pressure	NOUN
ejpam-5156	14	12	.	.	PUNCT
ejpam-5156	15	1	if	if	SCONJ
ejpam-5156	15	2	these	these	DET
ejpam-5156	15	3	alliances	alliance	NOUN
ejpam-5156	15	4	were	be	AUX
ejpam-5156	15	5	also	also	ADV
ejpam-5156	15	6	dominating	dominate	VERB
ejpam-5156	15	7	,	,	PUNCT
ejpam-5156	15	8	then	then	ADV
ejpam-5156	15	9	they	they	PRON
ejpam-5156	15	10	are	be	AUX
ejpam-5156	15	11	called	call	VERB
ejpam-5156	15	12	global	global	ADJ
ejpam-5156	15	13	defensive	defensive	ADJ
ejpam-5156	15	14	alliances	alliance	NOUN
ejpam-5156	15	15	[	[	X
ejpam-5156	15	16	11	11	NUM
ejpam-5156	15	17	]	]	PUNCT
ejpam-5156	15	18	.	.	PUNCT
ejpam-5156	16	1	global	global	ADJ
ejpam-5156	16	2	offensive	offensive	ADJ
ejpam-5156	16	3	alliances	alliance	NOUN
ejpam-5156	16	4	and	and	CCONJ
ejpam-5156	16	5	global	global	ADJ
ejpam-5156	16	6	defensive	defensive	ADJ
ejpam-5156	16	7	alliances	alliance	NOUN
ejpam-5156	16	8	have	have	AUX
ejpam-5156	16	9	been	be	AUX
ejpam-5156	16	10	a	a	DET
ejpam-5156	16	11	focus	focus	NOUN
ejpam-5156	16	12	of	of	ADP
ejpam-5156	16	13	study	study	NOUN
ejpam-5156	16	14	among	among	ADP
ejpam-5156	16	15	mathematics	mathematics	NOUN
ejpam-5156	16	16	enthusiasts	enthusiast	NOUN
ejpam-5156	16	17	.	.	PUNCT
ejpam-5156	17	1	some	some	PRON
ejpam-5156	17	2	of	of	ADP
ejpam-5156	17	3	these	these	DET
ejpam-5156	17	4	studies	study	NOUN
ejpam-5156	17	5	include	include	VERB
ejpam-5156	17	6	global	global	ADJ
ejpam-5156	17	7	offensive	offensive	ADJ
ejpam-5156	17	8	alliances	alliance	NOUN
ejpam-5156	17	9	in	in	ADP
ejpam-5156	17	10	some	some	DET
ejpam-5156	17	11	special	special	ADJ
ejpam-5156	17	12	classes	class	NOUN
ejpam-5156	17	13	of	of	ADP
ejpam-5156	17	14	graphs	graph	NOUN
ejpam-5156	17	15	in	in	ADP
ejpam-5156	17	16	2011	2011	NUM
ejpam-5156	17	17	by	by	ADP
ejpam-5156	17	18	cabahug	cabahug	NOUN
ejpam-5156	17	19	and	and	CCONJ
ejpam-5156	17	20	isla	isla	NOUN
ejpam-5156	18	1	[	[	X
ejpam-5156	18	2	3	3	NUM
ejpam-5156	18	3	]	]	PUNCT
ejpam-5156	18	4	,	,	PUNCT
ejpam-5156	18	5	global	global	ADJ
ejpam-5156	18	6	defensive	defensive	ADJ
ejpam-5156	18	7	alliances	alliance	NOUN
ejpam-5156	18	8	in	in	ADP
ejpam-5156	18	9	the	the	DET
ejpam-5156	18	10	lexicographic	lexicographic	ADJ
ejpam-5156	18	11	product	product	NOUN
ejpam-5156	18	12	of	of	ADP
ejpam-5156	18	13	paths	path	NOUN
ejpam-5156	18	14	and	and	CCONJ
ejpam-5156	18	15	cycles	cycle	NOUN
ejpam-5156	18	16	in	in	ADP
ejpam-5156	18	17	2020	2020	NUM
ejpam-5156	18	18	by	by	ADP
ejpam-5156	18	19	barbosa	barbosa	PROPN
ejpam-5156	18	20	,	,	PUNCT
ejpam-5156	18	21	dourado	dourado	NOUN
ejpam-5156	18	22	,	,	PUNCT
ejpam-5156	18	23	and	and	CCONJ
ejpam-5156	18	24	da	da	NOUN
ejpam-5156	18	25	∗corresponding	∗corresponde	VERB
ejpam-5156	18	26	author	author	NOUN
ejpam-5156	18	27	.	.	PUNCT
ejpam-5156	19	1	doi	doi	NOUN
ejpam-5156	19	2	:	:	PUNCT
ejpam-5156	19	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5156	https://doi.org/10.29020/nybg.ejpam.v17i3.5156	PROPN
ejpam-5156	19	4	email	email	NOUN
ejpam-5156	19	5	addresses	address	VERB
ejpam-5156	19	6	:	:	PUNCT
ejpam-5156	19	7	coleocint@gmail.com	coleocint@gmail.com	X
ejpam-5156	19	8	(	(	PUNCT
ejpam-5156	19	9	l.	l.	PROPN
ejpam-5156	19	10	consistente	consistente	PROPN
ejpam-5156	19	11	)	)	PUNCT
ejpam-5156	19	12	,	,	PUNCT
ejpam-5156	19	13	isaganicabahugjr@cmu.edu.ph	isaganicabahugjr@cmu.edu.ph	PROPN
ejpam-5156	19	14	(	(	PUNCT
ejpam-5156	19	15	i.	i.	PROPN
ejpam-5156	19	16	cabahug	cabahug	PROPN
ejpam-5156	19	17	,	,	PUNCT
ejpam-5156	19	18	jr	jr	PROPN
ejpam-5156	19	19	.	.	PUNCT
ejpam-5156	19	20	)	)	PUNCT
ejpam-5156	19	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5156	19	22	2196	2196	NUM
ejpam-5156	20	1	©	©	ADP
ejpam-5156	20	2	2024	2024	NUM
ejpam-5156	20	3	ejpam	ejpam	NOUN
ejpam-5156	20	4	all	all	DET
ejpam-5156	20	5	rights	right	NOUN
ejpam-5156	20	6	reserved	reserve	VERB
ejpam-5156	20	7	.	.	PUNCT
ejpam-5156	21	1	l.	l.	PROPN
ejpam-5156	21	2	consistente	consistente	PROPN
ejpam-5156	21	3	,	,	PUNCT
ejpam-5156	21	4	i.	i.	PROPN
ejpam-5156	21	5	cabahug	cabahug	PROPN
ejpam-5156	21	6	,	,	PUNCT
ejpam-5156	21	7	jr	jr	PROPN
ejpam-5156	21	8	.	.	PROPN
ejpam-5156	21	9	/	/	SYM
ejpam-5156	21	10	eur	eur	PROPN
ejpam-5156	21	11	.	.	PUNCT
ejpam-5156	22	1	j.	j.	PROPN
ejpam-5156	22	2	pure	pure	PROPN
ejpam-5156	22	3	appl	appl	PROPN
ejpam-5156	22	4	.	.	PROPN
ejpam-5156	22	5	math	math	PROPN
ejpam-5156	22	6	,	,	PUNCT
ejpam-5156	22	7	17	17	NUM
ejpam-5156	22	8	(	(	PUNCT
ejpam-5156	22	9	3	3	NUM
ejpam-5156	22	10	)	)	PUNCT
ejpam-5156	22	11	(	(	PUNCT
ejpam-5156	22	12	2024	2024	NUM
ejpam-5156	22	13	)	)	PUNCT
ejpam-5156	22	14	,	,	PUNCT
ejpam-5156	22	15	2196	2196	NUM
ejpam-5156	22	16	-	-	SYM
ejpam-5156	22	17	2209	2209	NUM
ejpam-5156	22	18	2197	2197	NUM
ejpam-5156	22	19	silva	silva	NOUN
ejpam-5156	23	1	[	[	X
ejpam-5156	23	2	1	1	NUM
ejpam-5156	23	3	]	]	PUNCT
ejpam-5156	23	4	,	,	PUNCT
ejpam-5156	23	5	and	and	CCONJ
ejpam-5156	23	6	global	global	ADJ
ejpam-5156	23	7	defensive	defensive	ADJ
ejpam-5156	23	8	k	k	NOUN
ejpam-5156	23	9	-	-	PUNCT
ejpam-5156	23	10	alliances	alliance	NOUN
ejpam-5156	23	11	in	in	ADP
ejpam-5156	23	12	directed	direct	VERB
ejpam-5156	23	13	graphs	graph	NOUN
ejpam-5156	23	14	focusing	focus	VERB
ejpam-5156	23	15	on	on	ADP
ejpam-5156	23	16	combinatorial	combinatorial	ADJ
ejpam-5156	23	17	and	and	CCONJ
ejpam-5156	23	18	computational	computational	ADJ
ejpam-5156	23	19	issues	issue	NOUN
ejpam-5156	23	20	in	in	ADP
ejpam-5156	23	21	2020	2020	NUM
ejpam-5156	23	22	by	by	ADP
ejpam-5156	23	23	mojdeh	mojdeh	NOUN
ejpam-5156	23	24	,	,	PUNCT
ejpam-5156	23	25	samadi	samadi	NOUN
ejpam-5156	23	26	,	,	PUNCT
ejpam-5156	23	27	and	and	CCONJ
ejpam-5156	23	28	yero	yero	NOUN
ejpam-5156	23	29	.	.	PUNCT
ejpam-5156	24	1	moreover	moreover	ADV
ejpam-5156	24	2	,	,	PUNCT
ejpam-5156	24	3	in	in	ADP
ejpam-5156	24	4	2022	2022	NUM
ejpam-5156	24	5	,	,	PUNCT
ejpam-5156	24	6	gaikwad	gaikwad	NOUN
ejpam-5156	24	7	and	and	CCONJ
ejpam-5156	24	8	maity	maity	NOUN
ejpam-5156	24	9	studied	study	VERB
ejpam-5156	24	10	globally	globally	ADV
ejpam-5156	24	11	minimal	minimal	ADJ
ejpam-5156	24	12	defensive	defensive	ADJ
ejpam-5156	24	13	alliances	alliance	NOUN
ejpam-5156	24	14	[	[	X
ejpam-5156	24	15	9	9	NUM
ejpam-5156	24	16	]	]	PUNCT
ejpam-5156	24	17	.	.	PUNCT
ejpam-5156	25	1	domination	domination	NOUN
ejpam-5156	25	2	in	in	ADP
ejpam-5156	25	3	graphs	graph	NOUN
ejpam-5156	25	4	is	be	AUX
ejpam-5156	25	5	a	a	DET
ejpam-5156	25	6	growing	grow	VERB
ejpam-5156	25	7	area	area	NOUN
ejpam-5156	25	8	of	of	ADP
ejpam-5156	25	9	research	research	NOUN
ejpam-5156	25	10	.	.	PUNCT
ejpam-5156	26	1	some	some	DET
ejpam-5156	26	2	recent	recent	ADJ
ejpam-5156	26	3	studies	study	NOUN
ejpam-5156	26	4	on	on	ADP
ejpam-5156	26	5	domination	domination	NOUN
ejpam-5156	26	6	can	can	AUX
ejpam-5156	26	7	be	be	AUX
ejpam-5156	26	8	found	find	VERB
ejpam-5156	26	9	in	in	ADP
ejpam-5156	26	10	[	[	X
ejpam-5156	26	11	4	4	NUM
ejpam-5156	26	12	]	]	PUNCT
ejpam-5156	26	13	,	,	PUNCT
ejpam-5156	26	14	[	[	X
ejpam-5156	26	15	6	6	NUM
ejpam-5156	26	16	]	]	PUNCT
ejpam-5156	26	17	,	,	PUNCT
ejpam-5156	26	18	and	and	CCONJ
ejpam-5156	26	19	[	[	X
ejpam-5156	26	20	14	14	NUM
ejpam-5156	26	21	]	]	PUNCT
ejpam-5156	26	22	.	.	PUNCT
ejpam-5156	27	1	on	on	ADP
ejpam-5156	27	2	the	the	DET
ejpam-5156	27	3	other	other	ADJ
ejpam-5156	27	4	hand	hand	NOUN
ejpam-5156	27	5	,	,	PUNCT
ejpam-5156	27	6	in	in	ADP
ejpam-5156	27	7	1999	1999	NUM
ejpam-5156	27	8	,	,	PUNCT
ejpam-5156	27	9	hedetniemi	hedetniemi	ADV
ejpam-5156	27	10	and	and	CCONJ
ejpam-5156	27	11	colleagues	colleague	NOUN
ejpam-5156	27	12	introduced	introduce	VERB
ejpam-5156	27	13	the	the	DET
ejpam-5156	27	14	notion	notion	NOUN
ejpam-5156	27	15	of	of	ADP
ejpam-5156	27	16	a	a	DET
ejpam-5156	27	17	restrained	restrain	VERB
ejpam-5156	27	18	dominating	dominating	NOUN
ejpam-5156	27	19	set	set	VERB
ejpam-5156	27	20	wherein	wherein	SCONJ
ejpam-5156	27	21	the	the	DET
ejpam-5156	27	22	subgraph	subgraph	NOUN
ejpam-5156	27	23	induced	induce	VERB
ejpam-5156	27	24	by	by	ADP
ejpam-5156	27	25	its	its	PRON
ejpam-5156	27	26	complement	complement	NOUN
ejpam-5156	27	27	has	have	AUX
ejpam-5156	27	28	no	no	DET
ejpam-5156	27	29	isolated	isolate	VERB
ejpam-5156	27	30	vertices	vertex	NOUN
ejpam-5156	27	31	[	[	X
ejpam-5156	27	32	7	7	NUM
ejpam-5156	27	33	]	]	PUNCT
ejpam-5156	27	34	.	.	PUNCT
ejpam-5156	28	1	some	some	DET
ejpam-5156	28	2	studies	study	NOUN
ejpam-5156	28	3	related	relate	VERB
ejpam-5156	28	4	to	to	ADP
ejpam-5156	28	5	restrained	restrained	ADJ
ejpam-5156	28	6	domination	domination	NOUN
ejpam-5156	28	7	include	include	VERB
ejpam-5156	28	8	fair	fair	ADJ
ejpam-5156	28	9	restrained	restrained	ADJ
ejpam-5156	28	10	domination	domination	NOUN
ejpam-5156	28	11	in	in	ADP
ejpam-5156	28	12	graphs	graph	NOUN
ejpam-5156	28	13	in	in	ADP
ejpam-5156	28	14	2020	2020	NUM
ejpam-5156	28	15	by	by	ADP
ejpam-5156	28	16	enriquez	enriquez	PROPN
ejpam-5156	28	17	[	[	X
ejpam-5156	28	18	8	8	NUM
ejpam-5156	28	19	]	]	PUNCT
ejpam-5156	28	20	and	and	CCONJ
ejpam-5156	28	21	restrained	restrain	VERB
ejpam-5156	28	22	double	double	ADJ
ejpam-5156	28	23	roman	roman	ADJ
ejpam-5156	28	24	domination	domination	NOUN
ejpam-5156	28	25	of	of	ADP
ejpam-5156	28	26	a	a	DET
ejpam-5156	28	27	graph	graph	NOUN
ejpam-5156	28	28	in	in	ADP
ejpam-5156	28	29	2022	2022	NUM
ejpam-5156	28	30	by	by	ADP
ejpam-5156	28	31	mojdeh	mojdeh	NOUN
ejpam-5156	28	32	,	,	PUNCT
ejpam-5156	28	33	masoumi	masoumi	NOUN
ejpam-5156	28	34	,	,	PUNCT
ejpam-5156	28	35	and	and	CCONJ
ejpam-5156	28	36	volkmann	volkmann	PROPN
ejpam-5156	29	1	[	[	X
ejpam-5156	29	2	13	13	NUM
ejpam-5156	29	3	]	]	PUNCT
ejpam-5156	29	4	.	.	PUNCT
ejpam-5156	30	1	although	although	SCONJ
ejpam-5156	30	2	global	global	ADJ
ejpam-5156	30	3	defensive	defensive	ADJ
ejpam-5156	30	4	alliance	alliance	NOUN
ejpam-5156	30	5	forms	form	VERB
ejpam-5156	30	6	a	a	DET
ejpam-5156	30	7	defensive	defensive	ADJ
ejpam-5156	30	8	alliance	alliance	NOUN
ejpam-5156	30	9	that	that	PRON
ejpam-5156	30	10	is	be	AUX
ejpam-5156	30	11	also	also	ADV
ejpam-5156	30	12	a	a	DET
ejpam-5156	30	13	dominating	dominating	NOUN
ejpam-5156	30	14	set	set	NOUN
ejpam-5156	30	15	,	,	PUNCT
ejpam-5156	30	16	it	it	PRON
ejpam-5156	30	17	could	could	AUX
ejpam-5156	30	18	not	not	PART
ejpam-5156	30	19	guarantee	guarantee	VERB
ejpam-5156	30	20	an	an	DET
ejpam-5156	30	21	alliance	alliance	NOUN
ejpam-5156	30	22	where	where	SCONJ
ejpam-5156	30	23	non	non	NOUN
ejpam-5156	30	24	-	-	ADJ
ejpam-5156	30	25	members	member	NOUN
ejpam-5156	30	26	were	be	AUX
ejpam-5156	30	27	also	also	ADV
ejpam-5156	30	28	adjacent	adjacent	ADJ
ejpam-5156	30	29	to	to	ADP
ejpam-5156	30	30	at	at	ADV
ejpam-5156	30	31	least	least	ADV
ejpam-5156	30	32	one	one	NUM
ejpam-5156	30	33	non	non	ADJ
ejpam-5156	30	34	-	-	NOUN
ejpam-5156	30	35	member	member	NOUN
ejpam-5156	30	36	.	.	PUNCT
ejpam-5156	31	1	to	to	PART
ejpam-5156	31	2	address	address	VERB
ejpam-5156	31	3	this	this	PRON
ejpam-5156	31	4	,	,	PUNCT
ejpam-5156	31	5	a	a	DET
ejpam-5156	31	6	new	new	ADJ
ejpam-5156	31	7	type	type	NOUN
ejpam-5156	31	8	of	of	ADP
ejpam-5156	31	9	alliance	alliance	NOUN
ejpam-5156	31	10	had	have	VERB
ejpam-5156	31	11	to	to	PART
ejpam-5156	31	12	be	be	AUX
ejpam-5156	31	13	formed	form	VERB
ejpam-5156	31	14	.	.	PUNCT
ejpam-5156	32	1	with	with	ADP
ejpam-5156	32	2	this	this	PRON
ejpam-5156	32	3	in	in	ADP
ejpam-5156	32	4	mind	mind	NOUN
ejpam-5156	32	5	,	,	PUNCT
ejpam-5156	32	6	the	the	DET
ejpam-5156	32	7	authors	author	NOUN
ejpam-5156	32	8	decided	decide	VERB
ejpam-5156	32	9	to	to	PART
ejpam-5156	32	10	introduce	introduce	VERB
ejpam-5156	32	11	restrained	restrained	ADJ
ejpam-5156	32	12	global	global	ADJ
ejpam-5156	32	13	defensive	defensive	ADJ
ejpam-5156	32	14	alliances	alliance	NOUN
ejpam-5156	32	15	in	in	ADP
ejpam-5156	32	16	graphs	graph	NOUN
ejpam-5156	32	17	.	.	PUNCT
ejpam-5156	33	1	using	use	VERB
ejpam-5156	33	2	this	this	DET
ejpam-5156	33	3	alliance	alliance	NOUN
ejpam-5156	33	4	as	as	ADP
ejpam-5156	33	5	a	a	DET
ejpam-5156	33	6	basis	basis	NOUN
ejpam-5156	33	7	,	,	PUNCT
ejpam-5156	33	8	the	the	DET
ejpam-5156	33	9	authors	author	NOUN
ejpam-5156	33	10	aim	aim	VERB
ejpam-5156	33	11	to	to	PART
ejpam-5156	33	12	contribute	contribute	VERB
ejpam-5156	33	13	new	new	ADJ
ejpam-5156	33	14	insights	insight	NOUN
ejpam-5156	33	15	to	to	ADP
ejpam-5156	33	16	applications	application	NOUN
ejpam-5156	33	17	related	relate	VERB
ejpam-5156	33	18	to	to	ADP
ejpam-5156	33	19	strategic	strategic	ADJ
ejpam-5156	33	20	interactions	interaction	NOUN
ejpam-5156	33	21	and	and	CCONJ
ejpam-5156	33	22	mutual	mutual	ADJ
ejpam-5156	33	23	support	support	NOUN
ejpam-5156	33	24	within	within	ADP
ejpam-5156	33	25	networks	network	NOUN
ejpam-5156	33	26	by	by	ADP
ejpam-5156	33	27	establishing	establish	VERB
ejpam-5156	33	28	certain	certain	ADJ
ejpam-5156	33	29	characterizations	characterization	NOUN
ejpam-5156	33	30	,	,	PUNCT
ejpam-5156	33	31	developing	develop	VERB
ejpam-5156	33	32	formulas	formula	NOUN
ejpam-5156	33	33	for	for	ADP
ejpam-5156	33	34	the	the	DET
ejpam-5156	33	35	restrained	restrain	VERB
ejpam-5156	33	36	global	global	ADJ
ejpam-5156	33	37	defensive	defensive	ADJ
ejpam-5156	33	38	alliance	alliance	NOUN
ejpam-5156	33	39	number	number	NOUN
ejpam-5156	33	40	,	,	PUNCT
ejpam-5156	33	41	and	and	CCONJ
ejpam-5156	33	42	determining	determine	VERB
ejpam-5156	33	43	some	some	PRON
ejpam-5156	33	44	of	of	ADP
ejpam-5156	33	45	its	its	PRON
ejpam-5156	33	46	inherent	inherent	ADJ
ejpam-5156	33	47	properties	property	NOUN
ejpam-5156	33	48	on	on	ADP
ejpam-5156	33	49	complete	complete	ADJ
ejpam-5156	33	50	,	,	PUNCT
ejpam-5156	33	51	complete	complete	ADJ
ejpam-5156	33	52	bipartite	bipartite	NOUN
ejpam-5156	33	53	,	,	PUNCT
ejpam-5156	33	54	and	and	CCONJ
ejpam-5156	33	55	path	path	NOUN
ejpam-5156	33	56	graphs	graph	NOUN
ejpam-5156	33	57	.	.	PUNCT
ejpam-5156	34	1	2	2	X
ejpam-5156	34	2	.	.	X
ejpam-5156	34	3	terminology	terminology	NOUN
ejpam-5156	34	4	and	and	CCONJ
ejpam-5156	34	5	notation	notation	NOUN
ejpam-5156	34	6	a	a	DET
ejpam-5156	34	7	graph	graph	NOUN
ejpam-5156	34	8	g	g	PROPN
ejpam-5156	34	9	is	be	AUX
ejpam-5156	34	10	a	a	DET
ejpam-5156	34	11	finite	finite	NOUN
ejpam-5156	34	12	nonempty	nonempty	ADV
ejpam-5156	34	13	set	set	VERB
ejpam-5156	34	14	v	v	NOUN
ejpam-5156	34	15	(	(	PUNCT
ejpam-5156	34	16	g	g	NOUN
ejpam-5156	34	17	)	)	PUNCT
ejpam-5156	34	18	of	of	ADP
ejpam-5156	34	19	objects	object	NOUN
ejpam-5156	34	20	called	call	VERB
ejpam-5156	34	21	vertices	vertex	NOUN
ejpam-5156	34	22	(	(	PUNCT
ejpam-5156	34	23	the	the	DET
ejpam-5156	34	24	singular	singular	NOUN
ejpam-5156	34	25	is	be	AUX
ejpam-5156	34	26	vertex	vertex	NOUN
ejpam-5156	34	27	)	)	PUNCT
ejpam-5156	34	28	together	together	ADV
ejpam-5156	34	29	with	with	ADP
ejpam-5156	34	30	a	a	DET
ejpam-5156	34	31	possibly	possibly	ADV
ejpam-5156	34	32	empty	empty	ADJ
ejpam-5156	34	33	set	set	VERB
ejpam-5156	34	34	e(g	e(g	NOUN
ejpam-5156	34	35	)	)	PUNCT
ejpam-5156	34	36	of	of	ADP
ejpam-5156	34	37	2	2	NUM
ejpam-5156	34	38	-	-	PUNCT
ejpam-5156	34	39	element	element	NOUN
ejpam-5156	34	40	subsets	subset	NOUN
ejpam-5156	34	41	of	of	ADP
ejpam-5156	34	42	v	v	NOUN
ejpam-5156	34	43	(	(	PUNCT
ejpam-5156	34	44	g	g	NOUN
ejpam-5156	34	45	)	)	PUNCT
ejpam-5156	34	46	called	call	VERB
ejpam-5156	34	47	edges	edge	NOUN
ejpam-5156	34	48	.	.	PUNCT
ejpam-5156	35	1	here	here	ADV
ejpam-5156	35	2	,	,	PUNCT
ejpam-5156	35	3	v	v	X
ejpam-5156	35	4	(	(	PUNCT
ejpam-5156	35	5	g	g	NOUN
ejpam-5156	35	6	)	)	PUNCT
ejpam-5156	35	7	is	be	AUX
ejpam-5156	35	8	the	the	DET
ejpam-5156	35	9	vertex	vertex	NOUN
ejpam-5156	35	10	set	set	NOUN
ejpam-5156	35	11	of	of	ADP
ejpam-5156	35	12	a	a	DET
ejpam-5156	35	13	graph	graph	NOUN
ejpam-5156	35	14	g	g	NOUN
ejpam-5156	35	15	while	while	SCONJ
ejpam-5156	35	16	e(g	e(g	PROPN
ejpam-5156	35	17	)	)	PUNCT
ejpam-5156	35	18	is	be	AUX
ejpam-5156	35	19	the	the	DET
ejpam-5156	35	20	edge	edge	NOUN
ejpam-5156	35	21	set	set	NOUN
ejpam-5156	35	22	of	of	ADP
ejpam-5156	35	23	graph	graph	NOUN
ejpam-5156	35	24	g	g	PROPN
ejpam-5156	35	25	[	[	X
ejpam-5156	35	26	5	5	NUM
ejpam-5156	35	27	]	]	PUNCT
ejpam-5156	35	28	.	.	PUNCT
ejpam-5156	36	1	an	an	DET
ejpam-5156	36	2	edge	edge	NOUN
ejpam-5156	36	3	joining	join	VERB
ejpam-5156	36	4	a	a	DET
ejpam-5156	36	5	vertex	vertex	NOUN
ejpam-5156	36	6	to	to	ADP
ejpam-5156	36	7	itself	itself	PRON
ejpam-5156	36	8	is	be	AUX
ejpam-5156	36	9	called	call	VERB
ejpam-5156	36	10	a	a	DET
ejpam-5156	36	11	loop	loop	NOUN
ejpam-5156	36	12	.	.	PUNCT
ejpam-5156	37	1	two	two	NUM
ejpam-5156	37	2	or	or	CCONJ
ejpam-5156	37	3	more	more	ADJ
ejpam-5156	37	4	edges	edge	NOUN
ejpam-5156	37	5	that	that	PRON
ejpam-5156	37	6	join	join	VERB
ejpam-5156	37	7	the	the	DET
ejpam-5156	37	8	same	same	ADJ
ejpam-5156	37	9	pair	pair	NOUN
ejpam-5156	37	10	of	of	ADP
ejpam-5156	37	11	distinct	distinct	ADJ
ejpam-5156	37	12	vertices	vertex	NOUN
ejpam-5156	37	13	are	be	AUX
ejpam-5156	37	14	called	call	VERB
ejpam-5156	37	15	parallel	parallel	ADJ
ejpam-5156	37	16	edges	edge	NOUN
ejpam-5156	37	17	.	.	PUNCT
ejpam-5156	38	1	if	if	SCONJ
ejpam-5156	38	2	a	a	DET
ejpam-5156	38	3	graph	graph	NOUN
ejpam-5156	38	4	has	have	VERB
ejpam-5156	38	5	no	no	DET
ejpam-5156	38	6	loops	loop	NOUN
ejpam-5156	38	7	and	and	CCONJ
ejpam-5156	38	8	parallel	parallel	ADJ
ejpam-5156	38	9	edges	edge	NOUN
ejpam-5156	38	10	then	then	ADV
ejpam-5156	38	11	it	it	PRON
ejpam-5156	38	12	is	be	AUX
ejpam-5156	38	13	a	a	DET
ejpam-5156	38	14	simple	simple	ADJ
ejpam-5156	38	15	graph	graph	NOUN
ejpam-5156	38	16	.	.	PUNCT
ejpam-5156	39	1	the	the	DET
ejpam-5156	39	2	order	order	NOUN
ejpam-5156	39	3	of	of	ADP
ejpam-5156	39	4	a	a	DET
ejpam-5156	39	5	graph	graph	NOUN
ejpam-5156	39	6	g	g	NOUN
ejpam-5156	39	7	refers	refer	VERB
ejpam-5156	39	8	to	to	ADP
ejpam-5156	39	9	the	the	DET
ejpam-5156	39	10	number	number	NOUN
ejpam-5156	39	11	of	of	ADP
ejpam-5156	39	12	vertices	vertex	NOUN
ejpam-5156	39	13	in	in	ADP
ejpam-5156	39	14	g	g	PROPN
ejpam-5156	39	15	while	while	SCONJ
ejpam-5156	39	16	the	the	DET
ejpam-5156	39	17	size	size	NOUN
ejpam-5156	39	18	of	of	ADP
ejpam-5156	39	19	a	a	DET
ejpam-5156	39	20	graph	graph	NOUN
ejpam-5156	39	21	g	g	NOUN
ejpam-5156	39	22	refers	refer	VERB
ejpam-5156	39	23	to	to	ADP
ejpam-5156	39	24	the	the	DET
ejpam-5156	39	25	number	number	NOUN
ejpam-5156	39	26	of	of	ADP
ejpam-5156	39	27	edges	edge	NOUN
ejpam-5156	39	28	in	in	ADP
ejpam-5156	39	29	g	g	PROPN
ejpam-5156	39	30	[	[	X
ejpam-5156	39	31	5	5	NUM
ejpam-5156	39	32	]	]	PUNCT
ejpam-5156	39	33	.	.	PUNCT
ejpam-5156	40	1	if	if	SCONJ
ejpam-5156	40	2	uv	uv	NOUN
ejpam-5156	40	3	is	be	AUX
ejpam-5156	40	4	an	an	DET
ejpam-5156	40	5	edge	edge	NOUN
ejpam-5156	40	6	of	of	ADP
ejpam-5156	40	7	a	a	DET
ejpam-5156	40	8	graph	graph	NOUN
ejpam-5156	40	9	g	g	NOUN
ejpam-5156	40	10	,	,	PUNCT
ejpam-5156	40	11	then	then	ADV
ejpam-5156	40	12	u	u	NOUN
ejpam-5156	40	13	and	and	CCONJ
ejpam-5156	40	14	v	v	NOUN
ejpam-5156	40	15	are	be	AUX
ejpam-5156	40	16	adjacent	adjacent	ADJ
ejpam-5156	40	17	vertices	vertex	NOUN
ejpam-5156	40	18	.	.	PUNCT
ejpam-5156	41	1	two	two	NUM
ejpam-5156	41	2	adjacent	adjacent	ADJ
ejpam-5156	41	3	vertices	vertex	NOUN
ejpam-5156	41	4	are	be	AUX
ejpam-5156	41	5	referred	refer	VERB
ejpam-5156	41	6	to	to	ADP
ejpam-5156	41	7	as	as	ADP
ejpam-5156	41	8	neighbors	neighbor	NOUN
ejpam-5156	41	9	of	of	ADP
ejpam-5156	41	10	each	each	DET
ejpam-5156	41	11	other	other	ADJ
ejpam-5156	41	12	.	.	PUNCT
ejpam-5156	42	1	the	the	DET
ejpam-5156	42	2	set	set	NOUN
ejpam-5156	42	3	of	of	ADP
ejpam-5156	42	4	neighbors	neighbor	NOUN
ejpam-5156	42	5	of	of	ADP
ejpam-5156	42	6	a	a	DET
ejpam-5156	42	7	vertex	vertex	NOUN
ejpam-5156	42	8	v	v	NOUN
ejpam-5156	42	9	is	be	AUX
ejpam-5156	42	10	called	call	VERB
ejpam-5156	42	11	the	the	DET
ejpam-5156	42	12	open	open	ADJ
ejpam-5156	42	13	neighborhood	neighborhood	NOUN
ejpam-5156	42	14	of	of	ADP
ejpam-5156	42	15	v(or	v(or	NOUN
ejpam-5156	42	16	simply	simply	ADV
ejpam-5156	42	17	the	the	DET
ejpam-5156	42	18	neighborhood	neighborhood	NOUN
ejpam-5156	42	19	of	of	ADP
ejpam-5156	42	20	v	v	NOUN
ejpam-5156	42	21	)	)	PUNCT
ejpam-5156	42	22	and	and	CCONJ
ejpam-5156	42	23	is	be	AUX
ejpam-5156	42	24	denoted	denote	VERB
ejpam-5156	42	25	by	by	ADP
ejpam-5156	42	26	ng(v	ng(v	NOUN
ejpam-5156	42	27	)	)	PUNCT
ejpam-5156	42	28	,	,	PUNCT
ejpam-5156	42	29	or	or	CCONJ
ejpam-5156	42	30	n(v	n(v	PROPN
ejpam-5156	42	31	)	)	PUNCT
ejpam-5156	42	32	if	if	SCONJ
ejpam-5156	42	33	the	the	DET
ejpam-5156	42	34	graph	graph	NOUN
ejpam-5156	42	35	g	g	NOUN
ejpam-5156	42	36	is	be	AUX
ejpam-5156	42	37	understood	understand	VERB
ejpam-5156	42	38	.	.	PUNCT
ejpam-5156	43	1	the	the	DET
ejpam-5156	43	2	set	set	ADJ
ejpam-5156	43	3	n	n	PROPN
ejpam-5156	43	4	[	[	X
ejpam-5156	43	5	v	v	X
ejpam-5156	43	6	]	]	X
ejpam-5156	43	7	=	=	SYM
ejpam-5156	43	8	n(υ	n(υ	NOUN
ejpam-5156	43	9	)	)	PUNCT
ejpam-5156	43	10	⋃	⋃	NOUN
ejpam-5156	43	11	{	{	PUNCT
ejpam-5156	43	12	υ	υ	NOUN
ejpam-5156	43	13	}	}	PUNCT
ejpam-5156	43	14	is	be	AUX
ejpam-5156	43	15	called	call	VERB
ejpam-5156	43	16	the	the	DET
ejpam-5156	43	17	closed	closed	ADJ
ejpam-5156	43	18	neighborhood	neighborhood	NOUN
ejpam-5156	43	19	of	of	ADP
ejpam-5156	43	20	v	v	NOUN
ejpam-5156	43	21	[	[	X
ejpam-5156	43	22	5	5	NUM
ejpam-5156	43	23	]	]	PUNCT
ejpam-5156	43	24	.	.	PUNCT
ejpam-5156	44	1	the	the	DET
ejpam-5156	44	2	degree	degree	NOUN
ejpam-5156	44	3	of	of	ADP
ejpam-5156	44	4	a	a	DET
ejpam-5156	44	5	vertex	vertex	NOUN
ejpam-5156	44	6	v	v	NOUN
ejpam-5156	44	7	in	in	ADP
ejpam-5156	44	8	a	a	DET
ejpam-5156	44	9	graph	graph	NOUN
ejpam-5156	44	10	g	g	NOUN
ejpam-5156	44	11	,	,	PUNCT
ejpam-5156	44	12	denoted	denote	VERB
ejpam-5156	44	13	by	by	ADP
ejpam-5156	44	14	deg	deg	PROPN
ejpam-5156	44	15	v	v	PROPN
ejpam-5156	44	16	,	,	PUNCT
ejpam-5156	44	17	is	be	AUX
ejpam-5156	44	18	the	the	DET
ejpam-5156	44	19	number	number	NOUN
ejpam-5156	44	20	of	of	ADP
ejpam-5156	44	21	vertices	vertex	NOUN
ejpam-5156	44	22	in	in	ADP
ejpam-5156	44	23	g	g	PROPN
ejpam-5156	44	24	that	that	PRON
ejpam-5156	44	25	are	be	AUX
ejpam-5156	44	26	adjacent	adjacent	ADJ
ejpam-5156	44	27	to	to	ADP
ejpam-5156	44	28	v.	v.	ADP
ejpam-5156	44	29	the	the	DET
ejpam-5156	44	30	largest	large	ADJ
ejpam-5156	44	31	degree	degree	NOUN
ejpam-5156	44	32	among	among	ADP
ejpam-5156	44	33	the	the	DET
ejpam-5156	44	34	vertices	vertex	NOUN
ejpam-5156	44	35	of	of	ADP
ejpam-5156	44	36	g	g	PROPN
ejpam-5156	44	37	is	be	AUX
ejpam-5156	44	38	called	call	VERB
ejpam-5156	44	39	the	the	DET
ejpam-5156	44	40	maximum	maximum	ADJ
ejpam-5156	44	41	degree	degree	NOUN
ejpam-5156	44	42	of	of	ADP
ejpam-5156	44	43	g	g	NOUN
ejpam-5156	44	44	,	,	PUNCT
ejpam-5156	44	45	denoted	denote	VERB
ejpam-5156	44	46	by	by	ADP
ejpam-5156	44	47	△	△	PROPN
ejpam-5156	44	48	(	(	PUNCT
ejpam-5156	44	49	g	g	NOUN
ejpam-5156	44	50	)	)	PUNCT
ejpam-5156	44	51	,	,	PUNCT
ejpam-5156	44	52	while	while	SCONJ
ejpam-5156	44	53	the	the	DET
ejpam-5156	44	54	smallest	small	ADJ
ejpam-5156	44	55	degree	degree	NOUN
ejpam-5156	44	56	among	among	ADP
ejpam-5156	44	57	the	the	DET
ejpam-5156	44	58	vertices	vertex	NOUN
ejpam-5156	44	59	of	of	ADP
ejpam-5156	44	60	g	g	PROPN
ejpam-5156	44	61	is	be	AUX
ejpam-5156	44	62	called	call	VERB
ejpam-5156	44	63	the	the	DET
ejpam-5156	44	64	minimum	minimum	NOUN
ejpam-5156	44	65	degree	degree	NOUN
ejpam-5156	44	66	of	of	ADP
ejpam-5156	44	67	g	g	NOUN
ejpam-5156	44	68	,	,	PUNCT
ejpam-5156	44	69	denoted	denote	VERB
ejpam-5156	44	70	by	by	ADP
ejpam-5156	44	71	δ(g	δ(g	NOUN
ejpam-5156	44	72	)	)	PUNCT
ejpam-5156	45	1	[	[	X
ejpam-5156	45	2	5	5	NUM
ejpam-5156	45	3	]	]	PUNCT
ejpam-5156	45	4	.	.	PUNCT
ejpam-5156	46	1	a	a	DET
ejpam-5156	46	2	vertex	vertex	NOUN
ejpam-5156	46	3	of	of	ADP
ejpam-5156	46	4	degree	degree	NOUN
ejpam-5156	46	5	0	0	PUNCT
ejpam-5156	46	6	is	be	AUX
ejpam-5156	46	7	referred	refer	VERB
ejpam-5156	46	8	to	to	ADP
ejpam-5156	46	9	as	as	ADP
ejpam-5156	46	10	an	an	DET
ejpam-5156	46	11	isolated	isolated	ADJ
ejpam-5156	46	12	vertex	vertex	NOUN
ejpam-5156	46	13	and	and	CCONJ
ejpam-5156	46	14	a	a	DET
ejpam-5156	46	15	vertex	vertex	NOUN
ejpam-5156	46	16	of	of	ADP
ejpam-5156	46	17	degree	degree	NOUN
ejpam-5156	46	18	1	1	NUM
ejpam-5156	46	19	is	be	AUX
ejpam-5156	46	20	an	an	DET
ejpam-5156	46	21	end	end	NOUN
ejpam-5156	46	22	-	-	PUNCT
ejpam-5156	46	23	vertex	vertex	NOUN
ejpam-5156	46	24	or	or	CCONJ
ejpam-5156	46	25	a	a	DET
ejpam-5156	46	26	leaf	leaf	NOUN
ejpam-5156	46	27	[	[	X
ejpam-5156	46	28	5	5	NUM
ejpam-5156	46	29	]	]	PUNCT
ejpam-5156	46	30	.	.	PUNCT
ejpam-5156	47	1	for	for	ADP
ejpam-5156	47	2	an	an	DET
ejpam-5156	47	3	integer	integer	NOUN
ejpam-5156	47	4	n	n	PRON
ejpam-5156	47	5	≥	≥	NOUN
ejpam-5156	47	6	1	1	NUM
ejpam-5156	47	7	,	,	PUNCT
ejpam-5156	47	8	the	the	DET
ejpam-5156	47	9	path	path	NOUN
ejpam-5156	47	10	pn	pn	PROPN
ejpam-5156	47	11	is	be	AUX
ejpam-5156	47	12	a	a	DET
ejpam-5156	47	13	graph	graph	NOUN
ejpam-5156	47	14	of	of	ADP
ejpam-5156	47	15	order	order	NOUN
ejpam-5156	47	16	n	n	NOUN
ejpam-5156	47	17	and	and	CCONJ
ejpam-5156	47	18	size	size	NOUN
ejpam-5156	47	19	n−	n−	PROPN
ejpam-5156	47	20	1	1	NUM
ejpam-5156	47	21	whose	whose	DET
ejpam-5156	47	22	vertices	vertex	NOUN
ejpam-5156	47	23	can	can	AUX
ejpam-5156	47	24	be	be	AUX
ejpam-5156	47	25	labeled	label	VERB
ejpam-5156	47	26	by	by	ADP
ejpam-5156	47	27	v0	v0	PROPN
ejpam-5156	47	28	,	,	PUNCT
ejpam-5156	47	29	v1	v1	NOUN
ejpam-5156	47	30	,	,	PUNCT
ejpam-5156	47	31	...	...	PUNCT
ejpam-5156	47	32	,	,	PUNCT
ejpam-5156	47	33	vn−1	vn−1	ADJ
ejpam-5156	47	34	and	and	CCONJ
ejpam-5156	47	35	whose	whose	DET
ejpam-5156	47	36	edges	edge	NOUN
ejpam-5156	47	37	are	be	AUX
ejpam-5156	47	38	vivi+1	vivi+1	ADJ
ejpam-5156	47	39	for	for	ADP
ejpam-5156	47	40	i	i	PRON
ejpam-5156	47	41	=	=	NOUN
ejpam-5156	47	42	0	0	NUM
ejpam-5156	47	43	,	,	PUNCT
ejpam-5156	47	44	1	1	NUM
ejpam-5156	47	45	,	,	PUNCT
ejpam-5156	47	46	2	2	NUM
ejpam-5156	47	47	,	,	PUNCT
ejpam-5156	47	48	...	...	PUNCT
ejpam-5156	47	49	,	,	PUNCT
ejpam-5156	47	50	n−	n−	NOUN
ejpam-5156	47	51	2	2	NUM
ejpam-5156	47	52	[	[	X
ejpam-5156	47	53	5	5	NUM
ejpam-5156	47	54	]	]	PUNCT
ejpam-5156	47	55	.	.	PUNCT
ejpam-5156	48	1	a	a	DET
ejpam-5156	48	2	complete	complete	ADJ
ejpam-5156	48	3	graph	graph	NOUN
ejpam-5156	48	4	of	of	ADP
ejpam-5156	48	5	order	order	NOUN
ejpam-5156	48	6	n	n	CCONJ
ejpam-5156	48	7	,	,	PUNCT
ejpam-5156	48	8	denoted	denote	VERB
ejpam-5156	48	9	by	by	ADP
ejpam-5156	48	10	kn	kn	PROPN
ejpam-5156	48	11	,	,	PUNCT
ejpam-5156	48	12	is	be	AUX
ejpam-5156	48	13	graph	graph	NOUN
ejpam-5156	48	14	with	with	ADP
ejpam-5156	48	15	n	n	ADP
ejpam-5156	48	16	vertices	vertex	NOUN
ejpam-5156	48	17	where	where	SCONJ
ejpam-5156	48	18	in	in	ADP
ejpam-5156	48	19	every	every	DET
ejpam-5156	48	20	pair	pair	NOUN
ejpam-5156	48	21	of	of	ADP
ejpam-5156	48	22	distinct	distinct	ADJ
ejpam-5156	48	23	vertices	vertex	NOUN
ejpam-5156	48	24	are	be	AUX
ejpam-5156	48	25	adjacent	adjacent	ADJ
ejpam-5156	48	26	[	[	X
ejpam-5156	48	27	10	10	NUM
ejpam-5156	48	28	]	]	PUNCT
ejpam-5156	48	29	.	.	PUNCT
ejpam-5156	49	1	an	an	DET
ejpam-5156	49	2	empty	empty	ADJ
ejpam-5156	49	3	graph	graph	NOUN
ejpam-5156	49	4	of	of	ADP
ejpam-5156	49	5	order	order	NOUN
ejpam-5156	49	6	n	n	NOUN
ejpam-5156	49	7	is	be	AUX
ejpam-5156	49	8	graph	graph	VERB
ejpam-5156	49	9	with	with	ADP
ejpam-5156	49	10	n	n	ADP
ejpam-5156	49	11	vertices	vertex	NOUN
ejpam-5156	49	12	where	where	SCONJ
ejpam-5156	49	13	in	in	ADP
ejpam-5156	49	14	every	every	DET
ejpam-5156	49	15	pair	pair	NOUN
ejpam-5156	49	16	of	of	ADP
ejpam-5156	49	17	distinct	distinct	ADJ
ejpam-5156	49	18	vertices	vertex	NOUN
ejpam-5156	49	19	are	be	AUX
ejpam-5156	49	20	not	not	PART
ejpam-5156	49	21	adjacent	adjacent	ADJ
ejpam-5156	49	22	[	[	X
ejpam-5156	49	23	5	5	NUM
ejpam-5156	49	24	]	]	PUNCT
ejpam-5156	49	25	.	.	PUNCT
ejpam-5156	50	1	a	a	DET
ejpam-5156	50	2	graph	graph	NOUN
ejpam-5156	50	3	g	g	NOUN
ejpam-5156	50	4	is	be	AUX
ejpam-5156	50	5	a	a	DET
ejpam-5156	50	6	complete	complete	ADJ
ejpam-5156	50	7	bipartite	bipartite	NOUN
ejpam-5156	50	8	graph	graph	NOUN
ejpam-5156	50	9	if	if	SCONJ
ejpam-5156	50	10	v	v	X
ejpam-5156	50	11	(	(	PUNCT
ejpam-5156	50	12	g	g	NOUN
ejpam-5156	50	13	)	)	PUNCT
ejpam-5156	50	14	can	can	AUX
ejpam-5156	50	15	be	be	AUX
ejpam-5156	50	16	partitioned	partition	VERB
ejpam-5156	50	17	into	into	ADP
ejpam-5156	50	18	two	two	NUM
ejpam-5156	50	19	sets	set	NOUN
ejpam-5156	50	20	a1	a1	NOUN
ejpam-5156	50	21	and	and	CCONJ
ejpam-5156	50	22	a2	a2	PROPN
ejpam-5156	50	23	(	(	PUNCT
ejpam-5156	50	24	called	call	VERB
ejpam-5156	50	25	partite	partite	ADJ
ejpam-5156	50	26	sets	set	NOUN
ejpam-5156	50	27	)	)	PUNCT
ejpam-5156	50	28	so	so	ADV
ejpam-5156	50	29	l.	l.	PROPN
ejpam-5156	50	30	consistente	consistente	PROPN
ejpam-5156	50	31	,	,	PUNCT
ejpam-5156	50	32	i.	i.	PROPN
ejpam-5156	50	33	cabahug	cabahug	PROPN
ejpam-5156	50	34	,	,	PUNCT
ejpam-5156	50	35	jr	jr	PROPN
ejpam-5156	50	36	.	.	PROPN
ejpam-5156	50	37	/	/	SYM
ejpam-5156	50	38	eur	eur	PROPN
ejpam-5156	50	39	.	.	PUNCT
ejpam-5156	51	1	j.	j.	PROPN
ejpam-5156	51	2	pure	pure	PROPN
ejpam-5156	51	3	appl	appl	PROPN
ejpam-5156	51	4	.	.	PROPN
ejpam-5156	51	5	math	math	PROPN
ejpam-5156	51	6	,	,	PUNCT
ejpam-5156	51	7	17	17	NUM
ejpam-5156	51	8	(	(	PUNCT
ejpam-5156	51	9	3	3	NUM
ejpam-5156	51	10	)	)	PUNCT
ejpam-5156	51	11	(	(	PUNCT
ejpam-5156	51	12	2024	2024	NUM
ejpam-5156	51	13	)	)	PUNCT
ejpam-5156	51	14	,	,	PUNCT
ejpam-5156	51	15	2196	2196	NUM
ejpam-5156	51	16	-	-	SYM
ejpam-5156	51	17	2209	2209	NUM
ejpam-5156	51	18	2198	2198	NUM
ejpam-5156	51	19	that	that	PRON
ejpam-5156	51	20	uv	uv	NOUN
ejpam-5156	51	21	is	be	AUX
ejpam-5156	51	22	an	an	DET
ejpam-5156	51	23	edge	edge	NOUN
ejpam-5156	51	24	of	of	ADP
ejpam-5156	51	25	g	g	NOUN
ejpam-5156	51	26	if	if	SCONJ
ejpam-5156	51	27	and	and	CCONJ
ejpam-5156	51	28	only	only	ADV
ejpam-5156	51	29	if	if	SCONJ
ejpam-5156	51	30	u	u	PROPN
ejpam-5156	51	31	∈	∈	PROPN
ejpam-5156	51	32	a1	a1	NOUN
ejpam-5156	51	33	and	and	CCONJ
ejpam-5156	51	34	v	v	ADP
ejpam-5156	51	35	∈	∈	PROPN
ejpam-5156	51	36	a2	a2	PROPN
ejpam-5156	51	37	.	.	PUNCT
ejpam-5156	52	1	if	if	SCONJ
ejpam-5156	52	2	|a1|	|a1|	NOUN
ejpam-5156	52	3	=	=	SYM
ejpam-5156	52	4	m	m	NOUN
ejpam-5156	52	5	and	and	CCONJ
ejpam-5156	52	6	|a2|	|a2|	NOUN
ejpam-5156	52	7	=	=	SYM
ejpam-5156	52	8	n	n	CCONJ
ejpam-5156	52	9	,	,	PUNCT
ejpam-5156	52	10	then	then	ADV
ejpam-5156	52	11	this	this	DET
ejpam-5156	52	12	complete	complete	ADJ
ejpam-5156	52	13	bipartite	bipartite	NOUN
ejpam-5156	52	14	graph	graph	NOUN
ejpam-5156	52	15	,	,	PUNCT
ejpam-5156	52	16	denoted	denote	VERB
ejpam-5156	52	17	by	by	ADP
ejpam-5156	52	18	km	km	PROPN
ejpam-5156	52	19	,	,	PUNCT
ejpam-5156	52	20	n	n	PROPN
ejpam-5156	52	21	(	(	PUNCT
ejpam-5156	52	22	or	or	CCONJ
ejpam-5156	52	23	kn	kn	PROPN
ejpam-5156	52	24	,	,	PUNCT
ejpam-5156	52	25	m	m	PROPN
ejpam-5156	52	26	)	)	PUNCT
ejpam-5156	52	27	,	,	PUNCT
ejpam-5156	52	28	has	have	VERB
ejpam-5156	52	29	order	order	NOUN
ejpam-5156	52	30	m+	m+	NUM
ejpam-5156	52	31	n	n	NOUN
ejpam-5156	52	32	and	and	CCONJ
ejpam-5156	52	33	size	size	PROPN
ejpam-5156	52	34	mn	mn	PROPN
ejpam-5156	52	35	.	.	PUNCT
ejpam-5156	53	1	the	the	DET
ejpam-5156	53	2	complete	complete	ADJ
ejpam-5156	53	3	bipartite	bipartite	PROPN
ejpam-5156	53	4	graph	graph	NOUN
ejpam-5156	53	5	k1,n	k1,n	PROPN
ejpam-5156	53	6	is	be	AUX
ejpam-5156	53	7	called	call	VERB
ejpam-5156	53	8	a	a	DET
ejpam-5156	53	9	star	star	NOUN
ejpam-5156	53	10	[	[	X
ejpam-5156	53	11	5	5	NUM
ejpam-5156	53	12	]	]	PUNCT
ejpam-5156	53	13	.	.	PUNCT
ejpam-5156	54	1	a	a	DET
ejpam-5156	54	2	graph	graph	NOUN
ejpam-5156	54	3	h	h	NOUN
ejpam-5156	54	4	is	be	AUX
ejpam-5156	54	5	a	a	DET
ejpam-5156	54	6	subgraph	subgraph	NOUN
ejpam-5156	54	7	of	of	ADP
ejpam-5156	54	8	a	a	DET
ejpam-5156	54	9	graph	graph	NOUN
ejpam-5156	54	10	g	g	NOUN
ejpam-5156	54	11	if	if	SCONJ
ejpam-5156	54	12	the	the	DET
ejpam-5156	54	13	vertex	vertex	NOUN
ejpam-5156	54	14	set	set	VERB
ejpam-5156	54	15	v	v	NOUN
ejpam-5156	54	16	(	(	PUNCT
ejpam-5156	54	17	h	h	NOUN
ejpam-5156	54	18	)	)	PUNCT
ejpam-5156	54	19	of	of	ADP
ejpam-5156	54	20	h	h	NOUN
ejpam-5156	54	21	is	be	AUX
ejpam-5156	54	22	contained	contain	VERB
ejpam-5156	54	23	in	in	ADP
ejpam-5156	54	24	the	the	DET
ejpam-5156	54	25	vertex	vertex	NOUN
ejpam-5156	54	26	set	set	VERB
ejpam-5156	54	27	v	v	NOUN
ejpam-5156	54	28	(	(	PUNCT
ejpam-5156	54	29	g	g	NOUN
ejpam-5156	54	30	)	)	PUNCT
ejpam-5156	54	31	of	of	ADP
ejpam-5156	54	32	g	g	PROPN
ejpam-5156	54	33	and	and	CCONJ
ejpam-5156	54	34	all	all	DET
ejpam-5156	54	35	edges	edge	NOUN
ejpam-5156	54	36	of	of	ADP
ejpam-5156	54	37	h	h	NOUN
ejpam-5156	54	38	are	be	AUX
ejpam-5156	54	39	edges	edge	NOUN
ejpam-5156	54	40	in	in	ADP
ejpam-5156	54	41	g	g	PROPN
ejpam-5156	54	42	,	,	PUNCT
ejpam-5156	54	43	i.e	i.e	PROPN
ejpam-5156	54	44	,	,	PUNCT
ejpam-5156	54	45	v	v	ADJ
ejpam-5156	54	46	(	(	PUNCT
ejpam-5156	54	47	h	h	NOUN
ejpam-5156	54	48	)	)	PUNCT
ejpam-5156	54	49	⊆	⊆	NUM
ejpam-5156	54	50	v	v	NOUN
ejpam-5156	54	51	(	(	PUNCT
ejpam-5156	54	52	g	g	NOUN
ejpam-5156	54	53	)	)	PUNCT
ejpam-5156	54	54	and	and	CCONJ
ejpam-5156	54	55	e(h	e(h	NOUN
ejpam-5156	54	56	)	)	PUNCT
ejpam-5156	54	57	⊆	⊆	NUM
ejpam-5156	54	58	e(g	e(g	PROPN
ejpam-5156	54	59	)	)	PUNCT
ejpam-5156	54	60	.	.	PUNCT
ejpam-5156	55	1	for	for	ADP
ejpam-5156	55	2	any	any	DET
ejpam-5156	55	3	vertex	vertex	NOUN
ejpam-5156	55	4	subset	subset	NOUN
ejpam-5156	55	5	s	s	PART
ejpam-5156	55	6	⊆	⊆	NUM
ejpam-5156	55	7	v	v	NOUN
ejpam-5156	55	8	(	(	PUNCT
ejpam-5156	55	9	g	g	NOUN
ejpam-5156	55	10	)	)	PUNCT
ejpam-5156	55	11	,	,	PUNCT
ejpam-5156	55	12	the	the	DET
ejpam-5156	55	13	induced	induced	ADJ
ejpam-5156	55	14	subgraph	subgraph	NOUN
ejpam-5156	55	15	by	by	ADP
ejpam-5156	55	16	s	s	PRON
ejpam-5156	55	17	denoted	denote	VERB
ejpam-5156	55	18	by	by	ADP
ejpam-5156	55	19	⟨s⟩g	⟨s⟩g	NOUN
ejpam-5156	55	20	contains	contain	VERB
ejpam-5156	55	21	all	all	DET
ejpam-5156	55	22	the	the	DET
ejpam-5156	55	23	edges	edge	NOUN
ejpam-5156	55	24	of	of	ADP
ejpam-5156	55	25	e(g	e(g	NOUN
ejpam-5156	55	26	)	)	PUNCT
ejpam-5156	55	27	whose	whose	DET
ejpam-5156	55	28	extremities	extremity	NOUN
ejpam-5156	55	29	belong	belong	VERB
ejpam-5156	55	30	to	to	ADP
ejpam-5156	55	31	s	s	PRON
ejpam-5156	55	32	[	[	X
ejpam-5156	55	33	2	2	NUM
ejpam-5156	55	34	]	]	PUNCT
ejpam-5156	55	35	.	.	PUNCT
ejpam-5156	56	1	a	a	DET
ejpam-5156	56	2	set	set	NOUN
ejpam-5156	56	3	s	s	NOUN
ejpam-5156	56	4	of	of	ADP
ejpam-5156	56	5	vertices	vertex	NOUN
ejpam-5156	56	6	of	of	ADP
ejpam-5156	56	7	g	g	PROPN
ejpam-5156	56	8	is	be	AUX
ejpam-5156	56	9	a	a	DET
ejpam-5156	56	10	dominating	dominating	NOUN
ejpam-5156	56	11	set	set	NOUN
ejpam-5156	56	12	if	if	SCONJ
ejpam-5156	56	13	every	every	DET
ejpam-5156	56	14	vertex	vertex	NOUN
ejpam-5156	56	15	in	in	ADP
ejpam-5156	56	16	v	v	NOUN
ejpam-5156	56	17	(	(	PUNCT
ejpam-5156	56	18	g)∖s	g)∖	NOUN
ejpam-5156	56	19	is	be	AUX
ejpam-5156	56	20	adjacent	adjacent	ADJ
ejpam-5156	56	21	to	to	ADP
ejpam-5156	56	22	at	at	ADV
ejpam-5156	56	23	least	least	ADV
ejpam-5156	56	24	one	one	NUM
ejpam-5156	56	25	vertex	vertex	NOUN
ejpam-5156	56	26	in	in	ADP
ejpam-5156	56	27	s.	s.	PROPN
ejpam-5156	56	28	the	the	DET
ejpam-5156	56	29	minimum	minimum	ADJ
ejpam-5156	56	30	cardinality	cardinality	NOUN
ejpam-5156	56	31	among	among	ADP
ejpam-5156	56	32	the	the	DET
ejpam-5156	56	33	dominating	dominating	NOUN
ejpam-5156	56	34	sets	set	NOUN
ejpam-5156	56	35	of	of	ADP
ejpam-5156	56	36	g	g	PROPN
ejpam-5156	56	37	is	be	AUX
ejpam-5156	56	38	called	call	VERB
ejpam-5156	56	39	the	the	DET
ejpam-5156	56	40	domination	domination	NOUN
ejpam-5156	56	41	number	number	NOUN
ejpam-5156	56	42	of	of	ADP
ejpam-5156	56	43	g	g	NOUN
ejpam-5156	56	44	and	and	CCONJ
ejpam-5156	56	45	is	be	AUX
ejpam-5156	56	46	denoted	denote	VERB
ejpam-5156	56	47	by	by	ADP
ejpam-5156	56	48	γ(g	γ(g	PROPN
ejpam-5156	56	49	)	)	PUNCT
ejpam-5156	56	50	.	.	PUNCT
ejpam-5156	57	1	a	a	DET
ejpam-5156	57	2	dominating	dominating	NOUN
ejpam-5156	57	3	set	set	NOUN
ejpam-5156	57	4	of	of	ADP
ejpam-5156	57	5	cardinality	cardinality	PROPN
ejpam-5156	57	6	γ(g	γ(g	PROPN
ejpam-5156	57	7	)	)	PUNCT
ejpam-5156	57	8	is	be	AUX
ejpam-5156	57	9	then	then	ADV
ejpam-5156	57	10	referred	refer	VERB
ejpam-5156	57	11	to	to	ADP
ejpam-5156	57	12	as	as	ADP
ejpam-5156	57	13	a	a	DET
ejpam-5156	57	14	minimum	minimum	ADJ
ejpam-5156	57	15	dominating	dominating	NOUN
ejpam-5156	57	16	set	set	NOUN
ejpam-5156	57	17	[	[	X
ejpam-5156	57	18	5	5	NUM
ejpam-5156	57	19	]	]	PUNCT
ejpam-5156	57	20	.	.	PUNCT
ejpam-5156	58	1	a	a	DET
ejpam-5156	58	2	restrained	restrain	VERB
ejpam-5156	58	3	dominating	dominating	NOUN
ejpam-5156	58	4	set	set	VERB
ejpam-5156	58	5	in	in	ADP
ejpam-5156	58	6	a	a	DET
ejpam-5156	58	7	graph	graph	NOUN
ejpam-5156	58	8	g	g	NOUN
ejpam-5156	58	9	is	be	AUX
ejpam-5156	58	10	a	a	DET
ejpam-5156	58	11	set	set	NOUN
ejpam-5156	58	12	s	s	NOUN
ejpam-5156	58	13	⊆	⊆	NUM
ejpam-5156	58	14	v	v	NOUN
ejpam-5156	58	15	(	(	PUNCT
ejpam-5156	58	16	g	g	NOUN
ejpam-5156	58	17	)	)	PUNCT
ejpam-5156	58	18	where	where	SCONJ
ejpam-5156	58	19	every	every	DET
ejpam-5156	58	20	vertex	vertex	NOUN
ejpam-5156	58	21	in	in	ADP
ejpam-5156	58	22	v	v	NOUN
ejpam-5156	58	23	(	(	PUNCT
ejpam-5156	58	24	g)∖s	g)∖	NOUN
ejpam-5156	58	25	is	be	AUX
ejpam-5156	58	26	adjacent	adjacent	ADJ
ejpam-5156	58	27	to	to	ADP
ejpam-5156	58	28	a	a	DET
ejpam-5156	58	29	vertex	vertex	NOUN
ejpam-5156	58	30	in	in	ADP
ejpam-5156	58	31	s	s	PRON
ejpam-5156	58	32	as	as	ADV
ejpam-5156	58	33	well	well	ADV
ejpam-5156	58	34	as	as	ADP
ejpam-5156	58	35	another	another	DET
ejpam-5156	58	36	vertex	vertex	NOUN
ejpam-5156	58	37	in	in	ADP
ejpam-5156	58	38	v	v	NOUN
ejpam-5156	58	39	(	(	PUNCT
ejpam-5156	58	40	g)∖s	g)∖	NOUN
ejpam-5156	58	41	.	.	PUNCT
ejpam-5156	59	1	in	in	ADP
ejpam-5156	59	2	this	this	DET
ejpam-5156	59	3	case	case	NOUN
ejpam-5156	59	4	,	,	PUNCT
ejpam-5156	59	5	the	the	DET
ejpam-5156	59	6	induced	induced	ADJ
ejpam-5156	59	7	subgraph	subgraph	NOUN
ejpam-5156	59	8	⟨v	⟨v	NOUN
ejpam-5156	59	9	(	(	PUNCT
ejpam-5156	59	10	g	g	NOUN
ejpam-5156	59	11	)	)	PUNCT
ejpam-5156	59	12	∖	∖	X
ejpam-5156	59	13	s⟩	s⟩	PROPN
ejpam-5156	59	14	has	have	VERB
ejpam-5156	59	15	no	no	DET
ejpam-5156	59	16	isolated	isolated	ADJ
ejpam-5156	59	17	vertices	vertex	NOUN
ejpam-5156	59	18	.	.	PUNCT
ejpam-5156	60	1	the	the	DET
ejpam-5156	60	2	restrained	restrained	ADJ
ejpam-5156	60	3	domination	domination	NOUN
ejpam-5156	60	4	number	number	NOUN
ejpam-5156	60	5	of	of	ADP
ejpam-5156	60	6	g	g	NOUN
ejpam-5156	60	7	,	,	PUNCT
ejpam-5156	60	8	denoted	denote	VERB
ejpam-5156	60	9	by	by	ADP
ejpam-5156	60	10	γr(g	γr(g	PROPN
ejpam-5156	60	11	)	)	PUNCT
ejpam-5156	60	12	,	,	PUNCT
ejpam-5156	60	13	is	be	AUX
ejpam-5156	60	14	the	the	DET
ejpam-5156	60	15	smallest	small	ADJ
ejpam-5156	60	16	cardinality	cardinality	NOUN
ejpam-5156	60	17	of	of	ADP
ejpam-5156	60	18	a	a	DET
ejpam-5156	60	19	restrained	restrained	ADJ
ejpam-5156	60	20	dominating	dominating	NOUN
ejpam-5156	60	21	set	set	NOUN
ejpam-5156	60	22	of	of	ADP
ejpam-5156	60	23	g	g	PROPN
ejpam-5156	60	24	[	[	X
ejpam-5156	60	25	7	7	NUM
ejpam-5156	60	26	]	]	PUNCT
ejpam-5156	60	27	.	.	PUNCT
ejpam-5156	61	1	a	a	DET
ejpam-5156	61	2	defensive	defensive	ADJ
ejpam-5156	61	3	alliance	alliance	NOUN
ejpam-5156	61	4	in	in	ADP
ejpam-5156	61	5	a	a	DET
ejpam-5156	61	6	graph	graph	NOUN
ejpam-5156	61	7	g	g	NOUN
ejpam-5156	61	8	is	be	AUX
ejpam-5156	61	9	a	a	DET
ejpam-5156	61	10	nonempty	nonempty	ADJ
ejpam-5156	61	11	set	set	NOUN
ejpam-5156	61	12	of	of	ADP
ejpam-5156	61	13	vertices	vertex	NOUN
ejpam-5156	61	14	s	s	PART
ejpam-5156	61	15	⊆	⊆	NUM
ejpam-5156	61	16	v	v	NOUN
ejpam-5156	61	17	(	(	PUNCT
ejpam-5156	61	18	g	g	NOUN
ejpam-5156	61	19	)	)	PUNCT
ejpam-5156	61	20	if	if	SCONJ
ejpam-5156	61	21	for	for	ADP
ejpam-5156	61	22	every	every	DET
ejpam-5156	61	23	vertex	vertex	NOUN
ejpam-5156	61	24	v	v	ADP
ejpam-5156	61	25	∈	∈	PROPN
ejpam-5156	61	26	s	s	NOUN
ejpam-5156	61	27	,	,	PUNCT
ejpam-5156	61	28	|n	|n	X
ejpam-5156	62	1	[	[	X
ejpam-5156	62	2	v]∩s|	v]∩s|	ADP
ejpam-5156	62	3	≥	≥	NOUN
ejpam-5156	62	4	|n(v)∩	|n(v)∩	PUNCT
ejpam-5156	62	5	(	(	PUNCT
ejpam-5156	62	6	v	v	X
ejpam-5156	62	7	(	(	PUNCT
ejpam-5156	62	8	g)∖s)|	g)∖s)|	PROPN
ejpam-5156	62	9	.	.	PUNCT
ejpam-5156	63	1	a	a	DET
ejpam-5156	63	2	defensive	defensive	ADJ
ejpam-5156	63	3	alliance	alliance	NOUN
ejpam-5156	63	4	s	s	PART
ejpam-5156	63	5	is	be	AUX
ejpam-5156	63	6	called	call	VERB
ejpam-5156	63	7	global	global	ADJ
ejpam-5156	63	8	if	if	SCONJ
ejpam-5156	63	9	it	it	PRON
ejpam-5156	63	10	effects	effect	VERB
ejpam-5156	63	11	every	every	DET
ejpam-5156	63	12	vertex	vertex	NOUN
ejpam-5156	63	13	in	in	ADP
ejpam-5156	63	14	v	v	NOUN
ejpam-5156	63	15	(	(	PUNCT
ejpam-5156	63	16	g)∖	g)∖	PROPN
ejpam-5156	63	17	s	s	PROPN
ejpam-5156	63	18	,	,	PUNCT
ejpam-5156	63	19	that	that	ADV
ejpam-5156	63	20	is	is	ADV
ejpam-5156	63	21	,	,	PUNCT
ejpam-5156	63	22	every	every	DET
ejpam-5156	63	23	vertex	vertex	NOUN
ejpam-5156	63	24	in	in	ADP
ejpam-5156	63	25	v	v	NOUN
ejpam-5156	63	26	(	(	PUNCT
ejpam-5156	63	27	g)∖	g)∖	PROPN
ejpam-5156	63	28	s	s	PROPN
ejpam-5156	63	29	is	be	AUX
ejpam-5156	63	30	adjacent	adjacent	ADJ
ejpam-5156	63	31	to	to	ADP
ejpam-5156	63	32	at	at	ADV
ejpam-5156	63	33	least	least	ADV
ejpam-5156	63	34	one	one	NUM
ejpam-5156	63	35	member	member	NOUN
ejpam-5156	63	36	of	of	ADP
ejpam-5156	63	37	the	the	DET
ejpam-5156	63	38	alliance	alliance	NOUN
ejpam-5156	63	39	s.	s.	PROPN
ejpam-5156	63	40	in	in	ADP
ejpam-5156	63	41	this	this	DET
ejpam-5156	63	42	case	case	NOUN
ejpam-5156	63	43	,	,	PUNCT
ejpam-5156	63	44	s	s	VERB
ejpam-5156	63	45	is	be	AUX
ejpam-5156	63	46	a	a	DET
ejpam-5156	63	47	dominating	dominating	NOUN
ejpam-5156	63	48	set	set	NOUN
ejpam-5156	63	49	.	.	PUNCT
ejpam-5156	64	1	the	the	DET
ejpam-5156	64	2	global	global	ADJ
ejpam-5156	64	3	defensive	defensive	ADJ
ejpam-5156	64	4	alliance	alliance	NOUN
ejpam-5156	64	5	number	number	NOUN
ejpam-5156	64	6	of	of	ADP
ejpam-5156	64	7	g	g	NOUN
ejpam-5156	64	8	,	,	PUNCT
ejpam-5156	64	9	denoted	denote	VERB
ejpam-5156	64	10	γa(g	γa(g	ADP
ejpam-5156	64	11	)	)	PUNCT
ejpam-5156	64	12	,	,	PUNCT
ejpam-5156	64	13	is	be	AUX
ejpam-5156	64	14	the	the	DET
ejpam-5156	64	15	minimum	minimum	ADJ
ejpam-5156	64	16	size	size	NOUN
ejpam-5156	64	17	around	around	ADP
ejpam-5156	64	18	all	all	DET
ejpam-5156	64	19	the	the	DET
ejpam-5156	64	20	global	global	ADJ
ejpam-5156	64	21	defensive	defensive	ADJ
ejpam-5156	64	22	alliances	alliance	NOUN
ejpam-5156	64	23	of	of	ADP
ejpam-5156	64	24	g	g	PROPN
ejpam-5156	64	25	[	[	X
ejpam-5156	64	26	11	11	NUM
ejpam-5156	64	27	]	]	SYM
ejpam-5156	64	28	.	.	PUNCT
ejpam-5156	65	1	3	3	X
ejpam-5156	65	2	.	.	X
ejpam-5156	65	3	results	result	VERB
ejpam-5156	65	4	this	this	DET
ejpam-5156	65	5	paper	paper	NOUN
ejpam-5156	65	6	utilized	utilize	VERB
ejpam-5156	65	7	the	the	DET
ejpam-5156	65	8	following	follow	VERB
ejpam-5156	65	9	terms	term	NOUN
ejpam-5156	65	10	to	to	PART
ejpam-5156	65	11	denote	denote	VERB
ejpam-5156	65	12	specific	specific	ADJ
ejpam-5156	65	13	concepts	concept	NOUN
ejpam-5156	65	14	:	:	PUNCT
ejpam-5156	65	15	ds	ds	ADP
ejpam-5156	65	16	signified	signify	VERB
ejpam-5156	65	17	dominating	dominating	NOUN
ejpam-5156	65	18	set	set	NOUN
ejpam-5156	65	19	,	,	PUNCT
ejpam-5156	65	20	da	da	PROPN
ejpam-5156	65	21	represented	represent	VERB
ejpam-5156	65	22	defensive	defensive	ADJ
ejpam-5156	65	23	alliance	alliance	NOUN
ejpam-5156	65	24	,	,	PUNCT
ejpam-5156	65	25	rds	rd	NOUN
ejpam-5156	65	26	stood	stand	VERB
ejpam-5156	65	27	for	for	ADP
ejpam-5156	65	28	restrained	restrained	ADJ
ejpam-5156	65	29	dominating	dominating	NOUN
ejpam-5156	65	30	set	set	NOUN
ejpam-5156	65	31	,	,	PUNCT
ejpam-5156	65	32	gda	gda	PROPN
ejpam-5156	65	33	indicated	indicate	VERB
ejpam-5156	65	34	global	global	ADJ
ejpam-5156	65	35	defensive	defensive	ADJ
ejpam-5156	65	36	alliance	alliance	NOUN
ejpam-5156	65	37	,	,	PUNCT
ejpam-5156	65	38	and	and	CCONJ
ejpam-5156	65	39	rgda	rgda	NOUN
ejpam-5156	65	40	denoted	denote	VERB
ejpam-5156	65	41	restrained	restrained	ADJ
ejpam-5156	65	42	global	global	ADJ
ejpam-5156	65	43	defensive	defensive	ADJ
ejpam-5156	65	44	alliance	alliance	NOUN
ejpam-5156	65	45	.	.	PUNCT
ejpam-5156	66	1	moreover	moreover	ADV
ejpam-5156	66	2	,	,	PUNCT
ejpam-5156	66	3	if	if	SCONJ
ejpam-5156	66	4	g	g	PROPN
ejpam-5156	66	5	is	be	AUX
ejpam-5156	66	6	a	a	DET
ejpam-5156	66	7	graph	graph	NOUN
ejpam-5156	66	8	,	,	PUNCT
ejpam-5156	66	9	its	its	PRON
ejpam-5156	66	10	vertex	vertex	NOUN
ejpam-5156	66	11	set	set	VERB
ejpam-5156	66	12	v	v	NOUN
ejpam-5156	66	13	(	(	PUNCT
ejpam-5156	66	14	g	g	NOUN
ejpam-5156	66	15	)	)	PUNCT
ejpam-5156	66	16	and	and	CCONJ
ejpam-5156	66	17	edge	edge	VERB
ejpam-5156	66	18	set	set	VERB
ejpam-5156	66	19	e(g	e(g	PROPN
ejpam-5156	66	20	)	)	PUNCT
ejpam-5156	66	21	are	be	AUX
ejpam-5156	66	22	denoted	denote	VERB
ejpam-5156	66	23	as	as	ADP
ejpam-5156	66	24	v	v	NOUN
ejpam-5156	66	25	and	and	CCONJ
ejpam-5156	66	26	e	e	NOUN
ejpam-5156	66	27	,	,	PUNCT
ejpam-5156	66	28	respectively	respectively	ADV
ejpam-5156	66	29	.	.	PUNCT
ejpam-5156	67	1	additionally	additionally	ADV
ejpam-5156	67	2	,	,	PUNCT
ejpam-5156	67	3	graphs	graph	NOUN
ejpam-5156	67	4	considered	consider	VERB
ejpam-5156	67	5	is	be	AUX
ejpam-5156	67	6	this	this	DET
ejpam-5156	67	7	paper	paper	NOUN
ejpam-5156	67	8	are	be	AUX
ejpam-5156	67	9	simple	simple	ADJ
ejpam-5156	67	10	,	,	PUNCT
ejpam-5156	67	11	finite	finite	ADJ
ejpam-5156	67	12	,	,	PUNCT
ejpam-5156	67	13	and	and	CCONJ
ejpam-5156	67	14	undirected	undirected	ADJ
ejpam-5156	67	15	graphs	graph	NOUN
ejpam-5156	67	16	.	.	PUNCT
ejpam-5156	68	1	definition	definition	NOUN
ejpam-5156	68	2	1	1	NUM
ejpam-5156	68	3	.	.	PUNCT
ejpam-5156	69	1	a	a	DET
ejpam-5156	69	2	restrained	restrained	ADJ
ejpam-5156	69	3	global	global	ADJ
ejpam-5156	69	4	defensive	defensive	ADJ
ejpam-5156	69	5	alliance	alliance	NOUN
ejpam-5156	69	6	of	of	ADP
ejpam-5156	69	7	a	a	DET
ejpam-5156	69	8	graph	graph	NOUN
ejpam-5156	69	9	g	g	NOUN
ejpam-5156	69	10	=	=	PUNCT
ejpam-5156	69	11	(	(	PUNCT
ejpam-5156	69	12	v	v	NOUN
ejpam-5156	69	13	,	,	PUNCT
ejpam-5156	69	14	e	e	NOUN
ejpam-5156	69	15	)	)	PUNCT
ejpam-5156	69	16	is	be	AUX
ejpam-5156	69	17	a	a	DET
ejpam-5156	69	18	set	set	NOUN
ejpam-5156	69	19	s	s	NOUN
ejpam-5156	69	20	of	of	ADP
ejpam-5156	69	21	vertices	vertex	NOUN
ejpam-5156	69	22	of	of	ADP
ejpam-5156	69	23	g	g	NOUN
ejpam-5156	69	24	that	that	PRON
ejpam-5156	69	25	is	be	AUX
ejpam-5156	69	26	a	a	DET
ejpam-5156	69	27	restrained	restrain	VERB
ejpam-5156	69	28	dominating	dominating	NOUN
ejpam-5156	69	29	set	set	NOUN
ejpam-5156	69	30	and	and	CCONJ
ejpam-5156	69	31	global	global	ADJ
ejpam-5156	69	32	defensive	defensive	ADJ
ejpam-5156	69	33	alliance	alliance	NOUN
ejpam-5156	69	34	.	.	PUNCT
ejpam-5156	70	1	a	a	DET
ejpam-5156	70	2	set	set	NOUN
ejpam-5156	70	3	s	s	NOUN
ejpam-5156	70	4	with	with	ADP
ejpam-5156	70	5	the	the	DET
ejpam-5156	70	6	least	least	ADJ
ejpam-5156	70	7	number	number	NOUN
ejpam-5156	70	8	of	of	ADP
ejpam-5156	70	9	vertices	vertex	NOUN
ejpam-5156	70	10	is	be	AUX
ejpam-5156	70	11	called	call	VERB
ejpam-5156	70	12	a	a	DET
ejpam-5156	70	13	minimum	minimum	ADJ
ejpam-5156	70	14	restrained	restrain	VERB
ejpam-5156	70	15	global	global	ADJ
ejpam-5156	70	16	defensive	defensive	ADJ
ejpam-5156	70	17	alliance	alliance	NOUN
ejpam-5156	70	18	.	.	PUNCT
ejpam-5156	71	1	the	the	DET
ejpam-5156	71	2	cardinality	cardinality	NOUN
ejpam-5156	71	3	of	of	ADP
ejpam-5156	71	4	a	a	DET
ejpam-5156	71	5	minimum	minimum	ADJ
ejpam-5156	71	6	restrained	restrain	VERB
ejpam-5156	71	7	global	global	ADJ
ejpam-5156	71	8	defensive	defensive	ADJ
ejpam-5156	71	9	alliance	alliance	NOUN
ejpam-5156	71	10	is	be	AUX
ejpam-5156	71	11	called	call	VERB
ejpam-5156	71	12	the	the	DET
ejpam-5156	71	13	restrained	restrained	ADJ
ejpam-5156	71	14	global	global	ADJ
ejpam-5156	71	15	defensive	defensive	ADJ
ejpam-5156	71	16	alliance	alliance	NOUN
ejpam-5156	71	17	number	number	NOUN
ejpam-5156	71	18	denoted	denote	VERB
ejpam-5156	71	19	by	by	ADP
ejpam-5156	71	20	γra(g	γra(g	PROPN
ejpam-5156	71	21	)	)	PUNCT
ejpam-5156	71	22	.	.	PUNCT
ejpam-5156	71	23	example	example	NOUN
ejpam-5156	72	1	1	1	NUM
ejpam-5156	72	2	.	.	PUNCT
ejpam-5156	73	1	in	in	ADP
ejpam-5156	73	2	figure	figure	NOUN
ejpam-5156	73	3	1	1	NUM
ejpam-5156	73	4	,	,	PUNCT
ejpam-5156	73	5	consider	consider	VERB
ejpam-5156	73	6	a	a	DET
ejpam-5156	73	7	set	set	NOUN
ejpam-5156	73	8	s	s	PART
ejpam-5156	73	9	=	=	SYM
ejpam-5156	73	10	{	{	PUNCT
ejpam-5156	73	11	v0	v0	NOUN
ejpam-5156	73	12	,	,	PUNCT
ejpam-5156	73	13	v1	v1	NOUN
ejpam-5156	73	14	}	}	PUNCT
ejpam-5156	73	15	in	in	ADP
ejpam-5156	73	16	k4	k4	PROPN
ejpam-5156	73	17	=	=	SYM
ejpam-5156	73	18	(	(	PUNCT
ejpam-5156	73	19	v	v	NOUN
ejpam-5156	73	20	,	,	PUNCT
ejpam-5156	73	21	e	e	NOUN
ejpam-5156	73	22	)	)	PUNCT
ejpam-5156	73	23	.	.	PUNCT
ejpam-5156	74	1	notice	notice	VERB
ejpam-5156	74	2	that	that	SCONJ
ejpam-5156	74	3	v	v	X
ejpam-5156	74	4	∖	∖	X
ejpam-5156	74	5	s	s	PART
ejpam-5156	74	6	=	=	PUNCT
ejpam-5156	74	7	{	{	PUNCT
ejpam-5156	74	8	v2	v2	PROPN
ejpam-5156	74	9	,	,	PUNCT
ejpam-5156	74	10	v3	v3	PROPN
ejpam-5156	74	11	}	}	PUNCT
ejpam-5156	74	12	,	,	PUNCT
ejpam-5156	74	13	and	and	CCONJ
ejpam-5156	74	14	both	both	CCONJ
ejpam-5156	74	15	v2	v2	PROPN
ejpam-5156	74	16	and	and	CCONJ
ejpam-5156	74	17	v3	v3	PROPN
ejpam-5156	74	18	are	be	AUX
ejpam-5156	74	19	adjacent	adjacent	ADJ
ejpam-5156	74	20	to	to	ADP
ejpam-5156	74	21	v0	v0	PROPN
ejpam-5156	74	22	.	.	PUNCT
ejpam-5156	75	1	this	this	PRON
ejpam-5156	75	2	means	mean	VERB
ejpam-5156	75	3	that	that	SCONJ
ejpam-5156	75	4	s	s	VERB
ejpam-5156	75	5	is	be	AUX
ejpam-5156	75	6	a	a	DET
ejpam-5156	75	7	ds	ds	NOUN
ejpam-5156	75	8	.	.	PUNCT
ejpam-5156	76	1	moreover	moreover	ADV
ejpam-5156	76	2	,	,	PUNCT
ejpam-5156	76	3	⟨v	⟨v	PROPN
ejpam-5156	76	4	∖	∖	PROPN
ejpam-5156	76	5	s⟩	s⟩	INTJ
ejpam-5156	76	6	has	have	VERB
ejpam-5156	76	7	no	no	DET
ejpam-5156	76	8	isolated	isolate	VERB
ejpam-5156	76	9	vertices	vertex	NOUN
ejpam-5156	76	10	since	since	SCONJ
ejpam-5156	76	11	v2	v2	PROPN
ejpam-5156	76	12	is	be	AUX
ejpam-5156	76	13	adjacent	adjacent	ADJ
ejpam-5156	76	14	to	to	ADP
ejpam-5156	76	15	v3	v3	PROPN
ejpam-5156	76	16	.	.	PUNCT
ejpam-5156	77	1	this	this	PRON
ejpam-5156	77	2	means	mean	VERB
ejpam-5156	77	3	that	that	SCONJ
ejpam-5156	77	4	s	s	VERB
ejpam-5156	77	5	is	be	AUX
ejpam-5156	77	6	an	an	DET
ejpam-5156	77	7	rds	rd	NOUN
ejpam-5156	77	8	.	.	PUNCT
ejpam-5156	78	1	now	now	ADV
ejpam-5156	78	2	,	,	PUNCT
ejpam-5156	78	3	it	it	PRON
ejpam-5156	78	4	remains	remain	VERB
ejpam-5156	78	5	to	to	PART
ejpam-5156	78	6	show	show	VERB
ejpam-5156	78	7	that	that	SCONJ
ejpam-5156	78	8	s	s	VERB
ejpam-5156	78	9	is	be	AUX
ejpam-5156	78	10	a	a	DET
ejpam-5156	78	11	da	da	X
ejpam-5156	78	12	.	.	PUNCT
ejpam-5156	78	13	observe	observe	VERB
ejpam-5156	78	14	that	that	SCONJ
ejpam-5156	78	15	|n	|n	NOUN
ejpam-5156	78	16	[	[	X
ejpam-5156	78	17	v0	v0	X
ejpam-5156	78	18	]	]	PUNCT
ejpam-5156	78	19	∩	∩	NOUN
ejpam-5156	78	20	s|	s|	NOUN
ejpam-5156	78	21	=	=	SYM
ejpam-5156	78	22	|{v0	|{v0	NOUN
ejpam-5156	78	23	,	,	PUNCT
ejpam-5156	78	24	v1}|	v1}|	X
ejpam-5156	78	25	=	=	SYM
ejpam-5156	78	26	2	2	NUM
ejpam-5156	78	27	≥	≥	NOUN
ejpam-5156	78	28	2	2	NUM
ejpam-5156	78	29	=	=	SYM
ejpam-5156	78	30	|{v2	|{v2	NOUN
ejpam-5156	78	31	,	,	PUNCT
ejpam-5156	78	32	v3}|	v3}|	NOUN
ejpam-5156	78	33	=	=	SYM
ejpam-5156	78	34	|n(v0	|n(v0	PROPN
ejpam-5156	78	35	)	)	PUNCT
ejpam-5156	78	36	∩	∩	NOUN
ejpam-5156	78	37	(	(	PUNCT
ejpam-5156	78	38	v	v	X
ejpam-5156	78	39	∖	∖	PROPN
ejpam-5156	78	40	s)|	s)|	PROPN
ejpam-5156	78	41	l.	l.	PROPN
ejpam-5156	78	42	consistente	consistente	PROPN
ejpam-5156	78	43	,	,	PUNCT
ejpam-5156	78	44	i.	i.	PROPN
ejpam-5156	78	45	cabahug	cabahug	PROPN
ejpam-5156	78	46	,	,	PUNCT
ejpam-5156	78	47	jr	jr	PROPN
ejpam-5156	78	48	.	.	PROPN
ejpam-5156	78	49	/	/	SYM
ejpam-5156	78	50	eur	eur	PROPN
ejpam-5156	78	51	.	.	PUNCT
ejpam-5156	79	1	j.	j.	PROPN
ejpam-5156	79	2	pure	pure	PROPN
ejpam-5156	79	3	appl	appl	PROPN
ejpam-5156	79	4	.	.	PROPN
ejpam-5156	79	5	math	math	PROPN
ejpam-5156	79	6	,	,	PUNCT
ejpam-5156	79	7	17	17	NUM
ejpam-5156	79	8	(	(	PUNCT
ejpam-5156	79	9	3	3	NUM
ejpam-5156	79	10	)	)	PUNCT
ejpam-5156	79	11	(	(	PUNCT
ejpam-5156	79	12	2024	2024	NUM
ejpam-5156	79	13	)	)	PUNCT
ejpam-5156	79	14	,	,	PUNCT
ejpam-5156	79	15	2196	2196	NUM
ejpam-5156	79	16	-	-	SYM
ejpam-5156	79	17	2209	2209	NUM
ejpam-5156	79	18	2199	2199	NUM
ejpam-5156	79	19	and	and	CCONJ
ejpam-5156	79	20	|n	|n	ADJ
ejpam-5156	79	21	[	[	X
ejpam-5156	79	22	v1	v1	NOUN
ejpam-5156	79	23	]	]	PUNCT
ejpam-5156	79	24	∩	∩	NOUN
ejpam-5156	79	25	s|	s|	NOUN
ejpam-5156	79	26	=	=	SYM
ejpam-5156	79	27	|{v0	|{v0	NOUN
ejpam-5156	79	28	,	,	PUNCT
ejpam-5156	79	29	v1}|	v1}|	X
ejpam-5156	79	30	=	=	SYM
ejpam-5156	79	31	2	2	NUM
ejpam-5156	79	32	≥	≥	NOUN
ejpam-5156	79	33	2	2	NUM
ejpam-5156	79	34	=	=	SYM
ejpam-5156	79	35	|{v2	|{v2	NOUN
ejpam-5156	79	36	,	,	PUNCT
ejpam-5156	79	37	v3}|	v3}|	NOUN
ejpam-5156	79	38	=	=	SYM
ejpam-5156	79	39	|n(v1	|n(v1	NOUN
ejpam-5156	79	40	)	)	PUNCT
ejpam-5156	79	41	∩	∩	NOUN
ejpam-5156	79	42	(	(	PUNCT
ejpam-5156	79	43	v	v	NUM
ejpam-5156	79	44	∖	∖	PROPN
ejpam-5156	79	45	s)|	s)|	NOUN
ejpam-5156	79	46	.	.	PUNCT
ejpam-5156	80	1	hence	hence	ADV
ejpam-5156	80	2	,	,	PUNCT
ejpam-5156	80	3	s	s	VERB
ejpam-5156	80	4	is	be	AUX
ejpam-5156	80	5	a	a	DET
ejpam-5156	80	6	da	da	NOUN
ejpam-5156	80	7	.	.	PUNCT
ejpam-5156	81	1	this	this	PRON
ejpam-5156	81	2	implies	imply	VERB
ejpam-5156	81	3	that	that	SCONJ
ejpam-5156	81	4	s	s	VERB
ejpam-5156	81	5	is	be	AUX
ejpam-5156	81	6	also	also	ADV
ejpam-5156	81	7	a	a	DET
ejpam-5156	81	8	gda	gda	NOUN
ejpam-5156	81	9	.	.	PUNCT
ejpam-5156	82	1	therefore	therefore	ADV
ejpam-5156	82	2	,	,	PUNCT
ejpam-5156	82	3	by	by	ADP
ejpam-5156	82	4	definition	definition	NOUN
ejpam-5156	82	5	1	1	NUM
ejpam-5156	82	6	,	,	PUNCT
ejpam-5156	82	7	s	s	VERB
ejpam-5156	82	8	is	be	AUX
ejpam-5156	82	9	an	an	DET
ejpam-5156	82	10	rgda	rgda	NOUN
ejpam-5156	82	11	.	.	PUNCT
ejpam-5156	83	1	figure	figure	NOUN
ejpam-5156	83	2	1	1	NUM
ejpam-5156	83	3	:	:	PUNCT
ejpam-5156	83	4	a	a	DET
ejpam-5156	83	5	complete	complete	ADJ
ejpam-5156	83	6	graph	graph	NOUN
ejpam-5156	83	7	k4	k4	PROPN
ejpam-5156	83	8	.	.	PUNCT
ejpam-5156	84	1	theorem	theorem	NOUN
ejpam-5156	84	2	1	1	NUM
ejpam-5156	84	3	.	.	PUNCT
ejpam-5156	85	1	let	let	VERB
ejpam-5156	85	2	g	g	PROPN
ejpam-5156	85	3	=	=	SYM
ejpam-5156	85	4	(	(	PUNCT
ejpam-5156	85	5	v	v	NOUN
ejpam-5156	85	6	,	,	PUNCT
ejpam-5156	85	7	e	e	NOUN
ejpam-5156	85	8	)	)	PUNCT
ejpam-5156	85	9	be	be	VERB
ejpam-5156	85	10	any	any	DET
ejpam-5156	85	11	graph	graph	NOUN
ejpam-5156	85	12	of	of	ADP
ejpam-5156	85	13	order	order	NOUN
ejpam-5156	85	14	n	n	PRON
ejpam-5156	85	15	≥	≥	NOUN
ejpam-5156	85	16	1	1	NUM
ejpam-5156	85	17	.	.	PUNCT
ejpam-5156	86	1	then	then	ADV
ejpam-5156	86	2	the	the	DET
ejpam-5156	86	3	set	set	NOUN
ejpam-5156	86	4	v	v	NOUN
ejpam-5156	86	5	is	be	AUX
ejpam-5156	86	6	a	a	DET
ejpam-5156	86	7	restrained	restrained	ADJ
ejpam-5156	86	8	global	global	ADJ
ejpam-5156	86	9	defensive	defensive	ADJ
ejpam-5156	86	10	alliance	alliance	NOUN
ejpam-5156	86	11	in	in	ADP
ejpam-5156	86	12	g.	g.	PROPN
ejpam-5156	86	13	as	as	ADP
ejpam-5156	86	14	consequence	consequence	NOUN
ejpam-5156	86	15	,	,	PUNCT
ejpam-5156	86	16	γra(g	γra(g	ADJ
ejpam-5156	86	17	)	)	PUNCT
ejpam-5156	86	18	≤	≤	NUM
ejpam-5156	86	19	n.	n.	NOUN
ejpam-5156	86	20	proof	proof	NOUN
ejpam-5156	86	21	.	.	PUNCT
ejpam-5156	87	1	let	let	VERB
ejpam-5156	87	2	g	g	PROPN
ejpam-5156	87	3	=	=	SYM
ejpam-5156	87	4	(	(	PUNCT
ejpam-5156	87	5	v	v	NOUN
ejpam-5156	87	6	,	,	PUNCT
ejpam-5156	87	7	e	e	NOUN
ejpam-5156	87	8	)	)	PUNCT
ejpam-5156	87	9	be	be	VERB
ejpam-5156	87	10	any	any	DET
ejpam-5156	87	11	graph	graph	NOUN
ejpam-5156	87	12	of	of	ADP
ejpam-5156	87	13	order	order	NOUN
ejpam-5156	87	14	n	n	PRON
ejpam-5156	87	15	≥	≥	NOUN
ejpam-5156	87	16	1	1	NUM
ejpam-5156	87	17	.	.	PUNCT
ejpam-5156	88	1	since	since	SCONJ
ejpam-5156	88	2	v	v	NOUN
ejpam-5156	88	3	dominates	dominate	VERB
ejpam-5156	88	4	itself	itself	PRON
ejpam-5156	88	5	and	and	CCONJ
ejpam-5156	88	6	v	v	ADP
ejpam-5156	88	7	∖	∖	PRON
ejpam-5156	88	8	v	v	NOUN
ejpam-5156	88	9	is	be	AUX
ejpam-5156	88	10	empty	empty	ADJ
ejpam-5156	88	11	,	,	PUNCT
ejpam-5156	88	12	it	it	PRON
ejpam-5156	88	13	vacuously	vacuously	ADV
ejpam-5156	88	14	implies	imply	VERB
ejpam-5156	88	15	that	that	SCONJ
ejpam-5156	88	16	v	v	NOUN
ejpam-5156	88	17	is	be	AUX
ejpam-5156	88	18	an	an	DET
ejpam-5156	88	19	rds	rd	NOUN
ejpam-5156	88	20	.	.	PUNCT
ejpam-5156	89	1	for	for	ADP
ejpam-5156	89	2	the	the	DET
ejpam-5156	89	3	same	same	ADJ
ejpam-5156	89	4	reason	reason	NOUN
ejpam-5156	89	5	,	,	PUNCT
ejpam-5156	89	6	notice	notice	VERB
ejpam-5156	89	7	that	that	SCONJ
ejpam-5156	89	8	for	for	ADP
ejpam-5156	89	9	every	every	DET
ejpam-5156	89	10	v	v	NUM
ejpam-5156	89	11	∈	∈	PROPN
ejpam-5156	89	12	v	v	NOUN
ejpam-5156	89	13	,	,	PUNCT
ejpam-5156	89	14	|n	|n	X
ejpam-5156	89	15	[	[	X
ejpam-5156	89	16	v	v	X
ejpam-5156	89	17	]	]	X
ejpam-5156	89	18	∩	∩	NOUN
ejpam-5156	89	19	v	v	ADP
ejpam-5156	89	20	|	|	ADV
ejpam-5156	89	21	=	=	PUNCT
ejpam-5156	89	22	|n	|n	X
ejpam-5156	89	23	[	[	X
ejpam-5156	89	24	v]|	v]|	PROPN
ejpam-5156	89	25	≥	≥	NOUN
ejpam-5156	89	26	0	0	NUM
ejpam-5156	89	27	=	=	SYM
ejpam-5156	89	28	|∅|	|∅|	PROPN
ejpam-5156	89	29	=	=	SYM
ejpam-5156	89	30	|n(v	|n(v	PROPN
ejpam-5156	89	31	)	)	PUNCT
ejpam-5156	89	32	∩	∩	NOUN
ejpam-5156	89	33	(	(	PUNCT
ejpam-5156	89	34	v	v	NUM
ejpam-5156	89	35	∖	∖	NOUN
ejpam-5156	89	36	v	v	NOUN
ejpam-5156	89	37	)	)	PUNCT
ejpam-5156	89	38	|	|	ADV
ejpam-5156	89	39	.	.	PUNCT
ejpam-5156	90	1	hence	hence	ADV
ejpam-5156	90	2	,	,	PUNCT
ejpam-5156	90	3	v	v	PRON
ejpam-5156	90	4	is	be	AUX
ejpam-5156	90	5	a	a	DET
ejpam-5156	90	6	da	da	NOUN
ejpam-5156	90	7	in	in	ADP
ejpam-5156	90	8	g.	g.	PROPN
ejpam-5156	91	1	so	so	ADV
ejpam-5156	91	2	,	,	PUNCT
ejpam-5156	91	3	v	v	NOUN
ejpam-5156	91	4	is	be	AUX
ejpam-5156	91	5	an	an	DET
ejpam-5156	91	6	rgda	rgda	NOUN
ejpam-5156	91	7	in	in	ADP
ejpam-5156	91	8	g.	g.	PROPN
ejpam-5156	91	9	now	now	ADV
ejpam-5156	91	10	,	,	PUNCT
ejpam-5156	91	11	if	if	SCONJ
ejpam-5156	91	12	no	no	DET
ejpam-5156	91	13	set	set	NOUN
ejpam-5156	91	14	w	w	PROPN
ejpam-5156	91	15	⊂	⊂	PROPN
ejpam-5156	91	16	v	v	PROPN
ejpam-5156	91	17	is	be	AUX
ejpam-5156	91	18	an	an	DET
ejpam-5156	91	19	rgda	rgda	NOUN
ejpam-5156	91	20	in	in	ADP
ejpam-5156	91	21	g	g	NOUN
ejpam-5156	91	22	,	,	PUNCT
ejpam-5156	91	23	then	then	ADV
ejpam-5156	91	24	γra(g	γra(g	ADJ
ejpam-5156	91	25	)	)	PUNCT
ejpam-5156	91	26	=	=	SYM
ejpam-5156	92	1	|v	|v	PROPN
ejpam-5156	92	2	|	|	ADV
ejpam-5156	92	3	=	=	PUNCT
ejpam-5156	92	4	n.	n.	NOUN
ejpam-5156	92	5	on	on	ADP
ejpam-5156	92	6	the	the	DET
ejpam-5156	92	7	other	other	ADJ
ejpam-5156	92	8	hand	hand	NOUN
ejpam-5156	92	9	,	,	PUNCT
ejpam-5156	92	10	if	if	SCONJ
ejpam-5156	92	11	there	there	PRON
ejpam-5156	92	12	exist	exist	VERB
ejpam-5156	92	13	a	a	DET
ejpam-5156	92	14	set	set	NOUN
ejpam-5156	92	15	w	w	PROPN
ejpam-5156	92	16	⊂	⊂	PROPN
ejpam-5156	92	17	v	v	ADP
ejpam-5156	92	18	that	that	PRON
ejpam-5156	92	19	is	be	AUX
ejpam-5156	92	20	also	also	ADV
ejpam-5156	92	21	an	an	DET
ejpam-5156	92	22	rgda	rgda	NOUN
ejpam-5156	92	23	in	in	ADP
ejpam-5156	92	24	g	g	PROPN
ejpam-5156	92	25	,	,	PUNCT
ejpam-5156	92	26	then	then	ADV
ejpam-5156	92	27	γra(g	γra(g	PROPN
ejpam-5156	92	28	)	)	PUNCT
ejpam-5156	92	29	<	<	X
ejpam-5156	92	30	n.	n.	PROPN
ejpam-5156	92	31	hence	hence	ADV
ejpam-5156	92	32	,	,	PUNCT
ejpam-5156	92	33	γra(g	γra(g	PROPN
ejpam-5156	92	34	)	)	PUNCT
ejpam-5156	92	35	≤	≤	NUM
ejpam-5156	92	36	n.	n.	NOUN
ejpam-5156	92	37	theorem	theorem	NOUN
ejpam-5156	92	38	2	2	X
ejpam-5156	92	39	.	.	PUNCT
ejpam-5156	93	1	let	let	VERB
ejpam-5156	93	2	g	g	PROPN
ejpam-5156	93	3	=	=	SYM
ejpam-5156	93	4	(	(	PUNCT
ejpam-5156	93	5	v	v	NOUN
ejpam-5156	93	6	,	,	PUNCT
ejpam-5156	93	7	e	e	NOUN
ejpam-5156	93	8	)	)	PUNCT
ejpam-5156	93	9	be	be	AUX
ejpam-5156	93	10	a	a	DET
ejpam-5156	93	11	graph	graph	NOUN
ejpam-5156	93	12	with	with	ADP
ejpam-5156	93	13	leaf	leaf	NOUN
ejpam-5156	93	14	vertices	vertex	NOUN
ejpam-5156	93	15	.	.	PUNCT
ejpam-5156	94	1	if	if	SCONJ
ejpam-5156	94	2	s	s	VERB
ejpam-5156	94	3	⊆	⊆	NUM
ejpam-5156	94	4	v	v	NOUN
ejpam-5156	94	5	is	be	AUX
ejpam-5156	94	6	a	a	DET
ejpam-5156	94	7	restrained	restrained	ADJ
ejpam-5156	94	8	global	global	ADJ
ejpam-5156	94	9	defensive	defensive	ADJ
ejpam-5156	94	10	alliance	alliance	NOUN
ejpam-5156	94	11	in	in	ADP
ejpam-5156	94	12	g	g	PROPN
ejpam-5156	94	13	,	,	PUNCT
ejpam-5156	94	14	then	then	ADV
ejpam-5156	94	15	s	s	VERB
ejpam-5156	94	16	contains	contain	VERB
ejpam-5156	94	17	the	the	DET
ejpam-5156	94	18	leaf	leaf	NOUN
ejpam-5156	94	19	vertices	vertex	NOUN
ejpam-5156	94	20	of	of	ADP
ejpam-5156	94	21	g.	g.	NOUN
ejpam-5156	94	22	proof	proof	NOUN
ejpam-5156	94	23	.	.	PUNCT
ejpam-5156	95	1	let	let	VERB
ejpam-5156	95	2	s	s	PRON
ejpam-5156	95	3	be	be	AUX
ejpam-5156	95	4	an	an	DET
ejpam-5156	95	5	rgda	rgda	NOUN
ejpam-5156	95	6	in	in	ADP
ejpam-5156	95	7	g	g	PROPN
ejpam-5156	95	8	=	=	SYM
ejpam-5156	95	9	(	(	PUNCT
ejpam-5156	95	10	v	v	NOUN
ejpam-5156	95	11	,	,	PUNCT
ejpam-5156	95	12	e	e	NOUN
ejpam-5156	95	13	)	)	PUNCT
ejpam-5156	95	14	.	.	PUNCT
ejpam-5156	96	1	assume	assume	VERB
ejpam-5156	96	2	that	that	SCONJ
ejpam-5156	96	3	s	s	VERB
ejpam-5156	96	4	does	do	AUX
ejpam-5156	96	5	not	not	PART
ejpam-5156	96	6	contain	contain	VERB
ejpam-5156	96	7	all	all	DET
ejpam-5156	96	8	the	the	DET
ejpam-5156	96	9	leaf	leaf	NOUN
ejpam-5156	96	10	vertices	vertex	NOUN
ejpam-5156	96	11	of	of	ADP
ejpam-5156	96	12	g.	g.	PROPN
ejpam-5156	96	13	then	then	ADV
ejpam-5156	96	14	there	there	PRON
ejpam-5156	96	15	must	must	AUX
ejpam-5156	96	16	exist	exist	VERB
ejpam-5156	96	17	a	a	DET
ejpam-5156	96	18	leaf	leaf	NOUN
ejpam-5156	96	19	vertex	vertex	NOUN
ejpam-5156	96	20	v	v	ADP
ejpam-5156	96	21	∈	∈	NOUN
ejpam-5156	96	22	v	v	ADP
ejpam-5156	96	23	such	such	DET
ejpam-5156	96	24	that	that	DET
ejpam-5156	96	25	v	v	NOUN
ejpam-5156	96	26	/∈	/∈	PUNCT
ejpam-5156	97	1	s.	s.	PROPN
ejpam-5156	97	2	suppose	suppose	VERB
ejpam-5156	97	3	that	that	SCONJ
ejpam-5156	97	4	v	v	NOUN
ejpam-5156	97	5	is	be	AUX
ejpam-5156	97	6	adjacent	adjacent	ADJ
ejpam-5156	97	7	to	to	ADP
ejpam-5156	97	8	a	a	DET
ejpam-5156	97	9	vertex	vertex	NOUN
ejpam-5156	97	10	a	a	DET
ejpam-5156	97	11	∈	∈	NOUN
ejpam-5156	97	12	v	v	NOUN
ejpam-5156	97	13	.	.	PUNCT
ejpam-5156	98	1	this	this	PRON
ejpam-5156	98	2	leads	lead	VERB
ejpam-5156	98	3	to	to	ADP
ejpam-5156	98	4	the	the	DET
ejpam-5156	98	5	following	following	ADJ
ejpam-5156	98	6	cases	case	NOUN
ejpam-5156	98	7	:	:	PUNCT
ejpam-5156	98	8	case	case	NOUN
ejpam-5156	98	9	1	1	NUM
ejpam-5156	98	10	:	:	PUNCT
ejpam-5156	98	11	a	a	PRON
ejpam-5156	98	12	/∈	/∈	PUNCT
ejpam-5156	98	13	s.	s.	PROPN
ejpam-5156	98	14	then	then	ADV
ejpam-5156	98	15	no	no	DET
ejpam-5156	98	16	vertices	vertex	NOUN
ejpam-5156	98	17	in	in	ADP
ejpam-5156	98	18	s	s	VERB
ejpam-5156	98	19	can	can	AUX
ejpam-5156	98	20	dominate	dominate	VERB
ejpam-5156	98	21	v.	v.	ADP
ejpam-5156	98	22	this	this	DET
ejpam-5156	98	23	means	mean	VERB
ejpam-5156	98	24	that	that	SCONJ
ejpam-5156	98	25	s	s	VERB
ejpam-5156	98	26	is	be	AUX
ejpam-5156	98	27	not	not	PART
ejpam-5156	98	28	a	a	DET
ejpam-5156	98	29	ds	ds	NOUN
ejpam-5156	98	30	,	,	PUNCT
ejpam-5156	98	31	a	a	DET
ejpam-5156	98	32	contradiction	contradiction	NOUN
ejpam-5156	98	33	.	.	PUNCT
ejpam-5156	99	1	case	case	NOUN
ejpam-5156	99	2	2	2	NUM
ejpam-5156	99	3	:	:	PUNCT
ejpam-5156	99	4	a	a	DET
ejpam-5156	99	5	∈	∈	PROPN
ejpam-5156	99	6	s.	s.	PROPN
ejpam-5156	99	7	then	then	ADV
ejpam-5156	99	8	⟨v	⟨v	PROPN
ejpam-5156	99	9	∖	∖	PROPN
ejpam-5156	99	10	s⟩	s⟩	PROPN
ejpam-5156	99	11	contains	contain	VERB
ejpam-5156	99	12	an	an	DET
ejpam-5156	99	13	isolated	isolated	ADJ
ejpam-5156	99	14	vertex	vertex	NOUN
ejpam-5156	99	15	v.	v.	ADP
ejpam-5156	99	16	this	this	PRON
ejpam-5156	99	17	means	mean	VERB
ejpam-5156	99	18	that	that	SCONJ
ejpam-5156	99	19	s	s	VERB
ejpam-5156	99	20	is	be	AUX
ejpam-5156	99	21	not	not	PART
ejpam-5156	99	22	an	an	DET
ejpam-5156	99	23	rds	rd	NOUN
ejpam-5156	99	24	,	,	PUNCT
ejpam-5156	99	25	a	a	DET
ejpam-5156	99	26	contradiction	contradiction	NOUN
ejpam-5156	99	27	.	.	PUNCT
ejpam-5156	100	1	since	since	SCONJ
ejpam-5156	100	2	neither	neither	PRON
ejpam-5156	100	3	of	of	ADP
ejpam-5156	100	4	the	the	DET
ejpam-5156	100	5	cases	case	NOUN
ejpam-5156	100	6	holds	hold	VERB
ejpam-5156	100	7	,	,	PUNCT
ejpam-5156	100	8	then	then	ADV
ejpam-5156	100	9	v	v	X
ejpam-5156	100	10	∈	∈	PROPN
ejpam-5156	100	11	s.	s.	PROPN
ejpam-5156	100	12	therefore	therefore	ADV
ejpam-5156	100	13	,	,	PUNCT
ejpam-5156	100	14	every	every	DET
ejpam-5156	100	15	leaf	leaf	NOUN
ejpam-5156	100	16	vertex	vertex	NOUN
ejpam-5156	100	17	of	of	ADP
ejpam-5156	100	18	g	g	NOUN
ejpam-5156	100	19	must	must	AUX
ejpam-5156	100	20	be	be	AUX
ejpam-5156	100	21	in	in	ADP
ejpam-5156	100	22	s.	s.	PROPN
ejpam-5156	100	23	theorem	theorem	PROPN
ejpam-5156	100	24	3	3	X
ejpam-5156	100	25	.	.	PUNCT
ejpam-5156	101	1	let	let	VERB
ejpam-5156	101	2	g	g	PROPN
ejpam-5156	101	3	=	=	SYM
ejpam-5156	101	4	(	(	PUNCT
ejpam-5156	101	5	v	v	NOUN
ejpam-5156	101	6	,	,	PUNCT
ejpam-5156	101	7	e	e	NOUN
ejpam-5156	101	8	)	)	PUNCT
ejpam-5156	101	9	be	be	VERB
ejpam-5156	101	10	any	any	DET
ejpam-5156	101	11	graph	graph	NOUN
ejpam-5156	101	12	of	of	ADP
ejpam-5156	101	13	order	order	NOUN
ejpam-5156	101	14	n.	n.	NOUN
ejpam-5156	101	15	then	then	ADV
ejpam-5156	101	16	γra(g	γra(g	PROPN
ejpam-5156	101	17	)	)	PUNCT
ejpam-5156	101	18	=	=	SYM
ejpam-5156	101	19	1	1	NUM
ejpam-5156	101	20	if	if	SCONJ
ejpam-5156	101	21	and	and	CCONJ
ejpam-5156	101	22	only	only	ADV
ejpam-5156	101	23	if	if	SCONJ
ejpam-5156	101	24	g	g	PROPN
ejpam-5156	101	25	is	be	AUX
ejpam-5156	101	26	a	a	DET
ejpam-5156	101	27	trivial	trivial	ADJ
ejpam-5156	101	28	graph	graph	NOUN
ejpam-5156	101	29	.	.	PUNCT
ejpam-5156	102	1	l.	l.	PROPN
ejpam-5156	102	2	consistente	consistente	PROPN
ejpam-5156	102	3	,	,	PUNCT
ejpam-5156	102	4	i.	i.	PROPN
ejpam-5156	102	5	cabahug	cabahug	PROPN
ejpam-5156	102	6	,	,	PUNCT
ejpam-5156	102	7	jr	jr	PROPN
ejpam-5156	102	8	.	.	PROPN
ejpam-5156	102	9	/	/	SYM
ejpam-5156	102	10	eur	eur	PROPN
ejpam-5156	102	11	.	.	PUNCT
ejpam-5156	103	1	j.	j.	PROPN
ejpam-5156	103	2	pure	pure	PROPN
ejpam-5156	103	3	appl	appl	PROPN
ejpam-5156	103	4	.	.	PROPN
ejpam-5156	103	5	math	math	PROPN
ejpam-5156	103	6	,	,	PUNCT
ejpam-5156	103	7	17	17	NUM
ejpam-5156	103	8	(	(	PUNCT
ejpam-5156	103	9	3	3	NUM
ejpam-5156	103	10	)	)	PUNCT
ejpam-5156	103	11	(	(	PUNCT
ejpam-5156	103	12	2024	2024	NUM
ejpam-5156	103	13	)	)	PUNCT
ejpam-5156	103	14	,	,	PUNCT
ejpam-5156	103	15	2196	2196	NUM
ejpam-5156	103	16	-	-	SYM
ejpam-5156	103	17	2209	2209	NUM
ejpam-5156	103	18	2200	2200	NUM
ejpam-5156	103	19	proof	proof	NOUN
ejpam-5156	103	20	.	.	PUNCT
ejpam-5156	104	1	let	let	VERB
ejpam-5156	104	2	γra(g	γra(g	PROPN
ejpam-5156	104	3	)	)	PUNCT
ejpam-5156	104	4	=	=	SYM
ejpam-5156	105	1	1	1	X
ejpam-5156	105	2	.	.	PUNCT
ejpam-5156	105	3	by	by	ADP
ejpam-5156	105	4	theorem	theorem	NOUN
ejpam-5156	105	5	1	1	NUM
ejpam-5156	105	6	with	with	ADP
ejpam-5156	105	7	n	n	NOUN
ejpam-5156	105	8	=	=	SYM
ejpam-5156	105	9	1	1	NUM
ejpam-5156	105	10	,	,	PUNCT
ejpam-5156	105	11	a	a	DET
ejpam-5156	105	12	graph	graph	NOUN
ejpam-5156	105	13	containing	contain	VERB
ejpam-5156	105	14	a	a	DET
ejpam-5156	105	15	single	single	ADJ
ejpam-5156	105	16	vertex	vertex	NOUN
ejpam-5156	105	17	,	,	PUNCT
ejpam-5156	105	18	trivial	trivial	ADJ
ejpam-5156	105	19	graph	graph	NOUN
ejpam-5156	105	20	,	,	PUNCT
ejpam-5156	105	21	is	be	AUX
ejpam-5156	105	22	an	an	DET
ejpam-5156	105	23	rgda	rgda	NOUN
ejpam-5156	105	24	.	.	PUNCT
ejpam-5156	106	1	if	if	SCONJ
ejpam-5156	106	2	g	g	PROPN
ejpam-5156	106	3	is	be	AUX
ejpam-5156	106	4	a	a	DET
ejpam-5156	106	5	trivial	trivial	ADJ
ejpam-5156	106	6	graph	graph	NOUN
ejpam-5156	106	7	,	,	PUNCT
ejpam-5156	106	8	then	then	ADV
ejpam-5156	106	9	γra(g	γra(g	ADJ
ejpam-5156	106	10	)	)	PUNCT
ejpam-5156	106	11	=	=	SYM
ejpam-5156	106	12	1	1	X
ejpam-5156	106	13	.	.	PUNCT
ejpam-5156	107	1	so	so	ADV
ejpam-5156	107	2	,	,	PUNCT
ejpam-5156	107	3	g	g	PROPN
ejpam-5156	107	4	can	can	AUX
ejpam-5156	107	5	be	be	AUX
ejpam-5156	107	6	a	a	DET
ejpam-5156	107	7	trivial	trivial	ADJ
ejpam-5156	107	8	graph	graph	NOUN
ejpam-5156	107	9	.	.	PUNCT
ejpam-5156	108	1	now	now	ADV
ejpam-5156	108	2	,	,	PUNCT
ejpam-5156	108	3	assume	assume	VERB
ejpam-5156	108	4	that	that	SCONJ
ejpam-5156	108	5	g	g	PROPN
ejpam-5156	108	6	can	can	AUX
ejpam-5156	108	7	also	also	ADV
ejpam-5156	108	8	be	be	AUX
ejpam-5156	108	9	a	a	DET
ejpam-5156	108	10	nontrivial	nontrivial	ADJ
ejpam-5156	108	11	graph	graph	NOUN
ejpam-5156	108	12	with	with	ADP
ejpam-5156	108	13	order	order	NOUN
ejpam-5156	108	14	n	n	PRON
ejpam-5156	108	15	≥	≥	NOUN
ejpam-5156	108	16	2	2	NUM
ejpam-5156	108	17	.	.	PUNCT
ejpam-5156	109	1	then	then	ADV
ejpam-5156	109	2	there	there	PRON
ejpam-5156	109	3	must	must	AUX
ejpam-5156	109	4	exist	exist	VERB
ejpam-5156	109	5	a	a	DET
ejpam-5156	109	6	singleton	singleton	NOUN
ejpam-5156	109	7	set	set	NOUN
ejpam-5156	109	8	{	{	PUNCT
ejpam-5156	109	9	a	a	NOUN
ejpam-5156	109	10	}	}	PUNCT
ejpam-5156	109	11	⊂	⊂	PROPN
ejpam-5156	109	12	v	v	NOUN
ejpam-5156	109	13	that	that	PRON
ejpam-5156	109	14	is	be	AUX
ejpam-5156	109	15	an	an	DET
ejpam-5156	109	16	rgda	rgda	NOUN
ejpam-5156	109	17	in	in	ADP
ejpam-5156	109	18	g.	g.	PROPN
ejpam-5156	109	19	observe	observe	PROPN
ejpam-5156	109	20	,	,	PUNCT
ejpam-5156	109	21	case	case	NOUN
ejpam-5156	109	22	1	1	NUM
ejpam-5156	109	23	:	:	PUNCT
ejpam-5156	109	24	g	g	NOUN
ejpam-5156	109	25	has	have	VERB
ejpam-5156	109	26	order	order	NOUN
ejpam-5156	109	27	n	n	NOUN
ejpam-5156	109	28	=	=	SYM
ejpam-5156	109	29	2	2	NUM
ejpam-5156	109	30	.	.	PUNCT
ejpam-5156	110	1	then	then	ADV
ejpam-5156	110	2	⟨v	⟨v	NOUN
ejpam-5156	110	3	∖	∖	NOUN
ejpam-5156	110	4	{	{	PUNCT
ejpam-5156	110	5	a}⟩	a}⟩	PROPN
ejpam-5156	110	6	is	be	AUX
ejpam-5156	110	7	an	an	DET
ejpam-5156	110	8	isolated	isolated	ADJ
ejpam-5156	110	9	vertex	vertex	NOUN
ejpam-5156	110	10	.	.	PUNCT
ejpam-5156	111	1	so	so	ADV
ejpam-5156	111	2	,	,	PUNCT
ejpam-5156	111	3	{	{	PUNCT
ejpam-5156	111	4	a	a	PRON
ejpam-5156	111	5	}	}	PUNCT
ejpam-5156	111	6	is	be	AUX
ejpam-5156	111	7	not	not	PART
ejpam-5156	111	8	an	an	DET
ejpam-5156	111	9	rds	rd	NOUN
ejpam-5156	111	10	,	,	PUNCT
ejpam-5156	111	11	a	a	DET
ejpam-5156	111	12	contradiction	contradiction	NOUN
ejpam-5156	111	13	.	.	PUNCT
ejpam-5156	112	1	case	case	NOUN
ejpam-5156	112	2	2	2	NUM
ejpam-5156	112	3	:	:	PUNCT
ejpam-5156	112	4	g	g	NOUN
ejpam-5156	112	5	has	have	VERB
ejpam-5156	112	6	an	an	DET
ejpam-5156	112	7	order	order	NOUN
ejpam-5156	112	8	n	n	PRON
ejpam-5156	112	9	≥	≥	NOUN
ejpam-5156	112	10	3	3	NUM
ejpam-5156	112	11	.	.	PUNCT
ejpam-5156	113	1	then	then	ADV
ejpam-5156	113	2	,	,	PUNCT
ejpam-5156	113	3	knowing	know	VERB
ejpam-5156	113	4	that	that	SCONJ
ejpam-5156	113	5	g	g	PROPN
ejpam-5156	113	6	must	must	AUX
ejpam-5156	113	7	be	be	AUX
ejpam-5156	113	8	a	a	DET
ejpam-5156	113	9	ds	ds	NOUN
ejpam-5156	113	10	,	,	PUNCT
ejpam-5156	113	11	for	for	SCONJ
ejpam-5156	113	12	every	every	DET
ejpam-5156	113	13	a	a	DET
ejpam-5156	113	14	∈	∈	PROPN
ejpam-5156	113	15	{	{	PUNCT
ejpam-5156	113	16	a	a	PRON
ejpam-5156	113	17	}	}	PUNCT
ejpam-5156	113	18	implies	imply	VERB
ejpam-5156	113	19	|n	|n	NOUN
ejpam-5156	113	20	[	[	X
ejpam-5156	113	21	a	a	X
ejpam-5156	113	22	]	]	X
ejpam-5156	113	23	∩	∩	NOUN
ejpam-5156	113	24	{	{	PUNCT
ejpam-5156	113	25	a}|	a}|	NOUN
ejpam-5156	113	26	=	=	PUNCT
ejpam-5156	113	27	|{a}|	|{a}|	NUM
ejpam-5156	113	28	=	=	SYM
ejpam-5156	113	29	1	1	NUM
ejpam-5156	113	30	̸≥	̸≥	NUM
ejpam-5156	113	31	n−	n−	PROPN
ejpam-5156	113	32	1	1	NUM
ejpam-5156	113	33	=	=	SYM
ejpam-5156	113	34	|v	|v	PROPN
ejpam-5156	113	35	∖	∖	PROPN
ejpam-5156	113	36	{	{	PUNCT
ejpam-5156	113	37	a}|	a}|	PROPN
ejpam-5156	113	38	=	=	SYM
ejpam-5156	113	39	|n(a	|n(a	PROPN
ejpam-5156	113	40	)	)	PUNCT
ejpam-5156	113	41	∩	∩	NOUN
ejpam-5156	113	42	(	(	PUNCT
ejpam-5156	113	43	v	v	NUM
ejpam-5156	113	44	∖	∖	PRON
ejpam-5156	113	45	{	{	PUNCT
ejpam-5156	113	46	a})|	a})|	ADJ
ejpam-5156	113	47	.	.	PUNCT
ejpam-5156	114	1	so	so	ADV
ejpam-5156	114	2	,	,	PUNCT
ejpam-5156	114	3	{	{	PUNCT
ejpam-5156	114	4	a	a	PRON
ejpam-5156	114	5	}	}	PUNCT
ejpam-5156	114	6	is	be	AUX
ejpam-5156	114	7	not	not	PART
ejpam-5156	114	8	a	a	DET
ejpam-5156	114	9	da	da	NOUN
ejpam-5156	114	10	,	,	PUNCT
ejpam-5156	114	11	a	a	DET
ejpam-5156	114	12	contradiction	contradiction	NOUN
ejpam-5156	114	13	.	.	PUNCT
ejpam-5156	115	1	since	since	SCONJ
ejpam-5156	115	2	neither	neither	PRON
ejpam-5156	115	3	of	of	ADP
ejpam-5156	115	4	the	the	DET
ejpam-5156	115	5	cases	case	NOUN
ejpam-5156	115	6	holds	hold	VERB
ejpam-5156	115	7	,	,	PUNCT
ejpam-5156	115	8	g	g	PROPN
ejpam-5156	115	9	can	can	AUX
ejpam-5156	115	10	not	not	PART
ejpam-5156	115	11	be	be	AUX
ejpam-5156	115	12	a	a	DET
ejpam-5156	115	13	nontrivial	nontrivial	ADJ
ejpam-5156	115	14	graph	graph	NOUN
ejpam-5156	115	15	.	.	PUNCT
ejpam-5156	116	1	therefore	therefore	ADV
ejpam-5156	116	2	,	,	PUNCT
ejpam-5156	116	3	g	g	PROPN
ejpam-5156	116	4	must	must	AUX
ejpam-5156	116	5	be	be	AUX
ejpam-5156	116	6	a	a	DET
ejpam-5156	116	7	trivial	trivial	ADJ
ejpam-5156	116	8	graph	graph	NOUN
ejpam-5156	116	9	.	.	PUNCT
ejpam-5156	117	1	conversely	conversely	ADV
ejpam-5156	117	2	,	,	PUNCT
ejpam-5156	117	3	let	let	VERB
ejpam-5156	117	4	g	g	NOUN
ejpam-5156	117	5	=	=	SYM
ejpam-5156	117	6	(	(	PUNCT
ejpam-5156	117	7	v	v	NOUN
ejpam-5156	117	8	,	,	PUNCT
ejpam-5156	117	9	e	e	NOUN
ejpam-5156	117	10	)	)	PUNCT
ejpam-5156	117	11	be	be	AUX
ejpam-5156	117	12	a	a	DET
ejpam-5156	117	13	trivial	trivial	ADJ
ejpam-5156	117	14	graph	graph	NOUN
ejpam-5156	117	15	.	.	PUNCT
ejpam-5156	118	1	by	by	ADP
ejpam-5156	118	2	theorem	theorem	NOUN
ejpam-5156	118	3	1	1	NUM
ejpam-5156	118	4	,	,	PUNCT
ejpam-5156	118	5	v	v	NOUN
ejpam-5156	118	6	is	be	AUX
ejpam-5156	118	7	an	an	DET
ejpam-5156	118	8	rgda	rgda	NOUN
ejpam-5156	118	9	in	in	ADP
ejpam-5156	118	10	g.	g.	PROPN
ejpam-5156	118	11	since	since	SCONJ
ejpam-5156	118	12	an	an	DET
ejpam-5156	118	13	empty	empty	ADJ
ejpam-5156	118	14	set	set	NOUN
ejpam-5156	118	15	of	of	ADP
ejpam-5156	118	16	g	g	NOUN
ejpam-5156	118	17	can	can	AUX
ejpam-5156	118	18	not	not	PART
ejpam-5156	118	19	dominate	dominate	VERB
ejpam-5156	118	20	g	g	NOUN
ejpam-5156	118	21	,	,	PUNCT
ejpam-5156	118	22	then	then	ADV
ejpam-5156	118	23	v	v	NOUN
ejpam-5156	118	24	must	must	AUX
ejpam-5156	118	25	be	be	AUX
ejpam-5156	118	26	the	the	DET
ejpam-5156	118	27	minimum	minimum	ADJ
ejpam-5156	118	28	rgda	rgda	NOUN
ejpam-5156	118	29	in	in	ADP
ejpam-5156	118	30	g.	g.	PROPN
ejpam-5156	118	31	therefore	therefore	ADV
ejpam-5156	118	32	,	,	PUNCT
ejpam-5156	118	33	γra(g	γra(g	PROPN
ejpam-5156	118	34	)	)	PUNCT
ejpam-5156	118	35	=	=	PUNCT
ejpam-5156	119	1	|v	|v	PROPN
ejpam-5156	119	2	|	|	ADV
ejpam-5156	119	3	=	=	SYM
ejpam-5156	119	4	1	1	X
ejpam-5156	119	5	.	.	PUNCT
ejpam-5156	119	6	theorem	theorem	NOUN
ejpam-5156	119	7	4	4	NUM
ejpam-5156	119	8	.	.	PUNCT
ejpam-5156	120	1	let	let	VERB
ejpam-5156	120	2	g	g	PROPN
ejpam-5156	120	3	=	=	SYM
ejpam-5156	120	4	(	(	PUNCT
ejpam-5156	120	5	v	v	NOUN
ejpam-5156	120	6	,	,	PUNCT
ejpam-5156	120	7	e	e	NOUN
ejpam-5156	120	8	)	)	PUNCT
ejpam-5156	120	9	be	be	AUX
ejpam-5156	120	10	a	a	DET
ejpam-5156	120	11	graph	graph	NOUN
ejpam-5156	120	12	with	with	ADP
ejpam-5156	120	13	isolated	isolated	ADJ
ejpam-5156	120	14	vertices	vertex	NOUN
ejpam-5156	120	15	and	and	CCONJ
ejpam-5156	120	16	s	s	VERB
ejpam-5156	120	17	⊆	⊆	NUM
ejpam-5156	120	18	v	v	NOUN
ejpam-5156	120	19	be	be	AUX
ejpam-5156	120	20	any	any	DET
ejpam-5156	120	21	restrained	restrained	ADJ
ejpam-5156	120	22	global	global	ADJ
ejpam-5156	120	23	defensive	defensive	ADJ
ejpam-5156	120	24	alliance	alliance	NOUN
ejpam-5156	120	25	in	in	ADP
ejpam-5156	120	26	g.	g.	PROPN
ejpam-5156	120	27	if	if	SCONJ
ejpam-5156	120	28	v	v	NOUN
ejpam-5156	120	29	is	be	AUX
ejpam-5156	120	30	an	an	DET
ejpam-5156	120	31	isolated	isolated	ADJ
ejpam-5156	120	32	vertex	vertex	NOUN
ejpam-5156	120	33	in	in	ADP
ejpam-5156	120	34	g	g	PROPN
ejpam-5156	120	35	,	,	PUNCT
ejpam-5156	120	36	then	then	ADV
ejpam-5156	120	37	v	v	X
ejpam-5156	120	38	∈	∈	PROPN
ejpam-5156	120	39	s.	s.	PROPN
ejpam-5156	120	40	proof	proof	PROPN
ejpam-5156	120	41	.	.	PUNCT
ejpam-5156	121	1	let	let	VERB
ejpam-5156	121	2	s	s	PRON
ejpam-5156	121	3	be	be	AUX
ejpam-5156	121	4	an	an	DET
ejpam-5156	121	5	rgda	rgda	NOUN
ejpam-5156	121	6	in	in	ADP
ejpam-5156	121	7	g	g	PROPN
ejpam-5156	121	8	=	=	SYM
ejpam-5156	121	9	(	(	PUNCT
ejpam-5156	121	10	v	v	NOUN
ejpam-5156	121	11	,	,	PUNCT
ejpam-5156	121	12	e	e	NOUN
ejpam-5156	121	13	)	)	PUNCT
ejpam-5156	121	14	and	and	CCONJ
ejpam-5156	121	15	v	v	X
ejpam-5156	121	16	∈	∈	NOUN
ejpam-5156	121	17	g	g	NOUN
ejpam-5156	121	18	be	be	AUX
ejpam-5156	121	19	an	an	DET
ejpam-5156	121	20	isolated	isolated	ADJ
ejpam-5156	121	21	vertex	vertex	NOUN
ejpam-5156	121	22	.	.	PUNCT
ejpam-5156	122	1	assume	assume	VERB
ejpam-5156	122	2	that	that	SCONJ
ejpam-5156	122	3	v	v	X
ejpam-5156	122	4	/∈	/∈	PUNCT
ejpam-5156	122	5	s.	s.	PROPN
ejpam-5156	123	1	then	then	ADV
ejpam-5156	123	2	⟨v	⟨v	PROPN
ejpam-5156	123	3	∖	∖	PROPN
ejpam-5156	123	4	s⟩	s⟩	PROPN
ejpam-5156	123	5	contains	contain	VERB
ejpam-5156	123	6	an	an	DET
ejpam-5156	123	7	isolated	isolated	ADJ
ejpam-5156	123	8	vertex	vertex	NOUN
ejpam-5156	123	9	v.	v.	ADP
ejpam-5156	123	10	this	this	PRON
ejpam-5156	123	11	means	mean	VERB
ejpam-5156	123	12	that	that	SCONJ
ejpam-5156	123	13	s	s	VERB
ejpam-5156	123	14	is	be	AUX
ejpam-5156	123	15	not	not	PART
ejpam-5156	123	16	an	an	DET
ejpam-5156	123	17	rds	rd	NOUN
ejpam-5156	123	18	,	,	PUNCT
ejpam-5156	123	19	a	a	DET
ejpam-5156	123	20	contradiction	contradiction	NOUN
ejpam-5156	123	21	.	.	PUNCT
ejpam-5156	124	1	hence	hence	ADV
ejpam-5156	124	2	,	,	PUNCT
ejpam-5156	124	3	v	v	PROPN
ejpam-5156	124	4	∈	∈	PROPN
ejpam-5156	124	5	s.	s.	PROPN
ejpam-5156	124	6	corollary	corollary	NOUN
ejpam-5156	124	7	1	1	X
ejpam-5156	124	8	.	.	PUNCT
ejpam-5156	125	1	let	let	VERB
ejpam-5156	125	2	en	en	X
ejpam-5156	125	3	=	=	SYM
ejpam-5156	125	4	(	(	PUNCT
ejpam-5156	125	5	v	v	NOUN
ejpam-5156	125	6	,	,	PUNCT
ejpam-5156	125	7	e	e	NOUN
ejpam-5156	125	8	)	)	PUNCT
ejpam-5156	125	9	be	be	AUX
ejpam-5156	125	10	an	an	DET
ejpam-5156	125	11	empty	empty	ADJ
ejpam-5156	125	12	graph	graph	NOUN
ejpam-5156	125	13	of	of	ADP
ejpam-5156	125	14	order	order	NOUN
ejpam-5156	125	15	n	n	PRON
ejpam-5156	125	16	≥	≥	NOUN
ejpam-5156	125	17	1	1	NUM
ejpam-5156	125	18	.	.	PUNCT
ejpam-5156	126	1	then	then	ADV
ejpam-5156	126	2	,	,	PUNCT
ejpam-5156	126	3	γra(en	γra(en	X
ejpam-5156	126	4	)	)	PUNCT
ejpam-5156	126	5	=	=	SYM
ejpam-5156	126	6	n.	n.	NOUN
ejpam-5156	126	7	theorem	theorem	VERB
ejpam-5156	126	8	5	5	NUM
ejpam-5156	126	9	.	.	PUNCT
ejpam-5156	127	1	if	if	SCONJ
ejpam-5156	127	2	g	g	PROPN
ejpam-5156	127	3	=	=	SYM
ejpam-5156	127	4	(	(	PUNCT
ejpam-5156	127	5	v	v	NOUN
ejpam-5156	127	6	,	,	PUNCT
ejpam-5156	127	7	e	e	NOUN
ejpam-5156	127	8	)	)	PUNCT
ejpam-5156	127	9	is	be	AUX
ejpam-5156	127	10	any	any	DET
ejpam-5156	127	11	graph	graph	NOUN
ejpam-5156	127	12	with	with	ADP
ejpam-5156	127	13	restrained	restrained	ADJ
ejpam-5156	127	14	global	global	ADJ
ejpam-5156	127	15	defensive	defensive	ADJ
ejpam-5156	127	16	alliance	alliance	NOUN
ejpam-5156	127	17	s	s	PART
ejpam-5156	127	18	,	,	PUNCT
ejpam-5156	127	19	then	then	ADV
ejpam-5156	127	20	1	1	NUM
ejpam-5156	127	21	≤	≤	NUM
ejpam-5156	127	22	|s|	|s|	NOUN
ejpam-5156	127	23	≤	≤	ADJ
ejpam-5156	127	24	n.	n.	NOUN
ejpam-5156	127	25	proof	proof	NOUN
ejpam-5156	127	26	.	.	PUNCT
ejpam-5156	128	1	let	let	VERB
ejpam-5156	128	2	s	s	PRON
ejpam-5156	128	3	be	be	AUX
ejpam-5156	128	4	an	an	DET
ejpam-5156	128	5	rgda	rgda	NOUN
ejpam-5156	128	6	in	in	ADP
ejpam-5156	128	7	g	g	PROPN
ejpam-5156	128	8	=	=	SYM
ejpam-5156	128	9	(	(	PUNCT
ejpam-5156	128	10	v	v	NOUN
ejpam-5156	128	11	,	,	PUNCT
ejpam-5156	128	12	e	e	NOUN
ejpam-5156	128	13	)	)	PUNCT
ejpam-5156	128	14	.	.	PUNCT
ejpam-5156	129	1	by	by	ADP
ejpam-5156	129	2	theorem	theorem	NOUN
ejpam-5156	129	3	1	1	NUM
ejpam-5156	129	4	,	,	PUNCT
ejpam-5156	129	5	γra(g	γra(g	ADJ
ejpam-5156	129	6	)	)	PUNCT
ejpam-5156	129	7	≤	≤	PUNCT
ejpam-5156	129	8	n.	n.	NOUN
ejpam-5156	129	9	this	this	PRON
ejpam-5156	129	10	means	mean	VERB
ejpam-5156	129	11	that	that	SCONJ
ejpam-5156	129	12	|s|	|s|	VERB
ejpam-5156	129	13	≤	≤	PROPN
ejpam-5156	129	14	n.	n.	NOUN
ejpam-5156	129	15	since	since	SCONJ
ejpam-5156	129	16	s	s	PROPN
ejpam-5156	129	17	is	be	AUX
ejpam-5156	129	18	necessarily	necessarily	ADV
ejpam-5156	129	19	a	a	DET
ejpam-5156	129	20	nonempty	nonempty	ADJ
ejpam-5156	129	21	set	set	NOUN
ejpam-5156	129	22	,	,	PUNCT
ejpam-5156	129	23	then	then	ADV
ejpam-5156	129	24	|s|	|s|	NOUN
ejpam-5156	129	25	≥	≥	NOUN
ejpam-5156	129	26	1	1	NUM
ejpam-5156	129	27	.	.	PUNCT
ejpam-5156	130	1	therefore	therefore	ADV
ejpam-5156	130	2	,	,	PUNCT
ejpam-5156	130	3	1	1	NUM
ejpam-5156	130	4	≤	≤	NUM
ejpam-5156	130	5	|s|	|s|	PROPN
ejpam-5156	130	6	≤	≤	PROPN
ejpam-5156	130	7	n.	n.	NOUN
ejpam-5156	130	8	theorem	theorem	NOUN
ejpam-5156	130	9	6	6	NUM
ejpam-5156	130	10	.	.	PUNCT
ejpam-5156	131	1	let	let	VERB
ejpam-5156	131	2	kn	kn	PROPN
ejpam-5156	131	3	=	=	PUNCT
ejpam-5156	131	4	(	(	PUNCT
ejpam-5156	131	5	v	v	NOUN
ejpam-5156	131	6	,	,	PUNCT
ejpam-5156	131	7	e	e	NOUN
ejpam-5156	131	8	)	)	PUNCT
ejpam-5156	131	9	be	be	AUX
ejpam-5156	131	10	a	a	DET
ejpam-5156	131	11	complete	complete	ADJ
ejpam-5156	131	12	graph	graph	NOUN
ejpam-5156	131	13	of	of	ADP
ejpam-5156	131	14	order	order	NOUN
ejpam-5156	131	15	n	n	PRON
ejpam-5156	131	16	≥	≥	NOUN
ejpam-5156	131	17	4	4	NUM
ejpam-5156	131	18	.	.	PUNCT
ejpam-5156	132	1	then	then	ADV
ejpam-5156	132	2	s	s	VERB
ejpam-5156	132	3	⊆	⊆	NUM
ejpam-5156	132	4	v	v	NOUN
ejpam-5156	132	5	is	be	AUX
ejpam-5156	132	6	a	a	DET
ejpam-5156	132	7	restrained	restrained	ADJ
ejpam-5156	132	8	global	global	ADJ
ejpam-5156	132	9	defensive	defensive	ADJ
ejpam-5156	132	10	alliance	alliance	NOUN
ejpam-5156	132	11	if	if	SCONJ
ejpam-5156	132	12	and	and	CCONJ
ejpam-5156	132	13	only	only	ADV
ejpam-5156	132	14	if	if	SCONJ
ejpam-5156	132	15	the	the	DET
ejpam-5156	132	16	following	follow	VERB
ejpam-5156	132	17	holds	hold	VERB
ejpam-5156	132	18	:	:	PUNCT
ejpam-5156	132	19	i.	i.	PROPN
ejpam-5156	132	20	|s|	|s|	PUNCT
ejpam-5156	132	21	≥	≥	PROPN
ejpam-5156	132	22	⌈	⌈	SYM
ejpam-5156	132	23	n	n	CCONJ
ejpam-5156	132	24	2	2	NUM
ejpam-5156	132	25	⌉	⌉	X
ejpam-5156	132	26	;	;	PUNCT
ejpam-5156	132	27	ii	ii	X
ejpam-5156	132	28	.	.	PUNCT
ejpam-5156	132	29	|s|	|s|	PROPN
ejpam-5156	132	30	=	=	NOUN
ejpam-5156	132	31	̸	̸	NUM
ejpam-5156	132	32	n−	n−	NOUN
ejpam-5156	132	33	1	1	NUM
ejpam-5156	132	34	.	.	PUNCT
ejpam-5156	133	1	proof	proof	NOUN
ejpam-5156	133	2	.	.	PUNCT
ejpam-5156	134	1	let	let	VERB
ejpam-5156	134	2	s	s	PRON
ejpam-5156	134	3	be	be	AUX
ejpam-5156	134	4	an	an	DET
ejpam-5156	134	5	rgda	rgda	NOUN
ejpam-5156	134	6	in	in	ADP
ejpam-5156	134	7	kn	kn	PROPN
ejpam-5156	134	8	=	=	PUNCT
ejpam-5156	134	9	(	(	PUNCT
ejpam-5156	134	10	v	v	NOUN
ejpam-5156	134	11	,	,	PUNCT
ejpam-5156	134	12	e	e	NOUN
ejpam-5156	134	13	)	)	PUNCT
ejpam-5156	134	14	of	of	ADP
ejpam-5156	134	15	order	order	NOUN
ejpam-5156	134	16	n	n	PRON
ejpam-5156	134	17	≥	≥	NOUN
ejpam-5156	134	18	4	4	NUM
ejpam-5156	134	19	.	.	PUNCT
ejpam-5156	134	20	assume	assume	VERB
ejpam-5156	134	21	that	that	SCONJ
ejpam-5156	134	22	s	s	VERB
ejpam-5156	134	23	does	do	AUX
ejpam-5156	134	24	not	not	PART
ejpam-5156	134	25	satisfy	satisfy	VERB
ejpam-5156	134	26	i	i	PRON
ejpam-5156	134	27	and	and	CCONJ
ejpam-5156	134	28	ii	ii	PROPN
ejpam-5156	134	29	.	.	PUNCT
ejpam-5156	135	1	this	this	PRON
ejpam-5156	135	2	means	mean	VERB
ejpam-5156	135	3	that	that	SCONJ
ejpam-5156	135	4	either	either	CCONJ
ejpam-5156	135	5	|s|	|s|	PROPN
ejpam-5156	135	6	̸≥	̸≥	PROPN
ejpam-5156	135	7	⌈	⌈	NOUN
ejpam-5156	135	8	n	n	PRON
ejpam-5156	135	9	2	2	NUM
ejpam-5156	135	10	⌉	⌉	NOUN
ejpam-5156	135	11	or	or	CCONJ
ejpam-5156	135	12	|s|	|s|	PROPN
ejpam-5156	135	13	=	=	SYM
ejpam-5156	135	14	n−	n−	NOUN
ejpam-5156	135	15	1	1	NUM
ejpam-5156	135	16	.	.	PUNCT
ejpam-5156	135	17	l.	l.	PROPN
ejpam-5156	135	18	consistente	consistente	PROPN
ejpam-5156	135	19	,	,	PUNCT
ejpam-5156	135	20	i.	i.	PROPN
ejpam-5156	135	21	cabahug	cabahug	PROPN
ejpam-5156	135	22	,	,	PUNCT
ejpam-5156	135	23	jr	jr	PROPN
ejpam-5156	135	24	.	.	PROPN
ejpam-5156	135	25	/	/	SYM
ejpam-5156	135	26	eur	eur	PROPN
ejpam-5156	135	27	.	.	PUNCT
ejpam-5156	136	1	j.	j.	PROPN
ejpam-5156	136	2	pure	pure	PROPN
ejpam-5156	136	3	appl	appl	PROPN
ejpam-5156	136	4	.	.	PROPN
ejpam-5156	136	5	math	math	PROPN
ejpam-5156	136	6	,	,	PUNCT
ejpam-5156	136	7	17	17	NUM
ejpam-5156	136	8	(	(	PUNCT
ejpam-5156	136	9	3	3	NUM
ejpam-5156	136	10	)	)	PUNCT
ejpam-5156	136	11	(	(	PUNCT
ejpam-5156	136	12	2024	2024	NUM
ejpam-5156	136	13	)	)	PUNCT
ejpam-5156	136	14	,	,	PUNCT
ejpam-5156	136	15	2196	2196	NUM
ejpam-5156	136	16	-	-	SYM
ejpam-5156	136	17	2209	2209	NUM
ejpam-5156	136	18	2201	2201	NUM
ejpam-5156	136	19	case	case	NOUN
ejpam-5156	136	20	1	1	NUM
ejpam-5156	136	21	:	:	PUNCT
ejpam-5156	136	22	suppose	suppose	VERB
ejpam-5156	136	23	that	that	SCONJ
ejpam-5156	136	24	|s|	|s|	NOUN
ejpam-5156	136	25	̸≥	̸≥	PROPN
ejpam-5156	136	26	⌈	⌈	NOUN
ejpam-5156	136	27	n	n	PRON
ejpam-5156	136	28	2	2	NUM
ejpam-5156	136	29	⌉	⌉	X
ejpam-5156	136	30	.	.	PUNCT
ejpam-5156	137	1	since	since	SCONJ
ejpam-5156	137	2	s	s	PROPN
ejpam-5156	137	3	is	be	AUX
ejpam-5156	137	4	an	an	DET
ejpam-5156	137	5	rgda	rgda	NOUN
ejpam-5156	137	6	and	and	CCONJ
ejpam-5156	137	7	at	at	ADV
ejpam-5156	137	8	least	least	ADV
ejpam-5156	137	9	one	one	NUM
ejpam-5156	137	10	vertex	vertex	NOUN
ejpam-5156	137	11	is	be	AUX
ejpam-5156	137	12	necessary	necessary	ADJ
ejpam-5156	137	13	to	to	PART
ejpam-5156	137	14	dominate	dominate	VERB
ejpam-5156	137	15	kn	kn	PROPN
ejpam-5156	137	16	,	,	PUNCT
ejpam-5156	137	17	s	s	PART
ejpam-5156	137	18	must	must	AUX
ejpam-5156	137	19	not	not	PART
ejpam-5156	137	20	be	be	AUX
ejpam-5156	137	21	empty	empty	ADJ
ejpam-5156	137	22	.	.	PUNCT
ejpam-5156	138	1	then	then	ADV
ejpam-5156	138	2	for	for	ADP
ejpam-5156	138	3	every	every	DET
ejpam-5156	138	4	v	v	NOUN
ejpam-5156	138	5	∈	∈	NOUN
ejpam-5156	138	6	s	s	PART
ejpam-5156	138	7	implies	imply	VERB
ejpam-5156	138	8	|n	|n	ADJ
ejpam-5156	138	9	[	[	X
ejpam-5156	138	10	v	v	X
ejpam-5156	138	11	]	]	X
ejpam-5156	138	12	∩	∩	NOUN
ejpam-5156	138	13	s|	s|	NOUN
ejpam-5156	138	14	=	=	SYM
ejpam-5156	138	15	|s|	|s|	NOUN
ejpam-5156	138	16	̸≥	̸≥	PROPN
ejpam-5156	138	17	⌈n	⌈n	NOUN
ejpam-5156	138	18	2	2	NUM
ejpam-5156	138	19	⌉	⌉	PRON
ejpam-5156	138	20	≤	≤	NOUN
ejpam-5156	138	21	|v	|v	VERB
ejpam-5156	138	22	|	|	ADV
ejpam-5156	138	23	−	−	PROPN
ejpam-5156	138	24	|s|	|s|	PROPN
ejpam-5156	138	25	=	=	SYM
ejpam-5156	138	26	|n(v	|n(v	PROPN
ejpam-5156	138	27	)	)	PUNCT
ejpam-5156	138	28	∩	∩	NOUN
ejpam-5156	138	29	(	(	PUNCT
ejpam-5156	138	30	v	v	NUM
ejpam-5156	138	31	∖	∖	PROPN
ejpam-5156	138	32	s)|	s)|	NOUN
ejpam-5156	138	33	.	.	PUNCT
ejpam-5156	139	1	so	so	ADV
ejpam-5156	139	2	,	,	PUNCT
ejpam-5156	139	3	s	s	VERB
ejpam-5156	139	4	is	be	AUX
ejpam-5156	139	5	not	not	PART
ejpam-5156	139	6	a	a	DET
ejpam-5156	139	7	da	da	NOUN
ejpam-5156	139	8	,	,	PUNCT
ejpam-5156	139	9	a	a	DET
ejpam-5156	139	10	contradiction	contradiction	NOUN
ejpam-5156	139	11	.	.	PUNCT
ejpam-5156	140	1	therefore	therefore	ADV
ejpam-5156	140	2	,	,	PUNCT
ejpam-5156	140	3	|s|	|s|	VERB
ejpam-5156	140	4	≥	≥	NOUN
ejpam-5156	140	5	⌈	⌈	SYM
ejpam-5156	140	6	n	n	PRON
ejpam-5156	140	7	2	2	NUM
ejpam-5156	140	8	⌉	⌉	X
ejpam-5156	140	9	.	.	PUNCT
ejpam-5156	141	1	this	this	PRON
ejpam-5156	141	2	proves	prove	VERB
ejpam-5156	141	3	i.	i.	NOUN
ejpam-5156	141	4	case	case	NOUN
ejpam-5156	141	5	2	2	NUM
ejpam-5156	141	6	:	:	PUNCT
ejpam-5156	141	7	suppose	suppose	VERB
ejpam-5156	141	8	that	that	SCONJ
ejpam-5156	141	9	|s|	|s|	PROPN
ejpam-5156	141	10	=	=	SYM
ejpam-5156	141	11	n	n	CCONJ
ejpam-5156	141	12	−	−	PROPN
ejpam-5156	141	13	1	1	NUM
ejpam-5156	141	14	.	.	PUNCT
ejpam-5156	142	1	then	then	ADV
ejpam-5156	142	2	there	there	PRON
ejpam-5156	142	3	exists	exist	VERB
ejpam-5156	142	4	a	a	DET
ejpam-5156	142	5	unique	unique	ADJ
ejpam-5156	142	6	vertex	vertex	NOUN
ejpam-5156	142	7	a	a	DET
ejpam-5156	142	8	∈	∈	NOUN
ejpam-5156	142	9	v	v	ADP
ejpam-5156	142	10	such	such	DET
ejpam-5156	142	11	that	that	SCONJ
ejpam-5156	142	12	a	a	DET
ejpam-5156	142	13	/∈	/∈	PUNCT
ejpam-5156	142	14	s.	s.	PROPN
ejpam-5156	143	1	this	this	PRON
ejpam-5156	143	2	means	mean	VERB
ejpam-5156	143	3	that	that	SCONJ
ejpam-5156	143	4	a	a	PRON
ejpam-5156	143	5	is	be	AUX
ejpam-5156	143	6	not	not	PART
ejpam-5156	143	7	adjacent	adjacent	ADJ
ejpam-5156	143	8	to	to	ADP
ejpam-5156	143	9	another	another	DET
ejpam-5156	143	10	vertex	vertex	NOUN
ejpam-5156	143	11	in	in	ADP
ejpam-5156	143	12	v	v	NUM
ejpam-5156	143	13	∖	∖	X
ejpam-5156	143	14	s.	s.	PROPN
ejpam-5156	144	1	so	so	ADV
ejpam-5156	144	2	,	,	PUNCT
ejpam-5156	144	3	s	s	X
ejpam-5156	144	4	is	be	AUX
ejpam-5156	144	5	not	not	PART
ejpam-5156	144	6	an	an	DET
ejpam-5156	144	7	rds	rd	NOUN
ejpam-5156	144	8	,	,	PUNCT
ejpam-5156	144	9	a	a	DET
ejpam-5156	144	10	contradiction	contradiction	NOUN
ejpam-5156	144	11	.	.	PUNCT
ejpam-5156	145	1	hence	hence	ADV
ejpam-5156	145	2	,	,	PUNCT
ejpam-5156	145	3	|s|	|s|	NOUN
ejpam-5156	145	4	=	=	NOUN
ejpam-5156	145	5	̸	̸	NUM
ejpam-5156	145	6	n−	n−	NOUN
ejpam-5156	145	7	1	1	NUM
ejpam-5156	145	8	.	.	PUNCT
ejpam-5156	146	1	this	this	PRON
ejpam-5156	146	2	proves	prove	VERB
ejpam-5156	146	3	ii	ii	NOUN
ejpam-5156	146	4	.	.	PUNCT
ejpam-5156	147	1	hence	hence	ADV
ejpam-5156	147	2	,	,	PUNCT
ejpam-5156	147	3	i	i	PRON
ejpam-5156	147	4	and	and	CCONJ
ejpam-5156	147	5	ii	ii	PROPN
ejpam-5156	147	6	must	must	AUX
ejpam-5156	147	7	be	be	AUX
ejpam-5156	147	8	true	true	ADJ
ejpam-5156	147	9	.	.	PUNCT
ejpam-5156	148	1	conversely	conversely	ADV
ejpam-5156	148	2	,	,	PUNCT
ejpam-5156	148	3	let	let	VERB
ejpam-5156	148	4	s	s	PRON
ejpam-5156	148	5	⊆	⊆	NUM
ejpam-5156	148	6	v	v	NOUN
ejpam-5156	148	7	be	be	AUX
ejpam-5156	148	8	a	a	DET
ejpam-5156	148	9	set	set	NOUN
ejpam-5156	148	10	in	in	ADP
ejpam-5156	148	11	kn	kn	PROPN
ejpam-5156	148	12	=	=	PUNCT
ejpam-5156	148	13	(	(	PUNCT
ejpam-5156	148	14	v	v	NOUN
ejpam-5156	148	15	,	,	PUNCT
ejpam-5156	148	16	e	e	NOUN
ejpam-5156	148	17	)	)	PUNCT
ejpam-5156	148	18	,	,	PUNCT
ejpam-5156	148	19	of	of	ADP
ejpam-5156	148	20	order	order	NOUN
ejpam-5156	148	21	n	n	PRON
ejpam-5156	148	22	≥	≥	NOUN
ejpam-5156	148	23	4	4	NUM
ejpam-5156	148	24	,	,	PUNCT
ejpam-5156	148	25	that	that	PRON
ejpam-5156	148	26	satisfies	satisfy	VERB
ejpam-5156	148	27	i	i	PRON
ejpam-5156	148	28	and	and	CCONJ
ejpam-5156	148	29	ii	ii	PROPN
ejpam-5156	148	30	.	.	PUNCT
ejpam-5156	149	1	by	by	ADP
ejpam-5156	149	2	i	i	PRON
ejpam-5156	149	3	,	,	PUNCT
ejpam-5156	149	4	s	s	VERB
ejpam-5156	149	5	is	be	AUX
ejpam-5156	149	6	,	,	PUNCT
ejpam-5156	149	7	necessarily	necessarily	ADV
ejpam-5156	149	8	,	,	PUNCT
ejpam-5156	149	9	a	a	DET
ejpam-5156	149	10	nonempty	nonempty	ADV
ejpam-5156	149	11	set	set	VERB
ejpam-5156	149	12	and	and	CCONJ
ejpam-5156	149	13	for	for	ADP
ejpam-5156	149	14	every	every	DET
ejpam-5156	149	15	v	v	NUM
ejpam-5156	149	16	∈	∈	PROPN
ejpam-5156	149	17	s	s	NOUN
ejpam-5156	149	18	,	,	PUNCT
ejpam-5156	149	19	|n	|n	X
ejpam-5156	150	1	[	[	X
ejpam-5156	150	2	v	v	X
ejpam-5156	150	3	]	]	X
ejpam-5156	150	4	∩	∩	NOUN
ejpam-5156	150	5	s|	s|	NOUN
ejpam-5156	150	6	=	=	SYM
ejpam-5156	150	7	|s|	|s|	PROPN
ejpam-5156	150	8	≥	≥	NOUN
ejpam-5156	150	9	⌈n	⌈n	NOUN
ejpam-5156	150	10	2	2	NUM
ejpam-5156	150	11	⌉	⌉	X
ejpam-5156	150	12	≥	≥	NUM
ejpam-5156	150	13	n−	n−	NOUN
ejpam-5156	150	14	⌈n	⌈n	VERB
ejpam-5156	150	15	2	2	NUM
ejpam-5156	150	16	⌉	⌉	X
ejpam-5156	150	17	≥	≥	NUM
ejpam-5156	150	18	|v	|v	X
ejpam-5156	150	19	∖	∖	X
ejpam-5156	150	20	s|	s|	VERB
ejpam-5156	150	21	=	=	PUNCT
ejpam-5156	150	22	|n	|n	X
ejpam-5156	151	1	[	[	X
ejpam-5156	151	2	v	v	X
ejpam-5156	151	3	]	]	X
ejpam-5156	151	4	∩	∩	NOUN
ejpam-5156	151	5	(	(	PUNCT
ejpam-5156	151	6	v	v	NUM
ejpam-5156	151	7	∖	∖	PROPN
ejpam-5156	151	8	s)|	s)|	NOUN
ejpam-5156	151	9	.	.	PUNCT
ejpam-5156	152	1	so	so	ADV
ejpam-5156	152	2	,	,	PUNCT
ejpam-5156	152	3	s	s	VERB
ejpam-5156	152	4	is	be	AUX
ejpam-5156	152	5	a	a	DET
ejpam-5156	152	6	da	da	NOUN
ejpam-5156	152	7	.	.	PUNCT
ejpam-5156	153	1	since	since	SCONJ
ejpam-5156	153	2	every	every	DET
ejpam-5156	153	3	vertex	vertex	NOUN
ejpam-5156	153	4	in	in	ADP
ejpam-5156	153	5	kn	kn	PROPN
ejpam-5156	153	6	is	be	AUX
ejpam-5156	153	7	adjacent	adjacent	ADJ
ejpam-5156	153	8	to	to	ADP
ejpam-5156	153	9	one	one	NUM
ejpam-5156	153	10	another	another	DET
ejpam-5156	153	11	,	,	PUNCT
ejpam-5156	153	12	s	s	VERB
ejpam-5156	153	13	is	be	AUX
ejpam-5156	153	14	also	also	ADV
ejpam-5156	153	15	a	a	DET
ejpam-5156	153	16	ds	ds	NOUN
ejpam-5156	153	17	.	.	PUNCT
ejpam-5156	153	18	by	by	ADP
ejpam-5156	153	19	ii	ii	PROPN
ejpam-5156	153	20	,	,	PUNCT
ejpam-5156	153	21	⟨v	⟨v	PROPN
ejpam-5156	153	22	∖	∖	PROPN
ejpam-5156	153	23	s⟩	s⟩	NOUN
ejpam-5156	153	24	does	do	AUX
ejpam-5156	153	25	not	not	PART
ejpam-5156	153	26	contain	contain	VERB
ejpam-5156	153	27	an	an	DET
ejpam-5156	153	28	isolated	isolated	ADJ
ejpam-5156	153	29	vertex	vertex	NOUN
ejpam-5156	153	30	.	.	PUNCT
ejpam-5156	154	1	hence	hence	ADV
ejpam-5156	154	2	,	,	PUNCT
ejpam-5156	154	3	s	s	VERB
ejpam-5156	154	4	is	be	AUX
ejpam-5156	154	5	an	an	DET
ejpam-5156	154	6	rds	rd	NOUN
ejpam-5156	154	7	.	.	PUNCT
ejpam-5156	155	1	therefore	therefore	ADV
ejpam-5156	155	2	,	,	PUNCT
ejpam-5156	155	3	s	s	VERB
ejpam-5156	155	4	is	be	AUX
ejpam-5156	155	5	an	an	DET
ejpam-5156	155	6	rgda	rgda	NOUN
ejpam-5156	155	7	in	in	ADP
ejpam-5156	155	8	kn	kn	PROPN
ejpam-5156	155	9	.	.	PUNCT
ejpam-5156	155	10	corollary	corollary	PROPN
ejpam-5156	156	1	2	2	NUM
ejpam-5156	156	2	.	.	PUNCT
ejpam-5156	157	1	let	let	VERB
ejpam-5156	157	2	kn	kn	PROPN
ejpam-5156	157	3	=	=	PUNCT
ejpam-5156	157	4	(	(	PUNCT
ejpam-5156	157	5	v	v	NOUN
ejpam-5156	157	6	,	,	PUNCT
ejpam-5156	157	7	e	e	NOUN
ejpam-5156	157	8	)	)	PUNCT
ejpam-5156	157	9	be	be	AUX
ejpam-5156	157	10	a	a	DET
ejpam-5156	157	11	complete	complete	ADJ
ejpam-5156	157	12	graph	graph	NOUN
ejpam-5156	157	13	of	of	ADP
ejpam-5156	157	14	order	order	NOUN
ejpam-5156	157	15	n	n	PRON
ejpam-5156	157	16	≥	≥	NOUN
ejpam-5156	157	17	1	1	NUM
ejpam-5156	157	18	.	.	PUNCT
ejpam-5156	158	1	then	then	ADV
ejpam-5156	158	2	γra(kn	γra(kn	NOUN
ejpam-5156	158	3	)	)	PUNCT
ejpam-5156	159	1	=	=	PRON
ejpam-5156	159	2	{	{	PUNCT
ejpam-5156	159	3	|v	|v	PROPN
ejpam-5156	160	1	|	|	ADV
ejpam-5156	160	2	if	if	SCONJ
ejpam-5156	160	3	n	n	NOUN
ejpam-5156	160	4	=	=	SYM
ejpam-5156	160	5	1	1	NUM
ejpam-5156	160	6	,	,	PUNCT
ejpam-5156	160	7	2	2	NUM
ejpam-5156	160	8	,	,	PUNCT
ejpam-5156	160	9	3	3	NUM
ejpam-5156	160	10	;	;	PUNCT
ejpam-5156	160	11	⌈	⌈	NUM
ejpam-5156	160	12	n	n	PRON
ejpam-5156	160	13	2	2	NUM
ejpam-5156	160	14	⌉	⌉	X
ejpam-5156	160	15	if	if	SCONJ
ejpam-5156	160	16	n	n	PRON
ejpam-5156	160	17	≥	≥	NOUN
ejpam-5156	160	18	4	4	NUM
ejpam-5156	160	19	.	.	PUNCT
ejpam-5156	161	1	(	(	PUNCT
ejpam-5156	161	2	1	1	X
ejpam-5156	161	3	)	)	PUNCT
ejpam-5156	161	4	proof	proof	NOUN
ejpam-5156	161	5	.	.	PUNCT
ejpam-5156	162	1	let	let	VERB
ejpam-5156	162	2	s	s	PRON
ejpam-5156	162	3	be	be	AUX
ejpam-5156	162	4	an	an	DET
ejpam-5156	162	5	rgda	rgda	NOUN
ejpam-5156	162	6	in	in	ADP
ejpam-5156	162	7	kn	kn	PROPN
ejpam-5156	162	8	=	=	PUNCT
ejpam-5156	162	9	(	(	PUNCT
ejpam-5156	162	10	v	v	NOUN
ejpam-5156	162	11	,	,	PUNCT
ejpam-5156	162	12	e	e	NOUN
ejpam-5156	162	13	)	)	PUNCT
ejpam-5156	162	14	with	with	ADP
ejpam-5156	162	15	order	order	NOUN
ejpam-5156	162	16	n	n	PRON
ejpam-5156	162	17	≥	≥	NOUN
ejpam-5156	162	18	1	1	NUM
ejpam-5156	162	19	.	.	PUNCT
ejpam-5156	162	20	case	case	NOUN
ejpam-5156	162	21	1	1	NUM
ejpam-5156	162	22	:	:	PUNCT
ejpam-5156	162	23	n	n	NOUN
ejpam-5156	162	24	=	=	SYM
ejpam-5156	162	25	1	1	NUM
ejpam-5156	162	26	,	,	PUNCT
ejpam-5156	162	27	2	2	NUM
ejpam-5156	162	28	,	,	PUNCT
ejpam-5156	162	29	3	3	NUM
ejpam-5156	162	30	.	.	X
ejpam-5156	162	31	subcase	subcase	NOUN
ejpam-5156	162	32	1	1	NUM
ejpam-5156	162	33	:	:	PUNCT
ejpam-5156	162	34	n	n	NOUN
ejpam-5156	162	35	=	=	SYM
ejpam-5156	162	36	1	1	X
ejpam-5156	162	37	.	.	PUNCT
ejpam-5156	162	38	by	by	ADP
ejpam-5156	162	39	theorem	theorem	NOUN
ejpam-5156	162	40	1	1	NUM
ejpam-5156	162	41	,	,	PUNCT
ejpam-5156	162	42	v	v	NOUN
ejpam-5156	162	43	is	be	AUX
ejpam-5156	162	44	an	an	DET
ejpam-5156	162	45	rgda	rgda	ADJ
ejpam-5156	162	46	ink1	ink1	NOUN
ejpam-5156	162	47	.	.	PUNCT
ejpam-5156	163	1	sincek1	sincek1	NOUN
ejpam-5156	163	2	has	have	VERB
ejpam-5156	163	3	only	only	ADV
ejpam-5156	163	4	one	one	NUM
ejpam-5156	163	5	vertex	vertex	NOUN
ejpam-5156	163	6	,	,	PUNCT
ejpam-5156	163	7	then	then	ADV
ejpam-5156	163	8	v	v	NOUN
ejpam-5156	163	9	is	be	AUX
ejpam-5156	163	10	the	the	DET
ejpam-5156	163	11	minimum	minimum	ADJ
ejpam-5156	163	12	rgda	rgda	NOUN
ejpam-5156	163	13	in	in	ADP
ejpam-5156	163	14	k1	k1	PROPN
ejpam-5156	163	15	.	.	PUNCT
ejpam-5156	164	1	therefore	therefore	ADV
ejpam-5156	164	2	,	,	PUNCT
ejpam-5156	164	3	γra(k1	γra(k1	PROPN
ejpam-5156	164	4	)	)	PUNCT
ejpam-5156	164	5	=	=	PUNCT
ejpam-5156	164	6	|v	|v	PROPN
ejpam-5156	164	7	|	|	ADV
ejpam-5156	164	8	=	=	NOUN
ejpam-5156	164	9	1	1	X
ejpam-5156	164	10	.	.	PUNCT
ejpam-5156	164	11	subcase	subcase	NOUN
ejpam-5156	164	12	2	2	NUM
ejpam-5156	164	13	:	:	PUNCT
ejpam-5156	164	14	n	n	PROPN
ejpam-5156	164	15	=	=	SYM
ejpam-5156	164	16	2	2	X
ejpam-5156	164	17	.	.	X
ejpam-5156	164	18	notice	notice	VERB
ejpam-5156	164	19	that	that	SCONJ
ejpam-5156	164	20	every	every	DET
ejpam-5156	164	21	vertex	vertex	NOUN
ejpam-5156	164	22	in	in	ADP
ejpam-5156	164	23	v	v	NOUN
ejpam-5156	164	24	is	be	AUX
ejpam-5156	164	25	a	a	DET
ejpam-5156	164	26	leaf	leaf	NOUN
ejpam-5156	164	27	vertex	vertex	NOUN
ejpam-5156	164	28	.	.	PUNCT
ejpam-5156	165	1	by	by	ADP
ejpam-5156	165	2	theorem	theorem	NOUN
ejpam-5156	165	3	2	2	NUM
ejpam-5156	165	4	,	,	PUNCT
ejpam-5156	165	5	v	v	X
ejpam-5156	165	6	∈	∈	NOUN
ejpam-5156	165	7	s.	s.	PROPN
ejpam-5156	166	1	so	so	ADV
ejpam-5156	166	2	,	,	PUNCT
ejpam-5156	166	3	γra(k2	γra(k2	ADJ
ejpam-5156	166	4	)	)	PUNCT
ejpam-5156	166	5	=	=	SYM
ejpam-5156	166	6	|v	|v	PROPN
ejpam-5156	166	7	|	|	ADV
ejpam-5156	166	8	=	=	SYM
ejpam-5156	166	9	2	2	X
ejpam-5156	166	10	.	.	X
ejpam-5156	166	11	subcase	subcase	NOUN
ejpam-5156	166	12	3	3	NUM
ejpam-5156	166	13	:	:	PUNCT
ejpam-5156	166	14	n	n	PROPN
ejpam-5156	166	15	=	=	SYM
ejpam-5156	166	16	3	3	X
ejpam-5156	166	17	.	.	X
ejpam-5156	167	1	if	if	SCONJ
ejpam-5156	167	2	s	s	PROPN
ejpam-5156	167	3	is	be	AUX
ejpam-5156	167	4	a	a	DET
ejpam-5156	167	5	singleton	singleton	NOUN
ejpam-5156	167	6	set	set	NOUN
ejpam-5156	167	7	,	,	PUNCT
ejpam-5156	167	8	say	say	INTJ
ejpam-5156	167	9	,	,	PUNCT
ejpam-5156	167	10	s	s	PART
ejpam-5156	167	11	=	=	PUNCT
ejpam-5156	167	12	{	{	PUNCT
ejpam-5156	167	13	a	a	NOUN
ejpam-5156	167	14	}	}	PUNCT
ejpam-5156	167	15	where	where	SCONJ
ejpam-5156	167	16	a	a	DET
ejpam-5156	167	17	∈	∈	PROPN
ejpam-5156	167	18	v	v	NOUN
ejpam-5156	167	19	,	,	PUNCT
ejpam-5156	167	20	then	then	ADV
ejpam-5156	167	21	|n	|n	X
ejpam-5156	168	1	[	[	X
ejpam-5156	168	2	a	a	X
ejpam-5156	168	3	]	]	X
ejpam-5156	168	4	∩	∩	ADJ
ejpam-5156	168	5	s|	s|	NOUN
ejpam-5156	168	6	=	=	SYM
ejpam-5156	168	7	|{a}|	|{a}|	PUNCT
ejpam-5156	168	8	=	=	SYM
ejpam-5156	168	9	1	1	NUM
ejpam-5156	168	10	̸≥	̸≥	NUM
ejpam-5156	168	11	2	2	NUM
ejpam-5156	168	12	=	=	SYM
ejpam-5156	168	13	|{v	|{v	X
ejpam-5156	168	14	∖	∖	PROPN
ejpam-5156	168	15	{	{	PUNCT
ejpam-5156	168	16	a}}|	a}}|	NOUN
ejpam-5156	168	17	=	=	SYM
ejpam-5156	168	18	|n(a	|n(a	PROPN
ejpam-5156	168	19	)	)	PUNCT
ejpam-5156	168	20	∩	∩	NOUN
ejpam-5156	168	21	(	(	PUNCT
ejpam-5156	168	22	v	v	NUM
ejpam-5156	168	23	∖	∖	PROPN
ejpam-5156	168	24	s)|	s)|	NOUN
ejpam-5156	168	25	.	.	PUNCT
ejpam-5156	169	1	so	so	ADV
ejpam-5156	169	2	,	,	PUNCT
ejpam-5156	169	3	s	s	VERB
ejpam-5156	169	4	is	be	AUX
ejpam-5156	169	5	not	not	PART
ejpam-5156	169	6	a	a	DET
ejpam-5156	169	7	da	da	NOUN
ejpam-5156	169	8	,	,	PUNCT
ejpam-5156	169	9	a	a	DET
ejpam-5156	169	10	contradiction	contradiction	NOUN
ejpam-5156	169	11	.	.	PUNCT
ejpam-5156	170	1	hence	hence	ADV
ejpam-5156	170	2	,	,	PUNCT
ejpam-5156	170	3	s	s	VERB
ejpam-5156	170	4	̸=	̸=	PROPN
ejpam-5156	170	5	{	{	PUNCT
ejpam-5156	170	6	a	a	X
ejpam-5156	170	7	}	}	PUNCT
ejpam-5156	170	8	.	.	PUNCT
ejpam-5156	171	1	if	if	SCONJ
ejpam-5156	171	2	s	s	PROPN
ejpam-5156	171	3	has	have	VERB
ejpam-5156	171	4	two	two	NUM
ejpam-5156	171	5	vertices	vertex	NOUN
ejpam-5156	171	6	,	,	PUNCT
ejpam-5156	171	7	say	say	VERB
ejpam-5156	171	8	s	s	X
ejpam-5156	171	9	=	=	PUNCT
ejpam-5156	171	10	{	{	PUNCT
ejpam-5156	171	11	a	a	DET
ejpam-5156	171	12	,	,	PUNCT
ejpam-5156	171	13	b	b	NOUN
ejpam-5156	171	14	}	}	PUNCT
ejpam-5156	171	15	where	where	SCONJ
ejpam-5156	171	16	a	a	DET
ejpam-5156	171	17	,	,	PUNCT
ejpam-5156	171	18	b	b	PROPN
ejpam-5156	171	19	∈	∈	PROPN
ejpam-5156	171	20	v	v	NOUN
ejpam-5156	171	21	,	,	PUNCT
ejpam-5156	171	22	then	then	ADV
ejpam-5156	171	23	⟨v	⟨v	AUX
ejpam-5156	171	24	∖	∖	PROPN
ejpam-5156	171	25	s⟩	s⟩	PROPN
ejpam-5156	171	26	contains	contain	VERB
ejpam-5156	171	27	an	an	DET
ejpam-5156	171	28	isolated	isolated	ADJ
ejpam-5156	171	29	vertex	vertex	NOUN
ejpam-5156	171	30	c	c	PROPN
ejpam-5156	171	31	∈	∈	PROPN
ejpam-5156	171	32	v	v	ADP
ejpam-5156	171	33	∖s	∖s	PROPN
ejpam-5156	171	34	.	.	PUNCT
ejpam-5156	172	1	so	so	ADV
ejpam-5156	172	2	,	,	PUNCT
ejpam-5156	172	3	s	s	VERB
ejpam-5156	172	4	is	be	AUX
ejpam-5156	172	5	not	not	PART
ejpam-5156	172	6	an	an	DET
ejpam-5156	172	7	rds	rd	NOUN
ejpam-5156	172	8	,	,	PUNCT
ejpam-5156	172	9	a	a	DET
ejpam-5156	172	10	contradiction	contradiction	NOUN
ejpam-5156	172	11	.	.	PUNCT
ejpam-5156	173	1	hence	hence	ADV
ejpam-5156	173	2	,	,	PUNCT
ejpam-5156	173	3	s	s	VERB
ejpam-5156	173	4	̸=	̸=	PROPN
ejpam-5156	173	5	{	{	PUNCT
ejpam-5156	173	6	a	a	DET
ejpam-5156	173	7	,	,	PUNCT
ejpam-5156	173	8	b	b	NOUN
ejpam-5156	173	9	}	}	PUNCT
ejpam-5156	173	10	.	.	PUNCT
ejpam-5156	174	1	if	if	SCONJ
ejpam-5156	174	2	s	s	VERB
ejpam-5156	174	3	=	=	X
ejpam-5156	174	4	v	v	NOUN
ejpam-5156	174	5	,	,	PUNCT
ejpam-5156	174	6	then	then	ADV
ejpam-5156	174	7	by	by	ADP
ejpam-5156	174	8	theorem	theorem	NOUN
ejpam-5156	174	9	1	1	NUM
ejpam-5156	174	10	,	,	PUNCT
ejpam-5156	174	11	v	v	NOUN
ejpam-5156	174	12	is	be	AUX
ejpam-5156	174	13	an	an	DET
ejpam-5156	174	14	rgda	rgda	NOUN
ejpam-5156	174	15	in	in	ADP
ejpam-5156	174	16	k3	k3	PROPN
ejpam-5156	174	17	.	.	PUNCT
ejpam-5156	175	1	now	now	ADV
ejpam-5156	175	2	,	,	PUNCT
ejpam-5156	175	3	since	since	SCONJ
ejpam-5156	175	4	s	s	PART
ejpam-5156	175	5	=	=	SYM
ejpam-5156	175	6	v	v	NOUN
ejpam-5156	175	7	is	be	AUX
ejpam-5156	175	8	the	the	DET
ejpam-5156	175	9	only	only	ADJ
ejpam-5156	175	10	rgda	rgda	NOUN
ejpam-5156	175	11	in	in	ADP
ejpam-5156	175	12	k3	k3	PROPN
ejpam-5156	175	13	,	,	PUNCT
ejpam-5156	175	14	it	it	PRON
ejpam-5156	175	15	is	be	AUX
ejpam-5156	175	16	also	also	ADV
ejpam-5156	175	17	the	the	DET
ejpam-5156	175	18	minimum	minimum	ADJ
ejpam-5156	175	19	rgda	rgda	NOUN
ejpam-5156	175	20	in	in	ADP
ejpam-5156	175	21	k3	k3	PROPN
ejpam-5156	175	22	.	.	PUNCT
ejpam-5156	176	1	hence	hence	ADV
ejpam-5156	176	2	,	,	PUNCT
ejpam-5156	176	3	γra(k3	γra(k3	PROPN
ejpam-5156	176	4	)	)	PUNCT
ejpam-5156	176	5	=	=	SYM
ejpam-5156	176	6	|s|	|s|	PROPN
ejpam-5156	176	7	=	=	PUNCT
ejpam-5156	176	8	|v	|v	PROPN
ejpam-5156	177	1	|	|	NOUN
ejpam-5156	177	2	=	=	SYM
ejpam-5156	177	3	3	3	X
ejpam-5156	177	4	.	.	PUNCT
ejpam-5156	177	5	l.	l.	PROPN
ejpam-5156	177	6	consistente	consistente	PROPN
ejpam-5156	177	7	,	,	PUNCT
ejpam-5156	177	8	i.	i.	PROPN
ejpam-5156	177	9	cabahug	cabahug	PROPN
ejpam-5156	177	10	,	,	PUNCT
ejpam-5156	177	11	jr	jr	PROPN
ejpam-5156	177	12	.	.	PROPN
ejpam-5156	177	13	/	/	SYM
ejpam-5156	177	14	eur	eur	PROPN
ejpam-5156	177	15	.	.	PUNCT
ejpam-5156	178	1	j.	j.	PROPN
ejpam-5156	178	2	pure	pure	PROPN
ejpam-5156	178	3	appl	appl	PROPN
ejpam-5156	178	4	.	.	PROPN
ejpam-5156	178	5	math	math	PROPN
ejpam-5156	178	6	,	,	PUNCT
ejpam-5156	178	7	17	17	NUM
ejpam-5156	178	8	(	(	PUNCT
ejpam-5156	178	9	3	3	NUM
ejpam-5156	178	10	)	)	PUNCT
ejpam-5156	178	11	(	(	PUNCT
ejpam-5156	178	12	2024	2024	NUM
ejpam-5156	178	13	)	)	PUNCT
ejpam-5156	178	14	,	,	PUNCT
ejpam-5156	178	15	2196	2196	NUM
ejpam-5156	178	16	-	-	SYM
ejpam-5156	178	17	2209	2209	NUM
ejpam-5156	178	18	2202	2202	NUM
ejpam-5156	178	19	case	case	NOUN
ejpam-5156	178	20	2	2	NUM
ejpam-5156	178	21	:	:	PUNCT
ejpam-5156	178	22	v	v	NUM
ejpam-5156	178	23	≥	≥	NUM
ejpam-5156	178	24	4	4	NUM
ejpam-5156	178	25	.	.	PUNCT
ejpam-5156	178	26	by	by	ADP
ejpam-5156	178	27	theorem	theorem	NOUN
ejpam-5156	178	28	6(i	6(i	NUM
ejpam-5156	178	29	)	)	PUNCT
ejpam-5156	178	30	,	,	PUNCT
ejpam-5156	178	31	|s|	|s|	PRON
ejpam-5156	178	32	≥	≥	NOUN
ejpam-5156	178	33	⌈	⌈	SYM
ejpam-5156	178	34	n	n	PRON
ejpam-5156	178	35	2	2	NUM
ejpam-5156	178	36	⌉	⌉	X
ejpam-5156	178	37	.	.	PUNCT
ejpam-5156	179	1	this	this	PRON
ejpam-5156	179	2	implies	imply	VERB
ejpam-5156	179	3	that	that	SCONJ
ejpam-5156	179	4	the	the	DET
ejpam-5156	179	5	smallest	small	ADJ
ejpam-5156	179	6	value	value	NOUN
ejpam-5156	179	7	for	for	ADP
ejpam-5156	179	8	|s|	|s|	PROPN
ejpam-5156	179	9	is	be	AUX
ejpam-5156	179	10	⌈	⌈	NUM
ejpam-5156	179	11	n	n	PRON
ejpam-5156	179	12	2	2	NUM
ejpam-5156	179	13	⌉	⌉	X
ejpam-5156	179	14	.	.	PUNCT
ejpam-5156	180	1	therefore	therefore	ADV
ejpam-5156	180	2	,	,	PUNCT
ejpam-5156	180	3	γra(kn	γra(kn	NOUN
ejpam-5156	180	4	)	)	PUNCT
ejpam-5156	180	5	=	=	SYM
ejpam-5156	180	6	⌈	⌈	NOUN
ejpam-5156	180	7	n	n	CCONJ
ejpam-5156	180	8	2	2	NUM
ejpam-5156	180	9	⌉	⌉	X
ejpam-5156	180	10	.	.	PUNCT
ejpam-5156	181	1	theorem	theorem	ADJ
ejpam-5156	181	2	7	7	NUM
ejpam-5156	181	3	.	.	PUNCT
ejpam-5156	182	1	let	let	AUX
ejpam-5156	182	2	km	km	PROPN
ejpam-5156	182	3	,	,	PUNCT
ejpam-5156	182	4	n	n	NOUN
ejpam-5156	182	5	=	=	SYM
ejpam-5156	182	6	(	(	PUNCT
ejpam-5156	182	7	v	v	NOUN
ejpam-5156	182	8	,	,	PUNCT
ejpam-5156	182	9	e	e	NOUN
ejpam-5156	182	10	)	)	PUNCT
ejpam-5156	182	11	be	be	AUX
ejpam-5156	182	12	a	a	DET
ejpam-5156	182	13	complete	complete	ADJ
ejpam-5156	182	14	bipartite	bipartite	NOUN
ejpam-5156	182	15	graph	graph	NOUN
ejpam-5156	182	16	with	with	ADP
ejpam-5156	182	17	partite	partite	ADJ
ejpam-5156	182	18	sets	set	NOUN
ejpam-5156	182	19	a1	a1	NOUN
ejpam-5156	182	20	and	and	CCONJ
ejpam-5156	182	21	a2	a2	NOUN
ejpam-5156	182	22	such	such	ADJ
ejpam-5156	182	23	that	that	DET
ejpam-5156	182	24	|a1|	|a1|	NOUN
ejpam-5156	182	25	=	=	SYM
ejpam-5156	182	26	m	m	NOUN
ejpam-5156	182	27	and	and	CCONJ
ejpam-5156	182	28	|a2|	|a2|	VERB
ejpam-5156	182	29	=	=	SYM
ejpam-5156	182	30	n	n	PROPN
ejpam-5156	182	31	where	where	SCONJ
ejpam-5156	182	32	m	m	VERB
ejpam-5156	182	33	,	,	PUNCT
ejpam-5156	182	34	n	n	PRON
ejpam-5156	182	35	≥	≥	NOUN
ejpam-5156	182	36	2	2	NUM
ejpam-5156	182	37	.	.	PUNCT
ejpam-5156	183	1	then	then	ADV
ejpam-5156	183	2	s	s	VERB
ejpam-5156	183	3	⊆	⊆	NUM
ejpam-5156	183	4	v	v	NOUN
ejpam-5156	183	5	is	be	AUX
ejpam-5156	183	6	a	a	DET
ejpam-5156	183	7	restrained	restrained	ADJ
ejpam-5156	183	8	global	global	ADJ
ejpam-5156	183	9	defensive	defensive	ADJ
ejpam-5156	183	10	alliance	alliance	NOUN
ejpam-5156	183	11	if	if	SCONJ
ejpam-5156	183	12	and	and	CCONJ
ejpam-5156	183	13	only	only	ADV
ejpam-5156	183	14	if	if	SCONJ
ejpam-5156	183	15	the	the	DET
ejpam-5156	183	16	following	follow	VERB
ejpam-5156	183	17	holds	hold	VERB
ejpam-5156	183	18	:	:	PUNCT
ejpam-5156	183	19	i.	i.	PROPN
ejpam-5156	183	20	|s	|s	PROPN
ejpam-5156	184	1	∩a1|	∩a1|	PROPN
ejpam-5156	184	2	≥	≥	NUM
ejpam-5156	185	1	⌊	⌊	PROPN
ejpam-5156	185	2	m	m	PROPN
ejpam-5156	185	3	2	2	NUM
ejpam-5156	185	4	⌋	⌋	NOUN
ejpam-5156	185	5	and	and	CCONJ
ejpam-5156	185	6	|s	|s	PROPN
ejpam-5156	185	7	∩a2|	∩a2|	PROPN
ejpam-5156	185	8	≥	≥	PRON
ejpam-5156	185	9	⌊	⌊	VERB
ejpam-5156	185	10	n	n	DET
ejpam-5156	185	11	2	2	NUM
ejpam-5156	185	12	⌋	⌋	NOUN
ejpam-5156	185	13	;	;	PUNCT
ejpam-5156	185	14	ii	ii	X
ejpam-5156	185	15	.	.	PUNCT
ejpam-5156	186	1	|s	|s	PROPN
ejpam-5156	186	2	∩a1|	∩a1|	PROPN
ejpam-5156	187	1	=	=	PUNCT
ejpam-5156	187	2	m	m	NOUN
ejpam-5156	187	3	if	if	SCONJ
ejpam-5156	187	4	and	and	CCONJ
ejpam-5156	187	5	only	only	ADV
ejpam-5156	187	6	if	if	SCONJ
ejpam-5156	187	7	|s	|s	PROPN
ejpam-5156	187	8	∩a2|	∩a2|	PROPN
ejpam-5156	187	9	=	=	SYM
ejpam-5156	187	10	n.	n.	NOUN
ejpam-5156	187	11	proof	proof	NOUN
ejpam-5156	187	12	.	.	PUNCT
ejpam-5156	188	1	let	let	VERB
ejpam-5156	188	2	s	s	PRON
ejpam-5156	188	3	be	be	AUX
ejpam-5156	188	4	a	a	DET
ejpam-5156	188	5	rgda	rgda	NOUN
ejpam-5156	188	6	in	in	ADP
ejpam-5156	188	7	km	km	PROPN
ejpam-5156	188	8	,	,	PUNCT
ejpam-5156	188	9	n	n	NOUN
ejpam-5156	188	10	=	=	SYM
ejpam-5156	188	11	(	(	PUNCT
ejpam-5156	188	12	v	v	NOUN
ejpam-5156	188	13	,	,	PUNCT
ejpam-5156	188	14	e	e	NOUN
ejpam-5156	188	15	)	)	PUNCT
ejpam-5156	188	16	.	.	PUNCT
ejpam-5156	189	1	suppose	suppose	VERB
ejpam-5156	189	2	that	that	SCONJ
ejpam-5156	189	3	i	i	PRON
ejpam-5156	189	4	and	and	CCONJ
ejpam-5156	189	5	ii	ii	PROPN
ejpam-5156	189	6	are	be	AUX
ejpam-5156	189	7	false	false	ADJ
ejpam-5156	189	8	.	.	PUNCT
ejpam-5156	190	1	then	then	ADV
ejpam-5156	190	2	either	either	CCONJ
ejpam-5156	190	3	i	i	PRON
ejpam-5156	190	4	or	or	CCONJ
ejpam-5156	190	5	ii	ii	PROPN
ejpam-5156	190	6	is	be	AUX
ejpam-5156	190	7	not	not	PART
ejpam-5156	190	8	true	true	ADJ
ejpam-5156	190	9	.	.	PUNCT
ejpam-5156	191	1	case	case	NOUN
ejpam-5156	191	2	1	1	NUM
ejpam-5156	191	3	:	:	PUNCT
ejpam-5156	191	4	i	i	PRON
ejpam-5156	191	5	is	be	AUX
ejpam-5156	191	6	false	false	ADJ
ejpam-5156	191	7	.	.	PUNCT
ejpam-5156	192	1	then	then	ADV
ejpam-5156	192	2	either	either	CCONJ
ejpam-5156	192	3	|s	|s	PROPN
ejpam-5156	192	4	∩	∩	NOUN
ejpam-5156	192	5	a1|	a1|	VERB
ejpam-5156	192	6	̸≥	̸≥	PROPN
ejpam-5156	192	7	⌊	⌊	PROPN
ejpam-5156	192	8	m	m	PROPN
ejpam-5156	192	9	2	2	NUM
ejpam-5156	192	10	⌋	⌋	NOUN
ejpam-5156	192	11	or	or	CCONJ
ejpam-5156	192	12	|s	|s	PROPN
ejpam-5156	192	13	∩	∩	NOUN
ejpam-5156	192	14	a2|	a2|	PROPN
ejpam-5156	192	15	̸≥	̸≥	NUM
ejpam-5156	192	16	⌊	⌊	VERB
ejpam-5156	192	17	n	n	DET
ejpam-5156	192	18	2	2	NUM
ejpam-5156	192	19	⌋	⌋	NOUN
ejpam-5156	192	20	.	.	PUNCT
ejpam-5156	193	1	observe	observe	VERB
ejpam-5156	193	2	the	the	DET
ejpam-5156	193	3	following	follow	VERB
ejpam-5156	193	4	subcases	subcase	NOUN
ejpam-5156	193	5	:	:	PUNCT
ejpam-5156	193	6	subcase	subcase	NOUN
ejpam-5156	193	7	1	1	NUM
ejpam-5156	193	8	:	:	PUNCT
ejpam-5156	193	9	|s	|s	PROPN
ejpam-5156	193	10	∩a1|	∩a1|	PROPN
ejpam-5156	194	1	̸≥	̸≥	PUNCT
ejpam-5156	194	2	⌊	⌊	PROPN
ejpam-5156	194	3	m	m	PROPN
ejpam-5156	194	4	2	2	NUM
ejpam-5156	194	5	⌋	⌋	NOUN
ejpam-5156	194	6	.	.	PUNCT
ejpam-5156	195	1	since	since	SCONJ
ejpam-5156	195	2	s	s	PROPN
ejpam-5156	195	3	is	be	AUX
ejpam-5156	195	4	an	an	DET
ejpam-5156	195	5	rgda	rgda	NOUN
ejpam-5156	195	6	,	,	PUNCT
ejpam-5156	195	7	at	at	ADV
ejpam-5156	195	8	least	least	ADV
ejpam-5156	195	9	one	one	NUM
ejpam-5156	195	10	vertex	vertex	NOUN
ejpam-5156	195	11	in	in	ADP
ejpam-5156	195	12	a2	a2	PROPN
ejpam-5156	195	13	must	must	AUX
ejpam-5156	195	14	exist	exist	VERB
ejpam-5156	195	15	to	to	PART
ejpam-5156	195	16	dominate	dominate	VERB
ejpam-5156	195	17	all	all	DET
ejpam-5156	195	18	vertices	vertex	NOUN
ejpam-5156	195	19	in	in	ADP
ejpam-5156	195	20	a1	a1	NOUN
ejpam-5156	195	21	.	.	PUNCT
ejpam-5156	196	1	the	the	DET
ejpam-5156	196	2	same	same	ADJ
ejpam-5156	196	3	is	be	AUX
ejpam-5156	196	4	true	true	ADJ
ejpam-5156	196	5	for	for	ADP
ejpam-5156	196	6	the	the	DET
ejpam-5156	196	7	other	other	ADJ
ejpam-5156	196	8	partite	partite	ADJ
ejpam-5156	196	9	set	set	NOUN
ejpam-5156	196	10	.	.	PUNCT
ejpam-5156	197	1	so	so	ADV
ejpam-5156	197	2	,	,	PUNCT
ejpam-5156	197	3	|s	|s	PROPN
ejpam-5156	197	4	∩	∩	NOUN
ejpam-5156	197	5	a1|	a1|	NOUN
ejpam-5156	197	6	and	and	CCONJ
ejpam-5156	197	7	|s	|s	PROPN
ejpam-5156	197	8	∩a2|	∩a2|	PROPN
ejpam-5156	197	9	are	be	AUX
ejpam-5156	197	10	both	both	PRON
ejpam-5156	197	11	nonempty	nonempty	ADJ
ejpam-5156	197	12	.	.	PUNCT
ejpam-5156	198	1	then	then	ADV
ejpam-5156	198	2	for	for	ADP
ejpam-5156	198	3	every	every	DET
ejpam-5156	198	4	v	v	NUM
ejpam-5156	198	5	∈	∈	PROPN
ejpam-5156	198	6	s	s	PART
ejpam-5156	198	7	∩a2	∩a2	NOUN
ejpam-5156	198	8	,	,	PUNCT
ejpam-5156	198	9	|n	|n	AUX
ejpam-5156	199	1	[	[	X
ejpam-5156	199	2	v	v	X
ejpam-5156	199	3	]	]	X
ejpam-5156	199	4	∩	∩	NOUN
ejpam-5156	199	5	s|	s|	NOUN
ejpam-5156	199	6	=	=	SYM
ejpam-5156	199	7	|s	|s	X
ejpam-5156	199	8	∩a1|+	∩a1|+	X
ejpam-5156	199	9	|{v}|	|{v}|	PROPN
ejpam-5156	199	10	=	=	SYM
ejpam-5156	199	11	|s	|s	PROPN
ejpam-5156	199	12	∩a1|+	∩a1|+	NUM
ejpam-5156	199	13	1	1	NUM
ejpam-5156	199	14	̸≥	̸≥	PROPN
ejpam-5156	199	15	m−	m−	PROPN
ejpam-5156	199	16	|s	|s	PROPN
ejpam-5156	199	17	∩a1|	∩a1|	PROPN
ejpam-5156	199	18	=	=	PUNCT
ejpam-5156	199	19	|a1	|a1	NOUN
ejpam-5156	199	20	∖	∖	X
ejpam-5156	199	21	s|	s|	VERB
ejpam-5156	199	22	=	=	SYM
ejpam-5156	199	23	|n(v	|n(v	ADJ
ejpam-5156	199	24	)	)	PUNCT
ejpam-5156	199	25	∩	∩	NOUN
ejpam-5156	199	26	v	v	ADP
ejpam-5156	199	27	∖	∖	NOUN
ejpam-5156	199	28	s|	s|	VERB
ejpam-5156	199	29	.	.	PUNCT
ejpam-5156	200	1	so	so	ADV
ejpam-5156	200	2	,	,	PUNCT
ejpam-5156	200	3	s	s	VERB
ejpam-5156	200	4	is	be	AUX
ejpam-5156	200	5	not	not	PART
ejpam-5156	200	6	a	a	DET
ejpam-5156	200	7	da	da	NOUN
ejpam-5156	200	8	,	,	PUNCT
ejpam-5156	200	9	a	a	DET
ejpam-5156	200	10	contradiction	contradiction	NOUN
ejpam-5156	200	11	.	.	PUNCT
ejpam-5156	201	1	hence	hence	ADV
ejpam-5156	201	2	,	,	PUNCT
ejpam-5156	201	3	|s	|s	PROPN
ejpam-5156	201	4	∩a1|	∩a1|	PROPN
ejpam-5156	201	5	≥	≥	NUM
ejpam-5156	201	6	⌊	⌊	PROPN
ejpam-5156	201	7	m	m	PROPN
ejpam-5156	201	8	2	2	NUM
ejpam-5156	201	9	⌋	⌋	NOUN
ejpam-5156	201	10	.	.	PUNCT
ejpam-5156	202	1	subcase	subcase	PROPN
ejpam-5156	202	2	2	2	NUM
ejpam-5156	202	3	:	:	PUNCT
ejpam-5156	202	4	|s	|s	PROPN
ejpam-5156	202	5	∩a2|	∩a2|	PROPN
ejpam-5156	203	1	̸≥	̸≥	PUNCT
ejpam-5156	203	2	⌊	⌊	VERB
ejpam-5156	203	3	n	n	ADV
ejpam-5156	203	4	2	2	NUM
ejpam-5156	203	5	⌋	⌋	NOUN
ejpam-5156	203	6	.	.	PUNCT
ejpam-5156	204	1	using	use	VERB
ejpam-5156	204	2	similar	similar	ADJ
ejpam-5156	204	3	argument	argument	NOUN
ejpam-5156	204	4	as	as	ADP
ejpam-5156	204	5	subcase	subcase	NOUN
ejpam-5156	204	6	1	1	NUM
ejpam-5156	204	7	,	,	PUNCT
ejpam-5156	204	8	it	it	PRON
ejpam-5156	204	9	follows	follow	VERB
ejpam-5156	204	10	that	that	SCONJ
ejpam-5156	204	11	|s	|s	PROPN
ejpam-5156	204	12	∩a2|	∩a2|	PROPN
ejpam-5156	204	13	≥	≥	PRON
ejpam-5156	204	14	⌊	⌊	VERB
ejpam-5156	204	15	n	n	PRON
ejpam-5156	204	16	2	2	NUM
ejpam-5156	204	17	⌋	⌋	NOUN
ejpam-5156	204	18	.	.	PUNCT
ejpam-5156	205	1	therefore	therefore	ADV
ejpam-5156	205	2	,	,	PUNCT
ejpam-5156	205	3	|s	|s	PROPN
ejpam-5156	205	4	∩a1|	∩a1|	PROPN
ejpam-5156	205	5	≥	≥	NUM
ejpam-5156	205	6	⌊	⌊	PROPN
ejpam-5156	205	7	m	m	PROPN
ejpam-5156	205	8	2	2	NUM
ejpam-5156	205	9	⌋	⌋	NOUN
ejpam-5156	205	10	and	and	CCONJ
ejpam-5156	205	11	|s	|s	PROPN
ejpam-5156	205	12	∩a2|	∩a2|	PROPN
ejpam-5156	205	13	≥	≥	PRON
ejpam-5156	205	14	⌊	⌊	VERB
ejpam-5156	205	15	n	n	PRON
ejpam-5156	205	16	2	2	NUM
ejpam-5156	205	17	⌋	⌋	NOUN
ejpam-5156	205	18	.	.	PUNCT
ejpam-5156	206	1	this	this	PRON
ejpam-5156	206	2	proves	prove	VERB
ejpam-5156	206	3	i.	i.	NOUN
ejpam-5156	206	4	case	case	NOUN
ejpam-5156	206	5	2	2	NUM
ejpam-5156	206	6	:	:	PUNCT
ejpam-5156	206	7	ii	ii	NOUN
ejpam-5156	206	8	is	be	AUX
ejpam-5156	206	9	false	false	ADJ
ejpam-5156	206	10	.	.	PUNCT
ejpam-5156	207	1	then	then	ADV
ejpam-5156	207	2	either	either	CCONJ
ejpam-5156	207	3	|s	|s	PROPN
ejpam-5156	207	4	∩	∩	NOUN
ejpam-5156	207	5	a1|	a1|	NOUN
ejpam-5156	208	1	=	=	SYM
ejpam-5156	209	1	m	m	PROPN
ejpam-5156	209	2	and	and	CCONJ
ejpam-5156	209	3	|s	|s	PROPN
ejpam-5156	209	4	∩	∩	NOUN
ejpam-5156	209	5	a2|	a2|	NOUN
ejpam-5156	209	6	=	=	SYM
ejpam-5156	209	7	̸	̸	PUNCT
ejpam-5156	209	8	n	n	CCONJ
ejpam-5156	209	9	or	or	CCONJ
ejpam-5156	209	10	|s	|s	PROPN
ejpam-5156	209	11	∩	∩	NOUN
ejpam-5156	209	12	a2|	a2|	PROPN
ejpam-5156	209	13	=	=	PUNCT
ejpam-5156	209	14	n	n	PROPN
ejpam-5156	209	15	and	and	CCONJ
ejpam-5156	209	16	|s	|s	PROPN
ejpam-5156	209	17	∩a2|	∩a2|	PUNCT
ejpam-5156	210	1	=	=	X
ejpam-5156	210	2	̸	̸	PUNCT
ejpam-5156	210	3	m.	m.	NOUN
ejpam-5156	210	4	subcase	subcase	NOUN
ejpam-5156	210	5	1	1	NUM
ejpam-5156	210	6	:	:	PUNCT
ejpam-5156	210	7	|s	|s	PROPN
ejpam-5156	210	8	∩a1|	∩a1|	PROPN
ejpam-5156	210	9	=	=	PUNCT
ejpam-5156	210	10	m	m	PROPN
ejpam-5156	210	11	and	and	CCONJ
ejpam-5156	210	12	|s	|s	PROPN
ejpam-5156	210	13	∩a2|	∩a2|	PUNCT
ejpam-5156	211	1	=	=	X
ejpam-5156	211	2	̸	̸	PUNCT
ejpam-5156	211	3	n.	n.	NOUN
ejpam-5156	211	4	this	this	PRON
ejpam-5156	211	5	means	mean	VERB
ejpam-5156	211	6	that	that	PRON
ejpam-5156	211	7	a1∖s	a1∖	VERB
ejpam-5156	211	8	⊆	⊆	NUM
ejpam-5156	211	9	v	v	NOUN
ejpam-5156	211	10	∖s	∖s	PROPN
ejpam-5156	211	11	is	be	AUX
ejpam-5156	211	12	empty	empty	ADJ
ejpam-5156	211	13	and	and	CCONJ
ejpam-5156	211	14	a2∖s	a2∖s	NUM
ejpam-5156	211	15	⊆	⊆	NUM
ejpam-5156	211	16	v	v	ADP
ejpam-5156	211	17	∖s	∖s	PROPN
ejpam-5156	211	18	is	be	AUX
ejpam-5156	211	19	nonempty	nonempty	ADJ
ejpam-5156	211	20	.	.	PUNCT
ejpam-5156	212	1	since	since	SCONJ
ejpam-5156	212	2	every	every	DET
ejpam-5156	212	3	vertex	vertex	NOUN
ejpam-5156	212	4	in	in	ADP
ejpam-5156	212	5	a2	a2	PROPN
ejpam-5156	212	6	is	be	AUX
ejpam-5156	212	7	only	only	ADV
ejpam-5156	212	8	adjacent	adjacent	ADJ
ejpam-5156	212	9	to	to	ADP
ejpam-5156	212	10	vertices	vertex	NOUN
ejpam-5156	212	11	in	in	ADP
ejpam-5156	212	12	a1	a1	NOUN
ejpam-5156	212	13	,	,	PUNCT
ejpam-5156	212	14	then	then	ADV
ejpam-5156	212	15	every	every	DET
ejpam-5156	212	16	vertex	vertex	NOUN
ejpam-5156	212	17	v	v	ADP
ejpam-5156	212	18	∈	∈	PROPN
ejpam-5156	212	19	a2	a2	NOUN
ejpam-5156	212	20	∖	∖	X
ejpam-5156	212	21	s	s	PART
ejpam-5156	212	22	⊆	⊆	NUM
ejpam-5156	212	23	v	v	NOUN
ejpam-5156	212	24	∖	∖	PRON
ejpam-5156	212	25	s	s	PART
ejpam-5156	212	26	is	be	AUX
ejpam-5156	212	27	not	not	PART
ejpam-5156	212	28	adjacent	adjacent	ADJ
ejpam-5156	212	29	to	to	ADP
ejpam-5156	212	30	another	another	DET
ejpam-5156	212	31	vertex	vertex	NOUN
ejpam-5156	212	32	in	in	ADP
ejpam-5156	212	33	v	v	NUM
ejpam-5156	212	34	∖	∖	X
ejpam-5156	212	35	s.	s.	PROPN
ejpam-5156	212	36	hence	hence	PROPN
ejpam-5156	212	37	,	,	PUNCT
ejpam-5156	212	38	s	s	VERB
ejpam-5156	212	39	is	be	AUX
ejpam-5156	212	40	not	not	PART
ejpam-5156	212	41	an	an	DET
ejpam-5156	212	42	rds	rd	NOUN
ejpam-5156	212	43	,	,	PUNCT
ejpam-5156	212	44	a	a	DET
ejpam-5156	212	45	contradiction	contradiction	NOUN
ejpam-5156	212	46	.	.	PUNCT
ejpam-5156	213	1	l.	l.	PROPN
ejpam-5156	213	2	consistente	consistente	PROPN
ejpam-5156	213	3	,	,	PUNCT
ejpam-5156	213	4	i.	i.	PROPN
ejpam-5156	213	5	cabahug	cabahug	PROPN
ejpam-5156	213	6	,	,	PUNCT
ejpam-5156	213	7	jr	jr	PROPN
ejpam-5156	213	8	.	.	PROPN
ejpam-5156	213	9	/	/	SYM
ejpam-5156	213	10	eur	eur	PROPN
ejpam-5156	213	11	.	.	PUNCT
ejpam-5156	214	1	j.	j.	PROPN
ejpam-5156	214	2	pure	pure	PROPN
ejpam-5156	214	3	appl	appl	PROPN
ejpam-5156	214	4	.	.	PROPN
ejpam-5156	214	5	math	math	PROPN
ejpam-5156	214	6	,	,	PUNCT
ejpam-5156	214	7	17	17	NUM
ejpam-5156	214	8	(	(	PUNCT
ejpam-5156	214	9	3	3	NUM
ejpam-5156	214	10	)	)	PUNCT
ejpam-5156	214	11	(	(	PUNCT
ejpam-5156	214	12	2024	2024	NUM
ejpam-5156	214	13	)	)	PUNCT
ejpam-5156	214	14	,	,	PUNCT
ejpam-5156	214	15	2196	2196	NUM
ejpam-5156	214	16	-	-	SYM
ejpam-5156	214	17	2209	2209	NUM
ejpam-5156	214	18	2203	2203	NUM
ejpam-5156	214	19	subcase	subcase	NOUN
ejpam-5156	214	20	2	2	NUM
ejpam-5156	214	21	:	:	PUNCT
ejpam-5156	214	22	|s	|s	PROPN
ejpam-5156	214	23	∩a2|	∩a2|	PUNCT
ejpam-5156	215	1	=	=	SYM
ejpam-5156	215	2	n	n	PROPN
ejpam-5156	215	3	and	and	CCONJ
ejpam-5156	215	4	|s	|s	PROPN
ejpam-5156	215	5	∩a1|	∩a1|	PROPN
ejpam-5156	215	6	=	=	SYM
ejpam-5156	215	7	̸	̸	X
ejpam-5156	215	8	m.	m.	NOUN
ejpam-5156	215	9	since	since	SCONJ
ejpam-5156	215	10	a1	a1	NOUN
ejpam-5156	215	11	and	and	CCONJ
ejpam-5156	215	12	a2	a2	PROPN
ejpam-5156	215	13	are	be	AUX
ejpam-5156	215	14	arbitrary	arbitrary	ADJ
ejpam-5156	215	15	,	,	PUNCT
ejpam-5156	215	16	similar	similar	ADJ
ejpam-5156	215	17	argument	argument	NOUN
ejpam-5156	215	18	as	as	SCONJ
ejpam-5156	215	19	subcase	subcase	NOUN
ejpam-5156	215	20	1	1	NUM
ejpam-5156	215	21	holds	hold	NOUN
ejpam-5156	215	22	.	.	PUNCT
ejpam-5156	216	1	therefore	therefore	ADV
ejpam-5156	216	2	,	,	PUNCT
ejpam-5156	216	3	|s	|s	PROPN
ejpam-5156	216	4	∩a1|	∩a1|	PROPN
ejpam-5156	217	1	=	=	PUNCT
ejpam-5156	217	2	m	m	NOUN
ejpam-5156	217	3	if	if	SCONJ
ejpam-5156	217	4	and	and	CCONJ
ejpam-5156	217	5	only	only	ADV
ejpam-5156	217	6	if	if	SCONJ
ejpam-5156	217	7	|s	|s	PROPN
ejpam-5156	217	8	∩a2|	∩a2|	PROPN
ejpam-5156	218	1	=	=	PUNCT
ejpam-5156	218	2	n.	n.	NOUN
ejpam-5156	218	3	this	this	PRON
ejpam-5156	218	4	proves	prove	VERB
ejpam-5156	218	5	ii	ii	NOUN
ejpam-5156	218	6	.	.	PUNCT
ejpam-5156	219	1	conversely	conversely	ADV
ejpam-5156	219	2	,	,	PUNCT
ejpam-5156	219	3	let	let	VERB
ejpam-5156	219	4	s	s	PRON
ejpam-5156	219	5	⊆	⊆	NUM
ejpam-5156	219	6	v	v	NOUN
ejpam-5156	219	7	be	be	AUX
ejpam-5156	219	8	a	a	DET
ejpam-5156	219	9	set	set	NOUN
ejpam-5156	219	10	in	in	ADP
ejpam-5156	219	11	km	km	PROPN
ejpam-5156	219	12	,	,	PUNCT
ejpam-5156	219	13	n	n	NOUN
ejpam-5156	219	14	=	=	SYM
ejpam-5156	219	15	(	(	PUNCT
ejpam-5156	219	16	v	v	NOUN
ejpam-5156	219	17	,	,	PUNCT
ejpam-5156	219	18	e	e	NOUN
ejpam-5156	219	19	)	)	PUNCT
ejpam-5156	219	20	where	where	SCONJ
ejpam-5156	219	21	m	m	VERB
ejpam-5156	219	22	,	,	PUNCT
ejpam-5156	219	23	n	n	PRON
ejpam-5156	219	24	≥	≥	NOUN
ejpam-5156	219	25	2	2	NUM
ejpam-5156	219	26	that	that	PRON
ejpam-5156	219	27	satisfies	satisfy	VERB
ejpam-5156	219	28	i	i	PRON
ejpam-5156	219	29	and	and	CCONJ
ejpam-5156	219	30	ii	ii	PROPN
ejpam-5156	219	31	.	.	PUNCT
ejpam-5156	220	1	by	by	ADP
ejpam-5156	220	2	i	i	PROPN
ejpam-5156	220	3	,	,	PUNCT
ejpam-5156	220	4	|s	|s	PROPN
ejpam-5156	220	5	∩a1|	∩a1|	PROPN
ejpam-5156	220	6	≥	≥	NUM
ejpam-5156	220	7	⌊	⌊	VERB
ejpam-5156	220	8	2	2	NUM
ejpam-5156	220	9	2	2	NUM
ejpam-5156	220	10	⌋	⌋	NOUN
ejpam-5156	220	11	=	=	SYM
ejpam-5156	220	12	1	1	NUM
ejpam-5156	220	13	and	and	CCONJ
ejpam-5156	220	14	|s	|s	PROPN
ejpam-5156	220	15	∩a2|	∩a2|	PROPN
ejpam-5156	220	16	≥	≥	AUX
ejpam-5156	220	17	⌊	⌊	VERB
ejpam-5156	220	18	2	2	NUM
ejpam-5156	220	19	2	2	NUM
ejpam-5156	220	20	⌋	⌋	NOUN
ejpam-5156	220	21	=	=	SYM
ejpam-5156	220	22	1	1	NUM
ejpam-5156	220	23	,	,	PUNCT
ejpam-5156	220	24	so	so	ADV
ejpam-5156	220	25	,	,	PUNCT
ejpam-5156	220	26	s	s	NOUN
ejpam-5156	220	27	is	be	AUX
ejpam-5156	220	28	nonempty	nonempty	ADJ
ejpam-5156	220	29	and	and	CCONJ
ejpam-5156	220	30	a	a	DET
ejpam-5156	220	31	ds	ds	NOUN
ejpam-5156	220	32	.	.	PUNCT
ejpam-5156	221	1	moreover	moreover	ADV
ejpam-5156	221	2	,	,	PUNCT
ejpam-5156	221	3	for	for	ADP
ejpam-5156	221	4	every	every	DET
ejpam-5156	221	5	v	v	NOUN
ejpam-5156	221	6	∈	∈	NOUN
ejpam-5156	221	7	s	s	PART
ejpam-5156	221	8	∩a1	∩a1	PROPN
ejpam-5156	221	9	,	,	PUNCT
ejpam-5156	221	10	|n	|n	AUX
ejpam-5156	222	1	[	[	X
ejpam-5156	222	2	v	v	X
ejpam-5156	222	3	]	]	X
ejpam-5156	222	4	∩	∩	NOUN
ejpam-5156	222	5	s|	s|	NOUN
ejpam-5156	222	6	=	=	SYM
ejpam-5156	222	7	|a2	|a2	NOUN
ejpam-5156	222	8	∩	∩	PROPN
ejpam-5156	223	1	s|+	s|+	PROPN
ejpam-5156	223	2	|{v}|	|{v}|	PUNCT
ejpam-5156	223	3	≥	≥	X
ejpam-5156	223	4	⌊n	⌊n	SYM
ejpam-5156	223	5	2	2	NUM
ejpam-5156	223	6	⌋	⌋	NOUN
ejpam-5156	223	7	+	+	CCONJ
ejpam-5156	223	8	1	1	NUM
ejpam-5156	223	9	≥	≥	NOUN
ejpam-5156	223	10	n−	n−	NOUN
ejpam-5156	223	11	⌊n	⌊n	NOUN
ejpam-5156	223	12	2	2	NUM
ejpam-5156	223	13	⌋	⌋	NUM
ejpam-5156	223	14	≥	≥	X
ejpam-5156	223	15	|a2	|a2	ADV
ejpam-5156	223	16	∖	∖	X
ejpam-5156	223	17	s|	s|	VERB
ejpam-5156	223	18	=	=	SYM
ejpam-5156	223	19	|n(v	|n(v	ADJ
ejpam-5156	223	20	)	)	PUNCT
ejpam-5156	223	21	∩	∩	NOUN
ejpam-5156	223	22	(	(	PUNCT
ejpam-5156	223	23	v	v	NUM
ejpam-5156	223	24	∖	∖	PROPN
ejpam-5156	223	25	s)|	s)|	NOUN
ejpam-5156	223	26	.	.	PUNCT
ejpam-5156	224	1	on	on	ADP
ejpam-5156	224	2	the	the	DET
ejpam-5156	224	3	other	other	ADJ
ejpam-5156	224	4	hand	hand	NOUN
ejpam-5156	224	5	,	,	PUNCT
ejpam-5156	224	6	for	for	ADP
ejpam-5156	224	7	every	every	DET
ejpam-5156	224	8	w	w	PROPN
ejpam-5156	224	9	∈	∈	PROPN
ejpam-5156	224	10	s	s	PART
ejpam-5156	224	11	∩a2	∩a2	NOUN
ejpam-5156	224	12	,	,	PUNCT
ejpam-5156	224	13	|n	|n	AUX
ejpam-5156	225	1	[	[	X
ejpam-5156	225	2	w	w	X
ejpam-5156	225	3	]	]	X
ejpam-5156	225	4	∩	∩	NOUN
ejpam-5156	225	5	s|	s|	NOUN
ejpam-5156	225	6	=	=	SYM
ejpam-5156	225	7	|a1	|a1	NOUN
ejpam-5156	225	8	∩	∩	ADJ
ejpam-5156	225	9	s|+	s|+	PROPN
ejpam-5156	225	10	|{w}|	|{w}|	PUNCT
ejpam-5156	225	11	≥	≥	NOUN
ejpam-5156	225	12	⌊m	⌊m	ADP
ejpam-5156	225	13	2	2	NUM
ejpam-5156	225	14	⌋	⌋	NOUN
ejpam-5156	225	15	+	+	CCONJ
ejpam-5156	225	16	1	1	NUM
ejpam-5156	225	17	≥	≥	NOUN
ejpam-5156	225	18	m−	m−	PROPN
ejpam-5156	225	19	⌊m	⌊m	ADP
ejpam-5156	225	20	2	2	NUM
ejpam-5156	225	21	⌋	⌋	NUM
ejpam-5156	225	22	≥	≥	NOUN
ejpam-5156	225	23	|a1	|a1	NOUN
ejpam-5156	225	24	∖	∖	X
ejpam-5156	225	25	s|	s|	VERB
ejpam-5156	225	26	=	=	SYM
ejpam-5156	225	27	|n(w	|n(w	ADJ
ejpam-5156	225	28	)	)	PUNCT
ejpam-5156	225	29	∩	∩	NOUN
ejpam-5156	225	30	(	(	PUNCT
ejpam-5156	225	31	v	v	NUM
ejpam-5156	225	32	∖	∖	PROPN
ejpam-5156	225	33	s)|	s)|	NOUN
ejpam-5156	225	34	.	.	PUNCT
ejpam-5156	226	1	this	this	PRON
ejpam-5156	226	2	means	mean	VERB
ejpam-5156	226	3	that	that	SCONJ
ejpam-5156	226	4	s	s	VERB
ejpam-5156	226	5	is	be	AUX
ejpam-5156	226	6	a	a	DET
ejpam-5156	226	7	da	da	NOUN
ejpam-5156	226	8	in	in	ADP
ejpam-5156	226	9	km	km	PROPN
ejpam-5156	226	10	,	,	PUNCT
ejpam-5156	226	11	n.	n.	NOUN
ejpam-5156	226	12	by	by	ADP
ejpam-5156	226	13	i	i	PROPN
ejpam-5156	226	14	and	and	CCONJ
ejpam-5156	226	15	ii	ii	PROPN
ejpam-5156	226	16	,	,	PUNCT
ejpam-5156	226	17	it	it	PRON
ejpam-5156	226	18	is	be	AUX
ejpam-5156	226	19	guaranteed	guarantee	VERB
ejpam-5156	226	20	that	that	SCONJ
ejpam-5156	226	21	whenever	whenever	SCONJ
ejpam-5156	226	22	a1	a1	NOUN
ejpam-5156	226	23	∖	∖	X
ejpam-5156	226	24	s	s	PART
ejpam-5156	226	25	is	be	AUX
ejpam-5156	226	26	nonempty	nonempty	X
ejpam-5156	226	27	,	,	PUNCT
ejpam-5156	226	28	a2	a2	PROPN
ejpam-5156	226	29	∖	∖	X
ejpam-5156	226	30	s	s	PART
ejpam-5156	226	31	is	be	AUX
ejpam-5156	226	32	also	also	ADV
ejpam-5156	226	33	nonempty	nonempty	ADJ
ejpam-5156	226	34	.	.	PUNCT
ejpam-5156	227	1	since	since	SCONJ
ejpam-5156	227	2	every	every	DET
ejpam-5156	227	3	vertex	vertex	NOUN
ejpam-5156	227	4	in	in	ADP
ejpam-5156	227	5	a1	a1	NOUN
ejpam-5156	227	6	is	be	AUX
ejpam-5156	227	7	adjacent	adjacent	ADJ
ejpam-5156	227	8	to	to	ADP
ejpam-5156	227	9	a2	a2	PROPN
ejpam-5156	227	10	,	,	PUNCT
ejpam-5156	227	11	then	then	ADV
ejpam-5156	227	12	s	s	VERB
ejpam-5156	227	13	is	be	AUX
ejpam-5156	227	14	an	an	DET
ejpam-5156	227	15	rds	rd	NOUN
ejpam-5156	227	16	.	.	PUNCT
ejpam-5156	228	1	therefore	therefore	ADV
ejpam-5156	228	2	,	,	PUNCT
ejpam-5156	228	3	s	s	VERB
ejpam-5156	228	4	is	be	AUX
ejpam-5156	228	5	a	a	DET
ejpam-5156	228	6	rgds	rgds	NOUN
ejpam-5156	228	7	in	in	ADP
ejpam-5156	228	8	km	km	PROPN
ejpam-5156	228	9	,	,	PUNCT
ejpam-5156	228	10	n.	n.	NOUN
ejpam-5156	228	11	corollary	corollary	NOUN
ejpam-5156	229	1	3	3	X
ejpam-5156	229	2	.	.	PUNCT
ejpam-5156	230	1	let	let	AUX
ejpam-5156	230	2	km	km	PROPN
ejpam-5156	230	3	,	,	PUNCT
ejpam-5156	230	4	n	n	NOUN
ejpam-5156	230	5	=	=	SYM
ejpam-5156	230	6	(	(	PUNCT
ejpam-5156	230	7	v	v	NOUN
ejpam-5156	230	8	,	,	PUNCT
ejpam-5156	230	9	e	e	NOUN
ejpam-5156	230	10	)	)	PUNCT
ejpam-5156	230	11	be	be	AUX
ejpam-5156	230	12	a	a	DET
ejpam-5156	230	13	complete	complete	ADJ
ejpam-5156	230	14	bipartite	bipartite	NOUN
ejpam-5156	230	15	graph	graph	NOUN
ejpam-5156	230	16	.	.	PUNCT
ejpam-5156	231	1	if	if	SCONJ
ejpam-5156	231	2	m	m	PROPN
ejpam-5156	231	3	,	,	PUNCT
ejpam-5156	231	4	n	n	PRON
ejpam-5156	231	5	≥	≥	NOUN
ejpam-5156	231	6	2	2	NUM
ejpam-5156	231	7	,	,	PUNCT
ejpam-5156	231	8	then	then	ADV
ejpam-5156	231	9	γra(km	γra(km	NOUN
ejpam-5156	231	10	,	,	PUNCT
ejpam-5156	231	11	n	n	CCONJ
ejpam-5156	231	12	)	)	PUNCT
ejpam-5156	232	1	=	=	PUNCT
ejpam-5156	232	2	⌊	⌊	VERB
ejpam-5156	232	3	m	m	NUM
ejpam-5156	232	4	2	2	NUM
ejpam-5156	232	5	⌋	⌋	NOUN
ejpam-5156	233	1	+	+	CCONJ
ejpam-5156	233	2	⌊	⌊	PROPN
ejpam-5156	233	3	n	n	PRON
ejpam-5156	233	4	2	2	NUM
ejpam-5156	233	5	⌋	⌋	NOUN
ejpam-5156	233	6	.	.	PUNCT
ejpam-5156	234	1	proof	proof	NOUN
ejpam-5156	234	2	.	.	PUNCT
ejpam-5156	235	1	let	let	VERB
ejpam-5156	235	2	s	s	PRON
ejpam-5156	235	3	be	be	AUX
ejpam-5156	235	4	an	an	DET
ejpam-5156	235	5	rgda	rgda	NOUN
ejpam-5156	235	6	in	in	ADP
ejpam-5156	235	7	km	km	PROPN
ejpam-5156	235	8	,	,	PUNCT
ejpam-5156	235	9	n	n	NOUN
ejpam-5156	235	10	=	=	SYM
ejpam-5156	235	11	(	(	PUNCT
ejpam-5156	235	12	v	v	NOUN
ejpam-5156	235	13	,	,	PUNCT
ejpam-5156	235	14	e	e	NOUN
ejpam-5156	235	15	)	)	PUNCT
ejpam-5156	235	16	where	where	SCONJ
ejpam-5156	235	17	m	m	VERB
ejpam-5156	235	18	,	,	PUNCT
ejpam-5156	235	19	n	n	PRON
ejpam-5156	235	20	≥	≥	NOUN
ejpam-5156	235	21	2	2	NUM
ejpam-5156	235	22	,	,	PUNCT
ejpam-5156	235	23	and	and	CCONJ
ejpam-5156	235	24	a1	a1	NOUN
ejpam-5156	235	25	and	and	CCONJ
ejpam-5156	235	26	a2	a2	PROPN
ejpam-5156	235	27	be	be	VERB
ejpam-5156	235	28	its	its	PRON
ejpam-5156	235	29	partite	partite	ADJ
ejpam-5156	235	30	sets	set	NOUN
ejpam-5156	235	31	such	such	ADJ
ejpam-5156	235	32	that	that	DET
ejpam-5156	235	33	|a1|	|a1|	NOUN
ejpam-5156	235	34	=	=	SYM
ejpam-5156	235	35	m	m	NOUN
ejpam-5156	235	36	and	and	CCONJ
ejpam-5156	235	37	|a2|	|a2|	NOUN
ejpam-5156	235	38	=	=	SYM
ejpam-5156	235	39	n.	n.	NOUN
ejpam-5156	235	40	by	by	ADP
ejpam-5156	235	41	theorem	theorem	NOUN
ejpam-5156	235	42	7(i	7(i	NUM
ejpam-5156	235	43	)	)	PUNCT
ejpam-5156	235	44	,	,	PUNCT
ejpam-5156	235	45	|s	|s	PROPN
ejpam-5156	235	46	∩	∩	NOUN
ejpam-5156	235	47	a1|	a1|	X
ejpam-5156	235	48	≥	≥	NUM
ejpam-5156	235	49	⌊	⌊	PROPN
ejpam-5156	235	50	m	m	PROPN
ejpam-5156	235	51	2	2	NUM
ejpam-5156	235	52	⌋	⌋	NOUN
ejpam-5156	235	53	and	and	CCONJ
ejpam-5156	235	54	|s	|s	PROPN
ejpam-5156	235	55	∩	∩	NOUN
ejpam-5156	235	56	a2|	a2|	PROPN
ejpam-5156	235	57	≥	≥	NUM
ejpam-5156	235	58	⌊	⌊	VERB
ejpam-5156	235	59	n	n	DET
ejpam-5156	235	60	2	2	NUM
ejpam-5156	235	61	⌋	⌋	NOUN
ejpam-5156	235	62	.	.	PUNCT
ejpam-5156	236	1	now	now	ADV
ejpam-5156	236	2	,	,	PUNCT
ejpam-5156	236	3	if	if	SCONJ
ejpam-5156	236	4	x1	x1	PROPN
ejpam-5156	236	5	⊆	⊆	NUM
ejpam-5156	236	6	s	s	NOUN
ejpam-5156	236	7	∩	∩	NOUN
ejpam-5156	236	8	a1	a1	NOUN
ejpam-5156	236	9	such	such	DET
ejpam-5156	236	10	that	that	DET
ejpam-5156	236	11	|x1|	|x1|	NOUN
ejpam-5156	237	1	=	=	SYM
ejpam-5156	237	2	⌊	⌊	VERB
ejpam-5156	237	3	m	m	PROPN
ejpam-5156	237	4	2	2	NUM
ejpam-5156	237	5	⌋	⌋	NOUN
ejpam-5156	238	1	and	and	CCONJ
ejpam-5156	238	2	x2	x2	NOUN
ejpam-5156	238	3	⊆	⊆	NUM
ejpam-5156	238	4	s	s	NOUN
ejpam-5156	238	5	∩	∩	NOUN
ejpam-5156	238	6	a2	a2	NOUN
ejpam-5156	238	7	such	such	ADJ
ejpam-5156	238	8	that	that	DET
ejpam-5156	238	9	|x2|	|x2|	NOUN
ejpam-5156	238	10	=	=	PUNCT
ejpam-5156	239	1	⌊	⌊	VERB
ejpam-5156	239	2	n	n	ADV
ejpam-5156	239	3	2	2	NUM
ejpam-5156	239	4	⌋	⌋	NOUN
ejpam-5156	239	5	,	,	PUNCT
ejpam-5156	239	6	then	then	ADV
ejpam-5156	239	7	x1	x1	NUM
ejpam-5156	239	8	∪x2	∪x2	NOUN
ejpam-5156	240	1	=	=	PUNCT
ejpam-5156	240	2	x	x	PUNCT
ejpam-5156	240	3	⊆	⊆	NUM
ejpam-5156	240	4	s	s	NOUN
ejpam-5156	240	5	is	be	AUX
ejpam-5156	240	6	the	the	DET
ejpam-5156	240	7	minimum	minimum	ADJ
ejpam-5156	240	8	restrained	restrain	VERB
ejpam-5156	240	9	global	global	ADJ
ejpam-5156	240	10	defensive	defensive	ADJ
ejpam-5156	240	11	alliance	alliance	NOUN
ejpam-5156	240	12	in	in	ADP
ejpam-5156	240	13	km	km	PROPN
ejpam-5156	240	14	,	,	PUNCT
ejpam-5156	240	15	n.	n.	PROPN
ejpam-5156	240	16	therefore	therefore	ADV
ejpam-5156	240	17	,	,	PUNCT
ejpam-5156	240	18	γra(km	γra(km	NOUN
ejpam-5156	240	19	,	,	PUNCT
ejpam-5156	240	20	n	n	CCONJ
ejpam-5156	240	21	)	)	PUNCT
ejpam-5156	241	1	=	=	SYM
ejpam-5156	241	2	|x|	|x|	X
ejpam-5156	241	3	=	=	PUNCT
ejpam-5156	241	4	|x1|+	|x1|+	PROPN
ejpam-5156	241	5	|x2|	|x2|	NOUN
ejpam-5156	241	6	=	=	PROPN
ejpam-5156	241	7	⌊m	⌊m	ADP
ejpam-5156	241	8	2	2	NUM
ejpam-5156	241	9	⌋	⌋	NOUN
ejpam-5156	241	10	+	+	CCONJ
ejpam-5156	241	11	⌊n	⌊n	ADJ
ejpam-5156	241	12	2	2	NUM
ejpam-5156	241	13	⌋	⌋	NOUN
ejpam-5156	241	14	.	.	PUNCT
ejpam-5156	242	1	theorem	theorem	ADJ
ejpam-5156	242	2	8	8	NUM
ejpam-5156	242	3	.	.	PUNCT
ejpam-5156	243	1	(	(	PUNCT
ejpam-5156	243	2	path	path	NOUN
ejpam-5156	243	3	graph	graph	NOUN
ejpam-5156	243	4	)	)	PUNCT
ejpam-5156	243	5	let	let	VERB
ejpam-5156	243	6	pn	pn	VERB
ejpam-5156	243	7	=	=	SYM
ejpam-5156	243	8	(	(	PUNCT
ejpam-5156	243	9	v	v	NOUN
ejpam-5156	243	10	,	,	PUNCT
ejpam-5156	243	11	e	e	NOUN
ejpam-5156	243	12	)	)	PUNCT
ejpam-5156	243	13	be	be	AUX
ejpam-5156	243	14	a	a	DET
ejpam-5156	243	15	path	path	NOUN
ejpam-5156	243	16	graph	graph	NOUN
ejpam-5156	243	17	with	with	ADP
ejpam-5156	243	18	n	n	PRON
ejpam-5156	243	19	≥	≥	NUM
ejpam-5156	243	20	2	2	NUM
ejpam-5156	243	21	.	.	PUNCT
ejpam-5156	244	1	then	then	ADV
ejpam-5156	244	2	s	s	VERB
ejpam-5156	244	3	⊆	⊆	NUM
ejpam-5156	244	4	v	v	NOUN
ejpam-5156	244	5	is	be	AUX
ejpam-5156	244	6	a	a	DET
ejpam-5156	244	7	restrained	restrained	ADJ
ejpam-5156	244	8	global	global	ADJ
ejpam-5156	244	9	defensive	defensive	ADJ
ejpam-5156	244	10	alliance	alliance	NOUN
ejpam-5156	244	11	if	if	SCONJ
ejpam-5156	244	12	and	and	CCONJ
ejpam-5156	244	13	only	only	ADV
ejpam-5156	244	14	if	if	SCONJ
ejpam-5156	244	15	the	the	DET
ejpam-5156	244	16	following	follow	VERB
ejpam-5156	244	17	holds	hold	VERB
ejpam-5156	244	18	:	:	PUNCT
ejpam-5156	244	19	i.	i.	NOUN
ejpam-5156	244	20	the	the	DET
ejpam-5156	244	21	leaf	leaf	NOUN
ejpam-5156	244	22	vertices	vertex	NOUN
ejpam-5156	244	23	of	of	ADP
ejpam-5156	244	24	pn	pn	PROPN
ejpam-5156	244	25	are	be	AUX
ejpam-5156	244	26	in	in	ADP
ejpam-5156	244	27	s	s	PROPN
ejpam-5156	244	28	;	;	PUNCT
ejpam-5156	244	29	ii	ii	X
ejpam-5156	244	30	.	.	PUNCT
ejpam-5156	245	1	⟨s⟩	⟨s⟩	PROPN
ejpam-5156	245	2	has	have	VERB
ejpam-5156	245	3	no	no	DET
ejpam-5156	245	4	isolated	isolate	VERB
ejpam-5156	245	5	vertices	vertex	NOUN
ejpam-5156	245	6	that	that	PRON
ejpam-5156	245	7	are	be	AUX
ejpam-5156	245	8	not	not	PART
ejpam-5156	245	9	leaf	leaf	NOUN
ejpam-5156	245	10	vertices	vertex	NOUN
ejpam-5156	245	11	of	of	ADP
ejpam-5156	245	12	pn	pn	PROPN
ejpam-5156	245	13	;	;	PUNCT
ejpam-5156	245	14	iii	iii	PROPN
ejpam-5156	245	15	.	.	PROPN
ejpam-5156	245	16	⟨v	⟨v	PROPN
ejpam-5156	245	17	∖	∖	PROPN
ejpam-5156	245	18	s⟩	s⟩	VERB
ejpam-5156	245	19	,	,	PUNCT
ejpam-5156	245	20	where	where	SCONJ
ejpam-5156	245	21	s	s	VERB
ejpam-5156	245	22	⊂	⊂	PROPN
ejpam-5156	245	23	v	v	NOUN
ejpam-5156	245	24	,	,	PUNCT
ejpam-5156	245	25	forms	form	VERB
ejpam-5156	245	26	a	a	DET
ejpam-5156	245	27	class	class	NOUN
ejpam-5156	245	28	of	of	ADP
ejpam-5156	245	29	p2	p2	NOUN
ejpam-5156	245	30	.	.	PUNCT
ejpam-5156	246	1	proof	proof	NOUN
ejpam-5156	246	2	.	.	PUNCT
ejpam-5156	247	1	let	let	VERB
ejpam-5156	247	2	s	s	PRON
ejpam-5156	247	3	be	be	AUX
ejpam-5156	247	4	an	an	DET
ejpam-5156	247	5	rgda	rgda	NOUN
ejpam-5156	247	6	in	in	ADP
ejpam-5156	247	7	pn	pn	PROPN
ejpam-5156	247	8	=	=	SYM
ejpam-5156	247	9	(	(	PUNCT
ejpam-5156	247	10	v	v	NOUN
ejpam-5156	247	11	,	,	PUNCT
ejpam-5156	247	12	e	e	NOUN
ejpam-5156	247	13	)	)	PUNCT
ejpam-5156	247	14	with	with	ADP
ejpam-5156	247	15	n	n	PRON
ejpam-5156	247	16	≥	≥	NUM
ejpam-5156	247	17	2	2	NUM
ejpam-5156	247	18	.	.	PUNCT
ejpam-5156	247	19	suppose	suppose	VERB
ejpam-5156	247	20	that	that	SCONJ
ejpam-5156	247	21	i	i	PRON
ejpam-5156	247	22	,	,	PUNCT
ejpam-5156	247	23	ii	ii	PROPN
ejpam-5156	247	24	,	,	PUNCT
ejpam-5156	247	25	and	and	CCONJ
ejpam-5156	247	26	iii	iii	X
ejpam-5156	247	27	are	be	AUX
ejpam-5156	247	28	false	false	ADJ
ejpam-5156	247	29	.	.	PUNCT
ejpam-5156	248	1	then	then	ADV
ejpam-5156	248	2	either	either	CCONJ
ejpam-5156	248	3	i	i	PROPN
ejpam-5156	248	4	,	,	PUNCT
ejpam-5156	248	5	ii	ii	PROPN
ejpam-5156	248	6	or	or	CCONJ
ejpam-5156	248	7	iii	iii	NOUN
ejpam-5156	248	8	is	be	AUX
ejpam-5156	248	9	not	not	PART
ejpam-5156	248	10	true	true	ADJ
ejpam-5156	248	11	.	.	PUNCT
ejpam-5156	249	1	observe	observe	VERB
ejpam-5156	249	2	the	the	DET
ejpam-5156	249	3	following	follow	VERB
ejpam-5156	249	4	cases	case	NOUN
ejpam-5156	249	5	.	.	PUNCT
ejpam-5156	250	1	case	case	NOUN
ejpam-5156	250	2	1	1	NUM
ejpam-5156	250	3	:	:	PUNCT
ejpam-5156	250	4	i	i	PRON
ejpam-5156	250	5	is	be	AUX
ejpam-5156	250	6	false	false	ADJ
ejpam-5156	250	7	.	.	PUNCT
ejpam-5156	251	1	it	it	PRON
ejpam-5156	251	2	is	be	AUX
ejpam-5156	251	3	known	know	VERB
ejpam-5156	251	4	that	that	SCONJ
ejpam-5156	251	5	pn	pn	PROPN
ejpam-5156	251	6	has	have	VERB
ejpam-5156	251	7	leaf	leaf	NOUN
ejpam-5156	251	8	vertices	vertex	NOUN
ejpam-5156	251	9	.	.	PUNCT
ejpam-5156	252	1	by	by	ADP
ejpam-5156	252	2	theorem	theorem	NOUN
ejpam-5156	252	3	2	2	NUM
ejpam-5156	252	4	,	,	PUNCT
ejpam-5156	252	5	every	every	DET
ejpam-5156	252	6	leaf	leaf	NOUN
ejpam-5156	252	7	vertex	vertex	NOUN
ejpam-5156	252	8	must	must	AUX
ejpam-5156	252	9	be	be	AUX
ejpam-5156	252	10	in	in	ADP
ejpam-5156	252	11	s.	s.	PROPN
ejpam-5156	252	12	hence	hence	PROPN
ejpam-5156	252	13	,	,	PUNCT
ejpam-5156	252	14	the	the	DET
ejpam-5156	252	15	leaf	leaf	NOUN
ejpam-5156	252	16	vertices	vertex	NOUN
ejpam-5156	252	17	of	of	ADP
ejpam-5156	252	18	pn	pn	PROPN
ejpam-5156	252	19	must	must	AUX
ejpam-5156	252	20	be	be	AUX
ejpam-5156	252	21	in	in	ADP
ejpam-5156	252	22	s.	s.	PROPN
ejpam-5156	252	23	this	this	PRON
ejpam-5156	252	24	proves	prove	VERB
ejpam-5156	252	25	i.	i.	PROPN
ejpam-5156	252	26	l.	l.	PROPN
ejpam-5156	252	27	consistente	consistente	PROPN
ejpam-5156	252	28	,	,	PUNCT
ejpam-5156	252	29	i.	i.	PROPN
ejpam-5156	252	30	cabahug	cabahug	PROPN
ejpam-5156	252	31	,	,	PUNCT
ejpam-5156	252	32	jr	jr	PROPN
ejpam-5156	252	33	.	.	PROPN
ejpam-5156	252	34	/	/	SYM
ejpam-5156	252	35	eur	eur	PROPN
ejpam-5156	252	36	.	.	PUNCT
ejpam-5156	253	1	j.	j.	PROPN
ejpam-5156	253	2	pure	pure	PROPN
ejpam-5156	253	3	appl	appl	PROPN
ejpam-5156	253	4	.	.	PROPN
ejpam-5156	253	5	math	math	PROPN
ejpam-5156	253	6	,	,	PUNCT
ejpam-5156	253	7	17	17	NUM
ejpam-5156	253	8	(	(	PUNCT
ejpam-5156	253	9	3	3	NUM
ejpam-5156	253	10	)	)	PUNCT
ejpam-5156	253	11	(	(	PUNCT
ejpam-5156	253	12	2024	2024	NUM
ejpam-5156	253	13	)	)	PUNCT
ejpam-5156	253	14	,	,	PUNCT
ejpam-5156	253	15	2196	2196	NUM
ejpam-5156	253	16	-	-	SYM
ejpam-5156	253	17	2209	2209	NUM
ejpam-5156	253	18	2204	2204	NUM
ejpam-5156	253	19	case	case	NOUN
ejpam-5156	253	20	2	2	NUM
ejpam-5156	253	21	:	:	PUNCT
ejpam-5156	253	22	ii	ii	NOUN
ejpam-5156	253	23	is	be	AUX
ejpam-5156	253	24	false	false	ADJ
ejpam-5156	253	25	.	.	PUNCT
ejpam-5156	254	1	then	then	ADV
ejpam-5156	254	2	⟨s⟩	⟨s⟩	PROPN
ejpam-5156	254	3	has	have	AUX
ejpam-5156	254	4	atleast	atleast	VERB
ejpam-5156	254	5	one	one	NUM
ejpam-5156	254	6	isolated	isolate	VERB
ejpam-5156	254	7	vertex	vertex	NOUN
ejpam-5156	254	8	v	v	NOUN
ejpam-5156	254	9	that	that	PRON
ejpam-5156	254	10	is	be	AUX
ejpam-5156	254	11	not	not	PART
ejpam-5156	254	12	a	a	DET
ejpam-5156	254	13	leaf	leaf	NOUN
ejpam-5156	254	14	vertex	vertex	NOUN
ejpam-5156	254	15	of	of	ADP
ejpam-5156	254	16	pn	pn	PROPN
ejpam-5156	254	17	.	.	PUNCT
ejpam-5156	255	1	this	this	PRON
ejpam-5156	255	2	implies	imply	VERB
ejpam-5156	255	3	that	that	SCONJ
ejpam-5156	255	4	v	v	NOUN
ejpam-5156	255	5	is	be	AUX
ejpam-5156	255	6	adjacent	adjacent	ADJ
ejpam-5156	255	7	to	to	ADP
ejpam-5156	255	8	two	two	NUM
ejpam-5156	255	9	vertices	vertex	NOUN
ejpam-5156	255	10	w	w	NOUN
ejpam-5156	255	11	,	,	PUNCT
ejpam-5156	255	12	x	x	SYM
ejpam-5156	255	13	∈	∈	NOUN
ejpam-5156	255	14	v	v	NOUN
ejpam-5156	255	15	∖	∖	X
ejpam-5156	255	16	s.	s.	PROPN
ejpam-5156	256	1	so	so	ADV
ejpam-5156	256	2	,	,	PUNCT
ejpam-5156	256	3	|n	|n	X
ejpam-5156	256	4	[	[	X
ejpam-5156	256	5	v	v	X
ejpam-5156	256	6	]	]	X
ejpam-5156	256	7	∩	∩	NOUN
ejpam-5156	256	8	s|	s|	NOUN
ejpam-5156	256	9	=	=	PUNCT
ejpam-5156	256	10	|{v}|	|{v}|	PUNCT
ejpam-5156	256	11	=	=	SYM
ejpam-5156	256	12	1	1	NUM
ejpam-5156	256	13	̸≥	̸≥	NUM
ejpam-5156	256	14	2	2	NUM
ejpam-5156	256	15	=	=	SYM
ejpam-5156	256	16	|{w	|{w	NOUN
ejpam-5156	256	17	,	,	PUNCT
ejpam-5156	256	18	x}|	x}|	PROPN
ejpam-5156	256	19	=	=	SYM
ejpam-5156	256	20	|n(v	|n(v	PROPN
ejpam-5156	256	21	)	)	PUNCT
ejpam-5156	256	22	∩	∩	NOUN
ejpam-5156	256	23	(	(	PUNCT
ejpam-5156	256	24	v	v	NUM
ejpam-5156	256	25	∖	∖	PROPN
ejpam-5156	256	26	s)|	s)|	NOUN
ejpam-5156	256	27	.	.	PUNCT
ejpam-5156	257	1	hence	hence	ADV
ejpam-5156	257	2	,	,	PUNCT
ejpam-5156	257	3	s	s	VERB
ejpam-5156	257	4	is	be	AUX
ejpam-5156	257	5	not	not	PART
ejpam-5156	257	6	a	a	DET
ejpam-5156	257	7	da	da	NOUN
ejpam-5156	257	8	,	,	PUNCT
ejpam-5156	257	9	a	a	DET
ejpam-5156	257	10	contradiction	contradiction	NOUN
ejpam-5156	257	11	.	.	PUNCT
ejpam-5156	258	1	thus	thus	ADV
ejpam-5156	258	2	,	,	PUNCT
ejpam-5156	258	3	⟨s⟩	⟨s⟩	PROPN
ejpam-5156	258	4	has	have	VERB
ejpam-5156	258	5	no	no	DET
ejpam-5156	258	6	isolated	isolate	VERB
ejpam-5156	258	7	vertices	vertex	NOUN
ejpam-5156	258	8	that	that	PRON
ejpam-5156	258	9	are	be	AUX
ejpam-5156	258	10	not	not	PART
ejpam-5156	258	11	leaf	leaf	NOUN
ejpam-5156	258	12	vertices	vertex	NOUN
ejpam-5156	258	13	of	of	ADP
ejpam-5156	258	14	pn	pn	PROPN
ejpam-5156	258	15	.	.	PUNCT
ejpam-5156	259	1	this	this	PRON
ejpam-5156	259	2	proves	prove	VERB
ejpam-5156	259	3	ii	ii	NOUN
ejpam-5156	259	4	.	.	PUNCT
ejpam-5156	259	5	case	case	NOUN
ejpam-5156	259	6	3	3	NUM
ejpam-5156	259	7	:	:	SYM
ejpam-5156	259	8	iii	iii	X
ejpam-5156	259	9	is	be	AUX
ejpam-5156	259	10	false	false	ADJ
ejpam-5156	259	11	.	.	PUNCT
ejpam-5156	260	1	then	then	ADV
ejpam-5156	260	2	s	s	VERB
ejpam-5156	260	3	⊂	⊂	PROPN
ejpam-5156	260	4	v	v	PROPN
ejpam-5156	260	5	and	and	CCONJ
ejpam-5156	260	6	⟨v	⟨v	PROPN
ejpam-5156	260	7	∖	∖	PROPN
ejpam-5156	260	8	s⟩	s⟩	NOUN
ejpam-5156	260	9	does	do	AUX
ejpam-5156	260	10	not	not	PART
ejpam-5156	260	11	form	form	VERB
ejpam-5156	260	12	a	a	DET
ejpam-5156	260	13	class	class	NOUN
ejpam-5156	260	14	of	of	ADP
ejpam-5156	260	15	p2	p2	NOUN
ejpam-5156	260	16	.	.	PUNCT
ejpam-5156	261	1	this	this	PRON
ejpam-5156	261	2	implies	imply	VERB
ejpam-5156	261	3	that	that	SCONJ
ejpam-5156	261	4	there	there	PRON
ejpam-5156	261	5	exists	exist	VERB
ejpam-5156	261	6	a	a	DET
ejpam-5156	261	7	component	component	NOUN
ejpam-5156	261	8	in	in	ADP
ejpam-5156	261	9	⟨v	⟨v	NOUN
ejpam-5156	261	10	∖	∖	NOUN
ejpam-5156	261	11	s⟩	s⟩	VERB
ejpam-5156	261	12	that	that	PRON
ejpam-5156	261	13	is	be	AUX
ejpam-5156	261	14	not	not	PART
ejpam-5156	261	15	p2	p2	NOUN
ejpam-5156	261	16	.	.	PUNCT
ejpam-5156	262	1	observe	observe	VERB
ejpam-5156	262	2	the	the	DET
ejpam-5156	262	3	following	follow	VERB
ejpam-5156	262	4	cases	case	NOUN
ejpam-5156	262	5	:	:	PUNCT
ejpam-5156	262	6	subcase	subcase	NOUN
ejpam-5156	262	7	1	1	NUM
ejpam-5156	262	8	:	:	PUNCT
ejpam-5156	262	9	if	if	SCONJ
ejpam-5156	262	10	⟨v	⟨v	PROPN
ejpam-5156	262	11	∖	∖	PROPN
ejpam-5156	262	12	s⟩	s⟩	INTJ
ejpam-5156	262	13	has	have	VERB
ejpam-5156	262	14	a	a	DET
ejpam-5156	262	15	component	component	NOUN
ejpam-5156	262	16	p1	p1	NOUN
ejpam-5156	262	17	,	,	PUNCT
ejpam-5156	262	18	then	then	ADV
ejpam-5156	262	19	s	s	VERB
ejpam-5156	262	20	is	be	AUX
ejpam-5156	262	21	not	not	PART
ejpam-5156	262	22	an	an	DET
ejpam-5156	262	23	rds	rd	NOUN
ejpam-5156	262	24	,	,	PUNCT
ejpam-5156	262	25	a	a	DET
ejpam-5156	262	26	contradiction	contradiction	NOUN
ejpam-5156	262	27	.	.	PUNCT
ejpam-5156	263	1	subcase	subcase	NOUN
ejpam-5156	263	2	2	2	NUM
ejpam-5156	263	3	:	:	PUNCT
ejpam-5156	263	4	if	if	SCONJ
ejpam-5156	263	5	⟨v	⟨v	PROPN
ejpam-5156	263	6	∖	∖	PROPN
ejpam-5156	263	7	s⟩	s⟩	INTJ
ejpam-5156	263	8	has	have	VERB
ejpam-5156	263	9	a	a	DET
ejpam-5156	263	10	component	component	NOUN
ejpam-5156	263	11	pt	pt	NOUN
ejpam-5156	263	12	where	where	SCONJ
ejpam-5156	263	13	3	3	NUM
ejpam-5156	263	14	≤	≤	NOUN
ejpam-5156	263	15	t	t	PROPN
ejpam-5156	263	16	≤	≤	NOUN
ejpam-5156	263	17	n	n	CCONJ
ejpam-5156	263	18	,	,	PUNCT
ejpam-5156	263	19	then	then	ADV
ejpam-5156	263	20	s	s	AUX
ejpam-5156	263	21	can	can	AUX
ejpam-5156	263	22	only	only	ADV
ejpam-5156	263	23	dominate	dominate	VERB
ejpam-5156	263	24	the	the	DET
ejpam-5156	263	25	leaf	leaf	NOUN
ejpam-5156	263	26	vertices	vertex	NOUN
ejpam-5156	263	27	of	of	ADP
ejpam-5156	263	28	pt	pt	PROPN
ejpam-5156	263	29	.	.	PROPN
ejpam-5156	264	1	this	this	PRON
ejpam-5156	264	2	means	mean	VERB
ejpam-5156	264	3	that	that	SCONJ
ejpam-5156	264	4	s	s	VERB
ejpam-5156	264	5	is	be	AUX
ejpam-5156	264	6	not	not	PART
ejpam-5156	264	7	a	a	DET
ejpam-5156	264	8	ds	ds	NOUN
ejpam-5156	264	9	,	,	PUNCT
ejpam-5156	264	10	a	a	DET
ejpam-5156	264	11	contradiction	contradiction	NOUN
ejpam-5156	264	12	.	.	PUNCT
ejpam-5156	265	1	hence	hence	ADV
ejpam-5156	265	2	,	,	PUNCT
ejpam-5156	265	3	⟨v	⟨v	PROPN
ejpam-5156	265	4	∖	∖	NOUN
ejpam-5156	265	5	s⟩	s⟩	VERB
ejpam-5156	265	6	forms	form	VERB
ejpam-5156	265	7	a	a	DET
ejpam-5156	265	8	class	class	NOUN
ejpam-5156	265	9	of	of	ADP
ejpam-5156	265	10	p2	p2	NOUN
ejpam-5156	265	11	.	.	PUNCT
ejpam-5156	266	1	this	this	PRON
ejpam-5156	266	2	proves	prove	VERB
ejpam-5156	266	3	iii	iii	NOUN
ejpam-5156	266	4	.	.	PUNCT
ejpam-5156	267	1	conversely	conversely	ADV
ejpam-5156	267	2	,	,	PUNCT
ejpam-5156	267	3	let	let	VERB
ejpam-5156	267	4	s	s	PRON
ejpam-5156	267	5	⊆	⊆	NUM
ejpam-5156	267	6	v	v	NOUN
ejpam-5156	267	7	be	be	AUX
ejpam-5156	267	8	a	a	DET
ejpam-5156	267	9	set	set	NOUN
ejpam-5156	267	10	in	in	ADP
ejpam-5156	267	11	pn	pn	PROPN
ejpam-5156	267	12	=	=	SYM
ejpam-5156	267	13	(	(	PUNCT
ejpam-5156	267	14	v	v	NOUN
ejpam-5156	267	15	,	,	PUNCT
ejpam-5156	267	16	e	e	NOUN
ejpam-5156	267	17	)	)	PUNCT
ejpam-5156	267	18	,	,	PUNCT
ejpam-5156	267	19	with	with	ADP
ejpam-5156	267	20	n	n	PRON
ejpam-5156	267	21	≥	≥	NUM
ejpam-5156	267	22	2	2	NUM
ejpam-5156	267	23	that	that	PRON
ejpam-5156	267	24	satisfies	satisfy	VERB
ejpam-5156	267	25	i	i	PRON
ejpam-5156	267	26	,	,	PUNCT
ejpam-5156	267	27	ii	ii	PROPN
ejpam-5156	267	28	,	,	PUNCT
ejpam-5156	267	29	and	and	CCONJ
ejpam-5156	267	30	iii	iii	X
ejpam-5156	267	31	.	.	PUNCT
ejpam-5156	268	1	since	since	SCONJ
ejpam-5156	268	2	pn	pn	PROPN
ejpam-5156	268	3	contains	contain	VERB
ejpam-5156	268	4	leaf	leaf	NOUN
ejpam-5156	268	5	vertices	vertex	NOUN
ejpam-5156	268	6	,	,	PUNCT
ejpam-5156	268	7	by	by	ADP
ejpam-5156	268	8	i	i	PRON
ejpam-5156	268	9	,	,	PUNCT
ejpam-5156	268	10	s	s	VERB
ejpam-5156	268	11	is	be	AUX
ejpam-5156	268	12	a	a	DET
ejpam-5156	268	13	nonempty	nonempty	ADJ
ejpam-5156	268	14	set	set	VERB
ejpam-5156	268	15	.	.	PUNCT
ejpam-5156	269	1	by	by	ADP
ejpam-5156	269	2	i	i	PROPN
ejpam-5156	269	3	and	and	CCONJ
ejpam-5156	269	4	iii	iii	PROPN
ejpam-5156	269	5	,	,	PUNCT
ejpam-5156	269	6	the	the	DET
ejpam-5156	269	7	leaf	leaf	NOUN
ejpam-5156	269	8	vertices	vertex	NOUN
ejpam-5156	269	9	of	of	ADP
ejpam-5156	269	10	pn	pn	PROPN
ejpam-5156	269	11	are	be	AUX
ejpam-5156	269	12	in	in	ADP
ejpam-5156	269	13	s	s	PRON
ejpam-5156	269	14	and	and	CCONJ
ejpam-5156	269	15	⟨v	⟨v	NUM
ejpam-5156	269	16	∖	∖	PROPN
ejpam-5156	269	17	s⟩	s⟩	INTJ
ejpam-5156	269	18	form	form	VERB
ejpam-5156	269	19	a	a	DET
ejpam-5156	269	20	class	class	NOUN
ejpam-5156	269	21	of	of	ADP
ejpam-5156	269	22	p2	p2	NOUN
ejpam-5156	269	23	.	.	PUNCT
ejpam-5156	270	1	this	this	PRON
ejpam-5156	270	2	implies	imply	VERB
ejpam-5156	270	3	that	that	SCONJ
ejpam-5156	270	4	every	every	DET
ejpam-5156	270	5	vertex	vertex	NOUN
ejpam-5156	270	6	v	v	ADP
ejpam-5156	270	7	∈	∈	NOUN
ejpam-5156	270	8	v	v	ADP
ejpam-5156	270	9	∖	∖	X
ejpam-5156	270	10	s	s	PART
ejpam-5156	270	11	is	be	AUX
ejpam-5156	270	12	adjacent	adjacent	ADJ
ejpam-5156	270	13	to	to	ADP
ejpam-5156	270	14	a	a	DET
ejpam-5156	270	15	vertex	vertex	NOUN
ejpam-5156	270	16	in	in	ADP
ejpam-5156	270	17	s	s	PRON
ejpam-5156	270	18	and	and	CCONJ
ejpam-5156	270	19	another	another	DET
ejpam-5156	270	20	vertex	vertex	NOUN
ejpam-5156	270	21	in	in	ADP
ejpam-5156	270	22	v	v	NUM
ejpam-5156	270	23	∖	∖	X
ejpam-5156	270	24	s.	s.	PROPN
ejpam-5156	270	25	hence	hence	PROPN
ejpam-5156	270	26	,	,	PUNCT
ejpam-5156	270	27	s	s	VERB
ejpam-5156	270	28	is	be	AUX
ejpam-5156	270	29	an	an	DET
ejpam-5156	270	30	rds	rd	NOUN
ejpam-5156	270	31	.	.	PUNCT
ejpam-5156	271	1	in	in	ADP
ejpam-5156	271	2	pn	pn	PROPN
ejpam-5156	271	3	,	,	PUNCT
ejpam-5156	271	4	every	every	DET
ejpam-5156	271	5	vertex	vertex	NOUN
ejpam-5156	271	6	in	in	ADP
ejpam-5156	271	7	v	v	NOUN
ejpam-5156	271	8	is	be	AUX
ejpam-5156	271	9	adjacent	adjacent	ADJ
ejpam-5156	271	10	to	to	ADP
ejpam-5156	271	11	at	at	ADP
ejpam-5156	271	12	most	most	ADV
ejpam-5156	271	13	two	two	NUM
ejpam-5156	271	14	vertices	vertex	NOUN
ejpam-5156	271	15	.	.	PUNCT
ejpam-5156	272	1	so	so	ADV
ejpam-5156	272	2	,	,	PUNCT
ejpam-5156	272	3	by	by	ADP
ejpam-5156	272	4	i	i	PRON
ejpam-5156	272	5	and	and	CCONJ
ejpam-5156	272	6	ii	ii	PROPN
ejpam-5156	272	7	,	,	PUNCT
ejpam-5156	272	8	for	for	ADP
ejpam-5156	272	9	every	every	DET
ejpam-5156	272	10	a	a	DET
ejpam-5156	272	11	∈	∈	NOUN
ejpam-5156	272	12	s	s	PART
ejpam-5156	272	13	implies	imply	VERB
ejpam-5156	272	14	the	the	DET
ejpam-5156	272	15	following	follow	VERB
ejpam-5156	272	16	:	:	PUNCT
ejpam-5156	272	17	case	case	NOUN
ejpam-5156	272	18	1	1	NUM
ejpam-5156	272	19	:	:	PUNCT
ejpam-5156	272	20	a	a	PRON
ejpam-5156	272	21	is	be	AUX
ejpam-5156	272	22	a	a	DET
ejpam-5156	272	23	leaf	leaf	NOUN
ejpam-5156	272	24	vertex	vertex	NOUN
ejpam-5156	272	25	subcase	subcase	NOUN
ejpam-5156	272	26	1	1	NUM
ejpam-5156	272	27	:	:	PUNCT
ejpam-5156	272	28	a	a	PRON
ejpam-5156	272	29	is	be	AUX
ejpam-5156	272	30	adjacent	adjacent	ADJ
ejpam-5156	272	31	to	to	ADP
ejpam-5156	272	32	another	another	DET
ejpam-5156	272	33	vertex	vertex	NOUN
ejpam-5156	272	34	in	in	ADP
ejpam-5156	272	35	s.	s.	PROPN
ejpam-5156	272	36	then	then	ADV
ejpam-5156	272	37	|n	|n	X
ejpam-5156	272	38	[	[	X
ejpam-5156	272	39	a	a	X
ejpam-5156	272	40	]	]	X
ejpam-5156	272	41	∩	∩	ADJ
ejpam-5156	272	42	s|	s|	NOUN
ejpam-5156	272	43	=	=	SYM
ejpam-5156	272	44	2	2	NUM
ejpam-5156	272	45	≥	≥	NOUN
ejpam-5156	272	46	0	0	NUM
ejpam-5156	272	47	=	=	SYM
ejpam-5156	272	48	|n(a	|n(a	PROPN
ejpam-5156	272	49	)	)	PUNCT
ejpam-5156	272	50	∩	∩	NOUN
ejpam-5156	272	51	(	(	PUNCT
ejpam-5156	272	52	v	v	NUM
ejpam-5156	272	53	∖	∖	PROPN
ejpam-5156	272	54	s)|	s)|	PROPN
ejpam-5156	272	55	.	.	PUNCT
ejpam-5156	272	56	subcase	subcase	PROPN
ejpam-5156	272	57	2	2	NUM
ejpam-5156	272	58	:	:	PUNCT
ejpam-5156	272	59	a	a	PRON
ejpam-5156	272	60	is	be	AUX
ejpam-5156	272	61	not	not	PART
ejpam-5156	272	62	adjacent	adjacent	ADJ
ejpam-5156	272	63	to	to	ADP
ejpam-5156	272	64	another	another	DET
ejpam-5156	272	65	vertex	vertex	NOUN
ejpam-5156	272	66	in	in	ADP
ejpam-5156	272	67	s.	s.	PROPN
ejpam-5156	272	68	then	then	ADV
ejpam-5156	272	69	|n	|n	X
ejpam-5156	273	1	[	[	X
ejpam-5156	273	2	a	a	X
ejpam-5156	273	3	]	]	X
ejpam-5156	273	4	∩	∩	ADJ
ejpam-5156	273	5	s|	s|	NOUN
ejpam-5156	273	6	=	=	SYM
ejpam-5156	273	7	1	1	NUM
ejpam-5156	273	8	≥	≥	NOUN
ejpam-5156	273	9	1	1	NUM
ejpam-5156	273	10	=	=	SYM
ejpam-5156	273	11	|n(a	|n(a	PROPN
ejpam-5156	273	12	)	)	PUNCT
ejpam-5156	273	13	∩	∩	NOUN
ejpam-5156	273	14	(	(	PUNCT
ejpam-5156	273	15	v	v	NUM
ejpam-5156	273	16	∖	∖	PROPN
ejpam-5156	273	17	s)|	s)|	PROPN
ejpam-5156	273	18	.	.	PUNCT
ejpam-5156	274	1	case	case	NOUN
ejpam-5156	274	2	2	2	NUM
ejpam-5156	274	3	:	:	PUNCT
ejpam-5156	274	4	a	a	PRON
ejpam-5156	274	5	is	be	AUX
ejpam-5156	274	6	not	not	PART
ejpam-5156	274	7	a	a	DET
ejpam-5156	274	8	leaf	leaf	NOUN
ejpam-5156	274	9	vertex	vertex	NOUN
ejpam-5156	274	10	subcase	subcase	NOUN
ejpam-5156	274	11	1	1	NUM
ejpam-5156	274	12	:	:	PUNCT
ejpam-5156	274	13	a	a	PRON
ejpam-5156	274	14	is	be	AUX
ejpam-5156	274	15	adjacent	adjacent	ADJ
ejpam-5156	274	16	to	to	ADP
ejpam-5156	274	17	one	one	NUM
ejpam-5156	274	18	vertex	vertex	NOUN
ejpam-5156	274	19	in	in	ADP
ejpam-5156	274	20	s.	s.	PROPN
ejpam-5156	274	21	then	then	ADV
ejpam-5156	274	22	|n	|n	X
ejpam-5156	275	1	[	[	X
ejpam-5156	275	2	a	a	X
ejpam-5156	275	3	]	]	X
ejpam-5156	275	4	∩	∩	ADJ
ejpam-5156	275	5	s|	s|	NOUN
ejpam-5156	275	6	=	=	SYM
ejpam-5156	275	7	2	2	NUM
ejpam-5156	275	8	≥	≥	NOUN
ejpam-5156	275	9	1	1	NUM
ejpam-5156	275	10	=	=	SYM
ejpam-5156	275	11	|n(a	|n(a	PROPN
ejpam-5156	275	12	)	)	PUNCT
ejpam-5156	275	13	∩	∩	NOUN
ejpam-5156	275	14	(	(	PUNCT
ejpam-5156	275	15	v	v	NUM
ejpam-5156	275	16	∖	∖	PROPN
ejpam-5156	275	17	s)|	s)|	PROPN
ejpam-5156	275	18	.	.	PUNCT
ejpam-5156	275	19	subcase	subcase	PROPN
ejpam-5156	275	20	2	2	NUM
ejpam-5156	275	21	:	:	PUNCT
ejpam-5156	275	22	a	a	PRON
ejpam-5156	275	23	is	be	AUX
ejpam-5156	275	24	adjacent	adjacent	ADJ
ejpam-5156	275	25	to	to	ADP
ejpam-5156	275	26	two	two	NUM
ejpam-5156	275	27	vertices	vertex	NOUN
ejpam-5156	275	28	in	in	ADP
ejpam-5156	275	29	s.	s.	PROPN
ejpam-5156	275	30	then	then	ADV
ejpam-5156	275	31	|n	|n	X
ejpam-5156	276	1	[	[	X
ejpam-5156	276	2	a	a	X
ejpam-5156	276	3	]	]	X
ejpam-5156	276	4	∩	∩	NOUN
ejpam-5156	276	5	s|	s|	NOUN
ejpam-5156	276	6	=	=	SYM
ejpam-5156	276	7	3	3	NUM
ejpam-5156	276	8	≥	≥	NOUN
ejpam-5156	276	9	0	0	NUM
ejpam-5156	276	10	=	=	SYM
ejpam-5156	276	11	|n(a	|n(a	PROPN
ejpam-5156	276	12	)	)	PUNCT
ejpam-5156	276	13	∩	∩	NOUN
ejpam-5156	276	14	(	(	PUNCT
ejpam-5156	276	15	v	v	NUM
ejpam-5156	276	16	∖	∖	PROPN
ejpam-5156	276	17	s)|	s)|	NOUN
ejpam-5156	276	18	.	.	PUNCT
ejpam-5156	277	1	these	these	PRON
ejpam-5156	277	2	implies	imply	VERB
ejpam-5156	277	3	that	that	SCONJ
ejpam-5156	277	4	s	s	VERB
ejpam-5156	277	5	is	be	AUX
ejpam-5156	277	6	a	a	DET
ejpam-5156	277	7	da	da	NOUN
ejpam-5156	277	8	.	.	PUNCT
ejpam-5156	278	1	therefore	therefore	ADV
ejpam-5156	278	2	,	,	PUNCT
ejpam-5156	278	3	by	by	ADP
ejpam-5156	278	4	i	i	PROPN
ejpam-5156	278	5	,	,	PUNCT
ejpam-5156	278	6	ii	ii	PROPN
ejpam-5156	278	7	,	,	PUNCT
ejpam-5156	278	8	and	and	CCONJ
ejpam-5156	278	9	iii	iii	NOUN
ejpam-5156	278	10	,	,	PUNCT
ejpam-5156	278	11	s	s	VERB
ejpam-5156	278	12	is	be	AUX
ejpam-5156	278	13	an	an	DET
ejpam-5156	278	14	rgda	rgda	NOUN
ejpam-5156	278	15	in	in	ADP
ejpam-5156	278	16	pn	pn	PROPN
ejpam-5156	278	17	.	.	PUNCT
ejpam-5156	279	1	lemma	lemma	PROPN
ejpam-5156	279	2	1	1	X
ejpam-5156	279	3	.	.	PUNCT
ejpam-5156	280	1	let	let	VERB
ejpam-5156	280	2	pn	pn	VERB
ejpam-5156	280	3	=	=	SYM
ejpam-5156	280	4	(	(	PUNCT
ejpam-5156	280	5	v	v	NOUN
ejpam-5156	280	6	,	,	PUNCT
ejpam-5156	280	7	e	e	NOUN
ejpam-5156	280	8	)	)	PUNCT
ejpam-5156	280	9	,	,	PUNCT
ejpam-5156	281	1	n	n	X
ejpam-5156	281	2	≡	≡	PROPN
ejpam-5156	281	3	0	0	PUNCT
ejpam-5156	281	4	(	(	PUNCT
ejpam-5156	281	5	mod	mod	PROPN
ejpam-5156	281	6	4	4	NUM
ejpam-5156	281	7	)	)	PUNCT
ejpam-5156	281	8	,	,	PUNCT
ejpam-5156	281	9	be	be	AUX
ejpam-5156	281	10	a	a	DET
ejpam-5156	281	11	path	path	NOUN
ejpam-5156	281	12	graph	graph	NOUN
ejpam-5156	281	13	of	of	ADP
ejpam-5156	281	14	order	order	NOUN
ejpam-5156	281	15	n	n	PRON
ejpam-5156	281	16	≥	≥	NOUN
ejpam-5156	281	17	2	2	NUM
ejpam-5156	281	18	.	.	PUNCT
ejpam-5156	282	1	then	then	ADV
ejpam-5156	282	2	s	s	VERB
ejpam-5156	282	3	=	=	SYM
ejpam-5156	282	4	{	{	PUNCT
ejpam-5156	282	5	v0	v0	NOUN
ejpam-5156	282	6	,	,	PUNCT
ejpam-5156	282	7	vn−1	vn−1	ADJ
ejpam-5156	282	8	}	}	PUNCT
ejpam-5156	282	9	∪	∪	NOUN
ejpam-5156	282	10	{	{	PUNCT
ejpam-5156	282	11	v3	v3	PROPN
ejpam-5156	282	12	,	,	PUNCT
ejpam-5156	282	13	v4	v4	NOUN
ejpam-5156	282	14	,	,	PUNCT
ejpam-5156	282	15	v7	v7	NUM
ejpam-5156	282	16	,	,	PUNCT
ejpam-5156	282	17	v8	v8	PROPN
ejpam-5156	282	18	,	,	PUNCT
ejpam-5156	282	19	.	.	PUNCT
ejpam-5156	282	20	.	.	PUNCT
ejpam-5156	282	21	.	.	PUNCT
ejpam-5156	283	1	,	,	PUNCT
ejpam-5156	283	2	vn−5	vn−5	PROPN
ejpam-5156	283	3	,	,	PUNCT
ejpam-5156	283	4	vn−4	vn−4	NOUN
ejpam-5156	283	5	}	}	PUNCT
ejpam-5156	283	6	is	be	AUX
ejpam-5156	283	7	a	a	DET
ejpam-5156	283	8	minimum	minimum	ADJ
ejpam-5156	283	9	restrained	restrain	VERB
ejpam-5156	283	10	global	global	ADJ
ejpam-5156	283	11	defensive	defensive	ADJ
ejpam-5156	283	12	alliance	alliance	NOUN
ejpam-5156	283	13	in	in	ADP
ejpam-5156	283	14	pn	pn	PROPN
ejpam-5156	283	15	.	.	PROPN
ejpam-5156	283	16	l.	l.	PROPN
ejpam-5156	283	17	consistente	consistente	PROPN
ejpam-5156	283	18	,	,	PUNCT
ejpam-5156	283	19	i.	i.	PROPN
ejpam-5156	283	20	cabahug	cabahug	PROPN
ejpam-5156	283	21	,	,	PUNCT
ejpam-5156	283	22	jr	jr	PROPN
ejpam-5156	283	23	.	.	PROPN
ejpam-5156	283	24	/	/	SYM
ejpam-5156	283	25	eur	eur	PROPN
ejpam-5156	283	26	.	.	PUNCT
ejpam-5156	284	1	j.	j.	PROPN
ejpam-5156	284	2	pure	pure	PROPN
ejpam-5156	284	3	appl	appl	PROPN
ejpam-5156	284	4	.	.	PROPN
ejpam-5156	284	5	math	math	PROPN
ejpam-5156	284	6	,	,	PUNCT
ejpam-5156	284	7	17	17	NUM
ejpam-5156	284	8	(	(	PUNCT
ejpam-5156	284	9	3	3	NUM
ejpam-5156	284	10	)	)	PUNCT
ejpam-5156	284	11	(	(	PUNCT
ejpam-5156	284	12	2024	2024	NUM
ejpam-5156	284	13	)	)	PUNCT
ejpam-5156	284	14	,	,	PUNCT
ejpam-5156	284	15	2196	2196	NUM
ejpam-5156	284	16	-	-	SYM
ejpam-5156	284	17	2209	2209	NUM
ejpam-5156	284	18	2205	2205	NUM
ejpam-5156	284	19	proof	proof	NOUN
ejpam-5156	284	20	.	.	PUNCT
ejpam-5156	285	1	let	let	VERB
ejpam-5156	285	2	s	s	PRON
ejpam-5156	285	3	=	=	PUNCT
ejpam-5156	285	4	{	{	PUNCT
ejpam-5156	285	5	v0	v0	NOUN
ejpam-5156	285	6	,	,	PUNCT
ejpam-5156	285	7	vn−1	vn−1	ADJ
ejpam-5156	285	8	}	}	PUNCT
ejpam-5156	285	9	∪	∪	NOUN
ejpam-5156	285	10	{	{	PUNCT
ejpam-5156	285	11	v3	v3	PROPN
ejpam-5156	285	12	,	,	PUNCT
ejpam-5156	285	13	v4	v4	NOUN
ejpam-5156	285	14	,	,	PUNCT
ejpam-5156	285	15	v7	v7	NUM
ejpam-5156	285	16	,	,	PUNCT
ejpam-5156	285	17	v8	v8	PROPN
ejpam-5156	285	18	,	,	PUNCT
ejpam-5156	285	19	.	.	PUNCT
ejpam-5156	285	20	.	.	PUNCT
ejpam-5156	286	1	.	.	PUNCT
ejpam-5156	287	1	,	,	PUNCT
ejpam-5156	287	2	vn−5	vn−5	NOUN
ejpam-5156	287	3	,	,	PUNCT
ejpam-5156	287	4	vn−4	vn−4	NOUN
ejpam-5156	287	5	}	}	PUNCT
ejpam-5156	287	6	.	.	PUNCT
ejpam-5156	288	1	notice	notice	VERB
ejpam-5156	288	2	that	that	SCONJ
ejpam-5156	288	3	all	all	DET
ejpam-5156	288	4	the	the	DET
ejpam-5156	288	5	leaf	leaf	NOUN
ejpam-5156	288	6	vertices	vertex	NOUN
ejpam-5156	288	7	of	of	ADP
ejpam-5156	288	8	pn	pn	PROPN
ejpam-5156	288	9	are	be	AUX
ejpam-5156	288	10	in	in	ADP
ejpam-5156	288	11	s	s	PROPN
ejpam-5156	288	12	,	,	PUNCT
ejpam-5156	288	13	that	that	ADV
ejpam-5156	288	14	is	is	ADV
ejpam-5156	288	15	,	,	PUNCT
ejpam-5156	288	16	v0	v0	PROPN
ejpam-5156	288	17	,	,	PUNCT
ejpam-5156	288	18	vn−1	vn−1	PROPN
ejpam-5156	288	19	∈	∈	PROPN
ejpam-5156	288	20	s.	s.	PROPN
ejpam-5156	288	21	so	so	ADV
ejpam-5156	288	22	,	,	PUNCT
ejpam-5156	288	23	theorem	theorem	VERB
ejpam-5156	288	24	8	8	NUM
ejpam-5156	288	25	(	(	PUNCT
ejpam-5156	288	26	i	i	NOUN
ejpam-5156	288	27	)	)	PUNCT
ejpam-5156	288	28	is	be	AUX
ejpam-5156	288	29	satisfied	satisfied	ADJ
ejpam-5156	288	30	.	.	PUNCT
ejpam-5156	289	1	additionally	additionally	ADV
ejpam-5156	289	2	,	,	PUNCT
ejpam-5156	289	3	⟨{v3	⟨{v3	PROPN
ejpam-5156	289	4	,	,	PUNCT
ejpam-5156	289	5	v4	v4	NOUN
ejpam-5156	289	6	,	,	PUNCT
ejpam-5156	289	7	v7	v7	NUM
ejpam-5156	289	8	,	,	PUNCT
ejpam-5156	289	9	v8	v8	PROPN
ejpam-5156	289	10	,	,	PUNCT
ejpam-5156	289	11	.	.	PUNCT
ejpam-5156	289	12	.	.	PUNCT
ejpam-5156	289	13	.	.	PUNCT
ejpam-5156	290	1	,	,	PUNCT
ejpam-5156	290	2	vn−5	vn−5	PROPN
ejpam-5156	290	3	,	,	PUNCT
ejpam-5156	290	4	vn−4}⟩	vn−4}⟩	NOUN
ejpam-5156	290	5	has	have	VERB
ejpam-5156	290	6	no	no	DET
ejpam-5156	290	7	isolated	isolated	ADJ
ejpam-5156	290	8	vertices	vertex	NOUN
ejpam-5156	290	9	,	,	PUNCT
ejpam-5156	290	10	so	so	ADV
ejpam-5156	290	11	⟨s⟩	⟨s⟩	PROPN
ejpam-5156	290	12	has	have	VERB
ejpam-5156	290	13	no	no	DET
ejpam-5156	290	14	isolated	isolate	VERB
ejpam-5156	290	15	vertices	vertex	NOUN
ejpam-5156	290	16	that	that	PRON
ejpam-5156	290	17	are	be	AUX
ejpam-5156	290	18	not	not	PART
ejpam-5156	290	19	leaf	leaf	ADJ
ejpam-5156	290	20	.	.	PUNCT
ejpam-5156	291	1	this	this	PRON
ejpam-5156	291	2	means	mean	VERB
ejpam-5156	291	3	that	that	SCONJ
ejpam-5156	291	4	theorem	theorem	VERB
ejpam-5156	291	5	8	8	NUM
ejpam-5156	291	6	(	(	PUNCT
ejpam-5156	291	7	ii	ii	NOUN
ejpam-5156	291	8	)	)	PUNCT
ejpam-5156	291	9	is	be	AUX
ejpam-5156	291	10	satisfied	satisfied	ADJ
ejpam-5156	291	11	.	.	PUNCT
ejpam-5156	292	1	moreover	moreover	ADV
ejpam-5156	292	2	,	,	PUNCT
ejpam-5156	292	3	⟨v	⟨v	PROPN
ejpam-5156	292	4	∖	∖	NOUN
ejpam-5156	292	5	s⟩	s⟩	NOUN
ejpam-5156	293	1	=	=	PUNCT
ejpam-5156	293	2	⟨{v1	⟨{v1	NOUN
ejpam-5156	293	3	,	,	PUNCT
ejpam-5156	293	4	v2	v2	PROPN
ejpam-5156	293	5	,	,	PUNCT
ejpam-5156	293	6	v5	v5	PROPN
ejpam-5156	293	7	,	,	PUNCT
ejpam-5156	293	8	v6	v6	NOUN
ejpam-5156	293	9	,	,	PUNCT
ejpam-5156	293	10	.	.	PUNCT
ejpam-5156	293	11	.	.	PUNCT
ejpam-5156	294	1	.	.	PUNCT
ejpam-5156	295	1	,	,	PUNCT
ejpam-5156	295	2	vn−3	vn−3	PROPN
ejpam-5156	295	3	,	,	PUNCT
ejpam-5156	295	4	vn−2}⟩	vn−2}⟩	ADV
ejpam-5156	295	5	forms	form	VERB
ejpam-5156	295	6	a	a	DET
ejpam-5156	295	7	class	class	NOUN
ejpam-5156	295	8	of	of	ADP
ejpam-5156	295	9	p2	p2	NOUN
ejpam-5156	295	10	,	,	PUNCT
ejpam-5156	295	11	hence	hence	ADV
ejpam-5156	295	12	,	,	PUNCT
ejpam-5156	295	13	theorem	theorem	VERB
ejpam-5156	295	14	8	8	NUM
ejpam-5156	295	15	(	(	PUNCT
ejpam-5156	295	16	iii	iii	NOUN
ejpam-5156	295	17	)	)	PUNCT
ejpam-5156	295	18	is	be	AUX
ejpam-5156	295	19	satisfied	satisfied	ADJ
ejpam-5156	295	20	.	.	PUNCT
ejpam-5156	296	1	this	this	PRON
ejpam-5156	296	2	means	mean	VERB
ejpam-5156	296	3	that	that	SCONJ
ejpam-5156	296	4	,	,	PUNCT
ejpam-5156	296	5	by	by	ADP
ejpam-5156	296	6	theorem	theorem	NOUN
ejpam-5156	296	7	8	8	NUM
ejpam-5156	296	8	,	,	PUNCT
ejpam-5156	296	9	s	s	VERB
ejpam-5156	296	10	is	be	AUX
ejpam-5156	296	11	an	an	DET
ejpam-5156	296	12	rgda	rgda	NOUN
ejpam-5156	296	13	in	in	ADP
ejpam-5156	296	14	pn	pn	PROPN
ejpam-5156	296	15	.	.	PUNCT
ejpam-5156	297	1	now	now	ADV
ejpam-5156	297	2	,	,	PUNCT
ejpam-5156	297	3	suppose	suppose	VERB
ejpam-5156	297	4	that	that	SCONJ
ejpam-5156	297	5	w	w	PROPN
ejpam-5156	297	6	⊂	⊂	PROPN
ejpam-5156	297	7	s.	s.	PROPN
ejpam-5156	297	8	then	then	ADV
ejpam-5156	297	9	there	there	PRON
ejpam-5156	297	10	exists	exist	VERB
ejpam-5156	297	11	a	a	DET
ejpam-5156	297	12	vertex	vertex	NOUN
ejpam-5156	297	13	in	in	ADP
ejpam-5156	297	14	s	s	PRON
ejpam-5156	297	15	that	that	PRON
ejpam-5156	297	16	is	be	AUX
ejpam-5156	297	17	not	not	PART
ejpam-5156	297	18	in	in	ADP
ejpam-5156	297	19	w	w	PROPN
ejpam-5156	297	20	.	.	PUNCT
ejpam-5156	298	1	this	this	PRON
ejpam-5156	298	2	leads	lead	VERB
ejpam-5156	298	3	to	to	ADP
ejpam-5156	298	4	the	the	DET
ejpam-5156	298	5	following	following	ADJ
ejpam-5156	298	6	cases	case	NOUN
ejpam-5156	298	7	:	:	PUNCT
ejpam-5156	298	8	case	case	NOUN
ejpam-5156	298	9	1	1	NUM
ejpam-5156	298	10	:	:	PUNCT
ejpam-5156	298	11	atleast	atleast	ADJ
ejpam-5156	298	12	one	one	NUM
ejpam-5156	298	13	vertex	vertex	NOUN
ejpam-5156	298	14	in	in	ADP
ejpam-5156	298	15	{	{	PUNCT
ejpam-5156	298	16	v0	v0	NOUN
ejpam-5156	298	17	,	,	PUNCT
ejpam-5156	298	18	vn−1	vn−1	ADJ
ejpam-5156	298	19	}	}	PUNCT
ejpam-5156	298	20	is	be	AUX
ejpam-5156	298	21	not	not	PART
ejpam-5156	298	22	in	in	ADP
ejpam-5156	298	23	w	w	PROPN
ejpam-5156	298	24	.	.	PUNCT
ejpam-5156	299	1	then	then	ADV
ejpam-5156	299	2	theorem	theorem	VERB
ejpam-5156	299	3	8	8	NUM
ejpam-5156	299	4	(	(	PUNCT
ejpam-5156	299	5	i	i	NOUN
ejpam-5156	299	6	)	)	PUNCT
ejpam-5156	299	7	is	be	AUX
ejpam-5156	299	8	not	not	PART
ejpam-5156	299	9	satisfied	satisfied	ADJ
ejpam-5156	299	10	,	,	PUNCT
ejpam-5156	299	11	so	so	ADV
ejpam-5156	299	12	w	w	NOUN
ejpam-5156	299	13	is	be	AUX
ejpam-5156	299	14	not	not	PART
ejpam-5156	299	15	an	an	DET
ejpam-5156	299	16	rgda	rgda	NOUN
ejpam-5156	299	17	in	in	ADP
ejpam-5156	299	18	pn	pn	PROPN
ejpam-5156	299	19	.	.	PROPN
ejpam-5156	299	20	case	case	NOUN
ejpam-5156	299	21	2	2	NUM
ejpam-5156	299	22	:	:	PUNCT
ejpam-5156	299	23	atleast	atleast	ADJ
ejpam-5156	299	24	one	one	NUM
ejpam-5156	299	25	vertex	vertex	NOUN
ejpam-5156	299	26	in	in	ADP
ejpam-5156	299	27	{	{	PUNCT
ejpam-5156	299	28	v3	v3	PROPN
ejpam-5156	299	29	,	,	PUNCT
ejpam-5156	299	30	v4	v4	NOUN
ejpam-5156	299	31	,	,	PUNCT
ejpam-5156	299	32	v7	v7	NUM
ejpam-5156	299	33	,	,	PUNCT
ejpam-5156	299	34	v8	v8	PROPN
ejpam-5156	299	35	,	,	PUNCT
ejpam-5156	299	36	.	.	PUNCT
ejpam-5156	299	37	.	.	PUNCT
ejpam-5156	300	1	.	.	PUNCT
ejpam-5156	301	1	,	,	PUNCT
ejpam-5156	301	2	vn−5	vn−5	PROPN
ejpam-5156	301	3	,	,	PUNCT
ejpam-5156	301	4	vn−4	vn−4	NOUN
ejpam-5156	301	5	}	}	PUNCT
ejpam-5156	301	6	is	be	AUX
ejpam-5156	301	7	not	not	PART
ejpam-5156	301	8	in	in	ADP
ejpam-5156	301	9	w	w	PROPN
ejpam-5156	301	10	.	.	PUNCT
ejpam-5156	302	1	then	then	ADV
ejpam-5156	302	2	there	there	PRON
ejpam-5156	302	3	exists	exist	VERB
ejpam-5156	302	4	a	a	DET
ejpam-5156	302	5	class	class	NOUN
ejpam-5156	302	6	in	in	ADP
ejpam-5156	302	7	⟨v	⟨v	NOUN
ejpam-5156	302	8	∖	∖	PROPN
ejpam-5156	302	9	w	w	PROPN
ejpam-5156	302	10	⟩	⟩	NOUN
ejpam-5156	302	11	that	that	PRON
ejpam-5156	302	12	is	be	AUX
ejpam-5156	302	13	not	not	PART
ejpam-5156	302	14	p2	p2	ADJ
ejpam-5156	302	15	,	,	PUNCT
ejpam-5156	302	16	so	so	ADV
ejpam-5156	302	17	theorem	theorem	ADJ
ejpam-5156	302	18	8	8	NUM
ejpam-5156	302	19	(	(	PUNCT
ejpam-5156	302	20	iii	iii	NOUN
ejpam-5156	302	21	)	)	PUNCT
ejpam-5156	302	22	is	be	AUX
ejpam-5156	302	23	not	not	PART
ejpam-5156	302	24	satisfied	satisfied	ADJ
ejpam-5156	302	25	.	.	PUNCT
ejpam-5156	303	1	hence	hence	ADV
ejpam-5156	303	2	,	,	PUNCT
ejpam-5156	303	3	w	w	NOUN
ejpam-5156	303	4	is	be	AUX
ejpam-5156	303	5	not	not	PART
ejpam-5156	303	6	an	an	DET
ejpam-5156	303	7	rgda	rgda	NOUN
ejpam-5156	303	8	in	in	ADP
ejpam-5156	303	9	pn	pn	PROPN
ejpam-5156	303	10	.	.	PUNCT
ejpam-5156	303	11	therefore	therefore	ADV
ejpam-5156	303	12	,	,	PUNCT
ejpam-5156	303	13	s	s	VERB
ejpam-5156	303	14	is	be	AUX
ejpam-5156	303	15	a	a	DET
ejpam-5156	303	16	minimum	minimum	ADJ
ejpam-5156	303	17	rgda	rgda	NOUN
ejpam-5156	303	18	in	in	ADP
ejpam-5156	303	19	pn	pn	PROPN
ejpam-5156	303	20	.	.	PUNCT
ejpam-5156	304	1	lemma	lemma	PROPN
ejpam-5156	304	2	2	2	X
ejpam-5156	304	3	.	.	PUNCT
ejpam-5156	305	1	let	let	VERB
ejpam-5156	305	2	pn	pn	VERB
ejpam-5156	305	3	=	=	SYM
ejpam-5156	305	4	(	(	PUNCT
ejpam-5156	305	5	v	v	NOUN
ejpam-5156	305	6	,	,	PUNCT
ejpam-5156	305	7	e	e	NOUN
ejpam-5156	305	8	)	)	PUNCT
ejpam-5156	305	9	,	,	PUNCT
ejpam-5156	305	10	n	n	CCONJ
ejpam-5156	305	11	≡	≡	PROPN
ejpam-5156	305	12	1	1	NUM
ejpam-5156	305	13	(	(	PUNCT
ejpam-5156	305	14	mod	mod	NOUN
ejpam-5156	305	15	4	4	NUM
ejpam-5156	305	16	)	)	PUNCT
ejpam-5156	305	17	,	,	PUNCT
ejpam-5156	305	18	be	be	AUX
ejpam-5156	305	19	a	a	DET
ejpam-5156	305	20	path	path	NOUN
ejpam-5156	305	21	graph	graph	NOUN
ejpam-5156	305	22	of	of	ADP
ejpam-5156	305	23	order	order	NOUN
ejpam-5156	305	24	n	n	PRON
ejpam-5156	305	25	≥	≥	NOUN
ejpam-5156	305	26	2	2	NUM
ejpam-5156	305	27	.	.	PUNCT
ejpam-5156	306	1	then	then	ADV
ejpam-5156	306	2	s	s	VERB
ejpam-5156	306	3	=	=	SYM
ejpam-5156	306	4	{	{	PUNCT
ejpam-5156	306	5	v0	v0	NOUN
ejpam-5156	306	6	,	,	PUNCT
ejpam-5156	306	7	vn−1	vn−1	ADJ
ejpam-5156	306	8	}	}	PUNCT
ejpam-5156	306	9	∪	∪	NOUN
ejpam-5156	306	10	{	{	PUNCT
ejpam-5156	306	11	v3	v3	PROPN
ejpam-5156	306	12	,	,	PUNCT
ejpam-5156	306	13	v4	v4	NOUN
ejpam-5156	306	14	,	,	PUNCT
ejpam-5156	306	15	v7	v7	NUM
ejpam-5156	306	16	,	,	PUNCT
ejpam-5156	306	17	v8	v8	PROPN
ejpam-5156	306	18	,	,	PUNCT
ejpam-5156	306	19	.	.	PUNCT
ejpam-5156	306	20	.	.	PUNCT
ejpam-5156	306	21	.	.	PUNCT
ejpam-5156	307	1	,	,	PUNCT
ejpam-5156	307	2	vn−6	vn−6	PROPN
ejpam-5156	307	3	,	,	PUNCT
ejpam-5156	307	4	vn−5	vn−5	PROPN
ejpam-5156	307	5	}	}	PUNCT
ejpam-5156	307	6	∪	∪	NOUN
ejpam-5156	307	7	{	{	PUNCT
ejpam-5156	307	8	vn−2	vn−2	PROPN
ejpam-5156	307	9	}	}	PUNCT
ejpam-5156	307	10	is	be	AUX
ejpam-5156	307	11	a	a	DET
ejpam-5156	307	12	minimum	minimum	ADJ
ejpam-5156	307	13	restrained	restrain	VERB
ejpam-5156	307	14	global	global	ADJ
ejpam-5156	307	15	defensive	defensive	ADJ
ejpam-5156	307	16	alliance	alliance	NOUN
ejpam-5156	307	17	in	in	ADP
ejpam-5156	307	18	pn	pn	PROPN
ejpam-5156	307	19	.	.	PUNCT
ejpam-5156	307	20	proof	proof	NOUN
ejpam-5156	307	21	.	.	PUNCT
ejpam-5156	308	1	let	let	VERB
ejpam-5156	308	2	s	s	PRON
ejpam-5156	308	3	=	=	PUNCT
ejpam-5156	308	4	{	{	PUNCT
ejpam-5156	308	5	v0	v0	NOUN
ejpam-5156	308	6	,	,	PUNCT
ejpam-5156	308	7	vn−1	vn−1	ADJ
ejpam-5156	308	8	}	}	PUNCT
ejpam-5156	308	9	∪	∪	NOUN
ejpam-5156	308	10	{	{	PUNCT
ejpam-5156	308	11	v3	v3	PROPN
ejpam-5156	308	12	,	,	PUNCT
ejpam-5156	308	13	v4	v4	NOUN
ejpam-5156	308	14	,	,	PUNCT
ejpam-5156	308	15	v7	v7	NUM
ejpam-5156	308	16	,	,	PUNCT
ejpam-5156	308	17	v8	v8	PROPN
ejpam-5156	308	18	,	,	PUNCT
ejpam-5156	308	19	.	.	PUNCT
ejpam-5156	308	20	.	.	PUNCT
ejpam-5156	309	1	.	.	PUNCT
ejpam-5156	310	1	,	,	PUNCT
ejpam-5156	310	2	vn−6	vn−6	PROPN
ejpam-5156	310	3	,	,	PUNCT
ejpam-5156	310	4	vn−5	vn−5	PROPN
ejpam-5156	310	5	}	}	PUNCT
ejpam-5156	310	6	∪	∪	NOUN
ejpam-5156	310	7	{	{	PUNCT
ejpam-5156	310	8	vn−2	vn−2	NOUN
ejpam-5156	310	9	}	}	PUNCT
ejpam-5156	310	10	.	.	PUNCT
ejpam-5156	311	1	notice	notice	VERB
ejpam-5156	311	2	that	that	SCONJ
ejpam-5156	311	3	all	all	DET
ejpam-5156	311	4	the	the	DET
ejpam-5156	311	5	leaf	leaf	NOUN
ejpam-5156	311	6	vertices	vertex	NOUN
ejpam-5156	311	7	of	of	ADP
ejpam-5156	311	8	pn	pn	PROPN
ejpam-5156	311	9	are	be	AUX
ejpam-5156	311	10	in	in	ADP
ejpam-5156	311	11	s	s	PROPN
ejpam-5156	311	12	,	,	PUNCT
ejpam-5156	311	13	that	that	ADV
ejpam-5156	311	14	is	is	ADV
ejpam-5156	311	15	,	,	PUNCT
ejpam-5156	311	16	v0	v0	PROPN
ejpam-5156	311	17	,	,	PUNCT
ejpam-5156	311	18	vn−1	vn−1	PROPN
ejpam-5156	311	19	∈	∈	PROPN
ejpam-5156	311	20	s.	s.	PROPN
ejpam-5156	311	21	so	so	ADV
ejpam-5156	311	22	,	,	PUNCT
ejpam-5156	311	23	theorem	theorem	VERB
ejpam-5156	311	24	8	8	NUM
ejpam-5156	311	25	(	(	PUNCT
ejpam-5156	311	26	i	i	NOUN
ejpam-5156	311	27	)	)	PUNCT
ejpam-5156	311	28	is	be	AUX
ejpam-5156	311	29	satisfied	satisfied	ADJ
ejpam-5156	311	30	.	.	PUNCT
ejpam-5156	312	1	additionally	additionally	ADV
ejpam-5156	312	2	,	,	PUNCT
ejpam-5156	312	3	⟨{v3	⟨{v3	PROPN
ejpam-5156	312	4	,	,	PUNCT
ejpam-5156	312	5	v4	v4	NOUN
ejpam-5156	312	6	,	,	PUNCT
ejpam-5156	312	7	v7	v7	NUM
ejpam-5156	312	8	,	,	PUNCT
ejpam-5156	312	9	v8	v8	PROPN
ejpam-5156	312	10	,	,	PUNCT
ejpam-5156	312	11	.	.	PUNCT
ejpam-5156	312	12	.	.	PUNCT
ejpam-5156	312	13	.	.	PUNCT
ejpam-5156	313	1	,	,	PUNCT
ejpam-5156	313	2	vn−6	vn−6	PROPN
ejpam-5156	313	3	,	,	PUNCT
ejpam-5156	313	4	vn−5}⟩	vn−5}⟩	NOUN
ejpam-5156	313	5	has	have	VERB
ejpam-5156	313	6	no	no	DET
ejpam-5156	313	7	isolated	isolate	VERB
ejpam-5156	313	8	vertices	vertex	NOUN
ejpam-5156	313	9	and	and	CCONJ
ejpam-5156	313	10	vn−2	vn−2	PROPN
ejpam-5156	313	11	is	be	AUX
ejpam-5156	313	12	adjacent	adjacent	ADJ
ejpam-5156	313	13	to	to	ADP
ejpam-5156	313	14	vn−1	vn−1	PROPN
ejpam-5156	313	15	,	,	PUNCT
ejpam-5156	313	16	so	so	ADV
ejpam-5156	313	17	⟨s⟩	⟨s⟩	PROPN
ejpam-5156	313	18	has	have	VERB
ejpam-5156	313	19	no	no	DET
ejpam-5156	313	20	isolated	isolate	VERB
ejpam-5156	313	21	vertices	vertex	NOUN
ejpam-5156	313	22	that	that	PRON
ejpam-5156	313	23	are	be	AUX
ejpam-5156	313	24	not	not	PART
ejpam-5156	313	25	leaf	leaf	ADJ
ejpam-5156	313	26	.	.	PUNCT
ejpam-5156	314	1	this	this	PRON
ejpam-5156	314	2	means	mean	VERB
ejpam-5156	314	3	that	that	SCONJ
ejpam-5156	314	4	theorem	theorem	VERB
ejpam-5156	314	5	8	8	NUM
ejpam-5156	314	6	(	(	PUNCT
ejpam-5156	314	7	ii	ii	NOUN
ejpam-5156	314	8	)	)	PUNCT
ejpam-5156	314	9	is	be	AUX
ejpam-5156	314	10	satisfied	satisfied	ADJ
ejpam-5156	314	11	.	.	PUNCT
ejpam-5156	315	1	moreover	moreover	ADV
ejpam-5156	315	2	,	,	PUNCT
ejpam-5156	315	3	⟨v	⟨v	PROPN
ejpam-5156	315	4	∖	∖	NOUN
ejpam-5156	315	5	s⟩	s⟩	NOUN
ejpam-5156	316	1	=	=	PUNCT
ejpam-5156	316	2	⟨{v1	⟨{v1	NOUN
ejpam-5156	316	3	,	,	PUNCT
ejpam-5156	316	4	v2	v2	PROPN
ejpam-5156	316	5	,	,	PUNCT
ejpam-5156	316	6	v5	v5	PROPN
ejpam-5156	316	7	,	,	PUNCT
ejpam-5156	316	8	v6	v6	NOUN
ejpam-5156	316	9	,	,	PUNCT
ejpam-5156	316	10	.	.	PUNCT
ejpam-5156	316	11	.	.	PUNCT
ejpam-5156	317	1	.	.	PUNCT
ejpam-5156	318	1	,	,	PUNCT
ejpam-5156	318	2	vn−4	vn−4	NOUN
ejpam-5156	318	3	,	,	PUNCT
ejpam-5156	318	4	vn−3}⟩	vn−3}⟩	NOUN
ejpam-5156	318	5	forms	form	VERB
ejpam-5156	318	6	a	a	DET
ejpam-5156	318	7	class	class	NOUN
ejpam-5156	318	8	of	of	ADP
ejpam-5156	318	9	p2	p2	NOUN
ejpam-5156	318	10	,	,	PUNCT
ejpam-5156	318	11	hence	hence	ADV
ejpam-5156	318	12	,	,	PUNCT
ejpam-5156	318	13	theorem	theorem	VERB
ejpam-5156	318	14	8	8	NUM
ejpam-5156	318	15	(	(	PUNCT
ejpam-5156	318	16	iii	iii	NOUN
ejpam-5156	318	17	)	)	PUNCT
ejpam-5156	318	18	is	be	AUX
ejpam-5156	318	19	satisfied	satisfied	ADJ
ejpam-5156	318	20	.	.	PUNCT
ejpam-5156	319	1	this	this	PRON
ejpam-5156	319	2	means	mean	VERB
ejpam-5156	319	3	that	that	SCONJ
ejpam-5156	319	4	,	,	PUNCT
ejpam-5156	319	5	by	by	ADP
ejpam-5156	319	6	theorem	theorem	NOUN
ejpam-5156	319	7	8	8	NUM
ejpam-5156	319	8	,	,	PUNCT
ejpam-5156	319	9	s	s	VERB
ejpam-5156	319	10	is	be	AUX
ejpam-5156	319	11	an	an	DET
ejpam-5156	319	12	rgda	rgda	NOUN
ejpam-5156	319	13	in	in	ADP
ejpam-5156	319	14	pn	pn	PROPN
ejpam-5156	319	15	.	.	PUNCT
ejpam-5156	320	1	now	now	ADV
ejpam-5156	320	2	,	,	PUNCT
ejpam-5156	320	3	suppose	suppose	VERB
ejpam-5156	320	4	that	that	SCONJ
ejpam-5156	320	5	w	w	PROPN
ejpam-5156	320	6	⊂	⊂	PROPN
ejpam-5156	320	7	s.	s.	PROPN
ejpam-5156	320	8	then	then	ADV
ejpam-5156	320	9	there	there	PRON
ejpam-5156	320	10	exists	exist	VERB
ejpam-5156	320	11	a	a	DET
ejpam-5156	320	12	vertex	vertex	NOUN
ejpam-5156	320	13	in	in	ADP
ejpam-5156	320	14	s	s	PRON
ejpam-5156	320	15	that	that	PRON
ejpam-5156	320	16	is	be	AUX
ejpam-5156	320	17	not	not	PART
ejpam-5156	320	18	in	in	ADP
ejpam-5156	320	19	w	w	PROPN
ejpam-5156	320	20	.	.	PUNCT
ejpam-5156	321	1	this	this	PRON
ejpam-5156	321	2	leads	lead	VERB
ejpam-5156	321	3	to	to	ADP
ejpam-5156	321	4	the	the	DET
ejpam-5156	321	5	following	following	ADJ
ejpam-5156	321	6	cases	case	NOUN
ejpam-5156	321	7	:	:	PUNCT
ejpam-5156	321	8	case	case	NOUN
ejpam-5156	321	9	1	1	NUM
ejpam-5156	321	10	:	:	PUNCT
ejpam-5156	321	11	atleast	atleast	ADJ
ejpam-5156	321	12	one	one	NUM
ejpam-5156	321	13	vertex	vertex	NOUN
ejpam-5156	321	14	in	in	ADP
ejpam-5156	321	15	{	{	PUNCT
ejpam-5156	321	16	v0	v0	NOUN
ejpam-5156	321	17	,	,	PUNCT
ejpam-5156	321	18	vn−1	vn−1	ADJ
ejpam-5156	321	19	}	}	PUNCT
ejpam-5156	321	20	is	be	AUX
ejpam-5156	321	21	not	not	PART
ejpam-5156	321	22	in	in	ADP
ejpam-5156	321	23	w	w	PROPN
ejpam-5156	321	24	.	.	PUNCT
ejpam-5156	322	1	then	then	ADV
ejpam-5156	322	2	theorem	theorem	VERB
ejpam-5156	322	3	8	8	NUM
ejpam-5156	322	4	(	(	PUNCT
ejpam-5156	322	5	i	i	NOUN
ejpam-5156	322	6	)	)	PUNCT
ejpam-5156	322	7	is	be	AUX
ejpam-5156	322	8	not	not	PART
ejpam-5156	322	9	satisfied	satisfied	ADJ
ejpam-5156	322	10	,	,	PUNCT
ejpam-5156	322	11	so	so	ADV
ejpam-5156	322	12	w	w	NOUN
ejpam-5156	322	13	is	be	AUX
ejpam-5156	322	14	not	not	PART
ejpam-5156	322	15	an	an	DET
ejpam-5156	322	16	rgda	rgda	NOUN
ejpam-5156	322	17	in	in	ADP
ejpam-5156	322	18	pn	pn	PROPN
ejpam-5156	322	19	.	.	PROPN
ejpam-5156	322	20	case	case	NOUN
ejpam-5156	322	21	2	2	NUM
ejpam-5156	322	22	:	:	PUNCT
ejpam-5156	322	23	atleast	atleast	ADJ
ejpam-5156	322	24	one	one	NUM
ejpam-5156	322	25	vertex	vertex	NOUN
ejpam-5156	322	26	in	in	ADP
ejpam-5156	322	27	{	{	PUNCT
ejpam-5156	322	28	v3	v3	PROPN
ejpam-5156	322	29	,	,	PUNCT
ejpam-5156	322	30	v4	v4	NOUN
ejpam-5156	322	31	,	,	PUNCT
ejpam-5156	322	32	v7	v7	NUM
ejpam-5156	322	33	,	,	PUNCT
ejpam-5156	322	34	v8	v8	PROPN
ejpam-5156	322	35	,	,	PUNCT
ejpam-5156	322	36	.	.	PUNCT
ejpam-5156	322	37	.	.	PUNCT
ejpam-5156	323	1	.	.	PUNCT
ejpam-5156	324	1	,	,	PUNCT
ejpam-5156	324	2	vn−6	vn−6	PROPN
ejpam-5156	324	3	,	,	PUNCT
ejpam-5156	324	4	vn−5	vn−5	PROPN
ejpam-5156	324	5	}	}	PUNCT
ejpam-5156	324	6	∪	∪	NOUN
ejpam-5156	324	7	{	{	PUNCT
ejpam-5156	324	8	vn−2	vn−2	NOUN
ejpam-5156	324	9	}	}	PUNCT
ejpam-5156	324	10	is	be	AUX
ejpam-5156	324	11	not	not	PART
ejpam-5156	324	12	in	in	ADP
ejpam-5156	324	13	w	w	PROPN
ejpam-5156	324	14	.	.	PUNCT
ejpam-5156	325	1	then	then	ADV
ejpam-5156	325	2	there	there	PRON
ejpam-5156	325	3	exists	exist	VERB
ejpam-5156	325	4	a	a	DET
ejpam-5156	325	5	class	class	NOUN
ejpam-5156	325	6	in	in	ADP
ejpam-5156	325	7	⟨v	⟨v	NOUN
ejpam-5156	325	8	∖	∖	PROPN
ejpam-5156	325	9	s⟩	s⟩	VERB
ejpam-5156	325	10	that	that	PRON
ejpam-5156	325	11	is	be	AUX
ejpam-5156	325	12	not	not	PART
ejpam-5156	325	13	p2	p2	ADJ
ejpam-5156	325	14	,	,	PUNCT
ejpam-5156	325	15	so	so	ADV
ejpam-5156	325	16	theorem	theorem	ADJ
ejpam-5156	325	17	8	8	NUM
ejpam-5156	325	18	(	(	PUNCT
ejpam-5156	325	19	iii	iii	NOUN
ejpam-5156	325	20	)	)	PUNCT
ejpam-5156	325	21	is	be	AUX
ejpam-5156	325	22	not	not	PART
ejpam-5156	325	23	satisfied	satisfied	ADJ
ejpam-5156	325	24	.	.	PUNCT
ejpam-5156	326	1	hence	hence	ADV
ejpam-5156	326	2	,	,	PUNCT
ejpam-5156	326	3	w	w	NOUN
ejpam-5156	326	4	is	be	AUX
ejpam-5156	326	5	not	not	PART
ejpam-5156	326	6	an	an	DET
ejpam-5156	326	7	rgda	rgda	NOUN
ejpam-5156	326	8	in	in	ADP
ejpam-5156	326	9	pn	pn	PROPN
ejpam-5156	326	10	.	.	PUNCT
ejpam-5156	326	11	therefore	therefore	ADV
ejpam-5156	326	12	,	,	PUNCT
ejpam-5156	326	13	s	s	VERB
ejpam-5156	326	14	is	be	AUX
ejpam-5156	326	15	a	a	DET
ejpam-5156	326	16	minimum	minimum	ADJ
ejpam-5156	326	17	rgda	rgda	NOUN
ejpam-5156	326	18	in	in	ADP
ejpam-5156	326	19	pn	pn	PROPN
ejpam-5156	326	20	.	.	PUNCT
ejpam-5156	327	1	lemma	lemma	PROPN
ejpam-5156	327	2	3	3	X
ejpam-5156	327	3	.	.	PUNCT
ejpam-5156	328	1	let	let	VERB
ejpam-5156	328	2	pn	pn	VERB
ejpam-5156	328	3	=	=	SYM
ejpam-5156	328	4	(	(	PUNCT
ejpam-5156	328	5	v	v	NOUN
ejpam-5156	328	6	,	,	PUNCT
ejpam-5156	328	7	e	e	NOUN
ejpam-5156	328	8	)	)	PUNCT
ejpam-5156	328	9	,	,	PUNCT
ejpam-5156	329	1	n	n	CCONJ
ejpam-5156	329	2	≡	≡	PROPN
ejpam-5156	329	3	2	2	NUM
ejpam-5156	329	4	(	(	PUNCT
ejpam-5156	329	5	mod	mod	NOUN
ejpam-5156	329	6	4	4	NUM
ejpam-5156	329	7	)	)	PUNCT
ejpam-5156	329	8	,	,	PUNCT
ejpam-5156	329	9	be	be	AUX
ejpam-5156	329	10	a	a	DET
ejpam-5156	329	11	path	path	NOUN
ejpam-5156	329	12	graph	graph	NOUN
ejpam-5156	329	13	of	of	ADP
ejpam-5156	329	14	order	order	NOUN
ejpam-5156	329	15	n	n	PRON
ejpam-5156	329	16	≥	≥	NOUN
ejpam-5156	329	17	2	2	NUM
ejpam-5156	329	18	.	.	PUNCT
ejpam-5156	330	1	then	then	ADV
ejpam-5156	330	2	s	s	VERB
ejpam-5156	330	3	=	=	SYM
ejpam-5156	330	4	{	{	PUNCT
ejpam-5156	330	5	v0	v0	NOUN
ejpam-5156	330	6	,	,	PUNCT
ejpam-5156	330	7	vn−1	vn−1	ADJ
ejpam-5156	330	8	}	}	PUNCT
ejpam-5156	330	9	∪	∪	NOUN
ejpam-5156	330	10	{	{	PUNCT
ejpam-5156	330	11	v3	v3	PROPN
ejpam-5156	330	12	,	,	PUNCT
ejpam-5156	330	13	v4	v4	NOUN
ejpam-5156	330	14	,	,	PUNCT
ejpam-5156	330	15	v7	v7	NUM
ejpam-5156	330	16	,	,	PUNCT
ejpam-5156	330	17	v8	v8	PROPN
ejpam-5156	330	18	,	,	PUNCT
ejpam-5156	330	19	.	.	PUNCT
ejpam-5156	330	20	.	.	PUNCT
ejpam-5156	330	21	.	.	PUNCT
ejpam-5156	331	1	,	,	PUNCT
ejpam-5156	331	2	vn−3	vn−3	PROPN
ejpam-5156	331	3	,	,	PUNCT
ejpam-5156	331	4	vn−2	vn−2	PROPN
ejpam-5156	331	5	}	}	PUNCT
ejpam-5156	331	6	is	be	AUX
ejpam-5156	331	7	a	a	DET
ejpam-5156	331	8	minimum	minimum	ADJ
ejpam-5156	331	9	restrained	restrain	VERB
ejpam-5156	331	10	global	global	ADJ
ejpam-5156	331	11	defensive	defensive	ADJ
ejpam-5156	331	12	alliance	alliance	NOUN
ejpam-5156	331	13	in	in	ADP
ejpam-5156	331	14	pn	pn	PROPN
ejpam-5156	331	15	.	.	PROPN
ejpam-5156	331	16	l.	l.	PROPN
ejpam-5156	331	17	consistente	consistente	PROPN
ejpam-5156	331	18	,	,	PUNCT
ejpam-5156	331	19	i.	i.	PROPN
ejpam-5156	331	20	cabahug	cabahug	PROPN
ejpam-5156	331	21	,	,	PUNCT
ejpam-5156	331	22	jr	jr	PROPN
ejpam-5156	331	23	.	.	PROPN
ejpam-5156	331	24	/	/	SYM
ejpam-5156	331	25	eur	eur	PROPN
ejpam-5156	331	26	.	.	PUNCT
ejpam-5156	332	1	j.	j.	PROPN
ejpam-5156	332	2	pure	pure	PROPN
ejpam-5156	332	3	appl	appl	PROPN
ejpam-5156	332	4	.	.	PROPN
ejpam-5156	332	5	math	math	PROPN
ejpam-5156	332	6	,	,	PUNCT
ejpam-5156	332	7	17	17	NUM
ejpam-5156	332	8	(	(	PUNCT
ejpam-5156	332	9	3	3	NUM
ejpam-5156	332	10	)	)	PUNCT
ejpam-5156	332	11	(	(	PUNCT
ejpam-5156	332	12	2024	2024	NUM
ejpam-5156	332	13	)	)	PUNCT
ejpam-5156	332	14	,	,	PUNCT
ejpam-5156	332	15	2196	2196	NUM
ejpam-5156	332	16	-	-	SYM
ejpam-5156	332	17	2209	2209	NUM
ejpam-5156	332	18	2206	2206	NUM
ejpam-5156	332	19	proof	proof	NOUN
ejpam-5156	332	20	.	.	PUNCT
ejpam-5156	333	1	let	let	VERB
ejpam-5156	333	2	s	s	PRON
ejpam-5156	333	3	=	=	PUNCT
ejpam-5156	333	4	{	{	PUNCT
ejpam-5156	333	5	v0	v0	NOUN
ejpam-5156	333	6	,	,	PUNCT
ejpam-5156	333	7	vn−1	vn−1	ADJ
ejpam-5156	333	8	}	}	PUNCT
ejpam-5156	333	9	∪	∪	NOUN
ejpam-5156	333	10	{	{	PUNCT
ejpam-5156	333	11	v3	v3	PROPN
ejpam-5156	333	12	,	,	PUNCT
ejpam-5156	333	13	v4	v4	NOUN
ejpam-5156	333	14	,	,	PUNCT
ejpam-5156	333	15	v7	v7	NUM
ejpam-5156	333	16	,	,	PUNCT
ejpam-5156	333	17	v8	v8	PROPN
ejpam-5156	333	18	,	,	PUNCT
ejpam-5156	333	19	.	.	PUNCT
ejpam-5156	333	20	.	.	PUNCT
ejpam-5156	334	1	.	.	PUNCT
ejpam-5156	335	1	,	,	PUNCT
ejpam-5156	335	2	vn−3	vn−3	PROPN
ejpam-5156	335	3	,	,	PUNCT
ejpam-5156	335	4	vn−2	vn−2	PROPN
ejpam-5156	335	5	}	}	PUNCT
ejpam-5156	335	6	.	.	PUNCT
ejpam-5156	336	1	notice	notice	VERB
ejpam-5156	336	2	that	that	SCONJ
ejpam-5156	336	3	all	all	DET
ejpam-5156	336	4	the	the	DET
ejpam-5156	336	5	leaf	leaf	NOUN
ejpam-5156	336	6	vertices	vertex	NOUN
ejpam-5156	336	7	of	of	ADP
ejpam-5156	336	8	pn	pn	PROPN
ejpam-5156	336	9	are	be	AUX
ejpam-5156	336	10	in	in	ADP
ejpam-5156	336	11	s	s	PROPN
ejpam-5156	336	12	,	,	PUNCT
ejpam-5156	336	13	that	that	ADV
ejpam-5156	336	14	is	is	ADV
ejpam-5156	336	15	,	,	PUNCT
ejpam-5156	336	16	v0	v0	PROPN
ejpam-5156	336	17	,	,	PUNCT
ejpam-5156	336	18	vn−1	vn−1	PROPN
ejpam-5156	336	19	∈	∈	PROPN
ejpam-5156	336	20	s.	s.	PROPN
ejpam-5156	336	21	so	so	ADV
ejpam-5156	336	22	,	,	PUNCT
ejpam-5156	336	23	theorem	theorem	VERB
ejpam-5156	336	24	8	8	NUM
ejpam-5156	336	25	(	(	PUNCT
ejpam-5156	336	26	i	i	NOUN
ejpam-5156	336	27	)	)	PUNCT
ejpam-5156	336	28	is	be	AUX
ejpam-5156	336	29	satisfied	satisfied	ADJ
ejpam-5156	336	30	.	.	PUNCT
ejpam-5156	337	1	additionally	additionally	ADV
ejpam-5156	337	2	,	,	PUNCT
ejpam-5156	337	3	⟨{v3	⟨{v3	PROPN
ejpam-5156	337	4	,	,	PUNCT
ejpam-5156	337	5	v4	v4	NOUN
ejpam-5156	337	6	,	,	PUNCT
ejpam-5156	337	7	v7	v7	NUM
ejpam-5156	337	8	,	,	PUNCT
ejpam-5156	337	9	v8	v8	PROPN
ejpam-5156	337	10	,	,	PUNCT
ejpam-5156	337	11	.	.	PUNCT
ejpam-5156	337	12	.	.	PUNCT
ejpam-5156	338	1	.	.	PUNCT
ejpam-5156	339	1	,	,	PUNCT
ejpam-5156	339	2	vn−3	vn−3	PROPN
ejpam-5156	339	3	,	,	PUNCT
ejpam-5156	339	4	vn−2}}⟩	vn−2}}⟩	NOUN
ejpam-5156	339	5	has	have	VERB
ejpam-5156	339	6	no	no	DET
ejpam-5156	339	7	isolated	isolated	ADJ
ejpam-5156	339	8	vertices	vertex	NOUN
ejpam-5156	339	9	,	,	PUNCT
ejpam-5156	339	10	so	so	ADV
ejpam-5156	339	11	⟨s⟩	⟨s⟩	PROPN
ejpam-5156	339	12	has	have	VERB
ejpam-5156	339	13	no	no	DET
ejpam-5156	339	14	isolated	isolate	VERB
ejpam-5156	339	15	vertices	vertex	NOUN
ejpam-5156	339	16	that	that	PRON
ejpam-5156	339	17	are	be	AUX
ejpam-5156	339	18	not	not	PART
ejpam-5156	339	19	leaf	leaf	ADJ
ejpam-5156	339	20	.	.	PUNCT
ejpam-5156	340	1	this	this	PRON
ejpam-5156	340	2	means	mean	VERB
ejpam-5156	340	3	that	that	SCONJ
ejpam-5156	340	4	theorem	theorem	VERB
ejpam-5156	340	5	8	8	NUM
ejpam-5156	340	6	(	(	PUNCT
ejpam-5156	340	7	ii	ii	NOUN
ejpam-5156	340	8	)	)	PUNCT
ejpam-5156	340	9	is	be	AUX
ejpam-5156	340	10	satisfied	satisfied	ADJ
ejpam-5156	340	11	.	.	PUNCT
ejpam-5156	341	1	moreover	moreover	ADV
ejpam-5156	341	2	,	,	PUNCT
ejpam-5156	341	3	⟨v	⟨v	PROPN
ejpam-5156	341	4	∖	∖	NOUN
ejpam-5156	341	5	s⟩	s⟩	NOUN
ejpam-5156	342	1	=	=	PUNCT
ejpam-5156	342	2	⟨{v1	⟨{v1	NOUN
ejpam-5156	342	3	,	,	PUNCT
ejpam-5156	342	4	v2	v2	PROPN
ejpam-5156	342	5	,	,	PUNCT
ejpam-5156	342	6	v5	v5	PROPN
ejpam-5156	342	7	,	,	PUNCT
ejpam-5156	342	8	v6	v6	NOUN
ejpam-5156	342	9	,	,	PUNCT
ejpam-5156	342	10	.	.	PUNCT
ejpam-5156	342	11	.	.	PUNCT
ejpam-5156	343	1	.	.	PUNCT
ejpam-5156	344	1	,	,	PUNCT
ejpam-5156	344	2	vn−5	vn−5	PROPN
ejpam-5156	344	3	,	,	PUNCT
ejpam-5156	344	4	vn−4}⟩	vn−4}⟩	NOUN
ejpam-5156	344	5	forms	form	VERB
ejpam-5156	344	6	a	a	DET
ejpam-5156	344	7	class	class	NOUN
ejpam-5156	344	8	of	of	ADP
ejpam-5156	344	9	p2	p2	NOUN
ejpam-5156	344	10	,	,	PUNCT
ejpam-5156	344	11	hence	hence	ADV
ejpam-5156	344	12	,	,	PUNCT
ejpam-5156	344	13	theorem	theorem	VERB
ejpam-5156	344	14	8	8	NUM
ejpam-5156	344	15	(	(	PUNCT
ejpam-5156	344	16	iii	iii	NOUN
ejpam-5156	344	17	)	)	PUNCT
ejpam-5156	344	18	is	be	AUX
ejpam-5156	344	19	satisfied	satisfied	ADJ
ejpam-5156	344	20	.	.	PUNCT
ejpam-5156	345	1	this	this	PRON
ejpam-5156	345	2	means	mean	VERB
ejpam-5156	345	3	that	that	SCONJ
ejpam-5156	345	4	,	,	PUNCT
ejpam-5156	345	5	by	by	ADP
ejpam-5156	345	6	theorem	theorem	NOUN
ejpam-5156	345	7	8	8	NUM
ejpam-5156	345	8	,	,	PUNCT
ejpam-5156	345	9	s	s	VERB
ejpam-5156	345	10	is	be	AUX
ejpam-5156	345	11	an	an	DET
ejpam-5156	345	12	rgda	rgda	NOUN
ejpam-5156	345	13	in	in	ADP
ejpam-5156	345	14	pn	pn	PROPN
ejpam-5156	345	15	.	.	PUNCT
ejpam-5156	346	1	now	now	ADV
ejpam-5156	346	2	,	,	PUNCT
ejpam-5156	346	3	suppose	suppose	VERB
ejpam-5156	346	4	that	that	SCONJ
ejpam-5156	346	5	w	w	PROPN
ejpam-5156	346	6	⊂	⊂	PROPN
ejpam-5156	346	7	s.	s.	PROPN
ejpam-5156	346	8	then	then	ADV
ejpam-5156	346	9	there	there	PRON
ejpam-5156	346	10	exists	exist	VERB
ejpam-5156	346	11	a	a	DET
ejpam-5156	346	12	vertex	vertex	NOUN
ejpam-5156	346	13	in	in	ADP
ejpam-5156	346	14	s	s	PRON
ejpam-5156	346	15	that	that	PRON
ejpam-5156	346	16	is	be	AUX
ejpam-5156	346	17	not	not	PART
ejpam-5156	346	18	in	in	ADP
ejpam-5156	346	19	w	w	PROPN
ejpam-5156	346	20	.	.	PUNCT
ejpam-5156	347	1	this	this	PRON
ejpam-5156	347	2	leads	lead	VERB
ejpam-5156	347	3	to	to	ADP
ejpam-5156	347	4	the	the	DET
ejpam-5156	347	5	following	following	ADJ
ejpam-5156	347	6	cases	case	NOUN
ejpam-5156	347	7	:	:	PUNCT
ejpam-5156	347	8	case	case	NOUN
ejpam-5156	347	9	1	1	NUM
ejpam-5156	347	10	:	:	PUNCT
ejpam-5156	347	11	atleast	atleast	ADJ
ejpam-5156	347	12	one	one	NUM
ejpam-5156	347	13	vertex	vertex	NOUN
ejpam-5156	347	14	in	in	ADP
ejpam-5156	347	15	{	{	PUNCT
ejpam-5156	347	16	v0	v0	NOUN
ejpam-5156	347	17	,	,	PUNCT
ejpam-5156	347	18	vn−1	vn−1	ADJ
ejpam-5156	347	19	}	}	PUNCT
ejpam-5156	347	20	is	be	AUX
ejpam-5156	347	21	not	not	PART
ejpam-5156	347	22	in	in	ADP
ejpam-5156	347	23	w	w	PROPN
ejpam-5156	347	24	.	.	PUNCT
ejpam-5156	348	1	then	then	ADV
ejpam-5156	348	2	theorem	theorem	VERB
ejpam-5156	348	3	8	8	NUM
ejpam-5156	348	4	(	(	PUNCT
ejpam-5156	348	5	i	i	NOUN
ejpam-5156	348	6	)	)	PUNCT
ejpam-5156	348	7	is	be	AUX
ejpam-5156	348	8	not	not	PART
ejpam-5156	348	9	satisfied	satisfied	ADJ
ejpam-5156	348	10	,	,	PUNCT
ejpam-5156	348	11	so	so	ADV
ejpam-5156	348	12	w	w	NOUN
ejpam-5156	348	13	is	be	AUX
ejpam-5156	348	14	not	not	PART
ejpam-5156	348	15	an	an	DET
ejpam-5156	348	16	rgda	rgda	NOUN
ejpam-5156	348	17	in	in	ADP
ejpam-5156	348	18	pn	pn	PROPN
ejpam-5156	348	19	.	.	PROPN
ejpam-5156	348	20	case	case	NOUN
ejpam-5156	348	21	2	2	NUM
ejpam-5156	348	22	:	:	PUNCT
ejpam-5156	348	23	atleast	atleast	ADJ
ejpam-5156	348	24	one	one	NUM
ejpam-5156	348	25	vertex	vertex	NOUN
ejpam-5156	348	26	in	in	ADP
ejpam-5156	348	27	{	{	PUNCT
ejpam-5156	348	28	v3	v3	PROPN
ejpam-5156	348	29	,	,	PUNCT
ejpam-5156	348	30	v4	v4	NOUN
ejpam-5156	348	31	,	,	PUNCT
ejpam-5156	348	32	v7	v7	NUM
ejpam-5156	348	33	,	,	PUNCT
ejpam-5156	348	34	v8	v8	PROPN
ejpam-5156	348	35	,	,	PUNCT
ejpam-5156	348	36	.	.	PUNCT
ejpam-5156	348	37	.	.	PUNCT
ejpam-5156	349	1	.	.	PUNCT
ejpam-5156	350	1	,	,	PUNCT
ejpam-5156	350	2	vn−3	vn−3	PROPN
ejpam-5156	350	3	,	,	PUNCT
ejpam-5156	350	4	vn−2	vn−2	PROPN
ejpam-5156	350	5	}	}	PUNCT
ejpam-5156	350	6	is	be	AUX
ejpam-5156	350	7	not	not	PART
ejpam-5156	350	8	in	in	ADP
ejpam-5156	350	9	w	w	PROPN
ejpam-5156	350	10	.	.	PUNCT
ejpam-5156	351	1	then	then	ADV
ejpam-5156	351	2	there	there	PRON
ejpam-5156	351	3	exists	exist	VERB
ejpam-5156	351	4	a	a	DET
ejpam-5156	351	5	class	class	NOUN
ejpam-5156	351	6	in	in	ADP
ejpam-5156	351	7	⟨v	⟨v	NOUN
ejpam-5156	351	8	∖	∖	PROPN
ejpam-5156	351	9	s⟩	s⟩	VERB
ejpam-5156	351	10	that	that	PRON
ejpam-5156	351	11	is	be	AUX
ejpam-5156	351	12	not	not	PART
ejpam-5156	351	13	p2	p2	ADJ
ejpam-5156	351	14	,	,	PUNCT
ejpam-5156	351	15	so	so	ADV
ejpam-5156	351	16	theorem	theorem	ADJ
ejpam-5156	351	17	8	8	NUM
ejpam-5156	351	18	(	(	PUNCT
ejpam-5156	351	19	iii	iii	NOUN
ejpam-5156	351	20	)	)	PUNCT
ejpam-5156	351	21	is	be	AUX
ejpam-5156	351	22	not	not	PART
ejpam-5156	351	23	satisfied	satisfied	ADJ
ejpam-5156	351	24	.	.	PUNCT
ejpam-5156	352	1	hence	hence	ADV
ejpam-5156	352	2	,	,	PUNCT
ejpam-5156	352	3	w	w	NOUN
ejpam-5156	352	4	is	be	AUX
ejpam-5156	352	5	not	not	PART
ejpam-5156	352	6	an	an	DET
ejpam-5156	352	7	rgda	rgda	NOUN
ejpam-5156	352	8	in	in	ADP
ejpam-5156	352	9	pn	pn	PROPN
ejpam-5156	352	10	.	.	PUNCT
ejpam-5156	352	11	therefore	therefore	ADV
ejpam-5156	352	12	,	,	PUNCT
ejpam-5156	352	13	s	s	VERB
ejpam-5156	352	14	is	be	AUX
ejpam-5156	352	15	a	a	DET
ejpam-5156	352	16	minimum	minimum	ADJ
ejpam-5156	352	17	rgda	rgda	NOUN
ejpam-5156	352	18	in	in	ADP
ejpam-5156	352	19	pn	pn	PROPN
ejpam-5156	352	20	.	.	PUNCT
ejpam-5156	353	1	lemma	lemma	PROPN
ejpam-5156	353	2	4	4	X
ejpam-5156	353	3	.	.	PUNCT
ejpam-5156	354	1	let	let	VERB
ejpam-5156	354	2	pn	pn	VERB
ejpam-5156	354	3	=	=	SYM
ejpam-5156	354	4	(	(	PUNCT
ejpam-5156	354	5	v	v	NOUN
ejpam-5156	354	6	,	,	PUNCT
ejpam-5156	354	7	e	e	NOUN
ejpam-5156	354	8	)	)	PUNCT
ejpam-5156	354	9	,	,	PUNCT
ejpam-5156	354	10	n	n	NUM
ejpam-5156	354	11	≡	≡	PROPN
ejpam-5156	354	12	3	3	NUM
ejpam-5156	354	13	(	(	PUNCT
ejpam-5156	354	14	mod	mod	NOUN
ejpam-5156	354	15	4	4	NUM
ejpam-5156	354	16	)	)	PUNCT
ejpam-5156	354	17	,	,	PUNCT
ejpam-5156	354	18	be	be	AUX
ejpam-5156	354	19	a	a	DET
ejpam-5156	354	20	path	path	NOUN
ejpam-5156	354	21	graph	graph	NOUN
ejpam-5156	354	22	of	of	ADP
ejpam-5156	354	23	order	order	NOUN
ejpam-5156	354	24	n	n	PRON
ejpam-5156	354	25	≥	≥	NOUN
ejpam-5156	354	26	2	2	NUM
ejpam-5156	354	27	.	.	PUNCT
ejpam-5156	355	1	then	then	ADV
ejpam-5156	355	2	s	s	VERB
ejpam-5156	355	3	=	=	SYM
ejpam-5156	355	4	{	{	PUNCT
ejpam-5156	355	5	v0	v0	NOUN
ejpam-5156	355	6	,	,	PUNCT
ejpam-5156	355	7	vn−1	vn−1	ADJ
ejpam-5156	355	8	}	}	PUNCT
ejpam-5156	355	9	∪	∪	NOUN
ejpam-5156	355	10	{	{	PUNCT
ejpam-5156	355	11	v3	v3	PROPN
ejpam-5156	355	12	,	,	PUNCT
ejpam-5156	355	13	v4	v4	NOUN
ejpam-5156	355	14	,	,	PUNCT
ejpam-5156	355	15	v7	v7	NUM
ejpam-5156	355	16	,	,	PUNCT
ejpam-5156	355	17	v8	v8	PROPN
ejpam-5156	355	18	,	,	PUNCT
ejpam-5156	355	19	.	.	PUNCT
ejpam-5156	355	20	.	.	PUNCT
ejpam-5156	355	21	.	.	PUNCT
ejpam-5156	356	1	,	,	PUNCT
ejpam-5156	356	2	vn−4	vn−4	NOUN
ejpam-5156	356	3	,	,	PUNCT
ejpam-5156	356	4	vn−3	vn−3	PROPN
ejpam-5156	356	5	}	}	PUNCT
ejpam-5156	356	6	∪	∪	NOUN
ejpam-5156	356	7	{	{	PUNCT
ejpam-5156	356	8	vn−2	vn−2	PROPN
ejpam-5156	356	9	}	}	PUNCT
ejpam-5156	356	10	is	be	AUX
ejpam-5156	356	11	a	a	DET
ejpam-5156	356	12	minimum	minimum	ADJ
ejpam-5156	356	13	restrained	restrain	VERB
ejpam-5156	356	14	global	global	ADJ
ejpam-5156	356	15	defensive	defensive	ADJ
ejpam-5156	356	16	alliance	alliance	NOUN
ejpam-5156	356	17	in	in	ADP
ejpam-5156	356	18	pn	pn	PROPN
ejpam-5156	356	19	.	.	PUNCT
ejpam-5156	356	20	proof	proof	NOUN
ejpam-5156	356	21	.	.	PUNCT
ejpam-5156	357	1	let	let	VERB
ejpam-5156	357	2	s	s	PRON
ejpam-5156	357	3	=	=	PUNCT
ejpam-5156	357	4	{	{	PUNCT
ejpam-5156	357	5	v0	v0	NOUN
ejpam-5156	357	6	,	,	PUNCT
ejpam-5156	357	7	vn−1	vn−1	ADJ
ejpam-5156	357	8	}	}	PUNCT
ejpam-5156	357	9	∪	∪	NOUN
ejpam-5156	357	10	{	{	PUNCT
ejpam-5156	357	11	v3	v3	PROPN
ejpam-5156	357	12	,	,	PUNCT
ejpam-5156	357	13	v4	v4	NOUN
ejpam-5156	357	14	,	,	PUNCT
ejpam-5156	357	15	v7	v7	NUM
ejpam-5156	357	16	,	,	PUNCT
ejpam-5156	357	17	v8	v8	PROPN
ejpam-5156	357	18	,	,	PUNCT
ejpam-5156	357	19	.	.	PUNCT
ejpam-5156	357	20	.	.	PUNCT
ejpam-5156	358	1	.	.	PUNCT
ejpam-5156	359	1	,	,	PUNCT
ejpam-5156	359	2	vn−4	vn−4	NOUN
ejpam-5156	359	3	,	,	PUNCT
ejpam-5156	359	4	vn−3	vn−3	PROPN
ejpam-5156	359	5	}	}	PUNCT
ejpam-5156	359	6	∪	∪	ADJ
ejpam-5156	359	7	{	{	PUNCT
ejpam-5156	359	8	vn−2	vn−2	NOUN
ejpam-5156	359	9	}	}	PUNCT
ejpam-5156	359	10	.	.	PUNCT
ejpam-5156	360	1	notice	notice	VERB
ejpam-5156	360	2	that	that	SCONJ
ejpam-5156	360	3	all	all	DET
ejpam-5156	360	4	the	the	DET
ejpam-5156	360	5	leaf	leaf	NOUN
ejpam-5156	360	6	vertices	vertex	NOUN
ejpam-5156	360	7	of	of	ADP
ejpam-5156	360	8	pn	pn	PROPN
ejpam-5156	360	9	are	be	AUX
ejpam-5156	360	10	in	in	ADP
ejpam-5156	360	11	s	s	PROPN
ejpam-5156	360	12	,	,	PUNCT
ejpam-5156	360	13	that	that	ADV
ejpam-5156	360	14	is	is	ADV
ejpam-5156	360	15	,	,	PUNCT
ejpam-5156	360	16	v0	v0	PROPN
ejpam-5156	360	17	,	,	PUNCT
ejpam-5156	360	18	vn−1	vn−1	PROPN
ejpam-5156	360	19	∈	∈	PROPN
ejpam-5156	360	20	s.	s.	PROPN
ejpam-5156	360	21	so	so	ADV
ejpam-5156	360	22	,	,	PUNCT
ejpam-5156	360	23	theorem	theorem	VERB
ejpam-5156	360	24	8	8	NUM
ejpam-5156	360	25	(	(	PUNCT
ejpam-5156	360	26	i	i	NOUN
ejpam-5156	360	27	)	)	PUNCT
ejpam-5156	360	28	is	be	AUX
ejpam-5156	360	29	satisfied	satisfied	ADJ
ejpam-5156	360	30	.	.	PUNCT
ejpam-5156	361	1	additionally	additionally	ADV
ejpam-5156	361	2	,	,	PUNCT
ejpam-5156	361	3	⟨{v3	⟨{v3	PROPN
ejpam-5156	361	4	,	,	PUNCT
ejpam-5156	361	5	v4	v4	NOUN
ejpam-5156	361	6	,	,	PUNCT
ejpam-5156	361	7	v7	v7	NUM
ejpam-5156	361	8	,	,	PUNCT
ejpam-5156	361	9	v8	v8	PROPN
ejpam-5156	361	10	,	,	PUNCT
ejpam-5156	361	11	.	.	PUNCT
ejpam-5156	361	12	.	.	PUNCT
ejpam-5156	362	1	.	.	PUNCT
ejpam-5156	363	1	,	,	PUNCT
ejpam-5156	363	2	vn−4	vn−4	NOUN
ejpam-5156	363	3	,	,	PUNCT
ejpam-5156	363	4	vn−3}⟩	vn−3}⟩	NOUN
ejpam-5156	363	5	has	have	VERB
ejpam-5156	363	6	no	no	DET
ejpam-5156	363	7	isolated	isolate	VERB
ejpam-5156	363	8	vertices	vertex	NOUN
ejpam-5156	363	9	and	and	CCONJ
ejpam-5156	363	10	vn−2	vn−2	PROPN
ejpam-5156	363	11	is	be	AUX
ejpam-5156	363	12	adjacent	adjacent	ADJ
ejpam-5156	363	13	to	to	ADP
ejpam-5156	363	14	vn−1	vn−1	PROPN
ejpam-5156	363	15	,	,	PUNCT
ejpam-5156	363	16	so	so	ADV
ejpam-5156	363	17	⟨s⟩	⟨s⟩	PROPN
ejpam-5156	363	18	has	have	VERB
ejpam-5156	363	19	no	no	DET
ejpam-5156	363	20	isolated	isolate	VERB
ejpam-5156	363	21	vertices	vertex	NOUN
ejpam-5156	363	22	that	that	PRON
ejpam-5156	363	23	are	be	AUX
ejpam-5156	363	24	not	not	PART
ejpam-5156	363	25	leaf	leaf	ADJ
ejpam-5156	363	26	.	.	PUNCT
ejpam-5156	364	1	this	this	PRON
ejpam-5156	364	2	means	mean	VERB
ejpam-5156	364	3	that	that	SCONJ
ejpam-5156	364	4	theorem	theorem	VERB
ejpam-5156	364	5	8	8	NUM
ejpam-5156	364	6	(	(	PUNCT
ejpam-5156	364	7	ii	ii	NOUN
ejpam-5156	364	8	)	)	PUNCT
ejpam-5156	364	9	is	be	AUX
ejpam-5156	364	10	satisfied	satisfied	ADJ
ejpam-5156	364	11	.	.	PUNCT
ejpam-5156	365	1	moreover	moreover	ADV
ejpam-5156	365	2	,	,	PUNCT
ejpam-5156	365	3	⟨v	⟨v	PROPN
ejpam-5156	365	4	∖	∖	NOUN
ejpam-5156	365	5	s⟩	s⟩	NOUN
ejpam-5156	366	1	=	=	PUNCT
ejpam-5156	366	2	⟨{v1	⟨{v1	NOUN
ejpam-5156	366	3	,	,	PUNCT
ejpam-5156	366	4	v2	v2	PROPN
ejpam-5156	366	5	,	,	PUNCT
ejpam-5156	366	6	v5	v5	PROPN
ejpam-5156	366	7	,	,	PUNCT
ejpam-5156	366	8	v6	v6	NOUN
ejpam-5156	366	9	,	,	PUNCT
ejpam-5156	366	10	.	.	PUNCT
ejpam-5156	366	11	.	.	PUNCT
ejpam-5156	367	1	.	.	PUNCT
ejpam-5156	368	1	,	,	PUNCT
ejpam-5156	368	2	vn−6	vn−6	PROPN
ejpam-5156	368	3	,	,	PUNCT
ejpam-5156	368	4	vn−5}⟩	vn−5}⟩	NOUN
ejpam-5156	368	5	forms	form	VERB
ejpam-5156	368	6	a	a	DET
ejpam-5156	368	7	class	class	NOUN
ejpam-5156	368	8	of	of	ADP
ejpam-5156	368	9	p2	p2	NOUN
ejpam-5156	368	10	,	,	PUNCT
ejpam-5156	368	11	hence	hence	ADV
ejpam-5156	368	12	,	,	PUNCT
ejpam-5156	368	13	theorem	theorem	VERB
ejpam-5156	368	14	8	8	NUM
ejpam-5156	368	15	(	(	PUNCT
ejpam-5156	368	16	iii	iii	NOUN
ejpam-5156	368	17	)	)	PUNCT
ejpam-5156	368	18	is	be	AUX
ejpam-5156	368	19	satisfied	satisfied	ADJ
ejpam-5156	368	20	.	.	PUNCT
ejpam-5156	369	1	this	this	PRON
ejpam-5156	369	2	means	mean	VERB
ejpam-5156	369	3	that	that	SCONJ
ejpam-5156	369	4	,	,	PUNCT
ejpam-5156	369	5	by	by	ADP
ejpam-5156	369	6	theorem	theorem	NOUN
ejpam-5156	369	7	8	8	NUM
ejpam-5156	369	8	,	,	PUNCT
ejpam-5156	369	9	s	s	VERB
ejpam-5156	369	10	is	be	AUX
ejpam-5156	369	11	an	an	DET
ejpam-5156	369	12	rgda	rgda	NOUN
ejpam-5156	369	13	in	in	ADP
ejpam-5156	369	14	pn	pn	PROPN
ejpam-5156	369	15	.	.	PUNCT
ejpam-5156	370	1	now	now	ADV
ejpam-5156	370	2	,	,	PUNCT
ejpam-5156	370	3	suppose	suppose	VERB
ejpam-5156	370	4	that	that	SCONJ
ejpam-5156	370	5	w	w	PROPN
ejpam-5156	370	6	⊂	⊂	PROPN
ejpam-5156	370	7	s.	s.	PROPN
ejpam-5156	370	8	then	then	ADV
ejpam-5156	370	9	there	there	PRON
ejpam-5156	370	10	exists	exist	VERB
ejpam-5156	370	11	a	a	DET
ejpam-5156	370	12	vertex	vertex	NOUN
ejpam-5156	370	13	in	in	ADP
ejpam-5156	370	14	s	s	PRON
ejpam-5156	370	15	that	that	PRON
ejpam-5156	370	16	is	be	AUX
ejpam-5156	370	17	not	not	PART
ejpam-5156	370	18	in	in	ADP
ejpam-5156	370	19	w	w	PROPN
ejpam-5156	370	20	.	.	PUNCT
ejpam-5156	371	1	this	this	PRON
ejpam-5156	371	2	leads	lead	VERB
ejpam-5156	371	3	to	to	ADP
ejpam-5156	371	4	the	the	DET
ejpam-5156	371	5	following	following	ADJ
ejpam-5156	371	6	cases	case	NOUN
ejpam-5156	371	7	:	:	PUNCT
ejpam-5156	371	8	case	case	NOUN
ejpam-5156	371	9	1	1	NUM
ejpam-5156	371	10	:	:	PUNCT
ejpam-5156	371	11	atleast	atleast	ADJ
ejpam-5156	371	12	one	one	NUM
ejpam-5156	371	13	vertex	vertex	NOUN
ejpam-5156	371	14	in	in	ADP
ejpam-5156	371	15	{	{	PUNCT
ejpam-5156	371	16	v0	v0	NOUN
ejpam-5156	371	17	,	,	PUNCT
ejpam-5156	371	18	vn−1	vn−1	ADJ
ejpam-5156	371	19	}	}	PUNCT
ejpam-5156	371	20	is	be	AUX
ejpam-5156	371	21	not	not	PART
ejpam-5156	371	22	in	in	ADP
ejpam-5156	371	23	w	w	PROPN
ejpam-5156	371	24	.	.	PUNCT
ejpam-5156	372	1	then	then	ADV
ejpam-5156	372	2	theorem	theorem	VERB
ejpam-5156	372	3	8	8	NUM
ejpam-5156	372	4	(	(	PUNCT
ejpam-5156	372	5	i	i	NOUN
ejpam-5156	372	6	)	)	PUNCT
ejpam-5156	372	7	is	be	AUX
ejpam-5156	372	8	not	not	PART
ejpam-5156	372	9	satisfied	satisfied	ADJ
ejpam-5156	372	10	,	,	PUNCT
ejpam-5156	372	11	so	so	ADV
ejpam-5156	372	12	w	w	NOUN
ejpam-5156	372	13	is	be	AUX
ejpam-5156	372	14	not	not	PART
ejpam-5156	372	15	an	an	DET
ejpam-5156	372	16	rgda	rgda	NOUN
ejpam-5156	372	17	in	in	ADP
ejpam-5156	372	18	pn	pn	PROPN
ejpam-5156	372	19	.	.	PROPN
ejpam-5156	372	20	case	case	NOUN
ejpam-5156	372	21	2	2	NUM
ejpam-5156	372	22	:	:	PUNCT
ejpam-5156	372	23	atleast	atleast	ADJ
ejpam-5156	372	24	one	one	NUM
ejpam-5156	372	25	vertex	vertex	NOUN
ejpam-5156	372	26	in	in	ADP
ejpam-5156	372	27	{	{	PUNCT
ejpam-5156	372	28	v3	v3	PROPN
ejpam-5156	372	29	,	,	PUNCT
ejpam-5156	372	30	v4	v4	NOUN
ejpam-5156	372	31	,	,	PUNCT
ejpam-5156	372	32	v7	v7	NUM
ejpam-5156	372	33	,	,	PUNCT
ejpam-5156	372	34	v8	v8	PROPN
ejpam-5156	372	35	,	,	PUNCT
ejpam-5156	372	36	.	.	PUNCT
ejpam-5156	372	37	.	.	PUNCT
ejpam-5156	373	1	.	.	PUNCT
ejpam-5156	374	1	,	,	PUNCT
ejpam-5156	374	2	vn−4	vn−4	NOUN
ejpam-5156	374	3	,	,	PUNCT
ejpam-5156	374	4	vn−3	vn−3	PROPN
ejpam-5156	374	5	}	}	PUNCT
ejpam-5156	374	6	∪	∪	NOUN
ejpam-5156	374	7	{	{	PUNCT
ejpam-5156	374	8	vn−2	vn−2	NOUN
ejpam-5156	374	9	}	}	PUNCT
ejpam-5156	374	10	is	be	AUX
ejpam-5156	374	11	not	not	PART
ejpam-5156	374	12	in	in	ADP
ejpam-5156	374	13	w	w	PROPN
ejpam-5156	374	14	.	.	PUNCT
ejpam-5156	375	1	then	then	ADV
ejpam-5156	375	2	there	there	PRON
ejpam-5156	375	3	exists	exist	VERB
ejpam-5156	375	4	a	a	DET
ejpam-5156	375	5	class	class	NOUN
ejpam-5156	375	6	in	in	ADP
ejpam-5156	375	7	⟨v	⟨v	NOUN
ejpam-5156	375	8	∖	∖	PROPN
ejpam-5156	375	9	s⟩	s⟩	VERB
ejpam-5156	375	10	that	that	PRON
ejpam-5156	375	11	is	be	AUX
ejpam-5156	375	12	not	not	PART
ejpam-5156	375	13	p2	p2	ADJ
ejpam-5156	375	14	,	,	PUNCT
ejpam-5156	375	15	so	so	ADV
ejpam-5156	375	16	theorem	theorem	ADJ
ejpam-5156	375	17	8	8	NUM
ejpam-5156	375	18	(	(	PUNCT
ejpam-5156	375	19	iii	iii	NOUN
ejpam-5156	375	20	)	)	PUNCT
ejpam-5156	375	21	is	be	AUX
ejpam-5156	375	22	not	not	PART
ejpam-5156	375	23	satisfied	satisfied	ADJ
ejpam-5156	375	24	.	.	PUNCT
ejpam-5156	376	1	hence	hence	ADV
ejpam-5156	376	2	,	,	PUNCT
ejpam-5156	376	3	w	w	NOUN
ejpam-5156	376	4	is	be	AUX
ejpam-5156	376	5	not	not	PART
ejpam-5156	376	6	an	an	DET
ejpam-5156	376	7	rgda	rgda	NOUN
ejpam-5156	376	8	in	in	ADP
ejpam-5156	376	9	pn	pn	PROPN
ejpam-5156	376	10	.	.	PUNCT
ejpam-5156	376	11	therefore	therefore	ADV
ejpam-5156	376	12	,	,	PUNCT
ejpam-5156	376	13	s	s	VERB
ejpam-5156	376	14	is	be	AUX
ejpam-5156	376	15	a	a	DET
ejpam-5156	376	16	minimum	minimum	ADJ
ejpam-5156	376	17	rgda	rgda	NOUN
ejpam-5156	376	18	in	in	ADP
ejpam-5156	376	19	pn	pn	PROPN
ejpam-5156	376	20	.	.	PROPN
ejpam-5156	376	21	corollary	corollary	ADJ
ejpam-5156	376	22	4	4	NUM
ejpam-5156	376	23	.	.	PUNCT
ejpam-5156	377	1	if	if	SCONJ
ejpam-5156	377	2	pn	pn	PROPN
ejpam-5156	377	3	=	=	SYM
ejpam-5156	377	4	(	(	PUNCT
ejpam-5156	377	5	v	v	NOUN
ejpam-5156	377	6	,	,	PUNCT
ejpam-5156	377	7	e	e	NOUN
ejpam-5156	377	8	)	)	PUNCT
ejpam-5156	377	9	is	be	AUX
ejpam-5156	377	10	a	a	DET
ejpam-5156	377	11	path	path	NOUN
ejpam-5156	377	12	graph	graph	NOUN
ejpam-5156	377	13	of	of	ADP
ejpam-5156	377	14	order	order	NOUN
ejpam-5156	377	15	n	n	PRON
ejpam-5156	377	16	≥	≥	NOUN
ejpam-5156	377	17	1	1	NUM
ejpam-5156	377	18	,	,	PUNCT
ejpam-5156	377	19	then	then	ADV
ejpam-5156	377	20	γra(pn	γra(pn	NUM
ejpam-5156	377	21	)	)	PUNCT
ejpam-5156	377	22	=	=	PUNCT
ejpam-5156	378	1			NOUN
ejpam-5156	378	2	n	n	PRON
ejpam-5156	378	3	2	2	NUM
ejpam-5156	378	4	n	n	CCONJ
ejpam-5156	378	5	≡	≡	PROPN
ejpam-5156	378	6	0	0	PUNCT
ejpam-5156	379	1	(	(	PUNCT
ejpam-5156	379	2	mod	mod	NOUN
ejpam-5156	379	3	4	4	NUM
ejpam-5156	379	4	)	)	SYM
ejpam-5156	379	5	n+1	n+1	NUM
ejpam-5156	379	6	2	2	NUM
ejpam-5156	379	7	n	n	CCONJ
ejpam-5156	379	8	≡	≡	PROPN
ejpam-5156	379	9	1	1	NUM
ejpam-5156	379	10	(	(	PUNCT
ejpam-5156	379	11	mod	mod	NOUN
ejpam-5156	379	12	4	4	NUM
ejpam-5156	379	13	)	)	PUNCT
ejpam-5156	379	14	n+2	n+2	ADV
ejpam-5156	379	15	2	2	NUM
ejpam-5156	379	16	n	n	CCONJ
ejpam-5156	379	17	≡	≡	PROPN
ejpam-5156	379	18	2	2	NUM
ejpam-5156	379	19	(	(	PUNCT
ejpam-5156	379	20	mod	mod	NOUN
ejpam-5156	379	21	4	4	NUM
ejpam-5156	379	22	)	)	PUNCT
ejpam-5156	379	23	n+3	n+3	PROPN
ejpam-5156	379	24	2	2	NUM
ejpam-5156	379	25	n	n	CCONJ
ejpam-5156	379	26	≡	≡	PROPN
ejpam-5156	379	27	3	3	NUM
ejpam-5156	379	28	(	(	PUNCT
ejpam-5156	379	29	mod	mod	NOUN
ejpam-5156	379	30	4	4	NUM
ejpam-5156	379	31	)	)	PUNCT
ejpam-5156	379	32	(	(	PUNCT
ejpam-5156	379	33	2	2	NUM
ejpam-5156	379	34	)	)	PUNCT
ejpam-5156	379	35	.	.	PUNCT
ejpam-5156	380	1	l.	l.	PROPN
ejpam-5156	380	2	consistente	consistente	PROPN
ejpam-5156	380	3	,	,	PUNCT
ejpam-5156	380	4	i.	i.	PROPN
ejpam-5156	380	5	cabahug	cabahug	PROPN
ejpam-5156	380	6	,	,	PUNCT
ejpam-5156	380	7	jr	jr	PROPN
ejpam-5156	380	8	.	.	PROPN
ejpam-5156	380	9	/	/	SYM
ejpam-5156	380	10	eur	eur	PROPN
ejpam-5156	380	11	.	.	PUNCT
ejpam-5156	381	1	j.	j.	PROPN
ejpam-5156	381	2	pure	pure	PROPN
ejpam-5156	381	3	appl	appl	PROPN
ejpam-5156	381	4	.	.	PROPN
ejpam-5156	381	5	math	math	PROPN
ejpam-5156	381	6	,	,	PUNCT
ejpam-5156	381	7	17	17	NUM
ejpam-5156	381	8	(	(	PUNCT
ejpam-5156	381	9	3	3	NUM
ejpam-5156	381	10	)	)	PUNCT
ejpam-5156	381	11	(	(	PUNCT
ejpam-5156	381	12	2024	2024	NUM
ejpam-5156	381	13	)	)	PUNCT
ejpam-5156	381	14	,	,	PUNCT
ejpam-5156	381	15	2196	2196	NUM
ejpam-5156	381	16	-	-	SYM
ejpam-5156	381	17	2209	2209	NUM
ejpam-5156	381	18	2207	2207	NUM
ejpam-5156	381	19	proof	proof	NOUN
ejpam-5156	381	20	.	.	PUNCT
ejpam-5156	382	1	let	let	VERB
ejpam-5156	382	2	pn	pn	VERB
ejpam-5156	382	3	=	=	SYM
ejpam-5156	382	4	(	(	PUNCT
ejpam-5156	382	5	v	v	NOUN
ejpam-5156	382	6	,	,	PUNCT
ejpam-5156	382	7	e	e	NOUN
ejpam-5156	382	8	)	)	PUNCT
ejpam-5156	382	9	be	be	AUX
ejpam-5156	382	10	a	a	DET
ejpam-5156	382	11	path	path	NOUN
ejpam-5156	382	12	graph	graph	NOUN
ejpam-5156	382	13	of	of	ADP
ejpam-5156	382	14	order	order	NOUN
ejpam-5156	382	15	n	n	PRON
ejpam-5156	382	16	≥	≥	NOUN
ejpam-5156	382	17	2	2	X
ejpam-5156	382	18	.	.	X
ejpam-5156	382	19	observe	observe	VERB
ejpam-5156	382	20	the	the	DET
ejpam-5156	382	21	following	follow	VERB
ejpam-5156	382	22	cases	case	NOUN
ejpam-5156	382	23	:	:	PUNCT
ejpam-5156	382	24	case	case	NOUN
ejpam-5156	382	25	1	1	NUM
ejpam-5156	382	26	:	:	PUNCT
ejpam-5156	383	1	n	n	NUM
ejpam-5156	383	2	≡	≡	PROPN
ejpam-5156	383	3	0	0	PUNCT
ejpam-5156	384	1	(	(	PUNCT
ejpam-5156	384	2	mod	mod	PROPN
ejpam-5156	384	3	4	4	NUM
ejpam-5156	384	4	)	)	PUNCT
ejpam-5156	384	5	.	.	PUNCT
ejpam-5156	385	1	let	let	VERB
ejpam-5156	385	2	s	s	PRON
ejpam-5156	385	3	=	=	PUNCT
ejpam-5156	385	4	{	{	PUNCT
ejpam-5156	385	5	v0	v0	NOUN
ejpam-5156	385	6	,	,	PUNCT
ejpam-5156	385	7	vn−1	vn−1	ADJ
ejpam-5156	385	8	}	}	PUNCT
ejpam-5156	385	9	∪	∪	NOUN
ejpam-5156	385	10	{	{	PUNCT
ejpam-5156	385	11	v3	v3	PROPN
ejpam-5156	385	12	,	,	PUNCT
ejpam-5156	385	13	v4	v4	NOUN
ejpam-5156	385	14	,	,	PUNCT
ejpam-5156	385	15	v7	v7	NUM
ejpam-5156	385	16	,	,	PUNCT
ejpam-5156	385	17	v8	v8	PROPN
ejpam-5156	385	18	,	,	PUNCT
ejpam-5156	385	19	.	.	PUNCT
ejpam-5156	385	20	.	.	PUNCT
ejpam-5156	386	1	.	.	PUNCT
ejpam-5156	387	1	,	,	PUNCT
ejpam-5156	387	2	vn−5	vn−5	NOUN
ejpam-5156	387	3	,	,	PUNCT
ejpam-5156	387	4	vn−4	vn−4	NOUN
ejpam-5156	387	5	}	}	PUNCT
ejpam-5156	387	6	.	.	PUNCT
ejpam-5156	388	1	by	by	ADP
ejpam-5156	388	2	lemma	lemma	PROPN
ejpam-5156	388	3	1	1	NUM
ejpam-5156	388	4	,	,	PUNCT
ejpam-5156	388	5	s	s	VERB
ejpam-5156	388	6	is	be	AUX
ejpam-5156	388	7	a	a	DET
ejpam-5156	388	8	minimum	minimum	ADJ
ejpam-5156	388	9	rgda	rgda	NOUN
ejpam-5156	388	10	in	in	ADP
ejpam-5156	388	11	pn	pn	PROPN
ejpam-5156	388	12	.	.	PUNCT
ejpam-5156	388	13	therefore	therefore	ADV
ejpam-5156	388	14	,	,	PUNCT
ejpam-5156	388	15	γra(pn	γra(pn	NUM
ejpam-5156	388	16	)	)	PUNCT
ejpam-5156	388	17	=	=	SYM
ejpam-5156	388	18	|s|	|s|	PROPN
ejpam-5156	388	19	=	=	PUNCT
ejpam-5156	388	20	|{v0	|{v0	NOUN
ejpam-5156	388	21	,	,	PUNCT
ejpam-5156	388	22	vn−1	vn−1	ADJ
ejpam-5156	388	23	}	}	PUNCT
ejpam-5156	388	24	∪	∪	NOUN
ejpam-5156	388	25	{	{	PUNCT
ejpam-5156	388	26	v3	v3	PROPN
ejpam-5156	388	27	,	,	PUNCT
ejpam-5156	388	28	v4	v4	NOUN
ejpam-5156	388	29	,	,	PUNCT
ejpam-5156	388	30	v7	v7	NUM
ejpam-5156	388	31	,	,	PUNCT
ejpam-5156	388	32	v8	v8	PROPN
ejpam-5156	388	33	,	,	PUNCT
ejpam-5156	388	34	.	.	PUNCT
ejpam-5156	388	35	.	.	PUNCT
ejpam-5156	389	1	.	.	PUNCT
ejpam-5156	390	1	,	,	PUNCT
ejpam-5156	390	2	vn−5	vn−5	NOUN
ejpam-5156	390	3	,	,	PUNCT
ejpam-5156	390	4	vn−4}|	vn−4}|	NOUN
ejpam-5156	390	5	=	=	SYM
ejpam-5156	390	6	2	2	NUM
ejpam-5156	390	7	+	+	NUM
ejpam-5156	390	8	n−	n−	NOUN
ejpam-5156	390	9	4	4	NUM
ejpam-5156	390	10	2	2	NUM
ejpam-5156	390	11	=	=	SYM
ejpam-5156	390	12	n−	n−	NOUN
ejpam-5156	390	13	4	4	NUM
ejpam-5156	390	14	+	+	CCONJ
ejpam-5156	390	15	4	4	NUM
ejpam-5156	390	16	2	2	NUM
ejpam-5156	390	17	=	=	SYM
ejpam-5156	390	18	n	n	PRON
ejpam-5156	390	19	2	2	NUM
ejpam-5156	390	20	.	.	PUNCT
ejpam-5156	391	1	case	case	NOUN
ejpam-5156	391	2	2	2	NUM
ejpam-5156	391	3	:	:	PUNCT
ejpam-5156	391	4	n	n	CCONJ
ejpam-5156	391	5	≡	≡	PROPN
ejpam-5156	391	6	1	1	NUM
ejpam-5156	391	7	(	(	PUNCT
ejpam-5156	391	8	mod	mod	NOUN
ejpam-5156	391	9	4	4	NUM
ejpam-5156	391	10	)	)	PUNCT
ejpam-5156	391	11	.	.	PUNCT
ejpam-5156	392	1	let	let	VERB
ejpam-5156	392	2	s	s	PRON
ejpam-5156	392	3	=	=	PUNCT
ejpam-5156	392	4	{	{	PUNCT
ejpam-5156	392	5	v0	v0	NOUN
ejpam-5156	392	6	,	,	PUNCT
ejpam-5156	392	7	vn−1	vn−1	ADJ
ejpam-5156	392	8	}	}	PUNCT
ejpam-5156	392	9	∪	∪	NOUN
ejpam-5156	392	10	{	{	PUNCT
ejpam-5156	392	11	v3	v3	PROPN
ejpam-5156	392	12	,	,	PUNCT
ejpam-5156	392	13	v4	v4	NOUN
ejpam-5156	392	14	,	,	PUNCT
ejpam-5156	392	15	v7	v7	NUM
ejpam-5156	392	16	,	,	PUNCT
ejpam-5156	392	17	v8	v8	PROPN
ejpam-5156	392	18	,	,	PUNCT
ejpam-5156	392	19	.	.	PUNCT
ejpam-5156	392	20	.	.	PUNCT
ejpam-5156	393	1	.	.	PUNCT
ejpam-5156	394	1	,	,	PUNCT
ejpam-5156	394	2	vn−6	vn−6	PROPN
ejpam-5156	394	3	,	,	PUNCT
ejpam-5156	394	4	vn−5	vn−5	PROPN
ejpam-5156	394	5	}	}	PUNCT
ejpam-5156	394	6	∪	∪	NOUN
ejpam-5156	394	7	{	{	PUNCT
ejpam-5156	394	8	vn−2	vn−2	NOUN
ejpam-5156	394	9	}	}	PUNCT
ejpam-5156	394	10	.	.	PUNCT
ejpam-5156	395	1	by	by	ADP
ejpam-5156	395	2	lemma	lemma	PROPN
ejpam-5156	395	3	2	2	NUM
ejpam-5156	395	4	,	,	PUNCT
ejpam-5156	395	5	s	s	VERB
ejpam-5156	395	6	is	be	AUX
ejpam-5156	395	7	a	a	DET
ejpam-5156	395	8	minimum	minimum	ADJ
ejpam-5156	395	9	rgda	rgda	NOUN
ejpam-5156	395	10	in	in	ADP
ejpam-5156	395	11	pn	pn	PROPN
ejpam-5156	395	12	.	.	PUNCT
ejpam-5156	395	13	therefore	therefore	ADV
ejpam-5156	395	14	,	,	PUNCT
ejpam-5156	395	15	γra(pn	γra(pn	NUM
ejpam-5156	395	16	)	)	PUNCT
ejpam-5156	395	17	=	=	SYM
ejpam-5156	395	18	|s|	|s|	PROPN
ejpam-5156	395	19	=	=	PUNCT
ejpam-5156	395	20	|{v0	|{v0	NOUN
ejpam-5156	395	21	,	,	PUNCT
ejpam-5156	395	22	vn−1	vn−1	ADJ
ejpam-5156	395	23	}	}	PUNCT
ejpam-5156	395	24	∪	∪	NOUN
ejpam-5156	395	25	{	{	PUNCT
ejpam-5156	395	26	v3	v3	PROPN
ejpam-5156	395	27	,	,	PUNCT
ejpam-5156	395	28	v4	v4	NOUN
ejpam-5156	395	29	,	,	PUNCT
ejpam-5156	395	30	v7	v7	NUM
ejpam-5156	395	31	,	,	PUNCT
ejpam-5156	395	32	v8	v8	PROPN
ejpam-5156	395	33	,	,	PUNCT
ejpam-5156	395	34	.	.	PUNCT
ejpam-5156	395	35	.	.	PUNCT
ejpam-5156	396	1	.	.	PUNCT
ejpam-5156	397	1	,	,	PUNCT
ejpam-5156	397	2	vn−6	vn−6	PROPN
ejpam-5156	397	3	,	,	PUNCT
ejpam-5156	397	4	vn−5	vn−5	PROPN
ejpam-5156	397	5	}	}	PUNCT
ejpam-5156	397	6	∪	∪	X
ejpam-5156	397	7	{	{	PUNCT
ejpam-5156	397	8	vn−2}|	vn−2}|	PROPN
ejpam-5156	397	9	=	=	SYM
ejpam-5156	397	10	2	2	NUM
ejpam-5156	397	11	+	+	NUM
ejpam-5156	397	12	n−	n−	NOUN
ejpam-5156	397	13	5	5	NUM
ejpam-5156	397	14	2	2	NUM
ejpam-5156	397	15	+	+	CCONJ
ejpam-5156	397	16	1	1	NUM
ejpam-5156	397	17	=	=	SYM
ejpam-5156	397	18	4	4	NUM
ejpam-5156	397	19	+	+	NUM
ejpam-5156	397	20	n−	n−	NOUN
ejpam-5156	397	21	5	5	NUM
ejpam-5156	397	22	+	+	CCONJ
ejpam-5156	397	23	2	2	NUM
ejpam-5156	397	24	2	2	NUM
ejpam-5156	397	25	=	=	SYM
ejpam-5156	397	26	n+	n+	NUM
ejpam-5156	397	27	1	1	NUM
ejpam-5156	397	28	2	2	NUM
ejpam-5156	397	29	.	.	PUNCT
ejpam-5156	398	1	case	case	NOUN
ejpam-5156	398	2	3	3	NUM
ejpam-5156	398	3	:	:	PUNCT
ejpam-5156	398	4	n	n	NUM
ejpam-5156	398	5	≡	≡	PROPN
ejpam-5156	398	6	2	2	NUM
ejpam-5156	398	7	(	(	PUNCT
ejpam-5156	398	8	mod	mod	NOUN
ejpam-5156	398	9	4	4	NUM
ejpam-5156	398	10	)	)	PUNCT
ejpam-5156	398	11	.	.	PUNCT
ejpam-5156	399	1	let	let	VERB
ejpam-5156	399	2	s	s	PRON
ejpam-5156	399	3	=	=	PUNCT
ejpam-5156	399	4	{	{	PUNCT
ejpam-5156	399	5	v0	v0	NOUN
ejpam-5156	399	6	,	,	PUNCT
ejpam-5156	399	7	vn−1	vn−1	ADJ
ejpam-5156	399	8	}	}	PUNCT
ejpam-5156	399	9	∪	∪	NOUN
ejpam-5156	399	10	{	{	PUNCT
ejpam-5156	399	11	v3	v3	PROPN
ejpam-5156	399	12	,	,	PUNCT
ejpam-5156	399	13	v4	v4	NOUN
ejpam-5156	399	14	,	,	PUNCT
ejpam-5156	399	15	v7	v7	NUM
ejpam-5156	399	16	,	,	PUNCT
ejpam-5156	399	17	v8	v8	PROPN
ejpam-5156	399	18	,	,	PUNCT
ejpam-5156	399	19	.	.	PUNCT
ejpam-5156	399	20	.	.	PUNCT
ejpam-5156	400	1	.	.	PUNCT
ejpam-5156	401	1	,	,	PUNCT
ejpam-5156	401	2	vn−3	vn−3	PROPN
ejpam-5156	401	3	,	,	PUNCT
ejpam-5156	401	4	vn−2	vn−2	PROPN
ejpam-5156	401	5	}	}	PUNCT
ejpam-5156	401	6	.	.	PUNCT
ejpam-5156	402	1	by	by	ADP
ejpam-5156	402	2	lemma	lemma	PROPN
ejpam-5156	402	3	3	3	NUM
ejpam-5156	402	4	,	,	PUNCT
ejpam-5156	402	5	s	s	VERB
ejpam-5156	402	6	is	be	AUX
ejpam-5156	402	7	a	a	DET
ejpam-5156	402	8	minimum	minimum	ADJ
ejpam-5156	402	9	rgda	rgda	NOUN
ejpam-5156	402	10	in	in	ADP
ejpam-5156	402	11	pn	pn	PROPN
ejpam-5156	402	12	.	.	PUNCT
ejpam-5156	402	13	therefore	therefore	ADV
ejpam-5156	402	14	,	,	PUNCT
ejpam-5156	402	15	γra(pn	γra(pn	NUM
ejpam-5156	402	16	)	)	PUNCT
ejpam-5156	402	17	=	=	SYM
ejpam-5156	402	18	|s|	|s|	PROPN
ejpam-5156	402	19	=	=	PUNCT
ejpam-5156	402	20	|{v0	|{v0	NOUN
ejpam-5156	402	21	,	,	PUNCT
ejpam-5156	402	22	vn−1	vn−1	ADJ
ejpam-5156	402	23	}	}	PUNCT
ejpam-5156	402	24	∪	∪	NOUN
ejpam-5156	402	25	{	{	PUNCT
ejpam-5156	402	26	v3	v3	PROPN
ejpam-5156	402	27	,	,	PUNCT
ejpam-5156	402	28	v4	v4	NOUN
ejpam-5156	402	29	,	,	PUNCT
ejpam-5156	402	30	v7	v7	NUM
ejpam-5156	402	31	,	,	PUNCT
ejpam-5156	402	32	v8	v8	PROPN
ejpam-5156	402	33	,	,	PUNCT
ejpam-5156	402	34	.	.	PUNCT
ejpam-5156	402	35	.	.	PUNCT
ejpam-5156	403	1	.	.	PUNCT
ejpam-5156	404	1	,	,	PUNCT
ejpam-5156	404	2	vn−3	vn−3	PROPN
ejpam-5156	404	3	,	,	PUNCT
ejpam-5156	404	4	vn−2}|	vn−2}|	PROPN
ejpam-5156	404	5	=	=	SYM
ejpam-5156	404	6	2	2	NUM
ejpam-5156	404	7	+	+	NUM
ejpam-5156	404	8	n−	n−	NOUN
ejpam-5156	404	9	2	2	NUM
ejpam-5156	404	10	2	2	NUM
ejpam-5156	404	11	=	=	SYM
ejpam-5156	404	12	4	4	NUM
ejpam-5156	404	13	+	+	NUM
ejpam-5156	404	14	n−	n−	NOUN
ejpam-5156	404	15	2	2	NUM
ejpam-5156	404	16	2	2	NUM
ejpam-5156	404	17	=	=	SYM
ejpam-5156	404	18	n+	n+	X
ejpam-5156	404	19	2	2	NUM
ejpam-5156	404	20	2	2	NUM
ejpam-5156	404	21	.	.	PUNCT
ejpam-5156	405	1	case	case	NOUN
ejpam-5156	405	2	4	4	NUM
ejpam-5156	405	3	:	:	PUNCT
ejpam-5156	405	4	n	n	NUM
ejpam-5156	405	5	≡	≡	PROPN
ejpam-5156	405	6	3	3	NUM
ejpam-5156	405	7	(	(	PUNCT
ejpam-5156	405	8	mod	mod	NOUN
ejpam-5156	405	9	4	4	NUM
ejpam-5156	405	10	)	)	PUNCT
ejpam-5156	405	11	.	.	PUNCT
ejpam-5156	406	1	let	let	VERB
ejpam-5156	406	2	s	s	PRON
ejpam-5156	406	3	=	=	PUNCT
ejpam-5156	406	4	{	{	PUNCT
ejpam-5156	406	5	v0	v0	NOUN
ejpam-5156	406	6	,	,	PUNCT
ejpam-5156	406	7	vn−1	vn−1	ADJ
ejpam-5156	406	8	}	}	PUNCT
ejpam-5156	406	9	∪	∪	NOUN
ejpam-5156	406	10	{	{	PUNCT
ejpam-5156	406	11	v3	v3	PROPN
ejpam-5156	406	12	,	,	PUNCT
ejpam-5156	406	13	v4	v4	NOUN
ejpam-5156	406	14	,	,	PUNCT
ejpam-5156	406	15	v7	v7	NUM
ejpam-5156	406	16	,	,	PUNCT
ejpam-5156	406	17	v8	v8	PROPN
ejpam-5156	406	18	,	,	PUNCT
ejpam-5156	406	19	.	.	PUNCT
ejpam-5156	406	20	.	.	PUNCT
ejpam-5156	407	1	.	.	PUNCT
ejpam-5156	408	1	,	,	PUNCT
ejpam-5156	408	2	vn−4	vn−4	NOUN
ejpam-5156	408	3	,	,	PUNCT
ejpam-5156	408	4	vn−3	vn−3	PROPN
ejpam-5156	408	5	}	}	PUNCT
ejpam-5156	408	6	∪	∪	ADJ
ejpam-5156	408	7	{	{	PUNCT
ejpam-5156	408	8	vn−2	vn−2	NOUN
ejpam-5156	408	9	}	}	PUNCT
ejpam-5156	408	10	.	.	PUNCT
ejpam-5156	409	1	references	reference	NOUN
ejpam-5156	409	2	2208	2208	NUM
ejpam-5156	409	3	by	by	ADP
ejpam-5156	409	4	lemma	lemma	PROPN
ejpam-5156	409	5	4	4	NUM
ejpam-5156	409	6	,	,	PUNCT
ejpam-5156	409	7	s	s	VERB
ejpam-5156	409	8	is	be	AUX
ejpam-5156	409	9	a	a	DET
ejpam-5156	409	10	minimum	minimum	ADJ
ejpam-5156	409	11	rgda	rgda	NOUN
ejpam-5156	409	12	in	in	ADP
ejpam-5156	409	13	pn	pn	PROPN
ejpam-5156	409	14	.	.	PUNCT
ejpam-5156	409	15	therefore	therefore	ADV
ejpam-5156	409	16	,	,	PUNCT
ejpam-5156	409	17	γra(pn	γra(pn	NUM
ejpam-5156	409	18	)	)	PUNCT
ejpam-5156	409	19	=	=	SYM
ejpam-5156	409	20	|s|	|s|	PROPN
ejpam-5156	409	21	=	=	PUNCT
ejpam-5156	409	22	|{v0	|{v0	NOUN
ejpam-5156	409	23	,	,	PUNCT
ejpam-5156	409	24	vn−1	vn−1	ADJ
ejpam-5156	409	25	}	}	PUNCT
ejpam-5156	409	26	∪	∪	NOUN
ejpam-5156	409	27	{	{	PUNCT
ejpam-5156	409	28	v3	v3	PROPN
ejpam-5156	409	29	,	,	PUNCT
ejpam-5156	409	30	v4	v4	NOUN
ejpam-5156	409	31	,	,	PUNCT
ejpam-5156	409	32	v7	v7	NUM
ejpam-5156	409	33	,	,	PUNCT
ejpam-5156	409	34	v8	v8	PROPN
ejpam-5156	409	35	,	,	PUNCT
ejpam-5156	409	36	.	.	PUNCT
ejpam-5156	409	37	.	.	PUNCT
ejpam-5156	410	1	.	.	PUNCT
ejpam-5156	411	1	,	,	PUNCT
ejpam-5156	411	2	vn−4	vn−4	NOUN
ejpam-5156	411	3	,	,	PUNCT
ejpam-5156	411	4	vn−3	vn−3	PROPN
ejpam-5156	411	5	}	}	PUNCT
ejpam-5156	411	6	∪	∪	X
ejpam-5156	411	7	{	{	PUNCT
ejpam-5156	411	8	vn−2}|	vn−2}|	PROPN
ejpam-5156	411	9	=	=	SYM
ejpam-5156	411	10	2	2	NUM
ejpam-5156	411	11	+	+	NUM
ejpam-5156	411	12	n−	n−	NOUN
ejpam-5156	411	13	3	3	NUM
ejpam-5156	411	14	2	2	NUM
ejpam-5156	411	15	+	+	CCONJ
ejpam-5156	411	16	1	1	NUM
ejpam-5156	411	17	=	=	SYM
ejpam-5156	411	18	4	4	NUM
ejpam-5156	411	19	+	+	NUM
ejpam-5156	411	20	n−	n−	NOUN
ejpam-5156	411	21	3	3	NUM
ejpam-5156	411	22	+	+	CCONJ
ejpam-5156	411	23	2	2	NUM
ejpam-5156	411	24	2	2	NUM
ejpam-5156	411	25	=	=	SYM
ejpam-5156	411	26	n+	n+	X
ejpam-5156	411	27	3	3	NUM
ejpam-5156	411	28	2	2	NUM
ejpam-5156	411	29	.	.	PUNCT
ejpam-5156	412	1	this	this	PRON
ejpam-5156	412	2	completes	complete	VERB
ejpam-5156	412	3	the	the	DET
ejpam-5156	412	4	proof	proof	NOUN
ejpam-5156	412	5	.	.	PUNCT
ejpam-5156	413	1	remark	remark	NOUN
ejpam-5156	413	2	1	1	NUM
ejpam-5156	413	3	.	.	PUNCT
ejpam-5156	414	1	if	if	SCONJ
ejpam-5156	414	2	p1	p1	PROPN
ejpam-5156	414	3	is	be	AUX
ejpam-5156	414	4	a	a	DET
ejpam-5156	414	5	path	path	NOUN
ejpam-5156	414	6	graph	graph	NOUN
ejpam-5156	414	7	of	of	ADP
ejpam-5156	414	8	order	order	NOUN
ejpam-5156	414	9	1	1	NUM
ejpam-5156	414	10	,	,	PUNCT
ejpam-5156	414	11	then	then	ADV
ejpam-5156	414	12	γra(p1	γra(p1	PROPN
ejpam-5156	414	13	)	)	PUNCT
ejpam-5156	415	1	=	=	SYM
ejpam-5156	415	2	1	1	X
ejpam-5156	415	3	.	.	PUNCT
ejpam-5156	415	4	acknowledgements	acknowledgement	NOUN
ejpam-5156	415	5	the	the	DET
ejpam-5156	415	6	authors	author	NOUN
ejpam-5156	415	7	extend	extend	VERB
ejpam-5156	415	8	their	their	PRON
ejpam-5156	415	9	sincere	sincere	ADJ
ejpam-5156	415	10	thanks	thank	NOUN
ejpam-5156	415	11	to	to	ADP
ejpam-5156	415	12	those	those	PRON
ejpam-5156	415	13	who	who	PRON
ejpam-5156	415	14	have	have	AUX
ejpam-5156	415	15	played	play	VERB
ejpam-5156	415	16	a	a	DET
ejpam-5156	415	17	crucial	crucial	ADJ
ejpam-5156	415	18	role	role	NOUN
ejpam-5156	415	19	in	in	ADP
ejpam-5156	415	20	the	the	DET
ejpam-5156	415	21	completion	completion	NOUN
ejpam-5156	415	22	of	of	ADP
ejpam-5156	415	23	this	this	DET
ejpam-5156	415	24	study	study	NOUN
ejpam-5156	415	25	.	.	PUNCT
ejpam-5156	416	1	a	a	DET
ejpam-5156	416	2	special	special	ADJ
ejpam-5156	416	3	note	note	NOUN
ejpam-5156	416	4	of	of	ADP
ejpam-5156	416	5	appreciation	appreciation	NOUN
ejpam-5156	416	6	is	be	AUX
ejpam-5156	416	7	directed	direct	VERB
ejpam-5156	416	8	to	to	ADP
ejpam-5156	416	9	the	the	DET
ejpam-5156	416	10	department	department	NOUN
ejpam-5156	416	11	of	of	ADP
ejpam-5156	416	12	science	science	NOUN
ejpam-5156	416	13	and	and	CCONJ
ejpam-5156	416	14	technology	technology	NOUN
ejpam-5156	416	15	-	-	PUNCT
ejpam-5156	416	16	science	science	NOUN
ejpam-5156	416	17	education	education	PROPN
ejpam-5156	416	18	institute	institute	PROPN
ejpam-5156	416	19	science	science	PROPN
ejpam-5156	416	20	and	and	CCONJ
ejpam-5156	416	21	technology	technology	NOUN
ejpam-5156	416	22	regional	regional	ADJ
ejpam-5156	416	23	alliance	alliance	NOUN
ejpam-5156	416	24	of	of	ADP
ejpam-5156	416	25	universities	university	NOUN
ejpam-5156	416	26	for	for	ADP
ejpam-5156	416	27	inclusive	inclusive	ADJ
ejpam-5156	416	28	national	national	ADJ
ejpam-5156	416	29	development	development	NOUN
ejpam-5156	416	30	(	(	PUNCT
ejpam-5156	416	31	dost	dost	NOUN
ejpam-5156	416	32	-	-	PUNCT
ejpam-5156	416	33	sei	sei	ADJ
ejpam-5156	416	34	strand	strand	NOUN
ejpam-5156	416	35	)	)	PUNCT
ejpam-5156	416	36	for	for	ADP
ejpam-5156	416	37	their	their	PRON
ejpam-5156	416	38	invaluable	invaluable	ADJ
ejpam-5156	416	39	assistance	assistance	NOUN
ejpam-5156	416	40	throughout	throughout	ADP
ejpam-5156	416	41	the	the	DET
ejpam-5156	416	42	research	research	NOUN
ejpam-5156	416	43	process	process	NOUN
ejpam-5156	416	44	.	.	PUNCT
ejpam-5156	417	1	references	reference	NOUN
ejpam-5156	417	2	[	[	X
ejpam-5156	417	3	1	1	NUM
ejpam-5156	417	4	]	]	X
ejpam-5156	417	5	r	r	NOUN
ejpam-5156	417	6	barbosa	barbosa	PROPN
ejpam-5156	417	7	,	,	PUNCT
ejpam-5156	417	8	m	m	PROPN
ejpam-5156	417	9	dourado	dourado	NOUN
ejpam-5156	417	10	,	,	PUNCT
ejpam-5156	417	11	and	and	CCONJ
ejpam-5156	417	12	l	l	PROPN
ejpam-5156	417	13	da	da	PROPN
ejpam-5156	417	14	silva	silva	PROPN
ejpam-5156	417	15	.	.	PUNCT
ejpam-5156	418	1	global	global	ADJ
ejpam-5156	418	2	defensive	defensive	ADJ
ejpam-5156	418	3	alliances	alliance	NOUN
ejpam-5156	418	4	in	in	ADP
ejpam-5156	418	5	the	the	DET
ejpam-5156	418	6	lexicographic	lexicographic	ADJ
ejpam-5156	418	7	product	product	NOUN
ejpam-5156	418	8	of	of	ADP
ejpam-5156	418	9	paths	path	NOUN
ejpam-5156	418	10	and	and	CCONJ
ejpam-5156	418	11	cycles	cycle	NOUN
ejpam-5156	418	12	.	.	PUNCT
ejpam-5156	419	1	discrete	discrete	ADJ
ejpam-5156	419	2	applied	apply	VERB
ejpam-5156	419	3	mathematics	mathematic	NOUN
ejpam-5156	419	4	,	,	PUNCT
ejpam-5156	419	5	283:168–188	283:168–188	NUM
ejpam-5156	419	6	,	,	PUNCT
ejpam-5156	419	7	2020	2020	NUM
ejpam-5156	419	8	.	.	PUNCT
ejpam-5156	420	1	[	[	X
ejpam-5156	420	2	2	2	NUM
ejpam-5156	420	3	]	]	SYM
ejpam-5156	420	4	f	f	PROPN
ejpam-5156	420	5	beggas	beggas	NOUN
ejpam-5156	420	6	.	.	PUNCT
ejpam-5156	421	1	decomposition	decomposition	NOUN
ejpam-5156	421	2	and	and	CCONJ
ejpam-5156	421	3	domination	domination	NOUN
ejpam-5156	421	4	of	of	ADP
ejpam-5156	421	5	some	some	DET
ejpam-5156	421	6	graphs	graph	NOUN
ejpam-5156	421	7	.	.	PUNCT
ejpam-5156	422	1	data	datum	NOUN
ejpam-5156	422	2	structures	structure	NOUN
ejpam-5156	422	3	and	and	CCONJ
ejpam-5156	422	4	algorithms	algorithm	NOUN
ejpam-5156	423	1	[	[	X
ejpam-5156	423	2	cs.ds	cs.ds	PROPN
ejpam-5156	423	3	]	]	X
ejpam-5156	423	4	,	,	PUNCT
ejpam-5156	423	5	university	university	PROPN
ejpam-5156	423	6	claude	claude	PROPN
ejpam-5156	423	7	bernard	bernard	PROPN
ejpam-5156	423	8	lyon	lyon	PROPN
ejpam-5156	423	9	,	,	PUNCT
ejpam-5156	423	10	2017	2017	NUM
ejpam-5156	423	11	.	.	PUNCT
ejpam-5156	424	1	[	[	X
ejpam-5156	424	2	3	3	X
ejpam-5156	424	3	]	]	X
ejpam-5156	424	4	i	i	PRON
ejpam-5156	424	5	cabahug	cabahug	VERB
ejpam-5156	424	6	and	and	CCONJ
ejpam-5156	424	7	r	r	PROPN
ejpam-5156	424	8	isla	isla	PROPN
ejpam-5156	424	9	.	.	PUNCT
ejpam-5156	425	1	global	global	ADJ
ejpam-5156	425	2	offensive	offensive	ADJ
ejpam-5156	425	3	alliances	alliance	NOUN
ejpam-5156	425	4	in	in	ADP
ejpam-5156	425	5	some	some	DET
ejpam-5156	425	6	special	special	ADJ
ejpam-5156	425	7	classes	class	NOUN
ejpam-5156	425	8	of	of	ADP
ejpam-5156	425	9	graphs	graph	NOUN
ejpam-5156	425	10	.	.	PUNCT
ejpam-5156	426	1	the	the	DET
ejpam-5156	426	2	mindanawan	mindanawan	PROPN
ejpam-5156	426	3	journal	journal	PROPN
ejpam-5156	426	4	of	of	ADP
ejpam-5156	426	5	mathematics	mathematic	NOUN
ejpam-5156	426	6	,	,	PUNCT
ejpam-5156	426	7	2:43–48	2:43–48	NUM
ejpam-5156	426	8	,	,	PUNCT
ejpam-5156	426	9	2011	2011	NUM
ejpam-5156	426	10	.	.	PUNCT
ejpam-5156	427	1	[	[	X
ejpam-5156	427	2	4	4	X
ejpam-5156	427	3	]	]	X
ejpam-5156	427	4	j	j	PROPN
ejpam-5156	427	5	cabulao	cabulao	PROPN
ejpam-5156	427	6	and	and	CCONJ
ejpam-5156	427	7	r	r	PROPN
ejpam-5156	427	8	isla	isla	PROPN
ejpam-5156	427	9	.	.	PUNCT
ejpam-5156	428	1	on	on	ADP
ejpam-5156	428	2	connected	connect	VERB
ejpam-5156	428	3	partial	partial	ADJ
ejpam-5156	428	4	domination	domination	NOUN
ejpam-5156	428	5	in	in	ADP
ejpam-5156	428	6	graphs	graph	NOUN
ejpam-5156	428	7	.	.	PUNCT
ejpam-5156	429	1	european	european	ADJ
ejpam-5156	429	2	journal	journal	PROPN
ejpam-5156	429	3	of	of	ADP
ejpam-5156	429	4	pure	pure	ADJ
ejpam-5156	429	5	and	and	CCONJ
ejpam-5156	429	6	applied	applied	ADJ
ejpam-5156	429	7	mathematics	mathematic	NOUN
ejpam-5156	429	8	,	,	PUNCT
ejpam-5156	429	9	14(4	14(4	NUM
ejpam-5156	429	10	)	)	PUNCT
ejpam-5156	429	11	,	,	PUNCT
ejpam-5156	429	12	2021	2021	NUM
ejpam-5156	429	13	.	.	PUNCT
ejpam-5156	430	1	[	[	X
ejpam-5156	430	2	5	5	NUM
ejpam-5156	430	3	]	]	PUNCT
ejpam-5156	430	4	g	g	PROPN
ejpam-5156	430	5	chartrand	chartrand	NOUN
ejpam-5156	430	6	,	,	PUNCT
ejpam-5156	430	7	l	l	PROPN
ejpam-5156	430	8	lesniak	lesniak	PROPN
ejpam-5156	430	9	,	,	PUNCT
ejpam-5156	430	10	and	and	CCONJ
ejpam-5156	430	11	p	p	PROPN
ejpam-5156	430	12	zhang	zhang	PROPN
ejpam-5156	430	13	.	.	PUNCT
ejpam-5156	430	14	graphs	graph	NOUN
ejpam-5156	430	15	and	and	CCONJ
ejpam-5156	430	16	digraphs	digraph	NOUN
ejpam-5156	430	17	.	.	PUNCT
ejpam-5156	431	1	chapman	chapman	NOUN
ejpam-5156	431	2	and	and	CCONJ
ejpam-5156	431	3	hall	hall	PROPN
ejpam-5156	431	4	/	/	SYM
ejpam-5156	431	5	crc	crc	PROPN
ejpam-5156	431	6	,	,	PUNCT
ejpam-5156	431	7	new	new	PROPN
ejpam-5156	431	8	york	york	PROPN
ejpam-5156	431	9	,	,	PUNCT
ejpam-5156	431	10	2015	2015	NUM
ejpam-5156	431	11	.	.	PUNCT
ejpam-5156	432	1	[	[	X
ejpam-5156	432	2	6	6	NUM
ejpam-5156	432	3	]	]	PUNCT
ejpam-5156	432	4	l	l	NOUN
ejpam-5156	432	5	consistente	consistente	NOUN
ejpam-5156	432	6	and	and	CCONJ
ejpam-5156	432	7	i	i	PRON
ejpam-5156	432	8	cabahug	cabahug	VERB
ejpam-5156	432	9	.	.	PUNCT
ejpam-5156	433	1	hinge	hinge	NOUN
ejpam-5156	433	2	total	total	ADJ
ejpam-5156	433	3	domination	domination	NOUN
ejpam-5156	433	4	in	in	ADP
ejpam-5156	433	5	graphs	graph	NOUN
ejpam-5156	433	6	.	.	PUNCT
ejpam-5156	434	1	asian	asian	ADJ
ejpam-5156	434	2	research	research	PROPN
ejpam-5156	434	3	journal	journal	NOUN
ejpam-5156	434	4	of	of	ADP
ejpam-5156	434	5	mathematics	mathematic	NOUN
ejpam-5156	434	6	,	,	PUNCT
ejpam-5156	434	7	18(9):25–34	18(9):25–34	NUM
ejpam-5156	434	8	,	,	PUNCT
ejpam-5156	434	9	2022	2022	NUM
ejpam-5156	434	10	.	.	PUNCT
ejpam-5156	435	1	[	[	X
ejpam-5156	435	2	7	7	X
ejpam-5156	435	3	]	]	X
ejpam-5156	435	4	g	g	PROPN
ejpam-5156	435	5	domke	domke	PROPN
ejpam-5156	435	6	,	,	PUNCT
ejpam-5156	435	7	s	s	VERB
ejpam-5156	435	8	hattingh	hattingh	NOUN
ejpam-5156	435	9	,	,	PUNCT
ejpam-5156	435	10	r	r	NOUN
ejpam-5156	435	11	laskar	laskar	PROPN
ejpam-5156	435	12	,	,	PUNCT
ejpam-5156	435	13	s	s	VERB
ejpam-5156	435	14	hedetniemi	hedetniemi	NOUN
ejpam-5156	435	15	,	,	PUNCT
ejpam-5156	435	16	r	r	NOUN
ejpam-5156	435	17	laskar	laskar	PROPN
ejpam-5156	435	18	,	,	PUNCT
ejpam-5156	435	19	and	and	CCONJ
ejpam-5156	435	20	l	l	NOUN
ejpam-5156	435	21	markus	markus	NOUN
ejpam-5156	435	22	.	.	PUNCT
ejpam-5156	436	1	restrained	restrained	ADJ
ejpam-5156	436	2	domination	domination	NOUN
ejpam-5156	436	3	in	in	ADP
ejpam-5156	436	4	graphs	graph	NOUN
ejpam-5156	436	5	.	.	PUNCT
ejpam-5156	437	1	discrete	discrete	ADJ
ejpam-5156	437	2	mathematics	mathematic	NOUN
ejpam-5156	437	3	,	,	PUNCT
ejpam-5156	437	4	203:61–69	203:61–69	NUM
ejpam-5156	437	5	,	,	PUNCT
ejpam-5156	437	6	1999	1999	NUM
ejpam-5156	437	7	.	.	PUNCT
ejpam-5156	438	1	references	reference	NOUN
ejpam-5156	438	2	2209	2209	NUM
ejpam-5156	439	1	[	[	X
ejpam-5156	439	2	8	8	NUM
ejpam-5156	439	3	]	]	X
ejpam-5156	439	4	e	e	X
ejpam-5156	439	5	enriquez	enriquez	PROPN
ejpam-5156	439	6	.	.	PUNCT
ejpam-5156	440	1	fair	fair	ADJ
ejpam-5156	440	2	restrained	restrained	ADJ
ejpam-5156	440	3	domination	domination	NOUN
ejpam-5156	440	4	in	in	ADP
ejpam-5156	440	5	graphs	graph	NOUN
ejpam-5156	440	6	.	.	PUNCT
ejpam-5156	441	1	international	international	ADJ
ejpam-5156	441	2	journal	journal	PROPN
ejpam-5156	441	3	of	of	ADP
ejpam-5156	441	4	mathematics	mathematics	NOUN
ejpam-5156	441	5	trends	trend	NOUN
ejpam-5156	441	6	and	and	CCONJ
ejpam-5156	441	7	technology	technology	NOUN
ejpam-5156	441	8	,	,	PUNCT
ejpam-5156	441	9	66(1):229–235	66(1):229–235	PROPN
ejpam-5156	441	10	,	,	PUNCT
ejpam-5156	441	11	2020	2020	NUM
ejpam-5156	441	12	.	.	PUNCT
ejpam-5156	442	1	[	[	X
ejpam-5156	442	2	9	9	NUM
ejpam-5156	442	3	]	]	X
ejpam-5156	442	4	a	a	DET
ejpam-5156	442	5	gaikwad	gaikwad	NOUN
ejpam-5156	442	6	and	and	CCONJ
ejpam-5156	442	7	s	s	VERB
ejpam-5156	442	8	maity	maity	NOUN
ejpam-5156	442	9	.	.	PUNCT
ejpam-5156	443	1	globally	globally	ADV
ejpam-5156	443	2	minimal	minimal	VERB
ejpam-5156	443	3	defensive	defensive	ADJ
ejpam-5156	443	4	alliances	alliance	NOUN
ejpam-5156	443	5	.	.	PUNCT
ejpam-5156	444	1	information	information	NOUN
ejpam-5156	444	2	processing	processing	NOUN
ejpam-5156	444	3	letters	letter	NOUN
ejpam-5156	444	4	,	,	PUNCT
ejpam-5156	444	5	177	177	NUM
ejpam-5156	444	6	,	,	PUNCT
ejpam-5156	444	7	2022	2022	NUM
ejpam-5156	444	8	.	.	PUNCT
ejpam-5156	445	1	[	[	X
ejpam-5156	445	2	10	10	NUM
ejpam-5156	445	3	]	]	X
ejpam-5156	445	4	f	f	PROPN
ejpam-5156	445	5	harary	harary	NOUN
ejpam-5156	445	6	.	.	PUNCT
ejpam-5156	446	1	graph	graph	NOUN
ejpam-5156	446	2	theory	theory	NOUN
ejpam-5156	446	3	.	.	PUNCT
ejpam-5156	447	1	united	united	PROPN
ejpam-5156	447	2	states	states	PROPN
ejpam-5156	447	3	of	of	ADP
ejpam-5156	447	4	america	america	PROPN
ejpam-5156	447	5	:	:	PUNCT
ejpam-5156	447	6	addison	addison	PROPN
ejpam-5156	447	7	-	-	PUNCT
ejpam-5156	447	8	wesley	wesley	PROPN
ejpam-5156	447	9	publishing	publishing	PROPN
ejpam-5156	447	10	company	company	PROPN
ejpam-5156	447	11	,	,	PUNCT
ejpam-5156	447	12	inc	inc	PROPN
ejpam-5156	447	13	.	.	PROPN
ejpam-5156	447	14	,	,	PUNCT
ejpam-5156	447	15	canada	canada	PROPN
ejpam-5156	447	16	,	,	PUNCT
ejpam-5156	447	17	1969	1969	NUM
ejpam-5156	447	18	.	.	PUNCT
ejpam-5156	448	1	[	[	X
ejpam-5156	448	2	11	11	NUM
ejpam-5156	448	3	]	]	PUNCT
ejpam-5156	448	4	t	t	PROPN
ejpam-5156	448	5	haynes	haynes	PROPN
ejpam-5156	448	6	,	,	PUNCT
ejpam-5156	448	7	s	s	VERB
ejpam-5156	448	8	hedetniemi	hedetniemi	ADV
ejpam-5156	448	9	,	,	PUNCT
ejpam-5156	448	10	and	and	CCONJ
ejpam-5156	448	11	m	m	PROPN
ejpam-5156	448	12	henning	henning	NOUN
ejpam-5156	448	13	.	.	PUNCT
ejpam-5156	449	1	global	global	ADJ
ejpam-5156	449	2	defensive	defensive	ADJ
ejpam-5156	449	3	alliances	alliance	NOUN
ejpam-5156	449	4	in	in	ADP
ejpam-5156	449	5	graphs	graph	NOUN
ejpam-5156	449	6	.	.	PUNCT
ejpam-5156	450	1	electronic	electronic	ADJ
ejpam-5156	450	2	journal	journal	NOUN
ejpam-5156	450	3	of	of	ADP
ejpam-5156	450	4	combinatorics	combinatoric	NOUN
ejpam-5156	450	5	,	,	PUNCT
ejpam-5156	450	6	10	10	NUM
ejpam-5156	450	7	,	,	PUNCT
ejpam-5156	450	8	2003	2003	NUM
ejpam-5156	450	9	.	.	PUNCT
ejpam-5156	451	1	[	[	X
ejpam-5156	451	2	12	12	NUM
ejpam-5156	451	3	]	]	X
ejpam-5156	451	4	p	p	X
ejpam-5156	451	5	kristiansen	kristiansen	PROPN
ejpam-5156	451	6	,	,	PUNCT
ejpam-5156	451	7	m	m	VERB
ejpam-5156	451	8	hedetniemi	hedetniemi	ADV
ejpam-5156	451	9	,	,	PUNCT
ejpam-5156	451	10	and	and	CCONJ
ejpam-5156	451	11	s.	s.	PROPN
ejpam-5156	451	12	hedetniemi	hedetniemi	PROPN
ejpam-5156	451	13	.	.	PUNCT
ejpam-5156	452	1	alliances	alliance	NOUN
ejpam-5156	452	2	in	in	ADP
ejpam-5156	452	3	graphs	graph	NOUN
ejpam-5156	452	4	.	.	PUNCT
ejpam-5156	453	1	journal	journal	NOUN
ejpam-5156	453	2	of	of	ADP
ejpam-5156	453	3	combinatorial	combinatorial	ADJ
ejpam-5156	453	4	mathematics	mathematic	NOUN
ejpam-5156	453	5	and	and	CCONJ
ejpam-5156	453	6	combinatorial	combinatorial	ADJ
ejpam-5156	453	7	computing	computing	NOUN
ejpam-5156	453	8	,	,	PUNCT
ejpam-5156	453	9	48:157–177	48:157–177	NUM
ejpam-5156	453	10	,	,	PUNCT
ejpam-5156	453	11	2004	2004	NUM
ejpam-5156	453	12	.	.	PUNCT
ejpam-5156	454	1	[	[	X
ejpam-5156	454	2	13	13	NUM
ejpam-5156	454	3	]	]	X
ejpam-5156	454	4	d	d	X
ejpam-5156	454	5	mojdeh	mojdeh	NOUN
ejpam-5156	454	6	,	,	PUNCT
ejpam-5156	454	7	i	i	PRON
ejpam-5156	454	8	masoumi	masoumi	NOUN
ejpam-5156	454	9	,	,	PUNCT
ejpam-5156	454	10	and	and	CCONJ
ejpam-5156	454	11	l	l	PROPN
ejpam-5156	454	12	volkmann	volkmann	PROPN
ejpam-5156	454	13	.	.	PUNCT
ejpam-5156	455	1	restrained	restrained	ADJ
ejpam-5156	455	2	double	double	ADJ
ejpam-5156	455	3	roman	roman	ADJ
ejpam-5156	455	4	domination	domination	NOUN
ejpam-5156	455	5	of	of	ADP
ejpam-5156	455	6	a	a	DET
ejpam-5156	455	7	graph	graph	NOUN
ejpam-5156	455	8	.	.	PUNCT
ejpam-5156	456	1	rairo	rairo	PROPN
ejpam-5156	456	2	.	.	PUNCT
ejpam-5156	457	1	recherche	recherche	PROPN
ejpam-5156	457	2	operationnelle	operationnelle	PROPN
ejpam-5156	457	3	,	,	PUNCT
ejpam-5156	457	4	56(4):2293–2304	56(4):2293–2304	NUM
ejpam-5156	457	5	,	,	PUNCT
ejpam-5156	457	6	2022	2022	NUM
ejpam-5156	457	7	.	.	PUNCT
ejpam-5156	458	1	[	[	X
ejpam-5156	458	2	14	14	NUM
ejpam-5156	458	3	]	]	X
ejpam-5156	458	4	m	m	VERB
ejpam-5156	458	5	ortega	ortega	PROPN
ejpam-5156	458	6	and	and	CCONJ
ejpam-5156	458	7	r	r	PROPN
ejpam-5156	458	8	isla	isla	PROPN
ejpam-5156	458	9	.	.	PUNCT
ejpam-5156	459	1	on	on	ADP
ejpam-5156	459	2	semitotal	semitotal	ADJ
ejpam-5156	459	3	k	k	ADJ
ejpam-5156	459	4	-	-	ADJ
ejpam-5156	459	5	fair	fair	ADJ
ejpam-5156	459	6	and	and	CCONJ
ejpam-5156	459	7	independent	independent	ADJ
ejpam-5156	459	8	k	k	ADJ
ejpam-5156	459	9	-	-	PUNCT
ejpam-5156	459	10	fair	fair	ADJ
ejpam-5156	459	11	domination	domination	NOUN
ejpam-5156	459	12	in	in	ADP
ejpam-5156	459	13	graphs	graph	NOUN
ejpam-5156	459	14	.	.	PUNCT
ejpam-5156	460	1	european	european	ADJ
ejpam-5156	460	2	journal	journal	PROPN
ejpam-5156	460	3	of	of	ADP
ejpam-5156	460	4	pure	pure	ADJ
ejpam-5156	460	5	and	and	CCONJ
ejpam-5156	460	6	applied	applied	ADJ
ejpam-5156	460	7	mathematics	mathematic	NOUN
ejpam-5156	460	8	,	,	PUNCT
ejpam-5156	460	9	13(4	13(4	NUM
ejpam-5156	460	10	)	)	PUNCT
ejpam-5156	460	11	,	,	PUNCT
ejpam-5156	460	12	2020	2020	NUM
ejpam-5156	460	13	.	.	PUNCT