id	sid	tid	token	lemma	pos
ejpam-4427	1	1	european	european	PROPN
ejpam-4427	1	2	journal	journal	PROPN
ejpam-4427	1	3	of	of	ADP
ejpam-4427	1	4	pure	pure	ADJ
ejpam-4427	1	5	and	and	CCONJ
ejpam-4427	1	6	applied	apply	VERB
ejpam-4427	1	7	mathematics	mathematic	NOUN
ejpam-4427	1	8	vol	vol	NOUN
ejpam-4427	1	9	.	.	PROPN
ejpam-4427	2	1	15	15	NUM
ejpam-4427	2	2	,	,	PUNCT
ejpam-4427	2	3	no	no	INTJ
ejpam-4427	2	4	.	.	NOUN
ejpam-4427	2	5	3	3	NUM
ejpam-4427	2	6	,	,	PUNCT
ejpam-4427	2	7	2022	2022	NUM
ejpam-4427	2	8	,	,	PUNCT
ejpam-4427	2	9	1229	1229	NUM
ejpam-4427	2	10	-	-	SYM
ejpam-4427	2	11	1236	1236	NUM
ejpam-4427	2	12	issn	issn	PROPN
ejpam-4427	2	13	1307	1307	NUM
ejpam-4427	2	14	-	-	SYM
ejpam-4427	2	15	5543	5543	NUM
ejpam-4427	2	16	–	–	PUNCT
ejpam-4427	3	1	ejpam.com	ejpam.com	X
ejpam-4427	3	2	published	publish	VERB
ejpam-4427	3	3	by	by	ADP
ejpam-4427	3	4	new	new	PROPN
ejpam-4427	3	5	york	york	PROPN
ejpam-4427	3	6	business	business	PROPN
ejpam-4427	3	7	global	global	PROPN
ejpam-4427	3	8	restrained	restrain	VERB
ejpam-4427	3	9	2	2	NUM
ejpam-4427	3	10	-	-	PUNCT
ejpam-4427	3	11	resolving	resolve	VERB
ejpam-4427	3	12	sets	set	NOUN
ejpam-4427	3	13	in	in	ADP
ejpam-4427	3	14	the	the	DET
ejpam-4427	3	15	join	join	NOUN
ejpam-4427	3	16	,	,	PUNCT
ejpam-4427	3	17	corona	corona	NOUN
ejpam-4427	3	18	and	and	CCONJ
ejpam-4427	3	19	lexicographic	lexicographic	ADJ
ejpam-4427	3	20	product	product	NOUN
ejpam-4427	3	21	of	of	ADP
ejpam-4427	3	22	two	two	NUM
ejpam-4427	3	23	graphs	graph	NOUN
ejpam-4427	3	24	jean	jean	PROPN
ejpam-4427	3	25	cabaro1,∗	cabaro1,∗	PROPN
ejpam-4427	3	26	,	,	PUNCT
ejpam-4427	3	27	helen	helen	PROPN
ejpam-4427	3	28	rara2	rara2	PROPN
ejpam-4427	3	29	1	1	NUM
ejpam-4427	3	30	mathematics	mathematics	PROPN
ejpam-4427	3	31	department	department	NOUN
ejpam-4427	3	32	,	,	PUNCT
ejpam-4427	3	33	college	college	NOUN
ejpam-4427	3	34	of	of	ADP
ejpam-4427	3	35	natural	natural	ADJ
ejpam-4427	3	36	sciences	science	NOUN
ejpam-4427	3	37	and	and	CCONJ
ejpam-4427	3	38	mathematics	mathematic	NOUN
ejpam-4427	3	39	,	,	PUNCT
ejpam-4427	3	40	mindanao	mindanao	PROPN
ejpam-4427	3	41	state	state	PROPN
ejpam-4427	3	42	university	university	NOUN
ejpam-4427	3	43	-	-	PUNCT
ejpam-4427	3	44	main	main	ADJ
ejpam-4427	3	45	campus	campus	NOUN
ejpam-4427	3	46	,	,	PUNCT
ejpam-4427	3	47	9700	9700	NUM
ejpam-4427	3	48	marawi	marawi	PROPN
ejpam-4427	3	49	city	city	PROPN
ejpam-4427	3	50	,	,	PUNCT
ejpam-4427	3	51	philippines	philippines	PROPN
ejpam-4427	3	52	2	2	NUM
ejpam-4427	3	53	department	department	NOUN
ejpam-4427	3	54	of	of	ADP
ejpam-4427	3	55	mathematics	mathematic	NOUN
ejpam-4427	3	56	and	and	CCONJ
ejpam-4427	3	57	statistics	statistic	NOUN
ejpam-4427	3	58	,	,	PUNCT
ejpam-4427	3	59	college	college	NOUN
ejpam-4427	3	60	of	of	ADP
ejpam-4427	3	61	science	science	NOUN
ejpam-4427	3	62	and	and	CCONJ
ejpam-4427	3	63	mathematics	mathematic	NOUN
ejpam-4427	3	64	,	,	PUNCT
ejpam-4427	3	65	center	center	NOUN
ejpam-4427	3	66	of	of	ADP
ejpam-4427	3	67	graph	graph	NOUN
ejpam-4427	3	68	theory	theory	NOUN
ejpam-4427	3	69	,	,	PUNCT
ejpam-4427	3	70	algebra	algebra	NOUN
ejpam-4427	3	71	,	,	PUNCT
ejpam-4427	3	72	and	and	CCONJ
ejpam-4427	3	73	analysis	analysis	NOUN
ejpam-4427	3	74	-	-	PUNCT
ejpam-4427	3	75	premier	premier	NOUN
ejpam-4427	3	76	research	research	NOUN
ejpam-4427	3	77	institute	institute	PROPN
ejpam-4427	3	78	of	of	ADP
ejpam-4427	3	79	science	science	NOUN
ejpam-4427	3	80	and	and	CCONJ
ejpam-4427	3	81	mathematics	mathematic	NOUN
ejpam-4427	3	82	,	,	PUNCT
ejpam-4427	3	83	mindanao	mindanao	PROPN
ejpam-4427	3	84	state	state	PROPN
ejpam-4427	3	85	university	university	PROPN
ejpam-4427	3	86	-	-	PUNCT
ejpam-4427	3	87	iligan	iligan	PROPN
ejpam-4427	3	88	institute	institute	PROPN
ejpam-4427	3	89	of	of	ADP
ejpam-4427	3	90	technology	technology	PROPN
ejpam-4427	3	91	,	,	PUNCT
ejpam-4427	3	92	9200	9200	NUM
ejpam-4427	3	93	iligan	iligan	ADJ
ejpam-4427	3	94	city	city	NOUN
ejpam-4427	3	95	,	,	PUNCT
ejpam-4427	3	96	philippines	philippine	NOUN
ejpam-4427	3	97	abstract	abstract	ADJ
ejpam-4427	3	98	.	.	PUNCT
ejpam-4427	4	1	let	let	VERB
ejpam-4427	4	2	g	g	PRON
ejpam-4427	4	3	be	be	AUX
ejpam-4427	4	4	a	a	DET
ejpam-4427	4	5	connected	connected	ADJ
ejpam-4427	4	6	graph	graph	NOUN
ejpam-4427	4	7	.	.	PUNCT
ejpam-4427	5	1	an	an	DET
ejpam-4427	5	2	ordered	order	VERB
ejpam-4427	5	3	set	set	NOUN
ejpam-4427	5	4	of	of	ADP
ejpam-4427	5	5	vertices	vertex	NOUN
ejpam-4427	5	6	{	{	PUNCT
ejpam-4427	5	7	v1	v1	NOUN
ejpam-4427	5	8	,	,	PUNCT
ejpam-4427	5	9	...	...	PUNCT
ejpam-4427	5	10	,	,	PUNCT
ejpam-4427	5	11	vl	vl	ADJ
ejpam-4427	5	12	}	}	PUNCT
ejpam-4427	5	13	is	be	AUX
ejpam-4427	5	14	a	a	DET
ejpam-4427	5	15	2	2	NUM
ejpam-4427	5	16	-	-	PUNCT
ejpam-4427	5	17	resolving	resolving	NOUN
ejpam-4427	5	18	set	set	NOUN
ejpam-4427	5	19	for	for	ADP
ejpam-4427	5	20	g	g	PROPN
ejpam-4427	5	21	if	if	SCONJ
ejpam-4427	5	22	,	,	PUNCT
ejpam-4427	5	23	for	for	ADP
ejpam-4427	5	24	any	any	DET
ejpam-4427	5	25	distinct	distinct	ADJ
ejpam-4427	5	26	vertices	vertex	NOUN
ejpam-4427	5	27	u	u	NOUN
ejpam-4427	5	28	,	,	PUNCT
ejpam-4427	5	29	w	w	PROPN
ejpam-4427	5	30	∈	∈	PROPN
ejpam-4427	5	31	v	v	ADP
ejpam-4427	5	32	(	(	PUNCT
ejpam-4427	5	33	g	g	NOUN
ejpam-4427	5	34	)	)	PUNCT
ejpam-4427	5	35	,	,	PUNCT
ejpam-4427	5	36	the	the	DET
ejpam-4427	5	37	lists	list	NOUN
ejpam-4427	5	38	of	of	ADP
ejpam-4427	5	39	distances	distance	NOUN
ejpam-4427	5	40	(	(	PUNCT
ejpam-4427	5	41	dg(u	dg(u	X
ejpam-4427	5	42	,	,	PUNCT
ejpam-4427	5	43	v1	v1	NOUN
ejpam-4427	5	44	)	)	PUNCT
ejpam-4427	5	45	,	,	PUNCT
ejpam-4427	5	46	...	...	PUNCT
ejpam-4427	5	47	,	,	PUNCT
ejpam-4427	5	48	dg(u	dg(u	X
ejpam-4427	5	49	,	,	PUNCT
ejpam-4427	5	50	vl	vl	NOUN
ejpam-4427	5	51	)	)	PUNCT
ejpam-4427	5	52	)	)	PUNCT
ejpam-4427	5	53	and	and	CCONJ
ejpam-4427	5	54	(	(	PUNCT
ejpam-4427	5	55	dg(w	dg(w	X
ejpam-4427	5	56	,	,	PUNCT
ejpam-4427	5	57	v1	v1	NOUN
ejpam-4427	5	58	)	)	PUNCT
ejpam-4427	5	59	,	,	PUNCT
ejpam-4427	5	60	...	...	PUNCT
ejpam-4427	5	61	,	,	PUNCT
ejpam-4427	5	62	dg(w	dg(w	X
ejpam-4427	5	63	,	,	PUNCT
ejpam-4427	5	64	vl	vl	NOUN
ejpam-4427	5	65	)	)	PUNCT
ejpam-4427	5	66	)	)	PUNCT
ejpam-4427	5	67	differ	differ	VERB
ejpam-4427	5	68	in	in	ADP
ejpam-4427	5	69	at	at	ADV
ejpam-4427	5	70	least	least	ADJ
ejpam-4427	5	71	2	2	NUM
ejpam-4427	5	72	positions	position	NOUN
ejpam-4427	5	73	.	.	PUNCT
ejpam-4427	6	1	a	a	DET
ejpam-4427	6	2	set	set	NOUN
ejpam-4427	6	3	s	s	NOUN
ejpam-4427	6	4	⊆	⊆	NUM
ejpam-4427	6	5	v	v	NOUN
ejpam-4427	6	6	(	(	PUNCT
ejpam-4427	6	7	g	g	NOUN
ejpam-4427	6	8	)	)	PUNCT
ejpam-4427	6	9	is	be	AUX
ejpam-4427	6	10	a	a	DET
ejpam-4427	6	11	restrained	restrained	ADJ
ejpam-4427	6	12	2	2	NUM
ejpam-4427	6	13	-	-	PUNCT
ejpam-4427	6	14	resolving	resolving	NOUN
ejpam-4427	6	15	set	set	NOUN
ejpam-4427	6	16	in	in	ADP
ejpam-4427	6	17	g	g	PROPN
ejpam-4427	6	18	if	if	SCONJ
ejpam-4427	6	19	s	s	VERB
ejpam-4427	6	20	is	be	AUX
ejpam-4427	6	21	a	a	DET
ejpam-4427	6	22	2	2	NUM
ejpam-4427	6	23	-	-	PUNCT
ejpam-4427	6	24	resolving	resolving	NOUN
ejpam-4427	6	25	set	set	NOUN
ejpam-4427	6	26	in	in	ADP
ejpam-4427	6	27	g	g	PROPN
ejpam-4427	6	28	and	and	CCONJ
ejpam-4427	6	29	s	s	PART
ejpam-4427	6	30	=	=	SYM
ejpam-4427	6	31	v	v	X
ejpam-4427	6	32	(	(	PUNCT
ejpam-4427	6	33	g	g	NOUN
ejpam-4427	6	34	)	)	PUNCT
ejpam-4427	6	35	or	or	CCONJ
ejpam-4427	6	36	⟨v	⟨v	NUM
ejpam-4427	6	37	(	(	PUNCT
ejpam-4427	6	38	g)\s⟩	g)\s⟩	PROPN
ejpam-4427	6	39	has	have	AUX
ejpam-4427	6	40	no	no	DET
ejpam-4427	6	41	isolated	isolated	ADJ
ejpam-4427	6	42	vertex	vertex	NOUN
ejpam-4427	6	43	.	.	PUNCT
ejpam-4427	7	1	the	the	DET
ejpam-4427	7	2	restrained	restrained	ADJ
ejpam-4427	7	3	2	2	NUM
ejpam-4427	7	4	-	-	PUNCT
ejpam-4427	7	5	resolving	resolve	VERB
ejpam-4427	7	6	number	number	NOUN
ejpam-4427	7	7	of	of	ADP
ejpam-4427	7	8	g	g	NOUN
ejpam-4427	7	9	,	,	PUNCT
ejpam-4427	7	10	denoted	denote	VERB
ejpam-4427	7	11	by	by	ADP
ejpam-4427	7	12	rdim2(g	rdim2(g	NOUN
ejpam-4427	7	13	)	)	PUNCT
ejpam-4427	7	14	,	,	PUNCT
ejpam-4427	7	15	is	be	AUX
ejpam-4427	7	16	the	the	DET
ejpam-4427	7	17	smallest	small	ADJ
ejpam-4427	7	18	cardinality	cardinality	NOUN
ejpam-4427	7	19	of	of	ADP
ejpam-4427	7	20	a	a	DET
ejpam-4427	7	21	restrained	restrained	ADJ
ejpam-4427	7	22	2	2	NUM
ejpam-4427	7	23	-	-	PUNCT
ejpam-4427	7	24	resolving	resolving	NOUN
ejpam-4427	7	25	set	set	VERB
ejpam-4427	7	26	in	in	ADP
ejpam-4427	7	27	g.	g.	PROPN
ejpam-4427	7	28	a	a	DET
ejpam-4427	7	29	restrained	restrain	VERB
ejpam-4427	7	30	2	2	NUM
ejpam-4427	7	31	-	-	PUNCT
ejpam-4427	7	32	resolving	resolve	VERB
ejpam-4427	7	33	set	set	NOUN
ejpam-4427	7	34	of	of	ADP
ejpam-4427	7	35	cardinality	cardinality	NOUN
ejpam-4427	7	36	rdim2(g	rdim2(g	NOUN
ejpam-4427	7	37	)	)	PUNCT
ejpam-4427	7	38	is	be	AUX
ejpam-4427	7	39	then	then	ADV
ejpam-4427	7	40	referred	refer	VERB
ejpam-4427	7	41	to	to	ADP
ejpam-4427	7	42	as	as	ADP
ejpam-4427	7	43	an	an	DET
ejpam-4427	7	44	rdim2	rdim2	NOUN
ejpam-4427	7	45	-	-	PUNCT
ejpam-4427	7	46	set	set	NOUN
ejpam-4427	7	47	in	in	ADP
ejpam-4427	7	48	g.	g.	PROPN
ejpam-4427	7	49	this	this	DET
ejpam-4427	7	50	study	study	NOUN
ejpam-4427	7	51	deals	deal	VERB
ejpam-4427	7	52	with	with	ADP
ejpam-4427	7	53	the	the	DET
ejpam-4427	7	54	concept	concept	NOUN
ejpam-4427	7	55	of	of	ADP
ejpam-4427	7	56	restrained	restrained	ADJ
ejpam-4427	7	57	2	2	NUM
ejpam-4427	7	58	-	-	PUNCT
ejpam-4427	7	59	resolving	resolve	VERB
ejpam-4427	7	60	set	set	NOUN
ejpam-4427	7	61	of	of	ADP
ejpam-4427	7	62	a	a	DET
ejpam-4427	7	63	graph	graph	NOUN
ejpam-4427	7	64	.	.	PUNCT
ejpam-4427	8	1	it	it	PRON
ejpam-4427	8	2	characterizes	characterize	VERB
ejpam-4427	8	3	the	the	DET
ejpam-4427	8	4	restrained	restrained	ADJ
ejpam-4427	8	5	2	2	NUM
ejpam-4427	8	6	-	-	PUNCT
ejpam-4427	8	7	resolving	resolve	VERB
ejpam-4427	8	8	set	set	NOUN
ejpam-4427	8	9	in	in	ADP
ejpam-4427	8	10	the	the	DET
ejpam-4427	8	11	join	join	NOUN
ejpam-4427	8	12	,	,	PUNCT
ejpam-4427	8	13	corona	corona	NOUN
ejpam-4427	8	14	and	and	CCONJ
ejpam-4427	8	15	lexicographic	lexicographic	ADJ
ejpam-4427	8	16	product	product	NOUN
ejpam-4427	8	17	of	of	ADP
ejpam-4427	8	18	two	two	NUM
ejpam-4427	8	19	graphs	graph	NOUN
ejpam-4427	8	20	and	and	CCONJ
ejpam-4427	8	21	determine	determine	VERB
ejpam-4427	8	22	the	the	DET
ejpam-4427	8	23	bounds	bound	NOUN
ejpam-4427	8	24	or	or	CCONJ
ejpam-4427	8	25	exact	exact	ADJ
ejpam-4427	8	26	values	value	NOUN
ejpam-4427	8	27	of	of	ADP
ejpam-4427	8	28	the	the	DET
ejpam-4427	8	29	2	2	NUM
ejpam-4427	8	30	-	-	PUNCT
ejpam-4427	8	31	resolving	resolve	VERB
ejpam-4427	8	32	dominating	dominating	NOUN
ejpam-4427	8	33	number	number	NOUN
ejpam-4427	8	34	of	of	ADP
ejpam-4427	8	35	these	these	DET
ejpam-4427	8	36	graphs	graph	NOUN
ejpam-4427	8	37	.	.	PUNCT
ejpam-4427	9	1	2020	2020	NUM
ejpam-4427	9	2	mathematics	mathematic	NOUN
ejpam-4427	9	3	subject	subject	NOUN
ejpam-4427	9	4	classifications	classification	NOUN
ejpam-4427	9	5	:	:	PUNCT
ejpam-4427	9	6	05c69	05c69	X
ejpam-4427	9	7	key	key	ADJ
ejpam-4427	9	8	words	word	NOUN
ejpam-4427	9	9	and	and	CCONJ
ejpam-4427	9	10	phrases	phrase	NOUN
ejpam-4427	9	11	:	:	PUNCT
ejpam-4427	9	12	2	2	NUM
ejpam-4427	9	13	-	-	PUNCT
ejpam-4427	9	14	resolving	resolve	VERB
ejpam-4427	9	15	set	set	NOUN
ejpam-4427	9	16	,	,	PUNCT
ejpam-4427	9	17	restrained	restrain	VERB
ejpam-4427	9	18	2	2	NUM
ejpam-4427	9	19	-	-	PUNCT
ejpam-4427	9	20	resolving	resolve	VERB
ejpam-4427	9	21	set	set	NOUN
ejpam-4427	9	22	,	,	PUNCT
ejpam-4427	9	23	restrained	restrain	VERB
ejpam-4427	9	24	2	2	NUM
ejpam-4427	9	25	-	-	PUNCT
ejpam-4427	9	26	resolving	resolve	VERB
ejpam-4427	9	27	number	number	NOUN
ejpam-4427	9	28	,	,	PUNCT
ejpam-4427	9	29	join	join	NOUN
ejpam-4427	9	30	,	,	PUNCT
ejpam-4427	9	31	corona	corona	PROPN
ejpam-4427	9	32	,	,	PUNCT
ejpam-4427	9	33	lexicographic	lexicographic	ADJ
ejpam-4427	9	34	product	product	NOUN
ejpam-4427	9	35	of	of	ADP
ejpam-4427	9	36	two	two	NUM
ejpam-4427	9	37	graphs	graph	NOUN
ejpam-4427	9	38	1	1	NUM
ejpam-4427	9	39	.	.	PUNCT
ejpam-4427	9	40	introduction	introduction	NOUN
ejpam-4427	9	41	the	the	DET
ejpam-4427	9	42	problem	problem	NOUN
ejpam-4427	9	43	of	of	ADP
ejpam-4427	9	44	uniquely	uniquely	ADV
ejpam-4427	9	45	determining	determine	VERB
ejpam-4427	9	46	the	the	DET
ejpam-4427	9	47	location	location	NOUN
ejpam-4427	9	48	of	of	ADP
ejpam-4427	9	49	an	an	DET
ejpam-4427	9	50	intruder	intruder	NOUN
ejpam-4427	9	51	in	in	ADP
ejpam-4427	9	52	a	a	DET
ejpam-4427	9	53	network	network	NOUN
ejpam-4427	9	54	was	be	AUX
ejpam-4427	9	55	the	the	DET
ejpam-4427	9	56	principal	principal	ADJ
ejpam-4427	9	57	motivation	motivation	NOUN
ejpam-4427	9	58	of	of	ADP
ejpam-4427	9	59	introducing	introduce	VERB
ejpam-4427	9	60	the	the	DET
ejpam-4427	9	61	concept	concept	NOUN
ejpam-4427	9	62	of	of	ADP
ejpam-4427	9	63	metric	metric	ADJ
ejpam-4427	9	64	dimension	dimension	NOUN
ejpam-4427	9	65	in	in	ADP
ejpam-4427	9	66	graphs	graph	NOUN
ejpam-4427	9	67	by	by	ADP
ejpam-4427	9	68	slater	slater	NOUN
ejpam-4427	10	1	[	[	X
ejpam-4427	10	2	8	8	NUM
ejpam-4427	10	3	]	]	PUNCT
ejpam-4427	10	4	,	,	PUNCT
ejpam-4427	10	5	where	where	SCONJ
ejpam-4427	10	6	the	the	DET
ejpam-4427	10	7	metric	metric	ADJ
ejpam-4427	10	8	generators	generator	NOUN
ejpam-4427	10	9	were	be	AUX
ejpam-4427	10	10	called	call	VERB
ejpam-4427	10	11	locating	locating	NOUN
ejpam-4427	10	12	sets	set	NOUN
ejpam-4427	10	13	.	.	PUNCT
ejpam-4427	11	1	the	the	DET
ejpam-4427	11	2	concept	concept	NOUN
ejpam-4427	11	3	of	of	ADP
ejpam-4427	11	4	metric	metric	ADJ
ejpam-4427	11	5	dimension	dimension	NOUN
ejpam-4427	11	6	of	of	ADP
ejpam-4427	11	7	a	a	DET
ejpam-4427	11	8	graph	graph	NOUN
ejpam-4427	11	9	was	be	AUX
ejpam-4427	11	10	also	also	ADV
ejpam-4427	11	11	introduced	introduce	VERB
ejpam-4427	11	12	independently	independently	ADV
ejpam-4427	11	13	by	by	ADP
ejpam-4427	11	14	harary	harary	NOUN
ejpam-4427	11	15	and	and	CCONJ
ejpam-4427	11	16	melter	melter	NOUN
ejpam-4427	11	17	in	in	ADP
ejpam-4427	11	18	[	[	X
ejpam-4427	11	19	4	4	X
ejpam-4427	11	20	]	]	PUNCT
ejpam-4427	11	21	where	where	SCONJ
ejpam-4427	11	22	metric	metric	ADJ
ejpam-4427	11	23	generators	generator	NOUN
ejpam-4427	11	24	were	be	AUX
ejpam-4427	11	25	called	call	VERB
ejpam-4427	11	26	resolving	resolve	VERB
ejpam-4427	11	27	sets	set	NOUN
ejpam-4427	11	28	.	.	PUNCT
ejpam-4427	12	1	bailey	bailey	NOUN
ejpam-4427	12	2	and	and	CCONJ
ejpam-4427	12	3	yero	yero	NOUN
ejpam-4427	12	4	in	in	ADP
ejpam-4427	12	5	[	[	X
ejpam-4427	12	6	1	1	NUM
ejpam-4427	12	7	]	]	PUNCT
ejpam-4427	12	8	demonstrated	demonstrate	VERB
ejpam-4427	12	9	a	a	DET
ejpam-4427	12	10	construction	construction	NOUN
ejpam-4427	12	11	of	of	ADP
ejpam-4427	12	12	error	error	NOUN
ejpam-4427	12	13	-	-	PUNCT
ejpam-4427	12	14	correcting	correct	VERB
ejpam-4427	12	15	codes	code	NOUN
ejpam-4427	12	16	from	from	ADP
ejpam-4427	12	17	graphs	graph	NOUN
ejpam-4427	12	18	by	by	ADP
ejpam-4427	12	19	means	mean	NOUN
ejpam-4427	12	20	of	of	ADP
ejpam-4427	12	21	k	k	ADJ
ejpam-4427	12	22	-	-	PUNCT
ejpam-4427	12	23	resolving	resolving	ADJ
ejpam-4427	12	24	sets	set	NOUN
ejpam-4427	12	25	,	,	PUNCT
ejpam-4427	12	26	and	and	CCONJ
ejpam-4427	12	27	present	present	VERB
ejpam-4427	12	28	a	a	DET
ejpam-4427	12	29	decoding	decode	VERB
ejpam-4427	12	30	algorithm	algorithm	NOUN
ejpam-4427	12	31	which	which	PRON
ejpam-4427	12	32	makes	make	VERB
ejpam-4427	12	33	use	use	NOUN
ejpam-4427	12	34	of	of	ADP
ejpam-4427	12	35	∗corresponding	∗corresponde	VERB
ejpam-4427	12	36	author	author	NOUN
ejpam-4427	12	37	.	.	PUNCT
ejpam-4427	13	1	doi	doi	NOUN
ejpam-4427	13	2	:	:	PUNCT
ejpam-4427	14	1	https://doi.org/10.29020/nybg.ejpam.v15i3.4427	https://doi.org/10.29020/nybg.ejpam.v15i3.4427	ADJ
ejpam-4427	14	2	email	email	NOUN
ejpam-4427	14	3	addresses	address	NOUN
ejpam-4427	14	4	:	:	PUNCT
ejpam-4427	14	5	amerjean1228@gmail.com	amerjean1228@gmail.com	X
ejpam-4427	14	6	(	(	PUNCT
ejpam-4427	14	7	j.	j.	PROPN
ejpam-4427	14	8	cabaro	cabaro	PROPN
ejpam-4427	14	9	)	)	PUNCT
ejpam-4427	14	10	,	,	PUNCT
ejpam-4427	14	11	helenrara@gmail.com	helenrara@gmail.com	X
ejpam-4427	14	12	(	(	PUNCT
ejpam-4427	14	13	h.	h.	PROPN
ejpam-4427	14	14	rara	rara	PROPN
ejpam-4427	14	15	)	)	PUNCT
ejpam-4427	14	16	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4427	14	17	1229	1229	NUM
ejpam-4427	15	1	©	©	PROPN
ejpam-4427	15	2	2022	2022	NUM
ejpam-4427	15	3	ejpam	ejpam	VERB
ejpam-4427	15	4	all	all	DET
ejpam-4427	15	5	rights	right	NOUN
ejpam-4427	15	6	reserved	reserve	VERB
ejpam-4427	15	7	.	.	PUNCT
ejpam-4427	16	1	j.	j.	PROPN
ejpam-4427	16	2	cabaro	cabaro	PROPN
ejpam-4427	16	3	,	,	PUNCT
ejpam-4427	16	4	h.	h.	PROPN
ejpam-4427	16	5	rara	rara	PROPN
ejpam-4427	16	6	/	/	SYM
ejpam-4427	16	7	eur	eur	PROPN
ejpam-4427	16	8	.	.	PUNCT
ejpam-4427	17	1	j.	j.	PROPN
ejpam-4427	17	2	pure	pure	PROPN
ejpam-4427	17	3	appl	appl	PROPN
ejpam-4427	17	4	.	.	PROPN
ejpam-4427	17	5	math	math	PROPN
ejpam-4427	17	6	,	,	PUNCT
ejpam-4427	17	7	15	15	NUM
ejpam-4427	17	8	(	(	PUNCT
ejpam-4427	17	9	3	3	NUM
ejpam-4427	17	10	)	)	PUNCT
ejpam-4427	17	11	(	(	PUNCT
ejpam-4427	17	12	2022	2022	NUM
ejpam-4427	17	13	)	)	PUNCT
ejpam-4427	17	14	,	,	PUNCT
ejpam-4427	17	15	1229	1229	NUM
ejpam-4427	17	16	-	-	SYM
ejpam-4427	17	17	1236	1236	NUM
ejpam-4427	17	18	1230	1230	NUM
ejpam-4427	17	19	covering	covering	NOUN
ejpam-4427	17	20	designs	design	NOUN
ejpam-4427	17	21	.	.	PUNCT
ejpam-4427	18	1	in	in	ADP
ejpam-4427	18	2	[	[	X
ejpam-4427	18	3	6	6	NUM
ejpam-4427	18	4	]	]	PUNCT
ejpam-4427	18	5	,	,	PUNCT
ejpam-4427	18	6	the	the	DET
ejpam-4427	18	7	explicit	explicit	ADJ
ejpam-4427	18	8	interpretation	interpretation	NOUN
ejpam-4427	18	9	for	for	ADP
ejpam-4427	18	10	f	f	NOUN
ejpam-4427	18	11	-	-	PUNCT
ejpam-4427	18	12	index	index	NOUN
ejpam-4427	18	13	of	of	ADP
ejpam-4427	18	14	different	different	ADJ
ejpam-4427	18	15	forms	form	NOUN
ejpam-4427	18	16	of	of	ADP
ejpam-4427	18	17	corona	corona	NOUN
ejpam-4427	18	18	products	product	NOUN
ejpam-4427	18	19	involving	involve	VERB
ejpam-4427	18	20	zagreb	zagreb	PROPN
ejpam-4427	18	21	indices	index	NOUN
ejpam-4427	18	22	,	,	PUNCT
ejpam-4427	18	23	graph	graph	NOUN
ejpam-4427	18	24	size	size	NOUN
ejpam-4427	18	25	and	and	CCONJ
ejpam-4427	18	26	order	order	NOUN
ejpam-4427	18	27	are	be	AUX
ejpam-4427	18	28	obtained	obtain	VERB
ejpam-4427	18	29	.	.	PUNCT
ejpam-4427	19	1	the	the	DET
ejpam-4427	19	2	distance	distance	NOUN
ejpam-4427	19	3	between	between	ADP
ejpam-4427	19	4	two	two	NUM
ejpam-4427	19	5	vertices	vertex	NOUN
ejpam-4427	19	6	u	u	NOUN
ejpam-4427	19	7	and	and	CCONJ
ejpam-4427	19	8	v	v	NOUN
ejpam-4427	19	9	of	of	ADP
ejpam-4427	19	10	a	a	DET
ejpam-4427	19	11	graph	graph	NOUN
ejpam-4427	19	12	is	be	AUX
ejpam-4427	19	13	the	the	DET
ejpam-4427	19	14	length	length	NOUN
ejpam-4427	19	15	of	of	ADP
ejpam-4427	19	16	a	a	DET
ejpam-4427	19	17	shortest	short	ADJ
ejpam-4427	19	18	path	path	NOUN
ejpam-4427	19	19	between	between	ADP
ejpam-4427	19	20	u	u	NOUN
ejpam-4427	19	21	and	and	CCONJ
ejpam-4427	19	22	v	v	NOUN
ejpam-4427	19	23	,	,	PUNCT
ejpam-4427	19	24	and	and	CCONJ
ejpam-4427	19	25	we	we	PRON
ejpam-4427	19	26	denote	denote	VERB
ejpam-4427	19	27	this	this	PRON
ejpam-4427	19	28	by	by	ADP
ejpam-4427	19	29	dg(u	dg(u	NOUN
ejpam-4427	19	30	,	,	PUNCT
ejpam-4427	19	31	v	v	NOUN
ejpam-4427	19	32	)	)	PUNCT
ejpam-4427	19	33	.	.	PUNCT
ejpam-4427	20	1	in	in	ADP
ejpam-4427	20	2	recent	recent	ADJ
ejpam-4427	20	3	years	year	NOUN
ejpam-4427	20	4	,	,	PUNCT
ejpam-4427	20	5	much	much	ADJ
ejpam-4427	20	6	attention	attention	NOUN
ejpam-4427	20	7	has	have	AUX
ejpam-4427	20	8	been	be	AUX
ejpam-4427	20	9	paid	pay	VERB
ejpam-4427	20	10	to	to	ADP
ejpam-4427	20	11	the	the	DET
ejpam-4427	20	12	metric	metric	ADJ
ejpam-4427	20	13	dimension	dimension	NOUN
ejpam-4427	20	14	of	of	ADP
ejpam-4427	20	15	graphs	graph	NOUN
ejpam-4427	20	16	:	:	PUNCT
ejpam-4427	20	17	this	this	PRON
ejpam-4427	20	18	is	be	AUX
ejpam-4427	20	19	the	the	DET
ejpam-4427	20	20	smallest	small	ADJ
ejpam-4427	20	21	size	size	NOUN
ejpam-4427	20	22	of	of	ADP
ejpam-4427	20	23	a	a	DET
ejpam-4427	20	24	subset	subset	NOUN
ejpam-4427	20	25	of	of	ADP
ejpam-4427	20	26	vertices	vertex	NOUN
ejpam-4427	20	27	(	(	PUNCT
ejpam-4427	20	28	called	call	VERB
ejpam-4427	20	29	a	a	DET
ejpam-4427	20	30	resolving	resolving	NOUN
ejpam-4427	20	31	set	set	NOUN
ejpam-4427	20	32	)	)	PUNCT
ejpam-4427	20	33	with	with	ADP
ejpam-4427	20	34	the	the	DET
ejpam-4427	20	35	property	property	NOUN
ejpam-4427	20	36	that	that	PRON
ejpam-4427	20	37	the	the	DET
ejpam-4427	20	38	list	list	NOUN
ejpam-4427	20	39	of	of	ADP
ejpam-4427	20	40	distances	distance	NOUN
ejpam-4427	20	41	from	from	ADP
ejpam-4427	20	42	any	any	DET
ejpam-4427	20	43	vertex	vertex	NOUN
ejpam-4427	20	44	to	to	ADP
ejpam-4427	20	45	those	those	PRON
ejpam-4427	20	46	in	in	ADP
ejpam-4427	20	47	the	the	DET
ejpam-4427	20	48	set	set	NOUN
ejpam-4427	20	49	uniquely	uniquely	ADV
ejpam-4427	20	50	identifies	identify	VERB
ejpam-4427	20	51	that	that	SCONJ
ejpam-4427	20	52	vertex	vertex	NOUN
ejpam-4427	20	53	and	and	CCONJ
ejpam-4427	20	54	is	be	AUX
ejpam-4427	20	55	denoted	denote	VERB
ejpam-4427	20	56	by	by	ADP
ejpam-4427	20	57	dim(g	dim(g	PROPN
ejpam-4427	20	58	)	)	PUNCT
ejpam-4427	20	59	.	.	PUNCT
ejpam-4427	21	1	according	accord	VERB
ejpam-4427	21	2	to	to	ADP
ejpam-4427	21	3	the	the	DET
ejpam-4427	21	4	paper	paper	NOUN
ejpam-4427	21	5	of	of	ADP
ejpam-4427	21	6	saenpholphat	saenpholphat	PROPN
ejpam-4427	21	7	et	et	PROPN
ejpam-4427	21	8	al	al	PROPN
ejpam-4427	21	9	.	.	PUNCT
ejpam-4427	22	1	[	[	X
ejpam-4427	22	2	7	7	NUM
ejpam-4427	22	3	]	]	PUNCT
ejpam-4427	22	4	,	,	PUNCT
ejpam-4427	22	5	for	for	ADP
ejpam-4427	22	6	an	an	DET
ejpam-4427	22	7	ordered	order	VERB
ejpam-4427	22	8	set	set	NOUN
ejpam-4427	22	9	of	of	ADP
ejpam-4427	22	10	vertices	vertex	NOUN
ejpam-4427	22	11	w	w	NOUN
ejpam-4427	22	12	=	=	SYM
ejpam-4427	22	13	{	{	PUNCT
ejpam-4427	22	14	w1	w1	NOUN
ejpam-4427	22	15	,	,	PUNCT
ejpam-4427	22	16	w2	w2	NOUN
ejpam-4427	22	17	,	,	PUNCT
ejpam-4427	22	18	...	...	PUNCT
ejpam-4427	22	19	,	,	PUNCT
ejpam-4427	22	20	wk	wk	AUX
ejpam-4427	22	21	}	}	PUNCT
ejpam-4427	22	22	⊆	⊆	NUM
ejpam-4427	22	23	v	v	NOUN
ejpam-4427	22	24	(	(	PUNCT
ejpam-4427	22	25	g	g	NOUN
ejpam-4427	22	26	)	)	PUNCT
ejpam-4427	22	27	and	and	CCONJ
ejpam-4427	22	28	a	a	DET
ejpam-4427	22	29	vertex	vertex	NOUN
ejpam-4427	22	30	v	v	NOUN
ejpam-4427	22	31	in	in	ADP
ejpam-4427	22	32	g	g	PROPN
ejpam-4427	22	33	,	,	PUNCT
ejpam-4427	22	34	the	the	DET
ejpam-4427	22	35	k	k	NOUN
ejpam-4427	22	36	-	-	NOUN
ejpam-4427	22	37	vector	vector	NOUN
ejpam-4427	22	38	(	(	PUNCT
ejpam-4427	22	39	ordered	order	VERB
ejpam-4427	22	40	k	k	NOUN
ejpam-4427	22	41	-	-	PUNCT
ejpam-4427	22	42	tuple	tuple	ADJ
ejpam-4427	22	43	)	)	PUNCT
ejpam-4427	22	44	r(v	r(v	PROPN
ejpam-4427	22	45	/	/	SYM
ejpam-4427	22	46	w	w	NOUN
ejpam-4427	22	47	)	)	PUNCT
ejpam-4427	23	1	=	=	SYM
ejpam-4427	23	2	(	(	PUNCT
ejpam-4427	23	3	dg(v	dg(v	X
ejpam-4427	23	4	,	,	PUNCT
ejpam-4427	23	5	w1	w1	NOUN
ejpam-4427	23	6	)	)	PUNCT
ejpam-4427	23	7	,	,	PUNCT
ejpam-4427	23	8	dg(v	dg(v	X
ejpam-4427	23	9	,	,	PUNCT
ejpam-4427	23	10	w2	w2	NOUN
ejpam-4427	23	11	)	)	PUNCT
ejpam-4427	23	12	,	,	PUNCT
ejpam-4427	23	13	...	...	PUNCT
ejpam-4427	23	14	,	,	PUNCT
ejpam-4427	23	15	dg(v	dg(v	X
ejpam-4427	23	16	,	,	PUNCT
ejpam-4427	23	17	wk	wk	NOUN
ejpam-4427	23	18	)	)	PUNCT
ejpam-4427	23	19	)	)	PUNCT
ejpam-4427	23	20	is	be	AUX
ejpam-4427	23	21	referred	refer	VERB
ejpam-4427	23	22	to	to	ADP
ejpam-4427	23	23	as	as	ADP
ejpam-4427	23	24	the	the	DET
ejpam-4427	23	25	(	(	PUNCT
ejpam-4427	23	26	metric	metric	ADJ
ejpam-4427	23	27	)	)	PUNCT
ejpam-4427	23	28	representation	representation	NOUN
ejpam-4427	23	29	of	of	ADP
ejpam-4427	23	30	v	v	NOUN
ejpam-4427	23	31	with	with	ADP
ejpam-4427	23	32	respect	respect	NOUN
ejpam-4427	23	33	to	to	ADP
ejpam-4427	23	34	w	w	PROPN
ejpam-4427	23	35	.	.	PUNCT
ejpam-4427	24	1	the	the	DET
ejpam-4427	24	2	set	set	NOUN
ejpam-4427	24	3	w	w	NOUN
ejpam-4427	24	4	is	be	AUX
ejpam-4427	24	5	called	call	VERB
ejpam-4427	24	6	a	a	DET
ejpam-4427	24	7	resolving	resolving	NOUN
ejpam-4427	24	8	set	set	VERB
ejpam-4427	24	9	for	for	ADP
ejpam-4427	24	10	g	g	PROPN
ejpam-4427	24	11	if	if	SCONJ
ejpam-4427	24	12	distinct	distinct	ADJ
ejpam-4427	24	13	vertices	vertex	NOUN
ejpam-4427	24	14	have	have	VERB
ejpam-4427	24	15	distinct	distinct	ADJ
ejpam-4427	24	16	representation	representation	NOUN
ejpam-4427	24	17	with	with	ADP
ejpam-4427	24	18	respect	respect	NOUN
ejpam-4427	24	19	to	to	ADP
ejpam-4427	24	20	w	w	PROPN
ejpam-4427	24	21	.	.	PUNCT
ejpam-4427	25	1	hence	hence	ADV
ejpam-4427	25	2	,	,	PUNCT
ejpam-4427	25	3	if	if	SCONJ
ejpam-4427	25	4	w	w	NOUN
ejpam-4427	25	5	is	be	AUX
ejpam-4427	25	6	a	a	DET
ejpam-4427	25	7	resolving	resolving	NOUN
ejpam-4427	25	8	set	set	NOUN
ejpam-4427	25	9	of	of	ADP
ejpam-4427	25	10	cardinality	cardinality	PROPN
ejpam-4427	25	11	k	k	PROPN
ejpam-4427	25	12	for	for	ADP
ejpam-4427	25	13	a	a	DET
ejpam-4427	25	14	graph	graph	NOUN
ejpam-4427	25	15	g	g	NOUN
ejpam-4427	25	16	of	of	ADP
ejpam-4427	25	17	order	order	NOUN
ejpam-4427	25	18	n	n	CCONJ
ejpam-4427	25	19	,	,	PUNCT
ejpam-4427	25	20	then	then	ADV
ejpam-4427	25	21	the	the	DET
ejpam-4427	25	22	set	set	NOUN
ejpam-4427	25	23	{	{	PUNCT
ejpam-4427	25	24	r(v	r(v	PROPN
ejpam-4427	25	25	/	/	SYM
ejpam-4427	25	26	w	w	PROPN
ejpam-4427	25	27	)	)	PUNCT
ejpam-4427	25	28	:	:	PUNCT
ejpam-4427	25	29	v	v	X
ejpam-4427	25	30	∈	∈	PROPN
ejpam-4427	25	31	v	v	NOUN
ejpam-4427	25	32	(	(	PUNCT
ejpam-4427	25	33	g	g	NOUN
ejpam-4427	25	34	)	)	PUNCT
ejpam-4427	25	35	}	}	PUNCT
ejpam-4427	25	36	consists	consist	VERB
ejpam-4427	25	37	of	of	ADP
ejpam-4427	25	38	n	n	PRON
ejpam-4427	25	39	distinct	distinct	ADJ
ejpam-4427	25	40	k	k	NOUN
ejpam-4427	25	41	-	-	NOUN
ejpam-4427	25	42	vectors	vector	NOUN
ejpam-4427	25	43	.	.	PUNCT
ejpam-4427	26	1	a	a	DET
ejpam-4427	26	2	resolving	resolving	NOUN
ejpam-4427	26	3	set	set	NOUN
ejpam-4427	26	4	of	of	ADP
ejpam-4427	26	5	minimum	minimum	ADJ
ejpam-4427	26	6	cardinality	cardinality	NOUN
ejpam-4427	26	7	is	be	AUX
ejpam-4427	26	8	called	call	VERB
ejpam-4427	26	9	a	a	DET
ejpam-4427	26	10	minimum	minimum	ADJ
ejpam-4427	26	11	resolving	resolving	NOUN
ejpam-4427	26	12	set	set	VERB
ejpam-4427	26	13	or	or	CCONJ
ejpam-4427	26	14	a	a	DET
ejpam-4427	26	15	basis	basis	NOUN
ejpam-4427	26	16	,	,	PUNCT
ejpam-4427	26	17	and	and	CCONJ
ejpam-4427	26	18	the	the	DET
ejpam-4427	26	19	cardinality	cardinality	NOUN
ejpam-4427	26	20	of	of	ADP
ejpam-4427	26	21	a	a	DET
ejpam-4427	26	22	basis	basis	NOUN
ejpam-4427	26	23	for	for	ADP
ejpam-4427	26	24	g	g	PROPN
ejpam-4427	26	25	is	be	AUX
ejpam-4427	26	26	the	the	DET
ejpam-4427	26	27	dimension	dimension	NOUN
ejpam-4427	26	28	dim(g	dim(g	PROPN
ejpam-4427	26	29	)	)	PUNCT
ejpam-4427	26	30	of	of	ADP
ejpam-4427	26	31	g.	g.	PROPN
ejpam-4427	26	32	in	in	ADP
ejpam-4427	26	33	the	the	DET
ejpam-4427	26	34	paper	paper	NOUN
ejpam-4427	26	35	of	of	ADP
ejpam-4427	26	36	rara	rara	NOUN
ejpam-4427	26	37	and	and	CCONJ
ejpam-4427	26	38	cabaro	cabaro	VERB
ejpam-4427	27	1	[	[	X
ejpam-4427	27	2	5	5	NUM
ejpam-4427	27	3	]	]	PUNCT
ejpam-4427	27	4	,	,	PUNCT
ejpam-4427	27	5	an	an	DET
ejpam-4427	27	6	ordered	order	VERB
ejpam-4427	27	7	set	set	NOUN
ejpam-4427	27	8	of	of	ADP
ejpam-4427	27	9	vertices	vertex	NOUN
ejpam-4427	27	10	w	w	NOUN
ejpam-4427	27	11	=	=	SYM
ejpam-4427	27	12	{	{	PUNCT
ejpam-4427	27	13	w1	w1	NOUN
ejpam-4427	27	14	,	,	PUNCT
ejpam-4427	27	15	...	...	PUNCT
ejpam-4427	27	16	,	,	PUNCT
ejpam-4427	27	17	wl	wl	PROPN
ejpam-4427	27	18	}	}	PUNCT
ejpam-4427	27	19	is	be	AUX
ejpam-4427	27	20	a	a	DET
ejpam-4427	27	21	2	2	NUM
ejpam-4427	27	22	-	-	PUNCT
ejpam-4427	27	23	resolving	resolving	NOUN
ejpam-4427	27	24	set	set	NOUN
ejpam-4427	27	25	for	for	ADP
ejpam-4427	27	26	g	g	PROPN
ejpam-4427	27	27	if	if	SCONJ
ejpam-4427	27	28	,	,	PUNCT
ejpam-4427	27	29	for	for	ADP
ejpam-4427	27	30	any	any	DET
ejpam-4427	27	31	distinct	distinct	ADJ
ejpam-4427	27	32	vertices	vertex	NOUN
ejpam-4427	27	33	u	u	NOUN
ejpam-4427	27	34	,	,	PUNCT
ejpam-4427	27	35	v	v	NOUN
ejpam-4427	27	36	∈	∈	PROPN
ejpam-4427	27	37	v	v	NOUN
ejpam-4427	27	38	(	(	PUNCT
ejpam-4427	27	39	g	g	NOUN
ejpam-4427	27	40	)	)	PUNCT
ejpam-4427	27	41	,	,	PUNCT
ejpam-4427	27	42	the	the	DET
ejpam-4427	27	43	(	(	PUNCT
ejpam-4427	27	44	metric	metric	NOUN
ejpam-4427	27	45	)	)	PUNCT
ejpam-4427	27	46	representations	representation	VERB
ejpam-4427	27	47	r(u	r(u	PROPN
ejpam-4427	27	48	/	/	SYM
ejpam-4427	27	49	w	w	PROPN
ejpam-4427	27	50	)	)	PUNCT
ejpam-4427	27	51	and	and	CCONJ
ejpam-4427	27	52	r(v	r(v	PROPN
ejpam-4427	27	53	/	/	SYM
ejpam-4427	27	54	w	w	PROPN
ejpam-4427	27	55	)	)	PUNCT
ejpam-4427	27	56	of	of	ADP
ejpam-4427	27	57	u	u	NOUN
ejpam-4427	27	58	and	and	CCONJ
ejpam-4427	27	59	v	v	NOUN
ejpam-4427	27	60	,	,	PUNCT
ejpam-4427	27	61	respectively	respectively	ADV
ejpam-4427	27	62	differ	differ	VERB
ejpam-4427	27	63	in	in	ADP
ejpam-4427	27	64	at	at	ADV
ejpam-4427	27	65	least	least	ADJ
ejpam-4427	27	66	2	2	NUM
ejpam-4427	27	67	positions	position	NOUN
ejpam-4427	27	68	.	.	PUNCT
ejpam-4427	28	1	then	then	ADV
ejpam-4427	28	2	w	w	NOUN
ejpam-4427	28	3	is	be	AUX
ejpam-4427	28	4	said	say	VERB
ejpam-4427	28	5	to	to	PART
ejpam-4427	28	6	be	be	AUX
ejpam-4427	28	7	a	a	DET
ejpam-4427	28	8	2	2	NUM
ejpam-4427	28	9	-	-	PUNCT
ejpam-4427	28	10	resolving	resolving	NOUN
ejpam-4427	28	11	set	set	NOUN
ejpam-4427	28	12	for	for	ADP
ejpam-4427	28	13	g.	g.	PROPN
ejpam-4427	28	14	if	if	SCONJ
ejpam-4427	28	15	g	g	PROPN
ejpam-4427	28	16	has	have	VERB
ejpam-4427	28	17	a	a	DET
ejpam-4427	28	18	2	2	NUM
ejpam-4427	28	19	-	-	PUNCT
ejpam-4427	28	20	resolving	resolve	VERB
ejpam-4427	28	21	set	set	NOUN
ejpam-4427	28	22	,	,	PUNCT
ejpam-4427	28	23	the	the	DET
ejpam-4427	28	24	minimum	minimum	ADJ
ejpam-4427	28	25	cardinality	cardinality	NOUN
ejpam-4427	28	26	dim2(g	dim2(g	NOUN
ejpam-4427	28	27	)	)	PUNCT
ejpam-4427	28	28	is	be	AUX
ejpam-4427	28	29	called	call	VERB
ejpam-4427	28	30	the	the	DET
ejpam-4427	28	31	2	2	NUM
ejpam-4427	28	32	-	-	PUNCT
ejpam-4427	28	33	metric	metric	ADJ
ejpam-4427	28	34	dimension	dimension	NOUN
ejpam-4427	28	35	of	of	ADP
ejpam-4427	28	36	g.	g.	PROPN
ejpam-4427	28	37	if	if	SCONJ
ejpam-4427	28	38	k	k	PROPN
ejpam-4427	28	39	=	=	SYM
ejpam-4427	28	40	2	2	NUM
ejpam-4427	28	41	is	be	AUX
ejpam-4427	28	42	the	the	DET
ejpam-4427	28	43	largest	large	ADJ
ejpam-4427	28	44	integer	integer	NOUN
ejpam-4427	28	45	for	for	ADP
ejpam-4427	28	46	which	which	PRON
ejpam-4427	28	47	g	g	NOUN
ejpam-4427	28	48	has	have	VERB
ejpam-4427	28	49	a	a	DET
ejpam-4427	28	50	2	2	NUM
ejpam-4427	28	51	-	-	PUNCT
ejpam-4427	28	52	resolving	resolve	VERB
ejpam-4427	28	53	set	set	NOUN
ejpam-4427	28	54	,	,	PUNCT
ejpam-4427	28	55	then	then	ADV
ejpam-4427	28	56	we	we	PRON
ejpam-4427	28	57	say	say	VERB
ejpam-4427	28	58	that	that	SCONJ
ejpam-4427	28	59	g	g	PROPN
ejpam-4427	28	60	is	be	AUX
ejpam-4427	28	61	a	a	DET
ejpam-4427	28	62	2	2	NUM
ejpam-4427	28	63	-	-	PUNCT
ejpam-4427	28	64	metric	metric	ADJ
ejpam-4427	28	65	dimensional	dimensional	ADJ
ejpam-4427	28	66	graph	graph	NOUN
ejpam-4427	28	67	.	.	PUNCT
ejpam-4427	29	1	in	in	ADP
ejpam-4427	29	2	this	this	DET
ejpam-4427	29	3	paper	paper	NOUN
ejpam-4427	29	4	,	,	PUNCT
ejpam-4427	29	5	the	the	DET
ejpam-4427	29	6	concept	concept	NOUN
ejpam-4427	29	7	of	of	ADP
ejpam-4427	29	8	restrained	restrained	ADJ
ejpam-4427	29	9	2	2	NUM
ejpam-4427	29	10	-	-	PUNCT
ejpam-4427	29	11	resolving	resolve	VERB
ejpam-4427	29	12	set	set	NOUN
ejpam-4427	29	13	in	in	ADP
ejpam-4427	29	14	the	the	DET
ejpam-4427	29	15	join	join	NOUN
ejpam-4427	29	16	,	,	PUNCT
ejpam-4427	29	17	corona	corona	NOUN
ejpam-4427	29	18	and	and	CCONJ
ejpam-4427	29	19	lexicographic	lexicographic	ADJ
ejpam-4427	29	20	product	product	NOUN
ejpam-4427	29	21	of	of	ADP
ejpam-4427	29	22	two	two	NUM
ejpam-4427	29	23	graphs	graph	NOUN
ejpam-4427	29	24	is	be	AUX
ejpam-4427	29	25	discussed	discuss	VERB
ejpam-4427	29	26	.	.	PUNCT
ejpam-4427	30	1	2	2	X
ejpam-4427	30	2	.	.	X
ejpam-4427	30	3	preliminary	preliminary	ADJ
ejpam-4427	30	4	results	result	NOUN
ejpam-4427	30	5	in	in	ADP
ejpam-4427	30	6	this	this	DET
ejpam-4427	30	7	study	study	NOUN
ejpam-4427	30	8	,	,	PUNCT
ejpam-4427	30	9	we	we	PRON
ejpam-4427	30	10	consider	consider	VERB
ejpam-4427	30	11	finite	finite	NOUN
ejpam-4427	30	12	,	,	PUNCT
ejpam-4427	30	13	simple	simple	ADJ
ejpam-4427	30	14	and	and	CCONJ
ejpam-4427	30	15	connected	connected	ADJ
ejpam-4427	30	16	undirected	undirected	ADJ
ejpam-4427	30	17	graphs	graph	NOUN
ejpam-4427	30	18	.	.	PUNCT
ejpam-4427	31	1	for	for	ADP
ejpam-4427	31	2	basic	basic	ADJ
ejpam-4427	31	3	graph	graph	NOUN
ejpam-4427	31	4	-	-	PUNCT
ejpam-4427	31	5	theoretic	theoretic	NOUN
ejpam-4427	31	6	concepts	concept	NOUN
ejpam-4427	31	7	,	,	PUNCT
ejpam-4427	31	8	we	we	PRON
ejpam-4427	31	9	refer	refer	VERB
ejpam-4427	31	10	readers	reader	NOUN
ejpam-4427	31	11	to	to	ADP
ejpam-4427	31	12	[	[	X
ejpam-4427	31	13	3	3	NUM
ejpam-4427	31	14	]	]	PUNCT
ejpam-4427	31	15	.	.	PUNCT
ejpam-4427	32	1	remark	remark	PROPN
ejpam-4427	32	2	1	1	NUM
ejpam-4427	32	3	.	.	PUNCT
ejpam-4427	33	1	let	let	VERB
ejpam-4427	33	2	g	g	PRON
ejpam-4427	33	3	be	be	AUX
ejpam-4427	33	4	a	a	DET
ejpam-4427	33	5	connected	connected	ADJ
ejpam-4427	33	6	graph	graph	NOUN
ejpam-4427	33	7	.	.	PUNCT
ejpam-4427	34	1	then	then	ADV
ejpam-4427	34	2	every	every	DET
ejpam-4427	34	3	restrained	restrained	ADJ
ejpam-4427	34	4	2	2	NUM
ejpam-4427	34	5	-	-	PUNCT
ejpam-4427	34	6	resolving	resolving	NOUN
ejpam-4427	34	7	set	set	NOUN
ejpam-4427	34	8	in	in	ADP
ejpam-4427	34	9	g	g	PROPN
ejpam-4427	34	10	is	be	AUX
ejpam-4427	34	11	2	2	NUM
ejpam-4427	34	12	-	-	PUNCT
ejpam-4427	34	13	resolving	resolving	NOUN
ejpam-4427	34	14	.	.	PUNCT
ejpam-4427	35	1	hence	hence	ADV
ejpam-4427	35	2	,	,	PUNCT
ejpam-4427	35	3	dim2(g	dim2(g	NOUN
ejpam-4427	35	4	)	)	PUNCT
ejpam-4427	35	5	≤	≤	NOUN
ejpam-4427	35	6	rdim2(g	rdim2(g	VERB
ejpam-4427	35	7	)	)	PUNCT
ejpam-4427	35	8	.	.	PUNCT
ejpam-4427	36	1	proposition	proposition	NOUN
ejpam-4427	36	2	1	1	NUM
ejpam-4427	36	3	.	.	PUNCT
ejpam-4427	37	1	[	[	X
ejpam-4427	37	2	2	2	X
ejpam-4427	37	3	]	]	PUNCT
ejpam-4427	37	4	let	let	VERB
ejpam-4427	37	5	g	g	PRON
ejpam-4427	37	6	be	be	AUX
ejpam-4427	37	7	a	a	DET
ejpam-4427	37	8	connected	connected	ADJ
ejpam-4427	37	9	graph	graph	NOUN
ejpam-4427	37	10	of	of	ADP
ejpam-4427	37	11	order	order	NOUN
ejpam-4427	37	12	n	n	PRON
ejpam-4427	37	13	≥	≥	NOUN
ejpam-4427	37	14	2	2	NUM
ejpam-4427	37	15	.	.	PUNCT
ejpam-4427	37	16	then	then	ADV
ejpam-4427	37	17	dim2(g	dim2(g	NOUN
ejpam-4427	37	18	)	)	PUNCT
ejpam-4427	37	19	=	=	SYM
ejpam-4427	37	20	2	2	NUM
ejpam-4427	38	1	if	if	SCONJ
ejpam-4427	38	2	and	and	CCONJ
ejpam-4427	38	3	only	only	ADV
ejpam-4427	38	4	if	if	SCONJ
ejpam-4427	38	5	g	g	PROPN
ejpam-4427	38	6	∼=	∼=	PROPN
ejpam-4427	38	7	pn	pn	PROPN
ejpam-4427	38	8	.	.	PROPN
ejpam-4427	38	9	proposition	proposition	PROPN
ejpam-4427	38	10	2	2	NUM
ejpam-4427	38	11	.	.	PUNCT
ejpam-4427	38	12	dim2(kn	dim2(kn	PROPN
ejpam-4427	38	13	)	)	PUNCT
ejpam-4427	39	1	=	=	SYM
ejpam-4427	39	2	n	n	PROPN
ejpam-4427	39	3	for	for	ADP
ejpam-4427	39	4	n	n	PRON
ejpam-4427	39	5	≥	≥	NUM
ejpam-4427	39	6	2	2	NUM
ejpam-4427	39	7	.	.	PUNCT
ejpam-4427	39	8	proposition	proposition	NOUN
ejpam-4427	39	9	3	3	X
ejpam-4427	39	10	.	.	PUNCT
ejpam-4427	40	1	let	let	VERB
ejpam-4427	40	2	g	g	NOUN
ejpam-4427	40	3	be	be	AUX
ejpam-4427	40	4	any	any	DET
ejpam-4427	40	5	connected	connected	ADJ
ejpam-4427	40	6	graph	graph	NOUN
ejpam-4427	40	7	of	of	ADP
ejpam-4427	40	8	order	order	NOUN
ejpam-4427	40	9	n	n	PRON
ejpam-4427	40	10	≥	≥	NOUN
ejpam-4427	40	11	2	2	NUM
ejpam-4427	40	12	.	.	PUNCT
ejpam-4427	40	13	i.	i.	NOUN
ejpam-4427	40	14	rdim2(g	rdim2(g	VERB
ejpam-4427	40	15	)	)	PUNCT
ejpam-4427	40	16	=	=	SYM
ejpam-4427	40	17	2	2	NUM
ejpam-4427	40	18	if	if	SCONJ
ejpam-4427	40	19	and	and	CCONJ
ejpam-4427	40	20	only	only	ADV
ejpam-4427	40	21	if	if	SCONJ
ejpam-4427	40	22	g	g	PROPN
ejpam-4427	40	23	∼=	∼=	PROPN
ejpam-4427	40	24	pn	pn	NOUN
ejpam-4427	40	25	,	,	PUNCT
ejpam-4427	40	26	n	n	CCONJ
ejpam-4427	40	27	̸=	̸=	PROPN
ejpam-4427	40	28	3	3	NUM
ejpam-4427	40	29	.	.	X
ejpam-4427	40	30	ii	ii	PROPN
ejpam-4427	40	31	.	.	PUNCT
ejpam-4427	41	1	rdim2(kn	rdim2(kn	NOUN
ejpam-4427	41	2	)	)	PUNCT
ejpam-4427	42	1	=	=	SYM
ejpam-4427	42	2	n.	n.	PROPN
ejpam-4427	42	3	j.	j.	PROPN
ejpam-4427	42	4	cabaro	cabaro	PROPN
ejpam-4427	42	5	,	,	PUNCT
ejpam-4427	42	6	h.	h.	PROPN
ejpam-4427	42	7	rara	rara	PROPN
ejpam-4427	42	8	/	/	SYM
ejpam-4427	42	9	eur	eur	PROPN
ejpam-4427	42	10	.	.	PUNCT
ejpam-4427	43	1	j.	j.	PROPN
ejpam-4427	43	2	pure	pure	PROPN
ejpam-4427	43	3	appl	appl	PROPN
ejpam-4427	43	4	.	.	PROPN
ejpam-4427	43	5	math	math	PROPN
ejpam-4427	43	6	,	,	PUNCT
ejpam-4427	43	7	15	15	NUM
ejpam-4427	43	8	(	(	PUNCT
ejpam-4427	43	9	3	3	NUM
ejpam-4427	43	10	)	)	PUNCT
ejpam-4427	43	11	(	(	PUNCT
ejpam-4427	43	12	2022	2022	NUM
ejpam-4427	43	13	)	)	PUNCT
ejpam-4427	43	14	,	,	PUNCT
ejpam-4427	43	15	1229	1229	NUM
ejpam-4427	43	16	-	-	SYM
ejpam-4427	43	17	1236	1236	NUM
ejpam-4427	43	18	1231	1231	NUM
ejpam-4427	43	19	proof	proof	NOUN
ejpam-4427	43	20	.	.	PUNCT
ejpam-4427	44	1	i.	i.	PROPN
ejpam-4427	44	2	suppose	suppose	VERB
ejpam-4427	44	3	rdim2(g	rdim2(g	VERB
ejpam-4427	44	4	)	)	PUNCT
ejpam-4427	44	5	=	=	SYM
ejpam-4427	44	6	2	2	X
ejpam-4427	44	7	.	.	PUNCT
ejpam-4427	44	8	by	by	ADP
ejpam-4427	44	9	remark	remark	NOUN
ejpam-4427	44	10	1	1	NUM
ejpam-4427	44	11	,	,	PUNCT
ejpam-4427	44	12	dim2(g	dim2(g	NOUN
ejpam-4427	44	13	)	)	PUNCT
ejpam-4427	45	1	=	=	SYM
ejpam-4427	45	2	2	2	X
ejpam-4427	45	3	.	.	X
ejpam-4427	45	4	hence	hence	ADV
ejpam-4427	45	5	,	,	PUNCT
ejpam-4427	45	6	by	by	ADP
ejpam-4427	45	7	proposition	proposition	NOUN
ejpam-4427	45	8	1	1	NUM
ejpam-4427	45	9	,	,	PUNCT
ejpam-4427	45	10	g	g	PROPN
ejpam-4427	45	11	=	=	SYM
ejpam-4427	45	12	pn	pn	PROPN
ejpam-4427	45	13	.	.	PROPN
ejpam-4427	46	1	since	since	SCONJ
ejpam-4427	46	2	rdim2(p3	rdim2(p3	PROPN
ejpam-4427	46	3	)	)	PUNCT
ejpam-4427	46	4	=	=	SYM
ejpam-4427	47	1	3	3	X
ejpam-4427	47	2	,	,	PUNCT
ejpam-4427	47	3	g	g	PROPN
ejpam-4427	47	4	=	=	PUNCT
ejpam-4427	47	5	pn	pn	PROPN
ejpam-4427	47	6	except	except	SCONJ
ejpam-4427	47	7	n	n	PROPN
ejpam-4427	47	8	=	=	SYM
ejpam-4427	47	9	3	3	X
ejpam-4427	47	10	.	.	PUNCT
ejpam-4427	48	1	conversely	conversely	ADV
ejpam-4427	48	2	,	,	PUNCT
ejpam-4427	48	3	if	if	SCONJ
ejpam-4427	48	4	g	g	PROPN
ejpam-4427	48	5	=	=	PUNCT
ejpam-4427	48	6	pn	pn	PROPN
ejpam-4427	48	7	=	=	PUNCT
ejpam-4427	49	1	[	[	X
ejpam-4427	49	2	v1	v1	NOUN
ejpam-4427	49	3	,	,	PUNCT
ejpam-4427	49	4	v2	v2	PROPN
ejpam-4427	49	5	,	,	PUNCT
ejpam-4427	49	6	...	...	PUNCT
ejpam-4427	49	7	,	,	PUNCT
ejpam-4427	49	8	vn	vn	X
ejpam-4427	49	9	]	]	PUNCT
ejpam-4427	49	10	,	,	PUNCT
ejpam-4427	49	11	then	then	ADV
ejpam-4427	49	12	s	s	VERB
ejpam-4427	49	13	=	=	NOUN
ejpam-4427	49	14	{	{	PUNCT
ejpam-4427	49	15	v1	v1	PROPN
ejpam-4427	49	16	,	,	PUNCT
ejpam-4427	49	17	vn	vn	PROPN
ejpam-4427	49	18	}	}	PUNCT
ejpam-4427	49	19	is	be	AUX
ejpam-4427	49	20	a	a	DET
ejpam-4427	49	21	restrained	restrained	ADJ
ejpam-4427	49	22	2	2	NUM
ejpam-4427	49	23	-	-	PUNCT
ejpam-4427	49	24	resolving	resolve	VERB
ejpam-4427	49	25	set	set	NOUN
ejpam-4427	49	26	of	of	ADP
ejpam-4427	49	27	g.	g.	PROPN
ejpam-4427	49	28	hence	hence	ADV
ejpam-4427	49	29	,	,	PUNCT
ejpam-4427	49	30	rdim2(g	rdim2(g	ADJ
ejpam-4427	49	31	)	)	PUNCT
ejpam-4427	49	32	=	=	SYM
ejpam-4427	49	33	2	2	NUM
ejpam-4427	49	34	.	.	X
ejpam-4427	49	35	ii	ii	PROPN
ejpam-4427	49	36	.	.	PUNCT
ejpam-4427	50	1	by	by	ADP
ejpam-4427	50	2	proposition	proposition	NOUN
ejpam-4427	50	3	2	2	NUM
ejpam-4427	50	4	,	,	PUNCT
ejpam-4427	50	5	s	s	PART
ejpam-4427	50	6	=	=	SYM
ejpam-4427	50	7	v	v	PROPN
ejpam-4427	50	8	(	(	PUNCT
ejpam-4427	50	9	kn	kn	PROPN
ejpam-4427	50	10	)	)	PUNCT
ejpam-4427	50	11	is	be	AUX
ejpam-4427	50	12	the	the	DET
ejpam-4427	50	13	only	only	ADJ
ejpam-4427	50	14	2	2	NUM
ejpam-4427	50	15	-	-	PUNCT
ejpam-4427	50	16	resolving	resolve	VERB
ejpam-4427	50	17	set	set	NOUN
ejpam-4427	50	18	of	of	ADP
ejpam-4427	50	19	kn	kn	PROPN
ejpam-4427	50	20	.	.	PUNCT
ejpam-4427	51	1	thus	thus	ADV
ejpam-4427	51	2	,	,	PUNCT
ejpam-4427	51	3	rdim2(kn	rdim2(kn	NOUN
ejpam-4427	51	4	)	)	PUNCT
ejpam-4427	52	1	=	=	PUNCT
ejpam-4427	52	2	n.	n.	NOUN
ejpam-4427	52	3	3	3	X
ejpam-4427	52	4	.	.	PUNCT
ejpam-4427	53	1	restrained	restrain	VERB
ejpam-4427	53	2	2	2	NUM
ejpam-4427	53	3	-	-	PUNCT
ejpam-4427	53	4	resolving	resolve	VERB
ejpam-4427	53	5	sets	set	NOUN
ejpam-4427	53	6	in	in	ADP
ejpam-4427	53	7	the	the	DET
ejpam-4427	53	8	join	join	NOUN
ejpam-4427	53	9	of	of	ADP
ejpam-4427	53	10	graphs	graph	NOUN
ejpam-4427	53	11	definition	definition	NOUN
ejpam-4427	53	12	1	1	NUM
ejpam-4427	53	13	.	.	PUNCT
ejpam-4427	54	1	let	let	VERB
ejpam-4427	54	2	g	g	NOUN
ejpam-4427	54	3	be	be	AUX
ejpam-4427	54	4	any	any	DET
ejpam-4427	54	5	nontrivial	nontrivial	ADJ
ejpam-4427	54	6	connected	connect	VERB
ejpam-4427	54	7	graph	graph	NOUN
ejpam-4427	54	8	and	and	CCONJ
ejpam-4427	54	9	s	s	VERB
ejpam-4427	54	10	⊆	⊆	NUM
ejpam-4427	54	11	v	v	NOUN
ejpam-4427	54	12	(	(	PUNCT
ejpam-4427	54	13	g	g	NOUN
ejpam-4427	54	14	)	)	PUNCT
ejpam-4427	54	15	.	.	PUNCT
ejpam-4427	55	1	a	a	DET
ejpam-4427	55	2	set	set	NOUN
ejpam-4427	55	3	s	s	PART
ejpam-4427	55	4	⊂	⊂	X
ejpam-4427	55	5	v	v	X
ejpam-4427	55	6	(	(	PUNCT
ejpam-4427	55	7	g	g	NOUN
ejpam-4427	55	8	)	)	PUNCT
ejpam-4427	55	9	is	be	AUX
ejpam-4427	55	10	a	a	DET
ejpam-4427	55	11	2	2	NUM
ejpam-4427	55	12	-	-	PUNCT
ejpam-4427	55	13	locating	locate	VERB
ejpam-4427	55	14	set	set	NOUN
ejpam-4427	55	15	of	of	ADP
ejpam-4427	55	16	g	g	NOUN
ejpam-4427	55	17	if	if	SCONJ
ejpam-4427	55	18	it	it	PRON
ejpam-4427	55	19	satisfies	satisfy	VERB
ejpam-4427	55	20	the	the	DET
ejpam-4427	55	21	following	follow	VERB
ejpam-4427	55	22	conditions	condition	NOUN
ejpam-4427	55	23	:	:	PUNCT
ejpam-4427	55	24	(	(	PUNCT
ejpam-4427	55	25	i	i	NOUN
ejpam-4427	55	26	)	)	PUNCT
ejpam-4427	55	27	|(ng(x)	|(ng(x)	PROPN
ejpam-4427	55	28	△	△	NOUN
ejpam-4427	55	29	ng(y	ng(y	NUM
ejpam-4427	55	30	)	)	PUNCT
ejpam-4427	55	31	)	)	PUNCT
ejpam-4427	56	1	∩	∩	NOUN
ejpam-4427	56	2	s|	s|	VERB
ejpam-4427	56	3	≥	≥	NOUN
ejpam-4427	56	4	2	2	NUM
ejpam-4427	56	5	,	,	PUNCT
ejpam-4427	56	6	for	for	ADP
ejpam-4427	56	7	all	all	DET
ejpam-4427	56	8	x	x	NOUN
ejpam-4427	56	9	,	,	PUNCT
ejpam-4427	56	10	y	y	PROPN
ejpam-4427	56	11	∈	∈	PROPN
ejpam-4427	56	12	v	v	X
ejpam-4427	56	13	(	(	PUNCT
ejpam-4427	56	14	g)\s	g)\s	VERB
ejpam-4427	56	15	with	with	ADP
ejpam-4427	56	16	x	x	PROPN
ejpam-4427	56	17	̸=	̸=	PROPN
ejpam-4427	56	18	y	y	PROPN
ejpam-4427	56	19	(	(	PUNCT
ejpam-4427	56	20	ii	ii	PROPN
ejpam-4427	56	21	)	)	PUNCT
ejpam-4427	56	22	(	(	PUNCT
ejpam-4427	56	23	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-4427	56	24	)	)	PUNCT
ejpam-4427	56	25	)	)	PUNCT
ejpam-4427	56	26	∩	∩	PROPN
ejpam-4427	56	27	s	s	PART
ejpam-4427	56	28	̸=	̸=	PROPN
ejpam-4427	56	29	∅	∅	NOUN
ejpam-4427	56	30	or	or	CCONJ
ejpam-4427	56	31	(	(	PUNCT
ejpam-4427	56	32	ng(w)\ng[v]\s	ng(w)\ng[v]\s	PROPN
ejpam-4427	56	33	̸=	̸=	PROPN
ejpam-4427	56	34	∅	∅	NOUN
ejpam-4427	56	35	,	,	PUNCT
ejpam-4427	56	36	for	for	ADP
ejpam-4427	56	37	all	all	PRON
ejpam-4427	56	38	v	v	ADP
ejpam-4427	56	39	∈	∈	NOUN
ejpam-4427	56	40	s	s	NOUN
ejpam-4427	56	41	and	and	CCONJ
ejpam-4427	56	42	for	for	ADP
ejpam-4427	56	43	all	all	DET
ejpam-4427	56	44	w	w	PROPN
ejpam-4427	56	45	∈	∈	PROPN
ejpam-4427	56	46	v(g)\s	v(g)\s	NOUN
ejpam-4427	56	47	.	.	PUNCT
ejpam-4427	57	1	the	the	DET
ejpam-4427	57	2	2	2	NUM
ejpam-4427	57	3	-	-	PUNCT
ejpam-4427	57	4	locating	locate	VERB
ejpam-4427	57	5	number	number	NOUN
ejpam-4427	57	6	of	of	ADP
ejpam-4427	57	7	g	g	NOUN
ejpam-4427	57	8	,	,	PUNCT
ejpam-4427	57	9	denoted	denote	VERB
ejpam-4427	57	10	by	by	ADP
ejpam-4427	57	11	ln2(g	ln2(g	NOUN
ejpam-4427	57	12	)	)	PUNCT
ejpam-4427	57	13	,	,	PUNCT
ejpam-4427	57	14	is	be	AUX
ejpam-4427	57	15	the	the	DET
ejpam-4427	57	16	smallest	small	ADJ
ejpam-4427	57	17	cardinality	cardinality	NOUN
ejpam-4427	57	18	of	of	ADP
ejpam-4427	57	19	a	a	DET
ejpam-4427	57	20	2	2	NUM
ejpam-4427	57	21	-	-	PUNCT
ejpam-4427	57	22	locating	locate	VERB
ejpam-4427	57	23	set	set	NOUN
ejpam-4427	57	24	of	of	ADP
ejpam-4427	57	25	g.	g.	PROPN
ejpam-4427	57	26	a	a	DET
ejpam-4427	57	27	2	2	NUM
ejpam-4427	57	28	-	-	PUNCT
ejpam-4427	57	29	locating	locate	VERB
ejpam-4427	57	30	set	set	NOUN
ejpam-4427	57	31	of	of	ADP
ejpam-4427	57	32	g	g	NOUN
ejpam-4427	57	33	of	of	ADP
ejpam-4427	57	34	cardinality	cardinality	PROPN
ejpam-4427	57	35	ln2(g	ln2(g	PROPN
ejpam-4427	57	36	)	)	PUNCT
ejpam-4427	57	37	is	be	AUX
ejpam-4427	57	38	referred	refer	VERB
ejpam-4427	57	39	to	to	ADP
ejpam-4427	57	40	as	as	ADP
ejpam-4427	57	41	an	an	DET
ejpam-4427	57	42	ln2	ln2	NOUN
ejpam-4427	57	43	-	-	PUNCT
ejpam-4427	57	44	set	set	NOUN
ejpam-4427	57	45	of	of	ADP
ejpam-4427	57	46	g.	g.	PROPN
ejpam-4427	57	47	definition	definition	NOUN
ejpam-4427	57	48	2	2	NUM
ejpam-4427	57	49	.	.	PUNCT
ejpam-4427	58	1	let	let	VERB
ejpam-4427	58	2	g	g	NOUN
ejpam-4427	58	3	be	be	AUX
ejpam-4427	58	4	any	any	DET
ejpam-4427	58	5	nontrivial	nontrivial	ADJ
ejpam-4427	58	6	connected	connect	VERB
ejpam-4427	58	7	graph	graph	NOUN
ejpam-4427	58	8	and	and	CCONJ
ejpam-4427	58	9	s	s	VERB
ejpam-4427	58	10	⊆	⊆	NUM
ejpam-4427	58	11	v	v	NOUN
ejpam-4427	58	12	(	(	PUNCT
ejpam-4427	58	13	g	g	NOUN
ejpam-4427	58	14	)	)	PUNCT
ejpam-4427	58	15	.	.	PUNCT
ejpam-4427	59	1	s	s	PART
ejpam-4427	59	2	is	be	AUX
ejpam-4427	59	3	a	a	DET
ejpam-4427	59	4	(	(	PUNCT
ejpam-4427	59	5	2	2	NUM
ejpam-4427	59	6	,	,	PUNCT
ejpam-4427	59	7	2)-locating	2)-locating	NUM
ejpam-4427	59	8	(	(	PUNCT
ejpam-4427	59	9	(	(	PUNCT
ejpam-4427	59	10	2	2	NUM
ejpam-4427	59	11	,	,	PUNCT
ejpam-4427	59	12	1)-locating	1)-locating	NUM
ejpam-4427	59	13	,	,	PUNCT
ejpam-4427	59	14	respectively	respectively	ADV
ejpam-4427	59	15	)	)	PUNCT
ejpam-4427	59	16	set	set	VERB
ejpam-4427	59	17	in	in	ADP
ejpam-4427	59	18	g	g	PROPN
ejpam-4427	59	19	if	if	SCONJ
ejpam-4427	59	20	s	s	NOUN
ejpam-4427	59	21	is	be	AUX
ejpam-4427	59	22	2	2	NUM
ejpam-4427	59	23	-	-	PUNCT
ejpam-4427	59	24	locating	locate	VERB
ejpam-4427	59	25	and	and	CCONJ
ejpam-4427	59	26	|ng(y	|ng(y	NUM
ejpam-4427	59	27	)	)	PUNCT
ejpam-4427	59	28	∩	∩	NOUN
ejpam-4427	59	29	s|	s|	VERB
ejpam-4427	59	30	≤	≤	NUM
ejpam-4427	59	31	|s|	|s|	PROPN
ejpam-4427	59	32	−	−	PROPN
ejpam-4427	59	33	2	2	NUM
ejpam-4427	59	34	(	(	PUNCT
ejpam-4427	59	35	|ng(y	|ng(y	NUM
ejpam-4427	59	36	)	)	PUNCT
ejpam-4427	59	37	∩	∩	NOUN
ejpam-4427	59	38	s|	s|	VERB
ejpam-4427	59	39	≤	≤	NUM
ejpam-4427	59	40	|s|	|s|	PROPN
ejpam-4427	59	41	−	−	PROPN
ejpam-4427	59	42	1	1	NUM
ejpam-4427	59	43	,	,	PUNCT
ejpam-4427	59	44	respectively	respectively	ADV
ejpam-4427	59	45	)	)	PUNCT
ejpam-4427	59	46	,	,	PUNCT
ejpam-4427	59	47	for	for	ADP
ejpam-4427	59	48	all	all	DET
ejpam-4427	59	49	y	y	PROPN
ejpam-4427	59	50	∈	∈	PROPN
ejpam-4427	59	51	v	v	NOUN
ejpam-4427	59	52	(	(	PUNCT
ejpam-4427	59	53	g	g	NOUN
ejpam-4427	59	54	)	)	PUNCT
ejpam-4427	59	55	.	.	PUNCT
ejpam-4427	60	1	the	the	DET
ejpam-4427	60	2	(	(	PUNCT
ejpam-4427	60	3	2	2	NUM
ejpam-4427	60	4	,	,	PUNCT
ejpam-4427	60	5	2)-locating	2)-locating	NUM
ejpam-4427	60	6	(	(	PUNCT
ejpam-4427	60	7	(	(	PUNCT
ejpam-4427	60	8	2	2	NUM
ejpam-4427	60	9	,	,	PUNCT
ejpam-4427	60	10	1)-locating	1)-locating	NUM
ejpam-4427	60	11	,	,	PUNCT
ejpam-4427	60	12	respectively	respectively	ADV
ejpam-4427	60	13	)	)	PUNCT
ejpam-4427	60	14	number	number	NOUN
ejpam-4427	60	15	ofg	ofg	PROPN
ejpam-4427	60	16	,	,	PUNCT
ejpam-4427	60	17	denoted	denote	VERB
ejpam-4427	60	18	by	by	ADP
ejpam-4427	60	19	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4427	60	20	)	)	PUNCT
ejpam-4427	60	21	(	(	PUNCT
ejpam-4427	60	22	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4427	60	23	)	)	PUNCT
ejpam-4427	60	24	,	,	PUNCT
ejpam-4427	60	25	respectively	respectively	ADV
ejpam-4427	60	26	)	)	PUNCT
ejpam-4427	60	27	,	,	PUNCT
ejpam-4427	60	28	is	be	AUX
ejpam-4427	60	29	the	the	DET
ejpam-4427	60	30	smallest	small	ADJ
ejpam-4427	60	31	cardinality	cardinality	NOUN
ejpam-4427	60	32	of	of	ADP
ejpam-4427	60	33	a	a	DET
ejpam-4427	60	34	(	(	PUNCT
ejpam-4427	60	35	2	2	NUM
ejpam-4427	60	36	,	,	PUNCT
ejpam-4427	60	37	2)-locating	2)-locating	NUM
ejpam-4427	60	38	(	(	PUNCT
ejpam-4427	60	39	(	(	PUNCT
ejpam-4427	60	40	2	2	NUM
ejpam-4427	60	41	,	,	PUNCT
ejpam-4427	60	42	1)-locating	1)-locating	NUM
ejpam-4427	60	43	,	,	PUNCT
ejpam-4427	60	44	respectively	respectively	ADV
ejpam-4427	60	45	)	)	PUNCT
ejpam-4427	60	46	set	set	VERB
ejpam-4427	60	47	in	in	ADP
ejpam-4427	60	48	g.	g.	PROPN
ejpam-4427	60	49	a	a	PRON
ejpam-4427	60	50	(	(	PUNCT
ejpam-4427	60	51	2	2	NUM
ejpam-4427	60	52	,	,	PUNCT
ejpam-4427	60	53	2)-locating	2)-locating	NUM
ejpam-4427	60	54	(	(	PUNCT
ejpam-4427	60	55	(	(	PUNCT
ejpam-4427	60	56	2	2	NUM
ejpam-4427	60	57	,	,	PUNCT
ejpam-4427	60	58	1)-locating	1)-locating	NUM
ejpam-4427	60	59	,	,	PUNCT
ejpam-4427	60	60	respectively	respectively	ADV
ejpam-4427	60	61	)	)	PUNCT
ejpam-4427	60	62	set	set	VERB
ejpam-4427	60	63	in	in	ADP
ejpam-4427	60	64	g	g	NOUN
ejpam-4427	60	65	of	of	ADP
ejpam-4427	60	66	cardinality	cardinality	NOUN
ejpam-4427	60	67	ln(2,2)(g	ln(2,2)(g	PROPN
ejpam-4427	60	68	)	)	PUNCT
ejpam-4427	60	69	(	(	PUNCT
ejpam-4427	60	70	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4427	60	71	)	)	PUNCT
ejpam-4427	60	72	,	,	PUNCT
ejpam-4427	60	73	respectively	respectively	ADV
ejpam-4427	60	74	)	)	PUNCT
ejpam-4427	60	75	is	be	AUX
ejpam-4427	60	76	referred	refer	VERB
ejpam-4427	60	77	to	to	ADP
ejpam-4427	60	78	as	as	ADP
ejpam-4427	60	79	an	an	DET
ejpam-4427	60	80	ln(2,2)-set	ln(2,2)-set	NOUN
ejpam-4427	60	81	(	(	PUNCT
ejpam-4427	60	82	ln(2,1)-set	ln(2,1)-set	PROPN
ejpam-4427	60	83	,	,	PUNCT
ejpam-4427	60	84	respectively	respectively	ADV
ejpam-4427	60	85	)	)	PUNCT
ejpam-4427	60	86	in	in	ADP
ejpam-4427	60	87	g.	g.	PROPN
ejpam-4427	60	88	theorem	theorem	PROPN
ejpam-4427	60	89	1	1	X
ejpam-4427	60	90	.	.	PUNCT
ejpam-4427	61	1	let	let	VERB
ejpam-4427	61	2	g	g	NOUN
ejpam-4427	61	3	andh	andh	NOUN
ejpam-4427	61	4	be	be	AUX
ejpam-4427	61	5	nontrivial	nontrivial	ADJ
ejpam-4427	61	6	connected	connected	ADJ
ejpam-4427	61	7	graphs	graph	NOUN
ejpam-4427	61	8	.	.	PUNCT
ejpam-4427	62	1	a	a	DET
ejpam-4427	62	2	proper	proper	ADJ
ejpam-4427	62	3	subset	subset	NOUN
ejpam-4427	62	4	s	s	NOUN
ejpam-4427	62	5	of	of	ADP
ejpam-4427	62	6	v	v	NOUN
ejpam-4427	62	7	(	(	PUNCT
ejpam-4427	62	8	g+h	g+h	PROPN
ejpam-4427	62	9	)	)	PUNCT
ejpam-4427	62	10	is	be	AUX
ejpam-4427	62	11	a	a	DET
ejpam-4427	62	12	2	2	NUM
ejpam-4427	62	13	-	-	PUNCT
ejpam-4427	62	14	resolving	resolving	NOUN
ejpam-4427	62	15	set	set	NOUN
ejpam-4427	62	16	in	in	ADP
ejpam-4427	62	17	g	g	PROPN
ejpam-4427	63	1	+	+	NOUN
ejpam-4427	63	2	h	h	NOUN
ejpam-4427	63	3	if	if	SCONJ
ejpam-4427	63	4	and	and	CCONJ
ejpam-4427	63	5	only	only	ADV
ejpam-4427	63	6	if	if	SCONJ
ejpam-4427	63	7	sg	sg	PROPN
ejpam-4427	63	8	=	=	SYM
ejpam-4427	63	9	v	v	PROPN
ejpam-4427	63	10	(	(	PUNCT
ejpam-4427	63	11	g	g	NOUN
ejpam-4427	63	12	)	)	PUNCT
ejpam-4427	63	13	∩	∩	NOUN
ejpam-4427	63	14	s	s	NOUN
ejpam-4427	63	15	and	and	CCONJ
ejpam-4427	63	16	sh	sh	PROPN
ejpam-4427	63	17	=	=	SYM
ejpam-4427	63	18	v	v	PROPN
ejpam-4427	63	19	(	(	PUNCT
ejpam-4427	63	20	h	h	NOUN
ejpam-4427	63	21	)	)	PUNCT
ejpam-4427	63	22	∩	∩	NOUN
ejpam-4427	63	23	s	s	NOUN
ejpam-4427	63	24	are	be	AUX
ejpam-4427	63	25	2	2	NUM
ejpam-4427	63	26	-	-	PUNCT
ejpam-4427	63	27	locating	locate	VERB
ejpam-4427	63	28	sets	set	NOUN
ejpam-4427	63	29	in	in	ADP
ejpam-4427	63	30	g	g	PROPN
ejpam-4427	63	31	and	and	CCONJ
ejpam-4427	63	32	h	h	NOUN
ejpam-4427	63	33	,	,	PUNCT
ejpam-4427	63	34	respectively	respectively	ADV
ejpam-4427	63	35	,	,	PUNCT
ejpam-4427	63	36	where	where	SCONJ
ejpam-4427	63	37	sg	sg	NOUN
ejpam-4427	63	38	or	or	CCONJ
ejpam-4427	63	39	sh	sh	PROPN
ejpam-4427	63	40	is	be	AUX
ejpam-4427	63	41	a	a	DET
ejpam-4427	63	42	(	(	PUNCT
ejpam-4427	63	43	2	2	NUM
ejpam-4427	63	44	,	,	PUNCT
ejpam-4427	63	45	2)-locating	2)-locating	NUM
ejpam-4427	63	46	set	set	NOUN
ejpam-4427	63	47	or	or	CCONJ
ejpam-4427	63	48	sg	sg	PROPN
ejpam-4427	64	1	and	and	CCONJ
ejpam-4427	64	2	sh	sh	PROPN
ejpam-4427	64	3	are	be	AUX
ejpam-4427	64	4	(	(	PUNCT
ejpam-4427	64	5	2	2	NUM
ejpam-4427	64	6	,	,	PUNCT
ejpam-4427	64	7	1)-locating	1)-locating	NUM
ejpam-4427	64	8	sets	set	NOUN
ejpam-4427	64	9	.	.	PUNCT
ejpam-4427	65	1	theorem	theorem	NOUN
ejpam-4427	65	2	2	2	NUM
ejpam-4427	65	3	.	.	PUNCT
ejpam-4427	66	1	let	let	VERB
ejpam-4427	66	2	g	g	NOUN
ejpam-4427	66	3	and	and	CCONJ
ejpam-4427	66	4	h	h	NOUN
ejpam-4427	66	5	be	be	AUX
ejpam-4427	66	6	nontrivial	nontrivial	ADJ
ejpam-4427	66	7	connected	connected	ADJ
ejpam-4427	66	8	graphs	graph	NOUN
ejpam-4427	66	9	.	.	PUNCT
ejpam-4427	67	1	a	a	DET
ejpam-4427	67	2	set	set	NOUN
ejpam-4427	67	3	s	s	NOUN
ejpam-4427	67	4	⊆	⊆	NUM
ejpam-4427	67	5	v	v	NOUN
ejpam-4427	67	6	(	(	PUNCT
ejpam-4427	67	7	g	g	PROPN
ejpam-4427	67	8	+	+	NOUN
ejpam-4427	67	9	h	h	NOUN
ejpam-4427	67	10	)	)	PUNCT
ejpam-4427	67	11	is	be	AUX
ejpam-4427	67	12	a	a	DET
ejpam-4427	67	13	restrained	restrained	ADJ
ejpam-4427	67	14	2	2	NUM
ejpam-4427	67	15	-	-	PUNCT
ejpam-4427	67	16	resolving	resolving	NOUN
ejpam-4427	67	17	set	set	NOUN
ejpam-4427	67	18	in	in	ADP
ejpam-4427	67	19	g	g	PROPN
ejpam-4427	68	1	+	+	NOUN
ejpam-4427	68	2	h	h	NOUN
ejpam-4427	68	3	if	if	SCONJ
ejpam-4427	68	4	and	and	CCONJ
ejpam-4427	68	5	only	only	ADV
ejpam-4427	68	6	if	if	SCONJ
ejpam-4427	68	7	sg	sg	PROPN
ejpam-4427	68	8	=	=	SYM
ejpam-4427	68	9	v	v	NOUN
ejpam-4427	68	10	(	(	PUNCT
ejpam-4427	68	11	g)∩s	g)∩s	PROPN
ejpam-4427	68	12	and	and	CCONJ
ejpam-4427	68	13	sh	sh	PROPN
ejpam-4427	68	14	=	=	SYM
ejpam-4427	68	15	v	v	PROPN
ejpam-4427	68	16	(	(	PUNCT
ejpam-4427	68	17	h)∩s	h)∩s	PROPN
ejpam-4427	68	18	are	be	AUX
ejpam-4427	68	19	2	2	NUM
ejpam-4427	68	20	-	-	PUNCT
ejpam-4427	68	21	locating	locate	VERB
ejpam-4427	68	22	sets	set	NOUN
ejpam-4427	68	23	in	in	ADP
ejpam-4427	68	24	g	g	PROPN
ejpam-4427	68	25	and	and	CCONJ
ejpam-4427	68	26	h	h	NOUN
ejpam-4427	68	27	,	,	PUNCT
ejpam-4427	68	28	respectively	respectively	ADV
ejpam-4427	68	29	where	where	SCONJ
ejpam-4427	68	30	sg	sg	PROPN
ejpam-4427	68	31	or	or	CCONJ
ejpam-4427	68	32	sh	sh	PROPN
ejpam-4427	68	33	is	be	AUX
ejpam-4427	68	34	a	a	DET
ejpam-4427	68	35	(	(	PUNCT
ejpam-4427	68	36	2	2	NUM
ejpam-4427	68	37	,	,	PUNCT
ejpam-4427	68	38	2)-locating	2)-locating	NUM
ejpam-4427	68	39	set	set	NOUN
ejpam-4427	68	40	or	or	CCONJ
ejpam-4427	68	41	sg	sg	PROPN
ejpam-4427	68	42	and	and	CCONJ
ejpam-4427	68	43	sh	sh	PROPN
ejpam-4427	68	44	are	be	AUX
ejpam-4427	68	45	(	(	PUNCT
ejpam-4427	68	46	2	2	NUM
ejpam-4427	68	47	,	,	PUNCT
ejpam-4427	68	48	1)-locating	1)-locating	NUM
ejpam-4427	68	49	sets	set	NOUN
ejpam-4427	68	50	and	and	CCONJ
ejpam-4427	68	51	one	one	NUM
ejpam-4427	68	52	of	of	ADP
ejpam-4427	68	53	the	the	DET
ejpam-4427	68	54	following	follow	VERB
ejpam-4427	68	55	holds	hold	VERB
ejpam-4427	68	56	:	:	PUNCT
ejpam-4427	68	57	(	(	PUNCT
ejpam-4427	68	58	i	i	NOUN
ejpam-4427	68	59	)	)	PUNCT
ejpam-4427	68	60	sg	sg	PROPN
ejpam-4427	68	61	=	=	SYM
ejpam-4427	68	62	v	v	PROPN
ejpam-4427	68	63	(	(	PUNCT
ejpam-4427	68	64	g	g	NOUN
ejpam-4427	68	65	)	)	PUNCT
ejpam-4427	68	66	and	and	CCONJ
ejpam-4427	68	67	sh	sh	PROPN
ejpam-4427	68	68	is	be	AUX
ejpam-4427	68	69	a	a	DET
ejpam-4427	68	70	restrained	restrained	ADJ
ejpam-4427	68	71	2	2	NUM
ejpam-4427	68	72	-	-	PUNCT
ejpam-4427	68	73	locating	locate	VERB
ejpam-4427	68	74	set	set	NOUN
ejpam-4427	68	75	in	in	ADP
ejpam-4427	68	76	h	h	NOUN
ejpam-4427	68	77	;	;	PUNCT
ejpam-4427	68	78	(	(	PUNCT
ejpam-4427	68	79	ii	ii	NOUN
ejpam-4427	68	80	)	)	PUNCT
ejpam-4427	69	1	sh	sh	PROPN
ejpam-4427	70	1	=	=	SYM
ejpam-4427	70	2	v	v	PROPN
ejpam-4427	70	3	(	(	PUNCT
ejpam-4427	70	4	h	h	NOUN
ejpam-4427	70	5	)	)	PUNCT
ejpam-4427	70	6	and	and	CCONJ
ejpam-4427	70	7	sg	sg	PROPN
ejpam-4427	70	8	is	be	AUX
ejpam-4427	70	9	a	a	DET
ejpam-4427	70	10	restrained	restrained	ADJ
ejpam-4427	70	11	2	2	NUM
ejpam-4427	70	12	-	-	PUNCT
ejpam-4427	70	13	locating	locate	VERB
ejpam-4427	70	14	set	set	NOUN
ejpam-4427	70	15	in	in	ADP
ejpam-4427	70	16	g	g	NOUN
ejpam-4427	70	17	;	;	PUNCT
ejpam-4427	70	18	(	(	PUNCT
ejpam-4427	70	19	iii	iii	X
ejpam-4427	70	20	)	)	PUNCT
ejpam-4427	70	21	sg	sg	ADP
ejpam-4427	70	22	̸=	̸=	PROPN
ejpam-4427	70	23	v	v	NOUN
ejpam-4427	70	24	(	(	PUNCT
ejpam-4427	70	25	g	g	NOUN
ejpam-4427	70	26	)	)	PUNCT
ejpam-4427	70	27	and	and	CCONJ
ejpam-4427	70	28	sh	sh	INTJ
ejpam-4427	70	29	̸=	̸=	PROPN
ejpam-4427	70	30	v	v	NOUN
ejpam-4427	70	31	(	(	PUNCT
ejpam-4427	70	32	h	h	NOUN
ejpam-4427	70	33	)	)	PUNCT
ejpam-4427	70	34	.	.	PUNCT
ejpam-4427	71	1	j.	j.	PROPN
ejpam-4427	71	2	cabaro	cabaro	PROPN
ejpam-4427	71	3	,	,	PUNCT
ejpam-4427	71	4	h.	h.	PROPN
ejpam-4427	71	5	rara	rara	PROPN
ejpam-4427	71	6	/	/	SYM
ejpam-4427	71	7	eur	eur	PROPN
ejpam-4427	71	8	.	.	PUNCT
ejpam-4427	72	1	j.	j.	PROPN
ejpam-4427	72	2	pure	pure	PROPN
ejpam-4427	72	3	appl	appl	PROPN
ejpam-4427	72	4	.	.	PROPN
ejpam-4427	72	5	math	math	PROPN
ejpam-4427	72	6	,	,	PUNCT
ejpam-4427	72	7	15	15	NUM
ejpam-4427	72	8	(	(	PUNCT
ejpam-4427	72	9	3	3	NUM
ejpam-4427	72	10	)	)	PUNCT
ejpam-4427	72	11	(	(	PUNCT
ejpam-4427	72	12	2022	2022	NUM
ejpam-4427	72	13	)	)	PUNCT
ejpam-4427	72	14	,	,	PUNCT
ejpam-4427	72	15	1229	1229	NUM
ejpam-4427	72	16	-	-	SYM
ejpam-4427	72	17	1236	1236	NUM
ejpam-4427	72	18	1232	1232	NUM
ejpam-4427	72	19	proof	proof	NOUN
ejpam-4427	72	20	.	.	PUNCT
ejpam-4427	73	1	let	let	VERB
ejpam-4427	73	2	s	s	PRON
ejpam-4427	73	3	⊆	⊆	NUM
ejpam-4427	73	4	v	v	NOUN
ejpam-4427	73	5	(	(	PUNCT
ejpam-4427	73	6	g+h	g+h	NOUN
ejpam-4427	73	7	)	)	PUNCT
ejpam-4427	73	8	be	be	AUX
ejpam-4427	73	9	a	a	DET
ejpam-4427	73	10	restrained	restrained	ADJ
ejpam-4427	73	11	2	2	NUM
ejpam-4427	73	12	-	-	PUNCT
ejpam-4427	73	13	resolving	resolving	NOUN
ejpam-4427	73	14	set	set	VERB
ejpam-4427	73	15	in	in	ADP
ejpam-4427	73	16	g+h	g+h	PROPN
ejpam-4427	73	17	.	.	PUNCT
ejpam-4427	74	1	then	then	ADV
ejpam-4427	74	2	by	by	ADP
ejpam-4427	74	3	theorem	theorem	NOUN
ejpam-4427	74	4	1	1	NUM
ejpam-4427	74	5	,	,	PUNCT
ejpam-4427	74	6	sg	sg	ADP
ejpam-4427	74	7	=	=	SYM
ejpam-4427	74	8	v	v	PROPN
ejpam-4427	74	9	(	(	PUNCT
ejpam-4427	74	10	g)∩s	g)∩s	PROPN
ejpam-4427	74	11	and	and	CCONJ
ejpam-4427	74	12	sh	sh	PROPN
ejpam-4427	74	13	=	=	SYM
ejpam-4427	74	14	v	v	PROPN
ejpam-4427	74	15	(	(	PUNCT
ejpam-4427	74	16	h)∩s	h)∩s	PROPN
ejpam-4427	74	17	are	be	AUX
ejpam-4427	74	18	2	2	NUM
ejpam-4427	74	19	-	-	PUNCT
ejpam-4427	74	20	locating	locate	VERB
ejpam-4427	74	21	sets	set	NOUN
ejpam-4427	74	22	in	in	ADP
ejpam-4427	74	23	g	g	PROPN
ejpam-4427	74	24	and	and	CCONJ
ejpam-4427	74	25	h	h	NOUN
ejpam-4427	74	26	,	,	PUNCT
ejpam-4427	74	27	respectively	respectively	ADV
ejpam-4427	74	28	,	,	PUNCT
ejpam-4427	74	29	where	where	SCONJ
ejpam-4427	74	30	sg	sg	NOUN
ejpam-4427	74	31	or	or	CCONJ
ejpam-4427	74	32	sh	sh	PROPN
ejpam-4427	74	33	is	be	AUX
ejpam-4427	74	34	a	a	DET
ejpam-4427	74	35	(	(	PUNCT
ejpam-4427	74	36	2	2	NUM
ejpam-4427	74	37	,	,	PUNCT
ejpam-4427	74	38	2)-locating	2)-locating	NUM
ejpam-4427	74	39	set	set	NOUN
ejpam-4427	74	40	or	or	CCONJ
ejpam-4427	74	41	sg	sg	PROPN
ejpam-4427	74	42	and	and	CCONJ
ejpam-4427	74	43	sh	sh	PROPN
ejpam-4427	74	44	are	be	AUX
ejpam-4427	74	45	(	(	PUNCT
ejpam-4427	74	46	2	2	NUM
ejpam-4427	74	47	,	,	PUNCT
ejpam-4427	74	48	1)-locating	1)-locating	NUM
ejpam-4427	74	49	sets	set	NOUN
ejpam-4427	74	50	.	.	PUNCT
ejpam-4427	75	1	to	to	PART
ejpam-4427	75	2	show	show	VERB
ejpam-4427	75	3	that	that	SCONJ
ejpam-4427	75	4	(	(	PUNCT
ejpam-4427	75	5	i	i	NOUN
ejpam-4427	75	6	)	)	PUNCT
ejpam-4427	75	7	,	,	PUNCT
ejpam-4427	75	8	(	(	PUNCT
ejpam-4427	75	9	ii	ii	NOUN
ejpam-4427	75	10	)	)	PUNCT
ejpam-4427	75	11	,	,	PUNCT
ejpam-4427	75	12	and	and	CCONJ
ejpam-4427	75	13	(	(	PUNCT
ejpam-4427	75	14	iii	iii	X
ejpam-4427	75	15	)	)	PUNCT
ejpam-4427	75	16	hold	hold	NOUN
ejpam-4427	75	17	we	we	PRON
ejpam-4427	75	18	consider	consider	VERB
ejpam-4427	75	19	the	the	DET
ejpam-4427	75	20	following	follow	VERB
ejpam-4427	75	21	cases	case	NOUN
ejpam-4427	75	22	:	:	PUNCT
ejpam-4427	75	23	case	case	NOUN
ejpam-4427	75	24	1	1	NUM
ejpam-4427	75	25	.	.	PUNCT
ejpam-4427	75	26	sg	sg	PROPN
ejpam-4427	75	27	=	=	SYM
ejpam-4427	75	28	v	v	PROPN
ejpam-4427	75	29	(	(	PUNCT
ejpam-4427	75	30	g	g	NOUN
ejpam-4427	75	31	)	)	PUNCT
ejpam-4427	75	32	.	.	PUNCT
ejpam-4427	76	1	suppose	suppose	VERB
ejpam-4427	76	2	that	that	SCONJ
ejpam-4427	76	3	sh	sh	PROPN
ejpam-4427	76	4	̸=	̸=	PROPN
ejpam-4427	76	5	v	v	PROPN
ejpam-4427	76	6	(	(	PUNCT
ejpam-4427	76	7	h	h	NOUN
ejpam-4427	76	8	)	)	PUNCT
ejpam-4427	76	9	.	.	PUNCT
ejpam-4427	77	1	since	since	SCONJ
ejpam-4427	77	2	⟨v	⟨v	PROPN
ejpam-4427	77	3	(	(	PUNCT
ejpam-4427	77	4	g+h)\s⟩	g+h)\s⟩	PROPN
ejpam-4427	77	5	=	=	SYM
ejpam-4427	77	6	⟨v	⟨v	PROPN
ejpam-4427	77	7	(	(	PUNCT
ejpam-4427	77	8	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4427	77	9	and	and	CCONJ
ejpam-4427	77	10	⟨v	⟨v	NUM
ejpam-4427	77	11	(	(	PUNCT
ejpam-4427	77	12	g+h)\s⟩	g+h)\s⟩	PROPN
ejpam-4427	77	13	has	have	VERB
ejpam-4427	77	14	no	no	DET
ejpam-4427	77	15	isolated	isolated	ADJ
ejpam-4427	77	16	vertex	vertex	NOUN
ejpam-4427	77	17	,	,	PUNCT
ejpam-4427	77	18	it	it	PRON
ejpam-4427	77	19	follows	follow	VERB
ejpam-4427	77	20	that	that	PRON
ejpam-4427	77	21	⟨v	⟨v	PROPN
ejpam-4427	77	22	(	(	PUNCT
ejpam-4427	77	23	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4427	77	24	has	have	VERB
ejpam-4427	77	25	no	no	DET
ejpam-4427	77	26	isolated	isolated	ADJ
ejpam-4427	77	27	vertex	vertex	NOUN
ejpam-4427	77	28	.	.	PUNCT
ejpam-4427	78	1	thus	thus	ADV
ejpam-4427	78	2	,	,	PUNCT
ejpam-4427	78	3	sh	sh	PROPN
ejpam-4427	78	4	is	be	AUX
ejpam-4427	78	5	a	a	DET
ejpam-4427	78	6	restrained	restrained	ADJ
ejpam-4427	78	7	2	2	NUM
ejpam-4427	78	8	-	-	PUNCT
ejpam-4427	78	9	locating	locate	VERB
ejpam-4427	78	10	set	set	NOUN
ejpam-4427	78	11	in	in	ADP
ejpam-4427	78	12	h.	h.	PROPN
ejpam-4427	78	13	hence	hence	ADV
ejpam-4427	78	14	,	,	PUNCT
ejpam-4427	78	15	(	(	PUNCT
ejpam-4427	78	16	i	i	NOUN
ejpam-4427	78	17	)	)	PUNCT
ejpam-4427	78	18	holds	hold	VERB
ejpam-4427	78	19	.	.	PUNCT
ejpam-4427	79	1	case	case	NOUN
ejpam-4427	79	2	2	2	NUM
ejpam-4427	79	3	.	.	PUNCT
ejpam-4427	79	4	suppose	suppose	VERB
ejpam-4427	79	5	that	that	SCONJ
ejpam-4427	79	6	sg	sg	PROPN
ejpam-4427	79	7	̸=	̸=	PROPN
ejpam-4427	79	8	v	v	NOUN
ejpam-4427	79	9	(	(	PUNCT
ejpam-4427	79	10	g	g	NOUN
ejpam-4427	79	11	)	)	PUNCT
ejpam-4427	79	12	.	.	PUNCT
ejpam-4427	80	1	if	if	SCONJ
ejpam-4427	80	2	sh	sh	PROPN
ejpam-4427	80	3	̸=	̸=	PROPN
ejpam-4427	80	4	v	v	NOUN
ejpam-4427	80	5	(	(	PUNCT
ejpam-4427	80	6	h	h	NOUN
ejpam-4427	80	7	)	)	PUNCT
ejpam-4427	80	8	,	,	PUNCT
ejpam-4427	80	9	then	then	ADV
ejpam-4427	80	10	(	(	PUNCT
ejpam-4427	80	11	iii	iii	NOUN
ejpam-4427	80	12	)	)	PUNCT
ejpam-4427	80	13	holds	hold	VERB
ejpam-4427	80	14	.	.	PUNCT
ejpam-4427	80	15	suppose	suppose	VERB
ejpam-4427	80	16	that	that	SCONJ
ejpam-4427	80	17	sh	sh	PROPN
ejpam-4427	80	18	=	=	SYM
ejpam-4427	80	19	v	v	PROPN
ejpam-4427	80	20	(	(	PUNCT
ejpam-4427	80	21	h	h	NOUN
ejpam-4427	80	22	)	)	PUNCT
ejpam-4427	80	23	.	.	PUNCT
ejpam-4427	81	1	then	then	ADV
ejpam-4427	81	2	⟨v	⟨v	X
ejpam-4427	81	3	(	(	PUNCT
ejpam-4427	81	4	g+h)\s⟩	g+h)\s⟩	PROPN
ejpam-4427	81	5	=	=	SYM
ejpam-4427	81	6	⟨v	⟨v	PROPN
ejpam-4427	81	7	(	(	PUNCT
ejpam-4427	81	8	g)\sg⟩	g)\sg⟩	X
ejpam-4427	81	9	has	have	AUX
ejpam-4427	81	10	no	no	DET
ejpam-4427	81	11	isolated	isolated	ADJ
ejpam-4427	81	12	vertex	vertex	NOUN
ejpam-4427	81	13	.	.	PUNCT
ejpam-4427	82	1	hence	hence	ADV
ejpam-4427	82	2	,	,	PUNCT
ejpam-4427	82	3	sg	sg	PROPN
ejpam-4427	82	4	is	be	AUX
ejpam-4427	82	5	a	a	DET
ejpam-4427	82	6	restrained	restrained	ADJ
ejpam-4427	82	7	2	2	NUM
ejpam-4427	82	8	-	-	PUNCT
ejpam-4427	82	9	locating	locate	VERB
ejpam-4427	82	10	set	set	NOUN
ejpam-4427	82	11	in	in	ADP
ejpam-4427	82	12	g.	g.	PROPN
ejpam-4427	82	13	thus	thus	ADV
ejpam-4427	82	14	,	,	PUNCT
ejpam-4427	82	15	(	(	PUNCT
ejpam-4427	82	16	ii	ii	NOUN
ejpam-4427	82	17	)	)	PUNCT
ejpam-4427	82	18	holds	hold	VERB
ejpam-4427	82	19	.	.	PUNCT
ejpam-4427	83	1	for	for	ADP
ejpam-4427	83	2	the	the	DET
ejpam-4427	83	3	converse	converse	NOUN
ejpam-4427	83	4	,	,	PUNCT
ejpam-4427	83	5	suppose	suppose	VERB
ejpam-4427	83	6	that	that	SCONJ
ejpam-4427	83	7	sg	sg	PROPN
ejpam-4427	83	8	and	and	CCONJ
ejpam-4427	83	9	sh	sh	PROPN
ejpam-4427	83	10	are	be	AUX
ejpam-4427	83	11	2	2	NUM
ejpam-4427	83	12	-	-	PUNCT
ejpam-4427	83	13	locating	locate	VERB
ejpam-4427	83	14	sets	set	NOUN
ejpam-4427	83	15	in	in	ADP
ejpam-4427	83	16	g	g	PROPN
ejpam-4427	83	17	and	and	CCONJ
ejpam-4427	83	18	h	h	NOUN
ejpam-4427	83	19	,	,	PUNCT
ejpam-4427	83	20	respectively	respectively	ADV
ejpam-4427	83	21	,	,	PUNCT
ejpam-4427	83	22	where	where	SCONJ
ejpam-4427	83	23	sg	sg	NOUN
ejpam-4427	83	24	or	or	CCONJ
ejpam-4427	83	25	sh	sh	PROPN
ejpam-4427	83	26	is	be	AUX
ejpam-4427	83	27	a	a	DET
ejpam-4427	83	28	(	(	PUNCT
ejpam-4427	83	29	2	2	NUM
ejpam-4427	83	30	,	,	PUNCT
ejpam-4427	83	31	2)-locating	2)-locating	NUM
ejpam-4427	83	32	set	set	NOUN
ejpam-4427	83	33	or	or	CCONJ
ejpam-4427	83	34	sg	sg	PROPN
ejpam-4427	83	35	and	and	CCONJ
ejpam-4427	83	36	sh	sh	PROPN
ejpam-4427	83	37	are	be	AUX
ejpam-4427	83	38	(	(	PUNCT
ejpam-4427	83	39	2	2	NUM
ejpam-4427	83	40	,	,	PUNCT
ejpam-4427	83	41	1)-locating	1)-locating	NUM
ejpam-4427	83	42	sets	set	NOUN
ejpam-4427	83	43	.	.	PUNCT
ejpam-4427	84	1	then	then	ADV
ejpam-4427	84	2	by	by	ADP
ejpam-4427	84	3	theorem	theorem	NOUN
ejpam-4427	84	4	1	1	NUM
ejpam-4427	84	5	,	,	PUNCT
ejpam-4427	84	6	s	s	VERB
ejpam-4427	84	7	is	be	AUX
ejpam-4427	84	8	a	a	DET
ejpam-4427	84	9	2	2	NUM
ejpam-4427	84	10	-	-	PUNCT
ejpam-4427	84	11	resolving	resolving	NOUN
ejpam-4427	84	12	set	set	NOUN
ejpam-4427	84	13	in	in	ADP
ejpam-4427	84	14	g	g	PROPN
ejpam-4427	84	15	+	+	PROPN
ejpam-4427	84	16	h.	h.	PROPN
ejpam-4427	84	17	suppose	suppose	VERB
ejpam-4427	84	18	that	that	SCONJ
ejpam-4427	84	19	sg	sg	VERB
ejpam-4427	84	20	=	=	SYM
ejpam-4427	84	21	v	v	PROPN
ejpam-4427	84	22	(	(	PUNCT
ejpam-4427	84	23	g	g	NOUN
ejpam-4427	84	24	)	)	PUNCT
ejpam-4427	84	25	.	.	PUNCT
ejpam-4427	85	1	if	if	SCONJ
ejpam-4427	85	2	sh	sh	PROPN
ejpam-4427	85	3	=	=	SYM
ejpam-4427	85	4	v	v	PROPN
ejpam-4427	85	5	(	(	PUNCT
ejpam-4427	85	6	h	h	NOUN
ejpam-4427	85	7	)	)	PUNCT
ejpam-4427	85	8	,	,	PUNCT
ejpam-4427	85	9	then	then	ADV
ejpam-4427	85	10	s	s	VERB
ejpam-4427	85	11	=	=	SYM
ejpam-4427	85	12	v	v	PROPN
ejpam-4427	85	13	(	(	PUNCT
ejpam-4427	85	14	g	g	PROPN
ejpam-4427	85	15	+	+	NOUN
ejpam-4427	85	16	h	h	NOUN
ejpam-4427	85	17	)	)	PUNCT
ejpam-4427	85	18	is	be	AUX
ejpam-4427	85	19	a	a	DET
ejpam-4427	85	20	restrained	restrained	ADJ
ejpam-4427	85	21	2	2	NUM
ejpam-4427	85	22	-	-	PUNCT
ejpam-4427	85	23	resolving	resolving	NOUN
ejpam-4427	85	24	set	set	NOUN
ejpam-4427	85	25	in	in	ADP
ejpam-4427	85	26	g	g	PROPN
ejpam-4427	85	27	+	+	CCONJ
ejpam-4427	85	28	h.	h.	NOUN
ejpam-4427	85	29	if	if	SCONJ
ejpam-4427	85	30	sh	sh	PROPN
ejpam-4427	85	31	̸=	̸=	PROPN
ejpam-4427	85	32	v	v	NOUN
ejpam-4427	85	33	(	(	PUNCT
ejpam-4427	85	34	h	h	NOUN
ejpam-4427	85	35	)	)	PUNCT
ejpam-4427	85	36	,	,	PUNCT
ejpam-4427	85	37	then	then	ADV
ejpam-4427	85	38	by	by	ADP
ejpam-4427	85	39	(	(	PUNCT
ejpam-4427	85	40	i	i	NOUN
ejpam-4427	85	41	)	)	PUNCT
ejpam-4427	85	42	⟨v	⟨v	CCONJ
ejpam-4427	85	43	(	(	PUNCT
ejpam-4427	85	44	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4427	85	45	has	have	AUX
ejpam-4427	85	46	no	no	DET
ejpam-4427	85	47	isolated	isolated	ADJ
ejpam-4427	85	48	vertex	vertex	NOUN
ejpam-4427	85	49	.	.	PUNCT
ejpam-4427	86	1	since	since	SCONJ
ejpam-4427	86	2	v	v	NOUN
ejpam-4427	86	3	(	(	PUNCT
ejpam-4427	86	4	g+h)\s	g+h)\s	PROPN
ejpam-4427	86	5	=	=	SYM
ejpam-4427	86	6	v	v	NOUN
ejpam-4427	86	7	(	(	PUNCT
ejpam-4427	86	8	h)\sh	h)\sh	PROPN
ejpam-4427	86	9	,	,	PUNCT
ejpam-4427	86	10	s	s	VERB
ejpam-4427	86	11	is	be	AUX
ejpam-4427	86	12	a	a	DET
ejpam-4427	86	13	restrained	restrained	ADJ
ejpam-4427	86	14	2	2	NUM
ejpam-4427	86	15	-	-	PUNCT
ejpam-4427	86	16	resolving	resolving	NOUN
ejpam-4427	86	17	set	set	NOUN
ejpam-4427	86	18	in	in	ADP
ejpam-4427	86	19	g	g	PROPN
ejpam-4427	86	20	+	+	PROPN
ejpam-4427	86	21	h.	h.	PROPN
ejpam-4427	86	22	similarly	similarly	ADV
ejpam-4427	86	23	,	,	PUNCT
ejpam-4427	86	24	if	if	SCONJ
ejpam-4427	86	25	(	(	PUNCT
ejpam-4427	86	26	ii	ii	NOUN
ejpam-4427	86	27	)	)	PUNCT
ejpam-4427	86	28	holds	hold	VERB
ejpam-4427	86	29	,	,	PUNCT
ejpam-4427	86	30	then	then	ADV
ejpam-4427	86	31	s	s	VERB
ejpam-4427	86	32	is	be	AUX
ejpam-4427	86	33	a	a	DET
ejpam-4427	86	34	restrained	restrained	ADJ
ejpam-4427	86	35	2	2	NUM
ejpam-4427	86	36	-	-	PUNCT
ejpam-4427	86	37	resolving	resolving	NOUN
ejpam-4427	86	38	set	set	VERB
ejpam-4427	86	39	in	in	ADP
ejpam-4427	86	40	g+h	g+h	PROPN
ejpam-4427	86	41	.	.	PUNCT
ejpam-4427	87	1	finally	finally	ADV
ejpam-4427	87	2	,	,	PUNCT
ejpam-4427	87	3	suppose	suppose	VERB
ejpam-4427	87	4	that	that	SCONJ
ejpam-4427	87	5	sg	sg	PROPN
ejpam-4427	87	6	̸=	̸=	PROPN
ejpam-4427	87	7	v	v	NOUN
ejpam-4427	87	8	(	(	PUNCT
ejpam-4427	87	9	g	g	NOUN
ejpam-4427	87	10	)	)	PUNCT
ejpam-4427	87	11	and	and	CCONJ
ejpam-4427	87	12	sh	sh	INTJ
ejpam-4427	87	13	̸=	̸=	PROPN
ejpam-4427	87	14	v	v	NOUN
ejpam-4427	87	15	(	(	PUNCT
ejpam-4427	87	16	h	h	NOUN
ejpam-4427	87	17	)	)	PUNCT
ejpam-4427	87	18	.	.	PUNCT
ejpam-4427	88	1	then	then	ADV
ejpam-4427	88	2	clearly	clearly	ADV
ejpam-4427	88	3	,	,	PUNCT
ejpam-4427	88	4	s	s	VERB
ejpam-4427	88	5	is	be	AUX
ejpam-4427	88	6	a	a	DET
ejpam-4427	88	7	restrained	restrained	ADJ
ejpam-4427	88	8	2	2	NUM
ejpam-4427	88	9	-	-	PUNCT
ejpam-4427	88	10	resolving	resolving	NOUN
ejpam-4427	88	11	set	set	VERB
ejpam-4427	88	12	in	in	ADP
ejpam-4427	88	13	g+h	g+h	PROPN
ejpam-4427	88	14	.	.	PUNCT
ejpam-4427	89	1	corollary	corollary	ADJ
ejpam-4427	89	2	1	1	NUM
ejpam-4427	89	3	.	.	PUNCT
ejpam-4427	90	1	let	let	VERB
ejpam-4427	90	2	g	g	NOUN
ejpam-4427	90	3	and	and	CCONJ
ejpam-4427	90	4	h	h	NOUN
ejpam-4427	90	5	be	be	AUX
ejpam-4427	90	6	connected	connect	VERB
ejpam-4427	90	7	non	non	ADJ
ejpam-4427	90	8	-	-	ADJ
ejpam-4427	90	9	trivial	trivial	ADJ
ejpam-4427	90	10	graphs	graph	NOUN
ejpam-4427	90	11	of	of	ADP
ejpam-4427	90	12	order	order	NOUN
ejpam-4427	90	13	m	m	VERB
ejpam-4427	90	14	and	and	CCONJ
ejpam-4427	90	15	n	n	CCONJ
ejpam-4427	90	16	,	,	PUNCT
ejpam-4427	90	17	respectively	respectively	ADV
ejpam-4427	90	18	.	.	PUNCT
ejpam-4427	91	1	then	then	ADV
ejpam-4427	91	2	rdim2(g+h	rdim2(g+h	NUM
ejpam-4427	91	3	)	)	PUNCT
ejpam-4427	92	1	=	=	PUNCT
ejpam-4427	93	1			PRON
ejpam-4427	93	2	m+	m+	NUM
ejpam-4427	93	3	n	n	CCONJ
ejpam-4427	93	4	,	,	PUNCT
ejpam-4427	93	5	if	if	SCONJ
ejpam-4427	93	6	rln2(g	rln2(g	NOUN
ejpam-4427	93	7	)	)	PUNCT
ejpam-4427	93	8	=	=	SYM
ejpam-4427	93	9	m	m	NOUN
ejpam-4427	93	10	and	and	CCONJ
ejpam-4427	93	11	rln2(h	rln2(h	NUM
ejpam-4427	93	12	)	)	PUNCT
ejpam-4427	93	13	=	=	PRON
ejpam-4427	93	14	n	n	PRON
ejpam-4427	93	15	min{rln(2,2)(g	min{rln(2,2)(g	NOUN
ejpam-4427	93	16	)	)	PUNCT
ejpam-4427	93	17	+	+	NUM
ejpam-4427	93	18	rln2(h	rln2(h	NOUN
ejpam-4427	93	19	)	)	PUNCT
ejpam-4427	93	20	,	,	PUNCT
ejpam-4427	93	21	rln2(g	rln2(g	NUM
ejpam-4427	93	22	)	)	PUNCT
ejpam-4427	93	23	+	+	CCONJ
ejpam-4427	93	24	rln(2,2)(h	rln(2,2)(h	PROPN
ejpam-4427	93	25	)	)	PUNCT
ejpam-4427	93	26	,	,	PUNCT
ejpam-4427	93	27	rln(2,1)(g	rln(2,1)(g	PROPN
ejpam-4427	93	28	)	)	PUNCT
ejpam-4427	93	29	+	+	NUM
ejpam-4427	93	30	rln(2,1)(h	rln(2,1)(h	PROPN
ejpam-4427	93	31	)	)	PUNCT
ejpam-4427	93	32	}	}	PUNCT
ejpam-4427	93	33	,	,	PUNCT
ejpam-4427	93	34	otherwise	otherwise	ADV
ejpam-4427	93	35	the	the	DET
ejpam-4427	93	36	set	set	NOUN
ejpam-4427	93	37	consisting	consisting	NOUN
ejpam-4427	93	38	of	of	ADP
ejpam-4427	93	39	the	the	DET
ejpam-4427	93	40	shaded	shade	VERB
ejpam-4427	93	41	vertices	vertex	NOUN
ejpam-4427	93	42	in	in	ADP
ejpam-4427	93	43	figure	figure	NOUN
ejpam-4427	93	44	1	1	NUM
ejpam-4427	93	45	is	be	AUX
ejpam-4427	93	46	a	a	DET
ejpam-4427	93	47	restrained	restrained	ADJ
ejpam-4427	93	48	2	2	NUM
ejpam-4427	93	49	-	-	PUNCT
ejpam-4427	93	50	resolving	resolve	VERB
ejpam-4427	93	51	set	set	NOUN
ejpam-4427	93	52	of	of	ADP
ejpam-4427	93	53	the	the	DET
ejpam-4427	93	54	join	join	NOUN
ejpam-4427	93	55	p5	p5	PROPN
ejpam-4427	93	56	+	+	CCONJ
ejpam-4427	93	57	p6	p6	PROPN
ejpam-4427	93	58	.	.	PUNCT
ejpam-4427	94	1	theorem	theorem	NOUN
ejpam-4427	94	2	3	3	X
ejpam-4427	94	3	.	.	PUNCT
ejpam-4427	95	1	let	let	VERB
ejpam-4427	95	2	g	g	PRON
ejpam-4427	95	3	be	be	AUX
ejpam-4427	95	4	a	a	DET
ejpam-4427	95	5	connected	connected	ADJ
ejpam-4427	95	6	non	non	ADJ
ejpam-4427	95	7	-	-	ADJ
ejpam-4427	95	8	trivial	trivial	ADJ
ejpam-4427	95	9	graph	graph	NOUN
ejpam-4427	95	10	and	and	CCONJ
ejpam-4427	95	11	let	let	VERB
ejpam-4427	95	12	k1	k1	NOUN
ejpam-4427	95	13	=	=	SYM
ejpam-4427	95	14	{	{	PUNCT
ejpam-4427	95	15	v	v	NOUN
ejpam-4427	95	16	}	}	PUNCT
ejpam-4427	95	17	.	.	PUNCT
ejpam-4427	96	1	then	then	ADV
ejpam-4427	96	2	s	s	VERB
ejpam-4427	96	3	⊆	⊆	NUM
ejpam-4427	96	4	v	v	NOUN
ejpam-4427	96	5	(	(	PUNCT
ejpam-4427	96	6	k1	k1	NOUN
ejpam-4427	96	7	+	+	CCONJ
ejpam-4427	96	8	g	g	NOUN
ejpam-4427	96	9	)	)	PUNCT
ejpam-4427	96	10	is	be	AUX
ejpam-4427	96	11	a	a	DET
ejpam-4427	96	12	restrained	restrained	ADJ
ejpam-4427	96	13	2	2	NUM
ejpam-4427	96	14	-	-	PUNCT
ejpam-4427	96	15	resolving	resolve	VERB
ejpam-4427	96	16	set	set	NOUN
ejpam-4427	96	17	of	of	ADP
ejpam-4427	96	18	k1	k1	NOUN
ejpam-4427	96	19	+	+	CCONJ
ejpam-4427	96	20	g	g	NOUN
ejpam-4427	96	21	if	if	SCONJ
ejpam-4427	97	1	and	and	CCONJ
ejpam-4427	97	2	only	only	ADV
ejpam-4427	97	3	if	if	SCONJ
ejpam-4427	97	4	either	either	PRON
ejpam-4427	97	5	v	v	NOUN
ejpam-4427	97	6	/∈	/∈	PUNCT
ejpam-4427	97	7	s	s	PART
ejpam-4427	97	8	and	and	CCONJ
ejpam-4427	97	9	s	s	VERB
ejpam-4427	97	10	is	be	AUX
ejpam-4427	97	11	a	a	DET
ejpam-4427	97	12	(	(	PUNCT
ejpam-4427	97	13	2	2	NUM
ejpam-4427	97	14	,	,	PUNCT
ejpam-4427	97	15	2)-locating	2)-locating	NUM
ejpam-4427	97	16	set	set	VERB
ejpam-4427	97	17	in	in	ADP
ejpam-4427	97	18	g	g	NOUN
ejpam-4427	97	19	with	with	ADP
ejpam-4427	97	20	v	v	NOUN
ejpam-4427	97	21	(	(	PUNCT
ejpam-4427	97	22	g	g	NOUN
ejpam-4427	97	23	)	)	PUNCT
ejpam-4427	97	24	̸=	̸=	PROPN
ejpam-4427	97	25	s	s	PART
ejpam-4427	97	26	or	or	CCONJ
ejpam-4427	97	27	s	s	NOUN
ejpam-4427	97	28	=	=	PUNCT
ejpam-4427	97	29	{	{	PUNCT
ejpam-4427	97	30	v	v	NOUN
ejpam-4427	97	31	}	}	PUNCT
ejpam-4427	97	32	∪	∪	NOUN
ejpam-4427	97	33	t	t	PROPN
ejpam-4427	97	34	,	,	PUNCT
ejpam-4427	97	35	where	where	SCONJ
ejpam-4427	97	36	t	t	PROPN
ejpam-4427	97	37	is	be	AUX
ejpam-4427	97	38	a	a	DET
ejpam-4427	97	39	restrained	restrained	ADJ
ejpam-4427	97	40	(	(	PUNCT
ejpam-4427	97	41	2	2	NUM
ejpam-4427	97	42	,	,	PUNCT
ejpam-4427	97	43	1)-locating	1)-locating	NUM
ejpam-4427	97	44	set	set	VERB
ejpam-4427	97	45	in	in	ADP
ejpam-4427	97	46	g.	g.	PROPN
ejpam-4427	97	47	corollary	corollary	PROPN
ejpam-4427	97	48	2	2	PROPN
ejpam-4427	97	49	.	.	PUNCT
ejpam-4427	98	1	let	let	VERB
ejpam-4427	98	2	g	g	PRON
ejpam-4427	98	3	be	be	AUX
ejpam-4427	98	4	a	a	DET
ejpam-4427	98	5	connected	connected	ADJ
ejpam-4427	98	6	nontrivial	nontrivial	ADJ
ejpam-4427	98	7	graph	graph	NOUN
ejpam-4427	98	8	of	of	ADP
ejpam-4427	98	9	order	order	NOUN
ejpam-4427	98	10	m.	m.	NOUN
ejpam-4427	98	11	then	then	ADV
ejpam-4427	98	12	rdim2(k1	rdim2(k1	VERB
ejpam-4427	98	13	+	+	PROPN
ejpam-4427	98	14	g	g	NOUN
ejpam-4427	98	15	)	)	PUNCT
ejpam-4427	99	1	=	=	PRON
ejpam-4427	99	2	{	{	PUNCT
ejpam-4427	99	3	1	1	NUM
ejpam-4427	99	4	+	+	NOUN
ejpam-4427	99	5	m	m	PROPN
ejpam-4427	99	6	,	,	PUNCT
ejpam-4427	99	7	if	if	SCONJ
ejpam-4427	99	8	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4427	99	9	)	)	PUNCT
ejpam-4427	99	10	=	=	SYM
ejpam-4427	99	11	m	m	NOUN
ejpam-4427	99	12	and	and	CCONJ
ejpam-4427	99	13	rln(2,1)(g	rln(2,1)(g	ADJ
ejpam-4427	99	14	)	)	PUNCT
ejpam-4427	99	15	=	=	NUM
ejpam-4427	99	16	m	m	PRON
ejpam-4427	99	17	min	min	NOUN
ejpam-4427	99	18	{	{	PUNCT
ejpam-4427	99	19	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4427	99	20	)	)	PUNCT
ejpam-4427	99	21	,	,	PUNCT
ejpam-4427	99	22	rln(2,1)(g	rln(2,1)(g	PROPN
ejpam-4427	99	23	)	)	PUNCT
ejpam-4427	99	24	+	+	CCONJ
ejpam-4427	99	25	1	1	NUM
ejpam-4427	99	26	}	}	PUNCT
ejpam-4427	99	27	,	,	PUNCT
ejpam-4427	99	28	otherwise	otherwise	ADV
ejpam-4427	99	29	.	.	PUNCT
ejpam-4427	100	1	j.	j.	PROPN
ejpam-4427	100	2	cabaro	cabaro	PROPN
ejpam-4427	100	3	,	,	PUNCT
ejpam-4427	100	4	h.	h.	PROPN
ejpam-4427	100	5	rara	rara	PROPN
ejpam-4427	100	6	/	/	SYM
ejpam-4427	100	7	eur	eur	PROPN
ejpam-4427	100	8	.	.	PUNCT
ejpam-4427	101	1	j.	j.	PROPN
ejpam-4427	101	2	pure	pure	PROPN
ejpam-4427	101	3	appl	appl	PROPN
ejpam-4427	101	4	.	.	PROPN
ejpam-4427	101	5	math	math	PROPN
ejpam-4427	101	6	,	,	PUNCT
ejpam-4427	101	7	15	15	NUM
ejpam-4427	101	8	(	(	PUNCT
ejpam-4427	101	9	3	3	NUM
ejpam-4427	101	10	)	)	PUNCT
ejpam-4427	101	11	(	(	PUNCT
ejpam-4427	101	12	2022	2022	NUM
ejpam-4427	101	13	)	)	PUNCT
ejpam-4427	101	14	,	,	PUNCT
ejpam-4427	101	15	1229	1229	NUM
ejpam-4427	101	16	-	-	SYM
ejpam-4427	101	17	1236	1236	NUM
ejpam-4427	101	18	1233	1233	NUM
ejpam-4427	101	19	....................................	....................................	PUNCT
ejpam-4427	101	20	....................................	....................................	PUNCT
ejpam-4427	102	1	....................................	....................................	PUNCT
ejpam-4427	102	2	....................................	....................................	PUNCT
ejpam-4427	103	1	....................................	....................................	PUNCT
ejpam-4427	103	2	....................................	....................................	PUNCT
ejpam-4427	104	1	....................................	....................................	PUNCT
ejpam-4427	104	2	....................................	....................................	PUNCT
ejpam-4427	105	1	....................................	....................................	PUNCT
ejpam-4427	105	2	....................................	....................................	PUNCT
ejpam-4427	106	1	....................................	....................................	PUNCT
ejpam-4427	106	2	.........	.........	PUNCT
ejpam-4427	106	3	........	........	PUNCT
ejpam-4427	106	4	........	........	PUNCT
ejpam-4427	106	5	........	........	PUNCT
ejpam-4427	106	6	........	........	PUNCT
ejpam-4427	106	7	........	........	PUNCT
ejpam-4427	106	8	........	........	PUNCT
ejpam-4427	106	9	........	........	PUNCT
ejpam-4427	106	10	........	........	PUNCT
ejpam-4427	106	11	........	........	PUNCT
ejpam-4427	106	12	........	........	PUNCT
ejpam-4427	107	1	....	....	PUNCT
ejpam-4427	107	2	.........	.........	PUNCT
ejpam-4427	107	3	........	........	PUNCT
ejpam-4427	107	4	........	........	PUNCT
ejpam-4427	107	5	........	........	PUNCT
ejpam-4427	107	6	........	........	PUNCT
ejpam-4427	107	7	........	........	PUNCT
ejpam-4427	107	8	........	........	PUNCT
ejpam-4427	107	9	........	........	PUNCT
ejpam-4427	107	10	........	........	PUNCT
ejpam-4427	107	11	........	........	PUNCT
ejpam-4427	107	12	........	........	PUNCT
ejpam-4427	108	1	....	....	PUNCT
ejpam-4427	108	2	.........	.........	PUNCT
ejpam-4427	108	3	........	........	PUNCT
ejpam-4427	108	4	........	........	PUNCT
ejpam-4427	108	5	........	........	PUNCT
ejpam-4427	108	6	........	........	PUNCT
ejpam-4427	108	7	........	........	PUNCT
ejpam-4427	108	8	........	........	PUNCT
ejpam-4427	108	9	........	........	PUNCT
ejpam-4427	108	10	........	........	PUNCT
ejpam-4427	108	11	........	........	PUNCT
ejpam-4427	108	12	........	........	PUNCT
ejpam-4427	109	1	....	....	PUNCT
ejpam-4427	109	2	.........	.........	PUNCT
ejpam-4427	109	3	........	........	PUNCT
ejpam-4427	109	4	........	........	PUNCT
ejpam-4427	109	5	........	........	PUNCT
ejpam-4427	109	6	........	........	PUNCT
ejpam-4427	109	7	........	........	PUNCT
ejpam-4427	109	8	........	........	PUNCT
ejpam-4427	109	9	........	........	PUNCT
ejpam-4427	109	10	........	........	PUNCT
ejpam-4427	109	11	........	........	PUNCT
ejpam-4427	109	12	........	........	PUNCT
ejpam-4427	110	1	....	....	PUNCT
ejpam-4427	110	2	..........	..........	PUNCT
ejpam-4427	111	1	.........	.........	PUNCT
ejpam-4427	111	2	.........	.........	PUNCT
ejpam-4427	112	1	.........	.........	PUNCT
ejpam-4427	112	2	.........	.........	PUNCT
ejpam-4427	113	1	.........	.........	PUNCT
ejpam-4427	113	2	.........	.........	PUNCT
ejpam-4427	114	1	.........	.........	PUNCT
ejpam-4427	114	2	.........	.........	PUNCT
ejpam-4427	115	1	.........	.........	PUNCT
ejpam-4427	115	2	.........	.........	PUNCT
ejpam-4427	116	1	.........	.........	PUNCT
ejpam-4427	116	2	.........	.........	PUNCT
ejpam-4427	117	1	.........	.........	PUNCT
ejpam-4427	117	2	.........	.........	PUNCT
ejpam-4427	118	1	.........	.........	PUNCT
ejpam-4427	118	2	.........	.........	PUNCT
ejpam-4427	119	1	.........	.........	PUNCT
ejpam-4427	119	2	.........	.........	PUNCT
ejpam-4427	120	1	.........	.........	PUNCT
ejpam-4427	120	2	.........	.........	PUNCT
ejpam-4427	121	1	.........	.........	PUNCT
ejpam-4427	121	2	.........	.........	PUNCT
ejpam-4427	122	1	.........	.........	PUNCT
ejpam-4427	122	2	.........	.........	PUNCT
ejpam-4427	123	1	.........	.........	PUNCT
ejpam-4427	123	2	.........	.........	PUNCT
ejpam-4427	124	1	.........	.........	PUNCT
ejpam-4427	124	2	.........	.........	PUNCT
ejpam-4427	125	1	.........	.........	PUNCT
ejpam-4427	125	2	.........	.........	PUNCT
ejpam-4427	126	1	.........	.........	PUNCT
ejpam-4427	126	2	.........	.........	PUNCT
ejpam-4427	127	1	.........	.........	PUNCT
ejpam-4427	127	2	.........	.........	PUNCT
ejpam-4427	128	1	.........	.........	PUNCT
ejpam-4427	128	2	.........	.........	PUNCT
ejpam-4427	129	1	.........	.........	PUNCT
ejpam-4427	129	2	.........	.........	PUNCT
ejpam-4427	130	1	.........	.........	PUNCT
ejpam-4427	130	2	.........	.........	PUNCT
ejpam-4427	131	1	.........	.........	PUNCT
ejpam-4427	131	2	.........	.........	PUNCT
ejpam-4427	132	1	.........	.........	PUNCT
ejpam-4427	132	2	.........	.........	PUNCT
ejpam-4427	133	1	.........	.........	PUNCT
ejpam-4427	133	2	.........	.........	PUNCT
ejpam-4427	134	1	.........	.........	PUNCT
ejpam-4427	134	2	.........	.........	PUNCT
ejpam-4427	135	1	.........	.........	PUNCT
ejpam-4427	135	2	.........	.........	PUNCT
ejpam-4427	136	1	.........	.........	PUNCT
ejpam-4427	136	2	.........	.........	PUNCT
ejpam-4427	137	1	.........	.........	PUNCT
ejpam-4427	137	2	.........	.........	PUNCT
ejpam-4427	137	3	.........	.........	PUNCT
ejpam-4427	137	4	.	.	PUNCT
ejpam-4427	138	1	.........	.........	PUNCT
ejpam-4427	138	2	........	........	PUNCT
ejpam-4427	138	3	........	........	PUNCT
ejpam-4427	138	4	........	........	PUNCT
ejpam-4427	138	5	........	........	PUNCT
ejpam-4427	138	6	........	........	PUNCT
ejpam-4427	138	7	........	........	PUNCT
ejpam-4427	138	8	........	........	PUNCT
ejpam-4427	138	9	........	........	PUNCT
ejpam-4427	138	10	........	........	PUNCT
ejpam-4427	139	1	........	........	PUNCT
ejpam-4427	139	2	....	....	PUNCT
ejpam-4427	140	1	.........	.........	PUNCT
ejpam-4427	140	2	........	........	PUNCT
ejpam-4427	140	3	........	........	PUNCT
ejpam-4427	140	4	........	........	PUNCT
ejpam-4427	140	5	........	........	PUNCT
ejpam-4427	140	6	........	........	PUNCT
ejpam-4427	140	7	........	........	PUNCT
ejpam-4427	140	8	........	........	PUNCT
ejpam-4427	140	9	........	........	PUNCT
ejpam-4427	140	10	........	........	PUNCT
ejpam-4427	141	1	........	........	PUNCT
ejpam-4427	141	2	....	....	PUNCT
ejpam-4427	142	1	.........	.........	PUNCT
ejpam-4427	142	2	........	........	PUNCT
ejpam-4427	142	3	........	........	PUNCT
ejpam-4427	142	4	........	........	PUNCT
ejpam-4427	142	5	........	........	PUNCT
ejpam-4427	142	6	........	........	PUNCT
ejpam-4427	142	7	........	........	PUNCT
ejpam-4427	142	8	........	........	PUNCT
ejpam-4427	142	9	........	........	PUNCT
ejpam-4427	142	10	........	........	PUNCT
ejpam-4427	143	1	........	........	PUNCT
ejpam-4427	143	2	....	....	PUNCT
ejpam-4427	144	1	.........	.........	PUNCT
ejpam-4427	144	2	........	........	PUNCT
ejpam-4427	144	3	........	........	PUNCT
ejpam-4427	144	4	........	........	PUNCT
ejpam-4427	144	5	........	........	PUNCT
ejpam-4427	144	6	........	........	PUNCT
ejpam-4427	144	7	........	........	PUNCT
ejpam-4427	144	8	........	........	PUNCT
ejpam-4427	144	9	........	........	PUNCT
ejpam-4427	144	10	........	........	PUNCT
ejpam-4427	145	1	........	........	PUNCT
ejpam-4427	145	2	....	....	PUNCT
ejpam-4427	146	1	.........	.........	PUNCT
ejpam-4427	146	2	........	........	PUNCT
ejpam-4427	146	3	........	........	PUNCT
ejpam-4427	146	4	........	........	PUNCT
ejpam-4427	146	5	........	........	PUNCT
ejpam-4427	146	6	........	........	PUNCT
ejpam-4427	146	7	........	........	PUNCT
ejpam-4427	146	8	........	........	PUNCT
ejpam-4427	146	9	........	........	PUNCT
ejpam-4427	146	10	........	........	PUNCT
ejpam-4427	146	11	........	........	PUNCT
ejpam-4427	147	1	....	....	PUNCT
ejpam-4427	147	2	.................................	.................................	PUNCT
ejpam-4427	147	3	................................	................................	PUNCT
ejpam-4427	147	4	................................	................................	PUNCT
ejpam-4427	147	5	................................	................................	PUNCT
ejpam-4427	147	6	................................	................................	PUNCT
ejpam-4427	147	7	................................	................................	PUNCT
ejpam-4427	147	8	...........	...........	PUNCT
ejpam-4427	147	9	............................................................................................................................................................................................................	............................................................................................................................................................................................................	PUNCT
ejpam-4427	148	1	..........................................................................................................................................................................................................................................................	..........................................................................................................................................................................................................................................................	NUM
ejpam-4427	149	1	...................................................................................................................................................................................................................................................................................................................................	...................................................................................................................................................................................................................................................................................................................................	PROPN
ejpam-4427	149	2	...........................................................................................................................................................................................................................................................................................................................................................................................................................	...........................................................................................................................................................................................................................................................................................................................................................................................................................	PRON
ejpam-4427	149	3	..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4427	150	1	..............	..............	PUNCT
ejpam-4427	150	2	.............	.............	PUNCT
ejpam-4427	150	3	.............	.............	PUNCT
ejpam-4427	150	4	.............	.............	PUNCT
ejpam-4427	150	5	.............	.............	PUNCT
ejpam-4427	150	6	.............	.............	PUNCT
ejpam-4427	150	7	.............	.............	PUNCT
ejpam-4427	150	8	.............	.............	PUNCT
ejpam-4427	150	9	.............	.............	PUNCT
ejpam-4427	150	10	.............	.............	PUNCT
ejpam-4427	150	11	.............	.............	PUNCT
ejpam-4427	150	12	.............	.............	PUNCT
ejpam-4427	150	13	.............	.............	PUNCT
ejpam-4427	150	14	.............	.............	PUNCT
ejpam-4427	150	15	.............	.............	PUNCT
ejpam-4427	150	16	.............	.............	PUNCT
ejpam-4427	150	17	.............	.............	PUNCT
ejpam-4427	150	18	.............	.............	PUNCT
ejpam-4427	150	19	.............	.............	PUNCT
ejpam-4427	150	20	..	..	PUNCT
ejpam-4427	150	21	.................................	.................................	PUNCT
ejpam-4427	150	22	................................	................................	PUNCT
ejpam-4427	150	23	................................	................................	PUNCT
ejpam-4427	150	24	................................	................................	PUNCT
ejpam-4427	150	25	................................	................................	PUNCT
ejpam-4427	150	26	................................	................................	PUNCT
ejpam-4427	150	27	...........	...........	PUNCT
ejpam-4427	150	28	............................................................................................................................................................................................................	............................................................................................................................................................................................................	PUNCT
ejpam-4427	151	1	..........................................................................................................................................................................................................................................................	..........................................................................................................................................................................................................................................................	NUM
ejpam-4427	152	1	...................................................................................................................................................................................................................................................................................................................................	...................................................................................................................................................................................................................................................................................................................................	PROPN
ejpam-4427	152	2	...........................................................................................................................................................................................................................................................................................................................................................................................................................	...........................................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4427	153	1	...........	...........	PUNCT
ejpam-4427	153	2	..........	..........	PUNCT
ejpam-4427	154	1	..........	..........	PUNCT
ejpam-4427	154	2	..........	..........	PUNCT
ejpam-4427	155	1	..........	..........	PUNCT
ejpam-4427	155	2	..........	..........	PUNCT
ejpam-4427	156	1	..........	..........	PUNCT
ejpam-4427	156	2	..........	..........	PUNCT
ejpam-4427	157	1	..........	..........	PUNCT
ejpam-4427	157	2	..........	..........	PUNCT
ejpam-4427	158	1	..........	..........	PUNCT
ejpam-4427	158	2	..........	..........	PUNCT
ejpam-4427	159	1	..........	..........	PUNCT
ejpam-4427	159	2	..........	..........	PUNCT
ejpam-4427	160	1	..........	..........	PUNCT
ejpam-4427	160	2	..........	..........	PUNCT
ejpam-4427	161	1	..........	..........	PUNCT
ejpam-4427	161	2	..........	..........	PUNCT
ejpam-4427	162	1	..........	..........	PUNCT
ejpam-4427	162	2	..........	..........	PUNCT
ejpam-4427	163	1	..........	..........	PUNCT
ejpam-4427	163	2	..........	..........	PUNCT
ejpam-4427	164	1	..........	..........	PUNCT
ejpam-4427	164	2	..........	..........	PUNCT
ejpam-4427	165	1	..........	..........	PUNCT
ejpam-4427	165	2	..........	..........	PUNCT
ejpam-4427	166	1	..........	..........	PUNCT
ejpam-4427	166	2	..........	..........	PUNCT
ejpam-4427	167	1	..........	..........	PUNCT
ejpam-4427	167	2	..........	..........	PUNCT
ejpam-4427	168	1	..........	..........	PUNCT
ejpam-4427	168	2	..........	..........	PUNCT
ejpam-4427	169	1	..	..	PUNCT
ejpam-4427	169	2	..............	..............	PUNCT
ejpam-4427	169	3	.............	.............	PUNCT
ejpam-4427	169	4	.............	.............	PUNCT
ejpam-4427	169	5	.............	.............	PUNCT
ejpam-4427	169	6	.............	.............	PUNCT
ejpam-4427	169	7	.............	.............	PUNCT
ejpam-4427	169	8	.............	.............	PUNCT
ejpam-4427	169	9	.............	.............	PUNCT
ejpam-4427	169	10	.............	.............	PUNCT
ejpam-4427	169	11	.............	.............	PUNCT
ejpam-4427	169	12	.............	.............	PUNCT
ejpam-4427	169	13	.............	.............	PUNCT
ejpam-4427	169	14	.............	.............	PUNCT
ejpam-4427	169	15	.............	.............	PUNCT
ejpam-4427	169	16	.............	.............	PUNCT
ejpam-4427	169	17	.............	.............	PUNCT
ejpam-4427	169	18	.............	.............	PUNCT
ejpam-4427	169	19	.............	.............	PUNCT
ejpam-4427	169	20	.............	.............	PUNCT
ejpam-4427	169	21	..	..	PUNCT
ejpam-4427	169	22	.................................	.................................	PUNCT
ejpam-4427	169	23	................................	................................	PUNCT
ejpam-4427	169	24	................................	................................	PUNCT
ejpam-4427	169	25	................................	................................	PUNCT
ejpam-4427	169	26	................................	................................	PUNCT
ejpam-4427	169	27	................................	................................	PUNCT
ejpam-4427	169	28	...........	...........	PUNCT
ejpam-4427	169	29	............................................................................................................................................................................................................	............................................................................................................................................................................................................	PUNCT
ejpam-4427	170	1	..........................................................................................................................................................................................................................................................	..........................................................................................................................................................................................................................................................	NUM
ejpam-4427	170	2	...................................................................................................................................................................................................................................................................................................................................	...................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4427	171	1	..........	..........	PUNCT
ejpam-4427	171	2	..........	..........	PUNCT
ejpam-4427	172	1	.........	.........	PUNCT
ejpam-4427	172	2	..........	..........	PUNCT
ejpam-4427	173	1	..........	..........	PUNCT
ejpam-4427	173	2	.........	.........	PUNCT
ejpam-4427	174	1	.........	.........	PUNCT
ejpam-4427	174	2	..........	..........	PUNCT
ejpam-4427	175	1	.........	.........	PUNCT
ejpam-4427	175	2	.........	.........	PUNCT
ejpam-4427	176	1	..........	..........	PUNCT
ejpam-4427	176	2	.........	.........	PUNCT
ejpam-4427	177	1	..........	..........	PUNCT
ejpam-4427	177	2	..........	..........	PUNCT
ejpam-4427	178	1	.........	.........	PUNCT
ejpam-4427	178	2	.........	.........	PUNCT
ejpam-4427	179	1	..........	..........	PUNCT
ejpam-4427	179	2	.........	.........	PUNCT
ejpam-4427	180	1	.........	.........	PUNCT
ejpam-4427	180	2	..........	..........	PUNCT
ejpam-4427	181	1	.........	.........	PUNCT
ejpam-4427	181	2	..........	..........	PUNCT
ejpam-4427	182	1	..........	..........	PUNCT
ejpam-4427	182	2	.........	.........	PUNCT
ejpam-4427	183	1	.........	.........	PUNCT
ejpam-4427	183	2	..........	..........	PUNCT
ejpam-4427	184	1	.........	.........	PUNCT
ejpam-4427	184	2	.........	.........	PUNCT
ejpam-4427	185	1	..........	..........	PUNCT
ejpam-4427	185	2	.........	.........	PUNCT
ejpam-4427	186	1	..........	..........	PUNCT
ejpam-4427	186	2	..........	..........	PUNCT
ejpam-4427	187	1	.........	.........	PUNCT
ejpam-4427	187	2	.........	.........	PUNCT
ejpam-4427	188	1	..........	..........	PUNCT
ejpam-4427	188	2	.........	.........	PUNCT
ejpam-4427	189	1	.........	.........	PUNCT
ejpam-4427	189	2	..........	..........	PUNCT
ejpam-4427	190	1	.........	.........	PUNCT
ejpam-4427	190	2	..........	..........	PUNCT
ejpam-4427	191	1	..........	..........	PUNCT
ejpam-4427	191	2	.........	.........	PUNCT
ejpam-4427	192	1	.........	.........	PUNCT
ejpam-4427	192	2	....	....	PUNCT
ejpam-4427	192	3	...........	...........	PUNCT
ejpam-4427	192	4	..........	..........	PUNCT
ejpam-4427	193	1	..........	..........	PUNCT
ejpam-4427	193	2	..........	..........	PUNCT
ejpam-4427	194	1	..........	..........	PUNCT
ejpam-4427	194	2	..........	..........	PUNCT
ejpam-4427	195	1	..........	..........	PUNCT
ejpam-4427	195	2	..........	..........	PUNCT
ejpam-4427	196	1	..........	..........	PUNCT
ejpam-4427	196	2	..........	..........	PUNCT
ejpam-4427	197	1	..........	..........	PUNCT
ejpam-4427	197	2	..........	..........	PUNCT
ejpam-4427	198	1	..........	..........	PUNCT
ejpam-4427	198	2	..........	..........	PUNCT
ejpam-4427	199	1	..........	..........	PUNCT
ejpam-4427	199	2	..........	..........	PUNCT
ejpam-4427	200	1	..........	..........	PUNCT
ejpam-4427	200	2	..........	..........	PUNCT
ejpam-4427	201	1	..........	..........	PUNCT
ejpam-4427	201	2	..........	..........	PUNCT
ejpam-4427	202	1	..........	..........	PUNCT
ejpam-4427	202	2	..........	..........	PUNCT
ejpam-4427	203	1	..........	..........	PUNCT
ejpam-4427	203	2	..........	..........	PUNCT
ejpam-4427	204	1	..........	..........	PUNCT
ejpam-4427	204	2	..........	..........	PUNCT
ejpam-4427	205	1	..........	..........	PUNCT
ejpam-4427	205	2	..........	..........	PUNCT
ejpam-4427	206	1	..........	..........	PUNCT
ejpam-4427	206	2	..........	..........	PUNCT
ejpam-4427	207	1	..........	..........	PUNCT
ejpam-4427	207	2	..........	..........	PUNCT
ejpam-4427	208	1	..	..	PUNCT
ejpam-4427	208	2	..............	..............	PUNCT
ejpam-4427	208	3	.............	.............	PUNCT
ejpam-4427	208	4	.............	.............	PUNCT
ejpam-4427	208	5	.............	.............	PUNCT
ejpam-4427	208	6	.............	.............	PUNCT
ejpam-4427	208	7	.............	.............	PUNCT
ejpam-4427	208	8	.............	.............	PUNCT
ejpam-4427	208	9	.............	.............	PUNCT
ejpam-4427	208	10	.............	.............	PUNCT
ejpam-4427	208	11	.............	.............	PUNCT
ejpam-4427	208	12	.............	.............	PUNCT
ejpam-4427	208	13	.............	.............	PUNCT
ejpam-4427	208	14	.............	.............	PUNCT
ejpam-4427	208	15	.............	.............	PUNCT
ejpam-4427	208	16	.............	.............	PUNCT
ejpam-4427	208	17	.............	.............	PUNCT
ejpam-4427	208	18	.............	.............	PUNCT
ejpam-4427	208	19	.............	.............	PUNCT
ejpam-4427	208	20	.............	.............	PUNCT
ejpam-4427	208	21	..	..	PUNCT
ejpam-4427	208	22	.................................	.................................	PUNCT
ejpam-4427	208	23	................................	................................	PUNCT
ejpam-4427	208	24	................................	................................	PUNCT
ejpam-4427	208	25	................................	................................	PUNCT
ejpam-4427	208	26	................................	................................	PUNCT
ejpam-4427	208	27	................................	................................	PUNCT
ejpam-4427	208	28	...........	...........	PUNCT
ejpam-4427	208	29	............................................................................................................................................................................................................	............................................................................................................................................................................................................	PUNCT
ejpam-4427	209	1	..........................................................................................................................................................................................................................................................	..........................................................................................................................................................................................................................................................	PUNCT
ejpam-4427	210	1	..........	..........	PUNCT
ejpam-4427	211	1	.........	.........	PUNCT
ejpam-4427	212	1	.........	.........	PUNCT
ejpam-4427	213	1	.........	.........	PUNCT
ejpam-4427	214	1	.........	.........	PUNCT
ejpam-4427	215	1	.........	.........	PUNCT
ejpam-4427	216	1	.........	.........	PUNCT
ejpam-4427	217	1	.........	.........	PUNCT
ejpam-4427	218	1	.........	.........	PUNCT
ejpam-4427	219	1	.........	.........	PUNCT
ejpam-4427	220	1	.........	.........	PUNCT
ejpam-4427	221	1	.........	.........	PUNCT
ejpam-4427	222	1	.........	.........	PUNCT
ejpam-4427	223	1	.........	.........	PUNCT
ejpam-4427	224	1	.........	.........	PUNCT
ejpam-4427	225	1	.........	.........	PUNCT
ejpam-4427	226	1	.........	.........	PUNCT
ejpam-4427	227	1	.........	.........	PUNCT
ejpam-4427	228	1	.........	.........	PUNCT
ejpam-4427	229	1	.........	.........	PUNCT
ejpam-4427	230	1	.........	.........	PUNCT
ejpam-4427	231	1	.........	.........	PUNCT
ejpam-4427	232	1	.........	.........	PUNCT
ejpam-4427	233	1	.........	.........	PUNCT
ejpam-4427	234	1	.........	.........	PUNCT
ejpam-4427	235	1	.........	.........	PUNCT
ejpam-4427	236	1	.........	.........	PUNCT
ejpam-4427	237	1	.........	.........	PUNCT
ejpam-4427	238	1	.........	.........	PUNCT
ejpam-4427	239	1	.........	.........	PUNCT
ejpam-4427	240	1	.........	.........	PUNCT
ejpam-4427	241	1	.........	.........	PUNCT
ejpam-4427	242	1	.........	.........	PUNCT
ejpam-4427	243	1	.........	.........	PUNCT
ejpam-4427	244	1	.........	.........	PUNCT
ejpam-4427	245	1	.........	.........	PUNCT
ejpam-4427	246	1	.........	.........	PUNCT
ejpam-4427	247	1	.........	.........	PUNCT
ejpam-4427	248	1	.........	.........	PUNCT
ejpam-4427	249	1	.........	.........	PUNCT
ejpam-4427	250	1	.........	.........	PUNCT
ejpam-4427	251	1	.........	.........	PUNCT
ejpam-4427	252	1	.........	.........	PUNCT
ejpam-4427	253	1	.........	.........	PUNCT
ejpam-4427	254	1	.........	.........	PUNCT
ejpam-4427	255	1	.........	.........	PUNCT
ejpam-4427	256	1	.........	.........	PUNCT
ejpam-4427	257	1	.........	.........	PUNCT
ejpam-4427	258	1	.........	.........	PUNCT
ejpam-4427	259	1	.........	.........	PUNCT
ejpam-4427	260	1	.........	.........	PUNCT
ejpam-4427	261	1	.........	.........	PUNCT
ejpam-4427	262	1	.........	.........	PUNCT
ejpam-4427	263	1	.........	.........	PUNCT
ejpam-4427	264	1	.........	.........	PUNCT
ejpam-4427	265	1	.........	.........	PUNCT
ejpam-4427	265	2	.	.	PUNCT
ejpam-4427	266	1	...........	...........	PUNCT
ejpam-4427	266	2	.........	.........	PUNCT
ejpam-4427	267	1	.........	.........	PUNCT
ejpam-4427	267	2	..........	..........	PUNCT
ejpam-4427	268	1	.........	.........	PUNCT
ejpam-4427	268	2	.........	.........	PUNCT
ejpam-4427	269	1	..........	..........	PUNCT
ejpam-4427	269	2	.........	.........	PUNCT
ejpam-4427	270	1	..........	..........	PUNCT
ejpam-4427	270	2	..........	..........	PUNCT
ejpam-4427	271	1	.........	.........	PUNCT
ejpam-4427	271	2	.........	.........	PUNCT
ejpam-4427	272	1	..........	..........	PUNCT
ejpam-4427	272	2	.........	.........	PUNCT
ejpam-4427	273	1	.........	.........	PUNCT
ejpam-4427	273	2	..........	..........	PUNCT
ejpam-4427	274	1	.........	.........	PUNCT
ejpam-4427	274	2	..........	..........	PUNCT
ejpam-4427	275	1	..........	..........	PUNCT
ejpam-4427	275	2	.........	.........	PUNCT
ejpam-4427	276	1	.........	.........	PUNCT
ejpam-4427	276	2	..........	..........	PUNCT
ejpam-4427	277	1	.........	.........	PUNCT
ejpam-4427	277	2	.........	.........	PUNCT
ejpam-4427	278	1	..........	..........	PUNCT
ejpam-4427	278	2	.........	.........	PUNCT
ejpam-4427	279	1	..........	..........	PUNCT
ejpam-4427	279	2	..........	..........	PUNCT
ejpam-4427	280	1	.........	.........	PUNCT
ejpam-4427	280	2	.........	.........	PUNCT
ejpam-4427	281	1	..........	..........	PUNCT
ejpam-4427	281	2	.........	.........	PUNCT
ejpam-4427	282	1	.........	.........	PUNCT
ejpam-4427	282	2	..........	..........	PUNCT
ejpam-4427	283	1	.........	.........	PUNCT
ejpam-4427	283	2	..........	..........	PUNCT
ejpam-4427	284	1	..........	..........	PUNCT
ejpam-4427	284	2	.........	.........	PUNCT
ejpam-4427	285	1	.........	.........	PUNCT
ejpam-4427	285	2	..........	..........	PUNCT
ejpam-4427	286	1	.........	.........	PUNCT
ejpam-4427	286	2	.........	.........	PUNCT
ejpam-4427	287	1	..........	..........	PUNCT
ejpam-4427	287	2	....	....	PUNCT
ejpam-4427	287	3	...........	...........	PUNCT
ejpam-4427	287	4	..........	..........	PUNCT
ejpam-4427	288	1	..........	..........	PUNCT
ejpam-4427	288	2	..........	..........	PUNCT
ejpam-4427	289	1	..........	..........	PUNCT
ejpam-4427	289	2	..........	..........	PUNCT
ejpam-4427	290	1	..........	..........	PUNCT
ejpam-4427	290	2	..........	..........	PUNCT
ejpam-4427	291	1	..........	..........	PUNCT
ejpam-4427	291	2	..........	..........	PUNCT
ejpam-4427	292	1	..........	..........	PUNCT
ejpam-4427	292	2	..........	..........	PUNCT
ejpam-4427	293	1	..........	..........	PUNCT
ejpam-4427	293	2	..........	..........	PUNCT
ejpam-4427	294	1	..........	..........	PUNCT
ejpam-4427	294	2	..........	..........	PUNCT
ejpam-4427	295	1	..........	..........	PUNCT
ejpam-4427	295	2	..........	..........	PUNCT
ejpam-4427	296	1	..........	..........	PUNCT
ejpam-4427	296	2	..........	..........	PUNCT
ejpam-4427	297	1	..........	..........	PUNCT
ejpam-4427	297	2	..........	..........	PUNCT
ejpam-4427	298	1	..........	..........	PUNCT
ejpam-4427	298	2	..........	..........	PUNCT
ejpam-4427	299	1	..........	..........	PUNCT
ejpam-4427	299	2	..........	..........	PUNCT
ejpam-4427	300	1	..........	..........	PUNCT
ejpam-4427	300	2	..........	..........	PUNCT
ejpam-4427	301	1	..........	..........	PUNCT
ejpam-4427	301	2	..........	..........	PUNCT
ejpam-4427	302	1	..........	..........	PUNCT
ejpam-4427	302	2	..........	..........	PUNCT
ejpam-4427	303	1	..	..	PUNCT
ejpam-4427	303	2	..............	..............	PUNCT
ejpam-4427	303	3	.............	.............	PUNCT
ejpam-4427	303	4	.............	.............	PUNCT
ejpam-4427	303	5	.............	.............	PUNCT
ejpam-4427	303	6	.............	.............	PUNCT
ejpam-4427	303	7	.............	.............	PUNCT
ejpam-4427	303	8	.............	.............	PUNCT
ejpam-4427	303	9	.............	.............	PUNCT
ejpam-4427	303	10	.............	.............	PUNCT
ejpam-4427	303	11	.............	.............	PUNCT
ejpam-4427	303	12	.............	.............	PUNCT
ejpam-4427	303	13	.............	.............	PUNCT
ejpam-4427	303	14	.............	.............	PUNCT
ejpam-4427	303	15	.............	.............	PUNCT
ejpam-4427	303	16	.............	.............	PUNCT
ejpam-4427	303	17	.............	.............	PUNCT
ejpam-4427	303	18	.............	.............	PUNCT
ejpam-4427	303	19	.............	.............	PUNCT
ejpam-4427	303	20	.............	.............	PUNCT
ejpam-4427	303	21	..	..	PUNCT
ejpam-4427	303	22	.................................	.................................	PUNCT
ejpam-4427	303	23	................................	................................	PUNCT
ejpam-4427	303	24	................................	................................	PUNCT
ejpam-4427	303	25	................................	................................	PUNCT
ejpam-4427	303	26	................................	................................	PUNCT
ejpam-4427	303	27	................................	................................	PUNCT
ejpam-4427	303	28	...........	...........	PUNCT
ejpam-4427	303	29	............................................................................................................................................................................................................	............................................................................................................................................................................................................	PUNCT
ejpam-4427	304	1	p5	p5	ADJ
ejpam-4427	304	2	+	+	CCONJ
ejpam-4427	304	3	p6	p6	ADJ
ejpam-4427	304	4	:	:	PUNCT
ejpam-4427	304	5	•	•	NUM
ejpam-4427	304	6	•	•	NOUN
ejpam-4427	304	7	•	•	NUM
ejpam-4427	304	8	•	•	NUM
ejpam-4427	304	9	•	•	NUM
ejpam-4427	304	10	•	•	NOUN
ejpam-4427	304	11	•	•	NUM
ejpam-4427	304	12	figure	figure	NOUN
ejpam-4427	304	13	1	1	NUM
ejpam-4427	304	14	:	:	PUNCT
ejpam-4427	304	15	a	a	DET
ejpam-4427	304	16	graph	graph	NOUN
ejpam-4427	304	17	p5	p5	ADJ
ejpam-4427	304	18	+	+	CCONJ
ejpam-4427	304	19	p6	p6	VERB
ejpam-4427	304	20	with	with	ADP
ejpam-4427	304	21	rdim2(p5	rdim2(p5	NOUN
ejpam-4427	304	22	+	+	CCONJ
ejpam-4427	304	23	p6	p6	ADJ
ejpam-4427	304	24	)	)	PUNCT
ejpam-4427	304	25	=	=	NOUN
ejpam-4427	304	26	7	7	NUM
ejpam-4427	304	27	4	4	NUM
ejpam-4427	304	28	.	.	PUNCT
ejpam-4427	305	1	restrained	restrain	VERB
ejpam-4427	305	2	2	2	NUM
ejpam-4427	305	3	-	-	PUNCT
ejpam-4427	305	4	resolving	resolve	VERB
ejpam-4427	305	5	sets	set	NOUN
ejpam-4427	305	6	in	in	ADP
ejpam-4427	305	7	the	the	DET
ejpam-4427	305	8	corona	corona	NOUN
ejpam-4427	305	9	of	of	ADP
ejpam-4427	305	10	graphs	graph	NOUN
ejpam-4427	305	11	theorem	theorem	VERB
ejpam-4427	305	12	4	4	NUM
ejpam-4427	305	13	.	.	PUNCT
ejpam-4427	306	1	let	let	VERB
ejpam-4427	306	2	g	g	NOUN
ejpam-4427	306	3	and	and	CCONJ
ejpam-4427	306	4	h	h	NOUN
ejpam-4427	306	5	be	be	AUX
ejpam-4427	306	6	nontrivial	nontrivial	ADJ
ejpam-4427	306	7	connected	connected	ADJ
ejpam-4427	306	8	graphs	graph	NOUN
ejpam-4427	306	9	.	.	PUNCT
ejpam-4427	307	1	a	a	DET
ejpam-4427	307	2	set	set	NOUN
ejpam-4427	307	3	s	s	NOUN
ejpam-4427	307	4	⊆	⊆	NUM
ejpam-4427	307	5	v	v	NOUN
ejpam-4427	307	6	(	(	PUNCT
ejpam-4427	307	7	g	g	PROPN
ejpam-4427	307	8	◦	◦	NOUN
ejpam-4427	307	9	h	h	NOUN
ejpam-4427	307	10	)	)	PUNCT
ejpam-4427	307	11	is	be	AUX
ejpam-4427	307	12	a	a	DET
ejpam-4427	307	13	2	2	NUM
ejpam-4427	307	14	-	-	PUNCT
ejpam-4427	307	15	resolving	resolve	VERB
ejpam-4427	307	16	set	set	NOUN
ejpam-4427	307	17	of	of	ADP
ejpam-4427	307	18	g	g	PROPN
ejpam-4427	307	19	◦	◦	NOUN
ejpam-4427	307	20	h	h	NOUN
ejpam-4427	307	21	if	if	SCONJ
ejpam-4427	308	1	and	and	CCONJ
ejpam-4427	308	2	only	only	ADV
ejpam-4427	308	3	if	if	SCONJ
ejpam-4427	308	4	s	s	NOUN
ejpam-4427	308	5	=	=	X
ejpam-4427	308	6	a∪b	a∪b	ADJ
ejpam-4427	308	7	,	,	PUNCT
ejpam-4427	308	8	where	where	SCONJ
ejpam-4427	308	9	a	a	DET
ejpam-4427	308	10	⊆	⊆	NUM
ejpam-4427	308	11	v	v	NOUN
ejpam-4427	308	12	(	(	PUNCT
ejpam-4427	308	13	g	g	NOUN
ejpam-4427	308	14	)	)	PUNCT
ejpam-4427	308	15	and	and	CCONJ
ejpam-4427	308	16	b	b	X
ejpam-4427	308	17	=	=	SYM
ejpam-4427	308	18	⋃	⋃	NOUN
ejpam-4427	308	19	{	{	PUNCT
ejpam-4427	308	20	sv	sv	NOUN
ejpam-4427	308	21	:	:	PUNCT
ejpam-4427	308	22	sv	sv	PROPN
ejpam-4427	308	23	is	be	AUX
ejpam-4427	308	24	a	a	DET
ejpam-4427	308	25	2	2	NUM
ejpam-4427	308	26	-	-	PUNCT
ejpam-4427	308	27	resolving	resolve	VERB
ejpam-4427	308	28	set	set	NOUN
ejpam-4427	308	29	of	of	ADP
ejpam-4427	308	30	hv	hv	PROPN
ejpam-4427	308	31	,	,	PUNCT
ejpam-4427	308	32	for	for	ADP
ejpam-4427	308	33	all	all	PRON
ejpam-4427	308	34	v	v	ADP
ejpam-4427	308	35	∈	∈	NUM
ejpam-4427	308	36	v	v	NOUN
ejpam-4427	308	37	(	(	PUNCT
ejpam-4427	308	38	g	g	NOUN
ejpam-4427	308	39	)	)	PUNCT
ejpam-4427	308	40	}	}	PUNCT
ejpam-4427	308	41	.	.	PUNCT
ejpam-4427	309	1	theorem	theorem	NOUN
ejpam-4427	309	2	5	5	NUM
ejpam-4427	309	3	.	.	PUNCT
ejpam-4427	310	1	let	let	VERB
ejpam-4427	310	2	g	g	NOUN
ejpam-4427	310	3	and	and	CCONJ
ejpam-4427	310	4	h	h	NOUN
ejpam-4427	310	5	be	be	AUX
ejpam-4427	310	6	nontrivial	nontrivial	ADJ
ejpam-4427	310	7	connected	connected	ADJ
ejpam-4427	310	8	graphs	graph	NOUN
ejpam-4427	310	9	.	.	PUNCT
ejpam-4427	311	1	a	a	DET
ejpam-4427	311	2	set	set	NOUN
ejpam-4427	311	3	s	s	NOUN
ejpam-4427	311	4	⊆	⊆	NUM
ejpam-4427	311	5	v	v	NOUN
ejpam-4427	311	6	(	(	PUNCT
ejpam-4427	311	7	g	g	PROPN
ejpam-4427	311	8	◦	◦	NOUN
ejpam-4427	311	9	h	h	NOUN
ejpam-4427	311	10	)	)	PUNCT
ejpam-4427	311	11	is	be	AUX
ejpam-4427	311	12	a	a	DET
ejpam-4427	311	13	restrained	restrained	ADJ
ejpam-4427	311	14	2	2	NUM
ejpam-4427	311	15	-	-	PUNCT
ejpam-4427	311	16	resolving	resolving	NOUN
ejpam-4427	311	17	set	set	NOUN
ejpam-4427	311	18	in	in	ADP
ejpam-4427	311	19	g	g	PROPN
ejpam-4427	311	20	◦	◦	NOUN
ejpam-4427	311	21	h	h	NOUN
ejpam-4427	311	22	if	if	SCONJ
ejpam-4427	312	1	and	and	CCONJ
ejpam-4427	312	2	only	only	ADV
ejpam-4427	312	3	if	if	SCONJ
ejpam-4427	312	4	s	s	VERB
ejpam-4427	312	5	=	=	NOUN
ejpam-4427	312	6	a	a	PRON
ejpam-4427	312	7	∪	∪	X
ejpam-4427	312	8	(	(	PUNCT
ejpam-4427	312	9	⋃	⋃	NOUN
ejpam-4427	312	10	v∈v	v∈v	NOUN
ejpam-4427	312	11	(	(	PUNCT
ejpam-4427	312	12	g	g	NOUN
ejpam-4427	312	13	)	)	PUNCT
ejpam-4427	312	14	sv	sv	NOUN
ejpam-4427	312	15	)	)	PUNCT
ejpam-4427	312	16	satisfying	satisfy	VERB
ejpam-4427	312	17	the	the	DET
ejpam-4427	312	18	following	follow	VERB
ejpam-4427	312	19	conditions	condition	NOUN
ejpam-4427	312	20	.	.	PUNCT
ejpam-4427	313	1	(	(	PUNCT
ejpam-4427	313	2	i	i	NOUN
ejpam-4427	313	3	)	)	PUNCT
ejpam-4427	313	4	a	a	DET
ejpam-4427	313	5	⊆	⊆	NUM
ejpam-4427	313	6	v	v	NOUN
ejpam-4427	313	7	(	(	PUNCT
ejpam-4427	313	8	g	g	NOUN
ejpam-4427	313	9	)	)	PUNCT
ejpam-4427	313	10	(	(	PUNCT
ejpam-4427	313	11	ii	ii	NOUN
ejpam-4427	313	12	)	)	PUNCT
ejpam-4427	313	13	sv	sv	PROPN
ejpam-4427	313	14	is	be	AUX
ejpam-4427	313	15	a	a	DET
ejpam-4427	313	16	2	2	NUM
ejpam-4427	313	17	-	-	PUNCT
ejpam-4427	313	18	resolving	resolving	NOUN
ejpam-4427	313	19	set	set	NOUN
ejpam-4427	313	20	for	for	ADP
ejpam-4427	313	21	each	each	DET
ejpam-4427	313	22	v	v	NUM
ejpam-4427	313	23	∈	∈	PROPN
ejpam-4427	313	24	v	v	NOUN
ejpam-4427	313	25	(	(	PUNCT
ejpam-4427	313	26	g)\a	g)\a	PROPN
ejpam-4427	313	27	(	(	PUNCT
ejpam-4427	313	28	iii	iii	NOUN
ejpam-4427	313	29	)	)	PUNCT
ejpam-4427	313	30	sv	sv	PROPN
ejpam-4427	313	31	is	be	AUX
ejpam-4427	313	32	a	a	DET
ejpam-4427	313	33	restrained	restrained	ADJ
ejpam-4427	313	34	2	2	NUM
ejpam-4427	313	35	-	-	PUNCT
ejpam-4427	313	36	resolving	resolving	NOUN
ejpam-4427	313	37	set	set	NOUN
ejpam-4427	313	38	for	for	ADP
ejpam-4427	313	39	each	each	DET
ejpam-4427	313	40	v	v	ADP
ejpam-4427	313	41	∈	∈	PRON
ejpam-4427	313	42	a	a	DET
ejpam-4427	313	43	(	(	PUNCT
ejpam-4427	313	44	iv	iv	NOUN
ejpam-4427	313	45	)	)	PUNCT
ejpam-4427	313	46	w	w	PROPN
ejpam-4427	313	47	∈	∈	PROPN
ejpam-4427	313	48	ng(v	ng(v	PUNCT
ejpam-4427	313	49	(	(	PUNCT
ejpam-4427	313	50	g)\a	g)\a	NOUN
ejpam-4427	313	51	)	)	PUNCT
ejpam-4427	313	52	for	for	ADP
ejpam-4427	313	53	each	each	DET
ejpam-4427	313	54	w	w	PROPN
ejpam-4427	313	55	∈	∈	PROPN
ejpam-4427	313	56	v	v	NOUN
ejpam-4427	313	57	(	(	PUNCT
ejpam-4427	313	58	g)\a	g)\a	NOUN
ejpam-4427	313	59	with	with	ADP
ejpam-4427	313	60	sw	sw	PROPN
ejpam-4427	313	61	=	=	SYM
ejpam-4427	313	62	v	v	PROPN
ejpam-4427	313	63	(	(	PUNCT
ejpam-4427	313	64	hw	hw	NOUN
ejpam-4427	313	65	)	)	PUNCT
ejpam-4427	313	66	.	.	PUNCT
ejpam-4427	314	1	proof	proof	NOUN
ejpam-4427	314	2	.	.	PUNCT
ejpam-4427	315	1	suppose	suppose	VERB
ejpam-4427	315	2	s	s	PRON
ejpam-4427	315	3	is	be	AUX
ejpam-4427	315	4	a	a	DET
ejpam-4427	315	5	restrained	restrained	ADJ
ejpam-4427	315	6	2	2	NUM
ejpam-4427	315	7	-	-	PUNCT
ejpam-4427	315	8	resolving	resolving	NOUN
ejpam-4427	315	9	set	set	NOUN
ejpam-4427	315	10	in	in	ADP
ejpam-4427	315	11	g	g	PROPN
ejpam-4427	315	12	◦	◦	PROPN
ejpam-4427	315	13	h.	h.	PROPN
ejpam-4427	315	14	let	let	VERB
ejpam-4427	315	15	a	a	DET
ejpam-4427	315	16	=	=	X
ejpam-4427	315	17	v	v	X
ejpam-4427	315	18	(	(	PUNCT
ejpam-4427	315	19	g	g	NOUN
ejpam-4427	315	20	)	)	PUNCT
ejpam-4427	315	21	∩	∩	PROPN
ejpam-4427	315	22	s	s	NOUN
ejpam-4427	315	23	and	and	CCONJ
ejpam-4427	315	24	sv	sv	X
ejpam-4427	315	25	=	=	SYM
ejpam-4427	315	26	s	s	PROPN
ejpam-4427	315	27	∩	∩	ADJ
ejpam-4427	315	28	v	v	X
ejpam-4427	315	29	(	(	PUNCT
ejpam-4427	315	30	hv	hv	PROPN
ejpam-4427	315	31	)	)	PUNCT
ejpam-4427	315	32	for	for	ADP
ejpam-4427	315	33	all	all	DET
ejpam-4427	315	34	v	v	ADP
ejpam-4427	315	35	∈	∈	NOUN
ejpam-4427	315	36	v	v	NOUN
ejpam-4427	315	37	(	(	PUNCT
ejpam-4427	315	38	g	g	NOUN
ejpam-4427	315	39	)	)	PUNCT
ejpam-4427	315	40	.	.	PUNCT
ejpam-4427	316	1	then	then	ADV
ejpam-4427	316	2	s	s	VERB
ejpam-4427	316	3	=	=	PUNCT
ejpam-4427	316	4	a	a	PRON
ejpam-4427	316	5	∪	∪	X
ejpam-4427	316	6	(	(	PUNCT
ejpam-4427	316	7	⋃	⋃	NOUN
ejpam-4427	316	8	v∈v	v∈v	NOUN
ejpam-4427	316	9	(	(	PUNCT
ejpam-4427	316	10	g	g	NOUN
ejpam-4427	316	11	)	)	PUNCT
ejpam-4427	316	12	sv	sv	NOUN
ejpam-4427	316	13	)	)	PUNCT
ejpam-4427	316	14	where	where	SCONJ
ejpam-4427	316	15	a	a	DET
ejpam-4427	316	16	⊆	⊆	NUM
ejpam-4427	316	17	v	v	NOUN
ejpam-4427	316	18	(	(	PUNCT
ejpam-4427	316	19	g	g	NOUN
ejpam-4427	316	20	)	)	PUNCT
ejpam-4427	316	21	and	and	CCONJ
ejpam-4427	316	22	sv	sv	X
ejpam-4427	316	23	⊆	⊆	NUM
ejpam-4427	316	24	v	v	X
ejpam-4427	316	25	(	(	PUNCT
ejpam-4427	316	26	hv	hv	PROPN
ejpam-4427	316	27	)	)	PUNCT
ejpam-4427	316	28	for	for	ADP
ejpam-4427	316	29	each	each	DET
ejpam-4427	316	30	v	v	NUM
ejpam-4427	316	31	∈	∈	PROPN
ejpam-4427	316	32	v	v	NOUN
ejpam-4427	316	33	(	(	PUNCT
ejpam-4427	316	34	g	g	NOUN
ejpam-4427	316	35	)	)	PUNCT
ejpam-4427	316	36	.	.	PUNCT
ejpam-4427	317	1	by	by	ADP
ejpam-4427	317	2	theorem	theorem	NOUN
ejpam-4427	317	3	4	4	NUM
ejpam-4427	317	4	,	,	PUNCT
ejpam-4427	317	5	sv	sv	X
ejpam-4427	317	6	is	be	AUX
ejpam-4427	317	7	a	a	DET
ejpam-4427	317	8	2	2	NUM
ejpam-4427	317	9	-	-	PUNCT
ejpam-4427	317	10	resolving	resolving	NOUN
ejpam-4427	317	11	set	set	VERB
ejpam-4427	317	12	in	in	ADP
ejpam-4427	317	13	hv	hv	PROPN
ejpam-4427	317	14	for	for	ADP
ejpam-4427	317	15	every	every	DET
ejpam-4427	317	16	v	v	NUM
ejpam-4427	317	17	∈	∈	PROPN
ejpam-4427	317	18	v	v	NOUN
ejpam-4427	317	19	(	(	PUNCT
ejpam-4427	317	20	g	g	NOUN
ejpam-4427	317	21	)	)	PUNCT
ejpam-4427	317	22	.	.	PUNCT
ejpam-4427	318	1	since	since	SCONJ
ejpam-4427	318	2	s	s	PROPN
ejpam-4427	318	3	is	be	AUX
ejpam-4427	318	4	a	a	DET
ejpam-4427	318	5	restrained	restrained	ADJ
ejpam-4427	318	6	2	2	NUM
ejpam-4427	318	7	-	-	PUNCT
ejpam-4427	318	8	resolving	resolving	NOUN
ejpam-4427	318	9	set	set	VERB
ejpam-4427	318	10	in	in	ADP
ejpam-4427	318	11	g	g	ADP
ejpam-4427	318	12	◦	◦	NOUN
ejpam-4427	318	13	h	h	NOUN
ejpam-4427	318	14	,	,	PUNCT
ejpam-4427	318	15	s	s	NOUN
ejpam-4427	318	16	=	=	SYM
ejpam-4427	318	17	v	v	X
ejpam-4427	318	18	(	(	PUNCT
ejpam-4427	318	19	g	g	PROPN
ejpam-4427	318	20	◦	◦	NOUN
ejpam-4427	318	21	h	h	NOUN
ejpam-4427	318	22	)	)	PUNCT
ejpam-4427	318	23	or	or	CCONJ
ejpam-4427	318	24	⟨v	⟨v	NUM
ejpam-4427	318	25	(	(	PUNCT
ejpam-4427	318	26	g	g	PROPN
ejpam-4427	318	27	◦	◦	NOUN
ejpam-4427	318	28	h)\s⟩	h)\s⟩	PROPN
ejpam-4427	318	29	has	have	VERB
ejpam-4427	318	30	no	no	DET
ejpam-4427	318	31	isolated	isolated	ADJ
ejpam-4427	318	32	vertex	vertex	NOUN
ejpam-4427	318	33	.	.	PUNCT
ejpam-4427	319	1	let	let	VERB
ejpam-4427	319	2	v	v	NUM
ejpam-4427	319	3	∈	∈	VERB
ejpam-4427	319	4	a.	a.	NOUN
ejpam-4427	319	5	if	if	SCONJ
ejpam-4427	319	6	sv	sv	PROPN
ejpam-4427	319	7	=	=	SYM
ejpam-4427	319	8	v	v	PROPN
ejpam-4427	319	9	(	(	PUNCT
ejpam-4427	319	10	hv	hv	PROPN
ejpam-4427	319	11	)	)	PUNCT
ejpam-4427	319	12	,	,	PUNCT
ejpam-4427	319	13	then	then	ADV
ejpam-4427	319	14	sv	sv	PROPN
ejpam-4427	319	15	is	be	AUX
ejpam-4427	319	16	a	a	DET
ejpam-4427	319	17	restrained	restrained	ADJ
ejpam-4427	319	18	2	2	NUM
ejpam-4427	319	19	-	-	PUNCT
ejpam-4427	319	20	resolving	resolve	VERB
ejpam-4427	319	21	set	set	NOUN
ejpam-4427	319	22	of	of	ADP
ejpam-4427	319	23	hv	hv	PROPN
ejpam-4427	319	24	.	.	PROPN
ejpam-4427	319	25	suppose	suppose	VERB
ejpam-4427	320	1	sv	sv	PROPN
ejpam-4427	320	2	̸=	̸=	PROPN
ejpam-4427	320	3	v	v	PROPN
ejpam-4427	320	4	(	(	PUNCT
ejpam-4427	320	5	hv	hv	PROPN
ejpam-4427	320	6	)	)	PUNCT
ejpam-4427	320	7	.	.	PUNCT
ejpam-4427	321	1	since	since	SCONJ
ejpam-4427	321	2	v	v	NUM
ejpam-4427	321	3	∈	∈	PROPN
ejpam-4427	321	4	a	a	PRON
ejpam-4427	321	5	,	,	PUNCT
ejpam-4427	321	6	⟨v	⟨v	NOUN
ejpam-4427	321	7	(	(	PUNCT
ejpam-4427	321	8	hv)\sv⟩	hv)\sv⟩	NOUN
ejpam-4427	321	9	must	must	AUX
ejpam-4427	321	10	have	have	VERB
ejpam-4427	321	11	no	no	DET
ejpam-4427	321	12	isolated	isolate	VERB
ejpam-4427	321	13	vertex	vertex	NOUN
ejpam-4427	321	14	.	.	PUNCT
ejpam-4427	322	1	hence	hence	ADV
ejpam-4427	322	2	,	,	PUNCT
ejpam-4427	322	3	sv	sv	PROPN
ejpam-4427	322	4	is	be	AUX
ejpam-4427	322	5	a	a	DET
ejpam-4427	322	6	restrained	restrained	ADJ
ejpam-4427	322	7	2	2	NUM
ejpam-4427	322	8	-	-	PUNCT
ejpam-4427	322	9	resolving	resolve	VERB
ejpam-4427	322	10	set	set	VERB
ejpam-4427	322	11	in	in	ADP
ejpam-4427	322	12	hv	hv	PROPN
ejpam-4427	322	13	.	.	PUNCT
ejpam-4427	323	1	next	next	ADV
ejpam-4427	323	2	,	,	PUNCT
ejpam-4427	323	3	let	let	VERB
ejpam-4427	323	4	w	w	PROPN
ejpam-4427	323	5	∈	∈	PROPN
ejpam-4427	323	6	v	v	NOUN
ejpam-4427	323	7	(	(	PUNCT
ejpam-4427	323	8	g)\a	g)\a	NOUN
ejpam-4427	323	9	with	with	ADP
ejpam-4427	323	10	sw	sw	PROPN
ejpam-4427	323	11	=	=	SYM
ejpam-4427	323	12	v	v	PROPN
ejpam-4427	323	13	(	(	PUNCT
ejpam-4427	323	14	hw	hw	NOUN
ejpam-4427	323	15	)	)	PUNCT
ejpam-4427	323	16	.	.	PUNCT
ejpam-4427	324	1	since	since	SCONJ
ejpam-4427	324	2	v	v	NOUN
ejpam-4427	324	3	(	(	PUNCT
ejpam-4427	324	4	g	g	NOUN
ejpam-4427	324	5	◦	◦	NOUN
ejpam-4427	324	6	h)\s	h)\s	NOUN
ejpam-4427	324	7	has	have	VERB
ejpam-4427	324	8	no	no	DET
ejpam-4427	324	9	isolated	isolated	ADJ
ejpam-4427	324	10	vertex	vertex	NOUN
ejpam-4427	324	11	,	,	PUNCT
ejpam-4427	324	12	w	w	PROPN
ejpam-4427	324	13	∈	∈	PROPN
ejpam-4427	324	14	ng(v	ng(v	PUNCT
ejpam-4427	324	15	(	(	PUNCT
ejpam-4427	324	16	g)\a	g)\a	NOUN
ejpam-4427	324	17	)	)	PUNCT
ejpam-4427	324	18	.	.	PUNCT
ejpam-4427	325	1	hence	hence	ADV
ejpam-4427	325	2	,	,	PUNCT
ejpam-4427	325	3	(	(	PUNCT
ejpam-4427	325	4	i)-(iv	i)-(iv	X
ejpam-4427	325	5	)	)	PUNCT
ejpam-4427	325	6	hold	hold	VERB
ejpam-4427	325	7	.	.	PUNCT
ejpam-4427	326	1	j.	j.	PROPN
ejpam-4427	326	2	cabaro	cabaro	PROPN
ejpam-4427	326	3	,	,	PUNCT
ejpam-4427	326	4	h.	h.	PROPN
ejpam-4427	326	5	rara	rara	PROPN
ejpam-4427	326	6	/	/	SYM
ejpam-4427	326	7	eur	eur	PROPN
ejpam-4427	326	8	.	.	PUNCT
ejpam-4427	327	1	j.	j.	PROPN
ejpam-4427	327	2	pure	pure	PROPN
ejpam-4427	327	3	appl	appl	PROPN
ejpam-4427	327	4	.	.	PROPN
ejpam-4427	327	5	math	math	PROPN
ejpam-4427	327	6	,	,	PUNCT
ejpam-4427	327	7	15	15	NUM
ejpam-4427	327	8	(	(	PUNCT
ejpam-4427	327	9	3	3	NUM
ejpam-4427	327	10	)	)	PUNCT
ejpam-4427	327	11	(	(	PUNCT
ejpam-4427	327	12	2022	2022	NUM
ejpam-4427	327	13	)	)	PUNCT
ejpam-4427	327	14	,	,	PUNCT
ejpam-4427	327	15	1229	1229	NUM
ejpam-4427	327	16	-	-	SYM
ejpam-4427	327	17	1236	1236	NUM
ejpam-4427	327	18	1234	1234	NUM
ejpam-4427	327	19	conversely	conversely	ADV
ejpam-4427	327	20	,	,	PUNCT
ejpam-4427	327	21	let	let	VERB
ejpam-4427	327	22	s	s	VERB
ejpam-4427	327	23	=	=	NOUN
ejpam-4427	327	24	a	a	DET
ejpam-4427	327	25	∪	∪	X
ejpam-4427	327	26	(	(	PUNCT
ejpam-4427	327	27	⋃	⋃	NOUN
ejpam-4427	327	28	v∈v	v∈v	NOUN
ejpam-4427	327	29	(	(	PUNCT
ejpam-4427	327	30	g	g	NOUN
ejpam-4427	327	31	)	)	PUNCT
ejpam-4427	327	32	sv	sv	NOUN
ejpam-4427	327	33	)	)	PUNCT
ejpam-4427	327	34	,	,	PUNCT
ejpam-4427	327	35	where	where	SCONJ
ejpam-4427	327	36	a	a	DET
ejpam-4427	327	37	⊆	⊆	NUM
ejpam-4427	327	38	v	v	NOUN
ejpam-4427	327	39	(	(	PUNCT
ejpam-4427	327	40	g	g	NOUN
ejpam-4427	327	41	)	)	PUNCT
ejpam-4427	327	42	and	and	CCONJ
ejpam-4427	327	43	sv	sv	X
ejpam-4427	327	44	⊆	⊆	NUM
ejpam-4427	327	45	v	v	X
ejpam-4427	327	46	(	(	PUNCT
ejpam-4427	327	47	hv	hv	PROPN
ejpam-4427	327	48	)	)	PUNCT
ejpam-4427	327	49	for	for	ADP
ejpam-4427	327	50	each	each	PRON
ejpam-4427	327	51	v	v	NUM
ejpam-4427	327	52	∈	∈	PROPN
ejpam-4427	327	53	v	v	NOUN
ejpam-4427	327	54	(	(	PUNCT
ejpam-4427	327	55	g	g	NOUN
ejpam-4427	327	56	)	)	PUNCT
ejpam-4427	327	57	satisfying	satisfying	NOUN
ejpam-4427	327	58	(	(	PUNCT
ejpam-4427	327	59	i)-(iv	i)-(iv	ADJ
ejpam-4427	327	60	)	)	PUNCT
ejpam-4427	327	61	.	.	PUNCT
ejpam-4427	328	1	by	by	ADP
ejpam-4427	328	2	theorem	theorem	NOUN
ejpam-4427	328	3	4	4	NUM
ejpam-4427	328	4	,	,	PUNCT
ejpam-4427	328	5	s	s	VERB
ejpam-4427	328	6	is	be	AUX
ejpam-4427	328	7	a	a	DET
ejpam-4427	328	8	2	2	NUM
ejpam-4427	328	9	-	-	PUNCT
ejpam-4427	328	10	resolving	resolving	NOUN
ejpam-4427	328	11	set	set	NOUN
ejpam-4427	328	12	in	in	ADP
ejpam-4427	328	13	g	g	PROPN
ejpam-4427	328	14	◦	◦	NOUN
ejpam-4427	328	15	h.	h.	PROPN
ejpam-4427	329	1	moreover	moreover	ADV
ejpam-4427	329	2	,	,	PUNCT
ejpam-4427	329	3	because	because	SCONJ
ejpam-4427	329	4	of	of	ADP
ejpam-4427	329	5	(	(	PUNCT
ejpam-4427	329	6	i)-(iv	i)-(iv	NOUN
ejpam-4427	329	7	)	)	PUNCT
ejpam-4427	329	8	,	,	PUNCT
ejpam-4427	329	9	s	s	VERB
ejpam-4427	329	10	is	be	AUX
ejpam-4427	329	11	a	a	DET
ejpam-4427	329	12	restrained	restrained	ADJ
ejpam-4427	329	13	2	2	NUM
ejpam-4427	329	14	-	-	PUNCT
ejpam-4427	329	15	resolving	resolving	NOUN
ejpam-4427	329	16	set	set	NOUN
ejpam-4427	329	17	in	in	ADP
ejpam-4427	329	18	g	g	PROPN
ejpam-4427	329	19	◦	◦	NOUN
ejpam-4427	329	20	h.	h.	NOUN
ejpam-4427	329	21	corollary	corollary	ADJ
ejpam-4427	330	1	3	3	X
ejpam-4427	330	2	.	.	PUNCT
ejpam-4427	331	1	let	let	VERB
ejpam-4427	331	2	g	g	NOUN
ejpam-4427	331	3	and	and	CCONJ
ejpam-4427	331	4	h	h	NOUN
ejpam-4427	331	5	be	be	AUX
ejpam-4427	331	6	nontrivial	nontrivial	ADJ
ejpam-4427	331	7	connected	connected	ADJ
ejpam-4427	331	8	graphs	graph	NOUN
ejpam-4427	331	9	,	,	PUNCT
ejpam-4427	331	10	where	where	SCONJ
ejpam-4427	331	11	|v	|v	PROPN
ejpam-4427	331	12	(	(	PUNCT
ejpam-4427	331	13	g)|	g)|	PROPN
ejpam-4427	331	14	=	=	NOUN
ejpam-4427	331	15	n.	n.	NOUN
ejpam-4427	331	16	then	then	ADV
ejpam-4427	331	17	rdim2(g	rdim2(g	VERB
ejpam-4427	331	18	◦	◦	NOUN
ejpam-4427	331	19	h	h	NOUN
ejpam-4427	331	20	)	)	PUNCT
ejpam-4427	331	21	=	=	SYM
ejpam-4427	331	22	n	n	PROPN
ejpam-4427	331	23	·	·	PUNCT
ejpam-4427	331	24	dim2(h	dim2(h	NUM
ejpam-4427	331	25	)	)	PUNCT
ejpam-4427	331	26	.	.	PUNCT
ejpam-4427	332	1	the	the	DET
ejpam-4427	332	2	set	set	NOUN
ejpam-4427	332	3	consisting	consisting	NOUN
ejpam-4427	332	4	of	of	ADP
ejpam-4427	332	5	the	the	DET
ejpam-4427	332	6	shaded	shade	VERB
ejpam-4427	332	7	vertices	vertex	NOUN
ejpam-4427	332	8	in	in	ADP
ejpam-4427	332	9	figure	figure	NOUN
ejpam-4427	332	10	2	2	NUM
ejpam-4427	332	11	is	be	AUX
ejpam-4427	332	12	a	a	DET
ejpam-4427	332	13	restrained	restrained	ADJ
ejpam-4427	332	14	2	2	NUM
ejpam-4427	332	15	-	-	PUNCT
ejpam-4427	332	16	resolving	resolve	VERB
ejpam-4427	332	17	set	set	NOUN
ejpam-4427	332	18	of	of	ADP
ejpam-4427	332	19	the	the	DET
ejpam-4427	332	20	corona	corona	NOUN
ejpam-4427	332	21	p4	p4	PROPN
ejpam-4427	332	22	◦	◦	PROPN
ejpam-4427	332	23	c5	c5	PROPN
ejpam-4427	332	24	.	.	PUNCT
ejpam-4427	333	1	....................................	....................................	PUNCT
ejpam-4427	333	2	....................................	....................................	PUNCT
ejpam-4427	334	1	....................................	....................................	PUNCT
ejpam-4427	334	2	....................................	....................................	PUNCT
ejpam-4427	335	1	....................................	....................................	PUNCT
ejpam-4427	335	2	....................................	....................................	PUNCT
ejpam-4427	336	1	....................................	....................................	PUNCT
ejpam-4427	336	2	....................................	....................................	PUNCT
ejpam-4427	337	1	....................................	....................................	PUNCT
ejpam-4427	337	2	....................................	....................................	PUNCT
ejpam-4427	338	1	....................................	....................................	PUNCT
ejpam-4427	338	2	....................................	....................................	PUNCT
ejpam-4427	339	1	....................................	....................................	PUNCT
ejpam-4427	339	2	....................................	....................................	PUNCT
ejpam-4427	340	1	....................................	....................................	PUNCT
ejpam-4427	340	2	....................................	....................................	PUNCT
ejpam-4427	341	1	....................................	....................................	PUNCT
ejpam-4427	341	2	....................................	....................................	PUNCT
ejpam-4427	342	1	....................................	....................................	PUNCT
ejpam-4427	342	2	........................................................................	........................................................................	PUNCT
ejpam-4427	343	1	....................................	....................................	PUNCT
ejpam-4427	343	2	....................................	....................................	PUNCT
ejpam-4427	344	1	....................................	....................................	PUNCT
ejpam-4427	344	2	......................................................................................................................................................................................................	......................................................................................................................................................................................................	INTJ
ejpam-4427	345	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	INTJ
ejpam-4427	345	2	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4427	346	1	...............................................................	...............................................................	PUNCT
ejpam-4427	346	2	......................................................................................................................................................	......................................................................................................................................................	PUNCT
ejpam-4427	346	3	........	........	PUNCT
ejpam-4427	346	4	........	........	PUNCT
ejpam-4427	346	5	........	........	PUNCT
ejpam-4427	346	6	........	........	PUNCT
ejpam-4427	346	7	........	........	PUNCT
ejpam-4427	346	8	........	........	PUNCT
ejpam-4427	346	9	........	........	PUNCT
ejpam-4427	346	10	........	........	PUNCT
ejpam-4427	346	11	........	........	PUNCT
ejpam-4427	346	12	........	........	PUNCT
ejpam-4427	346	13	........	........	PUNCT
ejpam-4427	346	14	........	........	PUNCT
ejpam-4427	346	15	........	........	PUNCT
ejpam-4427	346	16	........	........	PUNCT
ejpam-4427	346	17	........	........	PUNCT
ejpam-4427	346	18	........	........	PUNCT
ejpam-4427	346	19	........	........	PUNCT
ejpam-4427	346	20	...........	...........	PUNCT
ejpam-4427	346	21	..........	..........	PUNCT
ejpam-4427	347	1	..........	..........	PUNCT
ejpam-4427	347	2	..........	..........	PUNCT
ejpam-4427	348	1	..........	..........	PUNCT
ejpam-4427	348	2	..........	..........	PUNCT
ejpam-4427	349	1	..........	..........	PUNCT
ejpam-4427	349	2	..........	..........	PUNCT
ejpam-4427	350	1	..........	..........	PUNCT
ejpam-4427	350	2	..........	..........	PUNCT
ejpam-4427	351	1	..........	..........	PUNCT
ejpam-4427	351	2	..........	..........	PUNCT
ejpam-4427	352	1	..........	..........	PUNCT
ejpam-4427	352	2	..........	..........	PUNCT
ejpam-4427	352	3	............	............	PUNCT
ejpam-4427	352	4	...........	...........	PUNCT
ejpam-4427	352	5	...........	...........	PUNCT
ejpam-4427	352	6	...........	...........	PUNCT
ejpam-4427	352	7	...........	...........	PUNCT
ejpam-4427	352	8	.......	.......	PUNCT
ejpam-4427	352	9	........................................................................	........................................................................	PUNCT
ejpam-4427	352	10	..........................	..........................	PUNCT
ejpam-4427	352	11	.........................	.........................	PUNCT
ejpam-4427	353	1	.....................	.....................	PUNCT
ejpam-4427	353	2	........................................................................	........................................................................	PUNCT
ejpam-4427	354	1	..........	..........	PUNCT
ejpam-4427	354	2	.........	.........	PUNCT
ejpam-4427	355	1	.........	.........	PUNCT
ejpam-4427	355	2	.........	.........	PUNCT
ejpam-4427	356	1	.........	.........	PUNCT
ejpam-4427	356	2	.........	.........	PUNCT
ejpam-4427	356	3	.........	.........	PUNCT
ejpam-4427	356	4	........	........	PUNCT
ejpam-4427	356	5	............	............	PUNCT
ejpam-4427	356	6	...........	...........	PUNCT
ejpam-4427	356	7	...........	...........	PUNCT
ejpam-4427	356	8	...........	...........	PUNCT
ejpam-4427	356	9	...........	...........	PUNCT
ejpam-4427	356	10	.......	.......	PUNCT
ejpam-4427	356	11	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4427	356	12	............	............	PUNCT
ejpam-4427	356	13	...........	...........	PUNCT
ejpam-4427	356	14	...........	...........	PUNCT
ejpam-4427	356	15	...........	...........	PUNCT
ejpam-4427	356	16	...........	...........	PUNCT
ejpam-4427	356	17	.......	.......	PUNCT
ejpam-4427	357	1	..........	..........	PUNCT
ejpam-4427	357	2	.........	.........	PUNCT
ejpam-4427	358	1	.........	.........	PUNCT
ejpam-4427	358	2	.........	.........	PUNCT
ejpam-4427	359	1	.........	.........	PUNCT
ejpam-4427	359	2	.........	.........	PUNCT
ejpam-4427	359	3	.........	.........	PUNCT
ejpam-4427	360	1	........	........	PUNCT
ejpam-4427	360	2	........................................................................	........................................................................	PUNCT
ejpam-4427	360	3	..........................	..........................	PUNCT
ejpam-4427	360	4	.........................	.........................	PUNCT
ejpam-4427	360	5	.....................	.....................	PUNCT
ejpam-4427	361	1	........................................................................	........................................................................	PUNCT
ejpam-4427	361	2	...............................................................	...............................................................	PUNCT
ejpam-4427	361	3	...........	...........	PUNCT
ejpam-4427	361	4	..........	..........	PUNCT
ejpam-4427	362	1	..........	..........	PUNCT
ejpam-4427	362	2	..........	..........	PUNCT
ejpam-4427	363	1	..........	..........	PUNCT
ejpam-4427	363	2	..........	..........	PUNCT
ejpam-4427	364	1	..........	..........	PUNCT
ejpam-4427	364	2	..........	..........	PUNCT
ejpam-4427	365	1	..........	..........	PUNCT
ejpam-4427	365	2	..........	..........	PUNCT
ejpam-4427	366	1	..........	..........	PUNCT
ejpam-4427	366	2	..........	..........	PUNCT
ejpam-4427	367	1	..........	..........	PUNCT
ejpam-4427	367	2	..........	..........	PUNCT
ejpam-4427	368	1	.........	.........	PUNCT
ejpam-4427	368	2	........	........	PUNCT
ejpam-4427	368	3	........	........	PUNCT
ejpam-4427	368	4	........	........	PUNCT
ejpam-4427	368	5	........	........	PUNCT
ejpam-4427	368	6	........	........	PUNCT
ejpam-4427	368	7	........	........	PUNCT
ejpam-4427	368	8	........	........	PUNCT
ejpam-4427	368	9	........	........	PUNCT
ejpam-4427	368	10	........	........	PUNCT
ejpam-4427	368	11	........	........	PUNCT
ejpam-4427	368	12	........	........	PUNCT
ejpam-4427	368	13	........	........	PUNCT
ejpam-4427	368	14	........	........	PUNCT
ejpam-4427	368	15	........	........	PUNCT
ejpam-4427	368	16	........	........	PUNCT
ejpam-4427	368	17	........	........	PUNCT
ejpam-4427	369	1	........	........	PUNCT
ejpam-4427	369	2	.............................................................................................................................................	.............................................................................................................................................	PUNCT
ejpam-4427	370	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4427	370	2	...............................................................	...............................................................	PUNCT
ejpam-4427	371	1	........................................................................	........................................................................	PUNCT
ejpam-4427	371	2	..........................	..........................	PUNCT
ejpam-4427	371	3	.........................	.........................	PUNCT
ejpam-4427	372	1	.....................	.....................	PUNCT
ejpam-4427	372	2	........................................................................	........................................................................	PUNCT
ejpam-4427	373	1	..........	..........	PUNCT
ejpam-4427	373	2	.........	.........	PUNCT
ejpam-4427	374	1	.........	.........	PUNCT
ejpam-4427	374	2	.........	.........	PUNCT
ejpam-4427	375	1	.........	.........	PUNCT
ejpam-4427	375	2	.........	.........	PUNCT
ejpam-4427	375	3	.........	.........	PUNCT
ejpam-4427	375	4	........	........	PUNCT
ejpam-4427	375	5	............	............	PUNCT
ejpam-4427	375	6	...........	...........	PUNCT
ejpam-4427	375	7	...........	...........	PUNCT
ejpam-4427	375	8	...........	...........	PUNCT
ejpam-4427	375	9	...........	...........	PUNCT
ejpam-4427	375	10	.......	.......	PUNCT
ejpam-4427	375	11	......................................................................................................................................................	......................................................................................................................................................	PUNCT
ejpam-4427	375	12	........	........	PUNCT
ejpam-4427	375	13	........	........	PUNCT
ejpam-4427	375	14	........	........	PUNCT
ejpam-4427	375	15	........	........	PUNCT
ejpam-4427	375	16	........	........	PUNCT
ejpam-4427	375	17	........	........	PUNCT
ejpam-4427	375	18	........	........	PUNCT
ejpam-4427	375	19	........	........	PUNCT
ejpam-4427	375	20	........	........	PUNCT
ejpam-4427	375	21	........	........	PUNCT
ejpam-4427	375	22	........	........	PUNCT
ejpam-4427	375	23	........	........	PUNCT
ejpam-4427	375	24	........	........	PUNCT
ejpam-4427	375	25	........	........	PUNCT
ejpam-4427	375	26	........	........	PUNCT
ejpam-4427	375	27	........	........	PUNCT
ejpam-4427	375	28	........	........	PUNCT
ejpam-4427	375	29	...........	...........	PUNCT
ejpam-4427	376	1	..........	..........	PUNCT
ejpam-4427	376	2	..........	..........	PUNCT
ejpam-4427	377	1	..........	..........	PUNCT
ejpam-4427	377	2	..........	..........	PUNCT
ejpam-4427	378	1	..........	..........	PUNCT
ejpam-4427	378	2	..........	..........	PUNCT
ejpam-4427	379	1	..........	..........	PUNCT
ejpam-4427	379	2	..........	..........	PUNCT
ejpam-4427	380	1	..........	..........	PUNCT
ejpam-4427	380	2	..........	..........	PUNCT
ejpam-4427	381	1	..........	..........	PUNCT
ejpam-4427	381	2	..........	..........	PUNCT
ejpam-4427	382	1	..........	..........	PUNCT
ejpam-4427	382	2	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4427	383	1	...............................................................	...............................................................	PUNCT
ejpam-4427	383	2	........................................................................	........................................................................	PUNCT
ejpam-4427	384	1	..........................	..........................	PUNCT
ejpam-4427	384	2	.........................	.........................	PUNCT
ejpam-4427	385	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	385	2	..........	..........	PUNCT
ejpam-4427	386	1	.........	.........	PUNCT
ejpam-4427	386	2	.........	.........	PUNCT
ejpam-4427	387	1	.........	.........	PUNCT
ejpam-4427	387	2	.........	.........	PUNCT
ejpam-4427	388	1	.........	.........	PUNCT
ejpam-4427	388	2	.........	.........	PUNCT
ejpam-4427	388	3	........	........	PUNCT
ejpam-4427	388	4	............	............	PUNCT
ejpam-4427	388	5	...........	...........	PUNCT
ejpam-4427	388	6	...........	...........	PUNCT
ejpam-4427	388	7	...........	...........	PUNCT
ejpam-4427	388	8	...........	...........	PUNCT
ejpam-4427	388	9	.......	.......	PUNCT
ejpam-4427	388	10	...........	...........	PUNCT
ejpam-4427	388	11	..........	..........	PUNCT
ejpam-4427	389	1	..........	..........	PUNCT
ejpam-4427	389	2	..........	..........	PUNCT
ejpam-4427	390	1	..........	..........	PUNCT
ejpam-4427	390	2	..........	..........	PUNCT
ejpam-4427	391	1	..........	..........	PUNCT
ejpam-4427	391	2	..........	..........	PUNCT
ejpam-4427	392	1	..........	..........	PUNCT
ejpam-4427	392	2	..........	..........	PUNCT
ejpam-4427	393	1	..........	..........	PUNCT
ejpam-4427	393	2	..........	..........	PUNCT
ejpam-4427	394	1	..........	..........	PUNCT
ejpam-4427	394	2	..........	..........	PUNCT
ejpam-4427	395	1	.........	.........	PUNCT
ejpam-4427	395	2	........	........	PUNCT
ejpam-4427	395	3	........	........	PUNCT
ejpam-4427	395	4	........	........	PUNCT
ejpam-4427	395	5	........	........	PUNCT
ejpam-4427	395	6	........	........	PUNCT
ejpam-4427	395	7	........	........	PUNCT
ejpam-4427	395	8	........	........	PUNCT
ejpam-4427	395	9	........	........	PUNCT
ejpam-4427	395	10	........	........	PUNCT
ejpam-4427	395	11	........	........	PUNCT
ejpam-4427	395	12	........	........	PUNCT
ejpam-4427	395	13	........	........	PUNCT
ejpam-4427	395	14	........	........	PUNCT
ejpam-4427	395	15	........	........	PUNCT
ejpam-4427	395	16	........	........	PUNCT
ejpam-4427	395	17	........	........	PUNCT
ejpam-4427	396	1	........	........	PUNCT
ejpam-4427	396	2	.............................................................................................................................................	.............................................................................................................................................	PUNCT
ejpam-4427	397	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	397	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	398	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	398	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	399	1	•	•	NUM
ejpam-4427	399	2	••	••	NOUN
ejpam-4427	399	3	•	•	NOUN
ejpam-4427	399	4	••	••	NOUN
ejpam-4427	399	5	•	•	NUM
ejpam-4427	399	6	•	•	NOUN
ejpam-4427	399	7	•	•	NOUN
ejpam-4427	399	8	••	••	NOUN
ejpam-4427	399	9	•	•	NUM
ejpam-4427	399	10	figure	figure	NOUN
ejpam-4427	399	11	2	2	NUM
ejpam-4427	399	12	:	:	PUNCT
ejpam-4427	399	13	a	a	DET
ejpam-4427	399	14	graph	graph	NOUN
ejpam-4427	399	15	p4	p4	ADJ
ejpam-4427	399	16	◦	◦	PROPN
ejpam-4427	399	17	c5	c5	PROPN
ejpam-4427	399	18	with	with	ADP
ejpam-4427	399	19	rdim2(p4	rdim2(p4	NOUN
ejpam-4427	399	20	◦	◦	PROPN
ejpam-4427	399	21	c5	c5	PROPN
ejpam-4427	399	22	)	)	PUNCT
ejpam-4427	400	1	=	=	NOUN
ejpam-4427	400	2	12	12	NUM
ejpam-4427	400	3	5	5	NUM
ejpam-4427	400	4	.	.	PUNCT
ejpam-4427	401	1	restrained	restrain	VERB
ejpam-4427	401	2	2	2	NUM
ejpam-4427	401	3	-	-	PUNCT
ejpam-4427	401	4	resolving	resolve	VERB
ejpam-4427	401	5	sets	set	NOUN
ejpam-4427	401	6	in	in	ADP
ejpam-4427	401	7	the	the	DET
ejpam-4427	401	8	lexicographic	lexicographic	ADJ
ejpam-4427	401	9	product	product	NOUN
ejpam-4427	401	10	of	of	ADP
ejpam-4427	401	11	graphs	graph	NOUN
ejpam-4427	401	12	definition	definition	NOUN
ejpam-4427	401	13	3	3	NUM
ejpam-4427	401	14	.	.	PUNCT
ejpam-4427	402	1	a	a	DET
ejpam-4427	402	2	vertex	vertex	NOUN
ejpam-4427	402	3	x	x	PRON
ejpam-4427	402	4	is	be	AUX
ejpam-4427	402	5	said	say	VERB
ejpam-4427	402	6	to	to	PART
ejpam-4427	402	7	be	be	AUX
ejpam-4427	402	8	1	1	NUM
ejpam-4427	402	9	-	-	PUNCT
ejpam-4427	402	10	equidistant	equidistant	NOUN
ejpam-4427	402	11	to	to	ADP
ejpam-4427	402	12	y	y	PRON
ejpam-4427	402	13	if	if	SCONJ
ejpam-4427	402	14	xy	xy	PROPN
ejpam-4427	402	15	∈	∈	PROPN
ejpam-4427	402	16	e(g	e(g	PROPN
ejpam-4427	402	17	)	)	PUNCT
ejpam-4427	402	18	and	and	CCONJ
ejpam-4427	402	19	dg(x	dg(x	NUM
ejpam-4427	402	20	,	,	PUNCT
ejpam-4427	402	21	z	z	NOUN
ejpam-4427	402	22	)	)	PUNCT
ejpam-4427	402	23	=	=	SYM
ejpam-4427	402	24	dg(y	dg(y	ADJ
ejpam-4427	402	25	,	,	PUNCT
ejpam-4427	402	26	z	z	NOUN
ejpam-4427	402	27	)	)	PUNCT
ejpam-4427	402	28	,	,	PUNCT
ejpam-4427	402	29	for	for	ADP
ejpam-4427	402	30	all	all	DET
ejpam-4427	402	31	z	z	NOUN
ejpam-4427	402	32	∈	∈	PROPN
ejpam-4427	402	33	v	v	NOUN
ejpam-4427	402	34	(	(	PUNCT
ejpam-4427	402	35	g)\	g)\	X
ejpam-4427	402	36	{	{	PUNCT
ejpam-4427	402	37	x	x	PROPN
ejpam-4427	402	38	,	,	PUNCT
ejpam-4427	402	39	y	y	NOUN
ejpam-4427	402	40	}	}	PUNCT
ejpam-4427	402	41	and	and	CCONJ
ejpam-4427	402	42	it	it	PRON
ejpam-4427	402	43	is	be	AUX
ejpam-4427	402	44	2	2	NUM
ejpam-4427	402	45	-	-	PUNCT
ejpam-4427	402	46	equidistant	equidistant	NOUN
ejpam-4427	402	47	to	to	ADP
ejpam-4427	402	48	y	y	PRON
ejpam-4427	402	49	if	if	SCONJ
ejpam-4427	402	50	dg(x	dg(x	NUM
ejpam-4427	402	51	,	,	PUNCT
ejpam-4427	402	52	y	y	NOUN
ejpam-4427	402	53	)	)	PUNCT
ejpam-4427	402	54	=	=	SYM
ejpam-4427	402	55	2	2	NUM
ejpam-4427	402	56	and	and	CCONJ
ejpam-4427	402	57	dg(x	dg(x	NUM
ejpam-4427	402	58	,	,	PUNCT
ejpam-4427	402	59	z	z	NOUN
ejpam-4427	402	60	)	)	PUNCT
ejpam-4427	403	1	=	=	NOUN
ejpam-4427	403	2	dg(w	dg(w	NOUN
ejpam-4427	403	3	,	,	PUNCT
ejpam-4427	403	4	z	z	NOUN
ejpam-4427	403	5	)	)	PUNCT
ejpam-4427	403	6	,	,	PUNCT
ejpam-4427	403	7	for	for	ADP
ejpam-4427	403	8	all	all	DET
ejpam-4427	403	9	z	z	NOUN
ejpam-4427	403	10	∈	∈	PROPN
ejpam-4427	403	11	v	v	NOUN
ejpam-4427	403	12	(	(	PUNCT
ejpam-4427	403	13	g)\	g)\	X
ejpam-4427	403	14	{	{	PUNCT
ejpam-4427	403	15	x	x	NOUN
ejpam-4427	403	16	,	,	PUNCT
ejpam-4427	403	17	w	w	NOUN
ejpam-4427	403	18	}	}	PUNCT
ejpam-4427	403	19	.	.	PUNCT
ejpam-4427	404	1	a	a	DET
ejpam-4427	404	2	vertex	vertex	NOUN
ejpam-4427	404	3	is	be	AUX
ejpam-4427	404	4	called	call	VERB
ejpam-4427	404	5	a	a	DET
ejpam-4427	404	6	free	free	ADJ
ejpam-4427	404	7	-	-	PUNCT
ejpam-4427	404	8	vertex	vertex	NOUN
ejpam-4427	404	9	in	in	ADP
ejpam-4427	404	10	g	g	PROPN
ejpam-4427	404	11	if	if	SCONJ
ejpam-4427	404	12	it	it	PRON
ejpam-4427	404	13	is	be	AUX
ejpam-4427	404	14	neither	neither	PRON
ejpam-4427	404	15	1	1	NUM
ejpam-4427	404	16	-	-	PUNCT
ejpam-4427	404	17	equidistant	equidistant	ADJ
ejpam-4427	404	18	nor	nor	CCONJ
ejpam-4427	404	19	2	2	NUM
ejpam-4427	404	20	-	-	PUNCT
ejpam-4427	404	21	equidistant	equidistant	NOUN
ejpam-4427	404	22	to	to	ADP
ejpam-4427	404	23	any	any	DET
ejpam-4427	404	24	vertex	vertex	NOUN
ejpam-4427	404	25	.	.	PUNCT
ejpam-4427	405	1	the	the	DET
ejpam-4427	405	2	set	set	NOUN
ejpam-4427	405	3	containing	contain	VERB
ejpam-4427	405	4	all	all	PRON
ejpam-4427	405	5	1	1	NUM
ejpam-4427	405	6	-	-	PUNCT
ejpam-4427	405	7	equidistant	equidistant	ADJ
ejpam-4427	405	8	,	,	PUNCT
ejpam-4427	405	9	2	2	NUM
ejpam-4427	405	10	-	-	PUNCT
ejpam-4427	405	11	equidistant	equidistant	ADJ
ejpam-4427	405	12	,	,	PUNCT
ejpam-4427	405	13	and	and	CCONJ
ejpam-4427	405	14	free	free	ADJ
ejpam-4427	405	15	-	-	PUNCT
ejpam-4427	405	16	vertices	vertex	NOUN
ejpam-4427	405	17	in	in	ADP
ejpam-4427	405	18	g	g	PROPN
ejpam-4427	405	19	are	be	AUX
ejpam-4427	405	20	denoted	denote	VERB
ejpam-4427	405	21	by	by	ADP
ejpam-4427	405	22	eq1(g	eq1(g	PROPN
ejpam-4427	405	23	)	)	PUNCT
ejpam-4427	405	24	,	,	PUNCT
ejpam-4427	405	25	eq2(g	eq2(g	PROPN
ejpam-4427	405	26	)	)	PUNCT
ejpam-4427	405	27	and	and	CCONJ
ejpam-4427	405	28	fr(g	fr(g	NUM
ejpam-4427	405	29	)	)	PUNCT
ejpam-4427	405	30	,	,	PUNCT
ejpam-4427	405	31	respectively	respectively	ADV
ejpam-4427	405	32	.	.	PUNCT
ejpam-4427	406	1	theorem	theorem	VERB
ejpam-4427	406	2	6	6	NUM
ejpam-4427	406	3	.	.	PUNCT
ejpam-4427	407	1	let	let	VERB
ejpam-4427	407	2	g	g	NOUN
ejpam-4427	407	3	and	and	CCONJ
ejpam-4427	407	4	h	h	PROPN
ejpam-4427	407	5	be	be	VERB
ejpam-4427	407	6	non	non	ADJ
ejpam-4427	407	7	-	-	ADJ
ejpam-4427	407	8	trivial	trivial	ADJ
ejpam-4427	407	9	connected	connected	ADJ
ejpam-4427	407	10	graphs	graph	NOUN
ejpam-4427	407	11	.	.	PUNCT
ejpam-4427	408	1	then	then	ADV
ejpam-4427	408	2	w	w	NOUN
ejpam-4427	408	3	=	=	PUNCT
ejpam-4427	408	4	⋃	⋃	PROPN
ejpam-4427	408	5	x∈s	x∈s	NOUN
ejpam-4427	408	6	[	[	PUNCT
ejpam-4427	408	7	{	{	PUNCT
ejpam-4427	408	8	x	x	NOUN
ejpam-4427	408	9	}	}	PUNCT
ejpam-4427	408	10	×	×	NOUN
ejpam-4427	408	11	tx	tx	PROPN
ejpam-4427	408	12	]	]	PUNCT
ejpam-4427	408	13	,	,	PUNCT
ejpam-4427	408	14	where	where	SCONJ
ejpam-4427	408	15	s	s	VERB
ejpam-4427	408	16	⊆	⊆	NUM
ejpam-4427	408	17	v	v	NOUN
ejpam-4427	408	18	(	(	PUNCT
ejpam-4427	408	19	g	g	NOUN
ejpam-4427	408	20	)	)	PUNCT
ejpam-4427	408	21	and	and	CCONJ
ejpam-4427	408	22	tx	tx	VERB
ejpam-4427	408	23	⊆	⊆	NUM
ejpam-4427	408	24	v	v	NOUN
ejpam-4427	408	25	(	(	PUNCT
ejpam-4427	408	26	h	h	NOUN
ejpam-4427	408	27	)	)	PUNCT
ejpam-4427	408	28	for	for	ADP
ejpam-4427	408	29	each	each	DET
ejpam-4427	408	30	x	x	SYM
ejpam-4427	408	31	∈	∈	PROPN
ejpam-4427	408	32	s	s	NOUN
ejpam-4427	408	33	,	,	PUNCT
ejpam-4427	408	34	is	be	AUX
ejpam-4427	408	35	a	a	DET
ejpam-4427	408	36	2	2	NUM
ejpam-4427	408	37	-	-	PUNCT
ejpam-4427	408	38	resolving	resolving	NOUN
ejpam-4427	408	39	set	set	VERB
ejpam-4427	408	40	in	in	ADP
ejpam-4427	408	41	g[h	g[h	PROPN
ejpam-4427	408	42	]	]	PUNCT
ejpam-4427	408	43	if	if	SCONJ
ejpam-4427	408	44	and	and	CCONJ
ejpam-4427	408	45	only	only	ADV
ejpam-4427	408	46	if	if	SCONJ
ejpam-4427	408	47	(	(	PUNCT
ejpam-4427	408	48	i	i	NOUN
ejpam-4427	408	49	)	)	PUNCT
ejpam-4427	408	50	s	s	PART
ejpam-4427	408	51	=	=	SYM
ejpam-4427	408	52	v	v	X
ejpam-4427	408	53	(	(	PUNCT
ejpam-4427	408	54	g	g	NOUN
ejpam-4427	408	55	)	)	PUNCT
ejpam-4427	408	56	(	(	PUNCT
ejpam-4427	408	57	ii	ii	NOUN
ejpam-4427	408	58	)	)	PUNCT
ejpam-4427	408	59	tx	tx	PROPN
ejpam-4427	408	60	is	be	AUX
ejpam-4427	408	61	a	a	DET
ejpam-4427	408	62	2	2	NUM
ejpam-4427	408	63	-	-	PUNCT
ejpam-4427	408	64	locating	locate	VERB
ejpam-4427	408	65	set	set	NOUN
ejpam-4427	408	66	in	in	ADP
ejpam-4427	408	67	h	h	NOUN
ejpam-4427	408	68	for	for	ADP
ejpam-4427	408	69	every	every	DET
ejpam-4427	408	70	x	x	SYM
ejpam-4427	408	71	∈	∈	PROPN
ejpam-4427	408	72	v	v	NOUN
ejpam-4427	408	73	(	(	PUNCT
ejpam-4427	408	74	g	g	NOUN
ejpam-4427	408	75	)	)	PUNCT
ejpam-4427	408	76	;	;	PUNCT
ejpam-4427	408	77	(	(	PUNCT
ejpam-4427	408	78	iii	iii	X
ejpam-4427	408	79	)	)	PUNCT
ejpam-4427	408	80	tx	tx	NOUN
ejpam-4427	409	1	and	and	CCONJ
ejpam-4427	409	2	ty	ty	INTJ
ejpam-4427	409	3	are	be	AUX
ejpam-4427	409	4	(	(	PUNCT
ejpam-4427	409	5	2	2	NUM
ejpam-4427	409	6	,	,	PUNCT
ejpam-4427	409	7	1)-locating	1)-locating	NUM
ejpam-4427	409	8	sets	set	NOUN
ejpam-4427	409	9	or	or	CCONJ
ejpam-4427	409	10	one	one	NUM
ejpam-4427	409	11	of	of	ADP
ejpam-4427	409	12	tx	tx	PROPN
ejpam-4427	410	1	and	and	CCONJ
ejpam-4427	410	2	ty	ty	PRON
ejpam-4427	410	3	is	be	AUX
ejpam-4427	410	4	a	a	DET
ejpam-4427	410	5	(	(	PUNCT
ejpam-4427	410	6	2	2	NUM
ejpam-4427	410	7	,	,	PUNCT
ejpam-4427	410	8	2)-locating	2)-locating	NUM
ejpam-4427	410	9	set	set	VERB
ejpam-4427	410	10	in	in	ADP
ejpam-4427	410	11	h	h	NOUN
ejpam-4427	410	12	whenever	whenever	SCONJ
ejpam-4427	410	13	x	x	X
ejpam-4427	410	14	,	,	PUNCT
ejpam-4427	410	15	y	y	PROPN
ejpam-4427	410	16	∈	∈	PROPN
ejpam-4427	410	17	eq1(g	eq1(g	PROPN
ejpam-4427	410	18	)	)	PUNCT
ejpam-4427	410	19	;	;	PUNCT
ejpam-4427	410	20	and	and	CCONJ
ejpam-4427	410	21	(	(	PUNCT
ejpam-4427	410	22	iv	iv	X
ejpam-4427	410	23	)	)	PUNCT
ejpam-4427	410	24	tx	tx	PROPN
ejpam-4427	411	1	and	and	CCONJ
ejpam-4427	411	2	ty	ty	INTJ
ejpam-4427	411	3	are	be	AUX
ejpam-4427	411	4	(	(	PUNCT
ejpam-4427	411	5	2	2	NUM
ejpam-4427	411	6	-	-	PUNCT
ejpam-4427	411	7	locating	locating	NOUN
ejpam-4427	411	8	)	)	PUNCT
ejpam-4427	411	9	dominating	dominating	NOUN
ejpam-4427	411	10	sets	set	NOUN
ejpam-4427	411	11	inh	inh	NOUN
ejpam-4427	411	12	or	or	CCONJ
ejpam-4427	411	13	one	one	NUM
ejpam-4427	411	14	of	of	ADP
ejpam-4427	411	15	tx	tx	PROPN
ejpam-4427	412	1	and	and	CCONJ
ejpam-4427	412	2	ty	ty	PRON
ejpam-4427	412	3	is	be	AUX
ejpam-4427	412	4	a	a	DET
ejpam-4427	412	5	2	2	NUM
ejpam-4427	412	6	-	-	PUNCT
ejpam-4427	412	7	dominating	dominating	NOUN
ejpam-4427	412	8	set	set	NOUN
ejpam-4427	412	9	whenever	whenever	SCONJ
ejpam-4427	412	10	x	x	X
ejpam-4427	412	11	,	,	PUNCT
ejpam-4427	412	12	y	y	PROPN
ejpam-4427	412	13	∈	∈	PROPN
ejpam-4427	412	14	eq2(g	eq2(g	VERB
ejpam-4427	412	15	)	)	PUNCT
ejpam-4427	412	16	.	.	PUNCT
ejpam-4427	413	1	j.	j.	PROPN
ejpam-4427	413	2	cabaro	cabaro	PROPN
ejpam-4427	413	3	,	,	PUNCT
ejpam-4427	413	4	h.	h.	PROPN
ejpam-4427	413	5	rara	rara	PROPN
ejpam-4427	413	6	/	/	SYM
ejpam-4427	413	7	eur	eur	PROPN
ejpam-4427	413	8	.	.	PUNCT
ejpam-4427	414	1	j.	j.	PROPN
ejpam-4427	414	2	pure	pure	PROPN
ejpam-4427	414	3	appl	appl	PROPN
ejpam-4427	414	4	.	.	PROPN
ejpam-4427	414	5	math	math	PROPN
ejpam-4427	414	6	,	,	PUNCT
ejpam-4427	414	7	15	15	NUM
ejpam-4427	414	8	(	(	PUNCT
ejpam-4427	414	9	3	3	NUM
ejpam-4427	414	10	)	)	PUNCT
ejpam-4427	414	11	(	(	PUNCT
ejpam-4427	414	12	2022	2022	NUM
ejpam-4427	414	13	)	)	PUNCT
ejpam-4427	414	14	,	,	PUNCT
ejpam-4427	414	15	1229	1229	NUM
ejpam-4427	414	16	-	-	SYM
ejpam-4427	414	17	1236	1236	NUM
ejpam-4427	414	18	1235	1235	NUM
ejpam-4427	414	19	theorem	theorem	NOUN
ejpam-4427	414	20	7	7	NUM
ejpam-4427	414	21	.	.	PUNCT
ejpam-4427	415	1	let	let	VERB
ejpam-4427	415	2	g	g	NOUN
ejpam-4427	415	3	and	and	CCONJ
ejpam-4427	415	4	h	h	PROPN
ejpam-4427	415	5	be	be	VERB
ejpam-4427	415	6	non	non	ADJ
ejpam-4427	415	7	-	-	ADJ
ejpam-4427	415	8	trivial	trivial	ADJ
ejpam-4427	415	9	connected	connected	ADJ
ejpam-4427	415	10	graphs	graph	NOUN
ejpam-4427	415	11	.	.	PUNCT
ejpam-4427	416	1	then	then	ADV
ejpam-4427	416	2	w	w	NOUN
ejpam-4427	416	3	=	=	PUNCT
ejpam-4427	416	4	⋃	⋃	PROPN
ejpam-4427	416	5	x∈s	x∈s	NOUN
ejpam-4427	416	6	[	[	PUNCT
ejpam-4427	416	7	{	{	PUNCT
ejpam-4427	416	8	x	x	NOUN
ejpam-4427	416	9	}	}	PUNCT
ejpam-4427	416	10	×	×	NOUN
ejpam-4427	416	11	tx	tx	PROPN
ejpam-4427	416	12	]	]	PUNCT
ejpam-4427	416	13	,	,	PUNCT
ejpam-4427	416	14	where	where	SCONJ
ejpam-4427	416	15	s	s	VERB
ejpam-4427	416	16	⊆	⊆	NUM
ejpam-4427	416	17	v	v	NOUN
ejpam-4427	416	18	(	(	PUNCT
ejpam-4427	416	19	g	g	NOUN
ejpam-4427	416	20	)	)	PUNCT
ejpam-4427	416	21	and	and	CCONJ
ejpam-4427	416	22	tx	tx	VERB
ejpam-4427	416	23	⊆	⊆	NUM
ejpam-4427	416	24	v	v	NOUN
ejpam-4427	416	25	(	(	PUNCT
ejpam-4427	416	26	h	h	NOUN
ejpam-4427	416	27	)	)	PUNCT
ejpam-4427	416	28	for	for	ADP
ejpam-4427	416	29	each	each	DET
ejpam-4427	416	30	x	x	SYM
ejpam-4427	416	31	∈	∈	PROPN
ejpam-4427	416	32	s	s	NOUN
ejpam-4427	416	33	,	,	PUNCT
ejpam-4427	416	34	is	be	AUX
ejpam-4427	416	35	a	a	DET
ejpam-4427	416	36	restrained	restrained	ADJ
ejpam-4427	416	37	2	2	NUM
ejpam-4427	416	38	-	-	PUNCT
ejpam-4427	416	39	resolving	resolving	NOUN
ejpam-4427	416	40	set	set	VERB
ejpam-4427	416	41	in	in	ADP
ejpam-4427	416	42	g[h	g[h	PROPN
ejpam-4427	416	43	]	]	PUNCT
ejpam-4427	416	44	if	if	SCONJ
ejpam-4427	416	45	and	and	CCONJ
ejpam-4427	416	46	only	only	ADV
ejpam-4427	416	47	if	if	SCONJ
ejpam-4427	416	48	(	(	PUNCT
ejpam-4427	416	49	i	i	NOUN
ejpam-4427	416	50	)	)	PUNCT
ejpam-4427	416	51	s	s	PART
ejpam-4427	416	52	=	=	SYM
ejpam-4427	416	53	v	v	X
ejpam-4427	416	54	(	(	PUNCT
ejpam-4427	416	55	g	g	NOUN
ejpam-4427	416	56	)	)	PUNCT
ejpam-4427	416	57	(	(	PUNCT
ejpam-4427	416	58	ii	ii	NOUN
ejpam-4427	416	59	)	)	PUNCT
ejpam-4427	416	60	tx	tx	PROPN
ejpam-4427	416	61	is	be	AUX
ejpam-4427	416	62	a	a	DET
ejpam-4427	416	63	2	2	NUM
ejpam-4427	416	64	-	-	PUNCT
ejpam-4427	416	65	locating	locate	VERB
ejpam-4427	416	66	set	set	NOUN
ejpam-4427	416	67	in	in	ADP
ejpam-4427	416	68	h	h	NOUN
ejpam-4427	416	69	for	for	ADP
ejpam-4427	416	70	all	all	PRON
ejpam-4427	416	71	x	x	SYM
ejpam-4427	416	72	∈	∈	PROPN
ejpam-4427	416	73	v	v	NOUN
ejpam-4427	416	74	(	(	PUNCT
ejpam-4427	416	75	g	g	NOUN
ejpam-4427	416	76	)	)	PUNCT
ejpam-4427	416	77	;	;	PUNCT
ejpam-4427	416	78	(	(	PUNCT
ejpam-4427	416	79	iii	iii	X
ejpam-4427	416	80	)	)	PUNCT
ejpam-4427	416	81	tx	tx	PROPN
ejpam-4427	416	82	is	be	AUX
ejpam-4427	416	83	a	a	DET
ejpam-4427	416	84	restrained	restrained	ADJ
ejpam-4427	416	85	2	2	NUM
ejpam-4427	416	86	-	-	PUNCT
ejpam-4427	416	87	locating	locate	VERB
ejpam-4427	416	88	set	set	NOUN
ejpam-4427	416	89	for	for	ADP
ejpam-4427	416	90	each	each	PRON
ejpam-4427	416	91	x	x	PUNCT
ejpam-4427	416	92	with	with	ADP
ejpam-4427	416	93	ty	ty	NOUN
ejpam-4427	416	94	=	=	SYM
ejpam-4427	416	95	v	v	NOUN
ejpam-4427	416	96	(	(	PUNCT
ejpam-4427	416	97	h	h	NOUN
ejpam-4427	416	98	)	)	PUNCT
ejpam-4427	416	99	,	,	PUNCT
ejpam-4427	416	100	for	for	ADP
ejpam-4427	416	101	all	all	DET
ejpam-4427	416	102	y	y	PROPN
ejpam-4427	416	103	∈	∈	PROPN
ejpam-4427	416	104	ng(x	ng(x	NUM
ejpam-4427	416	105	)	)	PUNCT
ejpam-4427	416	106	;	;	PUNCT
ejpam-4427	416	107	(	(	PUNCT
ejpam-4427	416	108	iv	iv	X
ejpam-4427	416	109	)	)	PUNCT
ejpam-4427	416	110	tx	tx	PROPN
ejpam-4427	416	111	and	and	CCONJ
ejpam-4427	416	112	ty	ty	INTJ
ejpam-4427	416	113	are	be	AUX
ejpam-4427	416	114	(	(	PUNCT
ejpam-4427	416	115	2	2	NUM
ejpam-4427	416	116	,	,	PUNCT
ejpam-4427	416	117	1)-locating	1)-locating	NUM
ejpam-4427	416	118	sets	set	NOUN
ejpam-4427	416	119	or	or	CCONJ
ejpam-4427	416	120	one	one	NUM
ejpam-4427	416	121	of	of	ADP
ejpam-4427	416	122	tx	tx	PROPN
ejpam-4427	416	123	and	and	CCONJ
ejpam-4427	416	124	ty	ty	PRON
ejpam-4427	416	125	is	be	AUX
ejpam-4427	416	126	a	a	DET
ejpam-4427	416	127	(	(	PUNCT
ejpam-4427	416	128	2	2	NUM
ejpam-4427	416	129	,	,	PUNCT
ejpam-4427	416	130	2)-locating	2)-locating	NUM
ejpam-4427	416	131	set	set	VERB
ejpam-4427	416	132	in	in	ADP
ejpam-4427	416	133	h	h	NOUN
ejpam-4427	416	134	whenever	whenever	SCONJ
ejpam-4427	416	135	x	x	X
ejpam-4427	416	136	,	,	PUNCT
ejpam-4427	416	137	y	y	PROPN
ejpam-4427	416	138	∈	∈	PROPN
ejpam-4427	416	139	eq1(g	eq1(g	PROPN
ejpam-4427	416	140	)	)	PUNCT
ejpam-4427	416	141	;	;	PUNCT
ejpam-4427	416	142	and	and	CCONJ
ejpam-4427	416	143	(	(	PUNCT
ejpam-4427	416	144	v	v	NOUN
ejpam-4427	416	145	)	)	PUNCT
ejpam-4427	416	146	tx	tx	NOUN
ejpam-4427	416	147	and	and	CCONJ
ejpam-4427	416	148	ty	ty	INTJ
ejpam-4427	416	149	are	be	AUX
ejpam-4427	416	150	(	(	PUNCT
ejpam-4427	416	151	2	2	NUM
ejpam-4427	416	152	-	-	PUNCT
ejpam-4427	416	153	locating	locating	NOUN
ejpam-4427	416	154	)	)	PUNCT
ejpam-4427	416	155	dominating	dominating	NOUN
ejpam-4427	416	156	sets	set	NOUN
ejpam-4427	416	157	in	in	ADP
ejpam-4427	416	158	h	h	NOUN
ejpam-4427	416	159	or	or	CCONJ
ejpam-4427	416	160	if	if	SCONJ
ejpam-4427	416	161	one	one	NUM
ejpam-4427	416	162	of	of	ADP
ejpam-4427	416	163	tx	tx	PROPN
ejpam-4427	416	164	and	and	CCONJ
ejpam-4427	416	165	ty	ty	INTJ
ejpam-4427	416	166	,	,	PUNCT
ejpam-4427	416	167	say	say	VERB
ejpam-4427	416	168	tx	tx	PROPN
ejpam-4427	416	169	is	be	AUX
ejpam-4427	416	170	not	not	PART
ejpam-4427	416	171	dominating	dominate	VERB
ejpam-4427	416	172	,	,	PUNCT
ejpam-4427	416	173	then	then	ADV
ejpam-4427	416	174	ty	ty	PRON
ejpam-4427	416	175	is	be	VERB
ejpam-4427	416	176	2	2	NUM
ejpam-4427	416	177	-	-	PUNCT
ejpam-4427	416	178	dominating	dominate	VERB
ejpam-4427	416	179	whenever	whenever	SCONJ
ejpam-4427	416	180	x	x	X
ejpam-4427	416	181	,	,	PUNCT
ejpam-4427	416	182	y	y	PROPN
ejpam-4427	416	183	∈	∈	PROPN
ejpam-4427	416	184	eq2(g	eq2(g	VERB
ejpam-4427	416	185	)	)	PUNCT
ejpam-4427	416	186	.	.	PUNCT
ejpam-4427	417	1	proof	proof	NOUN
ejpam-4427	417	2	.	.	PUNCT
ejpam-4427	418	1	suppose	suppose	VERB
ejpam-4427	418	2	w	w	PROPN
ejpam-4427	418	3	=	=	PUNCT
ejpam-4427	418	4	⋃	⋃	PROPN
ejpam-4427	418	5	x∈s	x∈s	NOUN
ejpam-4427	418	6	[	[	PUNCT
ejpam-4427	418	7	{	{	PUNCT
ejpam-4427	418	8	x}×tx	x}×tx	X
ejpam-4427	418	9	]	]	PUNCT
ejpam-4427	418	10	where	where	SCONJ
ejpam-4427	418	11	s	s	VERB
ejpam-4427	418	12	⊆	⊆	NUM
ejpam-4427	418	13	v	v	NOUN
ejpam-4427	418	14	(	(	PUNCT
ejpam-4427	418	15	g	g	NOUN
ejpam-4427	418	16	)	)	PUNCT
ejpam-4427	418	17	and	and	CCONJ
ejpam-4427	418	18	tx	tx	VERB
ejpam-4427	418	19	⊆	⊆	NUM
ejpam-4427	418	20	v	v	NOUN
ejpam-4427	418	21	(	(	PUNCT
ejpam-4427	418	22	h	h	NOUN
ejpam-4427	418	23	)	)	PUNCT
ejpam-4427	418	24	is	be	AUX
ejpam-4427	418	25	a	a	DET
ejpam-4427	418	26	restrained	restrain	VERB
ejpam-4427	418	27	2resolving	2resolving	NUM
ejpam-4427	418	28	set	set	VERB
ejpam-4427	418	29	in	in	ADP
ejpam-4427	418	30	g[h	g[h	PROPN
ejpam-4427	418	31	]	]	PUNCT
ejpam-4427	418	32	.	.	PUNCT
ejpam-4427	419	1	then	then	ADV
ejpam-4427	419	2	by	by	ADP
ejpam-4427	419	3	theorem	theorem	NOUN
ejpam-4427	419	4	6	6	NUM
ejpam-4427	419	5	,	,	PUNCT
ejpam-4427	419	6	(	(	PUNCT
ejpam-4427	419	7	i	i	NOUN
ejpam-4427	419	8	)	)	PUNCT
ejpam-4427	419	9	,	,	PUNCT
ejpam-4427	419	10	(	(	PUNCT
ejpam-4427	419	11	ii	ii	NOUN
ejpam-4427	419	12	)	)	PUNCT
ejpam-4427	419	13	,	,	PUNCT
ejpam-4427	419	14	(	(	PUNCT
ejpam-4427	419	15	iv	iv	X
ejpam-4427	419	16	)	)	PUNCT
ejpam-4427	419	17	and	and	CCONJ
ejpam-4427	419	18	(	(	PUNCT
ejpam-4427	419	19	v	v	NOUN
ejpam-4427	419	20	)	)	PUNCT
ejpam-4427	419	21	hold	hold	NOUN
ejpam-4427	419	22	.	.	PUNCT
ejpam-4427	420	1	now	now	ADV
ejpam-4427	420	2	,	,	PUNCT
ejpam-4427	420	3	let	let	VERB
ejpam-4427	420	4	x	x	PUNCT
ejpam-4427	420	5	∈	∈	PROPN
ejpam-4427	420	6	v	v	X
ejpam-4427	420	7	(	(	PUNCT
ejpam-4427	420	8	g	g	NOUN
ejpam-4427	420	9	)	)	PUNCT
ejpam-4427	420	10	with	with	ADP
ejpam-4427	420	11	ty	ty	NOUN
ejpam-4427	420	12	=	=	SYM
ejpam-4427	420	13	v	v	NOUN
ejpam-4427	420	14	(	(	PUNCT
ejpam-4427	420	15	h	h	NOUN
ejpam-4427	420	16	)	)	PUNCT
ejpam-4427	420	17	,	,	PUNCT
ejpam-4427	420	18	for	for	ADP
ejpam-4427	420	19	all	all	DET
ejpam-4427	420	20	y	y	PROPN
ejpam-4427	420	21	∈	∈	PROPN
ejpam-4427	420	22	ng(x	ng(x	NUM
ejpam-4427	420	23	)	)	PUNCT
ejpam-4427	420	24	.	.	PUNCT
ejpam-4427	421	1	suppose	suppose	VERB
ejpam-4427	421	2	that	that	SCONJ
ejpam-4427	421	3	tx	tx	PROPN
ejpam-4427	421	4	is	be	AUX
ejpam-4427	421	5	not	not	PART
ejpam-4427	421	6	restrained	restrain	VERB
ejpam-4427	421	7	2	2	NUM
ejpam-4427	421	8	-	-	PUNCT
ejpam-4427	421	9	locating	locate	VERB
ejpam-4427	421	10	set	set	NOUN
ejpam-4427	421	11	.	.	PUNCT
ejpam-4427	422	1	then	then	ADV
ejpam-4427	422	2	⟨v	⟨v	CCONJ
ejpam-4427	422	3	(	(	PUNCT
ejpam-4427	422	4	h)\tx⟩	h)\tx⟩	X
ejpam-4427	422	5	has	have	VERB
ejpam-4427	422	6	an	an	DET
ejpam-4427	422	7	isolated	isolated	ADJ
ejpam-4427	422	8	vertex	vertex	NOUN
ejpam-4427	422	9	,	,	PUNCT
ejpam-4427	422	10	say	say	VERB
ejpam-4427	422	11	u.	u.	NOUN
ejpam-4427	422	12	thus	thus	ADV
ejpam-4427	422	13	,	,	PUNCT
ejpam-4427	422	14	(	(	PUNCT
ejpam-4427	422	15	x	x	NOUN
ejpam-4427	422	16	,	,	PUNCT
ejpam-4427	422	17	u	u	NOUN
ejpam-4427	422	18	)	)	PUNCT
ejpam-4427	422	19	is	be	AUX
ejpam-4427	422	20	an	an	DET
ejpam-4427	422	21	isolated	isolated	ADJ
ejpam-4427	422	22	vertex	vertex	NOUN
ejpam-4427	422	23	in	in	ADP
ejpam-4427	422	24	⟨v	⟨v	PROPN
ejpam-4427	422	25	(	(	PUNCT
ejpam-4427	422	26	g[h])\w	g[h])\w	INTJ
ejpam-4427	422	27	⟩	⟩	NOUN
ejpam-4427	422	28	,	,	PUNCT
ejpam-4427	422	29	contrary	contrary	ADJ
ejpam-4427	422	30	to	to	ADP
ejpam-4427	422	31	the	the	DET
ejpam-4427	422	32	assumption	assumption	NOUN
ejpam-4427	422	33	that	that	SCONJ
ejpam-4427	422	34	w	w	NOUN
ejpam-4427	422	35	is	be	AUX
ejpam-4427	422	36	a	a	DET
ejpam-4427	422	37	restrained	restrained	ADJ
ejpam-4427	422	38	2	2	NUM
ejpam-4427	422	39	-	-	PUNCT
ejpam-4427	422	40	resolving	resolving	NOUN
ejpam-4427	422	41	set	set	VERB
ejpam-4427	422	42	in	in	ADP
ejpam-4427	422	43	g[h	g[h	NOUN
ejpam-4427	422	44	]	]	PUNCT
ejpam-4427	422	45	.	.	PUNCT
ejpam-4427	423	1	hence	hence	ADV
ejpam-4427	423	2	,	,	PUNCT
ejpam-4427	423	3	tx	tx	PROPN
ejpam-4427	423	4	is	be	AUX
ejpam-4427	423	5	a	a	DET
ejpam-4427	423	6	restrained	restrained	ADJ
ejpam-4427	423	7	2	2	NUM
ejpam-4427	423	8	-	-	PUNCT
ejpam-4427	423	9	locating	locate	VERB
ejpam-4427	423	10	set	set	NOUN
ejpam-4427	423	11	.	.	PUNCT
ejpam-4427	424	1	for	for	ADP
ejpam-4427	424	2	the	the	DET
ejpam-4427	424	3	converse	converse	NOUN
ejpam-4427	424	4	,	,	PUNCT
ejpam-4427	424	5	suppose	suppose	VERB
ejpam-4427	424	6	that	that	SCONJ
ejpam-4427	424	7	(	(	PUNCT
ejpam-4427	424	8	i	i	NOUN
ejpam-4427	424	9	)	)	PUNCT
ejpam-4427	424	10	,	,	PUNCT
ejpam-4427	424	11	(	(	PUNCT
ejpam-4427	424	12	ii	ii	NOUN
ejpam-4427	424	13	)	)	PUNCT
ejpam-4427	424	14	,	,	PUNCT
ejpam-4427	424	15	(	(	PUNCT
ejpam-4427	424	16	iii	iii	NOUN
ejpam-4427	424	17	)	)	PUNCT
ejpam-4427	424	18	,	,	PUNCT
ejpam-4427	424	19	and	and	CCONJ
ejpam-4427	424	20	(	(	PUNCT
ejpam-4427	424	21	iv	iv	X
ejpam-4427	424	22	)	)	PUNCT
ejpam-4427	424	23	hold	hold	NOUN
ejpam-4427	424	24	.	.	PUNCT
ejpam-4427	425	1	then	then	ADV
ejpam-4427	425	2	by	by	ADP
ejpam-4427	425	3	theorem	theorem	NOUN
ejpam-4427	425	4	6	6	NUM
ejpam-4427	425	5	,	,	PUNCT
ejpam-4427	425	6	w	w	NOUN
ejpam-4427	425	7	=	=	PUNCT
ejpam-4427	425	8	⋃	⋃	PROPN
ejpam-4427	425	9	x∈s	x∈s	NOUN
ejpam-4427	425	10	[	[	PUNCT
ejpam-4427	425	11	{	{	PUNCT
ejpam-4427	425	12	x}×tx	x}×tx	X
ejpam-4427	425	13	]	]	X
ejpam-4427	425	14	is	be	AUX
ejpam-4427	425	15	a	a	DET
ejpam-4427	425	16	2	2	NUM
ejpam-4427	425	17	-	-	PUNCT
ejpam-4427	425	18	resolving	resolving	NOUN
ejpam-4427	425	19	set	set	VERB
ejpam-4427	425	20	in	in	ADP
ejpam-4427	425	21	g[h	g[h	NOUN
ejpam-4427	425	22	]	]	PUNCT
ejpam-4427	425	23	.	.	PUNCT
ejpam-4427	426	1	if	if	SCONJ
ejpam-4427	426	2	w	w	PROPN
ejpam-4427	426	3	=	=	SYM
ejpam-4427	426	4	v	v	NOUN
ejpam-4427	426	5	(	(	PUNCT
ejpam-4427	426	6	g[h	g[h	PROPN
ejpam-4427	426	7	]	]	PUNCT
ejpam-4427	426	8	)	)	PUNCT
ejpam-4427	426	9	,	,	PUNCT
ejpam-4427	426	10	then	then	ADV
ejpam-4427	426	11	w	w	PROPN
ejpam-4427	426	12	is	be	AUX
ejpam-4427	426	13	a	a	DET
ejpam-4427	426	14	restrained	restrained	ADJ
ejpam-4427	426	15	2	2	NUM
ejpam-4427	426	16	-	-	PUNCT
ejpam-4427	426	17	resolving	resolving	NOUN
ejpam-4427	426	18	set	set	VERB
ejpam-4427	426	19	in	in	ADP
ejpam-4427	426	20	g[h	g[h	PROPN
ejpam-4427	426	21	]	]	PUNCT
ejpam-4427	426	22	.	.	PUNCT
ejpam-4427	427	1	suppose	suppose	VERB
ejpam-4427	427	2	that	that	SCONJ
ejpam-4427	427	3	w	w	PROPN
ejpam-4427	427	4	̸=	̸=	PROPN
ejpam-4427	427	5	v	v	NOUN
ejpam-4427	427	6	(	(	PUNCT
ejpam-4427	427	7	g[h	g[h	PROPN
ejpam-4427	427	8	]	]	PUNCT
ejpam-4427	427	9	)	)	PUNCT
ejpam-4427	427	10	.	.	PUNCT
ejpam-4427	428	1	let	let	VERB
ejpam-4427	428	2	(	(	PUNCT
ejpam-4427	428	3	x	x	NOUN
ejpam-4427	428	4	,	,	PUNCT
ejpam-4427	428	5	a	a	DET
ejpam-4427	428	6	)	)	PUNCT
ejpam-4427	428	7	∈	∈	NOUN
ejpam-4427	428	8	v	v	NOUN
ejpam-4427	428	9	(	(	PUNCT
ejpam-4427	428	10	g[h])\w	g[h])\w	INTJ
ejpam-4427	428	11	.	.	PUNCT
ejpam-4427	429	1	if	if	SCONJ
ejpam-4427	429	2	ty	ty	NUM
ejpam-4427	429	3	̸=	̸=	PROPN
ejpam-4427	429	4	v	v	NOUN
ejpam-4427	429	5	(	(	PUNCT
ejpam-4427	429	6	h	h	NOUN
ejpam-4427	429	7	)	)	PUNCT
ejpam-4427	429	8	,	,	PUNCT
ejpam-4427	429	9	for	for	ADP
ejpam-4427	429	10	all	all	DET
ejpam-4427	429	11	y	y	PROPN
ejpam-4427	429	12	∈	∈	PROPN
ejpam-4427	429	13	ng(x	ng(x	NUM
ejpam-4427	429	14	)	)	PUNCT
ejpam-4427	429	15	,	,	PUNCT
ejpam-4427	429	16	then	then	ADV
ejpam-4427	429	17	⟨v	⟨v	NUM
ejpam-4427	429	18	(	(	PUNCT
ejpam-4427	429	19	g[h])\w	g[h])\w	INTJ
ejpam-4427	429	20	⟩	⟩	PROPN
ejpam-4427	429	21	has	have	VERB
ejpam-4427	429	22	no	no	DET
ejpam-4427	429	23	isolated	isolated	ADJ
ejpam-4427	429	24	vertex	vertex	NOUN
ejpam-4427	429	25	.	.	PUNCT
ejpam-4427	430	1	if	if	SCONJ
ejpam-4427	430	2	ty	ty	PRON
ejpam-4427	430	3	=	=	SYM
ejpam-4427	430	4	v	v	NOUN
ejpam-4427	430	5	(	(	PUNCT
ejpam-4427	430	6	h	h	NOUN
ejpam-4427	430	7	)	)	PUNCT
ejpam-4427	430	8	,	,	PUNCT
ejpam-4427	430	9	for	for	ADP
ejpam-4427	430	10	some	some	DET
ejpam-4427	430	11	y	y	PROPN
ejpam-4427	430	12	∈	∈	PROPN
ejpam-4427	430	13	ng(x	ng(x	NUM
ejpam-4427	430	14	)	)	PUNCT
ejpam-4427	430	15	,	,	PUNCT
ejpam-4427	430	16	then	then	ADV
ejpam-4427	430	17	by	by	ADP
ejpam-4427	430	18	(	(	PUNCT
ejpam-4427	430	19	iii	iii	NOUN
ejpam-4427	430	20	)	)	PUNCT
ejpam-4427	430	21	,	,	PUNCT
ejpam-4427	430	22	tx	tx	PROPN
ejpam-4427	430	23	is	be	AUX
ejpam-4427	430	24	a	a	DET
ejpam-4427	430	25	restrained	restrained	ADJ
ejpam-4427	430	26	2	2	NUM
ejpam-4427	430	27	-	-	PUNCT
ejpam-4427	430	28	locating	locate	VERB
ejpam-4427	430	29	set	set	NOUN
ejpam-4427	430	30	.	.	PUNCT
ejpam-4427	431	1	thus	thus	ADV
ejpam-4427	431	2	,	,	PUNCT
ejpam-4427	431	3	v	v	X
ejpam-4427	431	4	(	(	PUNCT
ejpam-4427	431	5	h)\tx	h)\tx	PROPN
ejpam-4427	431	6	has	have	VERB
ejpam-4427	431	7	no	no	DET
ejpam-4427	431	8	isolated	isolated	ADJ
ejpam-4427	431	9	vertex	vertex	NOUN
ejpam-4427	431	10	.	.	PUNCT
ejpam-4427	432	1	hence	hence	ADV
ejpam-4427	432	2	,	,	PUNCT
ejpam-4427	432	3	⟨v	⟨v	PROPN
ejpam-4427	432	4	(	(	PUNCT
ejpam-4427	432	5	g[h])\w	g[h])\w	INTJ
ejpam-4427	432	6	⟩	⟩	PROPN
ejpam-4427	432	7	has	have	VERB
ejpam-4427	432	8	no	no	DET
ejpam-4427	432	9	isolated	isolated	ADJ
ejpam-4427	432	10	vertex	vertex	NOUN
ejpam-4427	432	11	.	.	PUNCT
ejpam-4427	433	1	therefore	therefore	ADV
ejpam-4427	433	2	,	,	PUNCT
ejpam-4427	433	3	w	w	PROPN
ejpam-4427	433	4	is	be	AUX
ejpam-4427	433	5	a	a	DET
ejpam-4427	433	6	restrained	restrained	ADJ
ejpam-4427	433	7	2	2	NUM
ejpam-4427	433	8	-	-	PUNCT
ejpam-4427	433	9	resolving	resolving	NOUN
ejpam-4427	433	10	set	set	VERB
ejpam-4427	433	11	in	in	ADP
ejpam-4427	433	12	g[h	g[h	PROPN
ejpam-4427	433	13	]	]	PUNCT
ejpam-4427	433	14	.	.	PUNCT
ejpam-4427	434	1	the	the	DET
ejpam-4427	434	2	following	follow	VERB
ejpam-4427	434	3	corollaries	corollary	NOUN
ejpam-4427	434	4	are	be	AUX
ejpam-4427	434	5	the	the	DET
ejpam-4427	434	6	direct	direct	ADJ
ejpam-4427	434	7	consequences	consequence	NOUN
ejpam-4427	434	8	of	of	ADP
ejpam-4427	434	9	theorem	theorem	ADJ
ejpam-4427	434	10	7	7	NUM
ejpam-4427	434	11	.	.	PUNCT
ejpam-4427	434	12	corollary	corollary	ADJ
ejpam-4427	434	13	4	4	NUM
ejpam-4427	434	14	.	.	PUNCT
ejpam-4427	435	1	let	let	VERB
ejpam-4427	435	2	g	g	NOUN
ejpam-4427	435	3	and	and	CCONJ
ejpam-4427	435	4	h	h	NOUN
ejpam-4427	435	5	be	be	AUX
ejpam-4427	435	6	nontrivial	nontrivial	ADJ
ejpam-4427	435	7	connected	connect	VERB
ejpam-4427	435	8	graphs	graph	NOUN
ejpam-4427	435	9	such	such	ADJ
ejpam-4427	435	10	that	that	SCONJ
ejpam-4427	435	11	g	g	PROPN
ejpam-4427	435	12	is	be	AUX
ejpam-4427	435	13	not	not	PART
ejpam-4427	435	14	freeequidistant	freeequidistant	ADJ
ejpam-4427	435	15	.	.	PUNCT
ejpam-4427	436	1	then	then	ADV
ejpam-4427	436	2	,	,	PUNCT
ejpam-4427	436	3	rdim2(g[h	rdim2(g[h	VERB
ejpam-4427	436	4	]	]	PUNCT
ejpam-4427	436	5	)	)	PUNCT
ejpam-4427	436	6	≤	≤	NOUN
ejpam-4427	437	1	n	n	CCONJ
ejpam-4427	437	2	·	·	PUNCT
ejpam-4427	437	3	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4427	437	4	)	)	PUNCT
ejpam-4427	438	1	+	+	NOUN
ejpam-4427	438	2	m	m	NOUN
ejpam-4427	438	3	·	·	PUNCT
ejpam-4427	438	4	γ2l(h	γ2l(h	PROPN
ejpam-4427	438	5	)	)	PUNCT
ejpam-4427	439	1	+	+	CCONJ
ejpam-4427	439	2	p	p	X
ejpam-4427	439	3	·	·	PUNCT
ejpam-4427	439	4	rln2(h	rln2(h	NUM
ejpam-4427	439	5	)	)	PUNCT
ejpam-4427	439	6	,	,	PUNCT
ejpam-4427	439	7	where	where	SCONJ
ejpam-4427	439	8	n+m+	n+m+	VERB
ejpam-4427	439	9	p	p	X
ejpam-4427	439	10	=	=	X
ejpam-4427	439	11	|v	|v	X
ejpam-4427	439	12	(	(	PUNCT
ejpam-4427	439	13	g)|	g)|	NOUN
ejpam-4427	439	14	with	with	ADP
ejpam-4427	439	15	|eq1(g)|	|eq1(g)|	NOUN
ejpam-4427	439	16	=	=	SYM
ejpam-4427	439	17	n	n	CCONJ
ejpam-4427	439	18	,	,	PUNCT
ejpam-4427	439	19	|eq2(g)|	|eq2(g)|	X
ejpam-4427	439	20	=	=	PUNCT
ejpam-4427	439	21	m	m	VERB
ejpam-4427	439	22	and	and	CCONJ
ejpam-4427	439	23	|fr(g)|	|fr(g)|	X
ejpam-4427	439	24	=	=	SYM
ejpam-4427	440	1	p.	p.	NOUN
ejpam-4427	440	2	the	the	DET
ejpam-4427	440	3	following	follow	VERB
ejpam-4427	440	4	result	result	NOUN
ejpam-4427	440	5	follows	follow	VERB
ejpam-4427	440	6	from	from	ADP
ejpam-4427	440	7	theorem	theorem	ADJ
ejpam-4427	440	8	7	7	NUM
ejpam-4427	440	9	.	.	PUNCT
ejpam-4427	440	10	corollary	corollary	ADJ
ejpam-4427	440	11	5	5	NUM
ejpam-4427	440	12	.	.	PUNCT
ejpam-4427	440	13	letg	letg	NOUN
ejpam-4427	440	14	andh	andh	NOUN
ejpam-4427	440	15	be	be	VERB
ejpam-4427	440	16	non	non	ADJ
ejpam-4427	440	17	-	-	ADJ
ejpam-4427	440	18	trivial	trivial	ADJ
ejpam-4427	440	19	connected	connected	ADJ
ejpam-4427	440	20	graphs	graph	NOUN
ejpam-4427	440	21	such	such	ADJ
ejpam-4427	440	22	thatg	thatg	PROPN
ejpam-4427	440	23	is	be	AUX
ejpam-4427	440	24	free	free	ADJ
ejpam-4427	440	25	-	-	PUNCT
ejpam-4427	440	26	equidistant	equidistant	NOUN
ejpam-4427	440	27	.	.	PUNCT
ejpam-4427	441	1	then	then	ADV
ejpam-4427	441	2	rdim2(g[h	rdim2(g[h	VERB
ejpam-4427	441	3	]	]	PUNCT
ejpam-4427	441	4	)	)	PUNCT
ejpam-4427	442	1	=	=	PRON
ejpam-4427	442	2	{	{	PUNCT
ejpam-4427	442	3	|v	|v	PROPN
ejpam-4427	442	4	(	(	PUNCT
ejpam-4427	442	5	g)|	g)|	PROPN
ejpam-4427	442	6	·	·	SYM
ejpam-4427	442	7	ln2(h	ln2(h	PROPN
ejpam-4427	442	8	)	)	PUNCT
ejpam-4427	442	9	,	,	PUNCT
ejpam-4427	442	10	if	if	SCONJ
ejpam-4427	442	11	ln2(h	ln2(h	PROPN
ejpam-4427	442	12	)	)	PUNCT
ejpam-4427	442	13	̸=	̸=	PROPN
ejpam-4427	442	14	|v	|v	NOUN
ejpam-4427	442	15	(	(	PUNCT
ejpam-4427	442	16	h)|	h)|	PROPN
ejpam-4427	442	17	|v	|v	PROPN
ejpam-4427	442	18	(	(	PUNCT
ejpam-4427	442	19	g)|	g)|	NOUN
ejpam-4427	442	20	·	·	PUNCT
ejpam-4427	442	21	rln2(h	rln2(h	NUM
ejpam-4427	442	22	)	)	PUNCT
ejpam-4427	442	23	,	,	PUNCT
ejpam-4427	442	24	otherwise	otherwise	ADV
ejpam-4427	442	25	.	.	PUNCT
ejpam-4427	443	1	the	the	DET
ejpam-4427	443	2	set	set	NOUN
ejpam-4427	443	3	consisting	consisting	NOUN
ejpam-4427	443	4	of	of	ADP
ejpam-4427	443	5	the	the	DET
ejpam-4427	443	6	shaded	shade	VERB
ejpam-4427	443	7	vertices	vertex	NOUN
ejpam-4427	443	8	in	in	ADP
ejpam-4427	443	9	figure	figure	NOUN
ejpam-4427	443	10	3	3	NUM
ejpam-4427	443	11	is	be	AUX
ejpam-4427	443	12	a	a	DET
ejpam-4427	443	13	restrained	restrained	ADJ
ejpam-4427	443	14	2	2	NUM
ejpam-4427	443	15	-	-	PUNCT
ejpam-4427	443	16	resolving	resolve	VERB
ejpam-4427	443	17	set	set	NOUN
ejpam-4427	443	18	of	of	ADP
ejpam-4427	443	19	the	the	DET
ejpam-4427	443	20	lexicographic	lexicographic	ADJ
ejpam-4427	443	21	product	product	NOUN
ejpam-4427	443	22	p4[p3	p4[p3	NOUN
ejpam-4427	443	23	]	]	X
ejpam-4427	443	24	.	.	PUNCT
ejpam-4427	444	1	references	reference	NOUN
ejpam-4427	444	2	1236	1236	NUM
ejpam-4427	444	3	....................................	....................................	PUNCT
ejpam-4427	444	4	....................................	....................................	PUNCT
ejpam-4427	445	1	....................................	....................................	PUNCT
ejpam-4427	445	2	....................................	....................................	PUNCT
ejpam-4427	446	1	....................................	....................................	PUNCT
ejpam-4427	446	2	....................................	....................................	PUNCT
ejpam-4427	447	1	....................................	....................................	PUNCT
ejpam-4427	447	2	....................................	....................................	PUNCT
ejpam-4427	448	1	....................................	....................................	PUNCT
ejpam-4427	448	2	....................................	....................................	PUNCT
ejpam-4427	449	1	....................................	....................................	PUNCT
ejpam-4427	449	2	....................................	....................................	PUNCT
ejpam-4427	450	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	450	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	451	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	451	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	452	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	452	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	453	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	453	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4427	453	3	.........	.........	PUNCT
ejpam-4427	453	4	........	........	PUNCT
ejpam-4427	453	5	........	........	PUNCT
ejpam-4427	453	6	........	........	PUNCT
ejpam-4427	453	7	........	........	PUNCT
ejpam-4427	453	8	........	........	PUNCT
ejpam-4427	453	9	........	........	PUNCT
ejpam-4427	453	10	........	........	PUNCT
ejpam-4427	453	11	........	........	PUNCT
ejpam-4427	453	12	........	........	PUNCT
ejpam-4427	453	13	........	........	PUNCT
ejpam-4427	454	1	....	....	PUNCT
ejpam-4427	454	2	.........	.........	PUNCT
ejpam-4427	454	3	........	........	PUNCT
ejpam-4427	454	4	........	........	PUNCT
ejpam-4427	454	5	........	........	PUNCT
ejpam-4427	454	6	........	........	PUNCT
ejpam-4427	454	7	........	........	PUNCT
ejpam-4427	454	8	........	........	PUNCT
ejpam-4427	454	9	........	........	PUNCT
ejpam-4427	454	10	........	........	PUNCT
ejpam-4427	454	11	........	........	PUNCT
ejpam-4427	454	12	........	........	PUNCT
ejpam-4427	455	1	....	....	PUNCT
ejpam-4427	455	2	.........	.........	PUNCT
ejpam-4427	455	3	........	........	PUNCT
ejpam-4427	455	4	........	........	PUNCT
ejpam-4427	455	5	........	........	PUNCT
ejpam-4427	455	6	........	........	PUNCT
ejpam-4427	455	7	........	........	PUNCT
ejpam-4427	455	8	........	........	PUNCT
ejpam-4427	455	9	........	........	PUNCT
ejpam-4427	455	10	........	........	PUNCT
ejpam-4427	455	11	........	........	PUNCT
ejpam-4427	455	12	........	........	PUNCT
ejpam-4427	456	1	....	....	PUNCT
ejpam-4427	456	2	.........	.........	PUNCT
ejpam-4427	456	3	........	........	PUNCT
ejpam-4427	456	4	........	........	PUNCT
ejpam-4427	456	5	........	........	PUNCT
ejpam-4427	456	6	........	........	PUNCT
ejpam-4427	456	7	........	........	PUNCT
ejpam-4427	456	8	........	........	PUNCT
ejpam-4427	456	9	........	........	PUNCT
ejpam-4427	456	10	........	........	PUNCT
ejpam-4427	456	11	........	........	PUNCT
ejpam-4427	456	12	........	........	PUNCT
ejpam-4427	457	1	....	....	PUNCT
ejpam-4427	457	2	.........	.........	PUNCT
ejpam-4427	457	3	........	........	PUNCT
ejpam-4427	457	4	........	........	PUNCT
ejpam-4427	457	5	........	........	PUNCT
ejpam-4427	457	6	........	........	PUNCT
ejpam-4427	457	7	........	........	PUNCT
ejpam-4427	457	8	........	........	PUNCT
ejpam-4427	457	9	........	........	PUNCT
ejpam-4427	457	10	........	........	PUNCT
ejpam-4427	457	11	........	........	PUNCT
ejpam-4427	457	12	........	........	PUNCT
ejpam-4427	458	1	....	....	PUNCT
ejpam-4427	458	2	.........	.........	PUNCT
ejpam-4427	458	3	........	........	PUNCT
ejpam-4427	458	4	........	........	PUNCT
ejpam-4427	458	5	........	........	PUNCT
ejpam-4427	458	6	........	........	PUNCT
ejpam-4427	458	7	........	........	PUNCT
ejpam-4427	458	8	........	........	PUNCT
ejpam-4427	458	9	........	........	PUNCT
ejpam-4427	458	10	........	........	PUNCT
ejpam-4427	458	11	........	........	PUNCT
ejpam-4427	458	12	........	........	PUNCT
ejpam-4427	459	1	....	....	PUNCT
ejpam-4427	459	2	.........	.........	PUNCT
ejpam-4427	459	3	........	........	PUNCT
ejpam-4427	459	4	........	........	PUNCT
ejpam-4427	459	5	........	........	PUNCT
ejpam-4427	459	6	........	........	PUNCT
ejpam-4427	459	7	........	........	PUNCT
ejpam-4427	459	8	........	........	PUNCT
ejpam-4427	459	9	........	........	PUNCT
ejpam-4427	459	10	........	........	PUNCT
ejpam-4427	459	11	........	........	PUNCT
ejpam-4427	459	12	........	........	PUNCT
ejpam-4427	460	1	....	....	PUNCT
ejpam-4427	460	2	.........	.........	PUNCT
ejpam-4427	460	3	........	........	PUNCT
ejpam-4427	460	4	........	........	PUNCT
ejpam-4427	460	5	........	........	PUNCT
ejpam-4427	460	6	........	........	PUNCT
ejpam-4427	460	7	........	........	PUNCT
ejpam-4427	460	8	........	........	PUNCT
ejpam-4427	460	9	........	........	PUNCT
ejpam-4427	460	10	........	........	PUNCT
ejpam-4427	460	11	........	........	PUNCT
ejpam-4427	460	12	........	........	PUNCT
ejpam-4427	461	1	....	....	PUNCT
ejpam-4427	461	2	............	............	PUNCT
ejpam-4427	461	3	...........	...........	PUNCT
ejpam-4427	461	4	...........	...........	PUNCT
ejpam-4427	461	5	...........	...........	PUNCT
ejpam-4427	461	6	...........	...........	PUNCT
ejpam-4427	461	7	...........	...........	PUNCT
ejpam-4427	461	8	...........	...........	PUNCT
ejpam-4427	461	9	...........	...........	PUNCT
ejpam-4427	461	10	...........	...........	PUNCT
ejpam-4427	461	11	...........	...........	PUNCT
ejpam-4427	461	12	...........	...........	PUNCT
ejpam-4427	461	13	...........	...........	PUNCT
ejpam-4427	461	14	...	...	PUNCT
ejpam-4427	461	15	.........	.........	PUNCT
ejpam-4427	461	16	........	........	PUNCT
ejpam-4427	461	17	........	........	PUNCT
ejpam-4427	461	18	........	........	PUNCT
ejpam-4427	461	19	........	........	PUNCT
ejpam-4427	461	20	........	........	PUNCT
ejpam-4427	461	21	........	........	PUNCT
ejpam-4427	461	22	........	........	PUNCT
ejpam-4427	461	23	........	........	PUNCT
ejpam-4427	461	24	........	........	PUNCT
ejpam-4427	461	25	........	........	PUNCT
ejpam-4427	462	1	....	....	PUNCT
ejpam-4427	462	2	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4427	463	1	.........................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................	PUNCT
ejpam-4427	463	2	...........	...........	PUNCT
ejpam-4427	463	3	...........	...........	PUNCT
ejpam-4427	463	4	...........	...........	PUNCT
ejpam-4427	463	5	...........	...........	PUNCT
ejpam-4427	463	6	...........	...........	PUNCT
ejpam-4427	463	7	...........	...........	PUNCT
ejpam-4427	463	8	...........	...........	PUNCT
ejpam-4427	463	9	...........	...........	PUNCT
ejpam-4427	463	10	...........	...........	PUNCT
ejpam-4427	463	11	...........	...........	PUNCT
ejpam-4427	463	12	...........	...........	PUNCT
ejpam-4427	463	13	...	...	PUNCT
ejpam-4427	464	1	...................	...................	PUNCT
ejpam-4427	464	2	..................	..................	PUNCT
ejpam-4427	465	1	..................	..................	PUNCT
ejpam-4427	465	2	..................	..................	PUNCT
ejpam-4427	466	1	..................	..................	PUNCT
ejpam-4427	466	2	..................	..................	PUNCT
ejpam-4427	467	1	..................	..................	PUNCT
ejpam-4427	467	2	..................	..................	PUNCT
ejpam-4427	468	1	..................	..................	PUNCT
ejpam-4427	468	2	..................	..................	PUNCT
ejpam-4427	469	1	..................	..................	PUNCT
ejpam-4427	469	2	..................	..................	PUNCT
ejpam-4427	470	1	....	....	PUNCT
ejpam-4427	470	2	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4427	471	1	.........................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................	PUNCT
ejpam-4427	471	2	...........	...........	PUNCT
ejpam-4427	471	3	...........	...........	PUNCT
ejpam-4427	471	4	...........	...........	PUNCT
ejpam-4427	471	5	...........	...........	PUNCT
ejpam-4427	471	6	...........	...........	PUNCT
ejpam-4427	471	7	...........	...........	PUNCT
ejpam-4427	471	8	...........	...........	PUNCT
ejpam-4427	471	9	...........	...........	PUNCT
ejpam-4427	471	10	...........	...........	PUNCT
ejpam-4427	471	11	...........	...........	PUNCT
ejpam-4427	471	12	...........	...........	PUNCT
ejpam-4427	471	13	...	...	PUNCT
ejpam-4427	472	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4427	472	2	.............................................................................................................................................................................................................................	.............................................................................................................................................................................................................................	PUNCT
ejpam-4427	472	3	...................	...................	PUNCT
ejpam-4427	472	4	..................	..................	PUNCT
ejpam-4427	472	5	..................	..................	PUNCT
ejpam-4427	472	6	..................	..................	PUNCT
ejpam-4427	472	7	..................	..................	PUNCT
ejpam-4427	472	8	..................	..................	PUNCT
ejpam-4427	472	9	..................	..................	PUNCT
ejpam-4427	472	10	..................	..................	PUNCT
ejpam-4427	472	11	..................	..................	PUNCT
ejpam-4427	472	12	..................	..................	PUNCT
ejpam-4427	472	13	..................	..................	PUNCT
ejpam-4427	472	14	..................	..................	PUNCT
ejpam-4427	473	1	....	....	PUNCT
ejpam-4427	473	2	............	............	PUNCT
ejpam-4427	473	3	...........	...........	PUNCT
ejpam-4427	473	4	...........	...........	PUNCT
ejpam-4427	473	5	...........	...........	PUNCT
ejpam-4427	473	6	...........	...........	PUNCT
ejpam-4427	473	7	...........	...........	PUNCT
ejpam-4427	473	8	...........	...........	PUNCT
ejpam-4427	473	9	...........	...........	PUNCT
ejpam-4427	473	10	...........	...........	PUNCT
ejpam-4427	473	11	...........	...........	PUNCT
ejpam-4427	473	12	...........	...........	PUNCT
ejpam-4427	473	13	...........	...........	PUNCT
ejpam-4427	473	14	...	...	PUNCT
ejpam-4427	473	15	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4427	473	16	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4427	474	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4427	474	2	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4427	474	3	............	............	PUNCT
ejpam-4427	475	1	...........	...........	PUNCT
ejpam-4427	475	2	...........	...........	PUNCT
ejpam-4427	475	3	...........	...........	PUNCT
ejpam-4427	475	4	...........	...........	PUNCT
ejpam-4427	475	5	...........	...........	PUNCT
ejpam-4427	475	6	...........	...........	PUNCT
ejpam-4427	475	7	...........	...........	PUNCT
ejpam-4427	475	8	...........	...........	PUNCT
ejpam-4427	475	9	...........	...........	PUNCT
ejpam-4427	475	10	...........	...........	PUNCT
ejpam-4427	475	11	...........	...........	PUNCT
ejpam-4427	475	12	...	...	PUNCT
ejpam-4427	475	13	...................	...................	PUNCT
ejpam-4427	476	1	..................	..................	PUNCT
ejpam-4427	476	2	..................	..................	PUNCT
ejpam-4427	477	1	..................	..................	PUNCT
ejpam-4427	477	2	..................	..................	PUNCT
ejpam-4427	478	1	..................	..................	PUNCT
ejpam-4427	478	2	..................	..................	PUNCT
ejpam-4427	479	1	..................	..................	PUNCT
ejpam-4427	479	2	..................	..................	PUNCT
ejpam-4427	480	1	..................	..................	PUNCT
ejpam-4427	480	2	..................	..................	PUNCT
ejpam-4427	481	1	..................	..................	PUNCT
ejpam-4427	481	2	....	....	PUNCT
ejpam-4427	481	3	............	............	PUNCT
ejpam-4427	481	4	...........	...........	PUNCT
ejpam-4427	481	5	...........	...........	PUNCT
ejpam-4427	481	6	...........	...........	PUNCT
ejpam-4427	481	7	...........	...........	PUNCT
ejpam-4427	481	8	...........	...........	PUNCT
ejpam-4427	481	9	...........	...........	PUNCT
ejpam-4427	481	10	...........	...........	PUNCT
ejpam-4427	481	11	...........	...........	PUNCT
ejpam-4427	481	12	...........	...........	PUNCT
ejpam-4427	481	13	...........	...........	PUNCT
ejpam-4427	481	14	...........	...........	PUNCT
ejpam-4427	481	15	...	...	PUNCT
ejpam-4427	482	1	•	•	NUM
ejpam-4427	482	2	•	•	NUM
ejpam-4427	482	3	•	•	NUM
ejpam-4427	482	4	•	•	NUM
ejpam-4427	482	5	•	•	NUM
ejpam-4427	482	6	•	•	NUM
ejpam-4427	482	7	•	•	NOUN
ejpam-4427	482	8	•	•	NUM
ejpam-4427	482	9	figure	figure	NOUN
ejpam-4427	482	10	3	3	NUM
ejpam-4427	482	11	:	:	PUNCT
ejpam-4427	482	12	a	a	DET
ejpam-4427	482	13	graph	graph	NOUN
ejpam-4427	482	14	p4[p3	p4[p3	NOUN
ejpam-4427	482	15	]	]	X
ejpam-4427	482	16	with	with	ADP
ejpam-4427	482	17	rdim2	rdim2	PROPN
ejpam-4427	483	1	p4[p3	p4[p3	NOUN
ejpam-4427	483	2	]	]	X
ejpam-4427	483	3	=	=	SYM
ejpam-4427	483	4	8	8	NUM
ejpam-4427	483	5	acknowledgements	acknowledgement	NOUN
ejpam-4427	483	6	the	the	DET
ejpam-4427	483	7	authors	author	NOUN
ejpam-4427	483	8	would	would	AUX
ejpam-4427	483	9	like	like	VERB
ejpam-4427	483	10	to	to	PART
ejpam-4427	483	11	thank	thank	VERB
ejpam-4427	483	12	the	the	DET
ejpam-4427	483	13	commission	commission	NOUN
ejpam-4427	483	14	on	on	ADP
ejpam-4427	483	15	higher	high	ADJ
ejpam-4427	483	16	education	education	NOUN
ejpam-4427	483	17	(	(	PUNCT
ejpam-4427	483	18	ched	che	VERB
ejpam-4427	483	19	)	)	PUNCT
ejpam-4427	483	20	and	and	CCONJ
ejpam-4427	483	21	mindanao	mindanao	PROPN
ejpam-4427	483	22	state	state	PROPN
ejpam-4427	483	23	university	university	PROPN
ejpam-4427	483	24	-	-	PUNCT
ejpam-4427	483	25	marawi	marawi	PROPN
ejpam-4427	483	26	and	and	CCONJ
ejpam-4427	483	27	msu	msu	PROPN
ejpam-4427	483	28	-	-	PUNCT
ejpam-4427	483	29	iligan	iligan	PROPN
ejpam-4427	483	30	institute	institute	PROPN
ejpam-4427	483	31	of	of	ADP
ejpam-4427	483	32	technology	technology	PROPN
ejpam-4427	483	33	,	,	PUNCT
ejpam-4427	483	34	philippines	philippine	NOUN
ejpam-4427	483	35	.	.	PUNCT
ejpam-4427	484	1	references	reference	NOUN
ejpam-4427	484	2	[	[	X
ejpam-4427	484	3	1	1	NUM
ejpam-4427	484	4	]	]	X
ejpam-4427	484	5	r	r	NOUN
ejpam-4427	484	6	bailey	bailey	NOUN
ejpam-4427	484	7	and	and	CCONJ
ejpam-4427	484	8	i	i	PRON
ejpam-4427	484	9	yero	yero	PROPN
ejpam-4427	484	10	.	.	PUNCT
ejpam-4427	485	1	error	error	NOUN
ejpam-4427	485	2	-	-	PUNCT
ejpam-4427	485	3	correcting	correct	VERB
ejpam-4427	485	4	codes	code	NOUN
ejpam-4427	485	5	from	from	ADP
ejpam-4427	485	6	k	k	ADJ
ejpam-4427	485	7	-	-	PUNCT
ejpam-4427	485	8	resolving	resolving	ADJ
ejpam-4427	485	9	sets	set	NOUN
ejpam-4427	485	10	.	.	PUNCT
ejpam-4427	486	1	discussiones	discussione	NOUN
ejpam-4427	486	2	mathematicae	mathematicae	VERB
ejpam-4427	486	3	,	,	PUNCT
ejpam-4427	486	4	graph	graph	NOUN
ejpam-4427	486	5	theory	theory	NOUN
ejpam-4427	486	6	,	,	PUNCT
ejpam-4427	486	7	39:341–355	39:341–355	PROPN
ejpam-4427	486	8	,	,	PUNCT
ejpam-4427	486	9	2019	2019	NUM
ejpam-4427	486	10	.	.	PUNCT
ejpam-4427	487	1	[	[	X
ejpam-4427	487	2	2	2	NUM
ejpam-4427	487	3	]	]	SYM
ejpam-4427	487	4	j	j	PROPN
ejpam-4427	487	5	estrada	estrada	PROPN
ejpam-4427	487	6	-	-	PUNCT
ejpam-4427	487	7	moreno	moreno	PROPN
ejpam-4427	487	8	,	,	PUNCT
ejpam-4427	487	9	a	a	DET
ejpam-4427	487	10	rodriguez	rodriguez	NOUN
ejpam-4427	487	11	-	-	PUNCT
ejpam-4427	487	12	velasquez	velasquez	PROPN
ejpam-4427	487	13	and	and	CCONJ
ejpam-4427	487	14	i	i	PRON
ejpam-4427	487	15	yero	yero	NOUN
ejpam-4427	487	16	.	.	PUNCT
ejpam-4427	488	1	the	the	DET
ejpam-4427	488	2	k	k	ADJ
ejpam-4427	488	3	-	-	ADJ
ejpam-4427	488	4	metric	metric	ADJ
ejpam-4427	488	5	dimension	dimension	NOUN
ejpam-4427	488	6	of	of	ADP
ejpam-4427	488	7	a	a	DET
ejpam-4427	488	8	graph	graph	NOUN
ejpam-4427	488	9	.	.	PUNCT
ejpam-4427	489	1	applied	apply	VERB
ejpam-4427	489	2	math	math	NOUN
ejpam-4427	489	3	information	information	NOUN
ejpam-4427	489	4	science	science	NOUN
ejpam-4427	489	5	.	.	PUNCT
ejpam-4427	489	6	,	,	PUNCT
ejpam-4427	489	7	9:2829–2840	9:2829–2840	NUM
ejpam-4427	489	8	,	,	PUNCT
ejpam-4427	489	9	2015	2015	NUM
ejpam-4427	489	10	.	.	PUNCT
ejpam-4427	490	1	[	[	X
ejpam-4427	490	2	3	3	X
ejpam-4427	490	3	]	]	X
ejpam-4427	490	4	f	f	PROPN
ejpam-4427	490	5	harary	harary	NOUN
ejpam-4427	490	6	.	.	PUNCT
ejpam-4427	491	1	graph	graph	NOUN
ejpam-4427	491	2	theory	theory	NOUN
ejpam-4427	491	3	.	.	PUNCT
ejpam-4427	492	1	addison	addison	PROPN
ejpam-4427	492	2	-	-	PUNCT
ejpam-4427	492	3	wesley	wesley	PROPN
ejpam-4427	492	4	publishing	publishing	PROPN
ejpam-4427	492	5	company	company	NOUN
ejpam-4427	492	6	,	,	PUNCT
ejpam-4427	492	7	usa	usa	PROPN
ejpam-4427	492	8	,	,	PUNCT
ejpam-4427	492	9	1969	1969	NUM
ejpam-4427	492	10	.	.	PUNCT
ejpam-4427	493	1	[	[	X
ejpam-4427	493	2	4	4	X
ejpam-4427	493	3	]	]	X
ejpam-4427	493	4	f	f	PROPN
ejpam-4427	493	5	harary	harary	NOUN
ejpam-4427	493	6	and	and	CCONJ
ejpam-4427	493	7	r	r	NOUN
ejpam-4427	493	8	melter	melter	NOUN
ejpam-4427	493	9	.	.	PUNCT
ejpam-4427	494	1	on	on	ADP
ejpam-4427	494	2	the	the	DET
ejpam-4427	494	3	metric	metric	ADJ
ejpam-4427	494	4	dimension	dimension	NOUN
ejpam-4427	494	5	of	of	ADP
ejpam-4427	494	6	a	a	DET
ejpam-4427	494	7	graph	graph	NOUN
ejpam-4427	494	8	.	.	PUNCT
ejpam-4427	495	1	ars	ars	PROPN
ejpam-4427	495	2	combinatoria	combinatoria	PROPN
ejpam-4427	495	3	,	,	PUNCT
ejpam-4427	495	4	2	2	NUM
ejpam-4427	495	5	,	,	PUNCT
ejpam-4427	495	6	1976	1976	NUM
ejpam-4427	495	7	.	.	PUNCT
ejpam-4427	496	1	[	[	X
ejpam-4427	496	2	5	5	NUM
ejpam-4427	496	3	]	]	PUNCT
ejpam-4427	496	4	h	h	NOUN
ejpam-4427	496	5	rara	rara	NOUN
ejpam-4427	496	6	and	and	CCONJ
ejpam-4427	496	7	j	j	PROPN
ejpam-4427	496	8	cabaro	cabaro	NOUN
ejpam-4427	496	9	.	.	PUNCT
ejpam-4427	497	1	on	on	ADP
ejpam-4427	497	2	2	2	NUM
ejpam-4427	497	3	-	-	PUNCT
ejpam-4427	497	4	resolving	resolve	VERB
ejpam-4427	497	5	sets	set	NOUN
ejpam-4427	497	6	in	in	ADP
ejpam-4427	497	7	the	the	DET
ejpam-4427	497	8	join	join	NOUN
ejpam-4427	497	9	and	and	CCONJ
ejpam-4427	497	10	corona	corona	NOUN
ejpam-4427	497	11	of	of	ADP
ejpam-4427	497	12	graphs	graph	NOUN
ejpam-4427	497	13	.	.	PUNCT
ejpam-4427	498	1	european	european	ADJ
ejpam-4427	498	2	journal	journal	PROPN
ejpam-4427	498	3	of	of	ADP
ejpam-4427	498	4	pure	pure	ADJ
ejpam-4427	498	5	and	and	CCONJ
ejpam-4427	498	6	applied	applied	ADJ
ejpam-4427	498	7	mathematics	mathematic	NOUN
ejpam-4427	498	8	,	,	PUNCT
ejpam-4427	498	9	14:773–782	14:773–782	NUM
ejpam-4427	498	10	,	,	PUNCT
ejpam-4427	498	11	2021	2021	NUM
ejpam-4427	498	12	.	.	PUNCT
ejpam-4427	499	1	[	[	X
ejpam-4427	499	2	6	6	NUM
ejpam-4427	499	3	]	]	SYM
ejpam-4427	499	4	v	v	PART
ejpam-4427	499	5	lokesha	lokesha	VERB
ejpam-4427	499	6	a	a	DET
ejpam-4427	499	7	s	s	NOUN
ejpam-4427	499	8	cevik	cevik	NOUN
ejpam-4427	499	9	,	,	PUNCT
ejpam-4427	499	10	jain	jain	NOUN
ejpam-4427	499	11	and	and	CCONJ
ejpam-4427	499	12	i.	i.	PROPN
ejpam-4427	499	13	cangul	cangul	PROPN
ejpam-4427	499	14	.	.	PUNCT
ejpam-4427	500	1	new	new	ADJ
ejpam-4427	500	2	results	result	NOUN
ejpam-4427	500	3	on	on	ADP
ejpam-4427	500	4	the	the	DET
ejpam-4427	500	5	f	f	NOUN
ejpam-4427	500	6	-	-	PUNCT
ejpam-4427	500	7	index	index	NOUN
ejpam-4427	500	8	of	of	ADP
ejpam-4427	500	9	graphs	graph	NOUN
ejpam-4427	500	10	based	base	VERB
ejpam-4427	500	11	on	on	ADP
ejpam-4427	500	12	corona	corona	NOUN
ejpam-4427	500	13	-	-	PUNCT
ejpam-4427	500	14	type	type	NOUN
ejpam-4427	500	15	of	of	ADP
ejpam-4427	500	16	graphs	graph	NOUN
ejpam-4427	500	17	.	.	PUNCT
ejpam-4427	501	1	proc	proc	NOUN
ejpam-4427	501	2	.	.	PUNCT
ejpam-4427	502	1	of	of	ADP
ejpam-4427	502	2	the	the	DET
ejpam-4427	502	3	jangjeon	jangjeon	PROPN
ejpam-4427	502	4	mathematical	mathematical	PROPN
ejpam-4427	502	5	society	society	NOUN
ejpam-4427	502	6	,	,	PUNCT
ejpam-4427	502	7	23(2):141–147	23(2):141–147	PROPN
ejpam-4427	502	8	,	,	PUNCT
ejpam-4427	502	9	2020	2020	NUM
ejpam-4427	503	1	.	.	PUNCT
ejpam-4427	504	1	[	[	X
ejpam-4427	504	2	7	7	NUM
ejpam-4427	504	3	]	]	SYM
ejpam-4427	504	4	v	v	ADP
ejpam-4427	504	5	saenpholphat	saenpholphat	NOUN
ejpam-4427	504	6	and	and	CCONJ
ejpam-4427	504	7	p	p	PROPN
ejpam-4427	504	8	zang	zang	PROPN
ejpam-4427	504	9	.	.	PUNCT
ejpam-4427	505	1	on	on	ADP
ejpam-4427	505	2	connected	connected	ADJ
ejpam-4427	505	3	resolvability	resolvability	NOUN
ejpam-4427	505	4	of	of	ADP
ejpam-4427	505	5	graphs	graph	NOUN
ejpam-4427	505	6	.	.	PUNCT
ejpam-4427	506	1	australian	australian	ADJ
ejpam-4427	506	2	journal	journal	NOUN
ejpam-4427	506	3	of	of	ADP
ejpam-4427	506	4	combinatorics	combinatoric	NOUN
ejpam-4427	506	5	,	,	PUNCT
ejpam-4427	506	6	28:25–37	28:25–37	NUM
ejpam-4427	506	7	,	,	PUNCT
ejpam-4427	506	8	2003	2003	NUM
ejpam-4427	506	9	.	.	PUNCT
ejpam-4427	507	1	[	[	X
ejpam-4427	507	2	8	8	NUM
ejpam-4427	507	3	]	]	X
ejpam-4427	507	4	p.	p.	PROPN
ejpam-4427	507	5	slater	slater	PROPN
ejpam-4427	507	6	.	.	PUNCT
ejpam-4427	508	1	congressus	congressus	PROPN
ejpam-4427	508	2	numerantium	numerantium	PROPN
ejpam-4427	508	3	,	,	PUNCT
ejpam-4427	508	4	.	.	PUNCT
ejpam-4427	508	5	,	,	PUNCT
ejpam-4427	509	1	14:549–559	14:549–559	NUM
ejpam-4427	509	2	,	,	PUNCT
ejpam-4427	509	3	1975	1975	NUM
ejpam-4427	509	4	.	.	PUNCT