id	sid	tid	token	lemma	pos
ejpam-4426	1	1	european	european	PROPN
ejpam-4426	1	2	journal	journal	PROPN
ejpam-4426	1	3	of	of	ADP
ejpam-4426	1	4	pure	pure	ADJ
ejpam-4426	1	5	and	and	CCONJ
ejpam-4426	1	6	applied	apply	VERB
ejpam-4426	1	7	mathematics	mathematic	NOUN
ejpam-4426	1	8	vol	vol	NOUN
ejpam-4426	1	9	.	.	PROPN
ejpam-4426	2	1	15	15	NUM
ejpam-4426	2	2	,	,	PUNCT
ejpam-4426	2	3	no	no	INTJ
ejpam-4426	2	4	.	.	NOUN
ejpam-4426	2	5	3	3	NUM
ejpam-4426	2	6	,	,	PUNCT
ejpam-4426	2	7	2022	2022	NUM
ejpam-4426	2	8	,	,	PUNCT
ejpam-4426	2	9	1417	1417	NUM
ejpam-4426	2	10	-	-	SYM
ejpam-4426	2	11	1425	1425	NUM
ejpam-4426	2	12	issn	issn	PROPN
ejpam-4426	2	13	1307	1307	NUM
ejpam-4426	2	14	-	-	SYM
ejpam-4426	2	15	5543	5543	NUM
ejpam-4426	2	16	–	–	PUNCT
ejpam-4426	3	1	ejpam.com	ejpam.com	X
ejpam-4426	3	2	published	publish	VERB
ejpam-4426	3	3	by	by	ADP
ejpam-4426	3	4	new	new	PROPN
ejpam-4426	3	5	york	york	PROPN
ejpam-4426	3	6	business	business	PROPN
ejpam-4426	3	7	global	global	ADJ
ejpam-4426	3	8	on	on	ADP
ejpam-4426	3	9	2	2	NUM
ejpam-4426	3	10	-	-	PUNCT
ejpam-4426	3	11	resolving	resolve	VERB
ejpam-4426	3	12	dominating	dominating	NOUN
ejpam-4426	3	13	sets	set	NOUN
ejpam-4426	3	14	in	in	ADP
ejpam-4426	3	15	the	the	DET
ejpam-4426	3	16	join	join	NOUN
ejpam-4426	3	17	,	,	PUNCT
ejpam-4426	3	18	corona	corona	NOUN
ejpam-4426	3	19	and	and	CCONJ
ejpam-4426	3	20	lexicographic	lexicographic	ADJ
ejpam-4426	3	21	product	product	NOUN
ejpam-4426	3	22	of	of	ADP
ejpam-4426	3	23	two	two	NUM
ejpam-4426	3	24	graphs	graph	NOUN
ejpam-4426	3	25	jean	jean	PROPN
ejpam-4426	3	26	cabaro1,∗	cabaro1,∗	PROPN
ejpam-4426	3	27	,	,	PUNCT
ejpam-4426	3	28	helen	helen	PROPN
ejpam-4426	3	29	rara2	rara2	PROPN
ejpam-4426	3	30	1	1	NUM
ejpam-4426	3	31	mathematics	mathematics	PROPN
ejpam-4426	3	32	department	department	NOUN
ejpam-4426	3	33	,	,	PUNCT
ejpam-4426	3	34	college	college	NOUN
ejpam-4426	3	35	of	of	ADP
ejpam-4426	3	36	natural	natural	ADJ
ejpam-4426	3	37	sciences	science	NOUN
ejpam-4426	3	38	and	and	CCONJ
ejpam-4426	3	39	mathematics	mathematic	NOUN
ejpam-4426	3	40	,	,	PUNCT
ejpam-4426	3	41	mindanao	mindanao	PROPN
ejpam-4426	3	42	state	state	PROPN
ejpam-4426	3	43	university	university	NOUN
ejpam-4426	3	44	-	-	PUNCT
ejpam-4426	3	45	main	main	ADJ
ejpam-4426	3	46	campus	campus	NOUN
ejpam-4426	3	47	,	,	PUNCT
ejpam-4426	3	48	9700	9700	NUM
ejpam-4426	3	49	marawi	marawi	PROPN
ejpam-4426	3	50	city	city	PROPN
ejpam-4426	3	51	,	,	PUNCT
ejpam-4426	3	52	philippines	philippines	PROPN
ejpam-4426	3	53	2	2	NUM
ejpam-4426	3	54	department	department	NOUN
ejpam-4426	3	55	of	of	ADP
ejpam-4426	3	56	mathematics	mathematic	NOUN
ejpam-4426	3	57	and	and	CCONJ
ejpam-4426	3	58	statistics	statistic	NOUN
ejpam-4426	3	59	,	,	PUNCT
ejpam-4426	3	60	college	college	NOUN
ejpam-4426	3	61	of	of	ADP
ejpam-4426	3	62	science	science	NOUN
ejpam-4426	3	63	and	and	CCONJ
ejpam-4426	3	64	mathematics	mathematic	NOUN
ejpam-4426	3	65	,	,	PUNCT
ejpam-4426	3	66	center	center	NOUN
ejpam-4426	3	67	of	of	ADP
ejpam-4426	3	68	graph	graph	NOUN
ejpam-4426	3	69	theory	theory	NOUN
ejpam-4426	3	70	,	,	PUNCT
ejpam-4426	3	71	algebra	algebra	NOUN
ejpam-4426	3	72	,	,	PUNCT
ejpam-4426	3	73	and	and	CCONJ
ejpam-4426	3	74	analysis	analysis	NOUN
ejpam-4426	3	75	-	-	PUNCT
ejpam-4426	3	76	premier	premier	NOUN
ejpam-4426	3	77	research	research	NOUN
ejpam-4426	3	78	institute	institute	PROPN
ejpam-4426	3	79	of	of	ADP
ejpam-4426	3	80	science	science	NOUN
ejpam-4426	3	81	and	and	CCONJ
ejpam-4426	3	82	mathematics	mathematic	NOUN
ejpam-4426	3	83	,	,	PUNCT
ejpam-4426	3	84	mindanao	mindanao	PROPN
ejpam-4426	3	85	state	state	PROPN
ejpam-4426	3	86	university	university	PROPN
ejpam-4426	3	87	-	-	PUNCT
ejpam-4426	3	88	iligan	iligan	PROPN
ejpam-4426	3	89	institute	institute	PROPN
ejpam-4426	3	90	of	of	ADP
ejpam-4426	3	91	technology	technology	PROPN
ejpam-4426	3	92	,	,	PUNCT
ejpam-4426	3	93	9200	9200	NUM
ejpam-4426	3	94	iligan	iligan	ADJ
ejpam-4426	3	95	city	city	NOUN
ejpam-4426	3	96	,	,	PUNCT
ejpam-4426	3	97	philippines	philippine	NOUN
ejpam-4426	3	98	abstract	abstract	ADJ
ejpam-4426	3	99	.	.	PUNCT
ejpam-4426	4	1	let	let	VERB
ejpam-4426	4	2	g	g	PRON
ejpam-4426	4	3	be	be	AUX
ejpam-4426	4	4	a	a	DET
ejpam-4426	4	5	connected	connected	ADJ
ejpam-4426	4	6	graph	graph	NOUN
ejpam-4426	4	7	.	.	PUNCT
ejpam-4426	5	1	an	an	DET
ejpam-4426	5	2	ordered	order	VERB
ejpam-4426	5	3	set	set	NOUN
ejpam-4426	5	4	of	of	ADP
ejpam-4426	5	5	vertices	vertex	NOUN
ejpam-4426	5	6	{	{	PUNCT
ejpam-4426	5	7	v1	v1	NOUN
ejpam-4426	5	8	,	,	PUNCT
ejpam-4426	5	9	...	...	PUNCT
ejpam-4426	5	10	,	,	PUNCT
ejpam-4426	5	11	vl	vl	ADJ
ejpam-4426	5	12	}	}	PUNCT
ejpam-4426	5	13	is	be	AUX
ejpam-4426	5	14	a	a	DET
ejpam-4426	5	15	2	2	NUM
ejpam-4426	5	16	-	-	PUNCT
ejpam-4426	5	17	resolving	resolving	NOUN
ejpam-4426	5	18	set	set	NOUN
ejpam-4426	5	19	for	for	ADP
ejpam-4426	5	20	g	g	PROPN
ejpam-4426	5	21	if	if	SCONJ
ejpam-4426	5	22	,	,	PUNCT
ejpam-4426	5	23	for	for	ADP
ejpam-4426	5	24	any	any	DET
ejpam-4426	5	25	distinct	distinct	ADJ
ejpam-4426	5	26	vertices	vertex	NOUN
ejpam-4426	5	27	u	u	NOUN
ejpam-4426	5	28	,	,	PUNCT
ejpam-4426	5	29	w	w	PROPN
ejpam-4426	5	30	∈	∈	PROPN
ejpam-4426	5	31	v	v	ADP
ejpam-4426	5	32	(	(	PUNCT
ejpam-4426	5	33	g	g	NOUN
ejpam-4426	5	34	)	)	PUNCT
ejpam-4426	5	35	,	,	PUNCT
ejpam-4426	5	36	the	the	DET
ejpam-4426	5	37	lists	list	NOUN
ejpam-4426	5	38	of	of	ADP
ejpam-4426	5	39	distances	distance	NOUN
ejpam-4426	5	40	(	(	PUNCT
ejpam-4426	5	41	dg(u	dg(u	X
ejpam-4426	5	42	,	,	PUNCT
ejpam-4426	5	43	v1	v1	NOUN
ejpam-4426	5	44	)	)	PUNCT
ejpam-4426	5	45	,	,	PUNCT
ejpam-4426	5	46	...	...	PUNCT
ejpam-4426	5	47	,	,	PUNCT
ejpam-4426	5	48	dg(u	dg(u	X
ejpam-4426	5	49	,	,	PUNCT
ejpam-4426	5	50	vl	vl	NOUN
ejpam-4426	5	51	)	)	PUNCT
ejpam-4426	5	52	)	)	PUNCT
ejpam-4426	5	53	and	and	CCONJ
ejpam-4426	5	54	(	(	PUNCT
ejpam-4426	5	55	dg(w	dg(w	X
ejpam-4426	5	56	,	,	PUNCT
ejpam-4426	5	57	v1	v1	NOUN
ejpam-4426	5	58	)	)	PUNCT
ejpam-4426	5	59	,	,	PUNCT
ejpam-4426	5	60	...	...	PUNCT
ejpam-4426	5	61	,	,	PUNCT
ejpam-4426	5	62	dg(w	dg(w	X
ejpam-4426	5	63	,	,	PUNCT
ejpam-4426	5	64	vl	vl	NOUN
ejpam-4426	5	65	)	)	PUNCT
ejpam-4426	5	66	)	)	PUNCT
ejpam-4426	5	67	differ	differ	VERB
ejpam-4426	5	68	in	in	ADP
ejpam-4426	5	69	at	at	ADV
ejpam-4426	5	70	least	least	ADJ
ejpam-4426	5	71	2	2	NUM
ejpam-4426	5	72	positions	position	NOUN
ejpam-4426	5	73	.	.	PUNCT
ejpam-4426	6	1	a	a	DET
ejpam-4426	6	2	2	2	NUM
ejpam-4426	6	3	-	-	PUNCT
ejpam-4426	6	4	resolving	resolve	VERB
ejpam-4426	6	5	set	set	NOUN
ejpam-4426	6	6	s	s	PROPN
ejpam-4426	6	7	⊆	⊆	NUM
ejpam-4426	6	8	v	v	NOUN
ejpam-4426	6	9	(	(	PUNCT
ejpam-4426	6	10	g	g	NOUN
ejpam-4426	6	11	)	)	PUNCT
ejpam-4426	6	12	which	which	PRON
ejpam-4426	6	13	is	be	AUX
ejpam-4426	6	14	dominating	dominate	VERB
ejpam-4426	6	15	is	be	AUX
ejpam-4426	6	16	called	call	VERB
ejpam-4426	6	17	a	a	DET
ejpam-4426	6	18	2	2	NUM
ejpam-4426	6	19	-	-	PUNCT
ejpam-4426	6	20	resolving	resolve	VERB
ejpam-4426	6	21	dominating	dominating	NOUN
ejpam-4426	6	22	set	set	NOUN
ejpam-4426	6	23	or	or	CCONJ
ejpam-4426	6	24	simply	simply	ADV
ejpam-4426	6	25	2r	2r	NUM
ejpam-4426	6	26	-	-	PUNCT
ejpam-4426	6	27	dominating	dominate	VERB
ejpam-4426	6	28	set	set	NOUN
ejpam-4426	6	29	in	in	ADP
ejpam-4426	6	30	g.	g.	PROPN
ejpam-4426	6	31	the	the	DET
ejpam-4426	6	32	minimum	minimum	ADJ
ejpam-4426	6	33	cardinality	cardinality	NOUN
ejpam-4426	6	34	of	of	ADP
ejpam-4426	6	35	a	a	DET
ejpam-4426	6	36	2	2	NUM
ejpam-4426	6	37	-	-	PUNCT
ejpam-4426	6	38	resolving	resolve	VERB
ejpam-4426	6	39	dominating	dominating	NOUN
ejpam-4426	6	40	set	set	VERB
ejpam-4426	6	41	in	in	ADP
ejpam-4426	6	42	g	g	NOUN
ejpam-4426	6	43	,	,	PUNCT
ejpam-4426	6	44	denoted	denote	VERB
ejpam-4426	6	45	by	by	ADP
ejpam-4426	6	46	γ2r(g	γ2r(g	PROPN
ejpam-4426	6	47	)	)	PUNCT
ejpam-4426	6	48	,	,	PUNCT
ejpam-4426	6	49	is	be	AUX
ejpam-4426	6	50	called	call	VERB
ejpam-4426	6	51	the	the	DET
ejpam-4426	6	52	2r	2r	NUM
ejpam-4426	6	53	-	-	PUNCT
ejpam-4426	6	54	domination	domination	NOUN
ejpam-4426	6	55	number	number	NOUN
ejpam-4426	6	56	of	of	ADP
ejpam-4426	6	57	g.	g.	PROPN
ejpam-4426	6	58	any	any	DET
ejpam-4426	6	59	2r	2r	NUM
ejpam-4426	6	60	-	-	PUNCT
ejpam-4426	6	61	dominating	dominate	VERB
ejpam-4426	6	62	set	set	NOUN
ejpam-4426	6	63	of	of	ADP
ejpam-4426	6	64	cardinality	cardinality	NOUN
ejpam-4426	6	65	γ2r(g	γ2r(g	PROPN
ejpam-4426	6	66	)	)	PUNCT
ejpam-4426	7	1	is	be	AUX
ejpam-4426	7	2	then	then	ADV
ejpam-4426	7	3	referred	refer	VERB
ejpam-4426	7	4	to	to	ADP
ejpam-4426	7	5	as	as	ADP
ejpam-4426	7	6	a	a	DET
ejpam-4426	7	7	γ2r	γ2r	ADV
ejpam-4426	7	8	-	-	PUNCT
ejpam-4426	7	9	set	set	NOUN
ejpam-4426	7	10	in	in	ADP
ejpam-4426	7	11	g.	g.	PROPN
ejpam-4426	7	12	this	this	DET
ejpam-4426	7	13	study	study	NOUN
ejpam-4426	7	14	deals	deal	VERB
ejpam-4426	7	15	with	with	ADP
ejpam-4426	7	16	the	the	DET
ejpam-4426	7	17	concept	concept	NOUN
ejpam-4426	7	18	of	of	ADP
ejpam-4426	7	19	2	2	NUM
ejpam-4426	7	20	-	-	PUNCT
ejpam-4426	7	21	resolving	resolve	VERB
ejpam-4426	7	22	dominating	dominating	NOUN
ejpam-4426	7	23	set	set	NOUN
ejpam-4426	7	24	of	of	ADP
ejpam-4426	7	25	a	a	DET
ejpam-4426	7	26	graph	graph	NOUN
ejpam-4426	7	27	.	.	PUNCT
ejpam-4426	8	1	it	it	PRON
ejpam-4426	8	2	characterizes	characterize	VERB
ejpam-4426	8	3	the	the	DET
ejpam-4426	8	4	2	2	NUM
ejpam-4426	8	5	-	-	PUNCT
ejpam-4426	8	6	resolving	resolve	VERB
ejpam-4426	8	7	dominating	dominating	NOUN
ejpam-4426	8	8	set	set	VERB
ejpam-4426	8	9	in	in	ADP
ejpam-4426	8	10	the	the	DET
ejpam-4426	8	11	join	join	NOUN
ejpam-4426	8	12	,	,	PUNCT
ejpam-4426	8	13	corona	corona	NOUN
ejpam-4426	8	14	and	and	CCONJ
ejpam-4426	8	15	lexicographic	lexicographic	ADJ
ejpam-4426	8	16	product	product	NOUN
ejpam-4426	8	17	of	of	ADP
ejpam-4426	8	18	two	two	NUM
ejpam-4426	8	19	graphs	graph	NOUN
ejpam-4426	8	20	and	and	CCONJ
ejpam-4426	8	21	determine	determine	VERB
ejpam-4426	8	22	the	the	DET
ejpam-4426	8	23	bounds	bound	NOUN
ejpam-4426	8	24	or	or	CCONJ
ejpam-4426	8	25	exact	exact	ADJ
ejpam-4426	8	26	values	value	NOUN
ejpam-4426	8	27	of	of	ADP
ejpam-4426	8	28	the	the	DET
ejpam-4426	8	29	2	2	NUM
ejpam-4426	8	30	-	-	PUNCT
ejpam-4426	8	31	resolving	resolve	VERB
ejpam-4426	8	32	dominating	dominating	NOUN
ejpam-4426	8	33	number	number	NOUN
ejpam-4426	8	34	of	of	ADP
ejpam-4426	8	35	these	these	DET
ejpam-4426	8	36	graphs	graph	NOUN
ejpam-4426	8	37	.	.	PUNCT
ejpam-4426	9	1	2020	2020	NUM
ejpam-4426	9	2	mathematics	mathematic	NOUN
ejpam-4426	9	3	subject	subject	NOUN
ejpam-4426	9	4	classifications	classification	NOUN
ejpam-4426	9	5	:	:	PUNCT
ejpam-4426	9	6	05c62	05c62	NUM
ejpam-4426	9	7	key	key	ADJ
ejpam-4426	9	8	words	word	NOUN
ejpam-4426	9	9	and	and	CCONJ
ejpam-4426	9	10	phrases	phrase	NOUN
ejpam-4426	9	11	:	:	PUNCT
ejpam-4426	9	12	2	2	NUM
ejpam-4426	9	13	-	-	PUNCT
ejpam-4426	9	14	resolving	resolve	VERB
ejpam-4426	9	15	set	set	NOUN
ejpam-4426	9	16	,	,	PUNCT
ejpam-4426	9	17	2	2	NUM
ejpam-4426	9	18	-	-	PUNCT
ejpam-4426	9	19	resolving	resolve	VERB
ejpam-4426	9	20	dominating	dominating	NOUN
ejpam-4426	9	21	set	set	NOUN
ejpam-4426	9	22	,	,	PUNCT
ejpam-4426	9	23	2r	2r	NUM
ejpam-4426	9	24	-	-	PUNCT
ejpam-4426	9	25	domination	domination	NOUN
ejpam-4426	9	26	number	number	NOUN
ejpam-4426	9	27	,	,	PUNCT
ejpam-4426	9	28	join	join	NOUN
ejpam-4426	9	29	,	,	PUNCT
ejpam-4426	9	30	corona	corona	PROPN
ejpam-4426	9	31	,	,	PUNCT
ejpam-4426	9	32	lexicographic	lexicographic	ADJ
ejpam-4426	9	33	product	product	NOUN
ejpam-4426	9	34	of	of	ADP
ejpam-4426	9	35	two	two	NUM
ejpam-4426	9	36	graphs	graph	NOUN
ejpam-4426	9	37	1	1	NUM
ejpam-4426	9	38	.	.	PUNCT
ejpam-4426	9	39	introduction	introduction	NOUN
ejpam-4426	9	40	the	the	DET
ejpam-4426	9	41	problem	problem	NOUN
ejpam-4426	9	42	of	of	ADP
ejpam-4426	9	43	uniquely	uniquely	ADV
ejpam-4426	9	44	determining	determine	VERB
ejpam-4426	9	45	the	the	DET
ejpam-4426	9	46	location	location	NOUN
ejpam-4426	9	47	of	of	ADP
ejpam-4426	9	48	an	an	DET
ejpam-4426	9	49	intruder	intruder	NOUN
ejpam-4426	9	50	in	in	ADP
ejpam-4426	9	51	a	a	DET
ejpam-4426	9	52	network	network	NOUN
ejpam-4426	9	53	was	be	AUX
ejpam-4426	9	54	the	the	DET
ejpam-4426	9	55	principal	principal	ADJ
ejpam-4426	9	56	motivation	motivation	NOUN
ejpam-4426	9	57	of	of	ADP
ejpam-4426	9	58	introducing	introduce	VERB
ejpam-4426	9	59	the	the	DET
ejpam-4426	9	60	concept	concept	NOUN
ejpam-4426	9	61	of	of	ADP
ejpam-4426	9	62	metric	metric	ADJ
ejpam-4426	9	63	dimension	dimension	NOUN
ejpam-4426	9	64	in	in	ADP
ejpam-4426	9	65	graphs	graph	NOUN
ejpam-4426	9	66	by	by	ADP
ejpam-4426	9	67	slater	slater	NOUN
ejpam-4426	10	1	[	[	X
ejpam-4426	10	2	7	7	NUM
ejpam-4426	10	3	]	]	PUNCT
ejpam-4426	10	4	,	,	PUNCT
ejpam-4426	10	5	where	where	SCONJ
ejpam-4426	10	6	the	the	DET
ejpam-4426	10	7	metric	metric	ADJ
ejpam-4426	10	8	generators	generator	NOUN
ejpam-4426	10	9	were	be	AUX
ejpam-4426	10	10	called	call	VERB
ejpam-4426	10	11	locating	locating	NOUN
ejpam-4426	10	12	sets	set	NOUN
ejpam-4426	10	13	.	.	PUNCT
ejpam-4426	11	1	the	the	DET
ejpam-4426	11	2	concept	concept	NOUN
ejpam-4426	11	3	of	of	ADP
ejpam-4426	11	4	metric	metric	ADJ
ejpam-4426	11	5	dimension	dimension	NOUN
ejpam-4426	11	6	of	of	ADP
ejpam-4426	11	7	a	a	DET
ejpam-4426	11	8	graph	graph	NOUN
ejpam-4426	11	9	was	be	AUX
ejpam-4426	11	10	also	also	ADV
ejpam-4426	11	11	introduced	introduce	VERB
ejpam-4426	11	12	independently	independently	ADV
ejpam-4426	11	13	by	by	ADP
ejpam-4426	11	14	harary	harary	NOUN
ejpam-4426	11	15	and	and	CCONJ
ejpam-4426	11	16	melter	melter	NOUN
ejpam-4426	11	17	in	in	ADP
ejpam-4426	11	18	[	[	X
ejpam-4426	11	19	3	3	X
ejpam-4426	11	20	]	]	PUNCT
ejpam-4426	11	21	where	where	SCONJ
ejpam-4426	11	22	metric	metric	ADJ
ejpam-4426	11	23	generators	generator	NOUN
ejpam-4426	11	24	were	be	AUX
ejpam-4426	11	25	called	call	VERB
ejpam-4426	11	26	resolving	resolve	VERB
ejpam-4426	11	27	sets	set	NOUN
ejpam-4426	11	28	.	.	PUNCT
ejpam-4426	12	1	bailey	bailey	NOUN
ejpam-4426	12	2	and	and	CCONJ
ejpam-4426	12	3	yero	yero	NOUN
ejpam-4426	12	4	in	in	ADP
ejpam-4426	12	5	[	[	X
ejpam-4426	12	6	6	6	NUM
ejpam-4426	12	7	]	]	PUNCT
ejpam-4426	12	8	demonstrated	demonstrate	VERB
ejpam-4426	12	9	a	a	DET
ejpam-4426	12	10	construction	construction	NOUN
ejpam-4426	12	11	of	of	ADP
ejpam-4426	12	12	error	error	NOUN
ejpam-4426	12	13	-	-	PUNCT
ejpam-4426	12	14	correcting	correct	VERB
ejpam-4426	12	15	codes	code	NOUN
ejpam-4426	12	16	from	from	ADP
ejpam-4426	12	17	graphs	graph	NOUN
ejpam-4426	12	18	by	by	ADP
ejpam-4426	12	19	means	mean	NOUN
ejpam-4426	12	20	of	of	ADP
ejpam-4426	12	21	k	k	ADJ
ejpam-4426	12	22	-	-	PUNCT
ejpam-4426	12	23	resolving	resolving	ADJ
ejpam-4426	12	24	sets	set	NOUN
ejpam-4426	12	25	,	,	PUNCT
ejpam-4426	12	26	and	and	CCONJ
ejpam-4426	12	27	present	present	VERB
ejpam-4426	12	28	a	a	DET
ejpam-4426	12	29	decoding	decode	VERB
ejpam-4426	12	30	algorithm	algorithm	NOUN
ejpam-4426	12	31	which	which	PRON
ejpam-4426	12	32	makes	make	VERB
ejpam-4426	12	33	use	use	NOUN
ejpam-4426	12	34	of	of	ADP
ejpam-4426	12	35	covering	cover	VERB
ejpam-4426	12	36	designs	design	NOUN
ejpam-4426	12	37	.	.	PUNCT
ejpam-4426	13	1	∗corresponding	∗corresponde	VERB
ejpam-4426	13	2	author	author	NOUN
ejpam-4426	13	3	.	.	PUNCT
ejpam-4426	14	1	doi	doi	NOUN
ejpam-4426	14	2	:	:	PUNCT
ejpam-4426	14	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4426	https://doi.org/10.29020/nybg.ejpam.v15i3.4426	NOUN
ejpam-4426	14	4	email	email	NOUN
ejpam-4426	14	5	addresses	address	VERB
ejpam-4426	14	6	:	:	PUNCT
ejpam-4426	14	7	amerjean1228@gmail.com	amerjean1228@gmail.com	X
ejpam-4426	14	8	(	(	PUNCT
ejpam-4426	14	9	j.	j.	PROPN
ejpam-4426	14	10	cabaro	cabaro	PROPN
ejpam-4426	14	11	)	)	PUNCT
ejpam-4426	14	12	,	,	PUNCT
ejpam-4426	14	13	helenrara@gmail.com	helenrara@gmail.com	X
ejpam-4426	14	14	(	(	PUNCT
ejpam-4426	14	15	h.	h.	PROPN
ejpam-4426	14	16	rara	rara	PROPN
ejpam-4426	14	17	)	)	PUNCT
ejpam-4426	14	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4426	14	19	1417	1417	NUM
ejpam-4426	15	1	©	©	PROPN
ejpam-4426	15	2	2022	2022	NUM
ejpam-4426	15	3	ejpam	ejpam	VERB
ejpam-4426	15	4	all	all	DET
ejpam-4426	15	5	rights	right	NOUN
ejpam-4426	15	6	reserved	reserve	VERB
ejpam-4426	15	7	.	.	PUNCT
ejpam-4426	16	1	j.	j.	PROPN
ejpam-4426	16	2	cabaro	cabaro	PROPN
ejpam-4426	16	3	,	,	PUNCT
ejpam-4426	16	4	h.	h.	PROPN
ejpam-4426	16	5	rara	rara	PROPN
ejpam-4426	16	6	/	/	SYM
ejpam-4426	16	7	eur	eur	PROPN
ejpam-4426	16	8	.	.	PUNCT
ejpam-4426	17	1	j.	j.	PROPN
ejpam-4426	17	2	pure	pure	PROPN
ejpam-4426	17	3	appl	appl	PROPN
ejpam-4426	17	4	.	.	PROPN
ejpam-4426	17	5	math	math	PROPN
ejpam-4426	17	6	,	,	PUNCT
ejpam-4426	17	7	15	15	NUM
ejpam-4426	17	8	(	(	PUNCT
ejpam-4426	17	9	3	3	NUM
ejpam-4426	17	10	)	)	PUNCT
ejpam-4426	17	11	(	(	PUNCT
ejpam-4426	17	12	2022	2022	NUM
ejpam-4426	17	13	)	)	PUNCT
ejpam-4426	17	14	,	,	PUNCT
ejpam-4426	17	15	1417	1417	NUM
ejpam-4426	17	16	-	-	SYM
ejpam-4426	17	17	1425	1425	NUM
ejpam-4426	17	18	1418	1418	NUM
ejpam-4426	17	19	the	the	DET
ejpam-4426	17	20	distance	distance	NOUN
ejpam-4426	17	21	between	between	ADP
ejpam-4426	17	22	two	two	NUM
ejpam-4426	17	23	vertices	vertex	NOUN
ejpam-4426	17	24	u	u	NOUN
ejpam-4426	17	25	and	and	CCONJ
ejpam-4426	17	26	v	v	NOUN
ejpam-4426	17	27	of	of	ADP
ejpam-4426	17	28	a	a	DET
ejpam-4426	17	29	graph	graph	NOUN
ejpam-4426	17	30	is	be	AUX
ejpam-4426	17	31	the	the	DET
ejpam-4426	17	32	length	length	NOUN
ejpam-4426	17	33	of	of	ADP
ejpam-4426	17	34	a	a	DET
ejpam-4426	17	35	shortest	short	ADJ
ejpam-4426	17	36	path	path	NOUN
ejpam-4426	17	37	between	between	ADP
ejpam-4426	17	38	u	u	NOUN
ejpam-4426	17	39	and	and	CCONJ
ejpam-4426	17	40	v	v	NOUN
ejpam-4426	17	41	,	,	PUNCT
ejpam-4426	17	42	and	and	CCONJ
ejpam-4426	17	43	we	we	PRON
ejpam-4426	17	44	denote	denote	VERB
ejpam-4426	17	45	this	this	PRON
ejpam-4426	17	46	by	by	ADP
ejpam-4426	17	47	dg(u	dg(u	NOUN
ejpam-4426	17	48	,	,	PUNCT
ejpam-4426	17	49	v	v	NOUN
ejpam-4426	17	50	)	)	PUNCT
ejpam-4426	17	51	.	.	PUNCT
ejpam-4426	18	1	in	in	ADP
ejpam-4426	18	2	recent	recent	ADJ
ejpam-4426	18	3	years	year	NOUN
ejpam-4426	18	4	,	,	PUNCT
ejpam-4426	18	5	much	much	ADJ
ejpam-4426	18	6	attention	attention	NOUN
ejpam-4426	18	7	has	have	AUX
ejpam-4426	18	8	been	be	AUX
ejpam-4426	18	9	paid	pay	VERB
ejpam-4426	18	10	to	to	ADP
ejpam-4426	18	11	the	the	DET
ejpam-4426	18	12	metric	metric	ADJ
ejpam-4426	18	13	dimension	dimension	NOUN
ejpam-4426	18	14	of	of	ADP
ejpam-4426	18	15	graphs	graph	NOUN
ejpam-4426	18	16	:	:	PUNCT
ejpam-4426	18	17	this	this	PRON
ejpam-4426	18	18	is	be	AUX
ejpam-4426	18	19	the	the	DET
ejpam-4426	18	20	smallest	small	ADJ
ejpam-4426	18	21	size	size	NOUN
ejpam-4426	18	22	of	of	ADP
ejpam-4426	18	23	a	a	DET
ejpam-4426	18	24	subset	subset	NOUN
ejpam-4426	18	25	of	of	ADP
ejpam-4426	18	26	vertices	vertex	NOUN
ejpam-4426	18	27	(	(	PUNCT
ejpam-4426	18	28	called	call	VERB
ejpam-4426	18	29	a	a	DET
ejpam-4426	18	30	resolving	resolving	NOUN
ejpam-4426	18	31	set	set	NOUN
ejpam-4426	18	32	)	)	PUNCT
ejpam-4426	18	33	with	with	ADP
ejpam-4426	18	34	the	the	DET
ejpam-4426	18	35	property	property	NOUN
ejpam-4426	18	36	that	that	PRON
ejpam-4426	18	37	the	the	DET
ejpam-4426	18	38	list	list	NOUN
ejpam-4426	18	39	of	of	ADP
ejpam-4426	18	40	distances	distance	NOUN
ejpam-4426	18	41	from	from	ADP
ejpam-4426	18	42	any	any	DET
ejpam-4426	18	43	vertex	vertex	NOUN
ejpam-4426	18	44	to	to	ADP
ejpam-4426	18	45	those	those	PRON
ejpam-4426	18	46	in	in	ADP
ejpam-4426	18	47	the	the	DET
ejpam-4426	18	48	set	set	NOUN
ejpam-4426	18	49	uniquely	uniquely	ADV
ejpam-4426	18	50	identifies	identify	VERB
ejpam-4426	18	51	that	that	SCONJ
ejpam-4426	18	52	vertex	vertex	NOUN
ejpam-4426	18	53	and	and	CCONJ
ejpam-4426	18	54	is	be	AUX
ejpam-4426	18	55	denoted	denote	VERB
ejpam-4426	18	56	by	by	ADP
ejpam-4426	18	57	dim(g	dim(g	PROPN
ejpam-4426	18	58	)	)	PUNCT
ejpam-4426	18	59	.	.	PUNCT
ejpam-4426	19	1	according	accord	VERB
ejpam-4426	19	2	to	to	ADP
ejpam-4426	19	3	the	the	DET
ejpam-4426	19	4	paper	paper	NOUN
ejpam-4426	19	5	of	of	ADP
ejpam-4426	19	6	saenpholphat	saenpholphat	PROPN
ejpam-4426	19	7	et	et	PROPN
ejpam-4426	19	8	al	al	PROPN
ejpam-4426	19	9	.	.	PUNCT
ejpam-4426	20	1	[	[	X
ejpam-4426	20	2	8	8	NUM
ejpam-4426	20	3	]	]	PUNCT
ejpam-4426	20	4	,	,	PUNCT
ejpam-4426	20	5	for	for	ADP
ejpam-4426	20	6	an	an	DET
ejpam-4426	20	7	ordered	order	VERB
ejpam-4426	20	8	set	set	NOUN
ejpam-4426	20	9	of	of	ADP
ejpam-4426	20	10	vertices	vertex	NOUN
ejpam-4426	20	11	w	w	NOUN
ejpam-4426	20	12	=	=	SYM
ejpam-4426	20	13	{	{	PUNCT
ejpam-4426	20	14	w1	w1	NOUN
ejpam-4426	20	15	,	,	PUNCT
ejpam-4426	20	16	w2	w2	NOUN
ejpam-4426	20	17	,	,	PUNCT
ejpam-4426	20	18	...	...	PUNCT
ejpam-4426	20	19	,	,	PUNCT
ejpam-4426	20	20	wk	wk	AUX
ejpam-4426	20	21	}	}	PUNCT
ejpam-4426	20	22	⊆	⊆	NUM
ejpam-4426	20	23	v	v	NOUN
ejpam-4426	20	24	(	(	PUNCT
ejpam-4426	20	25	g	g	NOUN
ejpam-4426	20	26	)	)	PUNCT
ejpam-4426	20	27	and	and	CCONJ
ejpam-4426	20	28	a	a	DET
ejpam-4426	20	29	vertex	vertex	NOUN
ejpam-4426	20	30	v	v	NOUN
ejpam-4426	20	31	in	in	ADP
ejpam-4426	20	32	g	g	PROPN
ejpam-4426	20	33	,	,	PUNCT
ejpam-4426	20	34	the	the	DET
ejpam-4426	20	35	k	k	NOUN
ejpam-4426	20	36	-	-	NOUN
ejpam-4426	20	37	vector	vector	NOUN
ejpam-4426	20	38	(	(	PUNCT
ejpam-4426	20	39	ordered	order	VERB
ejpam-4426	20	40	k	k	NOUN
ejpam-4426	20	41	-	-	PUNCT
ejpam-4426	20	42	tuple	tuple	ADJ
ejpam-4426	20	43	)	)	PUNCT
ejpam-4426	20	44	r(v	r(v	PROPN
ejpam-4426	20	45	/	/	SYM
ejpam-4426	20	46	w	w	NOUN
ejpam-4426	20	47	)	)	PUNCT
ejpam-4426	21	1	=	=	SYM
ejpam-4426	21	2	(	(	PUNCT
ejpam-4426	21	3	dg(v	dg(v	X
ejpam-4426	21	4	,	,	PUNCT
ejpam-4426	21	5	w1	w1	NOUN
ejpam-4426	21	6	)	)	PUNCT
ejpam-4426	21	7	,	,	PUNCT
ejpam-4426	21	8	dg(v	dg(v	X
ejpam-4426	21	9	,	,	PUNCT
ejpam-4426	21	10	w2	w2	NOUN
ejpam-4426	21	11	)	)	PUNCT
ejpam-4426	21	12	,	,	PUNCT
ejpam-4426	21	13	...	...	PUNCT
ejpam-4426	21	14	,	,	PUNCT
ejpam-4426	21	15	dg(v	dg(v	X
ejpam-4426	21	16	,	,	PUNCT
ejpam-4426	21	17	wk	wk	NOUN
ejpam-4426	21	18	)	)	PUNCT
ejpam-4426	21	19	)	)	PUNCT
ejpam-4426	21	20	is	be	AUX
ejpam-4426	21	21	referred	refer	VERB
ejpam-4426	21	22	to	to	ADP
ejpam-4426	21	23	as	as	ADP
ejpam-4426	21	24	the	the	DET
ejpam-4426	21	25	(	(	PUNCT
ejpam-4426	21	26	metric	metric	ADJ
ejpam-4426	21	27	)	)	PUNCT
ejpam-4426	21	28	representation	representation	NOUN
ejpam-4426	21	29	of	of	ADP
ejpam-4426	21	30	v	v	NOUN
ejpam-4426	21	31	with	with	ADP
ejpam-4426	21	32	respect	respect	NOUN
ejpam-4426	21	33	to	to	ADP
ejpam-4426	21	34	w	w	PROPN
ejpam-4426	21	35	.	.	PUNCT
ejpam-4426	22	1	the	the	DET
ejpam-4426	22	2	set	set	NOUN
ejpam-4426	22	3	w	w	NOUN
ejpam-4426	22	4	is	be	AUX
ejpam-4426	22	5	called	call	VERB
ejpam-4426	22	6	a	a	DET
ejpam-4426	22	7	resolving	resolving	NOUN
ejpam-4426	22	8	set	set	VERB
ejpam-4426	22	9	for	for	ADP
ejpam-4426	22	10	g	g	PROPN
ejpam-4426	22	11	if	if	SCONJ
ejpam-4426	22	12	distinct	distinct	ADJ
ejpam-4426	22	13	vertices	vertex	NOUN
ejpam-4426	22	14	have	have	VERB
ejpam-4426	22	15	distinct	distinct	ADJ
ejpam-4426	22	16	representation	representation	NOUN
ejpam-4426	22	17	with	with	ADP
ejpam-4426	22	18	respect	respect	NOUN
ejpam-4426	22	19	to	to	ADP
ejpam-4426	22	20	w	w	PROPN
ejpam-4426	22	21	.	.	PUNCT
ejpam-4426	23	1	hence	hence	ADV
ejpam-4426	23	2	,	,	PUNCT
ejpam-4426	23	3	if	if	SCONJ
ejpam-4426	23	4	w	w	NOUN
ejpam-4426	23	5	is	be	AUX
ejpam-4426	23	6	a	a	DET
ejpam-4426	23	7	resolving	resolving	NOUN
ejpam-4426	23	8	set	set	NOUN
ejpam-4426	23	9	of	of	ADP
ejpam-4426	23	10	cardinality	cardinality	PROPN
ejpam-4426	23	11	k	k	PROPN
ejpam-4426	23	12	for	for	ADP
ejpam-4426	23	13	a	a	DET
ejpam-4426	23	14	graph	graph	NOUN
ejpam-4426	23	15	g	g	NOUN
ejpam-4426	23	16	of	of	ADP
ejpam-4426	23	17	order	order	NOUN
ejpam-4426	23	18	n	n	CCONJ
ejpam-4426	23	19	,	,	PUNCT
ejpam-4426	23	20	then	then	ADV
ejpam-4426	23	21	the	the	DET
ejpam-4426	23	22	set	set	NOUN
ejpam-4426	23	23	{	{	PUNCT
ejpam-4426	23	24	r(v	r(v	PROPN
ejpam-4426	23	25	/	/	SYM
ejpam-4426	23	26	w	w	PROPN
ejpam-4426	23	27	)	)	PUNCT
ejpam-4426	23	28	:	:	PUNCT
ejpam-4426	23	29	v	v	X
ejpam-4426	23	30	∈	∈	PROPN
ejpam-4426	23	31	v	v	NOUN
ejpam-4426	23	32	(	(	PUNCT
ejpam-4426	23	33	g	g	NOUN
ejpam-4426	23	34	)	)	PUNCT
ejpam-4426	23	35	}	}	PUNCT
ejpam-4426	23	36	consists	consist	VERB
ejpam-4426	23	37	of	of	ADP
ejpam-4426	23	38	n	n	PRON
ejpam-4426	23	39	distinct	distinct	ADJ
ejpam-4426	23	40	k	k	NOUN
ejpam-4426	23	41	-	-	NOUN
ejpam-4426	23	42	vectors	vector	NOUN
ejpam-4426	23	43	.	.	PUNCT
ejpam-4426	24	1	a	a	DET
ejpam-4426	24	2	resolving	resolving	NOUN
ejpam-4426	24	3	set	set	NOUN
ejpam-4426	24	4	of	of	ADP
ejpam-4426	24	5	minimum	minimum	ADJ
ejpam-4426	24	6	cardinality	cardinality	NOUN
ejpam-4426	24	7	is	be	AUX
ejpam-4426	24	8	called	call	VERB
ejpam-4426	24	9	a	a	DET
ejpam-4426	24	10	minimum	minimum	ADJ
ejpam-4426	24	11	resolving	resolving	NOUN
ejpam-4426	24	12	set	set	VERB
ejpam-4426	24	13	or	or	CCONJ
ejpam-4426	24	14	a	a	DET
ejpam-4426	24	15	basis	basis	NOUN
ejpam-4426	24	16	,	,	PUNCT
ejpam-4426	24	17	and	and	CCONJ
ejpam-4426	24	18	the	the	DET
ejpam-4426	24	19	cardinality	cardinality	NOUN
ejpam-4426	24	20	of	of	ADP
ejpam-4426	24	21	a	a	DET
ejpam-4426	24	22	basis	basis	NOUN
ejpam-4426	24	23	for	for	ADP
ejpam-4426	24	24	g	g	PROPN
ejpam-4426	24	25	is	be	AUX
ejpam-4426	24	26	the	the	DET
ejpam-4426	24	27	dimension	dimension	NOUN
ejpam-4426	24	28	dim(g	dim(g	PROPN
ejpam-4426	24	29	)	)	PUNCT
ejpam-4426	24	30	of	of	ADP
ejpam-4426	24	31	g.	g.	PROPN
ejpam-4426	24	32	in	in	ADP
ejpam-4426	24	33	the	the	DET
ejpam-4426	24	34	paper	paper	NOUN
ejpam-4426	24	35	of	of	ADP
ejpam-4426	24	36	rara	rara	NOUN
ejpam-4426	24	37	and	and	CCONJ
ejpam-4426	24	38	cabaro	cabaro	VERB
ejpam-4426	25	1	[	[	X
ejpam-4426	25	2	4	4	NUM
ejpam-4426	25	3	]	]	PUNCT
ejpam-4426	25	4	,	,	PUNCT
ejpam-4426	25	5	an	an	DET
ejpam-4426	25	6	ordered	order	VERB
ejpam-4426	25	7	set	set	NOUN
ejpam-4426	25	8	of	of	ADP
ejpam-4426	25	9	vertices	vertex	NOUN
ejpam-4426	25	10	w	w	NOUN
ejpam-4426	25	11	=	=	SYM
ejpam-4426	25	12	{	{	PUNCT
ejpam-4426	25	13	w1	w1	NOUN
ejpam-4426	25	14	,	,	PUNCT
ejpam-4426	25	15	...	...	PUNCT
ejpam-4426	25	16	,	,	PUNCT
ejpam-4426	25	17	wl	wl	PROPN
ejpam-4426	25	18	}	}	PUNCT
ejpam-4426	25	19	is	be	AUX
ejpam-4426	25	20	a	a	DET
ejpam-4426	25	21	2	2	NUM
ejpam-4426	25	22	-	-	PUNCT
ejpam-4426	25	23	resolving	resolving	NOUN
ejpam-4426	25	24	set	set	NOUN
ejpam-4426	25	25	for	for	ADP
ejpam-4426	25	26	g	g	PROPN
ejpam-4426	25	27	if	if	SCONJ
ejpam-4426	25	28	,	,	PUNCT
ejpam-4426	25	29	for	for	ADP
ejpam-4426	25	30	any	any	DET
ejpam-4426	25	31	distinct	distinct	ADJ
ejpam-4426	25	32	vertices	vertex	NOUN
ejpam-4426	25	33	u	u	NOUN
ejpam-4426	25	34	,	,	PUNCT
ejpam-4426	25	35	v	v	NOUN
ejpam-4426	25	36	∈	∈	PROPN
ejpam-4426	25	37	v	v	NOUN
ejpam-4426	25	38	(	(	PUNCT
ejpam-4426	25	39	g	g	NOUN
ejpam-4426	25	40	)	)	PUNCT
ejpam-4426	25	41	,	,	PUNCT
ejpam-4426	25	42	the	the	DET
ejpam-4426	25	43	(	(	PUNCT
ejpam-4426	25	44	metric	metric	NOUN
ejpam-4426	25	45	)	)	PUNCT
ejpam-4426	25	46	representations	representation	VERB
ejpam-4426	25	47	r(u	r(u	PROPN
ejpam-4426	25	48	/	/	SYM
ejpam-4426	25	49	w	w	PROPN
ejpam-4426	25	50	)	)	PUNCT
ejpam-4426	25	51	and	and	CCONJ
ejpam-4426	25	52	r(v	r(v	PROPN
ejpam-4426	25	53	/	/	SYM
ejpam-4426	25	54	w	w	PROPN
ejpam-4426	25	55	)	)	PUNCT
ejpam-4426	25	56	of	of	ADP
ejpam-4426	25	57	u	u	NOUN
ejpam-4426	25	58	and	and	CCONJ
ejpam-4426	25	59	v	v	NOUN
ejpam-4426	25	60	,	,	PUNCT
ejpam-4426	25	61	respectively	respectively	ADV
ejpam-4426	25	62	differ	differ	VERB
ejpam-4426	25	63	in	in	ADP
ejpam-4426	25	64	at	at	ADV
ejpam-4426	25	65	least	least	ADJ
ejpam-4426	25	66	2	2	NUM
ejpam-4426	25	67	positions	position	NOUN
ejpam-4426	25	68	.	.	PUNCT
ejpam-4426	26	1	then	then	ADV
ejpam-4426	26	2	w	w	NOUN
ejpam-4426	26	3	is	be	AUX
ejpam-4426	26	4	said	say	VERB
ejpam-4426	26	5	to	to	PART
ejpam-4426	26	6	be	be	AUX
ejpam-4426	26	7	a	a	DET
ejpam-4426	26	8	2	2	NUM
ejpam-4426	26	9	-	-	PUNCT
ejpam-4426	26	10	resolving	resolving	NOUN
ejpam-4426	26	11	set	set	NOUN
ejpam-4426	26	12	for	for	ADP
ejpam-4426	26	13	g.	g.	PROPN
ejpam-4426	26	14	if	if	SCONJ
ejpam-4426	26	15	g	g	PROPN
ejpam-4426	26	16	has	have	VERB
ejpam-4426	26	17	a	a	DET
ejpam-4426	26	18	2	2	NUM
ejpam-4426	26	19	-	-	PUNCT
ejpam-4426	26	20	resolving	resolve	VERB
ejpam-4426	26	21	set	set	NOUN
ejpam-4426	26	22	,	,	PUNCT
ejpam-4426	26	23	the	the	DET
ejpam-4426	26	24	minimum	minimum	ADJ
ejpam-4426	26	25	cardinality	cardinality	NOUN
ejpam-4426	26	26	dim2(g	dim2(g	NOUN
ejpam-4426	26	27	)	)	PUNCT
ejpam-4426	26	28	is	be	AUX
ejpam-4426	26	29	called	call	VERB
ejpam-4426	26	30	the	the	DET
ejpam-4426	26	31	2	2	NUM
ejpam-4426	26	32	-	-	PUNCT
ejpam-4426	26	33	metric	metric	ADJ
ejpam-4426	26	34	dimension	dimension	NOUN
ejpam-4426	26	35	of	of	ADP
ejpam-4426	26	36	g.	g.	PROPN
ejpam-4426	26	37	if	if	SCONJ
ejpam-4426	26	38	k	k	PROPN
ejpam-4426	26	39	=	=	SYM
ejpam-4426	26	40	2	2	NUM
ejpam-4426	26	41	is	be	AUX
ejpam-4426	26	42	the	the	DET
ejpam-4426	26	43	largest	large	ADJ
ejpam-4426	26	44	integer	integer	NOUN
ejpam-4426	26	45	for	for	ADP
ejpam-4426	26	46	which	which	PRON
ejpam-4426	26	47	g	g	NOUN
ejpam-4426	26	48	has	have	VERB
ejpam-4426	26	49	a	a	DET
ejpam-4426	26	50	2	2	NUM
ejpam-4426	26	51	-	-	PUNCT
ejpam-4426	26	52	resolving	resolve	VERB
ejpam-4426	26	53	set	set	NOUN
ejpam-4426	26	54	,	,	PUNCT
ejpam-4426	26	55	then	then	ADV
ejpam-4426	26	56	we	we	PRON
ejpam-4426	26	57	say	say	VERB
ejpam-4426	26	58	that	that	SCONJ
ejpam-4426	26	59	g	g	PROPN
ejpam-4426	26	60	is	be	AUX
ejpam-4426	26	61	a	a	DET
ejpam-4426	26	62	2	2	NUM
ejpam-4426	26	63	-	-	PUNCT
ejpam-4426	26	64	metric	metric	ADJ
ejpam-4426	26	65	dimensional	dimensional	ADJ
ejpam-4426	26	66	graph	graph	NOUN
ejpam-4426	26	67	.	.	PUNCT
ejpam-4426	27	1	in	in	ADP
ejpam-4426	27	2	this	this	DET
ejpam-4426	27	3	paper	paper	NOUN
ejpam-4426	27	4	,	,	PUNCT
ejpam-4426	27	5	the	the	DET
ejpam-4426	27	6	concept	concept	NOUN
ejpam-4426	27	7	of	of	ADP
ejpam-4426	27	8	2	2	NUM
ejpam-4426	27	9	-	-	PUNCT
ejpam-4426	27	10	resolving	resolve	VERB
ejpam-4426	27	11	dominating	dominating	NOUN
ejpam-4426	27	12	set	set	VERB
ejpam-4426	27	13	in	in	ADP
ejpam-4426	27	14	the	the	DET
ejpam-4426	27	15	join	join	NOUN
ejpam-4426	27	16	,	,	PUNCT
ejpam-4426	27	17	corona	corona	NOUN
ejpam-4426	27	18	and	and	CCONJ
ejpam-4426	27	19	lexicographic	lexicographic	ADJ
ejpam-4426	27	20	product	product	NOUN
ejpam-4426	27	21	of	of	ADP
ejpam-4426	27	22	two	two	NUM
ejpam-4426	27	23	graphs	graph	NOUN
ejpam-4426	27	24	is	be	AUX
ejpam-4426	27	25	discussed	discuss	VERB
ejpam-4426	27	26	.	.	PUNCT
ejpam-4426	28	1	2	2	X
ejpam-4426	28	2	.	.	X
ejpam-4426	28	3	preliminary	preliminary	ADJ
ejpam-4426	28	4	results	result	NOUN
ejpam-4426	28	5	in	in	ADP
ejpam-4426	28	6	this	this	DET
ejpam-4426	28	7	study	study	NOUN
ejpam-4426	28	8	,	,	PUNCT
ejpam-4426	28	9	we	we	PRON
ejpam-4426	28	10	consider	consider	VERB
ejpam-4426	28	11	finite	finite	NOUN
ejpam-4426	28	12	,	,	PUNCT
ejpam-4426	28	13	simple	simple	ADJ
ejpam-4426	28	14	and	and	CCONJ
ejpam-4426	28	15	connected	connected	ADJ
ejpam-4426	28	16	undirected	undirected	ADJ
ejpam-4426	28	17	graphs	graph	NOUN
ejpam-4426	28	18	.	.	PUNCT
ejpam-4426	29	1	for	for	ADP
ejpam-4426	29	2	basic	basic	ADJ
ejpam-4426	29	3	graph	graph	NOUN
ejpam-4426	29	4	-	-	PUNCT
ejpam-4426	29	5	theoretic	theoretic	NOUN
ejpam-4426	29	6	concepts	concept	NOUN
ejpam-4426	29	7	,	,	PUNCT
ejpam-4426	29	8	we	we	PRON
ejpam-4426	29	9	refer	refer	VERB
ejpam-4426	29	10	readers	reader	NOUN
ejpam-4426	29	11	to	to	ADP
ejpam-4426	29	12	[	[	X
ejpam-4426	29	13	5	5	NUM
ejpam-4426	29	14	]	]	PUNCT
ejpam-4426	29	15	.	.	PUNCT
ejpam-4426	30	1	theorem	theorem	NOUN
ejpam-4426	30	2	1	1	NUM
ejpam-4426	30	3	.	.	PUNCT
ejpam-4426	31	1	[	[	X
ejpam-4426	31	2	2	2	X
ejpam-4426	31	3	]	]	PUNCT
ejpam-4426	31	4	let	let	VERB
ejpam-4426	31	5	g	g	NOUN
ejpam-4426	31	6	and	and	CCONJ
ejpam-4426	31	7	h	h	NOUN
ejpam-4426	31	8	be	be	VERB
ejpam-4426	31	9	two	two	NUM
ejpam-4426	31	10	nontrivial	nontrivial	ADJ
ejpam-4426	31	11	graphs	graph	NOUN
ejpam-4426	31	12	such	such	ADJ
ejpam-4426	31	13	that	that	SCONJ
ejpam-4426	31	14	g	g	PROPN
ejpam-4426	31	15	is	be	AUX
ejpam-4426	31	16	connected	connect	VERB
ejpam-4426	31	17	.	.	PUNCT
ejpam-4426	32	1	then	then	ADV
ejpam-4426	32	2	the	the	DET
ejpam-4426	32	3	following	follow	VERB
ejpam-4426	32	4	assertions	assertion	NOUN
ejpam-4426	32	5	hold	hold	VERB
ejpam-4426	32	6	for	for	ADP
ejpam-4426	32	7	any	any	DET
ejpam-4426	32	8	a	a	NOUN
ejpam-4426	32	9	,	,	PUNCT
ejpam-4426	32	10	c	c	PROPN
ejpam-4426	32	11	∈	∈	PROPN
ejpam-4426	32	12	v	v	ADP
ejpam-4426	32	13	(	(	PUNCT
ejpam-4426	32	14	g	g	NOUN
ejpam-4426	32	15	)	)	PUNCT
ejpam-4426	32	16	and	and	CCONJ
ejpam-4426	32	17	b	b	X
ejpam-4426	32	18	,	,	PUNCT
ejpam-4426	32	19	d	d	PROPN
ejpam-4426	32	20	∈	∈	PROPN
ejpam-4426	32	21	v	v	ADP
ejpam-4426	32	22	(	(	PUNCT
ejpam-4426	32	23	h	h	NOUN
ejpam-4426	32	24	)	)	PUNCT
ejpam-4426	32	25	such	such	ADJ
ejpam-4426	32	26	that	that	SCONJ
ejpam-4426	32	27	a	a	DET
ejpam-4426	32	28	̸=	̸=	PROPN
ejpam-4426	32	29	c.	c.	NOUN
ejpam-4426	32	30	(	(	PUNCT
ejpam-4426	32	31	i	i	NOUN
ejpam-4426	32	32	)	)	PUNCT
ejpam-4426	32	33	ng[h](a	ng[h](a	PROPN
ejpam-4426	32	34	,	,	PUNCT
ejpam-4426	32	35	b	b	NOUN
ejpam-4426	32	36	)	)	PUNCT
ejpam-4426	32	37	=	=	SYM
ejpam-4426	32	38	(	(	PUNCT
ejpam-4426	32	39	{	{	PUNCT
ejpam-4426	32	40	a	a	DET
ejpam-4426	32	41	}	}	PUNCT
ejpam-4426	32	42	×nh	×nh	NOUN
ejpam-4426	32	43	{	{	PUNCT
ejpam-4426	32	44	b	b	NOUN
ejpam-4426	32	45	}	}	PUNCT
ejpam-4426	32	46	)	)	PUNCT
ejpam-4426	32	47	∪	∪	ADP
ejpam-4426	32	48	{	{	PUNCT
ejpam-4426	32	49	ng	ng	PROPN
ejpam-4426	32	50	{	{	PUNCT
ejpam-4426	32	51	a	a	PROPN
ejpam-4426	32	52	}	}	PUNCT
ejpam-4426	32	53	×	×	NOUN
ejpam-4426	32	54	v	v	NOUN
ejpam-4426	32	55	(	(	PUNCT
ejpam-4426	32	56	h	h	NOUN
ejpam-4426	32	57	)	)	PUNCT
ejpam-4426	32	58	}	}	PUNCT
ejpam-4426	32	59	(	(	PUNCT
ejpam-4426	32	60	ii	ii	NOUN
ejpam-4426	32	61	)	)	PUNCT
ejpam-4426	32	62	dg[h]((a	dg[h]((a	PROPN
ejpam-4426	32	63	,	,	PUNCT
ejpam-4426	32	64	b	b	NOUN
ejpam-4426	32	65	)	)	PUNCT
ejpam-4426	32	66	,	,	PUNCT
ejpam-4426	32	67	(	(	PUNCT
ejpam-4426	32	68	c	c	X
ejpam-4426	32	69	,	,	PUNCT
ejpam-4426	32	70	d	d	NOUN
ejpam-4426	32	71	)	)	PUNCT
ejpam-4426	32	72	)	)	PUNCT
ejpam-4426	32	73	=	=	SYM
ejpam-4426	32	74	dg(a	dg(a	X
ejpam-4426	32	75	,	,	PUNCT
ejpam-4426	32	76	c	c	NOUN
ejpam-4426	32	77	)	)	PUNCT
ejpam-4426	32	78	(	(	PUNCT
ejpam-4426	32	79	iii	iii	X
ejpam-4426	32	80	)	)	PUNCT
ejpam-4426	32	81	dg[h](a	dg[h](a	NOUN
ejpam-4426	32	82	,	,	PUNCT
ejpam-4426	32	83	b	b	NOUN
ejpam-4426	32	84	)	)	PUNCT
ejpam-4426	32	85	,	,	PUNCT
ejpam-4426	32	86	(	(	PUNCT
ejpam-4426	32	87	a	a	PRON
ejpam-4426	32	88	,	,	PUNCT
ejpam-4426	32	89	d	d	NOUN
ejpam-4426	32	90	)	)	PUNCT
ejpam-4426	32	91	=	=	SYM
ejpam-4426	32	92	min	min	NOUN
ejpam-4426	32	93	{	{	PUNCT
ejpam-4426	32	94	dh(b	dh(b	PROPN
ejpam-4426	32	95	,	,	PUNCT
ejpam-4426	32	96	d	d	NOUN
ejpam-4426	32	97	)	)	PUNCT
ejpam-4426	32	98	,	,	PUNCT
ejpam-4426	32	99	2	2	NUM
ejpam-4426	32	100	}	}	PUNCT
ejpam-4426	32	101	.	.	PUNCT
ejpam-4426	33	1	proposition	proposition	NOUN
ejpam-4426	33	2	1	1	NUM
ejpam-4426	33	3	.	.	PUNCT
ejpam-4426	34	1	[	[	X
ejpam-4426	34	2	1	1	X
ejpam-4426	34	3	]	]	PUNCT
ejpam-4426	34	4	let	let	VERB
ejpam-4426	34	5	g	g	PRON
ejpam-4426	34	6	be	be	AUX
ejpam-4426	34	7	a	a	DET
ejpam-4426	34	8	connected	connected	ADJ
ejpam-4426	34	9	graph	graph	NOUN
ejpam-4426	34	10	of	of	ADP
ejpam-4426	34	11	order	order	NOUN
ejpam-4426	34	12	n	n	PRON
ejpam-4426	34	13	≥	≥	NOUN
ejpam-4426	34	14	2	2	NUM
ejpam-4426	34	15	.	.	PUNCT
ejpam-4426	34	16	then	then	ADV
ejpam-4426	34	17	dim2(g	dim2(g	NOUN
ejpam-4426	34	18	)	)	PUNCT
ejpam-4426	34	19	=	=	SYM
ejpam-4426	34	20	2	2	NUM
ejpam-4426	35	1	if	if	SCONJ
ejpam-4426	35	2	and	and	CCONJ
ejpam-4426	35	3	only	only	ADV
ejpam-4426	35	4	if	if	SCONJ
ejpam-4426	35	5	g	g	PROPN
ejpam-4426	35	6	∼=	∼=	PROPN
ejpam-4426	35	7	pn	pn	PROPN
ejpam-4426	35	8	.	.	PROPN
ejpam-4426	35	9	proposition	proposition	PROPN
ejpam-4426	35	10	2	2	NUM
ejpam-4426	35	11	.	.	PUNCT
ejpam-4426	35	12	dim2(kn	dim2(kn	PROPN
ejpam-4426	35	13	)	)	PUNCT
ejpam-4426	36	1	=	=	SYM
ejpam-4426	36	2	n	n	PROPN
ejpam-4426	36	3	for	for	ADP
ejpam-4426	36	4	n	n	PRON
ejpam-4426	36	5	≥	≥	NUM
ejpam-4426	36	6	2	2	NUM
ejpam-4426	36	7	.	.	PUNCT
ejpam-4426	37	1	j.	j.	PROPN
ejpam-4426	37	2	cabaro	cabaro	PROPN
ejpam-4426	37	3	,	,	PUNCT
ejpam-4426	37	4	h.	h.	PROPN
ejpam-4426	37	5	rara	rara	PROPN
ejpam-4426	37	6	/	/	SYM
ejpam-4426	37	7	eur	eur	PROPN
ejpam-4426	37	8	.	.	PUNCT
ejpam-4426	38	1	j.	j.	PROPN
ejpam-4426	38	2	pure	pure	PROPN
ejpam-4426	38	3	appl	appl	PROPN
ejpam-4426	38	4	.	.	PROPN
ejpam-4426	38	5	math	math	PROPN
ejpam-4426	38	6	,	,	PUNCT
ejpam-4426	38	7	15	15	NUM
ejpam-4426	38	8	(	(	PUNCT
ejpam-4426	38	9	3	3	NUM
ejpam-4426	38	10	)	)	PUNCT
ejpam-4426	38	11	(	(	PUNCT
ejpam-4426	38	12	2022	2022	NUM
ejpam-4426	38	13	)	)	PUNCT
ejpam-4426	38	14	,	,	PUNCT
ejpam-4426	38	15	1417	1417	NUM
ejpam-4426	38	16	-	-	SYM
ejpam-4426	38	17	1425	1425	NUM
ejpam-4426	38	18	1419	1419	NUM
ejpam-4426	38	19	remark	remark	NOUN
ejpam-4426	38	20	1	1	NUM
ejpam-4426	38	21	.	.	PUNCT
ejpam-4426	39	1	for	for	ADP
ejpam-4426	39	2	any	any	DET
ejpam-4426	39	3	connected	connected	ADJ
ejpam-4426	39	4	graph	graph	NOUN
ejpam-4426	39	5	g	g	NOUN
ejpam-4426	39	6	of	of	ADP
ejpam-4426	39	7	order	order	NOUN
ejpam-4426	39	8	n	n	PRON
ejpam-4426	39	9	≥	≥	NOUN
ejpam-4426	39	10	2	2	NUM
ejpam-4426	39	11	,	,	PUNCT
ejpam-4426	39	12	1	1	NUM
ejpam-4426	39	13	<	<	X
ejpam-4426	39	14	γ2r(g	γ2r(g	PROPN
ejpam-4426	39	15	)	)	PUNCT
ejpam-4426	39	16	≤	≤	NUM
ejpam-4426	39	17	n.	n.	NOUN
ejpam-4426	39	18	remark	remark	NOUN
ejpam-4426	39	19	2	2	NUM
ejpam-4426	39	20	.	.	X
ejpam-4426	39	21	for	for	ADP
ejpam-4426	39	22	any	any	DET
ejpam-4426	39	23	connected	connected	ADJ
ejpam-4426	39	24	graph	graph	NOUN
ejpam-4426	39	25	g	g	NOUN
ejpam-4426	39	26	of	of	ADP
ejpam-4426	39	27	order	order	NOUN
ejpam-4426	39	28	n	n	PRON
ejpam-4426	39	29	≥	≥	NOUN
ejpam-4426	39	30	2	2	NUM
ejpam-4426	39	31	,	,	PUNCT
ejpam-4426	39	32	dim2(g	dim2(g	NOUN
ejpam-4426	39	33	)	)	PUNCT
ejpam-4426	39	34	≤	≤	NOUN
ejpam-4426	39	35	γ2r(g	γ2r(g	PROPN
ejpam-4426	39	36	)	)	PUNCT
ejpam-4426	39	37	.	.	PUNCT
ejpam-4426	40	1	remark	remark	NOUN
ejpam-4426	40	2	3	3	NUM
ejpam-4426	40	3	.	.	PUNCT
ejpam-4426	40	4	for	for	ADP
ejpam-4426	40	5	n	n	PRON
ejpam-4426	40	6	≥	≥	NUM
ejpam-4426	40	7	2	2	NUM
ejpam-4426	40	8	,	,	PUNCT
ejpam-4426	40	9	γ2r(kn	γ2r(kn	NUM
ejpam-4426	40	10	)	)	PUNCT
ejpam-4426	40	11	=	=	SYM
ejpam-4426	40	12	n.	n.	NOUN
ejpam-4426	40	13	theorem	theorem	NOUN
ejpam-4426	40	14	2	2	X
ejpam-4426	40	15	.	.	PUNCT
ejpam-4426	41	1	let	let	VERB
ejpam-4426	41	2	g	g	PRON
ejpam-4426	41	3	be	be	AUX
ejpam-4426	41	4	a	a	DET
ejpam-4426	41	5	nontrivial	nontrivial	ADJ
ejpam-4426	41	6	connected	connect	VERB
ejpam-4426	41	7	graph	graph	NOUN
ejpam-4426	41	8	of	of	ADP
ejpam-4426	41	9	order	order	NOUN
ejpam-4426	41	10	n	n	PRON
ejpam-4426	41	11	≥	≥	NOUN
ejpam-4426	41	12	2	2	NUM
ejpam-4426	41	13	.	.	PUNCT
ejpam-4426	42	1	then	then	ADV
ejpam-4426	42	2	γ2r(g	γ2r(g	PROPN
ejpam-4426	42	3	)	)	PUNCT
ejpam-4426	43	1	=	=	SYM
ejpam-4426	43	2	2	2	NUM
ejpam-4426	43	3	if	if	SCONJ
ejpam-4426	43	4	and	and	CCONJ
ejpam-4426	43	5	only	only	ADV
ejpam-4426	43	6	if	if	SCONJ
ejpam-4426	43	7	g	g	PROPN
ejpam-4426	43	8	∼=	∼=	PROPN
ejpam-4426	43	9	pn	pn	NOUN
ejpam-4426	43	10	,	,	PUNCT
ejpam-4426	43	11	for	for	ADP
ejpam-4426	43	12	2	2	NUM
ejpam-4426	43	13	≤	≤	NOUN
ejpam-4426	43	14	n	n	CCONJ
ejpam-4426	43	15	≤	≤	NOUN
ejpam-4426	43	16	4	4	NUM
ejpam-4426	43	17	.	.	PUNCT
ejpam-4426	44	1	proof	proof	NOUN
ejpam-4426	44	2	.	.	PUNCT
ejpam-4426	45	1	suppose	suppose	VERB
ejpam-4426	45	2	that	that	SCONJ
ejpam-4426	45	3	γ2r(g	γ2r(g	PROPN
ejpam-4426	45	4	)	)	PUNCT
ejpam-4426	46	1	=	=	SYM
ejpam-4426	47	1	2	2	X
ejpam-4426	47	2	.	.	X
ejpam-4426	47	3	let	let	VERB
ejpam-4426	47	4	s	s	VERB
ejpam-4426	47	5	=	=	PUNCT
ejpam-4426	47	6	{	{	PUNCT
ejpam-4426	47	7	x	x	PROPN
ejpam-4426	47	8	,	,	PUNCT
ejpam-4426	47	9	y	y	PROPN
ejpam-4426	47	10	}	}	PUNCT
ejpam-4426	47	11	be	be	AUX
ejpam-4426	47	12	a	a	DET
ejpam-4426	47	13	γ2r	γ2r	ADV
ejpam-4426	47	14	-	-	PUNCT
ejpam-4426	47	15	set	set	NOUN
ejpam-4426	47	16	in	in	ADP
ejpam-4426	47	17	g.	g.	NOUN
ejpam-4426	47	18	by	by	ADP
ejpam-4426	47	19	remark	remark	NOUN
ejpam-4426	47	20	2	2	NUM
ejpam-4426	47	21	and	and	CCONJ
ejpam-4426	47	22	proposition	proposition	NOUN
ejpam-4426	47	23	1	1	NUM
ejpam-4426	47	24	,	,	PUNCT
ejpam-4426	47	25	g	g	PROPN
ejpam-4426	47	26	∼=	∼=	PROPN
ejpam-4426	47	27	pn	pn	NOUN
ejpam-4426	47	28	.	.	PUNCT
ejpam-4426	48	1	moreover	moreover	ADV
ejpam-4426	48	2	,	,	PUNCT
ejpam-4426	48	3	x	x	PUNCT
ejpam-4426	48	4	and	and	CCONJ
ejpam-4426	48	5	y	y	PROPN
ejpam-4426	48	6	are	be	AUX
ejpam-4426	48	7	the	the	DET
ejpam-4426	48	8	end	end	NOUN
ejpam-4426	48	9	vertices	vertex	NOUN
ejpam-4426	48	10	in	in	ADP
ejpam-4426	48	11	g.	g.	PROPN
ejpam-4426	48	12	since	since	SCONJ
ejpam-4426	48	13	s	s	PROPN
ejpam-4426	48	14	is	be	AUX
ejpam-4426	48	15	a	a	DET
ejpam-4426	48	16	dominating	dominating	NOUN
ejpam-4426	48	17	set	set	NOUN
ejpam-4426	48	18	in	in	ADP
ejpam-4426	48	19	g	g	PROPN
ejpam-4426	48	20	,	,	PUNCT
ejpam-4426	48	21	2	2	NUM
ejpam-4426	48	22	≤	≤	NOUN
ejpam-4426	48	23	n	n	CCONJ
ejpam-4426	48	24	≤	≤	NOUN
ejpam-4426	48	25	4	4	NUM
ejpam-4426	48	26	.	.	PUNCT
ejpam-4426	49	1	the	the	DET
ejpam-4426	49	2	converse	converse	NOUN
ejpam-4426	49	3	follows	follow	VERB
ejpam-4426	49	4	immediately	immediately	ADV
ejpam-4426	49	5	from	from	ADP
ejpam-4426	49	6	proposition	proposition	NOUN
ejpam-4426	49	7	1	1	NUM
ejpam-4426	49	8	.	.	PUNCT
ejpam-4426	49	9	theorem	theorem	NOUN
ejpam-4426	49	10	3	3	X
ejpam-4426	49	11	.	.	PUNCT
ejpam-4426	50	1	let	let	VERB
ejpam-4426	50	2	g	g	PRON
ejpam-4426	50	3	be	be	AUX
ejpam-4426	50	4	a	a	DET
ejpam-4426	50	5	connected	connected	ADJ
ejpam-4426	50	6	graph	graph	NOUN
ejpam-4426	50	7	of	of	ADP
ejpam-4426	50	8	order	order	NOUN
ejpam-4426	50	9	n	n	PRON
ejpam-4426	50	10	≥	≥	NOUN
ejpam-4426	50	11	2	2	NUM
ejpam-4426	50	12	.	.	PUNCT
ejpam-4426	51	1	if	if	SCONJ
ejpam-4426	51	2	g	g	PROPN
ejpam-4426	51	3	∈	∈	PROPN
ejpam-4426	51	4	{	{	PUNCT
ejpam-4426	51	5	kn	kn	PROPN
ejpam-4426	51	6	,	,	PUNCT
ejpam-4426	51	7	f3	f3	ADJ
ejpam-4426	51	8	,	,	PUNCT
ejpam-4426	51	9	p2	p2	PROPN
ejpam-4426	51	10	+	+	CCONJ
ejpam-4426	51	11	p3,km	p3,km	NOUN
ejpam-4426	51	12	,	,	PUNCT
ejpam-4426	51	13	n−m	n−m	PROPN
ejpam-4426	51	14	}	}	PUNCT
ejpam-4426	51	15	,	,	PUNCT
ejpam-4426	51	16	where	where	SCONJ
ejpam-4426	51	17	m	m	PROPN
ejpam-4426	51	18	≥	≥	NOUN
ejpam-4426	51	19	2	2	NUM
ejpam-4426	51	20	,	,	PUNCT
ejpam-4426	51	21	then	then	ADV
ejpam-4426	51	22	γ2r(g	γ2r(g	PROPN
ejpam-4426	51	23	)	)	PUNCT
ejpam-4426	51	24	=	=	PUNCT
ejpam-4426	52	1	n.	n.	ADJ
ejpam-4426	52	2	example	example	NOUN
ejpam-4426	53	1	1	1	X
ejpam-4426	53	2	.	.	PUNCT
ejpam-4426	54	1	the	the	DET
ejpam-4426	54	2	sets	set	NOUN
ejpam-4426	54	3	s1	s1	NOUN
ejpam-4426	54	4	=	=	PUNCT
ejpam-4426	54	5	{	{	PUNCT
ejpam-4426	54	6	b	b	PROPN
ejpam-4426	54	7	,	,	PUNCT
ejpam-4426	54	8	e	e	NOUN
ejpam-4426	54	9	,	,	PUNCT
ejpam-4426	54	10	g	g	NOUN
ejpam-4426	54	11	}	}	PUNCT
ejpam-4426	54	12	and	and	CCONJ
ejpam-4426	54	13	s2	s2	VERB
ejpam-4426	54	14	=	=	PUNCT
ejpam-4426	54	15	{	{	PUNCT
ejpam-4426	54	16	a	a	X
ejpam-4426	54	17	,	,	PUNCT
ejpam-4426	54	18	d	d	NOUN
ejpam-4426	54	19	,	,	PUNCT
ejpam-4426	54	20	e	e	NOUN
ejpam-4426	54	21	,	,	PUNCT
ejpam-4426	54	22	g	g	NOUN
ejpam-4426	54	23	}	}	PUNCT
ejpam-4426	54	24	in	in	ADP
ejpam-4426	54	25	figure	figure	NOUN
ejpam-4426	54	26	1	1	NUM
ejpam-4426	54	27	are	be	AUX
ejpam-4426	54	28	2	2	NUM
ejpam-4426	54	29	-	-	PUNCT
ejpam-4426	54	30	resolving	resolve	VERB
ejpam-4426	54	31	dominating	dominating	NOUN
ejpam-4426	54	32	sets	set	NOUN
ejpam-4426	54	33	in	in	ADP
ejpam-4426	54	34	g.	g.	PROPN
ejpam-4426	54	35	moreover	moreover	ADV
ejpam-4426	54	36	,	,	PUNCT
ejpam-4426	54	37	s1	s1	PROPN
ejpam-4426	54	38	is	be	AUX
ejpam-4426	54	39	a	a	DET
ejpam-4426	54	40	γ2r	γ2r	ADV
ejpam-4426	54	41	-	-	PUNCT
ejpam-4426	54	42	set	set	NOUN
ejpam-4426	54	43	in	in	ADP
ejpam-4426	54	44	g.	g.	PROPN
ejpam-4426	54	45	thus	thus	ADV
ejpam-4426	54	46	,	,	PUNCT
ejpam-4426	54	47	γ2r(g	γ2r(g	PROPN
ejpam-4426	54	48	)	)	PUNCT
ejpam-4426	54	49	=	=	SYM
ejpam-4426	55	1	3	3	X
ejpam-4426	55	2	.	.	PUNCT
ejpam-4426	55	3	....................................	....................................	PUNCT
ejpam-4426	55	4	....................................	....................................	PUNCT
ejpam-4426	55	5	....................................	....................................	PUNCT
ejpam-4426	55	6	....................................	....................................	PUNCT
ejpam-4426	55	7	....................................	....................................	PUNCT
ejpam-4426	55	8	........................................................................	........................................................................	PUNCT
ejpam-4426	55	9	.........	.........	PUNCT
ejpam-4426	55	10	........	........	PUNCT
ejpam-4426	55	11	........	........	PUNCT
ejpam-4426	55	12	........	........	PUNCT
ejpam-4426	55	13	........	........	PUNCT
ejpam-4426	55	14	........	........	PUNCT
ejpam-4426	55	15	........	........	PUNCT
ejpam-4426	55	16	........	........	PUNCT
ejpam-4426	55	17	........	........	PUNCT
ejpam-4426	55	18	........	........	PUNCT
ejpam-4426	55	19	........	........	PUNCT
ejpam-4426	56	1	....	....	PUNCT
ejpam-4426	56	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	56	3	.........	.........	PUNCT
ejpam-4426	56	4	........	........	PUNCT
ejpam-4426	56	5	........	........	PUNCT
ejpam-4426	56	6	........	........	PUNCT
ejpam-4426	56	7	........	........	PUNCT
ejpam-4426	56	8	........	........	PUNCT
ejpam-4426	56	9	........	........	PUNCT
ejpam-4426	56	10	........	........	PUNCT
ejpam-4426	56	11	........	........	PUNCT
ejpam-4426	56	12	........	........	PUNCT
ejpam-4426	56	13	........	........	PUNCT
ejpam-4426	57	1	....	....	PUNCT
ejpam-4426	57	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	57	3	.........	.........	PUNCT
ejpam-4426	57	4	........	........	PUNCT
ejpam-4426	57	5	........	........	PUNCT
ejpam-4426	57	6	........	........	PUNCT
ejpam-4426	57	7	........	........	PUNCT
ejpam-4426	57	8	........	........	PUNCT
ejpam-4426	57	9	........	........	PUNCT
ejpam-4426	57	10	........	........	PUNCT
ejpam-4426	57	11	........	........	PUNCT
ejpam-4426	57	12	........	........	PUNCT
ejpam-4426	57	13	........	........	PUNCT
ejpam-4426	58	1	.........................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................	PUNCT
ejpam-4426	59	1	g	g	NOUN
ejpam-4426	59	2	:	:	PUNCT
ejpam-4426	59	3	a	a	DET
ejpam-4426	59	4	b	b	NOUN
ejpam-4426	59	5	c	c	NOUN
ejpam-4426	59	6	d	d	X
ejpam-4426	59	7	e	e	X
ejpam-4426	59	8	f	f	PROPN
ejpam-4426	59	9	g	g	PROPN
ejpam-4426	59	10	figure	figure	NOUN
ejpam-4426	59	11	1	1	NUM
ejpam-4426	59	12	:	:	PUNCT
ejpam-4426	59	13	a	a	DET
ejpam-4426	59	14	graph	graph	NOUN
ejpam-4426	59	15	g	g	NOUN
ejpam-4426	59	16	with	with	ADP
ejpam-4426	59	17	γ2r(g	γ2r(g	PROPN
ejpam-4426	59	18	)	)	PUNCT
ejpam-4426	59	19	=	=	SYM
ejpam-4426	60	1	3	3	NUM
ejpam-4426	60	2	example	example	NOUN
ejpam-4426	60	3	2	2	NUM
ejpam-4426	60	4	.	.	X
ejpam-4426	60	5	consider	consider	VERB
ejpam-4426	60	6	the	the	DET
ejpam-4426	60	7	graph	graph	NOUN
ejpam-4426	60	8	g	g	NOUN
ejpam-4426	60	9	in	in	ADP
ejpam-4426	60	10	figure	figure	NOUN
ejpam-4426	60	11	2	2	NUM
ejpam-4426	60	12	.	.	PUNCT
ejpam-4426	61	1	the	the	DET
ejpam-4426	61	2	ordered	order	VERB
ejpam-4426	61	3	set	set	NOUN
ejpam-4426	61	4	of	of	ADP
ejpam-4426	61	5	vertices	vertex	NOUN
ejpam-4426	61	6	w	w	NOUN
ejpam-4426	61	7	=	=	SYM
ejpam-4426	61	8	{	{	PUNCT
ejpam-4426	61	9	u1	u1	NOUN
ejpam-4426	61	10	,	,	PUNCT
ejpam-4426	61	11	u2	u2	NOUN
ejpam-4426	61	12	,	,	PUNCT
ejpam-4426	61	13	u3	u3	PROPN
ejpam-4426	61	14	}	}	PUNCT
ejpam-4426	61	15	is	be	AUX
ejpam-4426	61	16	a	a	DET
ejpam-4426	61	17	2	2	NUM
ejpam-4426	61	18	-	-	PUNCT
ejpam-4426	61	19	resolving	resolving	NOUN
ejpam-4426	61	20	set	set	NOUN
ejpam-4426	61	21	for	for	ADP
ejpam-4426	61	22	the	the	DET
ejpam-4426	61	23	graph	graph	NOUN
ejpam-4426	61	24	g	g	NOUN
ejpam-4426	61	25	since	since	SCONJ
ejpam-4426	61	26	the	the	DET
ejpam-4426	61	27	representations	representation	NOUN
ejpam-4426	61	28	rg(u1	rg(u1	NOUN
ejpam-4426	61	29	/	/	SYM
ejpam-4426	61	30	w3	w3	PROPN
ejpam-4426	61	31	)	)	PUNCT
ejpam-4426	62	1	=	=	PUNCT
ejpam-4426	62	2	(	(	PUNCT
ejpam-4426	62	3	0	0	NUM
ejpam-4426	62	4	,	,	PUNCT
ejpam-4426	62	5	1	1	NUM
ejpam-4426	62	6	,	,	PUNCT
ejpam-4426	62	7	2	2	NUM
ejpam-4426	62	8	)	)	PUNCT
ejpam-4426	62	9	,	,	PUNCT
ejpam-4426	62	10	rg(u2,w3	rg(u2,w3	NOUN
ejpam-4426	62	11	)	)	PUNCT
ejpam-4426	63	1	=	=	SYM
ejpam-4426	63	2	(	(	PUNCT
ejpam-4426	63	3	1	1	NUM
ejpam-4426	63	4	,	,	PUNCT
ejpam-4426	63	5	0	0	NUM
ejpam-4426	63	6	,	,	PUNCT
ejpam-4426	63	7	1	1	NUM
ejpam-4426	63	8	)	)	PUNCT
ejpam-4426	63	9	,	,	PUNCT
ejpam-4426	63	10	rg(u3	rg(u3	PROPN
ejpam-4426	63	11	/	/	SYM
ejpam-4426	63	12	w3	w3	PROPN
ejpam-4426	63	13	)	)	PUNCT
ejpam-4426	63	14	=	=	PUNCT
ejpam-4426	64	1	(	(	PUNCT
ejpam-4426	64	2	2	2	NUM
ejpam-4426	64	3	,	,	PUNCT
ejpam-4426	64	4	1	1	NUM
ejpam-4426	64	5	,	,	PUNCT
ejpam-4426	64	6	0	0	NUM
ejpam-4426	64	7	)	)	PUNCT
ejpam-4426	64	8	,	,	PUNCT
ejpam-4426	64	9	rg(u4	rg(u4	NOUN
ejpam-4426	64	10	/	/	SYM
ejpam-4426	64	11	w3	w3	PROPN
ejpam-4426	64	12	)	)	PUNCT
ejpam-4426	65	1	=	=	PUNCT
ejpam-4426	65	2	(	(	PUNCT
ejpam-4426	65	3	2	2	NUM
ejpam-4426	65	4	,	,	PUNCT
ejpam-4426	65	5	2	2	NUM
ejpam-4426	65	6	,	,	PUNCT
ejpam-4426	65	7	1	1	NUM
ejpam-4426	65	8	)	)	PUNCT
ejpam-4426	65	9	,	,	PUNCT
ejpam-4426	65	10	rg(u5	rg(u5	NOUN
ejpam-4426	65	11	/	/	SYM
ejpam-4426	65	12	w3	w3	PROPN
ejpam-4426	65	13	)	)	PUNCT
ejpam-4426	65	14	=	=	PUNCT
ejpam-4426	66	1	(	(	PUNCT
ejpam-4426	66	2	1	1	NUM
ejpam-4426	66	3	,	,	PUNCT
ejpam-4426	66	4	2	2	NUM
ejpam-4426	66	5	,	,	PUNCT
ejpam-4426	66	6	2	2	NUM
ejpam-4426	66	7	)	)	PUNCT
ejpam-4426	66	8	and	and	CCONJ
ejpam-4426	66	9	rg(u6	rg(u6	NOUN
ejpam-4426	66	10	/	/	SYM
ejpam-4426	66	11	w3	w3	NOUN
ejpam-4426	66	12	)	)	PUNCT
ejpam-4426	66	13	=	=	PUNCT
ejpam-4426	67	1	(	(	PUNCT
ejpam-4426	67	2	3	3	NUM
ejpam-4426	67	3	,	,	PUNCT
ejpam-4426	67	4	3	3	NUM
ejpam-4426	67	5	,	,	PUNCT
ejpam-4426	67	6	2	2	NUM
ejpam-4426	67	7	)	)	PUNCT
ejpam-4426	67	8	differ	differ	VERB
ejpam-4426	67	9	in	in	ADP
ejpam-4426	67	10	at	at	ADV
ejpam-4426	67	11	least	least	ADJ
ejpam-4426	67	12	2	2	NUM
ejpam-4426	67	13	positions	position	NOUN
ejpam-4426	67	14	.	.	PUNCT
ejpam-4426	68	1	but	but	CCONJ
ejpam-4426	68	2	w	w	NOUN
ejpam-4426	68	3	is	be	AUX
ejpam-4426	68	4	not	not	PART
ejpam-4426	68	5	a	a	DET
ejpam-4426	68	6	dominating	dominating	NOUN
ejpam-4426	68	7	set	set	NOUN
ejpam-4426	68	8	of	of	ADP
ejpam-4426	68	9	g.	g.	PROPN
ejpam-4426	68	10	3	3	NUM
ejpam-4426	68	11	.	.	NOUN
ejpam-4426	68	12	2	2	NUM
ejpam-4426	68	13	-	-	PUNCT
ejpam-4426	68	14	resolving	resolve	VERB
ejpam-4426	68	15	dominating	dominating	NOUN
ejpam-4426	68	16	sets	set	NOUN
ejpam-4426	68	17	in	in	ADP
ejpam-4426	68	18	the	the	DET
ejpam-4426	68	19	join	join	NOUN
ejpam-4426	68	20	of	of	ADP
ejpam-4426	68	21	graphs	graph	NOUN
ejpam-4426	68	22	definition	definition	NOUN
ejpam-4426	68	23	1	1	NUM
ejpam-4426	68	24	.	.	PUNCT
ejpam-4426	69	1	let	let	VERB
ejpam-4426	69	2	g	g	NOUN
ejpam-4426	69	3	be	be	AUX
ejpam-4426	69	4	any	any	DET
ejpam-4426	69	5	nontrivial	nontrivial	ADJ
ejpam-4426	69	6	connected	connect	VERB
ejpam-4426	69	7	graph	graph	NOUN
ejpam-4426	69	8	and	and	CCONJ
ejpam-4426	69	9	s	s	VERB
ejpam-4426	69	10	⊆	⊆	NUM
ejpam-4426	69	11	v	v	NOUN
ejpam-4426	69	12	(	(	PUNCT
ejpam-4426	69	13	g	g	NOUN
ejpam-4426	69	14	)	)	PUNCT
ejpam-4426	69	15	.	.	PUNCT
ejpam-4426	70	1	a	a	DET
ejpam-4426	70	2	set	set	NOUN
ejpam-4426	70	3	s	s	PART
ejpam-4426	70	4	⊂	⊂	X
ejpam-4426	70	5	v	v	X
ejpam-4426	70	6	(	(	PUNCT
ejpam-4426	70	7	g	g	NOUN
ejpam-4426	70	8	)	)	PUNCT
ejpam-4426	70	9	is	be	AUX
ejpam-4426	70	10	a	a	DET
ejpam-4426	70	11	2	2	NUM
ejpam-4426	70	12	-	-	PUNCT
ejpam-4426	70	13	locating	locate	VERB
ejpam-4426	70	14	set	set	NOUN
ejpam-4426	70	15	of	of	ADP
ejpam-4426	70	16	g	g	NOUN
ejpam-4426	70	17	if	if	SCONJ
ejpam-4426	70	18	it	it	PRON
ejpam-4426	70	19	satisfies	satisfy	VERB
ejpam-4426	70	20	the	the	DET
ejpam-4426	70	21	following	follow	VERB
ejpam-4426	70	22	conditions	condition	NOUN
ejpam-4426	70	23	:	:	PUNCT
ejpam-4426	70	24	(	(	PUNCT
ejpam-4426	70	25	i	i	NOUN
ejpam-4426	70	26	)	)	PUNCT
ejpam-4426	70	27	|(ng(x)	|(ng(x)	PROPN
ejpam-4426	70	28	△	△	NOUN
ejpam-4426	70	29	ng(y	ng(y	NUM
ejpam-4426	70	30	)	)	PUNCT
ejpam-4426	70	31	)	)	PUNCT
ejpam-4426	71	1	∩	∩	NOUN
ejpam-4426	71	2	s|	s|	VERB
ejpam-4426	71	3	≥	≥	NOUN
ejpam-4426	71	4	2	2	NUM
ejpam-4426	71	5	,	,	PUNCT
ejpam-4426	71	6	for	for	ADP
ejpam-4426	71	7	all	all	DET
ejpam-4426	71	8	x	x	NOUN
ejpam-4426	71	9	,	,	PUNCT
ejpam-4426	71	10	y	y	PROPN
ejpam-4426	71	11	∈	∈	PROPN
ejpam-4426	71	12	v	v	X
ejpam-4426	71	13	(	(	PUNCT
ejpam-4426	71	14	g)\s	g)\s	VERB
ejpam-4426	71	15	with	with	ADP
ejpam-4426	71	16	x	x	PROPN
ejpam-4426	71	17	̸=	̸=	PROPN
ejpam-4426	71	18	y	y	PROPN
ejpam-4426	71	19	j.	j.	PROPN
ejpam-4426	71	20	cabaro	cabaro	PROPN
ejpam-4426	71	21	,	,	PUNCT
ejpam-4426	71	22	h.	h.	PROPN
ejpam-4426	71	23	rara	rara	PROPN
ejpam-4426	71	24	/	/	SYM
ejpam-4426	71	25	eur	eur	PROPN
ejpam-4426	71	26	.	.	PUNCT
ejpam-4426	72	1	j.	j.	PROPN
ejpam-4426	72	2	pure	pure	PROPN
ejpam-4426	72	3	appl	appl	PROPN
ejpam-4426	72	4	.	.	PROPN
ejpam-4426	72	5	math	math	PROPN
ejpam-4426	72	6	,	,	PUNCT
ejpam-4426	72	7	15	15	NUM
ejpam-4426	72	8	(	(	PUNCT
ejpam-4426	72	9	3	3	NUM
ejpam-4426	72	10	)	)	PUNCT
ejpam-4426	72	11	(	(	PUNCT
ejpam-4426	72	12	2022	2022	NUM
ejpam-4426	72	13	)	)	PUNCT
ejpam-4426	72	14	,	,	PUNCT
ejpam-4426	72	15	1417	1417	NUM
ejpam-4426	72	16	-	-	SYM
ejpam-4426	72	17	1425	1425	NUM
ejpam-4426	72	18	1420	1420	NUM
ejpam-4426	72	19	....................................	....................................	PUNCT
ejpam-4426	72	20	....................................	....................................	PUNCT
ejpam-4426	73	1	....................................	....................................	PUNCT
ejpam-4426	73	2	....................................	....................................	PUNCT
ejpam-4426	74	1	....................................	....................................	PUNCT
ejpam-4426	74	2	....................................	....................................	PUNCT
ejpam-4426	75	1	.........	.........	PUNCT
ejpam-4426	75	2	........	........	PUNCT
ejpam-4426	75	3	........	........	PUNCT
ejpam-4426	75	4	........	........	PUNCT
ejpam-4426	75	5	........	........	PUNCT
ejpam-4426	75	6	........	........	PUNCT
ejpam-4426	75	7	........	........	PUNCT
ejpam-4426	75	8	........	........	PUNCT
ejpam-4426	75	9	........	........	PUNCT
ejpam-4426	75	10	........	........	PUNCT
ejpam-4426	76	1	........	........	PUNCT
ejpam-4426	76	2	....	....	PUNCT
ejpam-4426	77	1	...................	...................	PUNCT
ejpam-4426	77	2	..................	..................	PUNCT
ejpam-4426	78	1	..................	..................	PUNCT
ejpam-4426	78	2	..................	..................	PUNCT
ejpam-4426	79	1	..................	..................	PUNCT
ejpam-4426	79	2	...............	...............	PUNCT
ejpam-4426	80	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4426	80	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	80	3	............	............	PUNCT
ejpam-4426	80	4	...........	...........	PUNCT
ejpam-4426	80	5	...........	...........	PUNCT
ejpam-4426	80	6	...........	...........	PUNCT
ejpam-4426	80	7	...........	...........	PUNCT
ejpam-4426	80	8	...........	...........	PUNCT
ejpam-4426	80	9	...........	...........	PUNCT
ejpam-4426	80	10	...........	...........	PUNCT
ejpam-4426	80	11	...........	...........	PUNCT
ejpam-4426	80	12	...........	...........	PUNCT
ejpam-4426	80	13	...........	...........	PUNCT
ejpam-4426	80	14	...........	...........	PUNCT
ejpam-4426	80	15	...	...	PUNCT
ejpam-4426	80	16	..........................................................................................................	..........................................................................................................	PUNCT
ejpam-4426	81	1	g	g	NOUN
ejpam-4426	81	2	:	:	PUNCT
ejpam-4426	81	3	u1	u1	PROPN
ejpam-4426	81	4	u2	u2	PROPN
ejpam-4426	81	5	u3	u3	PROPN
ejpam-4426	81	6	u4	u4	PROPN
ejpam-4426	81	7	u5	u5	PROPN
ejpam-4426	81	8	u6	u6	PROPN
ejpam-4426	81	9	•	•	ADP
ejpam-4426	81	10	•	•	NOUN
ejpam-4426	81	11	•	•	NUM
ejpam-4426	81	12	figure	figure	NOUN
ejpam-4426	81	13	2	2	NUM
ejpam-4426	81	14	:	:	PUNCT
ejpam-4426	81	15	a	a	DET
ejpam-4426	81	16	graph	graph	NOUN
ejpam-4426	81	17	g	g	NOUN
ejpam-4426	81	18	with	with	ADP
ejpam-4426	81	19	dim2(g	dim2(g	NOUN
ejpam-4426	81	20	)	)	PUNCT
ejpam-4426	81	21	=	=	SYM
ejpam-4426	81	22	3	3	NUM
ejpam-4426	81	23	(	(	PUNCT
ejpam-4426	81	24	ii	ii	NOUN
ejpam-4426	81	25	)	)	PUNCT
ejpam-4426	81	26	(	(	PUNCT
ejpam-4426	81	27	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-4426	81	28	)	)	PUNCT
ejpam-4426	81	29	)	)	PUNCT
ejpam-4426	82	1	∩	∩	PROPN
ejpam-4426	82	2	s	s	PART
ejpam-4426	82	3	̸=	̸=	PROPN
ejpam-4426	82	4	∅	∅	NOUN
ejpam-4426	82	5	or	or	CCONJ
ejpam-4426	82	6	(	(	PUNCT
ejpam-4426	82	7	ng(w)\ng[v]\s	ng(w)\ng[v]\s	PROPN
ejpam-4426	82	8	̸=	̸=	PROPN
ejpam-4426	82	9	∅	∅	NOUN
ejpam-4426	82	10	,	,	PUNCT
ejpam-4426	82	11	for	for	ADP
ejpam-4426	82	12	all	all	PRON
ejpam-4426	82	13	v	v	ADP
ejpam-4426	82	14	∈	∈	NOUN
ejpam-4426	82	15	s	s	NOUN
ejpam-4426	82	16	and	and	CCONJ
ejpam-4426	82	17	for	for	ADP
ejpam-4426	82	18	all	all	DET
ejpam-4426	82	19	w	w	PROPN
ejpam-4426	82	20	∈	∈	PROPN
ejpam-4426	82	21	v(g)\s	v(g)\s	NOUN
ejpam-4426	82	22	.	.	PUNCT
ejpam-4426	83	1	the	the	DET
ejpam-4426	83	2	2	2	NUM
ejpam-4426	83	3	-	-	PUNCT
ejpam-4426	83	4	locating	locate	VERB
ejpam-4426	83	5	number	number	NOUN
ejpam-4426	83	6	of	of	ADP
ejpam-4426	83	7	g	g	NOUN
ejpam-4426	83	8	,	,	PUNCT
ejpam-4426	83	9	denoted	denote	VERB
ejpam-4426	83	10	by	by	ADP
ejpam-4426	83	11	ln2(g	ln2(g	NOUN
ejpam-4426	83	12	)	)	PUNCT
ejpam-4426	83	13	,	,	PUNCT
ejpam-4426	83	14	is	be	AUX
ejpam-4426	83	15	the	the	DET
ejpam-4426	83	16	smallest	small	ADJ
ejpam-4426	83	17	cardinality	cardinality	NOUN
ejpam-4426	83	18	of	of	ADP
ejpam-4426	83	19	a	a	DET
ejpam-4426	83	20	2	2	NUM
ejpam-4426	83	21	-	-	PUNCT
ejpam-4426	83	22	locating	locate	VERB
ejpam-4426	83	23	set	set	NOUN
ejpam-4426	83	24	of	of	ADP
ejpam-4426	83	25	g.	g.	PROPN
ejpam-4426	83	26	a	a	DET
ejpam-4426	83	27	2	2	NUM
ejpam-4426	83	28	-	-	PUNCT
ejpam-4426	83	29	locating	locate	VERB
ejpam-4426	83	30	set	set	NOUN
ejpam-4426	83	31	of	of	ADP
ejpam-4426	83	32	g	g	NOUN
ejpam-4426	83	33	of	of	ADP
ejpam-4426	83	34	cardinality	cardinality	PROPN
ejpam-4426	83	35	ln2(g	ln2(g	PROPN
ejpam-4426	83	36	)	)	PUNCT
ejpam-4426	83	37	is	be	AUX
ejpam-4426	83	38	referred	refer	VERB
ejpam-4426	83	39	to	to	ADP
ejpam-4426	83	40	as	as	ADP
ejpam-4426	83	41	an	an	DET
ejpam-4426	83	42	ln2	ln2	NOUN
ejpam-4426	83	43	-	-	PUNCT
ejpam-4426	83	44	set	set	NOUN
ejpam-4426	83	45	of	of	ADP
ejpam-4426	83	46	g.	g.	PROPN
ejpam-4426	83	47	definition	definition	NOUN
ejpam-4426	83	48	2	2	NUM
ejpam-4426	83	49	.	.	PUNCT
ejpam-4426	84	1	let	let	VERB
ejpam-4426	84	2	g	g	NOUN
ejpam-4426	84	3	be	be	AUX
ejpam-4426	84	4	any	any	DET
ejpam-4426	84	5	nontrivial	nontrivial	ADJ
ejpam-4426	84	6	connected	connect	VERB
ejpam-4426	84	7	graph	graph	NOUN
ejpam-4426	84	8	and	and	CCONJ
ejpam-4426	84	9	s	s	VERB
ejpam-4426	84	10	⊆	⊆	NUM
ejpam-4426	84	11	v	v	NOUN
ejpam-4426	84	12	(	(	PUNCT
ejpam-4426	84	13	g	g	NOUN
ejpam-4426	84	14	)	)	PUNCT
ejpam-4426	84	15	.	.	PUNCT
ejpam-4426	85	1	s	s	PART
ejpam-4426	85	2	is	be	AUX
ejpam-4426	85	3	a	a	DET
ejpam-4426	85	4	(	(	PUNCT
ejpam-4426	85	5	2	2	NUM
ejpam-4426	85	6	,	,	PUNCT
ejpam-4426	85	7	2)locating	2)locating	NUM
ejpam-4426	85	8	(	(	PUNCT
ejpam-4426	85	9	(	(	PUNCT
ejpam-4426	85	10	2	2	NUM
ejpam-4426	85	11	,	,	PUNCT
ejpam-4426	85	12	1)-locating	1)-locating	NUM
ejpam-4426	85	13	,	,	PUNCT
ejpam-4426	85	14	respectively	respectively	ADV
ejpam-4426	85	15	)	)	PUNCT
ejpam-4426	85	16	set	set	VERB
ejpam-4426	85	17	in	in	ADP
ejpam-4426	85	18	g	g	PROPN
ejpam-4426	85	19	if	if	SCONJ
ejpam-4426	85	20	s	s	NOUN
ejpam-4426	85	21	is	be	AUX
ejpam-4426	85	22	2	2	NUM
ejpam-4426	85	23	-	-	PUNCT
ejpam-4426	85	24	locating	locate	VERB
ejpam-4426	85	25	and	and	CCONJ
ejpam-4426	85	26	|ng(y)∩	|ng(y)∩	NOUN
ejpam-4426	85	27	s|	s|	VERB
ejpam-4426	85	28	≤	≤	NUM
ejpam-4426	85	29	|s|	|s|	PROPN
ejpam-4426	85	30	−	−	PROPN
ejpam-4426	85	31	2	2	NUM
ejpam-4426	85	32	(	(	PUNCT
ejpam-4426	85	33	|ng(y)∩s|	|ng(y)∩s|	NOUN
ejpam-4426	85	34	≤	≤	X
ejpam-4426	85	35	|s|−	|s|−	NOUN
ejpam-4426	85	36	1	1	NUM
ejpam-4426	85	37	,	,	PUNCT
ejpam-4426	85	38	respectively	respectively	ADV
ejpam-4426	85	39	)	)	PUNCT
ejpam-4426	85	40	,	,	PUNCT
ejpam-4426	85	41	for	for	ADP
ejpam-4426	85	42	all	all	DET
ejpam-4426	85	43	y	y	PROPN
ejpam-4426	85	44	∈	∈	PROPN
ejpam-4426	85	45	v	v	NOUN
ejpam-4426	85	46	(	(	PUNCT
ejpam-4426	85	47	g	g	NOUN
ejpam-4426	85	48	)	)	PUNCT
ejpam-4426	85	49	.	.	PUNCT
ejpam-4426	86	1	the	the	DET
ejpam-4426	86	2	(	(	PUNCT
ejpam-4426	86	3	2	2	NUM
ejpam-4426	86	4	,	,	PUNCT
ejpam-4426	86	5	2)-locating	2)-locating	NUM
ejpam-4426	86	6	(	(	PUNCT
ejpam-4426	86	7	(	(	PUNCT
ejpam-4426	86	8	2	2	NUM
ejpam-4426	86	9	,	,	PUNCT
ejpam-4426	86	10	1)-locating	1)-locating	NUM
ejpam-4426	86	11	,	,	PUNCT
ejpam-4426	86	12	respectively	respectively	ADV
ejpam-4426	86	13	)	)	PUNCT
ejpam-4426	86	14	number	number	NOUN
ejpam-4426	86	15	of	of	ADP
ejpam-4426	86	16	g	g	NOUN
ejpam-4426	86	17	,	,	PUNCT
ejpam-4426	86	18	denoted	denote	VERB
ejpam-4426	86	19	by	by	ADP
ejpam-4426	86	20	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4426	86	21	)	)	PUNCT
ejpam-4426	86	22	(	(	PUNCT
ejpam-4426	86	23	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4426	86	24	)	)	PUNCT
ejpam-4426	86	25	,	,	PUNCT
ejpam-4426	86	26	respectively	respectively	ADV
ejpam-4426	86	27	)	)	PUNCT
ejpam-4426	86	28	,	,	PUNCT
ejpam-4426	86	29	is	be	AUX
ejpam-4426	86	30	the	the	DET
ejpam-4426	86	31	smallest	small	ADJ
ejpam-4426	86	32	cardinality	cardinality	NOUN
ejpam-4426	86	33	of	of	ADP
ejpam-4426	86	34	a	a	DET
ejpam-4426	86	35	(	(	PUNCT
ejpam-4426	86	36	2	2	NUM
ejpam-4426	86	37	,	,	PUNCT
ejpam-4426	86	38	2)-locating	2)-locating	NUM
ejpam-4426	86	39	(	(	PUNCT
ejpam-4426	86	40	(	(	PUNCT
ejpam-4426	86	41	2	2	NUM
ejpam-4426	86	42	,	,	PUNCT
ejpam-4426	86	43	1)-locating	1)-locating	NUM
ejpam-4426	86	44	,	,	PUNCT
ejpam-4426	86	45	respectively	respectively	ADV
ejpam-4426	86	46	)	)	PUNCT
ejpam-4426	86	47	set	set	VERB
ejpam-4426	86	48	in	in	ADP
ejpam-4426	86	49	g.	g.	PROPN
ejpam-4426	86	50	a	a	PRON
ejpam-4426	86	51	(	(	PUNCT
ejpam-4426	86	52	2	2	NUM
ejpam-4426	86	53	,	,	PUNCT
ejpam-4426	86	54	2)-locating	2)-locating	NUM
ejpam-4426	86	55	(	(	PUNCT
ejpam-4426	86	56	(	(	PUNCT
ejpam-4426	86	57	2	2	NUM
ejpam-4426	86	58	,	,	PUNCT
ejpam-4426	86	59	1)-locating	1)-locating	NUM
ejpam-4426	86	60	,	,	PUNCT
ejpam-4426	86	61	respectively	respectively	ADV
ejpam-4426	86	62	)	)	PUNCT
ejpam-4426	86	63	set	set	VERB
ejpam-4426	86	64	in	in	ADP
ejpam-4426	86	65	g	g	NOUN
ejpam-4426	86	66	of	of	ADP
ejpam-4426	86	67	cardinality	cardinality	NOUN
ejpam-4426	86	68	ln(2,2)(g	ln(2,2)(g	PROPN
ejpam-4426	86	69	)	)	PUNCT
ejpam-4426	86	70	(	(	PUNCT
ejpam-4426	86	71	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4426	86	72	)	)	PUNCT
ejpam-4426	86	73	,	,	PUNCT
ejpam-4426	86	74	respectively	respectively	ADV
ejpam-4426	86	75	)	)	PUNCT
ejpam-4426	86	76	is	be	AUX
ejpam-4426	86	77	referred	refer	VERB
ejpam-4426	86	78	to	to	ADP
ejpam-4426	86	79	as	as	ADP
ejpam-4426	86	80	an	an	DET
ejpam-4426	86	81	ln(2,2)-set	ln(2,2)-set	NOUN
ejpam-4426	86	82	(	(	PUNCT
ejpam-4426	86	83	ln(2,1)-set	ln(2,1)-set	PROPN
ejpam-4426	86	84	,	,	PUNCT
ejpam-4426	86	85	respectively	respectively	ADV
ejpam-4426	86	86	)	)	PUNCT
ejpam-4426	86	87	in	in	ADP
ejpam-4426	86	88	g.	g.	PROPN
ejpam-4426	86	89	theorem	theorem	VERB
ejpam-4426	86	90	4	4	NUM
ejpam-4426	86	91	.	.	PUNCT
ejpam-4426	87	1	[	[	X
ejpam-4426	87	2	4	4	X
ejpam-4426	87	3	]	]	PUNCT
ejpam-4426	87	4	let	let	VERB
ejpam-4426	87	5	g	g	PRON
ejpam-4426	87	6	be	be	AUX
ejpam-4426	87	7	a	a	DET
ejpam-4426	87	8	connected	connected	ADJ
ejpam-4426	87	9	graph	graph	NOUN
ejpam-4426	87	10	of	of	ADP
ejpam-4426	87	11	order	order	NOUN
ejpam-4426	87	12	greater	great	ADJ
ejpam-4426	87	13	than	than	ADP
ejpam-4426	87	14	3	3	NUM
ejpam-4426	87	15	and	and	CCONJ
ejpam-4426	87	16	let	let	VERB
ejpam-4426	87	17	k1	k1	NOUN
ejpam-4426	87	18	=	=	SYM
ejpam-4426	87	19	{	{	PUNCT
ejpam-4426	87	20	v	v	NOUN
ejpam-4426	87	21	}	}	PUNCT
ejpam-4426	87	22	.	.	PUNCT
ejpam-4426	88	1	then	then	ADV
ejpam-4426	88	2	s	s	VERB
ejpam-4426	88	3	⊆	⊆	NUM
ejpam-4426	88	4	v	v	NOUN
ejpam-4426	88	5	(	(	PUNCT
ejpam-4426	88	6	k1	k1	NOUN
ejpam-4426	88	7	+	+	CCONJ
ejpam-4426	88	8	g	g	NOUN
ejpam-4426	88	9	)	)	PUNCT
ejpam-4426	88	10	is	be	AUX
ejpam-4426	88	11	a	a	DET
ejpam-4426	88	12	2	2	NUM
ejpam-4426	88	13	-	-	PUNCT
ejpam-4426	88	14	resolving	resolve	VERB
ejpam-4426	88	15	set	set	NOUN
ejpam-4426	88	16	of	of	ADP
ejpam-4426	88	17	k1	k1	NOUN
ejpam-4426	88	18	+	+	CCONJ
ejpam-4426	88	19	g	g	NOUN
ejpam-4426	88	20	if	if	SCONJ
ejpam-4426	88	21	and	and	CCONJ
ejpam-4426	88	22	only	only	ADV
ejpam-4426	88	23	if	if	SCONJ
ejpam-4426	88	24	either	either	PRON
ejpam-4426	88	25	v	v	NOUN
ejpam-4426	88	26	/∈	/∈	PUNCT
ejpam-4426	88	27	s	s	PART
ejpam-4426	88	28	and	and	CCONJ
ejpam-4426	88	29	s	s	VERB
ejpam-4426	88	30	is	be	AUX
ejpam-4426	88	31	a	a	DET
ejpam-4426	88	32	(	(	PUNCT
ejpam-4426	88	33	2	2	NUM
ejpam-4426	88	34	,	,	PUNCT
ejpam-4426	88	35	2)-locating	2)-locating	NUM
ejpam-4426	88	36	set	set	VERB
ejpam-4426	88	37	in	in	ADP
ejpam-4426	88	38	g	g	PROPN
ejpam-4426	88	39	or	or	CCONJ
ejpam-4426	88	40	s	s	NOUN
ejpam-4426	88	41	=	=	PUNCT
ejpam-4426	88	42	{	{	PUNCT
ejpam-4426	88	43	v	v	NOUN
ejpam-4426	88	44	}	}	PUNCT
ejpam-4426	88	45	∪	∪	NOUN
ejpam-4426	88	46	t	t	PROPN
ejpam-4426	88	47	,	,	PUNCT
ejpam-4426	88	48	where	where	SCONJ
ejpam-4426	88	49	t	t	PROPN
ejpam-4426	88	50	is	be	AUX
ejpam-4426	88	51	a	a	DET
ejpam-4426	88	52	(	(	PUNCT
ejpam-4426	88	53	2	2	NUM
ejpam-4426	88	54	,	,	PUNCT
ejpam-4426	88	55	1)-locating	1)-locating	NUM
ejpam-4426	88	56	set	set	VERB
ejpam-4426	88	57	in	in	ADP
ejpam-4426	88	58	g.	g.	PROPN
ejpam-4426	88	59	theorem	theorem	VERB
ejpam-4426	88	60	5	5	NUM
ejpam-4426	88	61	.	.	PUNCT
ejpam-4426	89	1	[	[	X
ejpam-4426	89	2	4	4	X
ejpam-4426	89	3	]	]	PUNCT
ejpam-4426	89	4	let	let	VERB
ejpam-4426	89	5	g	g	NOUN
ejpam-4426	89	6	and	and	CCONJ
ejpam-4426	89	7	h	h	NOUN
ejpam-4426	89	8	be	be	AUX
ejpam-4426	89	9	nontrivial	nontrivial	ADJ
ejpam-4426	89	10	connected	connected	ADJ
ejpam-4426	89	11	graphs	graph	NOUN
ejpam-4426	89	12	.	.	PUNCT
ejpam-4426	90	1	a	a	DET
ejpam-4426	90	2	proper	proper	ADJ
ejpam-4426	90	3	subset	subset	NOUN
ejpam-4426	90	4	s	s	NOUN
ejpam-4426	90	5	of	of	ADP
ejpam-4426	90	6	v	v	NOUN
ejpam-4426	90	7	(	(	PUNCT
ejpam-4426	90	8	g+h	g+h	PROPN
ejpam-4426	90	9	)	)	PUNCT
ejpam-4426	90	10	is	be	AUX
ejpam-4426	90	11	a	a	DET
ejpam-4426	90	12	2	2	NUM
ejpam-4426	90	13	-	-	PUNCT
ejpam-4426	90	14	resolving	resolving	NOUN
ejpam-4426	90	15	set	set	NOUN
ejpam-4426	90	16	in	in	ADP
ejpam-4426	90	17	g+h	g+h	PROPN
ejpam-4426	90	18	if	if	SCONJ
ejpam-4426	90	19	and	and	CCONJ
ejpam-4426	90	20	only	only	ADV
ejpam-4426	90	21	if	if	SCONJ
ejpam-4426	90	22	sg	sg	PROPN
ejpam-4426	90	23	=	=	SYM
ejpam-4426	90	24	v	v	NOUN
ejpam-4426	90	25	(	(	PUNCT
ejpam-4426	90	26	g)∩s	g)∩s	PROPN
ejpam-4426	90	27	and	and	CCONJ
ejpam-4426	90	28	sh	sh	PROPN
ejpam-4426	90	29	=	=	SYM
ejpam-4426	90	30	v	v	PROPN
ejpam-4426	90	31	(	(	PUNCT
ejpam-4426	90	32	h)∩s	h)∩s	PROPN
ejpam-4426	90	33	are	be	AUX
ejpam-4426	90	34	2	2	NUM
ejpam-4426	90	35	-	-	PUNCT
ejpam-4426	90	36	locating	locate	VERB
ejpam-4426	90	37	sets	set	NOUN
ejpam-4426	90	38	in	in	ADP
ejpam-4426	90	39	g	g	PROPN
ejpam-4426	90	40	and	and	CCONJ
ejpam-4426	90	41	h	h	NOUN
ejpam-4426	90	42	,	,	PUNCT
ejpam-4426	90	43	respectively	respectively	ADV
ejpam-4426	90	44	,	,	PUNCT
ejpam-4426	90	45	where	where	SCONJ
ejpam-4426	90	46	sg	sg	NOUN
ejpam-4426	90	47	or	or	CCONJ
ejpam-4426	90	48	sh	sh	PROPN
ejpam-4426	90	49	is	be	AUX
ejpam-4426	90	50	a	a	DET
ejpam-4426	90	51	(	(	PUNCT
ejpam-4426	90	52	2	2	NUM
ejpam-4426	90	53	,	,	PUNCT
ejpam-4426	90	54	2)-locating	2)-locating	NUM
ejpam-4426	90	55	set	set	NOUN
ejpam-4426	90	56	or	or	CCONJ
ejpam-4426	90	57	sg	sg	PROPN
ejpam-4426	90	58	and	and	CCONJ
ejpam-4426	90	59	sh	sh	PROPN
ejpam-4426	90	60	are	be	AUX
ejpam-4426	90	61	(	(	PUNCT
ejpam-4426	90	62	2	2	NUM
ejpam-4426	90	63	,	,	PUNCT
ejpam-4426	90	64	1)-locating	1)-locating	NUM
ejpam-4426	90	65	sets	set	NOUN
ejpam-4426	90	66	.	.	PUNCT
ejpam-4426	91	1	theorem	theorem	NOUN
ejpam-4426	91	2	6	6	NUM
ejpam-4426	91	3	.	.	PUNCT
ejpam-4426	92	1	let	let	VERB
ejpam-4426	92	2	g	g	PRON
ejpam-4426	92	3	be	be	AUX
ejpam-4426	92	4	a	a	DET
ejpam-4426	92	5	connected	connected	ADJ
ejpam-4426	92	6	non	non	ADJ
ejpam-4426	92	7	-	-	ADJ
ejpam-4426	92	8	trivial	trivial	ADJ
ejpam-4426	92	9	graph	graph	NOUN
ejpam-4426	92	10	and	and	CCONJ
ejpam-4426	92	11	let	let	VERB
ejpam-4426	92	12	k1	k1	NOUN
ejpam-4426	92	13	=	=	SYM
ejpam-4426	92	14	{	{	PUNCT
ejpam-4426	92	15	v	v	NOUN
ejpam-4426	92	16	}	}	PUNCT
ejpam-4426	92	17	.	.	PUNCT
ejpam-4426	93	1	then	then	ADV
ejpam-4426	93	2	s	s	VERB
ejpam-4426	93	3	⊆	⊆	NUM
ejpam-4426	93	4	v	v	NOUN
ejpam-4426	93	5	(	(	PUNCT
ejpam-4426	93	6	k1	k1	NOUN
ejpam-4426	93	7	+	+	NOUN
ejpam-4426	93	8	g	g	NOUN
ejpam-4426	93	9	)	)	PUNCT
ejpam-4426	93	10	is	be	AUX
ejpam-4426	93	11	a	a	DET
ejpam-4426	93	12	2	2	NUM
ejpam-4426	93	13	-	-	PUNCT
ejpam-4426	93	14	resolving	resolve	VERB
ejpam-4426	93	15	dominating	dominating	NOUN
ejpam-4426	93	16	set	set	VERB
ejpam-4426	93	17	in	in	ADP
ejpam-4426	93	18	k1	k1	NOUN
ejpam-4426	93	19	+	+	ADP
ejpam-4426	93	20	g	g	PROPN
ejpam-4426	93	21	if	if	SCONJ
ejpam-4426	94	1	and	and	CCONJ
ejpam-4426	94	2	only	only	ADV
ejpam-4426	94	3	if	if	SCONJ
ejpam-4426	94	4	it	it	PRON
ejpam-4426	94	5	is	be	AUX
ejpam-4426	94	6	a	a	DET
ejpam-4426	94	7	2	2	NUM
ejpam-4426	94	8	-	-	PUNCT
ejpam-4426	94	9	resolving	resolving	NOUN
ejpam-4426	94	10	set	set	VERB
ejpam-4426	94	11	in	in	ADP
ejpam-4426	94	12	k1	k1	PROPN
ejpam-4426	94	13	+	+	PROPN
ejpam-4426	94	14	g.	g.	NOUN
ejpam-4426	94	15	proof	proof	NOUN
ejpam-4426	94	16	.	.	PUNCT
ejpam-4426	95	1	let	let	VERB
ejpam-4426	95	2	s	s	PRON
ejpam-4426	95	3	⊆	⊆	NUM
ejpam-4426	95	4	v	v	NOUN
ejpam-4426	95	5	(	(	PUNCT
ejpam-4426	95	6	k1	k1	NOUN
ejpam-4426	95	7	+	+	CCONJ
ejpam-4426	95	8	g	g	NOUN
ejpam-4426	95	9	)	)	PUNCT
ejpam-4426	95	10	be	be	VERB
ejpam-4426	95	11	a	a	DET
ejpam-4426	95	12	2	2	NUM
ejpam-4426	95	13	-	-	PUNCT
ejpam-4426	95	14	resolving	resolve	VERB
ejpam-4426	95	15	dominating	dominating	NOUN
ejpam-4426	95	16	set	set	VERB
ejpam-4426	95	17	in	in	ADP
ejpam-4426	95	18	k1	k1	PROPN
ejpam-4426	95	19	+	+	CCONJ
ejpam-4426	95	20	g.	g.	PROPN
ejpam-4426	95	21	then	then	ADV
ejpam-4426	95	22	,	,	PUNCT
ejpam-4426	95	23	s	s	VERB
ejpam-4426	95	24	is	be	AUX
ejpam-4426	95	25	a	a	DET
ejpam-4426	95	26	2	2	NUM
ejpam-4426	95	27	-	-	PUNCT
ejpam-4426	95	28	resolving	resolving	NOUN
ejpam-4426	95	29	set	set	VERB
ejpam-4426	95	30	in	in	ADP
ejpam-4426	95	31	k1	k1	NOUN
ejpam-4426	96	1	+	+	PROPN
ejpam-4426	96	2	g	g	NOUN
ejpam-4426	96	3	by	by	ADP
ejpam-4426	96	4	the	the	DET
ejpam-4426	96	5	definition	definition	NOUN
ejpam-4426	96	6	of	of	ADP
ejpam-4426	96	7	2	2	NUM
ejpam-4426	96	8	-	-	PUNCT
ejpam-4426	96	9	resolving	resolve	VERB
ejpam-4426	96	10	dominating	dominating	NOUN
ejpam-4426	96	11	set	set	NOUN
ejpam-4426	96	12	.	.	PUNCT
ejpam-4426	97	1	conversely	conversely	ADV
ejpam-4426	97	2	,	,	PUNCT
ejpam-4426	97	3	if	if	SCONJ
ejpam-4426	97	4	s	s	VERB
ejpam-4426	97	5	is	be	AUX
ejpam-4426	97	6	a	a	DET
ejpam-4426	97	7	2	2	NUM
ejpam-4426	97	8	-	-	PUNCT
ejpam-4426	97	9	resolving	resolving	NOUN
ejpam-4426	97	10	set	set	VERB
ejpam-4426	97	11	in	in	ADP
ejpam-4426	97	12	k1	k1	NOUN
ejpam-4426	97	13	+	+	CCONJ
ejpam-4426	97	14	g	g	NOUN
ejpam-4426	97	15	,	,	PUNCT
ejpam-4426	97	16	then	then	ADV
ejpam-4426	97	17	by	by	ADP
ejpam-4426	97	18	theorem	theorem	NOUN
ejpam-4426	97	19	4	4	NUM
ejpam-4426	97	20	,	,	PUNCT
ejpam-4426	97	21	s	s	VERB
ejpam-4426	97	22	is	be	AUX
ejpam-4426	97	23	a	a	DET
ejpam-4426	97	24	2	2	NUM
ejpam-4426	97	25	-	-	PUNCT
ejpam-4426	97	26	locating	locate	VERB
ejpam-4426	97	27	set	set	NOUN
ejpam-4426	97	28	.	.	PUNCT
ejpam-4426	98	1	hence	hence	ADV
ejpam-4426	98	2	,	,	PUNCT
ejpam-4426	98	3	s	s	VERB
ejpam-4426	98	4	is	be	AUX
ejpam-4426	98	5	a	a	DET
ejpam-4426	98	6	dominating	dominating	NOUN
ejpam-4426	98	7	set	set	VERB
ejpam-4426	98	8	in	in	ADP
ejpam-4426	98	9	k1	k1	PROPN
ejpam-4426	98	10	+	+	CCONJ
ejpam-4426	98	11	g.	g.	PROPN
ejpam-4426	98	12	thus	thus	ADV
ejpam-4426	98	13	,	,	PUNCT
ejpam-4426	98	14	s	s	VERB
ejpam-4426	98	15	is	be	AUX
ejpam-4426	98	16	a	a	DET
ejpam-4426	98	17	2	2	NUM
ejpam-4426	98	18	-	-	PUNCT
ejpam-4426	98	19	resolving	resolve	VERB
ejpam-4426	98	20	dominating	dominating	NOUN
ejpam-4426	98	21	set	set	VERB
ejpam-4426	98	22	in	in	ADP
ejpam-4426	98	23	k1	k1	PROPN
ejpam-4426	98	24	+	+	PROPN
ejpam-4426	98	25	g.	g.	PROPN
ejpam-4426	98	26	corollary	corollary	NOUN
ejpam-4426	98	27	1	1	NUM
ejpam-4426	98	28	.	.	PUNCT
ejpam-4426	99	1	γ2r(k1	γ2r(k1	PROPN
ejpam-4426	100	1	+	+	NOUN
ejpam-4426	100	2	g	g	NOUN
ejpam-4426	100	3	)	)	PUNCT
ejpam-4426	100	4	=	=	SYM
ejpam-4426	100	5	dim2(k1	dim2(k1	PROPN
ejpam-4426	100	6	+	+	NOUN
ejpam-4426	100	7	g	g	NOUN
ejpam-4426	100	8	)	)	PUNCT
ejpam-4426	100	9	.	.	PUNCT
ejpam-4426	101	1	j.	j.	PROPN
ejpam-4426	101	2	cabaro	cabaro	PROPN
ejpam-4426	101	3	,	,	PUNCT
ejpam-4426	101	4	h.	h.	PROPN
ejpam-4426	101	5	rara	rara	PROPN
ejpam-4426	101	6	/	/	SYM
ejpam-4426	101	7	eur	eur	PROPN
ejpam-4426	101	8	.	.	PUNCT
ejpam-4426	102	1	j.	j.	PROPN
ejpam-4426	102	2	pure	pure	PROPN
ejpam-4426	102	3	appl	appl	PROPN
ejpam-4426	102	4	.	.	PROPN
ejpam-4426	102	5	math	math	PROPN
ejpam-4426	102	6	,	,	PUNCT
ejpam-4426	102	7	15	15	NUM
ejpam-4426	102	8	(	(	PUNCT
ejpam-4426	102	9	3	3	NUM
ejpam-4426	102	10	)	)	PUNCT
ejpam-4426	102	11	(	(	PUNCT
ejpam-4426	102	12	2022	2022	NUM
ejpam-4426	102	13	)	)	PUNCT
ejpam-4426	102	14	,	,	PUNCT
ejpam-4426	102	15	1417	1417	NUM
ejpam-4426	102	16	-	-	SYM
ejpam-4426	102	17	1425	1425	NUM
ejpam-4426	102	18	1421	1421	NUM
ejpam-4426	102	19	theorem	theorem	NOUN
ejpam-4426	102	20	7	7	NUM
ejpam-4426	102	21	.	.	PUNCT
ejpam-4426	103	1	let	let	VERB
ejpam-4426	103	2	g	g	NOUN
ejpam-4426	103	3	andh	andh	NOUN
ejpam-4426	103	4	be	be	AUX
ejpam-4426	103	5	nontrivial	nontrivial	ADJ
ejpam-4426	103	6	connected	connected	ADJ
ejpam-4426	103	7	graphs	graph	NOUN
ejpam-4426	103	8	.	.	PUNCT
ejpam-4426	104	1	a	a	DET
ejpam-4426	104	2	proper	proper	ADJ
ejpam-4426	104	3	subset	subset	NOUN
ejpam-4426	104	4	s	s	NOUN
ejpam-4426	104	5	of	of	ADP
ejpam-4426	104	6	v	v	NOUN
ejpam-4426	104	7	(	(	PUNCT
ejpam-4426	104	8	g+h	g+h	PROPN
ejpam-4426	104	9	)	)	PUNCT
ejpam-4426	104	10	is	be	AUX
ejpam-4426	104	11	a	a	DET
ejpam-4426	104	12	2	2	NUM
ejpam-4426	104	13	-	-	PUNCT
ejpam-4426	104	14	resolving	resolve	VERB
ejpam-4426	104	15	dominating	dominating	NOUN
ejpam-4426	104	16	set	set	VERB
ejpam-4426	104	17	in	in	ADP
ejpam-4426	104	18	g+h	g+h	PROPN
ejpam-4426	104	19	if	if	SCONJ
ejpam-4426	104	20	and	and	CCONJ
ejpam-4426	104	21	only	only	ADV
ejpam-4426	104	22	if	if	SCONJ
ejpam-4426	104	23	it	it	PRON
ejpam-4426	104	24	is	be	AUX
ejpam-4426	104	25	a	a	DET
ejpam-4426	104	26	2	2	NUM
ejpam-4426	104	27	-	-	PUNCT
ejpam-4426	104	28	resolving	resolving	NOUN
ejpam-4426	104	29	set	set	VERB
ejpam-4426	104	30	in	in	ADP
ejpam-4426	104	31	g+h	g+h	PROPN
ejpam-4426	104	32	.	.	PUNCT
ejpam-4426	105	1	proof	proof	NOUN
ejpam-4426	105	2	.	.	PUNCT
ejpam-4426	106	1	let	let	VERB
ejpam-4426	106	2	s	s	PRON
ejpam-4426	106	3	⊆	⊆	NUM
ejpam-4426	106	4	v	v	NOUN
ejpam-4426	106	5	(	(	PUNCT
ejpam-4426	106	6	g	g	PROPN
ejpam-4426	106	7	+	+	NOUN
ejpam-4426	106	8	h	h	NOUN
ejpam-4426	106	9	)	)	PUNCT
ejpam-4426	106	10	be	be	VERB
ejpam-4426	106	11	a	a	DET
ejpam-4426	106	12	2	2	NUM
ejpam-4426	106	13	-	-	PUNCT
ejpam-4426	106	14	resolving	resolve	VERB
ejpam-4426	106	15	dominating	dominating	NOUN
ejpam-4426	106	16	set	set	VERB
ejpam-4426	106	17	in	in	ADP
ejpam-4426	106	18	g	g	PROPN
ejpam-4426	106	19	+	+	CCONJ
ejpam-4426	106	20	h.	h.	PROPN
ejpam-4426	106	21	then	then	ADV
ejpam-4426	106	22	,	,	PUNCT
ejpam-4426	106	23	s	s	VERB
ejpam-4426	106	24	is	be	AUX
ejpam-4426	106	25	a	a	DET
ejpam-4426	106	26	2	2	NUM
ejpam-4426	106	27	-	-	PUNCT
ejpam-4426	106	28	resolving	resolving	NOUN
ejpam-4426	106	29	set	set	VERB
ejpam-4426	106	30	in	in	ADP
ejpam-4426	106	31	g+h	g+h	PROPN
ejpam-4426	106	32	.	.	PUNCT
ejpam-4426	107	1	conversely	conversely	ADV
ejpam-4426	107	2	,	,	PUNCT
ejpam-4426	107	3	if	if	SCONJ
ejpam-4426	107	4	s	s	VERB
ejpam-4426	107	5	is	be	AUX
ejpam-4426	107	6	a	a	DET
ejpam-4426	107	7	2	2	NUM
ejpam-4426	107	8	-	-	PUNCT
ejpam-4426	107	9	resolving	resolving	NOUN
ejpam-4426	107	10	set	set	NOUN
ejpam-4426	107	11	in	in	ADP
ejpam-4426	107	12	g	g	PROPN
ejpam-4426	108	1	+	+	CCONJ
ejpam-4426	108	2	h	h	NOUN
ejpam-4426	108	3	,	,	PUNCT
ejpam-4426	108	4	then	then	ADV
ejpam-4426	108	5	by	by	ADP
ejpam-4426	108	6	theorem	theorem	NOUN
ejpam-4426	108	7	5	5	NUM
ejpam-4426	108	8	,	,	PUNCT
ejpam-4426	108	9	s	s	VERB
ejpam-4426	108	10	is	be	AUX
ejpam-4426	108	11	a	a	DET
ejpam-4426	108	12	2	2	NUM
ejpam-4426	108	13	-	-	PUNCT
ejpam-4426	108	14	locating	locate	VERB
ejpam-4426	108	15	set	set	NOUN
ejpam-4426	108	16	.	.	PUNCT
ejpam-4426	109	1	hence	hence	ADV
ejpam-4426	109	2	,	,	PUNCT
ejpam-4426	109	3	s	s	VERB
ejpam-4426	109	4	is	be	AUX
ejpam-4426	109	5	a	a	DET
ejpam-4426	109	6	dominating	dominating	NOUN
ejpam-4426	109	7	set	set	NOUN
ejpam-4426	109	8	in	in	ADP
ejpam-4426	109	9	g	g	PROPN
ejpam-4426	109	10	+	+	PROPN
ejpam-4426	109	11	h.	h.	PROPN
ejpam-4426	109	12	thus	thus	ADV
ejpam-4426	109	13	,	,	PUNCT
ejpam-4426	109	14	s	s	VERB
ejpam-4426	109	15	is	be	AUX
ejpam-4426	109	16	a	a	DET
ejpam-4426	109	17	2	2	NUM
ejpam-4426	109	18	-	-	PUNCT
ejpam-4426	109	19	resolving	resolve	VERB
ejpam-4426	109	20	dominating	dominating	NOUN
ejpam-4426	109	21	set	set	VERB
ejpam-4426	109	22	in	in	ADP
ejpam-4426	109	23	g+h	g+h	PROPN
ejpam-4426	109	24	.	.	PUNCT
ejpam-4426	110	1	corollary	corollary	ADJ
ejpam-4426	110	2	2	2	NUM
ejpam-4426	110	3	.	.	PUNCT
ejpam-4426	111	1	let	let	VERB
ejpam-4426	111	2	g	g	NOUN
ejpam-4426	111	3	and	and	CCONJ
ejpam-4426	111	4	h	h	NOUN
ejpam-4426	111	5	be	be	AUX
ejpam-4426	111	6	connected	connect	VERB
ejpam-4426	111	7	nontrivial	nontrivial	ADJ
ejpam-4426	111	8	graphs	graph	NOUN
ejpam-4426	111	9	.	.	PUNCT
ejpam-4426	112	1	then	then	ADV
ejpam-4426	112	2	,	,	PUNCT
ejpam-4426	112	3	γ2r(g+h	γ2r(g+h	PROPN
ejpam-4426	112	4	)	)	PUNCT
ejpam-4426	112	5	=	=	SYM
ejpam-4426	112	6	dim2(g+h	dim2(g+h	PROPN
ejpam-4426	112	7	)	)	PUNCT
ejpam-4426	112	8	.	.	PUNCT
ejpam-4426	113	1	the	the	DET
ejpam-4426	113	2	set	set	NOUN
ejpam-4426	113	3	consisting	consisting	NOUN
ejpam-4426	113	4	of	of	ADP
ejpam-4426	113	5	the	the	DET
ejpam-4426	113	6	shaded	shade	VERB
ejpam-4426	113	7	vertices	vertex	NOUN
ejpam-4426	113	8	in	in	ADP
ejpam-4426	113	9	figure	figure	NOUN
ejpam-4426	113	10	3	3	NUM
ejpam-4426	113	11	is	be	AUX
ejpam-4426	113	12	a	a	DET
ejpam-4426	113	13	2	2	NUM
ejpam-4426	113	14	-	-	PUNCT
ejpam-4426	113	15	resolving	resolve	VERB
ejpam-4426	113	16	dominating	dominating	NOUN
ejpam-4426	113	17	set	set	NOUN
ejpam-4426	113	18	of	of	ADP
ejpam-4426	113	19	the	the	DET
ejpam-4426	113	20	join	join	NOUN
ejpam-4426	113	21	p5	p5	PROPN
ejpam-4426	113	22	+	+	CCONJ
ejpam-4426	113	23	p6	p6	PROPN
ejpam-4426	113	24	.	.	PUNCT
ejpam-4426	113	25	....................................	....................................	PUNCT
ejpam-4426	114	1	....................................	....................................	PUNCT
ejpam-4426	114	2	....................................	....................................	PUNCT
ejpam-4426	115	1	....................................	....................................	PUNCT
ejpam-4426	115	2	....................................	....................................	PUNCT
ejpam-4426	116	1	....................................	....................................	PUNCT
ejpam-4426	116	2	....................................	....................................	PUNCT
ejpam-4426	117	1	....................................	....................................	PUNCT
ejpam-4426	117	2	....................................	....................................	PUNCT
ejpam-4426	118	1	....................................	....................................	PUNCT
ejpam-4426	118	2	....................................	....................................	PUNCT
ejpam-4426	119	1	.........	.........	PUNCT
ejpam-4426	119	2	........	........	PUNCT
ejpam-4426	119	3	........	........	PUNCT
ejpam-4426	119	4	........	........	PUNCT
ejpam-4426	119	5	........	........	PUNCT
ejpam-4426	119	6	........	........	PUNCT
ejpam-4426	119	7	........	........	PUNCT
ejpam-4426	119	8	........	........	PUNCT
ejpam-4426	119	9	........	........	PUNCT
ejpam-4426	120	1	......	......	PUNCT
ejpam-4426	120	2	.........	.........	PUNCT
ejpam-4426	120	3	........	........	PUNCT
ejpam-4426	120	4	........	........	PUNCT
ejpam-4426	120	5	........	........	PUNCT
ejpam-4426	120	6	........	........	PUNCT
ejpam-4426	120	7	........	........	PUNCT
ejpam-4426	120	8	........	........	PUNCT
ejpam-4426	120	9	........	........	PUNCT
ejpam-4426	120	10	........	........	PUNCT
ejpam-4426	121	1	......	......	PUNCT
ejpam-4426	121	2	.........	.........	PUNCT
ejpam-4426	121	3	........	........	PUNCT
ejpam-4426	121	4	........	........	PUNCT
ejpam-4426	121	5	........	........	PUNCT
ejpam-4426	121	6	........	........	PUNCT
ejpam-4426	121	7	........	........	PUNCT
ejpam-4426	121	8	........	........	PUNCT
ejpam-4426	121	9	........	........	PUNCT
ejpam-4426	121	10	........	........	PUNCT
ejpam-4426	122	1	......	......	PUNCT
ejpam-4426	122	2	.........	.........	PUNCT
ejpam-4426	122	3	........	........	PUNCT
ejpam-4426	122	4	........	........	PUNCT
ejpam-4426	122	5	........	........	PUNCT
ejpam-4426	122	6	........	........	PUNCT
ejpam-4426	122	7	........	........	PUNCT
ejpam-4426	122	8	........	........	PUNCT
ejpam-4426	122	9	........	........	PUNCT
ejpam-4426	122	10	........	........	PUNCT
ejpam-4426	123	1	......	......	PUNCT
ejpam-4426	123	2	..........	..........	PUNCT
ejpam-4426	124	1	.........	.........	PUNCT
ejpam-4426	124	2	.........	.........	PUNCT
ejpam-4426	125	1	.........	.........	PUNCT
ejpam-4426	125	2	.........	.........	PUNCT
ejpam-4426	126	1	.........	.........	PUNCT
ejpam-4426	126	2	.........	.........	PUNCT
ejpam-4426	127	1	.........	.........	PUNCT
ejpam-4426	127	2	.........	.........	PUNCT
ejpam-4426	128	1	.........	.........	PUNCT
ejpam-4426	128	2	.........	.........	PUNCT
ejpam-4426	129	1	.........	.........	PUNCT
ejpam-4426	129	2	.........	.........	PUNCT
ejpam-4426	130	1	.........	.........	PUNCT
ejpam-4426	130	2	.........	.........	PUNCT
ejpam-4426	131	1	.........	.........	PUNCT
ejpam-4426	131	2	.........	.........	PUNCT
ejpam-4426	132	1	.........	.........	PUNCT
ejpam-4426	132	2	.........	.........	PUNCT
ejpam-4426	133	1	.........	.........	PUNCT
ejpam-4426	133	2	.........	.........	PUNCT
ejpam-4426	134	1	.........	.........	PUNCT
ejpam-4426	134	2	.........	.........	PUNCT
ejpam-4426	135	1	.........	.........	PUNCT
ejpam-4426	135	2	.........	.........	PUNCT
ejpam-4426	136	1	.........	.........	PUNCT
ejpam-4426	136	2	.........	.........	PUNCT
ejpam-4426	137	1	.........	.........	PUNCT
ejpam-4426	137	2	.........	.........	PUNCT
ejpam-4426	138	1	.........	.........	PUNCT
ejpam-4426	138	2	.........	.........	PUNCT
ejpam-4426	139	1	.........	.........	PUNCT
ejpam-4426	139	2	.........	.........	PUNCT
ejpam-4426	140	1	.........	.........	PUNCT
ejpam-4426	140	2	.........	.........	PUNCT
ejpam-4426	141	1	.........	.........	PUNCT
ejpam-4426	141	2	.........	.........	PUNCT
ejpam-4426	142	1	.........	.........	PUNCT
ejpam-4426	142	2	.........	.........	PUNCT
ejpam-4426	143	1	.........	.........	PUNCT
ejpam-4426	143	2	.........	.........	PUNCT
ejpam-4426	144	1	.........	.........	PUNCT
ejpam-4426	144	2	.........	.........	PUNCT
ejpam-4426	145	1	.........	.........	PUNCT
ejpam-4426	145	2	.........	.........	PUNCT
ejpam-4426	146	1	.........	.........	PUNCT
ejpam-4426	146	2	.........	.........	PUNCT
ejpam-4426	147	1	.........	.........	PUNCT
ejpam-4426	147	2	.........	.........	PUNCT
ejpam-4426	147	3	........	........	PUNCT
ejpam-4426	147	4	........	........	PUNCT
ejpam-4426	147	5	........	........	PUNCT
ejpam-4426	147	6	........	........	PUNCT
ejpam-4426	147	7	........	........	PUNCT
ejpam-4426	147	8	........	........	PUNCT
ejpam-4426	147	9	........	........	PUNCT
ejpam-4426	147	10	........	........	PUNCT
ejpam-4426	148	1	......	......	PUNCT
ejpam-4426	148	2	.........	.........	PUNCT
ejpam-4426	148	3	........	........	PUNCT
ejpam-4426	148	4	........	........	PUNCT
ejpam-4426	148	5	........	........	PUNCT
ejpam-4426	148	6	........	........	PUNCT
ejpam-4426	148	7	........	........	PUNCT
ejpam-4426	148	8	........	........	PUNCT
ejpam-4426	148	9	........	........	PUNCT
ejpam-4426	148	10	........	........	PUNCT
ejpam-4426	149	1	......	......	PUNCT
ejpam-4426	149	2	.........	.........	PUNCT
ejpam-4426	149	3	........	........	PUNCT
ejpam-4426	149	4	........	........	PUNCT
ejpam-4426	149	5	........	........	PUNCT
ejpam-4426	149	6	........	........	PUNCT
ejpam-4426	149	7	........	........	PUNCT
ejpam-4426	149	8	........	........	PUNCT
ejpam-4426	149	9	........	........	PUNCT
ejpam-4426	149	10	........	........	PUNCT
ejpam-4426	150	1	......	......	PUNCT
ejpam-4426	150	2	.........	.........	PUNCT
ejpam-4426	150	3	........	........	PUNCT
ejpam-4426	150	4	........	........	PUNCT
ejpam-4426	150	5	........	........	PUNCT
ejpam-4426	150	6	........	........	PUNCT
ejpam-4426	150	7	........	........	PUNCT
ejpam-4426	150	8	........	........	PUNCT
ejpam-4426	150	9	........	........	PUNCT
ejpam-4426	150	10	........	........	PUNCT
ejpam-4426	151	1	......	......	PUNCT
ejpam-4426	151	2	.........	.........	PUNCT
ejpam-4426	151	3	........	........	PUNCT
ejpam-4426	151	4	........	........	PUNCT
ejpam-4426	151	5	........	........	PUNCT
ejpam-4426	151	6	........	........	PUNCT
ejpam-4426	151	7	........	........	PUNCT
ejpam-4426	151	8	........	........	PUNCT
ejpam-4426	151	9	........	........	PUNCT
ejpam-4426	151	10	........	........	PUNCT
ejpam-4426	151	11	......	......	PUNCT
ejpam-4426	151	12	.................................	.................................	PUNCT
ejpam-4426	151	13	................................	................................	PUNCT
ejpam-4426	151	14	................................	................................	PUNCT
ejpam-4426	151	15	................................	................................	PUNCT
ejpam-4426	151	16	................................	................................	PUNCT
ejpam-4426	151	17	.............	.............	PUNCT
ejpam-4426	151	18	..............................................................................................................................................................................	..............................................................................................................................................................................	PUNCT
ejpam-4426	152	1	.....................................................................................................................................................................................................................	.....................................................................................................................................................................................................................	PUNCT
ejpam-4426	152	2	...................................................................................................................................................................................................................................................................................	...................................................................................................................................................................................................................................................................................	PROPN
ejpam-4426	152	3	..............................................................................................................................................................................................................................................................................................................................................................	..............................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4426	153	1	.................................................................................................................................................................................................................................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4426	153	2	..............	..............	PUNCT
ejpam-4426	153	3	.............	.............	PUNCT
ejpam-4426	153	4	.............	.............	PUNCT
ejpam-4426	153	5	.............	.............	PUNCT
ejpam-4426	153	6	.............	.............	PUNCT
ejpam-4426	153	7	.............	.............	PUNCT
ejpam-4426	153	8	.............	.............	PUNCT
ejpam-4426	153	9	.............	.............	PUNCT
ejpam-4426	153	10	.............	.............	PUNCT
ejpam-4426	153	11	.............	.............	PUNCT
ejpam-4426	153	12	.............	.............	PUNCT
ejpam-4426	153	13	.............	.............	PUNCT
ejpam-4426	153	14	.............	.............	PUNCT
ejpam-4426	153	15	.............	.............	PUNCT
ejpam-4426	153	16	.............	.............	PUNCT
ejpam-4426	153	17	.............	.............	PUNCT
ejpam-4426	154	1	....	....	PUNCT
ejpam-4426	154	2	.................................	.................................	PUNCT
ejpam-4426	154	3	................................	................................	PUNCT
ejpam-4426	154	4	................................	................................	PUNCT
ejpam-4426	154	5	................................	................................	PUNCT
ejpam-4426	154	6	................................	................................	PUNCT
ejpam-4426	154	7	.............	.............	PUNCT
ejpam-4426	154	8	..............................................................................................................................................................................	..............................................................................................................................................................................	PUNCT
ejpam-4426	155	1	.....................................................................................................................................................................................................................	.....................................................................................................................................................................................................................	PUNCT
ejpam-4426	155	2	...................................................................................................................................................................................................................................................................................	...................................................................................................................................................................................................................................................................................	PROPN
ejpam-4426	155	3	..............................................................................................................................................................................................................................................................................................................................................................	..............................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4426	155	4	...........	...........	PUNCT
ejpam-4426	155	5	..........	..........	PUNCT
ejpam-4426	156	1	..........	..........	PUNCT
ejpam-4426	156	2	..........	..........	PUNCT
ejpam-4426	157	1	..........	..........	PUNCT
ejpam-4426	157	2	..........	..........	PUNCT
ejpam-4426	158	1	..........	..........	PUNCT
ejpam-4426	158	2	..........	..........	PUNCT
ejpam-4426	159	1	..........	..........	PUNCT
ejpam-4426	159	2	..........	..........	PUNCT
ejpam-4426	160	1	..........	..........	PUNCT
ejpam-4426	160	2	..........	..........	PUNCT
ejpam-4426	161	1	..........	..........	PUNCT
ejpam-4426	161	2	..........	..........	PUNCT
ejpam-4426	162	1	..........	..........	PUNCT
ejpam-4426	162	2	..........	..........	PUNCT
ejpam-4426	163	1	..........	..........	PUNCT
ejpam-4426	163	2	..........	..........	PUNCT
ejpam-4426	164	1	..........	..........	PUNCT
ejpam-4426	164	2	..........	..........	PUNCT
ejpam-4426	165	1	..........	..........	PUNCT
ejpam-4426	165	2	..........	..........	PUNCT
ejpam-4426	166	1	..........	..........	PUNCT
ejpam-4426	166	2	..........	..........	PUNCT
ejpam-4426	167	1	..........	..........	PUNCT
ejpam-4426	167	2	..........	..........	PUNCT
ejpam-4426	168	1	..........	..........	PUNCT
ejpam-4426	168	2	....	....	PUNCT
ejpam-4426	169	1	..............	..............	PUNCT
ejpam-4426	169	2	.............	.............	PUNCT
ejpam-4426	169	3	.............	.............	PUNCT
ejpam-4426	169	4	.............	.............	PUNCT
ejpam-4426	169	5	.............	.............	PUNCT
ejpam-4426	169	6	.............	.............	PUNCT
ejpam-4426	169	7	.............	.............	PUNCT
ejpam-4426	169	8	.............	.............	PUNCT
ejpam-4426	169	9	.............	.............	PUNCT
ejpam-4426	169	10	.............	.............	PUNCT
ejpam-4426	169	11	.............	.............	PUNCT
ejpam-4426	169	12	.............	.............	PUNCT
ejpam-4426	169	13	.............	.............	PUNCT
ejpam-4426	169	14	.............	.............	PUNCT
ejpam-4426	169	15	.............	.............	PUNCT
ejpam-4426	169	16	.............	.............	PUNCT
ejpam-4426	170	1	....	....	PUNCT
ejpam-4426	170	2	.................................	.................................	PUNCT
ejpam-4426	170	3	................................	................................	PUNCT
ejpam-4426	170	4	................................	................................	PUNCT
ejpam-4426	170	5	................................	................................	PUNCT
ejpam-4426	170	6	................................	................................	PUNCT
ejpam-4426	171	1	.............	.............	PUNCT
ejpam-4426	171	2	..............................................................................................................................................................................	..............................................................................................................................................................................	PUNCT
ejpam-4426	171	3	.....................................................................................................................................................................................................................	.....................................................................................................................................................................................................................	PUNCT
ejpam-4426	172	1	...................................................................................................................................................................................................................................................................................	...................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4426	172	2	..........	..........	PUNCT
ejpam-4426	173	1	.........	.........	PUNCT
ejpam-4426	173	2	.........	.........	PUNCT
ejpam-4426	174	1	.........	.........	PUNCT
ejpam-4426	174	2	.........	.........	PUNCT
ejpam-4426	175	1	.........	.........	PUNCT
ejpam-4426	175	2	.........	.........	PUNCT
ejpam-4426	176	1	.........	.........	PUNCT
ejpam-4426	176	2	.........	.........	PUNCT
ejpam-4426	177	1	.........	.........	PUNCT
ejpam-4426	177	2	.........	.........	PUNCT
ejpam-4426	178	1	.........	.........	PUNCT
ejpam-4426	178	2	.........	.........	PUNCT
ejpam-4426	179	1	.........	.........	PUNCT
ejpam-4426	179	2	.........	.........	PUNCT
ejpam-4426	180	1	.........	.........	PUNCT
ejpam-4426	180	2	.........	.........	PUNCT
ejpam-4426	181	1	.........	.........	PUNCT
ejpam-4426	181	2	.........	.........	PUNCT
ejpam-4426	182	1	.........	.........	PUNCT
ejpam-4426	182	2	.........	.........	PUNCT
ejpam-4426	183	1	.........	.........	PUNCT
ejpam-4426	183	2	.........	.........	PUNCT
ejpam-4426	184	1	.........	.........	PUNCT
ejpam-4426	184	2	.........	.........	PUNCT
ejpam-4426	185	1	.........	.........	PUNCT
ejpam-4426	185	2	.........	.........	PUNCT
ejpam-4426	186	1	.........	.........	PUNCT
ejpam-4426	186	2	.........	.........	PUNCT
ejpam-4426	187	1	.........	.........	PUNCT
ejpam-4426	187	2	.........	.........	PUNCT
ejpam-4426	188	1	.........	.........	PUNCT
ejpam-4426	188	2	.........	.........	PUNCT
ejpam-4426	189	1	.........	.........	PUNCT
ejpam-4426	189	2	.........	.........	PUNCT
ejpam-4426	190	1	.........	.........	PUNCT
ejpam-4426	190	2	.........	.........	PUNCT
ejpam-4426	191	1	.........	.........	PUNCT
ejpam-4426	191	2	.......	.......	PUNCT
ejpam-4426	191	3	...........	...........	PUNCT
ejpam-4426	191	4	..........	..........	PUNCT
ejpam-4426	192	1	..........	..........	PUNCT
ejpam-4426	192	2	..........	..........	PUNCT
ejpam-4426	193	1	..........	..........	PUNCT
ejpam-4426	193	2	..........	..........	PUNCT
ejpam-4426	194	1	..........	..........	PUNCT
ejpam-4426	194	2	..........	..........	PUNCT
ejpam-4426	195	1	..........	..........	PUNCT
ejpam-4426	195	2	..........	..........	PUNCT
ejpam-4426	196	1	..........	..........	PUNCT
ejpam-4426	196	2	..........	..........	PUNCT
ejpam-4426	197	1	..........	..........	PUNCT
ejpam-4426	197	2	..........	..........	PUNCT
ejpam-4426	198	1	..........	..........	PUNCT
ejpam-4426	198	2	..........	..........	PUNCT
ejpam-4426	199	1	..........	..........	PUNCT
ejpam-4426	199	2	..........	..........	PUNCT
ejpam-4426	200	1	..........	..........	PUNCT
ejpam-4426	200	2	..........	..........	PUNCT
ejpam-4426	201	1	..........	..........	PUNCT
ejpam-4426	201	2	..........	..........	PUNCT
ejpam-4426	202	1	..........	..........	PUNCT
ejpam-4426	202	2	..........	..........	PUNCT
ejpam-4426	203	1	..........	..........	PUNCT
ejpam-4426	203	2	..........	..........	PUNCT
ejpam-4426	204	1	..........	..........	PUNCT
ejpam-4426	204	2	....	....	PUNCT
ejpam-4426	205	1	..............	..............	PUNCT
ejpam-4426	205	2	.............	.............	PUNCT
ejpam-4426	205	3	.............	.............	PUNCT
ejpam-4426	205	4	.............	.............	PUNCT
ejpam-4426	205	5	.............	.............	PUNCT
ejpam-4426	205	6	.............	.............	PUNCT
ejpam-4426	205	7	.............	.............	PUNCT
ejpam-4426	205	8	.............	.............	PUNCT
ejpam-4426	205	9	.............	.............	PUNCT
ejpam-4426	205	10	.............	.............	PUNCT
ejpam-4426	205	11	.............	.............	PUNCT
ejpam-4426	205	12	.............	.............	PUNCT
ejpam-4426	205	13	.............	.............	PUNCT
ejpam-4426	205	14	.............	.............	PUNCT
ejpam-4426	205	15	.............	.............	PUNCT
ejpam-4426	205	16	.............	.............	PUNCT
ejpam-4426	206	1	....	....	PUNCT
ejpam-4426	206	2	.................................	.................................	PUNCT
ejpam-4426	206	3	................................	................................	PUNCT
ejpam-4426	206	4	................................	................................	PUNCT
ejpam-4426	206	5	................................	................................	PUNCT
ejpam-4426	206	6	................................	................................	PUNCT
ejpam-4426	206	7	.............	.............	PUNCT
ejpam-4426	206	8	..............................................................................................................................................................................	..............................................................................................................................................................................	PUNCT
ejpam-4426	206	9	.....................................................................................................................................................................................................................	.....................................................................................................................................................................................................................	PUNCT
ejpam-4426	207	1	..........	..........	PUNCT
ejpam-4426	207	2	.........	.........	PUNCT
ejpam-4426	208	1	.........	.........	PUNCT
ejpam-4426	208	2	.........	.........	PUNCT
ejpam-4426	209	1	.........	.........	PUNCT
ejpam-4426	209	2	.........	.........	PUNCT
ejpam-4426	210	1	.........	.........	PUNCT
ejpam-4426	210	2	.........	.........	PUNCT
ejpam-4426	211	1	.........	.........	PUNCT
ejpam-4426	211	2	.........	.........	PUNCT
ejpam-4426	212	1	.........	.........	PUNCT
ejpam-4426	212	2	.........	.........	PUNCT
ejpam-4426	213	1	.........	.........	PUNCT
ejpam-4426	213	2	.........	.........	PUNCT
ejpam-4426	214	1	.........	.........	PUNCT
ejpam-4426	214	2	.........	.........	PUNCT
ejpam-4426	215	1	.........	.........	PUNCT
ejpam-4426	215	2	.........	.........	PUNCT
ejpam-4426	216	1	.........	.........	PUNCT
ejpam-4426	216	2	.........	.........	PUNCT
ejpam-4426	217	1	.........	.........	PUNCT
ejpam-4426	217	2	.........	.........	PUNCT
ejpam-4426	218	1	.........	.........	PUNCT
ejpam-4426	218	2	.........	.........	PUNCT
ejpam-4426	219	1	.........	.........	PUNCT
ejpam-4426	219	2	.........	.........	PUNCT
ejpam-4426	220	1	.........	.........	PUNCT
ejpam-4426	220	2	.........	.........	PUNCT
ejpam-4426	221	1	.........	.........	PUNCT
ejpam-4426	221	2	.........	.........	PUNCT
ejpam-4426	222	1	.........	.........	PUNCT
ejpam-4426	222	2	.........	.........	PUNCT
ejpam-4426	223	1	.........	.........	PUNCT
ejpam-4426	223	2	.........	.........	PUNCT
ejpam-4426	224	1	.........	.........	PUNCT
ejpam-4426	224	2	.........	.........	PUNCT
ejpam-4426	225	1	.........	.........	PUNCT
ejpam-4426	225	2	.........	.........	PUNCT
ejpam-4426	226	1	.........	.........	PUNCT
ejpam-4426	226	2	.........	.........	PUNCT
ejpam-4426	227	1	.........	.........	PUNCT
ejpam-4426	227	2	.........	.........	PUNCT
ejpam-4426	228	1	.........	.........	PUNCT
ejpam-4426	228	2	.........	.........	PUNCT
ejpam-4426	229	1	.........	.........	PUNCT
ejpam-4426	229	2	.........	.........	PUNCT
ejpam-4426	230	1	.........	.........	PUNCT
ejpam-4426	230	2	.........	.........	PUNCT
ejpam-4426	231	1	..........	..........	PUNCT
ejpam-4426	231	2	.........	.........	PUNCT
ejpam-4426	232	1	.........	.........	PUNCT
ejpam-4426	232	2	.........	.........	PUNCT
ejpam-4426	233	1	.........	.........	PUNCT
ejpam-4426	233	2	.........	.........	PUNCT
ejpam-4426	234	1	.........	.........	PUNCT
ejpam-4426	234	2	.........	.........	PUNCT
ejpam-4426	235	1	.........	.........	PUNCT
ejpam-4426	235	2	.........	.........	PUNCT
ejpam-4426	236	1	.........	.........	PUNCT
ejpam-4426	236	2	.........	.........	PUNCT
ejpam-4426	237	1	.........	.........	PUNCT
ejpam-4426	237	2	.........	.........	PUNCT
ejpam-4426	238	1	.........	.........	PUNCT
ejpam-4426	238	2	.........	.........	PUNCT
ejpam-4426	239	1	.........	.........	PUNCT
ejpam-4426	239	2	.........	.........	PUNCT
ejpam-4426	240	1	.........	.........	PUNCT
ejpam-4426	240	2	.........	.........	PUNCT
ejpam-4426	241	1	.........	.........	PUNCT
ejpam-4426	241	2	.........	.........	PUNCT
ejpam-4426	242	1	.........	.........	PUNCT
ejpam-4426	242	2	.........	.........	PUNCT
ejpam-4426	243	1	.........	.........	PUNCT
ejpam-4426	243	2	.........	.........	PUNCT
ejpam-4426	244	1	.........	.........	PUNCT
ejpam-4426	244	2	.........	.........	PUNCT
ejpam-4426	245	1	.........	.........	PUNCT
ejpam-4426	245	2	.........	.........	PUNCT
ejpam-4426	246	1	.........	.........	PUNCT
ejpam-4426	246	2	.........	.........	PUNCT
ejpam-4426	247	1	.........	.........	PUNCT
ejpam-4426	247	2	.........	.........	PUNCT
ejpam-4426	248	1	.........	.........	PUNCT
ejpam-4426	248	2	.........	.........	PUNCT
ejpam-4426	249	1	.........	.........	PUNCT
ejpam-4426	249	2	.........	.........	PUNCT
ejpam-4426	249	3	.......	.......	PUNCT
ejpam-4426	249	4	...........	...........	PUNCT
ejpam-4426	249	5	..........	..........	PUNCT
ejpam-4426	250	1	..........	..........	PUNCT
ejpam-4426	250	2	..........	..........	PUNCT
ejpam-4426	251	1	..........	..........	PUNCT
ejpam-4426	251	2	..........	..........	PUNCT
ejpam-4426	252	1	..........	..........	PUNCT
ejpam-4426	252	2	..........	..........	PUNCT
ejpam-4426	253	1	..........	..........	PUNCT
ejpam-4426	253	2	..........	..........	PUNCT
ejpam-4426	254	1	..........	..........	PUNCT
ejpam-4426	254	2	..........	..........	PUNCT
ejpam-4426	255	1	..........	..........	PUNCT
ejpam-4426	255	2	..........	..........	PUNCT
ejpam-4426	256	1	..........	..........	PUNCT
ejpam-4426	256	2	..........	..........	PUNCT
ejpam-4426	257	1	..........	..........	PUNCT
ejpam-4426	257	2	..........	..........	PUNCT
ejpam-4426	258	1	..........	..........	PUNCT
ejpam-4426	258	2	..........	..........	PUNCT
ejpam-4426	259	1	..........	..........	PUNCT
ejpam-4426	259	2	..........	..........	PUNCT
ejpam-4426	260	1	..........	..........	PUNCT
ejpam-4426	260	2	..........	..........	PUNCT
ejpam-4426	261	1	..........	..........	PUNCT
ejpam-4426	261	2	..........	..........	PUNCT
ejpam-4426	262	1	..........	..........	PUNCT
ejpam-4426	262	2	....	....	PUNCT
ejpam-4426	263	1	..............	..............	PUNCT
ejpam-4426	263	2	.............	.............	PUNCT
ejpam-4426	263	3	.............	.............	PUNCT
ejpam-4426	263	4	.............	.............	PUNCT
ejpam-4426	263	5	.............	.............	PUNCT
ejpam-4426	263	6	.............	.............	PUNCT
ejpam-4426	263	7	.............	.............	PUNCT
ejpam-4426	263	8	.............	.............	PUNCT
ejpam-4426	263	9	.............	.............	PUNCT
ejpam-4426	263	10	.............	.............	PUNCT
ejpam-4426	263	11	.............	.............	PUNCT
ejpam-4426	263	12	.............	.............	PUNCT
ejpam-4426	263	13	.............	.............	PUNCT
ejpam-4426	263	14	.............	.............	PUNCT
ejpam-4426	263	15	.............	.............	PUNCT
ejpam-4426	263	16	.............	.............	PUNCT
ejpam-4426	264	1	....	....	PUNCT
ejpam-4426	264	2	.................................	.................................	PUNCT
ejpam-4426	264	3	................................	................................	PUNCT
ejpam-4426	264	4	................................	................................	PUNCT
ejpam-4426	264	5	................................	................................	PUNCT
ejpam-4426	264	6	................................	................................	PUNCT
ejpam-4426	264	7	.............	.............	PUNCT
ejpam-4426	265	1	..............................................................................................................................................................................	..............................................................................................................................................................................	PUNCT
ejpam-4426	266	1	•	•	NUM
ejpam-4426	266	2	•	•	NUM
ejpam-4426	266	3	•	•	NUM
ejpam-4426	266	4	•	•	NUM
ejpam-4426	266	5	•	•	NUM
ejpam-4426	266	6	•	•	NOUN
ejpam-4426	266	7	•	•	NUM
ejpam-4426	266	8	figure	figure	NOUN
ejpam-4426	266	9	3	3	NUM
ejpam-4426	266	10	:	:	PUNCT
ejpam-4426	266	11	a	a	DET
ejpam-4426	266	12	graph	graph	NOUN
ejpam-4426	266	13	p5	p5	ADJ
ejpam-4426	266	14	+	+	CCONJ
ejpam-4426	266	15	p6	p6	VERB
ejpam-4426	266	16	with	with	ADP
ejpam-4426	266	17	γ2r(p5	γ2r(p5	PROPN
ejpam-4426	266	18	+	+	CCONJ
ejpam-4426	266	19	p6	p6	PROPN
ejpam-4426	266	20	)	)	PUNCT
ejpam-4426	267	1	=	=	NOUN
ejpam-4426	268	1	7	7	NUM
ejpam-4426	268	2	4	4	NUM
ejpam-4426	268	3	.	.	NOUN
ejpam-4426	268	4	2	2	NUM
ejpam-4426	268	5	-	-	PUNCT
ejpam-4426	268	6	resolving	resolve	VERB
ejpam-4426	268	7	dominating	dominating	NOUN
ejpam-4426	268	8	sets	set	NOUN
ejpam-4426	268	9	in	in	ADP
ejpam-4426	268	10	the	the	DET
ejpam-4426	268	11	corona	corona	NOUN
ejpam-4426	268	12	of	of	ADP
ejpam-4426	268	13	graphs	graph	NOUN
ejpam-4426	268	14	theorem	theorem	VERB
ejpam-4426	268	15	8	8	NUM
ejpam-4426	268	16	.	.	PUNCT
ejpam-4426	269	1	[	[	X
ejpam-4426	269	2	4	4	X
ejpam-4426	269	3	]	]	PUNCT
ejpam-4426	269	4	let	let	VERB
ejpam-4426	269	5	g	g	NOUN
ejpam-4426	269	6	and	and	CCONJ
ejpam-4426	269	7	h	h	NOUN
ejpam-4426	269	8	be	be	AUX
ejpam-4426	269	9	nontrivial	nontrivial	ADJ
ejpam-4426	269	10	connected	connected	ADJ
ejpam-4426	269	11	graphs	graph	NOUN
ejpam-4426	269	12	.	.	PUNCT
ejpam-4426	270	1	a	a	DET
ejpam-4426	270	2	set	set	NOUN
ejpam-4426	270	3	s	s	NOUN
ejpam-4426	270	4	⊆	⊆	NUM
ejpam-4426	270	5	v	v	NOUN
ejpam-4426	270	6	(	(	PUNCT
ejpam-4426	270	7	g	g	PROPN
ejpam-4426	270	8	◦	◦	NOUN
ejpam-4426	270	9	h	h	NOUN
ejpam-4426	270	10	)	)	PUNCT
ejpam-4426	270	11	is	be	AUX
ejpam-4426	270	12	a	a	DET
ejpam-4426	270	13	2	2	NUM
ejpam-4426	270	14	-	-	PUNCT
ejpam-4426	270	15	resolving	resolve	VERB
ejpam-4426	270	16	set	set	NOUN
ejpam-4426	270	17	of	of	ADP
ejpam-4426	270	18	g	g	PROPN
ejpam-4426	270	19	◦	◦	NOUN
ejpam-4426	270	20	h	h	NOUN
ejpam-4426	270	21	if	if	SCONJ
ejpam-4426	271	1	and	and	CCONJ
ejpam-4426	271	2	only	only	ADV
ejpam-4426	271	3	if	if	SCONJ
ejpam-4426	271	4	s	s	NOUN
ejpam-4426	271	5	=	=	X
ejpam-4426	271	6	a∪b	a∪b	ADJ
ejpam-4426	271	7	,	,	PUNCT
ejpam-4426	271	8	where	where	SCONJ
ejpam-4426	271	9	a	a	DET
ejpam-4426	271	10	⊆	⊆	NUM
ejpam-4426	271	11	v	v	NOUN
ejpam-4426	271	12	(	(	PUNCT
ejpam-4426	271	13	g	g	NOUN
ejpam-4426	271	14	)	)	PUNCT
ejpam-4426	271	15	and	and	CCONJ
ejpam-4426	271	16	b	b	X
ejpam-4426	271	17	=	=	SYM
ejpam-4426	271	18	⋃	⋃	NOUN
ejpam-4426	271	19	{	{	PUNCT
ejpam-4426	271	20	sv	sv	NOUN
ejpam-4426	271	21	:	:	PUNCT
ejpam-4426	271	22	sv	sv	PROPN
ejpam-4426	271	23	is	be	AUX
ejpam-4426	271	24	a	a	DET
ejpam-4426	271	25	2	2	NUM
ejpam-4426	271	26	-	-	PUNCT
ejpam-4426	271	27	resolving	resolve	VERB
ejpam-4426	271	28	set	set	NOUN
ejpam-4426	271	29	of	of	ADP
ejpam-4426	271	30	hv	hv	PROPN
ejpam-4426	271	31	,	,	PUNCT
ejpam-4426	271	32	for	for	ADP
ejpam-4426	271	33	all	all	PRON
ejpam-4426	271	34	v	v	ADP
ejpam-4426	271	35	∈	∈	NUM
ejpam-4426	271	36	v	v	NOUN
ejpam-4426	271	37	(	(	PUNCT
ejpam-4426	271	38	g	g	NOUN
ejpam-4426	271	39	)	)	PUNCT
ejpam-4426	271	40	}	}	PUNCT
ejpam-4426	271	41	.	.	PUNCT
ejpam-4426	272	1	theorem	theorem	VERB
ejpam-4426	272	2	9	9	NUM
ejpam-4426	272	3	.	.	PUNCT
ejpam-4426	273	1	let	let	VERB
ejpam-4426	273	2	g	g	NOUN
ejpam-4426	273	3	and	and	CCONJ
ejpam-4426	273	4	h	h	NOUN
ejpam-4426	273	5	be	be	AUX
ejpam-4426	273	6	nontrivial	nontrivial	ADJ
ejpam-4426	273	7	connected	connected	ADJ
ejpam-4426	273	8	graphs	graph	NOUN
ejpam-4426	273	9	.	.	PUNCT
ejpam-4426	274	1	then	then	ADV
ejpam-4426	274	2	s	s	VERB
ejpam-4426	274	3	⊆	⊆	NUM
ejpam-4426	274	4	v	v	NOUN
ejpam-4426	274	5	(	(	PUNCT
ejpam-4426	274	6	g	g	PROPN
ejpam-4426	274	7	◦	◦	NOUN
ejpam-4426	274	8	h	h	NOUN
ejpam-4426	274	9	)	)	PUNCT
ejpam-4426	274	10	is	be	AUX
ejpam-4426	274	11	a	a	DET
ejpam-4426	274	12	2	2	NUM
ejpam-4426	274	13	-	-	PUNCT
ejpam-4426	274	14	resolving	resolve	VERB
ejpam-4426	274	15	dominating	dominating	NOUN
ejpam-4426	274	16	set	set	VERB
ejpam-4426	274	17	in	in	ADP
ejpam-4426	274	18	g	g	PROPN
ejpam-4426	274	19	◦	◦	NOUN
ejpam-4426	274	20	h	h	NOUN
ejpam-4426	274	21	if	if	SCONJ
ejpam-4426	275	1	and	and	CCONJ
ejpam-4426	275	2	only	only	ADV
ejpam-4426	275	3	if	if	SCONJ
ejpam-4426	275	4	s	s	VERB
ejpam-4426	275	5	=	=	NOUN
ejpam-4426	275	6	a	a	PRON
ejpam-4426	275	7	∪	∪	X
ejpam-4426	275	8	(	(	PUNCT
ejpam-4426	275	9	⋃	⋃	NOUN
ejpam-4426	275	10	v∈v	v∈v	NOUN
ejpam-4426	275	11	(	(	PUNCT
ejpam-4426	275	12	g	g	NOUN
ejpam-4426	275	13	)	)	PUNCT
ejpam-4426	275	14	sv	sv	NOUN
ejpam-4426	275	15	)	)	PUNCT
ejpam-4426	275	16	,	,	PUNCT
ejpam-4426	275	17	where	where	SCONJ
ejpam-4426	275	18	a	a	DET
ejpam-4426	275	19	⊆	⊆	NUM
ejpam-4426	275	20	v	v	NOUN
ejpam-4426	275	21	(	(	PUNCT
ejpam-4426	275	22	g	g	NOUN
ejpam-4426	275	23	)	)	PUNCT
ejpam-4426	275	24	,	,	PUNCT
ejpam-4426	275	25	sv	sv	PROPN
ejpam-4426	275	26	is	be	AUX
ejpam-4426	275	27	a	a	DET
ejpam-4426	275	28	2	2	NUM
ejpam-4426	275	29	-	-	PUNCT
ejpam-4426	275	30	resolving	resolving	NOUN
ejpam-4426	275	31	set	set	NOUN
ejpam-4426	275	32	for	for	ADP
ejpam-4426	275	33	each	each	DET
ejpam-4426	275	34	v	v	ADP
ejpam-4426	275	35	∈	∈	PROPN
ejpam-4426	275	36	a	a	PRON
ejpam-4426	275	37	and	and	CCONJ
ejpam-4426	275	38	sv	sv	PROPN
ejpam-4426	275	39	is	be	AUX
ejpam-4426	275	40	a	a	DET
ejpam-4426	275	41	2	2	NUM
ejpam-4426	275	42	-	-	PUNCT
ejpam-4426	275	43	resolving	resolve	VERB
ejpam-4426	275	44	dominating	dominating	NOUN
ejpam-4426	275	45	set	set	NOUN
ejpam-4426	275	46	for	for	ADP
ejpam-4426	275	47	each	each	DET
ejpam-4426	275	48	v	v	NUM
ejpam-4426	275	49	∈	∈	PROPN
ejpam-4426	275	50	v	v	NOUN
ejpam-4426	275	51	(	(	PUNCT
ejpam-4426	275	52	g)\a	g)\a	PROPN
ejpam-4426	275	53	.	.	PUNCT
ejpam-4426	276	1	j.	j.	PROPN
ejpam-4426	276	2	cabaro	cabaro	PROPN
ejpam-4426	276	3	,	,	PUNCT
ejpam-4426	276	4	h.	h.	PROPN
ejpam-4426	276	5	rara	rara	PROPN
ejpam-4426	276	6	/	/	SYM
ejpam-4426	276	7	eur	eur	PROPN
ejpam-4426	276	8	.	.	PUNCT
ejpam-4426	277	1	j.	j.	PROPN
ejpam-4426	277	2	pure	pure	PROPN
ejpam-4426	277	3	appl	appl	PROPN
ejpam-4426	277	4	.	.	PROPN
ejpam-4426	277	5	math	math	PROPN
ejpam-4426	277	6	,	,	PUNCT
ejpam-4426	277	7	15	15	NUM
ejpam-4426	277	8	(	(	PUNCT
ejpam-4426	277	9	3	3	NUM
ejpam-4426	277	10	)	)	PUNCT
ejpam-4426	277	11	(	(	PUNCT
ejpam-4426	277	12	2022	2022	NUM
ejpam-4426	277	13	)	)	PUNCT
ejpam-4426	277	14	,	,	PUNCT
ejpam-4426	277	15	1417	1417	NUM
ejpam-4426	277	16	-	-	SYM
ejpam-4426	277	17	1425	1425	NUM
ejpam-4426	277	18	1422	1422	NUM
ejpam-4426	277	19	proof	proof	NOUN
ejpam-4426	277	20	.	.	PUNCT
ejpam-4426	278	1	suppose	suppose	VERB
ejpam-4426	278	2	s	s	NOUN
ejpam-4426	278	3	is	be	AUX
ejpam-4426	278	4	a	a	DET
ejpam-4426	278	5	2	2	NUM
ejpam-4426	278	6	-	-	PUNCT
ejpam-4426	278	7	resolving	resolve	VERB
ejpam-4426	278	8	dominating	dominating	NOUN
ejpam-4426	278	9	set	set	VERB
ejpam-4426	278	10	in	in	ADP
ejpam-4426	278	11	g	g	PROPN
ejpam-4426	278	12	◦	◦	PROPN
ejpam-4426	278	13	h.	h.	PROPN
ejpam-4426	278	14	let	let	VERB
ejpam-4426	278	15	a	a	DET
ejpam-4426	278	16	=	=	X
ejpam-4426	278	17	v	v	X
ejpam-4426	278	18	(	(	PUNCT
ejpam-4426	278	19	g	g	NOUN
ejpam-4426	278	20	)	)	PUNCT
ejpam-4426	278	21	∩	∩	PROPN
ejpam-4426	278	22	s	s	NOUN
ejpam-4426	278	23	and	and	CCONJ
ejpam-4426	278	24	sv	sv	X
ejpam-4426	278	25	=	=	SYM
ejpam-4426	278	26	s	s	PROPN
ejpam-4426	278	27	∩	∩	ADJ
ejpam-4426	278	28	v	v	X
ejpam-4426	278	29	(	(	PUNCT
ejpam-4426	278	30	hv	hv	PROPN
ejpam-4426	278	31	)	)	PUNCT
ejpam-4426	278	32	for	for	ADP
ejpam-4426	278	33	all	all	DET
ejpam-4426	278	34	v	v	ADP
ejpam-4426	278	35	∈	∈	NOUN
ejpam-4426	278	36	v	v	NOUN
ejpam-4426	278	37	(	(	PUNCT
ejpam-4426	278	38	g	g	NOUN
ejpam-4426	278	39	)	)	PUNCT
ejpam-4426	278	40	.	.	PUNCT
ejpam-4426	279	1	then	then	ADV
ejpam-4426	279	2	s	s	VERB
ejpam-4426	279	3	=	=	PUNCT
ejpam-4426	279	4	a	a	PRON
ejpam-4426	279	5	∪	∪	X
ejpam-4426	279	6	(	(	PUNCT
ejpam-4426	279	7	⋃	⋃	NOUN
ejpam-4426	279	8	v∈v	v∈v	NOUN
ejpam-4426	279	9	(	(	PUNCT
ejpam-4426	279	10	g	g	NOUN
ejpam-4426	279	11	)	)	PUNCT
ejpam-4426	279	12	sv	sv	NOUN
ejpam-4426	279	13	)	)	PUNCT
ejpam-4426	279	14	where	where	SCONJ
ejpam-4426	279	15	a	a	DET
ejpam-4426	279	16	⊆	⊆	NUM
ejpam-4426	279	17	v	v	NOUN
ejpam-4426	279	18	(	(	PUNCT
ejpam-4426	279	19	g	g	NOUN
ejpam-4426	279	20	)	)	PUNCT
ejpam-4426	279	21	and	and	CCONJ
ejpam-4426	279	22	sv	sv	X
ejpam-4426	279	23	⊆	⊆	NUM
ejpam-4426	279	24	v	v	X
ejpam-4426	279	25	(	(	PUNCT
ejpam-4426	279	26	hv	hv	NOUN
ejpam-4426	279	27	)	)	PUNCT
ejpam-4426	279	28	.	.	PUNCT
ejpam-4426	280	1	by	by	ADP
ejpam-4426	280	2	theorem	theorem	NOUN
ejpam-4426	280	3	8	8	NUM
ejpam-4426	280	4	,	,	PUNCT
ejpam-4426	280	5	sv	sv	X
ejpam-4426	280	6	is	be	AUX
ejpam-4426	280	7	a	a	DET
ejpam-4426	280	8	2	2	NUM
ejpam-4426	280	9	-	-	PUNCT
ejpam-4426	280	10	resolving	resolving	NOUN
ejpam-4426	280	11	set	set	VERB
ejpam-4426	280	12	in	in	ADP
ejpam-4426	280	13	hv	hv	PROPN
ejpam-4426	280	14	for	for	ADP
ejpam-4426	280	15	each	each	DET
ejpam-4426	280	16	v	v	ADP
ejpam-4426	280	17	∈	∈	PROPN
ejpam-4426	280	18	a.	a.	NOUN
ejpam-4426	280	19	if	if	SCONJ
ejpam-4426	280	20	v	v	NUM
ejpam-4426	280	21	∈	∈	PROPN
ejpam-4426	280	22	v	v	NOUN
ejpam-4426	280	23	(	(	PUNCT
ejpam-4426	280	24	g)\a	g)\a	NOUN
ejpam-4426	280	25	,	,	PUNCT
ejpam-4426	280	26	then	then	ADV
ejpam-4426	280	27	sv	sv	PROPN
ejpam-4426	280	28	is	be	AUX
ejpam-4426	280	29	a	a	DET
ejpam-4426	280	30	2	2	NUM
ejpam-4426	280	31	-	-	PUNCT
ejpam-4426	280	32	resolving	resolve	VERB
ejpam-4426	280	33	dominating	dominating	NOUN
ejpam-4426	280	34	set	set	VERB
ejpam-4426	280	35	in	in	ADP
ejpam-4426	280	36	g	g	PROPN
ejpam-4426	280	37	◦	◦	NOUN
ejpam-4426	280	38	h.	h.	NOUN
ejpam-4426	280	39	conversely	conversely	ADV
ejpam-4426	280	40	,	,	PUNCT
ejpam-4426	280	41	let	let	VERB
ejpam-4426	280	42	s	s	VERB
ejpam-4426	280	43	=	=	NOUN
ejpam-4426	280	44	a	a	DET
ejpam-4426	280	45	∪	∪	X
ejpam-4426	280	46	(	(	PUNCT
ejpam-4426	280	47	⋃	⋃	NOUN
ejpam-4426	280	48	v∈v	v∈v	NOUN
ejpam-4426	280	49	(	(	PUNCT
ejpam-4426	280	50	g	g	NOUN
ejpam-4426	280	51	)	)	PUNCT
ejpam-4426	280	52	sv	sv	NOUN
ejpam-4426	280	53	)	)	PUNCT
ejpam-4426	280	54	where	where	SCONJ
ejpam-4426	280	55	a	a	DET
ejpam-4426	280	56	⊆	⊆	NUM
ejpam-4426	280	57	v	v	NOUN
ejpam-4426	280	58	(	(	PUNCT
ejpam-4426	280	59	g	g	NOUN
ejpam-4426	280	60	)	)	PUNCT
ejpam-4426	280	61	and	and	CCONJ
ejpam-4426	280	62	sv	sv	X
ejpam-4426	280	63	⊆	⊆	NUM
ejpam-4426	280	64	v	v	X
ejpam-4426	280	65	(	(	PUNCT
ejpam-4426	280	66	hv	hv	NOUN
ejpam-4426	280	67	)	)	PUNCT
ejpam-4426	280	68	satisfying	satisfy	VERB
ejpam-4426	280	69	the	the	DET
ejpam-4426	280	70	given	give	VERB
ejpam-4426	280	71	conditions	condition	NOUN
ejpam-4426	280	72	.	.	PUNCT
ejpam-4426	281	1	by	by	ADP
ejpam-4426	281	2	theorem	theorem	NOUN
ejpam-4426	281	3	8	8	NUM
ejpam-4426	281	4	,	,	PUNCT
ejpam-4426	281	5	s	s	VERB
ejpam-4426	281	6	is	be	AUX
ejpam-4426	281	7	a	a	DET
ejpam-4426	281	8	2	2	NUM
ejpam-4426	281	9	-	-	PUNCT
ejpam-4426	281	10	resolving	resolving	NOUN
ejpam-4426	281	11	set	set	NOUN
ejpam-4426	281	12	in	in	ADP
ejpam-4426	281	13	g	g	PROPN
ejpam-4426	281	14	◦	◦	PROPN
ejpam-4426	281	15	h.	h.	PROPN
ejpam-4426	281	16	let	let	VERB
ejpam-4426	281	17	x	x	SYM
ejpam-4426	281	18	∈	∈	PROPN
ejpam-4426	281	19	v	v	X
ejpam-4426	281	20	(	(	PUNCT
ejpam-4426	281	21	g	g	NOUN
ejpam-4426	281	22	◦	◦	NOUN
ejpam-4426	281	23	h)\s	h)\s	NOUN
ejpam-4426	281	24	and	and	CCONJ
ejpam-4426	281	25	let	let	VERB
ejpam-4426	281	26	v	v	VERB
ejpam-4426	281	27	∈	∈	VERB
ejpam-4426	281	28	a	a	DET
ejpam-4426	281	29	such	such	ADJ
ejpam-4426	281	30	that	that	SCONJ
ejpam-4426	281	31	x	x	SYM
ejpam-4426	281	32	∈	∈	NOUN
ejpam-4426	281	33	v	v	NOUN
ejpam-4426	281	34	(	(	PUNCT
ejpam-4426	281	35	v	v	PROPN
ejpam-4426	281	36	+	+	PROPN
ejpam-4426	281	37	hv	hv	NOUN
ejpam-4426	281	38	)	)	PUNCT
ejpam-4426	281	39	.	.	PUNCT
ejpam-4426	282	1	then	then	ADV
ejpam-4426	282	2	xv	xv	PROPN
ejpam-4426	282	3	∈	∈	PROPN
ejpam-4426	282	4	e(g	e(g	PROPN
ejpam-4426	282	5	◦	◦	PROPN
ejpam-4426	282	6	h	h	NOUN
ejpam-4426	282	7	)	)	PUNCT
ejpam-4426	282	8	.	.	PUNCT
ejpam-4426	283	1	if	if	SCONJ
ejpam-4426	283	2	v	v	NUM
ejpam-4426	283	3	∈	∈	PROPN
ejpam-4426	283	4	v	v	NOUN
ejpam-4426	283	5	(	(	PUNCT
ejpam-4426	283	6	g)\a	g)\a	NOUN
ejpam-4426	283	7	,	,	PUNCT
ejpam-4426	283	8	then	then	ADV
ejpam-4426	283	9	there	there	PRON
ejpam-4426	283	10	exists	exist	VERB
ejpam-4426	283	11	y	y	PROPN
ejpam-4426	283	12	∈	∈	PROPN
ejpam-4426	283	13	sv	sv	INTJ
ejpam-4426	283	14	such	such	ADJ
ejpam-4426	283	15	that	that	SCONJ
ejpam-4426	283	16	xy	xy	PROPN
ejpam-4426	283	17	∈	∈	PROPN
ejpam-4426	283	18	e(g	e(g	PROPN
ejpam-4426	283	19	◦	◦	PROPN
ejpam-4426	283	20	h	h	NOUN
ejpam-4426	283	21	)	)	PUNCT
ejpam-4426	283	22	.	.	PUNCT
ejpam-4426	284	1	therefore	therefore	ADV
ejpam-4426	284	2	,	,	PUNCT
ejpam-4426	284	3	s	s	VERB
ejpam-4426	284	4	is	be	AUX
ejpam-4426	284	5	a	a	DET
ejpam-4426	284	6	dominating	dominating	NOUN
ejpam-4426	284	7	set	set	VERB
ejpam-4426	284	8	in	in	ADP
ejpam-4426	284	9	g	g	PROPN
ejpam-4426	284	10	◦	◦	NOUN
ejpam-4426	284	11	h.	h.	NOUN
ejpam-4426	284	12	hence	hence	ADV
ejpam-4426	284	13	,	,	PUNCT
ejpam-4426	284	14	s	s	VERB
ejpam-4426	284	15	is	be	AUX
ejpam-4426	284	16	a	a	DET
ejpam-4426	284	17	2	2	NUM
ejpam-4426	284	18	-	-	PUNCT
ejpam-4426	284	19	resolving	resolve	VERB
ejpam-4426	284	20	dominating	dominating	NOUN
ejpam-4426	284	21	set	set	VERB
ejpam-4426	284	22	in	in	ADP
ejpam-4426	284	23	g	g	PROPN
ejpam-4426	284	24	◦	◦	NOUN
ejpam-4426	284	25	h.	h.	NOUN
ejpam-4426	284	26	corollary	corollary	ADJ
ejpam-4426	284	27	3	3	X
ejpam-4426	284	28	.	.	PUNCT
ejpam-4426	285	1	let	let	VERB
ejpam-4426	285	2	g	g	NOUN
ejpam-4426	285	3	and	and	CCONJ
ejpam-4426	285	4	h	h	NOUN
ejpam-4426	285	5	be	be	AUX
ejpam-4426	285	6	nontrivial	nontrivial	ADJ
ejpam-4426	285	7	connected	connected	ADJ
ejpam-4426	285	8	graphs	graph	NOUN
ejpam-4426	285	9	,	,	PUNCT
ejpam-4426	285	10	where	where	SCONJ
ejpam-4426	285	11	|v	|v	PROPN
ejpam-4426	285	12	(	(	PUNCT
ejpam-4426	285	13	g)|	g)|	PROPN
ejpam-4426	285	14	=	=	PUNCT
ejpam-4426	285	15	n.	n.	NOUN
ejpam-4426	285	16	then	then	ADV
ejpam-4426	285	17	γ2r(g	γ2r(g	PROPN
ejpam-4426	285	18	◦	◦	NOUN
ejpam-4426	285	19	h	h	NOUN
ejpam-4426	285	20	)	)	PUNCT
ejpam-4426	285	21	≤	≤	NUM
ejpam-4426	285	22	min	min	NOUN
ejpam-4426	285	23	{	{	PUNCT
ejpam-4426	285	24	n(1	n(1	NOUN
ejpam-4426	285	25	+	+	CCONJ
ejpam-4426	285	26	dim2(h	dim2(h	NOUN
ejpam-4426	285	27	)	)	PUNCT
ejpam-4426	285	28	)	)	PUNCT
ejpam-4426	285	29	,	,	PUNCT
ejpam-4426	285	30	nγ2r(h	nγ2r(h	NOUN
ejpam-4426	285	31	)	)	PUNCT
ejpam-4426	285	32	}	}	PUNCT
ejpam-4426	285	33	.	.	PUNCT
ejpam-4426	286	1	the	the	DET
ejpam-4426	286	2	set	set	NOUN
ejpam-4426	286	3	consisting	consisting	NOUN
ejpam-4426	286	4	of	of	ADP
ejpam-4426	286	5	the	the	DET
ejpam-4426	286	6	shaded	shade	VERB
ejpam-4426	286	7	vertices	vertex	NOUN
ejpam-4426	286	8	in	in	ADP
ejpam-4426	286	9	figure	figure	NOUN
ejpam-4426	286	10	4	4	NUM
ejpam-4426	286	11	is	be	AUX
ejpam-4426	286	12	a	a	DET
ejpam-4426	286	13	2	2	NUM
ejpam-4426	286	14	-	-	PUNCT
ejpam-4426	286	15	resolving	resolve	VERB
ejpam-4426	286	16	dominating	dominating	NOUN
ejpam-4426	286	17	set	set	NOUN
ejpam-4426	286	18	of	of	ADP
ejpam-4426	286	19	the	the	DET
ejpam-4426	286	20	corona	corona	NOUN
ejpam-4426	286	21	p4	p4	PROPN
ejpam-4426	286	22	◦	◦	PROPN
ejpam-4426	286	23	c5	c5	PROPN
ejpam-4426	286	24	.	.	PUNCT
ejpam-4426	287	1	....................................	....................................	PUNCT
ejpam-4426	287	2	....................................	....................................	PUNCT
ejpam-4426	288	1	....................................	....................................	PUNCT
ejpam-4426	288	2	....................................	....................................	PUNCT
ejpam-4426	289	1	....................................	....................................	PUNCT
ejpam-4426	289	2	....................................	....................................	PUNCT
ejpam-4426	290	1	....................................	....................................	PUNCT
ejpam-4426	290	2	....................................	....................................	PUNCT
ejpam-4426	291	1	....................................	....................................	PUNCT
ejpam-4426	291	2	....................................	....................................	PUNCT
ejpam-4426	292	1	....................................	....................................	PUNCT
ejpam-4426	292	2	....................................	....................................	PUNCT
ejpam-4426	293	1	....................................	....................................	PUNCT
ejpam-4426	293	2	....................................	....................................	PUNCT
ejpam-4426	294	1	....................................	....................................	PUNCT
ejpam-4426	294	2	....................................	....................................	PUNCT
ejpam-4426	295	1	....................................	....................................	PUNCT
ejpam-4426	295	2	....................................	....................................	PUNCT
ejpam-4426	296	1	....................................	....................................	PUNCT
ejpam-4426	296	2	........................................................................	........................................................................	PUNCT
ejpam-4426	297	1	....................................	....................................	PUNCT
ejpam-4426	297	2	....................................	....................................	PUNCT
ejpam-4426	298	1	....................................	....................................	PUNCT
ejpam-4426	298	2	......................................................................................................................................................................................................	......................................................................................................................................................................................................	INTJ
ejpam-4426	299	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	INTJ
ejpam-4426	299	2	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4426	300	1	...............................................................	...............................................................	PUNCT
ejpam-4426	300	2	......................................................................................................................................................	......................................................................................................................................................	PUNCT
ejpam-4426	300	3	........	........	PUNCT
ejpam-4426	300	4	........	........	PUNCT
ejpam-4426	300	5	........	........	PUNCT
ejpam-4426	300	6	........	........	PUNCT
ejpam-4426	300	7	........	........	PUNCT
ejpam-4426	300	8	........	........	PUNCT
ejpam-4426	300	9	........	........	PUNCT
ejpam-4426	300	10	........	........	PUNCT
ejpam-4426	300	11	........	........	PUNCT
ejpam-4426	300	12	........	........	PUNCT
ejpam-4426	300	13	........	........	PUNCT
ejpam-4426	300	14	........	........	PUNCT
ejpam-4426	300	15	........	........	PUNCT
ejpam-4426	300	16	........	........	PUNCT
ejpam-4426	300	17	........	........	PUNCT
ejpam-4426	300	18	........	........	PUNCT
ejpam-4426	300	19	........	........	PUNCT
ejpam-4426	300	20	...........	...........	PUNCT
ejpam-4426	300	21	..........	..........	PUNCT
ejpam-4426	301	1	..........	..........	PUNCT
ejpam-4426	301	2	..........	..........	PUNCT
ejpam-4426	302	1	..........	..........	PUNCT
ejpam-4426	302	2	..........	..........	PUNCT
ejpam-4426	303	1	..........	..........	PUNCT
ejpam-4426	303	2	..........	..........	PUNCT
ejpam-4426	304	1	..........	..........	PUNCT
ejpam-4426	304	2	..........	..........	PUNCT
ejpam-4426	305	1	..........	..........	PUNCT
ejpam-4426	305	2	..........	..........	PUNCT
ejpam-4426	306	1	..........	..........	PUNCT
ejpam-4426	306	2	..........	..........	PUNCT
ejpam-4426	306	3	............	............	PUNCT
ejpam-4426	306	4	...........	...........	PUNCT
ejpam-4426	306	5	...........	...........	PUNCT
ejpam-4426	306	6	...........	...........	PUNCT
ejpam-4426	306	7	...........	...........	PUNCT
ejpam-4426	306	8	.......	.......	PUNCT
ejpam-4426	306	9	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	307	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	307	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	308	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	308	2	........................................................................	........................................................................	PUNCT
ejpam-4426	308	3	..........................	..........................	PUNCT
ejpam-4426	308	4	.........................	.........................	PUNCT
ejpam-4426	309	1	.....................	.....................	PUNCT
ejpam-4426	309	2	........................................................................	........................................................................	PUNCT
ejpam-4426	310	1	..........	..........	PUNCT
ejpam-4426	310	2	.........	.........	PUNCT
ejpam-4426	311	1	.........	.........	PUNCT
ejpam-4426	311	2	.........	.........	PUNCT
ejpam-4426	312	1	.........	.........	PUNCT
ejpam-4426	312	2	.........	.........	PUNCT
ejpam-4426	312	3	.........	.........	PUNCT
ejpam-4426	312	4	........	........	PUNCT
ejpam-4426	312	5	............	............	PUNCT
ejpam-4426	312	6	...........	...........	PUNCT
ejpam-4426	312	7	...........	...........	PUNCT
ejpam-4426	312	8	...........	...........	PUNCT
ejpam-4426	312	9	...........	...........	PUNCT
ejpam-4426	312	10	.......	.......	PUNCT
ejpam-4426	312	11	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4426	312	12	............	............	PUNCT
ejpam-4426	312	13	...........	...........	PUNCT
ejpam-4426	312	14	...........	...........	PUNCT
ejpam-4426	312	15	...........	...........	PUNCT
ejpam-4426	312	16	...........	...........	PUNCT
ejpam-4426	312	17	.......	.......	PUNCT
ejpam-4426	313	1	..........	..........	PUNCT
ejpam-4426	313	2	.........	.........	PUNCT
ejpam-4426	314	1	.........	.........	PUNCT
ejpam-4426	314	2	.........	.........	PUNCT
ejpam-4426	315	1	.........	.........	PUNCT
ejpam-4426	315	2	.........	.........	PUNCT
ejpam-4426	315	3	.........	.........	PUNCT
ejpam-4426	316	1	........	........	PUNCT
ejpam-4426	316	2	........................................................................	........................................................................	PUNCT
ejpam-4426	316	3	..........................	..........................	PUNCT
ejpam-4426	316	4	.........................	.........................	PUNCT
ejpam-4426	316	5	.....................	.....................	PUNCT
ejpam-4426	317	1	........................................................................	........................................................................	PUNCT
ejpam-4426	317	2	...............................................................	...............................................................	PUNCT
ejpam-4426	317	3	...........	...........	PUNCT
ejpam-4426	317	4	..........	..........	PUNCT
ejpam-4426	318	1	..........	..........	PUNCT
ejpam-4426	318	2	..........	..........	PUNCT
ejpam-4426	319	1	..........	..........	PUNCT
ejpam-4426	319	2	..........	..........	PUNCT
ejpam-4426	320	1	..........	..........	PUNCT
ejpam-4426	320	2	..........	..........	PUNCT
ejpam-4426	321	1	..........	..........	PUNCT
ejpam-4426	321	2	..........	..........	PUNCT
ejpam-4426	322	1	..........	..........	PUNCT
ejpam-4426	322	2	..........	..........	PUNCT
ejpam-4426	323	1	..........	..........	PUNCT
ejpam-4426	323	2	..........	..........	PUNCT
ejpam-4426	324	1	.........	.........	PUNCT
ejpam-4426	324	2	........	........	PUNCT
ejpam-4426	324	3	........	........	PUNCT
ejpam-4426	324	4	........	........	PUNCT
ejpam-4426	324	5	........	........	PUNCT
ejpam-4426	324	6	........	........	PUNCT
ejpam-4426	324	7	........	........	PUNCT
ejpam-4426	324	8	........	........	PUNCT
ejpam-4426	324	9	........	........	PUNCT
ejpam-4426	324	10	........	........	PUNCT
ejpam-4426	324	11	........	........	PUNCT
ejpam-4426	324	12	........	........	PUNCT
ejpam-4426	324	13	........	........	PUNCT
ejpam-4426	324	14	........	........	PUNCT
ejpam-4426	324	15	........	........	PUNCT
ejpam-4426	324	16	........	........	PUNCT
ejpam-4426	324	17	........	........	PUNCT
ejpam-4426	325	1	........	........	PUNCT
ejpam-4426	325	2	.............................................................................................................................................	.............................................................................................................................................	PUNCT
ejpam-4426	326	1	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4426	326	2	...............................................................	...............................................................	PUNCT
ejpam-4426	327	1	........................................................................	........................................................................	PUNCT
ejpam-4426	327	2	..........................	..........................	PUNCT
ejpam-4426	327	3	.........................	.........................	PUNCT
ejpam-4426	328	1	.....................	.....................	PUNCT
ejpam-4426	328	2	........................................................................	........................................................................	PUNCT
ejpam-4426	329	1	..........	..........	PUNCT
ejpam-4426	329	2	.........	.........	PUNCT
ejpam-4426	330	1	.........	.........	PUNCT
ejpam-4426	330	2	.........	.........	PUNCT
ejpam-4426	331	1	.........	.........	PUNCT
ejpam-4426	331	2	.........	.........	PUNCT
ejpam-4426	331	3	.........	.........	PUNCT
ejpam-4426	331	4	........	........	PUNCT
ejpam-4426	331	5	............	............	PUNCT
ejpam-4426	331	6	...........	...........	PUNCT
ejpam-4426	331	7	...........	...........	PUNCT
ejpam-4426	331	8	...........	...........	PUNCT
ejpam-4426	331	9	...........	...........	PUNCT
ejpam-4426	331	10	.......	.......	PUNCT
ejpam-4426	331	11	......................................................................................................................................................	......................................................................................................................................................	PUNCT
ejpam-4426	331	12	........	........	PUNCT
ejpam-4426	331	13	........	........	PUNCT
ejpam-4426	331	14	........	........	PUNCT
ejpam-4426	331	15	........	........	PUNCT
ejpam-4426	331	16	........	........	PUNCT
ejpam-4426	331	17	........	........	PUNCT
ejpam-4426	331	18	........	........	PUNCT
ejpam-4426	331	19	........	........	PUNCT
ejpam-4426	331	20	........	........	PUNCT
ejpam-4426	331	21	........	........	PUNCT
ejpam-4426	331	22	........	........	PUNCT
ejpam-4426	331	23	........	........	PUNCT
ejpam-4426	331	24	........	........	PUNCT
ejpam-4426	331	25	........	........	PUNCT
ejpam-4426	331	26	........	........	PUNCT
ejpam-4426	331	27	........	........	PUNCT
ejpam-4426	331	28	........	........	PUNCT
ejpam-4426	331	29	...........	...........	PUNCT
ejpam-4426	332	1	..........	..........	PUNCT
ejpam-4426	332	2	..........	..........	PUNCT
ejpam-4426	333	1	..........	..........	PUNCT
ejpam-4426	333	2	..........	..........	PUNCT
ejpam-4426	334	1	..........	..........	PUNCT
ejpam-4426	334	2	..........	..........	PUNCT
ejpam-4426	335	1	..........	..........	PUNCT
ejpam-4426	335	2	..........	..........	PUNCT
ejpam-4426	336	1	..........	..........	PUNCT
ejpam-4426	336	2	..........	..........	PUNCT
ejpam-4426	337	1	..........	..........	PUNCT
ejpam-4426	337	2	..........	..........	PUNCT
ejpam-4426	338	1	..........	..........	PUNCT
ejpam-4426	338	2	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4426	339	1	...............................................................	...............................................................	PUNCT
ejpam-4426	339	2	........................................................................	........................................................................	PUNCT
ejpam-4426	340	1	..........................	..........................	PUNCT
ejpam-4426	340	2	.........................	.........................	PUNCT
ejpam-4426	341	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	341	2	..........	..........	PUNCT
ejpam-4426	342	1	.........	.........	PUNCT
ejpam-4426	342	2	.........	.........	PUNCT
ejpam-4426	343	1	.........	.........	PUNCT
ejpam-4426	343	2	.........	.........	PUNCT
ejpam-4426	344	1	.........	.........	PUNCT
ejpam-4426	344	2	.........	.........	PUNCT
ejpam-4426	344	3	........	........	PUNCT
ejpam-4426	344	4	............	............	PUNCT
ejpam-4426	344	5	...........	...........	PUNCT
ejpam-4426	344	6	...........	...........	PUNCT
ejpam-4426	344	7	...........	...........	PUNCT
ejpam-4426	344	8	...........	...........	PUNCT
ejpam-4426	344	9	.......	.......	PUNCT
ejpam-4426	344	10	...........	...........	PUNCT
ejpam-4426	344	11	..........	..........	PUNCT
ejpam-4426	345	1	..........	..........	PUNCT
ejpam-4426	345	2	..........	..........	PUNCT
ejpam-4426	346	1	..........	..........	PUNCT
ejpam-4426	346	2	..........	..........	PUNCT
ejpam-4426	347	1	..........	..........	PUNCT
ejpam-4426	347	2	..........	..........	PUNCT
ejpam-4426	348	1	..........	..........	PUNCT
ejpam-4426	348	2	..........	..........	PUNCT
ejpam-4426	349	1	..........	..........	PUNCT
ejpam-4426	349	2	..........	..........	PUNCT
ejpam-4426	350	1	..........	..........	PUNCT
ejpam-4426	350	2	..........	..........	PUNCT
ejpam-4426	351	1	.........	.........	PUNCT
ejpam-4426	351	2	........	........	PUNCT
ejpam-4426	351	3	........	........	PUNCT
ejpam-4426	351	4	........	........	PUNCT
ejpam-4426	351	5	........	........	PUNCT
ejpam-4426	351	6	........	........	PUNCT
ejpam-4426	351	7	........	........	PUNCT
ejpam-4426	351	8	........	........	PUNCT
ejpam-4426	351	9	........	........	PUNCT
ejpam-4426	351	10	........	........	PUNCT
ejpam-4426	351	11	........	........	PUNCT
ejpam-4426	351	12	........	........	PUNCT
ejpam-4426	351	13	........	........	PUNCT
ejpam-4426	351	14	........	........	PUNCT
ejpam-4426	351	15	........	........	PUNCT
ejpam-4426	351	16	........	........	PUNCT
ejpam-4426	351	17	........	........	PUNCT
ejpam-4426	352	1	........	........	PUNCT
ejpam-4426	352	2	.............................................................................................................................................	.............................................................................................................................................	PUNCT
ejpam-4426	353	1	•	•	NUM
ejpam-4426	353	2	••	••	NOUN
ejpam-4426	353	3	•	•	NOUN
ejpam-4426	353	4	••	••	NOUN
ejpam-4426	353	5	•	•	NUM
ejpam-4426	353	6	•	•	NOUN
ejpam-4426	353	7	•	•	NOUN
ejpam-4426	353	8	••	••	NOUN
ejpam-4426	353	9	•	•	NUM
ejpam-4426	353	10	figure	figure	NOUN
ejpam-4426	353	11	4	4	NUM
ejpam-4426	353	12	:	:	PUNCT
ejpam-4426	353	13	a	a	DET
ejpam-4426	353	14	graph	graph	NOUN
ejpam-4426	353	15	p4	p4	ADJ
ejpam-4426	353	16	◦	◦	PROPN
ejpam-4426	353	17	c5	c5	PROPN
ejpam-4426	353	18	with	with	ADP
ejpam-4426	353	19	γ2r(p4	γ2r(p4	PROPN
ejpam-4426	353	20	◦	◦	PROPN
ejpam-4426	353	21	c5	c5	PROPN
ejpam-4426	353	22	)	)	PUNCT
ejpam-4426	353	23	=	=	NOUN
ejpam-4426	354	1	12	12	NUM
ejpam-4426	354	2	5	5	NUM
ejpam-4426	354	3	.	.	SYM
ejpam-4426	354	4	2	2	NUM
ejpam-4426	354	5	-	-	PUNCT
ejpam-4426	354	6	resolving	resolve	VERB
ejpam-4426	354	7	dominating	dominating	NOUN
ejpam-4426	354	8	sets	set	NOUN
ejpam-4426	354	9	in	in	ADP
ejpam-4426	354	10	the	the	DET
ejpam-4426	354	11	lexicographic	lexicographic	ADJ
ejpam-4426	354	12	product	product	NOUN
ejpam-4426	354	13	of	of	ADP
ejpam-4426	354	14	graphs	graph	NOUN
ejpam-4426	354	15	definition	definition	NOUN
ejpam-4426	354	16	3	3	NUM
ejpam-4426	354	17	.	.	PUNCT
ejpam-4426	355	1	a	a	DET
ejpam-4426	355	2	vertex	vertex	NOUN
ejpam-4426	355	3	x	x	PRON
ejpam-4426	355	4	is	be	AUX
ejpam-4426	355	5	said	say	VERB
ejpam-4426	355	6	to	to	PART
ejpam-4426	355	7	be	be	AUX
ejpam-4426	355	8	1	1	NUM
ejpam-4426	355	9	-	-	PUNCT
ejpam-4426	355	10	equidistant	equidistant	NOUN
ejpam-4426	355	11	to	to	ADP
ejpam-4426	355	12	y	y	PRON
ejpam-4426	355	13	if	if	SCONJ
ejpam-4426	355	14	xy	xy	PROPN
ejpam-4426	355	15	∈	∈	PROPN
ejpam-4426	355	16	e(g	e(g	PROPN
ejpam-4426	355	17	)	)	PUNCT
ejpam-4426	355	18	and	and	CCONJ
ejpam-4426	355	19	dg(x	dg(x	NUM
ejpam-4426	355	20	,	,	PUNCT
ejpam-4426	355	21	z	z	NOUN
ejpam-4426	355	22	)	)	PUNCT
ejpam-4426	355	23	=	=	SYM
ejpam-4426	355	24	dg(y	dg(y	ADJ
ejpam-4426	355	25	,	,	PUNCT
ejpam-4426	355	26	z	z	NOUN
ejpam-4426	355	27	)	)	PUNCT
ejpam-4426	355	28	,	,	PUNCT
ejpam-4426	355	29	for	for	ADP
ejpam-4426	355	30	all	all	DET
ejpam-4426	355	31	z	z	NOUN
ejpam-4426	355	32	∈	∈	PROPN
ejpam-4426	355	33	v	v	NOUN
ejpam-4426	355	34	(	(	PUNCT
ejpam-4426	355	35	g)\	g)\	X
ejpam-4426	355	36	{	{	PUNCT
ejpam-4426	355	37	x	x	PROPN
ejpam-4426	355	38	,	,	PUNCT
ejpam-4426	355	39	y	y	NOUN
ejpam-4426	355	40	}	}	PUNCT
ejpam-4426	355	41	and	and	CCONJ
ejpam-4426	355	42	it	it	PRON
ejpam-4426	355	43	is	be	AUX
ejpam-4426	355	44	2	2	NUM
ejpam-4426	355	45	-	-	PUNCT
ejpam-4426	355	46	equidistant	equidistant	NOUN
ejpam-4426	355	47	to	to	ADP
ejpam-4426	355	48	y	y	PRON
ejpam-4426	355	49	if	if	SCONJ
ejpam-4426	355	50	dg(x	dg(x	NUM
ejpam-4426	355	51	,	,	PUNCT
ejpam-4426	355	52	y	y	NOUN
ejpam-4426	355	53	)	)	PUNCT
ejpam-4426	355	54	=	=	SYM
ejpam-4426	355	55	2	2	NUM
ejpam-4426	355	56	and	and	CCONJ
ejpam-4426	355	57	dg(x	dg(x	NUM
ejpam-4426	355	58	,	,	PUNCT
ejpam-4426	355	59	z	z	NOUN
ejpam-4426	355	60	)	)	PUNCT
ejpam-4426	356	1	=	=	NOUN
ejpam-4426	356	2	dg(w	dg(w	NOUN
ejpam-4426	356	3	,	,	PUNCT
ejpam-4426	356	4	z	z	NOUN
ejpam-4426	356	5	)	)	PUNCT
ejpam-4426	356	6	,	,	PUNCT
ejpam-4426	356	7	for	for	ADP
ejpam-4426	356	8	all	all	DET
ejpam-4426	356	9	z	z	NOUN
ejpam-4426	356	10	∈	∈	PROPN
ejpam-4426	356	11	v	v	NOUN
ejpam-4426	356	12	(	(	PUNCT
ejpam-4426	356	13	g)\	g)\	X
ejpam-4426	356	14	{	{	PUNCT
ejpam-4426	356	15	x	x	NOUN
ejpam-4426	356	16	,	,	PUNCT
ejpam-4426	356	17	w	w	NOUN
ejpam-4426	356	18	}	}	PUNCT
ejpam-4426	356	19	.	.	PUNCT
ejpam-4426	357	1	a	a	DET
ejpam-4426	357	2	vertex	vertex	NOUN
ejpam-4426	357	3	is	be	AUX
ejpam-4426	357	4	called	call	VERB
ejpam-4426	357	5	a	a	DET
ejpam-4426	357	6	free	free	ADJ
ejpam-4426	357	7	-	-	PUNCT
ejpam-4426	357	8	vertex	vertex	NOUN
ejpam-4426	357	9	in	in	ADP
ejpam-4426	357	10	g	g	PROPN
ejpam-4426	357	11	if	if	SCONJ
ejpam-4426	357	12	it	it	PRON
ejpam-4426	357	13	is	be	AUX
ejpam-4426	357	14	neither	neither	PRON
ejpam-4426	357	15	1	1	NUM
ejpam-4426	357	16	-	-	PUNCT
ejpam-4426	357	17	equidistant	equidistant	ADJ
ejpam-4426	357	18	nor	nor	CCONJ
ejpam-4426	357	19	2	2	NUM
ejpam-4426	357	20	-	-	PUNCT
ejpam-4426	357	21	equidistant	equidistant	NOUN
ejpam-4426	357	22	to	to	ADP
ejpam-4426	357	23	any	any	DET
ejpam-4426	357	24	vertex	vertex	NOUN
ejpam-4426	357	25	.	.	PUNCT
ejpam-4426	358	1	the	the	DET
ejpam-4426	358	2	set	set	NOUN
ejpam-4426	358	3	containing	contain	VERB
ejpam-4426	358	4	all	all	PRON
ejpam-4426	358	5	1	1	NUM
ejpam-4426	358	6	-	-	PUNCT
ejpam-4426	358	7	equidistant	equidistant	ADJ
ejpam-4426	358	8	,	,	PUNCT
ejpam-4426	358	9	2	2	NUM
ejpam-4426	358	10	-	-	PUNCT
ejpam-4426	358	11	equidistant	equidistant	ADJ
ejpam-4426	358	12	,	,	PUNCT
ejpam-4426	358	13	and	and	CCONJ
ejpam-4426	358	14	free	free	ADJ
ejpam-4426	358	15	-	-	PUNCT
ejpam-4426	358	16	vertices	vertex	NOUN
ejpam-4426	358	17	in	in	ADP
ejpam-4426	358	18	g	g	PROPN
ejpam-4426	358	19	are	be	AUX
ejpam-4426	358	20	denoted	denote	VERB
ejpam-4426	358	21	by	by	ADP
ejpam-4426	358	22	eq1(g	eq1(g	PROPN
ejpam-4426	358	23	)	)	PUNCT
ejpam-4426	358	24	,	,	PUNCT
ejpam-4426	358	25	eq2(g	eq2(g	PROPN
ejpam-4426	358	26	)	)	PUNCT
ejpam-4426	358	27	and	and	CCONJ
ejpam-4426	358	28	fr(g	fr(g	NUM
ejpam-4426	358	29	)	)	PUNCT
ejpam-4426	358	30	,	,	PUNCT
ejpam-4426	358	31	respectively	respectively	ADV
ejpam-4426	358	32	.	.	PUNCT
ejpam-4426	359	1	theorem	theorem	VERB
ejpam-4426	359	2	10	10	NUM
ejpam-4426	359	3	.	.	PUNCT
ejpam-4426	360	1	let	let	VERB
ejpam-4426	360	2	g	g	NOUN
ejpam-4426	360	3	and	and	CCONJ
ejpam-4426	360	4	h	h	PROPN
ejpam-4426	360	5	be	be	VERB
ejpam-4426	360	6	non	non	ADJ
ejpam-4426	360	7	-	-	ADJ
ejpam-4426	360	8	trivial	trivial	ADJ
ejpam-4426	360	9	connected	connected	ADJ
ejpam-4426	360	10	graphs	graph	NOUN
ejpam-4426	360	11	.	.	PUNCT
ejpam-4426	361	1	then	then	ADV
ejpam-4426	361	2	w	w	NOUN
ejpam-4426	361	3	=	=	PUNCT
ejpam-4426	361	4	⋃	⋃	PROPN
ejpam-4426	361	5	x∈s	x∈s	NOUN
ejpam-4426	361	6	[	[	PUNCT
ejpam-4426	361	7	{	{	PUNCT
ejpam-4426	361	8	x	x	NOUN
ejpam-4426	361	9	}	}	PUNCT
ejpam-4426	361	10	×	×	NOUN
ejpam-4426	361	11	tx	tx	PROPN
ejpam-4426	361	12	]	]	PUNCT
ejpam-4426	361	13	,	,	PUNCT
ejpam-4426	361	14	where	where	SCONJ
ejpam-4426	361	15	s	s	VERB
ejpam-4426	361	16	⊆	⊆	NUM
ejpam-4426	361	17	v	v	NOUN
ejpam-4426	361	18	(	(	PUNCT
ejpam-4426	361	19	g	g	NOUN
ejpam-4426	361	20	)	)	PUNCT
ejpam-4426	361	21	and	and	CCONJ
ejpam-4426	361	22	tx	tx	VERB
ejpam-4426	361	23	⊆	⊆	NUM
ejpam-4426	361	24	v	v	NOUN
ejpam-4426	361	25	(	(	PUNCT
ejpam-4426	361	26	h	h	NOUN
ejpam-4426	361	27	)	)	PUNCT
ejpam-4426	361	28	for	for	ADP
ejpam-4426	361	29	each	each	DET
ejpam-4426	361	30	x	x	SYM
ejpam-4426	361	31	∈	∈	PROPN
ejpam-4426	361	32	s	s	NOUN
ejpam-4426	361	33	,	,	PUNCT
ejpam-4426	361	34	is	be	AUX
ejpam-4426	361	35	a	a	DET
ejpam-4426	361	36	2	2	NUM
ejpam-4426	361	37	-	-	PUNCT
ejpam-4426	361	38	resolving	resolving	NOUN
ejpam-4426	361	39	set	set	VERB
ejpam-4426	361	40	in	in	ADP
ejpam-4426	361	41	g[h	g[h	PROPN
ejpam-4426	361	42	]	]	PUNCT
ejpam-4426	361	43	if	if	SCONJ
ejpam-4426	361	44	and	and	CCONJ
ejpam-4426	361	45	only	only	ADV
ejpam-4426	361	46	if	if	SCONJ
ejpam-4426	361	47	(	(	PUNCT
ejpam-4426	361	48	i	i	NOUN
ejpam-4426	361	49	)	)	PUNCT
ejpam-4426	361	50	s	s	PART
ejpam-4426	361	51	=	=	SYM
ejpam-4426	361	52	v	v	X
ejpam-4426	361	53	(	(	PUNCT
ejpam-4426	361	54	g	g	NOUN
ejpam-4426	361	55	)	)	PUNCT
ejpam-4426	361	56	j.	j.	PROPN
ejpam-4426	361	57	cabaro	cabaro	PROPN
ejpam-4426	361	58	,	,	PUNCT
ejpam-4426	361	59	h.	h.	PROPN
ejpam-4426	361	60	rara	rara	PROPN
ejpam-4426	361	61	/	/	SYM
ejpam-4426	361	62	eur	eur	PROPN
ejpam-4426	361	63	.	.	PUNCT
ejpam-4426	362	1	j.	j.	PROPN
ejpam-4426	362	2	pure	pure	PROPN
ejpam-4426	362	3	appl	appl	PROPN
ejpam-4426	362	4	.	.	PROPN
ejpam-4426	362	5	math	math	PROPN
ejpam-4426	362	6	,	,	PUNCT
ejpam-4426	362	7	15	15	NUM
ejpam-4426	362	8	(	(	PUNCT
ejpam-4426	362	9	3	3	NUM
ejpam-4426	362	10	)	)	PUNCT
ejpam-4426	362	11	(	(	PUNCT
ejpam-4426	362	12	2022	2022	NUM
ejpam-4426	362	13	)	)	PUNCT
ejpam-4426	362	14	,	,	PUNCT
ejpam-4426	362	15	1417	1417	NUM
ejpam-4426	362	16	-	-	SYM
ejpam-4426	362	17	1425	1425	NUM
ejpam-4426	362	18	1423	1423	NUM
ejpam-4426	362	19	(	(	PUNCT
ejpam-4426	362	20	ii	ii	NOUN
ejpam-4426	362	21	)	)	PUNCT
ejpam-4426	362	22	tx	tx	PROPN
ejpam-4426	362	23	is	be	AUX
ejpam-4426	362	24	a	a	DET
ejpam-4426	362	25	2	2	NUM
ejpam-4426	362	26	-	-	PUNCT
ejpam-4426	362	27	locating	locate	VERB
ejpam-4426	362	28	set	set	NOUN
ejpam-4426	362	29	in	in	ADP
ejpam-4426	362	30	h	h	NOUN
ejpam-4426	362	31	for	for	ADP
ejpam-4426	362	32	every	every	DET
ejpam-4426	362	33	x	x	SYM
ejpam-4426	362	34	∈	∈	PROPN
ejpam-4426	362	35	v	v	NOUN
ejpam-4426	362	36	(	(	PUNCT
ejpam-4426	362	37	g	g	NOUN
ejpam-4426	362	38	)	)	PUNCT
ejpam-4426	362	39	;	;	PUNCT
ejpam-4426	362	40	(	(	PUNCT
ejpam-4426	362	41	iii	iii	X
ejpam-4426	362	42	)	)	PUNCT
ejpam-4426	362	43	tx	tx	NOUN
ejpam-4426	363	1	and	and	CCONJ
ejpam-4426	363	2	ty	ty	INTJ
ejpam-4426	363	3	are	be	AUX
ejpam-4426	363	4	(	(	PUNCT
ejpam-4426	363	5	2	2	NUM
ejpam-4426	363	6	,	,	PUNCT
ejpam-4426	363	7	1)-locating	1)-locating	NUM
ejpam-4426	363	8	sets	set	NOUN
ejpam-4426	363	9	or	or	CCONJ
ejpam-4426	363	10	one	one	NUM
ejpam-4426	363	11	of	of	ADP
ejpam-4426	363	12	tx	tx	PROPN
ejpam-4426	364	1	and	and	CCONJ
ejpam-4426	364	2	ty	ty	PRON
ejpam-4426	364	3	is	be	AUX
ejpam-4426	364	4	a	a	DET
ejpam-4426	364	5	(	(	PUNCT
ejpam-4426	364	6	2	2	NUM
ejpam-4426	364	7	,	,	PUNCT
ejpam-4426	364	8	2)-locating	2)-locating	NUM
ejpam-4426	364	9	set	set	VERB
ejpam-4426	364	10	in	in	ADP
ejpam-4426	364	11	h	h	NOUN
ejpam-4426	364	12	whenever	whenever	SCONJ
ejpam-4426	364	13	x	x	X
ejpam-4426	364	14	,	,	PUNCT
ejpam-4426	364	15	y	y	PROPN
ejpam-4426	364	16	∈	∈	PROPN
ejpam-4426	364	17	eq1(g	eq1(g	PROPN
ejpam-4426	364	18	)	)	PUNCT
ejpam-4426	364	19	;	;	PUNCT
ejpam-4426	364	20	and	and	CCONJ
ejpam-4426	364	21	(	(	PUNCT
ejpam-4426	364	22	iv	iv	X
ejpam-4426	364	23	)	)	PUNCT
ejpam-4426	364	24	tx	tx	PROPN
ejpam-4426	365	1	and	and	CCONJ
ejpam-4426	365	2	ty	ty	INTJ
ejpam-4426	365	3	are	be	AUX
ejpam-4426	365	4	(	(	PUNCT
ejpam-4426	365	5	2	2	NUM
ejpam-4426	365	6	-	-	PUNCT
ejpam-4426	365	7	locating	locating	NOUN
ejpam-4426	365	8	)	)	PUNCT
ejpam-4426	365	9	dominating	dominating	NOUN
ejpam-4426	365	10	sets	set	NOUN
ejpam-4426	365	11	inh	inh	NOUN
ejpam-4426	365	12	or	or	CCONJ
ejpam-4426	365	13	one	one	NUM
ejpam-4426	365	14	of	of	ADP
ejpam-4426	365	15	tx	tx	PROPN
ejpam-4426	366	1	and	and	CCONJ
ejpam-4426	366	2	ty	ty	PRON
ejpam-4426	366	3	is	be	AUX
ejpam-4426	366	4	a	a	DET
ejpam-4426	366	5	2	2	NUM
ejpam-4426	366	6	-	-	PUNCT
ejpam-4426	366	7	dominating	dominating	NOUN
ejpam-4426	366	8	set	set	NOUN
ejpam-4426	366	9	whenever	whenever	SCONJ
ejpam-4426	366	10	x	x	X
ejpam-4426	366	11	,	,	PUNCT
ejpam-4426	366	12	y	y	PROPN
ejpam-4426	366	13	∈	∈	PROPN
ejpam-4426	366	14	eq2(g	eq2(g	VERB
ejpam-4426	366	15	)	)	PUNCT
ejpam-4426	366	16	.	.	PUNCT
ejpam-4426	367	1	proof	proof	NOUN
ejpam-4426	367	2	.	.	PUNCT
ejpam-4426	368	1	suppose	suppose	VERB
ejpam-4426	368	2	w	w	PROPN
ejpam-4426	368	3	=	=	PUNCT
ejpam-4426	368	4	⋃	⋃	PROPN
ejpam-4426	368	5	x∈s	x∈s	NOUN
ejpam-4426	368	6	[	[	PUNCT
ejpam-4426	368	7	{	{	PUNCT
ejpam-4426	368	8	x	x	NOUN
ejpam-4426	368	9	}	}	PUNCT
ejpam-4426	368	10	×	×	NOUN
ejpam-4426	368	11	tx	tx	PROPN
ejpam-4426	368	12	]	]	PUNCT
ejpam-4426	368	13	is	be	AUX
ejpam-4426	368	14	a	a	DET
ejpam-4426	368	15	2	2	NUM
ejpam-4426	368	16	-	-	PUNCT
ejpam-4426	368	17	resolving	resolving	NOUN
ejpam-4426	368	18	set	set	VERB
ejpam-4426	368	19	in	in	ADP
ejpam-4426	368	20	g[h	g[h	PROPN
ejpam-4426	368	21	]	]	PUNCT
ejpam-4426	368	22	.	.	PUNCT
ejpam-4426	369	1	suppose	suppose	VERB
ejpam-4426	369	2	there	there	PRON
ejpam-4426	369	3	exists	exist	VERB
ejpam-4426	369	4	x	x	X
ejpam-4426	369	5	∈	∈	PROPN
ejpam-4426	369	6	v	v	NOUN
ejpam-4426	369	7	(	(	PUNCT
ejpam-4426	369	8	g)\s	g)\s	NOUN
ejpam-4426	369	9	.	.	PUNCT
ejpam-4426	370	1	pick	pick	VERB
ejpam-4426	370	2	a	a	PRON
ejpam-4426	370	3	,	,	PUNCT
ejpam-4426	370	4	b	b	PROPN
ejpam-4426	370	5	∈	∈	PROPN
ejpam-4426	370	6	v	v	NOUN
ejpam-4426	370	7	(	(	PUNCT
ejpam-4426	370	8	h	h	NOUN
ejpam-4426	370	9	)	)	PUNCT
ejpam-4426	370	10	,	,	PUNCT
ejpam-4426	370	11	where	where	SCONJ
ejpam-4426	370	12	a	a	DET
ejpam-4426	370	13	̸=	̸=	PROPN
ejpam-4426	370	14	b.	b.	NOUN
ejpam-4426	370	15	then	then	ADV
ejpam-4426	370	16	(	(	PUNCT
ejpam-4426	370	17	x	x	X
ejpam-4426	370	18	,	,	PUNCT
ejpam-4426	370	19	a	a	PRON
ejpam-4426	370	20	)	)	PUNCT
ejpam-4426	370	21	,	,	PUNCT
ejpam-4426	370	22	(	(	PUNCT
ejpam-4426	370	23	x	x	NOUN
ejpam-4426	370	24	,	,	PUNCT
ejpam-4426	370	25	b	b	NOUN
ejpam-4426	370	26	)	)	PUNCT
ejpam-4426	370	27	/∈	/∈	PUNCT
ejpam-4426	371	1	w	w	NOUN
ejpam-4426	371	2	and	and	CCONJ
ejpam-4426	371	3	(	(	PUNCT
ejpam-4426	371	4	x	x	NOUN
ejpam-4426	371	5	,	,	PUNCT
ejpam-4426	371	6	a	a	PRON
ejpam-4426	371	7	)	)	PUNCT
ejpam-4426	371	8	̸=	̸=	PROPN
ejpam-4426	371	9	(	(	PUNCT
ejpam-4426	371	10	x	x	X
ejpam-4426	371	11	,	,	PUNCT
ejpam-4426	371	12	b	b	NOUN
ejpam-4426	371	13	)	)	PUNCT
ejpam-4426	371	14	.	.	PUNCT
ejpam-4426	372	1	since	since	SCONJ
ejpam-4426	372	2	x	x	PROPN
ejpam-4426	372	3	/∈	/∈	PROPN
ejpam-4426	372	4	s	s	PART
ejpam-4426	372	5	and	and	CCONJ
ejpam-4426	372	6	dg[h]((x	dg[h]((x	NOUN
ejpam-4426	372	7	,	,	PUNCT
ejpam-4426	372	8	a	a	PRON
ejpam-4426	372	9	)	)	PUNCT
ejpam-4426	372	10	,	,	PUNCT
ejpam-4426	372	11	(	(	PUNCT
ejpam-4426	372	12	y	y	NOUN
ejpam-4426	372	13	,	,	PUNCT
ejpam-4426	372	14	p	p	NOUN
ejpam-4426	372	15	)	)	PUNCT
ejpam-4426	372	16	)	)	PUNCT
ejpam-4426	372	17	=	=	PUNCT
ejpam-4426	372	18	dg[h]((x	dg[h]((x	X
ejpam-4426	372	19	,	,	PUNCT
ejpam-4426	372	20	b	b	NOUN
ejpam-4426	372	21	)	)	PUNCT
ejpam-4426	372	22	,	,	PUNCT
ejpam-4426	372	23	(	(	PUNCT
ejpam-4426	372	24	y	y	NOUN
ejpam-4426	372	25	,	,	PUNCT
ejpam-4426	372	26	p	p	NOUN
ejpam-4426	372	27	)	)	PUNCT
ejpam-4426	372	28	)	)	PUNCT
ejpam-4426	372	29	for	for	ADP
ejpam-4426	372	30	all	all	DET
ejpam-4426	372	31	y	y	PROPN
ejpam-4426	372	32	∈	∈	PROPN
ejpam-4426	372	33	v	v	NOUN
ejpam-4426	372	34	(	(	PUNCT
ejpam-4426	372	35	g)\	g)\	X
ejpam-4426	372	36	{	{	PUNCT
ejpam-4426	372	37	x	x	NOUN
ejpam-4426	372	38	}	}	PUNCT
ejpam-4426	372	39	and	and	CCONJ
ejpam-4426	372	40	for	for	ADP
ejpam-4426	372	41	all	all	DET
ejpam-4426	372	42	p	p	NOUN
ejpam-4426	372	43	∈	∈	PROPN
ejpam-4426	372	44	v	v	NOUN
ejpam-4426	372	45	(	(	PUNCT
ejpam-4426	372	46	h	h	NOUN
ejpam-4426	372	47	)	)	PUNCT
ejpam-4426	372	48	,	,	PUNCT
ejpam-4426	372	49	rg[h]((x	rg[h]((x	NOUN
ejpam-4426	372	50	,	,	PUNCT
ejpam-4426	372	51	a)/w	a)/w	NOUN
ejpam-4426	372	52	)	)	PUNCT
ejpam-4426	372	53	=	=	PUNCT
ejpam-4426	372	54	rg[h]((x	rg[h]((x	NOUN
ejpam-4426	372	55	,	,	PUNCT
ejpam-4426	372	56	b)/w	b)/w	NOUN
ejpam-4426	372	57	)	)	PUNCT
ejpam-4426	372	58	.	.	PUNCT
ejpam-4426	373	1	this	this	PRON
ejpam-4426	373	2	implies	imply	VERB
ejpam-4426	373	3	that	that	SCONJ
ejpam-4426	373	4	w	w	NOUN
ejpam-4426	373	5	is	be	AUX
ejpam-4426	373	6	not	not	PART
ejpam-4426	373	7	a	a	DET
ejpam-4426	373	8	2	2	NUM
ejpam-4426	373	9	-	-	PUNCT
ejpam-4426	373	10	resolving	resolve	VERB
ejpam-4426	373	11	set	set	NOUN
ejpam-4426	373	12	of	of	ADP
ejpam-4426	373	13	g[h	g[h	PROPN
ejpam-4426	373	14	]	]	PUNCT
ejpam-4426	373	15	,	,	PUNCT
ejpam-4426	373	16	a	a	DET
ejpam-4426	373	17	contradiction	contradiction	NOUN
ejpam-4426	373	18	to	to	ADP
ejpam-4426	373	19	the	the	DET
ejpam-4426	373	20	assumption	assumption	NOUN
ejpam-4426	373	21	on	on	ADP
ejpam-4426	373	22	w	w	PROPN
ejpam-4426	373	23	.	.	PUNCT
ejpam-4426	374	1	therefore	therefore	ADV
ejpam-4426	374	2	,	,	PUNCT
ejpam-4426	374	3	s	s	VERB
ejpam-4426	374	4	=	=	SYM
ejpam-4426	374	5	v	v	X
ejpam-4426	374	6	(	(	PUNCT
ejpam-4426	374	7	g	g	NOUN
ejpam-4426	374	8	)	)	PUNCT
ejpam-4426	374	9	.	.	PUNCT
ejpam-4426	375	1	to	to	PART
ejpam-4426	375	2	prove	prove	VERB
ejpam-4426	375	3	(	(	PUNCT
ejpam-4426	375	4	ii	ii	NOUN
ejpam-4426	375	5	)	)	PUNCT
ejpam-4426	375	6	,	,	PUNCT
ejpam-4426	375	7	let	let	VERB
ejpam-4426	375	8	x	x	PUNCT
ejpam-4426	375	9	∈	∈	PROPN
ejpam-4426	375	10	v	v	X
ejpam-4426	375	11	(	(	PUNCT
ejpam-4426	375	12	g	g	NOUN
ejpam-4426	375	13	)	)	PUNCT
ejpam-4426	375	14	and	and	CCONJ
ejpam-4426	375	15	p	p	X
ejpam-4426	375	16	,	,	PUNCT
ejpam-4426	375	17	q	q	PROPN
ejpam-4426	375	18	∈	∈	PROPN
ejpam-4426	375	19	v	v	ADP
ejpam-4426	375	20	(	(	PUNCT
ejpam-4426	375	21	h	h	NOUN
ejpam-4426	375	22	)	)	PUNCT
ejpam-4426	375	23	where	where	SCONJ
ejpam-4426	375	24	p	p	PROPN
ejpam-4426	375	25	̸=	̸=	PROPN
ejpam-4426	375	26	q.	q.	NOUN
ejpam-4426	375	27	then	then	ADV
ejpam-4426	375	28	(	(	PUNCT
ejpam-4426	375	29	x	x	X
ejpam-4426	375	30	,	,	PUNCT
ejpam-4426	375	31	p	p	NOUN
ejpam-4426	375	32	)	)	PUNCT
ejpam-4426	375	33	̸=	̸=	PROPN
ejpam-4426	375	34	(	(	PUNCT
ejpam-4426	375	35	x	x	X
ejpam-4426	375	36	,	,	PUNCT
ejpam-4426	375	37	q	q	NOUN
ejpam-4426	375	38	)	)	PUNCT
ejpam-4426	375	39	.	.	PUNCT
ejpam-4426	376	1	if	if	SCONJ
ejpam-4426	376	2	p	p	X
ejpam-4426	376	3	,	,	PUNCT
ejpam-4426	376	4	q	q	NOUN
ejpam-4426	376	5	/∈	/∈	PUNCT
ejpam-4426	377	1	tx	tx	INTJ
ejpam-4426	377	2	or	or	CCONJ
ejpam-4426	377	3	[	[	X
ejpam-4426	377	4	p	p	X
ejpam-4426	377	5	∈	∈	PROPN
ejpam-4426	377	6	tx	tx	NOUN
ejpam-4426	377	7	and	and	CCONJ
ejpam-4426	377	8	q	q	NOUN
ejpam-4426	377	9	/∈	/∈	PUNCT
ejpam-4426	378	1	tx	tx	PROPN
ejpam-4426	378	2	]	]	PUNCT
ejpam-4426	378	3	,	,	PUNCT
ejpam-4426	378	4	then	then	ADV
ejpam-4426	378	5	(	(	PUNCT
ejpam-4426	378	6	x	x	X
ejpam-4426	378	7	,	,	PUNCT
ejpam-4426	378	8	p	p	NOUN
ejpam-4426	378	9	)	)	PUNCT
ejpam-4426	378	10	,	,	PUNCT
ejpam-4426	378	11	(	(	PUNCT
ejpam-4426	378	12	x	x	X
ejpam-4426	378	13	,	,	PUNCT
ejpam-4426	378	14	q	q	NOUN
ejpam-4426	378	15	)	)	PUNCT
ejpam-4426	378	16	/∈	/∈	PUNCT
ejpam-4426	379	1	w	w	NOUN
ejpam-4426	379	2	or	or	CCONJ
ejpam-4426	379	3	[	[	X
ejpam-4426	379	4	(	(	PUNCT
ejpam-4426	379	5	x	x	X
ejpam-4426	379	6	,	,	PUNCT
ejpam-4426	379	7	p	p	NOUN
ejpam-4426	379	8	)	)	PUNCT
ejpam-4426	379	9	∈	∈	PROPN
ejpam-4426	379	10	w	w	NOUN
ejpam-4426	379	11	and	and	CCONJ
ejpam-4426	379	12	(	(	PUNCT
ejpam-4426	379	13	x	x	NOUN
ejpam-4426	379	14	,	,	PUNCT
ejpam-4426	379	15	q	q	NOUN
ejpam-4426	379	16	)	)	PUNCT
ejpam-4426	379	17	/∈	/∈	PUNCT
ejpam-4426	380	1	w	w	NOUN
ejpam-4426	380	2	]	]	X
ejpam-4426	380	3	.	.	PUNCT
ejpam-4426	381	1	since	since	SCONJ
ejpam-4426	381	2	w	w	PROPN
ejpam-4426	381	3	is	be	AUX
ejpam-4426	381	4	a	a	DET
ejpam-4426	381	5	2	2	NUM
ejpam-4426	381	6	-	-	PUNCT
ejpam-4426	381	7	resolving	resolving	NOUN
ejpam-4426	381	8	set	set	VERB
ejpam-4426	381	9	in	in	ADP
ejpam-4426	381	10	g[h	g[h	PROPN
ejpam-4426	381	11	]	]	PUNCT
ejpam-4426	381	12	,	,	PUNCT
ejpam-4426	381	13	rg[h]((x	rg[h]((x	NOUN
ejpam-4426	381	14	,	,	PUNCT
ejpam-4426	381	15	p)/w	p)/w	PROPN
ejpam-4426	381	16	)	)	PUNCT
ejpam-4426	381	17	and	and	CCONJ
ejpam-4426	381	18	rg[h]((x	rg[h]((x	NOUN
ejpam-4426	381	19	,	,	PUNCT
ejpam-4426	381	20	q)/w	q)/w	PROPN
ejpam-4426	381	21	)	)	PUNCT
ejpam-4426	381	22	differ	differ	VERB
ejpam-4426	381	23	in	in	ADP
ejpam-4426	381	24	at	at	ADV
ejpam-4426	381	25	least	least	ADJ
ejpam-4426	381	26	2	2	NUM
ejpam-4426	381	27	positions	position	NOUN
ejpam-4426	381	28	.	.	PUNCT
ejpam-4426	382	1	hence	hence	ADV
ejpam-4426	382	2	,	,	PUNCT
ejpam-4426	382	3	by	by	ADP
ejpam-4426	382	4	theorem	theorem	NOUN
ejpam-4426	382	5	1(iii	1(iii	NUM
ejpam-4426	382	6	)	)	PUNCT
ejpam-4426	382	7	and	and	CCONJ
ejpam-4426	382	8	definition	definition	NOUN
ejpam-4426	382	9	1	1	NUM
ejpam-4426	382	10	,	,	PUNCT
ejpam-4426	382	11	tx	tx	PROPN
ejpam-4426	382	12	is	be	AUX
ejpam-4426	382	13	a	a	DET
ejpam-4426	382	14	2	2	NUM
ejpam-4426	382	15	-	-	PUNCT
ejpam-4426	382	16	locating	locate	VERB
ejpam-4426	382	17	set	set	NOUN
ejpam-4426	382	18	in	in	ADP
ejpam-4426	382	19	h.	h.	PROPN
ejpam-4426	382	20	thus	thus	ADV
ejpam-4426	382	21	,	,	PUNCT
ejpam-4426	382	22	(	(	PUNCT
ejpam-4426	382	23	ii	ii	NOUN
ejpam-4426	382	24	)	)	PUNCT
ejpam-4426	382	25	follows	follow	VERB
ejpam-4426	382	26	.	.	PUNCT
ejpam-4426	383	1	to	to	PART
ejpam-4426	383	2	prove	prove	VERB
ejpam-4426	383	3	(	(	PUNCT
ejpam-4426	383	4	iii	iii	NOUN
ejpam-4426	383	5	)	)	PUNCT
ejpam-4426	383	6	,	,	PUNCT
ejpam-4426	383	7	let	let	VERB
ejpam-4426	383	8	x	x	PRON
ejpam-4426	383	9	and	and	CCONJ
ejpam-4426	383	10	y	y	PROPN
ejpam-4426	383	11	be	be	AUX
ejpam-4426	383	12	adjacent	adjacent	ADJ
ejpam-4426	383	13	vertices	vertex	NOUN
ejpam-4426	383	14	of	of	ADP
ejpam-4426	383	15	g	g	NOUN
ejpam-4426	383	16	with	with	ADP
ejpam-4426	383	17	dg(x	dg(x	NUM
ejpam-4426	383	18	,	,	PUNCT
ejpam-4426	383	19	z	z	NOUN
ejpam-4426	383	20	)	)	PUNCT
ejpam-4426	383	21	=	=	SYM
ejpam-4426	383	22	dg(y	dg(y	ADJ
ejpam-4426	383	23	,	,	PUNCT
ejpam-4426	383	24	z	z	NOUN
ejpam-4426	383	25	)	)	PUNCT
ejpam-4426	383	26	,	,	PUNCT
ejpam-4426	383	27	for	for	ADP
ejpam-4426	383	28	all	all	DET
ejpam-4426	383	29	z	z	NOUN
ejpam-4426	383	30	∈	∈	PROPN
ejpam-4426	383	31	v	v	NOUN
ejpam-4426	383	32	(	(	PUNCT
ejpam-4426	383	33	g)\	g)\	X
ejpam-4426	383	34	{	{	PUNCT
ejpam-4426	383	35	x	x	PROPN
ejpam-4426	383	36	,	,	PUNCT
ejpam-4426	383	37	y	y	PROPN
ejpam-4426	383	38	}	}	PUNCT
ejpam-4426	383	39	.	.	PUNCT
ejpam-4426	384	1	let	let	VERB
ejpam-4426	384	2	a	a	DET
ejpam-4426	384	3	,	,	PUNCT
ejpam-4426	384	4	b	b	PROPN
ejpam-4426	384	5	∈	∈	PROPN
ejpam-4426	384	6	v	v	NOUN
ejpam-4426	384	7	(	(	PUNCT
ejpam-4426	384	8	h	h	NOUN
ejpam-4426	384	9	)	)	PUNCT
ejpam-4426	384	10	,	,	PUNCT
ejpam-4426	384	11	a	a	DET
ejpam-4426	384	12	̸=	̸=	PROPN
ejpam-4426	384	13	b.	b.	NOUN
ejpam-4426	384	14	since	since	SCONJ
ejpam-4426	384	15	w	w	PROPN
ejpam-4426	384	16	is	be	AUX
ejpam-4426	384	17	2	2	NUM
ejpam-4426	384	18	-	-	PUNCT
ejpam-4426	384	19	resolving	resolving	NOUN
ejpam-4426	384	20	,	,	PUNCT
ejpam-4426	384	21	rg[h]((x	rg[h]((x	NOUN
ejpam-4426	384	22	,	,	PUNCT
ejpam-4426	384	23	a)/w	a)/w	PROPN
ejpam-4426	384	24	)	)	PUNCT
ejpam-4426	384	25	and	and	CCONJ
ejpam-4426	384	26	rg[h]((y	rg[h]((y	NOUN
ejpam-4426	384	27	,	,	PUNCT
ejpam-4426	384	28	b)/w	b)/w	PROPN
ejpam-4426	384	29	)	)	PUNCT
ejpam-4426	384	30	differ	differ	VERB
ejpam-4426	384	31	in	in	ADP
ejpam-4426	384	32	at	at	ADV
ejpam-4426	384	33	least	least	ADJ
ejpam-4426	384	34	2	2	NUM
ejpam-4426	384	35	positions	position	NOUN
ejpam-4426	384	36	.	.	PUNCT
ejpam-4426	385	1	by	by	ADP
ejpam-4426	385	2	assumption	assumption	NOUN
ejpam-4426	385	3	,	,	PUNCT
ejpam-4426	385	4	it	it	PRON
ejpam-4426	385	5	is	be	AUX
ejpam-4426	385	6	not	not	PART
ejpam-4426	385	7	possible	possible	ADJ
ejpam-4426	385	8	that	that	SCONJ
ejpam-4426	385	9	nh(a	nh(a	NUM
ejpam-4426	385	10	)	)	PUNCT
ejpam-4426	385	11	∩	∩	NOUN
ejpam-4426	385	12	tx	tx	PROPN
ejpam-4426	385	13	=	=	PUNCT
ejpam-4426	385	14	tx	tx	PROPN
ejpam-4426	385	15	and	and	CCONJ
ejpam-4426	385	16	nh(b	nh(b	NOUN
ejpam-4426	385	17	)	)	PUNCT
ejpam-4426	385	18	∩	∩	NOUN
ejpam-4426	386	1	ty	ty	INTJ
ejpam-4426	386	2	=	=	SYM
ejpam-4426	386	3	ty	ty	INTJ
ejpam-4426	386	4	.	.	PUNCT
ejpam-4426	387	1	if	if	SCONJ
ejpam-4426	387	2	tx	tx	PROPN
ejpam-4426	387	3	or	or	CCONJ
ejpam-4426	387	4	ty	ty	INTJ
ejpam-4426	387	5	is	be	AUX
ejpam-4426	387	6	(	(	PUNCT
ejpam-4426	387	7	2	2	NUM
ejpam-4426	387	8	,	,	PUNCT
ejpam-4426	387	9	2)-locating	2)-locating	NUM
ejpam-4426	387	10	,	,	PUNCT
ejpam-4426	387	11	then	then	ADV
ejpam-4426	387	12	we	we	PRON
ejpam-4426	387	13	are	be	AUX
ejpam-4426	387	14	done	do	VERB
ejpam-4426	387	15	.	.	PUNCT
ejpam-4426	388	1	otherwise	otherwise	ADV
ejpam-4426	388	2	,	,	PUNCT
ejpam-4426	388	3	tx	tx	PROPN
ejpam-4426	388	4	and	and	CCONJ
ejpam-4426	388	5	ty	ty	INTJ
ejpam-4426	388	6	are	be	AUX
ejpam-4426	388	7	(	(	PUNCT
ejpam-4426	388	8	2	2	NUM
ejpam-4426	388	9	,	,	PUNCT
ejpam-4426	388	10	1)-locating	1)-locating	NUM
ejpam-4426	388	11	.	.	PUNCT
ejpam-4426	389	1	to	to	PART
ejpam-4426	389	2	prove	prove	VERB
ejpam-4426	389	3	(	(	PUNCT
ejpam-4426	389	4	iv	iv	NUM
ejpam-4426	389	5	)	)	PUNCT
ejpam-4426	389	6	,	,	PUNCT
ejpam-4426	389	7	let	let	VERB
ejpam-4426	389	8	x	x	PRON
ejpam-4426	389	9	,	,	PUNCT
ejpam-4426	389	10	y	y	PROPN
ejpam-4426	389	11	∈	∈	PROPN
ejpam-4426	389	12	v	v	ADP
ejpam-4426	389	13	(	(	PUNCT
ejpam-4426	389	14	g	g	NOUN
ejpam-4426	389	15	)	)	PUNCT
ejpam-4426	389	16	where	where	SCONJ
ejpam-4426	389	17	dg(x	dg(x	NUM
ejpam-4426	389	18	,	,	PUNCT
ejpam-4426	389	19	y	y	NOUN
ejpam-4426	389	20	)	)	PUNCT
ejpam-4426	389	21	=	=	SYM
ejpam-4426	389	22	2	2	NUM
ejpam-4426	389	23	and	and	CCONJ
ejpam-4426	389	24	dg(x	dg(x	NUM
ejpam-4426	389	25	,	,	PUNCT
ejpam-4426	389	26	z	z	NOUN
ejpam-4426	389	27	)	)	PUNCT
ejpam-4426	389	28	=	=	SYM
ejpam-4426	389	29	dg(y	dg(y	ADJ
ejpam-4426	389	30	,	,	PUNCT
ejpam-4426	389	31	z	z	NOUN
ejpam-4426	389	32	)	)	PUNCT
ejpam-4426	389	33	,	,	PUNCT
ejpam-4426	389	34	for	for	ADP
ejpam-4426	389	35	all	all	DET
ejpam-4426	389	36	z	z	NOUN
ejpam-4426	389	37	∈	∈	PROPN
ejpam-4426	389	38	v	v	NOUN
ejpam-4426	389	39	(	(	PUNCT
ejpam-4426	389	40	g)\	g)\	X
ejpam-4426	389	41	{	{	PUNCT
ejpam-4426	389	42	x	x	PROPN
ejpam-4426	389	43	,	,	PUNCT
ejpam-4426	389	44	y	y	PROPN
ejpam-4426	389	45	}	}	PUNCT
ejpam-4426	389	46	.	.	PUNCT
ejpam-4426	390	1	let	let	VERB
ejpam-4426	390	2	a	a	DET
ejpam-4426	390	3	,	,	PUNCT
ejpam-4426	390	4	b	b	PROPN
ejpam-4426	390	5	∈	∈	PROPN
ejpam-4426	390	6	v	v	NOUN
ejpam-4426	390	7	(	(	PUNCT
ejpam-4426	390	8	h	h	NOUN
ejpam-4426	390	9	)	)	PUNCT
ejpam-4426	390	10	,	,	PUNCT
ejpam-4426	390	11	a	a	DET
ejpam-4426	390	12	̸=	̸=	PROPN
ejpam-4426	390	13	b.	b.	PROPN
ejpam-4426	390	14	suppose	suppose	VERB
ejpam-4426	390	15	one	one	NUM
ejpam-4426	390	16	of	of	ADP
ejpam-4426	390	17	tx	tx	PROPN
ejpam-4426	390	18	and	and	CCONJ
ejpam-4426	390	19	ty	ty	INTJ
ejpam-4426	390	20	,	,	PUNCT
ejpam-4426	390	21	say	say	VERB
ejpam-4426	390	22	tx	tx	PROPN
ejpam-4426	390	23	is	be	AUX
ejpam-4426	390	24	not	not	PART
ejpam-4426	390	25	a	a	DET
ejpam-4426	390	26	dominating	dominating	NOUN
ejpam-4426	390	27	set	set	NOUN
ejpam-4426	390	28	in	in	ADP
ejpam-4426	390	29	h.	h.	PROPN
ejpam-4426	390	30	pick	pick	VERB
ejpam-4426	390	31	a	a	DET
ejpam-4426	390	32	∈	∈	PROPN
ejpam-4426	390	33	v	v	NOUN
ejpam-4426	390	34	(	(	PUNCT
ejpam-4426	390	35	h)\nh	h)\nh	PROPN
ejpam-4426	391	1	[	[	X
ejpam-4426	391	2	tx	tx	X
ejpam-4426	391	3	]	]	PUNCT
ejpam-4426	391	4	and	and	CCONJ
ejpam-4426	391	5	let	let	VERB
ejpam-4426	391	6	b	b	X
ejpam-4426	391	7	∈	∈	PROPN
ejpam-4426	391	8	v	v	X
ejpam-4426	391	9	(	(	PUNCT
ejpam-4426	391	10	h)\ty	h)\ty	PROPN
ejpam-4426	391	11	.	.	PUNCT
ejpam-4426	392	1	since	since	SCONJ
ejpam-4426	392	2	dg[h]((x	dg[h]((x	PROPN
ejpam-4426	392	3	,	,	PUNCT
ejpam-4426	392	4	a	a	PRON
ejpam-4426	392	5	)	)	PUNCT
ejpam-4426	392	6	,	,	PUNCT
ejpam-4426	392	7	(	(	PUNCT
ejpam-4426	392	8	z	z	NOUN
ejpam-4426	392	9	,	,	PUNCT
ejpam-4426	392	10	q	q	NOUN
ejpam-4426	392	11	)	)	PUNCT
ejpam-4426	392	12	)	)	PUNCT
ejpam-4426	392	13	=	=	SYM
ejpam-4426	392	14	2	2	NUM
ejpam-4426	392	15	,	,	PUNCT
ejpam-4426	392	16	for	for	ADP
ejpam-4426	392	17	all	all	DET
ejpam-4426	392	18	(	(	PUNCT
ejpam-4426	392	19	z	z	NOUN
ejpam-4426	392	20	,	,	PUNCT
ejpam-4426	392	21	q	q	NOUN
ejpam-4426	392	22	)	)	PUNCT
ejpam-4426	392	23	,	,	PUNCT
ejpam-4426	392	24	it	it	PRON
ejpam-4426	392	25	follows	follow	VERB
ejpam-4426	392	26	that	that	SCONJ
ejpam-4426	392	27	|nh(b)∩ty|	|nh(b)∩ty|	ADV
ejpam-4426	392	28	≥	≥	NOUN
ejpam-4426	392	29	2	2	NUM
ejpam-4426	392	30	,	,	PUNCT
ejpam-4426	392	31	i.e.	i.e.	X
ejpam-4426	392	32	,	,	PUNCT
ejpam-4426	392	33	ty	ty	INTJ
ejpam-4426	392	34	is	be	AUX
ejpam-4426	392	35	a	a	DET
ejpam-4426	392	36	2	2	NUM
ejpam-4426	392	37	-	-	PUNCT
ejpam-4426	392	38	dominating	dominating	NOUN
ejpam-4426	392	39	set	set	NOUN
ejpam-4426	392	40	.	.	PUNCT
ejpam-4426	393	1	conversely	conversely	ADV
ejpam-4426	393	2	,	,	PUNCT
ejpam-4426	393	3	suppose	suppose	VERB
ejpam-4426	393	4	(	(	PUNCT
ejpam-4426	393	5	i),(ii	i),(ii	PROPN
ejpam-4426	393	6	)	)	PUNCT
ejpam-4426	393	7	,	,	PUNCT
ejpam-4426	393	8	(	(	PUNCT
ejpam-4426	393	9	iii	iii	NOUN
ejpam-4426	393	10	)	)	PUNCT
ejpam-4426	393	11	and	and	CCONJ
ejpam-4426	393	12	(	(	PUNCT
ejpam-4426	393	13	iv	iv	X
ejpam-4426	393	14	)	)	PUNCT
ejpam-4426	393	15	hold	hold	NOUN
ejpam-4426	393	16	.	.	PUNCT
ejpam-4426	394	1	let	let	VERB
ejpam-4426	394	2	(	(	PUNCT
ejpam-4426	394	3	x	x	X
ejpam-4426	394	4	,	,	PUNCT
ejpam-4426	394	5	a	a	PRON
ejpam-4426	394	6	)	)	PUNCT
ejpam-4426	394	7	,	,	PUNCT
ejpam-4426	394	8	(	(	PUNCT
ejpam-4426	394	9	y	y	PROPN
ejpam-4426	394	10	,	,	PUNCT
ejpam-4426	394	11	b	b	NOUN
ejpam-4426	394	12	)	)	PUNCT
ejpam-4426	394	13	∈	∈	NOUN
ejpam-4426	394	14	v	v	NOUN
ejpam-4426	394	15	(	(	PUNCT
ejpam-4426	394	16	g[h	g[h	PROPN
ejpam-4426	394	17	]	]	PUNCT
ejpam-4426	394	18	)	)	PUNCT
ejpam-4426	394	19	,	,	PUNCT
ejpam-4426	394	20	(	(	PUNCT
ejpam-4426	394	21	x	x	X
ejpam-4426	394	22	,	,	PUNCT
ejpam-4426	394	23	a	a	PRON
ejpam-4426	394	24	)	)	PUNCT
ejpam-4426	394	25	̸=	̸=	PROPN
ejpam-4426	394	26	(	(	PUNCT
ejpam-4426	394	27	y	y	PROPN
ejpam-4426	394	28	,	,	PUNCT
ejpam-4426	394	29	b	b	NOUN
ejpam-4426	394	30	)	)	PUNCT
ejpam-4426	394	31	.	.	PUNCT
ejpam-4426	395	1	consider	consider	VERB
ejpam-4426	395	2	the	the	DET
ejpam-4426	395	3	following	follow	VERB
ejpam-4426	395	4	cases	case	NOUN
ejpam-4426	395	5	.	.	PUNCT
ejpam-4426	396	1	case	case	NOUN
ejpam-4426	396	2	1	1	NUM
ejpam-4426	396	3	.	.	PUNCT
ejpam-4426	396	4	x	x	X
ejpam-4426	397	1	=	=	PUNCT
ejpam-4426	397	2	y	y	PROPN
ejpam-4426	397	3	supppose	supppose	PROPN
ejpam-4426	397	4	(	(	PUNCT
ejpam-4426	397	5	x	x	X
ejpam-4426	397	6	,	,	PUNCT
ejpam-4426	397	7	a	a	PRON
ejpam-4426	397	8	)	)	PUNCT
ejpam-4426	397	9	,	,	PUNCT
ejpam-4426	397	10	(	(	PUNCT
ejpam-4426	397	11	y	y	NOUN
ejpam-4426	397	12	,	,	PUNCT
ejpam-4426	397	13	b	b	NOUN
ejpam-4426	397	14	)	)	PUNCT
ejpam-4426	397	15	/∈	/∈	PUNCT
ejpam-4426	398	1	w	w	INTJ
ejpam-4426	398	2	.	.	PUNCT
ejpam-4426	399	1	then	then	ADV
ejpam-4426	399	2	a	a	DET
ejpam-4426	399	3	̸=	̸=	PROPN
ejpam-4426	399	4	b	b	PROPN
ejpam-4426	399	5	and	and	CCONJ
ejpam-4426	399	6	a	a	DET
ejpam-4426	399	7	,	,	PUNCT
ejpam-4426	399	8	b	b	PROPN
ejpam-4426	399	9	/∈	/∈	PUNCT
ejpam-4426	400	1	tx	tx	PROPN
ejpam-4426	401	1	=	=	SYM
ejpam-4426	402	1	ty	ty	INTJ
ejpam-4426	402	2	.	.	PUNCT
ejpam-4426	403	1	by	by	ADP
ejpam-4426	403	2	(	(	PUNCT
ejpam-4426	403	3	ii	ii	NOUN
ejpam-4426	403	4	)	)	PUNCT
ejpam-4426	403	5	,	,	PUNCT
ejpam-4426	403	6	tx	tx	PROPN
ejpam-4426	403	7	is	be	AUX
ejpam-4426	403	8	a	a	DET
ejpam-4426	403	9	2	2	NUM
ejpam-4426	403	10	-	-	PUNCT
ejpam-4426	403	11	locating	locate	VERB
ejpam-4426	403	12	set	set	NOUN
ejpam-4426	403	13	.	.	PUNCT
ejpam-4426	404	1	hence	hence	ADV
ejpam-4426	404	2	,	,	PUNCT
ejpam-4426	404	3	by	by	ADP
ejpam-4426	404	4	theore	theore	NOUN
ejpam-4426	404	5	1(iii	1(iii	NUM
ejpam-4426	404	6	)	)	PUNCT
ejpam-4426	404	7	and	and	CCONJ
ejpam-4426	404	8	by	by	ADP
ejpam-4426	404	9	definition	definition	NOUN
ejpam-4426	404	10	1	1	NUM
ejpam-4426	404	11	,	,	PUNCT
ejpam-4426	404	12	rg[h]((x	rg[h]((x	NOUN
ejpam-4426	404	13	,	,	PUNCT
ejpam-4426	404	14	a)/w	a)/w	PROPN
ejpam-4426	404	15	)	)	PUNCT
ejpam-4426	404	16	and	and	CCONJ
ejpam-4426	404	17	rg[h]((y	rg[h]((y	NOUN
ejpam-4426	404	18	,	,	PUNCT
ejpam-4426	404	19	b)/w	b)/w	PROPN
ejpam-4426	404	20	)	)	PUNCT
ejpam-4426	404	21	differ	differ	VERB
ejpam-4426	404	22	in	in	ADP
ejpam-4426	404	23	at	at	ADV
ejpam-4426	404	24	least	least	ADV
ejpam-4426	404	25	two	two	NUM
ejpam-4426	404	26	positions	position	NOUN
ejpam-4426	404	27	.	.	PUNCT
ejpam-4426	405	1	on	on	ADP
ejpam-4426	405	2	the	the	DET
ejpam-4426	405	3	other	other	ADJ
ejpam-4426	405	4	hand	hand	NOUN
ejpam-4426	405	5	,	,	PUNCT
ejpam-4426	405	6	if	if	SCONJ
ejpam-4426	405	7	(	(	PUNCT
ejpam-4426	405	8	x	x	NOUN
ejpam-4426	405	9	,	,	PUNCT
ejpam-4426	405	10	a	a	PRON
ejpam-4426	405	11	)	)	PUNCT
ejpam-4426	405	12	∈	∈	PROPN
ejpam-4426	405	13	w	w	PROPN
ejpam-4426	405	14	,	,	PUNCT
ejpam-4426	405	15	(	(	PUNCT
ejpam-4426	405	16	y	y	PROPN
ejpam-4426	405	17	,	,	PUNCT
ejpam-4426	405	18	b	b	NOUN
ejpam-4426	405	19	)	)	PUNCT
ejpam-4426	405	20	/∈	/∈	PUNCT
ejpam-4426	406	1	w	w	NOUN
ejpam-4426	406	2	,	,	PUNCT
ejpam-4426	406	3	then	then	ADV
ejpam-4426	406	4	a	a	DET
ejpam-4426	406	5	∈	∈	PROPN
ejpam-4426	406	6	tx	tx	PROPN
ejpam-4426	406	7	,	,	PUNCT
ejpam-4426	406	8	b	b	PROPN
ejpam-4426	406	9	/∈	/∈	PROPN
ejpam-4426	407	1	ty	ty	INTJ
ejpam-4426	407	2	.	.	PUNCT
ejpam-4426	408	1	using	use	VERB
ejpam-4426	408	2	similar	similar	ADJ
ejpam-4426	408	3	argument	argument	NOUN
ejpam-4426	408	4	as	as	ADP
ejpam-4426	408	5	in	in	ADP
ejpam-4426	408	6	above	above	ADV
ejpam-4426	408	7	,	,	PUNCT
ejpam-4426	408	8	rg[h]((x	rg[h]((x	NOUN
ejpam-4426	408	9	,	,	PUNCT
ejpam-4426	408	10	a)/w	a)/w	PROPN
ejpam-4426	408	11	)	)	PUNCT
ejpam-4426	408	12	and	and	CCONJ
ejpam-4426	408	13	rg[h]((y	rg[h]((y	NOUN
ejpam-4426	408	14	,	,	PUNCT
ejpam-4426	408	15	b)/w	b)/w	PROPN
ejpam-4426	408	16	)	)	PUNCT
ejpam-4426	408	17	differ	differ	VERB
ejpam-4426	408	18	in	in	ADP
ejpam-4426	408	19	at	at	ADV
ejpam-4426	408	20	least	least	ADJ
ejpam-4426	408	21	2	2	NUM
ejpam-4426	408	22	positions	position	NOUN
ejpam-4426	408	23	.	.	PUNCT
ejpam-4426	409	1	case	case	NOUN
ejpam-4426	409	2	2	2	NUM
ejpam-4426	409	3	.	.	PUNCT
ejpam-4426	409	4	x	x	X
ejpam-4426	410	1	̸=	̸=	PROPN
ejpam-4426	410	2	y.	y.	NOUN
ejpam-4426	410	3	subcase	subcase	VERB
ejpam-4426	410	4	2.1	2.1	NUM
ejpam-4426	410	5	xy	xy	PROPN
ejpam-4426	410	6	∈	∈	PROPN
ejpam-4426	410	7	e(g	e(g	PROPN
ejpam-4426	410	8	)	)	PUNCT
ejpam-4426	410	9	.	.	PUNCT
ejpam-4426	411	1	if	if	SCONJ
ejpam-4426	411	2	dg(x	dg(x	NUM
ejpam-4426	411	3	,	,	PUNCT
ejpam-4426	411	4	z	z	X
ejpam-4426	411	5	)	)	PUNCT
ejpam-4426	411	6	̸=	̸=	PROPN
ejpam-4426	411	7	dg(y	dg(y	NOUN
ejpam-4426	411	8	,	,	PUNCT
ejpam-4426	411	9	z	z	NOUN
ejpam-4426	411	10	)	)	PUNCT
ejpam-4426	411	11	for	for	ADP
ejpam-4426	411	12	some	some	DET
ejpam-4426	411	13	z	z	NOUN
ejpam-4426	411	14	∈	∈	PROPN
ejpam-4426	411	15	v	v	NOUN
ejpam-4426	411	16	(	(	PUNCT
ejpam-4426	411	17	g)\	g)\	X
ejpam-4426	411	18	{	{	PUNCT
ejpam-4426	411	19	x	x	PROPN
ejpam-4426	411	20	,	,	PUNCT
ejpam-4426	411	21	y	y	PROPN
ejpam-4426	411	22	}	}	PUNCT
ejpam-4426	411	23	,	,	PUNCT
ejpam-4426	411	24	then	then	ADV
ejpam-4426	411	25	rg[h]((x	rg[h]((x	VERB
ejpam-4426	411	26	,	,	PUNCT
ejpam-4426	411	27	a)/w	a)/w	PROPN
ejpam-4426	411	28	)	)	PUNCT
ejpam-4426	411	29	and	and	CCONJ
ejpam-4426	411	30	rg[h]((y	rg[h]((y	NOUN
ejpam-4426	411	31	,	,	PUNCT
ejpam-4426	411	32	b)/w	b)/w	PROPN
ejpam-4426	411	33	)	)	PUNCT
ejpam-4426	411	34	differ	differ	VERB
ejpam-4426	411	35	in	in	ADP
ejpam-4426	411	36	at	at	ADV
ejpam-4426	411	37	least	least	ADJ
ejpam-4426	411	38	2	2	NUM
ejpam-4426	411	39	positions	position	NOUN
ejpam-4426	411	40	since	since	SCONJ
ejpam-4426	411	41	h	h	NOUN
ejpam-4426	411	42	is	be	AUX
ejpam-4426	411	43	nontrivial	nontrivial	ADJ
ejpam-4426	411	44	.	.	PUNCT
ejpam-4426	412	1	suppose	suppose	VERB
ejpam-4426	412	2	dg(x	dg(x	NUM
ejpam-4426	412	3	,	,	PUNCT
ejpam-4426	412	4	z	z	NOUN
ejpam-4426	412	5	)	)	PUNCT
ejpam-4426	412	6	=	=	SYM
ejpam-4426	413	1	dg(y	dg(y	ADJ
ejpam-4426	413	2	,	,	PUNCT
ejpam-4426	413	3	z	z	NOUN
ejpam-4426	413	4	)	)	PUNCT
ejpam-4426	413	5	,	,	PUNCT
ejpam-4426	413	6	for	for	ADP
ejpam-4426	413	7	all	all	DET
ejpam-4426	413	8	z	z	NOUN
ejpam-4426	413	9	∈	∈	PROPN
ejpam-4426	413	10	v	v	NOUN
ejpam-4426	413	11	(	(	PUNCT
ejpam-4426	413	12	g)\	g)\	X
ejpam-4426	413	13	{	{	PUNCT
ejpam-4426	413	14	x	x	PROPN
ejpam-4426	413	15	,	,	PUNCT
ejpam-4426	413	16	y	y	PROPN
ejpam-4426	413	17	}	}	PUNCT
ejpam-4426	413	18	.	.	PUNCT
ejpam-4426	414	1	then	then	ADV
ejpam-4426	414	2	by	by	ADP
ejpam-4426	414	3	(	(	PUNCT
ejpam-4426	414	4	iii	iii	NOUN
ejpam-4426	414	5	)	)	PUNCT
ejpam-4426	414	6	,	,	PUNCT
ejpam-4426	414	7	tx	tx	PROPN
ejpam-4426	414	8	and	and	CCONJ
ejpam-4426	414	9	ty	ty	INTJ
ejpam-4426	414	10	are	be	AUX
ejpam-4426	414	11	(	(	PUNCT
ejpam-4426	414	12	2	2	NUM
ejpam-4426	414	13	,	,	PUNCT
ejpam-4426	414	14	1)-locating	1)-locating	NUM
ejpam-4426	414	15	sets	set	NOUN
ejpam-4426	414	16	in	in	ADP
ejpam-4426	414	17	h	h	NOUN
ejpam-4426	414	18	or	or	CCONJ
ejpam-4426	414	19	one	one	NUM
ejpam-4426	414	20	of	of	ADP
ejpam-4426	414	21	tx	tx	PROPN
ejpam-4426	414	22	and	and	CCONJ
ejpam-4426	414	23	ty	ty	PRON
ejpam-4426	414	24	is	be	AUX
ejpam-4426	414	25	a	a	DET
ejpam-4426	414	26	(	(	PUNCT
ejpam-4426	414	27	2	2	NUM
ejpam-4426	414	28	,	,	PUNCT
ejpam-4426	414	29	2)-locating	2)-locating	NUM
ejpam-4426	414	30	set	set	VERB
ejpam-4426	414	31	in	in	ADP
ejpam-4426	414	32	h.	h.	PROPN
ejpam-4426	414	33	hence	hence	ADV
ejpam-4426	414	34	,	,	PUNCT
ejpam-4426	414	35	by	by	ADP
ejpam-4426	414	36	definition	definition	NOUN
ejpam-4426	414	37	1	1	NUM
ejpam-4426	414	38	,	,	PUNCT
ejpam-4426	414	39	rg[h]((x	rg[h]((x	NOUN
ejpam-4426	414	40	,	,	PUNCT
ejpam-4426	414	41	a)/w	a)/w	PROPN
ejpam-4426	414	42	)	)	PUNCT
ejpam-4426	414	43	and	and	CCONJ
ejpam-4426	414	44	rg[h]((y	rg[h]((y	NOUN
ejpam-4426	414	45	,	,	PUNCT
ejpam-4426	414	46	b)/w	b)/w	PROPN
ejpam-4426	414	47	)	)	PUNCT
ejpam-4426	414	48	differ	differ	VERB
ejpam-4426	414	49	in	in	ADP
ejpam-4426	414	50	at	at	ADV
ejpam-4426	414	51	least	least	ADJ
ejpam-4426	414	52	2	2	NUM
ejpam-4426	414	53	positions	position	NOUN
ejpam-4426	414	54	.	.	PUNCT
ejpam-4426	415	1	j.	j.	PROPN
ejpam-4426	415	2	cabaro	cabaro	PROPN
ejpam-4426	415	3	,	,	PUNCT
ejpam-4426	415	4	h.	h.	PROPN
ejpam-4426	415	5	rara	rara	PROPN
ejpam-4426	415	6	/	/	SYM
ejpam-4426	415	7	eur	eur	PROPN
ejpam-4426	415	8	.	.	PUNCT
ejpam-4426	416	1	j.	j.	PROPN
ejpam-4426	416	2	pure	pure	PROPN
ejpam-4426	416	3	appl	appl	PROPN
ejpam-4426	416	4	.	.	PROPN
ejpam-4426	416	5	math	math	PROPN
ejpam-4426	416	6	,	,	PUNCT
ejpam-4426	416	7	15	15	NUM
ejpam-4426	416	8	(	(	PUNCT
ejpam-4426	416	9	3	3	NUM
ejpam-4426	416	10	)	)	PUNCT
ejpam-4426	416	11	(	(	PUNCT
ejpam-4426	416	12	2022	2022	NUM
ejpam-4426	416	13	)	)	PUNCT
ejpam-4426	416	14	,	,	PUNCT
ejpam-4426	416	15	1417	1417	NUM
ejpam-4426	416	16	-	-	SYM
ejpam-4426	416	17	1425	1425	NUM
ejpam-4426	416	18	1424	1424	NUM
ejpam-4426	416	19	subcase	subcase	NOUN
ejpam-4426	416	20	2.2	2.2	NUM
ejpam-4426	416	21	xy	xy	NOUN
ejpam-4426	416	22	/∈	/∈	PUNCT
ejpam-4426	417	1	e(g	e(g	NOUN
ejpam-4426	417	2	)	)	PUNCT
ejpam-4426	418	1	if	if	SCONJ
ejpam-4426	418	2	dg(x	dg(x	NUM
ejpam-4426	418	3	,	,	PUNCT
ejpam-4426	418	4	y	y	PROPN
ejpam-4426	418	5	)	)	PUNCT
ejpam-4426	418	6	>	>	X
ejpam-4426	419	1	2	2	NUM
ejpam-4426	419	2	,	,	PUNCT
ejpam-4426	419	3	then	then	ADV
ejpam-4426	419	4	it	it	PRON
ejpam-4426	419	5	follows	follow	VERB
ejpam-4426	419	6	that	that	SCONJ
ejpam-4426	419	7	rg[h]((x	rg[h]((x	NOUN
ejpam-4426	419	8	,	,	PUNCT
ejpam-4426	419	9	a)/w	a)/w	PROPN
ejpam-4426	419	10	)	)	PUNCT
ejpam-4426	419	11	and	and	CCONJ
ejpam-4426	419	12	rg[h]((y	rg[h]((y	NOUN
ejpam-4426	419	13	,	,	PUNCT
ejpam-4426	419	14	b)/w	b)/w	PROPN
ejpam-4426	419	15	)	)	PUNCT
ejpam-4426	419	16	differ	differ	VERB
ejpam-4426	419	17	in	in	ADP
ejpam-4426	419	18	at	at	ADV
ejpam-4426	419	19	least	least	ADJ
ejpam-4426	419	20	2	2	NUM
ejpam-4426	419	21	positions	position	NOUN
ejpam-4426	419	22	.	.	PUNCT
ejpam-4426	420	1	if	if	SCONJ
ejpam-4426	420	2	dg(x	dg(x	NUM
ejpam-4426	420	3	,	,	PUNCT
ejpam-4426	420	4	y	y	NOUN
ejpam-4426	420	5	)	)	PUNCT
ejpam-4426	420	6	=	=	SYM
ejpam-4426	420	7	2	2	NUM
ejpam-4426	420	8	and	and	CCONJ
ejpam-4426	420	9	dg(x	dg(x	NUM
ejpam-4426	420	10	,	,	PUNCT
ejpam-4426	420	11	z	z	X
ejpam-4426	420	12	)	)	PUNCT
ejpam-4426	420	13	̸=	̸=	PROPN
ejpam-4426	421	1	dg(y	dg(y	NOUN
ejpam-4426	421	2	,	,	PUNCT
ejpam-4426	421	3	z	z	NOUN
ejpam-4426	421	4	)	)	PUNCT
ejpam-4426	422	1	for	for	ADP
ejpam-4426	422	2	some	some	DET
ejpam-4426	422	3	z	z	NOUN
ejpam-4426	422	4	∈	∈	PROPN
ejpam-4426	422	5	v	v	NOUN
ejpam-4426	422	6	(	(	PUNCT
ejpam-4426	422	7	g)\	g)\	X
ejpam-4426	422	8	{	{	PUNCT
ejpam-4426	422	9	x	x	PROPN
ejpam-4426	422	10	,	,	PUNCT
ejpam-4426	422	11	y	y	PROPN
ejpam-4426	422	12	}	}	PUNCT
ejpam-4426	422	13	,	,	PUNCT
ejpam-4426	422	14	then	then	ADV
ejpam-4426	422	15	it	it	PRON
ejpam-4426	422	16	follows	follow	VERB
ejpam-4426	422	17	that	that	SCONJ
ejpam-4426	422	18	rg[h]((x	rg[h]((x	NOUN
ejpam-4426	422	19	,	,	PUNCT
ejpam-4426	422	20	a)/w	a)/w	PROPN
ejpam-4426	422	21	)	)	PUNCT
ejpam-4426	422	22	and	and	CCONJ
ejpam-4426	422	23	rg[h]((y	rg[h]((y	NOUN
ejpam-4426	422	24	,	,	PUNCT
ejpam-4426	422	25	b)/w	b)/w	PROPN
ejpam-4426	422	26	)	)	PUNCT
ejpam-4426	422	27	differ	differ	VERB
ejpam-4426	422	28	in	in	ADP
ejpam-4426	422	29	at	at	ADV
ejpam-4426	422	30	least	least	ADJ
ejpam-4426	422	31	2	2	NUM
ejpam-4426	422	32	positions	position	NOUN
ejpam-4426	422	33	.	.	PUNCT
ejpam-4426	423	1	suppose	suppose	VERB
ejpam-4426	423	2	dg(x	dg(x	PROPN
ejpam-4426	423	3	,	,	PUNCT
ejpam-4426	423	4	y	y	NOUN
ejpam-4426	423	5	)	)	PUNCT
ejpam-4426	423	6	=	=	SYM
ejpam-4426	423	7	2	2	NUM
ejpam-4426	423	8	and	and	CCONJ
ejpam-4426	423	9	dg(x	dg(x	NUM
ejpam-4426	423	10	,	,	PUNCT
ejpam-4426	423	11	z	z	NOUN
ejpam-4426	423	12	)	)	PUNCT
ejpam-4426	423	13	=	=	SYM
ejpam-4426	424	1	dg(y	dg(y	ADJ
ejpam-4426	424	2	,	,	PUNCT
ejpam-4426	424	3	z	z	NOUN
ejpam-4426	424	4	)	)	PUNCT
ejpam-4426	424	5	,	,	PUNCT
ejpam-4426	424	6	for	for	ADP
ejpam-4426	424	7	all	all	DET
ejpam-4426	424	8	z	z	NOUN
ejpam-4426	424	9	∈	∈	PROPN
ejpam-4426	424	10	v	v	NOUN
ejpam-4426	424	11	(	(	PUNCT
ejpam-4426	424	12	g)\	g)\	X
ejpam-4426	424	13	{	{	PUNCT
ejpam-4426	424	14	x	x	PROPN
ejpam-4426	424	15	,	,	PUNCT
ejpam-4426	424	16	y	y	PROPN
ejpam-4426	424	17	}	}	PUNCT
ejpam-4426	424	18	.	.	PUNCT
ejpam-4426	425	1	suppose	suppose	VERB
ejpam-4426	425	2	(	(	PUNCT
ejpam-4426	425	3	x	x	X
ejpam-4426	425	4	,	,	PUNCT
ejpam-4426	425	5	a	a	PRON
ejpam-4426	425	6	)	)	PUNCT
ejpam-4426	425	7	,	,	PUNCT
ejpam-4426	425	8	(	(	PUNCT
ejpam-4426	425	9	y	y	NOUN
ejpam-4426	425	10	,	,	PUNCT
ejpam-4426	425	11	b	b	NOUN
ejpam-4426	425	12	)	)	PUNCT
ejpam-4426	425	13	/∈	/∈	PUNCT
ejpam-4426	426	1	w	w	INTJ
ejpam-4426	426	2	.	.	PUNCT
ejpam-4426	427	1	then	then	ADV
ejpam-4426	427	2	a	a	DET
ejpam-4426	427	3	/∈	/∈	INTJ
ejpam-4426	427	4	tx	tx	NOUN
ejpam-4426	428	1	and	and	CCONJ
ejpam-4426	428	2	y	y	PROPN
ejpam-4426	428	3	/∈	/∈	PUNCT
ejpam-4426	429	1	ty	ty	INTJ
ejpam-4426	429	2	.	.	PUNCT
ejpam-4426	430	1	if	if	SCONJ
ejpam-4426	430	2	tx	tx	PROPN
ejpam-4426	430	3	and	and	CCONJ
ejpam-4426	430	4	ty	ty	PRON
ejpam-4426	430	5	are	be	AUX
ejpam-4426	430	6	both	both	PRON
ejpam-4426	430	7	dominating	dominate	VERB
ejpam-4426	430	8	,	,	PUNCT
ejpam-4426	430	9	then	then	ADV
ejpam-4426	430	10	rg[h]((x	rg[h]((x	VERB
ejpam-4426	430	11	,	,	PUNCT
ejpam-4426	430	12	a)/w	a)/w	PROPN
ejpam-4426	430	13	)	)	PUNCT
ejpam-4426	430	14	and	and	CCONJ
ejpam-4426	430	15	rg[h]((y	rg[h]((y	NOUN
ejpam-4426	430	16	,	,	PUNCT
ejpam-4426	430	17	b)/w	b)/w	PROPN
ejpam-4426	430	18	)	)	PUNCT
ejpam-4426	430	19	differ	differ	VERB
ejpam-4426	430	20	in	in	ADP
ejpam-4426	430	21	at	at	ADV
ejpam-4426	430	22	least	least	ADJ
ejpam-4426	430	23	2	2	NUM
ejpam-4426	430	24	positions	position	NOUN
ejpam-4426	430	25	.	.	PUNCT
ejpam-4426	431	1	if	if	SCONJ
ejpam-4426	431	2	one	one	NUM
ejpam-4426	431	3	,	,	PUNCT
ejpam-4426	431	4	say	say	VERB
ejpam-4426	431	5	ty	ty	INTJ
ejpam-4426	431	6	,	,	PUNCT
ejpam-4426	431	7	is	be	AUX
ejpam-4426	431	8	a	a	DET
ejpam-4426	431	9	2	2	NUM
ejpam-4426	431	10	-	-	PUNCT
ejpam-4426	431	11	dominating	dominating	NOUN
ejpam-4426	431	12	set	set	NOUN
ejpam-4426	431	13	,	,	PUNCT
ejpam-4426	431	14	then	then	ADV
ejpam-4426	431	15	rg[h]((x	rg[h]((x	VERB
ejpam-4426	431	16	,	,	PUNCT
ejpam-4426	431	17	a)/w	a)/w	PROPN
ejpam-4426	431	18	)	)	PUNCT
ejpam-4426	431	19	and	and	CCONJ
ejpam-4426	431	20	rg[h]((y	rg[h]((y	NOUN
ejpam-4426	431	21	,	,	PUNCT
ejpam-4426	431	22	b)/w	b)/w	PROPN
ejpam-4426	431	23	)	)	PUNCT
ejpam-4426	431	24	differ	differ	VERB
ejpam-4426	431	25	in	in	ADP
ejpam-4426	431	26	at	at	ADV
ejpam-4426	431	27	least	least	ADJ
ejpam-4426	431	28	2	2	NUM
ejpam-4426	431	29	positions	position	NOUN
ejpam-4426	431	30	.	.	PUNCT
ejpam-4426	432	1	similarly	similarly	ADV
ejpam-4426	432	2	,	,	PUNCT
ejpam-4426	432	3	if	if	SCONJ
ejpam-4426	432	4	(	(	PUNCT
ejpam-4426	432	5	x	x	NOUN
ejpam-4426	432	6	,	,	PUNCT
ejpam-4426	432	7	a	a	PRON
ejpam-4426	432	8	)	)	PUNCT
ejpam-4426	432	9	∈	∈	PROPN
ejpam-4426	432	10	w	w	PROPN
ejpam-4426	432	11	,	,	PUNCT
ejpam-4426	432	12	(	(	PUNCT
ejpam-4426	432	13	y	y	PROPN
ejpam-4426	432	14	,	,	PUNCT
ejpam-4426	432	15	b	b	NOUN
ejpam-4426	432	16	)	)	PUNCT
ejpam-4426	432	17	/∈	/∈	PUNCT
ejpam-4426	433	1	w	w	NOUN
ejpam-4426	433	2	,	,	PUNCT
ejpam-4426	433	3	then	then	ADV
ejpam-4426	433	4	rg[h]((x	rg[h]((x	VERB
ejpam-4426	433	5	,	,	PUNCT
ejpam-4426	433	6	a)/w	a)/w	PROPN
ejpam-4426	433	7	)	)	PUNCT
ejpam-4426	433	8	and	and	CCONJ
ejpam-4426	433	9	rg[h]((y	rg[h]((y	NOUN
ejpam-4426	433	10	,	,	PUNCT
ejpam-4426	433	11	b)/w	b)/w	PROPN
ejpam-4426	433	12	)	)	PUNCT
ejpam-4426	433	13	differ	differ	VERB
ejpam-4426	433	14	in	in	ADP
ejpam-4426	433	15	at	at	ADV
ejpam-4426	433	16	least	least	ADJ
ejpam-4426	433	17	2	2	NUM
ejpam-4426	433	18	positions	position	NOUN
ejpam-4426	433	19	.	.	PUNCT
ejpam-4426	434	1	accordingly	accordingly	ADV
ejpam-4426	434	2	,	,	PUNCT
ejpam-4426	434	3	w	w	PROPN
ejpam-4426	434	4	is	be	AUX
ejpam-4426	434	5	a	a	DET
ejpam-4426	434	6	2	2	NUM
ejpam-4426	434	7	-	-	PUNCT
ejpam-4426	434	8	resolving	resolve	VERB
ejpam-4426	434	9	set	set	NOUN
ejpam-4426	434	10	of	of	ADP
ejpam-4426	434	11	g[h	g[h	PROPN
ejpam-4426	434	12	]	]	PUNCT
ejpam-4426	434	13	.	.	PUNCT
ejpam-4426	435	1	theorem	theorem	NOUN
ejpam-4426	435	2	11	11	NUM
ejpam-4426	435	3	.	.	PUNCT
ejpam-4426	436	1	let	let	VERB
ejpam-4426	436	2	g	g	NOUN
ejpam-4426	436	3	and	and	CCONJ
ejpam-4426	436	4	h	h	PROPN
ejpam-4426	436	5	be	be	VERB
ejpam-4426	436	6	non	non	ADJ
ejpam-4426	436	7	-	-	ADJ
ejpam-4426	436	8	trivial	trivial	ADJ
ejpam-4426	436	9	connected	connected	ADJ
ejpam-4426	436	10	graphs	graph	NOUN
ejpam-4426	436	11	.	.	PUNCT
ejpam-4426	437	1	then	then	ADV
ejpam-4426	437	2	w	w	NOUN
ejpam-4426	437	3	=	=	PUNCT
ejpam-4426	437	4	⋃	⋃	PROPN
ejpam-4426	437	5	x∈s	x∈s	NOUN
ejpam-4426	437	6	[	[	PUNCT
ejpam-4426	437	7	{	{	PUNCT
ejpam-4426	437	8	x	x	NOUN
ejpam-4426	437	9	}	}	PUNCT
ejpam-4426	437	10	×	×	NOUN
ejpam-4426	437	11	tx	tx	PROPN
ejpam-4426	437	12	]	]	PUNCT
ejpam-4426	437	13	,	,	PUNCT
ejpam-4426	437	14	where	where	SCONJ
ejpam-4426	437	15	s	s	VERB
ejpam-4426	437	16	⊆	⊆	NUM
ejpam-4426	437	17	v	v	NOUN
ejpam-4426	437	18	(	(	PUNCT
ejpam-4426	437	19	g	g	NOUN
ejpam-4426	437	20	)	)	PUNCT
ejpam-4426	437	21	and	and	CCONJ
ejpam-4426	437	22	tx	tx	VERB
ejpam-4426	437	23	⊆	⊆	NUM
ejpam-4426	437	24	v	v	NOUN
ejpam-4426	437	25	(	(	PUNCT
ejpam-4426	437	26	h	h	NOUN
ejpam-4426	437	27	)	)	PUNCT
ejpam-4426	437	28	for	for	ADP
ejpam-4426	437	29	each	each	DET
ejpam-4426	437	30	x	x	SYM
ejpam-4426	437	31	∈	∈	PROPN
ejpam-4426	437	32	s	s	NOUN
ejpam-4426	437	33	,	,	PUNCT
ejpam-4426	437	34	is	be	AUX
ejpam-4426	437	35	a	a	DET
ejpam-4426	437	36	2	2	NUM
ejpam-4426	437	37	-	-	PUNCT
ejpam-4426	437	38	resolving	resolve	VERB
ejpam-4426	437	39	dominating	dominating	NOUN
ejpam-4426	437	40	set	set	VERB
ejpam-4426	437	41	in	in	ADP
ejpam-4426	437	42	g[h	g[h	PROPN
ejpam-4426	437	43	]	]	PUNCT
ejpam-4426	437	44	if	if	SCONJ
ejpam-4426	437	45	and	and	CCONJ
ejpam-4426	437	46	only	only	ADV
ejpam-4426	437	47	if	if	SCONJ
ejpam-4426	437	48	it	it	PRON
ejpam-4426	437	49	is	be	AUX
ejpam-4426	437	50	a	a	DET
ejpam-4426	437	51	2	2	NUM
ejpam-4426	437	52	-	-	PUNCT
ejpam-4426	437	53	resolving	resolving	NOUN
ejpam-4426	437	54	set	set	VERB
ejpam-4426	437	55	in	in	ADP
ejpam-4426	437	56	g[h	g[h	NOUN
ejpam-4426	437	57	]	]	PUNCT
ejpam-4426	437	58	.	.	PUNCT
ejpam-4426	438	1	proof	proof	NOUN
ejpam-4426	438	2	.	.	PUNCT
ejpam-4426	439	1	the	the	DET
ejpam-4426	439	2	proof	proof	NOUN
ejpam-4426	439	3	is	be	AUX
ejpam-4426	439	4	similar	similar	ADJ
ejpam-4426	439	5	to	to	ADP
ejpam-4426	439	6	that	that	PRON
ejpam-4426	439	7	of	of	ADP
ejpam-4426	439	8	theorem	theorem	ADJ
ejpam-4426	439	9	10	10	NUM
ejpam-4426	439	10	.	.	PUNCT
ejpam-4426	439	11	corollary	corollary	ADJ
ejpam-4426	439	12	4	4	NUM
ejpam-4426	439	13	.	.	PUNCT
ejpam-4426	440	1	let	let	VERB
ejpam-4426	440	2	g	g	NOUN
ejpam-4426	440	3	and	and	CCONJ
ejpam-4426	440	4	h	h	NOUN
ejpam-4426	440	5	be	be	AUX
ejpam-4426	440	6	nontrivial	nontrivial	ADJ
ejpam-4426	440	7	connected	connect	VERB
ejpam-4426	440	8	graphs	graph	NOUN
ejpam-4426	440	9	such	such	ADJ
ejpam-4426	440	10	that	that	SCONJ
ejpam-4426	440	11	g	g	PROPN
ejpam-4426	440	12	is	be	AUX
ejpam-4426	440	13	not	not	PART
ejpam-4426	440	14	freeequidistant	freeequidistant	ADJ
ejpam-4426	440	15	.	.	PUNCT
ejpam-4426	441	1	then	then	ADV
ejpam-4426	441	2	,	,	PUNCT
ejpam-4426	441	3	γ2r(g[h	γ2r(g[h	PROPN
ejpam-4426	441	4	]	]	PUNCT
ejpam-4426	441	5	)	)	PUNCT
ejpam-4426	442	1	=	=	SYM
ejpam-4426	442	2	dim2(g[h	dim2(g[h	NOUN
ejpam-4426	442	3	]	]	PUNCT
ejpam-4426	442	4	)	)	PUNCT
ejpam-4426	442	5	.	.	PUNCT
ejpam-4426	443	1	the	the	DET
ejpam-4426	443	2	set	set	NOUN
ejpam-4426	443	3	consisting	consisting	NOUN
ejpam-4426	443	4	of	of	ADP
ejpam-4426	443	5	the	the	DET
ejpam-4426	443	6	shaded	shade	VERB
ejpam-4426	443	7	vertices	vertex	NOUN
ejpam-4426	443	8	in	in	ADP
ejpam-4426	443	9	figure	figure	NOUN
ejpam-4426	443	10	5	5	NUM
ejpam-4426	443	11	is	be	AUX
ejpam-4426	443	12	a	a	DET
ejpam-4426	443	13	2	2	NUM
ejpam-4426	443	14	-	-	PUNCT
ejpam-4426	443	15	resolving	resolve	VERB
ejpam-4426	443	16	dominating	dominating	NOUN
ejpam-4426	443	17	set	set	NOUN
ejpam-4426	443	18	of	of	ADP
ejpam-4426	443	19	the	the	DET
ejpam-4426	443	20	lexicographic	lexicographic	ADJ
ejpam-4426	443	21	product	product	NOUN
ejpam-4426	443	22	p4[p3	p4[p3	NOUN
ejpam-4426	443	23	]	]	PROPN
ejpam-4426	443	24	.	.	PUNCT
ejpam-4426	443	25	....................................	....................................	PUNCT
ejpam-4426	444	1	....................................	....................................	PUNCT
ejpam-4426	444	2	....................................	....................................	PUNCT
ejpam-4426	445	1	....................................	....................................	PUNCT
ejpam-4426	445	2	....................................	....................................	PUNCT
ejpam-4426	446	1	....................................	....................................	PUNCT
ejpam-4426	446	2	....................................	....................................	PUNCT
ejpam-4426	447	1	....................................	....................................	PUNCT
ejpam-4426	447	2	....................................	....................................	PUNCT
ejpam-4426	448	1	....................................	....................................	PUNCT
ejpam-4426	448	2	....................................	....................................	PUNCT
ejpam-4426	449	1	....................................	....................................	PUNCT
ejpam-4426	449	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	450	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	450	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	451	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	451	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	452	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	452	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	453	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-4426	453	2	.........	.........	PUNCT
ejpam-4426	453	3	........	........	PUNCT
ejpam-4426	453	4	........	........	PUNCT
ejpam-4426	453	5	........	........	PUNCT
ejpam-4426	453	6	........	........	PUNCT
ejpam-4426	453	7	........	........	PUNCT
ejpam-4426	453	8	........	........	PUNCT
ejpam-4426	453	9	........	........	PUNCT
ejpam-4426	453	10	........	........	PUNCT
ejpam-4426	453	11	........	........	PUNCT
ejpam-4426	454	1	........	........	PUNCT
ejpam-4426	454	2	....	....	PUNCT
ejpam-4426	455	1	.........	.........	PUNCT
ejpam-4426	455	2	........	........	PUNCT
ejpam-4426	455	3	........	........	PUNCT
ejpam-4426	455	4	........	........	PUNCT
ejpam-4426	455	5	........	........	PUNCT
ejpam-4426	455	6	........	........	PUNCT
ejpam-4426	455	7	........	........	PUNCT
ejpam-4426	455	8	........	........	PUNCT
ejpam-4426	455	9	........	........	PUNCT
ejpam-4426	455	10	........	........	PUNCT
ejpam-4426	456	1	........	........	PUNCT
ejpam-4426	456	2	....	....	PUNCT
ejpam-4426	457	1	.........	.........	PUNCT
ejpam-4426	457	2	........	........	PUNCT
ejpam-4426	457	3	........	........	PUNCT
ejpam-4426	457	4	........	........	PUNCT
ejpam-4426	457	5	........	........	PUNCT
ejpam-4426	457	6	........	........	PUNCT
ejpam-4426	457	7	........	........	PUNCT
ejpam-4426	457	8	........	........	PUNCT
ejpam-4426	457	9	........	........	PUNCT
ejpam-4426	457	10	........	........	PUNCT
ejpam-4426	458	1	........	........	PUNCT
ejpam-4426	458	2	....	....	PUNCT
ejpam-4426	459	1	.........	.........	PUNCT
ejpam-4426	459	2	........	........	PUNCT
ejpam-4426	459	3	........	........	PUNCT
ejpam-4426	459	4	........	........	PUNCT
ejpam-4426	459	5	........	........	PUNCT
ejpam-4426	459	6	........	........	PUNCT
ejpam-4426	459	7	........	........	PUNCT
ejpam-4426	459	8	........	........	PUNCT
ejpam-4426	459	9	........	........	PUNCT
ejpam-4426	459	10	........	........	PUNCT
ejpam-4426	460	1	........	........	PUNCT
ejpam-4426	460	2	....	....	PUNCT
ejpam-4426	461	1	.........	.........	PUNCT
ejpam-4426	461	2	........	........	PUNCT
ejpam-4426	461	3	........	........	PUNCT
ejpam-4426	461	4	........	........	PUNCT
ejpam-4426	461	5	........	........	PUNCT
ejpam-4426	461	6	........	........	PUNCT
ejpam-4426	461	7	........	........	PUNCT
ejpam-4426	461	8	........	........	PUNCT
ejpam-4426	461	9	........	........	PUNCT
ejpam-4426	461	10	........	........	PUNCT
ejpam-4426	462	1	........	........	PUNCT
ejpam-4426	462	2	....	....	PUNCT
ejpam-4426	463	1	.........	.........	PUNCT
ejpam-4426	463	2	........	........	PUNCT
ejpam-4426	463	3	........	........	PUNCT
ejpam-4426	463	4	........	........	PUNCT
ejpam-4426	463	5	........	........	PUNCT
ejpam-4426	463	6	........	........	PUNCT
ejpam-4426	463	7	........	........	PUNCT
ejpam-4426	463	8	........	........	PUNCT
ejpam-4426	463	9	........	........	PUNCT
ejpam-4426	463	10	........	........	PUNCT
ejpam-4426	464	1	........	........	PUNCT
ejpam-4426	464	2	....	....	PUNCT
ejpam-4426	465	1	.........	.........	PUNCT
ejpam-4426	465	2	........	........	PUNCT
ejpam-4426	465	3	........	........	PUNCT
ejpam-4426	465	4	........	........	PUNCT
ejpam-4426	465	5	........	........	PUNCT
ejpam-4426	465	6	........	........	PUNCT
ejpam-4426	465	7	........	........	PUNCT
ejpam-4426	465	8	........	........	PUNCT
ejpam-4426	465	9	........	........	PUNCT
ejpam-4426	465	10	........	........	PUNCT
ejpam-4426	466	1	........	........	PUNCT
ejpam-4426	466	2	....	....	PUNCT
ejpam-4426	467	1	.........	.........	PUNCT
ejpam-4426	467	2	........	........	PUNCT
ejpam-4426	467	3	........	........	PUNCT
ejpam-4426	467	4	........	........	PUNCT
ejpam-4426	467	5	........	........	PUNCT
ejpam-4426	467	6	........	........	PUNCT
ejpam-4426	467	7	........	........	PUNCT
ejpam-4426	467	8	........	........	PUNCT
ejpam-4426	467	9	........	........	PUNCT
ejpam-4426	467	10	........	........	PUNCT
ejpam-4426	468	1	........	........	PUNCT
ejpam-4426	468	2	....	....	PUNCT
ejpam-4426	468	3	............	............	PUNCT
ejpam-4426	468	4	...........	...........	PUNCT
ejpam-4426	468	5	...........	...........	PUNCT
ejpam-4426	468	6	...........	...........	PUNCT
ejpam-4426	468	7	...........	...........	PUNCT
ejpam-4426	468	8	...........	...........	PUNCT
ejpam-4426	468	9	...........	...........	PUNCT
ejpam-4426	468	10	...........	...........	PUNCT
ejpam-4426	468	11	...........	...........	PUNCT
ejpam-4426	468	12	...........	...........	PUNCT
ejpam-4426	468	13	...........	...........	PUNCT
ejpam-4426	468	14	...........	...........	PUNCT
ejpam-4426	468	15	...	...	PUNCT
ejpam-4426	468	16	.........	.........	PUNCT
ejpam-4426	468	17	........	........	PUNCT
ejpam-4426	468	18	........	........	PUNCT
ejpam-4426	468	19	........	........	PUNCT
ejpam-4426	468	20	........	........	PUNCT
ejpam-4426	468	21	........	........	PUNCT
ejpam-4426	468	22	........	........	PUNCT
ejpam-4426	468	23	........	........	PUNCT
ejpam-4426	468	24	........	........	PUNCT
ejpam-4426	468	25	........	........	PUNCT
ejpam-4426	469	1	........	........	PUNCT
ejpam-4426	469	2	....	....	PUNCT
ejpam-4426	470	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4426	470	2	.........................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................	PUNCT
ejpam-4426	471	1	...........	...........	PUNCT
ejpam-4426	471	2	...........	...........	PUNCT
ejpam-4426	471	3	...........	...........	PUNCT
ejpam-4426	471	4	...........	...........	PUNCT
ejpam-4426	471	5	...........	...........	PUNCT
ejpam-4426	471	6	...........	...........	PUNCT
ejpam-4426	471	7	...........	...........	PUNCT
ejpam-4426	471	8	...........	...........	PUNCT
ejpam-4426	471	9	...........	...........	PUNCT
ejpam-4426	471	10	...........	...........	PUNCT
ejpam-4426	471	11	...........	...........	PUNCT
ejpam-4426	471	12	...	...	PUNCT
ejpam-4426	471	13	...................	...................	PUNCT
ejpam-4426	472	1	..................	..................	PUNCT
ejpam-4426	472	2	..................	..................	PUNCT
ejpam-4426	473	1	..................	..................	PUNCT
ejpam-4426	473	2	..................	..................	PUNCT
ejpam-4426	474	1	..................	..................	PUNCT
ejpam-4426	474	2	..................	..................	PUNCT
ejpam-4426	475	1	..................	..................	PUNCT
ejpam-4426	475	2	..................	..................	PUNCT
ejpam-4426	476	1	..................	..................	PUNCT
ejpam-4426	476	2	..................	..................	PUNCT
ejpam-4426	477	1	..................	..................	PUNCT
ejpam-4426	477	2	....	....	PUNCT
ejpam-4426	478	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4426	478	2	.........................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................	PUNCT
ejpam-4426	479	1	...........	...........	PUNCT
ejpam-4426	479	2	...........	...........	PUNCT
ejpam-4426	479	3	...........	...........	PUNCT
ejpam-4426	479	4	...........	...........	PUNCT
ejpam-4426	479	5	...........	...........	PUNCT
ejpam-4426	479	6	...........	...........	PUNCT
ejpam-4426	479	7	...........	...........	PUNCT
ejpam-4426	479	8	...........	...........	PUNCT
ejpam-4426	479	9	...........	...........	PUNCT
ejpam-4426	479	10	...........	...........	PUNCT
ejpam-4426	479	11	...........	...........	PUNCT
ejpam-4426	479	12	...	...	PUNCT
ejpam-4426	480	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4426	480	2	.............................................................................................................................................................................................................................	.............................................................................................................................................................................................................................	PUNCT
ejpam-4426	480	3	...................	...................	PUNCT
ejpam-4426	480	4	..................	..................	PUNCT
ejpam-4426	480	5	..................	..................	PUNCT
ejpam-4426	480	6	..................	..................	PUNCT
ejpam-4426	480	7	..................	..................	PUNCT
ejpam-4426	480	8	..................	..................	PUNCT
ejpam-4426	480	9	..................	..................	PUNCT
ejpam-4426	480	10	..................	..................	PUNCT
ejpam-4426	480	11	..................	..................	PUNCT
ejpam-4426	480	12	..................	..................	PUNCT
ejpam-4426	480	13	..................	..................	PUNCT
ejpam-4426	480	14	..................	..................	PUNCT
ejpam-4426	481	1	....	....	PUNCT
ejpam-4426	481	2	............	............	PUNCT
ejpam-4426	481	3	...........	...........	PUNCT
ejpam-4426	481	4	...........	...........	PUNCT
ejpam-4426	481	5	...........	...........	PUNCT
ejpam-4426	481	6	...........	...........	PUNCT
ejpam-4426	481	7	...........	...........	PUNCT
ejpam-4426	481	8	...........	...........	PUNCT
ejpam-4426	481	9	...........	...........	PUNCT
ejpam-4426	481	10	...........	...........	PUNCT
ejpam-4426	481	11	...........	...........	PUNCT
ejpam-4426	481	12	...........	...........	PUNCT
ejpam-4426	481	13	...........	...........	PUNCT
ejpam-4426	481	14	...	...	PUNCT
ejpam-4426	481	15	......................................................................................................................................................................................................	......................................................................................................................................................................................................	PUNCT
ejpam-4426	481	16	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4426	482	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4426	482	2	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-4426	482	3	............	............	PUNCT
ejpam-4426	483	1	...........	...........	PUNCT
ejpam-4426	483	2	...........	...........	PUNCT
ejpam-4426	483	3	...........	...........	PUNCT
ejpam-4426	483	4	...........	...........	PUNCT
ejpam-4426	483	5	...........	...........	PUNCT
ejpam-4426	483	6	...........	...........	PUNCT
ejpam-4426	483	7	...........	...........	PUNCT
ejpam-4426	483	8	...........	...........	PUNCT
ejpam-4426	483	9	...........	...........	PUNCT
ejpam-4426	483	10	...........	...........	PUNCT
ejpam-4426	483	11	...........	...........	PUNCT
ejpam-4426	483	12	...	...	PUNCT
ejpam-4426	483	13	...................	...................	PUNCT
ejpam-4426	484	1	..................	..................	PUNCT
ejpam-4426	484	2	..................	..................	PUNCT
ejpam-4426	485	1	..................	..................	PUNCT
ejpam-4426	485	2	..................	..................	PUNCT
ejpam-4426	486	1	..................	..................	PUNCT
ejpam-4426	486	2	..................	..................	PUNCT
ejpam-4426	487	1	..................	..................	PUNCT
ejpam-4426	487	2	..................	..................	PUNCT
ejpam-4426	488	1	..................	..................	PUNCT
ejpam-4426	488	2	..................	..................	PUNCT
ejpam-4426	489	1	..................	..................	PUNCT
ejpam-4426	489	2	....	....	PUNCT
ejpam-4426	489	3	............	............	PUNCT
ejpam-4426	489	4	...........	...........	PUNCT
ejpam-4426	489	5	...........	...........	PUNCT
ejpam-4426	489	6	...........	...........	PUNCT
ejpam-4426	489	7	...........	...........	PUNCT
ejpam-4426	489	8	...........	...........	PUNCT
ejpam-4426	489	9	...........	...........	PUNCT
ejpam-4426	489	10	...........	...........	PUNCT
ejpam-4426	489	11	...........	...........	PUNCT
ejpam-4426	489	12	...........	...........	PUNCT
ejpam-4426	489	13	...........	...........	PUNCT
ejpam-4426	489	14	...........	...........	PUNCT
ejpam-4426	489	15	...	...	PUNCT
ejpam-4426	490	1	•	•	NUM
ejpam-4426	490	2	•	•	NUM
ejpam-4426	490	3	•	•	NUM
ejpam-4426	490	4	•	•	NUM
ejpam-4426	490	5	•	•	NUM
ejpam-4426	490	6	•	•	NUM
ejpam-4426	490	7	•	•	NOUN
ejpam-4426	490	8	•	•	NUM
ejpam-4426	490	9	figure	figure	NOUN
ejpam-4426	490	10	5	5	NUM
ejpam-4426	490	11	:	:	PUNCT
ejpam-4426	490	12	a	a	DET
ejpam-4426	490	13	graph	graph	NOUN
ejpam-4426	490	14	p4[p3	p4[p3	NOUN
ejpam-4426	490	15	]	]	X
ejpam-4426	490	16	with	with	ADP
ejpam-4426	490	17	γ2rp4[p3	γ2rp4[p3	NOUN
ejpam-4426	490	18	]	]	X
ejpam-4426	491	1	=	=	SYM
ejpam-4426	491	2	8	8	NUM
ejpam-4426	491	3	references	reference	NOUN
ejpam-4426	491	4	1425	1425	NUM
ejpam-4426	491	5	acknowledgements	acknowledgement	NOUN
ejpam-4426	491	6	the	the	DET
ejpam-4426	491	7	authors	author	NOUN
ejpam-4426	491	8	would	would	AUX
ejpam-4426	491	9	like	like	VERB
ejpam-4426	491	10	to	to	PART
ejpam-4426	491	11	thank	thank	VERB
ejpam-4426	491	12	the	the	DET
ejpam-4426	491	13	commission	commission	NOUN
ejpam-4426	491	14	on	on	ADP
ejpam-4426	491	15	higher	high	ADJ
ejpam-4426	491	16	education	education	NOUN
ejpam-4426	491	17	(	(	PUNCT
ejpam-4426	491	18	ched	che	VERB
ejpam-4426	491	19	)	)	PUNCT
ejpam-4426	491	20	and	and	CCONJ
ejpam-4426	491	21	mindanao	mindanao	PROPN
ejpam-4426	491	22	state	state	PROPN
ejpam-4426	491	23	university	university	PROPN
ejpam-4426	491	24	-	-	PUNCT
ejpam-4426	491	25	marawi	marawi	PROPN
ejpam-4426	491	26	and	and	CCONJ
ejpam-4426	491	27	msu	msu	PROPN
ejpam-4426	491	28	-	-	PUNCT
ejpam-4426	491	29	iligan	iligan	PROPN
ejpam-4426	491	30	institute	institute	PROPN
ejpam-4426	491	31	of	of	ADP
ejpam-4426	491	32	technology	technology	PROPN
ejpam-4426	491	33	,	,	PUNCT
ejpam-4426	491	34	philippines	philippine	NOUN
ejpam-4426	491	35	.	.	PUNCT
ejpam-4426	492	1	references	reference	NOUN
ejpam-4426	492	2	[	[	X
ejpam-4426	492	3	1	1	NUM
ejpam-4426	492	4	]	]	X
ejpam-4426	492	5	estrada	estrada	PROPN
ejpam-4426	492	6	-	-	PUNCT
ejpam-4426	492	7	moreno	moreno	PROPN
ejpam-4426	492	8	a	a	PROPN
ejpam-4426	492	9	,	,	PUNCT
ejpam-4426	492	10	rodriguez	rodriguez	PROPN
ejpam-4426	492	11	-	-	PUNCT
ejpam-4426	492	12	velasquez	velasquez	PROPN
ejpam-4426	492	13	j	j	PROPN
ejpam-4426	492	14	,	,	PUNCT
ejpam-4426	492	15	and	and	CCONJ
ejpam-4426	492	16	i	i	PRON
ejpam-4426	492	17	yero	yero	NOUN
ejpam-4426	492	18	.	.	PUNCT
ejpam-4426	493	1	the	the	DET
ejpam-4426	493	2	k	k	ADJ
ejpam-4426	493	3	-	-	ADJ
ejpam-4426	493	4	metric	metric	ADJ
ejpam-4426	493	5	dimension	dimension	NOUN
ejpam-4426	493	6	of	of	ADP
ejpam-4426	493	7	a	a	DET
ejpam-4426	493	8	graph	graph	NOUN
ejpam-4426	493	9	.	.	PUNCT
ejpam-4426	494	1	applied	apply	VERB
ejpam-4426	494	2	math	math	NOUN
ejpam-4426	494	3	information	information	NOUN
ejpam-4426	494	4	science	science	NOUN
ejpam-4426	494	5	.	.	PUNCT
ejpam-4426	494	6	,	,	PUNCT
ejpam-4426	494	7	9:2829–2840	9:2829–2840	NUM
ejpam-4426	494	8	,	,	PUNCT
ejpam-4426	494	9	2015	2015	NUM
ejpam-4426	494	10	.	.	PUNCT
ejpam-4426	495	1	[	[	X
ejpam-4426	495	2	2	2	X
ejpam-4426	495	3	]	]	X
ejpam-4426	495	4	kuziak	kuziak	PROPN
ejpam-4426	495	5	d.	d.	PROPN
ejpam-4426	495	6	,	,	PUNCT
ejpam-4426	495	7	rodriguez	rodriguez	PROPN
ejpam-4426	495	8	-	-	PUNCT
ejpam-4426	495	9	velasquez	velasquez	PROPN
ejpam-4426	495	10	j.	j.	PROPN
ejpam-4426	495	11	,	,	PUNCT
ejpam-4426	495	12	and	and	CCONJ
ejpam-4426	495	13	i	i	PRON
ejpam-4426	495	14	yero	yero	PROPN
ejpam-4426	495	15	.	.	PROPN
ejpam-4426	495	16	closed	close	VERB
ejpam-4426	495	17	formulae	formulae	ADJ
ejpam-4426	495	18	for	for	ADP
ejpam-4426	495	19	the	the	DET
ejpam-4426	495	20	strong	strong	ADJ
ejpam-4426	495	21	metric	metric	ADJ
ejpam-4426	495	22	dimension	dimension	NOUN
ejpam-4426	495	23	of	of	ADP
ejpam-4426	495	24	lexicographic	lexicographic	ADJ
ejpam-4426	495	25	product	product	NOUN
ejpam-4426	495	26	graphs	graph	NOUN
ejpam-4426	495	27	.	.	PUNCT
ejpam-4426	496	1	discussiones	discussione	NOUN
ejpam-4426	496	2	mathematicae	mathematicae	PROPN
ejpam-4426	496	3	graph	graph	NOUN
ejpam-4426	496	4	theory	theory	NOUN
ejpam-4426	496	5	,	,	PUNCT
ejpam-4426	496	6	.	.	PUNCT
ejpam-4426	496	7	,	,	PUNCT
ejpam-4426	496	8	36(4):1051–1064	36(4):1051–1064	NUM
ejpam-4426	496	9	,	,	PUNCT
ejpam-4426	496	10	2016	2016	NUM
ejpam-4426	496	11	.	.	PUNCT
ejpam-4426	497	1	[	[	X
ejpam-4426	497	2	3	3	NUM
ejpam-4426	497	3	]	]	X
ejpam-4426	497	4	harary	harary	NOUN
ejpam-4426	497	5	f	f	PROPN
ejpam-4426	497	6	and	and	CCONJ
ejpam-4426	497	7	r	r	NOUN
ejpam-4426	497	8	melter	melter	NOUN
ejpam-4426	497	9	.	.	PUNCT
ejpam-4426	498	1	on	on	ADP
ejpam-4426	498	2	the	the	DET
ejpam-4426	498	3	metric	metric	ADJ
ejpam-4426	498	4	dimension	dimension	NOUN
ejpam-4426	498	5	of	of	ADP
ejpam-4426	498	6	a	a	DET
ejpam-4426	498	7	graph	graph	NOUN
ejpam-4426	498	8	.	.	PUNCT
ejpam-4426	499	1	ars	ars	PROPN
ejpam-4426	499	2	combinatoria	combinatoria	PROPN
ejpam-4426	499	3	,	,	PUNCT
ejpam-4426	499	4	2	2	NUM
ejpam-4426	499	5	,	,	PUNCT
ejpam-4426	499	6	1976	1976	NUM
ejpam-4426	499	7	.	.	PUNCT
ejpam-4426	500	1	[	[	X
ejpam-4426	500	2	4	4	X
ejpam-4426	500	3	]	]	ADJ
ejpam-4426	500	4	rara	rara	NOUN
ejpam-4426	500	5	h	h	NOUN
ejpam-4426	500	6	and	and	CCONJ
ejpam-4426	500	7	j	j	PROPN
ejpam-4426	500	8	cabaro	cabaro	NOUN
ejpam-4426	500	9	.	.	PUNCT
ejpam-4426	501	1	on	on	ADP
ejpam-4426	501	2	2	2	NUM
ejpam-4426	501	3	-	-	PUNCT
ejpam-4426	501	4	resolving	resolve	VERB
ejpam-4426	501	5	sets	set	NOUN
ejpam-4426	501	6	in	in	ADP
ejpam-4426	501	7	the	the	DET
ejpam-4426	501	8	join	join	NOUN
ejpam-4426	501	9	and	and	CCONJ
ejpam-4426	501	10	corona	corona	NOUN
ejpam-4426	501	11	of	of	ADP
ejpam-4426	501	12	graphs	graph	NOUN
ejpam-4426	501	13	.	.	PUNCT
ejpam-4426	502	1	european	european	ADJ
ejpam-4426	502	2	journal	journal	PROPN
ejpam-4426	502	3	of	of	ADP
ejpam-4426	502	4	pure	pure	ADJ
ejpam-4426	502	5	and	and	CCONJ
ejpam-4426	502	6	applied	applied	ADJ
ejpam-4426	502	7	mathematics	mathematic	NOUN
ejpam-4426	502	8	,	,	PUNCT
ejpam-4426	502	9	14:773–782	14:773–782	NUM
ejpam-4426	502	10	,	,	PUNCT
ejpam-4426	502	11	2021	2021	NUM
ejpam-4426	502	12	.	.	PUNCT
ejpam-4426	503	1	[	[	X
ejpam-4426	503	2	5	5	NUM
ejpam-4426	503	3	]	]	SYM
ejpam-4426	503	4	f	f	PROPN
ejpam-4426	503	5	harary	harary	NOUN
ejpam-4426	503	6	.	.	PUNCT
ejpam-4426	504	1	graph	graph	NOUN
ejpam-4426	504	2	theory	theory	NOUN
ejpam-4426	504	3	.	.	PUNCT
ejpam-4426	505	1	addison	addison	PROPN
ejpam-4426	505	2	-	-	PUNCT
ejpam-4426	505	3	wesley	wesley	PROPN
ejpam-4426	505	4	publishing	publishing	PROPN
ejpam-4426	505	5	company	company	NOUN
ejpam-4426	505	6	,	,	PUNCT
ejpam-4426	505	7	usa	usa	PROPN
ejpam-4426	505	8	,	,	PUNCT
ejpam-4426	505	9	1969	1969	NUM
ejpam-4426	505	10	.	.	PUNCT
ejpam-4426	506	1	[	[	X
ejpam-4426	506	2	6	6	NUM
ejpam-4426	506	3	]	]	SYM
ejpam-4426	506	4	bailey	bailey	NOUN
ejpam-4426	506	5	r	r	NOUN
ejpam-4426	506	6	and	and	CCONJ
ejpam-4426	506	7	i	i	PRON
ejpam-4426	506	8	yero	yero	NOUN
ejpam-4426	506	9	.	.	PUNCT
ejpam-4426	507	1	error	error	NOUN
ejpam-4426	507	2	-	-	PUNCT
ejpam-4426	507	3	correcting	correct	VERB
ejpam-4426	507	4	codes	code	NOUN
ejpam-4426	507	5	from	from	ADP
ejpam-4426	507	6	k	k	ADJ
ejpam-4426	507	7	-	-	PUNCT
ejpam-4426	507	8	resolving	resolving	ADJ
ejpam-4426	507	9	sets	set	NOUN
ejpam-4426	507	10	.	.	PUNCT
ejpam-4426	508	1	discussiones	discussione	NOUN
ejpam-4426	508	2	mathematicae	mathematicae	VERB
ejpam-4426	508	3	,	,	PUNCT
ejpam-4426	508	4	graph	graph	NOUN
ejpam-4426	508	5	theory	theory	NOUN
ejpam-4426	508	6	,	,	PUNCT
ejpam-4426	508	7	39:341–355	39:341–355	PROPN
ejpam-4426	508	8	,	,	PUNCT
ejpam-4426	508	9	2019	2019	NUM
ejpam-4426	508	10	.	.	PUNCT
ejpam-4426	509	1	[	[	X
ejpam-4426	509	2	7	7	X
ejpam-4426	509	3	]	]	PUNCT
ejpam-4426	509	4	p.	p.	PROPN
ejpam-4426	509	5	j.	j.	PROPN
ejpam-4426	509	6	slater	slater	PROPN
ejpam-4426	509	7	.	.	PUNCT
ejpam-4426	510	1	leaves	leave	NOUN
ejpam-4426	510	2	of	of	ADP
ejpam-4426	510	3	trees	tree	NOUN
ejpam-4426	510	4	.	.	PUNCT
ejpam-4426	511	1	congressus	congressus	PROPN
ejpam-4426	511	2	numerantium	numerantium	PROPN
ejpam-4426	511	3	,	,	PUNCT
ejpam-4426	511	4	.	.	PUNCT
ejpam-4426	511	5	,	,	PUNCT
ejpam-4426	512	1	14:549–559	14:549–559	NUM
ejpam-4426	512	2	,	,	PUNCT
ejpam-4426	512	3	1975	1975	NUM
ejpam-4426	512	4	.	.	PUNCT
ejpam-4426	513	1	[	[	X
ejpam-4426	513	2	8	8	X
ejpam-4426	513	3	]	]	PUNCT
ejpam-4426	513	4	saenpholphat	saenpholphat	PRON
ejpam-4426	513	5	v	v	NOUN
ejpam-4426	513	6	and	and	CCONJ
ejpam-4426	513	7	p	p	PROPN
ejpam-4426	513	8	zang	zang	PROPN
ejpam-4426	513	9	.	.	PUNCT
ejpam-4426	514	1	on	on	ADP
ejpam-4426	514	2	connected	connected	ADJ
ejpam-4426	514	3	resolvability	resolvability	NOUN
ejpam-4426	514	4	of	of	ADP
ejpam-4426	514	5	graphs	graph	NOUN
ejpam-4426	514	6	.	.	PUNCT
ejpam-4426	515	1	australian	australian	ADJ
ejpam-4426	515	2	journal	journal	NOUN
ejpam-4426	515	3	of	of	ADP
ejpam-4426	515	4	combinatorics	combinatoric	NOUN
ejpam-4426	515	5	,	,	PUNCT
ejpam-4426	515	6	28:25–37	28:25–37	NUM
ejpam-4426	515	7	,	,	PUNCT
ejpam-4426	515	8	2003	2003	NUM
ejpam-4426	515	9	.	.	PUNCT