id	sid	tid	token	lemma	pos
ejpam-4829	1	1	european	european	PROPN
ejpam-4829	1	2	journal	journal	PROPN
ejpam-4829	1	3	of	of	ADP
ejpam-4829	1	4	pure	pure	ADJ
ejpam-4829	1	5	and	and	CCONJ
ejpam-4829	1	6	applied	apply	VERB
ejpam-4829	1	7	mathematics	mathematic	NOUN
ejpam-4829	1	8	vol	vol	NOUN
ejpam-4829	1	9	.	.	PUNCT
ejpam-4829	2	1	16	16	NUM
ejpam-4829	2	2	,	,	PUNCT
ejpam-4829	2	3	no	no	INTJ
ejpam-4829	2	4	.	.	NOUN
ejpam-4829	2	5	4	4	NUM
ejpam-4829	2	6	,	,	PUNCT
ejpam-4829	2	7	2023	2023	NUM
ejpam-4829	2	8	,	,	PUNCT
ejpam-4829	2	9	2786	2786	NUM
ejpam-4829	2	10	-	-	SYM
ejpam-4829	2	11	2797	2797	NUM
ejpam-4829	2	12	issn	issn	PROPN
ejpam-4829	2	13	1307	1307	NUM
ejpam-4829	2	14	-	-	SYM
ejpam-4829	2	15	5543	5543	NUM
ejpam-4829	2	16	–	–	PUNCT
ejpam-4829	2	17	ejpam.com	ejpam.com	X
ejpam-4829	2	18	published	publish	VERB
ejpam-4829	2	19	by	by	ADP
ejpam-4829	2	20	new	new	PROPN
ejpam-4829	2	21	york	york	PROPN
ejpam-4829	2	22	business	business	PROPN
ejpam-4829	2	23	global	global	ADJ
ejpam-4829	2	24	prime	prime	ADJ
ejpam-4829	2	25	graph	graph	NOUN
ejpam-4829	2	26	generation	generation	NOUN
ejpam-4829	2	27	through	through	ADP
ejpam-4829	2	28	single	single	ADJ
ejpam-4829	2	29	edge	edge	NOUN
ejpam-4829	2	30	addition	addition	NOUN
ejpam-4829	2	31	:	:	PUNCT
ejpam-4829	2	32	characterizing	characterize	VERB
ejpam-4829	2	33	a	a	DET
ejpam-4829	2	34	class	class	NOUN
ejpam-4829	2	35	of	of	ADP
ejpam-4829	2	36	graphs	graph	NOUN
ejpam-4829	2	37	ayesha	ayesha	PROPN
ejpam-4829	2	38	alorini1,2	alorini1,2	PROPN
ejpam-4829	2	39	,	,	PUNCT
ejpam-4829	2	40	aymen	ayman	NOUN
ejpam-4829	2	41	ben	ben	PROPN
ejpam-4829	2	42	amira1	amira1	PROPN
ejpam-4829	2	43	,	,	PUNCT
ejpam-4829	2	44	mohammad	mohammad	PROPN
ejpam-4829	2	45	alzohairi1	alzohairi1	PROPN
ejpam-4829	2	46	,	,	PUNCT
ejpam-4829	2	47	moncef	moncef	PROPN
ejpam-4829	2	48	bouaziz1,∗	bouaziz1,∗	PROPN
ejpam-4829	2	49	1	1	NUM
ejpam-4829	2	50	department	department	NOUN
ejpam-4829	2	51	of	of	ADP
ejpam-4829	2	52	mathematics	mathematic	NOUN
ejpam-4829	2	53	,	,	PUNCT
ejpam-4829	2	54	college	college	NOUN
ejpam-4829	2	55	of	of	ADP
ejpam-4829	2	56	sciences	sciences	PROPN
ejpam-4829	2	57	,	,	PUNCT
ejpam-4829	2	58	king	king	NOUN
ejpam-4829	2	59	saud	saud	PROPN
ejpam-4829	2	60	university	university	PROPN
ejpam-4829	2	61	,	,	PUNCT
ejpam-4829	2	62	riyadh	riyadh	PROPN
ejpam-4829	2	63	,	,	PUNCT
ejpam-4829	2	64	saudi	saudi	PROPN
ejpam-4829	2	65	arabia	arabia	PROPN
ejpam-4829	2	66	2	2	NUM
ejpam-4829	2	67	department	department	NOUN
ejpam-4829	2	68	of	of	ADP
ejpam-4829	2	69	mathematics	mathematic	NOUN
ejpam-4829	2	70	,	,	PUNCT
ejpam-4829	2	71	college	college	NOUN
ejpam-4829	2	72	of	of	ADP
ejpam-4829	2	73	sciences	science	NOUN
ejpam-4829	2	74	,	,	PUNCT
ejpam-4829	2	75	imam	imam	PROPN
ejpam-4829	2	76	mohammad	mohammad	PROPN
ejpam-4829	2	77	ibn	ibn	PROPN
ejpam-4829	2	78	saud	saud	PROPN
ejpam-4829	2	79	university	university	PROPN
ejpam-4829	2	80	,	,	PUNCT
ejpam-4829	2	81	riyadh	riyadh	PROPN
ejpam-4829	2	82	,	,	PUNCT
ejpam-4829	2	83	saudi	saudi	PROPN
ejpam-4829	2	84	arabia	arabia	PROPN
ejpam-4829	2	85	abstract	abstract	NOUN
ejpam-4829	2	86	.	.	PUNCT
ejpam-4829	3	1	a	a	DET
ejpam-4829	3	2	graph	graph	NOUN
ejpam-4829	3	3	g	g	NOUN
ejpam-4829	3	4	consists	consist	VERB
ejpam-4829	3	5	of	of	ADP
ejpam-4829	3	6	a	a	DET
ejpam-4829	3	7	finite	finite	NOUN
ejpam-4829	3	8	set	set	VERB
ejpam-4829	3	9	v	v	NOUN
ejpam-4829	3	10	(	(	PUNCT
ejpam-4829	3	11	g	g	NOUN
ejpam-4829	3	12	)	)	PUNCT
ejpam-4829	3	13	of	of	ADP
ejpam-4829	3	14	vertices	vertex	NOUN
ejpam-4829	3	15	with	with	ADP
ejpam-4829	3	16	a	a	DET
ejpam-4829	3	17	collection	collection	NOUN
ejpam-4829	3	18	e(g	e(g	NOUN
ejpam-4829	3	19	)	)	PUNCT
ejpam-4829	3	20	of	of	ADP
ejpam-4829	3	21	unordered	unordered	ADJ
ejpam-4829	3	22	pairs	pair	NOUN
ejpam-4829	3	23	of	of	ADP
ejpam-4829	3	24	distinct	distinct	ADJ
ejpam-4829	3	25	vertices	vertex	NOUN
ejpam-4829	3	26	called	call	VERB
ejpam-4829	3	27	edge	edge	NOUN
ejpam-4829	3	28	set	set	NOUN
ejpam-4829	3	29	of	of	ADP
ejpam-4829	3	30	g.	g.	PROPN
ejpam-4829	3	31	let	let	VERB
ejpam-4829	3	32	g	g	NOUN
ejpam-4829	3	33	be	be	AUX
ejpam-4829	3	34	a	a	DET
ejpam-4829	3	35	graph	graph	NOUN
ejpam-4829	3	36	.	.	PUNCT
ejpam-4829	4	1	a	a	DET
ejpam-4829	4	2	set	set	NOUN
ejpam-4829	4	3	m	m	NOUN
ejpam-4829	4	4	of	of	ADP
ejpam-4829	4	5	vertices	vertex	NOUN
ejpam-4829	4	6	is	be	AUX
ejpam-4829	4	7	a	a	DET
ejpam-4829	4	8	module	module	NOUN
ejpam-4829	4	9	of	of	ADP
ejpam-4829	4	10	g	g	PROPN
ejpam-4829	4	11	if	if	SCONJ
ejpam-4829	4	12	,	,	PUNCT
ejpam-4829	4	13	for	for	ADP
ejpam-4829	4	14	vertices	vertex	NOUN
ejpam-4829	4	15	x	x	PUNCT
ejpam-4829	4	16	and	and	CCONJ
ejpam-4829	4	17	y	y	PROPN
ejpam-4829	4	18	in	in	ADP
ejpam-4829	4	19	m	m	PROPN
ejpam-4829	4	20	and	and	CCONJ
ejpam-4829	4	21	each	each	DET
ejpam-4829	4	22	vertex	vertex	NOUN
ejpam-4829	4	23	z	z	PROPN
ejpam-4829	4	24	outside	outside	ADP
ejpam-4829	4	25	m	m	PROPN
ejpam-4829	4	26	,	,	PUNCT
ejpam-4829	4	27	{	{	PUNCT
ejpam-4829	4	28	z	z	NOUN
ejpam-4829	4	29	,	,	PUNCT
ejpam-4829	4	30	x	x	NOUN
ejpam-4829	4	31	}	}	PUNCT
ejpam-4829	4	32	∈	∈	PROPN
ejpam-4829	4	33	e(g	e(g	NOUN
ejpam-4829	4	34	)	)	PUNCT
ejpam-4829	4	35	⇐	⇐	ADJ
ejpam-4829	4	36	⇒	⇒	PROPN
ejpam-4829	4	37	{	{	PUNCT
ejpam-4829	4	38	z	z	PROPN
ejpam-4829	4	39	,	,	PUNCT
ejpam-4829	4	40	y	y	PROPN
ejpam-4829	4	41	}	}	PUNCT
ejpam-4829	4	42	∈	∈	PROPN
ejpam-4829	4	43	e(g	e(g	PROPN
ejpam-4829	4	44	)	)	PUNCT
ejpam-4829	4	45	.	.	PUNCT
ejpam-4829	5	1	thus	thus	ADV
ejpam-4829	5	2	,	,	PUNCT
ejpam-4829	5	3	a	a	DET
ejpam-4829	5	4	module	module	NOUN
ejpam-4829	5	5	of	of	ADP
ejpam-4829	5	6	g	g	PROPN
ejpam-4829	5	7	is	be	AUX
ejpam-4829	5	8	a	a	DET
ejpam-4829	5	9	set	set	NOUN
ejpam-4829	5	10	m	m	NOUN
ejpam-4829	5	11	of	of	ADP
ejpam-4829	5	12	vertices	vertex	NOUN
ejpam-4829	5	13	indistinguishable	indistinguishable	ADJ
ejpam-4829	5	14	by	by	ADP
ejpam-4829	5	15	the	the	DET
ejpam-4829	5	16	vertices	vertex	NOUN
ejpam-4829	5	17	outside	outside	ADP
ejpam-4829	5	18	m	m	PROPN
ejpam-4829	5	19	.	.	PUNCT
ejpam-4829	6	1	the	the	DET
ejpam-4829	6	2	empty	empty	ADJ
ejpam-4829	6	3	set	set	NOUN
ejpam-4829	6	4	,	,	PUNCT
ejpam-4829	6	5	the	the	DET
ejpam-4829	6	6	singleton	singleton	NOUN
ejpam-4829	6	7	sets	set	NOUN
ejpam-4829	6	8	and	and	CCONJ
ejpam-4829	6	9	the	the	DET
ejpam-4829	6	10	full	full	ADJ
ejpam-4829	6	11	set	set	NOUN
ejpam-4829	6	12	of	of	ADP
ejpam-4829	6	13	vertices	vertex	NOUN
ejpam-4829	6	14	represent	represent	VERB
ejpam-4829	6	15	the	the	DET
ejpam-4829	6	16	trivial	trivial	ADJ
ejpam-4829	6	17	modules	module	NOUN
ejpam-4829	6	18	.	.	PUNCT
ejpam-4829	7	1	a	a	DET
ejpam-4829	7	2	graph	graph	NOUN
ejpam-4829	7	3	is	be	AUX
ejpam-4829	7	4	indecomposable	indecomposable	ADJ
ejpam-4829	7	5	if	if	SCONJ
ejpam-4829	7	6	all	all	DET
ejpam-4829	7	7	its	its	PRON
ejpam-4829	7	8	modules	module	NOUN
ejpam-4829	7	9	are	be	AUX
ejpam-4829	7	10	trivial	trivial	ADJ
ejpam-4829	7	11	,	,	PUNCT
ejpam-4829	7	12	otherwise	otherwise	ADV
ejpam-4829	7	13	it	it	PRON
ejpam-4829	7	14	is	be	AUX
ejpam-4829	7	15	decomposable	decomposable	ADJ
ejpam-4829	7	16	.	.	PUNCT
ejpam-4829	8	1	indecomposable	indecomposable	ADJ
ejpam-4829	8	2	graphs	graph	NOUN
ejpam-4829	8	3	with	with	ADP
ejpam-4829	8	4	at	at	ADV
ejpam-4829	8	5	least	least	ADV
ejpam-4829	8	6	four	four	NUM
ejpam-4829	8	7	vertices	vertex	NOUN
ejpam-4829	8	8	are	be	AUX
ejpam-4829	8	9	prime	prime	ADJ
ejpam-4829	8	10	graphs	graph	NOUN
ejpam-4829	8	11	.	.	PUNCT
ejpam-4829	9	1	the	the	DET
ejpam-4829	9	2	introduction	introduction	NOUN
ejpam-4829	9	3	and	and	CCONJ
ejpam-4829	9	4	the	the	DET
ejpam-4829	9	5	study	study	NOUN
ejpam-4829	9	6	of	of	ADP
ejpam-4829	9	7	the	the	DET
ejpam-4829	9	8	construction	construction	NOUN
ejpam-4829	9	9	of	of	ADP
ejpam-4829	9	10	prime	prime	ADJ
ejpam-4829	9	11	graphs	graph	NOUN
ejpam-4829	9	12	obtained	obtain	VERB
ejpam-4829	9	13	from	from	ADP
ejpam-4829	9	14	a	a	DET
ejpam-4829	9	15	given	give	VERB
ejpam-4829	9	16	decomposable	decomposable	ADJ
ejpam-4829	9	17	graph	graph	NOUN
ejpam-4829	9	18	by	by	ADP
ejpam-4829	9	19	adding	add	VERB
ejpam-4829	9	20	one	one	NUM
ejpam-4829	9	21	edge	edge	NOUN
ejpam-4829	9	22	constitue	constitue	NOUN
ejpam-4829	9	23	the	the	DET
ejpam-4829	9	24	central	central	ADJ
ejpam-4829	9	25	points	point	NOUN
ejpam-4829	9	26	of	of	ADP
ejpam-4829	9	27	this	this	DET
ejpam-4829	9	28	paper	paper	NOUN
ejpam-4829	9	29	.	.	PUNCT
ejpam-4829	10	1	2020	2020	NUM
ejpam-4829	10	2	mathematics	mathematic	NOUN
ejpam-4829	10	3	subject	subject	NOUN
ejpam-4829	10	4	classifications	classification	NOUN
ejpam-4829	10	5	:	:	PUNCT
ejpam-4829	10	6	05c60	05c60	NOUN
ejpam-4829	10	7	key	key	ADJ
ejpam-4829	10	8	words	word	NOUN
ejpam-4829	10	9	and	and	CCONJ
ejpam-4829	10	10	phrases	phrase	NOUN
ejpam-4829	10	11	:	:	PUNCT
ejpam-4829	10	12	module	module	NOUN
ejpam-4829	10	13	,	,	PUNCT
ejpam-4829	10	14	prime	prime	ADJ
ejpam-4829	10	15	,	,	PUNCT
ejpam-4829	10	16	decomposable	decomposable	ADJ
ejpam-4829	10	17	,	,	PUNCT
ejpam-4829	10	18	prime	prime	ADJ
ejpam-4829	10	19	frame	frame	NOUN
ejpam-4829	10	20	,	,	PUNCT
ejpam-4829	10	21	isomorphism	isomorphism	NOUN
ejpam-4829	10	22	.	.	PUNCT
ejpam-4829	11	1	1	1	X
ejpam-4829	11	2	.	.	X
ejpam-4829	11	3	introduction	introduction	NOUN
ejpam-4829	11	4	our	our	PRON
ejpam-4829	11	5	notations	notation	NOUN
ejpam-4829	11	6	and	and	CCONJ
ejpam-4829	11	7	terminology	terminology	NOUN
ejpam-4829	11	8	follow	follow	VERB
ejpam-4829	11	9	[	[	X
ejpam-4829	11	10	1	1	NUM
ejpam-4829	11	11	]	]	PUNCT
ejpam-4829	11	12	.	.	PUNCT
ejpam-4829	12	1	all	all	DET
ejpam-4829	12	2	graphs	graph	NOUN
ejpam-4829	12	3	mentioned	mention	VERB
ejpam-4829	12	4	in	in	ADP
ejpam-4829	12	5	this	this	DET
ejpam-4829	12	6	paper	paper	NOUN
ejpam-4829	12	7	are	be	AUX
ejpam-4829	12	8	finite	finite	ADJ
ejpam-4829	12	9	.	.	PUNCT
ejpam-4829	12	10	without	without	ADP
ejpam-4829	12	11	loops	loop	NOUN
ejpam-4829	12	12	and	and	CCONJ
ejpam-4829	12	13	multiple	multiple	ADJ
ejpam-4829	12	14	edges	edge	NOUN
ejpam-4829	12	15	,	,	PUNCT
ejpam-4829	12	16	these	these	DET
ejpam-4829	12	17	graphs	graph	NOUN
ejpam-4829	12	18	are	be	AUX
ejpam-4829	12	19	called	call	VERB
ejpam-4829	12	20	simple	simple	ADJ
ejpam-4829	12	21	graphs	graph	NOUN
ejpam-4829	12	22	.	.	PUNCT
ejpam-4829	13	1	a	a	DET
ejpam-4829	13	2	graph	graph	NOUN
ejpam-4829	13	3	g	g	NOUN
ejpam-4829	13	4	consists	consist	VERB
ejpam-4829	13	5	of	of	ADP
ejpam-4829	13	6	a	a	DET
ejpam-4829	13	7	finite	finite	NOUN
ejpam-4829	13	8	set	set	VERB
ejpam-4829	13	9	v	v	NOUN
ejpam-4829	13	10	(	(	PUNCT
ejpam-4829	13	11	g	g	NOUN
ejpam-4829	13	12	)	)	PUNCT
ejpam-4829	13	13	of	of	ADP
ejpam-4829	13	14	vertices	vertex	NOUN
ejpam-4829	13	15	called	call	VERB
ejpam-4829	13	16	vertex	vertex	NOUN
ejpam-4829	13	17	set	set	VERB
ejpam-4829	13	18	with	with	ADP
ejpam-4829	13	19	a	a	DET
ejpam-4829	13	20	collection	collection	NOUN
ejpam-4829	13	21	e(g	e(g	NOUN
ejpam-4829	13	22	)	)	PUNCT
ejpam-4829	13	23	of	of	ADP
ejpam-4829	13	24	pairs	pair	NOUN
ejpam-4829	13	25	of	of	ADP
ejpam-4829	13	26	distinct	distinct	ADJ
ejpam-4829	13	27	vertices	vertex	NOUN
ejpam-4829	13	28	(	(	PUNCT
ejpam-4829	13	29	edge	edge	NOUN
ejpam-4829	13	30	set	set	NOUN
ejpam-4829	13	31	of	of	ADP
ejpam-4829	13	32	g	g	NOUN
ejpam-4829	13	33	)	)	PUNCT
ejpam-4829	13	34	.	.	PUNCT
ejpam-4829	14	1	such	such	DET
ejpam-4829	14	2	a	a	DET
ejpam-4829	14	3	graph	graph	NOUN
ejpam-4829	14	4	is	be	AUX
ejpam-4829	14	5	denoted	denote	VERB
ejpam-4829	14	6	by	by	ADP
ejpam-4829	14	7	(	(	PUNCT
ejpam-4829	14	8	v	v	NOUN
ejpam-4829	14	9	(	(	PUNCT
ejpam-4829	14	10	g	g	NOUN
ejpam-4829	14	11	)	)	PUNCT
ejpam-4829	14	12	,	,	PUNCT
ejpam-4829	14	13	e(g	e(g	PROPN
ejpam-4829	14	14	)	)	PUNCT
ejpam-4829	14	15	)	)	PUNCT
ejpam-4829	15	1	(	(	PUNCT
ejpam-4829	15	2	simply	simply	ADV
ejpam-4829	15	3	(	(	PUNCT
ejpam-4829	15	4	v	v	NOUN
ejpam-4829	15	5	,	,	PUNCT
ejpam-4829	15	6	e	e	NOUN
ejpam-4829	15	7	)	)	PUNCT
ejpam-4829	15	8	)	)	PUNCT
ejpam-4829	15	9	.	.	PUNCT
ejpam-4829	16	1	an	an	DET
ejpam-4829	16	2	empty	empty	ADJ
ejpam-4829	16	3	graph	graph	NOUN
ejpam-4829	16	4	is	be	AUX
ejpam-4829	16	5	a	a	DET
ejpam-4829	16	6	graph	graph	NOUN
ejpam-4829	16	7	without	without	ADP
ejpam-4829	16	8	edges	edge	NOUN
ejpam-4829	16	9	while	while	SCONJ
ejpam-4829	16	10	a	a	DET
ejpam-4829	16	11	complete	complete	ADJ
ejpam-4829	16	12	graph	graph	NOUN
ejpam-4829	16	13	is	be	AUX
ejpam-4829	16	14	a	a	DET
ejpam-4829	16	15	graph	graph	NOUN
ejpam-4829	16	16	with	with	ADP
ejpam-4829	16	17	all	all	DET
ejpam-4829	16	18	possible	possible	ADJ
ejpam-4829	16	19	edges	edge	NOUN
ejpam-4829	16	20	.	.	PUNCT
ejpam-4829	17	1	two	two	NUM
ejpam-4829	17	2	distinct	distinct	ADJ
ejpam-4829	17	3	vertices	vertex	NOUN
ejpam-4829	17	4	u	u	NOUN
ejpam-4829	17	5	and	and	CCONJ
ejpam-4829	17	6	v	v	NOUN
ejpam-4829	17	7	of	of	ADP
ejpam-4829	17	8	a	a	DET
ejpam-4829	17	9	graph	graph	NOUN
ejpam-4829	17	10	g	g	NOUN
ejpam-4829	17	11	are	be	AUX
ejpam-4829	17	12	adjacent	adjacent	ADJ
ejpam-4829	17	13	if	if	SCONJ
ejpam-4829	17	14	{	{	PUNCT
ejpam-4829	17	15	u	u	NOUN
ejpam-4829	17	16	,	,	PUNCT
ejpam-4829	17	17	v	v	NOUN
ejpam-4829	17	18	}	}	PUNCT
ejpam-4829	17	19	∈	∈	PROPN
ejpam-4829	17	20	e(g	e(g	PROPN
ejpam-4829	17	21	)	)	PUNCT
ejpam-4829	17	22	.	.	PUNCT
ejpam-4829	18	1	an	an	DET
ejpam-4829	18	2	edge	edge	NOUN
ejpam-4829	18	3	{	{	PUNCT
ejpam-4829	18	4	u	u	NOUN
ejpam-4829	18	5	,	,	PUNCT
ejpam-4829	18	6	v	v	NOUN
ejpam-4829	18	7	}	}	PUNCT
ejpam-4829	18	8	of	of	ADP
ejpam-4829	18	9	g	g	PROPN
ejpam-4829	18	10	is	be	AUX
ejpam-4829	18	11	denoted	denote	VERB
ejpam-4829	18	12	by	by	ADP
ejpam-4829	18	13	uv	uv	NOUN
ejpam-4829	18	14	while	while	SCONJ
ejpam-4829	18	15	u	u	NOUN
ejpam-4829	18	16	and	and	CCONJ
ejpam-4829	18	17	v	v	NOUN
ejpam-4829	18	18	are	be	AUX
ejpam-4829	18	19	called	call	VERB
ejpam-4829	18	20	endpoints	endpoint	NOUN
ejpam-4829	18	21	of	of	ADP
ejpam-4829	18	22	the	the	DET
ejpam-4829	18	23	edge	edge	NOUN
ejpam-4829	18	24	uv	uv	NOUN
ejpam-4829	18	25	.	.	PUNCT
ejpam-4829	19	1	two	two	NUM
ejpam-4829	19	2	distinct	distinct	ADJ
ejpam-4829	19	3	edges	edge	NOUN
ejpam-4829	19	4	e	e	NOUN
ejpam-4829	19	5	and	and	CCONJ
ejpam-4829	19	6	e′	e′	PROPN
ejpam-4829	19	7	of	of	ADP
ejpam-4829	19	8	a	a	DET
ejpam-4829	19	9	graph	graph	NOUN
ejpam-4829	19	10	g	g	NOUN
ejpam-4829	19	11	are	be	AUX
ejpam-4829	19	12	adjacent	adjacent	ADJ
ejpam-4829	19	13	edges	edge	NOUN
ejpam-4829	19	14	if	if	SCONJ
ejpam-4829	19	15	they	they	PRON
ejpam-4829	19	16	have	have	VERB
ejpam-4829	19	17	a	a	DET
ejpam-4829	19	18	common	common	ADJ
ejpam-4829	19	19	endpoint	endpoint	NOUN
ejpam-4829	19	20	.	.	PUNCT
ejpam-4829	20	1	a	a	DET
ejpam-4829	20	2	neighbor	neighbor	NOUN
ejpam-4829	20	3	of	of	ADP
ejpam-4829	20	4	a	a	DET
ejpam-4829	20	5	vertex	vertex	NOUN
ejpam-4829	20	6	u	u	NOUN
ejpam-4829	20	7	in	in	ADP
ejpam-4829	20	8	a	a	DET
ejpam-4829	20	9	graph	graph	NOUN
ejpam-4829	20	10	g	g	NOUN
ejpam-4829	20	11	is	be	AUX
ejpam-4829	20	12	a	a	DET
ejpam-4829	20	13	vertex	vertex	NOUN
ejpam-4829	20	14	adjacent	adjacent	ADJ
ejpam-4829	20	15	to	to	ADP
ejpam-4829	20	16	u	u	PRON
ejpam-4829	20	17	,	,	PUNCT
ejpam-4829	20	18	the	the	DET
ejpam-4829	20	19	neighborhood	neighborhood	NOUN
ejpam-4829	20	20	of	of	ADP
ejpam-4829	20	21	u	u	PRON
ejpam-4829	20	22	denoted	denote	VERB
ejpam-4829	20	23	by	by	ADP
ejpam-4829	20	24	ng(u	ng(u	NOUN
ejpam-4829	20	25	)	)	PUNCT
ejpam-4829	20	26	∗corresponding	∗corresponde	VERB
ejpam-4829	20	27	author	author	NOUN
ejpam-4829	20	28	.	.	PUNCT
ejpam-4829	21	1	doi	doi	NOUN
ejpam-4829	21	2	:	:	PUNCT
ejpam-4829	21	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4829	https://doi.org/10.29020/nybg.ejpam.v16i4.4829	NOUN
ejpam-4829	21	4	email	email	NOUN
ejpam-4829	21	5	addresses	address	NOUN
ejpam-4829	21	6	:	:	PUNCT
ejpam-4829	21	7	aaalorini@imamu.edu.sa	aaalorini@imamu.edu.sa	PROPN
ejpam-4829	21	8	(	(	PUNCT
ejpam-4829	21	9	a.	a.	NOUN
ejpam-4829	21	10	alorini	alorini	PROPN
ejpam-4829	21	11	)	)	PUNCT
ejpam-4829	21	12	,	,	PUNCT
ejpam-4829	21	13	abenamira@ksu.edu.sa	abenamira@ksu.edu.sa	PROPN
ejpam-4829	21	14	(	(	PUNCT
ejpam-4829	21	15	a.	a.	PROPN
ejpam-4829	21	16	ben	ben	PROPN
ejpam-4829	21	17	amira	amira	PROPN
ejpam-4829	21	18	)	)	PUNCT
ejpam-4829	21	19	,	,	PUNCT
ejpam-4829	21	20	mzohairi@gmail.com	mzohairi@gmail.com	X
ejpam-4829	21	21	(	(	PUNCT
ejpam-4829	21	22	m.	m.	NOUN
ejpam-4829	21	23	alzohairi	alzohairi	PROPN
ejpam-4829	21	24	)	)	PUNCT
ejpam-4829	21	25	,	,	PUNCT
ejpam-4829	21	26	mbouaziz@ksu.edu.sa	mbouaziz@ksu.edu.sa	NOUN
ejpam-4829	21	27	(	(	PUNCT
ejpam-4829	21	28	m.	m.	NOUN
ejpam-4829	21	29	bouaziz	bouaziz	PROPN
ejpam-4829	21	30	)	)	PUNCT
ejpam-4829	21	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4829	21	32	2786	2786	NUM
ejpam-4829	22	1	©	©	ADP
ejpam-4829	22	2	2023	2023	NUM
ejpam-4829	22	3	ejpam	ejpam	NOUN
ejpam-4829	22	4	all	all	DET
ejpam-4829	22	5	rights	right	NOUN
ejpam-4829	22	6	reserved	reserve	VERB
ejpam-4829	22	7	.	.	PUNCT
ejpam-4829	23	1	m.	m.	NOUN
ejpam-4829	23	2	bouaziz	bouaziz	PROPN
ejpam-4829	23	3	et	et	PROPN
ejpam-4829	23	4	al	al	PROPN
ejpam-4829	23	5	.	.	PUNCT
ejpam-4829	23	6	/	/	SYM
ejpam-4829	23	7	eur	eur	PROPN
ejpam-4829	23	8	.	.	PUNCT
ejpam-4829	24	1	j.	j.	PROPN
ejpam-4829	24	2	pure	pure	PROPN
ejpam-4829	24	3	appl	appl	PROPN
ejpam-4829	24	4	.	.	PROPN
ejpam-4829	24	5	math	math	PROPN
ejpam-4829	24	6	,	,	PUNCT
ejpam-4829	24	7	16	16	NUM
ejpam-4829	24	8	(	(	PUNCT
ejpam-4829	24	9	4	4	NUM
ejpam-4829	24	10	)	)	PUNCT
ejpam-4829	24	11	(	(	PUNCT
ejpam-4829	24	12	2023	2023	NUM
ejpam-4829	24	13	)	)	PUNCT
ejpam-4829	24	14	,	,	PUNCT
ejpam-4829	24	15	2786	2786	NUM
ejpam-4829	24	16	-	-	SYM
ejpam-4829	24	17	2797	2797	NUM
ejpam-4829	24	18	2787	2787	NUM
ejpam-4829	24	19	is	be	AUX
ejpam-4829	24	20	the	the	DET
ejpam-4829	24	21	set	set	NOUN
ejpam-4829	24	22	of	of	ADP
ejpam-4829	24	23	neighbors	neighbor	NOUN
ejpam-4829	24	24	of	of	ADP
ejpam-4829	24	25	u	u	NOUN
ejpam-4829	24	26	and	and	CCONJ
ejpam-4829	24	27	the	the	DET
ejpam-4829	24	28	neighborhood	neighborhood	NOUN
ejpam-4829	24	29	of	of	ADP
ejpam-4829	24	30	a	a	DET
ejpam-4829	24	31	subset	subset	NOUN
ejpam-4829	24	32	x	x	X
ejpam-4829	24	33	of	of	ADP
ejpam-4829	24	34	v	v	NOUN
ejpam-4829	24	35	(	(	PUNCT
ejpam-4829	24	36	g	g	NOUN
ejpam-4829	24	37	)	)	PUNCT
ejpam-4829	24	38	represented	represent	VERB
ejpam-4829	24	39	by	by	ADP
ejpam-4829	24	40	ng(x	ng(x	NUM
ejpam-4829	24	41	)	)	PUNCT
ejpam-4829	24	42	is	be	AUX
ejpam-4829	24	43	the	the	DET
ejpam-4829	24	44	union	union	NOUN
ejpam-4829	24	45	of	of	ADP
ejpam-4829	24	46	the	the	DET
ejpam-4829	24	47	neighborhoods	neighborhood	NOUN
ejpam-4829	24	48	of	of	ADP
ejpam-4829	24	49	every	every	DET
ejpam-4829	24	50	vertex	vertex	NOUN
ejpam-4829	24	51	in	in	ADP
ejpam-4829	24	52	x.	x.	NOUN
ejpam-4829	24	53	the	the	DET
ejpam-4829	24	54	degree	degree	NOUN
ejpam-4829	24	55	of	of	ADP
ejpam-4829	24	56	u	u	PRON
ejpam-4829	24	57	denoted	denote	VERB
ejpam-4829	24	58	by	by	ADP
ejpam-4829	24	59	dg(u	dg(u	NOUN
ejpam-4829	24	60	)	)	PUNCT
ejpam-4829	24	61	is	be	AUX
ejpam-4829	24	62	dg(u	dg(u	NOUN
ejpam-4829	24	63	)	)	PUNCT
ejpam-4829	24	64	=	=	SYM
ejpam-4829	24	65	|ng(u)|	|ng(u)|	NOUN
ejpam-4829	24	66	.	.	PUNCT
ejpam-4829	25	1	the	the	DET
ejpam-4829	25	2	complement	complement	NOUN
ejpam-4829	25	3	of	of	ADP
ejpam-4829	25	4	a	a	DET
ejpam-4829	25	5	graph	graph	NOUN
ejpam-4829	25	6	g	g	NOUN
ejpam-4829	25	7	is	be	AUX
ejpam-4829	25	8	the	the	DET
ejpam-4829	25	9	graph	graph	NOUN
ejpam-4829	25	10	g	g	ADP
ejpam-4829	25	11	such	such	DET
ejpam-4829	25	12	that	that	PRON
ejpam-4829	25	13	v	v	NOUN
ejpam-4829	25	14	(	(	PUNCT
ejpam-4829	25	15	g	g	NOUN
ejpam-4829	25	16	)	)	PUNCT
ejpam-4829	25	17	=	=	NOUN
ejpam-4829	25	18	v	v	X
ejpam-4829	25	19	(	(	PUNCT
ejpam-4829	25	20	g	g	NOUN
ejpam-4829	25	21	)	)	PUNCT
ejpam-4829	25	22	and	and	CCONJ
ejpam-4829	25	23	e(g	e(g	PROPN
ejpam-4829	25	24	)	)	PUNCT
ejpam-4829	26	1	=	=	PRON
ejpam-4829	26	2	{	{	PUNCT
ejpam-4829	26	3	{	{	PUNCT
ejpam-4829	26	4	u	u	NOUN
ejpam-4829	26	5	,	,	PUNCT
ejpam-4829	26	6	v	v	NOUN
ejpam-4829	26	7	}	}	PUNCT
ejpam-4829	26	8	:	:	PUNCT
ejpam-4829	26	9	u	u	PROPN
ejpam-4829	26	10	̸=	̸=	PROPN
ejpam-4829	26	11	v	v	ADP
ejpam-4829	26	12	∈	∈	PROPN
ejpam-4829	26	13	v	v	NOUN
ejpam-4829	26	14	(	(	PUNCT
ejpam-4829	26	15	g	g	NOUN
ejpam-4829	26	16	)	)	PUNCT
ejpam-4829	26	17	,	,	PUNCT
ejpam-4829	26	18	{	{	PUNCT
ejpam-4829	26	19	u	u	NOUN
ejpam-4829	26	20	,	,	PUNCT
ejpam-4829	26	21	v	v	NOUN
ejpam-4829	26	22	}	}	PUNCT
ejpam-4829	26	23	/∈	/∈	PUNCT
ejpam-4829	26	24	e(g	e(g	NOUN
ejpam-4829	26	25	)	)	PUNCT
ejpam-4829	26	26	}	}	PUNCT
ejpam-4829	26	27	.	.	PUNCT
ejpam-4829	27	1	for	for	ADP
ejpam-4829	27	2	undefined	undefined	ADJ
ejpam-4829	27	3	notions	notion	NOUN
ejpam-4829	27	4	and	and	CCONJ
ejpam-4829	27	5	notations	notation	NOUN
ejpam-4829	27	6	in	in	ADP
ejpam-4829	27	7	the	the	DET
ejpam-4829	27	8	graph	graph	NOUN
ejpam-4829	27	9	theory	theory	NOUN
ejpam-4829	27	10	,	,	PUNCT
ejpam-4829	27	11	see	see	VERB
ejpam-4829	27	12	[	[	X
ejpam-4829	27	13	8	8	NUM
ejpam-4829	27	14	]	]	PUNCT
ejpam-4829	27	15	.	.	PUNCT
ejpam-4829	28	1	in	in	ADP
ejpam-4829	28	2	particular	particular	ADJ
ejpam-4829	28	3	,	,	PUNCT
ejpam-4829	28	4	a	a	DET
ejpam-4829	28	5	graph	graph	NOUN
ejpam-4829	28	6	h	h	NOUN
ejpam-4829	28	7	=	=	SYM
ejpam-4829	28	8	(	(	PUNCT
ejpam-4829	28	9	w	w	PROPN
ejpam-4829	28	10	,	,	PUNCT
ejpam-4829	28	11	f	f	PROPN
ejpam-4829	28	12	)	)	PUNCT
ejpam-4829	28	13	is	be	AUX
ejpam-4829	28	14	a	a	DET
ejpam-4829	28	15	subgraph	subgraph	NOUN
ejpam-4829	28	16	of	of	ADP
ejpam-4829	28	17	a	a	DET
ejpam-4829	28	18	graph	graph	NOUN
ejpam-4829	28	19	g	g	NOUN
ejpam-4829	28	20	=	=	PUNCT
ejpam-4829	28	21	(	(	PUNCT
ejpam-4829	28	22	v	v	NOUN
ejpam-4829	28	23	,	,	PUNCT
ejpam-4829	28	24	e	e	NOUN
ejpam-4829	28	25	)	)	PUNCT
ejpam-4829	28	26	if	if	SCONJ
ejpam-4829	28	27	w	w	PROPN
ejpam-4829	28	28	⊆	⊆	NUM
ejpam-4829	28	29	v	v	NOUN
ejpam-4829	28	30	and	and	CCONJ
ejpam-4829	28	31	f	f	PROPN
ejpam-4829	28	32	⊆	⊆	PROPN
ejpam-4829	28	33	e.	e.	PROPN
ejpam-4829	28	34	given	give	VERB
ejpam-4829	28	35	a	a	DET
ejpam-4829	28	36	subset	subset	NOUN
ejpam-4829	28	37	x	x	PUNCT
ejpam-4829	28	38	of	of	ADP
ejpam-4829	28	39	the	the	DET
ejpam-4829	28	40	vertex	vertex	NOUN
ejpam-4829	28	41	set	set	NOUN
ejpam-4829	28	42	of	of	ADP
ejpam-4829	28	43	a	a	DET
ejpam-4829	28	44	graph	graph	NOUN
ejpam-4829	28	45	g	g	NOUN
ejpam-4829	28	46	=	=	PUNCT
ejpam-4829	28	47	(	(	PUNCT
ejpam-4829	28	48	v	v	NOUN
ejpam-4829	28	49	,	,	PUNCT
ejpam-4829	28	50	e	e	NOUN
ejpam-4829	28	51	)	)	PUNCT
ejpam-4829	28	52	,	,	PUNCT
ejpam-4829	28	53	the	the	DET
ejpam-4829	28	54	subgraph	subgraph	NOUN
ejpam-4829	28	55	g[x	g[x	NOUN
ejpam-4829	28	56	]	]	X
ejpam-4829	28	57	=	=	SYM
ejpam-4829	28	58	(	(	PUNCT
ejpam-4829	28	59	x	x	X
ejpam-4829	28	60	,	,	PUNCT
ejpam-4829	28	61	e	e	NOUN
ejpam-4829	28	62	∩	∩	X
ejpam-4829	28	63	{	{	PUNCT
ejpam-4829	28	64	xy	xy	PROPN
ejpam-4829	28	65	,	,	PUNCT
ejpam-4829	28	66	x	x	PUNCT
ejpam-4829	28	67	̸=	̸=	PROPN
ejpam-4829	28	68	y	y	PROPN
ejpam-4829	28	69	∈	∈	PROPN
ejpam-4829	28	70	x	x	NOUN
ejpam-4829	28	71	}	}	PUNCT
ejpam-4829	28	72	)	)	PUNCT
ejpam-4829	28	73	is	be	AUX
ejpam-4829	28	74	called	call	VERB
ejpam-4829	28	75	the	the	DET
ejpam-4829	28	76	subgraph	subgraph	NOUN
ejpam-4829	28	77	induced	induce	VERB
ejpam-4829	28	78	by	by	ADP
ejpam-4829	28	79	x.	x.	NOUN
ejpam-4829	28	80	the	the	DET
ejpam-4829	28	81	subgraph	subgraph	PROPN
ejpam-4829	28	82	g[v	g[v	PROPN
ejpam-4829	28	83	(	(	PUNCT
ejpam-4829	28	84	g	g	NOUN
ejpam-4829	28	85	)	)	PUNCT
ejpam-4829	28	86	\x	\x	NOUN
ejpam-4829	28	87	]	]	PUNCT
ejpam-4829	28	88	is	be	AUX
ejpam-4829	28	89	denoted	denote	VERB
ejpam-4829	28	90	by	by	ADP
ejpam-4829	28	91	g−x	g−x	NOUN
ejpam-4829	28	92	.	.	PUNCT
ejpam-4829	29	1	considering	consider	VERB
ejpam-4829	29	2	a	a	DET
ejpam-4829	29	3	vertex	vertex	NOUN
ejpam-4829	29	4	x	x	NOUN
ejpam-4829	29	5	,	,	PUNCT
ejpam-4829	29	6	the	the	DET
ejpam-4829	29	7	subgraph	subgraph	NOUN
ejpam-4829	29	8	g−	g−	PROPN
ejpam-4829	29	9	{	{	PUNCT
ejpam-4829	29	10	x	x	NOUN
ejpam-4829	29	11	}	}	PUNCT
ejpam-4829	29	12	is	be	AUX
ejpam-4829	29	13	also	also	ADV
ejpam-4829	29	14	denoted	denote	VERB
ejpam-4829	29	15	by	by	ADP
ejpam-4829	29	16	g−	g−	PROPN
ejpam-4829	29	17	x.	x.	NOUN
ejpam-4829	29	18	for	for	ADP
ejpam-4829	29	19	a	a	DET
ejpam-4829	29	20	vertex	vertex	NOUN
ejpam-4829	29	21	u	u	NOUN
ejpam-4829	29	22	outside	outside	ADP
ejpam-4829	29	23	a	a	DET
ejpam-4829	29	24	vertex	vertex	NOUN
ejpam-4829	29	25	subset	subset	NOUN
ejpam-4829	29	26	x	x	PUNCT
ejpam-4829	29	27	of	of	ADP
ejpam-4829	29	28	a	a	DET
ejpam-4829	29	29	graph	graph	NOUN
ejpam-4829	29	30	g	g	NOUN
ejpam-4829	29	31	,	,	PUNCT
ejpam-4829	30	1	u	u	NOUN
ejpam-4829	30	2	∼g	∼g	PROPN
ejpam-4829	30	3	x	x	PUNCT
ejpam-4829	30	4	denotes	denote	NOUN
ejpam-4829	30	5	when	when	SCONJ
ejpam-4829	30	6	u	u	NOUN
ejpam-4829	30	7	is	be	AUX
ejpam-4829	30	8	either	either	ADV
ejpam-4829	30	9	adjacent	adjacent	ADJ
ejpam-4829	30	10	to	to	ADP
ejpam-4829	30	11	all	all	PRON
ejpam-4829	30	12	or	or	CCONJ
ejpam-4829	30	13	none	none	NOUN
ejpam-4829	30	14	of	of	ADP
ejpam-4829	30	15	the	the	DET
ejpam-4829	30	16	elements	element	NOUN
ejpam-4829	30	17	of	of	ADP
ejpam-4829	30	18	x.	x.	NOUN
ejpam-4829	30	19	in	in	ADP
ejpam-4829	30	20	a	a	DET
ejpam-4829	30	21	graph	graph	NOUN
ejpam-4829	30	22	g	g	NOUN
ejpam-4829	30	23	,	,	PUNCT
ejpam-4829	30	24	a	a	DET
ejpam-4829	30	25	vertex	vertex	NOUN
ejpam-4829	30	26	subset	subset	NOUN
ejpam-4829	30	27	m	m	AUX
ejpam-4829	30	28	is	be	AUX
ejpam-4829	30	29	a	a	DET
ejpam-4829	30	30	module	module	NOUN
ejpam-4829	30	31	of	of	ADP
ejpam-4829	30	32	g	g	PROPN
ejpam-4829	30	33	if	if	SCONJ
ejpam-4829	30	34	every	every	DET
ejpam-4829	30	35	vertex	vertex	NOUN
ejpam-4829	30	36	outside	outside	ADP
ejpam-4829	30	37	m	m	PROPN
ejpam-4829	30	38	is	be	AUX
ejpam-4829	30	39	either	either	ADV
ejpam-4829	30	40	adjacent	adjacent	ADJ
ejpam-4829	30	41	to	to	ADP
ejpam-4829	30	42	all	all	PRON
ejpam-4829	30	43	or	or	CCONJ
ejpam-4829	30	44	none	none	NOUN
ejpam-4829	30	45	of	of	ADP
ejpam-4829	30	46	the	the	DET
ejpam-4829	30	47	elements	element	NOUN
ejpam-4829	30	48	of	of	ADP
ejpam-4829	30	49	m	m	PROPN
ejpam-4829	30	50	.	.	PUNCT
ejpam-4829	31	1	this	this	DET
ejpam-4829	31	2	concept	concept	NOUN
ejpam-4829	31	3	was	be	AUX
ejpam-4829	31	4	introduced	introduce	VERB
ejpam-4829	31	5	in	in	ADP
ejpam-4829	31	6	[	[	X
ejpam-4829	31	7	6	6	NUM
ejpam-4829	31	8	]	]	PUNCT
ejpam-4829	31	9	.	.	PUNCT
ejpam-4829	32	1	the	the	DET
ejpam-4829	32	2	empty	empty	ADJ
ejpam-4829	32	3	set	set	NOUN
ejpam-4829	32	4	,	,	PUNCT
ejpam-4829	32	5	the	the	DET
ejpam-4829	32	6	singleton	singleton	NOUN
ejpam-4829	32	7	sets	set	NOUN
ejpam-4829	32	8	and	and	CCONJ
ejpam-4829	32	9	the	the	DET
ejpam-4829	32	10	full	full	ADJ
ejpam-4829	32	11	set	set	NOUN
ejpam-4829	32	12	v	v	NOUN
ejpam-4829	32	13	(	(	PUNCT
ejpam-4829	32	14	g	g	NOUN
ejpam-4829	32	15	)	)	PUNCT
ejpam-4829	32	16	of	of	ADP
ejpam-4829	32	17	vertices	vertex	NOUN
ejpam-4829	32	18	are	be	AUX
ejpam-4829	32	19	trivial	trivial	ADJ
ejpam-4829	32	20	modules	module	NOUN
ejpam-4829	32	21	.	.	PUNCT
ejpam-4829	33	1	a	a	DET
ejpam-4829	33	2	module	module	NOUN
ejpam-4829	33	3	of	of	ADP
ejpam-4829	33	4	a	a	DET
ejpam-4829	33	5	graph	graph	NOUN
ejpam-4829	33	6	g	g	ADP
ejpam-4829	33	7	distinct	distinct	ADJ
ejpam-4829	33	8	from	from	ADP
ejpam-4829	33	9	v	v	NUM
ejpam-4829	33	10	(	(	PUNCT
ejpam-4829	33	11	g	g	NOUN
ejpam-4829	33	12	)	)	PUNCT
ejpam-4829	33	13	is	be	AUX
ejpam-4829	33	14	a	a	DET
ejpam-4829	33	15	proper	proper	ADJ
ejpam-4829	33	16	module	module	NOUN
ejpam-4829	33	17	of	of	ADP
ejpam-4829	33	18	g.	g.	PROPN
ejpam-4829	33	19	a	a	DET
ejpam-4829	33	20	graph	graph	NOUN
ejpam-4829	33	21	is	be	AUX
ejpam-4829	33	22	indecomposable	indecomposable	ADJ
ejpam-4829	33	23	if	if	SCONJ
ejpam-4829	33	24	all	all	DET
ejpam-4829	33	25	its	its	PRON
ejpam-4829	33	26	modules	module	NOUN
ejpam-4829	33	27	are	be	AUX
ejpam-4829	33	28	trivial	trivial	ADJ
ejpam-4829	33	29	,	,	PUNCT
ejpam-4829	33	30	otherwise	otherwise	ADV
ejpam-4829	33	31	it	it	PRON
ejpam-4829	33	32	is	be	AUX
ejpam-4829	33	33	decomposable	decomposable	ADJ
ejpam-4829	33	34	.	.	PUNCT
ejpam-4829	34	1	clearly	clearly	ADV
ejpam-4829	34	2	,	,	PUNCT
ejpam-4829	34	3	all	all	DET
ejpam-4829	34	4	graphs	graph	NOUN
ejpam-4829	34	5	with	with	ADP
ejpam-4829	34	6	at	at	ADP
ejpam-4829	34	7	most	most	ADV
ejpam-4829	34	8	two	two	NUM
ejpam-4829	34	9	vertices	vertex	NOUN
ejpam-4829	34	10	are	be	AUX
ejpam-4829	34	11	indecomposable	indecomposable	ADJ
ejpam-4829	34	12	.	.	PUNCT
ejpam-4829	35	1	given	give	VERB
ejpam-4829	35	2	a	a	DET
ejpam-4829	35	3	3	3	NUM
ejpam-4829	35	4	-	-	PUNCT
ejpam-4829	35	5	vertex	vertex	NOUN
ejpam-4829	35	6	graph	graph	NOUN
ejpam-4829	35	7	g	g	NOUN
ejpam-4829	35	8	,	,	PUNCT
ejpam-4829	35	9	if	if	SCONJ
ejpam-4829	35	10	g	g	PROPN
ejpam-4829	35	11	is	be	AUX
ejpam-4829	35	12	complete	complete	ADJ
ejpam-4829	35	13	or	or	CCONJ
ejpam-4829	35	14	empty	empty	ADJ
ejpam-4829	35	15	,	,	PUNCT
ejpam-4829	35	16	then	then	ADV
ejpam-4829	35	17	each	each	DET
ejpam-4829	35	18	2	2	NUM
ejpam-4829	35	19	-	-	PUNCT
ejpam-4829	35	20	element	element	NOUN
ejpam-4829	35	21	vertex	vertex	NOUN
ejpam-4829	35	22	subset	subset	NOUN
ejpam-4829	35	23	is	be	AUX
ejpam-4829	35	24	a	a	DET
ejpam-4829	35	25	non	non	ADJ
ejpam-4829	35	26	-	-	ADJ
ejpam-4829	35	27	trivial	trivial	ADJ
ejpam-4829	35	28	module	module	NOUN
ejpam-4829	35	29	of	of	ADP
ejpam-4829	35	30	g	g	NOUN
ejpam-4829	35	31	,	,	PUNCT
ejpam-4829	35	32	otherwise	otherwise	ADV
ejpam-4829	35	33	g	g	PROPN
ejpam-4829	35	34	has	have	VERB
ejpam-4829	35	35	a	a	DET
ejpam-4829	35	36	unique	unique	ADJ
ejpam-4829	35	37	nontrivial	nontrivial	NOUN
ejpam-4829	35	38	module	module	NOUN
ejpam-4829	35	39	{	{	PUNCT
ejpam-4829	35	40	u	u	NOUN
ejpam-4829	35	41	,	,	PUNCT
ejpam-4829	35	42	v	v	NOUN
ejpam-4829	35	43	}	}	PUNCT
ejpam-4829	35	44	where	where	SCONJ
ejpam-4829	35	45	uv	uv	NOUN
ejpam-4829	35	46	is	be	AUX
ejpam-4829	35	47	the	the	DET
ejpam-4829	35	48	unique	unique	ADJ
ejpam-4829	35	49	edge	edge	NOUN
ejpam-4829	35	50	of	of	ADP
ejpam-4829	35	51	g	g	NOUN
ejpam-4829	35	52	or	or	CCONJ
ejpam-4829	35	53	g.	g.	PROPN
ejpam-4829	35	54	thus	thus	ADV
ejpam-4829	35	55	,	,	PUNCT
ejpam-4829	35	56	all	all	DET
ejpam-4829	35	57	3	3	NUM
ejpam-4829	35	58	-	-	PUNCT
ejpam-4829	35	59	vertex	vertex	NOUN
ejpam-4829	35	60	graphs	graph	NOUN
ejpam-4829	35	61	are	be	AUX
ejpam-4829	35	62	decomposable	decomposable	ADJ
ejpam-4829	35	63	.	.	PUNCT
ejpam-4829	36	1	indecomposable	indecomposable	ADJ
ejpam-4829	36	2	graphs	graph	NOUN
ejpam-4829	36	3	with	with	ADP
ejpam-4829	36	4	at	at	ADV
ejpam-4829	36	5	least	least	ADV
ejpam-4829	36	6	four	four	NUM
ejpam-4829	36	7	vertices	vertex	NOUN
ejpam-4829	36	8	are	be	AUX
ejpam-4829	36	9	called	call	VERB
ejpam-4829	36	10	prime	prime	ADJ
ejpam-4829	36	11	graphs	graph	NOUN
ejpam-4829	36	12	.	.	PUNCT
ejpam-4829	37	1	an	an	DET
ejpam-4829	37	2	isomorphism	isomorphism	NOUN
ejpam-4829	37	3	f	f	PROPN
ejpam-4829	37	4	from	from	ADP
ejpam-4829	37	5	a	a	DET
ejpam-4829	37	6	graph	graph	NOUN
ejpam-4829	37	7	g	g	NOUN
ejpam-4829	37	8	=	=	PUNCT
ejpam-4829	37	9	(	(	PUNCT
ejpam-4829	37	10	v	v	NOUN
ejpam-4829	37	11	,	,	PUNCT
ejpam-4829	37	12	e	e	NOUN
ejpam-4829	37	13	)	)	PUNCT
ejpam-4829	37	14	onto	onto	ADP
ejpam-4829	37	15	a	a	DET
ejpam-4829	37	16	graph	graph	NOUN
ejpam-4829	37	17	g′	g′	NOUN
ejpam-4829	37	18	=	=	SYM
ejpam-4829	37	19	(	(	PUNCT
ejpam-4829	37	20	v	v	NOUN
ejpam-4829	37	21	′	′	NUM
ejpam-4829	37	22	,	,	PUNCT
ejpam-4829	37	23	e′	e′	X
ejpam-4829	37	24	)	)	PUNCT
ejpam-4829	37	25	is	be	AUX
ejpam-4829	37	26	a	a	DET
ejpam-4829	37	27	bijection	bijection	NOUN
ejpam-4829	37	28	from	from	ADP
ejpam-4829	37	29	v	v	NOUN
ejpam-4829	37	30	onto	onto	ADP
ejpam-4829	37	31	v	v	NOUN
ejpam-4829	37	32	′	′	NUM
ejpam-4829	37	33	such	such	ADJ
ejpam-4829	37	34	that	that	PRON
ejpam-4829	37	35	for	for	ADP
ejpam-4829	37	36	all	all	DET
ejpam-4829	37	37	x	x	NOUN
ejpam-4829	37	38	,	,	PUNCT
ejpam-4829	37	39	y	y	PROPN
ejpam-4829	37	40	∈	∈	PROPN
ejpam-4829	37	41	v	v	NOUN
ejpam-4829	37	42	,	,	PUNCT
ejpam-4829	37	43	xy	xy	PROPN
ejpam-4829	37	44	∈	∈	PROPN
ejpam-4829	37	45	e	e	PROPN
ejpam-4829	37	46	⇔	⇔	X
ejpam-4829	37	47	f(x)f(y	f(x)f(y	NOUN
ejpam-4829	37	48	)	)	PUNCT
ejpam-4829	37	49	∈	∈	NOUN
ejpam-4829	38	1	e′.	e′.	NOUN
ejpam-4829	39	1	we	we	PRON
ejpam-4829	39	2	denote	denote	VERB
ejpam-4829	39	3	g	g	PROPN
ejpam-4829	39	4	≃	≃	PROPN
ejpam-4829	39	5	g′	g′	NOUN
ejpam-4829	39	6	the	the	DET
ejpam-4829	39	7	graphsg	graphsg	NOUN
ejpam-4829	39	8	andg′	andg′	ADJ
ejpam-4829	39	9	which	which	PRON
ejpam-4829	39	10	are	be	AUX
ejpam-4829	39	11	called	call	VERB
ejpam-4829	39	12	isomorphic	isomorphic	ADJ
ejpam-4829	39	13	if	if	SCONJ
ejpam-4829	39	14	there	there	PRON
ejpam-4829	39	15	is	be	VERB
ejpam-4829	39	16	an	an	DET
ejpam-4829	39	17	isomorphism	isomorphism	NOUN
ejpam-4829	39	18	fromg	fromg	NOUN
ejpam-4829	39	19	ontog′.	ontog′.	NOUN
ejpam-4829	39	20	in	in	ADP
ejpam-4829	39	21	order	order	NOUN
ejpam-4829	39	22	to	to	PART
ejpam-4829	39	23	state	state	VERB
ejpam-4829	39	24	our	our	PRON
ejpam-4829	39	25	theorem	theorem	NOUN
ejpam-4829	39	26	,	,	PUNCT
ejpam-4829	39	27	we	we	PRON
ejpam-4829	39	28	introduce	introduce	VERB
ejpam-4829	39	29	the	the	DET
ejpam-4829	39	30	following	follow	VERB
ejpam-4829	39	31	new	new	ADJ
ejpam-4829	39	32	graphs	graph	NOUN
ejpam-4829	39	33	,	,	PUNCT
ejpam-4829	39	34	along	along	ADP
ejpam-4829	39	35	with	with	ADP
ejpam-4829	39	36	some	some	DET
ejpam-4829	39	37	known	know	VERB
ejpam-4829	39	38	graphs	graph	NOUN
ejpam-4829	39	39	.	.	PUNCT
ejpam-4829	40	1	recall	recall	VERB
ejpam-4829	40	2	the	the	DET
ejpam-4829	40	3	known	know	VERB
ejpam-4829	40	4	small	small	ADJ
ejpam-4829	40	5	graphs	graph	NOUN
ejpam-4829	40	6	used	use	VERB
ejpam-4829	40	7	in	in	ADP
ejpam-4829	40	8	this	this	DET
ejpam-4829	40	9	paper	paper	NOUN
ejpam-4829	40	10	.	.	PUNCT
ejpam-4829	41	1	first	first	ADV
ejpam-4829	41	2	,	,	PUNCT
ejpam-4829	41	3	the	the	DET
ejpam-4829	41	4	graph	graph	NOUN
ejpam-4829	41	5	p4	p4	NOUN
ejpam-4829	41	6	=	=	PUNCT
ejpam-4829	41	7	(	(	PUNCT
ejpam-4829	41	8	{	{	PUNCT
ejpam-4829	41	9	v1	v1	NOUN
ejpam-4829	41	10	,	,	PUNCT
ejpam-4829	41	11	v2	v2	PROPN
ejpam-4829	41	12	,	,	PUNCT
ejpam-4829	41	13	v3	v3	PROPN
ejpam-4829	41	14	,	,	PUNCT
ejpam-4829	41	15	v4	v4	PROPN
ejpam-4829	41	16	}	}	PUNCT
ejpam-4829	41	17	,	,	PUNCT
ejpam-4829	41	18	{	{	PUNCT
ejpam-4829	41	19	v1v2	v1v2	NOUN
ejpam-4829	41	20	,	,	PUNCT
ejpam-4829	41	21	v2v3	v2v3	PROPN
ejpam-4829	41	22	,	,	PUNCT
ejpam-4829	41	23	v3v4	v3v4	NOUN
ejpam-4829	41	24	}	}	PUNCT
ejpam-4829	41	25	)	)	PUNCT
ejpam-4829	41	26	(	(	PUNCT
ejpam-4829	41	27	illustrated	illustrate	VERB
ejpam-4829	41	28	in	in	ADP
ejpam-4829	41	29	figure	figure	NOUN
ejpam-4829	41	30	1	1	NUM
ejpam-4829	41	31	)	)	PUNCT
ejpam-4829	41	32	.	.	PUNCT
ejpam-4829	42	1	second	second	ADJ
ejpam-4829	42	2	,	,	PUNCT
ejpam-4829	42	3	the	the	DET
ejpam-4829	42	4	graph	graph	NOUN
ejpam-4829	42	5	β	β	X
ejpam-4829	42	6	=	=	SYM
ejpam-4829	42	7	(	(	PUNCT
ejpam-4829	42	8	{	{	PUNCT
ejpam-4829	42	9	a	a	X
ejpam-4829	42	10	,	,	PUNCT
ejpam-4829	42	11	a′	a′	PROPN
ejpam-4829	42	12	,	,	PUNCT
ejpam-4829	42	13	x	x	PROPN
ejpam-4829	42	14	,	,	PUNCT
ejpam-4829	42	15	x′	x′	NUM
ejpam-4829	42	16	,	,	PUNCT
ejpam-4829	42	17	y	y	PROPN
ejpam-4829	42	18	}	}	PUNCT
ejpam-4829	42	19	,	,	PUNCT
ejpam-4829	42	20	{	{	PUNCT
ejpam-4829	42	21	ax′	ax′	NOUN
ejpam-4829	42	22	,	,	PUNCT
ejpam-4829	42	23	ay	ay	INTJ
ejpam-4829	42	24	,	,	PUNCT
ejpam-4829	42	25	aa′	aa′	ADJ
ejpam-4829	42	26	,	,	PUNCT
ejpam-4829	42	27	a′x′	a′x′	ADJ
ejpam-4829	42	28	,	,	PUNCT
ejpam-4829	42	29	a′y	a′y	ADJ
ejpam-4829	42	30	,	,	PUNCT
ejpam-4829	42	31	xy	xy	NOUN
ejpam-4829	42	32	}	}	PUNCT
ejpam-4829	42	33	)	)	PUNCT
ejpam-4829	42	34	(	(	PUNCT
ejpam-4829	42	35	shown	show	VERB
ejpam-4829	42	36	in	in	ADP
ejpam-4829	42	37	figure	figure	NOUN
ejpam-4829	42	38	2	2	NUM
ejpam-4829	42	39	)	)	PUNCT
ejpam-4829	42	40	.	.	PUNCT
ejpam-4829	43	1	finally	finally	ADV
ejpam-4829	43	2	,	,	PUNCT
ejpam-4829	43	3	the	the	DET
ejpam-4829	43	4	taurus	taurus	NOUN
ejpam-4829	43	5	(	(	PUNCT
ejpam-4829	43	6	resp	resp	NOUN
ejpam-4829	43	7	.	.	PUNCT
ejpam-4829	44	1	the	the	DET
ejpam-4829	44	2	house	house	NOUN
ejpam-4829	44	3	)	)	PUNCT
ejpam-4829	44	4	is	be	AUX
ejpam-4829	44	5	the	the	DET
ejpam-4829	44	6	graph	graph	NOUN
ejpam-4829	44	7	with	with	ADP
ejpam-4829	44	8	the	the	DET
ejpam-4829	44	9	vertex	vertex	NOUN
ejpam-4829	44	10	set	set	NOUN
ejpam-4829	44	11	{	{	PUNCT
ejpam-4829	44	12	a	a	X
ejpam-4829	44	13	,	,	PUNCT
ejpam-4829	44	14	x1	x1	PROPN
ejpam-4829	44	15	,	,	PUNCT
ejpam-4829	44	16	x′1	x′1	PROPN
ejpam-4829	44	17	,	,	PUNCT
ejpam-4829	44	18	x2	x2	PROPN
ejpam-4829	44	19	,	,	PUNCT
ejpam-4829	44	20	x′2	x′2	NOUN
ejpam-4829	44	21	}	}	PUNCT
ejpam-4829	44	22	and	and	CCONJ
ejpam-4829	44	23	the	the	DET
ejpam-4829	44	24	edge	edge	NOUN
ejpam-4829	44	25	set	set	NOUN
ejpam-4829	44	26	{	{	PUNCT
ejpam-4829	44	27	ax′1	ax′1	PROPN
ejpam-4829	44	28	,	,	PUNCT
ejpam-4829	44	29	ax′2	ax′2	PROPN
ejpam-4829	44	30	,	,	PUNCT
ejpam-4829	44	31	x′1x′2	x′1x′2	PROPN
ejpam-4829	44	32	,	,	PUNCT
ejpam-4829	44	33	x1x′1	x1x′1	PROPN
ejpam-4829	44	34	,	,	PUNCT
ejpam-4829	44	35	x2x′2	x2x′2	PROPN
ejpam-4829	44	36	}	}	PUNCT
ejpam-4829	44	37	,	,	PUNCT
ejpam-4829	44	38	(	(	PUNCT
ejpam-4829	44	39	resp	resp	NOUN
ejpam-4829	44	40	.	.	PUNCT
ejpam-4829	45	1	{	{	PUNCT
ejpam-4829	45	2	ax′1	ax′1	NOUN
ejpam-4829	45	3	,	,	PUNCT
ejpam-4829	45	4	ax′2	ax′2	PROPN
ejpam-4829	45	5	,	,	PUNCT
ejpam-4829	45	6	x′1x′2	x′1x′2	PROPN
ejpam-4829	45	7	,	,	PUNCT
ejpam-4829	45	8	x1x′1	x1x′1	PROPN
ejpam-4829	45	9	,	,	PUNCT
ejpam-4829	45	10	x2x′2	x2x′2	PROPN
ejpam-4829	45	11	,	,	PUNCT
ejpam-4829	45	12	x1x2	x1x2	ADJ
ejpam-4829	45	13	}	}	PUNCT
ejpam-4829	45	14	)	)	PUNCT
ejpam-4829	45	15	as	as	SCONJ
ejpam-4829	45	16	illustrated	illustrate	VERB
ejpam-4829	45	17	in	in	ADP
ejpam-4829	45	18	figure	figure	NOUN
ejpam-4829	45	19	3	3	NUM
ejpam-4829	45	20	.	.	PUNCT
ejpam-4829	45	21	v1	v1	PROPN
ejpam-4829	45	22	v2	v2	PROPN
ejpam-4829	45	23	v3	v3	PROPN
ejpam-4829	45	24	v4	v4	PROPN
ejpam-4829	45	25	figure	figure	NOUN
ejpam-4829	45	26	1	1	NUM
ejpam-4829	45	27	:	:	PUNCT
ejpam-4829	45	28	p4	p4	ADJ
ejpam-4829	45	29	x′	x′	PROPN
ejpam-4829	45	30	a	a	DET
ejpam-4829	45	31	a′	a′	PROPN
ejpam-4829	45	32	y	y	NOUN
ejpam-4829	45	33	x	x	PRON
ejpam-4829	45	34	figure	figure	NOUN
ejpam-4829	45	35	2	2	NUM
ejpam-4829	45	36	:	:	PUNCT
ejpam-4829	45	37	β	β	X
ejpam-4829	45	38	m.	m.	PROPN
ejpam-4829	45	39	bouaziz	bouaziz	PROPN
ejpam-4829	45	40	et	et	PROPN
ejpam-4829	45	41	al	al	PROPN
ejpam-4829	45	42	.	.	PUNCT
ejpam-4829	45	43	/	/	SYM
ejpam-4829	45	44	eur	eur	PROPN
ejpam-4829	45	45	.	.	PUNCT
ejpam-4829	46	1	j.	j.	PROPN
ejpam-4829	46	2	pure	pure	PROPN
ejpam-4829	46	3	appl	appl	PROPN
ejpam-4829	46	4	.	.	PROPN
ejpam-4829	46	5	math	math	PROPN
ejpam-4829	46	6	,	,	PUNCT
ejpam-4829	46	7	16	16	NUM
ejpam-4829	46	8	(	(	PUNCT
ejpam-4829	46	9	4	4	NUM
ejpam-4829	46	10	)	)	PUNCT
ejpam-4829	46	11	(	(	PUNCT
ejpam-4829	46	12	2023	2023	NUM
ejpam-4829	46	13	)	)	PUNCT
ejpam-4829	46	14	,	,	PUNCT
ejpam-4829	46	15	2786	2786	NUM
ejpam-4829	46	16	-	-	SYM
ejpam-4829	46	17	2797	2797	NUM
ejpam-4829	46	18	2788	2788	NUM
ejpam-4829	47	1	x1	x1	NOUN
ejpam-4829	48	1	x2	x2	NOUN
ejpam-4829	48	2	x′	x′	PROPN
ejpam-4829	48	3	1	1	NUM
ejpam-4829	48	4	x′	x′	PROPN
ejpam-4829	48	5	2	2	NUM
ejpam-4829	48	6	a	a	DET
ejpam-4829	48	7	taurus	taurus	NOUN
ejpam-4829	48	8	x1	x1	PROPN
ejpam-4829	49	1	x2	x2	PROPN
ejpam-4829	49	2	x′	x′	PROPN
ejpam-4829	49	3	1	1	NUM
ejpam-4829	49	4	x′	x′	PROPN
ejpam-4829	49	5	2	2	NUM
ejpam-4829	49	6	a	a	DET
ejpam-4829	49	7	house	house	NOUN
ejpam-4829	49	8	figure	figure	NOUN
ejpam-4829	49	9	3	3	NUM
ejpam-4829	49	10	:	:	PUNCT
ejpam-4829	49	11	taurus	taurus	PROPN
ejpam-4829	49	12	and	and	CCONJ
ejpam-4829	49	13	house	house	PROPN
ejpam-4829	49	14	let	let	VERB
ejpam-4829	49	15	’s	’s	PRON
ejpam-4829	49	16	define	define	VERB
ejpam-4829	49	17	the	the	DET
ejpam-4829	49	18	following	follow	VERB
ejpam-4829	49	19	two	two	NUM
ejpam-4829	49	20	graph	graph	NOUN
ejpam-4829	49	21	families	family	NOUN
ejpam-4829	49	22	:	:	PUNCT
ejpam-4829	49	23	definition	definition	NOUN
ejpam-4829	49	24	1	1	NUM
ejpam-4829	49	25	.	.	PUNCT
ejpam-4829	50	1	let	let	VERB
ejpam-4829	50	2	k	k	NOUN
ejpam-4829	50	3	and	and	CCONJ
ejpam-4829	50	4	q	q	AUX
ejpam-4829	50	5	be	be	AUX
ejpam-4829	50	6	two	two	NUM
ejpam-4829	50	7	non	non	ADJ
ejpam-4829	50	8	-	-	ADJ
ejpam-4829	50	9	negative	negative	ADJ
ejpam-4829	50	10	integers	integer	NOUN
ejpam-4829	50	11	with	with	ADP
ejpam-4829	50	12	k	k	PROPN
ejpam-4829	50	13	≥	≥	NUM
ejpam-4829	50	14	2	2	NUM
ejpam-4829	50	15	.	.	PUNCT
ejpam-4829	51	1	a	a	DET
ejpam-4829	51	2	palace	palace	NOUN
ejpam-4829	51	3	pk	pk	NOUN
ejpam-4829	51	4	,	,	PUNCT
ejpam-4829	51	5	q	q	PUNCT
ejpam-4829	51	6	is	be	AUX
ejpam-4829	51	7	a	a	DET
ejpam-4829	51	8	graph	graph	NOUN
ejpam-4829	51	9	(	(	PUNCT
ejpam-4829	51	10	v	v	NOUN
ejpam-4829	51	11	,	,	PUNCT
ejpam-4829	51	12	e	e	NOUN
ejpam-4829	51	13	)	)	PUNCT
ejpam-4829	51	14	satisfying	satisfy	VERB
ejpam-4829	51	15	the	the	DET
ejpam-4829	51	16	following	following	NOUN
ejpam-4829	51	17	:	:	PUNCT
ejpam-4829	51	18	there	there	PRON
ejpam-4829	51	19	is	be	VERB
ejpam-4829	51	20	a	a	DET
ejpam-4829	51	21	∈	∈	NOUN
ejpam-4829	51	22	v	v	ADP
ejpam-4829	51	23	such	such	ADJ
ejpam-4829	51	24	that	that	SCONJ
ejpam-4829	51	25	,	,	PUNCT
ejpam-4829	51	26	by	by	ADP
ejpam-4829	51	27	denoting	denote	VERB
ejpam-4829	51	28	z	z	NOUN
ejpam-4829	51	29	=	=	SYM
ejpam-4829	51	30	npk	npk	NOUN
ejpam-4829	51	31	,	,	PUNCT
ejpam-4829	51	32	q	q	X
ejpam-4829	51	33	(	(	PUNCT
ejpam-4829	51	34	a	a	NOUN
ejpam-4829	51	35	)	)	PUNCT
ejpam-4829	51	36	and	and	CCONJ
ejpam-4829	51	37	x	x	X
ejpam-4829	51	38	=	=	SYM
ejpam-4829	51	39	v	v	NOUN
ejpam-4829	51	40	\	\	PROPN
ejpam-4829	51	41	(	(	PUNCT
ejpam-4829	51	42	z	z	NOUN
ejpam-4829	51	43	∪	∪	VERB
ejpam-4829	51	44	{	{	PUNCT
ejpam-4829	51	45	a	a	NOUN
ejpam-4829	51	46	}	}	PUNCT
ejpam-4829	51	47	)	)	PUNCT
ejpam-4829	51	48	,	,	PUNCT
ejpam-4829	51	49	|z|	|z|	NOUN
ejpam-4829	51	50	≥	≥	NOUN
ejpam-4829	51	51	k	k	NOUN
ejpam-4829	51	52	,	,	PUNCT
ejpam-4829	51	53	|x|	|x|	PROPN
ejpam-4829	51	54	=	=	SYM
ejpam-4829	51	55	k	k	PROPN
ejpam-4829	51	56	and	and	CCONJ
ejpam-4829	51	57	|z|−k	|z|−k	PROPN
ejpam-4829	52	1	=	=	SYM
ejpam-4829	52	2	q.	q.	PROPN
ejpam-4829	52	3	moreover	moreover	ADV
ejpam-4829	52	4	,	,	PUNCT
ejpam-4829	52	5	by	by	ADP
ejpam-4829	52	6	denoting	denote	VERB
ejpam-4829	52	7	x	x	X
ejpam-4829	52	8	=	=	SYM
ejpam-4829	52	9	{	{	PUNCT
ejpam-4829	52	10	x1	x1	PROPN
ejpam-4829	52	11	,	,	PUNCT
ejpam-4829	52	12	x2	x2	PROPN
ejpam-4829	52	13	,	,	PUNCT
ejpam-4829	52	14	.	.	PUNCT
ejpam-4829	52	15	.	.	PUNCT
ejpam-4829	52	16	.	.	PUNCT
ejpam-4829	53	1	,	,	PUNCT
ejpam-4829	53	2	xk	xk	PROPN
ejpam-4829	53	3	}	}	PUNCT
ejpam-4829	53	4	,	,	PUNCT
ejpam-4829	53	5	there	there	PRON
ejpam-4829	53	6	is	be	VERB
ejpam-4829	53	7	a	a	DET
ejpam-4829	53	8	k	k	ADJ
ejpam-4829	53	9	-	-	ADJ
ejpam-4829	53	10	element	element	NOUN
ejpam-4829	53	11	subset	subset	NOUN
ejpam-4829	53	12	x	x	X
ejpam-4829	54	1	′	′	NUM
ejpam-4829	54	2	=	=	SYM
ejpam-4829	54	3	{	{	PUNCT
ejpam-4829	54	4	x′1	x′1	PROPN
ejpam-4829	54	5	,	,	PUNCT
ejpam-4829	54	6	x′2	x′2	NOUN
ejpam-4829	54	7	,	,	PUNCT
ejpam-4829	54	8	.	.	PUNCT
ejpam-4829	54	9	.	.	PUNCT
ejpam-4829	54	10	.	.	PUNCT
ejpam-4829	55	1	,	,	PUNCT
ejpam-4829	55	2	x′k	x′k	PROPN
ejpam-4829	55	3	}	}	PUNCT
ejpam-4829	55	4	of	of	ADP
ejpam-4829	55	5	z	z	NOUN
ejpam-4829	55	6	such	such	ADJ
ejpam-4829	55	7	that	that	DET
ejpam-4829	55	8	pk	pk	NOUN
ejpam-4829	55	9	,	,	PUNCT
ejpam-4829	55	10	q[x	q[x	PROPN
ejpam-4829	55	11	′	′	NUM
ejpam-4829	55	12	]	]	X
ejpam-4829	55	13	is	be	AUX
ejpam-4829	55	14	a	a	DET
ejpam-4829	55	15	complete	complete	ADJ
ejpam-4829	55	16	graph	graph	NOUN
ejpam-4829	55	17	,	,	PUNCT
ejpam-4829	55	18	the	the	DET
ejpam-4829	55	19	set	set	NOUN
ejpam-4829	55	20	of	of	ADP
ejpam-4829	55	21	edges	edge	NOUN
ejpam-4829	55	22	between	between	ADP
ejpam-4829	55	23	x	x	PUNCT
ejpam-4829	55	24	and	and	CCONJ
ejpam-4829	55	25	x	x	SYM
ejpam-4829	55	26	′	′	NOUN
ejpam-4829	55	27	is	be	AUX
ejpam-4829	55	28	{	{	PUNCT
ejpam-4829	55	29	xix′i	xix′i	NOUN
ejpam-4829	55	30	:	:	PUNCT
ejpam-4829	55	31	1	1	NUM
ejpam-4829	55	32	≤	≤	NUM
ejpam-4829	56	1	i	i	X
ejpam-4829	56	2	≤	≤	PUNCT
ejpam-4829	57	1	k	k	X
ejpam-4829	57	2	}	}	PUNCT
ejpam-4829	57	3	and	and	CCONJ
ejpam-4829	57	4	the	the	DET
ejpam-4829	57	5	subset	subset	NOUN
ejpam-4829	57	6	y	y	PROPN
ejpam-4829	57	7	=	=	SYM
ejpam-4829	57	8	z	z	NOUN
ejpam-4829	57	9	\x	\x	NOUN
ejpam-4829	57	10	′	′	NUM
ejpam-4829	57	11	satisfies	satisfy	VERB
ejpam-4829	57	12	the	the	DET
ejpam-4829	57	13	following	follow	VERB
ejpam-4829	57	14	conditions	condition	NOUN
ejpam-4829	57	15	:	:	PUNCT
ejpam-4829	57	16	(	(	PUNCT
ejpam-4829	57	17	i	i	NOUN
ejpam-4829	57	18	)	)	PUNCT
ejpam-4829	57	19	for	for	ADP
ejpam-4829	57	20	every	every	DET
ejpam-4829	57	21	y	y	PROPN
ejpam-4829	57	22	∈	∈	PROPN
ejpam-4829	57	23	y	y	PROPN
ejpam-4829	57	24	,	,	PUNCT
ejpam-4829	57	25	pk	pk	NOUN
ejpam-4829	57	26	,	,	PUNCT
ejpam-4829	57	27	q[{a	q[{a	PROPN
ejpam-4829	57	28	,	,	PUNCT
ejpam-4829	57	29	y	y	PROPN
ejpam-4829	57	30	}	}	PUNCT
ejpam-4829	57	31	∪x	∪x	NOUN
ejpam-4829	57	32	′	′	NOUN
ejpam-4829	57	33	]	]	PUNCT
ejpam-4829	57	34	is	be	AUX
ejpam-4829	57	35	a	a	DET
ejpam-4829	57	36	complete	complete	ADJ
ejpam-4829	57	37	graph	graph	NOUN
ejpam-4829	57	38	.	.	PUNCT
ejpam-4829	58	1	(	(	PUNCT
ejpam-4829	58	2	ii	ii	NOUN
ejpam-4829	58	3	)	)	PUNCT
ejpam-4829	58	4	for	for	ADP
ejpam-4829	58	5	every	every	DET
ejpam-4829	58	6	y	y	PROPN
ejpam-4829	58	7	∈	∈	PROPN
ejpam-4829	58	8	y	y	PROPN
ejpam-4829	58	9	,	,	PUNCT
ejpam-4829	58	10	either	either	CCONJ
ejpam-4829	58	11	1	1	NUM
ejpam-4829	58	12	<	<	X
ejpam-4829	58	13	|npk	|npk	PROPN
ejpam-4829	58	14	,	,	PUNCT
ejpam-4829	58	15	q	q	X
ejpam-4829	59	1	[	[	X
ejpam-4829	59	2	x∪{y}](y)|	x∪{y}](y)|	X
ejpam-4829	59	3	<	<	X
ejpam-4829	59	4	k	k	PROPN
ejpam-4829	59	5	or	or	CCONJ
ejpam-4829	59	6	(	(	PUNCT
ejpam-4829	59	7	|npk	|npk	ADJ
ejpam-4829	59	8	,	,	PUNCT
ejpam-4829	59	9	q	q	X
ejpam-4829	60	1	[	[	X
ejpam-4829	60	2	x∪{y}](y)|	x∪{y}](y)|	PROPN
ejpam-4829	60	3	∈	∈	PROPN
ejpam-4829	60	4	{	{	PUNCT
ejpam-4829	60	5	1	1	NUM
ejpam-4829	60	6	,	,	PUNCT
ejpam-4829	60	7	k	k	NOUN
ejpam-4829	60	8	}	}	PUNCT
ejpam-4829	60	9	and	and	CCONJ
ejpam-4829	60	10	∃	∃	PROPN
ejpam-4829	60	11	z	z	PROPN
ejpam-4829	60	12	∈	∈	PROPN
ejpam-4829	60	13	y	y	PROPN
ejpam-4829	60	14	\	\	PROPN
ejpam-4829	60	15	{	{	PUNCT
ejpam-4829	60	16	y	y	NOUN
ejpam-4829	60	17	}	}	PUNCT
ejpam-4829	60	18	such	such	ADJ
ejpam-4829	60	19	that	that	PRON
ejpam-4829	60	20	zy	zy	PROPN
ejpam-4829	60	21	/∈	/∈	PUNCT
ejpam-4829	60	22	e	e	X
ejpam-4829	60	23	)	)	PUNCT
ejpam-4829	60	24	.	.	PUNCT
ejpam-4829	61	1	(	(	PUNCT
ejpam-4829	61	2	iii	iii	X
ejpam-4829	61	3	)	)	PUNCT
ejpam-4829	61	4	for	for	ADP
ejpam-4829	61	5	any	any	DET
ejpam-4829	61	6	y1	y1	NOUN
ejpam-4829	61	7	̸=	̸=	PROPN
ejpam-4829	61	8	y2	y2	NOUN
ejpam-4829	61	9	∈	∈	PROPN
ejpam-4829	61	10	y	y	PROPN
ejpam-4829	61	11	,	,	PUNCT
ejpam-4829	61	12	npk	npk	NOUN
ejpam-4829	61	13	,	,	PUNCT
ejpam-4829	61	14	q	q	X
ejpam-4829	62	1	[	[	X
ejpam-4829	62	2	x∪y1](y1	x∪y1](y1	PROPN
ejpam-4829	62	3	)	)	PUNCT
ejpam-4829	62	4	̸=	̸=	PROPN
ejpam-4829	62	5	npk	npk	NOUN
ejpam-4829	62	6	,	,	PUNCT
ejpam-4829	62	7	q	q	X
ejpam-4829	63	1	[	[	X
ejpam-4829	63	2	x∪y2](y2	x∪y2](y2	PROPN
ejpam-4829	63	3	)	)	PUNCT
ejpam-4829	63	4	.	.	PUNCT
ejpam-4829	64	1	x1	x1	NUM
ejpam-4829	65	1	x2	x2	INTJ
ejpam-4829	65	2	.	.	PUNCT
ejpam-4829	65	3	.	.	PUNCT
ejpam-4829	65	4	.	.	PUNCT
ejpam-4829	66	1	xkx	xkx	NOUN
ejpam-4829	66	2	yx′	yx′	NUM
ejpam-4829	66	3	1	1	NUM
ejpam-4829	66	4	x′	x′	PROPN
ejpam-4829	66	5	2	2	NUM
ejpam-4829	66	6	.	.	PUNCT
ejpam-4829	66	7	.	.	PUNCT
ejpam-4829	66	8	.	.	PUNCT
ejpam-4829	67	1	x′	x′	X
ejpam-4829	68	1	k	k	NOUN
ejpam-4829	69	1	x	x	PUNCT
ejpam-4829	69	2	′	′	NUM
ejpam-4829	69	3	a	a	DET
ejpam-4829	69	4	y1	y1	NOUN
ejpam-4829	69	5	yq	yq	PROPN
ejpam-4829	69	6	.	.	PUNCT
ejpam-4829	69	7	.	.	PUNCT
ejpam-4829	69	8	.	.	PUNCT
ejpam-4829	70	1	xi	xi	X
ejpam-4829	70	2	xjxs	xjxs	PROPN
ejpam-4829	70	3	figure	figure	NOUN
ejpam-4829	70	4	4	4	NUM
ejpam-4829	70	5	:	:	PUNCT
ejpam-4829	70	6	palace	palace	NOUN
ejpam-4829	70	7	pk	pk	PROPN
ejpam-4829	70	8	,	,	PUNCT
ejpam-4829	70	9	q	q	X
ejpam-4829	70	10	(	(	PUNCT
ejpam-4829	70	11	k	k	X
ejpam-4829	70	12	≥	≥	NUM
ejpam-4829	70	13	2	2	NUM
ejpam-4829	70	14	,	,	PUNCT
ejpam-4829	70	15	q	q	X
ejpam-4829	70	16	≥	≥	NOUN
ejpam-4829	70	17	0	0	NUM
ejpam-4829	70	18	)	)	PUNCT
ejpam-4829	70	19	definition	definition	NOUN
ejpam-4829	70	20	2	2	NUM
ejpam-4829	70	21	.	.	PUNCT
ejpam-4829	71	1	let	let	VERB
ejpam-4829	71	2	k	k	PROPN
ejpam-4829	71	3	≥	≥	NUM
ejpam-4829	71	4	2	2	NUM
ejpam-4829	71	5	and	and	CCONJ
ejpam-4829	71	6	q	q	ADJ
ejpam-4829	71	7	be	be	AUX
ejpam-4829	71	8	two	two	NUM
ejpam-4829	71	9	non	non	ADJ
ejpam-4829	71	10	-	-	ADJ
ejpam-4829	71	11	negative	negative	ADJ
ejpam-4829	71	12	integers	integer	NOUN
ejpam-4829	71	13	.	.	PUNCT
ejpam-4829	72	1	a	a	DET
ejpam-4829	72	2	palace	palace	NOUN
ejpam-4829	72	3	βk	βk	NOUN
ejpam-4829	72	4	,	,	PUNCT
ejpam-4829	72	5	q	q	PUNCT
ejpam-4829	72	6	is	be	AUX
ejpam-4829	72	7	a	a	DET
ejpam-4829	72	8	graph	graph	NOUN
ejpam-4829	72	9	obtained	obtain	VERB
ejpam-4829	72	10	from	from	ADP
ejpam-4829	72	11	a	a	DET
ejpam-4829	72	12	palace	palace	NOUN
ejpam-4829	72	13	pk	pk	NOUN
ejpam-4829	72	14	,	,	PUNCT
ejpam-4829	72	15	q	q	NOUN
ejpam-4829	72	16	by	by	ADP
ejpam-4829	72	17	replacing	replace	VERB
ejpam-4829	72	18	the	the	DET
ejpam-4829	72	19	module	module	NOUN
ejpam-4829	72	20	{	{	PUNCT
ejpam-4829	72	21	a	a	NOUN
ejpam-4829	72	22	}	}	PUNCT
ejpam-4829	72	23	with	with	ADP
ejpam-4829	72	24	the	the	DET
ejpam-4829	72	25	module	module	NOUN
ejpam-4829	72	26	{	{	PUNCT
ejpam-4829	72	27	a	a	PRON
ejpam-4829	72	28	,	,	PUNCT
ejpam-4829	72	29	a′	a′	PROPN
ejpam-4829	72	30	}	}	PUNCT
ejpam-4829	72	31	where	where	SCONJ
ejpam-4829	72	32	βk	βk	NOUN
ejpam-4829	72	33	,	,	PUNCT
ejpam-4829	72	34	q[{a	q[{a	PROPN
ejpam-4829	72	35	,	,	PUNCT
ejpam-4829	72	36	a′	a′	PROPN
ejpam-4829	72	37	}	}	PUNCT
ejpam-4829	72	38	]	]	PUNCT
ejpam-4829	72	39	is	be	AUX
ejpam-4829	72	40	isomorphic	isomorphic	ADJ
ejpam-4829	72	41	to	to	ADP
ejpam-4829	72	42	the	the	DET
ejpam-4829	72	43	graph	graph	NOUN
ejpam-4829	72	44	k2	k2	NOUN
ejpam-4829	72	45	,	,	PUNCT
ejpam-4829	72	46	as	as	SCONJ
ejpam-4829	72	47	illustrated	illustrate	VERB
ejpam-4829	72	48	in	in	ADP
ejpam-4829	72	49	figure	figure	NOUN
ejpam-4829	72	50	5	5	NUM
ejpam-4829	72	51	.	.	PUNCT
ejpam-4829	73	1	notation	notation	NOUN
ejpam-4829	73	2	:	:	PUNCT
ejpam-4829	73	3	the	the	DET
ejpam-4829	73	4	family	family	NOUN
ejpam-4829	73	5	of	of	ADP
ejpam-4829	73	6	graphs	graph	NOUN
ejpam-4829	73	7	isomorphic	isomorphic	ADJ
ejpam-4829	73	8	to	to	ADP
ejpam-4829	73	9	the	the	DET
ejpam-4829	73	10	graph	graph	NOUN
ejpam-4829	73	11	β	β	X
ejpam-4829	73	12	or	or	CCONJ
ejpam-4829	73	13	a	a	DET
ejpam-4829	73	14	palace	palace	NOUN
ejpam-4829	73	15	βk	βk	NOUN
ejpam-4829	73	16	,	,	PUNCT
ejpam-4829	73	17	q	q	X
ejpam-4829	73	18	,	,	PUNCT
ejpam-4829	73	19	for	for	ADP
ejpam-4829	73	20	some	some	PRON
ejpam-4829	73	21	k	k	PROPN
ejpam-4829	73	22	≥	≥	NUM
ejpam-4829	73	23	2	2	NUM
ejpam-4829	73	24	and	and	CCONJ
ejpam-4829	73	25	q	q	ADJ
ejpam-4829	73	26	≥	≥	NOUN
ejpam-4829	73	27	0	0	NUM
ejpam-4829	73	28	,	,	PUNCT
ejpam-4829	73	29	m.	m.	NOUN
ejpam-4829	73	30	bouaziz	bouaziz	PROPN
ejpam-4829	73	31	et	et	PROPN
ejpam-4829	73	32	al	al	PROPN
ejpam-4829	73	33	.	.	PUNCT
ejpam-4829	73	34	/	/	SYM
ejpam-4829	73	35	eur	eur	PROPN
ejpam-4829	73	36	.	.	PUNCT
ejpam-4829	74	1	j.	j.	PROPN
ejpam-4829	74	2	pure	pure	PROPN
ejpam-4829	74	3	appl	appl	PROPN
ejpam-4829	74	4	.	.	PROPN
ejpam-4829	74	5	math	math	PROPN
ejpam-4829	74	6	,	,	PUNCT
ejpam-4829	74	7	16	16	NUM
ejpam-4829	74	8	(	(	PUNCT
ejpam-4829	74	9	4	4	NUM
ejpam-4829	74	10	)	)	PUNCT
ejpam-4829	74	11	(	(	PUNCT
ejpam-4829	74	12	2023	2023	NUM
ejpam-4829	74	13	)	)	PUNCT
ejpam-4829	74	14	,	,	PUNCT
ejpam-4829	74	15	2786	2786	NUM
ejpam-4829	74	16	-	-	SYM
ejpam-4829	74	17	2797	2797	NUM
ejpam-4829	74	18	2789	2789	NUM
ejpam-4829	74	19	x1	x1	NOUN
ejpam-4829	74	20	x2	x2	PROPN
ejpam-4829	74	21	.	.	PUNCT
ejpam-4829	74	22	.	.	PUNCT
ejpam-4829	75	1	.	.	PUNCT
ejpam-4829	76	1	xkx	xkx	NOUN
ejpam-4829	76	2	yx′	yx′	NUM
ejpam-4829	76	3	1	1	NUM
ejpam-4829	76	4	x′	x′	PROPN
ejpam-4829	76	5	2	2	NUM
ejpam-4829	76	6	.	.	PUNCT
ejpam-4829	76	7	.	.	PUNCT
ejpam-4829	76	8	.	.	PUNCT
ejpam-4829	77	1	x′	x′	X
ejpam-4829	78	1	k	k	NOUN
ejpam-4829	79	1	x	x	PUNCT
ejpam-4829	79	2	′	′	NUM
ejpam-4829	79	3	a	a	DET
ejpam-4829	79	4	a′	a′	PROPN
ejpam-4829	79	5	y1	y1	PROPN
ejpam-4829	79	6	yq	yq	PROPN
ejpam-4829	79	7	.	.	PUNCT
ejpam-4829	79	8	.	.	PUNCT
ejpam-4829	79	9	.	.	PUNCT
ejpam-4829	79	10	.	.	PUNCT
ejpam-4829	79	11	.	.	PUNCT
ejpam-4829	79	12	.	.	PUNCT
ejpam-4829	80	1	xi	xi	X
ejpam-4829	80	2	xjxs	xjxs	PROPN
ejpam-4829	80	3	figure	figure	NOUN
ejpam-4829	80	4	5	5	NUM
ejpam-4829	80	5	:	:	PUNCT
ejpam-4829	80	6	palace	palace	NOUN
ejpam-4829	80	7	βk	βk	NOUN
ejpam-4829	80	8	,	,	PUNCT
ejpam-4829	80	9	q	q	X
ejpam-4829	81	1	(	(	PUNCT
ejpam-4829	81	2	k	k	X
ejpam-4829	81	3	≥	≥	NUM
ejpam-4829	81	4	2	2	NUM
ejpam-4829	81	5	,	,	PUNCT
ejpam-4829	81	6	q	q	X
ejpam-4829	81	7	≥	≥	NOUN
ejpam-4829	81	8	0	0	NUM
ejpam-4829	81	9	)	)	PUNCT
ejpam-4829	81	10	is	be	AUX
ejpam-4829	81	11	denoted	denote	VERB
ejpam-4829	81	12	by	by	ADP
ejpam-4829	81	13	b.	b.	PROPN
ejpam-4829	81	14	1.1	1.1	NUM
ejpam-4829	81	15	.	.	PUNCT
ejpam-4829	82	1	gallai	gallai	NOUN
ejpam-4829	82	2	’s	’s	PART
ejpam-4829	82	3	decomposition	decomposition	NOUN
ejpam-4829	82	4	let	let	VERB
ejpam-4829	82	5	g	g	NOUN
ejpam-4829	82	6	=	=	SYM
ejpam-4829	82	7	(	(	PUNCT
ejpam-4829	82	8	v	v	NOUN
ejpam-4829	82	9	,	,	PUNCT
ejpam-4829	82	10	e	e	NOUN
ejpam-4829	82	11	)	)	PUNCT
ejpam-4829	82	12	be	be	AUX
ejpam-4829	82	13	a	a	DET
ejpam-4829	82	14	graph	graph	NOUN
ejpam-4829	82	15	.	.	PUNCT
ejpam-4829	83	1	an	an	DET
ejpam-4829	83	2	equivalence	equivalence	NOUN
ejpam-4829	83	3	relation	relation	NOUN
ejpam-4829	83	4	is	be	AUX
ejpam-4829	83	5	denoted	denote	VERB
ejpam-4829	83	6	by	by	ADP
ejpam-4829	83	7	∼=	∼=	PROPN
ejpam-4829	83	8	between	between	ADP
ejpam-4829	83	9	the	the	DET
ejpam-4829	83	10	pairs	pair	NOUN
ejpam-4829	83	11	of	of	ADP
ejpam-4829	83	12	vertices	vertex	NOUN
ejpam-4829	83	13	of	of	ADP
ejpam-4829	83	14	g	g	NOUN
ejpam-4829	83	15	for	for	ADP
ejpam-4829	83	16	x	x	SYM
ejpam-4829	83	17	and	and	CCONJ
ejpam-4829	83	18	y	y	PROPN
ejpam-4829	83	19	as	as	ADV
ejpam-4829	83	20	well	well	ADV
ejpam-4829	83	21	as	as	ADP
ejpam-4829	83	22	u	u	NOUN
ejpam-4829	83	23	and	and	CCONJ
ejpam-4829	83	24	v.	v.	ADP
ejpam-4829	83	25	xy	xy	PROPN
ejpam-4829	83	26	∈	∈	PROPN
ejpam-4829	83	27	e	e	NOUN
ejpam-4829	83	28	if	if	SCONJ
ejpam-4829	83	29	and	and	CCONJ
ejpam-4829	83	30	only	only	ADV
ejpam-4829	83	31	if	if	SCONJ
ejpam-4829	83	32	uv	uv	NOUN
ejpam-4829	83	33	∈	∈	NOUN
ejpam-4829	83	34	e	e	NOUN
ejpam-4829	83	35	defines	define	VERB
ejpam-4829	83	36	{	{	PUNCT
ejpam-4829	83	37	x	x	NOUN
ejpam-4829	83	38	,	,	PUNCT
ejpam-4829	83	39	y	y	NOUN
ejpam-4829	83	40	}	}	PUNCT
ejpam-4829	83	41	∼=	∼=	PROPN
ejpam-4829	83	42	{	{	PUNCT
ejpam-4829	83	43	u	u	NOUN
ejpam-4829	83	44	,	,	PUNCT
ejpam-4829	83	45	v	v	NOUN
ejpam-4829	83	46	}	}	PUNCT
ejpam-4829	83	47	.	.	PUNCT
ejpam-4829	84	1	to	to	PART
ejpam-4829	84	2	recall	recall	VERB
ejpam-4829	84	3	the	the	DET
ejpam-4829	84	4	basic	basic	ADJ
ejpam-4829	84	5	properties	property	NOUN
ejpam-4829	84	6	of	of	ADP
ejpam-4829	84	7	the	the	DET
ejpam-4829	84	8	modules	module	NOUN
ejpam-4829	84	9	,	,	PUNCT
ejpam-4829	84	10	we	we	PRON
ejpam-4829	84	11	introduce	introduce	VERB
ejpam-4829	84	12	the	the	DET
ejpam-4829	84	13	following	following	ADJ
ejpam-4829	84	14	notation	notation	NOUN
ejpam-4829	84	15	:	:	PUNCT
ejpam-4829	84	16	given	give	VERB
ejpam-4829	84	17	a	a	DET
ejpam-4829	84	18	graph	graph	NOUN
ejpam-4829	84	19	g	g	NOUN
ejpam-4829	84	20	on	on	ADP
ejpam-4829	84	21	the	the	DET
ejpam-4829	84	22	vertex	vertex	NOUN
ejpam-4829	84	23	set	set	VERB
ejpam-4829	84	24	v	v	ADP
ejpam-4829	84	25	and	and	CCONJ
ejpam-4829	84	26	two	two	NUM
ejpam-4829	84	27	disjoint	disjoint	ADJ
ejpam-4829	84	28	vertex	vertex	NOUN
ejpam-4829	84	29	subsets	subset	NOUN
ejpam-4829	84	30	x	x	PUNCT
ejpam-4829	84	31	and	and	CCONJ
ejpam-4829	84	32	y	y	PROPN
ejpam-4829	84	33	of	of	ADP
ejpam-4829	84	34	v	v	NUM
ejpam-4829	84	35	,	,	PUNCT
ejpam-4829	84	36	x	x	X
ejpam-4829	84	37	and	and	CCONJ
ejpam-4829	84	38	y	y	PROPN
ejpam-4829	84	39	are	be	AUX
ejpam-4829	84	40	equivalent	equivalent	ADJ
ejpam-4829	84	41	(	(	PUNCT
ejpam-4829	84	42	x	x	SYM
ejpam-4829	84	43	∼	∼	NOUN
ejpam-4829	84	44	y	y	PROPN
ejpam-4829	84	45	)	)	PUNCT
ejpam-4829	84	46	if	if	SCONJ
ejpam-4829	84	47	,	,	PUNCT
ejpam-4829	84	48	for	for	ADP
ejpam-4829	84	49	any	any	DET
ejpam-4829	84	50	vertices	vertex	NOUN
ejpam-4829	84	51	x	x	PUNCT
ejpam-4829	84	52	and	and	CCONJ
ejpam-4829	84	53	x′	x′	PROPN
ejpam-4829	84	54	in	in	ADP
ejpam-4829	84	55	x	x	PROPN
ejpam-4829	84	56	and	and	CCONJ
ejpam-4829	84	57	y	y	PROPN
ejpam-4829	84	58	and	and	CCONJ
ejpam-4829	84	59	y′	y′	PROPN
ejpam-4829	84	60	in	in	ADP
ejpam-4829	84	61	y	y	PROPN
ejpam-4829	84	62	,	,	PUNCT
ejpam-4829	84	63	{	{	PUNCT
ejpam-4829	84	64	x	x	NOUN
ejpam-4829	84	65	,	,	PUNCT
ejpam-4829	84	66	y	y	NOUN
ejpam-4829	84	67	}	}	PUNCT
ejpam-4829	84	68	∼=	∼=	PROPN
ejpam-4829	84	69	{	{	PUNCT
ejpam-4829	84	70	x′	x′	NUM
ejpam-4829	84	71	,	,	PUNCT
ejpam-4829	84	72	y′	y′	NUM
ejpam-4829	84	73	}	}	PUNCT
ejpam-4829	84	74	.	.	PUNCT
ejpam-4829	85	1	proposition	proposition	NOUN
ejpam-4829	85	2	1	1	NUM
ejpam-4829	85	3	.	.	PUNCT
ejpam-4829	86	1	let	let	VERB
ejpam-4829	86	2	g	g	PRON
ejpam-4829	86	3	be	be	AUX
ejpam-4829	86	4	a	a	DET
ejpam-4829	86	5	graph	graph	NOUN
ejpam-4829	86	6	on	on	ADP
ejpam-4829	86	7	the	the	DET
ejpam-4829	86	8	set	set	NOUN
ejpam-4829	86	9	of	of	ADP
ejpam-4829	86	10	vertices	vertex	NOUN
ejpam-4829	86	11	v	v	NOUN
ejpam-4829	86	12	.	.	PUNCT
ejpam-4829	87	1	(	(	PUNCT
ejpam-4829	87	2	i	i	NOUN
ejpam-4829	87	3	)	)	PUNCT
ejpam-4829	87	4	∅	∅	NOUN
ejpam-4829	87	5	,	,	PUNCT
ejpam-4829	87	6	v	v	NOUN
ejpam-4829	87	7	and	and	CCONJ
ejpam-4829	87	8	{	{	PUNCT
ejpam-4829	87	9	u	u	NOUN
ejpam-4829	87	10	}	}	PUNCT
ejpam-4829	87	11	where	where	SCONJ
ejpam-4829	87	12	u	u	PROPN
ejpam-4829	87	13	∈	∈	PROPN
ejpam-4829	87	14	v	v	NOUN
ejpam-4829	87	15	are	be	AUX
ejpam-4829	87	16	modules	module	NOUN
ejpam-4829	87	17	of	of	ADP
ejpam-4829	87	18	g.	g.	PROPN
ejpam-4829	87	19	(	(	PUNCT
ejpam-4829	87	20	ii	ii	PROPN
ejpam-4829	87	21	)	)	PUNCT
ejpam-4829	87	22	considering	consider	VERB
ejpam-4829	87	23	a	a	DET
ejpam-4829	87	24	non	non	ADJ
ejpam-4829	87	25	-	-	ADJ
ejpam-4829	87	26	empty	empty	ADJ
ejpam-4829	87	27	vertex	vertex	NOUN
ejpam-4829	87	28	subset	subset	NOUN
ejpam-4829	87	29	w	w	NOUN
ejpam-4829	87	30	of	of	ADP
ejpam-4829	87	31	v	v	NOUN
ejpam-4829	87	32	,	,	PUNCT
ejpam-4829	87	33	if	if	SCONJ
ejpam-4829	87	34	m	m	NOUN
ejpam-4829	87	35	is	be	AUX
ejpam-4829	87	36	a	a	DET
ejpam-4829	87	37	module	module	NOUN
ejpam-4829	87	38	of	of	ADP
ejpam-4829	87	39	g	g	NOUN
ejpam-4829	87	40	,	,	PUNCT
ejpam-4829	87	41	then	then	ADV
ejpam-4829	87	42	m	m	VERB
ejpam-4829	87	43	∩w	∩w	ADJ
ejpam-4829	87	44	is	be	AUX
ejpam-4829	87	45	a	a	DET
ejpam-4829	87	46	module	module	NOUN
ejpam-4829	87	47	of	of	ADP
ejpam-4829	87	48	g[w	g[w	PROPN
ejpam-4829	87	49	]	]	PUNCT
ejpam-4829	87	50	.	.	PUNCT
ejpam-4829	88	1	(	(	PUNCT
ejpam-4829	88	2	iii	iii	X
ejpam-4829	88	3	)	)	PUNCT
ejpam-4829	88	4	if	if	SCONJ
ejpam-4829	88	5	m	m	PROPN
ejpam-4829	88	6	and	and	CCONJ
ejpam-4829	88	7	n	n	PROPN
ejpam-4829	88	8	are	be	AUX
ejpam-4829	88	9	modules	module	NOUN
ejpam-4829	88	10	of	of	ADP
ejpam-4829	88	11	g	g	NOUN
ejpam-4829	88	12	,	,	PUNCT
ejpam-4829	88	13	then	then	ADV
ejpam-4829	88	14	m	m	PROPN
ejpam-4829	88	15	∩n	∩n	PROPN
ejpam-4829	88	16	is	be	AUX
ejpam-4829	88	17	a	a	DET
ejpam-4829	88	18	module	module	NOUN
ejpam-4829	88	19	of	of	ADP
ejpam-4829	88	20	g.	g.	PROPN
ejpam-4829	88	21	(	(	PUNCT
ejpam-4829	88	22	iv	iv	X
ejpam-4829	88	23	)	)	PUNCT
ejpam-4829	88	24	if	if	SCONJ
ejpam-4829	88	25	m	m	VERB
ejpam-4829	88	26	and	and	CCONJ
ejpam-4829	88	27	n	n	PROPN
ejpam-4829	88	28	are	be	AUX
ejpam-4829	88	29	modules	module	NOUN
ejpam-4829	88	30	of	of	ADP
ejpam-4829	88	31	g	g	NOUN
ejpam-4829	88	32	such	such	ADJ
ejpam-4829	88	33	that	that	SCONJ
ejpam-4829	88	34	m	m	PROPN
ejpam-4829	88	35	∩n	∩n	NOUN
ejpam-4829	88	36	̸=	̸=	PROPN
ejpam-4829	88	37	∅	∅	NOUN
ejpam-4829	88	38	,	,	PUNCT
ejpam-4829	88	39	then	then	ADV
ejpam-4829	88	40	m	m	VERB
ejpam-4829	88	41	∪n	∪n	PROPN
ejpam-4829	88	42	is	be	AUX
ejpam-4829	88	43	a	a	DET
ejpam-4829	88	44	module	module	NOUN
ejpam-4829	88	45	of	of	ADP
ejpam-4829	88	46	g.	g.	PROPN
ejpam-4829	88	47	(	(	PUNCT
ejpam-4829	88	48	v	v	NOUN
ejpam-4829	88	49	)	)	PUNCT
ejpam-4829	88	50	if	if	SCONJ
ejpam-4829	88	51	m	m	VERB
ejpam-4829	88	52	and	and	CCONJ
ejpam-4829	88	53	n	n	PROPN
ejpam-4829	88	54	are	be	AUX
ejpam-4829	88	55	modules	module	NOUN
ejpam-4829	88	56	of	of	ADP
ejpam-4829	88	57	g	g	NOUN
ejpam-4829	88	58	such	such	ADJ
ejpam-4829	88	59	that	that	SCONJ
ejpam-4829	88	60	m	m	VERB
ejpam-4829	88	61	\n	\n	PUNCT
ejpam-4829	88	62	̸=	̸=	PROPN
ejpam-4829	88	63	∅	∅	NOUN
ejpam-4829	88	64	,	,	PUNCT
ejpam-4829	88	65	then	then	ADV
ejpam-4829	88	66	n	n	CCONJ
ejpam-4829	88	67	\m	\m	NOUN
ejpam-4829	88	68	is	be	AUX
ejpam-4829	88	69	a	a	DET
ejpam-4829	88	70	module	module	NOUN
ejpam-4829	88	71	of	of	ADP
ejpam-4829	88	72	g.	g.	PROPN
ejpam-4829	88	73	(	(	PUNCT
ejpam-4829	88	74	vi	vi	PROPN
ejpam-4829	88	75	)	)	PUNCT
ejpam-4829	88	76	if	if	SCONJ
ejpam-4829	88	77	m	m	VERB
ejpam-4829	88	78	and	and	CCONJ
ejpam-4829	88	79	n	n	PRON
ejpam-4829	88	80	are	be	AUX
ejpam-4829	88	81	disjoint	disjoint	NOUN
ejpam-4829	88	82	modules	module	NOUN
ejpam-4829	88	83	of	of	ADP
ejpam-4829	88	84	g	g	NOUN
ejpam-4829	88	85	,	,	PUNCT
ejpam-4829	88	86	then	then	ADV
ejpam-4829	88	87	m	m	VERB
ejpam-4829	88	88	∼	∼	NOUN
ejpam-4829	88	89	n	n	ADV
ejpam-4829	88	90	.	.	PUNCT
ejpam-4829	89	1	a	a	DET
ejpam-4829	89	2	partition	partition	NOUN
ejpam-4829	89	3	p	p	NOUN
ejpam-4829	89	4	of	of	ADP
ejpam-4829	89	5	the	the	DET
ejpam-4829	89	6	vertex	vertex	NOUN
ejpam-4829	89	7	set	set	VERB
ejpam-4829	89	8	v	v	NOUN
ejpam-4829	89	9	(	(	PUNCT
ejpam-4829	89	10	g	g	NOUN
ejpam-4829	89	11	)	)	PUNCT
ejpam-4829	89	12	of	of	ADP
ejpam-4829	89	13	a	a	DET
ejpam-4829	89	14	graph	graph	NOUN
ejpam-4829	89	15	g	g	NOUN
ejpam-4829	89	16	is	be	AUX
ejpam-4829	89	17	a	a	DET
ejpam-4829	89	18	modular	modular	ADJ
ejpam-4829	89	19	partition	partition	NOUN
ejpam-4829	89	20	of	of	ADP
ejpam-4829	89	21	g	g	PROPN
ejpam-4829	89	22	if	if	SCONJ
ejpam-4829	89	23	all	all	DET
ejpam-4829	89	24	its	its	PRON
ejpam-4829	89	25	elements	element	NOUN
ejpam-4829	89	26	are	be	AUX
ejpam-4829	89	27	modules	module	NOUN
ejpam-4829	89	28	of	of	ADP
ejpam-4829	89	29	g.	g.	PROPN
ejpam-4829	89	30	based	base	VERB
ejpam-4829	89	31	on	on	ADP
ejpam-4829	89	32	the	the	DET
ejpam-4829	89	33	last	last	ADJ
ejpam-4829	89	34	assertion	assertion	NOUN
ejpam-4829	89	35	of	of	ADP
ejpam-4829	89	36	proposition	proposition	NOUN
ejpam-4829	89	37	1	1	NUM
ejpam-4829	89	38	,	,	PUNCT
ejpam-4829	89	39	it	it	PRON
ejpam-4829	89	40	follows	follow	VERB
ejpam-4829	89	41	that	that	SCONJ
ejpam-4829	89	42	m.	m.	NOUN
ejpam-4829	89	43	bouaziz	bouaziz	PROPN
ejpam-4829	89	44	et	et	PROPN
ejpam-4829	90	1	al	al	PROPN
ejpam-4829	90	2	.	.	PUNCT
ejpam-4829	90	3	/	/	SYM
ejpam-4829	90	4	eur	eur	PROPN
ejpam-4829	90	5	.	.	PUNCT
ejpam-4829	91	1	j.	j.	PROPN
ejpam-4829	91	2	pure	pure	PROPN
ejpam-4829	91	3	appl	appl	PROPN
ejpam-4829	91	4	.	.	PROPN
ejpam-4829	91	5	math	math	PROPN
ejpam-4829	91	6	,	,	PUNCT
ejpam-4829	91	7	16	16	NUM
ejpam-4829	91	8	(	(	PUNCT
ejpam-4829	91	9	4	4	NUM
ejpam-4829	91	10	)	)	PUNCT
ejpam-4829	91	11	(	(	PUNCT
ejpam-4829	91	12	2023	2023	NUM
ejpam-4829	91	13	)	)	PUNCT
ejpam-4829	91	14	,	,	PUNCT
ejpam-4829	91	15	2786	2786	NUM
ejpam-4829	91	16	-	-	SYM
ejpam-4829	91	17	2797	2797	NUM
ejpam-4829	91	18	2790	2790	NUM
ejpam-4829	91	19	the	the	DET
ejpam-4829	91	20	elements	element	NOUN
ejpam-4829	91	21	of	of	ADP
ejpam-4829	91	22	p	p	NOUN
ejpam-4829	91	23	may	may	AUX
ejpam-4829	91	24	be	be	AUX
ejpam-4829	91	25	considered	consider	VERB
ejpam-4829	91	26	as	as	ADP
ejpam-4829	91	27	the	the	DET
ejpam-4829	91	28	vertices	vertex	NOUN
ejpam-4829	91	29	of	of	ADP
ejpam-4829	91	30	a	a	DET
ejpam-4829	91	31	new	new	ADJ
ejpam-4829	91	32	graph	graph	NOUN
ejpam-4829	91	33	.	.	PUNCT
ejpam-4829	92	1	the	the	DET
ejpam-4829	92	2	quotient	quotient	NOUN
ejpam-4829	92	3	of	of	ADP
ejpam-4829	92	4	g	g	NOUN
ejpam-4829	92	5	by	by	ADP
ejpam-4829	92	6	p	p	PROPN
ejpam-4829	92	7	is	be	AUX
ejpam-4829	92	8	g	g	NOUN
ejpam-4829	92	9	/	/	SYM
ejpam-4829	92	10	p	p	NOUN
ejpam-4829	92	11	defined	define	VERB
ejpam-4829	92	12	on	on	ADP
ejpam-4829	92	13	p	p	NOUN
ejpam-4829	92	14	as	as	SCONJ
ejpam-4829	92	15	follows	follow	VERB
ejpam-4829	92	16	:	:	PUNCT
ejpam-4829	92	17	for	for	ADP
ejpam-4829	92	18	the	the	DET
ejpam-4829	92	19	distinct	distinct	ADJ
ejpam-4829	92	20	elements	element	NOUN
ejpam-4829	92	21	x	x	PUNCT
ejpam-4829	92	22	and	and	CCONJ
ejpam-4829	92	23	y	y	PROPN
ejpam-4829	92	24	of	of	ADP
ejpam-4829	92	25	p	p	X
ejpam-4829	92	26	,	,	PUNCT
ejpam-4829	92	27	xy	xy	PROPN
ejpam-4829	92	28	∈	∈	PROPN
ejpam-4829	92	29	e(g	e(g	PROPN
ejpam-4829	92	30	/	/	SYM
ejpam-4829	93	1	p	p	NOUN
ejpam-4829	93	2	)	)	PUNCT
ejpam-4829	93	3	if	if	SCONJ
ejpam-4829	93	4	xy	xy	PROPN
ejpam-4829	93	5	∈	∈	PROPN
ejpam-4829	93	6	e(g	e(g	PROPN
ejpam-4829	93	7	)	)	PUNCT
ejpam-4829	93	8	for	for	ADP
ejpam-4829	93	9	every	every	DET
ejpam-4829	93	10	x	x	NOUN
ejpam-4829	93	11	and	and	CCONJ
ejpam-4829	93	12	y	y	PROPN
ejpam-4829	93	13	where	where	SCONJ
ejpam-4829	93	14	x	x	SYM
ejpam-4829	93	15	∈	∈	PROPN
ejpam-4829	93	16	x	x	X
ejpam-4829	93	17	and	and	CCONJ
ejpam-4829	93	18	y	y	PROPN
ejpam-4829	93	19	∈	∈	PROPN
ejpam-4829	93	20	y	y	PROPN
ejpam-4829	93	21	.	.	PUNCT
ejpam-4829	94	1	a	a	DET
ejpam-4829	94	2	module	module	NOUN
ejpam-4829	94	3	x	x	PUNCT
ejpam-4829	94	4	of	of	ADP
ejpam-4829	94	5	a	a	DET
ejpam-4829	94	6	graph	graph	NOUN
ejpam-4829	94	7	g	g	NOUN
ejpam-4829	94	8	is	be	AUX
ejpam-4829	94	9	a	a	DET
ejpam-4829	94	10	strong	strong	ADJ
ejpam-4829	94	11	module	module	NOUN
ejpam-4829	94	12	of	of	ADP
ejpam-4829	94	13	g	g	PROPN
ejpam-4829	94	14	if	if	SCONJ
ejpam-4829	94	15	,	,	PUNCT
ejpam-4829	94	16	for	for	ADP
ejpam-4829	94	17	every	every	DET
ejpam-4829	94	18	module	module	NOUN
ejpam-4829	94	19	y	y	NOUN
ejpam-4829	94	20	of	of	ADP
ejpam-4829	94	21	g	g	PROPN
ejpam-4829	94	22	,	,	PUNCT
ejpam-4829	94	23	x	x	SYM
ejpam-4829	94	24	∩	∩	ADJ
ejpam-4829	94	25	y	y	PROPN
ejpam-4829	94	26	̸=	̸=	PROPN
ejpam-4829	94	27	∅.	∅.	PRON
ejpam-4829	94	28	hence	hence	ADV
ejpam-4829	94	29	,	,	PUNCT
ejpam-4829	94	30	either	either	CCONJ
ejpam-4829	94	31	x	x	SYM
ejpam-4829	94	32	⊆	⊆	NUM
ejpam-4829	94	33	y	y	NOUN
ejpam-4829	94	34	or	or	CCONJ
ejpam-4829	94	35	y	y	PROPN
ejpam-4829	94	36	⊆	⊆	NUM
ejpam-4829	94	37	x.	x.	NOUN
ejpam-4829	95	1	if	if	SCONJ
ejpam-4829	95	2	|	|	ADV
ejpam-4829	95	3	v	v	ADJ
ejpam-4829	95	4	(	(	PUNCT
ejpam-4829	95	5	g	g	NOUN
ejpam-4829	95	6	)	)	PUNCT
ejpam-4829	95	7	|≥	|≥	ADJ
ejpam-4829	95	8	2	2	NUM
ejpam-4829	95	9	,	,	PUNCT
ejpam-4829	95	10	then	then	ADV
ejpam-4829	95	11	p(g	p(g	NOUN
ejpam-4829	95	12	)	)	PUNCT
ejpam-4829	95	13	denotes	denote	VERB
ejpam-4829	95	14	the	the	DET
ejpam-4829	95	15	family	family	NOUN
ejpam-4829	95	16	of	of	ADP
ejpam-4829	95	17	maximal	maximal	ADJ
ejpam-4829	95	18	proper	proper	ADJ
ejpam-4829	95	19	strong	strong	ADJ
ejpam-4829	95	20	modules	module	NOUN
ejpam-4829	95	21	of	of	ADP
ejpam-4829	95	22	g	g	NOUN
ejpam-4829	95	23	,	,	PUNCT
ejpam-4829	95	24	equipped	equip	VERB
ejpam-4829	95	25	with	with	ADP
ejpam-4829	95	26	the	the	DET
ejpam-4829	95	27	inclusion	inclusion	NOUN
ejpam-4829	95	28	.	.	PUNCT
ejpam-4829	96	1	the	the	DET
ejpam-4829	96	2	following	follow	VERB
ejpam-4829	96	3	theorem	theorem	NOUN
ejpam-4829	96	4	shows	show	VERB
ejpam-4829	96	5	gallai	gallai	NOUN
ejpam-4829	96	6	’s	’s	PART
ejpam-4829	96	7	decomposition	decomposition	NOUN
ejpam-4829	96	8	result	result	NOUN
ejpam-4829	96	9	.	.	PUNCT
ejpam-4829	97	1	theorem	theorem	NOUN
ejpam-4829	97	2	1	1	NUM
ejpam-4829	97	3	.	.	PUNCT
ejpam-4829	98	1	[	[	X
ejpam-4829	98	2	4	4	NUM
ejpam-4829	98	3	,	,	PUNCT
ejpam-4829	98	4	5	5	NUM
ejpam-4829	98	5	]	]	PUNCT
ejpam-4829	98	6	let	let	VERB
ejpam-4829	98	7	g	g	PRON
ejpam-4829	98	8	be	be	AUX
ejpam-4829	98	9	a	a	DET
ejpam-4829	98	10	graph	graph	NOUN
ejpam-4829	98	11	with	with	ADP
ejpam-4829	98	12	at	at	ADV
ejpam-4829	98	13	least	least	ADV
ejpam-4829	98	14	two	two	NUM
ejpam-4829	98	15	vertices	vertex	NOUN
ejpam-4829	98	16	.	.	PUNCT
ejpam-4829	99	1	the	the	DET
ejpam-4829	99	2	class	class	PROPN
ejpam-4829	99	3	p(g	p(g	PROPN
ejpam-4829	99	4	)	)	PUNCT
ejpam-4829	99	5	is	be	AUX
ejpam-4829	99	6	a	a	DET
ejpam-4829	99	7	modular	modular	ADJ
ejpam-4829	99	8	partition	partition	NOUN
ejpam-4829	99	9	of	of	ADP
ejpam-4829	99	10	g	g	PROPN
ejpam-4829	99	11	and	and	CCONJ
ejpam-4829	99	12	the	the	DET
ejpam-4829	99	13	quotient	quotient	NOUN
ejpam-4829	99	14	g	g	PROPN
ejpam-4829	99	15	/	/	SYM
ejpam-4829	99	16	p(g	p(g	NOUN
ejpam-4829	99	17	)	)	PUNCT
ejpam-4829	99	18	is	be	AUX
ejpam-4829	99	19	a	a	DET
ejpam-4829	99	20	prime	prime	ADJ
ejpam-4829	99	21	,	,	PUNCT
ejpam-4829	99	22	complete	complete	ADJ
ejpam-4829	99	23	or	or	CCONJ
ejpam-4829	99	24	empty	empty	ADJ
ejpam-4829	99	25	graph	graph	NOUN
ejpam-4829	99	26	.	.	PUNCT
ejpam-4829	100	1	taking	take	VERB
ejpam-4829	100	2	in	in	ADP
ejpam-4829	100	3	consideration	consideration	NOUN
ejpam-4829	100	4	a	a	DET
ejpam-4829	100	5	graph	graph	NOUN
ejpam-4829	100	6	g	g	NOUN
ejpam-4829	100	7	with	with	ADP
ejpam-4829	100	8	more	more	ADJ
ejpam-4829	100	9	than	than	ADP
ejpam-4829	100	10	one	one	NUM
ejpam-4829	100	11	vertex	vertex	NOUN
ejpam-4829	100	12	,	,	PUNCT
ejpam-4829	100	13	the	the	DET
ejpam-4829	100	14	elements	element	NOUN
ejpam-4829	100	15	of	of	ADP
ejpam-4829	100	16	p(g	p(g	NOUN
ejpam-4829	100	17	)	)	PUNCT
ejpam-4829	100	18	are	be	AUX
ejpam-4829	100	19	the	the	DET
ejpam-4829	100	20	modular	modular	ADJ
ejpam-4829	100	21	components	component	NOUN
ejpam-4829	100	22	of	of	ADP
ejpam-4829	100	23	g	g	PROPN
ejpam-4829	100	24	,	,	PUNCT
ejpam-4829	100	25	p(g	p(g	NOUN
ejpam-4829	100	26	)	)	PUNCT
ejpam-4829	100	27	is	be	AUX
ejpam-4829	100	28	its	its	PRON
ejpam-4829	100	29	canonical	canonical	ADJ
ejpam-4829	100	30	partition	partition	NOUN
ejpam-4829	100	31	and	and	CCONJ
ejpam-4829	100	32	the	the	DET
ejpam-4829	100	33	quotient	quotient	NOUN
ejpam-4829	100	34	g	g	PROPN
ejpam-4829	100	35	/	/	SYM
ejpam-4829	100	36	p(g	p(g	NOUN
ejpam-4829	100	37	)	)	PUNCT
ejpam-4829	100	38	is	be	AUX
ejpam-4829	100	39	its	its	PRON
ejpam-4829	100	40	frame	frame	NOUN
ejpam-4829	100	41	.	.	PUNCT
ejpam-4829	101	1	2	2	X
ejpam-4829	101	2	.	.	X
ejpam-4829	101	3	preliminary	preliminary	ADJ
ejpam-4829	101	4	results	result	NOUN
ejpam-4829	101	5	2.1	2.1	NUM
ejpam-4829	101	6	.	.	PUNCT
ejpam-4829	102	1	prime	prime	ADJ
ejpam-4829	102	2	graphs	graph	NOUN
ejpam-4829	102	3	and	and	CCONJ
ejpam-4829	102	4	their	their	PRON
ejpam-4829	102	5	prime	prime	ADJ
ejpam-4829	102	6	subgraphs	subgraphs	NOUN
ejpam-4829	102	7	ehrenfeucht	ehrenfeucht	NOUN
ejpam-4829	102	8	and	and	CCONJ
ejpam-4829	102	9	rozenberg	rozenberg	NOUN
ejpam-4829	103	1	[	[	X
ejpam-4829	103	2	3	3	NUM
ejpam-4829	103	3	]	]	PUNCT
ejpam-4829	103	4	constructed	construct	VERB
ejpam-4829	103	5	prime	prime	ADJ
ejpam-4829	103	6	subgraphs	subgraph	NOUN
ejpam-4829	103	7	of	of	ADP
ejpam-4829	103	8	a	a	DET
ejpam-4829	103	9	larger	large	ADJ
ejpam-4829	103	10	size	size	NOUN
ejpam-4829	103	11	than	than	ADP
ejpam-4829	103	12	a	a	DET
ejpam-4829	103	13	given	give	VERB
ejpam-4829	103	14	prime	prime	ADJ
ejpam-4829	103	15	subgraph	subgraph	NOUN
ejpam-4829	103	16	as	as	SCONJ
ejpam-4829	103	17	follows	follow	VERB
ejpam-4829	103	18	.	.	PUNCT
ejpam-4829	104	1	let	let	VERB
ejpam-4829	104	2	g	g	PROPN
ejpam-4829	104	3	=	=	SYM
ejpam-4829	104	4	(	(	PUNCT
ejpam-4829	104	5	v	v	NOUN
ejpam-4829	104	6	,	,	PUNCT
ejpam-4829	104	7	e	e	NOUN
ejpam-4829	104	8	)	)	PUNCT
ejpam-4829	104	9	be	be	AUX
ejpam-4829	104	10	a	a	DET
ejpam-4829	104	11	graph	graph	NOUN
ejpam-4829	104	12	.	.	PUNCT
ejpam-4829	105	1	given	give	VERB
ejpam-4829	105	2	a	a	DET
ejpam-4829	105	3	proper	proper	ADJ
ejpam-4829	105	4	subset	subset	NOUN
ejpam-4829	105	5	x	x	PUNCT
ejpam-4829	105	6	of	of	ADP
ejpam-4829	105	7	v	v	NOUN
ejpam-4829	105	8	such	such	ADJ
ejpam-4829	105	9	that	that	PRON
ejpam-4829	105	10	g[x	g[x	NOUN
ejpam-4829	105	11	]	]	PUNCT
ejpam-4829	105	12	is	be	AUX
ejpam-4829	105	13	prime	prime	ADJ
ejpam-4829	105	14	,	,	PUNCT
ejpam-4829	105	15	consider	consider	VERB
ejpam-4829	105	16	the	the	DET
ejpam-4829	105	17	following	follow	VERB
ejpam-4829	105	18	subsets	subset	NOUN
ejpam-4829	105	19	of	of	ADP
ejpam-4829	105	20	v	v	NOUN
ejpam-4829	105	21	\x	\x	NOUN
ejpam-4829	105	22	:	:	PUNCT
ejpam-4829	105	23	•	•	NUM
ejpam-4829	105	24	ext(x	ext(x	NOUN
ejpam-4829	105	25	)	)	PUNCT
ejpam-4829	105	26	is	be	AUX
ejpam-4829	105	27	the	the	DET
ejpam-4829	105	28	set	set	NOUN
ejpam-4829	105	29	of	of	ADP
ejpam-4829	105	30	x	x	PROPN
ejpam-4829	105	31	∈	∈	PROPN
ejpam-4829	105	32	v	v	ADP
ejpam-4829	105	33	\x	\x	NOUN
ejpam-4829	105	34	such	such	ADJ
ejpam-4829	105	35	that	that	SCONJ
ejpam-4829	105	36	g[x	g[x	ADP
ejpam-4829	105	37	∪	∪	ADP
ejpam-4829	105	38	{	{	PUNCT
ejpam-4829	105	39	x	x	NOUN
ejpam-4829	105	40	}	}	PUNCT
ejpam-4829	105	41	]	]	PUNCT
ejpam-4829	105	42	is	be	AUX
ejpam-4829	105	43	prime	prime	ADJ
ejpam-4829	105	44	.	.	PUNCT
ejpam-4829	106	1	•	•	NUM
ejpam-4829	106	2	⟨x⟩	⟨x⟩	PROPN
ejpam-4829	106	3	is	be	AUX
ejpam-4829	106	4	the	the	DET
ejpam-4829	106	5	set	set	NOUN
ejpam-4829	106	6	of	of	ADP
ejpam-4829	106	7	x	x	PROPN
ejpam-4829	106	8	∈	∈	PROPN
ejpam-4829	106	9	v	v	ADP
ejpam-4829	106	10	\x	\x	NOUN
ejpam-4829	106	11	such	such	ADJ
ejpam-4829	106	12	that	that	SCONJ
ejpam-4829	106	13	x	x	PRON
ejpam-4829	106	14	is	be	AUX
ejpam-4829	106	15	a	a	DET
ejpam-4829	106	16	module	module	NOUN
ejpam-4829	106	17	of	of	ADP
ejpam-4829	106	18	g[x	g[x	ADP
ejpam-4829	106	19	∪	∪	X
ejpam-4829	106	20	{	{	PUNCT
ejpam-4829	106	21	x	x	NOUN
ejpam-4829	106	22	}	}	PUNCT
ejpam-4829	106	23	]	]	PUNCT
ejpam-4829	106	24	.	.	PUNCT
ejpam-4829	107	1	•	•	NUM
ejpam-4829	107	2	for	for	ADP
ejpam-4829	107	3	u	u	PROPN
ejpam-4829	107	4	∈	∈	PROPN
ejpam-4829	107	5	x	x	PROPN
ejpam-4829	107	6	,	,	PUNCT
ejpam-4829	107	7	x(u	x(u	PROPN
ejpam-4829	107	8	)	)	PUNCT
ejpam-4829	107	9	is	be	AUX
ejpam-4829	107	10	the	the	DET
ejpam-4829	107	11	set	set	NOUN
ejpam-4829	107	12	of	of	ADP
ejpam-4829	107	13	x	x	PROPN
ejpam-4829	107	14	∈	∈	PROPN
ejpam-4829	107	15	v	v	ADP
ejpam-4829	107	16	\x	\x	NOUN
ejpam-4829	107	17	such	such	ADJ
ejpam-4829	107	18	that	that	SCONJ
ejpam-4829	107	19	{	{	PUNCT
ejpam-4829	107	20	x	x	NOUN
ejpam-4829	107	21	,	,	PUNCT
ejpam-4829	107	22	u	u	NOUN
ejpam-4829	107	23	}	}	PUNCT
ejpam-4829	107	24	is	be	AUX
ejpam-4829	107	25	a	a	DET
ejpam-4829	107	26	module	module	NOUN
ejpam-4829	107	27	of	of	ADP
ejpam-4829	107	28	g[x	g[x	ADP
ejpam-4829	107	29	∪	∪	X
ejpam-4829	107	30	{	{	PUNCT
ejpam-4829	107	31	x	x	NOUN
ejpam-4829	107	32	}	}	PUNCT
ejpam-4829	107	33	]	]	PUNCT
ejpam-4829	107	34	.	.	PUNCT
ejpam-4829	108	1	the	the	DET
ejpam-4829	108	2	family	family	NOUN
ejpam-4829	108	3	of	of	ADP
ejpam-4829	108	4	the	the	DET
ejpam-4829	108	5	non	non	ADJ
ejpam-4829	108	6	-	-	ADJ
ejpam-4829	108	7	empty	empty	ADJ
ejpam-4829	108	8	elements	element	NOUN
ejpam-4829	108	9	of	of	ADP
ejpam-4829	108	10	the	the	DET
ejpam-4829	108	11	union	union	NOUN
ejpam-4829	108	12	{	{	PUNCT
ejpam-4829	108	13	ext(x	ext(x	PROPN
ejpam-4829	108	14	)	)	PUNCT
ejpam-4829	108	15	,	,	PUNCT
ejpam-4829	108	16	⟨x⟩	⟨x⟩	PROPN
ejpam-4829	108	17	}	}	PUNCT
ejpam-4829	108	18	∪	∪	X
ejpam-4829	108	19	{	{	PUNCT
ejpam-4829	108	20	x(u	x(u	PROPN
ejpam-4829	108	21	)	)	PUNCT
ejpam-4829	108	22	:	:	PUNCT
ejpam-4829	108	23	u	u	NOUN
ejpam-4829	108	24	∈	∈	PROPN
ejpam-4829	108	25	x	x	PRON
ejpam-4829	108	26	}	}	PUNCT
ejpam-4829	108	27	is	be	AUX
ejpam-4829	108	28	denoted	denote	VERB
ejpam-4829	108	29	by	by	ADP
ejpam-4829	108	30	px	px	NOUN
ejpam-4829	108	31	.	.	PUNCT
ejpam-4829	109	1	lemma	lemma	PROPN
ejpam-4829	109	2	1	1	NUM
ejpam-4829	109	3	.	.	PUNCT
ejpam-4829	110	1	[	[	X
ejpam-4829	110	2	3	3	NUM
ejpam-4829	110	3	]	]	PUNCT
ejpam-4829	110	4	taking	take	VERB
ejpam-4829	110	5	into	into	ADP
ejpam-4829	110	6	account	account	NOUN
ejpam-4829	110	7	a	a	DET
ejpam-4829	110	8	graph	graph	NOUN
ejpam-4829	110	9	g	g	NOUN
ejpam-4829	110	10	=	=	SYM
ejpam-4829	110	11	(	(	PUNCT
ejpam-4829	110	12	v	v	NOUN
ejpam-4829	110	13	,	,	PUNCT
ejpam-4829	110	14	e	e	NOUN
ejpam-4829	110	15	)	)	PUNCT
ejpam-4829	110	16	,	,	PUNCT
ejpam-4829	110	17	consider	consider	VERB
ejpam-4829	110	18	a	a	DET
ejpam-4829	110	19	proper	proper	ADJ
ejpam-4829	110	20	subset	subset	NOUN
ejpam-4829	110	21	x	x	PUNCT
ejpam-4829	110	22	of	of	ADP
ejpam-4829	110	23	v	v	NOUN
ejpam-4829	110	24	such	such	ADJ
ejpam-4829	110	25	that	that	PRON
ejpam-4829	110	26	g[x	g[x	NOUN
ejpam-4829	110	27	]	]	PUNCT
ejpam-4829	110	28	is	be	AUX
ejpam-4829	110	29	prime	prime	ADJ
ejpam-4829	110	30	.	.	PUNCT
ejpam-4829	111	1	the	the	DET
ejpam-4829	111	2	family	family	NOUN
ejpam-4829	111	3	px	px	PROPN
ejpam-4829	111	4	realizes	realize	VERB
ejpam-4829	111	5	a	a	DET
ejpam-4829	111	6	partition	partition	NOUN
ejpam-4829	111	7	of	of	ADP
ejpam-4829	111	8	v	v	NOUN
ejpam-4829	111	9	\x	\x	NOUN
ejpam-4829	111	10	.	.	PUNCT
ejpam-4829	112	1	moreover	moreover	ADV
ejpam-4829	112	2	,	,	PUNCT
ejpam-4829	112	3	the	the	DET
ejpam-4829	112	4	following	follow	VERB
ejpam-4829	112	5	assertions	assertion	NOUN
ejpam-4829	112	6	hold	hold	VERB
ejpam-4829	112	7	.	.	PUNCT
ejpam-4829	113	1	1	1	X
ejpam-4829	113	2	)	)	PUNCT
ejpam-4829	113	3	let	let	VERB
ejpam-4829	113	4	u	u	PRON
ejpam-4829	113	5	∈	∈	NOUN
ejpam-4829	113	6	x.	x.	NOUN
ejpam-4829	113	7	for	for	ADP
ejpam-4829	113	8	x	x	PROPN
ejpam-4829	113	9	∈	∈	PROPN
ejpam-4829	113	10	x(u	x(u	PROPN
ejpam-4829	113	11	)	)	PUNCT
ejpam-4829	113	12	and	and	CCONJ
ejpam-4829	113	13	y	y	PROPN
ejpam-4829	113	14	∈	∈	PROPN
ejpam-4829	113	15	v	v	ADP
ejpam-4829	113	16	\	\	PUNCT
ejpam-4829	113	17	(	(	PUNCT
ejpam-4829	113	18	x	x	X
ejpam-4829	113	19	∪x(u	∪x(u	PROPN
ejpam-4829	113	20	)	)	PUNCT
ejpam-4829	113	21	)	)	PUNCT
ejpam-4829	113	22	,	,	PUNCT
ejpam-4829	113	23	if	if	SCONJ
ejpam-4829	113	24	g[x	g[x	ADP
ejpam-4829	113	25	∪	∪	ADP
ejpam-4829	113	26	{	{	PUNCT
ejpam-4829	113	27	x	x	NOUN
ejpam-4829	113	28	,	,	PUNCT
ejpam-4829	113	29	y	y	PROPN
ejpam-4829	113	30	}	}	PUNCT
ejpam-4829	113	31	]	]	PUNCT
ejpam-4829	113	32	is	be	AUX
ejpam-4829	113	33	not	not	PART
ejpam-4829	113	34	prime	prime	ADJ
ejpam-4829	113	35	,	,	PUNCT
ejpam-4829	113	36	then	then	ADV
ejpam-4829	113	37	{	{	PUNCT
ejpam-4829	113	38	u	u	NOUN
ejpam-4829	113	39	,	,	PUNCT
ejpam-4829	113	40	x	x	PRON
ejpam-4829	113	41	}	}	PUNCT
ejpam-4829	113	42	is	be	AUX
ejpam-4829	113	43	a	a	DET
ejpam-4829	113	44	module	module	NOUN
ejpam-4829	113	45	of	of	ADP
ejpam-4829	113	46	g[x	g[x	ADP
ejpam-4829	113	47	∪	∪	X
ejpam-4829	113	48	{	{	PUNCT
ejpam-4829	113	49	x	x	NOUN
ejpam-4829	113	50	,	,	PUNCT
ejpam-4829	113	51	y	y	PROPN
ejpam-4829	113	52	}	}	PUNCT
ejpam-4829	113	53	]	]	PUNCT
ejpam-4829	113	54	.	.	PUNCT
ejpam-4829	114	1	2	2	X
ejpam-4829	114	2	)	)	PUNCT
ejpam-4829	114	3	for	for	ADP
ejpam-4829	114	4	x	x	PROPN
ejpam-4829	114	5	∈	∈	PROPN
ejpam-4829	114	6	⟨x⟩	⟨x⟩	PROPN
ejpam-4829	114	7	and	and	CCONJ
ejpam-4829	114	8	y	y	PROPN
ejpam-4829	114	9	∈	∈	PROPN
ejpam-4829	114	10	v	v	ADP
ejpam-4829	114	11	\	\	PUNCT
ejpam-4829	114	12	(	(	PUNCT
ejpam-4829	114	13	x	x	SYM
ejpam-4829	114	14	∪	∪	ADP
ejpam-4829	114	15	⟨x⟩	⟨x⟩	NUM
ejpam-4829	114	16	)	)	PUNCT
ejpam-4829	114	17	,	,	PUNCT
ejpam-4829	114	18	if	if	SCONJ
ejpam-4829	114	19	g[x	g[x	ADP
ejpam-4829	114	20	∪	∪	ADP
ejpam-4829	114	21	{	{	PUNCT
ejpam-4829	114	22	x	x	NOUN
ejpam-4829	114	23	,	,	PUNCT
ejpam-4829	114	24	y	y	PROPN
ejpam-4829	114	25	}	}	PUNCT
ejpam-4829	114	26	]	]	PUNCT
ejpam-4829	114	27	is	be	AUX
ejpam-4829	114	28	not	not	PART
ejpam-4829	114	29	prime	prime	ADJ
ejpam-4829	114	30	,	,	PUNCT
ejpam-4829	114	31	then	then	ADV
ejpam-4829	114	32	x	x	PUNCT
ejpam-4829	114	33	∪	∪	X
ejpam-4829	114	34	{	{	PUNCT
ejpam-4829	114	35	y	y	NOUN
ejpam-4829	114	36	}	}	PUNCT
ejpam-4829	114	37	is	be	AUX
ejpam-4829	114	38	a	a	DET
ejpam-4829	114	39	module	module	NOUN
ejpam-4829	114	40	of	of	ADP
ejpam-4829	114	41	g[x	g[x	ADP
ejpam-4829	114	42	∪	∪	X
ejpam-4829	114	43	{	{	PUNCT
ejpam-4829	114	44	x	x	NOUN
ejpam-4829	114	45	,	,	PUNCT
ejpam-4829	114	46	y	y	PROPN
ejpam-4829	114	47	}	}	PUNCT
ejpam-4829	114	48	]	]	PUNCT
ejpam-4829	114	49	.	.	PUNCT
ejpam-4829	115	1	3	3	X
ejpam-4829	115	2	)	)	PUNCT
ejpam-4829	115	3	for	for	ADP
ejpam-4829	115	4	two	two	NUM
ejpam-4829	115	5	distinct	distinct	ADJ
ejpam-4829	115	6	vertices	vertex	NOUN
ejpam-4829	115	7	x	x	PUNCT
ejpam-4829	115	8	and	and	CCONJ
ejpam-4829	115	9	y	y	PROPN
ejpam-4829	115	10	in	in	ADP
ejpam-4829	115	11	ext(x	ext(x	PROPN
ejpam-4829	115	12	)	)	PUNCT
ejpam-4829	115	13	,	,	PUNCT
ejpam-4829	115	14	if	if	SCONJ
ejpam-4829	115	15	g[x	g[x	ADP
ejpam-4829	115	16	∪{x	∪{x	NOUN
ejpam-4829	115	17	,	,	PUNCT
ejpam-4829	115	18	y	y	NOUN
ejpam-4829	115	19	}	}	PUNCT
ejpam-4829	115	20	]	]	PUNCT
ejpam-4829	115	21	is	be	AUX
ejpam-4829	115	22	not	not	PART
ejpam-4829	115	23	prime	prime	ADJ
ejpam-4829	115	24	,	,	PUNCT
ejpam-4829	115	25	then	then	ADV
ejpam-4829	115	26	{	{	PUNCT
ejpam-4829	115	27	x	x	NOUN
ejpam-4829	115	28	,	,	PUNCT
ejpam-4829	115	29	y	y	PRON
ejpam-4829	115	30	}	}	PUNCT
ejpam-4829	115	31	is	be	AUX
ejpam-4829	115	32	a	a	DET
ejpam-4829	115	33	module	module	NOUN
ejpam-4829	115	34	of	of	ADP
ejpam-4829	115	35	g[x	g[x	ADP
ejpam-4829	115	36	∪	∪	X
ejpam-4829	115	37	{	{	PUNCT
ejpam-4829	115	38	x	x	NOUN
ejpam-4829	115	39	,	,	PUNCT
ejpam-4829	115	40	y	y	PROPN
ejpam-4829	115	41	}	}	PUNCT
ejpam-4829	115	42	]	]	PUNCT
ejpam-4829	115	43	.	.	PUNCT
ejpam-4829	116	1	d.	d.	PROPN
ejpam-4829	116	2	p.	p.	PROPN
ejpam-4829	116	3	sumner	sumner	PROPN
ejpam-4829	116	4	obtained	obtain	VERB
ejpam-4829	116	5	the	the	DET
ejpam-4829	116	6	following	following	ADJ
ejpam-4829	116	7	result	result	NOUN
ejpam-4829	116	8	:	:	PUNCT
ejpam-4829	116	9	lemma	lemma	PROPN
ejpam-4829	116	10	2	2	X
ejpam-4829	116	11	.	.	PUNCT
ejpam-4829	117	1	[	[	X
ejpam-4829	117	2	7	7	X
ejpam-4829	117	3	]	]	X
ejpam-4829	117	4	if	if	SCONJ
ejpam-4829	117	5	g	g	PROPN
ejpam-4829	117	6	is	be	AUX
ejpam-4829	117	7	a	a	DET
ejpam-4829	117	8	prime	prime	ADJ
ejpam-4829	117	9	graph	graph	NOUN
ejpam-4829	117	10	,	,	PUNCT
ejpam-4829	117	11	then	then	ADV
ejpam-4829	117	12	g	g	PROPN
ejpam-4829	117	13	contains	contain	VERB
ejpam-4829	117	14	a	a	DET
ejpam-4829	117	15	path	path	NOUN
ejpam-4829	117	16	p4	p4	NOUN
ejpam-4829	117	17	as	as	ADP
ejpam-4829	117	18	an	an	DET
ejpam-4829	117	19	induced	induced	ADJ
ejpam-4829	117	20	subgraph	subgraph	NOUN
ejpam-4829	117	21	.	.	PUNCT
ejpam-4829	118	1	m.	m.	PROPN
ejpam-4829	118	2	bouaziz	bouaziz	PROPN
ejpam-4829	118	3	et	et	PROPN
ejpam-4829	118	4	al	al	PROPN
ejpam-4829	118	5	.	.	PUNCT
ejpam-4829	118	6	/	/	SYM
ejpam-4829	118	7	eur	eur	PROPN
ejpam-4829	118	8	.	.	PUNCT
ejpam-4829	119	1	j.	j.	PROPN
ejpam-4829	119	2	pure	pure	PROPN
ejpam-4829	119	3	appl	appl	PROPN
ejpam-4829	119	4	.	.	PROPN
ejpam-4829	119	5	math	math	PROPN
ejpam-4829	119	6	,	,	PUNCT
ejpam-4829	119	7	16	16	NUM
ejpam-4829	119	8	(	(	PUNCT
ejpam-4829	119	9	4	4	NUM
ejpam-4829	119	10	)	)	PUNCT
ejpam-4829	119	11	(	(	PUNCT
ejpam-4829	119	12	2023	2023	NUM
ejpam-4829	119	13	)	)	PUNCT
ejpam-4829	119	14	,	,	PUNCT
ejpam-4829	119	15	2786	2786	NUM
ejpam-4829	119	16	-	-	SYM
ejpam-4829	119	17	2797	2797	NUM
ejpam-4829	119	18	2791	2791	NUM
ejpam-4829	119	19	2.2	2.2	NUM
ejpam-4829	119	20	.	.	PUNCT
ejpam-4829	120	1	prime	prime	ADJ
ejpam-4829	120	2	graphs	graph	NOUN
ejpam-4829	120	3	and	and	CCONJ
ejpam-4829	120	4	their	their	PRON
ejpam-4829	120	5	subgraphs	subgraph	NOUN
ejpam-4829	120	6	with	with	ADP
ejpam-4829	120	7	prime	prime	ADJ
ejpam-4829	120	8	frames	frame	NOUN
ejpam-4829	120	9	the	the	DET
ejpam-4829	120	10	following	follow	VERB
ejpam-4829	120	11	notations	notation	NOUN
ejpam-4829	120	12	introduced	introduce	VERB
ejpam-4829	120	13	by	by	ADP
ejpam-4829	120	14	y.	y.	PROPN
ejpam-4829	120	15	boudabbous	boudabbous	PROPN
ejpam-4829	120	16	and	and	CCONJ
ejpam-4829	120	17	p.	p.	PROPN
ejpam-4829	120	18	ille	ille	NOUN
ejpam-4829	121	1	[	[	X
ejpam-4829	121	2	2	2	X
ejpam-4829	121	3	]	]	PUNCT
ejpam-4829	121	4	generalize	generalize	VERB
ejpam-4829	121	5	those	those	PRON
ejpam-4829	121	6	mentioned	mention	VERB
ejpam-4829	121	7	in	in	ADP
ejpam-4829	121	8	the	the	DET
ejpam-4829	121	9	previous	previous	ADJ
ejpam-4829	121	10	section	section	NOUN
ejpam-4829	121	11	.	.	PUNCT
ejpam-4829	122	1	given	give	VERB
ejpam-4829	122	2	a	a	DET
ejpam-4829	122	3	proper	proper	ADJ
ejpam-4829	122	4	vertex	vertex	NOUN
ejpam-4829	122	5	subset	subset	NOUN
ejpam-4829	122	6	x	x	PUNCT
ejpam-4829	122	7	of	of	ADP
ejpam-4829	122	8	a	a	DET
ejpam-4829	122	9	graph	graph	NOUN
ejpam-4829	122	10	g	g	ADP
ejpam-4829	122	11	such	such	ADJ
ejpam-4829	122	12	that	that	SCONJ
ejpam-4829	122	13	|x|	|x|	PROPN
ejpam-4829	122	14	≥	≥	NUM
ejpam-4829	122	15	4	4	NUM
ejpam-4829	122	16	and	and	CCONJ
ejpam-4829	122	17	the	the	DET
ejpam-4829	122	18	frame	frame	NOUN
ejpam-4829	122	19	of	of	ADP
ejpam-4829	122	20	g[x	g[x	NOUN
ejpam-4829	122	21	]	]	PUNCT
ejpam-4829	122	22	is	be	AUX
ejpam-4829	122	23	prime	prime	ADJ
ejpam-4829	122	24	,	,	PUNCT
ejpam-4829	122	25	consider	consider	VERB
ejpam-4829	122	26	the	the	DET
ejpam-4829	122	27	following	follow	VERB
ejpam-4829	122	28	subsets	subset	NOUN
ejpam-4829	122	29	of	of	ADP
ejpam-4829	122	30	v	v	NOUN
ejpam-4829	122	31	(	(	PUNCT
ejpam-4829	122	32	g	g	NOUN
ejpam-4829	122	33	)	)	PUNCT
ejpam-4829	122	34	\x	\x	NOUN
ejpam-4829	122	35	:	:	PUNCT
ejpam-4829	122	36	•	•	NUM
ejpam-4829	122	37	⟨x⟩	⟨x⟩	PROPN
ejpam-4829	122	38	is	be	AUX
ejpam-4829	122	39	the	the	DET
ejpam-4829	122	40	set	set	NOUN
ejpam-4829	122	41	of	of	ADP
ejpam-4829	122	42	x	x	PUNCT
ejpam-4829	122	43	outside	outside	ADV
ejpam-4829	122	44	x	x	INTJ
ejpam-4829	122	45	such	such	ADJ
ejpam-4829	122	46	that	that	SCONJ
ejpam-4829	122	47	x	x	PRON
ejpam-4829	122	48	is	be	AUX
ejpam-4829	122	49	a	a	DET
ejpam-4829	122	50	module	module	NOUN
ejpam-4829	122	51	of	of	ADP
ejpam-4829	122	52	g[x	g[x	ADP
ejpam-4829	122	53	∪	∪	X
ejpam-4829	122	54	{	{	PUNCT
ejpam-4829	122	55	x	x	NOUN
ejpam-4829	122	56	}	}	PUNCT
ejpam-4829	122	57	]	]	PUNCT
ejpam-4829	122	58	.	.	PUNCT
ejpam-4829	123	1	•	•	NUM
ejpam-4829	123	2	ext(x	ext(x	NOUN
ejpam-4829	123	3	)	)	PUNCT
ejpam-4829	123	4	is	be	AUX
ejpam-4829	123	5	the	the	DET
ejpam-4829	123	6	set	set	NOUN
ejpam-4829	123	7	of	of	ADP
ejpam-4829	123	8	x	x	PUNCT
ejpam-4829	123	9	outside	outside	ADV
ejpam-4829	123	10	x	x	INTJ
ejpam-4829	123	11	such	such	ADJ
ejpam-4829	123	12	that	that	SCONJ
ejpam-4829	123	13	the	the	DET
ejpam-4829	123	14	frame	frame	NOUN
ejpam-4829	123	15	of	of	ADP
ejpam-4829	123	16	g[x	g[x	ADP
ejpam-4829	123	17	∪	∪	X
ejpam-4829	123	18	{	{	PUNCT
ejpam-4829	123	19	x	x	NOUN
ejpam-4829	123	20	}	}	PUNCT
ejpam-4829	123	21	]	]	PUNCT
ejpam-4829	123	22	is	be	AUX
ejpam-4829	123	23	prime	prime	ADJ
ejpam-4829	123	24	and	and	CCONJ
ejpam-4829	123	25	{	{	PUNCT
ejpam-4829	123	26	x	x	NOUN
ejpam-4829	123	27	}	}	PUNCT
ejpam-4829	123	28	∈	∈	PROPN
ejpam-4829	123	29	p(g[x	p(g[x	NOUN
ejpam-4829	123	30	∪	∪	X
ejpam-4829	123	31	{	{	PUNCT
ejpam-4829	123	32	x	x	NOUN
ejpam-4829	123	33	}	}	PUNCT
ejpam-4829	123	34	]	]	PUNCT
ejpam-4829	123	35	)	)	PUNCT
ejpam-4829	123	36	.	.	PUNCT
ejpam-4829	124	1	•	•	NOUN
ejpam-4829	124	2	for	for	ADP
ejpam-4829	124	3	each	each	DET
ejpam-4829	124	4	c	c	PROPN
ejpam-4829	124	5	in	in	ADP
ejpam-4829	124	6	p(g[x	p(g[x	PROPN
ejpam-4829	124	7	]	]	PUNCT
ejpam-4829	124	8	)	)	PUNCT
ejpam-4829	124	9	,	,	PUNCT
ejpam-4829	124	10	x(c	x(c	PROPN
ejpam-4829	124	11	)	)	PUNCT
ejpam-4829	124	12	is	be	AUX
ejpam-4829	124	13	the	the	DET
ejpam-4829	124	14	set	set	NOUN
ejpam-4829	124	15	of	of	ADP
ejpam-4829	124	16	x	x	PUNCT
ejpam-4829	124	17	outside	outside	ADV
ejpam-4829	124	18	x	x	INTJ
ejpam-4829	124	19	such	such	ADJ
ejpam-4829	124	20	that	that	SCONJ
ejpam-4829	124	21	the	the	DET
ejpam-4829	124	22	frame	frame	NOUN
ejpam-4829	124	23	of	of	ADP
ejpam-4829	124	24	g[x	g[x	ADP
ejpam-4829	124	25	∪	∪	X
ejpam-4829	124	26	{	{	PUNCT
ejpam-4829	124	27	x	x	NOUN
ejpam-4829	124	28	}	}	PUNCT
ejpam-4829	124	29	]	]	PUNCT
ejpam-4829	124	30	is	be	AUX
ejpam-4829	124	31	prime	prime	ADJ
ejpam-4829	124	32	and	and	CCONJ
ejpam-4829	124	33	c	c	NOUN
ejpam-4829	124	34	∪	∪	X
ejpam-4829	124	35	{	{	PUNCT
ejpam-4829	124	36	x	x	NOUN
ejpam-4829	124	37	}	}	PUNCT
ejpam-4829	124	38	∈	∈	PROPN
ejpam-4829	124	39	p(g[x	p(g[x	NOUN
ejpam-4829	124	40	∪	∪	X
ejpam-4829	124	41	{	{	PUNCT
ejpam-4829	124	42	x	x	NOUN
ejpam-4829	124	43	}	}	PUNCT
ejpam-4829	124	44	]	]	PUNCT
ejpam-4829	124	45	)	)	PUNCT
ejpam-4829	124	46	.	.	PUNCT
ejpam-4829	125	1	the	the	DET
ejpam-4829	125	2	family	family	NOUN
ejpam-4829	125	3	of	of	ADP
ejpam-4829	125	4	the	the	DET
ejpam-4829	125	5	non	non	ADJ
ejpam-4829	125	6	-	-	ADJ
ejpam-4829	125	7	empty	empty	ADJ
ejpam-4829	125	8	elements	element	NOUN
ejpam-4829	125	9	of	of	ADP
ejpam-4829	125	10	the	the	DET
ejpam-4829	125	11	union	union	NOUN
ejpam-4829	125	12	{	{	PUNCT
ejpam-4829	125	13	ext(x	ext(x	PROPN
ejpam-4829	125	14	)	)	PUNCT
ejpam-4829	125	15	,	,	PUNCT
ejpam-4829	125	16	⟨x⟩	⟨x⟩	PROPN
ejpam-4829	125	17	}	}	PUNCT
ejpam-4829	125	18	∪	∪	X
ejpam-4829	125	19	{	{	PUNCT
ejpam-4829	125	20	x(c	x(c	PROPN
ejpam-4829	125	21	)	)	PUNCT
ejpam-4829	125	22	:	:	PUNCT
ejpam-4829	126	1	c	c	X
ejpam-4829	126	2	∈	∈	PROPN
ejpam-4829	126	3	p(g[x	p(g[x	X
ejpam-4829	126	4	]	]	X
ejpam-4829	126	5	)	)	PUNCT
ejpam-4829	126	6	}	}	PUNCT
ejpam-4829	126	7	is	be	AUX
ejpam-4829	126	8	denoted	denote	VERB
ejpam-4829	126	9	by	by	ADP
ejpam-4829	126	10	qx	qx	PROPN
ejpam-4829	126	11	.	.	PUNCT
ejpam-4829	127	1	the	the	DET
ejpam-4829	127	2	following	follow	VERB
ejpam-4829	127	3	theorem	theorem	NOUN
ejpam-4829	127	4	is	be	AUX
ejpam-4829	127	5	essential	essential	ADJ
ejpam-4829	127	6	to	to	PART
ejpam-4829	127	7	prove	prove	VERB
ejpam-4829	127	8	some	some	DET
ejpam-4829	127	9	results	result	NOUN
ejpam-4829	127	10	in	in	ADP
ejpam-4829	127	11	this	this	DET
ejpam-4829	127	12	paper	paper	NOUN
ejpam-4829	127	13	.	.	PUNCT
ejpam-4829	128	1	theorem	theorem	NOUN
ejpam-4829	128	2	2	2	NUM
ejpam-4829	128	3	.	.	PUNCT
ejpam-4829	129	1	[	[	X
ejpam-4829	129	2	2	2	NUM
ejpam-4829	129	3	]	]	PUNCT
ejpam-4829	129	4	taking	take	VERB
ejpam-4829	129	5	into	into	ADP
ejpam-4829	129	6	account	account	NOUN
ejpam-4829	129	7	a	a	DET
ejpam-4829	129	8	graph	graph	NOUN
ejpam-4829	129	9	g	g	NOUN
ejpam-4829	129	10	=	=	SYM
ejpam-4829	129	11	(	(	PUNCT
ejpam-4829	129	12	v	v	NOUN
ejpam-4829	129	13	,	,	PUNCT
ejpam-4829	129	14	e	e	NOUN
ejpam-4829	129	15	)	)	PUNCT
ejpam-4829	129	16	,	,	PUNCT
ejpam-4829	129	17	consider	consider	VERB
ejpam-4829	129	18	a	a	DET
ejpam-4829	129	19	proper	proper	ADJ
ejpam-4829	129	20	vertex	vertex	NOUN
ejpam-4829	129	21	subset	subset	NOUN
ejpam-4829	129	22	x	x	PUNCT
ejpam-4829	129	23	of	of	ADP
ejpam-4829	129	24	g	g	NOUN
ejpam-4829	129	25	with	with	ADP
ejpam-4829	129	26	at	at	ADV
ejpam-4829	129	27	least	least	ADV
ejpam-4829	129	28	four	four	NUM
ejpam-4829	129	29	vertices	vertex	NOUN
ejpam-4829	129	30	such	such	ADJ
ejpam-4829	129	31	that	that	SCONJ
ejpam-4829	129	32	the	the	DET
ejpam-4829	129	33	frame	frame	NOUN
ejpam-4829	129	34	of	of	ADP
ejpam-4829	129	35	g[x	g[x	NOUN
ejpam-4829	129	36	]	]	PUNCT
ejpam-4829	129	37	is	be	AUX
ejpam-4829	129	38	prime	prime	ADJ
ejpam-4829	129	39	.	.	PUNCT
ejpam-4829	130	1	1	1	X
ejpam-4829	130	2	)	)	PUNCT
ejpam-4829	130	3	the	the	DET
ejpam-4829	130	4	family	family	NOUN
ejpam-4829	130	5	qx	qx	PROPN
ejpam-4829	130	6	forms	form	VERB
ejpam-4829	130	7	a	a	DET
ejpam-4829	130	8	partition	partition	NOUN
ejpam-4829	130	9	of	of	ADP
ejpam-4829	130	10	v	v	NOUN
ejpam-4829	130	11	\x	\x	NOUN
ejpam-4829	130	12	.	.	PUNCT
ejpam-4829	131	1	2	2	X
ejpam-4829	131	2	)	)	PUNCT
ejpam-4829	131	3	if	if	SCONJ
ejpam-4829	131	4	the	the	DET
ejpam-4829	131	5	graph	graph	NOUN
ejpam-4829	131	6	g	g	NOUN
ejpam-4829	131	7	is	be	AUX
ejpam-4829	131	8	prime	prime	ADJ
ejpam-4829	131	9	,	,	PUNCT
ejpam-4829	131	10	then	then	ADV
ejpam-4829	131	11	there	there	PRON
ejpam-4829	131	12	are	be	VERB
ejpam-4829	131	13	two	two	NUM
ejpam-4829	131	14	vertices	vertex	NOUN
ejpam-4829	131	15	x	x	PUNCT
ejpam-4829	131	16	and	and	CCONJ
ejpam-4829	131	17	y	y	PROPN
ejpam-4829	131	18	outside	outside	ADV
ejpam-4829	131	19	x	x	INTJ
ejpam-4829	131	20	such	such	ADJ
ejpam-4829	131	21	that	that	SCONJ
ejpam-4829	131	22	the	the	DET
ejpam-4829	131	23	frame	frame	NOUN
ejpam-4829	131	24	of	of	ADP
ejpam-4829	131	25	g[x	g[x	ADP
ejpam-4829	131	26	∪	∪	X
ejpam-4829	131	27	{	{	PUNCT
ejpam-4829	131	28	x	x	NOUN
ejpam-4829	131	29	,	,	PUNCT
ejpam-4829	131	30	y	y	PROPN
ejpam-4829	131	31	}	}	PUNCT
ejpam-4829	131	32	]	]	PUNCT
ejpam-4829	131	33	is	be	AUX
ejpam-4829	131	34	prime	prime	ADJ
ejpam-4829	131	35	and	and	CCONJ
ejpam-4829	131	36	{	{	PUNCT
ejpam-4829	131	37	x	x	NOUN
ejpam-4829	131	38	}	}	PUNCT
ejpam-4829	131	39	,	,	PUNCT
ejpam-4829	131	40	{	{	PUNCT
ejpam-4829	131	41	y	y	NOUN
ejpam-4829	131	42	}	}	PUNCT
ejpam-4829	131	43	∈	∈	PROPN
ejpam-4829	131	44	p(g[x	p(g[x	NOUN
ejpam-4829	131	45	∪	∪	X
ejpam-4829	131	46	{	{	PUNCT
ejpam-4829	131	47	x	x	NOUN
ejpam-4829	131	48	,	,	PUNCT
ejpam-4829	131	49	y	y	PROPN
ejpam-4829	131	50	}	}	PUNCT
ejpam-4829	131	51	]	]	PUNCT
ejpam-4829	131	52	)	)	PUNCT
ejpam-4829	131	53	.	.	PUNCT
ejpam-4829	132	1	more	more	ADV
ejpam-4829	132	2	precisely	precisely	ADV
ejpam-4829	132	3	:	:	PUNCT
ejpam-4829	132	4	(	(	PUNCT
ejpam-4829	132	5	i	i	NOUN
ejpam-4829	132	6	)	)	PUNCT
ejpam-4829	132	7	if	if	SCONJ
ejpam-4829	132	8	⟨x⟩	⟨x⟩	PROPN
ejpam-4829	132	9	=	=	NOUN
ejpam-4829	132	10	̸	̸	ADJ
ejpam-4829	132	11	∅	∅	NOUN
ejpam-4829	132	12	,	,	PUNCT
ejpam-4829	132	13	then	then	ADV
ejpam-4829	132	14	there	there	PRON
ejpam-4829	132	15	is	be	VERB
ejpam-4829	132	16	a	a	DET
ejpam-4829	132	17	vertex	vertex	NOUN
ejpam-4829	132	18	x	x	PUNCT
ejpam-4829	132	19	in	in	ADP
ejpam-4829	132	20	⟨x⟩	⟨x⟩	PROPN
ejpam-4829	132	21	and	and	CCONJ
ejpam-4829	132	22	a	a	DET
ejpam-4829	132	23	vertex	vertex	NOUN
ejpam-4829	132	24	y	y	PROPN
ejpam-4829	132	25	outside	outside	ADV
ejpam-4829	132	26	x	x	PUNCT
ejpam-4829	132	27	∪	∪	ADP
ejpam-4829	132	28	⟨x⟩	⟨x⟩	PROPN
ejpam-4829	132	29	such	such	ADJ
ejpam-4829	132	30	that	that	SCONJ
ejpam-4829	132	31	the	the	DET
ejpam-4829	132	32	frame	frame	NOUN
ejpam-4829	132	33	of	of	ADP
ejpam-4829	132	34	g[x	g[x	ADP
ejpam-4829	132	35	∪	∪	X
ejpam-4829	132	36	{	{	PUNCT
ejpam-4829	132	37	x	x	NOUN
ejpam-4829	132	38	,	,	PUNCT
ejpam-4829	132	39	y	y	PROPN
ejpam-4829	132	40	}	}	PUNCT
ejpam-4829	132	41	]	]	PUNCT
ejpam-4829	132	42	is	be	AUX
ejpam-4829	132	43	prime	prime	ADJ
ejpam-4829	132	44	and	and	CCONJ
ejpam-4829	132	45	{	{	PUNCT
ejpam-4829	132	46	x	x	NOUN
ejpam-4829	132	47	}	}	PUNCT
ejpam-4829	132	48	,	,	PUNCT
ejpam-4829	132	49	{	{	PUNCT
ejpam-4829	132	50	y	y	NOUN
ejpam-4829	132	51	}	}	PUNCT
ejpam-4829	132	52	∈	∈	PROPN
ejpam-4829	132	53	p(g[x	p(g[x	NOUN
ejpam-4829	132	54	∪	∪	X
ejpam-4829	132	55	{	{	PUNCT
ejpam-4829	132	56	x	x	NOUN
ejpam-4829	132	57	,	,	PUNCT
ejpam-4829	132	58	y	y	PROPN
ejpam-4829	132	59	}	}	PUNCT
ejpam-4829	132	60	]	]	PUNCT
ejpam-4829	132	61	)	)	PUNCT
ejpam-4829	132	62	.	.	PUNCT
ejpam-4829	133	1	(	(	PUNCT
ejpam-4829	133	2	ii	ii	NOUN
ejpam-4829	133	3	)	)	PUNCT
ejpam-4829	133	4	given	give	VERB
ejpam-4829	133	5	an	an	DET
ejpam-4829	133	6	element	element	NOUN
ejpam-4829	133	7	c	c	NOUN
ejpam-4829	133	8	of	of	ADP
ejpam-4829	133	9	p(g[x	p(g[x	PROPN
ejpam-4829	133	10	]	]	PUNCT
ejpam-4829	133	11	)	)	PUNCT
ejpam-4829	133	12	,	,	PUNCT
ejpam-4829	133	13	if	if	SCONJ
ejpam-4829	133	14	|c	|c	ADJ
ejpam-4829	133	15	∪x(c)|	∪x(c)|	PROPN
ejpam-4829	133	16	≥	≥	NOUN
ejpam-4829	133	17	2	2	NUM
ejpam-4829	133	18	and	and	CCONJ
ejpam-4829	133	19	ext(x	ext(x	NUM
ejpam-4829	133	20	)	)	PUNCT
ejpam-4829	134	1	=	=	NOUN
ejpam-4829	134	2	∅	∅	NOUN
ejpam-4829	134	3	,	,	PUNCT
ejpam-4829	134	4	then	then	ADV
ejpam-4829	134	5	there	there	PRON
ejpam-4829	134	6	is	be	VERB
ejpam-4829	134	7	a	a	DET
ejpam-4829	134	8	vertex	vertex	NOUN
ejpam-4829	134	9	x	x	PUNCT
ejpam-4829	134	10	in	in	ADP
ejpam-4829	134	11	x(c	x(c	PROPN
ejpam-4829	134	12	)	)	PUNCT
ejpam-4829	134	13	and	and	CCONJ
ejpam-4829	134	14	a	a	DET
ejpam-4829	134	15	vertex	vertex	NOUN
ejpam-4829	134	16	y	y	PROPN
ejpam-4829	134	17	outside	outside	ADV
ejpam-4829	134	18	x	x	PUNCT
ejpam-4829	134	19	∪	∪	ADP
ejpam-4829	134	20	x(c	x(c	PROPN
ejpam-4829	134	21	)	)	PUNCT
ejpam-4829	134	22	such	such	ADJ
ejpam-4829	134	23	that	that	SCONJ
ejpam-4829	134	24	the	the	DET
ejpam-4829	134	25	frame	frame	NOUN
ejpam-4829	134	26	of	of	ADP
ejpam-4829	134	27	g[x	g[x	ADP
ejpam-4829	134	28	∪	∪	X
ejpam-4829	134	29	{	{	PUNCT
ejpam-4829	134	30	x	x	NOUN
ejpam-4829	134	31	,	,	PUNCT
ejpam-4829	134	32	y	y	PROPN
ejpam-4829	134	33	}	}	PUNCT
ejpam-4829	134	34	]	]	PUNCT
ejpam-4829	134	35	is	be	AUX
ejpam-4829	134	36	prime	prime	ADJ
ejpam-4829	134	37	and	and	CCONJ
ejpam-4829	134	38	{	{	PUNCT
ejpam-4829	134	39	x	x	NOUN
ejpam-4829	134	40	}	}	PUNCT
ejpam-4829	134	41	,	,	PUNCT
ejpam-4829	134	42	{	{	PUNCT
ejpam-4829	134	43	y	y	NOUN
ejpam-4829	134	44	}	}	PUNCT
ejpam-4829	134	45	∈	∈	PROPN
ejpam-4829	134	46	p(g[x	p(g[x	NOUN
ejpam-4829	134	47	∪	∪	X
ejpam-4829	134	48	{	{	PUNCT
ejpam-4829	134	49	x	x	NOUN
ejpam-4829	134	50	,	,	PUNCT
ejpam-4829	134	51	y	y	PROPN
ejpam-4829	134	52	}	}	PUNCT
ejpam-4829	134	53	]	]	PUNCT
ejpam-4829	134	54	)	)	PUNCT
ejpam-4829	134	55	.	.	PUNCT
ejpam-4829	135	1	3	3	X
ejpam-4829	135	2	.	.	X
ejpam-4829	135	3	main	main	ADJ
ejpam-4829	135	4	result	result	NOUN
ejpam-4829	135	5	proposition	proposition	NOUN
ejpam-4829	135	6	2	2	X
ejpam-4829	135	7	.	.	PUNCT
ejpam-4829	136	1	let	let	VERB
ejpam-4829	136	2	k	k	NOUN
ejpam-4829	136	3	and	and	CCONJ
ejpam-4829	136	4	q	q	AUX
ejpam-4829	136	5	be	be	AUX
ejpam-4829	136	6	non	non	ADJ
ejpam-4829	136	7	-	-	ADJ
ejpam-4829	136	8	negative	negative	ADJ
ejpam-4829	136	9	integers	integer	NOUN
ejpam-4829	136	10	with	with	ADP
ejpam-4829	136	11	k	k	PROPN
ejpam-4829	136	12	≥	≥	NUM
ejpam-4829	136	13	2	2	NUM
ejpam-4829	136	14	.	.	PUNCT
ejpam-4829	137	1	let	let	VERB
ejpam-4829	137	2	g	g	PRON
ejpam-4829	137	3	be	be	AUX
ejpam-4829	137	4	a	a	DET
ejpam-4829	137	5	graph	graph	NOUN
ejpam-4829	137	6	.	.	PUNCT
ejpam-4829	138	1	if	if	SCONJ
ejpam-4829	138	2	g	g	PROPN
ejpam-4829	138	3	is	be	AUX
ejpam-4829	138	4	a	a	DET
ejpam-4829	138	5	pk	pk	NOUN
ejpam-4829	138	6	,	,	PUNCT
ejpam-4829	138	7	q	q	NOUN
ejpam-4829	138	8	graph	graph	NOUN
ejpam-4829	138	9	,	,	PUNCT
ejpam-4829	138	10	then	then	ADV
ejpam-4829	138	11	g	g	PROPN
ejpam-4829	138	12	is	be	AUX
ejpam-4829	138	13	prime	prime	ADJ
ejpam-4829	138	14	.	.	PUNCT
ejpam-4829	139	1	proof	proof	NOUN
ejpam-4829	139	2	.	.	PUNCT
ejpam-4829	140	1	let	let	VERB
ejpam-4829	140	2	k	k	NOUN
ejpam-4829	140	3	and	and	CCONJ
ejpam-4829	140	4	q	q	AUX
ejpam-4829	140	5	be	be	AUX
ejpam-4829	140	6	non	non	ADJ
ejpam-4829	140	7	-	-	ADJ
ejpam-4829	140	8	negative	negative	ADJ
ejpam-4829	140	9	integers	integer	NOUN
ejpam-4829	140	10	with	with	ADP
ejpam-4829	140	11	k	k	PROPN
ejpam-4829	140	12	≥	≥	NUM
ejpam-4829	140	13	2	2	NUM
ejpam-4829	140	14	.	.	PUNCT
ejpam-4829	141	1	let	let	VERB
ejpam-4829	141	2	g	g	PRON
ejpam-4829	141	3	be	be	AUX
ejpam-4829	141	4	a	a	DET
ejpam-4829	141	5	pk	pk	NOUN
ejpam-4829	141	6	,	,	PUNCT
ejpam-4829	141	7	q	q	NOUN
ejpam-4829	141	8	graph	graph	NOUN
ejpam-4829	141	9	.	.	PUNCT
ejpam-4829	142	1	first	first	ADV
ejpam-4829	142	2	,	,	PUNCT
ejpam-4829	142	3	if	if	SCONJ
ejpam-4829	142	4	q	q	X
ejpam-4829	142	5	=	=	SYM
ejpam-4829	142	6	0	0	NUM
ejpam-4829	142	7	,	,	PUNCT
ejpam-4829	142	8	then	then	ADV
ejpam-4829	142	9	g	g	PROPN
ejpam-4829	142	10	is	be	AUX
ejpam-4829	142	11	a	a	DET
ejpam-4829	142	12	pk,0	pk,0	PROPN
ejpam-4829	142	13	graph	graph	NOUN
ejpam-4829	142	14	.	.	PUNCT
ejpam-4829	143	1	assume	assume	VERB
ejpam-4829	143	2	that	that	SCONJ
ejpam-4829	143	3	|xk|	|xk|	PROPN
ejpam-4829	143	4	=	=	PUNCT
ejpam-4829	143	5	|x	|x	NOUN
ejpam-4829	143	6	′	′	NUM
ejpam-4829	143	7	k|	k|	NOUN
ejpam-4829	143	8	=	=	PUNCT
ejpam-4829	144	1	k	k	PROPN
ejpam-4829	144	2	where	where	SCONJ
ejpam-4829	144	3	xk	xk	PROPN
ejpam-4829	144	4	=	=	PUNCT
ejpam-4829	144	5	{	{	PUNCT
ejpam-4829	144	6	x1	x1	PROPN
ejpam-4829	144	7	,	,	PUNCT
ejpam-4829	144	8	x2	x2	PROPN
ejpam-4829	144	9	,	,	PUNCT
ejpam-4829	144	10	...	...	PUNCT
ejpam-4829	144	11	,	,	PUNCT
ejpam-4829	144	12	xk	xk	ADJ
ejpam-4829	144	13	}	}	PUNCT
ejpam-4829	144	14	and	and	CCONJ
ejpam-4829	144	15	x	x	SYM
ejpam-4829	144	16	′	′	NUM
ejpam-4829	144	17	k	k	X
ejpam-4829	145	1	=	=	PUNCT
ejpam-4829	145	2	{	{	PUNCT
ejpam-4829	145	3	x′1	x′1	PROPN
ejpam-4829	145	4	,	,	PUNCT
ejpam-4829	145	5	x′2	x′2	NOUN
ejpam-4829	145	6	,	,	PUNCT
ejpam-4829	145	7	...	...	PUNCT
ejpam-4829	145	8	,	,	PUNCT
ejpam-4829	145	9	x′k	x′k	PRON
ejpam-4829	145	10	}	}	PUNCT
ejpam-4829	145	11	are	be	AUX
ejpam-4829	145	12	m.	m.	NOUN
ejpam-4829	145	13	bouaziz	bouaziz	PROPN
ejpam-4829	145	14	et	et	PROPN
ejpam-4829	146	1	al	al	PROPN
ejpam-4829	146	2	.	.	PUNCT
ejpam-4829	146	3	/	/	SYM
ejpam-4829	146	4	eur	eur	PROPN
ejpam-4829	146	5	.	.	PUNCT
ejpam-4829	147	1	j.	j.	PROPN
ejpam-4829	147	2	pure	pure	PROPN
ejpam-4829	147	3	appl	appl	PROPN
ejpam-4829	147	4	.	.	PROPN
ejpam-4829	147	5	math	math	PROPN
ejpam-4829	147	6	,	,	PUNCT
ejpam-4829	147	7	16	16	NUM
ejpam-4829	147	8	(	(	PUNCT
ejpam-4829	147	9	4	4	NUM
ejpam-4829	147	10	)	)	PUNCT
ejpam-4829	147	11	(	(	PUNCT
ejpam-4829	147	12	2023	2023	NUM
ejpam-4829	147	13	)	)	PUNCT
ejpam-4829	147	14	,	,	PUNCT
ejpam-4829	147	15	2786	2786	NUM
ejpam-4829	147	16	-	-	SYM
ejpam-4829	147	17	2797	2797	NUM
ejpam-4829	147	18	2792	2792	NUM
ejpam-4829	147	19	two	two	NUM
ejpam-4829	147	20	disjoint	disjoint	NOUN
ejpam-4829	147	21	sets	set	NOUN
ejpam-4829	147	22	.	.	PUNCT
ejpam-4829	148	1	using	use	VERB
ejpam-4829	148	2	the	the	DET
ejpam-4829	148	3	induction	induction	NOUN
ejpam-4829	148	4	on	on	ADP
ejpam-4829	148	5	k	k	PROPN
ejpam-4829	148	6	(	(	PUNCT
ejpam-4829	148	7	k	k	PROPN
ejpam-4829	148	8	=	=	SYM
ejpam-4829	148	9	|x|	|x|	PROPN
ejpam-4829	148	10	)	)	PUNCT
ejpam-4829	148	11	,	,	PUNCT
ejpam-4829	148	12	we	we	PRON
ejpam-4829	148	13	prove	prove	VERB
ejpam-4829	148	14	that	that	SCONJ
ejpam-4829	148	15	g	g	PROPN
ejpam-4829	148	16	is	be	AUX
ejpam-4829	148	17	a	a	DET
ejpam-4829	148	18	prime	prime	ADJ
ejpam-4829	148	19	graph	graph	NOUN
ejpam-4829	148	20	.	.	PUNCT
ejpam-4829	149	1	on	on	ADP
ejpam-4829	149	2	the	the	DET
ejpam-4829	149	3	one	one	NUM
ejpam-4829	149	4	hand	hand	NOUN
ejpam-4829	149	5	,	,	PUNCT
ejpam-4829	149	6	if	if	SCONJ
ejpam-4829	149	7	k	k	PROPN
ejpam-4829	149	8	=	=	SYM
ejpam-4829	149	9	2	2	NUM
ejpam-4829	149	10	,	,	PUNCT
ejpam-4829	149	11	then	then	ADV
ejpam-4829	149	12	g	g	PROPN
ejpam-4829	149	13	is	be	AUX
ejpam-4829	149	14	the	the	DET
ejpam-4829	149	15	taurus	taurus	NOUN
ejpam-4829	149	16	(	(	PUNCT
ejpam-4829	149	17	resp	resp	NOUN
ejpam-4829	149	18	.	.	PUNCT
ejpam-4829	150	1	the	the	DET
ejpam-4829	150	2	house	house	NOUN
ejpam-4829	150	3	)	)	PUNCT
ejpam-4829	150	4	where	where	SCONJ
ejpam-4829	150	5	x1	x1	PROPN
ejpam-4829	150	6	is	be	AUX
ejpam-4829	150	7	nonadjacent	nonadjacent	ADJ
ejpam-4829	150	8	(	(	PUNCT
ejpam-4829	150	9	resp	resp	NOUN
ejpam-4829	150	10	.	.	PUNCT
ejpam-4829	151	1	adjacent	adjacent	ADJ
ejpam-4829	151	2	)	)	PUNCT
ejpam-4829	151	3	to	to	ADP
ejpam-4829	151	4	x2	x2	PROPN
ejpam-4829	151	5	.	.	PUNCT
ejpam-4829	152	1	thus	thus	ADV
ejpam-4829	152	2	,	,	PUNCT
ejpam-4829	152	3	g	g	PROPN
ejpam-4829	152	4	is	be	AUX
ejpam-4829	152	5	a	a	DET
ejpam-4829	152	6	prime	prime	ADJ
ejpam-4829	152	7	graph	graph	NOUN
ejpam-4829	152	8	.	.	PUNCT
ejpam-4829	153	1	on	on	ADP
ejpam-4829	153	2	the	the	DET
ejpam-4829	153	3	other	other	ADJ
ejpam-4829	153	4	hand	hand	NOUN
ejpam-4829	153	5	,	,	PUNCT
ejpam-4829	153	6	k	k	PROPN
ejpam-4829	153	7	≥	≥	NUM
ejpam-4829	153	8	2	2	X
ejpam-4829	153	9	.	.	PUNCT
ejpam-4829	153	10	assume	assume	VERB
ejpam-4829	153	11	that	that	SCONJ
ejpam-4829	153	12	,	,	PUNCT
ejpam-4829	153	13	for	for	ADP
ejpam-4829	153	14	every	every	DET
ejpam-4829	153	15	pk,0	pk,0	PROPN
ejpam-4829	153	16	graph	graph	NOUN
ejpam-4829	153	17	h	h	PROPN
ejpam-4829	153	18	,	,	PUNCT
ejpam-4829	153	19	h	h	PROPN
ejpam-4829	153	20	is	be	AUX
ejpam-4829	153	21	prime	prime	ADJ
ejpam-4829	153	22	.	.	PUNCT
ejpam-4829	154	1	we	we	PRON
ejpam-4829	154	2	prove	prove	VERB
ejpam-4829	154	3	that	that	SCONJ
ejpam-4829	154	4	every	every	DET
ejpam-4829	154	5	pk+1,0	pk+1,0	PROPN
ejpam-4829	154	6	graph	graph	NOUN
ejpam-4829	154	7	h	h	NOUN
ejpam-4829	154	8	′	′	NOUN
ejpam-4829	154	9	is	be	AUX
ejpam-4829	154	10	prime	prime	ADJ
ejpam-4829	154	11	.	.	PUNCT
ejpam-4829	155	1	let	let	VERB
ejpam-4829	155	2	xk+1	xk+1	NOUN
ejpam-4829	156	1	=	=	SYM
ejpam-4829	156	2	xk	xk	PROPN
ejpam-4829	156	3	∪	∪	X
ejpam-4829	156	4	{	{	PUNCT
ejpam-4829	156	5	xk+1	xk+1	ADJ
ejpam-4829	156	6	}	}	PUNCT
ejpam-4829	156	7	and	and	CCONJ
ejpam-4829	156	8	x	x	AUX
ejpam-4829	156	9	′	′	NUM
ejpam-4829	156	10	k+1	k+1	X
ejpam-4829	157	1	=	=	PUNCT
ejpam-4829	157	2	x	x	PUNCT
ejpam-4829	158	1	′	′	NUM
ejpam-4829	159	1	k	k	NOUN
ejpam-4829	159	2	∪	∪	X
ejpam-4829	159	3	{	{	PUNCT
ejpam-4829	159	4	x′k+1	x′k+1	NOUN
ejpam-4829	159	5	}	}	PUNCT
ejpam-4829	159	6	such	such	ADJ
ejpam-4829	159	7	that	that	PRON
ejpam-4829	159	8	x′k+1xk+1	x′k+1xk+1	VERB
ejpam-4829	159	9	∈	∈	PROPN
ejpam-4829	159	10	e(h	e(h	PROPN
ejpam-4829	159	11	′	′	NOUN
ejpam-4829	159	12	)	)	PUNCT
ejpam-4829	159	13	and	and	CCONJ
ejpam-4829	159	14	s	s	X
ejpam-4829	159	15	=	=	SYM
ejpam-4829	159	16	xk	xk	PROPN
ejpam-4829	159	17	∪x	∪x	NOUN
ejpam-4829	160	1	′	′	NUM
ejpam-4829	160	2	k	k	PROPN
ejpam-4829	160	3	∪{a	∪{a	PROPN
ejpam-4829	160	4	}	}	PUNCT
ejpam-4829	160	5	.	.	PUNCT
ejpam-4829	161	1	based	base	VERB
ejpam-4829	161	2	on	on	ADP
ejpam-4829	161	3	definition	definition	NOUN
ejpam-4829	161	4	1	1	NUM
ejpam-4829	161	5	,	,	PUNCT
ejpam-4829	161	6	there	there	PRON
ejpam-4829	161	7	is	be	VERB
ejpam-4829	161	8	a	a	DET
ejpam-4829	161	9	pk,0	pk,0	PROPN
ejpam-4829	161	10	graph	graph	NOUN
ejpam-4829	161	11	h1	h1	VERB
ejpam-4829	161	12	such	such	DET
ejpam-4829	161	13	that	that	SCONJ
ejpam-4829	161	14	h	h	NOUN
ejpam-4829	161	15	′[s	′[s	NOUN
ejpam-4829	161	16	]	]	X
ejpam-4829	161	17	≃	≃	NOUN
ejpam-4829	161	18	h1	h1	PROPN
ejpam-4829	161	19	.	.	PUNCT
ejpam-4829	162	1	then	then	ADV
ejpam-4829	162	2	,	,	PUNCT
ejpam-4829	162	3	by	by	ADP
ejpam-4829	162	4	the	the	DET
ejpam-4829	162	5	induction	induction	NOUN
ejpam-4829	162	6	hypothesis	hypothesis	NOUN
ejpam-4829	162	7	,	,	PUNCT
ejpam-4829	162	8	h	h	NOUN
ejpam-4829	162	9	′[s	′[s	NOUN
ejpam-4829	162	10	]	]	PUNCT
ejpam-4829	162	11	is	be	AUX
ejpam-4829	162	12	prime	prime	ADJ
ejpam-4829	162	13	.	.	PUNCT
ejpam-4829	163	1	using	use	VERB
ejpam-4829	163	2	the	the	DET
ejpam-4829	163	3	definition	definition	NOUN
ejpam-4829	163	4	of	of	ADP
ejpam-4829	163	5	the	the	DET
ejpam-4829	163	6	graph	graph	NOUN
ejpam-4829	163	7	h	h	NOUN
ejpam-4829	163	8	′	′	NOUN
ejpam-4829	163	9	,	,	PUNCT
ejpam-4829	163	10	{	{	PUNCT
ejpam-4829	163	11	a	a	PRON
ejpam-4829	163	12	,	,	PUNCT
ejpam-4829	163	13	x′k+1	x′k+1	PROPN
ejpam-4829	163	14	}	}	PUNCT
ejpam-4829	163	15	is	be	AUX
ejpam-4829	163	16	adjacent	adjacent	ADJ
ejpam-4829	163	17	to	to	ADP
ejpam-4829	163	18	x	x	PROPN
ejpam-4829	163	19	′	′	NUM
ejpam-4829	164	1	k	k	NOUN
ejpam-4829	164	2	but	but	CCONJ
ejpam-4829	164	3	non	non	ADJ
ejpam-4829	164	4	-	-	ADJ
ejpam-4829	164	5	adjacent	adjacent	ADJ
ejpam-4829	164	6	to	to	ADP
ejpam-4829	164	7	xk	xk	PROPN
ejpam-4829	164	8	.	.	PUNCT
ejpam-4829	164	9	thus	thus	ADV
ejpam-4829	164	10	,	,	PUNCT
ejpam-4829	164	11	x′k+1	x′k+1	PUNCT
ejpam-4829	164	12	∈	∈	PROPN
ejpam-4829	164	13	s(a	s(a	PROPN
ejpam-4829	164	14	)	)	PUNCT
ejpam-4829	164	15	.	.	PUNCT
ejpam-4829	165	1	according	accord	VERB
ejpam-4829	165	2	to	to	ADP
ejpam-4829	165	3	the	the	DET
ejpam-4829	165	4	definition	definition	NOUN
ejpam-4829	165	5	of	of	ADP
ejpam-4829	165	6	the	the	DET
ejpam-4829	165	7	graph	graph	NOUN
ejpam-4829	165	8	h	h	NOUN
ejpam-4829	165	9	′	′	NUM
ejpam-4829	165	10	,	,	PUNCT
ejpam-4829	165	11	xk+1	xk+1	PROPN
ejpam-4829	165	12	is	be	AUX
ejpam-4829	165	13	adjacent	adjacent	ADJ
ejpam-4829	165	14	to	to	ADP
ejpam-4829	165	15	x′k+1	x′k+1	PUNCT
ejpam-4829	165	16	but	but	CCONJ
ejpam-4829	165	17	non	non	ADJ
ejpam-4829	165	18	-	-	ADJ
ejpam-4829	165	19	adjacent	adjacent	ADJ
ejpam-4829	165	20	to	to	ADP
ejpam-4829	165	21	the	the	DET
ejpam-4829	165	22	vertex	vertex	NOUN
ejpam-4829	165	23	a.	a.	NOUN
ejpam-4829	165	24	consequently	consequently	ADV
ejpam-4829	165	25	,	,	PUNCT
ejpam-4829	165	26	{	{	PUNCT
ejpam-4829	165	27	a	a	PRON
ejpam-4829	165	28	,	,	PUNCT
ejpam-4829	165	29	x′k+1	x′k+1	PROPN
ejpam-4829	165	30	}	}	PUNCT
ejpam-4829	165	31	is	be	AUX
ejpam-4829	165	32	not	not	PART
ejpam-4829	165	33	a	a	DET
ejpam-4829	165	34	module	module	NOUN
ejpam-4829	165	35	in	in	ADP
ejpam-4829	165	36	g[s	g[s	PROPN
ejpam-4829	165	37	∪	∪	ADJ
ejpam-4829	165	38	{	{	PUNCT
ejpam-4829	165	39	xk+1	xk+1	PROPN
ejpam-4829	165	40	,	,	PUNCT
ejpam-4829	165	41	x	x	NOUN
ejpam-4829	165	42	′	′	NUM
ejpam-4829	165	43	k+1	k+1	NOUN
ejpam-4829	165	44	}	}	PUNCT
ejpam-4829	165	45	]	]	PUNCT
ejpam-4829	165	46	.	.	PUNCT
ejpam-4829	166	1	based	base	VERB
ejpam-4829	166	2	on	on	ADP
ejpam-4829	166	3	assertion	assertion	NOUN
ejpam-4829	166	4	1	1	NUM
ejpam-4829	166	5	of	of	ADP
ejpam-4829	166	6	lemma	lemma	PROPN
ejpam-4829	166	7	1	1	NUM
ejpam-4829	166	8	,	,	PUNCT
ejpam-4829	166	9	h	h	NOUN
ejpam-4829	166	10	′	′	NOUN
ejpam-4829	166	11	is	be	AUX
ejpam-4829	166	12	prime	prime	ADJ
ejpam-4829	166	13	.	.	PUNCT
ejpam-4829	167	1	second	second	ADJ
ejpam-4829	167	2	,	,	PUNCT
ejpam-4829	167	3	q	q	X
ejpam-4829	167	4	≥	≥	NOUN
ejpam-4829	167	5	1	1	X
ejpam-4829	167	6	.	.	PUNCT
ejpam-4829	168	1	let	let	VERB
ejpam-4829	168	2	a	a	DET
ejpam-4829	168	3	∈	∈	PROPN
ejpam-4829	168	4	v	v	NOUN
ejpam-4829	168	5	.	.	PUNCT
ejpam-4829	169	1	consider	consider	VERB
ejpam-4829	169	2	x	x	PRON
ejpam-4829	169	3	,	,	PUNCT
ejpam-4829	169	4	x	x	PROPN
ejpam-4829	169	5	′	′	NUM
ejpam-4829	169	6	,	,	PUNCT
ejpam-4829	169	7	y	y	PROPN
ejpam-4829	169	8	and	and	CCONJ
ejpam-4829	169	9	z	z	PROPN
ejpam-4829	169	10	as	as	SCONJ
ejpam-4829	169	11	mentioned	mention	VERB
ejpam-4829	169	12	in	in	ADP
ejpam-4829	169	13	definition	definition	NOUN
ejpam-4829	169	14	1	1	NUM
ejpam-4829	169	15	.	.	PUNCT
ejpam-4829	169	16	suppose	suppose	VERB
ejpam-4829	170	1	w	w	NOUN
ejpam-4829	170	2	=	=	SYM
ejpam-4829	170	3	x	x	X
ejpam-4829	170	4	∪x	∪x	NOUN
ejpam-4829	170	5	′	′	NUM
ejpam-4829	170	6	∪	∪	X
ejpam-4829	170	7	{	{	PUNCT
ejpam-4829	170	8	a	a	NOUN
ejpam-4829	170	9	}	}	PUNCT
ejpam-4829	170	10	.	.	PUNCT
ejpam-4829	171	1	y	y	PROPN
ejpam-4829	171	2	̸=	̸=	PROPN
ejpam-4829	171	3	∅.	∅.	ADV
ejpam-4829	171	4	on	on	ADP
ejpam-4829	171	5	the	the	DET
ejpam-4829	171	6	contrary	contrary	NOUN
ejpam-4829	171	7	,	,	PUNCT
ejpam-4829	171	8	consider	consider	VERB
ejpam-4829	171	9	a	a	DET
ejpam-4829	171	10	non	non	ADJ
ejpam-4829	171	11	-	-	ADJ
ejpam-4829	171	12	trivial	trivial	ADJ
ejpam-4829	171	13	module	module	NOUN
ejpam-4829	171	14	m	m	PROPN
ejpam-4829	171	15	of	of	ADP
ejpam-4829	171	16	g.	g.	PROPN
ejpam-4829	172	1	the	the	DET
ejpam-4829	172	2	fact	fact	NOUN
ejpam-4829	172	3	that	that	SCONJ
ejpam-4829	172	4	g[w	g[w	PROPN
ejpam-4829	172	5	]	]	PUNCT
ejpam-4829	172	6	is	be	AUX
ejpam-4829	172	7	prime	prime	ADJ
ejpam-4829	172	8	implies	imply	VERB
ejpam-4829	172	9	that	that	SCONJ
ejpam-4829	172	10	m	m	VERB
ejpam-4829	172	11	∩w	∩w	ADJ
ejpam-4829	173	1	=	=	PUNCT
ejpam-4829	173	2	w	w	X
ejpam-4829	173	3	,	,	PUNCT
ejpam-4829	173	4	m	m	VERB
ejpam-4829	173	5	∩w	∩w	VERB
ejpam-4829	173	6	is	be	AUX
ejpam-4829	173	7	empty	empty	ADJ
ejpam-4829	173	8	or	or	CCONJ
ejpam-4829	173	9	m	m	VERB
ejpam-4829	173	10	∩w	∩w	ADJ
ejpam-4829	173	11	is	be	AUX
ejpam-4829	173	12	a	a	DET
ejpam-4829	173	13	singleton	singleton	NOUN
ejpam-4829	173	14	.	.	PUNCT
ejpam-4829	174	1	firstly	firstly	ADV
ejpam-4829	174	2	,	,	PUNCT
ejpam-4829	174	3	if	if	SCONJ
ejpam-4829	174	4	m∩w	m∩w	PROPN
ejpam-4829	174	5	=	=	PROPN
ejpam-4829	174	6	w	w	PROPN
ejpam-4829	174	7	,	,	PUNCT
ejpam-4829	174	8	then	then	ADV
ejpam-4829	174	9	w	w	PROPN
ejpam-4829	174	10	⊂	⊂	PROPN
ejpam-4829	174	11	m	m	VERB
ejpam-4829	174	12	.	.	PUNCT
ejpam-4829	175	1	let	let	VERB
ejpam-4829	175	2	y	y	PROPN
ejpam-4829	175	3	∈	∈	PROPN
ejpam-4829	175	4	v	v	ADP
ejpam-4829	175	5	\m	\m	NOUN
ejpam-4829	175	6	.	.	PUNCT
ejpam-4829	176	1	as	as	ADP
ejpam-4829	176	2	a	a	DET
ejpam-4829	176	3	consequence	consequence	NOUN
ejpam-4829	176	4	,	,	PUNCT
ejpam-4829	176	5	y	y	PROPN
ejpam-4829	176	6	∼	∼	NOUN
ejpam-4829	176	7	w	w	NOUN
ejpam-4829	176	8	.	.	PUNCT
ejpam-4829	177	1	thus	thus	ADV
ejpam-4829	177	2	,	,	PUNCT
ejpam-4829	177	3	|ng[x∪{y}](y)|	|ng[x∪{y}](y)|	PROPN
ejpam-4829	177	4	=	=	SYM
ejpam-4829	177	5	k	k	PROPN
ejpam-4829	177	6	and	and	CCONJ
ejpam-4829	177	7	by	by	ADP
ejpam-4829	177	8	definition	definition	NOUN
ejpam-4829	177	9	y	y	PROPN
ejpam-4829	177	10	is	be	AUX
ejpam-4829	177	11	unique	unique	ADJ
ejpam-4829	177	12	in	in	ADP
ejpam-4829	177	13	y	y	PROPN
ejpam-4829	177	14	.	.	PUNCT
ejpam-4829	178	1	there	there	PRON
ejpam-4829	178	2	is	be	VERB
ejpam-4829	178	3	z	z	PROPN
ejpam-4829	178	4	∈	∈	PROPN
ejpam-4829	178	5	y	y	PROPN
ejpam-4829	178	6	\{y	\{y	PROPN
ejpam-4829	178	7	}	}	PUNCT
ejpam-4829	178	8	such	such	ADJ
ejpam-4829	178	9	that	that	PRON
ejpam-4829	178	10	zy	zy	PROPN
ejpam-4829	178	11	/∈	/∈	PUNCT
ejpam-4829	179	1	e	e	NOUN
ejpam-4829	179	2	and	and	CCONJ
ejpam-4829	179	3	there	there	PRON
ejpam-4829	179	4	is	be	VERB
ejpam-4829	179	5	x	x	X
ejpam-4829	179	6	∈	∈	PROPN
ejpam-4829	179	7	x	x	PUNCT
ejpam-4829	179	8	such	such	ADJ
ejpam-4829	179	9	that	that	DET
ejpam-4829	179	10	zx	zx	NOUN
ejpam-4829	179	11	/∈	/∈	PUNCT
ejpam-4829	180	1	e	e	NOUN
ejpam-4829	180	2	and	and	CCONJ
ejpam-4829	180	3	,	,	PUNCT
ejpam-4829	180	4	for	for	ADP
ejpam-4829	180	5	all	all	PRON
ejpam-4829	180	6	x′	x′	PROPN
ejpam-4829	180	7	∈	∈	PROPN
ejpam-4829	180	8	x	x	SYM
ejpam-4829	180	9	′	′	NUM
ejpam-4829	180	10	,	,	PUNCT
ejpam-4829	180	11	zx′	zx′	PROPN
ejpam-4829	180	12	∈	∈	NOUN
ejpam-4829	180	13	e	e	NOUN
ejpam-4829	180	14	,	,	PUNCT
ejpam-4829	180	15	which	which	PRON
ejpam-4829	180	16	is	be	AUX
ejpam-4829	180	17	a	a	DET
ejpam-4829	180	18	contradiction	contradiction	NOUN
ejpam-4829	180	19	.	.	PUNCT
ejpam-4829	181	1	secondly	secondly	ADV
ejpam-4829	181	2	,	,	PUNCT
ejpam-4829	181	3	if	if	SCONJ
ejpam-4829	181	4	m∩w	m∩w	NOUN
ejpam-4829	181	5	=	=	NOUN
ejpam-4829	181	6	∅	∅	NOUN
ejpam-4829	181	7	,	,	PUNCT
ejpam-4829	181	8	then	then	ADV
ejpam-4829	181	9	m	m	PROPN
ejpam-4829	181	10	⊂	⊂	PROPN
ejpam-4829	181	11	y	y	PROPN
ejpam-4829	181	12	,	,	PUNCT
ejpam-4829	181	13	which	which	PRON
ejpam-4829	181	14	contradicts	contradict	VERB
ejpam-4829	181	15	the	the	DET
ejpam-4829	181	16	fact	fact	NOUN
ejpam-4829	181	17	that	that	SCONJ
ejpam-4829	181	18	ng[x∪{y1}](y1	ng[x∪{y1}](y1	PROPN
ejpam-4829	181	19	)	)	PUNCT
ejpam-4829	181	20	̸=	̸=	PROPN
ejpam-4829	181	21	ng[x∪{y2}](y2	ng[x∪{y2}](y2	PROPN
ejpam-4829	181	22	)	)	PUNCT
ejpam-4829	181	23	for	for	ADP
ejpam-4829	181	24	any	any	DET
ejpam-4829	181	25	y1	y1	NOUN
ejpam-4829	181	26	̸=	̸=	PROPN
ejpam-4829	181	27	y2	y2	NOUN
ejpam-4829	181	28	∈	∈	PROPN
ejpam-4829	181	29	y	y	PROPN
ejpam-4829	181	30	.	.	PUNCT
ejpam-4829	182	1	thirdly	thirdly	ADV
ejpam-4829	182	2	,	,	PUNCT
ejpam-4829	182	3	there	there	PRON
ejpam-4829	182	4	is	be	VERB
ejpam-4829	182	5	α	α	NOUN
ejpam-4829	182	6	in	in	ADP
ejpam-4829	182	7	v	v	ADP
ejpam-4829	182	8	such	such	ADJ
ejpam-4829	182	9	that	that	SCONJ
ejpam-4829	182	10	m	m	VERB
ejpam-4829	182	11	∩w	∩w	ADJ
ejpam-4829	183	1	=	=	X
ejpam-4829	184	1	{	{	PUNCT
ejpam-4829	184	2	α	α	NOUN
ejpam-4829	184	3	}	}	PUNCT
ejpam-4829	184	4	.	.	PUNCT
ejpam-4829	185	1	let	let	VERB
ejpam-4829	185	2	t	t	PROPN
ejpam-4829	185	3	∈	∈	PROPN
ejpam-4829	185	4	m	m	VERB
ejpam-4829	185	5	\	\	NOUN
ejpam-4829	185	6	{	{	PUNCT
ejpam-4829	185	7	α	α	NOUN
ejpam-4829	185	8	}	}	PUNCT
ejpam-4829	185	9	,	,	PUNCT
ejpam-4829	186	1	t	t	PROPN
ejpam-4829	186	2	∈	∈	PROPN
ejpam-4829	186	3	y	y	PROPN
ejpam-4829	186	4	.	.	PUNCT
ejpam-4829	187	1	then	then	ADV
ejpam-4829	187	2	,	,	PUNCT
ejpam-4829	187	3	there	there	PRON
ejpam-4829	187	4	is	be	VERB
ejpam-4829	187	5	x	x	X
ejpam-4829	187	6	∈	∈	PROPN
ejpam-4829	187	7	x	x	PUNCT
ejpam-4829	187	8	such	such	ADJ
ejpam-4829	187	9	that	that	DET
ejpam-4829	187	10	xt	xt	PROPN
ejpam-4829	187	11	∈	∈	PROPN
ejpam-4829	187	12	e.	e.	PROPN
ejpam-4829	187	13	α	α	PROPN
ejpam-4829	187	14	̸=	̸=	PROPN
ejpam-4829	187	15	a	a	DET
ejpam-4829	187	16	because	because	NOUN
ejpam-4829	187	17	,	,	PUNCT
ejpam-4829	187	18	for	for	ADP
ejpam-4829	187	19	all	all	DET
ejpam-4829	187	20	x	x	SYM
ejpam-4829	187	21	∈	∈	PROPN
ejpam-4829	187	22	x	x	NOUN
ejpam-4829	187	23	,	,	PUNCT
ejpam-4829	187	24	ax	ax	NOUN
ejpam-4829	187	25	/∈	/∈	PUNCT
ejpam-4829	187	26	e	e	NOUN
ejpam-4829	187	27	and	and	CCONJ
ejpam-4829	187	28	tx	tx	PROPN
ejpam-4829	187	29	∈	∈	PROPN
ejpam-4829	187	30	e.	e.	PROPN
ejpam-4829	187	31	α	α	PROPN
ejpam-4829	187	32	/∈	/∈	PUNCT
ejpam-4829	187	33	x	x	PUNCT
ejpam-4829	187	34	since	since	SCONJ
ejpam-4829	187	35	,	,	PUNCT
ejpam-4829	187	36	for	for	ADP
ejpam-4829	187	37	every	every	DET
ejpam-4829	187	38	x	x	SYM
ejpam-4829	187	39	∈	∈	PROPN
ejpam-4829	187	40	x	x	NOUN
ejpam-4829	187	41	,	,	PUNCT
ejpam-4829	187	42	ax	ax	NOUN
ejpam-4829	187	43	/∈	/∈	PUNCT
ejpam-4829	187	44	e	e	NOUN
ejpam-4829	187	45	and	and	CCONJ
ejpam-4829	187	46	at	at	ADP
ejpam-4829	187	47	∈	∈	PROPN
ejpam-4829	187	48	e.	e.	PROPN
ejpam-4829	187	49	otherwise	otherwise	ADV
ejpam-4829	187	50	,	,	PUNCT
ejpam-4829	187	51	there	there	PRON
ejpam-4829	187	52	is	be	VERB
ejpam-4829	187	53	x′	x′	PROPN
ejpam-4829	187	54	∈	∈	PROPN
ejpam-4829	187	55	x	x	PUNCT
ejpam-4829	187	56	′	′	NUM
ejpam-4829	187	57	such	such	ADJ
ejpam-4829	187	58	that	that	SCONJ
ejpam-4829	187	59	α	α	NOUN
ejpam-4829	187	60	=	=	PUNCT
ejpam-4829	187	61	x′.	x′.	PROPN
ejpam-4829	187	62	then	then	ADV
ejpam-4829	187	63	,	,	PUNCT
ejpam-4829	187	64	there	there	PRON
ejpam-4829	187	65	is	be	VERB
ejpam-4829	187	66	x	x	X
ejpam-4829	187	67	∈	∈	PROPN
ejpam-4829	187	68	x	x	PUNCT
ejpam-4829	187	69	such	such	ADJ
ejpam-4829	187	70	that	that	DET
ejpam-4829	187	71	xx′	xx′	PROPN
ejpam-4829	187	72	/∈	/∈	PUNCT
ejpam-4829	188	1	e	e	NOUN
ejpam-4829	188	2	and	and	CCONJ
ejpam-4829	188	3	ax′	ax′	PROPN
ejpam-4829	188	4	∈	∈	PROPN
ejpam-4829	188	5	e	e	NOUN
ejpam-4829	188	6	,	,	PUNCT
ejpam-4829	188	7	which	which	PRON
ejpam-4829	188	8	is	be	AUX
ejpam-4829	188	9	a	a	DET
ejpam-4829	188	10	contradiction	contradiction	NOUN
ejpam-4829	188	11	.	.	PUNCT
ejpam-4829	189	1	thus	thus	ADV
ejpam-4829	189	2	,	,	PUNCT
ejpam-4829	189	3	α	α	PROPN
ejpam-4829	189	4	/∈	/∈	PUNCT
ejpam-4829	190	1	x	x	PROPN
ejpam-4829	190	2	′.	′.	PROPN
ejpam-4829	190	3	therefore	therefore	ADV
ejpam-4829	190	4	,	,	PUNCT
ejpam-4829	190	5	g	g	PROPN
ejpam-4829	190	6	is	be	AUX
ejpam-4829	190	7	prime	prime	ADJ
ejpam-4829	190	8	.	.	PUNCT
ejpam-4829	191	1	lemma	lemma	PROPN
ejpam-4829	191	2	3	3	X
ejpam-4829	191	3	.	.	PUNCT
ejpam-4829	192	1	let	let	VERB
ejpam-4829	192	2	h	h	PRON
ejpam-4829	192	3	be	be	AUX
ejpam-4829	192	4	a	a	DET
ejpam-4829	192	5	decomposable	decomposable	ADJ
ejpam-4829	192	6	graph	graph	NOUN
ejpam-4829	192	7	with	with	ADP
ejpam-4829	192	8	a	a	DET
ejpam-4829	192	9	prime	prime	ADJ
ejpam-4829	192	10	frame	frame	NOUN
ejpam-4829	192	11	.	.	PUNCT
ejpam-4829	193	1	for	for	ADP
ejpam-4829	193	2	any	any	DET
ejpam-4829	193	3	module	module	NOUN
ejpam-4829	193	4	m	m	NOUN
ejpam-4829	193	5	∈	∈	NOUN
ejpam-4829	193	6	p(h	p(h	NOUN
ejpam-4829	193	7	)	)	PUNCT
ejpam-4829	193	8	,	,	PUNCT
ejpam-4829	193	9	there	there	PRON
ejpam-4829	193	10	are	be	VERB
ejpam-4829	193	11	two	two	NUM
ejpam-4829	193	12	distinct	distinct	ADJ
ejpam-4829	193	13	vertices	vertex	NOUN
ejpam-4829	193	14	y	y	PROPN
ejpam-4829	193	15	,	,	PUNCT
ejpam-4829	193	16	z	z	PROPN
ejpam-4829	193	17	∈	∈	PROPN
ejpam-4829	193	18	v	v	ADP
ejpam-4829	193	19	(	(	PUNCT
ejpam-4829	193	20	h	h	NOUN
ejpam-4829	193	21	)	)	PUNCT
ejpam-4829	193	22	\m	\m	NOUN
ejpam-4829	193	23	such	such	ADJ
ejpam-4829	193	24	that	that	SCONJ
ejpam-4829	193	25	y	y	PROPN
ejpam-4829	193	26	∈	∈	PROPN
ejpam-4829	193	27	nh(m	nh(m	X
ejpam-4829	193	28	)	)	PUNCT
ejpam-4829	193	29	,	,	PUNCT
ejpam-4829	193	30	z	z	NOUN
ejpam-4829	193	31	/∈	/∈	PUNCT
ejpam-4829	193	32	nh(m	nh(m	NUM
ejpam-4829	193	33	)	)	PUNCT
ejpam-4829	193	34	and	and	CCONJ
ejpam-4829	193	35	yz	yz	PROPN
ejpam-4829	193	36	/∈	/∈	PUNCT
ejpam-4829	193	37	e(h	e(h	PROPN
ejpam-4829	193	38	)	)	PUNCT
ejpam-4829	193	39	.	.	PUNCT
ejpam-4829	194	1	proof	proof	NOUN
ejpam-4829	194	2	.	.	PUNCT
ejpam-4829	195	1	let	let	VERB
ejpam-4829	195	2	h	h	NOUN
ejpam-4829	195	3	=	=	PUNCT
ejpam-4829	195	4	(	(	PUNCT
ejpam-4829	195	5	v	v	NOUN
ejpam-4829	195	6	,	,	PUNCT
ejpam-4829	195	7	e	e	NOUN
ejpam-4829	195	8	)	)	PUNCT
ejpam-4829	195	9	be	be	AUX
ejpam-4829	195	10	a	a	DET
ejpam-4829	195	11	decomposable	decomposable	ADJ
ejpam-4829	195	12	graph	graph	NOUN
ejpam-4829	195	13	with	with	ADP
ejpam-4829	195	14	a	a	DET
ejpam-4829	195	15	prime	prime	ADJ
ejpam-4829	195	16	frame	frame	NOUN
ejpam-4829	195	17	.	.	PUNCT
ejpam-4829	196	1	let	let	VERB
ejpam-4829	196	2	m	m	PRON
ejpam-4829	196	3	∈	∈	NOUN
ejpam-4829	196	4	p(h	p(h	NOUN
ejpam-4829	196	5	)	)	PUNCT
ejpam-4829	196	6	be	be	AUX
ejpam-4829	196	7	a	a	DET
ejpam-4829	196	8	module	module	NOUN
ejpam-4829	196	9	of	of	ADP
ejpam-4829	196	10	h.	h.	PROPN
ejpam-4829	196	11	as	as	SCONJ
ejpam-4829	196	12	h	h	NOUN
ejpam-4829	196	13	has	have	VERB
ejpam-4829	196	14	a	a	DET
ejpam-4829	196	15	prime	prime	ADJ
ejpam-4829	196	16	frame	frame	NOUN
ejpam-4829	196	17	,	,	PUNCT
ejpam-4829	196	18	nh(m	nh(m	NOUN
ejpam-4829	196	19	)	)	PUNCT
ejpam-4829	196	20	̸=	̸=	NOUN
ejpam-4829	196	21	∅	∅	NOUN
ejpam-4829	196	22	and	and	CCONJ
ejpam-4829	196	23	v	v	ADP
ejpam-4829	196	24	\	\	PROPN
ejpam-4829	196	25	(	(	PUNCT
ejpam-4829	196	26	m	m	NOUN
ejpam-4829	196	27	∪nh(m	∪nh(m	NOUN
ejpam-4829	196	28	)	)	PUNCT
ejpam-4829	196	29	)	)	PUNCT
ejpam-4829	197	1	̸=	̸=	PROPN
ejpam-4829	197	2	∅.	∅.	VERB
ejpam-4829	197	3	on	on	ADP
ejpam-4829	197	4	the	the	DET
ejpam-4829	197	5	contrary	contrary	NOUN
ejpam-4829	197	6	,	,	PUNCT
ejpam-4829	197	7	suppose	suppose	VERB
ejpam-4829	197	8	that	that	SCONJ
ejpam-4829	197	9	,	,	PUNCT
ejpam-4829	197	10	for	for	ADP
ejpam-4829	197	11	any	any	DET
ejpam-4829	197	12	y	y	PROPN
ejpam-4829	197	13	∈	∈	PROPN
ejpam-4829	197	14	nh(m	nh(m	X
ejpam-4829	197	15	)	)	PUNCT
ejpam-4829	197	16	and	and	CCONJ
ejpam-4829	197	17	z	z	NOUN
ejpam-4829	197	18	/∈	/∈	PUNCT
ejpam-4829	198	1	(	(	PUNCT
ejpam-4829	198	2	m	m	NOUN
ejpam-4829	198	3	∪	∪	ADJ
ejpam-4829	198	4	nh(m	nh(m	NOUN
ejpam-4829	198	5	)	)	PUNCT
ejpam-4829	198	6	)	)	PUNCT
ejpam-4829	198	7	,	,	PUNCT
ejpam-4829	198	8	yz	yz	PROPN
ejpam-4829	198	9	∈	∈	PROPN
ejpam-4829	198	10	e.	e.	PROPN
ejpam-4829	198	11	it	it	PRON
ejpam-4829	198	12	follows	follow	VERB
ejpam-4829	198	13	that	that	SCONJ
ejpam-4829	198	14	∀y	∀y	PROPN
ejpam-4829	198	15	∈	∈	PROPN
ejpam-4829	198	16	nh(m	nh(m	X
ejpam-4829	198	17	)	)	PUNCT
ejpam-4829	198	18	and	and	CCONJ
ejpam-4829	198	19	∀t	∀t	PROPN
ejpam-4829	198	20	∈	∈	PROPN
ejpam-4829	198	21	v	v	ADP
ejpam-4829	198	22	\nh(m	\nh(m	PROPN
ejpam-4829	198	23	)	)	PUNCT
ejpam-4829	198	24	,	,	PUNCT
ejpam-4829	198	25	yt	yt	PROPN
ejpam-4829	198	26	∈	∈	PROPN
ejpam-4829	198	27	e.	e.	PROPN
ejpam-4829	198	28	then	then	ADV
ejpam-4829	198	29	,	,	PUNCT
ejpam-4829	198	30	{	{	PUNCT
ejpam-4829	198	31	nh(m	nh(m	ADJ
ejpam-4829	198	32	)	)	PUNCT
ejpam-4829	198	33	,	,	PUNCT
ejpam-4829	198	34	(	(	PUNCT
ejpam-4829	198	35	v	v	NOUN
ejpam-4829	198	36	\nh(m	\nh(m	NUM
ejpam-4829	198	37	)	)	PUNCT
ejpam-4829	198	38	)	)	PUNCT
ejpam-4829	198	39	}	}	PUNCT
ejpam-4829	198	40	m.	m.	NOUN
ejpam-4829	198	41	bouaziz	bouaziz	PROPN
ejpam-4829	198	42	et	et	PROPN
ejpam-4829	198	43	al	al	PROPN
ejpam-4829	198	44	.	.	PUNCT
ejpam-4829	198	45	/	/	SYM
ejpam-4829	198	46	eur	eur	PROPN
ejpam-4829	198	47	.	.	PUNCT
ejpam-4829	199	1	j.	j.	PROPN
ejpam-4829	199	2	pure	pure	PROPN
ejpam-4829	199	3	appl	appl	PROPN
ejpam-4829	199	4	.	.	PROPN
ejpam-4829	199	5	math	math	PROPN
ejpam-4829	199	6	,	,	PUNCT
ejpam-4829	199	7	16	16	NUM
ejpam-4829	199	8	(	(	PUNCT
ejpam-4829	199	9	4	4	NUM
ejpam-4829	199	10	)	)	PUNCT
ejpam-4829	199	11	(	(	PUNCT
ejpam-4829	199	12	2023	2023	NUM
ejpam-4829	199	13	)	)	PUNCT
ejpam-4829	199	14	,	,	PUNCT
ejpam-4829	199	15	2786	2786	NUM
ejpam-4829	199	16	-	-	SYM
ejpam-4829	199	17	2797	2797	NUM
ejpam-4829	199	18	2793	2793	NUM
ejpam-4829	199	19	is	be	AUX
ejpam-4829	199	20	a	a	DET
ejpam-4829	199	21	modular	modular	ADJ
ejpam-4829	199	22	partition	partition	NOUN
ejpam-4829	199	23	of	of	ADP
ejpam-4829	199	24	h	h	NOUN
ejpam-4829	199	25	with	with	ADP
ejpam-4829	199	26	two	two	NUM
ejpam-4829	199	27	elements	element	NOUN
ejpam-4829	199	28	.	.	PUNCT
ejpam-4829	200	1	as	as	ADP
ejpam-4829	200	2	m	m	PROPN
ejpam-4829	200	3	̸=	̸=	PROPN
ejpam-4829	200	4	v	v	ADP
ejpam-4829	200	5	\nh(m	\nh(m	NOUN
ejpam-4829	200	6	)	)	PUNCT
ejpam-4829	200	7	,	,	PUNCT
ejpam-4829	200	8	m	m	VERB
ejpam-4829	200	9	⊂	⊂	PROPN
ejpam-4829	200	10	v	v	ADP
ejpam-4829	200	11	\nh(m	\nh(m	PROPN
ejpam-4829	200	12	)	)	PUNCT
ejpam-4829	200	13	,	,	PUNCT
ejpam-4829	200	14	which	which	PRON
ejpam-4829	200	15	contradict	contradict	VERB
ejpam-4829	200	16	the	the	DET
ejpam-4829	200	17	fact	fact	NOUN
ejpam-4829	200	18	that	that	SCONJ
ejpam-4829	200	19	m	m	VERB
ejpam-4829	200	20	∈	∈	NOUN
ejpam-4829	200	21	p(h	p(h	NOUN
ejpam-4829	200	22	)	)	PUNCT
ejpam-4829	200	23	.	.	PUNCT
ejpam-4829	201	1	to	to	PART
ejpam-4829	201	2	prove	prove	VERB
ejpam-4829	201	3	the	the	DET
ejpam-4829	201	4	main	main	ADJ
ejpam-4829	201	5	result	result	NOUN
ejpam-4829	201	6	,	,	PUNCT
ejpam-4829	201	7	we	we	PRON
ejpam-4829	201	8	use	use	VERB
ejpam-4829	201	9	the	the	DET
ejpam-4829	201	10	following	follow	VERB
ejpam-4829	201	11	five	five	NUM
ejpam-4829	201	12	lemmas	lemmas	ADJ
ejpam-4829	201	13	.	.	PUNCT
ejpam-4829	202	1	lemma	lemma	PROPN
ejpam-4829	202	2	4	4	X
ejpam-4829	202	3	.	.	PUNCT
ejpam-4829	203	1	let	let	VERB
ejpam-4829	203	2	g	g	PRON
ejpam-4829	203	3	be	be	AUX
ejpam-4829	203	4	a	a	DET
ejpam-4829	203	5	decomposable	decomposable	ADJ
ejpam-4829	203	6	graph	graph	NOUN
ejpam-4829	203	7	with	with	ADP
ejpam-4829	203	8	a	a	DET
ejpam-4829	203	9	prime	prime	ADJ
ejpam-4829	203	10	frame	frame	NOUN
ejpam-4829	203	11	such	such	ADJ
ejpam-4829	203	12	that	that	SCONJ
ejpam-4829	203	13	g	g	PROPN
ejpam-4829	203	14	∈	∈	PROPN
ejpam-4829	203	15	b.	b.	PROPN
ejpam-4829	204	1	if	if	SCONJ
ejpam-4829	204	2	e	e	PROPN
ejpam-4829	204	3	is	be	AUX
ejpam-4829	204	4	an	an	DET
ejpam-4829	204	5	edge	edge	NOUN
ejpam-4829	204	6	in	in	ADP
ejpam-4829	204	7	g	g	NOUN
ejpam-4829	204	8	,	,	PUNCT
ejpam-4829	204	9	then	then	ADV
ejpam-4829	204	10	g+	g+	PROPN
ejpam-4829	204	11	e	e	NOUN
ejpam-4829	204	12	is	be	AUX
ejpam-4829	204	13	a	a	DET
ejpam-4829	204	14	decomposable	decomposable	ADJ
ejpam-4829	204	15	graph	graph	NOUN
ejpam-4829	204	16	.	.	PUNCT
ejpam-4829	205	1	proof	proof	NOUN
ejpam-4829	205	2	.	.	PUNCT
ejpam-4829	206	1	let	let	VERB
ejpam-4829	206	2	g	g	PROPN
ejpam-4829	206	3	∈	∈	PROPN
ejpam-4829	206	4	b	b	PROPN
ejpam-4829	206	5	and	and	CCONJ
ejpam-4829	206	6	e	e	PROPN
ejpam-4829	206	7	∈	∈	PROPN
ejpam-4829	206	8	g.	g.	NOUN
ejpam-4829	206	9	consider	consider	VERB
ejpam-4829	206	10	the	the	DET
ejpam-4829	206	11	graph	graph	NOUN
ejpam-4829	206	12	h	h	NOUN
ejpam-4829	206	13	=	=	PUNCT
ejpam-4829	206	14	g+	g+	PROPN
ejpam-4829	207	1	e.	e.	PROPN
ejpam-4829	207	2	firstly	firstly	ADV
ejpam-4829	207	3	,	,	PUNCT
ejpam-4829	207	4	if	if	SCONJ
ejpam-4829	207	5	|v	|v	PROPN
ejpam-4829	207	6	(	(	PUNCT
ejpam-4829	207	7	g)|	g)|	NOUN
ejpam-4829	207	8	=	=	SYM
ejpam-4829	207	9	5	5	NUM
ejpam-4829	207	10	,	,	PUNCT
ejpam-4829	207	11	then	then	ADV
ejpam-4829	207	12	g	g	PROPN
ejpam-4829	207	13	≃	≃	NOUN
ejpam-4829	207	14	β	β	X
ejpam-4829	207	15	.	.	PUNCT
ejpam-4829	208	1	if	if	SCONJ
ejpam-4829	208	2	e	e	PROPN
ejpam-4829	208	3	is	be	AUX
ejpam-4829	208	4	one	one	NUM
ejpam-4829	208	5	of	of	ADP
ejpam-4829	208	6	the	the	DET
ejpam-4829	208	7	edges	edge	NOUN
ejpam-4829	208	8	x′x	x′x	PROPN
ejpam-4829	208	9	and	and	CCONJ
ejpam-4829	208	10	x′y	x′y	PROPN
ejpam-4829	208	11	,	,	PUNCT
ejpam-4829	208	12	then	then	ADV
ejpam-4829	208	13	{	{	PUNCT
ejpam-4829	208	14	a	a	PRON
ejpam-4829	208	15	,	,	PUNCT
ejpam-4829	208	16	a′	a′	PROPN
ejpam-4829	208	17	}	}	PUNCT
ejpam-4829	208	18	is	be	AUX
ejpam-4829	208	19	still	still	ADV
ejpam-4829	208	20	a	a	DET
ejpam-4829	208	21	module	module	NOUN
ejpam-4829	208	22	in	in	ADP
ejpam-4829	208	23	g+	g+	PROPN
ejpam-4829	208	24	e.	e.	PROPN
ejpam-4829	208	25	thus	thus	ADV
ejpam-4829	208	26	,	,	PUNCT
ejpam-4829	208	27	g+	g+	ADP
ejpam-4829	208	28	e	e	NOUN
ejpam-4829	208	29	is	be	AUX
ejpam-4829	208	30	a	a	DET
ejpam-4829	208	31	decomposable	decomposable	ADJ
ejpam-4829	208	32	graph	graph	NOUN
ejpam-4829	208	33	.	.	PUNCT
ejpam-4829	209	1	otherwise	otherwise	ADV
ejpam-4829	209	2	,	,	PUNCT
ejpam-4829	209	3	e	e	X
ejpam-4829	209	4	=	=	PUNCT
ejpam-4829	209	5	ax	ax	NOUN
ejpam-4829	209	6	or	or	CCONJ
ejpam-4829	209	7	e	e	NOUN
ejpam-4829	209	8	=	=	PROPN
ejpam-4829	209	9	a′x	a′x	PROPN
ejpam-4829	209	10	.	.	PUNCT
ejpam-4829	210	1	without	without	ADP
ejpam-4829	210	2	loss	loss	NOUN
ejpam-4829	210	3	of	of	ADP
ejpam-4829	210	4	generality	generality	NOUN
ejpam-4829	210	5	,	,	PUNCT
ejpam-4829	210	6	we	we	PRON
ejpam-4829	210	7	add	add	VERB
ejpam-4829	210	8	ax	ax	NOUN
ejpam-4829	210	9	.	.	PUNCT
ejpam-4829	211	1	then	then	ADV
ejpam-4829	211	2	,	,	PUNCT
ejpam-4829	211	3	{	{	PUNCT
ejpam-4829	211	4	x	x	NOUN
ejpam-4829	211	5	,	,	PUNCT
ejpam-4829	211	6	x′	x′	NUM
ejpam-4829	211	7	,	,	PUNCT
ejpam-4829	211	8	a′	a′	PROPN
ejpam-4829	211	9	,	,	PUNCT
ejpam-4829	211	10	y	y	PRON
ejpam-4829	211	11	}	}	PUNCT
ejpam-4829	211	12	is	be	AUX
ejpam-4829	211	13	a	a	DET
ejpam-4829	211	14	non	non	ADJ
ejpam-4829	211	15	-	-	ADJ
ejpam-4829	211	16	trivial	trivial	ADJ
ejpam-4829	211	17	module	module	NOUN
ejpam-4829	211	18	.	.	PUNCT
ejpam-4829	212	1	as	as	ADP
ejpam-4829	212	2	a	a	DET
ejpam-4829	212	3	result	result	NOUN
ejpam-4829	212	4	,	,	PUNCT
ejpam-4829	212	5	g+	g+	X
ejpam-4829	212	6	e	e	NOUN
ejpam-4829	212	7	is	be	AUX
ejpam-4829	212	8	a	a	DET
ejpam-4829	212	9	decomposable	decomposable	ADJ
ejpam-4829	212	10	graph	graph	NOUN
ejpam-4829	212	11	.	.	PUNCT
ejpam-4829	213	1	secondly	secondly	ADV
ejpam-4829	213	2	,	,	PUNCT
ejpam-4829	213	3	|v	|v	PROPN
ejpam-4829	213	4	(	(	PUNCT
ejpam-4829	213	5	g)|	g)|	X
ejpam-4829	213	6	≥	≥	NOUN
ejpam-4829	213	7	6	6	NUM
ejpam-4829	213	8	.	.	PUNCT
ejpam-4829	214	1	if	if	SCONJ
ejpam-4829	214	2	the	the	DET
ejpam-4829	214	3	edge	edge	NOUN
ejpam-4829	214	4	e	e	NOUN
ejpam-4829	214	5	=	=	PUNCT
ejpam-4829	214	6	αβ	αβ	INTJ
ejpam-4829	214	7	where	where	SCONJ
ejpam-4829	214	8	α	α	NOUN
ejpam-4829	214	9	and	and	CCONJ
ejpam-4829	214	10	β	β	X
ejpam-4829	214	11	are	be	AUX
ejpam-4829	214	12	two	two	NUM
ejpam-4829	214	13	vertices	vertex	NOUN
ejpam-4829	214	14	in	in	ADP
ejpam-4829	214	15	x	x	PUNCT
ejpam-4829	214	16	∪	∪	PROPN
ejpam-4829	214	17	y	y	PROPN
ejpam-4829	214	18	,	,	PUNCT
ejpam-4829	214	19	then	then	ADV
ejpam-4829	214	20	{	{	PUNCT
ejpam-4829	214	21	a	a	PRON
ejpam-4829	214	22	,	,	PUNCT
ejpam-4829	214	23	a′	a′	PROPN
ejpam-4829	214	24	}	}	PUNCT
ejpam-4829	214	25	is	be	AUX
ejpam-4829	214	26	still	still	ADV
ejpam-4829	214	27	a	a	DET
ejpam-4829	214	28	module	module	NOUN
ejpam-4829	214	29	in	in	ADP
ejpam-4829	214	30	g+	g+	PROPN
ejpam-4829	214	31	e.	e.	PROPN
ejpam-4829	214	32	thus	thus	ADV
ejpam-4829	214	33	,	,	PUNCT
ejpam-4829	214	34	g+	g+	ADP
ejpam-4829	214	35	e	e	NOUN
ejpam-4829	214	36	is	be	AUX
ejpam-4829	214	37	a	a	DET
ejpam-4829	214	38	decomposable	decomposable	ADJ
ejpam-4829	214	39	graph	graph	NOUN
ejpam-4829	214	40	.	.	PUNCT
ejpam-4829	215	1	otherwise	otherwise	ADV
ejpam-4829	215	2	,	,	PUNCT
ejpam-4829	215	3	e	e	X
ejpam-4829	215	4	=	=	PUNCT
ejpam-4829	215	5	ax	ax	NOUN
ejpam-4829	215	6	or	or	CCONJ
ejpam-4829	215	7	e	e	NOUN
ejpam-4829	215	8	=	=	SYM
ejpam-4829	215	9	a′x	a′x	PROPN
ejpam-4829	215	10	for	for	ADP
ejpam-4829	215	11	x	x	SYM
ejpam-4829	215	12	∈	∈	PROPN
ejpam-4829	215	13	x.	x.	NOUN
ejpam-4829	215	14	assume	assume	VERB
ejpam-4829	215	15	,	,	PUNCT
ejpam-4829	215	16	without	without	ADP
ejpam-4829	215	17	loss	loss	NOUN
ejpam-4829	215	18	of	of	ADP
ejpam-4829	215	19	generality	generality	NOUN
ejpam-4829	215	20	,	,	PUNCT
ejpam-4829	215	21	that	that	SCONJ
ejpam-4829	215	22	e	e	NOUN
ejpam-4829	215	23	=	=	PUNCT
ejpam-4829	215	24	ax	ax	NOUN
ejpam-4829	215	25	and	and	CCONJ
ejpam-4829	215	26	there	there	PRON
ejpam-4829	215	27	is	be	VERB
ejpam-4829	215	28	exactly	exactly	ADV
ejpam-4829	215	29	one	one	NUM
ejpam-4829	215	30	vertex	vertex	NOUN
ejpam-4829	215	31	x′	x′	PROPN
ejpam-4829	215	32	in	in	ADP
ejpam-4829	215	33	x	x	X
ejpam-4829	215	34	′	′	NUM
ejpam-4829	215	35	such	such	ADJ
ejpam-4829	215	36	that	that	SCONJ
ejpam-4829	215	37	xx′	xx′	PROPN
ejpam-4829	215	38	∈	∈	PROPN
ejpam-4829	215	39	e.	e.	PROPN
ejpam-4829	215	40	thus	thus	ADV
ejpam-4829	215	41	,	,	PUNCT
ejpam-4829	215	42	{	{	PUNCT
ejpam-4829	215	43	ax′	ax′	NOUN
ejpam-4829	215	44	}	}	PUNCT
ejpam-4829	215	45	is	be	AUX
ejpam-4829	215	46	a	a	DET
ejpam-4829	215	47	module	module	NOUN
ejpam-4829	215	48	in	in	ADP
ejpam-4829	215	49	g+	g+	PROPN
ejpam-4829	215	50	e.	e.	PROPN
ejpam-4829	215	51	therefore	therefore	ADV
ejpam-4829	215	52	,	,	PUNCT
ejpam-4829	215	53	g+	g+	PROPN
ejpam-4829	215	54	e	e	NOUN
ejpam-4829	215	55	is	be	AUX
ejpam-4829	215	56	a	a	DET
ejpam-4829	215	57	decomposable	decomposable	ADJ
ejpam-4829	215	58	graph	graph	NOUN
ejpam-4829	215	59	.	.	PUNCT
ejpam-4829	216	1	lemma	lemma	PROPN
ejpam-4829	216	2	5	5	X
ejpam-4829	216	3	.	.	PUNCT
ejpam-4829	217	1	let	let	VERB
ejpam-4829	217	2	g	g	PRON
ejpam-4829	217	3	be	be	AUX
ejpam-4829	217	4	a	a	DET
ejpam-4829	217	5	decomposable	decomposable	ADJ
ejpam-4829	217	6	graph	graph	NOUN
ejpam-4829	217	7	with	with	ADP
ejpam-4829	217	8	a	a	DET
ejpam-4829	217	9	prime	prime	ADJ
ejpam-4829	217	10	frame	frame	NOUN
ejpam-4829	217	11	containing	contain	VERB
ejpam-4829	217	12	only	only	ADV
ejpam-4829	217	13	one	one	NUM
ejpam-4829	217	14	nontrivial	nontrivial	ADJ
ejpam-4829	217	15	module	module	NOUN
ejpam-4829	217	16	m	m	NOUN
ejpam-4829	217	17	.	.	PUNCT
ejpam-4829	218	1	if	if	SCONJ
ejpam-4829	218	2	g[m	g[m	NOUN
ejpam-4829	218	3	]	]	PUNCT
ejpam-4829	218	4	=	=	SYM
ejpam-4829	218	5	k2	k2	PROPN
ejpam-4829	218	6	,	,	PUNCT
ejpam-4829	218	7	then	then	ADV
ejpam-4829	218	8	there	there	PRON
ejpam-4829	218	9	is	be	VERB
ejpam-4829	218	10	an	an	DET
ejpam-4829	218	11	edge	edge	NOUN
ejpam-4829	218	12	e	e	NOUN
ejpam-4829	218	13	in	in	ADP
ejpam-4829	218	14	g	g	PROPN
ejpam-4829	218	15	such	such	DET
ejpam-4829	218	16	that	that	DET
ejpam-4829	218	17	g+	g+	NOUN
ejpam-4829	218	18	e	e	NOUN
ejpam-4829	218	19	is	be	AUX
ejpam-4829	218	20	prime	prime	ADJ
ejpam-4829	218	21	.	.	PUNCT
ejpam-4829	219	1	proof	proof	NOUN
ejpam-4829	219	2	.	.	PUNCT
ejpam-4829	220	1	let	let	VERB
ejpam-4829	220	2	g	g	PROPN
ejpam-4829	220	3	=	=	SYM
ejpam-4829	220	4	(	(	PUNCT
ejpam-4829	220	5	v	v	NOUN
ejpam-4829	220	6	,	,	PUNCT
ejpam-4829	220	7	e	e	NOUN
ejpam-4829	220	8	)	)	PUNCT
ejpam-4829	220	9	be	be	AUX
ejpam-4829	220	10	a	a	DET
ejpam-4829	220	11	decomposable	decomposable	ADJ
ejpam-4829	220	12	graph	graph	NOUN
ejpam-4829	220	13	with	with	ADP
ejpam-4829	220	14	a	a	DET
ejpam-4829	220	15	prime	prime	ADJ
ejpam-4829	220	16	frame	frame	NOUN
ejpam-4829	220	17	containing	contain	VERB
ejpam-4829	220	18	only	only	ADV
ejpam-4829	220	19	one	one	NUM
ejpam-4829	220	20	non	non	ADJ
ejpam-4829	220	21	-	-	ADJ
ejpam-4829	220	22	trivial	trivial	ADJ
ejpam-4829	220	23	module	module	NOUN
ejpam-4829	220	24	m	m	NOUN
ejpam-4829	220	25	=	=	PUNCT
ejpam-4829	220	26	{	{	PUNCT
ejpam-4829	220	27	a	a	PRON
ejpam-4829	220	28	,	,	PUNCT
ejpam-4829	220	29	a′	a′	ADJ
ejpam-4829	220	30	}	}	PUNCT
ejpam-4829	220	31	such	such	ADJ
ejpam-4829	220	32	that	that	DET
ejpam-4829	220	33	g[m	g[m	NOUN
ejpam-4829	220	34	]	]	PUNCT
ejpam-4829	220	35	=	=	SYM
ejpam-4829	220	36	k2	k2	PROPN
ejpam-4829	220	37	and	and	CCONJ
ejpam-4829	220	38	e	e	NOUN
ejpam-4829	220	39	∈	∈	PROPN
ejpam-4829	220	40	e(g	e(g	PROPN
ejpam-4829	220	41	)	)	PUNCT
ejpam-4829	220	42	.	.	PUNCT
ejpam-4829	221	1	consider	consider	VERB
ejpam-4829	221	2	h	h	NOUN
ejpam-4829	221	3	=	=	SYM
ejpam-4829	221	4	g+	g+	PROPN
ejpam-4829	221	5	e.	e.	PROPN
ejpam-4829	221	6	based	base	VERB
ejpam-4829	221	7	on	on	ADP
ejpam-4829	221	8	lemma	lemma	PROPN
ejpam-4829	221	9	3	3	NUM
ejpam-4829	221	10	,	,	PUNCT
ejpam-4829	221	11	there	there	PRON
ejpam-4829	221	12	is	be	VERB
ejpam-4829	221	13	x	x	X
ejpam-4829	221	14	/∈	/∈	PUNCT
ejpam-4829	221	15	ng(m	ng(m	PROPN
ejpam-4829	221	16	)	)	PUNCT
ejpam-4829	221	17	and	and	CCONJ
ejpam-4829	221	18	x′	x′	PROPN
ejpam-4829	221	19	∈	∈	PROPN
ejpam-4829	221	20	ng(m	ng(m	VERB
ejpam-4829	221	21	)	)	PUNCT
ejpam-4829	221	22	such	such	ADJ
ejpam-4829	221	23	that	that	DET
ejpam-4829	221	24	xx′	xx′	PROPN
ejpam-4829	221	25	/∈	/∈	PUNCT
ejpam-4829	222	1	e(g	e(g	PROPN
ejpam-4829	222	2	)	)	PUNCT
ejpam-4829	222	3	.	.	PUNCT
ejpam-4829	223	1	if	if	SCONJ
ejpam-4829	223	2	e	e	NOUN
ejpam-4829	223	3	=	=	SYM
ejpam-4829	223	4	ax	ax	NOUN
ejpam-4829	223	5	,	,	PUNCT
ejpam-4829	223	6	then	then	ADV
ejpam-4829	223	7	h[{x	h[{x	NUM
ejpam-4829	223	8	,	,	PUNCT
ejpam-4829	223	9	a	a	PRON
ejpam-4829	223	10	,	,	PUNCT
ejpam-4829	223	11	x′	x′	NUM
ejpam-4829	223	12	,	,	PUNCT
ejpam-4829	223	13	a′	a′	PROPN
ejpam-4829	223	14	}	}	PUNCT
ejpam-4829	223	15	]	]	PUNCT
ejpam-4829	223	16	is	be	AUX
ejpam-4829	223	17	a	a	DET
ejpam-4829	223	18	p4	p4	ADJ
ejpam-4829	223	19	.	.	PUNCT
ejpam-4829	224	1	h	h	NOUN
ejpam-4829	225	1	−	−	PROPN
ejpam-4829	225	2	a	a	DET
ejpam-4829	225	3	=	=	X
ejpam-4829	225	4	g	g	PROPN
ejpam-4829	225	5	−	−	PROPN
ejpam-4829	226	1	a	a	PRON
ejpam-4829	226	2	is	be	AUX
ejpam-4829	226	3	prime	prime	ADJ
ejpam-4829	226	4	.	.	PUNCT
ejpam-4829	227	1	as	as	ADP
ejpam-4829	227	2	h[{x	h[{x	NOUN
ejpam-4829	227	3	,	,	PUNCT
ejpam-4829	227	4	a	a	DET
ejpam-4829	227	5	,	,	PUNCT
ejpam-4829	227	6	x′	x′	NUM
ejpam-4829	227	7	,	,	PUNCT
ejpam-4829	227	8	a′	a′	PROPN
ejpam-4829	227	9	}	}	PUNCT
ejpam-4829	227	10	]	]	PUNCT
ejpam-4829	227	11	is	be	AUX
ejpam-4829	227	12	a	a	DET
ejpam-4829	227	13	path	path	NOUN
ejpam-4829	227	14	p4	p4	NOUN
ejpam-4829	227	15	,	,	PUNCT
ejpam-4829	227	16	in	in	ADP
ejpam-4829	227	17	h	h	NOUN
ejpam-4829	227	18	,	,	PUNCT
ejpam-4829	227	19	a	a	PRON
ejpam-4829	227	20	/∈	/∈	NOUN
ejpam-4829	227	21	⟨v	⟨v	NOUN
ejpam-4829	227	22	\	\	PROPN
ejpam-4829	227	23	{	{	PUNCT
ejpam-4829	227	24	a}⟩	a}⟩	PROPN
ejpam-4829	227	25	,	,	PUNCT
ejpam-4829	227	26	a	a	PRON
ejpam-4829	227	27	/∈	/∈	PUNCT
ejpam-4829	227	28	(	(	PUNCT
ejpam-4829	227	29	v	v	NOUN
ejpam-4829	227	30	\	\	PROPN
ejpam-4829	227	31	{	{	PUNCT
ejpam-4829	227	32	a	a	NOUN
ejpam-4829	227	33	}	}	PUNCT
ejpam-4829	227	34	)	)	PUNCT
ejpam-4829	227	35	(	(	PUNCT
ejpam-4829	227	36	a′	a′	PROPN
ejpam-4829	227	37	)	)	PUNCT
ejpam-4829	227	38	,	,	PUNCT
ejpam-4829	227	39	a	a	DET
ejpam-4829	227	40	/∈	/∈	PUNCT
ejpam-4829	227	41	(	(	PUNCT
ejpam-4829	227	42	v	v	NOUN
ejpam-4829	227	43	\	\	PROPN
ejpam-4829	227	44	{	{	PUNCT
ejpam-4829	227	45	a	a	NOUN
ejpam-4829	227	46	}	}	PUNCT
ejpam-4829	227	47	)	)	PUNCT
ejpam-4829	227	48	(	(	PUNCT
ejpam-4829	227	49	x	x	X
ejpam-4829	227	50	)	)	PUNCT
ejpam-4829	227	51	and	and	CCONJ
ejpam-4829	227	52	a	a	DET
ejpam-4829	227	53	/∈	/∈	INTJ
ejpam-4829	227	54	(	(	PUNCT
ejpam-4829	227	55	v	v	NOUN
ejpam-4829	227	56	\	\	PROPN
ejpam-4829	227	57	{	{	PUNCT
ejpam-4829	227	58	a	a	NOUN
ejpam-4829	227	59	}	}	PUNCT
ejpam-4829	227	60	)	)	PUNCT
ejpam-4829	227	61	(	(	PUNCT
ejpam-4829	227	62	x′	x′	NUM
ejpam-4829	227	63	)	)	PUNCT
ejpam-4829	227	64	.	.	PUNCT
ejpam-4829	228	1	if	if	SCONJ
ejpam-4829	228	2	h	h	NOUN
ejpam-4829	228	3	is	be	AUX
ejpam-4829	228	4	not	not	PART
ejpam-4829	228	5	prime	prime	ADJ
ejpam-4829	228	6	,	,	PUNCT
ejpam-4829	228	7	then	then	ADV
ejpam-4829	228	8	there	there	PRON
ejpam-4829	228	9	is	be	VERB
ejpam-4829	228	10	y	y	PROPN
ejpam-4829	228	11	in	in	ADP
ejpam-4829	228	12	v	v	NOUN
ejpam-4829	228	13	\	\	NOUN
ejpam-4829	228	14	{	{	PUNCT
ejpam-4829	228	15	a	a	PRON
ejpam-4829	228	16	,	,	PUNCT
ejpam-4829	228	17	a′	a′	PROPN
ejpam-4829	228	18	,	,	PUNCT
ejpam-4829	228	19	x	x	NOUN
ejpam-4829	228	20	,	,	PUNCT
ejpam-4829	228	21	x′	x′	NUM
ejpam-4829	228	22	}	}	PUNCT
ejpam-4829	228	23	such	such	ADJ
ejpam-4829	228	24	that	that	SCONJ
ejpam-4829	228	25	a	a	DET
ejpam-4829	228	26	∈	∈	PROPN
ejpam-4829	228	27	(	(	PUNCT
ejpam-4829	228	28	v	v	NOUN
ejpam-4829	228	29	\	\	PROPN
ejpam-4829	228	30	{	{	PUNCT
ejpam-4829	228	31	a	a	NOUN
ejpam-4829	228	32	}	}	PUNCT
ejpam-4829	228	33	)	)	PUNCT
ejpam-4829	228	34	(	(	PUNCT
ejpam-4829	228	35	y	y	NOUN
ejpam-4829	228	36	)	)	PUNCT
ejpam-4829	228	37	.	.	PUNCT
ejpam-4829	229	1	hence	hence	ADV
ejpam-4829	229	2	,	,	PUNCT
ejpam-4829	229	3	a′y	a′y	ADJ
ejpam-4829	229	4	/∈	/∈	PUNCT
ejpam-4829	229	5	e(h	e(h	PROPN
ejpam-4829	229	6	)	)	PUNCT
ejpam-4829	229	7	because	because	SCONJ
ejpam-4829	229	8	a′a	a′a	PROPN
ejpam-4829	229	9	/∈	/∈	PUNCT
ejpam-4829	229	10	e(h	e(h	PROPN
ejpam-4829	229	11	)	)	PUNCT
ejpam-4829	229	12	.	.	PUNCT
ejpam-4829	230	1	thus	thus	ADV
ejpam-4829	230	2	,	,	PUNCT
ejpam-4829	230	3	ya	ya	PROPN
ejpam-4829	230	4	/∈	/∈	PUNCT
ejpam-4829	230	5	e(h	e(h	PROPN
ejpam-4829	230	6	)	)	PUNCT
ejpam-4829	230	7	and	and	CCONJ
ejpam-4829	230	8	{	{	PUNCT
ejpam-4829	230	9	xy	xy	PROPN
ejpam-4829	230	10	,	,	PUNCT
ejpam-4829	230	11	x′y	x′y	PROPN
ejpam-4829	230	12	}	}	PUNCT
ejpam-4829	230	13	⊆	⊆	NUM
ejpam-4829	230	14	e(h	e(h	NOUN
ejpam-4829	230	15	)	)	PUNCT
ejpam-4829	230	16	.	.	PUNCT
ejpam-4829	231	1	in	in	ADP
ejpam-4829	231	2	this	this	DET
ejpam-4829	231	3	case	case	NOUN
ejpam-4829	231	4	,	,	PUNCT
ejpam-4829	231	5	we	we	PRON
ejpam-4829	231	6	choose	choose	VERB
ejpam-4829	231	7	the	the	DET
ejpam-4829	231	8	graph	graph	NOUN
ejpam-4829	231	9	h	h	NOUN
ejpam-4829	231	10	′	′	NUM
ejpam-4829	232	1	=	=	PUNCT
ejpam-4829	232	2	g	g	PROPN
ejpam-4829	232	3	+	+	X
ejpam-4829	232	4	e′	e′	PROPN
ejpam-4829	232	5	where	where	SCONJ
ejpam-4829	232	6	e′	e′	PROPN
ejpam-4829	232	7	=	=	SYM
ejpam-4829	232	8	ay	ay	PROPN
ejpam-4829	232	9	.	.	PUNCT
ejpam-4829	232	10	notice	notice	NOUN
ejpam-4829	232	11	that	that	SCONJ
ejpam-4829	232	12	h	h	PROPN
ejpam-4829	232	13	′[{a	′[{a	PROPN
ejpam-4829	232	14	,	,	PUNCT
ejpam-4829	232	15	a′	a′	PROPN
ejpam-4829	232	16	,	,	PUNCT
ejpam-4829	232	17	x	x	PROPN
ejpam-4829	232	18	,	,	PUNCT
ejpam-4829	232	19	x′	x′	NUM
ejpam-4829	232	20	,	,	PUNCT
ejpam-4829	232	21	y	y	PROPN
ejpam-4829	232	22	}	}	PUNCT
ejpam-4829	232	23	]	]	PUNCT
ejpam-4829	232	24	is	be	AUX
ejpam-4829	232	25	a	a	DET
ejpam-4829	232	26	taurus	taurus	NOUN
ejpam-4829	232	27	.	.	PUNCT
ejpam-4829	233	1	h	h	NOUN
ejpam-4829	234	1	′	′	NUM
ejpam-4829	235	1	−	−	NOUN
ejpam-4829	235	2	a	a	DET
ejpam-4829	235	3	=	=	NOUN
ejpam-4829	235	4	g	g	PROPN
ejpam-4829	235	5	−	−	PROPN
ejpam-4829	235	6	a	a	PRON
ejpam-4829	235	7	is	be	AUX
ejpam-4829	235	8	prime	prime	ADJ
ejpam-4829	235	9	.	.	PUNCT
ejpam-4829	236	1	since	since	SCONJ
ejpam-4829	236	2	h	h	PROPN
ejpam-4829	236	3	′[{a	′[{a	PROPN
ejpam-4829	236	4	,	,	PUNCT
ejpam-4829	236	5	a′	a′	PROPN
ejpam-4829	236	6	,	,	PUNCT
ejpam-4829	236	7	x	x	PROPN
ejpam-4829	236	8	,	,	PUNCT
ejpam-4829	236	9	x′	x′	NUM
ejpam-4829	236	10	,	,	PUNCT
ejpam-4829	236	11	y	y	PROPN
ejpam-4829	236	12	}	}	PUNCT
ejpam-4829	236	13	]	]	PUNCT
ejpam-4829	236	14	is	be	AUX
ejpam-4829	236	15	a	a	DET
ejpam-4829	236	16	taurus	taurus	NOUN
ejpam-4829	236	17	,	,	PUNCT
ejpam-4829	236	18	a	a	PRON
ejpam-4829	236	19	/∈	/∈	NOUN
ejpam-4829	236	20	⟨v	⟨v	NOUN
ejpam-4829	236	21	\	\	PROPN
ejpam-4829	236	22	{	{	PUNCT
ejpam-4829	236	23	a}⟩	a}⟩	PROPN
ejpam-4829	236	24	and	and	CCONJ
ejpam-4829	236	25	a	a	DET
ejpam-4829	236	26	/∈	/∈	INTJ
ejpam-4829	236	27	(	(	PUNCT
ejpam-4829	236	28	v	v	NOUN
ejpam-4829	236	29	\	\	PROPN
ejpam-4829	236	30	{	{	PUNCT
ejpam-4829	236	31	a	a	NOUN
ejpam-4829	236	32	}	}	PUNCT
ejpam-4829	236	33	)	)	PUNCT
ejpam-4829	236	34	(	(	PUNCT
ejpam-4829	236	35	α	α	X
ejpam-4829	236	36	)	)	PUNCT
ejpam-4829	236	37	with	with	ADP
ejpam-4829	236	38	α	α	PROPN
ejpam-4829	236	39	∈	∈	PROPN
ejpam-4829	236	40	{	{	PUNCT
ejpam-4829	236	41	a′	a′	PROPN
ejpam-4829	236	42	,	,	PUNCT
ejpam-4829	236	43	x	x	NOUN
ejpam-4829	236	44	,	,	PUNCT
ejpam-4829	236	45	x′	x′	NUM
ejpam-4829	236	46	,	,	PUNCT
ejpam-4829	236	47	y	y	PROPN
ejpam-4829	236	48	}	}	PUNCT
ejpam-4829	236	49	.	.	PUNCT
ejpam-4829	237	1	we	we	PRON
ejpam-4829	237	2	prove	prove	VERB
ejpam-4829	237	3	that	that	SCONJ
ejpam-4829	237	4	h	h	NOUN
ejpam-4829	237	5	′	′	NOUN
ejpam-4829	237	6	is	be	AUX
ejpam-4829	237	7	prime	prime	ADJ
ejpam-4829	237	8	using	use	VERB
ejpam-4829	237	9	contradiction	contradiction	NOUN
ejpam-4829	237	10	.	.	PUNCT
ejpam-4829	238	1	assume	assume	VERB
ejpam-4829	238	2	that	that	SCONJ
ejpam-4829	238	3	h	h	PROPN
ejpam-4829	238	4	′	′	NOUN
ejpam-4829	238	5	is	be	AUX
ejpam-4829	238	6	not	not	PART
ejpam-4829	238	7	prime	prime	ADJ
ejpam-4829	238	8	.	.	PUNCT
ejpam-4829	239	1	then	then	ADV
ejpam-4829	239	2	,	,	PUNCT
ejpam-4829	239	3	there	there	PRON
ejpam-4829	239	4	is	be	VERB
ejpam-4829	239	5	z	z	NOUN
ejpam-4829	239	6	in	in	ADP
ejpam-4829	239	7	v	v	NOUN
ejpam-4829	239	8	\	\	NOUN
ejpam-4829	239	9	{	{	PUNCT
ejpam-4829	239	10	a	a	PRON
ejpam-4829	239	11	,	,	PUNCT
ejpam-4829	239	12	a′	a′	PROPN
ejpam-4829	239	13	,	,	PUNCT
ejpam-4829	239	14	x	x	PROPN
ejpam-4829	239	15	,	,	PUNCT
ejpam-4829	239	16	x′	x′	NUM
ejpam-4829	239	17	,	,	PUNCT
ejpam-4829	239	18	y	y	PROPN
ejpam-4829	239	19	}	}	PUNCT
ejpam-4829	239	20	such	such	ADJ
ejpam-4829	239	21	that	that	SCONJ
ejpam-4829	239	22	a	a	DET
ejpam-4829	239	23	∈	∈	PROPN
ejpam-4829	239	24	(	(	PUNCT
ejpam-4829	239	25	v	v	NOUN
ejpam-4829	239	26	\	\	PROPN
ejpam-4829	239	27	{	{	PUNCT
ejpam-4829	239	28	a	a	NOUN
ejpam-4829	239	29	}	}	PUNCT
ejpam-4829	239	30	)	)	PUNCT
ejpam-4829	239	31	(	(	PUNCT
ejpam-4829	239	32	z	z	NOUN
ejpam-4829	239	33	)	)	PUNCT
ejpam-4829	239	34	.	.	PUNCT
ejpam-4829	240	1	moreover	moreover	ADV
ejpam-4829	240	2	,	,	PUNCT
ejpam-4829	240	3	za′	za′	NOUN
ejpam-4829	240	4	/∈	/∈	PUNCT
ejpam-4829	241	1	e(h	e(h	PROPN
ejpam-4829	241	2	′	′	NOUN
ejpam-4829	241	3	)	)	PUNCT
ejpam-4829	241	4	because	because	SCONJ
ejpam-4829	241	5	aa′	aa′	ADV
ejpam-4829	241	6	/∈	/∈	VERB
ejpam-4829	242	1	e(h	e(h	PROPN
ejpam-4829	242	2	′	′	NOUN
ejpam-4829	242	3	)	)	PUNCT
ejpam-4829	242	4	.	.	PUNCT
ejpam-4829	243	1	as	as	ADP
ejpam-4829	243	2	{	{	PUNCT
ejpam-4829	243	3	a	a	PRON
ejpam-4829	243	4	,	,	PUNCT
ejpam-4829	243	5	a′	a′	ADJ
ejpam-4829	243	6	}	}	PUNCT
ejpam-4829	243	7	is	be	AUX
ejpam-4829	243	8	a	a	DET
ejpam-4829	243	9	module	module	NOUN
ejpam-4829	243	10	in	in	ADP
ejpam-4829	243	11	g	g	PROPN
ejpam-4829	243	12	,	,	PUNCT
ejpam-4829	243	13	za	za	PROPN
ejpam-4829	243	14	/∈	/∈	PUNCT
ejpam-4829	244	1	e(h	e(h	PROPN
ejpam-4829	244	2	′	′	NOUN
ejpam-4829	244	3	)	)	PUNCT
ejpam-4829	244	4	,	,	PUNCT
ejpam-4829	244	5	{	{	PUNCT
ejpam-4829	244	6	x′z	x′z	X
ejpam-4829	244	7	,	,	PUNCT
ejpam-4829	244	8	yz	yz	PROPN
ejpam-4829	244	9	}	}	PUNCT
ejpam-4829	244	10	⊆	⊆	NUM
ejpam-4829	244	11	e(h	e(h	PROPN
ejpam-4829	244	12	′	′	NUM
ejpam-4829	244	13	)	)	PUNCT
ejpam-4829	244	14	and	and	CCONJ
ejpam-4829	244	15	xz	xz	PROPN
ejpam-4829	244	16	/∈	/∈	PUNCT
ejpam-4829	245	1	e(h	e(h	PROPN
ejpam-4829	245	2	′	′	NOUN
ejpam-4829	245	3	)	)	PUNCT
ejpam-4829	245	4	.	.	PUNCT
ejpam-4829	246	1	knowing	know	VERB
ejpam-4829	246	2	that	that	SCONJ
ejpam-4829	246	3	za	za	PROPN
ejpam-4829	246	4	/∈	/∈	PUNCT
ejpam-4829	247	1	e(h	e(h	PROPN
ejpam-4829	247	2	′	′	NOUN
ejpam-4829	247	3	)	)	PUNCT
ejpam-4829	248	1	and	and	CCONJ
ejpam-4829	248	2	zy	zy	PROPN
ejpam-4829	248	3	∈	∈	PROPN
ejpam-4829	248	4	e(h	e(h	PROPN
ejpam-4829	248	5	′	′	NOUN
ejpam-4829	248	6	)	)	PUNCT
ejpam-4829	248	7	contradict	contradict	VERB
ejpam-4829	248	8	the	the	DET
ejpam-4829	248	9	fact	fact	NOUN
ejpam-4829	248	10	that	that	SCONJ
ejpam-4829	248	11	{	{	PUNCT
ejpam-4829	248	12	a	a	X
ejpam-4829	248	13	,	,	PUNCT
ejpam-4829	248	14	y	y	NOUN
ejpam-4829	248	15	}	}	PUNCT
ejpam-4829	248	16	is	be	AUX
ejpam-4829	248	17	a	a	DET
ejpam-4829	248	18	module	module	NOUN
ejpam-4829	248	19	in	in	ADP
ejpam-4829	248	20	h	h	NOUN
ejpam-4829	248	21	,	,	PUNCT
ejpam-4829	248	22	h	h	NOUN
ejpam-4829	248	23	′	′	NOUN
ejpam-4829	248	24	is	be	AUX
ejpam-4829	248	25	prime	prime	ADJ
ejpam-4829	248	26	.	.	PUNCT
ejpam-4829	249	1	lemma	lemma	PROPN
ejpam-4829	249	2	6	6	NUM
ejpam-4829	249	3	.	.	PUNCT
ejpam-4829	250	1	let	let	VERB
ejpam-4829	250	2	g	g	PRON
ejpam-4829	250	3	be	be	AUX
ejpam-4829	250	4	a	a	DET
ejpam-4829	250	5	decomposable	decomposable	ADJ
ejpam-4829	250	6	graph	graph	NOUN
ejpam-4829	250	7	with	with	ADP
ejpam-4829	250	8	a	a	DET
ejpam-4829	250	9	prime	prime	ADJ
ejpam-4829	250	10	frame	frame	NOUN
ejpam-4829	250	11	containing	contain	VERB
ejpam-4829	250	12	only	only	ADV
ejpam-4829	250	13	one	one	NUM
ejpam-4829	250	14	nontrivial	nontrivial	ADJ
ejpam-4829	250	15	module	module	NOUN
ejpam-4829	250	16	m	m	NOUN
ejpam-4829	250	17	.	.	PUNCT
ejpam-4829	251	1	if	if	SCONJ
ejpam-4829	251	2	g[m	g[m	NOUN
ejpam-4829	251	3	]	]	PUNCT
ejpam-4829	251	4	=	=	SYM
ejpam-4829	251	5	k2	k2	PROPN
ejpam-4829	251	6	and	and	CCONJ
ejpam-4829	251	7	g	g	PROPN
ejpam-4829	251	8	/∈	/∈	PROPN
ejpam-4829	252	1	b	b	NOUN
ejpam-4829	252	2	,	,	PUNCT
ejpam-4829	252	3	then	then	ADV
ejpam-4829	252	4	an	an	DET
ejpam-4829	252	5	edge	edge	NOUN
ejpam-4829	252	6	e	e	NOUN
ejpam-4829	252	7	exists	exist	VERB
ejpam-4829	252	8	in	in	ADP
ejpam-4829	252	9	g	g	PROPN
ejpam-4829	252	10	such	such	ADJ
ejpam-4829	252	11	that	that	PRON
ejpam-4829	252	12	g	g	PROPN
ejpam-4829	253	1	+	+	CCONJ
ejpam-4829	253	2	e	e	NOUN
ejpam-4829	253	3	is	be	AUX
ejpam-4829	253	4	prime	prime	ADJ
ejpam-4829	253	5	.	.	PUNCT
ejpam-4829	254	1	m.	m.	NOUN
ejpam-4829	254	2	bouaziz	bouaziz	PROPN
ejpam-4829	254	3	et	et	PROPN
ejpam-4829	254	4	al	al	PROPN
ejpam-4829	254	5	.	.	PUNCT
ejpam-4829	254	6	/	/	SYM
ejpam-4829	254	7	eur	eur	PROPN
ejpam-4829	254	8	.	.	PUNCT
ejpam-4829	255	1	j.	j.	PROPN
ejpam-4829	255	2	pure	pure	PROPN
ejpam-4829	255	3	appl	appl	PROPN
ejpam-4829	255	4	.	.	PROPN
ejpam-4829	255	5	math	math	PROPN
ejpam-4829	255	6	,	,	PUNCT
ejpam-4829	255	7	16	16	NUM
ejpam-4829	255	8	(	(	PUNCT
ejpam-4829	255	9	4	4	NUM
ejpam-4829	255	10	)	)	PUNCT
ejpam-4829	255	11	(	(	PUNCT
ejpam-4829	255	12	2023	2023	NUM
ejpam-4829	255	13	)	)	PUNCT
ejpam-4829	255	14	,	,	PUNCT
ejpam-4829	255	15	2786	2786	NUM
ejpam-4829	255	16	-	-	SYM
ejpam-4829	255	17	2797	2797	NUM
ejpam-4829	255	18	2794	2794	NUM
ejpam-4829	255	19	proof	proof	NOUN
ejpam-4829	255	20	.	.	PUNCT
ejpam-4829	256	1	let	let	VERB
ejpam-4829	256	2	g	g	PROPN
ejpam-4829	256	3	=	=	SYM
ejpam-4829	256	4	(	(	PUNCT
ejpam-4829	256	5	v	v	NOUN
ejpam-4829	256	6	,	,	PUNCT
ejpam-4829	256	7	e	e	NOUN
ejpam-4829	256	8	)	)	PUNCT
ejpam-4829	256	9	be	be	AUX
ejpam-4829	256	10	a	a	DET
ejpam-4829	256	11	decomposable	decomposable	ADJ
ejpam-4829	256	12	graph	graph	NOUN
ejpam-4829	256	13	with	with	ADP
ejpam-4829	256	14	a	a	DET
ejpam-4829	256	15	prime	prime	ADJ
ejpam-4829	256	16	frame	frame	NOUN
ejpam-4829	256	17	containing	contain	VERB
ejpam-4829	256	18	only	only	ADV
ejpam-4829	256	19	one	one	NUM
ejpam-4829	256	20	non	non	ADJ
ejpam-4829	256	21	-	-	ADJ
ejpam-4829	256	22	trivial	trivial	ADJ
ejpam-4829	256	23	module	module	NOUN
ejpam-4829	256	24	m	m	NOUN
ejpam-4829	256	25	=	=	PUNCT
ejpam-4829	256	26	{	{	PUNCT
ejpam-4829	256	27	a	a	PRON
ejpam-4829	256	28	,	,	PUNCT
ejpam-4829	256	29	a′	a′	ADJ
ejpam-4829	256	30	}	}	PUNCT
ejpam-4829	256	31	such	such	ADJ
ejpam-4829	256	32	that	that	DET
ejpam-4829	256	33	g[m	g[m	NOUN
ejpam-4829	256	34	]	]	PUNCT
ejpam-4829	256	35	=	=	SYM
ejpam-4829	256	36	k2	k2	PROPN
ejpam-4829	256	37	and	and	CCONJ
ejpam-4829	256	38	g	g	PROPN
ejpam-4829	256	39	/∈	/∈	PROPN
ejpam-4829	256	40	b.	b.	PROPN
ejpam-4829	257	1	let	let	VERB
ejpam-4829	257	2	e	e	PROPN
ejpam-4829	257	3	∈	∈	PROPN
ejpam-4829	257	4	e(g	e(g	PROPN
ejpam-4829	257	5	)	)	PUNCT
ejpam-4829	257	6	.	.	PUNCT
ejpam-4829	258	1	consider	consider	VERB
ejpam-4829	258	2	that	that	DET
ejpam-4829	258	3	h	h	NOUN
ejpam-4829	258	4	=	=	PRON
ejpam-4829	258	5	g+	g+	PROPN
ejpam-4829	258	6	e.	e.	PROPN
ejpam-4829	258	7	suppose	suppose	VERB
ejpam-4829	258	8	z	z	NOUN
ejpam-4829	258	9	=	=	SYM
ejpam-4829	258	10	ng(m	ng(m	X
ejpam-4829	258	11	)	)	PUNCT
ejpam-4829	258	12	,	,	PUNCT
ejpam-4829	258	13	x	x	X
ejpam-4829	258	14	=	=	PUNCT
ejpam-4829	258	15	v	v	NOUN
ejpam-4829	258	16	\	\	PROPN
ejpam-4829	258	17	(	(	PUNCT
ejpam-4829	258	18	z	z	NOUN
ejpam-4829	258	19	∪	∪	VERB
ejpam-4829	258	20	{	{	PUNCT
ejpam-4829	258	21	a	a	PRON
ejpam-4829	258	22	,	,	PUNCT
ejpam-4829	258	23	a′	a′	NOUN
ejpam-4829	258	24	}	}	PUNCT
ejpam-4829	258	25	)	)	PUNCT
ejpam-4829	258	26	.	.	PUNCT
ejpam-4829	259	1	let	let	VERB
ejpam-4829	259	2	w	w	NOUN
ejpam-4829	259	3	=	=	SYM
ejpam-4829	259	4	v	v	NOUN
ejpam-4829	259	5	\	\	PROPN
ejpam-4829	259	6	{	{	PUNCT
ejpam-4829	259	7	a	a	NOUN
ejpam-4829	259	8	}	}	PUNCT
ejpam-4829	259	9	.	.	PUNCT
ejpam-4829	260	1	since	since	SCONJ
ejpam-4829	260	2	the	the	DET
ejpam-4829	260	3	frame	frame	NOUN
ejpam-4829	260	4	of	of	ADP
ejpam-4829	260	5	g	g	PROPN
ejpam-4829	260	6	is	be	AUX
ejpam-4829	260	7	prime	prime	ADJ
ejpam-4829	260	8	,	,	PUNCT
ejpam-4829	260	9	x	x	PUNCT
ejpam-4829	260	10	̸=	̸=	NOUN
ejpam-4829	260	11	∅	∅	NOUN
ejpam-4829	260	12	and	and	CCONJ
ejpam-4829	260	13	z	z	PROPN
ejpam-4829	260	14	̸=	̸=	PROPN
ejpam-4829	260	15	∅.	∅.	ADV
ejpam-4829	260	16	let	let	VERB
ejpam-4829	260	17	b	b	NOUN
ejpam-4829	260	18	=	=	PRON
ejpam-4829	260	19	{	{	PUNCT
ejpam-4829	260	20	b	b	NOUN
ejpam-4829	260	21	:	:	PUNCT
ejpam-4829	260	22	b	b	X
ejpam-4829	260	23	∈	∈	PROPN
ejpam-4829	260	24	x	x	X
ejpam-4829	260	25	and	and	CCONJ
ejpam-4829	260	26	bz	bz	PROPN
ejpam-4829	260	27	/∈	/∈	PUNCT
ejpam-4829	261	1	e	e	NOUN
ejpam-4829	261	2	,	,	PUNCT
ejpam-4829	261	3	∀z	∀z	PROPN
ejpam-4829	261	4	∈	∈	PROPN
ejpam-4829	262	1	z	z	PROPN
ejpam-4829	262	2	}	}	PUNCT
ejpam-4829	262	3	(	(	PUNCT
ejpam-4829	262	4	b	b	X
ejpam-4829	262	5	̸=	̸=	PROPN
ejpam-4829	262	6	x	x	PUNCT
ejpam-4829	262	7	because	because	SCONJ
ejpam-4829	262	8	the	the	DET
ejpam-4829	262	9	frame	frame	NOUN
ejpam-4829	262	10	is	be	AUX
ejpam-4829	262	11	prime	prime	ADJ
ejpam-4829	262	12	)	)	PUNCT
ejpam-4829	262	13	.	.	PUNCT
ejpam-4829	263	1	firstly	firstly	ADV
ejpam-4829	263	2	,	,	PUNCT
ejpam-4829	263	3	b	b	PROPN
ejpam-4829	263	4	̸=	̸=	PROPN
ejpam-4829	263	5	∅.	∅.	ADV
ejpam-4829	263	6	as	as	ADP
ejpam-4829	263	7	g−	g−	PROPN
ejpam-4829	263	8	a	a	PRON
ejpam-4829	263	9	is	be	AUX
ejpam-4829	263	10	prime	prime	ADJ
ejpam-4829	263	11	,	,	PUNCT
ejpam-4829	263	12	there	there	PRON
ejpam-4829	263	13	is	be	VERB
ejpam-4829	263	14	y	y	PROPN
ejpam-4829	263	15	∈	∈	PROPN
ejpam-4829	263	16	b	b	PROPN
ejpam-4829	263	17	and	and	CCONJ
ejpam-4829	263	18	x	x	SYM
ejpam-4829	263	19	∈	∈	PROPN
ejpam-4829	263	20	x	x	NOUN
ejpam-4829	263	21	\b	\b	NOUN
ejpam-4829	263	22	such	such	ADJ
ejpam-4829	263	23	that	that	SCONJ
ejpam-4829	263	24	xy	xy	PROPN
ejpam-4829	263	25	∈	∈	PROPN
ejpam-4829	263	26	e.	e.	PROPN
ejpam-4829	263	27	consider	consider	VERB
ejpam-4829	263	28	h	h	NOUN
ejpam-4829	263	29	=	=	SYM
ejpam-4829	263	30	g+	g+	NOUN
ejpam-4829	263	31	e	e	X
ejpam-4829	263	32	where	where	SCONJ
ejpam-4829	263	33	e	e	NOUN
ejpam-4829	263	34	=	=	SYM
ejpam-4829	263	35	ay	ay	PROPN
ejpam-4829	263	36	.	.	PUNCT
ejpam-4829	263	37	notice	notice	NOUN
ejpam-4829	263	38	that	that	SCONJ
ejpam-4829	263	39	g−	g−	VERB
ejpam-4829	263	40	a	a	DET
ejpam-4829	263	41	=	=	ADJ
ejpam-4829	263	42	h	h	NOUN
ejpam-4829	263	43	−	−	PROPN
ejpam-4829	263	44	a	a	PRON
ejpam-4829	263	45	is	be	AUX
ejpam-4829	263	46	prime	prime	ADJ
ejpam-4829	263	47	.	.	PUNCT
ejpam-4829	264	1	knowing	know	VERB
ejpam-4829	264	2	that	that	SCONJ
ejpam-4829	264	3	,	,	PUNCT
ejpam-4829	264	4	ax	ax	NOUN
ejpam-4829	264	5	/∈	/∈	PUNCT
ejpam-4829	264	6	e(h	e(h	PROPN
ejpam-4829	264	7	)	)	PUNCT
ejpam-4829	264	8	and	and	CCONJ
ejpam-4829	264	9	aa′	aa′	ADV
ejpam-4829	264	10	∈	∈	PROPN
ejpam-4829	264	11	e(h	e(h	PROPN
ejpam-4829	264	12	)	)	PUNCT
ejpam-4829	264	13	,	,	PUNCT
ejpam-4829	264	14	a	a	PRON
ejpam-4829	264	15	/∈	/∈	PUNCT
ejpam-4829	264	16	⟨w	⟨w	NOUN
ejpam-4829	264	17	⟩	⟩	NOUN
ejpam-4829	264	18	in	in	ADP
ejpam-4829	264	19	h.	h.	PROPN
ejpam-4829	264	20	as	as	ADP
ejpam-4829	264	21	ya	ya	PROPN
ejpam-4829	264	22	∈	∈	PROPN
ejpam-4829	264	23	e(h	e(h	PROPN
ejpam-4829	264	24	)	)	PUNCT
ejpam-4829	264	25	and	and	CCONJ
ejpam-4829	264	26	ya′	ya′	PROPN
ejpam-4829	264	27	/∈	/∈	PUNCT
ejpam-4829	265	1	e(h	e(h	PROPN
ejpam-4829	265	2	)	)	PUNCT
ejpam-4829	265	3	,	,	PUNCT
ejpam-4829	266	1	a	a	DET
ejpam-4829	266	2	/∈	/∈	NOUN
ejpam-4829	266	3	w	w	NOUN
ejpam-4829	266	4	(	(	PUNCT
ejpam-4829	266	5	a′	a′	PROPN
ejpam-4829	266	6	)	)	PUNCT
ejpam-4829	266	7	in	in	ADP
ejpam-4829	266	8	h.	h.	PROPN
ejpam-4829	266	9	since	since	SCONJ
ejpam-4829	266	10	,	,	PUNCT
ejpam-4829	266	11	for	for	ADP
ejpam-4829	266	12	all	all	PRON
ejpam-4829	266	13	β	β	X
ejpam-4829	266	14	∈	∈	PROPN
ejpam-4829	267	1	z	z	X
ejpam-4829	267	2	,	,	PUNCT
ejpam-4829	267	3	yβ	yβ	NOUN
ejpam-4829	267	4	/∈	/∈	PUNCT
ejpam-4829	267	5	e(h	e(h	PROPN
ejpam-4829	267	6	)	)	PUNCT
ejpam-4829	267	7	and	and	CCONJ
ejpam-4829	267	8	ya	ya	PROPN
ejpam-4829	267	9	∈	∈	PROPN
ejpam-4829	267	10	e(h	e(h	PROPN
ejpam-4829	267	11	)	)	PUNCT
ejpam-4829	267	12	,	,	PUNCT
ejpam-4829	267	13	a	a	DET
ejpam-4829	267	14	/∈	/∈	NOUN
ejpam-4829	267	15	w	w	NOUN
ejpam-4829	267	16	(	(	PUNCT
ejpam-4829	267	17	β	β	NOUN
ejpam-4829	267	18	)	)	PUNCT
ejpam-4829	267	19	in	in	ADP
ejpam-4829	267	20	h.	h.	PROPN
ejpam-4829	267	21	knowing	know	VERB
ejpam-4829	267	22	that	that	SCONJ
ejpam-4829	267	23	,	,	PUNCT
ejpam-4829	267	24	for	for	ADP
ejpam-4829	267	25	all	all	PRON
ejpam-4829	267	26	α	α	DET
ejpam-4829	267	27	∈	∈	NOUN
ejpam-4829	267	28	x	x	SYM
ejpam-4829	267	29	\	\	PROPN
ejpam-4829	267	30	{	{	PUNCT
ejpam-4829	267	31	y	y	NOUN
ejpam-4829	267	32	}	}	PUNCT
ejpam-4829	267	33	,	,	PUNCT
ejpam-4829	267	34	a′a	a′a	PROPN
ejpam-4829	267	35	∈	∈	PROPN
ejpam-4829	267	36	e(h	e(h	X
ejpam-4829	267	37	)	)	PUNCT
ejpam-4829	267	38	and	and	CCONJ
ejpam-4829	267	39	a′α	a′α	ADV
ejpam-4829	267	40	/∈	/∈	PUNCT
ejpam-4829	267	41	e(h	e(h	PROPN
ejpam-4829	267	42	)	)	PUNCT
ejpam-4829	267	43	,	,	PUNCT
ejpam-4829	267	44	a	a	DET
ejpam-4829	267	45	/∈	/∈	NOUN
ejpam-4829	267	46	w	w	NOUN
ejpam-4829	267	47	(	(	PUNCT
ejpam-4829	267	48	α	α	NOUN
ejpam-4829	267	49	)	)	PUNCT
ejpam-4829	267	50	in	in	ADP
ejpam-4829	267	51	h.	h.	PROPN
ejpam-4829	267	52	given	give	VERB
ejpam-4829	267	53	that	that	PRON
ejpam-4829	267	54	xa	xa	PROPN
ejpam-4829	267	55	/∈	/∈	PUNCT
ejpam-4829	267	56	e(h	e(h	PROPN
ejpam-4829	267	57	)	)	PUNCT
ejpam-4829	267	58	and	and	CCONJ
ejpam-4829	267	59	xy	xy	PROPN
ejpam-4829	267	60	∈	∈	PROPN
ejpam-4829	267	61	e(h	e(h	PROPN
ejpam-4829	267	62	)	)	PUNCT
ejpam-4829	267	63	,	,	PUNCT
ejpam-4829	267	64	a	a	DET
ejpam-4829	267	65	/∈	/∈	NOUN
ejpam-4829	267	66	w	w	NOUN
ejpam-4829	267	67	(	(	PUNCT
ejpam-4829	267	68	y	y	NOUN
ejpam-4829	267	69	)	)	PUNCT
ejpam-4829	267	70	in	in	ADP
ejpam-4829	267	71	h.	h.	PROPN
ejpam-4829	267	72	thus	thus	ADV
ejpam-4829	267	73	,	,	PUNCT
ejpam-4829	267	74	using	use	VERB
ejpam-4829	267	75	lemma	lemma	PROPN
ejpam-4829	267	76	1	1	NUM
ejpam-4829	267	77	in	in	ADP
ejpam-4829	267	78	h	h	NOUN
ejpam-4829	267	79	,	,	PUNCT
ejpam-4829	267	80	a	a	DET
ejpam-4829	267	81	∈	∈	NOUN
ejpam-4829	267	82	ext(w	ext(w	ADP
ejpam-4829	267	83	)	)	PUNCT
ejpam-4829	267	84	.	.	PUNCT
ejpam-4829	268	1	therefore	therefore	ADV
ejpam-4829	268	2	,	,	PUNCT
ejpam-4829	268	3	h	h	NOUN
ejpam-4829	268	4	=	=	PUNCT
ejpam-4829	268	5	g+	g+	NOUN
ejpam-4829	268	6	e	e	NOUN
ejpam-4829	268	7	is	be	AUX
ejpam-4829	268	8	prime	prime	ADJ
ejpam-4829	268	9	.	.	PUNCT
ejpam-4829	269	1	secondly	secondly	ADV
ejpam-4829	269	2	,	,	PUNCT
ejpam-4829	269	3	b	b	X
ejpam-4829	269	4	=	=	PUNCT
ejpam-4829	269	5	∅.	∅.	AUX
ejpam-4829	269	6	distinguish	distinguish	VERB
ejpam-4829	269	7	two	two	NUM
ejpam-4829	269	8	cases	case	NOUN
ejpam-4829	269	9	:	:	PUNCT
ejpam-4829	269	10	first	first	ADV
ejpam-4829	269	11	,	,	PUNCT
ejpam-4829	269	12	assume	assume	VERB
ejpam-4829	269	13	that	that	SCONJ
ejpam-4829	269	14	there	there	PRON
ejpam-4829	269	15	is	be	VERB
ejpam-4829	269	16	x	x	X
ejpam-4829	269	17	∈	∈	PROPN
ejpam-4829	269	18	x	x	SYM
ejpam-4829	269	19	where	where	SCONJ
ejpam-4829	269	20	,	,	PUNCT
ejpam-4829	269	21	for	for	ADP
ejpam-4829	269	22	all	all	PRON
ejpam-4829	269	23	x′	x′	PROPN
ejpam-4829	269	24	∈	∈	PROPN
ejpam-4829	269	25	z	z	PROPN
ejpam-4829	269	26	,	,	PUNCT
ejpam-4829	269	27	{	{	PUNCT
ejpam-4829	269	28	a	a	X
ejpam-4829	269	29	,	,	PUNCT
ejpam-4829	269	30	x′	x′	NUM
ejpam-4829	269	31	}	}	PUNCT
ejpam-4829	269	32	is	be	AUX
ejpam-4829	269	33	not	not	PART
ejpam-4829	269	34	a	a	DET
ejpam-4829	269	35	module	module	NOUN
ejpam-4829	269	36	in	in	ADP
ejpam-4829	269	37	h	h	NOUN
ejpam-4829	269	38	=	=	NOUN
ejpam-4829	269	39	g+	g+	NOUN
ejpam-4829	269	40	ax	ax	NOUN
ejpam-4829	269	41	.	.	PUNCT
ejpam-4829	269	42	notice	notice	VERB
ejpam-4829	269	43	that	that	SCONJ
ejpam-4829	269	44	h	h	NOUN
ejpam-4829	270	1	−	−	NOUN
ejpam-4829	270	2	a	a	DET
ejpam-4829	270	3	=	=	PUNCT
ejpam-4829	270	4	g−	g−	PROPN
ejpam-4829	270	5	a	a	PRON
ejpam-4829	270	6	is	be	AUX
ejpam-4829	270	7	prime	prime	ADJ
ejpam-4829	270	8	.	.	PUNCT
ejpam-4829	271	1	as	as	ADP
ejpam-4829	271	2	x	x	X
ejpam-4829	271	3	̸=	̸=	PROPN
ejpam-4829	271	4	∅	∅	NOUN
ejpam-4829	271	5	and	and	CCONJ
ejpam-4829	271	6	aa′	aa′	ADV
ejpam-4829	271	7	∈	∈	PROPN
ejpam-4829	271	8	e(h	e(h	PROPN
ejpam-4829	271	9	)	)	PUNCT
ejpam-4829	271	10	,	,	PUNCT
ejpam-4829	271	11	a	a	DET
ejpam-4829	271	12	/∈	/∈	PUNCT
ejpam-4829	271	13	⟨w	⟨w	NOUN
ejpam-4829	271	14	⟩	⟩	NOUN
ejpam-4829	271	15	in	in	ADP
ejpam-4829	271	16	h.	h.	PROPN
ejpam-4829	271	17	knowing	know	VERB
ejpam-4829	271	18	that	that	SCONJ
ejpam-4829	271	19	,	,	PUNCT
ejpam-4829	271	20	for	for	ADP
ejpam-4829	271	21	all	all	DET
ejpam-4829	271	22	t	t	NOUN
ejpam-4829	271	23	∈	∈	NOUN
ejpam-4829	271	24	x	x	SYM
ejpam-4829	271	25	\	\	X
ejpam-4829	271	26	{	{	PUNCT
ejpam-4829	271	27	x	x	X
ejpam-4829	271	28	}	}	PUNCT
ejpam-4829	271	29	,	,	PUNCT
ejpam-4829	271	30	a′t	a′t	PROPN
ejpam-4829	271	31	/∈	/∈	PUNCT
ejpam-4829	271	32	e(h	e(h	NOUN
ejpam-4829	271	33	)	)	PUNCT
ejpam-4829	271	34	and	and	CCONJ
ejpam-4829	271	35	a′a	a′a	PROPN
ejpam-4829	271	36	∈	∈	PROPN
ejpam-4829	271	37	e	e	PROPN
ejpam-4829	271	38	,	,	PUNCT
ejpam-4829	271	39	a	a	PRON
ejpam-4829	271	40	/∈	/∈	NOUN
ejpam-4829	271	41	w	w	NOUN
ejpam-4829	271	42	(	(	PUNCT
ejpam-4829	271	43	t	t	NOUN
ejpam-4829	271	44	)	)	PUNCT
ejpam-4829	271	45	in	in	ADP
ejpam-4829	271	46	h.	h.	PROPN
ejpam-4829	271	47	since	since	SCONJ
ejpam-4829	271	48	a′a	a′a	PROPN
ejpam-4829	271	49	∈	∈	PROPN
ejpam-4829	271	50	e(h	e(h	X
ejpam-4829	271	51	)	)	PUNCT
ejpam-4829	271	52	and	and	CCONJ
ejpam-4829	271	53	a′x	a′x	PROPN
ejpam-4829	271	54	/∈	/∈	PUNCT
ejpam-4829	272	1	e(h	e(h	PROPN
ejpam-4829	272	2	)	)	PUNCT
ejpam-4829	272	3	,	,	PUNCT
ejpam-4829	272	4	a	a	DET
ejpam-4829	272	5	/∈	/∈	NOUN
ejpam-4829	272	6	w	w	NOUN
ejpam-4829	272	7	(	(	PUNCT
ejpam-4829	272	8	x	x	NOUN
ejpam-4829	272	9	)	)	PUNCT
ejpam-4829	272	10	in	in	ADP
ejpam-4829	272	11	h.	h.	PROPN
ejpam-4829	272	12	given	give	VERB
ejpam-4829	272	13	that	that	PRON
ejpam-4829	272	14	,	,	PUNCT
ejpam-4829	272	15	for	for	ADP
ejpam-4829	272	16	all	all	PRON
ejpam-4829	272	17	x′	x′	PROPN
ejpam-4829	272	18	∈	∈	PROPN
ejpam-4829	272	19	z	z	PROPN
ejpam-4829	272	20	,	,	PUNCT
ejpam-4829	272	21	{	{	PUNCT
ejpam-4829	272	22	a	a	X
ejpam-4829	272	23	,	,	PUNCT
ejpam-4829	272	24	x′	x′	NUM
ejpam-4829	272	25	}	}	PUNCT
ejpam-4829	272	26	is	be	AUX
ejpam-4829	272	27	not	not	PART
ejpam-4829	272	28	a	a	DET
ejpam-4829	272	29	module	module	NOUN
ejpam-4829	272	30	in	in	ADP
ejpam-4829	272	31	h	h	NOUN
ejpam-4829	272	32	,	,	PUNCT
ejpam-4829	272	33	a	a	PRON
ejpam-4829	272	34	/∈	/∈	NOUN
ejpam-4829	273	1	w	w	NOUN
ejpam-4829	273	2	(	(	PUNCT
ejpam-4829	273	3	x′	x′	NUM
ejpam-4829	273	4	)	)	PUNCT
ejpam-4829	273	5	in	in	ADP
ejpam-4829	273	6	h.	h.	PROPN
ejpam-4829	273	7	as	as	ADP
ejpam-4829	273	8	xa	xa	PROPN
ejpam-4829	273	9	∈	∈	PROPN
ejpam-4829	273	10	e(h	e(h	PROPN
ejpam-4829	273	11	)	)	PUNCT
ejpam-4829	273	12	and	and	CCONJ
ejpam-4829	273	13	xa′	xa′	PROPN
ejpam-4829	273	14	/∈	/∈	PUNCT
ejpam-4829	274	1	e(h	e(h	PROPN
ejpam-4829	274	2	)	)	PUNCT
ejpam-4829	274	3	,	,	PUNCT
ejpam-4829	274	4	a	a	DET
ejpam-4829	274	5	/∈	/∈	NOUN
ejpam-4829	274	6	w	w	NOUN
ejpam-4829	274	7	(	(	PUNCT
ejpam-4829	274	8	a′	a′	PROPN
ejpam-4829	274	9	)	)	PUNCT
ejpam-4829	274	10	in	in	ADP
ejpam-4829	274	11	h.	h.	PROPN
ejpam-4829	274	12	as	as	ADP
ejpam-4829	274	13	a	a	DET
ejpam-4829	274	14	consequence	consequence	NOUN
ejpam-4829	274	15	,	,	PUNCT
ejpam-4829	274	16	based	base	VERB
ejpam-4829	274	17	on	on	ADP
ejpam-4829	274	18	by	by	ADP
ejpam-4829	274	19	lemma	lemma	PROPN
ejpam-4829	274	20	1	1	NUM
ejpam-4829	274	21	,	,	PUNCT
ejpam-4829	274	22	a	a	DET
ejpam-4829	274	23	∈	∈	NOUN
ejpam-4829	274	24	ext(w	ext(w	ADP
ejpam-4829	274	25	)	)	PUNCT
ejpam-4829	274	26	.	.	PUNCT
ejpam-4829	275	1	therefore	therefore	ADV
ejpam-4829	275	2	,	,	PUNCT
ejpam-4829	275	3	h	h	NOUN
ejpam-4829	275	4	is	be	AUX
ejpam-4829	275	5	prime	prime	ADJ
ejpam-4829	275	6	.	.	PUNCT
ejpam-4829	276	1	second	second	ADJ
ejpam-4829	276	2	,	,	PUNCT
ejpam-4829	276	3	assume	assume	VERB
ejpam-4829	276	4	that	that	SCONJ
ejpam-4829	276	5	,	,	PUNCT
ejpam-4829	276	6	for	for	ADP
ejpam-4829	276	7	all	all	DET
ejpam-4829	276	8	x	x	SYM
ejpam-4829	276	9	∈	∈	PROPN
ejpam-4829	276	10	x	x	NOUN
ejpam-4829	276	11	,	,	PUNCT
ejpam-4829	276	12	there	there	PRON
ejpam-4829	276	13	is	be	VERB
ejpam-4829	276	14	x′	x′	PROPN
ejpam-4829	276	15	∈	∈	PROPN
ejpam-4829	276	16	z	z	NOUN
ejpam-4829	276	17	such	such	ADJ
ejpam-4829	276	18	that	that	SCONJ
ejpam-4829	276	19	{	{	PUNCT
ejpam-4829	276	20	a	a	PRON
ejpam-4829	276	21	,	,	PUNCT
ejpam-4829	276	22	x′	x′	NUM
ejpam-4829	276	23	}	}	PUNCT
ejpam-4829	276	24	is	be	AUX
ejpam-4829	276	25	a	a	DET
ejpam-4829	276	26	new	new	ADJ
ejpam-4829	276	27	module	module	NOUN
ejpam-4829	276	28	in	in	ADP
ejpam-4829	276	29	h	h	NOUN
ejpam-4829	276	30	=	=	NOUN
ejpam-4829	276	31	g+	g+	NOUN
ejpam-4829	276	32	ax	ax	NOUN
ejpam-4829	276	33	.	.	PUNCT
ejpam-4829	277	1	since	since	SCONJ
ejpam-4829	277	2	a′a	a′a	PROPN
ejpam-4829	277	3	∈	∈	PROPN
ejpam-4829	277	4	e(h	e(h	PROPN
ejpam-4829	277	5	)	)	PUNCT
ejpam-4829	277	6	and	and	CCONJ
ejpam-4829	277	7	xa	xa	PROPN
ejpam-4829	277	8	∈	∈	PROPN
ejpam-4829	277	9	e(h	e(h	PROPN
ejpam-4829	277	10	)	)	PUNCT
ejpam-4829	277	11	,	,	PUNCT
ejpam-4829	277	12	a′x′	a′x′	PROPN
ejpam-4829	277	13	∈	∈	PROPN
ejpam-4829	277	14	e(h	e(h	PROPN
ejpam-4829	277	15	)	)	PUNCT
ejpam-4829	277	16	and	and	CCONJ
ejpam-4829	277	17	x′x	x′x	PROPN
ejpam-4829	277	18	∈	∈	PROPN
ejpam-4829	277	19	e(h	e(h	PROPN
ejpam-4829	277	20	)	)	PUNCT
ejpam-4829	277	21	.	.	PUNCT
ejpam-4829	278	1	we	we	PRON
ejpam-4829	278	2	show	show	VERB
ejpam-4829	278	3	that	that	SCONJ
ejpam-4829	278	4	,	,	PUNCT
ejpam-4829	278	5	for	for	ADP
ejpam-4829	278	6	all	all	DET
ejpam-4829	278	7	t	t	NOUN
ejpam-4829	278	8	∈	∈	NOUN
ejpam-4829	278	9	v	v	ADP
ejpam-4829	278	10	\	\	PROPN
ejpam-4829	278	11	{	{	PUNCT
ejpam-4829	278	12	a	a	PRON
ejpam-4829	278	13	,	,	PUNCT
ejpam-4829	278	14	a′	a′	PROPN
ejpam-4829	278	15	,	,	PUNCT
ejpam-4829	278	16	x	x	NOUN
ejpam-4829	278	17	,	,	PUNCT
ejpam-4829	278	18	x′	x′	NUM
ejpam-4829	278	19	}	}	PUNCT
ejpam-4829	278	20	,	,	PUNCT
ejpam-4829	278	21	t	t	PROPN
ejpam-4829	278	22	∼h	∼h	PROPN
ejpam-4829	278	23	{	{	PUNCT
ejpam-4829	278	24	a	a	PRON
ejpam-4829	278	25	,	,	PUNCT
ejpam-4829	278	26	a′	a′	PROPN
ejpam-4829	278	27	,	,	PUNCT
ejpam-4829	278	28	x′	x′	NUM
ejpam-4829	278	29	}	}	PUNCT
ejpam-4829	278	30	.	.	PUNCT
ejpam-4829	279	1	indeed	indeed	ADV
ejpam-4829	279	2	,	,	PUNCT
ejpam-4829	279	3	as	as	ADP
ejpam-4829	279	4	{	{	PUNCT
ejpam-4829	279	5	a	a	PRON
ejpam-4829	279	6	,	,	PUNCT
ejpam-4829	279	7	a′	a′	ADJ
ejpam-4829	279	8	}	}	PUNCT
ejpam-4829	279	9	is	be	AUX
ejpam-4829	279	10	a	a	DET
ejpam-4829	279	11	module	module	NOUN
ejpam-4829	279	12	in	in	ADP
ejpam-4829	279	13	g	g	PROPN
ejpam-4829	279	14	,	,	PUNCT
ejpam-4829	279	15	for	for	ADP
ejpam-4829	279	16	all	all	DET
ejpam-4829	279	17	t	t	NOUN
ejpam-4829	279	18	∈	∈	PROPN
ejpam-4829	279	19	v	v	X
ejpam-4829	279	20	\{a	\{a	NOUN
ejpam-4829	279	21	,	,	PUNCT
ejpam-4829	279	22	a′	a′	ADJ
ejpam-4829	279	23	}	}	PUNCT
ejpam-4829	279	24	,	,	PUNCT
ejpam-4829	279	25	t	t	PROPN
ejpam-4829	279	26	∼g	∼g	PROPN
ejpam-4829	279	27	{	{	PUNCT
ejpam-4829	279	28	a	a	X
ejpam-4829	279	29	,	,	PUNCT
ejpam-4829	279	30	a′	a′	PROPN
ejpam-4829	279	31	}	}	PUNCT
ejpam-4829	279	32	.	.	PUNCT
ejpam-4829	280	1	hence	hence	ADV
ejpam-4829	280	2	,	,	PUNCT
ejpam-4829	280	3	t	t	PROPN
ejpam-4829	280	4	∼h	∼h	PROPN
ejpam-4829	280	5	{	{	PUNCT
ejpam-4829	280	6	a	a	PRON
ejpam-4829	280	7	,	,	PUNCT
ejpam-4829	280	8	a′	a′	PROPN
ejpam-4829	280	9	}	}	PUNCT
ejpam-4829	280	10	.	.	PUNCT
ejpam-4829	281	1	given	give	VERB
ejpam-4829	281	2	that	that	SCONJ
ejpam-4829	281	3	{	{	PUNCT
ejpam-4829	281	4	a	a	PRON
ejpam-4829	281	5	,	,	PUNCT
ejpam-4829	281	6	x′	x′	NUM
ejpam-4829	281	7	}	}	PUNCT
ejpam-4829	281	8	is	be	AUX
ejpam-4829	281	9	a	a	DET
ejpam-4829	281	10	module	module	NOUN
ejpam-4829	281	11	in	in	ADP
ejpam-4829	281	12	h	h	NOUN
ejpam-4829	281	13	,	,	PUNCT
ejpam-4829	281	14	for	for	ADP
ejpam-4829	281	15	all	all	DET
ejpam-4829	281	16	t	t	NOUN
ejpam-4829	281	17	∈	∈	NOUN
ejpam-4829	281	18	v	v	ADP
ejpam-4829	281	19	\	\	PROPN
ejpam-4829	281	20	{	{	PUNCT
ejpam-4829	281	21	a	a	PRON
ejpam-4829	281	22	,	,	PUNCT
ejpam-4829	281	23	a′	a′	PROPN
ejpam-4829	281	24	,	,	PUNCT
ejpam-4829	281	25	x	x	NOUN
ejpam-4829	281	26	,	,	PUNCT
ejpam-4829	281	27	x′	x′	NUM
ejpam-4829	281	28	}	}	PUNCT
ejpam-4829	281	29	,	,	PUNCT
ejpam-4829	281	30	t	t	PROPN
ejpam-4829	281	31	∼h	∼h	PROPN
ejpam-4829	281	32	{	{	PUNCT
ejpam-4829	281	33	a	a	PRON
ejpam-4829	281	34	,	,	PUNCT
ejpam-4829	281	35	x′	x′	NUM
ejpam-4829	281	36	}	}	PUNCT
ejpam-4829	281	37	.	.	PUNCT
ejpam-4829	282	1	thus	thus	ADV
ejpam-4829	282	2	,	,	PUNCT
ejpam-4829	282	3	for	for	ADP
ejpam-4829	282	4	all	all	DET
ejpam-4829	282	5	t	t	NOUN
ejpam-4829	282	6	∈	∈	NOUN
ejpam-4829	282	7	v	v	ADP
ejpam-4829	282	8	\	\	PROPN
ejpam-4829	282	9	{	{	PUNCT
ejpam-4829	282	10	a	a	PRON
ejpam-4829	282	11	,	,	PUNCT
ejpam-4829	282	12	a′	a′	PROPN
ejpam-4829	282	13	,	,	PUNCT
ejpam-4829	282	14	x	x	NOUN
ejpam-4829	282	15	,	,	PUNCT
ejpam-4829	282	16	x′	x′	NUM
ejpam-4829	282	17	}	}	PUNCT
ejpam-4829	282	18	,	,	PUNCT
ejpam-4829	282	19	t	t	PROPN
ejpam-4829	282	20	∼h	∼h	PROPN
ejpam-4829	282	21	{	{	PUNCT
ejpam-4829	282	22	a	a	PRON
ejpam-4829	282	23	,	,	PUNCT
ejpam-4829	282	24	a′	a′	PROPN
ejpam-4829	282	25	,	,	PUNCT
ejpam-4829	282	26	x′	x′	NUM
ejpam-4829	282	27	}	}	PUNCT
ejpam-4829	282	28	.	.	PUNCT
ejpam-4829	283	1	let	let	VERB
ejpam-4829	283	2	x	x	X
ejpam-4829	283	3	′	′	PRON
ejpam-4829	283	4	be	be	AUX
ejpam-4829	283	5	the	the	DET
ejpam-4829	283	6	greatest	great	ADJ
ejpam-4829	283	7	clique	clique	NOUN
ejpam-4829	283	8	of	of	ADP
ejpam-4829	283	9	z	z	PROPN
ejpam-4829	283	10	(	(	PUNCT
ejpam-4829	283	11	i.e.	i.e.	X
ejpam-4829	283	12	g[x	g[x	ADP
ejpam-4829	283	13	′	′	NOUN
ejpam-4829	283	14	]	]	X
ejpam-4829	283	15	is	be	AUX
ejpam-4829	283	16	a	a	DET
ejpam-4829	283	17	complete	complete	ADJ
ejpam-4829	283	18	graph	graph	NOUN
ejpam-4829	283	19	)	)	PUNCT
ejpam-4829	283	20	such	such	ADJ
ejpam-4829	283	21	that	that	SCONJ
ejpam-4829	283	22	x	x	X
ejpam-4829	284	1	′	′	NUM
ejpam-4829	284	2	=	=	PUNCT
ejpam-4829	284	3	{	{	PUNCT
ejpam-4829	284	4	x′	x′	PROPN
ejpam-4829	284	5	:	:	PUNCT
ejpam-4829	284	6	x′	x′	PROPN
ejpam-4829	284	7	∈	∈	PROPN
ejpam-4829	284	8	z	z	PROPN
ejpam-4829	284	9	and	and	CCONJ
ejpam-4829	284	10	|ng[x∪{x′}](x	|ng[x∪{x′}](x	NUM
ejpam-4829	284	11	′)|	′)|	NOUN
ejpam-4829	284	12	=	=	SYM
ejpam-4829	284	13	1	1	NUM
ejpam-4829	284	14	}	}	PUNCT
ejpam-4829	284	15	and	and	CCONJ
ejpam-4829	284	16	x	x	PUNCT
ejpam-4829	284	17	′′	′′	NOUN
ejpam-4829	284	18	=	=	SYM
ejpam-4829	284	19	z	z	NOUN
ejpam-4829	284	20	\x	\x	NOUN
ejpam-4829	284	21	′.	′.	NOUN
ejpam-4829	284	22	as	as	ADP
ejpam-4829	284	23	g	g	PROPN
ejpam-4829	284	24	−	−	PROPN
ejpam-4829	284	25	a	a	PRON
ejpam-4829	284	26	is	be	AUX
ejpam-4829	284	27	prime	prime	ADJ
ejpam-4829	284	28	,	,	PUNCT
ejpam-4829	284	29	for	for	ADP
ejpam-4829	284	30	all	all	DET
ejpam-4829	284	31	x	x	SYM
ejpam-4829	284	32	∈	∈	PROPN
ejpam-4829	284	33	x	x	NOUN
ejpam-4829	284	34	,	,	PUNCT
ejpam-4829	284	35	there	there	PRON
ejpam-4829	284	36	is	be	VERB
ejpam-4829	284	37	a	a	DET
ejpam-4829	284	38	unique	unique	ADJ
ejpam-4829	284	39	x′	x′	PROPN
ejpam-4829	284	40	∈	∈	NOUN
ejpam-4829	284	41	x	x	PUNCT
ejpam-4829	285	1	′	′	NUM
ejpam-4829	285	2	such	such	ADJ
ejpam-4829	285	3	that	that	SCONJ
ejpam-4829	285	4	xx′	xx′	PROPN
ejpam-4829	285	5	∈	∈	PROPN
ejpam-4829	285	6	e(g	e(g	PROPN
ejpam-4829	285	7	)	)	PUNCT
ejpam-4829	285	8	.	.	PUNCT
ejpam-4829	286	1	as	as	ADP
ejpam-4829	286	2	a	a	DET
ejpam-4829	286	3	result	result	NOUN
ejpam-4829	286	4	,	,	PUNCT
ejpam-4829	286	5	|x|	|x|	PROPN
ejpam-4829	286	6	=	=	SYM
ejpam-4829	286	7	|x	|x	PROPN
ejpam-4829	286	8	′|	′|	PROPN
ejpam-4829	286	9	.	.	PUNCT
ejpam-4829	287	1	if	if	SCONJ
ejpam-4829	287	2	x	x	NUM
ejpam-4829	287	3	′′	′′	NOUN
ejpam-4829	287	4	=	=	NOUN
ejpam-4829	287	5	∅	∅	NOUN
ejpam-4829	287	6	,	,	PUNCT
ejpam-4829	287	7	then	then	ADV
ejpam-4829	287	8	g	g	PROPN
ejpam-4829	287	9	is	be	AUX
ejpam-4829	287	10	a	a	DET
ejpam-4829	287	11	βk,0	βk,0	PROPN
ejpam-4829	287	12	graph	graph	NOUN
ejpam-4829	287	13	,	,	PUNCT
ejpam-4829	287	14	which	which	PRON
ejpam-4829	287	15	contradicts	contradict	VERB
ejpam-4829	287	16	the	the	DET
ejpam-4829	287	17	fact	fact	NOUN
ejpam-4829	287	18	that	that	SCONJ
ejpam-4829	287	19	g	g	PROPN
ejpam-4829	287	20	/∈	/∈	PROPN
ejpam-4829	287	21	b.	b.	PROPN
ejpam-4829	287	22	otherwise	otherwise	ADV
ejpam-4829	287	23	,	,	PUNCT
ejpam-4829	287	24	x	x	X
ejpam-4829	287	25	′′	′′	PROPN
ejpam-4829	287	26	̸=	̸=	PROPN
ejpam-4829	287	27	∅	∅	NOUN
ejpam-4829	287	28	and	and	CCONJ
ejpam-4829	287	29	q	q	ADJ
ejpam-4829	287	30	≥	≥	NUM
ejpam-4829	287	31	1	1	NUM
ejpam-4829	287	32	.	.	PUNCT
ejpam-4829	288	1	since	since	SCONJ
ejpam-4829	288	2	g	g	PROPN
ejpam-4829	288	3	is	be	AUX
ejpam-4829	288	4	not	not	PART
ejpam-4829	288	5	a	a	DET
ejpam-4829	288	6	βk	βk	NOUN
ejpam-4829	288	7	,	,	PUNCT
ejpam-4829	288	8	q	q	NOUN
ejpam-4829	288	9	graph	graph	NOUN
ejpam-4829	288	10	and	and	CCONJ
ejpam-4829	288	11	g	g	NOUN
ejpam-4829	288	12	−	−	PROPN
ejpam-4829	288	13	a	a	DET
ejpam-4829	288	14	=	=	NOUN
ejpam-4829	288	15	h	h	NOUN
ejpam-4829	288	16	−	−	PROPN
ejpam-4829	288	17	a	a	PRON
ejpam-4829	288	18	is	be	AUX
ejpam-4829	288	19	prime	prime	ADJ
ejpam-4829	288	20	,	,	PUNCT
ejpam-4829	288	21	m.	m.	NOUN
ejpam-4829	288	22	bouaziz	bouaziz	PROPN
ejpam-4829	288	23	et	et	PROPN
ejpam-4829	288	24	al	al	PROPN
ejpam-4829	288	25	.	.	PUNCT
ejpam-4829	288	26	/	/	SYM
ejpam-4829	288	27	eur	eur	PROPN
ejpam-4829	288	28	.	.	PUNCT
ejpam-4829	289	1	j.	j.	PROPN
ejpam-4829	289	2	pure	pure	PROPN
ejpam-4829	289	3	appl	appl	PROPN
ejpam-4829	289	4	.	.	PROPN
ejpam-4829	289	5	math	math	PROPN
ejpam-4829	289	6	,	,	PUNCT
ejpam-4829	289	7	16	16	NUM
ejpam-4829	289	8	(	(	PUNCT
ejpam-4829	289	9	4	4	NUM
ejpam-4829	289	10	)	)	PUNCT
ejpam-4829	289	11	(	(	PUNCT
ejpam-4829	289	12	2023	2023	NUM
ejpam-4829	289	13	)	)	PUNCT
ejpam-4829	289	14	,	,	PUNCT
ejpam-4829	289	15	2786	2786	NUM
ejpam-4829	289	16	-	-	SYM
ejpam-4829	289	17	2797	2797	NUM
ejpam-4829	289	18	2795	2795	NUM
ejpam-4829	289	19	g−	g−	PROPN
ejpam-4829	289	20	a	a	PRON
ejpam-4829	289	21	is	be	AUX
ejpam-4829	289	22	not	not	PART
ejpam-4829	289	23	a	a	DET
ejpam-4829	289	24	pk	pk	NOUN
ejpam-4829	289	25	,	,	PUNCT
ejpam-4829	289	26	q	q	NOUN
ejpam-4829	289	27	graph	graph	NOUN
ejpam-4829	289	28	and	and	CCONJ
ejpam-4829	289	29	k	k	PROPN
ejpam-4829	289	30	≥	≥	NUM
ejpam-4829	289	31	3	3	X
ejpam-4829	289	32	.	.	PUNCT
ejpam-4829	290	1	we	we	PRON
ejpam-4829	290	2	distinguish	distinguish	VERB
ejpam-4829	290	3	two	two	NUM
ejpam-4829	290	4	subcases	subcase	NOUN
ejpam-4829	290	5	.	.	PUNCT
ejpam-4829	291	1	in	in	ADP
ejpam-4829	291	2	the	the	DET
ejpam-4829	291	3	first	first	ADJ
ejpam-4829	291	4	subcase	subcase	NOUN
ejpam-4829	291	5	,	,	PUNCT
ejpam-4829	291	6	there	there	PRON
ejpam-4829	291	7	is	be	VERB
ejpam-4829	291	8	y	y	PROPN
ejpam-4829	291	9	∈	∈	PROPN
ejpam-4829	291	10	x	x	PUNCT
ejpam-4829	292	1	′′	′′	NOUN
ejpam-4829	292	2	such	such	ADJ
ejpam-4829	292	3	that	that	SCONJ
ejpam-4829	292	4	|ng[x∪{y}](y)|	|ng[x∪{y}](y)|	PROPN
ejpam-4829	292	5	=	=	SYM
ejpam-4829	292	6	1	1	NUM
ejpam-4829	292	7	(	(	PUNCT
ejpam-4829	292	8	resp	resp	NOUN
ejpam-4829	292	9	.	.	PUNCT
ejpam-4829	293	1	|ng[x∪{y}](y)|	|ng[x∪{y}](y)|	PROPN
ejpam-4829	293	2	=	=	SYM
ejpam-4829	293	3	k	k	PROPN
ejpam-4829	293	4	)	)	PUNCT
ejpam-4829	293	5	and	and	CCONJ
ejpam-4829	293	6	∀t	∀t	PROPN
ejpam-4829	293	7	∈	∈	NOUN
ejpam-4829	293	8	x	x	X
ejpam-4829	293	9	′′	′′	PROPN
ejpam-4829	293	10	\	\	NOUN
ejpam-4829	293	11	{	{	PUNCT
ejpam-4829	293	12	y	y	NOUN
ejpam-4829	293	13	}	}	PUNCT
ejpam-4829	293	14	,	,	PUNCT
ejpam-4829	294	1	ty	ty	INTJ
ejpam-4829	294	2	∈	∈	PROPN
ejpam-4829	294	3	e.	e.	PROPN
ejpam-4829	294	4	thus	thus	ADV
ejpam-4829	294	5	,	,	PUNCT
ejpam-4829	294	6	y	y	PROPN
ejpam-4829	294	7	∈	∈	PROPN
ejpam-4829	294	8	x	x	SYM
ejpam-4829	294	9	′	′	NOUN
ejpam-4829	294	10	,	,	PUNCT
ejpam-4829	294	11	which	which	PRON
ejpam-4829	294	12	contradicts	contradict	VERB
ejpam-4829	294	13	the	the	DET
ejpam-4829	294	14	fact	fact	NOUN
ejpam-4829	294	15	that	that	SCONJ
ejpam-4829	294	16	x	x	SYM
ejpam-4829	294	17	′	′	NOUN
ejpam-4829	294	18	is	be	AUX
ejpam-4829	294	19	the	the	DET
ejpam-4829	294	20	greatest	great	ADJ
ejpam-4829	294	21	clique	clique	NOUN
ejpam-4829	294	22	of	of	ADP
ejpam-4829	294	23	z	z	PROPN
ejpam-4829	294	24	(	(	PUNCT
ejpam-4829	294	25	resp	resp	NOUN
ejpam-4829	294	26	.	.	PUNCT
ejpam-4829	295	1	y	y	PROPN
ejpam-4829	295	2	∈	∈	PROPN
ejpam-4829	295	3	⟨v	⟨v	PUNCT
ejpam-4829	295	4	\	\	NOUN
ejpam-4829	295	5	{	{	PUNCT
ejpam-4829	295	6	y}⟩	y}⟩	PROPN
ejpam-4829	295	7	,	,	PUNCT
ejpam-4829	295	8	which	which	PRON
ejpam-4829	295	9	contradicts	contradict	VERB
ejpam-4829	295	10	the	the	DET
ejpam-4829	295	11	fact	fact	NOUN
ejpam-4829	295	12	that	that	SCONJ
ejpam-4829	295	13	g−	g−	PROPN
ejpam-4829	295	14	a	a	PRON
ejpam-4829	295	15	is	be	AUX
ejpam-4829	295	16	prime	prime	ADJ
ejpam-4829	295	17	)	)	PUNCT
ejpam-4829	295	18	.	.	PUNCT
ejpam-4829	296	1	in	in	ADP
ejpam-4829	296	2	the	the	DET
ejpam-4829	296	3	second	second	ADJ
ejpam-4829	296	4	subcase	subcase	NOUN
ejpam-4829	296	5	,	,	PUNCT
ejpam-4829	296	6	there	there	PRON
ejpam-4829	296	7	is	be	VERB
ejpam-4829	296	8	y	y	PROPN
ejpam-4829	296	9	̸=	̸=	PROPN
ejpam-4829	296	10	z	z	NOUN
ejpam-4829	296	11	∈	∈	PROPN
ejpam-4829	296	12	x	x	X
ejpam-4829	297	1	′′	′′	NOUN
ejpam-4829	297	2	such	such	ADJ
ejpam-4829	297	3	that	that	DET
ejpam-4829	297	4	ng[x∪{y}](y	ng[x∪{y}](y	NOUN
ejpam-4829	297	5	)	)	PUNCT
ejpam-4829	297	6	=	=	SYM
ejpam-4829	297	7	ng[x∪{z}](z	ng[x∪{z}](z	PROPN
ejpam-4829	297	8	)	)	PUNCT
ejpam-4829	297	9	,	,	PUNCT
ejpam-4829	297	10	so	so	CCONJ
ejpam-4829	297	11	{	{	PUNCT
ejpam-4829	297	12	y	y	PROPN
ejpam-4829	297	13	,	,	PUNCT
ejpam-4829	297	14	z	z	NOUN
ejpam-4829	297	15	}	}	PUNCT
ejpam-4829	297	16	is	be	AUX
ejpam-4829	297	17	a	a	DET
ejpam-4829	297	18	non	non	ADJ
ejpam-4829	297	19	-	-	ADJ
ejpam-4829	297	20	trivial	trivial	ADJ
ejpam-4829	297	21	module	module	NOUN
ejpam-4829	297	22	in	in	ADP
ejpam-4829	297	23	g−	g−	PROPN
ejpam-4829	297	24	a	a	PRON
ejpam-4829	297	25	,	,	PUNCT
ejpam-4829	297	26	which	which	PRON
ejpam-4829	297	27	contradicts	contradict	VERB
ejpam-4829	297	28	the	the	DET
ejpam-4829	297	29	fact	fact	NOUN
ejpam-4829	297	30	that	that	SCONJ
ejpam-4829	297	31	g−	g−	PROPN
ejpam-4829	297	32	a	a	PRON
ejpam-4829	297	33	is	be	AUX
ejpam-4829	297	34	prime	prime	ADJ
ejpam-4829	297	35	.	.	PUNCT
ejpam-4829	298	1	lemma	lemma	PROPN
ejpam-4829	298	2	7	7	X
ejpam-4829	298	3	.	.	PUNCT
ejpam-4829	299	1	let	let	VERB
ejpam-4829	299	2	g	g	PRON
ejpam-4829	299	3	be	be	AUX
ejpam-4829	299	4	a	a	DET
ejpam-4829	299	5	decomposable	decomposable	ADJ
ejpam-4829	299	6	graph	graph	NOUN
ejpam-4829	299	7	with	with	ADP
ejpam-4829	299	8	a	a	DET
ejpam-4829	299	9	prime	prime	ADJ
ejpam-4829	299	10	frame	frame	NOUN
ejpam-4829	299	11	containing	contain	VERB
ejpam-4829	299	12	only	only	ADV
ejpam-4829	299	13	one	one	NUM
ejpam-4829	299	14	nontrivial	nontrivial	ADJ
ejpam-4829	299	15	module	module	NOUN
ejpam-4829	299	16	m	m	NOUN
ejpam-4829	299	17	.	.	PUNCT
ejpam-4829	300	1	if	if	SCONJ
ejpam-4829	300	2	g[m	g[m	NOUN
ejpam-4829	300	3	]	]	PUNCT
ejpam-4829	300	4	is	be	AUX
ejpam-4829	300	5	a	a	DET
ejpam-4829	300	6	prime	prime	ADJ
ejpam-4829	300	7	graph	graph	NOUN
ejpam-4829	300	8	,	,	PUNCT
ejpam-4829	300	9	then	then	ADV
ejpam-4829	300	10	there	there	PRON
ejpam-4829	300	11	is	be	VERB
ejpam-4829	300	12	an	an	DET
ejpam-4829	300	13	edge	edge	NOUN
ejpam-4829	300	14	e	e	NOUN
ejpam-4829	300	15	in	in	ADP
ejpam-4829	300	16	g	g	PROPN
ejpam-4829	300	17	such	such	DET
ejpam-4829	300	18	that	that	DET
ejpam-4829	300	19	g+	g+	NOUN
ejpam-4829	300	20	e	e	NOUN
ejpam-4829	300	21	is	be	AUX
ejpam-4829	300	22	prime	prime	ADJ
ejpam-4829	300	23	.	.	PUNCT
ejpam-4829	301	1	proof	proof	NOUN
ejpam-4829	301	2	.	.	PUNCT
ejpam-4829	302	1	let	let	VERB
ejpam-4829	302	2	g	g	PRON
ejpam-4829	302	3	be	be	AUX
ejpam-4829	302	4	a	a	DET
ejpam-4829	302	5	decomposable	decomposable	ADJ
ejpam-4829	302	6	graph	graph	NOUN
ejpam-4829	302	7	on	on	ADP
ejpam-4829	302	8	v	v	NOUN
ejpam-4829	302	9	with	with	ADP
ejpam-4829	302	10	a	a	DET
ejpam-4829	302	11	prime	prime	ADJ
ejpam-4829	302	12	frame	frame	NOUN
ejpam-4829	302	13	containing	contain	VERB
ejpam-4829	302	14	only	only	ADV
ejpam-4829	302	15	one	one	NUM
ejpam-4829	302	16	non	non	ADJ
ejpam-4829	302	17	-	-	ADJ
ejpam-4829	302	18	trivial	trivial	ADJ
ejpam-4829	302	19	module	module	NOUN
ejpam-4829	302	20	m	m	VERB
ejpam-4829	302	21	such	such	ADJ
ejpam-4829	302	22	that	that	DET
ejpam-4829	302	23	g[m	g[m	NOUN
ejpam-4829	302	24	]	]	PUNCT
ejpam-4829	302	25	is	be	AUX
ejpam-4829	302	26	a	a	DET
ejpam-4829	302	27	prime	prime	ADJ
ejpam-4829	302	28	graph	graph	NOUN
ejpam-4829	302	29	.	.	PUNCT
ejpam-4829	303	1	suppose	suppose	VERB
ejpam-4829	303	2	a	a	DET
ejpam-4829	303	3	∈	∈	NOUN
ejpam-4829	303	4	m	m	NOUN
ejpam-4829	303	5	and	and	CCONJ
ejpam-4829	303	6	x	x	X
ejpam-4829	303	7	=	=	NOUN
ejpam-4829	303	8	v	v	NOUN
ejpam-4829	303	9	\{a	\{a	NOUN
ejpam-4829	303	10	}	}	PUNCT
ejpam-4829	303	11	.	.	PUNCT
ejpam-4829	304	1	since	since	SCONJ
ejpam-4829	304	2	the	the	DET
ejpam-4829	304	3	frame	frame	NOUN
ejpam-4829	304	4	of	of	ADP
ejpam-4829	304	5	g	g	PROPN
ejpam-4829	304	6	is	be	AUX
ejpam-4829	304	7	prime	prime	ADJ
ejpam-4829	304	8	and	and	CCONJ
ejpam-4829	304	9	the	the	DET
ejpam-4829	304	10	only	only	ADJ
ejpam-4829	304	11	non	non	ADJ
ejpam-4829	304	12	-	-	ADJ
ejpam-4829	304	13	trivial	trivial	ADJ
ejpam-4829	304	14	module	module	NOUN
ejpam-4829	304	15	is	be	AUX
ejpam-4829	304	16	m	m	PRON
ejpam-4829	304	17	,	,	PUNCT
ejpam-4829	304	18	there	there	PRON
ejpam-4829	304	19	is	be	VERB
ejpam-4829	304	20	b	b	PROPN
ejpam-4829	304	21	∈	∈	NOUN
ejpam-4829	304	22	v	v	ADP
ejpam-4829	304	23	\m	\m	NOUN
ejpam-4829	304	24	such	such	ADJ
ejpam-4829	304	25	that	that	DET
ejpam-4829	304	26	b	b	NOUN
ejpam-4829	304	27	/∈	/∈	PUNCT
ejpam-4829	304	28	ng(m	ng(m	NUM
ejpam-4829	304	29	)	)	PUNCT
ejpam-4829	304	30	.	.	PUNCT
ejpam-4829	305	1	consider	consider	VERB
ejpam-4829	305	2	e	e	NOUN
ejpam-4829	305	3	=	=	PROPN
ejpam-4829	305	4	ab	ab	PROPN
ejpam-4829	305	5	and	and	CCONJ
ejpam-4829	306	1	h	h	NOUN
ejpam-4829	306	2	=	=	PUNCT
ejpam-4829	306	3	g+	g+	PROPN
ejpam-4829	306	4	e.	e.	PROPN
ejpam-4829	307	1	it	it	PRON
ejpam-4829	307	2	’s	’	VERB
ejpam-4829	307	3	clear	clear	ADJ
ejpam-4829	307	4	that	that	SCONJ
ejpam-4829	307	5	h	h	NOUN
ejpam-4829	308	1	−	−	NOUN
ejpam-4829	308	2	a	a	DET
ejpam-4829	308	3	=	=	PUNCT
ejpam-4829	308	4	g−	g−	PROPN
ejpam-4829	308	5	a	a	PRON
ejpam-4829	308	6	is	be	AUX
ejpam-4829	308	7	a	a	DET
ejpam-4829	308	8	graph	graph	NOUN
ejpam-4829	308	9	with	with	ADP
ejpam-4829	308	10	a	a	DET
ejpam-4829	308	11	prime	prime	ADJ
ejpam-4829	308	12	frame	frame	NOUN
ejpam-4829	308	13	having	have	VERB
ejpam-4829	308	14	only	only	ADV
ejpam-4829	308	15	non	non	ADJ
ejpam-4829	308	16	-	-	ADJ
ejpam-4829	308	17	trivial	trivial	ADJ
ejpam-4829	308	18	module	module	NOUN
ejpam-4829	308	19	m	m	NOUN
ejpam-4829	308	20	\	\	PUNCT
ejpam-4829	308	21	{	{	PUNCT
ejpam-4829	308	22	a	a	NOUN
ejpam-4829	308	23	}	}	PUNCT
ejpam-4829	308	24	.	.	PUNCT
ejpam-4829	309	1	as	as	ADP
ejpam-4829	309	2	b	b	PROPN
ejpam-4829	309	3	/∈	/∈	PUNCT
ejpam-4829	309	4	nh(m	nh(m	PUNCT
ejpam-4829	309	5	\	\	PROPN
ejpam-4829	309	6	{	{	PUNCT
ejpam-4829	309	7	a	a	NOUN
ejpam-4829	309	8	}	}	PUNCT
ejpam-4829	309	9	)	)	PUNCT
ejpam-4829	309	10	and	and	CCONJ
ejpam-4829	309	11	ab	ab	PROPN
ejpam-4829	309	12	∈	∈	PROPN
ejpam-4829	309	13	e(h	e(h	PROPN
ejpam-4829	309	14	)	)	PUNCT
ejpam-4829	309	15	,	,	PUNCT
ejpam-4829	309	16	a	a	DET
ejpam-4829	309	17	/∈	/∈	PUNCT
ejpam-4829	309	18	x(m	x(m	PROPN
ejpam-4829	309	19	\	\	PROPN
ejpam-4829	310	1	{	{	PUNCT
ejpam-4829	310	2	a	a	X
ejpam-4829	310	3	}	}	PUNCT
ejpam-4829	310	4	)	)	PUNCT
ejpam-4829	310	5	in	in	ADP
ejpam-4829	310	6	h.	h.	PROPN
ejpam-4829	310	7	given	give	VERB
ejpam-4829	310	8	that	that	DET
ejpam-4829	310	9	g[m	g[m	NOUN
ejpam-4829	310	10	]	]	PUNCT
ejpam-4829	310	11	is	be	AUX
ejpam-4829	310	12	prime	prime	ADJ
ejpam-4829	310	13	,	,	PUNCT
ejpam-4829	310	14	there	there	PRON
ejpam-4829	310	15	are	be	VERB
ejpam-4829	310	16	two	two	NUM
ejpam-4829	310	17	vertices	vertex	NOUN
ejpam-4829	310	18	y	y	PROPN
ejpam-4829	310	19	,	,	PUNCT
ejpam-4829	310	20	z	z	PROPN
ejpam-4829	310	21	∈	∈	PROPN
ejpam-4829	310	22	m	m	VERB
ejpam-4829	310	23	\	\	NOUN
ejpam-4829	310	24	{	{	PUNCT
ejpam-4829	310	25	a	a	NOUN
ejpam-4829	310	26	}	}	PUNCT
ejpam-4829	310	27	such	such	ADJ
ejpam-4829	310	28	that	that	SCONJ
ejpam-4829	310	29	ya	ya	PROPN
ejpam-4829	310	30	∈	∈	PROPN
ejpam-4829	310	31	e(g	e(g	PROPN
ejpam-4829	310	32	)	)	PUNCT
ejpam-4829	310	33	and	and	CCONJ
ejpam-4829	310	34	za	za	PROPN
ejpam-4829	310	35	/∈	/∈	PUNCT
ejpam-4829	310	36	e(g	e(g	PROPN
ejpam-4829	310	37	)	)	PUNCT
ejpam-4829	310	38	.	.	PUNCT
ejpam-4829	311	1	thus	thus	ADV
ejpam-4829	311	2	,	,	PUNCT
ejpam-4829	311	3	a	a	DET
ejpam-4829	311	4	/∈	/∈	PUNCT
ejpam-4829	311	5	⟨x⟩	⟨x⟩	PROPN
ejpam-4829	311	6	in	in	ADP
ejpam-4829	311	7	h.	h.	PROPN
ejpam-4829	311	8	for	for	ADP
ejpam-4829	311	9	all	all	DET
ejpam-4829	311	10	t	t	NOUN
ejpam-4829	311	11	∈	∈	PROPN
ejpam-4829	311	12	(	(	PUNCT
ejpam-4829	311	13	v	v	NOUN
ejpam-4829	311	14	\	\	PROPN
ejpam-4829	311	15	m	m	PROPN
ejpam-4829	311	16	)	)	PUNCT
ejpam-4829	311	17	,	,	PUNCT
ejpam-4829	311	18	t	t	PROPN
ejpam-4829	311	19	∈	∈	PROPN
ejpam-4829	311	20	ng(m	ng(m	PROPN
ejpam-4829	311	21	)	)	PUNCT
ejpam-4829	311	22	or	or	CCONJ
ejpam-4829	311	23	t	t	PROPN
ejpam-4829	311	24	/∈	/∈	PUNCT
ejpam-4829	311	25	ng(m	ng(m	PROPN
ejpam-4829	311	26	)	)	PUNCT
ejpam-4829	311	27	.	.	PUNCT
ejpam-4829	312	1	if	if	SCONJ
ejpam-4829	312	2	t	t	PROPN
ejpam-4829	312	3	∈	∈	PROPN
ejpam-4829	312	4	ng(m	ng(m	NOUN
ejpam-4829	312	5	)	)	PUNCT
ejpam-4829	312	6	,	,	PUNCT
ejpam-4829	312	7	then	then	ADV
ejpam-4829	312	8	zt	zt	PROPN
ejpam-4829	312	9	∈	∈	PROPN
ejpam-4829	312	10	e(g	e(g	PROPN
ejpam-4829	312	11	)	)	PUNCT
ejpam-4829	312	12	.	.	PUNCT
ejpam-4829	313	1	as	as	ADP
ejpam-4829	313	2	a	a	DET
ejpam-4829	313	3	result	result	NOUN
ejpam-4829	313	4	,	,	PUNCT
ejpam-4829	313	5	a	a	DET
ejpam-4829	313	6	/∈	/∈	PUNCT
ejpam-4829	313	7	x(t	x(t	PROPN
ejpam-4829	313	8	)	)	PUNCT
ejpam-4829	313	9	in	in	ADP
ejpam-4829	313	10	h.	h.	PROPN
ejpam-4829	313	11	if	if	SCONJ
ejpam-4829	313	12	t	t	PROPN
ejpam-4829	313	13	/∈	/∈	PUNCT
ejpam-4829	313	14	ng(m	ng(m	PROPN
ejpam-4829	313	15	)	)	PUNCT
ejpam-4829	313	16	,	,	PUNCT
ejpam-4829	313	17	then	then	ADV
ejpam-4829	313	18	yt	yt	X
ejpam-4829	313	19	/∈	/∈	PUNCT
ejpam-4829	313	20	e(g	e(g	PROPN
ejpam-4829	313	21	)	)	PUNCT
ejpam-4829	313	22	.	.	PUNCT
ejpam-4829	314	1	thus	thus	ADV
ejpam-4829	314	2	,	,	PUNCT
ejpam-4829	314	3	a	a	DET
ejpam-4829	314	4	/∈	/∈	PUNCT
ejpam-4829	314	5	x(t	x(t	PROPN
ejpam-4829	314	6	)	)	PUNCT
ejpam-4829	314	7	in	in	ADP
ejpam-4829	314	8	h.	h.	PROPN
ejpam-4829	314	9	therefore	therefore	ADV
ejpam-4829	314	10	,	,	PUNCT
ejpam-4829	314	11	using	use	VERB
ejpam-4829	314	12	assertion	assertion	NOUN
ejpam-4829	314	13	1	1	NUM
ejpam-4829	314	14	of	of	ADP
ejpam-4829	314	15	theorem	theorem	NOUN
ejpam-4829	314	16	2	2	NUM
ejpam-4829	314	17	,	,	PUNCT
ejpam-4829	314	18	a	a	DET
ejpam-4829	314	19	∈	∈	PROPN
ejpam-4829	314	20	ext(x	ext(x	PROPN
ejpam-4829	314	21	)	)	PUNCT
ejpam-4829	314	22	in	in	ADP
ejpam-4829	314	23	h.	h.	PROPN
ejpam-4829	314	24	based	base	VERB
ejpam-4829	314	25	on	on	ADP
ejpam-4829	314	26	assertion	assertion	NOUN
ejpam-4829	314	27	2	2	NUM
ejpam-4829	314	28	of	of	ADP
ejpam-4829	314	29	theorem	theorem	NOUN
ejpam-4829	314	30	2	2	NUM
ejpam-4829	314	31	,	,	PUNCT
ejpam-4829	314	32	if	if	SCONJ
ejpam-4829	314	33	n	n	PRON
ejpam-4829	314	34	∈	∈	NOUN
ejpam-4829	314	35	p(h	p(h	NOUN
ejpam-4829	314	36	)	)	PUNCT
ejpam-4829	314	37	where	where	SCONJ
ejpam-4829	314	38	n	n	PRON
ejpam-4829	314	39	is	be	AUX
ejpam-4829	314	40	a	a	DET
ejpam-4829	314	41	non	non	ADJ
ejpam-4829	314	42	-	-	ADJ
ejpam-4829	314	43	trivial	trivial	ADJ
ejpam-4829	314	44	module	module	NOUN
ejpam-4829	314	45	,	,	PUNCT
ejpam-4829	314	46	then	then	ADV
ejpam-4829	314	47	n	n	PRON
ejpam-4829	314	48	is	be	AUX
ejpam-4829	314	49	a	a	DET
ejpam-4829	314	50	non	non	ADJ
ejpam-4829	314	51	-	-	ADJ
ejpam-4829	314	52	singleton	singleton	ADJ
ejpam-4829	314	53	module	module	NOUN
ejpam-4829	314	54	of	of	ADP
ejpam-4829	314	55	h[m	h[m	PROPN
ejpam-4829	314	56	\	\	NOUN
ejpam-4829	314	57	{	{	PUNCT
ejpam-4829	314	58	a	a	NOUN
ejpam-4829	314	59	}	}	PUNCT
ejpam-4829	314	60	]	]	PUNCT
ejpam-4829	314	61	.	.	PUNCT
ejpam-4829	315	1	hence	hence	ADV
ejpam-4829	315	2	,	,	PUNCT
ejpam-4829	315	3	n	n	PRON
ejpam-4829	315	4	is	be	AUX
ejpam-4829	315	5	a	a	DET
ejpam-4829	315	6	module	module	NOUN
ejpam-4829	315	7	of	of	ADP
ejpam-4829	315	8	h	h	NOUN
ejpam-4829	315	9	−	−	PROPN
ejpam-4829	315	10	a.	a.	NOUN
ejpam-4829	316	1	moreover	moreover	ADV
ejpam-4829	316	2	,	,	PUNCT
ejpam-4829	316	3	a	a	DET
ejpam-4829	316	4	∼h	∼h	PROPN
ejpam-4829	316	5	n	n	NOUN
ejpam-4829	316	6	.	.	PUNCT
ejpam-4829	317	1	then	then	ADV
ejpam-4829	317	2	,	,	PUNCT
ejpam-4829	317	3	a	a	DET
ejpam-4829	317	4	∼g	∼g	NOUN
ejpam-4829	317	5	n	n	PRON
ejpam-4829	317	6	contradicts	contradict	VERB
ejpam-4829	317	7	the	the	DET
ejpam-4829	317	8	fact	fact	NOUN
ejpam-4829	317	9	that	that	SCONJ
ejpam-4829	317	10	g[m	g[m	NOUN
ejpam-4829	317	11	]	]	PUNCT
ejpam-4829	317	12	is	be	AUX
ejpam-4829	317	13	prime	prime	ADJ
ejpam-4829	317	14	.	.	PUNCT
ejpam-4829	318	1	consequently	consequently	ADV
ejpam-4829	318	2	,	,	PUNCT
ejpam-4829	318	3	h	h	NOUN
ejpam-4829	318	4	does	do	AUX
ejpam-4829	318	5	not	not	PART
ejpam-4829	318	6	contain	contain	VERB
ejpam-4829	318	7	any	any	DET
ejpam-4829	318	8	non	non	ADJ
ejpam-4829	318	9	-	-	ADJ
ejpam-4829	318	10	trivial	trivial	ADJ
ejpam-4829	318	11	module	module	NOUN
ejpam-4829	318	12	.	.	PUNCT
ejpam-4829	319	1	therefore	therefore	ADV
ejpam-4829	319	2	,	,	PUNCT
ejpam-4829	319	3	h	h	NOUN
ejpam-4829	319	4	is	be	AUX
ejpam-4829	319	5	a	a	DET
ejpam-4829	319	6	prime	prime	ADJ
ejpam-4829	319	7	graph	graph	NOUN
ejpam-4829	319	8	.	.	PUNCT
ejpam-4829	320	1	lemma	lemma	PROPN
ejpam-4829	320	2	8	8	NUM
ejpam-4829	320	3	.	.	PUNCT
ejpam-4829	321	1	let	let	VERB
ejpam-4829	321	2	g	g	PRON
ejpam-4829	321	3	be	be	AUX
ejpam-4829	321	4	a	a	DET
ejpam-4829	321	5	decomposable	decomposable	ADJ
ejpam-4829	321	6	graph	graph	NOUN
ejpam-4829	321	7	with	with	ADP
ejpam-4829	321	8	an	an	DET
ejpam-4829	321	9	empty	empty	ADJ
ejpam-4829	321	10	frame	frame	NOUN
ejpam-4829	321	11	containing	contain	VERB
ejpam-4829	321	12	only	only	ADV
ejpam-4829	321	13	one	one	NUM
ejpam-4829	321	14	nontrivial	nontrivial	ADJ
ejpam-4829	321	15	module	module	NOUN
ejpam-4829	321	16	m	m	NOUN
ejpam-4829	321	17	.	.	PUNCT
ejpam-4829	322	1	if	if	SCONJ
ejpam-4829	322	2	|m	|m	PRON
ejpam-4829	322	3	|	|	ADV
ejpam-4829	322	4	=	=	SYM
ejpam-4829	322	5	|v	|v	PROPN
ejpam-4829	322	6	(	(	PUNCT
ejpam-4829	322	7	g)|	g)|	INTJ
ejpam-4829	322	8	−	−	PROPN
ejpam-4829	322	9	1	1	NUM
ejpam-4829	322	10	and	and	CCONJ
ejpam-4829	322	11	g[m	g[m	NOUN
ejpam-4829	322	12	]	]	PUNCT
ejpam-4829	322	13	is	be	AUX
ejpam-4829	322	14	a	a	DET
ejpam-4829	322	15	prime	prime	ADJ
ejpam-4829	322	16	graph	graph	NOUN
ejpam-4829	322	17	,	,	PUNCT
ejpam-4829	322	18	then	then	ADV
ejpam-4829	322	19	an	an	DET
ejpam-4829	322	20	edge	edge	NOUN
ejpam-4829	322	21	e	e	NOUN
ejpam-4829	322	22	exists	exist	VERB
ejpam-4829	322	23	in	in	ADP
ejpam-4829	322	24	g	g	PROPN
ejpam-4829	322	25	such	such	DET
ejpam-4829	322	26	that	that	DET
ejpam-4829	322	27	g+	g+	NOUN
ejpam-4829	322	28	e	e	NOUN
ejpam-4829	322	29	is	be	AUX
ejpam-4829	322	30	prime	prime	ADJ
ejpam-4829	322	31	.	.	PUNCT
ejpam-4829	323	1	proof	proof	NOUN
ejpam-4829	323	2	.	.	PUNCT
ejpam-4829	324	1	let	let	VERB
ejpam-4829	324	2	g	g	PRON
ejpam-4829	324	3	be	be	AUX
ejpam-4829	324	4	a	a	DET
ejpam-4829	324	5	decomposable	decomposable	ADJ
ejpam-4829	324	6	graph	graph	NOUN
ejpam-4829	324	7	on	on	ADP
ejpam-4829	324	8	v	v	NOUN
ejpam-4829	324	9	with	with	ADP
ejpam-4829	324	10	an	an	DET
ejpam-4829	324	11	empty	empty	ADJ
ejpam-4829	324	12	frame	frame	NOUN
ejpam-4829	324	13	containing	contain	VERB
ejpam-4829	324	14	only	only	ADV
ejpam-4829	324	15	one	one	NUM
ejpam-4829	324	16	non	non	ADJ
ejpam-4829	324	17	-	-	ADJ
ejpam-4829	324	18	trivial	trivial	ADJ
ejpam-4829	324	19	module	module	NOUN
ejpam-4829	324	20	m	m	VERB
ejpam-4829	324	21	such	such	ADJ
ejpam-4829	324	22	that	that	PRON
ejpam-4829	324	23	v	v	NOUN
ejpam-4829	324	24	(	(	PUNCT
ejpam-4829	324	25	g	g	NOUN
ejpam-4829	324	26	)	)	PUNCT
ejpam-4829	324	27	=	=	PUNCT
ejpam-4829	325	1	m	m	VERB
ejpam-4829	325	2	∪	∪	ADJ
ejpam-4829	325	3	{	{	PUNCT
ejpam-4829	325	4	b	b	NOUN
ejpam-4829	325	5	}	}	PUNCT
ejpam-4829	325	6	and	and	CCONJ
ejpam-4829	325	7	g[m	g[m	NOUN
ejpam-4829	325	8	]	]	PUNCT
ejpam-4829	325	9	is	be	AUX
ejpam-4829	325	10	a	a	DET
ejpam-4829	325	11	prime	prime	ADJ
ejpam-4829	325	12	graph	graph	NOUN
ejpam-4829	325	13	.	.	PUNCT
ejpam-4829	326	1	let	let	VERB
ejpam-4829	326	2	p	p	NOUN
ejpam-4829	326	3	=	=	X
ejpam-4829	326	4	(	(	PUNCT
ejpam-4829	326	5	x1	x1	PROPN
ejpam-4829	326	6	,	,	PUNCT
ejpam-4829	326	7	x2	x2	PROPN
ejpam-4829	326	8	,	,	PUNCT
ejpam-4829	326	9	.	.	PUNCT
ejpam-4829	326	10	.	.	PUNCT
ejpam-4829	326	11	.	.	PUNCT
ejpam-4829	327	1	,	,	PUNCT
ejpam-4829	327	2	xk	xk	AUX
ejpam-4829	327	3	)	)	PUNCT
ejpam-4829	327	4	be	be	VERB
ejpam-4829	327	5	the	the	DET
ejpam-4829	327	6	longest	long	ADJ
ejpam-4829	327	7	prime	prime	ADJ
ejpam-4829	327	8	path	path	NOUN
ejpam-4829	327	9	in	in	ADP
ejpam-4829	327	10	g[m	g[m	NOUN
ejpam-4829	327	11	]	]	PUNCT
ejpam-4829	327	12	with	with	ADP
ejpam-4829	327	13	length	length	NOUN
ejpam-4829	327	14	k.	k.	NOUN
ejpam-4829	327	15	using	use	VERB
ejpam-4829	327	16	lemma	lemma	PROPN
ejpam-4829	327	17	2	2	NUM
ejpam-4829	327	18	,	,	PUNCT
ejpam-4829	327	19	k	k	X
ejpam-4829	327	20	≥	≥	NUM
ejpam-4829	327	21	4	4	X
ejpam-4829	327	22	.	.	PUNCT
ejpam-4829	328	1	consider	consider	VERB
ejpam-4829	328	2	e	e	NOUN
ejpam-4829	328	3	=	=	PRON
ejpam-4829	328	4	bx1	bx1	VERB
ejpam-4829	328	5	and	and	CCONJ
ejpam-4829	328	6	h	h	NOUN
ejpam-4829	329	1	=	=	NOUN
ejpam-4829	329	2	g	g	PROPN
ejpam-4829	329	3	+	+	PROPN
ejpam-4829	329	4	e.	e.	PROPN
ejpam-4829	329	5	h	h	PROPN
ejpam-4829	330	1	−	−	PROPN
ejpam-4829	330	2	b	b	PROPN
ejpam-4829	330	3	=	=	PUNCT
ejpam-4829	330	4	g	g	PROPN
ejpam-4829	330	5	−	−	PROPN
ejpam-4829	330	6	b	b	NOUN
ejpam-4829	330	7	=	=	NOUN
ejpam-4829	330	8	g[m	g[m	NOUN
ejpam-4829	330	9	]	]	PUNCT
ejpam-4829	330	10	is	be	AUX
ejpam-4829	330	11	a	a	DET
ejpam-4829	330	12	prime	prime	ADJ
ejpam-4829	330	13	graph	graph	NOUN
ejpam-4829	330	14	.	.	PUNCT
ejpam-4829	331	1	as	as	ADP
ejpam-4829	331	2	h[{b	h[{b	PROPN
ejpam-4829	331	3	,	,	PUNCT
ejpam-4829	331	4	x1	x1	PROPN
ejpam-4829	331	5	,	,	PUNCT
ejpam-4829	331	6	x2	x2	PROPN
ejpam-4829	331	7	,	,	PUNCT
ejpam-4829	331	8	.	.	PUNCT
ejpam-4829	331	9	.	.	PUNCT
ejpam-4829	331	10	.	.	PUNCT
ejpam-4829	332	1	,	,	PUNCT
ejpam-4829	332	2	xk	xk	PROPN
ejpam-4829	332	3	}	}	PUNCT
ejpam-4829	332	4	]	]	PUNCT
ejpam-4829	332	5	is	be	AUX
ejpam-4829	332	6	a	a	DET
ejpam-4829	332	7	path	path	NOUN
ejpam-4829	332	8	of	of	ADP
ejpam-4829	332	9	a	a	DET
ejpam-4829	332	10	length	length	NOUN
ejpam-4829	332	11	greater	great	ADJ
ejpam-4829	332	12	than	than	ADP
ejpam-4829	332	13	4	4	NUM
ejpam-4829	332	14	,	,	PUNCT
ejpam-4829	332	15	h[{b	h[{b	PROPN
ejpam-4829	332	16	,	,	PUNCT
ejpam-4829	332	17	x1	x1	PROPN
ejpam-4829	332	18	,	,	PUNCT
ejpam-4829	332	19	x2	x2	PROPN
ejpam-4829	332	20	,	,	PUNCT
ejpam-4829	332	21	.	.	PUNCT
ejpam-4829	332	22	.	.	PUNCT
ejpam-4829	333	1	.	.	PUNCT
ejpam-4829	334	1	,	,	PUNCT
ejpam-4829	334	2	xk	xk	PROPN
ejpam-4829	334	3	}	}	PUNCT
ejpam-4829	334	4	]	]	PUNCT
ejpam-4829	334	5	is	be	AUX
ejpam-4829	334	6	prime	prime	ADJ
ejpam-4829	334	7	.	.	PUNCT
ejpam-4829	335	1	hence	hence	ADV
ejpam-4829	335	2	,	,	PUNCT
ejpam-4829	335	3	b	b	X
ejpam-4829	335	4	/∈	/∈	PUNCT
ejpam-4829	336	1	⟨m⟩	⟨m⟩	NOUN
ejpam-4829	336	2	in	in	ADP
ejpam-4829	336	3	h	h	PROPN
ejpam-4829	336	4	and	and	CCONJ
ejpam-4829	336	5	b	b	PROPN
ejpam-4829	336	6	/∈	/∈	PUNCT
ejpam-4829	336	7	m(xi	m(xi	PROPN
ejpam-4829	336	8	)	)	PUNCT
ejpam-4829	336	9	in	in	ADP
ejpam-4829	336	10	h	h	NOUN
ejpam-4829	336	11	for	for	ADP
ejpam-4829	336	12	all	all	DET
ejpam-4829	336	13	1	1	NUM
ejpam-4829	336	14	≤	≤	NUM
ejpam-4829	336	15	i	i	PRON
ejpam-4829	336	16	≤	≤	PROPN
ejpam-4829	336	17	k.	k.	INTJ
ejpam-4829	337	1	if	if	SCONJ
ejpam-4829	337	2	h	h	NOUN
ejpam-4829	337	3	is	be	AUX
ejpam-4829	337	4	not	not	PART
ejpam-4829	337	5	prime	prime	ADJ
ejpam-4829	337	6	,	,	PUNCT
ejpam-4829	337	7	then	then	ADV
ejpam-4829	337	8	,	,	PUNCT
ejpam-4829	337	9	using	use	VERB
ejpam-4829	337	10	lemma	lemma	PROPN
ejpam-4829	337	11	1	1	NUM
ejpam-4829	337	12	,	,	PUNCT
ejpam-4829	337	13	there	there	PRON
ejpam-4829	337	14	is	be	VERB
ejpam-4829	337	15	t	t	PROPN
ejpam-4829	337	16	∈	∈	PROPN
ejpam-4829	337	17	m	m	VERB
ejpam-4829	337	18	\	\	NOUN
ejpam-4829	337	19	{	{	PUNCT
ejpam-4829	337	20	x1	x1	PROPN
ejpam-4829	337	21	,	,	PUNCT
ejpam-4829	337	22	x2	x2	PROPN
ejpam-4829	337	23	,	,	PUNCT
ejpam-4829	337	24	.	.	PUNCT
ejpam-4829	337	25	.	.	PUNCT
ejpam-4829	337	26	.	.	PUNCT
ejpam-4829	338	1	,	,	PUNCT
ejpam-4829	338	2	xk	xk	X
ejpam-4829	338	3	}	}	PUNCT
ejpam-4829	338	4	such	such	DET
ejpam-4829	338	5	that	that	DET
ejpam-4829	338	6	b	b	PROPN
ejpam-4829	338	7	∈	∈	PROPN
ejpam-4829	338	8	m(t	m(t	NOUN
ejpam-4829	338	9	)	)	PUNCT
ejpam-4829	338	10	.	.	PUNCT
ejpam-4829	339	1	thus	thus	ADV
ejpam-4829	339	2	,	,	PUNCT
ejpam-4829	339	3	h[{t	h[{t	PROPN
ejpam-4829	339	4	,	,	PUNCT
ejpam-4829	339	5	x1	x1	PROPN
ejpam-4829	339	6	,	,	PUNCT
ejpam-4829	339	7	x2	x2	PROPN
ejpam-4829	339	8	,	,	PUNCT
ejpam-4829	339	9	.	.	PUNCT
ejpam-4829	339	10	.	.	PUNCT
ejpam-4829	339	11	.	.	PUNCT
ejpam-4829	339	12	,	,	PUNCT
ejpam-4829	340	1	xk	xk	PROPN
ejpam-4829	340	2	}	}	PUNCT
ejpam-4829	340	3	]	]	PUNCT
ejpam-4829	340	4	=	=	SYM
ejpam-4829	340	5	g[{t	g[{t	PROPN
ejpam-4829	340	6	,	,	PUNCT
ejpam-4829	340	7	x1	x1	PROPN
ejpam-4829	340	8	,	,	PUNCT
ejpam-4829	340	9	x2	x2	PROPN
ejpam-4829	340	10	,	,	PUNCT
ejpam-4829	340	11	.	.	PUNCT
ejpam-4829	340	12	.	.	PUNCT
ejpam-4829	340	13	.	.	PUNCT
ejpam-4829	341	1	,	,	PUNCT
ejpam-4829	341	2	xk	xk	PROPN
ejpam-4829	341	3	}	}	PUNCT
ejpam-4829	341	4	]	]	PUNCT
ejpam-4829	341	5	is	be	AUX
ejpam-4829	341	6	a	a	DET
ejpam-4829	341	7	path	path	NOUN
ejpam-4829	341	8	of	of	ADP
ejpam-4829	341	9	length	length	NOUN
ejpam-4829	341	10	k	k	PROPN
ejpam-4829	342	1	+	+	CCONJ
ejpam-4829	342	2	1	1	NUM
ejpam-4829	342	3	,	,	PUNCT
ejpam-4829	342	4	which	which	PRON
ejpam-4829	342	5	is	be	AUX
ejpam-4829	342	6	a	a	DET
ejpam-4829	342	7	contradiction	contradiction	NOUN
ejpam-4829	342	8	.	.	PUNCT
ejpam-4829	343	1	as	as	ADP
ejpam-4829	343	2	a	a	DET
ejpam-4829	343	3	consequence	consequence	NOUN
ejpam-4829	343	4	,	,	PUNCT
ejpam-4829	343	5	based	base	VERB
ejpam-4829	343	6	on	on	ADP
ejpam-4829	343	7	lemma	lemma	PROPN
ejpam-4829	343	8	1	1	NUM
ejpam-4829	343	9	,	,	PUNCT
ejpam-4829	343	10	b	b	PROPN
ejpam-4829	343	11	∈	∈	PROPN
ejpam-4829	343	12	ext(m	ext(m	PROPN
ejpam-4829	343	13	)	)	PUNCT
ejpam-4829	343	14	.	.	PUNCT
ejpam-4829	344	1	therefore	therefore	ADV
ejpam-4829	344	2	,	,	PUNCT
ejpam-4829	344	3	h	h	NOUN
ejpam-4829	344	4	is	be	AUX
ejpam-4829	344	5	a	a	DET
ejpam-4829	344	6	prime	prime	ADJ
ejpam-4829	344	7	graph	graph	NOUN
ejpam-4829	344	8	.	.	PUNCT
ejpam-4829	345	1	our	our	PRON
ejpam-4829	345	2	main	main	ADJ
ejpam-4829	345	3	result	result	NOUN
ejpam-4829	345	4	is	be	AUX
ejpam-4829	345	5	the	the	DET
ejpam-4829	345	6	following	follow	VERB
ejpam-4829	345	7	theorem	theorem	NOUN
ejpam-4829	345	8	:	:	PUNCT
ejpam-4829	345	9	m.	m.	NOUN
ejpam-4829	345	10	bouaziz	bouaziz	PROPN
ejpam-4829	345	11	et	et	PROPN
ejpam-4829	345	12	al	al	PROPN
ejpam-4829	345	13	.	.	PUNCT
ejpam-4829	345	14	/	/	SYM
ejpam-4829	345	15	eur	eur	PROPN
ejpam-4829	345	16	.	.	PUNCT
ejpam-4829	346	1	j.	j.	PROPN
ejpam-4829	346	2	pure	pure	PROPN
ejpam-4829	346	3	appl	appl	PROPN
ejpam-4829	346	4	.	.	PROPN
ejpam-4829	346	5	math	math	PROPN
ejpam-4829	346	6	,	,	PUNCT
ejpam-4829	346	7	16	16	NUM
ejpam-4829	346	8	(	(	PUNCT
ejpam-4829	346	9	4	4	NUM
ejpam-4829	346	10	)	)	PUNCT
ejpam-4829	346	11	(	(	PUNCT
ejpam-4829	346	12	2023	2023	NUM
ejpam-4829	346	13	)	)	PUNCT
ejpam-4829	346	14	,	,	PUNCT
ejpam-4829	346	15	2786	2786	NUM
ejpam-4829	346	16	-	-	SYM
ejpam-4829	346	17	2797	2797	NUM
ejpam-4829	346	18	2796	2796	NUM
ejpam-4829	346	19	theorem	theorem	NOUN
ejpam-4829	346	20	3	3	NUM
ejpam-4829	346	21	.	.	PUNCT
ejpam-4829	347	1	let	let	VERB
ejpam-4829	347	2	g	g	PRON
ejpam-4829	347	3	be	be	AUX
ejpam-4829	347	4	a	a	DET
ejpam-4829	347	5	decomposable	decomposable	ADJ
ejpam-4829	347	6	graph	graph	NOUN
ejpam-4829	347	7	with	with	ADP
ejpam-4829	347	8	at	at	ADV
ejpam-4829	347	9	least	least	ADV
ejpam-4829	347	10	4	4	NUM
ejpam-4829	347	11	vertices	vertex	NOUN
ejpam-4829	347	12	having	have	VERB
ejpam-4829	347	13	exactly	exactly	ADV
ejpam-4829	347	14	one	one	NUM
ejpam-4829	347	15	non	non	ADJ
ejpam-4829	347	16	-	-	ADJ
ejpam-4829	347	17	trivial	trivial	ADJ
ejpam-4829	347	18	module	module	NOUN
ejpam-4829	347	19	m	m	NOUN
ejpam-4829	347	20	.	.	PUNCT
ejpam-4829	348	1	there	there	PRON
ejpam-4829	348	2	is	be	VERB
ejpam-4829	348	3	an	an	DET
ejpam-4829	348	4	edge	edge	NOUN
ejpam-4829	348	5	e	e	NOUN
ejpam-4829	348	6	in	in	ADP
ejpam-4829	348	7	g	g	PROPN
ejpam-4829	349	1	such	such	ADJ
ejpam-4829	349	2	that	that	DET
ejpam-4829	349	3	g	g	PROPN
ejpam-4829	349	4	+	+	CCONJ
ejpam-4829	349	5	e	e	NOUN
ejpam-4829	349	6	is	be	AUX
ejpam-4829	349	7	a	a	DET
ejpam-4829	349	8	prime	prime	ADJ
ejpam-4829	349	9	graph	graph	NOUN
ejpam-4829	349	10	if	if	SCONJ
ejpam-4829	349	11	and	and	CCONJ
ejpam-4829	349	12	only	only	ADV
ejpam-4829	349	13	if	if	SCONJ
ejpam-4829	349	14	one	one	NUM
ejpam-4829	349	15	of	of	ADP
ejpam-4829	349	16	the	the	DET
ejpam-4829	349	17	following	follow	VERB
ejpam-4829	349	18	assertions	assertion	NOUN
ejpam-4829	349	19	holds	hold	VERB
ejpam-4829	349	20	.	.	PUNCT
ejpam-4829	350	1	(	(	PUNCT
ejpam-4829	350	2	i	i	NOUN
ejpam-4829	350	3	)	)	PUNCT
ejpam-4829	350	4	g	g	PROPN
ejpam-4829	350	5	has	have	VERB
ejpam-4829	350	6	a	a	DET
ejpam-4829	350	7	prime	prime	ADJ
ejpam-4829	350	8	frame	frame	NOUN
ejpam-4829	350	9	and	and	CCONJ
ejpam-4829	350	10	g[m	g[m	NOUN
ejpam-4829	350	11	]	]	PUNCT
ejpam-4829	350	12	is	be	AUX
ejpam-4829	350	13	a	a	DET
ejpam-4829	350	14	prime	prime	ADJ
ejpam-4829	350	15	graph	graph	NOUN
ejpam-4829	350	16	or	or	CCONJ
ejpam-4829	350	17	k2	k2	NOUN
ejpam-4829	350	18	.	.	PUNCT
ejpam-4829	351	1	(	(	PUNCT
ejpam-4829	351	2	ii	ii	NOUN
ejpam-4829	351	3	)	)	PUNCT
ejpam-4829	351	4	g	g	PROPN
ejpam-4829	351	5	has	have	VERB
ejpam-4829	351	6	a	a	DET
ejpam-4829	351	7	prime	prime	ADJ
ejpam-4829	351	8	frame	frame	NOUN
ejpam-4829	351	9	,	,	PUNCT
ejpam-4829	351	10	g[m	g[m	NOUN
ejpam-4829	351	11	]	]	PUNCT
ejpam-4829	351	12	is	be	AUX
ejpam-4829	351	13	k2	k2	ADJ
ejpam-4829	351	14	and	and	CCONJ
ejpam-4829	351	15	g	g	PROPN
ejpam-4829	351	16	/∈	/∈	PROPN
ejpam-4829	352	1	b.	b.	PROPN
ejpam-4829	353	1	(	(	PUNCT
ejpam-4829	353	2	iii	iii	X
ejpam-4829	353	3	)	)	PUNCT
ejpam-4829	353	4	g	g	NOUN
ejpam-4829	353	5	has	have	VERB
ejpam-4829	353	6	an	an	DET
ejpam-4829	353	7	empty	empty	ADJ
ejpam-4829	353	8	frame	frame	NOUN
ejpam-4829	353	9	and	and	CCONJ
ejpam-4829	353	10	g[m	g[m	NOUN
ejpam-4829	353	11	]	]	PUNCT
ejpam-4829	353	12	is	be	AUX
ejpam-4829	353	13	a	a	DET
ejpam-4829	353	14	prime	prime	ADJ
ejpam-4829	353	15	graph	graph	NOUN
ejpam-4829	353	16	with	with	ADP
ejpam-4829	353	17	|m	|m	NOUN
ejpam-4829	354	1	|	|	ADV
ejpam-4829	354	2	=	=	SYM
ejpam-4829	354	3	|v	|v	PROPN
ejpam-4829	354	4	(	(	PUNCT
ejpam-4829	354	5	g)|	g)|	INTJ
ejpam-4829	354	6	−	−	NOUN
ejpam-4829	354	7	1	1	NUM
ejpam-4829	354	8	.	.	PUNCT
ejpam-4829	355	1	proof	proof	NOUN
ejpam-4829	355	2	.	.	PUNCT
ejpam-4829	356	1	let	let	VERB
ejpam-4829	356	2	g	g	PRON
ejpam-4829	356	3	be	be	AUX
ejpam-4829	356	4	a	a	DET
ejpam-4829	356	5	decomposable	decomposable	ADJ
ejpam-4829	356	6	graph	graph	NOUN
ejpam-4829	356	7	with	with	ADP
ejpam-4829	356	8	at	at	ADV
ejpam-4829	356	9	least	least	ADV
ejpam-4829	356	10	4	4	NUM
ejpam-4829	356	11	vertices	vertex	NOUN
ejpam-4829	356	12	having	have	VERB
ejpam-4829	356	13	exactly	exactly	ADV
ejpam-4829	356	14	one	one	NUM
ejpam-4829	356	15	non	non	ADJ
ejpam-4829	356	16	-	-	ADJ
ejpam-4829	356	17	trivial	trivial	ADJ
ejpam-4829	356	18	module	module	NOUN
ejpam-4829	356	19	m	m	NOUN
ejpam-4829	356	20	.	.	PUNCT
ejpam-4829	357	1	on	on	ADP
ejpam-4829	357	2	the	the	DET
ejpam-4829	357	3	one	one	NUM
ejpam-4829	357	4	hand	hand	NOUN
ejpam-4829	357	5	,	,	PUNCT
ejpam-4829	357	6	if	if	SCONJ
ejpam-4829	357	7	g	g	PROPN
ejpam-4829	357	8	has	have	VERB
ejpam-4829	357	9	a	a	DET
ejpam-4829	357	10	prime	prime	ADJ
ejpam-4829	357	11	frame	frame	NOUN
ejpam-4829	357	12	,	,	PUNCT
ejpam-4829	357	13	then	then	ADV
ejpam-4829	357	14	g[m	g[m	VERB
ejpam-4829	357	15	]	]	PUNCT
ejpam-4829	357	16	is	be	AUX
ejpam-4829	357	17	k2	k2	ADJ
ejpam-4829	357	18	,	,	PUNCT
ejpam-4829	357	19	k2	k2	ADJ
ejpam-4829	357	20	or	or	CCONJ
ejpam-4829	357	21	prime	prime	NOUN
ejpam-4829	357	22	.	.	PUNCT
ejpam-4829	358	1	first	first	ADV
ejpam-4829	358	2	,	,	PUNCT
ejpam-4829	358	3	if	if	SCONJ
ejpam-4829	358	4	g[m	g[m	NOUN
ejpam-4829	358	5	]	]	PUNCT
ejpam-4829	358	6	=	=	SYM
ejpam-4829	358	7	k2	k2	PROPN
ejpam-4829	358	8	,	,	PUNCT
ejpam-4829	358	9	then	then	ADV
ejpam-4829	358	10	,	,	PUNCT
ejpam-4829	358	11	according	accord	VERB
ejpam-4829	358	12	to	to	ADP
ejpam-4829	358	13	lemma	lemma	PROPN
ejpam-4829	358	14	5	5	NUM
ejpam-4829	358	15	,	,	PUNCT
ejpam-4829	358	16	there	there	PRON
ejpam-4829	358	17	is	be	VERB
ejpam-4829	358	18	an	an	DET
ejpam-4829	358	19	edge	edge	NOUN
ejpam-4829	358	20	e	e	NOUN
ejpam-4829	358	21	in	in	ADP
ejpam-4829	358	22	g	g	PROPN
ejpam-4829	358	23	such	such	DET
ejpam-4829	358	24	that	that	DET
ejpam-4829	358	25	g+	g+	NOUN
ejpam-4829	358	26	e	e	NOUN
ejpam-4829	358	27	is	be	AUX
ejpam-4829	358	28	prime	prime	ADJ
ejpam-4829	358	29	.	.	PUNCT
ejpam-4829	359	1	second	second	ADJ
ejpam-4829	359	2	,	,	PUNCT
ejpam-4829	359	3	if	if	SCONJ
ejpam-4829	359	4	g[m	g[m	NOUN
ejpam-4829	359	5	]	]	PUNCT
ejpam-4829	359	6	=	=	SYM
ejpam-4829	359	7	k2	k2	PROPN
ejpam-4829	359	8	and	and	CCONJ
ejpam-4829	359	9	g	g	PROPN
ejpam-4829	359	10	/∈	/∈	PROPN
ejpam-4829	360	1	b	b	NOUN
ejpam-4829	360	2	,	,	PUNCT
ejpam-4829	360	3	then	then	ADV
ejpam-4829	360	4	,	,	PUNCT
ejpam-4829	360	5	based	base	VERB
ejpam-4829	360	6	on	on	ADP
ejpam-4829	360	7	lemma	lemma	PROPN
ejpam-4829	360	8	6	6	NUM
ejpam-4829	360	9	,	,	PUNCT
ejpam-4829	360	10	there	there	PRON
ejpam-4829	360	11	is	be	VERB
ejpam-4829	360	12	an	an	DET
ejpam-4829	360	13	edge	edge	NOUN
ejpam-4829	360	14	e	e	NOUN
ejpam-4829	360	15	in	in	ADP
ejpam-4829	360	16	g	g	PROPN
ejpam-4829	360	17	such	such	DET
ejpam-4829	360	18	that	that	DET
ejpam-4829	360	19	g+	g+	NOUN
ejpam-4829	360	20	e	e	NOUN
ejpam-4829	360	21	is	be	AUX
ejpam-4829	360	22	prime	prime	ADJ
ejpam-4829	360	23	.	.	PUNCT
ejpam-4829	361	1	third	third	ADJ
ejpam-4829	361	2	,	,	PUNCT
ejpam-4829	361	3	if	if	SCONJ
ejpam-4829	361	4	g[m	g[m	NOUN
ejpam-4829	361	5	]	]	PUNCT
ejpam-4829	361	6	is	be	AUX
ejpam-4829	361	7	a	a	DET
ejpam-4829	361	8	prime	prime	ADJ
ejpam-4829	361	9	graph	graph	NOUN
ejpam-4829	361	10	,	,	PUNCT
ejpam-4829	361	11	then	then	ADV
ejpam-4829	361	12	,	,	PUNCT
ejpam-4829	361	13	using	use	VERB
ejpam-4829	361	14	lemma	lemma	PROPN
ejpam-4829	361	15	7	7	NUM
ejpam-4829	361	16	,	,	PUNCT
ejpam-4829	361	17	there	there	PRON
ejpam-4829	361	18	is	be	VERB
ejpam-4829	361	19	an	an	DET
ejpam-4829	361	20	edge	edge	NOUN
ejpam-4829	361	21	e	e	NOUN
ejpam-4829	361	22	in	in	ADP
ejpam-4829	361	23	g	g	PROPN
ejpam-4829	361	24	such	such	DET
ejpam-4829	361	25	that	that	DET
ejpam-4829	361	26	g+	g+	NOUN
ejpam-4829	361	27	e	e	NOUN
ejpam-4829	361	28	is	be	AUX
ejpam-4829	361	29	prime	prime	ADJ
ejpam-4829	361	30	.	.	PUNCT
ejpam-4829	362	1	on	on	ADP
ejpam-4829	362	2	the	the	DET
ejpam-4829	362	3	other	other	ADJ
ejpam-4829	362	4	hand	hand	NOUN
ejpam-4829	362	5	,	,	PUNCT
ejpam-4829	362	6	if	if	SCONJ
ejpam-4829	362	7	g	g	PROPN
ejpam-4829	362	8	has	have	VERB
ejpam-4829	362	9	an	an	DET
ejpam-4829	362	10	empty	empty	ADJ
ejpam-4829	362	11	frame	frame	NOUN
ejpam-4829	362	12	and	and	CCONJ
ejpam-4829	362	13	v	v	NOUN
ejpam-4829	362	14	(	(	PUNCT
ejpam-4829	362	15	g	g	NOUN
ejpam-4829	362	16	)	)	PUNCT
ejpam-4829	362	17	=	=	PUNCT
ejpam-4829	362	18	m	m	VERB
ejpam-4829	362	19	∪	∪	ADJ
ejpam-4829	362	20	{	{	PUNCT
ejpam-4829	362	21	b	b	NOUN
ejpam-4829	362	22	}	}	PUNCT
ejpam-4829	362	23	where	where	SCONJ
ejpam-4829	362	24	g[m	g[m	NOUN
ejpam-4829	362	25	]	]	PUNCT
ejpam-4829	362	26	is	be	AUX
ejpam-4829	362	27	a	a	DET
ejpam-4829	362	28	prime	prime	ADJ
ejpam-4829	362	29	graph	graph	NOUN
ejpam-4829	362	30	,	,	PUNCT
ejpam-4829	362	31	then	then	ADV
ejpam-4829	362	32	,	,	PUNCT
ejpam-4829	362	33	based	base	VERB
ejpam-4829	362	34	on	on	ADP
ejpam-4829	362	35	lemma	lemma	PROPN
ejpam-4829	362	36	8	8	NUM
ejpam-4829	362	37	,	,	PUNCT
ejpam-4829	362	38	there	there	PRON
ejpam-4829	362	39	is	be	VERB
ejpam-4829	362	40	an	an	DET
ejpam-4829	362	41	edge	edge	NOUN
ejpam-4829	362	42	e	e	NOUN
ejpam-4829	362	43	in	in	ADP
ejpam-4829	362	44	g	g	PROPN
ejpam-4829	362	45	such	such	DET
ejpam-4829	362	46	that	that	DET
ejpam-4829	362	47	g+	g+	NOUN
ejpam-4829	362	48	e	e	NOUN
ejpam-4829	362	49	is	be	AUX
ejpam-4829	362	50	prime	prime	ADJ
ejpam-4829	362	51	.	.	PUNCT
ejpam-4829	363	1	inversely	inversely	ADV
ejpam-4829	363	2	,	,	PUNCT
ejpam-4829	363	3	assume	assume	VERB
ejpam-4829	363	4	that	that	SCONJ
ejpam-4829	363	5	there	there	PRON
ejpam-4829	363	6	is	be	VERB
ejpam-4829	363	7	e	e	NOUN
ejpam-4829	363	8	in	in	ADP
ejpam-4829	363	9	g	g	PROPN
ejpam-4829	363	10	where	where	SCONJ
ejpam-4829	363	11	g+	g+	PROPN
ejpam-4829	363	12	e	e	NOUN
ejpam-4829	363	13	is	be	AUX
ejpam-4829	363	14	prime	prime	ADJ
ejpam-4829	363	15	.	.	PUNCT
ejpam-4829	364	1	it	it	PRON
ejpam-4829	364	2	’s	’	VERB
ejpam-4829	364	3	clear	clear	ADJ
ejpam-4829	364	4	that	that	SCONJ
ejpam-4829	364	5	the	the	DET
ejpam-4829	364	6	frame	frame	NOUN
ejpam-4829	364	7	of	of	ADP
ejpam-4829	364	8	g	g	PROPN
ejpam-4829	364	9	is	be	AUX
ejpam-4829	364	10	not	not	PART
ejpam-4829	364	11	complete	complete	ADJ
ejpam-4829	364	12	.	.	PUNCT
ejpam-4829	365	1	on	on	ADP
ejpam-4829	365	2	the	the	DET
ejpam-4829	365	3	one	one	NUM
ejpam-4829	365	4	hand	hand	NOUN
ejpam-4829	365	5	,	,	PUNCT
ejpam-4829	365	6	if	if	SCONJ
ejpam-4829	365	7	the	the	DET
ejpam-4829	365	8	frame	frame	NOUN
ejpam-4829	365	9	of	of	ADP
ejpam-4829	365	10	g	g	PROPN
ejpam-4829	365	11	is	be	AUX
ejpam-4829	365	12	prime	prime	ADJ
ejpam-4829	365	13	since	since	SCONJ
ejpam-4829	365	14	m	m	PROPN
ejpam-4829	365	15	is	be	AUX
ejpam-4829	365	16	the	the	DET
ejpam-4829	365	17	only	only	ADJ
ejpam-4829	365	18	non	non	ADJ
ejpam-4829	365	19	-	-	ADJ
ejpam-4829	365	20	trivial	trivial	ADJ
ejpam-4829	365	21	module	module	NOUN
ejpam-4829	365	22	in	in	ADP
ejpam-4829	365	23	g	g	PROPN
ejpam-4829	365	24	,	,	PUNCT
ejpam-4829	365	25	then	then	ADV
ejpam-4829	365	26	m	m	VERB
ejpam-4829	365	27	does	do	AUX
ejpam-4829	365	28	not	not	PART
ejpam-4829	365	29	contain	contain	VERB
ejpam-4829	365	30	any	any	DET
ejpam-4829	365	31	non	non	ADJ
ejpam-4829	365	32	-	-	ADJ
ejpam-4829	365	33	trivial	trivial	ADJ
ejpam-4829	365	34	module	module	NOUN
ejpam-4829	365	35	.	.	PUNCT
ejpam-4829	366	1	thus	thus	ADV
ejpam-4829	366	2	,	,	PUNCT
ejpam-4829	366	3	g[m	g[m	NOUN
ejpam-4829	366	4	]	]	PUNCT
ejpam-4829	366	5	is	be	AUX
ejpam-4829	366	6	a	a	DET
ejpam-4829	366	7	prime	prime	ADJ
ejpam-4829	366	8	graph	graph	NOUN
ejpam-4829	366	9	or	or	CCONJ
ejpam-4829	366	10	g[m	g[m	NOUN
ejpam-4829	366	11	]	]	PUNCT
ejpam-4829	366	12	∈	∈	PROPN
ejpam-4829	366	13	{	{	PUNCT
ejpam-4829	366	14	k2,k2	k2,k2	PROPN
ejpam-4829	366	15	}	}	PUNCT
ejpam-4829	366	16	.	.	PUNCT
ejpam-4829	367	1	assume	assume	VERB
ejpam-4829	367	2	that	that	SCONJ
ejpam-4829	367	3	g[m	g[m	NOUN
ejpam-4829	367	4	]	]	PUNCT
ejpam-4829	367	5	=	=	SYM
ejpam-4829	367	6	k2	k2	PROPN
ejpam-4829	367	7	.	.	PUNCT
ejpam-4829	368	1	as	as	SCONJ
ejpam-4829	368	2	g	g	PROPN
ejpam-4829	368	3	+	+	CCONJ
ejpam-4829	368	4	e	e	NOUN
ejpam-4829	368	5	is	be	AUX
ejpam-4829	368	6	prime	prime	ADJ
ejpam-4829	368	7	,	,	PUNCT
ejpam-4829	368	8	the	the	DET
ejpam-4829	368	9	lemma	lemma	PROPN
ejpam-4829	368	10	4	4	NUM
ejpam-4829	368	11	implies	imply	VERB
ejpam-4829	368	12	g	g	PROPN
ejpam-4829	368	13	/∈	/∈	PROPN
ejpam-4829	368	14	b.	b.	PROPN
ejpam-4829	369	1	on	on	ADP
ejpam-4829	369	2	the	the	DET
ejpam-4829	369	3	other	other	ADJ
ejpam-4829	369	4	hand	hand	NOUN
ejpam-4829	369	5	,	,	PUNCT
ejpam-4829	369	6	if	if	SCONJ
ejpam-4829	369	7	the	the	DET
ejpam-4829	369	8	frame	frame	NOUN
ejpam-4829	369	9	is	be	AUX
ejpam-4829	369	10	empty	empty	ADJ
ejpam-4829	369	11	knowing	know	VERB
ejpam-4829	369	12	that	that	SCONJ
ejpam-4829	369	13	each	each	DET
ejpam-4829	369	14	element	element	NOUN
ejpam-4829	369	15	of	of	ADP
ejpam-4829	369	16	p(g	p(g	NOUN
ejpam-4829	369	17	)	)	PUNCT
ejpam-4829	369	18	is	be	AUX
ejpam-4829	369	19	a	a	DET
ejpam-4829	369	20	module	module	NOUN
ejpam-4829	369	21	of	of	ADP
ejpam-4829	369	22	g	g	PROPN
ejpam-4829	369	23	and	and	CCONJ
ejpam-4829	369	24	g	g	PROPN
ejpam-4829	369	25	contains	contain	VERB
ejpam-4829	369	26	only	only	ADV
ejpam-4829	369	27	one	one	NUM
ejpam-4829	369	28	non	non	ADJ
ejpam-4829	369	29	-	-	ADJ
ejpam-4829	369	30	trivial	trivial	ADJ
ejpam-4829	369	31	module	module	NOUN
ejpam-4829	369	32	m	m	NOUN
ejpam-4829	369	33	,	,	PUNCT
ejpam-4829	369	34	then	then	ADV
ejpam-4829	369	35	v	v	NOUN
ejpam-4829	369	36	\	\	NOUN
ejpam-4829	369	37	m	m	VERB
ejpam-4829	369	38	is	be	AUX
ejpam-4829	369	39	a	a	DET
ejpam-4829	369	40	module	module	NOUN
ejpam-4829	369	41	.	.	PUNCT
ejpam-4829	370	1	given	give	VERB
ejpam-4829	370	2	that	that	SCONJ
ejpam-4829	370	3	m	m	NOUN
ejpam-4829	370	4	is	be	AUX
ejpam-4829	370	5	the	the	DET
ejpam-4829	370	6	unique	unique	ADJ
ejpam-4829	370	7	non	non	ADJ
ejpam-4829	370	8	-	-	ADJ
ejpam-4829	370	9	trivial	trivial	ADJ
ejpam-4829	370	10	module	module	NOUN
ejpam-4829	370	11	,	,	PUNCT
ejpam-4829	370	12	v	v	ADP
ejpam-4829	370	13	\m	\m	NOUN
ejpam-4829	370	14	is	be	AUX
ejpam-4829	370	15	a	a	DET
ejpam-4829	370	16	trivial	trivial	ADJ
ejpam-4829	370	17	module	module	NOUN
ejpam-4829	370	18	.	.	PUNCT
ejpam-4829	371	1	thus	thus	ADV
ejpam-4829	371	2	,	,	PUNCT
ejpam-4829	371	3	v	v	ADP
ejpam-4829	371	4	\m	\m	NOUN
ejpam-4829	371	5	is	be	AUX
ejpam-4829	371	6	a	a	DET
ejpam-4829	371	7	singleton	singleton	NOUN
ejpam-4829	371	8	.	.	PUNCT
ejpam-4829	372	1	therefore	therefore	ADV
ejpam-4829	372	2	,	,	PUNCT
ejpam-4829	372	3	the	the	DET
ejpam-4829	372	4	frame	frame	NOUN
ejpam-4829	372	5	of	of	ADP
ejpam-4829	372	6	g	g	PROPN
ejpam-4829	372	7	is	be	AUX
ejpam-4829	372	8	isomorphic	isomorphic	ADJ
ejpam-4829	372	9	to	to	ADP
ejpam-4829	372	10	k2	k2	ADJ
ejpam-4829	372	11	,	,	PUNCT
ejpam-4829	372	12	g[m	g[m	NOUN
ejpam-4829	372	13	]	]	PUNCT
ejpam-4829	372	14	is	be	AUX
ejpam-4829	372	15	a	a	DET
ejpam-4829	372	16	prime	prime	ADJ
ejpam-4829	372	17	graph	graph	NOUN
ejpam-4829	372	18	and	and	CCONJ
ejpam-4829	372	19	|m	|m	NOUN
ejpam-4829	372	20	|	|	ADV
ejpam-4829	372	21	=	=	SYM
ejpam-4829	372	22	|v	|v	PROPN
ejpam-4829	372	23	(	(	PUNCT
ejpam-4829	372	24	g)|	g)|	INTJ
ejpam-4829	372	25	−	−	NOUN
ejpam-4829	372	26	1	1	NUM
ejpam-4829	372	27	.	.	PUNCT
ejpam-4829	373	1	acknowledgements	acknowledgement	NOUN
ejpam-4829	373	2	the	the	DET
ejpam-4829	373	3	authors	author	NOUN
ejpam-4829	373	4	would	would	AUX
ejpam-4829	373	5	like	like	VERB
ejpam-4829	373	6	to	to	PART
ejpam-4829	373	7	extend	extend	VERB
ejpam-4829	373	8	their	their	PRON
ejpam-4829	373	9	sincere	sincere	ADJ
ejpam-4829	373	10	appreciations	appreciation	NOUN
ejpam-4829	373	11	to	to	ADP
ejpam-4829	373	12	the	the	DET
ejpam-4829	373	13	researchers	researcher	NOUN
ejpam-4829	373	14	supporting	support	VERB
ejpam-4829	373	15	program	program	NOUN
ejpam-4829	373	16	for	for	ADP
ejpam-4829	373	17	its	its	PRON
ejpam-4829	373	18	funding	funding	NOUN
ejpam-4829	373	19	of	of	ADP
ejpam-4829	373	20	this	this	DET
ejpam-4829	373	21	research	research	NOUN
ejpam-4829	373	22	through	through	ADP
ejpam-4829	373	23	the	the	DET
ejpam-4829	373	24	researchers	researcher	NOUN
ejpam-4829	373	25	supporting	support	VERB
ejpam-4829	373	26	references	reference	NOUN
ejpam-4829	373	27	2797	2797	NUM
ejpam-4829	373	28	project	project	NOUN
ejpam-4829	373	29	number	number	NOUN
ejpam-4829	373	30	(	(	PUNCT
ejpam-4829	373	31	rspd2023r1063	rspd2023r1063	NOUN
ejpam-4829	373	32	)	)	PUNCT
ejpam-4829	373	33	.	.	PUNCT
ejpam-4829	374	1	the	the	DET
ejpam-4829	374	2	authors	author	NOUN
ejpam-4829	374	3	are	be	AUX
ejpam-4829	374	4	pleased	pleased	ADJ
ejpam-4829	374	5	to	to	PART
ejpam-4829	374	6	thank	thank	VERB
ejpam-4829	374	7	the	the	DET
ejpam-4829	374	8	anonymous	anonymous	ADJ
ejpam-4829	374	9	referees	referee	NOUN
ejpam-4829	374	10	for	for	ADP
ejpam-4829	374	11	their	their	PRON
ejpam-4829	374	12	careful	careful	ADJ
ejpam-4829	374	13	reading	reading	NOUN
ejpam-4829	374	14	and	and	CCONJ
ejpam-4829	374	15	helpful	helpful	ADJ
ejpam-4829	374	16	suggestions	suggestion	NOUN
ejpam-4829	374	17	.	.	PUNCT
ejpam-4829	375	1	the	the	DET
ejpam-4829	375	2	authors	author	NOUN
ejpam-4829	375	3	are	be	AUX
ejpam-4829	375	4	grateful	grateful	ADJ
ejpam-4829	375	5	to	to	ADP
ejpam-4829	375	6	youssef	youssef	PROPN
ejpam-4829	375	7	boudabbous	boudabbous	ADJ
ejpam-4829	375	8	for	for	ADP
ejpam-4829	375	9	suggesting	suggest	VERB
ejpam-4829	375	10	the	the	DET
ejpam-4829	375	11	problem	problem	NOUN
ejpam-4829	375	12	for	for	ADP
ejpam-4829	375	13	this	this	DET
ejpam-4829	375	14	research	research	NOUN
ejpam-4829	375	15	paper	paper	NOUN
ejpam-4829	375	16	.	.	PUNCT
ejpam-4829	376	1	references	reference	NOUN
ejpam-4829	376	2	[	[	X
ejpam-4829	376	3	1	1	X
ejpam-4829	376	4	]	]	X
ejpam-4829	376	5	ja	ja	PROPN
ejpam-4829	376	6	bondy	bondy	PROPN
ejpam-4829	376	7	.	.	PUNCT
ejpam-4829	377	1	basic	basic	ADJ
ejpam-4829	377	2	graph	graph	NOUN
ejpam-4829	377	3	theory	theory	NOUN
ejpam-4829	377	4	:	:	PUNCT
ejpam-4829	377	5	paths	path	NOUN
ejpam-4829	377	6	and	and	CCONJ
ejpam-4829	377	7	circuits	circuit	NOUN
ejpam-4829	377	8	.	.	PUNCT
ejpam-4829	378	1	handbook	handbook	NOUN
ejpam-4829	378	2	of	of	ADP
ejpam-4829	378	3	combinatorics	combinatoric	NOUN
ejpam-4829	378	4	,	,	PUNCT
ejpam-4829	378	5	1:3–10	1:3–10	NUM
ejpam-4829	378	6	,	,	PUNCT
ejpam-4829	378	7	1995	1995	NUM
ejpam-4829	378	8	.	.	PUNCT
ejpam-4829	379	1	[	[	X
ejpam-4829	379	2	2	2	NUM
ejpam-4829	379	3	]	]	X
ejpam-4829	379	4	y	y	PROPN
ejpam-4829	379	5	boudabbous	boudabbous	ADJ
ejpam-4829	379	6	and	and	CCONJ
ejpam-4829	379	7	p	p	PROPN
ejpam-4829	379	8	ille	ille	PROPN
ejpam-4829	379	9	.	.	PUNCT
ejpam-4829	380	1	cut	cut	NOUN
ejpam-4829	380	2	-	-	PUNCT
ejpam-4829	380	3	primitive	primitive	ADJ
ejpam-4829	380	4	directed	direct	VERB
ejpam-4829	380	5	graphs	graph	NOUN
ejpam-4829	380	6	versus	versus	ADP
ejpam-4829	380	7	clan	clan	NOUN
ejpam-4829	380	8	-	-	PUNCT
ejpam-4829	380	9	primitive	primitive	ADJ
ejpam-4829	380	10	directed	direct	VERB
ejpam-4829	380	11	graphs	graph	NOUN
ejpam-4829	380	12	.	.	PUNCT
ejpam-4829	381	1	adv	adv	INTJ
ejpam-4829	381	2	.	.	PUNCT
ejpam-4829	382	1	pure	pure	ADJ
ejpam-4829	382	2	appl	appl	PROPN
ejpam-4829	382	3	.	.	PUNCT
ejpam-4829	382	4	math	math	PROPN
ejpam-4829	382	5	,	,	PUNCT
ejpam-4829	382	6	1:223–231	1:223–231	PROPN
ejpam-4829	382	7	,	,	PUNCT
ejpam-4829	382	8	2010	2010	NUM
ejpam-4829	382	9	.	.	PUNCT
ejpam-4829	383	1	[	[	X
ejpam-4829	383	2	3	3	X
ejpam-4829	383	3	]	]	PUNCT
ejpam-4829	383	4	a	a	DET
ejpam-4829	383	5	ehrenfeucht	ehrenfeucht	NOUN
ejpam-4829	383	6	and	and	CCONJ
ejpam-4829	383	7	g	g	PROPN
ejpam-4829	383	8	rozenberg	rozenberg	PROPN
ejpam-4829	383	9	.	.	PUNCT
ejpam-4829	384	1	primitivity	primitivity	NOUN
ejpam-4829	384	2	is	be	AUX
ejpam-4829	384	3	hereditary	hereditary	ADJ
ejpam-4829	384	4	for	for	ADP
ejpam-4829	384	5	2	2	NUM
ejpam-4829	384	6	-	-	PUNCT
ejpam-4829	384	7	structures	structure	NOUN
ejpam-4829	384	8	,	,	PUNCT
ejpam-4829	384	9	fundamental	fundamental	ADJ
ejpam-4829	384	10	study	study	NOUN
ejpam-4829	384	11	.	.	PUNCT
ejpam-4829	385	1	theoret	theoret	ADJ
ejpam-4829	385	2	.	.	PUNCT
ejpam-4829	386	1	comput	comput	NOUN
ejpam-4829	386	2	.	.	PUNCT
ejpam-4829	387	1	sci	sci	PROPN
ejpam-4829	387	2	,	,	PUNCT
ejpam-4829	387	3	3(70):343–358	3(70):343–358	NOUN
ejpam-4829	387	4	,	,	PUNCT
ejpam-4829	387	5	1990	1990	NUM
ejpam-4829	387	6	.	.	PUNCT
ejpam-4829	388	1	[	[	X
ejpam-4829	388	2	4	4	NUM
ejpam-4829	388	3	]	]	PUNCT
ejpam-4829	388	4	t	t	NOUN
ejpam-4829	388	5	gallai	gallai	NOUN
ejpam-4829	388	6	.	.	PUNCT
ejpam-4829	389	1	transitiv	transitiv	PROPN
ejpam-4829	389	2	orientierbare	orientierbare	PROPN
ejpam-4829	389	3	graphen	graphen	PROPN
ejpam-4829	389	4	.	.	PUNCT
ejpam-4829	390	1	acta	acta	PROPN
ejpam-4829	390	2	math	math	PROPN
ejpam-4829	390	3	.	.	PUNCT
ejpam-4829	391	1	acad	acad	PROPN
ejpam-4829	391	2	.	.	PUNCT
ejpam-4829	392	1	sci	sci	PROPN
ejpam-4829	392	2	.	.	PROPN
ejpam-4829	392	3	hungar	hungar	PROPN
ejpam-4829	392	4	,	,	PUNCT
ejpam-4829	392	5	18:25–66	18:25–66	NUM
ejpam-4829	392	6	,	,	PUNCT
ejpam-4829	392	7	1967	1967	NUM
ejpam-4829	392	8	.	.	PUNCT
ejpam-4829	393	1	[	[	X
ejpam-4829	393	2	5	5	X
ejpam-4829	393	3	]	]	PUNCT
ejpam-4829	393	4	f	f	NOUN
ejpam-4829	393	5	maffray	maffray	NOUN
ejpam-4829	393	6	and	and	CCONJ
ejpam-4829	393	7	m	m	VERB
ejpam-4829	393	8	preissmann	preissmann	NOUN
ejpam-4829	393	9	.	.	PUNCT
ejpam-4829	394	1	a	a	DET
ejpam-4829	394	2	translation	translation	NOUN
ejpam-4829	394	3	of	of	ADP
ejpam-4829	394	4	tibor	tibor	PROPN
ejpam-4829	394	5	gallai	gallai	PROPN
ejpam-4829	394	6	’s	’s	PART
ejpam-4829	394	7	paper	paper	NOUN
ejpam-4829	394	8	:	:	PUNCT
ejpam-4829	394	9	transitiv	transitiv	PROPN
ejpam-4829	394	10	orientierbare	orientierbare	NOUN
ejpam-4829	394	11	graphen	graphen	PROPN
ejpam-4829	394	12	.	.	PUNCT
ejpam-4829	395	1	in	in	ADP
ejpam-4829	395	2	:	:	PUNCT
ejpam-4829	395	3	perfect	perfect	ADJ
ejpam-4829	395	4	graphs	graph	NOUN
ejpam-4829	395	5	,	,	PUNCT
ejpam-4829	395	6	j.l	j.l	PROPN
ejpam-4829	395	7	.	.	PROPN
ejpam-4829	395	8	ramirez	ramirez	PROPN
ejpam-4829	395	9	-	-	PUNCT
ejpam-4829	395	10	alfonsin	alfonsin	PROPN
ejpam-4829	395	11	and	and	CCONJ
ejpam-4829	395	12	b.a	b.a	PROPN
ejpam-4829	395	13	.	.	PROPN
ejpam-4829	395	14	reed	reed	PROPN
ejpam-4829	395	15	eds	eds	PROPN
ejpam-4829	395	16	.	.	PROPN
ejpam-4829	395	17	,	,	PUNCT
ejpam-4829	395	18	j.	j.	PROPN
ejpam-4829	395	19	wiley	wiley	PROPN
ejpam-4829	395	20	,	,	PUNCT
ejpam-4829	395	21	pages	page	NOUN
ejpam-4829	395	22	25–66	25–66	NUM
ejpam-4829	395	23	,	,	PUNCT
ejpam-4829	395	24	2001	2001	NUM
ejpam-4829	395	25	.	.	PUNCT
ejpam-4829	396	1	[	[	X
ejpam-4829	396	2	6	6	NUM
ejpam-4829	396	3	]	]	PUNCT
ejpam-4829	396	4	j	j	PROPN
ejpam-4829	396	5	spinrad	spinrad	NOUN
ejpam-4829	396	6	.	.	PUNCT
ejpam-4829	397	1	p4	p4	ADJ
ejpam-4829	397	2	-	-	PUNCT
ejpam-4829	397	3	trees	tree	NOUN
ejpam-4829	397	4	and	and	CCONJ
ejpam-4829	397	5	substitution	substitution	NOUN
ejpam-4829	397	6	decomposition	decomposition	NOUN
ejpam-4829	397	7	.	.	PUNCT
ejpam-4829	398	1	discrete	discrete	ADJ
ejpam-4829	398	2	applied	applied	ADJ
ejpam-4829	398	3	mathematics	mathematic	NOUN
ejpam-4829	398	4	,	,	PUNCT
ejpam-4829	398	5	3(39):263–291	3(39):263–291	NUM
ejpam-4829	398	6	,	,	PUNCT
ejpam-4829	398	7	1992	1992	NUM
ejpam-4829	398	8	.	.	PUNCT
ejpam-4829	399	1	[	[	X
ejpam-4829	399	2	7	7	X
ejpam-4829	399	3	]	]	X
ejpam-4829	399	4	d	d	X
ejpam-4829	399	5	p	p	PROPN
ejpam-4829	399	6	sumner	sumner	PROPN
ejpam-4829	399	7	.	.	PUNCT
ejpam-4829	400	1	graphs	graph	NOUN
ejpam-4829	400	2	indecomposable	indecomposable	ADJ
ejpam-4829	400	3	with	with	ADP
ejpam-4829	400	4	respect	respect	NOUN
ejpam-4829	400	5	to	to	ADP
ejpam-4829	400	6	the	the	DET
ejpam-4829	400	7	x	x	NOUN
ejpam-4829	400	8	-	-	NOUN
ejpam-4829	400	9	join	join	VERB
ejpam-4829	400	10	.	.	PUNCT
ejpam-4829	401	1	discrete	discrete	ADJ
ejpam-4829	401	2	mathematics	mathematic	NOUN
ejpam-4829	401	3	,	,	PUNCT
ejpam-4829	401	4	6(39):281–298	6(39):281–298	NUM
ejpam-4829	401	5	,	,	PUNCT
ejpam-4829	401	6	1971	1971	NUM
ejpam-4829	401	7	.	.	PUNCT
ejpam-4829	402	1	[	[	X
ejpam-4829	402	2	8	8	NUM
ejpam-4829	402	3	]	]	X
ejpam-4829	402	4	d	d	X
ejpam-4829	402	5	west	west	PROPN
ejpam-4829	402	6	.	.	PUNCT
ejpam-4829	403	1	introduction	introduction	NOUN
ejpam-4829	403	2	to	to	AUX
ejpam-4829	403	3	graph	graph	NOUN
ejpam-4829	403	4	theory	theory	NOUN
ejpam-4829	403	5	,	,	PUNCT
ejpam-4829	403	6	second	second	ADJ
ejpam-4829	403	7	ed	ed	NOUN
ejpam-4829	403	8	.	.	PUNCT
ejpam-4829	403	9	prentice	prentice	PROPN
ejpam-4829	403	10	hall	hall	PROPN
ejpam-4829	403	11	,	,	PUNCT
ejpam-4829	403	12	2001	2001	NUM
ejpam-4829	403	13	.	.	PUNCT