id	sid	tid	token	lemma	pos
ejpam-3977	1	1	european	european	PROPN
ejpam-3977	1	2	journal	journal	PROPN
ejpam-3977	1	3	of	of	ADP
ejpam-3977	1	4	pure	pure	ADJ
ejpam-3977	1	5	and	and	CCONJ
ejpam-3977	1	6	applied	apply	VERB
ejpam-3977	1	7	mathematics	mathematic	NOUN
ejpam-3977	1	8	vol	vol	NOUN
ejpam-3977	1	9	.	.	PUNCT
ejpam-3977	2	1	14	14	NUM
ejpam-3977	2	2	,	,	PUNCT
ejpam-3977	2	3	no	no	INTJ
ejpam-3977	2	4	.	.	NOUN
ejpam-3977	2	5	3	3	NUM
ejpam-3977	2	6	,	,	PUNCT
ejpam-3977	2	7	2021	2021	NUM
ejpam-3977	2	8	,	,	PUNCT
ejpam-3977	2	9	773	773	NUM
ejpam-3977	2	10	-	-	SYM
ejpam-3977	2	11	782	782	NUM
ejpam-3977	2	12	issn	issn	PROPN
ejpam-3977	2	13	1307	1307	NUM
ejpam-3977	2	14	-	-	SYM
ejpam-3977	2	15	5543	5543	NUM
ejpam-3977	2	16	–	–	PUNCT
ejpam-3977	2	17	ejpam.com	ejpam.com	X
ejpam-3977	2	18	published	publish	VERB
ejpam-3977	2	19	by	by	ADP
ejpam-3977	2	20	new	new	PROPN
ejpam-3977	2	21	york	york	PROPN
ejpam-3977	2	22	business	business	PROPN
ejpam-3977	2	23	global	global	ADJ
ejpam-3977	2	24	on	on	ADP
ejpam-3977	2	25	2	2	NUM
ejpam-3977	2	26	-	-	PUNCT
ejpam-3977	2	27	resolving	resolve	VERB
ejpam-3977	2	28	sets	set	NOUN
ejpam-3977	2	29	in	in	ADP
ejpam-3977	2	30	the	the	DET
ejpam-3977	2	31	join	join	NOUN
ejpam-3977	2	32	and	and	CCONJ
ejpam-3977	2	33	corona	corona	NOUN
ejpam-3977	2	34	of	of	ADP
ejpam-3977	2	35	graphs†	graphs†	ADJ
ejpam-3977	2	36	jean	jean	PROPN
ejpam-3977	2	37	cabaro1	cabaro1	PROPN
ejpam-3977	2	38	,	,	PUNCT
ejpam-3977	2	39	helen	helen	PROPN
ejpam-3977	2	40	rara2	rara2	PROPN
ejpam-3977	2	41	1	1	NUM
ejpam-3977	2	42	mathematics	mathematics	PROPN
ejpam-3977	2	43	department	department	NOUN
ejpam-3977	2	44	,	,	PUNCT
ejpam-3977	2	45	college	college	NOUN
ejpam-3977	2	46	of	of	ADP
ejpam-3977	2	47	natural	natural	ADJ
ejpam-3977	2	48	sciences	science	NOUN
ejpam-3977	2	49	and	and	CCONJ
ejpam-3977	2	50	mathematics	mathematic	NOUN
ejpam-3977	2	51	,	,	PUNCT
ejpam-3977	2	52	mindanao	mindanao	PROPN
ejpam-3977	2	53	state	state	PROPN
ejpam-3977	2	54	university	university	NOUN
ejpam-3977	2	55	-	-	PUNCT
ejpam-3977	2	56	main	main	ADJ
ejpam-3977	2	57	campus	campus	NOUN
ejpam-3977	2	58	,	,	PUNCT
ejpam-3977	2	59	9700	9700	NUM
ejpam-3977	2	60	marawi	marawi	PROPN
ejpam-3977	2	61	city	city	PROPN
ejpam-3977	2	62	,	,	PUNCT
ejpam-3977	2	63	philippines	philippines	PROPN
ejpam-3977	2	64	2	2	NUM
ejpam-3977	2	65	department	department	NOUN
ejpam-3977	2	66	of	of	ADP
ejpam-3977	2	67	mathematics	mathematic	NOUN
ejpam-3977	2	68	and	and	CCONJ
ejpam-3977	2	69	statistics	statistic	NOUN
ejpam-3977	2	70	,	,	PUNCT
ejpam-3977	2	71	college	college	NOUN
ejpam-3977	2	72	of	of	ADP
ejpam-3977	2	73	science	science	NOUN
ejpam-3977	2	74	and	and	CCONJ
ejpam-3977	2	75	mathematics	mathematic	NOUN
ejpam-3977	2	76	,	,	PUNCT
ejpam-3977	2	77	center	center	NOUN
ejpam-3977	2	78	of	of	ADP
ejpam-3977	2	79	graph	graph	NOUN
ejpam-3977	2	80	theory	theory	NOUN
ejpam-3977	2	81	,	,	PUNCT
ejpam-3977	2	82	algebra	algebra	NOUN
ejpam-3977	2	83	,	,	PUNCT
ejpam-3977	2	84	and	and	CCONJ
ejpam-3977	2	85	analysis	analysis	NOUN
ejpam-3977	2	86	-	-	PUNCT
ejpam-3977	2	87	premier	premier	NOUN
ejpam-3977	2	88	research	research	NOUN
ejpam-3977	2	89	institute	institute	PROPN
ejpam-3977	2	90	of	of	ADP
ejpam-3977	2	91	science	science	NOUN
ejpam-3977	2	92	and	and	CCONJ
ejpam-3977	2	93	mathematics	mathematic	NOUN
ejpam-3977	2	94	,	,	PUNCT
ejpam-3977	2	95	mindanao	mindanao	PROPN
ejpam-3977	2	96	state	state	PROPN
ejpam-3977	2	97	university	university	PROPN
ejpam-3977	2	98	-	-	PUNCT
ejpam-3977	2	99	iligan	iligan	PROPN
ejpam-3977	2	100	institute	institute	PROPN
ejpam-3977	2	101	of	of	ADP
ejpam-3977	2	102	technology	technology	PROPN
ejpam-3977	2	103	,	,	PUNCT
ejpam-3977	2	104	9200	9200	NUM
ejpam-3977	2	105	iligan	iligan	ADJ
ejpam-3977	2	106	city	city	NOUN
ejpam-3977	2	107	,	,	PUNCT
ejpam-3977	3	1	philippines	philippine	NOUN
ejpam-3977	3	2	abstract	abstract	ADJ
ejpam-3977	3	3	.	.	PUNCT
ejpam-3977	4	1	let	let	VERB
ejpam-3977	4	2	g	g	PRON
ejpam-3977	4	3	be	be	AUX
ejpam-3977	4	4	a	a	DET
ejpam-3977	4	5	connected	connected	ADJ
ejpam-3977	4	6	graph	graph	NOUN
ejpam-3977	4	7	.	.	PUNCT
ejpam-3977	5	1	an	an	DET
ejpam-3977	5	2	ordered	order	VERB
ejpam-3977	5	3	set	set	NOUN
ejpam-3977	5	4	of	of	ADP
ejpam-3977	5	5	vertices	vertex	NOUN
ejpam-3977	5	6	{	{	PUNCT
ejpam-3977	5	7	v1	v1	NOUN
ejpam-3977	5	8	,	,	PUNCT
ejpam-3977	5	9	...	...	PUNCT
ejpam-3977	5	10	,	,	PUNCT
ejpam-3977	5	11	vl	vl	ADJ
ejpam-3977	5	12	}	}	PUNCT
ejpam-3977	5	13	is	be	AUX
ejpam-3977	5	14	a	a	DET
ejpam-3977	5	15	2	2	NUM
ejpam-3977	5	16	-	-	PUNCT
ejpam-3977	5	17	resolving	resolving	NOUN
ejpam-3977	5	18	set	set	NOUN
ejpam-3977	5	19	in	in	ADP
ejpam-3977	5	20	g	g	PROPN
ejpam-3977	5	21	if	if	SCONJ
ejpam-3977	5	22	,	,	PUNCT
ejpam-3977	5	23	for	for	ADP
ejpam-3977	5	24	any	any	DET
ejpam-3977	5	25	distinct	distinct	ADJ
ejpam-3977	5	26	vertices	vertex	NOUN
ejpam-3977	5	27	u	u	NOUN
ejpam-3977	5	28	,	,	PUNCT
ejpam-3977	5	29	w	w	PROPN
ejpam-3977	5	30	∈	∈	PROPN
ejpam-3977	5	31	v	v	ADP
ejpam-3977	5	32	(	(	PUNCT
ejpam-3977	5	33	g	g	NOUN
ejpam-3977	5	34	)	)	PUNCT
ejpam-3977	5	35	,	,	PUNCT
ejpam-3977	5	36	the	the	DET
ejpam-3977	5	37	lists	list	NOUN
ejpam-3977	5	38	of	of	ADP
ejpam-3977	5	39	distances	distance	NOUN
ejpam-3977	5	40	(	(	PUNCT
ejpam-3977	5	41	dg(u	dg(u	X
ejpam-3977	5	42	,	,	PUNCT
ejpam-3977	5	43	v1	v1	NOUN
ejpam-3977	5	44	)	)	PUNCT
ejpam-3977	5	45	,	,	PUNCT
ejpam-3977	5	46	...	...	PUNCT
ejpam-3977	5	47	,	,	PUNCT
ejpam-3977	5	48	dg(u	dg(u	X
ejpam-3977	5	49	,	,	PUNCT
ejpam-3977	5	50	vl	vl	NOUN
ejpam-3977	5	51	)	)	PUNCT
ejpam-3977	5	52	)	)	PUNCT
ejpam-3977	5	53	and	and	CCONJ
ejpam-3977	5	54	(	(	PUNCT
ejpam-3977	5	55	dg(w	dg(w	X
ejpam-3977	5	56	,	,	PUNCT
ejpam-3977	5	57	v1	v1	NOUN
ejpam-3977	5	58	)	)	PUNCT
ejpam-3977	5	59	,	,	PUNCT
ejpam-3977	5	60	...	...	PUNCT
ejpam-3977	5	61	,	,	PUNCT
ejpam-3977	5	62	dg(w	dg(w	X
ejpam-3977	5	63	,	,	PUNCT
ejpam-3977	5	64	vl	vl	NOUN
ejpam-3977	5	65	)	)	PUNCT
ejpam-3977	5	66	)	)	PUNCT
ejpam-3977	5	67	differ	differ	VERB
ejpam-3977	5	68	in	in	ADP
ejpam-3977	5	69	at	at	ADV
ejpam-3977	5	70	least	least	ADJ
ejpam-3977	5	71	2	2	NUM
ejpam-3977	5	72	positions	position	NOUN
ejpam-3977	5	73	.	.	PUNCT
ejpam-3977	6	1	if	if	SCONJ
ejpam-3977	6	2	g	g	PROPN
ejpam-3977	6	3	has	have	VERB
ejpam-3977	6	4	a	a	DET
ejpam-3977	6	5	2	2	NUM
ejpam-3977	6	6	-	-	PUNCT
ejpam-3977	6	7	resolving	resolve	VERB
ejpam-3977	6	8	set	set	NOUN
ejpam-3977	6	9	,	,	PUNCT
ejpam-3977	6	10	we	we	PRON
ejpam-3977	6	11	denote	denote	VERB
ejpam-3977	6	12	the	the	DET
ejpam-3977	6	13	least	least	ADJ
ejpam-3977	6	14	size	size	NOUN
ejpam-3977	6	15	of	of	ADP
ejpam-3977	6	16	a	a	DET
ejpam-3977	6	17	2	2	NUM
ejpam-3977	6	18	-	-	PUNCT
ejpam-3977	6	19	resolving	resolving	NOUN
ejpam-3977	6	20	set	set	VERB
ejpam-3977	6	21	by	by	ADP
ejpam-3977	6	22	dim2(g	dim2(g	NOUN
ejpam-3977	6	23	)	)	PUNCT
ejpam-3977	6	24	,	,	PUNCT
ejpam-3977	6	25	the	the	DET
ejpam-3977	6	26	2	2	NUM
ejpam-3977	6	27	-	-	PUNCT
ejpam-3977	6	28	metric	metric	ADJ
ejpam-3977	6	29	dimension	dimension	NOUN
ejpam-3977	6	30	of	of	ADP
ejpam-3977	6	31	g.	g.	PROPN
ejpam-3977	6	32	a	a	DET
ejpam-3977	6	33	2	2	NUM
ejpam-3977	6	34	-	-	PUNCT
ejpam-3977	6	35	resolving	resolve	VERB
ejpam-3977	6	36	set	set	NOUN
ejpam-3977	6	37	of	of	ADP
ejpam-3977	6	38	size	size	NOUN
ejpam-3977	6	39	dim2(g	dim2(g	NOUN
ejpam-3977	6	40	)	)	PUNCT
ejpam-3977	6	41	is	be	AUX
ejpam-3977	6	42	called	call	VERB
ejpam-3977	6	43	a	a	DET
ejpam-3977	6	44	2	2	NUM
ejpam-3977	6	45	-	-	PUNCT
ejpam-3977	6	46	metric	metric	ADJ
ejpam-3977	6	47	basis	basis	NOUN
ejpam-3977	6	48	for	for	ADP
ejpam-3977	6	49	g.	g.	PROPN
ejpam-3977	6	50	this	this	DET
ejpam-3977	6	51	study	study	NOUN
ejpam-3977	6	52	deals	deal	VERB
ejpam-3977	6	53	with	with	ADP
ejpam-3977	6	54	the	the	DET
ejpam-3977	6	55	concept	concept	NOUN
ejpam-3977	6	56	of	of	ADP
ejpam-3977	6	57	2	2	NUM
ejpam-3977	6	58	-	-	PUNCT
ejpam-3977	6	59	resolving	resolve	VERB
ejpam-3977	6	60	set	set	NOUN
ejpam-3977	6	61	of	of	ADP
ejpam-3977	6	62	a	a	DET
ejpam-3977	6	63	graph	graph	NOUN
ejpam-3977	6	64	.	.	PUNCT
ejpam-3977	7	1	it	it	PRON
ejpam-3977	7	2	characterizes	characterize	VERB
ejpam-3977	7	3	the	the	DET
ejpam-3977	7	4	2	2	NUM
ejpam-3977	7	5	-	-	PUNCT
ejpam-3977	7	6	resolving	resolving	NOUN
ejpam-3977	7	7	set	set	NOUN
ejpam-3977	7	8	in	in	ADP
ejpam-3977	7	9	the	the	DET
ejpam-3977	7	10	join	join	NOUN
ejpam-3977	7	11	and	and	CCONJ
ejpam-3977	7	12	corona	corona	NOUN
ejpam-3977	7	13	of	of	ADP
ejpam-3977	7	14	graphs	graph	NOUN
ejpam-3977	7	15	and	and	CCONJ
ejpam-3977	7	16	determine	determine	VERB
ejpam-3977	7	17	the	the	DET
ejpam-3977	7	18	exact	exact	ADJ
ejpam-3977	7	19	values	value	NOUN
ejpam-3977	7	20	of	of	ADP
ejpam-3977	7	21	the	the	DET
ejpam-3977	7	22	2	2	NUM
ejpam-3977	7	23	-	-	PUNCT
ejpam-3977	7	24	metric	metric	ADJ
ejpam-3977	7	25	dimension	dimension	NOUN
ejpam-3977	7	26	of	of	ADP
ejpam-3977	7	27	these	these	DET
ejpam-3977	7	28	graphs	graph	NOUN
ejpam-3977	7	29	.	.	PUNCT
ejpam-3977	8	1	2020	2020	NUM
ejpam-3977	8	2	mathematics	mathematic	NOUN
ejpam-3977	8	3	subject	subject	NOUN
ejpam-3977	8	4	classifications	classification	NOUN
ejpam-3977	8	5	:	:	PUNCT
ejpam-3977	8	6	05c69	05c69	X
ejpam-3977	8	7	key	key	ADJ
ejpam-3977	8	8	words	word	NOUN
ejpam-3977	8	9	and	and	CCONJ
ejpam-3977	8	10	phrases	phrase	NOUN
ejpam-3977	8	11	:	:	PUNCT
ejpam-3977	8	12	2	2	NUM
ejpam-3977	8	13	-	-	PUNCT
ejpam-3977	8	14	resolving	resolve	VERB
ejpam-3977	8	15	set	set	NOUN
ejpam-3977	8	16	,	,	PUNCT
ejpam-3977	8	17	2	2	NUM
ejpam-3977	8	18	-	-	PUNCT
ejpam-3977	8	19	metric	metric	ADJ
ejpam-3977	8	20	dimension	dimension	NOUN
ejpam-3977	8	21	,	,	PUNCT
ejpam-3977	8	22	2	2	NUM
ejpam-3977	8	23	-	-	PUNCT
ejpam-3977	8	24	metric	metric	ADJ
ejpam-3977	8	25	basis	basis	NOUN
ejpam-3977	8	26	,	,	PUNCT
ejpam-3977	8	27	corona	corona	PROPN
ejpam-3977	8	28	1	1	NUM
ejpam-3977	8	29	.	.	PUNCT
ejpam-3977	9	1	introduction	introduction	NOUN
ejpam-3977	9	2	the	the	DET
ejpam-3977	9	3	problem	problem	NOUN
ejpam-3977	9	4	of	of	ADP
ejpam-3977	9	5	uniquely	uniquely	ADV
ejpam-3977	9	6	determining	determine	VERB
ejpam-3977	9	7	the	the	DET
ejpam-3977	9	8	location	location	NOUN
ejpam-3977	9	9	of	of	ADP
ejpam-3977	9	10	an	an	DET
ejpam-3977	9	11	intruder	intruder	NOUN
ejpam-3977	9	12	in	in	ADP
ejpam-3977	9	13	a	a	DET
ejpam-3977	9	14	network	network	NOUN
ejpam-3977	9	15	was	be	AUX
ejpam-3977	9	16	the	the	DET
ejpam-3977	9	17	principal	principal	ADJ
ejpam-3977	9	18	motivation	motivation	NOUN
ejpam-3977	9	19	of	of	ADP
ejpam-3977	9	20	introducing	introduce	VERB
ejpam-3977	9	21	the	the	DET
ejpam-3977	9	22	concept	concept	NOUN
ejpam-3977	9	23	of	of	ADP
ejpam-3977	9	24	metric	metric	ADJ
ejpam-3977	9	25	dimension	dimension	NOUN
ejpam-3977	9	26	in	in	ADP
ejpam-3977	9	27	graphs	graph	NOUN
ejpam-3977	9	28	by	by	ADP
ejpam-3977	9	29	slater	slater	NOUN
ejpam-3977	9	30	[	[	X
ejpam-3977	9	31	10	10	NUM
ejpam-3977	9	32	]	]	PUNCT
ejpam-3977	9	33	,	,	PUNCT
ejpam-3977	9	34	where	where	SCONJ
ejpam-3977	9	35	the	the	DET
ejpam-3977	9	36	metric	metric	ADJ
ejpam-3977	9	37	generators	generator	NOUN
ejpam-3977	9	38	were	be	AUX
ejpam-3977	9	39	called	call	VERB
ejpam-3977	9	40	locating	locating	NOUN
ejpam-3977	9	41	sets	set	NOUN
ejpam-3977	9	42	.	.	PUNCT
ejpam-3977	10	1	the	the	DET
ejpam-3977	10	2	concept	concept	NOUN
ejpam-3977	10	3	of	of	ADP
ejpam-3977	10	4	metric	metric	ADJ
ejpam-3977	10	5	dimension	dimension	NOUN
ejpam-3977	10	6	of	of	ADP
ejpam-3977	10	7	a	a	DET
ejpam-3977	10	8	graph	graph	NOUN
ejpam-3977	10	9	was	be	AUX
ejpam-3977	10	10	also	also	ADV
ejpam-3977	10	11	introduced	introduce	VERB
ejpam-3977	10	12	independently	independently	ADV
ejpam-3977	10	13	by	by	ADP
ejpam-3977	10	14	harary	harary	NOUN
ejpam-3977	10	15	and	and	CCONJ
ejpam-3977	10	16	melter	melter	NOUN
ejpam-3977	10	17	in	in	ADP
ejpam-3977	10	18	[	[	X
ejpam-3977	10	19	4	4	X
ejpam-3977	10	20	]	]	PUNCT
ejpam-3977	10	21	where	where	SCONJ
ejpam-3977	10	22	metric	metric	ADJ
ejpam-3977	10	23	generators	generator	NOUN
ejpam-3977	10	24	were	be	AUX
ejpam-3977	10	25	called	call	VERB
ejpam-3977	10	26	resolving	resolve	VERB
ejpam-3977	10	27	sets	set	NOUN
ejpam-3977	10	28	.	.	PUNCT
ejpam-3977	11	1	in	in	ADP
ejpam-3977	11	2	[	[	X
ejpam-3977	11	3	6	6	NUM
ejpam-3977	11	4	]	]	PUNCT
ejpam-3977	11	5	,	,	PUNCT
ejpam-3977	11	6	monsanto	monsanto	PROPN
ejpam-3977	11	7	,	,	PUNCT
ejpam-3977	11	8	acal	acal	ADJ
ejpam-3977	11	9	and	and	CCONJ
ejpam-3977	11	10	rara	rara	NOUN
ejpam-3977	11	11	discussed	discuss	VERB
ejpam-3977	11	12	the	the	DET
ejpam-3977	11	13	strong	strong	ADJ
ejpam-3977	11	14	resolving	resolve	VERB
ejpam-3977	11	15	dominating	dominating	NOUN
ejpam-3977	11	16	sets	set	NOUN
ejpam-3977	11	17	in	in	ADP
ejpam-3977	11	18	the	the	DET
ejpam-3977	11	19	join	join	NOUN
ejpam-3977	11	20	and	and	CCONJ
ejpam-3977	11	21	corona	corona	NOUN
ejpam-3977	11	22	of	of	ADP
ejpam-3977	11	23	graphs	graph	NOUN
ejpam-3977	11	24	while	while	SCONJ
ejpam-3977	11	25	in	in	ADP
ejpam-3977	11	26	[	[	PUNCT
ejpam-3977	11	27	5	5	NUM
ejpam-3977	11	28	]	]	PUNCT
ejpam-3977	11	29	,	,	PUNCT
ejpam-3977	11	30	monsanto	monsanto	PROPN
ejpam-3977	11	31	and	and	CCONJ
ejpam-3977	11	32	rara	rara	NOUN
ejpam-3977	11	33	discussed	discuss	VERB
ejpam-3977	11	34	the	the	DET
ejpam-3977	11	35	resolving	resolve	VERB
ejpam-3977	11	36	restrained	restrained	ADJ
ejpam-3977	11	37	domination	domination	NOUN
ejpam-3977	11	38	in	in	ADP
ejpam-3977	11	39	graphs	graph	NOUN
ejpam-3977	11	40	.	.	PUNCT
ejpam-3977	12	1	bailey	bailey	NOUN
ejpam-3977	12	2	and	and	CCONJ
ejpam-3977	12	3	yero	yero	NOUN
ejpam-3977	12	4	in	in	ADP
ejpam-3977	12	5	[	[	X
ejpam-3977	12	6	1	1	NUM
ejpam-3977	12	7	]	]	PUNCT
ejpam-3977	12	8	demonstrated	demonstrate	VERB
ejpam-3977	12	9	a	a	DET
ejpam-3977	12	10	construction	construction	NOUN
ejpam-3977	12	11	of	of	ADP
ejpam-3977	12	12	error	error	NOUN
ejpam-3977	12	13	-	-	PUNCT
ejpam-3977	12	14	correcting	correct	VERB
ejpam-3977	12	15	codes	code	NOUN
ejpam-3977	12	16	from	from	ADP
ejpam-3977	12	17	graphs	graph	NOUN
ejpam-3977	12	18	by	by	ADP
ejpam-3977	12	19	means	mean	NOUN
ejpam-3977	12	20	of	of	ADP
ejpam-3977	12	21	k	k	ADJ
ejpam-3977	12	22	-	-	PUNCT
ejpam-3977	12	23	resolving	resolving	ADJ
ejpam-3977	12	24	sets	set	NOUN
ejpam-3977	12	25	,	,	PUNCT
ejpam-3977	12	26	and	and	CCONJ
ejpam-3977	12	27	present	present	VERB
ejpam-3977	12	28	a	a	DET
ejpam-3977	12	29	decoding	decode	VERB
ejpam-3977	12	30	algorithm	algorithm	NOUN
ejpam-3977	12	31	which	which	PRON
ejpam-3977	12	32	makes	make	VERB
ejpam-3977	12	33	use	use	NOUN
ejpam-3977	12	34	of	of	ADP
ejpam-3977	12	35	covering	cover	VERB
ejpam-3977	12	36	designs	design	NOUN
ejpam-3977	12	37	.	.	PUNCT
ejpam-3977	13	1	the	the	DET
ejpam-3977	13	2	distance	distance	NOUN
ejpam-3977	13	3	between	between	ADP
ejpam-3977	13	4	two	two	NUM
ejpam-3977	13	5	vertices	vertex	NOUN
ejpam-3977	13	6	u	u	NOUN
ejpam-3977	13	7	and	and	CCONJ
ejpam-3977	13	8	v	v	NOUN
ejpam-3977	13	9	of	of	ADP
ejpam-3977	13	10	a	a	DET
ejpam-3977	13	11	graph	graph	NOUN
ejpam-3977	13	12	is	be	AUX
ejpam-3977	13	13	the	the	DET
ejpam-3977	13	14	length	length	NOUN
ejpam-3977	13	15	of	of	ADP
ejpam-3977	13	16	a	a	DET
ejpam-3977	13	17	shortest	short	ADJ
ejpam-3977	13	18	path	path	NOUN
ejpam-3977	13	19	†the	†the	DET
ejpam-3977	13	20	authors	author	NOUN
ejpam-3977	13	21	would	would	AUX
ejpam-3977	13	22	like	like	VERB
ejpam-3977	13	23	to	to	PART
ejpam-3977	13	24	thank	thank	VERB
ejpam-3977	13	25	the	the	DET
ejpam-3977	13	26	commission	commission	NOUN
ejpam-3977	13	27	on	on	ADP
ejpam-3977	13	28	higher	high	ADJ
ejpam-3977	13	29	education	education	NOUN
ejpam-3977	13	30	(	(	PUNCT
ejpam-3977	13	31	ched	che	VERB
ejpam-3977	13	32	)	)	PUNCT
ejpam-3977	13	33	and	and	CCONJ
ejpam-3977	13	34	mindanao	mindanao	PROPN
ejpam-3977	13	35	state	state	PROPN
ejpam-3977	13	36	university	university	PROPN
ejpam-3977	13	37	-	-	PUNCT
ejpam-3977	13	38	marawi	marawi	PROPN
ejpam-3977	13	39	and	and	CCONJ
ejpam-3977	13	40	msu	msu	PROPN
ejpam-3977	13	41	-	-	PUNCT
ejpam-3977	13	42	iligan	iligan	PROPN
ejpam-3977	13	43	institute	institute	PROPN
ejpam-3977	13	44	of	of	ADP
ejpam-3977	13	45	technology	technology	PROPN
ejpam-3977	13	46	,	,	PUNCT
ejpam-3977	13	47	philippines	philippine	NOUN
ejpam-3977	13	48	.	.	PUNCT
ejpam-3977	14	1	doi	doi	NOUN
ejpam-3977	14	2	:	:	PUNCT
ejpam-3977	14	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3977	https://doi.org/10.29020/nybg.ejpam.v14i3.3977	ADJ
ejpam-3977	14	4	email	email	NOUN
ejpam-3977	14	5	addresses	address	VERB
ejpam-3977	14	6	:	:	PUNCT
ejpam-3977	14	7	amerjean1228@gmail.com	amerjean1228@gmail.com	X
ejpam-3977	14	8	(	(	PUNCT
ejpam-3977	14	9	j.	j.	PROPN
ejpam-3977	14	10	cabaro	cabaro	PROPN
ejpam-3977	14	11	)	)	PUNCT
ejpam-3977	14	12	,	,	PUNCT
ejpam-3977	14	13	helenrara@gmail.com	helenrara@gmail.com	X
ejpam-3977	14	14	(	(	PUNCT
ejpam-3977	14	15	h.	h.	PROPN
ejpam-3977	14	16	rara	rara	PROPN
ejpam-3977	14	17	)	)	PUNCT
ejpam-3977	14	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3977	15	1	773	773	NUM
ejpam-3977	16	1	©	©	NOUN
ejpam-3977	16	2	2021	2021	NUM
ejpam-3977	16	3	ejpam	ejpam	VERB
ejpam-3977	16	4	all	all	DET
ejpam-3977	16	5	rights	right	NOUN
ejpam-3977	16	6	reserved	reserve	VERB
ejpam-3977	16	7	.	.	PUNCT
ejpam-3977	17	1	j.	j.	PROPN
ejpam-3977	17	2	cabaro	cabaro	PROPN
ejpam-3977	17	3	,	,	PUNCT
ejpam-3977	17	4	h.	h.	PROPN
ejpam-3977	17	5	rara	rara	PROPN
ejpam-3977	17	6	/	/	SYM
ejpam-3977	17	7	eur	eur	PROPN
ejpam-3977	17	8	.	.	PUNCT
ejpam-3977	18	1	j.	j.	PROPN
ejpam-3977	18	2	pure	pure	PROPN
ejpam-3977	18	3	appl	appl	PROPN
ejpam-3977	18	4	.	.	PROPN
ejpam-3977	18	5	math	math	PROPN
ejpam-3977	18	6	,	,	PUNCT
ejpam-3977	18	7	14	14	NUM
ejpam-3977	18	8	(	(	PUNCT
ejpam-3977	18	9	3	3	NUM
ejpam-3977	18	10	)	)	PUNCT
ejpam-3977	18	11	(	(	PUNCT
ejpam-3977	18	12	2021	2021	NUM
ejpam-3977	18	13	)	)	PUNCT
ejpam-3977	18	14	,	,	PUNCT
ejpam-3977	18	15	773	773	NUM
ejpam-3977	18	16	-	-	SYM
ejpam-3977	18	17	782	782	NUM
ejpam-3977	18	18	774	774	NUM
ejpam-3977	18	19	between	between	ADP
ejpam-3977	18	20	u	u	NOUN
ejpam-3977	18	21	and	and	CCONJ
ejpam-3977	18	22	v	v	NOUN
ejpam-3977	18	23	,	,	PUNCT
ejpam-3977	18	24	and	and	CCONJ
ejpam-3977	18	25	we	we	PRON
ejpam-3977	18	26	denote	denote	VERB
ejpam-3977	18	27	this	this	PRON
ejpam-3977	18	28	by	by	ADP
ejpam-3977	18	29	dg(u	dg(u	NOUN
ejpam-3977	18	30	,	,	PUNCT
ejpam-3977	18	31	v	v	NOUN
ejpam-3977	18	32	)	)	PUNCT
ejpam-3977	18	33	.	.	PUNCT
ejpam-3977	19	1	in	in	ADP
ejpam-3977	19	2	recent	recent	ADJ
ejpam-3977	19	3	years	year	NOUN
ejpam-3977	19	4	,	,	PUNCT
ejpam-3977	19	5	much	much	ADJ
ejpam-3977	19	6	attention	attention	NOUN
ejpam-3977	19	7	has	have	AUX
ejpam-3977	19	8	been	be	AUX
ejpam-3977	19	9	paid	pay	VERB
ejpam-3977	19	10	to	to	ADP
ejpam-3977	19	11	the	the	DET
ejpam-3977	19	12	metric	metric	ADJ
ejpam-3977	19	13	dimension	dimension	NOUN
ejpam-3977	19	14	of	of	ADP
ejpam-3977	19	15	graphs	graph	NOUN
ejpam-3977	19	16	:	:	PUNCT
ejpam-3977	19	17	this	this	PRON
ejpam-3977	19	18	is	be	AUX
ejpam-3977	19	19	the	the	DET
ejpam-3977	19	20	smallest	small	ADJ
ejpam-3977	19	21	size	size	NOUN
ejpam-3977	19	22	of	of	ADP
ejpam-3977	19	23	a	a	DET
ejpam-3977	19	24	subset	subset	NOUN
ejpam-3977	19	25	of	of	ADP
ejpam-3977	19	26	vertices	vertex	NOUN
ejpam-3977	19	27	(	(	PUNCT
ejpam-3977	19	28	called	call	VERB
ejpam-3977	19	29	a	a	DET
ejpam-3977	19	30	resolving	resolving	NOUN
ejpam-3977	19	31	set	set	NOUN
ejpam-3977	19	32	)	)	PUNCT
ejpam-3977	19	33	with	with	ADP
ejpam-3977	19	34	the	the	DET
ejpam-3977	19	35	property	property	NOUN
ejpam-3977	19	36	that	that	PRON
ejpam-3977	19	37	the	the	DET
ejpam-3977	19	38	list	list	NOUN
ejpam-3977	19	39	of	of	ADP
ejpam-3977	19	40	distances	distance	NOUN
ejpam-3977	19	41	from	from	ADP
ejpam-3977	19	42	any	any	DET
ejpam-3977	19	43	vertex	vertex	NOUN
ejpam-3977	19	44	to	to	ADP
ejpam-3977	19	45	those	those	PRON
ejpam-3977	19	46	in	in	ADP
ejpam-3977	19	47	the	the	DET
ejpam-3977	19	48	set	set	NOUN
ejpam-3977	19	49	uniquely	uniquely	ADV
ejpam-3977	19	50	identifies	identify	VERB
ejpam-3977	19	51	that	that	SCONJ
ejpam-3977	19	52	vertex	vertex	NOUN
ejpam-3977	19	53	and	and	CCONJ
ejpam-3977	19	54	is	be	AUX
ejpam-3977	19	55	denoted	denote	VERB
ejpam-3977	19	56	by	by	ADP
ejpam-3977	19	57	dim(g	dim(g	PROPN
ejpam-3977	19	58	)	)	PUNCT
ejpam-3977	19	59	.	.	PUNCT
ejpam-3977	20	1	according	accord	VERB
ejpam-3977	20	2	to	to	ADP
ejpam-3977	20	3	the	the	DET
ejpam-3977	20	4	paper	paper	NOUN
ejpam-3977	20	5	of	of	ADP
ejpam-3977	20	6	saenpholphat	saenpholphat	PROPN
ejpam-3977	20	7	et	et	PROPN
ejpam-3977	20	8	al	al	PROPN
ejpam-3977	20	9	.	.	PUNCT
ejpam-3977	21	1	[	[	X
ejpam-3977	21	2	9	9	NUM
ejpam-3977	21	3	]	]	PUNCT
ejpam-3977	21	4	,	,	PUNCT
ejpam-3977	21	5	for	for	ADP
ejpam-3977	21	6	an	an	DET
ejpam-3977	21	7	ordered	order	VERB
ejpam-3977	21	8	set	set	NOUN
ejpam-3977	21	9	of	of	ADP
ejpam-3977	21	10	vertices	vertex	NOUN
ejpam-3977	21	11	w	w	NOUN
ejpam-3977	21	12	=	=	SYM
ejpam-3977	21	13	{	{	PUNCT
ejpam-3977	21	14	w1	w1	NOUN
ejpam-3977	21	15	,	,	PUNCT
ejpam-3977	21	16	w2	w2	NOUN
ejpam-3977	21	17	,	,	PUNCT
ejpam-3977	21	18	...	...	PUNCT
ejpam-3977	21	19	,	,	PUNCT
ejpam-3977	21	20	wk	wk	ADP
ejpam-3977	21	21	}	}	PUNCT
ejpam-3977	21	22	⊆	⊆	NUM
ejpam-3977	21	23	v	v	NOUN
ejpam-3977	21	24	(	(	PUNCT
ejpam-3977	21	25	g	g	NOUN
ejpam-3977	21	26	)	)	PUNCT
ejpam-3977	21	27	and	and	CCONJ
ejpam-3977	21	28	a	a	DET
ejpam-3977	21	29	vertex	vertex	NOUN
ejpam-3977	21	30	v	v	NOUN
ejpam-3977	21	31	in	in	ADP
ejpam-3977	21	32	g	g	PROPN
ejpam-3977	21	33	,	,	PUNCT
ejpam-3977	21	34	the	the	DET
ejpam-3977	21	35	k	k	NOUN
ejpam-3977	21	36	-	-	NOUN
ejpam-3977	21	37	vector	vector	NOUN
ejpam-3977	21	38	(	(	PUNCT
ejpam-3977	21	39	ordered	order	VERB
ejpam-3977	21	40	k	k	NOUN
ejpam-3977	21	41	-	-	PUNCT
ejpam-3977	21	42	tuple	tuple	ADJ
ejpam-3977	21	43	)	)	PUNCT
ejpam-3977	21	44	r(v	r(v	PROPN
ejpam-3977	21	45	/	/	SYM
ejpam-3977	21	46	w	w	NOUN
ejpam-3977	21	47	)	)	PUNCT
ejpam-3977	22	1	=	=	SYM
ejpam-3977	22	2	(	(	PUNCT
ejpam-3977	22	3	dg(v	dg(v	X
ejpam-3977	22	4	,	,	PUNCT
ejpam-3977	22	5	w1	w1	NOUN
ejpam-3977	22	6	)	)	PUNCT
ejpam-3977	22	7	,	,	PUNCT
ejpam-3977	22	8	dg(v	dg(v	X
ejpam-3977	22	9	,	,	PUNCT
ejpam-3977	22	10	w2	w2	NOUN
ejpam-3977	22	11	)	)	PUNCT
ejpam-3977	22	12	,	,	PUNCT
ejpam-3977	22	13	...	...	PUNCT
ejpam-3977	22	14	,	,	PUNCT
ejpam-3977	22	15	dg(v	dg(v	X
ejpam-3977	22	16	,	,	PUNCT
ejpam-3977	22	17	wk	wk	NOUN
ejpam-3977	22	18	)	)	PUNCT
ejpam-3977	22	19	)	)	PUNCT
ejpam-3977	22	20	is	be	AUX
ejpam-3977	22	21	referred	refer	VERB
ejpam-3977	22	22	to	to	ADP
ejpam-3977	22	23	as	as	ADP
ejpam-3977	22	24	the	the	DET
ejpam-3977	22	25	(	(	PUNCT
ejpam-3977	22	26	metric	metric	ADJ
ejpam-3977	22	27	)	)	PUNCT
ejpam-3977	22	28	representation	representation	NOUN
ejpam-3977	22	29	of	of	ADP
ejpam-3977	22	30	v	v	NOUN
ejpam-3977	22	31	with	with	ADP
ejpam-3977	22	32	respect	respect	NOUN
ejpam-3977	22	33	to	to	ADP
ejpam-3977	22	34	w	w	PROPN
ejpam-3977	22	35	.	.	PUNCT
ejpam-3977	23	1	the	the	DET
ejpam-3977	23	2	set	set	NOUN
ejpam-3977	23	3	w	w	NOUN
ejpam-3977	23	4	is	be	AUX
ejpam-3977	23	5	called	call	VERB
ejpam-3977	23	6	a	a	DET
ejpam-3977	23	7	resolving	resolving	NOUN
ejpam-3977	23	8	set	set	VERB
ejpam-3977	23	9	for	for	ADP
ejpam-3977	23	10	g	g	PROPN
ejpam-3977	23	11	if	if	SCONJ
ejpam-3977	23	12	distinct	distinct	ADJ
ejpam-3977	23	13	vertices	vertex	NOUN
ejpam-3977	23	14	have	have	VERB
ejpam-3977	23	15	distinct	distinct	ADJ
ejpam-3977	23	16	representation	representation	NOUN
ejpam-3977	23	17	with	with	ADP
ejpam-3977	23	18	respect	respect	NOUN
ejpam-3977	23	19	to	to	ADP
ejpam-3977	23	20	w	w	PROPN
ejpam-3977	23	21	.	.	PUNCT
ejpam-3977	24	1	hence	hence	ADV
ejpam-3977	24	2	,	,	PUNCT
ejpam-3977	24	3	if	if	SCONJ
ejpam-3977	24	4	w	w	NOUN
ejpam-3977	24	5	is	be	AUX
ejpam-3977	24	6	a	a	DET
ejpam-3977	24	7	resolving	resolving	NOUN
ejpam-3977	24	8	set	set	NOUN
ejpam-3977	24	9	of	of	ADP
ejpam-3977	24	10	cardinality	cardinality	PROPN
ejpam-3977	24	11	k	k	PROPN
ejpam-3977	24	12	for	for	ADP
ejpam-3977	24	13	a	a	DET
ejpam-3977	24	14	graph	graph	NOUN
ejpam-3977	24	15	g	g	NOUN
ejpam-3977	24	16	of	of	ADP
ejpam-3977	24	17	order	order	NOUN
ejpam-3977	24	18	n	n	CCONJ
ejpam-3977	24	19	,	,	PUNCT
ejpam-3977	24	20	then	then	ADV
ejpam-3977	24	21	the	the	DET
ejpam-3977	24	22	set	set	NOUN
ejpam-3977	24	23	{	{	PUNCT
ejpam-3977	24	24	r(v	r(v	PROPN
ejpam-3977	24	25	/	/	SYM
ejpam-3977	24	26	w	w	PROPN
ejpam-3977	24	27	)	)	PUNCT
ejpam-3977	24	28	:	:	PUNCT
ejpam-3977	24	29	v	v	X
ejpam-3977	24	30	∈	∈	PROPN
ejpam-3977	24	31	v	v	NOUN
ejpam-3977	24	32	(	(	PUNCT
ejpam-3977	24	33	g	g	NOUN
ejpam-3977	24	34	)	)	PUNCT
ejpam-3977	24	35	}	}	PUNCT
ejpam-3977	24	36	consists	consist	VERB
ejpam-3977	24	37	of	of	ADP
ejpam-3977	24	38	n	n	PRON
ejpam-3977	24	39	distinct	distinct	ADJ
ejpam-3977	24	40	k	k	NOUN
ejpam-3977	24	41	-	-	NOUN
ejpam-3977	24	42	vectors	vector	NOUN
ejpam-3977	24	43	.	.	PUNCT
ejpam-3977	25	1	a	a	DET
ejpam-3977	25	2	resolving	resolving	NOUN
ejpam-3977	25	3	set	set	NOUN
ejpam-3977	25	4	of	of	ADP
ejpam-3977	25	5	minimum	minimum	ADJ
ejpam-3977	25	6	cardinality	cardinality	NOUN
ejpam-3977	25	7	is	be	AUX
ejpam-3977	25	8	called	call	VERB
ejpam-3977	25	9	a	a	DET
ejpam-3977	25	10	minimum	minimum	ADJ
ejpam-3977	25	11	resolving	resolving	NOUN
ejpam-3977	25	12	set	set	VERB
ejpam-3977	25	13	or	or	CCONJ
ejpam-3977	25	14	a	a	DET
ejpam-3977	25	15	basis	basis	NOUN
ejpam-3977	25	16	,	,	PUNCT
ejpam-3977	25	17	and	and	CCONJ
ejpam-3977	25	18	the	the	DET
ejpam-3977	25	19	cardinality	cardinality	NOUN
ejpam-3977	25	20	of	of	ADP
ejpam-3977	25	21	a	a	DET
ejpam-3977	25	22	basis	basis	NOUN
ejpam-3977	25	23	for	for	ADP
ejpam-3977	25	24	g	g	PROPN
ejpam-3977	25	25	is	be	AUX
ejpam-3977	25	26	the	the	DET
ejpam-3977	25	27	dimension	dimension	NOUN
ejpam-3977	25	28	dim(g	dim(g	PROPN
ejpam-3977	25	29	)	)	PUNCT
ejpam-3977	25	30	of	of	ADP
ejpam-3977	25	31	g.	g.	PROPN
ejpam-3977	25	32	in	in	ADP
ejpam-3977	25	33	the	the	DET
ejpam-3977	25	34	paper	paper	NOUN
ejpam-3977	25	35	of	of	ADP
ejpam-3977	25	36	bailey	bailey	PROPN
ejpam-3977	25	37	et	et	PROPN
ejpam-3977	25	38	al.[1	al.[1	PROPN
ejpam-3977	25	39	]	]	PUNCT
ejpam-3977	25	40	,	,	PUNCT
ejpam-3977	25	41	an	an	DET
ejpam-3977	25	42	ordered	order	VERB
ejpam-3977	25	43	set	set	NOUN
ejpam-3977	25	44	of	of	ADP
ejpam-3977	25	45	vertices	vertex	NOUN
ejpam-3977	25	46	w	w	NOUN
ejpam-3977	25	47	=	=	SYM
ejpam-3977	25	48	{	{	PUNCT
ejpam-3977	25	49	w1	w1	NOUN
ejpam-3977	25	50	,	,	PUNCT
ejpam-3977	25	51	...	...	PUNCT
ejpam-3977	25	52	,	,	PUNCT
ejpam-3977	25	53	wl	wl	PROPN
ejpam-3977	25	54	}	}	PUNCT
ejpam-3977	25	55	is	be	AUX
ejpam-3977	25	56	a	a	DET
ejpam-3977	25	57	kresolving	kresolving	NOUN
ejpam-3977	25	58	set	set	VERB
ejpam-3977	25	59	for	for	ADP
ejpam-3977	25	60	g	g	PROPN
ejpam-3977	25	61	if	if	SCONJ
ejpam-3977	25	62	,	,	PUNCT
ejpam-3977	25	63	for	for	ADP
ejpam-3977	25	64	any	any	DET
ejpam-3977	25	65	distinct	distinct	ADJ
ejpam-3977	25	66	vertices	vertex	NOUN
ejpam-3977	25	67	u	u	NOUN
ejpam-3977	25	68	,	,	PUNCT
ejpam-3977	25	69	v	v	NOUN
ejpam-3977	25	70	∈	∈	PROPN
ejpam-3977	25	71	v	v	NOUN
ejpam-3977	25	72	(	(	PUNCT
ejpam-3977	25	73	g	g	NOUN
ejpam-3977	25	74	)	)	PUNCT
ejpam-3977	25	75	,	,	PUNCT
ejpam-3977	25	76	the	the	DET
ejpam-3977	25	77	(	(	PUNCT
ejpam-3977	25	78	metric	metric	NOUN
ejpam-3977	25	79	)	)	PUNCT
ejpam-3977	25	80	representations	representation	VERB
ejpam-3977	25	81	r(u	r(u	PROPN
ejpam-3977	25	82	/	/	SYM
ejpam-3977	25	83	w	w	PROPN
ejpam-3977	25	84	)	)	PUNCT
ejpam-3977	25	85	and	and	CCONJ
ejpam-3977	25	86	r(v	r(v	PROPN
ejpam-3977	25	87	/	/	SYM
ejpam-3977	25	88	w	w	PROPN
ejpam-3977	25	89	)	)	PUNCT
ejpam-3977	25	90	of	of	ADP
ejpam-3977	25	91	u	u	NOUN
ejpam-3977	25	92	and	and	CCONJ
ejpam-3977	25	93	v	v	NOUN
ejpam-3977	25	94	,	,	PUNCT
ejpam-3977	25	95	respectively	respectively	ADV
ejpam-3977	25	96	differ	differ	VERB
ejpam-3977	25	97	in	in	ADP
ejpam-3977	25	98	at	at	ADP
ejpam-3977	25	99	least	least	ADJ
ejpam-3977	25	100	k	k	NOUN
ejpam-3977	25	101	positions	position	NOUN
ejpam-3977	25	102	.	.	PUNCT
ejpam-3977	26	1	if	if	SCONJ
ejpam-3977	26	2	k	k	PROPN
ejpam-3977	26	3	=	=	SYM
ejpam-3977	26	4	1	1	NUM
ejpam-3977	26	5	,	,	PUNCT
ejpam-3977	26	6	then	then	ADV
ejpam-3977	26	7	the	the	DET
ejpam-3977	26	8	k	k	NOUN
ejpam-3977	26	9	-	-	PUNCT
ejpam-3977	26	10	resolving	resolving	ADJ
ejpam-3977	26	11	set	set	NOUN
ejpam-3977	26	12	is	be	AUX
ejpam-3977	26	13	called	call	VERB
ejpam-3977	26	14	a	a	DET
ejpam-3977	26	15	resolving	resolving	NOUN
ejpam-3977	26	16	set	set	VERB
ejpam-3977	26	17	for	for	ADP
ejpam-3977	26	18	g.	g.	PROPN
ejpam-3977	26	19	if	if	SCONJ
ejpam-3977	26	20	g	g	PROPN
ejpam-3977	26	21	has	have	VERB
ejpam-3977	26	22	a	a	DET
ejpam-3977	26	23	k	k	ADJ
ejpam-3977	26	24	-	-	ADJ
ejpam-3977	26	25	resolving	resolving	ADJ
ejpam-3977	26	26	set	set	NOUN
ejpam-3977	26	27	,	,	PUNCT
ejpam-3977	26	28	the	the	DET
ejpam-3977	26	29	minimum	minimum	ADJ
ejpam-3977	26	30	cardinality	cardinality	PROPN
ejpam-3977	26	31	dimk(g	dimk(g	PROPN
ejpam-3977	26	32	)	)	PUNCT
ejpam-3977	26	33	is	be	AUX
ejpam-3977	26	34	called	call	VERB
ejpam-3977	26	35	the	the	DET
ejpam-3977	26	36	k	k	ADJ
ejpam-3977	26	37	-	-	ADJ
ejpam-3977	26	38	metric	metric	ADJ
ejpam-3977	26	39	dimension	dimension	NOUN
ejpam-3977	26	40	of	of	ADP
ejpam-3977	26	41	g.	g.	PROPN
ejpam-3977	26	42	in	in	ADP
ejpam-3977	26	43	this	this	DET
ejpam-3977	26	44	paper	paper	NOUN
ejpam-3977	26	45	,	,	PUNCT
ejpam-3977	26	46	the	the	DET
ejpam-3977	26	47	concept	concept	NOUN
ejpam-3977	26	48	of	of	ADP
ejpam-3977	26	49	2	2	NUM
ejpam-3977	26	50	-	-	PUNCT
ejpam-3977	26	51	resolving	resolving	NOUN
ejpam-3977	26	52	set	set	NOUN
ejpam-3977	26	53	in	in	ADP
ejpam-3977	26	54	the	the	DET
ejpam-3977	26	55	join	join	NOUN
ejpam-3977	26	56	and	and	CCONJ
ejpam-3977	26	57	corona	corona	NOUN
ejpam-3977	26	58	of	of	ADP
ejpam-3977	26	59	graphs	graph	NOUN
ejpam-3977	26	60	is	be	AUX
ejpam-3977	26	61	discussed	discuss	VERB
ejpam-3977	26	62	.	.	PUNCT
ejpam-3977	27	1	2	2	X
ejpam-3977	27	2	.	.	X
ejpam-3977	27	3	preliminary	preliminary	ADJ
ejpam-3977	27	4	results	result	NOUN
ejpam-3977	27	5	in	in	ADP
ejpam-3977	27	6	this	this	DET
ejpam-3977	27	7	study	study	NOUN
ejpam-3977	27	8	,	,	PUNCT
ejpam-3977	27	9	we	we	PRON
ejpam-3977	27	10	consider	consider	VERB
ejpam-3977	27	11	finite	finite	NOUN
ejpam-3977	27	12	,	,	PUNCT
ejpam-3977	27	13	simple	simple	ADJ
ejpam-3977	27	14	and	and	CCONJ
ejpam-3977	27	15	connected	connected	ADJ
ejpam-3977	27	16	undirected	undirected	ADJ
ejpam-3977	27	17	graphs	graph	NOUN
ejpam-3977	27	18	.	.	PUNCT
ejpam-3977	28	1	for	for	ADP
ejpam-3977	28	2	basic	basic	ADJ
ejpam-3977	28	3	graph	graph	NOUN
ejpam-3977	28	4	-	-	PUNCT
ejpam-3977	28	5	theoretic	theoretic	NOUN
ejpam-3977	28	6	concepts	concept	NOUN
ejpam-3977	28	7	,	,	PUNCT
ejpam-3977	28	8	we	we	PRON
ejpam-3977	28	9	refer	refer	VERB
ejpam-3977	28	10	readers	reader	NOUN
ejpam-3977	28	11	to	to	ADP
ejpam-3977	28	12	[	[	X
ejpam-3977	28	13	3	3	NUM
ejpam-3977	28	14	]	]	PUNCT
ejpam-3977	28	15	.	.	PUNCT
ejpam-3977	29	1	remark	remark	PROPN
ejpam-3977	29	2	1	1	NUM
ejpam-3977	29	3	.	.	PUNCT
ejpam-3977	30	1	let	let	VERB
ejpam-3977	30	2	g	g	NOUN
ejpam-3977	30	3	be	be	AUX
ejpam-3977	30	4	any	any	DET
ejpam-3977	30	5	connected	connected	ADJ
ejpam-3977	30	6	graph	graph	NOUN
ejpam-3977	30	7	of	of	ADP
ejpam-3977	30	8	order	order	NOUN
ejpam-3977	30	9	n	n	PRON
ejpam-3977	30	10	≥	≥	NOUN
ejpam-3977	30	11	2	2	NUM
ejpam-3977	30	12	.	.	PUNCT
ejpam-3977	31	1	then	then	ADV
ejpam-3977	31	2	the	the	DET
ejpam-3977	31	3	vertex	vertex	NOUN
ejpam-3977	31	4	set	set	NOUN
ejpam-3977	31	5	of	of	ADP
ejpam-3977	31	6	g	g	PROPN
ejpam-3977	31	7	is	be	AUX
ejpam-3977	31	8	a	a	DET
ejpam-3977	31	9	2	2	NUM
ejpam-3977	31	10	-	-	PUNCT
ejpam-3977	31	11	resolving	resolving	NOUN
ejpam-3977	31	12	set	set	VERB
ejpam-3977	31	13	in	in	ADP
ejpam-3977	31	14	g.	g.	PROPN
ejpam-3977	31	15	hence	hence	ADV
ejpam-3977	31	16	,	,	PUNCT
ejpam-3977	31	17	2	2	NUM
ejpam-3977	31	18	≤	≤	NUM
ejpam-3977	31	19	dim2(g	dim2(g	NOUN
ejpam-3977	31	20	)	)	PUNCT
ejpam-3977	31	21	≤	≤	NOUN
ejpam-3977	31	22	n.	n.	NOUN
ejpam-3977	31	23	proposition	proposition	NOUN
ejpam-3977	31	24	1.[7	1.[7	NUM
ejpam-3977	31	25	]	]	PUNCT
ejpam-3977	31	26	dim2(g	dim2(g	NOUN
ejpam-3977	31	27	)	)	PUNCT
ejpam-3977	31	28	=	=	SYM
ejpam-3977	31	29	2	2	NUM
ejpam-3977	31	30	if	if	SCONJ
ejpam-3977	31	31	and	and	CCONJ
ejpam-3977	31	32	only	only	ADV
ejpam-3977	31	33	if	if	SCONJ
ejpam-3977	31	34	g	g	PROPN
ejpam-3977	31	35	∼=	∼=	PROPN
ejpam-3977	31	36	pn	pn	NOUN
ejpam-3977	31	37	,	,	PUNCT
ejpam-3977	31	38	n	n	PRON
ejpam-3977	31	39	≥	≥	NOUN
ejpam-3977	31	40	2	2	NUM
ejpam-3977	31	41	.	.	PUNCT
ejpam-3977	31	42	proposition	proposition	NOUN
ejpam-3977	31	43	2	2	NUM
ejpam-3977	31	44	.	.	X
ejpam-3977	32	1	for	for	ADP
ejpam-3977	32	2	any	any	DET
ejpam-3977	32	3	complete	complete	ADJ
ejpam-3977	32	4	graph	graph	NOUN
ejpam-3977	32	5	kn	kn	NOUN
ejpam-3977	32	6	of	of	ADP
ejpam-3977	32	7	order	order	NOUN
ejpam-3977	32	8	n	n	PRON
ejpam-3977	32	9	≥	≥	NOUN
ejpam-3977	32	10	2	2	NUM
ejpam-3977	32	11	,	,	PUNCT
ejpam-3977	32	12	dim2(kn	dim2(kn	PROPN
ejpam-3977	32	13	)	)	PUNCT
ejpam-3977	32	14	=	=	SYM
ejpam-3977	32	15	n.	n.	NOUN
ejpam-3977	32	16	theorem	theorem	VERB
ejpam-3977	32	17	1	1	NUM
ejpam-3977	32	18	.	.	PUNCT
ejpam-3977	33	1	every	every	DET
ejpam-3977	33	2	2	2	NUM
ejpam-3977	33	3	-	-	PUNCT
ejpam-3977	33	4	resolving	resolving	NOUN
ejpam-3977	33	5	set	set	NOUN
ejpam-3977	33	6	in	in	ADP
ejpam-3977	33	7	a	a	DET
ejpam-3977	33	8	connected	connected	ADJ
ejpam-3977	33	9	graph	graph	NOUN
ejpam-3977	33	10	g	g	PROPN
ejpam-3977	33	11	is	be	AUX
ejpam-3977	33	12	a	a	DET
ejpam-3977	33	13	resolving	resolving	NOUN
ejpam-3977	33	14	set	set	VERB
ejpam-3977	33	15	in	in	ADP
ejpam-3977	33	16	g.	g.	PROPN
ejpam-3977	33	17	hence	hence	ADV
ejpam-3977	33	18	,	,	PUNCT
ejpam-3977	33	19	dim(g	dim(g	PROPN
ejpam-3977	33	20	)	)	PUNCT
ejpam-3977	33	21	≤	≤	NOUN
ejpam-3977	33	22	dim2(g	dim2(g	NOUN
ejpam-3977	33	23	)	)	PUNCT
ejpam-3977	33	24	.	.	PUNCT
ejpam-3977	34	1	remark	remark	PROPN
ejpam-3977	34	2	2	2	NUM
ejpam-3977	34	3	.	.	PUNCT
ejpam-3977	34	4	a	a	DET
ejpam-3977	34	5	superset	superset	NOUN
ejpam-3977	34	6	of	of	ADP
ejpam-3977	34	7	a	a	DET
ejpam-3977	34	8	2	2	NUM
ejpam-3977	34	9	-	-	PUNCT
ejpam-3977	34	10	resolving	resolve	VERB
ejpam-3977	34	11	set	set	NOUN
ejpam-3977	34	12	is	be	AUX
ejpam-3977	34	13	a	a	DET
ejpam-3977	34	14	2	2	NUM
ejpam-3977	34	15	-	-	PUNCT
ejpam-3977	34	16	resolving	resolve	VERB
ejpam-3977	34	17	set	set	NOUN
ejpam-3977	34	18	.	.	PUNCT
ejpam-3977	35	1	remark	remark	PROPN
ejpam-3977	35	2	3	3	NUM
ejpam-3977	35	3	.	.	PUNCT
ejpam-3977	36	1	let	let	VERB
ejpam-3977	36	2	s	s	PRON
ejpam-3977	36	3	⊆	⊆	NUM
ejpam-3977	36	4	v	v	NOUN
ejpam-3977	36	5	(	(	PUNCT
ejpam-3977	36	6	g	g	NOUN
ejpam-3977	36	7	)	)	PUNCT
ejpam-3977	36	8	.	.	PUNCT
ejpam-3977	37	1	for	for	ADP
ejpam-3977	37	2	any	any	DET
ejpam-3977	37	3	pair	pair	NOUN
ejpam-3977	37	4	of	of	ADP
ejpam-3977	37	5	vertices	vertex	NOUN
ejpam-3977	37	6	x	x	X
ejpam-3977	37	7	,	,	PUNCT
ejpam-3977	37	8	y	y	PROPN
ejpam-3977	37	9	∈	∈	PROPN
ejpam-3977	37	10	s	s	PROPN
ejpam-3977	37	11	,	,	PUNCT
ejpam-3977	37	12	r(x	r(x	PROPN
ejpam-3977	37	13	/	/	SYM
ejpam-3977	37	14	s	s	NOUN
ejpam-3977	37	15	)	)	PUNCT
ejpam-3977	37	16	and	and	CCONJ
ejpam-3977	37	17	r(y	r(y	VERB
ejpam-3977	37	18	/	/	SYM
ejpam-3977	37	19	s	s	PART
ejpam-3977	37	20	)	)	PUNCT
ejpam-3977	37	21	differ	differ	VERB
ejpam-3977	37	22	in	in	ADP
ejpam-3977	37	23	at	at	ADV
ejpam-3977	37	24	least	least	ADJ
ejpam-3977	37	25	2	2	NUM
ejpam-3977	37	26	positions	position	NOUN
ejpam-3977	37	27	.	.	PUNCT
ejpam-3977	38	1	hence	hence	ADV
ejpam-3977	38	2	,	,	PUNCT
ejpam-3977	38	3	to	to	PART
ejpam-3977	38	4	prove	prove	VERB
ejpam-3977	38	5	that	that	SCONJ
ejpam-3977	38	6	s	s	VERB
ejpam-3977	38	7	is	be	AUX
ejpam-3977	38	8	a	a	DET
ejpam-3977	38	9	2	2	NUM
ejpam-3977	38	10	-	-	PUNCT
ejpam-3977	38	11	resolving	resolving	NOUN
ejpam-3977	38	12	set	set	NOUN
ejpam-3977	38	13	in	in	ADP
ejpam-3977	38	14	g	g	NOUN
ejpam-3977	38	15	,	,	PUNCT
ejpam-3977	38	16	we	we	PRON
ejpam-3977	38	17	only	only	ADV
ejpam-3977	38	18	need	need	VERB
ejpam-3977	38	19	to	to	PART
ejpam-3977	38	20	show	show	VERB
ejpam-3977	38	21	that	that	SCONJ
ejpam-3977	38	22	for	for	ADP
ejpam-3977	38	23	every	every	DET
ejpam-3977	38	24	pair	pair	NOUN
ejpam-3977	38	25	of	of	ADP
ejpam-3977	38	26	vertices	vertex	NOUN
ejpam-3977	38	27	x	x	X
ejpam-3977	38	28	,	,	PUNCT
ejpam-3977	38	29	y	y	PROPN
ejpam-3977	38	30	∈	∈	PROPN
ejpam-3977	38	31	v	v	ADP
ejpam-3977	38	32	(	(	PUNCT
ejpam-3977	38	33	g	g	NOUN
ejpam-3977	38	34	)	)	PUNCT
ejpam-3977	38	35	where	where	SCONJ
ejpam-3977	38	36	x	x	PUNCT
ejpam-3977	38	37	∈	∈	PROPN
ejpam-3977	38	38	s	s	X
ejpam-3977	38	39	and	and	CCONJ
ejpam-3977	38	40	y	y	PROPN
ejpam-3977	38	41	∈	∈	PROPN
ejpam-3977	38	42	v	v	X
ejpam-3977	38	43	(	(	PUNCT
ejpam-3977	38	44	g)\s	g)\s	NOUN
ejpam-3977	38	45	or	or	CCONJ
ejpam-3977	38	46	both	both	DET
ejpam-3977	38	47	x	x	NOUN
ejpam-3977	38	48	,	,	PUNCT
ejpam-3977	38	49	y	y	PROPN
ejpam-3977	38	50	∈	∈	PROPN
ejpam-3977	38	51	v	v	X
ejpam-3977	38	52	(	(	PUNCT
ejpam-3977	38	53	g)\s	g)\s	NOUN
ejpam-3977	38	54	,	,	PUNCT
ejpam-3977	38	55	r(x	r(x	PROPN
ejpam-3977	38	56	/	/	SYM
ejpam-3977	38	57	s	s	NOUN
ejpam-3977	38	58	)	)	PUNCT
ejpam-3977	38	59	and	and	CCONJ
ejpam-3977	38	60	r(y	r(y	VERB
ejpam-3977	38	61	/	/	SYM
ejpam-3977	38	62	s	s	PART
ejpam-3977	38	63	)	)	PUNCT
ejpam-3977	38	64	differ	differ	VERB
ejpam-3977	38	65	in	in	ADP
ejpam-3977	38	66	at	at	ADV
ejpam-3977	38	67	least	least	ADJ
ejpam-3977	38	68	2	2	NUM
ejpam-3977	38	69	positions	position	NOUN
ejpam-3977	38	70	.	.	PUNCT
ejpam-3977	39	1	j.	j.	PROPN
ejpam-3977	39	2	cabaro	cabaro	PROPN
ejpam-3977	39	3	,	,	PUNCT
ejpam-3977	39	4	h.	h.	PROPN
ejpam-3977	39	5	rara	rara	PROPN
ejpam-3977	39	6	/	/	SYM
ejpam-3977	39	7	eur	eur	PROPN
ejpam-3977	39	8	.	.	PUNCT
ejpam-3977	40	1	j.	j.	PROPN
ejpam-3977	40	2	pure	pure	PROPN
ejpam-3977	40	3	appl	appl	PROPN
ejpam-3977	40	4	.	.	PROPN
ejpam-3977	40	5	math	math	PROPN
ejpam-3977	40	6	,	,	PUNCT
ejpam-3977	40	7	14	14	NUM
ejpam-3977	40	8	(	(	PUNCT
ejpam-3977	40	9	3	3	NUM
ejpam-3977	40	10	)	)	PUNCT
ejpam-3977	40	11	(	(	PUNCT
ejpam-3977	40	12	2021	2021	NUM
ejpam-3977	40	13	)	)	PUNCT
ejpam-3977	40	14	,	,	PUNCT
ejpam-3977	40	15	773	773	NUM
ejpam-3977	40	16	-	-	SYM
ejpam-3977	40	17	782	782	NUM
ejpam-3977	41	1	775	775	NUM
ejpam-3977	41	2	3	3	NUM
ejpam-3977	41	3	.	.	NOUN
ejpam-3977	41	4	2	2	NUM
ejpam-3977	41	5	-	-	PUNCT
ejpam-3977	41	6	resolving	resolve	VERB
ejpam-3977	41	7	sets	set	NOUN
ejpam-3977	41	8	in	in	ADP
ejpam-3977	41	9	the	the	DET
ejpam-3977	41	10	join	join	NOUN
ejpam-3977	41	11	of	of	ADP
ejpam-3977	41	12	graphs	graph	NOUN
ejpam-3977	41	13	definition	definition	NOUN
ejpam-3977	41	14	1.[2	1.[2	NUM
ejpam-3977	41	15	]	]	X
ejpam-3977	41	16	the	the	DET
ejpam-3977	41	17	join	join	NOUN
ejpam-3977	41	18	g	g	PROPN
ejpam-3977	41	19	+	+	CCONJ
ejpam-3977	41	20	h	h	NOUN
ejpam-3977	41	21	of	of	ADP
ejpam-3977	41	22	two	two	NUM
ejpam-3977	41	23	graphs	graph	NOUN
ejpam-3977	41	24	g	g	NOUN
ejpam-3977	41	25	and	and	CCONJ
ejpam-3977	41	26	h	h	NOUN
ejpam-3977	41	27	is	be	AUX
ejpam-3977	41	28	the	the	DET
ejpam-3977	41	29	graph	graph	NOUN
ejpam-3977	41	30	with	with	ADP
ejpam-3977	41	31	vertex	vertex	NOUN
ejpam-3977	41	32	set	set	VERB
ejpam-3977	41	33	v	v	NOUN
ejpam-3977	41	34	(	(	PUNCT
ejpam-3977	41	35	g	g	PROPN
ejpam-3977	41	36	+	+	NOUN
ejpam-3977	41	37	h	h	NOUN
ejpam-3977	41	38	)	)	PUNCT
ejpam-3977	42	1	=	=	NOUN
ejpam-3977	42	2	v	v	X
ejpam-3977	42	3	(	(	PUNCT
ejpam-3977	42	4	g	g	NOUN
ejpam-3977	42	5	)	)	PUNCT
ejpam-3977	42	6	∪	∪	NOUN
ejpam-3977	42	7	v	v	NOUN
ejpam-3977	42	8	(	(	PUNCT
ejpam-3977	42	9	h	h	NOUN
ejpam-3977	42	10	)	)	PUNCT
ejpam-3977	42	11	and	and	CCONJ
ejpam-3977	42	12	edge	edge	NOUN
ejpam-3977	42	13	set	set	VERB
ejpam-3977	42	14	e(g	e(g	PROPN
ejpam-3977	42	15	+	+	CCONJ
ejpam-3977	42	16	h	h	NOUN
ejpam-3977	42	17	)	)	PUNCT
ejpam-3977	42	18	=	=	SYM
ejpam-3977	42	19	e(g	e(g	PROPN
ejpam-3977	42	20	)	)	PUNCT
ejpam-3977	42	21	∪	∪	ADP
ejpam-3977	42	22	e(h	e(h	PROPN
ejpam-3977	42	23	)	)	PUNCT
ejpam-3977	42	24	∪	∪	NOUN
ejpam-3977	42	25	{	{	PUNCT
ejpam-3977	42	26	uv	uv	NOUN
ejpam-3977	42	27	:	:	PUNCT
ejpam-3977	42	28	u	u	PROPN
ejpam-3977	42	29	∈	∈	PROPN
ejpam-3977	42	30	v	v	ADP
ejpam-3977	42	31	(	(	PUNCT
ejpam-3977	42	32	g	g	NOUN
ejpam-3977	42	33	)	)	PUNCT
ejpam-3977	42	34	,	,	PUNCT
ejpam-3977	42	35	v	v	X
ejpam-3977	42	36	∈	∈	PROPN
ejpam-3977	42	37	v	v	NOUN
ejpam-3977	42	38	(	(	PUNCT
ejpam-3977	42	39	h	h	NOUN
ejpam-3977	42	40	)	)	PUNCT
ejpam-3977	42	41	}	}	PUNCT
ejpam-3977	42	42	.	.	PUNCT
ejpam-3977	43	1	note	note	VERB
ejpam-3977	43	2	that	that	SCONJ
ejpam-3977	43	3	the	the	DET
ejpam-3977	43	4	star	star	NOUN
ejpam-3977	43	5	k1,n	k1,n	PROPN
ejpam-3977	43	6	can	can	AUX
ejpam-3977	43	7	be	be	AUX
ejpam-3977	43	8	expressed	express	VERB
ejpam-3977	43	9	as	as	ADP
ejpam-3977	43	10	the	the	DET
ejpam-3977	43	11	join	join	NOUN
ejpam-3977	43	12	of	of	ADP
ejpam-3977	43	13	the	the	DET
ejpam-3977	43	14	trivial	trivial	ADJ
ejpam-3977	43	15	graph	graph	NOUN
ejpam-3977	43	16	k1	k1	NOUN
ejpam-3977	43	17	and	and	CCONJ
ejpam-3977	43	18	the	the	DET
ejpam-3977	43	19	empty	empty	ADJ
ejpam-3977	43	20	graph	graph	NOUN
ejpam-3977	43	21	kn	kn	PROPN
ejpam-3977	43	22	of	of	ADP
ejpam-3977	43	23	order	order	NOUN
ejpam-3977	43	24	n	n	CCONJ
ejpam-3977	43	25	,	,	PUNCT
ejpam-3977	43	26	that	that	ADV
ejpam-3977	43	27	is	is	ADV
ejpam-3977	43	28	,	,	PUNCT
ejpam-3977	43	29	k1,n	k1,n	PROPN
ejpam-3977	43	30	=	=	PROPN
ejpam-3977	43	31	k1	k1	PROPN
ejpam-3977	43	32	+	+	X
ejpam-3977	43	33	kn	kn	PROPN
ejpam-3977	43	34	.	.	PUNCT
ejpam-3977	44	1	the	the	DET
ejpam-3977	44	2	graphs	graph	NOUN
ejpam-3977	44	3	fn	fn	NOUN
ejpam-3977	44	4	=	=	SYM
ejpam-3977	44	5	k1	k1	PROPN
ejpam-3977	44	6	+	+	CCONJ
ejpam-3977	44	7	pn	pn	PROPN
ejpam-3977	44	8	and	and	CCONJ
ejpam-3977	44	9	wn	wn	PROPN
ejpam-3977	44	10	=	=	PROPN
ejpam-3977	44	11	k1	k1	PROPN
ejpam-3977	45	1	+	+	CCONJ
ejpam-3977	45	2	cn	cn	NOUN
ejpam-3977	45	3	of	of	ADP
ejpam-3977	45	4	orders	order	NOUN
ejpam-3977	45	5	n	n	X
ejpam-3977	45	6	+	+	CCONJ
ejpam-3977	45	7	1	1	NUM
ejpam-3977	45	8	are	be	AUX
ejpam-3977	45	9	called	call	VERB
ejpam-3977	45	10	fan	fan	NOUN
ejpam-3977	45	11	and	and	CCONJ
ejpam-3977	45	12	wheel	wheel	NOUN
ejpam-3977	45	13	,	,	PUNCT
ejpam-3977	45	14	respectively	respectively	ADV
ejpam-3977	45	15	.	.	PUNCT
ejpam-3977	46	1	definition	definition	NOUN
ejpam-3977	46	2	2	2	NUM
ejpam-3977	46	3	.	.	PUNCT
ejpam-3977	47	1	let	let	VERB
ejpam-3977	47	2	g	g	NOUN
ejpam-3977	47	3	=	=	SYM
ejpam-3977	47	4	(	(	PUNCT
ejpam-3977	47	5	(	(	PUNCT
ejpam-3977	47	6	v	v	NOUN
ejpam-3977	47	7	(	(	PUNCT
ejpam-3977	47	8	g	g	NOUN
ejpam-3977	47	9	)	)	PUNCT
ejpam-3977	47	10	,	,	PUNCT
ejpam-3977	47	11	e(g	e(g	PROPN
ejpam-3977	47	12	)	)	PUNCT
ejpam-3977	47	13	)	)	PUNCT
ejpam-3977	48	1	be	be	AUX
ejpam-3977	48	2	a	a	DET
ejpam-3977	48	3	connected	connected	ADJ
ejpam-3977	48	4	graph	graph	NOUN
ejpam-3977	48	5	.	.	PUNCT
ejpam-3977	49	1	the	the	DET
ejpam-3977	49	2	open	open	ADJ
ejpam-3977	49	3	neighborhood	neighborhood	NOUN
ejpam-3977	49	4	ng(v	ng(v	PUNCT
ejpam-3977	49	5	)	)	PUNCT
ejpam-3977	49	6	=	=	PRON
ejpam-3977	49	7	{	{	PUNCT
ejpam-3977	49	8	u	u	NOUN
ejpam-3977	49	9	∈	∈	PROPN
ejpam-3977	49	10	v	v	NOUN
ejpam-3977	49	11	(	(	PUNCT
ejpam-3977	49	12	g	g	NOUN
ejpam-3977	49	13	)	)	PUNCT
ejpam-3977	49	14	:	:	PUNCT
ejpam-3977	49	15	uv	uv	PROPN
ejpam-3977	49	16	∈	∈	PROPN
ejpam-3977	49	17	e(g	e(g	PROPN
ejpam-3977	49	18	)	)	PUNCT
ejpam-3977	49	19	}	}	PUNCT
ejpam-3977	49	20	.	.	PUNCT
ejpam-3977	50	1	any	any	DET
ejpam-3977	50	2	element	element	NOUN
ejpam-3977	50	3	u	u	NOUN
ejpam-3977	50	4	of	of	ADP
ejpam-3977	50	5	ng(v	ng(v	PUNCT
ejpam-3977	50	6	)	)	PUNCT
ejpam-3977	50	7	is	be	AUX
ejpam-3977	50	8	called	call	VERB
ejpam-3977	50	9	a	a	DET
ejpam-3977	50	10	neighbor	neighbor	NOUN
ejpam-3977	50	11	of	of	ADP
ejpam-3977	50	12	v.	v.	ADP
ejpam-3977	50	13	the	the	DET
ejpam-3977	50	14	notation	notation	NOUN
ejpam-3977	50	15	x	x	SYM
ejpam-3977	50	16	∈	∈	PROPN
ejpam-3977	50	17	v	v	X
ejpam-3977	50	18	(	(	PUNCT
ejpam-3977	50	19	g)\s	g)\s	NOUN
ejpam-3977	50	20	means	mean	VERB
ejpam-3977	50	21	that	that	SCONJ
ejpam-3977	50	22	x	x	PUNCT
ejpam-3977	50	23	∈	∈	NOUN
ejpam-3977	50	24	v	v	X
ejpam-3977	50	25	(	(	PUNCT
ejpam-3977	50	26	g	g	NOUN
ejpam-3977	50	27	)	)	PUNCT
ejpam-3977	50	28	but	but	CCONJ
ejpam-3977	50	29	not	not	PART
ejpam-3977	50	30	in	in	ADP
ejpam-3977	50	31	s.	s.	PROPN
ejpam-3977	50	32	definition	definition	NOUN
ejpam-3977	50	33	3	3	X
ejpam-3977	50	34	.	.	PUNCT
ejpam-3977	51	1	let	let	VERB
ejpam-3977	51	2	g	g	NOUN
ejpam-3977	51	3	be	be	AUX
ejpam-3977	51	4	any	any	DET
ejpam-3977	51	5	nontrivial	nontrivial	ADJ
ejpam-3977	51	6	connected	connect	VERB
ejpam-3977	51	7	graph	graph	NOUN
ejpam-3977	51	8	and	and	CCONJ
ejpam-3977	51	9	s	s	VERB
ejpam-3977	51	10	⊆	⊆	NUM
ejpam-3977	51	11	v	v	NOUN
ejpam-3977	51	12	(	(	PUNCT
ejpam-3977	51	13	g	g	NOUN
ejpam-3977	51	14	)	)	PUNCT
ejpam-3977	51	15	.	.	PUNCT
ejpam-3977	52	1	then	then	ADV
ejpam-3977	52	2	s	s	VERB
ejpam-3977	52	3	is	be	AUX
ejpam-3977	52	4	a	a	DET
ejpam-3977	52	5	2	2	NUM
ejpam-3977	52	6	-	-	PUNCT
ejpam-3977	52	7	locating	locate	VERB
ejpam-3977	52	8	set	set	NOUN
ejpam-3977	52	9	of	of	ADP
ejpam-3977	52	10	g	g	PROPN
ejpam-3977	52	11	if	if	SCONJ
ejpam-3977	52	12	∀x	∀x	NUM
ejpam-3977	52	13	,	,	PUNCT
ejpam-3977	52	14	y	y	PROPN
ejpam-3977	52	15	∈	∈	PROPN
ejpam-3977	52	16	v	v	NOUN
ejpam-3977	52	17	(	(	PUNCT
ejpam-3977	52	18	g	g	NOUN
ejpam-3977	52	19	)	)	PUNCT
ejpam-3977	52	20	,	,	PUNCT
ejpam-3977	52	21	x	x	X
ejpam-3977	52	22	6=	6=	PROPN
ejpam-3977	52	23	y	y	PROPN
ejpam-3977	52	24	,	,	PUNCT
ejpam-3977	52	25	the	the	DET
ejpam-3977	52	26	following	follow	VERB
ejpam-3977	52	27	are	be	AUX
ejpam-3977	52	28	satisfied	satisfied	ADJ
ejpam-3977	52	29	:	:	PUNCT
ejpam-3977	52	30	(	(	PUNCT
ejpam-3977	52	31	i	i	NOUN
ejpam-3977	52	32	)	)	PUNCT
ejpam-3977	52	33	if	if	SCONJ
ejpam-3977	52	34	x	x	X
ejpam-3977	52	35	,	,	PUNCT
ejpam-3977	52	36	y	y	PROPN
ejpam-3977	52	37	∈	∈	PROPN
ejpam-3977	52	38	v	v	X
ejpam-3977	52	39	(	(	PUNCT
ejpam-3977	52	40	g)\s	g)\s	NOUN
ejpam-3977	52	41	,	,	PUNCT
ejpam-3977	52	42	then	then	ADV
ejpam-3977	52	43	∃w	∃w	PROPN
ejpam-3977	52	44	,	,	PUNCT
ejpam-3977	52	45	z	z	PROPN
ejpam-3977	52	46	∈	∈	PROPN
ejpam-3977	52	47	s	s	PROPN
ejpam-3977	52	48	,	,	PUNCT
ejpam-3977	52	49	w	w	PROPN
ejpam-3977	52	50	6=	6=	PROPN
ejpam-3977	52	51	z	z	NOUN
ejpam-3977	52	52	such	such	ADJ
ejpam-3977	52	53	that	that	SCONJ
ejpam-3977	52	54	either	either	ADV
ejpam-3977	52	55	:	:	PUNCT
ejpam-3977	52	56	(	(	PUNCT
ejpam-3977	52	57	a	a	X
ejpam-3977	52	58	)	)	PUNCT
ejpam-3977	52	59	w	w	NOUN
ejpam-3977	52	60	,	,	PUNCT
ejpam-3977	52	61	z	z	NOUN
ejpam-3977	52	62	∈	∈	PROPN
ejpam-3977	52	63	(	(	PUNCT
ejpam-3977	52	64	ng(x))\ng(y	ng(x))\ng(y	NOUN
ejpam-3977	52	65	)	)	PUNCT
ejpam-3977	52	66	,	,	PUNCT
ejpam-3977	52	67	or	or	CCONJ
ejpam-3977	52	68	(	(	PUNCT
ejpam-3977	52	69	b	b	X
ejpam-3977	52	70	)	)	PUNCT
ejpam-3977	52	71	w	w	NOUN
ejpam-3977	52	72	,	,	PUNCT
ejpam-3977	52	73	z	z	NOUN
ejpam-3977	52	74	∈	∈	PROPN
ejpam-3977	52	75	(	(	PUNCT
ejpam-3977	52	76	ng(y))\ng(x	ng(y))\ng(x	NOUN
ejpam-3977	52	77	)	)	PUNCT
ejpam-3977	52	78	,	,	PUNCT
ejpam-3977	52	79	or	or	CCONJ
ejpam-3977	52	80	(	(	PUNCT
ejpam-3977	52	81	c	c	X
ejpam-3977	52	82	)	)	PUNCT
ejpam-3977	52	83	w	w	NOUN
ejpam-3977	52	84	∈	∈	PROPN
ejpam-3977	52	85	(	(	PUNCT
ejpam-3977	52	86	ng(x))\ng(y	ng(x))\ng(y	NOUN
ejpam-3977	52	87	)	)	PUNCT
ejpam-3977	52	88	and	and	CCONJ
ejpam-3977	52	89	z	z	NOUN
ejpam-3977	52	90	∈	∈	PROPN
ejpam-3977	52	91	(	(	PUNCT
ejpam-3977	52	92	ng(y))\ng(x	ng(y))\ng(x	NOUN
ejpam-3977	52	93	)	)	PUNCT
ejpam-3977	52	94	.	.	PUNCT
ejpam-3977	53	1	(	(	PUNCT
ejpam-3977	53	2	ii	ii	NOUN
ejpam-3977	53	3	)	)	PUNCT
ejpam-3977	53	4	if	if	SCONJ
ejpam-3977	53	5	x	x	PUNCT
ejpam-3977	53	6	∈	∈	PROPN
ejpam-3977	53	7	s	s	PROPN
ejpam-3977	53	8	,	,	PUNCT
ejpam-3977	53	9	y	y	PROPN
ejpam-3977	53	10	∈	∈	PROPN
ejpam-3977	53	11	v	v	X
ejpam-3977	53	12	(	(	PUNCT
ejpam-3977	53	13	g)\s	g)\s	NOUN
ejpam-3977	53	14	,	,	PUNCT
ejpam-3977	53	15	then	then	ADV
ejpam-3977	53	16	∃p	∃p	PROPN
ejpam-3977	53	17	∈	∈	PROPN
ejpam-3977	53	18	(	(	PUNCT
ejpam-3977	53	19	ng(x	ng(x	NUM
ejpam-3977	53	20	)	)	PUNCT
ejpam-3977	53	21	∩	∩	ADJ
ejpam-3977	53	22	s)\ng(y	s)\ng(y	X
ejpam-3977	53	23	)	)	PUNCT
ejpam-3977	53	24	or	or	CCONJ
ejpam-3977	53	25	p	p	NOUN
ejpam-3977	53	26	∈	∈	PROPN
ejpam-3977	53	27	(	(	PUNCT
ejpam-3977	53	28	ng(y	ng(y	NOUN
ejpam-3977	53	29	)	)	PUNCT
ejpam-3977	53	30	∩	∩	NOUN
ejpam-3977	53	31	s)\ng(x	s)\ng(x	NOUN
ejpam-3977	53	32	)	)	PUNCT
ejpam-3977	53	33	.	.	PUNCT
ejpam-3977	54	1	the	the	DET
ejpam-3977	54	2	2	2	NUM
ejpam-3977	54	3	-	-	PUNCT
ejpam-3977	54	4	locating	locate	VERB
ejpam-3977	54	5	number	number	NOUN
ejpam-3977	54	6	of	of	ADP
ejpam-3977	54	7	g	g	NOUN
ejpam-3977	54	8	,	,	PUNCT
ejpam-3977	54	9	denoted	denote	VERB
ejpam-3977	54	10	by	by	ADP
ejpam-3977	54	11	ln2(g	ln2(g	NOUN
ejpam-3977	54	12	)	)	PUNCT
ejpam-3977	54	13	,	,	PUNCT
ejpam-3977	54	14	is	be	AUX
ejpam-3977	54	15	the	the	DET
ejpam-3977	54	16	smallest	small	ADJ
ejpam-3977	54	17	cardinality	cardinality	NOUN
ejpam-3977	54	18	of	of	ADP
ejpam-3977	54	19	a	a	DET
ejpam-3977	54	20	2	2	NUM
ejpam-3977	54	21	-	-	PUNCT
ejpam-3977	54	22	locating	locate	VERB
ejpam-3977	54	23	set	set	NOUN
ejpam-3977	54	24	of	of	ADP
ejpam-3977	54	25	g.	g.	PROPN
ejpam-3977	54	26	a	a	DET
ejpam-3977	54	27	2	2	NUM
ejpam-3977	54	28	-	-	PUNCT
ejpam-3977	54	29	locating	locate	VERB
ejpam-3977	54	30	set	set	NOUN
ejpam-3977	54	31	of	of	ADP
ejpam-3977	54	32	g	g	NOUN
ejpam-3977	54	33	of	of	ADP
ejpam-3977	54	34	cardinality	cardinality	PROPN
ejpam-3977	54	35	ln2(g	ln2(g	PROPN
ejpam-3977	54	36	)	)	PUNCT
ejpam-3977	54	37	is	be	AUX
ejpam-3977	54	38	referred	refer	VERB
ejpam-3977	54	39	to	to	ADP
ejpam-3977	54	40	as	as	ADP
ejpam-3977	54	41	ln2	ln2	NOUN
ejpam-3977	54	42	-	-	PUNCT
ejpam-3977	54	43	set	set	NOUN
ejpam-3977	54	44	of	of	ADP
ejpam-3977	54	45	g.	g.	PROPN
ejpam-3977	54	46	example	example	NOUN
ejpam-3977	55	1	1	1	X
ejpam-3977	55	2	.	.	PUNCT
ejpam-3977	56	1	the	the	DET
ejpam-3977	56	2	sets	set	NOUN
ejpam-3977	56	3	s1	s1	NOUN
ejpam-3977	56	4	=	=	PUNCT
ejpam-3977	56	5	{	{	PUNCT
ejpam-3977	56	6	c	c	NOUN
ejpam-3977	56	7	,	,	PUNCT
ejpam-3977	56	8	d	d	NOUN
ejpam-3977	56	9	,	,	PUNCT
ejpam-3977	56	10	e	e	NOUN
ejpam-3977	56	11	,	,	PUNCT
ejpam-3977	56	12	f	f	NOUN
ejpam-3977	56	13	}	}	PUNCT
ejpam-3977	56	14	and	and	CCONJ
ejpam-3977	56	15	s2	s2	VERB
ejpam-3977	56	16	=	=	PUNCT
ejpam-3977	56	17	{	{	PUNCT
ejpam-3977	56	18	a	a	PRON
ejpam-3977	56	19	,	,	PUNCT
ejpam-3977	56	20	b	b	NOUN
ejpam-3977	56	21	,	,	PUNCT
ejpam-3977	56	22	c	c	NOUN
ejpam-3977	56	23	,	,	PUNCT
ejpam-3977	56	24	f	f	X
ejpam-3977	56	25	}	}	PUNCT
ejpam-3977	56	26	are	be	AUX
ejpam-3977	56	27	2	2	NUM
ejpam-3977	56	28	-	-	PUNCT
ejpam-3977	56	29	locating	locate	VERB
ejpam-3977	56	30	sets	set	NOUN
ejpam-3977	56	31	in	in	ADP
ejpam-3977	56	32	g	g	NOUN
ejpam-3977	56	33	in	in	ADP
ejpam-3977	56	34	figure1	figure1	PROPN
ejpam-3977	56	35	.	.	PUNCT
ejpam-3977	57	1	moreover	moreover	ADV
ejpam-3977	57	2	,	,	PUNCT
ejpam-3977	57	3	s1	s1	PROPN
ejpam-3977	57	4	and	and	CCONJ
ejpam-3977	57	5	s2	s2	PROPN
ejpam-3977	57	6	are	be	AUX
ejpam-3977	57	7	ln2	ln2	ADV
ejpam-3977	57	8	-	-	PUNCT
ejpam-3977	57	9	set	set	NOUN
ejpam-3977	57	10	in	in	ADP
ejpam-3977	57	11	g.	g.	PROPN
ejpam-3977	57	12	thus	thus	ADV
ejpam-3977	57	13	,	,	PUNCT
ejpam-3977	57	14	ln2(g	ln2(g	PROPN
ejpam-3977	57	15	)	)	PUNCT
ejpam-3977	57	16	=	=	SYM
ejpam-3977	57	17	|s1|	|s1|	NOUN
ejpam-3977	57	18	=	=	SYM
ejpam-3977	57	19	|s2|	|s2|	NOUN
ejpam-3977	57	20	=	=	NOUN
ejpam-3977	57	21	4	4	NUM
ejpam-3977	57	22	.	.	PUNCT
ejpam-3977	57	23	....................................	....................................	PUNCT
ejpam-3977	58	1	....................................	....................................	PUNCT
ejpam-3977	58	2	....................................	....................................	PUNCT
ejpam-3977	59	1	....................................	....................................	PUNCT
ejpam-3977	59	2	....................................	....................................	PUNCT
ejpam-3977	60	1	....................................	....................................	PUNCT
ejpam-3977	60	2	.........	.........	PUNCT
ejpam-3977	60	3	........	........	PUNCT
ejpam-3977	60	4	........	........	PUNCT
ejpam-3977	60	5	........	........	PUNCT
ejpam-3977	60	6	........	........	PUNCT
ejpam-3977	60	7	........	........	PUNCT
ejpam-3977	60	8	........	........	PUNCT
ejpam-3977	60	9	........	........	PUNCT
ejpam-3977	60	10	........	........	PUNCT
ejpam-3977	60	11	........	........	PUNCT
ejpam-3977	60	12	........	........	PUNCT
ejpam-3977	61	1	....	....	PUNCT
ejpam-3977	61	2	.........	.........	PUNCT
ejpam-3977	61	3	........	........	PUNCT
ejpam-3977	61	4	........	........	PUNCT
ejpam-3977	61	5	........	........	PUNCT
ejpam-3977	61	6	........	........	PUNCT
ejpam-3977	61	7	........	........	PUNCT
ejpam-3977	61	8	........	........	PUNCT
ejpam-3977	61	9	........	........	PUNCT
ejpam-3977	61	10	........	........	PUNCT
ejpam-3977	61	11	........	........	PUNCT
ejpam-3977	61	12	........	........	PUNCT
ejpam-3977	62	1	....	....	PUNCT
ejpam-3977	62	2	...................	...................	PUNCT
ejpam-3977	63	1	..................	..................	PUNCT
ejpam-3977	63	2	..................	..................	PUNCT
ejpam-3977	64	1	..................	..................	PUNCT
ejpam-3977	64	2	..................	..................	PUNCT
ejpam-3977	65	1	..................	..................	PUNCT
ejpam-3977	65	2	..................	..................	PUNCT
ejpam-3977	66	1	..................	..................	PUNCT
ejpam-3977	66	2	..................	..................	PUNCT
ejpam-3977	67	1	..................	..................	PUNCT
ejpam-3977	67	2	..................	..................	PUNCT
ejpam-3977	67	3	..................	..................	PUNCT
ejpam-3977	67	4	......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-3977	67	5	.........	.........	PUNCT
ejpam-3977	68	1	........	........	PUNCT
ejpam-3977	68	2	........	........	PUNCT
ejpam-3977	68	3	........	........	PUNCT
ejpam-3977	68	4	........	........	PUNCT
ejpam-3977	68	5	........	........	PUNCT
ejpam-3977	68	6	........	........	PUNCT
ejpam-3977	68	7	........	........	PUNCT
ejpam-3977	68	8	........	........	PUNCT
ejpam-3977	68	9	........	........	PUNCT
ejpam-3977	68	10	........	........	PUNCT
ejpam-3977	69	1	....	....	PUNCT
ejpam-3977	69	2	.........	.........	PUNCT
ejpam-3977	69	3	........	........	PUNCT
ejpam-3977	69	4	........	........	PUNCT
ejpam-3977	69	5	........	........	PUNCT
ejpam-3977	69	6	........	........	PUNCT
ejpam-3977	69	7	........	........	PUNCT
ejpam-3977	69	8	........	........	PUNCT
ejpam-3977	69	9	........	........	PUNCT
ejpam-3977	69	10	........	........	PUNCT
ejpam-3977	69	11	........	........	PUNCT
ejpam-3977	69	12	........	........	PUNCT
ejpam-3977	70	1	....	....	PUNCT
ejpam-3977	70	2	g	g	NOUN
ejpam-3977	70	3	:	:	PUNCT
ejpam-3977	70	4	a	a	DET
ejpam-3977	70	5	b	b	NOUN
ejpam-3977	70	6	c	c	NOUN
ejpam-3977	70	7	d	d	X
ejpam-3977	70	8	e	e	X
ejpam-3977	70	9	f	f	PROPN
ejpam-3977	70	10	figure	figure	NOUN
ejpam-3977	70	11	1	1	NUM
ejpam-3977	70	12	:	:	PUNCT
ejpam-3977	70	13	a	a	DET
ejpam-3977	70	14	graph	graph	NOUN
ejpam-3977	70	15	g	g	NOUN
ejpam-3977	70	16	with	with	ADP
ejpam-3977	70	17	ln2	ln2	ADJ
ejpam-3977	70	18	=	=	SYM
ejpam-3977	70	19	4	4	NUM
ejpam-3977	70	20	remark	remark	NOUN
ejpam-3977	70	21	4	4	NUM
ejpam-3977	70	22	.	.	PUNCT
ejpam-3977	71	1	every	every	DET
ejpam-3977	71	2	2	2	NUM
ejpam-3977	71	3	-	-	PUNCT
ejpam-3977	71	4	locating	locate	VERB
ejpam-3977	71	5	set	set	NOUN
ejpam-3977	71	6	in	in	ADP
ejpam-3977	71	7	g	g	PROPN
ejpam-3977	71	8	is	be	AUX
ejpam-3977	71	9	a	a	DET
ejpam-3977	71	10	2	2	NUM
ejpam-3977	71	11	-	-	PUNCT
ejpam-3977	71	12	resolving	resolving	NOUN
ejpam-3977	71	13	set	set	VERB
ejpam-3977	71	14	in	in	ADP
ejpam-3977	71	15	g.	g.	PROPN
ejpam-3977	71	16	however	however	ADV
ejpam-3977	71	17	,	,	PUNCT
ejpam-3977	71	18	a	a	DET
ejpam-3977	71	19	2	2	NUM
ejpam-3977	71	20	-	-	PUNCT
ejpam-3977	71	21	resolving	resolving	NOUN
ejpam-3977	71	22	set	set	NOUN
ejpam-3977	71	23	in	in	ADP
ejpam-3977	71	24	g	g	NOUN
ejpam-3977	71	25	need	need	AUX
ejpam-3977	71	26	not	not	PART
ejpam-3977	71	27	be	be	AUX
ejpam-3977	71	28	a	a	DET
ejpam-3977	71	29	2	2	NUM
ejpam-3977	71	30	-	-	PUNCT
ejpam-3977	71	31	locating	locate	VERB
ejpam-3977	71	32	set	set	NOUN
ejpam-3977	71	33	in	in	ADP
ejpam-3977	71	34	g.	g.	PROPN
ejpam-3977	71	35	thus	thus	ADV
ejpam-3977	71	36	,	,	PUNCT
ejpam-3977	71	37	dim2(g	dim2(g	NOUN
ejpam-3977	71	38	)	)	PUNCT
ejpam-3977	71	39	≤	≤	NOUN
ejpam-3977	71	40	ln2(g	ln2(g	PROPN
ejpam-3977	71	41	)	)	PUNCT
ejpam-3977	71	42	.	.	PUNCT
ejpam-3977	72	1	j.	j.	PROPN
ejpam-3977	72	2	cabaro	cabaro	PROPN
ejpam-3977	72	3	,	,	PUNCT
ejpam-3977	72	4	h.	h.	PROPN
ejpam-3977	72	5	rara	rara	PROPN
ejpam-3977	72	6	/	/	SYM
ejpam-3977	72	7	eur	eur	PROPN
ejpam-3977	72	8	.	.	PUNCT
ejpam-3977	73	1	j.	j.	PROPN
ejpam-3977	73	2	pure	pure	PROPN
ejpam-3977	73	3	appl	appl	PROPN
ejpam-3977	73	4	.	.	PROPN
ejpam-3977	73	5	math	math	PROPN
ejpam-3977	73	6	,	,	PUNCT
ejpam-3977	73	7	14	14	NUM
ejpam-3977	73	8	(	(	PUNCT
ejpam-3977	73	9	3	3	NUM
ejpam-3977	73	10	)	)	PUNCT
ejpam-3977	73	11	(	(	PUNCT
ejpam-3977	73	12	2021	2021	NUM
ejpam-3977	73	13	)	)	PUNCT
ejpam-3977	73	14	,	,	PUNCT
ejpam-3977	73	15	773	773	NUM
ejpam-3977	73	16	-	-	SYM
ejpam-3977	73	17	782	782	NUM
ejpam-3977	73	18	776	776	NUM
ejpam-3977	73	19	example	example	NOUN
ejpam-3977	73	20	2	2	NUM
ejpam-3977	73	21	.	.	PUNCT
ejpam-3977	74	1	let	let	VERB
ejpam-3977	74	2	p6	p6	PROPN
ejpam-3977	74	3	=	=	PUNCT
ejpam-3977	75	1	[	[	X
ejpam-3977	75	2	v1	v1	NOUN
ejpam-3977	75	3	,	,	PUNCT
ejpam-3977	75	4	v2	v2	PROPN
ejpam-3977	75	5	,	,	PUNCT
ejpam-3977	75	6	...	...	PUNCT
ejpam-3977	75	7	,	,	PUNCT
ejpam-3977	75	8	v6	v6	PROPN
ejpam-3977	75	9	]	]	PUNCT
ejpam-3977	75	10	be	be	AUX
ejpam-3977	75	11	a	a	DET
ejpam-3977	75	12	path	path	NOUN
ejpam-3977	75	13	of	of	ADP
ejpam-3977	75	14	order	order	NOUN
ejpam-3977	75	15	6	6	NUM
ejpam-3977	75	16	and	and	CCONJ
ejpam-3977	75	17	s1	s1	PROPN
ejpam-3977	75	18	=	=	SYM
ejpam-3977	75	19	{	{	PUNCT
ejpam-3977	75	20	v1	v1	PROPN
ejpam-3977	75	21	,	,	PUNCT
ejpam-3977	75	22	v3	v3	PROPN
ejpam-3977	75	23	,	,	PUNCT
ejpam-3977	75	24	v5	v5	PROPN
ejpam-3977	75	25	,	,	PUNCT
ejpam-3977	75	26	v6	v6	NOUN
ejpam-3977	75	27	}	}	PUNCT
ejpam-3977	75	28	.	.	PUNCT
ejpam-3977	76	1	then	then	ADV
ejpam-3977	76	2	s1	s1	PROPN
ejpam-3977	76	3	is	be	AUX
ejpam-3977	76	4	both	both	PRON
ejpam-3977	76	5	2	2	NUM
ejpam-3977	76	6	-	-	PUNCT
ejpam-3977	76	7	locating	locate	VERB
ejpam-3977	76	8	and	and	CCONJ
ejpam-3977	76	9	2	2	NUM
ejpam-3977	76	10	-	-	PUNCT
ejpam-3977	76	11	resolving	resolve	VERB
ejpam-3977	76	12	set	set	VERB
ejpam-3977	76	13	in	in	ADP
ejpam-3977	76	14	p6	p6	PROPN
ejpam-3977	76	15	.	.	PUNCT
ejpam-3977	77	1	on	on	ADP
ejpam-3977	77	2	the	the	DET
ejpam-3977	77	3	other	other	ADJ
ejpam-3977	77	4	hand	hand	NOUN
ejpam-3977	77	5	,	,	PUNCT
ejpam-3977	77	6	s2	s2	NOUN
ejpam-3977	77	7	=	=	SYM
ejpam-3977	77	8	{	{	PUNCT
ejpam-3977	77	9	v2	v2	PROPN
ejpam-3977	77	10	,	,	PUNCT
ejpam-3977	77	11	v4	v4	PROPN
ejpam-3977	77	12	,	,	PUNCT
ejpam-3977	77	13	v6	v6	PROPN
ejpam-3977	77	14	}	}	PUNCT
ejpam-3977	77	15	is	be	AUX
ejpam-3977	77	16	a	a	DET
ejpam-3977	77	17	2	2	NUM
ejpam-3977	77	18	-	-	PUNCT
ejpam-3977	77	19	resolving	resolve	VERB
ejpam-3977	77	20	set	set	NOUN
ejpam-3977	77	21	but	but	CCONJ
ejpam-3977	77	22	not	not	PART
ejpam-3977	77	23	2	2	NUM
ejpam-3977	77	24	-	-	PUNCT
ejpam-3977	77	25	locating	locating	NOUN
ejpam-3977	77	26	.	.	PUNCT
ejpam-3977	77	27	example	example	NOUN
ejpam-3977	78	1	3	3	NUM
ejpam-3977	78	2	.	.	X
ejpam-3977	78	3	for	for	ADP
ejpam-3977	78	4	all	all	DET
ejpam-3977	78	5	n	n	PRON
ejpam-3977	78	6	≥	≥	NOUN
ejpam-3977	78	7	2	2	NUM
ejpam-3977	78	8	,	,	PUNCT
ejpam-3977	78	9	ln2(pn	ln2(pn	NOUN
ejpam-3977	78	10	)	)	PUNCT
ejpam-3977	78	11	=	=	PUNCT
ejpam-3977	78	12	⌈	⌈	SYM
ejpam-3977	78	13	n	n	CCONJ
ejpam-3977	78	14	+	+	CCONJ
ejpam-3977	78	15	1	1	NUM
ejpam-3977	78	16	2	2	NUM
ejpam-3977	78	17	⌉	⌉	X
ejpam-3977	78	18	.	.	PUNCT
ejpam-3977	79	1	example	example	NOUN
ejpam-3977	80	1	4	4	NUM
ejpam-3977	80	2	.	.	X
ejpam-3977	81	1	for	for	ADP
ejpam-3977	81	2	all	all	DET
ejpam-3977	81	3	n	n	PRON
ejpam-3977	81	4	≥	≥	NOUN
ejpam-3977	81	5	5	5	NUM
ejpam-3977	81	6	,	,	PUNCT
ejpam-3977	81	7	ln2(cn	ln2(cn	ADJ
ejpam-3977	81	8	)	)	PUNCT
ejpam-3977	81	9	=	=	PUNCT
ejpam-3977	81	10	⌈n	⌈n	NOUN
ejpam-3977	81	11	2	2	NUM
ejpam-3977	81	12	⌉	⌉	NOUN
ejpam-3977	81	13	and	and	CCONJ
ejpam-3977	81	14	ln2(c3	ln2(c3	NOUN
ejpam-3977	81	15	)	)	PUNCT
ejpam-3977	81	16	=	=	SYM
ejpam-3977	81	17	3	3	NUM
ejpam-3977	81	18	,	,	PUNCT
ejpam-3977	81	19	ln2(c4	ln2(c4	NOUN
ejpam-3977	81	20	)	)	PUNCT
ejpam-3977	81	21	=	=	SYM
ejpam-3977	81	22	4	4	X
ejpam-3977	81	23	.	.	X
ejpam-3977	81	24	definition	definition	NOUN
ejpam-3977	81	25	4	4	NUM
ejpam-3977	81	26	.	.	PUNCT
ejpam-3977	82	1	let	let	VERB
ejpam-3977	82	2	g	g	NOUN
ejpam-3977	82	3	be	be	AUX
ejpam-3977	82	4	any	any	DET
ejpam-3977	82	5	nontrivial	nontrivial	ADJ
ejpam-3977	82	6	connected	connect	VERB
ejpam-3977	82	7	graph	graph	NOUN
ejpam-3977	82	8	and	and	CCONJ
ejpam-3977	82	9	s	s	VERB
ejpam-3977	82	10	⊆	⊆	NUM
ejpam-3977	82	11	v	v	NOUN
ejpam-3977	82	12	(	(	PUNCT
ejpam-3977	82	13	g	g	NOUN
ejpam-3977	82	14	)	)	PUNCT
ejpam-3977	82	15	.	.	PUNCT
ejpam-3977	83	1	s	s	PART
ejpam-3977	83	2	is	be	AUX
ejpam-3977	83	3	a	a	DET
ejpam-3977	83	4	strictly	strictly	ADV
ejpam-3977	83	5	2	2	NUM
ejpam-3977	83	6	-	-	PUNCT
ejpam-3977	83	7	locating	locate	VERB
ejpam-3977	83	8	(	(	PUNCT
ejpam-3977	83	9	strictly	strictly	ADV
ejpam-3977	83	10	1	1	NUM
ejpam-3977	83	11	-	-	PUNCT
ejpam-3977	83	12	locating	locating	NOUN
ejpam-3977	83	13	)	)	PUNCT
ejpam-3977	83	14	set	set	NOUN
ejpam-3977	83	15	in	in	ADP
ejpam-3977	83	16	g	g	PROPN
ejpam-3977	83	17	if	if	SCONJ
ejpam-3977	83	18	s	s	NOUN
ejpam-3977	83	19	is	be	AUX
ejpam-3977	83	20	2	2	NUM
ejpam-3977	83	21	-	-	PUNCT
ejpam-3977	83	22	locating	locate	VERB
ejpam-3977	83	23	and	and	CCONJ
ejpam-3977	83	24	|ng(y	|ng(y	NUM
ejpam-3977	83	25	)	)	PUNCT
ejpam-3977	83	26	∩	∩	NOUN
ejpam-3977	83	27	s|	s|	VERB
ejpam-3977	83	28	≤	≤	NUM
ejpam-3977	83	29	|s|	|s|	PROPN
ejpam-3977	83	30	−	−	PROPN
ejpam-3977	83	31	2	2	NUM
ejpam-3977	83	32	(	(	PUNCT
ejpam-3977	83	33	|ng(y	|ng(y	NUM
ejpam-3977	83	34	)	)	PUNCT
ejpam-3977	83	35	∩	∩	NOUN
ejpam-3977	83	36	s|	s|	VERB
ejpam-3977	83	37	≤	≤	NUM
ejpam-3977	83	38	|s|	|s|	PROPN
ejpam-3977	83	39	−	−	PROPN
ejpam-3977	83	40	1	1	NUM
ejpam-3977	83	41	)	)	PUNCT
ejpam-3977	83	42	,	,	PUNCT
ejpam-3977	83	43	∀y	∀y	PROPN
ejpam-3977	83	44	∈	∈	PROPN
ejpam-3977	83	45	v	v	NOUN
ejpam-3977	83	46	(	(	PUNCT
ejpam-3977	83	47	g	g	NOUN
ejpam-3977	83	48	)	)	PUNCT
ejpam-3977	83	49	.	.	PUNCT
ejpam-3977	84	1	the	the	DET
ejpam-3977	84	2	strictly	strictly	ADV
ejpam-3977	84	3	2	2	NUM
ejpam-3977	84	4	-	-	PUNCT
ejpam-3977	84	5	locating	locate	VERB
ejpam-3977	84	6	(	(	PUNCT
ejpam-3977	84	7	strictly	strictly	ADV
ejpam-3977	84	8	1	1	NUM
ejpam-3977	84	9	-	-	PUNCT
ejpam-3977	84	10	locating	locate	VERB
ejpam-3977	84	11	)	)	PUNCT
ejpam-3977	84	12	number	number	NOUN
ejpam-3977	84	13	of	of	ADP
ejpam-3977	84	14	g	g	NOUN
ejpam-3977	84	15	,	,	PUNCT
ejpam-3977	84	16	denoted	denote	VERB
ejpam-3977	84	17	by	by	ADP
ejpam-3977	84	18	sln2(g	sln2(g	PRON
ejpam-3977	84	19	)	)	PUNCT
ejpam-3977	84	20	(	(	PUNCT
ejpam-3977	84	21	sln1(g	sln1(g	NOUN
ejpam-3977	84	22	)	)	PUNCT
ejpam-3977	84	23	)	)	PUNCT
ejpam-3977	84	24	,	,	PUNCT
ejpam-3977	84	25	is	be	AUX
ejpam-3977	84	26	the	the	DET
ejpam-3977	84	27	smallest	small	ADJ
ejpam-3977	84	28	cardinality	cardinality	NOUN
ejpam-3977	84	29	of	of	ADP
ejpam-3977	84	30	a	a	DET
ejpam-3977	84	31	strictly	strictly	ADV
ejpam-3977	84	32	2	2	NUM
ejpam-3977	84	33	-	-	PUNCT
ejpam-3977	84	34	locating	locate	VERB
ejpam-3977	84	35	(	(	PUNCT
ejpam-3977	84	36	strictly	strictly	ADV
ejpam-3977	84	37	1	1	NUM
ejpam-3977	84	38	-	-	PUNCT
ejpam-3977	84	39	locating	locating	NOUN
ejpam-3977	84	40	)	)	PUNCT
ejpam-3977	84	41	set	set	VERB
ejpam-3977	84	42	in	in	ADP
ejpam-3977	84	43	g.	g.	PROPN
ejpam-3977	84	44	a	a	DET
ejpam-3977	84	45	strictly	strictly	ADV
ejpam-3977	84	46	2	2	NUM
ejpam-3977	84	47	-	-	PUNCT
ejpam-3977	84	48	locating	locate	VERB
ejpam-3977	84	49	(	(	PUNCT
ejpam-3977	84	50	strictly	strictly	ADV
ejpam-3977	84	51	1	1	NUM
ejpam-3977	84	52	-	-	PUNCT
ejpam-3977	84	53	locating	locating	NOUN
ejpam-3977	84	54	)	)	PUNCT
ejpam-3977	84	55	set	set	NOUN
ejpam-3977	84	56	in	in	ADP
ejpam-3977	84	57	g	g	NOUN
ejpam-3977	84	58	of	of	ADP
ejpam-3977	84	59	cardinality	cardinality	NOUN
ejpam-3977	84	60	sln2(g	sln2(g	NUM
ejpam-3977	84	61	)	)	PUNCT
ejpam-3977	84	62	(	(	PUNCT
ejpam-3977	84	63	sln1(g	sln1(g	NOUN
ejpam-3977	84	64	)	)	PUNCT
ejpam-3977	84	65	)	)	PUNCT
ejpam-3977	84	66	is	be	AUX
ejpam-3977	84	67	referred	refer	VERB
ejpam-3977	84	68	to	to	ADP
ejpam-3977	84	69	as	as	ADP
ejpam-3977	84	70	sln2	sln2	NOUN
ejpam-3977	84	71	-	-	PUNCT
ejpam-3977	84	72	set	set	VERB
ejpam-3977	84	73	(	(	PUNCT
ejpam-3977	84	74	sln1	sln1	NOUN
ejpam-3977	84	75	-	-	PUNCT
ejpam-3977	84	76	set	set	NOUN
ejpam-3977	84	77	)	)	PUNCT
ejpam-3977	84	78	in	in	ADP
ejpam-3977	84	79	g.	g.	PROPN
ejpam-3977	84	80	example	example	NOUN
ejpam-3977	85	1	5	5	NUM
ejpam-3977	85	2	.	.	PUNCT
ejpam-3977	86	1	the	the	DET
ejpam-3977	86	2	set	set	ADJ
ejpam-3977	86	3	s2	s2	NOUN
ejpam-3977	86	4	=	=	PUNCT
ejpam-3977	86	5	{	{	PUNCT
ejpam-3977	86	6	a	a	PRON
ejpam-3977	86	7	,	,	PUNCT
ejpam-3977	86	8	b	b	NOUN
ejpam-3977	86	9	,	,	PUNCT
ejpam-3977	86	10	c	c	NOUN
ejpam-3977	86	11	,	,	PUNCT
ejpam-3977	86	12	f	f	X
ejpam-3977	86	13	}	}	PUNCT
ejpam-3977	86	14	is	be	AUX
ejpam-3977	86	15	a	a	DET
ejpam-3977	86	16	strictly	strictly	ADV
ejpam-3977	86	17	1	1	NUM
ejpam-3977	86	18	-	-	PUNCT
ejpam-3977	86	19	locating	locate	VERB
ejpam-3977	86	20	set	set	NOUN
ejpam-3977	86	21	in	in	ADP
ejpam-3977	86	22	g	g	NOUN
ejpam-3977	86	23	in	in	ADP
ejpam-3977	86	24	figure	figure	NOUN
ejpam-3977	86	25	1	1	NUM
ejpam-3977	86	26	.	.	PUNCT
ejpam-3977	87	1	moreover	moreover	ADV
ejpam-3977	87	2	,	,	PUNCT
ejpam-3977	87	3	s2	s2	PROPN
ejpam-3977	87	4	is	be	AUX
ejpam-3977	87	5	a	a	DET
ejpam-3977	87	6	sln1	sln1	NOUN
ejpam-3977	87	7	-	-	PUNCT
ejpam-3977	87	8	set	set	VERB
ejpam-3977	87	9	in	in	ADP
ejpam-3977	87	10	g.	g.	PROPN
ejpam-3977	87	11	thus	thus	ADV
ejpam-3977	87	12	,	,	PUNCT
ejpam-3977	87	13	sln1(g	sln1(g	X
ejpam-3977	87	14	)	)	PUNCT
ejpam-3977	87	15	=	=	SYM
ejpam-3977	87	16	4	4	NUM
ejpam-3977	87	17	.	.	NOUN
ejpam-3977	87	18	example	example	NOUN
ejpam-3977	87	19	6	6	NUM
ejpam-3977	87	20	.	.	PUNCT
ejpam-3977	88	1	the	the	DET
ejpam-3977	88	2	set	set	NOUN
ejpam-3977	88	3	s	s	PART
ejpam-3977	88	4	=	=	NOUN
ejpam-3977	88	5	{	{	PUNCT
ejpam-3977	88	6	u1	u1	NOUN
ejpam-3977	88	7	,	,	PUNCT
ejpam-3977	88	8	u3	u3	PROPN
ejpam-3977	88	9	,	,	PUNCT
ejpam-3977	88	10	u5	u5	PROPN
ejpam-3977	88	11	,	,	PUNCT
ejpam-3977	88	12	u7	u7	PROPN
ejpam-3977	88	13	}	}	PUNCT
ejpam-3977	88	14	is	be	AUX
ejpam-3977	88	15	a	a	DET
ejpam-3977	88	16	strictly	strictly	ADV
ejpam-3977	88	17	2	2	NUM
ejpam-3977	88	18	-	-	PUNCT
ejpam-3977	88	19	locating	locate	VERB
ejpam-3977	88	20	set	set	NOUN
ejpam-3977	88	21	in	in	ADP
ejpam-3977	88	22	p7	p7	NOUN
ejpam-3977	88	23	in	in	ADP
ejpam-3977	88	24	figure	figure	NOUN
ejpam-3977	88	25	2	2	NUM
ejpam-3977	88	26	.	.	PUNCT
ejpam-3977	89	1	moreover	moreover	ADV
ejpam-3977	89	2	,	,	PUNCT
ejpam-3977	89	3	s	s	VERB
ejpam-3977	89	4	is	be	AUX
ejpam-3977	89	5	a	a	DET
ejpam-3977	89	6	sln2	sln2	NOUN
ejpam-3977	89	7	-	-	PUNCT
ejpam-3977	89	8	set	set	VERB
ejpam-3977	89	9	in	in	ADP
ejpam-3977	89	10	p7	p7	PROPN
ejpam-3977	89	11	.	.	PUNCT
ejpam-3977	90	1	thus	thus	ADV
ejpam-3977	90	2	,	,	PUNCT
ejpam-3977	90	3	sln2(p7	sln2(p7	PROPN
ejpam-3977	90	4	)	)	PUNCT
ejpam-3977	90	5	=	=	PUNCT
ejpam-3977	90	6	4	4	X
ejpam-3977	90	7	.	.	PUNCT
ejpam-3977	90	8	....................................	....................................	PUNCT
ejpam-3977	90	9	....................................	....................................	PUNCT
ejpam-3977	90	10	....................................	....................................	PUNCT
ejpam-3977	90	11	....................................	....................................	PUNCT
ejpam-3977	90	12	....................................	....................................	PUNCT
ejpam-3977	90	13	....................................	....................................	PUNCT
ejpam-3977	90	14	.................................................................................................................................	.................................................................................................................................	PUNCT
ejpam-3977	90	15	.............................................................................................	.............................................................................................	PUNCT
ejpam-3977	91	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-3977	91	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-3977	91	3	.............................................................................................	.............................................................................................	PUNCT
ejpam-3977	92	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-3977	92	2	g	g	NOUN
ejpam-3977	92	3	:	:	PUNCT
ejpam-3977	92	4	u1	u1	PROPN
ejpam-3977	92	5	u2	u2	PROPN
ejpam-3977	92	6	u3	u3	PROPN
ejpam-3977	92	7	u4	u4	PROPN
ejpam-3977	92	8	u5	u5	PROPN
ejpam-3977	92	9	u6	u6	PROPN
ejpam-3977	92	10	u7	u7	PROPN
ejpam-3977	92	11	figure	figure	NOUN
ejpam-3977	92	12	2	2	NUM
ejpam-3977	92	13	:	:	PUNCT
ejpam-3977	92	14	a	a	DET
ejpam-3977	92	15	graph	graph	NOUN
ejpam-3977	92	16	p7	p7	VERB
ejpam-3977	92	17	with	with	ADP
ejpam-3977	92	18	sln2	sln2	NOUN
ejpam-3977	92	19	=	=	SYM
ejpam-3977	92	20	4	4	NUM
ejpam-3977	92	21	example	example	NOUN
ejpam-3977	92	22	7	7	NUM
ejpam-3977	92	23	.	.	X
ejpam-3977	93	1	for	for	ADP
ejpam-3977	93	2	all	all	DET
ejpam-3977	93	3	n	n	PRON
ejpam-3977	93	4	≥	≥	NOUN
ejpam-3977	93	5	4	4	NUM
ejpam-3977	93	6	,	,	PUNCT
ejpam-3977	93	7	sln1(pn	sln1(pn	NOUN
ejpam-3977	93	8	)	)	PUNCT
ejpam-3977	93	9	=	=	SYM
ejpam-3977	93	10	{	{	PUNCT
ejpam-3977	93	11	n	n	ADV
ejpam-3977	93	12	2	2	NUM
ejpam-3977	93	13	+	+	NUM
ejpam-3977	93	14	1	1	NUM
ejpam-3977	93	15	,	,	PUNCT
ejpam-3977	93	16	n	n	X
ejpam-3977	93	17	is	be	AUX
ejpam-3977	93	18	even⌈	even⌈	NOUN
ejpam-3977	93	19	n	n	CCONJ
ejpam-3977	93	20	2	2	NUM
ejpam-3977	93	21	⌉	⌉	X
ejpam-3977	93	22	,	,	PUNCT
ejpam-3977	93	23	n	n	X
ejpam-3977	93	24	is	be	AUX
ejpam-3977	93	25	odd	odd	ADJ
ejpam-3977	93	26	example	example	NOUN
ejpam-3977	93	27	8	8	NUM
ejpam-3977	93	28	.	.	PUNCT
ejpam-3977	94	1	for	for	ADP
ejpam-3977	94	2	all	all	DET
ejpam-3977	94	3	n	n	PRON
ejpam-3977	94	4	≥	≥	NUM
ejpam-3977	94	5	5	5	NUM
ejpam-3977	94	6	,	,	PUNCT
ejpam-3977	94	7	sln1(cn	sln1(cn	NOUN
ejpam-3977	94	8	)	)	PUNCT
ejpam-3977	94	9	=	=	NOUN
ejpam-3977	94	10	{	{	PUNCT
ejpam-3977	94	11	n	n	ADV
ejpam-3977	94	12	2	2	NUM
ejpam-3977	94	13	,	,	PUNCT
ejpam-3977	94	14	n	n	X
ejpam-3977	94	15	is	be	AUX
ejpam-3977	94	16	even⌈	even⌈	NOUN
ejpam-3977	94	17	n	n	CCONJ
ejpam-3977	94	18	2	2	NUM
ejpam-3977	94	19	⌉	⌉	X
ejpam-3977	94	20	,	,	PUNCT
ejpam-3977	94	21	n	n	X
ejpam-3977	94	22	is	be	AUX
ejpam-3977	94	23	odd	odd	ADJ
ejpam-3977	94	24	example	example	NOUN
ejpam-3977	95	1	9	9	NUM
ejpam-3977	95	2	.	.	PUNCT
ejpam-3977	96	1	for	for	ADP
ejpam-3977	96	2	all	all	DET
ejpam-3977	96	3	n	n	PRON
ejpam-3977	96	4	≥	≥	NUM
ejpam-3977	96	5	6	6	NUM
ejpam-3977	96	6	,	,	PUNCT
ejpam-3977	96	7	sln2(pn	sln2(pn	NUM
ejpam-3977	96	8	)	)	PUNCT
ejpam-3977	96	9	=	=	NOUN
ejpam-3977	96	10	{	{	PUNCT
ejpam-3977	96	11	n	n	ADV
ejpam-3977	96	12	2	2	NUM
ejpam-3977	96	13	+	+	NUM
ejpam-3977	96	14	1	1	NUM
ejpam-3977	96	15	,	,	PUNCT
ejpam-3977	96	16	n	n	X
ejpam-3977	96	17	is	be	AUX
ejpam-3977	96	18	even⌈	even⌈	NOUN
ejpam-3977	96	19	n	n	CCONJ
ejpam-3977	96	20	2	2	NUM
ejpam-3977	96	21	⌉	⌉	X
ejpam-3977	96	22	,	,	PUNCT
ejpam-3977	96	23	n	n	X
ejpam-3977	96	24	is	be	AUX
ejpam-3977	96	25	odd	odd	ADJ
ejpam-3977	96	26	example	example	NOUN
ejpam-3977	96	27	10	10	NUM
ejpam-3977	96	28	.	.	PUNCT
ejpam-3977	97	1	for	for	ADP
ejpam-3977	97	2	all	all	DET
ejpam-3977	97	3	n	n	PRON
ejpam-3977	97	4	≥	≥	NOUN
ejpam-3977	97	5	7	7	NUM
ejpam-3977	97	6	,	,	PUNCT
ejpam-3977	97	7	sln2(cn	sln2(cn	NOUN
ejpam-3977	97	8	)	)	PUNCT
ejpam-3977	97	9	=	=	PUNCT
ejpam-3977	97	10	{	{	PUNCT
ejpam-3977	97	11	n	n	ADV
ejpam-3977	97	12	2	2	NUM
ejpam-3977	97	13	,	,	PUNCT
ejpam-3977	97	14	n	n	X
ejpam-3977	97	15	is	be	AUX
ejpam-3977	97	16	even⌈	even⌈	NOUN
ejpam-3977	97	17	n	n	CCONJ
ejpam-3977	97	18	2	2	NUM
ejpam-3977	97	19	⌉	⌉	X
ejpam-3977	97	20	,	,	PUNCT
ejpam-3977	97	21	n	n	X
ejpam-3977	97	22	is	be	AUX
ejpam-3977	97	23	odd	odd	ADJ
ejpam-3977	97	24	remark	remark	NOUN
ejpam-3977	97	25	5	5	NUM
ejpam-3977	97	26	.	.	PUNCT
ejpam-3977	98	1	every	every	DET
ejpam-3977	98	2	strictly	strictly	ADV
ejpam-3977	98	3	2	2	NUM
ejpam-3977	98	4	-	-	PUNCT
ejpam-3977	98	5	locating	locate	VERB
ejpam-3977	98	6	set	set	NOUN
ejpam-3977	98	7	in	in	ADP
ejpam-3977	98	8	g	g	PROPN
ejpam-3977	98	9	is	be	AUX
ejpam-3977	98	10	strictly	strictly	ADV
ejpam-3977	98	11	1	1	NUM
ejpam-3977	98	12	-	-	PUNCT
ejpam-3977	98	13	locating	locating	NOUN
ejpam-3977	98	14	.	.	PUNCT
ejpam-3977	99	1	however	however	ADV
ejpam-3977	99	2	,	,	PUNCT
ejpam-3977	99	3	strictly	strictly	ADV
ejpam-3977	99	4	1	1	NUM
ejpam-3977	99	5	-	-	PUNCT
ejpam-3977	99	6	locating	locate	VERB
ejpam-3977	99	7	set	set	NOUN
ejpam-3977	99	8	in	in	ADP
ejpam-3977	99	9	g	g	NOUN
ejpam-3977	99	10	need	need	AUX
ejpam-3977	99	11	not	not	PART
ejpam-3977	99	12	be	be	AUX
ejpam-3977	99	13	a	a	DET
ejpam-3977	99	14	strictly	strictly	ADV
ejpam-3977	99	15	2	2	NUM
ejpam-3977	99	16	-	-	PUNCT
ejpam-3977	99	17	locating	locate	VERB
ejpam-3977	99	18	set	set	NOUN
ejpam-3977	99	19	in	in	ADP
ejpam-3977	99	20	g.	g.	PROPN
ejpam-3977	99	21	theorem	theorem	PROPN
ejpam-3977	99	22	2	2	NUM
ejpam-3977	99	23	.	.	PUNCT
ejpam-3977	100	1	a	a	DET
ejpam-3977	100	2	proper	proper	ADJ
ejpam-3977	100	3	subset	subset	NOUN
ejpam-3977	100	4	s	s	NOUN
ejpam-3977	100	5	of	of	ADP
ejpam-3977	100	6	v	v	NOUN
ejpam-3977	100	7	(	(	PUNCT
ejpam-3977	100	8	k1	k1	NOUN
ejpam-3977	100	9	+	+	CCONJ
ejpam-3977	100	10	kn	kn	PROPN
ejpam-3977	100	11	)	)	PUNCT
ejpam-3977	100	12	is	be	AUX
ejpam-3977	100	13	a	a	DET
ejpam-3977	100	14	2	2	NUM
ejpam-3977	100	15	-	-	PUNCT
ejpam-3977	100	16	resolving	resolving	NOUN
ejpam-3977	100	17	set	set	VERB
ejpam-3977	100	18	in	in	ADP
ejpam-3977	100	19	k1	k1	NOUN
ejpam-3977	100	20	+	+	CCONJ
ejpam-3977	100	21	kn	kn	PROPN
ejpam-3977	100	22	if	if	SCONJ
ejpam-3977	100	23	and	and	CCONJ
ejpam-3977	100	24	only	only	ADV
ejpam-3977	100	25	if	if	SCONJ
ejpam-3977	100	26	s	s	VERB
ejpam-3977	100	27	=	=	SYM
ejpam-3977	100	28	v	v	PROPN
ejpam-3977	100	29	(	(	PUNCT
ejpam-3977	100	30	kn	kn	PROPN
ejpam-3977	100	31	)	)	PUNCT
ejpam-3977	100	32	,	,	PUNCT
ejpam-3977	100	33	∀n	∀n	NUM
ejpam-3977	100	34	≥	≥	NOUN
ejpam-3977	100	35	2	2	X
ejpam-3977	100	36	.	.	PUNCT
ejpam-3977	100	37	j.	j.	PROPN
ejpam-3977	100	38	cabaro	cabaro	PROPN
ejpam-3977	100	39	,	,	PUNCT
ejpam-3977	100	40	h.	h.	PROPN
ejpam-3977	100	41	rara	rara	PROPN
ejpam-3977	100	42	/	/	SYM
ejpam-3977	100	43	eur	eur	PROPN
ejpam-3977	100	44	.	.	PUNCT
ejpam-3977	101	1	j.	j.	PROPN
ejpam-3977	101	2	pure	pure	PROPN
ejpam-3977	101	3	appl	appl	PROPN
ejpam-3977	101	4	.	.	PROPN
ejpam-3977	101	5	math	math	PROPN
ejpam-3977	101	6	,	,	PUNCT
ejpam-3977	101	7	14	14	NUM
ejpam-3977	101	8	(	(	PUNCT
ejpam-3977	101	9	3	3	NUM
ejpam-3977	101	10	)	)	PUNCT
ejpam-3977	101	11	(	(	PUNCT
ejpam-3977	101	12	2021	2021	NUM
ejpam-3977	101	13	)	)	PUNCT
ejpam-3977	101	14	,	,	PUNCT
ejpam-3977	101	15	773	773	NUM
ejpam-3977	101	16	-	-	SYM
ejpam-3977	101	17	782	782	NUM
ejpam-3977	101	18	777	777	NUM
ejpam-3977	101	19	proof	proof	NOUN
ejpam-3977	101	20	.	.	PUNCT
ejpam-3977	102	1	let	let	VERB
ejpam-3977	102	2	s	s	PRON
ejpam-3977	102	3	be	be	AUX
ejpam-3977	102	4	a	a	DET
ejpam-3977	102	5	proper	proper	ADJ
ejpam-3977	102	6	subset	subset	NOUN
ejpam-3977	102	7	of	of	ADP
ejpam-3977	102	8	v	v	NOUN
ejpam-3977	102	9	(	(	PUNCT
ejpam-3977	102	10	k1	k1	NOUN
ejpam-3977	102	11	+	+	CCONJ
ejpam-3977	102	12	kn	kn	PROPN
ejpam-3977	102	13	)	)	PUNCT
ejpam-3977	102	14	.	.	PUNCT
ejpam-3977	103	1	suppose	suppose	VERB
ejpam-3977	103	2	s	s	NOUN
ejpam-3977	103	3	is	be	AUX
ejpam-3977	103	4	a	a	DET
ejpam-3977	103	5	2	2	NUM
ejpam-3977	103	6	-	-	PUNCT
ejpam-3977	103	7	resolving	resolving	NOUN
ejpam-3977	103	8	set	set	VERB
ejpam-3977	103	9	in	in	ADP
ejpam-3977	103	10	k1	k1	PROPN
ejpam-3977	103	11	+	+	CCONJ
ejpam-3977	103	12	kn	kn	PROPN
ejpam-3977	103	13	and	and	CCONJ
ejpam-3977	103	14	suppose	suppose	VERB
ejpam-3977	103	15	∃x	∃x	PROPN
ejpam-3977	103	16	∈	∈	PROPN
ejpam-3977	103	17	v	v	NOUN
ejpam-3977	103	18	(	(	PUNCT
ejpam-3977	103	19	kn)\s	kn)\s	NOUN
ejpam-3977	103	20	.	.	PUNCT
ejpam-3977	104	1	then	then	ADV
ejpam-3977	104	2	r(x	r(x	PROPN
ejpam-3977	104	3	/	/	SYM
ejpam-3977	104	4	s	s	PART
ejpam-3977	104	5	)	)	PUNCT
ejpam-3977	104	6	and	and	CCONJ
ejpam-3977	104	7	r(y	r(y	VERB
ejpam-3977	104	8	/	/	SYM
ejpam-3977	104	9	s	s	PART
ejpam-3977	104	10	)	)	PUNCT
ejpam-3977	104	11	differ	differ	VERB
ejpam-3977	104	12	in	in	ADP
ejpam-3977	104	13	at	at	ADP
ejpam-3977	104	14	most	most	ADV
ejpam-3977	104	15	one	one	NUM
ejpam-3977	104	16	position	position	NOUN
ejpam-3977	104	17	for	for	ADP
ejpam-3977	104	18	each	each	DET
ejpam-3977	104	19	y	y	PROPN
ejpam-3977	104	20	∈	∈	PROPN
ejpam-3977	104	21	v	v	PROPN
ejpam-3977	104	22	(	(	PUNCT
ejpam-3977	104	23	kn	kn	PROPN
ejpam-3977	104	24	)	)	PUNCT
ejpam-3977	104	25	.	.	PUNCT
ejpam-3977	105	1	thus	thus	ADV
ejpam-3977	105	2	,	,	PUNCT
ejpam-3977	105	3	s	s	VERB
ejpam-3977	105	4	=	=	SYM
ejpam-3977	105	5	v	v	PROPN
ejpam-3977	105	6	(	(	PUNCT
ejpam-3977	105	7	kn	kn	PROPN
ejpam-3977	105	8	)	)	PUNCT
ejpam-3977	105	9	.	.	PUNCT
ejpam-3977	106	1	conversely	conversely	ADV
ejpam-3977	106	2	,	,	PUNCT
ejpam-3977	106	3	let	let	VERB
ejpam-3977	106	4	s	s	PRON
ejpam-3977	106	5	=	=	NOUN
ejpam-3977	106	6	v	v	PROPN
ejpam-3977	106	7	(	(	PUNCT
ejpam-3977	106	8	kn	kn	PROPN
ejpam-3977	106	9	)	)	PUNCT
ejpam-3977	106	10	and	and	CCONJ
ejpam-3977	106	11	x	x	PUNCT
ejpam-3977	106	12	∈	∈	PROPN
ejpam-3977	106	13	v	v	NOUN
ejpam-3977	106	14	(	(	PUNCT
ejpam-3977	106	15	k1	k1	NOUN
ejpam-3977	106	16	)	)	PUNCT
ejpam-3977	106	17	.	.	PUNCT
ejpam-3977	107	1	then	then	ADV
ejpam-3977	107	2	,	,	PUNCT
ejpam-3977	107	3	r(x	r(x	PROPN
ejpam-3977	107	4	/	/	SYM
ejpam-3977	107	5	s	s	NOUN
ejpam-3977	107	6	)	)	PUNCT
ejpam-3977	107	7	=	=	SYM
ejpam-3977	107	8	(	(	PUNCT
ejpam-3977	107	9	1	1	NUM
ejpam-3977	107	10	,	,	PUNCT
ejpam-3977	107	11	...	...	PUNCT
ejpam-3977	107	12	,	,	PUNCT
ejpam-3977	107	13	1	1	X
ejpam-3977	107	14	)	)	PUNCT
ejpam-3977	107	15	and	and	CCONJ
ejpam-3977	107	16	r(y	r(y	VERB
ejpam-3977	107	17	/	/	SYM
ejpam-3977	107	18	s	s	NOUN
ejpam-3977	107	19	)	)	PUNCT
ejpam-3977	107	20	=	=	SYM
ejpam-3977	107	21	(	(	PUNCT
ejpam-3977	107	22	...	...	PUNCT
ejpam-3977	107	23	,	,	PUNCT
ejpam-3977	107	24	2	2	NUM
ejpam-3977	107	25	,	,	PUNCT
ejpam-3977	107	26	2	2	NUM
ejpam-3977	107	27	,	,	PUNCT
ejpam-3977	107	28	2	2	NUM
ejpam-3977	107	29	,	,	PUNCT
ejpam-3977	107	30	0	0	NUM
ejpam-3977	107	31	,	,	PUNCT
ejpam-3977	107	32	2	2	NUM
ejpam-3977	107	33	,	,	PUNCT
ejpam-3977	107	34	...	...	PUNCT
ejpam-3977	107	35	)	)	PUNCT
ejpam-3977	108	1	for	for	ADP
ejpam-3977	108	2	each	each	DET
ejpam-3977	108	3	y	y	PROPN
ejpam-3977	108	4	∈	∈	PROPN
ejpam-3977	108	5	v	v	PROPN
ejpam-3977	108	6	(	(	PUNCT
ejpam-3977	108	7	kn	kn	PROPN
ejpam-3977	108	8	)	)	PUNCT
ejpam-3977	108	9	.	.	PUNCT
ejpam-3977	109	1	thus	thus	ADV
ejpam-3977	109	2	,	,	PUNCT
ejpam-3977	109	3	r(x	r(x	PROPN
ejpam-3977	109	4	/	/	SYM
ejpam-3977	109	5	s	s	NOUN
ejpam-3977	109	6	)	)	PUNCT
ejpam-3977	109	7	and	and	CCONJ
ejpam-3977	109	8	r(y	r(y	VERB
ejpam-3977	109	9	/	/	SYM
ejpam-3977	109	10	s	s	PART
ejpam-3977	109	11	)	)	PUNCT
ejpam-3977	109	12	differ	differ	VERB
ejpam-3977	109	13	in	in	ADP
ejpam-3977	109	14	at	at	ADV
ejpam-3977	109	15	least	least	ADV
ejpam-3977	109	16	two	two	NUM
ejpam-3977	109	17	positions	position	NOUN
ejpam-3977	109	18	.	.	PUNCT
ejpam-3977	110	1	therefore	therefore	ADV
ejpam-3977	110	2	s	s	VERB
ejpam-3977	110	3	is	be	AUX
ejpam-3977	110	4	a	a	DET
ejpam-3977	110	5	2	2	NUM
ejpam-3977	110	6	-	-	PUNCT
ejpam-3977	110	7	resolving	resolve	VERB
ejpam-3977	110	8	set	set	NOUN
ejpam-3977	110	9	of	of	ADP
ejpam-3977	110	10	k1	k1	PROPN
ejpam-3977	110	11	+	+	CCONJ
ejpam-3977	110	12	kn	kn	PROPN
ejpam-3977	110	13	.	.	PROPN
ejpam-3977	110	14	corollary	corollary	ADJ
ejpam-3977	110	15	1	1	NUM
ejpam-3977	110	16	.	.	PUNCT
ejpam-3977	110	17	dim2(k1	dim2(k1	PROPN
ejpam-3977	110	18	+	+	CCONJ
ejpam-3977	110	19	kn	kn	PROPN
ejpam-3977	110	20	)	)	PUNCT
ejpam-3977	110	21	=	=	SYM
ejpam-3977	110	22	|v	|v	PROPN
ejpam-3977	110	23	(	(	PUNCT
ejpam-3977	110	24	kn)|	kn)|	PROPN
ejpam-3977	110	25	.	.	PUNCT
ejpam-3977	111	1	theorem	theorem	NOUN
ejpam-3977	111	2	3	3	X
ejpam-3977	111	3	.	.	PUNCT
ejpam-3977	112	1	let	let	VERB
ejpam-3977	112	2	g	g	PRON
ejpam-3977	112	3	be	be	AUX
ejpam-3977	112	4	a	a	DET
ejpam-3977	112	5	connected	connected	ADJ
ejpam-3977	112	6	non	non	ADJ
ejpam-3977	112	7	-	-	ADJ
ejpam-3977	112	8	trivial	trivial	ADJ
ejpam-3977	112	9	graph	graph	NOUN
ejpam-3977	112	10	and	and	CCONJ
ejpam-3977	112	11	let	let	VERB
ejpam-3977	112	12	k1	k1	NOUN
ejpam-3977	112	13	=	=	SYM
ejpam-3977	112	14	{	{	PUNCT
ejpam-3977	112	15	v	v	NOUN
ejpam-3977	112	16	}	}	PUNCT
ejpam-3977	112	17	.	.	PUNCT
ejpam-3977	113	1	then	then	ADV
ejpam-3977	113	2	s	s	VERB
ejpam-3977	113	3	⊆	⊆	NUM
ejpam-3977	113	4	v	v	NOUN
ejpam-3977	113	5	(	(	PUNCT
ejpam-3977	113	6	k1	k1	NOUN
ejpam-3977	113	7	+	+	CCONJ
ejpam-3977	113	8	g	g	NOUN
ejpam-3977	113	9	)	)	PUNCT
ejpam-3977	113	10	is	be	AUX
ejpam-3977	113	11	a	a	DET
ejpam-3977	113	12	2	2	NUM
ejpam-3977	113	13	-	-	PUNCT
ejpam-3977	113	14	resolving	resolve	VERB
ejpam-3977	113	15	set	set	NOUN
ejpam-3977	113	16	of	of	ADP
ejpam-3977	113	17	k1	k1	NOUN
ejpam-3977	113	18	+	+	CCONJ
ejpam-3977	113	19	g	g	NOUN
ejpam-3977	113	20	if	if	SCONJ
ejpam-3977	113	21	and	and	CCONJ
ejpam-3977	113	22	only	only	ADV
ejpam-3977	113	23	if	if	SCONJ
ejpam-3977	113	24	either	either	PRON
ejpam-3977	113	25	v	v	NOUN
ejpam-3977	113	26	/∈	/∈	PUNCT
ejpam-3977	113	27	s	s	PART
ejpam-3977	113	28	and	and	CCONJ
ejpam-3977	113	29	s	s	VERB
ejpam-3977	113	30	is	be	AUX
ejpam-3977	113	31	strictly	strictly	ADV
ejpam-3977	113	32	2	2	NUM
ejpam-3977	113	33	-	-	PUNCT
ejpam-3977	113	34	locating	locate	VERB
ejpam-3977	113	35	set	set	NOUN
ejpam-3977	113	36	of	of	ADP
ejpam-3977	113	37	g	g	PROPN
ejpam-3977	113	38	or	or	CCONJ
ejpam-3977	113	39	s	s	NOUN
ejpam-3977	113	40	=	=	PUNCT
ejpam-3977	113	41	{	{	PUNCT
ejpam-3977	113	42	v	v	NOUN
ejpam-3977	113	43	}	}	PUNCT
ejpam-3977	113	44	∪	∪	NOUN
ejpam-3977	113	45	t	t	PROPN
ejpam-3977	113	46	,	,	PUNCT
ejpam-3977	113	47	where	where	SCONJ
ejpam-3977	113	48	t	t	PROPN
ejpam-3977	113	49	is	be	AUX
ejpam-3977	113	50	a	a	DET
ejpam-3977	113	51	strictly	strictly	ADV
ejpam-3977	113	52	1	1	NUM
ejpam-3977	113	53	-	-	PUNCT
ejpam-3977	113	54	locating	locate	VERB
ejpam-3977	113	55	set	set	NOUN
ejpam-3977	113	56	in	in	ADP
ejpam-3977	113	57	g.	g.	PROPN
ejpam-3977	113	58	proof	proof	PROPN
ejpam-3977	113	59	.	.	PUNCT
ejpam-3977	114	1	let	let	VERB
ejpam-3977	114	2	s	s	PRON
ejpam-3977	114	3	⊆	⊆	NUM
ejpam-3977	114	4	v	v	NOUN
ejpam-3977	114	5	(	(	PUNCT
ejpam-3977	114	6	k1	k1	NOUN
ejpam-3977	114	7	+	+	NOUN
ejpam-3977	114	8	g	g	NOUN
ejpam-3977	114	9	)	)	PUNCT
ejpam-3977	114	10	be	be	VERB
ejpam-3977	114	11	a	a	DET
ejpam-3977	114	12	2	2	NUM
ejpam-3977	114	13	-	-	PUNCT
ejpam-3977	114	14	resolving	resolve	VERB
ejpam-3977	114	15	set	set	NOUN
ejpam-3977	114	16	of	of	ADP
ejpam-3977	114	17	k1	k1	PROPN
ejpam-3977	114	18	+	+	PROPN
ejpam-3977	114	19	g.	g.	NOUN
ejpam-3977	115	1	if	if	SCONJ
ejpam-3977	115	2	v	v	NUM
ejpam-3977	115	3	/∈	/∈	PUNCT
ejpam-3977	116	1	s	s	X
ejpam-3977	116	2	,	,	PUNCT
ejpam-3977	116	3	then	then	ADV
ejpam-3977	116	4	s	s	VERB
ejpam-3977	116	5	⊆	⊆	NUM
ejpam-3977	116	6	v	v	NOUN
ejpam-3977	116	7	(	(	PUNCT
ejpam-3977	116	8	g	g	NOUN
ejpam-3977	116	9	)	)	PUNCT
ejpam-3977	116	10	is	be	AUX
ejpam-3977	116	11	2	2	NUM
ejpam-3977	116	12	-	-	PUNCT
ejpam-3977	116	13	locating	locate	VERB
ejpam-3977	116	14	set	set	NOUN
ejpam-3977	116	15	in	in	ADP
ejpam-3977	116	16	g.	g.	PROPN
ejpam-3977	116	17	suppose	suppose	VERB
ejpam-3977	116	18	there	there	PRON
ejpam-3977	116	19	exists	exist	VERB
ejpam-3977	116	20	y	y	PROPN
ejpam-3977	116	21	∈	∈	PROPN
ejpam-3977	116	22	v	v	ADP
ejpam-3977	116	23	(	(	PUNCT
ejpam-3977	116	24	g	g	NOUN
ejpam-3977	116	25	)	)	PUNCT
ejpam-3977	116	26	such	such	ADJ
ejpam-3977	116	27	that	that	SCONJ
ejpam-3977	116	28	|ng(y)∩s|	|ng(y)∩s|	PROPN
ejpam-3977	116	29	>	>	X
ejpam-3977	116	30	|s|	|s|	PROPN
ejpam-3977	116	31	−	−	PROPN
ejpam-3977	116	32	2	2	NUM
ejpam-3977	116	33	.	.	PUNCT
ejpam-3977	116	34	then	then	ADV
ejpam-3977	116	35	r(v	r(v	PROPN
ejpam-3977	116	36	/	/	SYM
ejpam-3977	116	37	s	s	PART
ejpam-3977	116	38	)	)	PUNCT
ejpam-3977	116	39	and	and	CCONJ
ejpam-3977	116	40	r(y	r(y	VERB
ejpam-3977	116	41	/	/	SYM
ejpam-3977	116	42	s	s	PART
ejpam-3977	116	43	)	)	PUNCT
ejpam-3977	116	44	differ	differ	VERB
ejpam-3977	116	45	in	in	ADP
ejpam-3977	116	46	at	at	ADP
ejpam-3977	116	47	most	most	ADV
ejpam-3977	116	48	one	one	NUM
ejpam-3977	116	49	position	position	NOUN
ejpam-3977	116	50	,	,	PUNCT
ejpam-3977	116	51	contrary	contrary	ADV
ejpam-3977	116	52	to	to	ADP
ejpam-3977	116	53	our	our	PRON
ejpam-3977	116	54	assumption	assumption	NOUN
ejpam-3977	116	55	that	that	SCONJ
ejpam-3977	116	56	s	s	VERB
ejpam-3977	116	57	is	be	AUX
ejpam-3977	116	58	a	a	DET
ejpam-3977	116	59	2	2	NUM
ejpam-3977	116	60	-	-	PUNCT
ejpam-3977	116	61	resolving	resolving	NOUN
ejpam-3977	116	62	set	set	VERB
ejpam-3977	116	63	in	in	ADP
ejpam-3977	116	64	k1	k1	PROPN
ejpam-3977	116	65	+	+	CCONJ
ejpam-3977	116	66	g.	g.	PROPN
ejpam-3977	116	67	hence	hence	ADV
ejpam-3977	116	68	,	,	PUNCT
ejpam-3977	116	69	s	s	VERB
ejpam-3977	116	70	is	be	AUX
ejpam-3977	116	71	a	a	DET
ejpam-3977	116	72	strictly	strictly	ADV
ejpam-3977	116	73	2	2	NUM
ejpam-3977	116	74	-	-	PUNCT
ejpam-3977	116	75	locating	locate	VERB
ejpam-3977	116	76	set	set	NOUN
ejpam-3977	116	77	of	of	ADP
ejpam-3977	116	78	k1	k1	PROPN
ejpam-3977	116	79	+	+	CCONJ
ejpam-3977	116	80	g.	g.	PROPN
ejpam-3977	116	81	next	next	ADV
ejpam-3977	116	82	,	,	PUNCT
ejpam-3977	116	83	suppose	suppose	VERB
ejpam-3977	116	84	that	that	SCONJ
ejpam-3977	116	85	s	s	VERB
ejpam-3977	116	86	=	=	X
ejpam-3977	116	87	t	t	X
ejpam-3977	116	88	∪	∪	X
ejpam-3977	116	89	{	{	PUNCT
ejpam-3977	116	90	v	v	NOUN
ejpam-3977	116	91	}	}	PUNCT
ejpam-3977	116	92	,	,	PUNCT
ejpam-3977	116	93	where	where	SCONJ
ejpam-3977	116	94	t	t	NOUN
ejpam-3977	116	95	=	=	SYM
ejpam-3977	116	96	v	v	PROPN
ejpam-3977	116	97	(	(	PUNCT
ejpam-3977	116	98	g	g	NOUN
ejpam-3977	116	99	)	)	PUNCT
ejpam-3977	116	100	∩	∩	PROPN
ejpam-3977	116	101	s.	s.	PROPN
ejpam-3977	116	102	then	then	ADV
ejpam-3977	116	103	∅	∅	VERB
ejpam-3977	116	104	6=	6=	ADP
ejpam-3977	116	105	t	t	PROPN
ejpam-3977	116	106	⊆	⊆	NUM
ejpam-3977	116	107	v	v	NOUN
ejpam-3977	116	108	(	(	PUNCT
ejpam-3977	116	109	g	g	NOUN
ejpam-3977	116	110	)	)	PUNCT
ejpam-3977	116	111	.	.	PUNCT
ejpam-3977	117	1	thus	thus	ADV
ejpam-3977	117	2	,	,	PUNCT
ejpam-3977	117	3	t	t	PROPN
ejpam-3977	117	4	is	be	AUX
ejpam-3977	117	5	a	a	DET
ejpam-3977	117	6	2	2	NUM
ejpam-3977	117	7	-	-	PUNCT
ejpam-3977	117	8	locating	locate	VERB
ejpam-3977	117	9	set	set	NOUN
ejpam-3977	117	10	in	in	ADP
ejpam-3977	117	11	g.	g.	PROPN
ejpam-3977	117	12	since	since	SCONJ
ejpam-3977	117	13	s	s	PROPN
ejpam-3977	117	14	is	be	AUX
ejpam-3977	117	15	a	a	DET
ejpam-3977	117	16	2	2	NUM
ejpam-3977	117	17	-	-	PUNCT
ejpam-3977	117	18	resolving	resolve	VERB
ejpam-3977	117	19	set	set	NOUN
ejpam-3977	117	20	and	and	CCONJ
ejpam-3977	117	21	v	v	ADP
ejpam-3977	117	22	∈	∈	PROPN
ejpam-3977	117	23	s	s	PROPN
ejpam-3977	117	24	,	,	PUNCT
ejpam-3977	117	25	t	t	PROPN
ejpam-3977	117	26	is	be	AUX
ejpam-3977	117	27	strictly	strictly	ADV
ejpam-3977	117	28	1	1	NUM
ejpam-3977	117	29	-	-	PUNCT
ejpam-3977	117	30	locating	locate	VERB
ejpam-3977	117	31	set	set	NOUN
ejpam-3977	117	32	in	in	ADP
ejpam-3977	117	33	g.	g.	PROPN
ejpam-3977	117	34	for	for	ADP
ejpam-3977	117	35	the	the	DET
ejpam-3977	117	36	converse	converse	NOUN
ejpam-3977	117	37	,	,	PUNCT
ejpam-3977	117	38	let	let	VERB
ejpam-3977	117	39	x	x	PRON
ejpam-3977	117	40	,	,	PUNCT
ejpam-3977	117	41	y	y	PROPN
ejpam-3977	117	42	∈	∈	PROPN
ejpam-3977	117	43	v	v	PROPN
ejpam-3977	117	44	(	(	PUNCT
ejpam-3977	117	45	k1	k1	NOUN
ejpam-3977	117	46	+	+	CCONJ
ejpam-3977	117	47	g	g	NOUN
ejpam-3977	117	48	)	)	PUNCT
ejpam-3977	117	49	.	.	PUNCT
ejpam-3977	118	1	first	first	ADV
ejpam-3977	118	2	,	,	PUNCT
ejpam-3977	118	3	assume	assume	VERB
ejpam-3977	118	4	that	that	SCONJ
ejpam-3977	118	5	v	v	AUX
ejpam-3977	118	6	/∈	/∈	PUNCT
ejpam-3977	118	7	s	s	PART
ejpam-3977	118	8	and	and	CCONJ
ejpam-3977	118	9	s	s	VERB
ejpam-3977	118	10	is	be	AUX
ejpam-3977	118	11	a	a	DET
ejpam-3977	118	12	strictly	strictly	ADV
ejpam-3977	118	13	2	2	NUM
ejpam-3977	118	14	-	-	PUNCT
ejpam-3977	118	15	locating	locate	VERB
ejpam-3977	118	16	set	set	NOUN
ejpam-3977	118	17	in	in	ADP
ejpam-3977	118	18	g.	g.	PROPN
ejpam-3977	118	19	consider	consider	VERB
ejpam-3977	118	20	the	the	DET
ejpam-3977	118	21	following	follow	VERB
ejpam-3977	118	22	cases	case	NOUN
ejpam-3977	118	23	.	.	PUNCT
ejpam-3977	119	1	case	case	NOUN
ejpam-3977	119	2	1	1	NUM
ejpam-3977	119	3	.	.	NUM
ejpam-3977	120	1	x	x	X
ejpam-3977	120	2	,	,	PUNCT
ejpam-3977	120	3	y	y	PROPN
ejpam-3977	120	4	∈	∈	PROPN
ejpam-3977	120	5	s	s	X
ejpam-3977	120	6	by	by	ADP
ejpam-3977	120	7	remark	remark	NOUN
ejpam-3977	120	8	3	3	NUM
ejpam-3977	120	9	,	,	PUNCT
ejpam-3977	120	10	rk1+g(x	rk1+g(x	NOUN
ejpam-3977	120	11	/	/	SYM
ejpam-3977	120	12	s	s	NOUN
ejpam-3977	120	13	)	)	PUNCT
ejpam-3977	120	14	and	and	CCONJ
ejpam-3977	120	15	rk1+g(y	rk1+g(y	PROPN
ejpam-3977	120	16	/	/	SYM
ejpam-3977	120	17	s	s	PART
ejpam-3977	120	18	)	)	PUNCT
ejpam-3977	120	19	differ	differ	VERB
ejpam-3977	120	20	in	in	ADP
ejpam-3977	120	21	at	at	ADV
ejpam-3977	120	22	least	least	ADJ
ejpam-3977	120	23	2	2	NUM
ejpam-3977	120	24	positions	position	NOUN
ejpam-3977	120	25	,	,	PUNCT
ejpam-3977	120	26	the	the	DET
ejpam-3977	120	27	xth	xth	PROPN
ejpam-3977	120	28	and	and	CCONJ
ejpam-3977	120	29	yth	yth	PROPN
ejpam-3977	120	30	positions	position	NOUN
ejpam-3977	120	31	.	.	PUNCT
ejpam-3977	121	1	case	case	NOUN
ejpam-3977	121	2	2	2	NUM
ejpam-3977	121	3	.	.	NUM
ejpam-3977	121	4	x	x	X
ejpam-3977	121	5	,	,	PUNCT
ejpam-3977	121	6	y	y	PROPN
ejpam-3977	121	7	∈	∈	PROPN
ejpam-3977	121	8	v	v	NOUN
ejpam-3977	121	9	(	(	PUNCT
ejpam-3977	121	10	g)\s	g)\s	NOUN
ejpam-3977	121	11	by	by	ADP
ejpam-3977	121	12	definition	definition	NOUN
ejpam-3977	121	13	3(i	3(i	NUM
ejpam-3977	121	14	)	)	PUNCT
ejpam-3977	121	15	,	,	PUNCT
ejpam-3977	121	16	rk1+g(x	rk1+g(x	NOUN
ejpam-3977	121	17	/	/	SYM
ejpam-3977	121	18	s	s	NOUN
ejpam-3977	121	19	)	)	PUNCT
ejpam-3977	121	20	and	and	CCONJ
ejpam-3977	121	21	rk1+g(y	rk1+g(y	PROPN
ejpam-3977	121	22	/	/	SYM
ejpam-3977	121	23	s	s	PART
ejpam-3977	121	24	)	)	PUNCT
ejpam-3977	121	25	differ	differ	VERB
ejpam-3977	121	26	in	in	ADP
ejpam-3977	121	27	the	the	DET
ejpam-3977	121	28	zth	zth	NOUN
ejpam-3977	121	29	and	and	CCONJ
ejpam-3977	121	30	wth	wth	NOUN
ejpam-3977	121	31	positions	position	NOUN
ejpam-3977	121	32	,	,	PUNCT
ejpam-3977	121	33	for	for	ADP
ejpam-3977	121	34	some	some	DET
ejpam-3977	121	35	distinct	distinct	ADJ
ejpam-3977	121	36	vertices	vertex	NOUN
ejpam-3977	121	37	z	z	NOUN
ejpam-3977	121	38	,	,	PUNCT
ejpam-3977	121	39	w	w	PROPN
ejpam-3977	121	40	∈	∈	PROPN
ejpam-3977	121	41	s.	s.	PROPN
ejpam-3977	121	42	case	case	NOUN
ejpam-3977	121	43	3	3	X
ejpam-3977	121	44	.	.	PUNCT
ejpam-3977	121	45	x	x	PUNCT
ejpam-3977	121	46	∈	∈	PROPN
ejpam-3977	121	47	s	s	PROPN
ejpam-3977	121	48	,	,	PUNCT
ejpam-3977	121	49	y	y	PROPN
ejpam-3977	121	50	∈	∈	PROPN
ejpam-3977	121	51	v	v	NOUN
ejpam-3977	121	52	(	(	PUNCT
ejpam-3977	121	53	g)\s	g)\s	NOUN
ejpam-3977	121	54	by	by	ADP
ejpam-3977	121	55	definition	definition	NOUN
ejpam-3977	121	56	3(ii	3(ii	NUM
ejpam-3977	121	57	)	)	PUNCT
ejpam-3977	121	58	,	,	PUNCT
ejpam-3977	121	59	there	there	PRON
ejpam-3977	121	60	exists	exist	VERB
ejpam-3977	121	61	z	z	PROPN
ejpam-3977	121	62	∈	∈	PROPN
ejpam-3977	121	63	(	(	PUNCT
ejpam-3977	121	64	ng(x	ng(x	NUM
ejpam-3977	121	65	)	)	PUNCT
ejpam-3977	121	66	∩	∩	ADJ
ejpam-3977	121	67	s)\ng(y	s)\ng(y	PROPN
ejpam-3977	121	68	)	)	PUNCT
ejpam-3977	121	69	or	or	CCONJ
ejpam-3977	121	70	z	z	NOUN
ejpam-3977	121	71	∈	∈	PROPN
ejpam-3977	121	72	(	(	PUNCT
ejpam-3977	121	73	ng(y	ng(y	NOUN
ejpam-3977	121	74	)	)	PUNCT
ejpam-3977	121	75	∩	∩	NOUN
ejpam-3977	121	76	s)\ng(x	s)\ng(x	NOUN
ejpam-3977	121	77	)	)	PUNCT
ejpam-3977	121	78	.	.	PUNCT
ejpam-3977	122	1	hence	hence	ADV
ejpam-3977	122	2	,	,	PUNCT
ejpam-3977	122	3	rk1+g(x	rk1+g(x	NOUN
ejpam-3977	122	4	/	/	SYM
ejpam-3977	122	5	s	s	NOUN
ejpam-3977	122	6	)	)	PUNCT
ejpam-3977	122	7	and	and	CCONJ
ejpam-3977	122	8	rk1+g(y	rk1+g(y	PROPN
ejpam-3977	122	9	/	/	SYM
ejpam-3977	122	10	s	s	PART
ejpam-3977	122	11	)	)	PUNCT
ejpam-3977	122	12	differ	differ	VERB
ejpam-3977	122	13	in	in	ADP
ejpam-3977	122	14	the	the	DET
ejpam-3977	122	15	xth	xth	PROPN
ejpam-3977	122	16	and	and	CCONJ
ejpam-3977	122	17	zth	zth	NOUN
ejpam-3977	122	18	positions	position	NOUN
ejpam-3977	122	19	.	.	PUNCT
ejpam-3977	123	1	case	case	NOUN
ejpam-3977	123	2	4	4	NUM
ejpam-3977	123	3	.	.	PUNCT
ejpam-3977	123	4	x	x	X
ejpam-3977	124	1	=	=	SYM
ejpam-3977	124	2	v	v	PROPN
ejpam-3977	124	3	,	,	PUNCT
ejpam-3977	124	4	y	y	PROPN
ejpam-3977	124	5	∈	∈	PROPN
ejpam-3977	124	6	v	v	NOUN
ejpam-3977	124	7	(	(	PUNCT
ejpam-3977	124	8	g	g	NOUN
ejpam-3977	124	9	)	)	PUNCT
ejpam-3977	124	10	.	.	PUNCT
ejpam-3977	125	1	by	by	ADP
ejpam-3977	125	2	definition	definition	NOUN
ejpam-3977	125	3	4	4	NUM
ejpam-3977	125	4	,	,	PUNCT
ejpam-3977	125	5	∃u	∃u	PROPN
ejpam-3977	125	6	,	,	PUNCT
ejpam-3977	125	7	w	w	PROPN
ejpam-3977	125	8	∈	∈	PROPN
ejpam-3977	125	9	s\ng(y	s\ng(y	NOUN
ejpam-3977	125	10	)	)	PUNCT
ejpam-3977	125	11	,	,	PUNCT
ejpam-3977	125	12	u	u	PROPN
ejpam-3977	125	13	6=	6=	PROPN
ejpam-3977	125	14	w.	w.	PROPN
ejpam-3977	125	15	thus	thus	ADV
ejpam-3977	125	16	,	,	PUNCT
ejpam-3977	125	17	rk1+g(x	rk1+g(x	NOUN
ejpam-3977	125	18	/	/	SYM
ejpam-3977	125	19	s	s	NOUN
ejpam-3977	125	20	)	)	PUNCT
ejpam-3977	125	21	and	and	CCONJ
ejpam-3977	125	22	rk1+g(y	rk1+g(y	PROPN
ejpam-3977	125	23	/	/	SYM
ejpam-3977	125	24	s	s	PART
ejpam-3977	125	25	)	)	PUNCT
ejpam-3977	125	26	differ	differ	VERB
ejpam-3977	125	27	in	in	ADP
ejpam-3977	125	28	the	the	DET
ejpam-3977	125	29	uth	uth	NOUN
ejpam-3977	125	30	and	and	CCONJ
ejpam-3977	125	31	wth	wth	NOUN
ejpam-3977	125	32	positions	position	NOUN
ejpam-3977	125	33	.	.	PUNCT
ejpam-3977	126	1	next	next	ADV
ejpam-3977	126	2	,	,	PUNCT
ejpam-3977	126	3	suppose	suppose	VERB
ejpam-3977	126	4	s	s	VERB
ejpam-3977	126	5	=	=	SYM
ejpam-3977	126	6	{	{	PUNCT
ejpam-3977	126	7	v	v	NOUN
ejpam-3977	126	8	}	}	PUNCT
ejpam-3977	126	9	∪	∪	ADP
ejpam-3977	126	10	t	t	PROPN
ejpam-3977	126	11	where	where	SCONJ
ejpam-3977	126	12	t	t	PROPN
ejpam-3977	126	13	is	be	AUX
ejpam-3977	126	14	strictly	strictly	ADV
ejpam-3977	126	15	1	1	NUM
ejpam-3977	126	16	-	-	PUNCT
ejpam-3977	126	17	locating	locate	VERB
ejpam-3977	126	18	set	set	NOUN
ejpam-3977	126	19	in	in	ADP
ejpam-3977	126	20	g.	g.	PROPN
ejpam-3977	126	21	consider	consider	VERB
ejpam-3977	126	22	the	the	DET
ejpam-3977	126	23	following	follow	VERB
ejpam-3977	126	24	cases	case	NOUN
ejpam-3977	126	25	.	.	PUNCT
ejpam-3977	127	1	case	case	NOUN
ejpam-3977	127	2	1	1	NUM
ejpam-3977	127	3	.	.	NUM
ejpam-3977	128	1	x	x	X
ejpam-3977	128	2	,	,	PUNCT
ejpam-3977	128	3	y	y	PROPN
ejpam-3977	128	4	∈	∈	PROPN
ejpam-3977	128	5	s	s	X
ejpam-3977	128	6	by	by	ADP
ejpam-3977	128	7	remark	remark	NOUN
ejpam-3977	128	8	3	3	NUM
ejpam-3977	128	9	,	,	PUNCT
ejpam-3977	128	10	rk1+g(x	rk1+g(x	NOUN
ejpam-3977	128	11	/	/	SYM
ejpam-3977	128	12	s	s	NOUN
ejpam-3977	128	13	)	)	PUNCT
ejpam-3977	128	14	and	and	CCONJ
ejpam-3977	128	15	rk1+g(y	rk1+g(y	PROPN
ejpam-3977	128	16	/	/	SYM
ejpam-3977	128	17	s	s	PART
ejpam-3977	128	18	)	)	PUNCT
ejpam-3977	128	19	differ	differ	VERB
ejpam-3977	128	20	in	in	ADP
ejpam-3977	128	21	at	at	ADV
ejpam-3977	128	22	least	least	ADJ
ejpam-3977	128	23	2	2	NUM
ejpam-3977	128	24	positions	position	NOUN
ejpam-3977	128	25	,	,	PUNCT
ejpam-3977	128	26	the	the	DET
ejpam-3977	128	27	xth	xth	PROPN
ejpam-3977	128	28	and	and	CCONJ
ejpam-3977	128	29	yth	yth	PROPN
ejpam-3977	128	30	positions	position	NOUN
ejpam-3977	128	31	.	.	PUNCT
ejpam-3977	129	1	case	case	NOUN
ejpam-3977	129	2	2	2	NUM
ejpam-3977	129	3	.	.	NUM
ejpam-3977	129	4	x	x	X
ejpam-3977	129	5	,	,	PUNCT
ejpam-3977	129	6	y	y	PROPN
ejpam-3977	129	7	∈	∈	PROPN
ejpam-3977	129	8	v	v	PROPN
ejpam-3977	129	9	(	(	PUNCT
ejpam-3977	129	10	k1	k1	NOUN
ejpam-3977	129	11	+	+	CCONJ
ejpam-3977	129	12	g)\s	g)\s	NOUN
ejpam-3977	129	13	.	.	PUNCT
ejpam-3977	130	1	then	then	ADV
ejpam-3977	130	2	x	x	X
ejpam-3977	130	3	,	,	PUNCT
ejpam-3977	130	4	y	y	PROPN
ejpam-3977	130	5	∈	∈	PROPN
ejpam-3977	130	6	v	v	PROPN
ejpam-3977	130	7	(	(	PUNCT
ejpam-3977	130	8	g)\t	g)\t	NOUN
ejpam-3977	130	9	.	.	PUNCT
ejpam-3977	131	1	by	by	ADP
ejpam-3977	131	2	definition	definition	NOUN
ejpam-3977	131	3	3(i	3(i	NUM
ejpam-3977	131	4	)	)	PUNCT
ejpam-3977	131	5	,	,	PUNCT
ejpam-3977	131	6	rk1+g(x	rk1+g(x	NOUN
ejpam-3977	131	7	/	/	SYM
ejpam-3977	131	8	s	s	AUX
ejpam-3977	131	9	)	)	PUNCT
ejpam-3977	131	10	and	and	CCONJ
ejpam-3977	131	11	rk1+g(y	rk1+g(y	PROPN
ejpam-3977	131	12	/	/	SYM
ejpam-3977	131	13	s	s	PART
ejpam-3977	131	14	)	)	PUNCT
ejpam-3977	131	15	differ	differ	VERB
ejpam-3977	131	16	in	in	ADP
ejpam-3977	131	17	at	at	ADV
ejpam-3977	131	18	least	least	ADJ
ejpam-3977	131	19	2	2	NUM
ejpam-3977	131	20	positions	position	NOUN
ejpam-3977	131	21	.	.	PUNCT
ejpam-3977	132	1	case	case	NOUN
ejpam-3977	132	2	3	3	NUM
ejpam-3977	132	3	.	.	PUNCT
ejpam-3977	132	4	x	x	X
ejpam-3977	133	1	=	=	SYM
ejpam-3977	133	2	v	v	PROPN
ejpam-3977	133	3	,	,	PUNCT
ejpam-3977	133	4	y	y	PROPN
ejpam-3977	133	5	∈	∈	PROPN
ejpam-3977	133	6	v	v	NOUN
ejpam-3977	133	7	(	(	PUNCT
ejpam-3977	133	8	g	g	NOUN
ejpam-3977	133	9	)	)	PUNCT
ejpam-3977	133	10	.	.	PUNCT
ejpam-3977	134	1	by	by	ADP
ejpam-3977	134	2	definition	definition	NOUN
ejpam-3977	134	3	4	4	NUM
ejpam-3977	134	4	,	,	PUNCT
ejpam-3977	134	5	∃z	∃z	PROPN
ejpam-3977	134	6	∈	∈	PROPN
ejpam-3977	134	7	t\ng(y	t\ng(y	PROPN
ejpam-3977	134	8	)	)	PUNCT
ejpam-3977	134	9	.	.	PUNCT
ejpam-3977	135	1	thus	thus	ADV
ejpam-3977	135	2	,	,	PUNCT
ejpam-3977	135	3	rk1+g(x	rk1+g(x	NOUN
ejpam-3977	135	4	/	/	SYM
ejpam-3977	135	5	s	s	NOUN
ejpam-3977	135	6	)	)	PUNCT
ejpam-3977	135	7	and	and	CCONJ
ejpam-3977	135	8	rk1+g(y	rk1+g(y	PROPN
ejpam-3977	135	9	/	/	SYM
ejpam-3977	135	10	s	s	PART
ejpam-3977	135	11	)	)	PUNCT
ejpam-3977	135	12	differ	differ	VERB
ejpam-3977	135	13	in	in	ADP
ejpam-3977	135	14	the	the	DET
ejpam-3977	135	15	xth	xth	PROPN
ejpam-3977	135	16	j.	j.	PROPN
ejpam-3977	135	17	cabaro	cabaro	PROPN
ejpam-3977	135	18	,	,	PUNCT
ejpam-3977	135	19	h.	h.	PROPN
ejpam-3977	135	20	rara	rara	PROPN
ejpam-3977	135	21	/	/	SYM
ejpam-3977	135	22	eur	eur	PROPN
ejpam-3977	135	23	.	.	PUNCT
ejpam-3977	136	1	j.	j.	PROPN
ejpam-3977	136	2	pure	pure	PROPN
ejpam-3977	136	3	appl	appl	PROPN
ejpam-3977	136	4	.	.	PROPN
ejpam-3977	136	5	math	math	PROPN
ejpam-3977	136	6	,	,	PUNCT
ejpam-3977	136	7	14	14	NUM
ejpam-3977	136	8	(	(	PUNCT
ejpam-3977	136	9	3	3	NUM
ejpam-3977	136	10	)	)	PUNCT
ejpam-3977	136	11	(	(	PUNCT
ejpam-3977	136	12	2021	2021	NUM
ejpam-3977	136	13	)	)	PUNCT
ejpam-3977	136	14	,	,	PUNCT
ejpam-3977	136	15	773	773	NUM
ejpam-3977	136	16	-	-	SYM
ejpam-3977	136	17	782	782	NUM
ejpam-3977	136	18	778	778	NUM
ejpam-3977	136	19	and	and	CCONJ
ejpam-3977	136	20	zth	zth	NOUN
ejpam-3977	136	21	positions	position	NOUN
ejpam-3977	136	22	.	.	PUNCT
ejpam-3977	137	1	case	case	NOUN
ejpam-3977	137	2	4	4	NUM
ejpam-3977	137	3	.	.	PUNCT
ejpam-3977	137	4	x	x	SYM
ejpam-3977	137	5	∈	∈	PROPN
ejpam-3977	137	6	t	t	NOUN
ejpam-3977	137	7	,	,	PUNCT
ejpam-3977	137	8	y	y	PROPN
ejpam-3977	137	9	∈	∈	PROPN
ejpam-3977	137	10	v	v	PROPN
ejpam-3977	137	11	(	(	PUNCT
ejpam-3977	137	12	g)\t	g)\t	PROPN
ejpam-3977	137	13	.	.	PUNCT
ejpam-3977	138	1	since	since	SCONJ
ejpam-3977	138	2	t	t	PROPN
ejpam-3977	138	3	is	be	AUX
ejpam-3977	138	4	2	2	NUM
ejpam-3977	138	5	-	-	PUNCT
ejpam-3977	138	6	locating	locate	VERB
ejpam-3977	138	7	set	set	NOUN
ejpam-3977	138	8	in	in	ADP
ejpam-3977	138	9	g	g	NOUN
ejpam-3977	138	10	,	,	PUNCT
ejpam-3977	138	11	rg(x	rg(x	X
ejpam-3977	138	12	/	/	SYM
ejpam-3977	138	13	t	t	NOUN
ejpam-3977	138	14	)	)	PUNCT
ejpam-3977	138	15	and	and	CCONJ
ejpam-3977	138	16	rg(y	rg(y	NOUN
ejpam-3977	138	17	/	/	SYM
ejpam-3977	138	18	t	t	PROPN
ejpam-3977	138	19	)	)	PUNCT
ejpam-3977	138	20	differ	differ	VERB
ejpam-3977	138	21	in	in	ADP
ejpam-3977	138	22	at	at	ADV
ejpam-3977	138	23	least	least	ADJ
ejpam-3977	138	24	2	2	NUM
ejpam-3977	138	25	positions	position	NOUN
ejpam-3977	138	26	.	.	PUNCT
ejpam-3977	139	1	hence	hence	ADV
ejpam-3977	139	2	,	,	PUNCT
ejpam-3977	139	3	rk1+g(x	rk1+g(x	NOUN
ejpam-3977	139	4	/	/	SYM
ejpam-3977	139	5	s	s	NOUN
ejpam-3977	139	6	)	)	PUNCT
ejpam-3977	139	7	and	and	CCONJ
ejpam-3977	139	8	rk1+g(y	rk1+g(y	PROPN
ejpam-3977	139	9	/	/	SYM
ejpam-3977	139	10	s	s	PART
ejpam-3977	139	11	)	)	PUNCT
ejpam-3977	139	12	differ	differ	VERB
ejpam-3977	139	13	also	also	ADV
ejpam-3977	139	14	in	in	ADP
ejpam-3977	139	15	at	at	ADV
ejpam-3977	139	16	least	least	ADJ
ejpam-3977	139	17	2	2	NUM
ejpam-3977	139	18	positions	position	NOUN
ejpam-3977	139	19	.	.	PUNCT
ejpam-3977	140	1	therefore	therefore	ADV
ejpam-3977	140	2	,	,	PUNCT
ejpam-3977	140	3	s	s	VERB
ejpam-3977	140	4	is	be	AUX
ejpam-3977	140	5	a	a	DET
ejpam-3977	140	6	2	2	NUM
ejpam-3977	140	7	-	-	PUNCT
ejpam-3977	140	8	resolving	resolving	NOUN
ejpam-3977	140	9	set	set	VERB
ejpam-3977	140	10	in	in	ADP
ejpam-3977	140	11	k1	k1	PROPN
ejpam-3977	140	12	+	+	CCONJ
ejpam-3977	140	13	g.	g.	NOUN
ejpam-3977	140	14	the	the	DET
ejpam-3977	140	15	sets	set	NOUN
ejpam-3977	140	16	{	{	PUNCT
ejpam-3977	140	17	u	u	NOUN
ejpam-3977	140	18	,	,	PUNCT
ejpam-3977	140	19	u1	u1	NOUN
ejpam-3977	140	20	,	,	PUNCT
ejpam-3977	140	21	u3	u3	PROPN
ejpam-3977	140	22	,	,	PUNCT
ejpam-3977	140	23	u4	u4	PROPN
ejpam-3977	140	24	}	}	PUNCT
ejpam-3977	140	25	and	and	CCONJ
ejpam-3977	140	26	{	{	PUNCT
ejpam-3977	140	27	v	v	NOUN
ejpam-3977	140	28	,	,	PUNCT
ejpam-3977	140	29	v1	v1	NOUN
ejpam-3977	140	30	,	,	PUNCT
ejpam-3977	140	31	v3	v3	PROPN
ejpam-3977	140	32	,	,	PUNCT
ejpam-3977	140	33	v5	v5	PROPN
ejpam-3977	140	34	}	}	PUNCT
ejpam-3977	140	35	are	be	AUX
ejpam-3977	140	36	2	2	NUM
ejpam-3977	140	37	-	-	PUNCT
ejpam-3977	140	38	resolving	resolve	VERB
ejpam-3977	140	39	sets	set	NOUN
ejpam-3977	140	40	in	in	ADP
ejpam-3977	140	41	the	the	DET
ejpam-3977	140	42	join	join	NOUN
ejpam-3977	140	43	〈	〈	PROPN
ejpam-3977	140	44	u〉+	u〉+	PROPN
ejpam-3977	140	45	p5	p5	NOUN
ejpam-3977	140	46	and	and	CCONJ
ejpam-3977	140	47	〈	〈	PROPN
ejpam-3977	140	48	v〉+	v〉+	PROPN
ejpam-3977	140	49	c6	c6	PROPN
ejpam-3977	140	50	,	,	PUNCT
ejpam-3977	140	51	respectively	respectively	ADV
ejpam-3977	140	52	,	,	PUNCT
ejpam-3977	140	53	in	in	ADP
ejpam-3977	140	54	figure	figure	NOUN
ejpam-3977	140	55	3	3	NUM
ejpam-3977	140	56	.	.	PUNCT
ejpam-3977	140	57	....................................	....................................	PUNCT
ejpam-3977	140	58	....................................	....................................	PUNCT
ejpam-3977	141	1	....................................	....................................	PUNCT
ejpam-3977	141	2	....................................	....................................	PUNCT
ejpam-3977	142	1	....................................	....................................	PUNCT
ejpam-3977	142	2	....................................	....................................	PUNCT
ejpam-3977	143	1	....................................	....................................	PUNCT
ejpam-3977	143	2	....................................	....................................	PUNCT
ejpam-3977	144	1	....................................	....................................	PUNCT
ejpam-3977	144	2	....................................	....................................	PUNCT
ejpam-3977	145	1	....................................	....................................	PUNCT
ejpam-3977	145	2	....................................	....................................	PUNCT
ejpam-3977	146	1	..............	..............	PUNCT
ejpam-3977	146	2	.............	.............	PUNCT
ejpam-3977	146	3	.............	.............	PUNCT
ejpam-3977	146	4	.............	.............	PUNCT
ejpam-3977	146	5	.............	.............	PUNCT
ejpam-3977	146	6	.............	.............	PUNCT
ejpam-3977	146	7	.............	.............	PUNCT
ejpam-3977	146	8	.............	.............	PUNCT
ejpam-3977	146	9	.............	.............	PUNCT
ejpam-3977	146	10	.............	.............	PUNCT
ejpam-3977	146	11	.............	.............	PUNCT
ejpam-3977	146	12	.............	.............	PUNCT
ejpam-3977	146	13	.............	.............	PUNCT
ejpam-3977	146	14	.............	.............	PUNCT
ejpam-3977	146	15	.............	.............	PUNCT
ejpam-3977	146	16	.............	.............	PUNCT
ejpam-3977	146	17	.............	.............	PUNCT
ejpam-3977	146	18	.............	.............	PUNCT
ejpam-3977	146	19	.............	.............	PUNCT
ejpam-3977	146	20	..	..	PUNCT
ejpam-3977	146	21	.................................	.................................	PUNCT
ejpam-3977	146	22	................................	................................	PUNCT
ejpam-3977	146	23	................................	................................	PUNCT
ejpam-3977	146	24	................................	................................	PUNCT
ejpam-3977	146	25	................................	................................	PUNCT
ejpam-3977	146	26	................................	................................	PUNCT
ejpam-3977	146	27	...........	...........	PUNCT
ejpam-3977	146	28	............................................................................................................................................................................................................	............................................................................................................................................................................................................	PUNCT
ejpam-3977	147	1	..........................................................................................................................................................................................................................................................	..........................................................................................................................................................................................................................................................	PUNCT
ejpam-3977	147	2	.........	.........	PUNCT
ejpam-3977	148	1	........	........	PUNCT
ejpam-3977	148	2	........	........	PUNCT
ejpam-3977	148	3	........	........	PUNCT
ejpam-3977	148	4	........	........	PUNCT
ejpam-3977	148	5	........	........	PUNCT
ejpam-3977	148	6	........	........	PUNCT
ejpam-3977	148	7	........	........	PUNCT
ejpam-3977	148	8	........	........	PUNCT
ejpam-3977	148	9	........	........	PUNCT
ejpam-3977	148	10	........	........	PUNCT
ejpam-3977	149	1	....	....	PUNCT
ejpam-3977	149	2	.........	.........	PUNCT
ejpam-3977	149	3	........	........	PUNCT
ejpam-3977	149	4	........	........	PUNCT
ejpam-3977	149	5	........	........	PUNCT
ejpam-3977	149	6	........	........	PUNCT
ejpam-3977	149	7	........	........	PUNCT
ejpam-3977	149	8	........	........	PUNCT
ejpam-3977	149	9	........	........	PUNCT
ejpam-3977	149	10	........	........	PUNCT
ejpam-3977	149	11	........	........	PUNCT
ejpam-3977	149	12	........	........	PUNCT
ejpam-3977	150	1	....	....	PUNCT
ejpam-3977	150	2	.........	.........	PUNCT
ejpam-3977	150	3	........	........	PUNCT
ejpam-3977	150	4	........	........	PUNCT
ejpam-3977	150	5	........	........	PUNCT
ejpam-3977	150	6	........	........	PUNCT
ejpam-3977	150	7	........	........	PUNCT
ejpam-3977	150	8	........	........	PUNCT
ejpam-3977	150	9	........	........	PUNCT
ejpam-3977	150	10	........	........	PUNCT
ejpam-3977	150	11	........	........	PUNCT
ejpam-3977	150	12	........	........	PUNCT
ejpam-3977	151	1	....	....	PUNCT
ejpam-3977	151	2	............	............	PUNCT
ejpam-3977	151	3	...........	...........	PUNCT
ejpam-3977	151	4	...........	...........	PUNCT
ejpam-3977	151	5	...........	...........	PUNCT
ejpam-3977	151	6	...........	...........	PUNCT
ejpam-3977	151	7	...........	...........	PUNCT
ejpam-3977	151	8	...........	...........	PUNCT
ejpam-3977	151	9	...........	...........	PUNCT
ejpam-3977	151	10	...........	...........	PUNCT
ejpam-3977	151	11	...........	...........	PUNCT
ejpam-3977	151	12	...........	...........	PUNCT
ejpam-3977	151	13	...........	...........	PUNCT
ejpam-3977	151	14	...	...	PUNCT
ejpam-3977	151	15	..............	..............	PUNCT
ejpam-3977	151	16	.............	.............	PUNCT
ejpam-3977	151	17	.............	.............	PUNCT
ejpam-3977	151	18	.............	.............	PUNCT
ejpam-3977	151	19	.............	.............	PUNCT
ejpam-3977	151	20	.............	.............	PUNCT
ejpam-3977	151	21	.............	.............	PUNCT
ejpam-3977	151	22	.............	.............	PUNCT
ejpam-3977	151	23	.............	.............	PUNCT
ejpam-3977	151	24	.............	.............	PUNCT
ejpam-3977	151	25	.............	.............	PUNCT
ejpam-3977	151	26	.............	.............	PUNCT
ejpam-3977	151	27	.............	.............	PUNCT
ejpam-3977	151	28	.............	.............	PUNCT
ejpam-3977	151	29	.............	.............	PUNCT
ejpam-3977	151	30	.............	.............	PUNCT
ejpam-3977	151	31	.............	.............	PUNCT
ejpam-3977	151	32	.............	.............	PUNCT
ejpam-3977	151	33	.............	.............	PUNCT
ejpam-3977	151	34	..	..	PUNCT
ejpam-3977	151	35	..........................	..........................	PUNCT
ejpam-3977	151	36	.........................	.........................	PUNCT
ejpam-3977	151	37	.........................	.........................	PUNCT
ejpam-3977	151	38	.........................	.........................	PUNCT
ejpam-3977	151	39	.........................	.........................	PUNCT
ejpam-3977	151	40	.........................	.........................	PUNCT
ejpam-3977	151	41	.........................	.........................	PUNCT
ejpam-3977	151	42	.........................	.........................	PUNCT
ejpam-3977	151	43	.........................	.........................	PUNCT
ejpam-3977	151	44	.........................	.........................	PUNCT
ejpam-3977	151	45	.........................	.........................	PUNCT
ejpam-3977	151	46	.........................	.........................	PUNCT
ejpam-3977	152	1	................	................	PUNCT
ejpam-3977	152	2	.............................................................................................................................................................................................................................................................................................................................	.............................................................................................................................................................................................................................................................................................................................	PROPN
ejpam-3977	152	3	..........................................................................................................................................................................................................................................................	..........................................................................................................................................................................................................................................................	PUNCT
ejpam-3977	153	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-3977	153	2	...................	...................	PUNCT
ejpam-3977	154	1	..................	..................	PUNCT
ejpam-3977	154	2	..................	..................	PUNCT
ejpam-3977	155	1	..................	..................	PUNCT
ejpam-3977	155	2	..................	..................	PUNCT
ejpam-3977	155	3	...............	...............	PUNCT
ejpam-3977	155	4	..........................................................................................................	..........................................................................................................	PUNCT
ejpam-3977	156	1	.........	.........	PUNCT
ejpam-3977	156	2	........	........	PUNCT
ejpam-3977	156	3	........	........	PUNCT
ejpam-3977	156	4	........	........	PUNCT
ejpam-3977	156	5	........	........	PUNCT
ejpam-3977	156	6	........	........	PUNCT
ejpam-3977	156	7	........	........	PUNCT
ejpam-3977	156	8	........	........	PUNCT
ejpam-3977	156	9	........	........	PUNCT
ejpam-3977	156	10	........	........	PUNCT
ejpam-3977	156	11	........	........	PUNCT
ejpam-3977	156	12	........	........	PUNCT
ejpam-3977	156	13	........	........	PUNCT
ejpam-3977	156	14	........	........	PUNCT
ejpam-3977	156	15	........	........	PUNCT
ejpam-3977	156	16	........	........	PUNCT
ejpam-3977	156	17	........	........	PUNCT
ejpam-3977	156	18	........	........	PUNCT
ejpam-3977	156	19	........	........	PUNCT
ejpam-3977	156	20	........	........	PUNCT
ejpam-3977	156	21	........	........	PUNCT
ejpam-3977	156	22	........	........	PUNCT
ejpam-3977	157	1	........	........	PUNCT
ejpam-3977	157	2	........	........	PUNCT
ejpam-3977	158	1	.....	.....	PUNCT
ejpam-3977	158	2	...................	...................	PUNCT
ejpam-3977	159	1	..................	..................	PUNCT
ejpam-3977	159	2	..................	..................	PUNCT
ejpam-3977	160	1	..................	..................	PUNCT
ejpam-3977	160	2	..................	..................	PUNCT
ejpam-3977	161	1	.........................................................................................................................	.........................................................................................................................	PUNCT
ejpam-3977	161	2	{	{	PUNCT
ejpam-3977	161	3	u}+	u}+	NUM
ejpam-3977	161	4	p5	p5	ADJ
ejpam-3977	161	5	:	:	PUNCT
ejpam-3977	161	6	u1	u1	NOUN
ejpam-3977	161	7	u2	u2	PROPN
ejpam-3977	161	8	u3	u3	PROPN
ejpam-3977	161	9	u4	u4	PROPN
ejpam-3977	161	10	u	u	PROPN
ejpam-3977	161	11	{	{	PUNCT
ejpam-3977	161	12	v}+	v}+	PROPN
ejpam-3977	161	13	c6	c6	PROPN
ejpam-3977	161	14	:	:	PUNCT
ejpam-3977	161	15	v1	v1	VERB
ejpam-3977	161	16	v2	v2	PROPN
ejpam-3977	161	17	v3	v3	PROPN
ejpam-3977	161	18	v4	v4	PROPN
ejpam-3977	161	19	v5v6	v5v6	PROPN
ejpam-3977	161	20	v	v	NOUN
ejpam-3977	161	21	figure	figure	NOUN
ejpam-3977	161	22	3	3	NUM
ejpam-3977	161	23	:	:	PUNCT
ejpam-3977	161	24	the	the	DET
ejpam-3977	161	25	join	join	NOUN
ejpam-3977	161	26	{	{	PUNCT
ejpam-3977	161	27	u}+	u}+	NOUN
ejpam-3977	161	28	p5	p5	ADJ
ejpam-3977	161	29	with	with	ADP
ejpam-3977	161	30	dim2({u}+	dim2({u}+	PROPN
ejpam-3977	161	31	p5	p5	PROPN
ejpam-3977	161	32	)	)	PUNCT
ejpam-3977	161	33	=	=	SYM
ejpam-3977	161	34	4	4	NUM
ejpam-3977	161	35	and	and	CCONJ
ejpam-3977	161	36	the	the	DET
ejpam-3977	161	37	join	join	NOUN
ejpam-3977	161	38	{	{	PUNCT
ejpam-3977	161	39	v}+	v}+	ADP
ejpam-3977	161	40	c6	c6	PROPN
ejpam-3977	161	41	with	with	ADP
ejpam-3977	161	42	dim2({v}+	dim2({v}+	PROPN
ejpam-3977	161	43	c6	c6	PROPN
ejpam-3977	161	44	)	)	PUNCT
ejpam-3977	162	1	=	=	PUNCT
ejpam-3977	162	2	4	4	NUM
ejpam-3977	162	3	the	the	DET
ejpam-3977	162	4	next	next	ADJ
ejpam-3977	162	5	result	result	NOUN
ejpam-3977	162	6	follows	follow	VERB
ejpam-3977	162	7	immediately	immediately	ADV
ejpam-3977	162	8	from	from	ADP
ejpam-3977	162	9	theorem	theorem	ADJ
ejpam-3977	162	10	3	3	NUM
ejpam-3977	162	11	.	.	PUNCT
ejpam-3977	162	12	corollary	corollary	ADJ
ejpam-3977	162	13	2	2	NUM
ejpam-3977	162	14	.	.	PUNCT
ejpam-3977	162	15	dim2(k1	dim2(k1	PROPN
ejpam-3977	162	16	+	+	CCONJ
ejpam-3977	162	17	g	g	NOUN
ejpam-3977	162	18	)	)	PUNCT
ejpam-3977	162	19	=	=	SYM
ejpam-3977	162	20	min	min	NOUN
ejpam-3977	162	21	{	{	PUNCT
ejpam-3977	162	22	sln2(g	sln2(g	NUM
ejpam-3977	162	23	)	)	PUNCT
ejpam-3977	162	24	,	,	PUNCT
ejpam-3977	162	25	sln1(g	sln1(g	PUNCT
ejpam-3977	162	26	)	)	PUNCT
ejpam-3977	163	1	+	+	CCONJ
ejpam-3977	163	2	1	1	NUM
ejpam-3977	163	3	}	}	PUNCT
ejpam-3977	163	4	.	.	PUNCT
ejpam-3977	163	5	example	example	NOUN
ejpam-3977	164	1	11.[8	11.[8	NUM
ejpam-3977	164	2	]	]	PUNCT
ejpam-3977	164	3	for	for	ADP
ejpam-3977	164	4	any	any	DET
ejpam-3977	164	5	integer	integer	NOUN
ejpam-3977	164	6	n	n	PRON
ejpam-3977	164	7	≥	≥	NUM
ejpam-3977	164	8	6	6	NUM
ejpam-3977	164	9	,	,	PUNCT
ejpam-3977	164	10	dim2(f1,n	dim2(f1,n	NUM
ejpam-3977	164	11	)	)	PUNCT
ejpam-3977	164	12	=	=	SYM
ejpam-3977	164	13	⌈	⌈	X
ejpam-3977	164	14	(	(	PUNCT
ejpam-3977	164	15	n	n	PROPN
ejpam-3977	164	16	+	+	CCONJ
ejpam-3977	164	17	1	1	NUM
ejpam-3977	164	18	)	)	PUNCT
ejpam-3977	164	19	2	2	NUM
ejpam-3977	164	20	⌉	⌉	NOUN
ejpam-3977	164	21	=	=	NOUN
ejpam-3977	164	22	sln2(pn	sln2(pn	NUM
ejpam-3977	164	23	)	)	PUNCT
ejpam-3977	164	24	.	.	PUNCT
ejpam-3977	165	1	example	example	NOUN
ejpam-3977	166	1	12.[8	12.[8	NUM
ejpam-3977	166	2	]	]	PUNCT
ejpam-3977	166	3	for	for	ADP
ejpam-3977	166	4	any	any	DET
ejpam-3977	166	5	n	n	PRON
ejpam-3977	166	6	≥	≥	NOUN
ejpam-3977	166	7	7	7	NUM
ejpam-3977	166	8	,	,	PUNCT
ejpam-3977	166	9	dim2(w1,n	dim2(w1,n	X
ejpam-3977	166	10	)	)	PUNCT
ejpam-3977	166	11	=	=	PUNCT
ejpam-3977	166	12	⌈n	⌈n	NOUN
ejpam-3977	166	13	2	2	NUM
ejpam-3977	166	14	⌉	⌉	X
ejpam-3977	166	15	=	=	NOUN
ejpam-3977	166	16	sln2(cn	sln2(cn	NOUN
ejpam-3977	166	17	)	)	PUNCT
ejpam-3977	166	18	.	.	PUNCT
ejpam-3977	167	1	theorem	theorem	ADJ
ejpam-3977	167	2	4	4	NUM
ejpam-3977	167	3	.	.	PUNCT
ejpam-3977	168	1	let	let	VERB
ejpam-3977	168	2	g	g	NOUN
ejpam-3977	168	3	and	and	CCONJ
ejpam-3977	168	4	h	h	NOUN
ejpam-3977	168	5	be	be	AUX
ejpam-3977	168	6	nontrivial	nontrivial	ADJ
ejpam-3977	168	7	connected	connected	ADJ
ejpam-3977	168	8	graphs	graph	NOUN
ejpam-3977	168	9	.	.	PUNCT
ejpam-3977	169	1	a	a	DET
ejpam-3977	169	2	proper	proper	ADJ
ejpam-3977	169	3	subset	subset	NOUN
ejpam-3977	169	4	s	s	NOUN
ejpam-3977	169	5	of	of	ADP
ejpam-3977	169	6	v	v	NOUN
ejpam-3977	169	7	(	(	PUNCT
ejpam-3977	169	8	g+h	g+h	PROPN
ejpam-3977	169	9	)	)	PUNCT
ejpam-3977	169	10	is	be	AUX
ejpam-3977	169	11	a	a	DET
ejpam-3977	169	12	2	2	NUM
ejpam-3977	169	13	-	-	PUNCT
ejpam-3977	169	14	resolving	resolving	NOUN
ejpam-3977	169	15	set	set	NOUN
ejpam-3977	169	16	in	in	ADP
ejpam-3977	169	17	g	g	PROPN
ejpam-3977	170	1	+	+	NOUN
ejpam-3977	170	2	h	h	NOUN
ejpam-3977	170	3	if	if	SCONJ
ejpam-3977	170	4	and	and	CCONJ
ejpam-3977	170	5	only	only	ADV
ejpam-3977	170	6	if	if	SCONJ
ejpam-3977	170	7	sg	sg	PROPN
ejpam-3977	170	8	=	=	SYM
ejpam-3977	170	9	v	v	PROPN
ejpam-3977	170	10	(	(	PUNCT
ejpam-3977	170	11	h	h	NOUN
ejpam-3977	170	12	)	)	PUNCT
ejpam-3977	170	13	∩	∩	NOUN
ejpam-3977	170	14	s	s	NOUN
ejpam-3977	170	15	and	and	CCONJ
ejpam-3977	170	16	sh	sh	PROPN
ejpam-3977	170	17	=	=	SYM
ejpam-3977	170	18	v	v	PROPN
ejpam-3977	170	19	(	(	PUNCT
ejpam-3977	170	20	h	h	NOUN
ejpam-3977	170	21	)	)	PUNCT
ejpam-3977	170	22	∩	∩	NOUN
ejpam-3977	170	23	s	s	PART
ejpam-3977	170	24	are	be	AUX
ejpam-3977	170	25	2locating	2locating	NUM
ejpam-3977	170	26	sets	set	NOUN
ejpam-3977	170	27	in	in	ADP
ejpam-3977	170	28	g	g	PROPN
ejpam-3977	170	29	and	and	CCONJ
ejpam-3977	170	30	h	h	NOUN
ejpam-3977	170	31	respectively	respectively	ADV
ejpam-3977	170	32	where	where	SCONJ
ejpam-3977	170	33	sg	sg	PROPN
ejpam-3977	170	34	or	or	CCONJ
ejpam-3977	170	35	sh	sh	PROPN
ejpam-3977	170	36	is	be	AUX
ejpam-3977	170	37	strictly	strictly	ADV
ejpam-3977	170	38	2	2	NUM
ejpam-3977	170	39	-	-	PUNCT
ejpam-3977	170	40	locating	locate	VERB
ejpam-3977	170	41	set	set	NOUN
ejpam-3977	170	42	or	or	CCONJ
ejpam-3977	170	43	sg	sg	PROPN
ejpam-3977	170	44	and	and	CCONJ
ejpam-3977	170	45	sh	sh	PROPN
ejpam-3977	170	46	are	be	AUX
ejpam-3977	170	47	strictly	strictly	ADV
ejpam-3977	170	48	1	1	NUM
ejpam-3977	170	49	-	-	PUNCT
ejpam-3977	170	50	locating	locate	VERB
ejpam-3977	170	51	sets	set	NOUN
ejpam-3977	170	52	.	.	PUNCT
ejpam-3977	171	1	proof	proof	NOUN
ejpam-3977	171	2	.	.	PUNCT
ejpam-3977	172	1	suppose	suppose	VERB
ejpam-3977	172	2	s	s	PRON
ejpam-3977	172	3	is	be	AUX
ejpam-3977	172	4	a	a	DET
ejpam-3977	172	5	proper	proper	ADJ
ejpam-3977	172	6	subset	subset	NOUN
ejpam-3977	172	7	of	of	ADP
ejpam-3977	172	8	v	v	NOUN
ejpam-3977	172	9	(	(	PUNCT
ejpam-3977	172	10	g	g	PROPN
ejpam-3977	172	11	+	+	NOUN
ejpam-3977	172	12	h	h	NOUN
ejpam-3977	172	13	)	)	PUNCT
ejpam-3977	172	14	.	.	PUNCT
ejpam-3977	173	1	let	let	VERB
ejpam-3977	173	2	s	s	PRON
ejpam-3977	173	3	be	be	AUX
ejpam-3977	173	4	a	a	DET
ejpam-3977	173	5	2	2	NUM
ejpam-3977	173	6	-	-	PUNCT
ejpam-3977	173	7	resolving	resolving	NOUN
ejpam-3977	173	8	set	set	NOUN
ejpam-3977	173	9	in	in	ADP
ejpam-3977	173	10	g	g	PROPN
ejpam-3977	173	11	+	+	CCONJ
ejpam-3977	173	12	h.	h.	PROPN
ejpam-3977	173	13	let	let	VERB
ejpam-3977	173	14	sg	sg	PROPN
ejpam-3977	173	15	=	=	SYM
ejpam-3977	173	16	v	v	PROPN
ejpam-3977	173	17	(	(	PUNCT
ejpam-3977	173	18	g	g	NOUN
ejpam-3977	173	19	)	)	PUNCT
ejpam-3977	173	20	∩	∩	NOUN
ejpam-3977	173	21	s	s	NOUN
ejpam-3977	173	22	and	and	CCONJ
ejpam-3977	173	23	sh	sh	PROPN
ejpam-3977	173	24	=	=	SYM
ejpam-3977	173	25	v	v	PROPN
ejpam-3977	173	26	(	(	PUNCT
ejpam-3977	173	27	h	h	NOUN
ejpam-3977	173	28	)	)	PUNCT
ejpam-3977	173	29	∩	∩	PROPN
ejpam-3977	173	30	s.	s.	PROPN
ejpam-3977	173	31	then	then	ADV
ejpam-3977	173	32	s	s	VERB
ejpam-3977	173	33	=	=	PUNCT
ejpam-3977	173	34	sg	sg	X
ejpam-3977	173	35	∪	∪	VERB
ejpam-3977	173	36	sh	sh	PROPN
ejpam-3977	173	37	.	.	PUNCT
ejpam-3977	174	1	suppose	suppose	VERB
ejpam-3977	174	2	sg	sg	ADP
ejpam-3977	174	3	=	=	PUNCT
ejpam-3977	174	4	∅.	∅.	VERB
ejpam-3977	174	5	then	then	ADV
ejpam-3977	174	6	s	s	VERB
ejpam-3977	174	7	=	=	ADJ
ejpam-3977	174	8	sh	sh	INTJ
ejpam-3977	174	9	.	.	PUNCT
ejpam-3977	175	1	let	let	VERB
ejpam-3977	175	2	x	x	PRON
ejpam-3977	175	3	,	,	PUNCT
ejpam-3977	175	4	y	y	PROPN
ejpam-3977	175	5	∈	∈	PROPN
ejpam-3977	175	6	v	v	NOUN
ejpam-3977	175	7	(	(	PUNCT
ejpam-3977	175	8	g	g	NOUN
ejpam-3977	175	9	)	)	PUNCT
ejpam-3977	175	10	,	,	PUNCT
ejpam-3977	175	11	x	x	X
ejpam-3977	176	1	6=	6=	ADP
ejpam-3977	176	2	y.	y.	NOUN
ejpam-3977	176	3	then	then	ADV
ejpam-3977	176	4	rg+h(x	rg+h(x	PROPN
ejpam-3977	176	5	/	/	SYM
ejpam-3977	176	6	s	s	PART
ejpam-3977	176	7	)	)	PUNCT
ejpam-3977	176	8	=	=	SYM
ejpam-3977	176	9	rg+h(y	rg+h(y	PROPN
ejpam-3977	176	10	/	/	SYM
ejpam-3977	176	11	s	s	NOUN
ejpam-3977	176	12	)	)	PUNCT
ejpam-3977	176	13	=	=	SYM
ejpam-3977	176	14	(	(	PUNCT
ejpam-3977	176	15	1	1	NUM
ejpam-3977	176	16	,	,	PUNCT
ejpam-3977	176	17	...	...	PUNCT
ejpam-3977	176	18	,	,	PUNCT
ejpam-3977	176	19	1	1	NUM
ejpam-3977	176	20	)	)	PUNCT
ejpam-3977	176	21	.	.	PUNCT
ejpam-3977	177	1	a	a	DET
ejpam-3977	177	2	contradiction	contradiction	NOUN
ejpam-3977	177	3	to	to	ADP
ejpam-3977	177	4	the	the	DET
ejpam-3977	177	5	assumption	assumption	NOUN
ejpam-3977	177	6	of	of	ADP
ejpam-3977	177	7	s.	s.	PROPN
ejpam-3977	177	8	thus	thus	ADV
ejpam-3977	177	9	,	,	PUNCT
ejpam-3977	177	10	sg	sg	PROPN
ejpam-3977	177	11	6=	6=	X
ejpam-3977	177	12	∅.	∅.	ADP
ejpam-3977	177	13	similarly	similarly	ADV
ejpam-3977	177	14	,	,	PUNCT
ejpam-3977	177	15	sh	sh	PROPN
ejpam-3977	177	16	6=	6=	ADP
ejpam-3977	177	17	∅.	∅.	ADP
ejpam-3977	177	18	next	next	ADV
ejpam-3977	177	19	,	,	PUNCT
ejpam-3977	177	20	suppose	suppose	VERB
ejpam-3977	177	21	sg	sg	PROPN
ejpam-3977	177	22	or	or	CCONJ
ejpam-3977	177	23	sh	sh	INTJ
ejpam-3977	177	24	,	,	PUNCT
ejpam-3977	177	25	say	say	VERB
ejpam-3977	177	26	sg	sg	PROPN
ejpam-3977	177	27	is	be	AUX
ejpam-3977	177	28	not	not	PART
ejpam-3977	177	29	2	2	NUM
ejpam-3977	177	30	-	-	PUNCT
ejpam-3977	177	31	locating	locate	VERB
ejpam-3977	177	32	set	set	NOUN
ejpam-3977	177	33	in	in	ADP
ejpam-3977	177	34	g.	g.	PROPN
ejpam-3977	177	35	then	then	ADV
ejpam-3977	177	36	there	there	PRON
ejpam-3977	177	37	exist	exist	VERB
ejpam-3977	177	38	x	x	NOUN
ejpam-3977	177	39	,	,	PUNCT
ejpam-3977	177	40	y	y	PROPN
ejpam-3977	177	41	∈	∈	PROPN
ejpam-3977	177	42	v	v	NOUN
ejpam-3977	177	43	(	(	PUNCT
ejpam-3977	177	44	g	g	NOUN
ejpam-3977	177	45	)	)	PUNCT
ejpam-3977	177	46	,	,	PUNCT
ejpam-3977	177	47	x	x	X
ejpam-3977	178	1	6=	6=	ADP
ejpam-3977	178	2	y	y	PRON
ejpam-3977	178	3	such	such	ADJ
ejpam-3977	178	4	that	that	SCONJ
ejpam-3977	178	5	rg(x	rg(x	PROPN
ejpam-3977	178	6	/	/	SYM
ejpam-3977	178	7	sg	sg	NOUN
ejpam-3977	178	8	)	)	PUNCT
ejpam-3977	178	9	and	and	CCONJ
ejpam-3977	178	10	rg(y	rg(y	NOUN
ejpam-3977	178	11	/	/	SYM
ejpam-3977	178	12	sg	sg	PROPN
ejpam-3977	178	13	)	)	PUNCT
ejpam-3977	178	14	differ	differ	VERB
ejpam-3977	178	15	in	in	ADP
ejpam-3977	178	16	at	at	ADP
ejpam-3977	178	17	most	most	ADJ
ejpam-3977	178	18	1	1	NUM
ejpam-3977	178	19	position	position	NOUN
ejpam-3977	178	20	.	.	PUNCT
ejpam-3977	179	1	hence	hence	ADV
ejpam-3977	179	2	,	,	PUNCT
ejpam-3977	179	3	rg+h(x	rg+h(x	PROPN
ejpam-3977	179	4	/	/	SYM
ejpam-3977	179	5	s	s	NOUN
ejpam-3977	179	6	)	)	PUNCT
ejpam-3977	179	7	and	and	CCONJ
ejpam-3977	179	8	rg+h(y	rg+h(y	PRON
ejpam-3977	179	9	/	/	SYM
ejpam-3977	179	10	s	s	PART
ejpam-3977	179	11	)	)	PUNCT
ejpam-3977	179	12	differ	differ	VERB
ejpam-3977	179	13	also	also	ADV
ejpam-3977	179	14	in	in	ADP
ejpam-3977	179	15	at	at	ADP
ejpam-3977	179	16	most	most	ADV
ejpam-3977	179	17	one	one	NUM
ejpam-3977	179	18	position	position	NOUN
ejpam-3977	179	19	.	.	PUNCT
ejpam-3977	180	1	thus	thus	ADV
ejpam-3977	180	2	,	,	PUNCT
ejpam-3977	180	3	s	s	VERB
ejpam-3977	180	4	is	be	AUX
ejpam-3977	180	5	not	not	PART
ejpam-3977	180	6	2	2	NUM
ejpam-3977	180	7	-	-	PUNCT
ejpam-3977	180	8	resolving	resolve	VERB
ejpam-3977	180	9	set	set	NOUN
ejpam-3977	180	10	in	in	ADP
ejpam-3977	180	11	g	g	PROPN
ejpam-3977	180	12	+	+	CCONJ
ejpam-3977	180	13	h	h	NOUN
ejpam-3977	180	14	,	,	PUNCT
ejpam-3977	180	15	contrary	contrary	ADJ
ejpam-3977	180	16	to	to	ADP
ejpam-3977	180	17	our	our	PRON
ejpam-3977	180	18	assumption	assumption	NOUN
ejpam-3977	180	19	.	.	PUNCT
ejpam-3977	181	1	therefore	therefore	ADV
ejpam-3977	181	2	sg	sg	PROPN
ejpam-3977	181	3	and	and	CCONJ
ejpam-3977	181	4	sh	sh	PROPN
ejpam-3977	181	5	are	be	AUX
ejpam-3977	181	6	2	2	NUM
ejpam-3977	181	7	-	-	PUNCT
ejpam-3977	181	8	locating	locate	VERB
ejpam-3977	181	9	sets	set	NOUN
ejpam-3977	181	10	in	in	ADP
ejpam-3977	181	11	g	g	PROPN
ejpam-3977	181	12	j.	j.	PROPN
ejpam-3977	181	13	cabaro	cabaro	PROPN
ejpam-3977	181	14	,	,	PUNCT
ejpam-3977	181	15	h.	h.	PROPN
ejpam-3977	181	16	rara	rara	PROPN
ejpam-3977	181	17	/	/	SYM
ejpam-3977	181	18	eur	eur	PROPN
ejpam-3977	181	19	.	.	PUNCT
ejpam-3977	182	1	j.	j.	PROPN
ejpam-3977	182	2	pure	pure	PROPN
ejpam-3977	182	3	appl	appl	PROPN
ejpam-3977	182	4	.	.	PROPN
ejpam-3977	182	5	math	math	PROPN
ejpam-3977	182	6	,	,	PUNCT
ejpam-3977	182	7	14	14	NUM
ejpam-3977	182	8	(	(	PUNCT
ejpam-3977	182	9	3	3	NUM
ejpam-3977	182	10	)	)	PUNCT
ejpam-3977	182	11	(	(	PUNCT
ejpam-3977	182	12	2021	2021	NUM
ejpam-3977	182	13	)	)	PUNCT
ejpam-3977	182	14	,	,	PUNCT
ejpam-3977	182	15	773	773	NUM
ejpam-3977	182	16	-	-	SYM
ejpam-3977	182	17	782	782	NUM
ejpam-3977	182	18	779	779	NUM
ejpam-3977	182	19	and	and	CCONJ
ejpam-3977	182	20	h	h	NOUN
ejpam-3977	182	21	,	,	PUNCT
ejpam-3977	182	22	respectively	respectively	ADV
ejpam-3977	182	23	.	.	PUNCT
ejpam-3977	183	1	now	now	ADV
ejpam-3977	183	2	,	,	PUNCT
ejpam-3977	183	3	suppose	suppose	VERB
ejpam-3977	183	4	that	that	SCONJ
ejpam-3977	183	5	both	both	PRON
ejpam-3977	183	6	sg	sg	NOUN
ejpam-3977	183	7	and	and	CCONJ
ejpam-3977	183	8	sh	sh	PROPN
ejpam-3977	183	9	are	be	AUX
ejpam-3977	183	10	not	not	PART
ejpam-3977	183	11	strictly	strictly	ADV
ejpam-3977	183	12	2	2	NUM
ejpam-3977	183	13	-	-	PUNCT
ejpam-3977	183	14	locating	locate	VERB
ejpam-3977	183	15	sets	set	NOUN
ejpam-3977	183	16	.	.	PUNCT
ejpam-3977	184	1	then	then	ADV
ejpam-3977	184	2	|ng(x	|ng(x	X
ejpam-3977	184	3	)	)	PUNCT
ejpam-3977	184	4	∩	∩	NOUN
ejpam-3977	184	5	sg|	sg|	VERB
ejpam-3977	184	6	>	>	X
ejpam-3977	184	7	|sg|	|sg|	NOUN
ejpam-3977	184	8	−	−	PROPN
ejpam-3977	184	9	2	2	NUM
ejpam-3977	184	10	,	,	PUNCT
ejpam-3977	184	11	∀x	∀x	VERB
ejpam-3977	184	12	∈	∈	PROPN
ejpam-3977	184	13	v	v	NOUN
ejpam-3977	184	14	(	(	PUNCT
ejpam-3977	184	15	g	g	NOUN
ejpam-3977	184	16	)	)	PUNCT
ejpam-3977	184	17	and	and	CCONJ
ejpam-3977	184	18	|nh(y	|nh(y	X
ejpam-3977	184	19	)	)	PUNCT
ejpam-3977	184	20	∩	∩	NOUN
ejpam-3977	184	21	sh	sh	PROPN
ejpam-3977	184	22	|	|	ADV
ejpam-3977	184	23	>	>	X
ejpam-3977	184	24	|sh	|sh	ADP
ejpam-3977	184	25	|	|	ADV
ejpam-3977	184	26	−	−	PROPN
ejpam-3977	184	27	2	2	NUM
ejpam-3977	184	28	,	,	PUNCT
ejpam-3977	184	29	∀y	∀y	NUM
ejpam-3977	184	30	∈	∈	PROPN
ejpam-3977	184	31	v	v	NOUN
ejpam-3977	184	32	(	(	PUNCT
ejpam-3977	184	33	h	h	NOUN
ejpam-3977	184	34	)	)	PUNCT
ejpam-3977	184	35	.	.	PUNCT
ejpam-3977	185	1	hence	hence	ADV
ejpam-3977	185	2	either	either	DET
ejpam-3977	185	3	ng(x	ng(x	NUM
ejpam-3977	185	4	)	)	PUNCT
ejpam-3977	185	5	∩	∩	NOUN
ejpam-3977	185	6	sg	sg	ADP
ejpam-3977	185	7	=	=	PUNCT
ejpam-3977	185	8	sg	sg	PROPN
ejpam-3977	185	9	or	or	CCONJ
ejpam-3977	185	10	∃p	∃p	PROPN
ejpam-3977	185	11	∈	∈	PROPN
ejpam-3977	185	12	sg\ng(x	sg\ng(x	X
ejpam-3977	185	13	)	)	PUNCT
ejpam-3977	185	14	and	and	CCONJ
ejpam-3977	185	15	either	either	CCONJ
ejpam-3977	185	16	nh(y	nh(y	NOUN
ejpam-3977	185	17	)	)	PUNCT
ejpam-3977	185	18	∩	∩	NOUN
ejpam-3977	185	19	sh	sh	PROPN
ejpam-3977	185	20	=	=	PUNCT
ejpam-3977	185	21	sh	sh	PROPN
ejpam-3977	185	22	or	or	CCONJ
ejpam-3977	185	23	∃q	∃q	PROPN
ejpam-3977	185	24	∈	∈	PROPN
ejpam-3977	185	25	sh\nh(y	sh\nh(y	PROPN
ejpam-3977	185	26	)	)	PUNCT
ejpam-3977	185	27	.	.	PUNCT
ejpam-3977	186	1	since	since	SCONJ
ejpam-3977	186	2	s	s	PROPN
ejpam-3977	186	3	is	be	AUX
ejpam-3977	186	4	a	a	DET
ejpam-3977	186	5	2	2	NUM
ejpam-3977	186	6	-	-	PUNCT
ejpam-3977	186	7	locating	locate	VERB
ejpam-3977	186	8	set	set	NOUN
ejpam-3977	186	9	,	,	PUNCT
ejpam-3977	186	10	∃p	∃p	PROPN
ejpam-3977	186	11	∈	∈	PROPN
ejpam-3977	186	12	sg\ng(x	sg\ng(x	X
ejpam-3977	186	13	)	)	PUNCT
ejpam-3977	186	14	and	and	CCONJ
ejpam-3977	186	15	∃q	∃q	PROPN
ejpam-3977	186	16	∈	∈	PROPN
ejpam-3977	186	17	sh\nh(y	sh\nh(y	PROPN
ejpam-3977	186	18	)	)	PUNCT
ejpam-3977	186	19	.	.	PUNCT
ejpam-3977	187	1	thus	thus	ADV
ejpam-3977	187	2	,	,	PUNCT
ejpam-3977	187	3	sg	sg	PROPN
ejpam-3977	187	4	and	and	CCONJ
ejpam-3977	187	5	sh	sh	PROPN
ejpam-3977	187	6	are	be	AUX
ejpam-3977	187	7	both	both	PRON
ejpam-3977	187	8	strictly	strictly	ADV
ejpam-3977	187	9	1	1	NUM
ejpam-3977	187	10	-	-	PUNCT
ejpam-3977	187	11	locating	locate	VERB
ejpam-3977	187	12	sets	set	NOUN
ejpam-3977	187	13	.	.	PUNCT
ejpam-3977	188	1	for	for	ADP
ejpam-3977	188	2	the	the	DET
ejpam-3977	188	3	converse	converse	NOUN
ejpam-3977	188	4	,	,	PUNCT
ejpam-3977	188	5	suppose	suppose	VERB
ejpam-3977	188	6	that	that	SCONJ
ejpam-3977	188	7	sg	sg	PROPN
ejpam-3977	188	8	and	and	CCONJ
ejpam-3977	188	9	sh	sh	PROPN
ejpam-3977	188	10	are	be	AUX
ejpam-3977	188	11	2	2	NUM
ejpam-3977	188	12	-	-	PUNCT
ejpam-3977	188	13	locating	locate	VERB
ejpam-3977	188	14	sets	set	NOUN
ejpam-3977	188	15	in	in	ADP
ejpam-3977	188	16	g	g	PROPN
ejpam-3977	188	17	and	and	CCONJ
ejpam-3977	188	18	h	h	NOUN
ejpam-3977	188	19	,	,	PUNCT
ejpam-3977	188	20	respectively	respectively	ADV
ejpam-3977	188	21	where	where	SCONJ
ejpam-3977	188	22	sg	sg	NOUN
ejpam-3977	188	23	or	or	CCONJ
ejpam-3977	188	24	sh	sh	PROPN
ejpam-3977	188	25	is	be	AUX
ejpam-3977	188	26	strictly	strictly	ADV
ejpam-3977	188	27	2	2	NUM
ejpam-3977	188	28	-	-	PUNCT
ejpam-3977	188	29	locating	locate	VERB
ejpam-3977	188	30	set	set	NOUN
ejpam-3977	188	31	or	or	CCONJ
ejpam-3977	188	32	sg	sg	PROPN
ejpam-3977	188	33	and	and	CCONJ
ejpam-3977	188	34	sh	sh	PROPN
ejpam-3977	188	35	are	be	AUX
ejpam-3977	188	36	both	both	PRON
ejpam-3977	188	37	strictly	strictly	ADV
ejpam-3977	188	38	1	1	NUM
ejpam-3977	188	39	-	-	PUNCT
ejpam-3977	188	40	locating	locate	VERB
ejpam-3977	188	41	sets	set	NOUN
ejpam-3977	188	42	.	.	PUNCT
ejpam-3977	189	1	let	let	VERB
ejpam-3977	189	2	x	x	PRON
ejpam-3977	189	3	,	,	PUNCT
ejpam-3977	189	4	y	y	PROPN
ejpam-3977	189	5	∈	∈	PROPN
ejpam-3977	189	6	v	v	PROPN
ejpam-3977	189	7	(	(	PUNCT
ejpam-3977	189	8	g+h	g+h	NOUN
ejpam-3977	189	9	)	)	PUNCT
ejpam-3977	189	10	with	with	ADP
ejpam-3977	189	11	x	x	SYM
ejpam-3977	189	12	6=	6=	ADP
ejpam-3977	189	13	y.	y.	NOUN
ejpam-3977	189	14	if	if	SCONJ
ejpam-3977	189	15	x	x	PRON
ejpam-3977	189	16	,	,	PUNCT
ejpam-3977	189	17	y	y	PROPN
ejpam-3977	189	18	∈	∈	PROPN
ejpam-3977	189	19	v	v	NOUN
ejpam-3977	189	20	(	(	PUNCT
ejpam-3977	189	21	g	g	NOUN
ejpam-3977	189	22	)	)	PUNCT
ejpam-3977	189	23	,	,	PUNCT
ejpam-3977	189	24	then	then	ADV
ejpam-3977	189	25	rg(x	rg(x	NUM
ejpam-3977	189	26	/	/	SYM
ejpam-3977	189	27	sg	sg	PROPN
ejpam-3977	189	28	)	)	PUNCT
ejpam-3977	189	29	and	and	CCONJ
ejpam-3977	189	30	rg(y	rg(y	NOUN
ejpam-3977	189	31	/	/	SYM
ejpam-3977	189	32	sg	sg	PROPN
ejpam-3977	189	33	)	)	PUNCT
ejpam-3977	189	34	differ	differ	VERB
ejpam-3977	189	35	in	in	ADP
ejpam-3977	189	36	at	at	ADV
ejpam-3977	189	37	least	least	ADJ
ejpam-3977	189	38	2	2	NUM
ejpam-3977	189	39	positions	position	NOUN
ejpam-3977	189	40	since	since	SCONJ
ejpam-3977	189	41	sg	sg	PROPN
ejpam-3977	189	42	is	be	AUX
ejpam-3977	189	43	a	a	DET
ejpam-3977	189	44	2	2	NUM
ejpam-3977	189	45	-	-	PUNCT
ejpam-3977	189	46	locating	locate	VERB
ejpam-3977	189	47	set	set	NOUN
ejpam-3977	189	48	in	in	ADP
ejpam-3977	189	49	g.	g.	PROPN
ejpam-3977	189	50	hence	hence	ADV
ejpam-3977	189	51	,	,	PUNCT
ejpam-3977	189	52	rg+h(x	rg+h(x	PROPN
ejpam-3977	189	53	/	/	SYM
ejpam-3977	189	54	s	s	NOUN
ejpam-3977	189	55	)	)	PUNCT
ejpam-3977	189	56	and	and	CCONJ
ejpam-3977	189	57	rg+h(y	rg+h(y	PRON
ejpam-3977	189	58	/	/	SYM
ejpam-3977	189	59	s	s	PART
ejpam-3977	189	60	)	)	PUNCT
ejpam-3977	189	61	also	also	ADV
ejpam-3977	189	62	differ	differ	VERB
ejpam-3977	189	63	in	in	ADP
ejpam-3977	189	64	at	at	ADV
ejpam-3977	189	65	least	least	ADJ
ejpam-3977	189	66	2	2	NUM
ejpam-3977	189	67	positions	position	NOUN
ejpam-3977	189	68	.	.	PUNCT
ejpam-3977	190	1	similarly	similarly	ADV
ejpam-3977	190	2	,	,	PUNCT
ejpam-3977	190	3	if	if	SCONJ
ejpam-3977	190	4	x	x	X
ejpam-3977	190	5	,	,	PUNCT
ejpam-3977	190	6	y	y	PROPN
ejpam-3977	190	7	∈	∈	PROPN
ejpam-3977	190	8	v	v	PROPN
ejpam-3977	190	9	(	(	PUNCT
ejpam-3977	190	10	h	h	NOUN
ejpam-3977	190	11	)	)	PUNCT
ejpam-3977	190	12	,	,	PUNCT
ejpam-3977	190	13	then	then	ADV
ejpam-3977	190	14	rg+h(x	rg+h(x	PROPN
ejpam-3977	190	15	/	/	SYM
ejpam-3977	190	16	s	s	NOUN
ejpam-3977	190	17	)	)	PUNCT
ejpam-3977	190	18	and	and	CCONJ
ejpam-3977	190	19	rg+h(y	rg+h(y	PRON
ejpam-3977	190	20	/	/	SYM
ejpam-3977	190	21	s	s	PART
ejpam-3977	190	22	)	)	PUNCT
ejpam-3977	190	23	differ	differ	VERB
ejpam-3977	190	24	in	in	ADP
ejpam-3977	190	25	at	at	ADV
ejpam-3977	190	26	least	least	ADJ
ejpam-3977	190	27	2	2	NUM
ejpam-3977	190	28	positions	position	NOUN
ejpam-3977	190	29	.	.	PUNCT
ejpam-3977	191	1	suppose	suppose	VERB
ejpam-3977	191	2	that	that	SCONJ
ejpam-3977	191	3	x	x	SYM
ejpam-3977	191	4	∈	∈	NOUN
ejpam-3977	191	5	v	v	X
ejpam-3977	191	6	(	(	PUNCT
ejpam-3977	191	7	g	g	NOUN
ejpam-3977	191	8	)	)	PUNCT
ejpam-3977	191	9	and	and	CCONJ
ejpam-3977	191	10	y	y	PROPN
ejpam-3977	191	11	∈	∈	PROPN
ejpam-3977	191	12	v	v	ADP
ejpam-3977	191	13	(	(	PUNCT
ejpam-3977	191	14	h	h	NOUN
ejpam-3977	191	15	)	)	PUNCT
ejpam-3977	191	16	and	and	CCONJ
ejpam-3977	191	17	sg	sg	PROPN
ejpam-3977	191	18	is	be	AUX
ejpam-3977	191	19	strictly	strictly	ADV
ejpam-3977	191	20	2	2	NUM
ejpam-3977	191	21	-	-	PUNCT
ejpam-3977	191	22	locating	locate	VERB
ejpam-3977	191	23	set	set	NOUN
ejpam-3977	191	24	.	.	PUNCT
ejpam-3977	192	1	then	then	ADV
ejpam-3977	192	2	,	,	PUNCT
ejpam-3977	192	3	∃w	∃w	PROPN
ejpam-3977	192	4	,	,	PUNCT
ejpam-3977	192	5	z	z	PROPN
ejpam-3977	192	6	∈	∈	PROPN
ejpam-3977	192	7	sg\ng(x	sg\ng(x	NOUN
ejpam-3977	192	8	)	)	PUNCT
ejpam-3977	192	9	.	.	PUNCT
ejpam-3977	193	1	then	then	ADV
ejpam-3977	193	2	rg+h(x	rg+h(x	PROPN
ejpam-3977	193	3	/	/	SYM
ejpam-3977	193	4	s	s	NOUN
ejpam-3977	193	5	)	)	PUNCT
ejpam-3977	193	6	and	and	CCONJ
ejpam-3977	193	7	rg+h(y	rg+h(y	PRON
ejpam-3977	193	8	/	/	SYM
ejpam-3977	193	9	s	s	PART
ejpam-3977	193	10	)	)	PUNCT
ejpam-3977	193	11	differ	differ	VERB
ejpam-3977	193	12	in	in	ADP
ejpam-3977	193	13	the	the	DET
ejpam-3977	193	14	zth	zth	NOUN
ejpam-3977	193	15	and	and	CCONJ
ejpam-3977	193	16	wth	wth	NOUN
ejpam-3977	193	17	positions	position	NOUN
ejpam-3977	193	18	.	.	PUNCT
ejpam-3977	194	1	on	on	ADP
ejpam-3977	194	2	the	the	DET
ejpam-3977	194	3	other	other	ADJ
ejpam-3977	194	4	hand	hand	NOUN
ejpam-3977	194	5	,	,	PUNCT
ejpam-3977	194	6	if	if	SCONJ
ejpam-3977	194	7	sg	sg	PROPN
ejpam-3977	194	8	and	and	CCONJ
ejpam-3977	194	9	sh	sh	PROPN
ejpam-3977	194	10	are	be	AUX
ejpam-3977	194	11	strictly	strictly	ADV
ejpam-3977	194	12	1	1	NUM
ejpam-3977	194	13	-	-	PUNCT
ejpam-3977	194	14	locating	locate	VERB
ejpam-3977	194	15	sets	set	NOUN
ejpam-3977	194	16	,	,	PUNCT
ejpam-3977	194	17	then	then	ADV
ejpam-3977	194	18	∃p	∃p	PROPN
ejpam-3977	194	19	∈	∈	PROPN
ejpam-3977	194	20	sg\ng(x	sg\ng(x	X
ejpam-3977	194	21	)	)	PUNCT
ejpam-3977	194	22	and	and	CCONJ
ejpam-3977	194	23	q	q	PROPN
ejpam-3977	194	24	∈	∈	PROPN
ejpam-3977	194	25	sh\nh(y	sh\nh(y	PROPN
ejpam-3977	194	26	)	)	PUNCT
ejpam-3977	194	27	.	.	PUNCT
ejpam-3977	195	1	hence	hence	ADV
ejpam-3977	195	2	rg+h(x	rg+h(x	PROPN
ejpam-3977	195	3	/	/	SYM
ejpam-3977	195	4	s	s	NOUN
ejpam-3977	195	5	)	)	PUNCT
ejpam-3977	195	6	and	and	CCONJ
ejpam-3977	195	7	rg+h(y	rg+h(y	PRON
ejpam-3977	195	8	/	/	SYM
ejpam-3977	195	9	s	s	PART
ejpam-3977	195	10	)	)	PUNCT
ejpam-3977	195	11	differ	differ	VERB
ejpam-3977	195	12	in	in	ADP
ejpam-3977	195	13	pth	pth	NOUN
ejpam-3977	195	14	and	and	CCONJ
ejpam-3977	195	15	qth	qth	NOUN
ejpam-3977	195	16	positions	position	NOUN
ejpam-3977	195	17	.	.	PUNCT
ejpam-3977	196	1	therefore	therefore	ADV
ejpam-3977	196	2	,	,	PUNCT
ejpam-3977	196	3	s	s	VERB
ejpam-3977	196	4	is	be	AUX
ejpam-3977	196	5	a	a	DET
ejpam-3977	196	6	2	2	NUM
ejpam-3977	196	7	-	-	PUNCT
ejpam-3977	196	8	resolving	resolving	NOUN
ejpam-3977	196	9	set	set	NOUN
ejpam-3977	196	10	in	in	ADP
ejpam-3977	196	11	g	g	PROPN
ejpam-3977	196	12	+	+	CCONJ
ejpam-3977	196	13	h.	h.	PROPN
ejpam-3977	196	14	corollary	corollary	NOUN
ejpam-3977	196	15	3	3	X
ejpam-3977	196	16	.	.	PUNCT
ejpam-3977	197	1	let	let	VERB
ejpam-3977	197	2	g	g	NOUN
ejpam-3977	197	3	and	and	CCONJ
ejpam-3977	197	4	h	h	NOUN
ejpam-3977	197	5	be	be	AUX
ejpam-3977	197	6	connected	connect	VERB
ejpam-3977	197	7	nontrivial	nontrivial	ADJ
ejpam-3977	197	8	graphs	graph	NOUN
ejpam-3977	197	9	.	.	PUNCT
ejpam-3977	198	1	then	then	ADV
ejpam-3977	198	2	,	,	PUNCT
ejpam-3977	198	3	dim2(g	dim2(g	X
ejpam-3977	198	4	+	+	CCONJ
ejpam-3977	198	5	h	h	X
ejpam-3977	198	6	)	)	PUNCT
ejpam-3977	198	7	=	=	SYM
ejpam-3977	198	8	min	min	NOUN
ejpam-3977	198	9	{	{	PUNCT
ejpam-3977	198	10	sln2(g	sln2(g	NUM
ejpam-3977	198	11	)	)	PUNCT
ejpam-3977	198	12	+	+	CCONJ
ejpam-3977	198	13	ln2(h	ln2(h	PROPN
ejpam-3977	198	14	)	)	PUNCT
ejpam-3977	198	15	,	,	PUNCT
ejpam-3977	198	16	ln2(g	ln2(g	PROPN
ejpam-3977	198	17	)	)	PUNCT
ejpam-3977	198	18	+	+	NUM
ejpam-3977	198	19	sln2(h	sln2(h	NUM
ejpam-3977	198	20	)	)	PUNCT
ejpam-3977	198	21	,	,	PUNCT
ejpam-3977	198	22	sln1(g	sln1(g	X
ejpam-3977	198	23	)	)	PUNCT
ejpam-3977	198	24	+	+	NUM
ejpam-3977	198	25	sln1(h	sln1(h	NOUN
ejpam-3977	198	26	)	)	PUNCT
ejpam-3977	198	27	}	}	PUNCT
ejpam-3977	198	28	.	.	PUNCT
ejpam-3977	199	1	proof	proof	NOUN
ejpam-3977	199	2	.	.	PUNCT
ejpam-3977	200	1	let	let	VERB
ejpam-3977	200	2	s	s	PRON
ejpam-3977	200	3	be	be	AUX
ejpam-3977	200	4	a	a	DET
ejpam-3977	200	5	minimum	minimum	ADJ
ejpam-3977	200	6	2	2	NUM
ejpam-3977	200	7	-	-	PUNCT
ejpam-3977	200	8	resolving	resolve	VERB
ejpam-3977	200	9	set	set	NOUN
ejpam-3977	200	10	of	of	ADP
ejpam-3977	200	11	g	g	PROPN
ejpam-3977	200	12	+	+	CCONJ
ejpam-3977	200	13	h.	h.	PROPN
ejpam-3977	200	14	let	let	VERB
ejpam-3977	200	15	sg	sg	PROPN
ejpam-3977	200	16	=	=	SYM
ejpam-3977	200	17	v	v	PROPN
ejpam-3977	200	18	(	(	PUNCT
ejpam-3977	200	19	g	g	NOUN
ejpam-3977	200	20	)	)	PUNCT
ejpam-3977	200	21	∩	∩	NOUN
ejpam-3977	200	22	s	s	NOUN
ejpam-3977	200	23	and	and	CCONJ
ejpam-3977	200	24	sh	sh	PROPN
ejpam-3977	200	25	=	=	SYM
ejpam-3977	200	26	v	v	PROPN
ejpam-3977	200	27	(	(	PUNCT
ejpam-3977	200	28	h	h	NOUN
ejpam-3977	200	29	)	)	PUNCT
ejpam-3977	200	30	∩	∩	NOUN
ejpam-3977	200	31	s.	s.	PROPN
ejpam-3977	200	32	by	by	ADP
ejpam-3977	200	33	theorem	theorem	NOUN
ejpam-3977	200	34	4	4	NUM
ejpam-3977	200	35	,	,	PUNCT
ejpam-3977	200	36	sg	sg	PROPN
ejpam-3977	200	37	and	and	CCONJ
ejpam-3977	200	38	sh	sh	PROPN
ejpam-3977	200	39	are	be	AUX
ejpam-3977	200	40	2	2	NUM
ejpam-3977	200	41	-	-	PUNCT
ejpam-3977	200	42	locating	locate	VERB
ejpam-3977	200	43	sets	set	NOUN
ejpam-3977	200	44	in	in	ADP
ejpam-3977	200	45	g	g	PROPN
ejpam-3977	200	46	and	and	CCONJ
ejpam-3977	200	47	h	h	NOUN
ejpam-3977	200	48	,	,	PUNCT
ejpam-3977	200	49	respectively	respectively	ADV
ejpam-3977	200	50	where	where	SCONJ
ejpam-3977	200	51	sg	sg	NOUN
ejpam-3977	200	52	or	or	CCONJ
ejpam-3977	200	53	sh	sh	PROPN
ejpam-3977	200	54	is	be	AUX
ejpam-3977	200	55	strictly	strictly	ADV
ejpam-3977	200	56	2	2	NUM
ejpam-3977	200	57	-	-	PUNCT
ejpam-3977	200	58	locating	locate	VERB
ejpam-3977	200	59	set	set	NOUN
ejpam-3977	200	60	or	or	CCONJ
ejpam-3977	200	61	sg	sg	PROPN
ejpam-3977	200	62	and	and	CCONJ
ejpam-3977	200	63	sh	sh	PROPN
ejpam-3977	200	64	are	be	AUX
ejpam-3977	200	65	strictly	strictly	ADV
ejpam-3977	200	66	1	1	NUM
ejpam-3977	200	67	-	-	PUNCT
ejpam-3977	200	68	locating	locate	VERB
ejpam-3977	200	69	sets	set	NOUN
ejpam-3977	200	70	.	.	PUNCT
ejpam-3977	201	1	if	if	SCONJ
ejpam-3977	201	2	sg	sg	PROPN
ejpam-3977	201	3	is	be	AUX
ejpam-3977	201	4	strictly	strictly	ADV
ejpam-3977	201	5	2	2	NUM
ejpam-3977	201	6	-	-	PUNCT
ejpam-3977	201	7	locating	locate	VERB
ejpam-3977	201	8	set	set	NOUN
ejpam-3977	201	9	in	in	ADP
ejpam-3977	201	10	g	g	NOUN
ejpam-3977	201	11	,	,	PUNCT
ejpam-3977	201	12	then	then	ADV
ejpam-3977	201	13	sln2(g	sln2(g	NUM
ejpam-3977	201	14	)	)	PUNCT
ejpam-3977	201	15	+	+	CCONJ
ejpam-3977	201	16	ln2(h	ln2(h	PROPN
ejpam-3977	201	17	)	)	PUNCT
ejpam-3977	201	18	≤	≤	NUM
ejpam-3977	201	19	|sg|	|sg|	NOUN
ejpam-3977	201	20	+	+	CCONJ
ejpam-3977	201	21	|sh	|sh	PROPN
ejpam-3977	201	22	|	|	ADV
ejpam-3977	201	23	=	=	SYM
ejpam-3977	201	24	|s|	|s|	NOUN
ejpam-3977	201	25	=	=	NOUN
ejpam-3977	201	26	dim2(g	dim2(g	X
ejpam-3977	201	27	+	+	X
ejpam-3977	201	28	h	h	NOUN
ejpam-3977	201	29	)	)	PUNCT
ejpam-3977	201	30	.	.	PUNCT
ejpam-3977	202	1	if	if	SCONJ
ejpam-3977	202	2	sh	sh	PROPN
ejpam-3977	202	3	is	be	AUX
ejpam-3977	202	4	strictly	strictly	ADV
ejpam-3977	202	5	2	2	NUM
ejpam-3977	202	6	-	-	PUNCT
ejpam-3977	202	7	locating	locate	VERB
ejpam-3977	202	8	set	set	NOUN
ejpam-3977	202	9	in	in	ADP
ejpam-3977	202	10	h	h	NOUN
ejpam-3977	202	11	,	,	PUNCT
ejpam-3977	202	12	then	then	ADV
ejpam-3977	202	13	sln2(h	sln2(h	NUM
ejpam-3977	202	14	)	)	PUNCT
ejpam-3977	202	15	+	+	PUNCT
ejpam-3977	202	16	ln2(g	ln2(g	X
ejpam-3977	202	17	)	)	PUNCT
ejpam-3977	202	18	≤	≤	NUM
ejpam-3977	202	19	|sh	|sh	ADP
ejpam-3977	202	20	|	|	ADV
ejpam-3977	202	21	+	+	CCONJ
ejpam-3977	202	22	|sg|	|sg|	NOUN
ejpam-3977	202	23	=	=	SYM
ejpam-3977	202	24	|s|	|s|	NOUN
ejpam-3977	202	25	=	=	NOUN
ejpam-3977	202	26	dim2(g	dim2(g	X
ejpam-3977	202	27	+	+	X
ejpam-3977	202	28	h	h	NOUN
ejpam-3977	202	29	)	)	PUNCT
ejpam-3977	202	30	.	.	PUNCT
ejpam-3977	203	1	if	if	SCONJ
ejpam-3977	203	2	sg	sg	PROPN
ejpam-3977	203	3	and	and	CCONJ
ejpam-3977	203	4	sh	sh	PROPN
ejpam-3977	203	5	are	be	AUX
ejpam-3977	203	6	both	both	PRON
ejpam-3977	203	7	strictly	strictly	ADV
ejpam-3977	203	8	1	1	NUM
ejpam-3977	203	9	-	-	PUNCT
ejpam-3977	203	10	locating	locate	VERB
ejpam-3977	203	11	sets	set	NOUN
ejpam-3977	203	12	,	,	PUNCT
ejpam-3977	203	13	then	then	ADV
ejpam-3977	203	14	sln1(g	sln1(g	PUNCT
ejpam-3977	203	15	)	)	PUNCT
ejpam-3977	203	16	+	+	NUM
ejpam-3977	203	17	sln1(h	sln1(h	NOUN
ejpam-3977	203	18	)	)	PUNCT
ejpam-3977	203	19	≤	≤	NUM
ejpam-3977	203	20	|sg|	|sg|	NOUN
ejpam-3977	203	21	+	+	CCONJ
ejpam-3977	203	22	|sh	|sh	PROPN
ejpam-3977	203	23	|	|	ADV
ejpam-3977	203	24	=	=	SYM
ejpam-3977	203	25	|s|	|s|	NOUN
ejpam-3977	203	26	=	=	NOUN
ejpam-3977	203	27	dim2(g	dim2(g	X
ejpam-3977	203	28	+	+	X
ejpam-3977	203	29	h	h	NOUN
ejpam-3977	203	30	)	)	PUNCT
ejpam-3977	203	31	.	.	PUNCT
ejpam-3977	204	1	thus	thus	ADV
ejpam-3977	204	2	,	,	PUNCT
ejpam-3977	204	3	dim2(g	dim2(g	X
ejpam-3977	204	4	+	+	CCONJ
ejpam-3977	204	5	h	h	X
ejpam-3977	204	6	)	)	PUNCT
ejpam-3977	204	7	≥	≥	PROPN
ejpam-3977	204	8	min	min	NOUN
ejpam-3977	204	9	{	{	PUNCT
ejpam-3977	204	10	sln2(g	sln2(g	NUM
ejpam-3977	204	11	)	)	PUNCT
ejpam-3977	204	12	+	+	CCONJ
ejpam-3977	204	13	ln2(h	ln2(h	PROPN
ejpam-3977	204	14	)	)	PUNCT
ejpam-3977	204	15	,	,	PUNCT
ejpam-3977	204	16	ln2(g	ln2(g	PROPN
ejpam-3977	204	17	)	)	PUNCT
ejpam-3977	204	18	+	+	NUM
ejpam-3977	204	19	sln2(h	sln2(h	NUM
ejpam-3977	204	20	)	)	PUNCT
ejpam-3977	204	21	,	,	PUNCT
ejpam-3977	204	22	sln1(g	sln1(g	X
ejpam-3977	204	23	)	)	PUNCT
ejpam-3977	204	24	+	+	NUM
ejpam-3977	204	25	sln1(h	sln1(h	NOUN
ejpam-3977	204	26	)	)	PUNCT
ejpam-3977	204	27	}	}	PUNCT
ejpam-3977	204	28	.	.	PUNCT
ejpam-3977	205	1	next	next	ADV
ejpam-3977	205	2	suppose	suppose	VERB
ejpam-3977	205	3	that	that	SCONJ
ejpam-3977	205	4	sln1(g	sln1(g	PUNCT
ejpam-3977	205	5	)	)	PUNCT
ejpam-3977	205	6	+	+	NUM
ejpam-3977	205	7	sln1(h	sln1(h	NOUN
ejpam-3977	205	8	)	)	PUNCT
ejpam-3977	205	9	≤	≤	NOUN
ejpam-3977	205	10	sln2(g	sln2(g	PRON
ejpam-3977	205	11	)	)	PUNCT
ejpam-3977	205	12	+	+	CCONJ
ejpam-3977	205	13	ln2(h	ln2(h	PROPN
ejpam-3977	205	14	)	)	PUNCT
ejpam-3977	205	15	and	and	CCONJ
ejpam-3977	205	16	sln1(g	sln1(g	NUM
ejpam-3977	205	17	)	)	PUNCT
ejpam-3977	205	18	+	+	NUM
ejpam-3977	205	19	sln1(h	sln1(h	NOUN
ejpam-3977	205	20	)	)	PUNCT
ejpam-3977	205	21	≤	≤	NUM
ejpam-3977	205	22	ln2(g	ln2(g	PROPN
ejpam-3977	205	23	)	)	PUNCT
ejpam-3977	205	24	+	+	NUM
ejpam-3977	205	25	sln2(h	sln2(h	NUM
ejpam-3977	205	26	)	)	PUNCT
ejpam-3977	205	27	.	.	PUNCT
ejpam-3977	206	1	let	let	VERB
ejpam-3977	206	2	sg	sg	PART
ejpam-3977	206	3	be	be	AUX
ejpam-3977	206	4	a	a	DET
ejpam-3977	206	5	minimum	minimum	NOUN
ejpam-3977	206	6	strictly	strictly	ADV
ejpam-3977	206	7	1	1	NUM
ejpam-3977	206	8	-	-	PUNCT
ejpam-3977	206	9	locating	locate	VERB
ejpam-3977	206	10	set	set	NOUN
ejpam-3977	206	11	in	in	ADP
ejpam-3977	206	12	g	g	PROPN
ejpam-3977	206	13	and	and	CCONJ
ejpam-3977	206	14	sh	sh	PROPN
ejpam-3977	206	15	be	be	AUX
ejpam-3977	206	16	a	a	DET
ejpam-3977	206	17	minimum	minimum	NOUN
ejpam-3977	206	18	strictly	strictly	ADV
ejpam-3977	206	19	1	1	NUM
ejpam-3977	206	20	-	-	PUNCT
ejpam-3977	206	21	locating	locate	VERB
ejpam-3977	206	22	set	set	NOUN
ejpam-3977	206	23	in	in	ADP
ejpam-3977	206	24	h.	h.	PROPN
ejpam-3977	206	25	then	then	ADV
ejpam-3977	206	26	s	s	VERB
ejpam-3977	206	27	=	=	PUNCT
ejpam-3977	206	28	sg	sg	PROPN
ejpam-3977	206	29	∪	∪	NOUN
ejpam-3977	206	30	sh	sh	PROPN
ejpam-3977	206	31	is	be	AUX
ejpam-3977	206	32	a	a	DET
ejpam-3977	206	33	2	2	NUM
ejpam-3977	206	34	-	-	PUNCT
ejpam-3977	206	35	resolving	resolving	NOUN
ejpam-3977	206	36	set	set	NOUN
ejpam-3977	206	37	in	in	ADP
ejpam-3977	206	38	g	g	PROPN
ejpam-3977	207	1	+	+	CCONJ
ejpam-3977	207	2	h	h	NOUN
ejpam-3977	207	3	,	,	PUNCT
ejpam-3977	207	4	by	by	ADP
ejpam-3977	207	5	theorem	theorem	NOUN
ejpam-3977	207	6	4	4	NUM
ejpam-3977	207	7	.	.	PUNCT
ejpam-3977	208	1	hence	hence	ADV
ejpam-3977	208	2	dim2(g	dim2(g	PRON
ejpam-3977	208	3	+	+	CCONJ
ejpam-3977	208	4	h	h	X
ejpam-3977	208	5	)	)	PUNCT
ejpam-3977	208	6	≤	≤	NUM
ejpam-3977	208	7	|s|	|s|	PROPN
ejpam-3977	208	8	=	=	PUNCT
ejpam-3977	208	9	|sg|	|sg|	PROPN
ejpam-3977	208	10	+	+	CCONJ
ejpam-3977	208	11	|sh	|sh	PROPN
ejpam-3977	208	12	|	|	ADV
ejpam-3977	208	13	=	=	PUNCT
ejpam-3977	208	14	sln1(g	sln1(g	X
ejpam-3977	208	15	)	)	PUNCT
ejpam-3977	208	16	+	+	NUM
ejpam-3977	208	17	sln1(h	sln1(h	NOUN
ejpam-3977	208	18	)	)	PUNCT
ejpam-3977	208	19	.	.	PUNCT
ejpam-3977	209	1	therefore	therefore	ADV
ejpam-3977	209	2	,	,	PUNCT
ejpam-3977	209	3	dim2(g	dim2(g	X
ejpam-3977	209	4	+	+	CCONJ
ejpam-3977	209	5	h	h	X
ejpam-3977	209	6	)	)	PUNCT
ejpam-3977	209	7	≤	≤	NOUN
ejpam-3977	209	8	sln1(g	sln1(g	NOUN
ejpam-3977	209	9	)	)	PUNCT
ejpam-3977	209	10	+	+	NUM
ejpam-3977	209	11	sln1(h	sln1(h	NOUN
ejpam-3977	209	12	)	)	PUNCT
ejpam-3977	209	13	.	.	PUNCT
ejpam-3977	210	1	similarly	similarly	ADV
ejpam-3977	210	2	,	,	PUNCT
ejpam-3977	210	3	if	if	SCONJ
ejpam-3977	210	4	sln2(g	sln2(g	NUM
ejpam-3977	210	5	)	)	PUNCT
ejpam-3977	210	6	+	+	CCONJ
ejpam-3977	210	7	ln2(h	ln2(h	PROPN
ejpam-3977	210	8	)	)	PUNCT
ejpam-3977	210	9	≤	≤	NOUN
ejpam-3977	210	10	sln1(g	sln1(g	NOUN
ejpam-3977	210	11	)	)	PUNCT
ejpam-3977	210	12	+	+	NUM
ejpam-3977	210	13	sln1(h	sln1(h	NOUN
ejpam-3977	210	14	)	)	PUNCT
ejpam-3977	210	15	and	and	CCONJ
ejpam-3977	210	16	sln2(g	sln2(g	NUM
ejpam-3977	210	17	)	)	PUNCT
ejpam-3977	210	18	+	+	CCONJ
ejpam-3977	210	19	ln2(h	ln2(h	PROPN
ejpam-3977	210	20	)	)	PUNCT
ejpam-3977	210	21	≤	≤	NOUN
ejpam-3977	210	22	ln2(g	ln2(g	PROPN
ejpam-3977	210	23	)	)	PUNCT
ejpam-3977	210	24	+	+	NUM
ejpam-3977	210	25	sln2(h	sln2(h	NUM
ejpam-3977	210	26	)	)	PUNCT
ejpam-3977	210	27	,	,	PUNCT
ejpam-3977	210	28	then	then	ADV
ejpam-3977	210	29	dim2(g	dim2(g	PRON
ejpam-3977	210	30	+	+	CCONJ
ejpam-3977	210	31	h	h	X
ejpam-3977	210	32	)	)	PUNCT
ejpam-3977	210	33	≤	≤	NOUN
ejpam-3977	210	34	sln2(g	sln2(g	PRON
ejpam-3977	210	35	)	)	PUNCT
ejpam-3977	210	36	+	+	CCONJ
ejpam-3977	210	37	ln2(h	ln2(h	PROPN
ejpam-3977	210	38	)	)	PUNCT
ejpam-3977	210	39	.	.	PUNCT
ejpam-3977	211	1	also	also	ADV
ejpam-3977	211	2	,	,	PUNCT
ejpam-3977	211	3	if	if	SCONJ
ejpam-3977	211	4	ln2(g	ln2(g	NOUN
ejpam-3977	211	5	)	)	PUNCT
ejpam-3977	211	6	+	+	NUM
ejpam-3977	211	7	sln2(h	sln2(h	X
ejpam-3977	211	8	)	)	PUNCT
ejpam-3977	211	9	≤	≤	NOUN
ejpam-3977	211	10	sln2(g	sln2(g	PRON
ejpam-3977	211	11	)	)	PUNCT
ejpam-3977	211	12	+	+	CCONJ
ejpam-3977	211	13	ln2(h	ln2(h	PROPN
ejpam-3977	211	14	)	)	PUNCT
ejpam-3977	211	15	and	and	CCONJ
ejpam-3977	211	16	ln2(g	ln2(g	PROPN
ejpam-3977	211	17	)	)	PUNCT
ejpam-3977	211	18	+	+	NUM
ejpam-3977	211	19	sln2(h	sln2(h	X
ejpam-3977	211	20	)	)	PUNCT
ejpam-3977	211	21	≤	≤	NOUN
ejpam-3977	211	22	sln1(g	sln1(g	NOUN
ejpam-3977	211	23	)	)	PUNCT
ejpam-3977	211	24	+	+	NUM
ejpam-3977	211	25	sln1(h	sln1(h	NOUN
ejpam-3977	211	26	)	)	PUNCT
ejpam-3977	211	27	,	,	PUNCT
ejpam-3977	211	28	then	then	ADV
ejpam-3977	211	29	dim2(g	dim2(g	PRON
ejpam-3977	211	30	+	+	CCONJ
ejpam-3977	211	31	h	h	X
ejpam-3977	211	32	)	)	PUNCT
ejpam-3977	211	33	≤	≤	NOUN
ejpam-3977	211	34	ln2(g	ln2(g	PROPN
ejpam-3977	211	35	)	)	PUNCT
ejpam-3977	211	36	+	+	NUM
ejpam-3977	211	37	sln2(h	sln2(h	NUM
ejpam-3977	211	38	)	)	PUNCT
ejpam-3977	211	39	.	.	PUNCT
ejpam-3977	212	1	therefore	therefore	ADV
ejpam-3977	212	2	,	,	PUNCT
ejpam-3977	212	3	dim2(g	dim2(g	X
ejpam-3977	212	4	+	+	CCONJ
ejpam-3977	212	5	h	h	NOUN
ejpam-3977	212	6	)	)	PUNCT
ejpam-3977	212	7	=	=	SYM
ejpam-3977	212	8	min	min	NOUN
ejpam-3977	212	9	{	{	PUNCT
ejpam-3977	212	10	sln2(g	sln2(g	NUM
ejpam-3977	212	11	)	)	PUNCT
ejpam-3977	212	12	+	+	CCONJ
ejpam-3977	212	13	ln2(h	ln2(h	PROPN
ejpam-3977	212	14	)	)	PUNCT
ejpam-3977	212	15	,	,	PUNCT
ejpam-3977	212	16	ln2(g	ln2(g	PROPN
ejpam-3977	212	17	)	)	PUNCT
ejpam-3977	212	18	+	+	NUM
ejpam-3977	212	19	sln2(h	sln2(h	NUM
ejpam-3977	212	20	)	)	PUNCT
ejpam-3977	212	21	,	,	PUNCT
ejpam-3977	212	22	sln1(g	sln1(g	X
ejpam-3977	212	23	)	)	PUNCT
ejpam-3977	212	24	+	+	NUM
ejpam-3977	212	25	sln1(h	sln1(h	NOUN
ejpam-3977	212	26	)	)	PUNCT
ejpam-3977	212	27	}	}	PUNCT
ejpam-3977	212	28	.	.	PUNCT
ejpam-3977	213	1	example	example	NOUN
ejpam-3977	214	1	13	13	NUM
ejpam-3977	214	2	.	.	PUNCT
ejpam-3977	215	1	for	for	ADP
ejpam-3977	215	2	any	any	DET
ejpam-3977	215	3	n	n	CCONJ
ejpam-3977	215	4	,	,	PUNCT
ejpam-3977	215	5	m	m	VERB
ejpam-3977	215	6	≥	≥	NOUN
ejpam-3977	215	7	4	4	NUM
ejpam-3977	215	8	,	,	PUNCT
ejpam-3977	215	9	dim2(pn	dim2(pn	PROPN
ejpam-3977	215	10	+	+	CCONJ
ejpam-3977	215	11	pm	pm	NOUN
ejpam-3977	215	12	)	)	PUNCT
ejpam-3977	215	13	=	=	PUNCT
ejpam-3977	215	14			NOUN
ejpam-3977	215	15	(	(	PUNCT
ejpam-3977	215	16	n	n	ADV
ejpam-3977	215	17	2	2	NUM
ejpam-3977	215	18	+	+	NUM
ejpam-3977	215	19	1	1	NUM
ejpam-3977	215	20	)	)	PUNCT
ejpam-3977	215	21	+	+	CCONJ
ejpam-3977	215	22	(	(	PUNCT
ejpam-3977	215	23	m	m	VERB
ejpam-3977	215	24	2	2	NUM
ejpam-3977	215	25	+	+	NUM
ejpam-3977	215	26	1	1	NUM
ejpam-3977	215	27	)	)	PUNCT
ejpam-3977	215	28	,	,	PUNCT
ejpam-3977	215	29	if	if	SCONJ
ejpam-3977	215	30	n	n	CCONJ
ejpam-3977	215	31	,	,	PUNCT
ejpam-3977	215	32	m	m	VERB
ejpam-3977	215	33	even	even	ADV
ejpam-3977	215	34	(	(	PUNCT
ejpam-3977	215	35	n	n	ADV
ejpam-3977	215	36	2	2	NUM
ejpam-3977	215	37	+	+	NUM
ejpam-3977	215	38	1	1	NUM
ejpam-3977	215	39	)	)	PUNCT
ejpam-3977	215	40	+	+	PUNCT
ejpam-3977	215	41	⌈	⌈	NUM
ejpam-3977	215	42	m	m	VERB
ejpam-3977	215	43	2	2	NUM
ejpam-3977	215	44	⌉	⌉	NOUN
ejpam-3977	215	45	,	,	PUNCT
ejpam-3977	215	46	if	if	SCONJ
ejpam-3977	215	47	n	n	PRON
ejpam-3977	215	48	is	be	AUX
ejpam-3977	215	49	even	even	ADV
ejpam-3977	215	50	,	,	PUNCT
ejpam-3977	215	51	m	m	VERB
ejpam-3977	215	52	is	be	AUX
ejpam-3977	215	53	odd⌈	odd⌈	ADJ
ejpam-3977	215	54	n	n	DET
ejpam-3977	215	55	2	2	NUM
ejpam-3977	215	56	⌉	⌉	X
ejpam-3977	215	57	+	+	CCONJ
ejpam-3977	215	58	(	(	PUNCT
ejpam-3977	215	59	m	m	VERB
ejpam-3977	215	60	2	2	NUM
ejpam-3977	215	61	+	+	NUM
ejpam-3977	215	62	1	1	NUM
ejpam-3977	215	63	)	)	PUNCT
ejpam-3977	215	64	,	,	PUNCT
ejpam-3977	215	65	if	if	SCONJ
ejpam-3977	215	66	n	n	PRON
ejpam-3977	215	67	is	be	AUX
ejpam-3977	215	68	odd	odd	ADJ
ejpam-3977	215	69	,	,	PUNCT
ejpam-3977	215	70	m	m	VERB
ejpam-3977	215	71	is	be	AUX
ejpam-3977	215	72	even⌈	even⌈	NOUN
ejpam-3977	215	73	n	n	CCONJ
ejpam-3977	215	74	2	2	NUM
ejpam-3977	215	75	⌉	⌉	NOUN
ejpam-3977	215	76	+	+	CCONJ
ejpam-3977	215	77	⌈	⌈	NUM
ejpam-3977	215	78	m	m	VERB
ejpam-3977	215	79	2	2	NUM
ejpam-3977	215	80	⌉	⌉	NOUN
ejpam-3977	215	81	,	,	PUNCT
ejpam-3977	215	82	if	if	SCONJ
ejpam-3977	215	83	n	n	CCONJ
ejpam-3977	215	84	,	,	PUNCT
ejpam-3977	215	85	m	m	PROPN
ejpam-3977	215	86	odd	odd	ADJ
ejpam-3977	215	87	j.	j.	PROPN
ejpam-3977	215	88	cabaro	cabaro	PROPN
ejpam-3977	215	89	,	,	PUNCT
ejpam-3977	215	90	h.	h.	PROPN
ejpam-3977	215	91	rara	rara	PROPN
ejpam-3977	215	92	/	/	SYM
ejpam-3977	215	93	eur	eur	PROPN
ejpam-3977	215	94	.	.	PUNCT
ejpam-3977	216	1	j.	j.	PROPN
ejpam-3977	216	2	pure	pure	PROPN
ejpam-3977	216	3	appl	appl	PROPN
ejpam-3977	216	4	.	.	PROPN
ejpam-3977	216	5	math	math	PROPN
ejpam-3977	216	6	,	,	PUNCT
ejpam-3977	216	7	14	14	NUM
ejpam-3977	216	8	(	(	PUNCT
ejpam-3977	216	9	3	3	NUM
ejpam-3977	216	10	)	)	PUNCT
ejpam-3977	216	11	(	(	PUNCT
ejpam-3977	216	12	2021	2021	NUM
ejpam-3977	216	13	)	)	PUNCT
ejpam-3977	216	14	,	,	PUNCT
ejpam-3977	216	15	773	773	NUM
ejpam-3977	216	16	-	-	SYM
ejpam-3977	216	17	782	782	NUM
ejpam-3977	216	18	780	780	NUM
ejpam-3977	216	19	in	in	ADP
ejpam-3977	216	20	particular	particular	ADJ
ejpam-3977	216	21	,	,	PUNCT
ejpam-3977	216	22	for	for	ADP
ejpam-3977	216	23	n	n	NOUN
ejpam-3977	216	24	=	=	SYM
ejpam-3977	216	25	2	2	NUM
ejpam-3977	216	26	,	,	PUNCT
ejpam-3977	216	27	3	3	NUM
ejpam-3977	216	28	and	and	CCONJ
ejpam-3977	216	29	m	m	PROPN
ejpam-3977	216	30	=	=	ADJ
ejpam-3977	216	31	2	2	NUM
ejpam-3977	216	32	,	,	PUNCT
ejpam-3977	216	33	3	3	NUM
ejpam-3977	216	34	,	,	PUNCT
ejpam-3977	216	35	dim2(pn	dim2(pn	PROPN
ejpam-3977	216	36	+	+	CCONJ
ejpam-3977	216	37	pm	pm	NOUN
ejpam-3977	216	38	)	)	PUNCT
ejpam-3977	216	39	=	=	SYM
ejpam-3977	216	40	n	n	PROPN
ejpam-3977	216	41	+	+	NOUN
ejpam-3977	216	42	m	m	NUM
ejpam-3977	216	43	4	4	NUM
ejpam-3977	216	44	.	.	NOUN
ejpam-3977	217	1	2	2	NUM
ejpam-3977	217	2	-	-	PUNCT
ejpam-3977	217	3	resolving	resolve	VERB
ejpam-3977	217	4	sets	set	NOUN
ejpam-3977	217	5	in	in	ADP
ejpam-3977	217	6	the	the	DET
ejpam-3977	217	7	corona	corona	NOUN
ejpam-3977	217	8	of	of	ADP
ejpam-3977	217	9	graphs	graph	NOUN
ejpam-3977	217	10	definition	definition	NOUN
ejpam-3977	217	11	5	5	NUM
ejpam-3977	217	12	.	.	PUNCT
ejpam-3977	218	1	[	[	X
ejpam-3977	218	2	2	2	X
ejpam-3977	218	3	]	]	PUNCT
ejpam-3977	218	4	the	the	DET
ejpam-3977	218	5	corona	corona	NOUN
ejpam-3977	218	6	g	g	PROPN
ejpam-3977	218	7	◦	◦	NOUN
ejpam-3977	218	8	h	h	NOUN
ejpam-3977	218	9	of	of	ADP
ejpam-3977	218	10	two	two	NUM
ejpam-3977	218	11	graphs	graph	NOUN
ejpam-3977	218	12	g	g	NOUN
ejpam-3977	218	13	and	and	CCONJ
ejpam-3977	218	14	h	h	NOUN
ejpam-3977	218	15	is	be	AUX
ejpam-3977	218	16	the	the	DET
ejpam-3977	218	17	graph	graph	NOUN
ejpam-3977	218	18	obtained	obtain	VERB
ejpam-3977	218	19	by	by	ADP
ejpam-3977	218	20	taking	take	VERB
ejpam-3977	218	21	one	one	NUM
ejpam-3977	218	22	copy	copy	NOUN
ejpam-3977	218	23	of	of	ADP
ejpam-3977	218	24	g	g	NOUN
ejpam-3977	218	25	of	of	ADP
ejpam-3977	218	26	order	order	NOUN
ejpam-3977	218	27	n	n	NOUN
ejpam-3977	218	28	and	and	CCONJ
ejpam-3977	218	29	n	n	PRON
ejpam-3977	218	30	copies	copy	NOUN
ejpam-3977	218	31	of	of	ADP
ejpam-3977	218	32	h	h	NOUN
ejpam-3977	218	33	,	,	PUNCT
ejpam-3977	218	34	and	and	CCONJ
ejpam-3977	218	35	then	then	ADV
ejpam-3977	218	36	joining	join	VERB
ejpam-3977	218	37	the	the	DET
ejpam-3977	218	38	ith	ith	PROPN
ejpam-3977	218	39	vertex	vertex	NOUN
ejpam-3977	218	40	of	of	ADP
ejpam-3977	218	41	g	g	NOUN
ejpam-3977	218	42	to	to	ADP
ejpam-3977	218	43	every	every	DET
ejpam-3977	218	44	vertex	vertex	NOUN
ejpam-3977	218	45	in	in	ADP
ejpam-3977	218	46	the	the	DET
ejpam-3977	218	47	ith	ith	PROPN
ejpam-3977	218	48	copy	copy	NOUN
ejpam-3977	218	49	of	of	ADP
ejpam-3977	218	50	h.	h.	PROPN
ejpam-3977	218	51	for	for	ADP
ejpam-3977	218	52	every	every	DET
ejpam-3977	218	53	v	v	NUM
ejpam-3977	218	54	∈	∈	PROPN
ejpam-3977	218	55	v	v	NOUN
ejpam-3977	218	56	(	(	PUNCT
ejpam-3977	218	57	g	g	NOUN
ejpam-3977	218	58	)	)	PUNCT
ejpam-3977	218	59	,	,	PUNCT
ejpam-3977	218	60	denote	denote	VERB
ejpam-3977	218	61	by	by	ADP
ejpam-3977	218	62	hv	hv	PROPN
ejpam-3977	218	63	the	the	DET
ejpam-3977	218	64	copy	copy	NOUN
ejpam-3977	218	65	of	of	ADP
ejpam-3977	218	66	h	h	NOUN
ejpam-3977	218	67	whose	whose	DET
ejpam-3977	218	68	vertices	vertex	NOUN
ejpam-3977	218	69	are	be	AUX
ejpam-3977	218	70	attached	attach	VERB
ejpam-3977	218	71	one	one	NUM
ejpam-3977	218	72	by	by	ADP
ejpam-3977	218	73	one	one	NUM
ejpam-3977	218	74	to	to	ADP
ejpam-3977	218	75	the	the	DET
ejpam-3977	218	76	vertex	vertex	NOUN
ejpam-3977	218	77	v.	v.	ADP
ejpam-3977	218	78	subsequently	subsequently	ADV
ejpam-3977	218	79	,	,	PUNCT
ejpam-3977	218	80	denote	denote	VERB
ejpam-3977	218	81	by	by	ADP
ejpam-3977	218	82	v	v	PRON
ejpam-3977	219	1	+	+	CCONJ
ejpam-3977	219	2	hv	hv	NOUN
ejpam-3977	219	3	the	the	DET
ejpam-3977	219	4	subgraph	subgraph	NOUN
ejpam-3977	219	5	of	of	ADP
ejpam-3977	219	6	the	the	DET
ejpam-3977	219	7	corona	corona	NOUN
ejpam-3977	219	8	g	g	PROPN
ejpam-3977	219	9	◦	◦	NOUN
ejpam-3977	219	10	h	h	NOUN
ejpam-3977	219	11	corresponding	correspond	VERB
ejpam-3977	219	12	to	to	ADP
ejpam-3977	219	13	the	the	DET
ejpam-3977	219	14	join	join	NOUN
ejpam-3977	219	15	〈	〈	PROPN
ejpam-3977	219	16	{	{	PUNCT
ejpam-3977	219	17	v}〉+	v}〉+	PROPN
ejpam-3977	219	18	hv	hv	PROPN
ejpam-3977	219	19	,	,	PUNCT
ejpam-3977	219	20	v	v	NOUN
ejpam-3977	219	21	∈	∈	PROPN
ejpam-3977	219	22	v	v	NOUN
ejpam-3977	219	23	(	(	PUNCT
ejpam-3977	219	24	g	g	NOUN
ejpam-3977	219	25	)	)	PUNCT
ejpam-3977	219	26	.	.	PUNCT
ejpam-3977	220	1	the	the	DET
ejpam-3977	220	2	sets	set	NOUN
ejpam-3977	220	3	{	{	PUNCT
ejpam-3977	220	4	u1	u1	NOUN
ejpam-3977	220	5	,	,	PUNCT
ejpam-3977	220	6	u2	u2	NOUN
ejpam-3977	220	7	,	,	PUNCT
ejpam-3977	220	8	v1	v1	NOUN
ejpam-3977	220	9	,	,	PUNCT
ejpam-3977	220	10	v2	v2	PROPN
ejpam-3977	220	11	,	,	PUNCT
ejpam-3977	220	12	w1	w1	NOUN
ejpam-3977	220	13	,	,	PUNCT
ejpam-3977	220	14	w2	w2	NOUN
ejpam-3977	220	15	}	}	PUNCT
ejpam-3977	220	16	and	and	CCONJ
ejpam-3977	220	17	{	{	PUNCT
ejpam-3977	220	18	a1	a1	NOUN
ejpam-3977	220	19	,	,	PUNCT
ejpam-3977	220	20	a3	a3	NOUN
ejpam-3977	220	21	,	,	PUNCT
ejpam-3977	220	22	b1	b1	NOUN
ejpam-3977	220	23	,	,	PUNCT
ejpam-3977	220	24	b3	b3	PROPN
ejpam-3977	220	25	,	,	PUNCT
ejpam-3977	220	26	c1	c1	PROPN
ejpam-3977	220	27	,	,	PUNCT
ejpam-3977	220	28	c3	c3	PROPN
ejpam-3977	220	29	,	,	PUNCT
ejpam-3977	220	30	d1	d1	PROPN
ejpam-3977	220	31	,	,	PUNCT
ejpam-3977	220	32	d3	d3	PROPN
ejpam-3977	220	33	}	}	PUNCT
ejpam-3977	220	34	are	be	AUX
ejpam-3977	220	35	2	2	NUM
ejpam-3977	220	36	-	-	PUNCT
ejpam-3977	220	37	resolving	resolve	VERB
ejpam-3977	220	38	sets	set	NOUN
ejpam-3977	220	39	in	in	ADP
ejpam-3977	220	40	the	the	DET
ejpam-3977	220	41	coronas	coronas	PROPN
ejpam-3977	220	42	p3	p3	PROPN
ejpam-3977	220	43	◦	◦	PROPN
ejpam-3977	220	44	p2	p2	PROPN
ejpam-3977	220	45	and	and	CCONJ
ejpam-3977	220	46	c4	c4	NOUN
ejpam-3977	220	47	◦	◦	PROPN
ejpam-3977	220	48	p3	p3	PROPN
ejpam-3977	220	49	,	,	PUNCT
ejpam-3977	220	50	respectively	respectively	ADV
ejpam-3977	220	51	,	,	PUNCT
ejpam-3977	220	52	in	in	ADP
ejpam-3977	220	53	figure	figure	NOUN
ejpam-3977	220	54	4	4	NUM
ejpam-3977	220	55	.	.	PUNCT
ejpam-3977	220	56	....................................	....................................	PUNCT
ejpam-3977	221	1	....................................	....................................	PUNCT
ejpam-3977	221	2	........................................................................	........................................................................	PUNCT
ejpam-3977	222	1	....................................	....................................	PUNCT
ejpam-3977	222	2	........................................................................	........................................................................	PUNCT
ejpam-3977	223	1	....................................	....................................	PUNCT
ejpam-3977	223	2	....................................	....................................	PUNCT
ejpam-3977	224	1	....................................	....................................	PUNCT
ejpam-3977	224	2	....................................	....................................	PUNCT
ejpam-3977	225	1	....................................	....................................	PUNCT
ejpam-3977	225	2	....................................	....................................	PUNCT
ejpam-3977	226	1	....................................	....................................	PUNCT
ejpam-3977	226	2	....................................	....................................	PUNCT
ejpam-3977	227	1	....................................	....................................	PUNCT
ejpam-3977	227	2	....................................	....................................	PUNCT
ejpam-3977	228	1	....................................	....................................	PUNCT
ejpam-3977	228	2	....................................	....................................	PUNCT
ejpam-3977	229	1	....................................	....................................	PUNCT
ejpam-3977	229	2	....................................	....................................	PUNCT
ejpam-3977	230	1	....................................	....................................	PUNCT
ejpam-3977	230	2	............................................................................................................	............................................................................................................	PUNCT
ejpam-3977	231	1	..........	..........	PUNCT
ejpam-3977	231	2	.........	.........	PUNCT
ejpam-3977	232	1	.........	.........	PUNCT
ejpam-3977	232	2	.........	.........	PUNCT
ejpam-3977	233	1	.........	.........	PUNCT
ejpam-3977	233	2	.........	.........	PUNCT
ejpam-3977	234	1	.........	.........	PUNCT
ejpam-3977	234	2	.........	.........	PUNCT
ejpam-3977	235	1	.........	.........	PUNCT
ejpam-3977	235	2	.........	.........	PUNCT
ejpam-3977	236	1	.........	.........	PUNCT
ejpam-3977	236	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3977	236	3	.............................................................................................	.............................................................................................	PUNCT
ejpam-3977	237	1	...........................................................................................................................................................	...........................................................................................................................................................	PUNCT
ejpam-3977	237	2	.........	.........	PUNCT
ejpam-3977	238	1	.........	.........	PUNCT
ejpam-3977	238	2	.........	.........	PUNCT
ejpam-3977	239	1	.........	.........	PUNCT
ejpam-3977	239	2	.........	.........	PUNCT
ejpam-3977	240	1	.........	.........	PUNCT
ejpam-3977	240	2	.........	.........	PUNCT
ejpam-3977	241	1	.........	.........	PUNCT
ejpam-3977	241	2	.........	.........	PUNCT
ejpam-3977	242	1	.........	.........	PUNCT
ejpam-3977	242	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3977	242	3	.............................................................................................	.............................................................................................	PUNCT
ejpam-3977	243	1	...........................................................................................................................................................	...........................................................................................................................................................	PUNCT
ejpam-3977	243	2	.........	.........	PUNCT
ejpam-3977	244	1	.........	.........	PUNCT
ejpam-3977	244	2	.........	.........	PUNCT
ejpam-3977	245	1	.........	.........	PUNCT
ejpam-3977	245	2	.........	.........	PUNCT
ejpam-3977	246	1	.........	.........	PUNCT
ejpam-3977	246	2	.........	.........	PUNCT
ejpam-3977	247	1	.........	.........	PUNCT
ejpam-3977	247	2	.........	.........	PUNCT
ejpam-3977	248	1	.........	.........	PUNCT
ejpam-3977	248	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-3977	248	3	.............................................................................................	.............................................................................................	PUNCT
ejpam-3977	249	1	.........	.........	PUNCT
ejpam-3977	249	2	........	........	PUNCT
ejpam-3977	249	3	........	........	PUNCT
ejpam-3977	249	4	........	........	PUNCT
ejpam-3977	249	5	........	........	PUNCT
ejpam-3977	249	6	.	.	PUNCT
ejpam-3977	250	1	.........	.........	PUNCT
ejpam-3977	250	2	........	........	PUNCT
ejpam-3977	250	3	........	........	PUNCT
ejpam-3977	250	4	........	........	PUNCT
ejpam-3977	251	1	........	........	PUNCT
ejpam-3977	251	2	.	.	PUNCT
ejpam-3977	252	1	.............................................................................................	.............................................................................................	PUNCT
ejpam-3977	252	2	..........................................................................................................	..........................................................................................................	PUNCT
ejpam-3977	253	1	...................	...................	PUNCT
ejpam-3977	253	2	..................	..................	PUNCT
ejpam-3977	254	1	..................	..................	PUNCT
ejpam-3977	254	2	..................	..................	PUNCT
ejpam-3977	255	1	..................	..................	PUNCT
ejpam-3977	255	2	...............	...............	PUNCT
ejpam-3977	256	1	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-3977	256	2	..........	..........	PUNCT
ejpam-3977	257	1	.........	.........	PUNCT
ejpam-3977	257	2	.........	.........	PUNCT
ejpam-3977	258	1	.........	.........	PUNCT
ejpam-3977	258	2	.........	.........	PUNCT
ejpam-3977	259	1	.........	.........	PUNCT
ejpam-3977	259	2	.........	.........	PUNCT
ejpam-3977	260	1	.........	.........	PUNCT
ejpam-3977	260	2	.........	.........	PUNCT
ejpam-3977	261	1	.........	.........	PUNCT
ejpam-3977	261	2	.........	.........	PUNCT
ejpam-3977	262	1	......	......	PUNCT
ejpam-3977	262	2	.........	.........	PUNCT
ejpam-3977	262	3	........	........	PUNCT
ejpam-3977	262	4	........	........	PUNCT
ejpam-3977	262	5	........	........	PUNCT
ejpam-3977	262	6	........	........	PUNCT
ejpam-3977	262	7	........	........	PUNCT
ejpam-3977	262	8	........	........	PUNCT
ejpam-3977	262	9	........	........	PUNCT
ejpam-3977	262	10	........	........	PUNCT
ejpam-3977	262	11	........	........	PUNCT
ejpam-3977	262	12	........	........	PUNCT
ejpam-3977	262	13	........................................................................................................................................................	........................................................................................................................................................	PROPN
ejpam-3977	262	14	..........................................	..........................................	PUNCT
ejpam-3977	262	15	............	............	PUNCT
ejpam-3977	262	16	...........	...........	PUNCT
ejpam-3977	262	17	...........	...........	PUNCT
ejpam-3977	262	18	...........	...........	PUNCT
ejpam-3977	262	19	...........	...........	PUNCT
ejpam-3977	262	20	...........	...........	PUNCT
ejpam-3977	262	21	...........	...........	PUNCT
ejpam-3977	262	22	...........	...........	PUNCT
ejpam-3977	262	23	...........	...........	PUNCT
ejpam-3977	262	24	...........	...........	PUNCT
ejpam-3977	262	25	...........	...........	PUNCT
ejpam-3977	262	26	...........	...........	PUNCT
ejpam-3977	262	27	...	...	PUNCT
ejpam-3977	262	28	...................	...................	PUNCT
ejpam-3977	263	1	..................	..................	PUNCT
ejpam-3977	263	2	..................	..................	PUNCT
ejpam-3977	264	1	..................	..................	PUNCT
ejpam-3977	264	2	..................	..................	PUNCT
ejpam-3977	264	3	...............	...............	PUNCT
ejpam-3977	265	1	.......................................................................................................................................................................................................	.......................................................................................................................................................................................................	PUNCT
ejpam-3977	265	2	.........	.........	PUNCT
ejpam-3977	265	3	........	........	PUNCT
ejpam-3977	265	4	........	........	PUNCT
ejpam-3977	265	5	........	........	PUNCT
ejpam-3977	265	6	........	........	PUNCT
ejpam-3977	265	7	.	.	PUNCT
ejpam-3977	265	8	.........	.........	PUNCT
ejpam-3977	266	1	........	........	PUNCT
ejpam-3977	266	2	........	........	PUNCT
ejpam-3977	266	3	........	........	PUNCT
ejpam-3977	266	4	........	........	PUNCT
ejpam-3977	266	5	.	.	PUNCT
ejpam-3977	266	6	............	............	PUNCT
ejpam-3977	267	1	...........	...........	PUNCT
ejpam-3977	267	2	...........	...........	PUNCT
ejpam-3977	267	3	...........	...........	PUNCT
ejpam-3977	267	4	...........	...........	PUNCT
ejpam-3977	267	5	...........	...........	PUNCT
ejpam-3977	267	6	...........	...........	PUNCT
ejpam-3977	267	7	...........	...........	PUNCT
ejpam-3977	267	8	...........	...........	PUNCT
ejpam-3977	267	9	...........	...........	PUNCT
ejpam-3977	267	10	...........	...........	PUNCT
ejpam-3977	267	11	...........	...........	PUNCT
ejpam-3977	267	12	...	...	PUNCT
ejpam-3977	267	13	...................................................................................................................	...................................................................................................................	PUNCT
ejpam-3977	267	14	........	........	PUNCT
ejpam-3977	267	15	........	........	PUNCT
ejpam-3977	267	16	........	........	PUNCT
ejpam-3977	267	17	........	........	PUNCT
ejpam-3977	267	18	........	........	PUNCT
ejpam-3977	267	19	........	........	PUNCT
ejpam-3977	267	20	........	........	PUNCT
ejpam-3977	267	21	........	........	PUNCT
ejpam-3977	267	22	........	........	PUNCT
ejpam-3977	267	23	........	........	PUNCT
ejpam-3977	268	1	....	....	PUNCT
ejpam-3977	268	2	..........	..........	PUNCT
ejpam-3977	269	1	.........	.........	PUNCT
ejpam-3977	269	2	.........	.........	PUNCT
ejpam-3977	270	1	.........	.........	PUNCT
ejpam-3977	270	2	.........	.........	PUNCT
ejpam-3977	271	1	.........	.........	PUNCT
ejpam-3977	271	2	.........	.........	PUNCT
ejpam-3977	272	1	.........	.........	PUNCT
ejpam-3977	272	2	.........	.........	PUNCT
ejpam-3977	273	1	.........	.........	PUNCT
ejpam-3977	273	2	.........	.........	PUNCT
ejpam-3977	274	1	......	......	PUNCT
ejpam-3977	274	2	........................................................................................................................................	........................................................................................................................................	PUNCT
ejpam-3977	274	3	..........................................	..........................................	PUNCT
ejpam-3977	274	4	..........................................	..........................................	PUNCT
ejpam-3977	275	1	p3	p3	PROPN
ejpam-3977	275	2	◦	◦	NOUN
ejpam-3977	275	3	p2	p2	PROPN
ejpam-3977	275	4	:	:	PUNCT
ejpam-3977	275	5	u1	u1	NOUN
ejpam-3977	275	6	u2	u2	PROPN
ejpam-3977	275	7	v1	v1	PROPN
ejpam-3977	275	8	v2	v2	PROPN
ejpam-3977	275	9	w1	w1	NOUN
ejpam-3977	275	10	w2	w2	NOUN
ejpam-3977	275	11	u	u	PROPN
ejpam-3977	275	12	v	v	PROPN
ejpam-3977	275	13	w	w	PROPN
ejpam-3977	275	14	c4	c4	PROPN
ejpam-3977	275	15	◦	◦	PROPN
ejpam-3977	275	16	p3	p3	PROPN
ejpam-3977	275	17	:	:	PUNCT
ejpam-3977	275	18	a	a	DET
ejpam-3977	275	19	a1	a1	NOUN
ejpam-3977	275	20	a2	a2	PROPN
ejpam-3977	275	21	a3	a3	PROPN
ejpam-3977	275	22	b	b	PROPN
ejpam-3977	275	23	b1	b1	PROPN
ejpam-3977	275	24	b2	b2	NOUN
ejpam-3977	275	25	b3	b3	PROPN
ejpam-3977	275	26	c	c	PROPN
ejpam-3977	275	27	c1	c1	PROPN
ejpam-3977	275	28	c2	c2	PROPN
ejpam-3977	275	29	c3	c3	PROPN
ejpam-3977	275	30	d	d	PROPN
ejpam-3977	275	31	d1	d1	PROPN
ejpam-3977	275	32	d2	d2	PROPN
ejpam-3977	275	33	d3	d3	PROPN
ejpam-3977	275	34	figure	figure	NOUN
ejpam-3977	275	35	4	4	NUM
ejpam-3977	275	36	:	:	PUNCT
ejpam-3977	275	37	the	the	DET
ejpam-3977	275	38	corona	corona	PROPN
ejpam-3977	275	39	p3	p3	PROPN
ejpam-3977	275	40	◦	◦	PROPN
ejpam-3977	275	41	p2	p2	PROPN
ejpam-3977	275	42	with	with	ADP
ejpam-3977	275	43	dim2(p3	dim2(p3	PROPN
ejpam-3977	275	44	+	+	CCONJ
ejpam-3977	275	45	p2	p2	NOUN
ejpam-3977	275	46	)	)	PUNCT
ejpam-3977	275	47	=	=	SYM
ejpam-3977	275	48	6	6	NUM
ejpam-3977	275	49	and	and	CCONJ
ejpam-3977	275	50	the	the	DET
ejpam-3977	275	51	corona	corona	NOUN
ejpam-3977	275	52	c4	c4	NOUN
ejpam-3977	275	53	◦	◦	PROPN
ejpam-3977	275	54	p3	p3	PROPN
ejpam-3977	275	55	with	with	ADP
ejpam-3977	275	56	dim2(c4	dim2(c4	PROPN
ejpam-3977	275	57	◦	◦	NOUN
ejpam-3977	275	58	p3	p3	NOUN
ejpam-3977	275	59	)	)	PUNCT
ejpam-3977	275	60	=	=	SYM
ejpam-3977	275	61	8	8	NUM
ejpam-3977	275	62	remark	remark	NOUN
ejpam-3977	275	63	6	6	NUM
ejpam-3977	275	64	.	.	PUNCT
ejpam-3977	276	1	let	let	VERB
ejpam-3977	276	2	v	v	NUM
ejpam-3977	276	3	∈	∈	PROPN
ejpam-3977	276	4	v	v	NOUN
ejpam-3977	276	5	(	(	PUNCT
ejpam-3977	276	6	g	g	NOUN
ejpam-3977	276	7	)	)	PUNCT
ejpam-3977	276	8	.	.	PUNCT
ejpam-3977	277	1	for	for	ADP
ejpam-3977	277	2	every	every	DET
ejpam-3977	277	3	x	x	PROPN
ejpam-3977	277	4	,	,	PUNCT
ejpam-3977	277	5	y	y	PROPN
ejpam-3977	277	6	∈	∈	PROPN
ejpam-3977	277	7	v	v	PROPN
ejpam-3977	277	8	(	(	PUNCT
ejpam-3977	277	9	hv	hv	PROPN
ejpam-3977	277	10	)	)	PUNCT
ejpam-3977	277	11	,	,	PUNCT
ejpam-3977	277	12	dg	dg	PROPN
ejpam-3977	277	13	◦	◦	NOUN
ejpam-3977	277	14	h(x	h(x	PROPN
ejpam-3977	277	15	,	,	PUNCT
ejpam-3977	277	16	w	w	PROPN
ejpam-3977	277	17	)	)	PUNCT
ejpam-3977	277	18	=	=	SYM
ejpam-3977	277	19	dg	dg	NOUN
ejpam-3977	277	20	◦	◦	NOUN
ejpam-3977	277	21	h(y	h(y	ADV
ejpam-3977	277	22	,	,	PUNCT
ejpam-3977	277	23	w	w	NOUN
ejpam-3977	277	24	)	)	PUNCT
ejpam-3977	277	25	and	and	CCONJ
ejpam-3977	277	26	dg	dg	AUX
ejpam-3977	277	27	◦	◦	NOUN
ejpam-3977	277	28	h(v	h(v	PROPN
ejpam-3977	277	29	,	,	PUNCT
ejpam-3977	277	30	w	w	NOUN
ejpam-3977	277	31	)	)	PUNCT
ejpam-3977	277	32	+	+	CCONJ
ejpam-3977	277	33	1	1	NUM
ejpam-3977	277	34	=	=	SYM
ejpam-3977	277	35	dg	dg	NOUN
ejpam-3977	277	36	◦	◦	NOUN
ejpam-3977	277	37	h(x	h(x	PROPN
ejpam-3977	277	38	,	,	PUNCT
ejpam-3977	277	39	w	w	NOUN
ejpam-3977	277	40	)	)	PUNCT
ejpam-3977	277	41	for	for	ADP
ejpam-3977	277	42	every	every	DET
ejpam-3977	277	43	w	w	PROPN
ejpam-3977	277	44	∈	∈	PROPN
ejpam-3977	277	45	v	v	NOUN
ejpam-3977	277	46	(	(	PUNCT
ejpam-3977	277	47	g	g	PROPN
ejpam-3977	277	48	◦	◦	PROPN
ejpam-3977	277	49	h)\v	h)\v	PROPN
ejpam-3977	277	50	(	(	PUNCT
ejpam-3977	277	51	hv	hv	PROPN
ejpam-3977	277	52	)	)	PUNCT
ejpam-3977	277	53	.	.	PUNCT
ejpam-3977	278	1	remark	remark	PROPN
ejpam-3977	278	2	7	7	NUM
ejpam-3977	278	3	.	.	PUNCT
ejpam-3977	279	1	let	let	VERB
ejpam-3977	279	2	g	g	NOUN
ejpam-3977	279	3	and	and	CCONJ
ejpam-3977	279	4	h	h	PROPN
ejpam-3977	279	5	be	be	VERB
ejpam-3977	279	6	non	non	ADJ
ejpam-3977	279	7	-	-	ADJ
ejpam-3977	279	8	trivial	trivial	ADJ
ejpam-3977	279	9	connectd	connectd	VERB
ejpam-3977	279	10	graphs	graph	NOUN
ejpam-3977	279	11	,	,	PUNCT
ejpam-3977	279	12	c	c	PROPN
ejpam-3977	279	13	⊆	⊆	NUM
ejpam-3977	279	14	v	v	NOUN
ejpam-3977	279	15	(	(	PUNCT
ejpam-3977	279	16	g	g	PROPN
ejpam-3977	279	17	◦	◦	NOUN
ejpam-3977	279	18	h	h	NOUN
ejpam-3977	279	19	)	)	PUNCT
ejpam-3977	279	20	and	and	CCONJ
ejpam-3977	279	21	sv	sv	X
ejpam-3977	279	22	=	=	SYM
ejpam-3977	279	23	v	v	PROPN
ejpam-3977	279	24	(	(	PUNCT
ejpam-3977	279	25	hv	hv	NOUN
ejpam-3977	279	26	)	)	PUNCT
ejpam-3977	279	27	∩	∩	NOUN
ejpam-3977	279	28	c	c	X
ejpam-3977	279	29	where	where	SCONJ
ejpam-3977	279	30	v	v	X
ejpam-3977	279	31	∈	∈	NOUN
ejpam-3977	279	32	v	v	NOUN
ejpam-3977	279	33	(	(	PUNCT
ejpam-3977	279	34	g	g	NOUN
ejpam-3977	279	35	)	)	PUNCT
ejpam-3977	279	36	.	.	PUNCT
ejpam-3977	280	1	for	for	ADP
ejpam-3977	280	2	each	each	DET
ejpam-3977	280	3	x	x	SYM
ejpam-3977	280	4	∈	∈	PROPN
ejpam-3977	280	5	v	v	ADP
ejpam-3977	280	6	(	(	PUNCT
ejpam-3977	280	7	hv	hv	PROPN
ejpam-3977	280	8	)	)	PUNCT
ejpam-3977	280	9	\	\	PROPN
ejpam-3977	280	10	sv	sv	PROPN
ejpam-3977	280	11	and	and	CCONJ
ejpam-3977	280	12	z	z	PROPN
ejpam-3977	280	13	∈	∈	PROPN
ejpam-3977	280	14	sv	sv	PROPN
ejpam-3977	280	15	,	,	PUNCT
ejpam-3977	280	16	dg	dg	PROPN
ejpam-3977	280	17	◦	◦	NOUN
ejpam-3977	280	18	h(x	h(x	PROPN
ejpam-3977	280	19	,	,	PUNCT
ejpam-3977	280	20	z	z	NOUN
ejpam-3977	280	21	)	)	PUNCT
ejpam-3977	280	22	=	=	PRON
ejpam-3977	280	23	{	{	PUNCT
ejpam-3977	280	24	1	1	NUM
ejpam-3977	280	25	if	if	SCONJ
ejpam-3977	280	26	z	z	PROPN
ejpam-3977	280	27	∈	∈	PROPN
ejpam-3977	280	28	nhv(x	nhv(x	PROPN
ejpam-3977	280	29	)	)	PUNCT
ejpam-3977	280	30	2	2	NUM
ejpam-3977	280	31	otherwise	otherwise	ADV
ejpam-3977	280	32	theorem	theorem	VERB
ejpam-3977	280	33	5	5	NUM
ejpam-3977	280	34	.	.	PUNCT
ejpam-3977	280	35	let	let	VERB
ejpam-3977	280	36	g	g	NOUN
ejpam-3977	280	37	and	and	CCONJ
ejpam-3977	280	38	h	h	NOUN
ejpam-3977	280	39	be	be	AUX
ejpam-3977	280	40	nontrivial	nontrivial	ADJ
ejpam-3977	280	41	connected	connected	ADJ
ejpam-3977	280	42	graphs	graph	NOUN
ejpam-3977	280	43	.	.	PUNCT
ejpam-3977	281	1	a	a	DET
ejpam-3977	281	2	proper	proper	ADJ
ejpam-3977	281	3	subset	subset	NOUN
ejpam-3977	281	4	s	s	NOUN
ejpam-3977	281	5	of	of	ADP
ejpam-3977	281	6	v	v	NOUN
ejpam-3977	281	7	(	(	PUNCT
ejpam-3977	281	8	g	g	PROPN
ejpam-3977	281	9	◦	◦	NOUN
ejpam-3977	281	10	h	h	NOUN
ejpam-3977	281	11	)	)	PUNCT
ejpam-3977	281	12	is	be	AUX
ejpam-3977	281	13	a	a	DET
ejpam-3977	281	14	2	2	NUM
ejpam-3977	281	15	-	-	PUNCT
ejpam-3977	281	16	resolving	resolve	VERB
ejpam-3977	281	17	set	set	NOUN
ejpam-3977	281	18	of	of	ADP
ejpam-3977	281	19	g	g	PROPN
ejpam-3977	281	20	◦	◦	NOUN
ejpam-3977	281	21	h	h	NOUN
ejpam-3977	281	22	if	if	SCONJ
ejpam-3977	282	1	and	and	CCONJ
ejpam-3977	282	2	only	only	ADV
ejpam-3977	282	3	if	if	SCONJ
ejpam-3977	282	4	s	s	VERB
ejpam-3977	282	5	=	=	PUNCT
ejpam-3977	282	6	a	a	PRON
ejpam-3977	282	7	∪b	∪b	NOUN
ejpam-3977	282	8	,	,	PUNCT
ejpam-3977	282	9	where	where	SCONJ
ejpam-3977	282	10	a	a	DET
ejpam-3977	282	11	⊆	⊆	NUM
ejpam-3977	282	12	v	v	NOUN
ejpam-3977	282	13	(	(	PUNCT
ejpam-3977	282	14	g	g	NOUN
ejpam-3977	282	15	)	)	PUNCT
ejpam-3977	282	16	and	and	CCONJ
ejpam-3977	282	17	b	b	X
ejpam-3977	282	18	=	=	SYM
ejpam-3977	282	19	⋃	⋃	NOUN
ejpam-3977	282	20	{	{	PUNCT
ejpam-3977	282	21	sv	sv	NOUN
ejpam-3977	282	22	:	:	PUNCT
ejpam-3977	282	23	sv	sv	PROPN
ejpam-3977	282	24	is	be	AUX
ejpam-3977	282	25	a	a	DET
ejpam-3977	282	26	2	2	NUM
ejpam-3977	282	27	-	-	PUNCT
ejpam-3977	282	28	resolving	resolve	VERB
ejpam-3977	282	29	set	set	NOUN
ejpam-3977	282	30	of	of	ADP
ejpam-3977	282	31	hv	hv	PROPN
ejpam-3977	282	32	,	,	PUNCT
ejpam-3977	282	33	∀v	∀v	PROPN
ejpam-3977	282	34	∈	∈	PROPN
ejpam-3977	282	35	v	v	NOUN
ejpam-3977	282	36	(	(	PUNCT
ejpam-3977	282	37	g	g	NOUN
ejpam-3977	282	38	)	)	PUNCT
ejpam-3977	282	39	}	}	PUNCT
ejpam-3977	282	40	.	.	PUNCT
ejpam-3977	283	1	j.	j.	PROPN
ejpam-3977	283	2	cabaro	cabaro	PROPN
ejpam-3977	283	3	,	,	PUNCT
ejpam-3977	283	4	h.	h.	PROPN
ejpam-3977	283	5	rara	rara	PROPN
ejpam-3977	283	6	/	/	SYM
ejpam-3977	283	7	eur	eur	PROPN
ejpam-3977	283	8	.	.	PUNCT
ejpam-3977	284	1	j.	j.	PROPN
ejpam-3977	284	2	pure	pure	PROPN
ejpam-3977	284	3	appl	appl	PROPN
ejpam-3977	284	4	.	.	PROPN
ejpam-3977	284	5	math	math	PROPN
ejpam-3977	284	6	,	,	PUNCT
ejpam-3977	284	7	14	14	NUM
ejpam-3977	284	8	(	(	PUNCT
ejpam-3977	284	9	3	3	NUM
ejpam-3977	284	10	)	)	PUNCT
ejpam-3977	284	11	(	(	PUNCT
ejpam-3977	284	12	2021	2021	NUM
ejpam-3977	284	13	)	)	PUNCT
ejpam-3977	284	14	,	,	PUNCT
ejpam-3977	284	15	773	773	NUM
ejpam-3977	284	16	-	-	SYM
ejpam-3977	284	17	782	782	NUM
ejpam-3977	284	18	781	781	NUM
ejpam-3977	284	19	proof	proof	NOUN
ejpam-3977	284	20	.	.	PUNCT
ejpam-3977	285	1	suppose	suppose	VERB
ejpam-3977	285	2	s	s	NOUN
ejpam-3977	285	3	is	be	AUX
ejpam-3977	285	4	a	a	DET
ejpam-3977	285	5	2	2	NUM
ejpam-3977	285	6	-	-	PUNCT
ejpam-3977	285	7	resolving	resolving	NOUN
ejpam-3977	285	8	set	set	NOUN
ejpam-3977	285	9	in	in	ADP
ejpam-3977	285	10	g	g	PROPN
ejpam-3977	285	11	◦	◦	NOUN
ejpam-3977	285	12	h.	h.	NOUN
ejpam-3977	285	13	let	let	VERB
ejpam-3977	285	14	a	a	DET
ejpam-3977	285	15	=	=	X
ejpam-3977	285	16	v	v	NOUN
ejpam-3977	285	17	(	(	PUNCT
ejpam-3977	285	18	g)∩c	g)∩c	NOUN
ejpam-3977	285	19	and	and	CCONJ
ejpam-3977	285	20	sv	sv	NOUN
ejpam-3977	285	21	=	=	SYM
ejpam-3977	285	22	s∩v	s∩v	PROPN
ejpam-3977	285	23	(	(	PUNCT
ejpam-3977	285	24	hv	hv	PROPN
ejpam-3977	285	25	)	)	PUNCT
ejpam-3977	285	26	for	for	ADP
ejpam-3977	285	27	all	all	PRON
ejpam-3977	285	28	v	v	ADP
ejpam-3977	285	29	∈	∈	NOUN
ejpam-3977	285	30	v	v	NOUN
ejpam-3977	285	31	(	(	PUNCT
ejpam-3977	285	32	g	g	NOUN
ejpam-3977	285	33	)	)	PUNCT
ejpam-3977	285	34	.	.	PUNCT
ejpam-3977	286	1	then	then	ADV
ejpam-3977	286	2	s	s	VERB
ejpam-3977	286	3	=	=	SYM
ejpam-3977	286	4	a∪	a∪	PROPN
ejpam-3977	286	5	(	(	PUNCT
ejpam-3977	286	6	⋃	⋃	NOUN
ejpam-3977	286	7	v∈v	v∈v	NOUN
ejpam-3977	286	8	(	(	PUNCT
ejpam-3977	286	9	g	g	NOUN
ejpam-3977	286	10	)	)	PUNCT
ejpam-3977	286	11	sv	sv	NOUN
ejpam-3977	286	12	)	)	PUNCT
ejpam-3977	286	13	where	where	SCONJ
ejpam-3977	286	14	a	a	DET
ejpam-3977	286	15	⊆	⊆	NUM
ejpam-3977	286	16	v	v	NOUN
ejpam-3977	286	17	(	(	PUNCT
ejpam-3977	286	18	g	g	NOUN
ejpam-3977	286	19	)	)	PUNCT
ejpam-3977	286	20	and	and	CCONJ
ejpam-3977	286	21	sv	sv	X
ejpam-3977	286	22	⊆	⊆	NUM
ejpam-3977	286	23	v	v	X
ejpam-3977	286	24	(	(	PUNCT
ejpam-3977	286	25	hv	hv	PROPN
ejpam-3977	286	26	)	)	PUNCT
ejpam-3977	286	27	.	.	PUNCT
ejpam-3977	287	1	suppose	suppose	VERB
ejpam-3977	287	2	sv	sv	X
ejpam-3977	288	1	=	=	NOUN
ejpam-3977	288	2	∅	∅	NOUN
ejpam-3977	288	3	for	for	ADP
ejpam-3977	288	4	some	some	DET
ejpam-3977	288	5	v	v	ADP
ejpam-3977	288	6	∈	∈	NOUN
ejpam-3977	288	7	v	v	NOUN
ejpam-3977	288	8	(	(	PUNCT
ejpam-3977	288	9	g	g	NOUN
ejpam-3977	288	10	)	)	PUNCT
ejpam-3977	288	11	.	.	PUNCT
ejpam-3977	289	1	let	let	VERB
ejpam-3977	289	2	x	x	PRON
ejpam-3977	289	3	,	,	PUNCT
ejpam-3977	289	4	y	y	PROPN
ejpam-3977	289	5	∈	∈	PROPN
ejpam-3977	289	6	v	v	PROPN
ejpam-3977	289	7	(	(	PUNCT
ejpam-3977	289	8	hv	hv	PROPN
ejpam-3977	289	9	)	)	PUNCT
ejpam-3977	289	10	.	.	PUNCT
ejpam-3977	290	1	then	then	ADV
ejpam-3977	290	2	rg	rg	PROPN
ejpam-3977	290	3	◦	◦	PROPN
ejpam-3977	290	4	h(x	h(x	PROPN
ejpam-3977	290	5	/	/	SYM
ejpam-3977	290	6	s	s	PROPN
ejpam-3977	290	7	)	)	PUNCT
ejpam-3977	290	8	=	=	SYM
ejpam-3977	291	1	rg	rg	VERB
ejpam-3977	291	2	◦	◦	NOUN
ejpam-3977	291	3	h(y	h(y	ADV
ejpam-3977	291	4	/	/	SYM
ejpam-3977	291	5	s	s	NOUN
ejpam-3977	291	6	)	)	PUNCT
ejpam-3977	291	7	which	which	PRON
ejpam-3977	291	8	is	be	AUX
ejpam-3977	291	9	a	a	DET
ejpam-3977	291	10	contradiction	contradiction	NOUN
ejpam-3977	291	11	to	to	ADP
ejpam-3977	291	12	the	the	DET
ejpam-3977	291	13	assumption	assumption	NOUN
ejpam-3977	291	14	of	of	ADP
ejpam-3977	291	15	s.	s.	PROPN
ejpam-3977	291	16	thus	thus	ADV
ejpam-3977	291	17	sv	sv	PROPN
ejpam-3977	292	1	6=	6=	ADP
ejpam-3977	292	2	∅.	∅.	ADP
ejpam-3977	292	3	now	now	ADV
ejpam-3977	292	4	,	,	PUNCT
ejpam-3977	292	5	we	we	PRON
ejpam-3977	292	6	claim	claim	VERB
ejpam-3977	292	7	that	that	SCONJ
ejpam-3977	292	8	sv	sv	PROPN
ejpam-3977	292	9	is	be	AUX
ejpam-3977	292	10	a	a	DET
ejpam-3977	292	11	2	2	NUM
ejpam-3977	292	12	-	-	PUNCT
ejpam-3977	292	13	resolving	resolving	NOUN
ejpam-3977	292	14	set	set	VERB
ejpam-3977	292	15	in	in	ADP
ejpam-3977	292	16	hv	hv	PROPN
ejpam-3977	292	17	for	for	ADP
ejpam-3977	292	18	each	each	DET
ejpam-3977	292	19	v	v	NUM
ejpam-3977	292	20	∈	∈	PROPN
ejpam-3977	292	21	v	v	NOUN
ejpam-3977	292	22	(	(	PUNCT
ejpam-3977	292	23	g	g	NOUN
ejpam-3977	292	24	)	)	PUNCT
ejpam-3977	292	25	.	.	PUNCT
ejpam-3977	293	1	let	let	VERB
ejpam-3977	293	2	p	p	PRON
ejpam-3977	293	3	,	,	PUNCT
ejpam-3977	293	4	q	q	PROPN
ejpam-3977	293	5	∈	∈	PROPN
ejpam-3977	293	6	v	v	ADP
ejpam-3977	293	7	(	(	PUNCT
ejpam-3977	293	8	hv	hv	PROPN
ejpam-3977	293	9	)	)	PUNCT
ejpam-3977	293	10	where	where	SCONJ
ejpam-3977	293	11	p	p	PROPN
ejpam-3977	293	12	6=	6=	PROPN
ejpam-3977	293	13	q.	q.	PROPN
ejpam-3977	293	14	since	since	SCONJ
ejpam-3977	293	15	s	s	PROPN
ejpam-3977	293	16	is	be	AUX
ejpam-3977	293	17	a	a	DET
ejpam-3977	293	18	2	2	NUM
ejpam-3977	293	19	-	-	PUNCT
ejpam-3977	293	20	resolving	resolving	NOUN
ejpam-3977	293	21	set	set	NOUN
ejpam-3977	293	22	in	in	ADP
ejpam-3977	293	23	g	g	PROPN
ejpam-3977	293	24	◦	◦	NOUN
ejpam-3977	293	25	h	h	NOUN
ejpam-3977	293	26	,	,	PUNCT
ejpam-3977	293	27	rg	rg	NOUN
ejpam-3977	293	28	◦	◦	NOUN
ejpam-3977	293	29	h(p	h(p	NOUN
ejpam-3977	293	30	/	/	SYM
ejpam-3977	293	31	s	s	NOUN
ejpam-3977	293	32	)	)	PUNCT
ejpam-3977	293	33	and	and	CCONJ
ejpam-3977	293	34	rg	rg	NOUN
ejpam-3977	293	35	◦	◦	NOUN
ejpam-3977	293	36	h(q	h(q	ADV
ejpam-3977	293	37	/	/	SYM
ejpam-3977	293	38	s	s	X
ejpam-3977	293	39	)	)	PUNCT
ejpam-3977	293	40	differ	differ	VERB
ejpam-3977	293	41	in	in	ADP
ejpam-3977	293	42	at	at	ADV
ejpam-3977	293	43	least	least	ADJ
ejpam-3977	293	44	2	2	NUM
ejpam-3977	293	45	positions	position	NOUN
ejpam-3977	293	46	.	.	PUNCT
ejpam-3977	294	1	by	by	ADP
ejpam-3977	294	2	remark	remark	NOUN
ejpam-3977	294	3	6	6	NUM
ejpam-3977	294	4	,	,	PUNCT
ejpam-3977	294	5	rhv(p	rhv(p	PROPN
ejpam-3977	294	6	/	/	SYM
ejpam-3977	294	7	sv	sv	NOUN
ejpam-3977	294	8	)	)	PUNCT
ejpam-3977	294	9	and	and	CCONJ
ejpam-3977	294	10	rhv(q	rhv(q	PROPN
ejpam-3977	294	11	/	/	SYM
ejpam-3977	294	12	sv	sv	NOUN
ejpam-3977	294	13	)	)	PUNCT
ejpam-3977	294	14	must	must	AUX
ejpam-3977	294	15	differ	differ	VERB
ejpam-3977	294	16	in	in	ADP
ejpam-3977	294	17	at	at	ADV
ejpam-3977	294	18	least	least	ADJ
ejpam-3977	294	19	2	2	NUM
ejpam-3977	294	20	positions	position	NOUN
ejpam-3977	294	21	.	.	PUNCT
ejpam-3977	295	1	thus	thus	ADV
ejpam-3977	295	2	sv	sv	PROPN
ejpam-3977	295	3	is	be	AUX
ejpam-3977	295	4	a	a	DET
ejpam-3977	295	5	2	2	NUM
ejpam-3977	295	6	-	-	PUNCT
ejpam-3977	295	7	resolving	resolving	NOUN
ejpam-3977	295	8	set	set	NOUN
ejpam-3977	295	9	in	in	ADP
ejpam-3977	295	10	hv	hv	PROPN
ejpam-3977	295	11	.	.	PUNCT
ejpam-3977	296	1	conversely	conversely	ADV
ejpam-3977	296	2	,	,	PUNCT
ejpam-3977	296	3	let	let	VERB
ejpam-3977	296	4	s	s	VERB
ejpam-3977	296	5	=	=	NOUN
ejpam-3977	296	6	a	a	DET
ejpam-3977	296	7	∪	∪	X
ejpam-3977	296	8	(	(	PUNCT
ejpam-3977	296	9	⋃	⋃	NOUN
ejpam-3977	296	10	v∈v	v∈v	NOUN
ejpam-3977	296	11	(	(	PUNCT
ejpam-3977	296	12	g	g	NOUN
ejpam-3977	296	13	)	)	PUNCT
ejpam-3977	296	14	sv	sv	NOUN
ejpam-3977	296	15	)	)	PUNCT
ejpam-3977	296	16	where	where	SCONJ
ejpam-3977	296	17	a	a	DET
ejpam-3977	296	18	⊆	⊆	NUM
ejpam-3977	296	19	v	v	NOUN
ejpam-3977	296	20	(	(	PUNCT
ejpam-3977	296	21	g	g	NOUN
ejpam-3977	296	22	)	)	PUNCT
ejpam-3977	296	23	and	and	CCONJ
ejpam-3977	296	24	sv	sv	X
ejpam-3977	296	25	⊆	⊆	NUM
ejpam-3977	296	26	v	v	X
ejpam-3977	296	27	(	(	PUNCT
ejpam-3977	296	28	hv	hv	NOUN
ejpam-3977	296	29	)	)	PUNCT
ejpam-3977	296	30	satisfying	satisfy	VERB
ejpam-3977	296	31	the	the	DET
ejpam-3977	296	32	given	give	VERB
ejpam-3977	296	33	conditions	condition	NOUN
ejpam-3977	296	34	.	.	PUNCT
ejpam-3977	297	1	let	let	VERB
ejpam-3977	297	2	x	x	PRON
ejpam-3977	297	3	,	,	PUNCT
ejpam-3977	297	4	y	y	PROPN
ejpam-3977	297	5	∈	∈	PROPN
ejpam-3977	297	6	v	v	NOUN
ejpam-3977	297	7	(	(	PUNCT
ejpam-3977	297	8	g	g	PROPN
ejpam-3977	297	9	◦	◦	NOUN
ejpam-3977	297	10	h	h	NOUN
ejpam-3977	297	11	)	)	PUNCT
ejpam-3977	297	12	with	with	ADP
ejpam-3977	297	13	x	x	SYM
ejpam-3977	297	14	6=	6=	ADP
ejpam-3977	297	15	y	y	PROPN
ejpam-3977	297	16	and	and	CCONJ
ejpam-3977	297	17	let	let	VERB
ejpam-3977	297	18	u	u	NOUN
ejpam-3977	297	19	,	,	PUNCT
ejpam-3977	297	20	v	v	PROPN
ejpam-3977	297	21	∈	∈	PROPN
ejpam-3977	297	22	v	v	NOUN
ejpam-3977	297	23	(	(	PUNCT
ejpam-3977	297	24	g	g	NOUN
ejpam-3977	297	25	)	)	PUNCT
ejpam-3977	297	26	such	such	ADJ
ejpam-3977	297	27	that	that	SCONJ
ejpam-3977	297	28	x	x	SYM
ejpam-3977	297	29	∈	∈	NOUN
ejpam-3977	297	30	v	v	X
ejpam-3977	297	31	(	(	PUNCT
ejpam-3977	297	32	u	u	NOUN
ejpam-3977	297	33	+	+	X
ejpam-3977	297	34	hu	hu	PROPN
ejpam-3977	297	35	)	)	PUNCT
ejpam-3977	297	36	and	and	CCONJ
ejpam-3977	297	37	y	y	PROPN
ejpam-3977	297	38	∈	∈	PROPN
ejpam-3977	297	39	v	v	ADP
ejpam-3977	297	40	(	(	PUNCT
ejpam-3977	297	41	v	v	NOUN
ejpam-3977	297	42	+	+	CCONJ
ejpam-3977	297	43	hv	hv	PROPN
ejpam-3977	297	44	)	)	PUNCT
ejpam-3977	297	45	.	.	PUNCT
ejpam-3977	298	1	case	case	NOUN
ejpam-3977	298	2	1	1	NUM
ejpam-3977	298	3	.	.	X
ejpam-3977	298	4	u	u	NOUN
ejpam-3977	299	1	=	=	PROPN
ejpam-3977	299	2	v	v	NUM
ejpam-3977	299	3	subcase	subcase	NOUN
ejpam-3977	299	4	1.1	1.1	NUM
ejpam-3977	299	5	x	x	NOUN
ejpam-3977	299	6	,	,	PUNCT
ejpam-3977	299	7	y	y	PROPN
ejpam-3977	299	8	∈	∈	PROPN
ejpam-3977	299	9	v	v	PROPN
ejpam-3977	299	10	(	(	PUNCT
ejpam-3977	299	11	hv	hv	PROPN
ejpam-3977	299	12	)	)	PUNCT
ejpam-3977	299	13	since	since	SCONJ
ejpam-3977	299	14	sv	sv	PROPN
ejpam-3977	299	15	is	be	AUX
ejpam-3977	299	16	a	a	DET
ejpam-3977	299	17	2	2	NUM
ejpam-3977	299	18	-	-	PUNCT
ejpam-3977	299	19	resolving	resolve	VERB
ejpam-3977	299	20	set	set	NOUN
ejpam-3977	299	21	,	,	PUNCT
ejpam-3977	299	22	rhv(x	rhv(x	PROPN
ejpam-3977	299	23	/	/	SYM
ejpam-3977	299	24	sv	sv	PROPN
ejpam-3977	299	25	)	)	PUNCT
ejpam-3977	299	26	and	and	CCONJ
ejpam-3977	299	27	rhv(y	rhv(y	PROPN
ejpam-3977	299	28	/	/	SYM
ejpam-3977	299	29	sv	sv	NOUN
ejpam-3977	299	30	)	)	PUNCT
ejpam-3977	299	31	differ	differ	VERB
ejpam-3977	299	32	in	in	ADP
ejpam-3977	299	33	at	at	ADV
ejpam-3977	299	34	least	least	ADJ
ejpam-3977	299	35	2	2	NUM
ejpam-3977	299	36	positions	position	NOUN
ejpam-3977	299	37	.	.	PUNCT
ejpam-3977	300	1	by	by	ADP
ejpam-3977	300	2	remark	remark	NOUN
ejpam-3977	300	3	6	6	NUM
ejpam-3977	300	4	,	,	PUNCT
ejpam-3977	300	5	rg	rg	NOUN
ejpam-3977	300	6	◦	◦	NOUN
ejpam-3977	300	7	h(x	h(x	PROPN
ejpam-3977	300	8	/	/	SYM
ejpam-3977	300	9	s	s	PROPN
ejpam-3977	300	10	)	)	PUNCT
ejpam-3977	300	11	and	and	CCONJ
ejpam-3977	300	12	rg	rg	PRON
ejpam-3977	300	13	◦	◦	NOUN
ejpam-3977	300	14	h(y	h(y	ADV
ejpam-3977	300	15	/	/	SYM
ejpam-3977	300	16	s	s	X
ejpam-3977	300	17	)	)	PUNCT
ejpam-3977	300	18	differ	differ	VERB
ejpam-3977	300	19	in	in	ADP
ejpam-3977	300	20	at	at	ADV
ejpam-3977	300	21	least	least	ADJ
ejpam-3977	300	22	2	2	NUM
ejpam-3977	300	23	positions	position	NOUN
ejpam-3977	300	24	.	.	PUNCT
ejpam-3977	301	1	subcase	subcase	VERB
ejpam-3977	301	2	1.2	1.2	NUM
ejpam-3977	301	3	x	x	SYM
ejpam-3977	301	4	=	=	SYM
ejpam-3977	301	5	v	v	NOUN
ejpam-3977	302	1	and	and	CCONJ
ejpam-3977	302	2	y	y	PROPN
ejpam-3977	302	3	∈	∈	PROPN
ejpam-3977	302	4	v	v	PROPN
ejpam-3977	302	5	(	(	PUNCT
ejpam-3977	302	6	hv	hv	PROPN
ejpam-3977	302	7	)	)	PUNCT
ejpam-3977	302	8	since	since	SCONJ
ejpam-3977	302	9	g	g	PROPN
ejpam-3977	302	10	is	be	AUX
ejpam-3977	302	11	nontrivial	nontrivial	ADJ
ejpam-3977	302	12	and	and	CCONJ
ejpam-3977	302	13	connected	connect	VERB
ejpam-3977	302	14	,	,	PUNCT
ejpam-3977	302	15	∃w	∃w	PROPN
ejpam-3977	302	16	∈	∈	PROPN
ejpam-3977	302	17	ng(v	ng(v	PUNCT
ejpam-3977	302	18	)	)	PUNCT
ejpam-3977	302	19	and	and	CCONJ
ejpam-3977	302	20	|sw|	|sw|	PROPN
ejpam-3977	302	21	≥	≥	NOUN
ejpam-3977	302	22	2	2	NUM
ejpam-3977	302	23	.	.	PUNCT
ejpam-3977	303	1	by	by	ADP
ejpam-3977	303	2	remark	remark	NOUN
ejpam-3977	303	3	6	6	NUM
ejpam-3977	303	4	,	,	PUNCT
ejpam-3977	303	5	rg	rg	NOUN
ejpam-3977	303	6	◦	◦	NOUN
ejpam-3977	303	7	h(x	h(x	PROPN
ejpam-3977	303	8	/	/	SYM
ejpam-3977	303	9	s	s	AUX
ejpam-3977	303	10	)	)	PUNCT
ejpam-3977	303	11	and	and	CCONJ
ejpam-3977	303	12	rg	rg	PRON
ejpam-3977	303	13	◦	◦	NOUN
ejpam-3977	303	14	h(y	h(y	ADV
ejpam-3977	303	15	/	/	SYM
ejpam-3977	303	16	s	s	X
ejpam-3977	303	17	)	)	PUNCT
ejpam-3977	303	18	differ	differ	VERB
ejpam-3977	303	19	in	in	ADP
ejpam-3977	303	20	at	at	ADV
ejpam-3977	303	21	least	least	ADJ
ejpam-3977	303	22	2	2	NUM
ejpam-3977	303	23	positions	position	NOUN
ejpam-3977	303	24	.	.	PUNCT
ejpam-3977	304	1	case	case	NOUN
ejpam-3977	304	2	2	2	NUM
ejpam-3977	304	3	.	.	X
ejpam-3977	304	4	u	u	PROPN
ejpam-3977	304	5	6=	6=	PROPN
ejpam-3977	304	6	v	v	NUM
ejpam-3977	304	7	subcase	subcase	NOUN
ejpam-3977	304	8	2.1	2.1	NUM
ejpam-3977	304	9	x	x	SYM
ejpam-3977	304	10	∈	∈	PROPN
ejpam-3977	304	11	v	v	NOUN
ejpam-3977	304	12	(	(	PUNCT
ejpam-3977	304	13	hu	hu	PROPN
ejpam-3977	304	14	)	)	PUNCT
ejpam-3977	304	15	,	,	PUNCT
ejpam-3977	304	16	y	y	PROPN
ejpam-3977	304	17	∈	∈	PROPN
ejpam-3977	304	18	v	v	ADP
ejpam-3977	304	19	(	(	PUNCT
ejpam-3977	304	20	hv	hv	NOUN
ejpam-3977	304	21	)	)	PUNCT
ejpam-3977	304	22	note	note	NOUN
ejpam-3977	304	23	that	that	SCONJ
ejpam-3977	304	24	rg	rg	AUX
ejpam-3977	304	25	◦	◦	NOUN
ejpam-3977	304	26	h(x	h(x	PROPN
ejpam-3977	304	27	/	/	SYM
ejpam-3977	304	28	sv	sv	PROPN
ejpam-3977	304	29	)	)	PUNCT
ejpam-3977	304	30	has	have	VERB
ejpam-3977	304	31	components	component	NOUN
ejpam-3977	304	32	greater	great	ADJ
ejpam-3977	304	33	than	than	ADP
ejpam-3977	304	34	or	or	CCONJ
ejpam-3977	304	35	equal	equal	ADJ
ejpam-3977	304	36	to	to	ADP
ejpam-3977	304	37	3	3	NUM
ejpam-3977	304	38	and	and	CCONJ
ejpam-3977	304	39	rg	rg	PRON
ejpam-3977	304	40	◦	◦	NOUN
ejpam-3977	304	41	h(y	h(y	PRON
ejpam-3977	304	42	/	/	SYM
ejpam-3977	304	43	sv	sv	NOUN
ejpam-3977	304	44	)	)	PUNCT
ejpam-3977	304	45	has	have	VERB
ejpam-3977	304	46	components	component	NOUN
ejpam-3977	304	47	less	less	ADJ
ejpam-3977	304	48	than	than	ADP
ejpam-3977	304	49	or	or	CCONJ
ejpam-3977	304	50	equal	equal	ADJ
ejpam-3977	304	51	to	to	ADP
ejpam-3977	304	52	2	2	NUM
ejpam-3977	304	53	.	.	PUNCT
ejpam-3977	305	1	since	since	SCONJ
ejpam-3977	305	2	|sv|	|sv|	PROPN
ejpam-3977	305	3	≥	≥	PROPN
ejpam-3977	305	4	2	2	NUM
ejpam-3977	305	5	,	,	PUNCT
ejpam-3977	305	6	rg	rg	NOUN
ejpam-3977	305	7	◦	◦	NOUN
ejpam-3977	305	8	h(x	h(x	PROPN
ejpam-3977	305	9	/	/	SYM
ejpam-3977	305	10	s	s	PROPN
ejpam-3977	305	11	)	)	PUNCT
ejpam-3977	305	12	and	and	CCONJ
ejpam-3977	305	13	rg	rg	PRON
ejpam-3977	305	14	◦	◦	NOUN
ejpam-3977	305	15	h(y	h(y	ADV
ejpam-3977	305	16	/	/	SYM
ejpam-3977	305	17	s	s	X
ejpam-3977	305	18	)	)	PUNCT
ejpam-3977	305	19	differ	differ	VERB
ejpam-3977	305	20	in	in	ADP
ejpam-3977	305	21	at	at	ADV
ejpam-3977	305	22	least	least	ADJ
ejpam-3977	305	23	2	2	NUM
ejpam-3977	305	24	positions	position	NOUN
ejpam-3977	305	25	.	.	PUNCT
ejpam-3977	306	1	subcase	subcase	VERB
ejpam-3977	306	2	2.2	2.2	NUM
ejpam-3977	306	3	x	x	SYM
ejpam-3977	306	4	=	=	SYM
ejpam-3977	306	5	u	u	NOUN
ejpam-3977	306	6	,	,	PUNCT
ejpam-3977	306	7	y	y	PROPN
ejpam-3977	306	8	∈	∈	PROPN
ejpam-3977	306	9	v	v	NOUN
ejpam-3977	306	10	(	(	PUNCT
ejpam-3977	306	11	v	v	NOUN
ejpam-3977	306	12	+	+	CCONJ
ejpam-3977	306	13	hv	hv	NOUN
ejpam-3977	306	14	)	)	PUNCT
ejpam-3977	306	15	since	since	SCONJ
ejpam-3977	306	16	|su|	|su|	PROPN
ejpam-3977	306	17	≥	≥	NOUN
ejpam-3977	306	18	2	2	NUM
ejpam-3977	306	19	,	,	PUNCT
ejpam-3977	306	20	rg	rg	NOUN
ejpam-3977	306	21	◦	◦	NOUN
ejpam-3977	306	22	h(x	h(x	PROPN
ejpam-3977	306	23	/	/	SYM
ejpam-3977	306	24	su	su	PROPN
ejpam-3977	306	25	)	)	PUNCT
ejpam-3977	306	26	and	and	CCONJ
ejpam-3977	306	27	rg	rg	PRON
ejpam-3977	306	28	◦	◦	NOUN
ejpam-3977	306	29	h(y	h(y	PRON
ejpam-3977	306	30	/	/	SYM
ejpam-3977	306	31	su	su	NOUN
ejpam-3977	306	32	)	)	PUNCT
ejpam-3977	306	33	differ	differ	VERB
ejpam-3977	306	34	in	in	ADP
ejpam-3977	306	35	at	at	ADV
ejpam-3977	306	36	least	least	ADJ
ejpam-3977	306	37	2	2	NUM
ejpam-3977	306	38	positions	position	NOUN
ejpam-3977	306	39	.	.	PUNCT
ejpam-3977	307	1	hence	hence	ADV
ejpam-3977	307	2	,	,	PUNCT
ejpam-3977	307	3	rg	rg	PROPN
ejpam-3977	307	4	◦	◦	NOUN
ejpam-3977	307	5	h(x	h(x	PROPN
ejpam-3977	307	6	/	/	SYM
ejpam-3977	307	7	s	s	PROPN
ejpam-3977	307	8	)	)	PUNCT
ejpam-3977	307	9	and	and	CCONJ
ejpam-3977	307	10	rg	rg	PRON
ejpam-3977	307	11	◦	◦	NOUN
ejpam-3977	307	12	h(y	h(y	ADV
ejpam-3977	307	13	/	/	SYM
ejpam-3977	307	14	s	s	X
ejpam-3977	307	15	)	)	PUNCT
ejpam-3977	307	16	differ	differ	VERB
ejpam-3977	307	17	in	in	ADP
ejpam-3977	307	18	at	at	ADV
ejpam-3977	307	19	least	least	ADJ
ejpam-3977	307	20	2	2	NUM
ejpam-3977	307	21	positions	position	NOUN
ejpam-3977	307	22	.	.	PUNCT
ejpam-3977	308	1	therefore	therefore	ADV
ejpam-3977	308	2	,	,	PUNCT
ejpam-3977	308	3	in	in	ADP
ejpam-3977	308	4	any	any	DET
ejpam-3977	308	5	case	case	NOUN
ejpam-3977	308	6	,	,	PUNCT
ejpam-3977	308	7	s	s	VERB
ejpam-3977	308	8	is	be	AUX
ejpam-3977	308	9	a	a	DET
ejpam-3977	308	10	2	2	NUM
ejpam-3977	308	11	-	-	PUNCT
ejpam-3977	308	12	resolving	resolving	NOUN
ejpam-3977	308	13	set	set	NOUN
ejpam-3977	308	14	in	in	ADP
ejpam-3977	308	15	g	g	PROPN
ejpam-3977	308	16	◦	◦	NOUN
ejpam-3977	308	17	h.	h.	NOUN
ejpam-3977	308	18	corollary	corollary	ADJ
ejpam-3977	308	19	4	4	NUM
ejpam-3977	308	20	.	.	PUNCT
ejpam-3977	309	1	let	let	VERB
ejpam-3977	309	2	g	g	NOUN
ejpam-3977	309	3	and	and	CCONJ
ejpam-3977	309	4	h	h	NOUN
ejpam-3977	309	5	be	be	AUX
ejpam-3977	309	6	nontrivial	nontrivial	ADJ
ejpam-3977	309	7	connected	connected	ADJ
ejpam-3977	309	8	graphs	graph	NOUN
ejpam-3977	309	9	,	,	PUNCT
ejpam-3977	309	10	where	where	SCONJ
ejpam-3977	309	11	|v	|v	PROPN
ejpam-3977	309	12	(	(	PUNCT
ejpam-3977	309	13	g)|	g)|	PROPN
ejpam-3977	309	14	=	=	NOUN
ejpam-3977	309	15	n.	n.	NOUN
ejpam-3977	309	16	then	then	ADV
ejpam-3977	309	17	dim2(g	dim2(g	PRON
ejpam-3977	309	18	◦	◦	NOUN
ejpam-3977	309	19	h	h	NOUN
ejpam-3977	309	20	)	)	PUNCT
ejpam-3977	309	21	=	=	SYM
ejpam-3977	309	22	n	n	PROPN
ejpam-3977	309	23	·	·	PUNCT
ejpam-3977	309	24	dim2(h	dim2(h	NUM
ejpam-3977	309	25	)	)	PUNCT
ejpam-3977	309	26	.	.	PUNCT
ejpam-3977	310	1	proof	proof	NOUN
ejpam-3977	310	2	.	.	PUNCT
ejpam-3977	311	1	let	let	VERB
ejpam-3977	311	2	s	s	PRON
ejpam-3977	311	3	be	be	AUX
ejpam-3977	311	4	a	a	DET
ejpam-3977	311	5	minimum	minimum	ADJ
ejpam-3977	311	6	2	2	NUM
ejpam-3977	311	7	-	-	PUNCT
ejpam-3977	311	8	resolving	resolve	VERB
ejpam-3977	311	9	set	set	NOUN
ejpam-3977	311	10	of	of	ADP
ejpam-3977	311	11	g	g	PROPN
ejpam-3977	311	12	◦	◦	NOUN
ejpam-3977	311	13	h.	h.	NOUN
ejpam-3977	311	14	then	then	ADV
ejpam-3977	311	15	by	by	ADP
ejpam-3977	311	16	theorem	theorem	NOUN
ejpam-3977	311	17	5	5	NUM
ejpam-3977	311	18	,	,	PUNCT
ejpam-3977	311	19	s	s	PART
ejpam-3977	311	20	=	=	X
ejpam-3977	311	21	a∪b	a∪b	NOUN
ejpam-3977	311	22	,	,	PUNCT
ejpam-3977	311	23	where	where	SCONJ
ejpam-3977	311	24	a	a	DET
ejpam-3977	311	25	⊆	⊆	NUM
ejpam-3977	311	26	v	v	NOUN
ejpam-3977	311	27	(	(	PUNCT
ejpam-3977	311	28	g	g	NOUN
ejpam-3977	311	29	)	)	PUNCT
ejpam-3977	311	30	and	and	CCONJ
ejpam-3977	311	31	b	b	X
ejpam-3977	311	32	=	=	PUNCT
ejpam-3977	311	33	⋃	⋃	PROPN
ejpam-3977	311	34	sv	sv	NOUN
ejpam-3977	311	35	,	,	PUNCT
ejpam-3977	311	36	v	v	NOUN
ejpam-3977	311	37	∈	∈	PROPN
ejpam-3977	311	38	v	v	NOUN
ejpam-3977	311	39	(	(	PUNCT
ejpam-3977	311	40	g	g	NOUN
ejpam-3977	311	41	)	)	PUNCT
ejpam-3977	311	42	and	and	CCONJ
ejpam-3977	311	43	sv	sv	PROPN
ejpam-3977	311	44	is	be	AUX
ejpam-3977	311	45	a	a	DET
ejpam-3977	311	46	2	2	NUM
ejpam-3977	311	47	-	-	PUNCT
ejpam-3977	311	48	resolving	resolving	NOUN
ejpam-3977	311	49	set	set	NOUN
ejpam-3977	311	50	in	in	ADP
ejpam-3977	311	51	h.	h.	PROPN
ejpam-3977	311	52	hence	hence	ADV
ejpam-3977	311	53	,	,	PUNCT
ejpam-3977	311	54	dim2(g	dim2(g	NOUN
ejpam-3977	311	55	◦	◦	NOUN
ejpam-3977	311	56	h	h	NOUN
ejpam-3977	311	57	)	)	PUNCT
ejpam-3977	311	58	=	=	PUNCT
ejpam-3977	311	59	|s|	|s|	NOUN
ejpam-3977	312	1	=	=	SYM
ejpam-3977	313	1	|a|+	|a|+	NOUN
ejpam-3977	313	2	|b|	|b|	PUNCT
ejpam-3977	313	3	≥	≥	AUX
ejpam-3977	313	4	|a|+	|a|+	VERB
ejpam-3977	313	5	|v	|v	X
ejpam-3977	313	6	(	(	PUNCT
ejpam-3977	313	7	g)|	g)|	NOUN
ejpam-3977	313	8	·	·	PUNCT
ejpam-3977	313	9	dim2(h	dim2(h	X
ejpam-3977	313	10	)	)	PUNCT
ejpam-3977	313	11	=	=	PUNCT
ejpam-3977	313	12	|a|+	|a|+	VERB
ejpam-3977	313	13	n.dim2(h	n.dim2(h	NUM
ejpam-3977	313	14	)	)	PUNCT
ejpam-3977	313	15	≥	≥	NOUN
ejpam-3977	313	16	n	n	CCONJ
ejpam-3977	313	17	·	·	PUNCT
ejpam-3977	313	18	dim2(h	dim2(h	NUM
ejpam-3977	313	19	)	)	PUNCT
ejpam-3977	313	20	.	.	PUNCT
ejpam-3977	314	1	now	now	ADV
ejpam-3977	314	2	,	,	PUNCT
ejpam-3977	314	3	let	let	VERB
ejpam-3977	314	4	c	c	PRON
ejpam-3977	314	5	be	be	AUX
ejpam-3977	314	6	a	a	DET
ejpam-3977	314	7	minimum	minimum	ADJ
ejpam-3977	314	8	2	2	NUM
ejpam-3977	314	9	-	-	PUNCT
ejpam-3977	314	10	resolving	resolving	NOUN
ejpam-3977	314	11	set	set	NOUN
ejpam-3977	314	12	in	in	ADP
ejpam-3977	314	13	h.	h.	PROPN
ejpam-3977	314	14	for	for	ADP
ejpam-3977	314	15	each	each	DET
ejpam-3977	314	16	v	v	NUM
ejpam-3977	314	17	∈	∈	PROPN
ejpam-3977	314	18	v	v	NOUN
ejpam-3977	314	19	(	(	PUNCT
ejpam-3977	314	20	g	g	NOUN
ejpam-3977	314	21	)	)	PUNCT
ejpam-3977	314	22	,	,	PUNCT
ejpam-3977	314	23	choose	choose	VERB
ejpam-3977	314	24	cv	cv	PROPN
ejpam-3977	314	25	⊆	⊆	NUM
ejpam-3977	314	26	v	v	PROPN
ejpam-3977	314	27	(	(	PUNCT
ejpam-3977	314	28	hv	hv	NOUN
ejpam-3977	314	29	)	)	PUNCT
ejpam-3977	314	30	with	with	ADP
ejpam-3977	314	31	〈	〈	PROPN
ejpam-3977	314	32	cv	cv	PROPN
ejpam-3977	314	33	〉	〉	PROPN
ejpam-3977	314	34	∼=	∼=	PROPN
ejpam-3977	314	35	〈	〈	PROPN
ejpam-3977	314	36	c	c	PROPN
ejpam-3977	314	37	〉	〉	NUM
ejpam-3977	314	38	.	.	PUNCT
ejpam-3977	315	1	then	then	ADV
ejpam-3977	315	2	d	d	NOUN
ejpam-3977	315	3	=	=	PUNCT
ejpam-3977	315	4	⋃	⋃	NOUN
ejpam-3977	315	5	v∈v	v∈v	NOUN
ejpam-3977	315	6	(	(	PUNCT
ejpam-3977	315	7	g)cv	g)cv	PROPN
ejpam-3977	315	8	is	be	AUX
ejpam-3977	315	9	a	a	DET
ejpam-3977	315	10	2	2	NUM
ejpam-3977	315	11	-	-	PUNCT
ejpam-3977	315	12	resolving	resolving	NOUN
ejpam-3977	315	13	set	set	NOUN
ejpam-3977	315	14	in	in	ADP
ejpam-3977	315	15	g	g	ADP
ejpam-3977	315	16	◦	◦	NOUN
ejpam-3977	315	17	h	h	NOUN
ejpam-3977	315	18	by	by	ADP
ejpam-3977	315	19	theorem	theorem	NOUN
ejpam-3977	315	20	5	5	NUM
ejpam-3977	315	21	.	.	PUNCT
ejpam-3977	316	1	hence	hence	ADV
ejpam-3977	316	2	,	,	PUNCT
ejpam-3977	316	3	references	reference	NOUN
ejpam-3977	316	4	782	782	NUM
ejpam-3977	316	5	dim2(g	dim2(g	NOUN
ejpam-3977	316	6	◦	◦	NOUN
ejpam-3977	316	7	h	h	NOUN
ejpam-3977	316	8	)	)	PUNCT
ejpam-3977	316	9	≤	≤	NUM
ejpam-3977	316	10	|d|	|d|	PROPN
ejpam-3977	316	11	=	=	PUNCT
ejpam-3977	317	1	|	|	ADV
ejpam-3977	317	2	⋃	⋃	ADJ
ejpam-3977	317	3	v∈v	v∈v	NOUN
ejpam-3977	317	4	(	(	PUNCT
ejpam-3977	317	5	g	g	NOUN
ejpam-3977	317	6	)	)	PUNCT
ejpam-3977	317	7	cv|	cv|	NOUN
ejpam-3977	317	8	=	=	SYM
ejpam-3977	317	9	n	n	NOUN
ejpam-3977	317	10	·	·	PUNCT
ejpam-3977	317	11	|cv|	|cv|	X
ejpam-3977	317	12	=	=	SYM
ejpam-3977	317	13	n	n	PROPN
ejpam-3977	317	14	·	·	PUNCT
ejpam-3977	317	15	|c|	|c|	PROPN
ejpam-3977	317	16	=	=	SYM
ejpam-3977	317	17	n	n	PROPN
ejpam-3977	317	18	·	·	PUNCT
ejpam-3977	317	19	dim2(h	dim2(h	NUM
ejpam-3977	317	20	)	)	PUNCT
ejpam-3977	317	21	.	.	PUNCT
ejpam-3977	318	1	therefore	therefore	ADV
ejpam-3977	318	2	,	,	PUNCT
ejpam-3977	318	3	dim2(g	dim2(g	NOUN
ejpam-3977	318	4	◦	◦	NOUN
ejpam-3977	318	5	h	h	NOUN
ejpam-3977	318	6	)	)	PUNCT
ejpam-3977	318	7	=	=	SYM
ejpam-3977	318	8	n	n	PROPN
ejpam-3977	318	9	·	·	PUNCT
ejpam-3977	318	10	dim2(h	dim2(h	NUM
ejpam-3977	318	11	)	)	PUNCT
ejpam-3977	318	12	.	.	PUNCT
ejpam-3977	319	1	example	example	NOUN
ejpam-3977	320	1	14	14	NUM
ejpam-3977	320	2	.	.	PUNCT
ejpam-3977	321	1	for	for	ADP
ejpam-3977	321	2	any	any	DET
ejpam-3977	321	3	integer	integer	NOUN
ejpam-3977	321	4	n	n	PRON
ejpam-3977	321	5	≥	≥	NOUN
ejpam-3977	321	6	2	2	NUM
ejpam-3977	321	7	and	and	CCONJ
ejpam-3977	321	8	m	m	PROPN
ejpam-3977	321	9	≥	≥	NOUN
ejpam-3977	321	10	5	5	NUM
ejpam-3977	321	11	,	,	PUNCT
ejpam-3977	321	12	dim2(g	dim2(g	NOUN
ejpam-3977	321	13	◦	◦	NOUN
ejpam-3977	321	14	cm	cm	NUM
ejpam-3977	321	15	)	)	PUNCT
ejpam-3977	322	1	=	=	PRON
ejpam-3977	322	2	{	{	PUNCT
ejpam-3977	322	3	n	n	PROPN
ejpam-3977	322	4	(	(	PUNCT
ejpam-3977	322	5	⌈	⌈	NOUN
ejpam-3977	322	6	m	m	PROPN
ejpam-3977	322	7	2	2	NUM
ejpam-3977	322	8	⌉	⌉	NOUN
ejpam-3977	322	9	)	)	PUNCT
ejpam-3977	322	10	,	,	PUNCT
ejpam-3977	322	11	if	if	SCONJ
ejpam-3977	322	12	m	m	PROPN
ejpam-3977	322	13	is	be	AUX
ejpam-3977	322	14	odd	odd	ADJ
ejpam-3977	322	15	n	n	CCONJ
ejpam-3977	322	16	(	(	PUNCT
ejpam-3977	322	17	m	m	PROPN
ejpam-3977	322	18	2	2	NUM
ejpam-3977	322	19	)	)	PUNCT
ejpam-3977	322	20	,	,	PUNCT
ejpam-3977	322	21	if	if	SCONJ
ejpam-3977	322	22	m	m	NOUN
ejpam-3977	322	23	is	be	AUX
ejpam-3977	322	24	even	even	ADV
ejpam-3977	322	25	example	example	NOUN
ejpam-3977	322	26	15	15	NUM
ejpam-3977	322	27	.	.	PUNCT
ejpam-3977	323	1	for	for	ADP
ejpam-3977	323	2	any	any	DET
ejpam-3977	323	3	integer	integer	NOUN
ejpam-3977	323	4	n	n	CCONJ
ejpam-3977	323	5	,	,	PUNCT
ejpam-3977	323	6	m	m	VERB
ejpam-3977	323	7	≥	≥	NOUN
ejpam-3977	323	8	2	2	NUM
ejpam-3977	323	9	,	,	PUNCT
ejpam-3977	323	10	dim2(g	dim2(g	NOUN
ejpam-3977	323	11	◦	◦	NOUN
ejpam-3977	323	12	pm	pm	NOUN
ejpam-3977	323	13	)	)	PUNCT
ejpam-3977	323	14	=	=	PRON
ejpam-3977	323	15	{	{	PUNCT
ejpam-3977	323	16	n	n	PROPN
ejpam-3977	323	17	(	(	PUNCT
ejpam-3977	323	18	⌈	⌈	NOUN
ejpam-3977	323	19	m	m	PROPN
ejpam-3977	323	20	2	2	NUM
ejpam-3977	323	21	⌉	⌉	NOUN
ejpam-3977	323	22	)	)	PUNCT
ejpam-3977	323	23	,	,	PUNCT
ejpam-3977	323	24	if	if	SCONJ
ejpam-3977	323	25	m	m	PROPN
ejpam-3977	323	26	is	be	AUX
ejpam-3977	323	27	odd	odd	ADJ
ejpam-3977	323	28	n	n	PART
ejpam-3977	323	29	[	[	X
ejpam-3977	323	30	(	(	PUNCT
ejpam-3977	323	31	m	m	NOUN
ejpam-3977	323	32	2	2	NUM
ejpam-3977	323	33	)	)	PUNCT
ejpam-3977	323	34	+	+	CCONJ
ejpam-3977	323	35	1	1	X
ejpam-3977	323	36	]	]	PUNCT
ejpam-3977	323	37	,	,	PUNCT
ejpam-3977	323	38	if	if	SCONJ
ejpam-3977	323	39	m	m	NOUN
ejpam-3977	323	40	is	be	AUX
ejpam-3977	323	41	even	even	ADV
ejpam-3977	323	42	references	reference	NOUN
ejpam-3977	323	43	[	[	X
ejpam-3977	323	44	1	1	NUM
ejpam-3977	323	45	]	]	X
ejpam-3977	323	46	r	r	NOUN
ejpam-3977	323	47	bailey	bailey	NOUN
ejpam-3977	323	48	and	and	CCONJ
ejpam-3977	323	49	i	i	PRON
ejpam-3977	323	50	yero	yero	PROPN
ejpam-3977	323	51	.	.	PUNCT
ejpam-3977	324	1	error	error	NOUN
ejpam-3977	324	2	-	-	PUNCT
ejpam-3977	324	3	correcting	correct	VERB
ejpam-3977	324	4	codes	code	NOUN
ejpam-3977	324	5	from	from	ADP
ejpam-3977	324	6	k	k	ADJ
ejpam-3977	324	7	-	-	PUNCT
ejpam-3977	324	8	resolving	resolving	ADJ
ejpam-3977	324	9	sets	set	NOUN
ejpam-3977	324	10	.	.	PUNCT
ejpam-3977	325	1	discussiones	discussione	NOUN
ejpam-3977	325	2	mathematicae	mathematicae	VERB
ejpam-3977	325	3	,	,	PUNCT
ejpam-3977	325	4	graph	graph	NOUN
ejpam-3977	325	5	theory	theory	NOUN
ejpam-3977	325	6	,	,	PUNCT
ejpam-3977	325	7	39:341–355	39:341–355	PROPN
ejpam-3977	325	8	,	,	PUNCT
ejpam-3977	325	9	2019	2019	NUM
ejpam-3977	325	10	.	.	PUNCT
ejpam-3977	326	1	[	[	X
ejpam-3977	326	2	2	2	X
ejpam-3977	326	3	]	]	PUNCT
ejpam-3977	326	4	g	g	NOUN
ejpam-3977	326	5	chartrand	chartrand	NOUN
ejpam-3977	326	6	and	and	CCONJ
ejpam-3977	326	7	p	p	PROPN
ejpam-3977	326	8	zhang	zhang	PROPN
ejpam-3977	326	9	.	.	PUNCT
ejpam-3977	326	10	graphs	graph	NOUN
ejpam-3977	326	11	and	and	CCONJ
ejpam-3977	326	12	digraphs	digraph	NOUN
ejpam-3977	326	13	.	.	PUNCT
ejpam-3977	327	1	wmu	wmu	PROPN
ejpam-3977	327	2	,	,	PUNCT
ejpam-3977	327	3	kalamazoo	kalamazoo	PROPN
ejpam-3977	327	4	,	,	PUNCT
ejpam-3977	327	5	usa	usa	PROPN
ejpam-3977	327	6	,	,	PUNCT
ejpam-3977	327	7	sixth	sixth	ADJ
ejpam-3977	327	8	edition	edition	NOUN
ejpam-3977	327	9	,	,	PUNCT
ejpam-3977	327	10	2016	2016	NUM
ejpam-3977	327	11	.	.	PUNCT
ejpam-3977	328	1	[	[	X
ejpam-3977	328	2	3	3	X
ejpam-3977	328	3	]	]	X
ejpam-3977	328	4	f	f	PROPN
ejpam-3977	328	5	harary	harary	NOUN
ejpam-3977	328	6	.	.	PUNCT
ejpam-3977	329	1	graph	graph	NOUN
ejpam-3977	329	2	theory	theory	NOUN
ejpam-3977	329	3	.	.	PUNCT
ejpam-3977	330	1	addison	addison	PROPN
ejpam-3977	330	2	-	-	PUNCT
ejpam-3977	330	3	wesley	wesley	PROPN
ejpam-3977	330	4	publishing	publishing	PROPN
ejpam-3977	330	5	company	company	NOUN
ejpam-3977	330	6	,	,	PUNCT
ejpam-3977	330	7	usa	usa	PROPN
ejpam-3977	330	8	,	,	PUNCT
ejpam-3977	330	9	1969	1969	NUM
ejpam-3977	330	10	.	.	PUNCT
ejpam-3977	331	1	[	[	X
ejpam-3977	331	2	4	4	X
ejpam-3977	331	3	]	]	X
ejpam-3977	331	4	f	f	PROPN
ejpam-3977	331	5	harary	harary	NOUN
ejpam-3977	331	6	and	and	CCONJ
ejpam-3977	331	7	r	r	NOUN
ejpam-3977	331	8	melter	melter	NOUN
ejpam-3977	331	9	.	.	PUNCT
ejpam-3977	332	1	on	on	ADP
ejpam-3977	332	2	the	the	DET
ejpam-3977	332	3	metric	metric	ADJ
ejpam-3977	332	4	dimension	dimension	NOUN
ejpam-3977	332	5	of	of	ADP
ejpam-3977	332	6	a	a	DET
ejpam-3977	332	7	graph	graph	NOUN
ejpam-3977	332	8	.	.	PUNCT
ejpam-3977	332	9	ars	ars	PROPN
ejpam-3977	332	10	combinatoria	combinatoria	PROPN
ejpam-3977	332	11	.	.	PUNCT
ejpam-3977	332	12	,	,	PUNCT
ejpam-3977	332	13	2:191–195	2:191–195	NUM
ejpam-3977	332	14	,	,	PUNCT
ejpam-3977	332	15	1976	1976	NUM
ejpam-3977	332	16	.	.	PUNCT
ejpam-3977	333	1	[	[	X
ejpam-3977	333	2	5	5	X
ejpam-3977	333	3	]	]	PUNCT
ejpam-3977	333	4	g	g	PROPN
ejpam-3977	333	5	monsanto	monsanto	PROPN
ejpam-3977	333	6	and	and	CCONJ
ejpam-3977	333	7	h	h	PROPN
ejpam-3977	333	8	rara	rara	NOUN
ejpam-3977	333	9	.	.	PUNCT
ejpam-3977	334	1	resolving	resolve	VERB
ejpam-3977	334	2	restrained	restrained	ADJ
ejpam-3977	334	3	domination	domination	NOUN
ejpam-3977	334	4	in	in	ADP
ejpam-3977	334	5	graphs	graph	NOUN
ejpam-3977	334	6	.	.	PUNCT
ejpam-3977	335	1	european	european	ADJ
ejpam-3977	335	2	journal	journal	PROPN
ejpam-3977	335	3	of	of	ADP
ejpam-3977	335	4	pure	pure	ADJ
ejpam-3977	335	5	and	and	CCONJ
ejpam-3977	335	6	applied	applied	ADJ
ejpam-3977	335	7	mathematics	mathematic	NOUN
ejpam-3977	335	8	.	.	PUNCT
ejpam-3977	335	9	,	,	PUNCT
ejpam-3977	335	10	2021(accepted	2021(accepted	NUM
ejpam-3977	335	11	)	)	PUNCT
ejpam-3977	335	12	.	.	PUNCT
ejpam-3977	336	1	[	[	X
ejpam-3977	336	2	6	6	NUM
ejpam-3977	336	3	]	]	X
ejpam-3977	336	4	p	p	X
ejpam-3977	336	5	acal	acal	ADJ
ejpam-3977	336	6	g	g	PROPN
ejpam-3977	336	7	monsanto	monsanto	PROPN
ejpam-3977	336	8	and	and	CCONJ
ejpam-3977	336	9	h	h	PROPN
ejpam-3977	336	10	rara	rara	NOUN
ejpam-3977	336	11	.	.	PUNCT
ejpam-3977	337	1	on	on	ADP
ejpam-3977	337	2	strong	strong	ADJ
ejpam-3977	337	3	resolving	resolving	NOUN
ejpam-3977	337	4	domination	domination	NOUN
ejpam-3977	337	5	in	in	ADP
ejpam-3977	337	6	the	the	DET
ejpam-3977	337	7	join	join	NOUN
ejpam-3977	337	8	and	and	CCONJ
ejpam-3977	337	9	corona	corona	NOUN
ejpam-3977	337	10	of	of	ADP
ejpam-3977	337	11	graphs	graph	NOUN
ejpam-3977	337	12	.	.	PUNCT
ejpam-3977	338	1	european	european	ADJ
ejpam-3977	338	2	journal	journal	PROPN
ejpam-3977	338	3	of	of	ADP
ejpam-3977	338	4	pure	pure	ADJ
ejpam-3977	338	5	and	and	CCONJ
ejpam-3977	338	6	applied	applied	ADJ
ejpam-3977	338	7	mathematics	mathematic	NOUN
ejpam-3977	338	8	.	.	PUNCT
ejpam-3977	338	9	,	,	PUNCT
ejpam-3977	338	10	13:170–179	13:170–179	NUM
ejpam-3977	338	11	,	,	PUNCT
ejpam-3977	338	12	2020	2020	NUM
ejpam-3977	338	13	.	.	PUNCT
ejpam-3977	339	1	[	[	X
ejpam-3977	339	2	7	7	X
ejpam-3977	339	3	]	]	PUNCT
ejpam-3977	339	4	a	a	DET
ejpam-3977	339	5	estrada	estrada	PROPN
ejpam-3977	339	6	-	-	PUNCT
ejpam-3977	339	7	moreno	moreno	PROPN
ejpam-3977	339	8	j	j	PROPN
ejpam-3977	339	9	rodriguez	rodriguez	PROPN
ejpam-3977	339	10	-	-	PUNCT
ejpam-3977	339	11	velasquez	velasquez	PROPN
ejpam-3977	339	12	and	and	CCONJ
ejpam-3977	339	13	i	i	PRON
ejpam-3977	339	14	yero	yero	NOUN
ejpam-3977	339	15	.	.	PUNCT
ejpam-3977	340	1	the	the	DET
ejpam-3977	340	2	k	k	ADJ
ejpam-3977	340	3	-	-	ADJ
ejpam-3977	340	4	metric	metric	ADJ
ejpam-3977	340	5	dimension	dimension	NOUN
ejpam-3977	340	6	of	of	ADP
ejpam-3977	340	7	a	a	DET
ejpam-3977	340	8	graph	graph	NOUN
ejpam-3977	340	9	.	.	PUNCT
ejpam-3977	341	1	applied	apply	VERB
ejpam-3977	341	2	mathematics	mathematic	NOUN
ejpam-3977	341	3	and	and	CCONJ
ejpam-3977	341	4	information	information	NOUN
ejpam-3977	341	5	sciences	science	NOUN
ejpam-3977	341	6	,	,	PUNCT
ejpam-3977	341	7	9:2829–2840	9:2829–2840	NUM
ejpam-3977	341	8	,	,	PUNCT
ejpam-3977	341	9	2015	2015	NUM
ejpam-3977	341	10	.	.	PUNCT
ejpam-3977	342	1	[	[	X
ejpam-3977	342	2	8	8	NUM
ejpam-3977	342	3	]	]	PUNCT
ejpam-3977	342	4	a	a	DET
ejpam-3977	342	5	estrada	estrada	PROPN
ejpam-3977	342	6	-	-	PUNCT
ejpam-3977	342	7	moreno	moreno	PROPN
ejpam-3977	342	8	j	j	PROPN
ejpam-3977	342	9	rodriguez	rodriguez	PROPN
ejpam-3977	342	10	-	-	PUNCT
ejpam-3977	342	11	velasquez	velasquez	PROPN
ejpam-3977	342	12	and	and	CCONJ
ejpam-3977	342	13	i	i	PRON
ejpam-3977	342	14	yero	yero	NOUN
ejpam-3977	342	15	.	.	PUNCT
ejpam-3977	343	1	the	the	DET
ejpam-3977	343	2	k	k	ADJ
ejpam-3977	343	3	-	-	ADJ
ejpam-3977	343	4	metric	metric	ADJ
ejpam-3977	343	5	dimension	dimension	NOUN
ejpam-3977	343	6	of	of	ADP
ejpam-3977	343	7	corona	corona	NOUN
ejpam-3977	343	8	product	product	NOUN
ejpam-3977	343	9	graphs	graph	NOUN
ejpam-3977	343	10	.	.	PUNCT
ejpam-3977	344	1	the	the	DET
ejpam-3977	344	2	bulletin	bulletin	NOUN
ejpam-3977	344	3	of	of	ADP
ejpam-3977	344	4	the	the	DET
ejpam-3977	344	5	malaysian	malaysian	ADJ
ejpam-3977	344	6	mathematical	mathematical	ADJ
ejpam-3977	344	7	society	society	NOUN
ejpam-3977	344	8	.	.	PUNCT
ejpam-3977	344	9	,	,	PUNCT
ejpam-3977	344	10	39:135	39:135	NUM
ejpam-3977	344	11	–	–	PUNCT
ejpam-3977	344	12	156	156	NUM
ejpam-3977	344	13	,	,	PUNCT
ejpam-3977	344	14	2016	2016	NUM
ejpam-3977	344	15	.	.	PUNCT
ejpam-3977	345	1	[	[	X
ejpam-3977	345	2	9	9	NUM
ejpam-3977	345	3	]	]	SYM
ejpam-3977	345	4	v	v	NOUN
ejpam-3977	345	5	saenpholphat	saenpholphat	NOUN
ejpam-3977	346	1	and	and	CCONJ
ejpam-3977	346	2	p	p	PROPN
ejpam-3977	346	3	zang	zang	PROPN
ejpam-3977	346	4	.	.	PUNCT
ejpam-3977	347	1	on	on	ADP
ejpam-3977	347	2	connected	connected	ADJ
ejpam-3977	347	3	resolvability	resolvability	NOUN
ejpam-3977	347	4	of	of	ADP
ejpam-3977	347	5	graphs	graph	NOUN
ejpam-3977	347	6	.	.	PUNCT
ejpam-3977	348	1	australian	australian	ADJ
ejpam-3977	348	2	journal	journal	NOUN
ejpam-3977	348	3	of	of	ADP
ejpam-3977	348	4	combinatorics	combinatoric	NOUN
ejpam-3977	348	5	.	.	PUNCT
ejpam-3977	348	6	,	,	PUNCT
ejpam-3977	348	7	28:25–37	28:25–37	NUM
ejpam-3977	348	8	,	,	PUNCT
ejpam-3977	348	9	2003	2003	NUM
ejpam-3977	348	10	.	.	PUNCT
ejpam-3977	349	1	[	[	X
ejpam-3977	349	2	10	10	NUM
ejpam-3977	349	3	]	]	X
ejpam-3977	349	4	p	p	X
ejpam-3977	349	5	slater	slater	PROPN
ejpam-3977	349	6	.	.	PUNCT
ejpam-3977	350	1	congressus	congressus	PROPN
ejpam-3977	350	2	numerantium	numerantium	PROPN
ejpam-3977	350	3	,	,	PUNCT
ejpam-3977	350	4	14:549–559	14:549–559	NUM
ejpam-3977	350	5	,	,	PUNCT
ejpam-3977	350	6	1975	1975	NUM
ejpam-3977	350	7	.	.	PUNCT