id	sid	tid	token	lemma	pos
ejpam-4144	1	1	european	european	PROPN
ejpam-4144	1	2	journal	journal	PROPN
ejpam-4144	1	3	of	of	ADP
ejpam-4144	1	4	pure	pure	ADJ
ejpam-4144	1	5	and	and	CCONJ
ejpam-4144	1	6	applied	apply	VERB
ejpam-4144	1	7	mathematics	mathematic	NOUN
ejpam-4144	1	8	vol	vol	NOUN
ejpam-4144	1	9	.	.	PUNCT
ejpam-4144	2	1	14	14	NUM
ejpam-4144	2	2	,	,	PUNCT
ejpam-4144	2	3	no	no	INTJ
ejpam-4144	2	4	.	.	NOUN
ejpam-4144	2	5	4	4	NUM
ejpam-4144	2	6	,	,	PUNCT
ejpam-4144	2	7	2021	2021	NUM
ejpam-4144	2	8	,	,	PUNCT
ejpam-4144	2	9	1415	1415	NUM
ejpam-4144	2	10	-	-	SYM
ejpam-4144	2	11	1428	1428	NUM
ejpam-4144	2	12	issn	issn	PROPN
ejpam-4144	2	13	1307	1307	NUM
ejpam-4144	2	14	-	-	SYM
ejpam-4144	2	15	5543	5543	NUM
ejpam-4144	2	16	–	–	PUNCT
ejpam-4144	2	17	ejpam.com	ejpam.com	X
ejpam-4144	2	18	published	publish	VERB
ejpam-4144	2	19	by	by	ADP
ejpam-4144	2	20	new	new	PROPN
ejpam-4144	2	21	york	york	PROPN
ejpam-4144	2	22	business	business	PROPN
ejpam-4144	2	23	global	global	ADJ
ejpam-4144	2	24	revisiting	revisiting	ADJ
ejpam-4144	2	25	domination	domination	NOUN
ejpam-4144	2	26	,	,	PUNCT
ejpam-4144	2	27	hop	hop	NOUN
ejpam-4144	2	28	domination	domination	NOUN
ejpam-4144	2	29	,	,	PUNCT
ejpam-4144	2	30	and	and	CCONJ
ejpam-4144	2	31	global	global	ADJ
ejpam-4144	2	32	hop	hop	NOUN
ejpam-4144	2	33	domination	domination	NOUN
ejpam-4144	2	34	in	in	ADP
ejpam-4144	2	35	graphs	graph	NOUN
ejpam-4144	2	36	gemma	gemma	PROPN
ejpam-4144	2	37	salasalan1,∗	salasalan1,∗	PROPN
ejpam-4144	2	38	,	,	PUNCT
ejpam-4144	2	39	sergio	sergio	PROPN
ejpam-4144	2	40	r.	r.	PROPN
ejpam-4144	2	41	canoy	canoy	PROPN
ejpam-4144	2	42	,	,	PUNCT
ejpam-4144	2	43	jr.2,3	jr.2,3	PROPN
ejpam-4144	2	44	1	1	NUM
ejpam-4144	2	45	department	department	NOUN
ejpam-4144	2	46	of	of	ADP
ejpam-4144	2	47	arts	art	NOUN
ejpam-4144	2	48	and	and	CCONJ
ejpam-4144	2	49	sciences	sciences	PROPN
ejpam-4144	2	50	,	,	PUNCT
ejpam-4144	2	51	institute	institute	NOUN
ejpam-4144	2	52	of	of	ADP
ejpam-4144	2	53	teacher	teacher	NOUN
ejpam-4144	2	54	education	education	NOUN
ejpam-4144	2	55	,	,	PUNCT
ejpam-4144	2	56	arts	art	NOUN
ejpam-4144	2	57	and	and	CCONJ
ejpam-4144	2	58	sciences	science	NOUN
ejpam-4144	2	59	,	,	PUNCT
ejpam-4144	2	60	davao	davao	PROPN
ejpam-4144	2	61	del	del	PROPN
ejpam-4144	2	62	sur	sur	PROPN
ejpam-4144	2	63	state	state	PROPN
ejpam-4144	2	64	college	college	PROPN
ejpam-4144	2	65	,	,	PUNCT
ejpam-4144	2	66	matti	matti	PROPN
ejpam-4144	2	67	,	,	PUNCT
ejpam-4144	2	68	digos	digos	PROPN
ejpam-4144	2	69	city	city	PROPN
ejpam-4144	2	70	,	,	PUNCT
ejpam-4144	2	71	davao	davao	PROPN
ejpam-4144	2	72	del	del	PROPN
ejpam-4144	2	73	sur	sur	PROPN
ejpam-4144	2	74	,	,	PUNCT
ejpam-4144	2	75	philippines	philippines	PROPN
ejpam-4144	2	76	2	2	NUM
ejpam-4144	2	77	department	department	NOUN
ejpam-4144	2	78	of	of	ADP
ejpam-4144	2	79	mathematics	mathematic	NOUN
ejpam-4144	2	80	and	and	CCONJ
ejpam-4144	2	81	statistics	statistic	NOUN
ejpam-4144	2	82	,	,	PUNCT
ejpam-4144	2	83	college	college	NOUN
ejpam-4144	2	84	of	of	ADP
ejpam-4144	2	85	science	science	NOUN
ejpam-4144	2	86	and	and	CCONJ
ejpam-4144	2	87	mathematics	mathematic	NOUN
ejpam-4144	2	88	,	,	PUNCT
ejpam-4144	2	89	msu	msu	PROPN
ejpam-4144	2	90	-	-	PUNCT
ejpam-4144	2	91	iligan	iligan	PROPN
ejpam-4144	2	92	institute	institute	PROPN
ejpam-4144	2	93	of	of	ADP
ejpam-4144	2	94	technology	technology	PROPN
ejpam-4144	2	95	,	,	PUNCT
ejpam-4144	2	96	,	,	PUNCT
ejpam-4144	2	97	9200	9200	NUM
ejpam-4144	2	98	iligan	iligan	ADJ
ejpam-4144	2	99	city	city	NOUN
ejpam-4144	2	100	,	,	PUNCT
ejpam-4144	2	101	philippines	philippine	NOUN
ejpam-4144	2	102	3	3	NUM
ejpam-4144	2	103	center	center	NOUN
ejpam-4144	2	104	of	of	ADP
ejpam-4144	2	105	graph	graph	NOUN
ejpam-4144	2	106	theory	theory	NOUN
ejpam-4144	2	107	,	,	PUNCT
ejpam-4144	2	108	algebra	algebra	NOUN
ejpam-4144	2	109	and	and	CCONJ
ejpam-4144	2	110	analysis	analysis	NOUN
ejpam-4144	2	111	,	,	PUNCT
ejpam-4144	2	112	premier	premier	PROPN
ejpam-4144	2	113	research	research	PROPN
ejpam-4144	2	114	institute	institute	PROPN
ejpam-4144	2	115	of	of	ADP
ejpam-4144	2	116	science	science	NOUN
ejpam-4144	2	117	and	and	CCONJ
ejpam-4144	2	118	mathematics	mathematic	NOUN
ejpam-4144	2	119	,	,	PUNCT
ejpam-4144	2	120	msu	msu	PROPN
ejpam-4144	2	121	-	-	PUNCT
ejpam-4144	2	122	iligan	iligan	PROPN
ejpam-4144	2	123	institute	institute	PROPN
ejpam-4144	2	124	of	of	ADP
ejpam-4144	2	125	technology	technology	PROPN
ejpam-4144	2	126	,	,	PUNCT
ejpam-4144	2	127	9200	9200	NUM
ejpam-4144	2	128	iligan	iligan	ADJ
ejpam-4144	2	129	city	city	NOUN
ejpam-4144	2	130	,	,	PUNCT
ejpam-4144	2	131	philippines	philippine	NOUN
ejpam-4144	2	132	abstract	abstract	ADJ
ejpam-4144	2	133	.	.	PUNCT
ejpam-4144	3	1	a	a	DET
ejpam-4144	3	2	set	set	NOUN
ejpam-4144	3	3	s	s	NOUN
ejpam-4144	3	4	⊆	⊆	NUM
ejpam-4144	3	5	v	v	NOUN
ejpam-4144	3	6	(	(	PUNCT
ejpam-4144	3	7	g	g	NOUN
ejpam-4144	3	8	)	)	PUNCT
ejpam-4144	3	9	is	be	AUX
ejpam-4144	3	10	a	a	DET
ejpam-4144	3	11	hop	hop	NOUN
ejpam-4144	3	12	dominating	dominating	NOUN
ejpam-4144	3	13	set	set	NOUN
ejpam-4144	3	14	of	of	ADP
ejpam-4144	3	15	g	g	PROPN
ejpam-4144	3	16	if	if	SCONJ
ejpam-4144	3	17	for	for	ADP
ejpam-4144	3	18	each	each	PRON
ejpam-4144	3	19	v	v	NUM
ejpam-4144	3	20	∈	∈	PROPN
ejpam-4144	3	21	v	v	NOUN
ejpam-4144	3	22	(	(	PUNCT
ejpam-4144	3	23	g	g	NOUN
ejpam-4144	3	24	)	)	PUNCT
ejpam-4144	3	25	\	\	PROPN
ejpam-4144	4	1	s	s	X
ejpam-4144	4	2	,	,	PUNCT
ejpam-4144	4	3	there	there	PRON
ejpam-4144	4	4	exists	exist	VERB
ejpam-4144	4	5	w	w	PROPN
ejpam-4144	4	6	∈	∈	PROPN
ejpam-4144	4	7	s	s	VERB
ejpam-4144	5	1	such	such	ADJ
ejpam-4144	5	2	that	that	PRON
ejpam-4144	5	3	dg(v	dg(v	ADJ
ejpam-4144	5	4	,	,	PUNCT
ejpam-4144	5	5	w	w	NOUN
ejpam-4144	5	6	)	)	PUNCT
ejpam-4144	5	7	=	=	SYM
ejpam-4144	5	8	2	2	X
ejpam-4144	5	9	.	.	PUNCT
ejpam-4144	6	1	it	it	PRON
ejpam-4144	6	2	is	be	AUX
ejpam-4144	6	3	a	a	DET
ejpam-4144	6	4	global	global	ADJ
ejpam-4144	6	5	hop	hop	NOUN
ejpam-4144	6	6	dominating	dominating	NOUN
ejpam-4144	6	7	set	set	NOUN
ejpam-4144	6	8	of	of	ADP
ejpam-4144	6	9	g	g	PROPN
ejpam-4144	6	10	if	if	SCONJ
ejpam-4144	6	11	it	it	PRON
ejpam-4144	6	12	is	be	AUX
ejpam-4144	6	13	a	a	DET
ejpam-4144	6	14	hop	hop	NOUN
ejpam-4144	6	15	dominating	dominating	NOUN
ejpam-4144	6	16	set	set	NOUN
ejpam-4144	6	17	of	of	ADP
ejpam-4144	6	18	both	both	CCONJ
ejpam-4144	6	19	g	g	PROPN
ejpam-4144	6	20	and	and	CCONJ
ejpam-4144	6	21	the	the	DET
ejpam-4144	6	22	complement	complement	NOUN
ejpam-4144	6	23	g	g	PROPN
ejpam-4144	6	24	of	of	ADP
ejpam-4144	6	25	g.	g.	PROPN
ejpam-4144	6	26	the	the	DET
ejpam-4144	6	27	minimum	minimum	ADJ
ejpam-4144	6	28	cardinality	cardinality	NOUN
ejpam-4144	6	29	of	of	ADP
ejpam-4144	6	30	a	a	DET
ejpam-4144	6	31	hop	hop	NOUN
ejpam-4144	6	32	dominating	dominating	NOUN
ejpam-4144	6	33	(	(	PUNCT
ejpam-4144	6	34	global	global	ADJ
ejpam-4144	6	35	hop	hop	NOUN
ejpam-4144	6	36	dominating	dominating	NOUN
ejpam-4144	6	37	)	)	PUNCT
ejpam-4144	6	38	set	set	NOUN
ejpam-4144	6	39	of	of	ADP
ejpam-4144	6	40	g	g	NOUN
ejpam-4144	6	41	,	,	PUNCT
ejpam-4144	6	42	denoted	denote	VERB
ejpam-4144	6	43	by	by	ADP
ejpam-4144	6	44	γh(g	γh(g	NOUN
ejpam-4144	6	45	)	)	PUNCT
ejpam-4144	6	46	(	(	PUNCT
ejpam-4144	6	47	resp	resp	NOUN
ejpam-4144	6	48	.	.	PUNCT
ejpam-4144	7	1	γgh(g	γgh(g	NOUN
ejpam-4144	7	2	)	)	PUNCT
ejpam-4144	7	3	)	)	PUNCT
ejpam-4144	7	4	,	,	PUNCT
ejpam-4144	7	5	is	be	AUX
ejpam-4144	7	6	called	call	VERB
ejpam-4144	7	7	the	the	DET
ejpam-4144	7	8	hop	hop	NOUN
ejpam-4144	7	9	domination	domination	NOUN
ejpam-4144	7	10	(	(	PUNCT
ejpam-4144	7	11	resp	resp	NOUN
ejpam-4144	7	12	.	.	PUNCT
ejpam-4144	8	1	global	global	ADJ
ejpam-4144	8	2	hop	hop	PROPN
ejpam-4144	8	3	domination	domination	NOUN
ejpam-4144	8	4	)	)	PUNCT
ejpam-4144	8	5	number	number	NOUN
ejpam-4144	8	6	of	of	ADP
ejpam-4144	8	7	g.	g.	PROPN
ejpam-4144	8	8	in	in	ADP
ejpam-4144	8	9	this	this	DET
ejpam-4144	8	10	paper	paper	NOUN
ejpam-4144	8	11	,	,	PUNCT
ejpam-4144	8	12	we	we	PRON
ejpam-4144	8	13	give	give	VERB
ejpam-4144	8	14	some	some	DET
ejpam-4144	8	15	realization	realization	NOUN
ejpam-4144	8	16	results	result	NOUN
ejpam-4144	8	17	involving	involve	VERB
ejpam-4144	8	18	domination	domination	NOUN
ejpam-4144	8	19	,	,	PUNCT
ejpam-4144	8	20	hop	hop	NOUN
ejpam-4144	8	21	domination	domination	NOUN
ejpam-4144	8	22	,	,	PUNCT
ejpam-4144	8	23	and	and	CCONJ
ejpam-4144	8	24	global	global	ADJ
ejpam-4144	8	25	hop	hop	NOUN
ejpam-4144	8	26	domination	domination	NOUN
ejpam-4144	8	27	parameters	parameter	NOUN
ejpam-4144	8	28	.	.	PUNCT
ejpam-4144	9	1	also	also	ADV
ejpam-4144	9	2	,	,	PUNCT
ejpam-4144	9	3	we	we	PRON
ejpam-4144	9	4	give	give	VERB
ejpam-4144	9	5	a	a	DET
ejpam-4144	9	6	rectification	rectification	NOUN
ejpam-4144	9	7	of	of	ADP
ejpam-4144	9	8	a	a	DET
ejpam-4144	9	9	result	result	NOUN
ejpam-4144	9	10	found	find	VERB
ejpam-4144	9	11	in	in	ADP
ejpam-4144	9	12	a	a	DET
ejpam-4144	9	13	recent	recent	ADJ
ejpam-4144	9	14	paper	paper	NOUN
ejpam-4144	9	15	of	of	ADP
ejpam-4144	9	16	the	the	DET
ejpam-4144	9	17	authors	author	NOUN
ejpam-4144	9	18	and	and	CCONJ
ejpam-4144	9	19	use	use	VERB
ejpam-4144	9	20	this	this	PRON
ejpam-4144	9	21	to	to	PART
ejpam-4144	9	22	prove	prove	VERB
ejpam-4144	9	23	some	some	DET
ejpam-4144	9	24	results	result	NOUN
ejpam-4144	9	25	in	in	ADP
ejpam-4144	9	26	this	this	DET
ejpam-4144	9	27	paper	paper	NOUN
ejpam-4144	9	28	.	.	PUNCT
ejpam-4144	10	1	2020	2020	NUM
ejpam-4144	10	2	mathematics	mathematic	NOUN
ejpam-4144	10	3	subject	subject	NOUN
ejpam-4144	10	4	classifications	classification	NOUN
ejpam-4144	10	5	:	:	PUNCT
ejpam-4144	10	6	05c69	05c69	X
ejpam-4144	10	7	key	key	ADJ
ejpam-4144	10	8	words	word	NOUN
ejpam-4144	10	9	and	and	CCONJ
ejpam-4144	10	10	phrases	phrase	NOUN
ejpam-4144	10	11	:	:	PUNCT
ejpam-4144	10	12	domination	domination	NOUN
ejpam-4144	10	13	,	,	PUNCT
ejpam-4144	10	14	hop	hop	NOUN
ejpam-4144	10	15	domination	domination	NOUN
ejpam-4144	10	16	,	,	PUNCT
ejpam-4144	10	17	global	global	ADJ
ejpam-4144	10	18	hop	hop	NOUN
ejpam-4144	10	19	domination	domination	PROPN
ejpam-4144	10	20	,	,	PUNCT
ejpam-4144	10	21	complementary	complementary	ADJ
ejpam-4144	10	22	prism	prism	NOUN
ejpam-4144	10	23	,	,	PUNCT
ejpam-4144	10	24	shadow	shadow	NOUN
ejpam-4144	10	25	graph	graph	NOUN
ejpam-4144	10	26	1	1	NUM
ejpam-4144	10	27	.	.	PUNCT
ejpam-4144	11	1	introduction	introduction	NOUN
ejpam-4144	11	2	domination	domination	NOUN
ejpam-4144	11	3	has	have	AUX
ejpam-4144	11	4	been	be	AUX
ejpam-4144	11	5	a	a	DET
ejpam-4144	11	6	topic	topic	NOUN
ejpam-4144	11	7	of	of	ADP
ejpam-4144	11	8	interest	interest	NOUN
ejpam-4144	11	9	to	to	ADP
ejpam-4144	11	10	many	many	ADJ
ejpam-4144	11	11	researchers	researcher	NOUN
ejpam-4144	11	12	in	in	ADP
ejpam-4144	11	13	the	the	DET
ejpam-4144	11	14	field	field	NOUN
ejpam-4144	11	15	of	of	ADP
ejpam-4144	11	16	graph	graph	NOUN
ejpam-4144	11	17	theory	theory	NOUN
ejpam-4144	11	18	.	.	PUNCT
ejpam-4144	12	1	by	by	ADP
ejpam-4144	12	2	imposing	impose	VERB
ejpam-4144	12	3	certain	certain	ADJ
ejpam-4144	12	4	additional	additional	ADJ
ejpam-4144	12	5	conditions	condition	NOUN
ejpam-4144	12	6	or	or	CCONJ
ejpam-4144	12	7	formulating	formulate	VERB
ejpam-4144	12	8	similar	similar	ADJ
ejpam-4144	12	9	conditions	condition	NOUN
ejpam-4144	12	10	from	from	ADP
ejpam-4144	12	11	the	the	DET
ejpam-4144	12	12	standard	standard	ADJ
ejpam-4144	12	13	concept	concept	NOUN
ejpam-4144	12	14	,	,	PUNCT
ejpam-4144	12	15	a	a	DET
ejpam-4144	12	16	variant	variant	NOUN
ejpam-4144	12	17	can	can	AUX
ejpam-4144	12	18	then	then	ADV
ejpam-4144	12	19	be	be	AUX
ejpam-4144	12	20	obtained	obtain	VERB
ejpam-4144	12	21	.	.	PUNCT
ejpam-4144	13	1	indeed	indeed	ADV
ejpam-4144	13	2	,	,	PUNCT
ejpam-4144	13	3	the	the	DET
ejpam-4144	13	4	domination	domination	NOUN
ejpam-4144	13	5	concept	concept	NOUN
ejpam-4144	13	6	yielded	yield	VERB
ejpam-4144	13	7	several	several	ADJ
ejpam-4144	13	8	variations	variation	NOUN
ejpam-4144	13	9	which	which	PRON
ejpam-4144	13	10	have	have	AUX
ejpam-4144	13	11	been	be	AUX
ejpam-4144	13	12	investigated	investigate	VERB
ejpam-4144	13	13	by	by	ADP
ejpam-4144	13	14	researchers	researcher	NOUN
ejpam-4144	13	15	.	.	PUNCT
ejpam-4144	14	1	some	some	PRON
ejpam-4144	14	2	of	of	ADP
ejpam-4144	14	3	these	these	DET
ejpam-4144	14	4	variants	variant	NOUN
ejpam-4144	14	5	can	can	AUX
ejpam-4144	14	6	be	be	AUX
ejpam-4144	14	7	found	find	VERB
ejpam-4144	14	8	in	in	ADP
ejpam-4144	14	9	[	[	X
ejpam-4144	14	10	1	1	NUM
ejpam-4144	14	11	]	]	PUNCT
ejpam-4144	14	12	,	,	PUNCT
ejpam-4144	14	13	[	[	X
ejpam-4144	14	14	2	2	NUM
ejpam-4144	14	15	]	]	PUNCT
ejpam-4144	14	16	,	,	PUNCT
ejpam-4144	14	17	[	[	X
ejpam-4144	14	18	3	3	NUM
ejpam-4144	14	19	]	]	PUNCT
ejpam-4144	14	20	,	,	PUNCT
ejpam-4144	14	21	[	[	X
ejpam-4144	14	22	4	4	NUM
ejpam-4144	14	23	]	]	PUNCT
ejpam-4144	14	24	,	,	PUNCT
ejpam-4144	14	25	[	[	X
ejpam-4144	14	26	6	6	NUM
ejpam-4144	14	27	]	]	PUNCT
ejpam-4144	14	28	,	,	PUNCT
ejpam-4144	14	29	[	[	X
ejpam-4144	14	30	7	7	NUM
ejpam-4144	14	31	]	]	PUNCT
ejpam-4144	14	32	,	,	PUNCT
ejpam-4144	14	33	[	[	X
ejpam-4144	14	34	8	8	NUM
ejpam-4144	14	35	]	]	PUNCT
ejpam-4144	14	36	,	,	PUNCT
ejpam-4144	14	37	[	[	X
ejpam-4144	14	38	9	9	NUM
ejpam-4144	14	39	]	]	PUNCT
ejpam-4144	14	40	,	,	PUNCT
ejpam-4144	14	41	[	[	X
ejpam-4144	14	42	10	10	NUM
ejpam-4144	14	43	]	]	PUNCT
ejpam-4144	14	44	and	and	CCONJ
ejpam-4144	14	45	[	[	X
ejpam-4144	14	46	14	14	NUM
ejpam-4144	14	47	]	]	PUNCT
ejpam-4144	14	48	.	.	PUNCT
ejpam-4144	15	1	shortly	shortly	ADV
ejpam-4144	15	2	after	after	SCONJ
ejpam-4144	15	3	natarajan	natarajan	PROPN
ejpam-4144	15	4	and	and	CCONJ
ejpam-4144	15	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4144	15	6	[	[	X
ejpam-4144	15	7	13	13	NUM
ejpam-4144	15	8	]	]	PUNCT
ejpam-4144	15	9	introduced	introduce	VERB
ejpam-4144	15	10	and	and	CCONJ
ejpam-4144	15	11	studied	study	VERB
ejpam-4144	15	12	the	the	DET
ejpam-4144	15	13	concept	concept	NOUN
ejpam-4144	15	14	of	of	ADP
ejpam-4144	15	15	hop	hop	NOUN
ejpam-4144	15	16	domination	domination	NOUN
ejpam-4144	15	17	in	in	ADP
ejpam-4144	15	18	a	a	DET
ejpam-4144	15	19	graph	graph	NOUN
ejpam-4144	15	20	,	,	PUNCT
ejpam-4144	15	21	some	some	DET
ejpam-4144	15	22	variants	variant	NOUN
ejpam-4144	15	23	of	of	ADP
ejpam-4144	15	24	the	the	DET
ejpam-4144	15	25	concept	concept	NOUN
ejpam-4144	15	26	emerged	emerge	VERB
ejpam-4144	15	27	.	.	PUNCT
ejpam-4144	16	1	the	the	DET
ejpam-4144	16	2	concept	concept	NOUN
ejpam-4144	16	3	and	and	CCONJ
ejpam-4144	16	4	some	some	PRON
ejpam-4144	16	5	of	of	ADP
ejpam-4144	16	6	its	its	PRON
ejpam-4144	16	7	variants	variant	NOUN
ejpam-4144	16	8	are	be	AUX
ejpam-4144	16	9	studied	study	VERB
ejpam-4144	16	10	in	in	ADP
ejpam-4144	16	11	[	[	X
ejpam-4144	16	12	5	5	NUM
ejpam-4144	16	13	]	]	PUNCT
ejpam-4144	16	14	,	,	PUNCT
ejpam-4144	16	15	[	[	X
ejpam-4144	16	16	11	11	NUM
ejpam-4144	16	17	]	]	PUNCT
ejpam-4144	16	18	,	,	PUNCT
ejpam-4144	16	19	[	[	X
ejpam-4144	16	20	12	12	NUM
ejpam-4144	16	21	]	]	PUNCT
ejpam-4144	16	22	,	,	PUNCT
ejpam-4144	16	23	[	[	X
ejpam-4144	16	24	15	15	NUM
ejpam-4144	16	25	]	]	PUNCT
ejpam-4144	16	26	,	,	PUNCT
ejpam-4144	16	27	and	and	CCONJ
ejpam-4144	16	28	[	[	X
ejpam-4144	16	29	16	16	NUM
ejpam-4144	16	30	]	]	PUNCT
ejpam-4144	16	31	.	.	PUNCT
ejpam-4144	17	1	in	in	ADP
ejpam-4144	17	2	this	this	DET
ejpam-4144	17	3	paper	paper	NOUN
ejpam-4144	17	4	,	,	PUNCT
ejpam-4144	17	5	we	we	PRON
ejpam-4144	17	6	show	show	VERB
ejpam-4144	17	7	that	that	SCONJ
ejpam-4144	17	8	the	the	DET
ejpam-4144	17	9	standard	standard	ADJ
ejpam-4144	17	10	domination	domination	NOUN
ejpam-4144	17	11	and	and	CCONJ
ejpam-4144	17	12	hop	hop	NOUN
ejpam-4144	17	13	domination	domination	NOUN
ejpam-4144	17	14	parameters	parameter	NOUN
ejpam-4144	17	15	are	be	AUX
ejpam-4144	17	16	generally	generally	ADV
ejpam-4144	17	17	non	non	ADJ
ejpam-4144	17	18	-	-	ADJ
ejpam-4144	17	19	comparable	comparable	ADJ
ejpam-4144	17	20	.	.	PUNCT
ejpam-4144	18	1	it	it	PRON
ejpam-4144	18	2	∗corresponding	∗corresponde	VERB
ejpam-4144	18	3	author	author	NOUN
ejpam-4144	18	4	.	.	PUNCT
ejpam-4144	19	1	doi	doi	NOUN
ejpam-4144	19	2	:	:	PUNCT
ejpam-4144	19	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4144	https://doi.org/10.29020/nybg.ejpam.v14i4.4144	ADJ
ejpam-4144	19	4	email	email	NOUN
ejpam-4144	19	5	addresses	address	VERB
ejpam-4144	19	6	:	:	PUNCT
ejpam-4144	19	7	gemma.salasalan@g.msuiit.edu.ph	gemma.salasalan@g.msuiit.edu.ph	PROPN
ejpam-4144	19	8	(	(	PUNCT
ejpam-4144	19	9	g.	g.	PROPN
ejpam-4144	19	10	salasalan	salasalan	NOUN
ejpam-4144	19	11	)	)	PUNCT
ejpam-4144	19	12	,	,	PUNCT
ejpam-4144	19	13	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4144	19	14	(	(	PUNCT
ejpam-4144	19	15	s.	s.	PROPN
ejpam-4144	19	16	canoy	canoy	PROPN
ejpam-4144	19	17	,	,	PUNCT
ejpam-4144	19	18	jr	jr	PROPN
ejpam-4144	19	19	.	.	PUNCT
ejpam-4144	19	20	)	)	PUNCT
ejpam-4144	19	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4144	20	1	1415	1415	NUM
ejpam-4144	20	2	©	©	NOUN
ejpam-4144	20	3	2021	2021	NUM
ejpam-4144	20	4	ejpam	ejpam	VERB
ejpam-4144	20	5	all	all	DET
ejpam-4144	20	6	rights	right	NOUN
ejpam-4144	20	7	reserved	reserve	VERB
ejpam-4144	20	8	.	.	PUNCT
ejpam-4144	21	1	g.	g.	PROPN
ejpam-4144	21	2	salasalan	salasalan	PROPN
ejpam-4144	21	3	,	,	PUNCT
ejpam-4144	21	4	s.	s.	PROPN
ejpam-4144	21	5	canoy	canoy	PROPN
ejpam-4144	21	6	,	,	PUNCT
ejpam-4144	21	7	jr	jr	PROPN
ejpam-4144	21	8	.	.	PROPN
ejpam-4144	21	9	/	/	SYM
ejpam-4144	21	10	eur	eur	PROPN
ejpam-4144	21	11	.	.	PUNCT
ejpam-4144	22	1	j.	j.	PROPN
ejpam-4144	22	2	pure	pure	PROPN
ejpam-4144	22	3	appl	appl	PROPN
ejpam-4144	22	4	.	.	PROPN
ejpam-4144	22	5	math	math	PROPN
ejpam-4144	22	6	,	,	PUNCT
ejpam-4144	22	7	14	14	NUM
ejpam-4144	22	8	(	(	PUNCT
ejpam-4144	22	9	4	4	NUM
ejpam-4144	22	10	)	)	PUNCT
ejpam-4144	22	11	(	(	PUNCT
ejpam-4144	22	12	2021	2021	NUM
ejpam-4144	22	13	)	)	PUNCT
ejpam-4144	22	14	,	,	PUNCT
ejpam-4144	22	15	1415	1415	NUM
ejpam-4144	22	16	-	-	SYM
ejpam-4144	22	17	1428	1428	NUM
ejpam-4144	22	18	1416	1416	NUM
ejpam-4144	22	19	is	be	AUX
ejpam-4144	22	20	shown	show	VERB
ejpam-4144	22	21	that	that	SCONJ
ejpam-4144	22	22	the	the	DET
ejpam-4144	22	23	absolute	absolute	ADJ
ejpam-4144	22	24	difference	difference	NOUN
ejpam-4144	22	25	of	of	ADP
ejpam-4144	22	26	these	these	DET
ejpam-4144	22	27	parameters	parameter	NOUN
ejpam-4144	22	28	can	can	AUX
ejpam-4144	22	29	be	be	AUX
ejpam-4144	22	30	made	make	VERB
ejpam-4144	22	31	arbitrarily	arbitrarily	ADV
ejpam-4144	22	32	large	large	ADJ
ejpam-4144	22	33	.	.	PUNCT
ejpam-4144	23	1	further	far	ADV
ejpam-4144	23	2	,	,	PUNCT
ejpam-4144	23	3	we	we	PRON
ejpam-4144	23	4	rectify	rectify	VERB
ejpam-4144	23	5	a	a	DET
ejpam-4144	23	6	result	result	NOUN
ejpam-4144	23	7	found	find	VERB
ejpam-4144	23	8	in	in	ADP
ejpam-4144	23	9	[	[	X
ejpam-4144	23	10	16	16	NUM
ejpam-4144	23	11	]	]	PUNCT
ejpam-4144	23	12	and	and	CCONJ
ejpam-4144	23	13	use	use	VERB
ejpam-4144	23	14	the	the	DET
ejpam-4144	23	15	corrected	correct	VERB
ejpam-4144	23	16	result	result	NOUN
ejpam-4144	23	17	to	to	PART
ejpam-4144	23	18	prove	prove	VERB
ejpam-4144	23	19	some	some	DET
ejpam-4144	23	20	results	result	NOUN
ejpam-4144	23	21	in	in	ADP
ejpam-4144	23	22	this	this	DET
ejpam-4144	23	23	paper	paper	NOUN
ejpam-4144	23	24	.	.	PUNCT
ejpam-4144	24	1	let	let	VERB
ejpam-4144	24	2	g	g	PROPN
ejpam-4144	24	3	=	=	SYM
ejpam-4144	24	4	(	(	PUNCT
ejpam-4144	24	5	v	v	NOUN
ejpam-4144	24	6	(	(	PUNCT
ejpam-4144	24	7	g	g	NOUN
ejpam-4144	24	8	)	)	PUNCT
ejpam-4144	24	9	,	,	PUNCT
ejpam-4144	24	10	e(g	e(g	PROPN
ejpam-4144	24	11	)	)	PUNCT
ejpam-4144	24	12	)	)	PUNCT
ejpam-4144	25	1	be	be	AUX
ejpam-4144	25	2	a	a	DET
ejpam-4144	25	3	simple	simple	ADJ
ejpam-4144	25	4	undirected	undirected	ADJ
ejpam-4144	25	5	graph	graph	NOUN
ejpam-4144	25	6	.	.	PUNCT
ejpam-4144	26	1	the	the	DET
ejpam-4144	26	2	distance	distance	NOUN
ejpam-4144	26	3	between	between	ADP
ejpam-4144	26	4	two	two	NUM
ejpam-4144	26	5	vertices	vertex	NOUN
ejpam-4144	26	6	u	u	NOUN
ejpam-4144	26	7	and	and	CCONJ
ejpam-4144	26	8	v	v	NOUN
ejpam-4144	26	9	of	of	ADP
ejpam-4144	26	10	g	g	NOUN
ejpam-4144	26	11	,	,	PUNCT
ejpam-4144	26	12	denoted	denote	VERB
ejpam-4144	26	13	by	by	ADP
ejpam-4144	26	14	dg(u	dg(u	NOUN
ejpam-4144	26	15	,	,	PUNCT
ejpam-4144	26	16	v	v	NOUN
ejpam-4144	26	17	)	)	PUNCT
ejpam-4144	26	18	,	,	PUNCT
ejpam-4144	26	19	is	be	AUX
ejpam-4144	26	20	equal	equal	ADJ
ejpam-4144	26	21	to	to	ADP
ejpam-4144	26	22	the	the	DET
ejpam-4144	26	23	length	length	NOUN
ejpam-4144	26	24	of	of	ADP
ejpam-4144	26	25	a	a	DET
ejpam-4144	26	26	shortest	short	ADJ
ejpam-4144	26	27	path	path	NOUN
ejpam-4144	26	28	connecting	connect	VERB
ejpam-4144	26	29	u	u	NOUN
ejpam-4144	26	30	and	and	CCONJ
ejpam-4144	26	31	v.	v.	ADP
ejpam-4144	26	32	any	any	DET
ejpam-4144	26	33	path	path	NOUN
ejpam-4144	26	34	connecting	connect	VERB
ejpam-4144	26	35	u	u	NOUN
ejpam-4144	26	36	and	and	CCONJ
ejpam-4144	26	37	v	v	NOUN
ejpam-4144	26	38	of	of	ADP
ejpam-4144	26	39	length	length	NOUN
ejpam-4144	26	40	dg(u	dg(u	ADJ
ejpam-4144	26	41	,	,	PUNCT
ejpam-4144	26	42	v	v	NOUN
ejpam-4144	26	43	)	)	PUNCT
ejpam-4144	26	44	is	be	AUX
ejpam-4144	26	45	called	call	VERB
ejpam-4144	26	46	a	a	DET
ejpam-4144	26	47	u	u	NOUN
ejpam-4144	26	48	-	-	NOUN
ejpam-4144	26	49	v	v	ADJ
ejpam-4144	26	50	geodesic	geodesic	NOUN
ejpam-4144	26	51	.	.	PUNCT
ejpam-4144	27	1	the	the	DET
ejpam-4144	27	2	open	open	ADJ
ejpam-4144	27	3	neighbourhood	neighbourhood	NOUN
ejpam-4144	27	4	of	of	ADP
ejpam-4144	27	5	a	a	DET
ejpam-4144	27	6	vertex	vertex	NOUN
ejpam-4144	27	7	v	v	NOUN
ejpam-4144	27	8	of	of	ADP
ejpam-4144	27	9	g	g	PROPN
ejpam-4144	27	10	is	be	AUX
ejpam-4144	27	11	the	the	DET
ejpam-4144	27	12	set	set	NOUN
ejpam-4144	27	13	ng(v	ng(v	PUNCT
ejpam-4144	27	14	)	)	PUNCT
ejpam-4144	27	15	=	=	SYM
ejpam-4144	28	1	{	{	PUNCT
ejpam-4144	28	2	u	u	NOUN
ejpam-4144	28	3	∈	∈	PROPN
ejpam-4144	28	4	v	v	NOUN
ejpam-4144	28	5	(	(	PUNCT
ejpam-4144	28	6	g	g	NOUN
ejpam-4144	28	7	)	)	PUNCT
ejpam-4144	28	8	:	:	PUNCT
ejpam-4144	28	9	uv	uv	PROPN
ejpam-4144	28	10	∈	∈	PROPN
ejpam-4144	28	11	e(g	e(g	PROPN
ejpam-4144	28	12	)	)	PUNCT
ejpam-4144	28	13	}	}	PUNCT
ejpam-4144	28	14	and	and	CCONJ
ejpam-4144	28	15	its	its	PRON
ejpam-4144	28	16	closed	closed	ADJ
ejpam-4144	28	17	neighbourhood	neighbourhood	NOUN
ejpam-4144	28	18	is	be	AUX
ejpam-4144	28	19	the	the	DET
ejpam-4144	28	20	set	set	NOUN
ejpam-4144	28	21	ng[v	ng[v	NOUN
ejpam-4144	28	22	]	]	X
ejpam-4144	28	23	=	=	SYM
ejpam-4144	28	24	ng(v	ng(v	X
ejpam-4144	28	25	)	)	PUNCT
ejpam-4144	28	26	∪	∪	ADP
ejpam-4144	28	27	{	{	PUNCT
ejpam-4144	28	28	v	v	NOUN
ejpam-4144	28	29	}	}	PUNCT
ejpam-4144	28	30	.	.	PUNCT
ejpam-4144	29	1	the	the	DET
ejpam-4144	29	2	open	open	ADJ
ejpam-4144	29	3	neighbourhood	neighbourhood	NOUN
ejpam-4144	29	4	of	of	ADP
ejpam-4144	29	5	a	a	DET
ejpam-4144	29	6	subset	subset	NOUN
ejpam-4144	29	7	s	s	NOUN
ejpam-4144	29	8	of	of	ADP
ejpam-4144	29	9	v	v	NOUN
ejpam-4144	29	10	(	(	PUNCT
ejpam-4144	29	11	g	g	NOUN
ejpam-4144	29	12	)	)	PUNCT
ejpam-4144	29	13	is	be	AUX
ejpam-4144	29	14	the	the	DET
ejpam-4144	29	15	set	set	NOUN
ejpam-4144	29	16	ng(s	ng(s	NOUN
ejpam-4144	29	17	)	)	PUNCT
ejpam-4144	29	18	=	=	SYM
ejpam-4144	29	19	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-4144	29	20	)	)	PUNCT
ejpam-4144	29	21	and	and	CCONJ
ejpam-4144	29	22	its	its	PRON
ejpam-4144	29	23	closed	closed	ADJ
ejpam-4144	29	24	neighbourhood	neighbourhood	NOUN
ejpam-4144	29	25	is	be	AUX
ejpam-4144	29	26	the	the	DET
ejpam-4144	29	27	set	set	VERB
ejpam-4144	29	28	ng[s	ng[	NOUN
ejpam-4144	29	29	]	]	PUNCT
ejpam-4144	29	30	=	=	SYM
ejpam-4144	29	31	ng(s	ng(s	X
ejpam-4144	29	32	)	)	PUNCT
ejpam-4144	29	33	∪	∪	ADP
ejpam-4144	29	34	s.	s.	PROPN
ejpam-4144	29	35	the	the	DET
ejpam-4144	29	36	degree	degree	NOUN
ejpam-4144	29	37	of	of	ADP
ejpam-4144	29	38	v	v	NOUN
ejpam-4144	29	39	,	,	PUNCT
ejpam-4144	29	40	denoted	denote	VERB
ejpam-4144	29	41	by	by	ADP
ejpam-4144	29	42	degg(v	degg(v	PROPN
ejpam-4144	29	43	)	)	PUNCT
ejpam-4144	29	44	,	,	PUNCT
ejpam-4144	29	45	is	be	AUX
ejpam-4144	29	46	equal	equal	ADJ
ejpam-4144	29	47	to	to	ADP
ejpam-4144	29	48	|ng(v)|	|ng(v)|	NOUN
ejpam-4144	29	49	.	.	PUNCT
ejpam-4144	30	1	a	a	DET
ejpam-4144	30	2	vertex	vertex	NOUN
ejpam-4144	30	3	v	v	NOUN
ejpam-4144	30	4	is	be	AUX
ejpam-4144	30	5	called	call	VERB
ejpam-4144	30	6	a	a	DET
ejpam-4144	30	7	leaf	leaf	NOUN
ejpam-4144	30	8	in	in	ADP
ejpam-4144	30	9	g	g	PROPN
ejpam-4144	30	10	if	if	SCONJ
ejpam-4144	30	11	degg(v	degg(v	X
ejpam-4144	30	12	)	)	PUNCT
ejpam-4144	30	13	=	=	SYM
ejpam-4144	31	1	1	1	X
ejpam-4144	31	2	.	.	PUNCT
ejpam-4144	32	1	the	the	DET
ejpam-4144	32	2	open	open	ADJ
ejpam-4144	32	3	hop	hop	NOUN
ejpam-4144	32	4	neighbourhood	neighbourhood	NOUN
ejpam-4144	32	5	of	of	ADP
ejpam-4144	32	6	a	a	DET
ejpam-4144	32	7	vertex	vertex	NOUN
ejpam-4144	32	8	v	v	NOUN
ejpam-4144	32	9	of	of	ADP
ejpam-4144	32	10	g	g	PROPN
ejpam-4144	32	11	is	be	AUX
ejpam-4144	32	12	the	the	DET
ejpam-4144	32	13	set	set	NOUN
ejpam-4144	32	14	ng(v	ng(v	PUNCT
ejpam-4144	32	15	,	,	PUNCT
ejpam-4144	32	16	2	2	X
ejpam-4144	32	17	)	)	PUNCT
ejpam-4144	32	18	=	=	PRON
ejpam-4144	32	19	{	{	PUNCT
ejpam-4144	32	20	w	w	NOUN
ejpam-4144	32	21	∈	∈	PROPN
ejpam-4144	32	22	v	v	ADP
ejpam-4144	32	23	(	(	PUNCT
ejpam-4144	32	24	g	g	NOUN
ejpam-4144	32	25	)	)	PUNCT
ejpam-4144	32	26	:	:	PUNCT
ejpam-4144	32	27	dg(v	dg(v	X
ejpam-4144	32	28	,	,	PUNCT
ejpam-4144	32	29	w	w	NOUN
ejpam-4144	32	30	)	)	PUNCT
ejpam-4144	32	31	=	=	SYM
ejpam-4144	32	32	2	2	X
ejpam-4144	32	33	}	}	PUNCT
ejpam-4144	32	34	and	and	CCONJ
ejpam-4144	32	35	its	its	PRON
ejpam-4144	32	36	closed	closed	ADJ
ejpam-4144	32	37	hop	hop	NOUN
ejpam-4144	32	38	neighbourhood	neighbourhood	NOUN
ejpam-4144	32	39	is	be	AUX
ejpam-4144	32	40	the	the	DET
ejpam-4144	32	41	set	set	NOUN
ejpam-4144	32	42	ng[v	ng[v	PROPN
ejpam-4144	32	43	,	,	PUNCT
ejpam-4144	32	44	2	2	NUM
ejpam-4144	32	45	]	]	PUNCT
ejpam-4144	32	46	=	=	PUNCT
ejpam-4144	32	47	ng(v	ng(v	X
ejpam-4144	32	48	,	,	PUNCT
ejpam-4144	32	49	2	2	X
ejpam-4144	32	50	)	)	PUNCT
ejpam-4144	32	51	∪	∪	NOUN
ejpam-4144	32	52	{	{	PUNCT
ejpam-4144	32	53	v	v	NOUN
ejpam-4144	32	54	}	}	PUNCT
ejpam-4144	32	55	.	.	PUNCT
ejpam-4144	33	1	the	the	DET
ejpam-4144	33	2	open	open	ADJ
ejpam-4144	33	3	hop	hop	NOUN
ejpam-4144	33	4	neighbourhood	neighbourhood	NOUN
ejpam-4144	33	5	of	of	ADP
ejpam-4144	33	6	a	a	DET
ejpam-4144	33	7	subset	subset	NOUN
ejpam-4144	33	8	s	s	NOUN
ejpam-4144	33	9	of	of	ADP
ejpam-4144	33	10	v	v	NOUN
ejpam-4144	33	11	(	(	PUNCT
ejpam-4144	33	12	g	g	NOUN
ejpam-4144	33	13	)	)	PUNCT
ejpam-4144	33	14	is	be	AUX
ejpam-4144	33	15	the	the	DET
ejpam-4144	33	16	set	set	NOUN
ejpam-4144	33	17	ng(s	ng(s	NOUN
ejpam-4144	33	18	,	,	PUNCT
ejpam-4144	33	19	2	2	X
ejpam-4144	33	20	)	)	PUNCT
ejpam-4144	33	21	=	=	SYM
ejpam-4144	33	22	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-4144	33	23	,	,	PUNCT
ejpam-4144	33	24	2	2	NUM
ejpam-4144	33	25	)	)	PUNCT
ejpam-4144	33	26	and	and	CCONJ
ejpam-4144	33	27	its	its	PRON
ejpam-4144	33	28	closed	closed	ADJ
ejpam-4144	33	29	hop	hop	NOUN
ejpam-4144	33	30	neighbourhood	neighbourhood	NOUN
ejpam-4144	33	31	is	be	AUX
ejpam-4144	33	32	the	the	DET
ejpam-4144	33	33	set	set	VERB
ejpam-4144	33	34	ng[s	ng[	NOUN
ejpam-4144	33	35	,	,	PUNCT
ejpam-4144	33	36	2	2	NUM
ejpam-4144	33	37	]	]	PUNCT
ejpam-4144	33	38	=	=	PUNCT
ejpam-4144	33	39	ng(s	ng(s	NOUN
ejpam-4144	33	40	,	,	PUNCT
ejpam-4144	33	41	2	2	X
ejpam-4144	33	42	)	)	PUNCT
ejpam-4144	33	43	∪	∪	ADP
ejpam-4144	33	44	s.	s.	PROPN
ejpam-4144	33	45	a	a	DET
ejpam-4144	33	46	set	set	NOUN
ejpam-4144	33	47	s	s	PROPN
ejpam-4144	33	48	⊆	⊆	NUM
ejpam-4144	33	49	v	v	NOUN
ejpam-4144	33	50	(	(	PUNCT
ejpam-4144	33	51	g	g	NOUN
ejpam-4144	33	52	)	)	PUNCT
ejpam-4144	33	53	is	be	AUX
ejpam-4144	33	54	a	a	DET
ejpam-4144	33	55	dominating	dominating	NOUN
ejpam-4144	33	56	set	set	NOUN
ejpam-4144	33	57	of	of	ADP
ejpam-4144	33	58	g	g	PROPN
ejpam-4144	33	59	if	if	SCONJ
ejpam-4144	33	60	ng[s	ng[	NOUN
ejpam-4144	33	61	]	]	PUNCT
ejpam-4144	33	62	=	=	SYM
ejpam-4144	33	63	v	v	NOUN
ejpam-4144	33	64	(	(	PUNCT
ejpam-4144	33	65	g	g	NOUN
ejpam-4144	33	66	)	)	PUNCT
ejpam-4144	33	67	.	.	PUNCT
ejpam-4144	34	1	a	a	DET
ejpam-4144	34	2	vertex	vertex	NOUN
ejpam-4144	34	3	v	v	NOUN
ejpam-4144	34	4	of	of	ADP
ejpam-4144	34	5	g	g	PROPN
ejpam-4144	34	6	is	be	AUX
ejpam-4144	34	7	a	a	DET
ejpam-4144	34	8	dominating	dominating	NOUN
ejpam-4144	34	9	vertex	vertex	NOUN
ejpam-4144	34	10	if	if	SCONJ
ejpam-4144	34	11	{	{	PUNCT
ejpam-4144	34	12	v	v	NOUN
ejpam-4144	34	13	}	}	PUNCT
ejpam-4144	34	14	is	be	AUX
ejpam-4144	34	15	a	a	DET
ejpam-4144	34	16	dominating	dominating	NOUN
ejpam-4144	34	17	set	set	NOUN
ejpam-4144	34	18	of	of	ADP
ejpam-4144	34	19	g.	g.	PROPN
ejpam-4144	34	20	the	the	DET
ejpam-4144	34	21	smallest	small	ADJ
ejpam-4144	34	22	cardinality	cardinality	NOUN
ejpam-4144	34	23	of	of	ADP
ejpam-4144	34	24	a	a	DET
ejpam-4144	34	25	dominating	dominating	NOUN
ejpam-4144	34	26	set	set	NOUN
ejpam-4144	34	27	of	of	ADP
ejpam-4144	34	28	g	g	NOUN
ejpam-4144	34	29	,	,	PUNCT
ejpam-4144	34	30	denoted	denote	VERB
ejpam-4144	34	31	by	by	ADP
ejpam-4144	34	32	γ(g	γ(g	PROPN
ejpam-4144	34	33	)	)	PUNCT
ejpam-4144	34	34	,	,	PUNCT
ejpam-4144	34	35	is	be	AUX
ejpam-4144	34	36	called	call	VERB
ejpam-4144	34	37	the	the	DET
ejpam-4144	34	38	domination	domination	NOUN
ejpam-4144	34	39	number	number	NOUN
ejpam-4144	34	40	of	of	ADP
ejpam-4144	34	41	g.	g.	PROPN
ejpam-4144	34	42	a	a	DET
ejpam-4144	34	43	dominating	dominating	NOUN
ejpam-4144	34	44	set	set	NOUN
ejpam-4144	34	45	of	of	ADP
ejpam-4144	34	46	g	g	NOUN
ejpam-4144	34	47	with	with	ADP
ejpam-4144	34	48	with	with	ADP
ejpam-4144	34	49	cardinality	cardinality	PROPN
ejpam-4144	34	50	γ(g	γ(g	PROPN
ejpam-4144	34	51	)	)	PUNCT
ejpam-4144	34	52	is	be	AUX
ejpam-4144	34	53	called	call	VERB
ejpam-4144	34	54	a	a	DET
ejpam-4144	34	55	γ	γ	NOUN
ejpam-4144	34	56	-	-	PUNCT
ejpam-4144	34	57	set	set	NOUN
ejpam-4144	34	58	of	of	ADP
ejpam-4144	34	59	g.	g.	PROPN
ejpam-4144	34	60	a	a	DET
ejpam-4144	34	61	set	set	NOUN
ejpam-4144	34	62	s	s	PROPN
ejpam-4144	34	63	⊆	⊆	NUM
ejpam-4144	34	64	v	v	NOUN
ejpam-4144	34	65	(	(	PUNCT
ejpam-4144	34	66	g	g	NOUN
ejpam-4144	34	67	)	)	PUNCT
ejpam-4144	34	68	is	be	AUX
ejpam-4144	34	69	a	a	DET
ejpam-4144	34	70	hop	hop	NOUN
ejpam-4144	34	71	dominating	dominating	NOUN
ejpam-4144	34	72	set	set	NOUN
ejpam-4144	34	73	of	of	ADP
ejpam-4144	34	74	g	g	PROPN
ejpam-4144	34	75	if	if	SCONJ
ejpam-4144	34	76	for	for	ADP
ejpam-4144	34	77	each	each	DET
ejpam-4144	34	78	x	x	SYM
ejpam-4144	34	79	∈	∈	PROPN
ejpam-4144	35	1	v	v	ADP
ejpam-4144	35	2	(	(	PUNCT
ejpam-4144	35	3	g	g	NOUN
ejpam-4144	35	4	)	)	PUNCT
ejpam-4144	35	5	\	\	PROPN
ejpam-4144	36	1	s	s	X
ejpam-4144	36	2	,	,	PUNCT
ejpam-4144	36	3	there	there	PRON
ejpam-4144	36	4	exists	exist	VERB
ejpam-4144	36	5	z	z	PROPN
ejpam-4144	36	6	∈	∈	PROPN
ejpam-4144	36	7	s	s	VERB
ejpam-4144	36	8	such	such	ADJ
ejpam-4144	36	9	that	that	PRON
ejpam-4144	36	10	dg(x	dg(x	NOUN
ejpam-4144	36	11	,	,	PUNCT
ejpam-4144	36	12	z	z	NOUN
ejpam-4144	36	13	)	)	PUNCT
ejpam-4144	36	14	=	=	SYM
ejpam-4144	36	15	2	2	X
ejpam-4144	36	16	.	.	X
ejpam-4144	36	17	the	the	DET
ejpam-4144	36	18	smallest	small	ADJ
ejpam-4144	36	19	cardinality	cardinality	NOUN
ejpam-4144	36	20	of	of	ADP
ejpam-4144	36	21	a	a	DET
ejpam-4144	36	22	hop	hop	NOUN
ejpam-4144	36	23	dominating	dominating	NOUN
ejpam-4144	36	24	set	set	NOUN
ejpam-4144	36	25	of	of	ADP
ejpam-4144	36	26	g	g	NOUN
ejpam-4144	36	27	,	,	PUNCT
ejpam-4144	36	28	denoted	denote	VERB
ejpam-4144	36	29	by	by	ADP
ejpam-4144	36	30	γh(g	γh(g	NOUN
ejpam-4144	36	31	)	)	PUNCT
ejpam-4144	36	32	,	,	PUNCT
ejpam-4144	36	33	is	be	AUX
ejpam-4144	36	34	called	call	VERB
ejpam-4144	36	35	the	the	DET
ejpam-4144	36	36	hop	hop	NOUN
ejpam-4144	36	37	domination	domination	NOUN
ejpam-4144	36	38	number	number	NOUN
ejpam-4144	36	39	of	of	ADP
ejpam-4144	36	40	g.	g.	PROPN
ejpam-4144	36	41	a	a	DET
ejpam-4144	36	42	hop	hop	NOUN
ejpam-4144	36	43	dominating	dominating	NOUN
ejpam-4144	36	44	set	set	NOUN
ejpam-4144	36	45	of	of	ADP
ejpam-4144	36	46	g	g	PROPN
ejpam-4144	36	47	with	with	ADP
ejpam-4144	36	48	cardinality	cardinality	NOUN
ejpam-4144	36	49	γh(g	γh(g	NOUN
ejpam-4144	36	50	)	)	PUNCT
ejpam-4144	36	51	is	be	AUX
ejpam-4144	36	52	called	call	VERB
ejpam-4144	36	53	a	a	DET
ejpam-4144	36	54	γh	γh	ADV
ejpam-4144	36	55	-	-	PUNCT
ejpam-4144	36	56	set	set	NOUN
ejpam-4144	36	57	of	of	ADP
ejpam-4144	36	58	g.	g.	PROPN
ejpam-4144	36	59	a	a	DET
ejpam-4144	36	60	set	set	NOUN
ejpam-4144	36	61	s	s	PROPN
ejpam-4144	36	62	⊆	⊆	NUM
ejpam-4144	36	63	v	v	NOUN
ejpam-4144	36	64	(	(	PUNCT
ejpam-4144	36	65	g	g	NOUN
ejpam-4144	36	66	)	)	PUNCT
ejpam-4144	36	67	is	be	AUX
ejpam-4144	36	68	a	a	DET
ejpam-4144	36	69	global	global	ADJ
ejpam-4144	36	70	hop	hop	NOUN
ejpam-4144	36	71	dominating	dominating	NOUN
ejpam-4144	36	72	set	set	NOUN
ejpam-4144	36	73	of	of	ADP
ejpam-4144	36	74	g	g	PROPN
ejpam-4144	36	75	if	if	SCONJ
ejpam-4144	36	76	it	it	PRON
ejpam-4144	36	77	is	be	AUX
ejpam-4144	36	78	a	a	DET
ejpam-4144	36	79	hop	hop	NOUN
ejpam-4144	36	80	dominating	dominating	NOUN
ejpam-4144	36	81	set	set	NOUN
ejpam-4144	36	82	of	of	ADP
ejpam-4144	36	83	g	g	PROPN
ejpam-4144	36	84	and	and	CCONJ
ejpam-4144	36	85	g.	g.	NOUN
ejpam-4144	36	86	the	the	DET
ejpam-4144	36	87	smallest	small	ADJ
ejpam-4144	36	88	cardinality	cardinality	NOUN
ejpam-4144	36	89	of	of	ADP
ejpam-4144	36	90	a	a	DET
ejpam-4144	36	91	global	global	ADJ
ejpam-4144	36	92	hop	hop	NOUN
ejpam-4144	36	93	dominating	dominating	NOUN
ejpam-4144	36	94	set	set	NOUN
ejpam-4144	36	95	of	of	ADP
ejpam-4144	36	96	g	g	NOUN
ejpam-4144	36	97	,	,	PUNCT
ejpam-4144	36	98	denoted	denote	VERB
ejpam-4144	36	99	by	by	ADP
ejpam-4144	36	100	γgh(g	γgh(g	NOUN
ejpam-4144	36	101	)	)	PUNCT
ejpam-4144	36	102	,	,	PUNCT
ejpam-4144	36	103	is	be	AUX
ejpam-4144	36	104	called	call	VERB
ejpam-4144	36	105	the	the	DET
ejpam-4144	36	106	global	global	ADJ
ejpam-4144	36	107	hop	hop	NOUN
ejpam-4144	36	108	domination	domination	NOUN
ejpam-4144	36	109	number	number	NOUN
ejpam-4144	36	110	of	of	ADP
ejpam-4144	36	111	g.	g.	PROPN
ejpam-4144	36	112	a	a	DET
ejpam-4144	36	113	global	global	ADJ
ejpam-4144	36	114	hop	hop	NOUN
ejpam-4144	36	115	dominating	dominating	NOUN
ejpam-4144	36	116	set	set	NOUN
ejpam-4144	36	117	of	of	ADP
ejpam-4144	36	118	g	g	NOUN
ejpam-4144	36	119	with	with	ADP
ejpam-4144	36	120	cardinality	cardinality	NOUN
ejpam-4144	36	121	γgh(g	γgh(g	NOUN
ejpam-4144	36	122	)	)	PUNCT
ejpam-4144	36	123	is	be	AUX
ejpam-4144	36	124	called	call	VERB
ejpam-4144	36	125	a	a	DET
ejpam-4144	36	126	γgh	γgh	PROPN
ejpam-4144	36	127	-	-	PUNCT
ejpam-4144	36	128	set	set	NOUN
ejpam-4144	36	129	of	of	ADP
ejpam-4144	36	130	g.	g.	PROPN
ejpam-4144	36	131	2	2	NUM
ejpam-4144	36	132	.	.	PUNCT
ejpam-4144	37	1	results	result	NOUN
ejpam-4144	37	2	we	we	PRON
ejpam-4144	37	3	note	note	VERB
ejpam-4144	37	4	that	that	SCONJ
ejpam-4144	37	5	although	although	SCONJ
ejpam-4144	37	6	hop	hop	NOUN
ejpam-4144	37	7	domination	domination	NOUN
ejpam-4144	37	8	is	be	AUX
ejpam-4144	37	9	,	,	PUNCT
ejpam-4144	37	10	in	in	ADP
ejpam-4144	37	11	some	some	DET
ejpam-4144	37	12	sense	sense	NOUN
ejpam-4144	37	13	,	,	PUNCT
ejpam-4144	37	14	a	a	DET
ejpam-4144	37	15	variation	variation	NOUN
ejpam-4144	37	16	of	of	ADP
ejpam-4144	37	17	the	the	DET
ejpam-4144	37	18	standard	standard	ADJ
ejpam-4144	37	19	domination	domination	NOUN
ejpam-4144	37	20	concept	concept	NOUN
ejpam-4144	37	21	,	,	PUNCT
ejpam-4144	37	22	the	the	DET
ejpam-4144	37	23	associated	associated	ADJ
ejpam-4144	37	24	parameters	parameter	NOUN
ejpam-4144	37	25	are	be	AUX
ejpam-4144	37	26	,	,	PUNCT
ejpam-4144	37	27	in	in	ADP
ejpam-4144	37	28	general	general	ADJ
ejpam-4144	37	29	,	,	PUNCT
ejpam-4144	37	30	not	not	PART
ejpam-4144	37	31	comparable	comparable	ADJ
ejpam-4144	37	32	.	.	PUNCT
ejpam-4144	38	1	our	our	PRON
ejpam-4144	38	2	first	first	ADJ
ejpam-4144	38	3	simple	simple	ADJ
ejpam-4144	38	4	result	result	NOUN
ejpam-4144	38	5	says	say	VERB
ejpam-4144	38	6	that	that	SCONJ
ejpam-4144	38	7	the	the	DET
ejpam-4144	38	8	absolute	absolute	ADJ
ejpam-4144	38	9	difference	difference	NOUN
ejpam-4144	38	10	of	of	ADP
ejpam-4144	38	11	the	the	DET
ejpam-4144	38	12	domination	domination	NOUN
ejpam-4144	38	13	number	number	NOUN
ejpam-4144	38	14	and	and	CCONJ
ejpam-4144	38	15	hop	hop	NOUN
ejpam-4144	38	16	domination	domination	NOUN
ejpam-4144	38	17	number	number	NOUN
ejpam-4144	38	18	can	can	AUX
ejpam-4144	38	19	be	be	AUX
ejpam-4144	38	20	made	make	VERB
ejpam-4144	38	21	arbitrarily	arbitrarily	ADV
ejpam-4144	38	22	large	large	ADJ
ejpam-4144	38	23	.	.	PUNCT
ejpam-4144	39	1	proposition	proposition	NOUN
ejpam-4144	39	2	1	1	NUM
ejpam-4144	39	3	.	.	PUNCT
ejpam-4144	40	1	each	each	PRON
ejpam-4144	40	2	of	of	ADP
ejpam-4144	40	3	the	the	DET
ejpam-4144	40	4	following	following	ADJ
ejpam-4144	40	5	statements	statement	NOUN
ejpam-4144	40	6	holds	hold	VERB
ejpam-4144	40	7	.	.	PUNCT
ejpam-4144	41	1	(	(	PUNCT
ejpam-4144	41	2	i	i	NOUN
ejpam-4144	41	3	)	)	PUNCT
ejpam-4144	41	4	for	for	ADP
ejpam-4144	41	5	each	each	DET
ejpam-4144	41	6	integer	integer	NOUN
ejpam-4144	41	7	n	n	PRON
ejpam-4144	41	8	≥	≥	NOUN
ejpam-4144	41	9	1	1	NUM
ejpam-4144	41	10	,	,	PUNCT
ejpam-4144	41	11	there	there	PRON
ejpam-4144	41	12	exists	exist	VERB
ejpam-4144	41	13	a	a	DET
ejpam-4144	41	14	connected	connected	ADJ
ejpam-4144	41	15	graph	graph	NOUN
ejpam-4144	41	16	g	g	ADP
ejpam-4144	41	17	such	such	ADJ
ejpam-4144	41	18	that	that	PRON
ejpam-4144	41	19	γh(g)−γ(g	γh(g)−γ(g	PROPN
ejpam-4144	41	20	)	)	PUNCT
ejpam-4144	42	1	=	=	SYM
ejpam-4144	42	2	n.	n.	NOUN
ejpam-4144	42	3	(	(	PUNCT
ejpam-4144	42	4	ii	ii	NOUN
ejpam-4144	42	5	)	)	PUNCT
ejpam-4144	42	6	for	for	ADP
ejpam-4144	42	7	each	each	DET
ejpam-4144	42	8	integer	integer	NOUN
ejpam-4144	42	9	n	n	PRON
ejpam-4144	42	10	≥	≥	NOUN
ejpam-4144	42	11	1	1	NUM
ejpam-4144	42	12	,	,	PUNCT
ejpam-4144	42	13	there	there	PRON
ejpam-4144	42	14	exists	exist	VERB
ejpam-4144	42	15	a	a	DET
ejpam-4144	42	16	connected	connected	ADJ
ejpam-4144	42	17	graph	graph	NOUN
ejpam-4144	42	18	g	g	ADP
ejpam-4144	42	19	such	such	ADJ
ejpam-4144	42	20	that	that	SCONJ
ejpam-4144	42	21	γ(g)−γh(g	γ(g)−γh(g	NOUN
ejpam-4144	42	22	)	)	PUNCT
ejpam-4144	42	23	=	=	SYM
ejpam-4144	43	1	n.	n.	NOUN
ejpam-4144	43	2	proof	proof	NOUN
ejpam-4144	43	3	.	.	PUNCT
ejpam-4144	44	1	(	(	PUNCT
ejpam-4144	44	2	i	i	NOUN
ejpam-4144	44	3	)	)	PUNCT
ejpam-4144	44	4	letg	letg	PROPN
ejpam-4144	44	5	=	=	SYM
ejpam-4144	44	6	kn+1	kn+1	PROPN
ejpam-4144	44	7	.	.	PUNCT
ejpam-4144	45	1	then	then	ADV
ejpam-4144	45	2	γ(g	γ(g	PROPN
ejpam-4144	45	3	)	)	PUNCT
ejpam-4144	45	4	=	=	SYM
ejpam-4144	45	5	1	1	NUM
ejpam-4144	45	6	and	and	CCONJ
ejpam-4144	45	7	γh(g	γh(g	NOUN
ejpam-4144	45	8	)	)	PUNCT
ejpam-4144	46	1	=	=	PUNCT
ejpam-4144	46	2	n+1	n+1	PROPN
ejpam-4144	46	3	.	.	PUNCT
ejpam-4144	46	4	hence	hence	ADV
ejpam-4144	46	5	,	,	PUNCT
ejpam-4144	46	6	γh(g)−γ(g	γh(g)−γ(g	PROPN
ejpam-4144	46	7	)	)	PUNCT
ejpam-4144	46	8	=	=	SYM
ejpam-4144	46	9	n.	n.	NOUN
ejpam-4144	46	10	(	(	PUNCT
ejpam-4144	46	11	ii	ii	NOUN
ejpam-4144	46	12	)	)	PUNCT
ejpam-4144	46	13	consider	consider	VERB
ejpam-4144	46	14	the	the	DET
ejpam-4144	46	15	star	star	NOUN
ejpam-4144	46	16	k1,n+2	k1,n+2	PROPN
ejpam-4144	46	17	with	with	ADP
ejpam-4144	46	18	vertices	vertex	NOUN
ejpam-4144	46	19	v0	v0	NOUN
ejpam-4144	46	20	,	,	PUNCT
ejpam-4144	46	21	v1	v1	NOUN
ejpam-4144	46	22	,	,	PUNCT
ejpam-4144	46	23	v2	v2	NOUN
ejpam-4144	46	24	,	,	PUNCT
ejpam-4144	46	25	.	.	PUNCT
ejpam-4144	46	26	.	.	PUNCT
ejpam-4144	47	1	.	.	PUNCT
ejpam-4144	48	1	,	,	PUNCT
ejpam-4144	48	2	vn+1	vn+1	PROPN
ejpam-4144	48	3	,	,	PUNCT
ejpam-4144	48	4	vn+2	vn+2	PROPN
ejpam-4144	48	5	,	,	PUNCT
ejpam-4144	48	6	where	where	SCONJ
ejpam-4144	48	7	v0	v0	NOUN
ejpam-4144	48	8	is	be	AUX
ejpam-4144	48	9	the	the	DET
ejpam-4144	48	10	central	central	ADJ
ejpam-4144	48	11	vertex	vertex	NOUN
ejpam-4144	48	12	.	.	PUNCT
ejpam-4144	49	1	let	let	VERB
ejpam-4144	49	2	g	g	NOUN
ejpam-4144	49	3	(	(	PUNCT
ejpam-4144	49	4	see	see	VERB
ejpam-4144	49	5	figure	figure	NOUN
ejpam-4144	49	6	1	1	NUM
ejpam-4144	49	7	)	)	PUNCT
ejpam-4144	49	8	be	be	AUX
ejpam-4144	49	9	the	the	DET
ejpam-4144	49	10	graph	graph	NOUN
ejpam-4144	49	11	obtained	obtain	VERB
ejpam-4144	49	12	from	from	ADP
ejpam-4144	49	13	k1,n+2	k1,n+2	PROPN
ejpam-4144	49	14	by	by	ADP
ejpam-4144	49	15	adding	add	VERB
ejpam-4144	49	16	n+	n+	ADP
ejpam-4144	49	17	2	2	NUM
ejpam-4144	49	18	pendant	pendant	ADJ
ejpam-4144	49	19	edges	edge	NOUN
ejpam-4144	49	20	v1w1	v1w1	NOUN
ejpam-4144	49	21	,	,	PUNCT
ejpam-4144	49	22	v2w2	v2w2	NOUN
ejpam-4144	49	23	,	,	PUNCT
ejpam-4144	49	24	.	.	PUNCT
ejpam-4144	49	25	.	.	PUNCT
ejpam-4144	50	1	.	.	PUNCT
ejpam-4144	51	1	,	,	PUNCT
ejpam-4144	51	2	vn+1wn+1	vn+1wn+1	NOUN
ejpam-4144	51	3	,	,	PUNCT
ejpam-4144	51	4	vn+2wn+2	vn+2wn+2	X
ejpam-4144	51	5	.	.	PUNCT
ejpam-4144	52	1	let	let	VERB
ejpam-4144	52	2	s1	s1	PROPN
ejpam-4144	52	3	=	=	SYM
ejpam-4144	52	4	{	{	PUNCT
ejpam-4144	52	5	v1	v1	PROPN
ejpam-4144	52	6	,	,	PUNCT
ejpam-4144	52	7	v2	v2	PROPN
ejpam-4144	52	8	,	,	PUNCT
ejpam-4144	52	9	.	.	PUNCT
ejpam-4144	52	10	.	.	PUNCT
ejpam-4144	53	1	.	.	PUNCT
ejpam-4144	54	1	,	,	PUNCT
ejpam-4144	54	2	vn	vn	X
ejpam-4144	54	3	,	,	PUNCT
ejpam-4144	54	4	vn+1	vn+1	PROPN
ejpam-4144	54	5	,	,	PUNCT
ejpam-4144	54	6	vn+2	vn+2	PROPN
ejpam-4144	54	7	}	}	PUNCT
ejpam-4144	54	8	g.	g.	NOUN
ejpam-4144	54	9	salasalan	salasalan	NOUN
ejpam-4144	54	10	,	,	PUNCT
ejpam-4144	54	11	s.	s.	PROPN
ejpam-4144	54	12	canoy	canoy	PROPN
ejpam-4144	54	13	,	,	PUNCT
ejpam-4144	54	14	jr	jr	PROPN
ejpam-4144	54	15	.	.	PROPN
ejpam-4144	54	16	/	/	SYM
ejpam-4144	54	17	eur	eur	PROPN
ejpam-4144	54	18	.	.	PUNCT
ejpam-4144	55	1	j.	j.	PROPN
ejpam-4144	55	2	pure	pure	PROPN
ejpam-4144	55	3	appl	appl	PROPN
ejpam-4144	55	4	.	.	PROPN
ejpam-4144	55	5	math	math	PROPN
ejpam-4144	55	6	,	,	PUNCT
ejpam-4144	55	7	14	14	NUM
ejpam-4144	55	8	(	(	PUNCT
ejpam-4144	55	9	4	4	NUM
ejpam-4144	55	10	)	)	PUNCT
ejpam-4144	55	11	(	(	PUNCT
ejpam-4144	55	12	2021	2021	NUM
ejpam-4144	55	13	)	)	PUNCT
ejpam-4144	55	14	,	,	PUNCT
ejpam-4144	55	15	1415	1415	NUM
ejpam-4144	55	16	-	-	SYM
ejpam-4144	55	17	1428	1428	NUM
ejpam-4144	55	18	1417	1417	NUM
ejpam-4144	55	19	.........	.........	PUNCT
ejpam-4144	55	20	........	........	PUNCT
ejpam-4144	55	21	........	........	PUNCT
ejpam-4144	55	22	........	........	PUNCT
ejpam-4144	55	23	........	........	PUNCT
ejpam-4144	55	24	........	........	PUNCT
ejpam-4144	55	25	........	........	PUNCT
ejpam-4144	55	26	........	........	PUNCT
ejpam-4144	55	27	........	........	PUNCT
ejpam-4144	55	28	...	...	PUNCT
ejpam-4144	56	1	....................................	....................................	PUNCT
ejpam-4144	56	2	.........	.........	PUNCT
ejpam-4144	56	3	........	........	PUNCT
ejpam-4144	56	4	........	........	PUNCT
ejpam-4144	56	5	........	........	PUNCT
ejpam-4144	56	6	........	........	PUNCT
ejpam-4144	56	7	........	........	PUNCT
ejpam-4144	56	8	........	........	PUNCT
ejpam-4144	56	9	........	........	PUNCT
ejpam-4144	56	10	........	........	PUNCT
ejpam-4144	56	11	...	...	PUNCT
ejpam-4144	57	1	....................................	....................................	PUNCT
ejpam-4144	57	2	....................................	....................................	PUNCT
ejpam-4144	57	3	............	............	PUNCT
ejpam-4144	57	4	...........	...........	PUNCT
ejpam-4144	57	5	...........	...........	PUNCT
ejpam-4144	57	6	...........	...........	PUNCT
ejpam-4144	57	7	...........	...........	PUNCT
ejpam-4144	57	8	...........	...........	PUNCT
ejpam-4144	57	9	....	....	PUNCT
ejpam-4144	58	1	....................................	....................................	PUNCT
ejpam-4144	58	2	............	............	PUNCT
ejpam-4144	58	3	...........	...........	PUNCT
ejpam-4144	58	4	...........	...........	PUNCT
ejpam-4144	58	5	...........	...........	PUNCT
ejpam-4144	58	6	...........	...........	PUNCT
ejpam-4144	58	7	...........	...........	PUNCT
ejpam-4144	58	8	....	....	PUNCT
ejpam-4144	58	9	....................................	....................................	PUNCT
ejpam-4144	59	1	....................................	....................................	PUNCT
ejpam-4144	59	2	..........................	..........................	PUNCT
ejpam-4144	60	1	.........................	.........................	PUNCT
ejpam-4144	60	2	.........................	.........................	PUNCT
ejpam-4144	61	1	....	....	PUNCT
ejpam-4144	61	2	....................................	....................................	PUNCT
ejpam-4144	62	1	..........................	..........................	PUNCT
ejpam-4144	62	2	.........................	.........................	PUNCT
ejpam-4144	63	1	.........................	.........................	PUNCT
ejpam-4144	63	2	....	....	PUNCT
ejpam-4144	64	1	....................................	....................................	PUNCT
ejpam-4144	64	2	....................................	....................................	PUNCT
ejpam-4144	64	3	.......................................................................	.......................................................................	PUNCT
ejpam-4144	65	1	....................................	....................................	PUNCT
ejpam-4144	65	2	.......................................................................	.......................................................................	PUNCT
ejpam-4144	65	3	....................................	....................................	PUNCT
ejpam-4144	66	1	....................................	....................................	PUNCT
ejpam-4144	67	1	v1	v1	NOUN
ejpam-4144	67	2	w1	w1	NOUN
ejpam-4144	67	3	w2	w2	PROPN
ejpam-4144	67	4	w3	w3	PROPN
ejpam-4144	67	5	wn+2	wn+2	PROPN
ejpam-4144	67	6	v0	v0	PROPN
ejpam-4144	67	7	v2	v2	PROPN
ejpam-4144	67	8	v3	v3	PROPN
ejpam-4144	67	9	vn+2	vn+2	PRON
ejpam-4144	67	10	...	...	PUNCT
ejpam-4144	68	1	g	g	NOUN
ejpam-4144	68	2	figure	figure	NOUN
ejpam-4144	68	3	1	1	NUM
ejpam-4144	68	4	and	and	CCONJ
ejpam-4144	68	5	s2	s2	PROPN
ejpam-4144	68	6	=	=	SYM
ejpam-4144	68	7	{	{	PUNCT
ejpam-4144	68	8	v0	v0	NOUN
ejpam-4144	68	9	,	,	PUNCT
ejpam-4144	68	10	v1	v1	NOUN
ejpam-4144	68	11	}	}	PUNCT
ejpam-4144	68	12	.	.	PUNCT
ejpam-4144	69	1	clearly	clearly	ADV
ejpam-4144	69	2	,	,	PUNCT
ejpam-4144	69	3	s1	s1	PROPN
ejpam-4144	69	4	and	and	CCONJ
ejpam-4144	69	5	s2	s2	PROPN
ejpam-4144	69	6	are	be	AUX
ejpam-4144	69	7	γ	γ	NOUN
ejpam-4144	69	8	-	-	PUNCT
ejpam-4144	69	9	set	set	ADJ
ejpam-4144	69	10	and	and	CCONJ
ejpam-4144	69	11	γh	γh	NOUN
ejpam-4144	69	12	-	-	PUNCT
ejpam-4144	69	13	set	set	NOUN
ejpam-4144	69	14	of	of	ADP
ejpam-4144	69	15	g	g	NOUN
ejpam-4144	69	16	,	,	PUNCT
ejpam-4144	69	17	respectively	respectively	ADV
ejpam-4144	69	18	.	.	PUNCT
ejpam-4144	70	1	thus	thus	ADV
ejpam-4144	70	2	,	,	PUNCT
ejpam-4144	70	3	γ(g)−	γ(g)−	NOUN
ejpam-4144	70	4	γh(g	γh(g	NOUN
ejpam-4144	70	5	)	)	PUNCT
ejpam-4144	70	6	=	=	SYM
ejpam-4144	70	7	(	(	PUNCT
ejpam-4144	70	8	n+	n+	NUM
ejpam-4144	70	9	2)−	2)−	NUM
ejpam-4144	70	10	2	2	NUM
ejpam-4144	70	11	=	=	SYM
ejpam-4144	70	12	n.	n.	NOUN
ejpam-4144	70	13	the	the	DET
ejpam-4144	70	14	next	next	ADJ
ejpam-4144	70	15	result	result	NOUN
ejpam-4144	70	16	is	be	AUX
ejpam-4144	70	17	,	,	PUNCT
ejpam-4144	70	18	in	in	ADP
ejpam-4144	70	19	fact	fact	NOUN
ejpam-4144	70	20	,	,	PUNCT
ejpam-4144	70	21	a	a	DET
ejpam-4144	70	22	realization	realization	NOUN
ejpam-4144	70	23	problem	problem	NOUN
ejpam-4144	70	24	.	.	PUNCT
ejpam-4144	71	1	theorem	theorem	NOUN
ejpam-4144	71	2	1	1	NUM
ejpam-4144	71	3	.	.	PUNCT
ejpam-4144	72	1	let	let	VERB
ejpam-4144	72	2	a	a	PRON
ejpam-4144	72	3	and	and	CCONJ
ejpam-4144	72	4	b	b	NOUN
ejpam-4144	72	5	be	be	AUX
ejpam-4144	72	6	positive	positive	ADJ
ejpam-4144	72	7	integers	integer	NOUN
ejpam-4144	72	8	.	.	PUNCT
ejpam-4144	73	1	then	then	ADV
ejpam-4144	73	2	each	each	PRON
ejpam-4144	73	3	of	of	ADP
ejpam-4144	73	4	the	the	DET
ejpam-4144	73	5	following	following	ADJ
ejpam-4144	73	6	statements	statement	NOUN
ejpam-4144	73	7	holds	hold	VERB
ejpam-4144	73	8	.	.	PUNCT
ejpam-4144	74	1	(	(	PUNCT
ejpam-4144	74	2	i	i	NOUN
ejpam-4144	74	3	)	)	PUNCT
ejpam-4144	74	4	if	if	SCONJ
ejpam-4144	74	5	2	2	NUM
ejpam-4144	74	6	≤	≤	NOUN
ejpam-4144	74	7	a	a	DET
ejpam-4144	74	8	≤	≤	NUM
ejpam-4144	74	9	b	b	NOUN
ejpam-4144	74	10	,	,	PUNCT
ejpam-4144	74	11	then	then	ADV
ejpam-4144	74	12	there	there	PRON
ejpam-4144	74	13	exists	exist	VERB
ejpam-4144	74	14	a	a	DET
ejpam-4144	74	15	connected	connected	ADJ
ejpam-4144	74	16	graph	graph	NOUN
ejpam-4144	74	17	g	g	ADP
ejpam-4144	74	18	such	such	ADJ
ejpam-4144	74	19	that	that	PRON
ejpam-4144	74	20	γh(g	γh(g	NOUN
ejpam-4144	74	21	)	)	PUNCT
ejpam-4144	74	22	=	=	SYM
ejpam-4144	74	23	a	a	PROPN
ejpam-4144	74	24	and	and	CCONJ
ejpam-4144	74	25	γ(g	γ(g	PROPN
ejpam-4144	74	26	)	)	PUNCT
ejpam-4144	75	1	=	=	SYM
ejpam-4144	75	2	b.	b.	PROPN
ejpam-4144	75	3	(	(	PUNCT
ejpam-4144	75	4	ii	ii	PROPN
ejpam-4144	75	5	)	)	PUNCT
ejpam-4144	75	6	if	if	SCONJ
ejpam-4144	75	7	3	3	NUM
ejpam-4144	75	8	≤	≤	NOUN
ejpam-4144	75	9	a	a	DET
ejpam-4144	75	10	≤	≤	NUM
ejpam-4144	75	11	b	b	NOUN
ejpam-4144	75	12	,	,	PUNCT
ejpam-4144	75	13	then	then	ADV
ejpam-4144	75	14	there	there	PRON
ejpam-4144	75	15	exists	exist	VERB
ejpam-4144	75	16	a	a	DET
ejpam-4144	75	17	graph	graph	NOUN
ejpam-4144	75	18	h	h	NOUN
ejpam-4144	75	19	such	such	ADJ
ejpam-4144	75	20	that	that	DET
ejpam-4144	75	21	γ(h	γ(h	NOUN
ejpam-4144	75	22	)	)	PUNCT
ejpam-4144	75	23	=	=	PUNCT
ejpam-4144	75	24	a	a	PRON
ejpam-4144	75	25	and	and	CCONJ
ejpam-4144	75	26	γh(h	γh(h	NUM
ejpam-4144	75	27	)	)	PUNCT
ejpam-4144	75	28	=	=	SYM
ejpam-4144	75	29	b.	b.	NOUN
ejpam-4144	75	30	proof	proof	NOUN
ejpam-4144	75	31	.	.	PUNCT
ejpam-4144	76	1	(	(	PUNCT
ejpam-4144	76	2	i	i	NOUN
ejpam-4144	76	3	)	)	PUNCT
ejpam-4144	76	4	suppose	suppose	VERB
ejpam-4144	76	5	first	first	ADV
ejpam-4144	76	6	that	that	SCONJ
ejpam-4144	76	7	a	a	DET
ejpam-4144	76	8	=	=	X
ejpam-4144	76	9	b.	b.	NOUN
ejpam-4144	76	10	consider	consider	VERB
ejpam-4144	76	11	the	the	DET
ejpam-4144	76	12	graph	graph	NOUN
ejpam-4144	76	13	g	g	NOUN
ejpam-4144	76	14	in	in	ADP
ejpam-4144	76	15	figure	figure	NOUN
ejpam-4144	76	16	2	2	NUM
ejpam-4144	76	17	.	.	PUNCT
ejpam-4144	76	18	clearly	clearly	ADV
ejpam-4144	76	19	,	,	PUNCT
ejpam-4144	76	20	s1	s1	PROPN
ejpam-4144	76	21	=	=	PUNCT
ejpam-4144	76	22	{	{	PUNCT
ejpam-4144	76	23	x1	x1	PROPN
ejpam-4144	76	24	,	,	PUNCT
ejpam-4144	76	25	x2	x2	PROPN
ejpam-4144	76	26	,	,	PUNCT
ejpam-4144	76	27	.	.	PUNCT
ejpam-4144	76	28	.	.	PUNCT
ejpam-4144	76	29	.	.	PUNCT
ejpam-4144	77	1	,	,	PUNCT
ejpam-4144	77	2	xa	xa	PROPN
ejpam-4144	77	3	}	}	PUNCT
ejpam-4144	77	4	is	be	AUX
ejpam-4144	77	5	a	a	DET
ejpam-4144	77	6	γh	γh	ADV
ejpam-4144	77	7	-	-	PUNCT
ejpam-4144	77	8	set	set	VERB
ejpam-4144	77	9	and	and	CCONJ
ejpam-4144	77	10	s2	s2	NOUN
ejpam-4144	77	11	=	=	SYM
ejpam-4144	77	12	{	{	PUNCT
ejpam-4144	77	13	y1	y1	PROPN
ejpam-4144	77	14	,	,	PUNCT
ejpam-4144	77	15	y2	y2	PROPN
ejpam-4144	77	16	,	,	PUNCT
ejpam-4144	77	17	.	.	PUNCT
ejpam-4144	77	18	.	.	PUNCT
ejpam-4144	78	1	.	.	PUNCT
ejpam-4144	79	1	,	,	PUNCT
ejpam-4144	79	2	ya	ya	PRON
ejpam-4144	79	3	}	}	PUNCT
ejpam-4144	79	4	is	be	AUX
ejpam-4144	79	5	a	a	DET
ejpam-4144	79	6	γ	γ	NOUN
ejpam-4144	79	7	-	-	PUNCT
ejpam-4144	79	8	set	set	NOUN
ejpam-4144	79	9	of	of	ADP
ejpam-4144	79	10	g.	g.	PROPN
ejpam-4144	79	11	hence	hence	ADV
ejpam-4144	79	12	,	,	PUNCT
ejpam-4144	79	13	γh(g	γh(g	NOUN
ejpam-4144	79	14	)	)	PUNCT
ejpam-4144	79	15	=	=	PUNCT
ejpam-4144	79	16	γ(g	γ(g	PROPN
ejpam-4144	79	17	)	)	PUNCT
ejpam-4144	80	1	=	=	PUNCT
ejpam-4144	80	2	a.	a.	NOUN
ejpam-4144	80	3	.........	.........	PUNCT
ejpam-4144	80	4	........	........	PUNCT
ejpam-4144	80	5	........	........	PUNCT
ejpam-4144	80	6	........	........	PUNCT
ejpam-4144	80	7	........	........	PUNCT
ejpam-4144	80	8	........	........	PUNCT
ejpam-4144	80	9	........	........	PUNCT
ejpam-4144	80	10	........	........	PUNCT
ejpam-4144	80	11	........	........	PUNCT
ejpam-4144	80	12	...	...	PUNCT
ejpam-4144	80	13	....................................	....................................	PUNCT
ejpam-4144	80	14	.........	.........	PUNCT
ejpam-4144	80	15	........	........	PUNCT
ejpam-4144	80	16	........	........	PUNCT
ejpam-4144	80	17	........	........	PUNCT
ejpam-4144	80	18	........	........	PUNCT
ejpam-4144	80	19	........	........	PUNCT
ejpam-4144	80	20	........	........	PUNCT
ejpam-4144	80	21	........	........	PUNCT
ejpam-4144	80	22	........	........	PUNCT
ejpam-4144	80	23	...	...	PUNCT
ejpam-4144	80	24	....................................	....................................	PUNCT
ejpam-4144	80	25	....................................	....................................	PUNCT
ejpam-4144	80	26	.........	.........	PUNCT
ejpam-4144	80	27	........	........	PUNCT
ejpam-4144	80	28	........	........	PUNCT
ejpam-4144	80	29	........	........	PUNCT
ejpam-4144	80	30	........	........	PUNCT
ejpam-4144	80	31	........	........	PUNCT
ejpam-4144	80	32	........	........	PUNCT
ejpam-4144	80	33	........	........	PUNCT
ejpam-4144	80	34	........	........	PUNCT
ejpam-4144	80	35	...	...	PUNCT
ejpam-4144	80	36	....................................	....................................	PUNCT
ejpam-4144	80	37	.........	.........	PUNCT
ejpam-4144	80	38	........	........	PUNCT
ejpam-4144	80	39	........	........	PUNCT
ejpam-4144	80	40	........	........	PUNCT
ejpam-4144	80	41	........	........	PUNCT
ejpam-4144	80	42	........	........	PUNCT
ejpam-4144	80	43	........	........	PUNCT
ejpam-4144	80	44	........	........	PUNCT
ejpam-4144	80	45	........	........	PUNCT
ejpam-4144	80	46	...	...	PUNCT
ejpam-4144	80	47	....................................	....................................	PUNCT
ejpam-4144	80	48	....................................	....................................	PUNCT
ejpam-4144	80	49	.........	.........	PUNCT
ejpam-4144	80	50	........	........	PUNCT
ejpam-4144	80	51	........	........	PUNCT
ejpam-4144	80	52	........	........	PUNCT
ejpam-4144	80	53	........	........	PUNCT
ejpam-4144	80	54	........	........	PUNCT
ejpam-4144	80	55	........	........	PUNCT
ejpam-4144	80	56	........	........	PUNCT
ejpam-4144	80	57	........	........	PUNCT
ejpam-4144	80	58	...	...	PUNCT
ejpam-4144	80	59	....................................	....................................	PUNCT
ejpam-4144	80	60	.........	.........	PUNCT
ejpam-4144	80	61	........	........	PUNCT
ejpam-4144	80	62	........	........	PUNCT
ejpam-4144	80	63	........	........	PUNCT
ejpam-4144	80	64	........	........	PUNCT
ejpam-4144	80	65	........	........	PUNCT
ejpam-4144	80	66	........	........	PUNCT
ejpam-4144	80	67	........	........	PUNCT
ejpam-4144	80	68	........	........	PUNCT
ejpam-4144	80	69	...	...	PUNCT
ejpam-4144	80	70	....................................	....................................	PUNCT
ejpam-4144	80	71	....................................	....................................	PUNCT
ejpam-4144	80	72	.........	.........	PUNCT
ejpam-4144	80	73	........	........	PUNCT
ejpam-4144	80	74	........	........	PUNCT
ejpam-4144	80	75	........	........	PUNCT
ejpam-4144	80	76	........	........	PUNCT
ejpam-4144	80	77	........	........	PUNCT
ejpam-4144	80	78	........	........	PUNCT
ejpam-4144	80	79	........	........	PUNCT
ejpam-4144	80	80	........	........	PUNCT
ejpam-4144	80	81	...	...	PUNCT
ejpam-4144	80	82	....................................	....................................	PUNCT
ejpam-4144	80	83	.........	.........	PUNCT
ejpam-4144	80	84	........	........	PUNCT
ejpam-4144	80	85	........	........	PUNCT
ejpam-4144	80	86	........	........	PUNCT
ejpam-4144	80	87	........	........	PUNCT
ejpam-4144	80	88	........	........	PUNCT
ejpam-4144	80	89	........	........	PUNCT
ejpam-4144	80	90	........	........	PUNCT
ejpam-4144	80	91	........	........	PUNCT
ejpam-4144	80	92	...	...	PUNCT
ejpam-4144	80	93	....................................	....................................	PUNCT
ejpam-4144	80	94	....................................	....................................	PUNCT
ejpam-4144	80	95	.........	.........	PUNCT
ejpam-4144	80	96	........	........	PUNCT
ejpam-4144	80	97	........	........	PUNCT
ejpam-4144	80	98	........	........	PUNCT
ejpam-4144	80	99	........	........	PUNCT
ejpam-4144	80	100	........	........	PUNCT
ejpam-4144	80	101	........	........	PUNCT
ejpam-4144	80	102	........	........	PUNCT
ejpam-4144	80	103	........	........	PUNCT
ejpam-4144	80	104	...	...	PUNCT
ejpam-4144	80	105	....................................	....................................	PUNCT
ejpam-4144	80	106	.........	.........	PUNCT
ejpam-4144	80	107	........	........	PUNCT
ejpam-4144	80	108	........	........	PUNCT
ejpam-4144	80	109	........	........	PUNCT
ejpam-4144	80	110	........	........	PUNCT
ejpam-4144	80	111	........	........	PUNCT
ejpam-4144	80	112	........	........	PUNCT
ejpam-4144	80	113	........	........	PUNCT
ejpam-4144	80	114	........	........	PUNCT
ejpam-4144	80	115	...	...	PUNCT
ejpam-4144	81	1	....................................	....................................	PUNCT
ejpam-4144	81	2	....................................	....................................	PUNCT
ejpam-4144	82	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4144	82	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4144	83	1	....................................	....................................	PUNCT
ejpam-4144	83	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4144	84	1	....................................	....................................	PUNCT
ejpam-4144	85	1	y1	y1	INTJ
ejpam-4144	85	2	y2	y2	NOUN
ejpam-4144	85	3	y3	y3	NOUN
ejpam-4144	85	4	ya−1	ya−1	NOUN
ejpam-4144	85	5	ya	ya	PROPN
ejpam-4144	85	6	x1	x1	NOUN
ejpam-4144	86	1	x2	x2	PROPN
ejpam-4144	86	2	x3	x3	PROPN
ejpam-4144	86	3	xa−1	xa−1	PROPN
ejpam-4144	86	4	xa	xa	PROPN
ejpam-4144	86	5	.	.	PUNCT
ejpam-4144	86	6	.	.	PUNCT
ejpam-4144	86	7	.	.	PUNCT
ejpam-4144	87	1	g	g	NOUN
ejpam-4144	87	2	figure	figure	NOUN
ejpam-4144	87	3	2	2	NUM
ejpam-4144	87	4	next	next	ADV
ejpam-4144	87	5	,	,	PUNCT
ejpam-4144	87	6	suppose	suppose	VERB
ejpam-4144	87	7	a	a	DET
ejpam-4144	87	8	<	<	X
ejpam-4144	87	9	b	b	NOUN
ejpam-4144	87	10	and	and	CCONJ
ejpam-4144	87	11	let	let	VERB
ejpam-4144	87	12	m	m	NOUN
ejpam-4144	87	13	=	=	SYM
ejpam-4144	88	1	b	b	X
ejpam-4144	88	2	−	−	NOUN
ejpam-4144	88	3	a.	a.	NOUN
ejpam-4144	88	4	consider	consider	VERB
ejpam-4144	88	5	the	the	DET
ejpam-4144	88	6	graph	graph	NOUN
ejpam-4144	88	7	g	g	NOUN
ejpam-4144	88	8	in	in	ADP
ejpam-4144	88	9	figure	figure	NOUN
ejpam-4144	88	10	3	3	NUM
ejpam-4144	88	11	.	.	X
ejpam-4144	88	12	one	one	PRON
ejpam-4144	88	13	can	can	AUX
ejpam-4144	88	14	easily	easily	ADV
ejpam-4144	88	15	see	see	VERB
ejpam-4144	88	16	that	that	PRON
ejpam-4144	88	17	set	set	NOUN
ejpam-4144	88	18	s	s	X
ejpam-4144	88	19	=	=	PUNCT
ejpam-4144	88	20	{	{	PUNCT
ejpam-4144	88	21	x1	x1	PROPN
ejpam-4144	88	22	,	,	PUNCT
ejpam-4144	88	23	x2	x2	PROPN
ejpam-4144	88	24	,	,	PUNCT
ejpam-4144	88	25	.	.	PUNCT
ejpam-4144	88	26	.	.	PUNCT
ejpam-4144	89	1	.	.	PUNCT
ejpam-4144	90	1	,	,	PUNCT
ejpam-4144	90	2	xa	xa	PROPN
ejpam-4144	90	3	}	}	PUNCT
ejpam-4144	90	4	is	be	AUX
ejpam-4144	90	5	a	a	DET
ejpam-4144	90	6	γh	γh	ADV
ejpam-4144	90	7	-	-	PUNCT
ejpam-4144	90	8	set	set	NOUN
ejpam-4144	90	9	of	of	ADP
ejpam-4144	90	10	g.	g.	PROPN
ejpam-4144	90	11	hence	hence	ADV
ejpam-4144	90	12	,	,	PUNCT
ejpam-4144	90	13	γh(g	γh(g	NOUN
ejpam-4144	90	14	)	)	PUNCT
ejpam-4144	90	15	=	=	SYM
ejpam-4144	90	16	|s|	|s|	NOUN
ejpam-4144	90	17	=	=	NOUN
ejpam-4144	90	18	a.	a.	NOUN
ejpam-4144	90	19	the	the	DET
ejpam-4144	90	20	set	set	NOUN
ejpam-4144	90	21	s′	s′	PUNCT
ejpam-4144	90	22	=	=	PUNCT
ejpam-4144	90	23	{	{	PUNCT
ejpam-4144	90	24	y1	y1	NOUN
ejpam-4144	90	25	,	,	PUNCT
ejpam-4144	90	26	y2	y2	PROPN
ejpam-4144	90	27	,	,	PUNCT
ejpam-4144	90	28	.	.	PUNCT
ejpam-4144	90	29	.	.	PUNCT
ejpam-4144	91	1	.	.	PUNCT
ejpam-4144	92	1	,	,	PUNCT
ejpam-4144	92	2	ya	ya	PROPN
ejpam-4144	92	3	,	,	PUNCT
ejpam-4144	92	4	z1	z1	PROPN
ejpam-4144	92	5	,	,	PUNCT
ejpam-4144	92	6	z2	z2	PROPN
ejpam-4144	92	7	,	,	PUNCT
ejpam-4144	92	8	.	.	PUNCT
ejpam-4144	92	9	.	.	PUNCT
ejpam-4144	92	10	.	.	PUNCT
ejpam-4144	93	1	,	,	PUNCT
ejpam-4144	93	2	zm	zm	PROPN
ejpam-4144	93	3	}	}	PUNCT
ejpam-4144	93	4	is	be	AUX
ejpam-4144	93	5	a	a	DET
ejpam-4144	93	6	γ	γ	NOUN
ejpam-4144	93	7	-	-	PUNCT
ejpam-4144	93	8	set	set	NOUN
ejpam-4144	93	9	of	of	ADP
ejpam-4144	93	10	g	g	PROPN
ejpam-4144	93	11	and	and	CCONJ
ejpam-4144	93	12	so	so	ADV
ejpam-4144	93	13	γ(g	γ(g	PROPN
ejpam-4144	93	14	)	)	PUNCT
ejpam-4144	94	1	=	=	PUNCT
ejpam-4144	94	2	|s′|	|s′|	NOUN
ejpam-4144	94	3	=	=	PUNCT
ejpam-4144	94	4	a+m	a+m	NUM
ejpam-4144	94	5	=	=	SYM
ejpam-4144	94	6	b.	b.	PROPN
ejpam-4144	94	7	g.	g.	PROPN
ejpam-4144	94	8	salasalan	salasalan	PROPN
ejpam-4144	94	9	,	,	PUNCT
ejpam-4144	94	10	s.	s.	PROPN
ejpam-4144	94	11	canoy	canoy	PROPN
ejpam-4144	94	12	,	,	PUNCT
ejpam-4144	94	13	jr	jr	PROPN
ejpam-4144	94	14	.	.	PROPN
ejpam-4144	94	15	/	/	SYM
ejpam-4144	94	16	eur	eur	PROPN
ejpam-4144	94	17	.	.	PUNCT
ejpam-4144	95	1	j.	j.	PROPN
ejpam-4144	95	2	pure	pure	PROPN
ejpam-4144	95	3	appl	appl	PROPN
ejpam-4144	95	4	.	.	PROPN
ejpam-4144	95	5	math	math	PROPN
ejpam-4144	95	6	,	,	PUNCT
ejpam-4144	95	7	14	14	NUM
ejpam-4144	95	8	(	(	PUNCT
ejpam-4144	95	9	4	4	NUM
ejpam-4144	95	10	)	)	PUNCT
ejpam-4144	95	11	(	(	PUNCT
ejpam-4144	95	12	2021	2021	NUM
ejpam-4144	95	13	)	)	PUNCT
ejpam-4144	95	14	,	,	PUNCT
ejpam-4144	95	15	1415	1415	NUM
ejpam-4144	95	16	-	-	SYM
ejpam-4144	95	17	1428	1428	NUM
ejpam-4144	95	18	1418	1418	NUM
ejpam-4144	95	19	.........	.........	PUNCT
ejpam-4144	95	20	........	........	PUNCT
ejpam-4144	95	21	........	........	PUNCT
ejpam-4144	95	22	........	........	PUNCT
ejpam-4144	95	23	........	........	PUNCT
ejpam-4144	95	24	........	........	PUNCT
ejpam-4144	95	25	........	........	PUNCT
ejpam-4144	95	26	........	........	PUNCT
ejpam-4144	95	27	........	........	PUNCT
ejpam-4144	95	28	...	...	PUNCT
ejpam-4144	96	1	....................................	....................................	PUNCT
ejpam-4144	96	2	.........	.........	PUNCT
ejpam-4144	96	3	........	........	PUNCT
ejpam-4144	96	4	........	........	PUNCT
ejpam-4144	96	5	........	........	PUNCT
ejpam-4144	96	6	........	........	PUNCT
ejpam-4144	96	7	........	........	PUNCT
ejpam-4144	96	8	........	........	PUNCT
ejpam-4144	96	9	........	........	PUNCT
ejpam-4144	96	10	........	........	PUNCT
ejpam-4144	96	11	...	...	PUNCT
ejpam-4144	97	1	....................................	....................................	PUNCT
ejpam-4144	97	2	....................................	....................................	PUNCT
ejpam-4144	97	3	.........	.........	PUNCT
ejpam-4144	97	4	........	........	PUNCT
ejpam-4144	97	5	........	........	PUNCT
ejpam-4144	97	6	........	........	PUNCT
ejpam-4144	97	7	........	........	PUNCT
ejpam-4144	97	8	........	........	PUNCT
ejpam-4144	97	9	........	........	PUNCT
ejpam-4144	97	10	........	........	PUNCT
ejpam-4144	97	11	........	........	PUNCT
ejpam-4144	97	12	...	...	PUNCT
ejpam-4144	98	1	....................................	....................................	PUNCT
ejpam-4144	98	2	.........	.........	PUNCT
ejpam-4144	98	3	........	........	PUNCT
ejpam-4144	98	4	........	........	PUNCT
ejpam-4144	98	5	........	........	PUNCT
ejpam-4144	98	6	........	........	PUNCT
ejpam-4144	98	7	........	........	PUNCT
ejpam-4144	98	8	........	........	PUNCT
ejpam-4144	98	9	........	........	PUNCT
ejpam-4144	98	10	........	........	PUNCT
ejpam-4144	98	11	...	...	PUNCT
ejpam-4144	99	1	....................................	....................................	PUNCT
ejpam-4144	99	2	....................................	....................................	PUNCT
ejpam-4144	99	3	.........	.........	PUNCT
ejpam-4144	99	4	........	........	PUNCT
ejpam-4144	99	5	........	........	PUNCT
ejpam-4144	99	6	........	........	PUNCT
ejpam-4144	99	7	........	........	PUNCT
ejpam-4144	99	8	........	........	PUNCT
ejpam-4144	99	9	........	........	PUNCT
ejpam-4144	99	10	........	........	PUNCT
ejpam-4144	99	11	........	........	PUNCT
ejpam-4144	99	12	...	...	PUNCT
ejpam-4144	100	1	....................................	....................................	PUNCT
ejpam-4144	100	2	.........	.........	PUNCT
ejpam-4144	100	3	........	........	PUNCT
ejpam-4144	100	4	........	........	PUNCT
ejpam-4144	100	5	........	........	PUNCT
ejpam-4144	100	6	........	........	PUNCT
ejpam-4144	100	7	........	........	PUNCT
ejpam-4144	100	8	........	........	PUNCT
ejpam-4144	100	9	........	........	PUNCT
ejpam-4144	100	10	........	........	PUNCT
ejpam-4144	100	11	...	...	PUNCT
ejpam-4144	101	1	....................................	....................................	PUNCT
ejpam-4144	101	2	....................................	....................................	PUNCT
ejpam-4144	101	3	.........	.........	PUNCT
ejpam-4144	101	4	........	........	PUNCT
ejpam-4144	101	5	........	........	PUNCT
ejpam-4144	101	6	........	........	PUNCT
ejpam-4144	101	7	........	........	PUNCT
ejpam-4144	101	8	........	........	PUNCT
ejpam-4144	101	9	........	........	PUNCT
ejpam-4144	101	10	........	........	PUNCT
ejpam-4144	101	11	........	........	PUNCT
ejpam-4144	101	12	...	...	PUNCT
ejpam-4144	102	1	....................................	....................................	PUNCT
ejpam-4144	102	2	.........	.........	PUNCT
ejpam-4144	102	3	........	........	PUNCT
ejpam-4144	102	4	........	........	PUNCT
ejpam-4144	102	5	........	........	PUNCT
ejpam-4144	102	6	........	........	PUNCT
ejpam-4144	102	7	........	........	PUNCT
ejpam-4144	102	8	........	........	PUNCT
ejpam-4144	102	9	........	........	PUNCT
ejpam-4144	102	10	........	........	PUNCT
ejpam-4144	102	11	...	...	PUNCT
ejpam-4144	103	1	....................................	....................................	PUNCT
ejpam-4144	103	2	....................................	....................................	PUNCT
ejpam-4144	103	3	.........	.........	PUNCT
ejpam-4144	103	4	........	........	PUNCT
ejpam-4144	103	5	........	........	PUNCT
ejpam-4144	103	6	........	........	PUNCT
ejpam-4144	103	7	........	........	PUNCT
ejpam-4144	103	8	........	........	PUNCT
ejpam-4144	103	9	........	........	PUNCT
ejpam-4144	103	10	........	........	PUNCT
ejpam-4144	103	11	........	........	PUNCT
ejpam-4144	103	12	...	...	PUNCT
ejpam-4144	104	1	....................................	....................................	PUNCT
ejpam-4144	104	2	.........	.........	PUNCT
ejpam-4144	104	3	........	........	PUNCT
ejpam-4144	104	4	........	........	PUNCT
ejpam-4144	104	5	........	........	PUNCT
ejpam-4144	104	6	........	........	PUNCT
ejpam-4144	104	7	........	........	PUNCT
ejpam-4144	104	8	........	........	PUNCT
ejpam-4144	104	9	........	........	PUNCT
ejpam-4144	104	10	........	........	PUNCT
ejpam-4144	104	11	...	...	PUNCT
ejpam-4144	105	1	....................................	....................................	PUNCT
ejpam-4144	105	2	....................................	....................................	PUNCT
ejpam-4144	106	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4144	106	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4144	107	1	....................................	....................................	PUNCT
ejpam-4144	107	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4144	108	1	....................................	....................................	PUNCT
ejpam-4144	108	2	............	............	PUNCT
ejpam-4144	108	3	...........	...........	PUNCT
ejpam-4144	108	4	...........	...........	PUNCT
ejpam-4144	108	5	...........	...........	PUNCT
ejpam-4144	108	6	...........	...........	PUNCT
ejpam-4144	108	7	...........	...........	PUNCT
ejpam-4144	108	8	....	....	PUNCT
ejpam-4144	109	1	....................................	....................................	PUNCT
ejpam-4144	109	2	............	............	PUNCT
ejpam-4144	109	3	...........	...........	PUNCT
ejpam-4144	109	4	...........	...........	PUNCT
ejpam-4144	109	5	...........	...........	PUNCT
ejpam-4144	109	6	...........	...........	PUNCT
ejpam-4144	109	7	...........	...........	PUNCT
ejpam-4144	109	8	....	....	PUNCT
ejpam-4144	109	9	....................................	....................................	PUNCT
ejpam-4144	110	1	....................................	....................................	PUNCT
ejpam-4144	110	2	..........................	..........................	PUNCT
ejpam-4144	111	1	.........................	.........................	PUNCT
ejpam-4144	111	2	.........................	.........................	PUNCT
ejpam-4144	112	1	....	....	PUNCT
ejpam-4144	112	2	....................................	....................................	PUNCT
ejpam-4144	113	1	..........................	..........................	PUNCT
ejpam-4144	113	2	.........................	.........................	PUNCT
ejpam-4144	114	1	.........................	.........................	PUNCT
ejpam-4144	114	2	....	....	PUNCT
ejpam-4144	115	1	....................................	....................................	PUNCT
ejpam-4144	115	2	....................................	....................................	PUNCT
ejpam-4144	115	3	.......................................................................	.......................................................................	PUNCT
ejpam-4144	116	1	....................................	....................................	PUNCT
ejpam-4144	116	2	.......................................................................	.......................................................................	PUNCT
ejpam-4144	117	1	....................................	....................................	PUNCT
ejpam-4144	117	2	....................................	....................................	PUNCT
ejpam-4144	118	1	y1	y1	INTJ
ejpam-4144	118	2	y2	y2	NOUN
ejpam-4144	118	3	y3	y3	NOUN
ejpam-4144	118	4	ya−1	ya−1	NOUN
ejpam-4144	118	5	ya	ya	PROPN
ejpam-4144	119	1	x1	x1	NOUN
ejpam-4144	120	1	x2	x2	PROPN
ejpam-4144	120	2	x3	x3	PROPN
ejpam-4144	120	3	xa−1	xa−1	PROPN
ejpam-4144	120	4	xa	xa	PROPN
ejpam-4144	120	5	z1	z1	PROPN
ejpam-4144	120	6	z2	z2	PROPN
ejpam-4144	120	7	zm	zm	PROPN
ejpam-4144	120	8	.	.	PUNCT
ejpam-4144	120	9	.	.	PUNCT
ejpam-4144	120	10	.	.	PUNCT
ejpam-4144	121	1	...	...	PUNCT
ejpam-4144	122	1	g	g	PRON
ejpam-4144	122	2	figure	figure	NOUN
ejpam-4144	122	3	3	3	NUM
ejpam-4144	122	4	(	(	PUNCT
ejpam-4144	122	5	ii	ii	NOUN
ejpam-4144	122	6	)	)	PUNCT
ejpam-4144	122	7	the	the	DET
ejpam-4144	122	8	case	case	NOUN
ejpam-4144	122	9	a	a	DET
ejpam-4144	122	10	=	=	SYM
ejpam-4144	122	11	b	b	NOUN
ejpam-4144	122	12	is	be	AUX
ejpam-4144	122	13	similar	similar	ADJ
ejpam-4144	122	14	to	to	ADP
ejpam-4144	122	15	the	the	DET
ejpam-4144	122	16	first	first	ADJ
ejpam-4144	122	17	case	case	NOUN
ejpam-4144	122	18	of	of	ADP
ejpam-4144	122	19	(	(	PUNCT
ejpam-4144	122	20	i	i	NOUN
ejpam-4144	122	21	)	)	PUNCT
ejpam-4144	122	22	.	.	PUNCT
ejpam-4144	123	1	suppose	suppose	VERB
ejpam-4144	123	2	a	a	DET
ejpam-4144	123	3	<	<	X
ejpam-4144	123	4	b	b	NOUN
ejpam-4144	123	5	and	and	CCONJ
ejpam-4144	123	6	let	let	VERB
ejpam-4144	123	7	m	m	NOUN
ejpam-4144	123	8	=	=	SYM
ejpam-4144	124	1	b	b	X
ejpam-4144	124	2	−	−	NOUN
ejpam-4144	124	3	a.	a.	NOUN
ejpam-4144	124	4	consider	consider	VERB
ejpam-4144	124	5	graph	graph	NOUN
ejpam-4144	124	6	h	h	NOUN
ejpam-4144	124	7	=	=	NOUN
ejpam-4144	124	8	g	g	PROPN
ejpam-4144	124	9	∪	∪	ADJ
ejpam-4144	124	10	km+1	km+1	PROPN
ejpam-4144	124	11	,	,	PUNCT
ejpam-4144	124	12	where	where	SCONJ
ejpam-4144	124	13	v	v	NOUN
ejpam-4144	124	14	(	(	PUNCT
ejpam-4144	124	15	km+1	km+1	PROPN
ejpam-4144	124	16	)	)	PUNCT
ejpam-4144	124	17	=	=	SYM
ejpam-4144	124	18	{	{	PUNCT
ejpam-4144	124	19	v1	v1	PROPN
ejpam-4144	124	20	,	,	PUNCT
ejpam-4144	124	21	v2	v2	PROPN
ejpam-4144	124	22	,	,	PUNCT
ejpam-4144	124	23	.	.	PUNCT
ejpam-4144	124	24	.	.	PUNCT
ejpam-4144	125	1	.	.	PUNCT
ejpam-4144	126	1	,	,	PUNCT
ejpam-4144	126	2	vm	vm	PROPN
ejpam-4144	126	3	,	,	PUNCT
ejpam-4144	126	4	vm+1	vm+1	NOUN
ejpam-4144	126	5	}	}	PUNCT
ejpam-4144	126	6	and	and	CCONJ
ejpam-4144	126	7	g	g	PROPN
ejpam-4144	126	8	is	be	AUX
ejpam-4144	126	9	the	the	DET
ejpam-4144	126	10	graph	graph	NOUN
ejpam-4144	126	11	in	in	ADP
ejpam-4144	126	12	figure	figure	NOUN
ejpam-4144	126	13	4	4	NUM
ejpam-4144	126	14	.	.	PUNCT
ejpam-4144	127	1	then	then	ADV
ejpam-4144	127	2	s	s	VERB
ejpam-4144	127	3	=	=	SYM
ejpam-4144	127	4	{	{	PUNCT
ejpam-4144	127	5	y1	y1	PROPN
ejpam-4144	127	6	,	,	PUNCT
ejpam-4144	127	7	y2	y2	PROPN
ejpam-4144	127	8	,	,	PUNCT
ejpam-4144	127	9	.	.	PUNCT
ejpam-4144	127	10	.	.	PUNCT
ejpam-4144	127	11	.	.	PUNCT
ejpam-4144	128	1	,	,	PUNCT
ejpam-4144	128	2	ya−1	ya−1	NOUN
ejpam-4144	128	3	,	,	PUNCT
ejpam-4144	128	4	v1	v1	PROPN
ejpam-4144	128	5	}	}	PUNCT
ejpam-4144	128	6	is	be	AUX
ejpam-4144	128	7	a	a	DET
ejpam-4144	128	8	γ	γ	NOUN
ejpam-4144	128	9	-	-	PUNCT
ejpam-4144	128	10	set	set	VERB
ejpam-4144	128	11	and	and	CCONJ
ejpam-4144	128	12	s′	s′	ADJ
ejpam-4144	128	13	=	=	PUNCT
ejpam-4144	128	14	{	{	PUNCT
ejpam-4144	128	15	x1	x1	PROPN
ejpam-4144	128	16	,	,	PUNCT
ejpam-4144	128	17	x2	x2	PROPN
ejpam-4144	128	18	,	,	PUNCT
ejpam-4144	128	19	.	.	PUNCT
ejpam-4144	128	20	.	.	PUNCT
ejpam-4144	129	1	.	.	PUNCT
ejpam-4144	130	1	,	,	PUNCT
ejpam-4144	130	2	xa−1}∪	xa−1}∪	PROPN
ejpam-4144	130	3	.........	.........	PUNCT
ejpam-4144	130	4	........	........	PUNCT
ejpam-4144	130	5	........	........	PUNCT
ejpam-4144	130	6	........	........	PUNCT
ejpam-4144	130	7	........	........	PUNCT
ejpam-4144	130	8	........	........	PUNCT
ejpam-4144	130	9	........	........	PUNCT
ejpam-4144	130	10	........	........	PUNCT
ejpam-4144	130	11	........	........	PUNCT
ejpam-4144	130	12	...	...	PUNCT
ejpam-4144	131	1	....................................	....................................	PUNCT
ejpam-4144	131	2	.........	.........	PUNCT
ejpam-4144	131	3	........	........	PUNCT
ejpam-4144	131	4	........	........	PUNCT
ejpam-4144	131	5	........	........	PUNCT
ejpam-4144	131	6	........	........	PUNCT
ejpam-4144	131	7	........	........	PUNCT
ejpam-4144	131	8	........	........	PUNCT
ejpam-4144	131	9	........	........	PUNCT
ejpam-4144	131	10	........	........	PUNCT
ejpam-4144	131	11	...	...	PUNCT
ejpam-4144	132	1	....................................	....................................	PUNCT
ejpam-4144	132	2	....................................	....................................	PUNCT
ejpam-4144	132	3	.........	.........	PUNCT
ejpam-4144	132	4	........	........	PUNCT
ejpam-4144	132	5	........	........	PUNCT
ejpam-4144	132	6	........	........	PUNCT
ejpam-4144	132	7	........	........	PUNCT
ejpam-4144	132	8	........	........	PUNCT
ejpam-4144	132	9	........	........	PUNCT
ejpam-4144	132	10	........	........	PUNCT
ejpam-4144	132	11	........	........	PUNCT
ejpam-4144	132	12	...	...	PUNCT
ejpam-4144	133	1	....................................	....................................	PUNCT
ejpam-4144	133	2	.........	.........	PUNCT
ejpam-4144	133	3	........	........	PUNCT
ejpam-4144	133	4	........	........	PUNCT
ejpam-4144	133	5	........	........	PUNCT
ejpam-4144	133	6	........	........	PUNCT
ejpam-4144	133	7	........	........	PUNCT
ejpam-4144	133	8	........	........	PUNCT
ejpam-4144	133	9	........	........	PUNCT
ejpam-4144	133	10	........	........	PUNCT
ejpam-4144	133	11	...	...	PUNCT
ejpam-4144	134	1	....................................	....................................	PUNCT
ejpam-4144	134	2	....................................	....................................	PUNCT
ejpam-4144	134	3	.........	.........	PUNCT
ejpam-4144	134	4	........	........	PUNCT
ejpam-4144	134	5	........	........	PUNCT
ejpam-4144	134	6	........	........	PUNCT
ejpam-4144	134	7	........	........	PUNCT
ejpam-4144	134	8	........	........	PUNCT
ejpam-4144	134	9	........	........	PUNCT
ejpam-4144	134	10	........	........	PUNCT
ejpam-4144	134	11	........	........	PUNCT
ejpam-4144	134	12	...	...	PUNCT
ejpam-4144	135	1	....................................	....................................	PUNCT
ejpam-4144	135	2	.........	.........	PUNCT
ejpam-4144	135	3	........	........	PUNCT
ejpam-4144	135	4	........	........	PUNCT
ejpam-4144	135	5	........	........	PUNCT
ejpam-4144	135	6	........	........	PUNCT
ejpam-4144	135	7	........	........	PUNCT
ejpam-4144	135	8	........	........	PUNCT
ejpam-4144	135	9	........	........	PUNCT
ejpam-4144	135	10	........	........	PUNCT
ejpam-4144	135	11	...	...	PUNCT
ejpam-4144	136	1	....................................	....................................	PUNCT
ejpam-4144	136	2	....................................	....................................	PUNCT
ejpam-4144	136	3	.........	.........	PUNCT
ejpam-4144	136	4	........	........	PUNCT
ejpam-4144	136	5	........	........	PUNCT
ejpam-4144	136	6	........	........	PUNCT
ejpam-4144	136	7	........	........	PUNCT
ejpam-4144	136	8	........	........	PUNCT
ejpam-4144	136	9	........	........	PUNCT
ejpam-4144	136	10	........	........	PUNCT
ejpam-4144	136	11	........	........	PUNCT
ejpam-4144	136	12	...	...	PUNCT
ejpam-4144	137	1	....................................	....................................	PUNCT
ejpam-4144	137	2	.........	.........	PUNCT
ejpam-4144	137	3	........	........	PUNCT
ejpam-4144	137	4	........	........	PUNCT
ejpam-4144	137	5	........	........	PUNCT
ejpam-4144	137	6	........	........	PUNCT
ejpam-4144	137	7	........	........	PUNCT
ejpam-4144	137	8	........	........	PUNCT
ejpam-4144	137	9	........	........	PUNCT
ejpam-4144	137	10	........	........	PUNCT
ejpam-4144	137	11	...	...	PUNCT
ejpam-4144	138	1	....................................	....................................	PUNCT
ejpam-4144	138	2	....................................	....................................	PUNCT
ejpam-4144	138	3	.........	.........	PUNCT
ejpam-4144	138	4	........	........	PUNCT
ejpam-4144	138	5	........	........	PUNCT
ejpam-4144	138	6	........	........	PUNCT
ejpam-4144	138	7	........	........	PUNCT
ejpam-4144	138	8	........	........	PUNCT
ejpam-4144	138	9	........	........	PUNCT
ejpam-4144	138	10	........	........	PUNCT
ejpam-4144	138	11	........	........	PUNCT
ejpam-4144	138	12	...	...	PUNCT
ejpam-4144	139	1	....................................	....................................	PUNCT
ejpam-4144	139	2	.........	.........	PUNCT
ejpam-4144	139	3	........	........	PUNCT
ejpam-4144	139	4	........	........	PUNCT
ejpam-4144	139	5	........	........	PUNCT
ejpam-4144	139	6	........	........	PUNCT
ejpam-4144	139	7	........	........	PUNCT
ejpam-4144	139	8	........	........	PUNCT
ejpam-4144	139	9	........	........	PUNCT
ejpam-4144	139	10	........	........	PUNCT
ejpam-4144	139	11	...	...	PUNCT
ejpam-4144	140	1	....................................	....................................	PUNCT
ejpam-4144	140	2	....................................	....................................	PUNCT
ejpam-4144	141	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4144	141	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4144	142	1	....................................	....................................	PUNCT
ejpam-4144	142	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4144	143	1	....................................	....................................	PUNCT
ejpam-4144	144	1	y1	y1	INTJ
ejpam-4144	144	2	y2	y2	NOUN
ejpam-4144	144	3	y3	y3	PROPN
ejpam-4144	144	4	ya−2	ya−2	PROPN
ejpam-4144	144	5	ya−1	ya−1	NOUN
ejpam-4144	144	6	x1	x1	PROPN
ejpam-4144	145	1	x2	x2	PROPN
ejpam-4144	145	2	x3	x3	PROPN
ejpam-4144	145	3	xa−2	xa−2	PROPN
ejpam-4144	145	4	xa−1	xa−1	PROPN
ejpam-4144	145	5	.	.	PUNCT
ejpam-4144	145	6	.	.	PUNCT
ejpam-4144	145	7	.	.	PUNCT
ejpam-4144	146	1	g	g	NOUN
ejpam-4144	146	2	figure	figure	NOUN
ejpam-4144	146	3	4	4	NUM
ejpam-4144	146	4	v	v	NOUN
ejpam-4144	146	5	(	(	PUNCT
ejpam-4144	146	6	km+1	km+1	PROPN
ejpam-4144	146	7	)	)	PUNCT
ejpam-4144	146	8	is	be	AUX
ejpam-4144	146	9	a	a	DET
ejpam-4144	146	10	γh	γh	ADV
ejpam-4144	146	11	-	-	PUNCT
ejpam-4144	146	12	set	set	VERB
ejpam-4144	146	13	ofh	ofh	PROPN
ejpam-4144	146	14	.	.	PUNCT
ejpam-4144	147	1	therefore	therefore	ADV
ejpam-4144	147	2	,	,	PUNCT
ejpam-4144	147	3	γ(h	γ(h	NOUN
ejpam-4144	147	4	)	)	PUNCT
ejpam-4144	147	5	=	=	PUNCT
ejpam-4144	147	6	a	a	PRON
ejpam-4144	147	7	and	and	CCONJ
ejpam-4144	147	8	γh(h	γh(h	NUM
ejpam-4144	147	9	)	)	PUNCT
ejpam-4144	147	10	=	=	SYM
ejpam-4144	147	11	a−1+m+1	a−1+m+1	PROPN
ejpam-4144	147	12	=	=	SYM
ejpam-4144	147	13	a+m	a+m	NUM
ejpam-4144	147	14	=	=	SYM
ejpam-4144	147	15	b.	b.	PROPN
ejpam-4144	148	1	it	it	PRON
ejpam-4144	148	2	must	must	AUX
ejpam-4144	148	3	be	be	AUX
ejpam-4144	148	4	clear	clear	ADJ
ejpam-4144	148	5	that	that	SCONJ
ejpam-4144	148	6	every	every	DET
ejpam-4144	148	7	global	global	ADJ
ejpam-4144	148	8	hop	hop	NOUN
ejpam-4144	148	9	dominating	dominating	NOUN
ejpam-4144	148	10	set	set	NOUN
ejpam-4144	148	11	is	be	AUX
ejpam-4144	148	12	a	a	DET
ejpam-4144	148	13	hop	hop	NOUN
ejpam-4144	148	14	dominating	dominate	VERB
ejpam-4144	148	15	a	a	DET
ejpam-4144	148	16	set	set	NOUN
ejpam-4144	148	17	and	and	CCONJ
ejpam-4144	148	18	a	a	DET
ejpam-4144	148	19	set	set	NOUN
ejpam-4144	148	20	is	be	AUX
ejpam-4144	148	21	a	a	DET
ejpam-4144	148	22	global	global	ADJ
ejpam-4144	148	23	hop	hop	NOUN
ejpam-4144	148	24	dominating	dominating	NOUN
ejpam-4144	148	25	set	set	NOUN
ejpam-4144	148	26	of	of	ADP
ejpam-4144	148	27	a	a	DET
ejpam-4144	148	28	graph	graph	NOUN
ejpam-4144	148	29	g	g	NOUN
ejpam-4144	148	30	if	if	SCONJ
ejpam-4144	149	1	and	and	CCONJ
ejpam-4144	149	2	only	only	ADV
ejpam-4144	149	3	if	if	SCONJ
ejpam-4144	149	4	it	it	PRON
ejpam-4144	149	5	is	be	AUX
ejpam-4144	149	6	a	a	DET
ejpam-4144	149	7	global	global	ADJ
ejpam-4144	149	8	hop	hop	NOUN
ejpam-4144	149	9	dominating	dominating	NOUN
ejpam-4144	149	10	set	set	NOUN
ejpam-4144	149	11	of	of	ADP
ejpam-4144	149	12	g.	g.	PROPN
ejpam-4144	149	13	the	the	DET
ejpam-4144	149	14	following	follow	VERB
ejpam-4144	149	15	remark	remark	NOUN
ejpam-4144	149	16	is	be	AUX
ejpam-4144	149	17	immediate	immediate	ADJ
ejpam-4144	149	18	from	from	ADP
ejpam-4144	149	19	these	these	DET
ejpam-4144	149	20	facts	fact	NOUN
ejpam-4144	149	21	.	.	PUNCT
ejpam-4144	150	1	remark	remark	PROPN
ejpam-4144	150	2	1	1	NUM
ejpam-4144	150	3	.	.	PUNCT
ejpam-4144	151	1	for	for	ADP
ejpam-4144	151	2	any	any	DET
ejpam-4144	151	3	graph	graph	NOUN
ejpam-4144	151	4	g	g	NOUN
ejpam-4144	151	5	,	,	PUNCT
ejpam-4144	151	6	γh(g	γh(g	NOUN
ejpam-4144	151	7	)	)	PUNCT
ejpam-4144	151	8	≤	≤	NUM
ejpam-4144	151	9	γgh(g	γgh(g	NOUN
ejpam-4144	151	10	)	)	PUNCT
ejpam-4144	151	11	and	and	CCONJ
ejpam-4144	151	12	γgh(g	γgh(g	NOUN
ejpam-4144	151	13	)	)	PUNCT
ejpam-4144	151	14	=	=	SYM
ejpam-4144	151	15	γgh(g	γgh(g	NOUN
ejpam-4144	151	16	)	)	PUNCT
ejpam-4144	151	17	.	.	PUNCT
ejpam-4144	152	1	it	it	PRON
ejpam-4144	152	2	was	be	AUX
ejpam-4144	152	3	pointed	point	VERB
ejpam-4144	152	4	out	out	ADP
ejpam-4144	152	5	in	in	ADP
ejpam-4144	152	6	[	[	X
ejpam-4144	152	7	16	16	NUM
ejpam-4144	152	8	]	]	PUNCT
ejpam-4144	152	9	that	that	SCONJ
ejpam-4144	152	10	1	1	NUM
ejpam-4144	152	11	≤	≤	NUM
ejpam-4144	152	12	γgh(g	γgh(g	NOUN
ejpam-4144	152	13	)	)	PUNCT
ejpam-4144	152	14	≤	≤	NOUN
ejpam-4144	152	15	|v	|v	X
ejpam-4144	152	16	(	(	PUNCT
ejpam-4144	152	17	g)|	g)|	NOUN
ejpam-4144	152	18	for	for	ADP
ejpam-4144	152	19	any	any	DET
ejpam-4144	152	20	graph	graph	NOUN
ejpam-4144	152	21	g	g	NOUN
ejpam-4144	152	22	and	and	CCONJ
ejpam-4144	152	23	that	that	SCONJ
ejpam-4144	152	24	γgh(g	γgh(g	NOUN
ejpam-4144	152	25	)	)	PUNCT
ejpam-4144	152	26	=	=	SYM
ejpam-4144	152	27	1	1	NUM
ejpam-4144	152	28	if	if	SCONJ
ejpam-4144	152	29	and	and	CCONJ
ejpam-4144	152	30	only	only	ADV
ejpam-4144	152	31	if	if	SCONJ
ejpam-4144	152	32	g	g	PROPN
ejpam-4144	152	33	=	=	PROPN
ejpam-4144	152	34	k1	k1	PROPN
ejpam-4144	152	35	.	.	PUNCT
ejpam-4144	153	1	the	the	DET
ejpam-4144	153	2	next	next	ADJ
ejpam-4144	153	3	result	result	NOUN
ejpam-4144	153	4	is	be	AUX
ejpam-4144	153	5	a	a	DET
ejpam-4144	153	6	rectification	rectification	NOUN
ejpam-4144	153	7	of	of	ADP
ejpam-4144	153	8	theorem	theorem	ADJ
ejpam-4144	153	9	3.3	3.3	NUM
ejpam-4144	153	10	in	in	ADP
ejpam-4144	153	11	[	[	X
ejpam-4144	153	12	16	16	NUM
ejpam-4144	153	13	]	]	PUNCT
ejpam-4144	153	14	.	.	PUNCT
ejpam-4144	154	1	theorem	theorem	NOUN
ejpam-4144	154	2	2	2	NUM
ejpam-4144	154	3	.	.	PUNCT
ejpam-4144	154	4	(	(	PUNCT
ejpam-4144	154	5	theorem	theorem	VERB
ejpam-4144	154	6	3.3	3.3	NUM
ejpam-4144	154	7	in	in	ADP
ejpam-4144	154	8	[	[	X
ejpam-4144	154	9	16	16	NUM
ejpam-4144	154	10	]	]	PUNCT
ejpam-4144	154	11	)	)	PUNCT
ejpam-4144	154	12	let	let	VERB
ejpam-4144	154	13	g	g	PRON
ejpam-4144	154	14	be	be	AUX
ejpam-4144	154	15	a	a	DET
ejpam-4144	154	16	graph	graph	NOUN
ejpam-4144	154	17	of	of	ADP
ejpam-4144	154	18	order	order	NOUN
ejpam-4144	154	19	n	n	PRON
ejpam-4144	154	20	≥	≥	NOUN
ejpam-4144	154	21	1	1	NUM
ejpam-4144	154	22	.	.	PUNCT
ejpam-4144	155	1	then	then	ADV
ejpam-4144	155	2	γgh(g	γgh(g	NOUN
ejpam-4144	155	3	)	)	PUNCT
ejpam-4144	155	4	=	=	SYM
ejpam-4144	156	1	n	n	NOUN
ejpam-4144	156	2	if	if	SCONJ
ejpam-4144	156	3	and	and	CCONJ
ejpam-4144	156	4	only	only	ADV
ejpam-4144	156	5	if	if	SCONJ
ejpam-4144	156	6	every	every	DET
ejpam-4144	156	7	component	component	NOUN
ejpam-4144	156	8	of	of	ADP
ejpam-4144	156	9	g	g	PROPN
ejpam-4144	156	10	or	or	CCONJ
ejpam-4144	156	11	g	g	PROPN
ejpam-4144	156	12	is	be	AUX
ejpam-4144	156	13	complete	complete	ADJ
ejpam-4144	156	14	.	.	PUNCT
ejpam-4144	157	1	moreover	moreover	ADV
ejpam-4144	157	2	,	,	PUNCT
ejpam-4144	157	3	if	if	SCONJ
ejpam-4144	157	4	g	g	PROPN
ejpam-4144	157	5	is	be	AUX
ejpam-4144	157	6	connected	connect	VERB
ejpam-4144	157	7	,	,	PUNCT
ejpam-4144	157	8	then	then	ADV
ejpam-4144	157	9	for	for	ADP
ejpam-4144	157	10	each	each	DET
ejpam-4144	157	11	v	v	NUM
ejpam-4144	157	12	∈	∈	PROPN
ejpam-4144	157	13	v	v	NOUN
ejpam-4144	157	14	(	(	PUNCT
ejpam-4144	157	15	g	g	NOUN
ejpam-4144	157	16	)	)	PUNCT
ejpam-4144	157	17	,	,	PUNCT
ejpam-4144	157	18	we	we	PRON
ejpam-4144	157	19	have	have	AUX
ejpam-4144	157	20	(	(	PUNCT
ejpam-4144	157	21	i	i	NOUN
ejpam-4144	157	22	)	)	PUNCT
ejpam-4144	157	23	v	v	NOUN
ejpam-4144	157	24	(	(	PUNCT
ejpam-4144	157	25	g	g	NOUN
ejpam-4144	157	26	)	)	PUNCT
ejpam-4144	157	27	\ng(v	\ng(v	NOUN
ejpam-4144	157	28	)	)	PUNCT
ejpam-4144	157	29	is	be	AUX
ejpam-4144	157	30	an	an	DET
ejpam-4144	157	31	independent	independent	ADJ
ejpam-4144	157	32	set	set	NOUN
ejpam-4144	157	33	,	,	PUNCT
ejpam-4144	157	34	and	and	CCONJ
ejpam-4144	157	35	(	(	PUNCT
ejpam-4144	157	36	ii	ii	NOUN
ejpam-4144	157	37	)	)	PUNCT
ejpam-4144	157	38	ng(v	ng(v	PUNCT
ejpam-4144	157	39	)	)	PUNCT
ejpam-4144	157	40	=	=	SYM
ejpam-4144	157	41	ng(a	ng(a	NOUN
ejpam-4144	157	42	)	)	PUNCT
ejpam-4144	157	43	for	for	ADP
ejpam-4144	157	44	each	each	DET
ejpam-4144	157	45	a	a	DET
ejpam-4144	157	46	∈	∈	PROPN
ejpam-4144	157	47	v	v	NOUN
ejpam-4144	157	48	(	(	PUNCT
ejpam-4144	157	49	g	g	NOUN
ejpam-4144	157	50	)	)	PUNCT
ejpam-4144	157	51	\ng(v	\ng(v	NOUN
ejpam-4144	157	52	)	)	PUNCT
ejpam-4144	157	53	.	.	PUNCT
ejpam-4144	158	1	proof	proof	NOUN
ejpam-4144	158	2	.	.	PUNCT
ejpam-4144	159	1	suppose	suppose	VERB
ejpam-4144	159	2	γgh(g	γgh(g	NOUN
ejpam-4144	159	3	)	)	PUNCT
ejpam-4144	159	4	=	=	SYM
ejpam-4144	159	5	n.	n.	NOUN
ejpam-4144	159	6	assume	assume	VERB
ejpam-4144	159	7	first	first	ADV
ejpam-4144	159	8	that	that	SCONJ
ejpam-4144	159	9	g	g	PROPN
ejpam-4144	159	10	is	be	AUX
ejpam-4144	159	11	disconnected	disconnect	VERB
ejpam-4144	159	12	and	and	CCONJ
ejpam-4144	159	13	suppose	suppose	VERB
ejpam-4144	159	14	that	that	SCONJ
ejpam-4144	159	15	g	g	PROPN
ejpam-4144	159	16	has	have	VERB
ejpam-4144	159	17	a	a	DET
ejpam-4144	159	18	component	component	NOUN
ejpam-4144	159	19	c	c	NOUN
ejpam-4144	159	20	which	which	PRON
ejpam-4144	159	21	is	be	AUX
ejpam-4144	159	22	not	not	PART
ejpam-4144	159	23	complete	complete	ADJ
ejpam-4144	159	24	.	.	PUNCT
ejpam-4144	160	1	then	then	ADV
ejpam-4144	160	2	there	there	PRON
ejpam-4144	160	3	exist	exist	VERB
ejpam-4144	160	4	distinct	distinct	ADJ
ejpam-4144	160	5	vertices	vertex	NOUN
ejpam-4144	160	6	x	x	X
ejpam-4144	160	7	,	,	PUNCT
ejpam-4144	160	8	y	y	PROPN
ejpam-4144	160	9	∈	∈	PROPN
ejpam-4144	160	10	v	v	NOUN
ejpam-4144	160	11	(	(	PUNCT
ejpam-4144	160	12	c	c	NOUN
ejpam-4144	160	13	)	)	PUNCT
ejpam-4144	160	14	such	such	ADJ
ejpam-4144	160	15	that	that	DET
ejpam-4144	160	16	dg(x	dg(x	PROPN
ejpam-4144	160	17	,	,	PUNCT
ejpam-4144	160	18	y	y	NOUN
ejpam-4144	160	19	)	)	PUNCT
ejpam-4144	160	20	=	=	SYM
ejpam-4144	160	21	dc(x	dc(x	NOUN
ejpam-4144	160	22	,	,	PUNCT
ejpam-4144	160	23	y	y	NOUN
ejpam-4144	160	24	)	)	PUNCT
ejpam-4144	160	25	=	=	SYM
ejpam-4144	161	1	2	2	X
ejpam-4144	161	2	.	.	X
ejpam-4144	161	3	let	let	VERB
ejpam-4144	161	4	s	s	NOUN
ejpam-4144	161	5	=	=	X
ejpam-4144	161	6	v	v	ADJ
ejpam-4144	161	7	(	(	PUNCT
ejpam-4144	161	8	g	g	NOUN
ejpam-4144	161	9	)	)	PUNCT
ejpam-4144	161	10	\	\	NOUN
ejpam-4144	161	11	{	{	PUNCT
ejpam-4144	161	12	x	x	NOUN
ejpam-4144	161	13	}	}	PUNCT
ejpam-4144	161	14	.	.	PUNCT
ejpam-4144	162	1	then	then	ADV
ejpam-4144	162	2	s	s	VERB
ejpam-4144	162	3	is	be	AUX
ejpam-4144	162	4	a	a	DET
ejpam-4144	162	5	hop	hop	NOUN
ejpam-4144	162	6	dominating	dominating	NOUN
ejpam-4144	162	7	set	set	NOUN
ejpam-4144	162	8	of	of	ADP
ejpam-4144	162	9	g.	g.	PROPN
ejpam-4144	162	10	let	let	VERB
ejpam-4144	162	11	z	z	NOUN
ejpam-4144	162	12	∈	∈	PROPN
ejpam-4144	162	13	c	c	NOUN
ejpam-4144	162	14	such	such	ADJ
ejpam-4144	162	15	that	that	SCONJ
ejpam-4144	162	16	[	[	X
ejpam-4144	162	17	x	x	X
ejpam-4144	162	18	,	,	PUNCT
ejpam-4144	162	19	z	z	PROPN
ejpam-4144	162	20	,	,	PUNCT
ejpam-4144	162	21	y	y	PROPN
ejpam-4144	162	22	]	]	X
ejpam-4144	162	23	is	be	AUX
ejpam-4144	162	24	an	an	DET
ejpam-4144	162	25	x	x	NOUN
ejpam-4144	162	26	-	-	NOUN
ejpam-4144	162	27	y	y	ADJ
ejpam-4144	162	28	geodesic	geodesic	NOUN
ejpam-4144	162	29	in	in	ADP
ejpam-4144	162	30	g.	g.	PROPN
ejpam-4144	162	31	let	let	VERB
ejpam-4144	162	32	c	c	NOUN
ejpam-4144	162	33	′	′	VERB
ejpam-4144	162	34	be	be	AUX
ejpam-4144	162	35	a	a	DET
ejpam-4144	162	36	component	component	NOUN
ejpam-4144	162	37	of	of	ADP
ejpam-4144	162	38	g.	g.	PROPN
ejpam-4144	162	39	salasalan	salasalan	PROPN
ejpam-4144	162	40	,	,	PUNCT
ejpam-4144	162	41	s.	s.	PROPN
ejpam-4144	162	42	canoy	canoy	PROPN
ejpam-4144	162	43	,	,	PUNCT
ejpam-4144	162	44	jr	jr	PROPN
ejpam-4144	162	45	.	.	PROPN
ejpam-4144	162	46	/	/	SYM
ejpam-4144	162	47	eur	eur	PROPN
ejpam-4144	162	48	.	.	PUNCT
ejpam-4144	163	1	j.	j.	PROPN
ejpam-4144	163	2	pure	pure	PROPN
ejpam-4144	163	3	appl	appl	PROPN
ejpam-4144	163	4	.	.	PROPN
ejpam-4144	163	5	math	math	PROPN
ejpam-4144	163	6	,	,	PUNCT
ejpam-4144	163	7	14	14	NUM
ejpam-4144	163	8	(	(	PUNCT
ejpam-4144	163	9	4	4	NUM
ejpam-4144	163	10	)	)	PUNCT
ejpam-4144	163	11	(	(	PUNCT
ejpam-4144	163	12	2021	2021	NUM
ejpam-4144	163	13	)	)	PUNCT
ejpam-4144	163	14	,	,	PUNCT
ejpam-4144	163	15	1415	1415	NUM
ejpam-4144	163	16	-	-	SYM
ejpam-4144	163	17	1428	1428	NUM
ejpam-4144	163	18	1419	1419	NUM
ejpam-4144	163	19	g	g	NOUN
ejpam-4144	163	20	with	with	ADP
ejpam-4144	163	21	c	c	NOUN
ejpam-4144	163	22	′	′	NOUN
ejpam-4144	163	23	̸=	̸=	PROPN
ejpam-4144	163	24	c	c	NOUN
ejpam-4144	163	25	and	and	CCONJ
ejpam-4144	163	26	pick	pick	VERB
ejpam-4144	163	27	any	any	DET
ejpam-4144	163	28	w	w	PROPN
ejpam-4144	163	29	∈	∈	PROPN
ejpam-4144	163	30	c	c	NOUN
ejpam-4144	163	31	′.	′.	NOUN
ejpam-4144	163	32	then	then	ADV
ejpam-4144	163	33	[	[	X
ejpam-4144	163	34	x	x	X
ejpam-4144	163	35	,	,	PUNCT
ejpam-4144	163	36	w	w	PROPN
ejpam-4144	163	37	,	,	PUNCT
ejpam-4144	163	38	z	z	X
ejpam-4144	163	39	]	]	X
ejpam-4144	163	40	is	be	AUX
ejpam-4144	163	41	an	an	DET
ejpam-4144	163	42	x	x	ADJ
ejpam-4144	163	43	-	-	NOUN
ejpam-4144	163	44	z	z	ADJ
ejpam-4144	163	45	geodesic	geodesic	NOUN
ejpam-4144	163	46	in	in	ADP
ejpam-4144	163	47	g.	g.	PROPN
ejpam-4144	163	48	it	it	PRON
ejpam-4144	163	49	follows	follow	VERB
ejpam-4144	163	50	that	that	SCONJ
ejpam-4144	163	51	dg(x	dg(x	ADV
ejpam-4144	163	52	,	,	PUNCT
ejpam-4144	163	53	z	z	NOUN
ejpam-4144	163	54	)	)	PUNCT
ejpam-4144	163	55	=	=	SYM
ejpam-4144	163	56	2	2	X
ejpam-4144	163	57	.	.	PUNCT
ejpam-4144	164	1	thus	thus	ADV
ejpam-4144	164	2	,	,	PUNCT
ejpam-4144	164	3	s	s	VERB
ejpam-4144	164	4	is	be	AUX
ejpam-4144	164	5	a	a	DET
ejpam-4144	164	6	hop	hop	NOUN
ejpam-4144	164	7	dominating	dominating	NOUN
ejpam-4144	164	8	set	set	NOUN
ejpam-4144	164	9	of	of	ADP
ejpam-4144	164	10	g	g	NOUN
ejpam-4144	164	11	,	,	PUNCT
ejpam-4144	164	12	showing	show	VERB
ejpam-4144	164	13	that	that	SCONJ
ejpam-4144	164	14	s	s	VERB
ejpam-4144	164	15	is	be	AUX
ejpam-4144	164	16	a	a	DET
ejpam-4144	164	17	global	global	ADJ
ejpam-4144	164	18	hop	hop	NOUN
ejpam-4144	164	19	dominating	dominating	NOUN
ejpam-4144	164	20	set	set	NOUN
ejpam-4144	164	21	of	of	ADP
ejpam-4144	164	22	g.	g.	PROPN
ejpam-4144	164	23	therefore	therefore	ADV
ejpam-4144	164	24	,	,	PUNCT
ejpam-4144	164	25	γgh(g	γgh(g	PROPN
ejpam-4144	164	26	)	)	PUNCT
ejpam-4144	164	27	≤	≤	NUM
ejpam-4144	164	28	|s|	|s|	PROPN
ejpam-4144	164	29	=	=	SYM
ejpam-4144	164	30	n−1	n−1	PROPN
ejpam-4144	164	31	,	,	PUNCT
ejpam-4144	164	32	a	a	DET
ejpam-4144	164	33	contradiction	contradiction	NOUN
ejpam-4144	164	34	.	.	PUNCT
ejpam-4144	165	1	accordingly	accordingly	ADV
ejpam-4144	165	2	,	,	PUNCT
ejpam-4144	165	3	every	every	DET
ejpam-4144	165	4	component	component	NOUN
ejpam-4144	165	5	of	of	ADP
ejpam-4144	165	6	g	g	PROPN
ejpam-4144	165	7	is	be	AUX
ejpam-4144	165	8	complete	complete	ADJ
ejpam-4144	165	9	.	.	PUNCT
ejpam-4144	166	1	next	next	ADV
ejpam-4144	166	2	,	,	PUNCT
ejpam-4144	166	3	suppose	suppose	VERB
ejpam-4144	166	4	that	that	SCONJ
ejpam-4144	166	5	g	g	PROPN
ejpam-4144	166	6	is	be	AUX
ejpam-4144	166	7	connected	connect	VERB
ejpam-4144	166	8	.	.	PUNCT
ejpam-4144	167	1	suppose	suppose	VERB
ejpam-4144	167	2	further	far	ADV
ejpam-4144	167	3	that	that	SCONJ
ejpam-4144	167	4	g	g	PROPN
ejpam-4144	167	5	is	be	AUX
ejpam-4144	167	6	connected	connect	VERB
ejpam-4144	167	7	.	.	PUNCT
ejpam-4144	168	1	then	then	ADV
ejpam-4144	168	2	,	,	PUNCT
ejpam-4144	168	3	clearly	clearly	ADV
ejpam-4144	168	4	,	,	PUNCT
ejpam-4144	168	5	g	g	PROPN
ejpam-4144	168	6	̸=	̸=	PROPN
ejpam-4144	168	7	kn	kn	PROPN
ejpam-4144	168	8	.	.	PUNCT
ejpam-4144	169	1	let	let	VERB
ejpam-4144	169	2	u	u	NOUN
ejpam-4144	169	3	,	,	PUNCT
ejpam-4144	169	4	v	v	PROPN
ejpam-4144	169	5	∈	∈	PROPN
ejpam-4144	169	6	v	v	NOUN
ejpam-4144	169	7	(	(	PUNCT
ejpam-4144	169	8	g	g	NOUN
ejpam-4144	169	9	)	)	PUNCT
ejpam-4144	169	10	be	be	AUX
ejpam-4144	169	11	such	such	ADJ
ejpam-4144	169	12	that	that	SCONJ
ejpam-4144	169	13	dg(u	dg(u	ADJ
ejpam-4144	169	14	,	,	PUNCT
ejpam-4144	169	15	v	v	NOUN
ejpam-4144	169	16	)	)	PUNCT
ejpam-4144	169	17	=	=	SYM
ejpam-4144	169	18	2	2	NUM
ejpam-4144	169	19	and	and	CCONJ
ejpam-4144	169	20	let	let	VERB
ejpam-4144	169	21	[	[	X
ejpam-4144	169	22	u	u	NOUN
ejpam-4144	169	23	,	,	PUNCT
ejpam-4144	169	24	p	p	X
ejpam-4144	169	25	,	,	PUNCT
ejpam-4144	169	26	v	v	NOUN
ejpam-4144	169	27	]	]	PUNCT
ejpam-4144	169	28	be	be	AUX
ejpam-4144	169	29	a	a	DET
ejpam-4144	169	30	u	u	NOUN
ejpam-4144	169	31	-	-	NOUN
ejpam-4144	169	32	v	v	ADJ
ejpam-4144	169	33	geodesic	geodesic	NOUN
ejpam-4144	169	34	in	in	ADP
ejpam-4144	169	35	g.	g.	PROPN
ejpam-4144	169	36	then	then	ADV
ejpam-4144	169	37	s∗	s∗	PROPN
ejpam-4144	169	38	=	=	SYM
ejpam-4144	169	39	v	v	PROPN
ejpam-4144	169	40	(	(	PUNCT
ejpam-4144	169	41	g	g	NOUN
ejpam-4144	169	42	)	)	PUNCT
ejpam-4144	169	43	\	\	NOUN
ejpam-4144	170	1	{	{	PUNCT
ejpam-4144	170	2	u	u	NOUN
ejpam-4144	170	3	}	}	PUNCT
ejpam-4144	170	4	is	be	AUX
ejpam-4144	170	5	a	a	DET
ejpam-4144	170	6	hop	hop	NOUN
ejpam-4144	170	7	dominating	dominating	NOUN
ejpam-4144	170	8	set	set	NOUN
ejpam-4144	170	9	of	of	ADP
ejpam-4144	170	10	g.	g.	PROPN
ejpam-4144	170	11	since	since	SCONJ
ejpam-4144	170	12	up	up	ADV
ejpam-4144	170	13	/∈	/∈	PUNCT
ejpam-4144	171	1	e(g	e(g	PROPN
ejpam-4144	171	2	)	)	PUNCT
ejpam-4144	171	3	,	,	PUNCT
ejpam-4144	171	4	it	it	PRON
ejpam-4144	171	5	follows	follow	VERB
ejpam-4144	171	6	that	that	SCONJ
ejpam-4144	171	7	dg(u	dg(u	ADJ
ejpam-4144	171	8	,	,	PUNCT
ejpam-4144	171	9	p	p	NOUN
ejpam-4144	171	10	)	)	PUNCT
ejpam-4144	171	11	≥	≥	NOUN
ejpam-4144	171	12	2	2	NUM
ejpam-4144	171	13	.	.	PUNCT
ejpam-4144	172	1	it	it	PRON
ejpam-4144	172	2	follows	follow	VERB
ejpam-4144	172	3	that	that	SCONJ
ejpam-4144	172	4	there	there	PRON
ejpam-4144	172	5	exists	exist	VERB
ejpam-4144	172	6	q	q	PROPN
ejpam-4144	172	7	∈	∈	PROPN
ejpam-4144	172	8	s	s	VERB
ejpam-4144	172	9	such	such	ADJ
ejpam-4144	173	1	that	that	PRON
ejpam-4144	173	2	dg(u	dg(u	ADJ
ejpam-4144	173	3	,	,	PUNCT
ejpam-4144	173	4	q	q	X
ejpam-4144	173	5	)	)	PUNCT
ejpam-4144	173	6	=	=	SYM
ejpam-4144	173	7	2	2	X
ejpam-4144	173	8	.	.	PUNCT
ejpam-4144	173	9	this	this	PRON
ejpam-4144	173	10	shows	show	VERB
ejpam-4144	173	11	that	that	SCONJ
ejpam-4144	173	12	s∗	s∗	PROPN
ejpam-4144	173	13	is	be	AUX
ejpam-4144	173	14	hop	hop	NOUN
ejpam-4144	173	15	dominating	dominate	VERB
ejpam-4144	173	16	set	set	NOUN
ejpam-4144	173	17	of	of	ADP
ejpam-4144	173	18	g.	g.	PROPN
ejpam-4144	173	19	thus	thus	ADV
ejpam-4144	173	20	,	,	PUNCT
ejpam-4144	173	21	s∗	s∗	PROPN
ejpam-4144	173	22	is	be	AUX
ejpam-4144	173	23	a	a	DET
ejpam-4144	173	24	global	global	ADJ
ejpam-4144	173	25	hop	hop	NOUN
ejpam-4144	173	26	dominating	dominating	NOUN
ejpam-4144	173	27	set	set	NOUN
ejpam-4144	173	28	of	of	ADP
ejpam-4144	173	29	g	g	NOUN
ejpam-4144	173	30	and	and	CCONJ
ejpam-4144	173	31	γgh(g	γgh(g	NOUN
ejpam-4144	173	32	)	)	PUNCT
ejpam-4144	173	33	≤	≤	NOUN
ejpam-4144	173	34	|s∗|	|s∗|	NUM
ejpam-4144	174	1	=	=	SYM
ejpam-4144	174	2	n	n	PRON
ejpam-4144	174	3	−	−	PROPN
ejpam-4144	174	4	1	1	NUM
ejpam-4144	174	5	,	,	PUNCT
ejpam-4144	174	6	a	a	DET
ejpam-4144	174	7	contradiction	contradiction	NOUN
ejpam-4144	174	8	.	.	PUNCT
ejpam-4144	175	1	therefore	therefore	ADV
ejpam-4144	175	2	,	,	PUNCT
ejpam-4144	175	3	g	g	PROPN
ejpam-4144	175	4	is	be	AUX
ejpam-4144	175	5	disconnected	disconnect	VERB
ejpam-4144	175	6	.	.	PUNCT
ejpam-4144	176	1	since	since	SCONJ
ejpam-4144	176	2	γgh(g	γgh(g	NOUN
ejpam-4144	176	3	)	)	PUNCT
ejpam-4144	176	4	=	=	SYM
ejpam-4144	176	5	γgh(g	γgh(g	PROPN
ejpam-4144	176	6	)	)	PUNCT
ejpam-4144	176	7	=	=	SYM
ejpam-4144	176	8	n	n	CCONJ
ejpam-4144	176	9	,	,	PUNCT
ejpam-4144	176	10	this	this	PRON
ejpam-4144	176	11	would	would	AUX
ejpam-4144	176	12	imply	imply	VERB
ejpam-4144	176	13	that	that	SCONJ
ejpam-4144	176	14	every	every	DET
ejpam-4144	176	15	component	component	NOUN
ejpam-4144	176	16	of	of	ADP
ejpam-4144	176	17	g	g	PROPN
ejpam-4144	176	18	is	be	AUX
ejpam-4144	176	19	complete	complete	ADJ
ejpam-4144	176	20	(	(	PUNCT
ejpam-4144	176	21	as	as	ADP
ejpam-4144	176	22	in	in	ADP
ejpam-4144	176	23	the	the	DET
ejpam-4144	176	24	first	first	ADJ
ejpam-4144	176	25	case	case	NOUN
ejpam-4144	176	26	applied	apply	VERB
ejpam-4144	176	27	to	to	ADP
ejpam-4144	176	28	g	g	NOUN
ejpam-4144	176	29	)	)	PUNCT
ejpam-4144	176	30	.	.	PUNCT
ejpam-4144	177	1	for	for	ADP
ejpam-4144	177	2	the	the	DET
ejpam-4144	177	3	converse	converse	NOUN
ejpam-4144	177	4	,	,	PUNCT
ejpam-4144	177	5	suppose	suppose	VERB
ejpam-4144	177	6	first	first	ADV
ejpam-4144	177	7	that	that	SCONJ
ejpam-4144	177	8	every	every	DET
ejpam-4144	177	9	component	component	NOUN
ejpam-4144	177	10	of	of	ADP
ejpam-4144	177	11	g	g	PROPN
ejpam-4144	177	12	is	be	AUX
ejpam-4144	177	13	complete	complete	ADJ
ejpam-4144	177	14	.	.	PUNCT
ejpam-4144	178	1	then	then	ADV
ejpam-4144	178	2	,	,	PUNCT
ejpam-4144	178	3	clearly	clearly	ADV
ejpam-4144	178	4	,	,	PUNCT
ejpam-4144	178	5	s	s	NOUN
ejpam-4144	178	6	=	=	SYM
ejpam-4144	178	7	v	v	X
ejpam-4144	178	8	(	(	PUNCT
ejpam-4144	178	9	g	g	NOUN
ejpam-4144	178	10	)	)	PUNCT
ejpam-4144	178	11	is	be	AUX
ejpam-4144	178	12	the	the	DET
ejpam-4144	178	13	only	only	ADJ
ejpam-4144	178	14	hop	hop	NOUN
ejpam-4144	178	15	dominating	dominating	NOUN
ejpam-4144	178	16	set	set	NOUN
ejpam-4144	178	17	of	of	ADP
ejpam-4144	178	18	g.	g.	PROPN
ejpam-4144	178	19	it	it	PRON
ejpam-4144	178	20	follows	follow	VERB
ejpam-4144	178	21	that	that	SCONJ
ejpam-4144	178	22	s	s	VERB
ejpam-4144	178	23	is	be	AUX
ejpam-4144	178	24	the	the	DET
ejpam-4144	178	25	only	only	ADJ
ejpam-4144	178	26	global	global	ADJ
ejpam-4144	178	27	hop	hop	NOUN
ejpam-4144	178	28	dominating	dominating	NOUN
ejpam-4144	178	29	set	set	NOUN
ejpam-4144	178	30	of	of	ADP
ejpam-4144	178	31	g.	g.	PROPN
ejpam-4144	178	32	if	if	SCONJ
ejpam-4144	178	33	every	every	DET
ejpam-4144	178	34	component	component	NOUN
ejpam-4144	178	35	of	of	ADP
ejpam-4144	178	36	g	g	PROPN
ejpam-4144	178	37	is	be	AUX
ejpam-4144	178	38	complete	complete	ADJ
ejpam-4144	178	39	,	,	PUNCT
ejpam-4144	178	40	then	then	ADV
ejpam-4144	178	41	s	s	VERB
ejpam-4144	178	42	is	be	AUX
ejpam-4144	178	43	the	the	DET
ejpam-4144	178	44	only	only	ADJ
ejpam-4144	178	45	global	global	ADJ
ejpam-4144	178	46	hop	hop	NOUN
ejpam-4144	178	47	dominating	dominating	NOUN
ejpam-4144	178	48	set	set	NOUN
ejpam-4144	178	49	of	of	ADP
ejpam-4144	178	50	g.	g.	PROPN
ejpam-4144	178	51	therefore	therefore	ADV
ejpam-4144	178	52	,	,	PUNCT
ejpam-4144	178	53	γgh(g	γgh(g	PROPN
ejpam-4144	178	54	)	)	PUNCT
ejpam-4144	179	1	=	=	VERB
ejpam-4144	179	2	n.	n.	PROPN
ejpam-4144	179	3	now	now	ADV
ejpam-4144	179	4	suppose	suppose	VERB
ejpam-4144	179	5	g	g	PROPN
ejpam-4144	179	6	is	be	AUX
ejpam-4144	179	7	connected	connect	VERB
ejpam-4144	179	8	and	and	CCONJ
ejpam-4144	179	9	let	let	VERB
ejpam-4144	180	1	v	v	NUM
ejpam-4144	180	2	∈	∈	PROPN
ejpam-4144	180	3	v	v	NOUN
ejpam-4144	180	4	(	(	PUNCT
ejpam-4144	180	5	g	g	NOUN
ejpam-4144	180	6	)	)	PUNCT
ejpam-4144	180	7	=	=	NOUN
ejpam-4144	180	8	v	v	X
ejpam-4144	180	9	(	(	PUNCT
ejpam-4144	180	10	g	g	NOUN
ejpam-4144	180	11	)	)	PUNCT
ejpam-4144	180	12	.	.	PUNCT
ejpam-4144	181	1	suppose	suppose	VERB
ejpam-4144	181	2	there	there	PRON
ejpam-4144	181	3	exist	exist	VERB
ejpam-4144	181	4	distinct	distinct	ADJ
ejpam-4144	181	5	vertices	vertex	NOUN
ejpam-4144	181	6	a	a	PRON
ejpam-4144	181	7	,	,	PUNCT
ejpam-4144	181	8	b	b	PROPN
ejpam-4144	181	9	∈	∈	PROPN
ejpam-4144	181	10	v	v	NOUN
ejpam-4144	181	11	(	(	PUNCT
ejpam-4144	181	12	g	g	NOUN
ejpam-4144	181	13	)	)	PUNCT
ejpam-4144	181	14	\ng(v	\ng(v	NOUN
ejpam-4144	181	15	)	)	PUNCT
ejpam-4144	181	16	such	such	ADJ
ejpam-4144	181	17	that	that	SCONJ
ejpam-4144	181	18	ab	ab	PROPN
ejpam-4144	181	19	∈	∈	PROPN
ejpam-4144	181	20	e(g	e(g	PROPN
ejpam-4144	181	21	)	)	PUNCT
ejpam-4144	181	22	.	.	PUNCT
ejpam-4144	182	1	then	then	ADV
ejpam-4144	182	2	[	[	X
ejpam-4144	182	3	a	a	X
ejpam-4144	182	4	,	,	PUNCT
ejpam-4144	182	5	v	v	NOUN
ejpam-4144	182	6	,	,	PUNCT
ejpam-4144	182	7	b	b	AUX
ejpam-4144	182	8	]	]	X
ejpam-4144	182	9	is	be	AUX
ejpam-4144	182	10	an	an	DET
ejpam-4144	182	11	a	a	PRON
ejpam-4144	182	12	-	-	PUNCT
ejpam-4144	182	13	b	b	NOUN
ejpam-4144	182	14	geodesic	geodesic	NOUN
ejpam-4144	182	15	in	in	ADP
ejpam-4144	182	16	g	g	NOUN
ejpam-4144	182	17	,	,	PUNCT
ejpam-4144	182	18	implying	imply	VERB
ejpam-4144	182	19	that	that	PRON
ejpam-4144	182	20	sa	sa	PROPN
ejpam-4144	182	21	=	=	SYM
ejpam-4144	182	22	v	v	PROPN
ejpam-4144	182	23	(	(	PUNCT
ejpam-4144	182	24	g)\{a	g)\{a	PROPN
ejpam-4144	182	25	}	}	PUNCT
ejpam-4144	182	26	is	be	AUX
ejpam-4144	182	27	a	a	DET
ejpam-4144	182	28	hop	hop	NOUN
ejpam-4144	182	29	dominating	dominating	NOUN
ejpam-4144	182	30	set	set	NOUN
ejpam-4144	182	31	of	of	ADP
ejpam-4144	182	32	g.	g.	PROPN
ejpam-4144	182	33	now	now	ADV
ejpam-4144	182	34	,	,	PUNCT
ejpam-4144	182	35	since	since	SCONJ
ejpam-4144	182	36	a	a	DET
ejpam-4144	182	37	∈	∈	PROPN
ejpam-4144	182	38	v	v	NOUN
ejpam-4144	182	39	(	(	PUNCT
ejpam-4144	182	40	g)\ng(v	g)\ng(v	PROPN
ejpam-4144	182	41	)	)	PUNCT
ejpam-4144	182	42	,	,	PUNCT
ejpam-4144	182	43	it	it	PRON
ejpam-4144	182	44	follows	follow	VERB
ejpam-4144	182	45	that	that	SCONJ
ejpam-4144	182	46	dg(a	dg(a	X
ejpam-4144	182	47	,	,	PUNCT
ejpam-4144	182	48	v	v	NOUN
ejpam-4144	182	49	)	)	PUNCT
ejpam-4144	182	50	≥	≥	NOUN
ejpam-4144	182	51	2	2	NUM
ejpam-4144	182	52	.	.	PUNCT
ejpam-4144	183	1	this	this	PRON
ejpam-4144	183	2	implies	imply	VERB
ejpam-4144	183	3	that	that	SCONJ
ejpam-4144	183	4	there	there	PRON
ejpam-4144	183	5	exists	exist	VERB
ejpam-4144	183	6	w	w	PROPN
ejpam-4144	183	7	∈	∈	PROPN
ejpam-4144	183	8	sa	sa	NOUN
ejpam-4144	183	9	such	such	ADJ
ejpam-4144	183	10	that	that	PRON
ejpam-4144	183	11	dg(a	dg(a	PROPN
ejpam-4144	183	12	,	,	PUNCT
ejpam-4144	183	13	w	w	NOUN
ejpam-4144	183	14	)	)	PUNCT
ejpam-4144	183	15	=	=	SYM
ejpam-4144	183	16	2	2	NUM
ejpam-4144	183	17	,	,	PUNCT
ejpam-4144	183	18	showing	show	VERB
ejpam-4144	183	19	that	that	PRON
ejpam-4144	183	20	sa	sa	PROPN
ejpam-4144	183	21	is	be	AUX
ejpam-4144	183	22	also	also	ADV
ejpam-4144	183	23	a	a	DET
ejpam-4144	183	24	hop	hop	NOUN
ejpam-4144	183	25	dominating	dominating	NOUN
ejpam-4144	183	26	set	set	NOUN
ejpam-4144	183	27	of	of	ADP
ejpam-4144	183	28	g.	g.	PROPN
ejpam-4144	183	29	hence	hence	ADV
ejpam-4144	183	30	,	,	PUNCT
ejpam-4144	183	31	γgh(g	γgh(g	PROPN
ejpam-4144	183	32	)	)	PUNCT
ejpam-4144	183	33	≤	≤	NOUN
ejpam-4144	183	34	|sa|	|sa|	NUM
ejpam-4144	184	1	=	=	SYM
ejpam-4144	185	1	n	n	CCONJ
ejpam-4144	185	2	−	−	PROPN
ejpam-4144	185	3	1	1	NUM
ejpam-4144	185	4	,	,	PUNCT
ejpam-4144	185	5	a	a	DET
ejpam-4144	185	6	contradiction	contradiction	NOUN
ejpam-4144	185	7	.	.	PUNCT
ejpam-4144	186	1	therefore	therefore	ADV
ejpam-4144	186	2	,	,	PUNCT
ejpam-4144	186	3	v	v	X
ejpam-4144	186	4	(	(	PUNCT
ejpam-4144	186	5	g	g	NOUN
ejpam-4144	186	6	)	)	PUNCT
ejpam-4144	186	7	\	\	NOUN
ejpam-4144	186	8	ng(v	ng(v	PUNCT
ejpam-4144	186	9	)	)	PUNCT
ejpam-4144	186	10	is	be	AUX
ejpam-4144	186	11	an	an	DET
ejpam-4144	186	12	independent	independent	ADJ
ejpam-4144	186	13	set	set	NOUN
ejpam-4144	186	14	,	,	PUNCT
ejpam-4144	186	15	showing	show	VERB
ejpam-4144	186	16	that	that	SCONJ
ejpam-4144	186	17	(	(	PUNCT
ejpam-4144	186	18	i	i	NOUN
ejpam-4144	186	19	)	)	PUNCT
ejpam-4144	186	20	holds	hold	VERB
ejpam-4144	186	21	.	.	PUNCT
ejpam-4144	187	1	next	next	ADV
ejpam-4144	187	2	,	,	PUNCT
ejpam-4144	187	3	let	let	VERB
ejpam-4144	187	4	a	a	DET
ejpam-4144	187	5	∈	∈	PROPN
ejpam-4144	187	6	v	v	NOUN
ejpam-4144	187	7	(	(	PUNCT
ejpam-4144	187	8	g	g	NOUN
ejpam-4144	187	9	)	)	PUNCT
ejpam-4144	187	10	\ng(v	\ng(v	NOUN
ejpam-4144	187	11	)	)	PUNCT
ejpam-4144	187	12	.	.	PUNCT
ejpam-4144	188	1	let	let	VERB
ejpam-4144	188	2	cv	cv	PROPN
ejpam-4144	188	3	be	be	AUX
ejpam-4144	188	4	the	the	DET
ejpam-4144	188	5	component	component	NOUN
ejpam-4144	188	6	of	of	ADP
ejpam-4144	188	7	g	g	NOUN
ejpam-4144	188	8	with	with	ADP
ejpam-4144	188	9	v	v	PROPN
ejpam-4144	188	10	∈	∈	PROPN
ejpam-4144	188	11	cv	cv	PROPN
ejpam-4144	188	12	.	.	PROPN
ejpam-4144	189	1	since	since	SCONJ
ejpam-4144	189	2	a	a	DET
ejpam-4144	189	3	∈	∈	NOUN
ejpam-4144	189	4	ng(v	ng(v	PUNCT
ejpam-4144	189	5	)	)	PUNCT
ejpam-4144	189	6	and	and	CCONJ
ejpam-4144	189	7	cv	cv	PROPN
ejpam-4144	189	8	is	be	AUX
ejpam-4144	189	9	complete	complete	ADJ
ejpam-4144	189	10	,	,	PUNCT
ejpam-4144	189	11	ng(a	ng(a	PRON
ejpam-4144	189	12	)	)	PUNCT
ejpam-4144	189	13	=	=	PUNCT
ejpam-4144	189	14	ng(v	ng(v	X
ejpam-4144	189	15	)	)	PUNCT
ejpam-4144	189	16	.	.	PUNCT
ejpam-4144	190	1	this	this	PRON
ejpam-4144	190	2	shows	show	VERB
ejpam-4144	190	3	that	that	SCONJ
ejpam-4144	190	4	(	(	PUNCT
ejpam-4144	190	5	ii	ii	NOUN
ejpam-4144	190	6	)	)	PUNCT
ejpam-4144	190	7	holds	hold	VERB
ejpam-4144	190	8	.	.	PUNCT
ejpam-4144	191	1	the	the	DET
ejpam-4144	191	2	next	next	ADJ
ejpam-4144	191	3	result	result	NOUN
ejpam-4144	191	4	is	be	AUX
ejpam-4144	191	5	a	a	DET
ejpam-4144	191	6	consequence	consequence	NOUN
ejpam-4144	191	7	of	of	ADP
ejpam-4144	191	8	theorem	theorem	ADJ
ejpam-4144	191	9	2	2	NUM
ejpam-4144	191	10	.	.	PUNCT
ejpam-4144	191	11	corollary	corollary	ADJ
ejpam-4144	191	12	1	1	NUM
ejpam-4144	191	13	.	.	NUM
ejpam-4144	191	14	γgh(kn	γgh(kn	NOUN
ejpam-4144	191	15	)	)	PUNCT
ejpam-4144	191	16	=	=	PUNCT
ejpam-4144	191	17	γgh(k1,n−1	γgh(k1,n−1	X
ejpam-4144	191	18	)	)	PUNCT
ejpam-4144	191	19	=	=	SYM
ejpam-4144	192	1	n	n	PROPN
ejpam-4144	192	2	for	for	ADP
ejpam-4144	192	3	all	all	DET
ejpam-4144	192	4	integer	integer	NOUN
ejpam-4144	192	5	n	n	PRON
ejpam-4144	192	6	≥	≥	NUM
ejpam-4144	192	7	2	2	NUM
ejpam-4144	192	8	.	.	PUNCT
ejpam-4144	192	9	theorem	theorem	NOUN
ejpam-4144	192	10	3	3	X
ejpam-4144	192	11	.	.	PUNCT
ejpam-4144	193	1	let	let	VERB
ejpam-4144	193	2	a	a	PRON
ejpam-4144	193	3	and	and	CCONJ
ejpam-4144	193	4	b	b	NOUN
ejpam-4144	193	5	be	be	AUX
ejpam-4144	193	6	positive	positive	ADJ
ejpam-4144	193	7	integers	integer	NOUN
ejpam-4144	193	8	such	such	ADJ
ejpam-4144	193	9	that	that	SCONJ
ejpam-4144	193	10	2	2	NUM
ejpam-4144	193	11	≤	≤	NUM
ejpam-4144	193	12	a	a	DET
ejpam-4144	193	13	≤	≤	PROPN
ejpam-4144	193	14	b.	b.	NOUN
ejpam-4144	194	1	then	then	ADV
ejpam-4144	194	2	there	there	PRON
ejpam-4144	194	3	exists	exist	VERB
ejpam-4144	194	4	a	a	DET
ejpam-4144	194	5	connected	connected	ADJ
ejpam-4144	194	6	graph	graph	NOUN
ejpam-4144	194	7	g	g	ADP
ejpam-4144	194	8	such	such	ADJ
ejpam-4144	194	9	that	that	PRON
ejpam-4144	194	10	γh(g	γh(g	NOUN
ejpam-4144	194	11	)	)	PUNCT
ejpam-4144	194	12	=	=	SYM
ejpam-4144	194	13	a	a	PRON
ejpam-4144	194	14	and	and	CCONJ
ejpam-4144	194	15	γgh(g	γgh(g	NOUN
ejpam-4144	194	16	)	)	PUNCT
ejpam-4144	194	17	=	=	SYM
ejpam-4144	194	18	b.	b.	NOUN
ejpam-4144	194	19	proof	proof	NOUN
ejpam-4144	194	20	.	.	PUNCT
ejpam-4144	195	1	consider	consider	VERB
ejpam-4144	195	2	the	the	DET
ejpam-4144	195	3	following	follow	VERB
ejpam-4144	195	4	cases	case	NOUN
ejpam-4144	195	5	:	:	PUNCT
ejpam-4144	195	6	case	case	NOUN
ejpam-4144	195	7	1	1	NUM
ejpam-4144	195	8	.	.	PUNCT
ejpam-4144	196	1	a	a	DET
ejpam-4144	196	2	=	=	X
ejpam-4144	196	3	b	b	NOUN
ejpam-4144	196	4	let	let	VERB
ejpam-4144	196	5	g	g	PROPN
ejpam-4144	196	6	=	=	SYM
ejpam-4144	196	7	ka	ka	PROPN
ejpam-4144	196	8	.	.	PUNCT
ejpam-4144	197	1	then	then	ADV
ejpam-4144	197	2	g	g	PROPN
ejpam-4144	197	3	=	=	SYM
ejpam-4144	197	4	ka	ka	PROPN
ejpam-4144	197	5	.	.	PUNCT
ejpam-4144	197	6	by	by	ADP
ejpam-4144	197	7	theorem	theorem	NOUN
ejpam-4144	197	8	2	2	NUM
ejpam-4144	197	9	,	,	PUNCT
ejpam-4144	197	10	γh(g	γh(g	NOUN
ejpam-4144	197	11	)	)	PUNCT
ejpam-4144	197	12	=	=	SYM
ejpam-4144	197	13	γgh(g	γgh(g	PROPN
ejpam-4144	197	14	)	)	PUNCT
ejpam-4144	197	15	=	=	NOUN
ejpam-4144	197	16	a.	a.	NOUN
ejpam-4144	197	17	case	case	NOUN
ejpam-4144	197	18	2	2	NUM
ejpam-4144	197	19	.	.	PUNCT
ejpam-4144	198	1	a	a	DET
ejpam-4144	198	2	<	<	X
ejpam-4144	198	3	b	b	X
ejpam-4144	198	4	let	let	VERB
ejpam-4144	198	5	k	k	NOUN
ejpam-4144	198	6	=	=	PUNCT
ejpam-4144	198	7	b−	b−	NOUN
ejpam-4144	198	8	a.	a.	NOUN
ejpam-4144	198	9	let	let	VERB
ejpam-4144	198	10	v	v	X
ejpam-4144	198	11	(	(	PUNCT
ejpam-4144	198	12	ka−1	ka−1	PROPN
ejpam-4144	198	13	)	)	PUNCT
ejpam-4144	198	14	=	=	PRON
ejpam-4144	198	15	{	{	PUNCT
ejpam-4144	198	16	x1	x1	PROPN
ejpam-4144	198	17	,	,	PUNCT
ejpam-4144	198	18	x2	x2	PROPN
ejpam-4144	198	19	,	,	PUNCT
ejpam-4144	198	20	.	.	PUNCT
ejpam-4144	198	21	.	.	PUNCT
ejpam-4144	198	22	.	.	PUNCT
ejpam-4144	199	1	,	,	PUNCT
ejpam-4144	199	2	xa−1	xa−1	PROPN
ejpam-4144	199	3	}	}	PUNCT
ejpam-4144	199	4	and	and	CCONJ
ejpam-4144	199	5	consider	consider	VERB
ejpam-4144	199	6	the	the	DET
ejpam-4144	199	7	graph	graph	NOUN
ejpam-4144	199	8	g	g	NOUN
ejpam-4144	199	9	in	in	ADP
ejpam-4144	199	10	figure	figure	NOUN
ejpam-4144	199	11	5	5	NUM
ejpam-4144	199	12	obtained	obtain	VERB
ejpam-4144	199	13	from	from	ADP
ejpam-4144	199	14	⟨v⟩	⟨v⟩	PROPN
ejpam-4144	199	15	+	+	CCONJ
ejpam-4144	199	16	ka−1	ka−1	NOUN
ejpam-4144	199	17	by	by	ADP
ejpam-4144	199	18	adding	add	VERB
ejpam-4144	199	19	the	the	DET
ejpam-4144	199	20	edges	edge	NOUN
ejpam-4144	199	21	xiyj	xiyj	NOUN
ejpam-4144	199	22	for	for	ADP
ejpam-4144	199	23	i	i	PRON
ejpam-4144	199	24	∈	∈	PROPN
ejpam-4144	199	25	{	{	PUNCT
ejpam-4144	199	26	1	1	NUM
ejpam-4144	199	27	,	,	PUNCT
ejpam-4144	199	28	2	2	NUM
ejpam-4144	199	29	,	,	PUNCT
ejpam-4144	199	30	.	.	PUNCT
ejpam-4144	199	31	.	.	PUNCT
ejpam-4144	200	1	.	.	PUNCT
ejpam-4144	201	1	,	,	PUNCT
ejpam-4144	201	2	a	a	DET
ejpam-4144	201	3	−	−	NOUN
ejpam-4144	201	4	1	1	NUM
ejpam-4144	201	5	}	}	PUNCT
ejpam-4144	201	6	and	and	CCONJ
ejpam-4144	201	7	j	j	PROPN
ejpam-4144	201	8	∈	∈	PROPN
ejpam-4144	201	9	{	{	PUNCT
ejpam-4144	201	10	1	1	NUM
ejpam-4144	201	11	,	,	PUNCT
ejpam-4144	201	12	2	2	NUM
ejpam-4144	201	13	,	,	PUNCT
ejpam-4144	201	14	.	.	PUNCT
ejpam-4144	201	15	.	.	PUNCT
ejpam-4144	201	16	.	.	PUNCT
ejpam-4144	202	1	,	,	PUNCT
ejpam-4144	202	2	k	k	X
ejpam-4144	202	3	}	}	PUNCT
ejpam-4144	202	4	(	(	PUNCT
ejpam-4144	202	5	⟨v⟩	⟨v⟩	PROPN
ejpam-4144	202	6	is	be	AUX
ejpam-4144	202	7	the	the	DET
ejpam-4144	202	8	graph	graph	NOUN
ejpam-4144	202	9	induced	induce	VERB
ejpam-4144	202	10	by	by	ADP
ejpam-4144	202	11	{	{	PUNCT
ejpam-4144	202	12	v	v	NOUN
ejpam-4144	202	13	}	}	PUNCT
ejpam-4144	202	14	)	)	PUNCT
ejpam-4144	202	15	.	.	PUNCT
ejpam-4144	203	1	g.	g.	PROPN
ejpam-4144	203	2	salasalan	salasalan	PROPN
ejpam-4144	203	3	,	,	PUNCT
ejpam-4144	203	4	s.	s.	PROPN
ejpam-4144	203	5	canoy	canoy	PROPN
ejpam-4144	203	6	,	,	PUNCT
ejpam-4144	203	7	jr	jr	PROPN
ejpam-4144	203	8	.	.	PROPN
ejpam-4144	203	9	/	/	SYM
ejpam-4144	203	10	eur	eur	PROPN
ejpam-4144	203	11	.	.	PUNCT
ejpam-4144	204	1	j.	j.	PROPN
ejpam-4144	204	2	pure	pure	PROPN
ejpam-4144	204	3	appl	appl	PROPN
ejpam-4144	204	4	.	.	PROPN
ejpam-4144	204	5	math	math	PROPN
ejpam-4144	204	6	,	,	PUNCT
ejpam-4144	204	7	14	14	NUM
ejpam-4144	204	8	(	(	PUNCT
ejpam-4144	204	9	4	4	NUM
ejpam-4144	204	10	)	)	PUNCT
ejpam-4144	204	11	(	(	PUNCT
ejpam-4144	204	12	2021	2021	NUM
ejpam-4144	204	13	)	)	PUNCT
ejpam-4144	204	14	,	,	PUNCT
ejpam-4144	204	15	1415	1415	NUM
ejpam-4144	204	16	-	-	SYM
ejpam-4144	204	17	1428	1428	NUM
ejpam-4144	204	18	1420	1420	NUM
ejpam-4144	204	19	.............................................................................................................................................................................................	.............................................................................................................................................................................................	VERB
ejpam-4144	204	20	.................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................	PUNCT
ejpam-4144	204	21	....................................	....................................	PUNCT
ejpam-4144	204	22	...............	...............	PUNCT
ejpam-4144	204	23	..............	..............	PUNCT
ejpam-4144	204	24	..............	..............	PUNCT
ejpam-4144	204	25	..............	..............	PUNCT
ejpam-4144	204	26	..............	..............	PUNCT
ejpam-4144	204	27	..............	..............	PUNCT
ejpam-4144	204	28	..............	..............	PUNCT
ejpam-4144	204	29	..............	..............	PUNCT
ejpam-4144	204	30	..............	..............	PUNCT
ejpam-4144	204	31	..............	..............	PUNCT
ejpam-4144	205	1	..............	..............	PUNCT
ejpam-4144	206	1	..........	..........	PUNCT
ejpam-4144	207	1	....................................	....................................	PUNCT
ejpam-4144	208	1	...............	...............	PUNCT
ejpam-4144	209	1	..............	..............	PUNCT
ejpam-4144	210	1	..............	..............	PUNCT
ejpam-4144	211	1	..............	..............	PUNCT
ejpam-4144	212	1	..............	..............	PUNCT
ejpam-4144	213	1	..............	..............	PUNCT
ejpam-4144	214	1	..............	..............	PUNCT
ejpam-4144	215	1	..............	..............	PUNCT
ejpam-4144	216	1	..............	..............	PUNCT
ejpam-4144	217	1	..............	..............	PUNCT
ejpam-4144	218	1	..............	..............	PUNCT
ejpam-4144	219	1	..........	..........	PUNCT
ejpam-4144	220	1	....................................	....................................	PUNCT
ejpam-4144	220	2	..............................................................................................................................	..............................................................................................................................	PUNCT
ejpam-4144	221	1	..............................................................................................	..............................................................................................	PUNCT
ejpam-4144	222	1	....................................	....................................	PUNCT
ejpam-4144	223	1	....................................	....................................	PUNCT
ejpam-4144	224	1	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4144	225	1	....................................	....................................	PUNCT
ejpam-4144	226	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4144	227	1	....................................	....................................	PUNCT
ejpam-4144	228	1	..........	..........	PUNCT
ejpam-4144	229	1	.........	.........	PUNCT
ejpam-4144	230	1	.........	.........	PUNCT
ejpam-4144	231	1	.........	.........	PUNCT
ejpam-4144	232	1	.........	.........	PUNCT
ejpam-4144	233	1	.........	.........	PUNCT
ejpam-4144	234	1	.........	.........	PUNCT
ejpam-4144	235	1	.........	.........	PUNCT
ejpam-4144	236	1	.........	.........	PUNCT
ejpam-4144	237	1	.........	.........	PUNCT
ejpam-4144	238	1	.........	.........	PUNCT
ejpam-4144	239	1	.........	.........	PUNCT
ejpam-4144	240	1	.........	.........	PUNCT
ejpam-4144	241	1	....................................	....................................	PUNCT
ejpam-4144	242	1	....................................	....................................	PUNCT
ejpam-4144	243	1	........................................................................	........................................................................	PUNCT
ejpam-4144	244	1	.......................................................................	.......................................................................	PUNCT
ejpam-4144	245	1	.......................................................................	.......................................................................	PUNCT
ejpam-4144	246	1	....................................	....................................	PUNCT
ejpam-4144	246	2	..................................................	..................................................	PUNCT
ejpam-4144	246	3	.......................................................................	.......................................................................	PUNCT
ejpam-4144	246	4	.......................................................................	.......................................................................	PUNCT
ejpam-4144	246	5	.......................................................................	.......................................................................	PUNCT
ejpam-4144	247	1	.......................	.......................	PUNCT
ejpam-4144	247	2	....................................	....................................	PUNCT
ejpam-4144	248	1	..........................................................................................................................................................................................................................................................	..........................................................................................................................................................................................................................................................	PUNCT
ejpam-4144	248	2	..............................................................................................................................................................................................................................................................................................	..............................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4144	249	1	....................................	....................................	PUNCT
ejpam-4144	249	2	..............................................................................................................................................................................................................................................................................................	..............................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4144	250	1	....................................	....................................	PUNCT
ejpam-4144	250	2	....................................	....................................	PUNCT
ejpam-4144	250	3	...............	...............	PUNCT
ejpam-4144	251	1	..............	..............	PUNCT
ejpam-4144	251	2	..............	..............	PUNCT
ejpam-4144	252	1	..............	..............	PUNCT
ejpam-4144	252	2	..............	..............	PUNCT
ejpam-4144	253	1	..............	..............	PUNCT
ejpam-4144	253	2	..............	..............	PUNCT
ejpam-4144	254	1	..............	..............	PUNCT
ejpam-4144	254	2	..............	..............	PUNCT
ejpam-4144	255	1	..............	..............	PUNCT
ejpam-4144	255	2	..............	..............	PUNCT
ejpam-4144	256	1	..............	..............	PUNCT
ejpam-4144	256	2	..............	..............	PUNCT
ejpam-4144	257	1	..............	..............	PUNCT
ejpam-4144	257	2	....................................	....................................	PUNCT
ejpam-4144	257	3	...............	...............	PUNCT
ejpam-4144	258	1	..............	..............	PUNCT
ejpam-4144	258	2	..............	..............	PUNCT
ejpam-4144	259	1	..............	..............	PUNCT
ejpam-4144	259	2	..............	..............	PUNCT
ejpam-4144	260	1	..............	..............	PUNCT
ejpam-4144	260	2	..............	..............	PUNCT
ejpam-4144	261	1	..............	..............	PUNCT
ejpam-4144	261	2	..............	..............	PUNCT
ejpam-4144	262	1	..............	..............	PUNCT
ejpam-4144	262	2	..............	..............	PUNCT
ejpam-4144	263	1	..............	..............	PUNCT
ejpam-4144	263	2	..............	..............	PUNCT
ejpam-4144	264	1	..............	..............	PUNCT
ejpam-4144	264	2	....................................	....................................	PUNCT
ejpam-4144	265	1	..........................	..........................	PUNCT
ejpam-4144	265	2	.........................	.........................	PUNCT
ejpam-4144	266	1	.........................	.........................	PUNCT
ejpam-4144	266	2	.........................	.........................	PUNCT
ejpam-4144	266	3	.........................	.........................	PUNCT
ejpam-4144	266	4	.........................	.........................	PUNCT
ejpam-4144	266	5	....................	....................	PUNCT
ejpam-4144	266	6	......................................	......................................	PUNCT
ejpam-4144	266	7	.........................	.........................	PUNCT
ejpam-4144	266	8	.........................	.........................	PUNCT
ejpam-4144	266	9	.........................	.........................	PUNCT
ejpam-4144	266	10	.........................	.........................	PUNCT
ejpam-4144	266	11	.........................	.........................	PUNCT
ejpam-4144	266	12	.........................	.........................	PUNCT
ejpam-4144	266	13	...................	...................	PUNCT
ejpam-4144	266	14	.	.	PUNCT
ejpam-4144	267	1	...................................	...................................	PUNCT
ejpam-4144	267	2	...........................................................................................................................................................................	...........................................................................................................................................................................	PUNCT
ejpam-4144	268	1	....................................	....................................	PUNCT
ejpam-4144	268	2	....................................	....................................	PUNCT
ejpam-4144	268	3	............	............	PUNCT
ejpam-4144	268	4	...........	...........	PUNCT
ejpam-4144	268	5	...........	...........	PUNCT
ejpam-4144	268	6	...........	...........	PUNCT
ejpam-4144	268	7	...........	...........	PUNCT
ejpam-4144	268	8	...........	...........	PUNCT
ejpam-4144	268	9	...........	...........	PUNCT
ejpam-4144	268	10	...........	...........	PUNCT
ejpam-4144	268	11	...........	...........	PUNCT
ejpam-4144	268	12	...........	...........	PUNCT
ejpam-4144	268	13	...........	...........	PUNCT
ejpam-4144	268	14	...........	...........	PUNCT
ejpam-4144	268	15	...........	...........	PUNCT
ejpam-4144	268	16	...........	...........	PUNCT
ejpam-4144	268	17	...........	...........	PUNCT
ejpam-4144	268	18	...........	...........	PUNCT
ejpam-4144	268	19	...........	...........	PUNCT
ejpam-4144	268	20	...........	...........	PUNCT
ejpam-4144	268	21	...........	...........	PUNCT
ejpam-4144	268	22	...........	...........	PUNCT
ejpam-4144	268	23	...........	...........	PUNCT
ejpam-4144	268	24	...........	...........	PUNCT
ejpam-4144	268	25	...........	...........	PUNCT
ejpam-4144	268	26	...........	...........	PUNCT
ejpam-4144	268	27	...........	...........	PUNCT
ejpam-4144	268	28	...........	...........	PUNCT
ejpam-4144	268	29	...........	...........	PUNCT
ejpam-4144	268	30	...........	...........	PUNCT
ejpam-4144	269	1	.....	.....	PUNCT
ejpam-4144	269	2	....................................	....................................	PUNCT
ejpam-4144	269	3	............	............	PUNCT
ejpam-4144	269	4	...........	...........	PUNCT
ejpam-4144	269	5	...........	...........	PUNCT
ejpam-4144	269	6	...........	...........	PUNCT
ejpam-4144	269	7	...........	...........	PUNCT
ejpam-4144	269	8	...........	...........	PUNCT
ejpam-4144	269	9	...........	...........	PUNCT
ejpam-4144	269	10	...........	...........	PUNCT
ejpam-4144	269	11	...........	...........	PUNCT
ejpam-4144	269	12	...........	...........	PUNCT
ejpam-4144	269	13	...........	...........	PUNCT
ejpam-4144	269	14	...........	...........	PUNCT
ejpam-4144	269	15	...........	...........	PUNCT
ejpam-4144	269	16	...........	...........	PUNCT
ejpam-4144	269	17	...........	...........	PUNCT
ejpam-4144	269	18	...........	...........	PUNCT
ejpam-4144	269	19	...........	...........	PUNCT
ejpam-4144	269	20	...........	...........	PUNCT
ejpam-4144	269	21	...........	...........	PUNCT
ejpam-4144	269	22	...........	...........	PUNCT
ejpam-4144	269	23	...........	...........	PUNCT
ejpam-4144	269	24	...........	...........	PUNCT
ejpam-4144	269	25	...........	...........	PUNCT
ejpam-4144	269	26	...........	...........	PUNCT
ejpam-4144	269	27	...........	...........	PUNCT
ejpam-4144	269	28	...........	...........	PUNCT
ejpam-4144	269	29	...........	...........	PUNCT
ejpam-4144	269	30	...........	...........	PUNCT
ejpam-4144	269	31	.....	.....	PUNCT
ejpam-4144	269	32	.	.	PUNCT
ejpam-4144	269	33	...................................	...................................	PUNCT
ejpam-4144	270	1	..............	..............	PUNCT
ejpam-4144	270	2	.............	.............	PUNCT
ejpam-4144	270	3	.............	.............	PUNCT
ejpam-4144	270	4	.............	.............	PUNCT
ejpam-4144	270	5	.............	.............	PUNCT
ejpam-4144	270	6	.............	.............	PUNCT
ejpam-4144	270	7	.............	.............	PUNCT
ejpam-4144	270	8	.............	.............	PUNCT
ejpam-4144	270	9	.............	.............	PUNCT
ejpam-4144	270	10	.............	.............	PUNCT
ejpam-4144	270	11	.............	.............	PUNCT
ejpam-4144	270	12	.............	.............	PUNCT
ejpam-4144	270	13	.............	.............	PUNCT
ejpam-4144	270	14	.............	.............	PUNCT
ejpam-4144	270	15	.............	.............	PUNCT
ejpam-4144	270	16	.............	.............	PUNCT
ejpam-4144	270	17	.............	.............	PUNCT
ejpam-4144	270	18	.............	.............	PUNCT
ejpam-4144	270	19	.............	.............	PUNCT
ejpam-4144	270	20	.............	.............	PUNCT
ejpam-4144	270	21	.............	.............	PUNCT
ejpam-4144	270	22	...	...	PUNCT
ejpam-4144	271	1	....................................	....................................	PUNCT
ejpam-4144	271	2	..............	..............	PUNCT
ejpam-4144	271	3	.............	.............	PUNCT
ejpam-4144	271	4	.............	.............	PUNCT
ejpam-4144	271	5	.............	.............	PUNCT
ejpam-4144	271	6	.............	.............	PUNCT
ejpam-4144	271	7	.............	.............	PUNCT
ejpam-4144	271	8	.............	.............	PUNCT
ejpam-4144	271	9	.............	.............	PUNCT
ejpam-4144	271	10	.............	.............	PUNCT
ejpam-4144	271	11	.............	.............	PUNCT
ejpam-4144	271	12	.............	.............	PUNCT
ejpam-4144	271	13	.............	.............	PUNCT
ejpam-4144	271	14	.............	.............	PUNCT
ejpam-4144	271	15	.............	.............	PUNCT
ejpam-4144	271	16	.............	.............	PUNCT
ejpam-4144	271	17	.............	.............	PUNCT
ejpam-4144	271	18	.............	.............	PUNCT
ejpam-4144	271	19	.............	.............	PUNCT
ejpam-4144	271	20	.............	.............	PUNCT
ejpam-4144	271	21	.............	.............	PUNCT
ejpam-4144	271	22	.............	.............	PUNCT
ejpam-4144	271	23	...	...	PUNCT
ejpam-4144	272	1	....	....	PUNCT
ejpam-4144	272	2	................................	................................	PUNCT
ejpam-4144	272	3	.................................	.................................	PUNCT
ejpam-4144	272	4	................................	................................	PUNCT
ejpam-4144	272	5	................................	................................	PUNCT
ejpam-4144	272	6	................................	................................	PUNCT
ejpam-4144	272	7	................................	................................	PUNCT
ejpam-4144	272	8	................................	................................	PUNCT
ejpam-4144	272	9	................................	................................	PUNCT
ejpam-4144	272	10	.	.	PUNCT
ejpam-4144	273	1	....................................	....................................	PUNCT
ejpam-4144	273	2	....................................	....................................	PUNCT
ejpam-4144	274	1	v	v	X
ejpam-4144	274	2	x1	x1	NOUN
ejpam-4144	275	1	x2	x2	PROPN
ejpam-4144	275	2	xa−1	xa−1	PROPN
ejpam-4144	275	3	...	...	PUNCT
ejpam-4144	276	1	y1	y1	INTJ
ejpam-4144	276	2	y2	y2	INTJ
ejpam-4144	276	3	yk	yk	INTJ
ejpam-4144	276	4	...	...	PUNCT
ejpam-4144	277	1	g	g	NOUN
ejpam-4144	277	2	figure	figure	NOUN
ejpam-4144	277	3	5	5	NUM
ejpam-4144	277	4	let	let	VERB
ejpam-4144	277	5	s	s	VERB
ejpam-4144	277	6	=	=	NOUN
ejpam-4144	277	7	{	{	PUNCT
ejpam-4144	277	8	v	v	NOUN
ejpam-4144	277	9	}	}	PUNCT
ejpam-4144	277	10	∪	∪	NOUN
ejpam-4144	277	11	v	v	NOUN
ejpam-4144	277	12	(	(	PUNCT
ejpam-4144	277	13	ka−1	ka−1	PROPN
ejpam-4144	277	14	)	)	PUNCT
ejpam-4144	277	15	=	=	PRON
ejpam-4144	277	16	{	{	PUNCT
ejpam-4144	277	17	v	v	NOUN
ejpam-4144	277	18	,	,	PUNCT
ejpam-4144	277	19	x1	x1	PROPN
ejpam-4144	277	20	,	,	PUNCT
ejpam-4144	277	21	x2	x2	PROPN
ejpam-4144	277	22	,	,	PUNCT
ejpam-4144	277	23	.	.	PUNCT
ejpam-4144	277	24	.	.	PUNCT
ejpam-4144	278	1	.	.	PUNCT
ejpam-4144	279	1	,	,	PUNCT
ejpam-4144	279	2	xa−1	xa−1	PROPN
ejpam-4144	279	3	}	}	PUNCT
ejpam-4144	279	4	.	.	PUNCT
ejpam-4144	280	1	since	since	SCONJ
ejpam-4144	280	2	every	every	DET
ejpam-4144	280	3	vertex	vertex	NOUN
ejpam-4144	280	4	xi	xi	X
ejpam-4144	280	5	(	(	PUNCT
ejpam-4144	280	6	1	1	NUM
ejpam-4144	280	7	≤	≤	NUM
ejpam-4144	280	8	i	i	PRON
ejpam-4144	280	9	≤	≤	ADJ
ejpam-4144	280	10	a−	a−	PROPN
ejpam-4144	280	11	1	1	NUM
ejpam-4144	280	12	)	)	PUNCT
ejpam-4144	280	13	is	be	AUX
ejpam-4144	280	14	a	a	DET
ejpam-4144	280	15	dominating	dominating	NOUN
ejpam-4144	280	16	vertex	vertex	NOUN
ejpam-4144	280	17	of	of	ADP
ejpam-4144	280	18	g	g	PROPN
ejpam-4144	280	19	,	,	PUNCT
ejpam-4144	280	20	it	it	PRON
ejpam-4144	280	21	follows	follow	VERB
ejpam-4144	280	22	that	that	SCONJ
ejpam-4144	280	23	each	each	DET
ejpam-4144	280	24	xi	xi	X
ejpam-4144	280	25	is	be	AUX
ejpam-4144	280	26	in	in	ADP
ejpam-4144	280	27	every	every	DET
ejpam-4144	280	28	γh	γh	ADV
ejpam-4144	280	29	-	-	PUNCT
ejpam-4144	280	30	set	set	NOUN
ejpam-4144	280	31	of	of	ADP
ejpam-4144	280	32	g.	g.	PROPN
ejpam-4144	280	33	since	since	SCONJ
ejpam-4144	280	34	dg(v	dg(v	PROPN
ejpam-4144	280	35	,	,	PUNCT
ejpam-4144	280	36	yj	yj	PROPN
ejpam-4144	280	37	)	)	PUNCT
ejpam-4144	280	38	=	=	SYM
ejpam-4144	280	39	2	2	NUM
ejpam-4144	280	40	for	for	ADP
ejpam-4144	280	41	all	all	DET
ejpam-4144	280	42	j	j	PROPN
ejpam-4144	280	43	∈	∈	PROPN
ejpam-4144	280	44	{	{	PUNCT
ejpam-4144	280	45	1	1	NUM
ejpam-4144	280	46	,	,	PUNCT
ejpam-4144	280	47	2	2	NUM
ejpam-4144	280	48	,	,	PUNCT
ejpam-4144	280	49	.	.	PUNCT
ejpam-4144	280	50	.	.	PUNCT
ejpam-4144	281	1	.	.	PUNCT
ejpam-4144	282	1	,	,	PUNCT
ejpam-4144	282	2	k	k	X
ejpam-4144	282	3	}	}	PUNCT
ejpam-4144	282	4	,	,	PUNCT
ejpam-4144	282	5	it	it	PRON
ejpam-4144	282	6	follows	follow	VERB
ejpam-4144	282	7	that	that	SCONJ
ejpam-4144	282	8	s	s	VERB
ejpam-4144	282	9	is	be	AUX
ejpam-4144	282	10	a	a	DET
ejpam-4144	282	11	γh	γh	ADV
ejpam-4144	282	12	-	-	PUNCT
ejpam-4144	282	13	set	set	NOUN
ejpam-4144	282	14	of	of	ADP
ejpam-4144	282	15	g.	g.	PROPN
ejpam-4144	282	16	hence	hence	ADV
ejpam-4144	282	17	,	,	PUNCT
ejpam-4144	282	18	γh(g	γh(g	NOUN
ejpam-4144	282	19	)	)	PUNCT
ejpam-4144	283	1	=	=	SYM
ejpam-4144	283	2	a.	a.	NOUN
ejpam-4144	283	3	now	now	ADV
ejpam-4144	283	4	,	,	PUNCT
ejpam-4144	283	5	the	the	DET
ejpam-4144	283	6	complement	complement	NOUN
ejpam-4144	283	7	g	g	NOUN
ejpam-4144	283	8	of	of	ADP
ejpam-4144	283	9	g	g	PROPN
ejpam-4144	283	10	is	be	AUX
ejpam-4144	283	11	the	the	DET
ejpam-4144	283	12	graph	graph	NOUN
ejpam-4144	283	13	isomorphic	isomorphic	ADJ
ejpam-4144	283	14	to	to	ADP
ejpam-4144	283	15	(	(	PUNCT
ejpam-4144	283	16	k1	k1	X
ejpam-4144	283	17	+	+	CCONJ
ejpam-4144	283	18	kk	kk	PROPN
ejpam-4144	283	19	)	)	PUNCT
ejpam-4144	283	20	∪	∪	PROPN
ejpam-4144	283	21	ka−1	ka−1	PROPN
ejpam-4144	283	22	.	.	PUNCT
ejpam-4144	284	1	by	by	ADP
ejpam-4144	284	2	theorem	theorem	ADJ
ejpam-4144	284	3	2	2	NUM
ejpam-4144	284	4	,	,	PUNCT
ejpam-4144	284	5	γgh(g	γgh(g	NOUN
ejpam-4144	284	6	)	)	PUNCT
ejpam-4144	284	7	=	=	SYM
ejpam-4144	284	8	|v	|v	X
ejpam-4144	284	9	(	(	PUNCT
ejpam-4144	284	10	g)|	g)|	NOUN
ejpam-4144	284	11	=	=	SYM
ejpam-4144	284	12	(	(	PUNCT
ejpam-4144	284	13	k	k	PROPN
ejpam-4144	284	14	+	+	PROPN
ejpam-4144	284	15	1	1	NUM
ejpam-4144	284	16	)	)	PUNCT
ejpam-4144	284	17	+	+	CCONJ
ejpam-4144	284	18	(	(	PUNCT
ejpam-4144	284	19	a−	a−	PROPN
ejpam-4144	284	20	1	1	NUM
ejpam-4144	284	21	)	)	PUNCT
ejpam-4144	284	22	=	=	SYM
ejpam-4144	284	23	b.	b.	PROPN
ejpam-4144	284	24	corollary	corollary	NOUN
ejpam-4144	284	25	2	2	NUM
ejpam-4144	284	26	.	.	PUNCT
ejpam-4144	284	27	for	for	ADP
ejpam-4144	284	28	each	each	DET
ejpam-4144	284	29	positive	positive	ADJ
ejpam-4144	284	30	integer	integer	NOUN
ejpam-4144	284	31	n	n	CCONJ
ejpam-4144	284	32	,	,	PUNCT
ejpam-4144	284	33	there	there	PRON
ejpam-4144	284	34	exists	exist	VERB
ejpam-4144	284	35	a	a	DET
ejpam-4144	284	36	connected	connected	ADJ
ejpam-4144	284	37	graph	graph	NOUN
ejpam-4144	284	38	g	g	ADP
ejpam-4144	284	39	such	such	ADJ
ejpam-4144	284	40	that	that	DET
ejpam-4144	284	41	γgh(g)−	γgh(g)−	NOUN
ejpam-4144	284	42	γh(g	γh(g	NOUN
ejpam-4144	284	43	)	)	PUNCT
ejpam-4144	284	44	=	=	VERB
ejpam-4144	284	45	n.	n.	NOUN
ejpam-4144	284	46	in	in	ADP
ejpam-4144	284	47	other	other	ADJ
ejpam-4144	284	48	words	word	NOUN
ejpam-4144	284	49	,	,	PUNCT
ejpam-4144	284	50	the	the	DET
ejpam-4144	284	51	difference	difference	NOUN
ejpam-4144	284	52	γgh−	γgh−	PROPN
ejpam-4144	284	53	γh	γh	ADV
ejpam-4144	284	54	can	can	AUX
ejpam-4144	284	55	be	be	AUX
ejpam-4144	284	56	made	make	VERB
ejpam-4144	284	57	arbitrarily	arbitrarily	ADV
ejpam-4144	284	58	large	large	ADJ
ejpam-4144	284	59	.	.	PUNCT
ejpam-4144	285	1	proof	proof	NOUN
ejpam-4144	285	2	.	.	PUNCT
ejpam-4144	286	1	let	let	VERB
ejpam-4144	286	2	n	n	PRON
ejpam-4144	286	3	be	be	AUX
ejpam-4144	286	4	a	a	DET
ejpam-4144	286	5	positive	positive	ADJ
ejpam-4144	286	6	integer	integer	NOUN
ejpam-4144	286	7	.	.	PUNCT
ejpam-4144	287	1	by	by	ADP
ejpam-4144	287	2	theorem	theorem	NOUN
ejpam-4144	287	3	3	3	NUM
ejpam-4144	287	4	,	,	PUNCT
ejpam-4144	287	5	there	there	PRON
ejpam-4144	287	6	exists	exist	VERB
ejpam-4144	287	7	a	a	DET
ejpam-4144	287	8	connected	connected	ADJ
ejpam-4144	287	9	graph	graph	NOUN
ejpam-4144	287	10	g	g	ADP
ejpam-4144	287	11	such	such	ADJ
ejpam-4144	287	12	that	that	PRON
ejpam-4144	287	13	γh(g	γh(g	NOUN
ejpam-4144	287	14	)	)	PUNCT
ejpam-4144	287	15	=	=	SYM
ejpam-4144	288	1	n+	n+	ADP
ejpam-4144	288	2	1	1	NUM
ejpam-4144	288	3	and	and	CCONJ
ejpam-4144	288	4	γgh(g	γgh(g	NOUN
ejpam-4144	288	5	)	)	PUNCT
ejpam-4144	289	1	=	=	SYM
ejpam-4144	289	2	2n+	2n+	NUM
ejpam-4144	290	1	1	1	NUM
ejpam-4144	290	2	.	.	PUNCT
ejpam-4144	291	1	hence	hence	ADV
ejpam-4144	291	2	,	,	PUNCT
ejpam-4144	291	3	γgh(g)−	γgh(g)−	NOUN
ejpam-4144	291	4	γh(g	γh(g	NOUN
ejpam-4144	291	5	)	)	PUNCT
ejpam-4144	291	6	=	=	VERB
ejpam-4144	291	7	n.	n.	NOUN
ejpam-4144	291	8	for	for	ADP
ejpam-4144	291	9	a	a	DET
ejpam-4144	291	10	graph	graph	NOUN
ejpam-4144	291	11	g	g	NOUN
ejpam-4144	291	12	,	,	PUNCT
ejpam-4144	291	13	the	the	DET
ejpam-4144	291	14	complementary	complementary	ADJ
ejpam-4144	291	15	prism	prism	NOUN
ejpam-4144	291	16	,	,	PUNCT
ejpam-4144	291	17	denoted	denote	VERB
ejpam-4144	291	18	by	by	ADP
ejpam-4144	291	19	gg	gg	PROPN
ejpam-4144	291	20	,	,	PUNCT
ejpam-4144	291	21	is	be	AUX
ejpam-4144	291	22	formed	form	VERB
ejpam-4144	291	23	from	from	ADP
ejpam-4144	291	24	the	the	DET
ejpam-4144	291	25	disjoint	disjoint	PROPN
ejpam-4144	291	26	union	union	NOUN
ejpam-4144	291	27	of	of	ADP
ejpam-4144	291	28	g	g	PROPN
ejpam-4144	291	29	and	and	CCONJ
ejpam-4144	291	30	its	its	PRON
ejpam-4144	291	31	complement	complement	NOUN
ejpam-4144	291	32	g	g	NOUN
ejpam-4144	291	33	by	by	ADP
ejpam-4144	291	34	adding	add	VERB
ejpam-4144	291	35	a	a	DET
ejpam-4144	291	36	perfect	perfect	ADJ
ejpam-4144	291	37	matching	matching	NOUN
ejpam-4144	291	38	between	between	ADP
ejpam-4144	291	39	corresponding	corresponding	ADJ
ejpam-4144	291	40	vertices	vertex	NOUN
ejpam-4144	291	41	of	of	ADP
ejpam-4144	291	42	g	g	PROPN
ejpam-4144	291	43	and	and	CCONJ
ejpam-4144	291	44	g.	g.	NOUN
ejpam-4144	291	45	for	for	ADP
ejpam-4144	291	46	each	each	DET
ejpam-4144	291	47	v	v	NUM
ejpam-4144	291	48	∈	∈	PROPN
ejpam-4144	291	49	v	v	NOUN
ejpam-4144	291	50	(	(	PUNCT
ejpam-4144	291	51	g	g	NOUN
ejpam-4144	291	52	)	)	PUNCT
ejpam-4144	291	53	,	,	PUNCT
ejpam-4144	291	54	let	let	VERB
ejpam-4144	291	55	v	v	PART
ejpam-4144	291	56	denote	denote	VERB
ejpam-4144	291	57	the	the	DET
ejpam-4144	291	58	vertex	vertex	NOUN
ejpam-4144	291	59	corresponding	correspond	VERB
ejpam-4144	291	60	to	to	ADP
ejpam-4144	291	61	v	v	NOUN
ejpam-4144	291	62	in	in	ADP
ejpam-4144	291	63	g.	g.	PROPN
ejpam-4144	291	64	in	in	ADP
ejpam-4144	291	65	simple	simple	ADJ
ejpam-4144	291	66	terms	term	NOUN
ejpam-4144	291	67	,	,	PUNCT
ejpam-4144	291	68	the	the	DET
ejpam-4144	291	69	graph	graph	NOUN
ejpam-4144	291	70	gg	gg	NOUN
ejpam-4144	291	71	is	be	AUX
ejpam-4144	291	72	formed	form	VERB
ejpam-4144	291	73	from	from	ADP
ejpam-4144	291	74	g	g	PROPN
ejpam-4144	291	75	∪g	∪g	NUM
ejpam-4144	291	76	by	by	ADP
ejpam-4144	291	77	adding	add	VERB
ejpam-4144	291	78	the	the	DET
ejpam-4144	291	79	edge	edge	NOUN
ejpam-4144	291	80	vv	vv	NOUN
ejpam-4144	291	81	for	for	ADP
ejpam-4144	291	82	every	every	DET
ejpam-4144	291	83	vertex	vertex	NOUN
ejpam-4144	291	84	v	v	ADP
ejpam-4144	291	85	∈	∈	NOUN
ejpam-4144	291	86	v	v	NOUN
ejpam-4144	291	87	(	(	PUNCT
ejpam-4144	291	88	g	g	NOUN
ejpam-4144	291	89	)	)	PUNCT
ejpam-4144	291	90	.	.	PUNCT
ejpam-4144	292	1	the	the	DET
ejpam-4144	292	2	next	next	ADJ
ejpam-4144	292	3	result	result	NOUN
ejpam-4144	292	4	gives	give	VERB
ejpam-4144	292	5	bounds	bound	NOUN
ejpam-4144	292	6	for	for	ADP
ejpam-4144	292	7	the	the	DET
ejpam-4144	292	8	domination	domination	NOUN
ejpam-4144	292	9	number	number	NOUN
ejpam-4144	292	10	of	of	ADP
ejpam-4144	292	11	the	the	DET
ejpam-4144	292	12	complementary	complementary	ADJ
ejpam-4144	292	13	prism	prism	NOUN
ejpam-4144	292	14	of	of	ADP
ejpam-4144	292	15	a	a	DET
ejpam-4144	292	16	graph	graph	NOUN
ejpam-4144	292	17	.	.	PUNCT
ejpam-4144	293	1	theorem	theorem	NOUN
ejpam-4144	293	2	4	4	NUM
ejpam-4144	293	3	.	.	PUNCT
ejpam-4144	294	1	[	[	X
ejpam-4144	294	2	10	10	NUM
ejpam-4144	294	3	]	]	PUNCT
ejpam-4144	294	4	for	for	ADP
ejpam-4144	294	5	any	any	DET
ejpam-4144	294	6	graph	graph	NOUN
ejpam-4144	294	7	g	g	NOUN
ejpam-4144	294	8	,	,	PUNCT
ejpam-4144	294	9	max{γ(g	max{γ(g	PROPN
ejpam-4144	294	10	)	)	PUNCT
ejpam-4144	294	11	,	,	PUNCT
ejpam-4144	294	12	γ(g	γ(g	PROPN
ejpam-4144	294	13	)	)	PUNCT
ejpam-4144	294	14	}	}	PUNCT
ejpam-4144	294	15	≤	≤	NUM
ejpam-4144	294	16	γ(gg	γ(gg	NUM
ejpam-4144	294	17	)	)	PUNCT
ejpam-4144	294	18	≤	≤	PROPN
ejpam-4144	294	19	γ(g	γ(g	PROPN
ejpam-4144	294	20	)	)	PUNCT
ejpam-4144	295	1	+	+	PROPN
ejpam-4144	295	2	γ(g	γ(g	PROPN
ejpam-4144	295	3	)	)	PUNCT
ejpam-4144	295	4	.	.	PUNCT
ejpam-4144	296	1	theorem	theorem	NOUN
ejpam-4144	296	2	5	5	NUM
ejpam-4144	296	3	.	.	PUNCT
ejpam-4144	297	1	let	let	VERB
ejpam-4144	297	2	g	g	PRON
ejpam-4144	297	3	be	be	AUX
ejpam-4144	297	4	a	a	DET
ejpam-4144	297	5	connected	connected	ADJ
ejpam-4144	297	6	graph	graph	NOUN
ejpam-4144	297	7	of	of	ADP
ejpam-4144	297	8	order	order	NOUN
ejpam-4144	297	9	n.	n.	NOUN
ejpam-4144	297	10	then	then	ADV
ejpam-4144	297	11	each	each	PRON
ejpam-4144	297	12	of	of	ADP
ejpam-4144	297	13	following	follow	VERB
ejpam-4144	297	14	holds	hold	NOUN
ejpam-4144	297	15	.	.	PUNCT
ejpam-4144	298	1	(	(	PUNCT
ejpam-4144	298	2	i	i	NOUN
ejpam-4144	298	3	)	)	PUNCT
ejpam-4144	298	4	if	if	SCONJ
ejpam-4144	298	5	g	g	PROPN
ejpam-4144	298	6	is	be	AUX
ejpam-4144	298	7	a	a	DET
ejpam-4144	298	8	non	non	ADJ
ejpam-4144	298	9	-	-	ADJ
ejpam-4144	298	10	trivial	trivial	ADJ
ejpam-4144	298	11	graph	graph	NOUN
ejpam-4144	298	12	such	such	ADJ
ejpam-4144	298	13	that	that	PRON
ejpam-4144	298	14	γ(g	γ(g	PROPN
ejpam-4144	298	15	)	)	PUNCT
ejpam-4144	298	16	=	=	SYM
ejpam-4144	299	1	1	1	NUM
ejpam-4144	299	2	,	,	PUNCT
ejpam-4144	299	3	then	then	ADV
ejpam-4144	299	4	γ(gg	γ(gg	ADJ
ejpam-4144	299	5	)	)	PUNCT
ejpam-4144	299	6	=	=	SYM
ejpam-4144	300	1	1	1	NUM
ejpam-4144	300	2	+	+	NUM
ejpam-4144	300	3	γ(g	γ(g	PROPN
ejpam-4144	300	4	\	\	PROPN
ejpam-4144	300	5	v	v	NOUN
ejpam-4144	300	6	)	)	PUNCT
ejpam-4144	300	7	,	,	PUNCT
ejpam-4144	300	8	where	where	SCONJ
ejpam-4144	300	9	v	v	NOUN
ejpam-4144	300	10	is	be	AUX
ejpam-4144	300	11	a	a	DET
ejpam-4144	300	12	dominating	dominating	NOUN
ejpam-4144	300	13	vertex	vertex	NOUN
ejpam-4144	300	14	of	of	ADP
ejpam-4144	300	15	g.	g.	PROPN
ejpam-4144	300	16	in	in	ADP
ejpam-4144	300	17	particular	particular	ADJ
ejpam-4144	300	18	,	,	PUNCT
ejpam-4144	300	19	γ(knkn	γ(knkn	NOUN
ejpam-4144	300	20	)	)	PUNCT
ejpam-4144	301	1	=	=	SYM
ejpam-4144	301	2	n.	n.	NOUN
ejpam-4144	301	3	(	(	PUNCT
ejpam-4144	301	4	ii	ii	NOUN
ejpam-4144	301	5	)	)	PUNCT
ejpam-4144	301	6	if	if	SCONJ
ejpam-4144	301	7	n	n	PRON
ejpam-4144	301	8	≥	≥	NOUN
ejpam-4144	301	9	1	1	NUM
ejpam-4144	301	10	,	,	PUNCT
ejpam-4144	301	11	then	then	ADV
ejpam-4144	301	12	γh(gg	γh(gg	PROPN
ejpam-4144	301	13	)	)	PUNCT
ejpam-4144	301	14	=	=	SYM
ejpam-4144	302	1	2	2	X
ejpam-4144	302	2	.	.	X
ejpam-4144	302	3	in	in	ADP
ejpam-4144	302	4	particular	particular	ADJ
ejpam-4144	302	5	,	,	PUNCT
ejpam-4144	302	6	{	{	PUNCT
ejpam-4144	302	7	v	v	NOUN
ejpam-4144	302	8	,	,	PUNCT
ejpam-4144	302	9	v	v	NOUN
ejpam-4144	302	10	}	}	PUNCT
ejpam-4144	302	11	is	be	AUX
ejpam-4144	302	12	γh	γh	ADV
ejpam-4144	302	13	-	-	PUNCT
ejpam-4144	302	14	set	set	NOUN
ejpam-4144	302	15	of	of	ADP
ejpam-4144	302	16	gg	gg	NOUN
ejpam-4144	302	17	for	for	ADP
ejpam-4144	302	18	each	each	DET
ejpam-4144	302	19	v	v	NUM
ejpam-4144	302	20	∈	∈	PROPN
ejpam-4144	302	21	v	v	NOUN
ejpam-4144	302	22	(	(	PUNCT
ejpam-4144	302	23	g	g	NOUN
ejpam-4144	302	24	)	)	PUNCT
ejpam-4144	302	25	.	.	PUNCT
ejpam-4144	303	1	(	(	PUNCT
ejpam-4144	303	2	iii	iii	X
ejpam-4144	303	3	)	)	PUNCT
ejpam-4144	303	4	if	if	SCONJ
ejpam-4144	303	5	n	n	PRON
ejpam-4144	303	6	≥	≥	NOUN
ejpam-4144	303	7	2	2	NUM
ejpam-4144	303	8	,	,	PUNCT
ejpam-4144	303	9	then	then	ADV
ejpam-4144	303	10	γgh(gg	γgh(gg	NUM
ejpam-4144	303	11	)	)	PUNCT
ejpam-4144	303	12	≤	≤	NUM
ejpam-4144	303	13	min{n	min{n	NOUN
ejpam-4144	303	14	,	,	PUNCT
ejpam-4144	303	15	2γgh(g	2γgh(g	NUM
ejpam-4144	303	16	)	)	PUNCT
ejpam-4144	303	17	}	}	PUNCT
ejpam-4144	303	18	.	.	PUNCT
ejpam-4144	304	1	proof	proof	NOUN
ejpam-4144	304	2	.	.	PUNCT
ejpam-4144	305	1	(	(	PUNCT
ejpam-4144	305	2	i	i	NOUN
ejpam-4144	305	3	)	)	PUNCT
ejpam-4144	305	4	let	let	VERB
ejpam-4144	305	5	v	v	PART
ejpam-4144	305	6	be	be	AUX
ejpam-4144	305	7	a	a	DET
ejpam-4144	305	8	dominating	dominating	NOUN
ejpam-4144	305	9	vertex	vertex	NOUN
ejpam-4144	305	10	of	of	ADP
ejpam-4144	305	11	g	g	NOUN
ejpam-4144	305	12	and	and	CCONJ
ejpam-4144	305	13	let	let	VERB
ejpam-4144	305	14	d	d	PRON
ejpam-4144	305	15	be	be	AUX
ejpam-4144	305	16	a	a	DET
ejpam-4144	305	17	dominating	dominating	NOUN
ejpam-4144	305	18	set	set	NOUN
ejpam-4144	305	19	of	of	ADP
ejpam-4144	305	20	g	g	PROPN
ejpam-4144	305	21	\	\	PUNCT
ejpam-4144	306	1	v.	v.	CCONJ
ejpam-4144	306	2	since	since	SCONJ
ejpam-4144	306	3	(	(	PUNCT
ejpam-4144	306	4	v	v	NOUN
ejpam-4144	306	5	(	(	PUNCT
ejpam-4144	306	6	g)\{v})∪{v	g)\{v})∪{v	NOUN
ejpam-4144	306	7	}	}	PUNCT
ejpam-4144	306	8	⊆	⊆	NUM
ejpam-4144	306	9	ngg(v	ngg(v	NOUN
ejpam-4144	306	10	)	)	PUNCT
ejpam-4144	306	11	and	and	CCONJ
ejpam-4144	306	12	v	v	NOUN
ejpam-4144	306	13	(	(	PUNCT
ejpam-4144	306	14	g)\{v	g)\{v	PROPN
ejpam-4144	306	15	}	}	PUNCT
ejpam-4144	306	16	⊆	⊆	NUM
ejpam-4144	306	17	ngg(d	ngg(d	NOUN
ejpam-4144	306	18	)	)	PUNCT
ejpam-4144	306	19	,	,	PUNCT
ejpam-4144	306	20	s	s	NOUN
ejpam-4144	306	21	=	=	SYM
ejpam-4144	306	22	d∪{v	d∪{v	NOUN
ejpam-4144	306	23	}	}	PUNCT
ejpam-4144	306	24	is	be	AUX
ejpam-4144	306	25	a	a	DET
ejpam-4144	306	26	dominating	dominating	NOUN
ejpam-4144	306	27	set	set	NOUN
ejpam-4144	306	28	of	of	ADP
ejpam-4144	306	29	gg	gg	PROPN
ejpam-4144	306	30	.	.	PUNCT
ejpam-4144	307	1	this	this	PRON
ejpam-4144	307	2	implies	imply	VERB
ejpam-4144	307	3	that	that	SCONJ
ejpam-4144	307	4	γ(gg	γ(gg	ADJ
ejpam-4144	307	5	)	)	PUNCT
ejpam-4144	307	6	≤	≤	NUM
ejpam-4144	307	7	1	1	NUM
ejpam-4144	307	8	+	+	NUM
ejpam-4144	307	9	|d|	|d|	NOUN
ejpam-4144	307	10	=	=	SYM
ejpam-4144	307	11	1	1	NUM
ejpam-4144	307	12	+	+	NUM
ejpam-4144	307	13	γ(g	γ(g	PROPN
ejpam-4144	307	14	\	\	PROPN
ejpam-4144	307	15	v	v	NOUN
ejpam-4144	307	16	)	)	PUNCT
ejpam-4144	307	17	.	.	PUNCT
ejpam-4144	308	1	g.	g.	PROPN
ejpam-4144	308	2	salasalan	salasalan	PROPN
ejpam-4144	308	3	,	,	PUNCT
ejpam-4144	308	4	s.	s.	PROPN
ejpam-4144	308	5	canoy	canoy	PROPN
ejpam-4144	308	6	,	,	PUNCT
ejpam-4144	308	7	jr	jr	PROPN
ejpam-4144	308	8	.	.	PROPN
ejpam-4144	308	9	/	/	SYM
ejpam-4144	308	10	eur	eur	PROPN
ejpam-4144	308	11	.	.	PUNCT
ejpam-4144	309	1	j.	j.	PROPN
ejpam-4144	309	2	pure	pure	PROPN
ejpam-4144	309	3	appl	appl	PROPN
ejpam-4144	309	4	.	.	PROPN
ejpam-4144	309	5	math	math	PROPN
ejpam-4144	309	6	,	,	PUNCT
ejpam-4144	309	7	14	14	NUM
ejpam-4144	309	8	(	(	PUNCT
ejpam-4144	309	9	4	4	NUM
ejpam-4144	309	10	)	)	PUNCT
ejpam-4144	309	11	(	(	PUNCT
ejpam-4144	309	12	2021	2021	NUM
ejpam-4144	309	13	)	)	PUNCT
ejpam-4144	309	14	,	,	PUNCT
ejpam-4144	309	15	1415	1415	NUM
ejpam-4144	309	16	-	-	SYM
ejpam-4144	309	17	1428	1428	NUM
ejpam-4144	309	18	1421	1421	NUM
ejpam-4144	309	19	suppose	suppose	VERB
ejpam-4144	309	20	now	now	ADV
ejpam-4144	309	21	that	that	SCONJ
ejpam-4144	309	22	s0	s0	PROPN
ejpam-4144	309	23	is	be	AUX
ejpam-4144	309	24	a	a	DET
ejpam-4144	309	25	γ	γ	NOUN
ejpam-4144	309	26	-	-	PUNCT
ejpam-4144	309	27	set	set	NOUN
ejpam-4144	309	28	of	of	ADP
ejpam-4144	309	29	gg	gg	PROPN
ejpam-4144	309	30	.	.	PUNCT
ejpam-4144	310	1	since	since	SCONJ
ejpam-4144	310	2	v	v	NOUN
ejpam-4144	310	3	is	be	AUX
ejpam-4144	310	4	a	a	DET
ejpam-4144	310	5	dominating	dominating	NOUN
ejpam-4144	310	6	vertex	vertex	NOUN
ejpam-4144	310	7	of	of	ADP
ejpam-4144	310	8	g	g	PROPN
ejpam-4144	310	9	,	,	PUNCT
ejpam-4144	310	10	v	v	NOUN
ejpam-4144	310	11	is	be	AUX
ejpam-4144	310	12	an	an	DET
ejpam-4144	310	13	isolated	isolated	ADJ
ejpam-4144	310	14	vertex	vertex	NOUN
ejpam-4144	310	15	of	of	ADP
ejpam-4144	310	16	g	g	PROPN
ejpam-4144	310	17	(	(	PUNCT
ejpam-4144	310	18	and	and	CCONJ
ejpam-4144	310	19	so	so	ADV
ejpam-4144	310	20	a	a	DET
ejpam-4144	310	21	leaf	leaf	NOUN
ejpam-4144	310	22	in	in	ADP
ejpam-4144	310	23	gg	gg	PROPN
ejpam-4144	310	24	)	)	PUNCT
ejpam-4144	310	25	.	.	PUNCT
ejpam-4144	311	1	hence	hence	ADV
ejpam-4144	311	2	,	,	PUNCT
ejpam-4144	311	3	v	v	PROPN
ejpam-4144	311	4	∈	∈	NOUN
ejpam-4144	311	5	s0	s0	NOUN
ejpam-4144	311	6	or	or	CCONJ
ejpam-4144	311	7	v	v	ADP
ejpam-4144	311	8	∈	∈	PROPN
ejpam-4144	311	9	s0	s0	NOUN
ejpam-4144	311	10	.	.	PUNCT
ejpam-4144	311	11	suppose	suppose	VERB
ejpam-4144	311	12	v	v	X
ejpam-4144	311	13	/∈	/∈	SYM
ejpam-4144	311	14	s0	s0	PROPN
ejpam-4144	311	15	.	.	PUNCT
ejpam-4144	312	1	then	then	ADV
ejpam-4144	312	2	v	v	ADP
ejpam-4144	312	3	∈	∈	PROPN
ejpam-4144	312	4	s0	s0	PROPN
ejpam-4144	312	5	.	.	PUNCT
ejpam-4144	312	6	suppose	suppose	VERB
ejpam-4144	312	7	s1	s1	PROPN
ejpam-4144	312	8	=	=	SYM
ejpam-4144	312	9	s0∩v	s0∩v	PROPN
ejpam-4144	312	10	(	(	PUNCT
ejpam-4144	312	11	g	g	NOUN
ejpam-4144	312	12	)	)	PUNCT
ejpam-4144	312	13	=	=	PUNCT
ejpam-4144	312	14	∅.	∅.	NOUN
ejpam-4144	312	15	since	since	SCONJ
ejpam-4144	312	16	ngg(w)∩v	ngg(w)∩v	PROPN
ejpam-4144	312	17	(	(	PUNCT
ejpam-4144	312	18	g	g	NOUN
ejpam-4144	312	19	)	)	PUNCT
ejpam-4144	312	20	=	=	SYM
ejpam-4144	312	21	{	{	PUNCT
ejpam-4144	312	22	w	w	NOUN
ejpam-4144	312	23	}	}	PUNCT
ejpam-4144	312	24	for	for	ADP
ejpam-4144	312	25	each	each	DET
ejpam-4144	312	26	w	w	PROPN
ejpam-4144	312	27	∈	∈	PROPN
ejpam-4144	312	28	v	v	ADP
ejpam-4144	312	29	(	(	PUNCT
ejpam-4144	312	30	g	g	NOUN
ejpam-4144	312	31	)	)	PUNCT
ejpam-4144	312	32	,	,	PUNCT
ejpam-4144	312	33	it	it	PRON
ejpam-4144	312	34	follows	follow	VERB
ejpam-4144	312	35	that	that	SCONJ
ejpam-4144	312	36	s0	s0	PROPN
ejpam-4144	312	37	=	=	SYM
ejpam-4144	312	38	v	v	PROPN
ejpam-4144	312	39	(	(	PUNCT
ejpam-4144	312	40	g	g	NOUN
ejpam-4144	312	41	)	)	PUNCT
ejpam-4144	312	42	.	.	PUNCT
ejpam-4144	313	1	hence	hence	ADV
ejpam-4144	313	2	,	,	PUNCT
ejpam-4144	313	3	γ(gg	γ(gg	ADJ
ejpam-4144	313	4	)	)	PUNCT
ejpam-4144	313	5	=	=	SYM
ejpam-4144	313	6	|s0|	|s0|	NOUN
ejpam-4144	313	7	=	=	SYM
ejpam-4144	313	8	n	n	NUM
ejpam-4144	313	9	≥	≥	NOUN
ejpam-4144	313	10	1+γ(g\v	1+γ(g\v	NUM
ejpam-4144	313	11	)	)	PUNCT
ejpam-4144	313	12	.	.	PUNCT
ejpam-4144	314	1	suppose	suppose	VERB
ejpam-4144	314	2	s1	s1	PROPN
ejpam-4144	314	3	̸=	̸=	PROPN
ejpam-4144	314	4	∅	∅	NOUN
ejpam-4144	314	5	and	and	CCONJ
ejpam-4144	314	6	let	let	VERB
ejpam-4144	314	7	s2	s2	NOUN
ejpam-4144	314	8	=	=	SYM
ejpam-4144	314	9	s0	s0	PROPN
ejpam-4144	314	10	∩	∩	NOUN
ejpam-4144	314	11	(	(	PUNCT
ejpam-4144	314	12	v	v	NOUN
ejpam-4144	314	13	(	(	PUNCT
ejpam-4144	314	14	g	g	NOUN
ejpam-4144	314	15	)	)	PUNCT
ejpam-4144	314	16	\	\	NOUN
ejpam-4144	314	17	{	{	PUNCT
ejpam-4144	314	18	v	v	NOUN
ejpam-4144	314	19	}	}	PUNCT
ejpam-4144	314	20	)	)	PUNCT
ejpam-4144	314	21	.	.	PUNCT
ejpam-4144	315	1	if	if	SCONJ
ejpam-4144	315	2	s2	s2	PROPN
ejpam-4144	315	3	is	be	AUX
ejpam-4144	315	4	a	a	DET
ejpam-4144	315	5	dominating	dominating	NOUN
ejpam-4144	315	6	of	of	ADP
ejpam-4144	315	7	g	g	NOUN
ejpam-4144	315	8	\	\	PROPN
ejpam-4144	315	9	v	v	NOUN
ejpam-4144	315	10	,	,	PUNCT
ejpam-4144	315	11	then	then	ADV
ejpam-4144	315	12	γ(gg	γ(gg	ADJ
ejpam-4144	315	13	)	)	PUNCT
ejpam-4144	315	14	=	=	PUNCT
ejpam-4144	315	15	|s0|	|s0|	NOUN
ejpam-4144	315	16	≥	≥	NOUN
ejpam-4144	315	17	1	1	NUM
ejpam-4144	315	18	+	+	NUM
ejpam-4144	315	19	γ(g	γ(g	PROPN
ejpam-4144	315	20	\	\	PROPN
ejpam-4144	315	21	v	v	NOUN
ejpam-4144	315	22	)	)	PUNCT
ejpam-4144	315	23	.	.	PUNCT
ejpam-4144	316	1	suppose	suppose	VERB
ejpam-4144	316	2	r	r	NOUN
ejpam-4144	316	3	=	=	SYM
ejpam-4144	316	4	v	v	NOUN
ejpam-4144	316	5	(	(	PUNCT
ejpam-4144	316	6	g	g	NOUN
ejpam-4144	316	7	\	\	PROPN
ejpam-4144	316	8	v	v	NOUN
ejpam-4144	316	9	)	)	PUNCT
ejpam-4144	316	10	\	\	NOUN
ejpam-4144	317	1	ng\v[s2	ng\v[s2	PROPN
ejpam-4144	317	2	]	]	PUNCT
ejpam-4144	317	3	̸=	̸=	PROPN
ejpam-4144	317	4	∅	∅	NOUN
ejpam-4144	317	5	and	and	CCONJ
ejpam-4144	317	6	set	set	VERB
ejpam-4144	317	7	rg	rg	X
ejpam-4144	317	8	=	=	PUNCT
ejpam-4144	317	9	{	{	PUNCT
ejpam-4144	317	10	w	w	PROPN
ejpam-4144	317	11	∈	∈	PROPN
ejpam-4144	317	12	v	v	ADP
ejpam-4144	317	13	(	(	PUNCT
ejpam-4144	317	14	g	g	NOUN
ejpam-4144	317	15	)	)	PUNCT
ejpam-4144	317	16	\	\	NOUN
ejpam-4144	317	17	{	{	PUNCT
ejpam-4144	317	18	v	v	NOUN
ejpam-4144	317	19	}	}	PUNCT
ejpam-4144	317	20	:	:	PUNCT
ejpam-4144	317	21	w	w	X
ejpam-4144	317	22	∈	∈	PROPN
ejpam-4144	317	23	r	r	NOUN
ejpam-4144	317	24	}	}	PUNCT
ejpam-4144	317	25	.	.	PUNCT
ejpam-4144	318	1	then	then	ADV
ejpam-4144	318	2	necessarily	necessarily	ADV
ejpam-4144	318	3	,	,	PUNCT
ejpam-4144	318	4	rg	rg	PROPN
ejpam-4144	318	5	⊆	⊆	NUM
ejpam-4144	318	6	s1	s1	NOUN
ejpam-4144	318	7	.	.	PUNCT
ejpam-4144	319	1	thus	thus	ADV
ejpam-4144	319	2	,	,	PUNCT
ejpam-4144	319	3	γ(gg	γ(gg	ADJ
ejpam-4144	319	4	)	)	PUNCT
ejpam-4144	319	5	=	=	SYM
ejpam-4144	319	6	|s0|	|s0|	NOUN
ejpam-4144	319	7	=	=	SYM
ejpam-4144	319	8	1	1	NUM
ejpam-4144	319	9	+	+	NUM
ejpam-4144	319	10	|s1|+	|s1|+	NOUN
ejpam-4144	319	11	|s2|	|s2|	NOUN
ejpam-4144	319	12	≥	≥	NOUN
ejpam-4144	319	13	1	1	NUM
ejpam-4144	319	14	+	+	CCONJ
ejpam-4144	319	15	|rg|+	|rg|+	PROPN
ejpam-4144	319	16	|s2|	|s2|	PROPN
ejpam-4144	319	17	≥	≥	NOUN
ejpam-4144	319	18	1+γ(g\v	1+γ(g\v	NUM
ejpam-4144	319	19	)	)	PUNCT
ejpam-4144	319	20	.	.	PUNCT
ejpam-4144	320	1	next	next	ADV
ejpam-4144	320	2	,	,	PUNCT
ejpam-4144	320	3	suppose	suppose	VERB
ejpam-4144	320	4	that	that	SCONJ
ejpam-4144	320	5	v	v	ADP
ejpam-4144	320	6	∈	∈	PROPN
ejpam-4144	320	7	s0	s0	NOUN
ejpam-4144	320	8	.	.	PUNCT
ejpam-4144	321	1	since	since	SCONJ
ejpam-4144	321	2	s0	s0	PROPN
ejpam-4144	321	3	is	be	AUX
ejpam-4144	321	4	a	a	DET
ejpam-4144	321	5	γ	γ	NOUN
ejpam-4144	321	6	-	-	PUNCT
ejpam-4144	321	7	set	set	NOUN
ejpam-4144	321	8	of	of	ADP
ejpam-4144	321	9	gg	gg	NOUN
ejpam-4144	321	10	and	and	CCONJ
ejpam-4144	321	11	v	v	NOUN
ejpam-4144	321	12	is	be	AUX
ejpam-4144	321	13	a	a	DET
ejpam-4144	321	14	leaf	leaf	NOUN
ejpam-4144	321	15	of	of	ADP
ejpam-4144	321	16	gg	gg	PROPN
ejpam-4144	321	17	,	,	PUNCT
ejpam-4144	321	18	v	v	PROPN
ejpam-4144	321	19	/∈	/∈	PUNCT
ejpam-4144	321	20	s.	s.	PROPN
ejpam-4144	321	21	let	let	VERB
ejpam-4144	321	22	d1	d1	PROPN
ejpam-4144	321	23	=	=	SYM
ejpam-4144	321	24	(	(	PUNCT
ejpam-4144	321	25	v	v	NOUN
ejpam-4144	321	26	(	(	PUNCT
ejpam-4144	321	27	g	g	NOUN
ejpam-4144	321	28	)	)	PUNCT
ejpam-4144	321	29	\	\	NOUN
ejpam-4144	321	30	{	{	PUNCT
ejpam-4144	321	31	v	v	NOUN
ejpam-4144	321	32	}	}	PUNCT
ejpam-4144	321	33	)	)	PUNCT
ejpam-4144	321	34	∩	∩	PROPN
ejpam-4144	321	35	s0	s0	PROPN
ejpam-4144	321	36	.	.	PUNCT
ejpam-4144	322	1	if	if	SCONJ
ejpam-4144	322	2	d1	d1	NOUN
ejpam-4144	322	3	=	=	SYM
ejpam-4144	322	4	∅	∅	NOUN
ejpam-4144	322	5	,	,	PUNCT
ejpam-4144	322	6	then	then	ADV
ejpam-4144	322	7	d2	d2	PROPN
ejpam-4144	322	8	=	=	SYM
ejpam-4144	322	9	(	(	PUNCT
ejpam-4144	322	10	v	v	NOUN
ejpam-4144	322	11	(	(	PUNCT
ejpam-4144	322	12	g	g	NOUN
ejpam-4144	322	13	)	)	PUNCT
ejpam-4144	322	14	∩	∩	NOUN
ejpam-4144	322	15	s0	s0	NOUN
ejpam-4144	322	16	must	must	AUX
ejpam-4144	322	17	be	be	AUX
ejpam-4144	322	18	a	a	DET
ejpam-4144	322	19	dominating	dominating	NOUN
ejpam-4144	322	20	set	set	NOUN
ejpam-4144	322	21	of	of	ADP
ejpam-4144	322	22	g	g	PROPN
ejpam-4144	322	23	\	\	PROPN
ejpam-4144	323	1	v.	v.	ADP
ejpam-4144	323	2	it	it	PRON
ejpam-4144	323	3	follows	follow	VERB
ejpam-4144	323	4	that	that	SCONJ
ejpam-4144	323	5	γ(gg	γ(gg	ADJ
ejpam-4144	323	6	)	)	PUNCT
ejpam-4144	323	7	=	=	PUNCT
ejpam-4144	323	8	|s0|	|s0|	NOUN
ejpam-4144	323	9	≥	≥	NOUN
ejpam-4144	323	10	1	1	NUM
ejpam-4144	323	11	+	+	CCONJ
ejpam-4144	323	12	γ(g	γ(g	PROPN
ejpam-4144	323	13	\	\	PROPN
ejpam-4144	324	1	v	v	NOUN
ejpam-4144	324	2	)	)	PUNCT
ejpam-4144	324	3	.	.	PUNCT
ejpam-4144	325	1	suppose	suppose	VERB
ejpam-4144	325	2	that	that	SCONJ
ejpam-4144	325	3	d1	d1	PROPN
ejpam-4144	325	4	̸=	̸=	PROPN
ejpam-4144	325	5	∅.	∅.	VERB
ejpam-4144	325	6	if	if	SCONJ
ejpam-4144	325	7	d2	d2	NOUN
ejpam-4144	325	8	=	=	SYM
ejpam-4144	325	9	∅	∅	NOUN
ejpam-4144	325	10	,	,	PUNCT
ejpam-4144	325	11	then	then	ADV
ejpam-4144	325	12	d1	d1	PROPN
ejpam-4144	325	13	=	=	SYM
ejpam-4144	325	14	v	v	PROPN
ejpam-4144	325	15	(	(	PUNCT
ejpam-4144	325	16	g	g	NOUN
ejpam-4144	325	17	)	)	PUNCT
ejpam-4144	325	18	\	\	NOUN
ejpam-4144	326	1	{	{	PUNCT
ejpam-4144	326	2	v	v	NOUN
ejpam-4144	326	3	}	}	PUNCT
ejpam-4144	326	4	.	.	PUNCT
ejpam-4144	327	1	it	it	PRON
ejpam-4144	327	2	follows	follow	VERB
ejpam-4144	327	3	that	that	SCONJ
ejpam-4144	327	4	s0	s0	PROPN
ejpam-4144	327	5	=	=	SYM
ejpam-4144	327	6	v	v	PROPN
ejpam-4144	327	7	(	(	PUNCT
ejpam-4144	327	8	g	g	NOUN
ejpam-4144	327	9	)	)	PUNCT
ejpam-4144	327	10	and	and	CCONJ
ejpam-4144	327	11	γ(gg	γ(gg	NUM
ejpam-4144	327	12	)	)	PUNCT
ejpam-4144	327	13	=	=	SYM
ejpam-4144	327	14	|s0|	|s0|	NOUN
ejpam-4144	327	15	=	=	SYM
ejpam-4144	327	16	n	n	X
ejpam-4144	327	17	≥	≥	NOUN
ejpam-4144	327	18	1	1	NUM
ejpam-4144	327	19	+	+	CCONJ
ejpam-4144	327	20	γ(g	γ(g	PROPN
ejpam-4144	327	21	\	\	PROPN
ejpam-4144	327	22	v	v	NOUN
ejpam-4144	327	23	)	)	PUNCT
ejpam-4144	327	24	.	.	PUNCT
ejpam-4144	328	1	suppose	suppose	VERB
ejpam-4144	328	2	d2	d2	PROPN
ejpam-4144	328	3	̸=	̸=	PROPN
ejpam-4144	328	4	∅	∅	NOUN
ejpam-4144	328	5	and	and	CCONJ
ejpam-4144	328	6	let	let	VERB
ejpam-4144	328	7	d∗	d∗	NOUN
ejpam-4144	328	8	2	2	NUM
ejpam-4144	328	9	=	=	SYM
ejpam-4144	328	10	v	v	NOUN
ejpam-4144	328	11	(	(	PUNCT
ejpam-4144	328	12	g	g	NOUN
ejpam-4144	328	13	\	\	PROPN
ejpam-4144	328	14	v	v	NOUN
ejpam-4144	328	15	)	)	PUNCT
ejpam-4144	328	16	\	\	NOUN
ejpam-4144	328	17	ng\v[d2].since	ng\v[d2].since	NOUN
ejpam-4144	328	18	s0	s0	PROPN
ejpam-4144	328	19	is	be	AUX
ejpam-4144	328	20	a	a	DET
ejpam-4144	328	21	γ	γ	NOUN
ejpam-4144	328	22	-	-	PUNCT
ejpam-4144	328	23	set	set	VERB
ejpam-4144	328	24	and	and	CCONJ
ejpam-4144	328	25	v	v	ADP
ejpam-4144	328	26	∈	∈	PROPN
ejpam-4144	328	27	s0	s0	NOUN
ejpam-4144	328	28	,	,	PUNCT
ejpam-4144	328	29	it	it	PRON
ejpam-4144	328	30	follows	follow	VERB
ejpam-4144	328	31	that	that	SCONJ
ejpam-4144	328	32	d∗	d∗	VERB
ejpam-4144	328	33	2	2	NUM
ejpam-4144	328	34	=	=	SYM
ejpam-4144	328	35	{	{	PUNCT
ejpam-4144	328	36	x	x	X
ejpam-4144	328	37	:	:	PUNCT
ejpam-4144	328	38	x	x	SYM
ejpam-4144	328	39	∈	∈	NOUN
ejpam-4144	328	40	d1	d1	NOUN
ejpam-4144	328	41	}	}	PUNCT
ejpam-4144	328	42	and	and	CCONJ
ejpam-4144	328	43	|d∗	|d∗	PROPN
ejpam-4144	328	44	2|	2|	PROPN
ejpam-4144	328	45	=	=	PUNCT
ejpam-4144	328	46	|d1|	|d1|	PROPN
ejpam-4144	328	47	.	.	PUNCT
ejpam-4144	329	1	clearly	clearly	ADV
ejpam-4144	329	2	,	,	PUNCT
ejpam-4144	329	3	d′	d′	X
ejpam-4144	329	4	=	=	SYM
ejpam-4144	329	5	d2	d2	PROPN
ejpam-4144	329	6	∪d∗	∪d∗	NUM
ejpam-4144	329	7	2	2	NUM
ejpam-4144	329	8	is	be	AUX
ejpam-4144	329	9	a	a	DET
ejpam-4144	329	10	dominating	dominating	NOUN
ejpam-4144	329	11	set	set	NOUN
ejpam-4144	329	12	of	of	ADP
ejpam-4144	329	13	g	g	PROPN
ejpam-4144	329	14	\	\	PROPN
ejpam-4144	329	15	v	v	NOUN
ejpam-4144	329	16	and	and	CCONJ
ejpam-4144	329	17	so	so	ADV
ejpam-4144	329	18	γ(gg	γ(gg	ADJ
ejpam-4144	329	19	)	)	PUNCT
ejpam-4144	329	20	=	=	SYM
ejpam-4144	329	21	|s0|	|s0|	NOUN
ejpam-4144	329	22	=	=	SYM
ejpam-4144	329	23	1	1	NUM
ejpam-4144	329	24	+	+	NUM
ejpam-4144	329	25	|d1|+	|d1|+	NOUN
ejpam-4144	329	26	|d2|	|d2|	NOUN
ejpam-4144	329	27	=	=	SYM
ejpam-4144	329	28	1	1	NUM
ejpam-4144	329	29	+	+	CCONJ
ejpam-4144	329	30	|d′|	|d′|	PROPN
ejpam-4144	329	31	≥	≥	NUM
ejpam-4144	329	32	1	1	NUM
ejpam-4144	329	33	+	+	CCONJ
ejpam-4144	329	34	γ(g	γ(g	PROPN
ejpam-4144	329	35	\	\	PROPN
ejpam-4144	329	36	v	v	NOUN
ejpam-4144	329	37	)	)	PUNCT
ejpam-4144	329	38	.	.	PUNCT
ejpam-4144	330	1	this	this	PRON
ejpam-4144	330	2	proves	prove	VERB
ejpam-4144	330	3	the	the	DET
ejpam-4144	330	4	desired	desire	VERB
ejpam-4144	330	5	equality	equality	NOUN
ejpam-4144	330	6	.	.	PUNCT
ejpam-4144	331	1	thus	thus	ADV
ejpam-4144	331	2	,	,	PUNCT
ejpam-4144	331	3	in	in	ADP
ejpam-4144	331	4	particular	particular	ADJ
ejpam-4144	331	5	,	,	PUNCT
ejpam-4144	331	6	if	if	SCONJ
ejpam-4144	331	7	g	g	PROPN
ejpam-4144	331	8	=	=	SYM
ejpam-4144	331	9	kn	kn	PROPN
ejpam-4144	331	10	,	,	PUNCT
ejpam-4144	331	11	then	then	ADV
ejpam-4144	331	12	γ(knkn	γ(knkn	NOUN
ejpam-4144	331	13	)	)	PUNCT
ejpam-4144	332	1	=	=	SYM
ejpam-4144	332	2	n.	n.	NOUN
ejpam-4144	332	3	(	(	PUNCT
ejpam-4144	332	4	ii	ii	NOUN
ejpam-4144	332	5	)	)	PUNCT
ejpam-4144	332	6	if	if	SCONJ
ejpam-4144	332	7	n	n	NOUN
ejpam-4144	332	8	=	=	SYM
ejpam-4144	332	9	1	1	NUM
ejpam-4144	332	10	,	,	PUNCT
ejpam-4144	332	11	then	then	ADV
ejpam-4144	332	12	gg	gg	PROPN
ejpam-4144	332	13	=	=	SYM
ejpam-4144	332	14	k2	k2	PROPN
ejpam-4144	332	15	.	.	PUNCT
ejpam-4144	333	1	hence	hence	ADV
ejpam-4144	333	2	,	,	PUNCT
ejpam-4144	333	3	γh(gg	γh(gg	PROPN
ejpam-4144	333	4	)	)	PUNCT
ejpam-4144	333	5	=	=	SYM
ejpam-4144	334	1	2	2	X
ejpam-4144	334	2	.	.	X
ejpam-4144	334	3	suppose	suppose	VERB
ejpam-4144	334	4	n	n	PRON
ejpam-4144	334	5	≥	≥	NOUN
ejpam-4144	334	6	2	2	NUM
ejpam-4144	334	7	.	.	PUNCT
ejpam-4144	335	1	let	let	VERB
ejpam-4144	335	2	v	v	NUM
ejpam-4144	335	3	∈	∈	PROPN
ejpam-4144	335	4	v	v	NOUN
ejpam-4144	335	5	(	(	PUNCT
ejpam-4144	335	6	g	g	NOUN
ejpam-4144	335	7	)	)	PUNCT
ejpam-4144	335	8	and	and	CCONJ
ejpam-4144	335	9	let	let	VERB
ejpam-4144	335	10	s	s	AUX
ejpam-4144	335	11	=	=	PUNCT
ejpam-4144	335	12	{	{	PUNCT
ejpam-4144	335	13	v	v	NOUN
ejpam-4144	335	14	,	,	PUNCT
ejpam-4144	335	15	v	v	NOUN
ejpam-4144	335	16	}	}	PUNCT
ejpam-4144	335	17	.	.	PUNCT
ejpam-4144	336	1	let	let	VERB
ejpam-4144	336	2	w	w	NOUN
ejpam-4144	336	3	∈	∈	PROPN
ejpam-4144	336	4	v	v	ADP
ejpam-4144	336	5	(	(	PUNCT
ejpam-4144	336	6	g	g	NOUN
ejpam-4144	336	7	)	)	PUNCT
ejpam-4144	336	8	\	\	NOUN
ejpam-4144	336	9	{	{	PUNCT
ejpam-4144	336	10	v	v	NOUN
ejpam-4144	336	11	}	}	PUNCT
ejpam-4144	336	12	.	.	PUNCT
ejpam-4144	337	1	if	if	SCONJ
ejpam-4144	337	2	wv	wv	PROPN
ejpam-4144	337	3	∈	∈	PROPN
ejpam-4144	337	4	e(g	e(g	PROPN
ejpam-4144	337	5	)	)	PUNCT
ejpam-4144	337	6	,	,	PUNCT
ejpam-4144	337	7	then	then	ADV
ejpam-4144	337	8	[	[	X
ejpam-4144	337	9	w	w	X
ejpam-4144	337	10	,	,	PUNCT
ejpam-4144	337	11	v	v	NOUN
ejpam-4144	337	12	,	,	PUNCT
ejpam-4144	337	13	v	v	NOUN
ejpam-4144	337	14	]	]	PUNCT
ejpam-4144	337	15	is	be	AUX
ejpam-4144	337	16	a	a	DET
ejpam-4144	337	17	w	w	NOUN
ejpam-4144	337	18	-	-	PUNCT
ejpam-4144	337	19	v	v	NOUN
ejpam-4144	337	20	geodesic	geodesic	NOUN
ejpam-4144	337	21	in	in	ADP
ejpam-4144	337	22	gg	gg	PROPN
ejpam-4144	337	23	.	.	PUNCT
ejpam-4144	338	1	if	if	SCONJ
ejpam-4144	338	2	wv	wv	PROPN
ejpam-4144	338	3	/∈	/∈	PUNCT
ejpam-4144	338	4	e(g	e(g	PROPN
ejpam-4144	338	5	)	)	PUNCT
ejpam-4144	338	6	,	,	PUNCT
ejpam-4144	338	7	then	then	ADV
ejpam-4144	338	8	w	w	PROPN
ejpam-4144	338	9	v	v	PROPN
ejpam-4144	338	10	∈	∈	PROPN
ejpam-4144	338	11	e(g	e(g	PROPN
ejpam-4144	338	12	)	)	PUNCT
ejpam-4144	338	13	.	.	PUNCT
ejpam-4144	339	1	it	it	PRON
ejpam-4144	339	2	follows	follow	VERB
ejpam-4144	339	3	that	that	SCONJ
ejpam-4144	339	4	[	[	X
ejpam-4144	339	5	w	w	NOUN
ejpam-4144	339	6	,	,	PUNCT
ejpam-4144	339	7	w	w	PROPN
ejpam-4144	339	8	,	,	PUNCT
ejpam-4144	339	9	v	v	NOUN
ejpam-4144	339	10	]	]	PUNCT
ejpam-4144	339	11	is	be	AUX
ejpam-4144	339	12	a	a	DET
ejpam-4144	339	13	w	w	NOUN
ejpam-4144	339	14	-	-	PUNCT
ejpam-4144	339	15	v	v	NOUN
ejpam-4144	339	16	geodesic	geodesic	NOUN
ejpam-4144	339	17	in	in	ADP
ejpam-4144	339	18	gg	gg	PROPN
ejpam-4144	339	19	.	.	PUNCT
ejpam-4144	340	1	next	next	ADV
ejpam-4144	340	2	,	,	PUNCT
ejpam-4144	340	3	let	let	VERB
ejpam-4144	340	4	z	z	NOUN
ejpam-4144	340	5	∈	∈	PROPN
ejpam-4144	340	6	v	v	ADP
ejpam-4144	340	7	(	(	PUNCT
ejpam-4144	340	8	g	g	NOUN
ejpam-4144	340	9	)	)	PUNCT
ejpam-4144	340	10	\	\	NOUN
ejpam-4144	340	11	{	{	PUNCT
ejpam-4144	340	12	v	v	NOUN
ejpam-4144	340	13	}	}	PUNCT
ejpam-4144	340	14	.	.	PUNCT
ejpam-4144	341	1	if	if	SCONJ
ejpam-4144	341	2	z	z	PROPN
ejpam-4144	341	3	v	v	ADP
ejpam-4144	341	4	∈	∈	PROPN
ejpam-4144	341	5	e(g	e(g	PROPN
ejpam-4144	341	6	)	)	PUNCT
ejpam-4144	341	7	,	,	PUNCT
ejpam-4144	341	8	then	then	ADV
ejpam-4144	341	9	[	[	X
ejpam-4144	341	10	z	z	NOUN
ejpam-4144	341	11	,	,	PUNCT
ejpam-4144	341	12	v	v	NOUN
ejpam-4144	341	13	,	,	PUNCT
ejpam-4144	341	14	v	v	NOUN
ejpam-4144	341	15	]	]	PUNCT
ejpam-4144	341	16	is	be	AUX
ejpam-4144	341	17	a	a	DET
ejpam-4144	341	18	z	z	NOUN
ejpam-4144	341	19	-	-	PUNCT
ejpam-4144	341	20	v	v	NOUN
ejpam-4144	341	21	geodesic	geodesic	NOUN
ejpam-4144	341	22	in	in	ADP
ejpam-4144	341	23	gg	gg	PROPN
ejpam-4144	341	24	.	.	PUNCT
ejpam-4144	342	1	if	if	SCONJ
ejpam-4144	342	2	z	z	PROPN
ejpam-4144	342	3	v	v	VERB
ejpam-4144	342	4	/∈	/∈	PUNCT
ejpam-4144	342	5	e(g	e(g	PROPN
ejpam-4144	342	6	)	)	PUNCT
ejpam-4144	342	7	,	,	PUNCT
ejpam-4144	342	8	then	then	ADV
ejpam-4144	342	9	zv	zv	PROPN
ejpam-4144	342	10	∈	∈	PROPN
ejpam-4144	342	11	e(g	e(g	PROPN
ejpam-4144	342	12	)	)	PUNCT
ejpam-4144	342	13	and	and	CCONJ
ejpam-4144	343	1	[	[	X
ejpam-4144	343	2	z	z	X
ejpam-4144	343	3	,	,	PUNCT
ejpam-4144	343	4	z	z	PROPN
ejpam-4144	343	5	,	,	PUNCT
ejpam-4144	343	6	v	v	NOUN
ejpam-4144	343	7	]	]	PUNCT
ejpam-4144	343	8	is	be	AUX
ejpam-4144	343	9	a	a	DET
ejpam-4144	343	10	z	z	NOUN
ejpam-4144	343	11	-	-	PUNCT
ejpam-4144	343	12	v	v	NOUN
ejpam-4144	343	13	geodesic	geodesic	NOUN
ejpam-4144	343	14	in	in	ADP
ejpam-4144	343	15	gg	gg	PROPN
ejpam-4144	343	16	.	.	PUNCT
ejpam-4144	344	1	thus	thus	ADV
ejpam-4144	344	2	,	,	PUNCT
ejpam-4144	344	3	s	s	VERB
ejpam-4144	344	4	is	be	AUX
ejpam-4144	344	5	a	a	DET
ejpam-4144	344	6	hop	hop	NOUN
ejpam-4144	344	7	dominating	dominating	NOUN
ejpam-4144	344	8	set	set	NOUN
ejpam-4144	344	9	of	of	ADP
ejpam-4144	344	10	g.	g.	PROPN
ejpam-4144	344	11	since	since	SCONJ
ejpam-4144	344	12	gg	gg	PROPN
ejpam-4144	344	13	is	be	AUX
ejpam-4144	344	14	non	non	ADJ
ejpam-4144	344	15	-	-	ADJ
ejpam-4144	344	16	trivial	trivial	ADJ
ejpam-4144	344	17	,	,	PUNCT
ejpam-4144	344	18	it	it	PRON
ejpam-4144	344	19	follows	follow	VERB
ejpam-4144	344	20	that	that	SCONJ
ejpam-4144	344	21	γh(gg	γh(gg	NOUN
ejpam-4144	344	22	)	)	PUNCT
ejpam-4144	345	1	=	=	SYM
ejpam-4144	345	2	2	2	X
ejpam-4144	345	3	.	.	PUNCT
ejpam-4144	345	4	(	(	PUNCT
ejpam-4144	345	5	iii	iii	NOUN
ejpam-4144	345	6	)	)	PUNCT
ejpam-4144	345	7	suppose	suppose	VERB
ejpam-4144	345	8	n	n	PRON
ejpam-4144	345	9	≥	≥	NOUN
ejpam-4144	345	10	2	2	NUM
ejpam-4144	345	11	.	.	PUNCT
ejpam-4144	346	1	let	let	VERB
ejpam-4144	346	2	s	s	NOUN
ejpam-4144	346	3	=	=	X
ejpam-4144	346	4	v	v	ADJ
ejpam-4144	346	5	(	(	PUNCT
ejpam-4144	346	6	g	g	NOUN
ejpam-4144	346	7	)	)	PUNCT
ejpam-4144	346	8	and	and	CCONJ
ejpam-4144	346	9	let	let	VERB
ejpam-4144	346	10	v	v	NUM
ejpam-4144	346	11	∈	∈	PROPN
ejpam-4144	346	12	v	v	NOUN
ejpam-4144	346	13	(	(	PUNCT
ejpam-4144	346	14	gg	gg	NOUN
ejpam-4144	346	15	)	)	PUNCT
ejpam-4144	346	16	\	\	PROPN
ejpam-4144	346	17	s	s	PART
ejpam-4144	346	18	=	=	SYM
ejpam-4144	346	19	v	v	NOUN
ejpam-4144	346	20	(	(	PUNCT
ejpam-4144	346	21	g	g	NOUN
ejpam-4144	346	22	)	)	PUNCT
ejpam-4144	346	23	.	.	PUNCT
ejpam-4144	347	1	since	since	SCONJ
ejpam-4144	347	2	g	g	PROPN
ejpam-4144	347	3	is	be	AUX
ejpam-4144	347	4	connected	connect	VERB
ejpam-4144	347	5	and	and	CCONJ
ejpam-4144	347	6	non	non	ADJ
ejpam-4144	347	7	-	-	ADJ
ejpam-4144	347	8	trivial	trivial	ADJ
ejpam-4144	347	9	,	,	PUNCT
ejpam-4144	347	10	we	we	PRON
ejpam-4144	347	11	may	may	AUX
ejpam-4144	347	12	choose	choose	VERB
ejpam-4144	347	13	any	any	DET
ejpam-4144	347	14	w	w	PROPN
ejpam-4144	347	15	∈	∈	PROPN
ejpam-4144	347	16	v	v	ADP
ejpam-4144	347	17	(	(	PUNCT
ejpam-4144	347	18	g	g	NOUN
ejpam-4144	347	19	)	)	PUNCT
ejpam-4144	347	20	∩	∩	NOUN
ejpam-4144	347	21	ng(v	ng(v	NUM
ejpam-4144	347	22	)	)	PUNCT
ejpam-4144	347	23	.	.	PUNCT
ejpam-4144	348	1	consequently	consequently	ADV
ejpam-4144	348	2	,	,	PUNCT
ejpam-4144	348	3	[	[	X
ejpam-4144	348	4	v	v	NOUN
ejpam-4144	348	5	,	,	PUNCT
ejpam-4144	348	6	v	v	NOUN
ejpam-4144	348	7	,	,	PUNCT
ejpam-4144	348	8	w	w	NOUN
ejpam-4144	348	9	]	]	X
ejpam-4144	348	10	is	be	AUX
ejpam-4144	348	11	a	a	DET
ejpam-4144	348	12	v	v	NOUN
ejpam-4144	348	13	-	-	PUNCT
ejpam-4144	348	14	w	w	NOUN
ejpam-4144	348	15	geodesic	geodesic	NOUN
ejpam-4144	348	16	in	in	ADP
ejpam-4144	348	17	gg	gg	PROPN
ejpam-4144	348	18	.	.	PUNCT
ejpam-4144	349	1	hence	hence	ADV
ejpam-4144	349	2	,	,	PUNCT
ejpam-4144	349	3	dgg(v	dgg(v	PROPN
ejpam-4144	349	4	,	,	PUNCT
ejpam-4144	349	5	w	w	NOUN
ejpam-4144	349	6	)	)	PUNCT
ejpam-4144	349	7	=	=	SYM
ejpam-4144	350	1	2	2	X
ejpam-4144	350	2	.	.	PUNCT
ejpam-4144	350	3	since	since	SCONJ
ejpam-4144	350	4	v	v	NOUN
ejpam-4144	350	5	was	be	AUX
ejpam-4144	350	6	arbitrarily	arbitrarily	ADV
ejpam-4144	350	7	chosen	choose	VERB
ejpam-4144	350	8	,	,	PUNCT
ejpam-4144	350	9	it	it	PRON
ejpam-4144	350	10	follows	follow	VERB
ejpam-4144	350	11	that	that	PRON
ejpam-4144	350	12	s	s	VERB
ejpam-4144	350	13	=	=	SYM
ejpam-4144	350	14	v	v	X
ejpam-4144	350	15	(	(	PUNCT
ejpam-4144	350	16	g	g	NOUN
ejpam-4144	350	17	)	)	PUNCT
ejpam-4144	350	18	is	be	AUX
ejpam-4144	350	19	a	a	DET
ejpam-4144	350	20	hop	hop	NOUN
ejpam-4144	350	21	dominating	dominating	NOUN
ejpam-4144	350	22	set	set	NOUN
ejpam-4144	350	23	of	of	ADP
ejpam-4144	350	24	gg	gg	PROPN
ejpam-4144	350	25	.	.	PUNCT
ejpam-4144	351	1	next	next	ADV
ejpam-4144	351	2	,	,	PUNCT
ejpam-4144	351	3	let	let	VERB
ejpam-4144	351	4	y	y	PROPN
ejpam-4144	351	5	∈	∈	PROPN
ejpam-4144	351	6	v	v	PROPN
ejpam-4144	351	7	(	(	PUNCT
ejpam-4144	351	8	gg	gg	NOUN
ejpam-4144	351	9	)	)	PUNCT
ejpam-4144	351	10	\	\	PUNCT
ejpam-4144	352	1	s.	s.	PROPN
ejpam-4144	352	2	then	then	ADV
ejpam-4144	352	3	yy	yy	INTJ
ejpam-4144	352	4	/∈	/∈	PUNCT
ejpam-4144	352	5	e(gg	e(gg	NUM
ejpam-4144	352	6	)	)	PUNCT
ejpam-4144	352	7	.	.	PUNCT
ejpam-4144	353	1	pick	pick	VERB
ejpam-4144	353	2	any	any	DET
ejpam-4144	353	3	x	x	SYM
ejpam-4144	353	4	∈	∈	PROPN
ejpam-4144	353	5	v	v	ADP
ejpam-4144	353	6	(	(	PUNCT
ejpam-4144	353	7	g	g	NOUN
ejpam-4144	353	8	)	)	PUNCT
ejpam-4144	353	9	\	\	NOUN
ejpam-4144	353	10	{	{	PUNCT
ejpam-4144	353	11	y	y	NOUN
ejpam-4144	353	12	}	}	PUNCT
ejpam-4144	353	13	.	.	PUNCT
ejpam-4144	354	1	if	if	SCONJ
ejpam-4144	354	2	xy	xy	PROPN
ejpam-4144	354	3	∈	∈	PROPN
ejpam-4144	354	4	e(gg	e(gg	PROPN
ejpam-4144	354	5	)	)	PUNCT
ejpam-4144	354	6	,	,	PUNCT
ejpam-4144	354	7	then	then	ADV
ejpam-4144	354	8	x	x	X
ejpam-4144	354	9	y	y	PROPN
ejpam-4144	354	10	∈	∈	PROPN
ejpam-4144	354	11	e(gg	e(gg	PROPN
ejpam-4144	354	12	)	)	PUNCT
ejpam-4144	354	13	.	.	PUNCT
ejpam-4144	355	1	since	since	SCONJ
ejpam-4144	355	2	yx	yx	PROPN
ejpam-4144	355	3	∈	∈	PROPN
ejpam-4144	355	4	e(gg	e(gg	PROPN
ejpam-4144	355	5	)	)	PUNCT
ejpam-4144	355	6	,	,	PUNCT
ejpam-4144	355	7	it	it	PRON
ejpam-4144	355	8	follows	follow	VERB
ejpam-4144	355	9	that	that	SCONJ
ejpam-4144	355	10	d	d	PROPN
ejpam-4144	355	11	gg	gg	X
ejpam-4144	355	12	(	(	PUNCT
ejpam-4144	355	13	y	y	PROPN
ejpam-4144	355	14	,	,	PUNCT
ejpam-4144	355	15	y	y	NOUN
ejpam-4144	355	16	)	)	PUNCT
ejpam-4144	355	17	=	=	SYM
ejpam-4144	356	1	2	2	X
ejpam-4144	356	2	.	.	X
ejpam-4144	357	1	if	if	SCONJ
ejpam-4144	357	2	xy	xy	PROPN
ejpam-4144	357	3	/∈	/∈	PUNCT
ejpam-4144	358	1	e(gg	e(gg	NUM
ejpam-4144	358	2	)	)	PUNCT
ejpam-4144	359	1	,	,	PUNCT
ejpam-4144	359	2	then	then	ADV
ejpam-4144	359	3	xy	xy	PROPN
ejpam-4144	359	4	∈	∈	PROPN
ejpam-4144	359	5	e(gg	e(gg	PROPN
ejpam-4144	359	6	)	)	PUNCT
ejpam-4144	359	7	.	.	PUNCT
ejpam-4144	360	1	since	since	SCONJ
ejpam-4144	360	2	xy	xy	PROPN
ejpam-4144	360	3	∈	∈	PROPN
ejpam-4144	360	4	e(gg	e(gg	PROPN
ejpam-4144	360	5	)	)	PUNCT
ejpam-4144	360	6	,	,	PUNCT
ejpam-4144	360	7	d	d	X
ejpam-4144	360	8	gg	gg	PROPN
ejpam-4144	360	9	(	(	PUNCT
ejpam-4144	360	10	y	y	PROPN
ejpam-4144	360	11	,	,	PUNCT
ejpam-4144	360	12	y	y	NOUN
ejpam-4144	360	13	)	)	PUNCT
ejpam-4144	360	14	=	=	SYM
ejpam-4144	360	15	2	2	X
ejpam-4144	360	16	.	.	PUNCT
ejpam-4144	361	1	this	this	PRON
ejpam-4144	361	2	shows	show	VERB
ejpam-4144	361	3	that	that	SCONJ
ejpam-4144	361	4	s	s	VERB
ejpam-4144	361	5	is	be	AUX
ejpam-4144	361	6	also	also	ADV
ejpam-4144	361	7	a	a	DET
ejpam-4144	361	8	hop	hop	NOUN
ejpam-4144	361	9	dominating	dominating	NOUN
ejpam-4144	361	10	set	set	NOUN
ejpam-4144	361	11	of	of	ADP
ejpam-4144	361	12	gg	gg	PROPN
ejpam-4144	361	13	.	.	PUNCT
ejpam-4144	362	1	therefore	therefore	ADV
ejpam-4144	362	2	,	,	PUNCT
ejpam-4144	362	3	s	s	VERB
ejpam-4144	362	4	is	be	AUX
ejpam-4144	362	5	a	a	DET
ejpam-4144	362	6	global	global	ADJ
ejpam-4144	362	7	hop	hop	NOUN
ejpam-4144	362	8	dominating	dominating	NOUN
ejpam-4144	362	9	set	set	NOUN
ejpam-4144	362	10	of	of	ADP
ejpam-4144	362	11	gg	gg	PROPN
ejpam-4144	362	12	and	and	CCONJ
ejpam-4144	362	13	γgh(gg	γgh(gg	NUM
ejpam-4144	362	14	)	)	PUNCT
ejpam-4144	362	15	≤	≤	NUM
ejpam-4144	362	16	|s|	|s|	PROPN
ejpam-4144	362	17	=	=	SYM
ejpam-4144	362	18	n.	n.	PROPN
ejpam-4144	362	19	now	now	ADV
ejpam-4144	362	20	let	let	VERB
ejpam-4144	362	21	sg	sg	PART
ejpam-4144	362	22	be	be	AUX
ejpam-4144	362	23	a	a	DET
ejpam-4144	362	24	global	global	ADJ
ejpam-4144	362	25	hop	hop	NOUN
ejpam-4144	362	26	dominating	dominating	NOUN
ejpam-4144	362	27	set	set	NOUN
ejpam-4144	362	28	of	of	ADP
ejpam-4144	362	29	g	g	PROPN
ejpam-4144	362	30	and	and	CCONJ
ejpam-4144	362	31	let	let	VERB
ejpam-4144	362	32	sg	sg	VERB
ejpam-4144	362	33	=	=	PUNCT
ejpam-4144	362	34	{	{	PUNCT
ejpam-4144	362	35	v	v	NOUN
ejpam-4144	362	36	:	:	PUNCT
ejpam-4144	362	37	v	v	NUM
ejpam-4144	362	38	∈	∈	PROPN
ejpam-4144	362	39	sg	sg	ADP
ejpam-4144	362	40	}	}	PUNCT
ejpam-4144	362	41	.	.	PUNCT
ejpam-4144	363	1	then	then	ADV
ejpam-4144	363	2	clearly	clearly	ADV
ejpam-4144	363	3	,	,	PUNCT
ejpam-4144	363	4	s′	s′	ADJ
ejpam-4144	363	5	=	=	NOUN
ejpam-4144	363	6	sg	sg	PART
ejpam-4144	363	7	∪	∪	ADJ
ejpam-4144	363	8	sg	sg	PROPN
ejpam-4144	363	9	is	be	AUX
ejpam-4144	363	10	a	a	DET
ejpam-4144	363	11	hop	hop	NOUN
ejpam-4144	363	12	dominating	dominating	NOUN
ejpam-4144	363	13	set	set	NOUN
ejpam-4144	363	14	of	of	ADP
ejpam-4144	363	15	both	both	DET
ejpam-4144	363	16	gg	gg	NOUN
ejpam-4144	363	17	and	and	CCONJ
ejpam-4144	363	18	gg	gg	PROPN
ejpam-4144	363	19	,	,	PUNCT
ejpam-4144	363	20	that	that	ADV
ejpam-4144	363	21	is	is	ADV
ejpam-4144	363	22	,	,	PUNCT
ejpam-4144	363	23	s′	s′	ADJ
ejpam-4144	363	24	is	be	AUX
ejpam-4144	363	25	a	a	DET
ejpam-4144	363	26	global	global	ADJ
ejpam-4144	363	27	hop	hop	NOUN
ejpam-4144	363	28	dominating	dominating	NOUN
ejpam-4144	363	29	set	set	NOUN
ejpam-4144	363	30	of	of	ADP
ejpam-4144	363	31	gg	gg	PROPN
ejpam-4144	363	32	.	.	PUNCT
ejpam-4144	364	1	thus	thus	ADV
ejpam-4144	364	2	,	,	PUNCT
ejpam-4144	364	3	in	in	ADP
ejpam-4144	364	4	particular	particular	ADJ
ejpam-4144	364	5	,	,	PUNCT
ejpam-4144	364	6	if	if	SCONJ
ejpam-4144	364	7	sg	sg	PROPN
ejpam-4144	364	8	is	be	AUX
ejpam-4144	364	9	a	a	DET
ejpam-4144	364	10	γgh	γgh	PROPN
ejpam-4144	364	11	-	-	PUNCT
ejpam-4144	364	12	set	set	NOUN
ejpam-4144	364	13	of	of	ADP
ejpam-4144	364	14	g	g	NOUN
ejpam-4144	364	15	,	,	PUNCT
ejpam-4144	364	16	then	then	ADV
ejpam-4144	364	17	s′	s′	ADJ
ejpam-4144	364	18	=	=	PUNCT
ejpam-4144	364	19	sg	sg	PART
ejpam-4144	364	20	∪sg	∪sg	PROPN
ejpam-4144	364	21	is	be	AUX
ejpam-4144	364	22	a	a	DET
ejpam-4144	364	23	global	global	ADJ
ejpam-4144	364	24	hop	hop	NOUN
ejpam-4144	364	25	dominating	dominating	NOUN
ejpam-4144	364	26	set	set	NOUN
ejpam-4144	364	27	of	of	ADP
ejpam-4144	364	28	gg	gg	PROPN
ejpam-4144	364	29	.	.	PUNCT
ejpam-4144	365	1	this	this	PRON
ejpam-4144	365	2	implies	imply	VERB
ejpam-4144	365	3	that	that	SCONJ
ejpam-4144	365	4	γgh(gg	γgh(gg	NUM
ejpam-4144	365	5	)	)	PUNCT
ejpam-4144	365	6	≤	≤	NOUN
ejpam-4144	365	7	|s′|	|s′|	NOUN
ejpam-4144	365	8	=	=	PUNCT
ejpam-4144	365	9	2γgh(g	2γgh(g	NUM
ejpam-4144	365	10	)	)	PUNCT
ejpam-4144	365	11	.	.	PUNCT
ejpam-4144	366	1	combining	combine	VERB
ejpam-4144	366	2	this	this	PRON
ejpam-4144	366	3	with	with	ADP
ejpam-4144	366	4	the	the	DET
ejpam-4144	366	5	first	first	ADJ
ejpam-4144	366	6	inequality	inequality	NOUN
ejpam-4144	366	7	,	,	PUNCT
ejpam-4144	366	8	we	we	PRON
ejpam-4144	366	9	find	find	VERB
ejpam-4144	366	10	that	that	SCONJ
ejpam-4144	366	11	the	the	DET
ejpam-4144	366	12	assertion	assertion	NOUN
ejpam-4144	366	13	in	in	ADP
ejpam-4144	366	14	(	(	PUNCT
ejpam-4144	366	15	iii	iii	NOUN
ejpam-4144	366	16	)	)	PUNCT
ejpam-4144	366	17	holds	hold	VERB
ejpam-4144	366	18	.	.	PUNCT
ejpam-4144	367	1	the	the	DET
ejpam-4144	367	2	bound	bind	VERB
ejpam-4144	367	3	given	give	VERB
ejpam-4144	367	4	in	in	ADP
ejpam-4144	367	5	theorem	theorem	ADJ
ejpam-4144	367	6	5(iii	5(iii	NUM
ejpam-4144	367	7	)	)	PUNCT
ejpam-4144	367	8	is	be	AUX
ejpam-4144	367	9	sharp	sharp	ADJ
ejpam-4144	367	10	.	.	PUNCT
ejpam-4144	368	1	to	to	PART
ejpam-4144	368	2	see	see	VERB
ejpam-4144	368	3	this	this	PRON
ejpam-4144	368	4	,	,	PUNCT
ejpam-4144	368	5	consider	consider	VERB
ejpam-4144	368	6	the	the	DET
ejpam-4144	368	7	graph	graph	NOUN
ejpam-4144	368	8	g	g	PROPN
ejpam-4144	368	9	=	=	PROPN
ejpam-4144	368	10	p3	p3	PROPN
ejpam-4144	368	11	and	and	CCONJ
ejpam-4144	368	12	the	the	DET
ejpam-4144	368	13	graph	graph	NOUN
ejpam-4144	368	14	h	h	NOUN
ejpam-4144	368	15	obtained	obtain	VERB
ejpam-4144	368	16	from	from	ADP
ejpam-4144	368	17	c4	c4	NOUN
ejpam-4144	368	18	by	by	ADP
ejpam-4144	368	19	adding	add	VERB
ejpam-4144	368	20	a	a	DET
ejpam-4144	368	21	pendant	pendant	ADJ
ejpam-4144	368	22	edge	edge	NOUN
ejpam-4144	368	23	.	.	PUNCT
ejpam-4144	369	1	it	it	PRON
ejpam-4144	369	2	can	can	AUX
ejpam-4144	369	3	be	be	AUX
ejpam-4144	369	4	verified	verify	VERB
ejpam-4144	369	5	that	that	SCONJ
ejpam-4144	369	6	γgh(gg	γgh(gg	NUM
ejpam-4144	369	7	)	)	PUNCT
ejpam-4144	370	1	=	=	SYM
ejpam-4144	370	2	|v	|v	PROPN
ejpam-4144	370	3	(	(	PUNCT
ejpam-4144	370	4	g)|	g)|	NOUN
ejpam-4144	370	5	=	=	SYM
ejpam-4144	370	6	3	3	NUM
ejpam-4144	370	7	and	and	CCONJ
ejpam-4144	370	8	γgh(hh	γgh(hh	NUM
ejpam-4144	370	9	)	)	PUNCT
ejpam-4144	370	10	=	=	SYM
ejpam-4144	370	11	2γgh(h	2γgh(h	NUM
ejpam-4144	370	12	)	)	PUNCT
ejpam-4144	370	13	=	=	SYM
ejpam-4144	370	14	4	4	NUM
ejpam-4144	370	15	<	<	SYM
ejpam-4144	370	16	5	5	NUM
ejpam-4144	370	17	=	=	SYM
ejpam-4144	370	18	|v	|v	X
ejpam-4144	370	19	(	(	PUNCT
ejpam-4144	370	20	h)|	h)|	PROPN
ejpam-4144	370	21	.	.	PUNCT
ejpam-4144	370	22	theorem	theorem	PROPN
ejpam-4144	370	23	6	6	NUM
ejpam-4144	370	24	.	.	PUNCT
ejpam-4144	371	1	let	let	VERB
ejpam-4144	371	2	g	g	PROPN
ejpam-4144	371	3	=	=	PUNCT
ejpam-4144	371	4	km1,m2,	km1,m2,	PROPN
ejpam-4144	371	5	...	...	PUNCT
ejpam-4144	371	6	,mk	,mk	PUNCT
ejpam-4144	371	7	be	be	AUX
ejpam-4144	371	8	a	a	DET
ejpam-4144	371	9	complete	complete	ADJ
ejpam-4144	371	10	multipartite	multipartite	ADJ
ejpam-4144	371	11	graph	graph	NOUN
ejpam-4144	371	12	such	such	ADJ
ejpam-4144	371	13	that	that	DET
ejpam-4144	371	14	m1	m1	PROPN
ejpam-4144	371	15	≤	≤	NUM
ejpam-4144	371	16	m2	m2	PROPN
ejpam-4144	371	17	≤	≤	PROPN
ejpam-4144	371	18	g.	g.	PROPN
ejpam-4144	371	19	salasalan	salasalan	NOUN
ejpam-4144	371	20	,	,	PUNCT
ejpam-4144	371	21	s.	s.	PROPN
ejpam-4144	371	22	canoy	canoy	PROPN
ejpam-4144	371	23	,	,	PUNCT
ejpam-4144	371	24	jr	jr	PROPN
ejpam-4144	371	25	.	.	PROPN
ejpam-4144	371	26	/	/	SYM
ejpam-4144	371	27	eur	eur	PROPN
ejpam-4144	371	28	.	.	PUNCT
ejpam-4144	372	1	j.	j.	PROPN
ejpam-4144	372	2	pure	pure	PROPN
ejpam-4144	372	3	appl	appl	PROPN
ejpam-4144	372	4	.	.	PROPN
ejpam-4144	372	5	math	math	PROPN
ejpam-4144	372	6	,	,	PUNCT
ejpam-4144	372	7	14	14	NUM
ejpam-4144	372	8	(	(	PUNCT
ejpam-4144	372	9	4	4	NUM
ejpam-4144	372	10	)	)	PUNCT
ejpam-4144	372	11	(	(	PUNCT
ejpam-4144	372	12	2021	2021	NUM
ejpam-4144	372	13	)	)	PUNCT
ejpam-4144	372	14	,	,	PUNCT
ejpam-4144	372	15	1415	1415	NUM
ejpam-4144	372	16	-	-	SYM
ejpam-4144	372	17	1428	1428	NUM
ejpam-4144	372	18	1422	1422	NUM
ejpam-4144	372	19	.	.	PUNCT
ejpam-4144	372	20	.	.	PUNCT
ejpam-4144	372	21	.	.	PUNCT
ejpam-4144	373	1	≤	≤	NUM
ejpam-4144	373	2	mk	mk	PROPN
ejpam-4144	373	3	and	and	CCONJ
ejpam-4144	373	4	k	k	PROPN
ejpam-4144	373	5	≥	≥	NUM
ejpam-4144	373	6	2	2	NUM
ejpam-4144	373	7	.	.	PUNCT
ejpam-4144	373	8	then	then	ADV
ejpam-4144	373	9	γ(gg	γ(gg	NUM
ejpam-4144	373	10	)	)	PUNCT
ejpam-4144	373	11	=	=	SYM
ejpam-4144	374	1			NOUN
ejpam-4144	374	2	k	k	NOUN
ejpam-4144	375	1	if	if	SCONJ
ejpam-4144	375	2	m1	m1	PROPN
ejpam-4144	375	3	=	=	NOUN
ejpam-4144	375	4	1	1	NUM
ejpam-4144	375	5	k	k	NOUN
ejpam-4144	375	6	+	+	NOUN
ejpam-4144	375	7	1	1	NUM
ejpam-4144	375	8	if	if	SCONJ
ejpam-4144	375	9	m1	m1	PROPN
ejpam-4144	375	10	=	=	SYM
ejpam-4144	375	11	2	2	NUM
ejpam-4144	375	12	k	k	NOUN
ejpam-4144	375	13	+	+	NOUN
ejpam-4144	375	14	2	2	NUM
ejpam-4144	375	15	if	if	SCONJ
ejpam-4144	375	16	m1	m1	PROPN
ejpam-4144	375	17	≥	≥	NOUN
ejpam-4144	375	18	3	3	X
ejpam-4144	375	19	.	.	PUNCT
ejpam-4144	375	20	proof	proof	NOUN
ejpam-4144	375	21	.	.	PUNCT
ejpam-4144	376	1	let	let	VERB
ejpam-4144	376	2	u1	u1	NOUN
ejpam-4144	376	3	,	,	PUNCT
ejpam-4144	376	4	u2	u2	NOUN
ejpam-4144	376	5	,	,	PUNCT
ejpam-4144	376	6	.	.	PUNCT
ejpam-4144	376	7	.	.	PUNCT
ejpam-4144	377	1	.	.	PUNCT
ejpam-4144	378	1	,	,	PUNCT
ejpam-4144	378	2	uk	uk	PROPN
ejpam-4144	378	3	be	be	VERB
ejpam-4144	378	4	the	the	DET
ejpam-4144	378	5	partite	partite	ADJ
ejpam-4144	378	6	sets	set	NOUN
ejpam-4144	378	7	of	of	ADP
ejpam-4144	378	8	g	g	NOUN
ejpam-4144	378	9	with	with	ADP
ejpam-4144	378	10	|ui|	|ui|	PROPN
ejpam-4144	378	11	=	=	SYM
ejpam-4144	378	12	mi	mi	PROPN
ejpam-4144	378	13	for	for	ADP
ejpam-4144	378	14	each	each	DET
ejpam-4144	378	15	i	i	PRON
ejpam-4144	378	16	∈	∈	PROPN
ejpam-4144	378	17	{	{	PUNCT
ejpam-4144	378	18	1	1	NUM
ejpam-4144	378	19	,	,	PUNCT
ejpam-4144	378	20	2	2	NUM
ejpam-4144	378	21	,	,	PUNCT
ejpam-4144	378	22	.	.	PUNCT
ejpam-4144	378	23	.	.	PUNCT
ejpam-4144	379	1	.	.	PUNCT
ejpam-4144	380	1	,	,	PUNCT
ejpam-4144	380	2	k	k	X
ejpam-4144	380	3	}	}	PUNCT
ejpam-4144	380	4	.	.	PUNCT
ejpam-4144	381	1	for	for	ADP
ejpam-4144	381	2	each	each	DET
ejpam-4144	381	3	i	i	PRON
ejpam-4144	381	4	∈	∈	PROPN
ejpam-4144	381	5	{	{	PUNCT
ejpam-4144	381	6	1	1	NUM
ejpam-4144	381	7	,	,	PUNCT
ejpam-4144	381	8	2	2	NUM
ejpam-4144	381	9	,	,	PUNCT
ejpam-4144	381	10	.	.	PUNCT
ejpam-4144	381	11	.	.	PUNCT
ejpam-4144	381	12	.	.	PUNCT
ejpam-4144	382	1	,	,	PUNCT
ejpam-4144	382	2	k	k	X
ejpam-4144	382	3	}	}	PUNCT
ejpam-4144	382	4	,	,	PUNCT
ejpam-4144	382	5	let	let	VERB
ejpam-4144	382	6	u	u	PRON
ejpam-4144	382	7	i	i	NOUN
ejpam-4144	382	8	=	=	PUNCT
ejpam-4144	382	9	{	{	PUNCT
ejpam-4144	382	10	v	v	NOUN
ejpam-4144	382	11	:	:	PUNCT
ejpam-4144	382	12	v	v	NUM
ejpam-4144	382	13	∈	∈	PROPN
ejpam-4144	382	14	ui	ui	PROPN
ejpam-4144	382	15	}	}	PUNCT
ejpam-4144	382	16	.	.	PUNCT
ejpam-4144	383	1	then	then	ADV
ejpam-4144	383	2	the	the	DET
ejpam-4144	383	3	induced	induced	ADJ
ejpam-4144	383	4	graphs	graph	NOUN
ejpam-4144	383	5	of	of	ADP
ejpam-4144	383	6	the	the	DET
ejpam-4144	383	7	sets	set	NOUN
ejpam-4144	383	8	u1	u1	NOUN
ejpam-4144	383	9	,	,	PUNCT
ejpam-4144	383	10	u2	u2	NOUN
ejpam-4144	383	11	,	,	PUNCT
ejpam-4144	383	12	.	.	PUNCT
ejpam-4144	383	13	.	.	PUNCT
ejpam-4144	383	14	.	.	PUNCT
ejpam-4144	384	1	,	,	PUNCT
ejpam-4144	384	2	uk	uk	PROPN
ejpam-4144	384	3	are	be	AUX
ejpam-4144	384	4	exactly	exactly	ADV
ejpam-4144	384	5	the	the	DET
ejpam-4144	384	6	(	(	PUNCT
ejpam-4144	384	7	complete	complete	ADJ
ejpam-4144	384	8	)	)	PUNCT
ejpam-4144	384	9	components	component	NOUN
ejpam-4144	384	10	of	of	ADP
ejpam-4144	384	11	g	g	PROPN
ejpam-4144	384	12	in	in	ADP
ejpam-4144	384	13	gg	gg	PROPN
ejpam-4144	384	14	.	.	PUNCT
ejpam-4144	385	1	suppose	suppose	VERB
ejpam-4144	385	2	first	first	ADV
ejpam-4144	385	3	that	that	DET
ejpam-4144	385	4	m1	m1	PROPN
ejpam-4144	385	5	=	=	SYM
ejpam-4144	385	6	1	1	NUM
ejpam-4144	385	7	,	,	PUNCT
ejpam-4144	385	8	say	say	VERB
ejpam-4144	385	9	u1	u1	NOUN
ejpam-4144	385	10	=	=	SYM
ejpam-4144	385	11	{	{	PUNCT
ejpam-4144	385	12	v	v	NOUN
ejpam-4144	385	13	}	}	PUNCT
ejpam-4144	385	14	.	.	PUNCT
ejpam-4144	386	1	then	then	ADV
ejpam-4144	386	2	v	v	NOUN
ejpam-4144	386	3	is	be	AUX
ejpam-4144	386	4	a	a	DET
ejpam-4144	386	5	dominating	dominating	NOUN
ejpam-4144	386	6	vertex	vertex	NOUN
ejpam-4144	386	7	of	of	ADP
ejpam-4144	386	8	g	g	PROPN
ejpam-4144	386	9	and	and	CCONJ
ejpam-4144	386	10	so	so	ADV
ejpam-4144	386	11	by	by	ADP
ejpam-4144	386	12	theorem	theorem	NOUN
ejpam-4144	386	13	5(i	5(i	NOUN
ejpam-4144	386	14	)	)	PUNCT
ejpam-4144	386	15	,	,	PUNCT
ejpam-4144	386	16	γ(gg	γ(gg	ADJ
ejpam-4144	386	17	)	)	PUNCT
ejpam-4144	386	18	=	=	SYM
ejpam-4144	386	19	1	1	NUM
ejpam-4144	386	20	+	+	NUM
ejpam-4144	386	21	γ(g	γ(g	PROPN
ejpam-4144	386	22	\	\	PROPN
ejpam-4144	386	23	v	v	NOUN
ejpam-4144	386	24	)	)	PUNCT
ejpam-4144	386	25	.	.	PUNCT
ejpam-4144	387	1	since	since	SCONJ
ejpam-4144	387	2	g	g	PROPN
ejpam-4144	387	3	\	\	PROPN
ejpam-4144	387	4	v	v	NOUN
ejpam-4144	387	5	is	be	AUX
ejpam-4144	387	6	the	the	DET
ejpam-4144	387	7	disjoint	disjoint	PROPN
ejpam-4144	387	8	union	union	NOUN
ejpam-4144	387	9	of	of	ADP
ejpam-4144	387	10	complete	complete	ADJ
ejpam-4144	387	11	graphs	graph	NOUN
ejpam-4144	387	12	⟨u2⟩	⟨u2⟩	ADJ
ejpam-4144	387	13	,	,	PUNCT
ejpam-4144	387	14	⟨u3⟩	⟨u3⟩	PROPN
ejpam-4144	387	15	,	,	PUNCT
ejpam-4144	387	16	.	.	PUNCT
ejpam-4144	387	17	.	.	PUNCT
ejpam-4144	388	1	.	.	PUNCT
ejpam-4144	389	1	,	,	PUNCT
ejpam-4144	389	2	⟨uk⟩	⟨uk⟩	NOUN
ejpam-4144	389	3	,	,	PUNCT
ejpam-4144	389	4	it	it	PRON
ejpam-4144	389	5	follows	follow	VERB
ejpam-4144	389	6	that	that	PRON
ejpam-4144	389	7	γ(g	γ(g	VERB
ejpam-4144	389	8	\	\	PROPN
ejpam-4144	389	9	v	v	NOUN
ejpam-4144	389	10	)	)	PUNCT
ejpam-4144	389	11	=	=	PUNCT
ejpam-4144	390	1	k	k	NOUN
ejpam-4144	391	1	−	−	NOUN
ejpam-4144	391	2	1	1	NUM
ejpam-4144	391	3	.	.	PUNCT
ejpam-4144	391	4	thus	thus	ADV
ejpam-4144	391	5	,	,	PUNCT
ejpam-4144	391	6	γ(gg	γ(gg	ADJ
ejpam-4144	391	7	)	)	PUNCT
ejpam-4144	391	8	=	=	VERB
ejpam-4144	392	1	k.	k.	PROPN
ejpam-4144	392	2	next	next	ADV
ejpam-4144	392	3	,	,	PUNCT
ejpam-4144	392	4	suppose	suppose	VERB
ejpam-4144	392	5	that	that	SCONJ
ejpam-4144	392	6	m1	m1	PROPN
ejpam-4144	392	7	=	=	SYM
ejpam-4144	392	8	2	2	NUM
ejpam-4144	392	9	,	,	PUNCT
ejpam-4144	392	10	say	say	VERB
ejpam-4144	392	11	u1	u1	NOUN
ejpam-4144	392	12	=	=	SYM
ejpam-4144	392	13	{	{	PUNCT
ejpam-4144	392	14	u	u	NOUN
ejpam-4144	392	15	,	,	PUNCT
ejpam-4144	392	16	v	v	NOUN
ejpam-4144	392	17	}	}	PUNCT
ejpam-4144	392	18	.	.	PUNCT
ejpam-4144	393	1	by	by	ADP
ejpam-4144	393	2	theorem	theorem	NOUN
ejpam-4144	393	3	4	4	NUM
ejpam-4144	393	4	,	,	PUNCT
ejpam-4144	393	5	max{γ(g	max{γ(g	PROPN
ejpam-4144	393	6	)	)	PUNCT
ejpam-4144	393	7	,	,	PUNCT
ejpam-4144	393	8	γ(g	γ(g	PROPN
ejpam-4144	393	9	)	)	PUNCT
ejpam-4144	393	10	}	}	PUNCT
ejpam-4144	393	11	=	=	SYM
ejpam-4144	393	12	k	k	NOUN
ejpam-4144	393	13	≤	≤	ADV
ejpam-4144	393	14	γ(gg	γ(gg	NUM
ejpam-4144	393	15	)	)	PUNCT
ejpam-4144	393	16	≤	≤	PUNCT
ejpam-4144	394	1	k	k	X
ejpam-4144	394	2	+	+	CCONJ
ejpam-4144	394	3	2	2	NUM
ejpam-4144	394	4	=	=	SYM
ejpam-4144	394	5	γ(g	γ(g	PROPN
ejpam-4144	394	6	)	)	PUNCT
ejpam-4144	395	1	+	+	PROPN
ejpam-4144	395	2	γ(g	γ(g	PROPN
ejpam-4144	395	3	)	)	PUNCT
ejpam-4144	395	4	.	.	PUNCT
ejpam-4144	396	1	for	for	ADP
ejpam-4144	396	2	each	each	DET
ejpam-4144	396	3	i	i	PRON
ejpam-4144	396	4	∈	∈	PROPN
ejpam-4144	396	5	{	{	PUNCT
ejpam-4144	396	6	2	2	NUM
ejpam-4144	396	7	.	.	PUNCT
ejpam-4144	396	8	.	.	PUNCT
ejpam-4144	396	9	.	.	PUNCT
ejpam-4144	397	1	,	,	PUNCT
ejpam-4144	397	2	k	k	X
ejpam-4144	397	3	}	}	PUNCT
ejpam-4144	397	4	,	,	PUNCT
ejpam-4144	397	5	choose	choose	VERB
ejpam-4144	397	6	any	any	DET
ejpam-4144	397	7	vi	vi	NOUN
ejpam-4144	397	8	∈	∈	PROPN
ejpam-4144	397	9	ui	ui	NOUN
ejpam-4144	397	10	and	and	CCONJ
ejpam-4144	397	11	let	let	VERB
ejpam-4144	397	12	s	s	PRON
ejpam-4144	397	13	=	=	PUNCT
ejpam-4144	397	14	{	{	PUNCT
ejpam-4144	397	15	u	u	NOUN
ejpam-4144	397	16	,	,	PUNCT
ejpam-4144	397	17	v	v	NOUN
ejpam-4144	397	18	}	}	PUNCT
ejpam-4144	397	19	∪	∪	NOUN
ejpam-4144	397	20	{	{	PUNCT
ejpam-4144	397	21	vi	vi	NOUN
ejpam-4144	397	22	:	:	PUNCT
ejpam-4144	397	23	i	i	PRON
ejpam-4144	397	24	∈	∈	PROPN
ejpam-4144	397	25	{	{	PUNCT
ejpam-4144	397	26	2	2	NUM
ejpam-4144	397	27	,	,	PUNCT
ejpam-4144	397	28	3	3	NUM
ejpam-4144	397	29	,	,	PUNCT
ejpam-4144	397	30	.	.	PUNCT
ejpam-4144	397	31	.	.	PUNCT
ejpam-4144	398	1	.	.	PUNCT
ejpam-4144	399	1	,	,	PUNCT
ejpam-4144	399	2	k	k	X
ejpam-4144	399	3	}	}	PUNCT
ejpam-4144	399	4	}	}	PUNCT
ejpam-4144	399	5	.	.	PUNCT
ejpam-4144	400	1	then	then	ADV
ejpam-4144	400	2	s	s	VERB
ejpam-4144	400	3	is	be	AUX
ejpam-4144	400	4	a	a	DET
ejpam-4144	400	5	dominating	dominating	NOUN
ejpam-4144	400	6	set	set	NOUN
ejpam-4144	400	7	of	of	ADP
ejpam-4144	400	8	gg	gg	PROPN
ejpam-4144	400	9	.	.	PUNCT
ejpam-4144	401	1	hence	hence	ADV
ejpam-4144	401	2	,	,	PUNCT
ejpam-4144	401	3	γ(gg	γ(gg	NUM
ejpam-4144	401	4	)	)	PUNCT
ejpam-4144	401	5	≤	≤	NUM
ejpam-4144	401	6	|s|	|s|	PROPN
ejpam-4144	401	7	=	=	SYM
ejpam-4144	401	8	2	2	NUM
ejpam-4144	401	9	+	+	CCONJ
ejpam-4144	401	10	k	k	NOUN
ejpam-4144	401	11	−	−	PROPN
ejpam-4144	401	12	1	1	NUM
ejpam-4144	401	13	=	=	SYM
ejpam-4144	401	14	k	k	PROPN
ejpam-4144	402	1	+	+	NOUN
ejpam-4144	402	2	1	1	X
ejpam-4144	402	3	.	.	PUNCT
ejpam-4144	402	4	let	let	VERB
ejpam-4144	402	5	s′	s′	PROPN
ejpam-4144	402	6	be	be	AUX
ejpam-4144	402	7	a	a	DET
ejpam-4144	402	8	γ	γ	NOUN
ejpam-4144	402	9	-	-	PUNCT
ejpam-4144	402	10	set	set	NOUN
ejpam-4144	402	11	of	of	ADP
ejpam-4144	402	12	gg	gg	PROPN
ejpam-4144	402	13	.	.	PUNCT
ejpam-4144	403	1	if	if	SCONJ
ejpam-4144	403	2	s′	s′	ADJ
ejpam-4144	403	3	∩	∩	NOUN
ejpam-4144	403	4	v	v	ADP
ejpam-4144	403	5	(	(	PUNCT
ejpam-4144	403	6	g	g	NOUN
ejpam-4144	403	7	)	)	PUNCT
ejpam-4144	403	8	=	=	NOUN
ejpam-4144	403	9	∅	∅	NOUN
ejpam-4144	403	10	or	or	CCONJ
ejpam-4144	403	11	s′	s′	ADJ
ejpam-4144	403	12	∩	∩	ADJ
ejpam-4144	403	13	v	v	ADJ
ejpam-4144	403	14	(	(	PUNCT
ejpam-4144	403	15	g	g	NOUN
ejpam-4144	403	16	)	)	PUNCT
ejpam-4144	403	17	=	=	NOUN
ejpam-4144	403	18	∅	∅	NOUN
ejpam-4144	403	19	,	,	PUNCT
ejpam-4144	403	20	then	then	ADV
ejpam-4144	403	21	|s′|	|s′|	NOUN
ejpam-4144	403	22	=	=	SYM
ejpam-4144	403	23	|v	|v	PROPN
ejpam-4144	403	24	(	(	PUNCT
ejpam-4144	403	25	g)|	g)|	PROPN
ejpam-4144	403	26	=	=	SYM
ejpam-4144	403	27	∑k	∑k	PROPN
ejpam-4144	403	28	i=1mi	i=1mi	X
ejpam-4144	403	29	≥	≥	NOUN
ejpam-4144	403	30	2k	2k	X
ejpam-4144	403	31	>	>	X
ejpam-4144	403	32	k	k	PROPN
ejpam-4144	404	1	+	+	PUNCT
ejpam-4144	404	2	1	1	NUM
ejpam-4144	404	3	which	which	PRON
ejpam-4144	404	4	is	be	AUX
ejpam-4144	404	5	not	not	PART
ejpam-4144	404	6	possible	possible	ADJ
ejpam-4144	404	7	.	.	PUNCT
ejpam-4144	405	1	thus	thus	ADV
ejpam-4144	405	2	,	,	PUNCT
ejpam-4144	405	3	s′	s′	ADJ
ejpam-4144	405	4	∩	∩	ADJ
ejpam-4144	405	5	v	v	NOUN
ejpam-4144	405	6	(	(	PUNCT
ejpam-4144	405	7	g	g	NOUN
ejpam-4144	405	8	)	)	PUNCT
ejpam-4144	405	9	̸=	̸=	PROPN
ejpam-4144	405	10	∅	∅	NOUN
ejpam-4144	405	11	and	and	CCONJ
ejpam-4144	405	12	s′	s′	ADJ
ejpam-4144	405	13	∩	∩	NOUN
ejpam-4144	405	14	v	v	ADJ
ejpam-4144	405	15	(	(	PUNCT
ejpam-4144	405	16	g	g	NOUN
ejpam-4144	405	17	)	)	PUNCT
ejpam-4144	405	18	̸=	̸=	PROPN
ejpam-4144	405	19	∅.	∅.	VERB
ejpam-4144	405	20	clearly	clearly	ADV
ejpam-4144	405	21	,	,	PUNCT
ejpam-4144	405	22	s′	s′	ADJ
ejpam-4144	405	23	∩	∩	NOUN
ejpam-4144	405	24	(	(	PUNCT
ejpam-4144	405	25	ui	ui	PROPN
ejpam-4144	405	26	∪	∪	PROPN
ejpam-4144	405	27	u	u	PROPN
ejpam-4144	405	28	i	i	NOUN
ejpam-4144	405	29	)	)	PUNCT
ejpam-4144	405	30	̸=	̸=	PROPN
ejpam-4144	405	31	∅	∅	NOUN
ejpam-4144	405	32	for	for	ADP
ejpam-4144	405	33	all	all	PRON
ejpam-4144	405	34	i	i	PRON
ejpam-4144	405	35	∈	∈	PROPN
ejpam-4144	405	36	{	{	PUNCT
ejpam-4144	405	37	1	1	NUM
ejpam-4144	405	38	,	,	PUNCT
ejpam-4144	405	39	2	2	NUM
ejpam-4144	405	40	,	,	PUNCT
ejpam-4144	405	41	.	.	PUNCT
ejpam-4144	405	42	.	.	PUNCT
ejpam-4144	405	43	.	.	PUNCT
ejpam-4144	406	1	,	,	PUNCT
ejpam-4144	406	2	k	k	X
ejpam-4144	406	3	}	}	PUNCT
ejpam-4144	406	4	.	.	PUNCT
ejpam-4144	407	1	suppose	suppose	VERB
ejpam-4144	407	2	s′	s′	ADJ
ejpam-4144	407	3	∩	∩	ADJ
ejpam-4144	407	4	u1	u1	NOUN
ejpam-4144	407	5	̸=	̸=	PROPN
ejpam-4144	407	6	∅.	∅.	ADV
ejpam-4144	407	7	if	if	SCONJ
ejpam-4144	407	8	|s′	|s′	NOUN
ejpam-4144	407	9	∩	∩	NOUN
ejpam-4144	407	10	u1|	u1|	PROPN
ejpam-4144	407	11	=	=	SYM
ejpam-4144	407	12	1	1	NUM
ejpam-4144	407	13	,	,	PUNCT
ejpam-4144	407	14	say	say	VERB
ejpam-4144	407	15	v	v	ADP
ejpam-4144	407	16	∈	∈	PROPN
ejpam-4144	407	17	s′	s′	ADJ
ejpam-4144	407	18	∩	∩	ADJ
ejpam-4144	407	19	u1	u1	NOUN
ejpam-4144	407	20	,	,	PUNCT
ejpam-4144	407	21	then	then	ADV
ejpam-4144	407	22	v	v	X
ejpam-4144	407	23	(	(	PUNCT
ejpam-4144	407	24	g	g	NOUN
ejpam-4144	407	25	)	)	PUNCT
ejpam-4144	407	26	\	\	NOUN
ejpam-4144	408	1	{	{	PUNCT
ejpam-4144	408	2	u	u	NOUN
ejpam-4144	408	3	,	,	PUNCT
ejpam-4144	408	4	v	v	NOUN
ejpam-4144	408	5	}	}	PUNCT
ejpam-4144	408	6	⊆	⊆	NUM
ejpam-4144	408	7	ngg(v	ngg(v	NOUN
ejpam-4144	408	8	)	)	PUNCT
ejpam-4144	408	9	.	.	PUNCT
ejpam-4144	409	1	since	since	SCONJ
ejpam-4144	409	2	s′	s′	ADJ
ejpam-4144	409	3	is	be	AUX
ejpam-4144	409	4	a	a	DET
ejpam-4144	409	5	γ	γ	NOUN
ejpam-4144	409	6	-	-	PUNCT
ejpam-4144	409	7	set	set	NOUN
ejpam-4144	409	8	of	of	ADP
ejpam-4144	409	9	gg	gg	NOUN
ejpam-4144	409	10	and	and	CCONJ
ejpam-4144	409	11	u	u	PROPN
ejpam-4144	409	12	/∈	/∈	PROPN
ejpam-4144	409	13	s′	s′	ADJ
ejpam-4144	409	14	,	,	PUNCT
ejpam-4144	409	15	|s′	|s′	NOUN
ejpam-4144	409	16	∩	∩	ADJ
ejpam-4144	409	17	u1|	u1|	PROPN
ejpam-4144	409	18	=	=	SYM
ejpam-4144	409	19	1	1	X
ejpam-4144	409	20	.	.	PUNCT
ejpam-4144	410	1	we	we	PRON
ejpam-4144	410	2	may	may	AUX
ejpam-4144	410	3	assume	assume	VERB
ejpam-4144	410	4	that	that	SCONJ
ejpam-4144	410	5	u	u	PROPN
ejpam-4144	410	6	∈	∈	PROPN
ejpam-4144	410	7	s′.	s′.	INTJ
ejpam-4144	410	8	let	let	VERB
ejpam-4144	410	9	j	j	PROPN
ejpam-4144	410	10	∈	∈	PROPN
ejpam-4144	410	11	{	{	PUNCT
ejpam-4144	410	12	2	2	NUM
ejpam-4144	410	13	,	,	PUNCT
ejpam-4144	410	14	3	3	NUM
ejpam-4144	410	15	,	,	PUNCT
ejpam-4144	410	16	.	.	PUNCT
ejpam-4144	410	17	.	.	PUNCT
ejpam-4144	410	18	.	.	PUNCT
ejpam-4144	411	1	,	,	PUNCT
ejpam-4144	411	2	k	k	X
ejpam-4144	411	3	}	}	PUNCT
ejpam-4144	411	4	and	and	CCONJ
ejpam-4144	411	5	suppose	suppose	VERB
ejpam-4144	411	6	that	that	SCONJ
ejpam-4144	411	7	s	s	VERB
ejpam-4144	411	8	∩	∩	ADJ
ejpam-4144	411	9	u	u	NOUN
ejpam-4144	411	10	j	j	NOUN
ejpam-4144	411	11	=	=	PUNCT
ejpam-4144	411	12	∅.	∅.	PROPN
ejpam-4144	411	13	then	then	ADV
ejpam-4144	411	14	necessarily	necessarily	ADV
ejpam-4144	411	15	,	,	PUNCT
ejpam-4144	411	16	uj	uj	PROPN
ejpam-4144	411	17	⊆	⊆	NUM
ejpam-4144	411	18	s′.	s′.	PROPN
ejpam-4144	411	19	pick	pick	VERB
ejpam-4144	411	20	any	any	DET
ejpam-4144	411	21	w	w	PROPN
ejpam-4144	411	22	∈	∈	PROPN
ejpam-4144	411	23	u	u	NOUN
ejpam-4144	411	24	j	j	PROPN
ejpam-4144	411	25	and	and	CCONJ
ejpam-4144	411	26	let	let	VERB
ejpam-4144	411	27	sw	sw	PROPN
ejpam-4144	411	28	=	=	SYM
ejpam-4144	411	29	(	(	PUNCT
ejpam-4144	411	30	s′	s′	X
ejpam-4144	411	31	\uj)∪	\uj)∪	NOUN
ejpam-4144	411	32	{	{	PUNCT
ejpam-4144	411	33	w	w	NOUN
ejpam-4144	411	34	}	}	PUNCT
ejpam-4144	411	35	.	.	PUNCT
ejpam-4144	412	1	then	then	ADV
ejpam-4144	412	2	sw	sw	PROPN
ejpam-4144	412	3	is	be	AUX
ejpam-4144	412	4	a	a	DET
ejpam-4144	412	5	dominating	dominating	NOUN
ejpam-4144	412	6	set	set	NOUN
ejpam-4144	412	7	of	of	ADP
ejpam-4144	412	8	gg	gg	PROPN
ejpam-4144	412	9	.	.	PUNCT
ejpam-4144	413	1	since	since	SCONJ
ejpam-4144	413	2	|uj	|uj	PROPN
ejpam-4144	413	3	|	|	ADV
ejpam-4144	413	4	≥	≥	NUM
ejpam-4144	413	5	2	2	NUM
ejpam-4144	413	6	,	,	PUNCT
ejpam-4144	413	7	γ(gg	γ(gg	NUM
ejpam-4144	413	8	)	)	PUNCT
ejpam-4144	413	9	=	=	PUNCT
ejpam-4144	413	10	|s′|	|s′|	NOUN
ejpam-4144	413	11	>	>	X
ejpam-4144	413	12	|sw|	|sw|	PROPN
ejpam-4144	413	13	,	,	PUNCT
ejpam-4144	413	14	a	a	DET
ejpam-4144	413	15	contradiction	contradiction	NOUN
ejpam-4144	413	16	.	.	PUNCT
ejpam-4144	414	1	therefore	therefore	ADV
ejpam-4144	414	2	,	,	PUNCT
ejpam-4144	414	3	s′	s′	ADJ
ejpam-4144	414	4	∩	∩	ADJ
ejpam-4144	414	5	u	u	PROPN
ejpam-4144	414	6	j	j	PROPN
ejpam-4144	414	7	̸=	̸=	PROPN
ejpam-4144	414	8	∅	∅	NOUN
ejpam-4144	414	9	for	for	ADP
ejpam-4144	414	10	each	each	DET
ejpam-4144	414	11	j	j	PROPN
ejpam-4144	414	12	∈	∈	PROPN
ejpam-4144	414	13	{	{	PUNCT
ejpam-4144	414	14	2	2	NUM
ejpam-4144	414	15	,	,	PUNCT
ejpam-4144	414	16	3	3	NUM
ejpam-4144	414	17	,	,	PUNCT
ejpam-4144	414	18	.	.	PUNCT
ejpam-4144	414	19	.	.	PUNCT
ejpam-4144	414	20	.	.	PUNCT
ejpam-4144	415	1	,	,	PUNCT
ejpam-4144	415	2	k	k	X
ejpam-4144	415	3	}	}	PUNCT
ejpam-4144	415	4	.	.	PUNCT
ejpam-4144	416	1	moreover	moreover	ADV
ejpam-4144	416	2	,	,	PUNCT
ejpam-4144	416	3	because	because	SCONJ
ejpam-4144	416	4	s′	s′	ADJ
ejpam-4144	416	5	is	be	AUX
ejpam-4144	416	6	a	a	DET
ejpam-4144	416	7	γ	γ	NOUN
ejpam-4144	416	8	-	-	PUNCT
ejpam-4144	416	9	set	set	NOUN
ejpam-4144	416	10	of	of	ADP
ejpam-4144	416	11	gg	gg	NOUN
ejpam-4144	416	12	,	,	PUNCT
ejpam-4144	416	13	|s′	|s′	NOUN
ejpam-4144	416	14	∩	∩	ADJ
ejpam-4144	416	15	u	u	NOUN
ejpam-4144	416	16	j	j	PROPN
ejpam-4144	417	1	|	|	ADV
ejpam-4144	417	2	=	=	NOUN
ejpam-4144	417	3	1	1	NUM
ejpam-4144	417	4	for	for	ADP
ejpam-4144	417	5	all	all	DET
ejpam-4144	417	6	j	j	PROPN
ejpam-4144	417	7	∈	∈	PROPN
ejpam-4144	417	8	{	{	PUNCT
ejpam-4144	417	9	2	2	NUM
ejpam-4144	417	10	,	,	PUNCT
ejpam-4144	417	11	3	3	NUM
ejpam-4144	417	12	,	,	PUNCT
ejpam-4144	417	13	.	.	PUNCT
ejpam-4144	417	14	.	.	PUNCT
ejpam-4144	417	15	.	.	PUNCT
ejpam-4144	418	1	,	,	PUNCT
ejpam-4144	418	2	k	k	X
ejpam-4144	418	3	}	}	PUNCT
ejpam-4144	418	4	.	.	PUNCT
ejpam-4144	419	1	thus	thus	ADV
ejpam-4144	419	2	,	,	PUNCT
ejpam-4144	419	3	γ(gg	γ(gg	ADJ
ejpam-4144	419	4	)	)	PUNCT
ejpam-4144	419	5	=	=	PUNCT
ejpam-4144	419	6	|s′|	|s′|	NOUN
ejpam-4144	419	7	≥	≥	PROPN
ejpam-4144	419	8	k	k	PROPN
ejpam-4144	420	1	+	+	NOUN
ejpam-4144	420	2	1	1	X
ejpam-4144	420	3	.	.	X
ejpam-4144	421	1	if	if	SCONJ
ejpam-4144	421	2	|s′	|s′	PROPN
ejpam-4144	421	3	∩	∩	NOUN
ejpam-4144	421	4	u1|	u1|	PROPN
ejpam-4144	421	5	=	=	SYM
ejpam-4144	421	6	2	2	NUM
ejpam-4144	421	7	,	,	PUNCT
ejpam-4144	421	8	then	then	ADV
ejpam-4144	421	9	s′	s′	ADJ
ejpam-4144	421	10	∩	∩	ADJ
ejpam-4144	421	11	u1	u1	NOUN
ejpam-4144	421	12	=	=	PUNCT
ejpam-4144	421	13	∅.	∅.	NOUN
ejpam-4144	421	14	since	since	SCONJ
ejpam-4144	421	15	s′	s′	ADJ
ejpam-4144	421	16	∩	∩	NOUN
ejpam-4144	421	17	(	(	PUNCT
ejpam-4144	421	18	ui	ui	PROPN
ejpam-4144	421	19	∪	∪	PROPN
ejpam-4144	421	20	u	u	PROPN
ejpam-4144	421	21	i	i	NOUN
ejpam-4144	421	22	)	)	PUNCT
ejpam-4144	421	23	̸=	̸=	PROPN
ejpam-4144	421	24	∅	∅	NOUN
ejpam-4144	421	25	for	for	ADP
ejpam-4144	421	26	all	all	PRON
ejpam-4144	421	27	i	i	PRON
ejpam-4144	421	28	∈	∈	PROPN
ejpam-4144	421	29	{	{	PUNCT
ejpam-4144	421	30	2	2	NUM
ejpam-4144	421	31	,	,	PUNCT
ejpam-4144	421	32	.	.	PUNCT
ejpam-4144	421	33	.	.	PUNCT
ejpam-4144	421	34	.	.	PUNCT
ejpam-4144	422	1	,	,	PUNCT
ejpam-4144	422	2	k	k	X
ejpam-4144	422	3	}	}	PUNCT
ejpam-4144	422	4	,	,	PUNCT
ejpam-4144	422	5	it	it	PRON
ejpam-4144	422	6	follows	follow	VERB
ejpam-4144	422	7	that	that	SCONJ
ejpam-4144	422	8	γ(gg	γ(gg	ADJ
ejpam-4144	422	9	)	)	PUNCT
ejpam-4144	422	10	=	=	PUNCT
ejpam-4144	422	11	|s′|	|s′|	NOUN
ejpam-4144	422	12	≥	≥	PROPN
ejpam-4144	422	13	k	k	PROPN
ejpam-4144	423	1	+	+	CCONJ
ejpam-4144	423	2	1	1	X
ejpam-4144	423	3	.	.	PUNCT
ejpam-4144	423	4	suppose	suppose	VERB
ejpam-4144	423	5	now	now	ADV
ejpam-4144	423	6	that	that	SCONJ
ejpam-4144	423	7	s′	s′	ADJ
ejpam-4144	423	8	∩	∩	ADJ
ejpam-4144	423	9	u1	u1	NOUN
ejpam-4144	423	10	=	=	PUNCT
ejpam-4144	423	11	∅.	∅.	NOUN
ejpam-4144	423	12	if	if	SCONJ
ejpam-4144	423	13	|s′	|s′	ADJ
ejpam-4144	423	14	∩	∩	NOUN
ejpam-4144	423	15	u1|	u1|	PROPN
ejpam-4144	423	16	=	=	SYM
ejpam-4144	423	17	1	1	NUM
ejpam-4144	423	18	,	,	PUNCT
ejpam-4144	423	19	then	then	ADV
ejpam-4144	423	20	there	there	PRON
ejpam-4144	423	21	exists	exist	VERB
ejpam-4144	423	22	j	j	PROPN
ejpam-4144	423	23	̸=	̸=	PROPN
ejpam-4144	423	24	1	1	NUM
ejpam-4144	423	25	such	such	ADJ
ejpam-4144	423	26	that	that	SCONJ
ejpam-4144	423	27	s′	s′	ADJ
ejpam-4144	423	28	∩	∩	ADJ
ejpam-4144	423	29	uj	uj	PROPN
ejpam-4144	423	30	̸=	̸=	PROPN
ejpam-4144	423	31	∅.	∅.	ADV
ejpam-4144	423	32	if	if	SCONJ
ejpam-4144	423	33	|s′	|s′	PROPN
ejpam-4144	423	34	∩	∩	X
ejpam-4144	423	35	uj	uj	NOUN
ejpam-4144	423	36	|	|	ADV
ejpam-4144	423	37	=	=	SYM
ejpam-4144	423	38	1	1	NUM
ejpam-4144	423	39	,	,	PUNCT
ejpam-4144	423	40	then	then	ADV
ejpam-4144	423	41	|s′	|s′	NOUN
ejpam-4144	423	42	∩	∩	ADJ
ejpam-4144	423	43	u	u	NOUN
ejpam-4144	423	44	j	j	PROPN
ejpam-4144	423	45	|	|	ADV
ejpam-4144	423	46	=	=	NOUN
ejpam-4144	423	47	̸	̸	NUM
ejpam-4144	423	48	0	0	NUM
ejpam-4144	423	49	.	.	PUNCT
ejpam-4144	424	1	since	since	SCONJ
ejpam-4144	424	2	s′	s′	ADJ
ejpam-4144	424	3	∩	∩	NOUN
ejpam-4144	424	4	(	(	PUNCT
ejpam-4144	424	5	ui	ui	PROPN
ejpam-4144	424	6	∪	∪	PROPN
ejpam-4144	424	7	u	u	PROPN
ejpam-4144	424	8	i	i	NOUN
ejpam-4144	424	9	)	)	PUNCT
ejpam-4144	424	10	̸=	̸=	PROPN
ejpam-4144	424	11	∅	∅	NOUN
ejpam-4144	424	12	for	for	ADP
ejpam-4144	424	13	all	all	PRON
ejpam-4144	424	14	i	i	PRON
ejpam-4144	424	15	∈	∈	PROPN
ejpam-4144	424	16	{	{	PUNCT
ejpam-4144	424	17	2	2	NUM
ejpam-4144	424	18	,	,	PUNCT
ejpam-4144	424	19	.	.	PUNCT
ejpam-4144	424	20	.	.	PUNCT
ejpam-4144	424	21	.	.	PUNCT
ejpam-4144	425	1	,	,	PUNCT
ejpam-4144	425	2	j	j	PROPN
ejpam-4144	425	3	−	−	PROPN
ejpam-4144	425	4	1	1	NUM
ejpam-4144	425	5	,	,	PUNCT
ejpam-4144	425	6	j	j	PROPN
ejpam-4144	425	7	+	+	PROPN
ejpam-4144	425	8	2	2	NUM
ejpam-4144	425	9	,	,	PUNCT
ejpam-4144	425	10	.	.	PUNCT
ejpam-4144	425	11	.	.	PUNCT
ejpam-4144	426	1	.	.	PUNCT
ejpam-4144	427	1	,	,	PUNCT
ejpam-4144	427	2	k	k	X
ejpam-4144	427	3	}	}	PUNCT
ejpam-4144	427	4	,	,	PUNCT
ejpam-4144	427	5	it	it	PRON
ejpam-4144	427	6	follows	follow	VERB
ejpam-4144	427	7	that	that	SCONJ
ejpam-4144	427	8	γ(gg	γ(gg	ADJ
ejpam-4144	427	9	)	)	PUNCT
ejpam-4144	427	10	=	=	PUNCT
ejpam-4144	427	11	|s′|	|s′|	NOUN
ejpam-4144	427	12	≥	≥	PROPN
ejpam-4144	427	13	k	k	PROPN
ejpam-4144	428	1	+	+	NOUN
ejpam-4144	428	2	1	1	X
ejpam-4144	428	3	.	.	X
ejpam-4144	429	1	if	if	SCONJ
ejpam-4144	429	2	|s′	|s′	PROPN
ejpam-4144	429	3	∩	∩	X
ejpam-4144	429	4	uj	uj	PROPN
ejpam-4144	429	5	|	|	ADV
ejpam-4144	429	6	≥	≥	NUM
ejpam-4144	429	7	2	2	NUM
ejpam-4144	429	8	,	,	PUNCT
ejpam-4144	429	9	then	then	ADV
ejpam-4144	429	10	clearly	clearly	ADV
ejpam-4144	429	11	,	,	PUNCT
ejpam-4144	429	12	γ(gg	γ(gg	NUM
ejpam-4144	429	13	)	)	PUNCT
ejpam-4144	429	14	=	=	PUNCT
ejpam-4144	429	15	|s′|	|s′|	NOUN
ejpam-4144	429	16	≥	≥	PROPN
ejpam-4144	429	17	k	k	PROPN
ejpam-4144	430	1	+	+	CCONJ
ejpam-4144	430	2	1	1	X
ejpam-4144	430	3	.	.	X
ejpam-4144	430	4	therefore	therefore	ADV
ejpam-4144	430	5	,	,	PUNCT
ejpam-4144	430	6	γ(gg	γ(gg	ADJ
ejpam-4144	430	7	)	)	PUNCT
ejpam-4144	430	8	=	=	SYM
ejpam-4144	431	1	k	k	PROPN
ejpam-4144	432	1	+	+	NOUN
ejpam-4144	432	2	1	1	X
ejpam-4144	432	3	.	.	PUNCT
ejpam-4144	432	4	finally	finally	ADV
ejpam-4144	432	5	,	,	PUNCT
ejpam-4144	432	6	let	let	VERB
ejpam-4144	432	7	m1	m1	PROPN
ejpam-4144	432	8	≥	≥	PRON
ejpam-4144	432	9	3	3	X
ejpam-4144	432	10	.	.	PUNCT
ejpam-4144	433	1	let	let	VERB
ejpam-4144	433	2	s	s	PRON
ejpam-4144	433	3	be	be	AUX
ejpam-4144	433	4	a	a	DET
ejpam-4144	433	5	γ	γ	NOUN
ejpam-4144	433	6	-	-	PUNCT
ejpam-4144	433	7	set	set	NOUN
ejpam-4144	433	8	of	of	ADP
ejpam-4144	433	9	gg	gg	PROPN
ejpam-4144	433	10	.	.	PUNCT
ejpam-4144	434	1	since	since	SCONJ
ejpam-4144	434	2	γ(gg	γ(gg	NUM
ejpam-4144	434	3	)	)	PUNCT
ejpam-4144	434	4	≤	≤	NOUN
ejpam-4144	434	5	k+2	k+2	PROPN
ejpam-4144	434	6	(	(	PUNCT
ejpam-4144	434	7	by	by	ADP
ejpam-4144	434	8	theorem	theorem	NOUN
ejpam-4144	434	9	4	4	NUM
ejpam-4144	434	10	)	)	PUNCT
ejpam-4144	434	11	and	and	CCONJ
ejpam-4144	434	12	|v	|v	PROPN
ejpam-4144	434	13	(	(	PUNCT
ejpam-4144	434	14	g)|	g)|	PROPN
ejpam-4144	434	15	=	=	SYM
ejpam-4144	434	16	∑k	∑k	PROPN
ejpam-4144	434	17	i=1mi	i=1mi	X
ejpam-4144	434	18	>	>	PUNCT
ejpam-4144	435	1	k	k	PROPN
ejpam-4144	436	1	+	+	CCONJ
ejpam-4144	436	2	2	2	NUM
ejpam-4144	436	3	,	,	PUNCT
ejpam-4144	436	4	s	s	VERB
ejpam-4144	436	5	∩	∩	ADJ
ejpam-4144	436	6	v	v	ADJ
ejpam-4144	436	7	(	(	PUNCT
ejpam-4144	436	8	g	g	NOUN
ejpam-4144	436	9	)	)	PUNCT
ejpam-4144	436	10	̸=	̸=	PROPN
ejpam-4144	436	11	∅	∅	NOUN
ejpam-4144	436	12	and	and	CCONJ
ejpam-4144	436	13	s	s	VERB
ejpam-4144	436	14	∩	∩	ADJ
ejpam-4144	436	15	v	v	ADJ
ejpam-4144	436	16	(	(	PUNCT
ejpam-4144	436	17	g	g	NOUN
ejpam-4144	436	18	)	)	PUNCT
ejpam-4144	436	19	̸=	̸=	PROPN
ejpam-4144	436	20	∅.	∅.	PRON
ejpam-4144	436	21	again	again	ADV
ejpam-4144	436	22	,	,	PUNCT
ejpam-4144	436	23	s	s	VERB
ejpam-4144	436	24	∩	∩	NOUN
ejpam-4144	436	25	(	(	PUNCT
ejpam-4144	436	26	ui	ui	PROPN
ejpam-4144	436	27	∪	∪	PROPN
ejpam-4144	436	28	u	u	PROPN
ejpam-4144	436	29	i	i	NOUN
ejpam-4144	436	30	)	)	PUNCT
ejpam-4144	436	31	̸=	̸=	PROPN
ejpam-4144	436	32	∅	∅	NOUN
ejpam-4144	436	33	for	for	ADP
ejpam-4144	436	34	each	each	DET
ejpam-4144	436	35	i	i	PRON
ejpam-4144	436	36	∈	∈	PROPN
ejpam-4144	436	37	{	{	PUNCT
ejpam-4144	436	38	1	1	NUM
ejpam-4144	436	39	,	,	PUNCT
ejpam-4144	436	40	2	2	NUM
ejpam-4144	436	41	,	,	PUNCT
ejpam-4144	436	42	.	.	PUNCT
ejpam-4144	436	43	.	.	PUNCT
ejpam-4144	437	1	.	.	PUNCT
ejpam-4144	438	1	,	,	PUNCT
ejpam-4144	438	2	k	k	X
ejpam-4144	438	3	}	}	PUNCT
ejpam-4144	438	4	.	.	PUNCT
ejpam-4144	439	1	suppose	suppose	VERB
ejpam-4144	439	2	s	s	VERB
ejpam-4144	439	3	∩	∩	ADJ
ejpam-4144	439	4	u1	u1	NOUN
ejpam-4144	439	5	=	=	PUNCT
ejpam-4144	439	6	∅.	∅.	NOUN
ejpam-4144	439	7	then	then	ADV
ejpam-4144	439	8	s	s	PART
ejpam-4144	439	9	∩	∩	ADJ
ejpam-4144	439	10	u1	u1	NOUN
ejpam-4144	439	11	̸=	̸=	PROPN
ejpam-4144	439	12	∅.	∅.	ADV
ejpam-4144	439	13	if	if	SCONJ
ejpam-4144	439	14	|s	|s	PROPN
ejpam-4144	439	15	∩	∩	NOUN
ejpam-4144	439	16	u1|	u1|	PROPN
ejpam-4144	439	17	≥	≥	NOUN
ejpam-4144	439	18	3	3	NUM
ejpam-4144	439	19	,	,	PUNCT
ejpam-4144	439	20	then	then	ADV
ejpam-4144	439	21	γ(gg	γ(gg	NUM
ejpam-4144	439	22	)	)	PUNCT
ejpam-4144	439	23	=	=	SYM
ejpam-4144	439	24	|s|	|s|	PROPN
ejpam-4144	439	25	≥	≥	NOUN
ejpam-4144	439	26	k	k	NOUN
ejpam-4144	440	1	+	+	CCONJ
ejpam-4144	440	2	2	2	X
ejpam-4144	440	3	.	.	PUNCT
ejpam-4144	440	4	so	so	ADV
ejpam-4144	440	5	suppose	suppose	VERB
ejpam-4144	440	6	that	that	SCONJ
ejpam-4144	440	7	|s	|s	PROPN
ejpam-4144	440	8	∩	∩	NOUN
ejpam-4144	440	9	u1|	u1|	PROPN
ejpam-4144	440	10	≤	≤	ADJ
ejpam-4144	440	11	2	2	NUM
ejpam-4144	440	12	.	.	PUNCT
ejpam-4144	441	1	then	then	ADV
ejpam-4144	441	2	there	there	PRON
ejpam-4144	441	3	exists	exist	VERB
ejpam-4144	441	4	j	j	PROPN
ejpam-4144	441	5	̸=	̸=	PROPN
ejpam-4144	441	6	1	1	NUM
ejpam-4144	441	7	such	such	ADJ
ejpam-4144	441	8	that	that	PRON
ejpam-4144	441	9	s	s	VERB
ejpam-4144	441	10	∩uj	∩uj	NOUN
ejpam-4144	441	11	̸=	̸=	PROPN
ejpam-4144	441	12	∅.	∅.	ADV
ejpam-4144	441	13	if	if	SCONJ
ejpam-4144	441	14	s	s	NOUN
ejpam-4144	441	15	∩uj	∩uj	NOUN
ejpam-4144	441	16	=	=	SYM
ejpam-4144	441	17	uj	uj	PROPN
ejpam-4144	441	18	,	,	PUNCT
ejpam-4144	441	19	then	then	ADV
ejpam-4144	441	20	γ(gg	γ(gg	NUM
ejpam-4144	441	21	)	)	PUNCT
ejpam-4144	441	22	=	=	SYM
ejpam-4144	441	23	|s|	|s|	PROPN
ejpam-4144	441	24	≥	≥	NOUN
ejpam-4144	441	25	k	k	NOUN
ejpam-4144	442	1	+	+	PROPN
ejpam-4144	442	2	2	2	X
ejpam-4144	442	3	.	.	X
ejpam-4144	443	1	if	if	SCONJ
ejpam-4144	443	2	s	s	PRON
ejpam-4144	443	3	∩uj	∩uj	NOUN
ejpam-4144	443	4	̸=	̸=	PROPN
ejpam-4144	443	5	uj	uj	PROPN
ejpam-4144	443	6	,	,	PUNCT
ejpam-4144	443	7	then	then	ADV
ejpam-4144	443	8	s	s	VERB
ejpam-4144	443	9	∩u	∩u	ADJ
ejpam-4144	443	10	j	j	PROPN
ejpam-4144	443	11	̸=	̸=	PROPN
ejpam-4144	443	12	∅.	∅.	PRON
ejpam-4144	443	13	hence	hence	ADV
ejpam-4144	443	14	,	,	PUNCT
ejpam-4144	443	15	if	if	SCONJ
ejpam-4144	443	16	|s∩u1|	|s∩u1|	ADV
ejpam-4144	443	17	=	=	SYM
ejpam-4144	443	18	2	2	NUM
ejpam-4144	443	19	,	,	PUNCT
ejpam-4144	443	20	then	then	ADV
ejpam-4144	443	21	γ(gg	γ(gg	NUM
ejpam-4144	443	22	)	)	PUNCT
ejpam-4144	443	23	=	=	SYM
ejpam-4144	443	24	|s|	|s|	PROPN
ejpam-4144	443	25	≥	≥	NOUN
ejpam-4144	443	26	k+2	k+2	NUM
ejpam-4144	443	27	.	.	PROPN
ejpam-4144	443	28	suppose	suppose	VERB
ejpam-4144	443	29	now	now	ADV
ejpam-4144	443	30	that	that	SCONJ
ejpam-4144	443	31	|s∩u1|	|s∩u1|	NOUN
ejpam-4144	443	32	=	=	SYM
ejpam-4144	443	33	1	1	X
ejpam-4144	443	34	.	.	PUNCT
ejpam-4144	443	35	suppose	suppose	VERB
ejpam-4144	443	36	further	far	ADV
ejpam-4144	443	37	that	that	SCONJ
ejpam-4144	443	38	|s	|s	PROPN
ejpam-4144	443	39	∩	∩	NOUN
ejpam-4144	443	40	(	(	PUNCT
ejpam-4144	443	41	uj	uj	PROPN
ejpam-4144	443	42	∪	∪	PROPN
ejpam-4144	443	43	u	u	PROPN
ejpam-4144	443	44	j)|	j)|	NOUN
ejpam-4144	443	45	=	=	SYM
ejpam-4144	443	46	2	2	X
ejpam-4144	443	47	.	.	PUNCT
ejpam-4144	443	48	then	then	ADV
ejpam-4144	443	49	there	there	PRON
ejpam-4144	443	50	exists	exist	VERB
ejpam-4144	443	51	r	r	PROPN
ejpam-4144	443	52	̸=	̸=	PROPN
ejpam-4144	443	53	1	1	NUM
ejpam-4144	443	54	,	,	PUNCT
ejpam-4144	443	55	j	j	PROPN
ejpam-4144	443	56	such	such	ADJ
ejpam-4144	443	57	that	that	SCONJ
ejpam-4144	443	58	|s	|s	PROPN
ejpam-4144	443	59	∩	∩	NOUN
ejpam-4144	443	60	(	(	PUNCT
ejpam-4144	443	61	ur	ur	INTJ
ejpam-4144	443	62	∪	∪	PROPN
ejpam-4144	443	63	u	u	PROPN
ejpam-4144	443	64	r)|	r)|	ADJ
ejpam-4144	443	65	≥	≥	NOUN
ejpam-4144	443	66	2	2	NUM
ejpam-4144	443	67	.	.	PUNCT
ejpam-4144	444	1	thus	thus	ADV
ejpam-4144	444	2	,	,	PUNCT
ejpam-4144	444	3	γ(gg	γ(gg	NUM
ejpam-4144	444	4	)	)	PUNCT
ejpam-4144	444	5	=	=	SYM
ejpam-4144	444	6	|s|	|s|	PROPN
ejpam-4144	444	7	≥	≥	NOUN
ejpam-4144	444	8	k	k	NOUN
ejpam-4144	445	1	+	+	CCONJ
ejpam-4144	445	2	2	2	X
ejpam-4144	445	3	.	.	PUNCT
ejpam-4144	445	4	next	next	ADV
ejpam-4144	445	5	,	,	PUNCT
ejpam-4144	445	6	suppose	suppose	VERB
ejpam-4144	445	7	that	that	SCONJ
ejpam-4144	445	8	s	s	VERB
ejpam-4144	445	9	∩	∩	ADJ
ejpam-4144	445	10	u1	u1	NOUN
ejpam-4144	445	11	̸=	̸=	PROPN
ejpam-4144	445	12	∅.	∅.	ADV
ejpam-4144	445	13	suppose	suppose	VERB
ejpam-4144	445	14	s	s	SYM
ejpam-4144	445	15	∩	∩	ADJ
ejpam-4144	445	16	uj	uj	PROPN
ejpam-4144	445	17	=	=	NOUN
ejpam-4144	445	18	∅	∅	NOUN
ejpam-4144	445	19	for	for	ADP
ejpam-4144	445	20	all	all	DET
ejpam-4144	445	21	j	j	PROPN
ejpam-4144	445	22	≥	≥	NUM
ejpam-4144	445	23	2	2	NUM
ejpam-4144	445	24	.	.	PUNCT
ejpam-4144	446	1	since	since	SCONJ
ejpam-4144	446	2	s	s	PROPN
ejpam-4144	446	3	is	be	AUX
ejpam-4144	446	4	a	a	DET
ejpam-4144	446	5	γ	γ	NOUN
ejpam-4144	446	6	-	-	PUNCT
ejpam-4144	446	7	set	set	NOUN
ejpam-4144	446	8	of	of	ADP
ejpam-4144	446	9	gg	gg	PROPN
ejpam-4144	446	10	and	and	CCONJ
ejpam-4144	446	11	uj	uj	VERB
ejpam-4144	446	12	⊆	⊆	NUM
ejpam-4144	446	13	ngg(s	ngg(s	NOUN
ejpam-4144	446	14	∩	∩	ADJ
ejpam-4144	446	15	u1	u1	NOUN
ejpam-4144	446	16	)	)	PUNCT
ejpam-4144	446	17	for	for	ADP
ejpam-4144	446	18	all	all	DET
ejpam-4144	446	19	j	j	PROPN
ejpam-4144	446	20	≥	≥	NUM
ejpam-4144	446	21	2	2	NUM
ejpam-4144	446	22	,	,	PUNCT
ejpam-4144	446	23	|s	|s	PROPN
ejpam-4144	446	24	∩	∩	PROPN
ejpam-4144	446	25	u	u	NOUN
ejpam-4144	446	26	j	j	PROPN
ejpam-4144	446	27	|	|	ADV
ejpam-4144	446	28	=	=	NOUN
ejpam-4144	446	29	1	1	NUM
ejpam-4144	446	30	for	for	ADP
ejpam-4144	446	31	all	all	DET
ejpam-4144	446	32	j	j	PROPN
ejpam-4144	446	33	≥	≥	NUM
ejpam-4144	446	34	2	2	NUM
ejpam-4144	446	35	and	and	CCONJ
ejpam-4144	446	36	|s|	|s|	PROPN
ejpam-4144	446	37	=	=	SYM
ejpam-4144	446	38	k−1	k−1	PROPN
ejpam-4144	446	39	+	+	X
ejpam-4144	446	40	|u1|	|u1|	ADJ
ejpam-4144	446	41	.	.	PUNCT
ejpam-4144	447	1	if	if	SCONJ
ejpam-4144	447	2	m1	m1	PROPN
ejpam-4144	447	3	=	=	SYM
ejpam-4144	447	4	|u1|	|u1|	X
ejpam-4144	447	5	=	=	SYM
ejpam-4144	447	6	3	3	NUM
ejpam-4144	447	7	,	,	PUNCT
ejpam-4144	447	8	then	then	ADV
ejpam-4144	447	9	|s|	|s|	PROPN
ejpam-4144	447	10	=	=	SYM
ejpam-4144	447	11	k−1	k−1	PROPN
ejpam-4144	447	12	+	+	PROPN
ejpam-4144	447	13	3	3	NUM
ejpam-4144	447	14	=	=	SYM
ejpam-4144	447	15	k+2	k+2	PROPN
ejpam-4144	447	16	.	.	PUNCT
ejpam-4144	448	1	however	however	ADV
ejpam-4144	448	2	,	,	PUNCT
ejpam-4144	448	3	if	if	SCONJ
ejpam-4144	448	4	m1	m1	PROPN
ejpam-4144	448	5	≥	≥	NOUN
ejpam-4144	448	6	4	4	NUM
ejpam-4144	448	7	,	,	PUNCT
ejpam-4144	448	8	then	then	ADV
ejpam-4144	448	9	|s|	|s|	PROPN
ejpam-4144	448	10	=	=	SYM
ejpam-4144	448	11	k−	k−	PROPN
ejpam-4144	448	12	1	1	NUM
ejpam-4144	448	13	+	+	NUM
ejpam-4144	448	14	|u1|	|u1|	ADJ
ejpam-4144	448	15	≥	≥	NOUN
ejpam-4144	448	16	k+3	k+3	PROPN
ejpam-4144	448	17	,	,	PUNCT
ejpam-4144	448	18	contrary	contrary	ADV
ejpam-4144	448	19	to	to	ADP
ejpam-4144	448	20	the	the	DET
ejpam-4144	448	21	fact	fact	NOUN
ejpam-4144	448	22	that	that	SCONJ
ejpam-4144	448	23	k+2	k+2	PROPN
ejpam-4144	448	24	is	be	AUX
ejpam-4144	448	25	an	an	DET
ejpam-4144	448	26	upper	upper	ADJ
ejpam-4144	448	27	bound	bind	VERB
ejpam-4144	448	28	of	of	ADP
ejpam-4144	448	29	|s|	|s|	PROPN
ejpam-4144	448	30	.	.	PUNCT
ejpam-4144	449	1	hence	hence	ADV
ejpam-4144	449	2	,	,	PUNCT
ejpam-4144	449	3	for	for	ADP
ejpam-4144	449	4	m1	m1	PROPN
ejpam-4144	449	5	≥	≥	NUM
ejpam-4144	449	6	4	4	NUM
ejpam-4144	449	7	,	,	PUNCT
ejpam-4144	449	8	there	there	PRON
ejpam-4144	449	9	exists	exist	VERB
ejpam-4144	449	10	j	j	PROPN
ejpam-4144	449	11	≥	≥	NUM
ejpam-4144	449	12	2	2	NUM
ejpam-4144	449	13	such	such	ADJ
ejpam-4144	449	14	that	that	SCONJ
ejpam-4144	449	15	|s	|s	PROPN
ejpam-4144	449	16	∩	∩	NOUN
ejpam-4144	449	17	(	(	PUNCT
ejpam-4144	449	18	uj	uj	PROPN
ejpam-4144	449	19	∪	∪	PROPN
ejpam-4144	449	20	u	u	PROPN
ejpam-4144	449	21	j)|	j)|	X
ejpam-4144	449	22	≥	≥	NOUN
ejpam-4144	449	23	2	2	NUM
ejpam-4144	449	24	.	.	PUNCT
ejpam-4144	450	1	since	since	SCONJ
ejpam-4144	450	2	|s	|s	PROPN
ejpam-4144	450	3	∩	∩	PROPN
ejpam-4144	450	4	(	(	PUNCT
ejpam-4144	450	5	u1	u1	PROPN
ejpam-4144	450	6	∪	∪	X
ejpam-4144	450	7	u1)|	u1)|	PROPN
ejpam-4144	450	8	≥	≥	NUM
ejpam-4144	450	9	2	2	NUM
ejpam-4144	450	10	,	,	PUNCT
ejpam-4144	450	11	s	s	PART
ejpam-4144	450	12	g.	g.	NOUN
ejpam-4144	450	13	salasalan	salasalan	NOUN
ejpam-4144	450	14	,	,	PUNCT
ejpam-4144	450	15	s.	s.	PROPN
ejpam-4144	450	16	canoy	canoy	PROPN
ejpam-4144	450	17	,	,	PUNCT
ejpam-4144	450	18	jr	jr	PROPN
ejpam-4144	450	19	.	.	PROPN
ejpam-4144	450	20	/	/	SYM
ejpam-4144	450	21	eur	eur	PROPN
ejpam-4144	450	22	.	.	PUNCT
ejpam-4144	451	1	j.	j.	PROPN
ejpam-4144	451	2	pure	pure	PROPN
ejpam-4144	451	3	appl	appl	PROPN
ejpam-4144	451	4	.	.	PROPN
ejpam-4144	451	5	math	math	PROPN
ejpam-4144	451	6	,	,	PUNCT
ejpam-4144	451	7	14	14	NUM
ejpam-4144	451	8	(	(	PUNCT
ejpam-4144	451	9	4	4	NUM
ejpam-4144	451	10	)	)	PUNCT
ejpam-4144	451	11	(	(	PUNCT
ejpam-4144	451	12	2021	2021	NUM
ejpam-4144	451	13	)	)	PUNCT
ejpam-4144	451	14	,	,	PUNCT
ejpam-4144	451	15	1415	1415	NUM
ejpam-4144	451	16	-	-	SYM
ejpam-4144	451	17	1428	1428	NUM
ejpam-4144	451	18	1423	1423	NUM
ejpam-4144	451	19	is	be	AUX
ejpam-4144	451	20	a	a	DET
ejpam-4144	451	21	γ	γ	NOUN
ejpam-4144	451	22	-	-	PUNCT
ejpam-4144	451	23	set	set	ADJ
ejpam-4144	451	24	,	,	PUNCT
ejpam-4144	451	25	γ(gg	γ(gg	NUM
ejpam-4144	451	26	)	)	PUNCT
ejpam-4144	451	27	=	=	SYM
ejpam-4144	451	28	|s|	|s|	PROPN
ejpam-4144	451	29	≥	≥	NOUN
ejpam-4144	451	30	k+2	k+2	PROPN
ejpam-4144	451	31	.	.	PROPN
ejpam-4144	452	1	note	note	VERB
ejpam-4144	452	2	that	that	SCONJ
ejpam-4144	452	3	we	we	PRON
ejpam-4144	452	4	obtain	obtain	VERB
ejpam-4144	452	5	the	the	DET
ejpam-4144	452	6	same	same	ADJ
ejpam-4144	452	7	implications	implication	NOUN
ejpam-4144	452	8	if	if	SCONJ
ejpam-4144	452	9	m1	m1	PROPN
ejpam-4144	452	10	=	=	PUNCT
ejpam-4144	452	11	3	3	NUM
ejpam-4144	452	12	and	and	CCONJ
ejpam-4144	452	13	s	s	PROPN
ejpam-4144	452	14	∩	∩	ADJ
ejpam-4144	452	15	uj	uj	PROPN
ejpam-4144	452	16	̸=	̸=	PROPN
ejpam-4144	452	17	∅	∅	NOUN
ejpam-4144	452	18	for	for	ADP
ejpam-4144	452	19	some	some	DET
ejpam-4144	452	20	j	j	PROPN
ejpam-4144	452	21	≥	≥	NUM
ejpam-4144	452	22	2	2	NUM
ejpam-4144	452	23	.	.	PUNCT
ejpam-4144	452	24	accordingly	accordingly	ADV
ejpam-4144	452	25	,	,	PUNCT
ejpam-4144	452	26	γ(gg	γ(gg	ADJ
ejpam-4144	452	27	)	)	PUNCT
ejpam-4144	452	28	=	=	SYM
ejpam-4144	453	1	k	k	PROPN
ejpam-4144	454	1	+	+	PROPN
ejpam-4144	454	2	2	2	X
ejpam-4144	454	3	.	.	AUX
ejpam-4144	454	4	given	give	VERB
ejpam-4144	454	5	a	a	DET
ejpam-4144	454	6	graph	graph	NOUN
ejpam-4144	454	7	g	g	NOUN
ejpam-4144	454	8	with	with	ADP
ejpam-4144	454	9	γ(g	γ(g	PROPN
ejpam-4144	454	10	)	)	PUNCT
ejpam-4144	454	11	=	=	SYM
ejpam-4144	454	12	1	1	NUM
ejpam-4144	454	13	,	,	PUNCT
ejpam-4144	454	14	we	we	PRON
ejpam-4144	454	15	denote	denote	VERB
ejpam-4144	454	16	by	by	ADP
ejpam-4144	454	17	dom(g	dom(g	NOUN
ejpam-4144	454	18	)	)	PUNCT
ejpam-4144	454	19	the	the	DET
ejpam-4144	454	20	set	set	NOUN
ejpam-4144	454	21	{	{	PUNCT
ejpam-4144	454	22	v	v	NOUN
ejpam-4144	454	23	∈	∈	PROPN
ejpam-4144	454	24	v	v	NOUN
ejpam-4144	454	25	(	(	PUNCT
ejpam-4144	454	26	g	g	NOUN
ejpam-4144	454	27	)	)	PUNCT
ejpam-4144	454	28	:	:	PUNCT
ejpam-4144	454	29	{	{	PUNCT
ejpam-4144	454	30	v	v	NOUN
ejpam-4144	454	31	}	}	PUNCT
ejpam-4144	454	32	is	be	AUX
ejpam-4144	454	33	a	a	DET
ejpam-4144	454	34	dominating	dominating	NOUN
ejpam-4144	454	35	set	set	NOUN
ejpam-4144	454	36	of	of	ADP
ejpam-4144	454	37	g	g	NOUN
ejpam-4144	454	38	}	}	PUNCT
ejpam-4144	454	39	.	.	PUNCT
ejpam-4144	455	1	lemma	lemma	PROPN
ejpam-4144	455	2	1	1	X
ejpam-4144	455	3	.	.	PUNCT
ejpam-4144	456	1	let	let	VERB
ejpam-4144	456	2	g	g	PRON
ejpam-4144	456	3	be	be	AUX
ejpam-4144	456	4	a	a	DET
ejpam-4144	456	5	graph	graph	NOUN
ejpam-4144	456	6	with	with	ADP
ejpam-4144	456	7	γ(g	γ(g	PROPN
ejpam-4144	456	8	)	)	PUNCT
ejpam-4144	456	9	=	=	SYM
ejpam-4144	456	10	1	1	NUM
ejpam-4144	456	11	and	and	CCONJ
ejpam-4144	456	12	let	let	VERB
ejpam-4144	456	13	s	s	PRON
ejpam-4144	456	14	be	be	AUX
ejpam-4144	456	15	a	a	DET
ejpam-4144	456	16	global	global	ADJ
ejpam-4144	456	17	hop	hop	NOUN
ejpam-4144	456	18	dominating	dominating	NOUN
ejpam-4144	456	19	set	set	NOUN
ejpam-4144	456	20	of	of	ADP
ejpam-4144	456	21	gg	gg	PROPN
ejpam-4144	456	22	.	.	PUNCT
ejpam-4144	457	1	if	if	SCONJ
ejpam-4144	457	2	v	v	NUM
ejpam-4144	457	3	∈	∈	PROPN
ejpam-4144	457	4	dom(g	dom(g	NOUN
ejpam-4144	457	5	)	)	PUNCT
ejpam-4144	457	6	,	,	PUNCT
ejpam-4144	457	7	then	then	ADV
ejpam-4144	457	8	v	v	X
ejpam-4144	457	9	∈	∈	PROPN
ejpam-4144	457	10	s	s	X
ejpam-4144	457	11	or	or	CCONJ
ejpam-4144	457	12	v	v	ADP
ejpam-4144	457	13	∈	∈	PROPN
ejpam-4144	457	14	s.	s.	PROPN
ejpam-4144	457	15	proof	proof	PROPN
ejpam-4144	457	16	.	.	PUNCT
ejpam-4144	458	1	let	let	VERB
ejpam-4144	458	2	v	v	X
ejpam-4144	458	3	∈	∈	VERB
ejpam-4144	458	4	dom(g	dom(g	NOUN
ejpam-4144	458	5	)	)	PUNCT
ejpam-4144	458	6	and	and	CCONJ
ejpam-4144	458	7	suppose	suppose	VERB
ejpam-4144	458	8	that	that	SCONJ
ejpam-4144	458	9	v	v	NOUN
ejpam-4144	458	10	,	,	PUNCT
ejpam-4144	458	11	v	v	NOUN
ejpam-4144	458	12	/∈	/∈	PUNCT
ejpam-4144	458	13	s.	s.	PROPN
ejpam-4144	458	14	since	since	SCONJ
ejpam-4144	458	15	s	s	PROPN
ejpam-4144	458	16	is	be	AUX
ejpam-4144	458	17	a	a	DET
ejpam-4144	458	18	global	global	ADJ
ejpam-4144	458	19	hop	hop	NOUN
ejpam-4144	458	20	dominating	dominating	NOUN
ejpam-4144	458	21	set	set	NOUN
ejpam-4144	458	22	of	of	ADP
ejpam-4144	458	23	gg	gg	PROPN
ejpam-4144	458	24	,	,	PUNCT
ejpam-4144	458	25	it	it	PRON
ejpam-4144	458	26	is	be	AUX
ejpam-4144	458	27	a	a	DET
ejpam-4144	458	28	hop	hop	NOUN
ejpam-4144	458	29	dominating	dominating	NOUN
ejpam-4144	458	30	set	set	NOUN
ejpam-4144	458	31	of	of	ADP
ejpam-4144	458	32	gg	gg	PROPN
ejpam-4144	458	33	.	.	PUNCT
ejpam-4144	459	1	as	as	ADP
ejpam-4144	459	2	v	v	ADP
ejpam-4144	459	3	∈	∈	NOUN
ejpam-4144	459	4	v	v	NOUN
ejpam-4144	459	5	(	(	PUNCT
ejpam-4144	459	6	gg	gg	NOUN
ejpam-4144	459	7	)	)	PUNCT
ejpam-4144	459	8	\	\	PROPN
ejpam-4144	460	1	s	s	X
ejpam-4144	460	2	,	,	PUNCT
ejpam-4144	460	3	there	there	PRON
ejpam-4144	460	4	exists	exist	VERB
ejpam-4144	460	5	z	z	PROPN
ejpam-4144	460	6	∈	∈	PROPN
ejpam-4144	460	7	s	s	VERB
ejpam-4144	461	1	such	such	ADJ
ejpam-4144	461	2	that	that	SCONJ
ejpam-4144	461	3	d	d	PROPN
ejpam-4144	461	4	gg	gg	PROPN
ejpam-4144	461	5	(	(	PUNCT
ejpam-4144	461	6	v	v	NOUN
ejpam-4144	461	7	,	,	PUNCT
ejpam-4144	461	8	z	z	NOUN
ejpam-4144	461	9	)	)	PUNCT
ejpam-4144	461	10	=	=	SYM
ejpam-4144	461	11	2	2	X
ejpam-4144	461	12	.	.	PUNCT
ejpam-4144	462	1	however	however	ADV
ejpam-4144	462	2	,	,	PUNCT
ejpam-4144	462	3	d	d	PROPN
ejpam-4144	462	4	gg	gg	X
ejpam-4144	462	5	(	(	PUNCT
ejpam-4144	462	6	v	v	NOUN
ejpam-4144	462	7	,	,	PUNCT
ejpam-4144	462	8	x	x	NOUN
ejpam-4144	462	9	)	)	PUNCT
ejpam-4144	462	10	=	=	SYM
ejpam-4144	462	11	1	1	NUM
ejpam-4144	462	12	for	for	ADP
ejpam-4144	462	13	all	all	DET
ejpam-4144	462	14	x	x	SYM
ejpam-4144	462	15	∈	∈	PROPN
ejpam-4144	462	16	v	v	NOUN
ejpam-4144	462	17	(	(	PUNCT
ejpam-4144	462	18	gg	gg	NOUN
ejpam-4144	462	19	)	)	PUNCT
ejpam-4144	462	20	\	\	PROPN
ejpam-4144	462	21	{	{	PUNCT
ejpam-4144	462	22	v	v	NOUN
ejpam-4144	462	23	,	,	PUNCT
ejpam-4144	462	24	v	v	NOUN
ejpam-4144	462	25	}	}	PUNCT
ejpam-4144	462	26	.	.	PUNCT
ejpam-4144	463	1	since	since	SCONJ
ejpam-4144	463	2	v	v	NUM
ejpam-4144	463	3	/∈	/∈	SYM
ejpam-4144	463	4	s	s	X
ejpam-4144	463	5	,	,	PUNCT
ejpam-4144	463	6	it	it	PRON
ejpam-4144	463	7	follows	follow	VERB
ejpam-4144	463	8	that	that	SCONJ
ejpam-4144	463	9	such	such	DET
ejpam-4144	463	10	a	a	DET
ejpam-4144	463	11	vertex	vertex	NOUN
ejpam-4144	463	12	z	z	NOUN
ejpam-4144	463	13	does	do	AUX
ejpam-4144	463	14	not	not	PART
ejpam-4144	463	15	exist	exist	VERB
ejpam-4144	463	16	,	,	PUNCT
ejpam-4144	463	17	contrary	contrary	ADV
ejpam-4144	463	18	to	to	ADP
ejpam-4144	463	19	the	the	DET
ejpam-4144	463	20	assumption	assumption	NOUN
ejpam-4144	463	21	that	that	SCONJ
ejpam-4144	463	22	s	s	VERB
ejpam-4144	463	23	is	be	AUX
ejpam-4144	463	24	a	a	DET
ejpam-4144	463	25	hop	hop	NOUN
ejpam-4144	463	26	dominating	dominating	NOUN
ejpam-4144	463	27	set	set	NOUN
ejpam-4144	463	28	of	of	ADP
ejpam-4144	463	29	of	of	ADP
ejpam-4144	463	30	gg	gg	PROPN
ejpam-4144	463	31	.	.	PUNCT
ejpam-4144	464	1	therefore	therefore	ADV
ejpam-4144	464	2	,	,	PUNCT
ejpam-4144	464	3	v	v	ADP
ejpam-4144	464	4	∈	∈	PROPN
ejpam-4144	464	5	s	s	NOUN
ejpam-4144	464	6	or	or	CCONJ
ejpam-4144	464	7	v	v	ADP
ejpam-4144	464	8	∈	∈	PROPN
ejpam-4144	464	9	s.	s.	PROPN
ejpam-4144	464	10	corollary	corollary	NOUN
ejpam-4144	464	11	3	3	PROPN
ejpam-4144	464	12	.	.	PUNCT
ejpam-4144	465	1	for	for	ADP
ejpam-4144	465	2	each	each	DET
ejpam-4144	465	3	positive	positive	ADJ
ejpam-4144	465	4	integer	integer	NOUN
ejpam-4144	465	5	n	n	PRON
ejpam-4144	465	6	≥	≥	NOUN
ejpam-4144	465	7	2	2	NUM
ejpam-4144	465	8	,	,	PUNCT
ejpam-4144	465	9	γgh(knkn	γgh(knkn	NUM
ejpam-4144	465	10	)	)	PUNCT
ejpam-4144	465	11	=	=	VERB
ejpam-4144	465	12	n.	n.	NOUN
ejpam-4144	465	13	proof	proof	NOUN
ejpam-4144	465	14	.	.	PUNCT
ejpam-4144	466	1	by	by	ADP
ejpam-4144	466	2	theorem	theorem	NOUN
ejpam-4144	466	3	5(iii	5(iii	NUM
ejpam-4144	466	4	)	)	PUNCT
ejpam-4144	466	5	,	,	PUNCT
ejpam-4144	466	6	γgh(knkn	γgh(knkn	NUM
ejpam-4144	466	7	)	)	PUNCT
ejpam-4144	466	8	≤	≤	NOUN
ejpam-4144	466	9	n.	n.	NOUN
ejpam-4144	466	10	let	let	VERB
ejpam-4144	466	11	s	s	PRON
ejpam-4144	466	12	be	be	AUX
ejpam-4144	466	13	a	a	DET
ejpam-4144	466	14	γgh	γgh	PROPN
ejpam-4144	466	15	-	-	PUNCT
ejpam-4144	466	16	set	set	NOUN
ejpam-4144	466	17	of	of	ADP
ejpam-4144	466	18	knkn	knkn	PROPN
ejpam-4144	466	19	.	.	PUNCT
ejpam-4144	467	1	since	since	SCONJ
ejpam-4144	467	2	dom(kn	dom(kn	NUM
ejpam-4144	467	3	)	)	PUNCT
ejpam-4144	467	4	=	=	SYM
ejpam-4144	467	5	v	v	X
ejpam-4144	467	6	(	(	PUNCT
ejpam-4144	467	7	kn	kn	PROPN
ejpam-4144	467	8	)	)	PUNCT
ejpam-4144	467	9	,	,	PUNCT
ejpam-4144	467	10	γgh(knkn	γgh(knkn	NUM
ejpam-4144	467	11	)	)	PUNCT
ejpam-4144	467	12	=	=	SYM
ejpam-4144	467	13	|s|	|s|	PROPN
ejpam-4144	467	14	≥	≥	NOUN
ejpam-4144	467	15	n	n	ADV
ejpam-4144	467	16	by	by	ADP
ejpam-4144	467	17	lemma	lemma	PROPN
ejpam-4144	467	18	1	1	NUM
ejpam-4144	467	19	.	.	PUNCT
ejpam-4144	467	20	therefore	therefore	ADV
ejpam-4144	467	21	,	,	PUNCT
ejpam-4144	467	22	γgh(knkn	γgh(knkn	NUM
ejpam-4144	467	23	)	)	PUNCT
ejpam-4144	467	24	=	=	SYM
ejpam-4144	467	25	n.	n.	NOUN
ejpam-4144	467	26	theorem	theorem	VERB
ejpam-4144	467	27	7	7	NUM
ejpam-4144	467	28	.	.	PUNCT
ejpam-4144	468	1	let	let	VERB
ejpam-4144	468	2	g	g	PROPN
ejpam-4144	468	3	=	=	PUNCT
ejpam-4144	468	4	km1,m2,	km1,m2,	PROPN
ejpam-4144	468	5	...	...	PUNCT
ejpam-4144	468	6	,mk	,mk	PUNCT
ejpam-4144	468	7	be	be	AUX
ejpam-4144	468	8	a	a	DET
ejpam-4144	468	9	complete	complete	ADJ
ejpam-4144	468	10	multipartite	multipartite	ADJ
ejpam-4144	468	11	graph	graph	NOUN
ejpam-4144	468	12	such	such	ADJ
ejpam-4144	468	13	that	that	SCONJ
ejpam-4144	468	14	1	1	NUM
ejpam-4144	468	15	≤	≤	NUM
ejpam-4144	468	16	m1	m1	NOUN
ejpam-4144	468	17	≤	≤	NUM
ejpam-4144	468	18	m2	m2	PROPN
ejpam-4144	468	19	≤	≤	PROPN
ejpam-4144	468	20	.	.	PUNCT
ejpam-4144	468	21	.	.	PUNCT
ejpam-4144	468	22	.	.	PUNCT
ejpam-4144	469	1	≤	≤	NUM
ejpam-4144	469	2	mk	mk	PROPN
ejpam-4144	469	3	,	,	PUNCT
ejpam-4144	469	4	where	where	SCONJ
ejpam-4144	469	5	k	k	PROPN
ejpam-4144	469	6	≥	≥	NUM
ejpam-4144	469	7	2	2	NUM
ejpam-4144	469	8	and	and	CCONJ
ejpam-4144	469	9	mj	mj	PROPN
ejpam-4144	469	10	≥	≥	NUM
ejpam-4144	469	11	2	2	NUM
ejpam-4144	469	12	for	for	ADP
ejpam-4144	469	13	some	some	DET
ejpam-4144	469	14	j	j	NOUN
ejpam-4144	469	15	with	with	ADP
ejpam-4144	469	16	1	1	NUM
ejpam-4144	469	17	≤	≤	NUM
ejpam-4144	469	18	j	j	PROPN
ejpam-4144	469	19	≤	≤	PROPN
ejpam-4144	469	20	k.	k.	PROPN
ejpam-4144	469	21	then	then	ADV
ejpam-4144	469	22	γgh(gg	γgh(gg	NUM
ejpam-4144	469	23	)	)	PUNCT
ejpam-4144	470	1	=	=	PRON
ejpam-4144	470	2	{	{	PUNCT
ejpam-4144	471	1	k	k	X
ejpam-4144	471	2	if	if	SCONJ
ejpam-4144	471	3	m1	m1	PROPN
ejpam-4144	471	4	=	=	PROPN
ejpam-4144	471	5	m2	m2	PROPN
ejpam-4144	471	6	=	=	SYM
ejpam-4144	471	7	1	1	NUM
ejpam-4144	471	8	and	and	CCONJ
ejpam-4144	471	9	k	k	PROPN
ejpam-4144	471	10	≥	≥	NUM
ejpam-4144	471	11	4	4	NUM
ejpam-4144	471	12	k	k	NOUN
ejpam-4144	471	13	+	+	CCONJ
ejpam-4144	471	14	1	1	NUM
ejpam-4144	471	15	otherwise	otherwise	ADV
ejpam-4144	471	16	.	.	PUNCT
ejpam-4144	472	1	proof	proof	NOUN
ejpam-4144	472	2	.	.	PUNCT
ejpam-4144	473	1	let	let	VERB
ejpam-4144	473	2	u1	u1	NOUN
ejpam-4144	473	3	,	,	PUNCT
ejpam-4144	473	4	u2	u2	NOUN
ejpam-4144	473	5	,	,	PUNCT
ejpam-4144	473	6	.	.	PUNCT
ejpam-4144	473	7	.	.	PUNCT
ejpam-4144	474	1	.	.	PUNCT
ejpam-4144	475	1	,	,	PUNCT
ejpam-4144	475	2	uk	uk	PROPN
ejpam-4144	475	3	be	be	VERB
ejpam-4144	475	4	the	the	DET
ejpam-4144	475	5	partite	partite	ADJ
ejpam-4144	475	6	sets	set	NOUN
ejpam-4144	475	7	of	of	ADP
ejpam-4144	475	8	g	g	NOUN
ejpam-4144	475	9	with	with	ADP
ejpam-4144	475	10	|ui|	|ui|	PROPN
ejpam-4144	475	11	=	=	SYM
ejpam-4144	475	12	mi	mi	PROPN
ejpam-4144	475	13	for	for	ADP
ejpam-4144	475	14	each	each	DET
ejpam-4144	475	15	i	i	PRON
ejpam-4144	475	16	∈	∈	PROPN
ejpam-4144	475	17	{	{	PUNCT
ejpam-4144	475	18	1	1	NUM
ejpam-4144	475	19	,	,	PUNCT
ejpam-4144	475	20	2	2	NUM
ejpam-4144	475	21	,	,	PUNCT
ejpam-4144	475	22	.	.	PUNCT
ejpam-4144	475	23	.	.	PUNCT
ejpam-4144	476	1	.	.	PUNCT
ejpam-4144	477	1	,	,	PUNCT
ejpam-4144	477	2	k	k	X
ejpam-4144	477	3	}	}	PUNCT
ejpam-4144	477	4	.	.	PUNCT
ejpam-4144	478	1	again	again	ADV
ejpam-4144	478	2	,	,	PUNCT
ejpam-4144	478	3	for	for	ADP
ejpam-4144	478	4	each	each	DET
ejpam-4144	478	5	i	i	PRON
ejpam-4144	478	6	∈	∈	PROPN
ejpam-4144	478	7	{	{	PUNCT
ejpam-4144	478	8	1	1	NUM
ejpam-4144	478	9	,	,	PUNCT
ejpam-4144	478	10	2	2	NUM
ejpam-4144	478	11	,	,	PUNCT
ejpam-4144	478	12	.	.	PUNCT
ejpam-4144	478	13	.	.	PUNCT
ejpam-4144	478	14	.	.	PUNCT
ejpam-4144	479	1	,	,	PUNCT
ejpam-4144	479	2	k	k	X
ejpam-4144	479	3	}	}	PUNCT
ejpam-4144	479	4	,	,	PUNCT
ejpam-4144	479	5	let	let	VERB
ejpam-4144	479	6	u	u	PRON
ejpam-4144	479	7	i	i	NOUN
ejpam-4144	479	8	=	=	PUNCT
ejpam-4144	479	9	{	{	PUNCT
ejpam-4144	479	10	v	v	NOUN
ejpam-4144	479	11	:	:	PUNCT
ejpam-4144	479	12	v	v	NUM
ejpam-4144	479	13	∈	∈	PROPN
ejpam-4144	479	14	ui	ui	PROPN
ejpam-4144	479	15	}	}	PUNCT
ejpam-4144	479	16	.	.	PUNCT
ejpam-4144	480	1	choose	choose	VERB
ejpam-4144	480	2	any	any	DET
ejpam-4144	480	3	vi	vi	NOUN
ejpam-4144	480	4	∈	∈	PROPN
ejpam-4144	480	5	ui	ui	NOUN
ejpam-4144	480	6	for	for	ADP
ejpam-4144	480	7	each	each	DET
ejpam-4144	480	8	i	i	PRON
ejpam-4144	480	9	∈	∈	PROPN
ejpam-4144	480	10	{	{	PUNCT
ejpam-4144	480	11	1	1	NUM
ejpam-4144	480	12	,	,	PUNCT
ejpam-4144	480	13	2	2	NUM
ejpam-4144	480	14	,	,	PUNCT
ejpam-4144	480	15	.	.	PUNCT
ejpam-4144	480	16	.	.	PUNCT
ejpam-4144	481	1	.	.	PUNCT
ejpam-4144	482	1	,	,	PUNCT
ejpam-4144	482	2	k	k	X
ejpam-4144	482	3	}	}	PUNCT
ejpam-4144	482	4	.	.	PUNCT
ejpam-4144	483	1	suppose	suppose	VERB
ejpam-4144	483	2	m1	m1	PROPN
ejpam-4144	483	3	=	=	SYM
ejpam-4144	483	4	m2	m2	PROPN
ejpam-4144	483	5	=	=	SYM
ejpam-4144	483	6	1	1	NUM
ejpam-4144	483	7	and	and	CCONJ
ejpam-4144	483	8	k	k	PROPN
ejpam-4144	483	9	≥	≥	NUM
ejpam-4144	483	10	4	4	NUM
ejpam-4144	483	11	.	.	PUNCT
ejpam-4144	483	12	then	then	ADV
ejpam-4144	483	13	u1	u1	VERB
ejpam-4144	483	14	=	=	SYM
ejpam-4144	483	15	{	{	PUNCT
ejpam-4144	483	16	v1	v1	NOUN
ejpam-4144	483	17	}	}	PUNCT
ejpam-4144	483	18	and	and	CCONJ
ejpam-4144	483	19	u2	u2	PROPN
ejpam-4144	483	20	=	=	PUNCT
ejpam-4144	483	21	{	{	PUNCT
ejpam-4144	483	22	v2	v2	NOUN
ejpam-4144	483	23	}	}	PUNCT
ejpam-4144	483	24	.	.	PUNCT
ejpam-4144	484	1	let	let	VERB
ejpam-4144	484	2	s	s	PRON
ejpam-4144	484	3	=	=	NOUN
ejpam-4144	484	4	{	{	PUNCT
ejpam-4144	484	5	v1	v1	PROPN
ejpam-4144	484	6	,	,	PUNCT
ejpam-4144	484	7	v2	v2	PROPN
ejpam-4144	484	8	,	,	PUNCT
ejpam-4144	484	9	v3	v3	PROPN
ejpam-4144	484	10	,	,	PUNCT
ejpam-4144	484	11	v4	v4	PROPN
ejpam-4144	484	12	,	,	PUNCT
ejpam-4144	484	13	.	.	PUNCT
ejpam-4144	484	14	.	.	PUNCT
ejpam-4144	485	1	.	.	PUNCT
ejpam-4144	486	1	,	,	PUNCT
ejpam-4144	486	2	vk	vk	ADP
ejpam-4144	486	3	}	}	PUNCT
ejpam-4144	486	4	.	.	PUNCT
ejpam-4144	487	1	then	then	ADV
ejpam-4144	487	2	dgg(v1	dgg(v1	NOUN
ejpam-4144	487	3	,	,	PUNCT
ejpam-4144	487	4	v2	v2	NOUN
ejpam-4144	487	5	)	)	PUNCT
ejpam-4144	487	6	=	=	SYM
ejpam-4144	487	7	2	2	NUM
ejpam-4144	487	8	and	and	CCONJ
ejpam-4144	487	9	dgg(v2	dgg(v2	PROPN
ejpam-4144	487	10	,	,	PUNCT
ejpam-4144	487	11	v1	v1	NOUN
ejpam-4144	487	12	)	)	PUNCT
ejpam-4144	487	13	=	=	SYM
ejpam-4144	488	1	2	2	X
ejpam-4144	488	2	.	.	X
ejpam-4144	488	3	for	for	ADP
ejpam-4144	488	4	each	each	DET
ejpam-4144	488	5	j	j	PROPN
ejpam-4144	488	6	∈	∈	PROPN
ejpam-4144	488	7	{	{	PUNCT
ejpam-4144	488	8	3	3	NUM
ejpam-4144	488	9	,	,	PUNCT
ejpam-4144	488	10	4	4	NUM
ejpam-4144	488	11	,	,	PUNCT
ejpam-4144	488	12	.	.	PUNCT
ejpam-4144	488	13	.	.	PUNCT
ejpam-4144	488	14	.	.	PUNCT
ejpam-4144	489	1	,	,	PUNCT
ejpam-4144	489	2	k	k	X
ejpam-4144	489	3	}	}	PUNCT
ejpam-4144	489	4	,	,	PUNCT
ejpam-4144	489	5	we	we	PRON
ejpam-4144	489	6	have	have	VERB
ejpam-4144	489	7	dgg(w	dgg(w	PROPN
ejpam-4144	489	8	,	,	PUNCT
ejpam-4144	489	9	v1	v1	NOUN
ejpam-4144	489	10	)	)	PUNCT
ejpam-4144	489	11	=	=	SYM
ejpam-4144	489	12	2	2	NUM
ejpam-4144	489	13	for	for	ADP
ejpam-4144	489	14	each	each	DET
ejpam-4144	489	15	w	w	PROPN
ejpam-4144	489	16	∈	∈	PROPN
ejpam-4144	489	17	uj	uj	PROPN
ejpam-4144	489	18	\	\	PROPN
ejpam-4144	489	19	s	s	PART
ejpam-4144	489	20	and	and	CCONJ
ejpam-4144	489	21	dgg(x	dgg(x	PROPN
ejpam-4144	489	22	,	,	PUNCT
ejpam-4144	489	23	vr	vr	NOUN
ejpam-4144	489	24	)	)	PUNCT
ejpam-4144	489	25	=	=	SYM
ejpam-4144	489	26	2	2	NUM
ejpam-4144	489	27	for	for	ADP
ejpam-4144	489	28	each	each	DET
ejpam-4144	489	29	x	x	SYM
ejpam-4144	489	30	∈	∈	PROPN
ejpam-4144	489	31	uj	uj	PROPN
ejpam-4144	489	32	,	,	PUNCT
ejpam-4144	489	33	where	where	SCONJ
ejpam-4144	489	34	r	r	NOUN
ejpam-4144	489	35	≥	≥	NUM
ejpam-4144	489	36	3	3	NUM
ejpam-4144	489	37	and	and	CCONJ
ejpam-4144	489	38	r	r	PROPN
ejpam-4144	489	39	̸=	̸=	PROPN
ejpam-4144	489	40	j.	j.	PROPN
ejpam-4144	489	41	thus	thus	ADV
ejpam-4144	489	42	,	,	PUNCT
ejpam-4144	489	43	s	s	VERB
ejpam-4144	489	44	is	be	AUX
ejpam-4144	489	45	a	a	DET
ejpam-4144	489	46	hop	hop	NOUN
ejpam-4144	489	47	dominating	dominating	NOUN
ejpam-4144	489	48	set	set	NOUN
ejpam-4144	489	49	of	of	ADP
ejpam-4144	489	50	gg	gg	PROPN
ejpam-4144	489	51	.	.	PUNCT
ejpam-4144	490	1	on	on	ADP
ejpam-4144	490	2	the	the	DET
ejpam-4144	490	3	other	other	ADJ
ejpam-4144	490	4	hand	hand	NOUN
ejpam-4144	490	5	,	,	PUNCT
ejpam-4144	490	6	d	d	PRON
ejpam-4144	490	7	gg	gg	PROPN
ejpam-4144	490	8	(	(	PUNCT
ejpam-4144	490	9	v1	v1	NOUN
ejpam-4144	490	10	,	,	PUNCT
ejpam-4144	490	11	v1	v1	NOUN
ejpam-4144	490	12	)	)	PUNCT
ejpam-4144	490	13	=	=	SYM
ejpam-4144	490	14	2	2	NUM
ejpam-4144	490	15	and	and	CCONJ
ejpam-4144	490	16	d	d	ADP
ejpam-4144	490	17	gg	gg	PROPN
ejpam-4144	490	18	(	(	PUNCT
ejpam-4144	490	19	v2	v2	PROPN
ejpam-4144	490	20	,	,	PUNCT
ejpam-4144	490	21	v2	v2	NOUN
ejpam-4144	490	22	)	)	PUNCT
ejpam-4144	490	23	=	=	SYM
ejpam-4144	491	1	2	2	X
ejpam-4144	491	2	.	.	X
ejpam-4144	491	3	for	for	ADP
ejpam-4144	491	4	each	each	DET
ejpam-4144	491	5	j	j	PROPN
ejpam-4144	491	6	∈	∈	PROPN
ejpam-4144	491	7	{	{	PUNCT
ejpam-4144	491	8	3	3	NUM
ejpam-4144	491	9	,	,	PUNCT
ejpam-4144	491	10	4	4	NUM
ejpam-4144	491	11	,	,	PUNCT
ejpam-4144	491	12	.	.	PUNCT
ejpam-4144	491	13	.	.	PUNCT
ejpam-4144	491	14	.	.	PUNCT
ejpam-4144	492	1	,	,	PUNCT
ejpam-4144	492	2	k	k	X
ejpam-4144	492	3	}	}	PUNCT
ejpam-4144	492	4	,	,	PUNCT
ejpam-4144	492	5	we	we	PRON
ejpam-4144	492	6	have	have	VERB
ejpam-4144	492	7	d	d	PROPN
ejpam-4144	492	8	gg	gg	X
ejpam-4144	492	9	(	(	PUNCT
ejpam-4144	492	10	w	w	PROPN
ejpam-4144	492	11	,	,	PUNCT
ejpam-4144	492	12	vj	vj	ADJ
ejpam-4144	492	13	)	)	PUNCT
ejpam-4144	492	14	=	=	SYM
ejpam-4144	492	15	2	2	NUM
ejpam-4144	492	16	for	for	ADP
ejpam-4144	492	17	each	each	DET
ejpam-4144	492	18	each	each	DET
ejpam-4144	492	19	w	w	PROPN
ejpam-4144	492	20	∈	∈	PROPN
ejpam-4144	492	21	uj	uj	PROPN
ejpam-4144	492	22	\	\	PROPN
ejpam-4144	492	23	s	s	PROPN
ejpam-4144	492	24	and	and	CCONJ
ejpam-4144	492	25	d	d	PROPN
ejpam-4144	492	26	gg	gg	PROPN
ejpam-4144	492	27	(	(	PUNCT
ejpam-4144	492	28	x	x	NOUN
ejpam-4144	492	29	,	,	PUNCT
ejpam-4144	492	30	v1	v1	NOUN
ejpam-4144	492	31	)	)	PUNCT
ejpam-4144	492	32	=	=	SYM
ejpam-4144	492	33	2	2	NUM
ejpam-4144	492	34	for	for	ADP
ejpam-4144	492	35	each	each	PRON
ejpam-4144	492	36	each	each	DET
ejpam-4144	492	37	x	x	SYM
ejpam-4144	492	38	∈	∈	PROPN
ejpam-4144	492	39	uj	uj	PROPN
ejpam-4144	492	40	.	.	PUNCT
ejpam-4144	493	1	thus	thus	ADV
ejpam-4144	493	2	,	,	PUNCT
ejpam-4144	493	3	s	s	VERB
ejpam-4144	493	4	is	be	AUX
ejpam-4144	493	5	a	a	DET
ejpam-4144	493	6	hop	hop	NOUN
ejpam-4144	493	7	dominating	dominating	NOUN
ejpam-4144	493	8	set	set	NOUN
ejpam-4144	493	9	of	of	ADP
ejpam-4144	493	10	gg	gg	PROPN
ejpam-4144	493	11	.	.	PUNCT
ejpam-4144	494	1	therefore	therefore	ADV
ejpam-4144	494	2	,	,	PUNCT
ejpam-4144	494	3	s	s	VERB
ejpam-4144	494	4	is	be	AUX
ejpam-4144	494	5	a	a	DET
ejpam-4144	494	6	global	global	ADJ
ejpam-4144	494	7	hop	hop	NOUN
ejpam-4144	494	8	dominating	dominating	NOUN
ejpam-4144	494	9	set	set	NOUN
ejpam-4144	494	10	of	of	ADP
ejpam-4144	494	11	gg	gg	PROPN
ejpam-4144	494	12	and	and	CCONJ
ejpam-4144	494	13	γgh(gg	γgh(gg	NUM
ejpam-4144	494	14	)	)	PUNCT
ejpam-4144	494	15	≤	≤	NUM
ejpam-4144	494	16	|s|	|s|	PROPN
ejpam-4144	494	17	=	=	SYM
ejpam-4144	494	18	k.	k.	PROPN
ejpam-4144	494	19	next	next	ADV
ejpam-4144	494	20	,	,	PUNCT
ejpam-4144	494	21	let	let	VERB
ejpam-4144	494	22	s0	s0	PROPN
ejpam-4144	494	23	be	be	AUX
ejpam-4144	494	24	a	a	DET
ejpam-4144	494	25	γgh	γgh	PROPN
ejpam-4144	494	26	-	-	PUNCT
ejpam-4144	494	27	set	set	NOUN
ejpam-4144	494	28	of	of	ADP
ejpam-4144	494	29	gg	gg	PROPN
ejpam-4144	494	30	.	.	PUNCT
ejpam-4144	494	31	suppose	suppose	VERB
ejpam-4144	494	32	there	there	PRON
ejpam-4144	494	33	exists	exist	VERB
ejpam-4144	494	34	j	j	PROPN
ejpam-4144	494	35	∈	∈	PROPN
ejpam-4144	494	36	{	{	PUNCT
ejpam-4144	494	37	1	1	NUM
ejpam-4144	494	38	,	,	PUNCT
ejpam-4144	494	39	2	2	NUM
ejpam-4144	494	40	,	,	PUNCT
ejpam-4144	494	41	.	.	PUNCT
ejpam-4144	494	42	.	.	PUNCT
ejpam-4144	495	1	.	.	PUNCT
ejpam-4144	496	1	,	,	PUNCT
ejpam-4144	496	2	k	k	X
ejpam-4144	496	3	}	}	PUNCT
ejpam-4144	496	4	such	such	ADJ
ejpam-4144	496	5	that	that	SCONJ
ejpam-4144	496	6	s0∩(uj∪u	s0∩(uj∪u	PROPN
ejpam-4144	496	7	j	j	PROPN
ejpam-4144	496	8	)	)	PUNCT
ejpam-4144	496	9	=	=	VERB
ejpam-4144	496	10	∅.	∅.	AUX
ejpam-4144	496	11	let	let	VERB
ejpam-4144	496	12	w	w	PROPN
ejpam-4144	496	13	∈	∈	PROPN
ejpam-4144	496	14	u	u	PROPN
ejpam-4144	496	15	j	j	PROPN
ejpam-4144	496	16	.	.	PUNCT
ejpam-4144	497	1	it	it	PRON
ejpam-4144	497	2	follows	follow	VERB
ejpam-4144	497	3	from	from	ADP
ejpam-4144	497	4	the	the	DET
ejpam-4144	497	5	adjacency	adjacency	NOUN
ejpam-4144	497	6	in	in	ADP
ejpam-4144	497	7	gg	gg	PROPN
ejpam-4144	497	8	that	that	SCONJ
ejpam-4144	497	9	d	d	PROPN
ejpam-4144	497	10	gg	gg	X
ejpam-4144	497	11	(	(	PUNCT
ejpam-4144	497	12	w	w	PROPN
ejpam-4144	497	13	,	,	PUNCT
ejpam-4144	497	14	p	p	NOUN
ejpam-4144	497	15	)	)	PUNCT
ejpam-4144	497	16	=	=	SYM
ejpam-4144	497	17	1	1	NUM
ejpam-4144	497	18	for	for	ADP
ejpam-4144	497	19	all	all	DET
ejpam-4144	497	20	p	p	NOUN
ejpam-4144	497	21	∈	∈	PROPN
ejpam-4144	497	22	v	v	NOUN
ejpam-4144	497	23	(	(	PUNCT
ejpam-4144	497	24	gg)\(u	gg)\(u	NOUN
ejpam-4144	497	25	j∪{w	j∪{w	PROPN
ejpam-4144	497	26	}	}	PUNCT
ejpam-4144	497	27	)	)	PUNCT
ejpam-4144	497	28	.	.	PUNCT
ejpam-4144	498	1	hence	hence	ADV
ejpam-4144	498	2	,	,	PUNCT
ejpam-4144	498	3	by	by	ADP
ejpam-4144	498	4	assumption	assumption	NOUN
ejpam-4144	498	5	,	,	PUNCT
ejpam-4144	498	6	there	there	PRON
ejpam-4144	498	7	exists	exist	VERB
ejpam-4144	498	8	no	no	DET
ejpam-4144	498	9	q	q	NOUN
ejpam-4144	498	10	∈	∈	PROPN
ejpam-4144	498	11	s0	s0	NOUN
ejpam-4144	498	12	with	with	ADP
ejpam-4144	498	13	d	d	PROPN
ejpam-4144	498	14	gg	gg	PROPN
ejpam-4144	498	15	(	(	PUNCT
ejpam-4144	498	16	w	w	PROPN
ejpam-4144	498	17	,	,	PUNCT
ejpam-4144	498	18	q	q	NOUN
ejpam-4144	498	19	)	)	PUNCT
ejpam-4144	498	20	=	=	SYM
ejpam-4144	498	21	2	2	NUM
ejpam-4144	498	22	,	,	PUNCT
ejpam-4144	498	23	contrary	contrary	ADV
ejpam-4144	498	24	to	to	ADP
ejpam-4144	498	25	the	the	DET
ejpam-4144	498	26	fact	fact	NOUN
ejpam-4144	498	27	that	that	SCONJ
ejpam-4144	498	28	s0	s0	PROPN
ejpam-4144	498	29	is	be	AUX
ejpam-4144	498	30	a	a	DET
ejpam-4144	498	31	hop	hop	NOUN
ejpam-4144	498	32	dominating	dominating	NOUN
ejpam-4144	498	33	set	set	NOUN
ejpam-4144	498	34	of	of	ADP
ejpam-4144	498	35	gg	gg	PROPN
ejpam-4144	498	36	.	.	PUNCT
ejpam-4144	499	1	therefore	therefore	ADV
ejpam-4144	499	2	,	,	PUNCT
ejpam-4144	499	3	s0∩(uj∪u	s0∩(uj∪u	PROPN
ejpam-4144	499	4	j	j	PROPN
ejpam-4144	499	5	)	)	PUNCT
ejpam-4144	499	6	̸=	̸=	PROPN
ejpam-4144	499	7	∅	∅	NOUN
ejpam-4144	499	8	for	for	ADP
ejpam-4144	499	9	each	each	DET
ejpam-4144	499	10	j	j	PROPN
ejpam-4144	499	11	∈	∈	PROPN
ejpam-4144	499	12	{	{	PUNCT
ejpam-4144	499	13	1	1	NUM
ejpam-4144	499	14	,	,	PUNCT
ejpam-4144	499	15	2	2	NUM
ejpam-4144	499	16	,	,	PUNCT
ejpam-4144	499	17	.	.	PUNCT
ejpam-4144	499	18	.	.	PUNCT
ejpam-4144	499	19	.	.	PUNCT
ejpam-4144	500	1	,	,	PUNCT
ejpam-4144	500	2	k	k	X
ejpam-4144	500	3	}	}	PUNCT
ejpam-4144	500	4	.	.	PUNCT
ejpam-4144	501	1	consequently	consequently	ADV
ejpam-4144	501	2	,	,	PUNCT
ejpam-4144	501	3	γgh(gg	γgh(gg	NUM
ejpam-4144	501	4	)	)	PUNCT
ejpam-4144	501	5	=	=	SYM
ejpam-4144	501	6	|s|	|s|	PROPN
ejpam-4144	501	7	≥	≥	PROPN
ejpam-4144	501	8	k.	k.	PROPN
ejpam-4144	501	9	accordingly	accordingly	ADV
ejpam-4144	501	10	,	,	PUNCT
ejpam-4144	501	11	γgh(gg	γgh(gg	NUM
ejpam-4144	501	12	)	)	PUNCT
ejpam-4144	501	13	=	=	SYM
ejpam-4144	501	14	k.	k.	PROPN
ejpam-4144	501	15	g.	g.	PROPN
ejpam-4144	501	16	salasalan	salasalan	PROPN
ejpam-4144	501	17	,	,	PUNCT
ejpam-4144	501	18	s.	s.	PROPN
ejpam-4144	501	19	canoy	canoy	PROPN
ejpam-4144	501	20	,	,	PUNCT
ejpam-4144	501	21	jr	jr	PROPN
ejpam-4144	501	22	.	.	PROPN
ejpam-4144	501	23	/	/	SYM
ejpam-4144	501	24	eur	eur	PROPN
ejpam-4144	501	25	.	.	PUNCT
ejpam-4144	502	1	j.	j.	PROPN
ejpam-4144	502	2	pure	pure	PROPN
ejpam-4144	502	3	appl	appl	PROPN
ejpam-4144	502	4	.	.	PROPN
ejpam-4144	502	5	math	math	PROPN
ejpam-4144	502	6	,	,	PUNCT
ejpam-4144	502	7	14	14	NUM
ejpam-4144	502	8	(	(	PUNCT
ejpam-4144	502	9	4	4	NUM
ejpam-4144	502	10	)	)	PUNCT
ejpam-4144	502	11	(	(	PUNCT
ejpam-4144	502	12	2021	2021	NUM
ejpam-4144	502	13	)	)	PUNCT
ejpam-4144	502	14	,	,	PUNCT
ejpam-4144	502	15	1415	1415	NUM
ejpam-4144	502	16	-	-	SYM
ejpam-4144	502	17	1428	1428	NUM
ejpam-4144	502	18	1424	1424	NUM
ejpam-4144	502	19	suppose	suppose	VERB
ejpam-4144	502	20	now	now	ADV
ejpam-4144	502	21	that	that	SCONJ
ejpam-4144	502	22	the	the	DET
ejpam-4144	502	23	conditions	condition	NOUN
ejpam-4144	502	24	m1	m1	NOUN
ejpam-4144	502	25	=	=	SYM
ejpam-4144	502	26	m2	m2	PROPN
ejpam-4144	502	27	=	=	SYM
ejpam-4144	502	28	1	1	NUM
ejpam-4144	502	29	and	and	CCONJ
ejpam-4144	502	30	k	k	PROPN
ejpam-4144	502	31	≥	≥	NUM
ejpam-4144	502	32	4	4	NUM
ejpam-4144	502	33	do	do	AUX
ejpam-4144	502	34	not	not	PART
ejpam-4144	502	35	hold	hold	VERB
ejpam-4144	502	36	.	.	PUNCT
ejpam-4144	503	1	let	let	VERB
ejpam-4144	503	2	s′	s′	ADJ
ejpam-4144	503	3	=	=	PUNCT
ejpam-4144	503	4	{	{	PUNCT
ejpam-4144	503	5	v1	v1	NOUN
ejpam-4144	503	6	,	,	PUNCT
ejpam-4144	503	7	v1	v1	NOUN
ejpam-4144	503	8	,	,	PUNCT
ejpam-4144	503	9	v2	v2	PROPN
ejpam-4144	503	10	,	,	PUNCT
ejpam-4144	503	11	v3	v3	PROPN
ejpam-4144	503	12	,	,	PUNCT
ejpam-4144	503	13	.	.	PUNCT
ejpam-4144	503	14	.	.	PUNCT
ejpam-4144	503	15	.	.	PUNCT
ejpam-4144	504	1	,	,	PUNCT
ejpam-4144	504	2	vk	vk	ADP
ejpam-4144	504	3	}	}	PUNCT
ejpam-4144	504	4	.	.	PUNCT
ejpam-4144	505	1	by	by	ADP
ejpam-4144	505	2	theorem	theorem	NOUN
ejpam-4144	505	3	5(ii	5(ii	NUM
ejpam-4144	505	4	)	)	PUNCT
ejpam-4144	505	5	,	,	PUNCT
ejpam-4144	505	6	{	{	PUNCT
ejpam-4144	505	7	v1	v1	NOUN
ejpam-4144	505	8	,	,	PUNCT
ejpam-4144	505	9	v1	v1	NOUN
ejpam-4144	505	10	}	}	PUNCT
ejpam-4144	505	11	is	be	AUX
ejpam-4144	505	12	a	a	DET
ejpam-4144	505	13	hop	hop	NOUN
ejpam-4144	505	14	dominating	dominating	NOUN
ejpam-4144	505	15	set	set	NOUN
ejpam-4144	505	16	of	of	ADP
ejpam-4144	505	17	gg	gg	PROPN
ejpam-4144	505	18	.	.	PUNCT
ejpam-4144	506	1	hence	hence	ADV
ejpam-4144	506	2	,	,	PUNCT
ejpam-4144	506	3	s	s	VERB
ejpam-4144	506	4	is	be	AUX
ejpam-4144	506	5	a	a	DET
ejpam-4144	506	6	hop	hop	NOUN
ejpam-4144	506	7	dominating	dominating	NOUN
ejpam-4144	506	8	set	set	NOUN
ejpam-4144	506	9	of	of	ADP
ejpam-4144	506	10	gg	gg	PROPN
ejpam-4144	506	11	.	.	PUNCT
ejpam-4144	507	1	let	let	VERB
ejpam-4144	507	2	v′	v′	NOUN
ejpam-4144	507	3	∈	∈	PROPN
ejpam-4144	507	4	uj	uj	PROPN
ejpam-4144	507	5	\	\	PROPN
ejpam-4144	507	6	{	{	PUNCT
ejpam-4144	507	7	v1	v1	NOUN
ejpam-4144	507	8	}	}	PUNCT
ejpam-4144	507	9	,	,	PUNCT
ejpam-4144	507	10	where	where	SCONJ
ejpam-4144	507	11	j	j	PROPN
ejpam-4144	507	12	∈	∈	PROPN
ejpam-4144	507	13	{	{	PUNCT
ejpam-4144	507	14	1	1	NUM
ejpam-4144	507	15	,	,	PUNCT
ejpam-4144	507	16	2	2	NUM
ejpam-4144	507	17	,	,	PUNCT
ejpam-4144	507	18	.	.	PUNCT
ejpam-4144	507	19	.	.	PUNCT
ejpam-4144	508	1	.	.	PUNCT
ejpam-4144	509	1	,	,	PUNCT
ejpam-4144	509	2	k	k	X
ejpam-4144	509	3	}	}	PUNCT
ejpam-4144	509	4	.	.	PUNCT
ejpam-4144	510	1	then	then	ADV
ejpam-4144	510	2	[	[	X
ejpam-4144	510	3	v′	v′	NOUN
ejpam-4144	510	4	,	,	PUNCT
ejpam-4144	510	5	v1	v1	NOUN
ejpam-4144	510	6	,	,	PUNCT
ejpam-4144	510	7	v2	v2	PROPN
ejpam-4144	510	8	]	]	PUNCT
ejpam-4144	510	9	is	be	AUX
ejpam-4144	510	10	a	a	DET
ejpam-4144	510	11	v′-v2	v′-v2	NOUN
ejpam-4144	510	12	geodesic	geodesic	NOUN
ejpam-4144	510	13	in	in	ADP
ejpam-4144	510	14	gg	gg	PROPN
ejpam-4144	510	15	.	.	PUNCT
ejpam-4144	511	1	hence	hence	ADV
ejpam-4144	511	2	,	,	PUNCT
ejpam-4144	511	3	d	d	PROPN
ejpam-4144	511	4	gg	gg	PROPN
ejpam-4144	511	5	(	(	PUNCT
ejpam-4144	511	6	v′	v′	PROPN
ejpam-4144	511	7	,	,	PUNCT
ejpam-4144	511	8	v2	v2	PROPN
ejpam-4144	511	9	)	)	PUNCT
ejpam-4144	511	10	=	=	SYM
ejpam-4144	511	11	2	2	X
ejpam-4144	511	12	.	.	X
ejpam-4144	511	13	let	let	VERB
ejpam-4144	511	14	j	j	PROPN
ejpam-4144	511	15	∈	∈	PROPN
ejpam-4144	511	16	{	{	PUNCT
ejpam-4144	511	17	1	1	NUM
ejpam-4144	511	18	,	,	PUNCT
ejpam-4144	511	19	2	2	NUM
ejpam-4144	511	20	,	,	PUNCT
ejpam-4144	511	21	.	.	PUNCT
ejpam-4144	511	22	.	.	PUNCT
ejpam-4144	512	1	.	.	PUNCT
ejpam-4144	513	1	,	,	PUNCT
ejpam-4144	513	2	k	k	X
ejpam-4144	513	3	}	}	PUNCT
ejpam-4144	513	4	and	and	CCONJ
ejpam-4144	513	5	pick	pick	VERB
ejpam-4144	513	6	any	any	DET
ejpam-4144	513	7	i	i	PROPN
ejpam-4144	513	8	∈	∈	PROPN
ejpam-4144	513	9	{	{	PUNCT
ejpam-4144	513	10	1	1	NUM
ejpam-4144	513	11	,	,	PUNCT
ejpam-4144	513	12	2	2	NUM
ejpam-4144	513	13	,	,	PUNCT
ejpam-4144	513	14	.	.	PUNCT
ejpam-4144	513	15	.	.	PUNCT
ejpam-4144	514	1	.	.	PUNCT
ejpam-4144	515	1	,	,	PUNCT
ejpam-4144	515	2	k	k	X
ejpam-4144	515	3	}	}	PUNCT
ejpam-4144	515	4	\	\	NOUN
ejpam-4144	515	5	{	{	PUNCT
ejpam-4144	515	6	j	j	NOUN
ejpam-4144	515	7	}	}	PUNCT
ejpam-4144	515	8	.	.	PUNCT
ejpam-4144	516	1	then	then	ADV
ejpam-4144	516	2	for	for	ADP
ejpam-4144	516	3	y	y	PROPN
ejpam-4144	516	4	∈	∈	PROPN
ejpam-4144	516	5	u	u	PROPN
ejpam-4144	516	6	j	j	PROPN
ejpam-4144	516	7	\{vj	\{vj	PROPN
ejpam-4144	516	8	}	}	PUNCT
ejpam-4144	516	9	,	,	PUNCT
ejpam-4144	516	10	we	we	PRON
ejpam-4144	516	11	find	find	VERB
ejpam-4144	516	12	that	that	SCONJ
ejpam-4144	516	13	[	[	X
ejpam-4144	516	14	y	y	PROPN
ejpam-4144	516	15	,	,	PUNCT
ejpam-4144	516	16	vi	vi	PROPN
ejpam-4144	516	17	,	,	PUNCT
ejpam-4144	516	18	vj	vj	X
ejpam-4144	516	19	]	]	PUNCT
ejpam-4144	516	20	is	be	AUX
ejpam-4144	516	21	a	a	DET
ejpam-4144	516	22	y	y	PROPN
ejpam-4144	516	23	-	-	PUNCT
ejpam-4144	516	24	vj	vj	PROPN
ejpam-4144	516	25	geodesic	geodesic	NOUN
ejpam-4144	516	26	in	in	ADP
ejpam-4144	516	27	gg	gg	PROPN
ejpam-4144	516	28	.	.	PUNCT
ejpam-4144	517	1	hence	hence	ADV
ejpam-4144	517	2	,	,	PUNCT
ejpam-4144	517	3	d	d	PROPN
ejpam-4144	517	4	gg	gg	PROPN
ejpam-4144	517	5	(	(	PUNCT
ejpam-4144	517	6	y	y	PROPN
ejpam-4144	517	7	,	,	PUNCT
ejpam-4144	517	8	vj	vj	PROPN
ejpam-4144	517	9	)	)	PUNCT
ejpam-4144	517	10	=	=	SYM
ejpam-4144	517	11	2	2	X
ejpam-4144	517	12	.	.	PUNCT
ejpam-4144	518	1	this	this	PRON
ejpam-4144	518	2	shows	show	VERB
ejpam-4144	518	3	that	that	SCONJ
ejpam-4144	518	4	s′	s′	ADJ
ejpam-4144	518	5	is	be	AUX
ejpam-4144	518	6	a	a	DET
ejpam-4144	518	7	hop	hop	NOUN
ejpam-4144	518	8	dominating	dominating	NOUN
ejpam-4144	518	9	set	set	NOUN
ejpam-4144	518	10	of	of	ADP
ejpam-4144	518	11	gg	gg	PROPN
ejpam-4144	518	12	.	.	PUNCT
ejpam-4144	519	1	therefore	therefore	ADV
ejpam-4144	519	2	,	,	PUNCT
ejpam-4144	519	3	s′	s′	PROPN
ejpam-4144	519	4	is	be	AUX
ejpam-4144	519	5	a	a	DET
ejpam-4144	519	6	global	global	ADJ
ejpam-4144	519	7	hop	hop	NOUN
ejpam-4144	519	8	dominating	dominating	NOUN
ejpam-4144	519	9	set	set	NOUN
ejpam-4144	519	10	of	of	ADP
ejpam-4144	519	11	gg	gg	PROPN
ejpam-4144	519	12	and	and	CCONJ
ejpam-4144	519	13	γgh(gg	γgh(gg	NUM
ejpam-4144	519	14	)	)	PUNCT
ejpam-4144	519	15	≤	≤	NOUN
ejpam-4144	519	16	|s′|	|s′|	NOUN
ejpam-4144	519	17	=	=	PUNCT
ejpam-4144	520	1	k	k	PROPN
ejpam-4144	521	1	+	+	NOUN
ejpam-4144	521	2	1	1	X
ejpam-4144	521	3	.	.	PUNCT
ejpam-4144	521	4	let	let	VERB
ejpam-4144	521	5	s0	s0	PROPN
ejpam-4144	521	6	be	be	AUX
ejpam-4144	521	7	a	a	DET
ejpam-4144	521	8	γgh	γgh	PROPN
ejpam-4144	521	9	-	-	PUNCT
ejpam-4144	521	10	set	set	NOUN
ejpam-4144	521	11	of	of	ADP
ejpam-4144	521	12	gg	gg	PROPN
ejpam-4144	521	13	.	.	PUNCT
ejpam-4144	522	1	as	as	SCONJ
ejpam-4144	522	2	shown	show	VERB
ejpam-4144	522	3	and	and	CCONJ
ejpam-4144	522	4	seen	see	VERB
ejpam-4144	522	5	earlier	early	ADJ
ejpam-4144	522	6	s0	s0	PROPN
ejpam-4144	522	7	∩	∩	NOUN
ejpam-4144	522	8	(	(	PUNCT
ejpam-4144	522	9	uj	uj	PROPN
ejpam-4144	522	10	∪	∪	PROPN
ejpam-4144	522	11	u	u	PROPN
ejpam-4144	522	12	j	j	PROPN
ejpam-4144	522	13	)	)	PUNCT
ejpam-4144	522	14	̸=	̸=	PROPN
ejpam-4144	522	15	∅	∅	NOUN
ejpam-4144	522	16	for	for	ADP
ejpam-4144	522	17	each	each	DET
ejpam-4144	522	18	j	j	PROPN
ejpam-4144	522	19	∈	∈	PROPN
ejpam-4144	522	20	{	{	PUNCT
ejpam-4144	522	21	1	1	NUM
ejpam-4144	522	22	,	,	PUNCT
ejpam-4144	522	23	2	2	NUM
ejpam-4144	522	24	,	,	PUNCT
ejpam-4144	522	25	.	.	PUNCT
ejpam-4144	522	26	.	.	PUNCT
ejpam-4144	523	1	.	.	PUNCT
ejpam-4144	524	1	,	,	PUNCT
ejpam-4144	524	2	k	k	X
ejpam-4144	524	3	}	}	PUNCT
ejpam-4144	524	4	.	.	PUNCT
ejpam-4144	525	1	next	next	ADV
ejpam-4144	525	2	,	,	PUNCT
ejpam-4144	525	3	suppose	suppose	VERB
ejpam-4144	525	4	there	there	PRON
ejpam-4144	525	5	exists	exist	VERB
ejpam-4144	525	6	j	j	PROPN
ejpam-4144	525	7	∈	∈	PROPN
ejpam-4144	525	8	{	{	PUNCT
ejpam-4144	525	9	1	1	NUM
ejpam-4144	525	10	,	,	PUNCT
ejpam-4144	525	11	2	2	NUM
ejpam-4144	525	12	,	,	PUNCT
ejpam-4144	525	13	.	.	PUNCT
ejpam-4144	525	14	.	.	PUNCT
ejpam-4144	525	15	.	.	PUNCT
ejpam-4144	526	1	,	,	PUNCT
ejpam-4144	526	2	k	k	X
ejpam-4144	526	3	}	}	PUNCT
ejpam-4144	526	4	with	with	ADP
ejpam-4144	526	5	mj	mj	PROPN
ejpam-4144	526	6	≥	≥	NUM
ejpam-4144	526	7	2	2	NUM
ejpam-4144	526	8	such	such	ADJ
ejpam-4144	526	9	that	that	DET
ejpam-4144	526	10	|s0	|s0	ADJ
ejpam-4144	526	11	∩	∩	ADJ
ejpam-4144	526	12	u	u	NOUN
ejpam-4144	526	13	j	j	PROPN
ejpam-4144	526	14	|	|	ADV
ejpam-4144	526	15	=	=	NOUN
ejpam-4144	526	16	0	0	X
ejpam-4144	526	17	.	.	PUNCT
ejpam-4144	527	1	let	let	VERB
ejpam-4144	527	2	a	a	DET
ejpam-4144	527	3	∈	∈	PROPN
ejpam-4144	527	4	u	u	X
ejpam-4144	527	5	j	j	PROPN
ejpam-4144	527	6	.	.	PUNCT
ejpam-4144	528	1	since	since	SCONJ
ejpam-4144	528	2	d	d	PROPN
ejpam-4144	528	3	gg	gg	X
ejpam-4144	528	4	(	(	PUNCT
ejpam-4144	528	5	a	a	DET
ejpam-4144	528	6	,	,	PUNCT
ejpam-4144	528	7	p	p	NOUN
ejpam-4144	528	8	)	)	PUNCT
ejpam-4144	528	9	=	=	SYM
ejpam-4144	528	10	1	1	NUM
ejpam-4144	528	11	for	for	ADP
ejpam-4144	528	12	p	p	PROPN
ejpam-4144	528	13	∈	∈	PROPN
ejpam-4144	528	14	v	v	ADP
ejpam-4144	528	15	(	(	PUNCT
ejpam-4144	528	16	gg	gg	NOUN
ejpam-4144	528	17	)	)	PUNCT
ejpam-4144	528	18	\	\	PUNCT
ejpam-4144	528	19	(	(	PUNCT
ejpam-4144	528	20	u	u	NOUN
ejpam-4144	528	21	j	j	PROPN
ejpam-4144	528	22	∪	∪	X
ejpam-4144	528	23	{	{	PUNCT
ejpam-4144	528	24	a	a	PRON
ejpam-4144	528	25	}	}	PUNCT
ejpam-4144	528	26	)	)	PUNCT
ejpam-4144	528	27	and	and	CCONJ
ejpam-4144	528	28	|s0	|s0	ADJ
ejpam-4144	528	29	∩	∩	ADJ
ejpam-4144	528	30	u	u	NOUN
ejpam-4144	528	31	j	j	PROPN
ejpam-4144	528	32	|	|	ADV
ejpam-4144	528	33	=	=	SYM
ejpam-4144	528	34	0	0	NUM
ejpam-4144	528	35	,	,	PUNCT
ejpam-4144	528	36	it	it	PRON
ejpam-4144	528	37	follows	follow	VERB
ejpam-4144	528	38	that	that	SCONJ
ejpam-4144	528	39	a	a	DET
ejpam-4144	528	40	∈	∈	PROPN
ejpam-4144	528	41	s0	s0	NOUN
ejpam-4144	528	42	.	.	PUNCT
ejpam-4144	529	1	thus	thus	ADV
ejpam-4144	529	2	,	,	PUNCT
ejpam-4144	529	3	uj	uj	PROPN
ejpam-4144	529	4	⊆	⊆	NUM
ejpam-4144	529	5	s0	s0	NOUN
ejpam-4144	529	6	.	.	PUNCT
ejpam-4144	530	1	since	since	SCONJ
ejpam-4144	530	2	mj	mj	PROPN
ejpam-4144	530	3	≥	≥	PROPN
ejpam-4144	530	4	2	2	NUM
ejpam-4144	530	5	,	,	PUNCT
ejpam-4144	530	6	it	it	PRON
ejpam-4144	530	7	follows	follow	VERB
ejpam-4144	530	8	that	that	SCONJ
ejpam-4144	530	9	γgh(gg	γgh(gg	NUM
ejpam-4144	530	10	)	)	PUNCT
ejpam-4144	530	11	=	=	SYM
ejpam-4144	530	12	|s0|	|s0|	NOUN
ejpam-4144	530	13	≥	≥	NOUN
ejpam-4144	530	14	k	k	PROPN
ejpam-4144	531	1	+	+	CCONJ
ejpam-4144	531	2	1	1	X
ejpam-4144	531	3	.	.	PUNCT
ejpam-4144	531	4	suppose	suppose	VERB
ejpam-4144	531	5	that	that	SCONJ
ejpam-4144	531	6	|s0	|s0	ADJ
ejpam-4144	531	7	∩	∩	ADJ
ejpam-4144	531	8	u	u	PROPN
ejpam-4144	531	9	j	j	PROPN
ejpam-4144	531	10	|	|	ADV
ejpam-4144	531	11	̸=	̸=	PROPN
ejpam-4144	531	12	0	0	NUM
ejpam-4144	531	13	for	for	ADP
ejpam-4144	531	14	each	each	DET
ejpam-4144	531	15	j	j	NOUN
ejpam-4144	531	16	with	with	ADP
ejpam-4144	531	17	mj	mj	PROPN
ejpam-4144	531	18	≥	≥	PROPN
ejpam-4144	531	19	2	2	NUM
ejpam-4144	531	20	.	.	PUNCT
ejpam-4144	532	1	if	if	SCONJ
ejpam-4144	532	2	|s0	|s0	ADJ
ejpam-4144	532	3	∩	∩	ADJ
ejpam-4144	532	4	u	u	PROPN
ejpam-4144	532	5	j	j	PROPN
ejpam-4144	532	6	|	|	ADV
ejpam-4144	532	7	≥	≥	NOUN
ejpam-4144	532	8	2	2	NUM
ejpam-4144	532	9	for	for	ADP
ejpam-4144	532	10	some	some	DET
ejpam-4144	532	11	j	j	NOUN
ejpam-4144	532	12	with	with	ADP
ejpam-4144	532	13	mj	mj	PROPN
ejpam-4144	532	14	≥	≥	PROPN
ejpam-4144	532	15	2	2	NUM
ejpam-4144	532	16	,	,	PUNCT
ejpam-4144	532	17	then	then	ADV
ejpam-4144	532	18	γgh(gg	γgh(gg	NUM
ejpam-4144	532	19	)	)	PUNCT
ejpam-4144	533	1	=	=	PRON
ejpam-4144	533	2	|s0|	|s0|	NOUN
ejpam-4144	533	3	≥	≥	NOUN
ejpam-4144	533	4	k	k	PROPN
ejpam-4144	534	1	+	+	CCONJ
ejpam-4144	534	2	1	1	X
ejpam-4144	534	3	.	.	PUNCT
ejpam-4144	534	4	suppose	suppose	VERB
ejpam-4144	534	5	that	that	SCONJ
ejpam-4144	534	6	|s0	|s0	ADJ
ejpam-4144	534	7	∩	∩	ADJ
ejpam-4144	534	8	u	u	NOUN
ejpam-4144	534	9	j	j	PROPN
ejpam-4144	534	10	|	|	ADV
ejpam-4144	534	11	=	=	NOUN
ejpam-4144	534	12	1	1	NUM
ejpam-4144	534	13	for	for	ADP
ejpam-4144	534	14	each	each	DET
ejpam-4144	534	15	j	j	NOUN
ejpam-4144	534	16	with	with	ADP
ejpam-4144	534	17	mj	mj	PROPN
ejpam-4144	534	18	≥	≥	PROPN
ejpam-4144	534	19	2	2	NUM
ejpam-4144	534	20	.	.	PUNCT
ejpam-4144	535	1	for	for	ADP
ejpam-4144	535	2	a	a	DET
ejpam-4144	535	3	j	j	NOUN
ejpam-4144	535	4	satisfying	satisfy	VERB
ejpam-4144	535	5	this	this	DET
ejpam-4144	535	6	property	property	NOUN
ejpam-4144	535	7	,	,	PUNCT
ejpam-4144	535	8	pick	pick	VERB
ejpam-4144	535	9	y	y	PROPN
ejpam-4144	535	10	∈	∈	PROPN
ejpam-4144	535	11	u	u	PROPN
ejpam-4144	535	12	j	j	PROPN
ejpam-4144	535	13	\	\	PROPN
ejpam-4144	535	14	s0	s0	PROPN
ejpam-4144	535	15	.	.	PUNCT
ejpam-4144	536	1	since	since	SCONJ
ejpam-4144	536	2	s	s	PROPN
ejpam-4144	536	3	is	be	AUX
ejpam-4144	536	4	a	a	DET
ejpam-4144	536	5	hop	hop	NOUN
ejpam-4144	536	6	dominating	dominating	NOUN
ejpam-4144	536	7	set	set	NOUN
ejpam-4144	536	8	of	of	ADP
ejpam-4144	536	9	gg	gg	PROPN
ejpam-4144	536	10	and	and	CCONJ
ejpam-4144	536	11	the	the	DET
ejpam-4144	536	12	induced	induced	ADJ
ejpam-4144	536	13	graph	graph	NOUN
ejpam-4144	536	14	of	of	ADP
ejpam-4144	536	15	u	u	PROPN
ejpam-4144	536	16	j	j	PROPN
ejpam-4144	536	17	is	be	AUX
ejpam-4144	536	18	a	a	DET
ejpam-4144	536	19	complete	complete	ADJ
ejpam-4144	536	20	graph	graph	NOUN
ejpam-4144	536	21	in	in	ADP
ejpam-4144	536	22	gg	gg	PROPN
ejpam-4144	536	23	,	,	PUNCT
ejpam-4144	536	24	it	it	PRON
ejpam-4144	536	25	follows	follow	VERB
ejpam-4144	536	26	that	that	SCONJ
ejpam-4144	536	27	there	there	PRON
ejpam-4144	536	28	exists	exist	VERB
ejpam-4144	536	29	r	r	PROPN
ejpam-4144	536	30	̸=	̸=	PROPN
ejpam-4144	536	31	j	j	PROPN
ejpam-4144	536	32	such	such	ADJ
ejpam-4144	536	33	z	z	NOUN
ejpam-4144	536	34	∈	∈	NOUN
ejpam-4144	536	35	ur	ur	INTJ
ejpam-4144	536	36	∩s0	∩s0	NOUN
ejpam-4144	536	37	and	and	CCONJ
ejpam-4144	536	38	dgg(y	dgg(y	PROPN
ejpam-4144	536	39	,	,	PUNCT
ejpam-4144	536	40	z	z	NOUN
ejpam-4144	536	41	)	)	PUNCT
ejpam-4144	536	42	=	=	SYM
ejpam-4144	537	1	2	2	X
ejpam-4144	537	2	.	.	X
ejpam-4144	538	1	if	if	SCONJ
ejpam-4144	538	2	an	an	DET
ejpam-4144	538	3	r	r	NOUN
ejpam-4144	538	4	exists	exist	VERB
ejpam-4144	538	5	such	such	ADJ
ejpam-4144	538	6	that	that	SCONJ
ejpam-4144	538	7	mr	mr	PROPN
ejpam-4144	538	8	≥	≥	PROPN
ejpam-4144	538	9	2	2	NUM
ejpam-4144	538	10	,	,	PUNCT
ejpam-4144	538	11	then	then	ADV
ejpam-4144	538	12	this	this	PRON
ejpam-4144	538	13	would	would	AUX
ejpam-4144	538	14	imply	imply	VERB
ejpam-4144	538	15	that	that	DET
ejpam-4144	538	16	γgh(gg	γgh(gg	NUM
ejpam-4144	538	17	)	)	PUNCT
ejpam-4144	538	18	=	=	SYM
ejpam-4144	538	19	|s0|	|s0|	NOUN
ejpam-4144	538	20	≥	≥	NOUN
ejpam-4144	538	21	k	k	PROPN
ejpam-4144	539	1	+	+	CCONJ
ejpam-4144	539	2	1	1	X
ejpam-4144	539	3	.	.	PUNCT
ejpam-4144	539	4	so	so	ADV
ejpam-4144	539	5	suppose	suppose	VERB
ejpam-4144	539	6	that	that	SCONJ
ejpam-4144	539	7	there	there	PRON
ejpam-4144	539	8	exists	exist	VERB
ejpam-4144	539	9	no	no	DET
ejpam-4144	539	10	such	such	ADJ
ejpam-4144	539	11	r	r	NOUN
ejpam-4144	539	12	with	with	ADP
ejpam-4144	539	13	mr	mr	PROPN
ejpam-4144	539	14	≥	≥	PROPN
ejpam-4144	539	15	2	2	NUM
ejpam-4144	539	16	.	.	PUNCT
ejpam-4144	540	1	then	then	ADV
ejpam-4144	540	2	mr	mr	PROPN
ejpam-4144	540	3	=	=	PROPN
ejpam-4144	540	4	1	1	NUM
ejpam-4144	540	5	and	and	CCONJ
ejpam-4144	540	6	r	r	NOUN
ejpam-4144	540	7	=	=	SYM
ejpam-4144	540	8	1	1	NUM
ejpam-4144	540	9	or	or	CCONJ
ejpam-4144	540	10	r	r	NOUN
ejpam-4144	540	11	=	=	SYM
ejpam-4144	540	12	2	2	NUM
ejpam-4144	540	13	,	,	PUNCT
ejpam-4144	540	14	say	say	VERB
ejpam-4144	540	15	ur	ur	INTJ
ejpam-4144	540	16	=	=	NOUN
ejpam-4144	540	17	u1	u1	NOUN
ejpam-4144	540	18	.	.	PUNCT
ejpam-4144	541	1	if	if	SCONJ
ejpam-4144	541	2	z	z	PROPN
ejpam-4144	541	3	∈	∈	PROPN
ejpam-4144	541	4	s0	s0	PROPN
ejpam-4144	541	5	,	,	PUNCT
ejpam-4144	541	6	then	then	ADV
ejpam-4144	541	7	γgh(gg	γgh(gg	NUM
ejpam-4144	541	8	)	)	PUNCT
ejpam-4144	541	9	=	=	PRON
ejpam-4144	541	10	|s0|	|s0|	NOUN
ejpam-4144	541	11	≥	≥	NOUN
ejpam-4144	541	12	k	k	PROPN
ejpam-4144	542	1	+	+	CCONJ
ejpam-4144	542	2	1	1	X
ejpam-4144	542	3	.	.	PUNCT
ejpam-4144	542	4	suppose	suppose	VERB
ejpam-4144	543	1	z	z	NOUN
ejpam-4144	543	2	/∈	/∈	PUNCT
ejpam-4144	543	3	s0	s0	PROPN
ejpam-4144	543	4	.	.	PUNCT
ejpam-4144	544	1	then	then	ADV
ejpam-4144	544	2	there	there	PRON
ejpam-4144	544	3	exists	exist	VERB
ejpam-4144	544	4	p	p	PROPN
ejpam-4144	544	5	∈	∈	PROPN
ejpam-4144	544	6	us	us	PROPN
ejpam-4144	544	7	∩	∩	ADJ
ejpam-4144	544	8	s0	s0	NOUN
ejpam-4144	544	9	for	for	ADP
ejpam-4144	544	10	some	some	PRON
ejpam-4144	544	11	s	s	PART
ejpam-4144	544	12	≥	≥	NOUN
ejpam-4144	544	13	2	2	NUM
ejpam-4144	544	14	such	such	ADJ
ejpam-4144	544	15	that	that	DET
ejpam-4144	544	16	dgg(z	dgg(z	PROPN
ejpam-4144	544	17	,	,	PUNCT
ejpam-4144	544	18	p	p	NOUN
ejpam-4144	544	19	)	)	PUNCT
ejpam-4144	545	1	=	=	SYM
ejpam-4144	545	2	2	2	X
ejpam-4144	545	3	.	.	X
ejpam-4144	546	1	if	if	SCONJ
ejpam-4144	546	2	ms	ms	PROPN
ejpam-4144	546	3	=	=	PROPN
ejpam-4144	546	4	1	1	NUM
ejpam-4144	546	5	,	,	PUNCT
ejpam-4144	546	6	then	then	ADV
ejpam-4144	546	7	s	s	VERB
ejpam-4144	546	8	=	=	SYM
ejpam-4144	546	9	2	2	NUM
ejpam-4144	546	10	and	and	CCONJ
ejpam-4144	546	11	j	j	NOUN
ejpam-4144	547	1	=	=	SYM
ejpam-4144	547	2	k	k	PROPN
ejpam-4144	547	3	=	=	SYM
ejpam-4144	547	4	3	3	NUM
ejpam-4144	547	5	by	by	ADP
ejpam-4144	547	6	assumption	assumption	NOUN
ejpam-4144	547	7	.	.	PUNCT
ejpam-4144	548	1	if	if	SCONJ
ejpam-4144	548	2	p	p	PROPN
ejpam-4144	548	3	∈	∈	PROPN
ejpam-4144	548	4	s0	s0	NOUN
ejpam-4144	548	5	,	,	PUNCT
ejpam-4144	548	6	then	then	ADV
ejpam-4144	548	7	γgh(gg	γgh(gg	NUM
ejpam-4144	548	8	)	)	PUNCT
ejpam-4144	548	9	=	=	PRON
ejpam-4144	548	10	|s0|	|s0|	NOUN
ejpam-4144	548	11	≥	≥	NOUN
ejpam-4144	548	12	k	k	PROPN
ejpam-4144	549	1	+	+	CCONJ
ejpam-4144	549	2	1	1	X
ejpam-4144	549	3	.	.	PUNCT
ejpam-4144	549	4	suppose	suppose	VERB
ejpam-4144	549	5	p	p	X
ejpam-4144	549	6	/∈	/∈	PUNCT
ejpam-4144	549	7	s0	s0	NOUN
ejpam-4144	549	8	and	and	CCONJ
ejpam-4144	549	9	let	let	VERB
ejpam-4144	549	10	s0	s0	PROPN
ejpam-4144	549	11	∩	∩	PROPN
ejpam-4144	549	12	u	u	PROPN
ejpam-4144	549	13	j	j	PROPN
ejpam-4144	549	14	=	=	PUNCT
ejpam-4144	549	15	{	{	PUNCT
ejpam-4144	549	16	q	q	X
ejpam-4144	549	17	}	}	PUNCT
ejpam-4144	549	18	.	.	PUNCT
ejpam-4144	550	1	since	since	SCONJ
ejpam-4144	550	2	s0	s0	PROPN
ejpam-4144	550	3	is	be	AUX
ejpam-4144	550	4	a	a	DET
ejpam-4144	550	5	hop	hop	NOUN
ejpam-4144	550	6	dominating	dominating	NOUN
ejpam-4144	550	7	set	set	NOUN
ejpam-4144	550	8	of	of	ADP
ejpam-4144	550	9	gg	gg	PROPN
ejpam-4144	550	10	,	,	PUNCT
ejpam-4144	550	11	z	z	PROPN
ejpam-4144	550	12	,	,	PUNCT
ejpam-4144	550	13	p	p	NOUN
ejpam-4144	550	14	/∈	/∈	PUNCT
ejpam-4144	550	15	s0	s0	PROPN
ejpam-4144	550	16	,	,	PUNCT
ejpam-4144	550	17	and	and	CCONJ
ejpam-4144	550	18	k	k	PROPN
ejpam-4144	550	19	=	=	SYM
ejpam-4144	550	20	3	3	NUM
ejpam-4144	550	21	,	,	PUNCT
ejpam-4144	550	22	we	we	PRON
ejpam-4144	550	23	must	must	AUX
ejpam-4144	550	24	have	have	VERB
ejpam-4144	550	25	q	q	PROPN
ejpam-4144	550	26	∈	∈	PROPN
ejpam-4144	550	27	s0	s0	NOUN
ejpam-4144	550	28	.	.	PUNCT
ejpam-4144	551	1	hence	hence	ADV
ejpam-4144	551	2	,	,	PUNCT
ejpam-4144	551	3	γgh(gg	γgh(gg	NUM
ejpam-4144	551	4	)	)	PUNCT
ejpam-4144	551	5	=	=	SYM
ejpam-4144	551	6	|s0|	|s0|	NOUN
ejpam-4144	551	7	≥	≥	NOUN
ejpam-4144	551	8	k	k	PROPN
ejpam-4144	552	1	+	+	CCONJ
ejpam-4144	552	2	1	1	X
ejpam-4144	552	3	.	.	PUNCT
ejpam-4144	552	4	now	now	ADV
ejpam-4144	552	5	,	,	PUNCT
ejpam-4144	552	6	if	if	SCONJ
ejpam-4144	552	7	ms	ms	PROPN
ejpam-4144	552	8	≥	≥	PROPN
ejpam-4144	552	9	2	2	NUM
ejpam-4144	552	10	,	,	PUNCT
ejpam-4144	552	11	then	then	ADV
ejpam-4144	552	12	s	s	VERB
ejpam-4144	552	13	=	=	SYM
ejpam-4144	552	14	k	k	X
ejpam-4144	552	15	by	by	ADP
ejpam-4144	552	16	assumption	assumption	NOUN
ejpam-4144	552	17	.	.	PUNCT
ejpam-4144	553	1	this	this	PRON
ejpam-4144	553	2	implies	imply	VERB
ejpam-4144	553	3	that	that	SCONJ
ejpam-4144	553	4	|s0∩(uj∪u	|s0∩(uj∪u	NUM
ejpam-4144	553	5	j)|	j)|	NOUN
ejpam-4144	553	6	≥	≥	NOUN
ejpam-4144	553	7	2	2	NUM
ejpam-4144	553	8	,	,	PUNCT
ejpam-4144	553	9	showing	show	VERB
ejpam-4144	553	10	that	that	SCONJ
ejpam-4144	553	11	γgh(gg	γgh(gg	NUM
ejpam-4144	553	12	)	)	PUNCT
ejpam-4144	553	13	=	=	SYM
ejpam-4144	553	14	|s0|	|s0|	NOUN
ejpam-4144	553	15	≥	≥	PROPN
ejpam-4144	553	16	k+1	k+1	X
ejpam-4144	553	17	.	.	PROPN
ejpam-4144	553	18	therefore	therefore	ADV
ejpam-4144	553	19	,	,	PUNCT
ejpam-4144	553	20	γgh(gg	γgh(gg	NUM
ejpam-4144	553	21	)	)	PUNCT
ejpam-4144	553	22	=	=	PUNCT
ejpam-4144	554	1	k+1	k+1	X
ejpam-4144	554	2	.	.	PUNCT
ejpam-4144	555	1	the	the	DET
ejpam-4144	555	2	shadow	shadow	NOUN
ejpam-4144	555	3	graph	graph	VERB
ejpam-4144	555	4	d2(g	d2(g	PROPN
ejpam-4144	555	5	)	)	PUNCT
ejpam-4144	555	6	of	of	ADP
ejpam-4144	555	7	a	a	DET
ejpam-4144	555	8	graph	graph	NOUN
ejpam-4144	555	9	g	g	NOUN
ejpam-4144	555	10	is	be	AUX
ejpam-4144	555	11	the	the	DET
ejpam-4144	555	12	graph	graph	NOUN
ejpam-4144	555	13	obtained	obtain	VERB
ejpam-4144	555	14	by	by	ADP
ejpam-4144	555	15	taking	take	VERB
ejpam-4144	555	16	two	two	NUM
ejpam-4144	555	17	copies	copy	NOUN
ejpam-4144	555	18	of	of	ADP
ejpam-4144	555	19	g	g	NOUN
ejpam-4144	555	20	,	,	PUNCT
ejpam-4144	555	21	say	say	VERB
ejpam-4144	555	22	g1	g1	PROPN
ejpam-4144	555	23	and	and	CCONJ
ejpam-4144	555	24	g2	g2	PROPN
ejpam-4144	555	25	,	,	PUNCT
ejpam-4144	555	26	and	and	CCONJ
ejpam-4144	555	27	joining	join	VERB
ejpam-4144	555	28	each	each	DET
ejpam-4144	555	29	vertex	vertex	NOUN
ejpam-4144	555	30	u	u	NOUN
ejpam-4144	555	31	∈	∈	PROPN
ejpam-4144	555	32	v	v	NOUN
ejpam-4144	555	33	(	(	PUNCT
ejpam-4144	555	34	g1	g1	PROPN
ejpam-4144	555	35	)	)	PUNCT
ejpam-4144	555	36	to	to	ADP
ejpam-4144	555	37	the	the	DET
ejpam-4144	555	38	neighbors	neighbor	NOUN
ejpam-4144	555	39	of	of	ADP
ejpam-4144	555	40	the	the	DET
ejpam-4144	555	41	corresponding	corresponding	ADJ
ejpam-4144	555	42	vertex	vertex	NOUN
ejpam-4144	555	43	u′	u′	PROPN
ejpam-4144	555	44	∈	∈	PROPN
ejpam-4144	555	45	v	v	NOUN
ejpam-4144	555	46	(	(	PUNCT
ejpam-4144	555	47	g2	g2	PROPN
ejpam-4144	555	48	)	)	PUNCT
ejpam-4144	555	49	.	.	PUNCT
ejpam-4144	556	1	lemma	lemma	PROPN
ejpam-4144	556	2	2	2	X
ejpam-4144	556	3	.	.	PUNCT
ejpam-4144	557	1	let	let	VERB
ejpam-4144	557	2	g	g	PRON
ejpam-4144	557	3	be	be	AUX
ejpam-4144	557	4	a	a	DET
ejpam-4144	557	5	non	non	ADJ
ejpam-4144	557	6	-	-	ADJ
ejpam-4144	557	7	trivial	trivial	ADJ
ejpam-4144	557	8	connected	connected	ADJ
ejpam-4144	557	9	graph	graph	NOUN
ejpam-4144	557	10	and	and	CCONJ
ejpam-4144	557	11	let	let	VERB
ejpam-4144	557	12	g1	g1	PROPN
ejpam-4144	557	13	and	and	CCONJ
ejpam-4144	557	14	g2	g2	PROPN
ejpam-4144	557	15	be	be	VERB
ejpam-4144	557	16	copies	copy	NOUN
ejpam-4144	557	17	of	of	ADP
ejpam-4144	557	18	g	g	NOUN
ejpam-4144	557	19	in	in	ADP
ejpam-4144	557	20	the	the	DET
ejpam-4144	557	21	graph	graph	NOUN
ejpam-4144	557	22	d2(g	d2(g	PROPN
ejpam-4144	557	23	)	)	PUNCT
ejpam-4144	557	24	.	.	PUNCT
ejpam-4144	558	1	if	if	SCONJ
ejpam-4144	558	2	w	w	PROPN
ejpam-4144	558	3	∈	∈	PROPN
ejpam-4144	558	4	v	v	X
ejpam-4144	558	5	(	(	PUNCT
ejpam-4144	558	6	g1	g1	PROPN
ejpam-4144	558	7	)	)	PUNCT
ejpam-4144	558	8	and	and	CCONJ
ejpam-4144	558	9	w′	w′	PROPN
ejpam-4144	558	10	∈	∈	PROPN
ejpam-4144	558	11	v	v	X
ejpam-4144	558	12	(	(	PUNCT
ejpam-4144	558	13	g2	g2	PROPN
ejpam-4144	558	14	)	)	PUNCT
ejpam-4144	558	15	is	be	AUX
ejpam-4144	558	16	the	the	DET
ejpam-4144	558	17	corresponding	corresponding	ADJ
ejpam-4144	558	18	vertex	vertex	NOUN
ejpam-4144	558	19	of	of	ADP
ejpam-4144	558	20	w	w	PROPN
ejpam-4144	558	21	,	,	PUNCT
ejpam-4144	558	22	then	then	ADV
ejpam-4144	558	23	nd2(g)[w	nd2(g)[w	X
ejpam-4144	558	24	,	,	PUNCT
ejpam-4144	558	25	2	2	X
ejpam-4144	558	26	]	]	PUNCT
ejpam-4144	558	27	=	=	SYM
ejpam-4144	558	28	ng1	ng1	NOUN
ejpam-4144	559	1	[	[	X
ejpam-4144	559	2	w	w	NOUN
ejpam-4144	559	3	,	,	PUNCT
ejpam-4144	559	4	2	2	NUM
ejpam-4144	559	5	]	]	PUNCT
ejpam-4144	559	6	∪ng2	∪ng2	PROPN
ejpam-4144	560	1	[	[	X
ejpam-4144	560	2	w	w	NOUN
ejpam-4144	560	3	′	′	NOUN
ejpam-4144	560	4	,	,	PUNCT
ejpam-4144	560	5	2	2	NUM
ejpam-4144	560	6	]	]	PUNCT
ejpam-4144	560	7	=	=	SYM
ejpam-4144	560	8	nd2(g)[w	nd2(g)[w	NOUN
ejpam-4144	560	9	′	′	NUM
ejpam-4144	560	10	,	,	PUNCT
ejpam-4144	560	11	2	2	NUM
ejpam-4144	560	12	]	]	PUNCT
ejpam-4144	560	13	.	.	PUNCT
ejpam-4144	561	1	proof	proof	NOUN
ejpam-4144	561	2	.	.	PUNCT
ejpam-4144	562	1	clearly	clearly	ADV
ejpam-4144	562	2	,	,	PUNCT
ejpam-4144	562	3	ng1	ng1	NOUN
ejpam-4144	563	1	[	[	X
ejpam-4144	563	2	w	w	NOUN
ejpam-4144	563	3	,	,	PUNCT
ejpam-4144	563	4	2	2	NUM
ejpam-4144	563	5	]	]	PUNCT
ejpam-4144	563	6	∪ng2	∪ng2	PROPN
ejpam-4144	564	1	[	[	X
ejpam-4144	564	2	w	w	NOUN
ejpam-4144	564	3	′	′	NOUN
ejpam-4144	564	4	,	,	PUNCT
ejpam-4144	564	5	2	2	NUM
ejpam-4144	564	6	]	]	PUNCT
ejpam-4144	564	7	⊆	⊆	NUM
ejpam-4144	564	8	nd2(g)[w	nd2(g)[w	X
ejpam-4144	564	9	,	,	PUNCT
ejpam-4144	564	10	2	2	NUM
ejpam-4144	564	11	]	]	PUNCT
ejpam-4144	564	12	.	.	PUNCT
ejpam-4144	565	1	now	now	ADV
ejpam-4144	565	2	let	let	VERB
ejpam-4144	565	3	x	x	X
ejpam-4144	565	4	∈	∈	PROPN
ejpam-4144	565	5	nd2(g)[w	nd2(g)[w	X
ejpam-4144	565	6	,	,	PUNCT
ejpam-4144	565	7	2	2	NUM
ejpam-4144	565	8	]	]	PUNCT
ejpam-4144	565	9	.	.	PUNCT
ejpam-4144	566	1	then	then	ADV
ejpam-4144	566	2	x	x	X
ejpam-4144	566	3	=	=	PUNCT
ejpam-4144	566	4	w	w	PROPN
ejpam-4144	566	5	or	or	CCONJ
ejpam-4144	566	6	dd2(g)(w	dd2(g)(w	ADJ
ejpam-4144	566	7	,	,	PUNCT
ejpam-4144	566	8	x	x	NOUN
ejpam-4144	566	9	)	)	PUNCT
ejpam-4144	566	10	=	=	SYM
ejpam-4144	566	11	2	2	X
ejpam-4144	566	12	.	.	PUNCT
ejpam-4144	566	13	suppose	suppose	VERB
ejpam-4144	566	14	first	first	ADV
ejpam-4144	566	15	that	that	SCONJ
ejpam-4144	566	16	x	x	PUNCT
ejpam-4144	566	17	∈	∈	NOUN
ejpam-4144	566	18	v	v	NOUN
ejpam-4144	566	19	(	(	PUNCT
ejpam-4144	566	20	g1	g1	PROPN
ejpam-4144	566	21	)	)	PUNCT
ejpam-4144	566	22	.	.	PUNCT
ejpam-4144	567	1	if	if	SCONJ
ejpam-4144	567	2	x	x	X
ejpam-4144	567	3	=	=	SYM
ejpam-4144	567	4	w	w	PROPN
ejpam-4144	567	5	,	,	PUNCT
ejpam-4144	567	6	then	then	ADV
ejpam-4144	567	7	x	x	SYM
ejpam-4144	567	8	∈	∈	PROPN
ejpam-4144	567	9	ng1	ng1	NOUN
ejpam-4144	568	1	[	[	X
ejpam-4144	568	2	w	w	NOUN
ejpam-4144	568	3	,	,	PUNCT
ejpam-4144	568	4	2	2	NUM
ejpam-4144	568	5	]	]	PUNCT
ejpam-4144	568	6	.	.	PUNCT
ejpam-4144	569	1	suppose	suppose	VERB
ejpam-4144	569	2	that	that	SCONJ
ejpam-4144	569	3	dd2(g)(w	dd2(g)(w	NOUN
ejpam-4144	569	4	,	,	PUNCT
ejpam-4144	569	5	x	x	NOUN
ejpam-4144	569	6	)	)	PUNCT
ejpam-4144	569	7	=	=	SYM
ejpam-4144	569	8	2	2	NUM
ejpam-4144	569	9	and	and	CCONJ
ejpam-4144	569	10	let	let	VERB
ejpam-4144	569	11	y	y	PROPN
ejpam-4144	569	12	∈	∈	PROPN
ejpam-4144	569	13	v	v	X
ejpam-4144	569	14	(	(	PUNCT
ejpam-4144	569	15	d2(g	d2(g	PROPN
ejpam-4144	569	16	)	)	PUNCT
ejpam-4144	569	17	)	)	PUNCT
ejpam-4144	569	18	such	such	ADJ
ejpam-4144	569	19	that	that	SCONJ
ejpam-4144	569	20	[	[	X
ejpam-4144	569	21	w	w	PROPN
ejpam-4144	569	22	,	,	PUNCT
ejpam-4144	569	23	y	y	PROPN
ejpam-4144	569	24	,	,	PUNCT
ejpam-4144	569	25	x	x	X
ejpam-4144	569	26	]	]	X
ejpam-4144	569	27	is	be	AUX
ejpam-4144	569	28	w	w	NOUN
ejpam-4144	569	29	-	-	PUNCT
ejpam-4144	569	30	x	x	NOUN
ejpam-4144	569	31	geodesic	geodesic	NOUN
ejpam-4144	569	32	in	in	ADP
ejpam-4144	569	33	d2(g	d2(g	PROPN
ejpam-4144	569	34	)	)	PUNCT
ejpam-4144	569	35	.	.	PUNCT
ejpam-4144	570	1	if	if	SCONJ
ejpam-4144	570	2	y	y	PROPN
ejpam-4144	570	3	∈	∈	PROPN
ejpam-4144	570	4	v	v	X
ejpam-4144	570	5	(	(	PUNCT
ejpam-4144	570	6	g1	g1	PROPN
ejpam-4144	570	7	)	)	PUNCT
ejpam-4144	570	8	,	,	PUNCT
ejpam-4144	570	9	then	then	ADV
ejpam-4144	570	10	[	[	X
ejpam-4144	570	11	w	w	PROPN
ejpam-4144	570	12	,	,	PUNCT
ejpam-4144	570	13	y	y	PROPN
ejpam-4144	570	14	,	,	PUNCT
ejpam-4144	570	15	x	x	X
ejpam-4144	570	16	]	]	X
ejpam-4144	570	17	is	be	AUX
ejpam-4144	570	18	a	a	DET
ejpam-4144	570	19	w	w	NOUN
ejpam-4144	570	20	-	-	PUNCT
ejpam-4144	570	21	x	x	ADJ
ejpam-4144	570	22	geodesic	geodesic	ADJ
ejpam-4144	570	23	ing1	ing1	NOUN
ejpam-4144	570	24	.	.	PUNCT
ejpam-4144	571	1	suppose	suppose	VERB
ejpam-4144	571	2	y	y	PROPN
ejpam-4144	571	3	∈	∈	PROPN
ejpam-4144	571	4	v	v	PROPN
ejpam-4144	571	5	(	(	PUNCT
ejpam-4144	571	6	g2	g2	PROPN
ejpam-4144	571	7	)	)	PUNCT
ejpam-4144	571	8	,	,	PUNCT
ejpam-4144	571	9	say	say	VERB
ejpam-4144	571	10	y	y	NOUN
ejpam-4144	571	11	=	=	PUNCT
ejpam-4144	572	1	u′.	u′.	NOUN
ejpam-4144	572	2	by	by	ADP
ejpam-4144	572	3	definition	definition	NOUN
ejpam-4144	572	4	of	of	ADP
ejpam-4144	572	5	d2(g	d2(g	PROPN
ejpam-4144	572	6	)	)	PUNCT
ejpam-4144	572	7	,	,	PUNCT
ejpam-4144	572	8	it	it	PRON
ejpam-4144	572	9	follows	follow	VERB
ejpam-4144	572	10	that	that	SCONJ
ejpam-4144	572	11	u	u	PROPN
ejpam-4144	572	12	∈	∈	PROPN
ejpam-4144	572	13	v	v	NOUN
ejpam-4144	572	14	(	(	PUNCT
ejpam-4144	572	15	g1	g1	PROPN
ejpam-4144	572	16	)	)	PUNCT
ejpam-4144	572	17	and	and	CCONJ
ejpam-4144	572	18	[	[	X
ejpam-4144	572	19	w	w	X
ejpam-4144	572	20	,	,	PUNCT
ejpam-4144	572	21	u	u	NOUN
ejpam-4144	572	22	,	,	PUNCT
ejpam-4144	572	23	x	x	X
ejpam-4144	572	24	]	]	X
ejpam-4144	572	25	is	be	AUX
ejpam-4144	572	26	a	a	DET
ejpam-4144	572	27	w	w	NOUN
ejpam-4144	572	28	-	-	PUNCT
ejpam-4144	572	29	x	x	NOUN
ejpam-4144	572	30	geodesic	geodesic	NOUN
ejpam-4144	572	31	in	in	ADP
ejpam-4144	572	32	g1	g1	NOUN
ejpam-4144	572	33	.	.	PUNCT
ejpam-4144	573	1	hence	hence	ADV
ejpam-4144	573	2	,	,	PUNCT
ejpam-4144	573	3	x	x	PUNCT
ejpam-4144	573	4	∈	∈	PROPN
ejpam-4144	573	5	ng1	ng1	NOUN
ejpam-4144	574	1	[	[	X
ejpam-4144	574	2	w	w	NOUN
ejpam-4144	574	3	,	,	PUNCT
ejpam-4144	574	4	2	2	NUM
ejpam-4144	574	5	]	]	PUNCT
ejpam-4144	574	6	.	.	PUNCT
ejpam-4144	575	1	next	next	ADV
ejpam-4144	575	2	,	,	PUNCT
ejpam-4144	575	3	suppose	suppose	VERB
ejpam-4144	575	4	that	that	SCONJ
ejpam-4144	575	5	x	x	X
ejpam-4144	575	6	=	=	PUNCT
ejpam-4144	575	7	z′	z′	NUM
ejpam-4144	575	8	∈	∈	PROPN
ejpam-4144	575	9	v	v	NOUN
ejpam-4144	575	10	(	(	PUNCT
ejpam-4144	575	11	g2	g2	PROPN
ejpam-4144	575	12	)	)	PUNCT
ejpam-4144	575	13	.	.	PUNCT
ejpam-4144	576	1	if	if	SCONJ
ejpam-4144	576	2	y	y	PROPN
ejpam-4144	576	3	∈	∈	PROPN
ejpam-4144	576	4	v	v	X
ejpam-4144	576	5	(	(	PUNCT
ejpam-4144	576	6	g1	g1	PROPN
ejpam-4144	576	7	)	)	PUNCT
ejpam-4144	576	8	,	,	PUNCT
ejpam-4144	576	9	then	then	ADV
ejpam-4144	576	10	[	[	X
ejpam-4144	576	11	w′	w′	NOUN
ejpam-4144	576	12	,	,	PUNCT
ejpam-4144	576	13	y′	y′	NUM
ejpam-4144	576	14	,	,	PUNCT
ejpam-4144	576	15	z′	z′	PROPN
ejpam-4144	576	16	]	]	X
ejpam-4144	576	17	is	be	AUX
ejpam-4144	576	18	a	a	DET
ejpam-4144	576	19	w	w	NOUN
ejpam-4144	576	20	-	-	PUNCT
ejpam-4144	576	21	x	x	NOUN
ejpam-4144	576	22	geodesic	geodesic	NOUN
ejpam-4144	576	23	in	in	ADP
ejpam-4144	576	24	g2	g2	PROPN
ejpam-4144	576	25	.	.	PUNCT
ejpam-4144	577	1	suppose	suppose	VERB
ejpam-4144	577	2	y	y	PROPN
ejpam-4144	577	3	∈	∈	PROPN
ejpam-4144	577	4	v	v	PROPN
ejpam-4144	577	5	(	(	PUNCT
ejpam-4144	577	6	g2	g2	PROPN
ejpam-4144	577	7	)	)	PUNCT
ejpam-4144	577	8	,	,	PUNCT
ejpam-4144	577	9	say	say	VERB
ejpam-4144	577	10	y	y	NOUN
ejpam-4144	577	11	=	=	PUNCT
ejpam-4144	578	1	u′.	u′.	NOUN
ejpam-4144	578	2	then	then	ADV
ejpam-4144	578	3	[	[	X
ejpam-4144	578	4	w′	w′	NOUN
ejpam-4144	578	5	,	,	PUNCT
ejpam-4144	578	6	u′	u′	PROPN
ejpam-4144	578	7	,	,	PUNCT
ejpam-4144	578	8	z′	z′	PROPN
ejpam-4144	578	9	]	]	X
ejpam-4144	578	10	is	be	AUX
ejpam-4144	578	11	w′-x	w′-x	ADJ
ejpam-4144	578	12	geodesic	geodesic	NOUN
ejpam-4144	578	13	in	in	ADP
ejpam-4144	578	14	g2	g2	PROPN
ejpam-4144	578	15	.	.	PUNCT
ejpam-4144	579	1	hence	hence	ADV
ejpam-4144	579	2	,	,	PUNCT
ejpam-4144	579	3	x	x	PUNCT
ejpam-4144	579	4	∈	∈	NOUN
ejpam-4144	579	5	ng2	ng2	NOUN
ejpam-4144	580	1	[	[	X
ejpam-4144	580	2	w	w	NOUN
ejpam-4144	580	3	′	′	NOUN
ejpam-4144	580	4	,	,	PUNCT
ejpam-4144	580	5	2	2	NUM
ejpam-4144	580	6	]	]	PUNCT
ejpam-4144	580	7	.	.	PUNCT
ejpam-4144	581	1	thus	thus	ADV
ejpam-4144	581	2	,	,	PUNCT
ejpam-4144	581	3	nd2(g)[w	nd2(g)[w	X
ejpam-4144	581	4	,	,	PUNCT
ejpam-4144	581	5	2	2	X
ejpam-4144	581	6	]	]	SYM
ejpam-4144	581	7	⊆	⊆	NUM
ejpam-4144	581	8	ng1	ng1	NOUN
ejpam-4144	581	9	[	[	X
ejpam-4144	581	10	w	w	NOUN
ejpam-4144	581	11	,	,	PUNCT
ejpam-4144	581	12	2	2	NUM
ejpam-4144	581	13	]	]	PUNCT
ejpam-4144	581	14	∪ng2	∪ng2	PROPN
ejpam-4144	582	1	[	[	X
ejpam-4144	582	2	w	w	NOUN
ejpam-4144	582	3	′	′	NOUN
ejpam-4144	582	4	,	,	PUNCT
ejpam-4144	582	5	2	2	NUM
ejpam-4144	582	6	]	]	PUNCT
ejpam-4144	582	7	,	,	PUNCT
ejpam-4144	582	8	showing	show	VERB
ejpam-4144	582	9	that	that	DET
ejpam-4144	582	10	g.	g.	PROPN
ejpam-4144	582	11	salasalan	salasalan	PROPN
ejpam-4144	582	12	,	,	PUNCT
ejpam-4144	582	13	s.	s.	PROPN
ejpam-4144	582	14	canoy	canoy	PROPN
ejpam-4144	582	15	,	,	PUNCT
ejpam-4144	582	16	jr	jr	PROPN
ejpam-4144	582	17	.	.	PROPN
ejpam-4144	582	18	/	/	SYM
ejpam-4144	582	19	eur	eur	PROPN
ejpam-4144	582	20	.	.	PUNCT
ejpam-4144	583	1	j.	j.	PROPN
ejpam-4144	583	2	pure	pure	PROPN
ejpam-4144	583	3	appl	appl	PROPN
ejpam-4144	583	4	.	.	PROPN
ejpam-4144	583	5	math	math	PROPN
ejpam-4144	583	6	,	,	PUNCT
ejpam-4144	583	7	14	14	NUM
ejpam-4144	583	8	(	(	PUNCT
ejpam-4144	583	9	4	4	NUM
ejpam-4144	583	10	)	)	PUNCT
ejpam-4144	583	11	(	(	PUNCT
ejpam-4144	583	12	2021	2021	NUM
ejpam-4144	583	13	)	)	PUNCT
ejpam-4144	583	14	,	,	PUNCT
ejpam-4144	583	15	1415	1415	NUM
ejpam-4144	583	16	-	-	SYM
ejpam-4144	583	17	1428	1428	NUM
ejpam-4144	583	18	1425	1425	NUM
ejpam-4144	583	19	nd2(g)[w	nd2(g)[w	NOUN
ejpam-4144	583	20	,	,	PUNCT
ejpam-4144	583	21	2	2	X
ejpam-4144	583	22	]	]	SYM
ejpam-4144	583	23	⊆	⊆	NUM
ejpam-4144	583	24	ng1	ng1	NOUN
ejpam-4144	583	25	[	[	X
ejpam-4144	583	26	w	w	NOUN
ejpam-4144	583	27	,	,	PUNCT
ejpam-4144	583	28	2	2	NUM
ejpam-4144	583	29	]	]	PUNCT
ejpam-4144	583	30	∪	∪	ADP
ejpam-4144	583	31	ng2	ng2	NOUN
ejpam-4144	584	1	[	[	X
ejpam-4144	584	2	w	w	NOUN
ejpam-4144	584	3	′	′	NOUN
ejpam-4144	584	4	,	,	PUNCT
ejpam-4144	584	5	2	2	NUM
ejpam-4144	584	6	]	]	PUNCT
ejpam-4144	584	7	.	.	PUNCT
ejpam-4144	585	1	similarly	similarly	ADV
ejpam-4144	585	2	,	,	PUNCT
ejpam-4144	585	3	nd2(g)[w	nd2(g)[w	NOUN
ejpam-4144	585	4	′	′	NUM
ejpam-4144	585	5	,	,	PUNCT
ejpam-4144	585	6	2	2	NUM
ejpam-4144	585	7	]	]	SYM
ejpam-4144	585	8	⊆	⊆	NUM
ejpam-4144	585	9	ng1	ng1	NOUN
ejpam-4144	585	10	[	[	X
ejpam-4144	585	11	w	w	NOUN
ejpam-4144	585	12	,	,	PUNCT
ejpam-4144	585	13	2	2	NUM
ejpam-4144	585	14	]	]	PUNCT
ejpam-4144	585	15	∪	∪	ADP
ejpam-4144	585	16	ng2	ng2	NOUN
ejpam-4144	586	1	[	[	X
ejpam-4144	586	2	w	w	NOUN
ejpam-4144	586	3	′	′	NOUN
ejpam-4144	586	4	,	,	PUNCT
ejpam-4144	586	5	2	2	NUM
ejpam-4144	586	6	]	]	PUNCT
ejpam-4144	586	7	.	.	PUNCT
ejpam-4144	587	1	therefore	therefore	ADV
ejpam-4144	587	2	,	,	PUNCT
ejpam-4144	587	3	nd2(g)[w	nd2(g)[w	X
ejpam-4144	587	4	,	,	PUNCT
ejpam-4144	587	5	2	2	X
ejpam-4144	587	6	]	]	PUNCT
ejpam-4144	587	7	=	=	SYM
ejpam-4144	587	8	ng1	ng1	NOUN
ejpam-4144	588	1	[	[	X
ejpam-4144	588	2	w	w	NOUN
ejpam-4144	588	3	,	,	PUNCT
ejpam-4144	588	4	2	2	NUM
ejpam-4144	588	5	]	]	PUNCT
ejpam-4144	588	6	∪ng2	∪ng2	PROPN
ejpam-4144	589	1	[	[	X
ejpam-4144	589	2	w	w	NOUN
ejpam-4144	589	3	′	′	NOUN
ejpam-4144	589	4	,	,	PUNCT
ejpam-4144	589	5	2	2	NUM
ejpam-4144	589	6	]	]	PUNCT
ejpam-4144	589	7	=	=	SYM
ejpam-4144	589	8	nd2(g)[w	nd2(g)[w	NOUN
ejpam-4144	589	9	′	′	NUM
ejpam-4144	589	10	,	,	PUNCT
ejpam-4144	589	11	2	2	NUM
ejpam-4144	589	12	]	]	PUNCT
ejpam-4144	589	13	.	.	PUNCT
ejpam-4144	590	1	a	a	DET
ejpam-4144	590	2	result	result	NOUN
ejpam-4144	590	3	in	in	ADP
ejpam-4144	590	4	[	[	X
ejpam-4144	590	5	13	13	NUM
ejpam-4144	590	6	]	]	PUNCT
ejpam-4144	590	7	says	say	VERB
ejpam-4144	590	8	that	that	SCONJ
ejpam-4144	590	9	γh(d2(g	γh(d2(g	NOUN
ejpam-4144	590	10	)	)	PUNCT
ejpam-4144	590	11	)	)	PUNCT
ejpam-4144	591	1	=	=	NOUN
ejpam-4144	591	2	γh(g	γh(g	NOUN
ejpam-4144	591	3	)	)	PUNCT
ejpam-4144	591	4	for	for	ADP
ejpam-4144	591	5	any	any	DET
ejpam-4144	591	6	graph	graph	NOUN
ejpam-4144	591	7	g.	g.	NOUN
ejpam-4144	591	8	this	this	PRON
ejpam-4144	591	9	,	,	PUNCT
ejpam-4144	591	10	however	however	ADV
ejpam-4144	591	11	,	,	PUNCT
ejpam-4144	591	12	is	be	AUX
ejpam-4144	591	13	not	not	PART
ejpam-4144	591	14	true	true	ADJ
ejpam-4144	591	15	if	if	SCONJ
ejpam-4144	591	16	g	g	PROPN
ejpam-4144	591	17	contains	contain	VERB
ejpam-4144	591	18	an	an	DET
ejpam-4144	591	19	isolated	isolated	ADJ
ejpam-4144	591	20	vertex	vertex	NOUN
ejpam-4144	591	21	.	.	PUNCT
ejpam-4144	592	1	indeed	indeed	ADV
ejpam-4144	592	2	,	,	PUNCT
ejpam-4144	592	3	if	if	SCONJ
ejpam-4144	592	4	g	g	PROPN
ejpam-4144	592	5	is	be	AUX
ejpam-4144	592	6	the	the	DET
ejpam-4144	592	7	trivial	trivial	ADJ
ejpam-4144	592	8	graph	graph	NOUN
ejpam-4144	592	9	and	and	CCONJ
ejpam-4144	592	10	h	h	NOUN
ejpam-4144	592	11	is	be	AUX
ejpam-4144	592	12	the	the	DET
ejpam-4144	592	13	(	(	PUNCT
ejpam-4144	592	14	disjoint	disjoint	NOUN
ejpam-4144	592	15	)	)	PUNCT
ejpam-4144	592	16	union	union	NOUN
ejpam-4144	592	17	k1	k1	PROPN
ejpam-4144	592	18	∪	∪	ADP
ejpam-4144	592	19	k1	k1	PROPN
ejpam-4144	592	20	∪	∪	NOUN
ejpam-4144	592	21	p2	p2	NOUN
ejpam-4144	592	22	,	,	PUNCT
ejpam-4144	592	23	then	then	ADV
ejpam-4144	592	24	d2(g	d2(g	NUM
ejpam-4144	592	25	)	)	PUNCT
ejpam-4144	592	26	=	=	SYM
ejpam-4144	592	27	k2	k2	NOUN
ejpam-4144	592	28	and	and	CCONJ
ejpam-4144	592	29	d2(g	d2(g	PROPN
ejpam-4144	592	30	)	)	PUNCT
ejpam-4144	592	31	=	=	SYM
ejpam-4144	592	32	k2	k2	PROPN
ejpam-4144	592	33	∪	∪	X
ejpam-4144	592	34	k2	k2	PROPN
ejpam-4144	592	35	∪	∪	X
ejpam-4144	592	36	c4	c4	NOUN
ejpam-4144	592	37	.	.	PUNCT
ejpam-4144	593	1	hence	hence	ADV
ejpam-4144	593	2	,	,	PUNCT
ejpam-4144	593	3	γh(d2(g	γh(d2(g	PROPN
ejpam-4144	593	4	)	)	PUNCT
ejpam-4144	593	5	)	)	PUNCT
ejpam-4144	594	1	=	=	SYM
ejpam-4144	594	2	2	2	NUM
ejpam-4144	594	3	̸=	̸=	PROPN
ejpam-4144	594	4	1	1	NUM
ejpam-4144	594	5	=	=	PUNCT
ejpam-4144	594	6	γh(g	γh(g	NOUN
ejpam-4144	594	7	)	)	PUNCT
ejpam-4144	594	8	and	and	CCONJ
ejpam-4144	594	9	γh(d2(h	γh(d2(h	PROPN
ejpam-4144	594	10	)	)	PUNCT
ejpam-4144	594	11	)	)	PUNCT
ejpam-4144	595	1	=	=	PUNCT
ejpam-4144	595	2	6	6	NUM
ejpam-4144	595	3	̸=	̸=	PROPN
ejpam-4144	595	4	4	4	NUM
ejpam-4144	595	5	=	=	NOUN
ejpam-4144	595	6	γh(g	γh(g	NOUN
ejpam-4144	595	7	)	)	PUNCT
ejpam-4144	595	8	.	.	PUNCT
ejpam-4144	596	1	theorem	theorem	ADJ
ejpam-4144	596	2	8	8	NUM
ejpam-4144	596	3	.	.	PUNCT
ejpam-4144	597	1	let	let	VERB
ejpam-4144	597	2	g	g	PRON
ejpam-4144	597	3	be	be	AUX
ejpam-4144	597	4	a	a	DET
ejpam-4144	597	5	non	non	ADJ
ejpam-4144	597	6	-	-	ADJ
ejpam-4144	597	7	trivial	trivial	ADJ
ejpam-4144	597	8	graph	graph	NOUN
ejpam-4144	597	9	.	.	PUNCT
ejpam-4144	598	1	then	then	ADV
ejpam-4144	598	2	the	the	DET
ejpam-4144	598	3	following	follow	VERB
ejpam-4144	598	4	hold	hold	NOUN
ejpam-4144	598	5	.	.	PUNCT
ejpam-4144	599	1	(	(	PUNCT
ejpam-4144	599	2	i	i	NOUN
ejpam-4144	599	3	)	)	PUNCT
ejpam-4144	599	4	if	if	SCONJ
ejpam-4144	599	5	g	g	PROPN
ejpam-4144	599	6	is	be	AUX
ejpam-4144	599	7	connected	connect	VERB
ejpam-4144	599	8	,	,	PUNCT
ejpam-4144	599	9	then	then	ADV
ejpam-4144	599	10	γh(d2(g	γh(d2(g	NOUN
ejpam-4144	599	11	)	)	PUNCT
ejpam-4144	599	12	)	)	PUNCT
ejpam-4144	600	1	=	=	NOUN
ejpam-4144	600	2	γh(g	γh(g	NOUN
ejpam-4144	600	3	)	)	PUNCT
ejpam-4144	600	4	.	.	PUNCT
ejpam-4144	601	1	(	(	PUNCT
ejpam-4144	601	2	ii	ii	NOUN
ejpam-4144	601	3	)	)	PUNCT
ejpam-4144	601	4	if	if	SCONJ
ejpam-4144	601	5	g	g	PROPN
ejpam-4144	601	6	is	be	AUX
ejpam-4144	601	7	disconnected	disconnect	VERB
ejpam-4144	601	8	with	with	ADP
ejpam-4144	601	9	r	r	NOUN
ejpam-4144	601	10	trivial	trivial	ADJ
ejpam-4144	601	11	components	component	NOUN
ejpam-4144	601	12	and	and	CCONJ
ejpam-4144	601	13	k	k	ADJ
ejpam-4144	601	14	non	non	ADJ
ejpam-4144	601	15	-	-	ADJ
ejpam-4144	601	16	trivial	trivial	ADJ
ejpam-4144	601	17	components	component	NOUN
ejpam-4144	601	18	g1,g2	g1,g2	PROPN
ejpam-4144	601	19	,	,	PUNCT
ejpam-4144	601	20	g3	g3	PROPN
ejpam-4144	601	21	,	,	PUNCT
ejpam-4144	601	22	.	.	PUNCT
ejpam-4144	601	23	.	.	PUNCT
ejpam-4144	601	24	.	.	PUNCT
ejpam-4144	602	1	,	,	PUNCT
ejpam-4144	602	2	gk	gk	PROPN
ejpam-4144	602	3	,	,	PUNCT
ejpam-4144	602	4	then	then	ADV
ejpam-4144	602	5	γh(d2(g	γh(d2(g	NOUN
ejpam-4144	602	6	)	)	PUNCT
ejpam-4144	602	7	)	)	PUNCT
ejpam-4144	603	1	=	=	PUNCT
ejpam-4144	603	2	2r	2r	NUM
ejpam-4144	604	1	+	+	CCONJ
ejpam-4144	604	2	∑k	∑k	PROPN
ejpam-4144	604	3	i=1	i=1	PROPN
ejpam-4144	604	4	γh(gk	γh(gk	NOUN
ejpam-4144	604	5	)	)	PUNCT
ejpam-4144	604	6	.	.	PUNCT
ejpam-4144	605	1	proof	proof	NOUN
ejpam-4144	605	2	.	.	PUNCT
ejpam-4144	606	1	(	(	PUNCT
ejpam-4144	606	2	i	i	NOUN
ejpam-4144	606	3	)	)	PUNCT
ejpam-4144	606	4	let	let	VERB
ejpam-4144	606	5	g1	g1	PROPN
ejpam-4144	606	6	and	and	CCONJ
ejpam-4144	606	7	g2	g2	PROPN
ejpam-4144	606	8	be	be	VERB
ejpam-4144	606	9	the	the	DET
ejpam-4144	606	10	two	two	NUM
ejpam-4144	606	11	copies	copy	NOUN
ejpam-4144	606	12	of	of	ADP
ejpam-4144	606	13	g	g	NOUN
ejpam-4144	606	14	in	in	ADP
ejpam-4144	606	15	the	the	DET
ejpam-4144	606	16	definition	definition	NOUN
ejpam-4144	606	17	of	of	ADP
ejpam-4144	606	18	d2(g	d2(g	PROPN
ejpam-4144	606	19	)	)	PUNCT
ejpam-4144	606	20	.	.	PUNCT
ejpam-4144	607	1	let	let	VERB
ejpam-4144	607	2	s	s	PRON
ejpam-4144	607	3	be	be	AUX
ejpam-4144	607	4	a	a	DET
ejpam-4144	607	5	γh	γh	ADV
ejpam-4144	607	6	-	-	PUNCT
ejpam-4144	607	7	set	set	NOUN
ejpam-4144	607	8	of	of	ADP
ejpam-4144	607	9	g1	g1	NOUN
ejpam-4144	607	10	and	and	CCONJ
ejpam-4144	607	11	let	let	VERB
ejpam-4144	607	12	v′	v′	NOUN
ejpam-4144	607	13	∈	∈	PROPN
ejpam-4144	607	14	v	v	NOUN
ejpam-4144	607	15	(	(	PUNCT
ejpam-4144	607	16	g2	g2	PROPN
ejpam-4144	607	17	)	)	PUNCT
ejpam-4144	607	18	.	.	PUNCT
ejpam-4144	608	1	if	if	SCONJ
ejpam-4144	608	2	the	the	DET
ejpam-4144	608	3	corresponding	correspond	VERB
ejpam-4144	608	4	vertex	vertex	NOUN
ejpam-4144	608	5	v	v	ADP
ejpam-4144	608	6	∈	∈	PROPN
ejpam-4144	608	7	v	v	NOUN
ejpam-4144	608	8	(	(	PUNCT
ejpam-4144	608	9	g1	g1	PROPN
ejpam-4144	608	10	)	)	PUNCT
ejpam-4144	608	11	is	be	AUX
ejpam-4144	608	12	in	in	ADP
ejpam-4144	608	13	s	s	PROPN
ejpam-4144	608	14	,	,	PUNCT
ejpam-4144	608	15	then	then	ADV
ejpam-4144	608	16	dd2(g)(v	dd2(g)(v	PROPN
ejpam-4144	608	17	,	,	PUNCT
ejpam-4144	608	18	v	v	NOUN
ejpam-4144	608	19	′	′	NOUN
ejpam-4144	608	20	)	)	PUNCT
ejpam-4144	608	21	=	=	SYM
ejpam-4144	609	1	2	2	X
ejpam-4144	609	2	.	.	PUNCT
ejpam-4144	609	3	so	so	ADV
ejpam-4144	609	4	suppose	suppose	VERB
ejpam-4144	609	5	v	v	X
ejpam-4144	609	6	/∈	/∈	PUNCT
ejpam-4144	609	7	s.	s.	PROPN
ejpam-4144	609	8	since	since	SCONJ
ejpam-4144	609	9	s	s	PROPN
ejpam-4144	609	10	is	be	AUX
ejpam-4144	609	11	a	a	DET
ejpam-4144	609	12	hop	hop	NOUN
ejpam-4144	609	13	dominating	dominating	NOUN
ejpam-4144	609	14	set	set	NOUN
ejpam-4144	609	15	of	of	ADP
ejpam-4144	609	16	g1	g1	NOUN
ejpam-4144	609	17	,	,	PUNCT
ejpam-4144	609	18	there	there	PRON
ejpam-4144	609	19	exists	exist	VERB
ejpam-4144	609	20	w	w	PROPN
ejpam-4144	609	21	∈	∈	PROPN
ejpam-4144	609	22	s	s	VERB
ejpam-4144	609	23	such	such	ADJ
ejpam-4144	609	24	that	that	PRON
ejpam-4144	609	25	dg1(v	dg1(v	PROPN
ejpam-4144	609	26	,	,	PUNCT
ejpam-4144	609	27	w	w	PROPN
ejpam-4144	609	28	)	)	PUNCT
ejpam-4144	609	29	=	=	SYM
ejpam-4144	609	30	2	2	X
ejpam-4144	609	31	.	.	X
ejpam-4144	609	32	let	let	VERB
ejpam-4144	609	33	[	[	X
ejpam-4144	609	34	v	v	ADP
ejpam-4144	609	35	,	,	PUNCT
ejpam-4144	609	36	z	z	PROPN
ejpam-4144	609	37	,	,	PUNCT
ejpam-4144	609	38	w	w	AUX
ejpam-4144	609	39	]	]	PUNCT
ejpam-4144	609	40	be	be	AUX
ejpam-4144	609	41	a	a	DET
ejpam-4144	609	42	v	v	NOUN
ejpam-4144	609	43	-	-	PUNCT
ejpam-4144	609	44	w	w	NOUN
ejpam-4144	609	45	geodesic	geodesic	NOUN
ejpam-4144	609	46	in	in	ADP
ejpam-4144	609	47	g1	g1	PROPN
ejpam-4144	609	48	.	.	PUNCT
ejpam-4144	610	1	then	then	ADV
ejpam-4144	610	2	v′z	v′z	PROPN
ejpam-4144	610	3	,	,	PUNCT
ejpam-4144	610	4	zw	zw	PROPN
ejpam-4144	610	5	∈	∈	PROPN
ejpam-4144	610	6	e(d2(g	e(d2(g	PROPN
ejpam-4144	610	7	)	)	PUNCT
ejpam-4144	610	8	)	)	PUNCT
ejpam-4144	610	9	.	.	PUNCT
ejpam-4144	611	1	since	since	SCONJ
ejpam-4144	611	2	v	v	NUM
ejpam-4144	611	3	/∈	/∈	PUNCT
ejpam-4144	611	4	ng1(w	ng1(w	NOUN
ejpam-4144	611	5	)	)	PUNCT
ejpam-4144	611	6	,	,	PUNCT
ejpam-4144	611	7	v′w	v′w	VERB
ejpam-4144	611	8	/∈	/∈	PUNCT
ejpam-4144	611	9	e(d2(g	e(d2(g	VERB
ejpam-4144	611	10	)	)	PUNCT
ejpam-4144	611	11	)	)	PUNCT
ejpam-4144	611	12	.	.	PUNCT
ejpam-4144	612	1	thus	thus	ADV
ejpam-4144	612	2	,	,	PUNCT
ejpam-4144	612	3	dd2(g)(w	dd2(g)(w	ADJ
ejpam-4144	612	4	,	,	PUNCT
ejpam-4144	612	5	v	v	NOUN
ejpam-4144	612	6	′	′	NOUN
ejpam-4144	612	7	)	)	PUNCT
ejpam-4144	612	8	=	=	SYM
ejpam-4144	613	1	2	2	X
ejpam-4144	613	2	.	.	X
ejpam-4144	613	3	therefore	therefore	ADV
ejpam-4144	613	4	,	,	PUNCT
ejpam-4144	613	5	s	s	VERB
ejpam-4144	613	6	is	be	AUX
ejpam-4144	613	7	a	a	DET
ejpam-4144	613	8	hop	hop	NOUN
ejpam-4144	613	9	dominating	dominating	NOUN
ejpam-4144	613	10	set	set	NOUN
ejpam-4144	613	11	of	of	ADP
ejpam-4144	613	12	d2(g	d2(g	PROPN
ejpam-4144	613	13	)	)	PUNCT
ejpam-4144	613	14	and	and	CCONJ
ejpam-4144	613	15	γh(d2(g	γh(d2(g	NOUN
ejpam-4144	613	16	)	)	PUNCT
ejpam-4144	613	17	≤	≤	NUM
ejpam-4144	613	18	|s|	|s|	PROPN
ejpam-4144	613	19	=	=	NOUN
ejpam-4144	613	20	γh(g	γh(g	NOUN
ejpam-4144	613	21	)	)	PUNCT
ejpam-4144	613	22	.	.	PUNCT
ejpam-4144	614	1	next	next	ADV
ejpam-4144	614	2	,	,	PUNCT
ejpam-4144	614	3	suppose	suppose	VERB
ejpam-4144	614	4	that	that	SCONJ
ejpam-4144	614	5	s′	s′	PROPN
ejpam-4144	614	6	is	be	AUX
ejpam-4144	614	7	a	a	DET
ejpam-4144	614	8	γh	γh	ADV
ejpam-4144	614	9	-	-	PUNCT
ejpam-4144	614	10	set	set	NOUN
ejpam-4144	614	11	of	of	ADP
ejpam-4144	614	12	d2(g	d2(g	PROPN
ejpam-4144	614	13	)	)	PUNCT
ejpam-4144	614	14	.	.	PUNCT
ejpam-4144	615	1	let	let	VERB
ejpam-4144	615	2	s1	s1	NOUN
ejpam-4144	615	3	=	=	PUNCT
ejpam-4144	615	4	s′∩v	s′∩v	PROPN
ejpam-4144	615	5	(	(	PUNCT
ejpam-4144	615	6	g1	g1	PROPN
ejpam-4144	615	7	)	)	PUNCT
ejpam-4144	615	8	and	and	CCONJ
ejpam-4144	615	9	s2	s2	VERB
ejpam-4144	615	10	=	=	SYM
ejpam-4144	615	11	s′∩v	s′∩v	PROPN
ejpam-4144	615	12	(	(	PUNCT
ejpam-4144	615	13	g2	g2	PROPN
ejpam-4144	615	14	)	)	PUNCT
ejpam-4144	615	15	.	.	PUNCT
ejpam-4144	616	1	if	if	SCONJ
ejpam-4144	616	2	s1	s1	PROPN
ejpam-4144	616	3	=	=	SYM
ejpam-4144	616	4	s′	s′	VERB
ejpam-4144	616	5	or	or	CCONJ
ejpam-4144	616	6	s2	s2	VERB
ejpam-4144	616	7	=	=	SYM
ejpam-4144	616	8	s′	s′	NOUN
ejpam-4144	616	9	,	,	PUNCT
ejpam-4144	616	10	then	then	ADV
ejpam-4144	616	11	s′	s′	ADJ
ejpam-4144	616	12	is	be	AUX
ejpam-4144	616	13	a	a	DET
ejpam-4144	616	14	hop	hop	NOUN
ejpam-4144	616	15	dominating	dominating	NOUN
ejpam-4144	616	16	set	set	NOUN
ejpam-4144	616	17	of	of	ADP
ejpam-4144	616	18	g1	g1	NOUN
ejpam-4144	616	19	or	or	CCONJ
ejpam-4144	616	20	g2	g2	PROPN
ejpam-4144	616	21	.	.	PUNCT
ejpam-4144	617	1	hence	hence	ADV
ejpam-4144	617	2	,	,	PUNCT
ejpam-4144	617	3	γh(d2(g	γh(d2(g	PROPN
ejpam-4144	617	4	)	)	PUNCT
ejpam-4144	617	5	=	=	PUNCT
ejpam-4144	617	6	|s′|	|s′|	NOUN
ejpam-4144	617	7	≥	≥	PRON
ejpam-4144	617	8	γh(g	γh(g	NOUN
ejpam-4144	617	9	)	)	PUNCT
ejpam-4144	617	10	.	.	PUNCT
ejpam-4144	617	11	suppose	suppose	VERB
ejpam-4144	617	12	s1	s1	PROPN
ejpam-4144	617	13	̸=	̸=	PROPN
ejpam-4144	617	14	∅	∅	NOUN
ejpam-4144	617	15	and	and	CCONJ
ejpam-4144	617	16	s2	s2	VERB
ejpam-4144	617	17	̸=	̸=	PROPN
ejpam-4144	617	18	∅.	∅.	ADV
ejpam-4144	617	19	if	if	SCONJ
ejpam-4144	617	20	s1	s1	PROPN
ejpam-4144	617	21	is	be	AUX
ejpam-4144	617	22	a	a	DET
ejpam-4144	617	23	hop	hop	NOUN
ejpam-4144	617	24	dominating	dominating	NOUN
ejpam-4144	617	25	set	set	NOUN
ejpam-4144	617	26	of	of	ADP
ejpam-4144	617	27	g1	g1	NOUN
ejpam-4144	617	28	or	or	CCONJ
ejpam-4144	617	29	s2	s2	NOUN
ejpam-4144	617	30	is	be	AUX
ejpam-4144	617	31	a	a	DET
ejpam-4144	617	32	hop	hop	NOUN
ejpam-4144	617	33	dominating	dominating	NOUN
ejpam-4144	617	34	set	set	NOUN
ejpam-4144	617	35	of	of	ADP
ejpam-4144	617	36	g2	g2	PROPN
ejpam-4144	617	37	,	,	PUNCT
ejpam-4144	617	38	then	then	ADV
ejpam-4144	617	39	,	,	PUNCT
ejpam-4144	617	40	as	as	SCONJ
ejpam-4144	617	41	seen	see	VERB
ejpam-4144	617	42	earlier	early	ADV
ejpam-4144	617	43	,	,	PUNCT
ejpam-4144	617	44	s1	s1	NOUN
ejpam-4144	617	45	or	or	CCONJ
ejpam-4144	617	46	s2	s2	NOUN
ejpam-4144	617	47	is	be	AUX
ejpam-4144	617	48	a	a	DET
ejpam-4144	617	49	hop	hop	NOUN
ejpam-4144	617	50	dominating	dominating	NOUN
ejpam-4144	617	51	set	set	NOUN
ejpam-4144	617	52	of	of	ADP
ejpam-4144	617	53	d2(g	d2(g	PROPN
ejpam-4144	617	54	)	)	PUNCT
ejpam-4144	617	55	,	,	PUNCT
ejpam-4144	617	56	contrary	contrary	ADV
ejpam-4144	617	57	to	to	ADP
ejpam-4144	617	58	the	the	DET
ejpam-4144	617	59	assumption	assumption	NOUN
ejpam-4144	617	60	that	that	SCONJ
ejpam-4144	617	61	s′	s′	ADJ
ejpam-4144	617	62	is	be	AUX
ejpam-4144	617	63	a	a	DET
ejpam-4144	617	64	γh	γh	ADV
ejpam-4144	617	65	-	-	PUNCT
ejpam-4144	617	66	set	set	NOUN
ejpam-4144	617	67	of	of	ADP
ejpam-4144	617	68	d2(g	d2(g	PROPN
ejpam-4144	617	69	)	)	PUNCT
ejpam-4144	617	70	.	.	PUNCT
ejpam-4144	618	1	hence	hence	ADV
ejpam-4144	618	2	,	,	PUNCT
ejpam-4144	618	3	none	none	NOUN
ejpam-4144	618	4	of	of	ADP
ejpam-4144	618	5	these	these	DET
ejpam-4144	618	6	two	two	NUM
ejpam-4144	618	7	sets	set	NOUN
ejpam-4144	618	8	is	be	AUX
ejpam-4144	618	9	a	a	DET
ejpam-4144	618	10	hop	hop	NOUN
ejpam-4144	618	11	dominating	dominating	NOUN
ejpam-4144	618	12	set	set	NOUN
ejpam-4144	618	13	.	.	PUNCT
ejpam-4144	619	1	let	let	VERB
ejpam-4144	619	2	dg	dg	VERB
ejpam-4144	619	3	=	=	PUNCT
ejpam-4144	619	4	{	{	PUNCT
ejpam-4144	619	5	v	v	NUM
ejpam-4144	619	6	∈	∈	NOUN
ejpam-4144	619	7	v	v	NOUN
ejpam-4144	619	8	(	(	PUNCT
ejpam-4144	619	9	g1	g1	PROPN
ejpam-4144	619	10	)	)	PUNCT
ejpam-4144	619	11	\	\	NOUN
ejpam-4144	620	1	s1	s1	NOUN
ejpam-4144	620	2	:	:	PUNCT
ejpam-4144	620	3	v	v	NUM
ejpam-4144	620	4	/∈	/∈	PUNCT
ejpam-4144	620	5	ng1(s1	ng1(s1	NUM
ejpam-4144	620	6	,	,	PUNCT
ejpam-4144	620	7	2	2	NUM
ejpam-4144	620	8	)	)	PUNCT
ejpam-4144	620	9	}	}	PUNCT
ejpam-4144	620	10	=	=	SYM
ejpam-4144	620	11	v	v	X
ejpam-4144	620	12	(	(	PUNCT
ejpam-4144	620	13	g1	g1	PROPN
ejpam-4144	620	14	)	)	PUNCT
ejpam-4144	620	15	\ng1	\ng1	VERB
ejpam-4144	621	1	[	[	X
ejpam-4144	621	2	s1	s1	NOUN
ejpam-4144	621	3	,	,	PUNCT
ejpam-4144	621	4	2	2	NUM
ejpam-4144	621	5	]	]	PUNCT
ejpam-4144	621	6	and	and	CCONJ
ejpam-4144	621	7	let	let	VERB
ejpam-4144	621	8	sg	sg	VERB
ejpam-4144	621	9	=	=	PUNCT
ejpam-4144	621	10	{	{	PUNCT
ejpam-4144	621	11	v	v	NUM
ejpam-4144	621	12	∈	∈	NOUN
ejpam-4144	621	13	v	v	NOUN
ejpam-4144	621	14	(	(	PUNCT
ejpam-4144	621	15	g1	g1	PROPN
ejpam-4144	621	16	)	)	PUNCT
ejpam-4144	621	17	\	\	NOUN
ejpam-4144	621	18	s1	s1	NOUN
ejpam-4144	621	19	:	:	PUNCT
ejpam-4144	621	20	v′	v′	PROPN
ejpam-4144	621	21	∈	∈	PROPN
ejpam-4144	621	22	s2	s2	PROPN
ejpam-4144	621	23	}	}	PUNCT
ejpam-4144	621	24	.	.	PUNCT
ejpam-4144	622	1	clearly	clearly	ADV
ejpam-4144	622	2	,	,	PUNCT
ejpam-4144	622	3	if	if	SCONJ
ejpam-4144	622	4	v	v	ADP
ejpam-4144	622	5	∈	∈	PROPN
ejpam-4144	622	6	sg	sg	PROPN
ejpam-4144	622	7	,	,	PUNCT
ejpam-4144	622	8	then	then	ADV
ejpam-4144	622	9	v′	v′	PROPN
ejpam-4144	622	10	∈	∈	PROPN
ejpam-4144	622	11	s2	s2	PROPN
ejpam-4144	622	12	.	.	PUNCT
ejpam-4144	623	1	now	now	ADV
ejpam-4144	623	2	let	let	VERB
ejpam-4144	623	3	y′	y′	NOUN
ejpam-4144	623	4	∈	∈	PROPN
ejpam-4144	623	5	s2	s2	PROPN
ejpam-4144	623	6	.	.	PUNCT
ejpam-4144	624	1	then	then	ADV
ejpam-4144	624	2	nd2(g)[y	nd2(g)[y	PROPN
ejpam-4144	624	3	′	′	NOUN
ejpam-4144	624	4	,	,	PUNCT
ejpam-4144	624	5	2	2	NUM
ejpam-4144	624	6	]	]	PUNCT
ejpam-4144	624	7	=	=	SYM
ejpam-4144	624	8	nd2(g)[y	nd2(g)[y	X
ejpam-4144	624	9	,	,	PUNCT
ejpam-4144	624	10	2	2	NUM
ejpam-4144	624	11	]	]	PUNCT
ejpam-4144	624	12	by	by	ADP
ejpam-4144	624	13	lemma	lemma	PROPN
ejpam-4144	624	14	2	2	NUM
ejpam-4144	624	15	.	.	PUNCT
ejpam-4144	624	16	since	since	SCONJ
ejpam-4144	624	17	s′	s′	ADJ
ejpam-4144	624	18	is	be	AUX
ejpam-4144	624	19	a	a	DET
ejpam-4144	624	20	γh	γh	ADV
ejpam-4144	624	21	-	-	PUNCT
ejpam-4144	624	22	set	set	NOUN
ejpam-4144	624	23	of	of	ADP
ejpam-4144	624	24	d2(g	d2(g	PROPN
ejpam-4144	624	25	)	)	PUNCT
ejpam-4144	624	26	,	,	PUNCT
ejpam-4144	624	27	it	it	PRON
ejpam-4144	624	28	follows	follow	VERB
ejpam-4144	624	29	that	that	SCONJ
ejpam-4144	624	30	y	y	PROPN
ejpam-4144	624	31	∈	∈	PROPN
ejpam-4144	624	32	v	v	PROPN
ejpam-4144	624	33	(	(	PUNCT
ejpam-4144	624	34	g1	g1	PROPN
ejpam-4144	624	35	)	)	PUNCT
ejpam-4144	624	36	\	\	NOUN
ejpam-4144	624	37	s1	s1	NOUN
ejpam-4144	624	38	,	,	PUNCT
ejpam-4144	624	39	that	that	ADV
ejpam-4144	624	40	is	is	ADV
ejpam-4144	624	41	,	,	PUNCT
ejpam-4144	624	42	y	y	PROPN
ejpam-4144	624	43	∈	∈	PROPN
ejpam-4144	624	44	sg	sg	PROPN
ejpam-4144	624	45	.	.	PUNCT
ejpam-4144	625	1	hence	hence	ADV
ejpam-4144	625	2	,	,	PUNCT
ejpam-4144	625	3	|sg|	|sg|	PROPN
ejpam-4144	625	4	=	=	SYM
ejpam-4144	625	5	|s2|	|s2|	NOUN
ejpam-4144	625	6	.	.	PUNCT
ejpam-4144	626	1	since	since	SCONJ
ejpam-4144	626	2	s′	s′	ADJ
ejpam-4144	626	3	is	be	AUX
ejpam-4144	626	4	a	a	DET
ejpam-4144	626	5	hop	hop	NOUN
ejpam-4144	626	6	dominating	dominating	NOUN
ejpam-4144	626	7	set	set	NOUN
ejpam-4144	626	8	of	of	ADP
ejpam-4144	626	9	d2(g	d2(g	PROPN
ejpam-4144	626	10	)	)	PUNCT
ejpam-4144	626	11	,	,	PUNCT
ejpam-4144	626	12	dg	dg	VERB
ejpam-4144	626	13	⊆	⊆	NUM
ejpam-4144	626	14	nd2(g)[s2	nd2(g)[s2	NOUN
ejpam-4144	626	15	,	,	PUNCT
ejpam-4144	626	16	2	2	NUM
ejpam-4144	626	17	]	]	PUNCT
ejpam-4144	626	18	.	.	PUNCT
ejpam-4144	627	1	this	this	PRON
ejpam-4144	627	2	means	mean	VERB
ejpam-4144	627	3	that	that	SCONJ
ejpam-4144	627	4	if	if	SCONJ
ejpam-4144	627	5	w	w	PROPN
ejpam-4144	627	6	∈	∈	PROPN
ejpam-4144	627	7	dg	dg	NOUN
ejpam-4144	627	8	,	,	PUNCT
ejpam-4144	627	9	then	then	ADV
ejpam-4144	627	10	there	there	PRON
ejpam-4144	627	11	exists	exist	VERB
ejpam-4144	627	12	z′	z′	NUM
ejpam-4144	627	13	∈	∈	PROPN
ejpam-4144	627	14	s2	s2	NOUN
ejpam-4144	627	15	such	such	ADJ
ejpam-4144	627	16	that	that	SCONJ
ejpam-4144	627	17	w	w	PROPN
ejpam-4144	627	18	∈	∈	PROPN
ejpam-4144	627	19	nd2(g)[z	nd2(g)[z	PUNCT
ejpam-4144	627	20	′	′	NUM
ejpam-4144	627	21	,	,	PUNCT
ejpam-4144	627	22	2	2	NUM
ejpam-4144	627	23	]	]	PUNCT
ejpam-4144	627	24	.	.	PUNCT
ejpam-4144	628	1	consequently	consequently	ADV
ejpam-4144	628	2	,	,	PUNCT
ejpam-4144	628	3	z	z	PROPN
ejpam-4144	628	4	∈	∈	PROPN
ejpam-4144	628	5	sg	sg	PROPN
ejpam-4144	628	6	and	and	CCONJ
ejpam-4144	628	7	by	by	ADP
ejpam-4144	628	8	lemma	lemma	PROPN
ejpam-4144	628	9	2	2	NUM
ejpam-4144	628	10	,	,	PUNCT
ejpam-4144	628	11	we	we	PRON
ejpam-4144	628	12	have	have	VERB
ejpam-4144	628	13	w	w	NOUN
ejpam-4144	628	14	∈	∈	PROPN
ejpam-4144	628	15	nd2(g)[z	nd2(g)[z	NUM
ejpam-4144	628	16	,	,	PUNCT
ejpam-4144	628	17	2	2	X
ejpam-4144	628	18	]	]	PUNCT
ejpam-4144	628	19	=	=	SYM
ejpam-4144	628	20	ng1	ng1	NOUN
ejpam-4144	629	1	[	[	X
ejpam-4144	629	2	z	z	X
ejpam-4144	629	3	,	,	PUNCT
ejpam-4144	629	4	2	2	NUM
ejpam-4144	629	5	]	]	PUNCT
ejpam-4144	629	6	.	.	PUNCT
ejpam-4144	630	1	thus	thus	ADV
ejpam-4144	630	2	,	,	PUNCT
ejpam-4144	630	3	dg	dg	VERB
ejpam-4144	630	4	⊆	⊆	NUM
ejpam-4144	630	5	ng1	ng1	NOUN
ejpam-4144	630	6	[	[	X
ejpam-4144	630	7	sg	sg	X
ejpam-4144	630	8	,	,	PUNCT
ejpam-4144	630	9	2	2	NUM
ejpam-4144	630	10	]	]	PUNCT
ejpam-4144	630	11	,	,	PUNCT
ejpam-4144	630	12	showing	show	VERB
ejpam-4144	630	13	that	that	SCONJ
ejpam-4144	630	14	s1	s1	NOUN
ejpam-4144	630	15	∪	∪	NOUN
ejpam-4144	630	16	sg	sg	PROPN
ejpam-4144	630	17	is	be	AUX
ejpam-4144	630	18	a	a	DET
ejpam-4144	630	19	hop	hop	NOUN
ejpam-4144	630	20	dominating	dominating	NOUN
ejpam-4144	630	21	set	set	NOUN
ejpam-4144	630	22	of	of	ADP
ejpam-4144	630	23	g1	g1	PROPN
ejpam-4144	630	24	.	.	PUNCT
ejpam-4144	631	1	therefore	therefore	ADV
ejpam-4144	631	2	,	,	PUNCT
ejpam-4144	631	3	γh(g	γh(g	NOUN
ejpam-4144	631	4	)	)	PUNCT
ejpam-4144	631	5	=	=	SYM
ejpam-4144	631	6	γh(g1	γh(g1	X
ejpam-4144	631	7	)	)	PUNCT
ejpam-4144	631	8	≤	≤	NOUN
ejpam-4144	631	9	|s1	|s1	PUNCT
ejpam-4144	631	10	∪	∪	ADJ
ejpam-4144	631	11	sg|	sg|	NOUN
ejpam-4144	631	12	=	=	SYM
ejpam-4144	631	13	γh(d2(g	γh(d2(g	NOUN
ejpam-4144	631	14	)	)	PUNCT
ejpam-4144	631	15	)	)	PUNCT
ejpam-4144	631	16	.	.	PUNCT
ejpam-4144	632	1	this	this	PRON
ejpam-4144	632	2	establishes	establish	VERB
ejpam-4144	632	3	the	the	DET
ejpam-4144	632	4	desired	desire	VERB
ejpam-4144	632	5	equality	equality	NOUN
ejpam-4144	632	6	.	.	PUNCT
ejpam-4144	633	1	(	(	PUNCT
ejpam-4144	633	2	ii	ii	X
ejpam-4144	633	3	)	)	PUNCT
ejpam-4144	633	4	this	this	PRON
ejpam-4144	633	5	follows	follow	VERB
ejpam-4144	633	6	from	from	ADP
ejpam-4144	633	7	(	(	PUNCT
ejpam-4144	633	8	i	i	NOUN
ejpam-4144	633	9	)	)	PUNCT
ejpam-4144	633	10	and	and	CCONJ
ejpam-4144	633	11	the	the	DET
ejpam-4144	633	12	fact	fact	NOUN
ejpam-4144	633	13	that	that	SCONJ
ejpam-4144	633	14	the	the	DET
ejpam-4144	633	15	hop	hop	NOUN
ejpam-4144	633	16	domination	domination	NOUN
ejpam-4144	633	17	of	of	ADP
ejpam-4144	633	18	a	a	DET
ejpam-4144	633	19	(	(	PUNCT
ejpam-4144	633	20	disconnected	disconnected	ADJ
ejpam-4144	633	21	)	)	PUNCT
ejpam-4144	633	22	graph	graph	NOUN
ejpam-4144	633	23	is	be	AUX
ejpam-4144	633	24	the	the	DET
ejpam-4144	633	25	sum	sum	NOUN
ejpam-4144	633	26	of	of	ADP
ejpam-4144	633	27	the	the	DET
ejpam-4144	633	28	hop	hop	NOUN
ejpam-4144	633	29	domination	domination	NOUN
ejpam-4144	633	30	numbers	number	NOUN
ejpam-4144	633	31	of	of	ADP
ejpam-4144	633	32	its	its	PRON
ejpam-4144	633	33	components	component	NOUN
ejpam-4144	633	34	.	.	PUNCT
ejpam-4144	634	1	theorem	theorem	NOUN
ejpam-4144	634	2	9	9	NUM
ejpam-4144	634	3	.	.	PUNCT
ejpam-4144	635	1	let	let	VERB
ejpam-4144	635	2	g	g	PRON
ejpam-4144	635	3	be	be	AUX
ejpam-4144	635	4	a	a	DET
ejpam-4144	635	5	non	non	ADJ
ejpam-4144	635	6	-	-	ADJ
ejpam-4144	635	7	trivial	trivial	ADJ
ejpam-4144	635	8	connected	connected	ADJ
ejpam-4144	635	9	graph	graph	NOUN
ejpam-4144	635	10	.	.	PUNCT
ejpam-4144	636	1	then	then	ADV
ejpam-4144	636	2	γgh(d2(g	γgh(d2(g	NUM
ejpam-4144	636	3	)	)	PUNCT
ejpam-4144	636	4	)	)	PUNCT
ejpam-4144	637	1	≤	≤	NUM
ejpam-4144	637	2	2γgh(g	2γgh(g	NOUN
ejpam-4144	637	3	)	)	PUNCT
ejpam-4144	637	4	.	.	PUNCT
ejpam-4144	638	1	proof	proof	NOUN
ejpam-4144	638	2	.	.	PUNCT
ejpam-4144	639	1	let	let	VERB
ejpam-4144	639	2	g1	g1	PROPN
ejpam-4144	639	3	and	and	CCONJ
ejpam-4144	639	4	g2	g2	PROPN
ejpam-4144	639	5	be	be	VERB
ejpam-4144	639	6	the	the	DET
ejpam-4144	639	7	two	two	NUM
ejpam-4144	639	8	copies	copy	NOUN
ejpam-4144	639	9	of	of	ADP
ejpam-4144	639	10	g	g	NOUN
ejpam-4144	639	11	in	in	ADP
ejpam-4144	639	12	the	the	DET
ejpam-4144	639	13	definition	definition	NOUN
ejpam-4144	639	14	of	of	ADP
ejpam-4144	639	15	d2(g	d2(g	PROPN
ejpam-4144	639	16	)	)	PUNCT
ejpam-4144	639	17	.	.	PUNCT
ejpam-4144	640	1	let	let	VERB
ejpam-4144	640	2	s1	s1	NOUN
ejpam-4144	640	3	be	be	AUX
ejpam-4144	640	4	a	a	DET
ejpam-4144	640	5	γgh	γgh	PROPN
ejpam-4144	640	6	-	-	PUNCT
ejpam-4144	640	7	set	set	NOUN
ejpam-4144	640	8	of	of	ADP
ejpam-4144	640	9	g1	g1	NOUN
ejpam-4144	640	10	and	and	CCONJ
ejpam-4144	640	11	let	let	VERB
ejpam-4144	640	12	s2	s2	VERB
ejpam-4144	640	13	=	=	PRON
ejpam-4144	640	14	{	{	PUNCT
ejpam-4144	640	15	v′	v′	NOUN
ejpam-4144	640	16	∈	∈	PROPN
ejpam-4144	640	17	v	v	NOUN
ejpam-4144	640	18	(	(	PUNCT
ejpam-4144	640	19	g2	g2	PROPN
ejpam-4144	640	20	)	)	PUNCT
ejpam-4144	640	21	:	:	PUNCT
ejpam-4144	640	22	v	v	X
ejpam-4144	640	23	∈	∈	NOUN
ejpam-4144	640	24	s1	s1	NOUN
ejpam-4144	640	25	}	}	PUNCT
ejpam-4144	640	26	.	.	PUNCT
ejpam-4144	641	1	then	then	ADV
ejpam-4144	641	2	s2	s2	PROPN
ejpam-4144	641	3	is	be	AUX
ejpam-4144	641	4	a	a	DET
ejpam-4144	641	5	γgh	γgh	PROPN
ejpam-4144	641	6	-	-	PUNCT
ejpam-4144	641	7	set	set	NOUN
ejpam-4144	641	8	of	of	ADP
ejpam-4144	641	9	g2	g2	PROPN
ejpam-4144	641	10	.	.	PUNCT
ejpam-4144	642	1	hence	hence	ADV
ejpam-4144	642	2	,	,	PUNCT
ejpam-4144	642	3	s	s	PART
ejpam-4144	642	4	=	=	NOUN
ejpam-4144	642	5	s1	s1	PROPN
ejpam-4144	642	6	∪	∪	X
ejpam-4144	642	7	s2	s2	NOUN
ejpam-4144	642	8	is	be	AUX
ejpam-4144	642	9	a	a	DET
ejpam-4144	642	10	hop	hop	NOUN
ejpam-4144	642	11	dominating	dominating	NOUN
ejpam-4144	642	12	set	set	NOUN
ejpam-4144	642	13	of	of	ADP
ejpam-4144	642	14	d2(g	d2(g	PROPN
ejpam-4144	642	15	)	)	PUNCT
ejpam-4144	642	16	.	.	PUNCT
ejpam-4144	643	1	since	since	SCONJ
ejpam-4144	643	2	s1	s1	PROPN
ejpam-4144	643	3	and	and	CCONJ
ejpam-4144	643	4	s2	s2	NOUN
ejpam-4144	643	5	are	be	AUX
ejpam-4144	643	6	also	also	ADV
ejpam-4144	643	7	γgh	γgh	ADJ
ejpam-4144	643	8	-	-	PUNCT
ejpam-4144	643	9	sets	set	NOUN
ejpam-4144	643	10	of	of	ADP
ejpam-4144	643	11	g1	g1	NOUN
ejpam-4144	643	12	and	and	CCONJ
ejpam-4144	643	13	g2	g2	PROPN
ejpam-4144	643	14	,	,	PUNCT
ejpam-4144	643	15	respectively	respectively	ADV
ejpam-4144	643	16	,	,	PUNCT
ejpam-4144	643	17	it	it	PRON
ejpam-4144	643	18	follows	follow	VERB
ejpam-4144	643	19	that	that	PRON
ejpam-4144	643	20	s	s	VERB
ejpam-4144	643	21	=	=	PUNCT
ejpam-4144	643	22	s1∪s2	s1∪s2	NOUN
ejpam-4144	643	23	is	be	AUX
ejpam-4144	643	24	a	a	DET
ejpam-4144	643	25	hop	hop	NOUN
ejpam-4144	643	26	dominating	dominating	NOUN
ejpam-4144	643	27	set	set	NOUN
ejpam-4144	643	28	of	of	ADP
ejpam-4144	643	29	d2(g	d2(g	PROPN
ejpam-4144	643	30	)	)	PUNCT
ejpam-4144	643	31	.	.	PUNCT
ejpam-4144	644	1	hence	hence	ADV
ejpam-4144	644	2	,	,	PUNCT
ejpam-4144	644	3	s	s	PART
ejpam-4144	644	4	=	=	NOUN
ejpam-4144	644	5	s1	s1	PROPN
ejpam-4144	644	6	∪	∪	X
ejpam-4144	644	7	s2	s2	NOUN
ejpam-4144	644	8	is	be	AUX
ejpam-4144	644	9	a	a	DET
ejpam-4144	644	10	global	global	ADJ
ejpam-4144	644	11	hop	hop	NOUN
ejpam-4144	644	12	dominating	dominating	NOUN
ejpam-4144	644	13	set	set	NOUN
ejpam-4144	644	14	of	of	ADP
ejpam-4144	644	15	d2(g	d2(g	PROPN
ejpam-4144	644	16	)	)	PUNCT
ejpam-4144	644	17	and	and	CCONJ
ejpam-4144	644	18	γgh(d2(g	γgh(d2(g	NUM
ejpam-4144	644	19	)	)	PUNCT
ejpam-4144	644	20	)	)	PUNCT
ejpam-4144	644	21	≤	≤	NUM
ejpam-4144	644	22	|s|	|s|	PROPN
ejpam-4144	644	23	=	=	PUNCT
ejpam-4144	644	24	2γgh(g	2γgh(g	NOUN
ejpam-4144	644	25	)	)	PUNCT
ejpam-4144	644	26	.	.	PUNCT
ejpam-4144	645	1	the	the	DET
ejpam-4144	645	2	next	next	ADJ
ejpam-4144	645	3	result	result	NOUN
ejpam-4144	645	4	is	be	AUX
ejpam-4144	645	5	easy	easy	ADJ
ejpam-4144	645	6	.	.	PUNCT
ejpam-4144	646	1	g.	g.	PROPN
ejpam-4144	646	2	salasalan	salasalan	PROPN
ejpam-4144	646	3	,	,	PUNCT
ejpam-4144	646	4	s.	s.	PROPN
ejpam-4144	646	5	canoy	canoy	PROPN
ejpam-4144	646	6	,	,	PUNCT
ejpam-4144	646	7	jr	jr	PROPN
ejpam-4144	646	8	.	.	PROPN
ejpam-4144	646	9	/	/	SYM
ejpam-4144	646	10	eur	eur	PROPN
ejpam-4144	646	11	.	.	PUNCT
ejpam-4144	647	1	j.	j.	PROPN
ejpam-4144	647	2	pure	pure	PROPN
ejpam-4144	647	3	appl	appl	PROPN
ejpam-4144	647	4	.	.	PROPN
ejpam-4144	647	5	math	math	PROPN
ejpam-4144	647	6	,	,	PUNCT
ejpam-4144	647	7	14	14	NUM
ejpam-4144	647	8	(	(	PUNCT
ejpam-4144	647	9	4	4	NUM
ejpam-4144	647	10	)	)	PUNCT
ejpam-4144	647	11	(	(	PUNCT
ejpam-4144	647	12	2021	2021	NUM
ejpam-4144	647	13	)	)	PUNCT
ejpam-4144	647	14	,	,	PUNCT
ejpam-4144	647	15	1415	1415	NUM
ejpam-4144	647	16	-	-	SYM
ejpam-4144	647	17	1428	1428	NUM
ejpam-4144	647	18	1426	1426	NUM
ejpam-4144	647	19	lemma	lemma	PROPN
ejpam-4144	647	20	3	3	X
ejpam-4144	647	21	.	.	PUNCT
ejpam-4144	648	1	let	let	VERB
ejpam-4144	648	2	g	g	PRON
ejpam-4144	648	3	be	be	AUX
ejpam-4144	648	4	a	a	DET
ejpam-4144	648	5	non	non	ADJ
ejpam-4144	648	6	-	-	ADJ
ejpam-4144	648	7	trivial	trivial	ADJ
ejpam-4144	648	8	graph	graph	NOUN
ejpam-4144	648	9	.	.	PUNCT
ejpam-4144	649	1	then	then	ADV
ejpam-4144	649	2	each	each	PRON
ejpam-4144	649	3	of	of	ADP
ejpam-4144	649	4	the	the	DET
ejpam-4144	649	5	following	following	ADJ
ejpam-4144	649	6	statements	statement	NOUN
ejpam-4144	649	7	is	be	AUX
ejpam-4144	649	8	true	true	ADJ
ejpam-4144	649	9	.	.	PUNCT
ejpam-4144	650	1	(	(	PUNCT
ejpam-4144	650	2	i	i	NOUN
ejpam-4144	650	3	)	)	PUNCT
ejpam-4144	650	4	d2(g	d2(g	X
ejpam-4144	650	5	)	)	PUNCT
ejpam-4144	650	6	is	be	AUX
ejpam-4144	650	7	not	not	PART
ejpam-4144	650	8	a	a	DET
ejpam-4144	650	9	complete	complete	ADJ
ejpam-4144	650	10	graph	graph	NOUN
ejpam-4144	650	11	.	.	PUNCT
ejpam-4144	651	1	(	(	PUNCT
ejpam-4144	651	2	ii	ii	X
ejpam-4144	651	3	)	)	PUNCT
ejpam-4144	651	4	d2(g	d2(g	PROPN
ejpam-4144	651	5	)	)	PUNCT
ejpam-4144	651	6	is	be	AUX
ejpam-4144	651	7	connected	connect	VERB
ejpam-4144	651	8	if	if	SCONJ
ejpam-4144	651	9	and	and	CCONJ
ejpam-4144	651	10	only	only	ADV
ejpam-4144	651	11	if	if	SCONJ
ejpam-4144	651	12	g	g	PROPN
ejpam-4144	651	13	is	be	AUX
ejpam-4144	651	14	connected	connect	VERB
ejpam-4144	651	15	.	.	PUNCT
ejpam-4144	652	1	lemma	lemma	PROPN
ejpam-4144	652	2	4	4	X
ejpam-4144	652	3	.	.	PUNCT
ejpam-4144	653	1	let	let	VERB
ejpam-4144	653	2	g	g	PRON
ejpam-4144	653	3	be	be	AUX
ejpam-4144	653	4	a	a	DET
ejpam-4144	653	5	graph	graph	NOUN
ejpam-4144	653	6	of	of	ADP
ejpam-4144	653	7	order	order	NOUN
ejpam-4144	653	8	n.	n.	NOUN
ejpam-4144	653	9	then	then	ADV
ejpam-4144	653	10	each	each	PRON
ejpam-4144	653	11	of	of	ADP
ejpam-4144	653	12	the	the	DET
ejpam-4144	653	13	following	following	ADJ
ejpam-4144	653	14	statements	statement	NOUN
ejpam-4144	653	15	is	be	AUX
ejpam-4144	653	16	true	true	ADJ
ejpam-4144	653	17	.	.	PUNCT
ejpam-4144	654	1	(	(	PUNCT
ejpam-4144	654	2	i	i	NOUN
ejpam-4144	654	3	)	)	PUNCT
ejpam-4144	654	4	every	every	DET
ejpam-4144	654	5	component	component	NOUN
ejpam-4144	654	6	of	of	ADP
ejpam-4144	654	7	d2(g	d2(g	PROPN
ejpam-4144	654	8	)	)	PUNCT
ejpam-4144	654	9	is	be	AUX
ejpam-4144	654	10	a	a	DET
ejpam-4144	654	11	complete	complete	ADJ
ejpam-4144	654	12	graph	graph	NOUN
ejpam-4144	654	13	if	if	SCONJ
ejpam-4144	654	14	and	and	CCONJ
ejpam-4144	654	15	only	only	ADV
ejpam-4144	654	16	if	if	SCONJ
ejpam-4144	654	17	g	g	PROPN
ejpam-4144	654	18	=	=	PROPN
ejpam-4144	654	19	kn	kn	PROPN
ejpam-4144	654	20	.	.	PUNCT
ejpam-4144	654	21	(	(	PUNCT
ejpam-4144	654	22	ii	ii	NOUN
ejpam-4144	654	23	)	)	PUNCT
ejpam-4144	654	24	every	every	DET
ejpam-4144	654	25	component	component	NOUN
ejpam-4144	654	26	of	of	ADP
ejpam-4144	654	27	d2(g	d2(g	PROPN
ejpam-4144	654	28	)	)	PUNCT
ejpam-4144	654	29	is	be	AUX
ejpam-4144	654	30	a	a	DET
ejpam-4144	654	31	complete	complete	ADJ
ejpam-4144	654	32	graph	graph	NOUN
ejpam-4144	655	1	if	if	SCONJ
ejpam-4144	655	2	and	and	CCONJ
ejpam-4144	655	3	only	only	ADV
ejpam-4144	655	4	if	if	SCONJ
ejpam-4144	655	5	g	g	PROPN
ejpam-4144	655	6	=	=	VERB
ejpam-4144	655	7	kn	kn	PROPN
ejpam-4144	655	8	or	or	CCONJ
ejpam-4144	655	9	g	g	PROPN
ejpam-4144	655	10	=	=	PUNCT
ejpam-4144	655	11	km1,m2,	km1,m2,	PROPN
ejpam-4144	655	12	...	...	PUNCT
ejpam-4144	655	13	,mk	,mk	PUNCT
ejpam-4144	655	14	,	,	PUNCT
ejpam-4144	655	15	where	where	SCONJ
ejpam-4144	655	16	k∑	k∑	PROPN
ejpam-4144	655	17	i=1	i=1	PROPN
ejpam-4144	655	18	mi	mi	PROPN
ejpam-4144	655	19	=	=	PROPN
ejpam-4144	655	20	n.	n.	PROPN
ejpam-4144	655	21	proof	proof	NOUN
ejpam-4144	655	22	.	.	PUNCT
ejpam-4144	656	1	let	let	VERB
ejpam-4144	656	2	g1	g1	PROPN
ejpam-4144	656	3	and	and	CCONJ
ejpam-4144	656	4	g2	g2	PROPN
ejpam-4144	656	5	be	be	VERB
ejpam-4144	656	6	the	the	DET
ejpam-4144	656	7	two	two	NUM
ejpam-4144	656	8	copies	copy	NOUN
ejpam-4144	656	9	of	of	ADP
ejpam-4144	656	10	g	g	NOUN
ejpam-4144	656	11	in	in	ADP
ejpam-4144	656	12	the	the	DET
ejpam-4144	656	13	definition	definition	NOUN
ejpam-4144	656	14	of	of	ADP
ejpam-4144	656	15	d2(g	d2(g	PROPN
ejpam-4144	656	16	)	)	PUNCT
ejpam-4144	656	17	.	.	PUNCT
ejpam-4144	657	1	(	(	PUNCT
ejpam-4144	657	2	i	i	NOUN
ejpam-4144	657	3	)	)	PUNCT
ejpam-4144	657	4	suppose	suppose	VERB
ejpam-4144	657	5	every	every	DET
ejpam-4144	657	6	component	component	NOUN
ejpam-4144	657	7	of	of	ADP
ejpam-4144	657	8	d2(g	d2(g	PROPN
ejpam-4144	657	9	)	)	PUNCT
ejpam-4144	657	10	is	be	AUX
ejpam-4144	657	11	a	a	DET
ejpam-4144	657	12	complete	complete	ADJ
ejpam-4144	657	13	graph	graph	NOUN
ejpam-4144	657	14	.	.	PUNCT
ejpam-4144	658	1	suppose	suppose	VERB
ejpam-4144	658	2	further	far	ADV
ejpam-4144	658	3	that	that	SCONJ
ejpam-4144	658	4	g	g	PROPN
ejpam-4144	658	5	has	have	VERB
ejpam-4144	658	6	a	a	DET
ejpam-4144	658	7	non	non	ADJ
ejpam-4144	658	8	-	-	ADJ
ejpam-4144	658	9	trivial	trivial	ADJ
ejpam-4144	658	10	component	component	NOUN
ejpam-4144	658	11	h.	h.	NOUN
ejpam-4144	658	12	then	then	ADV
ejpam-4144	658	13	d2(h	d2(h	PROPN
ejpam-4144	658	14	)	)	PUNCT
ejpam-4144	658	15	is	be	AUX
ejpam-4144	658	16	a	a	DET
ejpam-4144	658	17	component	component	NOUN
ejpam-4144	658	18	of	of	ADP
ejpam-4144	658	19	d2(g	d2(g	PROPN
ejpam-4144	658	20	)	)	PUNCT
ejpam-4144	658	21	which	which	PRON
ejpam-4144	658	22	is	be	AUX
ejpam-4144	658	23	not	not	PART
ejpam-4144	658	24	complete	complete	ADJ
ejpam-4144	658	25	by	by	ADP
ejpam-4144	658	26	lemma	lemma	PROPN
ejpam-4144	658	27	3	3	NUM
ejpam-4144	658	28	,	,	PUNCT
ejpam-4144	658	29	a	a	DET
ejpam-4144	658	30	contradiction	contradiction	NOUN
ejpam-4144	658	31	to	to	ADP
ejpam-4144	658	32	our	our	PRON
ejpam-4144	658	33	assumption	assumption	NOUN
ejpam-4144	658	34	of	of	ADP
ejpam-4144	658	35	d2(g	d2(g	PROPN
ejpam-4144	658	36	)	)	PUNCT
ejpam-4144	658	37	.	.	PUNCT
ejpam-4144	659	1	therefore	therefore	ADV
ejpam-4144	659	2	,	,	PUNCT
ejpam-4144	659	3	every	every	DET
ejpam-4144	659	4	component	component	NOUN
ejpam-4144	659	5	of	of	ADP
ejpam-4144	659	6	g	g	PROPN
ejpam-4144	659	7	is	be	AUX
ejpam-4144	659	8	trivial	trivial	ADJ
ejpam-4144	659	9	,	,	PUNCT
ejpam-4144	659	10	i.e.	i.e.	X
ejpam-4144	659	11	,	,	PUNCT
ejpam-4144	659	12	g	g	PROPN
ejpam-4144	659	13	=	=	SYM
ejpam-4144	659	14	kn	kn	PROPN
ejpam-4144	659	15	.	.	PUNCT
ejpam-4144	660	1	the	the	DET
ejpam-4144	660	2	converse	converse	NOUN
ejpam-4144	660	3	is	be	AUX
ejpam-4144	660	4	clear	clear	ADJ
ejpam-4144	660	5	.	.	PUNCT
ejpam-4144	661	1	(	(	PUNCT
ejpam-4144	661	2	ii	ii	NOUN
ejpam-4144	661	3	)	)	PUNCT
ejpam-4144	661	4	suppose	suppose	VERB
ejpam-4144	661	5	that	that	SCONJ
ejpam-4144	661	6	every	every	DET
ejpam-4144	661	7	component	component	NOUN
ejpam-4144	661	8	of	of	ADP
ejpam-4144	661	9	d2(g	d2(g	PROPN
ejpam-4144	661	10	)	)	PUNCT
ejpam-4144	661	11	is	be	AUX
ejpam-4144	661	12	a	a	DET
ejpam-4144	661	13	complete	complete	ADJ
ejpam-4144	661	14	graph	graph	NOUN
ejpam-4144	661	15	.	.	PUNCT
ejpam-4144	662	1	if	if	SCONJ
ejpam-4144	662	2	d2(g	d2(g	NOUN
ejpam-4144	662	3	)	)	PUNCT
ejpam-4144	662	4	is	be	AUX
ejpam-4144	662	5	connected	connect	VERB
ejpam-4144	662	6	,	,	PUNCT
ejpam-4144	662	7	then	then	ADV
ejpam-4144	662	8	d2(g	d2(g	NUM
ejpam-4144	662	9	)	)	PUNCT
ejpam-4144	662	10	=	=	SYM
ejpam-4144	662	11	k2n	k2n	NOUN
ejpam-4144	662	12	.	.	PUNCT
ejpam-4144	663	1	hence	hence	ADV
ejpam-4144	663	2	,	,	PUNCT
ejpam-4144	663	3	g	g	PROPN
ejpam-4144	663	4	=	=	PROPN
ejpam-4144	663	5	kn	kn	PROPN
ejpam-4144	663	6	.	.	PUNCT
ejpam-4144	664	1	next	next	ADV
ejpam-4144	664	2	,	,	PUNCT
ejpam-4144	664	3	suppose	suppose	VERB
ejpam-4144	664	4	that	that	SCONJ
ejpam-4144	664	5	d2(g	d2(g	PROPN
ejpam-4144	664	6	)	)	PUNCT
ejpam-4144	664	7	is	be	AUX
ejpam-4144	664	8	disconnected	disconnect	VERB
ejpam-4144	664	9	with	with	ADP
ejpam-4144	664	10	components	component	NOUN
ejpam-4144	664	11	c1	c1	PROPN
ejpam-4144	664	12	,	,	PUNCT
ejpam-4144	664	13	c2	c2	PROPN
ejpam-4144	664	14	,	,	PUNCT
ejpam-4144	664	15	.	.	PUNCT
ejpam-4144	664	16	.	.	PUNCT
ejpam-4144	665	1	.	.	PUNCT
ejpam-4144	666	1	,	,	PUNCT
ejpam-4144	666	2	ck	ck	INTJ
ejpam-4144	666	3	.	.	PUNCT
ejpam-4144	667	1	for	for	ADP
ejpam-4144	667	2	each	each	DET
ejpam-4144	667	3	i	i	PRON
ejpam-4144	667	4	∈	∈	PROPN
ejpam-4144	667	5	{	{	PUNCT
ejpam-4144	667	6	1	1	NUM
ejpam-4144	667	7	,	,	PUNCT
ejpam-4144	667	8	2	2	NUM
ejpam-4144	667	9	,	,	PUNCT
ejpam-4144	667	10	.	.	PUNCT
ejpam-4144	667	11	.	.	PUNCT
ejpam-4144	667	12	.	.	PUNCT
ejpam-4144	668	1	,	,	PUNCT
ejpam-4144	668	2	k	k	X
ejpam-4144	668	3	}	}	PUNCT
ejpam-4144	668	4	,	,	PUNCT
ejpam-4144	668	5	let	let	VERB
ejpam-4144	668	6	s1,i	s1,i	PROPN
ejpam-4144	668	7	=	=	SYM
ejpam-4144	668	8	v	v	PROPN
ejpam-4144	668	9	(	(	PUNCT
ejpam-4144	668	10	g1	g1	PROPN
ejpam-4144	668	11	)	)	PUNCT
ejpam-4144	668	12	∩	∩	ADJ
ejpam-4144	668	13	v	v	X
ejpam-4144	668	14	(	(	PUNCT
ejpam-4144	668	15	ci	ci	NOUN
ejpam-4144	668	16	)	)	PUNCT
ejpam-4144	668	17	,	,	PUNCT
ejpam-4144	669	1	s2,i	s2,i	PROPN
ejpam-4144	669	2	=	=	SYM
ejpam-4144	669	3	v	v	PROPN
ejpam-4144	669	4	(	(	PUNCT
ejpam-4144	669	5	g2	g2	PROPN
ejpam-4144	669	6	)	)	PUNCT
ejpam-4144	669	7	∩	∩	PROPN
ejpam-4144	669	8	v	v	X
ejpam-4144	669	9	(	(	PUNCT
ejpam-4144	669	10	ci	ci	NOUN
ejpam-4144	669	11	)	)	PUNCT
ejpam-4144	669	12	and	and	CCONJ
ejpam-4144	669	13	mi	mi	PROPN
ejpam-4144	669	14	=	=	SYM
ejpam-4144	670	1	|s1,i|	|s1,i|	PROPN
ejpam-4144	670	2	.	.	PUNCT
ejpam-4144	670	3	note	note	VERB
ejpam-4144	670	4	that	that	SCONJ
ejpam-4144	670	5	v	v	X
ejpam-4144	670	6	∈	∈	PROPN
ejpam-4144	670	7	s1,i	s1,i	PROPN
ejpam-4144	670	8	if	if	SCONJ
ejpam-4144	670	9	and	and	CCONJ
ejpam-4144	670	10	only	only	ADV
ejpam-4144	670	11	if	if	SCONJ
ejpam-4144	670	12	v′	v′	PROPN
ejpam-4144	670	13	∈	∈	PROPN
ejpam-4144	670	14	s2,i	s2,i	PROPN
ejpam-4144	670	15	and	and	CCONJ
ejpam-4144	670	16	that	that	SCONJ
ejpam-4144	670	17	ci	ci	NOUN
ejpam-4144	670	18	=	=	PUNCT
ejpam-4144	671	1	⟨s1,i∪s2,i⟩	⟨s1,i∪s2,i⟩	ADJ
ejpam-4144	671	2	for	for	ADP
ejpam-4144	671	3	each	each	DET
ejpam-4144	671	4	i	i	PRON
ejpam-4144	671	5	∈	∈	PROPN
ejpam-4144	671	6	{	{	PUNCT
ejpam-4144	671	7	1	1	NUM
ejpam-4144	671	8	,	,	PUNCT
ejpam-4144	671	9	2	2	NUM
ejpam-4144	671	10	,	,	PUNCT
ejpam-4144	671	11	.	.	PUNCT
ejpam-4144	671	12	.	.	PUNCT
ejpam-4144	672	1	.	.	PUNCT
ejpam-4144	673	1	,	,	PUNCT
ejpam-4144	673	2	k	k	X
ejpam-4144	673	3	}	}	PUNCT
ejpam-4144	673	4	.	.	PUNCT
ejpam-4144	674	1	let	let	VERB
ejpam-4144	674	2	i	i	PRON
ejpam-4144	674	3	,	,	PUNCT
ejpam-4144	674	4	j	j	PROPN
ejpam-4144	674	5	∈	∈	PROPN
ejpam-4144	674	6	{	{	PUNCT
ejpam-4144	674	7	1	1	NUM
ejpam-4144	674	8	,	,	PUNCT
ejpam-4144	674	9	2	2	NUM
ejpam-4144	674	10	,	,	PUNCT
ejpam-4144	674	11	.	.	PUNCT
ejpam-4144	674	12	.	.	PUNCT
ejpam-4144	675	1	.	.	PUNCT
ejpam-4144	676	1	,	,	PUNCT
ejpam-4144	676	2	k	k	X
ejpam-4144	676	3	}	}	PUNCT
ejpam-4144	676	4	with	with	ADP
ejpam-4144	676	5	i	i	PROPN
ejpam-4144	676	6	̸=	̸=	PROPN
ejpam-4144	676	7	j.	j.	PROPN
ejpam-4144	676	8	since	since	SCONJ
ejpam-4144	676	9	ci	ci	PROPN
ejpam-4144	676	10	and	and	CCONJ
ejpam-4144	676	11	cj	cj	NOUN
ejpam-4144	676	12	are	be	AUX
ejpam-4144	676	13	complete	complete	ADJ
ejpam-4144	676	14	subgraphs	subgraph	NOUN
ejpam-4144	676	15	(	(	PUNCT
ejpam-4144	676	16	components	component	NOUN
ejpam-4144	676	17	)	)	PUNCT
ejpam-4144	676	18	of	of	ADP
ejpam-4144	676	19	d2(g	d2(g	PROPN
ejpam-4144	676	20	)	)	PUNCT
ejpam-4144	676	21	,	,	PUNCT
ejpam-4144	676	22	it	it	PRON
ejpam-4144	676	23	follows	follow	VERB
ejpam-4144	676	24	that	that	SCONJ
ejpam-4144	676	25	in	in	ADP
ejpam-4144	676	26	graph	graph	NOUN
ejpam-4144	676	27	d2(g	d2(g	PROPN
ejpam-4144	676	28	)	)	PUNCT
ejpam-4144	676	29	,	,	PUNCT
ejpam-4144	676	30	s1,i	s1,i	PROPN
ejpam-4144	676	31	and	and	CCONJ
ejpam-4144	676	32	s1,j	s1,j	NOUN
ejpam-4144	676	33	are	be	AUX
ejpam-4144	676	34	independent	independent	ADJ
ejpam-4144	676	35	subsets	subset	NOUN
ejpam-4144	676	36	of	of	ADP
ejpam-4144	676	37	v	v	NOUN
ejpam-4144	676	38	(	(	PUNCT
ejpam-4144	676	39	g1	g1	PROPN
ejpam-4144	676	40	)	)	PUNCT
ejpam-4144	676	41	and	and	CCONJ
ejpam-4144	676	42	xy	xy	PROPN
ejpam-4144	676	43	∈	∈	PROPN
ejpam-4144	676	44	e(g1	e(g1	ADJ
ejpam-4144	676	45	)	)	PUNCT
ejpam-4144	676	46	for	for	ADP
ejpam-4144	676	47	each	each	DET
ejpam-4144	676	48	x	x	SYM
ejpam-4144	676	49	∈	∈	PROPN
ejpam-4144	676	50	s1,i	s1,i	PROPN
ejpam-4144	676	51	and	and	CCONJ
ejpam-4144	676	52	y	y	PROPN
ejpam-4144	676	53	∈	∈	PROPN
ejpam-4144	676	54	s1,j	s1,j	PROPN
ejpam-4144	676	55	.	.	PUNCT
ejpam-4144	677	1	it	it	PRON
ejpam-4144	677	2	follows	follow	VERB
ejpam-4144	677	3	that	that	SCONJ
ejpam-4144	677	4	g1	g1	PROPN
ejpam-4144	677	5	is	be	AUX
ejpam-4144	677	6	a	a	DET
ejpam-4144	677	7	complete	complete	ADJ
ejpam-4144	677	8	multipartite	multipartite	ADJ
ejpam-4144	677	9	graph	graph	NOUN
ejpam-4144	677	10	with	with	ADP
ejpam-4144	677	11	partite	partite	ADJ
ejpam-4144	677	12	sets	set	NOUN
ejpam-4144	677	13	s1,1	s1,1	PROPN
ejpam-4144	677	14	,	,	PUNCT
ejpam-4144	677	15	s1,2	s1,2	PROPN
ejpam-4144	677	16	,	,	PUNCT
ejpam-4144	677	17	.	.	PUNCT
ejpam-4144	677	18	.	.	PUNCT
ejpam-4144	678	1	.	.	PUNCT
ejpam-4144	679	1	,	,	PUNCT
ejpam-4144	680	1	s1,k	s1,k	PROPN
ejpam-4144	680	2	.	.	PUNCT
ejpam-4144	681	1	hence	hence	ADV
ejpam-4144	681	2	,	,	PUNCT
ejpam-4144	681	3	g	g	PROPN
ejpam-4144	681	4	=	=	SYM
ejpam-4144	681	5	km1,m2,	km1,m2,	PROPN
ejpam-4144	681	6	...	...	PUNCT
ejpam-4144	681	7	,mk	,mk	PUNCT
ejpam-4144	681	8	.	.	PUNCT
ejpam-4144	682	1	the	the	DET
ejpam-4144	682	2	converse	converse	NOUN
ejpam-4144	682	3	is	be	AUX
ejpam-4144	682	4	clear	clear	ADJ
ejpam-4144	682	5	.	.	PUNCT
ejpam-4144	683	1	theorem	theorem	ADJ
ejpam-4144	683	2	10	10	NUM
ejpam-4144	683	3	.	.	PUNCT
ejpam-4144	684	1	let	let	VERB
ejpam-4144	684	2	g	g	PRON
ejpam-4144	684	3	be	be	AUX
ejpam-4144	684	4	a	a	DET
ejpam-4144	684	5	graph	graph	NOUN
ejpam-4144	684	6	of	of	ADP
ejpam-4144	684	7	order	order	NOUN
ejpam-4144	684	8	n.	n.	NOUN
ejpam-4144	684	9	then	then	ADV
ejpam-4144	684	10	γgh(d2(g	γgh(d2(g	ADJ
ejpam-4144	684	11	)	)	PUNCT
ejpam-4144	684	12	)	)	PUNCT
ejpam-4144	685	1	=	=	SYM
ejpam-4144	685	2	2n	2n	NUM
ejpam-4144	685	3	if	if	SCONJ
ejpam-4144	685	4	and	and	CCONJ
ejpam-4144	685	5	only	only	ADV
ejpam-4144	685	6	if	if	SCONJ
ejpam-4144	685	7	g	g	PROPN
ejpam-4144	685	8	=	=	VERB
ejpam-4144	685	9	kn	kn	PROPN
ejpam-4144	685	10	or	or	CCONJ
ejpam-4144	685	11	g	g	PROPN
ejpam-4144	685	12	=	=	PUNCT
ejpam-4144	685	13	km1,m2,	km1,m2,	PROPN
ejpam-4144	685	14	...	...	PUNCT
ejpam-4144	685	15	,mk	,mk	PUNCT
ejpam-4144	685	16	,	,	PUNCT
ejpam-4144	685	17	where	where	SCONJ
ejpam-4144	685	18	k∑	k∑	PROPN
ejpam-4144	685	19	i=1	i=1	PROPN
ejpam-4144	685	20	mi	mi	PROPN
ejpam-4144	685	21	=	=	PROPN
ejpam-4144	685	22	n.	n.	PROPN
ejpam-4144	685	23	proof	proof	NOUN
ejpam-4144	685	24	.	.	PUNCT
ejpam-4144	686	1	by	by	ADP
ejpam-4144	686	2	theorem	theorem	NOUN
ejpam-4144	686	3	2	2	NUM
ejpam-4144	686	4	,	,	PUNCT
ejpam-4144	686	5	γgh(d2(g	γgh(d2(g	NUM
ejpam-4144	686	6	)	)	PUNCT
ejpam-4144	686	7	)	)	PUNCT
ejpam-4144	687	1	=	=	SYM
ejpam-4144	687	2	2n	2n	NUM
ejpam-4144	687	3	if	if	SCONJ
ejpam-4144	687	4	and	and	CCONJ
ejpam-4144	687	5	only	only	ADV
ejpam-4144	687	6	if	if	SCONJ
ejpam-4144	687	7	every	every	DET
ejpam-4144	687	8	component	component	NOUN
ejpam-4144	687	9	of	of	ADP
ejpam-4144	687	10	d2(g	d2(g	PROPN
ejpam-4144	687	11	)	)	PUNCT
ejpam-4144	687	12	or	or	CCONJ
ejpam-4144	687	13	d2(g	d2(g	PROPN
ejpam-4144	687	14	)	)	PUNCT
ejpam-4144	687	15	is	be	AUX
ejpam-4144	687	16	complete	complete	ADJ
ejpam-4144	687	17	.	.	PUNCT
ejpam-4144	688	1	thus	thus	ADV
ejpam-4144	688	2	by	by	ADP
ejpam-4144	688	3	lemma	lemma	PROPN
ejpam-4144	688	4	4	4	NUM
ejpam-4144	688	5	,	,	PUNCT
ejpam-4144	688	6	γgh(d2(g	γgh(d2(g	NUM
ejpam-4144	688	7	)	)	PUNCT
ejpam-4144	688	8	)	)	PUNCT
ejpam-4144	689	1	=	=	SYM
ejpam-4144	689	2	2n	2n	NUM
ejpam-4144	689	3	if	if	SCONJ
ejpam-4144	689	4	and	and	CCONJ
ejpam-4144	689	5	only	only	ADV
ejpam-4144	689	6	if	if	SCONJ
ejpam-4144	689	7	g	g	PROPN
ejpam-4144	689	8	=	=	VERB
ejpam-4144	689	9	kn	kn	PROPN
ejpam-4144	689	10	or	or	CCONJ
ejpam-4144	689	11	g	g	PROPN
ejpam-4144	689	12	=	=	PUNCT
ejpam-4144	689	13	km1,m2,	km1,m2,	PROPN
ejpam-4144	689	14	...	...	PUNCT
ejpam-4144	689	15	,mk	,mk	PUNCT
ejpam-4144	689	16	,	,	PUNCT
ejpam-4144	689	17	where	where	SCONJ
ejpam-4144	689	18	k∑	k∑	PROPN
ejpam-4144	689	19	i=1	i=1	PROPN
ejpam-4144	689	20	mi	mi	PROPN
ejpam-4144	689	21	=	=	PROPN
ejpam-4144	689	22	n.	n.	PROPN
ejpam-4144	689	23	note	note	NOUN
ejpam-4144	689	24	that	that	SCONJ
ejpam-4144	689	25	theorem	theorem	VERB
ejpam-4144	689	26	10	10	NUM
ejpam-4144	689	27	shows	show	VERB
ejpam-4144	689	28	that	that	SCONJ
ejpam-4144	689	29	the	the	DET
ejpam-4144	689	30	bound	bind	VERB
ejpam-4144	689	31	given	give	VERB
ejpam-4144	689	32	in	in	ADP
ejpam-4144	689	33	theorem	theorem	ADJ
ejpam-4144	689	34	9	9	NUM
ejpam-4144	689	35	is	be	AUX
ejpam-4144	689	36	tight	tight	ADJ
ejpam-4144	689	37	.	.	PUNCT
ejpam-4144	690	1	conclusion	conclusion	NOUN
ejpam-4144	690	2	:	:	PUNCT
ejpam-4144	690	3	the	the	DET
ejpam-4144	690	4	domination	domination	NOUN
ejpam-4144	690	5	and	and	CCONJ
ejpam-4144	690	6	hop	hop	NOUN
ejpam-4144	690	7	domination	domination	NOUN
ejpam-4144	690	8	parameters	parameter	NOUN
ejpam-4144	690	9	are	be	AUX
ejpam-4144	690	10	,	,	PUNCT
ejpam-4144	690	11	in	in	ADP
ejpam-4144	690	12	general	general	ADJ
ejpam-4144	690	13	,	,	PUNCT
ejpam-4144	690	14	not	not	PART
ejpam-4144	690	15	comparable	comparable	ADJ
ejpam-4144	690	16	.	.	PUNCT
ejpam-4144	691	1	however	however	ADV
ejpam-4144	691	2	,	,	PUNCT
ejpam-4144	691	3	a	a	DET
ejpam-4144	691	4	result	result	NOUN
ejpam-4144	691	5	shows	show	VERB
ejpam-4144	691	6	that	that	SCONJ
ejpam-4144	691	7	the	the	DET
ejpam-4144	691	8	absolute	absolute	ADJ
ejpam-4144	691	9	difference	difference	NOUN
ejpam-4144	691	10	of	of	ADP
ejpam-4144	691	11	the	the	DET
ejpam-4144	691	12	domination	domination	NOUN
ejpam-4144	691	13	number	number	NOUN
ejpam-4144	691	14	and	and	CCONJ
ejpam-4144	691	15	hop	hop	NOUN
ejpam-4144	691	16	domination	domination	NOUN
ejpam-4144	691	17	number	number	NOUN
ejpam-4144	691	18	can	can	AUX
ejpam-4144	691	19	be	be	AUX
ejpam-4144	691	20	made	make	VERB
ejpam-4144	691	21	arbitrarily	arbitrarily	ADV
ejpam-4144	691	22	large	large	ADJ
ejpam-4144	691	23	.	.	PUNCT
ejpam-4144	692	1	on	on	ADP
ejpam-4144	692	2	the	the	DET
ejpam-4144	692	3	other	other	ADJ
ejpam-4144	692	4	hand	hand	NOUN
ejpam-4144	692	5	,	,	PUNCT
ejpam-4144	692	6	a	a	DET
ejpam-4144	692	7	result	result	NOUN
ejpam-4144	692	8	shows	show	VERB
ejpam-4144	692	9	a	a	DET
ejpam-4144	692	10	relationship	relationship	NOUN
ejpam-4144	692	11	of	of	ADP
ejpam-4144	692	12	the	the	DET
ejpam-4144	692	13	hop	hop	NOUN
ejpam-4144	692	14	domination	domination	NOUN
ejpam-4144	692	15	and	and	CCONJ
ejpam-4144	692	16	global	global	ADJ
ejpam-4144	692	17	hop	hop	NOUN
ejpam-4144	692	18	domination	domination	NOUN
ejpam-4144	692	19	numbers	number	NOUN
ejpam-4144	692	20	.	.	PUNCT
ejpam-4144	693	1	references	reference	NOUN
ejpam-4144	693	2	1427	1427	NUM
ejpam-4144	693	3	for	for	ADP
ejpam-4144	693	4	any	any	DET
ejpam-4144	693	5	non	non	ADJ
ejpam-4144	693	6	-	-	ADJ
ejpam-4144	693	7	trivial	trivial	ADJ
ejpam-4144	693	8	connected	connected	ADJ
ejpam-4144	693	9	graph	graph	NOUN
ejpam-4144	693	10	g	g	NOUN
ejpam-4144	693	11	,	,	PUNCT
ejpam-4144	693	12	it	it	PRON
ejpam-4144	693	13	is	be	AUX
ejpam-4144	693	14	proved	prove	VERB
ejpam-4144	693	15	that	that	SCONJ
ejpam-4144	693	16	that	that	PRON
ejpam-4144	693	17	2γgh(g	2γgh(g	NOUN
ejpam-4144	693	18	)	)	PUNCT
ejpam-4144	693	19	is	be	AUX
ejpam-4144	693	20	a	a	DET
ejpam-4144	693	21	tight	tight	ADJ
ejpam-4144	693	22	bound	bind	VERB
ejpam-4144	693	23	for	for	ADP
ejpam-4144	693	24	the	the	DET
ejpam-4144	693	25	global	global	ADJ
ejpam-4144	693	26	hop	hop	PROPN
ejpam-4144	693	27	domination	domination	NOUN
ejpam-4144	693	28	number	number	NOUN
ejpam-4144	693	29	of	of	ADP
ejpam-4144	693	30	the	the	DET
ejpam-4144	693	31	shadow	shadow	NOUN
ejpam-4144	693	32	graph	graph	VERB
ejpam-4144	693	33	d2(g	d2(g	PROPN
ejpam-4144	693	34	)	)	PUNCT
ejpam-4144	693	35	of	of	ADP
ejpam-4144	693	36	g.	g.	PROPN
ejpam-4144	693	37	the	the	DET
ejpam-4144	693	38	authors	author	NOUN
ejpam-4144	693	39	are	be	AUX
ejpam-4144	693	40	still	still	ADV
ejpam-4144	693	41	unable	unable	ADJ
ejpam-4144	693	42	to	to	PART
ejpam-4144	693	43	show	show	VERB
ejpam-4144	693	44	that	that	SCONJ
ejpam-4144	693	45	the	the	DET
ejpam-4144	693	46	strict	strict	ADJ
ejpam-4144	693	47	inequality	inequality	NOUN
ejpam-4144	693	48	in	in	ADP
ejpam-4144	693	49	theorem	theorem	NOUN
ejpam-4144	693	50	9	9	NUM
ejpam-4144	693	51	is	be	AUX
ejpam-4144	693	52	also	also	ADV
ejpam-4144	693	53	attainable	attainable	ADJ
ejpam-4144	693	54	.	.	PUNCT
ejpam-4144	694	1	we	we	PRON
ejpam-4144	694	2	leave	leave	VERB
ejpam-4144	694	3	to	to	ADP
ejpam-4144	694	4	the	the	DET
ejpam-4144	694	5	interested	interested	ADJ
ejpam-4144	694	6	readers	reader	NOUN
ejpam-4144	694	7	to	to	PART
ejpam-4144	694	8	verify	verify	VERB
ejpam-4144	694	9	whether	whether	SCONJ
ejpam-4144	694	10	or	or	CCONJ
ejpam-4144	694	11	not	not	PART
ejpam-4144	694	12	equality	equality	NOUN
ejpam-4144	694	13	in	in	ADP
ejpam-4144	694	14	this	this	DET
ejpam-4144	694	15	result	result	NOUN
ejpam-4144	694	16	holds	hold	VERB
ejpam-4144	694	17	.	.	PUNCT
ejpam-4144	695	1	acknowledgements	acknowledgement	NOUN
ejpam-4144	695	2	the	the	DET
ejpam-4144	695	3	authors	author	NOUN
ejpam-4144	695	4	would	would	AUX
ejpam-4144	695	5	like	like	VERB
ejpam-4144	695	6	to	to	PART
ejpam-4144	695	7	thank	thank	VERB
ejpam-4144	695	8	the	the	DET
ejpam-4144	695	9	referees	referee	NOUN
ejpam-4144	695	10	for	for	ADP
ejpam-4144	695	11	reading	read	VERB
ejpam-4144	695	12	the	the	DET
ejpam-4144	695	13	initial	initial	ADJ
ejpam-4144	695	14	manuscript	manuscript	NOUN
ejpam-4144	695	15	and	and	CCONJ
ejpam-4144	695	16	the	the	DET
ejpam-4144	695	17	invaluable	invaluable	ADJ
ejpam-4144	695	18	comments	comment	NOUN
ejpam-4144	695	19	and	and	CCONJ
ejpam-4144	695	20	suggestion	suggestion	NOUN
ejpam-4144	695	21	they	they	PRON
ejpam-4144	695	22	have	have	AUX
ejpam-4144	695	23	given	give	VERB
ejpam-4144	695	24	.	.	PUNCT
ejpam-4144	696	1	also	also	ADV
ejpam-4144	696	2	,	,	PUNCT
ejpam-4144	696	3	the	the	DET
ejpam-4144	696	4	authors	author	NOUN
ejpam-4144	696	5	are	be	AUX
ejpam-4144	696	6	grateful	grateful	ADJ
ejpam-4144	696	7	to	to	ADP
ejpam-4144	696	8	the	the	DET
ejpam-4144	696	9	department	department	NOUN
ejpam-4144	696	10	of	of	ADP
ejpam-4144	696	11	science	science	NOUN
ejpam-4144	696	12	and	and	CCONJ
ejpam-4144	696	13	technology	technology	NOUN
ejpam-4144	696	14	accelerated	accelerate	VERB
ejpam-4144	696	15	science	science	NOUN
ejpam-4144	696	16	and	and	CCONJ
ejpam-4144	696	17	technology	technology	NOUN
ejpam-4144	696	18	and	and	CCONJ
ejpam-4144	696	19	human	human	ADJ
ejpam-4144	696	20	resource	resource	NOUN
ejpam-4144	696	21	development	development	NOUN
ejpam-4144	696	22	program	program	NOUN
ejpam-4144	696	23	(	(	PUNCT
ejpam-4144	696	24	dost	dost	NOUN
ejpam-4144	696	25	-	-	PUNCT
ejpam-4144	696	26	asthrdp	asthrdp	NOUN
ejpam-4144	696	27	)	)	PUNCT
ejpam-4144	696	28	,	,	PUNCT
ejpam-4144	696	29	philippines	philippine	NOUN
ejpam-4144	696	30	,	,	PUNCT
ejpam-4144	696	31	and	and	CCONJ
ejpam-4144	696	32	msu	msu	PROPN
ejpam-4144	696	33	-	-	PUNCT
ejpam-4144	696	34	iligan	iligan	PROPN
ejpam-4144	696	35	institute	institute	PROPN
ejpam-4144	696	36	of	of	ADP
ejpam-4144	696	37	technology	technology	NOUN
ejpam-4144	696	38	for	for	ADP
ejpam-4144	696	39	funding	fund	VERB
ejpam-4144	696	40	this	this	DET
ejpam-4144	696	41	research	research	NOUN
ejpam-4144	696	42	.	.	PUNCT
ejpam-4144	697	1	references	reference	NOUN
ejpam-4144	697	2	[	[	X
ejpam-4144	697	3	1	1	NUM
ejpam-4144	697	4	]	]	PUNCT
ejpam-4144	697	5	b.	b.	PROPN
ejpam-4144	697	6	arriola	arriola	PROPN
ejpam-4144	697	7	and	and	CCONJ
ejpam-4144	697	8	s.	s.	PROPN
ejpam-4144	697	9	jr	jr	PROPN
ejpam-4144	697	10	.	.	PROPN
ejpam-4144	698	1	canoy	canoy	PROPN
ejpam-4144	698	2	.	.	PUNCT
ejpam-4144	699	1	secure	secure	VERB
ejpam-4144	699	2	doubly	doubly	ADV
ejpam-4144	699	3	connected	connected	ADJ
ejpam-4144	699	4	domination	domination	NOUN
ejpam-4144	699	5	in	in	ADP
ejpam-4144	699	6	graphs	graph	NOUN
ejpam-4144	699	7	.	.	PUNCT
ejpam-4144	700	1	international	international	ADJ
ejpam-4144	700	2	journal	journal	PROPN
ejpam-4144	700	3	of	of	ADP
ejpam-4144	700	4	mathematical	mathematical	ADJ
ejpam-4144	700	5	analysis	analysis	NOUN
ejpam-4144	700	6	,	,	PUNCT
ejpam-4144	700	7	8:1571–1580	8:1571–1580	NUM
ejpam-4144	700	8	,	,	PUNCT
ejpam-4144	700	9	2014	2014	NUM
ejpam-4144	700	10	.	.	PUNCT
ejpam-4144	701	1	[	[	X
ejpam-4144	701	2	2	2	NUM
ejpam-4144	701	3	]	]	PUNCT
ejpam-4144	701	4	a.	a.	NOUN
ejpam-4144	701	5	cabaro	cabaro	NOUN
ejpam-4144	701	6	,	,	PUNCT
ejpam-4144	701	7	s.	s.	PROPN
ejpam-4144	701	8	jr	jr	PROPN
ejpam-4144	701	9	.	.	PROPN
ejpam-4144	701	10	canoy	canoy	PROPN
ejpam-4144	701	11	,	,	PUNCT
ejpam-4144	701	12	and	and	CCONJ
ejpam-4144	701	13	i.	i.	PROPN
ejpam-4144	701	14	aniversario	aniversario	PROPN
ejpam-4144	701	15	.	.	PUNCT
ejpam-4144	702	1	secure	secure	VERB
ejpam-4144	702	2	connected	connected	ADJ
ejpam-4144	702	3	domination	domination	NOUN
ejpam-4144	702	4	in	in	ADP
ejpam-4144	702	5	a	a	DET
ejpam-4144	702	6	graph	graph	NOUN
ejpam-4144	702	7	.	.	PUNCT
ejpam-4144	703	1	international	international	ADJ
ejpam-4144	703	2	journal	journal	PROPN
ejpam-4144	703	3	of	of	ADP
ejpam-4144	703	4	mathematical	mathematical	ADJ
ejpam-4144	703	5	analysis	analysis	NOUN
ejpam-4144	703	6	,	,	PUNCT
ejpam-4144	703	7	8(42):2065–2074	8(42):2065–2074	NUM
ejpam-4144	703	8	,	,	PUNCT
ejpam-4144	703	9	2014	2014	NUM
ejpam-4144	703	10	.	.	PUNCT
ejpam-4144	704	1	[	[	X
ejpam-4144	704	2	3	3	X
ejpam-4144	704	3	]	]	PUNCT
ejpam-4144	704	4	s.	s.	PROPN
ejpam-4144	704	5	jr	jr	PROPN
ejpam-4144	704	6	.	.	PROPN
ejpam-4144	704	7	canoy	canoy	PROPN
ejpam-4144	704	8	,	,	PUNCT
ejpam-4144	704	9	s.a	s.a	PROPN
ejpam-4144	704	10	.	.	PROPN
ejpam-4144	704	11	canoy	canoy	PROPN
ejpam-4144	704	12	,	,	PUNCT
ejpam-4144	704	13	and	and	CCONJ
ejpam-4144	704	14	m.	m.	NOUN
ejpam-4144	704	15	cruzate	cruzate	NOUN
ejpam-4144	704	16	.	.	PUNCT
ejpam-4144	705	1	global	global	ADJ
ejpam-4144	705	2	domination	domination	NOUN
ejpam-4144	705	3	in	in	ADP
ejpam-4144	705	4	a	a	DET
ejpam-4144	705	5	graph	graph	NOUN
ejpam-4144	705	6	.	.	PUNCT
ejpam-4144	706	1	advances	advance	NOUN
ejpam-4144	706	2	and	and	CCONJ
ejpam-4144	706	3	applications	application	NOUN
ejpam-4144	706	4	in	in	ADP
ejpam-4144	706	5	discrete	discrete	ADJ
ejpam-4144	706	6	mathematics	mathematic	NOUN
ejpam-4144	706	7	,	,	PUNCT
ejpam-4144	706	8	19(4):401–408	19(4):401–408	PROPN
ejpam-4144	706	9	,	,	PUNCT
ejpam-4144	706	10	2018	2018	NUM
ejpam-4144	706	11	.	.	PUNCT
ejpam-4144	707	1	[	[	X
ejpam-4144	707	2	4	4	X
ejpam-4144	707	3	]	]	PUNCT
ejpam-4144	707	4	s.	s.	PROPN
ejpam-4144	707	5	jr	jr	PROPN
ejpam-4144	707	6	.	.	PROPN
ejpam-4144	707	7	canoy	canoy	PROPN
ejpam-4144	707	8	and	and	CCONJ
ejpam-4144	707	9	g.	g.	PROPN
ejpam-4144	707	10	malacas	malacas	PROPN
ejpam-4144	707	11	.	.	PUNCT
ejpam-4144	708	1	determining	determine	VERB
ejpam-4144	708	2	the	the	DET
ejpam-4144	708	3	intruder	intruder	NOUN
ejpam-4144	708	4	’s	’s	PART
ejpam-4144	708	5	location	location	NOUN
ejpam-4144	708	6	in	in	ADP
ejpam-4144	708	7	a	a	DET
ejpam-4144	708	8	given	give	VERB
ejpam-4144	708	9	network	network	NOUN
ejpam-4144	708	10	:	:	PUNCT
ejpam-4144	708	11	locating	locate	VERB
ejpam-4144	708	12	-	-	PUNCT
ejpam-4144	708	13	dominating	dominating	NOUN
ejpam-4144	708	14	sets	set	NOUN
ejpam-4144	708	15	in	in	ADP
ejpam-4144	708	16	a	a	DET
ejpam-4144	708	17	graph	graph	NOUN
ejpam-4144	708	18	.	.	PUNCT
ejpam-4144	709	1	nrcp	nrcp	PROPN
ejpam-4144	709	2	research	research	PROPN
ejpam-4144	709	3	journal	journal	PROPN
ejpam-4144	709	4	.	.	PUNCT
ejpam-4144	709	5	,	,	PUNCT
ejpam-4144	709	6	13(1):1–8	13(1):1–8	NUM
ejpam-4144	709	7	,	,	PUNCT
ejpam-4144	709	8	2013	2013	NUM
ejpam-4144	709	9	.	.	PUNCT
ejpam-4144	710	1	[	[	X
ejpam-4144	710	2	5	5	X
ejpam-4144	710	3	]	]	PUNCT
ejpam-4144	710	4	s.	s.	PROPN
ejpam-4144	710	5	jr	jr	PROPN
ejpam-4144	710	6	.	.	PROPN
ejpam-4144	710	7	canoy	canoy	PROPN
ejpam-4144	710	8	,	,	PUNCT
ejpam-4144	710	9	r.	r.	NOUN
ejpam-4144	710	10	mollejon	mollejon	NOUN
ejpam-4144	710	11	,	,	PUNCT
ejpam-4144	710	12	and	and	CCONJ
ejpam-4144	710	13	j.g	j.g	PROPN
ejpam-4144	710	14	.	.	PROPN
ejpam-4144	710	15	canoy	canoy	PROPN
ejpam-4144	710	16	.	.	PUNCT
ejpam-4144	711	1	hop	hop	PROPN
ejpam-4144	711	2	dominating	dominating	NOUN
ejpam-4144	711	3	sets	set	NOUN
ejpam-4144	711	4	in	in	ADP
ejpam-4144	711	5	graphs	graph	NOUN
ejpam-4144	711	6	under	under	ADP
ejpam-4144	711	7	binary	binary	ADJ
ejpam-4144	711	8	operations	operation	NOUN
ejpam-4144	711	9	.	.	PUNCT
ejpam-4144	712	1	european	european	ADJ
ejpam-4144	712	2	journal	journal	PROPN
ejpam-4144	712	3	of	of	ADP
ejpam-4144	712	4	pure	pure	ADJ
ejpam-4144	712	5	and	and	CCONJ
ejpam-4144	712	6	applied	applied	ADJ
ejpam-4144	712	7	mathematics	mathematic	NOUN
ejpam-4144	712	8	,	,	PUNCT
ejpam-4144	712	9	12(4):1455	12(4):1455	NUM
ejpam-4144	712	10	–	–	PUNCT
ejpam-4144	712	11	1463	1463	NUM
ejpam-4144	712	12	,	,	PUNCT
ejpam-4144	712	13	2019	2019	NUM
ejpam-4144	712	14	.	.	PUNCT
ejpam-4144	713	1	[	[	X
ejpam-4144	713	2	6	6	NUM
ejpam-4144	713	3	]	]	PUNCT
ejpam-4144	713	4	h.	h.	NOUN
ejpam-4144	713	5	escuardo	escuardo	PROPN
ejpam-4144	713	6	,	,	PUNCT
ejpam-4144	713	7	r.	r.	PROPN
ejpam-4144	713	8	gera	gera	PROPN
ejpam-4144	713	9	,	,	PUNCT
ejpam-4144	713	10	a.	a.	PROPN
ejpam-4144	713	11	hansberg	hansberg	PROPN
ejpam-4144	713	12	,	,	PUNCT
ejpam-4144	713	13	a.j	a.j	PROPN
ejpam-4144	713	14	.	.	PROPN
ejpam-4144	713	15	rad	rad	PROPN
ejpam-4144	713	16	,	,	PUNCT
ejpam-4144	713	17	and	and	CCONJ
ejpam-4144	713	18	l.	l.	PROPN
ejpam-4144	713	19	volkman	volkman	PROPN
ejpam-4144	713	20	.	.	PUNCT
ejpam-4144	714	1	geodetic	geodetic	ADJ
ejpam-4144	714	2	domination	domination	NOUN
ejpam-4144	714	3	in	in	ADP
ejpam-4144	714	4	graphs	graph	NOUN
ejpam-4144	714	5	.	.	PUNCT
ejpam-4144	715	1	journal	journal	NOUN
ejpam-4144	715	2	of	of	ADP
ejpam-4144	715	3	combinatorial	combinatorial	ADJ
ejpam-4144	715	4	mathematics	mathematic	NOUN
ejpam-4144	715	5	and	and	CCONJ
ejpam-4144	715	6	combinatorial	combinatorial	ADJ
ejpam-4144	715	7	computing	computing	NOUN
ejpam-4144	715	8	,	,	PUNCT
ejpam-4144	715	9	77:89–101	77:89–101	NUM
ejpam-4144	715	10	,	,	PUNCT
ejpam-4144	715	11	2011	2011	NUM
ejpam-4144	715	12	.	.	PUNCT
ejpam-4144	716	1	[	[	X
ejpam-4144	716	2	7	7	X
ejpam-4144	716	3	]	]	X
ejpam-4144	716	4	t.	t.	PROPN
ejpam-4144	716	5	haynes	haynes	PROPN
ejpam-4144	716	6	,	,	PUNCT
ejpam-4144	716	7	s.	s.	PROPN
ejpam-4144	716	8	hedetniemi	hedetniemi	PROPN
ejpam-4144	716	9	,	,	PUNCT
ejpam-4144	716	10	and	and	CCONJ
ejpam-4144	716	11	p.	p.	PROPN
ejpam-4144	716	12	slater	slater	PROPN
ejpam-4144	716	13	.	.	PUNCT
ejpam-4144	717	1	domination	domination	NOUN
ejpam-4144	717	2	in	in	ADP
ejpam-4144	717	3	graphs	graph	NOUN
ejpam-4144	717	4	,	,	PUNCT
ejpam-4144	717	5	advanced	advanced	ADJ
ejpam-4144	717	6	topics	topic	NOUN
ejpam-4144	717	7	.	.	PUNCT
ejpam-4144	718	1	marcell	marcell	PROPN
ejpam-4144	718	2	dekker	dekker	PROPN
ejpam-4144	718	3	,	,	PUNCT
ejpam-4144	718	4	new	new	PROPN
ejpam-4144	718	5	york	york	PROPN
ejpam-4144	718	6	,	,	PUNCT
ejpam-4144	718	7	usa	usa	PROPN
ejpam-4144	718	8	,	,	PUNCT
ejpam-4144	718	9	1998	1998	NUM
ejpam-4144	718	10	.	.	PUNCT
ejpam-4144	719	1	[	[	X
ejpam-4144	719	2	8	8	X
ejpam-4144	719	3	]	]	PUNCT
ejpam-4144	719	4	t.	t.	PROPN
ejpam-4144	719	5	haynes	haynes	PROPN
ejpam-4144	719	6	,	,	PUNCT
ejpam-4144	719	7	s.	s.	PROPN
ejpam-4144	719	8	hedetniemi	hedetniemi	PROPN
ejpam-4144	719	9	,	,	PUNCT
ejpam-4144	719	10	and	and	CCONJ
ejpam-4144	719	11	p.	p.	PROPN
ejpam-4144	719	12	slater	slater	PROPN
ejpam-4144	719	13	.	.	PUNCT
ejpam-4144	720	1	fundamentals	fundamental	NOUN
ejpam-4144	720	2	of	of	ADP
ejpam-4144	720	3	domination	domination	NOUN
ejpam-4144	720	4	in	in	ADP
ejpam-4144	720	5	graphs	graph	NOUN
ejpam-4144	720	6	.	.	PUNCT
ejpam-4144	721	1	marcell	marcell	PROPN
ejpam-4144	721	2	dekker	dekker	PROPN
ejpam-4144	721	3	,	,	PUNCT
ejpam-4144	721	4	new	new	PROPN
ejpam-4144	721	5	york	york	PROPN
ejpam-4144	721	6	,	,	PUNCT
ejpam-4144	721	7	usa	usa	PROPN
ejpam-4144	721	8	,	,	PUNCT
ejpam-4144	721	9	1998	1998	NUM
ejpam-4144	721	10	.	.	PUNCT
ejpam-4144	722	1	[	[	X
ejpam-4144	722	2	9	9	NUM
ejpam-4144	722	3	]	]	PUNCT
ejpam-4144	722	4	t.	t.	PROPN
ejpam-4144	722	5	haynes	haynes	PROPN
ejpam-4144	722	6	,	,	PUNCT
ejpam-4144	722	7	m.	m.	NOUN
ejpam-4144	722	8	henning	henning	PROPN
ejpam-4144	722	9	,	,	PUNCT
ejpam-4144	722	10	and	and	CCONJ
ejpam-4144	722	11	j.	j.	PROPN
ejpam-4144	722	12	howard	howard	PROPN
ejpam-4144	722	13	.	.	PUNCT
ejpam-4144	723	1	locating	locate	VERB
ejpam-4144	723	2	and	and	CCONJ
ejpam-4144	723	3	total	total	ADJ
ejpam-4144	723	4	dominating	dominating	NOUN
ejpam-4144	723	5	sets	set	NOUN
ejpam-4144	723	6	in	in	ADP
ejpam-4144	723	7	trees	tree	NOUN
ejpam-4144	723	8	.	.	PUNCT
ejpam-4144	724	1	discrete	discrete	ADJ
ejpam-4144	724	2	applied	apply	VERB
ejpam-4144	724	3	mathematics	mathematic	NOUN
ejpam-4144	724	4	,	,	PUNCT
ejpam-4144	724	5	154(8):1293–1300	154(8):1293–1300	NUM
ejpam-4144	724	6	,	,	PUNCT
ejpam-4144	724	7	2006	2006	NUM
ejpam-4144	724	8	.	.	PUNCT
ejpam-4144	725	1	[	[	X
ejpam-4144	725	2	10	10	NUM
ejpam-4144	725	3	]	]	PUNCT
ejpam-4144	725	4	t.	t.	PROPN
ejpam-4144	725	5	haynes	haynes	PROPN
ejpam-4144	725	6	,	,	PUNCT
ejpam-4144	725	7	m.	m.	NOUN
ejpam-4144	725	8	henning	henning	PROPN
ejpam-4144	725	9	,	,	PUNCT
ejpam-4144	725	10	and	and	CCONJ
ejpam-4144	725	11	l.	l.	PROPN
ejpam-4144	725	12	van	van	PROPN
ejpam-4144	725	13	der	der	PROPN
ejpam-4144	725	14	merwe	merwe	PROPN
ejpam-4144	725	15	.	.	PUNCT
ejpam-4144	725	16	domination	domination	PROPN
ejpam-4144	725	17	and	and	CCONJ
ejpam-4144	725	18	total	total	ADJ
ejpam-4144	725	19	domination	domination	NOUN
ejpam-4144	725	20	in	in	ADP
ejpam-4144	725	21	complementary	complementary	ADJ
ejpam-4144	725	22	prisms	prism	NOUN
ejpam-4144	725	23	.	.	PUNCT
ejpam-4144	726	1	journal	journal	NOUN
ejpam-4144	726	2	of	of	ADP
ejpam-4144	726	3	combinatorial	combinatorial	ADJ
ejpam-4144	726	4	optimization	optimization	NOUN
ejpam-4144	726	5	,	,	PUNCT
ejpam-4144	726	6	18:23–37	18:23–37	PROPN
ejpam-4144	726	7	,	,	PUNCT
ejpam-4144	726	8	2009	2009	NUM
ejpam-4144	726	9	.	.	PUNCT
ejpam-4144	727	1	references	reference	NOUN
ejpam-4144	727	2	1428	1428	NUM
ejpam-4144	727	3	[	[	X
ejpam-4144	727	4	11	11	NUM
ejpam-4144	727	5	]	]	PUNCT
ejpam-4144	727	6	m.	m.	NOUN
ejpam-4144	727	7	henning	henning	PROPN
ejpam-4144	727	8	and	and	CCONJ
ejpam-4144	727	9	n.j	n.j	PROPN
ejpam-4144	727	10	.	.	PROPN
ejpam-4144	727	11	rad	rad	PROPN
ejpam-4144	727	12	.	.	PROPN
ejpam-4144	728	1	on	on	ADP
ejpam-4144	728	2	2	2	NUM
ejpam-4144	728	3	-	-	PUNCT
ejpam-4144	728	4	step	step	NOUN
ejpam-4144	728	5	and	and	CCONJ
ejpam-4144	728	6	hop	hop	NOUN
ejpam-4144	728	7	dominating	dominating	NOUN
ejpam-4144	728	8	sets	set	NOUN
ejpam-4144	728	9	in	in	ADP
ejpam-4144	728	10	graphs	graph	NOUN
ejpam-4144	728	11	.	.	PUNCT
ejpam-4144	729	1	graphs	graph	NOUN
ejpam-4144	729	2	and	and	CCONJ
ejpam-4144	729	3	combinatorics	combinatoric	NOUN
ejpam-4144	729	4	,	,	PUNCT
ejpam-4144	729	5	33(4):913–927	33(4):913–927	PROPN
ejpam-4144	729	6	,	,	PUNCT
ejpam-4144	729	7	2017	2017	NUM
ejpam-4144	729	8	.	.	PUNCT
ejpam-4144	730	1	[	[	X
ejpam-4144	730	2	12	12	NUM
ejpam-4144	730	3	]	]	X
ejpam-4144	730	4	g.	g.	PROPN
ejpam-4144	730	5	mahadevan	mahadevan	PROPN
ejpam-4144	730	6	and	and	CCONJ
ejpam-4144	730	7	v.	v.	ADP
ejpam-4144	730	8	vijayalakshmi	vijayalakshmi	NOUN
ejpam-4144	730	9	.	.	PUNCT
ejpam-4144	731	1	clone	clone	NOUN
ejpam-4144	731	2	hop	hop	NOUN
ejpam-4144	731	3	domination	domination	NOUN
ejpam-4144	731	4	number	number	NOUN
ejpam-4144	731	5	of	of	ADP
ejpam-4144	731	6	a	a	DET
ejpam-4144	731	7	graph	graph	NOUN
ejpam-4144	731	8	.	.	PUNCT
ejpam-4144	732	1	journal	journal	NOUN
ejpam-4144	732	2	of	of	ADP
ejpam-4144	732	3	discrete	discrete	ADJ
ejpam-4144	732	4	mathematical	mathematical	ADJ
ejpam-4144	732	5	sciences	science	NOUN
ejpam-4144	732	6	and	and	CCONJ
ejpam-4144	732	7	cryptography	cryptography	NOUN
ejpam-4144	732	8	,	,	PUNCT
ejpam-4144	732	9	22(5):719–729	22(5):719–729	PROPN
ejpam-4144	732	10	,	,	PUNCT
ejpam-4144	732	11	2019	2019	NUM
ejpam-4144	732	12	.	.	PUNCT
ejpam-4144	733	1	[	[	X
ejpam-4144	733	2	13	13	NUM
ejpam-4144	733	3	]	]	X
ejpam-4144	733	4	c.	c.	PROPN
ejpam-4144	733	5	natarajan	natarajan	PROPN
ejpam-4144	733	6	and	and	CCONJ
ejpam-4144	733	7	s.	s.	PROPN
ejpam-4144	733	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4144	733	9	.	.	PUNCT
ejpam-4144	734	1	hop	hop	PROPN
ejpam-4144	734	2	domination	domination	NOUN
ejpam-4144	734	3	in	in	ADP
ejpam-4144	734	4	graphs	graphs	PROPN
ejpam-4144	734	5	ii	ii	PROPN
ejpam-4144	734	6	.	.	PUNCT
ejpam-4144	734	7	versita	versita	PROPN
ejpam-4144	734	8	,	,	PUNCT
ejpam-4144	734	9	23(2):187	23(2):187	NUM
ejpam-4144	734	10	–	–	PUNCT
ejpam-4144	734	11	199	199	NUM
ejpam-4144	734	12	,	,	PUNCT
ejpam-4144	734	13	2015	2015	NUM
ejpam-4144	734	14	.	.	PUNCT
ejpam-4144	735	1	[	[	X
ejpam-4144	735	2	14	14	NUM
ejpam-4144	735	3	]	]	PUNCT
ejpam-4144	735	4	b.	b.	PROPN
ejpam-4144	735	5	omamalin	omamalin	PROPN
ejpam-4144	735	6	,	,	PUNCT
ejpam-4144	735	7	s.	s.	PROPN
ejpam-4144	735	8	jr	jr	PROPN
ejpam-4144	735	9	.	.	PROPN
ejpam-4144	735	10	canoy	canoy	PROPN
ejpam-4144	735	11	,	,	PUNCT
ejpam-4144	735	12	and	and	CCONJ
ejpam-4144	735	13	h.	h.	PROPN
ejpam-4144	735	14	rara	rara	PROPN
ejpam-4144	735	15	.	.	PUNCT
ejpam-4144	736	1	locating	locate	VERB
ejpam-4144	736	2	total	total	ADJ
ejpam-4144	736	3	dominating	dominating	NOUN
ejpam-4144	736	4	sets	set	NOUN
ejpam-4144	736	5	in	in	ADP
ejpam-4144	736	6	the	the	DET
ejpam-4144	736	7	join	join	NOUN
ejpam-4144	736	8	,	,	PUNCT
ejpam-4144	736	9	corona	corona	PROPN
ejpam-4144	736	10	,	,	PUNCT
ejpam-4144	736	11	and	and	CCONJ
ejpam-4144	736	12	composition	composition	NOUN
ejpam-4144	736	13	of	of	ADP
ejpam-4144	736	14	graphs	graph	NOUN
ejpam-4144	736	15	.	.	PUNCT
ejpam-4144	737	1	applied	apply	VERB
ejpam-4144	737	2	mathematical	mathematical	ADJ
ejpam-4144	737	3	sciences	science	NOUN
ejpam-4144	737	4	,	,	PUNCT
ejpam-4144	737	5	8(48):2363–2374	8(48):2363–2374	NUM
ejpam-4144	737	6	,	,	PUNCT
ejpam-4144	737	7	2014	2014	NUM
ejpam-4144	737	8	.	.	PUNCT
ejpam-4144	738	1	[	[	X
ejpam-4144	738	2	15	15	NUM
ejpam-4144	738	3	]	]	X
ejpam-4144	738	4	y.	y.	PROPN
ejpam-4144	738	5	pabilona	pabilona	PROPN
ejpam-4144	738	6	and	and	CCONJ
ejpam-4144	738	7	h.	h.	PROPN
ejpam-4144	738	8	rara	rara	PROPN
ejpam-4144	738	9	.	.	PUNCT
ejpam-4144	739	1	connected	connect	VERB
ejpam-4144	739	2	hop	hop	NOUN
ejpam-4144	739	3	domination	domination	NOUN
ejpam-4144	739	4	in	in	ADP
ejpam-4144	739	5	graphs	graph	NOUN
ejpam-4144	739	6	under	under	ADP
ejpam-4144	739	7	some	some	DET
ejpam-4144	739	8	binary	binary	ADJ
ejpam-4144	739	9	operations	operation	NOUN
ejpam-4144	739	10	.	.	PUNCT
ejpam-4144	740	1	asian	asian	ADJ
ejpam-4144	740	2	-	-	PUNCT
ejpam-4144	740	3	european	european	ADJ
ejpam-4144	740	4	journal	journal	NOUN
ejpam-4144	740	5	of	of	ADP
ejpam-4144	740	6	mathematics	mathematic	NOUN
ejpam-4144	740	7	,	,	PUNCT
ejpam-4144	740	8	11(5):1850075–1–1850075–11	11(5):1850075–1–1850075–11	NUM
ejpam-4144	740	9	,	,	PUNCT
ejpam-4144	740	10	2018	2018	NUM
ejpam-4144	740	11	.	.	PUNCT
ejpam-4144	741	1	[	[	X
ejpam-4144	741	2	16	16	NUM
ejpam-4144	741	3	]	]	X
ejpam-4144	741	4	g.	g.	PROPN
ejpam-4144	741	5	salasalan	salasalan	NOUN
ejpam-4144	741	6	and	and	CCONJ
ejpam-4144	741	7	s.	s.	PROPN
ejpam-4144	741	8	jr	jr	PROPN
ejpam-4144	741	9	.	.	PROPN
ejpam-4144	741	10	canoy	canoy	PROPN
ejpam-4144	741	11	.	.	PUNCT
ejpam-4144	742	1	global	global	ADJ
ejpam-4144	742	2	hop	hop	PROPN
ejpam-4144	742	3	domination	domination	PROPN
ejpam-4144	742	4	numbers	number	NOUN
ejpam-4144	742	5	of	of	ADP
ejpam-4144	742	6	graphs	graph	NOUN
ejpam-4144	742	7	.	.	PUNCT
ejpam-4144	743	1	european	european	ADJ
ejpam-4144	743	2	journal	journal	PROPN
ejpam-4144	743	3	of	of	ADP
ejpam-4144	743	4	pure	pure	ADJ
ejpam-4144	743	5	and	and	CCONJ
ejpam-4144	743	6	applied	applied	ADJ
ejpam-4144	743	7	mathematics	mathematic	NOUN
ejpam-4144	743	8	,	,	PUNCT
ejpam-4144	743	9	14(1):112–125	14(1):112–125	NUM
ejpam-4144	743	10	,	,	PUNCT
ejpam-4144	743	11	2021	2021	NUM
ejpam-4144	743	12	.	.	PUNCT