id	sid	tid	token	lemma	pos
ejpam-4946	1	1	european	european	PROPN
ejpam-4946	1	2	journal	journal	PROPN
ejpam-4946	1	3	of	of	ADP
ejpam-4946	1	4	pure	pure	ADJ
ejpam-4946	1	5	and	and	CCONJ
ejpam-4946	1	6	applied	apply	VERB
ejpam-4946	1	7	mathematics	mathematic	NOUN
ejpam-4946	1	8	vol	vol	NOUN
ejpam-4946	1	9	.	.	PROPN
ejpam-4946	2	1	17	17	NUM
ejpam-4946	2	2	,	,	PUNCT
ejpam-4946	2	3	no	no	INTJ
ejpam-4946	2	4	.	.	NOUN
ejpam-4946	2	5	1	1	NUM
ejpam-4946	2	6	,	,	PUNCT
ejpam-4946	2	7	2024	2024	NUM
ejpam-4946	2	8	,	,	PUNCT
ejpam-4946	2	9	124	124	NUM
ejpam-4946	2	10	-	-	SYM
ejpam-4946	2	11	134	134	NUM
ejpam-4946	2	12	issn	issn	PROPN
ejpam-4946	2	13	1307	1307	NUM
ejpam-4946	2	14	-	-	SYM
ejpam-4946	2	15	5543	5543	NUM
ejpam-4946	2	16	–	–	PUNCT
ejpam-4946	2	17	ejpam.com	ejpam.com	X
ejpam-4946	2	18	published	publish	VERB
ejpam-4946	2	19	by	by	ADP
ejpam-4946	2	20	new	new	PROPN
ejpam-4946	2	21	york	york	PROPN
ejpam-4946	2	22	business	business	PROPN
ejpam-4946	2	23	global	global	PROPN
ejpam-4946	2	24	j2	j2	PROPN
ejpam-4946	2	25	-	-	PUNCT
ejpam-4946	2	26	independence	independence	NOUN
ejpam-4946	2	27	parameters	parameter	NOUN
ejpam-4946	2	28	of	of	ADP
ejpam-4946	2	29	some	some	DET
ejpam-4946	2	30	graphs	graph	NOUN
ejpam-4946	2	31	javier	javier	PROPN
ejpam-4946	2	32	a.	a.	PROPN
ejpam-4946	2	33	hassan1	hassan1	PROPN
ejpam-4946	2	34	,	,	PUNCT
ejpam-4946	2	35	aziz	aziz	PROPN
ejpam-4946	2	36	b.	b.	PROPN
ejpam-4946	2	37	tapeing1,∗	tapeing1,∗	PROPN
ejpam-4946	2	38	,	,	PUNCT
ejpam-4946	2	39	hounam	hounam	PROPN
ejpam-4946	2	40	b.	b.	PROPN
ejpam-4946	2	41	copel1	copel1	PROPN
ejpam-4946	2	42	,	,	PUNCT
ejpam-4946	2	43	alcyn	alcyn	NOUN
ejpam-4946	2	44	bakkang2	bakkang2	NOUN
ejpam-4946	2	45	,	,	PUNCT
ejpam-4946	2	46	sharifa	sharifa	PROPN
ejpam-4946	2	47	dianne	dianne	PROPN
ejpam-4946	2	48	a.	a.	PROPN
ejpam-4946	2	49	aming3	aming3	PROPN
ejpam-4946	2	50	1mathematics	1mathematics	NUM
ejpam-4946	2	51	and	and	CCONJ
ejpam-4946	2	52	sciences	sciences	PROPN
ejpam-4946	2	53	department	department	PROPN
ejpam-4946	2	54	,	,	PUNCT
ejpam-4946	2	55	college	college	NOUN
ejpam-4946	2	56	of	of	ADP
ejpam-4946	2	57	arts	art	NOUN
ejpam-4946	2	58	and	and	CCONJ
ejpam-4946	2	59	sciences	science	NOUN
ejpam-4946	2	60	,	,	PUNCT
ejpam-4946	2	61	msu	msu	PROPN
ejpam-4946	2	62	tawi	tawi	PROPN
ejpam-4946	2	63	-	-	PUNCT
ejpam-4946	2	64	tawi	tawi	PROPN
ejpam-4946	2	65	college	college	PROPN
ejpam-4946	2	66	of	of	ADP
ejpam-4946	2	67	technology	technology	NOUN
ejpam-4946	2	68	and	and	CCONJ
ejpam-4946	2	69	oceanography	oceanography	NOUN
ejpam-4946	2	70	,	,	PUNCT
ejpam-4946	2	71	bongao	bongao	NOUN
ejpam-4946	2	72	,	,	PUNCT
ejpam-4946	2	73	tawi	tawi	NOUN
ejpam-4946	2	74	-	-	PUNCT
ejpam-4946	2	75	tawi	tawi	NOUN
ejpam-4946	2	76	,	,	PUNCT
ejpam-4946	2	77	philippines	philippine	NOUN
ejpam-4946	2	78	2	2	NUM
ejpam-4946	2	79	secondary	secondary	ADJ
ejpam-4946	2	80	education	education	NOUN
ejpam-4946	2	81	department	department	NOUN
ejpam-4946	2	82	,	,	PUNCT
ejpam-4946	2	83	college	college	NOUN
ejpam-4946	2	84	of	of	ADP
ejpam-4946	2	85	education	education	NOUN
ejpam-4946	2	86	,	,	PUNCT
ejpam-4946	2	87	msu	msu	PROPN
ejpam-4946	2	88	tawi	tawi	PROPN
ejpam-4946	2	89	-	-	PUNCT
ejpam-4946	2	90	tawi	tawi	PROPN
ejpam-4946	2	91	college	college	PROPN
ejpam-4946	2	92	of	of	ADP
ejpam-4946	2	93	technology	technology	NOUN
ejpam-4946	2	94	and	and	CCONJ
ejpam-4946	2	95	oceanography	oceanography	NOUN
ejpam-4946	2	96	,	,	PUNCT
ejpam-4946	2	97	bongao	bongao	NOUN
ejpam-4946	2	98	,	,	PUNCT
ejpam-4946	2	99	tawi	tawi	NOUN
ejpam-4946	2	100	-	-	PUNCT
ejpam-4946	2	101	tawi	tawi	NOUN
ejpam-4946	2	102	,	,	PUNCT
ejpam-4946	2	103	philippines	philippine	VERB
ejpam-4946	2	104	3	3	NUM
ejpam-4946	2	105	office	office	NOUN
ejpam-4946	2	106	of	of	ADP
ejpam-4946	2	107	the	the	DET
ejpam-4946	2	108	chancellor	chancellor	NOUN
ejpam-4946	2	109	,	,	PUNCT
ejpam-4946	2	110	msu	msu	PROPN
ejpam-4946	2	111	tawi	tawi	PROPN
ejpam-4946	2	112	-	-	PUNCT
ejpam-4946	2	113	tawi	tawi	PROPN
ejpam-4946	2	114	college	college	PROPN
ejpam-4946	2	115	of	of	ADP
ejpam-4946	2	116	technology	technology	NOUN
ejpam-4946	2	117	and	and	CCONJ
ejpam-4946	2	118	oceanography	oceanography	NOUN
ejpam-4946	2	119	,	,	PUNCT
ejpam-4946	2	120	bongao	bongao	NOUN
ejpam-4946	2	121	,	,	PUNCT
ejpam-4946	2	122	tawi	tawi	NOUN
ejpam-4946	2	123	-	-	PUNCT
ejpam-4946	2	124	tawi	tawi	NOUN
ejpam-4946	2	125	,	,	PUNCT
ejpam-4946	2	126	philippines	philippine	NOUN
ejpam-4946	2	127	abstract	abstract	ADJ
ejpam-4946	2	128	.	.	PUNCT
ejpam-4946	3	1	let	let	VERB
ejpam-4946	3	2	g	g	PRON
ejpam-4946	3	3	be	be	AUX
ejpam-4946	3	4	a	a	DET
ejpam-4946	3	5	graph	graph	NOUN
ejpam-4946	3	6	.	.	PUNCT
ejpam-4946	4	1	a	a	DET
ejpam-4946	4	2	subset	subset	NOUN
ejpam-4946	4	3	i	i	PRON
ejpam-4946	4	4	′	′	NUM
ejpam-4946	4	5	of	of	ADP
ejpam-4946	4	6	a	a	DET
ejpam-4946	4	7	vertex	vertex	NOUN
ejpam-4946	4	8	-	-	PUNCT
ejpam-4946	4	9	set	set	VERB
ejpam-4946	4	10	v	v	NOUN
ejpam-4946	4	11	(	(	PUNCT
ejpam-4946	4	12	g	g	NOUN
ejpam-4946	4	13	)	)	PUNCT
ejpam-4946	4	14	of	of	ADP
ejpam-4946	4	15	g	g	PROPN
ejpam-4946	4	16	is	be	AUX
ejpam-4946	4	17	called	call	VERB
ejpam-4946	4	18	a	a	DET
ejpam-4946	4	19	j2	j2	NOUN
ejpam-4946	4	20	-	-	PUNCT
ejpam-4946	4	21	independent	independent	NOUN
ejpam-4946	4	22	in	in	ADP
ejpam-4946	4	23	g	g	PROPN
ejpam-4946	4	24	if	if	SCONJ
ejpam-4946	4	25	for	for	ADP
ejpam-4946	4	26	every	every	DET
ejpam-4946	4	27	pair	pair	NOUN
ejpam-4946	4	28	of	of	ADP
ejpam-4946	4	29	distinct	distinct	ADJ
ejpam-4946	4	30	vertices	vertex	NOUN
ejpam-4946	4	31	a	a	DET
ejpam-4946	4	32	,	,	PUNCT
ejpam-4946	4	33	b	b	X
ejpam-4946	4	34	∈	∈	PROPN
ejpam-4946	4	35	i	i	PRON
ejpam-4946	4	36	′	′	VERB
ejpam-4946	4	37	,	,	PUNCT
ejpam-4946	4	38	dg(a	dg(a	X
ejpam-4946	4	39	,	,	PUNCT
ejpam-4946	4	40	b	b	X
ejpam-4946	4	41	)	)	PUNCT
ejpam-4946	4	42	̸=	̸=	PROPN
ejpam-4946	4	43	1	1	NUM
ejpam-4946	4	44	,	,	PUNCT
ejpam-4946	4	45	n2	n2	ADJ
ejpam-4946	4	46	g[a]\n2	g[a]\n2	NOUN
ejpam-4946	4	47	g[b	g[b	NOUN
ejpam-4946	4	48	]	]	PUNCT
ejpam-4946	4	49	̸=	̸=	PROPN
ejpam-4946	4	50	∅	∅	NOUN
ejpam-4946	4	51	and	and	CCONJ
ejpam-4946	4	52	n2	n2	ADJ
ejpam-4946	4	53	g[b]\n2	g[b]\n2	VERB
ejpam-4946	4	54	g[a	g[a	X
ejpam-4946	4	55	]	]	PUNCT
ejpam-4946	4	56	̸=	̸=	PROPN
ejpam-4946	4	57	∅.	∅.	ADP
ejpam-4946	4	58	the	the	DET
ejpam-4946	4	59	maximum	maximum	ADJ
ejpam-4946	4	60	cardinality	cardinality	NOUN
ejpam-4946	4	61	among	among	ADP
ejpam-4946	4	62	all	all	DET
ejpam-4946	4	63	j2	j2	PROPN
ejpam-4946	4	64	-	-	PUNCT
ejpam-4946	4	65	independent	independent	ADJ
ejpam-4946	4	66	sets	set	NOUN
ejpam-4946	4	67	in	in	ADP
ejpam-4946	4	68	g	g	NOUN
ejpam-4946	4	69	,	,	PUNCT
ejpam-4946	4	70	denoted	denote	VERB
ejpam-4946	4	71	by	by	ADP
ejpam-4946	4	72	αj2(g	αj2(g	PROPN
ejpam-4946	4	73	)	)	PUNCT
ejpam-4946	4	74	,	,	PUNCT
ejpam-4946	4	75	is	be	AUX
ejpam-4946	4	76	called	call	VERB
ejpam-4946	4	77	the	the	DET
ejpam-4946	4	78	j2	j2	PROPN
ejpam-4946	4	79	-	-	PUNCT
ejpam-4946	4	80	independence	independence	NOUN
ejpam-4946	4	81	number	number	NOUN
ejpam-4946	4	82	of	of	ADP
ejpam-4946	4	83	g.	g.	PROPN
ejpam-4946	4	84	any	any	DET
ejpam-4946	4	85	j2	j2	PROPN
ejpam-4946	4	86	-	-	PUNCT
ejpam-4946	4	87	independent	independent	ADJ
ejpam-4946	4	88	set	set	NOUN
ejpam-4946	5	1	i	i	PRON
ejpam-4946	5	2	′	′	VERB
ejpam-4946	6	1	satisfying	satisfy	VERB
ejpam-4946	6	2	|i	|i	NOUN
ejpam-4946	6	3	′|	′|	NUM
ejpam-4946	6	4	=	=	SYM
ejpam-4946	6	5	αj2(g	αj2(g	VERB
ejpam-4946	6	6	)	)	PUNCT
ejpam-4946	6	7	is	be	AUX
ejpam-4946	6	8	called	call	VERB
ejpam-4946	6	9	the	the	DET
ejpam-4946	6	10	maximum	maximum	ADJ
ejpam-4946	6	11	j2	j2	NOUN
ejpam-4946	6	12	-	-	PUNCT
ejpam-4946	6	13	independent	independent	ADJ
ejpam-4946	6	14	set	set	NOUN
ejpam-4946	6	15	of	of	ADP
ejpam-4946	6	16	g	g	NOUN
ejpam-4946	6	17	or	or	CCONJ
ejpam-4946	6	18	an	an	DET
ejpam-4946	6	19	αj2	αj2	NOUN
ejpam-4946	6	20	-	-	PUNCT
ejpam-4946	6	21	set	set	NOUN
ejpam-4946	6	22	of	of	ADP
ejpam-4946	6	23	g.	g.	PROPN
ejpam-4946	6	24	in	in	ADP
ejpam-4946	6	25	this	this	DET
ejpam-4946	6	26	paper	paper	NOUN
ejpam-4946	6	27	,	,	PUNCT
ejpam-4946	6	28	we	we	PRON
ejpam-4946	6	29	establish	establish	VERB
ejpam-4946	6	30	some	some	DET
ejpam-4946	6	31	bounds	bound	NOUN
ejpam-4946	6	32	of	of	ADP
ejpam-4946	6	33	this	this	DET
ejpam-4946	6	34	parameter	parameter	NOUN
ejpam-4946	6	35	on	on	ADP
ejpam-4946	6	36	a	a	DET
ejpam-4946	6	37	generalized	generalized	ADJ
ejpam-4946	6	38	graph	graph	NOUN
ejpam-4946	6	39	,	,	PUNCT
ejpam-4946	6	40	join	join	VERB
ejpam-4946	6	41	and	and	CCONJ
ejpam-4946	6	42	corona	corona	NOUN
ejpam-4946	6	43	of	of	ADP
ejpam-4946	6	44	two	two	NUM
ejpam-4946	6	45	graphs	graph	NOUN
ejpam-4946	6	46	.	.	PUNCT
ejpam-4946	7	1	we	we	PRON
ejpam-4946	7	2	characterize	characterize	VERB
ejpam-4946	7	3	j2independent	j2independent	NOUN
ejpam-4946	7	4	sets	set	NOUN
ejpam-4946	7	5	in	in	ADP
ejpam-4946	7	6	some	some	DET
ejpam-4946	7	7	families	family	NOUN
ejpam-4946	7	8	of	of	ADP
ejpam-4946	7	9	graphs	graph	NOUN
ejpam-4946	7	10	,	,	PUNCT
ejpam-4946	7	11	and	and	CCONJ
ejpam-4946	7	12	we	we	PRON
ejpam-4946	7	13	use	use	VERB
ejpam-4946	7	14	these	these	DET
ejpam-4946	7	15	results	result	NOUN
ejpam-4946	7	16	to	to	PART
ejpam-4946	7	17	derive	derive	VERB
ejpam-4946	7	18	the	the	DET
ejpam-4946	7	19	exact	exact	ADJ
ejpam-4946	7	20	values	value	NOUN
ejpam-4946	7	21	of	of	ADP
ejpam-4946	7	22	parameters	parameter	NOUN
ejpam-4946	7	23	of	of	ADP
ejpam-4946	7	24	these	these	DET
ejpam-4946	7	25	graphs	graph	NOUN
ejpam-4946	7	26	.	.	PUNCT
ejpam-4946	8	1	moreover	moreover	ADV
ejpam-4946	8	2	,	,	PUNCT
ejpam-4946	8	3	we	we	PRON
ejpam-4946	8	4	investigate	investigate	VERB
ejpam-4946	8	5	the	the	DET
ejpam-4946	8	6	connections	connection	NOUN
ejpam-4946	8	7	of	of	ADP
ejpam-4946	8	8	this	this	DET
ejpam-4946	8	9	new	new	ADJ
ejpam-4946	8	10	parameter	parameter	NOUN
ejpam-4946	8	11	with	with	ADP
ejpam-4946	8	12	other	other	ADJ
ejpam-4946	8	13	variants	variant	NOUN
ejpam-4946	8	14	of	of	ADP
ejpam-4946	8	15	independence	independence	NOUN
ejpam-4946	8	16	parameters	parameter	NOUN
ejpam-4946	8	17	.	.	PUNCT
ejpam-4946	9	1	in	in	ADP
ejpam-4946	9	2	fact	fact	NOUN
ejpam-4946	9	3	,	,	PUNCT
ejpam-4946	9	4	we	we	PRON
ejpam-4946	9	5	show	show	VERB
ejpam-4946	9	6	that	that	SCONJ
ejpam-4946	9	7	the	the	DET
ejpam-4946	9	8	j2	j2	PROPN
ejpam-4946	9	9	-	-	PUNCT
ejpam-4946	9	10	independence	independence	NOUN
ejpam-4946	9	11	number	number	NOUN
ejpam-4946	9	12	of	of	ADP
ejpam-4946	9	13	a	a	DET
ejpam-4946	9	14	graph	graph	NOUN
ejpam-4946	9	15	is	be	AUX
ejpam-4946	9	16	always	always	ADV
ejpam-4946	9	17	less	less	ADJ
ejpam-4946	9	18	than	than	ADP
ejpam-4946	9	19	or	or	CCONJ
ejpam-4946	9	20	equal	equal	ADJ
ejpam-4946	9	21	to	to	ADP
ejpam-4946	9	22	the	the	DET
ejpam-4946	9	23	standard	standard	ADJ
ejpam-4946	9	24	independence	independence	NOUN
ejpam-4946	9	25	number	number	NOUN
ejpam-4946	9	26	.	.	PUNCT
ejpam-4946	10	1	2020	2020	NUM
ejpam-4946	10	2	mathematics	mathematic	NOUN
ejpam-4946	10	3	subject	subject	NOUN
ejpam-4946	10	4	classifications	classification	NOUN
ejpam-4946	10	5	:	:	PUNCT
ejpam-4946	10	6	05c69	05c69	X
ejpam-4946	10	7	key	key	ADJ
ejpam-4946	10	8	words	word	NOUN
ejpam-4946	10	9	and	and	CCONJ
ejpam-4946	10	10	phrases	phrase	NOUN
ejpam-4946	10	11	:	:	PUNCT
ejpam-4946	10	12	independent	independent	ADJ
ejpam-4946	10	13	set	set	NOUN
ejpam-4946	10	14	,	,	PUNCT
ejpam-4946	10	15	j2	j2	PROPN
ejpam-4946	10	16	-	-	PUNCT
ejpam-4946	10	17	independent	independent	ADJ
ejpam-4946	10	18	set	set	NOUN
ejpam-4946	10	19	,	,	PUNCT
ejpam-4946	10	20	j2	j2	PROPN
ejpam-4946	10	21	-	-	PUNCT
ejpam-4946	10	22	independence	independence	NOUN
ejpam-4946	10	23	number	number	NOUN
ejpam-4946	10	24	1	1	NUM
ejpam-4946	10	25	.	.	PUNCT
ejpam-4946	10	26	introduction	introduction	NOUN
ejpam-4946	10	27	the	the	DET
ejpam-4946	10	28	independent	independent	ADJ
ejpam-4946	10	29	set	set	NOUN
ejpam-4946	10	30	in	in	ADP
ejpam-4946	10	31	graph	graph	NOUN
ejpam-4946	10	32	has	have	AUX
ejpam-4946	10	33	been	be	AUX
ejpam-4946	10	34	studied	study	VERB
ejpam-4946	10	35	excessively	excessively	ADV
ejpam-4946	10	36	and	and	CCONJ
ejpam-4946	10	37	one	one	NUM
ejpam-4946	10	38	of	of	ADP
ejpam-4946	10	39	the	the	DET
ejpam-4946	10	40	topics	topic	NOUN
ejpam-4946	10	41	in	in	ADP
ejpam-4946	10	42	graph	graph	NOUN
ejpam-4946	10	43	theory	theory	NOUN
ejpam-4946	10	44	which	which	PRON
ejpam-4946	10	45	has	have	AUX
ejpam-4946	10	46	been	be	AUX
ejpam-4946	10	47	growing	grow	VERB
ejpam-4946	10	48	rapidly	rapidly	ADV
ejpam-4946	10	49	.	.	PUNCT
ejpam-4946	11	1	moreover	moreover	ADV
ejpam-4946	11	2	,	,	PUNCT
ejpam-4946	11	3	the	the	DET
ejpam-4946	11	4	problem	problem	NOUN
ejpam-4946	11	5	of	of	ADP
ejpam-4946	11	6	finding	find	VERB
ejpam-4946	11	7	the	the	DET
ejpam-4946	11	8	maximum	maximum	ADJ
ejpam-4946	11	9	independent	independent	ADJ
ejpam-4946	11	10	set	set	NOUN
ejpam-4946	11	11	in	in	ADP
ejpam-4946	11	12	graphs	graph	NOUN
ejpam-4946	11	13	is	be	AUX
ejpam-4946	11	14	a	a	DET
ejpam-4946	11	15	fundamental	fundamental	ADJ
ejpam-4946	11	16	problem	problem	NOUN
ejpam-4946	11	17	not	not	PART
ejpam-4946	11	18	just	just	ADV
ejpam-4946	11	19	in	in	ADP
ejpam-4946	11	20	graph	graph	NOUN
ejpam-4946	11	21	theory	theory	NOUN
ejpam-4946	11	22	but	but	CCONJ
ejpam-4946	11	23	also	also	ADV
ejpam-4946	11	24	in	in	ADP
ejpam-4946	11	25	theoretical	theoretical	ADJ
ejpam-4946	11	26	computer	computer	NOUN
ejpam-4946	11	27	science	science	NOUN
ejpam-4946	11	28	.	.	PUNCT
ejpam-4946	12	1	a	a	DET
ejpam-4946	12	2	subset	subset	NOUN
ejpam-4946	12	3	v	v	ADP
ejpam-4946	12	4	′	′	NUM
ejpam-4946	12	5	of	of	ADP
ejpam-4946	12	6	the	the	DET
ejpam-4946	12	7	vertex	vertex	NOUN
ejpam-4946	12	8	-	-	PUNCT
ejpam-4946	12	9	set	set	VERB
ejpam-4946	12	10	v	v	NOUN
ejpam-4946	12	11	(	(	PUNCT
ejpam-4946	12	12	g	g	NOUN
ejpam-4946	12	13	)	)	PUNCT
ejpam-4946	12	14	of	of	ADP
ejpam-4946	12	15	a	a	DET
ejpam-4946	12	16	graph	graph	NOUN
ejpam-4946	12	17	g	g	NOUN
ejpam-4946	12	18	is	be	AUX
ejpam-4946	12	19	said	say	VERB
ejpam-4946	12	20	to	to	PART
ejpam-4946	12	21	be	be	AUX
ejpam-4946	12	22	an	an	DET
ejpam-4946	12	23	independent	independent	ADJ
ejpam-4946	12	24	if	if	SCONJ
ejpam-4946	12	25	no	no	DET
ejpam-4946	12	26	two	two	NUM
ejpam-4946	12	27	vertices	vertex	NOUN
ejpam-4946	12	28	in	in	ADP
ejpam-4946	12	29	v	v	NOUN
ejpam-4946	12	30	′	′	NOUN
ejpam-4946	12	31	are	be	AUX
ejpam-4946	12	32	adjacent	adjacent	ADJ
ejpam-4946	12	33	.	.	PUNCT
ejpam-4946	13	1	an	an	DET
ejpam-4946	13	2	independent	independent	ADJ
ejpam-4946	13	3	set	set	NOUN
ejpam-4946	13	4	is	be	AUX
ejpam-4946	13	5	∗corresponding	∗corresponde	VERB
ejpam-4946	13	6	author	author	NOUN
ejpam-4946	13	7	.	.	PUNCT
ejpam-4946	14	1	doi	doi	NOUN
ejpam-4946	14	2	:	:	PUNCT
ejpam-4946	14	3	https://doi.org/10.29020/nybg.ejpam.v17i1.4946	https://doi.org/10.29020/nybg.ejpam.v17i1.4946	NOUN
ejpam-4946	14	4	email	email	NOUN
ejpam-4946	14	5	addresses	address	NOUN
ejpam-4946	14	6	:	:	PUNCT
ejpam-4946	14	7	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-4946	14	8	(	(	PUNCT
ejpam-4946	14	9	j.	j.	PROPN
ejpam-4946	14	10	hassan	hassan	PROPN
ejpam-4946	14	11	)	)	PUNCT
ejpam-4946	15	1	aziztapeing@msutawi-tawi.edu.ph	aziztapeing@msutawi-tawi.edu.ph	PROPN
ejpam-4946	15	2	(	(	PUNCT
ejpam-4946	15	3	a.	a.	NOUN
ejpam-4946	15	4	tapeing	tapeing	NOUN
ejpam-4946	15	5	)	)	PUNCT
ejpam-4946	15	6	,	,	PUNCT
ejpam-4946	15	7	hounamcopel@msutawi-tawi.edu.ph	hounamcopel@msutawi-tawi.edu.ph	PROPN
ejpam-4946	15	8	(	(	PUNCT
ejpam-4946	15	9	h.	h.	PROPN
ejpam-4946	15	10	copel	copel	PROPN
ejpam-4946	15	11	)	)	PUNCT
ejpam-4946	15	12	alcynbakkang@msutawi-tawi.edu.ph	alcynbakkang@msutawi-tawi.edu.ph	PROPN
ejpam-4946	15	13	(	(	PUNCT
ejpam-4946	15	14	a.	a.	PROPN
ejpam-4946	15	15	bakkang	bakkang	PROPN
ejpam-4946	15	16	)	)	PUNCT
ejpam-4946	15	17	,	,	PUNCT
ejpam-4946	15	18	sharifadianneaming@msutawi-tawi.edu.ph	sharifadianneaming@msutawi-tawi.edu.ph	PROPN
ejpam-4946	15	19	(	(	PUNCT
ejpam-4946	15	20	s.	s.	PROPN
ejpam-4946	15	21	aming	aming	PROPN
ejpam-4946	15	22	)	)	PUNCT
ejpam-4946	15	23	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4946	15	24	124	124	NUM
ejpam-4946	15	25	©	©	ADP
ejpam-4946	15	26	2024	2024	NUM
ejpam-4946	15	27	ejpam	ejpam	NOUN
ejpam-4946	15	28	all	all	DET
ejpam-4946	15	29	rights	right	NOUN
ejpam-4946	15	30	reserved	reserve	VERB
ejpam-4946	15	31	.	.	PUNCT
ejpam-4946	16	1	a.	a.	NOUN
ejpam-4946	16	2	tapeing	tape	VERB
ejpam-4946	16	3	et	et	PROPN
ejpam-4946	16	4	al	al	PROPN
ejpam-4946	16	5	.	.	PUNCT
ejpam-4946	16	6	/	/	SYM
ejpam-4946	16	7	eur	eur	PROPN
ejpam-4946	16	8	.	.	PUNCT
ejpam-4946	17	1	j.	j.	PROPN
ejpam-4946	17	2	pure	pure	PROPN
ejpam-4946	17	3	appl	appl	PROPN
ejpam-4946	17	4	.	.	PROPN
ejpam-4946	17	5	math	math	PROPN
ejpam-4946	17	6	,	,	PUNCT
ejpam-4946	17	7	17	17	NUM
ejpam-4946	17	8	(	(	PUNCT
ejpam-4946	17	9	1	1	NUM
ejpam-4946	17	10	)	)	PUNCT
ejpam-4946	17	11	(	(	PUNCT
ejpam-4946	17	12	2024	2024	NUM
ejpam-4946	17	13	)	)	PUNCT
ejpam-4946	17	14	,	,	PUNCT
ejpam-4946	17	15	124	124	NUM
ejpam-4946	17	16	-	-	SYM
ejpam-4946	17	17	134	134	NUM
ejpam-4946	17	18	125	125	NUM
ejpam-4946	17	19	called	call	VERB
ejpam-4946	17	20	maximum	maximum	NOUN
ejpam-4946	17	21	if	if	SCONJ
ejpam-4946	17	22	it	it	PRON
ejpam-4946	17	23	is	be	AUX
ejpam-4946	17	24	of	of	ADP
ejpam-4946	17	25	largest	large	ADJ
ejpam-4946	17	26	cardinality	cardinality	NOUN
ejpam-4946	17	27	,	,	PUNCT
ejpam-4946	17	28	that	that	ADV
ejpam-4946	17	29	is	is	ADV
ejpam-4946	17	30	,	,	PUNCT
ejpam-4946	17	31	if	if	SCONJ
ejpam-4946	17	32	v	v	ADP
ejpam-4946	17	33	′	′	NOUN
ejpam-4946	17	34	∪{v	∪{v	NOUN
ejpam-4946	17	35	}	}	PUNCT
ejpam-4946	17	36	is	be	AUX
ejpam-4946	17	37	not	not	PART
ejpam-4946	17	38	an	an	DET
ejpam-4946	17	39	independent	independent	ADJ
ejpam-4946	17	40	set	set	NOUN
ejpam-4946	17	41	for	for	ADP
ejpam-4946	17	42	any	any	DET
ejpam-4946	17	43	v	v	NUM
ejpam-4946	17	44	∈	∈	NOUN
ejpam-4946	17	45	v	v	NOUN
ejpam-4946	17	46	(	(	PUNCT
ejpam-4946	17	47	g)\v	g)\v	NOUN
ejpam-4946	17	48	′	′	NOUN
ejpam-4946	17	49	,	,	PUNCT
ejpam-4946	17	50	and	and	CCONJ
ejpam-4946	17	51	it	it	PRON
ejpam-4946	17	52	is	be	AUX
ejpam-4946	17	53	denoted	denote	VERB
ejpam-4946	17	54	by	by	ADP
ejpam-4946	17	55	i(g	i(g	NOUN
ejpam-4946	17	56	)	)	PUNCT
ejpam-4946	17	57	to	to	PART
ejpam-4946	17	58	be	be	AUX
ejpam-4946	17	59	the	the	DET
ejpam-4946	17	60	number	number	NOUN
ejpam-4946	17	61	of	of	ADP
ejpam-4946	17	62	maximal	maximal	ADJ
ejpam-4946	17	63	independent	independent	ADJ
ejpam-4946	17	64	sets	set	NOUN
ejpam-4946	17	65	of	of	ADP
ejpam-4946	17	66	g.	g.	PROPN
ejpam-4946	17	67	in	in	ADP
ejpam-4946	17	68	1992	1992	NUM
ejpam-4946	17	69	,	,	PUNCT
ejpam-4946	17	70	jiuqiang	jiuqiang	PROPN
ejpam-4946	17	71	liu[8	liu[8	PROPN
ejpam-4946	17	72	]	]	PUNCT
ejpam-4946	17	73	developed	develop	VERB
ejpam-4946	17	74	new	new	ADJ
ejpam-4946	17	75	properties	property	NOUN
ejpam-4946	17	76	for	for	ADP
ejpam-4946	17	77	the	the	DET
ejpam-4946	17	78	number	number	NOUN
ejpam-4946	17	79	of	of	ADP
ejpam-4946	17	80	maximal	maximal	ADJ
ejpam-4946	17	81	independent	independent	ADJ
ejpam-4946	17	82	sets	set	NOUN
ejpam-4946	17	83	i(g	i(g	NOUN
ejpam-4946	17	84	)	)	PUNCT
ejpam-4946	17	85	and	and	CCONJ
ejpam-4946	17	86	the	the	DET
ejpam-4946	17	87	number	number	NOUN
ejpam-4946	17	88	of	of	ADP
ejpam-4946	17	89	maximum	maximum	ADJ
ejpam-4946	17	90	independent	independent	ADJ
ejpam-4946	17	91	sets	set	NOUN
ejpam-4946	17	92	im(g	im(g	PRON
ejpam-4946	17	93	)	)	PUNCT
ejpam-4946	17	94	,	,	PUNCT
ejpam-4946	17	95	as	as	ADV
ejpam-4946	17	96	well	well	ADV
ejpam-4946	17	97	as	as	ADP
ejpam-4946	17	98	determine	determine	VERB
ejpam-4946	17	99	the	the	DET
ejpam-4946	17	100	largest	large	ADJ
ejpam-4946	17	101	number	number	NOUN
ejpam-4946	17	102	of	of	ADP
ejpam-4946	17	103	maximal	maximal	ADJ
ejpam-4946	17	104	and	and	CCONJ
ejpam-4946	17	105	maximum	maximum	ADJ
ejpam-4946	17	106	independent	independent	ADJ
ejpam-4946	17	107	sets	set	NOUN
ejpam-4946	17	108	possible	possible	ADJ
ejpam-4946	17	109	in	in	ADP
ejpam-4946	17	110	a	a	DET
ejpam-4946	17	111	k	k	ADV
ejpam-4946	17	112	-	-	ADJ
ejpam-4946	17	113	connected	connected	ADJ
ejpam-4946	17	114	graph	graph	NOUN
ejpam-4946	17	115	of	of	ADP
ejpam-4946	17	116	order	order	NOUN
ejpam-4946	17	117	n(with	n(with	NOUN
ejpam-4946	17	118	n	n	ADV
ejpam-4946	17	119	large	large	ADJ
ejpam-4946	17	120	)	)	PUNCT
ejpam-4946	17	121	and	and	CCONJ
ejpam-4946	17	122	characterize	characterize	VERB
ejpam-4946	17	123	the	the	DET
ejpam-4946	17	124	respective	respective	ADJ
ejpam-4946	17	125	extremal	extremal	ADJ
ejpam-4946	17	126	graphs	graph	NOUN
ejpam-4946	17	127	.	.	PUNCT
ejpam-4946	18	1	in	in	ADP
ejpam-4946	18	2	[	[	X
ejpam-4946	18	3	1	1	NUM
ejpam-4946	18	4	]	]	PUNCT
ejpam-4946	18	5	,	,	PUNCT
ejpam-4946	18	6	established	establish	VERB
ejpam-4946	18	7	an	an	DET
ejpam-4946	18	8	upper	upper	ADJ
ejpam-4946	18	9	bound	bind	VERB
ejpam-4946	18	10	as	as	ADP
ejpam-4946	18	11	a	a	DET
ejpam-4946	18	12	tool	tool	NOUN
ejpam-4946	18	13	to	to	PART
ejpam-4946	18	14	prove	prove	VERB
ejpam-4946	18	15	that	that	SCONJ
ejpam-4946	18	16	the	the	DET
ejpam-4946	18	17	disjoint	disjoint	PROPN
ejpam-4946	18	18	union	union	NOUN
ejpam-4946	18	19	of	of	ADP
ejpam-4946	18	20	complete	complete	ADJ
ejpam-4946	18	21	bipartite	bipartite	PROPN
ejpam-4946	18	22	graphs	graph	NOUN
ejpam-4946	18	23	kd	kd	PROPN
ejpam-4946	18	24	,	,	PUNCT
ejpam-4946	18	25	d	d	PROPN
ejpam-4946	18	26	maximises	maximise	VERB
ejpam-4946	18	27	the	the	DET
ejpam-4946	18	28	number	number	NOUN
ejpam-4946	18	29	of	of	ADP
ejpam-4946	18	30	independent	independent	ADJ
ejpam-4946	18	31	sets	set	NOUN
ejpam-4946	18	32	of	of	ADP
ejpam-4946	18	33	a	a	DET
ejpam-4946	18	34	d	d	ADJ
ejpam-4946	18	35	-	-	ADJ
ejpam-4946	18	36	regular	regular	ADJ
ejpam-4946	18	37	graph	graph	NOUN
ejpam-4946	18	38	.	.	PUNCT
ejpam-4946	19	1	some	some	DET
ejpam-4946	19	2	variants	variant	NOUN
ejpam-4946	19	3	of	of	ADP
ejpam-4946	19	4	representing	represent	VERB
ejpam-4946	19	5	the	the	DET
ejpam-4946	19	6	independent	independent	ADJ
ejpam-4946	19	7	sets	set	NOUN
ejpam-4946	19	8	in	in	ADP
ejpam-4946	19	9	graphs	graph	NOUN
ejpam-4946	19	10	were	be	AUX
ejpam-4946	19	11	studied	study	VERB
ejpam-4946	19	12	by	by	ADP
ejpam-4946	19	13	some	some	DET
ejpam-4946	19	14	researchers	researcher	NOUN
ejpam-4946	19	15	(	(	PUNCT
ejpam-4946	19	16	see[1–4	see[1–4	NOUN
ejpam-4946	19	17	,	,	PUNCT
ejpam-4946	19	18	6	6	NUM
ejpam-4946	19	19	,	,	PUNCT
ejpam-4946	19	20	7	7	NUM
ejpam-4946	19	21	,	,	PUNCT
ejpam-4946	19	22	9–11	9–11	NOUN
ejpam-4946	19	23	]	]	PUNCT
ejpam-4946	19	24	)	)	PUNCT
ejpam-4946	19	25	.	.	PUNCT
ejpam-4946	20	1	in	in	ADP
ejpam-4946	20	2	2022	2022	NUM
ejpam-4946	20	3	,	,	PUNCT
ejpam-4946	20	4	j.	j.	PROPN
ejpam-4946	20	5	hassan	hassan	PROPN
ejpam-4946	20	6	et	et	PROPN
ejpam-4946	20	7	al	al	PROPN
ejpam-4946	20	8	.	.	PUNCT
ejpam-4946	21	1	[	[	X
ejpam-4946	21	2	6	6	NUM
ejpam-4946	21	3	]	]	PUNCT
ejpam-4946	21	4	introduced	introduce	VERB
ejpam-4946	21	5	the	the	DET
ejpam-4946	21	6	hop	hop	NOUN
ejpam-4946	21	7	independent	independent	ADJ
ejpam-4946	21	8	sets	set	NOUN
ejpam-4946	21	9	in	in	ADP
ejpam-4946	21	10	graphs	graph	NOUN
ejpam-4946	21	11	.	.	PUNCT
ejpam-4946	22	1	a	a	DET
ejpam-4946	22	2	subset	subset	NOUN
ejpam-4946	22	3	s	s	X
ejpam-4946	22	4	of	of	ADP
ejpam-4946	22	5	v	v	NOUN
ejpam-4946	22	6	(	(	PUNCT
ejpam-4946	22	7	g	g	NOUN
ejpam-4946	22	8	)	)	PUNCT
ejpam-4946	22	9	is	be	AUX
ejpam-4946	22	10	called	call	VERB
ejpam-4946	22	11	a	a	DET
ejpam-4946	22	12	hop	hop	NOUN
ejpam-4946	22	13	independent	independent	ADJ
ejpam-4946	22	14	if	if	SCONJ
ejpam-4946	22	15	for	for	ADP
ejpam-4946	22	16	every	every	DET
ejpam-4946	22	17	pair	pair	NOUN
ejpam-4946	22	18	of	of	ADP
ejpam-4946	22	19	distinct	distinct	ADJ
ejpam-4946	22	20	vertices	vertex	NOUN
ejpam-4946	22	21	x	x	X
ejpam-4946	22	22	,	,	PUNCT
ejpam-4946	22	23	y	y	PROPN
ejpam-4946	22	24	∈	∈	PROPN
ejpam-4946	22	25	s	s	PROPN
ejpam-4946	22	26	,	,	PUNCT
ejpam-4946	22	27	dg(x	dg(x	NUM
ejpam-4946	22	28	,	,	PUNCT
ejpam-4946	22	29	y	y	NOUN
ejpam-4946	22	30	)	)	PUNCT
ejpam-4946	22	31	̸=	̸=	PROPN
ejpam-4946	22	32	2	2	NUM
ejpam-4946	22	33	.	.	PUNCT
ejpam-4946	23	1	the	the	DET
ejpam-4946	23	2	maximum	maximum	ADJ
ejpam-4946	23	3	cardinality	cardinality	NOUN
ejpam-4946	23	4	of	of	ADP
ejpam-4946	23	5	a	a	DET
ejpam-4946	23	6	hop	hop	NOUN
ejpam-4946	23	7	independent	independent	ADJ
ejpam-4946	23	8	set	set	NOUN
ejpam-4946	23	9	in	in	ADP
ejpam-4946	23	10	g	g	NOUN
ejpam-4946	23	11	,	,	PUNCT
ejpam-4946	23	12	denoted	denote	VERB
ejpam-4946	23	13	by	by	ADP
ejpam-4946	23	14	αh(g	αh(g	NOUN
ejpam-4946	23	15	)	)	PUNCT
ejpam-4946	23	16	,	,	PUNCT
ejpam-4946	23	17	is	be	AUX
ejpam-4946	23	18	called	call	VERB
ejpam-4946	23	19	the	the	DET
ejpam-4946	23	20	hop	hop	NOUN
ejpam-4946	23	21	independence	independence	NOUN
ejpam-4946	23	22	number	number	NOUN
ejpam-4946	23	23	of	of	ADP
ejpam-4946	23	24	g.	g.	PROPN
ejpam-4946	23	25	any	any	DET
ejpam-4946	23	26	hop	hop	NOUN
ejpam-4946	23	27	independent	independent	ADJ
ejpam-4946	23	28	set	set	NOUN
ejpam-4946	23	29	s	s	PROPN
ejpam-4946	23	30	with	with	ADP
ejpam-4946	23	31	cardinality	cardinality	NOUN
ejpam-4946	23	32	equal	equal	ADJ
ejpam-4946	23	33	to	to	ADP
ejpam-4946	23	34	αh(g	αh(g	NOUN
ejpam-4946	23	35	)	)	PUNCT
ejpam-4946	23	36	is	be	AUX
ejpam-4946	23	37	called	call	VERB
ejpam-4946	23	38	an	an	DET
ejpam-4946	23	39	αh	αh	NOUN
ejpam-4946	23	40	-	-	PUNCT
ejpam-4946	23	41	set	set	NOUN
ejpam-4946	23	42	of	of	ADP
ejpam-4946	23	43	g.	g.	PROPN
ejpam-4946	23	44	they	they	PRON
ejpam-4946	23	45	have	have	AUX
ejpam-4946	23	46	shown	show	VERB
ejpam-4946	23	47	that	that	SCONJ
ejpam-4946	23	48	every	every	DET
ejpam-4946	23	49	maximum	maximum	ADJ
ejpam-4946	23	50	hop	hop	NOUN
ejpam-4946	23	51	independent	independent	ADJ
ejpam-4946	23	52	set	set	NOUN
ejpam-4946	23	53	in	in	ADP
ejpam-4946	23	54	a	a	DET
ejpam-4946	23	55	graph	graph	NOUN
ejpam-4946	23	56	is	be	AUX
ejpam-4946	23	57	a	a	DET
ejpam-4946	23	58	hop	hop	NOUN
ejpam-4946	23	59	dominating	dominating	NOUN
ejpam-4946	23	60	set	set	NOUN
ejpam-4946	23	61	,	,	PUNCT
ejpam-4946	23	62	that	that	ADV
ejpam-4946	23	63	is	is	ADV
ejpam-4946	23	64	,	,	PUNCT
ejpam-4946	23	65	the	the	DET
ejpam-4946	23	66	hop	hop	NOUN
ejpam-4946	23	67	independence	independence	NOUN
ejpam-4946	23	68	number	number	NOUN
ejpam-4946	23	69	of	of	ADP
ejpam-4946	23	70	a	a	DET
ejpam-4946	23	71	graph	graph	NOUN
ejpam-4946	23	72	g	g	NOUN
ejpam-4946	23	73	is	be	AUX
ejpam-4946	23	74	always	always	ADV
ejpam-4946	23	75	greater	great	ADJ
ejpam-4946	23	76	than	than	ADP
ejpam-4946	23	77	or	or	CCONJ
ejpam-4946	23	78	equal	equal	ADJ
ejpam-4946	23	79	to	to	ADP
ejpam-4946	23	80	the	the	DET
ejpam-4946	23	81	hop	hop	NOUN
ejpam-4946	23	82	domination	domination	NOUN
ejpam-4946	23	83	number	number	NOUN
ejpam-4946	23	84	of	of	ADP
ejpam-4946	23	85	a	a	DET
ejpam-4946	23	86	graph	graph	NOUN
ejpam-4946	23	87	.	.	PUNCT
ejpam-4946	24	1	they	they	PRON
ejpam-4946	24	2	have	have	AUX
ejpam-4946	24	3	characterized	characterize	VERB
ejpam-4946	24	4	this	this	DET
ejpam-4946	24	5	type	type	NOUN
ejpam-4946	24	6	of	of	ADP
ejpam-4946	24	7	set	set	NOUN
ejpam-4946	24	8	in	in	ADP
ejpam-4946	24	9	graphs	graph	NOUN
ejpam-4946	24	10	under	under	ADP
ejpam-4946	24	11	some	some	DET
ejpam-4946	24	12	binary	binary	ADJ
ejpam-4946	24	13	operations	operation	NOUN
ejpam-4946	24	14	such	such	ADJ
ejpam-4946	24	15	join	join	NOUN
ejpam-4946	24	16	,	,	PUNCT
ejpam-4946	24	17	corona	corona	PROPN
ejpam-4946	24	18	,	,	PUNCT
ejpam-4946	24	19	lexicographic	lexicographic	ADJ
ejpam-4946	24	20	product	product	NOUN
ejpam-4946	24	21	and	and	CCONJ
ejpam-4946	24	22	cartesian	cartesian	ADJ
ejpam-4946	24	23	product	product	NOUN
ejpam-4946	24	24	of	of	ADP
ejpam-4946	24	25	two	two	NUM
ejpam-4946	24	26	graphs	graph	NOUN
ejpam-4946	24	27	.	.	PUNCT
ejpam-4946	25	1	these	these	DET
ejpam-4946	25	2	characterizations	characterization	NOUN
ejpam-4946	25	3	had	have	AUX
ejpam-4946	25	4	been	be	AUX
ejpam-4946	25	5	used	use	VERB
ejpam-4946	25	6	to	to	PART
ejpam-4946	25	7	derive	derive	VERB
ejpam-4946	25	8	some	some	DET
ejpam-4946	25	9	formulas	formula	NOUN
ejpam-4946	25	10	of	of	ADP
ejpam-4946	25	11	a	a	DET
ejpam-4946	25	12	hop	hop	NOUN
ejpam-4946	25	13	independence	independence	NOUN
ejpam-4946	25	14	numbers	number	NOUN
ejpam-4946	25	15	of	of	ADP
ejpam-4946	25	16	these	these	DET
ejpam-4946	25	17	graphs	graph	NOUN
ejpam-4946	25	18	.	.	PUNCT
ejpam-4946	26	1	recently	recently	ADV
ejpam-4946	26	2	,	,	PUNCT
ejpam-4946	26	3	j.	j.	PROPN
ejpam-4946	26	4	hassan	hassan	PROPN
ejpam-4946	26	5	et	et	PROPN
ejpam-4946	26	6	al	al	PROPN
ejpam-4946	26	7	.	.	PUNCT
ejpam-4946	27	1	[	[	X
ejpam-4946	27	2	5	5	NUM
ejpam-4946	27	3	]	]	PUNCT
ejpam-4946	27	4	introduced	introduce	VERB
ejpam-4946	27	5	and	and	CCONJ
ejpam-4946	27	6	investigated	investigate	VERB
ejpam-4946	27	7	new	new	ADJ
ejpam-4946	27	8	concept	concept	NOUN
ejpam-4946	27	9	called	call	VERB
ejpam-4946	27	10	j2	j2	PROPN
ejpam-4946	27	11	-	-	PUNCT
ejpam-4946	27	12	hop	hop	PROPN
ejpam-4946	27	13	domination	domination	NOUN
ejpam-4946	27	14	.	.	PUNCT
ejpam-4946	28	1	a	a	DET
ejpam-4946	28	2	subset	subset	NOUN
ejpam-4946	28	3	t	t	NOUN
ejpam-4946	28	4	=	=	SYM
ejpam-4946	28	5	{	{	PUNCT
ejpam-4946	28	6	v1	v1	PROPN
ejpam-4946	28	7	,	,	PUNCT
ejpam-4946	28	8	v2	v2	PROPN
ejpam-4946	28	9	,	,	PUNCT
ejpam-4946	28	10	·	·	PUNCT
ejpam-4946	28	11	·	·	PUNCT
ejpam-4946	28	12	·	·	PUNCT
ejpam-4946	28	13	,	,	PUNCT
ejpam-4946	28	14	vm	vm	NOUN
ejpam-4946	28	15	}	}	PUNCT
ejpam-4946	28	16	of	of	ADP
ejpam-4946	28	17	vertices	vertex	NOUN
ejpam-4946	28	18	of	of	ADP
ejpam-4946	28	19	a	a	DET
ejpam-4946	28	20	graph	graph	NOUN
ejpam-4946	28	21	g	g	NOUN
ejpam-4946	28	22	is	be	AUX
ejpam-4946	28	23	called	call	VERB
ejpam-4946	28	24	a	a	DET
ejpam-4946	28	25	j2	j2	PROPN
ejpam-4946	28	26	-	-	PUNCT
ejpam-4946	28	27	set	set	VERB
ejpam-4946	28	28	if	if	SCONJ
ejpam-4946	28	29	n2	n2	PROPN
ejpam-4946	28	30	g[vi]\n2	g[vi]\n2	PROPN
ejpam-4946	28	31	g[vj	g[vj	PROPN
ejpam-4946	28	32	]	]	PUNCT
ejpam-4946	28	33	̸=	̸=	PROPN
ejpam-4946	28	34	∅	∅	NOUN
ejpam-4946	28	35	for	for	ADP
ejpam-4946	28	36	every	every	DET
ejpam-4946	28	37	i	i	PROPN
ejpam-4946	28	38	̸=	̸=	PROPN
ejpam-4946	28	39	j	j	PROPN
ejpam-4946	28	40	,	,	PUNCT
ejpam-4946	28	41	where	where	SCONJ
ejpam-4946	28	42	i	i	PRON
ejpam-4946	28	43	,	,	PUNCT
ejpam-4946	28	44	j	j	PROPN
ejpam-4946	28	45	∈	∈	PROPN
ejpam-4946	28	46	{	{	PUNCT
ejpam-4946	28	47	1	1	NUM
ejpam-4946	28	48	,	,	PUNCT
ejpam-4946	28	49	2	2	NUM
ejpam-4946	28	50	,	,	PUNCT
ejpam-4946	28	51	.	.	PUNCT
ejpam-4946	28	52	.	.	PUNCT
ejpam-4946	29	1	.	.	PUNCT
ejpam-4946	30	1	,	,	PUNCT
ejpam-4946	30	2	m	m	VERB
ejpam-4946	30	3	}	}	PUNCT
ejpam-4946	30	4	.	.	PUNCT
ejpam-4946	31	1	a	a	DET
ejpam-4946	31	2	j2	j2	PROPN
ejpam-4946	31	3	-	-	PUNCT
ejpam-4946	31	4	set	set	VERB
ejpam-4946	31	5	t	t	PROPN
ejpam-4946	31	6	is	be	AUX
ejpam-4946	31	7	called	call	VERB
ejpam-4946	31	8	a	a	DET
ejpam-4946	31	9	j2	j2	PROPN
ejpam-4946	31	10	-	-	PUNCT
ejpam-4946	31	11	hop	hop	NOUN
ejpam-4946	31	12	dominating	dominating	NOUN
ejpam-4946	31	13	in	in	ADP
ejpam-4946	31	14	g	g	PROPN
ejpam-4946	31	15	if	if	SCONJ
ejpam-4946	31	16	for	for	ADP
ejpam-4946	31	17	every	every	DET
ejpam-4946	31	18	a	a	DET
ejpam-4946	31	19	∈	∈	PROPN
ejpam-4946	31	20	v	v	NOUN
ejpam-4946	31	21	(	(	PUNCT
ejpam-4946	31	22	g	g	NOUN
ejpam-4946	31	23	)	)	PUNCT
ejpam-4946	31	24	\	\	PROPN
ejpam-4946	31	25	t	t	NOUN
ejpam-4946	31	26	,	,	PUNCT
ejpam-4946	31	27	there	there	PRON
ejpam-4946	31	28	exists	exist	VERB
ejpam-4946	31	29	b	b	PROPN
ejpam-4946	31	30	∈	∈	PROPN
ejpam-4946	31	31	t	t	NOUN
ejpam-4946	31	32	such	such	ADJ
ejpam-4946	31	33	that	that	PRON
ejpam-4946	31	34	dg(a	dg(a	PROPN
ejpam-4946	31	35	,	,	PUNCT
ejpam-4946	31	36	b	b	X
ejpam-4946	31	37	)	)	PUNCT
ejpam-4946	32	1	=	=	SYM
ejpam-4946	32	2	2	2	X
ejpam-4946	32	3	.	.	X
ejpam-4946	33	1	the	the	DET
ejpam-4946	33	2	j2	j2	PROPN
ejpam-4946	33	3	-	-	PUNCT
ejpam-4946	33	4	hop	hop	PROPN
ejpam-4946	33	5	domination	domination	NOUN
ejpam-4946	33	6	number	number	NOUN
ejpam-4946	33	7	of	of	ADP
ejpam-4946	33	8	g	g	NOUN
ejpam-4946	33	9	,	,	PUNCT
ejpam-4946	33	10	denoted	denote	VERB
ejpam-4946	33	11	by	by	ADP
ejpam-4946	33	12	γj2h(g	γj2h(g	NOUN
ejpam-4946	33	13	)	)	PUNCT
ejpam-4946	33	14	,	,	PUNCT
ejpam-4946	33	15	is	be	AUX
ejpam-4946	33	16	the	the	DET
ejpam-4946	33	17	maximum	maximum	ADJ
ejpam-4946	33	18	cardinality	cardinality	NOUN
ejpam-4946	33	19	among	among	ADP
ejpam-4946	33	20	all	all	DET
ejpam-4946	33	21	j2	j2	PROPN
ejpam-4946	33	22	-	-	PUNCT
ejpam-4946	33	23	hop	hop	NOUN
ejpam-4946	33	24	dominating	dominating	NOUN
ejpam-4946	33	25	sets	set	NOUN
ejpam-4946	33	26	in	in	ADP
ejpam-4946	33	27	g.	g.	PROPN
ejpam-4946	33	28	they	they	PRON
ejpam-4946	33	29	have	have	AUX
ejpam-4946	33	30	shown	show	VERB
ejpam-4946	33	31	that	that	SCONJ
ejpam-4946	33	32	every	every	DET
ejpam-4946	33	33	maximum	maximum	ADJ
ejpam-4946	33	34	hop	hop	NOUN
ejpam-4946	33	35	independent	independent	ADJ
ejpam-4946	33	36	set	set	NOUN
ejpam-4946	33	37	is	be	AUX
ejpam-4946	33	38	a	a	DET
ejpam-4946	33	39	j2	j2	PROPN
ejpam-4946	33	40	-	-	PUNCT
ejpam-4946	33	41	hop	hop	NOUN
ejpam-4946	33	42	dominating	dominating	NOUN
ejpam-4946	33	43	,	,	PUNCT
ejpam-4946	33	44	hence	hence	ADV
ejpam-4946	33	45	,	,	PUNCT
ejpam-4946	33	46	this	this	DET
ejpam-4946	33	47	parameter	parameter	NOUN
ejpam-4946	33	48	is	be	AUX
ejpam-4946	33	49	always	always	ADV
ejpam-4946	33	50	greater	great	ADJ
ejpam-4946	33	51	or	or	CCONJ
ejpam-4946	33	52	equal	equal	ADJ
ejpam-4946	33	53	compare	compare	NOUN
ejpam-4946	33	54	to	to	ADP
ejpam-4946	33	55	the	the	DET
ejpam-4946	33	56	hop	hop	NOUN
ejpam-4946	33	57	independence	independence	NOUN
ejpam-4946	33	58	parameter	parameter	NOUN
ejpam-4946	33	59	on	on	ADP
ejpam-4946	33	60	any	any	DET
ejpam-4946	33	61	graph	graph	NOUN
ejpam-4946	33	62	.	.	PUNCT
ejpam-4946	34	1	moreover	moreover	ADV
ejpam-4946	34	2	,	,	PUNCT
ejpam-4946	34	3	they	they	PRON
ejpam-4946	34	4	derived	derive	VERB
ejpam-4946	34	5	some	some	DET
ejpam-4946	34	6	lower	low	ADJ
ejpam-4946	34	7	and	and	CCONJ
ejpam-4946	34	8	upper	upper	ADJ
ejpam-4946	34	9	bounds	bound	NOUN
ejpam-4946	34	10	of	of	ADP
ejpam-4946	34	11	the	the	DET
ejpam-4946	34	12	parameter	parameter	NOUN
ejpam-4946	34	13	for	for	ADP
ejpam-4946	34	14	a	a	DET
ejpam-4946	34	15	generalized	generalized	ADJ
ejpam-4946	34	16	graph	graph	NOUN
ejpam-4946	34	17	,	,	PUNCT
ejpam-4946	34	18	join	join	VERB
ejpam-4946	34	19	and	and	CCONJ
ejpam-4946	34	20	corona	corona	NOUN
ejpam-4946	34	21	of	of	ADP
ejpam-4946	34	22	two	two	NUM
ejpam-4946	34	23	graphs	graph	NOUN
ejpam-4946	34	24	,	,	PUNCT
ejpam-4946	34	25	respectively	respectively	ADV
ejpam-4946	34	26	.	.	PUNCT
ejpam-4946	35	1	in	in	ADP
ejpam-4946	35	2	this	this	DET
ejpam-4946	35	3	paper	paper	NOUN
ejpam-4946	35	4	,	,	PUNCT
ejpam-4946	35	5	we	we	PRON
ejpam-4946	35	6	initiate	initiate	VERB
ejpam-4946	35	7	the	the	DET
ejpam-4946	35	8	study	study	NOUN
ejpam-4946	35	9	of	of	ADP
ejpam-4946	35	10	new	new	ADJ
ejpam-4946	35	11	variant	variant	NOUN
ejpam-4946	35	12	of	of	ADP
ejpam-4946	35	13	independence	independence	NOUN
ejpam-4946	35	14	called	call	VERB
ejpam-4946	35	15	j2	j2	PROPN
ejpam-4946	35	16	-	-	PUNCT
ejpam-4946	35	17	independence	independence	NOUN
ejpam-4946	35	18	.	.	PUNCT
ejpam-4946	36	1	a	a	DET
ejpam-4946	36	2	certain	certain	ADJ
ejpam-4946	36	3	subset	subset	NOUN
ejpam-4946	36	4	s	s	NOUN
ejpam-4946	36	5	of	of	ADP
ejpam-4946	36	6	a	a	DET
ejpam-4946	36	7	vertex	vertex	NOUN
ejpam-4946	36	8	-	-	PUNCT
ejpam-4946	36	9	set	set	VERB
ejpam-4946	36	10	v	v	NOUN
ejpam-4946	36	11	(	(	PUNCT
ejpam-4946	36	12	g	g	NOUN
ejpam-4946	36	13	)	)	PUNCT
ejpam-4946	36	14	of	of	ADP
ejpam-4946	36	15	g	g	PROPN
ejpam-4946	36	16	is	be	AUX
ejpam-4946	36	17	called	call	VERB
ejpam-4946	36	18	a	a	DET
ejpam-4946	36	19	j2	j2	NOUN
ejpam-4946	36	20	-	-	PUNCT
ejpam-4946	36	21	independent	independent	NOUN
ejpam-4946	36	22	if	if	SCONJ
ejpam-4946	36	23	s	s	NOUN
ejpam-4946	36	24	is	be	AUX
ejpam-4946	36	25	both	both	PRON
ejpam-4946	36	26	a	a	DET
ejpam-4946	36	27	j2	j2	PROPN
ejpam-4946	36	28	-	-	PUNCT
ejpam-4946	36	29	set	set	NOUN
ejpam-4946	36	30	and	and	CCONJ
ejpam-4946	36	31	an	an	DET
ejpam-4946	36	32	independent	independent	ADJ
ejpam-4946	36	33	set	set	NOUN
ejpam-4946	36	34	of	of	ADP
ejpam-4946	36	35	a	a	DET
ejpam-4946	36	36	graph	graph	NOUN
ejpam-4946	36	37	g.	g.	NOUN
ejpam-4946	36	38	we	we	PRON
ejpam-4946	36	39	investigate	investigate	VERB
ejpam-4946	36	40	its	its	PRON
ejpam-4946	36	41	properties	property	NOUN
ejpam-4946	36	42	and	and	CCONJ
ejpam-4946	36	43	its	its	PRON
ejpam-4946	36	44	relationships	relationship	NOUN
ejpam-4946	36	45	with	with	ADP
ejpam-4946	36	46	other	other	ADJ
ejpam-4946	36	47	variants	variant	NOUN
ejpam-4946	36	48	of	of	ADP
ejpam-4946	36	49	independence	independence	NOUN
ejpam-4946	36	50	.	.	PUNCT
ejpam-4946	37	1	further	far	ADV
ejpam-4946	37	2	,	,	PUNCT
ejpam-4946	37	3	we	we	PRON
ejpam-4946	37	4	characterize	characterize	VERB
ejpam-4946	37	5	j2	j2	NOUN
ejpam-4946	37	6	-	-	PUNCT
ejpam-4946	37	7	independent	independent	ADJ
ejpam-4946	37	8	sets	set	NOUN
ejpam-4946	37	9	in	in	ADP
ejpam-4946	37	10	some	some	DET
ejpam-4946	37	11	classes	class	NOUN
ejpam-4946	37	12	of	of	ADP
ejpam-4946	37	13	graphs	graph	NOUN
ejpam-4946	37	14	and	and	CCONJ
ejpam-4946	37	15	we	we	PRON
ejpam-4946	37	16	use	use	VERB
ejpam-4946	37	17	these	these	DET
ejpam-4946	37	18	results	result	NOUN
ejpam-4946	37	19	to	to	PART
ejpam-4946	37	20	determine	determine	VERB
ejpam-4946	37	21	the	the	DET
ejpam-4946	37	22	j2	j2	PROPN
ejpam-4946	37	23	-	-	PUNCT
ejpam-4946	37	24	independence	independence	NOUN
ejpam-4946	37	25	numbers	number	NOUN
ejpam-4946	37	26	of	of	ADP
ejpam-4946	37	27	these	these	DET
ejpam-4946	37	28	graphs	graph	NOUN
ejpam-4946	37	29	.	.	PUNCT
ejpam-4946	38	1	furthermore	furthermore	ADV
ejpam-4946	38	2	,	,	PUNCT
ejpam-4946	38	3	we	we	PRON
ejpam-4946	38	4	present	present	VERB
ejpam-4946	38	5	some	some	DET
ejpam-4946	38	6	lower	low	ADJ
ejpam-4946	38	7	bounds	bound	NOUN
ejpam-4946	38	8	of	of	ADP
ejpam-4946	38	9	the	the	DET
ejpam-4946	38	10	parameter	parameter	NOUN
ejpam-4946	38	11	on	on	ADP
ejpam-4946	38	12	the	the	DET
ejpam-4946	38	13	join	join	NOUN
ejpam-4946	38	14	and	and	CCONJ
ejpam-4946	38	15	corona	corona	NOUN
ejpam-4946	38	16	of	of	ADP
ejpam-4946	38	17	two	two	NUM
ejpam-4946	38	18	graphs	graph	NOUN
ejpam-4946	38	19	.	.	PUNCT
ejpam-4946	39	1	we	we	PRON
ejpam-4946	39	2	believe	believe	VERB
ejpam-4946	39	3	that	that	SCONJ
ejpam-4946	39	4	the	the	DET
ejpam-4946	39	5	results	result	NOUN
ejpam-4946	39	6	of	of	ADP
ejpam-4946	39	7	this	this	DET
ejpam-4946	39	8	study	study	NOUN
ejpam-4946	39	9	would	would	AUX
ejpam-4946	39	10	give	give	VERB
ejpam-4946	39	11	additional	additional	ADJ
ejpam-4946	39	12	insights	insight	NOUN
ejpam-4946	39	13	to	to	ADP
ejpam-4946	39	14	researchers	researcher	NOUN
ejpam-4946	39	15	in	in	ADP
ejpam-4946	39	16	the	the	DET
ejpam-4946	39	17	field	field	NOUN
ejpam-4946	39	18	and	and	CCONJ
ejpam-4946	39	19	would	would	AUX
ejpam-4946	39	20	help	help	VERB
ejpam-4946	39	21	them	they	PRON
ejpam-4946	39	22	for	for	ADP
ejpam-4946	39	23	more	more	ADJ
ejpam-4946	39	24	research	research	NOUN
ejpam-4946	39	25	directions	direction	NOUN
ejpam-4946	39	26	in	in	ADP
ejpam-4946	39	27	the	the	DET
ejpam-4946	39	28	future	future	NOUN
ejpam-4946	39	29	.	.	PUNCT
ejpam-4946	40	1	a.	a.	NOUN
ejpam-4946	40	2	tapeing	tape	VERB
ejpam-4946	40	3	et	et	PROPN
ejpam-4946	40	4	al	al	PROPN
ejpam-4946	40	5	.	.	PUNCT
ejpam-4946	40	6	/	/	SYM
ejpam-4946	40	7	eur	eur	PROPN
ejpam-4946	40	8	.	.	PUNCT
ejpam-4946	41	1	j.	j.	PROPN
ejpam-4946	41	2	pure	pure	PROPN
ejpam-4946	41	3	appl	appl	PROPN
ejpam-4946	41	4	.	.	PROPN
ejpam-4946	41	5	math	math	PROPN
ejpam-4946	41	6	,	,	PUNCT
ejpam-4946	41	7	17	17	NUM
ejpam-4946	41	8	(	(	PUNCT
ejpam-4946	41	9	1	1	NUM
ejpam-4946	41	10	)	)	PUNCT
ejpam-4946	41	11	(	(	PUNCT
ejpam-4946	41	12	2024	2024	NUM
ejpam-4946	41	13	)	)	PUNCT
ejpam-4946	41	14	,	,	PUNCT
ejpam-4946	41	15	124	124	NUM
ejpam-4946	41	16	-	-	SYM
ejpam-4946	41	17	134	134	NUM
ejpam-4946	41	18	126	126	NUM
ejpam-4946	41	19	2	2	NUM
ejpam-4946	41	20	.	.	PUNCT
ejpam-4946	41	21	terminology	terminology	NOUN
ejpam-4946	41	22	and	and	CCONJ
ejpam-4946	41	23	notation	notation	NOUN
ejpam-4946	41	24	let	let	VERB
ejpam-4946	41	25	g	g	NOUN
ejpam-4946	41	26	=	=	SYM
ejpam-4946	41	27	(	(	PUNCT
ejpam-4946	41	28	v	v	NOUN
ejpam-4946	41	29	(	(	PUNCT
ejpam-4946	41	30	g	g	NOUN
ejpam-4946	41	31	)	)	PUNCT
ejpam-4946	41	32	,	,	PUNCT
ejpam-4946	41	33	e(g	e(g	PROPN
ejpam-4946	41	34	)	)	PUNCT
ejpam-4946	41	35	)	)	PUNCT
ejpam-4946	41	36	be	be	AUX
ejpam-4946	41	37	a	a	DET
ejpam-4946	41	38	simple	simple	ADJ
ejpam-4946	41	39	and	and	CCONJ
ejpam-4946	41	40	undirected	undirected	ADJ
ejpam-4946	41	41	graph	graph	NOUN
ejpam-4946	41	42	.	.	PUNCT
ejpam-4946	42	1	two	two	NUM
ejpam-4946	42	2	vertices	vertex	NOUN
ejpam-4946	42	3	x	x	X
ejpam-4946	42	4	,	,	PUNCT
ejpam-4946	42	5	y	y	PROPN
ejpam-4946	42	6	of	of	ADP
ejpam-4946	42	7	g	g	PROPN
ejpam-4946	42	8	are	be	AUX
ejpam-4946	42	9	adjacent	adjacent	ADJ
ejpam-4946	42	10	,	,	PUNCT
ejpam-4946	42	11	or	or	CCONJ
ejpam-4946	42	12	neighbors	neighbor	NOUN
ejpam-4946	42	13	,	,	PUNCT
ejpam-4946	42	14	if	if	SCONJ
ejpam-4946	42	15	xy	xy	PROPN
ejpam-4946	42	16	is	be	AUX
ejpam-4946	42	17	an	an	DET
ejpam-4946	42	18	edge	edge	NOUN
ejpam-4946	42	19	of	of	ADP
ejpam-4946	42	20	g.	g.	PROPN
ejpam-4946	42	21	the	the	DET
ejpam-4946	42	22	open	open	ADJ
ejpam-4946	42	23	neighborhood	neighborhood	NOUN
ejpam-4946	42	24	of	of	ADP
ejpam-4946	42	25	x	x	PUNCT
ejpam-4946	42	26	in	in	ADP
ejpam-4946	42	27	g	g	PROPN
ejpam-4946	42	28	is	be	AUX
ejpam-4946	42	29	the	the	DET
ejpam-4946	42	30	set	set	NOUN
ejpam-4946	42	31	ng(x	ng(x	NUM
ejpam-4946	42	32	)	)	PUNCT
ejpam-4946	43	1	=	=	PRON
ejpam-4946	43	2	{	{	PUNCT
ejpam-4946	43	3	y	y	PROPN
ejpam-4946	43	4	∈	∈	PROPN
ejpam-4946	43	5	v	v	NOUN
ejpam-4946	43	6	(	(	PUNCT
ejpam-4946	43	7	g	g	NOUN
ejpam-4946	43	8	)	)	PUNCT
ejpam-4946	43	9	:	:	PUNCT
ejpam-4946	43	10	xy	xy	PROPN
ejpam-4946	43	11	∈	∈	PROPN
ejpam-4946	43	12	e(g	e(g	PROPN
ejpam-4946	43	13	)	)	PUNCT
ejpam-4946	43	14	}	}	PUNCT
ejpam-4946	43	15	.	.	PUNCT
ejpam-4946	44	1	the	the	DET
ejpam-4946	44	2	closed	closed	ADJ
ejpam-4946	44	3	neighborhood	neighborhood	NOUN
ejpam-4946	44	4	of	of	ADP
ejpam-4946	44	5	x	x	PUNCT
ejpam-4946	44	6	in	in	ADP
ejpam-4946	44	7	g	g	PROPN
ejpam-4946	44	8	is	be	AUX
ejpam-4946	44	9	the	the	DET
ejpam-4946	44	10	set	set	NOUN
ejpam-4946	44	11	ng[x	ng[x	PROPN
ejpam-4946	44	12	]	]	X
ejpam-4946	44	13	=	=	PUNCT
ejpam-4946	44	14	ng(x	ng(x	X
ejpam-4946	44	15	)	)	PUNCT
ejpam-4946	44	16	∪	∪	ADP
ejpam-4946	44	17	{	{	PUNCT
ejpam-4946	44	18	x	x	NOUN
ejpam-4946	44	19	}	}	PUNCT
ejpam-4946	44	20	.	.	PUNCT
ejpam-4946	45	1	if	if	SCONJ
ejpam-4946	45	2	x	x	PROPN
ejpam-4946	45	3	⊆	⊆	NUM
ejpam-4946	45	4	v	v	X
ejpam-4946	45	5	(	(	PUNCT
ejpam-4946	45	6	g	g	NOUN
ejpam-4946	45	7	)	)	PUNCT
ejpam-4946	45	8	,	,	PUNCT
ejpam-4946	45	9	the	the	DET
ejpam-4946	45	10	open	open	ADJ
ejpam-4946	45	11	neighborhood	neighborhood	NOUN
ejpam-4946	45	12	of	of	ADP
ejpam-4946	45	13	x	x	PUNCT
ejpam-4946	45	14	in	in	ADP
ejpam-4946	45	15	g	g	PROPN
ejpam-4946	45	16	is	be	AUX
ejpam-4946	45	17	the	the	DET
ejpam-4946	45	18	set	set	NOUN
ejpam-4946	45	19	ng(x	ng(x	NUM
ejpam-4946	45	20	)	)	PUNCT
ejpam-4946	46	1	=	=	SYM
ejpam-4946	46	2	⋃	⋃	NOUN
ejpam-4946	46	3	x∈x	x∈x	NOUN
ejpam-4946	46	4	ng(x	ng(x	NUM
ejpam-4946	46	5	)	)	PUNCT
ejpam-4946	46	6	.	.	PUNCT
ejpam-4946	47	1	the	the	DET
ejpam-4946	47	2	closed	closed	ADJ
ejpam-4946	47	3	neighborhood	neighborhood	NOUN
ejpam-4946	47	4	of	of	ADP
ejpam-4946	47	5	x	x	PUNCT
ejpam-4946	47	6	in	in	ADP
ejpam-4946	47	7	g	g	PROPN
ejpam-4946	47	8	is	be	AUX
ejpam-4946	47	9	the	the	DET
ejpam-4946	47	10	set	set	NOUN
ejpam-4946	47	11	ng[x	ng[x	PROPN
ejpam-4946	47	12	]	]	X
ejpam-4946	47	13	=	=	SYM
ejpam-4946	47	14	ng(x)∪x	ng(x)∪x	PROPN
ejpam-4946	47	15	.	.	PUNCT
ejpam-4946	48	1	a	a	DET
ejpam-4946	48	2	graph	graph	NOUN
ejpam-4946	48	3	g	g	NOUN
ejpam-4946	48	4	is	be	AUX
ejpam-4946	48	5	connected	connect	VERB
ejpam-4946	48	6	if	if	SCONJ
ejpam-4946	48	7	every	every	DET
ejpam-4946	48	8	pair	pair	NOUN
ejpam-4946	48	9	of	of	ADP
ejpam-4946	48	10	its	its	PRON
ejpam-4946	48	11	vertices	vertex	NOUN
ejpam-4946	48	12	can	can	AUX
ejpam-4946	48	13	be	be	AUX
ejpam-4946	48	14	joined	join	VERB
ejpam-4946	48	15	by	by	ADP
ejpam-4946	48	16	a	a	DET
ejpam-4946	48	17	path	path	NOUN
ejpam-4946	48	18	.	.	PUNCT
ejpam-4946	49	1	otherwise	otherwise	ADV
ejpam-4946	49	2	,	,	PUNCT
ejpam-4946	49	3	g	g	PROPN
ejpam-4946	49	4	is	be	AUX
ejpam-4946	49	5	disconnected	disconnect	VERB
ejpam-4946	49	6	.	.	PUNCT
ejpam-4946	50	1	a	a	DET
ejpam-4946	50	2	maximal	maximal	ADJ
ejpam-4946	50	3	connected	connected	ADJ
ejpam-4946	50	4	subgraph	subgraph	NOUN
ejpam-4946	50	5	(	(	PUNCT
ejpam-4946	50	6	not	not	PART
ejpam-4946	50	7	a	a	DET
ejpam-4946	50	8	subgraph	subgraph	NOUN
ejpam-4946	50	9	of	of	ADP
ejpam-4946	50	10	any	any	DET
ejpam-4946	50	11	connected	connected	ADJ
ejpam-4946	50	12	subgraph	subgraph	NOUN
ejpam-4946	50	13	)	)	PUNCT
ejpam-4946	50	14	of	of	ADP
ejpam-4946	50	15	g	g	PROPN
ejpam-4946	50	16	is	be	AUX
ejpam-4946	50	17	called	call	VERB
ejpam-4946	50	18	a	a	DET
ejpam-4946	50	19	component	component	NOUN
ejpam-4946	50	20	of	of	ADP
ejpam-4946	50	21	g.	g.	PROPN
ejpam-4946	50	22	a	a	DET
ejpam-4946	50	23	path	path	NOUN
ejpam-4946	50	24	graph	graph	NOUN
ejpam-4946	50	25	is	be	AUX
ejpam-4946	50	26	a	a	DET
ejpam-4946	50	27	non	non	ADJ
ejpam-4946	50	28	-	-	ADJ
ejpam-4946	50	29	empty	empty	ADJ
ejpam-4946	50	30	graph	graph	NOUN
ejpam-4946	50	31	with	with	ADP
ejpam-4946	50	32	vertex	vertex	NOUN
ejpam-4946	50	33	-	-	PUNCT
ejpam-4946	50	34	set	set	VERB
ejpam-4946	50	35	{	{	PUNCT
ejpam-4946	50	36	x1	x1	PROPN
ejpam-4946	50	37	,	,	PUNCT
ejpam-4946	50	38	x2	x2	PROPN
ejpam-4946	50	39	,	,	PUNCT
ejpam-4946	50	40	.	.	PUNCT
ejpam-4946	50	41	.	.	PUNCT
ejpam-4946	51	1	.	.	PUNCT
ejpam-4946	52	1	,	,	PUNCT
ejpam-4946	52	2	xn	xn	X
ejpam-4946	52	3	}	}	PUNCT
ejpam-4946	52	4	and	and	CCONJ
ejpam-4946	52	5	edge	edge	NOUN
ejpam-4946	52	6	-	-	PUNCT
ejpam-4946	52	7	set	set	NOUN
ejpam-4946	52	8	{	{	PUNCT
ejpam-4946	52	9	x1x2	x1x2	NOUN
ejpam-4946	52	10	,	,	PUNCT
ejpam-4946	52	11	x2x3	x2x3	PROPN
ejpam-4946	52	12	,	,	PUNCT
ejpam-4946	52	13	.	.	PUNCT
ejpam-4946	52	14	.	.	PUNCT
ejpam-4946	53	1	.	.	PUNCT
ejpam-4946	54	1	,	,	PUNCT
ejpam-4946	54	2	xn−1xn	xn−1xn	PROPN
ejpam-4946	54	3	}	}	PUNCT
ejpam-4946	54	4	,	,	PUNCT
ejpam-4946	54	5	where	where	SCONJ
ejpam-4946	54	6	the	the	DET
ejpam-4946	54	7	x	x	NOUN
ejpam-4946	54	8	′	′	NOUN
ejpam-4946	54	9	is	be	AUX
ejpam-4946	54	10	are	be	AUX
ejpam-4946	54	11	all	all	ADV
ejpam-4946	54	12	distinct	distinct	ADJ
ejpam-4946	54	13	.	.	PUNCT
ejpam-4946	55	1	the	the	DET
ejpam-4946	55	2	path	path	NOUN
ejpam-4946	55	3	of	of	ADP
ejpam-4946	55	4	order	order	NOUN
ejpam-4946	55	5	n	n	NOUN
ejpam-4946	55	6	is	be	AUX
ejpam-4946	55	7	denoted	denote	VERB
ejpam-4946	55	8	by	by	ADP
ejpam-4946	55	9	pn	pn	PROPN
ejpam-4946	55	10	.	.	PUNCT
ejpam-4946	56	1	if	if	SCONJ
ejpam-4946	56	2	g	g	PROPN
ejpam-4946	56	3	is	be	AUX
ejpam-4946	56	4	a	a	DET
ejpam-4946	56	5	graph	graph	NOUN
ejpam-4946	56	6	and	and	CCONJ
ejpam-4946	56	7	u	u	NOUN
ejpam-4946	56	8	and	and	CCONJ
ejpam-4946	56	9	v	v	NOUN
ejpam-4946	56	10	are	be	AUX
ejpam-4946	56	11	vertices	vertex	NOUN
ejpam-4946	56	12	of	of	ADP
ejpam-4946	56	13	g	g	NOUN
ejpam-4946	56	14	,	,	PUNCT
ejpam-4946	56	15	then	then	ADV
ejpam-4946	56	16	a	a	DET
ejpam-4946	56	17	path	path	NOUN
ejpam-4946	56	18	from	from	ADP
ejpam-4946	56	19	vertex	vertex	NOUN
ejpam-4946	56	20	u	u	NOUN
ejpam-4946	56	21	to	to	PART
ejpam-4946	56	22	vertex	vertex	NOUN
ejpam-4946	56	23	v	v	NOUN
ejpam-4946	56	24	is	be	AUX
ejpam-4946	56	25	sometimes	sometimes	ADV
ejpam-4946	56	26	called	call	VERB
ejpam-4946	56	27	a	a	DET
ejpam-4946	56	28	u	u	NOUN
ejpam-4946	56	29	-	-	NOUN
ejpam-4946	56	30	v	v	ADJ
ejpam-4946	56	31	path	path	NOUN
ejpam-4946	56	32	.	.	PUNCT
ejpam-4946	57	1	the	the	DET
ejpam-4946	57	2	cycle	cycle	NOUN
ejpam-4946	57	3	graph	graph	NOUN
ejpam-4946	57	4	cn	cn	NOUN
ejpam-4946	58	1	=	=	PUNCT
ejpam-4946	59	1	[	[	X
ejpam-4946	59	2	x1	x1	PROPN
ejpam-4946	59	3	,	,	PUNCT
ejpam-4946	59	4	x2	x2	PROPN
ejpam-4946	59	5	,	,	PUNCT
ejpam-4946	59	6	.	.	PUNCT
ejpam-4946	59	7	.	.	PUNCT
ejpam-4946	60	1	.	.	PUNCT
ejpam-4946	61	1	,	,	PUNCT
ejpam-4946	61	2	xn	xn	PROPN
ejpam-4946	61	3	,	,	PUNCT
ejpam-4946	61	4	x1	x1	PROPN
ejpam-4946	61	5	]	]	PUNCT
ejpam-4946	61	6	is	be	AUX
ejpam-4946	61	7	the	the	DET
ejpam-4946	61	8	graph	graph	NOUN
ejpam-4946	61	9	of	of	ADP
ejpam-4946	61	10	order	order	NOUN
ejpam-4946	61	11	n	n	PRON
ejpam-4946	61	12	≥	≥	NOUN
ejpam-4946	61	13	3	3	NUM
ejpam-4946	61	14	with	with	ADP
ejpam-4946	61	15	vertex	vertex	NOUN
ejpam-4946	61	16	-	-	PUNCT
ejpam-4946	61	17	set	set	VERB
ejpam-4946	61	18	{	{	PUNCT
ejpam-4946	61	19	x1	x1	PROPN
ejpam-4946	61	20	,	,	PUNCT
ejpam-4946	61	21	x2	x2	PROPN
ejpam-4946	61	22	,	,	PUNCT
ejpam-4946	61	23	.	.	PUNCT
ejpam-4946	61	24	.	.	PUNCT
ejpam-4946	62	1	.	.	PUNCT
ejpam-4946	63	1	,	,	PUNCT
ejpam-4946	63	2	xn	xn	X
ejpam-4946	63	3	}	}	PUNCT
ejpam-4946	63	4	and	and	CCONJ
ejpam-4946	63	5	edge	edge	NOUN
ejpam-4946	63	6	-	-	PUNCT
ejpam-4946	63	7	set	set	NOUN
ejpam-4946	63	8	{	{	PUNCT
ejpam-4946	63	9	x1x2	x1x2	NOUN
ejpam-4946	63	10	,	,	PUNCT
ejpam-4946	63	11	x2x3	x2x3	PROPN
ejpam-4946	63	12	,	,	PUNCT
ejpam-4946	63	13	.	.	PUNCT
ejpam-4946	63	14	.	.	PUNCT
ejpam-4946	64	1	.	.	PUNCT
ejpam-4946	65	1	,	,	PUNCT
ejpam-4946	65	2	xn−1xn	xn−1xn	PROPN
ejpam-4946	65	3	,	,	PUNCT
ejpam-4946	65	4	xnx1	xnx1	PROPN
ejpam-4946	65	5	}	}	PUNCT
ejpam-4946	65	6	.	.	PUNCT
ejpam-4946	66	1	a	a	DET
ejpam-4946	66	2	graph	graph	NOUN
ejpam-4946	66	3	is	be	AUX
ejpam-4946	66	4	complete	complete	ADJ
ejpam-4946	66	5	if	if	SCONJ
ejpam-4946	66	6	every	every	DET
ejpam-4946	66	7	pair	pair	NOUN
ejpam-4946	66	8	of	of	ADP
ejpam-4946	66	9	distinct	distinct	ADJ
ejpam-4946	66	10	vertices	vertex	NOUN
ejpam-4946	66	11	are	be	AUX
ejpam-4946	66	12	adjacent	adjacent	ADJ
ejpam-4946	66	13	.	.	PUNCT
ejpam-4946	67	1	a	a	DET
ejpam-4946	67	2	complete	complete	ADJ
ejpam-4946	67	3	graph	graph	NOUN
ejpam-4946	67	4	of	of	ADP
ejpam-4946	67	5	order	order	NOUN
ejpam-4946	67	6	n	n	NOUN
ejpam-4946	67	7	is	be	AUX
ejpam-4946	67	8	denoted	denote	VERB
ejpam-4946	67	9	by	by	ADP
ejpam-4946	67	10	kn	kn	PROPN
ejpam-4946	67	11	.	.	PUNCT
ejpam-4946	68	1	the	the	DET
ejpam-4946	68	2	complement	complement	NOUN
ejpam-4946	68	3	of	of	ADP
ejpam-4946	68	4	a	a	DET
ejpam-4946	68	5	graph	graph	NOUN
ejpam-4946	68	6	g	g	NOUN
ejpam-4946	68	7	,	,	PUNCT
ejpam-4946	68	8	denoted	denote	VERB
ejpam-4946	68	9	by	by	ADP
ejpam-4946	68	10	g	g	NOUN
ejpam-4946	68	11	,	,	PUNCT
ejpam-4946	68	12	is	be	AUX
ejpam-4946	68	13	the	the	DET
ejpam-4946	68	14	graph	graph	NOUN
ejpam-4946	68	15	with	with	ADP
ejpam-4946	68	16	v	v	NOUN
ejpam-4946	68	17	(	(	PUNCT
ejpam-4946	68	18	g	g	NOUN
ejpam-4946	68	19	)	)	PUNCT
ejpam-4946	68	20	=	=	NOUN
ejpam-4946	68	21	v	v	X
ejpam-4946	68	22	(	(	PUNCT
ejpam-4946	68	23	g	g	NOUN
ejpam-4946	68	24	)	)	PUNCT
ejpam-4946	68	25	and	and	CCONJ
ejpam-4946	68	26	e(g	e(g	PROPN
ejpam-4946	68	27	)	)	PUNCT
ejpam-4946	69	1	=	=	PRON
ejpam-4946	69	2	{	{	PUNCT
ejpam-4946	69	3	uv	uv	NOUN
ejpam-4946	69	4	:	:	PUNCT
ejpam-4946	69	5	u	u	NOUN
ejpam-4946	69	6	,	,	PUNCT
ejpam-4946	69	7	v	v	PROPN
ejpam-4946	69	8	∈	∈	PROPN
ejpam-4946	69	9	v	v	NOUN
ejpam-4946	69	10	(	(	PUNCT
ejpam-4946	69	11	g	g	NOUN
ejpam-4946	69	12	)	)	PUNCT
ejpam-4946	69	13	and	and	CCONJ
ejpam-4946	69	14	uv	uv	NOUN
ejpam-4946	69	15	/∈	/∈	PROPN
ejpam-4946	69	16	e(g	e(g	PROPN
ejpam-4946	69	17	)	)	PUNCT
ejpam-4946	69	18	}	}	PUNCT
ejpam-4946	69	19	.	.	PUNCT
ejpam-4946	70	1	let	let	VERB
ejpam-4946	70	2	g	g	NOUN
ejpam-4946	70	3	and	and	CCONJ
ejpam-4946	70	4	h	h	NOUN
ejpam-4946	70	5	be	be	VERB
ejpam-4946	70	6	any	any	DET
ejpam-4946	70	7	two	two	NUM
ejpam-4946	70	8	graphs	graph	NOUN
ejpam-4946	70	9	.	.	PUNCT
ejpam-4946	71	1	the	the	DET
ejpam-4946	71	2	join	join	NOUN
ejpam-4946	71	3	of	of	ADP
ejpam-4946	71	4	g	g	PROPN
ejpam-4946	71	5	and	and	CCONJ
ejpam-4946	71	6	h	h	NOUN
ejpam-4946	71	7	,	,	PUNCT
ejpam-4946	71	8	denoted	denote	VERB
ejpam-4946	71	9	by	by	ADP
ejpam-4946	71	10	g+h	g+h	PROPN
ejpam-4946	71	11	is	be	AUX
ejpam-4946	71	12	the	the	DET
ejpam-4946	71	13	graph	graph	NOUN
ejpam-4946	71	14	with	with	ADP
ejpam-4946	71	15	vertex	vertex	NOUN
ejpam-4946	71	16	set	set	VERB
ejpam-4946	71	17	v	v	NOUN
ejpam-4946	71	18	(	(	PUNCT
ejpam-4946	71	19	g+h	g+h	NOUN
ejpam-4946	71	20	)	)	PUNCT
ejpam-4946	72	1	=	=	SYM
ejpam-4946	72	2	v	v	X
ejpam-4946	72	3	(	(	PUNCT
ejpam-4946	72	4	g	g	NOUN
ejpam-4946	72	5	)	)	PUNCT
ejpam-4946	72	6	∪	∪	NOUN
ejpam-4946	72	7	v	v	NOUN
ejpam-4946	72	8	(	(	PUNCT
ejpam-4946	72	9	h	h	NOUN
ejpam-4946	72	10	)	)	PUNCT
ejpam-4946	72	11	and	and	CCONJ
ejpam-4946	72	12	edge	edge	NOUN
ejpam-4946	72	13	set	set	VERB
ejpam-4946	72	14	e(g+h	e(g+h	NUM
ejpam-4946	72	15	)	)	PUNCT
ejpam-4946	72	16	=	=	SYM
ejpam-4946	72	17	e(g	e(g	NOUN
ejpam-4946	72	18	)	)	PUNCT
ejpam-4946	72	19	∪	∪	ADP
ejpam-4946	72	20	e(h	e(h	PROPN
ejpam-4946	72	21	)	)	PUNCT
ejpam-4946	72	22	∪	∪	NOUN
ejpam-4946	72	23	{	{	PUNCT
ejpam-4946	72	24	uv	uv	NOUN
ejpam-4946	72	25	:	:	PUNCT
ejpam-4946	72	26	u	u	PROPN
ejpam-4946	72	27	∈	∈	PROPN
ejpam-4946	72	28	v	v	ADP
ejpam-4946	72	29	(	(	PUNCT
ejpam-4946	72	30	g	g	NOUN
ejpam-4946	72	31	)	)	PUNCT
ejpam-4946	72	32	,	,	PUNCT
ejpam-4946	72	33	v	v	X
ejpam-4946	72	34	∈	∈	PROPN
ejpam-4946	72	35	v	v	NOUN
ejpam-4946	72	36	(	(	PUNCT
ejpam-4946	72	37	h	h	NOUN
ejpam-4946	72	38	)	)	PUNCT
ejpam-4946	72	39	}	}	PUNCT
ejpam-4946	72	40	.	.	PUNCT
ejpam-4946	73	1	the	the	DET
ejpam-4946	73	2	corona	corona	NOUN
ejpam-4946	73	3	g	g	PROPN
ejpam-4946	73	4	and	and	CCONJ
ejpam-4946	73	5	h	h	NOUN
ejpam-4946	73	6	,	,	PUNCT
ejpam-4946	73	7	denoted	denote	VERB
ejpam-4946	73	8	by	by	ADP
ejpam-4946	73	9	g	g	PROPN
ejpam-4946	73	10	◦	◦	NOUN
ejpam-4946	73	11	h	h	NOUN
ejpam-4946	73	12	,	,	PUNCT
ejpam-4946	73	13	the	the	DET
ejpam-4946	73	14	graph	graph	NOUN
ejpam-4946	73	15	obtained	obtain	VERB
ejpam-4946	73	16	by	by	ADP
ejpam-4946	73	17	taking	take	VERB
ejpam-4946	73	18	one	one	NUM
ejpam-4946	73	19	copy	copy	NOUN
ejpam-4946	73	20	of	of	ADP
ejpam-4946	73	21	g	g	PROPN
ejpam-4946	73	22	and	and	CCONJ
ejpam-4946	73	23	|v	|v	PROPN
ejpam-4946	73	24	(	(	PUNCT
ejpam-4946	73	25	g)|	g)|	NOUN
ejpam-4946	73	26	copies	copy	NOUN
ejpam-4946	73	27	of	of	ADP
ejpam-4946	73	28	h	h	NOUN
ejpam-4946	73	29	,	,	PUNCT
ejpam-4946	73	30	and	and	CCONJ
ejpam-4946	73	31	then	then	ADV
ejpam-4946	73	32	joining	join	VERB
ejpam-4946	73	33	the	the	DET
ejpam-4946	73	34	ith	ith	PROPN
ejpam-4946	73	35	vertex	vertex	NOUN
ejpam-4946	73	36	of	of	ADP
ejpam-4946	73	37	g	g	NOUN
ejpam-4946	73	38	to	to	ADP
ejpam-4946	73	39	every	every	DET
ejpam-4946	73	40	vertex	vertex	NOUN
ejpam-4946	73	41	of	of	ADP
ejpam-4946	73	42	the	the	DET
ejpam-4946	73	43	ith	ith	PROPN
ejpam-4946	73	44	copy	copy	NOUN
ejpam-4946	73	45	of	of	ADP
ejpam-4946	73	46	h.	h.	PROPN
ejpam-4946	73	47	we	we	PRON
ejpam-4946	73	48	denote	denote	VERB
ejpam-4946	73	49	by	by	ADP
ejpam-4946	73	50	hv	hv	PROPN
ejpam-4946	73	51	the	the	DET
ejpam-4946	73	52	copy	copy	NOUN
ejpam-4946	73	53	of	of	ADP
ejpam-4946	73	54	h	h	NOUN
ejpam-4946	73	55	in	in	ADP
ejpam-4946	73	56	g	g	PROPN
ejpam-4946	73	57	◦	◦	NOUN
ejpam-4946	73	58	h	h	NOUN
ejpam-4946	73	59	corresponding	correspond	VERB
ejpam-4946	73	60	to	to	ADP
ejpam-4946	73	61	the	the	DET
ejpam-4946	73	62	vertex	vertex	NOUN
ejpam-4946	73	63	v	v	ADP
ejpam-4946	73	64	∈	∈	PROPN
ejpam-4946	73	65	g	g	NOUN
ejpam-4946	73	66	and	and	CCONJ
ejpam-4946	73	67	write	write	VERB
ejpam-4946	73	68	v	v	ADP
ejpam-4946	73	69	+	+	PROPN
ejpam-4946	73	70	hv	hv	NOUN
ejpam-4946	73	71	for	for	ADP
ejpam-4946	73	72	⟨{v}+hv⟩.	⟨{v}+hv⟩.	NOUN
ejpam-4946	73	73	the	the	DET
ejpam-4946	73	74	distance	distance	NOUN
ejpam-4946	73	75	dg(u	dg(u	X
ejpam-4946	73	76	,	,	PUNCT
ejpam-4946	73	77	v	v	NOUN
ejpam-4946	73	78	)	)	PUNCT
ejpam-4946	73	79	in	in	ADP
ejpam-4946	73	80	g	g	NOUN
ejpam-4946	73	81	of	of	ADP
ejpam-4946	73	82	two	two	NUM
ejpam-4946	73	83	vertices	vertex	NOUN
ejpam-4946	73	84	u	u	NOUN
ejpam-4946	73	85	,	,	PUNCT
ejpam-4946	73	86	v	v	PROPN
ejpam-4946	73	87	is	be	AUX
ejpam-4946	73	88	the	the	DET
ejpam-4946	73	89	length	length	NOUN
ejpam-4946	73	90	of	of	ADP
ejpam-4946	73	91	a	a	DET
ejpam-4946	73	92	shortest	short	ADJ
ejpam-4946	73	93	u	u	NOUN
ejpam-4946	73	94	-	-	NOUN
ejpam-4946	73	95	v	v	ADJ
ejpam-4946	73	96	path	path	NOUN
ejpam-4946	73	97	in	in	ADP
ejpam-4946	73	98	g.	g.	PROPN
ejpam-4946	73	99	the	the	DET
ejpam-4946	73	100	greatest	great	ADJ
ejpam-4946	73	101	distance	distance	NOUN
ejpam-4946	73	102	between	between	ADP
ejpam-4946	73	103	any	any	DET
ejpam-4946	73	104	two	two	NUM
ejpam-4946	73	105	vertices	vertex	NOUN
ejpam-4946	73	106	in	in	ADP
ejpam-4946	73	107	g	g	NOUN
ejpam-4946	73	108	,	,	PUNCT
ejpam-4946	73	109	denoted	denote	VERB
ejpam-4946	73	110	by	by	ADP
ejpam-4946	73	111	diam(g	diam(g	PROPN
ejpam-4946	73	112	)	)	PUNCT
ejpam-4946	73	113	,	,	PUNCT
ejpam-4946	73	114	is	be	AUX
ejpam-4946	73	115	called	call	VERB
ejpam-4946	73	116	the	the	DET
ejpam-4946	73	117	diameter	diameter	NOUN
ejpam-4946	73	118	of	of	ADP
ejpam-4946	73	119	g.	g.	PROPN
ejpam-4946	73	120	a	a	DET
ejpam-4946	73	121	subset	subset	NOUN
ejpam-4946	73	122	i	i	PRON
ejpam-4946	73	123	of	of	ADP
ejpam-4946	73	124	v	v	NOUN
ejpam-4946	73	125	(	(	PUNCT
ejpam-4946	73	126	g	g	NOUN
ejpam-4946	73	127	)	)	PUNCT
ejpam-4946	73	128	is	be	AUX
ejpam-4946	73	129	called	call	VERB
ejpam-4946	73	130	an	an	DET
ejpam-4946	73	131	independent	independent	ADJ
ejpam-4946	73	132	(	(	PUNCT
ejpam-4946	73	133	resp	resp	NOUN
ejpam-4946	73	134	.	.	PUNCT
ejpam-4946	74	1	hop	hop	PROPN
ejpam-4946	74	2	independent	independent	ADJ
ejpam-4946	74	3	)	)	PUNCT
ejpam-4946	74	4	if	if	SCONJ
ejpam-4946	74	5	for	for	ADP
ejpam-4946	74	6	every	every	DET
ejpam-4946	74	7	pair	pair	NOUN
ejpam-4946	74	8	of	of	ADP
ejpam-4946	74	9	distinct	distinct	ADJ
ejpam-4946	74	10	vertices	vertex	NOUN
ejpam-4946	74	11	x	x	X
ejpam-4946	74	12	,	,	PUNCT
ejpam-4946	74	13	y	y	PROPN
ejpam-4946	74	14	∈	∈	PROPN
ejpam-4946	74	15	i	i	PRON
ejpam-4946	74	16	,	,	PUNCT
ejpam-4946	74	17	dg(x	dg(x	X
ejpam-4946	74	18	,	,	PUNCT
ejpam-4946	74	19	y	y	NOUN
ejpam-4946	74	20	)	)	PUNCT
ejpam-4946	74	21	̸=	̸=	PROPN
ejpam-4946	74	22	1	1	NUM
ejpam-4946	74	23	(	(	PUNCT
ejpam-4946	74	24	resp	resp	NOUN
ejpam-4946	74	25	.	.	PUNCT
ejpam-4946	75	1	dg(x	dg(x	PROPN
ejpam-4946	75	2	,	,	PUNCT
ejpam-4946	75	3	y	y	NOUN
ejpam-4946	75	4	)	)	PUNCT
ejpam-4946	75	5	̸=	̸=	PROPN
ejpam-4946	75	6	2	2	NUM
ejpam-4946	75	7	)	)	PUNCT
ejpam-4946	75	8	.	.	PUNCT
ejpam-4946	76	1	the	the	DET
ejpam-4946	76	2	maximum	maximum	ADJ
ejpam-4946	76	3	cardinality	cardinality	NOUN
ejpam-4946	76	4	of	of	ADP
ejpam-4946	76	5	an	an	DET
ejpam-4946	76	6	independent	independent	ADJ
ejpam-4946	76	7	set	set	NOUN
ejpam-4946	76	8	(	(	PUNCT
ejpam-4946	76	9	resp	resp	NOUN
ejpam-4946	76	10	.	.	PUNCT
ejpam-4946	77	1	hop	hop	PROPN
ejpam-4946	77	2	independent	independent	ADJ
ejpam-4946	77	3	set	set	PROPN
ejpam-4946	77	4	)	)	PUNCT
ejpam-4946	77	5	in	in	ADP
ejpam-4946	77	6	g	g	NOUN
ejpam-4946	77	7	,	,	PUNCT
ejpam-4946	77	8	denoted	denote	VERB
ejpam-4946	77	9	by	by	ADP
ejpam-4946	77	10	α(g)(resp	α(g)(resp	PROPN
ejpam-4946	77	11	.	.	PUNCT
ejpam-4946	78	1	αh(g	αh(g	NOUN
ejpam-4946	78	2	)	)	PUNCT
ejpam-4946	79	1	)	)	PUNCT
ejpam-4946	79	2	,	,	PUNCT
ejpam-4946	79	3	is	be	AUX
ejpam-4946	79	4	called	call	VERB
ejpam-4946	79	5	the	the	DET
ejpam-4946	79	6	independence	independence	NOUN
ejpam-4946	79	7	(	(	PUNCT
ejpam-4946	79	8	resp	resp	NOUN
ejpam-4946	79	9	.	.	PUNCT
ejpam-4946	80	1	hop	hop	NOUN
ejpam-4946	80	2	independence	independence	NOUN
ejpam-4946	80	3	)	)	PUNCT
ejpam-4946	80	4	number	number	NOUN
ejpam-4946	80	5	of	of	ADP
ejpam-4946	80	6	g.	g.	PROPN
ejpam-4946	80	7	any	any	DET
ejpam-4946	80	8	independent	independent	ADJ
ejpam-4946	80	9	(	(	PUNCT
ejpam-4946	80	10	resp	resp	NOUN
ejpam-4946	80	11	.	.	PUNCT
ejpam-4946	81	1	hop	hop	PROPN
ejpam-4946	81	2	independent	independent	ADJ
ejpam-4946	81	3	)	)	PUNCT
ejpam-4946	81	4	set	set	VERB
ejpam-4946	81	5	i	i	PRON
ejpam-4946	81	6	with	with	ADP
ejpam-4946	81	7	cardinality	cardinality	NOUN
ejpam-4946	81	8	equal	equal	ADJ
ejpam-4946	81	9	to	to	ADP
ejpam-4946	81	10	α(g	α(g	NUM
ejpam-4946	81	11	)	)	PUNCT
ejpam-4946	81	12	(	(	PUNCT
ejpam-4946	81	13	resp	resp	NOUN
ejpam-4946	81	14	.	.	PUNCT
ejpam-4946	82	1	αh	αh	X
ejpam-4946	82	2	)	)	PUNCT
ejpam-4946	82	3	is	be	AUX
ejpam-4946	82	4	called	call	VERB
ejpam-4946	82	5	an	an	DET
ejpam-4946	82	6	α	α	NOUN
ejpam-4946	82	7	-	-	PUNCT
ejpam-4946	82	8	set	set	VERB
ejpam-4946	82	9	(	(	PUNCT
ejpam-4946	82	10	resp	resp	NOUN
ejpam-4946	82	11	.	.	PUNCT
ejpam-4946	83	1	αh	αh	X
ejpam-4946	83	2	-	-	PUNCT
ejpam-4946	83	3	set	set	NOUN
ejpam-4946	83	4	)	)	PUNCT
ejpam-4946	83	5	of	of	ADP
ejpam-4946	83	6	g.	g.	PROPN
ejpam-4946	83	7	3	3	NUM
ejpam-4946	83	8	.	.	PUNCT
ejpam-4946	84	1	results	result	NOUN
ejpam-4946	84	2	we	we	PRON
ejpam-4946	84	3	begin	begin	VERB
ejpam-4946	84	4	this	this	DET
ejpam-4946	84	5	section	section	NOUN
ejpam-4946	84	6	by	by	ADP
ejpam-4946	84	7	introducing	introduce	VERB
ejpam-4946	84	8	the	the	DET
ejpam-4946	84	9	concept	concept	NOUN
ejpam-4946	84	10	of	of	ADP
ejpam-4946	84	11	j2	j2	PROPN
ejpam-4946	84	12	-	-	PUNCT
ejpam-4946	84	13	independence	independence	NOUN
ejpam-4946	84	14	in	in	ADP
ejpam-4946	84	15	a	a	DET
ejpam-4946	84	16	graph	graph	NOUN
ejpam-4946	84	17	.	.	PUNCT
ejpam-4946	85	1	definition	definition	NOUN
ejpam-4946	85	2	1	1	NUM
ejpam-4946	85	3	.	.	PUNCT
ejpam-4946	86	1	let	let	VERB
ejpam-4946	86	2	g	g	PRON
ejpam-4946	86	3	be	be	AUX
ejpam-4946	86	4	a	a	DET
ejpam-4946	86	5	simple	simple	ADJ
ejpam-4946	86	6	graph	graph	NOUN
ejpam-4946	86	7	.	.	PUNCT
ejpam-4946	87	1	a	a	DET
ejpam-4946	87	2	subset	subset	NOUN
ejpam-4946	87	3	i	i	PRON
ejpam-4946	87	4	′	′	NUM
ejpam-4946	87	5	of	of	ADP
ejpam-4946	87	6	v	v	NOUN
ejpam-4946	87	7	(	(	PUNCT
ejpam-4946	87	8	g	g	NOUN
ejpam-4946	87	9	)	)	PUNCT
ejpam-4946	87	10	is	be	AUX
ejpam-4946	87	11	called	call	VERB
ejpam-4946	87	12	a	a	DET
ejpam-4946	87	13	j2	j2	PROPN
ejpam-4946	87	14	-	-	PUNCT
ejpam-4946	87	15	independent	independent	ADJ
ejpam-4946	87	16	a.	a.	NOUN
ejpam-4946	87	17	tapeing	tapeing	NOUN
ejpam-4946	87	18	et	et	PROPN
ejpam-4946	87	19	al	al	PROPN
ejpam-4946	87	20	.	.	PUNCT
ejpam-4946	87	21	/	/	SYM
ejpam-4946	87	22	eur	eur	PROPN
ejpam-4946	87	23	.	.	PUNCT
ejpam-4946	88	1	j.	j.	PROPN
ejpam-4946	88	2	pure	pure	PROPN
ejpam-4946	88	3	appl	appl	PROPN
ejpam-4946	88	4	.	.	PROPN
ejpam-4946	88	5	math	math	PROPN
ejpam-4946	88	6	,	,	PUNCT
ejpam-4946	88	7	17	17	NUM
ejpam-4946	88	8	(	(	PUNCT
ejpam-4946	88	9	1	1	NUM
ejpam-4946	88	10	)	)	PUNCT
ejpam-4946	88	11	(	(	PUNCT
ejpam-4946	88	12	2024	2024	NUM
ejpam-4946	88	13	)	)	PUNCT
ejpam-4946	88	14	,	,	PUNCT
ejpam-4946	88	15	124	124	NUM
ejpam-4946	88	16	-	-	SYM
ejpam-4946	88	17	134	134	NUM
ejpam-4946	88	18	127	127	NUM
ejpam-4946	88	19	in	in	ADP
ejpam-4946	88	20	g	g	PROPN
ejpam-4946	88	21	if	if	SCONJ
ejpam-4946	88	22	for	for	ADP
ejpam-4946	88	23	every	every	DET
ejpam-4946	88	24	pair	pair	NOUN
ejpam-4946	88	25	of	of	ADP
ejpam-4946	88	26	distinct	distinct	ADJ
ejpam-4946	88	27	vertices	vertex	NOUN
ejpam-4946	88	28	a	a	DET
ejpam-4946	88	29	,	,	PUNCT
ejpam-4946	88	30	b	b	X
ejpam-4946	88	31	∈	∈	PROPN
ejpam-4946	88	32	i	i	PRON
ejpam-4946	88	33	′	′	VERB
ejpam-4946	88	34	,	,	PUNCT
ejpam-4946	88	35	dg(a	dg(a	X
ejpam-4946	88	36	,	,	PUNCT
ejpam-4946	88	37	b	b	X
ejpam-4946	88	38	)	)	PUNCT
ejpam-4946	88	39	̸=	̸=	PROPN
ejpam-4946	88	40	1	1	NUM
ejpam-4946	88	41	,	,	PUNCT
ejpam-4946	88	42	n2	n2	ADJ
ejpam-4946	88	43	g[a]\n2	g[a]\n2	NOUN
ejpam-4946	88	44	g[b	g[b	NOUN
ejpam-4946	88	45	]	]	PUNCT
ejpam-4946	88	46	̸=	̸=	PROPN
ejpam-4946	88	47	∅	∅	NOUN
ejpam-4946	88	48	and	and	CCONJ
ejpam-4946	88	49	n2	n2	ADJ
ejpam-4946	88	50	g[b]\n2	g[b]\n2	VERB
ejpam-4946	88	51	g[a	g[a	X
ejpam-4946	88	52	]	]	PUNCT
ejpam-4946	88	53	̸=	̸=	PROPN
ejpam-4946	88	54	∅.	∅.	ADP
ejpam-4946	88	55	the	the	DET
ejpam-4946	88	56	maximum	maximum	ADJ
ejpam-4946	88	57	cardinality	cardinality	NOUN
ejpam-4946	88	58	among	among	ADP
ejpam-4946	88	59	all	all	DET
ejpam-4946	88	60	j2	j2	PROPN
ejpam-4946	88	61	-	-	PUNCT
ejpam-4946	88	62	independent	independent	ADJ
ejpam-4946	88	63	sets	set	NOUN
ejpam-4946	88	64	in	in	ADP
ejpam-4946	88	65	g	g	NOUN
ejpam-4946	88	66	,	,	PUNCT
ejpam-4946	88	67	denoted	denote	VERB
ejpam-4946	88	68	by	by	ADP
ejpam-4946	88	69	αj2(g	αj2(g	PROPN
ejpam-4946	88	70	)	)	PUNCT
ejpam-4946	88	71	,	,	PUNCT
ejpam-4946	88	72	is	be	AUX
ejpam-4946	88	73	called	call	VERB
ejpam-4946	88	74	the	the	DET
ejpam-4946	88	75	j2	j2	PROPN
ejpam-4946	88	76	-	-	PUNCT
ejpam-4946	88	77	independence	independence	NOUN
ejpam-4946	88	78	number	number	NOUN
ejpam-4946	88	79	of	of	ADP
ejpam-4946	88	80	g.	g.	PROPN
ejpam-4946	88	81	any	any	DET
ejpam-4946	88	82	j2	j2	PROPN
ejpam-4946	88	83	-	-	PUNCT
ejpam-4946	88	84	independent	independent	ADJ
ejpam-4946	88	85	set	set	NOUN
ejpam-4946	88	86	i	i	PRON
ejpam-4946	88	87	′	′	VERB
ejpam-4946	89	1	satisfying	satisfy	VERB
ejpam-4946	89	2	|i	|i	NOUN
ejpam-4946	89	3	′|	′|	NUM
ejpam-4946	89	4	=	=	SYM
ejpam-4946	89	5	αj2(g	αj2(g	VERB
ejpam-4946	89	6	)	)	PUNCT
ejpam-4946	89	7	is	be	AUX
ejpam-4946	89	8	called	call	VERB
ejpam-4946	89	9	the	the	DET
ejpam-4946	89	10	maximum	maximum	ADJ
ejpam-4946	89	11	j2	j2	NOUN
ejpam-4946	89	12	-	-	PUNCT
ejpam-4946	89	13	independent	independent	ADJ
ejpam-4946	89	14	set	set	NOUN
ejpam-4946	89	15	of	of	ADP
ejpam-4946	89	16	g	g	NOUN
ejpam-4946	89	17	or	or	CCONJ
ejpam-4946	89	18	an	an	DET
ejpam-4946	89	19	αj2	αj2	NOUN
ejpam-4946	89	20	-	-	PUNCT
ejpam-4946	89	21	set	set	NOUN
ejpam-4946	89	22	of	of	ADP
ejpam-4946	89	23	g.	g.	PROPN
ejpam-4946	89	24	example	example	NOUN
ejpam-4946	89	25	1	1	X
ejpam-4946	89	26	.	.	X
ejpam-4946	89	27	consider	consider	VERB
ejpam-4946	89	28	the	the	DET
ejpam-4946	89	29	graph	graph	NOUN
ejpam-4946	89	30	k	k	X
ejpam-4946	89	31	in	in	ADP
ejpam-4946	89	32	figure	figure	NOUN
ejpam-4946	89	33	1	1	NUM
ejpam-4946	89	34	.	.	PUNCT
ejpam-4946	90	1	let	let	VERB
ejpam-4946	90	2	i	i	PRON
ejpam-4946	90	3	=	=	PUNCT
ejpam-4946	90	4	{	{	PUNCT
ejpam-4946	90	5	a	a	X
ejpam-4946	90	6	,	,	PUNCT
ejpam-4946	90	7	d	d	NOUN
ejpam-4946	90	8	,	,	PUNCT
ejpam-4946	90	9	g	g	PROPN
ejpam-4946	90	10	,	,	PUNCT
ejpam-4946	90	11	h	h	NOUN
ejpam-4946	90	12	}	}	PUNCT
ejpam-4946	90	13	.	.	PUNCT
ejpam-4946	91	1	clearly	clearly	ADV
ejpam-4946	91	2	i	i	PRON
ejpam-4946	91	3	is	be	AUX
ejpam-4946	91	4	a	a	DET
ejpam-4946	91	5	maximum	maximum	ADJ
ejpam-4946	91	6	independent	independent	ADJ
ejpam-4946	91	7	set	set	NOUN
ejpam-4946	91	8	of	of	ADP
ejpam-4946	91	9	k.	k.	PROPN
ejpam-4946	91	10	notice	notice	VERB
ejpam-4946	92	1	that	that	SCONJ
ejpam-4946	92	2	n2	n2	PROPN
ejpam-4946	92	3	k	k	PROPN
ejpam-4946	93	1	[	[	X
ejpam-4946	93	2	a	a	X
ejpam-4946	93	3	]	]	X
ejpam-4946	93	4	=	=	X
ejpam-4946	93	5	{	{	PUNCT
ejpam-4946	93	6	a	a	X
ejpam-4946	93	7	,	,	PUNCT
ejpam-4946	93	8	d	d	NOUN
ejpam-4946	93	9	,	,	PUNCT
ejpam-4946	93	10	e	e	NOUN
ejpam-4946	93	11	}	}	PUNCT
ejpam-4946	93	12	,	,	PUNCT
ejpam-4946	93	13	n2	n2	PROPN
ejpam-4946	93	14	k	k	PROPN
ejpam-4946	94	1	[	[	X
ejpam-4946	94	2	d	d	X
ejpam-4946	94	3	]	]	X
ejpam-4946	94	4	=	=	X
ejpam-4946	94	5	{	{	PUNCT
ejpam-4946	94	6	a	a	X
ejpam-4946	94	7	,	,	PUNCT
ejpam-4946	94	8	d	d	NOUN
ejpam-4946	94	9	,	,	PUNCT
ejpam-4946	94	10	c	c	X
ejpam-4946	94	11	,	,	PUNCT
ejpam-4946	94	12	f	f	X
ejpam-4946	94	13	,	,	PUNCT
ejpam-4946	94	14	g	g	NOUN
ejpam-4946	94	15	}	}	PUNCT
ejpam-4946	94	16	,	,	PUNCT
ejpam-4946	95	1	n2	n2	PROPN
ejpam-4946	95	2	k	k	PROPN
ejpam-4946	96	1	[	[	X
ejpam-4946	96	2	g	g	X
ejpam-4946	96	3	]	]	X
ejpam-4946	96	4	=	=	X
ejpam-4946	96	5	{	{	PUNCT
ejpam-4946	96	6	c	c	NOUN
ejpam-4946	96	7	,	,	PUNCT
ejpam-4946	96	8	d	d	NOUN
ejpam-4946	96	9	,	,	PUNCT
ejpam-4946	96	10	g	g	PROPN
ejpam-4946	96	11	,	,	PUNCT
ejpam-4946	96	12	h	h	NOUN
ejpam-4946	96	13	}	}	PUNCT
ejpam-4946	96	14	,	,	PUNCT
ejpam-4946	96	15	and	and	CCONJ
ejpam-4946	96	16	n2	n2	PROPN
ejpam-4946	96	17	k	k	PROPN
ejpam-4946	97	1	[	[	X
ejpam-4946	97	2	h	h	X
ejpam-4946	97	3	]	]	X
ejpam-4946	97	4	=	=	X
ejpam-4946	97	5	{	{	PUNCT
ejpam-4946	97	6	e	e	NOUN
ejpam-4946	97	7	,	,	PUNCT
ejpam-4946	97	8	g	g	PROPN
ejpam-4946	97	9	,	,	PUNCT
ejpam-4946	97	10	h	h	NOUN
ejpam-4946	97	11	}	}	PUNCT
ejpam-4946	97	12	.	.	PUNCT
ejpam-4946	98	1	thus	thus	ADV
ejpam-4946	98	2	,	,	PUNCT
ejpam-4946	98	3	n2	n2	PROPN
ejpam-4946	98	4	k	k	PROPN
ejpam-4946	98	5	[	[	X
ejpam-4946	98	6	a]\n2	a]\n2	X
ejpam-4946	98	7	k	k	X
ejpam-4946	99	1	[	[	X
ejpam-4946	99	2	d	d	X
ejpam-4946	99	3	]	]	X
ejpam-4946	99	4	=	=	PUNCT
ejpam-4946	99	5	{	{	PUNCT
ejpam-4946	99	6	e	e	NOUN
ejpam-4946	99	7	}	}	PUNCT
ejpam-4946	99	8	,	,	PUNCT
ejpam-4946	99	9	n2	n2	PROPN
ejpam-4946	99	10	k	k	PROPN
ejpam-4946	100	1	[	[	X
ejpam-4946	100	2	a]\n2	a]\n2	PROPN
ejpam-4946	100	3	k	k	X
ejpam-4946	101	1	[	[	X
ejpam-4946	101	2	g	g	X
ejpam-4946	101	3	]	]	X
ejpam-4946	101	4	=	=	X
ejpam-4946	101	5	{	{	PUNCT
ejpam-4946	101	6	a	a	X
ejpam-4946	101	7	,	,	PUNCT
ejpam-4946	101	8	e	e	NOUN
ejpam-4946	101	9	}	}	PUNCT
ejpam-4946	101	10	,	,	PUNCT
ejpam-4946	101	11	n2	n2	PROPN
ejpam-4946	101	12	k	k	PROPN
ejpam-4946	102	1	[	[	X
ejpam-4946	102	2	a]\n2	a]\n2	PROPN
ejpam-4946	102	3	k	k	X
ejpam-4946	103	1	[	[	X
ejpam-4946	103	2	h	h	X
ejpam-4946	103	3	]	]	X
ejpam-4946	103	4	=	=	X
ejpam-4946	103	5	{	{	PUNCT
ejpam-4946	103	6	a	a	X
ejpam-4946	103	7	,	,	PUNCT
ejpam-4946	103	8	d	d	NOUN
ejpam-4946	103	9	}	}	PUNCT
ejpam-4946	103	10	,	,	PUNCT
ejpam-4946	103	11	n2	n2	PROPN
ejpam-4946	103	12	k	k	PROPN
ejpam-4946	104	1	[	[	X
ejpam-4946	104	2	d]\n2	d]\n2	X
ejpam-4946	104	3	k	k	X
ejpam-4946	105	1	[	[	X
ejpam-4946	105	2	a	a	X
ejpam-4946	105	3	]	]	X
ejpam-4946	105	4	=	=	X
ejpam-4946	105	5	{	{	PUNCT
ejpam-4946	105	6	c	c	NOUN
ejpam-4946	105	7	,	,	PUNCT
ejpam-4946	105	8	f	f	X
ejpam-4946	105	9	,	,	PUNCT
ejpam-4946	105	10	g	g	NOUN
ejpam-4946	105	11	}	}	PUNCT
ejpam-4946	105	12	,	,	PUNCT
ejpam-4946	105	13	n2	n2	PROPN
ejpam-4946	105	14	k	k	PROPN
ejpam-4946	106	1	[	[	X
ejpam-4946	106	2	d]\n2	d]\n2	PROPN
ejpam-4946	106	3	k	k	X
ejpam-4946	106	4	[	[	X
ejpam-4946	106	5	g	g	X
ejpam-4946	106	6	]	]	X
ejpam-4946	106	7	=	=	X
ejpam-4946	106	8	{	{	PUNCT
ejpam-4946	106	9	a	a	X
ejpam-4946	106	10	,	,	PUNCT
ejpam-4946	106	11	f	f	NOUN
ejpam-4946	106	12	}	}	PUNCT
ejpam-4946	106	13	,	,	PUNCT
ejpam-4946	106	14	n2	n2	PROPN
ejpam-4946	106	15	k	k	PROPN
ejpam-4946	107	1	[	[	X
ejpam-4946	107	2	d]\n2	d]\n2	PROPN
ejpam-4946	107	3	k	k	X
ejpam-4946	108	1	[	[	X
ejpam-4946	108	2	h	h	X
ejpam-4946	108	3	]	]	X
ejpam-4946	108	4	=	=	X
ejpam-4946	108	5	{	{	PUNCT
ejpam-4946	108	6	a	a	X
ejpam-4946	108	7	,	,	PUNCT
ejpam-4946	108	8	c	c	NOUN
ejpam-4946	108	9	,	,	PUNCT
ejpam-4946	108	10	d	d	NOUN
ejpam-4946	108	11	,	,	PUNCT
ejpam-4946	108	12	f	f	NOUN
ejpam-4946	108	13	}	}	PUNCT
ejpam-4946	108	14	,	,	PUNCT
ejpam-4946	108	15	n2	n2	PROPN
ejpam-4946	108	16	k	k	PROPN
ejpam-4946	109	1	[	[	X
ejpam-4946	109	2	g]\n2	g]\n2	X
ejpam-4946	109	3	k	k	X
ejpam-4946	110	1	[	[	X
ejpam-4946	110	2	a	a	X
ejpam-4946	110	3	]	]	X
ejpam-4946	110	4	=	=	X
ejpam-4946	110	5	{	{	PUNCT
ejpam-4946	110	6	c	c	NOUN
ejpam-4946	110	7	,	,	PUNCT
ejpam-4946	110	8	g	g	PROPN
ejpam-4946	110	9	,	,	PUNCT
ejpam-4946	110	10	h	h	NOUN
ejpam-4946	110	11	}	}	PUNCT
ejpam-4946	110	12	,	,	PUNCT
ejpam-4946	110	13	n2	n2	PROPN
ejpam-4946	110	14	k	k	PROPN
ejpam-4946	111	1	[	[	X
ejpam-4946	111	2	g]\n2	g]\n2	X
ejpam-4946	111	3	k	k	X
ejpam-4946	112	1	[	[	X
ejpam-4946	112	2	d	d	X
ejpam-4946	112	3	]	]	X
ejpam-4946	112	4	=	=	PUNCT
ejpam-4946	112	5	{	{	PUNCT
ejpam-4946	112	6	h	h	NOUN
ejpam-4946	112	7	}	}	PUNCT
ejpam-4946	112	8	,	,	PUNCT
ejpam-4946	112	9	n2	n2	PROPN
ejpam-4946	112	10	k	k	PROPN
ejpam-4946	113	1	[	[	X
ejpam-4946	113	2	g]\n2	g]\n2	X
ejpam-4946	113	3	k	k	X
ejpam-4946	114	1	[	[	X
ejpam-4946	114	2	h	h	X
ejpam-4946	114	3	]	]	X
ejpam-4946	114	4	=	=	X
ejpam-4946	114	5	{	{	PUNCT
ejpam-4946	114	6	c	c	NOUN
ejpam-4946	114	7	,	,	PUNCT
ejpam-4946	114	8	d	d	NOUN
ejpam-4946	114	9	}	}	PUNCT
ejpam-4946	114	10	,	,	PUNCT
ejpam-4946	114	11	n2	n2	PROPN
ejpam-4946	114	12	k	k	PROPN
ejpam-4946	115	1	[	[	X
ejpam-4946	115	2	h]\n2	h]\n2	X
ejpam-4946	115	3	k	k	PROPN
ejpam-4946	116	1	[	[	X
ejpam-4946	116	2	a	a	X
ejpam-4946	116	3	]	]	X
ejpam-4946	116	4	=	=	SYM
ejpam-4946	116	5	{	{	PUNCT
ejpam-4946	116	6	g	g	PROPN
ejpam-4946	116	7	,	,	PUNCT
ejpam-4946	116	8	h	h	NOUN
ejpam-4946	116	9	}	}	PUNCT
ejpam-4946	116	10	,	,	PUNCT
ejpam-4946	116	11	n2	n2	PROPN
ejpam-4946	116	12	k	k	PROPN
ejpam-4946	117	1	[	[	X
ejpam-4946	117	2	h]\n2	h]\n2	X
ejpam-4946	117	3	k	k	X
ejpam-4946	118	1	[	[	X
ejpam-4946	118	2	d	d	X
ejpam-4946	118	3	]	]	X
ejpam-4946	118	4	=	=	PUNCT
ejpam-4946	118	5	{	{	PUNCT
ejpam-4946	118	6	e	e	NOUN
ejpam-4946	118	7	,	,	PUNCT
ejpam-4946	118	8	h	h	NOUN
ejpam-4946	118	9	}	}	PUNCT
ejpam-4946	118	10	,	,	PUNCT
ejpam-4946	118	11	n2	n2	PROPN
ejpam-4946	118	12	k	k	PROPN
ejpam-4946	119	1	[	[	X
ejpam-4946	119	2	h]\n2	h]\n2	X
ejpam-4946	119	3	k	k	X
ejpam-4946	120	1	[	[	X
ejpam-4946	120	2	g	g	X
ejpam-4946	120	3	]	]	X
ejpam-4946	120	4	=	=	PUNCT
ejpam-4946	120	5	{	{	PUNCT
ejpam-4946	120	6	e	e	NOUN
ejpam-4946	120	7	}	}	PUNCT
ejpam-4946	120	8	.	.	PUNCT
ejpam-4946	121	1	therefore	therefore	ADV
ejpam-4946	121	2	,	,	PUNCT
ejpam-4946	121	3	i	i	PRON
ejpam-4946	121	4	is	be	AUX
ejpam-4946	121	5	a	a	DET
ejpam-4946	121	6	maximum	maximum	ADJ
ejpam-4946	121	7	j2	j2	NOUN
ejpam-4946	121	8	-	-	PUNCT
ejpam-4946	121	9	independent	independent	ADJ
ejpam-4946	121	10	set	set	NOUN
ejpam-4946	121	11	of	of	ADP
ejpam-4946	121	12	k	k	NOUN
ejpam-4946	121	13	,	,	PUNCT
ejpam-4946	121	14	and	and	CCONJ
ejpam-4946	121	15	so	so	ADV
ejpam-4946	121	16	αj2(k	αj2(k	NOUN
ejpam-4946	121	17	)	)	PUNCT
ejpam-4946	121	18	=	=	PUNCT
ejpam-4946	121	19	4	4	NUM
ejpam-4946	121	20	.	.	X
ejpam-4946	121	21	b	b	X
ejpam-4946	121	22	d	d	NOUN
ejpam-4946	121	23	e	e	X
ejpam-4946	121	24	f	f	PROPN
ejpam-4946	121	25	g	g	PROPN
ejpam-4946	121	26	h	h	NOUN
ejpam-4946	121	27	ca	can	AUX
ejpam-4946	121	28	k	k	NOUN
ejpam-4946	121	29	:	:	PUNCT
ejpam-4946	121	30	figure	figure	VERB
ejpam-4946	121	31	1	1	NUM
ejpam-4946	121	32	:	:	PUNCT
ejpam-4946	121	33	graph	graph	VERB
ejpam-4946	121	34	k	k	PROPN
ejpam-4946	121	35	with	with	ADP
ejpam-4946	121	36	αj2(k	αj2(k	NOUN
ejpam-4946	121	37	)	)	PUNCT
ejpam-4946	121	38	=	=	SYM
ejpam-4946	121	39	4	4	NUM
ejpam-4946	121	40	remark	remark	NOUN
ejpam-4946	121	41	1	1	NUM
ejpam-4946	121	42	.	.	PUNCT
ejpam-4946	122	1	let	let	VERB
ejpam-4946	122	2	g	g	PRON
ejpam-4946	122	3	be	be	AUX
ejpam-4946	122	4	a	a	DET
ejpam-4946	122	5	graph	graph	NOUN
ejpam-4946	122	6	.	.	PUNCT
ejpam-4946	123	1	then	then	ADV
ejpam-4946	123	2	(	(	PUNCT
ejpam-4946	123	3	i	i	NOUN
ejpam-4946	123	4	)	)	PUNCT
ejpam-4946	123	5	any	any	DET
ejpam-4946	123	6	singleton	singleton	NOUN
ejpam-4946	123	7	set	set	NOUN
ejpam-4946	123	8	{	{	PUNCT
ejpam-4946	123	9	x	x	NOUN
ejpam-4946	123	10	}	}	PUNCT
ejpam-4946	123	11	,	,	PUNCT
ejpam-4946	123	12	where	where	SCONJ
ejpam-4946	123	13	x	x	X
ejpam-4946	123	14	∈	∈	PROPN
ejpam-4946	123	15	v	v	X
ejpam-4946	123	16	(	(	PUNCT
ejpam-4946	123	17	g	g	NOUN
ejpam-4946	123	18	)	)	PUNCT
ejpam-4946	123	19	,	,	PUNCT
ejpam-4946	123	20	is	be	AUX
ejpam-4946	123	21	a	a	DET
ejpam-4946	123	22	j2	j2	PROPN
ejpam-4946	123	23	-	-	PUNCT
ejpam-4946	123	24	indeppendent	indeppendent	PROPN
ejpam-4946	123	25	set	set	NOUN
ejpam-4946	123	26	of	of	ADP
ejpam-4946	123	27	g	g	NOUN
ejpam-4946	123	28	;	;	PUNCT
ejpam-4946	123	29	and	and	CCONJ
ejpam-4946	123	30	(	(	PUNCT
ejpam-4946	123	31	ii	ii	NOUN
ejpam-4946	123	32	)	)	PUNCT
ejpam-4946	123	33	an	an	DET
ejpam-4946	123	34	independent	independent	ADJ
ejpam-4946	123	35	set	set	NOUN
ejpam-4946	123	36	i	i	PRON
ejpam-4946	123	37	may	may	AUX
ejpam-4946	123	38	not	not	PART
ejpam-4946	123	39	be	be	AUX
ejpam-4946	123	40	a	a	DET
ejpam-4946	123	41	j2	j2	NOUN
ejpam-4946	123	42	-	-	PUNCT
ejpam-4946	123	43	independent	independent	NOUN
ejpam-4946	123	44	in	in	ADP
ejpam-4946	123	45	g.	g.	PROPN
ejpam-4946	123	46	proposition	proposition	NOUN
ejpam-4946	123	47	1	1	X
ejpam-4946	123	48	.	.	PUNCT
ejpam-4946	124	1	let	let	VERB
ejpam-4946	124	2	g	g	PRON
ejpam-4946	124	3	be	be	AUX
ejpam-4946	124	4	a	a	DET
ejpam-4946	124	5	graph	graph	NOUN
ejpam-4946	124	6	.	.	PUNCT
ejpam-4946	125	1	then	then	ADV
ejpam-4946	125	2	(	(	PUNCT
ejpam-4946	125	3	i	i	NOUN
ejpam-4946	125	4	)	)	PUNCT
ejpam-4946	125	5	αj2(g	αj2(g	PROPN
ejpam-4946	125	6	)	)	PUNCT
ejpam-4946	125	7	≤	≤	NOUN
ejpam-4946	125	8	α(g	α(g	NUM
ejpam-4946	125	9	)	)	PUNCT
ejpam-4946	125	10	;	;	PUNCT
ejpam-4946	125	11	and	and	CCONJ
ejpam-4946	125	12	(	(	PUNCT
ejpam-4946	125	13	ii	ii	NOUN
ejpam-4946	125	14	)	)	PUNCT
ejpam-4946	125	15	1	1	NUM
ejpam-4946	125	16	≤	≤	NOUN
ejpam-4946	125	17	αj2(g	αj2(g	NOUN
ejpam-4946	125	18	)	)	PUNCT
ejpam-4946	125	19	≤	≤	NOUN
ejpam-4946	125	20	|v	|v	X
ejpam-4946	125	21	(	(	PUNCT
ejpam-4946	125	22	g)|	g)|	NOUN
ejpam-4946	125	23	.	.	PUNCT
ejpam-4946	126	1	proof	proof	NOUN
ejpam-4946	126	2	.	.	PUNCT
ejpam-4946	127	1	(	(	PUNCT
ejpam-4946	127	2	i	i	NOUN
ejpam-4946	127	3	)	)	PUNCT
ejpam-4946	127	4	let	let	VERB
ejpam-4946	127	5	g	g	NOUN
ejpam-4946	127	6	be	be	AUX
ejpam-4946	127	7	a	a	DET
ejpam-4946	127	8	graph	graph	NOUN
ejpam-4946	127	9	and	and	CCONJ
ejpam-4946	127	10	let	let	VERB
ejpam-4946	127	11	i	i	PRON
ejpam-4946	127	12	be	be	AUX
ejpam-4946	127	13	a	a	DET
ejpam-4946	127	14	maximum	maximum	ADJ
ejpam-4946	127	15	j2	j2	NOUN
ejpam-4946	127	16	-	-	PUNCT
ejpam-4946	127	17	independent	independent	ADJ
ejpam-4946	127	18	set	set	NOUN
ejpam-4946	127	19	of	of	ADP
ejpam-4946	127	20	g.	g.	PROPN
ejpam-4946	128	1	then	then	ADV
ejpam-4946	128	2	i	i	PRON
ejpam-4946	128	3	is	be	AUX
ejpam-4946	128	4	an	an	DET
ejpam-4946	128	5	independent	independent	ADJ
ejpam-4946	128	6	set	set	NOUN
ejpam-4946	128	7	in	in	ADP
ejpam-4946	128	8	g.	g.	PROPN
ejpam-4946	128	9	since	since	SCONJ
ejpam-4946	128	10	αg	αg	NOUN
ejpam-4946	128	11	is	be	AUX
ejpam-4946	128	12	the	the	DET
ejpam-4946	128	13	maximum	maximum	ADJ
ejpam-4946	128	14	cardinality	cardinality	NOUN
ejpam-4946	128	15	of	of	ADP
ejpam-4946	128	16	an	an	DET
ejpam-4946	128	17	independent	independent	ADJ
ejpam-4946	128	18	set	set	NOUN
ejpam-4946	128	19	in	in	ADP
ejpam-4946	128	20	g	g	NOUN
ejpam-4946	128	21	,	,	PUNCT
ejpam-4946	128	22	it	it	PRON
ejpam-4946	128	23	follows	follow	VERB
ejpam-4946	128	24	that	that	SCONJ
ejpam-4946	128	25	αj2(g	αj2(g	NOUN
ejpam-4946	128	26	)	)	PUNCT
ejpam-4946	128	27	=	=	PRON
ejpam-4946	128	28	|i|	|i|	VERB
ejpam-4946	128	29	≤	≤	NOUN
ejpam-4946	128	30	α(g	α(g	NUM
ejpam-4946	128	31	)	)	PUNCT
ejpam-4946	128	32	.	.	PUNCT
ejpam-4946	129	1	(	(	PUNCT
ejpam-4946	129	2	ii	ii	NOUN
ejpam-4946	129	3	)	)	PUNCT
ejpam-4946	129	4	since	since	SCONJ
ejpam-4946	129	5	every	every	DET
ejpam-4946	129	6	singleton	singleton	NOUN
ejpam-4946	129	7	set	set	NOUN
ejpam-4946	129	8	{	{	PUNCT
ejpam-4946	129	9	x	x	NOUN
ejpam-4946	129	10	}	}	PUNCT
ejpam-4946	129	11	,	,	PUNCT
ejpam-4946	129	12	where	where	SCONJ
ejpam-4946	129	13	x	x	X
ejpam-4946	129	14	∈	∈	PROPN
ejpam-4946	129	15	v	v	X
ejpam-4946	129	16	(	(	PUNCT
ejpam-4946	129	17	g	g	NOUN
ejpam-4946	129	18	)	)	PUNCT
ejpam-4946	129	19	,	,	PUNCT
ejpam-4946	129	20	is	be	AUX
ejpam-4946	129	21	a	a	DET
ejpam-4946	129	22	j2	j2	NOUN
ejpam-4946	129	23	-	-	PUNCT
ejpam-4946	129	24	independent	independent	NOUN
ejpam-4946	129	25	,	,	PUNCT
ejpam-4946	129	26	we	we	PRON
ejpam-4946	129	27	have	have	VERB
ejpam-4946	129	28	αj2(g	αj2(g	VERB
ejpam-4946	129	29	)	)	PUNCT
ejpam-4946	129	30	≥	≥	NOUN
ejpam-4946	129	31	1	1	NUM
ejpam-4946	129	32	.	.	PUNCT
ejpam-4946	130	1	morever	morever	PROPN
ejpam-4946	130	2	,	,	PUNCT
ejpam-4946	130	3	since	since	SCONJ
ejpam-4946	130	4	any	any	DET
ejpam-4946	130	5	j2	j2	NOUN
ejpam-4946	130	6	-	-	PUNCT
ejpam-4946	130	7	independent	independent	ADJ
ejpam-4946	130	8	set	set	NOUN
ejpam-4946	130	9	i	i	PRON
ejpam-4946	130	10	of	of	ADP
ejpam-4946	130	11	g	g	PROPN
ejpam-4946	130	12	is	be	AUX
ejpam-4946	130	13	always	always	ADV
ejpam-4946	130	14	a	a	DET
ejpam-4946	130	15	subset	subset	NOUN
ejpam-4946	130	16	of	of	ADP
ejpam-4946	130	17	v	v	NOUN
ejpam-4946	130	18	(	(	PUNCT
ejpam-4946	130	19	g	g	NOUN
ejpam-4946	130	20	)	)	PUNCT
ejpam-4946	130	21	,	,	PUNCT
ejpam-4946	130	22	it	it	PRON
ejpam-4946	130	23	follows	follow	VERB
ejpam-4946	130	24	that	that	SCONJ
ejpam-4946	130	25	αj2(g	αj2(g	NOUN
ejpam-4946	130	26	)	)	PUNCT
ejpam-4946	130	27	≤	≤	NOUN
ejpam-4946	130	28	|v	|v	X
ejpam-4946	130	29	(	(	PUNCT
ejpam-4946	130	30	g)|	g)|	NOUN
ejpam-4946	130	31	.	.	PUNCT
ejpam-4946	131	1	therefore	therefore	ADV
ejpam-4946	131	2	,	,	PUNCT
ejpam-4946	131	3	1	1	NUM
ejpam-4946	131	4	≤	≤	NOUN
ejpam-4946	131	5	αj2(g	αj2(g	NUM
ejpam-4946	131	6	)	)	PUNCT
ejpam-4946	131	7	≤	≤	NOUN
ejpam-4946	131	8	|v	|v	X
ejpam-4946	131	9	(	(	PUNCT
ejpam-4946	131	10	g)|	g)|	NOUN
ejpam-4946	131	11	.	.	PUNCT
ejpam-4946	132	1	a.	a.	NOUN
ejpam-4946	132	2	tapeing	tapeing	NOUN
ejpam-4946	132	3	et	et	PROPN
ejpam-4946	132	4	al	al	PROPN
ejpam-4946	132	5	.	.	PUNCT
ejpam-4946	132	6	/	/	SYM
ejpam-4946	132	7	eur	eur	PROPN
ejpam-4946	132	8	.	.	PUNCT
ejpam-4946	133	1	j.	j.	PROPN
ejpam-4946	133	2	pure	pure	PROPN
ejpam-4946	133	3	appl	appl	PROPN
ejpam-4946	133	4	.	.	PROPN
ejpam-4946	133	5	math	math	PROPN
ejpam-4946	133	6	,	,	PUNCT
ejpam-4946	133	7	17	17	NUM
ejpam-4946	133	8	(	(	PUNCT
ejpam-4946	133	9	1	1	NUM
ejpam-4946	133	10	)	)	PUNCT
ejpam-4946	133	11	(	(	PUNCT
ejpam-4946	133	12	2024	2024	NUM
ejpam-4946	133	13	)	)	PUNCT
ejpam-4946	133	14	,	,	PUNCT
ejpam-4946	133	15	124	124	NUM
ejpam-4946	133	16	-	-	SYM
ejpam-4946	133	17	134	134	NUM
ejpam-4946	133	18	128	128	NUM
ejpam-4946	133	19	remark	remark	NOUN
ejpam-4946	133	20	2	2	NUM
ejpam-4946	133	21	.	.	PUNCT
ejpam-4946	134	1	let	let	VERB
ejpam-4946	134	2	g	g	PRON
ejpam-4946	134	3	be	be	AUX
ejpam-4946	134	4	a	a	DET
ejpam-4946	134	5	graph	graph	NOUN
ejpam-4946	134	6	.	.	PUNCT
ejpam-4946	135	1	then	then	ADV
ejpam-4946	135	2	the	the	DET
ejpam-4946	135	3	difference	difference	NOUN
ejpam-4946	135	4	α(g)−αj2(g	α(g)−αj2(g	VERB
ejpam-4946	135	5	)	)	PUNCT
ejpam-4946	135	6	can	can	AUX
ejpam-4946	135	7	be	be	AUX
ejpam-4946	135	8	arbitrarily	arbitrarily	ADV
ejpam-4946	135	9	large	large	ADJ
ejpam-4946	135	10	.	.	PUNCT
ejpam-4946	136	1	to	to	PART
ejpam-4946	136	2	see	see	VERB
ejpam-4946	136	3	this	this	PRON
ejpam-4946	136	4	,	,	PUNCT
ejpam-4946	136	5	let	let	VERB
ejpam-4946	136	6	m	m	PRON
ejpam-4946	136	7	be	be	AUX
ejpam-4946	136	8	any	any	DET
ejpam-4946	136	9	positive	positive	ADJ
ejpam-4946	136	10	integer	integer	NOUN
ejpam-4946	136	11	and	and	CCONJ
ejpam-4946	136	12	consider	consider	VERB
ejpam-4946	136	13	the	the	DET
ejpam-4946	136	14	graph	graph	NOUN
ejpam-4946	136	15	g	g	NOUN
ejpam-4946	136	16	in	in	ADP
ejpam-4946	136	17	figure	figure	NOUN
ejpam-4946	136	18	2	2	NUM
ejpam-4946	136	19	.	.	PUNCT
ejpam-4946	137	1	let	let	VERB
ejpam-4946	137	2	i	i	PRON
ejpam-4946	137	3	=	=	SYM
ejpam-4946	137	4	{	{	PUNCT
ejpam-4946	137	5	v1	v1	PROPN
ejpam-4946	137	6	,	,	PUNCT
ejpam-4946	137	7	v2	v2	PROPN
ejpam-4946	137	8	,	,	PUNCT
ejpam-4946	137	9	.	.	PUNCT
ejpam-4946	137	10	.	.	PUNCT
ejpam-4946	138	1	.	.	PUNCT
ejpam-4946	139	1	,	,	PUNCT
ejpam-4946	139	2	vm+1	vm+1	NOUN
ejpam-4946	139	3	}	}	PUNCT
ejpam-4946	139	4	and	and	CCONJ
ejpam-4946	139	5	i	i	PRON
ejpam-4946	139	6	′	′	VERB
ejpam-4946	139	7	=	=	PUNCT
ejpam-4946	139	8	{	{	PUNCT
ejpam-4946	139	9	u	u	NOUN
ejpam-4946	139	10	}	}	PUNCT
ejpam-4946	139	11	.	.	PUNCT
ejpam-4946	140	1	then	then	ADV
ejpam-4946	140	2	i	i	PRON
ejpam-4946	140	3	is	be	AUX
ejpam-4946	140	4	a	a	DET
ejpam-4946	140	5	maximum	maximum	ADJ
ejpam-4946	140	6	independent	independent	ADJ
ejpam-4946	140	7	set	set	NOUN
ejpam-4946	140	8	of	of	ADP
ejpam-4946	140	9	g.	g.	PROPN
ejpam-4946	140	10	hence	hence	ADV
ejpam-4946	140	11	,	,	PUNCT
ejpam-4946	140	12	α(g	α(g	NUM
ejpam-4946	140	13	)	)	PUNCT
ejpam-4946	140	14	=	=	VERB
ejpam-4946	141	1	m+	m+	NUM
ejpam-4946	141	2	1	1	NUM
ejpam-4946	141	3	.	.	PUNCT
ejpam-4946	142	1	now	now	ADV
ejpam-4946	142	2	,	,	PUNCT
ejpam-4946	142	3	clearly	clearly	ADV
ejpam-4946	142	4	i	i	PRON
ejpam-4946	142	5	′	′	VERB
ejpam-4946	142	6	is	be	AUX
ejpam-4946	142	7	a	a	DET
ejpam-4946	142	8	j2	j2	NOUN
ejpam-4946	142	9	-	-	PUNCT
ejpam-4946	142	10	independent	independent	ADJ
ejpam-4946	142	11	set	set	NOUN
ejpam-4946	142	12	of	of	ADP
ejpam-4946	142	13	g.	g.	PROPN
ejpam-4946	142	14	since	since	SCONJ
ejpam-4946	142	15	dg(u	dg(u	NOUN
ejpam-4946	142	16	,	,	PUNCT
ejpam-4946	142	17	vi	vi	NOUN
ejpam-4946	142	18	)	)	PUNCT
ejpam-4946	142	19	=	=	SYM
ejpam-4946	142	20	1	1	NUM
ejpam-4946	142	21	for	for	ADP
ejpam-4946	142	22	each	each	DET
ejpam-4946	142	23	i	i	PRON
ejpam-4946	142	24	∈	∈	PROPN
ejpam-4946	142	25	{	{	PUNCT
ejpam-4946	142	26	1	1	NUM
ejpam-4946	142	27	,	,	PUNCT
ejpam-4946	142	28	2	2	NUM
ejpam-4946	142	29	,	,	PUNCT
ejpam-4946	142	30	.	.	PUNCT
ejpam-4946	142	31	.	.	PUNCT
ejpam-4946	143	1	.	.	PUNCT
ejpam-4946	144	1	,	,	PUNCT
ejpam-4946	144	2	m+1	m+1	NUM
ejpam-4946	144	3	}	}	PUNCT
ejpam-4946	144	4	,	,	PUNCT
ejpam-4946	144	5	and	and	CCONJ
ejpam-4946	144	6	n2	n2	PROPN
ejpam-4946	144	7	g[vs	g[vs	PROPN
ejpam-4946	144	8	]	]	PUNCT
ejpam-4946	144	9	=	=	PUNCT
ejpam-4946	144	10	n2	n2	PROPN
ejpam-4946	144	11	g[vt	g[vt	PROPN
ejpam-4946	144	12	]	]	X
ejpam-4946	144	13	∀	∀	X
ejpam-4946	144	14	s	s	PART
ejpam-4946	144	15	̸=	̸=	PROPN
ejpam-4946	144	16	t	t	PROPN
ejpam-4946	144	17	,	,	PUNCT
ejpam-4946	144	18	where	where	SCONJ
ejpam-4946	144	19	s	s	X
ejpam-4946	144	20	,	,	PUNCT
ejpam-4946	144	21	t	t	PROPN
ejpam-4946	144	22	∈	∈	PROPN
ejpam-4946	144	23	{	{	PUNCT
ejpam-4946	144	24	1	1	NUM
ejpam-4946	144	25	,	,	PUNCT
ejpam-4946	144	26	2	2	NUM
ejpam-4946	144	27	,	,	PUNCT
ejpam-4946	144	28	.	.	PUNCT
ejpam-4946	144	29	.	.	PUNCT
ejpam-4946	145	1	.	.	PUNCT
ejpam-4946	146	1	,	,	PUNCT
ejpam-4946	146	2	m+1	m+1	X
ejpam-4946	146	3	}	}	PUNCT
ejpam-4946	146	4	,	,	PUNCT
ejpam-4946	146	5	it	it	PRON
ejpam-4946	146	6	follows	follow	VERB
ejpam-4946	146	7	that	that	SCONJ
ejpam-4946	146	8	i	i	PRON
ejpam-4946	146	9	′	′	VERB
ejpam-4946	146	10	is	be	AUX
ejpam-4946	146	11	a	a	DET
ejpam-4946	146	12	maximum	maximum	ADJ
ejpam-4946	146	13	j2	j2	NOUN
ejpam-4946	146	14	-	-	PUNCT
ejpam-4946	146	15	independent	independent	ADJ
ejpam-4946	146	16	set	set	NOUN
ejpam-4946	146	17	of	of	ADP
ejpam-4946	146	18	g.	g.	PROPN
ejpam-4946	146	19	consequently	consequently	ADV
ejpam-4946	146	20	,	,	PUNCT
ejpam-4946	146	21	α(g)−	α(g)−	PROPN
ejpam-4946	146	22	αj2(g	αj2(g	PROPN
ejpam-4946	146	23	)	)	PUNCT
ejpam-4946	147	1	=	=	VERB
ejpam-4946	148	1	m+	m+	NUM
ejpam-4946	148	2	1−	1−	NUM
ejpam-4946	148	3	1	1	NUM
ejpam-4946	148	4	=	=	NOUN
ejpam-4946	148	5	m.	m.	NOUN
ejpam-4946	148	6	since	since	SCONJ
ejpam-4946	148	7	m	m	PROPN
ejpam-4946	148	8	can	can	AUX
ejpam-4946	148	9	be	be	AUX
ejpam-4946	148	10	made	make	VERB
ejpam-4946	148	11	arbitrarily	arbitrarily	ADV
ejpam-4946	148	12	large	large	ADJ
ejpam-4946	148	13	,	,	PUNCT
ejpam-4946	148	14	the	the	DET
ejpam-4946	148	15	assertion	assertion	NOUN
ejpam-4946	148	16	follows	follow	VERB
ejpam-4946	148	17	.	.	PUNCT
ejpam-4946	149	1	v2	v2	NOUN
ejpam-4946	149	2	v3v4	v3v4	PUNCT
ejpam-4946	149	3	v1	v1	PROPN
ejpam-4946	149	4	vm+1	vm+1	PROPN
ejpam-4946	149	5	v6	v6	NOUN
ejpam-4946	149	6	v5	v5	VERB
ejpam-4946	149	7	u	u	NOUN
ejpam-4946	149	8	g	g	NOUN
ejpam-4946	149	9	:	:	PUNCT
ejpam-4946	149	10	.	.	PUNCT
ejpam-4946	149	11	.	.	PUNCT
ejpam-4946	150	1	.	.	PUNCT
ejpam-4946	151	1	figure	figure	VERB
ejpam-4946	151	2	2	2	NUM
ejpam-4946	151	3	:	:	PUNCT
ejpam-4946	151	4	graph	graph	VERB
ejpam-4946	151	5	g	g	NOUN
ejpam-4946	151	6	with	with	ADP
ejpam-4946	151	7	α(g)−	α(g)−	NOUN
ejpam-4946	151	8	αj2(g	αj2(g	PROPN
ejpam-4946	151	9	)	)	PUNCT
ejpam-4946	152	1	=	=	NOUN
ejpam-4946	152	2	m	m	NOUN
ejpam-4946	152	3	theorem	theorem	ADJ
ejpam-4946	152	4	1	1	X
ejpam-4946	152	5	.	.	PUNCT
ejpam-4946	153	1	let	let	VERB
ejpam-4946	153	2	g	g	PRON
ejpam-4946	153	3	be	be	AUX
ejpam-4946	153	4	a	a	DET
ejpam-4946	153	5	graph	graph	NOUN
ejpam-4946	153	6	.	.	PUNCT
ejpam-4946	154	1	then	then	ADV
ejpam-4946	154	2	αj2(g	αj2(g	PROPN
ejpam-4946	154	3	)	)	PUNCT
ejpam-4946	155	1	=	=	SYM
ejpam-4946	155	2	|v	|v	PROPN
ejpam-4946	155	3	(	(	PUNCT
ejpam-4946	155	4	g)|	g)|	VERB
ejpam-4946	155	5	if	if	SCONJ
ejpam-4946	155	6	and	and	CCONJ
ejpam-4946	155	7	only	only	ADV
ejpam-4946	155	8	if	if	SCONJ
ejpam-4946	155	9	every	every	DET
ejpam-4946	155	10	component	component	NOUN
ejpam-4946	155	11	of	of	ADP
ejpam-4946	155	12	g	g	PROPN
ejpam-4946	155	13	is	be	AUX
ejpam-4946	155	14	trivial	trivial	ADJ
ejpam-4946	155	15	.	.	PUNCT
ejpam-4946	156	1	proof	proof	NOUN
ejpam-4946	156	2	.	.	PUNCT
ejpam-4946	157	1	suppose	suppose	VERB
ejpam-4946	157	2	that	that	SCONJ
ejpam-4946	157	3	αj2(g	αj2(g	NOUN
ejpam-4946	157	4	)	)	PUNCT
ejpam-4946	157	5	=	=	SYM
ejpam-4946	157	6	|v	|v	PROPN
ejpam-4946	157	7	(	(	PUNCT
ejpam-4946	157	8	g)|	g)|	INTJ
ejpam-4946	157	9	,	,	PUNCT
ejpam-4946	157	10	say	say	VERB
ejpam-4946	157	11	that	that	SCONJ
ejpam-4946	157	12	i	i	PRON
ejpam-4946	157	13	=	=	SYM
ejpam-4946	157	14	v	v	X
ejpam-4946	157	15	(	(	PUNCT
ejpam-4946	157	16	g	g	NOUN
ejpam-4946	157	17	)	)	PUNCT
ejpam-4946	157	18	is	be	AUX
ejpam-4946	157	19	the	the	DET
ejpam-4946	157	20	maximum	maximum	ADJ
ejpam-4946	157	21	j2independent	j2independent	PROPN
ejpam-4946	157	22	set	set	NOUN
ejpam-4946	157	23	of	of	ADP
ejpam-4946	157	24	g.	g.	PROPN
ejpam-4946	157	25	since	since	SCONJ
ejpam-4946	157	26	i	i	PRON
ejpam-4946	157	27	is	be	AUX
ejpam-4946	157	28	an	an	DET
ejpam-4946	157	29	independent	independent	ADJ
ejpam-4946	157	30	set	set	NOUN
ejpam-4946	157	31	of	of	ADP
ejpam-4946	157	32	g	g	NOUN
ejpam-4946	157	33	,	,	PUNCT
ejpam-4946	157	34	da(a	da(a	PROPN
ejpam-4946	157	35	,	,	PUNCT
ejpam-4946	157	36	b	b	X
ejpam-4946	157	37	)	)	PUNCT
ejpam-4946	157	38	̸=	̸=	NOUN
ejpam-4946	157	39	1	1	NUM
ejpam-4946	157	40	∀	∀	NOUN
ejpam-4946	157	41	a	a	PRON
ejpam-4946	157	42	,	,	PUNCT
ejpam-4946	157	43	b	b	X
ejpam-4946	157	44	∈	∈	PROPN
ejpam-4946	157	45	v	v	NOUN
ejpam-4946	157	46	(	(	PUNCT
ejpam-4946	157	47	g	g	NOUN
ejpam-4946	157	48	)	)	PUNCT
ejpam-4946	157	49	.	.	PUNCT
ejpam-4946	158	1	suppose	suppose	VERB
ejpam-4946	158	2	there	there	PRON
ejpam-4946	158	3	is	be	VERB
ejpam-4946	158	4	a	a	DET
ejpam-4946	158	5	component	component	NOUN
ejpam-4946	158	6	k	k	NOUN
ejpam-4946	158	7	of	of	ADP
ejpam-4946	158	8	g	g	PROPN
ejpam-4946	158	9	which	which	PRON
ejpam-4946	158	10	is	be	AUX
ejpam-4946	158	11	non	non	ADJ
ejpam-4946	158	12	-	-	ADJ
ejpam-4946	158	13	trivial	trivial	ADJ
ejpam-4946	158	14	.	.	PUNCT
ejpam-4946	159	1	then	then	ADV
ejpam-4946	159	2	there	there	PRON
ejpam-4946	159	3	exist	exist	VERB
ejpam-4946	159	4	x	x	NOUN
ejpam-4946	159	5	,	,	PUNCT
ejpam-4946	159	6	y	y	PROPN
ejpam-4946	159	7	∈	∈	PROPN
ejpam-4946	159	8	v	v	PROPN
ejpam-4946	159	9	(	(	PUNCT
ejpam-4946	159	10	k	k	NOUN
ejpam-4946	159	11	)	)	PUNCT
ejpam-4946	159	12	⊆	⊆	NUM
ejpam-4946	159	13	v	v	NOUN
ejpam-4946	159	14	(	(	PUNCT
ejpam-4946	159	15	g	g	NOUN
ejpam-4946	159	16	)	)	PUNCT
ejpam-4946	159	17	such	such	ADJ
ejpam-4946	159	18	that	that	SCONJ
ejpam-4946	159	19	dk(x	dk(x	PROPN
ejpam-4946	159	20	,	,	PUNCT
ejpam-4946	159	21	y	y	NOUN
ejpam-4946	159	22	)	)	PUNCT
ejpam-4946	159	23	=	=	SYM
ejpam-4946	159	24	dg(x	dg(x	X
ejpam-4946	159	25	,	,	PUNCT
ejpam-4946	159	26	y	y	NOUN
ejpam-4946	159	27	)	)	PUNCT
ejpam-4946	159	28	=	=	SYM
ejpam-4946	159	29	1	1	NUM
ejpam-4946	159	30	,	,	PUNCT
ejpam-4946	159	31	a	a	DET
ejpam-4946	159	32	contradiction	contradiction	NOUN
ejpam-4946	159	33	.	.	PUNCT
ejpam-4946	160	1	hence	hence	ADV
ejpam-4946	160	2	,	,	PUNCT
ejpam-4946	160	3	every	every	DET
ejpam-4946	160	4	component	component	NOUN
ejpam-4946	160	5	of	of	ADP
ejpam-4946	160	6	g	g	PROPN
ejpam-4946	160	7	is	be	AUX
ejpam-4946	160	8	trivial	trivial	ADJ
ejpam-4946	160	9	.	.	PUNCT
ejpam-4946	161	1	conversely	conversely	ADV
ejpam-4946	161	2	,	,	PUNCT
ejpam-4946	161	3	suppose	suppose	VERB
ejpam-4946	161	4	that	that	SCONJ
ejpam-4946	161	5	every	every	DET
ejpam-4946	161	6	componentk	componentk	NOUN
ejpam-4946	161	7	ofg	ofg	PROPN
ejpam-4946	161	8	is	be	AUX
ejpam-4946	161	9	trivial	trivial	ADJ
ejpam-4946	161	10	.	.	PUNCT
ejpam-4946	162	1	let	let	VERB
ejpam-4946	162	2	v	v	X
ejpam-4946	162	3	(	(	PUNCT
ejpam-4946	162	4	g	g	NOUN
ejpam-4946	162	5	)	)	PUNCT
ejpam-4946	162	6	=	=	SYM
ejpam-4946	162	7	{	{	PUNCT
ejpam-4946	162	8	a1	a1	PROPN
ejpam-4946	162	9	,	,	PUNCT
ejpam-4946	162	10	a2	a2	PROPN
ejpam-4946	162	11	,	,	PUNCT
ejpam-4946	162	12	.	.	PUNCT
ejpam-4946	162	13	.	.	PUNCT
ejpam-4946	163	1	.	.	PUNCT
ejpam-4946	164	1	,	,	PUNCT
ejpam-4946	164	2	am	be	AUX
ejpam-4946	164	3	}	}	PUNCT
ejpam-4946	164	4	,	,	PUNCT
ejpam-4946	164	5	m	m	PROPN
ejpam-4946	164	6	∈	∈	PROPN
ejpam-4946	164	7	n.	n.	NOUN
ejpam-4946	164	8	then	then	ADV
ejpam-4946	164	9	dg(ai	dg(ai	PROPN
ejpam-4946	164	10	,	,	PUNCT
ejpam-4946	164	11	aj	aj	PROPN
ejpam-4946	164	12	)	)	PUNCT
ejpam-4946	164	13	̸=	̸=	PROPN
ejpam-4946	164	14	1	1	NUM
ejpam-4946	164	15	and	and	CCONJ
ejpam-4946	164	16	ai	ai	PROPN
ejpam-4946	164	17	∈	∈	PROPN
ejpam-4946	164	18	n2	n2	NOUN
ejpam-4946	164	19	g[ai]\n2	g[ai]\n2	NOUN
ejpam-4946	164	20	g[aj	g[aj	PROPN
ejpam-4946	164	21	]	]	PUNCT
ejpam-4946	164	22	∀	∀	PUNCT
ejpam-4946	165	1	i	i	NOUN
ejpam-4946	165	2	̸=	̸=	PROPN
ejpam-4946	165	3	j	j	PROPN
ejpam-4946	165	4	,	,	PUNCT
ejpam-4946	165	5	where	where	SCONJ
ejpam-4946	165	6	i	i	PRON
ejpam-4946	165	7	,	,	PUNCT
ejpam-4946	165	8	j	j	PROPN
ejpam-4946	165	9	∈	∈	PROPN
ejpam-4946	165	10	{	{	PUNCT
ejpam-4946	165	11	1	1	NUM
ejpam-4946	165	12	,	,	PUNCT
ejpam-4946	165	13	2	2	NUM
ejpam-4946	165	14	,	,	PUNCT
ejpam-4946	165	15	.	.	PUNCT
ejpam-4946	165	16	.	.	PUNCT
ejpam-4946	165	17	.	.	PUNCT
ejpam-4946	166	1	,	,	PUNCT
ejpam-4946	166	2	m	m	VERB
ejpam-4946	166	3	}	}	PUNCT
ejpam-4946	166	4	.	.	PUNCT
ejpam-4946	167	1	thus	thus	ADV
ejpam-4946	167	2	,	,	PUNCT
ejpam-4946	167	3	n2	n2	PROPN
ejpam-4946	167	4	g[ai]\n2	g[ai]\n2	NOUN
ejpam-4946	167	5	g[aj	g[aj	PROPN
ejpam-4946	167	6	]	]	PUNCT
ejpam-4946	167	7	̸=	̸=	PROPN
ejpam-4946	167	8	∅	∅	VERB
ejpam-4946	167	9	∀	∀	NOUN
ejpam-4946	168	1	i	i	PRON
ejpam-4946	168	2	̸=	̸=	PROPN
ejpam-4946	168	3	j	j	PROPN
ejpam-4946	168	4	,	,	PUNCT
ejpam-4946	168	5	i	i	PRON
ejpam-4946	168	6	,	,	PUNCT
ejpam-4946	168	7	j	j	PROPN
ejpam-4946	168	8	∈	∈	PROPN
ejpam-4946	168	9	{	{	PUNCT
ejpam-4946	168	10	1	1	NUM
ejpam-4946	168	11	,	,	PUNCT
ejpam-4946	168	12	2	2	NUM
ejpam-4946	168	13	,	,	PUNCT
ejpam-4946	168	14	.	.	PUNCT
ejpam-4946	168	15	.	.	PUNCT
ejpam-4946	168	16	.	.	PUNCT
ejpam-4946	169	1	,	,	PUNCT
ejpam-4946	169	2	m	m	VERB
ejpam-4946	169	3	}	}	PUNCT
ejpam-4946	169	4	.	.	PUNCT
ejpam-4946	170	1	therefore	therefore	ADV
ejpam-4946	170	2	,	,	PUNCT
ejpam-4946	170	3	v	v	X
ejpam-4946	170	4	(	(	PUNCT
ejpam-4946	170	5	g	g	NOUN
ejpam-4946	170	6	)	)	PUNCT
ejpam-4946	170	7	is	be	AUX
ejpam-4946	170	8	a	a	DET
ejpam-4946	170	9	j2−	j2−	X
ejpam-4946	170	10	independent	independent	ADJ
ejpam-4946	170	11	set	set	NOUN
ejpam-4946	170	12	of	of	ADP
ejpam-4946	170	13	g	g	NOUN
ejpam-4946	170	14	,	,	PUNCT
ejpam-4946	170	15	and	and	CCONJ
ejpam-4946	170	16	so	so	ADV
ejpam-4946	170	17	αj2(g	αj2(g	ADJ
ejpam-4946	170	18	)	)	PUNCT
ejpam-4946	171	1	=	=	SYM
ejpam-4946	171	2	|v	|v	PROPN
ejpam-4946	171	3	(	(	PUNCT
ejpam-4946	171	4	g)|	g)|	NOUN
ejpam-4946	171	5	.	.	PUNCT
ejpam-4946	171	6	theorem	theorem	NOUN
ejpam-4946	171	7	2	2	NUM
ejpam-4946	171	8	.	.	PUNCT
ejpam-4946	172	1	let	let	VERB
ejpam-4946	172	2	g	g	PRON
ejpam-4946	172	3	be	be	AUX
ejpam-4946	172	4	a	a	DET
ejpam-4946	172	5	graph	graph	NOUN
ejpam-4946	172	6	.	.	PUNCT
ejpam-4946	173	1	if	if	SCONJ
ejpam-4946	173	2	g	g	PROPN
ejpam-4946	173	3	is	be	AUX
ejpam-4946	173	4	complete	complete	ADJ
ejpam-4946	173	5	,	,	PUNCT
ejpam-4946	173	6	then	then	ADV
ejpam-4946	173	7	αj2(g	αj2(g	ADJ
ejpam-4946	173	8	)	)	PUNCT
ejpam-4946	173	9	=	=	SYM
ejpam-4946	173	10	1	1	X
ejpam-4946	173	11	.	.	PUNCT
ejpam-4946	174	1	however	however	ADV
ejpam-4946	174	2	,	,	PUNCT
ejpam-4946	174	3	the	the	DET
ejpam-4946	174	4	converse	converse	NOUN
ejpam-4946	174	5	is	be	AUX
ejpam-4946	174	6	not	not	PART
ejpam-4946	174	7	true	true	ADJ
ejpam-4946	174	8	.	.	PUNCT
ejpam-4946	175	1	a.	a.	NOUN
ejpam-4946	175	2	tapeing	tapeing	NOUN
ejpam-4946	175	3	et	et	PROPN
ejpam-4946	175	4	al	al	PROPN
ejpam-4946	175	5	.	.	PUNCT
ejpam-4946	175	6	/	/	SYM
ejpam-4946	175	7	eur	eur	PROPN
ejpam-4946	175	8	.	.	PUNCT
ejpam-4946	176	1	j.	j.	PROPN
ejpam-4946	176	2	pure	pure	PROPN
ejpam-4946	176	3	appl	appl	PROPN
ejpam-4946	176	4	.	.	PROPN
ejpam-4946	176	5	math	math	PROPN
ejpam-4946	176	6	,	,	PUNCT
ejpam-4946	176	7	17	17	NUM
ejpam-4946	176	8	(	(	PUNCT
ejpam-4946	176	9	1	1	NUM
ejpam-4946	176	10	)	)	PUNCT
ejpam-4946	176	11	(	(	PUNCT
ejpam-4946	176	12	2024	2024	NUM
ejpam-4946	176	13	)	)	PUNCT
ejpam-4946	176	14	,	,	PUNCT
ejpam-4946	176	15	124	124	NUM
ejpam-4946	176	16	-	-	SYM
ejpam-4946	176	17	134	134	NUM
ejpam-4946	176	18	129	129	NUM
ejpam-4946	176	19	proof	proof	NOUN
ejpam-4946	176	20	.	.	PUNCT
ejpam-4946	177	1	let	let	VERB
ejpam-4946	177	2	g	g	PRON
ejpam-4946	177	3	be	be	AUX
ejpam-4946	177	4	a	a	DET
ejpam-4946	177	5	complete	complete	ADJ
ejpam-4946	177	6	graph	graph	NOUN
ejpam-4946	177	7	.	.	PUNCT
ejpam-4946	178	1	then	then	ADV
ejpam-4946	178	2	α(g	α(g	NUM
ejpam-4946	178	3	)	)	PUNCT
ejpam-4946	178	4	=	=	SYM
ejpam-4946	179	1	1	1	X
ejpam-4946	179	2	.	.	PUNCT
ejpam-4946	179	3	hence	hence	ADV
ejpam-4946	179	4	αj2(g	αj2(g	ADJ
ejpam-4946	179	5	)	)	PUNCT
ejpam-4946	179	6	=	=	SYM
ejpam-4946	179	7	1	1	NUM
ejpam-4946	179	8	by	by	ADP
ejpam-4946	179	9	proposition	proposition	NOUN
ejpam-4946	179	10	1	1	NUM
ejpam-4946	179	11	.	.	PUNCT
ejpam-4946	179	12	to	to	PART
ejpam-4946	179	13	see	see	VERB
ejpam-4946	179	14	that	that	SCONJ
ejpam-4946	179	15	the	the	DET
ejpam-4946	179	16	converse	converse	NOUN
ejpam-4946	179	17	is	be	AUX
ejpam-4946	179	18	not	not	PART
ejpam-4946	179	19	true	true	ADJ
ejpam-4946	179	20	,	,	PUNCT
ejpam-4946	179	21	consider	consider	VERB
ejpam-4946	179	22	p3	p3	NOUN
ejpam-4946	179	23	which	which	PRON
ejpam-4946	179	24	is	be	AUX
ejpam-4946	179	25	not	not	PART
ejpam-4946	179	26	complete	complete	ADJ
ejpam-4946	179	27	grph	grph	NOUN
ejpam-4946	179	28	.	.	PUNCT
ejpam-4946	180	1	let	let	VERB
ejpam-4946	180	2	v	v	X
ejpam-4946	180	3	(	(	PUNCT
ejpam-4946	180	4	p3	p3	PROPN
ejpam-4946	180	5	)	)	PUNCT
ejpam-4946	180	6	=	=	PRON
ejpam-4946	180	7	{	{	PUNCT
ejpam-4946	180	8	u1	u1	NOUN
ejpam-4946	180	9	,	,	PUNCT
ejpam-4946	180	10	u2	u2	NOUN
ejpam-4946	180	11	,	,	PUNCT
ejpam-4946	180	12	u3	u3	NOUN
ejpam-4946	180	13	}	}	PUNCT
ejpam-4946	180	14	.	.	PUNCT
ejpam-4946	181	1	observe	observe	VERB
ejpam-4946	181	2	that	that	SCONJ
ejpam-4946	181	3	n2	n2	PROPN
ejpam-4946	181	4	p3	p3	PROPN
ejpam-4946	182	1	[	[	X
ejpam-4946	182	2	u1	u1	X
ejpam-4946	182	3	]	]	X
ejpam-4946	182	4	=	=	SYM
ejpam-4946	182	5	n2	n2	PROPN
ejpam-4946	182	6	p3	p3	PROPN
ejpam-4946	182	7	[	[	X
ejpam-4946	182	8	u3	u3	X
ejpam-4946	182	9	]	]	PUNCT
ejpam-4946	182	10	.	.	PUNCT
ejpam-4946	183	1	thus	thus	ADV
ejpam-4946	183	2	,	,	PUNCT
ejpam-4946	183	3	u1	u1	NOUN
ejpam-4946	183	4	and	and	CCONJ
ejpam-4946	183	5	u3	u3	NOUN
ejpam-4946	183	6	can	can	AUX
ejpam-4946	183	7	not	not	PART
ejpam-4946	183	8	be	be	AUX
ejpam-4946	183	9	both	both	PRON
ejpam-4946	183	10	in	in	ADP
ejpam-4946	183	11	any	any	DET
ejpam-4946	183	12	j2	j2	NOUN
ejpam-4946	183	13	-	-	PUNCT
ejpam-4946	183	14	independent	independent	ADJ
ejpam-4946	183	15	set	set	NOUN
ejpam-4946	183	16	i	i	PRON
ejpam-4946	183	17	of	of	ADP
ejpam-4946	183	18	g.	g.	PROPN
ejpam-4946	183	19	since	since	SCONJ
ejpam-4946	183	20	dp3(u1	dp3(u1	NOUN
ejpam-4946	183	21	,	,	PUNCT
ejpam-4946	183	22	u2	u2	NOUN
ejpam-4946	183	23	)	)	PUNCT
ejpam-4946	183	24	=	=	SYM
ejpam-4946	183	25	1	1	NUM
ejpam-4946	183	26	=	=	SYM
ejpam-4946	183	27	dp3(u2	dp3(u2	PROPN
ejpam-4946	183	28	,	,	PUNCT
ejpam-4946	183	29	u3	u3	PROPN
ejpam-4946	183	30	)	)	PUNCT
ejpam-4946	183	31	,	,	PUNCT
ejpam-4946	183	32	either	either	CCONJ
ejpam-4946	183	33	{	{	PUNCT
ejpam-4946	183	34	u1	u1	NOUN
ejpam-4946	183	35	}	}	PUNCT
ejpam-4946	183	36	,	,	PUNCT
ejpam-4946	183	37	{	{	PUNCT
ejpam-4946	183	38	u2	u2	NOUN
ejpam-4946	183	39	}	}	PUNCT
ejpam-4946	183	40	or	or	CCONJ
ejpam-4946	183	41	{	{	PUNCT
ejpam-4946	183	42	u3	u3	NOUN
ejpam-4946	183	43	}	}	PUNCT
ejpam-4946	183	44	is	be	AUX
ejpam-4946	183	45	a	a	DET
ejpam-4946	183	46	maximum	maximum	ADJ
ejpam-4946	183	47	j2	j2	NOUN
ejpam-4946	183	48	-	-	PUNCT
ejpam-4946	183	49	independent	independent	ADJ
ejpam-4946	183	50	set	set	NOUN
ejpam-4946	183	51	of	of	ADP
ejpam-4946	183	52	p3	p3	PROPN
ejpam-4946	183	53	.	.	PUNCT
ejpam-4946	184	1	therefore	therefore	ADV
ejpam-4946	184	2	,	,	PUNCT
ejpam-4946	184	3	in	in	ADP
ejpam-4946	184	4	either	either	DET
ejpam-4946	184	5	case	case	NOUN
ejpam-4946	184	6	,	,	PUNCT
ejpam-4946	184	7	αj2(p3	αj2(p3	ADJ
ejpam-4946	184	8	)	)	PUNCT
ejpam-4946	184	9	=	=	SYM
ejpam-4946	184	10	1	1	NUM
ejpam-4946	184	11	,	,	PUNCT
ejpam-4946	184	12	and	and	CCONJ
ejpam-4946	184	13	so	so	ADV
ejpam-4946	184	14	the	the	DET
ejpam-4946	184	15	assertion	assertion	NOUN
ejpam-4946	184	16	follows	follow	VERB
ejpam-4946	184	17	.	.	PUNCT
ejpam-4946	185	1	theorem	theorem	NOUN
ejpam-4946	185	2	3	3	X
ejpam-4946	185	3	.	.	PUNCT
ejpam-4946	186	1	let	let	VERB
ejpam-4946	186	2	g	g	PRON
ejpam-4946	186	3	be	be	AUX
ejpam-4946	186	4	a	a	DET
ejpam-4946	186	5	graph	graph	NOUN
ejpam-4946	186	6	.	.	PUNCT
ejpam-4946	187	1	then	then	ADV
ejpam-4946	187	2	αj2(g	αj2(g	PROPN
ejpam-4946	187	3	)	)	PUNCT
ejpam-4946	187	4	=	=	SYM
ejpam-4946	187	5	α(g	α(g	NUM
ejpam-4946	187	6	)	)	PUNCT
ejpam-4946	187	7	if	if	SCONJ
ejpam-4946	187	8	and	and	CCONJ
ejpam-4946	187	9	only	only	ADV
ejpam-4946	187	10	if	if	SCONJ
ejpam-4946	187	11	g	g	PROPN
ejpam-4946	187	12	has	have	VERB
ejpam-4946	187	13	an	an	DET
ejpam-4946	187	14	α	α	NOUN
ejpam-4946	187	15	-	-	PUNCT
ejpam-4946	187	16	set	set	VERB
ejpam-4946	187	17	q	q	NOUN
ejpam-4946	187	18	such	such	ADJ
ejpam-4946	187	19	that	that	SCONJ
ejpam-4946	187	20	q	q	PROPN
ejpam-4946	187	21	forms	form	VERB
ejpam-4946	187	22	a	a	DET
ejpam-4946	187	23	j2	j2	NOUN
ejpam-4946	187	24	-	-	PUNCT
ejpam-4946	187	25	set	set	NOUN
ejpam-4946	187	26	in	in	ADP
ejpam-4946	187	27	g.	g.	PROPN
ejpam-4946	187	28	proof	proof	PROPN
ejpam-4946	187	29	.	.	PUNCT
ejpam-4946	188	1	suppose	suppose	VERB
ejpam-4946	188	2	that	that	SCONJ
ejpam-4946	188	3	αj2(g	αj2(g	NOUN
ejpam-4946	188	4	)	)	PUNCT
ejpam-4946	188	5	=	=	SYM
ejpam-4946	188	6	α(g	α(g	NUM
ejpam-4946	188	7	)	)	PUNCT
ejpam-4946	189	1	=	=	SYM
ejpam-4946	189	2	k	k	NOUN
ejpam-4946	189	3	,	,	PUNCT
ejpam-4946	189	4	say	say	VERB
ejpam-4946	189	5	q	q	X
ejpam-4946	189	6	=	=	PUNCT
ejpam-4946	189	7	{	{	PUNCT
ejpam-4946	189	8	w1	w1	NOUN
ejpam-4946	189	9	,	,	PUNCT
ejpam-4946	189	10	w2	w2	NOUN
ejpam-4946	189	11	,	,	PUNCT
ejpam-4946	189	12	.	.	PUNCT
ejpam-4946	189	13	.	.	PUNCT
ejpam-4946	189	14	.	.	PUNCT
ejpam-4946	190	1	,	,	PUNCT
ejpam-4946	190	2	wk	wk	X
ejpam-4946	190	3	}	}	PUNCT
ejpam-4946	190	4	is	be	AUX
ejpam-4946	190	5	a	a	DET
ejpam-4946	190	6	maximum	maximum	ADJ
ejpam-4946	190	7	j2	j2	NOUN
ejpam-4946	190	8	-	-	PUNCT
ejpam-4946	190	9	independent	independent	ADJ
ejpam-4946	190	10	set	set	NOUN
ejpam-4946	190	11	of	of	ADP
ejpam-4946	190	12	g.	g.	PROPN
ejpam-4946	191	1	then	then	ADV
ejpam-4946	191	2	q	q	X
ejpam-4946	191	3	is	be	AUX
ejpam-4946	191	4	an	an	DET
ejpam-4946	191	5	independent	independent	ADJ
ejpam-4946	191	6	set	set	NOUN
ejpam-4946	191	7	of	of	ADP
ejpam-4946	191	8	g.	g.	PROPN
ejpam-4946	191	9	since	since	SCONJ
ejpam-4946	191	10	αj2(g	αj2(g	PROPN
ejpam-4946	191	11	)	)	PUNCT
ejpam-4946	191	12	=	=	SYM
ejpam-4946	191	13	α(g	α(g	NUM
ejpam-4946	191	14	)	)	PUNCT
ejpam-4946	191	15	,	,	PUNCT
ejpam-4946	191	16	it	it	PRON
ejpam-4946	191	17	follows	follow	VERB
ejpam-4946	191	18	that	that	SCONJ
ejpam-4946	191	19	q	q	NOUN
ejpam-4946	191	20	is	be	AUX
ejpam-4946	191	21	an	an	DET
ejpam-4946	191	22	α	α	NOUN
ejpam-4946	191	23	-	-	PUNCT
ejpam-4946	191	24	set	set	NOUN
ejpam-4946	191	25	of	of	ADP
ejpam-4946	191	26	g.	g.	PROPN
ejpam-4946	191	27	since	since	SCONJ
ejpam-4946	191	28	q	q	PROPN
ejpam-4946	191	29	is	be	AUX
ejpam-4946	191	30	a	a	DET
ejpam-4946	191	31	j2	j2	NOUN
ejpam-4946	191	32	-	-	PUNCT
ejpam-4946	191	33	independent	independent	ADJ
ejpam-4946	191	34	set	set	NOUN
ejpam-4946	191	35	of	of	ADP
ejpam-4946	191	36	g	g	NOUN
ejpam-4946	191	37	,	,	PUNCT
ejpam-4946	191	38	q	q	PUNCT
ejpam-4946	191	39	is	be	AUX
ejpam-4946	191	40	a	a	DET
ejpam-4946	191	41	j2	j2	PROPN
ejpam-4946	191	42	-	-	PUNCT
ejpam-4946	191	43	set	set	NOUN
ejpam-4946	191	44	of	of	ADP
ejpam-4946	191	45	g.	g.	NOUN
ejpam-4946	191	46	conversely	conversely	ADV
ejpam-4946	191	47	,	,	PUNCT
ejpam-4946	191	48	suppose	suppose	VERB
ejpam-4946	191	49	g	g	PROPN
ejpam-4946	191	50	has	have	VERB
ejpam-4946	191	51	an	an	DET
ejpam-4946	191	52	α	α	NOUN
ejpam-4946	191	53	-	-	PUNCT
ejpam-4946	191	54	set	set	VERB
ejpam-4946	191	55	q	q	NOUN
ejpam-4946	191	56	of	of	ADP
ejpam-4946	191	57	g.	g.	PROPN
ejpam-4946	192	1	then	then	ADV
ejpam-4946	192	2	q	q	X
ejpam-4946	192	3	is	be	AUX
ejpam-4946	192	4	a	a	DET
ejpam-4946	192	5	maximum	maximum	ADJ
ejpam-4946	192	6	independent	independent	ADJ
ejpam-4946	192	7	set	set	NOUN
ejpam-4946	192	8	of	of	ADP
ejpam-4946	192	9	g.	g.	PROPN
ejpam-4946	192	10	since	since	SCONJ
ejpam-4946	192	11	q	q	PROPN
ejpam-4946	192	12	forms	form	VERB
ejpam-4946	192	13	a	a	DET
ejpam-4946	192	14	j2	j2	NOUN
ejpam-4946	192	15	-	-	PUNCT
ejpam-4946	192	16	set	set	NOUN
ejpam-4946	192	17	in	in	ADP
ejpam-4946	192	18	g	g	PROPN
ejpam-4946	192	19	,	,	PUNCT
ejpam-4946	192	20	it	it	PRON
ejpam-4946	192	21	follows	follow	VERB
ejpam-4946	192	22	that	that	SCONJ
ejpam-4946	192	23	q	q	NOUN
ejpam-4946	192	24	is	be	AUX
ejpam-4946	192	25	a	a	DET
ejpam-4946	192	26	maximum	maximum	ADJ
ejpam-4946	192	27	j2	j2	NOUN
ejpam-4946	192	28	-	-	PUNCT
ejpam-4946	192	29	independent	independent	ADJ
ejpam-4946	192	30	set	set	NOUN
ejpam-4946	192	31	of	of	ADP
ejpam-4946	192	32	g.	g.	PROPN
ejpam-4946	192	33	hence	hence	ADV
ejpam-4946	192	34	,	,	PUNCT
ejpam-4946	192	35	α(g	α(g	NUM
ejpam-4946	192	36	)	)	PUNCT
ejpam-4946	192	37	=	=	SYM
ejpam-4946	192	38	|q|	|q|	VERB
ejpam-4946	192	39	=	=	SYM
ejpam-4946	192	40	αj2(g	αj2(g	PROPN
ejpam-4946	192	41	)	)	PUNCT
ejpam-4946	192	42	.	.	PUNCT
ejpam-4946	193	1	theorem	theorem	ADJ
ejpam-4946	193	2	4	4	NUM
ejpam-4946	193	3	.	.	PUNCT
ejpam-4946	194	1	let	let	VERB
ejpam-4946	194	2	q	q	PART
ejpam-4946	194	3	be	be	AUX
ejpam-4946	194	4	a	a	DET
ejpam-4946	194	5	positive	positive	ADJ
ejpam-4946	194	6	integer	integer	NOUN
ejpam-4946	194	7	.	.	PUNCT
ejpam-4946	195	1	then	then	ADV
ejpam-4946	195	2	αj2(cq	αj2(cq	NOUN
ejpam-4946	195	3	)	)	PUNCT
ejpam-4946	196	1	=	=	SYM
ejpam-4946	197	1			NOUN
ejpam-4946	197	2	1	1	NUM
ejpam-4946	197	3	,	,	PUNCT
ejpam-4946	197	4	q	q	NOUN
ejpam-4946	197	5	=	=	SYM
ejpam-4946	197	6	3	3	NUM
ejpam-4946	197	7	,	,	PUNCT
ejpam-4946	197	8	4	4	NUM
ejpam-4946	197	9	2	2	NUM
ejpam-4946	197	10	,	,	PUNCT
ejpam-4946	197	11	q	q	NOUN
ejpam-4946	197	12	=	=	SYM
ejpam-4946	197	13	5	5	NUM
ejpam-4946	197	14	,	,	PUNCT
ejpam-4946	197	15	6	6	NUM
ejpam-4946	197	16	α(cq	α(cq	NOUN
ejpam-4946	197	17	)	)	PUNCT
ejpam-4946	197	18	,	,	PUNCT
ejpam-4946	197	19	q	q	X
ejpam-4946	197	20	≥	≥	NOUN
ejpam-4946	197	21	7	7	NUM
ejpam-4946	197	22	.	.	PUNCT
ejpam-4946	197	23	proof	proof	NOUN
ejpam-4946	197	24	.	.	PUNCT
ejpam-4946	198	1	clearly	clearly	ADV
ejpam-4946	198	2	,	,	PUNCT
ejpam-4946	198	3	αj2(c3	αj2(c3	NOUN
ejpam-4946	198	4	)	)	PUNCT
ejpam-4946	198	5	=	=	SYM
ejpam-4946	199	1	1	1	X
ejpam-4946	199	2	.	.	X
ejpam-4946	200	1	for	for	ADP
ejpam-4946	200	2	q	q	NOUN
ejpam-4946	200	3	=	=	SYM
ejpam-4946	200	4	4	4	NUM
ejpam-4946	200	5	,	,	PUNCT
ejpam-4946	200	6	let	let	VERB
ejpam-4946	200	7	v	v	X
ejpam-4946	200	8	(	(	PUNCT
ejpam-4946	200	9	c4	c4	NOUN
ejpam-4946	200	10	)	)	PUNCT
ejpam-4946	200	11	=	=	SYM
ejpam-4946	200	12	{	{	PUNCT
ejpam-4946	200	13	a1	a1	PROPN
ejpam-4946	200	14	,	,	PUNCT
ejpam-4946	200	15	a2	a2	PROPN
ejpam-4946	200	16	,	,	PUNCT
ejpam-4946	200	17	a3	a3	NOUN
ejpam-4946	200	18	,	,	PUNCT
ejpam-4946	200	19	a4	a4	NOUN
ejpam-4946	200	20	}	}	PUNCT
ejpam-4946	200	21	and	and	CCONJ
ejpam-4946	200	22	l	l	NOUN
ejpam-4946	200	23	=	=	SYM
ejpam-4946	200	24	{	{	PUNCT
ejpam-4946	200	25	a1	a1	PROPN
ejpam-4946	200	26	}	}	PUNCT
ejpam-4946	200	27	.	.	PUNCT
ejpam-4946	201	1	then	then	ADV
ejpam-4946	201	2	,	,	PUNCT
ejpam-4946	201	3	l	l	NOUN
ejpam-4946	201	4	is	be	AUX
ejpam-4946	201	5	a	a	DET
ejpam-4946	201	6	j2	j2	NOUN
ejpam-4946	201	7	-	-	PUNCT
ejpam-4946	201	8	independent	independent	ADJ
ejpam-4946	201	9	set	set	NOUN
ejpam-4946	201	10	of	of	ADP
ejpam-4946	201	11	cq	cq	PROPN
ejpam-4946	201	12	.	.	PUNCT
ejpam-4946	202	1	since	since	SCONJ
ejpam-4946	202	2	dc4(a1	dc4(a1	PROPN
ejpam-4946	202	3	,	,	PUNCT
ejpam-4946	202	4	a2	a2	NOUN
ejpam-4946	202	5	)	)	PUNCT
ejpam-4946	202	6	=	=	SYM
ejpam-4946	202	7	1	1	NUM
ejpam-4946	202	8	=	=	SYM
ejpam-4946	202	9	dc4(a1	dc4(a1	PROPN
ejpam-4946	202	10	,	,	PUNCT
ejpam-4946	202	11	a4	a4	NUM
ejpam-4946	202	12	)	)	PUNCT
ejpam-4946	202	13	and	and	CCONJ
ejpam-4946	202	14	n2	n2	ADJ
ejpam-4946	202	15	c4	c4	NOUN
ejpam-4946	202	16	[	[	X
ejpam-4946	202	17	a1	a1	NOUN
ejpam-4946	202	18	]	]	X
ejpam-4946	202	19	=	=	SYM
ejpam-4946	202	20	n2	n2	PROPN
ejpam-4946	202	21	c4	c4	NOUN
ejpam-4946	202	22	[	[	X
ejpam-4946	202	23	a3	a3	NOUN
ejpam-4946	202	24	]	]	PUNCT
ejpam-4946	202	25	,	,	PUNCT
ejpam-4946	202	26	it	it	PRON
ejpam-4946	202	27	follows	follow	VERB
ejpam-4946	202	28	that	that	SCONJ
ejpam-4946	202	29	l	l	NOUN
ejpam-4946	202	30	=	=	PRON
ejpam-4946	202	31	{	{	PUNCT
ejpam-4946	202	32	a1	a1	NOUN
ejpam-4946	202	33	}	}	PUNCT
ejpam-4946	202	34	is	be	AUX
ejpam-4946	202	35	a	a	DET
ejpam-4946	202	36	maximum	maximum	ADJ
ejpam-4946	202	37	j2	j2	NOUN
ejpam-4946	202	38	-	-	PUNCT
ejpam-4946	202	39	independent	independent	ADJ
ejpam-4946	202	40	set	set	NOUN
ejpam-4946	202	41	of	of	ADP
ejpam-4946	202	42	c4	c4	NOUN
ejpam-4946	202	43	.	.	PUNCT
ejpam-4946	203	1	thus	thus	ADV
ejpam-4946	203	2	,	,	PUNCT
ejpam-4946	203	3	αj2(c4	αj2(c4	NUM
ejpam-4946	203	4	)	)	PUNCT
ejpam-4946	203	5	=	=	SYM
ejpam-4946	203	6	1	1	X
ejpam-4946	203	7	.	.	X
ejpam-4946	203	8	for	for	ADP
ejpam-4946	203	9	q	q	NOUN
ejpam-4946	203	10	=	=	SYM
ejpam-4946	203	11	5	5	NUM
ejpam-4946	203	12	,	,	PUNCT
ejpam-4946	203	13	let	let	VERB
ejpam-4946	203	14	v	v	X
ejpam-4946	203	15	(	(	PUNCT
ejpam-4946	203	16	c5	c5	PROPN
ejpam-4946	203	17	)	)	PUNCT
ejpam-4946	203	18	=	=	PRON
ejpam-4946	203	19	{	{	PUNCT
ejpam-4946	203	20	a1	a1	PROPN
ejpam-4946	203	21	,	,	PUNCT
ejpam-4946	203	22	a2	a2	PROPN
ejpam-4946	203	23	,	,	PUNCT
ejpam-4946	203	24	a3	a3	NOUN
ejpam-4946	203	25	,	,	PUNCT
ejpam-4946	203	26	a4	a4	NOUN
ejpam-4946	203	27	,	,	PUNCT
ejpam-4946	203	28	a5	a5	PROPN
ejpam-4946	203	29	}	}	PUNCT
ejpam-4946	203	30	.	.	PUNCT
ejpam-4946	204	1	consider	consider	VERB
ejpam-4946	204	2	n	n	X
ejpam-4946	204	3	=	=	PUNCT
ejpam-4946	204	4	{	{	PUNCT
ejpam-4946	204	5	a1	a1	NOUN
ejpam-4946	204	6	,	,	PUNCT
ejpam-4946	204	7	a3	a3	NOUN
ejpam-4946	204	8	}	}	PUNCT
ejpam-4946	204	9	.	.	PUNCT
ejpam-4946	205	1	then	then	ADV
ejpam-4946	205	2	n	n	PRON
ejpam-4946	205	3	is	be	AUX
ejpam-4946	205	4	a	a	DET
ejpam-4946	205	5	maximum	maximum	ADJ
ejpam-4946	205	6	independent	independent	ADJ
ejpam-4946	205	7	set	set	NOUN
ejpam-4946	205	8	of	of	ADP
ejpam-4946	205	9	c5	c5	PROPN
ejpam-4946	205	10	.	.	PUNCT
ejpam-4946	206	1	note	note	VERB
ejpam-4946	206	2	that	that	SCONJ
ejpam-4946	206	3	n2	n2	PROPN
ejpam-4946	206	4	c5	c5	PROPN
ejpam-4946	206	5	[	[	X
ejpam-4946	206	6	a1	a1	PROPN
ejpam-4946	206	7	]	]	X
ejpam-4946	206	8	=	=	SYM
ejpam-4946	206	9	{	{	PUNCT
ejpam-4946	206	10	a1	a1	PROPN
ejpam-4946	206	11	,	,	PUNCT
ejpam-4946	206	12	a3	a3	NOUN
ejpam-4946	206	13	,	,	PUNCT
ejpam-4946	206	14	a4	a4	NOUN
ejpam-4946	206	15	}	}	PUNCT
ejpam-4946	206	16	and	and	CCONJ
ejpam-4946	206	17	n2	n2	PROPN
ejpam-4946	206	18	c3	c3	PROPN
ejpam-4946	206	19	[	[	X
ejpam-4946	206	20	a3	a3	NOUN
ejpam-4946	206	21	]	]	X
ejpam-4946	206	22	=	=	SYM
ejpam-4946	206	23	{	{	PUNCT
ejpam-4946	206	24	a1	a1	PROPN
ejpam-4946	206	25	,	,	PUNCT
ejpam-4946	206	26	a3	a3	NOUN
ejpam-4946	206	27	,	,	PUNCT
ejpam-4946	206	28	a5	a5	PROPN
ejpam-4946	206	29	}	}	PUNCT
ejpam-4946	206	30	.	.	PUNCT
ejpam-4946	207	1	thus	thus	ADV
ejpam-4946	207	2	,	,	PUNCT
ejpam-4946	207	3	n2	n2	PROPN
ejpam-4946	207	4	c5	c5	PROPN
ejpam-4946	207	5	[	[	X
ejpam-4946	207	6	a1]\n2	a1]\n2	PROPN
ejpam-4946	207	7	c5	c5	PROPN
ejpam-4946	208	1	[	[	X
ejpam-4946	208	2	a3	a3	NOUN
ejpam-4946	208	3	]	]	X
ejpam-4946	208	4	=	=	SYM
ejpam-4946	208	5	{	{	PUNCT
ejpam-4946	208	6	a4	a4	NOUN
ejpam-4946	208	7	}	}	PUNCT
ejpam-4946	208	8	=	=	NOUN
ejpam-4946	208	9	̸	̸	ADJ
ejpam-4946	208	10	∅	∅	NOUN
ejpam-4946	208	11	and	and	CCONJ
ejpam-4946	208	12	n2	n2	ADJ
ejpam-4946	208	13	c3	c3	NOUN
ejpam-4946	209	1	[	[	X
ejpam-4946	209	2	a3]\n2	a3]\n2	X
ejpam-4946	209	3	c5	c5	PROPN
ejpam-4946	209	4	[	[	X
ejpam-4946	209	5	a1	a1	PROPN
ejpam-4946	209	6	]	]	X
ejpam-4946	209	7	=	=	SYM
ejpam-4946	209	8	{	{	PUNCT
ejpam-4946	209	9	a5	a5	NOUN
ejpam-4946	209	10	}	}	PUNCT
ejpam-4946	209	11	=	=	NOUN
ejpam-4946	209	12	̸	̸	X
ejpam-4946	209	13	∅.	∅.	ADP
ejpam-4946	209	14	hence	hence	ADV
ejpam-4946	209	15	,	,	PUNCT
ejpam-4946	209	16	n	n	PRON
ejpam-4946	209	17	is	be	AUX
ejpam-4946	209	18	a	a	DET
ejpam-4946	209	19	maximum	maximum	ADJ
ejpam-4946	209	20	j2	j2	NOUN
ejpam-4946	209	21	-	-	PUNCT
ejpam-4946	209	22	independent	independent	ADJ
ejpam-4946	209	23	set	set	NOUN
ejpam-4946	209	24	in	in	ADP
ejpam-4946	209	25	c5	c5	PROPN
ejpam-4946	209	26	,	,	PUNCT
ejpam-4946	209	27	and	and	CCONJ
ejpam-4946	209	28	so	so	ADV
ejpam-4946	209	29	αj2(c5	αj2(c5	NOUN
ejpam-4946	209	30	)	)	PUNCT
ejpam-4946	209	31	=	=	SYM
ejpam-4946	209	32	2	2	X
ejpam-4946	209	33	.	.	X
ejpam-4946	209	34	similarly	similarly	ADV
ejpam-4946	209	35	,	,	PUNCT
ejpam-4946	209	36	αj2(c6	αj2(c6	NOUN
ejpam-4946	209	37	)	)	PUNCT
ejpam-4946	209	38	=	=	SYM
ejpam-4946	209	39	2	2	X
ejpam-4946	209	40	.	.	PUNCT
ejpam-4946	209	41	suppose	suppose	VERB
ejpam-4946	209	42	that	that	SCONJ
ejpam-4946	209	43	q	q	PROPN
ejpam-4946	209	44	≥	≥	NUM
ejpam-4946	209	45	7	7	NUM
ejpam-4946	209	46	.	.	PUNCT
ejpam-4946	210	1	let	let	VERB
ejpam-4946	210	2	v	v	NOUN
ejpam-4946	210	3	(	(	PUNCT
ejpam-4946	210	4	cq	cq	NOUN
ejpam-4946	210	5	)	)	PUNCT
ejpam-4946	210	6	=	=	SYM
ejpam-4946	210	7	{	{	PUNCT
ejpam-4946	210	8	v1	v1	PROPN
ejpam-4946	210	9	,	,	PUNCT
ejpam-4946	210	10	v2	v2	PROPN
ejpam-4946	210	11	,	,	PUNCT
ejpam-4946	210	12	.	.	PUNCT
ejpam-4946	210	13	.	.	PUNCT
ejpam-4946	211	1	.	.	PUNCT
ejpam-4946	212	1	,	,	PUNCT
ejpam-4946	212	2	vq	vq	PROPN
ejpam-4946	212	3	}	}	PUNCT
ejpam-4946	212	4	,	,	PUNCT
ejpam-4946	212	5	and	and	CCONJ
ejpam-4946	212	6	consider	consider	VERB
ejpam-4946	212	7	the	the	DET
ejpam-4946	212	8	following	follow	VERB
ejpam-4946	212	9	two	two	NUM
ejpam-4946	212	10	cases	case	NOUN
ejpam-4946	212	11	:	:	PUNCT
ejpam-4946	212	12	case	case	NOUN
ejpam-4946	212	13	1	1	NUM
ejpam-4946	212	14	.	.	PUNCT
ejpam-4946	213	1	q	q	PROPN
ejpam-4946	213	2	is	be	AUX
ejpam-4946	213	3	odd	odd	ADJ
ejpam-4946	213	4	let	let	VERB
ejpam-4946	213	5	q	q	NOUN
ejpam-4946	213	6	=	=	PUNCT
ejpam-4946	213	7	{	{	PUNCT
ejpam-4946	213	8	v1	v1	PROPN
ejpam-4946	213	9	,	,	PUNCT
ejpam-4946	213	10	v3	v3	PROPN
ejpam-4946	213	11	,	,	PUNCT
ejpam-4946	213	12	.	.	PUNCT
ejpam-4946	213	13	.	.	PUNCT
ejpam-4946	214	1	.	.	PUNCT
ejpam-4946	215	1	,	,	PUNCT
ejpam-4946	215	2	vn−4	vn−4	NOUN
ejpam-4946	215	3	,	,	PUNCT
ejpam-4946	215	4	vn−2	vn−2	PROPN
ejpam-4946	215	5	}	}	PUNCT
ejpam-4946	215	6	.	.	PUNCT
ejpam-4946	216	1	then	then	ADV
ejpam-4946	216	2	q	q	X
ejpam-4946	216	3	is	be	AUX
ejpam-4946	216	4	a	a	DET
ejpam-4946	216	5	maximum	maximum	ADJ
ejpam-4946	216	6	independent	independent	ADJ
ejpam-4946	216	7	set	set	NOUN
ejpam-4946	216	8	of	of	ADP
ejpam-4946	216	9	cq	cq	PROPN
ejpam-4946	216	10	,	,	PUNCT
ejpam-4946	216	11	and	and	CCONJ
ejpam-4946	216	12	so	so	ADV
ejpam-4946	216	13	α(cq	α(cq	PROPN
ejpam-4946	216	14	)	)	PUNCT
ejpam-4946	216	15	=	=	SYM
ejpam-4946	217	1	|q|	|q|	AUX
ejpam-4946	217	2	.	.	PUNCT
ejpam-4946	217	3	observe	observe	VERB
ejpam-4946	217	4	that	that	SCONJ
ejpam-4946	217	5	vn−1	vn−1	PROPN
ejpam-4946	217	6	∈	∈	PROPN
ejpam-4946	217	7	n2	n2	PROPN
ejpam-4946	217	8	cq	cq	PROPN
ejpam-4946	218	1	[	[	X
ejpam-4946	218	2	v1]\n2	v1]\n2	PROPN
ejpam-4946	218	3	cq	cq	NOUN
ejpam-4946	219	1	[	[	X
ejpam-4946	219	2	vj	vj	X
ejpam-4946	219	3	]	]	X
ejpam-4946	219	4	∀	∀	PUNCT
ejpam-4946	220	1	j	j	PROPN
ejpam-4946	220	2	̸=	̸=	PROPN
ejpam-4946	220	3	1	1	NUM
ejpam-4946	220	4	,	,	PUNCT
ejpam-4946	220	5	vr−2	vr−2	NOUN
ejpam-4946	220	6	∈	∈	PROPN
ejpam-4946	220	7	n2	n2	PROPN
ejpam-4946	220	8	cq	cq	PROPN
ejpam-4946	221	1	[	[	X
ejpam-4946	221	2	vr]\n2	vr]\n2	ADP
ejpam-4946	221	3	cq	cq	PROPN
ejpam-4946	222	1	[	[	X
ejpam-4946	222	2	vq	vq	X
ejpam-4946	222	3	]	]	X
ejpam-4946	222	4	∀	∀	X
ejpam-4946	223	1	r	r	NOUN
ejpam-4946	223	2	<	<	X
ejpam-4946	223	3	q	q	X
ejpam-4946	223	4	,	,	PUNCT
ejpam-4946	223	5	where	where	SCONJ
ejpam-4946	223	6	r	r	NOUN
ejpam-4946	223	7	,	,	PUNCT
ejpam-4946	223	8	q	q	NOUN
ejpam-4946	223	9	∈	∈	PROPN
ejpam-4946	223	10	{	{	PUNCT
ejpam-4946	223	11	3	3	NUM
ejpam-4946	223	12	,	,	PUNCT
ejpam-4946	223	13	5	5	NUM
ejpam-4946	223	14	,	,	PUNCT
ejpam-4946	223	15	.	.	PUNCT
ejpam-4946	223	16	.	.	PUNCT
ejpam-4946	224	1	.	.	PUNCT
ejpam-4946	225	1	,	,	PUNCT
ejpam-4946	226	1	n	n	CCONJ
ejpam-4946	226	2	−	−	PROPN
ejpam-4946	226	3	2	2	NUM
ejpam-4946	226	4	}	}	PUNCT
ejpam-4946	226	5	,	,	PUNCT
ejpam-4946	226	6	vs+2	vs+2	NUM
ejpam-4946	226	7	∈	∈	PROPN
ejpam-4946	226	8	n2	n2	NOUN
ejpam-4946	226	9	cq	cq	PROPN
ejpam-4946	227	1	[	[	X
ejpam-4946	227	2	vs]\n2	vs]\n2	PROPN
ejpam-4946	227	3	cq	cq	PROPN
ejpam-4946	228	1	[	[	X
ejpam-4946	228	2	vt	vt	X
ejpam-4946	228	3	]	]	X
ejpam-4946	228	4	∀	∀	X
ejpam-4946	228	5	s	s	PART
ejpam-4946	228	6	<	<	X
ejpam-4946	228	7	t	t	PROPN
ejpam-4946	228	8	,	,	PUNCT
ejpam-4946	228	9	where	where	SCONJ
ejpam-4946	228	10	s	s	X
ejpam-4946	228	11	,	,	PUNCT
ejpam-4946	228	12	t	t	PROPN
ejpam-4946	228	13	∈	∈	PROPN
ejpam-4946	228	14	{	{	PUNCT
ejpam-4946	228	15	3	3	NUM
ejpam-4946	228	16	,	,	PUNCT
ejpam-4946	228	17	5	5	NUM
ejpam-4946	228	18	,	,	PUNCT
ejpam-4946	228	19	.	.	PUNCT
ejpam-4946	228	20	.	.	PUNCT
ejpam-4946	229	1	.	.	PUNCT
ejpam-4946	230	1	,	,	PUNCT
ejpam-4946	231	1	n	n	CCONJ
ejpam-4946	231	2	−	−	PROPN
ejpam-4946	231	3	2	2	NUM
ejpam-4946	231	4	}	}	PUNCT
ejpam-4946	231	5	.	.	PUNCT
ejpam-4946	232	1	thus	thus	ADV
ejpam-4946	232	2	,	,	PUNCT
ejpam-4946	232	3	n2	n2	PROPN
ejpam-4946	232	4	cq	cq	PROPN
ejpam-4946	233	1	[	[	X
ejpam-4946	233	2	vi]\n2	vi]\n2	ADJ
ejpam-4946	233	3	cq	cq	NOUN
ejpam-4946	234	1	[	[	X
ejpam-4946	234	2	vj	vj	X
ejpam-4946	234	3	]	]	X
ejpam-4946	234	4	̸=	̸=	PROPN
ejpam-4946	234	5	∅	∅	NOUN
ejpam-4946	234	6	∀	∀	NOUN
ejpam-4946	235	1	i	i	PRON
ejpam-4946	235	2	̸=	̸=	PROPN
ejpam-4946	235	3	j	j	PROPN
ejpam-4946	235	4	,	,	PUNCT
ejpam-4946	235	5	where	where	SCONJ
ejpam-4946	235	6	i	i	PRON
ejpam-4946	235	7	,	,	PUNCT
ejpam-4946	235	8	j	j	PROPN
ejpam-4946	235	9	∈	∈	PROPN
ejpam-4946	235	10	{	{	PUNCT
ejpam-4946	235	11	1	1	NUM
ejpam-4946	235	12	,	,	PUNCT
ejpam-4946	235	13	3	3	NUM
ejpam-4946	235	14	,	,	PUNCT
ejpam-4946	235	15	.	.	PUNCT
ejpam-4946	235	16	.	.	PUNCT
ejpam-4946	236	1	.	.	PUNCT
ejpam-4946	237	1	,	,	PUNCT
ejpam-4946	238	1	n	n	CCONJ
ejpam-4946	238	2	−	−	PROPN
ejpam-4946	238	3	4	4	NUM
ejpam-4946	238	4	,	,	PUNCT
ejpam-4946	238	5	n	n	CCONJ
ejpam-4946	238	6	−	−	PROPN
ejpam-4946	238	7	2	2	NUM
ejpam-4946	238	8	}	}	PUNCT
ejpam-4946	238	9	,	,	PUNCT
ejpam-4946	238	10	showing	show	VERB
ejpam-4946	238	11	that	that	PRON
ejpam-4946	238	12	q	q	NOUN
ejpam-4946	238	13	is	be	AUX
ejpam-4946	238	14	a	a	DET
ejpam-4946	238	15	j2	j2	NOUN
ejpam-4946	238	16	-	-	PUNCT
ejpam-4946	238	17	set	set	NOUN
ejpam-4946	238	18	in	in	ADP
ejpam-4946	238	19	cq	cq	PROPN
ejpam-4946	238	20	.	.	PUNCT
ejpam-4946	239	1	hence	hence	ADV
ejpam-4946	239	2	,	,	PUNCT
ejpam-4946	239	3	q	q	PROPN
ejpam-4946	239	4	is	be	AUX
ejpam-4946	239	5	a	a	DET
ejpam-4946	239	6	maximum	maximum	ADJ
ejpam-4946	239	7	j2	j2	NOUN
ejpam-4946	239	8	-	-	PUNCT
ejpam-4946	239	9	independent	independent	ADJ
ejpam-4946	239	10	set	set	NOUN
ejpam-4946	239	11	of	of	ADP
ejpam-4946	239	12	cq	cq	PROPN
ejpam-4946	239	13	,	,	PUNCT
ejpam-4946	239	14	and	and	CCONJ
ejpam-4946	239	15	so	so	ADV
ejpam-4946	239	16	αj2(cq	αj2(cq	PROPN
ejpam-4946	239	17	)	)	PUNCT
ejpam-4946	240	1	=	=	SYM
ejpam-4946	240	2	|q|	|q|	VERB
ejpam-4946	240	3	=	=	SYM
ejpam-4946	240	4	α(cq	α(cq	PROPN
ejpam-4946	240	5	)	)	PUNCT
ejpam-4946	240	6	.	.	PUNCT
ejpam-4946	241	1	case	case	NOUN
ejpam-4946	241	2	2	2	NUM
ejpam-4946	241	3	.	.	PUNCT
ejpam-4946	242	1	q	q	PUNCT
ejpam-4946	242	2	is	be	AUX
ejpam-4946	242	3	even	even	ADV
ejpam-4946	242	4	let	let	VERB
ejpam-4946	242	5	r	r	NOUN
ejpam-4946	242	6	=	=	SYM
ejpam-4946	242	7	{	{	PUNCT
ejpam-4946	242	8	v1	v1	PROPN
ejpam-4946	242	9	,	,	PUNCT
ejpam-4946	242	10	v3	v3	PROPN
ejpam-4946	242	11	,	,	PUNCT
ejpam-4946	242	12	...	...	PUNCT
ejpam-4946	242	13	,	,	PUNCT
ejpam-4946	242	14	vn−3	vn−3	PROPN
ejpam-4946	242	15	,	,	PUNCT
ejpam-4946	242	16	vn−1	vn−1	ADJ
ejpam-4946	242	17	}	}	PUNCT
ejpam-4946	242	18	.	.	PUNCT
ejpam-4946	243	1	r	r	NOUN
ejpam-4946	243	2	is	be	AUX
ejpam-4946	243	3	a	a	DET
ejpam-4946	243	4	maximum	maximum	ADJ
ejpam-4946	243	5	independent	independent	ADJ
ejpam-4946	243	6	set	set	NOUN
ejpam-4946	243	7	of	of	ADP
ejpam-4946	243	8	cq	cq	PROPN
ejpam-4946	243	9	,	,	PUNCT
ejpam-4946	243	10	and	and	CCONJ
ejpam-4946	243	11	so	so	ADV
ejpam-4946	243	12	α(cq	α(cq	PROPN
ejpam-4946	243	13	)	)	PUNCT
ejpam-4946	243	14	=	=	SYM
ejpam-4946	243	15	|r|	|r|	NOUN
ejpam-4946	243	16	.notice	.notice	NOUN
ejpam-4946	243	17	that	that	PRON
ejpam-4946	243	18	vn−1	vn−1	PROPN
ejpam-4946	243	19	∈	∈	PROPN
ejpam-4946	243	20	n2	n2	PROPN
ejpam-4946	243	21	cq	cq	PROPN
ejpam-4946	244	1	[	[	X
ejpam-4946	244	2	v1]\n2	v1]\n2	PROPN
ejpam-4946	244	3	cq	cq	NOUN
ejpam-4946	245	1	[	[	X
ejpam-4946	245	2	vi	vi	X
ejpam-4946	245	3	]	]	X
ejpam-4946	245	4	∀	∀	NOUN
ejpam-4946	246	1	i	i	NOUN
ejpam-4946	246	2	̸=	̸=	PROPN
ejpam-4946	246	3	n−3	n−3	PROPN
ejpam-4946	246	4	,	,	PUNCT
ejpam-4946	246	5	n−1	n−1	PROPN
ejpam-4946	246	6	,	,	PUNCT
ejpam-4946	246	7	v1	v1	PROPN
ejpam-4946	246	8	∈	∈	PROPN
ejpam-4946	246	9	n2	n2	NOUN
ejpam-4946	246	10	cq	cq	PROPN
ejpam-4946	247	1	[	[	X
ejpam-4946	247	2	v1]\n2	v1]\n2	PROPN
ejpam-4946	247	3	cq	cq	NOUN
ejpam-4946	248	1	[	[	X
ejpam-4946	248	2	vn−3	vn−3	PROPN
ejpam-4946	248	3	]	]	X
ejpam-4946	248	4	,	,	PUNCT
ejpam-4946	248	5	v3	v3	PROPN
ejpam-4946	248	6	∈	∈	PROPN
ejpam-4946	248	7	n2	n2	PROPN
ejpam-4946	248	8	cq	cq	PROPN
ejpam-4946	249	1	[	[	X
ejpam-4946	249	2	v1]\n2	v1]\n2	X
ejpam-4946	249	3	cq	cq	NOUN
ejpam-4946	250	1	[	[	X
ejpam-4946	250	2	vn−1	vn−1	PROPN
ejpam-4946	250	3	]	]	PUNCT
ejpam-4946	250	4	,	,	PUNCT
ejpam-4946	250	5	vj−2	vj−2	NOUN
ejpam-4946	250	6	∈	∈	PROPN
ejpam-4946	250	7	n2	n2	NOUN
ejpam-4946	250	8	cq	cq	PROPN
ejpam-4946	251	1	[	[	X
ejpam-4946	251	2	vj	vj	X
ejpam-4946	251	3	]	]	X
ejpam-4946	251	4	\n2	\n2	PROPN
ejpam-4946	251	5	cq	cq	PROPN
ejpam-4946	252	1	[	[	X
ejpam-4946	252	2	vi	vi	X
ejpam-4946	252	3	]	]	PUNCT
ejpam-4946	252	4	.	.	PUNCT
ejpam-4946	252	5	∀	∀	PUNCT
ejpam-4946	253	1	i	i	PRON
ejpam-4946	253	2	>	>	X
ejpam-4946	253	3	j	j	PROPN
ejpam-4946	253	4	,	,	PUNCT
ejpam-4946	253	5	i	i	PRON
ejpam-4946	253	6	̸=	̸=	PROPN
ejpam-4946	253	7	n−	n−	NOUN
ejpam-4946	253	8	1	1	NUM
ejpam-4946	253	9	vt+2	vt+2	NUM
ejpam-4946	253	10	∈	∈	PROPN
ejpam-4946	253	11	n2	n2	NOUN
ejpam-4946	253	12	cq	cq	PROPN
ejpam-4946	254	1	[	[	X
ejpam-4946	254	2	vt]\n2	vt]\n2	X
ejpam-4946	254	3	cq	cq	NOUN
ejpam-4946	255	1	[	[	X
ejpam-4946	255	2	vs	vs	ADP
ejpam-4946	255	3	]	]	X
ejpam-4946	255	4	∀	∀	X
ejpam-4946	255	5	s	s	PART
ejpam-4946	255	6	<	<	X
ejpam-4946	255	7	t	t	PROPN
ejpam-4946	255	8	,	,	PUNCT
ejpam-4946	255	9	s	s	PART
ejpam-4946	255	10	̸=	̸=	PROPN
ejpam-4946	255	11	1	1	NUM
ejpam-4946	255	12	,	,	PUNCT
ejpam-4946	255	13	t	t	PROPN
ejpam-4946	255	14	̸=	̸=	PROPN
ejpam-4946	255	15	n−1	n−1	PROPN
ejpam-4946	255	16	,	,	PUNCT
ejpam-4946	255	17	vs	vs	ADP
ejpam-4946	255	18	∈	∈	PROPN
ejpam-4946	255	19	n2	n2	PROPN
ejpam-4946	255	20	cq	cq	PROPN
ejpam-4946	256	1	[	[	X
ejpam-4946	256	2	vs]\n2	vs]\n2	PROPN
ejpam-4946	256	3	cq	cq	NOUN
ejpam-4946	257	1	[	[	X
ejpam-4946	257	2	vn−1	vn−1	PROPN
ejpam-4946	257	3	]	]	X
ejpam-4946	257	4	∀	∀	X
ejpam-4946	257	5	s	s	PART
ejpam-4946	257	6	̸=	̸=	PROPN
ejpam-4946	257	7	n−3	n−3	PROPN
ejpam-4946	257	8	,	,	PUNCT
ejpam-4946	257	9	vn−5	vn−5	PROPN
ejpam-4946	257	10	∈	∈	PROPN
ejpam-4946	257	11	n2	n2	PROPN
ejpam-4946	257	12	cq	cq	PROPN
ejpam-4946	258	1	[	[	X
ejpam-4946	258	2	vn−3]\n2	vn−3]\n2	X
ejpam-4946	258	3	cq	cq	NOUN
ejpam-4946	259	1	[	[	X
ejpam-4946	259	2	vn−1	vn−1	PROPN
ejpam-4946	259	3	]	]	X
ejpam-4946	259	4	,	,	PUNCT
ejpam-4946	259	5	a.	a.	NOUN
ejpam-4946	259	6	tapeing	tapeing	NOUN
ejpam-4946	259	7	et	et	PROPN
ejpam-4946	259	8	al	al	PROPN
ejpam-4946	259	9	.	.	PUNCT
ejpam-4946	259	10	/	/	SYM
ejpam-4946	259	11	eur	eur	PROPN
ejpam-4946	259	12	.	.	PUNCT
ejpam-4946	260	1	j.	j.	PROPN
ejpam-4946	260	2	pure	pure	PROPN
ejpam-4946	260	3	appl	appl	PROPN
ejpam-4946	260	4	.	.	PROPN
ejpam-4946	260	5	math	math	PROPN
ejpam-4946	260	6	,	,	PUNCT
ejpam-4946	260	7	17	17	NUM
ejpam-4946	260	8	(	(	PUNCT
ejpam-4946	260	9	1	1	NUM
ejpam-4946	260	10	)	)	PUNCT
ejpam-4946	260	11	(	(	PUNCT
ejpam-4946	260	12	2024	2024	NUM
ejpam-4946	260	13	)	)	PUNCT
ejpam-4946	260	14	,	,	PUNCT
ejpam-4946	260	15	124	124	NUM
ejpam-4946	260	16	-	-	SYM
ejpam-4946	260	17	134	134	NUM
ejpam-4946	260	18	130	130	NUM
ejpam-4946	260	19	vn−1	vn−1	PROPN
ejpam-4946	260	20	∈	∈	PROPN
ejpam-4946	260	21	n2	n2	NOUN
ejpam-4946	260	22	cq	cq	PROPN
ejpam-4946	261	1	[	[	X
ejpam-4946	261	2	vn−1]\n2	vn−1]\n2	PROPN
ejpam-4946	261	3	cq	cq	PROPN
ejpam-4946	262	1	[	[	X
ejpam-4946	262	2	vm	vm	X
ejpam-4946	262	3	]	]	X
ejpam-4946	262	4	∀	∀	PUNCT
ejpam-4946	262	5	m	m	VERB
ejpam-4946	262	6	̸=	̸=	PROPN
ejpam-4946	262	7	1	1	NUM
ejpam-4946	262	8	,	,	PUNCT
ejpam-4946	262	9	n	n	CCONJ
ejpam-4946	262	10	−	−	PROPN
ejpam-4946	262	11	3	3	NUM
ejpam-4946	262	12	,	,	PUNCT
ejpam-4946	262	13	vn−3	vn−3	PROPN
ejpam-4946	262	14	∈	∈	PROPN
ejpam-4946	262	15	n2	n2	PROPN
ejpam-4946	262	16	cq	cq	PROPN
ejpam-4946	263	1	[	[	X
ejpam-4946	263	2	vn−1]\n2	vn−1]\n2	PROPN
ejpam-4946	263	3	cq	cq	X
ejpam-4946	264	1	[	[	X
ejpam-4946	264	2	v1	v1	NOUN
ejpam-4946	264	3	]	]	PUNCT
ejpam-4946	264	4	and	and	CCONJ
ejpam-4946	264	5	v1	v1	PROPN
ejpam-4946	264	6	∈	∈	PROPN
ejpam-4946	264	7	n2	n2	NOUN
ejpam-4946	264	8	cq	cq	PROPN
ejpam-4946	265	1	[	[	X
ejpam-4946	265	2	vn−1]\n2	vn−1]\n2	PROPN
ejpam-4946	265	3	cq	cq	X
ejpam-4946	266	1	[	[	X
ejpam-4946	266	2	vn−3	vn−3	PROPN
ejpam-4946	266	3	]	]	X
ejpam-4946	266	4	.	.	PUNCT
ejpam-4946	267	1	thus	thus	ADV
ejpam-4946	267	2	,	,	PUNCT
ejpam-4946	267	3	n	n	PROPN
ejpam-4946	267	4	2	2	NUM
ejpam-4946	267	5	cq	cq	NOUN
ejpam-4946	268	1	[	[	X
ejpam-4946	268	2	vi]\n2	vi]\n2	ADJ
ejpam-4946	268	3	cq	cq	NOUN
ejpam-4946	269	1	[	[	X
ejpam-4946	269	2	vj	vj	X
ejpam-4946	269	3	]	]	PUNCT
ejpam-4946	269	4	∀	∀	PUNCT
ejpam-4946	270	1	i	i	NOUN
ejpam-4946	270	2	̸=	̸=	PROPN
ejpam-4946	270	3	j	j	PROPN
ejpam-4946	270	4	,	,	PUNCT
ejpam-4946	270	5	i	i	PRON
ejpam-4946	270	6	,	,	PUNCT
ejpam-4946	270	7	j	j	PROPN
ejpam-4946	270	8	∈	∈	PROPN
ejpam-4946	270	9	{	{	PUNCT
ejpam-4946	270	10	1	1	NUM
ejpam-4946	270	11	,	,	PUNCT
ejpam-4946	270	12	3	3	NUM
ejpam-4946	270	13	,	,	PUNCT
ejpam-4946	270	14	.	.	PUNCT
ejpam-4946	270	15	.	.	PUNCT
ejpam-4946	271	1	.	.	PUNCT
ejpam-4946	272	1	,	,	PUNCT
ejpam-4946	273	1	n	n	CCONJ
ejpam-4946	273	2	−	−	PROPN
ejpam-4946	273	3	3	3	NUM
ejpam-4946	273	4	,	,	PUNCT
ejpam-4946	273	5	n	n	CCONJ
ejpam-4946	273	6	−	−	PROPN
ejpam-4946	273	7	1	1	NUM
ejpam-4946	273	8	}	}	PUNCT
ejpam-4946	273	9	and	and	CCONJ
ejpam-4946	273	10	so	so	ADV
ejpam-4946	273	11	r	r	NOUN
ejpam-4946	273	12	is	be	AUX
ejpam-4946	273	13	a	a	DET
ejpam-4946	273	14	j2	j2	NOUN
ejpam-4946	273	15	-	-	PUNCT
ejpam-4946	273	16	set	set	NOUN
ejpam-4946	273	17	in	in	ADP
ejpam-4946	273	18	cq	cq	PROPN
ejpam-4946	273	19	.	.	PUNCT
ejpam-4946	274	1	consequently	consequently	ADV
ejpam-4946	274	2	,	,	PUNCT
ejpam-4946	274	3	αj2(cq	αj2(cq	PROPN
ejpam-4946	274	4	)	)	PUNCT
ejpam-4946	274	5	=	=	SYM
ejpam-4946	274	6	|r|	|r|	NOUN
ejpam-4946	274	7	=	=	SYM
ejpam-4946	274	8	α(cq	α(cq	PROPN
ejpam-4946	274	9	)	)	PUNCT
ejpam-4946	274	10	for	for	ADP
ejpam-4946	274	11	all	all	DET
ejpam-4946	274	12	n	n	PRON
ejpam-4946	274	13	≥	≥	NUM
ejpam-4946	274	14	7	7	NUM
ejpam-4946	274	15	.	.	PUNCT
ejpam-4946	274	16	theorem	theorem	NOUN
ejpam-4946	274	17	5	5	NUM
ejpam-4946	274	18	.	.	PUNCT
ejpam-4946	275	1	let	let	VERB
ejpam-4946	275	2	m	m	PRON
ejpam-4946	275	3	and	and	CCONJ
ejpam-4946	275	4	n	n	ADV
ejpam-4946	275	5	be	be	AUX
ejpam-4946	275	6	positive	positive	ADJ
ejpam-4946	275	7	integers	integer	NOUN
ejpam-4946	275	8	.	.	PUNCT
ejpam-4946	276	1	then	then	ADV
ejpam-4946	276	2	αj2(km	αj2(km	NOUN
ejpam-4946	276	3	,	,	PUNCT
ejpam-4946	276	4	n	n	CCONJ
ejpam-4946	276	5	)	)	PUNCT
ejpam-4946	276	6	=	=	SYM
ejpam-4946	276	7	1	1	X
ejpam-4946	276	8	.	.	PUNCT
ejpam-4946	277	1	proof	proof	NOUN
ejpam-4946	277	2	.	.	PUNCT
ejpam-4946	278	1	let	let	VERB
ejpam-4946	278	2	v	v	NOUN
ejpam-4946	278	3	(	(	PUNCT
ejpam-4946	278	4	km	km	PROPN
ejpam-4946	278	5	,	,	PUNCT
ejpam-4946	278	6	n	n	CCONJ
ejpam-4946	278	7	)	)	PUNCT
ejpam-4946	278	8	=	=	SYM
ejpam-4946	278	9	{	{	PUNCT
ejpam-4946	278	10	u1	u1	NOUN
ejpam-4946	278	11	,	,	PUNCT
ejpam-4946	278	12	u2	u2	NOUN
ejpam-4946	278	13	,	,	PUNCT
ejpam-4946	278	14	.	.	PUNCT
ejpam-4946	278	15	.	.	PUNCT
ejpam-4946	279	1	.	.	PUNCT
ejpam-4946	280	1	,	,	PUNCT
ejpam-4946	280	2	um	um	INTJ
ejpam-4946	280	3	,	,	PUNCT
ejpam-4946	280	4	v1	v1	PROPN
ejpam-4946	280	5	,	,	PUNCT
ejpam-4946	280	6	v2	v2	NOUN
ejpam-4946	280	7	,	,	PUNCT
ejpam-4946	280	8	.	.	PUNCT
ejpam-4946	280	9	.	.	PUNCT
ejpam-4946	281	1	.	.	PUNCT
ejpam-4946	282	1	,	,	PUNCT
ejpam-4946	282	2	vn	vn	PROPN
ejpam-4946	282	3	}	}	PUNCT
ejpam-4946	282	4	,	,	PUNCT
ejpam-4946	282	5	where	where	SCONJ
ejpam-4946	282	6	v	v	NOUN
ejpam-4946	282	7	(	(	PUNCT
ejpam-4946	282	8	km	km	NOUN
ejpam-4946	282	9	)	)	PUNCT
ejpam-4946	282	10	=	=	PRON
ejpam-4946	282	11	{	{	PUNCT
ejpam-4946	282	12	u1	u1	NOUN
ejpam-4946	282	13	,	,	PUNCT
ejpam-4946	282	14	u2	u2	NOUN
ejpam-4946	282	15	,	,	PUNCT
ejpam-4946	282	16	.	.	PUNCT
ejpam-4946	282	17	.	.	PUNCT
ejpam-4946	282	18	.	.	PUNCT
ejpam-4946	283	1	,	,	PUNCT
ejpam-4946	283	2	um	um	INTJ
ejpam-4946	283	3	}	}	PUNCT
ejpam-4946	283	4	and	and	CCONJ
ejpam-4946	283	5	v	v	INTJ
ejpam-4946	283	6	(	(	PUNCT
ejpam-4946	283	7	kn	kn	PROPN
ejpam-4946	283	8	)	)	PUNCT
ejpam-4946	283	9	=	=	SYM
ejpam-4946	283	10	{	{	PUNCT
ejpam-4946	283	11	v1	v1	PROPN
ejpam-4946	283	12	,	,	PUNCT
ejpam-4946	283	13	v2	v2	PROPN
ejpam-4946	283	14	,	,	PUNCT
ejpam-4946	283	15	.	.	PUNCT
ejpam-4946	283	16	.	.	PUNCT
ejpam-4946	284	1	.	.	PUNCT
ejpam-4946	285	1	,	,	PUNCT
ejpam-4946	285	2	vn	vn	PROPN
ejpam-4946	285	3	}	}	PUNCT
ejpam-4946	285	4	.	.	PUNCT
ejpam-4946	286	1	consider	consider	VERB
ejpam-4946	286	2	m	m	NOUN
ejpam-4946	286	3	=	=	PUNCT
ejpam-4946	286	4	{	{	PUNCT
ejpam-4946	286	5	u1	u1	NOUN
ejpam-4946	286	6	}	}	PUNCT
ejpam-4946	286	7	.	.	PUNCT
ejpam-4946	287	1	then	then	ADV
ejpam-4946	287	2	m	m	PROPN
ejpam-4946	287	3	is	be	AUX
ejpam-4946	287	4	a	a	DET
ejpam-4946	287	5	j2	j2	NOUN
ejpam-4946	287	6	-	-	PUNCT
ejpam-4946	287	7	independent	independent	ADJ
ejpam-4946	287	8	set	set	NOUN
ejpam-4946	287	9	of	of	ADP
ejpam-4946	287	10	km	km	PROPN
ejpam-4946	287	11	,	,	PUNCT
ejpam-4946	287	12	n.	n.	PROPN
ejpam-4946	287	13	observe	observe	VERB
ejpam-4946	287	14	that	that	SCONJ
ejpam-4946	287	15	n2	n2	ADJ
ejpam-4946	287	16	km	km	PROPN
ejpam-4946	287	17	,	,	PUNCT
ejpam-4946	287	18	n	n	PROPN
ejpam-4946	287	19	[	[	X
ejpam-4946	287	20	ui	ui	X
ejpam-4946	287	21	]	]	X
ejpam-4946	287	22	=	=	PUNCT
ejpam-4946	287	23	n2	n2	PROPN
ejpam-4946	287	24	km	km	PROPN
ejpam-4946	287	25	,	,	PUNCT
ejpam-4946	287	26	n	n	PROPN
ejpam-4946	287	27	[	[	X
ejpam-4946	287	28	uj	uj	X
ejpam-4946	287	29	]	]	PUNCT
ejpam-4946	287	30	∀	∀	PUNCT
ejpam-4946	288	1	i	i	NOUN
ejpam-4946	288	2	̸=	̸=	PROPN
ejpam-4946	288	3	j	j	PROPN
ejpam-4946	288	4	,	,	PUNCT
ejpam-4946	288	5	where	where	SCONJ
ejpam-4946	288	6	i	i	PRON
ejpam-4946	288	7	,	,	PUNCT
ejpam-4946	288	8	j	j	PROPN
ejpam-4946	288	9	∈	∈	PROPN
ejpam-4946	288	10	{	{	PUNCT
ejpam-4946	288	11	1	1	NUM
ejpam-4946	288	12	,	,	PUNCT
ejpam-4946	288	13	2	2	NUM
ejpam-4946	288	14	,	,	PUNCT
ejpam-4946	288	15	.	.	PUNCT
ejpam-4946	288	16	.	.	PUNCT
ejpam-4946	288	17	.	.	PUNCT
ejpam-4946	289	1	,	,	PUNCT
ejpam-4946	289	2	m	m	VERB
ejpam-4946	289	3	}	}	PUNCT
ejpam-4946	289	4	and	and	CCONJ
ejpam-4946	289	5	n2	n2	ADJ
ejpam-4946	289	6	km	km	PROPN
ejpam-4946	289	7	,	,	PUNCT
ejpam-4946	289	8	n	n	X
ejpam-4946	289	9	[	[	X
ejpam-4946	289	10	vs	vs	ADP
ejpam-4946	289	11	]	]	X
ejpam-4946	289	12	=	=	PUNCT
ejpam-4946	289	13	n2	n2	ADJ
ejpam-4946	289	14	km	km	PROPN
ejpam-4946	289	15	,	,	PUNCT
ejpam-4946	289	16	n	n	PRON
ejpam-4946	289	17	[	[	X
ejpam-4946	289	18	vt	vt	X
ejpam-4946	289	19	]	]	X
ejpam-4946	289	20	∀	∀	NOUN
ejpam-4946	290	1	i	i	NOUN
ejpam-4946	290	2	̸=	̸=	PROPN
ejpam-4946	290	3	j	j	PROPN
ejpam-4946	290	4	,	,	PUNCT
ejpam-4946	290	5	i	i	PRON
ejpam-4946	290	6	,	,	PUNCT
ejpam-4946	290	7	j	j	PROPN
ejpam-4946	290	8	∈	∈	PROPN
ejpam-4946	290	9	{	{	PUNCT
ejpam-4946	290	10	1	1	NUM
ejpam-4946	290	11	,	,	PUNCT
ejpam-4946	290	12	2	2	NUM
ejpam-4946	290	13	,	,	PUNCT
ejpam-4946	290	14	.	.	PUNCT
ejpam-4946	290	15	.	.	PUNCT
ejpam-4946	291	1	.	.	PUNCT
ejpam-4946	291	2	,	,	PUNCT
ejpam-4946	291	3	n	n	CCONJ
ejpam-4946	291	4	}	}	PUNCT
ejpam-4946	291	5	.	.	PUNCT
ejpam-4946	292	1	since	since	SCONJ
ejpam-4946	292	2	ur	ur	INTJ
ejpam-4946	292	3	and	and	CCONJ
ejpam-4946	292	4	vq	vq	NOUN
ejpam-4946	292	5	are	be	AUX
ejpam-4946	292	6	adjacent	adjacent	ADJ
ejpam-4946	292	7	for	for	ADP
ejpam-4946	292	8	all	all	DET
ejpam-4946	292	9	r	r	NOUN
ejpam-4946	292	10	∈	∈	NOUN
ejpam-4946	292	11	{	{	PUNCT
ejpam-4946	292	12	1	1	NUM
ejpam-4946	292	13	,	,	PUNCT
ejpam-4946	292	14	2	2	NUM
ejpam-4946	292	15	,	,	PUNCT
ejpam-4946	292	16	.	.	PUNCT
ejpam-4946	292	17	.	.	PUNCT
ejpam-4946	293	1	.	.	PUNCT
ejpam-4946	294	1	,	,	PUNCT
ejpam-4946	294	2	m	m	VERB
ejpam-4946	294	3	}	}	PUNCT
ejpam-4946	294	4	and	and	CCONJ
ejpam-4946	294	5	q	q	ADJ
ejpam-4946	294	6	∈	∈	PROPN
ejpam-4946	294	7	{	{	PUNCT
ejpam-4946	294	8	1	1	NUM
ejpam-4946	294	9	,	,	PUNCT
ejpam-4946	294	10	2	2	NUM
ejpam-4946	294	11	,	,	PUNCT
ejpam-4946	294	12	.	.	PUNCT
ejpam-4946	294	13	.	.	PUNCT
ejpam-4946	294	14	.	.	PUNCT
ejpam-4946	295	1	,	,	PUNCT
ejpam-4946	295	2	n	n	CCONJ
ejpam-4946	295	3	}	}	PUNCT
ejpam-4946	295	4	,	,	PUNCT
ejpam-4946	295	5	it	it	PRON
ejpam-4946	295	6	follows	follow	VERB
ejpam-4946	295	7	that	that	SCONJ
ejpam-4946	295	8	m	m	PROPN
ejpam-4946	295	9	is	be	AUX
ejpam-4946	295	10	a	a	DET
ejpam-4946	295	11	maximum	maximum	ADJ
ejpam-4946	295	12	j2	j2	NOUN
ejpam-4946	295	13	-	-	PUNCT
ejpam-4946	295	14	independent	independent	ADJ
ejpam-4946	295	15	set	set	NOUN
ejpam-4946	295	16	of	of	ADP
ejpam-4946	295	17	km	km	PROPN
ejpam-4946	295	18	,	,	PUNCT
ejpam-4946	295	19	n.	n.	PROPN
ejpam-4946	295	20	therefore	therefore	ADV
ejpam-4946	295	21	,	,	PUNCT
ejpam-4946	295	22	αj2(km	αj2(km	NOUN
ejpam-4946	295	23	,	,	PUNCT
ejpam-4946	295	24	n	n	CCONJ
ejpam-4946	295	25	)	)	PUNCT
ejpam-4946	295	26	=	=	SYM
ejpam-4946	295	27	1	1	NUM
ejpam-4946	295	28	∀	∀	X
ejpam-4946	295	29	m	m	PROPN
ejpam-4946	295	30	,	,	PUNCT
ejpam-4946	295	31	n	n	PRON
ejpam-4946	295	32	≥	≥	NOUN
ejpam-4946	295	33	1	1	NUM
ejpam-4946	295	34	.	.	PUNCT
ejpam-4946	296	1	theorem	theorem	NOUN
ejpam-4946	296	2	6	6	NUM
ejpam-4946	296	3	.	.	PUNCT
ejpam-4946	297	1	let	let	VERB
ejpam-4946	297	2	s	s	PRON
ejpam-4946	297	3	and	and	CCONJ
ejpam-4946	297	4	t	t	PROPN
ejpam-4946	297	5	be	be	AUX
ejpam-4946	297	6	two	two	NUM
ejpam-4946	297	7	connected	connected	ADJ
ejpam-4946	297	8	graphs	graph	NOUN
ejpam-4946	297	9	.	.	PUNCT
ejpam-4946	298	1	a	a	DET
ejpam-4946	298	2	subset	subset	ADJ
ejpam-4946	298	3	l	l	NOUN
ejpam-4946	298	4	of	of	ADP
ejpam-4946	298	5	vertices	vertex	NOUN
ejpam-4946	298	6	of	of	ADP
ejpam-4946	298	7	s	s	NOUN
ejpam-4946	298	8	+	+	NUM
ejpam-4946	298	9	t	t	PROPN
ejpam-4946	298	10	is	be	AUX
ejpam-4946	298	11	a	a	DET
ejpam-4946	298	12	j2	j2	NOUN
ejpam-4946	298	13	-	-	PUNCT
ejpam-4946	298	14	independent	independent	ADJ
ejpam-4946	298	15	set	set	NOUN
ejpam-4946	298	16	of	of	ADP
ejpam-4946	298	17	s	s	PROPN
ejpam-4946	298	18	+	+	X
ejpam-4946	298	19	t	t	NOUN
ejpam-4946	299	1	if	if	SCONJ
ejpam-4946	299	2	one	one	NUM
ejpam-4946	299	3	of	of	ADP
ejpam-4946	299	4	the	the	DET
ejpam-4946	299	5	following	follow	VERB
ejpam-4946	299	6	holds	hold	NOUN
ejpam-4946	299	7	;	;	PUNCT
ejpam-4946	299	8	(	(	PUNCT
ejpam-4946	299	9	i	i	NOUN
ejpam-4946	299	10	)	)	PUNCT
ejpam-4946	299	11	l	l	NOUN
ejpam-4946	299	12	is	be	AUX
ejpam-4946	299	13	a	a	DET
ejpam-4946	299	14	j2	j2	NOUN
ejpam-4946	299	15	-	-	PUNCT
ejpam-4946	299	16	independent	independent	ADJ
ejpam-4946	299	17	set	set	NOUN
ejpam-4946	299	18	in	in	ADP
ejpam-4946	299	19	s	s	PROPN
ejpam-4946	299	20	(	(	PUNCT
ejpam-4946	299	21	ii	ii	NOUN
ejpam-4946	299	22	)	)	PUNCT
ejpam-4946	299	23	l	l	NOUN
ejpam-4946	299	24	is	be	AUX
ejpam-4946	299	25	a	a	DET
ejpam-4946	299	26	j2	j2	NOUN
ejpam-4946	299	27	-	-	PUNCT
ejpam-4946	299	28	independent	independent	ADJ
ejpam-4946	299	29	set	set	NOUN
ejpam-4946	299	30	in	in	ADP
ejpam-4946	299	31	t	t	NOUN
ejpam-4946	299	32	proof	proof	NOUN
ejpam-4946	299	33	.	.	PUNCT
ejpam-4946	300	1	suppose	suppose	VERB
ejpam-4946	300	2	that	that	SCONJ
ejpam-4946	300	3	l	l	NOUN
ejpam-4946	300	4	is	be	AUX
ejpam-4946	300	5	a	a	DET
ejpam-4946	300	6	j2	j2	NOUN
ejpam-4946	300	7	-	-	PUNCT
ejpam-4946	300	8	independent	independent	ADJ
ejpam-4946	300	9	set	set	NOUN
ejpam-4946	300	10	in	in	ADP
ejpam-4946	300	11	s.	s.	PROPN
ejpam-4946	300	12	then	then	ADV
ejpam-4946	300	13	l	l	PROPN
ejpam-4946	300	14	is	be	AUX
ejpam-4946	300	15	an	an	DET
ejpam-4946	300	16	independent	independent	ADJ
ejpam-4946	300	17	set	set	NOUN
ejpam-4946	300	18	in	in	ADP
ejpam-4946	300	19	s.	s.	PROPN
ejpam-4946	300	20	let	let	VERB
ejpam-4946	300	21	a	a	DET
ejpam-4946	300	22	,	,	PUNCT
ejpam-4946	300	23	b	b	X
ejpam-4946	300	24	∈	∈	PROPN
ejpam-4946	300	25	l.	l.	PROPN
ejpam-4946	300	26	then	then	ADV
ejpam-4946	300	27	ds(a	ds(a	VERB
ejpam-4946	300	28	,	,	PUNCT
ejpam-4946	300	29	b	b	X
ejpam-4946	300	30	)	)	PUNCT
ejpam-4946	300	31	̸=	̸=	PROPN
ejpam-4946	300	32	1	1	NUM
ejpam-4946	300	33	.	.	PUNCT
ejpam-4946	301	1	if	if	SCONJ
ejpam-4946	301	2	ds(a	ds(a	VERB
ejpam-4946	301	3	,	,	PUNCT
ejpam-4946	301	4	b	b	X
ejpam-4946	301	5	)	)	PUNCT
ejpam-4946	301	6	=	=	SYM
ejpam-4946	301	7	2	2	NUM
ejpam-4946	301	8	,	,	PUNCT
ejpam-4946	301	9	then	then	ADV
ejpam-4946	301	10	ds+t	ds+t	PROPN
ejpam-4946	301	11	(	(	PUNCT
ejpam-4946	301	12	a	a	DET
ejpam-4946	301	13	,	,	PUNCT
ejpam-4946	301	14	b	b	NOUN
ejpam-4946	301	15	)	)	PUNCT
ejpam-4946	301	16	=	=	SYM
ejpam-4946	301	17	2	2	NUM
ejpam-4946	301	18	̸=	̸=	PROPN
ejpam-4946	301	19	1	1	NUM
ejpam-4946	301	20	,	,	PUNCT
ejpam-4946	301	21	and	and	CCONJ
ejpam-4946	301	22	we	we	PRON
ejpam-4946	301	23	are	be	AUX
ejpam-4946	301	24	done	do	VERB
ejpam-4946	301	25	.	.	PUNCT
ejpam-4946	302	1	if	if	SCONJ
ejpam-4946	302	2	ds(a	ds(a	VERB
ejpam-4946	302	3	,	,	PUNCT
ejpam-4946	302	4	b	b	X
ejpam-4946	302	5	)	)	PUNCT
ejpam-4946	302	6	≥	≥	NOUN
ejpam-4946	302	7	3	3	NUM
ejpam-4946	302	8	,	,	PUNCT
ejpam-4946	302	9	then	then	ADV
ejpam-4946	302	10	ds+t	ds+t	PROPN
ejpam-4946	302	11	(	(	PUNCT
ejpam-4946	302	12	a	a	DET
ejpam-4946	302	13	,	,	PUNCT
ejpam-4946	302	14	b	b	NOUN
ejpam-4946	302	15	)	)	PUNCT
ejpam-4946	302	16	=	=	SYM
ejpam-4946	302	17	2	2	NUM
ejpam-4946	302	18	̸=	̸=	PROPN
ejpam-4946	302	19	1	1	NUM
ejpam-4946	302	20	.	.	PUNCT
ejpam-4946	303	1	therefore	therefore	ADV
ejpam-4946	303	2	,	,	PUNCT
ejpam-4946	303	3	l	l	NOUN
ejpam-4946	303	4	is	be	AUX
ejpam-4946	303	5	an	an	DET
ejpam-4946	303	6	independent	independent	ADJ
ejpam-4946	303	7	set	set	NOUN
ejpam-4946	303	8	of	of	ADP
ejpam-4946	303	9	s	s	NOUN
ejpam-4946	303	10	+	+	NUM
ejpam-4946	303	11	t.	t.	NOUN
ejpam-4946	303	12	it	it	PRON
ejpam-4946	303	13	suffices	suffice	VERB
ejpam-4946	303	14	to	to	PART
ejpam-4946	303	15	show	show	VERB
ejpam-4946	303	16	that	that	SCONJ
ejpam-4946	303	17	l	l	NOUN
ejpam-4946	303	18	is	be	AUX
ejpam-4946	303	19	a	a	DET
ejpam-4946	303	20	j2	j2	NOUN
ejpam-4946	303	21	-	-	PUNCT
ejpam-4946	303	22	set	set	NOUN
ejpam-4946	303	23	in	in	ADP
ejpam-4946	303	24	s	s	PROPN
ejpam-4946	303	25	+	+	X
ejpam-4946	303	26	t.	t.	NOUN
ejpam-4946	303	27	let	let	VERB
ejpam-4946	303	28	x	x	PRON
ejpam-4946	303	29	,	,	PUNCT
ejpam-4946	303	30	y	y	PROPN
ejpam-4946	303	31	∈	∈	PROPN
ejpam-4946	303	32	l.	l.	NOUN
ejpam-4946	303	33	since	since	SCONJ
ejpam-4946	303	34	l	l	PROPN
ejpam-4946	303	35	is	be	AUX
ejpam-4946	303	36	a	a	DET
ejpam-4946	303	37	j2	j2	NOUN
ejpam-4946	303	38	-	-	PUNCT
ejpam-4946	303	39	independent	independent	ADJ
ejpam-4946	303	40	set	set	NOUN
ejpam-4946	303	41	is	be	AUX
ejpam-4946	303	42	s	s	PRON
ejpam-4946	303	43	,	,	PUNCT
ejpam-4946	303	44	it	it	PRON
ejpam-4946	303	45	follows	follow	VERB
ejpam-4946	303	46	n2	n2	PROPN
ejpam-4946	303	47	s	s	PART
ejpam-4946	304	1	[	[	X
ejpam-4946	304	2	x]\n2	x]\n2	PROPN
ejpam-4946	304	3	s	s	PART
ejpam-4946	304	4	[	[	X
ejpam-4946	304	5	y	y	X
ejpam-4946	304	6	]	]	X
ejpam-4946	304	7	̸=	̸=	PROPN
ejpam-4946	304	8	∅	∅	NOUN
ejpam-4946	304	9	and	and	CCONJ
ejpam-4946	304	10	n2	n2	PROPN
ejpam-4946	304	11	s	s	PART
ejpam-4946	304	12	[	[	X
ejpam-4946	304	13	y]\n2	y]\n2	PROPN
ejpam-4946	304	14	s	s	PART
ejpam-4946	304	15	[	[	X
ejpam-4946	304	16	x	x	X
ejpam-4946	304	17	]	]	X
ejpam-4946	304	18	̸=	̸=	PROPN
ejpam-4946	304	19	∅.	∅.	ADV
ejpam-4946	304	20	assume	assume	VERB
ejpam-4946	304	21	that	that	SCONJ
ejpam-4946	304	22	ds(x	ds(x	PROPN
ejpam-4946	304	23	,	,	PUNCT
ejpam-4946	304	24	y	y	NOUN
ejpam-4946	304	25	)	)	PUNCT
ejpam-4946	304	26	=	=	SYM
ejpam-4946	304	27	2	2	X
ejpam-4946	304	28	.	.	PUNCT
ejpam-4946	304	29	since	since	SCONJ
ejpam-4946	304	30	l	l	NOUN
ejpam-4946	304	31	is	be	AUX
ejpam-4946	304	32	a	a	DET
ejpam-4946	304	33	j2	j2	NOUN
ejpam-4946	304	34	-	-	PUNCT
ejpam-4946	304	35	independent	independent	ADJ
ejpam-4946	304	36	set	set	NOUN
ejpam-4946	304	37	in	in	ADP
ejpam-4946	304	38	s	s	PROPN
ejpam-4946	304	39	,	,	PUNCT
ejpam-4946	304	40	there	there	PRON
ejpam-4946	304	41	exist	exist	VERB
ejpam-4946	304	42	w	w	NOUN
ejpam-4946	304	43	,	,	PUNCT
ejpam-4946	304	44	z	z	PROPN
ejpam-4946	304	45	∈	∈	PROPN
ejpam-4946	304	46	v	v	ADP
ejpam-4946	304	47	(	(	PUNCT
ejpam-4946	304	48	s	s	NOUN
ejpam-4946	304	49	)	)	PUNCT
ejpam-4946	304	50	such	such	ADJ
ejpam-4946	304	51	that	that	SCONJ
ejpam-4946	304	52	w	w	PROPN
ejpam-4946	304	53	∈	∈	PROPN
ejpam-4946	304	54	n2	n2	NOUN
ejpam-4946	304	55	s	s	PART
ejpam-4946	305	1	[	[	X
ejpam-4946	305	2	x]\n2	x]\n2	PROPN
ejpam-4946	305	3	s	s	PART
ejpam-4946	306	1	[	[	X
ejpam-4946	306	2	y	y	X
ejpam-4946	306	3	]	]	X
ejpam-4946	306	4	and	and	CCONJ
ejpam-4946	306	5	z	z	NOUN
ejpam-4946	306	6	∈	∈	PROPN
ejpam-4946	306	7	n2	n2	NOUN
ejpam-4946	306	8	s	s	PART
ejpam-4946	306	9	[	[	X
ejpam-4946	306	10	y]\n2	y]\n2	PROPN
ejpam-4946	306	11	s	s	PART
ejpam-4946	306	12	[	[	X
ejpam-4946	306	13	x	x	X
ejpam-4946	306	14	]	]	X
ejpam-4946	306	15	.	.	PUNCT
ejpam-4946	307	1	let	let	VERB
ejpam-4946	307	2	s	s	PRON
ejpam-4946	307	3	∈	∈	NOUN
ejpam-4946	307	4	ns(w	ns(w	NOUN
ejpam-4946	307	5	)	)	PUNCT
ejpam-4946	307	6	∩	∩	NOUN
ejpam-4946	307	7	ns(x	ns(x	PUNCT
ejpam-4946	307	8	)	)	PUNCT
ejpam-4946	307	9	and	and	CCONJ
ejpam-4946	307	10	t	t	PROPN
ejpam-4946	307	11	∈	∈	PROPN
ejpam-4946	307	12	ns(z	ns(z	NUM
ejpam-4946	307	13	)	)	PUNCT
ejpam-4946	307	14	∩	∩	NOUN
ejpam-4946	307	15	ns(y	ns(y	NUM
ejpam-4946	307	16	)	)	PUNCT
ejpam-4946	307	17	.	.	PUNCT
ejpam-4946	308	1	then	then	ADV
ejpam-4946	308	2	s	s	VERB
ejpam-4946	308	3	∈	∈	PROPN
ejpam-4946	308	4	n2	n2	NOUN
ejpam-4946	308	5	s+t	s+t	PROPN
ejpam-4946	309	1	[	[	X
ejpam-4946	309	2	y]\n2	y]\n2	PROPN
ejpam-4946	309	3	s+t	s+t	PROPN
ejpam-4946	310	1	[	[	X
ejpam-4946	310	2	x	x	X
ejpam-4946	310	3	]	]	X
ejpam-4946	310	4	and	and	CCONJ
ejpam-4946	310	5	t	t	PROPN
ejpam-4946	310	6	∈	∈	PROPN
ejpam-4946	310	7	n2	n2	NOUN
ejpam-4946	310	8	s+t	s+t	PROPN
ejpam-4946	311	1	[	[	X
ejpam-4946	311	2	x]\n2	x]\n2	PROPN
ejpam-4946	311	3	s+t	s+t	PROPN
ejpam-4946	312	1	[	[	X
ejpam-4946	312	2	y	y	X
ejpam-4946	312	3	]	]	X
ejpam-4946	312	4	.	.	PUNCT
ejpam-4946	313	1	thus	thus	ADV
ejpam-4946	313	2	,	,	PUNCT
ejpam-4946	313	3	l	l	NOUN
ejpam-4946	313	4	is	be	AUX
ejpam-4946	313	5	a	a	DET
ejpam-4946	313	6	j2set	j2set	NOUN
ejpam-4946	313	7	in	in	ADP
ejpam-4946	313	8	s	s	PROPN
ejpam-4946	313	9	+	+	CCONJ
ejpam-4946	313	10	t.	t.	NOUN
ejpam-4946	313	11	next	next	ADV
ejpam-4946	313	12	,	,	PUNCT
ejpam-4946	313	13	suppose	suppose	VERB
ejpam-4946	313	14	that	that	SCONJ
ejpam-4946	313	15	ds(x	ds(x	PROPN
ejpam-4946	313	16	,	,	PUNCT
ejpam-4946	313	17	y	y	PROPN
ejpam-4946	313	18	)	)	PUNCT
ejpam-4946	313	19	≥	≥	NOUN
ejpam-4946	313	20	3	3	NUM
ejpam-4946	313	21	.	.	PUNCT
ejpam-4946	314	1	let	let	VERB
ejpam-4946	314	2	u	u	PRON
ejpam-4946	314	3	∈	∈	NOUN
ejpam-4946	314	4	ns(x	ns(x	PUNCT
ejpam-4946	314	5	)	)	PUNCT
ejpam-4946	314	6	and	and	CCONJ
ejpam-4946	314	7	v	v	ADP
ejpam-4946	314	8	∈	∈	NUM
ejpam-4946	314	9	ns(y	ns(y	NUM
ejpam-4946	314	10	)	)	PUNCT
ejpam-4946	314	11	,	,	PUNCT
ejpam-4946	314	12	then	then	ADV
ejpam-4946	314	13	u	u	PROPN
ejpam-4946	314	14	∈	∈	PROPN
ejpam-4946	314	15	n2	n2	NOUN
ejpam-4946	314	16	s+t	s+t	PROPN
ejpam-4946	315	1	[	[	X
ejpam-4946	315	2	y]\n2	y]\n2	PROPN
ejpam-4946	315	3	s+t	s+t	PROPN
ejpam-4946	316	1	[	[	X
ejpam-4946	316	2	x	x	X
ejpam-4946	316	3	]	]	X
ejpam-4946	316	4	and	and	CCONJ
ejpam-4946	316	5	v	v	ADP
ejpam-4946	316	6	∈	∈	PROPN
ejpam-4946	316	7	n2	n2	NOUN
ejpam-4946	316	8	s+t	s+t	PROPN
ejpam-4946	317	1	[	[	X
ejpam-4946	317	2	x]\n2	x]\n2	PROPN
ejpam-4946	317	3	s+t	s+t	PROPN
ejpam-4946	318	1	[	[	X
ejpam-4946	318	2	y	y	X
ejpam-4946	318	3	]	]	X
ejpam-4946	318	4	.	.	PUNCT
ejpam-4946	319	1	hence	hence	ADV
ejpam-4946	319	2	,	,	PUNCT
ejpam-4946	319	3	l	l	PROPN
ejpam-4946	319	4	is	be	AUX
ejpam-4946	319	5	a	a	DET
ejpam-4946	319	6	j2	j2	NOUN
ejpam-4946	319	7	-	-	PUNCT
ejpam-4946	319	8	set	set	NOUN
ejpam-4946	319	9	in	in	ADP
ejpam-4946	319	10	s	s	PROPN
ejpam-4946	319	11	+	+	X
ejpam-4946	319	12	t	t	PROPN
ejpam-4946	319	13	,	,	PUNCT
ejpam-4946	319	14	showing	show	VERB
ejpam-4946	319	15	that	that	SCONJ
ejpam-4946	319	16	l	l	NOUN
ejpam-4946	319	17	is	be	AUX
ejpam-4946	319	18	a	a	DET
ejpam-4946	319	19	j2	j2	NOUN
ejpam-4946	319	20	-	-	PUNCT
ejpam-4946	319	21	independent	independent	ADJ
ejpam-4946	319	22	set	set	NOUN
ejpam-4946	319	23	in	in	ADP
ejpam-4946	319	24	s	s	PROPN
ejpam-4946	319	25	+	+	X
ejpam-4946	319	26	t.	t.	NOUN
ejpam-4946	319	27	similarly	similarly	ADV
ejpam-4946	319	28	,	,	PUNCT
ejpam-4946	319	29	if	if	SCONJ
ejpam-4946	319	30	l	l	NOUN
ejpam-4946	319	31	is	be	AUX
ejpam-4946	319	32	a	a	DET
ejpam-4946	319	33	j2	j2	NOUN
ejpam-4946	319	34	-	-	PUNCT
ejpam-4946	319	35	independent	independent	ADJ
ejpam-4946	319	36	set	set	NOUN
ejpam-4946	319	37	in	in	ADP
ejpam-4946	319	38	t	t	PROPN
ejpam-4946	319	39	,	,	PUNCT
ejpam-4946	319	40	then	then	ADV
ejpam-4946	319	41	l	l	PROPN
ejpam-4946	319	42	is	be	AUX
ejpam-4946	319	43	a	a	DET
ejpam-4946	319	44	j2	j2	NOUN
ejpam-4946	319	45	-	-	PUNCT
ejpam-4946	319	46	independent	independent	ADJ
ejpam-4946	319	47	set	set	NOUN
ejpam-4946	319	48	in	in	ADP
ejpam-4946	319	49	s	s	PROPN
ejpam-4946	319	50	+	+	NOUN
ejpam-4946	319	51	t.	t.	NOUN
ejpam-4946	319	52	corollary	corollary	ADJ
ejpam-4946	319	53	1	1	NUM
ejpam-4946	319	54	.	.	PUNCT
ejpam-4946	320	1	let	let	VERB
ejpam-4946	320	2	s	s	PRON
ejpam-4946	320	3	and	and	CCONJ
ejpam-4946	320	4	t	t	PROPN
ejpam-4946	320	5	be	be	AUX
ejpam-4946	320	6	two	two	NUM
ejpam-4946	320	7	connected	connected	ADJ
ejpam-4946	320	8	graphs	graph	NOUN
ejpam-4946	320	9	.	.	PUNCT
ejpam-4946	321	1	then	then	ADV
ejpam-4946	321	2	αj2(s	αj2(s	PROPN
ejpam-4946	321	3	+	+	CCONJ
ejpam-4946	321	4	t	t	PROPN
ejpam-4946	321	5	)	)	PUNCT
ejpam-4946	321	6	≥	≥	PROPN
ejpam-4946	321	7	max	max	PROPN
ejpam-4946	321	8	{	{	PUNCT
ejpam-4946	321	9	αj2(s	αj2(s	NOUN
ejpam-4946	321	10	)	)	PUNCT
ejpam-4946	321	11	,	,	PUNCT
ejpam-4946	321	12	αj2(t	αj2(t	PROPN
ejpam-4946	321	13	)	)	PUNCT
ejpam-4946	321	14	}	}	PUNCT
ejpam-4946	321	15	.	.	PUNCT
ejpam-4946	322	1	proof	proof	NOUN
ejpam-4946	322	2	.	.	PUNCT
ejpam-4946	323	1	let	let	VERB
ejpam-4946	323	2	l	l	NOUN
ejpam-4946	323	3	be	be	AUX
ejpam-4946	323	4	a	a	DET
ejpam-4946	323	5	maximum	maximum	ADJ
ejpam-4946	323	6	j2	j2	NOUN
ejpam-4946	323	7	-	-	PUNCT
ejpam-4946	323	8	independent	independent	ADJ
ejpam-4946	323	9	set	set	NOUN
ejpam-4946	323	10	of	of	ADP
ejpam-4946	323	11	s.	s.	PROPN
ejpam-4946	323	12	then	then	ADV
ejpam-4946	323	13	by	by	ADP
ejpam-4946	323	14	theorem	theorem	NOUN
ejpam-4946	323	15	6	6	NUM
ejpam-4946	323	16	,	,	PUNCT
ejpam-4946	323	17	l	l	NOUN
ejpam-4946	323	18	is	be	AUX
ejpam-4946	323	19	a	a	DET
ejpam-4946	323	20	j2	j2	NOUN
ejpam-4946	323	21	-	-	PUNCT
ejpam-4946	323	22	independent	independent	ADJ
ejpam-4946	323	23	set	set	NOUN
ejpam-4946	323	24	of	of	ADP
ejpam-4946	323	25	s	s	NOUN
ejpam-4946	323	26	+	+	X
ejpam-4946	323	27	t.	t.	NOUN
ejpam-4946	323	28	since	since	SCONJ
ejpam-4946	323	29	αj2(s	αj2(s	PROPN
ejpam-4946	323	30	+	+	CCONJ
ejpam-4946	323	31	t	t	NOUN
ejpam-4946	323	32	)	)	PUNCT
ejpam-4946	323	33	is	be	AUX
ejpam-4946	323	34	the	the	DET
ejpam-4946	323	35	maximum	maximum	ADJ
ejpam-4946	323	36	cardinality	cardinality	NOUN
ejpam-4946	323	37	among	among	ADP
ejpam-4946	323	38	all	all	DET
ejpam-4946	323	39	j2	j2	PROPN
ejpam-4946	323	40	-	-	PUNCT
ejpam-4946	323	41	independent	independent	ADJ
ejpam-4946	323	42	sets	set	NOUN
ejpam-4946	323	43	of	of	ADP
ejpam-4946	323	44	s	s	PROPN
ejpam-4946	323	45	+	+	NUM
ejpam-4946	323	46	t	t	PROPN
ejpam-4946	323	47	,	,	PUNCT
ejpam-4946	323	48	it	it	PRON
ejpam-4946	323	49	follows	follow	VERB
ejpam-4946	323	50	that	that	SCONJ
ejpam-4946	323	51	αj2(s	αj2(s	PROPN
ejpam-4946	323	52	+	+	CCONJ
ejpam-4946	323	53	t	t	PROPN
ejpam-4946	323	54	)	)	PUNCT
ejpam-4946	323	55	≥	≥	PROPN
ejpam-4946	323	56	|l|	|l|	NOUN
ejpam-4946	323	57	=	=	SYM
ejpam-4946	323	58	αj2(s	αj2(s	PROPN
ejpam-4946	323	59	)	)	PUNCT
ejpam-4946	323	60	.	.	PUNCT
ejpam-4946	324	1	similarly	similarly	ADV
ejpam-4946	324	2	,	,	PUNCT
ejpam-4946	324	3	if	if	SCONJ
ejpam-4946	324	4	l′	l′	NOUN
ejpam-4946	324	5	is	be	AUX
ejpam-4946	324	6	a	a	DET
ejpam-4946	324	7	maximum	maximum	ADJ
ejpam-4946	324	8	j2	j2	NOUN
ejpam-4946	324	9	-	-	PUNCT
ejpam-4946	324	10	independent	independent	ADJ
ejpam-4946	324	11	set	set	NOUN
ejpam-4946	324	12	of	of	ADP
ejpam-4946	324	13	t	t	PROPN
ejpam-4946	324	14	,	,	PUNCT
ejpam-4946	324	15	then	then	ADV
ejpam-4946	324	16	αj2(s	αj2(s	PROPN
ejpam-4946	324	17	+	+	CCONJ
ejpam-4946	324	18	t	t	PROPN
ejpam-4946	324	19	)	)	PUNCT
ejpam-4946	324	20	≥	≥	NOUN
ejpam-4946	324	21	∣∣l′∣∣	∣∣l′∣∣	NOUN
ejpam-4946	324	22	=	=	SYM
ejpam-4946	324	23	αj2(t	αj2(t	PROPN
ejpam-4946	324	24	)	)	PUNCT
ejpam-4946	324	25	.	.	PUNCT
ejpam-4946	325	1	a.	a.	NOUN
ejpam-4946	325	2	tapeing	tape	VERB
ejpam-4946	325	3	et	et	PROPN
ejpam-4946	325	4	al	al	PROPN
ejpam-4946	325	5	.	.	PUNCT
ejpam-4946	325	6	/	/	SYM
ejpam-4946	325	7	eur	eur	PROPN
ejpam-4946	325	8	.	.	PUNCT
ejpam-4946	326	1	j.	j.	PROPN
ejpam-4946	326	2	pure	pure	PROPN
ejpam-4946	326	3	appl	appl	PROPN
ejpam-4946	326	4	.	.	PROPN
ejpam-4946	326	5	math	math	PROPN
ejpam-4946	326	6	,	,	PUNCT
ejpam-4946	326	7	17	17	NUM
ejpam-4946	326	8	(	(	PUNCT
ejpam-4946	326	9	1	1	NUM
ejpam-4946	326	10	)	)	PUNCT
ejpam-4946	326	11	(	(	PUNCT
ejpam-4946	326	12	2024	2024	NUM
ejpam-4946	326	13	)	)	PUNCT
ejpam-4946	326	14	,	,	PUNCT
ejpam-4946	326	15	124	124	NUM
ejpam-4946	326	16	-	-	SYM
ejpam-4946	326	17	134	134	NUM
ejpam-4946	326	18	131	131	NUM
ejpam-4946	326	19	consequently	consequently	ADV
ejpam-4946	326	20	,	,	PUNCT
ejpam-4946	326	21	αj2(s	αj2(s	PROPN
ejpam-4946	326	22	+	+	CCONJ
ejpam-4946	326	23	t	t	PROPN
ejpam-4946	326	24	)	)	PUNCT
ejpam-4946	326	25	≥	≥	PROPN
ejpam-4946	326	26	max	max	PROPN
ejpam-4946	326	27	{	{	PUNCT
ejpam-4946	326	28	αj2(s	αj2(s	NOUN
ejpam-4946	326	29	)	)	PUNCT
ejpam-4946	326	30	,	,	PUNCT
ejpam-4946	326	31	αj2(t	αj2(t	PROPN
ejpam-4946	326	32	)	)	PUNCT
ejpam-4946	326	33	}	}	PUNCT
ejpam-4946	326	34	.	.	PUNCT
ejpam-4946	327	1	remark	remark	NOUN
ejpam-4946	327	2	3	3	NUM
ejpam-4946	327	3	.	.	PUNCT
ejpam-4946	328	1	the	the	DET
ejpam-4946	328	2	theorem	theorem	NOUN
ejpam-4946	328	3	6	6	NUM
ejpam-4946	328	4	does	do	AUX
ejpam-4946	328	5	not	not	PART
ejpam-4946	328	6	hold	hold	VERB
ejpam-4946	328	7	if	if	SCONJ
ejpam-4946	328	8	either	either	PRON
ejpam-4946	328	9	s	s	PRON
ejpam-4946	328	10	or	or	CCONJ
ejpam-4946	328	11	t	t	PROPN
ejpam-4946	328	12	is	be	AUX
ejpam-4946	328	13	disconnected	disconnect	VERB
ejpam-4946	328	14	.	.	PUNCT
ejpam-4946	329	1	consider	consider	VERB
ejpam-4946	329	2	the	the	DET
ejpam-4946	329	3	graph	graph	NOUN
ejpam-4946	329	4	k3	k3	VERB
ejpam-4946	329	5	+	+	CCONJ
ejpam-4946	329	6	p3	p3	NOUN
ejpam-4946	329	7	in	in	ADP
ejpam-4946	329	8	figure	figure	NOUN
ejpam-4946	329	9	3	3	NUM
ejpam-4946	329	10	,	,	PUNCT
ejpam-4946	329	11	where	where	SCONJ
ejpam-4946	329	12	s	s	VERB
ejpam-4946	329	13	=	=	SYM
ejpam-4946	329	14	k3	k3	PROPN
ejpam-4946	329	15	is	be	AUX
ejpam-4946	329	16	disconnected	disconnected	ADJ
ejpam-4946	329	17	and	and	CCONJ
ejpam-4946	329	18	t	t	NOUN
ejpam-4946	329	19	=	=	SYM
ejpam-4946	329	20	p3	p3	PROPN
ejpam-4946	329	21	.	.	PUNCT
ejpam-4946	330	1	let	let	VERB
ejpam-4946	330	2	s′	s′	ADJ
ejpam-4946	330	3	=	=	PUNCT
ejpam-4946	330	4	{	{	PUNCT
ejpam-4946	330	5	d	d	NOUN
ejpam-4946	330	6	,	,	PUNCT
ejpam-4946	330	7	e	e	NOUN
ejpam-4946	330	8	}	}	PUNCT
ejpam-4946	330	9	.	.	PUNCT
ejpam-4946	331	1	then	then	ADV
ejpam-4946	331	2	ds(d	ds(d	PUNCT
ejpam-4946	331	3	,	,	PUNCT
ejpam-4946	331	4	e	e	X
ejpam-4946	331	5	)	)	PUNCT
ejpam-4946	331	6	̸=	̸=	PROPN
ejpam-4946	331	7	1	1	NUM
ejpam-4946	331	8	,	,	PUNCT
ejpam-4946	331	9	d	d	PROPN
ejpam-4946	331	10	∈	∈	PROPN
ejpam-4946	331	11	n2	n2	NOUN
ejpam-4946	331	12	s	s	PART
ejpam-4946	332	1	[	[	X
ejpam-4946	332	2	d	d	X
ejpam-4946	332	3	]	]	X
ejpam-4946	332	4	\ns	\ns	PROPN
ejpam-4946	332	5	[	[	X
ejpam-4946	332	6	e	e	X
ejpam-4946	332	7	]	]	PUNCT
ejpam-4946	332	8	and	and	CCONJ
ejpam-4946	332	9	e	e	NOUN
ejpam-4946	332	10	∈	∈	PROPN
ejpam-4946	332	11	n2	n2	NOUN
ejpam-4946	332	12	s	s	X
ejpam-4946	332	13	[	[	X
ejpam-4946	332	14	e	e	X
ejpam-4946	332	15	]	]	X
ejpam-4946	332	16	\ns	\ns	PROPN
ejpam-4946	332	17	[	[	X
ejpam-4946	332	18	d	d	X
ejpam-4946	332	19	]	]	X
ejpam-4946	332	20	.	.	PUNCT
ejpam-4946	333	1	thus	thus	ADV
ejpam-4946	333	2	,	,	PUNCT
ejpam-4946	333	3	s′	s′	PROPN
ejpam-4946	333	4	is	be	AUX
ejpam-4946	333	5	a	a	DET
ejpam-4946	333	6	j2	j2	NOUN
ejpam-4946	333	7	-	-	PUNCT
ejpam-4946	333	8	independent	independent	ADJ
ejpam-4946	333	9	set	set	NOUN
ejpam-4946	333	10	in	in	ADP
ejpam-4946	333	11	s.	s.	PROPN
ejpam-4946	333	12	however	however	ADV
ejpam-4946	333	13	,	,	PUNCT
ejpam-4946	333	14	n2	n2	PROPN
ejpam-4946	333	15	s+t	s+t	PROPN
ejpam-4946	334	1	[	[	X
ejpam-4946	334	2	d	d	X
ejpam-4946	334	3	]	]	X
ejpam-4946	334	4	=	=	PUNCT
ejpam-4946	334	5	n2	n2	PROPN
ejpam-4946	334	6	s+t	s+t	PROPN
ejpam-4946	335	1	[	[	X
ejpam-4946	335	2	e	e	X
ejpam-4946	335	3	]	]	X
ejpam-4946	335	4	=	=	PUNCT
ejpam-4946	335	5	{	{	PUNCT
ejpam-4946	335	6	d	d	PROPN
ejpam-4946	335	7	,	,	PUNCT
ejpam-4946	335	8	e	e	NOUN
ejpam-4946	335	9	,	,	PUNCT
ejpam-4946	335	10	f	f	NOUN
ejpam-4946	335	11	}	}	PUNCT
ejpam-4946	335	12	.	.	PUNCT
ejpam-4946	336	1	hence	hence	ADV
ejpam-4946	336	2	,	,	PUNCT
ejpam-4946	336	3	s′	s′	PROPN
ejpam-4946	336	4	is	be	AUX
ejpam-4946	336	5	not	not	PART
ejpam-4946	336	6	a	a	DET
ejpam-4946	336	7	j2	j2	NOUN
ejpam-4946	336	8	-	-	PUNCT
ejpam-4946	336	9	set	set	NOUN
ejpam-4946	336	10	in	in	ADP
ejpam-4946	336	11	s	s	PROPN
ejpam-4946	336	12	+	+	X
ejpam-4946	336	13	t	t	NOUN
ejpam-4946	336	14	.	.	PUNCT
ejpam-4946	337	1	consequently	consequently	ADV
ejpam-4946	337	2	,	,	PUNCT
ejpam-4946	337	3	s′	s′	PROPN
ejpam-4946	337	4	is	be	AUX
ejpam-4946	337	5	not	not	PART
ejpam-4946	337	6	a	a	DET
ejpam-4946	337	7	j2	j2	NOUN
ejpam-4946	337	8	-	-	PUNCT
ejpam-4946	337	9	independent	independent	ADJ
ejpam-4946	337	10	set	set	NOUN
ejpam-4946	337	11	in	in	ADP
ejpam-4946	337	12	s	s	PROPN
ejpam-4946	337	13	+	+	X
ejpam-4946	337	14	t	t	NOUN
ejpam-4946	337	15	.	.	PUNCT
ejpam-4946	338	1	a	a	DET
ejpam-4946	338	2	b	b	NOUN
ejpam-4946	338	3	c	c	X
ejpam-4946	338	4	fed	fed	PROPN
ejpam-4946	338	5	g1	g1	PROPN
ejpam-4946	338	6	:	:	PUNCT
ejpam-4946	338	7	figure	figure	VERB
ejpam-4946	338	8	3	3	NUM
ejpam-4946	338	9	:	:	PUNCT
ejpam-4946	338	10	graph	graph	NOUN
ejpam-4946	338	11	k3	k3	VERB
ejpam-4946	338	12	+	+	CCONJ
ejpam-4946	338	13	p3	p3	PROPN
ejpam-4946	338	14	theorem	theorem	VERB
ejpam-4946	338	15	7	7	NUM
ejpam-4946	338	16	.	.	PUNCT
ejpam-4946	339	1	let	let	VERB
ejpam-4946	339	2	s	s	PRON
ejpam-4946	339	3	and	and	CCONJ
ejpam-4946	339	4	t	t	PROPN
ejpam-4946	339	5	be	be	AUX
ejpam-4946	339	6	connected	connect	VERB
ejpam-4946	339	7	graphs	graph	NOUN
ejpam-4946	339	8	.	.	PUNCT
ejpam-4946	340	1	if	if	SCONJ
ejpam-4946	340	2	w	w	NOUN
ejpam-4946	340	3	=	=	PUNCT
ejpam-4946	340	4	⋃	⋃	NOUN
ejpam-4946	340	5	a∈v	a∈v	NOUN
ejpam-4946	340	6	(	(	PUNCT
ejpam-4946	340	7	s	s	NOUN
ejpam-4946	340	8	)	)	PUNCT
ejpam-4946	340	9	ta	ta	ADP
ejpam-4946	340	10	,	,	PUNCT
ejpam-4946	340	11	where	where	SCONJ
ejpam-4946	340	12	ta	ta	PROPN
ejpam-4946	340	13	is	be	AUX
ejpam-4946	340	14	a	a	DET
ejpam-4946	340	15	j2independent	j2independent	ADJ
ejpam-4946	340	16	set	set	NOUN
ejpam-4946	340	17	of	of	ADP
ejpam-4946	340	18	t	t	PROPN
ejpam-4946	340	19	for	for	ADP
ejpam-4946	340	20	each	each	PRON
ejpam-4946	340	21	a	a	DET
ejpam-4946	340	22	∈	∈	PROPN
ejpam-4946	340	23	v	v	ADP
ejpam-4946	340	24	(	(	PUNCT
ejpam-4946	340	25	s	s	NOUN
ejpam-4946	340	26	)	)	PUNCT
ejpam-4946	340	27	,	,	PUNCT
ejpam-4946	340	28	then	then	ADV
ejpam-4946	340	29	w	w	PROPN
ejpam-4946	340	30	is	be	AUX
ejpam-4946	340	31	a	a	DET
ejpam-4946	340	32	j2	j2	NOUN
ejpam-4946	340	33	-	-	PUNCT
ejpam-4946	340	34	independent	independent	ADJ
ejpam-4946	340	35	set	set	NOUN
ejpam-4946	340	36	of	of	ADP
ejpam-4946	340	37	s	s	NOUN
ejpam-4946	340	38	◦	◦	NOUN
ejpam-4946	340	39	t.	t.	NOUN
ejpam-4946	340	40	moreover	moreover	ADV
ejpam-4946	340	41	,	,	PUNCT
ejpam-4946	340	42	αj2(s	αj2(s	PROPN
ejpam-4946	340	43	◦	◦	NOUN
ejpam-4946	340	44	t	t	PROPN
ejpam-4946	340	45	)	)	PUNCT
ejpam-4946	340	46	≥	≥	NOUN
ejpam-4946	340	47	αj2(t	αj2(t	PROPN
ejpam-4946	340	48	)	)	PUNCT
ejpam-4946	340	49	·	·	PUNCT
ejpam-4946	341	1	|v	|v	PROPN
ejpam-4946	341	2	(	(	PUNCT
ejpam-4946	341	3	s)|	s)|	NOUN
ejpam-4946	341	4	.	.	PUNCT
ejpam-4946	342	1	proof	proof	NOUN
ejpam-4946	342	2	.	.	PUNCT
ejpam-4946	343	1	let	let	VERB
ejpam-4946	343	2	w	w	NOUN
ejpam-4946	343	3	=	=	PUNCT
ejpam-4946	343	4	⋃	⋃	NOUN
ejpam-4946	343	5	a∈v	a∈v	NOUN
ejpam-4946	343	6	(	(	PUNCT
ejpam-4946	343	7	s	s	NOUN
ejpam-4946	343	8	)	)	PUNCT
ejpam-4946	343	9	ta	ta	ADP
ejpam-4946	343	10	,	,	PUNCT
ejpam-4946	343	11	where	where	SCONJ
ejpam-4946	343	12	ta	ta	PROPN
ejpam-4946	343	13	is	be	AUX
ejpam-4946	343	14	a	a	DET
ejpam-4946	343	15	j2	j2	NOUN
ejpam-4946	343	16	-	-	PUNCT
ejpam-4946	343	17	independent	independent	ADJ
ejpam-4946	343	18	set	set	NOUN
ejpam-4946	343	19	of	of	ADP
ejpam-4946	343	20	t	t	PROPN
ejpam-4946	343	21	for	for	ADP
ejpam-4946	343	22	each	each	PRON
ejpam-4946	343	23	a	a	DET
ejpam-4946	343	24	∈	∈	PROPN
ejpam-4946	343	25	v	v	ADP
ejpam-4946	343	26	(	(	PUNCT
ejpam-4946	343	27	s	s	NOUN
ejpam-4946	343	28	)	)	PUNCT
ejpam-4946	343	29	.	.	PUNCT
ejpam-4946	344	1	let	let	VERB
ejpam-4946	344	2	x	x	PRON
ejpam-4946	344	3	,	,	PUNCT
ejpam-4946	344	4	y	y	PROPN
ejpam-4946	344	5	∈	∈	PROPN
ejpam-4946	344	6	w.	w.	NOUN
ejpam-4946	344	7	if	if	SCONJ
ejpam-4946	344	8	x	x	PROPN
ejpam-4946	344	9	,	,	PUNCT
ejpam-4946	344	10	y	y	PROPN
ejpam-4946	344	11	∈	∈	PROPN
ejpam-4946	344	12	tc	tc	NOUN
ejpam-4946	344	13	for	for	ADP
ejpam-4946	344	14	some	some	DET
ejpam-4946	344	15	c	c	NOUN
ejpam-4946	344	16	∈	∈	PROPN
ejpam-4946	344	17	v	v	ADP
ejpam-4946	344	18	(	(	PUNCT
ejpam-4946	344	19	s	s	NOUN
ejpam-4946	344	20	)	)	PUNCT
ejpam-4946	344	21	,	,	PUNCT
ejpam-4946	344	22	then	then	ADV
ejpam-4946	344	23	ds	ds	PROPN
ejpam-4946	344	24	◦	◦	NOUN
ejpam-4946	344	25	t	t	NOUN
ejpam-4946	344	26	(	(	PUNCT
ejpam-4946	344	27	x	x	NOUN
ejpam-4946	344	28	,	,	PUNCT
ejpam-4946	344	29	y	y	NOUN
ejpam-4946	344	30	)	)	PUNCT
ejpam-4946	344	31	̸=	̸=	NOUN
ejpam-4946	344	32	1	1	NUM
ejpam-4946	344	33	because	because	SCONJ
ejpam-4946	344	34	tc	tc	NOUN
ejpam-4946	344	35	is	be	AUX
ejpam-4946	344	36	an	an	DET
ejpam-4946	344	37	independent	independent	ADJ
ejpam-4946	344	38	set	set	NOUN
ejpam-4946	344	39	of	of	ADP
ejpam-4946	344	40	t	t	PROPN
ejpam-4946	344	41	.	.	PUNCT
ejpam-4946	345	1	claim	claim	NOUN
ejpam-4946	345	2	:	:	PUNCT
ejpam-4946	345	3	n2	n2	PROPN
ejpam-4946	345	4	s	s	PROPN
ejpam-4946	345	5	◦	◦	NOUN
ejpam-4946	345	6	t	t	NOUN
ejpam-4946	345	7	[	[	X
ejpam-4946	345	8	x]\n2	x]\n2	PROPN
ejpam-4946	345	9	s	s	PART
ejpam-4946	345	10	◦	◦	NOUN
ejpam-4946	345	11	t	t	NOUN
ejpam-4946	345	12	[	[	X
ejpam-4946	345	13	y	y	X
ejpam-4946	345	14	]	]	X
ejpam-4946	345	15	̸=	̸=	PROPN
ejpam-4946	345	16	∅	∅	NOUN
ejpam-4946	345	17	and	and	CCONJ
ejpam-4946	345	18	n2	n2	PROPN
ejpam-4946	345	19	s	s	PROPN
ejpam-4946	345	20	◦	◦	NOUN
ejpam-4946	345	21	t	t	NOUN
ejpam-4946	345	22	[	[	X
ejpam-4946	345	23	y]\n2	y]\n2	PROPN
ejpam-4946	345	24	s	s	PROPN
ejpam-4946	345	25	◦	◦	NOUN
ejpam-4946	345	26	t	t	NOUN
ejpam-4946	346	1	[	[	X
ejpam-4946	346	2	x	x	X
ejpam-4946	346	3	]	]	X
ejpam-4946	346	4	̸=	̸=	PROPN
ejpam-4946	346	5	∅.	∅.	ADV
ejpam-4946	346	6	since	since	SCONJ
ejpam-4946	346	7	n2	n2	PROPN
ejpam-4946	346	8	t	t	PROPN
ejpam-4946	346	9	[	[	X
ejpam-4946	346	10	x]\n2	x]\n2	PROPN
ejpam-4946	346	11	t	t	PROPN
ejpam-4946	347	1	[	[	X
ejpam-4946	347	2	y	y	X
ejpam-4946	347	3	]	]	X
ejpam-4946	347	4	̸=	̸=	NOUN
ejpam-4946	347	5	∅	∅	NOUN
ejpam-4946	347	6	,	,	PUNCT
ejpam-4946	347	7	there	there	PRON
ejpam-4946	347	8	exists	exist	VERB
ejpam-4946	347	9	w	w	PROPN
ejpam-4946	347	10	∈	∈	PROPN
ejpam-4946	347	11	v	v	ADP
ejpam-4946	347	12	(	(	PUNCT
ejpam-4946	347	13	t	t	PROPN
ejpam-4946	347	14	)	)	PUNCT
ejpam-4946	347	15	such	such	ADJ
ejpam-4946	347	16	that	that	SCONJ
ejpam-4946	347	17	dt	dt	PROPN
ejpam-4946	347	18	(	(	PUNCT
ejpam-4946	347	19	x	x	X
ejpam-4946	347	20	,	,	PUNCT
ejpam-4946	347	21	w	w	NOUN
ejpam-4946	347	22	)	)	PUNCT
ejpam-4946	347	23	=	=	SYM
ejpam-4946	347	24	2	2	NUM
ejpam-4946	347	25	and	and	CCONJ
ejpam-4946	347	26	dt	dt	PROPN
ejpam-4946	347	27	(	(	PUNCT
ejpam-4946	347	28	y	y	PROPN
ejpam-4946	347	29	,	,	PUNCT
ejpam-4946	347	30	w	w	NOUN
ejpam-4946	347	31	)	)	PUNCT
ejpam-4946	347	32	̸=	̸=	PROPN
ejpam-4946	347	33	2	2	NUM
ejpam-4946	347	34	.	.	PUNCT
ejpam-4946	348	1	if	if	SCONJ
ejpam-4946	348	2	dt	dt	PROPN
ejpam-4946	348	3	(	(	PUNCT
ejpam-4946	348	4	x	x	NOUN
ejpam-4946	348	5	,	,	PUNCT
ejpam-4946	348	6	y	y	NOUN
ejpam-4946	348	7	)	)	PUNCT
ejpam-4946	348	8	=	=	SYM
ejpam-4946	348	9	2	2	NUM
ejpam-4946	348	10	,	,	PUNCT
ejpam-4946	348	11	,	,	PUNCT
ejpam-4946	348	12	then	then	ADV
ejpam-4946	348	13	dt	dt	X
ejpam-4946	348	14	(	(	PUNCT
ejpam-4946	348	15	y	y	PROPN
ejpam-4946	348	16	,	,	PUNCT
ejpam-4946	348	17	w	w	NOUN
ejpam-4946	348	18	)	)	PUNCT
ejpam-4946	348	19	̸=	̸=	PROPN
ejpam-4946	348	20	1	1	NUM
ejpam-4946	348	21	.	.	PUNCT
ejpam-4946	349	1	thus	thus	ADV
ejpam-4946	349	2	,	,	PUNCT
ejpam-4946	349	3	dt	dt	X
ejpam-4946	349	4	(	(	PUNCT
ejpam-4946	349	5	y	y	PROPN
ejpam-4946	349	6	,	,	PUNCT
ejpam-4946	349	7	w	w	PROPN
ejpam-4946	349	8	)	)	PUNCT
ejpam-4946	349	9	≥	≥	NOUN
ejpam-4946	349	10	3	3	NUM
ejpam-4946	349	11	.	.	PUNCT
ejpam-4946	350	1	let	let	VERB
ejpam-4946	350	2	t	t	PROPN
ejpam-4946	350	3	∈	∈	PROPN
ejpam-4946	350	4	nt	not	PART
ejpam-4946	350	5	(	(	PUNCT
ejpam-4946	350	6	x	x	X
ejpam-4946	350	7	)	)	PUNCT
ejpam-4946	350	8	∩nt	∩nt	NOUN
ejpam-4946	350	9	(	(	PUNCT
ejpam-4946	350	10	w	w	NOUN
ejpam-4946	350	11	)	)	PUNCT
ejpam-4946	350	12	.	.	PUNCT
ejpam-4946	351	1	then	then	ADV
ejpam-4946	351	2	t	t	PROPN
ejpam-4946	351	3	∈	∈	PROPN
ejpam-4946	351	4	n2	n2	PROPN
ejpam-4946	351	5	s	s	PROPN
ejpam-4946	351	6	◦	◦	NOUN
ejpam-4946	351	7	t	t	NOUN
ejpam-4946	351	8	[	[	X
ejpam-4946	351	9	y]\n2	y]\n2	PROPN
ejpam-4946	351	10	s	s	PROPN
ejpam-4946	351	11	◦	◦	NOUN
ejpam-4946	351	12	t	t	NOUN
ejpam-4946	351	13	[	[	X
ejpam-4946	351	14	x	x	X
ejpam-4946	351	15	]	]	X
ejpam-4946	351	16	.	.	PUNCT
ejpam-4946	352	1	hence	hence	ADV
ejpam-4946	352	2	,	,	PUNCT
ejpam-4946	352	3	n	n	PROPN
ejpam-4946	352	4	2	2	NUM
ejpam-4946	352	5	s	s	NOUN
ejpam-4946	352	6	◦	◦	NOUN
ejpam-4946	352	7	t	t	NOUN
ejpam-4946	352	8	[	[	X
ejpam-4946	352	9	y]\n2	y]\n2	PROPN
ejpam-4946	352	10	s	s	PROPN
ejpam-4946	352	11	◦	◦	NOUN
ejpam-4946	352	12	t	t	NOUN
ejpam-4946	352	13	[	[	X
ejpam-4946	352	14	x	x	X
ejpam-4946	352	15	]	]	X
ejpam-4946	352	16	̸=	̸=	PROPN
ejpam-4946	352	17	∅.	∅.	ADV
ejpam-4946	352	18	assume	assume	VERB
ejpam-4946	352	19	that	that	SCONJ
ejpam-4946	352	20	dt	dt	PROPN
ejpam-4946	352	21	(	(	PUNCT
ejpam-4946	352	22	x	x	NOUN
ejpam-4946	352	23	,	,	PUNCT
ejpam-4946	352	24	y	y	PROPN
ejpam-4946	352	25	)	)	PUNCT
ejpam-4946	352	26	≥	≥	NOUN
ejpam-4946	352	27	3	3	NUM
ejpam-4946	352	28	.	.	PUNCT
ejpam-4946	352	29	suppose	suppose	VERB
ejpam-4946	352	30	that	that	SCONJ
ejpam-4946	352	31	dt	dt	PROPN
ejpam-4946	352	32	(	(	PUNCT
ejpam-4946	352	33	y	y	PROPN
ejpam-4946	352	34	,	,	PUNCT
ejpam-4946	352	35	w	w	PROPN
ejpam-4946	352	36	)	)	PUNCT
ejpam-4946	352	37	=	=	SYM
ejpam-4946	352	38	1	1	X
ejpam-4946	352	39	.	.	PUNCT
ejpam-4946	352	40	let	let	VERB
ejpam-4946	352	41	v	v	X
ejpam-4946	352	42	∈	∈	PROPN
ejpam-4946	352	43	nt	not	PART
ejpam-4946	352	44	(	(	PUNCT
ejpam-4946	352	45	x	x	X
ejpam-4946	352	46	)	)	PUNCT
ejpam-4946	352	47	∩nt	∩nt	NOUN
ejpam-4946	352	48	(	(	PUNCT
ejpam-4946	352	49	w	w	NOUN
ejpam-4946	352	50	)	)	PUNCT
ejpam-4946	352	51	.	.	PUNCT
ejpam-4946	353	1	then	then	ADV
ejpam-4946	353	2	v	v	X
ejpam-4946	353	3	∈	∈	PROPN
ejpam-4946	353	4	n2	n2	NOUN
ejpam-4946	353	5	s	s	PROPN
ejpam-4946	353	6	◦	◦	NOUN
ejpam-4946	353	7	t	t	NOUN
ejpam-4946	353	8	[	[	X
ejpam-4946	353	9	y]\n2	y]\n2	PROPN
ejpam-4946	353	10	s	s	PROPN
ejpam-4946	353	11	◦	◦	NOUN
ejpam-4946	353	12	t	t	NOUN
ejpam-4946	353	13	[	[	X
ejpam-4946	353	14	x	x	X
ejpam-4946	353	15	]	]	X
ejpam-4946	353	16	.	.	PUNCT
ejpam-4946	354	1	thus	thus	ADV
ejpam-4946	354	2	,	,	PUNCT
ejpam-4946	354	3	n	n	PROPN
ejpam-4946	354	4	2	2	NUM
ejpam-4946	354	5	s	s	NOUN
ejpam-4946	354	6	◦	◦	NOUN
ejpam-4946	354	7	t	t	NOUN
ejpam-4946	354	8	[	[	X
ejpam-4946	354	9	y]\n2	y]\n2	PROPN
ejpam-4946	354	10	s	s	PROPN
ejpam-4946	354	11	◦	◦	NOUN
ejpam-4946	354	12	t	t	NOUN
ejpam-4946	354	13	[	[	X
ejpam-4946	354	14	x	x	X
ejpam-4946	354	15	]	]	X
ejpam-4946	354	16	̸=	̸=	PROPN
ejpam-4946	354	17	∅.	∅.	ADV
ejpam-4946	354	18	if	if	SCONJ
ejpam-4946	354	19	dt	dt	PROPN
ejpam-4946	354	20	(	(	PUNCT
ejpam-4946	354	21	y	y	PROPN
ejpam-4946	354	22	,	,	PUNCT
ejpam-4946	354	23	w	w	PROPN
ejpam-4946	354	24	)	)	PUNCT
ejpam-4946	354	25	≥	≥	NOUN
ejpam-4946	354	26	3	3	NUM
ejpam-4946	354	27	,	,	PUNCT
ejpam-4946	354	28	then	then	ADV
ejpam-4946	354	29	by	by	ADP
ejpam-4946	354	30	preceding	precede	VERB
ejpam-4946	354	31	argument	argument	NOUN
ejpam-4946	354	32	,	,	PUNCT
ejpam-4946	354	33	n2	n2	PROPN
ejpam-4946	354	34	s	s	PROPN
ejpam-4946	354	35	◦	◦	NOUN
ejpam-4946	354	36	t	t	NOUN
ejpam-4946	354	37	[	[	X
ejpam-4946	354	38	y]\n2	y]\n2	PROPN
ejpam-4946	354	39	s	s	PROPN
ejpam-4946	354	40	◦	◦	NOUN
ejpam-4946	354	41	t	t	NOUN
ejpam-4946	354	42	[	[	X
ejpam-4946	354	43	x	x	X
ejpam-4946	354	44	]	]	X
ejpam-4946	354	45	̸=	̸=	PROPN
ejpam-4946	354	46	∅.	∅.	PRON
ejpam-4946	354	47	similarly	similarly	ADV
ejpam-4946	354	48	,	,	PUNCT
ejpam-4946	354	49	if	if	SCONJ
ejpam-4946	354	50	n2	n2	PROPN
ejpam-4946	354	51	t	t	PROPN
ejpam-4946	354	52	[	[	X
ejpam-4946	354	53	y]\n2	y]\n2	PROPN
ejpam-4946	354	54	t	t	NOUN
ejpam-4946	355	1	[	[	X
ejpam-4946	355	2	x	x	X
ejpam-4946	355	3	]	]	X
ejpam-4946	355	4	̸=	̸=	PROPN
ejpam-4946	355	5	∅	∅	NOUN
ejpam-4946	355	6	,	,	PUNCT
ejpam-4946	355	7	then	then	ADV
ejpam-4946	355	8	a.	a.	NOUN
ejpam-4946	355	9	tapeing	tapeing	NOUN
ejpam-4946	355	10	et	et	PROPN
ejpam-4946	355	11	al	al	PROPN
ejpam-4946	355	12	.	.	PUNCT
ejpam-4946	355	13	/	/	SYM
ejpam-4946	355	14	eur	eur	PROPN
ejpam-4946	355	15	.	.	PUNCT
ejpam-4946	356	1	j.	j.	PROPN
ejpam-4946	356	2	pure	pure	PROPN
ejpam-4946	356	3	appl	appl	PROPN
ejpam-4946	356	4	.	.	PROPN
ejpam-4946	356	5	math	math	PROPN
ejpam-4946	356	6	,	,	PUNCT
ejpam-4946	356	7	17	17	NUM
ejpam-4946	356	8	(	(	PUNCT
ejpam-4946	356	9	1	1	NUM
ejpam-4946	356	10	)	)	PUNCT
ejpam-4946	356	11	(	(	PUNCT
ejpam-4946	356	12	2024	2024	NUM
ejpam-4946	356	13	)	)	PUNCT
ejpam-4946	356	14	,	,	PUNCT
ejpam-4946	356	15	124	124	NUM
ejpam-4946	356	16	-	-	SYM
ejpam-4946	356	17	134	134	NUM
ejpam-4946	356	18	132	132	NUM
ejpam-4946	356	19	n2	n2	NOUN
ejpam-4946	356	20	s	s	PROPN
ejpam-4946	356	21	◦	◦	NOUN
ejpam-4946	356	22	t	t	NOUN
ejpam-4946	356	23	[	[	X
ejpam-4946	356	24	x]\n2	x]\n2	PROPN
ejpam-4946	356	25	s	s	PART
ejpam-4946	356	26	◦	◦	NOUN
ejpam-4946	356	27	t	t	NOUN
ejpam-4946	356	28	[	[	X
ejpam-4946	356	29	y	y	X
ejpam-4946	356	30	]	]	X
ejpam-4946	356	31	̸=	̸=	PROPN
ejpam-4946	356	32	∅.	∅.	VERB
ejpam-4946	356	33	therefore	therefore	ADV
ejpam-4946	356	34	,	,	PUNCT
ejpam-4946	356	35	w	w	PROPN
ejpam-4946	356	36	is	be	AUX
ejpam-4946	356	37	a	a	DET
ejpam-4946	356	38	j2	j2	NOUN
ejpam-4946	356	39	-	-	PUNCT
ejpam-4946	356	40	independent	independent	ADJ
ejpam-4946	356	41	set	set	NOUN
ejpam-4946	356	42	of	of	ADP
ejpam-4946	356	43	s	s	NOUN
ejpam-4946	356	44	◦	◦	NOUN
ejpam-4946	356	45	t	t	NOUN
ejpam-4946	356	46	.	.	PUNCT
ejpam-4946	357	1	consequently	consequently	ADV
ejpam-4946	357	2	,	,	PUNCT
ejpam-4946	357	3	αj2(s	αj2(s	PROPN
ejpam-4946	357	4	◦	◦	NOUN
ejpam-4946	357	5	t	t	PROPN
ejpam-4946	357	6	)	)	PUNCT
ejpam-4946	357	7	≥	≥	NOUN
ejpam-4946	357	8	αj2(t	αj2(t	PROPN
ejpam-4946	357	9	)	)	PUNCT
ejpam-4946	357	10	·	·	PUNCT
ejpam-4946	358	1	|v	|v	PROPN
ejpam-4946	358	2	(	(	PUNCT
ejpam-4946	358	3	s)|	s)|	NOUN
ejpam-4946	358	4	.	.	PUNCT
ejpam-4946	359	1	remark	remark	PROPN
ejpam-4946	359	2	4	4	NUM
ejpam-4946	359	3	.	.	PUNCT
ejpam-4946	360	1	the	the	DET
ejpam-4946	360	2	theorem	theorem	NOUN
ejpam-4946	360	3	7	7	NUM
ejpam-4946	360	4	does	do	AUX
ejpam-4946	360	5	not	not	PART
ejpam-4946	360	6	hold	hold	VERB
ejpam-4946	360	7	if	if	SCONJ
ejpam-4946	360	8	t	t	PROPN
ejpam-4946	360	9	is	be	AUX
ejpam-4946	360	10	disconnected	disconnect	VERB
ejpam-4946	360	11	.	.	PUNCT
ejpam-4946	361	1	consider	consider	VERB
ejpam-4946	361	2	the	the	DET
ejpam-4946	361	3	graph	graph	NOUN
ejpam-4946	361	4	s	s	PART
ejpam-4946	361	5	◦	◦	NOUN
ejpam-4946	361	6	t	t	NOUN
ejpam-4946	361	7	in	in	ADP
ejpam-4946	361	8	figure	figure	NOUN
ejpam-4946	361	9	4	4	NUM
ejpam-4946	361	10	,	,	PUNCT
ejpam-4946	361	11	where	where	SCONJ
ejpam-4946	361	12	t	t	PROPN
ejpam-4946	361	13	is	be	AUX
ejpam-4946	361	14	disconnected	disconnect	VERB
ejpam-4946	361	15	.	.	PUNCT
ejpam-4946	362	1	let	let	VERB
ejpam-4946	362	2	b	b	NOUN
ejpam-4946	362	3	=	=	PRON
ejpam-4946	362	4	{	{	PUNCT
ejpam-4946	362	5	u1	u1	NOUN
ejpam-4946	362	6	,	,	PUNCT
ejpam-4946	362	7	u3	u3	PROPN
ejpam-4946	362	8	}	}	PUNCT
ejpam-4946	362	9	.	.	PUNCT
ejpam-4946	363	1	then	then	ADV
ejpam-4946	363	2	dt	dt	X
ejpam-4946	363	3	(	(	PUNCT
ejpam-4946	363	4	u1	u1	NOUN
ejpam-4946	363	5	,	,	PUNCT
ejpam-4946	363	6	u3	u3	NOUN
ejpam-4946	363	7	)	)	PUNCT
ejpam-4946	363	8	̸=	̸=	PROPN
ejpam-4946	363	9	1	1	NUM
ejpam-4946	363	10	.	.	PUNCT
ejpam-4946	364	1	hence	hence	ADV
ejpam-4946	364	2	,	,	PUNCT
ejpam-4946	364	3	b	b	PROPN
ejpam-4946	364	4	is	be	AUX
ejpam-4946	364	5	an	an	DET
ejpam-4946	364	6	independent	independent	ADJ
ejpam-4946	364	7	set	set	NOUN
ejpam-4946	364	8	of	of	ADP
ejpam-4946	364	9	t	t	PROPN
ejpam-4946	364	10	.	.	PUNCT
ejpam-4946	365	1	observe	observe	VERB
ejpam-4946	365	2	that	that	DET
ejpam-4946	365	3	n2	n2	PROPN
ejpam-4946	365	4	t	t	PROPN
ejpam-4946	365	5	[	[	X
ejpam-4946	365	6	u1	u1	X
ejpam-4946	365	7	]	]	X
ejpam-4946	365	8	=	=	SYM
ejpam-4946	365	9	{	{	PUNCT
ejpam-4946	365	10	u1	u1	NOUN
ejpam-4946	365	11	}	}	PUNCT
ejpam-4946	365	12	and	and	CCONJ
ejpam-4946	365	13	n2	n2	PROPN
ejpam-4946	365	14	t	t	PROPN
ejpam-4946	366	1	[	[	X
ejpam-4946	366	2	u3	u3	X
ejpam-4946	366	3	]	]	X
ejpam-4946	366	4	=	=	SYM
ejpam-4946	366	5	{	{	PUNCT
ejpam-4946	366	6	u3	u3	PROPN
ejpam-4946	366	7	}	}	PUNCT
ejpam-4946	366	8	.	.	PUNCT
ejpam-4946	367	1	thus	thus	ADV
ejpam-4946	367	2	,	,	PUNCT
ejpam-4946	367	3	n2	n2	PROPN
ejpam-4946	367	4	t	t	PROPN
ejpam-4946	367	5	[	[	X
ejpam-4946	367	6	u1]\n2	u1]\n2	PROPN
ejpam-4946	367	7	t	t	X
ejpam-4946	367	8	[	[	X
ejpam-4946	367	9	u3	u3	X
ejpam-4946	367	10	]	]	X
ejpam-4946	367	11	=	=	SYM
ejpam-4946	367	12	{	{	PUNCT
ejpam-4946	367	13	u1	u1	NOUN
ejpam-4946	367	14	}	}	PUNCT
ejpam-4946	367	15	̸=	̸=	PROPN
ejpam-4946	367	16	∅	∅	NOUN
ejpam-4946	367	17	and	and	CCONJ
ejpam-4946	367	18	n2	n2	PROPN
ejpam-4946	367	19	t	t	PROPN
ejpam-4946	368	1	[	[	X
ejpam-4946	368	2	u3]\n2	u3]\n2	X
ejpam-4946	368	3	t	t	NOUN
ejpam-4946	368	4	[	[	X
ejpam-4946	368	5	u1	u1	X
ejpam-4946	368	6	]	]	X
ejpam-4946	368	7	=	=	SYM
ejpam-4946	368	8	{	{	PUNCT
ejpam-4946	368	9	u3	u3	PROPN
ejpam-4946	368	10	}	}	PUNCT
ejpam-4946	368	11	̸=	̸=	PROPN
ejpam-4946	368	12	∅.	∅.	VERB
ejpam-4946	368	13	therefore	therefore	ADV
ejpam-4946	368	14	,	,	PUNCT
ejpam-4946	368	15	b	b	PROPN
ejpam-4946	368	16	is	be	AUX
ejpam-4946	368	17	a	a	DET
ejpam-4946	368	18	j2	j2	NOUN
ejpam-4946	368	19	-	-	PUNCT
ejpam-4946	368	20	independent	independent	ADJ
ejpam-4946	368	21	set	set	NOUN
ejpam-4946	368	22	of	of	ADP
ejpam-4946	368	23	t	t	PROPN
ejpam-4946	368	24	.	.	PUNCT
ejpam-4946	369	1	now	now	ADV
ejpam-4946	369	2	,	,	PUNCT
ejpam-4946	369	3	notice	notice	VERB
ejpam-4946	369	4	that	that	SCONJ
ejpam-4946	369	5	n2	n2	ADJ
ejpam-4946	369	6	t+s	t+s	X
ejpam-4946	369	7	[	[	X
ejpam-4946	369	8	u1	u1	NOUN
ejpam-4946	369	9	]	]	X
ejpam-4946	369	10	=	=	SYM
ejpam-4946	369	11	{	{	PUNCT
ejpam-4946	369	12	u1	u1	NOUN
ejpam-4946	369	13	,	,	PUNCT
ejpam-4946	369	14	u3	u3	PROPN
ejpam-4946	369	15	,	,	PUNCT
ejpam-4946	369	16	y	y	PROPN
ejpam-4946	369	17	}	}	PUNCT
ejpam-4946	369	18	⊆	⊆	NUM
ejpam-4946	369	19	{	{	PUNCT
ejpam-4946	369	20	u1	u1	NOUN
ejpam-4946	369	21	,	,	PUNCT
ejpam-4946	369	22	u2	u2	NOUN
ejpam-4946	369	23	,	,	PUNCT
ejpam-4946	369	24	u3	u3	NOUN
ejpam-4946	369	25	,	,	PUNCT
ejpam-4946	369	26	y	y	NOUN
ejpam-4946	369	27	}	}	PUNCT
ejpam-4946	369	28	=	=	SYM
ejpam-4946	369	29	n2	n2	NOUN
ejpam-4946	369	30	t+s	t+s	X
ejpam-4946	370	1	[	[	X
ejpam-4946	370	2	u3	u3	X
ejpam-4946	370	3	]	]	X
ejpam-4946	370	4	.	.	PUNCT
ejpam-4946	371	1	it	it	PRON
ejpam-4946	371	2	follows	follow	VERB
ejpam-4946	371	3	that	that	SCONJ
ejpam-4946	371	4	b	b	NOUN
ejpam-4946	371	5	is	be	AUX
ejpam-4946	371	6	not	not	PART
ejpam-4946	371	7	a	a	DET
ejpam-4946	371	8	j2	j2	PROPN
ejpam-4946	371	9	-	-	PUNCT
ejpam-4946	371	10	set	set	NOUN
ejpam-4946	371	11	of	of	ADP
ejpam-4946	371	12	s	s	PROPN
ejpam-4946	371	13	+	+	X
ejpam-4946	371	14	t	t	NOUN
ejpam-4946	371	15	.	.	PUNCT
ejpam-4946	372	1	consequently	consequently	ADV
ejpam-4946	372	2	,	,	PUNCT
ejpam-4946	372	3	b	b	PROPN
ejpam-4946	372	4	is	be	AUX
ejpam-4946	372	5	not	not	PART
ejpam-4946	372	6	a	a	DET
ejpam-4946	372	7	j2	j2	NOUN
ejpam-4946	372	8	-	-	PUNCT
ejpam-4946	372	9	independent	independent	ADJ
ejpam-4946	372	10	set	set	NOUN
ejpam-4946	372	11	of	of	ADP
ejpam-4946	372	12	s	s	PROPN
ejpam-4946	372	13	+	+	X
ejpam-4946	372	14	t	t	NOUN
ejpam-4946	372	15	.	.	PUNCT
ejpam-4946	373	1	s	s	VERB
ejpam-4946	373	2	:	:	PUNCT
ejpam-4946	373	3	t	t	NOUN
ejpam-4946	373	4	:	:	PUNCT
ejpam-4946	373	5	x	x	SYM
ejpam-4946	373	6	y	y	PROPN
ejpam-4946	373	7	z	z	PROPN
ejpam-4946	373	8	v1	v1	PROPN
ejpam-4946	373	9	v2	v2	PROPN
ejpam-4946	373	10	v3	v3	PROPN
ejpam-4946	373	11	v4	v4	PROPN
ejpam-4946	373	12	v5	v5	PROPN
ejpam-4946	373	13	v6	v6	NOUN
ejpam-4946	373	14	v7	v7	VERB
ejpam-4946	373	15	v8	v8	PROPN
ejpam-4946	373	16	v9	v9	PROPN
ejpam-4946	373	17	s	s	PART
ejpam-4946	373	18	◦	◦	NOUN
ejpam-4946	373	19	t	t	NOUN
ejpam-4946	373	20	:	:	PUNCT
ejpam-4946	373	21	figure	figure	VERB
ejpam-4946	373	22	4	4	NUM
ejpam-4946	373	23	:	:	PUNCT
ejpam-4946	373	24	graph	graph	NOUN
ejpam-4946	373	25	s	s	PART
ejpam-4946	373	26	◦	◦	NOUN
ejpam-4946	373	27	t	t	NOUN
ejpam-4946	373	28	theorem	theorem	VERB
ejpam-4946	373	29	8	8	NUM
ejpam-4946	373	30	.	.	PUNCT
ejpam-4946	374	1	let	let	VERB
ejpam-4946	374	2	g	g	PRON
ejpam-4946	374	3	be	be	AUX
ejpam-4946	374	4	a	a	DET
ejpam-4946	374	5	graph	graph	NOUN
ejpam-4946	374	6	.	.	PUNCT
ejpam-4946	375	1	then	then	ADV
ejpam-4946	375	2	the	the	DET
ejpam-4946	375	3	hop	hop	NOUN
ejpam-4946	375	4	independence	independence	NOUN
ejpam-4946	375	5	and	and	CCONJ
ejpam-4946	375	6	j2	j2	PROPN
ejpam-4946	375	7	-	-	PUNCT
ejpam-4946	375	8	independence	independence	NOUN
ejpam-4946	375	9	parameters	parameter	NOUN
ejpam-4946	375	10	are	be	AUX
ejpam-4946	375	11	incomparable	incomparable	ADJ
ejpam-4946	375	12	.	.	PUNCT
ejpam-4946	376	1	proof	proof	NOUN
ejpam-4946	376	2	.	.	PUNCT
ejpam-4946	377	1	consider	consider	VERB
ejpam-4946	377	2	the	the	DET
ejpam-4946	377	3	graph	graph	NOUN
ejpam-4946	377	4	g	g	NOUN
ejpam-4946	377	5	in	in	ADP
ejpam-4946	377	6	figure	figure	NOUN
ejpam-4946	377	7	5	5	NUM
ejpam-4946	377	8	.	.	PUNCT
ejpam-4946	378	1	let	let	VERB
ejpam-4946	378	2	q	q	NOUN
ejpam-4946	379	1	=	=	PUNCT
ejpam-4946	379	2	{	{	PUNCT
ejpam-4946	379	3	a	a	X
ejpam-4946	379	4	,	,	PUNCT
ejpam-4946	379	5	e	e	NOUN
ejpam-4946	379	6	}	}	PUNCT
ejpam-4946	379	7	,	,	PUNCT
ejpam-4946	379	8	then	then	ADV
ejpam-4946	379	9	q	q	X
ejpam-4946	379	10	is	be	AUX
ejpam-4946	379	11	an	an	DET
ejpam-4946	379	12	independent	independent	ADJ
ejpam-4946	379	13	set	set	NOUN
ejpam-4946	379	14	of	of	ADP
ejpam-4946	379	15	g.	g.	PROPN
ejpam-4946	379	16	observe	observe	VERB
ejpam-4946	379	17	that	that	DET
ejpam-4946	379	18	n2	n2	ADJ
ejpam-4946	379	19	g[a	g[a	NOUN
ejpam-4946	379	20	]	]	X
ejpam-4946	379	21	=	=	X
ejpam-4946	379	22	{	{	PUNCT
ejpam-4946	379	23	a	a	NOUN
ejpam-4946	379	24	,	,	PUNCT
ejpam-4946	379	25	h	h	NOUN
ejpam-4946	379	26	}	}	PUNCT
ejpam-4946	379	27	and	and	CCONJ
ejpam-4946	379	28	n2	n2	ADJ
ejpam-4946	379	29	g[e	g[e	X
ejpam-4946	379	30	]	]	X
ejpam-4946	379	31	=	=	SYM
ejpam-4946	379	32	{	{	PUNCT
ejpam-4946	379	33	d	d	PROPN
ejpam-4946	379	34	,	,	PUNCT
ejpam-4946	379	35	e	e	NOUN
ejpam-4946	379	36	,	,	PUNCT
ejpam-4946	379	37	g	g	NOUN
ejpam-4946	379	38	}	}	PUNCT
ejpam-4946	379	39	.	.	PUNCT
ejpam-4946	380	1	thus	thus	ADV
ejpam-4946	380	2	,	,	PUNCT
ejpam-4946	380	3	n2	n2	ADJ
ejpam-4946	380	4	g[a]\n2	g[a]\n2	X
ejpam-4946	380	5	g[e	g[e	X
ejpam-4946	380	6	]	]	X
ejpam-4946	380	7	=	=	X
ejpam-4946	380	8	{	{	PUNCT
ejpam-4946	380	9	a	a	NOUN
ejpam-4946	380	10	,	,	PUNCT
ejpam-4946	380	11	h	h	NOUN
ejpam-4946	380	12	}	}	PUNCT
ejpam-4946	380	13	=	=	NOUN
ejpam-4946	380	14	̸	̸	ADJ
ejpam-4946	380	15	∅	∅	NOUN
ejpam-4946	380	16	and	and	CCONJ
ejpam-4946	380	17	n2	n2	ADJ
ejpam-4946	380	18	g[e]\n2	g[e]\n2	NOUN
ejpam-4946	380	19	g[a	g[a	ADJ
ejpam-4946	380	20	]	]	X
ejpam-4946	380	21	=	=	PUNCT
ejpam-4946	380	22	{	{	PUNCT
ejpam-4946	380	23	d	d	PROPN
ejpam-4946	380	24	,	,	PUNCT
ejpam-4946	380	25	e	e	NOUN
ejpam-4946	380	26	,	,	PUNCT
ejpam-4946	380	27	g	g	NOUN
ejpam-4946	380	28	}	}	PUNCT
ejpam-4946	380	29	=	=	NOUN
ejpam-4946	380	30	̸	̸	ADJ
ejpam-4946	380	31	∅	∅	NOUN
ejpam-4946	380	32	and	and	CCONJ
ejpam-4946	380	33	so	so	ADV
ejpam-4946	380	34	q	q	X
ejpam-4946	380	35	is	be	AUX
ejpam-4946	380	36	a	a	DET
ejpam-4946	380	37	j2	j2	PROPN
ejpam-4946	380	38	independent	independent	ADJ
ejpam-4946	380	39	set	set	NOUN
ejpam-4946	380	40	of	of	ADP
ejpam-4946	380	41	g.	g.	PROPN
ejpam-4946	380	42	since	since	SCONJ
ejpam-4946	380	43	,	,	PUNCT
ejpam-4946	380	44	dg(a	dg(a	X
ejpam-4946	380	45	,	,	PUNCT
ejpam-4946	380	46	b	b	X
ejpam-4946	380	47	)	)	PUNCT
ejpam-4946	380	48	=	=	SYM
ejpam-4946	380	49	dg(a	dg(a	X
ejpam-4946	380	50	,	,	PUNCT
ejpam-4946	380	51	d	d	NOUN
ejpam-4946	380	52	)	)	PUNCT
ejpam-4946	380	53	=	=	SYM
ejpam-4946	381	1	dg(a	dg(a	X
ejpam-4946	381	2	,	,	PUNCT
ejpam-4946	381	3	c	c	NOUN
ejpam-4946	381	4	)	)	PUNCT
ejpam-4946	381	5	=	=	SYM
ejpam-4946	381	6	1	1	NUM
ejpam-4946	381	7	,	,	PUNCT
ejpam-4946	381	8	n2	n2	ADJ
ejpam-4946	381	9	g[a	g[a	NOUN
ejpam-4946	381	10	]	]	PUNCT
ejpam-4946	381	11	⊆	⊆	NUM
ejpam-4946	381	12	n2	n2	NOUN
ejpam-4946	381	13	g[h	g[h	PROPN
ejpam-4946	381	14	]	]	PUNCT
ejpam-4946	381	15	,	,	PUNCT
ejpam-4946	381	16	dg(e	dg(e	NOUN
ejpam-4946	381	17	,	,	PUNCT
ejpam-4946	381	18	f	f	X
ejpam-4946	381	19	)	)	PUNCT
ejpam-4946	381	20	=	=	SYM
ejpam-4946	381	21	1	1	NUM
ejpam-4946	381	22	=	=	SYM
ejpam-4946	381	23	dg(e	dg(e	NOUN
ejpam-4946	381	24	,	,	PUNCT
ejpam-4946	381	25	h	h	NOUN
ejpam-4946	381	26	)	)	PUNCT
ejpam-4946	381	27	and	and	CCONJ
ejpam-4946	381	28	n2	n2	ADJ
ejpam-4946	381	29	g[e	g[e	ADJ
ejpam-4946	381	30	]	]	X
ejpam-4946	381	31	=	=	SYM
ejpam-4946	381	32	n2	n2	NOUN
ejpam-4946	381	33	g[g	g[g	PROPN
ejpam-4946	381	34	]	]	PUNCT
ejpam-4946	381	35	,	,	PUNCT
ejpam-4946	381	36	it	it	PRON
ejpam-4946	381	37	follows	follow	VERB
ejpam-4946	381	38	that	that	SCONJ
ejpam-4946	381	39	q	q	NOUN
ejpam-4946	381	40	is	be	AUX
ejpam-4946	381	41	a	a	DET
ejpam-4946	381	42	maximum	maximum	ADJ
ejpam-4946	381	43	j2	j2	NOUN
ejpam-4946	381	44	-	-	PUNCT
ejpam-4946	381	45	independent	independent	ADJ
ejpam-4946	381	46	set	set	NOUN
ejpam-4946	381	47	of	of	ADP
ejpam-4946	381	48	g.	g.	PROPN
ejpam-4946	381	49	hence	hence	ADV
ejpam-4946	381	50	,	,	PUNCT
ejpam-4946	381	51	αj2(g	αj2(g	NUM
ejpam-4946	381	52	)	)	PUNCT
ejpam-4946	381	53	=	=	SYM
ejpam-4946	382	1	2	2	X
ejpam-4946	382	2	.	.	PUNCT
ejpam-4946	382	3	now	now	ADV
ejpam-4946	382	4	,	,	PUNCT
ejpam-4946	382	5	let	let	VERB
ejpam-4946	382	6	q′	q′	NOUN
ejpam-4946	382	7	=	=	VERB
ejpam-4946	382	8	{	{	PUNCT
ejpam-4946	382	9	a	a	PRON
ejpam-4946	382	10	,	,	PUNCT
ejpam-4946	382	11	b	b	NOUN
ejpam-4946	382	12	,	,	PUNCT
ejpam-4946	382	13	c	c	NOUN
ejpam-4946	382	14	,	,	PUNCT
ejpam-4946	382	15	d	d	NOUN
ejpam-4946	382	16	}	}	PUNCT
ejpam-4946	382	17	.	.	PUNCT
ejpam-4946	383	1	then	then	ADV
ejpam-4946	383	2	q′	q′	NOUN
ejpam-4946	383	3	is	be	AUX
ejpam-4946	383	4	a	a	DET
ejpam-4946	383	5	maximum	maximum	ADJ
ejpam-4946	383	6	hop	hop	NOUN
ejpam-4946	383	7	independent	independent	ADJ
ejpam-4946	383	8	set	set	NOUN
ejpam-4946	383	9	of	of	ADP
ejpam-4946	383	10	g.	g.	PROPN
ejpam-4946	383	11	therefore	therefore	ADV
ejpam-4946	383	12	,	,	PUNCT
ejpam-4946	383	13	αh(g	αh(g	NOUN
ejpam-4946	383	14	)	)	PUNCT
ejpam-4946	383	15	=	=	SYM
ejpam-4946	383	16	4	4	X
ejpam-4946	383	17	.	.	PUNCT
ejpam-4946	383	18	a.	a.	NOUN
ejpam-4946	383	19	tapeing	tapeing	NOUN
ejpam-4946	383	20	et	et	PROPN
ejpam-4946	383	21	al	al	PROPN
ejpam-4946	383	22	.	.	PUNCT
ejpam-4946	383	23	/	/	SYM
ejpam-4946	383	24	eur	eur	PROPN
ejpam-4946	383	25	.	.	PUNCT
ejpam-4946	384	1	j.	j.	PROPN
ejpam-4946	384	2	pure	pure	PROPN
ejpam-4946	384	3	appl	appl	PROPN
ejpam-4946	384	4	.	.	PROPN
ejpam-4946	384	5	math	math	PROPN
ejpam-4946	384	6	,	,	PUNCT
ejpam-4946	384	7	17	17	NUM
ejpam-4946	384	8	(	(	PUNCT
ejpam-4946	384	9	1	1	NUM
ejpam-4946	384	10	)	)	PUNCT
ejpam-4946	384	11	(	(	PUNCT
ejpam-4946	384	12	2024	2024	NUM
ejpam-4946	384	13	)	)	PUNCT
ejpam-4946	384	14	,	,	PUNCT
ejpam-4946	384	15	124	124	NUM
ejpam-4946	384	16	-	-	SYM
ejpam-4946	384	17	134	134	NUM
ejpam-4946	384	18	133	133	NUM
ejpam-4946	384	19	a	a	DET
ejpam-4946	384	20	b	b	NOUN
ejpam-4946	384	21	e	e	ADP
ejpam-4946	384	22	f	f	PROPN
ejpam-4946	384	23	g	g	PROPN
ejpam-4946	384	24	hdc	hdc	NOUN
ejpam-4946	384	25	g	g	PROPN
ejpam-4946	384	26	:	:	PUNCT
ejpam-4946	384	27	figure	figure	NOUN
ejpam-4946	384	28	5	5	NUM
ejpam-4946	384	29	:	:	PUNCT
ejpam-4946	384	30	graph	graph	VERB
ejpam-4946	384	31	g	g	NOUN
ejpam-4946	384	32	with	with	ADP
ejpam-4946	384	33	αh(g	αh(g	NOUN
ejpam-4946	384	34	)	)	PUNCT
ejpam-4946	384	35	=	=	SYM
ejpam-4946	384	36	4	4	NUM
ejpam-4946	384	37	and	and	CCONJ
ejpam-4946	384	38	α2	α2	ADJ
ejpam-4946	384	39	j(g	j(g	PROPN
ejpam-4946	384	40	)	)	PUNCT
ejpam-4946	385	1	=	=	SYM
ejpam-4946	385	2	2	2	NUM
ejpam-4946	385	3	next	next	ADV
ejpam-4946	385	4	consider	consider	VERB
ejpam-4946	385	5	the	the	DET
ejpam-4946	385	6	graph	graph	NOUN
ejpam-4946	385	7	k2	k2	NOUN
ejpam-4946	385	8	+	+	CCONJ
ejpam-4946	385	9	p13	p13	NOUN
ejpam-4946	385	10	in	in	ADP
ejpam-4946	385	11	figure	figure	NOUN
ejpam-4946	385	12	6	6	NUM
ejpam-4946	385	13	.	.	PUNCT
ejpam-4946	386	1	let	let	VERB
ejpam-4946	386	2	r	r	NOUN
ejpam-4946	386	3	=	=	PUNCT
ejpam-4946	386	4	{	{	PUNCT
ejpam-4946	386	5	a	a	X
ejpam-4946	386	6	,	,	PUNCT
ejpam-4946	386	7	d	d	NOUN
ejpam-4946	386	8	,	,	PUNCT
ejpam-4946	386	9	f	f	X
ejpam-4946	386	10	,	,	PUNCT
ejpam-4946	386	11	h	h	PROPN
ejpam-4946	386	12	,	,	PUNCT
ejpam-4946	386	13	j	j	PROPN
ejpam-4946	386	14	,	,	PUNCT
ejpam-4946	386	15	m	m	PROPN
ejpam-4946	386	16	}	}	PUNCT
ejpam-4946	386	17	.	.	PUNCT
ejpam-4946	387	1	then	then	ADV
ejpam-4946	387	2	,	,	PUNCT
ejpam-4946	387	3	r	r	NOUN
ejpam-4946	387	4	is	be	AUX
ejpam-4946	387	5	a	a	DET
ejpam-4946	387	6	maximum	maximum	ADJ
ejpam-4946	387	7	j2	j2	NOUN
ejpam-4946	387	8	-	-	PUNCT
ejpam-4946	387	9	independent	independent	ADJ
ejpam-4946	387	10	set	set	NOUN
ejpam-4946	387	11	of	of	ADP
ejpam-4946	387	12	k2	k2	NOUN
ejpam-4946	387	13	+	+	CCONJ
ejpam-4946	387	14	p13	p13	NOUN
ejpam-4946	387	15	,	,	PUNCT
ejpam-4946	387	16	and	and	CCONJ
ejpam-4946	387	17	so	so	ADV
ejpam-4946	387	18	α2	α2	ADJ
ejpam-4946	387	19	j(k2	j(k2	NOUN
ejpam-4946	387	20	+	+	CCONJ
ejpam-4946	387	21	p13	p13	NOUN
ejpam-4946	387	22	)	)	PUNCT
ejpam-4946	387	23	=	=	SYM
ejpam-4946	387	24	6	6	NUM
ejpam-4946	387	25	.	.	PUNCT
ejpam-4946	388	1	now	now	ADV
ejpam-4946	388	2	,	,	PUNCT
ejpam-4946	388	3	let	let	VERB
ejpam-4946	388	4	r′	r′	PROPN
ejpam-4946	388	5	=	=	PRON
ejpam-4946	388	6	{	{	PUNCT
ejpam-4946	388	7	a	a	PRON
ejpam-4946	388	8	,	,	PUNCT
ejpam-4946	388	9	b	b	NOUN
ejpam-4946	388	10	,	,	PUNCT
ejpam-4946	388	11	x	x	NOUN
ejpam-4946	388	12	,	,	PUNCT
ejpam-4946	388	13	y	y	PROPN
ejpam-4946	388	14	}	}	PUNCT
ejpam-4946	388	15	.	.	PUNCT
ejpam-4946	389	1	then	then	ADV
ejpam-4946	389	2	,	,	PUNCT
ejpam-4946	389	3	r′	r′	PROPN
ejpam-4946	389	4	is	be	AUX
ejpam-4946	389	5	a	a	DET
ejpam-4946	389	6	maximum	maximum	ADJ
ejpam-4946	389	7	hop	hop	NOUN
ejpam-4946	389	8	independent	independent	ADJ
ejpam-4946	389	9	set	set	VERB
ejpam-4946	389	10	k2	k2	PROPN
ejpam-4946	389	11	+	+	CCONJ
ejpam-4946	389	12	p13	p13	NOUN
ejpam-4946	389	13	.	.	PUNCT
ejpam-4946	390	1	hence	hence	ADV
ejpam-4946	390	2	,	,	PUNCT
ejpam-4946	390	3	αh(k2	αh(k2	NOUN
ejpam-4946	390	4	+	+	X
ejpam-4946	390	5	p13	p13	NOUN
ejpam-4946	390	6	)	)	PUNCT
ejpam-4946	390	7	=	=	SYM
ejpam-4946	390	8	4	4	X
ejpam-4946	390	9	.	.	PUNCT
ejpam-4946	391	1	a	a	DET
ejpam-4946	391	2	b	b	NOUN
ejpam-4946	391	3	c	c	NOUN
ejpam-4946	391	4	d	d	X
ejpam-4946	391	5	e	e	X
ejpam-4946	391	6	f	f	PROPN
ejpam-4946	391	7	g	g	PROPN
ejpam-4946	391	8	h	h	NOUN
ejpam-4946	392	1	i	i	PRON
ejpam-4946	392	2	j	j	PROPN
ejpam-4946	393	1	k	k	PROPN
ejpam-4946	393	2	l	l	PROPN
ejpam-4946	393	3	m	m	PROPN
ejpam-4946	393	4	k2	k2	NOUN
ejpam-4946	393	5	+	+	CCONJ
ejpam-4946	393	6	p13	p13	NOUN
ejpam-4946	393	7	:	:	PUNCT
ejpam-4946	393	8	x	x	SYM
ejpam-4946	393	9	y	y	NOUN
ejpam-4946	393	10	figure	figure	VERB
ejpam-4946	393	11	6	6	NUM
ejpam-4946	393	12	:	:	PUNCT
ejpam-4946	393	13	graph	graph	VERB
ejpam-4946	393	14	k2	k2	PROPN
ejpam-4946	393	15	+	+	CCONJ
ejpam-4946	393	16	p13	p13	NOUN
ejpam-4946	393	17	with	with	ADP
ejpam-4946	393	18	αh(k2	αh(k2	NOUN
ejpam-4946	393	19	+	+	X
ejpam-4946	393	20	p13	p13	NOUN
ejpam-4946	393	21	)	)	PUNCT
ejpam-4946	393	22	=	=	SYM
ejpam-4946	393	23	4	4	NUM
ejpam-4946	393	24	and	and	CCONJ
ejpam-4946	393	25	α2	α2	ADJ
ejpam-4946	393	26	j(k2	j(k2	NOUN
ejpam-4946	393	27	+	+	CCONJ
ejpam-4946	393	28	p13	p13	NOUN
ejpam-4946	393	29	)	)	PUNCT
ejpam-4946	393	30	=	=	NOUN
ejpam-4946	393	31	6	6	NUM
ejpam-4946	393	32	4	4	NUM
ejpam-4946	393	33	.	.	PUNCT
ejpam-4946	393	34	conclusion	conclusion	VERB
ejpam-4946	393	35	the	the	DET
ejpam-4946	393	36	concept	concept	NOUN
ejpam-4946	393	37	of	of	ADP
ejpam-4946	393	38	j2	j2	PROPN
ejpam-4946	393	39	-	-	PUNCT
ejpam-4946	393	40	independence	independence	NOUN
ejpam-4946	393	41	has	have	AUX
ejpam-4946	393	42	been	be	AUX
ejpam-4946	393	43	introduced	introduce	VERB
ejpam-4946	393	44	and	and	CCONJ
ejpam-4946	393	45	investigated	investigate	VERB
ejpam-4946	393	46	in	in	ADP
ejpam-4946	393	47	this	this	DET
ejpam-4946	393	48	study	study	NOUN
ejpam-4946	393	49	.	.	PUNCT
ejpam-4946	394	1	its	its	PRON
ejpam-4946	394	2	bounds	bound	NOUN
ejpam-4946	394	3	with	with	ADP
ejpam-4946	394	4	respect	respect	NOUN
ejpam-4946	394	5	to	to	ADP
ejpam-4946	394	6	the	the	DET
ejpam-4946	394	7	order	order	NOUN
ejpam-4946	394	8	of	of	ADP
ejpam-4946	394	9	a	a	DET
ejpam-4946	394	10	graph	graph	NOUN
ejpam-4946	394	11	and	and	CCONJ
ejpam-4946	394	12	other	other	ADJ
ejpam-4946	394	13	parameters	parameter	NOUN
ejpam-4946	394	14	have	have	AUX
ejpam-4946	394	15	been	be	AUX
ejpam-4946	394	16	determined	determine	VERB
ejpam-4946	394	17	.	.	PUNCT
ejpam-4946	395	1	it	it	PRON
ejpam-4946	395	2	was	be	AUX
ejpam-4946	395	3	shown	show	VERB
ejpam-4946	395	4	that	that	SCONJ
ejpam-4946	395	5	any	any	DET
ejpam-4946	395	6	graph	graph	NOUN
ejpam-4946	395	7	g	g	PROPN
ejpam-4946	395	8	admits	admit	VERB
ejpam-4946	395	9	a	a	DET
ejpam-4946	395	10	j2	j2	NOUN
ejpam-4946	395	11	-	-	PUNCT
ejpam-4946	395	12	independence	independence	NOUN
ejpam-4946	395	13	.	.	PUNCT
ejpam-4946	396	1	moreover	moreover	ADV
ejpam-4946	396	2	,	,	PUNCT
ejpam-4946	396	3	characterizations	characterization	NOUN
ejpam-4946	396	4	of	of	ADP
ejpam-4946	396	5	j2	j2	PROPN
ejpam-4946	396	6	-	-	PUNCT
ejpam-4946	396	7	independent	independent	ADJ
ejpam-4946	396	8	sets	set	NOUN
ejpam-4946	396	9	in	in	ADP
ejpam-4946	396	10	some	some	DET
ejpam-4946	396	11	classes	class	NOUN
ejpam-4946	396	12	of	of	ADP
ejpam-4946	396	13	graphs	graph	NOUN
ejpam-4946	396	14	have	have	AUX
ejpam-4946	396	15	been	be	AUX
ejpam-4946	396	16	presented	present	VERB
ejpam-4946	396	17	and	and	CCONJ
ejpam-4946	396	18	used	use	VERB
ejpam-4946	396	19	to	to	PART
ejpam-4946	396	20	determine	determine	VERB
ejpam-4946	396	21	the	the	DET
ejpam-4946	396	22	exact	exact	ADJ
ejpam-4946	396	23	values	value	NOUN
ejpam-4946	396	24	of	of	ADP
ejpam-4946	396	25	the	the	DET
ejpam-4946	396	26	parameter	parameter	NOUN
ejpam-4946	396	27	.	.	PUNCT
ejpam-4946	397	1	some	some	DET
ejpam-4946	397	2	graphs	graph	NOUN
ejpam-4946	397	3	that	that	PRON
ejpam-4946	397	4	were	be	AUX
ejpam-4946	397	5	not	not	PART
ejpam-4946	397	6	considered	consider	VERB
ejpam-4946	397	7	in	in	ADP
ejpam-4946	397	8	this	this	DET
ejpam-4946	397	9	study	study	NOUN
ejpam-4946	397	10	could	could	AUX
ejpam-4946	397	11	be	be	AUX
ejpam-4946	397	12	an	an	DET
ejpam-4946	397	13	interesting	interesting	ADJ
ejpam-4946	397	14	topic	topic	NOUN
ejpam-4946	397	15	to	to	PART
ejpam-4946	397	16	consider	consider	VERB
ejpam-4946	397	17	for	for	ADP
ejpam-4946	397	18	further	further	ADJ
ejpam-4946	397	19	investigation	investigation	NOUN
ejpam-4946	397	20	of	of	ADP
ejpam-4946	397	21	the	the	DET
ejpam-4946	397	22	concept	concept	NOUN
ejpam-4946	397	23	.	.	PUNCT
ejpam-4946	398	1	references	reference	NOUN
ejpam-4946	398	2	134	134	NUM
ejpam-4946	398	3	acknowledgements	acknowledgement	NOUN
ejpam-4946	398	4	the	the	DET
ejpam-4946	398	5	authors	author	NOUN
ejpam-4946	398	6	would	would	AUX
ejpam-4946	398	7	like	like	VERB
ejpam-4946	398	8	to	to	PART
ejpam-4946	398	9	thank	thank	VERB
ejpam-4946	398	10	mindanao	mindanao	PROPN
ejpam-4946	398	11	state	state	PROPN
ejpam-4946	398	12	university	university	PROPN
ejpam-4946	398	13	tawi	tawi	PROPN
ejpam-4946	398	14	-	-	PUNCT
ejpam-4946	398	15	tawi	tawi	PROPN
ejpam-4946	398	16	college	college	PROPN
ejpam-4946	398	17	of	of	ADP
ejpam-4946	398	18	technology	technology	NOUN
ejpam-4946	398	19	and	and	CCONJ
ejpam-4946	398	20	oceanography	oceanography	NOUN
ejpam-4946	398	21	for	for	ADP
ejpam-4946	398	22	funding	fund	VERB
ejpam-4946	398	23	this	this	DET
ejpam-4946	398	24	research	research	NOUN
ejpam-4946	398	25	.	.	PUNCT
ejpam-4946	399	1	moreover	moreover	ADV
ejpam-4946	399	2	,	,	PUNCT
ejpam-4946	399	3	the	the	DET
ejpam-4946	399	4	authors	author	NOUN
ejpam-4946	399	5	would	would	AUX
ejpam-4946	399	6	like	like	VERB
ejpam-4946	399	7	to	to	PART
ejpam-4946	399	8	thank	thank	VERB
ejpam-4946	399	9	the	the	DET
ejpam-4946	399	10	referees	referee	NOUN
ejpam-4946	399	11	for	for	ADP
ejpam-4946	399	12	their	their	PRON
ejpam-4946	399	13	invaluable	invaluable	ADJ
ejpam-4946	399	14	comments	comment	NOUN
ejpam-4946	399	15	and	and	CCONJ
ejpam-4946	399	16	suggestions	suggestion	NOUN
ejpam-4946	399	17	that	that	PRON
ejpam-4946	399	18	led	lead	VERB
ejpam-4946	399	19	to	to	ADP
ejpam-4946	399	20	the	the	DET
ejpam-4946	399	21	improvement	improvement	NOUN
ejpam-4946	399	22	of	of	ADP
ejpam-4946	399	23	the	the	DET
ejpam-4946	399	24	paper	paper	NOUN
ejpam-4946	399	25	.	.	PUNCT
ejpam-4946	400	1	references	reference	NOUN
ejpam-4946	400	2	[	[	X
ejpam-4946	400	3	1	1	NUM
ejpam-4946	400	4	]	]	PUNCT
ejpam-4946	400	5	e.	e.	PROPN
ejpam-4946	400	6	davies	davies	PROPN
ejpam-4946	400	7	,	,	PUNCT
ejpam-4946	400	8	m.	m.	PROPN
ejpam-4946	400	9	jenssen	jenssen	PROPN
ejpam-4946	400	10	,	,	PUNCT
ejpam-4946	400	11	w.	w.	PROPN
ejpam-4946	400	12	perkins	perkins	PROPN
ejpam-4946	400	13	,	,	PUNCT
ejpam-4946	400	14	and	and	CCONJ
ejpam-4946	400	15	b.	b.	PROPN
ejpam-4946	400	16	roberts	roberts	PROPN
ejpam-4946	400	17	.	.	PUNCT
ejpam-4946	401	1	independent	independent	ADJ
ejpam-4946	401	2	sets	set	NOUN
ejpam-4946	401	3	,	,	PUNCT
ejpam-4946	401	4	matchings	matching	NOUN
ejpam-4946	401	5	,	,	PUNCT
ejpam-4946	401	6	and	and	CCONJ
ejpam-4946	401	7	occupancy	occupancy	NOUN
ejpam-4946	401	8	fractions	fraction	NOUN
ejpam-4946	401	9	.	.	PUNCT
ejpam-4946	402	1	j.	j.	PROPN
ejpam-4946	402	2	lond	lond	PROPN
ejpam-4946	402	3	.	.	PUNCT
ejpam-4946	403	1	math	math	PROPN
ejpam-4946	403	2	.	.	PUNCT
ejpam-4946	404	1	soc	soc	PROPN
ejpam-4946	404	2	.	.	PUNCT
ejpam-4946	405	1	(	(	PUNCT
ejpam-4946	405	2	2	2	NUM
ejpam-4946	405	3	)	)	PUNCT
ejpam-4946	405	4	.	.	PUNCT
ejpam-4946	405	5	,	,	PUNCT
ejpam-4946	405	6	96(1):47–46	96(1):47–46	NUM
ejpam-4946	405	7	,	,	PUNCT
ejpam-4946	405	8	2017	2017	NUM
ejpam-4946	405	9	.	.	PUNCT
ejpam-4946	406	1	[	[	X
ejpam-4946	406	2	2	2	X
ejpam-4946	406	3	]	]	PUNCT
ejpam-4946	406	4	e.	e.	PROPN
ejpam-4946	406	5	davies	davies	PROPN
ejpam-4946	406	6	,	,	PUNCT
ejpam-4946	406	7	m.	m.	PROPN
ejpam-4946	406	8	jenssen	jenssen	PROPN
ejpam-4946	406	9	,	,	PUNCT
ejpam-4946	406	10	w.	w.	PROPN
ejpam-4946	406	11	perkins	perkins	PROPN
ejpam-4946	406	12	,	,	PUNCT
ejpam-4946	406	13	and	and	CCONJ
ejpam-4946	406	14	b.	b.	PROPN
ejpam-4946	406	15	roberts	roberts	PROPN
ejpam-4946	406	16	.	.	PUNCT
ejpam-4946	407	1	on	on	ADP
ejpam-4946	407	2	the	the	DET
ejpam-4946	407	3	average	average	ADJ
ejpam-4946	407	4	size	size	NOUN
ejpam-4946	407	5	of	of	ADP
ejpam-4946	407	6	independent	independent	ADJ
ejpam-4946	407	7	sets	set	NOUN
ejpam-4946	407	8	in	in	ADP
ejpam-4946	407	9	triangle	triangle	NOUN
ejpam-4946	407	10	-	-	PUNCT
ejpam-4946	407	11	free	free	ADJ
ejpam-4946	407	12	graphs	graph	NOUN
ejpam-4946	407	13	.	.	PUNCT
ejpam-4946	408	1	proc	proc	NOUN
ejpam-4946	408	2	.	.	PUNCT
ejpam-4946	409	1	amer	amer	PROPN
ejpam-4946	409	2	.	.	PUNCT
ejpam-4946	409	3	math	math	PROPN
ejpam-4946	409	4	.	.	PUNCT
ejpam-4946	410	1	soc	soc	PROPN
ejpam-4946	410	2	.	.	PUNCT
ejpam-4946	410	3	,	,	PUNCT
ejpam-4946	410	4	146(1):111–124	146(1):111–124	NUM
ejpam-4946	410	5	,	,	PUNCT
ejpam-4946	410	6	2018	2018	NUM
ejpam-4946	410	7	.	.	PUNCT
ejpam-4946	411	1	[	[	X
ejpam-4946	411	2	3	3	X
ejpam-4946	411	3	]	]	PUNCT
ejpam-4946	411	4	z.	z.	PROPN
ejpam-4946	411	5	furedi	furedi	PROPN
ejpam-4946	411	6	.	.	PUNCT
ejpam-4946	412	1	the	the	DET
ejpam-4946	412	2	number	number	NOUN
ejpam-4946	412	3	of	of	ADP
ejpam-4946	412	4	maximal	maximal	ADJ
ejpam-4946	412	5	independent	independent	ADJ
ejpam-4946	412	6	sets	set	NOUN
ejpam-4946	412	7	in	in	ADP
ejpam-4946	412	8	connected	connected	ADJ
ejpam-4946	412	9	graphs	graph	NOUN
ejpam-4946	412	10	,	,	PUNCT
ejpam-4946	412	11	.	.	PUNCT
ejpam-4946	413	1	j.	j.	PROPN
ejpam-4946	413	2	graph	graph	PROPN
ejpam-4946	413	3	theory	theory	NOUN
ejpam-4946	413	4	.	.	PUNCT
ejpam-4946	414	1	,	,	PUNCT
ejpam-4946	414	2	11(4):463–470	11(4):463–470	NOUN
ejpam-4946	414	3	,	,	PUNCT
ejpam-4946	414	4	2022	2022	NUM
ejpam-4946	414	5	.	.	PUNCT
ejpam-4946	415	1	[	[	X
ejpam-4946	415	2	4	4	NUM
ejpam-4946	415	3	]	]	X
ejpam-4946	415	4	j.r	j.r	PROPN
ejpam-4946	415	5	.	.	PROPN
ejpam-4946	415	6	griggs	griggs	PROPN
ejpam-4946	415	7	,	,	PUNCT
ejpam-4946	415	8	c.m	c.m	PROPN
ejpam-4946	415	9	.	.	PROPN
ejpam-4946	415	10	grinstead	grinstead	PROPN
ejpam-4946	415	11	,	,	PUNCT
ejpam-4946	415	12	and	and	CCONJ
ejpam-4946	415	13	d.r	d.r	PROPN
ejpam-4946	415	14	.	.	PROPN
ejpam-4946	415	15	guichard	guichard	PROPN
ejpam-4946	415	16	.	.	PUNCT
ejpam-4946	416	1	the	the	DET
ejpam-4946	416	2	number	number	NOUN
ejpam-4946	416	3	of	of	ADP
ejpam-4946	416	4	maximal	maximal	ADJ
ejpam-4946	416	5	independent	independent	ADJ
ejpam-4946	416	6	sets	set	NOUN
ejpam-4946	416	7	in	in	ADP
ejpam-4946	416	8	a	a	DET
ejpam-4946	416	9	connected	connected	ADJ
ejpam-4946	416	10	graph	graph	NOUN
ejpam-4946	416	11	.	.	PUNCT
ejpam-4946	416	12	discrete	discrete	ADJ
ejpam-4946	416	13	mathematics	mathematic	NOUN
ejpam-4946	416	14	.	.	PUNCT
ejpam-4946	416	15	,	,	PUNCT
ejpam-4946	416	16	68:211–220	68:211–220	PROPN
ejpam-4946	416	17	,	,	PUNCT
ejpam-4946	416	18	1988	1988	NUM
ejpam-4946	416	19	.	.	PUNCT
ejpam-4946	417	1	[	[	X
ejpam-4946	417	2	5	5	X
ejpam-4946	417	3	]	]	PUNCT
ejpam-4946	417	4	j.	j.	PROPN
ejpam-4946	417	5	hassan	hassan	PROPN
ejpam-4946	417	6	,	,	PUNCT
ejpam-4946	417	7	a	a	DET
ejpam-4946	417	8	bakkang	bakkang	NOUN
ejpam-4946	417	9	,	,	PUNCT
ejpam-4946	417	10	and	and	CCONJ
ejpam-4946	417	11	a.s	a.s	PROPN
ejpam-4946	417	12	.	.	PROPN
ejpam-4946	417	13	sappari	sappari	PROPN
ejpam-4946	417	14	.	.	PUNCT
ejpam-4946	418	1	j2	j2	PROPN
ejpam-4946	418	2	-	-	PUNCT
ejpam-4946	418	3	hop	hop	PROPN
ejpam-4946	418	4	domination	domination	NOUN
ejpam-4946	418	5	in	in	ADP
ejpam-4946	418	6	graphs	graph	NOUN
ejpam-4946	418	7	:	:	PUNCT
ejpam-4946	418	8	properties	property	NOUN
ejpam-4946	418	9	and	and	CCONJ
ejpam-4946	418	10	connections	connection	NOUN
ejpam-4946	418	11	with	with	ADP
ejpam-4946	418	12	other	other	ADJ
ejpam-4946	418	13	parameters	parameter	NOUN
ejpam-4946	418	14	.	.	PUNCT
ejpam-4946	419	1	eur	eur	PROPN
ejpam-4946	419	2	.	.	PUNCT
ejpam-4946	420	1	j.	j.	PROPN
ejpam-4946	420	2	pure	pure	PROPN
ejpam-4946	420	3	appl	appl	PROPN
ejpam-4946	420	4	.	.	PUNCT
ejpam-4946	420	5	math	math	PROPN
ejpam-4946	420	6	.	.	PUNCT
ejpam-4946	420	7	,	,	PUNCT
ejpam-4946	420	8	16(4):2118–2131	16(4):2118–2131	NUM
ejpam-4946	420	9	,	,	PUNCT
ejpam-4946	420	10	2022	2022	NUM
ejpam-4946	420	11	.	.	PUNCT
ejpam-4946	421	1	[	[	X
ejpam-4946	421	2	6	6	NUM
ejpam-4946	421	3	]	]	PUNCT
ejpam-4946	421	4	j.	j.	PROPN
ejpam-4946	421	5	hassan	hassan	PROPN
ejpam-4946	421	6	,	,	PUNCT
ejpam-4946	421	7	s.	s.	PROPN
ejpam-4946	421	8	canoy	canoy	PROPN
ejpam-4946	421	9	jr	jr	PROPN
ejpam-4946	421	10	.	.	PROPN
ejpam-4946	421	11	,	,	PUNCT
ejpam-4946	421	12	and	and	CCONJ
ejpam-4946	421	13	a.	a.	PROPN
ejpam-4946	421	14	aradais	aradais	PROPN
ejpam-4946	421	15	.	.	PUNCT
ejpam-4946	422	1	hop	hop	PROPN
ejpam-4946	422	2	independent	independent	ADJ
ejpam-4946	422	3	sets	set	NOUN
ejpam-4946	422	4	in	in	ADP
ejpam-4946	422	5	graphs	graph	NOUN
ejpam-4946	422	6	.	.	PUNCT
ejpam-4946	423	1	eur	eur	PROPN
ejpam-4946	423	2	.	.	PUNCT
ejpam-4946	424	1	j.	j.	PROPN
ejpam-4946	424	2	pure	pure	PROPN
ejpam-4946	424	3	appl	appl	PROPN
ejpam-4946	424	4	.	.	PUNCT
ejpam-4946	424	5	math	math	PROPN
ejpam-4946	424	6	.	.	PUNCT
ejpam-4946	424	7	,	,	PUNCT
ejpam-4946	424	8	15(2):467–477	15(2):467–477	PROPN
ejpam-4946	424	9	,	,	PUNCT
ejpam-4946	424	10	2022	2022	NUM
ejpam-4946	424	11	.	.	PUNCT
ejpam-4946	425	1	[	[	X
ejpam-4946	425	2	7	7	X
ejpam-4946	425	3	]	]	X
ejpam-4946	425	4	g.	g.	PROPN
ejpam-4946	425	5	hopkins	hopkins	PROPN
ejpam-4946	425	6	andw	andw	PROPN
ejpam-4946	425	7	.	.	PUNCT
ejpam-4946	426	1	staton	staton	PROPN
ejpam-4946	426	2	.	.	PUNCT
ejpam-4946	426	3	graphs	graph	NOUN
ejpam-4946	426	4	with	with	ADP
ejpam-4946	426	5	unique	unique	ADJ
ejpam-4946	426	6	maximum	maximum	ADJ
ejpam-4946	426	7	independent	independent	ADJ
ejpam-4946	426	8	sets	set	NOUN
ejpam-4946	426	9	.	.	PUNCT
ejpam-4946	426	10	.	.	PUNCT
ejpam-4946	427	1	discrete	discrete	ADJ
ejpam-4946	427	2	mathematics	mathematic	NOUN
ejpam-4946	427	3	.	.	PUNCT
ejpam-4946	427	4	,	,	PUNCT
ejpam-4946	427	5	57(2):245–251	57(2):245–251	PROPN
ejpam-4946	427	6	,	,	PUNCT
ejpam-4946	427	7	1985	1985	NUM
ejpam-4946	427	8	.	.	PUNCT
ejpam-4946	428	1	[	[	X
ejpam-4946	428	2	8	8	NUM
ejpam-4946	428	3	]	]	X
ejpam-4946	428	4	liu	liu	PROPN
ejpam-4946	428	5	jiuqiang	jiuqiang	PROPN
ejpam-4946	428	6	.	.	PUNCT
ejpam-4946	429	1	maximal	maximal	ADJ
ejpam-4946	429	2	and	and	CCONJ
ejpam-4946	429	3	maximum	maximum	ADJ
ejpam-4946	429	4	independent	independent	ADJ
ejpam-4946	429	5	sets	set	NOUN
ejpam-4946	429	6	in	in	ADP
ejpam-4946	429	7	graphs	graph	NOUN
ejpam-4946	429	8	.	.	PUNCT
ejpam-4946	430	1	dissertations	dissertation	NOUN
ejpam-4946	430	2	.	.	PUNCT
ejpam-4946	430	3	,	,	PUNCT
ejpam-4946	430	4	1985	1985	NUM
ejpam-4946	430	5	.	.	PUNCT
ejpam-4946	431	1	[	[	X
ejpam-4946	431	2	9	9	NUM
ejpam-4946	431	3	]	]	X
ejpam-4946	431	4	d.s	d.s	PROPN
ejpam-4946	431	5	.	.	PROPN
ejpam-4946	431	6	johnson	johnson	PROPN
ejpam-4946	431	7	,	,	PUNCT
ejpam-4946	431	8	m.	m.	NOUN
ejpam-4946	431	9	yannalcakis	yannalcakis	PROPN
ejpam-4946	431	10	,	,	PUNCT
ejpam-4946	431	11	and	and	CCONJ
ejpam-4946	431	12	c.j	c.j	PROPN
ejpam-4946	431	13	.	.	PROPN
ejpam-4946	431	14	papadimitriou	papadimitriou	NOUN
ejpam-4946	431	15	.	.	PUNCT
ejpam-4946	432	1	on	on	ADP
ejpam-4946	432	2	generating	generate	VERB
ejpam-4946	432	3	all	all	DET
ejpam-4946	432	4	maximal	maximal	ADJ
ejpam-4946	432	5	independent	independent	ADJ
ejpam-4946	432	6	sets	set	NOUN
ejpam-4946	432	7	.	.	PUNCT
ejpam-4946	432	8	.	.	PUNCT
ejpam-4946	433	1	inform	inform	VERB
ejpam-4946	433	2	.	.	PUNCT
ejpam-4946	433	3	process	process	NOUN
ejpam-4946	433	4	.	.	PUNCT
ejpam-4946	434	1	lett	lett	PROPN
ejpam-4946	434	2	.	.	PROPN
ejpam-4946	434	3	,	,	PUNCT
ejpam-4946	434	4	27:119–123	27:119–123	PROPN
ejpam-4946	434	5	,	,	PUNCT
ejpam-4946	434	6	1988	1988	NUM
ejpam-4946	434	7	.	.	PUNCT
ejpam-4946	435	1	[	[	X
ejpam-4946	435	2	10	10	NUM
ejpam-4946	435	3	]	]	X
ejpam-4946	435	4	h.s	h.s	PROPN
ejpam-4946	435	5	.	.	PROPN
ejpam-4946	435	6	wilf	wilf	PROPN
ejpam-4946	435	7	.	.	PUNCT
ejpam-4946	436	1	the	the	DET
ejpam-4946	436	2	number	number	NOUN
ejpam-4946	436	3	of	of	ADP
ejpam-4946	436	4	maximal	maximal	ADJ
ejpam-4946	436	5	independent	independent	ADJ
ejpam-4946	436	6	sets	set	NOUN
ejpam-4946	436	7	in	in	ADP
ejpam-4946	436	8	a	a	DET
ejpam-4946	436	9	tree	tree	NOUN
ejpam-4946	436	10	.	.	PUNCT
ejpam-4946	437	1	siam	siam	PROPN
ejpam-4946	437	2	j.	j.	PROPN
ejpam-4946	437	3	alg	alg	PROPN
ejpam-4946	437	4	.	.	PUNCT
ejpam-4946	438	1	disc	disc	PROPN
ejpam-4946	438	2	.	.	PUNCT
ejpam-4946	439	1	meth	meth	NOUN
ejpam-4946	439	2	.	.	PUNCT
ejpam-4946	439	3	,	,	PUNCT
ejpam-4946	439	4	7:125–130	7:125–130	NUM
ejpam-4946	439	5	,	,	PUNCT
ejpam-4946	439	6	1986	1986	NUM
ejpam-4946	439	7	.	.	PUNCT
ejpam-4946	440	1	[	[	X
ejpam-4946	440	2	11	11	NUM
ejpam-4946	440	3	]	]	PUNCT
ejpam-4946	440	4	j.	j.	PROPN
ejpam-4946	440	5	zito	zito	PROPN
ejpam-4946	440	6	.	.	PUNCT
ejpam-4946	441	1	the	the	DET
ejpam-4946	441	2	structure	structure	NOUN
ejpam-4946	441	3	and	and	CCONJ
ejpam-4946	441	4	maximum	maximum	ADJ
ejpam-4946	441	5	number	number	NOUN
ejpam-4946	441	6	of	of	ADP
ejpam-4946	441	7	maximum	maximum	ADJ
ejpam-4946	441	8	independent	independent	ADJ
ejpam-4946	441	9	sets	set	NOUN
ejpam-4946	441	10	in	in	ADP
ejpam-4946	441	11	trees	tree	NOUN
ejpam-4946	441	12	.	.	PUNCT
ejpam-4946	442	1	j.	j.	PROPN
ejpam-4946	442	2	graph	graph	PROPN
ejpam-4946	442	3	theory	theory	NOUN
ejpam-4946	442	4	.	.	PUNCT
ejpam-4946	442	5	,	,	PUNCT
ejpam-4946	442	6	15(2):207–221	15(2):207–221	NUM
ejpam-4946	442	7	,	,	PUNCT
ejpam-4946	442	8	1991	1991	NUM
ejpam-4946	442	9	.	.	PUNCT