id	sid	tid	token	lemma	pos
ejpam-5749	1	1	european	european	PROPN
ejpam-5749	1	2	journal	journal	PROPN
ejpam-5749	1	3	of	of	ADP
ejpam-5749	1	4	pure	pure	ADJ
ejpam-5749	1	5	and	and	CCONJ
ejpam-5749	1	6	applied	applied	ADJ
ejpam-5749	1	7	mathematics	mathematic	NOUN
ejpam-5749	1	8	2025	2025	NUM
ejpam-5749	1	9	,	,	PUNCT
ejpam-5749	1	10	vol	vol	NOUN
ejpam-5749	1	11	.	.	PROPN
ejpam-5749	1	12	18	18	NUM
ejpam-5749	1	13	,	,	PUNCT
ejpam-5749	1	14	issue	issue	NOUN
ejpam-5749	1	15	1	1	NUM
ejpam-5749	1	16	,	,	PUNCT
ejpam-5749	1	17	article	article	NOUN
ejpam-5749	1	18	number	number	NOUN
ejpam-5749	1	19	5749	5749	NUM
ejpam-5749	1	20	issn	issn	VERB
ejpam-5749	1	21	1307	1307	NUM
ejpam-5749	1	22	-	-	SYM
ejpam-5749	1	23	5543	5543	NUM
ejpam-5749	1	24	–	–	PUNCT
ejpam-5749	1	25	ejpam.com	ejpam.com	X
ejpam-5749	1	26	published	publish	VERB
ejpam-5749	1	27	by	by	ADP
ejpam-5749	1	28	new	new	PROPN
ejpam-5749	1	29	york	york	PROPN
ejpam-5749	1	30	business	business	PROPN
ejpam-5749	1	31	global	global	ADJ
ejpam-5749	1	32	semitotal	semitotal	ADJ
ejpam-5749	1	33	roman	roman	ADJ
ejpam-5749	1	34	domination	domination	NOUN
ejpam-5749	1	35	in	in	ADP
ejpam-5749	1	36	graphs	graphs	PROPN
ejpam-5749	1	37	brayan	brayan	PROPN
ejpam-5749	1	38	f.	f.	PROPN
ejpam-5749	1	39	bullang1	bullang1	PROPN
ejpam-5749	1	40	,	,	PUNCT
ejpam-5749	1	41	imelda	imelda	PROPN
ejpam-5749	1	42	s.	s.	PROPN
ejpam-5749	1	43	aniversario1,2	aniversario1,2	PROPN
ejpam-5749	1	44	,	,	PUNCT
ejpam-5749	2	1	alkajim	alkajim	VERB
ejpam-5749	2	2	a.	a.	NOUN
ejpam-5749	2	3	aradais2,3	aradais2,3	PROPN
ejpam-5749	2	4	,	,	PUNCT
ejpam-5749	2	5	ferdinand	ferdinand	PROPN
ejpam-5749	3	1	p.	p.	PROPN
ejpam-5749	4	1	jamil1,2	jamil1,2	PROPN
ejpam-5749	4	2	1	1	NUM
ejpam-5749	4	3	department	department	NOUN
ejpam-5749	4	4	of	of	ADP
ejpam-5749	4	5	mathematics	mathematic	NOUN
ejpam-5749	4	6	and	and	CCONJ
ejpam-5749	4	7	statistics	statistic	NOUN
ejpam-5749	4	8	,	,	PUNCT
ejpam-5749	4	9	college	college	NOUN
ejpam-5749	4	10	of	of	ADP
ejpam-5749	4	11	science	science	NOUN
ejpam-5749	4	12	and	and	CCONJ
ejpam-5749	4	13	mathematics	mathematic	NOUN
ejpam-5749	4	14	,	,	PUNCT
ejpam-5749	4	15	msu	msu	PROPN
ejpam-5749	4	16	-	-	PUNCT
ejpam-5749	4	17	iligan	iligan	PROPN
ejpam-5749	4	18	institute	institute	PROPN
ejpam-5749	4	19	of	of	ADP
ejpam-5749	4	20	technology	technology	PROPN
ejpam-5749	4	21	,	,	PUNCT
ejpam-5749	4	22	9200	9200	NUM
ejpam-5749	4	23	iligan	iligan	ADJ
ejpam-5749	4	24	city	city	NOUN
ejpam-5749	4	25	,	,	PUNCT
ejpam-5749	4	26	philippines	philippine	NOUN
ejpam-5749	4	27	2	2	NUM
ejpam-5749	4	28	center	center	NOUN
ejpam-5749	4	29	for	for	ADP
ejpam-5749	4	30	mathematical	mathematical	ADJ
ejpam-5749	4	31	and	and	CCONJ
ejpam-5749	4	32	theoretical	theoretical	ADJ
ejpam-5749	4	33	physical	physical	ADJ
ejpam-5749	4	34	sciences	science	NOUN
ejpam-5749	4	35	,	,	PUNCT
ejpam-5749	4	36	premier	premier	PROPN
ejpam-5749	4	37	research	research	PROPN
ejpam-5749	4	38	institute	institute	PROPN
ejpam-5749	4	39	of	of	ADP
ejpam-5749	4	40	science	science	NOUN
ejpam-5749	4	41	and	and	CCONJ
ejpam-5749	4	42	mathematics	mathematic	NOUN
ejpam-5749	4	43	,	,	PUNCT
ejpam-5749	4	44	msu	msu	PROPN
ejpam-5749	4	45	-	-	PUNCT
ejpam-5749	4	46	iligan	iligan	PROPN
ejpam-5749	4	47	institute	institute	PROPN
ejpam-5749	4	48	of	of	ADP
ejpam-5749	4	49	technology	technology	PROPN
ejpam-5749	4	50	,	,	PUNCT
ejpam-5749	4	51	9200	9200	NUM
ejpam-5749	4	52	iligan	iligan	ADJ
ejpam-5749	4	53	city	city	NOUN
ejpam-5749	4	54	,	,	PUNCT
ejpam-5749	4	55	philippines	philippine	NOUN
ejpam-5749	4	56	3	3	NUM
ejpam-5749	4	57	integrated	integrate	VERB
ejpam-5749	4	58	laboratory	laboratory	NOUN
ejpam-5749	4	59	school	school	NOUN
ejpam-5749	4	60	,	,	PUNCT
ejpam-5749	4	61	college	college	NOUN
ejpam-5749	4	62	of	of	ADP
ejpam-5749	4	63	education	education	NOUN
ejpam-5749	4	64	,	,	PUNCT
ejpam-5749	4	65	mindanao	mindanao	PROPN
ejpam-5749	4	66	state	state	PROPN
ejpam-5749	4	67	university	university	PROPN
ejpam-5749	4	68	tawi	tawi	PROPN
ejpam-5749	4	69	-	-	PUNCT
ejpam-5749	4	70	tawi	tawi	PROPN
ejpam-5749	4	71	college	college	PROPN
ejpam-5749	4	72	of	of	ADP
ejpam-5749	4	73	technology	technology	NOUN
ejpam-5749	4	74	and	and	CCONJ
ejpam-5749	4	75	oceanography	oceanography	NOUN
ejpam-5749	4	76	,	,	PUNCT
ejpam-5749	4	77	tawi	tawi	NOUN
ejpam-5749	4	78	-	-	PUNCT
ejpam-5749	4	79	tawi	tawi	NOUN
ejpam-5749	4	80	,	,	PUNCT
ejpam-5749	4	81	philippines	philippine	NOUN
ejpam-5749	4	82	abstract	abstract	ADJ
ejpam-5749	4	83	.	.	PUNCT
ejpam-5749	5	1	let	let	VERB
ejpam-5749	5	2	g	g	PRON
ejpam-5749	5	3	be	be	AUX
ejpam-5749	5	4	a	a	DET
ejpam-5749	5	5	nontrivial	nontrivial	ADJ
ejpam-5749	5	6	graph	graph	NOUN
ejpam-5749	5	7	without	without	ADP
ejpam-5749	5	8	isolated	isolated	ADJ
ejpam-5749	5	9	vertices	vertex	NOUN
ejpam-5749	5	10	.	.	PUNCT
ejpam-5749	6	1	a	a	DET
ejpam-5749	6	2	function	function	NOUN
ejpam-5749	6	3	f	f	NOUN
ejpam-5749	6	4	:	:	PUNCT
ejpam-5749	6	5	v	v	X
ejpam-5749	6	6	(	(	PUNCT
ejpam-5749	6	7	g	g	NOUN
ejpam-5749	6	8	)	)	PUNCT
ejpam-5749	6	9	→	→	SYM
ejpam-5749	6	10	{	{	PUNCT
ejpam-5749	6	11	0	0	NUM
ejpam-5749	6	12	,	,	PUNCT
ejpam-5749	6	13	1	1	NUM
ejpam-5749	6	14	,	,	PUNCT
ejpam-5749	6	15	2	2	NUM
ejpam-5749	6	16	}	}	PUNCT
ejpam-5749	6	17	is	be	AUX
ejpam-5749	6	18	a	a	DET
ejpam-5749	6	19	semitotal	semitotal	ADJ
ejpam-5749	6	20	roman	roman	ADJ
ejpam-5749	6	21	dominating	dominating	NOUN
ejpam-5749	6	22	function	function	NOUN
ejpam-5749	6	23	of	of	ADP
ejpam-5749	6	24	g	g	PROPN
ejpam-5749	6	25	if	if	SCONJ
ejpam-5749	6	26	for	for	ADP
ejpam-5749	6	27	each	each	PRON
ejpam-5749	6	28	v	v	NUM
ejpam-5749	6	29	∈	∈	PROPN
ejpam-5749	6	30	v	v	NOUN
ejpam-5749	6	31	(	(	PUNCT
ejpam-5749	6	32	g	g	NOUN
ejpam-5749	6	33	)	)	PUNCT
ejpam-5749	6	34	with	with	ADP
ejpam-5749	6	35	f(v	f(v	NOUN
ejpam-5749	6	36	)	)	PUNCT
ejpam-5749	6	37	=	=	SYM
ejpam-5749	6	38	0	0	NUM
ejpam-5749	6	39	,	,	PUNCT
ejpam-5749	6	40	there	there	PRON
ejpam-5749	6	41	exists	exist	VERB
ejpam-5749	6	42	u	u	PROPN
ejpam-5749	6	43	∈	∈	PROPN
ejpam-5749	6	44	v	v	ADP
ejpam-5749	6	45	(	(	PUNCT
ejpam-5749	6	46	g	g	NOUN
ejpam-5749	6	47	)	)	PUNCT
ejpam-5749	6	48	for	for	ADP
ejpam-5749	6	49	which	which	PRON
ejpam-5749	6	50	f(u	f(u	PROPN
ejpam-5749	6	51	)	)	PUNCT
ejpam-5749	6	52	=	=	SYM
ejpam-5749	6	53	2	2	NUM
ejpam-5749	6	54	and	and	CCONJ
ejpam-5749	6	55	uv	uv	NOUN
ejpam-5749	6	56	∈	∈	PROPN
ejpam-5749	6	57	e(g	e(g	PROPN
ejpam-5749	6	58	)	)	PUNCT
ejpam-5749	6	59	and	and	CCONJ
ejpam-5749	6	60	for	for	ADP
ejpam-5749	6	61	each	each	DET
ejpam-5749	6	62	v	v	NUM
ejpam-5749	6	63	∈	∈	PROPN
ejpam-5749	6	64	v	v	NOUN
ejpam-5749	6	65	(	(	PUNCT
ejpam-5749	6	66	g	g	NOUN
ejpam-5749	6	67	)	)	PUNCT
ejpam-5749	6	68	with	with	ADP
ejpam-5749	6	69	f(v	f(v	NOUN
ejpam-5749	6	70	)	)	PUNCT
ejpam-5749	6	71	̸=	̸=	PROPN
ejpam-5749	6	72	0	0	NUM
ejpam-5749	6	73	,	,	PUNCT
ejpam-5749	6	74	there	there	PRON
ejpam-5749	6	75	exists	exist	VERB
ejpam-5749	6	76	u	u	PROPN
ejpam-5749	6	77	∈	∈	PROPN
ejpam-5749	6	78	v	v	ADP
ejpam-5749	6	79	(	(	PUNCT
ejpam-5749	6	80	g	g	NOUN
ejpam-5749	6	81	)	)	PUNCT
ejpam-5749	6	82	for	for	ADP
ejpam-5749	6	83	which	which	PRON
ejpam-5749	6	84	f(u	f(u	PROPN
ejpam-5749	6	85	)	)	PUNCT
ejpam-5749	6	86	̸=	̸=	PROPN
ejpam-5749	6	87	0	0	NUM
ejpam-5749	6	88	and	and	CCONJ
ejpam-5749	6	89	dg(u	dg(u	X
ejpam-5749	6	90	,	,	PUNCT
ejpam-5749	6	91	v	v	NOUN
ejpam-5749	6	92	)	)	PUNCT
ejpam-5749	6	93	≤	≤	NOUN
ejpam-5749	6	94	2	2	NUM
ejpam-5749	6	95	.	.	PUNCT
ejpam-5749	6	96	the	the	DET
ejpam-5749	6	97	minimum	minimum	ADJ
ejpam-5749	6	98	weight	weight	NOUN
ejpam-5749	6	99	ωg(f	ωg(f	PRON
ejpam-5749	6	100	)	)	PUNCT
ejpam-5749	6	101	=	=	SYM
ejpam-5749	7	1	∑	∑	PUNCT
ejpam-5749	7	2	u∈v	u∈v	NOUN
ejpam-5749	7	3	(	(	PUNCT
ejpam-5749	7	4	g	g	NOUN
ejpam-5749	7	5	)	)	PUNCT
ejpam-5749	7	6	f(u	f(u	PROPN
ejpam-5749	7	7	)	)	PUNCT
ejpam-5749	7	8	of	of	ADP
ejpam-5749	7	9	a	a	DET
ejpam-5749	7	10	semitotal	semitotal	ADJ
ejpam-5749	7	11	roman	roman	ADJ
ejpam-5749	7	12	dominating	dominating	NOUN
ejpam-5749	7	13	function	function	NOUN
ejpam-5749	7	14	f	f	PROPN
ejpam-5749	7	15	of	of	ADP
ejpam-5749	7	16	g	g	PROPN
ejpam-5749	7	17	is	be	AUX
ejpam-5749	7	18	the	the	DET
ejpam-5749	7	19	semitotal	semitotal	ADJ
ejpam-5749	7	20	roman	roman	ADJ
ejpam-5749	7	21	domination	domination	NOUN
ejpam-5749	7	22	number	number	NOUN
ejpam-5749	7	23	of	of	ADP
ejpam-5749	7	24	g	g	NOUN
ejpam-5749	7	25	,	,	PUNCT
ejpam-5749	7	26	denoted	denote	VERB
ejpam-5749	7	27	by	by	ADP
ejpam-5749	7	28	γt2r(g	γt2r(g	NOUN
ejpam-5749	7	29	)	)	PUNCT
ejpam-5749	7	30	.	.	PUNCT
ejpam-5749	8	1	in	in	ADP
ejpam-5749	8	2	this	this	DET
ejpam-5749	8	3	paper	paper	NOUN
ejpam-5749	8	4	,	,	PUNCT
ejpam-5749	8	5	we	we	PRON
ejpam-5749	8	6	initiate	initiate	VERB
ejpam-5749	8	7	the	the	DET
ejpam-5749	8	8	study	study	NOUN
ejpam-5749	8	9	of	of	ADP
ejpam-5749	8	10	semitotal	semitotal	ADJ
ejpam-5749	8	11	roman	roman	ADJ
ejpam-5749	8	12	domination	domination	NOUN
ejpam-5749	8	13	.	.	PUNCT
ejpam-5749	9	1	we	we	PRON
ejpam-5749	9	2	characterize	characterize	VERB
ejpam-5749	9	3	graphs	graph	NOUN
ejpam-5749	9	4	g	g	NOUN
ejpam-5749	9	5	with	with	ADP
ejpam-5749	9	6	small	small	ADJ
ejpam-5749	9	7	values	value	NOUN
ejpam-5749	9	8	of	of	ADP
ejpam-5749	9	9	γt2r(g	γt2r(g	NUM
ejpam-5749	9	10	)	)	PUNCT
ejpam-5749	9	11	and	and	CCONJ
ejpam-5749	9	12	solve	solve	VERB
ejpam-5749	9	13	some	some	DET
ejpam-5749	9	14	realization	realization	NOUN
ejpam-5749	9	15	problems	problem	NOUN
ejpam-5749	9	16	with	with	ADP
ejpam-5749	9	17	other	other	ADJ
ejpam-5749	9	18	existing	exist	VERB
ejpam-5749	9	19	related	relate	VERB
ejpam-5749	9	20	concepts	concept	NOUN
ejpam-5749	9	21	.	.	PUNCT
ejpam-5749	10	1	we	we	PRON
ejpam-5749	10	2	also	also	ADV
ejpam-5749	10	3	investigate	investigate	VERB
ejpam-5749	10	4	the	the	DET
ejpam-5749	10	5	semitotal	semitotal	ADJ
ejpam-5749	10	6	roman	roman	ADJ
ejpam-5749	10	7	domination	domination	NOUN
ejpam-5749	10	8	in	in	ADP
ejpam-5749	10	9	the	the	DET
ejpam-5749	10	10	join	join	NOUN
ejpam-5749	10	11	,	,	PUNCT
ejpam-5749	10	12	corona	corona	NOUN
ejpam-5749	10	13	and	and	CCONJ
ejpam-5749	10	14	complimentary	complimentary	ADJ
ejpam-5749	10	15	prism	prism	NOUN
ejpam-5749	10	16	of	of	ADP
ejpam-5749	10	17	graphs	graph	NOUN
ejpam-5749	10	18	.	.	PUNCT
ejpam-5749	11	1	2020	2020	NUM
ejpam-5749	11	2	mathematics	mathematic	NOUN
ejpam-5749	11	3	subject	subject	NOUN
ejpam-5749	11	4	classifications	classification	NOUN
ejpam-5749	11	5	:	:	PUNCT
ejpam-5749	11	6	05c69	05c69	X
ejpam-5749	11	7	key	key	ADJ
ejpam-5749	11	8	words	word	NOUN
ejpam-5749	11	9	and	and	CCONJ
ejpam-5749	11	10	phrases	phrase	NOUN
ejpam-5749	11	11	:	:	PUNCT
ejpam-5749	11	12	semitotal	semitotal	ADJ
ejpam-5749	11	13	roman	roman	ADJ
ejpam-5749	11	14	dominating	dominating	NOUN
ejpam-5749	11	15	function	function	NOUN
ejpam-5749	11	16	,	,	PUNCT
ejpam-5749	11	17	semitotal	semitotal	ADJ
ejpam-5749	11	18	roman	roman	ADJ
ejpam-5749	11	19	domination	domination	NOUN
ejpam-5749	11	20	number	number	NOUN
ejpam-5749	11	21	,	,	PUNCT
ejpam-5749	11	22	roman	roman	ADJ
ejpam-5749	11	23	dominating	dominating	NOUN
ejpam-5749	11	24	function	function	NOUN
ejpam-5749	11	25	,	,	PUNCT
ejpam-5749	11	26	roman	roman	ADJ
ejpam-5749	11	27	domination	domination	NOUN
ejpam-5749	11	28	number	number	NOUN
ejpam-5749	11	29	,	,	PUNCT
ejpam-5749	11	30	total	total	ADJ
ejpam-5749	11	31	roman	roman	ADJ
ejpam-5749	11	32	dominating	dominating	NOUN
ejpam-5749	11	33	function	function	NOUN
ejpam-5749	11	34	,	,	PUNCT
ejpam-5749	11	35	and	and	CCONJ
ejpam-5749	11	36	total	total	ADJ
ejpam-5749	11	37	roman	roman	ADJ
ejpam-5749	11	38	domination	domination	NOUN
ejpam-5749	11	39	number	number	NOUN
ejpam-5749	11	40	1	1	NUM
ejpam-5749	11	41	.	.	PUNCT
ejpam-5749	12	1	introduction	introduction	NOUN
ejpam-5749	12	2	semitotal	semitotal	ADJ
ejpam-5749	12	3	domination	domination	NOUN
ejpam-5749	12	4	and	and	CCONJ
ejpam-5749	12	5	roman	roman	ADJ
ejpam-5749	12	6	domination	domination	NOUN
ejpam-5749	12	7	are	be	AUX
ejpam-5749	12	8	two	two	NUM
ejpam-5749	12	9	among	among	ADP
ejpam-5749	12	10	intriguing	intriguing	ADJ
ejpam-5749	12	11	concepts	concept	NOUN
ejpam-5749	12	12	in	in	ADP
ejpam-5749	12	13	domination	domination	NOUN
ejpam-5749	12	14	in	in	ADP
ejpam-5749	12	15	graphs	graph	NOUN
ejpam-5749	12	16	.	.	PUNCT
ejpam-5749	13	1	both	both	PRON
ejpam-5749	13	2	extend	extend	VERB
ejpam-5749	13	3	the	the	DET
ejpam-5749	13	4	classical	classical	ADJ
ejpam-5749	13	5	notion	notion	NOUN
ejpam-5749	13	6	of	of	ADP
ejpam-5749	13	7	domination	domination	NOUN
ejpam-5749	13	8	by	by	ADP
ejpam-5749	13	9	incorporating	incorporate	VERB
ejpam-5749	13	10	additional	additional	ADJ
ejpam-5749	13	11	structural	structural	ADJ
ejpam-5749	13	12	or	or	CCONJ
ejpam-5749	13	13	functional	functional	ADJ
ejpam-5749	13	14	constraints	constraint	NOUN
ejpam-5749	13	15	,	,	PUNCT
ejpam-5749	13	16	offering	offer	VERB
ejpam-5749	13	17	alternative	alternative	ADJ
ejpam-5749	13	18	perspective	perspective	NOUN
ejpam-5749	13	19	and	and	CCONJ
ejpam-5749	13	20	applications	application	NOUN
ejpam-5749	13	21	.	.	PUNCT
ejpam-5749	14	1	doi	doi	NOUN
ejpam-5749	14	2	:	:	PUNCT
ejpam-5749	14	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5749	https://doi.org/10.29020/nybg.ejpam.v18i1.5749	PROPN
ejpam-5749	14	4	email	email	NOUN
ejpam-5749	14	5	addresses	address	NOUN
ejpam-5749	14	6	:	:	PUNCT
ejpam-5749	15	1	brayan.bullang@g.msuiit.edu.ph	brayan.bullang@g.msuiit.edu.ph	PROPN
ejpam-5749	15	2	(	(	PUNCT
ejpam-5749	15	3	b.	b.	PROPN
ejpam-5749	15	4	bullang	bullang	PROPN
ejpam-5749	15	5	)	)	PUNCT
ejpam-5749	15	6	,	,	PUNCT
ejpam-5749	15	7	imelda.aniversario@g.msuiit.edu.ph	imelda.aniversario@g.msuiit.edu.ph	PROPN
ejpam-5749	15	8	(	(	PUNCT
ejpam-5749	15	9	i.	i.	PROPN
ejpam-5749	15	10	aniversario	aniversario	PROPN
ejpam-5749	15	11	)	)	PUNCT
ejpam-5749	15	12	,	,	PUNCT
ejpam-5749	15	13	alkajimaradais@msutawi-tawi.edu.ph	alkajimaradais@msutawi-tawi.edu.ph	PROPN
ejpam-5749	15	14	(	(	PUNCT
ejpam-5749	15	15	a.	a.	PROPN
ejpam-5749	15	16	aradais	aradais	PROPN
ejpam-5749	15	17	)	)	PUNCT
ejpam-5749	15	18	,	,	PUNCT
ejpam-5749	15	19	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-5749	15	20	(	(	PUNCT
ejpam-5749	15	21	f.	f.	PROPN
ejpam-5749	15	22	jamil	jamil	PROPN
ejpam-5749	15	23	)	)	PUNCT
ejpam-5749	15	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5749	16	1	1	1	NUM
ejpam-5749	16	2	copyright	copyright	NOUN
ejpam-5749	16	3	:	:	PUNCT
ejpam-5749	16	4	©	©	PROPN
ejpam-5749	16	5	2025	2025	NUM
ejpam-5749	16	6	the	the	DET
ejpam-5749	16	7	author(s	author(s	NOUN
ejpam-5749	16	8	)	)	PUNCT
ejpam-5749	16	9	.	.	PUNCT
ejpam-5749	17	1	(	(	PUNCT
ejpam-5749	17	2	cc	cc	NOUN
ejpam-5749	17	3	by	by	ADP
ejpam-5749	17	4	-	-	PUNCT
ejpam-5749	17	5	nc	nc	PROPN
ejpam-5749	17	6	4.0	4.0	NUM
ejpam-5749	17	7	)	)	PUNCT
ejpam-5749	17	8	b.	b.	PROPN
ejpam-5749	17	9	f.	f.	PROPN
ejpam-5749	17	10	bullang	bullang	PROPN
ejpam-5749	17	11	et	et	PROPN
ejpam-5749	17	12	al	al	PROPN
ejpam-5749	17	13	.	.	PUNCT
ejpam-5749	17	14	/	/	SYM
ejpam-5749	17	15	eur	eur	PROPN
ejpam-5749	17	16	.	.	PUNCT
ejpam-5749	18	1	j.	j.	PROPN
ejpam-5749	18	2	pure	pure	PROPN
ejpam-5749	18	3	appl	appl	PROPN
ejpam-5749	18	4	.	.	PROPN
ejpam-5749	18	5	math	math	PROPN
ejpam-5749	18	6	,	,	PUNCT
ejpam-5749	18	7	18	18	NUM
ejpam-5749	18	8	(	(	PUNCT
ejpam-5749	18	9	1	1	NUM
ejpam-5749	18	10	)	)	PUNCT
ejpam-5749	18	11	(	(	PUNCT
ejpam-5749	18	12	2025	2025	NUM
ejpam-5749	18	13	)	)	PUNCT
ejpam-5749	18	14	,	,	PUNCT
ejpam-5749	18	15	5749	5749	NUM
ejpam-5749	18	16	2	2	NUM
ejpam-5749	18	17	of	of	ADP
ejpam-5749	18	18	15	15	NUM
ejpam-5749	18	19	the	the	DET
ejpam-5749	18	20	semitotal	semitotal	ADJ
ejpam-5749	18	21	domination	domination	NOUN
ejpam-5749	18	22	in	in	ADP
ejpam-5749	18	23	graph	graph	NOUN
ejpam-5749	18	24	was	be	AUX
ejpam-5749	18	25	introduced	introduce	VERB
ejpam-5749	18	26	by	by	ADP
ejpam-5749	18	27	w.	w.	PROPN
ejpam-5749	18	28	goddard	goddard	PROPN
ejpam-5749	18	29	et	et	PROPN
ejpam-5749	18	30	al	al	PROPN
ejpam-5749	18	31	.	.	PUNCT
ejpam-5749	19	1	in	in	ADP
ejpam-5749	19	2	[	[	X
ejpam-5749	19	3	9	9	NUM
ejpam-5749	19	4	]	]	PUNCT
ejpam-5749	19	5	,	,	PUNCT
ejpam-5749	19	6	and	and	CCONJ
ejpam-5749	19	7	it	it	PRON
ejpam-5749	19	8	bridges	bridge	VERB
ejpam-5749	19	9	the	the	DET
ejpam-5749	19	10	gap	gap	NOUN
ejpam-5749	19	11	between	between	ADP
ejpam-5749	19	12	total	total	ADJ
ejpam-5749	19	13	domination	domination	NOUN
ejpam-5749	19	14	and	and	CCONJ
ejpam-5749	19	15	traditional	traditional	ADJ
ejpam-5749	19	16	domination	domination	NOUN
ejpam-5749	19	17	.	.	PUNCT
ejpam-5749	20	1	a	a	DET
ejpam-5749	20	2	semitotal	semitotal	ADJ
ejpam-5749	20	3	dominating	dominating	NOUN
ejpam-5749	20	4	set	set	NOUN
ejpam-5749	20	5	s	s	PART
ejpam-5749	20	6	requires	require	VERB
ejpam-5749	20	7	that	that	SCONJ
ejpam-5749	20	8	s	s	VERB
ejpam-5749	20	9	is	be	AUX
ejpam-5749	20	10	a	a	DET
ejpam-5749	20	11	dominating	dominating	NOUN
ejpam-5749	20	12	set	set	NOUN
ejpam-5749	20	13	,	,	PUNCT
ejpam-5749	20	14	but	but	CCONJ
ejpam-5749	20	15	unlike	unlike	ADP
ejpam-5749	20	16	the	the	DET
ejpam-5749	20	17	total	total	ADJ
ejpam-5749	20	18	domination	domination	NOUN
ejpam-5749	20	19	,	,	PUNCT
ejpam-5749	20	20	only	only	ADV
ejpam-5749	20	21	requires	require	VERB
ejpam-5749	20	22	that	that	SCONJ
ejpam-5749	20	23	each	each	DET
ejpam-5749	20	24	vertex	vertex	NOUN
ejpam-5749	20	25	in	in	ADP
ejpam-5749	20	26	s	s	PROPN
ejpam-5749	20	27	is	be	AUX
ejpam-5749	20	28	of	of	ADP
ejpam-5749	20	29	distance	distance	NOUN
ejpam-5749	20	30	1	1	NUM
ejpam-5749	20	31	or	or	CCONJ
ejpam-5749	20	32	2	2	NUM
ejpam-5749	20	33	from	from	ADP
ejpam-5749	20	34	at	at	ADV
ejpam-5749	20	35	least	least	ADV
ejpam-5749	20	36	one	one	NUM
ejpam-5749	20	37	vertex	vertex	NOUN
ejpam-5749	20	38	in	in	ADP
ejpam-5749	20	39	s.	s.	PROPN
ejpam-5749	20	40	it	it	PRON
ejpam-5749	20	41	has	have	VERB
ejpam-5749	20	42	practical	practical	ADJ
ejpam-5749	20	43	applications	application	NOUN
ejpam-5749	20	44	in	in	ADP
ejpam-5749	20	45	network	network	NOUN
ejpam-5749	20	46	resilience	resilience	NOUN
ejpam-5749	20	47	and	and	CCONJ
ejpam-5749	20	48	communication	communication	NOUN
ejpam-5749	20	49	.	.	PUNCT
ejpam-5749	21	1	roman	roman	ADJ
ejpam-5749	21	2	domination	domination	NOUN
ejpam-5749	21	3	,	,	PUNCT
ejpam-5749	21	4	which	which	PRON
ejpam-5749	21	5	draws	draw	VERB
ejpam-5749	21	6	inspiration	inspiration	NOUN
ejpam-5749	21	7	from	from	ADP
ejpam-5749	21	8	the	the	DET
ejpam-5749	21	9	roman	roman	ADJ
ejpam-5749	21	10	empire	empire	NOUN
ejpam-5749	21	11	’s	’s	PART
ejpam-5749	21	12	defense	defense	NOUN
ejpam-5749	21	13	strategies	strategy	NOUN
ejpam-5749	21	14	,	,	PUNCT
ejpam-5749	21	15	was	be	AUX
ejpam-5749	21	16	introduced	introduce	VERB
ejpam-5749	21	17	in	in	ADP
ejpam-5749	21	18	2004	2004	NUM
ejpam-5749	21	19	by	by	ADP
ejpam-5749	21	20	e.j	e.j	PROPN
ejpam-5749	21	21	.	.	PROPN
ejpam-5749	21	22	cockayne	cockayne	PROPN
ejpam-5749	21	23	et	et	PROPN
ejpam-5749	21	24	al	al	PROPN
ejpam-5749	21	25	.	.	PUNCT
ejpam-5749	22	1	[	[	X
ejpam-5749	22	2	8	8	NUM
ejpam-5749	22	3	]	]	PUNCT
ejpam-5749	22	4	.	.	PUNCT
ejpam-5749	23	1	in	in	ADP
ejpam-5749	23	2	this	this	DET
ejpam-5749	23	3	context	context	NOUN
ejpam-5749	23	4	,	,	PUNCT
ejpam-5749	23	5	a	a	DET
ejpam-5749	23	6	roman	roman	ADJ
ejpam-5749	23	7	dominating	dominating	NOUN
ejpam-5749	23	8	function	function	NOUN
ejpam-5749	23	9	assigns	assign	VERB
ejpam-5749	23	10	weights	weight	NOUN
ejpam-5749	23	11	(	(	PUNCT
ejpam-5749	23	12	0	0	NUM
ejpam-5749	23	13	,	,	PUNCT
ejpam-5749	23	14	1	1	NUM
ejpam-5749	23	15	,	,	PUNCT
ejpam-5749	23	16	or	or	CCONJ
ejpam-5749	23	17	2	2	NUM
ejpam-5749	23	18	)	)	PUNCT
ejpam-5749	23	19	to	to	ADP
ejpam-5749	23	20	the	the	DET
ejpam-5749	23	21	vertices	vertex	NOUN
ejpam-5749	23	22	of	of	ADP
ejpam-5749	23	23	a	a	DET
ejpam-5749	23	24	graph	graph	NOUN
ejpam-5749	23	25	such	such	ADJ
ejpam-5749	23	26	that	that	SCONJ
ejpam-5749	23	27	every	every	DET
ejpam-5749	23	28	vertex	vertex	NOUN
ejpam-5749	23	29	with	with	ADP
ejpam-5749	23	30	weight	weight	NOUN
ejpam-5749	23	31	0	0	NUM
ejpam-5749	23	32	has	have	VERB
ejpam-5749	23	33	an	an	DET
ejpam-5749	23	34	adjacent	adjacent	ADJ
ejpam-5749	23	35	vertex	vertex	NOUN
ejpam-5749	23	36	with	with	ADP
ejpam-5749	23	37	weight	weight	NOUN
ejpam-5749	23	38	2	2	NUM
ejpam-5749	23	39	.	.	PUNCT
ejpam-5749	24	1	it	it	PRON
ejpam-5749	24	2	reflects	reflect	VERB
ejpam-5749	24	3	a	a	DET
ejpam-5749	24	4	scenario	scenario	NOUN
ejpam-5749	24	5	where	where	SCONJ
ejpam-5749	24	6	resources	resource	NOUN
ejpam-5749	24	7	(	(	PUNCT
ejpam-5749	24	8	represented	represent	VERB
ejpam-5749	24	9	by	by	ADP
ejpam-5749	24	10	weights	weight	NOUN
ejpam-5749	24	11	)	)	PUNCT
ejpam-5749	24	12	are	be	AUX
ejpam-5749	24	13	allocated	allocate	VERB
ejpam-5749	24	14	to	to	PART
ejpam-5749	24	15	ensure	ensure	VERB
ejpam-5749	24	16	the	the	DET
ejpam-5749	24	17	protection	protection	NOUN
ejpam-5749	24	18	of	of	ADP
ejpam-5749	24	19	vulnerable	vulnerable	ADJ
ejpam-5749	24	20	nodes	node	NOUN
ejpam-5749	24	21	,	,	PUNCT
ejpam-5749	24	22	offering	offer	VERB
ejpam-5749	24	23	insights	insight	NOUN
ejpam-5749	24	24	into	into	ADP
ejpam-5749	24	25	resource	resource	NOUN
ejpam-5749	24	26	optimization	optimization	NOUN
ejpam-5749	24	27	and	and	CCONJ
ejpam-5749	24	28	strategic	strategic	ADJ
ejpam-5749	24	29	planning	planning	NOUN
ejpam-5749	24	30	in	in	ADP
ejpam-5749	24	31	networks	network	NOUN
ejpam-5749	24	32	.	.	PUNCT
ejpam-5749	25	1	since	since	SCONJ
ejpam-5749	25	2	its	its	PRON
ejpam-5749	25	3	introduction	introduction	NOUN
ejpam-5749	25	4	,	,	PUNCT
ejpam-5749	25	5	roman	roman	ADJ
ejpam-5749	25	6	domination	domination	NOUN
ejpam-5749	25	7	has	have	AUX
ejpam-5749	25	8	become	become	VERB
ejpam-5749	25	9	a	a	DET
ejpam-5749	25	10	very	very	ADV
ejpam-5749	25	11	active	active	ADJ
ejpam-5749	25	12	area	area	NOUN
ejpam-5749	25	13	of	of	ADP
ejpam-5749	25	14	research	research	NOUN
ejpam-5749	25	15	(	(	PUNCT
ejpam-5749	25	16	see	see	VERB
ejpam-5749	25	17	for	for	ADP
ejpam-5749	25	18	example	example	NOUN
ejpam-5749	25	19	[	[	X
ejpam-5749	25	20	1	1	NUM
ejpam-5749	25	21	]	]	PUNCT
ejpam-5749	25	22	,	,	PUNCT
ejpam-5749	25	23	[	[	X
ejpam-5749	25	24	6	6	NUM
ejpam-5749	25	25	]	]	PUNCT
ejpam-5749	25	26	,	,	PUNCT
ejpam-5749	25	27	[	[	X
ejpam-5749	25	28	8	8	NUM
ejpam-5749	25	29	]	]	PUNCT
ejpam-5749	25	30	,	,	PUNCT
ejpam-5749	25	31	[	[	X
ejpam-5749	25	32	11	11	NUM
ejpam-5749	25	33	]	]	PUNCT
ejpam-5749	25	34	,	,	PUNCT
ejpam-5749	25	35	[	[	X
ejpam-5749	25	36	16	16	NUM
ejpam-5749	25	37	]	]	PUNCT
ejpam-5749	25	38	,	,	PUNCT
ejpam-5749	25	39	[	[	X
ejpam-5749	25	40	17	17	NUM
ejpam-5749	25	41	]	]	PUNCT
ejpam-5749	25	42	,	,	PUNCT
ejpam-5749	25	43	[	[	X
ejpam-5749	25	44	18	18	NUM
ejpam-5749	25	45	]	]	NUM
ejpam-5749	25	46	)	)	PUNCT
ejpam-5749	25	47	.	.	PUNCT
ejpam-5749	26	1	part	part	NOUN
ejpam-5749	26	2	of	of	ADP
ejpam-5749	26	3	its	its	PRON
ejpam-5749	26	4	development	development	NOUN
ejpam-5749	26	5	was	be	AUX
ejpam-5749	26	6	the	the	DET
ejpam-5749	26	7	introduction	introduction	NOUN
ejpam-5749	26	8	of	of	ADP
ejpam-5749	26	9	the	the	DET
ejpam-5749	26	10	total	total	ADJ
ejpam-5749	26	11	roman	roman	ADJ
ejpam-5749	26	12	domination	domination	NOUN
ejpam-5749	26	13	in	in	ADP
ejpam-5749	26	14	2016	2016	NUM
ejpam-5749	26	15	by	by	ADP
ejpam-5749	26	16	a.	a.	NOUN
ejpam-5749	26	17	ahangar	ahangar	PROPN
ejpam-5749	26	18	et	et	PROPN
ejpam-5749	26	19	al	al	PROPN
ejpam-5749	26	20	.	.	PUNCT
ejpam-5749	27	1	[	[	X
ejpam-5749	27	2	1	1	NUM
ejpam-5749	27	3	]	]	PUNCT
ejpam-5749	27	4	,	,	PUNCT
ejpam-5749	27	5	some	some	PRON
ejpam-5749	27	6	of	of	ADP
ejpam-5749	27	7	the	the	DET
ejpam-5749	27	8	follow	follow	VERB
ejpam-5749	27	9	-	-	PUNCT
ejpam-5749	27	10	up	up	ADP
ejpam-5749	27	11	studies	study	NOUN
ejpam-5749	27	12	of	of	ADP
ejpam-5749	27	13	which	which	PRON
ejpam-5749	27	14	can	can	AUX
ejpam-5749	27	15	be	be	AUX
ejpam-5749	27	16	found	find	VERB
ejpam-5749	27	17	in	in	ADP
ejpam-5749	27	18	[	[	X
ejpam-5749	27	19	15	15	NUM
ejpam-5749	27	20	]	]	PUNCT
ejpam-5749	27	21	and	and	CCONJ
ejpam-5749	27	22	[	[	X
ejpam-5749	27	23	16	16	NUM
ejpam-5749	27	24	]	]	PUNCT
ejpam-5749	27	25	.	.	PUNCT
ejpam-5749	28	1	in	in	ADP
ejpam-5749	28	2	this	this	DET
ejpam-5749	28	3	paper	paper	NOUN
ejpam-5749	28	4	,	,	PUNCT
ejpam-5749	28	5	we	we	PRON
ejpam-5749	28	6	introduce	introduce	VERB
ejpam-5749	28	7	and	and	CCONJ
ejpam-5749	28	8	initiate	initiate	VERB
ejpam-5749	28	9	the	the	DET
ejpam-5749	28	10	study	study	NOUN
ejpam-5749	28	11	of	of	ADP
ejpam-5749	28	12	the	the	DET
ejpam-5749	28	13	semitotal	semitotal	ADJ
ejpam-5749	28	14	roman	roman	ADJ
ejpam-5749	28	15	domination	domination	NOUN
ejpam-5749	28	16	.	.	PUNCT
ejpam-5749	29	1	we	we	PRON
ejpam-5749	29	2	explore	explore	VERB
ejpam-5749	29	3	graphsg	graphsg	NOUN
ejpam-5749	29	4	with	with	ADP
ejpam-5749	29	5	values	value	NOUN
ejpam-5749	29	6	of	of	ADP
ejpam-5749	29	7	γt2r(g	γt2r(g	NOUN
ejpam-5749	29	8	)	)	PUNCT
ejpam-5749	29	9	equal	equal	ADJ
ejpam-5749	29	10	to	to	ADP
ejpam-5749	29	11	2	2	NUM
ejpam-5749	29	12	,	,	PUNCT
ejpam-5749	29	13	3	3	NUM
ejpam-5749	29	14	or	or	CCONJ
ejpam-5749	29	15	4	4	NUM
ejpam-5749	29	16	,	,	PUNCT
ejpam-5749	29	17	and	and	CCONJ
ejpam-5749	29	18	we	we	PRON
ejpam-5749	29	19	solve	solve	VERB
ejpam-5749	29	20	some	some	DET
ejpam-5749	29	21	realization	realization	NOUN
ejpam-5749	29	22	problems	problem	NOUN
ejpam-5749	29	23	involving	involve	VERB
ejpam-5749	29	24	the	the	DET
ejpam-5749	29	25	concept	concept	NOUN
ejpam-5749	29	26	with	with	ADP
ejpam-5749	29	27	other	other	ADJ
ejpam-5749	29	28	existing	exist	VERB
ejpam-5749	29	29	related	relate	VERB
ejpam-5749	29	30	concepts	concept	NOUN
ejpam-5749	29	31	.	.	PUNCT
ejpam-5749	30	1	we	we	PRON
ejpam-5749	30	2	also	also	ADV
ejpam-5749	30	3	investigate	investigate	VERB
ejpam-5749	30	4	the	the	DET
ejpam-5749	30	5	semitotal	semitotal	ADJ
ejpam-5749	30	6	roman	roman	ADJ
ejpam-5749	30	7	domination	domination	NOUN
ejpam-5749	30	8	in	in	ADP
ejpam-5749	30	9	the	the	DET
ejpam-5749	30	10	join	join	NOUN
ejpam-5749	30	11	,	,	PUNCT
ejpam-5749	30	12	corona	corona	NOUN
ejpam-5749	30	13	and	and	CCONJ
ejpam-5749	30	14	complimentary	complimentary	ADJ
ejpam-5749	30	15	prism	prism	NOUN
ejpam-5749	30	16	of	of	ADP
ejpam-5749	30	17	graphs	graph	NOUN
ejpam-5749	30	18	.	.	PUNCT
ejpam-5749	31	1	all	all	PRON
ejpam-5749	31	2	throughout	throughout	ADP
ejpam-5749	31	3	this	this	DET
ejpam-5749	31	4	paper	paper	NOUN
ejpam-5749	31	5	,	,	PUNCT
ejpam-5749	31	6	by	by	ADP
ejpam-5749	31	7	a	a	DET
ejpam-5749	31	8	graph	graph	NOUN
ejpam-5749	31	9	g	g	NOUN
ejpam-5749	31	10	we	we	PRON
ejpam-5749	31	11	mean	mean	VERB
ejpam-5749	31	12	simple	simple	ADJ
ejpam-5749	31	13	and	and	CCONJ
ejpam-5749	31	14	undirected	undirected	ADJ
ejpam-5749	31	15	.	.	PUNCT
ejpam-5749	32	1	we	we	PRON
ejpam-5749	32	2	refer	refer	VERB
ejpam-5749	32	3	to	to	ADP
ejpam-5749	32	4	[	[	X
ejpam-5749	32	5	5	5	NUM
ejpam-5749	32	6	]	]	PUNCT
ejpam-5749	32	7	for	for	ADP
ejpam-5749	32	8	all	all	DET
ejpam-5749	32	9	graph	graph	NOUN
ejpam-5749	32	10	terminologies	terminology	NOUN
ejpam-5749	32	11	we	we	PRON
ejpam-5749	32	12	used	use	VERB
ejpam-5749	32	13	but	but	CCONJ
ejpam-5749	32	14	are	be	AUX
ejpam-5749	32	15	not	not	PART
ejpam-5749	32	16	defined	define	VERB
ejpam-5749	32	17	here	here	ADV
ejpam-5749	32	18	.	.	PUNCT
ejpam-5749	33	1	as	as	ADP
ejpam-5749	33	2	usual	usual	ADJ
ejpam-5749	33	3	,	,	PUNCT
ejpam-5749	33	4	the	the	DET
ejpam-5749	33	5	symbols	symbol	NOUN
ejpam-5749	33	6	v	v	ADP
ejpam-5749	33	7	(	(	PUNCT
ejpam-5749	33	8	g	g	NOUN
ejpam-5749	33	9	)	)	PUNCT
ejpam-5749	33	10	and	and	CCONJ
ejpam-5749	33	11	e(g	e(g	PROPN
ejpam-5749	33	12	)	)	PUNCT
ejpam-5749	33	13	denote	denote	VERB
ejpam-5749	33	14	the	the	DET
ejpam-5749	33	15	vertex	vertex	NOUN
ejpam-5749	33	16	set	set	NOUN
ejpam-5749	33	17	and	and	CCONJ
ejpam-5749	33	18	edge	edge	NOUN
ejpam-5749	33	19	set	set	NOUN
ejpam-5749	33	20	,	,	PUNCT
ejpam-5749	33	21	respectively	respectively	ADV
ejpam-5749	33	22	,	,	PUNCT
ejpam-5749	33	23	of	of	ADP
ejpam-5749	33	24	g.	g.	NOUN
ejpam-5749	33	25	for	for	ADP
ejpam-5749	33	26	s	s	PROPN
ejpam-5749	33	27	⊆	⊆	NUM
ejpam-5749	33	28	v	v	NOUN
ejpam-5749	33	29	(	(	PUNCT
ejpam-5749	33	30	g	g	NOUN
ejpam-5749	33	31	)	)	PUNCT
ejpam-5749	33	32	,	,	PUNCT
ejpam-5749	33	33	|s|	|s|	PROPN
ejpam-5749	33	34	is	be	AUX
ejpam-5749	33	35	the	the	DET
ejpam-5749	33	36	cardinality	cardinality	NOUN
ejpam-5749	33	37	of	of	ADP
ejpam-5749	33	38	s.	s.	PROPN
ejpam-5749	33	39	in	in	ADP
ejpam-5749	33	40	particular	particular	ADJ
ejpam-5749	33	41	,	,	PUNCT
ejpam-5749	33	42	|v	|v	PROPN
ejpam-5749	33	43	(	(	PUNCT
ejpam-5749	33	44	g)|	g)|	NOUN
ejpam-5749	33	45	and	and	CCONJ
ejpam-5749	33	46	|e(g)|	|e(g)|	PROPN
ejpam-5749	33	47	are	be	AUX
ejpam-5749	33	48	the	the	DET
ejpam-5749	33	49	order	order	NOUN
ejpam-5749	33	50	and	and	CCONJ
ejpam-5749	33	51	size	size	NOUN
ejpam-5749	33	52	,	,	PUNCT
ejpam-5749	33	53	respectively	respectively	ADV
ejpam-5749	33	54	,	,	PUNCT
ejpam-5749	33	55	of	of	ADP
ejpam-5749	33	56	g.	g.	NOUN
ejpam-5749	33	57	given	give	VERB
ejpam-5749	33	58	two	two	NUM
ejpam-5749	33	59	graphs	graph	NOUN
ejpam-5749	33	60	g	g	NOUN
ejpam-5749	33	61	and	and	CCONJ
ejpam-5749	33	62	h	h	NOUN
ejpam-5749	33	63	with	with	ADP
ejpam-5749	33	64	disjoint	disjoint	ADJ
ejpam-5749	33	65	vertex	vertex	NOUN
ejpam-5749	33	66	sets	set	NOUN
ejpam-5749	33	67	,	,	PUNCT
ejpam-5749	33	68	the	the	DET
ejpam-5749	33	69	join	join	NOUN
ejpam-5749	33	70	g+h	g+h	PROPN
ejpam-5749	33	71	of	of	ADP
ejpam-5749	33	72	g	g	PROPN
ejpam-5749	33	73	and	and	CCONJ
ejpam-5749	33	74	h	h	NOUN
ejpam-5749	33	75	is	be	AUX
ejpam-5749	33	76	the	the	DET
ejpam-5749	33	77	graph	graph	NOUN
ejpam-5749	33	78	with	with	ADP
ejpam-5749	33	79	vertex	vertex	NOUN
ejpam-5749	33	80	set	set	VERB
ejpam-5749	33	81	v	v	NOUN
ejpam-5749	33	82	(	(	PUNCT
ejpam-5749	33	83	g)∪v	g)∪v	X
ejpam-5749	33	84	(	(	PUNCT
ejpam-5749	33	85	h	h	NOUN
ejpam-5749	33	86	)	)	PUNCT
ejpam-5749	33	87	and	and	CCONJ
ejpam-5749	33	88	edge	edge	VERB
ejpam-5749	33	89	set	set	VERB
ejpam-5749	33	90	e(g	e(g	NOUN
ejpam-5749	33	91	)	)	PUNCT
ejpam-5749	33	92	∪	∪	ADP
ejpam-5749	33	93	e(h)∪{uv	e(h)∪{uv	NOUN
ejpam-5749	33	94	:	:	PUNCT
ejpam-5749	33	95	u	u	PROPN
ejpam-5749	33	96	∈	∈	PROPN
ejpam-5749	33	97	v	v	ADP
ejpam-5749	33	98	(	(	PUNCT
ejpam-5749	33	99	g	g	NOUN
ejpam-5749	33	100	)	)	PUNCT
ejpam-5749	33	101	and	and	CCONJ
ejpam-5749	33	102	v	v	ADP
ejpam-5749	33	103	∈	∈	PROPN
ejpam-5749	33	104	v	v	NOUN
ejpam-5749	33	105	(	(	PUNCT
ejpam-5749	33	106	h	h	NOUN
ejpam-5749	33	107	)	)	PUNCT
ejpam-5749	33	108	}	}	PUNCT
ejpam-5749	33	109	.	.	PUNCT
ejpam-5749	34	1	the	the	DET
ejpam-5749	34	2	corona	corona	NOUN
ejpam-5749	34	3	g	g	ADP
ejpam-5749	34	4	◦	◦	NOUN
ejpam-5749	34	5	h	h	NOUN
ejpam-5749	34	6	of	of	ADP
ejpam-5749	34	7	graph	graph	NOUN
ejpam-5749	34	8	g	g	PROPN
ejpam-5749	34	9	and	and	CCONJ
ejpam-5749	34	10	h	h	NOUN
ejpam-5749	34	11	is	be	AUX
ejpam-5749	34	12	obtained	obtain	VERB
ejpam-5749	34	13	by	by	ADP
ejpam-5749	34	14	taking	take	VERB
ejpam-5749	34	15	one	one	NUM
ejpam-5749	34	16	copy	copy	NOUN
ejpam-5749	34	17	of	of	ADP
ejpam-5749	34	18	g	g	NOUN
ejpam-5749	34	19	of	of	ADP
ejpam-5749	34	20	order	order	NOUN
ejpam-5749	34	21	n	n	NOUN
ejpam-5749	34	22	and	and	CCONJ
ejpam-5749	34	23	n	n	PRON
ejpam-5749	34	24	copies	copy	NOUN
ejpam-5749	34	25	of	of	ADP
ejpam-5749	34	26	h	h	NOUN
ejpam-5749	34	27	,	,	PUNCT
ejpam-5749	34	28	and	and	CCONJ
ejpam-5749	34	29	then	then	ADV
ejpam-5749	34	30	joining	join	VERB
ejpam-5749	34	31	the	the	DET
ejpam-5749	34	32	ith	ith	PROPN
ejpam-5749	34	33	vertex	vertex	NOUN
ejpam-5749	34	34	of	of	ADP
ejpam-5749	34	35	g	g	NOUN
ejpam-5749	34	36	to	to	ADP
ejpam-5749	34	37	every	every	DET
ejpam-5749	34	38	vertex	vertex	NOUN
ejpam-5749	34	39	of	of	ADP
ejpam-5749	34	40	the	the	DET
ejpam-5749	34	41	ith	ith	PROPN
ejpam-5749	34	42	copy	copy	NOUN
ejpam-5749	34	43	of	of	ADP
ejpam-5749	34	44	h.	h.	PROPN
ejpam-5749	34	45	the	the	DET
ejpam-5749	34	46	complementary	complementary	ADJ
ejpam-5749	34	47	prism	prism	NOUN
ejpam-5749	34	48	,	,	PUNCT
ejpam-5749	34	49	denoted	denote	VERB
ejpam-5749	34	50	gg	gg	NOUN
ejpam-5749	34	51	,	,	PUNCT
ejpam-5749	34	52	is	be	AUX
ejpam-5749	34	53	formed	form	VERB
ejpam-5749	34	54	from	from	ADP
ejpam-5749	34	55	the	the	DET
ejpam-5749	34	56	disjoint	disjoint	PROPN
ejpam-5749	34	57	union	union	NOUN
ejpam-5749	34	58	of	of	ADP
ejpam-5749	34	59	g	g	PROPN
ejpam-5749	34	60	and	and	CCONJ
ejpam-5749	34	61	its	its	PRON
ejpam-5749	34	62	complement	complement	NOUN
ejpam-5749	34	63	g	g	NOUN
ejpam-5749	34	64	by	by	ADP
ejpam-5749	34	65	adding	add	VERB
ejpam-5749	34	66	a	a	DET
ejpam-5749	34	67	perfect	perfect	ADJ
ejpam-5749	34	68	matching	matching	NOUN
ejpam-5749	34	69	between	between	ADP
ejpam-5749	34	70	corresponding	corresponding	ADJ
ejpam-5749	34	71	vertices	vertex	NOUN
ejpam-5749	34	72	of	of	ADP
ejpam-5749	34	73	g	g	PROPN
ejpam-5749	34	74	and	and	CCONJ
ejpam-5749	34	75	g.	g.	NOUN
ejpam-5749	34	76	for	for	ADP
ejpam-5749	34	77	u	u	PROPN
ejpam-5749	34	78	∈	∈	PROPN
ejpam-5749	34	79	v	v	ADP
ejpam-5749	34	80	(	(	PUNCT
ejpam-5749	34	81	g	g	NOUN
ejpam-5749	34	82	)	)	PUNCT
ejpam-5749	34	83	,	,	PUNCT
ejpam-5749	34	84	the	the	DET
ejpam-5749	34	85	open	open	ADJ
ejpam-5749	34	86	neighborhood	neighborhood	NOUN
ejpam-5749	34	87	of	of	ADP
ejpam-5749	34	88	u	u	NOUN
ejpam-5749	34	89	is	be	AUX
ejpam-5749	34	90	the	the	DET
ejpam-5749	34	91	set	set	NOUN
ejpam-5749	34	92	ng(u	ng(u	NOUN
ejpam-5749	34	93	)	)	PUNCT
ejpam-5749	34	94	of	of	ADP
ejpam-5749	34	95	all	all	DET
ejpam-5749	34	96	vertices	vertex	NOUN
ejpam-5749	34	97	adjacent	adjacent	ADJ
ejpam-5749	34	98	to	to	PART
ejpam-5749	34	99	u.	u.	VERB
ejpam-5749	34	100	the	the	DET
ejpam-5749	34	101	closed	closed	ADJ
ejpam-5749	34	102	neighborhood	neighborhood	NOUN
ejpam-5749	34	103	of	of	ADP
ejpam-5749	34	104	u	u	NOUN
ejpam-5749	34	105	in	in	ADP
ejpam-5749	34	106	g	g	PROPN
ejpam-5749	34	107	is	be	AUX
ejpam-5749	34	108	the	the	DET
ejpam-5749	34	109	set	set	NOUN
ejpam-5749	34	110	ng[u	ng[u	PROPN
ejpam-5749	34	111	]	]	X
ejpam-5749	34	112	=	=	SYM
ejpam-5749	34	113	ng(u	ng(u	PROPN
ejpam-5749	34	114	)	)	PUNCT
ejpam-5749	34	115	∪	∪	NOUN
ejpam-5749	34	116	{	{	PUNCT
ejpam-5749	34	117	u	u	NOUN
ejpam-5749	34	118	}	}	PUNCT
ejpam-5749	34	119	.	.	PUNCT
ejpam-5749	35	1	for	for	ADP
ejpam-5749	35	2	s	s	PROPN
ejpam-5749	35	3	⊆	⊆	NUM
ejpam-5749	35	4	v	v	NOUN
ejpam-5749	35	5	(	(	PUNCT
ejpam-5749	35	6	g),the	g),the	X
ejpam-5749	35	7	open	open	ADJ
ejpam-5749	35	8	neighborhood	neighborhood	NOUN
ejpam-5749	35	9	of	of	ADP
ejpam-5749	35	10	s	s	NOUN
ejpam-5749	35	11	is	be	AUX
ejpam-5749	35	12	the	the	DET
ejpam-5749	35	13	set	set	NOUN
ejpam-5749	35	14	ng(s	ng(s	NOUN
ejpam-5749	35	15	)	)	PUNCT
ejpam-5749	35	16	=	=	SYM
ejpam-5749	35	17	∪u∈sng(u	∪u∈sng(u	PROPN
ejpam-5749	35	18	)	)	PUNCT
ejpam-5749	35	19	.	.	PUNCT
ejpam-5749	36	1	the	the	DET
ejpam-5749	36	2	closed	closed	ADJ
ejpam-5749	36	3	neighborhood	neighborhood	NOUN
ejpam-5749	36	4	of	of	ADP
ejpam-5749	36	5	s	s	NOUN
ejpam-5749	36	6	is	be	AUX
ejpam-5749	36	7	the	the	DET
ejpam-5749	36	8	set	set	ADJ
ejpam-5749	36	9	ng[s	ng[	NOUN
ejpam-5749	36	10	]	]	PUNCT
ejpam-5749	36	11	=	=	SYM
ejpam-5749	36	12	ng(s	ng(s	X
ejpam-5749	36	13	)	)	PUNCT
ejpam-5749	36	14	∪	∪	ADP
ejpam-5749	36	15	s.	s.	PROPN
ejpam-5749	36	16	a	a	DET
ejpam-5749	36	17	set	set	NOUN
ejpam-5749	36	18	s	s	PROPN
ejpam-5749	36	19	⊆	⊆	NUM
ejpam-5749	36	20	v	v	NOUN
ejpam-5749	36	21	(	(	PUNCT
ejpam-5749	36	22	g	g	NOUN
ejpam-5749	36	23	)	)	PUNCT
ejpam-5749	36	24	is	be	AUX
ejpam-5749	36	25	a	a	DET
ejpam-5749	36	26	dominating	dominating	NOUN
ejpam-5749	36	27	set	set	VERB
ejpam-5749	36	28	in	in	ADP
ejpam-5749	36	29	g	g	PROPN
ejpam-5749	36	30	if	if	SCONJ
ejpam-5749	36	31	ng[s	ng[	NOUN
ejpam-5749	36	32	]	]	PUNCT
ejpam-5749	36	33	=	=	SYM
ejpam-5749	36	34	v	v	NOUN
ejpam-5749	36	35	(	(	PUNCT
ejpam-5749	36	36	g	g	NOUN
ejpam-5749	36	37	)	)	PUNCT
ejpam-5749	36	38	.	.	PUNCT
ejpam-5749	37	1	the	the	DET
ejpam-5749	37	2	minimum	minimum	ADJ
ejpam-5749	37	3	cardinality	cardinality	NOUN
ejpam-5749	37	4	of	of	ADP
ejpam-5749	37	5	a	a	DET
ejpam-5749	37	6	dominating	dominating	NOUN
ejpam-5749	37	7	set	set	NOUN
ejpam-5749	37	8	in	in	ADP
ejpam-5749	37	9	g	g	NOUN
ejpam-5749	37	10	,	,	PUNCT
ejpam-5749	37	11	denoted	denote	VERB
ejpam-5749	37	12	by	by	ADP
ejpam-5749	37	13	γ(g	γ(g	PROPN
ejpam-5749	37	14	)	)	PUNCT
ejpam-5749	37	15	,	,	PUNCT
ejpam-5749	37	16	is	be	AUX
ejpam-5749	37	17	the	the	DET
ejpam-5749	37	18	domination	domination	NOUN
ejpam-5749	37	19	number	number	NOUN
ejpam-5749	37	20	of	of	ADP
ejpam-5749	37	21	g.	g.	PROPN
ejpam-5749	37	22	a	a	DET
ejpam-5749	37	23	dominating	dominating	NOUN
ejpam-5749	37	24	set	set	NOUN
ejpam-5749	37	25	s	s	NOUN
ejpam-5749	37	26	of	of	ADP
ejpam-5749	37	27	g	g	NOUN
ejpam-5749	37	28	with	with	ADP
ejpam-5749	37	29	|s|	|s|	PROPN
ejpam-5749	37	30	=	=	SYM
ejpam-5749	37	31	γ(g	γ(g	PROPN
ejpam-5749	37	32	)	)	PUNCT
ejpam-5749	37	33	is	be	AUX
ejpam-5749	37	34	called	call	VERB
ejpam-5749	37	35	a	a	DET
ejpam-5749	37	36	γ	γ	NOUN
ejpam-5749	37	37	-	-	PUNCT
ejpam-5749	37	38	set	set	NOUN
ejpam-5749	37	39	of	of	ADP
ejpam-5749	37	40	g.	g.	PROPN
ejpam-5749	37	41	the	the	DET
ejpam-5749	37	42	authors	author	NOUN
ejpam-5749	37	43	always	always	ADV
ejpam-5749	37	44	refer	refer	VERB
ejpam-5749	37	45	to	to	ADP
ejpam-5749	37	46	[	[	X
ejpam-5749	37	47	4	4	X
ejpam-5749	37	48	]	]	PUNCT
ejpam-5749	37	49	for	for	ADP
ejpam-5749	37	50	the	the	DET
ejpam-5749	37	51	introduction	introduction	NOUN
ejpam-5749	37	52	and	and	CCONJ
ejpam-5749	37	53	more	more	ADV
ejpam-5749	37	54	comprehensive	comprehensive	ADJ
ejpam-5749	37	55	discussion	discussion	NOUN
ejpam-5749	37	56	of	of	ADP
ejpam-5749	37	57	the	the	DET
ejpam-5749	37	58	development	development	NOUN
ejpam-5749	37	59	of	of	ADP
ejpam-5749	37	60	the	the	DET
ejpam-5749	37	61	concept	concept	NOUN
ejpam-5749	37	62	of	of	ADP
ejpam-5749	37	63	domination	domination	NOUN
ejpam-5749	37	64	in	in	ADP
ejpam-5749	37	65	graphs	graph	NOUN
ejpam-5749	37	66	.	.	PUNCT
ejpam-5749	38	1	provided	provide	VERB
ejpam-5749	38	2	that	that	SCONJ
ejpam-5749	38	3	g	g	PROPN
ejpam-5749	38	4	has	have	VERB
ejpam-5749	38	5	no	no	DET
ejpam-5749	38	6	isolated	isolated	ADJ
ejpam-5749	38	7	vertices	vertex	NOUN
ejpam-5749	38	8	,	,	PUNCT
ejpam-5749	38	9	a	a	DET
ejpam-5749	38	10	set	set	NOUN
ejpam-5749	38	11	s	s	NOUN
ejpam-5749	38	12	⊆	⊆	NUM
ejpam-5749	38	13	v	v	NOUN
ejpam-5749	38	14	(	(	PUNCT
ejpam-5749	38	15	g	g	NOUN
ejpam-5749	38	16	)	)	PUNCT
ejpam-5749	38	17	is	be	AUX
ejpam-5749	38	18	a	a	DET
ejpam-5749	38	19	total	total	ADJ
ejpam-5749	38	20	dominating	dominating	NOUN
ejpam-5749	38	21	set	set	VERB
ejpam-5749	38	22	in	in	ADP
ejpam-5749	38	23	g	g	PROPN
ejpam-5749	38	24	if	if	SCONJ
ejpam-5749	38	25	for	for	ADP
ejpam-5749	38	26	every	every	DET
ejpam-5749	38	27	v	v	NUM
ejpam-5749	38	28	∈	∈	NOUN
ejpam-5749	38	29	v	v	NOUN
ejpam-5749	38	30	(	(	PUNCT
ejpam-5749	38	31	g	g	NOUN
ejpam-5749	38	32	)	)	PUNCT
ejpam-5749	38	33	,	,	PUNCT
ejpam-5749	38	34	there	there	PRON
ejpam-5749	38	35	exists	exist	VERB
ejpam-5749	38	36	u	u	PROPN
ejpam-5749	38	37	∈	∈	PROPN
ejpam-5749	38	38	s	s	VERB
ejpam-5749	38	39	such	such	ADJ
ejpam-5749	38	40	that	that	DET
ejpam-5749	38	41	uv	uv	PROPN
ejpam-5749	38	42	∈	∈	PROPN
ejpam-5749	38	43	e(g	e(g	PROPN
ejpam-5749	38	44	)	)	PUNCT
ejpam-5749	38	45	.	.	PUNCT
ejpam-5749	39	1	the	the	DET
ejpam-5749	39	2	minimum	minimum	PROPN
ejpam-5749	39	3	cardinality	cardinality	PROPN
ejpam-5749	39	4	b.	b.	PROPN
ejpam-5749	39	5	f.	f.	PROPN
ejpam-5749	39	6	bullang	bullang	PROPN
ejpam-5749	39	7	et	et	PROPN
ejpam-5749	39	8	al	al	PROPN
ejpam-5749	39	9	.	.	PUNCT
ejpam-5749	39	10	/	/	SYM
ejpam-5749	39	11	eur	eur	PROPN
ejpam-5749	39	12	.	.	PUNCT
ejpam-5749	40	1	j.	j.	PROPN
ejpam-5749	40	2	pure	pure	PROPN
ejpam-5749	40	3	appl	appl	PROPN
ejpam-5749	40	4	.	.	PROPN
ejpam-5749	40	5	math	math	PROPN
ejpam-5749	40	6	,	,	PUNCT
ejpam-5749	40	7	18	18	NUM
ejpam-5749	40	8	(	(	PUNCT
ejpam-5749	40	9	1	1	NUM
ejpam-5749	40	10	)	)	PUNCT
ejpam-5749	40	11	(	(	PUNCT
ejpam-5749	40	12	2025	2025	NUM
ejpam-5749	40	13	)	)	PUNCT
ejpam-5749	40	14	,	,	PUNCT
ejpam-5749	40	15	5749	5749	NUM
ejpam-5749	40	16	3	3	NUM
ejpam-5749	40	17	of	of	ADP
ejpam-5749	40	18	15	15	NUM
ejpam-5749	40	19	of	of	ADP
ejpam-5749	40	20	a	a	DET
ejpam-5749	40	21	total	total	ADJ
ejpam-5749	40	22	dominating	dominating	NOUN
ejpam-5749	40	23	set	set	NOUN
ejpam-5749	40	24	in	in	ADP
ejpam-5749	40	25	g	g	NOUN
ejpam-5749	40	26	,	,	PUNCT
ejpam-5749	40	27	denoted	denote	VERB
ejpam-5749	40	28	by	by	ADP
ejpam-5749	40	29	γt(g	γt(g	NOUN
ejpam-5749	40	30	)	)	PUNCT
ejpam-5749	40	31	,	,	PUNCT
ejpam-5749	40	32	is	be	AUX
ejpam-5749	40	33	the	the	DET
ejpam-5749	40	34	total	total	ADJ
ejpam-5749	40	35	domination	domination	NOUN
ejpam-5749	40	36	number	number	NOUN
ejpam-5749	40	37	of	of	ADP
ejpam-5749	40	38	g.	g.	PROPN
ejpam-5749	40	39	a	a	DET
ejpam-5749	40	40	total	total	ADJ
ejpam-5749	40	41	dominating	dominating	NOUN
ejpam-5749	40	42	set	set	NOUN
ejpam-5749	40	43	s	s	VERB
ejpam-5749	40	44	in	in	ADP
ejpam-5749	40	45	g	g	NOUN
ejpam-5749	40	46	with	with	ADP
ejpam-5749	40	47	|s|	|s|	NOUN
ejpam-5749	40	48	=	=	SYM
ejpam-5749	40	49	γt(g	γt(g	X
ejpam-5749	40	50	)	)	PUNCT
ejpam-5749	40	51	is	be	AUX
ejpam-5749	40	52	called	call	VERB
ejpam-5749	40	53	a	a	DET
ejpam-5749	40	54	γt	γt	NOUN
ejpam-5749	40	55	-	-	NOUN
ejpam-5749	40	56	set	set	NOUN
ejpam-5749	40	57	of	of	ADP
ejpam-5749	40	58	g.	g.	PROPN
ejpam-5749	40	59	m.	m.	PROPN
ejpam-5749	40	60	henning	henning	PROPN
ejpam-5749	40	61	and	and	CCONJ
ejpam-5749	40	62	a.	a.	PROPN
ejpam-5749	40	63	yeo	yeo	PROPN
ejpam-5749	40	64	provides	provide	VERB
ejpam-5749	40	65	in	in	ADP
ejpam-5749	40	66	[	[	X
ejpam-5749	40	67	12	12	NUM
ejpam-5749	40	68	]	]	PUNCT
ejpam-5749	40	69	a	a	DET
ejpam-5749	40	70	very	very	ADV
ejpam-5749	40	71	comprehensive	comprehensive	ADJ
ejpam-5749	40	72	discussion	discussion	NOUN
ejpam-5749	40	73	of	of	ADP
ejpam-5749	40	74	total	total	ADJ
ejpam-5749	40	75	domination	domination	NOUN
ejpam-5749	40	76	,	,	PUNCT
ejpam-5749	40	77	including	include	VERB
ejpam-5749	40	78	its	its	PRON
ejpam-5749	40	79	history	history	NOUN
ejpam-5749	40	80	and	and	CCONJ
ejpam-5749	40	81	the	the	DET
ejpam-5749	40	82	succeeding	succeed	VERB
ejpam-5749	40	83	developments	development	NOUN
ejpam-5749	40	84	.	.	PUNCT
ejpam-5749	41	1	a	a	DET
ejpam-5749	41	2	set	set	NOUN
ejpam-5749	41	3	s	s	NOUN
ejpam-5749	41	4	⊆	⊆	NUM
ejpam-5749	41	5	v	v	NOUN
ejpam-5749	41	6	(	(	PUNCT
ejpam-5749	41	7	g	g	NOUN
ejpam-5749	41	8	)	)	PUNCT
ejpam-5749	41	9	is	be	AUX
ejpam-5749	41	10	a	a	DET
ejpam-5749	41	11	semitotal	semitotal	ADJ
ejpam-5749	41	12	dominating	dominating	NOUN
ejpam-5749	41	13	set	set	NOUN
ejpam-5749	41	14	in	in	ADP
ejpam-5749	41	15	g	g	PROPN
ejpam-5749	41	16	if	if	SCONJ
ejpam-5749	41	17	s	s	VERB
ejpam-5749	41	18	is	be	AUX
ejpam-5749	41	19	a	a	DET
ejpam-5749	41	20	dominating	dominating	NOUN
ejpam-5749	41	21	set	set	VERB
ejpam-5749	41	22	in	in	ADP
ejpam-5749	41	23	g	g	PROPN
ejpam-5749	41	24	such	such	ADJ
ejpam-5749	41	25	that	that	PRON
ejpam-5749	41	26	for	for	ADP
ejpam-5749	41	27	every	every	DET
ejpam-5749	41	28	x	x	SYM
ejpam-5749	41	29	∈	∈	PROPN
ejpam-5749	41	30	s	s	NOUN
ejpam-5749	41	31	,	,	PUNCT
ejpam-5749	41	32	there	there	PRON
ejpam-5749	41	33	exists	exist	VERB
ejpam-5749	41	34	y	y	PROPN
ejpam-5749	41	35	∈	∈	PROPN
ejpam-5749	41	36	s\{x	s\{x	PROPN
ejpam-5749	41	37	}	}	PUNCT
ejpam-5749	41	38	for	for	ADP
ejpam-5749	41	39	which	which	PRON
ejpam-5749	41	40	dg(x	dg(x	NUM
ejpam-5749	41	41	,	,	PUNCT
ejpam-5749	41	42	y	y	NOUN
ejpam-5749	41	43	)	)	PUNCT
ejpam-5749	41	44	≤	≤	NOUN
ejpam-5749	41	45	2	2	NUM
ejpam-5749	41	46	.	.	PUNCT
ejpam-5749	41	47	the	the	DET
ejpam-5749	41	48	smallest	small	ADJ
ejpam-5749	41	49	cardinality	cardinality	NOUN
ejpam-5749	41	50	of	of	ADP
ejpam-5749	41	51	a	a	DET
ejpam-5749	41	52	semitotal	semitotal	ADJ
ejpam-5749	41	53	dominating	dominating	NOUN
ejpam-5749	41	54	set	set	NOUN
ejpam-5749	41	55	in	in	ADP
ejpam-5749	41	56	g	g	NOUN
ejpam-5749	41	57	,	,	PUNCT
ejpam-5749	41	58	denoted	denote	VERB
ejpam-5749	41	59	by	by	ADP
ejpam-5749	41	60	γt2(g	γt2(g	PROPN
ejpam-5749	41	61	)	)	PUNCT
ejpam-5749	41	62	,	,	PUNCT
ejpam-5749	41	63	is	be	AUX
ejpam-5749	41	64	called	call	VERB
ejpam-5749	41	65	a	a	DET
ejpam-5749	41	66	semitotal	semitotal	ADJ
ejpam-5749	41	67	domination	domination	NOUN
ejpam-5749	41	68	number	number	NOUN
ejpam-5749	41	69	in	in	ADP
ejpam-5749	41	70	g.	g.	PROPN
ejpam-5749	41	71	a	a	DET
ejpam-5749	41	72	semitotal	semitotal	ADJ
ejpam-5749	41	73	dominating	dominating	NOUN
ejpam-5749	41	74	set	set	NOUN
ejpam-5749	41	75	s	s	VERB
ejpam-5749	41	76	in	in	ADP
ejpam-5749	41	77	g	g	NOUN
ejpam-5749	41	78	with	with	ADP
ejpam-5749	41	79	cardinality	cardinality	NOUN
ejpam-5749	41	80	γt2(g	γt2(g	PROPN
ejpam-5749	41	81	)	)	PUNCT
ejpam-5749	41	82	is	be	AUX
ejpam-5749	41	83	called	call	VERB
ejpam-5749	41	84	a	a	DET
ejpam-5749	41	85	γt2	γt2	NOUN
ejpam-5749	41	86	-	-	PUNCT
ejpam-5749	41	87	set	set	NOUN
ejpam-5749	41	88	of	of	ADP
ejpam-5749	41	89	g.	g.	PROPN
ejpam-5749	41	90	it	it	PRON
ejpam-5749	41	91	was	be	AUX
ejpam-5749	41	92	introduced	introduce	VERB
ejpam-5749	41	93	in	in	ADP
ejpam-5749	41	94	[	[	X
ejpam-5749	41	95	9	9	NUM
ejpam-5749	41	96	]	]	PUNCT
ejpam-5749	41	97	and	and	CCONJ
ejpam-5749	41	98	further	far	ADV
ejpam-5749	41	99	studied	study	VERB
ejpam-5749	41	100	in	in	ADP
ejpam-5749	41	101	[	[	X
ejpam-5749	41	102	1	1	NUM
ejpam-5749	41	103	,	,	PUNCT
ejpam-5749	41	104	10	10	NUM
ejpam-5749	41	105	,	,	PUNCT
ejpam-5749	41	106	13	13	NUM
ejpam-5749	41	107	,	,	PUNCT
ejpam-5749	41	108	14	14	NUM
ejpam-5749	41	109	,	,	PUNCT
ejpam-5749	41	110	16	16	NUM
ejpam-5749	41	111	]	]	PUNCT
ejpam-5749	41	112	.	.	PUNCT
ejpam-5749	42	1	a	a	DET
ejpam-5749	42	2	roman	roman	ADJ
ejpam-5749	42	3	dominating	dominating	NOUN
ejpam-5749	42	4	function	function	NOUN
ejpam-5749	42	5	(	(	PUNCT
ejpam-5749	42	6	rdf	rdf	NOUN
ejpam-5749	42	7	)	)	PUNCT
ejpam-5749	42	8	of	of	ADP
ejpam-5749	42	9	g	g	PROPN
ejpam-5749	42	10	is	be	AUX
ejpam-5749	42	11	a	a	DET
ejpam-5749	42	12	function	function	NOUN
ejpam-5749	42	13	f	f	NOUN
ejpam-5749	42	14	:	:	PUNCT
ejpam-5749	42	15	v	v	X
ejpam-5749	42	16	(	(	PUNCT
ejpam-5749	42	17	g	g	NOUN
ejpam-5749	42	18	)	)	PUNCT
ejpam-5749	42	19	→	→	SYM
ejpam-5749	42	20	{	{	PUNCT
ejpam-5749	42	21	0	0	NUM
ejpam-5749	42	22	,	,	PUNCT
ejpam-5749	42	23	1	1	NUM
ejpam-5749	42	24	,	,	PUNCT
ejpam-5749	42	25	2	2	NUM
ejpam-5749	42	26	}	}	PUNCT
ejpam-5749	42	27	such	such	ADJ
ejpam-5749	42	28	that	that	SCONJ
ejpam-5749	42	29	every	every	DET
ejpam-5749	42	30	vertex	vertex	NOUN
ejpam-5749	42	31	u	u	NOUN
ejpam-5749	42	32	∈	∈	PROPN
ejpam-5749	42	33	v	v	ADP
ejpam-5749	42	34	(	(	PUNCT
ejpam-5749	42	35	g	g	NOUN
ejpam-5749	42	36	)	)	PUNCT
ejpam-5749	42	37	for	for	ADP
ejpam-5749	42	38	which	which	PRON
ejpam-5749	42	39	f(u	f(u	PROPN
ejpam-5749	42	40	)	)	PUNCT
ejpam-5749	43	1	=	=	SYM
ejpam-5749	43	2	0	0	NUM
ejpam-5749	43	3	is	be	AUX
ejpam-5749	43	4	adjacent	adjacent	ADJ
ejpam-5749	43	5	to	to	ADP
ejpam-5749	43	6	at	at	ADV
ejpam-5749	43	7	least	least	ADV
ejpam-5749	43	8	one	one	NUM
ejpam-5749	43	9	vertex	vertex	NOUN
ejpam-5749	43	10	v	v	NOUN
ejpam-5749	43	11	for	for	ADP
ejpam-5749	43	12	which	which	PRON
ejpam-5749	43	13	f(v	f(v	NOUN
ejpam-5749	43	14	)	)	PUNCT
ejpam-5749	43	15	=	=	SYM
ejpam-5749	43	16	2	2	X
ejpam-5749	43	17	.	.	PUNCT
ejpam-5749	43	18	provided	provide	VERB
ejpam-5749	43	19	g	g	PROPN
ejpam-5749	43	20	has	have	VERB
ejpam-5749	43	21	no	no	DET
ejpam-5749	43	22	isolated	isolated	ADJ
ejpam-5749	43	23	vertices	vertex	NOUN
ejpam-5749	43	24	,	,	PUNCT
ejpam-5749	43	25	a	a	DET
ejpam-5749	43	26	total	total	ADJ
ejpam-5749	43	27	roman	roman	ADJ
ejpam-5749	43	28	dominating	dominating	NOUN
ejpam-5749	43	29	function	function	NOUN
ejpam-5749	43	30	of	of	ADP
ejpam-5749	43	31	g	g	PROPN
ejpam-5749	43	32	is	be	AUX
ejpam-5749	43	33	a	a	DET
ejpam-5749	43	34	dominating	dominate	VERB
ejpam-5749	43	35	roman	roman	ADJ
ejpam-5749	43	36	function	function	NOUN
ejpam-5749	44	1	f	f	NOUN
ejpam-5749	44	2	:	:	PUNCT
ejpam-5749	44	3	v	v	X
ejpam-5749	44	4	(	(	PUNCT
ejpam-5749	44	5	g	g	NOUN
ejpam-5749	44	6	)	)	PUNCT
ejpam-5749	44	7	→	→	SYM
ejpam-5749	44	8	{	{	PUNCT
ejpam-5749	44	9	0	0	NUM
ejpam-5749	44	10	,	,	PUNCT
ejpam-5749	44	11	1	1	NUM
ejpam-5749	44	12	,	,	PUNCT
ejpam-5749	44	13	2	2	NUM
ejpam-5749	44	14	}	}	PUNCT
ejpam-5749	44	15	such	such	ADJ
ejpam-5749	44	16	that	that	PRON
ejpam-5749	44	17	for	for	ADP
ejpam-5749	44	18	every	every	DET
ejpam-5749	44	19	v	v	NUM
ejpam-5749	44	20	∈	∈	PROPN
ejpam-5749	44	21	v	v	NOUN
ejpam-5749	44	22	(	(	PUNCT
ejpam-5749	44	23	g	g	NOUN
ejpam-5749	44	24	)	)	PUNCT
ejpam-5749	44	25	with	with	ADP
ejpam-5749	44	26	f(v	f(v	NOUN
ejpam-5749	44	27	)	)	PUNCT
ejpam-5749	44	28	̸=	̸=	PROPN
ejpam-5749	44	29	0	0	NUM
ejpam-5749	44	30	,	,	PUNCT
ejpam-5749	44	31	there	there	PRON
ejpam-5749	44	32	exists	exist	VERB
ejpam-5749	44	33	u	u	PROPN
ejpam-5749	44	34	∈	∈	PROPN
ejpam-5749	44	35	v	v	ADP
ejpam-5749	44	36	(	(	PUNCT
ejpam-5749	44	37	g	g	NOUN
ejpam-5749	44	38	)	)	PUNCT
ejpam-5749	44	39	with	with	ADP
ejpam-5749	44	40	f(u	f(u	PROPN
ejpam-5749	44	41	)	)	PUNCT
ejpam-5749	44	42	̸=	̸=	PROPN
ejpam-5749	44	43	0	0	NUM
ejpam-5749	45	1	and	and	CCONJ
ejpam-5749	45	2	uv	uv	NOUN
ejpam-5749	45	3	∈	∈	PROPN
ejpam-5749	45	4	v	v	ADP
ejpam-5749	45	5	(	(	PUNCT
ejpam-5749	45	6	g	g	NOUN
ejpam-5749	45	7	)	)	PUNCT
ejpam-5749	45	8	.	.	PUNCT
ejpam-5749	46	1	the	the	DET
ejpam-5749	46	2	roman	roman	ADJ
ejpam-5749	46	3	domination	domination	NOUN
ejpam-5749	46	4	number	number	NOUN
ejpam-5749	46	5	(	(	PUNCT
ejpam-5749	46	6	resp	resp	NOUN
ejpam-5749	46	7	.	.	PUNCT
ejpam-5749	47	1	total	total	ADJ
ejpam-5749	47	2	roman	roman	ADJ
ejpam-5749	47	3	domination	domination	NOUN
ejpam-5749	47	4	number	number	NOUN
ejpam-5749	47	5	)	)	PUNCT
ejpam-5749	47	6	of	of	ADP
ejpam-5749	47	7	g	g	PROPN
ejpam-5749	47	8	is	be	AUX
ejpam-5749	47	9	the	the	DET
ejpam-5749	47	10	minimum	minimum	ADJ
ejpam-5749	47	11	weight	weight	NOUN
ejpam-5749	47	12	ωg(f	ωg(f	PRON
ejpam-5749	47	13	)	)	PUNCT
ejpam-5749	47	14	=	=	SYM
ejpam-5749	47	15	∑	∑	PUNCT
ejpam-5749	47	16	v∈v	v∈v	PROPN
ejpam-5749	47	17	(	(	PUNCT
ejpam-5749	47	18	g	g	NOUN
ejpam-5749	47	19	)	)	PUNCT
ejpam-5749	47	20	f(v	f(v	NOUN
ejpam-5749	47	21	)	)	PUNCT
ejpam-5749	47	22	of	of	ADP
ejpam-5749	47	23	an	an	DET
ejpam-5749	47	24	rdf	rdf	NOUN
ejpam-5749	47	25	(	(	PUNCT
ejpam-5749	47	26	resp	resp	NOUN
ejpam-5749	47	27	.	.	PUNCT
ejpam-5749	48	1	trdf	trdf	PROPN
ejpam-5749	48	2	)	)	PUNCT
ejpam-5749	48	3	of	of	ADP
ejpam-5749	48	4	g.	g.	PROPN
ejpam-5749	49	1	we	we	PRON
ejpam-5749	49	2	write	write	VERB
ejpam-5749	49	3	f	f	PROPN
ejpam-5749	49	4	∈	∈	PROPN
ejpam-5749	49	5	rdf	rdf	NOUN
ejpam-5749	49	6	(	(	PUNCT
ejpam-5749	49	7	g	g	NOUN
ejpam-5749	49	8	)	)	PUNCT
ejpam-5749	49	9	and	and	CCONJ
ejpam-5749	49	10	f	f	PROPN
ejpam-5749	49	11	∈	∈	PROPN
ejpam-5749	49	12	trdf	trdf	PROPN
ejpam-5749	49	13	(	(	PUNCT
ejpam-5749	49	14	g	g	NOUN
ejpam-5749	49	15	)	)	PUNCT
ejpam-5749	49	16	to	to	PART
ejpam-5749	49	17	mean	mean	VERB
ejpam-5749	49	18	that	that	SCONJ
ejpam-5749	49	19	f	f	PROPN
ejpam-5749	49	20	is	be	AUX
ejpam-5749	49	21	an	an	DET
ejpam-5749	49	22	rdf	rdf	NOUN
ejpam-5749	49	23	and	and	CCONJ
ejpam-5749	49	24	trdf	trdf	NOUN
ejpam-5749	49	25	,	,	PUNCT
ejpam-5749	49	26	respectively	respectively	ADV
ejpam-5749	49	27	,	,	PUNCT
ejpam-5749	49	28	of	of	ADP
ejpam-5749	49	29	g.	g.	PROPN
ejpam-5749	49	30	an	an	DET
ejpam-5749	49	31	rdf	rdf	NOUN
ejpam-5749	49	32	(	(	PUNCT
ejpam-5749	49	33	resp	resp	NOUN
ejpam-5749	49	34	.	.	PUNCT
ejpam-5749	50	1	trdf	trdf	PROPN
ejpam-5749	50	2	)	)	PUNCT
ejpam-5749	50	3	with	with	ADP
ejpam-5749	50	4	ωg(f	ωg(f	NOUN
ejpam-5749	50	5	)	)	PUNCT
ejpam-5749	50	6	=	=	SYM
ejpam-5749	50	7	γr(g	γr(g	NOUN
ejpam-5749	50	8	)	)	PUNCT
ejpam-5749	50	9	is	be	AUX
ejpam-5749	50	10	referred	refer	VERB
ejpam-5749	50	11	to	to	ADP
ejpam-5749	50	12	as	as	ADP
ejpam-5749	50	13	a	a	DET
ejpam-5749	50	14	γr	γr	NOUN
ejpam-5749	50	15	-	-	PUNCT
ejpam-5749	50	16	function	function	NOUN
ejpam-5749	50	17	(	(	PUNCT
ejpam-5749	50	18	resp	resp	NOUN
ejpam-5749	50	19	.	.	PUNCT
ejpam-5749	51	1	γtr	γtr	NOUN
ejpam-5749	51	2	-	-	PUNCT
ejpam-5749	51	3	function	function	NOUN
ejpam-5749	51	4	)	)	PUNCT
ejpam-5749	51	5	of	of	ADP
ejpam-5749	51	6	g.	g.	PROPN
ejpam-5749	51	7	2	2	NUM
ejpam-5749	51	8	.	.	PUNCT
ejpam-5749	52	1	the	the	DET
ejpam-5749	52	2	semitotal	semitotal	ADJ
ejpam-5749	52	3	roman	roman	ADJ
ejpam-5749	52	4	domination	domination	NOUN
ejpam-5749	52	5	we	we	PRON
ejpam-5749	52	6	start	start	VERB
ejpam-5749	52	7	by	by	ADP
ejpam-5749	52	8	introducing	introduce	VERB
ejpam-5749	52	9	a	a	DET
ejpam-5749	52	10	semitotal	semitotal	ADJ
ejpam-5749	52	11	roman	roman	ADJ
ejpam-5749	52	12	dominating	dominating	NOUN
ejpam-5749	52	13	function	function	NOUN
ejpam-5749	52	14	.	.	PUNCT
ejpam-5749	53	1	a	a	DET
ejpam-5749	53	2	function	function	NOUN
ejpam-5749	53	3	f	f	NOUN
ejpam-5749	53	4	:	:	PUNCT
ejpam-5749	53	5	v	v	X
ejpam-5749	53	6	(	(	PUNCT
ejpam-5749	53	7	g	g	NOUN
ejpam-5749	53	8	)	)	PUNCT
ejpam-5749	53	9	→	→	SYM
ejpam-5749	53	10	{	{	PUNCT
ejpam-5749	53	11	0	0	NUM
ejpam-5749	53	12	,	,	PUNCT
ejpam-5749	53	13	1	1	NUM
ejpam-5749	53	14	,	,	PUNCT
ejpam-5749	53	15	2	2	NUM
ejpam-5749	53	16	}	}	PUNCT
ejpam-5749	53	17	is	be	AUX
ejpam-5749	53	18	a	a	DET
ejpam-5749	53	19	semitotal	semitotal	ADJ
ejpam-5749	53	20	roman	roman	ADJ
ejpam-5749	53	21	dominating	dominating	NOUN
ejpam-5749	53	22	function	function	NOUN
ejpam-5749	53	23	of	of	ADP
ejpam-5749	53	24	a	a	DET
ejpam-5749	53	25	graph	graph	NOUN
ejpam-5749	53	26	g	g	NOUN
ejpam-5749	53	27	,	,	PUNCT
ejpam-5749	53	28	and	and	CCONJ
ejpam-5749	53	29	write	write	VERB
ejpam-5749	53	30	f	f	PROPN
ejpam-5749	53	31	∈	∈	PROPN
ejpam-5749	53	32	srdf	srdf	NOUN
ejpam-5749	53	33	(	(	PUNCT
ejpam-5749	53	34	g	g	NOUN
ejpam-5749	53	35	)	)	PUNCT
ejpam-5749	53	36	,	,	PUNCT
ejpam-5749	53	37	if	if	SCONJ
ejpam-5749	53	38	each	each	PRON
ejpam-5749	53	39	of	of	ADP
ejpam-5749	53	40	the	the	DET
ejpam-5749	53	41	following	follow	VERB
ejpam-5749	53	42	holds	hold	VERB
ejpam-5749	53	43	:	:	PUNCT
ejpam-5749	53	44	(	(	PUNCT
ejpam-5749	53	45	i	i	NOUN
ejpam-5749	53	46	)	)	PUNCT
ejpam-5749	53	47	for	for	ADP
ejpam-5749	53	48	each	each	PRON
ejpam-5749	53	49	v	v	NUM
ejpam-5749	53	50	∈	∈	PROPN
ejpam-5749	53	51	v	v	NOUN
ejpam-5749	53	52	(	(	PUNCT
ejpam-5749	53	53	g	g	NOUN
ejpam-5749	53	54	)	)	PUNCT
ejpam-5749	53	55	with	with	ADP
ejpam-5749	53	56	f(v	f(v	NOUN
ejpam-5749	53	57	)	)	PUNCT
ejpam-5749	53	58	=	=	SYM
ejpam-5749	53	59	0	0	NUM
ejpam-5749	53	60	,	,	PUNCT
ejpam-5749	53	61	there	there	PRON
ejpam-5749	53	62	exists	exist	VERB
ejpam-5749	53	63	u	u	PROPN
ejpam-5749	53	64	∈	∈	PROPN
ejpam-5749	53	65	v	v	ADP
ejpam-5749	53	66	(	(	PUNCT
ejpam-5749	53	67	g	g	NOUN
ejpam-5749	53	68	)	)	PUNCT
ejpam-5749	53	69	with	with	ADP
ejpam-5749	53	70	f(u	f(u	PROPN
ejpam-5749	53	71	)	)	PUNCT
ejpam-5749	53	72	=	=	SYM
ejpam-5749	53	73	2	2	NUM
ejpam-5749	53	74	and	and	CCONJ
ejpam-5749	53	75	uv	uv	NOUN
ejpam-5749	53	76	∈	∈	PROPN
ejpam-5749	53	77	e(g	e(g	PROPN
ejpam-5749	53	78	)	)	PUNCT
ejpam-5749	53	79	;	;	PUNCT
ejpam-5749	53	80	(	(	PUNCT
ejpam-5749	53	81	ii	ii	NOUN
ejpam-5749	53	82	)	)	PUNCT
ejpam-5749	53	83	for	for	ADP
ejpam-5749	53	84	each	each	DET
ejpam-5749	53	85	v	v	NUM
ejpam-5749	53	86	∈	∈	PROPN
ejpam-5749	53	87	v	v	NOUN
ejpam-5749	53	88	(	(	PUNCT
ejpam-5749	53	89	g	g	NOUN
ejpam-5749	53	90	)	)	PUNCT
ejpam-5749	53	91	with	with	ADP
ejpam-5749	53	92	f(v	f(v	NOUN
ejpam-5749	53	93	)	)	PUNCT
ejpam-5749	53	94	̸=	̸=	PROPN
ejpam-5749	53	95	0	0	NUM
ejpam-5749	53	96	,	,	PUNCT
ejpam-5749	53	97	there	there	PRON
ejpam-5749	53	98	exists	exist	VERB
ejpam-5749	53	99	u	u	PROPN
ejpam-5749	53	100	∈	∈	PROPN
ejpam-5749	53	101	v	v	ADP
ejpam-5749	53	102	(	(	PUNCT
ejpam-5749	53	103	g	g	NOUN
ejpam-5749	53	104	)	)	PUNCT
ejpam-5749	53	105	for	for	ADP
ejpam-5749	53	106	which	which	PRON
ejpam-5749	53	107	f(u	f(u	PROPN
ejpam-5749	53	108	)	)	PUNCT
ejpam-5749	53	109	̸=	̸=	PROPN
ejpam-5749	53	110	0	0	NUM
ejpam-5749	53	111	and	and	CCONJ
ejpam-5749	53	112	dg(u	dg(u	X
ejpam-5749	53	113	,	,	PUNCT
ejpam-5749	53	114	v	v	NOUN
ejpam-5749	53	115	)	)	PUNCT
ejpam-5749	53	116	≤	≤	NOUN
ejpam-5749	53	117	2	2	NUM
ejpam-5749	53	118	.	.	PUNCT
ejpam-5749	54	1	the	the	DET
ejpam-5749	54	2	minimum	minimum	ADJ
ejpam-5749	54	3	weight	weight	NOUN
ejpam-5749	54	4	ωg(f	ωg(f	PRON
ejpam-5749	54	5	)	)	PUNCT
ejpam-5749	54	6	=	=	SYM
ejpam-5749	54	7	∑	∑	PUNCT
ejpam-5749	54	8	u∈v	u∈v	NOUN
ejpam-5749	54	9	(	(	PUNCT
ejpam-5749	54	10	g	g	NOUN
ejpam-5749	54	11	)	)	PUNCT
ejpam-5749	54	12	f(u	f(u	PROPN
ejpam-5749	54	13	)	)	PUNCT
ejpam-5749	54	14	of	of	ADP
ejpam-5749	54	15	a	a	DET
ejpam-5749	54	16	semitotal	semitotal	ADJ
ejpam-5749	54	17	roman	roman	ADJ
ejpam-5749	54	18	dominating	dominating	NOUN
ejpam-5749	54	19	function	function	NOUN
ejpam-5749	54	20	f	f	PROPN
ejpam-5749	54	21	of	of	ADP
ejpam-5749	54	22	g	g	PROPN
ejpam-5749	54	23	is	be	AUX
ejpam-5749	54	24	the	the	DET
ejpam-5749	54	25	semitotal	semitotal	ADJ
ejpam-5749	54	26	roman	roman	ADJ
ejpam-5749	54	27	domination	domination	NOUN
ejpam-5749	54	28	number	number	NOUN
ejpam-5749	54	29	of	of	ADP
ejpam-5749	54	30	g	g	NOUN
ejpam-5749	54	31	,	,	PUNCT
ejpam-5749	54	32	denoted	denote	VERB
ejpam-5749	54	33	by	by	ADP
ejpam-5749	54	34	γt2r(g	γt2r(g	NOUN
ejpam-5749	54	35	)	)	PUNCT
ejpam-5749	54	36	.	.	PUNCT
ejpam-5749	55	1	as	as	ADP
ejpam-5749	55	2	usual	usual	ADJ
ejpam-5749	55	3	,	,	PUNCT
ejpam-5749	55	4	we	we	PRON
ejpam-5749	55	5	write	write	VERB
ejpam-5749	55	6	f	f	PROPN
ejpam-5749	55	7	=	=	SYM
ejpam-5749	55	8	(	(	PUNCT
ejpam-5749	55	9	v0	v0	PROPN
ejpam-5749	55	10	,	,	PUNCT
ejpam-5749	55	11	v1	v1	NOUN
ejpam-5749	55	12	,	,	PUNCT
ejpam-5749	55	13	v2	v2	PROPN
ejpam-5749	55	14	)	)	PUNCT
ejpam-5749	55	15	for	for	ADP
ejpam-5749	55	16	a	a	DET
ejpam-5749	55	17	function	function	NOUN
ejpam-5749	56	1	f	f	NOUN
ejpam-5749	56	2	:	:	PUNCT
ejpam-5749	56	3	v	v	X
ejpam-5749	56	4	(	(	PUNCT
ejpam-5749	56	5	g	g	NOUN
ejpam-5749	56	6	)	)	PUNCT
ejpam-5749	56	7	→	→	SYM
ejpam-5749	56	8	{	{	PUNCT
ejpam-5749	56	9	0	0	NUM
ejpam-5749	56	10	,	,	PUNCT
ejpam-5749	56	11	1	1	NUM
ejpam-5749	56	12	,	,	PUNCT
ejpam-5749	56	13	2	2	NUM
ejpam-5749	56	14	}	}	PUNCT
ejpam-5749	56	15	of	of	ADP
ejpam-5749	56	16	a	a	DET
ejpam-5749	56	17	graph	graph	NOUN
ejpam-5749	56	18	g	g	PROPN
ejpam-5749	56	19	where	where	SCONJ
ejpam-5749	56	20	vi	vi	NOUN
ejpam-5749	56	21	=	=	PUNCT
ejpam-5749	56	22	{	{	PUNCT
ejpam-5749	56	23	v	v	NUM
ejpam-5749	56	24	∈	∈	NOUN
ejpam-5749	56	25	v	v	NOUN
ejpam-5749	56	26	(	(	PUNCT
ejpam-5749	56	27	g	g	NOUN
ejpam-5749	56	28	)	)	PUNCT
ejpam-5749	56	29	:	:	PUNCT
ejpam-5749	56	30	f(v	f(v	NOUN
ejpam-5749	56	31	)	)	PUNCT
ejpam-5749	57	1	=	=	SYM
ejpam-5749	57	2	i	i	PRON
ejpam-5749	57	3	for	for	ADP
ejpam-5749	57	4	each	each	DET
ejpam-5749	57	5	i	i	PRON
ejpam-5749	57	6	∈	∈	PROPN
ejpam-5749	57	7	{	{	PUNCT
ejpam-5749	57	8	0	0	NUM
ejpam-5749	57	9	,	,	PUNCT
ejpam-5749	57	10	1	1	NUM
ejpam-5749	57	11	,	,	PUNCT
ejpam-5749	57	12	2	2	NUM
ejpam-5749	57	13	}	}	PUNCT
ejpam-5749	57	14	}	}	PUNCT
ejpam-5749	57	15	.	.	PUNCT
ejpam-5749	58	1	more	more	ADV
ejpam-5749	58	2	precisely	precisely	ADV
ejpam-5749	58	3	,	,	PUNCT
ejpam-5749	58	4	f	f	PROPN
ejpam-5749	58	5	∈	∈	PROPN
ejpam-5749	58	6	srdf	srdf	NOUN
ejpam-5749	58	7	(	(	PUNCT
ejpam-5749	58	8	g	g	NOUN
ejpam-5749	58	9	)	)	PUNCT
ejpam-5749	58	10	if	if	SCONJ
ejpam-5749	58	11	and	and	CCONJ
ejpam-5749	58	12	only	only	ADV
ejpam-5749	58	13	if	if	SCONJ
ejpam-5749	58	14	v2	v2	PROPN
ejpam-5749	58	15	∩ng(v	∩ng(v	PROPN
ejpam-5749	58	16	)	)	PUNCT
ejpam-5749	58	17	̸=	̸=	PROPN
ejpam-5749	58	18	∅	∅	NOUN
ejpam-5749	58	19	for	for	ADP
ejpam-5749	58	20	each	each	DET
ejpam-5749	58	21	v	v	NOUN
ejpam-5749	58	22	∈	∈	PROPN
ejpam-5749	58	23	v0	v0	NOUN
ejpam-5749	58	24	and	and	CCONJ
ejpam-5749	58	25	v1	v1	VERB
ejpam-5749	58	26	∪	∪	X
ejpam-5749	58	27	v2	v2	NOUN
ejpam-5749	58	28	is	be	AUX
ejpam-5749	58	29	a	a	DET
ejpam-5749	58	30	semitotal	semitotal	ADJ
ejpam-5749	58	31	dominating	dominating	NOUN
ejpam-5749	58	32	set	set	NOUN
ejpam-5749	58	33	of	of	ADP
ejpam-5749	58	34	g.	g.	PROPN
ejpam-5749	58	35	in	in	ADP
ejpam-5749	58	36	this	this	DET
ejpam-5749	58	37	case	case	NOUN
ejpam-5749	58	38	,	,	PUNCT
ejpam-5749	58	39	ωg(f	ωg(f	NUM
ejpam-5749	58	40	)	)	PUNCT
ejpam-5749	58	41	=	=	PUNCT
ejpam-5749	58	42	|v1|+	|v1|+	DET
ejpam-5749	58	43	2|v2|	2|v2|	NUM
ejpam-5749	58	44	.	.	PUNCT
ejpam-5749	59	1	proposition	proposition	NOUN
ejpam-5749	59	2	1	1	NUM
ejpam-5749	59	3	.	.	PUNCT
ejpam-5749	60	1	let	let	VERB
ejpam-5749	60	2	g	g	NOUN
ejpam-5749	60	3	be	be	AUX
ejpam-5749	60	4	any	any	DET
ejpam-5749	60	5	graph	graph	NOUN
ejpam-5749	60	6	.	.	PUNCT
ejpam-5749	61	1	then	then	ADV
ejpam-5749	61	2	g	g	PROPN
ejpam-5749	61	3	admits	admit	VERB
ejpam-5749	61	4	a	a	DET
ejpam-5749	61	5	semitotal	semitotal	ADJ
ejpam-5749	61	6	roman	roman	ADJ
ejpam-5749	61	7	dominating	dominating	NOUN
ejpam-5749	61	8	function	function	NOUN
ejpam-5749	61	9	if	if	SCONJ
ejpam-5749	61	10	and	and	CCONJ
ejpam-5749	61	11	only	only	ADV
ejpam-5749	61	12	if	if	SCONJ
ejpam-5749	61	13	g	g	PROPN
ejpam-5749	61	14	has	have	VERB
ejpam-5749	61	15	no	no	DET
ejpam-5749	61	16	isolated	isolated	ADJ
ejpam-5749	61	17	vertices	vertex	NOUN
ejpam-5749	61	18	.	.	PUNCT
ejpam-5749	62	1	proposition	proposition	NOUN
ejpam-5749	62	2	2	2	NUM
ejpam-5749	62	3	.	.	PUNCT
ejpam-5749	63	1	for	for	ADP
ejpam-5749	63	2	all	all	DET
ejpam-5749	63	3	graphs	graph	NOUN
ejpam-5749	63	4	g	g	NOUN
ejpam-5749	63	5	without	without	ADP
ejpam-5749	63	6	isolated	isolated	ADJ
ejpam-5749	63	7	vertices	vertex	NOUN
ejpam-5749	63	8	,	,	PUNCT
ejpam-5749	63	9	γt2(g	γt2(g	NOUN
ejpam-5749	63	10	)	)	PUNCT
ejpam-5749	63	11	≤	≤	NOUN
ejpam-5749	63	12	γr(g	γr(g	NUM
ejpam-5749	63	13	)	)	PUNCT
ejpam-5749	63	14	≤	≤	NUM
ejpam-5749	63	15	γt2r(g	γt2r(g	NUM
ejpam-5749	63	16	)	)	PUNCT
ejpam-5749	63	17	≤	≤	PUNCT
ejpam-5749	63	18	min{γtr(g	min{γtr(g	PROPN
ejpam-5749	63	19	)	)	PUNCT
ejpam-5749	63	20	,	,	PUNCT
ejpam-5749	63	21	2γt2(g	2γt2(g	NUM
ejpam-5749	63	22	)	)	PUNCT
ejpam-5749	63	23	}	}	PUNCT
ejpam-5749	63	24	.	.	PUNCT
ejpam-5749	64	1	(	(	PUNCT
ejpam-5749	64	2	1	1	X
ejpam-5749	64	3	)	)	PUNCT
ejpam-5749	64	4	b.	b.	PROPN
ejpam-5749	64	5	f.	f.	PROPN
ejpam-5749	64	6	bullang	bullang	PROPN
ejpam-5749	64	7	et	et	PROPN
ejpam-5749	64	8	al	al	PROPN
ejpam-5749	64	9	.	.	PUNCT
ejpam-5749	64	10	/	/	SYM
ejpam-5749	64	11	eur	eur	PROPN
ejpam-5749	64	12	.	.	PUNCT
ejpam-5749	65	1	j.	j.	PROPN
ejpam-5749	65	2	pure	pure	PROPN
ejpam-5749	65	3	appl	appl	PROPN
ejpam-5749	65	4	.	.	PROPN
ejpam-5749	65	5	math	math	PROPN
ejpam-5749	65	6	,	,	PUNCT
ejpam-5749	65	7	18	18	NUM
ejpam-5749	65	8	(	(	PUNCT
ejpam-5749	65	9	1	1	NUM
ejpam-5749	65	10	)	)	PUNCT
ejpam-5749	65	11	(	(	PUNCT
ejpam-5749	65	12	2025	2025	NUM
ejpam-5749	65	13	)	)	PUNCT
ejpam-5749	65	14	,	,	PUNCT
ejpam-5749	65	15	5749	5749	NUM
ejpam-5749	65	16	4	4	NUM
ejpam-5749	65	17	of	of	ADP
ejpam-5749	65	18	15	15	NUM
ejpam-5749	65	19	proof	proof	NOUN
ejpam-5749	65	20	.	.	PUNCT
ejpam-5749	66	1	clearly	clearly	ADV
ejpam-5749	66	2	,	,	PUNCT
ejpam-5749	66	3	a	a	DET
ejpam-5749	66	4	total	total	ADJ
ejpam-5749	66	5	roman	roman	ADJ
ejpam-5749	66	6	dominating	dominating	NOUN
ejpam-5749	66	7	function	function	NOUN
ejpam-5749	66	8	is	be	AUX
ejpam-5749	66	9	a	a	DET
ejpam-5749	66	10	semitotal	semitotal	ADJ
ejpam-5749	66	11	roman	roman	ADJ
ejpam-5749	66	12	dominating	dominating	NOUN
ejpam-5749	66	13	function	function	NOUN
ejpam-5749	66	14	and	and	CCONJ
ejpam-5749	66	15	a	a	DET
ejpam-5749	66	16	semitotal	semitotal	ADJ
ejpam-5749	66	17	roman	roman	ADJ
ejpam-5749	66	18	dominating	dominating	NOUN
ejpam-5749	66	19	function	function	NOUN
ejpam-5749	66	20	ofg	ofg	PROPN
ejpam-5749	66	21	is	be	AUX
ejpam-5749	66	22	a	a	DET
ejpam-5749	66	23	roman	roman	ADJ
ejpam-5749	66	24	dominating	dominating	NOUN
ejpam-5749	66	25	function	function	NOUN
ejpam-5749	66	26	.	.	PUNCT
ejpam-5749	67	1	thus	thus	ADV
ejpam-5749	67	2	,	,	PUNCT
ejpam-5749	67	3	γr(g	γr(g	PROPN
ejpam-5749	67	4	)	)	PUNCT
ejpam-5749	67	5	≤	≤	NUM
ejpam-5749	67	6	γt2r(g	γt2r(g	NUM
ejpam-5749	67	7	)	)	PUNCT
ejpam-5749	67	8	≤	≤	NOUN
ejpam-5749	67	9	γtr(g	γtr(g	NUM
ejpam-5749	67	10	)	)	PUNCT
ejpam-5749	67	11	.	.	PUNCT
ejpam-5749	68	1	also	also	ADV
ejpam-5749	68	2	,	,	PUNCT
ejpam-5749	68	3	if	if	SCONJ
ejpam-5749	68	4	s	s	VERB
ejpam-5749	68	5	⊆	⊆	NUM
ejpam-5749	68	6	v	v	NOUN
ejpam-5749	68	7	(	(	PUNCT
ejpam-5749	68	8	g	g	NOUN
ejpam-5749	68	9	)	)	PUNCT
ejpam-5749	68	10	is	be	AUX
ejpam-5749	68	11	a	a	DET
ejpam-5749	68	12	semitotal	semitotal	ADJ
ejpam-5749	68	13	dominating	dominating	NOUN
ejpam-5749	68	14	set	set	NOUN
ejpam-5749	68	15	of	of	ADP
ejpam-5749	68	16	g	g	PROPN
ejpam-5749	68	17	,	,	PUNCT
ejpam-5749	68	18	then	then	ADV
ejpam-5749	68	19	f	f	PROPN
ejpam-5749	68	20	=	=	PUNCT
ejpam-5749	68	21	(	(	PUNCT
ejpam-5749	68	22	v	v	NOUN
ejpam-5749	68	23	(	(	PUNCT
ejpam-5749	68	24	g	g	NOUN
ejpam-5749	68	25	)	)	PUNCT
ejpam-5749	68	26	\	\	NOUN
ejpam-5749	68	27	s,∅	s,∅	NOUN
ejpam-5749	68	28	,	,	PUNCT
ejpam-5749	68	29	s	s	X
ejpam-5749	68	30	)	)	PUNCT
ejpam-5749	68	31	∈	∈	NOUN
ejpam-5749	68	32	srdf	srdf	NOUN
ejpam-5749	68	33	(	(	PUNCT
ejpam-5749	68	34	g	g	NOUN
ejpam-5749	68	35	)	)	PUNCT
ejpam-5749	68	36	,	,	PUNCT
ejpam-5749	68	37	showing	show	VERB
ejpam-5749	68	38	that	that	SCONJ
ejpam-5749	68	39	γt2r(g	γt2r(g	NOUN
ejpam-5749	68	40	)	)	PUNCT
ejpam-5749	68	41	≤	≤	NOUN
ejpam-5749	68	42	2γt2(g	2γt2(g	NUM
ejpam-5749	68	43	)	)	PUNCT
ejpam-5749	68	44	.	.	PUNCT
ejpam-5749	69	1	now	now	ADV
ejpam-5749	69	2	,	,	PUNCT
ejpam-5749	69	3	let	let	VERB
ejpam-5749	69	4	f	f	PROPN
ejpam-5749	69	5	=	=	SYM
ejpam-5749	69	6	(	(	PUNCT
ejpam-5749	69	7	v0	v0	PROPN
ejpam-5749	69	8	,	,	PUNCT
ejpam-5749	69	9	v1	v1	NOUN
ejpam-5749	69	10	,	,	PUNCT
ejpam-5749	69	11	v2	v2	NOUN
ejpam-5749	69	12	)	)	PUNCT
ejpam-5749	69	13	∈	∈	PROPN
ejpam-5749	69	14	rdf	rdf	NOUN
ejpam-5749	69	15	(	(	PUNCT
ejpam-5749	69	16	g	g	NOUN
ejpam-5749	69	17	)	)	PUNCT
ejpam-5749	69	18	.	.	PUNCT
ejpam-5749	70	1	then	then	ADV
ejpam-5749	70	2	s	s	VERB
ejpam-5749	70	3	=	=	NOUN
ejpam-5749	70	4	v1	v1	PROPN
ejpam-5749	70	5	∪	∪	NOUN
ejpam-5749	70	6	v2	v2	NOUN
ejpam-5749	70	7	is	be	AUX
ejpam-5749	70	8	a	a	DET
ejpam-5749	70	9	total	total	ADJ
ejpam-5749	70	10	dominating	dominating	NOUN
ejpam-5749	70	11	set	set	NOUN
ejpam-5749	70	12	of	of	ADP
ejpam-5749	70	13	g.	g.	PROPN
ejpam-5749	70	14	we	we	PRON
ejpam-5749	70	15	claim	claim	VERB
ejpam-5749	70	16	that	that	SCONJ
ejpam-5749	70	17	v1	v1	VERB
ejpam-5749	70	18	⊆	⊆	NUM
ejpam-5749	70	19	ng(s	ng(s	NOUN
ejpam-5749	70	20	,	,	PUNCT
ejpam-5749	70	21	2	2	NUM
ejpam-5749	70	22	)	)	PUNCT
ejpam-5749	70	23	.	.	PUNCT
ejpam-5749	71	1	let	let	VERB
ejpam-5749	71	2	x	x	PUNCT
ejpam-5749	71	3	∈	∈	PROPN
ejpam-5749	71	4	v1	v1	NOUN
ejpam-5749	71	5	.	.	PUNCT
ejpam-5749	72	1	suppose	suppose	VERB
ejpam-5749	72	2	that	that	SCONJ
ejpam-5749	72	3	dg(x	dg(x	PROPN
ejpam-5749	72	4	,	,	PUNCT
ejpam-5749	72	5	y	y	PROPN
ejpam-5749	72	6	)	)	PUNCT
ejpam-5749	72	7	≥	≥	NOUN
ejpam-5749	72	8	3	3	NUM
ejpam-5749	72	9	for	for	ADP
ejpam-5749	72	10	all	all	DET
ejpam-5749	72	11	y	y	PROPN
ejpam-5749	72	12	∈	∈	PROPN
ejpam-5749	72	13	s	s	PART
ejpam-5749	72	14	\	\	X
ejpam-5749	72	15	{	{	PUNCT
ejpam-5749	72	16	x	x	NOUN
ejpam-5749	72	17	}	}	PUNCT
ejpam-5749	72	18	.	.	PUNCT
ejpam-5749	73	1	since	since	SCONJ
ejpam-5749	73	2	x	x	PRON
ejpam-5749	73	3	is	be	AUX
ejpam-5749	73	4	not	not	PART
ejpam-5749	73	5	an	an	DET
ejpam-5749	73	6	isolated	isolated	ADJ
ejpam-5749	73	7	vertex	vertex	NOUN
ejpam-5749	73	8	,	,	PUNCT
ejpam-5749	73	9	there	there	PRON
ejpam-5749	73	10	exists	exist	VERB
ejpam-5749	73	11	z	z	PROPN
ejpam-5749	73	12	∈	∈	PROPN
ejpam-5749	73	13	ng(x	ng(x	NUM
ejpam-5749	73	14	)	)	PUNCT
ejpam-5749	73	15	∩	∩	PROPN
ejpam-5749	73	16	v0	v0	NOUN
ejpam-5749	73	17	.	.	PUNCT
ejpam-5749	74	1	then	then	ADV
ejpam-5749	74	2	there	there	PRON
ejpam-5749	74	3	exists	exist	VERB
ejpam-5749	74	4	w	w	PROPN
ejpam-5749	74	5	∈	∈	NOUN
ejpam-5749	74	6	v2	v2	NOUN
ejpam-5749	74	7	for	for	ADP
ejpam-5749	74	8	which	which	PRON
ejpam-5749	74	9	zw	zw	PROPN
ejpam-5749	74	10	∈	∈	PROPN
ejpam-5749	74	11	e(g	e(g	PROPN
ejpam-5749	74	12	)	)	PUNCT
ejpam-5749	74	13	,	,	PUNCT
ejpam-5749	74	14	implying	imply	VERB
ejpam-5749	74	15	that	that	SCONJ
ejpam-5749	74	16	dg(x	dg(x	CCONJ
ejpam-5749	74	17	,	,	PUNCT
ejpam-5749	74	18	w	w	NOUN
ejpam-5749	74	19	)	)	PUNCT
ejpam-5749	74	20	≤	≤	NUM
ejpam-5749	74	21	2	2	NUM
ejpam-5749	74	22	,	,	PUNCT
ejpam-5749	74	23	a	a	DET
ejpam-5749	74	24	contradiction	contradiction	NOUN
ejpam-5749	74	25	.	.	PUNCT
ejpam-5749	75	1	this	this	PRON
ejpam-5749	75	2	establishes	establish	VERB
ejpam-5749	75	3	the	the	DET
ejpam-5749	75	4	claim	claim	NOUN
ejpam-5749	75	5	,	,	PUNCT
ejpam-5749	75	6	which	which	PRON
ejpam-5749	75	7	implies	imply	VERB
ejpam-5749	75	8	that	that	PRON
ejpam-5749	75	9	s	s	VERB
ejpam-5749	75	10	\ng(s	\ng(s	NOUN
ejpam-5749	75	11	,	,	PUNCT
ejpam-5749	75	12	2	2	NUM
ejpam-5749	75	13	)	)	PUNCT
ejpam-5749	75	14	⊆	⊆	NUM
ejpam-5749	75	15	v2	v2	NOUN
ejpam-5749	75	16	.	.	PUNCT
ejpam-5749	76	1	for	for	ADP
ejpam-5749	76	2	each	each	DET
ejpam-5749	76	3	u	u	NOUN
ejpam-5749	76	4	∈	∈	PROPN
ejpam-5749	76	5	s	s	PART
ejpam-5749	76	6	\ng(s	\ng(s	NOUN
ejpam-5749	76	7	,	,	PUNCT
ejpam-5749	76	8	2	2	NUM
ejpam-5749	76	9	)	)	PUNCT
ejpam-5749	76	10	,	,	PUNCT
ejpam-5749	76	11	pick	pick	VERB
ejpam-5749	76	12	one	one	NUM
ejpam-5749	76	13	vu	vu	NOUN
ejpam-5749	76	14	∈	∈	PROPN
ejpam-5749	76	15	v	v	NOUN
ejpam-5749	76	16	(	(	PUNCT
ejpam-5749	76	17	g	g	NOUN
ejpam-5749	76	18	)	)	PUNCT
ejpam-5749	76	19	for	for	ADP
ejpam-5749	76	20	which	which	PRON
ejpam-5749	76	21	dg(u	dg(u	PROPN
ejpam-5749	76	22	,	,	PUNCT
ejpam-5749	76	23	vu	vu	X
ejpam-5749	76	24	)	)	PUNCT
ejpam-5749	76	25	≤	≤	NUM
ejpam-5749	76	26	2	2	NUM
ejpam-5749	76	27	.	.	PUNCT
ejpam-5749	77	1	if	if	SCONJ
ejpam-5749	77	2	s∗	s∗	PROPN
ejpam-5749	77	3	=	=	SYM
ejpam-5749	77	4	{	{	PUNCT
ejpam-5749	77	5	vu	vu	X
ejpam-5749	77	6	:	:	PUNCT
ejpam-5749	77	7	u	u	PROPN
ejpam-5749	77	8	∈	∈	PROPN
ejpam-5749	77	9	s	s	PART
ejpam-5749	77	10	\ng(s	\ng(s	NOUN
ejpam-5749	77	11	,	,	PUNCT
ejpam-5749	77	12	2	2	NUM
ejpam-5749	77	13	)	)	PUNCT
ejpam-5749	77	14	}	}	PUNCT
ejpam-5749	77	15	,	,	PUNCT
ejpam-5749	77	16	then	then	ADV
ejpam-5749	77	17	s	s	VERB
ejpam-5749	77	18	∪	∪	ADJ
ejpam-5749	77	19	s∗	s∗	PROPN
ejpam-5749	77	20	is	be	AUX
ejpam-5749	77	21	a	a	DET
ejpam-5749	77	22	semitotal	semitotal	ADJ
ejpam-5749	77	23	dominating	dominating	NOUN
ejpam-5749	77	24	set	set	NOUN
ejpam-5749	77	25	of	of	ADP
ejpam-5749	77	26	g	g	NOUN
ejpam-5749	77	27	with	with	ADP
ejpam-5749	77	28	|s∗|	|s∗|	NUM
ejpam-5749	77	29	≤	≤	NOUN
ejpam-5749	77	30	|v2|	|v2|	NOUN
ejpam-5749	77	31	.	.	PUNCT
ejpam-5749	78	1	thus	thus	ADV
ejpam-5749	78	2	,	,	PUNCT
ejpam-5749	78	3	γt2(g	γt2(g	NOUN
ejpam-5749	78	4	)	)	PUNCT
ejpam-5749	78	5	≤	≤	NUM
ejpam-5749	78	6	|s|+	|s|+	NOUN
ejpam-5749	78	7	|s∗|	|s∗|	NUM
ejpam-5749	78	8	≤	≤	NUM
ejpam-5749	78	9	|v1|+	|v1|+	PRON
ejpam-5749	78	10	2|v2|	2|v2|	NUM
ejpam-5749	78	11	=	=	SYM
ejpam-5749	78	12	γr(g	γr(g	NUM
ejpam-5749	78	13	)	)	PUNCT
ejpam-5749	78	14	.	.	PUNCT
ejpam-5749	79	1	the	the	DET
ejpam-5749	79	2	following	follow	VERB
ejpam-5749	79	3	examples	example	NOUN
ejpam-5749	79	4	show	show	VERB
ejpam-5749	79	5	that	that	SCONJ
ejpam-5749	79	6	the	the	DET
ejpam-5749	79	7	inequalities	inequality	NOUN
ejpam-5749	79	8	in	in	ADP
ejpam-5749	79	9	equation	equation	NOUN
ejpam-5749	79	10	1	1	NUM
ejpam-5749	79	11	are	be	AUX
ejpam-5749	79	12	sharp	sharp	ADJ
ejpam-5749	79	13	.	.	PUNCT
ejpam-5749	80	1	for	for	ADP
ejpam-5749	80	2	all	all	PRON
ejpam-5749	80	3	n	n	PRON
ejpam-5749	80	4	≥	≥	NUM
ejpam-5749	80	5	1	1	NUM
ejpam-5749	80	6	,	,	PUNCT
ejpam-5749	80	7	γr(k1,n	γr(k1,n	PROPN
ejpam-5749	80	8	)	)	PUNCT
ejpam-5749	80	9	<	<	X
ejpam-5749	80	10	γt2r(k1,n	γt2r(k1,n	NOUN
ejpam-5749	80	11	)	)	PUNCT
ejpam-5749	80	12	=	=	SYM
ejpam-5749	80	13	3	3	NUM
ejpam-5749	80	14	=	=	SYM
ejpam-5749	80	15	γtr(k1,n	γtr(k1,n	PROPN
ejpam-5749	80	16	)	)	PUNCT
ejpam-5749	80	17	<	<	X
ejpam-5749	80	18	2γt2(k1,n	2γt2(k1,n	NUM
ejpam-5749	80	19	)	)	PUNCT
ejpam-5749	80	20	.	.	PUNCT
ejpam-5749	81	1	on	on	ADP
ejpam-5749	81	2	the	the	DET
ejpam-5749	81	3	other	other	ADJ
ejpam-5749	81	4	hand	hand	NOUN
ejpam-5749	81	5	,	,	PUNCT
ejpam-5749	81	6	γr(p5	γr(p5	ADJ
ejpam-5749	81	7	)	)	PUNCT
ejpam-5749	81	8	=	=	SYM
ejpam-5749	81	9	γt2r(p5	γt2r(p5	ADJ
ejpam-5749	81	10	)	)	PUNCT
ejpam-5749	81	11	=	=	SYM
ejpam-5749	81	12	2γt2(p5	2γt2(p5	X
ejpam-5749	81	13	)	)	PUNCT
ejpam-5749	81	14	=	=	SYM
ejpam-5749	81	15	4	4	NUM
ejpam-5749	81	16	<	<	X
ejpam-5749	81	17	γtr(p5	γtr(p5	PROPN
ejpam-5749	81	18	)	)	PUNCT
ejpam-5749	81	19	.	.	PUNCT
ejpam-5749	82	1	proposition	proposition	NOUN
ejpam-5749	82	2	3	3	X
ejpam-5749	82	3	.	.	PUNCT
ejpam-5749	83	1	let	let	VERB
ejpam-5749	83	2	g	g	NOUN
ejpam-5749	83	3	be	be	AUX
ejpam-5749	83	4	any	any	DET
ejpam-5749	83	5	graph	graph	NOUN
ejpam-5749	83	6	without	without	ADP
ejpam-5749	83	7	isolated	isolated	ADJ
ejpam-5749	83	8	vertices	vertex	NOUN
ejpam-5749	83	9	,	,	PUNCT
ejpam-5749	83	10	and	and	CCONJ
ejpam-5749	83	11	let	let	VERB
ejpam-5749	83	12	f	f	PROPN
ejpam-5749	83	13	=	=	SYM
ejpam-5749	83	14	(	(	PUNCT
ejpam-5749	83	15	v0	v0	PROPN
ejpam-5749	83	16	,	,	PUNCT
ejpam-5749	83	17	v1	v1	NOUN
ejpam-5749	83	18	,	,	PUNCT
ejpam-5749	83	19	v2	v2	PROPN
ejpam-5749	83	20	)	)	PUNCT
ejpam-5749	83	21	be	be	AUX
ejpam-5749	83	22	a	a	DET
ejpam-5749	83	23	γt2r	γt2r	NOUN
ejpam-5749	83	24	-	-	PUNCT
ejpam-5749	83	25	function	function	NOUN
ejpam-5749	83	26	in	in	ADP
ejpam-5749	83	27	g.	g.	PROPN
ejpam-5749	84	1	then	then	ADV
ejpam-5749	84	2	each	each	PRON
ejpam-5749	84	3	of	of	ADP
ejpam-5749	84	4	the	the	DET
ejpam-5749	84	5	following	follow	VERB
ejpam-5749	84	6	holds	hold	VERB
ejpam-5749	84	7	:	:	PUNCT
ejpam-5749	84	8	(	(	PUNCT
ejpam-5749	84	9	i	i	NOUN
ejpam-5749	84	10	)	)	PUNCT
ejpam-5749	84	11	v0	v0	NOUN
ejpam-5749	84	12	=	=	SYM
ejpam-5749	84	13	∅	∅	NOUN
ejpam-5749	84	14	if	if	SCONJ
ejpam-5749	84	15	and	and	CCONJ
ejpam-5749	84	16	only	only	ADV
ejpam-5749	84	17	if	if	SCONJ
ejpam-5749	84	18	v2	v2	NOUN
ejpam-5749	84	19	=	=	NOUN
ejpam-5749	84	20	∅	∅	NOUN
ejpam-5749	84	21	;	;	PUNCT
ejpam-5749	84	22	and	and	CCONJ
ejpam-5749	84	23	(	(	PUNCT
ejpam-5749	84	24	ii	ii	NOUN
ejpam-5749	84	25	)	)	PUNCT
ejpam-5749	84	26	v1	v1	NOUN
ejpam-5749	84	27	=	=	SYM
ejpam-5749	84	28	∅	∅	NOUN
ejpam-5749	84	29	if	if	SCONJ
ejpam-5749	84	30	and	and	CCONJ
ejpam-5749	84	31	only	only	ADV
ejpam-5749	84	32	if	if	SCONJ
ejpam-5749	84	33	v2	v2	PROPN
ejpam-5749	84	34	is	be	AUX
ejpam-5749	84	35	a	a	DET
ejpam-5749	84	36	γt2	γt2	NOUN
ejpam-5749	84	37	-	-	PUNCT
ejpam-5749	84	38	set	set	NOUN
ejpam-5749	84	39	in	in	ADP
ejpam-5749	84	40	g.	g.	PROPN
ejpam-5749	84	41	proof	proof	PROPN
ejpam-5749	84	42	.	.	PUNCT
ejpam-5749	85	1	clearly	clearly	ADV
ejpam-5749	85	2	,	,	PUNCT
ejpam-5749	85	3	if	if	SCONJ
ejpam-5749	85	4	v2	v2	NOUN
ejpam-5749	85	5	=	=	NOUN
ejpam-5749	85	6	∅	∅	NOUN
ejpam-5749	85	7	,	,	PUNCT
ejpam-5749	85	8	then	then	ADV
ejpam-5749	85	9	v0	v0	NOUN
ejpam-5749	85	10	=	=	PUNCT
ejpam-5749	85	11	∅.	∅.	VERB
ejpam-5749	85	12	conversely	conversely	ADV
ejpam-5749	85	13	,	,	PUNCT
ejpam-5749	85	14	if	if	SCONJ
ejpam-5749	85	15	v0	v0	NOUN
ejpam-5749	85	16	=	=	SYM
ejpam-5749	85	17	∅	∅	NOUN
ejpam-5749	85	18	and	and	CCONJ
ejpam-5749	85	19	v2	v2	VERB
ejpam-5749	85	20	̸=	̸=	PROPN
ejpam-5749	85	21	∅	∅	NOUN
ejpam-5749	85	22	,	,	PUNCT
ejpam-5749	85	23	then	then	ADV
ejpam-5749	85	24	g	g	PROPN
ejpam-5749	85	25	=	=	SYM
ejpam-5749	85	26	(	(	PUNCT
ejpam-5749	85	27	v0	v0	NOUN
ejpam-5749	85	28	,	,	PUNCT
ejpam-5749	85	29	v1	v1	NOUN
ejpam-5749	85	30	∪	∪	ADJ
ejpam-5749	85	31	v2,∅	v2,∅	NOUN
ejpam-5749	85	32	)	)	PUNCT
ejpam-5749	85	33	∈	∈	NOUN
ejpam-5749	85	34	srdf	srdf	NOUN
ejpam-5749	85	35	(	(	PUNCT
ejpam-5749	85	36	g	g	NOUN
ejpam-5749	85	37	)	)	PUNCT
ejpam-5749	85	38	with	with	ADP
ejpam-5749	85	39	ωg(g	ωg(g	NOUN
ejpam-5749	85	40	)	)	PUNCT
ejpam-5749	85	41	=	=	PUNCT
ejpam-5749	85	42	|v1|+	|v1|+	ADV
ejpam-5749	85	43	|v2|	|v2|	ADV
ejpam-5749	85	44	<	<	X
ejpam-5749	85	45	ωg(f	ωg(f	NUM
ejpam-5749	85	46	)	)	PUNCT
ejpam-5749	85	47	,	,	PUNCT
ejpam-5749	85	48	a	a	DET
ejpam-5749	85	49	contradiction	contradiction	NOUN
ejpam-5749	85	50	.	.	PUNCT
ejpam-5749	86	1	this	this	PRON
ejpam-5749	86	2	proves	prove	VERB
ejpam-5749	86	3	(	(	PUNCT
ejpam-5749	86	4	i	i	NOUN
ejpam-5749	86	5	)	)	PUNCT
ejpam-5749	86	6	.	.	PUNCT
ejpam-5749	87	1	if	if	SCONJ
ejpam-5749	87	2	v1	v1	NOUN
ejpam-5749	87	3	=	=	SYM
ejpam-5749	87	4	∅	∅	NOUN
ejpam-5749	87	5	,	,	PUNCT
ejpam-5749	87	6	then	then	ADV
ejpam-5749	87	7	γt2r(g	γt2r(g	NUM
ejpam-5749	87	8	)	)	PUNCT
ejpam-5749	87	9	=	=	SYM
ejpam-5749	87	10	2|v2|	2|v2|	NUM
ejpam-5749	87	11	≥	≥	NOUN
ejpam-5749	87	12	2γt2(g	2γt2(g	NUM
ejpam-5749	87	13	)	)	PUNCT
ejpam-5749	87	14	.	.	PUNCT
ejpam-5749	88	1	then	then	ADV
ejpam-5749	88	2	inequality	inequality	NOUN
ejpam-5749	88	3	1	1	NUM
ejpam-5749	88	4	completes	complete	VERB
ejpam-5749	88	5	the	the	DET
ejpam-5749	88	6	equation	equation	NOUN
ejpam-5749	88	7	γt2r(g	γt2r(g	PRON
ejpam-5749	88	8	)	)	PUNCT
ejpam-5749	88	9	=	=	PUNCT
ejpam-5749	88	10	2γt2(g	2γt2(g	NUM
ejpam-5749	88	11	)	)	PUNCT
ejpam-5749	88	12	.	.	PUNCT
ejpam-5749	89	1	consequently	consequently	ADV
ejpam-5749	89	2	,	,	PUNCT
ejpam-5749	89	3	|v2|	|v2|	NOUN
ejpam-5749	89	4	=	=	SYM
ejpam-5749	89	5	γt2(g	γt2(g	NUM
ejpam-5749	89	6	)	)	PUNCT
ejpam-5749	89	7	and	and	CCONJ
ejpam-5749	89	8	v2	v2	PROPN
ejpam-5749	89	9	is	be	AUX
ejpam-5749	89	10	a	a	DET
ejpam-5749	89	11	γt2	γt2	NOUN
ejpam-5749	89	12	-	-	PUNCT
ejpam-5749	89	13	set	set	NOUN
ejpam-5749	89	14	of	of	ADP
ejpam-5749	89	15	g.	g.	NOUN
ejpam-5749	89	16	conversely	conversely	ADV
ejpam-5749	89	17	,	,	PUNCT
ejpam-5749	89	18	suppose	suppose	VERB
ejpam-5749	89	19	that	that	SCONJ
ejpam-5749	89	20	v2	v2	PROPN
ejpam-5749	89	21	is	be	AUX
ejpam-5749	89	22	a	a	DET
ejpam-5749	89	23	γt2	γt2	NOUN
ejpam-5749	89	24	-	-	PUNCT
ejpam-5749	89	25	set	set	NOUN
ejpam-5749	89	26	of	of	ADP
ejpam-5749	89	27	g.	g.	PROPN
ejpam-5749	89	28	then	then	ADV
ejpam-5749	89	29	inequality	inequality	NOUN
ejpam-5749	89	30	1	1	NUM
ejpam-5749	89	31	yields	yield	NOUN
ejpam-5749	89	32	|v1|	|v1|	NOUN
ejpam-5749	89	33	+	+	CCONJ
ejpam-5749	89	34	2γt2(g	2γt2(g	NUM
ejpam-5749	89	35	)	)	PUNCT
ejpam-5749	89	36	=	=	SYM
ejpam-5749	89	37	γt2r(g	γt2r(g	NUM
ejpam-5749	89	38	)	)	PUNCT
ejpam-5749	89	39	≤	≤	NOUN
ejpam-5749	89	40	2γt2(g	2γt2(g	NUM
ejpam-5749	89	41	)	)	PUNCT
ejpam-5749	89	42	,	,	PUNCT
ejpam-5749	89	43	showing	show	VERB
ejpam-5749	89	44	that	that	DET
ejpam-5749	89	45	v1	v1	NOUN
ejpam-5749	89	46	=	=	PUNCT
ejpam-5749	89	47	∅.	∅.	NOUN
ejpam-5749	89	48	this	this	DET
ejpam-5749	89	49	completes	complete	VERB
ejpam-5749	89	50	(	(	PUNCT
ejpam-5749	89	51	ii	ii	NOUN
ejpam-5749	89	52	)	)	PUNCT
ejpam-5749	89	53	.	.	PUNCT
ejpam-5749	90	1	proposition	proposition	NOUN
ejpam-5749	90	2	4	4	NUM
ejpam-5749	90	3	.	.	PUNCT
ejpam-5749	91	1	let	let	VERB
ejpam-5749	91	2	g	g	PRON
ejpam-5749	91	3	be	be	AUX
ejpam-5749	91	4	a	a	DET
ejpam-5749	91	5	graph	graph	NOUN
ejpam-5749	91	6	without	without	ADP
ejpam-5749	91	7	isolated	isolated	ADJ
ejpam-5749	91	8	vertices	vertex	NOUN
ejpam-5749	91	9	.	.	PUNCT
ejpam-5749	92	1	then	then	ADV
ejpam-5749	92	2	(	(	PUNCT
ejpam-5749	92	3	i	i	NOUN
ejpam-5749	92	4	)	)	PUNCT
ejpam-5749	92	5	γt2r(g	γt2r(g	NUM
ejpam-5749	92	6	)	)	PUNCT
ejpam-5749	92	7	=	=	PUNCT
ejpam-5749	92	8	γt2(g	γt2(g	VERB
ejpam-5749	92	9	)	)	PUNCT
ejpam-5749	92	10	if	if	SCONJ
ejpam-5749	92	11	and	and	CCONJ
ejpam-5749	92	12	only	only	ADV
ejpam-5749	92	13	if	if	SCONJ
ejpam-5749	92	14	g	g	PROPN
ejpam-5749	92	15	has	have	VERB
ejpam-5749	92	16	a	a	DET
ejpam-5749	92	17	γt2r	γt2r	NOUN
ejpam-5749	92	18	-	-	PUNCT
ejpam-5749	92	19	function	function	NOUN
ejpam-5749	92	20	f	f	NOUN
ejpam-5749	92	21	=	=	SYM
ejpam-5749	92	22	(	(	PUNCT
ejpam-5749	92	23	v0	v0	PROPN
ejpam-5749	92	24	,	,	PUNCT
ejpam-5749	92	25	v1	v1	NOUN
ejpam-5749	92	26	,	,	PUNCT
ejpam-5749	92	27	v2	v2	PROPN
ejpam-5749	92	28	)	)	PUNCT
ejpam-5749	92	29	for	for	ADP
ejpam-5749	92	30	which	which	PRON
ejpam-5749	92	31	v0	v0	NOUN
ejpam-5749	92	32	=	=	SYM
ejpam-5749	92	33	∅	∅	NOUN
ejpam-5749	92	34	;	;	PUNCT
ejpam-5749	92	35	and	and	CCONJ
ejpam-5749	92	36	(	(	PUNCT
ejpam-5749	92	37	ii	ii	NOUN
ejpam-5749	92	38	)	)	PUNCT
ejpam-5749	92	39	γt2r(g	γt2r(g	NUM
ejpam-5749	92	40	)	)	PUNCT
ejpam-5749	92	41	=	=	PUNCT
ejpam-5749	93	1	2γt2(g	2γt2(g	NUM
ejpam-5749	93	2	)	)	PUNCT
ejpam-5749	93	3	if	if	SCONJ
ejpam-5749	93	4	and	and	CCONJ
ejpam-5749	93	5	only	only	ADV
ejpam-5749	93	6	if	if	SCONJ
ejpam-5749	93	7	g	g	PROPN
ejpam-5749	93	8	has	have	VERB
ejpam-5749	93	9	a	a	DET
ejpam-5749	93	10	γt2r	γt2r	NOUN
ejpam-5749	93	11	-	-	PUNCT
ejpam-5749	93	12	function	function	NOUN
ejpam-5749	93	13	f	f	NOUN
ejpam-5749	93	14	=	=	SYM
ejpam-5749	93	15	(	(	PUNCT
ejpam-5749	93	16	v0	v0	PROPN
ejpam-5749	93	17	,	,	PUNCT
ejpam-5749	93	18	v1	v1	NOUN
ejpam-5749	93	19	,	,	PUNCT
ejpam-5749	93	20	v2	v2	PROPN
ejpam-5749	93	21	)	)	PUNCT
ejpam-5749	93	22	for	for	ADP
ejpam-5749	93	23	which	which	PRON
ejpam-5749	93	24	v2	v2	NOUN
ejpam-5749	93	25	is	be	AUX
ejpam-5749	93	26	a	a	DET
ejpam-5749	93	27	γt2	γt2	NOUN
ejpam-5749	93	28	-	-	PUNCT
ejpam-5749	93	29	set	set	NOUN
ejpam-5749	93	30	of	of	ADP
ejpam-5749	93	31	g.	g.	PROPN
ejpam-5749	93	32	proof	proof	NOUN
ejpam-5749	93	33	.	.	PUNCT
ejpam-5749	94	1	for	for	ADP
ejpam-5749	94	2	(	(	PUNCT
ejpam-5749	94	3	i	i	NOUN
ejpam-5749	94	4	)	)	PUNCT
ejpam-5749	94	5	,	,	PUNCT
ejpam-5749	94	6	suppose	suppose	VERB
ejpam-5749	94	7	that	that	SCONJ
ejpam-5749	94	8	γt2r(g	γt2r(g	PRON
ejpam-5749	94	9	)	)	PUNCT
ejpam-5749	94	10	=	=	PUNCT
ejpam-5749	94	11	γt2(g	γt2(g	NOUN
ejpam-5749	94	12	)	)	PUNCT
ejpam-5749	94	13	,	,	PUNCT
ejpam-5749	94	14	and	and	CCONJ
ejpam-5749	94	15	let	let	VERB
ejpam-5749	94	16	f	f	PROPN
ejpam-5749	94	17	=	=	SYM
ejpam-5749	94	18	(	(	PUNCT
ejpam-5749	94	19	v0	v0	PROPN
ejpam-5749	94	20	,	,	PUNCT
ejpam-5749	94	21	v1	v1	NOUN
ejpam-5749	94	22	,	,	PUNCT
ejpam-5749	94	23	v2	v2	PROPN
ejpam-5749	94	24	)	)	PUNCT
ejpam-5749	94	25	be	be	AUX
ejpam-5749	94	26	a	a	DET
ejpam-5749	94	27	γt2rfunction	γt2rfunction	NOUN
ejpam-5749	94	28	of	of	ADP
ejpam-5749	94	29	g.	g.	PROPN
ejpam-5749	94	30	then	then	ADV
ejpam-5749	94	31	|v1	|v1	PROPN
ejpam-5749	94	32	+	+	X
ejpam-5749	94	33	|v2|	|v2|	NOUN
ejpam-5749	94	34	=	=	SYM
ejpam-5749	94	35	|v1|+	|v1|+	DET
ejpam-5749	94	36	2|v2|	2|v2|	NUM
ejpam-5749	94	37	,	,	PUNCT
ejpam-5749	94	38	showing	show	VERB
ejpam-5749	94	39	that	that	SCONJ
ejpam-5749	94	40	v2	v2	NOUN
ejpam-5749	94	41	=	=	PUNCT
ejpam-5749	94	42	∅.	∅.	ADP
ejpam-5749	94	43	the	the	DET
ejpam-5749	94	44	converse	converse	NOUN
ejpam-5749	94	45	follows	follow	VERB
ejpam-5749	94	46	from	from	ADP
ejpam-5749	94	47	proposition	proposition	NOUN
ejpam-5749	94	48	3	3	NUM
ejpam-5749	94	49	.	.	PUNCT
ejpam-5749	94	50	b.	b.	PROPN
ejpam-5749	94	51	f.	f.	PROPN
ejpam-5749	94	52	bullang	bullang	PROPN
ejpam-5749	94	53	et	et	PROPN
ejpam-5749	94	54	al	al	PROPN
ejpam-5749	94	55	.	.	PUNCT
ejpam-5749	94	56	/	/	SYM
ejpam-5749	94	57	eur	eur	PROPN
ejpam-5749	94	58	.	.	PUNCT
ejpam-5749	95	1	j.	j.	PROPN
ejpam-5749	95	2	pure	pure	PROPN
ejpam-5749	95	3	appl	appl	PROPN
ejpam-5749	95	4	.	.	PROPN
ejpam-5749	95	5	math	math	PROPN
ejpam-5749	95	6	,	,	PUNCT
ejpam-5749	95	7	18	18	NUM
ejpam-5749	95	8	(	(	PUNCT
ejpam-5749	95	9	1	1	NUM
ejpam-5749	95	10	)	)	PUNCT
ejpam-5749	95	11	(	(	PUNCT
ejpam-5749	95	12	2025	2025	NUM
ejpam-5749	95	13	)	)	PUNCT
ejpam-5749	95	14	,	,	PUNCT
ejpam-5749	95	15	5749	5749	NUM
ejpam-5749	95	16	5	5	NUM
ejpam-5749	95	17	of	of	ADP
ejpam-5749	95	18	15	15	NUM
ejpam-5749	95	19	to	to	PART
ejpam-5749	95	20	prove	prove	VERB
ejpam-5749	95	21	(	(	PUNCT
ejpam-5749	95	22	ii	ii	NOUN
ejpam-5749	95	23	)	)	PUNCT
ejpam-5749	95	24	,	,	PUNCT
ejpam-5749	95	25	if	if	SCONJ
ejpam-5749	95	26	γt2r(g	γt2r(g	NUM
ejpam-5749	95	27	)	)	PUNCT
ejpam-5749	95	28	=	=	SYM
ejpam-5749	96	1	2γt2(g	2γt2(g	NUM
ejpam-5749	96	2	)	)	PUNCT
ejpam-5749	96	3	and	and	CCONJ
ejpam-5749	96	4	f	f	X
ejpam-5749	96	5	=	=	SYM
ejpam-5749	96	6	(	(	PUNCT
ejpam-5749	96	7	v0	v0	PROPN
ejpam-5749	96	8	,	,	PUNCT
ejpam-5749	96	9	v1	v1	NOUN
ejpam-5749	96	10	,	,	PUNCT
ejpam-5749	96	11	v2	v2	PROPN
ejpam-5749	96	12	)	)	PUNCT
ejpam-5749	96	13	is	be	AUX
ejpam-5749	96	14	a	a	DET
ejpam-5749	96	15	γt2rfunction	γt2rfunction	NOUN
ejpam-5749	96	16	of	of	ADP
ejpam-5749	96	17	g	g	NOUN
ejpam-5749	96	18	,	,	PUNCT
ejpam-5749	96	19	then	then	ADV
ejpam-5749	96	20	|v1|	|v1|	NOUN
ejpam-5749	96	21	+	+	CCONJ
ejpam-5749	96	22	2|v2|	2|v2|	NUM
ejpam-5749	96	23	=	=	SYM
ejpam-5749	96	24	2|v1|	2|v1|	NUM
ejpam-5749	96	25	+	+	CCONJ
ejpam-5749	96	26	2|v2|	2|v2|	NUM
ejpam-5749	96	27	.	.	PUNCT
ejpam-5749	97	1	necessarily	necessarily	ADV
ejpam-5749	97	2	,	,	PUNCT
ejpam-5749	97	3	v1	v1	NOUN
ejpam-5749	97	4	=	=	SYM
ejpam-5749	97	5	∅.	∅.	NOUN
ejpam-5749	97	6	by	by	ADP
ejpam-5749	97	7	proposition	proposition	NOUN
ejpam-5749	97	8	3	3	NUM
ejpam-5749	97	9	,	,	PUNCT
ejpam-5749	97	10	v2	v2	PROPN
ejpam-5749	97	11	is	be	AUX
ejpam-5749	97	12	a	a	DET
ejpam-5749	97	13	γt2	γt2	NOUN
ejpam-5749	97	14	-	-	PUNCT
ejpam-5749	97	15	set	set	NOUN
ejpam-5749	97	16	of	of	ADP
ejpam-5749	97	17	g.	g.	NOUN
ejpam-5749	97	18	conversely	conversely	ADV
ejpam-5749	97	19	,	,	PUNCT
ejpam-5749	97	20	by	by	ADP
ejpam-5749	97	21	proposition	proposition	NOUN
ejpam-5749	97	22	3	3	NUM
ejpam-5749	97	23	,	,	PUNCT
ejpam-5749	97	24	v1	v1	NOUN
ejpam-5749	97	25	=	=	SYM
ejpam-5749	97	26	∅	∅	NOUN
ejpam-5749	97	27	and	and	CCONJ
ejpam-5749	97	28	γt2r(g	γt2r(g	NUM
ejpam-5749	97	29	)	)	PUNCT
ejpam-5749	97	30	=	=	SYM
ejpam-5749	97	31	2|v2|	2|v2|	NUM
ejpam-5749	97	32	=	=	SYM
ejpam-5749	97	33	2γt2(g	2γt2(g	NUM
ejpam-5749	97	34	)	)	PUNCT
ejpam-5749	97	35	.	.	PUNCT
ejpam-5749	98	1	proposition	proposition	NOUN
ejpam-5749	98	2	5	5	NUM
ejpam-5749	98	3	.	.	PUNCT
ejpam-5749	99	1	let	let	VERB
ejpam-5749	99	2	g	g	PRON
ejpam-5749	99	3	be	be	AUX
ejpam-5749	99	4	a	a	DET
ejpam-5749	99	5	connected	connected	ADJ
ejpam-5749	99	6	graph	graph	NOUN
ejpam-5749	99	7	of	of	ADP
ejpam-5749	99	8	order	order	NOUN
ejpam-5749	99	9	n	n	PRON
ejpam-5749	99	10	≥	≥	NOUN
ejpam-5749	99	11	2	2	NUM
ejpam-5749	99	12	.	.	PUNCT
ejpam-5749	100	1	then	then	ADV
ejpam-5749	100	2	γt2r(g	γt2r(g	NUM
ejpam-5749	100	3	)	)	PUNCT
ejpam-5749	100	4	=	=	SYM
ejpam-5749	100	5	2	2	NUM
ejpam-5749	100	6	if	if	SCONJ
ejpam-5749	100	7	and	and	CCONJ
ejpam-5749	100	8	only	only	ADV
ejpam-5749	100	9	if	if	SCONJ
ejpam-5749	100	10	g	g	PROPN
ejpam-5749	100	11	=	=	SYM
ejpam-5749	100	12	k2	k2	PROPN
ejpam-5749	100	13	.	.	PUNCT
ejpam-5749	101	1	proof	proof	NOUN
ejpam-5749	101	2	.	.	PUNCT
ejpam-5749	102	1	let	let	VERB
ejpam-5749	102	2	g	g	PROPN
ejpam-5749	102	3	=	=	SYM
ejpam-5749	102	4	k2	k2	PROPN
ejpam-5749	102	5	,	,	PUNCT
ejpam-5749	102	6	then	then	ADV
ejpam-5749	102	7	γt2r(g	γt2r(g	NUM
ejpam-5749	102	8	)	)	PUNCT
ejpam-5749	102	9	=	=	SYM
ejpam-5749	103	1	2	2	X
ejpam-5749	103	2	.	.	X
ejpam-5749	103	3	conversely	conversely	ADV
ejpam-5749	103	4	,	,	PUNCT
ejpam-5749	103	5	assume	assume	VERB
ejpam-5749	103	6	that	that	SCONJ
ejpam-5749	103	7	γt2r(g	γt2r(g	PRON
ejpam-5749	103	8	)	)	PUNCT
ejpam-5749	103	9	=	=	SYM
ejpam-5749	103	10	2	2	NUM
ejpam-5749	103	11	and	and	CCONJ
ejpam-5749	103	12	let	let	VERB
ejpam-5749	103	13	f	f	PROPN
ejpam-5749	103	14	=	=	SYM
ejpam-5749	103	15	(	(	PUNCT
ejpam-5749	103	16	v0	v0	PROPN
ejpam-5749	103	17	,	,	PUNCT
ejpam-5749	103	18	v1	v1	NOUN
ejpam-5749	103	19	,	,	PUNCT
ejpam-5749	103	20	v2	v2	PROPN
ejpam-5749	103	21	)	)	PUNCT
ejpam-5749	103	22	be	be	AUX
ejpam-5749	103	23	a	a	DET
ejpam-5749	103	24	γt2r	γt2r	NOUN
ejpam-5749	103	25	-	-	PUNCT
ejpam-5749	103	26	function	function	NOUN
ejpam-5749	103	27	of	of	ADP
ejpam-5749	103	28	g.	g.	PROPN
ejpam-5749	103	29	since	since	SCONJ
ejpam-5749	103	30	v1	v1	PROPN
ejpam-5749	103	31	∪	∪	NOUN
ejpam-5749	103	32	v2	v2	NOUN
ejpam-5749	103	33	is	be	AUX
ejpam-5749	103	34	a	a	DET
ejpam-5749	103	35	semitotal	semitotal	ADJ
ejpam-5749	103	36	dominating	dominating	NOUN
ejpam-5749	103	37	set	set	NOUN
ejpam-5749	103	38	,	,	PUNCT
ejpam-5749	103	39	2	2	NUM
ejpam-5749	103	40	≤	≤	NOUN
ejpam-5749	103	41	|v1|	|v1|	NOUN
ejpam-5749	103	42	+	+	CCONJ
ejpam-5749	103	43	|v2|	|v2|	NOUN
ejpam-5749	103	44	≤	≤	NOUN
ejpam-5749	103	45	|v1|	|v1|	NOUN
ejpam-5749	103	46	+	+	CCONJ
ejpam-5749	103	47	2|v2|	2|v2|	NUM
ejpam-5749	103	48	=	=	SYM
ejpam-5749	103	49	2	2	X
ejpam-5749	103	50	.	.	X
ejpam-5749	103	51	necessarily	necessarily	ADV
ejpam-5749	103	52	,	,	PUNCT
ejpam-5749	103	53	v2	v2	NOUN
ejpam-5749	103	54	=	=	SYM
ejpam-5749	103	55	∅	∅	NOUN
ejpam-5749	103	56	and	and	CCONJ
ejpam-5749	103	57	,	,	PUNCT
ejpam-5749	103	58	by	by	ADP
ejpam-5749	103	59	proposition	proposition	NOUN
ejpam-5749	103	60	3	3	NUM
ejpam-5749	103	61	,	,	PUNCT
ejpam-5749	103	62	v0	v0	NOUN
ejpam-5749	103	63	=	=	PUNCT
ejpam-5749	103	64	∅.	∅.	NOUN
ejpam-5749	103	65	therefore	therefore	ADV
ejpam-5749	103	66	,	,	PUNCT
ejpam-5749	103	67	v	v	X
ejpam-5749	103	68	(	(	PUNCT
ejpam-5749	103	69	g	g	NOUN
ejpam-5749	103	70	)	)	PUNCT
ejpam-5749	103	71	=	=	SYM
ejpam-5749	103	72	v1	v1	NOUN
ejpam-5749	103	73	,	,	PUNCT
ejpam-5749	103	74	that	that	ADV
ejpam-5749	103	75	is	is	ADV
ejpam-5749	103	76	,	,	PUNCT
ejpam-5749	103	77	g	g	PROPN
ejpam-5749	103	78	=	=	SYM
ejpam-5749	103	79	k2	k2	PROPN
ejpam-5749	103	80	.	.	PUNCT
ejpam-5749	104	1	proposition	proposition	NOUN
ejpam-5749	104	2	6	6	NUM
ejpam-5749	104	3	.	.	PUNCT
ejpam-5749	105	1	let	let	VERB
ejpam-5749	105	2	g	g	PRON
ejpam-5749	105	3	be	be	AUX
ejpam-5749	105	4	a	a	DET
ejpam-5749	105	5	connected	connected	ADJ
ejpam-5749	105	6	graph	graph	NOUN
ejpam-5749	105	7	of	of	ADP
ejpam-5749	105	8	order	order	NOUN
ejpam-5749	105	9	n	n	PRON
ejpam-5749	105	10	≥	≥	NOUN
ejpam-5749	105	11	3	3	NUM
ejpam-5749	105	12	.	.	PUNCT
ejpam-5749	106	1	then	then	ADV
ejpam-5749	106	2	γt2r(g	γt2r(g	NUM
ejpam-5749	106	3	)	)	PUNCT
ejpam-5749	106	4	=	=	SYM
ejpam-5749	106	5	3	3	NUM
ejpam-5749	106	6	if	if	SCONJ
ejpam-5749	106	7	and	and	CCONJ
ejpam-5749	106	8	only	only	ADV
ejpam-5749	106	9	if	if	SCONJ
ejpam-5749	106	10	either	either	DET
ejpam-5749	106	11	γ(g	γ(g	PROPN
ejpam-5749	106	12	)	)	PUNCT
ejpam-5749	106	13	=	=	SYM
ejpam-5749	107	1	1	1	NUM
ejpam-5749	107	2	or	or	CCONJ
ejpam-5749	107	3	there	there	ADV
ejpam-5749	107	4	exist	exist	VERB
ejpam-5749	107	5	u	u	NOUN
ejpam-5749	107	6	and	and	CCONJ
ejpam-5749	107	7	v	v	NOUN
ejpam-5749	107	8	for	for	ADP
ejpam-5749	107	9	which	which	PRON
ejpam-5749	107	10	ng[v	ng[v	PROPN
ejpam-5749	107	11	]	]	X
ejpam-5749	107	12	=	=	SYM
ejpam-5749	107	13	v	v	X
ejpam-5749	107	14	(	(	PUNCT
ejpam-5749	107	15	g	g	NOUN
ejpam-5749	107	16	)	)	PUNCT
ejpam-5749	107	17	\	\	NOUN
ejpam-5749	107	18	{	{	PUNCT
ejpam-5749	107	19	u	u	NOUN
ejpam-5749	107	20	}	}	PUNCT
ejpam-5749	107	21	and	and	CCONJ
ejpam-5749	107	22	dg(u	dg(u	X
ejpam-5749	107	23	,	,	PUNCT
ejpam-5749	107	24	v	v	NOUN
ejpam-5749	107	25	)	)	PUNCT
ejpam-5749	107	26	=	=	SYM
ejpam-5749	107	27	2	2	X
ejpam-5749	107	28	.	.	PUNCT
ejpam-5749	107	29	proof	proof	NOUN
ejpam-5749	107	30	.	.	PUNCT
ejpam-5749	108	1	suppose	suppose	VERB
ejpam-5749	108	2	that	that	SCONJ
ejpam-5749	108	3	γt2r(g	γt2r(g	PRON
ejpam-5749	108	4	)	)	PUNCT
ejpam-5749	108	5	=	=	SYM
ejpam-5749	108	6	3	3	NUM
ejpam-5749	108	7	,	,	PUNCT
ejpam-5749	108	8	and	and	CCONJ
ejpam-5749	108	9	let	let	VERB
ejpam-5749	108	10	f	f	PROPN
ejpam-5749	108	11	=	=	SYM
ejpam-5749	108	12	(	(	PUNCT
ejpam-5749	108	13	v0	v0	PROPN
ejpam-5749	108	14	,	,	PUNCT
ejpam-5749	108	15	v1	v1	NOUN
ejpam-5749	108	16	,	,	PUNCT
ejpam-5749	108	17	v2	v2	PROPN
ejpam-5749	108	18	)	)	PUNCT
ejpam-5749	108	19	be	be	AUX
ejpam-5749	108	20	a	a	DET
ejpam-5749	108	21	γt2r	γt2r	NOUN
ejpam-5749	108	22	-	-	PUNCT
ejpam-5749	108	23	function	function	NOUN
ejpam-5749	108	24	of	of	ADP
ejpam-5749	108	25	g.	g.	PROPN
ejpam-5749	108	26	if	if	SCONJ
ejpam-5749	108	27	|v1|	|v1|	NUM
ejpam-5749	108	28	=	=	SYM
ejpam-5749	108	29	3	3	NUM
ejpam-5749	108	30	,	,	PUNCT
ejpam-5749	108	31	then	then	ADV
ejpam-5749	108	32	since	since	SCONJ
ejpam-5749	108	33	g	g	PROPN
ejpam-5749	108	34	is	be	AUX
ejpam-5749	108	35	connected	connect	VERB
ejpam-5749	108	36	,	,	PUNCT
ejpam-5749	108	37	g	g	NOUN
ejpam-5749	108	38	=	=	PUNCT
ejpam-5749	108	39	k3	k3	X
ejpam-5749	108	40	or	or	CCONJ
ejpam-5749	108	41	g	g	PROPN
ejpam-5749	108	42	=	=	PROPN
ejpam-5749	108	43	p3	p3	PROPN
ejpam-5749	108	44	.	.	PUNCT
ejpam-5749	109	1	in	in	ADP
ejpam-5749	109	2	any	any	DET
ejpam-5749	109	3	case	case	NOUN
ejpam-5749	109	4	,	,	PUNCT
ejpam-5749	109	5	γ(g	γ(g	PROPN
ejpam-5749	109	6	)	)	PUNCT
ejpam-5749	109	7	=	=	SYM
ejpam-5749	109	8	1	1	X
ejpam-5749	109	9	.	.	PUNCT
ejpam-5749	109	10	suppose	suppose	VERB
ejpam-5749	109	11	that	that	SCONJ
ejpam-5749	109	12	|v2|	|v2|	NOUN
ejpam-5749	109	13	=	=	SYM
ejpam-5749	109	14	1	1	NUM
ejpam-5749	109	15	=	=	NOUN
ejpam-5749	109	16	|v1|	|v1|	NOUN
ejpam-5749	109	17	,	,	PUNCT
ejpam-5749	109	18	say	say	VERB
ejpam-5749	109	19	v2	v2	NOUN
ejpam-5749	109	20	=	=	SYM
ejpam-5749	109	21	{	{	PUNCT
ejpam-5749	109	22	v	v	NOUN
ejpam-5749	109	23	}	}	PUNCT
ejpam-5749	109	24	and	and	CCONJ
ejpam-5749	109	25	v1	v1	VERB
ejpam-5749	109	26	=	=	SYM
ejpam-5749	109	27	{	{	PUNCT
ejpam-5749	109	28	u	u	NOUN
ejpam-5749	109	29	}	}	PUNCT
ejpam-5749	109	30	.	.	PUNCT
ejpam-5749	110	1	then	then	ADV
ejpam-5749	110	2	v0	v0	VERB
ejpam-5749	110	3	̸=	̸=	PROPN
ejpam-5749	110	4	∅	∅	NOUN
ejpam-5749	110	5	and	and	CCONJ
ejpam-5749	110	6	v0	v0	NOUN
ejpam-5749	110	7	=	=	SYM
ejpam-5749	110	8	v	v	PROPN
ejpam-5749	110	9	(	(	PUNCT
ejpam-5749	110	10	g	g	NOUN
ejpam-5749	110	11	)	)	PUNCT
ejpam-5749	110	12	\	\	NOUN
ejpam-5749	110	13	{	{	PUNCT
ejpam-5749	110	14	u	u	NOUN
ejpam-5749	110	15	}	}	PUNCT
ejpam-5749	110	16	⊆	⊆	NUM
ejpam-5749	110	17	ng[v	ng[v	NOUN
ejpam-5749	110	18	]	]	PUNCT
ejpam-5749	110	19	.	.	PUNCT
ejpam-5749	111	1	if	if	SCONJ
ejpam-5749	111	2	uv	uv	PROPN
ejpam-5749	111	3	∈	∈	PROPN
ejpam-5749	111	4	e(g	e(g	PROPN
ejpam-5749	111	5	)	)	PUNCT
ejpam-5749	111	6	,	,	PUNCT
ejpam-5749	111	7	then	then	ADV
ejpam-5749	111	8	ng[v	ng[v	X
ejpam-5749	111	9	]	]	X
ejpam-5749	111	10	=	=	SYM
ejpam-5749	111	11	v	v	X
ejpam-5749	111	12	(	(	PUNCT
ejpam-5749	111	13	g	g	NOUN
ejpam-5749	111	14	)	)	PUNCT
ejpam-5749	111	15	and	and	CCONJ
ejpam-5749	111	16	γ(g	γ(g	PROPN
ejpam-5749	111	17	)	)	PUNCT
ejpam-5749	111	18	=	=	PUNCT
ejpam-5749	112	1	1	1	X
ejpam-5749	112	2	.	.	PUNCT
ejpam-5749	112	3	otherwise	otherwise	ADV
ejpam-5749	112	4	,	,	PUNCT
ejpam-5749	112	5	dg(u	dg(u	X
ejpam-5749	112	6	,	,	PUNCT
ejpam-5749	112	7	v	v	NOUN
ejpam-5749	112	8	)	)	PUNCT
ejpam-5749	112	9	=	=	SYM
ejpam-5749	112	10	2	2	X
ejpam-5749	112	11	.	.	PUNCT
ejpam-5749	112	12	conversely	conversely	ADV
ejpam-5749	112	13	,	,	PUNCT
ejpam-5749	112	14	suppose	suppose	VERB
ejpam-5749	112	15	that	that	SCONJ
ejpam-5749	112	16	either	either	CCONJ
ejpam-5749	112	17	there	there	PRON
ejpam-5749	112	18	exists	exist	VERB
ejpam-5749	112	19	v	v	ADP
ejpam-5749	112	20	∈	∈	PROPN
ejpam-5749	112	21	v	v	NOUN
ejpam-5749	112	22	(	(	PUNCT
ejpam-5749	112	23	g	g	NOUN
ejpam-5749	112	24	)	)	PUNCT
ejpam-5749	112	25	for	for	ADP
ejpam-5749	112	26	which	which	PRON
ejpam-5749	112	27	ng[v	ng[v	PROPN
ejpam-5749	112	28	]	]	X
ejpam-5749	112	29	=	=	SYM
ejpam-5749	112	30	v	v	X
ejpam-5749	112	31	(	(	PUNCT
ejpam-5749	112	32	g	g	NOUN
ejpam-5749	112	33	)	)	PUNCT
ejpam-5749	112	34	or	or	CCONJ
ejpam-5749	112	35	there	there	PRON
ejpam-5749	112	36	exist	exist	VERB
ejpam-5749	112	37	u	u	NOUN
ejpam-5749	112	38	,	,	PUNCT
ejpam-5749	112	39	v	v	NOUN
ejpam-5749	112	40	∈	∈	PROPN
ejpam-5749	112	41	v	v	NOUN
ejpam-5749	112	42	(	(	PUNCT
ejpam-5749	112	43	g	g	NOUN
ejpam-5749	112	44	)	)	PUNCT
ejpam-5749	113	1	such	such	ADJ
ejpam-5749	113	2	that	that	DET
ejpam-5749	113	3	v	v	NOUN
ejpam-5749	113	4	(	(	PUNCT
ejpam-5749	113	5	g	g	NOUN
ejpam-5749	113	6	)	)	PUNCT
ejpam-5749	113	7	\	\	NOUN
ejpam-5749	113	8	{	{	PUNCT
ejpam-5749	113	9	u	u	NOUN
ejpam-5749	113	10	}	}	PUNCT
ejpam-5749	113	11	=	=	PUNCT
ejpam-5749	113	12	ng[v	ng[v	X
ejpam-5749	113	13	]	]	PUNCT
ejpam-5749	113	14	and	and	CCONJ
ejpam-5749	113	15	dg(u	dg(u	X
ejpam-5749	113	16	,	,	PUNCT
ejpam-5749	113	17	v	v	NOUN
ejpam-5749	113	18	)	)	PUNCT
ejpam-5749	113	19	=	=	SYM
ejpam-5749	113	20	2	2	X
ejpam-5749	113	21	.	.	X
ejpam-5749	113	22	in	in	ADP
ejpam-5749	113	23	any	any	DET
ejpam-5749	113	24	case	case	NOUN
ejpam-5749	113	25	,	,	PUNCT
ejpam-5749	113	26	let	let	VERB
ejpam-5749	113	27	v0	v0	NOUN
ejpam-5749	113	28	=	=	SYM
ejpam-5749	113	29	v	v	PROPN
ejpam-5749	113	30	(	(	PUNCT
ejpam-5749	113	31	g)\{u	g)\{u	PROPN
ejpam-5749	113	32	,	,	PUNCT
ejpam-5749	113	33	v	v	NOUN
ejpam-5749	113	34	}	}	PUNCT
ejpam-5749	113	35	,	,	PUNCT
ejpam-5749	113	36	v1	v1	NOUN
ejpam-5749	113	37	=	=	SYM
ejpam-5749	113	38	{	{	PUNCT
ejpam-5749	113	39	u	u	NOUN
ejpam-5749	113	40	}	}	PUNCT
ejpam-5749	113	41	and	and	CCONJ
ejpam-5749	113	42	v2	v2	NOUN
ejpam-5749	113	43	=	=	SYM
ejpam-5749	113	44	{	{	PUNCT
ejpam-5749	113	45	v	v	NOUN
ejpam-5749	113	46	}	}	PUNCT
ejpam-5749	113	47	.	.	PUNCT
ejpam-5749	114	1	then	then	ADV
ejpam-5749	114	2	f	f	PROPN
ejpam-5749	114	3	∈	∈	PROPN
ejpam-5749	114	4	srdf	srdf	NOUN
ejpam-5749	114	5	(	(	PUNCT
ejpam-5749	114	6	g	g	NOUN
ejpam-5749	114	7	)	)	PUNCT
ejpam-5749	114	8	so	so	SCONJ
ejpam-5749	114	9	that	that	SCONJ
ejpam-5749	114	10	γt2r(g	γt2r(g	NUM
ejpam-5749	114	11	)	)	PUNCT
ejpam-5749	114	12	≤	≤	NOUN
ejpam-5749	114	13	ωg(f	ωg(f	NOUN
ejpam-5749	114	14	)	)	PUNCT
ejpam-5749	114	15	=	=	SYM
ejpam-5749	115	1	3	3	X
ejpam-5749	115	2	.	.	PUNCT
ejpam-5749	115	3	since	since	SCONJ
ejpam-5749	115	4	n	n	PROPN
ejpam-5749	115	5	≥	≥	NOUN
ejpam-5749	115	6	3	3	NUM
ejpam-5749	115	7	,	,	PUNCT
ejpam-5749	115	8	proposition	proposition	NOUN
ejpam-5749	115	9	5	5	NUM
ejpam-5749	115	10	implies	imply	VERB
ejpam-5749	115	11	that	that	SCONJ
ejpam-5749	115	12	γt2r(g	γt2r(g	NUM
ejpam-5749	115	13	)	)	PUNCT
ejpam-5749	115	14	=	=	SYM
ejpam-5749	115	15	3	3	X
ejpam-5749	115	16	.	.	X
ejpam-5749	115	17	proposition	proposition	NOUN
ejpam-5749	115	18	7	7	NUM
ejpam-5749	115	19	.	.	PUNCT
ejpam-5749	116	1	let	let	VERB
ejpam-5749	116	2	g	g	PRON
ejpam-5749	116	3	be	be	AUX
ejpam-5749	116	4	a	a	DET
ejpam-5749	116	5	connected	connected	ADJ
ejpam-5749	116	6	graph	graph	NOUN
ejpam-5749	116	7	.	.	PUNCT
ejpam-5749	117	1	then	then	ADV
ejpam-5749	117	2	γt2r(g	γt2r(g	NUM
ejpam-5749	117	3	)	)	PUNCT
ejpam-5749	117	4	=	=	SYM
ejpam-5749	117	5	4	4	NUM
ejpam-5749	117	6	if	if	SCONJ
ejpam-5749	117	7	and	and	CCONJ
ejpam-5749	117	8	only	only	ADV
ejpam-5749	117	9	if	if	SCONJ
ejpam-5749	117	10	γ(g	γ(g	PROPN
ejpam-5749	117	11	)	)	PUNCT
ejpam-5749	117	12	≥	≥	NOUN
ejpam-5749	117	13	2	2	NUM
ejpam-5749	117	14	and	and	CCONJ
ejpam-5749	117	15	either	either	CCONJ
ejpam-5749	117	16	(	(	PUNCT
ejpam-5749	117	17	i	i	NOUN
ejpam-5749	117	18	)	)	PUNCT
ejpam-5749	117	19	γt2(g	γt2(g	ADJ
ejpam-5749	117	20	)	)	PUNCT
ejpam-5749	117	21	=	=	SYM
ejpam-5749	117	22	2	2	NUM
ejpam-5749	117	23	and	and	CCONJ
ejpam-5749	117	24	for	for	ADP
ejpam-5749	117	25	all	all	DET
ejpam-5749	117	26	γt2	γt2	NOUN
ejpam-5749	117	27	-	-	PUNCT
ejpam-5749	117	28	sets	set	NOUN
ejpam-5749	117	29	{	{	PUNCT
ejpam-5749	117	30	u	u	NOUN
ejpam-5749	117	31	,	,	PUNCT
ejpam-5749	117	32	v	v	NOUN
ejpam-5749	117	33	}	}	PUNCT
ejpam-5749	117	34	of	of	ADP
ejpam-5749	117	35	g	g	NOUN
ejpam-5749	117	36	,	,	PUNCT
ejpam-5749	117	37	ng(u)\ng(v	ng(u)\ng(v	ADJ
ejpam-5749	117	38	)	)	PUNCT
ejpam-5749	117	39	̸=	̸=	PROPN
ejpam-5749	117	40	∅	∅	NOUN
ejpam-5749	117	41	and	and	CCONJ
ejpam-5749	117	42	ng(v)\ng(u	ng(v)\ng(u	ADJ
ejpam-5749	117	43	)	)	PUNCT
ejpam-5749	117	44	̸=	̸=	PROPN
ejpam-5749	117	45	∅	∅	NOUN
ejpam-5749	117	46	;	;	PUNCT
ejpam-5749	117	47	or	or	CCONJ
ejpam-5749	117	48	(	(	PUNCT
ejpam-5749	117	49	ii	ii	NOUN
ejpam-5749	117	50	)	)	PUNCT
ejpam-5749	117	51	γt2(g	γt2(g	ADJ
ejpam-5749	117	52	)	)	PUNCT
ejpam-5749	117	53	=	=	SYM
ejpam-5749	117	54	3	3	NUM
ejpam-5749	117	55	and	and	CCONJ
ejpam-5749	117	56	g	g	PROPN
ejpam-5749	117	57	has	have	VERB
ejpam-5749	117	58	distinct	distinct	ADJ
ejpam-5749	117	59	vertices	vertex	NOUN
ejpam-5749	117	60	u	u	NOUN
ejpam-5749	117	61	,	,	PUNCT
ejpam-5749	117	62	v	v	NOUN
ejpam-5749	117	63	and	and	CCONJ
ejpam-5749	117	64	w	w	NOUN
ejpam-5749	117	65	for	for	ADP
ejpam-5749	117	66	which	which	PRON
ejpam-5749	117	67	v	v	ADP
ejpam-5749	117	68	(	(	PUNCT
ejpam-5749	117	69	g	g	NOUN
ejpam-5749	117	70	)	)	PUNCT
ejpam-5749	117	71	\	\	NOUN
ejpam-5749	117	72	{	{	PUNCT
ejpam-5749	117	73	u	u	NOUN
ejpam-5749	117	74	,	,	PUNCT
ejpam-5749	117	75	w	w	NOUN
ejpam-5749	117	76	}	}	PUNCT
ejpam-5749	117	77	=	=	PUNCT
ejpam-5749	117	78	ng[v	ng[v	X
ejpam-5749	117	79	]	]	PUNCT
ejpam-5749	117	80	and	and	CCONJ
ejpam-5749	117	81	dg(u	dg(u	X
ejpam-5749	117	82	,	,	PUNCT
ejpam-5749	117	83	v	v	NOUN
ejpam-5749	117	84	)	)	PUNCT
ejpam-5749	117	85	=	=	SYM
ejpam-5749	117	86	2	2	NUM
ejpam-5749	117	87	and	and	CCONJ
ejpam-5749	117	88	dg(w	dg(w	NOUN
ejpam-5749	117	89	,	,	PUNCT
ejpam-5749	117	90	v	v	NOUN
ejpam-5749	117	91	)	)	PUNCT
ejpam-5749	117	92	=	=	SYM
ejpam-5749	117	93	2	2	X
ejpam-5749	117	94	.	.	PUNCT
ejpam-5749	117	95	proof	proof	NOUN
ejpam-5749	117	96	.	.	PUNCT
ejpam-5749	118	1	suppose	suppose	VERB
ejpam-5749	118	2	that	that	SCONJ
ejpam-5749	118	3	γt2r(g	γt2r(g	PRON
ejpam-5749	118	4	)	)	PUNCT
ejpam-5749	118	5	=	=	SYM
ejpam-5749	119	1	4	4	X
ejpam-5749	119	2	.	.	PUNCT
ejpam-5749	119	3	by	by	ADP
ejpam-5749	119	4	proposition	proposition	NOUN
ejpam-5749	119	5	5	5	NUM
ejpam-5749	119	6	and	and	CCONJ
ejpam-5749	119	7	proposition	proposition	NOUN
ejpam-5749	119	8	6	6	NUM
ejpam-5749	119	9	,	,	PUNCT
ejpam-5749	119	10	γ(g	γ(g	PROPN
ejpam-5749	119	11	)	)	PUNCT
ejpam-5749	119	12	≥	≥	NOUN
ejpam-5749	119	13	2	2	NUM
ejpam-5749	119	14	.	.	PUNCT
ejpam-5749	120	1	let	let	VERB
ejpam-5749	120	2	f	f	PROPN
ejpam-5749	120	3	=	=	SYM
ejpam-5749	120	4	(	(	PUNCT
ejpam-5749	120	5	v0	v0	PROPN
ejpam-5749	120	6	,	,	PUNCT
ejpam-5749	120	7	v1	v1	NOUN
ejpam-5749	120	8	,	,	PUNCT
ejpam-5749	120	9	v2	v2	PROPN
ejpam-5749	120	10	)	)	PUNCT
ejpam-5749	120	11	is	be	AUX
ejpam-5749	120	12	a	a	DET
ejpam-5749	120	13	γt2r	γt2r	NOUN
ejpam-5749	120	14	-	-	PUNCT
ejpam-5749	120	15	function	function	NOUN
ejpam-5749	120	16	of	of	ADP
ejpam-5749	120	17	g.	g.	PROPN
ejpam-5749	120	18	in	in	ADP
ejpam-5749	120	19	view	view	NOUN
ejpam-5749	120	20	of	of	ADP
ejpam-5749	120	21	proposition	proposition	NOUN
ejpam-5749	120	22	3	3	NUM
ejpam-5749	120	23	,	,	PUNCT
ejpam-5749	120	24	if	if	SCONJ
ejpam-5749	120	25	v2	v2	NOUN
ejpam-5749	120	26	=	=	NOUN
ejpam-5749	120	27	∅	∅	NOUN
ejpam-5749	120	28	,	,	PUNCT
ejpam-5749	120	29	then	then	ADV
ejpam-5749	120	30	|v	|v	PROPN
ejpam-5749	120	31	(	(	PUNCT
ejpam-5749	120	32	g)|	g)|	NOUN
ejpam-5749	120	33	=	=	SYM
ejpam-5749	120	34	4	4	NUM
ejpam-5749	120	35	and	and	CCONJ
ejpam-5749	120	36	γt2r(g	γt2r(g	NUM
ejpam-5749	120	37	)	)	PUNCT
ejpam-5749	120	38	≤	≤	NOUN
ejpam-5749	120	39	3	3	NUM
ejpam-5749	120	40	,	,	PUNCT
ejpam-5749	120	41	a	a	DET
ejpam-5749	120	42	contradiction	contradiction	NOUN
ejpam-5749	120	43	.	.	PUNCT
ejpam-5749	121	1	thus	thus	ADV
ejpam-5749	121	2	,	,	PUNCT
ejpam-5749	121	3	either	either	ADV
ejpam-5749	121	4	|v2|	|v2|	ADV
ejpam-5749	121	5	=	=	SYM
ejpam-5749	121	6	2	2	NUM
ejpam-5749	121	7	and	and	CCONJ
ejpam-5749	121	8	v1	v1	NOUN
ejpam-5749	121	9	=	=	SYM
ejpam-5749	121	10	∅	∅	NOUN
ejpam-5749	121	11	or	or	CCONJ
ejpam-5749	121	12	|v2|	|v2|	NOUN
ejpam-5749	121	13	=	=	SYM
ejpam-5749	121	14	1	1	NUM
ejpam-5749	121	15	and	and	CCONJ
ejpam-5749	121	16	|v1|	|v1|	NOUN
ejpam-5749	121	17	=	=	SYM
ejpam-5749	121	18	2	2	X
ejpam-5749	121	19	.	.	PUNCT
ejpam-5749	121	20	by	by	ADP
ejpam-5749	121	21	proposition	proposition	NOUN
ejpam-5749	121	22	3	3	NUM
ejpam-5749	121	23	,	,	PUNCT
ejpam-5749	121	24	the	the	DET
ejpam-5749	121	25	former	former	ADJ
ejpam-5749	121	26	implies	imply	VERB
ejpam-5749	121	27	that	that	SCONJ
ejpam-5749	121	28	γt2(g	γt2(g	VERB
ejpam-5749	121	29	)	)	PUNCT
ejpam-5749	121	30	=	=	SYM
ejpam-5749	121	31	|v2|	|v2|	NOUN
ejpam-5749	121	32	=	=	SYM
ejpam-5749	121	33	2	2	NUM
ejpam-5749	121	34	and	and	CCONJ
ejpam-5749	121	35	,	,	PUNCT
ejpam-5749	121	36	by	by	ADP
ejpam-5749	121	37	proposition	proposition	NOUN
ejpam-5749	121	38	6	6	NUM
ejpam-5749	121	39	,	,	PUNCT
ejpam-5749	121	40	(	(	PUNCT
ejpam-5749	121	41	i	i	NOUN
ejpam-5749	121	42	)	)	PUNCT
ejpam-5749	121	43	holds	hold	VERB
ejpam-5749	121	44	.	.	PUNCT
ejpam-5749	122	1	now	now	ADV
ejpam-5749	122	2	,	,	PUNCT
ejpam-5749	122	3	suppose	suppose	VERB
ejpam-5749	122	4	that	that	SCONJ
ejpam-5749	122	5	v2	v2	PROPN
ejpam-5749	122	6	=	=	SYM
ejpam-5749	122	7	{	{	PUNCT
ejpam-5749	122	8	v	v	NOUN
ejpam-5749	122	9	}	}	PUNCT
ejpam-5749	122	10	and	and	CCONJ
ejpam-5749	122	11	v1	v1	VERB
ejpam-5749	122	12	=	=	SYM
ejpam-5749	122	13	{	{	PUNCT
ejpam-5749	122	14	u	u	NOUN
ejpam-5749	122	15	,	,	PUNCT
ejpam-5749	122	16	w	w	NOUN
ejpam-5749	122	17	}	}	PUNCT
ejpam-5749	122	18	.	.	PUNCT
ejpam-5749	123	1	since	since	SCONJ
ejpam-5749	123	2	v1	v1	NOUN
ejpam-5749	123	3	∪	∪	NOUN
ejpam-5749	123	4	v2	v2	NOUN
ejpam-5749	123	5	is	be	AUX
ejpam-5749	123	6	a	a	DET
ejpam-5749	123	7	semitotal	semitotal	ADJ
ejpam-5749	123	8	dominating	dominating	NOUN
ejpam-5749	123	9	set	set	NOUN
ejpam-5749	123	10	of	of	ADP
ejpam-5749	123	11	g	g	NOUN
ejpam-5749	123	12	,	,	PUNCT
ejpam-5749	123	13	γt2(g	γt2(g	NOUN
ejpam-5749	123	14	)	)	PUNCT
ejpam-5749	123	15	≤	≤	NOUN
ejpam-5749	124	1	3	3	NUM
ejpam-5749	124	2	.	.	PUNCT
ejpam-5749	125	1	if	if	SCONJ
ejpam-5749	125	2	γt2(g	γt2(g	NUM
ejpam-5749	125	3	)	)	PUNCT
ejpam-5749	125	4	=	=	SYM
ejpam-5749	125	5	2	2	NUM
ejpam-5749	125	6	,	,	PUNCT
ejpam-5749	125	7	then	then	ADV
ejpam-5749	125	8	(	(	PUNCT
ejpam-5749	125	9	i	i	NOUN
ejpam-5749	125	10	)	)	PUNCT
ejpam-5749	125	11	holds	hold	VERB
ejpam-5749	125	12	.	.	PUNCT
ejpam-5749	125	13	suppose	suppose	VERB
ejpam-5749	125	14	that	that	SCONJ
ejpam-5749	125	15	γt2(g	γt2(g	VERB
ejpam-5749	125	16	)	)	PUNCT
ejpam-5749	125	17	=	=	SYM
ejpam-5749	126	1	3	3	X
ejpam-5749	126	2	.	.	PUNCT
ejpam-5749	127	1	since	since	SCONJ
ejpam-5749	127	2	f	f	PROPN
ejpam-5749	127	3	∈	∈	PROPN
ejpam-5749	127	4	srdf	srdf	NOUN
ejpam-5749	127	5	(	(	PUNCT
ejpam-5749	127	6	g	g	NOUN
ejpam-5749	127	7	)	)	PUNCT
ejpam-5749	127	8	,	,	PUNCT
ejpam-5749	127	9	v	v	X
ejpam-5749	127	10	(	(	PUNCT
ejpam-5749	127	11	g	g	NOUN
ejpam-5749	127	12	)	)	PUNCT
ejpam-5749	127	13	\	\	NOUN
ejpam-5749	127	14	{	{	PUNCT
ejpam-5749	127	15	u	u	NOUN
ejpam-5749	127	16	,	,	PUNCT
ejpam-5749	127	17	w	w	NOUN
ejpam-5749	127	18	}	}	PUNCT
ejpam-5749	127	19	⊆	⊆	NUM
ejpam-5749	127	20	ng[v	ng[v	NOUN
ejpam-5749	127	21	]	]	PUNCT
ejpam-5749	127	22	.	.	PUNCT
ejpam-5749	127	23	suppose	suppose	VERB
ejpam-5749	127	24	that	that	SCONJ
ejpam-5749	127	25	uv	uv	PROPN
ejpam-5749	127	26	∈	∈	PROPN
ejpam-5749	127	27	e(g	e(g	PROPN
ejpam-5749	127	28	)	)	PUNCT
ejpam-5749	127	29	.	.	PUNCT
ejpam-5749	128	1	if	if	SCONJ
ejpam-5749	128	2	dg(u	dg(u	NOUN
ejpam-5749	128	3	,	,	PUNCT
ejpam-5749	128	4	w	w	NOUN
ejpam-5749	128	5	)	)	PUNCT
ejpam-5749	128	6	=	=	SYM
ejpam-5749	128	7	1	1	NUM
ejpam-5749	128	8	,	,	PUNCT
ejpam-5749	128	9	then	then	ADV
ejpam-5749	128	10	f∗	f∗	NOUN
ejpam-5749	128	11	=	=	SYM
ejpam-5749	128	12	(	(	PUNCT
ejpam-5749	128	13	v0∪{u	v0∪{u	PROPN
ejpam-5749	128	14	}	}	PUNCT
ejpam-5749	128	15	,	,	PUNCT
ejpam-5749	128	16	{	{	PUNCT
ejpam-5749	128	17	w	w	NOUN
ejpam-5749	128	18	}	}	PUNCT
ejpam-5749	128	19	,	,	PUNCT
ejpam-5749	128	20	{	{	PUNCT
ejpam-5749	128	21	v	v	NOUN
ejpam-5749	128	22	}	}	PUNCT
ejpam-5749	128	23	)	)	PUNCT
ejpam-5749	128	24	∈	∈	NOUN
ejpam-5749	128	25	srdf	srdf	NOUN
ejpam-5749	128	26	(	(	PUNCT
ejpam-5749	128	27	g	g	NOUN
ejpam-5749	128	28	)	)	PUNCT
ejpam-5749	128	29	with	with	ADP
ejpam-5749	128	30	ωg(f	ωg(f	NUM
ejpam-5749	128	31	∗	∗	NOUN
ejpam-5749	128	32	)	)	PUNCT
ejpam-5749	128	33	=	=	SYM
ejpam-5749	128	34	3	3	NUM
ejpam-5749	128	35	,	,	PUNCT
ejpam-5749	128	36	a	a	DET
ejpam-5749	128	37	contradiction	contradiction	NOUN
ejpam-5749	128	38	.	.	PUNCT
ejpam-5749	129	1	if	if	SCONJ
ejpam-5749	129	2	dg(u	dg(u	NOUN
ejpam-5749	129	3	,	,	PUNCT
ejpam-5749	129	4	w	w	NOUN
ejpam-5749	129	5	)	)	PUNCT
ejpam-5749	129	6	≥	≥	NOUN
ejpam-5749	129	7	2	2	NUM
ejpam-5749	129	8	and	and	CCONJ
ejpam-5749	129	9	p	p	NOUN
ejpam-5749	129	10	=	=	PUNCT
ejpam-5749	129	11	[	[	X
ejpam-5749	129	12	u	u	X
ejpam-5749	129	13	=	=	SYM
ejpam-5749	129	14	x1	x1	PROPN
ejpam-5749	129	15	,	,	PUNCT
ejpam-5749	129	16	x2	x2	PROPN
ejpam-5749	129	17	,	,	PUNCT
ejpam-5749	129	18	.	.	PUNCT
ejpam-5749	129	19	.	.	PUNCT
ejpam-5749	129	20	.	.	PUNCT
ejpam-5749	130	1	,	,	PUNCT
ejpam-5749	130	2	xk	xk	X
ejpam-5749	130	3	=	=	SYM
ejpam-5749	130	4	w	w	PROPN
ejpam-5749	130	5	]	]	X
ejpam-5749	130	6	is	be	AUX
ejpam-5749	130	7	a	a	DET
ejpam-5749	130	8	u	u	NOUN
ejpam-5749	130	9	-	-	NOUN
ejpam-5749	130	10	w	w	NOUN
ejpam-5749	130	11	geodesic	geodesic	NOUN
ejpam-5749	130	12	in	in	ADP
ejpam-5749	130	13	g	g	PROPN
ejpam-5749	130	14	,	,	PUNCT
ejpam-5749	130	15	then	then	ADV
ejpam-5749	130	16	xj	xj	PROPN
ejpam-5749	130	17	∈	∈	PROPN
ejpam-5749	130	18	v0	v0	NOUN
ejpam-5749	130	19	for	for	ADP
ejpam-5749	130	20	all	all	DET
ejpam-5749	130	21	j	j	PROPN
ejpam-5749	130	22	∈	∈	PROPN
ejpam-5749	130	23	{	{	PUNCT
ejpam-5749	130	24	2	2	NUM
ejpam-5749	130	25	,	,	PUNCT
ejpam-5749	130	26	3	3	NUM
ejpam-5749	130	27	,	,	PUNCT
ejpam-5749	130	28	.	.	PUNCT
ejpam-5749	130	29	.	.	PUNCT
ejpam-5749	131	1	.	.	PUNCT
ejpam-5749	132	1	,	,	PUNCT
ejpam-5749	133	1	k	k	PROPN
ejpam-5749	134	1	−	−	PROPN
ejpam-5749	135	1	1	1	NUM
ejpam-5749	135	2	}	}	PUNCT
ejpam-5749	135	3	.	.	PUNCT
ejpam-5749	136	1	since	since	SCONJ
ejpam-5749	136	2	xk−1v	xk−1v	PROPN
ejpam-5749	136	3	∈	∈	PROPN
ejpam-5749	136	4	e(g	e(g	PROPN
ejpam-5749	136	5	)	)	PUNCT
ejpam-5749	136	6	,	,	PUNCT
ejpam-5749	136	7	dg(w	dg(w	X
ejpam-5749	136	8	,	,	PUNCT
ejpam-5749	136	9	v	v	NOUN
ejpam-5749	136	10	)	)	PUNCT
ejpam-5749	136	11	=	=	SYM
ejpam-5749	136	12	2	2	X
ejpam-5749	136	13	.	.	PUNCT
ejpam-5749	136	14	thus	thus	ADV
ejpam-5749	136	15	,	,	PUNCT
ejpam-5749	136	16	f∗∗	f∗∗	PROPN
ejpam-5749	136	17	=	=	SYM
ejpam-5749	136	18	(	(	PUNCT
ejpam-5749	136	19	v0	v0	NOUN
ejpam-5749	136	20	∪	∪	X
ejpam-5749	136	21	{	{	PUNCT
ejpam-5749	136	22	u	u	NOUN
ejpam-5749	136	23	}	}	PUNCT
ejpam-5749	136	24	,	,	PUNCT
ejpam-5749	136	25	{	{	PUNCT
ejpam-5749	136	26	w	w	NOUN
ejpam-5749	136	27	}	}	PUNCT
ejpam-5749	136	28	,	,	PUNCT
ejpam-5749	136	29	{	{	PUNCT
ejpam-5749	136	30	v	v	NOUN
ejpam-5749	136	31	}	}	PUNCT
ejpam-5749	136	32	)	)	PUNCT
ejpam-5749	136	33	∈	∈	NOUN
ejpam-5749	136	34	srdf	srdf	NOUN
ejpam-5749	136	35	(	(	PUNCT
ejpam-5749	136	36	g	g	NOUN
ejpam-5749	136	37	)	)	PUNCT
ejpam-5749	136	38	with	with	ADP
ejpam-5749	136	39	ωg(f	ωg(f	NUM
ejpam-5749	136	40	∗∗	∗∗	NOUN
ejpam-5749	136	41	)	)	PUNCT
ejpam-5749	136	42	=	=	SYM
ejpam-5749	136	43	3	3	NUM
ejpam-5749	136	44	,	,	PUNCT
ejpam-5749	136	45	a	a	DET
ejpam-5749	136	46	contradiction	contradiction	NOUN
ejpam-5749	136	47	.	.	PUNCT
ejpam-5749	137	1	thus	thus	ADV
ejpam-5749	137	2	,	,	PUNCT
ejpam-5749	137	3	b.	b.	PROPN
ejpam-5749	137	4	f.	f.	PROPN
ejpam-5749	137	5	bullang	bullang	PROPN
ejpam-5749	137	6	et	et	PROPN
ejpam-5749	137	7	al	al	PROPN
ejpam-5749	137	8	.	.	PUNCT
ejpam-5749	137	9	/	/	SYM
ejpam-5749	137	10	eur	eur	PROPN
ejpam-5749	137	11	.	.	PUNCT
ejpam-5749	138	1	j.	j.	PROPN
ejpam-5749	138	2	pure	pure	PROPN
ejpam-5749	138	3	appl	appl	PROPN
ejpam-5749	138	4	.	.	PROPN
ejpam-5749	138	5	math	math	PROPN
ejpam-5749	138	6	,	,	PUNCT
ejpam-5749	138	7	18	18	NUM
ejpam-5749	138	8	(	(	PUNCT
ejpam-5749	138	9	1	1	NUM
ejpam-5749	138	10	)	)	PUNCT
ejpam-5749	138	11	(	(	PUNCT
ejpam-5749	138	12	2025	2025	NUM
ejpam-5749	138	13	)	)	PUNCT
ejpam-5749	138	14	,	,	PUNCT
ejpam-5749	138	15	5749	5749	NUM
ejpam-5749	138	16	6	6	NUM
ejpam-5749	138	17	of	of	ADP
ejpam-5749	138	18	15	15	NUM
ejpam-5749	138	19	uv	uv	NOUN
ejpam-5749	138	20	/∈	/∈	PUNCT
ejpam-5749	138	21	e(g	e(g	PROPN
ejpam-5749	138	22	)	)	PUNCT
ejpam-5749	138	23	.	.	PUNCT
ejpam-5749	139	1	similarly	similarly	ADV
ejpam-5749	139	2	,	,	PUNCT
ejpam-5749	139	3	wv	wv	PROPN
ejpam-5749	139	4	/∈	/∈	PUNCT
ejpam-5749	139	5	e(g	e(g	PROPN
ejpam-5749	139	6	)	)	PUNCT
ejpam-5749	139	7	.	.	PUNCT
ejpam-5749	140	1	therefore	therefore	ADV
ejpam-5749	140	2	,	,	PUNCT
ejpam-5749	140	3	ng[v	ng[v	X
ejpam-5749	140	4	]	]	X
ejpam-5749	140	5	=	=	SYM
ejpam-5749	140	6	v	v	X
ejpam-5749	140	7	(	(	PUNCT
ejpam-5749	140	8	g	g	NOUN
ejpam-5749	140	9	)	)	PUNCT
ejpam-5749	140	10	\	\	NOUN
ejpam-5749	140	11	{	{	PUNCT
ejpam-5749	140	12	u	u	NOUN
ejpam-5749	140	13	,	,	PUNCT
ejpam-5749	140	14	w	w	NOUN
ejpam-5749	140	15	}	}	PUNCT
ejpam-5749	140	16	.	.	PUNCT
ejpam-5749	141	1	suppose	suppose	VERB
ejpam-5749	141	2	that	that	SCONJ
ejpam-5749	141	3	dg(u	dg(u	ADJ
ejpam-5749	141	4	,	,	PUNCT
ejpam-5749	141	5	v	v	NOUN
ejpam-5749	141	6	)	)	PUNCT
ejpam-5749	141	7	≥	≥	NOUN
ejpam-5749	141	8	3	3	NUM
ejpam-5749	141	9	,	,	PUNCT
ejpam-5749	141	10	and	and	CCONJ
ejpam-5749	141	11	let	let	VERB
ejpam-5749	141	12	p	p	PRON
ejpam-5749	141	13	be	be	AUX
ejpam-5749	141	14	a	a	DET
ejpam-5749	141	15	v	v	NOUN
ejpam-5749	141	16	-	-	PUNCT
ejpam-5749	141	17	u	u	NOUN
ejpam-5749	141	18	geodesic	geodesic	NOUN
ejpam-5749	141	19	in	in	ADP
ejpam-5749	141	20	g.	g.	PROPN
ejpam-5749	141	21	since	since	SCONJ
ejpam-5749	141	22	ng[v	ng[v	PROPN
ejpam-5749	141	23	]	]	X
ejpam-5749	141	24	=	=	SYM
ejpam-5749	141	25	v	v	X
ejpam-5749	141	26	(	(	PUNCT
ejpam-5749	141	27	g)\{u	g)\{u	PROPN
ejpam-5749	141	28	,	,	PUNCT
ejpam-5749	141	29	w	w	NOUN
ejpam-5749	141	30	}	}	PUNCT
ejpam-5749	141	31	,	,	PUNCT
ejpam-5749	141	32	p	p	PROPN
ejpam-5749	141	33	has	have	VERB
ejpam-5749	141	34	length	length	NOUN
ejpam-5749	141	35	3	3	NUM
ejpam-5749	141	36	and	and	CCONJ
ejpam-5749	141	37	w	w	NOUN
ejpam-5749	141	38	lies	lie	NOUN
ejpam-5749	141	39	on	on	ADP
ejpam-5749	141	40	p	p	NOUN
ejpam-5749	141	41	so	so	SCONJ
ejpam-5749	141	42	that	that	SCONJ
ejpam-5749	141	43	dg(u	dg(u	ADJ
ejpam-5749	141	44	,	,	PUNCT
ejpam-5749	141	45	v	v	NOUN
ejpam-5749	141	46	)	)	PUNCT
ejpam-5749	141	47	=	=	SYM
ejpam-5749	141	48	2	2	NUM
ejpam-5749	141	49	and	and	CCONJ
ejpam-5749	141	50	uw	uw	PROPN
ejpam-5749	141	51	∈	∈	PROPN
ejpam-5749	141	52	e(g	e(g	PROPN
ejpam-5749	141	53	)	)	PUNCT
ejpam-5749	141	54	.	.	PUNCT
ejpam-5749	142	1	then	then	ADV
ejpam-5749	142	2	{	{	PUNCT
ejpam-5749	142	3	u	u	NOUN
ejpam-5749	142	4	,	,	PUNCT
ejpam-5749	142	5	v	v	NOUN
ejpam-5749	142	6	}	}	PUNCT
ejpam-5749	142	7	is	be	AUX
ejpam-5749	142	8	a	a	DET
ejpam-5749	142	9	γt2	γt2	NOUN
ejpam-5749	142	10	-	-	PUNCT
ejpam-5749	142	11	set	set	NOUN
ejpam-5749	142	12	of	of	ADP
ejpam-5749	142	13	g	g	NOUN
ejpam-5749	142	14	,	,	PUNCT
ejpam-5749	142	15	a	a	DET
ejpam-5749	142	16	contradiction	contradiction	NOUN
ejpam-5749	142	17	.	.	PUNCT
ejpam-5749	143	1	therefore	therefore	ADV
ejpam-5749	143	2	,	,	PUNCT
ejpam-5749	143	3	dg(u	dg(u	X
ejpam-5749	143	4	,	,	PUNCT
ejpam-5749	143	5	v	v	NOUN
ejpam-5749	143	6	)	)	PUNCT
ejpam-5749	143	7	=	=	SYM
ejpam-5749	143	8	2	2	NUM
ejpam-5749	143	9	=	=	SYM
ejpam-5749	143	10	dg(w	dg(w	X
ejpam-5749	143	11	,	,	PUNCT
ejpam-5749	143	12	v	v	NOUN
ejpam-5749	143	13	)	)	PUNCT
ejpam-5749	143	14	.	.	PUNCT
ejpam-5749	144	1	thus	thus	ADV
ejpam-5749	144	2	,	,	PUNCT
ejpam-5749	144	3	(	(	PUNCT
ejpam-5749	144	4	ii	ii	NOUN
ejpam-5749	144	5	)	)	PUNCT
ejpam-5749	144	6	holds	hold	VERB
ejpam-5749	144	7	.	.	PUNCT
ejpam-5749	145	1	conversely	conversely	ADV
ejpam-5749	145	2	,	,	PUNCT
ejpam-5749	145	3	assume	assume	VERB
ejpam-5749	145	4	that	that	SCONJ
ejpam-5749	145	5	γ(g	γ(g	PROPN
ejpam-5749	145	6	)	)	PUNCT
ejpam-5749	145	7	≥	≥	NOUN
ejpam-5749	145	8	2	2	NUM
ejpam-5749	145	9	.	.	PUNCT
ejpam-5749	145	10	suppose	suppose	VERB
ejpam-5749	145	11	that	that	SCONJ
ejpam-5749	145	12	(	(	PUNCT
ejpam-5749	145	13	i	i	NOUN
ejpam-5749	145	14	)	)	PUNCT
ejpam-5749	145	15	holds	hold	VERB
ejpam-5749	145	16	.	.	PUNCT
ejpam-5749	146	1	in	in	ADP
ejpam-5749	146	2	view	view	NOUN
ejpam-5749	146	3	of	of	ADP
ejpam-5749	146	4	proposition	proposition	NOUN
ejpam-5749	146	5	6	6	NUM
ejpam-5749	146	6	,	,	PUNCT
ejpam-5749	146	7	γt2r(g	γt2r(g	NUM
ejpam-5749	146	8	)	)	PUNCT
ejpam-5749	146	9	≥	≥	NOUN
ejpam-5749	146	10	4	4	NUM
ejpam-5749	146	11	.	.	PUNCT
ejpam-5749	146	12	now	now	ADV
ejpam-5749	146	13	let	let	VERB
ejpam-5749	146	14	s	s	PRON
ejpam-5749	146	15	=	=	PUNCT
ejpam-5749	146	16	{	{	PUNCT
ejpam-5749	146	17	u	u	NOUN
ejpam-5749	146	18	,	,	PUNCT
ejpam-5749	146	19	v	v	NOUN
ejpam-5749	146	20	}	}	PUNCT
ejpam-5749	146	21	be	be	AUX
ejpam-5749	146	22	a	a	DET
ejpam-5749	146	23	γt2	γt2	NOUN
ejpam-5749	146	24	-	-	PUNCT
ejpam-5749	146	25	set	set	NOUN
ejpam-5749	146	26	of	of	ADP
ejpam-5749	146	27	g.	g.	PROPN
ejpam-5749	146	28	since	since	SCONJ
ejpam-5749	146	29	f	f	PROPN
ejpam-5749	147	1	=	=	PUNCT
ejpam-5749	147	2	(	(	PUNCT
ejpam-5749	147	3	v	v	NOUN
ejpam-5749	147	4	(	(	PUNCT
ejpam-5749	147	5	g	g	NOUN
ejpam-5749	147	6	)	)	PUNCT
ejpam-5749	147	7	\	\	NOUN
ejpam-5749	148	1	{	{	PUNCT
ejpam-5749	148	2	u	u	NOUN
ejpam-5749	148	3	,	,	PUNCT
ejpam-5749	148	4	v},∅	v},∅	PROPN
ejpam-5749	148	5	,	,	PUNCT
ejpam-5749	148	6	{	{	PUNCT
ejpam-5749	148	7	u	u	NOUN
ejpam-5749	148	8	,	,	PUNCT
ejpam-5749	148	9	v	v	NOUN
ejpam-5749	148	10	}	}	PUNCT
ejpam-5749	148	11	)	)	PUNCT
ejpam-5749	148	12	∈	∈	NOUN
ejpam-5749	148	13	srdf	srdf	NOUN
ejpam-5749	148	14	(	(	PUNCT
ejpam-5749	148	15	g	g	NOUN
ejpam-5749	148	16	)	)	PUNCT
ejpam-5749	148	17	,	,	PUNCT
ejpam-5749	148	18	γt2r(g	γt2r(g	NUM
ejpam-5749	148	19	)	)	PUNCT
ejpam-5749	148	20	≤	≤	NOUN
ejpam-5749	148	21	ωg(f	ωg(f	NOUN
ejpam-5749	148	22	)	)	PUNCT
ejpam-5749	148	23	≤	≤	NUM
ejpam-5749	148	24	4	4	NUM
ejpam-5749	148	25	.	.	PUNCT
ejpam-5749	149	1	now	now	ADV
ejpam-5749	149	2	,	,	PUNCT
ejpam-5749	149	3	suppose	suppose	VERB
ejpam-5749	149	4	that	that	SCONJ
ejpam-5749	149	5	(	(	PUNCT
ejpam-5749	149	6	ii	ii	NOUN
ejpam-5749	149	7	)	)	PUNCT
ejpam-5749	149	8	holds	hold	VERB
ejpam-5749	149	9	.	.	PUNCT
ejpam-5749	150	1	since	since	SCONJ
ejpam-5749	150	2	γt2(g	γt2(g	NUM
ejpam-5749	150	3	)	)	PUNCT
ejpam-5749	150	4	=	=	SYM
ejpam-5749	150	5	3	3	NUM
ejpam-5749	150	6	,	,	PUNCT
ejpam-5749	150	7	γt2r(g	γt2r(g	NUM
ejpam-5749	150	8	)	)	PUNCT
ejpam-5749	150	9	≥	≥	NOUN
ejpam-5749	150	10	4	4	NUM
ejpam-5749	150	11	by	by	ADP
ejpam-5749	150	12	proposition	proposition	NOUN
ejpam-5749	150	13	6	6	NUM
ejpam-5749	150	14	.	.	PUNCT
ejpam-5749	151	1	moreover	moreover	ADV
ejpam-5749	151	2	,	,	PUNCT
ejpam-5749	151	3	since	since	SCONJ
ejpam-5749	151	4	f	f	PROPN
ejpam-5749	151	5	=	=	SYM
ejpam-5749	151	6	(	(	PUNCT
ejpam-5749	151	7	v	v	NOUN
ejpam-5749	151	8	(	(	PUNCT
ejpam-5749	151	9	g	g	NOUN
ejpam-5749	151	10	)	)	PUNCT
ejpam-5749	151	11	\	\	NOUN
ejpam-5749	151	12	{	{	PUNCT
ejpam-5749	151	13	u	u	NOUN
ejpam-5749	151	14	,	,	PUNCT
ejpam-5749	151	15	w	w	NOUN
ejpam-5749	151	16	}	}	PUNCT
ejpam-5749	151	17	,	,	PUNCT
ejpam-5749	151	18	{	{	PUNCT
ejpam-5749	151	19	u	u	NOUN
ejpam-5749	151	20	,	,	PUNCT
ejpam-5749	151	21	w	w	NOUN
ejpam-5749	151	22	}	}	PUNCT
ejpam-5749	151	23	,	,	PUNCT
ejpam-5749	151	24	{	{	PUNCT
ejpam-5749	151	25	v	v	NOUN
ejpam-5749	151	26	}	}	PUNCT
ejpam-5749	151	27	)	)	PUNCT
ejpam-5749	151	28	∈	∈	NOUN
ejpam-5749	151	29	srdf	srdf	NOUN
ejpam-5749	151	30	(	(	PUNCT
ejpam-5749	151	31	g	g	NOUN
ejpam-5749	151	32	)	)	PUNCT
ejpam-5749	151	33	,	,	PUNCT
ejpam-5749	151	34	γt2r(g	γt2r(g	NUM
ejpam-5749	151	35	)	)	PUNCT
ejpam-5749	151	36	≤	≤	NUM
ejpam-5749	151	37	wg(f	wg(f	NOUN
ejpam-5749	151	38	)	)	PUNCT
ejpam-5749	151	39	=	=	SYM
ejpam-5749	151	40	4	4	X
ejpam-5749	151	41	.	.	X
ejpam-5749	151	42	in	in	ADP
ejpam-5749	151	43	any	any	DET
ejpam-5749	151	44	case	case	NOUN
ejpam-5749	151	45	,	,	PUNCT
ejpam-5749	151	46	γt2r(g	γt2r(g	NUM
ejpam-5749	151	47	)	)	PUNCT
ejpam-5749	151	48	=	=	SYM
ejpam-5749	151	49	4	4	NUM
ejpam-5749	151	50	,	,	PUNCT
ejpam-5749	151	51	proposition	proposition	NOUN
ejpam-5749	151	52	6	6	NUM
ejpam-5749	151	53	asserts	assert	VERB
ejpam-5749	151	54	that	that	SCONJ
ejpam-5749	151	55	if	if	SCONJ
ejpam-5749	151	56	γt2r(g	γt2r(g	NUM
ejpam-5749	151	57	)	)	PUNCT
ejpam-5749	151	58	=	=	SYM
ejpam-5749	151	59	3	3	NUM
ejpam-5749	151	60	,	,	PUNCT
ejpam-5749	151	61	then	then	ADV
ejpam-5749	151	62	γt2(g	γt2(g	NUM
ejpam-5749	151	63	)	)	PUNCT
ejpam-5749	151	64	=	=	SYM
ejpam-5749	151	65	2	2	X
ejpam-5749	151	66	.	.	X
ejpam-5749	151	67	proposition	proposition	NOUN
ejpam-5749	151	68	7	7	NUM
ejpam-5749	151	69	also	also	ADV
ejpam-5749	151	70	provides	provide	VERB
ejpam-5749	151	71	that	that	SCONJ
ejpam-5749	151	72	the	the	DET
ejpam-5749	151	73	converse	converse	NOUN
ejpam-5749	151	74	need	need	AUX
ejpam-5749	151	75	not	not	PART
ejpam-5749	151	76	be	be	AUX
ejpam-5749	151	77	true	true	ADJ
ejpam-5749	151	78	.	.	PUNCT
ejpam-5749	152	1	in	in	ADP
ejpam-5749	152	2	particular	particular	ADJ
ejpam-5749	152	3	,	,	PUNCT
ejpam-5749	152	4	for	for	ADP
ejpam-5749	152	5	g2	g2	PROPN
ejpam-5749	152	6	in	in	ADP
ejpam-5749	152	7	figure	figure	NOUN
ejpam-5749	152	8	1	1	NUM
ejpam-5749	152	9	,	,	PUNCT
ejpam-5749	152	10	γt2(g2	γt2(g2	NUM
ejpam-5749	152	11	)	)	PUNCT
ejpam-5749	152	12	=	=	SYM
ejpam-5749	152	13	2	2	NUM
ejpam-5749	152	14	but	but	CCONJ
ejpam-5749	152	15	γt2r(g	γt2r(g	NUM
ejpam-5749	152	16	)	)	PUNCT
ejpam-5749	152	17	=	=	SYM
ejpam-5749	152	18	4	4	NUM
ejpam-5749	152	19	by	by	ADP
ejpam-5749	152	20	proposition	proposition	NOUN
ejpam-5749	152	21	7	7	NUM
ejpam-5749	152	22	.	.	PUNCT
ejpam-5749	153	1	the	the	DET
ejpam-5749	153	2	graph	graph	NOUN
ejpam-5749	153	3	g1	g1	NOUN
ejpam-5749	153	4	in	in	ADP
ejpam-5749	153	5	figure	figure	NOUN
ejpam-5749	153	6	1	1	NUM
ejpam-5749	153	7	provides	provide	VERB
ejpam-5749	153	8	a	a	DET
ejpam-5749	153	9	graph	graph	NOUN
ejpam-5749	153	10	which	which	PRON
ejpam-5749	153	11	perfectly	perfectly	ADV
ejpam-5749	153	12	satisfies	satisfy	VERB
ejpam-5749	153	13	condition	condition	NOUN
ejpam-5749	153	14	(	(	PUNCT
ejpam-5749	153	15	ii	ii	NOUN
ejpam-5749	153	16	)	)	PUNCT
ejpam-5749	153	17	of	of	ADP
ejpam-5749	153	18	proposition	proposition	NOUN
ejpam-5749	153	19	7	7	NUM
ejpam-5749	153	20	.	.	PUNCT
ejpam-5749	153	21	vu	vu	PROPN
ejpam-5749	153	22	w	w	PROPN
ejpam-5749	153	23	g1	g1	PROPN
ejpam-5749	153	24	:	:	PUNCT
ejpam-5749	153	25	v	v	X
ejpam-5749	153	26	u	u	NOUN
ejpam-5749	153	27	g2	g2	PROPN
ejpam-5749	153	28	:	:	PUNCT
ejpam-5749	153	29	figure	figure	VERB
ejpam-5749	153	30	1	1	NUM
ejpam-5749	153	31	:	:	PUNCT
ejpam-5749	153	32	graphs	graph	NOUN
ejpam-5749	153	33	satisfying	satisfy	VERB
ejpam-5749	153	34	the	the	DET
ejpam-5749	153	35	conditions	condition	NOUN
ejpam-5749	153	36	of	of	ADP
ejpam-5749	153	37	proposition	proposition	NOUN
ejpam-5749	153	38	7	7	NUM
ejpam-5749	153	39	proposition	proposition	NOUN
ejpam-5749	153	40	8	8	NUM
ejpam-5749	153	41	.	.	PUNCT
ejpam-5749	154	1	for	for	ADP
ejpam-5749	154	2	each	each	DET
ejpam-5749	154	3	positive	positive	ADJ
ejpam-5749	154	4	integer	integer	NOUN
ejpam-5749	154	5	n	n	NOUN
ejpam-5749	154	6	and	and	CCONJ
ejpam-5749	154	7	integer	integer	NOUN
ejpam-5749	154	8	0	0	NUM
ejpam-5749	154	9	≤	≤	NUM
ejpam-5749	154	10	k	k	NOUN
ejpam-5749	154	11	≤	≤	PROPN
ejpam-5749	154	12	n	n	CCONJ
ejpam-5749	154	13	,	,	PUNCT
ejpam-5749	154	14	there	there	PRON
ejpam-5749	154	15	exists	exist	VERB
ejpam-5749	154	16	a	a	DET
ejpam-5749	154	17	connected	connected	ADJ
ejpam-5749	154	18	graph	graph	NOUN
ejpam-5749	154	19	g	g	NOUN
ejpam-5749	154	20	for	for	ADP
ejpam-5749	154	21	which	which	PRON
ejpam-5749	154	22	γr(g	γr(g	NUM
ejpam-5749	154	23	)	)	PUNCT
ejpam-5749	155	1	=	=	SYM
ejpam-5749	155	2	4n	4n	NOUN
ejpam-5749	155	3	and	and	CCONJ
ejpam-5749	155	4	γt2r(g	γt2r(g	NUM
ejpam-5749	155	5	)	)	PUNCT
ejpam-5749	155	6	=	=	PUNCT
ejpam-5749	156	1	4n	4n	NOUN
ejpam-5749	156	2	+	+	X
ejpam-5749	156	3	k.	k.	X
ejpam-5749	156	4	consequently	consequently	ADV
ejpam-5749	156	5	,	,	PUNCT
ejpam-5749	156	6	the	the	DET
ejpam-5749	156	7	difference	difference	NOUN
ejpam-5749	156	8	γt2r(·)−	γt2r(·)−	X
ejpam-5749	156	9	γr	γr	X
ejpam-5749	156	10	(	(	PUNCT
ejpam-5749	156	11	·	·	PUNCT
ejpam-5749	156	12	)	)	PUNCT
ejpam-5749	156	13	can	can	AUX
ejpam-5749	156	14	be	be	AUX
ejpam-5749	156	15	made	make	VERB
ejpam-5749	156	16	arbitrarily	arbitrarily	ADV
ejpam-5749	156	17	large	large	ADJ
ejpam-5749	156	18	.	.	PUNCT
ejpam-5749	157	1	proof	proof	NOUN
ejpam-5749	157	2	.	.	PUNCT
ejpam-5749	158	1	we	we	PRON
ejpam-5749	158	2	consider	consider	VERB
ejpam-5749	158	3	the	the	DET
ejpam-5749	158	4	following	follow	VERB
ejpam-5749	158	5	cases	case	NOUN
ejpam-5749	158	6	:	:	PUNCT
ejpam-5749	158	7	case	case	NOUN
ejpam-5749	158	8	1	1	NUM
ejpam-5749	158	9	:	:	PUNCT
ejpam-5749	158	10	suppose	suppose	VERB
ejpam-5749	158	11	that	that	SCONJ
ejpam-5749	158	12	k	k	PROPN
ejpam-5749	158	13	=	=	PUNCT
ejpam-5749	158	14	0	0	X
ejpam-5749	158	15	.	.	PUNCT
ejpam-5749	158	16	consider	consider	VERB
ejpam-5749	158	17	the	the	DET
ejpam-5749	158	18	corona	corona	NOUN
ejpam-5749	158	19	g	g	NOUN
ejpam-5749	158	20	=	=	PUNCT
ejpam-5749	158	21	p2n	p2n	PROPN
ejpam-5749	158	22	◦	◦	NOUN
ejpam-5749	158	23	k4	k4	NOUN
ejpam-5749	158	24	provided	provide	VERB
ejpam-5749	158	25	in	in	ADP
ejpam-5749	158	26	figure	figure	NOUN
ejpam-5749	158	27	2	2	NUM
ejpam-5749	158	28	.	.	PUNCT
ejpam-5749	159	1	then	then	ADV
ejpam-5749	159	2	γr(g	γr(g	NUM
ejpam-5749	159	3	)	)	PUNCT
ejpam-5749	160	1	=	=	SYM
ejpam-5749	160	2	4n	4n	X
ejpam-5749	160	3	=	=	PUNCT
ejpam-5749	160	4	γt2r(g	γt2r(g	NUM
ejpam-5749	160	5	)	)	PUNCT
ejpam-5749	160	6	.	.	PUNCT
ejpam-5749	161	1	x1	x1	NUM
ejpam-5749	162	1	x2	x2	PROPN
ejpam-5749	162	2	x2n−1	x2n−1	PROPN
ejpam-5749	163	1	x2n	x2n	PROPN
ejpam-5749	163	2	·	·	PUNCT
ejpam-5749	163	3	·	·	PUNCT
ejpam-5749	163	4	·	·	PUNCT
ejpam-5749	163	5	figure	figure	NOUN
ejpam-5749	163	6	2	2	NUM
ejpam-5749	163	7	:	:	PUNCT
ejpam-5749	163	8	the	the	DET
ejpam-5749	163	9	graph	graph	NOUN
ejpam-5749	163	10	p2n	p2n	PUNCT
ejpam-5749	163	11	◦	◦	NOUN
ejpam-5749	163	12	k4	k4	NOUN
ejpam-5749	163	13	case	case	NOUN
ejpam-5749	163	14	2	2	NUM
ejpam-5749	163	15	:	:	PUNCT
ejpam-5749	163	16	suppose	suppose	VERB
ejpam-5749	163	17	that	that	SCONJ
ejpam-5749	163	18	k	k	PROPN
ejpam-5749	163	19	=	=	PUNCT
ejpam-5749	163	20	n.	n.	PROPN
ejpam-5749	163	21	in	in	ADP
ejpam-5749	163	22	this	this	DET
ejpam-5749	163	23	case	case	NOUN
ejpam-5749	163	24	take	take	VERB
ejpam-5749	163	25	the	the	DET
ejpam-5749	163	26	graph	graph	NOUN
ejpam-5749	163	27	g	g	NOUN
ejpam-5749	163	28	as	as	ADP
ejpam-5749	163	29	in	in	ADP
ejpam-5749	163	30	figure	figure	NOUN
ejpam-5749	163	31	3	3	NUM
ejpam-5749	163	32	obtained	obtain	VERB
ejpam-5749	163	33	from	from	ADP
ejpam-5749	163	34	p6n−2	p6n−2	PROPN
ejpam-5749	163	35	=	=	PUNCT
ejpam-5749	164	1	[	[	X
ejpam-5749	164	2	x1	x1	PROPN
ejpam-5749	164	3	,	,	PUNCT
ejpam-5749	164	4	x2	x2	PROPN
ejpam-5749	164	5	,	,	PUNCT
ejpam-5749	164	6	.	.	PUNCT
ejpam-5749	164	7	.	.	PUNCT
ejpam-5749	165	1	.	.	PUNCT
ejpam-5749	166	1	,	,	PUNCT
ejpam-5749	166	2	x6n−2	x6n−2	PROPN
ejpam-5749	166	3	]	]	PUNCT
ejpam-5749	166	4	by	by	ADP
ejpam-5749	166	5	joining	join	VERB
ejpam-5749	166	6	k4	k4	NOUN
ejpam-5749	166	7	with	with	ADP
ejpam-5749	166	8	x3j−2	x3j−2	PROPN
ejpam-5749	166	9	for	for	ADP
ejpam-5749	166	10	all	all	DET
ejpam-5749	166	11	j	j	NOUN
ejpam-5749	166	12	=	=	SYM
ejpam-5749	166	13	1	1	NUM
ejpam-5749	166	14	,	,	PUNCT
ejpam-5749	166	15	2	2	NUM
ejpam-5749	166	16	,	,	PUNCT
ejpam-5749	166	17	.	.	PUNCT
ejpam-5749	166	18	.	.	PUNCT
ejpam-5749	166	19	.	.	PUNCT
ejpam-5749	167	1	,	,	PUNCT
ejpam-5749	167	2	2n	2n	X
ejpam-5749	167	3	.	.	PUNCT
ejpam-5749	168	1	then	then	ADV
ejpam-5749	168	2	γr(g	γr(g	NUM
ejpam-5749	168	3	)	)	PUNCT
ejpam-5749	169	1	=	=	SYM
ejpam-5749	169	2	4n	4n	NOUN
ejpam-5749	169	3	and	and	CCONJ
ejpam-5749	169	4	γt2r(g	γt2r(g	NUM
ejpam-5749	169	5	)	)	PUNCT
ejpam-5749	169	6	=	=	PUNCT
ejpam-5749	170	1	4n+	4n+	NUM
ejpam-5749	170	2	k.	k.	NOUN
ejpam-5749	170	3	case	case	NOUN
ejpam-5749	170	4	3	3	X
ejpam-5749	170	5	:	:	PUNCT
ejpam-5749	170	6	finally	finally	ADV
ejpam-5749	170	7	,	,	PUNCT
ejpam-5749	170	8	suppose	suppose	VERB
ejpam-5749	170	9	that	that	SCONJ
ejpam-5749	170	10	1	1	NUM
ejpam-5749	170	11	≤	≤	NUM
ejpam-5749	170	12	k	k	NOUN
ejpam-5749	170	13	≤	≤	PROPN
ejpam-5749	170	14	n	n	CCONJ
ejpam-5749	170	15	−	−	PROPN
ejpam-5749	170	16	1	1	NUM
ejpam-5749	170	17	.	.	PUNCT
ejpam-5749	170	18	consider	consider	VERB
ejpam-5749	170	19	the	the	DET
ejpam-5749	170	20	graph	graph	NOUN
ejpam-5749	170	21	g	g	PROPN
ejpam-5749	170	22	obtained	obtain	VERB
ejpam-5749	170	23	from	from	ADP
ejpam-5749	170	24	p2n+4k	p2n+4k	NOUN
ejpam-5749	170	25	=	=	PUNCT
ejpam-5749	171	1	[	[	X
ejpam-5749	171	2	x1	x1	PROPN
ejpam-5749	171	3	,	,	PUNCT
ejpam-5749	171	4	x2	x2	PROPN
ejpam-5749	171	5	,	,	PUNCT
ejpam-5749	171	6	.	.	PUNCT
ejpam-5749	171	7	.	.	PUNCT
ejpam-5749	172	1	.	.	PUNCT
ejpam-5749	173	1	,	,	PUNCT
ejpam-5749	173	2	2n+4k	2n+4k	NUM
ejpam-5749	173	3	]	]	PUNCT
ejpam-5749	173	4	by	by	ADP
ejpam-5749	173	5	joining	join	VERB
ejpam-5749	173	6	k4	k4	PROPN
ejpam-5749	173	7	with	with	ADP
ejpam-5749	173	8	xj	xj	PROPN
ejpam-5749	173	9	for	for	ADP
ejpam-5749	173	10	all	all	DET
ejpam-5749	173	11	j	j	PROPN
ejpam-5749	173	12	∈	∈	PROPN
ejpam-5749	173	13	{	{	PUNCT
ejpam-5749	173	14	1	1	NUM
ejpam-5749	173	15	,	,	PUNCT
ejpam-5749	173	16	2	2	NUM
ejpam-5749	173	17	,	,	PUNCT
ejpam-5749	173	18	.	.	PUNCT
ejpam-5749	173	19	.	.	PUNCT
ejpam-5749	173	20	.	.	PUNCT
ejpam-5749	174	1	,	,	PUNCT
ejpam-5749	174	2	2n−	2n−	NUM
ejpam-5749	174	3	2k}∪	2k}∪	NUM
ejpam-5749	174	4	{	{	PUNCT
ejpam-5749	174	5	2n−	2n−	PROPN
ejpam-5749	174	6	2k	2k	NOUN
ejpam-5749	174	7	+	+	CCONJ
ejpam-5749	174	8	3l	3l	NUM
ejpam-5749	174	9	:	:	PUNCT
ejpam-5749	175	1	l	l	NOUN
ejpam-5749	175	2	=	=	SYM
ejpam-5749	175	3	1	1	NUM
ejpam-5749	175	4	,	,	PUNCT
ejpam-5749	175	5	2	2	NUM
ejpam-5749	175	6	,	,	PUNCT
ejpam-5749	175	7	.	.	PUNCT
ejpam-5749	175	8	.	.	PUNCT
ejpam-5749	175	9	.	.	PUNCT
ejpam-5749	176	1	,	,	PUNCT
ejpam-5749	176	2	2k	2k	NUM
ejpam-5749	176	3	}	}	PUNCT
ejpam-5749	176	4	(	(	PUNCT
ejpam-5749	176	5	see	see	VERB
ejpam-5749	176	6	figure	figure	NOUN
ejpam-5749	176	7	4	4	NUM
ejpam-5749	176	8	below	below	ADV
ejpam-5749	176	9	)	)	PUNCT
ejpam-5749	176	10	.	.	PUNCT
ejpam-5749	177	1	then	then	ADV
ejpam-5749	177	2	γr(g	γr(g	NUM
ejpam-5749	177	3	)	)	PUNCT
ejpam-5749	177	4	=	=	PUNCT
ejpam-5749	177	5	2(2n−	2(2n−	NUM
ejpam-5749	177	6	2k	2k	NUM
ejpam-5749	177	7	)	)	PUNCT
ejpam-5749	178	1	+	+	CCONJ
ejpam-5749	178	2	4k	4k	NUM
ejpam-5749	178	3	=	=	SYM
ejpam-5749	178	4	4n	4n	NOUN
ejpam-5749	178	5	and	and	CCONJ
ejpam-5749	178	6	γt2r(g	γt2r(g	NUM
ejpam-5749	178	7	)	)	PUNCT
ejpam-5749	178	8	=	=	SYM
ejpam-5749	178	9	2(2n−	2(2n−	NUM
ejpam-5749	178	10	2k	2k	NUM
ejpam-5749	178	11	)	)	PUNCT
ejpam-5749	179	1	+	+	CCONJ
ejpam-5749	179	2	(	(	PUNCT
ejpam-5749	179	3	4k	4k	X
ejpam-5749	179	4	+	+	CCONJ
ejpam-5749	179	5	k	k	X
ejpam-5749	179	6	)	)	PUNCT
ejpam-5749	179	7	=	=	SYM
ejpam-5749	180	1	4n+	4n+	NUM
ejpam-5749	180	2	k.	k.	PROPN
ejpam-5749	180	3	b.	b.	PROPN
ejpam-5749	180	4	f.	f.	PROPN
ejpam-5749	180	5	bullang	bullang	PROPN
ejpam-5749	180	6	et	et	PROPN
ejpam-5749	180	7	al	al	PROPN
ejpam-5749	180	8	.	.	PUNCT
ejpam-5749	180	9	/	/	SYM
ejpam-5749	180	10	eur	eur	PROPN
ejpam-5749	180	11	.	.	PUNCT
ejpam-5749	181	1	j.	j.	PROPN
ejpam-5749	181	2	pure	pure	PROPN
ejpam-5749	181	3	appl	appl	PROPN
ejpam-5749	181	4	.	.	PROPN
ejpam-5749	181	5	math	math	PROPN
ejpam-5749	181	6	,	,	PUNCT
ejpam-5749	181	7	18	18	NUM
ejpam-5749	181	8	(	(	PUNCT
ejpam-5749	181	9	1	1	NUM
ejpam-5749	181	10	)	)	PUNCT
ejpam-5749	181	11	(	(	PUNCT
ejpam-5749	181	12	2025	2025	NUM
ejpam-5749	181	13	)	)	PUNCT
ejpam-5749	181	14	,	,	PUNCT
ejpam-5749	181	15	5749	5749	NUM
ejpam-5749	181	16	7	7	NUM
ejpam-5749	181	17	of	of	ADP
ejpam-5749	181	18	15	15	NUM
ejpam-5749	182	1	x1	x1	NOUN
ejpam-5749	182	2	x2	x2	NOUN
ejpam-5749	182	3	x3	x3	PROPN
ejpam-5749	182	4	x4	x4	PROPN
ejpam-5749	182	5	x5	x5	PROPN
ejpam-5749	182	6	x6	x6	PROPN
ejpam-5749	182	7	x7	x7	NOUN
ejpam-5749	182	8	x6n−5	x6n−5	PROPN
ejpam-5749	182	9	x6n−4	x6n−4	PROPN
ejpam-5749	183	1	x6n−3	x6n−3	PROPN
ejpam-5749	183	2	x6n−2	x6n−2	PROPN
ejpam-5749	183	3	·	·	PUNCT
ejpam-5749	183	4	·	·	PUNCT
ejpam-5749	183	5	·	·	PUNCT
ejpam-5749	183	6	figure	figure	VERB
ejpam-5749	183	7	3	3	NUM
ejpam-5749	183	8	:	:	PUNCT
ejpam-5749	183	9	a	a	DET
ejpam-5749	183	10	graph	graph	NOUN
ejpam-5749	183	11	g	g	NOUN
ejpam-5749	183	12	with	with	ADP
ejpam-5749	183	13	γr(g	γr(g	NUM
ejpam-5749	183	14	)	)	PUNCT
ejpam-5749	184	1	=	=	SYM
ejpam-5749	184	2	4n	4n	NOUN
ejpam-5749	184	3	and	and	CCONJ
ejpam-5749	184	4	γt2r(g	γt2r(g	NUM
ejpam-5749	184	5	)	)	PUNCT
ejpam-5749	184	6	=	=	SYM
ejpam-5749	185	1	4n+	4n+	NUM
ejpam-5749	186	1	n	n	CCONJ
ejpam-5749	187	1	x1	x1	NUM
ejpam-5749	188	1	x2	x2	INTJ
ejpam-5749	188	2	x2n−2k−1	x2n−2k−1	PROPN
ejpam-5749	189	1	x2n−2k	x2n−2k	PROPN
ejpam-5749	189	2	x2n−2k+1	x2n−2k+1	VERB
ejpam-5749	189	3	x2n−2k+2	x2n−2k+2	PROPN
ejpam-5749	189	4	x2n−2k+3	x2n−2k+3	PROPN
ejpam-5749	189	5	x2n−2k+4	x2n−2k+4	PROPN
ejpam-5749	189	6	x2n−2k+5	x2n−2k+5	PROPN
ejpam-5749	189	7	x2n−2k+6	x2n−2k+6	PROPN
ejpam-5749	189	8	x2n−2k+7	x2n−2k+7	NOUN
ejpam-5749	189	9	x2n−2k+8	x2n−2k+8	VERB
ejpam-5749	189	10	x2n−2k+9	x2n−2k+9	PROPN
ejpam-5749	189	11	x2n+4k−3	x2n+4k−3	PROPN
ejpam-5749	189	12	x2n+4k−2	x2n+4k−2	PROPN
ejpam-5749	189	13	x2n+4k−1	x2n+4k−1	PROPN
ejpam-5749	189	14	x2n+4k	x2n+4k	PROPN
ejpam-5749	189	15	·	·	PUNCT
ejpam-5749	189	16	·	·	PUNCT
ejpam-5749	189	17	·	·	PUNCT
ejpam-5749	189	18	·	·	PUNCT
ejpam-5749	189	19	·	·	PUNCT
ejpam-5749	189	20	·	·	PUNCT
ejpam-5749	189	21	figure	figure	VERB
ejpam-5749	189	22	4	4	NUM
ejpam-5749	189	23	:	:	PUNCT
ejpam-5749	189	24	a	a	DET
ejpam-5749	189	25	graph	graph	NOUN
ejpam-5749	189	26	g	g	NOUN
ejpam-5749	189	27	with	with	ADP
ejpam-5749	189	28	γr(g	γr(g	NUM
ejpam-5749	189	29	)	)	PUNCT
ejpam-5749	190	1	=	=	SYM
ejpam-5749	190	2	4n	4n	NOUN
ejpam-5749	190	3	and	and	CCONJ
ejpam-5749	190	4	γt2r(g	γt2r(g	NUM
ejpam-5749	190	5	)	)	PUNCT
ejpam-5749	190	6	=	=	PUNCT
ejpam-5749	191	1	4n+	4n+	NUM
ejpam-5749	192	1	k	k	NOUN
ejpam-5749	192	2	,	,	PUNCT
ejpam-5749	192	3	1	1	NUM
ejpam-5749	192	4	≤	≤	NUM
ejpam-5749	192	5	k	k	X
ejpam-5749	192	6	≤	≤	PROPN
ejpam-5749	192	7	n−	n−	NOUN
ejpam-5749	192	8	1	1	NUM
ejpam-5749	192	9	proposition	proposition	NOUN
ejpam-5749	192	10	9	9	NUM
ejpam-5749	192	11	.	.	PUNCT
ejpam-5749	193	1	for	for	ADP
ejpam-5749	193	2	each	each	DET
ejpam-5749	193	3	positive	positive	ADJ
ejpam-5749	193	4	integer	integer	NOUN
ejpam-5749	193	5	n	n	NOUN
ejpam-5749	193	6	and	and	CCONJ
ejpam-5749	193	7	integer	integer	NOUN
ejpam-5749	193	8	0	0	NUM
ejpam-5749	193	9	≤	≤	NUM
ejpam-5749	193	10	k	k	NOUN
ejpam-5749	193	11	≤	≤	PROPN
ejpam-5749	193	12	n	n	CCONJ
ejpam-5749	193	13	,	,	PUNCT
ejpam-5749	193	14	there	there	PRON
ejpam-5749	193	15	exists	exist	VERB
ejpam-5749	193	16	a	a	DET
ejpam-5749	193	17	connected	connected	ADJ
ejpam-5749	193	18	graph	graph	NOUN
ejpam-5749	193	19	g	g	NOUN
ejpam-5749	193	20	for	for	ADP
ejpam-5749	193	21	which	which	PRON
ejpam-5749	193	22	γt2r(g	γt2r(g	NUM
ejpam-5749	193	23	)	)	PUNCT
ejpam-5749	194	1	=	=	NOUN
ejpam-5749	194	2	4n	4n	NOUN
ejpam-5749	194	3	and	and	CCONJ
ejpam-5749	194	4	γtr(g	γtr(g	NUM
ejpam-5749	194	5	)	)	PUNCT
ejpam-5749	194	6	=	=	PUNCT
ejpam-5749	195	1	4n	4n	NOUN
ejpam-5749	195	2	+	+	X
ejpam-5749	195	3	k.	k.	X
ejpam-5749	195	4	consequently	consequently	ADV
ejpam-5749	195	5	,	,	PUNCT
ejpam-5749	195	6	the	the	DET
ejpam-5749	195	7	difference	difference	NOUN
ejpam-5749	195	8	γtr(·)−	γtr(·)−	ADP
ejpam-5749	195	9	γt2r	γt2r	PROPN
ejpam-5749	195	10	(	(	PUNCT
ejpam-5749	195	11	·	·	PUNCT
ejpam-5749	195	12	)	)	PUNCT
ejpam-5749	195	13	can	can	AUX
ejpam-5749	195	14	be	be	AUX
ejpam-5749	195	15	made	make	VERB
ejpam-5749	195	16	arbitrarily	arbitrarily	ADV
ejpam-5749	195	17	large	large	ADJ
ejpam-5749	195	18	.	.	PUNCT
ejpam-5749	196	1	proof	proof	NOUN
ejpam-5749	196	2	.	.	PUNCT
ejpam-5749	197	1	for	for	ADP
ejpam-5749	197	2	k	k	PROPN
ejpam-5749	197	3	=	=	SYM
ejpam-5749	197	4	0	0	PROPN
ejpam-5749	197	5	,	,	PUNCT
ejpam-5749	197	6	we	we	PRON
ejpam-5749	197	7	take	take	VERB
ejpam-5749	197	8	the	the	DET
ejpam-5749	197	9	graph	graph	NOUN
ejpam-5749	197	10	g	g	NOUN
ejpam-5749	197	11	=	=	PUNCT
ejpam-5749	197	12	p2n	p2n	PROPN
ejpam-5749	197	13	◦	◦	NOUN
ejpam-5749	197	14	k4	k4	NOUN
ejpam-5749	197	15	in	in	ADP
ejpam-5749	197	16	figure	figure	NOUN
ejpam-5749	197	17	2	2	NUM
ejpam-5749	197	18	.	.	PUNCT
ejpam-5749	198	1	for	for	ADP
ejpam-5749	198	2	this	this	DET
ejpam-5749	198	3	graph	graph	NOUN
ejpam-5749	198	4	,	,	PUNCT
ejpam-5749	198	5	γt2r(g	γt2r(g	NUM
ejpam-5749	198	6	)	)	PUNCT
ejpam-5749	198	7	=	=	SYM
ejpam-5749	198	8	γtr(g	γtr(g	PROPN
ejpam-5749	198	9	)	)	PUNCT
ejpam-5749	198	10	=	=	SYM
ejpam-5749	198	11	4n	4n	X
ejpam-5749	198	12	.	.	PUNCT
ejpam-5749	198	13	suppose	suppose	VERB
ejpam-5749	198	14	that	that	SCONJ
ejpam-5749	198	15	k	k	PROPN
ejpam-5749	198	16	=	=	PUNCT
ejpam-5749	198	17	n.	n.	PROPN
ejpam-5749	198	18	consider	consider	VERB
ejpam-5749	198	19	the	the	DET
ejpam-5749	198	20	graph	graph	NOUN
ejpam-5749	198	21	g	g	NOUN
ejpam-5749	198	22	given	give	VERB
ejpam-5749	198	23	in	in	ADP
ejpam-5749	198	24	figure	figure	NOUN
ejpam-5749	198	25	5	5	NUM
ejpam-5749	198	26	obtained	obtain	VERB
ejpam-5749	198	27	from	from	ADP
ejpam-5749	198	28	p4n−1	p4n−1	NOUN
ejpam-5749	198	29	=	=	PUNCT
ejpam-5749	199	1	[	[	X
ejpam-5749	199	2	x1	x1	PROPN
ejpam-5749	199	3	,	,	PUNCT
ejpam-5749	199	4	x2	x2	PROPN
ejpam-5749	199	5	,	,	PUNCT
ejpam-5749	199	6	.	.	PUNCT
ejpam-5749	199	7	.	.	PUNCT
ejpam-5749	200	1	.	.	PUNCT
ejpam-5749	201	1	,	,	PUNCT
ejpam-5749	201	2	x4n−1	x4n−1	PROPN
ejpam-5749	201	3	]	]	PUNCT
ejpam-5749	201	4	by	by	ADP
ejpam-5749	201	5	joining	join	VERB
ejpam-5749	201	6	k4	k4	NOUN
ejpam-5749	201	7	with	with	ADP
ejpam-5749	201	8	x2j−1	x2j−1	PROPN
ejpam-5749	201	9	for	for	ADP
ejpam-5749	201	10	all	all	DET
ejpam-5749	201	11	j	j	NOUN
ejpam-5749	201	12	=	=	SYM
ejpam-5749	201	13	1	1	NUM
ejpam-5749	201	14	,	,	PUNCT
ejpam-5749	201	15	2	2	NUM
ejpam-5749	201	16	,	,	PUNCT
ejpam-5749	201	17	.	.	PUNCT
ejpam-5749	201	18	.	.	PUNCT
ejpam-5749	201	19	.	.	PUNCT
ejpam-5749	202	1	,	,	PUNCT
ejpam-5749	202	2	2n	2n	X
ejpam-5749	202	3	.	.	PUNCT
ejpam-5749	203	1	then	then	ADV
ejpam-5749	203	2	γt2r(g	γt2r(g	NUM
ejpam-5749	203	3	)	)	PUNCT
ejpam-5749	203	4	=	=	PUNCT
ejpam-5749	204	1	2(2n	2(2n	X
ejpam-5749	204	2	)	)	PUNCT
ejpam-5749	204	3	=	=	SYM
ejpam-5749	204	4	4n	4n	NOUN
ejpam-5749	204	5	and	and	CCONJ
ejpam-5749	204	6	γtr(g	γtr(g	NUM
ejpam-5749	204	7	)	)	PUNCT
ejpam-5749	204	8	=	=	PUNCT
ejpam-5749	204	9	2(2n	2(2n	NUM
ejpam-5749	204	10	)	)	PUNCT
ejpam-5749	205	1	+	+	NUM
ejpam-5749	205	2	n	n	NOUN
ejpam-5749	205	3	=	=	SYM
ejpam-5749	205	4	4n+	4n+	NUM
ejpam-5749	205	5	k.	k.	NOUN
ejpam-5749	206	1	x1	x1	PROPN
ejpam-5749	207	1	x2	x2	PROPN
ejpam-5749	207	2	x3	x3	PROPN
ejpam-5749	207	3	x4	x4	PROPN
ejpam-5749	207	4	x7	x7	VERB
ejpam-5749	207	5	x4n−3	x4n−3	PROPN
ejpam-5749	207	6	x4n−2	x4n−2	PROPN
ejpam-5749	207	7	x4n−1	x4n−1	PROPN
ejpam-5749	207	8	·	·	PUNCT
ejpam-5749	207	9	·	·	PUNCT
ejpam-5749	208	1	·	·	PUNCT
ejpam-5749	208	2	figure	figure	NOUN
ejpam-5749	208	3	5	5	NUM
ejpam-5749	208	4	:	:	PUNCT
ejpam-5749	208	5	a	a	DET
ejpam-5749	208	6	graph	graph	NOUN
ejpam-5749	208	7	g	g	NOUN
ejpam-5749	208	8	with	with	ADP
ejpam-5749	208	9	γr(g	γr(g	NUM
ejpam-5749	208	10	)	)	PUNCT
ejpam-5749	209	1	=	=	SYM
ejpam-5749	209	2	4n	4n	NOUN
ejpam-5749	209	3	and	and	CCONJ
ejpam-5749	209	4	γt2r(g	γt2r(g	NUM
ejpam-5749	209	5	)	)	PUNCT
ejpam-5749	209	6	=	=	SYM
ejpam-5749	210	1	4n+	4n+	NUM
ejpam-5749	210	2	n	n	CCONJ
ejpam-5749	210	3	now	now	ADV
ejpam-5749	210	4	,	,	PUNCT
ejpam-5749	210	5	suppose	suppose	VERB
ejpam-5749	210	6	that	that	SCONJ
ejpam-5749	210	7	1	1	NUM
ejpam-5749	210	8	≤	≤	NUM
ejpam-5749	210	9	k	k	PROPN
ejpam-5749	210	10	≤	≤	PROPN
ejpam-5749	210	11	n−1	n−1	PROPN
ejpam-5749	210	12	.	.	PUNCT
ejpam-5749	210	13	obtain	obtain	VERB
ejpam-5749	210	14	g	g	NOUN
ejpam-5749	210	15	as	as	ADP
ejpam-5749	210	16	the	the	DET
ejpam-5749	210	17	graph	graph	NOUN
ejpam-5749	210	18	in	in	ADP
ejpam-5749	210	19	figure	figure	NOUN
ejpam-5749	210	20	6	6	NUM
ejpam-5749	210	21	from	from	ADP
ejpam-5749	210	22	p2n+2k+1	p2n+2k+1	ADJ
ejpam-5749	210	23	=	=	PUNCT
ejpam-5749	211	1	[	[	X
ejpam-5749	211	2	x1	x1	PROPN
ejpam-5749	211	3	,	,	PUNCT
ejpam-5749	211	4	x2	x2	PROPN
ejpam-5749	211	5	,	,	PUNCT
ejpam-5749	211	6	.	.	PUNCT
ejpam-5749	211	7	.	.	PUNCT
ejpam-5749	211	8	.	.	PUNCT
ejpam-5749	212	1	,	,	PUNCT
ejpam-5749	212	2	x2n+2k+1	x2n+2k+1	PROPN
ejpam-5749	212	3	]	]	PUNCT
ejpam-5749	212	4	by	by	ADP
ejpam-5749	212	5	joiningk4	joiningk4	PROPN
ejpam-5749	212	6	with	with	ADP
ejpam-5749	212	7	xj	xj	PROPN
ejpam-5749	212	8	for	for	ADP
ejpam-5749	212	9	all	all	DET
ejpam-5749	212	10	j	j	PROPN
ejpam-5749	212	11	∈	∈	PROPN
ejpam-5749	212	12	{	{	PUNCT
ejpam-5749	212	13	1	1	NUM
ejpam-5749	212	14	,	,	PUNCT
ejpam-5749	212	15	2	2	NUM
ejpam-5749	212	16	,	,	PUNCT
ejpam-5749	212	17	.	.	PUNCT
ejpam-5749	212	18	.	.	PUNCT
ejpam-5749	213	1	.	.	PUNCT
ejpam-5749	214	1	,	,	PUNCT
ejpam-5749	214	2	2n−2k}∪{2n−2k+2l+1	2n−2k}∪{2n−2k+2l+1	X
ejpam-5749	214	3	:	:	PUNCT
ejpam-5749	215	1	l	l	NOUN
ejpam-5749	215	2	=	=	SYM
ejpam-5749	215	3	1	1	NUM
ejpam-5749	215	4	,	,	PUNCT
ejpam-5749	215	5	2	2	NUM
ejpam-5749	215	6	,	,	PUNCT
ejpam-5749	215	7	.	.	PUNCT
ejpam-5749	215	8	.	.	PUNCT
ejpam-5749	215	9	.	.	PUNCT
ejpam-5749	216	1	,	,	PUNCT
ejpam-5749	216	2	2k	2k	NUM
ejpam-5749	216	3	}	}	PUNCT
ejpam-5749	216	4	.	.	PUNCT
ejpam-5749	217	1	then	then	ADV
ejpam-5749	217	2	γt2r(g	γt2r(g	NUM
ejpam-5749	217	3	)	)	PUNCT
ejpam-5749	217	4	=	=	SYM
ejpam-5749	217	5	2(2n−	2(2n−	NUM
ejpam-5749	217	6	2k	2k	NUM
ejpam-5749	217	7	)	)	PUNCT
ejpam-5749	218	1	+	+	CCONJ
ejpam-5749	218	2	2(2k	2(2k	NUM
ejpam-5749	218	3	)	)	PUNCT
ejpam-5749	218	4	=	=	NOUN
ejpam-5749	219	1	4n	4n	NOUN
ejpam-5749	219	2	and	and	CCONJ
ejpam-5749	219	3	γtr(g	γtr(g	NUM
ejpam-5749	219	4	)	)	PUNCT
ejpam-5749	219	5	=	=	SYM
ejpam-5749	220	1	4n+	4n+	NUM
ejpam-5749	220	2	k.	k.	NOUN
ejpam-5749	220	3	proposition	proposition	PROPN
ejpam-5749	220	4	10	10	NUM
ejpam-5749	220	5	.	.	PUNCT
ejpam-5749	221	1	let	let	VERB
ejpam-5749	221	2	g	g	PRON
ejpam-5749	221	3	be	be	AUX
ejpam-5749	221	4	a	a	DET
ejpam-5749	221	5	disconnected	disconnected	ADJ
ejpam-5749	221	6	graph	graph	NOUN
ejpam-5749	221	7	without	without	ADP
ejpam-5749	221	8	isolated	isolated	ADJ
ejpam-5749	221	9	vertices	vertex	NOUN
ejpam-5749	221	10	,	,	PUNCT
ejpam-5749	221	11	and	and	CCONJ
ejpam-5749	221	12	let	let	VERB
ejpam-5749	221	13	c1	c1	PROPN
ejpam-5749	221	14	,	,	PUNCT
ejpam-5749	221	15	c2	c2	PROPN
ejpam-5749	221	16	,	,	PUNCT
ejpam-5749	221	17	...	...	PUNCT
ejpam-5749	221	18	,	,	PUNCT
ejpam-5749	221	19	ck	ck	INTJ
ejpam-5749	221	20	be	be	AUX
ejpam-5749	221	21	the	the	DET
ejpam-5749	221	22	components	component	NOUN
ejpam-5749	221	23	of	of	ADP
ejpam-5749	221	24	g.	g.	PROPN
ejpam-5749	221	25	then	then	ADV
ejpam-5749	221	26	γt2r(g	γt2r(g	NUM
ejpam-5749	221	27	)	)	PUNCT
ejpam-5749	222	1	=	=	PUNCT
ejpam-5749	223	1	∑k	∑k	PROPN
ejpam-5749	223	2	i=1	i=1	X
ejpam-5749	223	3	γt2r(ci	γt2r(ci	ADJ
ejpam-5749	223	4	)	)	PUNCT
ejpam-5749	223	5	.	.	PUNCT
ejpam-5749	224	1	b.	b.	PROPN
ejpam-5749	224	2	f.	f.	PROPN
ejpam-5749	224	3	bullang	bullang	PROPN
ejpam-5749	224	4	et	et	PROPN
ejpam-5749	224	5	al	al	PROPN
ejpam-5749	224	6	.	.	PUNCT
ejpam-5749	224	7	/	/	SYM
ejpam-5749	224	8	eur	eur	PROPN
ejpam-5749	224	9	.	.	PUNCT
ejpam-5749	225	1	j.	j.	PROPN
ejpam-5749	225	2	pure	pure	PROPN
ejpam-5749	225	3	appl	appl	PROPN
ejpam-5749	225	4	.	.	PROPN
ejpam-5749	225	5	math	math	PROPN
ejpam-5749	225	6	,	,	PUNCT
ejpam-5749	225	7	18	18	NUM
ejpam-5749	225	8	(	(	PUNCT
ejpam-5749	225	9	1	1	NUM
ejpam-5749	225	10	)	)	PUNCT
ejpam-5749	225	11	(	(	PUNCT
ejpam-5749	225	12	2025	2025	NUM
ejpam-5749	225	13	)	)	PUNCT
ejpam-5749	225	14	,	,	PUNCT
ejpam-5749	225	15	5749	5749	NUM
ejpam-5749	225	16	8	8	NUM
ejpam-5749	225	17	of	of	ADP
ejpam-5749	225	18	15	15	NUM
ejpam-5749	226	1	x1	x1	NUM
ejpam-5749	227	1	x2	x2	INTJ
ejpam-5749	227	2	x2n−2k−1	x2n−2k−1	PROPN
ejpam-5749	228	1	x2n−2k	x2n−2k	PROPN
ejpam-5749	228	2	x2n−2k+1	x2n−2k+1	VERB
ejpam-5749	228	3	x2n−2k+2	x2n−2k+2	PROPN
ejpam-5749	228	4	x2n−2k+3	x2n−2k+3	PROPN
ejpam-5749	228	5	x2n−2k+4	x2n−2k+4	PROPN
ejpam-5749	228	6	x2n−2k+5	x2n−2k+5	PROPN
ejpam-5749	228	7	x2n−2k+6	x2n−2k+6	PROPN
ejpam-5749	228	8	x2n−2k+7	x2n−2k+7	NOUN
ejpam-5749	228	9	x2n+2k−1	x2n+2k−1	NUM
ejpam-5749	228	10	x2n+2k	x2n+2k	PROPN
ejpam-5749	228	11	x2n+2k+1	x2n+2k+1	PUNCT
ejpam-5749	228	12	·	·	PUNCT
ejpam-5749	228	13	·	·	PUNCT
ejpam-5749	228	14	·	·	PUNCT
ejpam-5749	228	15	·	·	PUNCT
ejpam-5749	228	16	·	·	PUNCT
ejpam-5749	228	17	·	·	PUNCT
ejpam-5749	228	18	figure	figure	VERB
ejpam-5749	228	19	6	6	NUM
ejpam-5749	228	20	:	:	PUNCT
ejpam-5749	228	21	a	a	DET
ejpam-5749	228	22	graph	graph	NOUN
ejpam-5749	228	23	g	g	NOUN
ejpam-5749	228	24	with	with	ADP
ejpam-5749	228	25	γt2r(g	γt2r(g	NUM
ejpam-5749	228	26	)	)	PUNCT
ejpam-5749	228	27	=	=	NOUN
ejpam-5749	228	28	4n	4n	NOUN
ejpam-5749	228	29	and	and	CCONJ
ejpam-5749	228	30	γtr(g	γtr(g	NUM
ejpam-5749	228	31	)	)	PUNCT
ejpam-5749	228	32	=	=	SYM
ejpam-5749	229	1	4n+	4n+	NUM
ejpam-5749	230	1	k	k	NOUN
ejpam-5749	230	2	,	,	PUNCT
ejpam-5749	230	3	1	1	NUM
ejpam-5749	230	4	≤	≤	NUM
ejpam-5749	230	5	k	k	X
ejpam-5749	230	6	≤	≤	ADJ
ejpam-5749	230	7	n−	n−	NOUN
ejpam-5749	230	8	1	1	NUM
ejpam-5749	230	9	proof	proof	NOUN
ejpam-5749	230	10	.	.	PUNCT
ejpam-5749	231	1	let	let	VERB
ejpam-5749	231	2	f1	f1	NOUN
ejpam-5749	231	3	,	,	PUNCT
ejpam-5749	231	4	f2	f2	PROPN
ejpam-5749	231	5	,	,	PUNCT
ejpam-5749	231	6	...	...	PUNCT
ejpam-5749	231	7	,	,	PUNCT
ejpam-5749	231	8	fk	fk	INTJ
ejpam-5749	231	9	be	be	VERB
ejpam-5749	231	10	γt2r	γt2r	NOUN
ejpam-5749	231	11	-	-	PUNCT
ejpam-5749	231	12	functions	function	NOUN
ejpam-5749	231	13	of	of	ADP
ejpam-5749	231	14	c1	c1	NOUN
ejpam-5749	231	15	,	,	PUNCT
ejpam-5749	231	16	c2	c2	PROPN
ejpam-5749	231	17	,	,	PUNCT
ejpam-5749	231	18	...	...	PUNCT
ejpam-5749	231	19	,	,	PUNCT
ejpam-5749	231	20	ck	ck	INTJ
ejpam-5749	231	21	,	,	PUNCT
ejpam-5749	231	22	respectively	respectively	ADV
ejpam-5749	231	23	.	.	PUNCT
ejpam-5749	232	1	then	then	ADV
ejpam-5749	232	2	the	the	DET
ejpam-5749	232	3	function	function	NOUN
ejpam-5749	232	4	f	f	X
ejpam-5749	232	5	:	:	PUNCT
ejpam-5749	232	6	v	v	X
ejpam-5749	232	7	(	(	PUNCT
ejpam-5749	232	8	g	g	NOUN
ejpam-5749	232	9	)	)	PUNCT
ejpam-5749	232	10	→	→	SYM
ejpam-5749	232	11	{	{	PUNCT
ejpam-5749	232	12	0	0	NUM
ejpam-5749	232	13	,	,	PUNCT
ejpam-5749	232	14	1	1	NUM
ejpam-5749	232	15	,	,	PUNCT
ejpam-5749	232	16	2	2	NUM
ejpam-5749	232	17	}	}	PUNCT
ejpam-5749	232	18	given	give	VERB
ejpam-5749	232	19	by	by	ADP
ejpam-5749	232	20	f(x	f(x	PROPN
ejpam-5749	232	21	)	)	PUNCT
ejpam-5749	232	22	=	=	PUNCT
ejpam-5749	232	23			NOUN
ejpam-5749	232	24	f1(x	f1(x	NUM
ejpam-5749	232	25	)	)	PUNCT
ejpam-5749	232	26	,	,	PUNCT
ejpam-5749	232	27	if	if	SCONJ
ejpam-5749	232	28	x	x	SYM
ejpam-5749	232	29	∈	∈	PROPN
ejpam-5749	232	30	v	v	NOUN
ejpam-5749	232	31	(	(	PUNCT
ejpam-5749	232	32	c1	c1	PROPN
ejpam-5749	232	33	)	)	PUNCT
ejpam-5749	232	34	,	,	PUNCT
ejpam-5749	232	35	f2(x	f2(x	PROPN
ejpam-5749	232	36	)	)	PUNCT
ejpam-5749	232	37	,	,	PUNCT
ejpam-5749	232	38	if	if	SCONJ
ejpam-5749	232	39	x	x	SYM
ejpam-5749	232	40	∈	∈	PROPN
ejpam-5749	232	41	v	v	NOUN
ejpam-5749	232	42	(	(	PUNCT
ejpam-5749	232	43	c2	c2	PROPN
ejpam-5749	232	44	)	)	PUNCT
ejpam-5749	232	45	,	,	PUNCT
ejpam-5749	232	46	...	...	PUNCT
ejpam-5749	232	47	fk(x	fk(x	PROPN
ejpam-5749	232	48	)	)	PUNCT
ejpam-5749	232	49	,	,	PUNCT
ejpam-5749	232	50	if	if	SCONJ
ejpam-5749	232	51	x	x	SYM
ejpam-5749	232	52	∈	∈	PROPN
ejpam-5749	232	53	v	v	X
ejpam-5749	232	54	(	(	PUNCT
ejpam-5749	232	55	ck	ck	PROPN
ejpam-5749	232	56	)	)	PUNCT
ejpam-5749	232	57	,	,	PUNCT
ejpam-5749	232	58	is	be	AUX
ejpam-5749	232	59	a	a	DET
ejpam-5749	232	60	srdf	srdf	NOUN
ejpam-5749	232	61	of	of	ADP
ejpam-5749	232	62	g.	g.	PROPN
ejpam-5749	232	63	thus	thus	ADV
ejpam-5749	232	64	,	,	PUNCT
ejpam-5749	232	65	γt2r(g	γt2r(g	NUM
ejpam-5749	232	66	)	)	PUNCT
ejpam-5749	232	67	≤	≤	NOUN
ejpam-5749	232	68	ωg(f	ωg(f	NOUN
ejpam-5749	232	69	)	)	PUNCT
ejpam-5749	232	70	=	=	SYM
ejpam-5749	233	1	∑k	∑k	PROPN
ejpam-5749	233	2	i=1	i=1	X
ejpam-5749	233	3	γt2r(ci	γt2r(ci	ADJ
ejpam-5749	233	4	)	)	PUNCT
ejpam-5749	233	5	.	.	PUNCT
ejpam-5749	234	1	conversely	conversely	ADV
ejpam-5749	234	2	,	,	PUNCT
ejpam-5749	234	3	let	let	VERB
ejpam-5749	234	4	f	f	PRON
ejpam-5749	234	5	be	be	AUX
ejpam-5749	234	6	a	a	DET
ejpam-5749	234	7	γt2rfunction	γt2rfunction	NOUN
ejpam-5749	234	8	of	of	ADP
ejpam-5749	234	9	g.	g.	PROPN
ejpam-5749	234	10	then	then	ADV
ejpam-5749	234	11	,	,	PUNCT
ejpam-5749	234	12	for	for	ADP
ejpam-5749	234	13	each	each	DET
ejpam-5749	234	14	i	i	PRON
ejpam-5749	234	15	∈	∈	PROPN
ejpam-5749	234	16	{	{	PUNCT
ejpam-5749	234	17	1	1	NUM
ejpam-5749	234	18	,	,	PUNCT
ejpam-5749	234	19	2	2	NUM
ejpam-5749	234	20	,	,	PUNCT
ejpam-5749	234	21	.	.	PUNCT
ejpam-5749	234	22	.	.	PUNCT
ejpam-5749	235	1	.	.	PUNCT
ejpam-5749	236	1	,	,	PUNCT
ejpam-5749	236	2	k	k	X
ejpam-5749	236	3	}	}	PUNCT
ejpam-5749	236	4	,	,	PUNCT
ejpam-5749	236	5	the	the	DET
ejpam-5749	236	6	restriction	restriction	NOUN
ejpam-5749	236	7	f	f	PROPN
ejpam-5749	236	8	|ci	|ci	X
ejpam-5749	236	9	of	of	ADP
ejpam-5749	236	10	f	f	PROPN
ejpam-5749	236	11	to	to	PART
ejpam-5749	236	12	ci	ci	PROPN
ejpam-5749	236	13	is	be	AUX
ejpam-5749	236	14	a	a	DET
ejpam-5749	236	15	srdf	srdf	NOUN
ejpam-5749	236	16	of	of	ADP
ejpam-5749	236	17	c1	c1	NOUN
ejpam-5749	236	18	,	,	PUNCT
ejpam-5749	236	19	showing	show	VERB
ejpam-5749	236	20	γt2r(ci	γt2r(ci	ADJ
ejpam-5749	236	21	)	)	PUNCT
ejpam-5749	236	22	≤	≤	NUM
ejpam-5749	236	23	ωci(f	ωci(f	NUM
ejpam-5749	236	24	|ci	|ci	NUM
ejpam-5749	236	25	)	)	PUNCT
ejpam-5749	236	26	.	.	PUNCT
ejpam-5749	237	1	thus	thus	ADV
ejpam-5749	237	2	∑k	∑k	PROPN
ejpam-5749	237	3	i=1	i=1	X
ejpam-5749	237	4	γt2r(ci	γt2r(ci	ADJ
ejpam-5749	237	5	)	)	PUNCT
ejpam-5749	237	6	≤	≤	PUNCT
ejpam-5749	238	1	∑k	∑k	PROPN
ejpam-5749	238	2	i	i	PRON
ejpam-5749	238	3	=	=	PROPN
ejpam-5749	238	4	k	k	X
ejpam-5749	238	5	ωci(f	ωci(f	PROPN
ejpam-5749	238	6	)	)	PUNCT
ejpam-5749	238	7	=	=	SYM
ejpam-5749	238	8	ωg(f	ωg(f	X
ejpam-5749	238	9	)	)	PUNCT
ejpam-5749	238	10	=	=	PUNCT
ejpam-5749	238	11	γt2r(g	γt2r(g	NUM
ejpam-5749	238	12	)	)	PUNCT
ejpam-5749	238	13	.	.	PUNCT
ejpam-5749	239	1	proposition	proposition	NOUN
ejpam-5749	239	2	11	11	NUM
ejpam-5749	239	3	.	.	PUNCT
ejpam-5749	240	1	for	for	ADP
ejpam-5749	240	2	paths	path	NOUN
ejpam-5749	240	3	,	,	PUNCT
ejpam-5749	240	4	cycles	cycle	NOUN
ejpam-5749	240	5	and	and	CCONJ
ejpam-5749	240	6	complete	complete	ADJ
ejpam-5749	240	7	multipartite	multipartite	ADJ
ejpam-5749	240	8	graphs	graph	NOUN
ejpam-5749	240	9	,	,	PUNCT
ejpam-5749	240	10	we	we	PRON
ejpam-5749	240	11	have	have	VERB
ejpam-5749	240	12	the	the	DET
ejpam-5749	240	13	following	following	NOUN
ejpam-5749	240	14	:	:	PUNCT
ejpam-5749	240	15	(	(	PUNCT
ejpam-5749	240	16	i	i	NOUN
ejpam-5749	240	17	)	)	PUNCT
ejpam-5749	240	18	for	for	ADP
ejpam-5749	240	19	n	n	X
ejpam-5749	240	20	≥	≥	NUM
ejpam-5749	240	21	2	2	NUM
ejpam-5749	240	22	,	,	PUNCT
ejpam-5749	240	23	γt2r(pn	γt2r(pn	NOUN
ejpam-5749	240	24	)	)	PUNCT
ejpam-5749	240	25	=	=	SYM
ejpam-5749	241	1			PROPN
ejpam-5749	241	2	n	n	CCONJ
ejpam-5749	241	3	,	,	PUNCT
ejpam-5749	241	4	n	n	NOUN
ejpam-5749	241	5	=	=	SYM
ejpam-5749	241	6	2	2	NUM
ejpam-5749	241	7	,	,	PUNCT
ejpam-5749	241	8	3	3	NUM
ejpam-5749	241	9	,	,	PUNCT
ejpam-5749	241	10	3k	3k	X
ejpam-5749	241	11	+	+	CCONJ
ejpam-5749	241	12	r	r	NOUN
ejpam-5749	241	13	,	,	PUNCT
ejpam-5749	241	14	n	n	NOUN
ejpam-5749	241	15	=	=	SYM
ejpam-5749	241	16	4k	4k	NOUN
ejpam-5749	241	17	+	+	CCONJ
ejpam-5749	241	18	r	r	NOUN
ejpam-5749	241	19	and	and	CCONJ
ejpam-5749	241	20	0	0	NUM
ejpam-5749	241	21	≤	≤	NUM
ejpam-5749	241	22	r	r	NOUN
ejpam-5749	241	23	≤	≤	NUM
ejpam-5749	241	24	2	2	NUM
ejpam-5749	241	25	,	,	PUNCT
ejpam-5749	241	26	3k	3k	X
ejpam-5749	241	27	+	+	CCONJ
ejpam-5749	241	28	2	2	NUM
ejpam-5749	241	29	,	,	PUNCT
ejpam-5749	241	30	n	n	NOUN
ejpam-5749	241	31	=	=	SYM
ejpam-5749	241	32	4k	4k	NOUN
ejpam-5749	241	33	+	+	NOUN
ejpam-5749	241	34	3	3	X
ejpam-5749	241	35	.	.	PUNCT
ejpam-5749	241	36	(	(	PUNCT
ejpam-5749	241	37	ii	ii	NOUN
ejpam-5749	241	38	)	)	PUNCT
ejpam-5749	241	39	for	for	ADP
ejpam-5749	241	40	n	n	X
ejpam-5749	241	41	≥	≥	NUM
ejpam-5749	241	42	3	3	NUM
ejpam-5749	241	43	,	,	PUNCT
ejpam-5749	241	44	γt2r(cn	γt2r(cn	NOUN
ejpam-5749	241	45	)	)	PUNCT
ejpam-5749	242	1	=	=	PUNCT
ejpam-5749	243	1			NOUN
ejpam-5749	243	2	3	3	NUM
ejpam-5749	243	3	,	,	PUNCT
ejpam-5749	243	4	n	n	NOUN
ejpam-5749	243	5	=	=	SYM
ejpam-5749	243	6	3	3	NUM
ejpam-5749	243	7	,	,	PUNCT
ejpam-5749	243	8	3k	3k	X
ejpam-5749	243	9	+	+	CCONJ
ejpam-5749	243	10	r	r	NOUN
ejpam-5749	243	11	,	,	PUNCT
ejpam-5749	243	12	n	n	NOUN
ejpam-5749	243	13	=	=	SYM
ejpam-5749	243	14	4k	4k	NOUN
ejpam-5749	243	15	+	+	CCONJ
ejpam-5749	243	16	r	r	NOUN
ejpam-5749	243	17	and	and	CCONJ
ejpam-5749	243	18	0	0	NUM
ejpam-5749	243	19	≤	≤	NUM
ejpam-5749	243	20	r	r	NOUN
ejpam-5749	243	21	≤	≤	NUM
ejpam-5749	243	22	2	2	NUM
ejpam-5749	243	23	,	,	PUNCT
ejpam-5749	243	24	3k	3k	X
ejpam-5749	243	25	+	+	CCONJ
ejpam-5749	243	26	2	2	NUM
ejpam-5749	243	27	,	,	PUNCT
ejpam-5749	243	28	n	n	NOUN
ejpam-5749	243	29	=	=	SYM
ejpam-5749	243	30	4k	4k	NOUN
ejpam-5749	243	31	+	+	NOUN
ejpam-5749	243	32	3	3	X
ejpam-5749	243	33	.	.	X
ejpam-5749	243	34	(	(	PUNCT
ejpam-5749	243	35	iii	iii	NOUN
ejpam-5749	243	36	)	)	PUNCT
ejpam-5749	243	37	for	for	ADP
ejpam-5749	243	38	the	the	DET
ejpam-5749	243	39	complete	complete	ADJ
ejpam-5749	243	40	k	k	NOUN
ejpam-5749	243	41	-	-	ADJ
ejpam-5749	243	42	partite	partite	ADJ
ejpam-5749	243	43	g	g	PROPN
ejpam-5749	243	44	=	=	SYM
ejpam-5749	243	45	kn1,n2,	kn1,n2,	PROPN
ejpam-5749	243	46	...	...	PUNCT
ejpam-5749	243	47	,nk	,nk	PUNCT
ejpam-5749	243	48	with	with	ADP
ejpam-5749	243	49	2	2	NUM
ejpam-5749	243	50	≤	≤	NUM
ejpam-5749	243	51	n1	n1	PROPN
ejpam-5749	243	52	≤	≤	NOUN
ejpam-5749	243	53	n2	n2	NOUN
ejpam-5749	243	54	≤	≤	NOUN
ejpam-5749	243	55	·	·	PUNCT
ejpam-5749	243	56	·	·	PUNCT
ejpam-5749	243	57	·	·	PUNCT
ejpam-5749	243	58	≤	≤	NUM
ejpam-5749	243	59	nk	nk	PROPN
ejpam-5749	243	60	,	,	PUNCT
ejpam-5749	243	61	γt2r(g	γt2r(g	PRON
ejpam-5749	243	62	)	)	PUNCT
ejpam-5749	243	63	=	=	PRON
ejpam-5749	243	64	{	{	PUNCT
ejpam-5749	243	65	3	3	NUM
ejpam-5749	243	66	,	,	PUNCT
ejpam-5749	243	67	if	if	SCONJ
ejpam-5749	243	68	n1	n1	ADJ
ejpam-5749	243	69	=	=	SYM
ejpam-5749	243	70	2	2	NUM
ejpam-5749	243	71	;	;	PUNCT
ejpam-5749	243	72	4	4	NUM
ejpam-5749	243	73	,	,	PUNCT
ejpam-5749	243	74	otherwise	otherwise	ADV
ejpam-5749	243	75	.	.	PUNCT
ejpam-5749	244	1	proof	proof	NOUN
ejpam-5749	244	2	.	.	PUNCT
ejpam-5749	245	1	for	for	ADP
ejpam-5749	245	2	(	(	PUNCT
ejpam-5749	245	3	i	i	NOUN
ejpam-5749	245	4	)	)	PUNCT
ejpam-5749	245	5	,	,	PUNCT
ejpam-5749	245	6	if	if	SCONJ
ejpam-5749	245	7	n	n	NOUN
ejpam-5749	245	8	=	=	SYM
ejpam-5749	245	9	2	2	NUM
ejpam-5749	245	10	,	,	PUNCT
ejpam-5749	245	11	3	3	NUM
ejpam-5749	245	12	,	,	PUNCT
ejpam-5749	245	13	then	then	ADV
ejpam-5749	245	14	the	the	DET
ejpam-5749	245	15	result	result	NOUN
ejpam-5749	245	16	follows	follow	VERB
ejpam-5749	245	17	immediately	immediately	ADV
ejpam-5749	245	18	.	.	PUNCT
ejpam-5749	246	1	for	for	ADP
ejpam-5749	246	2	n	n	X
ejpam-5749	246	3	≥	≥	NOUN
ejpam-5749	246	4	4	4	NUM
ejpam-5749	246	5	,	,	PUNCT
ejpam-5749	246	6	write	write	VERB
ejpam-5749	246	7	n	n	PRON
ejpam-5749	246	8	=	=	SYM
ejpam-5749	246	9	4k	4k	NOUN
ejpam-5749	247	1	+	+	NOUN
ejpam-5749	247	2	r	r	VERB
ejpam-5749	247	3	where	where	SCONJ
ejpam-5749	247	4	0	0	NUM
ejpam-5749	247	5	≤	≤	NUM
ejpam-5749	247	6	r	r	NOUN
ejpam-5749	247	7	≤	≤	NUM
ejpam-5749	247	8	3	3	NUM
ejpam-5749	247	9	.	.	PUNCT
ejpam-5749	248	1	we	we	PRON
ejpam-5749	248	2	define	define	VERB
ejpam-5749	248	3	f	f	PROPN
ejpam-5749	248	4	=	=	SYM
ejpam-5749	248	5	(	(	PUNCT
ejpam-5749	248	6	v0	v0	PROPN
ejpam-5749	248	7	,	,	PUNCT
ejpam-5749	248	8	v1	v1	NOUN
ejpam-5749	248	9	,	,	PUNCT
ejpam-5749	248	10	v2	v2	PROPN
ejpam-5749	248	11	)	)	PUNCT
ejpam-5749	248	12	as	as	SCONJ
ejpam-5749	248	13	follows	follow	VERB
ejpam-5749	248	14	:	:	PUNCT
ejpam-5749	248	15	case	case	NOUN
ejpam-5749	248	16	1	1	NUM
ejpam-5749	248	17	:	:	PUNCT
ejpam-5749	248	18	suppose	suppose	VERB
ejpam-5749	248	19	that	that	SCONJ
ejpam-5749	248	20	r	r	NOUN
ejpam-5749	248	21	=	=	SYM
ejpam-5749	248	22	0	0	X
ejpam-5749	248	23	.	.	PUNCT
ejpam-5749	248	24	put	put	VERB
ejpam-5749	248	25	v2	v2	NOUN
ejpam-5749	248	26	=	=	PUNCT
ejpam-5749	248	27	{	{	PUNCT
ejpam-5749	248	28	x4l−2	x4l−2	NOUN
ejpam-5749	248	29	:	:	PUNCT
ejpam-5749	248	30	l	l	NOUN
ejpam-5749	248	31	=	=	SYM
ejpam-5749	248	32	1	1	NUM
ejpam-5749	248	33	,	,	PUNCT
ejpam-5749	248	34	2	2	NUM
ejpam-5749	248	35	,	,	PUNCT
ejpam-5749	248	36	.	.	PUNCT
ejpam-5749	248	37	.	.	PUNCT
ejpam-5749	248	38	.	.	PUNCT
ejpam-5749	249	1	,	,	PUNCT
ejpam-5749	249	2	k	k	X
ejpam-5749	249	3	}	}	PUNCT
ejpam-5749	249	4	,	,	PUNCT
ejpam-5749	249	5	v1	v1	NOUN
ejpam-5749	249	6	=	=	SYM
ejpam-5749	249	7	{	{	PUNCT
ejpam-5749	249	8	x4l	x4l	X
ejpam-5749	249	9	:	:	PUNCT
ejpam-5749	250	1	l	l	NOUN
ejpam-5749	250	2	=	=	SYM
ejpam-5749	250	3	1	1	NUM
ejpam-5749	250	4	,	,	PUNCT
ejpam-5749	250	5	2	2	NUM
ejpam-5749	250	6	,	,	PUNCT
ejpam-5749	250	7	.	.	PUNCT
ejpam-5749	250	8	.	.	PUNCT
ejpam-5749	250	9	.	.	PUNCT
ejpam-5749	251	1	,	,	PUNCT
ejpam-5749	251	2	k	k	X
ejpam-5749	251	3	}	}	PUNCT
ejpam-5749	251	4	and	and	CCONJ
ejpam-5749	251	5	v0	v0	PROPN
ejpam-5749	251	6	=	=	SYM
ejpam-5749	251	7	v	v	PROPN
ejpam-5749	251	8	(	(	PUNCT
ejpam-5749	251	9	pn	pn	NOUN
ejpam-5749	251	10	)	)	PUNCT
ejpam-5749	251	11	\	\	PUNCT
ejpam-5749	252	1	(	(	PUNCT
ejpam-5749	252	2	v1	v1	VERB
ejpam-5749	252	3	∪	∪	NOUN
ejpam-5749	252	4	v2	v2	NOUN
ejpam-5749	252	5	)	)	PUNCT
ejpam-5749	252	6	.	.	PUNCT
ejpam-5749	253	1	b.	b.	PROPN
ejpam-5749	253	2	f.	f.	PROPN
ejpam-5749	253	3	bullang	bullang	PROPN
ejpam-5749	253	4	et	et	PROPN
ejpam-5749	253	5	al	al	PROPN
ejpam-5749	253	6	.	.	PUNCT
ejpam-5749	253	7	/	/	SYM
ejpam-5749	253	8	eur	eur	PROPN
ejpam-5749	253	9	.	.	PUNCT
ejpam-5749	254	1	j.	j.	PROPN
ejpam-5749	254	2	pure	pure	PROPN
ejpam-5749	254	3	appl	appl	PROPN
ejpam-5749	254	4	.	.	PROPN
ejpam-5749	254	5	math	math	PROPN
ejpam-5749	254	6	,	,	PUNCT
ejpam-5749	254	7	18	18	NUM
ejpam-5749	254	8	(	(	PUNCT
ejpam-5749	254	9	1	1	NUM
ejpam-5749	254	10	)	)	PUNCT
ejpam-5749	254	11	(	(	PUNCT
ejpam-5749	254	12	2025	2025	NUM
ejpam-5749	254	13	)	)	PUNCT
ejpam-5749	254	14	,	,	PUNCT
ejpam-5749	254	15	5749	5749	NUM
ejpam-5749	254	16	9	9	NUM
ejpam-5749	254	17	of	of	ADP
ejpam-5749	254	18	15	15	NUM
ejpam-5749	254	19	case	case	NOUN
ejpam-5749	254	20	2	2	NUM
ejpam-5749	254	21	:	:	PUNCT
ejpam-5749	254	22	suppose	suppose	VERB
ejpam-5749	254	23	that	that	SCONJ
ejpam-5749	254	24	r	r	NOUN
ejpam-5749	254	25	=	=	SYM
ejpam-5749	254	26	1	1	X
ejpam-5749	254	27	.	.	PUNCT
ejpam-5749	254	28	put	put	VERB
ejpam-5749	254	29	v2	v2	NOUN
ejpam-5749	254	30	=	=	SYM
ejpam-5749	254	31	{	{	PUNCT
ejpam-5749	254	32	x4k	x4k	NOUN
ejpam-5749	254	33	,	,	PUNCT
ejpam-5749	254	34	x4l−2	x4l−2	NOUN
ejpam-5749	254	35	:	:	PUNCT
ejpam-5749	255	1	l	l	NOUN
ejpam-5749	255	2	=	=	SYM
ejpam-5749	255	3	1	1	NUM
ejpam-5749	255	4	,	,	PUNCT
ejpam-5749	255	5	2	2	NUM
ejpam-5749	255	6	,	,	PUNCT
ejpam-5749	255	7	.	.	PUNCT
ejpam-5749	255	8	.	.	PUNCT
ejpam-5749	255	9	.	.	PUNCT
ejpam-5749	256	1	,	,	PUNCT
ejpam-5749	256	2	k	k	X
ejpam-5749	256	3	}	}	PUNCT
ejpam-5749	256	4	,	,	PUNCT
ejpam-5749	256	5	v1	v1	NOUN
ejpam-5749	256	6	=	=	SYM
ejpam-5749	256	7	{	{	PUNCT
ejpam-5749	256	8	x4l	x4l	X
ejpam-5749	256	9	:	:	PUNCT
ejpam-5749	257	1	l	l	NOUN
ejpam-5749	257	2	=	=	SYM
ejpam-5749	257	3	1	1	NUM
ejpam-5749	257	4	,	,	PUNCT
ejpam-5749	257	5	2	2	NUM
ejpam-5749	257	6	,	,	PUNCT
ejpam-5749	257	7	.	.	PUNCT
ejpam-5749	257	8	.	.	PUNCT
ejpam-5749	257	9	.	.	PUNCT
ejpam-5749	258	1	,	,	PUNCT
ejpam-5749	259	1	k	k	PROPN
ejpam-5749	259	2	−	−	PROPN
ejpam-5749	260	1	1	1	NUM
ejpam-5749	260	2	}	}	PUNCT
ejpam-5749	260	3	and	and	CCONJ
ejpam-5749	260	4	v0	v0	PROPN
ejpam-5749	260	5	=	=	SYM
ejpam-5749	260	6	v	v	PROPN
ejpam-5749	260	7	(	(	PUNCT
ejpam-5749	260	8	pn	pn	NOUN
ejpam-5749	260	9	)	)	PUNCT
ejpam-5749	260	10	\	\	PUNCT
ejpam-5749	260	11	(	(	PUNCT
ejpam-5749	260	12	v1	v1	VERB
ejpam-5749	260	13	∪	∪	NOUN
ejpam-5749	260	14	v2	v2	NOUN
ejpam-5749	260	15	)	)	PUNCT
ejpam-5749	260	16	.	.	PUNCT
ejpam-5749	261	1	case	case	NOUN
ejpam-5749	261	2	3	3	X
ejpam-5749	261	3	:	:	PUNCT
ejpam-5749	261	4	suppose	suppose	VERB
ejpam-5749	261	5	that	that	SCONJ
ejpam-5749	261	6	r	r	NOUN
ejpam-5749	261	7	=	=	SYM
ejpam-5749	261	8	2	2	X
ejpam-5749	261	9	.	.	PUNCT
ejpam-5749	261	10	define	define	VERB
ejpam-5749	261	11	v2	v2	NOUN
ejpam-5749	261	12	=	=	PUNCT
ejpam-5749	261	13	{	{	PUNCT
ejpam-5749	261	14	x4l−2	x4l−2	NOUN
ejpam-5749	261	15	:	:	PUNCT
ejpam-5749	261	16	l	l	NOUN
ejpam-5749	261	17	=	=	SYM
ejpam-5749	261	18	1	1	NUM
ejpam-5749	261	19	,	,	PUNCT
ejpam-5749	261	20	2	2	NUM
ejpam-5749	261	21	,	,	PUNCT
ejpam-5749	261	22	.	.	PUNCT
ejpam-5749	261	23	.	.	PUNCT
ejpam-5749	262	1	.	.	PUNCT
ejpam-5749	263	1	,	,	PUNCT
ejpam-5749	263	2	k	k	PROPN
ejpam-5749	263	3	+	+	CCONJ
ejpam-5749	263	4	1	1	NUM
ejpam-5749	263	5	}	}	PUNCT
ejpam-5749	263	6	,	,	PUNCT
ejpam-5749	263	7	v1	v1	NOUN
ejpam-5749	263	8	=	=	SYM
ejpam-5749	263	9	{	{	PUNCT
ejpam-5749	263	10	x4l	x4l	X
ejpam-5749	263	11	:	:	PUNCT
ejpam-5749	264	1	l	l	NOUN
ejpam-5749	264	2	=	=	SYM
ejpam-5749	264	3	1	1	NUM
ejpam-5749	264	4	,	,	PUNCT
ejpam-5749	264	5	2	2	NUM
ejpam-5749	264	6	,	,	PUNCT
ejpam-5749	264	7	.	.	PUNCT
ejpam-5749	264	8	.	.	PUNCT
ejpam-5749	264	9	.	.	PUNCT
ejpam-5749	265	1	,	,	PUNCT
ejpam-5749	265	2	k	k	X
ejpam-5749	265	3	}	}	PUNCT
ejpam-5749	265	4	and	and	CCONJ
ejpam-5749	265	5	v0	v0	PROPN
ejpam-5749	265	6	=	=	SYM
ejpam-5749	265	7	v	v	PROPN
ejpam-5749	265	8	(	(	PUNCT
ejpam-5749	265	9	pn	pn	NOUN
ejpam-5749	265	10	)	)	PUNCT
ejpam-5749	265	11	\	\	PUNCT
ejpam-5749	266	1	(	(	PUNCT
ejpam-5749	266	2	v1	v1	VERB
ejpam-5749	266	3	∪	∪	NOUN
ejpam-5749	266	4	v2	v2	NOUN
ejpam-5749	266	5	)	)	PUNCT
ejpam-5749	266	6	.	.	PUNCT
ejpam-5749	267	1	case	case	NOUN
ejpam-5749	267	2	4	4	NUM
ejpam-5749	267	3	:	:	PUNCT
ejpam-5749	267	4	finally	finally	ADV
ejpam-5749	267	5	,	,	PUNCT
ejpam-5749	267	6	suppose	suppose	VERB
ejpam-5749	267	7	that	that	SCONJ
ejpam-5749	267	8	r	r	NOUN
ejpam-5749	267	9	=	=	SYM
ejpam-5749	267	10	3	3	X
ejpam-5749	267	11	.	.	PUNCT
ejpam-5749	267	12	define	define	VERB
ejpam-5749	267	13	v2	v2	NOUN
ejpam-5749	267	14	=	=	SYM
ejpam-5749	267	15	{	{	PUNCT
ejpam-5749	267	16	v4l−2	v4l−2	NOUN
ejpam-5749	267	17	:	:	PUNCT
ejpam-5749	267	18	l	l	NOUN
ejpam-5749	267	19	=	=	SYM
ejpam-5749	267	20	1	1	NUM
ejpam-5749	267	21	,	,	PUNCT
ejpam-5749	267	22	2	2	NUM
ejpam-5749	267	23	,	,	PUNCT
ejpam-5749	267	24	.	.	PUNCT
ejpam-5749	267	25	.	.	PUNCT
ejpam-5749	268	1	.	.	PUNCT
ejpam-5749	269	1	,	,	PUNCT
ejpam-5749	269	2	k	k	PROPN
ejpam-5749	269	3	+	+	CCONJ
ejpam-5749	269	4	1	1	NUM
ejpam-5749	269	5	}	}	PUNCT
ejpam-5749	269	6	,	,	PUNCT
ejpam-5749	269	7	v1	v1	NOUN
ejpam-5749	269	8	=	=	SYM
ejpam-5749	269	9	{	{	PUNCT
ejpam-5749	269	10	v4l	v4l	NOUN
ejpam-5749	269	11	:	:	PUNCT
ejpam-5749	270	1	l	l	NOUN
ejpam-5749	270	2	=	=	SYM
ejpam-5749	270	3	1	1	NUM
ejpam-5749	270	4	,	,	PUNCT
ejpam-5749	270	5	2	2	NUM
ejpam-5749	270	6	,	,	PUNCT
ejpam-5749	270	7	.	.	PUNCT
ejpam-5749	270	8	.	.	PUNCT
ejpam-5749	270	9	.	.	PUNCT
ejpam-5749	271	1	,	,	PUNCT
ejpam-5749	271	2	k	k	X
ejpam-5749	271	3	}	}	PUNCT
ejpam-5749	271	4	and	and	CCONJ
ejpam-5749	271	5	v0	v0	PROPN
ejpam-5749	271	6	=	=	SYM
ejpam-5749	271	7	v	v	PROPN
ejpam-5749	271	8	(	(	PUNCT
ejpam-5749	271	9	pn	pn	NOUN
ejpam-5749	271	10	)	)	PUNCT
ejpam-5749	271	11	\	\	PUNCT
ejpam-5749	272	1	(	(	PUNCT
ejpam-5749	272	2	v1	v1	VERB
ejpam-5749	272	3	∪	∪	NOUN
ejpam-5749	272	4	v2	v2	NOUN
ejpam-5749	272	5	)	)	PUNCT
ejpam-5749	272	6	.	.	PUNCT
ejpam-5749	273	1	in	in	ADP
ejpam-5749	273	2	any	any	DET
ejpam-5749	273	3	case	case	NOUN
ejpam-5749	273	4	,	,	PUNCT
ejpam-5749	273	5	f	f	PROPN
ejpam-5749	273	6	=	=	SYM
ejpam-5749	273	7	(	(	PUNCT
ejpam-5749	273	8	v0	v0	PROPN
ejpam-5749	273	9	,	,	PUNCT
ejpam-5749	273	10	v1	v1	NOUN
ejpam-5749	273	11	,	,	PUNCT
ejpam-5749	273	12	v2	v2	PROPN
ejpam-5749	273	13	)	)	PUNCT
ejpam-5749	273	14	is	be	AUX
ejpam-5749	273	15	a	a	DET
ejpam-5749	273	16	γt2r	γt2r	NOUN
ejpam-5749	273	17	-	-	PUNCT
ejpam-5749	273	18	function	function	NOUN
ejpam-5749	273	19	of	of	ADP
ejpam-5749	273	20	pn	pn	PROPN
ejpam-5749	273	21	with	with	ADP
ejpam-5749	273	22	ωpn(f	ωpn(f	PROPN
ejpam-5749	273	23	)	)	PUNCT
ejpam-5749	273	24	=	=	SYM
ejpam-5749	273	25	3k+r	3k+r	NUM
ejpam-5749	273	26	for	for	ADP
ejpam-5749	273	27	0	0	NUM
ejpam-5749	273	28	≤	≤	NUM
ejpam-5749	273	29	r	r	NOUN
ejpam-5749	273	30	≤	≤	NUM
ejpam-5749	273	31	2	2	NUM
ejpam-5749	273	32	and	and	CCONJ
ejpam-5749	273	33	ωpn(f	ωpn(f	NUM
ejpam-5749	273	34	)	)	PUNCT
ejpam-5749	273	35	=	=	SYM
ejpam-5749	273	36	3k	3k	NOUN
ejpam-5749	274	1	+	+	CCONJ
ejpam-5749	274	2	2	2	NUM
ejpam-5749	274	3	when	when	SCONJ
ejpam-5749	274	4	r	r	NOUN
ejpam-5749	274	5	=	=	SYM
ejpam-5749	274	6	3	3	NUM
ejpam-5749	274	7	.	.	NOUN
ejpam-5749	274	8	similar	similar	ADJ
ejpam-5749	274	9	arguments	argument	NOUN
ejpam-5749	274	10	prove	prove	VERB
ejpam-5749	274	11	statement	statement	NOUN
ejpam-5749	274	12	(	(	PUNCT
ejpam-5749	274	13	ii	ii	NOUN
ejpam-5749	274	14	)	)	PUNCT
ejpam-5749	274	15	.	.	PUNCT
ejpam-5749	275	1	whereas	whereas	ADV
ejpam-5749	275	2	,	,	PUNCT
ejpam-5749	275	3	statement	statement	NOUN
ejpam-5749	275	4	(	(	PUNCT
ejpam-5749	275	5	iii	iii	NOUN
ejpam-5749	275	6	)	)	PUNCT
ejpam-5749	275	7	follows	follow	VERB
ejpam-5749	275	8	from	from	ADP
ejpam-5749	275	9	proposition	proposition	NOUN
ejpam-5749	275	10	6	6	NUM
ejpam-5749	275	11	and	and	CCONJ
ejpam-5749	275	12	proposition	proposition	NOUN
ejpam-5749	275	13	7	7	NUM
ejpam-5749	275	14	.	.	NOUN
ejpam-5749	275	15	3	3	NUM
ejpam-5749	275	16	.	.	X
ejpam-5749	275	17	semitotal	semitotal	ADJ
ejpam-5749	275	18	roman	roman	ADJ
ejpam-5749	275	19	domination	domination	NOUN
ejpam-5749	275	20	in	in	ADP
ejpam-5749	275	21	graphs	graph	NOUN
ejpam-5749	275	22	under	under	ADP
ejpam-5749	275	23	some	some	DET
ejpam-5749	275	24	operations	operation	NOUN
ejpam-5749	275	25	here	here	ADV
ejpam-5749	275	26	we	we	PRON
ejpam-5749	275	27	investigate	investigate	VERB
ejpam-5749	275	28	the	the	DET
ejpam-5749	275	29	semitotal	semitotal	ADJ
ejpam-5749	275	30	roman	roman	ADJ
ejpam-5749	275	31	domination	domination	NOUN
ejpam-5749	275	32	in	in	ADP
ejpam-5749	275	33	the	the	DET
ejpam-5749	275	34	join	join	NOUN
ejpam-5749	275	35	,	,	PUNCT
ejpam-5749	275	36	corona	corona	NOUN
ejpam-5749	275	37	and	and	CCONJ
ejpam-5749	275	38	complementary	complementary	ADJ
ejpam-5749	275	39	prism	prism	NOUN
ejpam-5749	275	40	of	of	ADP
ejpam-5749	275	41	graphs	graph	NOUN
ejpam-5749	275	42	.	.	PUNCT
ejpam-5749	276	1	3.1	3.1	NUM
ejpam-5749	276	2	.	.	PUNCT
ejpam-5749	277	1	in	in	ADP
ejpam-5749	277	2	the	the	DET
ejpam-5749	277	3	join	join	NOUN
ejpam-5749	277	4	of	of	ADP
ejpam-5749	277	5	graphs	graph	NOUN
ejpam-5749	277	6	in	in	ADP
ejpam-5749	277	7	what	what	PRON
ejpam-5749	277	8	follows	follow	VERB
ejpam-5749	277	9	,	,	PUNCT
ejpam-5749	277	10	by	by	ADP
ejpam-5749	277	11	f	f	PROPN
ejpam-5749	277	12	|g	|g	NOUN
ejpam-5749	277	13	we	we	PRON
ejpam-5749	277	14	mean	mean	VERB
ejpam-5749	277	15	the	the	DET
ejpam-5749	277	16	restriction	restriction	NOUN
ejpam-5749	277	17	of	of	ADP
ejpam-5749	277	18	f	f	PROPN
ejpam-5749	277	19	to	to	PART
ejpam-5749	277	20	g.	g.	PROPN
ejpam-5749	277	21	theorem	theorem	PROPN
ejpam-5749	277	22	1	1	X
ejpam-5749	277	23	.	.	PUNCT
ejpam-5749	278	1	let	let	VERB
ejpam-5749	278	2	g	g	NOUN
ejpam-5749	279	1	and	and	CCONJ
ejpam-5749	279	2	h	h	NOUN
ejpam-5749	279	3	be	be	VERB
ejpam-5749	279	4	any	any	DET
ejpam-5749	279	5	graphs	graph	NOUN
ejpam-5749	279	6	and	and	CCONJ
ejpam-5749	279	7	f	f	NOUN
ejpam-5749	279	8	=	=	SYM
ejpam-5749	279	9	(	(	PUNCT
ejpam-5749	279	10	v0	v0	PROPN
ejpam-5749	279	11	,	,	PUNCT
ejpam-5749	279	12	v1	v1	NOUN
ejpam-5749	279	13	,	,	PUNCT
ejpam-5749	279	14	v2	v2	PROPN
ejpam-5749	279	15	)	)	PUNCT
ejpam-5749	279	16	:	:	PUNCT
ejpam-5749	279	17	v	v	X
ejpam-5749	279	18	(	(	PUNCT
ejpam-5749	279	19	g+h	g+h	NOUN
ejpam-5749	279	20	)	)	PUNCT
ejpam-5749	279	21	→	→	SYM
ejpam-5749	279	22	{	{	PUNCT
ejpam-5749	279	23	0	0	NUM
ejpam-5749	279	24	,	,	PUNCT
ejpam-5749	279	25	1	1	NUM
ejpam-5749	279	26	,	,	PUNCT
ejpam-5749	279	27	2	2	NUM
ejpam-5749	279	28	}	}	PUNCT
ejpam-5749	279	29	be	be	AUX
ejpam-5749	279	30	a	a	DET
ejpam-5749	279	31	function	function	NOUN
ejpam-5749	279	32	with	with	ADP
ejpam-5749	279	33	v0	v0	NOUN
ejpam-5749	279	34	̸=	̸=	PROPN
ejpam-5749	279	35	∅.	∅.	ADV
ejpam-5749	279	36	then	then	ADV
ejpam-5749	279	37	f	f	PROPN
ejpam-5749	279	38	∈	∈	PROPN
ejpam-5749	279	39	srdf	srdf	NOUN
ejpam-5749	279	40	(	(	PUNCT
ejpam-5749	279	41	g+h	g+h	NOUN
ejpam-5749	279	42	)	)	PUNCT
ejpam-5749	280	1	if	if	SCONJ
ejpam-5749	280	2	and	and	CCONJ
ejpam-5749	280	3	only	only	ADV
ejpam-5749	280	4	if	if	SCONJ
ejpam-5749	280	5	one	one	NUM
ejpam-5749	280	6	of	of	ADP
ejpam-5749	280	7	the	the	DET
ejpam-5749	280	8	following	follow	VERB
ejpam-5749	280	9	holds	hold	VERB
ejpam-5749	280	10	:	:	PUNCT
ejpam-5749	280	11	(	(	PUNCT
ejpam-5749	280	12	i	i	NOUN
ejpam-5749	280	13	)	)	PUNCT
ejpam-5749	280	14	v2	v2	VERB
ejpam-5749	280	15	⊆	⊆	NUM
ejpam-5749	280	16	v	v	NOUN
ejpam-5749	280	17	(	(	PUNCT
ejpam-5749	280	18	g	g	NOUN
ejpam-5749	280	19	)	)	PUNCT
ejpam-5749	280	20	,	,	PUNCT
ejpam-5749	280	21	f	f	PROPN
ejpam-5749	280	22	|g	|g	PROPN
ejpam-5749	280	23	∈	∈	PROPN
ejpam-5749	280	24	rdf	rdf	NOUN
ejpam-5749	280	25	(	(	PUNCT
ejpam-5749	280	26	g	g	NOUN
ejpam-5749	280	27	)	)	PUNCT
ejpam-5749	280	28	and	and	CCONJ
ejpam-5749	280	29	one	one	NUM
ejpam-5749	280	30	of	of	ADP
ejpam-5749	280	31	the	the	DET
ejpam-5749	280	32	following	following	NOUN
ejpam-5749	280	33	holds	hold	VERB
ejpam-5749	280	34	:	:	PUNCT
ejpam-5749	280	35	(	(	PUNCT
ejpam-5749	280	36	a	a	X
ejpam-5749	280	37	)	)	PUNCT
ejpam-5749	280	38	v1	v1	NOUN
ejpam-5749	280	39	∩	∩	ADJ
ejpam-5749	280	40	v	v	NOUN
ejpam-5749	280	41	(	(	PUNCT
ejpam-5749	280	42	h	h	NOUN
ejpam-5749	280	43	)	)	PUNCT
ejpam-5749	280	44	̸=	̸=	NOUN
ejpam-5749	280	45	∅	∅	NOUN
ejpam-5749	280	46	;	;	PUNCT
ejpam-5749	280	47	(	(	PUNCT
ejpam-5749	280	48	b	b	X
ejpam-5749	280	49	)	)	PUNCT
ejpam-5749	280	50	|(v1	|(v1	VERB
ejpam-5749	280	51	∪	∪	ADP
ejpam-5749	280	52	v2	v2	NOUN
ejpam-5749	280	53	)	)	PUNCT
ejpam-5749	280	54	∩	∩	ADJ
ejpam-5749	280	55	v	v	X
ejpam-5749	280	56	(	(	PUNCT
ejpam-5749	280	57	g)|	g)|	VERB
ejpam-5749	280	58	≥	≥	NOUN
ejpam-5749	280	59	2	2	NUM
ejpam-5749	280	60	;	;	PUNCT
ejpam-5749	280	61	(	(	PUNCT
ejpam-5749	280	62	ii	ii	NOUN
ejpam-5749	280	63	)	)	PUNCT
ejpam-5749	280	64	v2	v2	PROPN
ejpam-5749	280	65	⊆	⊆	NUM
ejpam-5749	280	66	v	v	NOUN
ejpam-5749	280	67	(	(	PUNCT
ejpam-5749	280	68	h	h	NOUN
ejpam-5749	280	69	)	)	PUNCT
ejpam-5749	280	70	,	,	PUNCT
ejpam-5749	280	71	f	f	PROPN
ejpam-5749	280	72	|h	|h	X
ejpam-5749	280	73	∈	∈	PROPN
ejpam-5749	280	74	rdf	rdf	NOUN
ejpam-5749	280	75	(	(	PUNCT
ejpam-5749	280	76	h	h	NOUN
ejpam-5749	280	77	)	)	PUNCT
ejpam-5749	280	78	,	,	PUNCT
ejpam-5749	280	79	and	and	CCONJ
ejpam-5749	280	80	one	one	NUM
ejpam-5749	280	81	of	of	ADP
ejpam-5749	280	82	the	the	DET
ejpam-5749	280	83	following	following	NOUN
ejpam-5749	280	84	holds	hold	VERB
ejpam-5749	280	85	:	:	PUNCT
ejpam-5749	280	86	(	(	PUNCT
ejpam-5749	280	87	a	a	X
ejpam-5749	280	88	)	)	PUNCT
ejpam-5749	280	89	v1	v1	NOUN
ejpam-5749	280	90	∩	∩	ADJ
ejpam-5749	280	91	v	v	NOUN
ejpam-5749	280	92	(	(	PUNCT
ejpam-5749	280	93	g	g	NOUN
ejpam-5749	280	94	)	)	PUNCT
ejpam-5749	280	95	̸=	̸=	PROPN
ejpam-5749	280	96	∅	∅	NOUN
ejpam-5749	280	97	;	;	PUNCT
ejpam-5749	280	98	(	(	PUNCT
ejpam-5749	280	99	b	b	X
ejpam-5749	280	100	)	)	PUNCT
ejpam-5749	280	101	|(v1	|(v1	VERB
ejpam-5749	280	102	∪	∪	ADP
ejpam-5749	280	103	v2	v2	NOUN
ejpam-5749	280	104	)	)	PUNCT
ejpam-5749	280	105	∩	∩	ADJ
ejpam-5749	280	106	v	v	X
ejpam-5749	280	107	(	(	PUNCT
ejpam-5749	280	108	h)|	h)|	PROPN
ejpam-5749	280	109	≥	≥	NOUN
ejpam-5749	280	110	2	2	NUM
ejpam-5749	280	111	;	;	PUNCT
ejpam-5749	280	112	(	(	PUNCT
ejpam-5749	280	113	iii	iii	X
ejpam-5749	280	114	)	)	PUNCT
ejpam-5749	280	115	v2	v2	NOUN
ejpam-5749	280	116	∩	∩	ADJ
ejpam-5749	280	117	v	v	NOUN
ejpam-5749	280	118	(	(	PUNCT
ejpam-5749	280	119	g	g	NOUN
ejpam-5749	280	120	)	)	PUNCT
ejpam-5749	280	121	̸=	̸=	PROPN
ejpam-5749	280	122	∅	∅	NOUN
ejpam-5749	280	123	and	and	CCONJ
ejpam-5749	280	124	v2	v2	VERB
ejpam-5749	280	125	∩	∩	ADJ
ejpam-5749	280	126	v	v	NOUN
ejpam-5749	280	127	(	(	PUNCT
ejpam-5749	280	128	h	h	NOUN
ejpam-5749	280	129	)	)	PUNCT
ejpam-5749	280	130	̸=	̸=	PROPN
ejpam-5749	280	131	∅.	∅.	PRON
ejpam-5749	280	132	proof	proof	NOUN
ejpam-5749	280	133	.	.	PUNCT
ejpam-5749	281	1	suppose	suppose	VERB
ejpam-5749	281	2	that	that	SCONJ
ejpam-5749	281	3	f	f	PROPN
ejpam-5749	281	4	∈	∈	PROPN
ejpam-5749	281	5	srdf	srdf	NOUN
ejpam-5749	281	6	(	(	PUNCT
ejpam-5749	281	7	g	g	NOUN
ejpam-5749	281	8	+	+	NOUN
ejpam-5749	281	9	h	h	NOUN
ejpam-5749	281	10	)	)	PUNCT
ejpam-5749	281	11	.	.	PUNCT
ejpam-5749	282	1	since	since	SCONJ
ejpam-5749	282	2	v0	v0	NOUN
ejpam-5749	282	3	̸=	̸=	PROPN
ejpam-5749	282	4	∅	∅	NOUN
ejpam-5749	282	5	,	,	PUNCT
ejpam-5749	282	6	v2	v2	PROPN
ejpam-5749	282	7	̸=	̸=	PROPN
ejpam-5749	282	8	∅.	∅.	ADV
ejpam-5749	282	9	suppose	suppose	VERB
ejpam-5749	282	10	that	that	SCONJ
ejpam-5749	282	11	v2	v2	PROPN
ejpam-5749	282	12	⊆	⊆	NUM
ejpam-5749	282	13	v	v	NOUN
ejpam-5749	282	14	(	(	PUNCT
ejpam-5749	282	15	g	g	NOUN
ejpam-5749	282	16	)	)	PUNCT
ejpam-5749	282	17	,	,	PUNCT
ejpam-5749	282	18	and	and	CCONJ
ejpam-5749	282	19	let	let	VERB
ejpam-5749	282	20	v	v	NUM
ejpam-5749	282	21	∈	∈	PROPN
ejpam-5749	282	22	v0	v0	NOUN
ejpam-5749	282	23	∩	∩	X
ejpam-5749	282	24	v	v	X
ejpam-5749	282	25	(	(	PUNCT
ejpam-5749	282	26	g	g	NOUN
ejpam-5749	282	27	)	)	PUNCT
ejpam-5749	282	28	.	.	PUNCT
ejpam-5749	283	1	then	then	ADV
ejpam-5749	283	2	there	there	PRON
ejpam-5749	283	3	exists	exist	VERB
ejpam-5749	283	4	u	u	PROPN
ejpam-5749	283	5	∈	∈	PROPN
ejpam-5749	283	6	v2	v2	NOUN
ejpam-5749	283	7	for	for	ADP
ejpam-5749	283	8	which	which	PRON
ejpam-5749	283	9	uv	uv	NOUN
ejpam-5749	283	10	∈	∈	PROPN
ejpam-5749	283	11	e(g	e(g	PROPN
ejpam-5749	284	1	+	+	NOUN
ejpam-5749	284	2	h	h	NOUN
ejpam-5749	284	3	)	)	PUNCT
ejpam-5749	284	4	.	.	PUNCT
ejpam-5749	285	1	since	since	SCONJ
ejpam-5749	285	2	v2	v2	PROPN
ejpam-5749	285	3	⊆	⊆	NUM
ejpam-5749	285	4	v	v	NOUN
ejpam-5749	285	5	(	(	PUNCT
ejpam-5749	285	6	g	g	NOUN
ejpam-5749	285	7	)	)	PUNCT
ejpam-5749	285	8	,	,	PUNCT
ejpam-5749	285	9	uv	uv	PROPN
ejpam-5749	285	10	∈	∈	PROPN
ejpam-5749	285	11	e(g	e(g	PROPN
ejpam-5749	285	12	)	)	PUNCT
ejpam-5749	285	13	.	.	PUNCT
ejpam-5749	286	1	accordingly	accordingly	ADV
ejpam-5749	286	2	,	,	PUNCT
ejpam-5749	286	3	f	f	PROPN
ejpam-5749	286	4	|g	|g	PROPN
ejpam-5749	286	5	∈	∈	PROPN
ejpam-5749	286	6	rdf	rdf	NOUN
ejpam-5749	286	7	(	(	PUNCT
ejpam-5749	286	8	g	g	NOUN
ejpam-5749	286	9	)	)	PUNCT
ejpam-5749	286	10	.	.	PUNCT
ejpam-5749	287	1	if	if	SCONJ
ejpam-5749	287	2	v1	v1	NOUN
ejpam-5749	287	3	∩	∩	ADJ
ejpam-5749	287	4	v	v	NOUN
ejpam-5749	287	5	(	(	PUNCT
ejpam-5749	287	6	h	h	NOUN
ejpam-5749	287	7	)	)	PUNCT
ejpam-5749	287	8	̸=	̸=	NOUN
ejpam-5749	287	9	∅	∅	NOUN
ejpam-5749	287	10	,	,	PUNCT
ejpam-5749	287	11	then	then	ADV
ejpam-5749	287	12	(	(	PUNCT
ejpam-5749	287	13	i)(a	i)(a	NOUN
ejpam-5749	287	14	)	)	PUNCT
ejpam-5749	287	15	holds	hold	VERB
ejpam-5749	287	16	.	.	PUNCT
ejpam-5749	288	1	suppose	suppose	VERB
ejpam-5749	288	2	that	that	SCONJ
ejpam-5749	288	3	v1	v1	NOUN
ejpam-5749	288	4	∩	∩	ADJ
ejpam-5749	288	5	v	v	X
ejpam-5749	288	6	(	(	PUNCT
ejpam-5749	288	7	h	h	NOUN
ejpam-5749	288	8	)	)	PUNCT
ejpam-5749	288	9	=	=	VERB
ejpam-5749	288	10	∅.	∅.	AUX
ejpam-5749	288	11	pick	pick	VERB
ejpam-5749	288	12	v	v	NUM
ejpam-5749	288	13	∈	∈	PROPN
ejpam-5749	288	14	v2	v2	NOUN
ejpam-5749	288	15	.	.	PUNCT
ejpam-5749	289	1	since	since	SCONJ
ejpam-5749	289	2	f	f	PROPN
ejpam-5749	289	3	∈	∈	PROPN
ejpam-5749	289	4	srdf	srdf	NOUN
ejpam-5749	289	5	(	(	PUNCT
ejpam-5749	289	6	g+h	g+h	PROPN
ejpam-5749	289	7	)	)	PUNCT
ejpam-5749	289	8	,	,	PUNCT
ejpam-5749	289	9	there	there	PRON
ejpam-5749	289	10	exists	exist	VERB
ejpam-5749	289	11	u	u	PROPN
ejpam-5749	289	12	∈	∈	PROPN
ejpam-5749	289	13	v1	v1	NOUN
ejpam-5749	289	14	∪	∪	NOUN
ejpam-5749	289	15	v2	v2	PROPN
ejpam-5749	289	16	for	for	ADP
ejpam-5749	289	17	which	which	PRON
ejpam-5749	289	18	1	1	NUM
ejpam-5749	289	19	≤	≤	NUM
ejpam-5749	289	20	dg+h(v	dg+h(v	PROPN
ejpam-5749	289	21	,	,	PUNCT
ejpam-5749	289	22	w	w	NOUN
ejpam-5749	289	23	)	)	PUNCT
ejpam-5749	289	24	≤	≤	NOUN
ejpam-5749	289	25	2	2	NUM
ejpam-5749	289	26	.	.	PUNCT
ejpam-5749	290	1	the	the	DET
ejpam-5749	290	2	assumptions	assumption	NOUN
ejpam-5749	290	3	imply	imply	VERB
ejpam-5749	290	4	that	that	SCONJ
ejpam-5749	290	5	w	w	PROPN
ejpam-5749	290	6	∈	∈	PROPN
ejpam-5749	290	7	v	v	ADP
ejpam-5749	290	8	(	(	PUNCT
ejpam-5749	290	9	g	g	NOUN
ejpam-5749	290	10	)	)	PUNCT
ejpam-5749	290	11	.	.	PUNCT
ejpam-5749	291	1	thus	thus	ADV
ejpam-5749	291	2	,	,	PUNCT
ejpam-5749	291	3	(	(	PUNCT
ejpam-5749	291	4	i)(b	i)(b	NUM
ejpam-5749	291	5	)	)	PUNCT
ejpam-5749	291	6	holds	hold	NOUN
ejpam-5749	291	7	.	.	PUNCT
ejpam-5749	292	1	similarly	similarly	ADV
ejpam-5749	292	2	,	,	PUNCT
ejpam-5749	292	3	if	if	SCONJ
ejpam-5749	292	4	v2	v2	PROPN
ejpam-5749	292	5	⊆	⊆	NUM
ejpam-5749	292	6	v	v	NOUN
ejpam-5749	292	7	(	(	PUNCT
ejpam-5749	292	8	h	h	NOUN
ejpam-5749	292	9	)	)	PUNCT
ejpam-5749	292	10	,	,	PUNCT
ejpam-5749	292	11	then	then	ADV
ejpam-5749	292	12	(	(	PUNCT
ejpam-5749	292	13	ii	ii	NOUN
ejpam-5749	292	14	)	)	PUNCT
ejpam-5749	292	15	holds	hold	VERB
ejpam-5749	292	16	.	.	PUNCT
ejpam-5749	293	1	clearly	clearly	ADV
ejpam-5749	293	2	,	,	PUNCT
ejpam-5749	293	3	if	if	SCONJ
ejpam-5749	293	4	both	both	PRON
ejpam-5749	293	5	(	(	PUNCT
ejpam-5749	293	6	i	i	NOUN
ejpam-5749	293	7	)	)	PUNCT
ejpam-5749	293	8	and	and	CCONJ
ejpam-5749	293	9	(	(	PUNCT
ejpam-5749	293	10	ii	ii	NOUN
ejpam-5749	293	11	)	)	PUNCT
ejpam-5749	293	12	do	do	AUX
ejpam-5749	293	13	not	not	PART
ejpam-5749	293	14	hold	hold	VERB
ejpam-5749	293	15	,	,	PUNCT
ejpam-5749	293	16	then	then	ADV
ejpam-5749	293	17	(	(	PUNCT
ejpam-5749	293	18	iii	iii	NOUN
ejpam-5749	293	19	)	)	PUNCT
ejpam-5749	293	20	holds	hold	NOUN
ejpam-5749	293	21	.	.	PUNCT
ejpam-5749	294	1	b.	b.	PROPN
ejpam-5749	294	2	f.	f.	PROPN
ejpam-5749	294	3	bullang	bullang	PROPN
ejpam-5749	294	4	et	et	PROPN
ejpam-5749	294	5	al	al	PROPN
ejpam-5749	294	6	.	.	PUNCT
ejpam-5749	294	7	/	/	SYM
ejpam-5749	294	8	eur	eur	PROPN
ejpam-5749	294	9	.	.	PUNCT
ejpam-5749	295	1	j.	j.	PROPN
ejpam-5749	295	2	pure	pure	PROPN
ejpam-5749	295	3	appl	appl	PROPN
ejpam-5749	295	4	.	.	PROPN
ejpam-5749	295	5	math	math	PROPN
ejpam-5749	295	6	,	,	PUNCT
ejpam-5749	295	7	18	18	NUM
ejpam-5749	295	8	(	(	PUNCT
ejpam-5749	295	9	1	1	NUM
ejpam-5749	295	10	)	)	PUNCT
ejpam-5749	295	11	(	(	PUNCT
ejpam-5749	295	12	2025	2025	NUM
ejpam-5749	295	13	)	)	PUNCT
ejpam-5749	295	14	,	,	PUNCT
ejpam-5749	295	15	5749	5749	NUM
ejpam-5749	295	16	10	10	NUM
ejpam-5749	295	17	of	of	ADP
ejpam-5749	295	18	15	15	NUM
ejpam-5749	295	19	conversely	conversely	ADV
ejpam-5749	295	20	,	,	PUNCT
ejpam-5749	295	21	assume	assume	VERB
ejpam-5749	295	22	that	that	SCONJ
ejpam-5749	295	23	(	(	PUNCT
ejpam-5749	295	24	i	i	NOUN
ejpam-5749	295	25	)	)	PUNCT
ejpam-5749	295	26	holds	hold	VERB
ejpam-5749	295	27	.	.	PUNCT
ejpam-5749	296	1	let	let	VERB
ejpam-5749	296	2	v	v	NUM
ejpam-5749	296	3	∈	∈	PROPN
ejpam-5749	296	4	v0	v0	NOUN
ejpam-5749	296	5	.	.	PUNCT
ejpam-5749	297	1	if	if	SCONJ
ejpam-5749	297	2	v	v	NUM
ejpam-5749	297	3	∈	∈	PROPN
ejpam-5749	297	4	v	v	NOUN
ejpam-5749	297	5	(	(	PUNCT
ejpam-5749	297	6	h	h	NOUN
ejpam-5749	297	7	)	)	PUNCT
ejpam-5749	297	8	,	,	PUNCT
ejpam-5749	297	9	then	then	ADV
ejpam-5749	297	10	pick	pick	VERB
ejpam-5749	297	11	any	any	DET
ejpam-5749	297	12	u	u	PROPN
ejpam-5749	297	13	∈	∈	PROPN
ejpam-5749	297	14	v2	v2	NOUN
ejpam-5749	297	15	.	.	PUNCT
ejpam-5749	298	1	if	if	SCONJ
ejpam-5749	298	2	v	v	NUM
ejpam-5749	298	3	∈	∈	PROPN
ejpam-5749	298	4	v	v	NOUN
ejpam-5749	298	5	(	(	PUNCT
ejpam-5749	298	6	g	g	NOUN
ejpam-5749	298	7	)	)	PUNCT
ejpam-5749	298	8	,	,	PUNCT
ejpam-5749	298	9	then	then	ADV
ejpam-5749	298	10	since	since	SCONJ
ejpam-5749	298	11	f	f	PROPN
ejpam-5749	298	12	|g	|g	PROPN
ejpam-5749	298	13	∈	∈	PROPN
ejpam-5749	298	14	rdf	rdf	NOUN
ejpam-5749	298	15	(	(	PUNCT
ejpam-5749	298	16	g	g	NOUN
ejpam-5749	298	17	)	)	PUNCT
ejpam-5749	298	18	,	,	PUNCT
ejpam-5749	298	19	there	there	PRON
ejpam-5749	298	20	exists	exist	VERB
ejpam-5749	298	21	u	u	PROPN
ejpam-5749	298	22	∈	∈	PROPN
ejpam-5749	298	23	v2	v2	NOUN
ejpam-5749	298	24	for	for	ADP
ejpam-5749	298	25	which	which	PRON
ejpam-5749	298	26	uv	uv	NOUN
ejpam-5749	298	27	∈	∈	PROPN
ejpam-5749	298	28	e(g	e(g	PROPN
ejpam-5749	298	29	)	)	PUNCT
ejpam-5749	298	30	.	.	PUNCT
ejpam-5749	299	1	in	in	ADP
ejpam-5749	299	2	any	any	DET
ejpam-5749	299	3	case	case	NOUN
ejpam-5749	299	4	,	,	PUNCT
ejpam-5749	299	5	uv	uv	NOUN
ejpam-5749	299	6	∈	∈	PROPN
ejpam-5749	299	7	e(g+h	e(g+h	NUM
ejpam-5749	299	8	)	)	PUNCT
ejpam-5749	299	9	.	.	PUNCT
ejpam-5749	300	1	let	let	VERB
ejpam-5749	300	2	v	v	NUM
ejpam-5749	300	3	∈	∈	PROPN
ejpam-5749	300	4	v1	v1	NOUN
ejpam-5749	300	5	∪	∪	X
ejpam-5749	300	6	v2	v2	NOUN
ejpam-5749	300	7	.	.	PUNCT
ejpam-5749	301	1	if	if	SCONJ
ejpam-5749	301	2	v	v	NUM
ejpam-5749	301	3	∈	∈	PROPN
ejpam-5749	301	4	v	v	NOUN
ejpam-5749	301	5	(	(	PUNCT
ejpam-5749	301	6	h	h	NOUN
ejpam-5749	301	7	)	)	PUNCT
ejpam-5749	301	8	,	,	PUNCT
ejpam-5749	301	9	then	then	ADV
ejpam-5749	301	10	v	v	X
ejpam-5749	301	11	∈	∈	NOUN
ejpam-5749	301	12	v1	v1	NOUN
ejpam-5749	301	13	and	and	CCONJ
ejpam-5749	301	14	uv	uv	NOUN
ejpam-5749	301	15	∈	∈	PROPN
ejpam-5749	301	16	e(g+h	e(g+h	NUM
ejpam-5749	301	17	)	)	PUNCT
ejpam-5749	301	18	for	for	ADP
ejpam-5749	301	19	all	all	DET
ejpam-5749	301	20	u	u	PROPN
ejpam-5749	301	21	∈	∈	PROPN
ejpam-5749	301	22	v2	v2	NOUN
ejpam-5749	301	23	⊆	⊆	NUM
ejpam-5749	301	24	v	v	NOUN
ejpam-5749	301	25	(	(	PUNCT
ejpam-5749	301	26	g	g	NOUN
ejpam-5749	301	27	)	)	PUNCT
ejpam-5749	301	28	.	.	PUNCT
ejpam-5749	301	29	suppose	suppose	VERB
ejpam-5749	301	30	that	that	SCONJ
ejpam-5749	301	31	v	v	NUM
ejpam-5749	301	32	∈	∈	PROPN
ejpam-5749	301	33	v	v	NOUN
ejpam-5749	301	34	(	(	PUNCT
ejpam-5749	301	35	g	g	NOUN
ejpam-5749	301	36	)	)	PUNCT
ejpam-5749	301	37	.	.	PUNCT
ejpam-5749	302	1	if	if	SCONJ
ejpam-5749	302	2	(	(	PUNCT
ejpam-5749	302	3	i)(a	i)(a	NOUN
ejpam-5749	302	4	)	)	PUNCT
ejpam-5749	302	5	holds	hold	VERB
ejpam-5749	302	6	,	,	PUNCT
ejpam-5749	302	7	then	then	ADV
ejpam-5749	302	8	dg+h(u	dg+h(u	PROPN
ejpam-5749	302	9	,	,	PUNCT
ejpam-5749	302	10	v	v	NOUN
ejpam-5749	302	11	)	)	PUNCT
ejpam-5749	302	12	=	=	SYM
ejpam-5749	302	13	1	1	NUM
ejpam-5749	302	14	for	for	ADP
ejpam-5749	302	15	all	all	DET
ejpam-5749	302	16	u	u	PRON
ejpam-5749	302	17	∈	∈	PROPN
ejpam-5749	302	18	v1	v1	NOUN
ejpam-5749	302	19	∩	∩	ADJ
ejpam-5749	302	20	v	v	X
ejpam-5749	302	21	(	(	PUNCT
ejpam-5749	302	22	h	h	NOUN
ejpam-5749	302	23	)	)	PUNCT
ejpam-5749	302	24	.	.	PUNCT
ejpam-5749	303	1	if	if	SCONJ
ejpam-5749	303	2	(	(	PUNCT
ejpam-5749	303	3	i)(b	i)(b	NUM
ejpam-5749	303	4	)	)	PUNCT
ejpam-5749	303	5	holds	hold	VERB
ejpam-5749	303	6	,	,	PUNCT
ejpam-5749	303	7	then	then	ADV
ejpam-5749	303	8	dg+h(u	dg+h(u	PROPN
ejpam-5749	303	9	,	,	PUNCT
ejpam-5749	303	10	v	v	NOUN
ejpam-5749	303	11	)	)	PUNCT
ejpam-5749	303	12	≤	≤	NUM
ejpam-5749	303	13	2	2	NUM
ejpam-5749	303	14	for	for	ADP
ejpam-5749	303	15	all	all	DET
ejpam-5749	303	16	u	u	NOUN
ejpam-5749	303	17	∈	∈	PROPN
ejpam-5749	303	18	[	[	X
ejpam-5749	303	19	(	(	PUNCT
ejpam-5749	303	20	v1	v1	VERB
ejpam-5749	303	21	∪	∪	NOUN
ejpam-5749	303	22	v2	v2	NOUN
ejpam-5749	303	23	)	)	PUNCT
ejpam-5749	303	24	∩	∩	ADJ
ejpam-5749	303	25	v	v	X
ejpam-5749	303	26	(	(	PUNCT
ejpam-5749	303	27	g	g	NOUN
ejpam-5749	303	28	)	)	PUNCT
ejpam-5749	303	29	]	]	PUNCT
ejpam-5749	303	30	\	\	PROPN
ejpam-5749	304	1	{	{	PUNCT
ejpam-5749	304	2	v	v	NOUN
ejpam-5749	304	3	}	}	PUNCT
ejpam-5749	304	4	.	.	PUNCT
ejpam-5749	305	1	accordingly	accordingly	ADV
ejpam-5749	305	2	,	,	PUNCT
ejpam-5749	305	3	f	f	PROPN
ejpam-5749	305	4	∈	∈	PROPN
ejpam-5749	305	5	srdf	srdf	NOUN
ejpam-5749	305	6	(	(	PUNCT
ejpam-5749	305	7	g	g	PROPN
ejpam-5749	305	8	+	+	PROPN
ejpam-5749	305	9	h	h	NOUN
ejpam-5749	305	10	)	)	PUNCT
ejpam-5749	305	11	.	.	PUNCT
ejpam-5749	306	1	similarly	similarly	ADV
ejpam-5749	306	2	,	,	PUNCT
ejpam-5749	306	3	if	if	SCONJ
ejpam-5749	306	4	(	(	PUNCT
ejpam-5749	306	5	ii	ii	NOUN
ejpam-5749	306	6	)	)	PUNCT
ejpam-5749	306	7	holds	hold	VERB
ejpam-5749	306	8	,	,	PUNCT
ejpam-5749	306	9	then	then	ADV
ejpam-5749	306	10	f	f	PROPN
ejpam-5749	306	11	∈	∈	PROPN
ejpam-5749	306	12	srdf	srdf	NOUN
ejpam-5749	306	13	(	(	PUNCT
ejpam-5749	306	14	g	g	PROPN
ejpam-5749	306	15	+	+	PROPN
ejpam-5749	306	16	h	h	NOUN
ejpam-5749	306	17	)	)	PUNCT
ejpam-5749	306	18	.	.	PUNCT
ejpam-5749	307	1	it	it	PRON
ejpam-5749	307	2	is	be	AUX
ejpam-5749	307	3	also	also	ADV
ejpam-5749	307	4	clear	clear	ADJ
ejpam-5749	307	5	that	that	SCONJ
ejpam-5749	307	6	if	if	SCONJ
ejpam-5749	307	7	(	(	PUNCT
ejpam-5749	307	8	iii	iii	NOUN
ejpam-5749	307	9	)	)	PUNCT
ejpam-5749	307	10	holds	hold	VERB
ejpam-5749	307	11	,	,	PUNCT
ejpam-5749	307	12	then	then	ADV
ejpam-5749	307	13	f	f	PROPN
ejpam-5749	307	14	∈	∈	PROPN
ejpam-5749	307	15	srdf	srdf	NOUN
ejpam-5749	307	16	(	(	PUNCT
ejpam-5749	307	17	g+h	g+h	NOUN
ejpam-5749	307	18	)	)	PUNCT
ejpam-5749	307	19	.	.	PUNCT
ejpam-5749	308	1	corollary	corollary	ADJ
ejpam-5749	308	2	1	1	NUM
ejpam-5749	308	3	.	.	PUNCT
ejpam-5749	309	1	let	let	VERB
ejpam-5749	309	2	g	g	NOUN
ejpam-5749	309	3	and	and	CCONJ
ejpam-5749	309	4	h	h	NOUN
ejpam-5749	309	5	be	be	VERB
ejpam-5749	309	6	any	any	DET
ejpam-5749	309	7	graphs	graph	NOUN
ejpam-5749	309	8	.	.	PUNCT
ejpam-5749	310	1	then	then	ADV
ejpam-5749	310	2	2	2	NUM
ejpam-5749	310	3	≤	≤	NUM
ejpam-5749	310	4	γtr(g+h	γtr(g+h	PROPN
ejpam-5749	310	5	)	)	PUNCT
ejpam-5749	310	6	≤	≤	NUM
ejpam-5749	310	7	4	4	NUM
ejpam-5749	310	8	.	.	PUNCT
ejpam-5749	311	1	(	(	PUNCT
ejpam-5749	311	2	2	2	X
ejpam-5749	311	3	)	)	PUNCT
ejpam-5749	311	4	proof	proof	NOUN
ejpam-5749	311	5	.	.	PUNCT
ejpam-5749	312	1	since	since	SCONJ
ejpam-5749	312	2	g	g	PROPN
ejpam-5749	312	3	+	+	CCONJ
ejpam-5749	312	4	h	h	NOUN
ejpam-5749	312	5	is	be	AUX
ejpam-5749	312	6	at	at	ADP
ejpam-5749	312	7	least	least	ADJ
ejpam-5749	312	8	p2	p2	NOUN
ejpam-5749	312	9	,	,	PUNCT
ejpam-5749	312	10	γt2r(g	γt2r(g	PROPN
ejpam-5749	312	11	+	+	NUM
ejpam-5749	312	12	h	h	NOUN
ejpam-5749	312	13	)	)	PUNCT
ejpam-5749	312	14	≥	≥	NOUN
ejpam-5749	312	15	2	2	NUM
ejpam-5749	312	16	by	by	ADP
ejpam-5749	312	17	proposition	proposition	NOUN
ejpam-5749	312	18	5	5	NUM
ejpam-5749	312	19	.	.	PUNCT
ejpam-5749	313	1	now	now	ADV
ejpam-5749	313	2	let	let	VERB
ejpam-5749	313	3	u	u	PRON
ejpam-5749	313	4	∈	∈	PROPN
ejpam-5749	313	5	v	v	ADP
ejpam-5749	313	6	(	(	PUNCT
ejpam-5749	313	7	g	g	NOUN
ejpam-5749	313	8	)	)	PUNCT
ejpam-5749	313	9	and	and	CCONJ
ejpam-5749	313	10	v	v	ADP
ejpam-5749	313	11	∈	∈	PROPN
ejpam-5749	313	12	v	v	NOUN
ejpam-5749	313	13	(	(	PUNCT
ejpam-5749	313	14	h	h	NOUN
ejpam-5749	313	15	)	)	PUNCT
ejpam-5749	313	16	.	.	PUNCT
ejpam-5749	314	1	define	define	VERB
ejpam-5749	314	2	v0	v0	PROPN
ejpam-5749	314	3	=	=	SYM
ejpam-5749	314	4	v	v	PROPN
ejpam-5749	314	5	(	(	PUNCT
ejpam-5749	314	6	g+h)∖	g+h)∖	X
ejpam-5749	314	7	{	{	PUNCT
ejpam-5749	314	8	u	u	PROPN
ejpam-5749	314	9	,	,	PUNCT
ejpam-5749	314	10	v	v	NOUN
ejpam-5749	314	11	}	}	PUNCT
ejpam-5749	314	12	,	,	PUNCT
ejpam-5749	314	13	v1	v1	NOUN
ejpam-5749	314	14	=	=	SYM
ejpam-5749	314	15	∅	∅	NOUN
ejpam-5749	314	16	and	and	CCONJ
ejpam-5749	314	17	v2	v2	NOUN
ejpam-5749	314	18	=	=	SYM
ejpam-5749	314	19	{	{	PUNCT
ejpam-5749	314	20	u	u	NOUN
ejpam-5749	314	21	,	,	PUNCT
ejpam-5749	314	22	v	v	NOUN
ejpam-5749	314	23	}	}	PUNCT
ejpam-5749	314	24	.	.	PUNCT
ejpam-5749	315	1	then	then	ADV
ejpam-5749	315	2	v2	v2	VERB
ejpam-5749	315	3	∩	∩	ADJ
ejpam-5749	315	4	v	v	NOUN
ejpam-5749	315	5	(	(	PUNCT
ejpam-5749	315	6	g	g	NOUN
ejpam-5749	315	7	)	)	PUNCT
ejpam-5749	315	8	̸=	̸=	PROPN
ejpam-5749	315	9	∅	∅	NOUN
ejpam-5749	315	10	and	and	CCONJ
ejpam-5749	315	11	v2	v2	VERB
ejpam-5749	315	12	∩	∩	ADJ
ejpam-5749	315	13	v	v	NOUN
ejpam-5749	315	14	(	(	PUNCT
ejpam-5749	315	15	h	h	NOUN
ejpam-5749	315	16	)	)	PUNCT
ejpam-5749	315	17	̸=	̸=	PROPN
ejpam-5749	315	18	∅.	∅.	VERB
ejpam-5749	315	19	by	by	ADP
ejpam-5749	315	20	theorem	theorem	NOUN
ejpam-5749	315	21	1	1	NUM
ejpam-5749	315	22	,	,	PUNCT
ejpam-5749	315	23	f	f	X
ejpam-5749	315	24	=	=	SYM
ejpam-5749	315	25	(	(	PUNCT
ejpam-5749	315	26	v0	v0	PROPN
ejpam-5749	315	27	,	,	PUNCT
ejpam-5749	315	28	v1	v1	NOUN
ejpam-5749	315	29	,	,	PUNCT
ejpam-5749	315	30	v2	v2	NOUN
ejpam-5749	315	31	)	)	PUNCT
ejpam-5749	315	32	∈	∈	PROPN
ejpam-5749	315	33	trd(g	trd(g	PROPN
ejpam-5749	316	1	+	+	NUM
ejpam-5749	316	2	h	h	NOUN
ejpam-5749	316	3	)	)	PUNCT
ejpam-5749	316	4	.	.	PUNCT
ejpam-5749	317	1	thus	thus	ADV
ejpam-5749	317	2	,	,	PUNCT
ejpam-5749	317	3	γt2r(g+h	γt2r(g+h	NOUN
ejpam-5749	317	4	)	)	PUNCT
ejpam-5749	317	5	≤	≤	NUM
ejpam-5749	317	6	wg+h(f	wg+h(f	NOUN
ejpam-5749	317	7	)	)	PUNCT
ejpam-5749	317	8	=	=	SYM
ejpam-5749	317	9	4	4	X
ejpam-5749	317	10	.	.	X
ejpam-5749	317	11	proposition	proposition	NOUN
ejpam-5749	317	12	12	12	NUM
ejpam-5749	317	13	.	.	PUNCT
ejpam-5749	318	1	let	let	VERB
ejpam-5749	318	2	g	g	NOUN
ejpam-5749	319	1	and	and	CCONJ
ejpam-5749	319	2	h	h	NOUN
ejpam-5749	319	3	be	be	VERB
ejpam-5749	319	4	any	any	DET
ejpam-5749	319	5	graphs	graph	NOUN
ejpam-5749	319	6	of	of	ADP
ejpam-5749	319	7	orders	order	NOUN
ejpam-5749	319	8	n	n	PRON
ejpam-5749	319	9	and	and	CCONJ
ejpam-5749	319	10	m	m	PROPN
ejpam-5749	319	11	,	,	PUNCT
ejpam-5749	319	12	respectively	respectively	ADV
ejpam-5749	319	13	.	.	PUNCT
ejpam-5749	320	1	then	then	ADV
ejpam-5749	320	2	(	(	PUNCT
ejpam-5749	320	3	i	i	NOUN
ejpam-5749	320	4	)	)	PUNCT
ejpam-5749	320	5	γt2r(g+h	γt2r(g+h	NOUN
ejpam-5749	320	6	)	)	PUNCT
ejpam-5749	321	1	=	=	SYM
ejpam-5749	321	2	2	2	NUM
ejpam-5749	321	3	if	if	SCONJ
ejpam-5749	321	4	and	and	CCONJ
ejpam-5749	321	5	only	only	ADV
ejpam-5749	321	6	if	if	SCONJ
ejpam-5749	321	7	n	n	NOUN
ejpam-5749	321	8	=	=	SYM
ejpam-5749	321	9	m	m	NOUN
ejpam-5749	321	10	=	=	NOUN
ejpam-5749	321	11	1	1	NUM
ejpam-5749	321	12	;	;	PUNCT
ejpam-5749	321	13	(	(	PUNCT
ejpam-5749	321	14	ii	ii	NOUN
ejpam-5749	321	15	)	)	PUNCT
ejpam-5749	321	16	γt2r(g+h	γt2r(g+h	NOUN
ejpam-5749	321	17	)	)	PUNCT
ejpam-5749	321	18	=	=	SYM
ejpam-5749	322	1	3	3	NUM
ejpam-5749	322	2	if	if	SCONJ
ejpam-5749	322	3	and	and	CCONJ
ejpam-5749	322	4	only	only	ADV
ejpam-5749	322	5	if	if	SCONJ
ejpam-5749	322	6	n	n	PRON
ejpam-5749	322	7	̸=	̸=	PROPN
ejpam-5749	322	8	1	1	NUM
ejpam-5749	322	9	or	or	CCONJ
ejpam-5749	322	10	m	m	PRON
ejpam-5749	322	11	̸=	̸=	PROPN
ejpam-5749	322	12	1	1	NUM
ejpam-5749	322	13	and	and	CCONJ
ejpam-5749	322	14	one	one	NUM
ejpam-5749	322	15	of	of	ADP
ejpam-5749	322	16	the	the	DET
ejpam-5749	322	17	following	following	NOUN
ejpam-5749	322	18	holds	hold	VERB
ejpam-5749	322	19	:	:	PUNCT
ejpam-5749	322	20	(	(	PUNCT
ejpam-5749	322	21	a	a	X
ejpam-5749	322	22	)	)	PUNCT
ejpam-5749	322	23	γ(g	γ(g	PROPN
ejpam-5749	322	24	)	)	PUNCT
ejpam-5749	322	25	=	=	SYM
ejpam-5749	322	26	1	1	NUM
ejpam-5749	322	27	or	or	CCONJ
ejpam-5749	322	28	γ(h	γ(h	NOUN
ejpam-5749	322	29	)	)	PUNCT
ejpam-5749	322	30	=	=	SYM
ejpam-5749	323	1	1	1	NUM
ejpam-5749	323	2	;	;	PUNCT
ejpam-5749	323	3	(	(	PUNCT
ejpam-5749	323	4	b	b	X
ejpam-5749	323	5	)	)	PUNCT
ejpam-5749	323	6	∆(g	∆(g	NOUN
ejpam-5749	323	7	)	)	PUNCT
ejpam-5749	324	1	=	=	PUNCT
ejpam-5749	324	2	n−	n−	NOUN
ejpam-5749	324	3	2	2	NUM
ejpam-5749	324	4	or	or	CCONJ
ejpam-5749	324	5	∆(h	∆(h	VERB
ejpam-5749	324	6	)	)	PUNCT
ejpam-5749	324	7	=	=	SYM
ejpam-5749	324	8	m−	m−	PROPN
ejpam-5749	324	9	2	2	NUM
ejpam-5749	324	10	.	.	PUNCT
ejpam-5749	325	1	(	(	PUNCT
ejpam-5749	325	2	iii	iii	NOUN
ejpam-5749	325	3	)	)	PUNCT
ejpam-5749	325	4	γt2r(g+h	γt2r(g+h	NOUN
ejpam-5749	325	5	)	)	PUNCT
ejpam-5749	326	1	=	=	SYM
ejpam-5749	326	2	4	4	NUM
ejpam-5749	326	3	if	if	SCONJ
ejpam-5749	326	4	and	and	CCONJ
ejpam-5749	326	5	only	only	ADV
ejpam-5749	326	6	if	if	SCONJ
ejpam-5749	326	7	∆(g	∆(g	NOUN
ejpam-5749	326	8	)	)	PUNCT
ejpam-5749	326	9	≤	≤	NUM
ejpam-5749	326	10	n−	n−	NOUN
ejpam-5749	326	11	3	3	NUM
ejpam-5749	326	12	and	and	CCONJ
ejpam-5749	326	13	∆(h	∆(h	NOUN
ejpam-5749	326	14	)	)	PUNCT
ejpam-5749	326	15	≤	≤	NOUN
ejpam-5749	326	16	m−	m−	PROPN
ejpam-5749	326	17	3	3	NUM
ejpam-5749	326	18	.	.	PUNCT
ejpam-5749	327	1	proof	proof	NOUN
ejpam-5749	327	2	.	.	PUNCT
ejpam-5749	328	1	by	by	ADP
ejpam-5749	328	2	proposition	proposition	NOUN
ejpam-5749	328	3	5	5	NUM
ejpam-5749	328	4	,	,	PUNCT
ejpam-5749	328	5	γt2r(g+h	γt2r(g+h	NOUN
ejpam-5749	328	6	)	)	PUNCT
ejpam-5749	328	7	=	=	SYM
ejpam-5749	328	8	2	2	NUM
ejpam-5749	328	9	if	if	SCONJ
ejpam-5749	328	10	and	and	CCONJ
ejpam-5749	328	11	only	only	ADV
ejpam-5749	328	12	if	if	SCONJ
ejpam-5749	328	13	g+h	g+h	NOUN
ejpam-5749	328	14	=	=	SYM
ejpam-5749	328	15	p2	p2	PROPN
ejpam-5749	328	16	.	.	PUNCT
ejpam-5749	329	1	thus	thus	ADV
ejpam-5749	329	2	,	,	PUNCT
ejpam-5749	329	3	(	(	PUNCT
ejpam-5749	329	4	i	i	NOUN
ejpam-5749	329	5	)	)	PUNCT
ejpam-5749	329	6	holds	hold	VERB
ejpam-5749	329	7	.	.	PUNCT
ejpam-5749	329	8	suppose	suppose	VERB
ejpam-5749	329	9	that	that	SCONJ
ejpam-5749	329	10	γt2r(g	γt2r(g	PROPN
ejpam-5749	329	11	+	+	NUM
ejpam-5749	329	12	h	h	NOUN
ejpam-5749	329	13	)	)	PUNCT
ejpam-5749	329	14	=	=	SYM
ejpam-5749	330	1	3	3	X
ejpam-5749	330	2	.	.	PUNCT
ejpam-5749	330	3	by	by	ADP
ejpam-5749	330	4	(	(	PUNCT
ejpam-5749	330	5	i	i	NOUN
ejpam-5749	330	6	)	)	PUNCT
ejpam-5749	330	7	,	,	PUNCT
ejpam-5749	330	8	g	g	PROPN
ejpam-5749	330	9	̸=	̸=	PROPN
ejpam-5749	330	10	k1	k1	NOUN
ejpam-5749	330	11	or	or	CCONJ
ejpam-5749	330	12	h	h	NOUN
ejpam-5749	330	13	̸=	̸=	PROPN
ejpam-5749	330	14	k1	k1	NOUN
ejpam-5749	330	15	.	.	PUNCT
ejpam-5749	331	1	if	if	SCONJ
ejpam-5749	331	2	γ(g	γ(g	PROPN
ejpam-5749	331	3	+	+	CCONJ
ejpam-5749	331	4	h	h	X
ejpam-5749	331	5	)	)	PUNCT
ejpam-5749	331	6	=	=	SYM
ejpam-5749	331	7	1	1	NUM
ejpam-5749	331	8	,	,	PUNCT
ejpam-5749	331	9	then	then	ADV
ejpam-5749	331	10	γ(g	γ(g	PROPN
ejpam-5749	331	11	)	)	PUNCT
ejpam-5749	331	12	=	=	SYM
ejpam-5749	331	13	1	1	NUM
ejpam-5749	331	14	or	or	CCONJ
ejpam-5749	331	15	γ(h	γ(h	NOUN
ejpam-5749	331	16	)	)	PUNCT
ejpam-5749	331	17	=	=	SYM
ejpam-5749	331	18	1	1	NUM
ejpam-5749	331	19	and	and	CCONJ
ejpam-5749	331	20	(	(	PUNCT
ejpam-5749	331	21	ii)(a	ii)(a	PROPN
ejpam-5749	331	22	)	)	PUNCT
ejpam-5749	331	23	holds	hold	VERB
ejpam-5749	331	24	.	.	PUNCT
ejpam-5749	332	1	otherwise	otherwise	ADV
ejpam-5749	332	2	,	,	PUNCT
ejpam-5749	332	3	by	by	ADP
ejpam-5749	332	4	proposition	proposition	NOUN
ejpam-5749	332	5	6	6	NUM
ejpam-5749	332	6	,	,	PUNCT
ejpam-5749	332	7	there	there	PRON
ejpam-5749	332	8	exists	exist	VERB
ejpam-5749	332	9	u	u	NOUN
ejpam-5749	332	10	,	,	PUNCT
ejpam-5749	332	11	v	v	NOUN
ejpam-5749	332	12	∈	∈	PROPN
ejpam-5749	332	13	v	v	NOUN
ejpam-5749	332	14	(	(	PUNCT
ejpam-5749	332	15	g+h	g+h	NOUN
ejpam-5749	332	16	)	)	PUNCT
ejpam-5749	332	17	for	for	ADP
ejpam-5749	332	18	which	which	PRON
ejpam-5749	332	19	ng+h	ng+h	ADV
ejpam-5749	332	20	[	[	X
ejpam-5749	332	21	v	v	X
ejpam-5749	332	22	]	]	X
ejpam-5749	332	23	=	=	SYM
ejpam-5749	332	24	v	v	NOUN
ejpam-5749	332	25	(	(	PUNCT
ejpam-5749	332	26	g+h	g+h	NOUN
ejpam-5749	332	27	)	)	PUNCT
ejpam-5749	332	28	\	\	NOUN
ejpam-5749	332	29	{	{	PUNCT
ejpam-5749	332	30	u	u	NOUN
ejpam-5749	332	31	}	}	PUNCT
ejpam-5749	332	32	and	and	CCONJ
ejpam-5749	332	33	dg+h(u	dg+h(u	PROPN
ejpam-5749	332	34	,	,	PUNCT
ejpam-5749	332	35	v	v	NOUN
ejpam-5749	332	36	)	)	PUNCT
ejpam-5749	332	37	=	=	SYM
ejpam-5749	332	38	2	2	X
ejpam-5749	332	39	.	.	X
ejpam-5749	332	40	necessarily	necessarily	ADV
ejpam-5749	332	41	,	,	PUNCT
ejpam-5749	332	42	either	either	CCONJ
ejpam-5749	332	43	u	u	NOUN
ejpam-5749	332	44	,	,	PUNCT
ejpam-5749	332	45	v	v	NOUN
ejpam-5749	332	46	∈	∈	PROPN
ejpam-5749	332	47	v	v	NOUN
ejpam-5749	332	48	(	(	PUNCT
ejpam-5749	332	49	g	g	NOUN
ejpam-5749	332	50	)	)	PUNCT
ejpam-5749	332	51	or	or	CCONJ
ejpam-5749	332	52	u	u	NOUN
ejpam-5749	332	53	,	,	PUNCT
ejpam-5749	332	54	v	v	PROPN
ejpam-5749	332	55	∈	∈	PROPN
ejpam-5749	332	56	v	v	NOUN
ejpam-5749	332	57	(	(	PUNCT
ejpam-5749	332	58	h	h	NOUN
ejpam-5749	332	59	)	)	PUNCT
ejpam-5749	332	60	.	.	PUNCT
ejpam-5749	333	1	this	this	PRON
ejpam-5749	333	2	means	mean	VERB
ejpam-5749	333	3	that	that	SCONJ
ejpam-5749	333	4	if	if	SCONJ
ejpam-5749	333	5	γ(g	γ(g	PROPN
ejpam-5749	333	6	)	)	PUNCT
ejpam-5749	333	7	̸=	̸=	PROPN
ejpam-5749	333	8	1	1	NUM
ejpam-5749	333	9	and	and	CCONJ
ejpam-5749	333	10	γ(h	γ(h	NOUN
ejpam-5749	333	11	)	)	PUNCT
ejpam-5749	333	12	̸=	̸=	PROPN
ejpam-5749	333	13	1	1	NUM
ejpam-5749	333	14	,	,	PUNCT
ejpam-5749	333	15	then	then	ADV
ejpam-5749	333	16	(	(	PUNCT
ejpam-5749	333	17	ii)(b	ii)(b	ADJ
ejpam-5749	333	18	)	)	PUNCT
ejpam-5749	333	19	holds	hold	VERB
ejpam-5749	333	20	.	.	PUNCT
ejpam-5749	334	1	conversely	conversely	ADV
ejpam-5749	334	2	,	,	PUNCT
ejpam-5749	334	3	if	if	SCONJ
ejpam-5749	334	4	g	g	PROPN
ejpam-5749	334	5	̸=	̸=	PROPN
ejpam-5749	334	6	k1	k1	NOUN
ejpam-5749	334	7	or	or	CCONJ
ejpam-5749	334	8	h	h	NOUN
ejpam-5749	334	9	̸=	̸=	PROPN
ejpam-5749	334	10	k1	k1	NOUN
ejpam-5749	334	11	,	,	PUNCT
ejpam-5749	334	12	then	then	ADV
ejpam-5749	334	13	γt2r(g	γt2r(g	X
ejpam-5749	334	14	+	+	NOUN
ejpam-5749	334	15	h	h	NOUN
ejpam-5749	334	16	)	)	PUNCT
ejpam-5749	334	17	≥	≥	NOUN
ejpam-5749	334	18	3	3	NUM
ejpam-5749	334	19	by	by	ADP
ejpam-5749	334	20	(	(	PUNCT
ejpam-5749	334	21	i	i	NOUN
ejpam-5749	334	22	)	)	PUNCT
ejpam-5749	334	23	.	.	PUNCT
ejpam-5749	335	1	if	if	SCONJ
ejpam-5749	335	2	(	(	PUNCT
ejpam-5749	335	3	ii)(a	ii)(a	NOUN
ejpam-5749	335	4	)	)	PUNCT
ejpam-5749	335	5	holds	hold	VERB
ejpam-5749	335	6	,	,	PUNCT
ejpam-5749	335	7	then	then	ADV
ejpam-5749	335	8	γ(g+h	γ(g+h	NUM
ejpam-5749	335	9	)	)	PUNCT
ejpam-5749	335	10	=	=	SYM
ejpam-5749	335	11	1	1	NUM
ejpam-5749	335	12	and	and	CCONJ
ejpam-5749	335	13	γt2r(g+h	γt2r(g+h	NOUN
ejpam-5749	335	14	)	)	PUNCT
ejpam-5749	336	1	=	=	SYM
ejpam-5749	336	2	3	3	NUM
ejpam-5749	336	3	(	(	PUNCT
ejpam-5749	336	4	by	by	ADP
ejpam-5749	336	5	proposition	proposition	NOUN
ejpam-5749	336	6	6	6	NUM
ejpam-5749	336	7	)	)	PUNCT
ejpam-5749	336	8	.	.	PUNCT
ejpam-5749	337	1	if	if	SCONJ
ejpam-5749	337	2	(	(	PUNCT
ejpam-5749	337	3	ii)(b	ii)(b	ADJ
ejpam-5749	337	4	)	)	PUNCT
ejpam-5749	337	5	holds	hold	VERB
ejpam-5749	337	6	,	,	PUNCT
ejpam-5749	337	7	then	then	ADV
ejpam-5749	337	8	∆(g	∆(g	NOUN
ejpam-5749	337	9	)	)	PUNCT
ejpam-5749	337	10	=	=	SYM
ejpam-5749	338	1	m+n−2	m+n−2	PROPN
ejpam-5749	338	2	.	.	PUNCT
ejpam-5749	339	1	thus	thus	ADV
ejpam-5749	339	2	,	,	PUNCT
ejpam-5749	339	3	there	there	PRON
ejpam-5749	339	4	exists	exist	VERB
ejpam-5749	339	5	u	u	NOUN
ejpam-5749	339	6	,	,	PUNCT
ejpam-5749	339	7	v	v	NOUN
ejpam-5749	339	8	∈	∈	PROPN
ejpam-5749	339	9	v	v	NOUN
ejpam-5749	339	10	(	(	PUNCT
ejpam-5749	339	11	g+h	g+h	NOUN
ejpam-5749	339	12	)	)	PUNCT
ejpam-5749	340	1	such	such	ADJ
ejpam-5749	340	2	that	that	SCONJ
ejpam-5749	340	3	ng+h	ng+h	PROPN
ejpam-5749	341	1	[	[	X
ejpam-5749	341	2	v	v	X
ejpam-5749	341	3	]	]	X
ejpam-5749	341	4	=	=	SYM
ejpam-5749	341	5	v	v	X
ejpam-5749	341	6	(	(	PUNCT
ejpam-5749	341	7	g+h)\{u	g+h)\{u	X
ejpam-5749	341	8	}	}	PUNCT
ejpam-5749	341	9	and	and	CCONJ
ejpam-5749	341	10	dg+h(u	dg+h(u	PROPN
ejpam-5749	341	11	,	,	PUNCT
ejpam-5749	341	12	v	v	NOUN
ejpam-5749	341	13	)	)	PUNCT
ejpam-5749	341	14	=	=	SYM
ejpam-5749	341	15	2	2	X
ejpam-5749	341	16	.	.	PUNCT
ejpam-5749	341	17	by	by	ADP
ejpam-5749	341	18	proposition	proposition	NOUN
ejpam-5749	341	19	6	6	NUM
ejpam-5749	341	20	,	,	PUNCT
ejpam-5749	341	21	γt2r(g+h	γt2r(g+h	NOUN
ejpam-5749	341	22	)	)	PUNCT
ejpam-5749	341	23	=	=	SYM
ejpam-5749	342	1	3	3	X
ejpam-5749	342	2	.	.	PUNCT
ejpam-5749	343	1	this	this	PRON
ejpam-5749	343	2	proves	prove	VERB
ejpam-5749	343	3	(	(	PUNCT
ejpam-5749	343	4	ii	ii	NOUN
ejpam-5749	343	5	)	)	PUNCT
ejpam-5749	343	6	.	.	PUNCT
ejpam-5749	344	1	statement	statement	NOUN
ejpam-5749	344	2	(	(	PUNCT
ejpam-5749	344	3	iii	iii	NOUN
ejpam-5749	344	4	)	)	PUNCT
ejpam-5749	344	5	follows	follow	VERB
ejpam-5749	344	6	immediately	immediately	ADV
ejpam-5749	344	7	from	from	ADP
ejpam-5749	344	8	statements	statement	NOUN
ejpam-5749	344	9	(	(	PUNCT
ejpam-5749	344	10	i	i	NOUN
ejpam-5749	344	11	)	)	PUNCT
ejpam-5749	344	12	and	and	CCONJ
ejpam-5749	344	13	(	(	PUNCT
ejpam-5749	344	14	ii	ii	NOUN
ejpam-5749	344	15	)	)	PUNCT
ejpam-5749	344	16	and	and	CCONJ
ejpam-5749	344	17	the	the	DET
ejpam-5749	344	18	inequality	inequality	NOUN
ejpam-5749	344	19	2	2	NUM
ejpam-5749	344	20	.	.	PUNCT
ejpam-5749	345	1	the	the	DET
ejpam-5749	345	2	join	join	NOUN
ejpam-5749	345	3	g	g	PROPN
ejpam-5749	345	4	+	+	CCONJ
ejpam-5749	345	5	h	h	NOUN
ejpam-5749	345	6	,	,	PUNCT
ejpam-5749	345	7	where	where	SCONJ
ejpam-5749	345	8	g	g	PROPN
ejpam-5749	345	9	=	=	SYM
ejpam-5749	345	10	k2	k2	PROPN
ejpam-5749	345	11	,	,	PUNCT
ejpam-5749	345	12	is	be	AUX
ejpam-5749	345	13	a	a	DET
ejpam-5749	345	14	good	good	ADJ
ejpam-5749	345	15	example	example	NOUN
ejpam-5749	345	16	of	of	ADP
ejpam-5749	345	17	proposition	proposition	NOUN
ejpam-5749	345	18	12(ii)(b	12(ii)(b	NUM
ejpam-5749	345	19	)	)	PUNCT
ejpam-5749	345	20	,	,	PUNCT
ejpam-5749	345	21	where	where	SCONJ
ejpam-5749	345	22	∆(g	∆(g	NOUN
ejpam-5749	345	23	)	)	PUNCT
ejpam-5749	345	24	=	=	SYM
ejpam-5749	346	1	n	n	CCONJ
ejpam-5749	346	2	−	−	NUM
ejpam-5749	346	3	2	2	NUM
ejpam-5749	346	4	=	=	SYM
ejpam-5749	346	5	0	0	X
ejpam-5749	346	6	.	.	PUNCT
ejpam-5749	347	1	proposition	proposition	NOUN
ejpam-5749	347	2	12(iii	12(iii	NOUN
ejpam-5749	347	3	)	)	PUNCT
ejpam-5749	347	4	also	also	ADV
ejpam-5749	347	5	implies	imply	VERB
ejpam-5749	347	6	that	that	SCONJ
ejpam-5749	347	7	γt2r(km	γt2r(km	NOUN
ejpam-5749	347	8	,	,	PUNCT
ejpam-5749	347	9	n	n	CCONJ
ejpam-5749	347	10	)	)	PUNCT
ejpam-5749	347	11	=	=	SYM
ejpam-5749	347	12	4	4	NUM
ejpam-5749	347	13	for	for	ADP
ejpam-5749	347	14	all	all	DET
ejpam-5749	347	15	integers	integer	NOUN
ejpam-5749	347	16	m	m	PRON
ejpam-5749	347	17	,	,	PUNCT
ejpam-5749	347	18	n	n	PRON
ejpam-5749	347	19	≥	≥	NOUN
ejpam-5749	347	20	3	3	NUM
ejpam-5749	347	21	.	.	PUNCT
ejpam-5749	347	22	b.	b.	PROPN
ejpam-5749	347	23	f.	f.	PROPN
ejpam-5749	347	24	bullang	bullang	PROPN
ejpam-5749	347	25	et	et	PROPN
ejpam-5749	347	26	al	al	PROPN
ejpam-5749	347	27	.	.	PUNCT
ejpam-5749	347	28	/	/	SYM
ejpam-5749	347	29	eur	eur	PROPN
ejpam-5749	347	30	.	.	PUNCT
ejpam-5749	348	1	j.	j.	PROPN
ejpam-5749	348	2	pure	pure	PROPN
ejpam-5749	348	3	appl	appl	PROPN
ejpam-5749	348	4	.	.	PROPN
ejpam-5749	348	5	math	math	PROPN
ejpam-5749	348	6	,	,	PUNCT
ejpam-5749	348	7	18	18	NUM
ejpam-5749	348	8	(	(	PUNCT
ejpam-5749	348	9	1	1	NUM
ejpam-5749	348	10	)	)	PUNCT
ejpam-5749	348	11	(	(	PUNCT
ejpam-5749	348	12	2025	2025	NUM
ejpam-5749	348	13	)	)	PUNCT
ejpam-5749	348	14	,	,	PUNCT
ejpam-5749	348	15	5749	5749	NUM
ejpam-5749	348	16	11	11	NUM
ejpam-5749	348	17	of	of	ADP
ejpam-5749	348	18	15	15	NUM
ejpam-5749	348	19	3.2	3.2	NUM
ejpam-5749	348	20	.	.	PUNCT
ejpam-5749	349	1	in	in	ADP
ejpam-5749	349	2	the	the	DET
ejpam-5749	349	3	corona	corona	NOUN
ejpam-5749	349	4	of	of	ADP
ejpam-5749	349	5	graphs	graph	NOUN
ejpam-5749	349	6	let	let	VERB
ejpam-5749	349	7	g	g	NOUN
ejpam-5749	349	8	and	and	CCONJ
ejpam-5749	349	9	h	h	NOUN
ejpam-5749	349	10	be	be	AUX
ejpam-5749	349	11	connected	connect	VERB
ejpam-5749	349	12	graphs	graph	NOUN
ejpam-5749	349	13	.	.	PUNCT
ejpam-5749	350	1	we	we	PRON
ejpam-5749	350	2	adapt	adapt	VERB
ejpam-5749	350	3	the	the	DET
ejpam-5749	350	4	notation	notation	NOUN
ejpam-5749	350	5	hv	hv	PROPN
ejpam-5749	350	6	to	to	PART
ejpam-5749	350	7	denote	denote	VERB
ejpam-5749	350	8	the	the	DET
ejpam-5749	350	9	copy	copy	NOUN
ejpam-5749	350	10	of	of	ADP
ejpam-5749	350	11	h	h	NOUN
ejpam-5749	350	12	whose	whose	DET
ejpam-5749	350	13	vertices	vertex	NOUN
ejpam-5749	350	14	is	be	AUX
ejpam-5749	350	15	joined	join	VERB
ejpam-5749	350	16	to	to	ADP
ejpam-5749	350	17	v	v	ADP
ejpam-5749	350	18	∈	∈	PROPN
ejpam-5749	350	19	v	v	NOUN
ejpam-5749	350	20	(	(	PUNCT
ejpam-5749	350	21	g	g	NOUN
ejpam-5749	350	22	)	)	PUNCT
ejpam-5749	350	23	.	.	PUNCT
ejpam-5749	351	1	theorem	theorem	NOUN
ejpam-5749	351	2	2	2	NUM
ejpam-5749	351	3	.	.	PUNCT
ejpam-5749	352	1	let	let	VERB
ejpam-5749	352	2	g	g	PRON
ejpam-5749	352	3	be	be	AUX
ejpam-5749	352	4	nontrivial	nontrivial	ADJ
ejpam-5749	352	5	connected	connect	VERB
ejpam-5749	352	6	graph	graph	NOUN
ejpam-5749	352	7	and	and	CCONJ
ejpam-5749	352	8	h	h	NOUN
ejpam-5749	352	9	be	be	AUX
ejpam-5749	352	10	any	any	DET
ejpam-5749	352	11	graph	graph	NOUN
ejpam-5749	352	12	,	,	PUNCT
ejpam-5749	352	13	and	and	CCONJ
ejpam-5749	352	14	let	let	VERB
ejpam-5749	352	15	f	f	PROPN
ejpam-5749	352	16	=	=	SYM
ejpam-5749	352	17	(	(	PUNCT
ejpam-5749	352	18	v0	v0	PROPN
ejpam-5749	352	19	,	,	PUNCT
ejpam-5749	352	20	v1	v1	NOUN
ejpam-5749	352	21	,	,	PUNCT
ejpam-5749	352	22	v2	v2	PROPN
ejpam-5749	352	23	)	)	PUNCT
ejpam-5749	352	24	:	:	PUNCT
ejpam-5749	353	1	v	v	X
ejpam-5749	353	2	(	(	PUNCT
ejpam-5749	353	3	g	g	PROPN
ejpam-5749	353	4	◦	◦	NOUN
ejpam-5749	353	5	h	h	NOUN
ejpam-5749	353	6	)	)	PUNCT
ejpam-5749	353	7	→	→	SYM
ejpam-5749	353	8	{	{	PUNCT
ejpam-5749	353	9	0	0	NUM
ejpam-5749	353	10	,	,	PUNCT
ejpam-5749	353	11	1	1	NUM
ejpam-5749	353	12	,	,	PUNCT
ejpam-5749	353	13	2	2	NUM
ejpam-5749	353	14	}	}	PUNCT
ejpam-5749	353	15	.	.	PUNCT
ejpam-5749	354	1	then	then	ADV
ejpam-5749	354	2	f	f	PROPN
ejpam-5749	354	3	∈	∈	PROPN
ejpam-5749	354	4	srdf	srdf	NOUN
ejpam-5749	354	5	(	(	PUNCT
ejpam-5749	354	6	g	g	PROPN
ejpam-5749	354	7	◦	◦	NOUN
ejpam-5749	354	8	h	h	NOUN
ejpam-5749	354	9	)	)	PUNCT
ejpam-5749	354	10	if	if	SCONJ
ejpam-5749	354	11	and	and	CCONJ
ejpam-5749	354	12	only	only	ADV
ejpam-5749	354	13	if	if	SCONJ
ejpam-5749	354	14	each	each	PRON
ejpam-5749	354	15	of	of	ADP
ejpam-5749	354	16	the	the	DET
ejpam-5749	354	17	following	follow	VERB
ejpam-5749	354	18	holds	hold	VERB
ejpam-5749	354	19	:	:	PUNCT
ejpam-5749	354	20	(	(	PUNCT
ejpam-5749	354	21	i	i	NOUN
ejpam-5749	354	22	)	)	PUNCT
ejpam-5749	354	23	for	for	ADP
ejpam-5749	354	24	each	each	DET
ejpam-5749	354	25	v	v	ADP
ejpam-5749	354	26	∈	∈	PROPN
ejpam-5749	354	27	v0	v0	NOUN
ejpam-5749	354	28	∩	∩	X
ejpam-5749	354	29	v	v	X
ejpam-5749	354	30	(	(	PUNCT
ejpam-5749	354	31	g	g	NOUN
ejpam-5749	354	32	)	)	PUNCT
ejpam-5749	354	33	,	,	PUNCT
ejpam-5749	354	34	f	f	PROPN
ejpam-5749	354	35	|hv	|hv	PROPN
ejpam-5749	354	36	∈	∈	PROPN
ejpam-5749	354	37	rdf	rdf	NOUN
ejpam-5749	354	38	(	(	PUNCT
ejpam-5749	354	39	hv	hv	NOUN
ejpam-5749	354	40	)	)	PUNCT
ejpam-5749	354	41	and	and	CCONJ
ejpam-5749	354	42	each	each	PRON
ejpam-5749	354	43	of	of	ADP
ejpam-5749	354	44	the	the	DET
ejpam-5749	354	45	following	following	NOUN
ejpam-5749	354	46	holds	hold	VERB
ejpam-5749	354	47	:	:	PUNCT
ejpam-5749	354	48	(	(	PUNCT
ejpam-5749	354	49	a	a	X
ejpam-5749	354	50	)	)	PUNCT
ejpam-5749	354	51	|(v1	|(v1	VERB
ejpam-5749	354	52	∪	∪	NOUN
ejpam-5749	354	53	v2	v2	NOUN
ejpam-5749	354	54	)	)	PUNCT
ejpam-5749	354	55	∩	∩	ADJ
ejpam-5749	354	56	v	v	X
ejpam-5749	354	57	(	(	PUNCT
ejpam-5749	354	58	hv)|	hv)|	VERB
ejpam-5749	354	59	≥	≥	NOUN
ejpam-5749	354	60	2	2	NUM
ejpam-5749	354	61	whenever	whenever	SCONJ
ejpam-5749	354	62	ng(v	ng(v	NOUN
ejpam-5749	354	63	)	)	PUNCT
ejpam-5749	354	64	⊆	⊆	NUM
ejpam-5749	354	65	v0	v0	NOUN
ejpam-5749	354	66	;	;	PUNCT
ejpam-5749	354	67	(	(	PUNCT
ejpam-5749	354	68	b	b	X
ejpam-5749	354	69	)	)	PUNCT
ejpam-5749	354	70	v2	v2	NOUN
ejpam-5749	354	71	∩	∩	ADJ
ejpam-5749	354	72	v	v	NOUN
ejpam-5749	354	73	(	(	PUNCT
ejpam-5749	354	74	hv	hv	NOUN
ejpam-5749	354	75	)	)	PUNCT
ejpam-5749	354	76	̸=	̸=	PROPN
ejpam-5749	354	77	∅	∅	NOUN
ejpam-5749	354	78	whenever	whenever	SCONJ
ejpam-5749	354	79	ng(v	ng(v	NOUN
ejpam-5749	354	80	)	)	PUNCT
ejpam-5749	354	81	∩	∩	ADJ
ejpam-5749	354	82	v2	v2	NOUN
ejpam-5749	354	83	=	=	SYM
ejpam-5749	354	84	∅.	∅.	X
ejpam-5749	354	85	(	(	PUNCT
ejpam-5749	354	86	ii	ii	NOUN
ejpam-5749	354	87	)	)	PUNCT
ejpam-5749	354	88	for	for	ADP
ejpam-5749	354	89	each	each	DET
ejpam-5749	354	90	v	v	NUM
ejpam-5749	354	91	∈	∈	PROPN
ejpam-5749	354	92	v1	v1	NOUN
ejpam-5749	354	93	∩	∩	ADJ
ejpam-5749	354	94	v	v	NOUN
ejpam-5749	354	95	(	(	PUNCT
ejpam-5749	354	96	g	g	NOUN
ejpam-5749	354	97	)	)	PUNCT
ejpam-5749	354	98	,	,	PUNCT
ejpam-5749	354	99	f	f	PROPN
ejpam-5749	354	100	|hv	|hv	PROPN
ejpam-5749	354	101	∈	∈	PROPN
ejpam-5749	354	102	rdf	rdf	NOUN
ejpam-5749	354	103	(	(	PUNCT
ejpam-5749	354	104	hv	hv	NOUN
ejpam-5749	354	105	)	)	PUNCT
ejpam-5749	354	106	.	.	PUNCT
ejpam-5749	355	1	(	(	PUNCT
ejpam-5749	355	2	iii	iii	X
ejpam-5749	355	3	)	)	PUNCT
ejpam-5749	355	4	for	for	ADP
ejpam-5749	355	5	each	each	PRON
ejpam-5749	355	6	v	v	NUM
ejpam-5749	355	7	∈	∈	PROPN
ejpam-5749	355	8	v2	v2	NOUN
ejpam-5749	355	9	∩	∩	ADJ
ejpam-5749	355	10	v	v	NOUN
ejpam-5749	355	11	(	(	PUNCT
ejpam-5749	355	12	g	g	NOUN
ejpam-5749	355	13	)	)	PUNCT
ejpam-5749	355	14	,	,	PUNCT
ejpam-5749	355	15	(	(	PUNCT
ejpam-5749	355	16	v1	v1	VERB
ejpam-5749	355	17	∪	∪	NOUN
ejpam-5749	355	18	v2	v2	NOUN
ejpam-5749	355	19	)	)	PUNCT
ejpam-5749	355	20	∩ng(v	∩ng(v	PROPN
ejpam-5749	355	21	,	,	PUNCT
ejpam-5749	355	22	2	2	NUM
ejpam-5749	355	23	)	)	PUNCT
ejpam-5749	355	24	̸=	̸=	NOUN
ejpam-5749	355	25	∅	∅	NOUN
ejpam-5749	355	26	whenever	whenever	SCONJ
ejpam-5749	355	27	v	v	X
ejpam-5749	355	28	(	(	PUNCT
ejpam-5749	355	29	hv	hv	PROPN
ejpam-5749	355	30	)	)	PUNCT
ejpam-5749	355	31	⊆	⊆	NUM
ejpam-5749	355	32	v0	v0	NOUN
ejpam-5749	355	33	.	.	PUNCT
ejpam-5749	356	1	proof	proof	NOUN
ejpam-5749	356	2	.	.	PUNCT
ejpam-5749	357	1	if	if	SCONJ
ejpam-5749	357	2	f	f	PROPN
ejpam-5749	357	3	∈	∈	PROPN
ejpam-5749	357	4	srdf	srdf	NOUN
ejpam-5749	357	5	(	(	PUNCT
ejpam-5749	357	6	g	g	NOUN
ejpam-5749	357	7	◦	◦	NOUN
ejpam-5749	357	8	h	h	NOUN
ejpam-5749	357	9	)	)	PUNCT
ejpam-5749	357	10	,	,	PUNCT
ejpam-5749	357	11	then	then	ADV
ejpam-5749	357	12	the	the	DET
ejpam-5749	357	13	statements	statement	NOUN
ejpam-5749	357	14	(	(	PUNCT
ejpam-5749	357	15	i)-(iii	i)-(iii	NOUN
ejpam-5749	357	16	)	)	PUNCT
ejpam-5749	357	17	are	be	AUX
ejpam-5749	357	18	clear	clear	ADJ
ejpam-5749	357	19	.	.	PUNCT
ejpam-5749	358	1	conversely	conversely	ADV
ejpam-5749	358	2	,	,	PUNCT
ejpam-5749	358	3	assume	assume	VERB
ejpam-5749	358	4	that	that	SCONJ
ejpam-5749	358	5	all	all	DET
ejpam-5749	358	6	conditions	condition	NOUN
ejpam-5749	358	7	(	(	PUNCT
ejpam-5749	358	8	i	i	NOUN
ejpam-5749	358	9	)	)	PUNCT
ejpam-5749	358	10	,	,	PUNCT
ejpam-5749	358	11	(	(	PUNCT
ejpam-5749	358	12	ii	ii	NOUN
ejpam-5749	358	13	)	)	PUNCT
ejpam-5749	358	14	and	and	CCONJ
ejpam-5749	358	15	(	(	PUNCT
ejpam-5749	358	16	iii	iii	X
ejpam-5749	358	17	)	)	PUNCT
ejpam-5749	358	18	hold	hold	NOUN
ejpam-5749	358	19	for	for	ADP
ejpam-5749	358	20	f	f	PROPN
ejpam-5749	358	21	.	.	PUNCT
ejpam-5749	359	1	first	first	ADV
ejpam-5749	359	2	,	,	PUNCT
ejpam-5749	359	3	let	let	VERB
ejpam-5749	359	4	x	x	X
ejpam-5749	359	5	∈	∈	PROPN
ejpam-5749	359	6	v0	v0	NOUN
ejpam-5749	359	7	and	and	CCONJ
ejpam-5749	359	8	let	let	VERB
ejpam-5749	359	9	v	v	NUM
ejpam-5749	359	10	∈	∈	PROPN
ejpam-5749	359	11	v	v	NOUN
ejpam-5749	359	12	(	(	PUNCT
ejpam-5749	359	13	g	g	NOUN
ejpam-5749	359	14	)	)	PUNCT
ejpam-5749	359	15	for	for	ADP
ejpam-5749	359	16	which	which	PRON
ejpam-5749	359	17	x	x	SYM
ejpam-5749	359	18	∈	∈	PROPN
ejpam-5749	359	19	v	v	NOUN
ejpam-5749	359	20	(	(	PUNCT
ejpam-5749	359	21	v	v	PROPN
ejpam-5749	359	22	+	+	PROPN
ejpam-5749	359	23	hv	hv	NOUN
ejpam-5749	359	24	)	)	PUNCT
ejpam-5749	359	25	.	.	PUNCT
ejpam-5749	360	1	suppose	suppose	VERB
ejpam-5749	360	2	that	that	SCONJ
ejpam-5749	360	3	x	x	X
ejpam-5749	361	1	=	=	PUNCT
ejpam-5749	361	2	v.	v.	ADP
ejpam-5749	361	3	if	if	SCONJ
ejpam-5749	361	4	ng(v	ng(v	NOUN
ejpam-5749	361	5	)	)	PUNCT
ejpam-5749	361	6	∩	∩	NOUN
ejpam-5749	361	7	v2	v2	PROPN
ejpam-5749	361	8	̸=	̸=	PROPN
ejpam-5749	361	9	∅	∅	NOUN
ejpam-5749	361	10	,	,	PUNCT
ejpam-5749	361	11	say	say	VERB
ejpam-5749	361	12	u	u	PROPN
ejpam-5749	361	13	∈	∈	PROPN
ejpam-5749	361	14	ng(v	ng(v	PUNCT
ejpam-5749	361	15	)	)	PUNCT
ejpam-5749	361	16	∩	∩	NOUN
ejpam-5749	361	17	v2	v2	PROPN
ejpam-5749	361	18	,	,	PUNCT
ejpam-5749	361	19	then	then	ADV
ejpam-5749	361	20	u	u	PROPN
ejpam-5749	361	21	∈	∈	PROPN
ejpam-5749	361	22	v2∩ng	v2∩ng	PROPN
ejpam-5749	361	23	◦	◦	NOUN
ejpam-5749	361	24	h(x	h(x	PROPN
ejpam-5749	361	25	)	)	PUNCT
ejpam-5749	361	26	.	.	PUNCT
ejpam-5749	362	1	if	if	SCONJ
ejpam-5749	362	2	,	,	PUNCT
ejpam-5749	362	3	on	on	ADP
ejpam-5749	362	4	the	the	DET
ejpam-5749	362	5	other	other	ADJ
ejpam-5749	362	6	hand	hand	NOUN
ejpam-5749	362	7	,	,	PUNCT
ejpam-5749	362	8	ng(v)∩v2	ng(v)∩v2	NOUN
ejpam-5749	362	9	=	=	SYM
ejpam-5749	362	10	∅	∅	NOUN
ejpam-5749	362	11	,	,	PUNCT
ejpam-5749	362	12	then	then	ADV
ejpam-5749	362	13	by	by	ADP
ejpam-5749	362	14	(	(	PUNCT
ejpam-5749	362	15	i)(b	i)(b	NUM
ejpam-5749	362	16	)	)	PUNCT
ejpam-5749	362	17	,	,	PUNCT
ejpam-5749	362	18	v2∩v	v2∩v	PROPN
ejpam-5749	362	19	(	(	PUNCT
ejpam-5749	362	20	hv	hv	NOUN
ejpam-5749	362	21	)	)	PUNCT
ejpam-5749	362	22	̸=	̸=	PROPN
ejpam-5749	362	23	∅.	∅.	AUX
ejpam-5749	362	24	pick	pick	VERB
ejpam-5749	362	25	u	u	PRON
ejpam-5749	362	26	∈	∈	PROPN
ejpam-5749	362	27	v2	v2	PROPN
ejpam-5749	362	28	∩	∩	ADJ
ejpam-5749	362	29	v	v	X
ejpam-5749	362	30	(	(	PUNCT
ejpam-5749	362	31	hv	hv	PROPN
ejpam-5749	362	32	)	)	PUNCT
ejpam-5749	362	33	.	.	PUNCT
ejpam-5749	363	1	then	then	ADV
ejpam-5749	363	2	u	u	PROPN
ejpam-5749	363	3	∈	∈	PROPN
ejpam-5749	363	4	v2	v2	PROPN
ejpam-5749	363	5	∩ng	∩ng	PROPN
ejpam-5749	363	6	◦	◦	NOUN
ejpam-5749	363	7	h(x	h(x	PROPN
ejpam-5749	363	8	)	)	PUNCT
ejpam-5749	363	9	.	.	PUNCT
ejpam-5749	363	10	suppose	suppose	VERB
ejpam-5749	363	11	that	that	SCONJ
ejpam-5749	363	12	x	x	PROPN
ejpam-5749	364	1	̸=	̸=	PROPN
ejpam-5749	364	2	v.	v.	ADV
ejpam-5749	364	3	if	if	SCONJ
ejpam-5749	364	4	v	v	PROPN
ejpam-5749	364	5	∈	∈	PROPN
ejpam-5749	364	6	v0	v0	NOUN
ejpam-5749	364	7	∪	∪	X
ejpam-5749	364	8	v1	v1	PROPN
ejpam-5749	364	9	,	,	PUNCT
ejpam-5749	364	10	then	then	ADV
ejpam-5749	364	11	since	since	SCONJ
ejpam-5749	364	12	f	f	PROPN
ejpam-5749	364	13	|hv	|hv	PROPN
ejpam-5749	364	14	∈	∈	PROPN
ejpam-5749	364	15	rdf	rdf	NOUN
ejpam-5749	364	16	(	(	PUNCT
ejpam-5749	364	17	hv	hv	NOUN
ejpam-5749	364	18	)	)	PUNCT
ejpam-5749	364	19	,	,	PUNCT
ejpam-5749	364	20	there	there	PRON
ejpam-5749	364	21	exists	exist	VERB
ejpam-5749	364	22	u	u	PROPN
ejpam-5749	364	23	∈	∈	PROPN
ejpam-5749	364	24	v2∩nhv(x	v2∩nhv(x	PROPN
ejpam-5749	364	25	)	)	PUNCT
ejpam-5749	364	26	.	.	PUNCT
ejpam-5749	365	1	this	this	PRON
ejpam-5749	365	2	means	mean	VERB
ejpam-5749	365	3	that	that	SCONJ
ejpam-5749	365	4	u	u	PROPN
ejpam-5749	365	5	∈	∈	PROPN
ejpam-5749	365	6	v2∩ng	v2∩ng	PROPN
ejpam-5749	365	7	◦	◦	NOUN
ejpam-5749	365	8	h(x	h(x	PROPN
ejpam-5749	365	9	)	)	PUNCT
ejpam-5749	365	10	.	.	PUNCT
ejpam-5749	366	1	and	and	CCONJ
ejpam-5749	366	2	,	,	PUNCT
ejpam-5749	366	3	if	if	SCONJ
ejpam-5749	366	4	v	v	NUM
ejpam-5749	366	5	∈	∈	PROPN
ejpam-5749	366	6	v2	v2	NOUN
ejpam-5749	366	7	,	,	PUNCT
ejpam-5749	366	8	then	then	ADV
ejpam-5749	366	9	v	v	ADP
ejpam-5749	366	10	∈	∈	PROPN
ejpam-5749	366	11	v2	v2	PROPN
ejpam-5749	366	12	∩ng	∩ng	PROPN
ejpam-5749	366	13	◦	◦	NOUN
ejpam-5749	366	14	h(x	h(x	PROPN
ejpam-5749	366	15	)	)	PUNCT
ejpam-5749	366	16	.	.	PUNCT
ejpam-5749	367	1	next	next	ADV
ejpam-5749	367	2	,	,	PUNCT
ejpam-5749	367	3	let	let	VERB
ejpam-5749	367	4	x	x	X
ejpam-5749	367	5	∈	∈	NOUN
ejpam-5749	367	6	v1	v1	NOUN
ejpam-5749	367	7	∪	∪	NOUN
ejpam-5749	367	8	v2	v2	NOUN
ejpam-5749	367	9	and	and	CCONJ
ejpam-5749	367	10	let	let	VERB
ejpam-5749	367	11	v	v	NUM
ejpam-5749	367	12	∈	∈	PROPN
ejpam-5749	367	13	v	v	NOUN
ejpam-5749	367	14	(	(	PUNCT
ejpam-5749	367	15	g	g	NOUN
ejpam-5749	367	16	)	)	PUNCT
ejpam-5749	367	17	for	for	ADP
ejpam-5749	367	18	which	which	PRON
ejpam-5749	367	19	x	x	SYM
ejpam-5749	367	20	∈	∈	PROPN
ejpam-5749	367	21	v	v	NOUN
ejpam-5749	367	22	(	(	PUNCT
ejpam-5749	367	23	v	v	NOUN
ejpam-5749	367	24	+	+	CCONJ
ejpam-5749	367	25	hv	hv	NOUN
ejpam-5749	367	26	)	)	PUNCT
ejpam-5749	367	27	.	.	PUNCT
ejpam-5749	368	1	if	if	SCONJ
ejpam-5749	368	2	x	x	X
ejpam-5749	368	3	=	=	SYM
ejpam-5749	368	4	v	v	ADP
ejpam-5749	368	5	∈	∈	PROPN
ejpam-5749	368	6	v1	v1	NOUN
ejpam-5749	368	7	,	,	PUNCT
ejpam-5749	368	8	then	then	ADV
ejpam-5749	368	9	since	since	SCONJ
ejpam-5749	368	10	f	f	PROPN
ejpam-5749	368	11	|hv	|hv	PROPN
ejpam-5749	368	12	∈	∈	PROPN
ejpam-5749	368	13	rdf	rdf	NOUN
ejpam-5749	368	14	(	(	PUNCT
ejpam-5749	368	15	hv	hv	NOUN
ejpam-5749	368	16	)	)	PUNCT
ejpam-5749	368	17	,	,	PUNCT
ejpam-5749	368	18	(	(	PUNCT
ejpam-5749	368	19	v1	v1	VERB
ejpam-5749	368	20	∪	∪	NOUN
ejpam-5749	368	21	v2	v2	NOUN
ejpam-5749	368	22	)	)	PUNCT
ejpam-5749	368	23	∩	∩	ADJ
ejpam-5749	368	24	v	v	X
ejpam-5749	368	25	(	(	PUNCT
ejpam-5749	368	26	hv	hv	NOUN
ejpam-5749	368	27	)	)	PUNCT
ejpam-5749	368	28	̸=	̸=	PROPN
ejpam-5749	368	29	∅.	∅.	PRON
ejpam-5749	368	30	then	then	ADV
ejpam-5749	368	31	1	1	NUM
ejpam-5749	368	32	≤	≤	NUM
ejpam-5749	368	33	dg	dg	PROPN
ejpam-5749	368	34	◦	◦	NOUN
ejpam-5749	368	35	h(x	h(x	PROPN
ejpam-5749	368	36	,	,	PUNCT
ejpam-5749	368	37	u	u	NOUN
ejpam-5749	368	38	)	)	PUNCT
ejpam-5749	368	39	≤	≤	NUM
ejpam-5749	368	40	2	2	NUM
ejpam-5749	368	41	for	for	ADP
ejpam-5749	368	42	all	all	DET
ejpam-5749	368	43	u	u	PROPN
ejpam-5749	368	44	∈	∈	NOUN
ejpam-5749	368	45	(	(	PUNCT
ejpam-5749	368	46	v1	v1	NOUN
ejpam-5749	368	47	∪	∪	NOUN
ejpam-5749	368	48	v2	v2	NOUN
ejpam-5749	368	49	)	)	PUNCT
ejpam-5749	368	50	∩	∩	ADJ
ejpam-5749	368	51	v	v	X
ejpam-5749	368	52	(	(	PUNCT
ejpam-5749	368	53	hv	hv	PROPN
ejpam-5749	368	54	)	)	PUNCT
ejpam-5749	368	55	.	.	PUNCT
ejpam-5749	368	56	suppose	suppose	VERB
ejpam-5749	368	57	x	x	SYM
ejpam-5749	368	58	=	=	SYM
ejpam-5749	368	59	v	v	ADP
ejpam-5749	368	60	∈	∈	PROPN
ejpam-5749	368	61	v2	v2	NOUN
ejpam-5749	368	62	.	.	PUNCT
ejpam-5749	369	1	if	if	SCONJ
ejpam-5749	369	2	v	v	X
ejpam-5749	369	3	(	(	PUNCT
ejpam-5749	369	4	hv	hv	NOUN
ejpam-5749	369	5	)	)	PUNCT
ejpam-5749	369	6	\	\	PROPN
ejpam-5749	369	7	v0	v0	PROPN
ejpam-5749	369	8	̸=	̸=	PROPN
ejpam-5749	369	9	∅	∅	NOUN
ejpam-5749	369	10	,	,	PUNCT
ejpam-5749	369	11	then	then	ADV
ejpam-5749	369	12	1	1	NUM
ejpam-5749	369	13	≤	≤	NUM
ejpam-5749	369	14	dg	dg	PROPN
ejpam-5749	369	15	◦	◦	NOUN
ejpam-5749	369	16	h(u	h(u	PROPN
ejpam-5749	369	17	,	,	PUNCT
ejpam-5749	369	18	x	x	NOUN
ejpam-5749	369	19	)	)	PUNCT
ejpam-5749	369	20	≤	≤	NUM
ejpam-5749	369	21	2	2	NUM
ejpam-5749	369	22	for	for	ADP
ejpam-5749	369	23	all	all	DET
ejpam-5749	369	24	u	u	PROPN
ejpam-5749	369	25	∈	∈	PROPN
ejpam-5749	369	26	v	v	ADP
ejpam-5749	369	27	(	(	PUNCT
ejpam-5749	369	28	hv	hv	NOUN
ejpam-5749	369	29	)	)	PUNCT
ejpam-5749	369	30	\v0	\v0	PROPN
ejpam-5749	369	31	.	.	PUNCT
ejpam-5749	370	1	if	if	SCONJ
ejpam-5749	370	2	v	v	X
ejpam-5749	370	3	(	(	PUNCT
ejpam-5749	370	4	hv	hv	PROPN
ejpam-5749	370	5	)	)	PUNCT
ejpam-5749	370	6	⊆	⊆	NUM
ejpam-5749	370	7	v0	v0	NOUN
ejpam-5749	370	8	,	,	PUNCT
ejpam-5749	370	9	then	then	ADV
ejpam-5749	370	10	by	by	ADP
ejpam-5749	370	11	(	(	PUNCT
ejpam-5749	370	12	iii	iii	NOUN
ejpam-5749	370	13	)	)	PUNCT
ejpam-5749	370	14	,	,	PUNCT
ejpam-5749	370	15	there	there	PRON
ejpam-5749	370	16	exists	exist	VERB
ejpam-5749	370	17	u	u	PROPN
ejpam-5749	370	18	∈	∈	PROPN
ejpam-5749	370	19	(	(	PUNCT
ejpam-5749	370	20	v1	v1	PROPN
ejpam-5749	370	21	∪v2)∩ng(x	∪v2)∩ng(x	NOUN
ejpam-5749	370	22	,	,	PUNCT
ejpam-5749	370	23	2	2	NUM
ejpam-5749	370	24	)	)	PUNCT
ejpam-5749	370	25	.	.	PUNCT
ejpam-5749	371	1	finally	finally	ADV
ejpam-5749	371	2	,	,	PUNCT
ejpam-5749	371	3	suppose	suppose	VERB
ejpam-5749	371	4	that	that	SCONJ
ejpam-5749	371	5	x	x	PROPN
ejpam-5749	371	6	̸=	̸=	PROPN
ejpam-5749	371	7	v.	v.	ADV
ejpam-5749	371	8	if	if	SCONJ
ejpam-5749	371	9	v	v	NUM
ejpam-5749	371	10	∈	∈	PROPN
ejpam-5749	371	11	v1	v1	NOUN
ejpam-5749	371	12	∪	∪	NOUN
ejpam-5749	371	13	v2	v2	NOUN
ejpam-5749	371	14	,	,	PUNCT
ejpam-5749	371	15	then	then	ADV
ejpam-5749	371	16	we	we	PRON
ejpam-5749	371	17	are	be	AUX
ejpam-5749	371	18	done	do	VERB
ejpam-5749	371	19	.	.	PUNCT
ejpam-5749	371	20	suppose	suppose	VERB
ejpam-5749	371	21	that	that	SCONJ
ejpam-5749	371	22	v	v	PROPN
ejpam-5749	371	23	∈	∈	PROPN
ejpam-5749	371	24	v0	v0	NOUN
ejpam-5749	371	25	.	.	PUNCT
ejpam-5749	372	1	if	if	SCONJ
ejpam-5749	372	2	ng(v	ng(v	NOUN
ejpam-5749	372	3	)	)	PUNCT
ejpam-5749	372	4	\	\	PROPN
ejpam-5749	372	5	v0	v0	PROPN
ejpam-5749	372	6	̸=	̸=	PROPN
ejpam-5749	372	7	∅	∅	NOUN
ejpam-5749	372	8	,	,	PUNCT
ejpam-5749	372	9	then	then	ADV
ejpam-5749	372	10	dg	dg	VERB
ejpam-5749	372	11	◦	◦	NOUN
ejpam-5749	372	12	h(x	h(x	PROPN
ejpam-5749	372	13	,	,	PUNCT
ejpam-5749	372	14	u	u	NOUN
ejpam-5749	372	15	)	)	PUNCT
ejpam-5749	372	16	≤	≤	NUM
ejpam-5749	372	17	2	2	NUM
ejpam-5749	372	18	for	for	ADP
ejpam-5749	372	19	all	all	DET
ejpam-5749	372	20	u	u	NOUN
ejpam-5749	372	21	∈	∈	NOUN
ejpam-5749	372	22	ng(v	ng(v	PUNCT
ejpam-5749	372	23	)	)	PUNCT
ejpam-5749	372	24	\	\	NOUN
ejpam-5749	372	25	v0	v0	PROPN
ejpam-5749	372	26	⊆	⊆	NUM
ejpam-5749	372	27	(	(	PUNCT
ejpam-5749	372	28	v1	v1	VERB
ejpam-5749	372	29	∪	∪	NOUN
ejpam-5749	372	30	v2	v2	NOUN
ejpam-5749	372	31	)	)	PUNCT
ejpam-5749	372	32	.	.	PUNCT
ejpam-5749	373	1	if	if	SCONJ
ejpam-5749	373	2	ng(v	ng(v	NOUN
ejpam-5749	373	3	)	)	PUNCT
ejpam-5749	373	4	⊆	⊆	NUM
ejpam-5749	373	5	v0	v0	NOUN
ejpam-5749	373	6	,	,	PUNCT
ejpam-5749	373	7	then	then	ADV
ejpam-5749	373	8	by	by	ADP
ejpam-5749	373	9	(	(	PUNCT
ejpam-5749	373	10	i)(a	i)(a	NOUN
ejpam-5749	373	11	)	)	PUNCT
ejpam-5749	373	12	,	,	PUNCT
ejpam-5749	373	13	there	there	PRON
ejpam-5749	373	14	exists	exist	VERB
ejpam-5749	373	15	u	u	PROPN
ejpam-5749	373	16	∈	∈	PROPN
ejpam-5749	373	17	(	(	PUNCT
ejpam-5749	373	18	v1	v1	NOUN
ejpam-5749	373	19	∪	∪	NOUN
ejpam-5749	373	20	v2	v2	NOUN
ejpam-5749	373	21	)	)	PUNCT
ejpam-5749	373	22	∩	∩	ADJ
ejpam-5749	373	23	v	v	X
ejpam-5749	373	24	(	(	PUNCT
ejpam-5749	373	25	hv	hv	PROPN
ejpam-5749	373	26	)	)	PUNCT
ejpam-5749	373	27	with	with	ADP
ejpam-5749	373	28	u	u	NOUN
ejpam-5749	373	29	̸=	̸=	PROPN
ejpam-5749	373	30	x.	x.	NOUN
ejpam-5749	373	31	here	here	ADV
ejpam-5749	373	32	,	,	PUNCT
ejpam-5749	373	33	dg	dg	PROPN
ejpam-5749	373	34	◦	◦	NOUN
ejpam-5749	373	35	h(x	h(x	PROPN
ejpam-5749	373	36	,	,	PUNCT
ejpam-5749	373	37	u	u	NOUN
ejpam-5749	373	38	)	)	PUNCT
ejpam-5749	373	39	≤	≤	NUM
ejpam-5749	373	40	2	2	NUM
ejpam-5749	373	41	.	.	PUNCT
ejpam-5749	374	1	the	the	DET
ejpam-5749	374	2	above	above	ADJ
ejpam-5749	374	3	results	result	NOUN
ejpam-5749	374	4	imply	imply	VERB
ejpam-5749	374	5	that	that	SCONJ
ejpam-5749	374	6	f	f	PROPN
ejpam-5749	374	7	∈	∈	PROPN
ejpam-5749	374	8	srdf	srdf	NOUN
ejpam-5749	374	9	(	(	PUNCT
ejpam-5749	374	10	g	g	PROPN
ejpam-5749	374	11	◦	◦	NOUN
ejpam-5749	374	12	h	h	NOUN
ejpam-5749	374	13	)	)	PUNCT
ejpam-5749	374	14	.	.	PUNCT
ejpam-5749	375	1	it	it	PRON
ejpam-5749	375	2	is	be	AUX
ejpam-5749	375	3	worth	worth	ADJ
ejpam-5749	375	4	noting	note	VERB
ejpam-5749	375	5	that	that	SCONJ
ejpam-5749	375	6	theorem	theorem	NOUN
ejpam-5749	375	7	2(i)(a	2(i)(a	NUM
ejpam-5749	375	8	)	)	PUNCT
ejpam-5749	375	9	does	do	AUX
ejpam-5749	375	10	not	not	PART
ejpam-5749	375	11	happen	happen	VERB
ejpam-5749	375	12	if	if	SCONJ
ejpam-5749	375	13	h	h	NOUN
ejpam-5749	375	14	=	=	SYM
ejpam-5749	375	15	k1	k1	PROPN
ejpam-5749	375	16	.	.	PUNCT
ejpam-5749	375	17	corollary	corollary	ADJ
ejpam-5749	375	18	2	2	NUM
ejpam-5749	375	19	.	.	PUNCT
ejpam-5749	376	1	let	let	VERB
ejpam-5749	376	2	g	g	PRON
ejpam-5749	376	3	be	be	AUX
ejpam-5749	376	4	a	a	DET
ejpam-5749	376	5	nontrivial	nontrivial	ADJ
ejpam-5749	376	6	connected	connect	VERB
ejpam-5749	376	7	graph	graph	NOUN
ejpam-5749	376	8	of	of	ADP
ejpam-5749	376	9	order	order	NOUN
ejpam-5749	376	10	n.	n.	NOUN
ejpam-5749	376	11	then	then	ADV
ejpam-5749	376	12	(	(	PUNCT
ejpam-5749	376	13	i	i	NOUN
ejpam-5749	376	14	)	)	PUNCT
ejpam-5749	376	15	γt2r(g	γt2r(g	PRON
ejpam-5749	376	16	◦	◦	NOUN
ejpam-5749	376	17	k1	k1	NOUN
ejpam-5749	376	18	)	)	PUNCT
ejpam-5749	376	19	=	=	PUNCT
ejpam-5749	376	20	n+	n+	NUM
ejpam-5749	376	21	γ(g	γ(g	PROPN
ejpam-5749	376	22	)	)	PUNCT
ejpam-5749	376	23	;	;	PUNCT
ejpam-5749	376	24	(	(	PUNCT
ejpam-5749	376	25	ii	ii	NOUN
ejpam-5749	376	26	)	)	PUNCT
ejpam-5749	376	27	γt2r(g	γt2r(g	PRON
ejpam-5749	376	28	◦	◦	NOUN
ejpam-5749	376	29	h	h	NOUN
ejpam-5749	376	30	)	)	PUNCT
ejpam-5749	376	31	=	=	SYM
ejpam-5749	376	32	2n	2n	NUM
ejpam-5749	376	33	for	for	ADP
ejpam-5749	376	34	all	all	DET
ejpam-5749	376	35	nontrivial	nontrivial	ADJ
ejpam-5749	376	36	graphs	graph	NOUN
ejpam-5749	376	37	h.	h.	NOUN
ejpam-5749	376	38	proof	proof	NOUN
ejpam-5749	376	39	.	.	PUNCT
ejpam-5749	377	1	in	in	ADP
ejpam-5749	377	2	the	the	DET
ejpam-5749	377	3	case	case	NOUN
ejpam-5749	377	4	where	where	SCONJ
ejpam-5749	377	5	h	h	NOUN
ejpam-5749	377	6	=	=	NOUN
ejpam-5749	377	7	k1	k1	PROPN
ejpam-5749	377	8	=	=	SYM
ejpam-5749	377	9	{	{	PUNCT
ejpam-5749	377	10	u	u	NOUN
ejpam-5749	377	11	}	}	PUNCT
ejpam-5749	377	12	,	,	PUNCT
ejpam-5749	377	13	we	we	PRON
ejpam-5749	377	14	define	define	VERB
ejpam-5749	377	15	for	for	ADP
ejpam-5749	377	16	each	each	PRON
ejpam-5749	377	17	v	v	NUM
ejpam-5749	377	18	∈	∈	PROPN
ejpam-5749	377	19	v	v	NOUN
ejpam-5749	377	20	(	(	PUNCT
ejpam-5749	377	21	g	g	NOUN
ejpam-5749	377	22	)	)	PUNCT
ejpam-5749	377	23	,	,	PUNCT
ejpam-5749	377	24	v	v	PROPN
ejpam-5749	377	25	(	(	PUNCT
ejpam-5749	377	26	hv	hv	NOUN
ejpam-5749	377	27	)	)	PUNCT
ejpam-5749	377	28	=	=	PRON
ejpam-5749	377	29	{	{	PUNCT
ejpam-5749	377	30	uv	uv	NOUN
ejpam-5749	377	31	}	}	PUNCT
ejpam-5749	377	32	.	.	PUNCT
ejpam-5749	378	1	let	let	VERB
ejpam-5749	378	2	s	s	PRON
ejpam-5749	378	3	⊆	⊆	NUM
ejpam-5749	378	4	v	v	NOUN
ejpam-5749	378	5	(	(	PUNCT
ejpam-5749	378	6	g	g	NOUN
ejpam-5749	378	7	)	)	PUNCT
ejpam-5749	378	8	be	be	AUX
ejpam-5749	378	9	a	a	DET
ejpam-5749	378	10	γ	γ	NOUN
ejpam-5749	378	11	-	-	PUNCT
ejpam-5749	378	12	set	set	NOUN
ejpam-5749	378	13	of	of	ADP
ejpam-5749	378	14	g.	g.	PROPN
ejpam-5749	378	15	define	define	VERB
ejpam-5749	378	16	v0	v0	PROPN
ejpam-5749	378	17	=	=	SYM
ejpam-5749	378	18	(	(	PUNCT
ejpam-5749	378	19	v	v	NOUN
ejpam-5749	378	20	(	(	PUNCT
ejpam-5749	378	21	g	g	NOUN
ejpam-5749	378	22	)	)	PUNCT
ejpam-5749	378	23	\s)∪	\s)∪	PROPN
ejpam-5749	378	24	(	(	PUNCT
ejpam-5749	378	25	∪v∈s{uv	∪v∈s{uv	NOUN
ejpam-5749	378	26	}	}	PUNCT
ejpam-5749	378	27	)	)	PUNCT
ejpam-5749	378	28	,	,	PUNCT
ejpam-5749	378	29	v1	v1	NOUN
ejpam-5749	378	30	=	=	SYM
ejpam-5749	378	31	∪v∈v	∪v∈v	X
ejpam-5749	378	32	(	(	PUNCT
ejpam-5749	378	33	g)\s{uv	g)\s{uv	NOUN
ejpam-5749	378	34	}	}	PUNCT
ejpam-5749	378	35	and	and	CCONJ
ejpam-5749	378	36	v2	v2	X
ejpam-5749	378	37	=	=	PUNCT
ejpam-5749	378	38	s.	s.	PROPN
ejpam-5749	378	39	it	it	PRON
ejpam-5749	378	40	is	be	AUX
ejpam-5749	378	41	easy	easy	ADJ
ejpam-5749	378	42	to	to	PART
ejpam-5749	378	43	see	see	VERB
ejpam-5749	378	44	that	that	PRON
ejpam-5749	378	45	f	f	PROPN
ejpam-5749	378	46	=	=	SYM
ejpam-5749	378	47	(	(	PUNCT
ejpam-5749	378	48	v0	v0	PROPN
ejpam-5749	378	49	,	,	PUNCT
ejpam-5749	378	50	v1	v1	NOUN
ejpam-5749	378	51	,	,	PUNCT
ejpam-5749	378	52	v2	v2	NOUN
ejpam-5749	378	53	)	)	PUNCT
ejpam-5749	378	54	∈	∈	NOUN
ejpam-5749	378	55	srdf	srdf	NOUN
ejpam-5749	378	56	(	(	PUNCT
ejpam-5749	378	57	g	g	PROPN
ejpam-5749	378	58	◦	◦	NOUN
ejpam-5749	378	59	h	h	NOUN
ejpam-5749	378	60	)	)	PUNCT
ejpam-5749	378	61	.	.	PUNCT
ejpam-5749	379	1	thus	thus	ADV
ejpam-5749	379	2	,	,	PUNCT
ejpam-5749	379	3	γt2r(g	γt2r(g	PRON
ejpam-5749	379	4	◦	◦	NOUN
ejpam-5749	379	5	h	h	NOUN
ejpam-5749	379	6	)	)	PUNCT
ejpam-5749	379	7	≤	≤	NUM
ejpam-5749	379	8	ωg	ωg	NOUN
ejpam-5749	379	9	◦	◦	NOUN
ejpam-5749	379	10	h(f	h(f	X
ejpam-5749	379	11	)	)	PUNCT
ejpam-5749	379	12	=	=	SYM
ejpam-5749	380	1	2|s|	2|s|	NUM
ejpam-5749	380	2	+	+	CCONJ
ejpam-5749	380	3	(	(	PUNCT
ejpam-5749	380	4	n	n	CCONJ
ejpam-5749	380	5	−	−	PROPN
ejpam-5749	380	6	|s|	|s|	PROPN
ejpam-5749	380	7	)	)	PUNCT
ejpam-5749	380	8	=	=	SYM
ejpam-5749	380	9	n	n	PROPN
ejpam-5749	380	10	+	+	NUM
ejpam-5749	380	11	γ(g	γ(g	PROPN
ejpam-5749	380	12	)	)	PUNCT
ejpam-5749	380	13	.	.	PUNCT
ejpam-5749	381	1	now	now	ADV
ejpam-5749	381	2	,	,	PUNCT
ejpam-5749	381	3	let	let	VERB
ejpam-5749	381	4	f	f	PROPN
ejpam-5749	381	5	=	=	SYM
ejpam-5749	381	6	(	(	PUNCT
ejpam-5749	381	7	v0	v0	PROPN
ejpam-5749	381	8	,	,	PUNCT
ejpam-5749	381	9	v1	v1	NOUN
ejpam-5749	381	10	,	,	PUNCT
ejpam-5749	381	11	v2	v2	PROPN
ejpam-5749	381	12	)	)	PUNCT
ejpam-5749	381	13	be	be	AUX
ejpam-5749	381	14	a	a	DET
ejpam-5749	381	15	γt2r	γt2r	NOUN
ejpam-5749	381	16	-	-	PUNCT
ejpam-5749	381	17	function	function	NOUN
ejpam-5749	381	18	of	of	ADP
ejpam-5749	381	19	b.	b.	PROPN
ejpam-5749	381	20	f.	f.	PROPN
ejpam-5749	381	21	bullang	bullang	PROPN
ejpam-5749	381	22	et	et	PROPN
ejpam-5749	381	23	al	al	PROPN
ejpam-5749	381	24	.	.	PUNCT
ejpam-5749	381	25	/	/	SYM
ejpam-5749	381	26	eur	eur	PROPN
ejpam-5749	381	27	.	.	PUNCT
ejpam-5749	382	1	j.	j.	PROPN
ejpam-5749	382	2	pure	pure	PROPN
ejpam-5749	382	3	appl	appl	PROPN
ejpam-5749	382	4	.	.	PROPN
ejpam-5749	382	5	math	math	PROPN
ejpam-5749	382	6	,	,	PUNCT
ejpam-5749	382	7	18	18	NUM
ejpam-5749	382	8	(	(	PUNCT
ejpam-5749	382	9	1	1	NUM
ejpam-5749	382	10	)	)	PUNCT
ejpam-5749	382	11	(	(	PUNCT
ejpam-5749	382	12	2025	2025	NUM
ejpam-5749	382	13	)	)	PUNCT
ejpam-5749	382	14	,	,	PUNCT
ejpam-5749	382	15	5749	5749	NUM
ejpam-5749	382	16	12	12	NUM
ejpam-5749	382	17	of	of	ADP
ejpam-5749	382	18	15	15	NUM
ejpam-5749	382	19	g	g	NOUN
ejpam-5749	382	20	◦	◦	NOUN
ejpam-5749	382	21	h.	h.	PROPN
ejpam-5749	382	22	since	since	SCONJ
ejpam-5749	382	23	f	f	PROPN
ejpam-5749	382	24	is	be	AUX
ejpam-5749	382	25	a	a	DET
ejpam-5749	382	26	γt2r	γt2r	NOUN
ejpam-5749	382	27	-	-	PUNCT
ejpam-5749	382	28	function	function	NOUN
ejpam-5749	382	29	,	,	PUNCT
ejpam-5749	382	30	f(u	f(u	PROPN
ejpam-5749	382	31	v	v	NOUN
ejpam-5749	382	32	)	)	PUNCT
ejpam-5749	382	33	=	=	SYM
ejpam-5749	382	34	1	1	NUM
ejpam-5749	382	35	for	for	ADP
ejpam-5749	382	36	all	all	DET
ejpam-5749	382	37	v	v	PRON
ejpam-5749	382	38	∈	∈	NOUN
ejpam-5749	382	39	v1	v1	NOUN
ejpam-5749	382	40	∩	∩	ADJ
ejpam-5749	382	41	v	v	NOUN
ejpam-5749	382	42	(	(	PUNCT
ejpam-5749	382	43	g	g	NOUN
ejpam-5749	382	44	)	)	PUNCT
ejpam-5749	382	45	and	and	CCONJ
ejpam-5749	382	46	f(uv	f(uv	NOUN
ejpam-5749	382	47	)	)	PUNCT
ejpam-5749	382	48	=	=	SYM
ejpam-5749	382	49	0	0	NUM
ejpam-5749	382	50	for	for	ADP
ejpam-5749	382	51	all	all	DET
ejpam-5749	382	52	v	v	NOUN
ejpam-5749	382	53	∈	∈	PROPN
ejpam-5749	382	54	v2	v2	NOUN
ejpam-5749	382	55	∩	∩	ADJ
ejpam-5749	382	56	v	v	NOUN
ejpam-5749	382	57	(	(	PUNCT
ejpam-5749	382	58	g	g	NOUN
ejpam-5749	382	59	)	)	PUNCT
ejpam-5749	382	60	.	.	PUNCT
ejpam-5749	383	1	let	let	VERB
ejpam-5749	383	2	x	x	PUNCT
ejpam-5749	383	3	=	=	PRON
ejpam-5749	383	4	{	{	PUNCT
ejpam-5749	383	5	v	v	NOUN
ejpam-5749	383	6	∈	∈	PROPN
ejpam-5749	383	7	v0	v0	NOUN
ejpam-5749	383	8	∩	∩	X
ejpam-5749	383	9	v	v	X
ejpam-5749	383	10	(	(	PUNCT
ejpam-5749	383	11	g	g	NOUN
ejpam-5749	383	12	)	)	PUNCT
ejpam-5749	383	13	:	:	PUNCT
ejpam-5749	383	14	f(uv	f(uv	X
ejpam-5749	383	15	)	)	PUNCT
ejpam-5749	383	16	=	=	SYM
ejpam-5749	383	17	2	2	X
ejpam-5749	383	18	}	}	PUNCT
ejpam-5749	383	19	,	,	PUNCT
ejpam-5749	383	20	y	y	PROPN
ejpam-5749	383	21	=	=	PRON
ejpam-5749	383	22	{	{	PUNCT
ejpam-5749	383	23	uv	uv	NOUN
ejpam-5749	383	24	:	:	PUNCT
ejpam-5749	383	25	v	v	NUM
ejpam-5749	383	26	∈	∈	NOUN
ejpam-5749	383	27	x	x	X
ejpam-5749	383	28	}	}	PUNCT
ejpam-5749	383	29	and	and	CCONJ
ejpam-5749	383	30	w	w	NOUN
ejpam-5749	383	31	=	=	PRON
ejpam-5749	383	32	{	{	PUNCT
ejpam-5749	383	33	uv	uv	NOUN
ejpam-5749	383	34	:	:	PUNCT
ejpam-5749	383	35	v	v	NUM
ejpam-5749	383	36	∈	∈	PROPN
ejpam-5749	383	37	v1	v1	NOUN
ejpam-5749	383	38	∩	∩	ADJ
ejpam-5749	383	39	v	v	NOUN
ejpam-5749	383	40	(	(	PUNCT
ejpam-5749	383	41	g	g	NOUN
ejpam-5749	383	42	)	)	PUNCT
ejpam-5749	383	43	}	}	PUNCT
ejpam-5749	383	44	,	,	PUNCT
ejpam-5749	383	45	and	and	CCONJ
ejpam-5749	383	46	define	define	VERB
ejpam-5749	383	47	v	v	NUM
ejpam-5749	383	48	∗	∗	NOUN
ejpam-5749	383	49	0	0	NUM
ejpam-5749	384	1	=	=	SYM
ejpam-5749	384	2	(	(	PUNCT
ejpam-5749	384	3	v0	v0	NOUN
ejpam-5749	384	4	\x	\x	NOUN
ejpam-5749	384	5	)	)	PUNCT
ejpam-5749	385	1	∪	∪	ADP
ejpam-5749	385	2	y	y	PROPN
ejpam-5749	385	3	∪w	∪w	PROPN
ejpam-5749	385	4	,	,	PUNCT
ejpam-5749	385	5	v	v	ADP
ejpam-5749	385	6	∗	∗	NOUN
ejpam-5749	385	7	1	1	NUM
ejpam-5749	385	8	=	=	SYM
ejpam-5749	385	9	v1	v1	NOUN
ejpam-5749	385	10	\	\	PUNCT
ejpam-5749	386	1	[	[	X
ejpam-5749	386	2	(	(	PUNCT
ejpam-5749	386	3	v1	v1	NOUN
ejpam-5749	386	4	∩	∩	ADJ
ejpam-5749	386	5	v	v	NOUN
ejpam-5749	386	6	(	(	PUNCT
ejpam-5749	386	7	g	g	NOUN
ejpam-5749	386	8	)	)	PUNCT
ejpam-5749	386	9	)	)	PUNCT
ejpam-5749	386	10	∪w	∪w	NUM
ejpam-5749	386	11	]	]	PUNCT
ejpam-5749	386	12	and	and	CCONJ
ejpam-5749	386	13	v	v	ADP
ejpam-5749	386	14	∗	∗	NOUN
ejpam-5749	386	15	2	2	NUM
ejpam-5749	386	16	=	=	SYM
ejpam-5749	386	17	(	(	PUNCT
ejpam-5749	386	18	(	(	PUNCT
ejpam-5749	386	19	v1	v1	VERB
ejpam-5749	386	20	∪	∪	NOUN
ejpam-5749	386	21	v2	v2	NOUN
ejpam-5749	386	22	)	)	PUNCT
ejpam-5749	386	23	∩	∩	ADJ
ejpam-5749	386	24	v	v	X
ejpam-5749	386	25	(	(	PUNCT
ejpam-5749	386	26	g	g	NOUN
ejpam-5749	386	27	)	)	PUNCT
ejpam-5749	386	28	)	)	PUNCT
ejpam-5749	387	1	∪x	∪x	X
ejpam-5749	387	2	.	.	PUNCT
ejpam-5749	388	1	first	first	ADV
ejpam-5749	388	2	,	,	PUNCT
ejpam-5749	388	3	we	we	PRON
ejpam-5749	388	4	claim	claim	VERB
ejpam-5749	388	5	that	that	SCONJ
ejpam-5749	388	6	g	g	PROPN
ejpam-5749	388	7	=	=	SYM
ejpam-5749	388	8	(	(	PUNCT
ejpam-5749	388	9	v	v	NOUN
ejpam-5749	388	10	∗	∗	NOUN
ejpam-5749	388	11	0	0	NUM
ejpam-5749	388	12	,	,	PUNCT
ejpam-5749	388	13	v	v	NOUN
ejpam-5749	388	14	∗	∗	NOUN
ejpam-5749	388	15	1	1	NUM
ejpam-5749	388	16	,	,	PUNCT
ejpam-5749	388	17	v	v	NOUN
ejpam-5749	388	18	∗	∗	X
ejpam-5749	388	19	2	2	NUM
ejpam-5749	388	20	)	)	PUNCT
ejpam-5749	388	21	∈	∈	NOUN
ejpam-5749	388	22	srdf	srdf	NOUN
ejpam-5749	388	23	(	(	PUNCT
ejpam-5749	388	24	g	g	PROPN
ejpam-5749	388	25	◦	◦	NOUN
ejpam-5749	388	26	h	h	NOUN
ejpam-5749	388	27	)	)	PUNCT
ejpam-5749	388	28	.	.	PUNCT
ejpam-5749	389	1	let	let	VERB
ejpam-5749	389	2	x	x	PUNCT
ejpam-5749	389	3	∈	∈	PROPN
ejpam-5749	389	4	v	v	ADP
ejpam-5749	389	5	∗	∗	NOUN
ejpam-5749	389	6	0	0	NUM
ejpam-5749	389	7	.	.	PUNCT
ejpam-5749	390	1	we	we	PRON
ejpam-5749	390	2	consider	consider	VERB
ejpam-5749	390	3	the	the	DET
ejpam-5749	390	4	following	follow	VERB
ejpam-5749	390	5	cases	case	NOUN
ejpam-5749	390	6	:	:	PUNCT
ejpam-5749	390	7	case	case	NOUN
ejpam-5749	390	8	1	1	NUM
ejpam-5749	390	9	:	:	PUNCT
ejpam-5749	390	10	suppose	suppose	VERB
ejpam-5749	390	11	x	x	X
ejpam-5749	390	12	∈	∈	PROPN
ejpam-5749	390	13	v0	v0	NOUN
ejpam-5749	390	14	\	\	PUNCT
ejpam-5749	390	15	x.	x.	NOUN
ejpam-5749	391	1	if	if	SCONJ
ejpam-5749	391	2	x	x	PRON
ejpam-5749	391	3	=	=	PUNCT
ejpam-5749	391	4	uv	uv	NOUN
ejpam-5749	391	5	for	for	ADP
ejpam-5749	391	6	some	some	DET
ejpam-5749	391	7	v	v	NOUN
ejpam-5749	391	8	,	,	PUNCT
ejpam-5749	391	9	then	then	ADV
ejpam-5749	391	10	v	v	ADP
ejpam-5749	391	11	∈	∈	PROPN
ejpam-5749	391	12	v2	v2	PROPN
ejpam-5749	391	13	∩	∩	ADJ
ejpam-5749	391	14	v	v	NOUN
ejpam-5749	391	15	(	(	PUNCT
ejpam-5749	391	16	g	g	NOUN
ejpam-5749	391	17	)	)	PUNCT
ejpam-5749	391	18	.	.	PUNCT
ejpam-5749	392	1	hence	hence	ADV
ejpam-5749	392	2	,	,	PUNCT
ejpam-5749	392	3	v	v	PROPN
ejpam-5749	392	4	∈	∈	PROPN
ejpam-5749	392	5	v	v	ADP
ejpam-5749	392	6	∗	∗	NOUN
ejpam-5749	392	7	2	2	NUM
ejpam-5749	392	8	∩ng	∩ng	NOUN
ejpam-5749	392	9	◦	◦	NOUN
ejpam-5749	392	10	h(x	h(x	PROPN
ejpam-5749	392	11	)	)	PUNCT
ejpam-5749	392	12	.	.	PUNCT
ejpam-5749	393	1	if	if	SCONJ
ejpam-5749	393	2	x	x	SYM
ejpam-5749	393	3	∈	∈	PROPN
ejpam-5749	393	4	v	v	X
ejpam-5749	393	5	(	(	PUNCT
ejpam-5749	393	6	g	g	NOUN
ejpam-5749	393	7	)	)	PUNCT
ejpam-5749	393	8	,	,	PUNCT
ejpam-5749	393	9	then	then	ADV
ejpam-5749	393	10	f(ux	f(ux	NOUN
ejpam-5749	393	11	)	)	PUNCT
ejpam-5749	393	12	̸=	̸=	PROPN
ejpam-5749	393	13	2	2	NUM
ejpam-5749	393	14	and	and	CCONJ
ejpam-5749	393	15	thus	thus	ADV
ejpam-5749	393	16	,	,	PUNCT
ejpam-5749	393	17	there	there	PRON
ejpam-5749	393	18	exists	exist	VERB
ejpam-5749	394	1	y	y	PROPN
ejpam-5749	394	2	∈	∈	PROPN
ejpam-5749	394	3	v2∩v	v2∩v	NOUN
ejpam-5749	394	4	(	(	PUNCT
ejpam-5749	394	5	g	g	NOUN
ejpam-5749	394	6	)	)	PUNCT
ejpam-5749	394	7	such	such	ADJ
ejpam-5749	394	8	that	that	SCONJ
ejpam-5749	394	9	xy	xy	PROPN
ejpam-5749	394	10	∈	∈	PROPN
ejpam-5749	394	11	e(g	e(g	PROPN
ejpam-5749	394	12	◦	◦	NOUN
ejpam-5749	394	13	h	h	NOUN
ejpam-5749	394	14	)	)	PUNCT
ejpam-5749	394	15	.	.	PUNCT
ejpam-5749	395	1	this	this	PRON
ejpam-5749	395	2	means	mean	VERB
ejpam-5749	395	3	that	that	SCONJ
ejpam-5749	395	4	y	y	PROPN
ejpam-5749	395	5	∈	∈	PROPN
ejpam-5749	395	6	v	v	ADP
ejpam-5749	395	7	∗	∗	NOUN
ejpam-5749	395	8	2	2	NUM
ejpam-5749	395	9	∩ng	∩ng	NOUN
ejpam-5749	395	10	◦	◦	NOUN
ejpam-5749	395	11	h(x	h(x	PROPN
ejpam-5749	395	12	)	)	PUNCT
ejpam-5749	395	13	.	.	PUNCT
ejpam-5749	396	1	case	case	NOUN
ejpam-5749	396	2	2	2	NUM
ejpam-5749	396	3	:	:	PUNCT
ejpam-5749	396	4	suppose	suppose	VERB
ejpam-5749	396	5	x	x	X
ejpam-5749	396	6	∈	∈	PROPN
ejpam-5749	396	7	y	y	PROPN
ejpam-5749	396	8	∪w	∪w	PROPN
ejpam-5749	396	9	.	.	PUNCT
ejpam-5749	397	1	then	then	ADV
ejpam-5749	397	2	x	x	X
ejpam-5749	397	3	=	=	PUNCT
ejpam-5749	397	4	uv	uv	NOUN
ejpam-5749	397	5	where	where	SCONJ
ejpam-5749	397	6	v	v	X
ejpam-5749	397	7	∈	∈	NOUN
ejpam-5749	397	8	x	x	X
ejpam-5749	397	9	or	or	CCONJ
ejpam-5749	397	10	v	v	ADP
ejpam-5749	397	11	∈	∈	NOUN
ejpam-5749	397	12	v1	v1	NOUN
ejpam-5749	397	13	∩	∩	ADJ
ejpam-5749	397	14	v	v	NOUN
ejpam-5749	397	15	(	(	PUNCT
ejpam-5749	397	16	g	g	NOUN
ejpam-5749	397	17	)	)	PUNCT
ejpam-5749	397	18	.	.	PUNCT
ejpam-5749	398	1	in	in	ADP
ejpam-5749	398	2	any	any	DET
ejpam-5749	398	3	case	case	NOUN
ejpam-5749	398	4	,	,	PUNCT
ejpam-5749	398	5	v	v	PROPN
ejpam-5749	398	6	∈	∈	NOUN
ejpam-5749	398	7	v	v	ADP
ejpam-5749	398	8	∗	∗	NOUN
ejpam-5749	398	9	2	2	NUM
ejpam-5749	398	10	∩ng	∩ng	NOUN
ejpam-5749	398	11	◦	◦	NOUN
ejpam-5749	398	12	h(x	h(x	PROPN
ejpam-5749	398	13	)	)	PUNCT
ejpam-5749	398	14	.	.	PUNCT
ejpam-5749	399	1	now	now	ADV
ejpam-5749	399	2	,	,	PUNCT
ejpam-5749	399	3	let	let	VERB
ejpam-5749	399	4	x	x	PUNCT
ejpam-5749	399	5	∈	∈	PROPN
ejpam-5749	399	6	v	v	ADP
ejpam-5749	399	7	∗	∗	NOUN
ejpam-5749	399	8	1	1	NUM
ejpam-5749	399	9	.	.	PUNCT
ejpam-5749	400	1	then	then	ADV
ejpam-5749	400	2	x	x	X
ejpam-5749	400	3	=	=	PUNCT
ejpam-5749	400	4	uv	uv	NOUN
ejpam-5749	400	5	∈	∈	PROPN
ejpam-5749	400	6	v1	v1	NOUN
ejpam-5749	400	7	with	with	ADP
ejpam-5749	400	8	v	v	NOUN
ejpam-5749	400	9	/∈	/∈	SYM
ejpam-5749	400	10	v1	v1	NOUN
ejpam-5749	400	11	∩	∩	ADJ
ejpam-5749	400	12	v	v	NOUN
ejpam-5749	400	13	(	(	PUNCT
ejpam-5749	400	14	g	g	NOUN
ejpam-5749	400	15	)	)	PUNCT
ejpam-5749	400	16	.	.	PUNCT
ejpam-5749	401	1	thus	thus	ADV
ejpam-5749	401	2	,	,	PUNCT
ejpam-5749	401	3	v	v	PROPN
ejpam-5749	401	4	∈	∈	PROPN
ejpam-5749	401	5	v0	v0	NOUN
ejpam-5749	401	6	∩	∩	X
ejpam-5749	401	7	v	v	X
ejpam-5749	401	8	(	(	PUNCT
ejpam-5749	401	9	g	g	NOUN
ejpam-5749	401	10	)	)	PUNCT
ejpam-5749	401	11	.	.	PUNCT
ejpam-5749	402	1	since	since	SCONJ
ejpam-5749	402	2	v	v	NUM
ejpam-5749	402	3	/∈	/∈	PUNCT
ejpam-5749	402	4	x	x	X
ejpam-5749	402	5	,	,	PUNCT
ejpam-5749	402	6	there	there	PRON
ejpam-5749	402	7	exists	exist	VERB
ejpam-5749	402	8	y	y	PROPN
ejpam-5749	402	9	∈	∈	PROPN
ejpam-5749	402	10	v2	v2	PROPN
ejpam-5749	402	11	∩ng(v	∩ng(v	PROPN
ejpam-5749	402	12	)	)	PUNCT
ejpam-5749	402	13	.	.	PUNCT
ejpam-5749	403	1	this	this	PRON
ejpam-5749	403	2	means	mean	VERB
ejpam-5749	403	3	that	that	SCONJ
ejpam-5749	403	4	dg	dg	AUX
ejpam-5749	403	5	◦	◦	NOUN
ejpam-5749	403	6	h(x	h(x	PROPN
ejpam-5749	403	7	,	,	PUNCT
ejpam-5749	403	8	y	y	PROPN
ejpam-5749	403	9	)	)	PUNCT
ejpam-5749	403	10	=	=	SYM
ejpam-5749	404	1	2	2	X
ejpam-5749	404	2	.	.	PUNCT
ejpam-5749	404	3	finally	finally	ADV
ejpam-5749	404	4	,	,	PUNCT
ejpam-5749	404	5	let	let	VERB
ejpam-5749	404	6	x	x	PUNCT
ejpam-5749	404	7	∈	∈	PROPN
ejpam-5749	404	8	v	v	ADP
ejpam-5749	404	9	∗	∗	NOUN
ejpam-5749	404	10	2	2	NUM
ejpam-5749	404	11	.	.	PUNCT
ejpam-5749	405	1	if	if	SCONJ
ejpam-5749	405	2	x	x	SYM
ejpam-5749	405	3	∈	∈	PROPN
ejpam-5749	405	4	x	x	NOUN
ejpam-5749	405	5	,	,	PUNCT
ejpam-5749	405	6	then	then	ADV
ejpam-5749	405	7	x	x	PART
ejpam-5749	405	8	∈	∈	PROPN
ejpam-5749	405	9	v0	v0	NOUN
ejpam-5749	405	10	∩	∩	X
ejpam-5749	405	11	v	v	X
ejpam-5749	405	12	(	(	PUNCT
ejpam-5749	405	13	g	g	NOUN
ejpam-5749	405	14	)	)	PUNCT
ejpam-5749	405	15	for	for	ADP
ejpam-5749	405	16	which	which	PRON
ejpam-5749	405	17	ux	ux	PROPN
ejpam-5749	405	18	∈	∈	PROPN
ejpam-5749	405	19	v2	v2	PROPN
ejpam-5749	405	20	,	,	PUNCT
ejpam-5749	405	21	and	and	CCONJ
ejpam-5749	405	22	there	there	PRON
ejpam-5749	405	23	exists	exist	VERB
ejpam-5749	405	24	y	y	PROPN
ejpam-5749	405	25	∈	∈	PROPN
ejpam-5749	405	26	v2	v2	PROPN
ejpam-5749	405	27	∩	∩	ADJ
ejpam-5749	405	28	v	v	NOUN
ejpam-5749	405	29	(	(	PUNCT
ejpam-5749	405	30	g	g	NOUN
ejpam-5749	405	31	)	)	PUNCT
ejpam-5749	405	32	so	so	SCONJ
ejpam-5749	405	33	that	that	SCONJ
ejpam-5749	405	34	dg	dg	VERB
ejpam-5749	405	35	◦	◦	NOUN
ejpam-5749	405	36	h(ux	h(ux	NOUN
ejpam-5749	405	37	,	,	PUNCT
ejpam-5749	405	38	y	y	NOUN
ejpam-5749	405	39	)	)	PUNCT
ejpam-5749	405	40	=	=	SYM
ejpam-5749	405	41	2	2	X
ejpam-5749	405	42	.	.	PUNCT
ejpam-5749	405	43	this	this	PRON
ejpam-5749	405	44	means	mean	VERB
ejpam-5749	405	45	that	that	SCONJ
ejpam-5749	405	46	dg	dg	AUX
ejpam-5749	405	47	◦	◦	NOUN
ejpam-5749	405	48	h(x	h(x	PROPN
ejpam-5749	405	49	,	,	PUNCT
ejpam-5749	405	50	y	y	PROPN
ejpam-5749	405	51	)	)	PUNCT
ejpam-5749	405	52	=	=	SYM
ejpam-5749	406	1	1	1	X
ejpam-5749	406	2	.	.	PUNCT
ejpam-5749	406	3	suppose	suppose	VERB
ejpam-5749	406	4	x	x	X
ejpam-5749	406	5	∈	∈	PROPN
ejpam-5749	406	6	(	(	PUNCT
ejpam-5749	406	7	v1	v1	NOUN
ejpam-5749	406	8	∪	∪	NOUN
ejpam-5749	406	9	v2	v2	NOUN
ejpam-5749	406	10	)	)	PUNCT
ejpam-5749	406	11	∩	∩	ADJ
ejpam-5749	406	12	v	v	X
ejpam-5749	406	13	(	(	PUNCT
ejpam-5749	406	14	g	g	NOUN
ejpam-5749	406	15	)	)	PUNCT
ejpam-5749	406	16	.	.	PUNCT
ejpam-5749	407	1	take	take	VERB
ejpam-5749	407	2	y	y	PROPN
ejpam-5749	407	3	∈	∈	PROPN
ejpam-5749	407	4	v	v	ADP
ejpam-5749	407	5	(	(	PUNCT
ejpam-5749	407	6	g	g	NOUN
ejpam-5749	407	7	)	)	PUNCT
ejpam-5749	407	8	such	such	ADJ
ejpam-5749	407	9	that	that	SCONJ
ejpam-5749	407	10	xy	xy	PROPN
ejpam-5749	407	11	∈	∈	PROPN
ejpam-5749	407	12	e(g	e(g	PROPN
ejpam-5749	407	13	)	)	PUNCT
ejpam-5749	407	14	.	.	PUNCT
ejpam-5749	408	1	if	if	SCONJ
ejpam-5749	408	2	y	y	PROPN
ejpam-5749	408	3	∈	∈	PROPN
ejpam-5749	408	4	v0	v0	PROPN
ejpam-5749	408	5	,	,	PUNCT
ejpam-5749	408	6	then	then	ADV
ejpam-5749	408	7	either	either	CCONJ
ejpam-5749	408	8	y	y	PROPN
ejpam-5749	408	9	∈	∈	PROPN
ejpam-5749	408	10	x	x	PUNCT
ejpam-5749	409	1	⊆	⊆	NUM
ejpam-5749	409	2	v	v	ADP
ejpam-5749	409	3	∗	∗	NOUN
ejpam-5749	409	4	2	2	NUM
ejpam-5749	409	5	or	or	CCONJ
ejpam-5749	409	6	uy	uy	PROPN
ejpam-5749	409	7	∈	∈	PROPN
ejpam-5749	409	8	v1	v1	NOUN
ejpam-5749	409	9	\	\	NOUN
ejpam-5749	409	10	w	w	ADP
ejpam-5749	409	11	⊆	⊆	NUM
ejpam-5749	409	12	v	v	ADP
ejpam-5749	409	13	∗	∗	NOUN
ejpam-5749	409	14	1	1	NUM
ejpam-5749	409	15	.	.	PUNCT
ejpam-5749	410	1	in	in	ADP
ejpam-5749	410	2	any	any	DET
ejpam-5749	410	3	case	case	NOUN
ejpam-5749	410	4	,	,	PUNCT
ejpam-5749	410	5	there	there	PRON
ejpam-5749	410	6	exists	exist	VERB
ejpam-5749	410	7	u	u	PROPN
ejpam-5749	410	8	∈	∈	PROPN
ejpam-5749	410	9	v	v	ADP
ejpam-5749	410	10	∗	∗	NOUN
ejpam-5749	410	11	1	1	NUM
ejpam-5749	410	12	∪	∪	NOUN
ejpam-5749	410	13	v	v	NOUN
ejpam-5749	410	14	∗	∗	NOUN
ejpam-5749	410	15	2	2	NUM
ejpam-5749	410	16	such	such	ADJ
ejpam-5749	410	17	that	that	SCONJ
ejpam-5749	410	18	1	1	NUM
ejpam-5749	410	19	≤	≤	NUM
ejpam-5749	410	20	dg	dg	PROPN
ejpam-5749	410	21	◦	◦	NOUN
ejpam-5749	410	22	h(x	h(x	PROPN
ejpam-5749	410	23	,	,	PUNCT
ejpam-5749	410	24	u	u	NOUN
ejpam-5749	410	25	)	)	PUNCT
ejpam-5749	410	26	≤	≤	NUM
ejpam-5749	410	27	2	2	NUM
ejpam-5749	410	28	.	.	PUNCT
ejpam-5749	411	1	then	then	ADV
ejpam-5749	411	2	since	since	SCONJ
ejpam-5749	411	3	ux	ux	PROPN
ejpam-5749	411	4	∈	∈	PROPN
ejpam-5749	411	5	v0	v0	NOUN
ejpam-5749	411	6	,	,	PUNCT
ejpam-5749	411	7	there	there	PRON
ejpam-5749	411	8	exists	exist	VERB
ejpam-5749	411	9	y	y	PROPN
ejpam-5749	411	10	∈	∈	PROPN
ejpam-5749	411	11	v2	v2	PROPN
ejpam-5749	411	12	such	such	ADJ
ejpam-5749	411	13	that	that	SCONJ
ejpam-5749	411	14	1	1	NUM
ejpam-5749	411	15	≤	≤	NUM
ejpam-5749	411	16	dg	dg	PROPN
ejpam-5749	411	17	◦	◦	NOUN
ejpam-5749	411	18	h(x	h(x	PROPN
ejpam-5749	411	19	,	,	PUNCT
ejpam-5749	411	20	y	y	PROPN
ejpam-5749	411	21	)	)	PUNCT
ejpam-5749	411	22	≤	≤	NOUN
ejpam-5749	411	23	2	2	NUM
ejpam-5749	411	24	.	.	PUNCT
ejpam-5749	412	1	on	on	ADP
ejpam-5749	412	2	the	the	DET
ejpam-5749	412	3	other	other	ADJ
ejpam-5749	412	4	hand	hand	NOUN
ejpam-5749	412	5	,	,	PUNCT
ejpam-5749	412	6	if	if	SCONJ
ejpam-5749	412	7	y	y	PROPN
ejpam-5749	412	8	∈	∈	PROPN
ejpam-5749	412	9	v1	v1	PROPN
ejpam-5749	412	10	∪	∪	NOUN
ejpam-5749	412	11	v2	v2	NOUN
ejpam-5749	412	12	,	,	PUNCT
ejpam-5749	412	13	then	then	ADV
ejpam-5749	412	14	y	y	PROPN
ejpam-5749	412	15	∈	∈	PROPN
ejpam-5749	412	16	v	v	ADP
ejpam-5749	412	17	∗	∗	NOUN
ejpam-5749	412	18	2	2	NUM
ejpam-5749	412	19	and	and	CCONJ
ejpam-5749	412	20	dg	dg	NOUN
ejpam-5749	412	21	◦	◦	NOUN
ejpam-5749	412	22	h(x	h(x	PROPN
ejpam-5749	412	23	,	,	PUNCT
ejpam-5749	412	24	y	y	PROPN
ejpam-5749	412	25	)	)	PUNCT
ejpam-5749	412	26	=	=	SYM
ejpam-5749	413	1	1	1	X
ejpam-5749	413	2	.	.	PUNCT
ejpam-5749	414	1	the	the	DET
ejpam-5749	414	2	above	above	ADJ
ejpam-5749	414	3	arguments	argument	NOUN
ejpam-5749	414	4	show	show	VERB
ejpam-5749	414	5	that	that	SCONJ
ejpam-5749	414	6	g	g	PROPN
ejpam-5749	414	7	∈	∈	PROPN
ejpam-5749	414	8	srdf	srdf	NOUN
ejpam-5749	414	9	(	(	PUNCT
ejpam-5749	414	10	g	g	PROPN
ejpam-5749	414	11	◦	◦	NOUN
ejpam-5749	414	12	h	h	NOUN
ejpam-5749	414	13	)	)	PUNCT
ejpam-5749	414	14	.	.	PUNCT
ejpam-5749	415	1	and	and	CCONJ
ejpam-5749	415	2	since	since	SCONJ
ejpam-5749	415	3	v	v	NOUN
ejpam-5749	415	4	(	(	PUNCT
ejpam-5749	415	5	g	g	NOUN
ejpam-5749	415	6	)	)	PUNCT
ejpam-5749	415	7	⊆	⊆	NUM
ejpam-5749	415	8	v	v	ADP
ejpam-5749	415	9	∗	∗	NOUN
ejpam-5749	415	10	0	0	NUM
ejpam-5749	415	11	,	,	PUNCT
ejpam-5749	415	12	v	v	NOUN
ejpam-5749	415	13	∗	∗	NOUN
ejpam-5749	415	14	2	2	NUM
ejpam-5749	415	15	is	be	AUX
ejpam-5749	415	16	a	a	DET
ejpam-5749	415	17	dominating	dominating	NOUN
ejpam-5749	415	18	set	set	NOUN
ejpam-5749	415	19	of	of	ADP
ejpam-5749	415	20	g.	g.	PROPN
ejpam-5749	415	21	moreover	moreover	ADV
ejpam-5749	415	22	,	,	PUNCT
ejpam-5749	415	23	since	since	SCONJ
ejpam-5749	415	24	x	x	X
ejpam-5749	415	25	=	=	PUNCT
ejpam-5749	415	26	v2	v2	PROPN
ejpam-5749	415	27	\	\	NOUN
ejpam-5749	415	28	(	(	PUNCT
ejpam-5749	415	29	v2	v2	PROPN
ejpam-5749	415	30	∩	∩	ADJ
ejpam-5749	415	31	v	v	NOUN
ejpam-5749	415	32	(	(	PUNCT
ejpam-5749	415	33	g	g	NOUN
ejpam-5749	415	34	)	)	PUNCT
ejpam-5749	415	35	and	and	CCONJ
ejpam-5749	415	36	|w	|w	ADJ
ejpam-5749	416	1	|	|	NOUN
ejpam-5749	416	2	=	=	PUNCT
ejpam-5749	416	3	|v1	|v1	PROPN
ejpam-5749	416	4	∩	∩	PROPN
ejpam-5749	416	5	v	v	X
ejpam-5749	416	6	(	(	PUNCT
ejpam-5749	416	7	g)|	g)|	PROPN
ejpam-5749	416	8	,	,	PUNCT
ejpam-5749	416	9	ωg	ωg	NOUN
ejpam-5749	416	10	◦	◦	NOUN
ejpam-5749	416	11	h(g	h(g	NOUN
ejpam-5749	416	12	)	)	PUNCT
ejpam-5749	416	13	=	=	SYM
ejpam-5749	416	14	|v	|v	PROPN
ejpam-5749	416	15	∗	∗	NOUN
ejpam-5749	416	16	1	1	NUM
ejpam-5749	416	17	|+	|+	NOUN
ejpam-5749	416	18	2|v	2|v	PROPN
ejpam-5749	416	19	∗	∗	NOUN
ejpam-5749	416	20	2	2	NUM
ejpam-5749	416	21	|	|	NOUN
ejpam-5749	416	22	=	=	SYM
ejpam-5749	416	23	|v1|	|v1|	NOUN
ejpam-5749	416	24	−	−	PROPN
ejpam-5749	416	25	2|v1	2|v1	NUM
ejpam-5749	416	26	∩	∩	X
ejpam-5749	416	27	v	v	X
ejpam-5749	416	28	(	(	PUNCT
ejpam-5749	416	29	g)|+	g)|+	PROPN
ejpam-5749	416	30	2[|v2|+	2[|v2|+	NUM
ejpam-5749	416	31	|v1	|v1	PROPN
ejpam-5749	416	32	∩	∩	PROPN
ejpam-5749	416	33	v	v	X
ejpam-5749	416	34	(	(	PUNCT
ejpam-5749	416	35	g)|	g)|	NOUN
ejpam-5749	416	36	]	]	PUNCT
ejpam-5749	416	37	=	=	PUNCT
ejpam-5749	416	38	|v1|+	|v1|+	PRON
ejpam-5749	416	39	2|v2|	2|v2|	NUM
ejpam-5749	416	40	=	=	SYM
ejpam-5749	416	41	γt2r(g	γt2r(g	PRON
ejpam-5749	416	42	◦	◦	NOUN
ejpam-5749	416	43	h	h	NOUN
ejpam-5749	416	44	)	)	PUNCT
ejpam-5749	416	45	.	.	PUNCT
ejpam-5749	417	1	thus	thus	ADV
ejpam-5749	417	2	,	,	PUNCT
ejpam-5749	417	3	n+	n+	PUNCT
ejpam-5749	417	4	γ(g	γ(g	NOUN
ejpam-5749	417	5	)	)	PUNCT
ejpam-5749	417	6	≤	≤	NOUN
ejpam-5749	417	7	n+	n+	ADP
ejpam-5749	417	8	|v	|v	PROPN
ejpam-5749	417	9	∗	∗	NOUN
ejpam-5749	417	10	2	2	NUM
ejpam-5749	417	11	|	|	ADV
ejpam-5749	417	12	=	=	SYM
ejpam-5749	417	13	|v	|v	PROPN
ejpam-5749	417	14	∗	∗	NOUN
ejpam-5749	417	15	1	1	NUM
ejpam-5749	417	16	|+	|+	NOUN
ejpam-5749	417	17	2|v	2|v	PROPN
ejpam-5749	417	18	∗	∗	NOUN
ejpam-5749	417	19	2	2	NUM
ejpam-5749	417	20	|	|	ADV
ejpam-5749	417	21	=	=	SYM
ejpam-5749	417	22	γt2r(g	γt2r(g	NUM
ejpam-5749	417	23	◦	◦	NOUN
ejpam-5749	417	24	h	h	NOUN
ejpam-5749	417	25	)	)	PUNCT
ejpam-5749	417	26	.	.	PUNCT
ejpam-5749	418	1	this	this	PRON
ejpam-5749	418	2	proves	prove	VERB
ejpam-5749	418	3	(	(	PUNCT
ejpam-5749	418	4	i	i	NOUN
ejpam-5749	418	5	)	)	PUNCT
ejpam-5749	418	6	.	.	PUNCT
ejpam-5749	419	1	to	to	PART
ejpam-5749	419	2	prove	prove	VERB
ejpam-5749	419	3	(	(	PUNCT
ejpam-5749	419	4	ii	ii	NOUN
ejpam-5749	419	5	)	)	PUNCT
ejpam-5749	419	6	,	,	PUNCT
ejpam-5749	419	7	since	since	SCONJ
ejpam-5749	419	8	f	f	PROPN
ejpam-5749	419	9	=	=	PUNCT
ejpam-5749	419	10	(	(	PUNCT
ejpam-5749	419	11	∪v∈v	∪v∈v	X
ejpam-5749	419	12	(	(	PUNCT
ejpam-5749	419	13	g)v	g)v	X
ejpam-5749	419	14	(	(	PUNCT
ejpam-5749	419	15	hv),∅	hv),∅	NOUN
ejpam-5749	419	16	,	,	PUNCT
ejpam-5749	419	17	v	v	ADJ
ejpam-5749	419	18	(	(	PUNCT
ejpam-5749	419	19	g	g	NOUN
ejpam-5749	419	20	)	)	PUNCT
ejpam-5749	419	21	)	)	PUNCT
ejpam-5749	420	1	∈	∈	NOUN
ejpam-5749	420	2	srdf	srdf	NOUN
ejpam-5749	420	3	(	(	PUNCT
ejpam-5749	420	4	g	g	NOUN
ejpam-5749	420	5	◦	◦	NOUN
ejpam-5749	420	6	h	h	NOUN
ejpam-5749	420	7	)	)	PUNCT
ejpam-5749	420	8	,	,	PUNCT
ejpam-5749	420	9	γt2r(g	γt2r(g	NOUN
ejpam-5749	420	10	◦	◦	NOUN
ejpam-5749	420	11	h	h	NOUN
ejpam-5749	420	12	)	)	PUNCT
ejpam-5749	420	13	≤	≤	NUM
ejpam-5749	420	14	2n	2n	NUM
ejpam-5749	420	15	.	.	PUNCT
ejpam-5749	421	1	to	to	PART
ejpam-5749	421	2	get	get	VERB
ejpam-5749	421	3	the	the	DET
ejpam-5749	421	4	other	other	ADJ
ejpam-5749	421	5	inequality	inequality	NOUN
ejpam-5749	421	6	,	,	PUNCT
ejpam-5749	421	7	let	let	VERB
ejpam-5749	421	8	f	f	PROPN
ejpam-5749	421	9	=	=	SYM
ejpam-5749	421	10	(	(	PUNCT
ejpam-5749	421	11	v0	v0	PROPN
ejpam-5749	421	12	,	,	PUNCT
ejpam-5749	421	13	v1	v1	NOUN
ejpam-5749	421	14	,	,	PUNCT
ejpam-5749	421	15	v2	v2	NOUN
ejpam-5749	421	16	)	)	PUNCT
ejpam-5749	421	17	∈	∈	NOUN
ejpam-5749	421	18	srdf	srdf	NOUN
ejpam-5749	421	19	(	(	PUNCT
ejpam-5749	421	20	g	g	PROPN
ejpam-5749	421	21	◦	◦	NOUN
ejpam-5749	421	22	h	h	NOUN
ejpam-5749	421	23	)	)	PUNCT
ejpam-5749	421	24	.	.	PUNCT
ejpam-5749	422	1	for	for	ADP
ejpam-5749	422	2	each	each	DET
ejpam-5749	422	3	v	v	NOUN
ejpam-5749	422	4	∈	∈	PROPN
ejpam-5749	422	5	v2	v2	NOUN
ejpam-5749	422	6	∩v	∩v	NOUN
ejpam-5749	422	7	(	(	PUNCT
ejpam-5749	422	8	g	g	NOUN
ejpam-5749	422	9	)	)	PUNCT
ejpam-5749	422	10	,	,	PUNCT
ejpam-5749	422	11	clearly	clearly	ADV
ejpam-5749	422	12	f(v	f(v	PROPN
ejpam-5749	422	13	(	(	PUNCT
ejpam-5749	422	14	hv	hv	NOUN
ejpam-5749	422	15	+	+	PROPN
ejpam-5749	422	16	v	v	NOUN
ejpam-5749	422	17	)	)	PUNCT
ejpam-5749	422	18	≥	≥	NOUN
ejpam-5749	422	19	2	2	NUM
ejpam-5749	422	20	.	.	X
ejpam-5749	423	1	for	for	ADP
ejpam-5749	423	2	each	each	DET
ejpam-5749	423	3	v	v	X
ejpam-5749	423	4	∈	∈	NOUN
ejpam-5749	423	5	(	(	PUNCT
ejpam-5749	423	6	v0	v0	NOUN
ejpam-5749	423	7	∪	∪	X
ejpam-5749	423	8	v1	v1	NOUN
ejpam-5749	423	9	)	)	PUNCT
ejpam-5749	423	10	∩	∩	ADJ
ejpam-5749	423	11	v	v	X
ejpam-5749	423	12	(	(	PUNCT
ejpam-5749	423	13	g	g	NOUN
ejpam-5749	423	14	)	)	PUNCT
ejpam-5749	423	15	,	,	PUNCT
ejpam-5749	423	16	since	since	SCONJ
ejpam-5749	423	17	f	f	PROPN
ejpam-5749	423	18	|hv	|hv	PROPN
ejpam-5749	423	19	∈	∈	PROPN
ejpam-5749	423	20	rdf	rdf	NOUN
ejpam-5749	423	21	(	(	PUNCT
ejpam-5749	423	22	hv	hv	NOUN
ejpam-5749	423	23	)	)	PUNCT
ejpam-5749	423	24	,	,	PUNCT
ejpam-5749	423	25	f(v	f(v	PROPN
ejpam-5749	423	26	(	(	PUNCT
ejpam-5749	423	27	hv	hv	NOUN
ejpam-5749	423	28	+	+	PROPN
ejpam-5749	423	29	v	v	NOUN
ejpam-5749	423	30	)	)	PUNCT
ejpam-5749	423	31	)	)	PUNCT
ejpam-5749	423	32	≥	≥	NOUN
ejpam-5749	424	1	2	2	NUM
ejpam-5749	424	2	.	.	PUNCT
ejpam-5749	424	3	thus	thus	ADV
ejpam-5749	424	4	,	,	PUNCT
ejpam-5749	424	5	ωg	ωg	VERB
ejpam-5749	424	6	◦	◦	NOUN
ejpam-5749	424	7	h(f	h(f	NOUN
ejpam-5749	424	8	)	)	PUNCT
ejpam-5749	424	9	≥	≥	PROPN
ejpam-5749	424	10	∑	∑	PUNCT
ejpam-5749	424	11	v∈v	v∈v	PROPN
ejpam-5749	424	12	(	(	PUNCT
ejpam-5749	424	13	g	g	NOUN
ejpam-5749	424	14	)	)	PUNCT
ejpam-5749	424	15	f(v	f(v	PROPN
ejpam-5749	424	16	(	(	PUNCT
ejpam-5749	424	17	hv	hv	NOUN
ejpam-5749	424	18	+	+	PROPN
ejpam-5749	424	19	v	v	NOUN
ejpam-5749	424	20	)	)	PUNCT
ejpam-5749	424	21	)	)	PUNCT
ejpam-5749	424	22	≥	≥	NOUN
ejpam-5749	424	23	2n	2n	NUM
ejpam-5749	424	24	.	.	PUNCT
ejpam-5749	425	1	3.3	3.3	NUM
ejpam-5749	425	2	.	.	PUNCT
ejpam-5749	426	1	in	in	ADP
ejpam-5749	426	2	the	the	DET
ejpam-5749	426	3	complementary	complementary	ADJ
ejpam-5749	426	4	prism	prism	NOUN
ejpam-5749	426	5	of	of	ADP
ejpam-5749	426	6	graphs	graph	NOUN
ejpam-5749	426	7	proposition	proposition	NOUN
ejpam-5749	426	8	13	13	NUM
ejpam-5749	426	9	.	.	PUNCT
ejpam-5749	427	1	let	let	VERB
ejpam-5749	427	2	g	g	PRON
ejpam-5749	427	3	be	be	AUX
ejpam-5749	427	4	a	a	DET
ejpam-5749	427	5	graph	graph	NOUN
ejpam-5749	427	6	of	of	ADP
ejpam-5749	427	7	order	order	NOUN
ejpam-5749	427	8	n.	n.	PROPN
ejpam-5749	427	9	then	then	ADV
ejpam-5749	427	10	b.	b.	PROPN
ejpam-5749	427	11	f.	f.	PROPN
ejpam-5749	427	12	bullang	bullang	PROPN
ejpam-5749	427	13	et	et	PROPN
ejpam-5749	427	14	al	al	PROPN
ejpam-5749	427	15	.	.	PUNCT
ejpam-5749	427	16	/	/	SYM
ejpam-5749	427	17	eur	eur	PROPN
ejpam-5749	427	18	.	.	PUNCT
ejpam-5749	428	1	j.	j.	PROPN
ejpam-5749	428	2	pure	pure	PROPN
ejpam-5749	428	3	appl	appl	PROPN
ejpam-5749	428	4	.	.	PROPN
ejpam-5749	428	5	math	math	PROPN
ejpam-5749	428	6	,	,	PUNCT
ejpam-5749	428	7	18	18	NUM
ejpam-5749	428	8	(	(	PUNCT
ejpam-5749	428	9	1	1	NUM
ejpam-5749	428	10	)	)	PUNCT
ejpam-5749	428	11	(	(	PUNCT
ejpam-5749	428	12	2025	2025	NUM
ejpam-5749	428	13	)	)	PUNCT
ejpam-5749	428	14	,	,	PUNCT
ejpam-5749	428	15	5749	5749	NUM
ejpam-5749	428	16	13	13	NUM
ejpam-5749	428	17	of	of	ADP
ejpam-5749	428	18	15	15	NUM
ejpam-5749	428	19	(	(	PUNCT
ejpam-5749	428	20	i	i	NOUN
ejpam-5749	428	21	)	)	PUNCT
ejpam-5749	428	22	γt2r(gg	γt2r(gg	ADJ
ejpam-5749	428	23	)	)	PUNCT
ejpam-5749	429	1	=	=	SYM
ejpam-5749	429	2	2	2	NUM
ejpam-5749	429	3	if	if	SCONJ
ejpam-5749	429	4	and	and	CCONJ
ejpam-5749	429	5	only	only	ADV
ejpam-5749	429	6	if	if	SCONJ
ejpam-5749	429	7	g	g	PROPN
ejpam-5749	429	8	=	=	PROPN
ejpam-5749	429	9	k1	k1	PROPN
ejpam-5749	429	10	.	.	PUNCT
ejpam-5749	429	11	(	(	PUNCT
ejpam-5749	429	12	ii	ii	NOUN
ejpam-5749	429	13	)	)	PUNCT
ejpam-5749	429	14	γt2r(gg	γt2r(gg	ADJ
ejpam-5749	429	15	)	)	PUNCT
ejpam-5749	430	1	=	=	SYM
ejpam-5749	430	2	3	3	NUM
ejpam-5749	430	3	if	if	SCONJ
ejpam-5749	430	4	and	and	CCONJ
ejpam-5749	430	5	only	only	ADV
ejpam-5749	430	6	if	if	SCONJ
ejpam-5749	430	7	g	g	PROPN
ejpam-5749	430	8	∈	∈	PROPN
ejpam-5749	430	9	{	{	PUNCT
ejpam-5749	430	10	k2,k2	k2,k2	PROPN
ejpam-5749	430	11	}	}	PUNCT
ejpam-5749	430	12	.	.	PUNCT
ejpam-5749	431	1	(	(	PUNCT
ejpam-5749	431	2	iii	iii	X
ejpam-5749	431	3	)	)	PUNCT
ejpam-5749	431	4	γt2r(gg	γt2r(gg	ADJ
ejpam-5749	431	5	)	)	PUNCT
ejpam-5749	432	1	=	=	SYM
ejpam-5749	432	2	4	4	NUM
ejpam-5749	432	3	if	if	SCONJ
ejpam-5749	432	4	and	and	CCONJ
ejpam-5749	432	5	only	only	ADV
ejpam-5749	432	6	if	if	SCONJ
ejpam-5749	432	7	either	either	CCONJ
ejpam-5749	432	8	(	(	PUNCT
ejpam-5749	432	9	a	a	X
ejpam-5749	432	10	)	)	PUNCT
ejpam-5749	432	11	g	g	PROPN
ejpam-5749	432	12	∈	∈	PROPN
ejpam-5749	432	13	{	{	PUNCT
ejpam-5749	432	14	k3,k3	k3,k3	PROPN
ejpam-5749	432	15	}	}	PUNCT
ejpam-5749	432	16	;	;	PUNCT
ejpam-5749	432	17	or	or	CCONJ
ejpam-5749	432	18	(	(	PUNCT
ejpam-5749	432	19	b	b	NOUN
ejpam-5749	432	20	)	)	PUNCT
ejpam-5749	432	21	g	g	PROPN
ejpam-5749	432	22	̸=	̸=	PROPN
ejpam-5749	432	23	k2	k2	NOUN
ejpam-5749	432	24	and	and	CCONJ
ejpam-5749	432	25	g	g	PROPN
ejpam-5749	432	26	(	(	PUNCT
ejpam-5749	432	27	resp	resp	NOUN
ejpam-5749	432	28	.	.	PUNCT
ejpam-5749	433	1	g	g	PROPN
ejpam-5749	433	2	̸=	̸=	PROPN
ejpam-5749	433	3	k2	k2	NOUN
ejpam-5749	433	4	and	and	CCONJ
ejpam-5749	433	5	g	g	NOUN
ejpam-5749	433	6	)	)	PUNCT
ejpam-5749	433	7	has	have	AUX
ejpam-5749	433	8	vertices	vertice	VERB
ejpam-5749	433	9	u	u	NOUN
ejpam-5749	433	10	and	and	CCONJ
ejpam-5749	433	11	v	v	NOUN
ejpam-5749	433	12	for	for	ADP
ejpam-5749	433	13	which	which	PRON
ejpam-5749	433	14	ng[v	ng[v	PROPN
ejpam-5749	433	15	]	]	X
ejpam-5749	433	16	=	=	SYM
ejpam-5749	433	17	v	v	X
ejpam-5749	433	18	(	(	PUNCT
ejpam-5749	433	19	g	g	NOUN
ejpam-5749	433	20	)	)	PUNCT
ejpam-5749	433	21	and	and	CCONJ
ejpam-5749	433	22	ng[u	ng[u	PROPN
ejpam-5749	433	23	]	]	X
ejpam-5749	433	24	=	=	SYM
ejpam-5749	433	25	{	{	PUNCT
ejpam-5749	433	26	u	u	NOUN
ejpam-5749	433	27	,	,	PUNCT
ejpam-5749	433	28	v	v	NOUN
ejpam-5749	433	29	}	}	PUNCT
ejpam-5749	433	30	(	(	PUNCT
ejpam-5749	433	31	resp	resp	NOUN
ejpam-5749	433	32	.	.	PUNCT
ejpam-5749	434	1	ng[v	ng[v	PUNCT
ejpam-5749	434	2	]	]	X
ejpam-5749	434	3	=	=	SYM
ejpam-5749	434	4	v	v	X
ejpam-5749	434	5	(	(	PUNCT
ejpam-5749	434	6	g	g	NOUN
ejpam-5749	434	7	)	)	PUNCT
ejpam-5749	434	8	and	and	CCONJ
ejpam-5749	434	9	ng[u	ng[u	PROPN
ejpam-5749	434	10	]	]	X
ejpam-5749	434	11	=	=	SYM
ejpam-5749	434	12	{	{	PUNCT
ejpam-5749	434	13	u	u	NOUN
ejpam-5749	434	14	,	,	PUNCT
ejpam-5749	434	15	v	v	NOUN
ejpam-5749	434	16	}	}	PUNCT
ejpam-5749	434	17	)	)	PUNCT
ejpam-5749	434	18	.	.	PUNCT
ejpam-5749	435	1	proof	proof	NOUN
ejpam-5749	435	2	.	.	PUNCT
ejpam-5749	436	1	by	by	ADP
ejpam-5749	436	2	proposition	proposition	NOUN
ejpam-5749	436	3	5	5	NUM
ejpam-5749	436	4	,	,	PUNCT
ejpam-5749	436	5	γt2r(gg	γt2r(gg	ADJ
ejpam-5749	436	6	)	)	PUNCT
ejpam-5749	436	7	=	=	SYM
ejpam-5749	436	8	2	2	NUM
ejpam-5749	436	9	if	if	SCONJ
ejpam-5749	436	10	and	and	CCONJ
ejpam-5749	436	11	only	only	ADV
ejpam-5749	436	12	if	if	SCONJ
ejpam-5749	436	13	gg	gg	PROPN
ejpam-5749	436	14	=	=	SYM
ejpam-5749	436	15	k2	k2	PROPN
ejpam-5749	436	16	.	.	PUNCT
ejpam-5749	437	1	thus	thus	ADV
ejpam-5749	437	2	,	,	PUNCT
ejpam-5749	437	3	(	(	PUNCT
ejpam-5749	437	4	i	i	NOUN
ejpam-5749	437	5	)	)	PUNCT
ejpam-5749	437	6	holds	hold	VERB
ejpam-5749	437	7	.	.	PUNCT
ejpam-5749	437	8	suppose	suppose	VERB
ejpam-5749	437	9	that	that	SCONJ
ejpam-5749	437	10	γt2r(gg	γt2r(gg	NOUN
ejpam-5749	437	11	)	)	PUNCT
ejpam-5749	437	12	=	=	SYM
ejpam-5749	438	1	3	3	X
ejpam-5749	438	2	.	.	PUNCT
ejpam-5749	438	3	since	since	SCONJ
ejpam-5749	438	4	gg	gg	PROPN
ejpam-5749	438	5	̸=	̸=	PROPN
ejpam-5749	438	6	k2	k2	NOUN
ejpam-5749	438	7	,	,	PUNCT
ejpam-5749	438	8	γ(gg	γ(gg	NUM
ejpam-5749	438	9	)	)	PUNCT
ejpam-5749	438	10	≥	≥	NOUN
ejpam-5749	438	11	2	2	NUM
ejpam-5749	438	12	by	by	ADP
ejpam-5749	438	13	(	(	PUNCT
ejpam-5749	438	14	i	i	NOUN
ejpam-5749	438	15	)	)	PUNCT
ejpam-5749	438	16	.	.	PUNCT
ejpam-5749	439	1	by	by	ADP
ejpam-5749	439	2	proposition	proposition	NOUN
ejpam-5749	439	3	6	6	NUM
ejpam-5749	439	4	,	,	PUNCT
ejpam-5749	439	5	gg	gg	PROPN
ejpam-5749	439	6	has	have	AUX
ejpam-5749	439	7	vertices	vertice	VERB
ejpam-5749	439	8	u	u	NOUN
ejpam-5749	439	9	and	and	CCONJ
ejpam-5749	439	10	v	v	NOUN
ejpam-5749	439	11	for	for	ADP
ejpam-5749	439	12	which	which	PRON
ejpam-5749	439	13	ngg[v	ngg[v	X
ejpam-5749	439	14	]	]	PUNCT
ejpam-5749	439	15	=	=	SYM
ejpam-5749	439	16	v	v	X
ejpam-5749	439	17	(	(	PUNCT
ejpam-5749	439	18	gg	gg	NOUN
ejpam-5749	439	19	)	)	PUNCT
ejpam-5749	439	20	\	\	NOUN
ejpam-5749	439	21	{	{	PUNCT
ejpam-5749	439	22	u	u	NOUN
ejpam-5749	439	23	}	}	PUNCT
ejpam-5749	439	24	and	and	CCONJ
ejpam-5749	439	25	dgg(u	dgg(u	PROPN
ejpam-5749	439	26	,	,	PUNCT
ejpam-5749	439	27	v	v	NOUN
ejpam-5749	439	28	)	)	PUNCT
ejpam-5749	440	1	=	=	SYM
ejpam-5749	440	2	2	2	X
ejpam-5749	440	3	.	.	PUNCT
ejpam-5749	441	1	this	this	PRON
ejpam-5749	441	2	is	be	AUX
ejpam-5749	441	3	possible	possible	ADJ
ejpam-5749	441	4	only	only	ADV
ejpam-5749	441	5	if	if	SCONJ
ejpam-5749	441	6	gg	gg	PROPN
ejpam-5749	441	7	=	=	SYM
ejpam-5749	441	8	p4	p4	ADJ
ejpam-5749	441	9	or	or	CCONJ
ejpam-5749	441	10	equivalently	equivalently	ADV
ejpam-5749	441	11	,	,	PUNCT
ejpam-5749	441	12	g	g	PROPN
ejpam-5749	441	13	∈	∈	PROPN
ejpam-5749	441	14	{	{	PUNCT
ejpam-5749	441	15	k2,k2	k2,k2	PROPN
ejpam-5749	441	16	}	}	PUNCT
ejpam-5749	441	17	.	.	PUNCT
ejpam-5749	442	1	the	the	DET
ejpam-5749	442	2	converse	converse	NOUN
ejpam-5749	442	3	of	of	ADP
ejpam-5749	442	4	(	(	PUNCT
ejpam-5749	442	5	ii	ii	NOUN
ejpam-5749	442	6	)	)	PUNCT
ejpam-5749	442	7	is	be	AUX
ejpam-5749	442	8	immediate	immediate	ADJ
ejpam-5749	442	9	.	.	PUNCT
ejpam-5749	443	1	suppose	suppose	VERB
ejpam-5749	443	2	that	that	SCONJ
ejpam-5749	443	3	γt2r(gg	γt2r(gg	NOUN
ejpam-5749	443	4	)	)	PUNCT
ejpam-5749	443	5	=	=	PUNCT
ejpam-5749	444	1	4	4	X
ejpam-5749	444	2	.	.	X
ejpam-5749	445	1	in	in	ADP
ejpam-5749	445	2	view	view	NOUN
ejpam-5749	445	3	of	of	ADP
ejpam-5749	445	4	proposition	proposition	NOUN
ejpam-5749	445	5	7	7	NUM
ejpam-5749	445	6	,	,	PUNCT
ejpam-5749	445	7	we	we	PRON
ejpam-5749	445	8	consider	consider	VERB
ejpam-5749	445	9	two	two	NUM
ejpam-5749	445	10	cases	case	NOUN
ejpam-5749	445	11	:	:	PUNCT
ejpam-5749	445	12	case	case	NOUN
ejpam-5749	445	13	1	1	NUM
ejpam-5749	445	14	:	:	PUNCT
ejpam-5749	445	15	suppose	suppose	VERB
ejpam-5749	445	16	that	that	SCONJ
ejpam-5749	445	17	γt2(gg	γt2(gg	PROPN
ejpam-5749	445	18	)	)	PUNCT
ejpam-5749	445	19	=	=	SYM
ejpam-5749	445	20	2	2	NUM
ejpam-5749	445	21	,	,	PUNCT
ejpam-5749	445	22	and	and	CCONJ
ejpam-5749	445	23	let	let	VERB
ejpam-5749	445	24	{	{	PUNCT
ejpam-5749	445	25	u	u	NOUN
ejpam-5749	445	26	,	,	PUNCT
ejpam-5749	445	27	v	v	NOUN
ejpam-5749	445	28	}	}	PUNCT
ejpam-5749	445	29	be	be	AUX
ejpam-5749	445	30	a	a	DET
ejpam-5749	445	31	γt2	γt2	NOUN
ejpam-5749	445	32	-	-	PUNCT
ejpam-5749	445	33	set	set	NOUN
ejpam-5749	445	34	of	of	ADP
ejpam-5749	445	35	gg	gg	PROPN
ejpam-5749	445	36	.	.	PUNCT
ejpam-5749	446	1	since	since	SCONJ
ejpam-5749	446	2	gg	gg	PROPN
ejpam-5749	446	3	̸=	̸=	PROPN
ejpam-5749	446	4	k2	k2	NOUN
ejpam-5749	446	5	,	,	PUNCT
ejpam-5749	446	6	if	if	SCONJ
ejpam-5749	446	7	dgg(u	dgg(u	X
ejpam-5749	446	8	,	,	PUNCT
ejpam-5749	446	9	v	v	NOUN
ejpam-5749	446	10	)	)	PUNCT
ejpam-5749	446	11	=	=	SYM
ejpam-5749	446	12	1	1	NUM
ejpam-5749	446	13	,	,	PUNCT
ejpam-5749	446	14	then	then	ADV
ejpam-5749	446	15	gg	gg	PROPN
ejpam-5749	446	16	=	=	SYM
ejpam-5749	446	17	p4	p4	ADJ
ejpam-5749	446	18	,	,	PUNCT
ejpam-5749	446	19	a	a	DET
ejpam-5749	446	20	contradiction	contradiction	NOUN
ejpam-5749	446	21	.	.	PUNCT
ejpam-5749	447	1	thus	thus	ADV
ejpam-5749	447	2	,	,	PUNCT
ejpam-5749	447	3	dgg(u	dgg(u	PROPN
ejpam-5749	447	4	,	,	PUNCT
ejpam-5749	447	5	v	v	NOUN
ejpam-5749	447	6	)	)	PUNCT
ejpam-5749	447	7	=	=	SYM
ejpam-5749	447	8	2	2	X
ejpam-5749	447	9	.	.	X
ejpam-5749	447	10	assume	assume	VERB
ejpam-5749	447	11	v	v	ADP
ejpam-5749	447	12	∈	∈	PROPN
ejpam-5749	447	13	v	v	NOUN
ejpam-5749	447	14	(	(	PUNCT
ejpam-5749	447	15	g	g	NOUN
ejpam-5749	447	16	)	)	PUNCT
ejpam-5749	447	17	.	.	PUNCT
ejpam-5749	448	1	necessarily	necessarily	ADV
ejpam-5749	448	2	,	,	PUNCT
ejpam-5749	448	3	u	u	PROPN
ejpam-5749	448	4	∈	∈	PROPN
ejpam-5749	448	5	v	v	NOUN
ejpam-5749	448	6	(	(	PUNCT
ejpam-5749	448	7	g	g	NOUN
ejpam-5749	448	8	)	)	PUNCT
ejpam-5749	448	9	and	and	CCONJ
ejpam-5749	448	10	u	u	NOUN
ejpam-5749	448	11	̸=	̸=	PROPN
ejpam-5749	448	12	v.	v.	CCONJ
ejpam-5749	448	13	since	since	SCONJ
ejpam-5749	448	14	{	{	PUNCT
ejpam-5749	448	15	u	u	NOUN
ejpam-5749	448	16	,	,	PUNCT
ejpam-5749	448	17	v	v	NOUN
ejpam-5749	448	18	}	}	PUNCT
ejpam-5749	448	19	is	be	AUX
ejpam-5749	448	20	a	a	DET
ejpam-5749	448	21	dominating	dominating	NOUN
ejpam-5749	448	22	set	set	NOUN
ejpam-5749	448	23	of	of	ADP
ejpam-5749	448	24	gg	gg	PROPN
ejpam-5749	448	25	,	,	PUNCT
ejpam-5749	448	26	ng[v	ng[v	X
ejpam-5749	448	27	]	]	PUNCT
ejpam-5749	448	28	=	=	SYM
ejpam-5749	448	29	v	v	X
ejpam-5749	448	30	(	(	PUNCT
ejpam-5749	448	31	g	g	NOUN
ejpam-5749	448	32	)	)	PUNCT
ejpam-5749	448	33	and	and	CCONJ
ejpam-5749	448	34	ng[u	ng[u	PROPN
ejpam-5749	448	35	]	]	X
ejpam-5749	448	36	=	=	SYM
ejpam-5749	448	37	v	v	X
ejpam-5749	448	38	(	(	PUNCT
ejpam-5749	448	39	g	g	NOUN
ejpam-5749	448	40	)	)	PUNCT
ejpam-5749	448	41	\	\	NOUN
ejpam-5749	448	42	{	{	PUNCT
ejpam-5749	448	43	v	v	NOUN
ejpam-5749	448	44	}	}	PUNCT
ejpam-5749	448	45	or	or	CCONJ
ejpam-5749	448	46	equivalently	equivalently	ADV
ejpam-5749	448	47	,	,	PUNCT
ejpam-5749	448	48	ng[u	ng[u	PROPN
ejpam-5749	448	49	]	]	X
ejpam-5749	448	50	=	=	SYM
ejpam-5749	448	51	{	{	PUNCT
ejpam-5749	448	52	u	u	NOUN
ejpam-5749	448	53	,	,	PUNCT
ejpam-5749	448	54	v	v	NOUN
ejpam-5749	448	55	}	}	PUNCT
ejpam-5749	448	56	.	.	PUNCT
ejpam-5749	449	1	case	case	NOUN
ejpam-5749	449	2	2	2	NUM
ejpam-5749	449	3	:	:	PUNCT
ejpam-5749	449	4	suppose	suppose	VERB
ejpam-5749	449	5	that	that	SCONJ
ejpam-5749	449	6	γt2(gg	γt2(gg	PROPN
ejpam-5749	449	7	)	)	PUNCT
ejpam-5749	449	8	=	=	SYM
ejpam-5749	449	9	3	3	NUM
ejpam-5749	449	10	and	and	CCONJ
ejpam-5749	449	11	u	u	NOUN
ejpam-5749	449	12	,	,	PUNCT
ejpam-5749	449	13	v	v	NOUN
ejpam-5749	449	14	and	and	CCONJ
ejpam-5749	449	15	w	w	NOUN
ejpam-5749	449	16	are	be	AUX
ejpam-5749	449	17	vertices	vertex	NOUN
ejpam-5749	449	18	of	of	ADP
ejpam-5749	449	19	gg	gg	NOUN
ejpam-5749	449	20	for	for	ADP
ejpam-5749	449	21	which	which	PRON
ejpam-5749	449	22	the	the	DET
ejpam-5749	449	23	following	follow	VERB
ejpam-5749	449	24	hold	hold	NOUN
ejpam-5749	449	25	:	:	PUNCT
ejpam-5749	449	26	(	(	PUNCT
ejpam-5749	449	27	a	a	X
ejpam-5749	449	28	)	)	PUNCT
ejpam-5749	449	29	v	v	NOUN
ejpam-5749	449	30	(	(	PUNCT
ejpam-5749	449	31	gg	gg	NOUN
ejpam-5749	449	32	)	)	PUNCT
ejpam-5749	449	33	\	\	NOUN
ejpam-5749	450	1	{	{	PUNCT
ejpam-5749	450	2	u	u	NOUN
ejpam-5749	450	3	,	,	PUNCT
ejpam-5749	450	4	w	w	NOUN
ejpam-5749	450	5	}	}	PUNCT
ejpam-5749	450	6	=	=	SYM
ejpam-5749	450	7	ngg[v	ngg[v	PROPN
ejpam-5749	450	8	]	]	PUNCT
ejpam-5749	450	9	;	;	PUNCT
ejpam-5749	450	10	(	(	PUNCT
ejpam-5749	450	11	b	b	X
ejpam-5749	450	12	)	)	PUNCT
ejpam-5749	450	13	dgg(u	dgg(u	PROPN
ejpam-5749	450	14	,	,	PUNCT
ejpam-5749	450	15	v	v	NOUN
ejpam-5749	450	16	)	)	PUNCT
ejpam-5749	450	17	=	=	SYM
ejpam-5749	450	18	2	2	NUM
ejpam-5749	450	19	and	and	CCONJ
ejpam-5749	450	20	dgg(w	dgg(w	PROPN
ejpam-5749	450	21	,	,	PUNCT
ejpam-5749	450	22	v	v	NOUN
ejpam-5749	450	23	)	)	PUNCT
ejpam-5749	450	24	=	=	SYM
ejpam-5749	450	25	2	2	X
ejpam-5749	450	26	.	.	X
ejpam-5749	450	27	wlog	wlog	PROPN
ejpam-5749	450	28	assume	assume	VERB
ejpam-5749	450	29	that	that	SCONJ
ejpam-5749	450	30	v	v	X
ejpam-5749	450	31	∈	∈	PROPN
ejpam-5749	450	32	v	v	NOUN
ejpam-5749	450	33	(	(	PUNCT
ejpam-5749	450	34	g	g	NOUN
ejpam-5749	450	35	)	)	PUNCT
ejpam-5749	450	36	.	.	PUNCT
ejpam-5749	451	1	if	if	SCONJ
ejpam-5749	451	2	u	u	PROPN
ejpam-5749	451	3	∈	∈	PROPN
ejpam-5749	451	4	v	v	X
ejpam-5749	451	5	(	(	PUNCT
ejpam-5749	451	6	g	g	NOUN
ejpam-5749	451	7	)	)	PUNCT
ejpam-5749	451	8	,	,	PUNCT
ejpam-5749	451	9	then	then	ADV
ejpam-5749	451	10	by	by	ADP
ejpam-5749	451	11	(	(	PUNCT
ejpam-5749	451	12	b	b	NOUN
ejpam-5749	451	13	)	)	PUNCT
ejpam-5749	451	14	,	,	PUNCT
ejpam-5749	451	15	dg(u	dg(u	X
ejpam-5749	451	16	,	,	PUNCT
ejpam-5749	451	17	v	v	NOUN
ejpam-5749	451	18	)	)	PUNCT
ejpam-5749	451	19	=	=	SYM
ejpam-5749	451	20	2	2	NUM
ejpam-5749	451	21	,	,	PUNCT
ejpam-5749	451	22	say	say	VERB
ejpam-5749	451	23	[	[	X
ejpam-5749	451	24	u	u	NOUN
ejpam-5749	451	25	,	,	PUNCT
ejpam-5749	451	26	z	z	PROPN
ejpam-5749	451	27	,	,	PUNCT
ejpam-5749	451	28	v	v	NOUN
ejpam-5749	451	29	]	]	PUNCT
ejpam-5749	451	30	is	be	AUX
ejpam-5749	451	31	a	a	DET
ejpam-5749	451	32	u	u	NOUN
ejpam-5749	451	33	-	-	NOUN
ejpam-5749	451	34	v	v	ADJ
ejpam-5749	451	35	geodesic	geodesic	NOUN
ejpam-5749	451	36	in	in	ADP
ejpam-5749	451	37	g.	g.	PROPN
ejpam-5749	451	38	then	then	ADV
ejpam-5749	451	39	by	by	ADP
ejpam-5749	451	40	(	(	PUNCT
ejpam-5749	451	41	a	a	X
ejpam-5749	451	42	)	)	PUNCT
ejpam-5749	451	43	,	,	PUNCT
ejpam-5749	451	44	u	u	PROPN
ejpam-5749	451	45	∈	∈	PROPN
ejpam-5749	451	46	ngg[v	ngg[v	PROPN
ejpam-5749	451	47	]	]	PUNCT
ejpam-5749	451	48	or	or	CCONJ
ejpam-5749	451	49	z	z	NOUN
ejpam-5749	451	50	∈	∈	PROPN
ejpam-5749	451	51	ngg[v	ngg[v	PROPN
ejpam-5749	451	52	]	]	PUNCT
ejpam-5749	451	53	,	,	PUNCT
ejpam-5749	451	54	which	which	PRON
ejpam-5749	451	55	is	be	AUX
ejpam-5749	451	56	impossible	impossible	ADJ
ejpam-5749	451	57	.	.	PUNCT
ejpam-5749	452	1	thus	thus	ADV
ejpam-5749	452	2	u	u	X
ejpam-5749	452	3	∈	∈	PROPN
ejpam-5749	452	4	v	v	NOUN
ejpam-5749	452	5	(	(	PUNCT
ejpam-5749	452	6	g	g	NOUN
ejpam-5749	452	7	)	)	PUNCT
ejpam-5749	452	8	.	.	PUNCT
ejpam-5749	453	1	similarly	similarly	ADV
ejpam-5749	453	2	,	,	PUNCT
ejpam-5749	453	3	w	w	PROPN
ejpam-5749	453	4	∈	∈	PROPN
ejpam-5749	453	5	v	v	ADP
ejpam-5749	453	6	(	(	PUNCT
ejpam-5749	453	7	g	g	NOUN
ejpam-5749	453	8	)	)	PUNCT
ejpam-5749	453	9	.	.	PUNCT
ejpam-5749	454	1	moreover	moreover	ADV
ejpam-5749	454	2	,	,	PUNCT
ejpam-5749	454	3	(	(	PUNCT
ejpam-5749	454	4	a	a	PRON
ejpam-5749	454	5	)	)	PUNCT
ejpam-5749	454	6	implies	imply	VERB
ejpam-5749	454	7	that	that	SCONJ
ejpam-5749	454	8	v	v	X
ejpam-5749	454	9	(	(	PUNCT
ejpam-5749	454	10	g	g	NOUN
ejpam-5749	454	11	)	)	PUNCT
ejpam-5749	454	12	=	=	SYM
ejpam-5749	454	13	{	{	PUNCT
ejpam-5749	454	14	v	v	NOUN
ejpam-5749	454	15	,	,	PUNCT
ejpam-5749	454	16	u	u	NOUN
ejpam-5749	454	17	,	,	PUNCT
ejpam-5749	454	18	w	w	NOUN
ejpam-5749	454	19	}	}	PUNCT
ejpam-5749	454	20	.	.	PUNCT
ejpam-5749	455	1	thus	thus	ADV
ejpam-5749	455	2	,	,	PUNCT
ejpam-5749	455	3	either	either	CCONJ
ejpam-5749	455	4	g	g	PROPN
ejpam-5749	455	5	=	=	PROPN
ejpam-5749	455	6	p3	p3	PROPN
ejpam-5749	455	7	or	or	CCONJ
ejpam-5749	455	8	g	g	NOUN
ejpam-5749	455	9	=	=	SYM
ejpam-5749	455	10	k3	k3	PROPN
ejpam-5749	455	11	.	.	PUNCT
ejpam-5749	456	1	but	but	CCONJ
ejpam-5749	456	2	if	if	SCONJ
ejpam-5749	456	3	g	g	PROPN
ejpam-5749	456	4	=	=	SYM
ejpam-5749	456	5	p3	p3	PROPN
ejpam-5749	456	6	,	,	PUNCT
ejpam-5749	456	7	then	then	ADV
ejpam-5749	456	8	g	g	PROPN
ejpam-5749	456	9	is	be	AUX
ejpam-5749	456	10	among	among	ADP
ejpam-5749	456	11	the	the	DET
ejpam-5749	456	12	graphs	graph	NOUN
ejpam-5749	456	13	described	describe	VERB
ejpam-5749	456	14	in	in	ADP
ejpam-5749	456	15	case	case	NOUN
ejpam-5749	456	16	1	1	NUM
ejpam-5749	456	17	.	.	PUNCT
ejpam-5749	457	1	thus	thus	ADV
ejpam-5749	457	2	,	,	PUNCT
ejpam-5749	457	3	g	g	PROPN
ejpam-5749	457	4	=	=	SYM
ejpam-5749	457	5	k3	k3	PROPN
ejpam-5749	457	6	.	.	PUNCT
ejpam-5749	458	1	the	the	DET
ejpam-5749	458	2	converse	converse	NOUN
ejpam-5749	458	3	of	of	ADP
ejpam-5749	458	4	(	(	PUNCT
ejpam-5749	458	5	iii	iii	NOUN
ejpam-5749	458	6	)	)	PUNCT
ejpam-5749	458	7	is	be	AUX
ejpam-5749	458	8	also	also	ADV
ejpam-5749	458	9	immediate	immediate	ADJ
ejpam-5749	458	10	.	.	PUNCT
ejpam-5749	459	1	corollary	corollary	ADJ
ejpam-5749	459	2	3	3	X
ejpam-5749	459	3	.	.	PUNCT
ejpam-5749	460	1	if	if	SCONJ
ejpam-5749	460	2	g	g	PROPN
ejpam-5749	460	3	is	be	AUX
ejpam-5749	460	4	a	a	DET
ejpam-5749	460	5	graph	graph	NOUN
ejpam-5749	460	6	with	with	ADP
ejpam-5749	460	7	isolated	isolated	ADJ
ejpam-5749	460	8	vertex	vertex	NOUN
ejpam-5749	460	9	v	v	ADP
ejpam-5749	460	10	such	such	ADJ
ejpam-5749	460	11	that	that	DET
ejpam-5749	460	12	γ(g	γ(g	PROPN
ejpam-5749	460	13	−	−	PROPN
ejpam-5749	460	14	v	v	NOUN
ejpam-5749	460	15	)	)	PUNCT
ejpam-5749	460	16	=	=	SYM
ejpam-5749	460	17	1	1	NUM
ejpam-5749	460	18	,	,	PUNCT
ejpam-5749	460	19	then	then	ADV
ejpam-5749	460	20	γt2r(gg	γt2r(gg	ADJ
ejpam-5749	460	21	)	)	PUNCT
ejpam-5749	461	1	=	=	SYM
ejpam-5749	461	2	4	4	X
ejpam-5749	461	3	.	.	X
ejpam-5749	461	4	proposition	proposition	NOUN
ejpam-5749	461	5	14	14	NUM
ejpam-5749	461	6	.	.	PUNCT
ejpam-5749	461	7	suppose	suppose	VERB
ejpam-5749	461	8	that	that	SCONJ
ejpam-5749	461	9	both	both	PRON
ejpam-5749	461	10	g	g	PROPN
ejpam-5749	461	11	and	and	CCONJ
ejpam-5749	461	12	g	g	PROPN
ejpam-5749	461	13	contain	contain	VERB
ejpam-5749	461	14	no	no	DET
ejpam-5749	461	15	isolated	isolated	ADJ
ejpam-5749	461	16	vertices	vertex	NOUN
ejpam-5749	461	17	.	.	PUNCT
ejpam-5749	462	1	then	then	ADV
ejpam-5749	462	2	max{γt2r(g	max{γt2r(g	ADJ
ejpam-5749	462	3	)	)	PUNCT
ejpam-5749	462	4	,	,	PUNCT
ejpam-5749	462	5	γt2r(g	γt2r(g	NUM
ejpam-5749	462	6	)	)	PUNCT
ejpam-5749	462	7	}	}	PUNCT
ejpam-5749	463	1	≤	≤	NUM
ejpam-5749	463	2	γt2r(gg	γt2r(gg	NOUN
ejpam-5749	463	3	)	)	PUNCT
ejpam-5749	463	4	≤	≤	NOUN
ejpam-5749	463	5	γt2r(g	γt2r(g	NUM
ejpam-5749	463	6	)	)	PUNCT
ejpam-5749	464	1	+	+	NUM
ejpam-5749	464	2	γt2r(g	γt2r(g	NUM
ejpam-5749	464	3	)	)	PUNCT
ejpam-5749	464	4	.	.	PUNCT
ejpam-5749	465	1	proof	proof	NOUN
ejpam-5749	465	2	.	.	PUNCT
ejpam-5749	466	1	let	let	VERB
ejpam-5749	466	2	f	f	PROPN
ejpam-5749	466	3	=	=	PRON
ejpam-5749	466	4	(	(	PUNCT
ejpam-5749	466	5	v	v	NOUN
ejpam-5749	466	6	f	f	PROPN
ejpam-5749	466	7	0	0	NUM
ejpam-5749	466	8	,	,	PUNCT
ejpam-5749	466	9	v	v	NOUN
ejpam-5749	466	10	f	f	PROPN
ejpam-5749	466	11	1	1	NUM
ejpam-5749	466	12	,	,	PUNCT
ejpam-5749	466	13	v	v	NOUN
ejpam-5749	466	14	f	f	PROPN
ejpam-5749	466	15	2	2	NUM
ejpam-5749	466	16	)	)	PUNCT
ejpam-5749	466	17	and	and	CCONJ
ejpam-5749	466	18	g	g	NOUN
ejpam-5749	466	19	=	=	SYM
ejpam-5749	466	20	(	(	PUNCT
ejpam-5749	466	21	v	v	NOUN
ejpam-5749	466	22	g	g	NOUN
ejpam-5749	466	23	0	0	NUM
ejpam-5749	466	24	,	,	PUNCT
ejpam-5749	466	25	v	v	ADP
ejpam-5749	466	26	g	g	PROPN
ejpam-5749	466	27	1	1	NUM
ejpam-5749	466	28	,	,	PUNCT
ejpam-5749	466	29	v	v	ADP
ejpam-5749	466	30	g	g	PROPN
ejpam-5749	466	31	2	2	NUM
ejpam-5749	466	32	)	)	PUNCT
ejpam-5749	466	33	be	be	AUX
ejpam-5749	466	34	a	a	DET
ejpam-5749	466	35	γt2r	γt2r	NOUN
ejpam-5749	466	36	-	-	PUNCT
ejpam-5749	466	37	functions	function	NOUN
ejpam-5749	466	38	of	of	ADP
ejpam-5749	466	39	g	g	NOUN
ejpam-5749	466	40	and	and	CCONJ
ejpam-5749	466	41	g	g	NOUN
ejpam-5749	466	42	,	,	PUNCT
ejpam-5749	466	43	respectively	respectively	ADV
ejpam-5749	466	44	.	.	PUNCT
ejpam-5749	467	1	it	it	PRON
ejpam-5749	467	2	is	be	AUX
ejpam-5749	467	3	straightforward	straightforward	ADJ
ejpam-5749	467	4	to	to	PART
ejpam-5749	467	5	show	show	VERB
ejpam-5749	467	6	that	that	SCONJ
ejpam-5749	467	7	f	f	PROPN
ejpam-5749	467	8	=	=	PRON
ejpam-5749	467	9	(	(	PUNCT
ejpam-5749	467	10	v	v	NOUN
ejpam-5749	467	11	f	f	PROPN
ejpam-5749	467	12	0	0	NUM
ejpam-5749	467	13	∪	∪	PROPN
ejpam-5749	467	14	v	v	ADP
ejpam-5749	467	15	g	g	NOUN
ejpam-5749	467	16	0	0	NUM
ejpam-5749	467	17	,	,	PUNCT
ejpam-5749	467	18	v	v	NOUN
ejpam-5749	467	19	f	f	PROPN
ejpam-5749	467	20	1	1	NUM
ejpam-5749	467	21	∪	∪	ADP
ejpam-5749	467	22	v	v	ADP
ejpam-5749	467	23	g	g	PROPN
ejpam-5749	467	24	1	1	NUM
ejpam-5749	467	25	,	,	PUNCT
ejpam-5749	467	26	v	v	NOUN
ejpam-5749	467	27	f	f	SYM
ejpam-5749	467	28	2	2	NUM
ejpam-5749	467	29	∪	∪	ADP
ejpam-5749	467	30	v	v	ADP
ejpam-5749	467	31	g	g	PROPN
ejpam-5749	467	32	2	2	NUM
ejpam-5749	467	33	)	)	PUNCT
ejpam-5749	467	34	∈	∈	NOUN
ejpam-5749	467	35	srdf	srdf	NOUN
ejpam-5749	467	36	(	(	PUNCT
ejpam-5749	467	37	gg	gg	NOUN
ejpam-5749	467	38	)	)	PUNCT
ejpam-5749	467	39	.	.	PUNCT
ejpam-5749	468	1	therefore	therefore	ADV
ejpam-5749	468	2	,	,	PUNCT
ejpam-5749	468	3	γt2r(gg	γt2r(gg	ADJ
ejpam-5749	468	4	)	)	PUNCT
ejpam-5749	468	5	≤	≤	NUM
ejpam-5749	468	6	ωgg(f	ωgg(f	NUM
ejpam-5749	468	7	)	)	PUNCT
ejpam-5749	468	8	=	=	PUNCT
ejpam-5749	468	9	γt2r(g	γt2r(g	NUM
ejpam-5749	468	10	)	)	PUNCT
ejpam-5749	469	1	+	+	NUM
ejpam-5749	469	2	γt2r(g	γt2r(g	NUM
ejpam-5749	469	3	)	)	PUNCT
ejpam-5749	469	4	.	.	PUNCT
ejpam-5749	470	1	to	to	PART
ejpam-5749	470	2	get	get	VERB
ejpam-5749	470	3	the	the	DET
ejpam-5749	470	4	other	other	ADJ
ejpam-5749	470	5	inequality	inequality	NOUN
ejpam-5749	470	6	,	,	PUNCT
ejpam-5749	470	7	let	let	VERB
ejpam-5749	470	8	p	p	NOUN
ejpam-5749	470	9	=	=	X
ejpam-5749	470	10	(	(	PUNCT
ejpam-5749	470	11	v0	v0	PROPN
ejpam-5749	470	12	,	,	PUNCT
ejpam-5749	470	13	v1	v1	NOUN
ejpam-5749	470	14	,	,	PUNCT
ejpam-5749	470	15	v2	v2	PROPN
ejpam-5749	470	16	)	)	PUNCT
ejpam-5749	470	17	be	be	AUX
ejpam-5749	470	18	a	a	DET
ejpam-5749	470	19	γt2r	γt2r	NOUN
ejpam-5749	470	20	-	-	PUNCT
ejpam-5749	470	21	function	function	NOUN
ejpam-5749	470	22	of	of	ADP
ejpam-5749	470	23	gg	gg	PROPN
ejpam-5749	470	24	.	.	PUNCT
ejpam-5749	471	1	let	let	VERB
ejpam-5749	471	2	a	a	DET
ejpam-5749	471	3	=	=	X
ejpam-5749	471	4	{	{	PUNCT
ejpam-5749	471	5	v	v	NOUN
ejpam-5749	471	6	∈	∈	PROPN
ejpam-5749	471	7	v0	v0	NOUN
ejpam-5749	471	8	∩	∩	X
ejpam-5749	471	9	v	v	X
ejpam-5749	471	10	(	(	PUNCT
ejpam-5749	471	11	g	g	NOUN
ejpam-5749	471	12	)	)	PUNCT
ejpam-5749	471	13	|	|	ADV
ejpam-5749	471	14	v2	v2	VERB
ejpam-5749	471	15	∩ngg(v	∩ngg(v	PUNCT
ejpam-5749	471	16	)	)	PUNCT
ejpam-5749	471	17	=	=	SYM
ejpam-5749	471	18	{	{	PUNCT
ejpam-5749	471	19	v	v	NOUN
ejpam-5749	471	20	}	}	PUNCT
ejpam-5749	471	21	and	and	CCONJ
ejpam-5749	471	22	ng(v	ng(v	NUM
ejpam-5749	471	23	)	)	PUNCT
ejpam-5749	471	24	⊆	⊆	NUM
ejpam-5749	471	25	v0	v0	NOUN
ejpam-5749	471	26	}	}	PUNCT
ejpam-5749	471	27	,	,	PUNCT
ejpam-5749	471	28	b.	b.	PROPN
ejpam-5749	471	29	f.	f.	PROPN
ejpam-5749	471	30	bullang	bullang	PROPN
ejpam-5749	471	31	et	et	PROPN
ejpam-5749	471	32	al	al	PROPN
ejpam-5749	471	33	.	.	PUNCT
ejpam-5749	471	34	/	/	SYM
ejpam-5749	471	35	eur	eur	PROPN
ejpam-5749	471	36	.	.	PUNCT
ejpam-5749	472	1	j.	j.	PROPN
ejpam-5749	472	2	pure	pure	PROPN
ejpam-5749	472	3	appl	appl	PROPN
ejpam-5749	472	4	.	.	PROPN
ejpam-5749	472	5	math	math	PROPN
ejpam-5749	472	6	,	,	PUNCT
ejpam-5749	472	7	18	18	NUM
ejpam-5749	472	8	(	(	PUNCT
ejpam-5749	472	9	1	1	NUM
ejpam-5749	472	10	)	)	PUNCT
ejpam-5749	472	11	(	(	PUNCT
ejpam-5749	472	12	2025	2025	NUM
ejpam-5749	472	13	)	)	PUNCT
ejpam-5749	472	14	,	,	PUNCT
ejpam-5749	472	15	5749	5749	NUM
ejpam-5749	472	16	14	14	NUM
ejpam-5749	472	17	of	of	ADP
ejpam-5749	472	18	15	15	NUM
ejpam-5749	472	19	b	b	NOUN
ejpam-5749	472	20	=	=	PRON
ejpam-5749	472	21	{	{	PUNCT
ejpam-5749	472	22	v	v	NOUN
ejpam-5749	472	23	∈	∈	PROPN
ejpam-5749	472	24	v0	v0	NOUN
ejpam-5749	472	25	∩	∩	X
ejpam-5749	472	26	v	v	X
ejpam-5749	472	27	(	(	PUNCT
ejpam-5749	472	28	g	g	NOUN
ejpam-5749	472	29	)	)	PUNCT
ejpam-5749	472	30	|	|	ADV
ejpam-5749	472	31	v2	v2	VERB
ejpam-5749	472	32	∩ngg(v	∩ngg(v	PUNCT
ejpam-5749	472	33	)	)	PUNCT
ejpam-5749	472	34	=	=	SYM
ejpam-5749	472	35	{	{	PUNCT
ejpam-5749	472	36	v	v	NOUN
ejpam-5749	472	37	}	}	PUNCT
ejpam-5749	472	38	and	and	CCONJ
ejpam-5749	472	39	ng(v	ng(v	NUM
ejpam-5749	472	40	)	)	PUNCT
ejpam-5749	472	41	∩	∩	NOUN
ejpam-5749	472	42	v1	v1	NOUN
ejpam-5749	472	43	̸=	̸=	PROPN
ejpam-5749	472	44	∅	∅	NOUN
ejpam-5749	472	45	}	}	PUNCT
ejpam-5749	472	46	,	,	PUNCT
ejpam-5749	472	47	and	and	CCONJ
ejpam-5749	472	48	c	c	X
ejpam-5749	472	49	=	=	PRON
ejpam-5749	472	50	{	{	PUNCT
ejpam-5749	472	51	v	v	NUM
ejpam-5749	472	52	∈	∈	NOUN
ejpam-5749	472	53	v	v	NOUN
ejpam-5749	472	54	(	(	PUNCT
ejpam-5749	472	55	g	g	NOUN
ejpam-5749	472	56	)	)	PUNCT
ejpam-5749	472	57	∩	∩	NOUN
ejpam-5749	472	58	(	(	PUNCT
ejpam-5749	472	59	v1	v1	NOUN
ejpam-5749	472	60	∪	∪	X
ejpam-5749	472	61	v2	v2	NOUN
ejpam-5749	472	62	)	)	PUNCT
ejpam-5749	473	1	|	|	ADV
ejpam-5749	473	2	(	(	PUNCT
ejpam-5749	473	3	v1	v1	VERB
ejpam-5749	473	4	∪	∪	X
ejpam-5749	473	5	v2	v2	NOUN
ejpam-5749	473	6	)	)	PUNCT
ejpam-5749	473	7	∩ngg(v	∩ngg(v	NOUN
ejpam-5749	473	8	,	,	PUNCT
ejpam-5749	473	9	2	2	X
ejpam-5749	473	10	)	)	PUNCT
ejpam-5749	473	11	⊆	⊆	NUM
ejpam-5749	473	12	v	v	NOUN
ejpam-5749	473	13	(	(	PUNCT
ejpam-5749	473	14	g	g	NOUN
ejpam-5749	473	15	)	)	PUNCT
ejpam-5749	473	16	}	}	PUNCT
ejpam-5749	473	17	.	.	PUNCT
ejpam-5749	474	1	for	for	ADP
ejpam-5749	474	2	each	each	DET
ejpam-5749	474	3	v	v	ADP
ejpam-5749	474	4	∈	∈	PRON
ejpam-5749	474	5	a	a	DET
ejpam-5749	474	6	∪	∪	ADJ
ejpam-5749	474	7	c	c	NOUN
ejpam-5749	474	8	,	,	PUNCT
ejpam-5749	474	9	choose	choose	VERB
ejpam-5749	474	10	exactly	exactly	ADV
ejpam-5749	474	11	one	one	NUM
ejpam-5749	474	12	uv	uv	NOUN
ejpam-5749	474	13	∈	∈	PROPN
ejpam-5749	474	14	ng(v	ng(v	PUNCT
ejpam-5749	474	15	)	)	PUNCT
ejpam-5749	474	16	and	and	CCONJ
ejpam-5749	474	17	let	let	VERB
ejpam-5749	474	18	d	d	NOUN
ejpam-5749	474	19	=	=	PRON
ejpam-5749	474	20	{	{	PUNCT
ejpam-5749	474	21	uv	uv	INTJ
ejpam-5749	474	22	|	|	NOUN
ejpam-5749	474	23	v	v	ADP
ejpam-5749	474	24	∈	∈	PROPN
ejpam-5749	474	25	a	a	PRON
ejpam-5749	474	26	}	}	PUNCT
ejpam-5749	474	27	and	and	CCONJ
ejpam-5749	474	28	e	e	NOUN
ejpam-5749	474	29	=	=	NOUN
ejpam-5749	474	30	{	{	PUNCT
ejpam-5749	474	31	uv	uv	INTJ
ejpam-5749	474	32	|	|	ADV
ejpam-5749	474	33	v	v	ADP
ejpam-5749	474	34	∈	∈	NOUN
ejpam-5749	474	35	c	c	NOUN
ejpam-5749	474	36	}	}	PUNCT
ejpam-5749	474	37	.	.	PUNCT
ejpam-5749	475	1	define	define	VERB
ejpam-5749	475	2	q	q	NOUN
ejpam-5749	475	3	=	=	SYM
ejpam-5749	475	4	(	(	PUNCT
ejpam-5749	475	5	v	v	NOUN
ejpam-5749	475	6	∗	∗	NOUN
ejpam-5749	475	7	0	0	NUM
ejpam-5749	475	8	,	,	PUNCT
ejpam-5749	475	9	v	v	NOUN
ejpam-5749	475	10	∗	∗	NOUN
ejpam-5749	475	11	1	1	NUM
ejpam-5749	475	12	,	,	PUNCT
ejpam-5749	475	13	v	v	NOUN
ejpam-5749	475	14	∗	∗	NOUN
ejpam-5749	475	15	2	2	NUM
ejpam-5749	475	16	)	)	PUNCT
ejpam-5749	475	17	by	by	ADP
ejpam-5749	475	18	v	v	NUM
ejpam-5749	475	19	∗	∗	NOUN
ejpam-5749	475	20	0	0	NUM
ejpam-5749	476	1	=	=	SYM
ejpam-5749	476	2	(	(	PUNCT
ejpam-5749	476	3	v0	v0	NOUN
ejpam-5749	476	4	∩	∩	X
ejpam-5749	476	5	v	v	NOUN
ejpam-5749	476	6	(	(	PUNCT
ejpam-5749	476	7	g))∖	g))∖	NOUN
ejpam-5749	476	8	(	(	PUNCT
ejpam-5749	476	9	a	a	PRON
ejpam-5749	476	10	∪b	∪b	PUNCT
ejpam-5749	476	11	∪d	∪d	NOUN
ejpam-5749	476	12	∪	∪	NOUN
ejpam-5749	476	13	e	e	PROPN
ejpam-5749	476	14	)	)	PUNCT
ejpam-5749	476	15	,	,	PUNCT
ejpam-5749	476	16	v	v	X
ejpam-5749	476	17	∗	∗	NOUN
ejpam-5749	476	18	1	1	NUM
ejpam-5749	476	19	=	=	SYM
ejpam-5749	476	20	(	(	PUNCT
ejpam-5749	476	21	v1	v1	PROPN
ejpam-5749	476	22	∩	∩	ADJ
ejpam-5749	476	23	v	v	NOUN
ejpam-5749	476	24	(	(	PUNCT
ejpam-5749	476	25	g	g	NOUN
ejpam-5749	476	26	)	)	PUNCT
ejpam-5749	476	27	)	)	PUNCT
ejpam-5749	476	28	∪a	∪a	X
ejpam-5749	476	29	∪b	∪b	PUNCT
ejpam-5749	476	30	∪d	∪d	X
ejpam-5749	476	31	∪	∪	NOUN
ejpam-5749	476	32	e	e	NOUN
ejpam-5749	476	33	,	,	PUNCT
ejpam-5749	476	34	and	and	CCONJ
ejpam-5749	476	35	v	v	ADP
ejpam-5749	476	36	∗	∗	NOUN
ejpam-5749	476	37	2	2	NUM
ejpam-5749	476	38	=	=	SYM
ejpam-5749	476	39	v2	v2	NOUN
ejpam-5749	476	40	∩	∩	NOUN
ejpam-5749	476	41	v	v	NOUN
ejpam-5749	476	42	(	(	PUNCT
ejpam-5749	476	43	g	g	NOUN
ejpam-5749	476	44	)	)	PUNCT
ejpam-5749	476	45	.	.	PUNCT
ejpam-5749	477	1	we	we	PRON
ejpam-5749	477	2	claim	claim	VERB
ejpam-5749	477	3	that	that	SCONJ
ejpam-5749	477	4	q	q	PROPN
ejpam-5749	477	5	∈	∈	NOUN
ejpam-5749	477	6	srdf	srdf	NOUN
ejpam-5749	477	7	(	(	PUNCT
ejpam-5749	477	8	g	g	NOUN
ejpam-5749	477	9	)	)	PUNCT
ejpam-5749	477	10	.	.	PUNCT
ejpam-5749	478	1	let	let	VERB
ejpam-5749	478	2	u	u	PRON
ejpam-5749	478	3	∈	∈	PROPN
ejpam-5749	478	4	v	v	ADP
ejpam-5749	478	5	∗	∗	NOUN
ejpam-5749	478	6	0	0	NUM
ejpam-5749	478	7	.	.	PUNCT
ejpam-5749	479	1	since	since	SCONJ
ejpam-5749	479	2	u	u	PROPN
ejpam-5749	479	3	∈	∈	PROPN
ejpam-5749	479	4	v0	v0	NOUN
ejpam-5749	479	5	,	,	PUNCT
ejpam-5749	479	6	there	there	PRON
ejpam-5749	479	7	exists	exist	VERB
ejpam-5749	479	8	v	v	ADP
ejpam-5749	479	9	∈	∈	PROPN
ejpam-5749	479	10	v2	v2	NOUN
ejpam-5749	479	11	for	for	ADP
ejpam-5749	479	12	which	which	PRON
ejpam-5749	479	13	uv	uv	NOUN
ejpam-5749	479	14	∈	∈	PROPN
ejpam-5749	479	15	e(gg	e(gg	PROPN
ejpam-5749	479	16	)	)	PUNCT
ejpam-5749	479	17	.	.	PUNCT
ejpam-5749	480	1	beacause	beacause	PROPN
ejpam-5749	480	2	u	u	PROPN
ejpam-5749	480	3	/∈	/∈	PUNCT
ejpam-5749	481	1	(	(	PUNCT
ejpam-5749	481	2	a	a	DET
ejpam-5749	481	3	∪	∪	ADJ
ejpam-5749	481	4	b	b	NOUN
ejpam-5749	481	5	)	)	PUNCT
ejpam-5749	481	6	,	,	PUNCT
ejpam-5749	481	7	v	v	X
ejpam-5749	481	8	∈	∈	PROPN
ejpam-5749	481	9	v	v	NOUN
ejpam-5749	481	10	(	(	PUNCT
ejpam-5749	481	11	g	g	NOUN
ejpam-5749	481	12	)	)	PUNCT
ejpam-5749	481	13	.	.	PUNCT
ejpam-5749	482	1	thus	thus	ADV
ejpam-5749	482	2	,	,	PUNCT
ejpam-5749	482	3	v	v	PROPN
ejpam-5749	482	4	∈	∈	PROPN
ejpam-5749	482	5	v	v	ADP
ejpam-5749	482	6	∗	∗	NOUN
ejpam-5749	482	7	2	2	NUM
ejpam-5749	482	8	and	and	CCONJ
ejpam-5749	482	9	uv	uv	NOUN
ejpam-5749	482	10	∈	∈	PROPN
ejpam-5749	482	11	e(g	e(g	PROPN
ejpam-5749	482	12	)	)	PUNCT
ejpam-5749	482	13	.	.	PUNCT
ejpam-5749	483	1	let	let	VERB
ejpam-5749	483	2	x	x	SYM
ejpam-5749	483	3	∈	∈	PROPN
ejpam-5749	483	4	v	v	ADP
ejpam-5749	483	5	∗	∗	NOUN
ejpam-5749	483	6	1	1	NUM
ejpam-5749	483	7	∪	∪	NOUN
ejpam-5749	483	8	v	v	NOUN
ejpam-5749	483	9	∗	∗	NOUN
ejpam-5749	483	10	2	2	NUM
ejpam-5749	483	11	.	.	PUNCT
ejpam-5749	484	1	we	we	PRON
ejpam-5749	484	2	consider	consider	VERB
ejpam-5749	484	3	the	the	DET
ejpam-5749	484	4	following	follow	VERB
ejpam-5749	484	5	cases	case	NOUN
ejpam-5749	484	6	:	:	PUNCT
ejpam-5749	484	7	case	case	NOUN
ejpam-5749	484	8	1	1	NUM
ejpam-5749	484	9	:	:	PUNCT
ejpam-5749	484	10	x	x	SYM
ejpam-5749	484	11	∈	∈	NOUN
ejpam-5749	484	12	v	v	ADP
ejpam-5749	484	13	∗	∗	NOUN
ejpam-5749	484	14	1	1	NUM
ejpam-5749	484	15	.	.	PUNCT
ejpam-5749	484	16	suppose	suppose	VERB
ejpam-5749	484	17	that	that	SCONJ
ejpam-5749	484	18	x	x	PUNCT
ejpam-5749	484	19	∈	∈	PROPN
ejpam-5749	484	20	v1	v1	NOUN
ejpam-5749	484	21	∩	∩	ADJ
ejpam-5749	484	22	v	v	NOUN
ejpam-5749	484	23	(	(	PUNCT
ejpam-5749	484	24	g	g	NOUN
ejpam-5749	484	25	)	)	PUNCT
ejpam-5749	484	26	.	.	PUNCT
ejpam-5749	485	1	then	then	ADV
ejpam-5749	485	2	there	there	PRON
ejpam-5749	485	3	exists	exist	VERB
ejpam-5749	485	4	y	y	PROPN
ejpam-5749	485	5	∈	∈	PROPN
ejpam-5749	485	6	v1	v1	PROPN
ejpam-5749	485	7	∪	∪	NOUN
ejpam-5749	485	8	v2	v2	NOUN
ejpam-5749	485	9	for	for	ADP
ejpam-5749	485	10	which	which	PRON
ejpam-5749	485	11	dgg(x	dgg(x	PROPN
ejpam-5749	485	12	,	,	PUNCT
ejpam-5749	485	13	y	y	NOUN
ejpam-5749	485	14	)	)	PUNCT
ejpam-5749	485	15	≤	≤	NOUN
ejpam-5749	485	16	2	2	NUM
ejpam-5749	485	17	.	.	PUNCT
ejpam-5749	486	1	if	if	SCONJ
ejpam-5749	486	2	x	x	PRON
ejpam-5749	486	3	/∈	/∈	PUNCT
ejpam-5749	487	1	c	c	X
ejpam-5749	487	2	,	,	PUNCT
ejpam-5749	487	3	then	then	ADV
ejpam-5749	487	4	y	y	PROPN
ejpam-5749	487	5	∈	∈	PROPN
ejpam-5749	487	6	(	(	PUNCT
ejpam-5749	487	7	v1∪v2)∩v	v1∪v2)∩v	PROPN
ejpam-5749	487	8	(	(	PUNCT
ejpam-5749	487	9	g	g	NOUN
ejpam-5749	487	10	)	)	PUNCT
ejpam-5749	488	1	⊆	⊆	NUM
ejpam-5749	488	2	v	v	ADP
ejpam-5749	488	3	∗	∗	NOUN
ejpam-5749	488	4	1	1	NUM
ejpam-5749	488	5	∪v	∪v	NOUN
ejpam-5749	488	6	∗	∗	NOUN
ejpam-5749	488	7	2	2	NUM
ejpam-5749	488	8	.	.	PUNCT
ejpam-5749	489	1	if	if	SCONJ
ejpam-5749	489	2	x	x	SYM
ejpam-5749	489	3	∈	∈	PROPN
ejpam-5749	489	4	c	c	X
ejpam-5749	489	5	,	,	PUNCT
ejpam-5749	489	6	then	then	ADV
ejpam-5749	489	7	there	there	PRON
ejpam-5749	489	8	exists	exist	VERB
ejpam-5749	489	9	ux	ux	PROPN
ejpam-5749	489	10	∈	∈	PROPN
ejpam-5749	489	11	ng(x)∩e	ng(x)∩e	PROPN
ejpam-5749	489	12	⊆	⊆	NUM
ejpam-5749	489	13	v	v	NOUN
ejpam-5749	489	14	∗	∗	NOUN
ejpam-5749	489	15	1	1	NUM
ejpam-5749	489	16	.	.	PUNCT
ejpam-5749	490	1	if	if	SCONJ
ejpam-5749	490	2	x	x	SYM
ejpam-5749	490	3	∈	∈	PROPN
ejpam-5749	490	4	a	a	PRON
ejpam-5749	490	5	,	,	PUNCT
ejpam-5749	490	6	then	then	ADV
ejpam-5749	490	7	there	there	PRON
ejpam-5749	490	8	exists	exist	VERB
ejpam-5749	490	9	ux	ux	PROPN
ejpam-5749	490	10	∈	∈	PROPN
ejpam-5749	490	11	ng(x	ng(x	NUM
ejpam-5749	490	12	)	)	PUNCT
ejpam-5749	490	13	∩	∩	NOUN
ejpam-5749	490	14	d	d	PROPN
ejpam-5749	490	15	⊆	⊆	NUM
ejpam-5749	490	16	v	v	ADP
ejpam-5749	490	17	∗	∗	NOUN
ejpam-5749	490	18	1	1	NUM
ejpam-5749	490	19	.	.	PUNCT
ejpam-5749	491	1	if	if	SCONJ
ejpam-5749	491	2	x	x	SYM
ejpam-5749	491	3	∈	∈	PROPN
ejpam-5749	491	4	d	d	NOUN
ejpam-5749	491	5	,	,	PUNCT
ejpam-5749	491	6	then	then	ADV
ejpam-5749	491	7	x	x	X
ejpam-5749	491	8	=	=	PUNCT
ejpam-5749	491	9	uv	uv	NOUN
ejpam-5749	491	10	for	for	ADP
ejpam-5749	491	11	some	some	DET
ejpam-5749	491	12	v	v	ADP
ejpam-5749	491	13	∈	∈	PRON
ejpam-5749	491	14	a	a	DET
ejpam-5749	491	15	⊆	⊆	NUM
ejpam-5749	491	16	v	v	NOUN
ejpam-5749	491	17	∗	∗	NOUN
ejpam-5749	491	18	1	1	NUM
ejpam-5749	491	19	and	and	CCONJ
ejpam-5749	491	20	v	v	ADP
ejpam-5749	491	21	∈	∈	PROPN
ejpam-5749	491	22	ng(x	ng(x	NUM
ejpam-5749	491	23	)	)	PUNCT
ejpam-5749	491	24	.	.	PUNCT
ejpam-5749	491	25	suppose	suppose	VERB
ejpam-5749	491	26	that	that	SCONJ
ejpam-5749	491	27	x	x	PROPN
ejpam-5749	491	28	∈	∈	PROPN
ejpam-5749	491	29	b.	b.	PROPN
ejpam-5749	491	30	since	since	SCONJ
ejpam-5749	491	31	ng(x	ng(x	NUM
ejpam-5749	491	32	)	)	PUNCT
ejpam-5749	491	33	∩	∩	NOUN
ejpam-5749	491	34	v1	v1	PROPN
ejpam-5749	491	35	̸=	̸=	PROPN
ejpam-5749	491	36	∅	∅	NOUN
ejpam-5749	491	37	,	,	PUNCT
ejpam-5749	491	38	say	say	VERB
ejpam-5749	491	39	y	y	PROPN
ejpam-5749	491	40	∈	∈	PROPN
ejpam-5749	491	41	ng(x	ng(x	NUM
ejpam-5749	491	42	)	)	PUNCT
ejpam-5749	491	43	∩	∩	NOUN
ejpam-5749	491	44	v1	v1	NOUN
ejpam-5749	491	45	,	,	PUNCT
ejpam-5749	491	46	we	we	PRON
ejpam-5749	491	47	have	have	VERB
ejpam-5749	491	48	y	y	PROPN
ejpam-5749	491	49	∈	∈	PROPN
ejpam-5749	491	50	v	v	ADP
ejpam-5749	491	51	∗	∗	NOUN
ejpam-5749	491	52	1	1	NUM
ejpam-5749	491	53	and	and	CCONJ
ejpam-5749	491	54	xy	xy	PROPN
ejpam-5749	491	55	∈	∈	PROPN
ejpam-5749	491	56	e(g	e(g	PROPN
ejpam-5749	491	57	)	)	PUNCT
ejpam-5749	491	58	.	.	PUNCT
ejpam-5749	492	1	finally	finally	ADV
ejpam-5749	492	2	,	,	PUNCT
ejpam-5749	492	3	suppose	suppose	VERB
ejpam-5749	492	4	x	x	X
ejpam-5749	492	5	∈	∈	PROPN
ejpam-5749	492	6	e.	e.	PROPN
ejpam-5749	492	7	then	then	ADV
ejpam-5749	492	8	x	x	X
ejpam-5749	493	1	=	=	PUNCT
ejpam-5749	493	2	uv	uv	NOUN
ejpam-5749	493	3	for	for	ADP
ejpam-5749	493	4	some	some	DET
ejpam-5749	493	5	v	v	ADP
ejpam-5749	493	6	∈	∈	PROPN
ejpam-5749	493	7	c.	c.	NOUN
ejpam-5749	493	8	this	this	PRON
ejpam-5749	493	9	means	mean	VERB
ejpam-5749	493	10	that	that	SCONJ
ejpam-5749	493	11	v	v	NUM
ejpam-5749	493	12	∈	∈	PROPN
ejpam-5749	493	13	v	v	ADP
ejpam-5749	493	14	∗	∗	NOUN
ejpam-5749	493	15	1	1	NUM
ejpam-5749	493	16	∪	∪	NOUN
ejpam-5749	493	17	v	v	NOUN
ejpam-5749	493	18	∗	∗	NOUN
ejpam-5749	493	19	2	2	NUM
ejpam-5749	493	20	and	and	CCONJ
ejpam-5749	493	21	xv	xv	PROPN
ejpam-5749	493	22	∈	∈	PROPN
ejpam-5749	493	23	e(g	e(g	PROPN
ejpam-5749	493	24	)	)	PUNCT
ejpam-5749	493	25	.	.	PUNCT
ejpam-5749	494	1	case	case	NOUN
ejpam-5749	494	2	2	2	NUM
ejpam-5749	494	3	:	:	PUNCT
ejpam-5749	494	4	x	x	SYM
ejpam-5749	494	5	∈	∈	NOUN
ejpam-5749	494	6	v	v	ADP
ejpam-5749	494	7	∗	∗	NOUN
ejpam-5749	494	8	2	2	NUM
ejpam-5749	494	9	.	.	PUNCT
ejpam-5749	495	1	then	then	ADV
ejpam-5749	495	2	there	there	PRON
ejpam-5749	495	3	exists	exist	VERB
ejpam-5749	495	4	y	y	PROPN
ejpam-5749	495	5	∈	∈	PROPN
ejpam-5749	495	6	v1	v1	PROPN
ejpam-5749	495	7	∪	∪	NOUN
ejpam-5749	495	8	v2	v2	NOUN
ejpam-5749	495	9	for	for	ADP
ejpam-5749	495	10	which	which	PRON
ejpam-5749	495	11	dgg(x	dgg(x	PROPN
ejpam-5749	495	12	,	,	PUNCT
ejpam-5749	495	13	y	y	NOUN
ejpam-5749	495	14	)	)	PUNCT
ejpam-5749	495	15	≤	≤	NOUN
ejpam-5749	495	16	2	2	NUM
ejpam-5749	495	17	.	.	PUNCT
ejpam-5749	496	1	if	if	SCONJ
ejpam-5749	496	2	x	x	PRON
ejpam-5749	496	3	/∈	/∈	PUNCT
ejpam-5749	497	1	c	c	X
ejpam-5749	497	2	,	,	PUNCT
ejpam-5749	497	3	then	then	ADV
ejpam-5749	497	4	y	y	PROPN
ejpam-5749	497	5	∈	∈	PROPN
ejpam-5749	497	6	v	v	ADP
ejpam-5749	497	7	(	(	PUNCT
ejpam-5749	497	8	g	g	NOUN
ejpam-5749	497	9	)	)	PUNCT
ejpam-5749	497	10	so	so	SCONJ
ejpam-5749	497	11	that	that	SCONJ
ejpam-5749	497	12	y	y	PROPN
ejpam-5749	497	13	∈	∈	PROPN
ejpam-5749	497	14	v	v	ADP
ejpam-5749	497	15	∗	∗	NOUN
ejpam-5749	497	16	1	1	NUM
ejpam-5749	497	17	∪	∪	NOUN
ejpam-5749	497	18	v	v	NOUN
ejpam-5749	497	19	∗	∗	NOUN
ejpam-5749	497	20	2	2	NUM
ejpam-5749	497	21	and	and	CCONJ
ejpam-5749	497	22	dg(x	dg(x	NUM
ejpam-5749	497	23	,	,	PUNCT
ejpam-5749	497	24	y	y	NOUN
ejpam-5749	497	25	)	)	PUNCT
ejpam-5749	497	26	≤	≤	NOUN
ejpam-5749	497	27	2	2	NUM
ejpam-5749	497	28	.	.	PUNCT
ejpam-5749	497	29	suppose	suppose	VERB
ejpam-5749	497	30	that	that	SCONJ
ejpam-5749	497	31	x	x	PROPN
ejpam-5749	497	32	∈	∈	PROPN
ejpam-5749	497	33	c.	c.	NOUN
ejpam-5749	497	34	then	then	ADV
ejpam-5749	497	35	ux	ux	PROPN
ejpam-5749	497	36	∈	∈	PROPN
ejpam-5749	497	37	e	e	PROPN
ejpam-5749	497	38	and	and	CCONJ
ejpam-5749	497	39	xux	xux	PROPN
ejpam-5749	497	40	∈	∈	PROPN
ejpam-5749	497	41	e(g	e(g	PROPN
ejpam-5749	497	42	)	)	PUNCT
ejpam-5749	497	43	.	.	PUNCT
ejpam-5749	498	1	accordingly	accordingly	ADV
ejpam-5749	498	2	,	,	PUNCT
ejpam-5749	498	3	q	q	X
ejpam-5749	498	4	=	=	SYM
ejpam-5749	498	5	(	(	PUNCT
ejpam-5749	498	6	v	v	NOUN
ejpam-5749	498	7	∗	∗	NOUN
ejpam-5749	498	8	0	0	NUM
ejpam-5749	498	9	,	,	PUNCT
ejpam-5749	498	10	v	v	NOUN
ejpam-5749	498	11	∗	∗	NOUN
ejpam-5749	498	12	1	1	NUM
ejpam-5749	498	13	,	,	PUNCT
ejpam-5749	498	14	v	v	NOUN
ejpam-5749	498	15	∗	∗	X
ejpam-5749	498	16	2	2	NUM
ejpam-5749	498	17	)	)	PUNCT
ejpam-5749	498	18	∈	∈	NOUN
ejpam-5749	498	19	srdf	srdf	NOUN
ejpam-5749	498	20	(	(	PUNCT
ejpam-5749	498	21	g	g	NOUN
ejpam-5749	498	22	)	)	PUNCT
ejpam-5749	498	23	,	,	PUNCT
ejpam-5749	498	24	showing	show	VERB
ejpam-5749	498	25	that	that	SCONJ
ejpam-5749	498	26	γt2r(gg	γt2r(gg	NOUN
ejpam-5749	498	27	)	)	PUNCT
ejpam-5749	498	28	=	=	SYM
ejpam-5749	498	29	ωgg(p	ωgg(p	X
ejpam-5749	498	30	)	)	PUNCT
ejpam-5749	498	31	≥	≥	NOUN
ejpam-5749	498	32	ωg(q	ωg(q	NOUN
ejpam-5749	498	33	)	)	PUNCT
ejpam-5749	498	34	≥	≥	NOUN
ejpam-5749	498	35	γt2r(g	γt2r(g	NUM
ejpam-5749	498	36	)	)	PUNCT
ejpam-5749	498	37	.	.	PUNCT
ejpam-5749	499	1	similarly	similarly	ADV
ejpam-5749	499	2	,	,	PUNCT
ejpam-5749	499	3	γt2r(gg	γt2r(gg	ADJ
ejpam-5749	499	4	)	)	PUNCT
ejpam-5749	499	5	≥	≥	NOUN
ejpam-5749	499	6	γt2r(g	γt2r(g	NUM
ejpam-5749	499	7	)	)	PUNCT
ejpam-5749	499	8	.	.	PUNCT
ejpam-5749	500	1	acknowledgment	acknowledgment	NOUN
ejpam-5749	500	2	:	:	PUNCT
ejpam-5749	500	3	the	the	DET
ejpam-5749	500	4	authors	author	NOUN
ejpam-5749	500	5	would	would	AUX
ejpam-5749	500	6	like	like	VERB
ejpam-5749	500	7	to	to	PART
ejpam-5749	500	8	thank	thank	VERB
ejpam-5749	500	9	the	the	DET
ejpam-5749	500	10	department	department	NOUN
ejpam-5749	500	11	of	of	ADP
ejpam-5749	500	12	science	science	NOUN
ejpam-5749	500	13	and	and	CCONJ
ejpam-5749	500	14	technology	technology	NOUN
ejpam-5749	500	15	accelerated	accelerate	VERB
ejpam-5749	500	16	science	science	NOUN
ejpam-5749	500	17	and	and	CCONJ
ejpam-5749	500	18	technology	technology	NOUN
ejpam-5749	500	19	human	human	ADJ
ejpam-5749	500	20	resource	resource	NOUN
ejpam-5749	500	21	development	development	NOUN
ejpam-5749	500	22	program	program	NOUN
ejpam-5749	500	23	(	(	PUNCT
ejpam-5749	500	24	dost	dost	NOUN
ejpam-5749	500	25	-	-	PUNCT
ejpam-5749	500	26	asthrdp)-philippines	asthrdp)-philippine	NOUN
ejpam-5749	500	27	,	,	PUNCT
ejpam-5749	500	28	and	and	CCONJ
ejpam-5749	500	29	msu	msu	PROPN
ejpam-5749	500	30	-	-	PUNCT
ejpam-5749	500	31	iligan	iligan	PROPN
ejpam-5749	500	32	institute	institute	PROPN
ejpam-5749	500	33	of	of	ADP
ejpam-5749	500	34	technology	technology	NOUN
ejpam-5749	500	35	for	for	ADP
ejpam-5749	500	36	funding	fund	VERB
ejpam-5749	500	37	this	this	DET
ejpam-5749	500	38	research	research	NOUN
ejpam-5749	500	39	.	.	PUNCT
ejpam-5749	501	1	b.	b.	PROPN
ejpam-5749	501	2	f.	f.	PROPN
ejpam-5749	501	3	bullang	bullang	PROPN
ejpam-5749	501	4	et	et	PROPN
ejpam-5749	501	5	al	al	PROPN
ejpam-5749	501	6	.	.	PUNCT
ejpam-5749	501	7	/	/	SYM
ejpam-5749	501	8	eur	eur	PROPN
ejpam-5749	501	9	.	.	PUNCT
ejpam-5749	502	1	j.	j.	PROPN
ejpam-5749	502	2	pure	pure	PROPN
ejpam-5749	502	3	appl	appl	PROPN
ejpam-5749	502	4	.	.	PROPN
ejpam-5749	502	5	math	math	PROPN
ejpam-5749	502	6	,	,	PUNCT
ejpam-5749	502	7	18	18	NUM
ejpam-5749	502	8	(	(	PUNCT
ejpam-5749	502	9	1	1	NUM
ejpam-5749	502	10	)	)	PUNCT
ejpam-5749	502	11	(	(	PUNCT
ejpam-5749	502	12	2025	2025	NUM
ejpam-5749	502	13	)	)	PUNCT
ejpam-5749	502	14	,	,	PUNCT
ejpam-5749	502	15	5749	5749	NUM
ejpam-5749	502	16	15	15	NUM
ejpam-5749	502	17	of	of	ADP
ejpam-5749	502	18	15	15	NUM
ejpam-5749	502	19	references	reference	NOUN
ejpam-5749	502	20	[	[	X
ejpam-5749	502	21	1	1	NUM
ejpam-5749	502	22	]	]	X
ejpam-5749	502	23	a.h	a.h	PROPN
ejpam-5749	502	24	.	.	PROPN
ejpam-5749	502	25	ahangar	ahangar	PROPN
ejpam-5749	502	26	,	,	PUNCT
ejpam-5749	502	27	m.	m.	NOUN
ejpam-5749	502	28	henning	henning	PROPN
ejpam-5749	502	29	,	,	PUNCT
ejpam-5749	502	30	v.	v.	CCONJ
ejpam-5749	502	31	samodivkin	samodivkin	NOUN
ejpam-5749	502	32	and	and	CCONJ
ejpam-5749	502	33	i.	i.	PROPN
ejpam-5749	502	34	yero	yero	PROPN
ejpam-5749	502	35	,	,	PUNCT
ejpam-5749	502	36	total	total	ADJ
ejpam-5749	502	37	roman	roman	ADJ
ejpam-5749	502	38	domination	domination	NOUN
ejpam-5749	502	39	in	in	ADP
ejpam-5749	502	40	graphs	graph	NOUN
ejpam-5749	502	41	.	.	PUNCT
ejpam-5749	503	1	applicable	applicable	ADJ
ejpam-5749	503	2	analysis	analysis	NOUN
ejpam-5749	503	3	and	and	CCONJ
ejpam-5749	503	4	discrete	discrete	ADJ
ejpam-5749	503	5	mathematics	mathematic	NOUN
ejpam-5749	503	6	,	,	PUNCT
ejpam-5749	503	7	vol	vol	NOUN
ejpam-5749	503	8	.	.	PROPN
ejpam-5749	503	9	10	10	NUM
ejpam-5749	503	10	,	,	PUNCT
ejpam-5749	503	11	no	no	INTJ
ejpam-5749	503	12	.	.	NOUN
ejpam-5749	503	13	2	2	NUM
ejpam-5749	503	14	(	(	PUNCT
ejpam-5749	503	15	october	october	PROPN
ejpam-5749	503	16	2016	2016	NUM
ejpam-5749	503	17	)	)	PUNCT
ejpam-5749	503	18	,	,	PUNCT
ejpam-5749	503	19	pp	pp	PROPN
ejpam-5749	503	20	.	.	PUNCT
ejpam-5749	504	1	501	501	NUM
ejpam-5749	504	2	-	-	SYM
ejpam-5749	504	3	517	517	NUM
ejpam-5749	504	4	.	.	PUNCT
ejpam-5749	505	1	[	[	X
ejpam-5749	505	2	2	2	NUM
ejpam-5749	505	3	]	]	PUNCT
ejpam-5749	505	4	i.	i.	NOUN
ejpam-5749	505	5	aniversario	aniversario	PROPN
ejpam-5749	505	6	,	,	PUNCT
ejpam-5749	505	7	s.	s.	PROPN
ejpam-5749	505	8	canoy	canoy	PROPN
ejpam-5749	505	9	jr	jr	PROPN
ejpam-5749	505	10	.	.	PROPN
ejpam-5749	505	11	,	,	PUNCT
ejpam-5749	505	12	and	and	CCONJ
ejpam-5749	505	13	f.p	f.p	PROPN
ejpam-5749	505	14	.	.	PROPN
ejpam-5749	505	15	jamil	jamil	PROPN
ejpam-5749	505	16	.	.	PUNCT
ejpam-5749	506	1	on	on	ADP
ejpam-5749	506	2	semitotal	semitotal	ADJ
ejpam-5749	506	3	domination	domination	NOUN
ejpam-5749	506	4	in	in	ADP
ejpam-5749	506	5	graphs	graph	NOUN
ejpam-5749	506	6	.	.	PUNCT
ejpam-5749	507	1	articles	article	NOUN
ejpam-5749	507	2	in	in	ADP
ejpam-5749	507	3	european	european	PROPN
ejpam-5749	507	4	journal	journal	PROPN
ejpam-5749	507	5	of	of	ADP
ejpam-5749	507	6	pure	pure	ADJ
ejpam-5749	507	7	and	and	CCONJ
ejpam-5749	507	8	applied	applied	ADJ
ejpam-5749	507	9	mathematics	mathematic	NOUN
ejpam-5749	507	10	,	,	PUNCT
ejpam-5749	507	11	october	october	PROPN
ejpam-5749	507	12	2019	2019	NUM
ejpam-5749	507	13	.	.	PUNCT
ejpam-5749	508	1	[	[	X
ejpam-5749	508	2	3	3	NUM
ejpam-5749	508	3	]	]	PUNCT
ejpam-5749	508	4	a.	a.	NOUN
ejpam-5749	508	5	aradais	aradais	PROPN
ejpam-5749	508	6	and	and	CCONJ
ejpam-5749	508	7	f.p	f.p	PROPN
ejpam-5749	508	8	.	.	PROPN
ejpam-5749	508	9	jamil	jamil	PROPN
ejpam-5749	508	10	,	,	PUNCT
ejpam-5749	508	11	outer	outer	ADV
ejpam-5749	508	12	-	-	PUNCT
ejpam-5749	508	13	connected	connect	VERB
ejpam-5749	508	14	semitotal	semitotal	ADJ
ejpam-5749	508	15	domination	domination	NOUN
ejpam-5749	508	16	in	in	ADP
ejpam-5749	508	17	graphs	graph	NOUN
ejpam-5749	508	18	,	,	PUNCT
ejpam-5749	508	19	2021	2021	NUM
ejpam-5749	508	20	,	,	PUNCT
ejpam-5749	508	21	eur	eur	PROPN
ejpam-5749	508	22	.	.	PUNCT
ejpam-5749	509	1	j.	j.	PROPN
ejpam-5749	509	2	pure	pure	PROPN
ejpam-5749	509	3	appl	appl	PROPN
ejpam-5749	509	4	.	.	PUNCT
ejpam-5749	509	5	math	math	PROPN
ejpam-5749	509	6	.	.	PUNCT
ejpam-5749	510	1	volume	volume	NOUN
ejpam-5749	510	2	15	15	NUM
ejpam-5749	510	3	pages	page	NOUN
ejpam-5749	510	4	1265	1265	NUM
ejpam-5749	510	5	-	-	SYM
ejpam-5749	510	6	1279	1279	NUM
ejpam-5749	510	7	,	,	PUNCT
ejpam-5749	510	8	(	(	PUNCT
ejpam-5749	510	9	2022	2022	NUM
ejpam-5749	510	10	)	)	PUNCT
ejpam-5749	510	11	.	.	PUNCT
ejpam-5749	511	1	[	[	X
ejpam-5749	511	2	4	4	X
ejpam-5749	511	3	]	]	X
ejpam-5749	511	4	b.	b.	PROPN
ejpam-5749	511	5	basavanagoud	basavanagoud	NOUN
ejpam-5749	511	6	,	,	PUNCT
ejpam-5749	511	7	and	and	CCONJ
ejpam-5749	511	8	s.m	s.m	PROPN
ejpam-5749	511	9	.	.	PROPN
ejpam-5749	511	10	hosamani	hosamani	PROPN
ejpam-5749	511	11	.	.	PUNCT
ejpam-5749	512	1	connected	connect	VERB
ejpam-5749	512	2	semitotal	semitotal	ADJ
ejpam-5749	512	3	-	-	PUNCT
ejpam-5749	512	4	point	point	NOUN
ejpam-5749	512	5	domination	domination	NOUN
ejpam-5749	512	6	in	in	ADP
ejpam-5749	512	7	graphs	graph	NOUN
ejpam-5749	512	8	.	.	PUNCT
ejpam-5749	513	1	international	international	ADJ
ejpam-5749	513	2	journal	journal	NOUN
ejpam-5749	513	3	of	of	ADP
ejpam-5749	513	4	advances	advance	NOUN
ejpam-5749	513	5	in	in	ADP
ejpam-5749	513	6	science	science	NOUN
ejpam-5749	513	7	and	and	CCONJ
ejpam-5749	513	8	technology	technology	NOUN
ejpam-5749	513	9	,	,	PUNCT
ejpam-5749	513	10	2011	2011	NUM
ejpam-5749	513	11	.	.	PUNCT
ejpam-5749	514	1	[	[	X
ejpam-5749	514	2	5	5	NUM
ejpam-5749	514	3	]	]	X
ejpam-5749	514	4	f.	f.	PROPN
ejpam-5749	514	5	buckley	buckley	PROPN
ejpam-5749	514	6	and	and	CCONJ
ejpam-5749	514	7	f.	f.	PROPN
ejpam-5749	514	8	harary	harary	PROPN
ejpam-5749	514	9	.	.	PUNCT
ejpam-5749	515	1	distance	distance	NOUN
ejpam-5749	515	2	in	in	ADP
ejpam-5749	515	3	graphs	graph	NOUN
ejpam-5749	515	4	.	.	PUNCT
ejpam-5749	516	1	redwood	redwood	NOUN
ejpam-5749	516	2	city	city	NOUN
ejpam-5749	516	3	,	,	PUNCT
ejpam-5749	516	4	ca	ca	PROPN
ejpam-5749	516	5	:	:	PUNCT
ejpam-5749	516	6	addison	addison	PROPN
ejpam-5749	516	7	-	-	PUNCT
ejpam-5749	516	8	wesley	wesley	PROPN
ejpam-5749	516	9	.	.	PUNCT
ejpam-5749	516	10	,	,	PUNCT
ejpam-5749	516	11	1990	1990	NUM
ejpam-5749	516	12	.	.	PUNCT
ejpam-5749	517	1	[	[	X
ejpam-5749	517	2	6	6	NUM
ejpam-5749	517	3	]	]	X
ejpam-5749	517	4	e.w	e.w	PROPN
ejpam-5749	517	5	.	.	PROPN
ejpam-5749	517	6	chambers	chamber	NOUN
ejpam-5749	517	7	,	,	PUNCT
ejpam-5749	517	8	et	et	NOUN
ejpam-5749	517	9	.	.	PUNCT
ejpam-5749	518	1	al	al	PROPN
ejpam-5749	518	2	..	..	PUNCT
ejpam-5749	518	3	extremal	extremal	ADJ
ejpam-5749	518	4	problems	problem	NOUN
ejpam-5749	518	5	for	for	ADP
ejpam-5749	518	6	roman	roman	ADJ
ejpam-5749	518	7	domination	domination	NOUN
ejpam-5749	518	8	.	.	PUNCT
ejpam-5749	519	1	society	society	NOUN
ejpam-5749	519	2	for	for	ADP
ejpam-5749	519	3	industrial	industrial	ADJ
ejpam-5749	519	4	and	and	CCONJ
ejpam-5749	519	5	applied	apply	VERB
ejpam-5749	519	6	mathematics	mathematics	NOUN
ejpam-5749	519	7	journals	journal	NOUN
ejpam-5749	519	8	for	for	ADP
ejpam-5749	519	9	discrete	discrete	ADJ
ejpam-5749	519	10	mathematics	mathematic	NOUN
ejpam-5749	519	11	.	.	PUNCT
ejpam-5749	520	1	2004	2004	NUM
ejpam-5749	520	2	.	.	PUNCT
ejpam-5749	521	1	[	[	X
ejpam-5749	521	2	7	7	NUM
ejpam-5749	521	3	]	]	X
ejpam-5749	521	4	e.j	e.j	PROPN
ejpam-5749	521	5	.	.	PROPN
ejpam-5749	521	6	cockayne	cockayne	PROPN
ejpam-5749	521	7	and	and	CCONJ
ejpam-5749	521	8	s.t	s.t	PROPN
ejpam-5749	521	9	.	.	PROPN
ejpam-5749	521	10	hedetniemi	hedetniemi	PROPN
ejpam-5749	521	11	.	.	PUNCT
ejpam-5749	522	1	towards	towards	ADP
ejpam-5749	522	2	a	a	DET
ejpam-5749	522	3	theory	theory	NOUN
ejpam-5749	522	4	of	of	ADP
ejpam-5749	522	5	domination	domination	NOUN
ejpam-5749	522	6	in	in	ADP
ejpam-5749	522	7	graphs	graph	NOUN
ejpam-5749	522	8	.	.	PUNCT
ejpam-5749	523	1	networks	network	NOUN
ejpam-5749	523	2	:	:	PUNCT
ejpam-5749	523	3	an	an	DET
ejpam-5749	523	4	international	international	ADJ
ejpam-5749	523	5	journal	journal	NOUN
ejpam-5749	523	6	.	.	PUNCT
ejpam-5749	524	1	1977	1977	NUM
ejpam-5749	524	2	.	.	PUNCT
ejpam-5749	525	1	[	[	X
ejpam-5749	525	2	8	8	NUM
ejpam-5749	525	3	]	]	SYM
ejpam-5749	525	4	e.j	e.j	PROPN
ejpam-5749	525	5	.	.	PROPN
ejpam-5749	525	6	cockayne	cockayne	PROPN
ejpam-5749	525	7	,	,	PUNCT
ejpam-5749	525	8	p.m.	p.m.	NOUN
ejpam-5749	526	1	dreyer	dreyer	PROPN
ejpam-5749	526	2	sr	sr	PROPN
ejpam-5749	526	3	.	.	PROPN
ejpam-5749	526	4	,	,	PUNCT
ejpam-5749	526	5	s.m	s.m	PROPN
ejpam-5749	526	6	.	.	PROPN
ejpam-5749	526	7	hedetniemi	hedetniemi	PROPN
ejpam-5749	526	8	,	,	PUNCT
ejpam-5749	526	9	s.t	s.t	PROPN
ejpam-5749	526	10	.	.	PROPN
ejpam-5749	526	11	hedetniemi	hedetniemi	PROPN
ejpam-5749	526	12	,	,	PUNCT
ejpam-5749	526	13	roman	roman	ADJ
ejpam-5749	526	14	domination	domination	NOUN
ejpam-5749	526	15	in	in	ADP
ejpam-5749	526	16	graphs	graph	NOUN
ejpam-5749	526	17	,	,	PUNCT
ejpam-5749	526	18	discrete	discrete	ADJ
ejpam-5749	526	19	mathematics	mathematic	NOUN
ejpam-5749	526	20	volume	volume	NOUN
ejpam-5749	526	21	278	278	NUM
ejpam-5749	526	22	,	,	PUNCT
ejpam-5749	526	23	issues	issue	NOUN
ejpam-5749	526	24	1–3	1–3	NUM
ejpam-5749	526	25	.	.	NOUN
ejpam-5749	526	26	2004	2004	NUM
ejpam-5749	526	27	.	.	PUNCT
ejpam-5749	527	1	[	[	X
ejpam-5749	527	2	9	9	NUM
ejpam-5749	527	3	]	]	PUNCT
ejpam-5749	527	4	w.	w.	PROPN
ejpam-5749	527	5	goddard	goddard	PROPN
ejpam-5749	527	6	,	,	PUNCT
ejpam-5749	527	7	m.	m.	NOUN
ejpam-5749	527	8	henning	henning	PROPN
ejpam-5749	527	9	and	and	CCONJ
ejpam-5749	527	10	c.	c.	PROPN
ejpam-5749	527	11	mcpillan	mcpillan	PROPN
ejpam-5749	527	12	,	,	PUNCT
ejpam-5749	527	13	semitotal	semitotal	ADJ
ejpam-5749	527	14	domination	domination	NOUN
ejpam-5749	527	15	in	in	ADP
ejpam-5749	527	16	graphs	graph	NOUN
ejpam-5749	527	17	,	,	PUNCT
ejpam-5749	527	18	utilitas	utilitas	PROPN
ejpam-5749	527	19	mathematica	mathematica	PROPN
ejpam-5749	527	20	,	,	PUNCT
ejpam-5749	527	21	vol	vol	NOUN
ejpam-5749	527	22	94	94	NUM
ejpam-5749	527	23	,	,	PUNCT
ejpam-5749	527	24	67	67	NUM
ejpam-5749	527	25	-	-	SYM
ejpam-5749	527	26	81	81	NUM
ejpam-5749	527	27	,	,	PUNCT
ejpam-5749	527	28	2014	2014	NUM
ejpam-5749	527	29	.	.	PUNCT
ejpam-5749	528	1	[	[	X
ejpam-5749	528	2	10	10	NUM
ejpam-5749	528	3	]	]	X
ejpam-5749	528	4	g.	g.	PROPN
ejpam-5749	528	5	hao	hao	PROPN
ejpam-5749	528	6	and	and	CCONJ
ejpam-5749	528	7	w.	w.	PROPN
ejpam-5749	528	8	zhuang	zhuang	PROPN
ejpam-5749	528	9	,	,	PUNCT
ejpam-5749	528	10	semitotal	semitotal	ADJ
ejpam-5749	528	11	domination	domination	NOUN
ejpam-5749	528	12	in	in	ADP
ejpam-5749	528	13	trees	tree	NOUN
ejpam-5749	528	14	,	,	PUNCT
ejpam-5749	528	15	discrete	discrete	ADJ
ejpam-5749	528	16	mathematics	mathematic	NOUN
ejpam-5749	528	17	and	and	CCONJ
ejpam-5749	528	18	theoretical	theoretical	ADJ
ejpam-5749	528	19	computer	computer	NOUN
ejpam-5749	528	20	science	science	NOUN
ejpam-5749	528	21	,	,	PUNCT
ejpam-5749	528	22	vol	vol	NOUN
ejpam-5749	528	23	.	.	PUNCT
ejpam-5749	528	24	20(2	20(2	NUM
ejpam-5749	528	25	)	)	PUNCT
ejpam-5749	528	26	,	,	PUNCT
ejpam-5749	528	27	1	1	NUM
ejpam-5749	528	28	-	-	SYM
ejpam-5749	528	29	11	11	NUM
ejpam-5749	528	30	,	,	PUNCT
ejpam-5749	528	31	2018	2018	NUM
ejpam-5749	528	32	.	.	PUNCT
ejpam-5749	529	1	[	[	X
ejpam-5749	529	2	11	11	NUM
ejpam-5749	529	3	]	]	X
ejpam-5749	529	4	m.a	m.a	PROPN
ejpam-5749	529	5	.	.	PROPN
ejpam-5749	529	6	henning	henning	PROPN
ejpam-5749	529	7	,	,	PUNCT
ejpam-5749	529	8	s.t	s.t	PROPN
ejpam-5749	529	9	.	.	PROPN
ejpam-5749	529	10	hedetniemi	hedetniemi	PROPN
ejpam-5749	529	11	.	.	PUNCT
ejpam-5749	530	1	defending	defend	VERB
ejpam-5749	530	2	the	the	DET
ejpam-5749	530	3	roman	roman	ADJ
ejpam-5749	530	4	empire	empire	NOUN
ejpam-5749	530	5	—	—	PUNCT
ejpam-5749	530	6	a	a	DET
ejpam-5749	530	7	new	new	ADJ
ejpam-5749	530	8	strategy	strategy	NOUN
ejpam-5749	530	9	,	,	PUNCT
ejpam-5749	530	10	discrete	discrete	ADJ
ejpam-5749	530	11	mathematics	mathematic	NOUN
ejpam-5749	530	12	volume	volume	NOUN
ejpam-5749	530	13	266	266	NUM
ejpam-5749	530	14	,	,	PUNCT
ejpam-5749	530	15	issues	issue	NOUN
ejpam-5749	530	16	1–3	1–3	NUM
ejpam-5749	530	17	.	.	NOUN
ejpam-5749	530	18	2003	2003	NUM
ejpam-5749	530	19	.	.	PUNCT
ejpam-5749	531	1	[	[	X
ejpam-5749	531	2	12	12	NUM
ejpam-5749	531	3	]	]	PUNCT
ejpam-5749	531	4	m.	m.	NOUN
ejpam-5749	531	5	henning	henning	PROPN
ejpam-5749	531	6	and	and	CCONJ
ejpam-5749	531	7	a.	a.	PROPN
ejpam-5749	531	8	yeo	yeo	PROPN
ejpam-5749	531	9	,	,	PUNCT
ejpam-5749	531	10	total	total	ADJ
ejpam-5749	531	11	domination	domination	NOUN
ejpam-5749	531	12	in	in	ADP
ejpam-5749	531	13	graphs	graph	NOUN
ejpam-5749	531	14	,	,	PUNCT
ejpam-5749	531	15	springer	springer	NOUN
ejpam-5749	531	16	monographs	monograph	NOUN
ejpam-5749	531	17	in	in	ADP
ejpam-5749	531	18	mathematics	mathematic	NOUN
ejpam-5749	531	19	,	,	PUNCT
ejpam-5749	531	20	springer	springer	NOUN
ejpam-5749	531	21	,	,	PUNCT
ejpam-5749	531	22	2013	2013	NUM
ejpam-5749	531	23	.	.	PUNCT
ejpam-5749	532	1	[	[	X
ejpam-5749	532	2	13	13	NUM
ejpam-5749	532	3	]	]	PUNCT
ejpam-5749	532	4	m.	m.	NOUN
ejpam-5749	532	5	henning	henning	PROPN
ejpam-5749	532	6	and	and	CCONJ
ejpam-5749	532	7	a.	a.	NOUN
ejpam-5749	532	8	marcon	marcon	PROPN
ejpam-5749	532	9	,	,	PUNCT
ejpam-5749	532	10	on	on	ADP
ejpam-5749	532	11	matching	match	VERB
ejpam-5749	532	12	and	and	CCONJ
ejpam-5749	532	13	semitotal	semitotal	ADJ
ejpam-5749	532	14	domination	domination	NOUN
ejpam-5749	532	15	in	in	ADP
ejpam-5749	532	16	graphs	graph	NOUN
ejpam-5749	532	17	,	,	PUNCT
ejpam-5749	532	18	discrete	discrete	ADJ
ejpam-5749	532	19	mathematics	mathematic	NOUN
ejpam-5749	532	20	,	,	PUNCT
ejpam-5749	532	21	vol	vol	NOUN
ejpam-5749	532	22	324(6	324(6	NUM
ejpam-5749	532	23	)	)	PUNCT
ejpam-5749	532	24	,	,	PUNCT
ejpam-5749	532	25	13	13	NUM
ejpam-5749	532	26	-	-	SYM
ejpam-5749	532	27	18	18	NUM
ejpam-5749	532	28	,	,	PUNCT
ejpam-5749	532	29	2014	2014	NUM
ejpam-5749	532	30	.	.	PUNCT
ejpam-5749	533	1	[	[	X
ejpam-5749	533	2	14	14	NUM
ejpam-5749	533	3	]	]	X
ejpam-5749	533	4	m.	m.	NOUN
ejpam-5749	533	5	henning	henning	PROPN
ejpam-5749	533	6	and	and	CCONJ
ejpam-5749	533	7	a.	a.	NOUN
ejpam-5749	533	8	marcon	marcon	PROPN
ejpam-5749	533	9	,	,	PUNCT
ejpam-5749	533	10	semitotal	semitotal	ADJ
ejpam-5749	533	11	domination	domination	NOUN
ejpam-5749	533	12	in	in	ADP
ejpam-5749	533	13	claw	claw	NOUN
ejpam-5749	533	14	-	-	PUNCT
ejpam-5749	533	15	free	free	ADJ
ejpam-5749	533	16	cubic	cubic	ADJ
ejpam-5749	533	17	graphs	graph	NOUN
ejpam-5749	533	18	,	,	PUNCT
ejpam-5749	533	19	annals	annal	NOUN
ejpam-5749	533	20	of	of	ADP
ejpam-5749	533	21	combinatorics	combinatoric	NOUN
ejpam-5749	533	22	,	,	PUNCT
ejpam-5749	533	23	vol	vol	NOUN
ejpam-5749	533	24	20(4	20(4	NOUN
ejpam-5749	533	25	)	)	PUNCT
ejpam-5749	533	26	,	,	PUNCT
ejpam-5749	533	27	799	799	NUM
ejpam-5749	533	28	-	-	SYM
ejpam-5749	533	29	813	813	NUM
ejpam-5749	533	30	,	,	PUNCT
ejpam-5749	533	31	2016	2016	NUM
ejpam-5749	533	32	.	.	PUNCT
ejpam-5749	534	1	[	[	X
ejpam-5749	534	2	15	15	NUM
ejpam-5749	534	3	]	]	PUNCT
ejpam-5749	534	4	a.martinez	a.martinez	NOUN
ejpam-5749	534	5	,	,	PUNCT
ejpam-5749	534	6	s.	s.	PROPN
ejpam-5749	534	7	garcia	garcia	PROPN
ejpam-5749	534	8	and	and	CCONJ
ejpam-5749	534	9	a.	a.	NOUN
ejpam-5749	534	10	garcia	garcia	PROPN
ejpam-5749	534	11	,	,	PUNCT
ejpam-5749	534	12	further	further	ADJ
ejpam-5749	534	13	results	result	NOUN
ejpam-5749	534	14	on	on	ADP
ejpam-5749	534	15	the	the	DET
ejpam-5749	534	16	total	total	ADJ
ejpam-5749	534	17	roman	roman	ADJ
ejpam-5749	534	18	domination	domination	NOUN
ejpam-5749	534	19	in	in	ADP
ejpam-5749	534	20	graphs	graph	NOUN
ejpam-5749	534	21	,	,	PUNCT
ejpam-5749	534	22	mathematics	mathematic	NOUN
ejpam-5749	534	23	,	,	PUNCT
ejpam-5749	534	24	vol	vol	NOUN
ejpam-5749	534	25	.	.	PUNCT
ejpam-5749	534	26	8(3	8(3	NUM
ejpam-5749	534	27	)	)	PUNCT
ejpam-5749	534	28	,	,	PUNCT
ejpam-5749	534	29	2020	2020	NUM
ejpam-5749	534	30	.	.	PUNCT
ejpam-5749	535	1	[	[	X
ejpam-5749	535	2	16	16	NUM
ejpam-5749	535	3	]	]	X
ejpam-5749	535	4	m.j	m.j	PROPN
ejpam-5749	535	5	.	.	PROPN
ejpam-5749	535	6	rivera	rivera	PROPN
ejpam-5749	535	7	and	and	CCONJ
ejpam-5749	535	8	f.p	f.p	PROPN
ejpam-5749	535	9	.	.	PROPN
ejpam-5749	535	10	jamil	jamil	PROPN
ejpam-5749	535	11	,	,	PUNCT
ejpam-5749	535	12	total	total	ADJ
ejpam-5749	535	13	roman	roman	ADJ
ejpam-5749	535	14	domination	domination	NOUN
ejpam-5749	535	15	in	in	ADP
ejpam-5749	535	16	the	the	DET
ejpam-5749	535	17	join	join	NOUN
ejpam-5749	535	18	,	,	PUNCT
ejpam-5749	535	19	corona	corona	NOUN
ejpam-5749	535	20	and	and	CCONJ
ejpam-5749	535	21	complementary	complementary	ADJ
ejpam-5749	535	22	prism	prism	NOUN
ejpam-5749	535	23	of	of	ADP
ejpam-5749	535	24	graphs	graph	NOUN
ejpam-5749	535	25	,	,	PUNCT
ejpam-5749	535	26	asia	asia	PROPN
ejpam-5749	535	27	pacific	pacific	PROPN
ejpam-5749	535	28	journal	journal	PROPN
ejpam-5749	535	29	of	of	ADP
ejpam-5749	535	30	science	science	NOUN
ejpam-5749	535	31	,	,	PUNCT
ejpam-5749	535	32	mathematics	mathematic	NOUN
ejpam-5749	535	33	and	and	CCONJ
ejpam-5749	535	34	engineering	engineering	NOUN
ejpam-5749	535	35	,	,	PUNCT
ejpam-5749	535	36	vol	vol	NOUN
ejpam-5749	535	37	.	.	PUNCT
ejpam-5749	535	38	7(2)(2021	7(2)(2021	NUM
ejpam-5749	535	39	)	)	PUNCT
ejpam-5749	535	40	,	,	PUNCT
ejpam-5749	535	41	pp	pp	ADP
ejpam-5749	535	42	37	37	NUM
ejpam-5749	535	43	-	-	SYM
ejpam-5749	535	44	48	48	NUM
ejpam-5749	535	45	.	.	PUNCT
ejpam-5749	536	1	[	[	X
ejpam-5749	536	2	17	17	NUM
ejpam-5749	536	3	]	]	X
ejpam-5749	536	4	c.s	c.s	PROPN
ejpam-5749	536	5	.	.	PROPN
ejpam-5749	536	6	revelle	revelle	PROPN
ejpam-5749	536	7	,	,	PUNCT
ejpam-5749	536	8	k.e	k.e	PROPN
ejpam-5749	536	9	.	.	PROPN
ejpam-5749	536	10	rosing	rosing	PROPN
ejpam-5749	536	11	,	,	PUNCT
ejpam-5749	536	12	defendens	defenden	VERB
ejpam-5749	536	13	imperium	imperium	NOUN
ejpam-5749	536	14	romanum	romanum	NOUN
ejpam-5749	536	15	:	:	PUNCT
ejpam-5749	536	16	a	a	DET
ejpam-5749	536	17	classical	classical	ADJ
ejpam-5749	536	18	problem	problem	NOUN
ejpam-5749	536	19	in	in	ADP
ejpam-5749	536	20	military	military	ADJ
ejpam-5749	536	21	strategy	strategy	NOUN
ejpam-5749	536	22	,	,	PUNCT
ejpam-5749	536	23	amer	amer	PROPN
ejpam-5749	536	24	.	.	PROPN
ejpam-5749	536	25	math	math	PROPN
ejpam-5749	536	26	.	.	PUNCT
ejpam-5749	537	1	monthly	monthly	ADJ
ejpam-5749	537	2	,	,	PUNCT
ejpam-5749	537	3	volume	volume	NOUN
ejpam-5749	537	4	107(7	107(7	NUM
ejpam-5749	537	5	)	)	PUNCT
ejpam-5749	537	6	pages	page	NOUN
ejpam-5749	537	7	585	585	NUM
ejpam-5749	537	8	-	-	SYM
ejpam-5749	537	9	594	594	NUM
ejpam-5749	537	10	,	,	PUNCT
ejpam-5749	537	11	(	(	PUNCT
ejpam-5749	537	12	2000	2000	NUM
ejpam-5749	537	13	)	)	PUNCT
ejpam-5749	537	14	.	.	PUNCT
ejpam-5749	538	1	[	[	X
ejpam-5749	538	2	18	18	NUM
ejpam-5749	538	3	]	]	X
ejpam-5749	538	4	i.	i.	PROPN
ejpam-5749	538	5	stewart	stewart	PROPN
ejpam-5749	538	6	,	,	PUNCT
ejpam-5749	538	7	defend	defend	VERB
ejpam-5749	538	8	the	the	DET
ejpam-5749	538	9	roman	roman	ADJ
ejpam-5749	538	10	empire	empire	NOUN
ejpam-5749	538	11	!	!	PUNCT
ejpam-5749	538	12	.	.	PUNCT
ejpam-5749	539	1	sci	sci	PROPN
ejpam-5749	539	2	.	.	PROPN
ejpam-5749	539	3	amer	amer	PROPN
ejpam-5749	539	4	.	.	PUNCT
ejpam-5749	540	1	volume	volume	NOUN
ejpam-5749	540	2	281(6	281(6	NUM
ejpam-5749	540	3	)	)	PUNCT
ejpam-5749	540	4	pages	page	NOUN
ejpam-5749	540	5	136	136	NUM
ejpam-5749	540	6	-	-	SYM
ejpam-5749	540	7	139	139	NUM
ejpam-5749	540	8	,	,	PUNCT
ejpam-5749	540	9	(	(	PUNCT
ejpam-5749	540	10	1999	1999	NUM
ejpam-5749	540	11	)	)	PUNCT
ejpam-5749	540	12	.	.	PUNCT