id	sid	tid	token	lemma	pos
ejpam-4451	1	1	european	european	PROPN
ejpam-4451	1	2	journal	journal	PROPN
ejpam-4451	1	3	of	of	ADP
ejpam-4451	1	4	pure	pure	ADJ
ejpam-4451	1	5	and	and	CCONJ
ejpam-4451	1	6	applied	apply	VERB
ejpam-4451	1	7	mathematics	mathematic	NOUN
ejpam-4451	1	8	vol	vol	NOUN
ejpam-4451	1	9	.	.	PROPN
ejpam-4451	2	1	15	15	NUM
ejpam-4451	2	2	,	,	PUNCT
ejpam-4451	2	3	no	no	INTJ
ejpam-4451	2	4	.	.	NOUN
ejpam-4451	2	5	3	3	NUM
ejpam-4451	2	6	,	,	PUNCT
ejpam-4451	2	7	2022	2022	NUM
ejpam-4451	2	8	,	,	PUNCT
ejpam-4451	2	9	1047	1047	NUM
ejpam-4451	2	10	-	-	SYM
ejpam-4451	2	11	1053	1053	NUM
ejpam-4451	2	12	issn	issn	PROPN
ejpam-4451	2	13	1307	1307	NUM
ejpam-4451	2	14	-	-	SYM
ejpam-4451	2	15	5543	5543	NUM
ejpam-4451	2	16	–	–	PUNCT
ejpam-4451	3	1	ejpam.com	ejpam.com	X
ejpam-4451	3	2	published	publish	VERB
ejpam-4451	3	3	by	by	ADP
ejpam-4451	3	4	new	new	PROPN
ejpam-4451	3	5	york	york	PROPN
ejpam-4451	3	6	business	business	PROPN
ejpam-4451	3	7	global	global	PROPN
ejpam-4451	3	8	restrained	restrain	VERB
ejpam-4451	3	9	2	2	NUM
ejpam-4451	3	10	-	-	PUNCT
ejpam-4451	3	11	resolving	resolve	VERB
ejpam-4451	3	12	dominating	dominating	NOUN
ejpam-4451	3	13	sets	set	NOUN
ejpam-4451	3	14	in	in	ADP
ejpam-4451	3	15	the	the	DET
ejpam-4451	3	16	join	join	NOUN
ejpam-4451	3	17	,	,	PUNCT
ejpam-4451	3	18	corona	corona	NOUN
ejpam-4451	3	19	and	and	CCONJ
ejpam-4451	3	20	lexicographic	lexicographic	ADJ
ejpam-4451	3	21	product	product	NOUN
ejpam-4451	3	22	of	of	ADP
ejpam-4451	3	23	two	two	NUM
ejpam-4451	3	24	graphs	graph	NOUN
ejpam-4451	3	25	jean	jean	PROPN
ejpam-4451	3	26	cabaro1,∗	cabaro1,∗	PROPN
ejpam-4451	3	27	,	,	PUNCT
ejpam-4451	3	28	helen	helen	PROPN
ejpam-4451	3	29	rara2	rara2	PROPN
ejpam-4451	3	30	1	1	NUM
ejpam-4451	3	31	mathematics	mathematics	PROPN
ejpam-4451	3	32	department	department	NOUN
ejpam-4451	3	33	,	,	PUNCT
ejpam-4451	3	34	college	college	NOUN
ejpam-4451	3	35	of	of	ADP
ejpam-4451	3	36	natural	natural	ADJ
ejpam-4451	3	37	sciences	science	NOUN
ejpam-4451	3	38	and	and	CCONJ
ejpam-4451	3	39	mathematics	mathematic	NOUN
ejpam-4451	3	40	,	,	PUNCT
ejpam-4451	3	41	mindanao	mindanao	PROPN
ejpam-4451	3	42	state	state	PROPN
ejpam-4451	3	43	university	university	NOUN
ejpam-4451	3	44	-	-	PUNCT
ejpam-4451	3	45	main	main	ADJ
ejpam-4451	3	46	campus	campus	NOUN
ejpam-4451	3	47	,	,	PUNCT
ejpam-4451	3	48	9700	9700	NUM
ejpam-4451	3	49	marawi	marawi	PROPN
ejpam-4451	3	50	city	city	PROPN
ejpam-4451	3	51	,	,	PUNCT
ejpam-4451	3	52	philippines	philippines	PROPN
ejpam-4451	3	53	2	2	NUM
ejpam-4451	3	54	department	department	NOUN
ejpam-4451	3	55	of	of	ADP
ejpam-4451	3	56	mathematics	mathematic	NOUN
ejpam-4451	3	57	and	and	CCONJ
ejpam-4451	3	58	statistics	statistic	NOUN
ejpam-4451	3	59	,	,	PUNCT
ejpam-4451	3	60	college	college	NOUN
ejpam-4451	3	61	of	of	ADP
ejpam-4451	3	62	science	science	NOUN
ejpam-4451	3	63	and	and	CCONJ
ejpam-4451	3	64	mathematics	mathematic	NOUN
ejpam-4451	3	65	,	,	PUNCT
ejpam-4451	3	66	center	center	NOUN
ejpam-4451	3	67	of	of	ADP
ejpam-4451	3	68	graph	graph	NOUN
ejpam-4451	3	69	theory	theory	NOUN
ejpam-4451	3	70	,	,	PUNCT
ejpam-4451	3	71	algebra	algebra	NOUN
ejpam-4451	3	72	,	,	PUNCT
ejpam-4451	3	73	and	and	CCONJ
ejpam-4451	3	74	analysis	analysis	NOUN
ejpam-4451	3	75	-	-	PUNCT
ejpam-4451	3	76	premier	premier	NOUN
ejpam-4451	3	77	research	research	NOUN
ejpam-4451	3	78	institute	institute	PROPN
ejpam-4451	3	79	of	of	ADP
ejpam-4451	3	80	science	science	NOUN
ejpam-4451	3	81	and	and	CCONJ
ejpam-4451	3	82	mathematics	mathematic	NOUN
ejpam-4451	3	83	,	,	PUNCT
ejpam-4451	3	84	mindanao	mindanao	PROPN
ejpam-4451	3	85	state	state	PROPN
ejpam-4451	3	86	university	university	PROPN
ejpam-4451	3	87	-	-	PUNCT
ejpam-4451	3	88	iligan	iligan	PROPN
ejpam-4451	3	89	institute	institute	PROPN
ejpam-4451	3	90	of	of	ADP
ejpam-4451	3	91	technology	technology	PROPN
ejpam-4451	3	92	,	,	PUNCT
ejpam-4451	3	93	9200	9200	NUM
ejpam-4451	3	94	iligan	iligan	ADJ
ejpam-4451	3	95	city	city	NOUN
ejpam-4451	3	96	,	,	PUNCT
ejpam-4451	3	97	philippines	philippine	NOUN
ejpam-4451	3	98	abstract	abstract	ADJ
ejpam-4451	3	99	.	.	PUNCT
ejpam-4451	4	1	let	let	VERB
ejpam-4451	4	2	g	g	PRON
ejpam-4451	4	3	be	be	AUX
ejpam-4451	4	4	a	a	DET
ejpam-4451	4	5	connected	connected	ADJ
ejpam-4451	4	6	graph	graph	NOUN
ejpam-4451	4	7	.	.	PUNCT
ejpam-4451	5	1	an	an	DET
ejpam-4451	5	2	ordered	order	VERB
ejpam-4451	5	3	set	set	NOUN
ejpam-4451	5	4	of	of	ADP
ejpam-4451	5	5	vertices	vertex	NOUN
ejpam-4451	5	6	{	{	PUNCT
ejpam-4451	5	7	v1	v1	NOUN
ejpam-4451	5	8	,	,	PUNCT
ejpam-4451	5	9	...	...	PUNCT
ejpam-4451	5	10	,	,	PUNCT
ejpam-4451	5	11	vl	vl	ADJ
ejpam-4451	5	12	}	}	PUNCT
ejpam-4451	5	13	is	be	AUX
ejpam-4451	5	14	a	a	DET
ejpam-4451	5	15	2	2	NUM
ejpam-4451	5	16	-	-	PUNCT
ejpam-4451	5	17	resolving	resolving	NOUN
ejpam-4451	5	18	set	set	NOUN
ejpam-4451	5	19	for	for	ADP
ejpam-4451	5	20	g	g	PROPN
ejpam-4451	5	21	if	if	SCONJ
ejpam-4451	5	22	,	,	PUNCT
ejpam-4451	5	23	for	for	ADP
ejpam-4451	5	24	any	any	DET
ejpam-4451	5	25	distinct	distinct	ADJ
ejpam-4451	5	26	vertices	vertex	NOUN
ejpam-4451	5	27	u	u	NOUN
ejpam-4451	5	28	,	,	PUNCT
ejpam-4451	5	29	w	w	PROPN
ejpam-4451	5	30	∈	∈	PROPN
ejpam-4451	5	31	v	v	ADP
ejpam-4451	5	32	(	(	PUNCT
ejpam-4451	5	33	g	g	NOUN
ejpam-4451	5	34	)	)	PUNCT
ejpam-4451	5	35	,	,	PUNCT
ejpam-4451	5	36	the	the	DET
ejpam-4451	5	37	lists	list	NOUN
ejpam-4451	5	38	of	of	ADP
ejpam-4451	5	39	distances	distance	NOUN
ejpam-4451	5	40	(	(	PUNCT
ejpam-4451	5	41	dg(u	dg(u	X
ejpam-4451	5	42	,	,	PUNCT
ejpam-4451	5	43	v1	v1	NOUN
ejpam-4451	5	44	)	)	PUNCT
ejpam-4451	5	45	,	,	PUNCT
ejpam-4451	5	46	...	...	PUNCT
ejpam-4451	5	47	,	,	PUNCT
ejpam-4451	5	48	dg(u	dg(u	X
ejpam-4451	5	49	,	,	PUNCT
ejpam-4451	5	50	vl	vl	NOUN
ejpam-4451	5	51	)	)	PUNCT
ejpam-4451	5	52	)	)	PUNCT
ejpam-4451	5	53	and	and	CCONJ
ejpam-4451	5	54	(	(	PUNCT
ejpam-4451	5	55	dg(w	dg(w	X
ejpam-4451	5	56	,	,	PUNCT
ejpam-4451	5	57	v1	v1	NOUN
ejpam-4451	5	58	)	)	PUNCT
ejpam-4451	5	59	,	,	PUNCT
ejpam-4451	5	60	...	...	PUNCT
ejpam-4451	5	61	,	,	PUNCT
ejpam-4451	5	62	dg(w	dg(w	X
ejpam-4451	5	63	,	,	PUNCT
ejpam-4451	5	64	vl	vl	NOUN
ejpam-4451	5	65	)	)	PUNCT
ejpam-4451	5	66	)	)	PUNCT
ejpam-4451	5	67	differ	differ	VERB
ejpam-4451	5	68	in	in	ADP
ejpam-4451	5	69	at	at	ADV
ejpam-4451	5	70	least	least	ADJ
ejpam-4451	5	71	2	2	NUM
ejpam-4451	5	72	positions	position	NOUN
ejpam-4451	5	73	.	.	PUNCT
ejpam-4451	6	1	a	a	DET
ejpam-4451	6	2	set	set	NOUN
ejpam-4451	6	3	s	s	NOUN
ejpam-4451	6	4	⊆	⊆	NUM
ejpam-4451	6	5	v	v	NOUN
ejpam-4451	6	6	(	(	PUNCT
ejpam-4451	6	7	g	g	NOUN
ejpam-4451	6	8	)	)	PUNCT
ejpam-4451	6	9	is	be	AUX
ejpam-4451	6	10	a	a	DET
ejpam-4451	6	11	restrained	restrained	ADJ
ejpam-4451	6	12	2	2	NUM
ejpam-4451	6	13	-	-	PUNCT
ejpam-4451	6	14	resolving	resolve	VERB
ejpam-4451	6	15	dominating	dominating	NOUN
ejpam-4451	6	16	set	set	VERB
ejpam-4451	6	17	in	in	ADP
ejpam-4451	6	18	g	g	PROPN
ejpam-4451	6	19	if	if	SCONJ
ejpam-4451	6	20	s	s	VERB
ejpam-4451	6	21	is	be	AUX
ejpam-4451	6	22	a	a	DET
ejpam-4451	6	23	2	2	NUM
ejpam-4451	6	24	-	-	PUNCT
ejpam-4451	6	25	resolving	resolve	VERB
ejpam-4451	6	26	dominating	dominating	NOUN
ejpam-4451	6	27	set	set	VERB
ejpam-4451	6	28	in	in	ADP
ejpam-4451	6	29	g	g	PROPN
ejpam-4451	6	30	and	and	CCONJ
ejpam-4451	6	31	s	s	PART
ejpam-4451	6	32	=	=	SYM
ejpam-4451	6	33	v	v	X
ejpam-4451	6	34	(	(	PUNCT
ejpam-4451	6	35	g	g	NOUN
ejpam-4451	6	36	)	)	PUNCT
ejpam-4451	6	37	or	or	CCONJ
ejpam-4451	6	38	⟨v	⟨v	NUM
ejpam-4451	6	39	(	(	PUNCT
ejpam-4451	6	40	g)\s⟩	g)\s⟩	PROPN
ejpam-4451	6	41	has	have	AUX
ejpam-4451	6	42	no	no	DET
ejpam-4451	6	43	isolated	isolated	ADJ
ejpam-4451	6	44	vertex	vertex	NOUN
ejpam-4451	6	45	.	.	PUNCT
ejpam-4451	7	1	the	the	DET
ejpam-4451	7	2	restrained	restrained	ADJ
ejpam-4451	7	3	2r	2r	NUM
ejpam-4451	7	4	-	-	PUNCT
ejpam-4451	7	5	domination	domination	NOUN
ejpam-4451	7	6	number	number	NOUN
ejpam-4451	7	7	of	of	ADP
ejpam-4451	7	8	g	g	NOUN
ejpam-4451	7	9	,	,	PUNCT
ejpam-4451	7	10	denoted	denote	VERB
ejpam-4451	7	11	by	by	ADP
ejpam-4451	7	12	γr2r(g	γr2r(g	NUM
ejpam-4451	7	13	)	)	PUNCT
ejpam-4451	7	14	,	,	PUNCT
ejpam-4451	7	15	is	be	AUX
ejpam-4451	7	16	the	the	DET
ejpam-4451	7	17	smallest	small	ADJ
ejpam-4451	7	18	cardinality	cardinality	NOUN
ejpam-4451	7	19	of	of	ADP
ejpam-4451	7	20	a	a	DET
ejpam-4451	7	21	restrained	restrained	ADJ
ejpam-4451	7	22	2	2	NUM
ejpam-4451	7	23	-	-	PUNCT
ejpam-4451	7	24	resolving	resolve	VERB
ejpam-4451	7	25	dominating	dominating	NOUN
ejpam-4451	7	26	set	set	VERB
ejpam-4451	7	27	in	in	ADP
ejpam-4451	7	28	g.	g.	PROPN
ejpam-4451	7	29	any	any	DET
ejpam-4451	7	30	restrained	restrained	ADJ
ejpam-4451	7	31	2	2	NUM
ejpam-4451	7	32	-	-	PUNCT
ejpam-4451	7	33	resolving	resolve	VERB
ejpam-4451	7	34	dominating	dominating	NOUN
ejpam-4451	7	35	set	set	NOUN
ejpam-4451	7	36	of	of	ADP
ejpam-4451	7	37	cardinality	cardinality	PROPN
ejpam-4451	7	38	γr2r(g	γr2r(g	NUM
ejpam-4451	7	39	)	)	PUNCT
ejpam-4451	7	40	is	be	AUX
ejpam-4451	7	41	referred	refer	VERB
ejpam-4451	7	42	to	to	ADP
ejpam-4451	7	43	as	as	ADP
ejpam-4451	7	44	a	a	DET
ejpam-4451	7	45	γr2r	γr2r	ADV
ejpam-4451	7	46	-	-	PUNCT
ejpam-4451	7	47	set	set	NOUN
ejpam-4451	7	48	in	in	ADP
ejpam-4451	7	49	g.	g.	PROPN
ejpam-4451	7	50	this	this	DET
ejpam-4451	7	51	study	study	NOUN
ejpam-4451	7	52	deals	deal	VERB
ejpam-4451	7	53	with	with	ADP
ejpam-4451	7	54	the	the	DET
ejpam-4451	7	55	concept	concept	NOUN
ejpam-4451	7	56	of	of	ADP
ejpam-4451	7	57	restrained	restrained	ADJ
ejpam-4451	7	58	2	2	NUM
ejpam-4451	7	59	-	-	PUNCT
ejpam-4451	7	60	resolving	resolve	VERB
ejpam-4451	7	61	dominating	dominating	NOUN
ejpam-4451	7	62	set	set	NOUN
ejpam-4451	7	63	of	of	ADP
ejpam-4451	7	64	a	a	DET
ejpam-4451	7	65	graph	graph	NOUN
ejpam-4451	7	66	.	.	PUNCT
ejpam-4451	8	1	it	it	PRON
ejpam-4451	8	2	characterizes	characterize	VERB
ejpam-4451	8	3	the	the	DET
ejpam-4451	8	4	restrained	restrained	ADJ
ejpam-4451	8	5	2	2	NUM
ejpam-4451	8	6	-	-	PUNCT
ejpam-4451	8	7	resolving	resolve	VERB
ejpam-4451	8	8	dominating	dominating	NOUN
ejpam-4451	8	9	set	set	VERB
ejpam-4451	8	10	in	in	ADP
ejpam-4451	8	11	the	the	DET
ejpam-4451	8	12	join	join	NOUN
ejpam-4451	8	13	,	,	PUNCT
ejpam-4451	8	14	corona	corona	NOUN
ejpam-4451	8	15	and	and	CCONJ
ejpam-4451	8	16	lexicographic	lexicographic	ADJ
ejpam-4451	8	17	product	product	NOUN
ejpam-4451	8	18	of	of	ADP
ejpam-4451	8	19	two	two	NUM
ejpam-4451	8	20	graphs	graph	NOUN
ejpam-4451	8	21	and	and	CCONJ
ejpam-4451	8	22	determine	determine	VERB
ejpam-4451	8	23	the	the	DET
ejpam-4451	8	24	bounds	bound	NOUN
ejpam-4451	8	25	or	or	CCONJ
ejpam-4451	8	26	exact	exact	ADJ
ejpam-4451	8	27	values	value	NOUN
ejpam-4451	8	28	of	of	ADP
ejpam-4451	8	29	the	the	DET
ejpam-4451	8	30	restrained	restrained	ADJ
ejpam-4451	8	31	2	2	NUM
ejpam-4451	8	32	-	-	PUNCT
ejpam-4451	8	33	resolving	resolve	VERB
ejpam-4451	8	34	domination	domination	NOUN
ejpam-4451	8	35	number	number	NOUN
ejpam-4451	8	36	of	of	ADP
ejpam-4451	8	37	these	these	DET
ejpam-4451	8	38	graphs	graph	NOUN
ejpam-4451	8	39	.	.	PUNCT
ejpam-4451	9	1	2020	2020	NUM
ejpam-4451	9	2	mathematics	mathematic	NOUN
ejpam-4451	9	3	subject	subject	NOUN
ejpam-4451	9	4	classifications	classification	NOUN
ejpam-4451	9	5	:	:	PUNCT
ejpam-4451	9	6	05c62	05c62	NUM
ejpam-4451	9	7	key	key	ADJ
ejpam-4451	9	8	words	word	NOUN
ejpam-4451	9	9	and	and	CCONJ
ejpam-4451	9	10	phrases	phrase	NOUN
ejpam-4451	9	11	:	:	PUNCT
ejpam-4451	9	12	restrained	restrain	VERB
ejpam-4451	9	13	2	2	NUM
ejpam-4451	9	14	-	-	PUNCT
ejpam-4451	9	15	resolving	resolve	VERB
ejpam-4451	9	16	set	set	NOUN
ejpam-4451	9	17	,	,	PUNCT
ejpam-4451	9	18	restrained	restrain	VERB
ejpam-4451	9	19	2	2	NUM
ejpam-4451	9	20	-	-	PUNCT
ejpam-4451	9	21	resolving	resolve	VERB
ejpam-4451	9	22	dominating	dominating	NOUN
ejpam-4451	9	23	set	set	NOUN
ejpam-4451	9	24	,	,	PUNCT
ejpam-4451	9	25	join	join	NOUN
ejpam-4451	9	26	,	,	PUNCT
ejpam-4451	9	27	corona	corona	PROPN
ejpam-4451	9	28	,	,	PUNCT
ejpam-4451	9	29	lexicographic	lexicographic	ADJ
ejpam-4451	9	30	product	product	NOUN
ejpam-4451	9	31	of	of	ADP
ejpam-4451	9	32	two	two	NUM
ejpam-4451	9	33	graphs	graph	NOUN
ejpam-4451	9	34	1	1	NUM
ejpam-4451	9	35	.	.	PUNCT
ejpam-4451	9	36	introduction	introduction	NOUN
ejpam-4451	9	37	the	the	DET
ejpam-4451	9	38	problem	problem	NOUN
ejpam-4451	9	39	of	of	ADP
ejpam-4451	9	40	uniquely	uniquely	ADV
ejpam-4451	9	41	determining	determine	VERB
ejpam-4451	9	42	the	the	DET
ejpam-4451	9	43	location	location	NOUN
ejpam-4451	9	44	of	of	ADP
ejpam-4451	9	45	an	an	DET
ejpam-4451	9	46	intruder	intruder	NOUN
ejpam-4451	9	47	in	in	ADP
ejpam-4451	9	48	a	a	DET
ejpam-4451	9	49	network	network	NOUN
ejpam-4451	9	50	was	be	AUX
ejpam-4451	9	51	the	the	DET
ejpam-4451	9	52	principal	principal	ADJ
ejpam-4451	9	53	motivation	motivation	NOUN
ejpam-4451	9	54	of	of	ADP
ejpam-4451	9	55	introducing	introduce	VERB
ejpam-4451	9	56	the	the	DET
ejpam-4451	9	57	concept	concept	NOUN
ejpam-4451	9	58	of	of	ADP
ejpam-4451	9	59	metric	metric	ADJ
ejpam-4451	9	60	dimension	dimension	NOUN
ejpam-4451	9	61	in	in	ADP
ejpam-4451	9	62	graphs	graph	NOUN
ejpam-4451	9	63	by	by	ADP
ejpam-4451	9	64	slater	slater	NOUN
ejpam-4451	10	1	[	[	X
ejpam-4451	10	2	9	9	NUM
ejpam-4451	10	3	]	]	PUNCT
ejpam-4451	10	4	,	,	PUNCT
ejpam-4451	10	5	where	where	SCONJ
ejpam-4451	10	6	the	the	DET
ejpam-4451	10	7	metric	metric	ADJ
ejpam-4451	10	8	generators	generator	NOUN
ejpam-4451	10	9	were	be	AUX
ejpam-4451	10	10	called	call	VERB
ejpam-4451	10	11	locating	locating	NOUN
ejpam-4451	10	12	sets	set	NOUN
ejpam-4451	10	13	.	.	PUNCT
ejpam-4451	11	1	the	the	DET
ejpam-4451	11	2	concept	concept	NOUN
ejpam-4451	11	3	of	of	ADP
ejpam-4451	11	4	metric	metric	ADJ
ejpam-4451	11	5	dimension	dimension	NOUN
ejpam-4451	11	6	of	of	ADP
ejpam-4451	11	7	a	a	DET
ejpam-4451	11	8	graph	graph	NOUN
ejpam-4451	11	9	was	be	AUX
ejpam-4451	11	10	also	also	ADV
ejpam-4451	11	11	introduced	introduce	VERB
ejpam-4451	11	12	independently	independently	ADV
ejpam-4451	11	13	by	by	ADP
ejpam-4451	11	14	harary	harary	NOUN
ejpam-4451	11	15	and	and	CCONJ
ejpam-4451	11	16	melter	melter	NOUN
ejpam-4451	11	17	in	in	ADP
ejpam-4451	11	18	[	[	X
ejpam-4451	11	19	4	4	X
ejpam-4451	11	20	]	]	PUNCT
ejpam-4451	11	21	where	where	SCONJ
ejpam-4451	11	22	metric	metric	ADJ
ejpam-4451	11	23	generators	generator	NOUN
ejpam-4451	11	24	were	be	AUX
ejpam-4451	11	25	called	call	VERB
ejpam-4451	11	26	resolving	resolve	VERB
ejpam-4451	11	27	sets	set	NOUN
ejpam-4451	11	28	.	.	PUNCT
ejpam-4451	12	1	bailey	bailey	NOUN
ejpam-4451	12	2	and	and	CCONJ
ejpam-4451	12	3	yero	yero	NOUN
ejpam-4451	12	4	in	in	ADP
ejpam-4451	12	5	[	[	X
ejpam-4451	12	6	1	1	NUM
ejpam-4451	12	7	]	]	PUNCT
ejpam-4451	12	8	demonstrated	demonstrate	VERB
ejpam-4451	12	9	a	a	DET
ejpam-4451	12	10	construction	construction	NOUN
ejpam-4451	12	11	of	of	ADP
ejpam-4451	12	12	error	error	NOUN
ejpam-4451	12	13	-	-	PUNCT
ejpam-4451	12	14	correcting	correct	VERB
ejpam-4451	12	15	codes	code	NOUN
ejpam-4451	12	16	from	from	ADP
ejpam-4451	12	17	graphs	graph	NOUN
ejpam-4451	12	18	by	by	ADP
ejpam-4451	12	19	means	mean	NOUN
ejpam-4451	12	20	of	of	ADP
ejpam-4451	12	21	k	k	ADJ
ejpam-4451	12	22	-	-	PUNCT
ejpam-4451	12	23	resolving	resolving	ADJ
ejpam-4451	12	24	sets	set	NOUN
ejpam-4451	12	25	,	,	PUNCT
ejpam-4451	12	26	and	and	CCONJ
ejpam-4451	12	27	present	present	VERB
ejpam-4451	12	28	a	a	DET
ejpam-4451	12	29	decoding	decode	VERB
ejpam-4451	12	30	algorithm	algorithm	NOUN
ejpam-4451	12	31	which	which	PRON
ejpam-4451	12	32	makes	make	VERB
ejpam-4451	12	33	use	use	NOUN
ejpam-4451	12	34	∗corresponding	∗corresponde	VERB
ejpam-4451	12	35	author	author	NOUN
ejpam-4451	12	36	.	.	PUNCT
ejpam-4451	13	1	doi	doi	NOUN
ejpam-4451	13	2	:	:	PUNCT
ejpam-4451	13	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4451	https://doi.org/10.29020/nybg.ejpam.v15i3.4451	PROPN
ejpam-4451	13	4	email	email	NOUN
ejpam-4451	13	5	addresses	address	NOUN
ejpam-4451	13	6	:	:	PUNCT
ejpam-4451	13	7	amerjean1228@gmail.com	amerjean1228@gmail.com	X
ejpam-4451	13	8	(	(	PUNCT
ejpam-4451	13	9	j.	j.	PROPN
ejpam-4451	13	10	cabaro	cabaro	PROPN
ejpam-4451	13	11	)	)	PUNCT
ejpam-4451	13	12	,	,	PUNCT
ejpam-4451	13	13	helenrara@gmail.com	helenrara@gmail.com	X
ejpam-4451	13	14	(	(	PUNCT
ejpam-4451	13	15	h.	h.	PROPN
ejpam-4451	13	16	rara	rara	PROPN
ejpam-4451	13	17	)	)	PUNCT
ejpam-4451	13	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4451	13	19	1047	1047	NUM
ejpam-4451	13	20	©	©	ADP
ejpam-4451	13	21	2022	2022	NUM
ejpam-4451	13	22	ejpam	ejpam	VERB
ejpam-4451	13	23	all	all	DET
ejpam-4451	13	24	rights	right	NOUN
ejpam-4451	13	25	reserved	reserve	VERB
ejpam-4451	13	26	.	.	PUNCT
ejpam-4451	14	1	j.	j.	PROPN
ejpam-4451	14	2	cabaro	cabaro	PROPN
ejpam-4451	14	3	,	,	PUNCT
ejpam-4451	14	4	h.	h.	PROPN
ejpam-4451	14	5	rara	rara	PROPN
ejpam-4451	14	6	/	/	SYM
ejpam-4451	14	7	eur	eur	PROPN
ejpam-4451	14	8	.	.	PUNCT
ejpam-4451	15	1	j.	j.	PROPN
ejpam-4451	15	2	pure	pure	PROPN
ejpam-4451	15	3	appl	appl	PROPN
ejpam-4451	15	4	.	.	PROPN
ejpam-4451	15	5	math	math	PROPN
ejpam-4451	15	6	,	,	PUNCT
ejpam-4451	15	7	15	15	NUM
ejpam-4451	15	8	(	(	PUNCT
ejpam-4451	15	9	3	3	NUM
ejpam-4451	15	10	)	)	PUNCT
ejpam-4451	15	11	(	(	PUNCT
ejpam-4451	15	12	2022	2022	NUM
ejpam-4451	15	13	)	)	PUNCT
ejpam-4451	15	14	,	,	PUNCT
ejpam-4451	15	15	1047	1047	NUM
ejpam-4451	15	16	-	-	SYM
ejpam-4451	15	17	1053	1053	NUM
ejpam-4451	15	18	1048	1048	NUM
ejpam-4451	15	19	of	of	ADP
ejpam-4451	15	20	covering	cover	VERB
ejpam-4451	15	21	designs	design	NOUN
ejpam-4451	15	22	.	.	PUNCT
ejpam-4451	16	1	the	the	DET
ejpam-4451	16	2	distance	distance	NOUN
ejpam-4451	16	3	between	between	ADP
ejpam-4451	16	4	two	two	NUM
ejpam-4451	16	5	vertices	vertex	NOUN
ejpam-4451	16	6	u	u	NOUN
ejpam-4451	16	7	and	and	CCONJ
ejpam-4451	16	8	v	v	NOUN
ejpam-4451	16	9	of	of	ADP
ejpam-4451	16	10	a	a	DET
ejpam-4451	16	11	graph	graph	NOUN
ejpam-4451	16	12	is	be	AUX
ejpam-4451	16	13	the	the	DET
ejpam-4451	16	14	length	length	NOUN
ejpam-4451	16	15	of	of	ADP
ejpam-4451	16	16	a	a	DET
ejpam-4451	16	17	shortest	short	ADJ
ejpam-4451	16	18	path	path	NOUN
ejpam-4451	16	19	between	between	ADP
ejpam-4451	16	20	u	u	NOUN
ejpam-4451	16	21	and	and	CCONJ
ejpam-4451	16	22	v	v	NOUN
ejpam-4451	16	23	,	,	PUNCT
ejpam-4451	16	24	and	and	CCONJ
ejpam-4451	16	25	we	we	PRON
ejpam-4451	16	26	denote	denote	VERB
ejpam-4451	16	27	this	this	PRON
ejpam-4451	16	28	by	by	ADP
ejpam-4451	16	29	dg(u	dg(u	NOUN
ejpam-4451	16	30	,	,	PUNCT
ejpam-4451	16	31	v	v	NOUN
ejpam-4451	16	32	)	)	PUNCT
ejpam-4451	16	33	.	.	PUNCT
ejpam-4451	17	1	in	in	ADP
ejpam-4451	17	2	recent	recent	ADJ
ejpam-4451	17	3	years	year	NOUN
ejpam-4451	17	4	,	,	PUNCT
ejpam-4451	17	5	much	much	ADJ
ejpam-4451	17	6	attention	attention	NOUN
ejpam-4451	17	7	has	have	AUX
ejpam-4451	17	8	been	be	AUX
ejpam-4451	17	9	paid	pay	VERB
ejpam-4451	17	10	to	to	ADP
ejpam-4451	17	11	the	the	DET
ejpam-4451	17	12	metric	metric	ADJ
ejpam-4451	17	13	dimension	dimension	NOUN
ejpam-4451	17	14	of	of	ADP
ejpam-4451	17	15	graphs	graph	NOUN
ejpam-4451	17	16	:	:	PUNCT
ejpam-4451	17	17	this	this	PRON
ejpam-4451	17	18	is	be	AUX
ejpam-4451	17	19	the	the	DET
ejpam-4451	17	20	smallest	small	ADJ
ejpam-4451	17	21	size	size	NOUN
ejpam-4451	17	22	of	of	ADP
ejpam-4451	17	23	a	a	DET
ejpam-4451	17	24	subset	subset	NOUN
ejpam-4451	17	25	of	of	ADP
ejpam-4451	17	26	vertices	vertex	NOUN
ejpam-4451	17	27	(	(	PUNCT
ejpam-4451	17	28	called	call	VERB
ejpam-4451	17	29	a	a	DET
ejpam-4451	17	30	resolving	resolving	NOUN
ejpam-4451	17	31	set	set	NOUN
ejpam-4451	17	32	)	)	PUNCT
ejpam-4451	17	33	with	with	ADP
ejpam-4451	17	34	the	the	DET
ejpam-4451	17	35	property	property	NOUN
ejpam-4451	17	36	that	that	PRON
ejpam-4451	17	37	the	the	DET
ejpam-4451	17	38	list	list	NOUN
ejpam-4451	17	39	of	of	ADP
ejpam-4451	17	40	distances	distance	NOUN
ejpam-4451	17	41	from	from	ADP
ejpam-4451	17	42	any	any	DET
ejpam-4451	17	43	vertex	vertex	NOUN
ejpam-4451	17	44	to	to	ADP
ejpam-4451	17	45	those	those	PRON
ejpam-4451	17	46	in	in	ADP
ejpam-4451	17	47	the	the	DET
ejpam-4451	17	48	set	set	NOUN
ejpam-4451	17	49	uniquely	uniquely	ADV
ejpam-4451	17	50	identifies	identify	VERB
ejpam-4451	17	51	that	that	SCONJ
ejpam-4451	17	52	vertex	vertex	NOUN
ejpam-4451	17	53	and	and	CCONJ
ejpam-4451	17	54	is	be	AUX
ejpam-4451	17	55	denoted	denote	VERB
ejpam-4451	17	56	by	by	ADP
ejpam-4451	17	57	dim(g	dim(g	PROPN
ejpam-4451	17	58	)	)	PUNCT
ejpam-4451	17	59	.	.	PUNCT
ejpam-4451	18	1	according	accord	VERB
ejpam-4451	18	2	to	to	ADP
ejpam-4451	18	3	the	the	DET
ejpam-4451	18	4	paper	paper	NOUN
ejpam-4451	18	5	of	of	ADP
ejpam-4451	18	6	saenpholphat	saenpholphat	PROPN
ejpam-4451	18	7	et	et	PROPN
ejpam-4451	18	8	al	al	PROPN
ejpam-4451	18	9	.	.	PUNCT
ejpam-4451	19	1	[	[	X
ejpam-4451	19	2	8	8	NUM
ejpam-4451	19	3	]	]	PUNCT
ejpam-4451	19	4	,	,	PUNCT
ejpam-4451	19	5	for	for	ADP
ejpam-4451	19	6	an	an	DET
ejpam-4451	19	7	ordered	order	VERB
ejpam-4451	19	8	set	set	NOUN
ejpam-4451	19	9	of	of	ADP
ejpam-4451	19	10	vertices	vertex	NOUN
ejpam-4451	19	11	w	w	NOUN
ejpam-4451	19	12	=	=	SYM
ejpam-4451	19	13	{	{	PUNCT
ejpam-4451	19	14	w1	w1	NOUN
ejpam-4451	19	15	,	,	PUNCT
ejpam-4451	19	16	w2	w2	NOUN
ejpam-4451	19	17	,	,	PUNCT
ejpam-4451	19	18	...	...	PUNCT
ejpam-4451	19	19	,	,	PUNCT
ejpam-4451	19	20	wk	wk	AUX
ejpam-4451	19	21	}	}	PUNCT
ejpam-4451	19	22	⊆	⊆	NUM
ejpam-4451	19	23	v	v	NOUN
ejpam-4451	19	24	(	(	PUNCT
ejpam-4451	19	25	g	g	NOUN
ejpam-4451	19	26	)	)	PUNCT
ejpam-4451	19	27	and	and	CCONJ
ejpam-4451	19	28	a	a	DET
ejpam-4451	19	29	vertex	vertex	NOUN
ejpam-4451	19	30	v	v	NOUN
ejpam-4451	19	31	in	in	ADP
ejpam-4451	19	32	g	g	PROPN
ejpam-4451	19	33	,	,	PUNCT
ejpam-4451	19	34	the	the	DET
ejpam-4451	19	35	k	k	NOUN
ejpam-4451	19	36	-	-	NOUN
ejpam-4451	19	37	vector	vector	NOUN
ejpam-4451	19	38	(	(	PUNCT
ejpam-4451	19	39	ordered	order	VERB
ejpam-4451	19	40	k	k	NOUN
ejpam-4451	19	41	-	-	PUNCT
ejpam-4451	19	42	tuple	tuple	ADJ
ejpam-4451	19	43	)	)	PUNCT
ejpam-4451	19	44	r(v	r(v	PROPN
ejpam-4451	19	45	/	/	SYM
ejpam-4451	19	46	w	w	NOUN
ejpam-4451	19	47	)	)	PUNCT
ejpam-4451	20	1	=	=	SYM
ejpam-4451	20	2	(	(	PUNCT
ejpam-4451	20	3	dg(v	dg(v	X
ejpam-4451	20	4	,	,	PUNCT
ejpam-4451	20	5	w1	w1	NOUN
ejpam-4451	20	6	)	)	PUNCT
ejpam-4451	20	7	,	,	PUNCT
ejpam-4451	20	8	dg(v	dg(v	X
ejpam-4451	20	9	,	,	PUNCT
ejpam-4451	20	10	w2	w2	NOUN
ejpam-4451	20	11	)	)	PUNCT
ejpam-4451	20	12	,	,	PUNCT
ejpam-4451	20	13	...	...	PUNCT
ejpam-4451	20	14	,	,	PUNCT
ejpam-4451	20	15	dg(v	dg(v	X
ejpam-4451	20	16	,	,	PUNCT
ejpam-4451	20	17	wk	wk	NOUN
ejpam-4451	20	18	)	)	PUNCT
ejpam-4451	20	19	)	)	PUNCT
ejpam-4451	20	20	is	be	AUX
ejpam-4451	20	21	referred	refer	VERB
ejpam-4451	20	22	to	to	ADP
ejpam-4451	20	23	as	as	ADP
ejpam-4451	20	24	the	the	DET
ejpam-4451	20	25	(	(	PUNCT
ejpam-4451	20	26	metric	metric	ADJ
ejpam-4451	20	27	)	)	PUNCT
ejpam-4451	20	28	representation	representation	NOUN
ejpam-4451	20	29	of	of	ADP
ejpam-4451	20	30	v	v	NOUN
ejpam-4451	20	31	with	with	ADP
ejpam-4451	20	32	respect	respect	NOUN
ejpam-4451	20	33	to	to	ADP
ejpam-4451	20	34	w	w	PROPN
ejpam-4451	20	35	.	.	PUNCT
ejpam-4451	21	1	the	the	DET
ejpam-4451	21	2	set	set	NOUN
ejpam-4451	21	3	w	w	NOUN
ejpam-4451	21	4	is	be	AUX
ejpam-4451	21	5	called	call	VERB
ejpam-4451	21	6	a	a	DET
ejpam-4451	21	7	resolving	resolving	NOUN
ejpam-4451	21	8	set	set	VERB
ejpam-4451	21	9	for	for	ADP
ejpam-4451	21	10	g	g	PROPN
ejpam-4451	21	11	if	if	SCONJ
ejpam-4451	21	12	distinct	distinct	ADJ
ejpam-4451	21	13	vertices	vertex	NOUN
ejpam-4451	21	14	have	have	VERB
ejpam-4451	21	15	distinct	distinct	ADJ
ejpam-4451	21	16	representation	representation	NOUN
ejpam-4451	21	17	with	with	ADP
ejpam-4451	21	18	respect	respect	NOUN
ejpam-4451	21	19	to	to	ADP
ejpam-4451	21	20	w	w	PROPN
ejpam-4451	21	21	.	.	PUNCT
ejpam-4451	22	1	hence	hence	ADV
ejpam-4451	22	2	,	,	PUNCT
ejpam-4451	22	3	if	if	SCONJ
ejpam-4451	22	4	w	w	NOUN
ejpam-4451	22	5	is	be	AUX
ejpam-4451	22	6	a	a	DET
ejpam-4451	22	7	resolving	resolving	NOUN
ejpam-4451	22	8	set	set	NOUN
ejpam-4451	22	9	of	of	ADP
ejpam-4451	22	10	cardinality	cardinality	PROPN
ejpam-4451	22	11	k	k	PROPN
ejpam-4451	22	12	for	for	ADP
ejpam-4451	22	13	a	a	DET
ejpam-4451	22	14	graph	graph	NOUN
ejpam-4451	22	15	g	g	NOUN
ejpam-4451	22	16	of	of	ADP
ejpam-4451	22	17	order	order	NOUN
ejpam-4451	22	18	n	n	CCONJ
ejpam-4451	22	19	,	,	PUNCT
ejpam-4451	22	20	then	then	ADV
ejpam-4451	22	21	the	the	DET
ejpam-4451	22	22	set	set	NOUN
ejpam-4451	22	23	{	{	PUNCT
ejpam-4451	22	24	r(v	r(v	PROPN
ejpam-4451	22	25	/	/	SYM
ejpam-4451	22	26	w	w	PROPN
ejpam-4451	22	27	)	)	PUNCT
ejpam-4451	22	28	:	:	PUNCT
ejpam-4451	22	29	v	v	X
ejpam-4451	22	30	∈	∈	PROPN
ejpam-4451	22	31	v	v	NOUN
ejpam-4451	22	32	(	(	PUNCT
ejpam-4451	22	33	g	g	NOUN
ejpam-4451	22	34	)	)	PUNCT
ejpam-4451	22	35	}	}	PUNCT
ejpam-4451	22	36	consists	consist	VERB
ejpam-4451	22	37	of	of	ADP
ejpam-4451	22	38	n	n	PRON
ejpam-4451	22	39	distinct	distinct	ADJ
ejpam-4451	22	40	k	k	NOUN
ejpam-4451	22	41	-	-	NOUN
ejpam-4451	22	42	vectors	vector	NOUN
ejpam-4451	22	43	.	.	PUNCT
ejpam-4451	23	1	a	a	DET
ejpam-4451	23	2	resolving	resolving	NOUN
ejpam-4451	23	3	set	set	NOUN
ejpam-4451	23	4	of	of	ADP
ejpam-4451	23	5	minimum	minimum	ADJ
ejpam-4451	23	6	cardinality	cardinality	NOUN
ejpam-4451	23	7	is	be	AUX
ejpam-4451	23	8	called	call	VERB
ejpam-4451	23	9	a	a	DET
ejpam-4451	23	10	minimum	minimum	ADJ
ejpam-4451	23	11	resolving	resolving	NOUN
ejpam-4451	23	12	set	set	VERB
ejpam-4451	23	13	or	or	CCONJ
ejpam-4451	23	14	a	a	DET
ejpam-4451	23	15	basis	basis	NOUN
ejpam-4451	23	16	,	,	PUNCT
ejpam-4451	23	17	and	and	CCONJ
ejpam-4451	23	18	the	the	DET
ejpam-4451	23	19	cardinality	cardinality	NOUN
ejpam-4451	23	20	of	of	ADP
ejpam-4451	23	21	a	a	DET
ejpam-4451	23	22	basis	basis	NOUN
ejpam-4451	23	23	for	for	ADP
ejpam-4451	23	24	g	g	PROPN
ejpam-4451	23	25	is	be	AUX
ejpam-4451	23	26	the	the	DET
ejpam-4451	23	27	dimension	dimension	NOUN
ejpam-4451	23	28	dim(g	dim(g	PROPN
ejpam-4451	23	29	)	)	PUNCT
ejpam-4451	23	30	of	of	ADP
ejpam-4451	23	31	g.	g.	PROPN
ejpam-4451	23	32	in	in	ADP
ejpam-4451	23	33	the	the	DET
ejpam-4451	23	34	paper	paper	NOUN
ejpam-4451	23	35	of	of	ADP
ejpam-4451	23	36	rara	rara	NOUN
ejpam-4451	23	37	and	and	CCONJ
ejpam-4451	23	38	cabaro	cabaro	VERB
ejpam-4451	24	1	[	[	X
ejpam-4451	24	2	5	5	NUM
ejpam-4451	24	3	]	]	PUNCT
ejpam-4451	24	4	,	,	PUNCT
ejpam-4451	24	5	an	an	DET
ejpam-4451	24	6	ordered	order	VERB
ejpam-4451	24	7	set	set	NOUN
ejpam-4451	24	8	of	of	ADP
ejpam-4451	24	9	vertices	vertex	NOUN
ejpam-4451	24	10	w	w	NOUN
ejpam-4451	24	11	=	=	SYM
ejpam-4451	24	12	{	{	PUNCT
ejpam-4451	24	13	w1	w1	NOUN
ejpam-4451	24	14	,	,	PUNCT
ejpam-4451	24	15	...	...	PUNCT
ejpam-4451	24	16	,	,	PUNCT
ejpam-4451	24	17	wl	wl	PROPN
ejpam-4451	24	18	}	}	PUNCT
ejpam-4451	24	19	is	be	AUX
ejpam-4451	24	20	a	a	DET
ejpam-4451	24	21	2	2	NUM
ejpam-4451	24	22	-	-	PUNCT
ejpam-4451	24	23	resolving	resolving	NOUN
ejpam-4451	24	24	set	set	NOUN
ejpam-4451	24	25	for	for	ADP
ejpam-4451	24	26	g	g	PROPN
ejpam-4451	24	27	if	if	SCONJ
ejpam-4451	24	28	,	,	PUNCT
ejpam-4451	24	29	for	for	ADP
ejpam-4451	24	30	any	any	DET
ejpam-4451	24	31	distinct	distinct	ADJ
ejpam-4451	24	32	vertices	vertex	NOUN
ejpam-4451	24	33	u	u	NOUN
ejpam-4451	24	34	,	,	PUNCT
ejpam-4451	24	35	v	v	NOUN
ejpam-4451	24	36	∈	∈	PROPN
ejpam-4451	24	37	v	v	NOUN
ejpam-4451	24	38	(	(	PUNCT
ejpam-4451	24	39	g	g	NOUN
ejpam-4451	24	40	)	)	PUNCT
ejpam-4451	24	41	,	,	PUNCT
ejpam-4451	24	42	the	the	DET
ejpam-4451	24	43	(	(	PUNCT
ejpam-4451	24	44	metric	metric	NOUN
ejpam-4451	24	45	)	)	PUNCT
ejpam-4451	24	46	representations	representation	VERB
ejpam-4451	24	47	r(u	r(u	PROPN
ejpam-4451	24	48	/	/	SYM
ejpam-4451	24	49	w	w	PROPN
ejpam-4451	24	50	)	)	PUNCT
ejpam-4451	24	51	and	and	CCONJ
ejpam-4451	24	52	r(v	r(v	PROPN
ejpam-4451	24	53	/	/	SYM
ejpam-4451	24	54	w	w	PROPN
ejpam-4451	24	55	)	)	PUNCT
ejpam-4451	24	56	of	of	ADP
ejpam-4451	24	57	u	u	NOUN
ejpam-4451	24	58	and	and	CCONJ
ejpam-4451	24	59	v	v	NOUN
ejpam-4451	24	60	,	,	PUNCT
ejpam-4451	24	61	respectively	respectively	ADV
ejpam-4451	24	62	differ	differ	VERB
ejpam-4451	24	63	in	in	ADP
ejpam-4451	24	64	at	at	ADV
ejpam-4451	24	65	least	least	ADJ
ejpam-4451	24	66	2	2	NUM
ejpam-4451	24	67	positions	position	NOUN
ejpam-4451	24	68	.	.	PUNCT
ejpam-4451	25	1	then	then	ADV
ejpam-4451	25	2	w	w	NOUN
ejpam-4451	25	3	is	be	AUX
ejpam-4451	25	4	said	say	VERB
ejpam-4451	25	5	to	to	PART
ejpam-4451	25	6	be	be	AUX
ejpam-4451	25	7	a	a	DET
ejpam-4451	25	8	2	2	NUM
ejpam-4451	25	9	-	-	PUNCT
ejpam-4451	25	10	resolving	resolving	NOUN
ejpam-4451	25	11	set	set	NOUN
ejpam-4451	25	12	for	for	ADP
ejpam-4451	25	13	g.	g.	PROPN
ejpam-4451	25	14	if	if	SCONJ
ejpam-4451	25	15	g	g	PROPN
ejpam-4451	25	16	has	have	VERB
ejpam-4451	25	17	a	a	DET
ejpam-4451	25	18	2	2	NUM
ejpam-4451	25	19	-	-	PUNCT
ejpam-4451	25	20	resolving	resolve	VERB
ejpam-4451	25	21	set	set	NOUN
ejpam-4451	25	22	,	,	PUNCT
ejpam-4451	25	23	the	the	DET
ejpam-4451	25	24	minimum	minimum	ADJ
ejpam-4451	25	25	cardinality	cardinality	NOUN
ejpam-4451	25	26	dim2(g	dim2(g	NOUN
ejpam-4451	25	27	)	)	PUNCT
ejpam-4451	25	28	is	be	AUX
ejpam-4451	25	29	called	call	VERB
ejpam-4451	25	30	the	the	DET
ejpam-4451	25	31	2	2	NUM
ejpam-4451	25	32	-	-	PUNCT
ejpam-4451	25	33	metric	metric	ADJ
ejpam-4451	25	34	dimension	dimension	NOUN
ejpam-4451	25	35	of	of	ADP
ejpam-4451	25	36	g.	g.	PROPN
ejpam-4451	25	37	if	if	SCONJ
ejpam-4451	25	38	k	k	PROPN
ejpam-4451	25	39	=	=	SYM
ejpam-4451	25	40	2	2	NUM
ejpam-4451	25	41	is	be	AUX
ejpam-4451	25	42	the	the	DET
ejpam-4451	25	43	largest	large	ADJ
ejpam-4451	25	44	integer	integer	NOUN
ejpam-4451	25	45	for	for	ADP
ejpam-4451	25	46	which	which	PRON
ejpam-4451	25	47	g	g	NOUN
ejpam-4451	25	48	has	have	VERB
ejpam-4451	25	49	a	a	DET
ejpam-4451	25	50	2	2	NUM
ejpam-4451	25	51	-	-	PUNCT
ejpam-4451	25	52	resolving	resolve	VERB
ejpam-4451	25	53	set	set	NOUN
ejpam-4451	25	54	,	,	PUNCT
ejpam-4451	25	55	then	then	ADV
ejpam-4451	25	56	we	we	PRON
ejpam-4451	25	57	say	say	VERB
ejpam-4451	25	58	that	that	SCONJ
ejpam-4451	25	59	g	g	PROPN
ejpam-4451	25	60	is	be	AUX
ejpam-4451	25	61	a	a	DET
ejpam-4451	25	62	2	2	NUM
ejpam-4451	25	63	-	-	PUNCT
ejpam-4451	25	64	metric	metric	ADJ
ejpam-4451	25	65	dimensional	dimensional	ADJ
ejpam-4451	25	66	graph	graph	NOUN
ejpam-4451	25	67	.	.	PUNCT
ejpam-4451	26	1	in	in	ADP
ejpam-4451	26	2	the	the	DET
ejpam-4451	26	3	paper	paper	NOUN
ejpam-4451	26	4	of	of	ADP
ejpam-4451	26	5	cabaro	cabaro	NOUN
ejpam-4451	26	6	and	and	CCONJ
ejpam-4451	26	7	rara	rara	NOUN
ejpam-4451	26	8	[	[	X
ejpam-4451	26	9	6	6	NUM
ejpam-4451	26	10	]	]	PUNCT
ejpam-4451	26	11	,	,	PUNCT
ejpam-4451	26	12	the	the	DET
ejpam-4451	26	13	concept	concept	NOUN
ejpam-4451	26	14	of	of	ADP
ejpam-4451	26	15	restrained	restrained	ADJ
ejpam-4451	26	16	2	2	NUM
ejpam-4451	26	17	-	-	PUNCT
ejpam-4451	26	18	resolving	resolve	VERB
ejpam-4451	26	19	set	set	NOUN
ejpam-4451	26	20	in	in	ADP
ejpam-4451	26	21	the	the	DET
ejpam-4451	26	22	join	join	NOUN
ejpam-4451	26	23	,	,	PUNCT
ejpam-4451	26	24	corona	corona	NOUN
ejpam-4451	26	25	and	and	CCONJ
ejpam-4451	26	26	lexicographic	lexicographic	ADJ
ejpam-4451	26	27	product	product	NOUN
ejpam-4451	26	28	of	of	ADP
ejpam-4451	26	29	two	two	NUM
ejpam-4451	26	30	graphs	graph	NOUN
ejpam-4451	26	31	was	be	AUX
ejpam-4451	26	32	discussed	discuss	VERB
ejpam-4451	26	33	.	.	PUNCT
ejpam-4451	27	1	in	in	ADP
ejpam-4451	27	2	this	this	DET
ejpam-4451	27	3	paper	paper	NOUN
ejpam-4451	27	4	,	,	PUNCT
ejpam-4451	27	5	the	the	DET
ejpam-4451	27	6	concept	concept	NOUN
ejpam-4451	27	7	of	of	ADP
ejpam-4451	27	8	restrained	restrained	ADJ
ejpam-4451	27	9	2	2	NUM
ejpam-4451	27	10	-	-	PUNCT
ejpam-4451	27	11	resolving	resolve	VERB
ejpam-4451	27	12	dominating	dominating	NOUN
ejpam-4451	27	13	set	set	VERB
ejpam-4451	27	14	in	in	ADP
ejpam-4451	27	15	the	the	DET
ejpam-4451	27	16	join	join	NOUN
ejpam-4451	27	17	,	,	PUNCT
ejpam-4451	27	18	corona	corona	NOUN
ejpam-4451	27	19	and	and	CCONJ
ejpam-4451	27	20	lexicographic	lexicographic	ADJ
ejpam-4451	27	21	product	product	NOUN
ejpam-4451	27	22	of	of	ADP
ejpam-4451	27	23	two	two	NUM
ejpam-4451	27	24	graphs	graph	NOUN
ejpam-4451	27	25	is	be	AUX
ejpam-4451	27	26	discussed	discuss	VERB
ejpam-4451	27	27	.	.	PUNCT
ejpam-4451	28	1	2	2	X
ejpam-4451	28	2	.	.	X
ejpam-4451	28	3	preliminary	preliminary	ADJ
ejpam-4451	28	4	results	result	NOUN
ejpam-4451	28	5	in	in	ADP
ejpam-4451	28	6	this	this	DET
ejpam-4451	28	7	study	study	NOUN
ejpam-4451	28	8	,	,	PUNCT
ejpam-4451	28	9	we	we	PRON
ejpam-4451	28	10	consider	consider	VERB
ejpam-4451	28	11	finite	finite	NOUN
ejpam-4451	28	12	,	,	PUNCT
ejpam-4451	28	13	simple	simple	ADJ
ejpam-4451	28	14	and	and	CCONJ
ejpam-4451	28	15	connected	connected	ADJ
ejpam-4451	28	16	undirected	undirected	ADJ
ejpam-4451	28	17	graphs	graph	NOUN
ejpam-4451	28	18	.	.	PUNCT
ejpam-4451	29	1	for	for	ADP
ejpam-4451	29	2	basic	basic	ADJ
ejpam-4451	29	3	graph	graph	NOUN
ejpam-4451	29	4	-	-	PUNCT
ejpam-4451	29	5	theoretic	theoretic	NOUN
ejpam-4451	29	6	concepts	concept	NOUN
ejpam-4451	29	7	,	,	PUNCT
ejpam-4451	29	8	we	we	PRON
ejpam-4451	29	9	refer	refer	VERB
ejpam-4451	29	10	readers	reader	NOUN
ejpam-4451	29	11	to	to	ADP
ejpam-4451	29	12	[	[	X
ejpam-4451	29	13	3	3	NUM
ejpam-4451	29	14	]	]	PUNCT
ejpam-4451	29	15	.	.	PUNCT
ejpam-4451	30	1	proposition	proposition	NOUN
ejpam-4451	30	2	1	1	NUM
ejpam-4451	30	3	.	.	PUNCT
ejpam-4451	31	1	[	[	X
ejpam-4451	31	2	2	2	X
ejpam-4451	31	3	]	]	PUNCT
ejpam-4451	31	4	let	let	VERB
ejpam-4451	31	5	g	g	PRON
ejpam-4451	31	6	be	be	AUX
ejpam-4451	31	7	a	a	DET
ejpam-4451	31	8	connected	connected	ADJ
ejpam-4451	31	9	graph	graph	NOUN
ejpam-4451	31	10	of	of	ADP
ejpam-4451	31	11	order	order	NOUN
ejpam-4451	31	12	n	n	PRON
ejpam-4451	31	13	≥	≥	NOUN
ejpam-4451	31	14	2	2	NUM
ejpam-4451	31	15	.	.	PUNCT
ejpam-4451	31	16	then	then	ADV
ejpam-4451	31	17	dim2(g	dim2(g	NOUN
ejpam-4451	31	18	)	)	PUNCT
ejpam-4451	31	19	=	=	SYM
ejpam-4451	31	20	2	2	NUM
ejpam-4451	31	21	if	if	SCONJ
ejpam-4451	31	22	and	and	CCONJ
ejpam-4451	31	23	only	only	ADV
ejpam-4451	31	24	if	if	SCONJ
ejpam-4451	31	25	g	g	PROPN
ejpam-4451	31	26	∼=	∼=	PROPN
ejpam-4451	31	27	pn	pn	PROPN
ejpam-4451	31	28	.	.	PROPN
ejpam-4451	31	29	remark	remark	PROPN
ejpam-4451	31	30	1	1	NUM
ejpam-4451	31	31	.	.	PUNCT
ejpam-4451	32	1	for	for	ADP
ejpam-4451	32	2	any	any	DET
ejpam-4451	32	3	connected	connected	ADJ
ejpam-4451	32	4	graph	graph	NOUN
ejpam-4451	32	5	g	g	NOUN
ejpam-4451	32	6	of	of	ADP
ejpam-4451	32	7	order	order	NOUN
ejpam-4451	32	8	n	n	PRON
ejpam-4451	32	9	≥	≥	NOUN
ejpam-4451	32	10	2	2	NUM
ejpam-4451	32	11	,	,	PUNCT
ejpam-4451	32	12	γ2r(g	γ2r(g	PROPN
ejpam-4451	32	13	)	)	PUNCT
ejpam-4451	32	14	≤	≤	NOUN
ejpam-4451	32	15	γr2r(g	γr2r(g	NUM
ejpam-4451	32	16	)	)	PUNCT
ejpam-4451	32	17	.	.	PUNCT
ejpam-4451	33	1	remark	remark	PROPN
ejpam-4451	33	2	2	2	NUM
ejpam-4451	33	3	.	.	PUNCT
ejpam-4451	33	4	for	for	ADP
ejpam-4451	33	5	n	n	PRON
ejpam-4451	33	6	≥	≥	NUM
ejpam-4451	33	7	2	2	NUM
ejpam-4451	33	8	,	,	PUNCT
ejpam-4451	33	9	γ2r(kn	γ2r(kn	PROPN
ejpam-4451	33	10	)	)	PUNCT
ejpam-4451	33	11	=	=	SYM
ejpam-4451	34	1	n	n	NOUN
ejpam-4451	34	2	=	=	PUNCT
ejpam-4451	34	3	γr2r(kn	γr2r(kn	NOUN
ejpam-4451	34	4	)	)	PUNCT
ejpam-4451	34	5	.	.	PUNCT
ejpam-4451	35	1	remark	remark	PROPN
ejpam-4451	35	2	3	3	NUM
ejpam-4451	35	3	.	.	PUNCT
ejpam-4451	36	1	let	let	VERB
ejpam-4451	36	2	g	g	PRON
ejpam-4451	36	3	be	be	AUX
ejpam-4451	36	4	a	a	DET
ejpam-4451	36	5	connected	connected	ADJ
ejpam-4451	36	6	graph	graph	NOUN
ejpam-4451	36	7	of	of	ADP
ejpam-4451	36	8	order	order	NOUN
ejpam-4451	36	9	n	n	PRON
ejpam-4451	36	10	≥	≥	NOUN
ejpam-4451	36	11	2	2	NUM
ejpam-4451	36	12	.	.	PUNCT
ejpam-4451	36	13	then	then	ADV
ejpam-4451	36	14	γr2r(g	γr2r(g	NUM
ejpam-4451	36	15	)	)	PUNCT
ejpam-4451	36	16	=	=	SYM
ejpam-4451	37	1	n	n	NOUN
ejpam-4451	37	2	if	if	SCONJ
ejpam-4451	37	3	and	and	CCONJ
ejpam-4451	37	4	only	only	ADV
ejpam-4451	37	5	if	if	SCONJ
ejpam-4451	37	6	g	g	PROPN
ejpam-4451	37	7	∼=	∼=	PROPN
ejpam-4451	37	8	kn	kn	NOUN
ejpam-4451	37	9	or	or	CCONJ
ejpam-4451	37	10	g	g	NOUN
ejpam-4451	37	11	∼=	∼=	PROPN
ejpam-4451	37	12	k1,n−1	k1,n−1	ADJ
ejpam-4451	37	13	or	or	CCONJ
ejpam-4451	37	14	g	g	NOUN
ejpam-4451	37	15	∼=	∼=	NOUN
ejpam-4451	37	16	c4	c4	NOUN
ejpam-4451	37	17	.	.	PUNCT
ejpam-4451	38	1	the	the	DET
ejpam-4451	38	2	following	follow	VERB
ejpam-4451	38	3	remark	remark	NOUN
ejpam-4451	38	4	follows	follow	VERB
ejpam-4451	38	5	from	from	ADP
ejpam-4451	38	6	proposition	proposition	NOUN
ejpam-4451	38	7	1	1	NUM
ejpam-4451	38	8	.	.	PUNCT
ejpam-4451	38	9	j.	j.	PROPN
ejpam-4451	38	10	cabaro	cabaro	PROPN
ejpam-4451	38	11	,	,	PUNCT
ejpam-4451	38	12	h.	h.	PROPN
ejpam-4451	38	13	rara	rara	PROPN
ejpam-4451	38	14	/	/	SYM
ejpam-4451	38	15	eur	eur	PROPN
ejpam-4451	38	16	.	.	PUNCT
ejpam-4451	39	1	j.	j.	PROPN
ejpam-4451	39	2	pure	pure	PROPN
ejpam-4451	39	3	appl	appl	PROPN
ejpam-4451	39	4	.	.	PROPN
ejpam-4451	39	5	math	math	PROPN
ejpam-4451	39	6	,	,	PUNCT
ejpam-4451	39	7	15	15	NUM
ejpam-4451	39	8	(	(	PUNCT
ejpam-4451	39	9	3	3	NUM
ejpam-4451	39	10	)	)	PUNCT
ejpam-4451	39	11	(	(	PUNCT
ejpam-4451	39	12	2022	2022	NUM
ejpam-4451	39	13	)	)	PUNCT
ejpam-4451	39	14	,	,	PUNCT
ejpam-4451	39	15	1047	1047	NUM
ejpam-4451	39	16	-	-	SYM
ejpam-4451	39	17	1053	1053	NUM
ejpam-4451	39	18	1049	1049	NUM
ejpam-4451	39	19	remark	remark	NOUN
ejpam-4451	39	20	4	4	NUM
ejpam-4451	39	21	.	.	PUNCT
ejpam-4451	40	1	let	let	VERB
ejpam-4451	40	2	g	g	PRON
ejpam-4451	40	3	be	be	AUX
ejpam-4451	40	4	a	a	DET
ejpam-4451	40	5	connected	connected	ADJ
ejpam-4451	40	6	graph	graph	NOUN
ejpam-4451	40	7	of	of	ADP
ejpam-4451	40	8	order	order	NOUN
ejpam-4451	40	9	n	n	PRON
ejpam-4451	40	10	≥	≥	NOUN
ejpam-4451	40	11	2	2	NUM
ejpam-4451	40	12	.	.	PUNCT
ejpam-4451	40	13	then	then	ADV
ejpam-4451	40	14	γr2r(g	γr2r(g	NUM
ejpam-4451	40	15	)	)	PUNCT
ejpam-4451	40	16	=	=	SYM
ejpam-4451	40	17	2	2	NUM
ejpam-4451	40	18	if	if	SCONJ
ejpam-4451	40	19	and	and	CCONJ
ejpam-4451	40	20	only	only	ADV
ejpam-4451	40	21	if	if	SCONJ
ejpam-4451	40	22	g	g	PROPN
ejpam-4451	40	23	∼=	∼=	PROPN
ejpam-4451	40	24	k2	k2	NOUN
ejpam-4451	40	25	or	or	CCONJ
ejpam-4451	40	26	g	g	NOUN
ejpam-4451	40	27	=	=	PUNCT
ejpam-4451	40	28	p4	p4	ADJ
ejpam-4451	40	29	.	.	PUNCT
ejpam-4451	41	1	proof	proof	NOUN
ejpam-4451	41	2	.	.	PUNCT
ejpam-4451	42	1	proof	proof	NOUN
ejpam-4451	42	2	follows	follow	VERB
ejpam-4451	42	3	immediately	immediately	ADV
ejpam-4451	42	4	from	from	ADP
ejpam-4451	42	5	proposition	proposition	NOUN
ejpam-4451	42	6	1	1	NUM
ejpam-4451	42	7	.	.	NOUN
ejpam-4451	43	1	3	3	X
ejpam-4451	43	2	.	.	PUNCT
ejpam-4451	43	3	restrained	restrain	VERB
ejpam-4451	43	4	2	2	NUM
ejpam-4451	43	5	-	-	PUNCT
ejpam-4451	43	6	resolving	resolve	VERB
ejpam-4451	43	7	dominating	dominating	NOUN
ejpam-4451	43	8	sets	set	NOUN
ejpam-4451	43	9	in	in	ADP
ejpam-4451	43	10	the	the	DET
ejpam-4451	43	11	join	join	NOUN
ejpam-4451	43	12	of	of	ADP
ejpam-4451	43	13	graphs	graph	NOUN
ejpam-4451	43	14	theorem	theorem	VERB
ejpam-4451	43	15	1	1	X
ejpam-4451	43	16	.	.	PUNCT
ejpam-4451	44	1	let	let	VERB
ejpam-4451	44	2	g	g	NOUN
ejpam-4451	44	3	and	and	CCONJ
ejpam-4451	44	4	h	h	NOUN
ejpam-4451	44	5	be	be	AUX
ejpam-4451	44	6	nontrivial	nontrivial	ADJ
ejpam-4451	44	7	connected	connected	ADJ
ejpam-4451	44	8	graphs	graph	NOUN
ejpam-4451	44	9	.	.	PUNCT
ejpam-4451	45	1	a	a	DET
ejpam-4451	45	2	set	set	NOUN
ejpam-4451	45	3	s	s	NOUN
ejpam-4451	45	4	⊆	⊆	NUM
ejpam-4451	45	5	v	v	NOUN
ejpam-4451	45	6	(	(	PUNCT
ejpam-4451	45	7	g	g	PROPN
ejpam-4451	45	8	+	+	NOUN
ejpam-4451	45	9	h	h	NOUN
ejpam-4451	45	10	)	)	PUNCT
ejpam-4451	45	11	is	be	AUX
ejpam-4451	45	12	a	a	DET
ejpam-4451	45	13	restrained	restrained	ADJ
ejpam-4451	45	14	2	2	NUM
ejpam-4451	45	15	-	-	PUNCT
ejpam-4451	45	16	resolving	resolving	NOUN
ejpam-4451	45	17	set	set	NOUN
ejpam-4451	45	18	in	in	ADP
ejpam-4451	45	19	g	g	PROPN
ejpam-4451	46	1	+	+	NOUN
ejpam-4451	46	2	h	h	NOUN
ejpam-4451	46	3	if	if	SCONJ
ejpam-4451	46	4	and	and	CCONJ
ejpam-4451	46	5	only	only	ADV
ejpam-4451	46	6	if	if	SCONJ
ejpam-4451	46	7	sg	sg	PROPN
ejpam-4451	46	8	=	=	SYM
ejpam-4451	46	9	v	v	NOUN
ejpam-4451	46	10	(	(	PUNCT
ejpam-4451	46	11	g)∩s	g)∩s	PROPN
ejpam-4451	46	12	and	and	CCONJ
ejpam-4451	46	13	sh	sh	PROPN
ejpam-4451	46	14	=	=	SYM
ejpam-4451	46	15	v	v	PROPN
ejpam-4451	46	16	(	(	PUNCT
ejpam-4451	46	17	h)∩s	h)∩s	PROPN
ejpam-4451	46	18	are	be	AUX
ejpam-4451	46	19	2	2	NUM
ejpam-4451	46	20	-	-	PUNCT
ejpam-4451	46	21	locating	locate	VERB
ejpam-4451	46	22	sets	set	NOUN
ejpam-4451	46	23	in	in	ADP
ejpam-4451	46	24	g	g	PROPN
ejpam-4451	46	25	and	and	CCONJ
ejpam-4451	46	26	h	h	NOUN
ejpam-4451	46	27	,	,	PUNCT
ejpam-4451	46	28	respectively	respectively	ADV
ejpam-4451	46	29	where	where	SCONJ
ejpam-4451	46	30	sg	sg	PROPN
ejpam-4451	46	31	or	or	CCONJ
ejpam-4451	46	32	sh	sh	PROPN
ejpam-4451	46	33	is	be	AUX
ejpam-4451	46	34	a	a	DET
ejpam-4451	46	35	(	(	PUNCT
ejpam-4451	46	36	2	2	NUM
ejpam-4451	46	37	,	,	PUNCT
ejpam-4451	46	38	2)-locating	2)-locating	NUM
ejpam-4451	46	39	set	set	NOUN
ejpam-4451	46	40	or	or	CCONJ
ejpam-4451	46	41	sg	sg	PROPN
ejpam-4451	46	42	and	and	CCONJ
ejpam-4451	46	43	sh	sh	PROPN
ejpam-4451	46	44	are	be	AUX
ejpam-4451	46	45	(	(	PUNCT
ejpam-4451	46	46	2	2	NUM
ejpam-4451	46	47	,	,	PUNCT
ejpam-4451	46	48	1)-locating	1)-locating	NUM
ejpam-4451	46	49	sets	set	NOUN
ejpam-4451	46	50	and	and	CCONJ
ejpam-4451	46	51	one	one	NUM
ejpam-4451	46	52	of	of	ADP
ejpam-4451	46	53	the	the	DET
ejpam-4451	46	54	following	follow	VERB
ejpam-4451	46	55	holds	hold	VERB
ejpam-4451	46	56	:	:	PUNCT
ejpam-4451	46	57	(	(	PUNCT
ejpam-4451	46	58	i	i	NOUN
ejpam-4451	46	59	)	)	PUNCT
ejpam-4451	46	60	sg	sg	PROPN
ejpam-4451	46	61	=	=	SYM
ejpam-4451	46	62	v	v	PROPN
ejpam-4451	46	63	(	(	PUNCT
ejpam-4451	46	64	g	g	NOUN
ejpam-4451	46	65	)	)	PUNCT
ejpam-4451	46	66	and	and	CCONJ
ejpam-4451	46	67	sh	sh	PROPN
ejpam-4451	46	68	is	be	AUX
ejpam-4451	46	69	a	a	DET
ejpam-4451	46	70	restrained	restrained	ADJ
ejpam-4451	46	71	2	2	NUM
ejpam-4451	46	72	-	-	PUNCT
ejpam-4451	46	73	locating	locate	VERB
ejpam-4451	46	74	set	set	NOUN
ejpam-4451	46	75	in	in	ADP
ejpam-4451	46	76	h	h	NOUN
ejpam-4451	46	77	;	;	PUNCT
ejpam-4451	46	78	(	(	PUNCT
ejpam-4451	46	79	ii	ii	NOUN
ejpam-4451	46	80	)	)	PUNCT
ejpam-4451	47	1	sh	sh	PROPN
ejpam-4451	48	1	=	=	SYM
ejpam-4451	48	2	v	v	PROPN
ejpam-4451	48	3	(	(	PUNCT
ejpam-4451	48	4	h	h	NOUN
ejpam-4451	48	5	)	)	PUNCT
ejpam-4451	48	6	and	and	CCONJ
ejpam-4451	48	7	sg	sg	PROPN
ejpam-4451	48	8	is	be	AUX
ejpam-4451	48	9	a	a	DET
ejpam-4451	48	10	restrained	restrained	ADJ
ejpam-4451	48	11	2	2	NUM
ejpam-4451	48	12	-	-	PUNCT
ejpam-4451	48	13	locating	locate	VERB
ejpam-4451	48	14	set	set	NOUN
ejpam-4451	48	15	in	in	ADP
ejpam-4451	48	16	g	g	NOUN
ejpam-4451	48	17	;	;	PUNCT
ejpam-4451	48	18	(	(	PUNCT
ejpam-4451	48	19	iii	iii	X
ejpam-4451	48	20	)	)	PUNCT
ejpam-4451	48	21	sg	sg	ADP
ejpam-4451	48	22	̸=	̸=	PROPN
ejpam-4451	48	23	v	v	NOUN
ejpam-4451	48	24	(	(	PUNCT
ejpam-4451	48	25	g	g	NOUN
ejpam-4451	48	26	)	)	PUNCT
ejpam-4451	48	27	and	and	CCONJ
ejpam-4451	48	28	sh	sh	INTJ
ejpam-4451	48	29	̸=	̸=	PROPN
ejpam-4451	48	30	v	v	NOUN
ejpam-4451	48	31	(	(	PUNCT
ejpam-4451	48	32	h	h	NOUN
ejpam-4451	48	33	)	)	PUNCT
ejpam-4451	48	34	.	.	PUNCT
ejpam-4451	49	1	theorem	theorem	NOUN
ejpam-4451	49	2	2	2	NUM
ejpam-4451	49	3	.	.	PUNCT
ejpam-4451	50	1	[	[	X
ejpam-4451	50	2	7	7	X
ejpam-4451	50	3	]	]	PUNCT
ejpam-4451	50	4	let	let	VERB
ejpam-4451	50	5	g	g	PRON
ejpam-4451	50	6	be	be	AUX
ejpam-4451	50	7	a	a	DET
ejpam-4451	50	8	connected	connected	ADJ
ejpam-4451	50	9	non	non	ADJ
ejpam-4451	50	10	-	-	ADJ
ejpam-4451	50	11	trivial	trivial	ADJ
ejpam-4451	50	12	graph	graph	NOUN
ejpam-4451	50	13	and	and	CCONJ
ejpam-4451	50	14	let	let	VERB
ejpam-4451	50	15	k1	k1	NOUN
ejpam-4451	50	16	=	=	SYM
ejpam-4451	50	17	{	{	PUNCT
ejpam-4451	50	18	v	v	NOUN
ejpam-4451	50	19	}	}	PUNCT
ejpam-4451	50	20	.	.	PUNCT
ejpam-4451	51	1	then	then	ADV
ejpam-4451	51	2	s	s	VERB
ejpam-4451	51	3	⊆	⊆	NUM
ejpam-4451	51	4	v	v	NOUN
ejpam-4451	51	5	(	(	PUNCT
ejpam-4451	51	6	k1	k1	NOUN
ejpam-4451	51	7	+	+	CCONJ
ejpam-4451	51	8	g	g	NOUN
ejpam-4451	51	9	)	)	PUNCT
ejpam-4451	51	10	is	be	AUX
ejpam-4451	51	11	a	a	DET
ejpam-4451	51	12	restrained	restrained	ADJ
ejpam-4451	51	13	2	2	NUM
ejpam-4451	51	14	-	-	PUNCT
ejpam-4451	51	15	resolving	resolve	VERB
ejpam-4451	51	16	set	set	NOUN
ejpam-4451	51	17	of	of	ADP
ejpam-4451	51	18	k1	k1	NOUN
ejpam-4451	51	19	+	+	CCONJ
ejpam-4451	51	20	g	g	NOUN
ejpam-4451	51	21	if	if	SCONJ
ejpam-4451	52	1	and	and	CCONJ
ejpam-4451	52	2	only	only	ADV
ejpam-4451	52	3	if	if	SCONJ
ejpam-4451	52	4	either	either	PRON
ejpam-4451	52	5	v	v	NOUN
ejpam-4451	52	6	/∈	/∈	PUNCT
ejpam-4451	52	7	s	s	PART
ejpam-4451	52	8	and	and	CCONJ
ejpam-4451	52	9	s	s	VERB
ejpam-4451	52	10	is	be	AUX
ejpam-4451	52	11	a	a	DET
ejpam-4451	52	12	(	(	PUNCT
ejpam-4451	52	13	2	2	NUM
ejpam-4451	52	14	,	,	PUNCT
ejpam-4451	52	15	2)-locating	2)-locating	NUM
ejpam-4451	52	16	set	set	VERB
ejpam-4451	52	17	in	in	ADP
ejpam-4451	52	18	g	g	NOUN
ejpam-4451	52	19	with	with	ADP
ejpam-4451	52	20	v	v	NOUN
ejpam-4451	52	21	(	(	PUNCT
ejpam-4451	52	22	g	g	NOUN
ejpam-4451	52	23	)	)	PUNCT
ejpam-4451	52	24	̸=	̸=	PROPN
ejpam-4451	52	25	s	s	PART
ejpam-4451	52	26	or	or	CCONJ
ejpam-4451	52	27	s	s	NOUN
ejpam-4451	52	28	=	=	PUNCT
ejpam-4451	52	29	{	{	PUNCT
ejpam-4451	52	30	v	v	NOUN
ejpam-4451	52	31	}	}	PUNCT
ejpam-4451	52	32	∪	∪	NOUN
ejpam-4451	52	33	t	t	PROPN
ejpam-4451	52	34	,	,	PUNCT
ejpam-4451	52	35	where	where	SCONJ
ejpam-4451	52	36	t	t	PROPN
ejpam-4451	52	37	is	be	AUX
ejpam-4451	52	38	a	a	DET
ejpam-4451	52	39	restrained	restrained	ADJ
ejpam-4451	52	40	(	(	PUNCT
ejpam-4451	52	41	2	2	NUM
ejpam-4451	52	42	,	,	PUNCT
ejpam-4451	52	43	1)-locating	1)-locating	NUM
ejpam-4451	52	44	set	set	VERB
ejpam-4451	52	45	in	in	ADP
ejpam-4451	52	46	g.	g.	PROPN
ejpam-4451	52	47	theorem	theorem	PROPN
ejpam-4451	53	1	3	3	X
ejpam-4451	53	2	.	.	PUNCT
ejpam-4451	54	1	let	let	VERB
ejpam-4451	54	2	g	g	NOUN
ejpam-4451	54	3	andh	andh	NOUN
ejpam-4451	54	4	be	be	AUX
ejpam-4451	54	5	nontrivial	nontrivial	ADJ
ejpam-4451	54	6	connected	connected	ADJ
ejpam-4451	54	7	graphs	graph	NOUN
ejpam-4451	54	8	.	.	PUNCT
ejpam-4451	55	1	a	a	DET
ejpam-4451	55	2	proper	proper	ADJ
ejpam-4451	55	3	subset	subset	NOUN
ejpam-4451	55	4	s	s	NOUN
ejpam-4451	55	5	of	of	ADP
ejpam-4451	55	6	v	v	NOUN
ejpam-4451	55	7	(	(	PUNCT
ejpam-4451	55	8	g+h	g+h	PROPN
ejpam-4451	55	9	)	)	PUNCT
ejpam-4451	55	10	is	be	AUX
ejpam-4451	55	11	a	a	DET
ejpam-4451	55	12	restrained	restrained	ADJ
ejpam-4451	55	13	2	2	NUM
ejpam-4451	55	14	-	-	PUNCT
ejpam-4451	55	15	resolving	resolve	VERB
ejpam-4451	55	16	dominating	dominating	NOUN
ejpam-4451	55	17	set	set	NOUN
ejpam-4451	55	18	ing+h	ing+h	PRON
ejpam-4451	55	19	if	if	SCONJ
ejpam-4451	55	20	and	and	CCONJ
ejpam-4451	55	21	only	only	ADV
ejpam-4451	55	22	if	if	SCONJ
ejpam-4451	55	23	s	s	NOUN
ejpam-4451	55	24	is	be	AUX
ejpam-4451	55	25	a	a	DET
ejpam-4451	55	26	restrained	restrained	ADJ
ejpam-4451	55	27	2	2	NUM
ejpam-4451	55	28	-	-	PUNCT
ejpam-4451	55	29	resolving	resolving	NOUN
ejpam-4451	55	30	set	set	VERB
ejpam-4451	55	31	in	in	ADP
ejpam-4451	55	32	g+h	g+h	PROPN
ejpam-4451	55	33	.	.	PUNCT
ejpam-4451	56	1	proof	proof	NOUN
ejpam-4451	56	2	.	.	PUNCT
ejpam-4451	57	1	let	let	VERB
ejpam-4451	57	2	s	s	PRON
ejpam-4451	57	3	⊆	⊆	NUM
ejpam-4451	57	4	v	v	NOUN
ejpam-4451	57	5	(	(	PUNCT
ejpam-4451	57	6	g+h	g+h	NOUN
ejpam-4451	57	7	)	)	PUNCT
ejpam-4451	57	8	be	be	AUX
ejpam-4451	57	9	a	a	DET
ejpam-4451	57	10	restrained	restrained	ADJ
ejpam-4451	57	11	2	2	NUM
ejpam-4451	57	12	-	-	PUNCT
ejpam-4451	57	13	resolving	resolve	VERB
ejpam-4451	57	14	dominating	dominating	NOUN
ejpam-4451	57	15	set	set	VERB
ejpam-4451	57	16	in	in	ADP
ejpam-4451	57	17	g+h	g+h	PROPN
ejpam-4451	57	18	.	.	PUNCT
ejpam-4451	58	1	then	then	ADV
ejpam-4451	58	2	s	s	VERB
ejpam-4451	58	3	is	be	AUX
ejpam-4451	58	4	a	a	DET
ejpam-4451	58	5	restrained	restrained	ADJ
ejpam-4451	58	6	2	2	NUM
ejpam-4451	58	7	-	-	PUNCT
ejpam-4451	58	8	resolving	resolving	NOUN
ejpam-4451	58	9	set	set	VERB
ejpam-4451	58	10	in	in	ADP
ejpam-4451	58	11	g+h	g+h	PROPN
ejpam-4451	58	12	.	.	PUNCT
ejpam-4451	59	1	conversely	conversely	ADV
ejpam-4451	59	2	,	,	PUNCT
ejpam-4451	59	3	if	if	SCONJ
ejpam-4451	59	4	s	s	VERB
ejpam-4451	59	5	is	be	AUX
ejpam-4451	59	6	a	a	DET
ejpam-4451	59	7	restrained	restrained	ADJ
ejpam-4451	59	8	2	2	NUM
ejpam-4451	59	9	-	-	PUNCT
ejpam-4451	59	10	resolving	resolving	NOUN
ejpam-4451	59	11	set	set	VERB
ejpam-4451	59	12	in	in	ADP
ejpam-4451	59	13	g+h	g+h	PROPN
ejpam-4451	59	14	,	,	PUNCT
ejpam-4451	59	15	then	then	ADV
ejpam-4451	59	16	by	by	ADP
ejpam-4451	59	17	theorem	theorem	NOUN
ejpam-4451	59	18	1	1	NUM
ejpam-4451	59	19	,	,	PUNCT
ejpam-4451	59	20	conditions	condition	NOUN
ejpam-4451	59	21	(	(	PUNCT
ejpam-4451	59	22	i	i	NOUN
ejpam-4451	59	23	)	)	PUNCT
ejpam-4451	59	24	,	,	PUNCT
ejpam-4451	59	25	(	(	PUNCT
ejpam-4451	59	26	ii	ii	NOUN
ejpam-4451	59	27	)	)	PUNCT
ejpam-4451	59	28	and	and	CCONJ
ejpam-4451	59	29	(	(	PUNCT
ejpam-4451	59	30	iii	iii	NOUN
ejpam-4451	59	31	)	)	PUNCT
ejpam-4451	59	32	hold	hold	NOUN
ejpam-4451	59	33	.	.	PUNCT
ejpam-4451	60	1	since	since	SCONJ
ejpam-4451	60	2	s	s	PROPN
ejpam-4451	60	3	is	be	AUX
ejpam-4451	60	4	a	a	DET
ejpam-4451	60	5	2	2	NUM
ejpam-4451	60	6	-	-	PUNCT
ejpam-4451	60	7	resolving	resolve	VERB
ejpam-4451	60	8	set	set	NOUN
ejpam-4451	60	9	,	,	PUNCT
ejpam-4451	60	10	sg	sg	ADP
ejpam-4451	60	11	̸=	̸=	PROPN
ejpam-4451	60	12	∅	∅	NOUN
ejpam-4451	60	13	and	and	CCONJ
ejpam-4451	60	14	sh	sh	PROPN
ejpam-4451	60	15	̸=	̸=	PROPN
ejpam-4451	60	16	∅.	∅.	ADV
ejpam-4451	60	17	thus	thus	ADV
ejpam-4451	60	18	,	,	PUNCT
ejpam-4451	60	19	s	s	PART
ejpam-4451	60	20	=	=	ADJ
ejpam-4451	60	21	sg∪sh	sg∪sh	PROPN
ejpam-4451	60	22	is	be	AUX
ejpam-4451	60	23	a	a	DET
ejpam-4451	60	24	dominating	dominating	NOUN
ejpam-4451	60	25	set	set	VERB
ejpam-4451	60	26	in	in	ADP
ejpam-4451	60	27	g	g	PROPN
ejpam-4451	60	28	+	+	PROPN
ejpam-4451	60	29	h.	h.	PROPN
ejpam-4451	60	30	therefore	therefore	ADV
ejpam-4451	60	31	,	,	PUNCT
ejpam-4451	60	32	s	s	VERB
ejpam-4451	60	33	is	be	AUX
ejpam-4451	60	34	a	a	DET
ejpam-4451	60	35	restrained	restrained	ADJ
ejpam-4451	60	36	2	2	NUM
ejpam-4451	60	37	-	-	PUNCT
ejpam-4451	60	38	resolving	resolve	VERB
ejpam-4451	60	39	dominating	dominating	NOUN
ejpam-4451	60	40	set	set	VERB
ejpam-4451	60	41	in	in	ADP
ejpam-4451	60	42	g+h	g+h	PROPN
ejpam-4451	60	43	.	.	PUNCT
ejpam-4451	61	1	corollary	corollary	ADJ
ejpam-4451	61	2	1	1	NUM
ejpam-4451	61	3	.	.	PUNCT
ejpam-4451	62	1	let	let	VERB
ejpam-4451	62	2	g	g	NOUN
ejpam-4451	63	1	and	and	CCONJ
ejpam-4451	63	2	h	h	PROPN
ejpam-4451	63	3	be	be	VERB
ejpam-4451	63	4	a	a	DET
ejpam-4451	63	5	connected	connected	ADJ
ejpam-4451	63	6	non	non	ADJ
ejpam-4451	63	7	-	-	ADJ
ejpam-4451	63	8	trivial	trivial	ADJ
ejpam-4451	63	9	graphs	graph	NOUN
ejpam-4451	63	10	of	of	ADP
ejpam-4451	63	11	order	order	NOUN
ejpam-4451	63	12	m	m	VERB
ejpam-4451	63	13	and	and	CCONJ
ejpam-4451	63	14	n	n	CCONJ
ejpam-4451	63	15	,	,	PUNCT
ejpam-4451	63	16	respectively	respectively	ADV
ejpam-4451	63	17	.	.	PUNCT
ejpam-4451	64	1	then	then	ADV
ejpam-4451	64	2	γr2r(g+h	γr2r(g+h	NOUN
ejpam-4451	64	3	)	)	PUNCT
ejpam-4451	64	4	=	=	SYM
ejpam-4451	65	1	rdim2(g+h	rdim2(g+h	NOUN
ejpam-4451	65	2	)	)	PUNCT
ejpam-4451	65	3	.	.	PUNCT
ejpam-4451	66	1	the	the	DET
ejpam-4451	66	2	set	set	NOUN
ejpam-4451	66	3	consisting	consisting	NOUN
ejpam-4451	66	4	of	of	ADP
ejpam-4451	66	5	the	the	DET
ejpam-4451	66	6	shaded	shade	VERB
ejpam-4451	66	7	vertices	vertex	NOUN
ejpam-4451	66	8	in	in	ADP
ejpam-4451	66	9	figure	figure	NOUN
ejpam-4451	66	10	1	1	NUM
ejpam-4451	66	11	is	be	AUX
ejpam-4451	66	12	a	a	DET
ejpam-4451	66	13	restrained	restrained	ADJ
ejpam-4451	66	14	2	2	NUM
ejpam-4451	66	15	-	-	PUNCT
ejpam-4451	66	16	resolving	resolve	VERB
ejpam-4451	66	17	dominating	dominating	NOUN
ejpam-4451	66	18	set	set	NOUN
ejpam-4451	66	19	of	of	ADP
ejpam-4451	66	20	the	the	DET
ejpam-4451	66	21	join	join	NOUN
ejpam-4451	66	22	p5	p5	PROPN
ejpam-4451	66	23	+	+	CCONJ
ejpam-4451	66	24	p6	p6	PROPN
ejpam-4451	66	25	.	.	PUNCT
ejpam-4451	67	1	j.	j.	PROPN
ejpam-4451	67	2	cabaro	cabaro	PROPN
ejpam-4451	67	3	,	,	PUNCT
ejpam-4451	67	4	h.	h.	PROPN
ejpam-4451	67	5	rara	rara	PROPN
ejpam-4451	67	6	/	/	SYM
ejpam-4451	67	7	eur	eur	PROPN
ejpam-4451	67	8	.	.	PUNCT
ejpam-4451	68	1	j.	j.	PROPN
ejpam-4451	68	2	pure	pure	PROPN
ejpam-4451	68	3	appl	appl	PROPN
ejpam-4451	68	4	.	.	PROPN
ejpam-4451	68	5	math	math	PROPN
ejpam-4451	68	6	,	,	PUNCT
ejpam-4451	68	7	15	15	NUM
ejpam-4451	68	8	(	(	PUNCT
ejpam-4451	68	9	3	3	NUM
ejpam-4451	68	10	)	)	PUNCT
ejpam-4451	68	11	(	(	PUNCT
ejpam-4451	68	12	2022	2022	NUM
ejpam-4451	68	13	)	)	PUNCT
ejpam-4451	68	14	,	,	PUNCT
ejpam-4451	68	15	1047	1047	NUM
ejpam-4451	68	16	-	-	SYM
ejpam-4451	68	17	1053	1053	NUM
ejpam-4451	68	18	1050	1050	NUM
ejpam-4451	68	19	....................................	....................................	PUNCT
ejpam-4451	68	20	....................................	....................................	PUNCT
ejpam-4451	69	1	....................................	....................................	PUNCT
ejpam-4451	69	2	....................................	....................................	PUNCT
ejpam-4451	70	1	....................................	....................................	PUNCT
ejpam-4451	70	2	....................................	....................................	PUNCT
ejpam-4451	71	1	....................................	....................................	PUNCT
ejpam-4451	71	2	....................................	....................................	PUNCT
ejpam-4451	72	1	....................................	....................................	PUNCT
ejpam-4451	72	2	....................................	....................................	PUNCT
ejpam-4451	73	1	....................................	....................................	PUNCT
ejpam-4451	73	2	.........	.........	PUNCT
ejpam-4451	73	3	........	........	PUNCT
ejpam-4451	73	4	........	........	PUNCT
ejpam-4451	73	5	........	........	PUNCT
ejpam-4451	73	6	........	........	PUNCT
ejpam-4451	73	7	........	........	PUNCT
ejpam-4451	73	8	........	........	PUNCT
ejpam-4451	73	9	........	........	PUNCT
ejpam-4451	73	10	........	........	PUNCT
ejpam-4451	73	11	.........	.........	PUNCT
ejpam-4451	73	12	........	........	PUNCT
ejpam-4451	73	13	........	........	PUNCT
ejpam-4451	73	14	........	........	PUNCT
ejpam-4451	73	15	........	........	PUNCT
ejpam-4451	73	16	........	........	PUNCT
ejpam-4451	73	17	........	........	PUNCT
ejpam-4451	73	18	........	........	PUNCT
ejpam-4451	73	19	........	........	PUNCT
ejpam-4451	73	20	.........	.........	PUNCT
ejpam-4451	73	21	........	........	PUNCT
ejpam-4451	73	22	........	........	PUNCT
ejpam-4451	73	23	........	........	PUNCT
ejpam-4451	73	24	........	........	PUNCT
ejpam-4451	73	25	........	........	PUNCT
ejpam-4451	73	26	........	........	PUNCT
ejpam-4451	73	27	........	........	PUNCT
ejpam-4451	73	28	........	........	PUNCT
ejpam-4451	73	29	.........	.........	PUNCT
ejpam-4451	73	30	........	........	PUNCT
ejpam-4451	73	31	........	........	PUNCT
ejpam-4451	73	32	........	........	PUNCT
ejpam-4451	73	33	........	........	PUNCT
ejpam-4451	73	34	........	........	PUNCT
ejpam-4451	73	35	........	........	PUNCT
ejpam-4451	73	36	........	........	PUNCT
ejpam-4451	73	37	........	........	PUNCT
ejpam-4451	74	1	..........	..........	PUNCT
ejpam-4451	74	2	.........	.........	PUNCT
ejpam-4451	75	1	.........	.........	PUNCT
ejpam-4451	75	2	.........	.........	PUNCT
ejpam-4451	76	1	.........	.........	PUNCT
ejpam-4451	76	2	.........	.........	PUNCT
ejpam-4451	77	1	.........	.........	PUNCT
ejpam-4451	77	2	.........	.........	PUNCT
ejpam-4451	78	1	.........	.........	PUNCT
ejpam-4451	78	2	.........	.........	PUNCT
ejpam-4451	79	1	.........	.........	PUNCT
ejpam-4451	79	2	.........	.........	PUNCT
ejpam-4451	80	1	.........	.........	PUNCT
ejpam-4451	80	2	.........	.........	PUNCT
ejpam-4451	81	1	.........	.........	PUNCT
ejpam-4451	81	2	.........	.........	PUNCT
ejpam-4451	82	1	.........	.........	PUNCT
ejpam-4451	82	2	.........	.........	PUNCT
ejpam-4451	83	1	.........	.........	PUNCT
ejpam-4451	83	2	.........	.........	PUNCT
ejpam-4451	84	1	.........	.........	PUNCT
ejpam-4451	84	2	.........	.........	PUNCT
ejpam-4451	85	1	.........	.........	PUNCT
ejpam-4451	85	2	.........	.........	PUNCT
ejpam-4451	86	1	.........	.........	PUNCT
ejpam-4451	86	2	.........	.........	PUNCT
ejpam-4451	87	1	.........	.........	PUNCT
ejpam-4451	87	2	.........	.........	PUNCT
ejpam-4451	88	1	.........	.........	PUNCT
ejpam-4451	88	2	.........	.........	PUNCT
ejpam-4451	89	1	.........	.........	PUNCT
ejpam-4451	89	2	.........	.........	PUNCT
ejpam-4451	90	1	.........	.........	PUNCT
ejpam-4451	90	2	.........	.........	PUNCT
ejpam-4451	91	1	.........	.........	PUNCT
ejpam-4451	91	2	.........	.........	PUNCT
ejpam-4451	92	1	.........	.........	PUNCT
ejpam-4451	92	2	.........	.........	PUNCT
ejpam-4451	93	1	.........	.........	PUNCT
ejpam-4451	93	2	.........	.........	PUNCT
ejpam-4451	94	1	.........	.........	PUNCT
ejpam-4451	94	2	.........	.........	PUNCT
ejpam-4451	95	1	.........	.........	PUNCT
ejpam-4451	95	2	.........	.........	PUNCT
ejpam-4451	96	1	....	....	PUNCT
ejpam-4451	96	2	.........	.........	PUNCT
ejpam-4451	96	3	........	........	PUNCT
ejpam-4451	96	4	........	........	PUNCT
ejpam-4451	96	5	........	........	PUNCT
ejpam-4451	96	6	........	........	PUNCT
ejpam-4451	96	7	........	........	PUNCT
ejpam-4451	96	8	........	........	PUNCT
ejpam-4451	96	9	........	........	PUNCT
ejpam-4451	96	10	........	........	PUNCT
ejpam-4451	96	11	.........	.........	PUNCT
ejpam-4451	96	12	........	........	PUNCT
ejpam-4451	96	13	........	........	PUNCT
ejpam-4451	96	14	........	........	PUNCT
ejpam-4451	96	15	........	........	PUNCT
ejpam-4451	96	16	........	........	PUNCT
ejpam-4451	96	17	........	........	PUNCT
ejpam-4451	96	18	........	........	PUNCT
ejpam-4451	96	19	........	........	PUNCT
ejpam-4451	96	20	.........	.........	PUNCT
ejpam-4451	96	21	........	........	PUNCT
ejpam-4451	96	22	........	........	PUNCT
ejpam-4451	96	23	........	........	PUNCT
ejpam-4451	96	24	........	........	PUNCT
ejpam-4451	96	25	........	........	PUNCT
ejpam-4451	96	26	........	........	PUNCT
ejpam-4451	96	27	........	........	PUNCT
ejpam-4451	96	28	........	........	PUNCT
ejpam-4451	96	29	.........	.........	PUNCT
ejpam-4451	96	30	........	........	PUNCT
ejpam-4451	96	31	........	........	PUNCT
ejpam-4451	96	32	........	........	PUNCT
ejpam-4451	96	33	........	........	PUNCT
ejpam-4451	96	34	........	........	PUNCT
ejpam-4451	96	35	........	........	PUNCT
ejpam-4451	96	36	........	........	PUNCT
ejpam-4451	96	37	........	........	PUNCT
ejpam-4451	96	38	.........	.........	PUNCT
ejpam-4451	96	39	........	........	PUNCT
ejpam-4451	96	40	........	........	PUNCT
ejpam-4451	96	41	........	........	PUNCT
ejpam-4451	96	42	........	........	PUNCT
ejpam-4451	96	43	........	........	PUNCT
ejpam-4451	96	44	........	........	PUNCT
ejpam-4451	96	45	........	........	PUNCT
ejpam-4451	96	46	........	........	PUNCT
ejpam-4451	96	47	.................................	.................................	PUNCT
ejpam-4451	96	48	................................	................................	PUNCT
ejpam-4451	96	49	................................	................................	PUNCT
ejpam-4451	96	50	................................	................................	PUNCT
ejpam-4451	96	51	................................	................................	PUNCT
ejpam-4451	96	52	.................................................................................................................................................................	.................................................................................................................................................................	PUNCT
ejpam-4451	97	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4451	97	2	................................................................................................................................................................................................................................................................	................................................................................................................................................................................................................................................................	PUNCT
ejpam-4451	98	1	......................................................................................................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................................................................................................	PROPN
ejpam-4451	98	2	.................................................................................................................................................................................................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4451	99	1	..............	..............	PUNCT
ejpam-4451	99	2	.............	.............	PUNCT
ejpam-4451	99	3	.............	.............	PUNCT
ejpam-4451	99	4	.............	.............	PUNCT
ejpam-4451	99	5	.............	.............	PUNCT
ejpam-4451	99	6	.............	.............	PUNCT
ejpam-4451	99	7	.............	.............	PUNCT
ejpam-4451	99	8	.............	.............	PUNCT
ejpam-4451	99	9	.............	.............	PUNCT
ejpam-4451	99	10	.............	.............	PUNCT
ejpam-4451	99	11	.............	.............	PUNCT
ejpam-4451	99	12	.............	.............	PUNCT
ejpam-4451	99	13	.............	.............	PUNCT
ejpam-4451	99	14	.............	.............	PUNCT
ejpam-4451	99	15	.............	.............	PUNCT
ejpam-4451	99	16	..	..	PUNCT
ejpam-4451	99	17	.................................	.................................	PUNCT
ejpam-4451	99	18	................................	................................	PUNCT
ejpam-4451	99	19	................................	................................	PUNCT
ejpam-4451	99	20	................................	................................	PUNCT
ejpam-4451	99	21	................................	................................	PUNCT
ejpam-4451	99	22	.................................................................................................................................................................	.................................................................................................................................................................	PUNCT
ejpam-4451	100	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4451	100	2	................................................................................................................................................................................................................................................................	................................................................................................................................................................................................................................................................	PUNCT
ejpam-4451	101	1	......................................................................................................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................................................................................................	PROPN
ejpam-4451	101	2	...........	...........	PUNCT
ejpam-4451	102	1	..........	..........	PUNCT
ejpam-4451	103	1	..........	..........	PUNCT
ejpam-4451	104	1	..........	..........	PUNCT
ejpam-4451	105	1	..........	..........	PUNCT
ejpam-4451	106	1	..........	..........	PUNCT
ejpam-4451	107	1	..........	..........	PUNCT
ejpam-4451	108	1	..........	..........	PUNCT
ejpam-4451	109	1	..........	..........	PUNCT
ejpam-4451	110	1	..........	..........	PUNCT
ejpam-4451	111	1	..........	..........	PUNCT
ejpam-4451	112	1	..........	..........	PUNCT
ejpam-4451	113	1	..........	..........	PUNCT
ejpam-4451	114	1	..........	..........	PUNCT
ejpam-4451	115	1	..........	..........	PUNCT
ejpam-4451	116	1	..........	..........	PUNCT
ejpam-4451	117	1	..........	..........	PUNCT
ejpam-4451	118	1	..........	..........	PUNCT
ejpam-4451	119	1	..........	..........	PUNCT
ejpam-4451	120	1	..........	..........	PUNCT
ejpam-4451	121	1	..........	..........	PUNCT
ejpam-4451	122	1	..........	..........	PUNCT
ejpam-4451	123	1	..........	..........	PUNCT
ejpam-4451	124	1	..........	..........	PUNCT
ejpam-4451	125	1	..........	..........	PUNCT
ejpam-4451	126	1	.....	.....	PUNCT
ejpam-4451	127	1	..............	..............	PUNCT
ejpam-4451	128	1	.............	.............	PUNCT
ejpam-4451	129	1	.............	.............	PUNCT
ejpam-4451	130	1	.............	.............	PUNCT
ejpam-4451	131	1	.............	.............	PUNCT
ejpam-4451	132	1	.............	.............	PUNCT
ejpam-4451	133	1	.............	.............	PUNCT
ejpam-4451	134	1	.............	.............	PUNCT
ejpam-4451	135	1	.............	.............	PUNCT
ejpam-4451	136	1	.............	.............	PUNCT
ejpam-4451	137	1	.............	.............	PUNCT
ejpam-4451	138	1	.............	.............	PUNCT
ejpam-4451	139	1	.............	.............	PUNCT
ejpam-4451	140	1	.............	.............	PUNCT
ejpam-4451	141	1	.............	.............	PUNCT
ejpam-4451	142	1	..	..	PUNCT
ejpam-4451	142	2	.................................	.................................	PUNCT
ejpam-4451	142	3	................................	................................	PUNCT
ejpam-4451	142	4	................................	................................	PUNCT
ejpam-4451	142	5	................................	................................	PUNCT
ejpam-4451	142	6	................................	................................	PUNCT
ejpam-4451	142	7	.................................................................................................................................................................	.................................................................................................................................................................	PUNCT
ejpam-4451	143	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4451	143	2	................................................................................................................................................................................................................................................................	................................................................................................................................................................................................................................................................	PUNCT
ejpam-4451	144	1	..........	..........	PUNCT
ejpam-4451	144	2	.........	.........	PUNCT
ejpam-4451	145	1	.........	.........	PUNCT
ejpam-4451	145	2	.........	.........	PUNCT
ejpam-4451	146	1	.........	.........	PUNCT
ejpam-4451	146	2	.........	.........	PUNCT
ejpam-4451	147	1	.........	.........	PUNCT
ejpam-4451	147	2	.........	.........	PUNCT
ejpam-4451	148	1	.........	.........	PUNCT
ejpam-4451	148	2	.........	.........	PUNCT
ejpam-4451	149	1	.........	.........	PUNCT
ejpam-4451	149	2	.........	.........	PUNCT
ejpam-4451	150	1	.........	.........	PUNCT
ejpam-4451	150	2	.........	.........	PUNCT
ejpam-4451	151	1	.........	.........	PUNCT
ejpam-4451	151	2	.........	.........	PUNCT
ejpam-4451	152	1	.........	.........	PUNCT
ejpam-4451	152	2	.........	.........	PUNCT
ejpam-4451	153	1	.........	.........	PUNCT
ejpam-4451	153	2	.........	.........	PUNCT
ejpam-4451	154	1	.........	.........	PUNCT
ejpam-4451	154	2	.........	.........	PUNCT
ejpam-4451	155	1	.........	.........	PUNCT
ejpam-4451	155	2	.........	.........	PUNCT
ejpam-4451	156	1	.........	.........	PUNCT
ejpam-4451	156	2	.........	.........	PUNCT
ejpam-4451	157	1	.........	.........	PUNCT
ejpam-4451	157	2	.........	.........	PUNCT
ejpam-4451	158	1	.........	.........	PUNCT
ejpam-4451	158	2	.........	.........	PUNCT
ejpam-4451	159	1	.........	.........	PUNCT
ejpam-4451	159	2	.........	.........	PUNCT
ejpam-4451	160	1	.........	.........	PUNCT
ejpam-4451	160	2	.........	.........	PUNCT
ejpam-4451	161	1	.........	.........	PUNCT
ejpam-4451	161	2	.........	.........	PUNCT
ejpam-4451	161	3	.	.	PUNCT
ejpam-4451	162	1	...........	...........	PUNCT
ejpam-4451	162	2	..........	..........	PUNCT
ejpam-4451	163	1	..........	..........	PUNCT
ejpam-4451	163	2	..........	..........	PUNCT
ejpam-4451	164	1	..........	..........	PUNCT
ejpam-4451	164	2	..........	..........	PUNCT
ejpam-4451	165	1	..........	..........	PUNCT
ejpam-4451	165	2	..........	..........	PUNCT
ejpam-4451	166	1	..........	..........	PUNCT
ejpam-4451	166	2	..........	..........	PUNCT
ejpam-4451	167	1	..........	..........	PUNCT
ejpam-4451	167	2	..........	..........	PUNCT
ejpam-4451	168	1	..........	..........	PUNCT
ejpam-4451	168	2	..........	..........	PUNCT
ejpam-4451	169	1	..........	..........	PUNCT
ejpam-4451	169	2	..........	..........	PUNCT
ejpam-4451	170	1	..........	..........	PUNCT
ejpam-4451	170	2	..........	..........	PUNCT
ejpam-4451	171	1	..........	..........	PUNCT
ejpam-4451	171	2	..........	..........	PUNCT
ejpam-4451	172	1	..........	..........	PUNCT
ejpam-4451	172	2	..........	..........	PUNCT
ejpam-4451	173	1	..........	..........	PUNCT
ejpam-4451	173	2	..........	..........	PUNCT
ejpam-4451	174	1	..........	..........	PUNCT
ejpam-4451	174	2	.....	.....	PUNCT
ejpam-4451	175	1	..............	..............	PUNCT
ejpam-4451	175	2	.............	.............	PUNCT
ejpam-4451	175	3	.............	.............	PUNCT
ejpam-4451	175	4	.............	.............	PUNCT
ejpam-4451	175	5	.............	.............	PUNCT
ejpam-4451	175	6	.............	.............	PUNCT
ejpam-4451	175	7	.............	.............	PUNCT
ejpam-4451	175	8	.............	.............	PUNCT
ejpam-4451	175	9	.............	.............	PUNCT
ejpam-4451	175	10	.............	.............	PUNCT
ejpam-4451	175	11	.............	.............	PUNCT
ejpam-4451	175	12	.............	.............	PUNCT
ejpam-4451	175	13	.............	.............	PUNCT
ejpam-4451	175	14	.............	.............	PUNCT
ejpam-4451	175	15	.............	.............	PUNCT
ejpam-4451	175	16	..	..	PUNCT
ejpam-4451	175	17	.................................	.................................	PUNCT
ejpam-4451	175	18	................................	................................	PUNCT
ejpam-4451	175	19	................................	................................	PUNCT
ejpam-4451	175	20	................................	................................	PUNCT
ejpam-4451	175	21	................................	................................	PUNCT
ejpam-4451	175	22	.................................................................................................................................................................	.................................................................................................................................................................	PUNCT
ejpam-4451	176	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4451	176	2	..........	..........	PUNCT
ejpam-4451	177	1	.........	.........	PUNCT
ejpam-4451	177	2	.........	.........	PUNCT
ejpam-4451	178	1	.........	.........	PUNCT
ejpam-4451	178	2	.........	.........	PUNCT
ejpam-4451	179	1	.........	.........	PUNCT
ejpam-4451	179	2	.........	.........	PUNCT
ejpam-4451	180	1	.........	.........	PUNCT
ejpam-4451	180	2	.........	.........	PUNCT
ejpam-4451	181	1	.........	.........	PUNCT
ejpam-4451	181	2	.........	.........	PUNCT
ejpam-4451	182	1	.........	.........	PUNCT
ejpam-4451	182	2	.........	.........	PUNCT
ejpam-4451	183	1	.........	.........	PUNCT
ejpam-4451	183	2	.........	.........	PUNCT
ejpam-4451	184	1	.........	.........	PUNCT
ejpam-4451	184	2	.........	.........	PUNCT
ejpam-4451	185	1	.........	.........	PUNCT
ejpam-4451	185	2	.........	.........	PUNCT
ejpam-4451	186	1	.........	.........	PUNCT
ejpam-4451	186	2	.........	.........	PUNCT
ejpam-4451	187	1	.........	.........	PUNCT
ejpam-4451	187	2	.........	.........	PUNCT
ejpam-4451	188	1	.........	.........	PUNCT
ejpam-4451	188	2	.........	.........	PUNCT
ejpam-4451	189	1	.........	.........	PUNCT
ejpam-4451	189	2	.........	.........	PUNCT
ejpam-4451	190	1	.........	.........	PUNCT
ejpam-4451	190	2	.........	.........	PUNCT
ejpam-4451	191	1	.........	.........	PUNCT
ejpam-4451	191	2	.........	.........	PUNCT
ejpam-4451	192	1	.........	.........	PUNCT
ejpam-4451	192	2	.........	.........	PUNCT
ejpam-4451	193	1	.........	.........	PUNCT
ejpam-4451	193	2	.........	.........	PUNCT
ejpam-4451	194	1	.........	.........	PUNCT
ejpam-4451	194	2	.........	.........	PUNCT
ejpam-4451	195	1	.........	.........	PUNCT
ejpam-4451	195	2	.........	.........	PUNCT
ejpam-4451	196	1	.........	.........	PUNCT
ejpam-4451	196	2	.........	.........	PUNCT
ejpam-4451	197	1	.........	.........	PUNCT
ejpam-4451	197	2	.........	.........	PUNCT
ejpam-4451	198	1	.........	.........	PUNCT
ejpam-4451	198	2	....	....	PUNCT
ejpam-4451	199	1	..........	..........	PUNCT
ejpam-4451	199	2	.........	.........	PUNCT
ejpam-4451	200	1	.........	.........	PUNCT
ejpam-4451	200	2	.........	.........	PUNCT
ejpam-4451	201	1	.........	.........	PUNCT
ejpam-4451	201	2	.........	.........	PUNCT
ejpam-4451	202	1	.........	.........	PUNCT
ejpam-4451	202	2	.........	.........	PUNCT
ejpam-4451	203	1	.........	.........	PUNCT
ejpam-4451	203	2	.........	.........	PUNCT
ejpam-4451	204	1	.........	.........	PUNCT
ejpam-4451	204	2	.........	.........	PUNCT
ejpam-4451	205	1	.........	.........	PUNCT
ejpam-4451	205	2	.........	.........	PUNCT
ejpam-4451	206	1	.........	.........	PUNCT
ejpam-4451	206	2	.........	.........	PUNCT
ejpam-4451	207	1	.........	.........	PUNCT
ejpam-4451	207	2	.........	.........	PUNCT
ejpam-4451	208	1	.........	.........	PUNCT
ejpam-4451	208	2	.........	.........	PUNCT
ejpam-4451	209	1	.........	.........	PUNCT
ejpam-4451	209	2	.........	.........	PUNCT
ejpam-4451	210	1	.........	.........	PUNCT
ejpam-4451	210	2	.........	.........	PUNCT
ejpam-4451	211	1	.........	.........	PUNCT
ejpam-4451	211	2	.........	.........	PUNCT
ejpam-4451	212	1	.........	.........	PUNCT
ejpam-4451	212	2	.........	.........	PUNCT
ejpam-4451	213	1	.........	.........	PUNCT
ejpam-4451	213	2	.........	.........	PUNCT
ejpam-4451	214	1	.........	.........	PUNCT
ejpam-4451	214	2	.........	.........	PUNCT
ejpam-4451	215	1	.........	.........	PUNCT
ejpam-4451	215	2	.........	.........	PUNCT
ejpam-4451	216	1	.........	.........	PUNCT
ejpam-4451	216	2	.........	.........	PUNCT
ejpam-4451	216	3	.	.	PUNCT
ejpam-4451	217	1	...........	...........	PUNCT
ejpam-4451	217	2	..........	..........	PUNCT
ejpam-4451	218	1	..........	..........	PUNCT
ejpam-4451	218	2	..........	..........	PUNCT
ejpam-4451	219	1	..........	..........	PUNCT
ejpam-4451	219	2	..........	..........	PUNCT
ejpam-4451	220	1	..........	..........	PUNCT
ejpam-4451	220	2	..........	..........	PUNCT
ejpam-4451	221	1	..........	..........	PUNCT
ejpam-4451	221	2	..........	..........	PUNCT
ejpam-4451	222	1	..........	..........	PUNCT
ejpam-4451	222	2	..........	..........	PUNCT
ejpam-4451	223	1	..........	..........	PUNCT
ejpam-4451	223	2	..........	..........	PUNCT
ejpam-4451	224	1	..........	..........	PUNCT
ejpam-4451	224	2	..........	..........	PUNCT
ejpam-4451	225	1	..........	..........	PUNCT
ejpam-4451	225	2	..........	..........	PUNCT
ejpam-4451	226	1	..........	..........	PUNCT
ejpam-4451	226	2	..........	..........	PUNCT
ejpam-4451	227	1	..........	..........	PUNCT
ejpam-4451	227	2	..........	..........	PUNCT
ejpam-4451	228	1	..........	..........	PUNCT
ejpam-4451	228	2	..........	..........	PUNCT
ejpam-4451	229	1	..........	..........	PUNCT
ejpam-4451	229	2	.....	.....	PUNCT
ejpam-4451	230	1	..............	..............	PUNCT
ejpam-4451	230	2	.............	.............	PUNCT
ejpam-4451	230	3	.............	.............	PUNCT
ejpam-4451	230	4	.............	.............	PUNCT
ejpam-4451	230	5	.............	.............	PUNCT
ejpam-4451	230	6	.............	.............	PUNCT
ejpam-4451	230	7	.............	.............	PUNCT
ejpam-4451	230	8	.............	.............	PUNCT
ejpam-4451	230	9	.............	.............	PUNCT
ejpam-4451	230	10	.............	.............	PUNCT
ejpam-4451	230	11	.............	.............	PUNCT
ejpam-4451	230	12	.............	.............	PUNCT
ejpam-4451	230	13	.............	.............	PUNCT
ejpam-4451	230	14	.............	.............	PUNCT
ejpam-4451	230	15	.............	.............	PUNCT
ejpam-4451	230	16	..	..	PUNCT
ejpam-4451	230	17	.................................	.................................	PUNCT
ejpam-4451	230	18	................................	................................	PUNCT
ejpam-4451	230	19	................................	................................	PUNCT
ejpam-4451	230	20	................................	................................	PUNCT
ejpam-4451	230	21	................................	................................	PUNCT
ejpam-4451	230	22	.................................................................................................................................................................	.................................................................................................................................................................	PUNCT
ejpam-4451	231	1	p5	p5	ADJ
ejpam-4451	231	2	+	+	CCONJ
ejpam-4451	231	3	p6	p6	ADJ
ejpam-4451	231	4	:	:	PUNCT
ejpam-4451	231	5	•	•	NUM
ejpam-4451	231	6	•	•	NOUN
ejpam-4451	231	7	•	•	NUM
ejpam-4451	231	8	•	•	NUM
ejpam-4451	231	9	•	•	NUM
ejpam-4451	231	10	•	•	NOUN
ejpam-4451	231	11	•	•	NUM
ejpam-4451	231	12	figure	figure	NOUN
ejpam-4451	231	13	1	1	NUM
ejpam-4451	231	14	:	:	PUNCT
ejpam-4451	231	15	a	a	DET
ejpam-4451	231	16	graph	graph	NOUN
ejpam-4451	231	17	p5	p5	ADJ
ejpam-4451	231	18	+	+	CCONJ
ejpam-4451	231	19	p6	p6	ADJ
ejpam-4451	231	20	with	with	ADP
ejpam-4451	231	21	γr2r(p5	γr2r(p5	PROPN
ejpam-4451	231	22	+	+	CCONJ
ejpam-4451	231	23	p6	p6	ADJ
ejpam-4451	231	24	)	)	PUNCT
ejpam-4451	231	25	=	=	SYM
ejpam-4451	231	26	7	7	NUM
ejpam-4451	231	27	theorem	theorem	NOUN
ejpam-4451	231	28	4	4	NUM
ejpam-4451	231	29	.	.	PUNCT
ejpam-4451	232	1	let	let	VERB
ejpam-4451	232	2	g	g	PRON
ejpam-4451	232	3	be	be	AUX
ejpam-4451	232	4	a	a	DET
ejpam-4451	232	5	connected	connected	ADJ
ejpam-4451	232	6	non	non	ADJ
ejpam-4451	232	7	-	-	ADJ
ejpam-4451	232	8	trivial	trivial	ADJ
ejpam-4451	232	9	graph	graph	NOUN
ejpam-4451	232	10	and	and	CCONJ
ejpam-4451	232	11	let	let	VERB
ejpam-4451	232	12	k1	k1	NOUN
ejpam-4451	232	13	=	=	SYM
ejpam-4451	232	14	{	{	PUNCT
ejpam-4451	232	15	v	v	NOUN
ejpam-4451	232	16	}	}	PUNCT
ejpam-4451	232	17	.	.	PUNCT
ejpam-4451	233	1	then	then	ADV
ejpam-4451	233	2	s	s	VERB
ejpam-4451	233	3	⊆	⊆	NUM
ejpam-4451	233	4	v	v	NOUN
ejpam-4451	233	5	(	(	PUNCT
ejpam-4451	233	6	k1	k1	NOUN
ejpam-4451	233	7	+	+	CCONJ
ejpam-4451	233	8	g	g	NOUN
ejpam-4451	233	9	)	)	PUNCT
ejpam-4451	233	10	is	be	AUX
ejpam-4451	233	11	a	a	DET
ejpam-4451	233	12	restrained	restrained	ADJ
ejpam-4451	233	13	2	2	NUM
ejpam-4451	233	14	-	-	PUNCT
ejpam-4451	233	15	resolving	resolve	VERB
ejpam-4451	233	16	dominating	dominating	NOUN
ejpam-4451	233	17	set	set	VERB
ejpam-4451	233	18	in	in	ADP
ejpam-4451	233	19	k1	k1	NOUN
ejpam-4451	233	20	+	+	CCONJ
ejpam-4451	233	21	g	g	NOUN
ejpam-4451	233	22	if	if	SCONJ
ejpam-4451	234	1	and	and	CCONJ
ejpam-4451	234	2	only	only	ADV
ejpam-4451	234	3	if	if	SCONJ
ejpam-4451	234	4	it	it	PRON
ejpam-4451	234	5	is	be	AUX
ejpam-4451	234	6	a	a	DET
ejpam-4451	234	7	restrained	restrained	ADJ
ejpam-4451	234	8	2	2	NUM
ejpam-4451	234	9	-	-	PUNCT
ejpam-4451	234	10	resolving	resolving	NOUN
ejpam-4451	234	11	set	set	VERB
ejpam-4451	234	12	in	in	ADP
ejpam-4451	234	13	k1	k1	PROPN
ejpam-4451	234	14	+	+	PROPN
ejpam-4451	234	15	g.	g.	NOUN
ejpam-4451	234	16	proof	proof	NOUN
ejpam-4451	234	17	.	.	PUNCT
ejpam-4451	235	1	suppose	suppose	VERB
ejpam-4451	235	2	s	s	PRON
ejpam-4451	235	3	is	be	AUX
ejpam-4451	235	4	a	a	DET
ejpam-4451	235	5	restrained	restrained	ADJ
ejpam-4451	235	6	2	2	NUM
ejpam-4451	235	7	-	-	PUNCT
ejpam-4451	235	8	resolving	resolve	VERB
ejpam-4451	235	9	dominating	dominating	NOUN
ejpam-4451	235	10	set	set	VERB
ejpam-4451	235	11	in	in	ADP
ejpam-4451	235	12	k1	k1	PROPN
ejpam-4451	235	13	+	+	CCONJ
ejpam-4451	235	14	g.	g.	PROPN
ejpam-4451	236	1	then	then	ADV
ejpam-4451	236	2	s	s	VERB
ejpam-4451	236	3	is	be	AUX
ejpam-4451	236	4	a	a	DET
ejpam-4451	236	5	restrained	restrained	ADJ
ejpam-4451	236	6	2	2	NUM
ejpam-4451	236	7	-	-	PUNCT
ejpam-4451	236	8	resolving	resolving	NOUN
ejpam-4451	236	9	in	in	ADP
ejpam-4451	236	10	k1	k1	PROPN
ejpam-4451	236	11	+	+	NOUN
ejpam-4451	236	12	g.	g.	NOUN
ejpam-4451	236	13	conversely	conversely	ADV
ejpam-4451	236	14	,	,	PUNCT
ejpam-4451	236	15	if	if	SCONJ
ejpam-4451	236	16	s	s	VERB
ejpam-4451	236	17	is	be	AUX
ejpam-4451	236	18	a	a	DET
ejpam-4451	236	19	restrained	restrained	ADJ
ejpam-4451	236	20	2	2	NUM
ejpam-4451	236	21	-	-	PUNCT
ejpam-4451	236	22	resolving	resolving	NOUN
ejpam-4451	236	23	set	set	VERB
ejpam-4451	236	24	in	in	ADP
ejpam-4451	236	25	k1	k1	NOUN
ejpam-4451	236	26	+	+	CCONJ
ejpam-4451	236	27	g	g	NOUN
ejpam-4451	236	28	,	,	PUNCT
ejpam-4451	236	29	then	then	ADV
ejpam-4451	236	30	by	by	ADP
ejpam-4451	236	31	theorem	theorem	NOUN
ejpam-4451	236	32	2	2	NUM
ejpam-4451	236	33	either	either	CCONJ
ejpam-4451	236	34	v	v	ADP
ejpam-4451	236	35	∈	∈	PROPN
ejpam-4451	236	36	s	s	PART
ejpam-4451	236	37	and	and	CCONJ
ejpam-4451	236	38	s	s	VERB
ejpam-4451	236	39	is	be	AUX
ejpam-4451	236	40	a	a	DET
ejpam-4451	236	41	(	(	PUNCT
ejpam-4451	236	42	2	2	NUM
ejpam-4451	236	43	,	,	PUNCT
ejpam-4451	236	44	2)-locating	2)-locating	NUM
ejpam-4451	236	45	set	set	VERB
ejpam-4451	236	46	in	in	ADP
ejpam-4451	236	47	g	g	NOUN
ejpam-4451	236	48	with	with	ADP
ejpam-4451	236	49	v	v	NOUN
ejpam-4451	236	50	(	(	PUNCT
ejpam-4451	236	51	g	g	NOUN
ejpam-4451	236	52	)	)	PUNCT
ejpam-4451	236	53	̸=	̸=	PROPN
ejpam-4451	236	54	s	s	PART
ejpam-4451	236	55	or	or	CCONJ
ejpam-4451	236	56	s	s	NOUN
ejpam-4451	236	57	=	=	PUNCT
ejpam-4451	236	58	{	{	PUNCT
ejpam-4451	236	59	v	v	NOUN
ejpam-4451	236	60	}	}	PUNCT
ejpam-4451	236	61	∪	∪	NOUN
ejpam-4451	236	62	t	t	PROPN
ejpam-4451	236	63	,	,	PUNCT
ejpam-4451	236	64	where	where	SCONJ
ejpam-4451	236	65	t	t	PROPN
ejpam-4451	236	66	is	be	AUX
ejpam-4451	236	67	a	a	DET
ejpam-4451	236	68	restrained	restrained	ADJ
ejpam-4451	236	69	(	(	PUNCT
ejpam-4451	236	70	2	2	NUM
ejpam-4451	236	71	,	,	PUNCT
ejpam-4451	236	72	1)-locating	1)-locating	NUM
ejpam-4451	236	73	set	set	VERB
ejpam-4451	236	74	in	in	ADP
ejpam-4451	236	75	g.	g.	PROPN
ejpam-4451	236	76	hence	hence	ADV
ejpam-4451	236	77	,	,	PUNCT
ejpam-4451	236	78	s	s	VERB
ejpam-4451	236	79	is	be	AUX
ejpam-4451	236	80	a	a	DET
ejpam-4451	236	81	restrained	restrained	ADJ
ejpam-4451	236	82	2	2	NUM
ejpam-4451	236	83	-	-	PUNCT
ejpam-4451	236	84	resolving	resolve	VERB
ejpam-4451	236	85	dominating	dominating	NOUN
ejpam-4451	236	86	set	set	VERB
ejpam-4451	236	87	in	in	ADP
ejpam-4451	236	88	k1	k1	PROPN
ejpam-4451	236	89	+	+	PROPN
ejpam-4451	236	90	g.	g.	PROPN
ejpam-4451	236	91	corollary	corollary	NOUN
ejpam-4451	236	92	2	2	PROPN
ejpam-4451	236	93	.	.	PUNCT
ejpam-4451	237	1	let	let	VERB
ejpam-4451	237	2	g	g	PRON
ejpam-4451	237	3	be	be	AUX
ejpam-4451	237	4	a	a	DET
ejpam-4451	237	5	connected	connected	ADJ
ejpam-4451	237	6	nontrivial	nontrivial	ADJ
ejpam-4451	237	7	graph	graph	NOUN
ejpam-4451	237	8	of	of	ADP
ejpam-4451	237	9	order	order	NOUN
ejpam-4451	237	10	m.	m.	NOUN
ejpam-4451	237	11	then	then	ADV
ejpam-4451	237	12	γr2r(k1	γr2r(k1	PROPN
ejpam-4451	237	13	+	+	PROPN
ejpam-4451	237	14	g	g	NOUN
ejpam-4451	237	15	)	)	PUNCT
ejpam-4451	238	1	=	=	PRON
ejpam-4451	238	2	{	{	PUNCT
ejpam-4451	238	3	1	1	NUM
ejpam-4451	238	4	+	+	NOUN
ejpam-4451	238	5	m	m	PROPN
ejpam-4451	238	6	,	,	PUNCT
ejpam-4451	238	7	if	if	SCONJ
ejpam-4451	238	8	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4451	238	9	)	)	PUNCT
ejpam-4451	238	10	=	=	SYM
ejpam-4451	238	11	m	m	NOUN
ejpam-4451	238	12	and	and	CCONJ
ejpam-4451	238	13	rln(2,1)(g	rln(2,1)(g	ADJ
ejpam-4451	238	14	)	)	PUNCT
ejpam-4451	238	15	=	=	NUM
ejpam-4451	238	16	m	m	PRON
ejpam-4451	238	17	min	min	NOUN
ejpam-4451	238	18	{	{	PUNCT
ejpam-4451	238	19	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4451	238	20	)	)	PUNCT
ejpam-4451	238	21	,	,	PUNCT
ejpam-4451	238	22	rln(2,1)(g	rln(2,1)(g	PROPN
ejpam-4451	238	23	)	)	PUNCT
ejpam-4451	238	24	+	+	CCONJ
ejpam-4451	238	25	1	1	NUM
ejpam-4451	238	26	}	}	PUNCT
ejpam-4451	238	27	,	,	PUNCT
ejpam-4451	238	28	otherwise	otherwise	ADV
ejpam-4451	238	29	.	.	PUNCT
ejpam-4451	239	1	4	4	X
ejpam-4451	239	2	.	.	X
ejpam-4451	239	3	restrained	restrain	VERB
ejpam-4451	239	4	2	2	NUM
ejpam-4451	239	5	-	-	PUNCT
ejpam-4451	239	6	resolving	resolve	VERB
ejpam-4451	239	7	dominating	dominating	NOUN
ejpam-4451	239	8	sets	set	NOUN
ejpam-4451	239	9	in	in	ADP
ejpam-4451	239	10	the	the	DET
ejpam-4451	239	11	corona	corona	NOUN
ejpam-4451	239	12	of	of	ADP
ejpam-4451	239	13	graphs	graph	NOUN
ejpam-4451	239	14	theorem	theorem	VERB
ejpam-4451	239	15	5	5	NUM
ejpam-4451	239	16	.	.	PUNCT
ejpam-4451	240	1	[	[	X
ejpam-4451	240	2	7	7	X
ejpam-4451	240	3	]	]	X
ejpam-4451	240	4	let	let	VERB
ejpam-4451	240	5	g	g	NOUN
ejpam-4451	240	6	and	and	CCONJ
ejpam-4451	240	7	h	h	NOUN
ejpam-4451	240	8	be	be	AUX
ejpam-4451	240	9	nontrivial	nontrivial	ADJ
ejpam-4451	240	10	connected	connected	ADJ
ejpam-4451	240	11	graphs	graph	NOUN
ejpam-4451	240	12	.	.	PUNCT
ejpam-4451	241	1	a	a	DET
ejpam-4451	241	2	set	set	NOUN
ejpam-4451	241	3	s	s	NOUN
ejpam-4451	241	4	⊆	⊆	NUM
ejpam-4451	241	5	v	v	NOUN
ejpam-4451	241	6	(	(	PUNCT
ejpam-4451	241	7	g	g	PROPN
ejpam-4451	241	8	◦	◦	NOUN
ejpam-4451	241	9	h	h	NOUN
ejpam-4451	241	10	)	)	PUNCT
ejpam-4451	241	11	is	be	AUX
ejpam-4451	241	12	a	a	DET
ejpam-4451	241	13	restrained	restrained	ADJ
ejpam-4451	241	14	2	2	NUM
ejpam-4451	241	15	-	-	PUNCT
ejpam-4451	241	16	resolving	resolving	NOUN
ejpam-4451	241	17	set	set	NOUN
ejpam-4451	241	18	in	in	ADP
ejpam-4451	241	19	g	g	PROPN
ejpam-4451	241	20	◦	◦	NOUN
ejpam-4451	241	21	h	h	NOUN
ejpam-4451	241	22	if	if	SCONJ
ejpam-4451	242	1	and	and	CCONJ
ejpam-4451	242	2	only	only	ADV
ejpam-4451	242	3	if	if	SCONJ
ejpam-4451	242	4	s	s	VERB
ejpam-4451	242	5	=	=	NOUN
ejpam-4451	242	6	a	a	PRON
ejpam-4451	242	7	∪	∪	X
ejpam-4451	242	8	(	(	PUNCT
ejpam-4451	242	9	⋃	⋃	NOUN
ejpam-4451	242	10	v∈v	v∈v	NOUN
ejpam-4451	242	11	(	(	PUNCT
ejpam-4451	242	12	g	g	NOUN
ejpam-4451	242	13	)	)	PUNCT
ejpam-4451	242	14	sv	sv	NOUN
ejpam-4451	242	15	)	)	PUNCT
ejpam-4451	242	16	satisfying	satisfy	VERB
ejpam-4451	242	17	the	the	DET
ejpam-4451	242	18	following	follow	VERB
ejpam-4451	242	19	conditions	condition	NOUN
ejpam-4451	242	20	.	.	PUNCT
ejpam-4451	243	1	(	(	PUNCT
ejpam-4451	243	2	i	i	NOUN
ejpam-4451	243	3	)	)	PUNCT
ejpam-4451	243	4	a	a	DET
ejpam-4451	243	5	⊆	⊆	NUM
ejpam-4451	243	6	v	v	NOUN
ejpam-4451	243	7	(	(	PUNCT
ejpam-4451	243	8	g	g	NOUN
ejpam-4451	243	9	)	)	PUNCT
ejpam-4451	243	10	(	(	PUNCT
ejpam-4451	243	11	ii	ii	NOUN
ejpam-4451	243	12	)	)	PUNCT
ejpam-4451	243	13	sv	sv	PROPN
ejpam-4451	243	14	is	be	AUX
ejpam-4451	243	15	a	a	DET
ejpam-4451	243	16	2	2	NUM
ejpam-4451	243	17	-	-	PUNCT
ejpam-4451	243	18	resolving	resolving	NOUN
ejpam-4451	243	19	set	set	NOUN
ejpam-4451	243	20	for	for	ADP
ejpam-4451	243	21	each	each	DET
ejpam-4451	243	22	v	v	NUM
ejpam-4451	243	23	∈	∈	PROPN
ejpam-4451	243	24	v	v	NOUN
ejpam-4451	243	25	(	(	PUNCT
ejpam-4451	243	26	g)\a	g)\a	PROPN
ejpam-4451	243	27	(	(	PUNCT
ejpam-4451	243	28	iii	iii	NOUN
ejpam-4451	243	29	)	)	PUNCT
ejpam-4451	243	30	sv	sv	PROPN
ejpam-4451	243	31	is	be	AUX
ejpam-4451	243	32	a	a	DET
ejpam-4451	243	33	restrained	restrained	ADJ
ejpam-4451	243	34	2	2	NUM
ejpam-4451	243	35	-	-	PUNCT
ejpam-4451	243	36	resolving	resolving	NOUN
ejpam-4451	243	37	set	set	NOUN
ejpam-4451	243	38	for	for	ADP
ejpam-4451	243	39	each	each	DET
ejpam-4451	243	40	v	v	ADP
ejpam-4451	243	41	∈	∈	PRON
ejpam-4451	243	42	a	a	DET
ejpam-4451	243	43	(	(	PUNCT
ejpam-4451	243	44	iv	iv	NOUN
ejpam-4451	243	45	)	)	PUNCT
ejpam-4451	243	46	w	w	PROPN
ejpam-4451	243	47	∈	∈	PROPN
ejpam-4451	243	48	ng(v	ng(v	PUNCT
ejpam-4451	243	49	(	(	PUNCT
ejpam-4451	243	50	g)\a	g)\a	NOUN
ejpam-4451	243	51	)	)	PUNCT
ejpam-4451	243	52	for	for	ADP
ejpam-4451	243	53	each	each	DET
ejpam-4451	243	54	w	w	PROPN
ejpam-4451	243	55	∈	∈	PROPN
ejpam-4451	243	56	v	v	NOUN
ejpam-4451	243	57	(	(	PUNCT
ejpam-4451	243	58	g)\a	g)\a	NOUN
ejpam-4451	243	59	with	with	ADP
ejpam-4451	243	60	sw	sw	PROPN
ejpam-4451	243	61	=	=	SYM
ejpam-4451	243	62	v	v	PROPN
ejpam-4451	243	63	(	(	PUNCT
ejpam-4451	243	64	hw	hw	NOUN
ejpam-4451	243	65	)	)	PUNCT
ejpam-4451	243	66	.	.	PUNCT
ejpam-4451	244	1	j.	j.	PROPN
ejpam-4451	244	2	cabaro	cabaro	PROPN
ejpam-4451	244	3	,	,	PUNCT
ejpam-4451	244	4	h.	h.	PROPN
ejpam-4451	244	5	rara	rara	PROPN
ejpam-4451	244	6	/	/	SYM
ejpam-4451	244	7	eur	eur	PROPN
ejpam-4451	244	8	.	.	PUNCT
ejpam-4451	245	1	j.	j.	PROPN
ejpam-4451	245	2	pure	pure	PROPN
ejpam-4451	245	3	appl	appl	PROPN
ejpam-4451	245	4	.	.	PROPN
ejpam-4451	245	5	math	math	PROPN
ejpam-4451	245	6	,	,	PUNCT
ejpam-4451	245	7	15	15	NUM
ejpam-4451	245	8	(	(	PUNCT
ejpam-4451	245	9	3	3	NUM
ejpam-4451	245	10	)	)	PUNCT
ejpam-4451	245	11	(	(	PUNCT
ejpam-4451	245	12	2022	2022	NUM
ejpam-4451	245	13	)	)	PUNCT
ejpam-4451	245	14	,	,	PUNCT
ejpam-4451	245	15	1047	1047	NUM
ejpam-4451	245	16	-	-	SYM
ejpam-4451	245	17	1053	1053	NUM
ejpam-4451	245	18	1051	1051	NUM
ejpam-4451	245	19	theorem	theorem	VERB
ejpam-4451	245	20	6	6	NUM
ejpam-4451	245	21	.	.	PUNCT
ejpam-4451	246	1	let	let	VERB
ejpam-4451	246	2	g	g	NOUN
ejpam-4451	246	3	and	and	CCONJ
ejpam-4451	246	4	h	h	NOUN
ejpam-4451	246	5	be	be	AUX
ejpam-4451	246	6	nontrivial	nontrivial	ADJ
ejpam-4451	246	7	connected	connected	ADJ
ejpam-4451	246	8	graphs	graph	NOUN
ejpam-4451	246	9	.	.	PUNCT
ejpam-4451	247	1	then	then	ADV
ejpam-4451	247	2	s	s	VERB
ejpam-4451	247	3	⊆	⊆	NUM
ejpam-4451	247	4	v	v	NOUN
ejpam-4451	247	5	(	(	PUNCT
ejpam-4451	247	6	g	g	PROPN
ejpam-4451	247	7	◦	◦	NOUN
ejpam-4451	247	8	h	h	NOUN
ejpam-4451	247	9	)	)	PUNCT
ejpam-4451	247	10	is	be	AUX
ejpam-4451	247	11	a	a	DET
ejpam-4451	247	12	restrained	restrained	ADJ
ejpam-4451	247	13	2	2	NUM
ejpam-4451	247	14	-	-	PUNCT
ejpam-4451	247	15	resolving	resolve	VERB
ejpam-4451	247	16	dominating	dominating	NOUN
ejpam-4451	247	17	set	set	VERB
ejpam-4451	247	18	in	in	ADP
ejpam-4451	247	19	g	g	PROPN
ejpam-4451	247	20	◦	◦	NOUN
ejpam-4451	247	21	h	h	NOUN
ejpam-4451	247	22	if	if	SCONJ
ejpam-4451	248	1	and	and	CCONJ
ejpam-4451	248	2	only	only	ADV
ejpam-4451	248	3	if	if	SCONJ
ejpam-4451	248	4	s	s	VERB
ejpam-4451	248	5	=	=	NOUN
ejpam-4451	248	6	a	a	DET
ejpam-4451	248	7	∪	∪	X
ejpam-4451	248	8	(	(	PUNCT
ejpam-4451	248	9	⋃	⋃	PROPN
ejpam-4451	248	10	v∈a	v∈a	NOUN
ejpam-4451	248	11	sv	sv	NOUN
ejpam-4451	248	12	)	)	PUNCT
ejpam-4451	248	13	(	(	PUNCT
ejpam-4451	248	14	⋃	⋃	ADP
ejpam-4451	248	15	w∈v	w∈v	PROPN
ejpam-4451	248	16	(	(	PUNCT
ejpam-4451	248	17	g)\a	g)\a	NOUN
ejpam-4451	248	18	sw	sw	PROPN
ejpam-4451	248	19	)	)	PUNCT
ejpam-4451	248	20	satisfying	satisfy	VERB
ejpam-4451	248	21	the	the	DET
ejpam-4451	248	22	following	follow	VERB
ejpam-4451	248	23	conditions	condition	NOUN
ejpam-4451	248	24	.	.	PUNCT
ejpam-4451	249	1	(	(	PUNCT
ejpam-4451	249	2	i	i	NOUN
ejpam-4451	249	3	)	)	PUNCT
ejpam-4451	249	4	a	a	DET
ejpam-4451	249	5	⊆	⊆	NUM
ejpam-4451	249	6	v	v	NOUN
ejpam-4451	249	7	(	(	PUNCT
ejpam-4451	249	8	g	g	NOUN
ejpam-4451	249	9	)	)	PUNCT
ejpam-4451	249	10	(	(	PUNCT
ejpam-4451	249	11	ii	ii	NOUN
ejpam-4451	249	12	)	)	PUNCT
ejpam-4451	249	13	sw	sw	PROPN
ejpam-4451	249	14	is	be	AUX
ejpam-4451	249	15	a	a	DET
ejpam-4451	249	16	2	2	NUM
ejpam-4451	249	17	-	-	PUNCT
ejpam-4451	249	18	resolving	resolve	VERB
ejpam-4451	249	19	dominating	dominating	NOUN
ejpam-4451	249	20	set	set	VERB
ejpam-4451	249	21	in	in	ADP
ejpam-4451	249	22	hw	hw	PRON
ejpam-4451	249	23	for	for	ADP
ejpam-4451	249	24	each	each	DET
ejpam-4451	249	25	w	w	PROPN
ejpam-4451	249	26	∈	∈	PROPN
ejpam-4451	249	27	v	v	NOUN
ejpam-4451	249	28	(	(	PUNCT
ejpam-4451	249	29	g)\a	g)\a	PROPN
ejpam-4451	249	30	(	(	PUNCT
ejpam-4451	249	31	iii	iii	NOUN
ejpam-4451	249	32	)	)	PUNCT
ejpam-4451	249	33	sv	sv	PROPN
ejpam-4451	249	34	is	be	AUX
ejpam-4451	249	35	a	a	DET
ejpam-4451	249	36	restrained	restrained	ADJ
ejpam-4451	249	37	2	2	NUM
ejpam-4451	249	38	-	-	PUNCT
ejpam-4451	249	39	resolving	resolving	NOUN
ejpam-4451	249	40	set	set	VERB
ejpam-4451	249	41	in	in	ADP
ejpam-4451	249	42	hv	hv	PROPN
ejpam-4451	249	43	for	for	ADP
ejpam-4451	249	44	each	each	PRON
ejpam-4451	249	45	v	v	ADP
ejpam-4451	249	46	∈	∈	PRON
ejpam-4451	249	47	a	a	DET
ejpam-4451	249	48	(	(	PUNCT
ejpam-4451	249	49	iv	iv	NOUN
ejpam-4451	249	50	)	)	PUNCT
ejpam-4451	249	51	w	w	PROPN
ejpam-4451	249	52	∈	∈	PROPN
ejpam-4451	249	53	ng(v	ng(v	PUNCT
ejpam-4451	249	54	(	(	PUNCT
ejpam-4451	249	55	g)\a	g)\a	NOUN
ejpam-4451	249	56	)	)	PUNCT
ejpam-4451	249	57	for	for	ADP
ejpam-4451	249	58	each	each	DET
ejpam-4451	249	59	w	w	PROPN
ejpam-4451	249	60	∈	∈	PROPN
ejpam-4451	249	61	v	v	NOUN
ejpam-4451	249	62	(	(	PUNCT
ejpam-4451	249	63	g)\a	g)\a	NOUN
ejpam-4451	249	64	with	with	ADP
ejpam-4451	249	65	sw	sw	PROPN
ejpam-4451	249	66	=	=	SYM
ejpam-4451	249	67	v	v	PROPN
ejpam-4451	249	68	(	(	PUNCT
ejpam-4451	249	69	hw	hw	NOUN
ejpam-4451	249	70	)	)	PUNCT
ejpam-4451	249	71	.	.	PUNCT
ejpam-4451	250	1	proof	proof	NOUN
ejpam-4451	250	2	.	.	PUNCT
ejpam-4451	251	1	suppose	suppose	VERB
ejpam-4451	251	2	s	s	PRON
ejpam-4451	251	3	is	be	AUX
ejpam-4451	251	4	a	a	DET
ejpam-4451	251	5	restrained	restrained	ADJ
ejpam-4451	251	6	2	2	NUM
ejpam-4451	251	7	-	-	PUNCT
ejpam-4451	251	8	resolving	resolve	VERB
ejpam-4451	251	9	dominating	dominating	NOUN
ejpam-4451	251	10	set	set	VERB
ejpam-4451	251	11	in	in	ADP
ejpam-4451	251	12	g	g	PROPN
ejpam-4451	251	13	◦	◦	NOUN
ejpam-4451	251	14	h.	h.	NOUN
ejpam-4451	251	15	by	by	ADP
ejpam-4451	251	16	theorem	theorem	ADJ
ejpam-4451	251	17	5	5	NUM
ejpam-4451	251	18	,	,	PUNCT
ejpam-4451	251	19	conditions	condition	NOUN
ejpam-4451	251	20	(	(	PUNCT
ejpam-4451	251	21	i	i	NOUN
ejpam-4451	251	22	)	)	PUNCT
ejpam-4451	251	23	,	,	PUNCT
ejpam-4451	251	24	(	(	PUNCT
ejpam-4451	251	25	ii	ii	NOUN
ejpam-4451	251	26	)	)	PUNCT
ejpam-4451	251	27	,	,	PUNCT
ejpam-4451	251	28	(	(	PUNCT
ejpam-4451	251	29	iii	iii	NOUN
ejpam-4451	251	30	)	)	PUNCT
ejpam-4451	251	31	and	and	CCONJ
ejpam-4451	251	32	(	(	PUNCT
ejpam-4451	251	33	iv	iv	X
ejpam-4451	251	34	)	)	PUNCT
ejpam-4451	251	35	hold	hold	NOUN
ejpam-4451	251	36	.	.	PUNCT
ejpam-4451	252	1	conversely	conversely	ADV
ejpam-4451	252	2	,	,	PUNCT
ejpam-4451	252	3	suppose	suppose	VERB
ejpam-4451	252	4	s	s	VERB
ejpam-4451	252	5	=	=	SYM
ejpam-4451	252	6	a∪	a∪	PROPN
ejpam-4451	252	7	(	(	PUNCT
ejpam-4451	252	8	⋃	⋃	PROPN
ejpam-4451	252	9	v∈a	v∈a	NOUN
ejpam-4451	252	10	sv	sv	PROPN
ejpam-4451	252	11	)	)	PUNCT
ejpam-4451	252	12	(	(	PUNCT
ejpam-4451	252	13	⋃	⋃	ADP
ejpam-4451	252	14	w∈v	w∈v	PROPN
ejpam-4451	252	15	(	(	PUNCT
ejpam-4451	252	16	g)\a	g)\a	NOUN
ejpam-4451	252	17	sw	sw	PROPN
ejpam-4451	252	18	)	)	PUNCT
ejpam-4451	252	19	satisfying	satisfy	VERB
ejpam-4451	252	20	the	the	DET
ejpam-4451	252	21	conditions	condition	NOUN
ejpam-4451	252	22	(	(	PUNCT
ejpam-4451	252	23	i),(ii),(iii	i),(ii),(iii	NOUN
ejpam-4451	252	24	)	)	PUNCT
ejpam-4451	252	25	and	and	CCONJ
ejpam-4451	252	26	(	(	PUNCT
ejpam-4451	252	27	iv	iv	X
ejpam-4451	252	28	)	)	PUNCT
ejpam-4451	252	29	.	.	PUNCT
ejpam-4451	253	1	then	then	ADV
ejpam-4451	253	2	by	by	ADP
ejpam-4451	253	3	theorem	theorem	NOUN
ejpam-4451	253	4	5	5	NUM
ejpam-4451	253	5	,	,	PUNCT
ejpam-4451	253	6	s	s	VERB
ejpam-4451	253	7	is	be	AUX
ejpam-4451	253	8	a	a	DET
ejpam-4451	253	9	restrained	restrained	ADJ
ejpam-4451	253	10	2	2	NUM
ejpam-4451	253	11	-	-	PUNCT
ejpam-4451	253	12	resolving	resolving	NOUN
ejpam-4451	253	13	set	set	VERB
ejpam-4451	253	14	ing	ing	PROPN
ejpam-4451	253	15	◦	◦	PROPN
ejpam-4451	253	16	h.	h.	PROPN
ejpam-4451	253	17	let	let	VERB
ejpam-4451	253	18	x	x	SYM
ejpam-4451	253	19	∈	∈	PROPN
ejpam-4451	253	20	v	v	X
ejpam-4451	253	21	(	(	PUNCT
ejpam-4451	253	22	g	g	NOUN
ejpam-4451	253	23	◦	◦	NOUN
ejpam-4451	253	24	h)\s	h)\s	NOUN
ejpam-4451	253	25	and	and	CCONJ
ejpam-4451	253	26	let	let	VERB
ejpam-4451	253	27	w	w	PROPN
ejpam-4451	253	28	∈	∈	PROPN
ejpam-4451	253	29	v	v	ADP
ejpam-4451	253	30	(	(	PUNCT
ejpam-4451	253	31	g	g	NOUN
ejpam-4451	253	32	)	)	PUNCT
ejpam-4451	253	33	such	such	ADJ
ejpam-4451	253	34	that	that	SCONJ
ejpam-4451	253	35	x	x	SYM
ejpam-4451	253	36	∈	∈	NOUN
ejpam-4451	253	37	v	v	NOUN
ejpam-4451	253	38	(	(	PUNCT
ejpam-4451	253	39	w	w	NOUN
ejpam-4451	253	40	+	+	NOUN
ejpam-4451	253	41	hw	hw	NOUN
ejpam-4451	253	42	)	)	PUNCT
ejpam-4451	253	43	.	.	PUNCT
ejpam-4451	254	1	if	if	SCONJ
ejpam-4451	254	2	w	w	PROPN
ejpam-4451	254	3	∈	∈	PROPN
ejpam-4451	254	4	s	s	PART
ejpam-4451	254	5	,	,	PUNCT
ejpam-4451	254	6	then	then	ADV
ejpam-4451	254	7	xw	xw	PROPN
ejpam-4451	254	8	∈	∈	PROPN
ejpam-4451	254	9	e(g	e(g	PROPN
ejpam-4451	254	10	◦	◦	PROPN
ejpam-4451	254	11	h	h	NOUN
ejpam-4451	254	12	)	)	PUNCT
ejpam-4451	254	13	.	.	PUNCT
ejpam-4451	255	1	if	if	SCONJ
ejpam-4451	255	2	w	w	PROPN
ejpam-4451	255	3	/∈	/∈	PROPN
ejpam-4451	255	4	s	s	ADP
ejpam-4451	255	5	,	,	PUNCT
ejpam-4451	255	6	then	then	ADV
ejpam-4451	255	7	x	x	X
ejpam-4451	255	8	/∈	/∈	PUNCT
ejpam-4451	255	9	sw	sw	PROPN
ejpam-4451	256	1	=	=	SYM
ejpam-4451	256	2	s	s	PROPN
ejpam-4451	256	3	∩	∩	ADJ
ejpam-4451	256	4	v	v	X
ejpam-4451	256	5	(	(	PUNCT
ejpam-4451	256	6	hw	hw	NOUN
ejpam-4451	256	7	)	)	PUNCT
ejpam-4451	256	8	,	,	PUNCT
ejpam-4451	256	9	where	where	SCONJ
ejpam-4451	256	10	sw	sw	PROPN
ejpam-4451	256	11	is	be	AUX
ejpam-4451	256	12	a	a	DET
ejpam-4451	256	13	2	2	NUM
ejpam-4451	256	14	-	-	PUNCT
ejpam-4451	256	15	resolving	resolve	VERB
ejpam-4451	256	16	dominating	dominating	NOUN
ejpam-4451	256	17	set	set	VERB
ejpam-4451	256	18	in	in	ADP
ejpam-4451	256	19	hw	hw	PRON
ejpam-4451	256	20	.	.	PUNCT
ejpam-4451	257	1	thus	thus	ADV
ejpam-4451	257	2	,	,	PUNCT
ejpam-4451	257	3	there	there	PRON
ejpam-4451	257	4	exists	exist	VERB
ejpam-4451	257	5	z	z	PROPN
ejpam-4451	257	6	∈	∈	PROPN
ejpam-4451	257	7	v	v	ADP
ejpam-4451	257	8	(	(	PUNCT
ejpam-4451	257	9	hw	hw	NOUN
ejpam-4451	257	10	)	)	PUNCT
ejpam-4451	257	11	∩	∩	NOUN
ejpam-4451	257	12	sw	sw	PROPN
ejpam-4451	257	13	such	such	ADJ
ejpam-4451	257	14	that	that	SCONJ
ejpam-4451	257	15	xz	xz	PROPN
ejpam-4451	257	16	∈	∈	PROPN
ejpam-4451	257	17	e(g	e(g	PROPN
ejpam-4451	257	18	◦	◦	PROPN
ejpam-4451	257	19	h	h	NOUN
ejpam-4451	257	20	)	)	PUNCT
ejpam-4451	257	21	.	.	PUNCT
ejpam-4451	258	1	therefore	therefore	ADV
ejpam-4451	258	2	,	,	PUNCT
ejpam-4451	258	3	s	s	VERB
ejpam-4451	258	4	is	be	AUX
ejpam-4451	258	5	a	a	DET
ejpam-4451	258	6	dominating	dominating	NOUN
ejpam-4451	258	7	set	set	VERB
ejpam-4451	258	8	in	in	ADP
ejpam-4451	258	9	g	g	PROPN
ejpam-4451	258	10	◦	◦	NOUN
ejpam-4451	258	11	h.	h.	PROPN
ejpam-4451	258	12	thus	thus	ADV
ejpam-4451	258	13	,	,	PUNCT
ejpam-4451	258	14	s	s	VERB
ejpam-4451	258	15	is	be	AUX
ejpam-4451	258	16	a	a	DET
ejpam-4451	258	17	restrained	restrained	ADJ
ejpam-4451	258	18	2	2	NUM
ejpam-4451	258	19	-	-	PUNCT
ejpam-4451	258	20	resolving	resolve	VERB
ejpam-4451	258	21	dominating	dominating	NOUN
ejpam-4451	258	22	set	set	VERB
ejpam-4451	258	23	in	in	ADP
ejpam-4451	258	24	g	g	PROPN
ejpam-4451	258	25	◦	◦	NOUN
ejpam-4451	258	26	h.	h.	NOUN
ejpam-4451	258	27	corollary	corollary	ADJ
ejpam-4451	258	28	3	3	X
ejpam-4451	258	29	.	.	PUNCT
ejpam-4451	259	1	let	let	VERB
ejpam-4451	259	2	g	g	NOUN
ejpam-4451	259	3	and	and	CCONJ
ejpam-4451	259	4	h	h	NOUN
ejpam-4451	259	5	be	be	AUX
ejpam-4451	259	6	nontrivial	nontrivial	ADJ
ejpam-4451	259	7	connected	connected	ADJ
ejpam-4451	259	8	graphs	graph	NOUN
ejpam-4451	259	9	,	,	PUNCT
ejpam-4451	260	1	where	where	SCONJ
ejpam-4451	260	2	|v	|v	PROPN
ejpam-4451	260	3	(	(	PUNCT
ejpam-4451	260	4	g)|	g)|	PROPN
ejpam-4451	260	5	=	=	NOUN
ejpam-4451	260	6	n.	n.	NOUN
ejpam-4451	260	7	then	then	ADV
ejpam-4451	260	8	γr2r(g	γr2r(g	NUM
ejpam-4451	260	9	◦	◦	NOUN
ejpam-4451	260	10	h	h	NOUN
ejpam-4451	260	11	)	)	PUNCT
ejpam-4451	260	12	≤	≤	NUM
ejpam-4451	260	13	min	min	NOUN
ejpam-4451	260	14	{	{	PUNCT
ejpam-4451	260	15	|v	|v	PROPN
ejpam-4451	260	16	(	(	PUNCT
ejpam-4451	260	17	g)|	g)|	PROPN
ejpam-4451	260	18	·	·	PUNCT
ejpam-4451	260	19	γ2r(h	γ2r(h	PROPN
ejpam-4451	260	20	)	)	PUNCT
ejpam-4451	260	21	,	,	PUNCT
ejpam-4451	260	22	|v	|v	PROPN
ejpam-4451	260	23	(	(	PUNCT
ejpam-4451	260	24	g)|(1	g)|(1	NOUN
ejpam-4451	260	25	+	+	CCONJ
ejpam-4451	260	26	rdim2(h	rdim2(h	NOUN
ejpam-4451	260	27	)	)	PUNCT
ejpam-4451	260	28	)	)	PUNCT
ejpam-4451	260	29	}	}	PUNCT
ejpam-4451	260	30	.	.	PUNCT
ejpam-4451	261	1	the	the	DET
ejpam-4451	261	2	set	set	NOUN
ejpam-4451	261	3	consisting	consisting	NOUN
ejpam-4451	261	4	of	of	ADP
ejpam-4451	261	5	the	the	DET
ejpam-4451	261	6	shaded	shade	VERB
ejpam-4451	261	7	vertices	vertex	NOUN
ejpam-4451	261	8	in	in	ADP
ejpam-4451	261	9	figure	figure	NOUN
ejpam-4451	261	10	2	2	NUM
ejpam-4451	261	11	is	be	AUX
ejpam-4451	261	12	a	a	DET
ejpam-4451	261	13	restrained	restrained	ADJ
ejpam-4451	261	14	2	2	NUM
ejpam-4451	261	15	-	-	PUNCT
ejpam-4451	261	16	resolving	resolve	VERB
ejpam-4451	261	17	dominating	dominating	NOUN
ejpam-4451	261	18	set	set	NOUN
ejpam-4451	261	19	of	of	ADP
ejpam-4451	261	20	the	the	DET
ejpam-4451	261	21	corona	corona	NOUN
ejpam-4451	261	22	p4	p4	PROPN
ejpam-4451	261	23	◦	◦	PROPN
ejpam-4451	261	24	c5	c5	PROPN
ejpam-4451	261	25	.	.	PUNCT
ejpam-4451	262	1	....................................	....................................	PUNCT
ejpam-4451	262	2	....................................	....................................	PUNCT
ejpam-4451	263	1	....................................	....................................	PUNCT
ejpam-4451	263	2	....................................	....................................	PUNCT
ejpam-4451	264	1	....................................	....................................	PUNCT
ejpam-4451	264	2	....................................	....................................	PUNCT
ejpam-4451	265	1	....................................	....................................	PUNCT
ejpam-4451	265	2	....................................	....................................	PUNCT
ejpam-4451	266	1	....................................	....................................	PUNCT
ejpam-4451	266	2	....................................	....................................	PUNCT
ejpam-4451	267	1	....................................	....................................	PUNCT
ejpam-4451	267	2	....................................	....................................	PUNCT
ejpam-4451	268	1	....................................	....................................	PUNCT
ejpam-4451	268	2	....................................	....................................	PUNCT
ejpam-4451	269	1	....................................	....................................	PUNCT
ejpam-4451	269	2	....................................	....................................	PUNCT
ejpam-4451	270	1	....................................	....................................	PUNCT
ejpam-4451	270	2	....................................	....................................	PUNCT
ejpam-4451	271	1	....................................	....................................	PUNCT
ejpam-4451	271	2	........................................................................	........................................................................	PUNCT
ejpam-4451	272	1	....................................	....................................	PUNCT
ejpam-4451	272	2	....................................	....................................	PUNCT
ejpam-4451	273	1	....................................	....................................	PUNCT
ejpam-4451	273	2	......................................................................................................................................................................................................	......................................................................................................................................................................................................	INTJ
ejpam-4451	274	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	INTJ
ejpam-4451	274	2	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4451	275	1	...............................................................	...............................................................	PUNCT
ejpam-4451	275	2	......................................................................................................................................................	......................................................................................................................................................	PUNCT
ejpam-4451	275	3	........	........	PUNCT
ejpam-4451	275	4	........	........	PUNCT
ejpam-4451	275	5	........	........	PUNCT
ejpam-4451	275	6	........	........	PUNCT
ejpam-4451	275	7	........	........	PUNCT
ejpam-4451	275	8	........	........	PUNCT
ejpam-4451	275	9	........	........	PUNCT
ejpam-4451	275	10	........	........	PUNCT
ejpam-4451	275	11	........	........	PUNCT
ejpam-4451	275	12	........	........	PUNCT
ejpam-4451	275	13	........	........	PUNCT
ejpam-4451	275	14	........	........	PUNCT
ejpam-4451	275	15	........	........	PUNCT
ejpam-4451	275	16	........	........	PUNCT
ejpam-4451	275	17	........	........	PUNCT
ejpam-4451	275	18	........	........	PUNCT
ejpam-4451	275	19	........	........	PUNCT
ejpam-4451	275	20	...........	...........	PUNCT
ejpam-4451	275	21	..........	..........	PUNCT
ejpam-4451	276	1	..........	..........	PUNCT
ejpam-4451	276	2	..........	..........	PUNCT
ejpam-4451	277	1	..........	..........	PUNCT
ejpam-4451	277	2	..........	..........	PUNCT
ejpam-4451	278	1	..........	..........	PUNCT
ejpam-4451	278	2	..........	..........	PUNCT
ejpam-4451	279	1	..........	..........	PUNCT
ejpam-4451	279	2	..........	..........	PUNCT
ejpam-4451	280	1	..........	..........	PUNCT
ejpam-4451	280	2	..........	..........	PUNCT
ejpam-4451	281	1	..........	..........	PUNCT
ejpam-4451	281	2	..........	..........	PUNCT
ejpam-4451	281	3	............	............	PUNCT
ejpam-4451	281	4	...........	...........	PUNCT
ejpam-4451	281	5	...........	...........	PUNCT
ejpam-4451	281	6	...........	...........	PUNCT
ejpam-4451	281	7	...........	...........	PUNCT
ejpam-4451	281	8	.......	.......	PUNCT
ejpam-4451	281	9	........................................................................	........................................................................	PUNCT
ejpam-4451	281	10	..........................	..........................	PUNCT
ejpam-4451	281	11	.........................	.........................	PUNCT
ejpam-4451	282	1	.....................	.....................	PUNCT
ejpam-4451	282	2	........................................................................	........................................................................	PUNCT
ejpam-4451	283	1	..........	..........	PUNCT
ejpam-4451	283	2	.........	.........	PUNCT
ejpam-4451	284	1	.........	.........	PUNCT
ejpam-4451	284	2	.........	.........	PUNCT
ejpam-4451	285	1	.........	.........	PUNCT
ejpam-4451	285	2	.........	.........	PUNCT
ejpam-4451	285	3	.........	.........	PUNCT
ejpam-4451	285	4	........	........	PUNCT
ejpam-4451	285	5	............	............	PUNCT
ejpam-4451	285	6	...........	...........	PUNCT
ejpam-4451	285	7	...........	...........	PUNCT
ejpam-4451	285	8	...........	...........	PUNCT
ejpam-4451	285	9	...........	...........	PUNCT
ejpam-4451	285	10	.......	.......	PUNCT
ejpam-4451	285	11	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4451	285	12	............	............	PUNCT
ejpam-4451	285	13	...........	...........	PUNCT
ejpam-4451	285	14	...........	...........	PUNCT
ejpam-4451	285	15	...........	...........	PUNCT
ejpam-4451	285	16	...........	...........	PUNCT
ejpam-4451	285	17	.......	.......	PUNCT
ejpam-4451	286	1	..........	..........	PUNCT
ejpam-4451	286	2	.........	.........	PUNCT
ejpam-4451	287	1	.........	.........	PUNCT
ejpam-4451	287	2	.........	.........	PUNCT
ejpam-4451	288	1	.........	.........	PUNCT
ejpam-4451	288	2	.........	.........	PUNCT
ejpam-4451	288	3	.........	.........	PUNCT
ejpam-4451	289	1	........	........	PUNCT
ejpam-4451	289	2	........................................................................	........................................................................	PUNCT
ejpam-4451	289	3	..........................	..........................	PUNCT
ejpam-4451	289	4	.........................	.........................	PUNCT
ejpam-4451	289	5	.....................	.....................	PUNCT
ejpam-4451	290	1	........................................................................	........................................................................	PUNCT
ejpam-4451	290	2	...............................................................	...............................................................	PUNCT
ejpam-4451	290	3	...........	...........	PUNCT
ejpam-4451	290	4	..........	..........	PUNCT
ejpam-4451	291	1	..........	..........	PUNCT
ejpam-4451	291	2	..........	..........	PUNCT
ejpam-4451	292	1	..........	..........	PUNCT
ejpam-4451	292	2	..........	..........	PUNCT
ejpam-4451	293	1	..........	..........	PUNCT
ejpam-4451	293	2	..........	..........	PUNCT
ejpam-4451	294	1	..........	..........	PUNCT
ejpam-4451	294	2	..........	..........	PUNCT
ejpam-4451	295	1	..........	..........	PUNCT
ejpam-4451	295	2	..........	..........	PUNCT
ejpam-4451	296	1	..........	..........	PUNCT
ejpam-4451	296	2	..........	..........	PUNCT
ejpam-4451	297	1	.........	.........	PUNCT
ejpam-4451	297	2	........	........	PUNCT
ejpam-4451	297	3	........	........	PUNCT
ejpam-4451	297	4	........	........	PUNCT
ejpam-4451	297	5	........	........	PUNCT
ejpam-4451	297	6	........	........	PUNCT
ejpam-4451	297	7	........	........	PUNCT
ejpam-4451	297	8	........	........	PUNCT
ejpam-4451	297	9	........	........	PUNCT
ejpam-4451	297	10	........	........	PUNCT
ejpam-4451	297	11	........	........	PUNCT
ejpam-4451	297	12	........	........	PUNCT
ejpam-4451	297	13	........	........	PUNCT
ejpam-4451	297	14	........	........	PUNCT
ejpam-4451	297	15	........	........	PUNCT
ejpam-4451	297	16	........	........	PUNCT
ejpam-4451	297	17	........	........	PUNCT
ejpam-4451	298	1	........	........	PUNCT
ejpam-4451	298	2	.............................................................................................................................................	.............................................................................................................................................	PUNCT
ejpam-4451	299	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4451	299	2	...............................................................	...............................................................	PUNCT
ejpam-4451	300	1	........................................................................	........................................................................	PUNCT
ejpam-4451	300	2	..........................	..........................	PUNCT
ejpam-4451	300	3	.........................	.........................	PUNCT
ejpam-4451	301	1	.....................	.....................	PUNCT
ejpam-4451	301	2	........................................................................	........................................................................	PUNCT
ejpam-4451	302	1	..........	..........	PUNCT
ejpam-4451	302	2	.........	.........	PUNCT
ejpam-4451	303	1	.........	.........	PUNCT
ejpam-4451	303	2	.........	.........	PUNCT
ejpam-4451	304	1	.........	.........	PUNCT
ejpam-4451	304	2	.........	.........	PUNCT
ejpam-4451	304	3	.........	.........	PUNCT
ejpam-4451	304	4	........	........	PUNCT
ejpam-4451	304	5	............	............	PUNCT
ejpam-4451	304	6	...........	...........	PUNCT
ejpam-4451	304	7	...........	...........	PUNCT
ejpam-4451	304	8	...........	...........	PUNCT
ejpam-4451	304	9	...........	...........	PUNCT
ejpam-4451	304	10	.......	.......	PUNCT
ejpam-4451	304	11	......................................................................................................................................................	......................................................................................................................................................	PUNCT
ejpam-4451	304	12	........	........	PUNCT
ejpam-4451	304	13	........	........	PUNCT
ejpam-4451	304	14	........	........	PUNCT
ejpam-4451	304	15	........	........	PUNCT
ejpam-4451	304	16	........	........	PUNCT
ejpam-4451	304	17	........	........	PUNCT
ejpam-4451	304	18	........	........	PUNCT
ejpam-4451	304	19	........	........	PUNCT
ejpam-4451	304	20	........	........	PUNCT
ejpam-4451	304	21	........	........	PUNCT
ejpam-4451	304	22	........	........	PUNCT
ejpam-4451	304	23	........	........	PUNCT
ejpam-4451	304	24	........	........	PUNCT
ejpam-4451	304	25	........	........	PUNCT
ejpam-4451	304	26	........	........	PUNCT
ejpam-4451	304	27	........	........	PUNCT
ejpam-4451	304	28	........	........	PUNCT
ejpam-4451	304	29	...........	...........	PUNCT
ejpam-4451	305	1	..........	..........	PUNCT
ejpam-4451	305	2	..........	..........	PUNCT
ejpam-4451	306	1	..........	..........	PUNCT
ejpam-4451	306	2	..........	..........	PUNCT
ejpam-4451	307	1	..........	..........	PUNCT
ejpam-4451	307	2	..........	..........	PUNCT
ejpam-4451	308	1	..........	..........	PUNCT
ejpam-4451	308	2	..........	..........	PUNCT
ejpam-4451	309	1	..........	..........	PUNCT
ejpam-4451	309	2	..........	..........	PUNCT
ejpam-4451	310	1	..........	..........	PUNCT
ejpam-4451	310	2	..........	..........	PUNCT
ejpam-4451	311	1	..........	..........	PUNCT
ejpam-4451	311	2	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4451	312	1	...............................................................	...............................................................	PUNCT
ejpam-4451	312	2	........................................................................	........................................................................	PUNCT
ejpam-4451	313	1	..........................	..........................	PUNCT
ejpam-4451	313	2	.........................	.........................	PUNCT
ejpam-4451	314	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	314	2	..........	..........	PUNCT
ejpam-4451	315	1	.........	.........	PUNCT
ejpam-4451	315	2	.........	.........	PUNCT
ejpam-4451	316	1	.........	.........	PUNCT
ejpam-4451	316	2	.........	.........	PUNCT
ejpam-4451	317	1	.........	.........	PUNCT
ejpam-4451	317	2	.........	.........	PUNCT
ejpam-4451	317	3	........	........	PUNCT
ejpam-4451	317	4	............	............	PUNCT
ejpam-4451	317	5	...........	...........	PUNCT
ejpam-4451	317	6	...........	...........	PUNCT
ejpam-4451	317	7	...........	...........	PUNCT
ejpam-4451	317	8	...........	...........	PUNCT
ejpam-4451	317	9	.......	.......	PUNCT
ejpam-4451	317	10	...........	...........	PUNCT
ejpam-4451	317	11	..........	..........	PUNCT
ejpam-4451	318	1	..........	..........	PUNCT
ejpam-4451	318	2	..........	..........	PUNCT
ejpam-4451	319	1	..........	..........	PUNCT
ejpam-4451	319	2	..........	..........	PUNCT
ejpam-4451	320	1	..........	..........	PUNCT
ejpam-4451	320	2	..........	..........	PUNCT
ejpam-4451	321	1	..........	..........	PUNCT
ejpam-4451	321	2	..........	..........	PUNCT
ejpam-4451	322	1	..........	..........	PUNCT
ejpam-4451	322	2	..........	..........	PUNCT
ejpam-4451	323	1	..........	..........	PUNCT
ejpam-4451	323	2	..........	..........	PUNCT
ejpam-4451	324	1	.........	.........	PUNCT
ejpam-4451	324	2	........	........	PUNCT
ejpam-4451	324	3	........	........	PUNCT
ejpam-4451	324	4	........	........	PUNCT
ejpam-4451	324	5	........	........	PUNCT
ejpam-4451	324	6	........	........	PUNCT
ejpam-4451	324	7	........	........	PUNCT
ejpam-4451	324	8	........	........	PUNCT
ejpam-4451	324	9	........	........	PUNCT
ejpam-4451	324	10	........	........	PUNCT
ejpam-4451	324	11	........	........	PUNCT
ejpam-4451	324	12	........	........	PUNCT
ejpam-4451	324	13	........	........	PUNCT
ejpam-4451	324	14	........	........	PUNCT
ejpam-4451	324	15	........	........	PUNCT
ejpam-4451	324	16	........	........	PUNCT
ejpam-4451	324	17	........	........	PUNCT
ejpam-4451	325	1	........	........	PUNCT
ejpam-4451	325	2	.............................................................................................................................................	.............................................................................................................................................	PUNCT
ejpam-4451	326	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	326	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	327	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	327	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	328	1	•	•	NUM
ejpam-4451	328	2	••	••	NOUN
ejpam-4451	328	3	•	•	NOUN
ejpam-4451	328	4	••	••	NOUN
ejpam-4451	328	5	•	•	NUM
ejpam-4451	328	6	•	•	NOUN
ejpam-4451	328	7	•	•	NOUN
ejpam-4451	328	8	••	••	NOUN
ejpam-4451	328	9	•	•	NUM
ejpam-4451	328	10	figure	figure	NOUN
ejpam-4451	328	11	2	2	NUM
ejpam-4451	328	12	:	:	PUNCT
ejpam-4451	328	13	a	a	DET
ejpam-4451	328	14	graph	graph	NOUN
ejpam-4451	328	15	p4	p4	ADJ
ejpam-4451	328	16	◦	◦	PROPN
ejpam-4451	328	17	c5	c5	PROPN
ejpam-4451	328	18	with	with	ADP
ejpam-4451	328	19	γr2r(p4	γr2r(p4	PROPN
ejpam-4451	328	20	◦	◦	PROPN
ejpam-4451	328	21	c5	c5	PROPN
ejpam-4451	328	22	)	)	PUNCT
ejpam-4451	329	1	=	=	PROPN
ejpam-4451	329	2	12	12	NUM
ejpam-4451	329	3	j.	j.	PROPN
ejpam-4451	329	4	cabaro	cabaro	PROPN
ejpam-4451	329	5	,	,	PUNCT
ejpam-4451	329	6	h.	h.	PROPN
ejpam-4451	329	7	rara	rara	PROPN
ejpam-4451	329	8	/	/	SYM
ejpam-4451	329	9	eur	eur	PROPN
ejpam-4451	329	10	.	.	PUNCT
ejpam-4451	330	1	j.	j.	PROPN
ejpam-4451	330	2	pure	pure	PROPN
ejpam-4451	330	3	appl	appl	PROPN
ejpam-4451	330	4	.	.	PROPN
ejpam-4451	330	5	math	math	PROPN
ejpam-4451	330	6	,	,	PUNCT
ejpam-4451	330	7	15	15	NUM
ejpam-4451	330	8	(	(	PUNCT
ejpam-4451	330	9	3	3	NUM
ejpam-4451	330	10	)	)	PUNCT
ejpam-4451	330	11	(	(	PUNCT
ejpam-4451	330	12	2022	2022	NUM
ejpam-4451	330	13	)	)	PUNCT
ejpam-4451	330	14	,	,	PUNCT
ejpam-4451	330	15	1047	1047	NUM
ejpam-4451	330	16	-	-	SYM
ejpam-4451	330	17	1053	1053	NUM
ejpam-4451	330	18	1052	1052	NUM
ejpam-4451	330	19	5	5	NUM
ejpam-4451	330	20	.	.	PUNCT
ejpam-4451	331	1	restrained	restrain	VERB
ejpam-4451	331	2	2	2	NUM
ejpam-4451	331	3	-	-	PUNCT
ejpam-4451	331	4	resolving	resolve	VERB
ejpam-4451	331	5	dominating	dominating	NOUN
ejpam-4451	331	6	sets	set	NOUN
ejpam-4451	331	7	in	in	ADP
ejpam-4451	331	8	the	the	DET
ejpam-4451	331	9	lexicographic	lexicographic	ADJ
ejpam-4451	331	10	product	product	NOUN
ejpam-4451	331	11	of	of	ADP
ejpam-4451	331	12	graphs	graph	NOUN
ejpam-4451	331	13	theorem	theorem	VERB
ejpam-4451	331	14	7	7	NUM
ejpam-4451	331	15	.	.	PUNCT
ejpam-4451	332	1	[	[	X
ejpam-4451	332	2	7	7	X
ejpam-4451	332	3	]	]	X
ejpam-4451	332	4	let	let	VERB
ejpam-4451	332	5	g	g	NOUN
ejpam-4451	332	6	and	and	CCONJ
ejpam-4451	332	7	h	h	PROPN
ejpam-4451	332	8	be	be	VERB
ejpam-4451	332	9	non	non	ADJ
ejpam-4451	332	10	-	-	ADJ
ejpam-4451	332	11	trivial	trivial	ADJ
ejpam-4451	332	12	connected	connected	ADJ
ejpam-4451	332	13	graphs	graph	NOUN
ejpam-4451	332	14	.	.	PUNCT
ejpam-4451	333	1	then	then	ADV
ejpam-4451	333	2	w	w	NOUN
ejpam-4451	333	3	=	=	PUNCT
ejpam-4451	333	4	⋃	⋃	PROPN
ejpam-4451	333	5	x∈s	x∈s	NOUN
ejpam-4451	333	6	[	[	PUNCT
ejpam-4451	333	7	{	{	PUNCT
ejpam-4451	333	8	x	x	NOUN
ejpam-4451	333	9	}	}	PUNCT
ejpam-4451	333	10	×	×	NOUN
ejpam-4451	333	11	tx	tx	PROPN
ejpam-4451	333	12	]	]	PUNCT
ejpam-4451	333	13	,	,	PUNCT
ejpam-4451	333	14	where	where	SCONJ
ejpam-4451	333	15	s	s	VERB
ejpam-4451	333	16	⊆	⊆	NUM
ejpam-4451	333	17	v	v	NOUN
ejpam-4451	333	18	(	(	PUNCT
ejpam-4451	333	19	g	g	NOUN
ejpam-4451	333	20	)	)	PUNCT
ejpam-4451	333	21	and	and	CCONJ
ejpam-4451	333	22	tx	tx	VERB
ejpam-4451	333	23	⊆	⊆	NUM
ejpam-4451	333	24	v	v	NOUN
ejpam-4451	333	25	(	(	PUNCT
ejpam-4451	333	26	h	h	NOUN
ejpam-4451	333	27	)	)	PUNCT
ejpam-4451	333	28	for	for	ADP
ejpam-4451	333	29	each	each	DET
ejpam-4451	333	30	x	x	SYM
ejpam-4451	333	31	∈	∈	PROPN
ejpam-4451	333	32	s	s	NOUN
ejpam-4451	333	33	,	,	PUNCT
ejpam-4451	333	34	is	be	AUX
ejpam-4451	333	35	a	a	DET
ejpam-4451	333	36	restrained	restrained	ADJ
ejpam-4451	333	37	2	2	NUM
ejpam-4451	333	38	-	-	PUNCT
ejpam-4451	333	39	resolving	resolving	NOUN
ejpam-4451	333	40	set	set	VERB
ejpam-4451	333	41	in	in	ADP
ejpam-4451	333	42	g[h	g[h	PROPN
ejpam-4451	333	43	]	]	PUNCT
ejpam-4451	333	44	if	if	SCONJ
ejpam-4451	333	45	and	and	CCONJ
ejpam-4451	333	46	only	only	ADV
ejpam-4451	333	47	if	if	SCONJ
ejpam-4451	333	48	(	(	PUNCT
ejpam-4451	333	49	i	i	NOUN
ejpam-4451	333	50	)	)	PUNCT
ejpam-4451	333	51	s	s	PART
ejpam-4451	333	52	=	=	SYM
ejpam-4451	333	53	v	v	X
ejpam-4451	333	54	(	(	PUNCT
ejpam-4451	333	55	g	g	NOUN
ejpam-4451	333	56	)	)	PUNCT
ejpam-4451	333	57	(	(	PUNCT
ejpam-4451	333	58	ii	ii	NOUN
ejpam-4451	333	59	)	)	PUNCT
ejpam-4451	333	60	tx	tx	PROPN
ejpam-4451	333	61	is	be	AUX
ejpam-4451	333	62	a	a	DET
ejpam-4451	333	63	2	2	NUM
ejpam-4451	333	64	-	-	PUNCT
ejpam-4451	333	65	locating	locate	VERB
ejpam-4451	333	66	set	set	NOUN
ejpam-4451	333	67	in	in	ADP
ejpam-4451	333	68	h	h	NOUN
ejpam-4451	333	69	for	for	ADP
ejpam-4451	333	70	all	all	PRON
ejpam-4451	333	71	x	x	SYM
ejpam-4451	333	72	∈	∈	PROPN
ejpam-4451	333	73	v	v	NOUN
ejpam-4451	333	74	(	(	PUNCT
ejpam-4451	333	75	g	g	NOUN
ejpam-4451	333	76	)	)	PUNCT
ejpam-4451	333	77	;	;	PUNCT
ejpam-4451	333	78	(	(	PUNCT
ejpam-4451	333	79	iii	iii	X
ejpam-4451	333	80	)	)	PUNCT
ejpam-4451	333	81	tx	tx	PROPN
ejpam-4451	333	82	is	be	AUX
ejpam-4451	333	83	a	a	DET
ejpam-4451	333	84	restrained	restrained	ADJ
ejpam-4451	333	85	2	2	NUM
ejpam-4451	333	86	-	-	PUNCT
ejpam-4451	333	87	locating	locate	VERB
ejpam-4451	333	88	set	set	NOUN
ejpam-4451	333	89	for	for	ADP
ejpam-4451	333	90	each	each	PRON
ejpam-4451	333	91	x	x	PUNCT
ejpam-4451	333	92	with	with	ADP
ejpam-4451	333	93	ty	ty	NOUN
ejpam-4451	333	94	=	=	SYM
ejpam-4451	333	95	v	v	NOUN
ejpam-4451	333	96	(	(	PUNCT
ejpam-4451	333	97	h	h	NOUN
ejpam-4451	333	98	)	)	PUNCT
ejpam-4451	333	99	,	,	PUNCT
ejpam-4451	333	100	for	for	ADP
ejpam-4451	333	101	all	all	DET
ejpam-4451	333	102	y	y	PROPN
ejpam-4451	333	103	∈	∈	PROPN
ejpam-4451	333	104	ng(x	ng(x	NUM
ejpam-4451	333	105	)	)	PUNCT
ejpam-4451	333	106	;	;	PUNCT
ejpam-4451	333	107	(	(	PUNCT
ejpam-4451	333	108	iv	iv	X
ejpam-4451	333	109	)	)	PUNCT
ejpam-4451	333	110	tx	tx	PROPN
ejpam-4451	333	111	and	and	CCONJ
ejpam-4451	333	112	ty	ty	INTJ
ejpam-4451	333	113	are	be	AUX
ejpam-4451	333	114	(	(	PUNCT
ejpam-4451	333	115	2	2	NUM
ejpam-4451	333	116	,	,	PUNCT
ejpam-4451	333	117	1)-locating	1)-locating	NUM
ejpam-4451	333	118	sets	set	NOUN
ejpam-4451	333	119	or	or	CCONJ
ejpam-4451	333	120	one	one	NUM
ejpam-4451	333	121	of	of	ADP
ejpam-4451	333	122	tx	tx	PROPN
ejpam-4451	333	123	and	and	CCONJ
ejpam-4451	333	124	ty	ty	PRON
ejpam-4451	333	125	is	be	AUX
ejpam-4451	333	126	a	a	DET
ejpam-4451	333	127	(	(	PUNCT
ejpam-4451	333	128	2	2	NUM
ejpam-4451	333	129	,	,	PUNCT
ejpam-4451	333	130	2)-locating	2)-locating	NUM
ejpam-4451	333	131	set	set	VERB
ejpam-4451	333	132	in	in	ADP
ejpam-4451	333	133	h	h	NOUN
ejpam-4451	333	134	whenever	whenever	SCONJ
ejpam-4451	333	135	x	x	X
ejpam-4451	333	136	,	,	PUNCT
ejpam-4451	333	137	y	y	PROPN
ejpam-4451	333	138	∈	∈	PROPN
ejpam-4451	333	139	eq1(g	eq1(g	PROPN
ejpam-4451	333	140	)	)	PUNCT
ejpam-4451	333	141	;	;	PUNCT
ejpam-4451	333	142	and	and	CCONJ
ejpam-4451	333	143	(	(	PUNCT
ejpam-4451	333	144	v	v	NOUN
ejpam-4451	333	145	)	)	PUNCT
ejpam-4451	333	146	tx	tx	NOUN
ejpam-4451	333	147	and	and	CCONJ
ejpam-4451	333	148	ty	ty	INTJ
ejpam-4451	333	149	are	be	AUX
ejpam-4451	333	150	(	(	PUNCT
ejpam-4451	333	151	2	2	NUM
ejpam-4451	333	152	-	-	PUNCT
ejpam-4451	333	153	locating	locating	NOUN
ejpam-4451	333	154	)	)	PUNCT
ejpam-4451	333	155	dominating	dominating	NOUN
ejpam-4451	333	156	sets	set	NOUN
ejpam-4451	333	157	in	in	ADP
ejpam-4451	333	158	h	h	NOUN
ejpam-4451	333	159	or	or	CCONJ
ejpam-4451	333	160	if	if	SCONJ
ejpam-4451	333	161	one	one	NUM
ejpam-4451	333	162	of	of	ADP
ejpam-4451	333	163	tx	tx	PROPN
ejpam-4451	333	164	and	and	CCONJ
ejpam-4451	333	165	ty	ty	INTJ
ejpam-4451	333	166	,	,	PUNCT
ejpam-4451	333	167	say	say	VERB
ejpam-4451	333	168	tx	tx	PROPN
ejpam-4451	333	169	is	be	AUX
ejpam-4451	333	170	not	not	PART
ejpam-4451	333	171	dominating	dominate	VERB
ejpam-4451	333	172	,	,	PUNCT
ejpam-4451	333	173	then	then	ADV
ejpam-4451	333	174	ty	ty	PRON
ejpam-4451	333	175	is	be	VERB
ejpam-4451	333	176	2	2	NUM
ejpam-4451	333	177	-	-	PUNCT
ejpam-4451	333	178	dominating	dominate	VERB
ejpam-4451	333	179	whenever	whenever	SCONJ
ejpam-4451	333	180	x	x	X
ejpam-4451	333	181	,	,	PUNCT
ejpam-4451	333	182	y	y	PROPN
ejpam-4451	333	183	∈	∈	PROPN
ejpam-4451	333	184	eq2(g	eq2(g	VERB
ejpam-4451	333	185	)	)	PUNCT
ejpam-4451	333	186	.	.	PUNCT
ejpam-4451	334	1	theorem	theorem	ADJ
ejpam-4451	334	2	8	8	NUM
ejpam-4451	334	3	.	.	PUNCT
ejpam-4451	335	1	let	let	VERB
ejpam-4451	335	2	g	g	NOUN
ejpam-4451	335	3	and	and	CCONJ
ejpam-4451	335	4	h	h	PROPN
ejpam-4451	335	5	be	be	VERB
ejpam-4451	335	6	non	non	ADJ
ejpam-4451	335	7	-	-	ADJ
ejpam-4451	335	8	trivial	trivial	ADJ
ejpam-4451	335	9	connected	connected	ADJ
ejpam-4451	335	10	graphs	graph	NOUN
ejpam-4451	335	11	.	.	PUNCT
ejpam-4451	336	1	then	then	ADV
ejpam-4451	336	2	w	w	NOUN
ejpam-4451	336	3	=	=	PUNCT
ejpam-4451	336	4	⋃	⋃	PROPN
ejpam-4451	336	5	x∈s	x∈s	NOUN
ejpam-4451	336	6	[	[	PUNCT
ejpam-4451	336	7	{	{	PUNCT
ejpam-4451	336	8	x	x	NOUN
ejpam-4451	336	9	}	}	PUNCT
ejpam-4451	336	10	×	×	NOUN
ejpam-4451	336	11	tx	tx	PROPN
ejpam-4451	336	12	]	]	PUNCT
ejpam-4451	336	13	,	,	PUNCT
ejpam-4451	336	14	where	where	SCONJ
ejpam-4451	336	15	s	s	VERB
ejpam-4451	336	16	⊆	⊆	NUM
ejpam-4451	336	17	v	v	NOUN
ejpam-4451	336	18	(	(	PUNCT
ejpam-4451	336	19	g	g	NOUN
ejpam-4451	336	20	)	)	PUNCT
ejpam-4451	336	21	and	and	CCONJ
ejpam-4451	336	22	tx	tx	VERB
ejpam-4451	336	23	⊆	⊆	NUM
ejpam-4451	336	24	v	v	NOUN
ejpam-4451	336	25	(	(	PUNCT
ejpam-4451	336	26	h	h	NOUN
ejpam-4451	336	27	)	)	PUNCT
ejpam-4451	336	28	for	for	ADP
ejpam-4451	336	29	each	each	DET
ejpam-4451	336	30	x	x	SYM
ejpam-4451	336	31	∈	∈	PROPN
ejpam-4451	336	32	s	s	NOUN
ejpam-4451	336	33	,	,	PUNCT
ejpam-4451	336	34	is	be	AUX
ejpam-4451	336	35	a	a	DET
ejpam-4451	336	36	restrained	restrained	ADJ
ejpam-4451	336	37	2	2	NUM
ejpam-4451	336	38	-	-	PUNCT
ejpam-4451	336	39	resolving	resolve	VERB
ejpam-4451	336	40	dominating	dominating	NOUN
ejpam-4451	336	41	set	set	VERB
ejpam-4451	336	42	in	in	ADP
ejpam-4451	336	43	g[h	g[h	PROPN
ejpam-4451	336	44	]	]	PUNCT
ejpam-4451	336	45	if	if	SCONJ
ejpam-4451	336	46	and	and	CCONJ
ejpam-4451	336	47	only	only	ADV
ejpam-4451	336	48	if	if	SCONJ
ejpam-4451	336	49	it	it	PRON
ejpam-4451	336	50	is	be	AUX
ejpam-4451	336	51	a	a	DET
ejpam-4451	336	52	restrained	restrained	ADJ
ejpam-4451	336	53	2	2	NUM
ejpam-4451	336	54	-	-	PUNCT
ejpam-4451	336	55	resolving	resolving	NOUN
ejpam-4451	336	56	set	set	VERB
ejpam-4451	336	57	in	in	ADP
ejpam-4451	336	58	g[h	g[h	NOUN
ejpam-4451	336	59	]	]	PUNCT
ejpam-4451	336	60	.	.	PUNCT
ejpam-4451	337	1	proof	proof	NOUN
ejpam-4451	337	2	.	.	PUNCT
ejpam-4451	338	1	suppose	suppose	VERB
ejpam-4451	338	2	w	w	PROPN
ejpam-4451	338	3	=	=	PUNCT
ejpam-4451	338	4	⋃	⋃	PROPN
ejpam-4451	338	5	x∈s	x∈s	NOUN
ejpam-4451	338	6	[	[	PUNCT
ejpam-4451	338	7	{	{	PUNCT
ejpam-4451	338	8	x	x	NOUN
ejpam-4451	338	9	}	}	PUNCT
ejpam-4451	338	10	×	×	NOUN
ejpam-4451	338	11	tx	tx	NOUN
ejpam-4451	338	12	]	]	PUNCT
ejpam-4451	338	13	where	where	SCONJ
ejpam-4451	338	14	s	s	VERB
ejpam-4451	338	15	⊆	⊆	NUM
ejpam-4451	338	16	v	v	NOUN
ejpam-4451	338	17	(	(	PUNCT
ejpam-4451	338	18	g	g	NOUN
ejpam-4451	338	19	)	)	PUNCT
ejpam-4451	338	20	and	and	CCONJ
ejpam-4451	338	21	tx	tx	VERB
ejpam-4451	338	22	⊆	⊆	NUM
ejpam-4451	338	23	v	v	NOUN
ejpam-4451	338	24	(	(	PUNCT
ejpam-4451	338	25	h	h	NOUN
ejpam-4451	338	26	)	)	PUNCT
ejpam-4451	338	27	is	be	AUX
ejpam-4451	338	28	a	a	DET
ejpam-4451	338	29	restrained	restrained	ADJ
ejpam-4451	338	30	2	2	NUM
ejpam-4451	338	31	-	-	PUNCT
ejpam-4451	338	32	resolving	resolve	VERB
ejpam-4451	338	33	dominating	dominating	NOUN
ejpam-4451	338	34	set	set	VERB
ejpam-4451	338	35	in	in	ADP
ejpam-4451	338	36	g[h	g[h	PROPN
ejpam-4451	338	37	]	]	PUNCT
ejpam-4451	338	38	.	.	PUNCT
ejpam-4451	339	1	then	then	ADV
ejpam-4451	339	2	w	w	PROPN
ejpam-4451	339	3	is	be	AUX
ejpam-4451	339	4	a	a	DET
ejpam-4451	339	5	restrained	restrained	ADJ
ejpam-4451	339	6	2	2	NUM
ejpam-4451	339	7	-	-	PUNCT
ejpam-4451	339	8	resolving	resolving	NOUN
ejpam-4451	339	9	set	set	VERB
ejpam-4451	339	10	in	in	ADP
ejpam-4451	339	11	g[h	g[h	NOUN
ejpam-4451	339	12	]	]	PUNCT
ejpam-4451	339	13	.	.	PUNCT
ejpam-4451	340	1	for	for	ADP
ejpam-4451	340	2	the	the	DET
ejpam-4451	340	3	converse	converse	NOUN
ejpam-4451	340	4	,	,	PUNCT
ejpam-4451	340	5	suppose	suppose	VERB
ejpam-4451	340	6	that	that	SCONJ
ejpam-4451	340	7	w	w	NOUN
ejpam-4451	340	8	is	be	AUX
ejpam-4451	340	9	a	a	DET
ejpam-4451	340	10	restrained	restrained	ADJ
ejpam-4451	340	11	2	2	NUM
ejpam-4451	340	12	-	-	PUNCT
ejpam-4451	340	13	resolving	resolving	NOUN
ejpam-4451	340	14	set	set	VERB
ejpam-4451	340	15	in	in	ADP
ejpam-4451	340	16	g[h	g[h	PROPN
ejpam-4451	340	17	]	]	PUNCT
ejpam-4451	340	18	.	.	PUNCT
ejpam-4451	341	1	then	then	ADV
ejpam-4451	341	2	by	by	ADP
ejpam-4451	341	3	theorem	theorem	NOUN
ejpam-4451	341	4	7	7	NUM
ejpam-4451	341	5	,	,	PUNCT
ejpam-4451	341	6	(	(	PUNCT
ejpam-4451	341	7	i)-(v	i)-(v	PROPN
ejpam-4451	341	8	)	)	PUNCT
ejpam-4451	341	9	hold	hold	VERB
ejpam-4451	341	10	.	.	PUNCT
ejpam-4451	342	1	since	since	SCONJ
ejpam-4451	342	2	w	w	PROPN
ejpam-4451	342	3	is	be	AUX
ejpam-4451	342	4	a	a	DET
ejpam-4451	342	5	2	2	NUM
ejpam-4451	342	6	-	-	PUNCT
ejpam-4451	342	7	resolving	resolve	VERB
ejpam-4451	342	8	set	set	NOUN
ejpam-4451	342	9	,	,	PUNCT
ejpam-4451	342	10	tx	tx	PROPN
ejpam-4451	342	11	̸=	̸=	PROPN
ejpam-4451	342	12	∅	∅	NOUN
ejpam-4451	342	13	for	for	ADP
ejpam-4451	342	14	every	every	DET
ejpam-4451	342	15	x	x	SYM
ejpam-4451	342	16	∈	∈	PROPN
ejpam-4451	342	17	v	v	NOUN
ejpam-4451	342	18	(	(	PUNCT
ejpam-4451	342	19	g	g	NOUN
ejpam-4451	342	20	)	)	PUNCT
ejpam-4451	342	21	.	.	PUNCT
ejpam-4451	343	1	thus	thus	ADV
ejpam-4451	343	2	,	,	PUNCT
ejpam-4451	343	3	w	w	PROPN
ejpam-4451	343	4	is	be	AUX
ejpam-4451	343	5	a	a	DET
ejpam-4451	343	6	dominating	dominating	NOUN
ejpam-4451	343	7	set	set	VERB
ejpam-4451	343	8	in	in	ADP
ejpam-4451	343	9	g[h	g[h	PROPN
ejpam-4451	343	10	]	]	PUNCT
ejpam-4451	343	11	.	.	PUNCT
ejpam-4451	344	1	therefore	therefore	ADV
ejpam-4451	344	2	,	,	PUNCT
ejpam-4451	344	3	w	w	PROPN
ejpam-4451	344	4	is	be	AUX
ejpam-4451	344	5	a	a	DET
ejpam-4451	344	6	restrained	restrained	ADJ
ejpam-4451	344	7	2	2	NUM
ejpam-4451	344	8	-	-	PUNCT
ejpam-4451	344	9	resolving	resolve	VERB
ejpam-4451	344	10	dominating	dominating	NOUN
ejpam-4451	344	11	set	set	VERB
ejpam-4451	344	12	in	in	ADP
ejpam-4451	344	13	g[h	g[h	PROPN
ejpam-4451	344	14	]	]	PUNCT
ejpam-4451	344	15	.	.	PUNCT
ejpam-4451	345	1	the	the	DET
ejpam-4451	345	2	following	follow	VERB
ejpam-4451	345	3	are	be	AUX
ejpam-4451	345	4	the	the	DET
ejpam-4451	345	5	direct	direct	ADJ
ejpam-4451	345	6	consequences	consequence	NOUN
ejpam-4451	345	7	of	of	ADP
ejpam-4451	345	8	theorem	theorem	ADJ
ejpam-4451	345	9	8	8	NUM
ejpam-4451	345	10	.	.	PUNCT
ejpam-4451	345	11	corollary	corollary	ADJ
ejpam-4451	345	12	4	4	NUM
ejpam-4451	345	13	.	.	PUNCT
ejpam-4451	346	1	let	let	VERB
ejpam-4451	346	2	g	g	NOUN
ejpam-4451	346	3	and	and	CCONJ
ejpam-4451	346	4	h	h	NOUN
ejpam-4451	346	5	be	be	AUX
ejpam-4451	346	6	nontrivial	nontrivial	ADJ
ejpam-4451	346	7	connected	connect	VERB
ejpam-4451	346	8	graphs	graph	NOUN
ejpam-4451	346	9	such	such	ADJ
ejpam-4451	346	10	that	that	SCONJ
ejpam-4451	346	11	g	g	PROPN
ejpam-4451	346	12	is	be	AUX
ejpam-4451	346	13	not	not	PART
ejpam-4451	346	14	freeequidistant	freeequidistant	ADJ
ejpam-4451	346	15	.	.	PUNCT
ejpam-4451	347	1	then	then	ADV
ejpam-4451	347	2	,	,	PUNCT
ejpam-4451	347	3	γr2r(g[h	γr2r(g[h	PROPN
ejpam-4451	347	4	]	]	X
ejpam-4451	347	5	)	)	PUNCT
ejpam-4451	347	6	=	=	SYM
ejpam-4451	347	7	rdim2(g[h	rdim2(g[h	PROPN
ejpam-4451	347	8	]	]	PUNCT
ejpam-4451	347	9	)	)	PUNCT
ejpam-4451	347	10	.	.	PUNCT
ejpam-4451	348	1	the	the	DET
ejpam-4451	348	2	following	following	ADJ
ejpam-4451	348	3	result	result	NOUN
ejpam-4451	348	4	follows	follow	VERB
ejpam-4451	348	5	from	from	ADP
ejpam-4451	348	6	theorem	theorem	ADJ
ejpam-4451	348	7	8	8	NUM
ejpam-4451	348	8	.	.	PUNCT
ejpam-4451	348	9	corollary	corollary	ADJ
ejpam-4451	348	10	5	5	NUM
ejpam-4451	348	11	.	.	PUNCT
ejpam-4451	348	12	letg	letg	NOUN
ejpam-4451	348	13	andh	andh	NOUN
ejpam-4451	348	14	be	be	VERB
ejpam-4451	348	15	non	non	ADJ
ejpam-4451	348	16	-	-	ADJ
ejpam-4451	348	17	trivial	trivial	ADJ
ejpam-4451	348	18	connected	connected	ADJ
ejpam-4451	348	19	graphs	graph	NOUN
ejpam-4451	348	20	such	such	ADJ
ejpam-4451	348	21	thatg	thatg	PROPN
ejpam-4451	348	22	is	be	AUX
ejpam-4451	348	23	free	free	ADJ
ejpam-4451	348	24	-	-	PUNCT
ejpam-4451	348	25	equidistant	equidistant	NOUN
ejpam-4451	348	26	.	.	PUNCT
ejpam-4451	349	1	then	then	ADV
ejpam-4451	349	2	γr2r(g[h	γr2r(g[h	X
ejpam-4451	349	3	]	]	X
ejpam-4451	349	4	)	)	PUNCT
ejpam-4451	349	5	=	=	SYM
ejpam-4451	349	6	rdim2(g[h	rdim2(g[h	PROPN
ejpam-4451	349	7	]	]	PUNCT
ejpam-4451	349	8	)	)	PUNCT
ejpam-4451	349	9	.	.	PUNCT
ejpam-4451	350	1	the	the	DET
ejpam-4451	350	2	set	set	NOUN
ejpam-4451	350	3	consisting	consisting	NOUN
ejpam-4451	350	4	of	of	ADP
ejpam-4451	350	5	the	the	DET
ejpam-4451	350	6	shaded	shade	VERB
ejpam-4451	350	7	vertices	vertex	NOUN
ejpam-4451	350	8	in	in	ADP
ejpam-4451	350	9	figure	figure	NOUN
ejpam-4451	350	10	3	3	NUM
ejpam-4451	350	11	is	be	AUX
ejpam-4451	350	12	a	a	DET
ejpam-4451	350	13	restrained	restrained	ADJ
ejpam-4451	350	14	2	2	NUM
ejpam-4451	350	15	-	-	PUNCT
ejpam-4451	350	16	resolving	resolve	VERB
ejpam-4451	350	17	dominating	dominating	NOUN
ejpam-4451	350	18	set	set	NOUN
ejpam-4451	350	19	of	of	ADP
ejpam-4451	350	20	the	the	DET
ejpam-4451	350	21	lexicographic	lexicographic	ADJ
ejpam-4451	350	22	product	product	NOUN
ejpam-4451	350	23	p4[p3	p4[p3	NOUN
ejpam-4451	350	24	]	]	X
ejpam-4451	350	25	.	.	PUNCT
ejpam-4451	351	1	references	reference	NOUN
ejpam-4451	351	2	1053	1053	NUM
ejpam-4451	351	3	....................................	....................................	PUNCT
ejpam-4451	351	4	....................................	....................................	PUNCT
ejpam-4451	352	1	....................................	....................................	PUNCT
ejpam-4451	352	2	....................................	....................................	PUNCT
ejpam-4451	353	1	....................................	....................................	PUNCT
ejpam-4451	353	2	....................................	....................................	PUNCT
ejpam-4451	354	1	....................................	....................................	PUNCT
ejpam-4451	354	2	....................................	....................................	PUNCT
ejpam-4451	355	1	....................................	....................................	PUNCT
ejpam-4451	355	2	....................................	....................................	PUNCT
ejpam-4451	356	1	....................................	....................................	PUNCT
ejpam-4451	356	2	....................................	....................................	PUNCT
ejpam-4451	357	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	357	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	358	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	358	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	359	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	359	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	360	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	360	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4451	360	3	.........	.........	PUNCT
ejpam-4451	360	4	........	........	PUNCT
ejpam-4451	360	5	........	........	PUNCT
ejpam-4451	360	6	........	........	PUNCT
ejpam-4451	360	7	........	........	PUNCT
ejpam-4451	360	8	........	........	PUNCT
ejpam-4451	360	9	........	........	PUNCT
ejpam-4451	360	10	........	........	PUNCT
ejpam-4451	360	11	........	........	PUNCT
ejpam-4451	360	12	........	........	PUNCT
ejpam-4451	360	13	........	........	PUNCT
ejpam-4451	361	1	....	....	PUNCT
ejpam-4451	361	2	.........	.........	PUNCT
ejpam-4451	361	3	........	........	PUNCT
ejpam-4451	361	4	........	........	PUNCT
ejpam-4451	361	5	........	........	PUNCT
ejpam-4451	361	6	........	........	PUNCT
ejpam-4451	361	7	........	........	PUNCT
ejpam-4451	361	8	........	........	PUNCT
ejpam-4451	361	9	........	........	PUNCT
ejpam-4451	361	10	........	........	PUNCT
ejpam-4451	361	11	........	........	PUNCT
ejpam-4451	361	12	........	........	PUNCT
ejpam-4451	362	1	....	....	PUNCT
ejpam-4451	362	2	.........	.........	PUNCT
ejpam-4451	362	3	........	........	PUNCT
ejpam-4451	362	4	........	........	PUNCT
ejpam-4451	362	5	........	........	PUNCT
ejpam-4451	362	6	........	........	PUNCT
ejpam-4451	362	7	........	........	PUNCT
ejpam-4451	362	8	........	........	PUNCT
ejpam-4451	362	9	........	........	PUNCT
ejpam-4451	362	10	........	........	PUNCT
ejpam-4451	362	11	........	........	PUNCT
ejpam-4451	362	12	........	........	PUNCT
ejpam-4451	363	1	....	....	PUNCT
ejpam-4451	363	2	.........	.........	PUNCT
ejpam-4451	363	3	........	........	PUNCT
ejpam-4451	363	4	........	........	PUNCT
ejpam-4451	363	5	........	........	PUNCT
ejpam-4451	363	6	........	........	PUNCT
ejpam-4451	363	7	........	........	PUNCT
ejpam-4451	363	8	........	........	PUNCT
ejpam-4451	363	9	........	........	PUNCT
ejpam-4451	363	10	........	........	PUNCT
ejpam-4451	363	11	........	........	PUNCT
ejpam-4451	363	12	........	........	PUNCT
ejpam-4451	364	1	....	....	PUNCT
ejpam-4451	364	2	.........	.........	PUNCT
ejpam-4451	364	3	........	........	PUNCT
ejpam-4451	364	4	........	........	PUNCT
ejpam-4451	364	5	........	........	PUNCT
ejpam-4451	364	6	........	........	PUNCT
ejpam-4451	364	7	........	........	PUNCT
ejpam-4451	364	8	........	........	PUNCT
ejpam-4451	364	9	........	........	PUNCT
ejpam-4451	364	10	........	........	PUNCT
ejpam-4451	364	11	........	........	PUNCT
ejpam-4451	364	12	........	........	PUNCT
ejpam-4451	365	1	....	....	PUNCT
ejpam-4451	365	2	.........	.........	PUNCT
ejpam-4451	365	3	........	........	PUNCT
ejpam-4451	365	4	........	........	PUNCT
ejpam-4451	365	5	........	........	PUNCT
ejpam-4451	365	6	........	........	PUNCT
ejpam-4451	365	7	........	........	PUNCT
ejpam-4451	365	8	........	........	PUNCT
ejpam-4451	365	9	........	........	PUNCT
ejpam-4451	365	10	........	........	PUNCT
ejpam-4451	365	11	........	........	PUNCT
ejpam-4451	365	12	........	........	PUNCT
ejpam-4451	366	1	....	....	PUNCT
ejpam-4451	366	2	.........	.........	PUNCT
ejpam-4451	366	3	........	........	PUNCT
ejpam-4451	366	4	........	........	PUNCT
ejpam-4451	366	5	........	........	PUNCT
ejpam-4451	366	6	........	........	PUNCT
ejpam-4451	366	7	........	........	PUNCT
ejpam-4451	366	8	........	........	PUNCT
ejpam-4451	366	9	........	........	PUNCT
ejpam-4451	366	10	........	........	PUNCT
ejpam-4451	366	11	........	........	PUNCT
ejpam-4451	366	12	........	........	PUNCT
ejpam-4451	367	1	....	....	PUNCT
ejpam-4451	367	2	.........	.........	PUNCT
ejpam-4451	367	3	........	........	PUNCT
ejpam-4451	367	4	........	........	PUNCT
ejpam-4451	367	5	........	........	PUNCT
ejpam-4451	367	6	........	........	PUNCT
ejpam-4451	367	7	........	........	PUNCT
ejpam-4451	367	8	........	........	PUNCT
ejpam-4451	367	9	........	........	PUNCT
ejpam-4451	367	10	........	........	PUNCT
ejpam-4451	367	11	........	........	PUNCT
ejpam-4451	367	12	........	........	PUNCT
ejpam-4451	368	1	....	....	PUNCT
ejpam-4451	368	2	............	............	PUNCT
ejpam-4451	368	3	...........	...........	PUNCT
ejpam-4451	368	4	...........	...........	PUNCT
ejpam-4451	368	5	...........	...........	PUNCT
ejpam-4451	368	6	...........	...........	PUNCT
ejpam-4451	368	7	...........	...........	PUNCT
ejpam-4451	368	8	...........	...........	PUNCT
ejpam-4451	368	9	...........	...........	PUNCT
ejpam-4451	368	10	...........	...........	PUNCT
ejpam-4451	368	11	...........	...........	PUNCT
ejpam-4451	368	12	...........	...........	PUNCT
ejpam-4451	368	13	...........	...........	PUNCT
ejpam-4451	368	14	...	...	PUNCT
ejpam-4451	368	15	.........	.........	PUNCT
ejpam-4451	368	16	........	........	PUNCT
ejpam-4451	368	17	........	........	PUNCT
ejpam-4451	368	18	........	........	PUNCT
ejpam-4451	368	19	........	........	PUNCT
ejpam-4451	368	20	........	........	PUNCT
ejpam-4451	368	21	........	........	PUNCT
ejpam-4451	368	22	........	........	PUNCT
ejpam-4451	368	23	........	........	PUNCT
ejpam-4451	368	24	........	........	PUNCT
ejpam-4451	368	25	........	........	PUNCT
ejpam-4451	369	1	....	....	PUNCT
ejpam-4451	369	2	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4451	370	1	.........................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................	PUNCT
ejpam-4451	370	2	...........	...........	PUNCT
ejpam-4451	370	3	...........	...........	PUNCT
ejpam-4451	370	4	...........	...........	PUNCT
ejpam-4451	370	5	...........	...........	PUNCT
ejpam-4451	370	6	...........	...........	PUNCT
ejpam-4451	370	7	...........	...........	PUNCT
ejpam-4451	370	8	...........	...........	PUNCT
ejpam-4451	370	9	...........	...........	PUNCT
ejpam-4451	370	10	...........	...........	PUNCT
ejpam-4451	370	11	...........	...........	PUNCT
ejpam-4451	370	12	...........	...........	PUNCT
ejpam-4451	370	13	...	...	PUNCT
ejpam-4451	371	1	...................	...................	PUNCT
ejpam-4451	371	2	..................	..................	PUNCT
ejpam-4451	372	1	..................	..................	PUNCT
ejpam-4451	372	2	..................	..................	PUNCT
ejpam-4451	373	1	..................	..................	PUNCT
ejpam-4451	373	2	..................	..................	PUNCT
ejpam-4451	374	1	..................	..................	PUNCT
ejpam-4451	374	2	..................	..................	PUNCT
ejpam-4451	375	1	..................	..................	PUNCT
ejpam-4451	375	2	..................	..................	PUNCT
ejpam-4451	376	1	..................	..................	PUNCT
ejpam-4451	376	2	..................	..................	PUNCT
ejpam-4451	377	1	....	....	PUNCT
ejpam-4451	377	2	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4451	378	1	.........................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................	PUNCT
ejpam-4451	378	2	...........	...........	PUNCT
ejpam-4451	378	3	...........	...........	PUNCT
ejpam-4451	378	4	...........	...........	PUNCT
ejpam-4451	378	5	...........	...........	PUNCT
ejpam-4451	378	6	...........	...........	PUNCT
ejpam-4451	378	7	...........	...........	PUNCT
ejpam-4451	378	8	...........	...........	PUNCT
ejpam-4451	378	9	...........	...........	PUNCT
ejpam-4451	378	10	...........	...........	PUNCT
ejpam-4451	378	11	...........	...........	PUNCT
ejpam-4451	378	12	...........	...........	PUNCT
ejpam-4451	378	13	...	...	PUNCT
ejpam-4451	379	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4451	379	2	.............................................................................................................................................................................................................................	.............................................................................................................................................................................................................................	PUNCT
ejpam-4451	379	3	...................	...................	PUNCT
ejpam-4451	379	4	..................	..................	PUNCT
ejpam-4451	379	5	..................	..................	PUNCT
ejpam-4451	379	6	..................	..................	PUNCT
ejpam-4451	379	7	..................	..................	PUNCT
ejpam-4451	379	8	..................	..................	PUNCT
ejpam-4451	379	9	..................	..................	PUNCT
ejpam-4451	379	10	..................	..................	PUNCT
ejpam-4451	379	11	..................	..................	PUNCT
ejpam-4451	379	12	..................	..................	PUNCT
ejpam-4451	379	13	..................	..................	PUNCT
ejpam-4451	379	14	..................	..................	PUNCT
ejpam-4451	380	1	....	....	PUNCT
ejpam-4451	380	2	............	............	PUNCT
ejpam-4451	380	3	...........	...........	PUNCT
ejpam-4451	380	4	...........	...........	PUNCT
ejpam-4451	380	5	...........	...........	PUNCT
ejpam-4451	380	6	...........	...........	PUNCT
ejpam-4451	380	7	...........	...........	PUNCT
ejpam-4451	380	8	...........	...........	PUNCT
ejpam-4451	380	9	...........	...........	PUNCT
ejpam-4451	380	10	...........	...........	PUNCT
ejpam-4451	380	11	...........	...........	PUNCT
ejpam-4451	380	12	...........	...........	PUNCT
ejpam-4451	380	13	...........	...........	PUNCT
ejpam-4451	380	14	...	...	PUNCT
ejpam-4451	380	15	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4451	380	16	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4451	381	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4451	381	2	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4451	381	3	............	............	PUNCT
ejpam-4451	382	1	...........	...........	PUNCT
ejpam-4451	382	2	...........	...........	PUNCT
ejpam-4451	382	3	...........	...........	PUNCT
ejpam-4451	382	4	...........	...........	PUNCT
ejpam-4451	382	5	...........	...........	PUNCT
ejpam-4451	382	6	...........	...........	PUNCT
ejpam-4451	382	7	...........	...........	PUNCT
ejpam-4451	382	8	...........	...........	PUNCT
ejpam-4451	382	9	...........	...........	PUNCT
ejpam-4451	382	10	...........	...........	PUNCT
ejpam-4451	382	11	...........	...........	PUNCT
ejpam-4451	382	12	...	...	PUNCT
ejpam-4451	382	13	...................	...................	PUNCT
ejpam-4451	383	1	..................	..................	PUNCT
ejpam-4451	383	2	..................	..................	PUNCT
ejpam-4451	384	1	..................	..................	PUNCT
ejpam-4451	384	2	..................	..................	PUNCT
ejpam-4451	385	1	..................	..................	PUNCT
ejpam-4451	385	2	..................	..................	PUNCT
ejpam-4451	386	1	..................	..................	PUNCT
ejpam-4451	386	2	..................	..................	PUNCT
ejpam-4451	387	1	..................	..................	PUNCT
ejpam-4451	387	2	..................	..................	PUNCT
ejpam-4451	388	1	..................	..................	PUNCT
ejpam-4451	388	2	....	....	PUNCT
ejpam-4451	388	3	............	............	PUNCT
ejpam-4451	388	4	...........	...........	PUNCT
ejpam-4451	388	5	...........	...........	PUNCT
ejpam-4451	388	6	...........	...........	PUNCT
ejpam-4451	388	7	...........	...........	PUNCT
ejpam-4451	388	8	...........	...........	PUNCT
ejpam-4451	388	9	...........	...........	PUNCT
ejpam-4451	388	10	...........	...........	PUNCT
ejpam-4451	388	11	...........	...........	PUNCT
ejpam-4451	388	12	...........	...........	PUNCT
ejpam-4451	388	13	...........	...........	PUNCT
ejpam-4451	388	14	...........	...........	PUNCT
ejpam-4451	388	15	...	...	PUNCT
ejpam-4451	389	1	•	•	NUM
ejpam-4451	389	2	•	•	NUM
ejpam-4451	389	3	•	•	NUM
ejpam-4451	389	4	•	•	NUM
ejpam-4451	389	5	•	•	NUM
ejpam-4451	389	6	•	•	NUM
ejpam-4451	389	7	•	•	NOUN
ejpam-4451	389	8	•	•	NUM
ejpam-4451	389	9	figure	figure	NOUN
ejpam-4451	389	10	3	3	NUM
ejpam-4451	389	11	:	:	PUNCT
ejpam-4451	389	12	a	a	DET
ejpam-4451	389	13	graph	graph	NOUN
ejpam-4451	389	14	p4[p3	p4[p3	NOUN
ejpam-4451	389	15	]	]	X
ejpam-4451	389	16	with	with	ADP
ejpam-4451	389	17	γr2r(p4[p3	γr2r(p4[p3	PROPN
ejpam-4451	389	18	]	]	X
ejpam-4451	389	19	)	)	PUNCT
ejpam-4451	389	20	=	=	SYM
ejpam-4451	389	21	8	8	NUM
ejpam-4451	389	22	acknowledgements	acknowledgement	NOUN
ejpam-4451	389	23	the	the	DET
ejpam-4451	389	24	authors	author	NOUN
ejpam-4451	389	25	would	would	AUX
ejpam-4451	389	26	like	like	VERB
ejpam-4451	389	27	to	to	PART
ejpam-4451	389	28	thank	thank	VERB
ejpam-4451	389	29	the	the	DET
ejpam-4451	389	30	commission	commission	NOUN
ejpam-4451	389	31	on	on	ADP
ejpam-4451	389	32	higher	high	ADJ
ejpam-4451	389	33	education	education	NOUN
ejpam-4451	389	34	(	(	PUNCT
ejpam-4451	389	35	ched	che	VERB
ejpam-4451	389	36	)	)	PUNCT
ejpam-4451	389	37	and	and	CCONJ
ejpam-4451	389	38	mindanao	mindanao	PROPN
ejpam-4451	389	39	state	state	PROPN
ejpam-4451	389	40	university	university	PROPN
ejpam-4451	389	41	-	-	PUNCT
ejpam-4451	389	42	marawi	marawi	PROPN
ejpam-4451	389	43	and	and	CCONJ
ejpam-4451	389	44	msu	msu	PROPN
ejpam-4451	389	45	-	-	PUNCT
ejpam-4451	389	46	iligan	iligan	PROPN
ejpam-4451	389	47	institute	institute	PROPN
ejpam-4451	389	48	of	of	ADP
ejpam-4451	389	49	technology	technology	PROPN
ejpam-4451	389	50	,	,	PUNCT
ejpam-4451	389	51	philippines	philippine	NOUN
ejpam-4451	389	52	.	.	PUNCT
ejpam-4451	390	1	references	reference	NOUN
ejpam-4451	390	2	[	[	X
ejpam-4451	390	3	1	1	NUM
ejpam-4451	390	4	]	]	X
ejpam-4451	390	5	r	r	NOUN
ejpam-4451	390	6	bailey	bailey	NOUN
ejpam-4451	390	7	and	and	CCONJ
ejpam-4451	390	8	i	i	PRON
ejpam-4451	390	9	yero	yero	PROPN
ejpam-4451	390	10	.	.	PUNCT
ejpam-4451	391	1	error	error	NOUN
ejpam-4451	391	2	-	-	PUNCT
ejpam-4451	391	3	correcting	correct	VERB
ejpam-4451	391	4	codes	code	NOUN
ejpam-4451	391	5	from	from	ADP
ejpam-4451	391	6	k	k	ADJ
ejpam-4451	391	7	-	-	PUNCT
ejpam-4451	391	8	resolving	resolving	ADJ
ejpam-4451	391	9	sets	set	NOUN
ejpam-4451	391	10	.	.	PUNCT
ejpam-4451	392	1	discussiones	discussione	NOUN
ejpam-4451	392	2	mathematicae	mathematicae	VERB
ejpam-4451	392	3	,	,	PUNCT
ejpam-4451	392	4	graph	graph	NOUN
ejpam-4451	392	5	theory	theory	NOUN
ejpam-4451	392	6	,	,	PUNCT
ejpam-4451	392	7	39:341–355	39:341–355	PROPN
ejpam-4451	392	8	,	,	PUNCT
ejpam-4451	392	9	2019	2019	NUM
ejpam-4451	392	10	.	.	PUNCT
ejpam-4451	393	1	[	[	X
ejpam-4451	393	2	2	2	NUM
ejpam-4451	393	3	]	]	SYM
ejpam-4451	393	4	j	j	PROPN
ejpam-4451	393	5	estrada	estrada	PROPN
ejpam-4451	393	6	-	-	PUNCT
ejpam-4451	393	7	moreno	moreno	PROPN
ejpam-4451	393	8	,	,	PUNCT
ejpam-4451	393	9	a	a	DET
ejpam-4451	393	10	rodriguez	rodriguez	NOUN
ejpam-4451	393	11	-	-	PUNCT
ejpam-4451	393	12	velasquez	velasquez	PROPN
ejpam-4451	393	13	and	and	CCONJ
ejpam-4451	393	14	i	i	PRON
ejpam-4451	393	15	yero	yero	NOUN
ejpam-4451	393	16	.	.	PUNCT
ejpam-4451	394	1	the	the	DET
ejpam-4451	394	2	k	k	ADJ
ejpam-4451	394	3	-	-	ADJ
ejpam-4451	394	4	metric	metric	ADJ
ejpam-4451	394	5	dimension	dimension	NOUN
ejpam-4451	394	6	of	of	ADP
ejpam-4451	394	7	a	a	DET
ejpam-4451	394	8	graph	graph	NOUN
ejpam-4451	394	9	.	.	PUNCT
ejpam-4451	395	1	applied	apply	VERB
ejpam-4451	395	2	math	math	NOUN
ejpam-4451	395	3	information	information	NOUN
ejpam-4451	395	4	science	science	NOUN
ejpam-4451	395	5	.	.	PUNCT
ejpam-4451	395	6	,	,	PUNCT
ejpam-4451	395	7	9:2829–2840	9:2829–2840	NUM
ejpam-4451	395	8	,	,	PUNCT
ejpam-4451	395	9	2015	2015	NUM
ejpam-4451	395	10	.	.	PUNCT
ejpam-4451	396	1	[	[	X
ejpam-4451	396	2	3	3	X
ejpam-4451	396	3	]	]	X
ejpam-4451	396	4	f	f	PROPN
ejpam-4451	396	5	harary	harary	NOUN
ejpam-4451	396	6	.	.	PUNCT
ejpam-4451	397	1	graph	graph	NOUN
ejpam-4451	397	2	theory	theory	NOUN
ejpam-4451	397	3	.	.	PUNCT
ejpam-4451	398	1	addison	addison	PROPN
ejpam-4451	398	2	-	-	PUNCT
ejpam-4451	398	3	wesley	wesley	PROPN
ejpam-4451	398	4	publishing	publishing	PROPN
ejpam-4451	398	5	company	company	NOUN
ejpam-4451	398	6	,	,	PUNCT
ejpam-4451	398	7	usa	usa	PROPN
ejpam-4451	398	8	,	,	PUNCT
ejpam-4451	398	9	1969	1969	NUM
ejpam-4451	398	10	.	.	PUNCT
ejpam-4451	399	1	[	[	X
ejpam-4451	399	2	4	4	X
ejpam-4451	399	3	]	]	X
ejpam-4451	399	4	f	f	PROPN
ejpam-4451	399	5	harary	harary	NOUN
ejpam-4451	399	6	and	and	CCONJ
ejpam-4451	399	7	r	r	NOUN
ejpam-4451	399	8	melter	melter	NOUN
ejpam-4451	399	9	.	.	PUNCT
ejpam-4451	400	1	on	on	ADP
ejpam-4451	400	2	the	the	DET
ejpam-4451	400	3	metric	metric	ADJ
ejpam-4451	400	4	dimension	dimension	NOUN
ejpam-4451	400	5	of	of	ADP
ejpam-4451	400	6	a	a	DET
ejpam-4451	400	7	graph	graph	NOUN
ejpam-4451	400	8	.	.	PUNCT
ejpam-4451	401	1	ars	ars	PROPN
ejpam-4451	401	2	combinatoria	combinatoria	PROPN
ejpam-4451	401	3	,	,	PUNCT
ejpam-4451	401	4	2	2	NUM
ejpam-4451	401	5	,	,	PUNCT
ejpam-4451	401	6	1976	1976	NUM
ejpam-4451	401	7	.	.	PUNCT
ejpam-4451	402	1	[	[	X
ejpam-4451	402	2	5	5	NUM
ejpam-4451	402	3	]	]	PUNCT
ejpam-4451	402	4	h	h	NOUN
ejpam-4451	402	5	rara	rara	NOUN
ejpam-4451	402	6	and	and	CCONJ
ejpam-4451	402	7	j	j	PROPN
ejpam-4451	402	8	cabaro	cabaro	NOUN
ejpam-4451	402	9	.	.	PUNCT
ejpam-4451	403	1	on	on	ADP
ejpam-4451	403	2	2	2	NUM
ejpam-4451	403	3	-	-	PUNCT
ejpam-4451	403	4	resolving	resolve	VERB
ejpam-4451	403	5	sets	set	NOUN
ejpam-4451	403	6	in	in	ADP
ejpam-4451	403	7	the	the	DET
ejpam-4451	403	8	join	join	NOUN
ejpam-4451	403	9	and	and	CCONJ
ejpam-4451	403	10	corona	corona	NOUN
ejpam-4451	403	11	of	of	ADP
ejpam-4451	403	12	graphs	graph	NOUN
ejpam-4451	403	13	.	.	PUNCT
ejpam-4451	404	1	european	european	ADJ
ejpam-4451	404	2	journal	journal	PROPN
ejpam-4451	404	3	of	of	ADP
ejpam-4451	404	4	pure	pure	ADJ
ejpam-4451	404	5	and	and	CCONJ
ejpam-4451	404	6	applied	applied	ADJ
ejpam-4451	404	7	mathematics	mathematic	NOUN
ejpam-4451	404	8	,	,	PUNCT
ejpam-4451	404	9	14:773–782	14:773–782	NUM
ejpam-4451	404	10	,	,	PUNCT
ejpam-4451	404	11	2021	2021	NUM
ejpam-4451	404	12	.	.	PUNCT
ejpam-4451	405	1	[	[	X
ejpam-4451	405	2	6	6	NUM
ejpam-4451	405	3	]	]	PUNCT
ejpam-4451	405	4	h	h	NOUN
ejpam-4451	405	5	rara	rara	NOUN
ejpam-4451	405	6	and	and	CCONJ
ejpam-4451	405	7	j	j	PROPN
ejpam-4451	405	8	cabaro	cabaro	NOUN
ejpam-4451	405	9	.	.	PUNCT
ejpam-4451	406	1	restrained	restrain	VERB
ejpam-4451	406	2	2	2	NUM
ejpam-4451	406	3	-	-	PUNCT
ejpam-4451	406	4	resolving	resolve	VERB
ejpam-4451	406	5	sets	set	NOUN
ejpam-4451	406	6	in	in	ADP
ejpam-4451	406	7	the	the	DET
ejpam-4451	406	8	join	join	NOUN
ejpam-4451	406	9	,	,	PUNCT
ejpam-4451	406	10	corona	corona	NOUN
ejpam-4451	406	11	and	and	CCONJ
ejpam-4451	406	12	lexicographic	lexicographic	ADJ
ejpam-4451	406	13	product	product	NOUN
ejpam-4451	406	14	of	of	ADP
ejpam-4451	406	15	two	two	NUM
ejpam-4451	406	16	graphs	graph	NOUN
ejpam-4451	406	17	.	.	PUNCT
ejpam-4451	407	1	european	european	ADJ
ejpam-4451	407	2	journal	journal	PROPN
ejpam-4451	407	3	of	of	ADP
ejpam-4451	407	4	pure	pure	ADJ
ejpam-4451	407	5	and	and	CCONJ
ejpam-4451	407	6	applied	applied	ADJ
ejpam-4451	407	7	mathematics	mathematic	NOUN
ejpam-4451	407	8	,	,	PUNCT
ejpam-4451	407	9	accepted	accept	VERB
ejpam-4451	407	10	:	:	PUNCT
ejpam-4451	407	11	to	to	PART
ejpam-4451	407	12	publish	publish	VERB
ejpam-4451	407	13	,	,	PUNCT
ejpam-4451	407	14	2022	2022	NUM
ejpam-4451	407	15	.	.	PUNCT
ejpam-4451	408	1	[	[	X
ejpam-4451	408	2	7	7	NUM
ejpam-4451	408	3	]	]	X
ejpam-4451	408	4	h	h	NOUN
ejpam-4451	408	5	rara	rara	NOUN
ejpam-4451	408	6	and	and	CCONJ
ejpam-4451	408	7	j	j	PROPN
ejpam-4451	408	8	cabaro	cabaro	NOUN
ejpam-4451	408	9	.	.	PUNCT
ejpam-4451	409	1	restrained	restrain	VERB
ejpam-4451	409	2	2	2	NUM
ejpam-4451	409	3	-	-	PUNCT
ejpam-4451	409	4	resolving	resolve	VERB
ejpam-4451	409	5	sets	set	NOUN
ejpam-4451	409	6	in	in	ADP
ejpam-4451	409	7	the	the	DET
ejpam-4451	409	8	join	join	NOUN
ejpam-4451	409	9	,	,	PUNCT
ejpam-4451	409	10	corona	corona	NOUN
ejpam-4451	409	11	and	and	CCONJ
ejpam-4451	409	12	lexicographic	lexicographic	ADJ
ejpam-4451	409	13	product	product	NOUN
ejpam-4451	409	14	of	of	ADP
ejpam-4451	409	15	two	two	NUM
ejpam-4451	409	16	graphs	graph	NOUN
ejpam-4451	409	17	.	.	PUNCT
ejpam-4451	410	1	european	european	ADJ
ejpam-4451	410	2	journal	journal	PROPN
ejpam-4451	410	3	of	of	ADP
ejpam-4451	410	4	pure	pure	ADJ
ejpam-4451	410	5	and	and	CCONJ
ejpam-4451	410	6	applied	applied	ADJ
ejpam-4451	410	7	mathematics	mathematic	NOUN
ejpam-4451	410	8	,	,	PUNCT
ejpam-4451	410	9	accepted	accept	VERB
ejpam-4451	410	10	:	:	PUNCT
ejpam-4451	410	11	to	to	PART
ejpam-4451	410	12	publish	publish	VERB
ejpam-4451	410	13	,	,	PUNCT
ejpam-4451	410	14	2022	2022	NUM
ejpam-4451	410	15	.	.	PUNCT
ejpam-4451	411	1	[	[	X
ejpam-4451	411	2	8	8	NUM
ejpam-4451	411	3	]	]	SYM
ejpam-4451	411	4	v	v	ADP
ejpam-4451	411	5	saenpholphat	saenpholphat	NOUN
ejpam-4451	412	1	and	and	CCONJ
ejpam-4451	412	2	p	p	PROPN
ejpam-4451	412	3	zang	zang	PROPN
ejpam-4451	412	4	.	.	PUNCT
ejpam-4451	413	1	on	on	ADP
ejpam-4451	413	2	connected	connected	ADJ
ejpam-4451	413	3	resolvability	resolvability	NOUN
ejpam-4451	413	4	of	of	ADP
ejpam-4451	413	5	graphs	graph	NOUN
ejpam-4451	413	6	.	.	PUNCT
ejpam-4451	414	1	australian	australian	ADJ
ejpam-4451	414	2	journal	journal	NOUN
ejpam-4451	414	3	of	of	ADP
ejpam-4451	414	4	combinatorics	combinatoric	NOUN
ejpam-4451	414	5	,	,	PUNCT
ejpam-4451	414	6	28:25–37	28:25–37	NUM
ejpam-4451	414	7	,	,	PUNCT
ejpam-4451	414	8	2003	2003	NUM
ejpam-4451	414	9	.	.	PUNCT
ejpam-4451	415	1	[	[	X
ejpam-4451	415	2	9	9	NUM
ejpam-4451	415	3	]	]	X
ejpam-4451	415	4	p.	p.	PROPN
ejpam-4451	415	5	slater	slater	PROPN
ejpam-4451	415	6	.	.	PUNCT
ejpam-4451	416	1	congressus	congressus	PROPN
ejpam-4451	416	2	numerantium	numerantium	PROPN
ejpam-4451	416	3	,	,	PUNCT
ejpam-4451	416	4	.	.	PUNCT
ejpam-4451	416	5	,	,	PUNCT
ejpam-4451	417	1	14:549–559	14:549–559	NUM
ejpam-4451	417	2	,	,	PUNCT
ejpam-4451	417	3	1975	1975	NUM
ejpam-4451	417	4	.	.	PUNCT