id	sid	tid	token	lemma	pos
cana-2576	1	1	communications	communication	NOUN
cana-2576	1	2	on	on	ADP
cana-2576	1	3	applied	apply	VERB
cana-2576	1	4	nonlinear	nonlinear	ADJ
cana-2576	1	5	analysis	analysis	NOUN
cana-2576	1	6	issn	issn	NOUN
cana-2576	1	7	:	:	PUNCT
cana-2576	1	8	1074	1074	NUM
cana-2576	1	9	-	-	PUNCT
cana-2576	1	10	133x	133x	NUM
cana-2576	1	11	vol	vol	NOUN
cana-2576	1	12	32	32	NUM
cana-2576	1	13	no	no	NOUN
cana-2576	1	14	.	.	PUNCT
cana-2576	2	1	3s	3s	NUM
cana-2576	2	2	(	(	PUNCT
cana-2576	2	3	2025	2025	NUM
cana-2576	2	4	)	)	PUNCT
cana-2576	2	5	154	154	NUM
cana-2576	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2576	2	7	relatively	relatively	ADV
cana-2576	2	8	prime	prime	ADJ
cana-2576	2	9	domination	domination	NOUN
cana-2576	2	10	number	number	NOUN
cana-2576	2	11	in	in	ADP
cana-2576	2	12	quadrilateral	quadrilateral	ADJ
cana-2576	2	13	snake	snake	NOUN
cana-2576	2	14	graphs	graph	NOUN
cana-2576	2	15	a.	a.	PROPN
cana-2576	2	16	anat	anat	PROPN
cana-2576	2	17	jaslin	jaslin	PROPN
cana-2576	2	18	jini1	jini1	PROPN
cana-2576	2	19	*	*	PROPN
cana-2576	2	20	,	,	PUNCT
cana-2576	2	21	a.	a.	NOUN
cana-2576	2	22	jancy	jancy	PROPN
cana-2576	2	23	vini1	vini1	PROPN
cana-2576	2	24	,	,	PUNCT
cana-2576	2	25	b.	b.	PROPN
cana-2576	2	26	shoba2	shoba2	PROPN
cana-2576	2	27	,	,	PUNCT
cana-2576	2	28	s.	s.	PROPN
cana-2576	2	29	manikanda	manikanda	PROPN
cana-2576	2	30	prabhu2	prabhu2	PROPN
cana-2576	2	31	,	,	PUNCT
cana-2576	2	32	p.	p.	NOUN
cana-2576	2	33	chellamani2	chellamani2	X
cana-2576	3	1	1department	1department	NUM
cana-2576	3	2	of	of	ADP
cana-2576	3	3	mathematics	mathematic	NOUN
cana-2576	3	4	,	,	PUNCT
cana-2576	3	5	holy	holy	PROPN
cana-2576	3	6	cross	cross	PROPN
cana-2576	3	7	college	college	PROPN
cana-2576	3	8	(	(	PUNCT
cana-2576	3	9	autonomous	autonomous	ADJ
cana-2576	3	10	)	)	PUNCT
cana-2576	3	11	,	,	PUNCT
cana-2576	3	12	nagercoil	nagercoil	NOUN
cana-2576	3	13	4	4	NUM
cana-2576	3	14	,	,	PUNCT
cana-2576	3	15	tamilnadu	tamilnadu	ADJ
cana-2576	3	16	,	,	PUNCT
cana-2576	3	17	india	india	PROPN
cana-2576	3	18	.	.	PUNCT
cana-2576	4	1	2department	2department	NUM
cana-2576	4	2	of	of	ADP
cana-2576	4	3	mathematics	mathematics	PROPN
cana-2576	4	4	,	,	PUNCT
cana-2576	4	5	st	st	PROPN
cana-2576	4	6	.	.	PROPN
cana-2576	4	7	joseph	joseph	PROPN
cana-2576	4	8	’s	’s	PART
cana-2576	4	9	college	college	PROPN
cana-2576	4	10	of	of	ADP
cana-2576	4	11	engineering	engineering	PROPN
cana-2576	4	12	,	,	PUNCT
cana-2576	4	13	omr	omr	PROPN
cana-2576	4	14	,	,	PUNCT
cana-2576	4	15	chennai	chennai	NOUN
cana-2576	4	16	–	–	PUNCT
cana-2576	4	17	600	600	NUM
cana-2576	4	18	119	119	NUM
cana-2576	4	19	,	,	PUNCT
cana-2576	4	20	tamil	tamil	PROPN
cana-2576	4	21	nadu	nadu	PROPN
cana-2576	4	22	,	,	PUNCT
cana-2576	4	23	india	india	PROPN
cana-2576	4	24	.	.	PUNCT
cana-2576	5	1	∗corresponding	∗corresponde	VERB
cana-2576	5	2	author	author	NOUN
cana-2576	5	3	:	:	PUNCT
cana-2576	5	4	anatjaslin@holycrossngl.edu.in	anatjaslin@holycrossngl.edu.in	NOUN
cana-2576	5	5	article	article	NOUN
cana-2576	5	6	history	history	NOUN
cana-2576	5	7	:	:	PUNCT
cana-2576	5	8	received	receive	VERB
cana-2576	5	9	:	:	PUNCT
cana-2576	5	10	23	23	NUM
cana-2576	5	11	-	-	SYM
cana-2576	5	12	09	09	NUM
cana-2576	5	13	-	-	PUNCT
cana-2576	5	14	2024	2024	NUM
cana-2576	5	15	revised	revise	VERB
cana-2576	5	16	:	:	PUNCT
cana-2576	5	17	04	04	NUM
cana-2576	5	18	-	-	SYM
cana-2576	5	19	11	11	NUM
cana-2576	5	20	-	-	PUNCT
cana-2576	5	21	2024	2024	NUM
cana-2576	5	22	accepted	accept	VERB
cana-2576	5	23	:	:	PUNCT
cana-2576	5	24	18	18	NUM
cana-2576	5	25	-	-	SYM
cana-2576	5	26	11	11	NUM
cana-2576	5	27	-	-	PUNCT
cana-2576	5	28	2024	2024	NUM
cana-2576	5	29	abstract	abstract	NOUN
cana-2576	5	30	:	:	PUNCT
cana-2576	5	31	a	a	DET
cana-2576	5	32	set	set	NOUN
cana-2576	5	33	𝑆	𝑆	PROPN
cana-2576	5	34	⊆	⊆	NUM
cana-2576	5	35	𝑉	𝑉	PROPN
cana-2576	5	36	is	be	AUX
cana-2576	5	37	said	say	VERB
cana-2576	5	38	to	to	PART
cana-2576	5	39	be	be	AUX
cana-2576	5	40	relatively	relatively	ADV
cana-2576	5	41	prime	prime	ADJ
cana-2576	5	42	dominating	dominating	NOUN
cana-2576	5	43	set	set	NOUN
cana-2576	5	44	if	if	SCONJ
cana-2576	5	45	it	it	PRON
cana-2576	5	46	is	be	AUX
cana-2576	5	47	a	a	DET
cana-2576	5	48	dominating	dominating	NOUN
cana-2576	5	49	set	set	VERB
cana-2576	5	50	with	with	ADP
cana-2576	5	51	at	at	ADV
cana-2576	5	52	least	least	ADV
cana-2576	5	53	two	two	NUM
cana-2576	5	54	elements	element	NOUN
cana-2576	5	55	and	and	CCONJ
cana-2576	5	56	for	for	ADP
cana-2576	5	57	every	every	DET
cana-2576	5	58	pair	pair	NOUN
cana-2576	5	59	of	of	ADP
cana-2576	5	60	vertices	vertex	NOUN
cana-2576	5	61	𝑢	𝑢	NOUN
cana-2576	5	62	and	and	CCONJ
cana-2576	5	63	𝑣	𝑣	X
cana-2576	5	64	in	in	ADP
cana-2576	5	65	𝑆	𝑆	PROPN
cana-2576	5	66	,	,	PUNCT
cana-2576	5	67	(	(	PUNCT
cana-2576	5	68	deg(𝑢	deg(𝑢	X
cana-2576	5	69	)	)	PUNCT
cana-2576	5	70	,	,	PUNCT
cana-2576	5	71	deg(𝑣	deg(𝑣	PROPN
cana-2576	5	72	)	)	PUNCT
cana-2576	5	73	)	)	PUNCT
cana-2576	6	1	=	=	PUNCT
cana-2576	6	2	1	1	X
cana-2576	6	3	.	.	PUNCT
cana-2576	7	1	the	the	DET
cana-2576	7	2	minimum	minimum	ADJ
cana-2576	7	3	cardinality	cardinality	NOUN
cana-2576	7	4	of	of	ADP
cana-2576	7	5	a	a	DET
cana-2576	7	6	relatively	relatively	ADV
cana-2576	7	7	prime	prime	ADJ
cana-2576	7	8	dominating	dominating	NOUN
cana-2576	7	9	set	set	NOUN
cana-2576	7	10	is	be	AUX
cana-2576	7	11	called	call	VERB
cana-2576	7	12	relatively	relatively	ADV
cana-2576	7	13	prime	prime	ADJ
cana-2576	7	14	domination	domination	NOUN
cana-2576	7	15	number	number	NOUN
cana-2576	7	16	and	and	CCONJ
cana-2576	7	17	it	it	PRON
cana-2576	7	18	is	be	AUX
cana-2576	7	19	denoted	denote	VERB
cana-2576	7	20	by	by	ADP
cana-2576	7	21	𝛾𝑟𝑝𝑑(𝐺	𝛾𝑟𝑝𝑑(𝐺	PROPN
cana-2576	7	22	)	)	PUNCT
cana-2576	7	23	.	.	PUNCT
cana-2576	8	1	if	if	SCONJ
cana-2576	8	2	there	there	PRON
cana-2576	8	3	is	be	VERB
cana-2576	8	4	no	no	DET
cana-2576	8	5	such	such	ADJ
cana-2576	8	6	pair	pair	NOUN
cana-2576	8	7	exist	exist	VERB
cana-2576	8	8	,	,	PUNCT
cana-2576	8	9	then	then	ADV
cana-2576	8	10	𝛾𝑟𝑝𝑑(𝐺	𝛾𝑟𝑝𝑑(𝐺	PROPN
cana-2576	8	11	)	)	PUNCT
cana-2576	8	12	=	=	SYM
cana-2576	8	13	0	0	X
cana-2576	8	14	.	.	PUNCT
cana-2576	9	1	for	for	ADP
cana-2576	9	2	a	a	DET
cana-2576	9	3	finite	finite	ADJ
cana-2576	9	4	undirected	undirected	ADJ
cana-2576	9	5	graph	graph	NOUN
cana-2576	9	6	𝐺(𝑉	𝐺(𝑉	PRON
cana-2576	9	7	,	,	PUNCT
cana-2576	9	8	𝐸	𝐸	PROPN
cana-2576	9	9	)	)	PUNCT
cana-2576	9	10	and	and	CCONJ
cana-2576	9	11	a	a	DET
cana-2576	9	12	subset	subset	NOUN
cana-2576	9	13			PROPN
cana-2576	9	14	v	v	PROPN
cana-2576	9	15	,	,	PUNCT
cana-2576	9	16	the	the	DET
cana-2576	9	17	switching	switching	NOUN
cana-2576	9	18	of	of	ADP
cana-2576	9	19	g	g	NOUN
cana-2576	9	20	by	by	ADP
cana-2576	9	21			PROPN
cana-2576	9	22	is	be	AUX
cana-2576	9	23	defined	define	VERB
cana-2576	9	24	as	as	ADP
cana-2576	9	25	the	the	DET
cana-2576	9	26	graph	graph	NOUN
cana-2576	9	27	g	g	PROPN
cana-2576	9	28	(	(	PUNCT
cana-2576	9	29	v	v	NOUN
cana-2576	9	30	,	,	PUNCT
cana-2576	9	31	e	e	ADJ
cana-2576	9	32	)	)	PUNCT
cana-2576	9	33	which	which	PRON
cana-2576	9	34	is	be	AUX
cana-2576	9	35	obtained	obtain	VERB
cana-2576	9	36	from	from	ADP
cana-2576	9	37	g	g	NOUN
cana-2576	9	38	by	by	ADP
cana-2576	9	39	removing	remove	VERB
cana-2576	9	40	all	all	DET
cana-2576	9	41	edges	edge	NOUN
cana-2576	9	42	between	between	ADP
cana-2576	9	43			PROPN
cana-2576	9	44	and	and	CCONJ
cana-2576	9	45	its	its	PRON
cana-2576	9	46	complement	complement	NOUN
cana-2576	9	47	v-	v-	NOUN
cana-2576	9	48	and	and	CCONJ
cana-2576	9	49	adding	add	VERB
cana-2576	9	50	as	as	ADP
cana-2576	9	51	edges	edge	NOUN
cana-2576	9	52	all	all	DET
cana-2576	9	53	non	non	NOUN
cana-2576	9	54	-	-	NOUN
cana-2576	9	55	edges	edge	NOUN
cana-2576	9	56	between	between	ADP
cana-2576	9	57			PROPN
cana-2576	9	58	and	and	CCONJ
cana-2576	9	59	v-	v-	NOUN
cana-2576	9	60	.	.	PUNCT
cana-2576	10	1	this	this	DET
cana-2576	10	2	article	article	NOUN
cana-2576	10	3	delves	delve	VERB
cana-2576	10	4	into	into	ADP
cana-2576	10	5	the	the	DET
cana-2576	10	6	discussion	discussion	NOUN
cana-2576	10	7	of	of	ADP
cana-2576	10	8	the	the	DET
cana-2576	10	9	relatively	relatively	ADV
cana-2576	10	10	prime	prime	ADJ
cana-2576	10	11	domination	domination	NOUN
cana-2576	10	12	number	number	NOUN
cana-2576	10	13	on	on	ADP
cana-2576	10	14	quadrilateral	quadrilateral	ADJ
cana-2576	10	15	snake	snake	NOUN
cana-2576	10	16	graphs	graph	NOUN
cana-2576	10	17	and	and	CCONJ
cana-2576	10	18	their	their	PRON
cana-2576	10	19	complements	complement	NOUN
cana-2576	10	20	.	.	PUNCT
cana-2576	11	1	the	the	DET
cana-2576	11	2	findings	finding	NOUN
cana-2576	11	3	reveal	reveal	VERB
cana-2576	11	4	that	that	SCONJ
cana-2576	11	5	for	for	ADP
cana-2576	11	6	quadrilateral	quadrilateral	ADJ
cana-2576	11	7	snake	snake	NOUN
cana-2576	11	8	graphs	graph	NOUN
cana-2576	11	9	,	,	PUNCT
cana-2576	11	10	the	the	DET
cana-2576	11	11	relatively	relatively	ADV
cana-2576	11	12	prime	prime	ADJ
cana-2576	11	13	domination	domination	NOUN
cana-2576	11	14	number	number	NOUN
cana-2576	11	15	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	11	16	)	)	PUNCT
cana-2576	11	17	equals	equal	VERB
cana-2576	11	18	either	either	DET
cana-2576	11	19	2	2	NUM
cana-2576	11	20	,	,	PUNCT
cana-2576	11	21	3	3	NUM
cana-2576	11	22	or	or	CCONJ
cana-2576	11	23	4	4	NUM
cana-2576	11	24	.	.	PUNCT
cana-2576	11	25	similarly	similarly	ADV
cana-2576	11	26	,	,	PUNCT
cana-2576	11	27	for	for	ADP
cana-2576	11	28	alternate	alternate	ADJ
cana-2576	11	29	quadrilateral	quadrilateral	ADJ
cana-2576	11	30	snake	snake	NOUN
cana-2576	11	31	graphs	graph	NOUN
cana-2576	11	32	,	,	PUNCT
cana-2576	11	33	the	the	DET
cana-2576	11	34	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	11	35	)	)	PUNCT
cana-2576	11	36	is	be	AUX
cana-2576	11	37	determined	determine	VERB
cana-2576	11	38	to	to	PART
cana-2576	11	39	be	be	AUX
cana-2576	11	40	2	2	NUM
cana-2576	11	41	,	,	PUNCT
cana-2576	11	42	3	3	NUM
cana-2576	11	43	or	or	CCONJ
cana-2576	11	44	4	4	NUM
cana-2576	11	45	.	.	PUNCT
cana-2576	12	1	in	in	ADP
cana-2576	12	2	the	the	DET
cana-2576	12	3	case	case	NOUN
cana-2576	12	4	of	of	ADP
cana-2576	12	5	double	double	ADJ
cana-2576	12	6	quadrilateral	quadrilateral	ADJ
cana-2576	12	7	snake	snake	NOUN
cana-2576	12	8	graphs	graph	NOUN
cana-2576	12	9	,	,	PUNCT
cana-2576	12	10	the	the	DET
cana-2576	12	11	relatively	relatively	ADV
cana-2576	12	12	prime	prime	ADJ
cana-2576	12	13	domination	domination	NOUN
cana-2576	12	14	number	number	NOUN
cana-2576	12	15	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	12	16	)	)	PUNCT
cana-2576	12	17	is	be	AUX
cana-2576	12	18	established	establish	VERB
cana-2576	12	19	as	as	ADP
cana-2576	12	20	2	2	NUM
cana-2576	12	21	,	,	PUNCT
cana-2576	12	22	3	3	NUM
cana-2576	12	23	,	,	PUNCT
cana-2576	12	24	4	4	NUM
cana-2576	12	25	,	,	PUNCT
cana-2576	12	26	6	6	NUM
cana-2576	12	27	or	or	CCONJ
cana-2576	12	28	7	7	NUM
cana-2576	12	29	,	,	PUNCT
cana-2576	12	30	while	while	SCONJ
cana-2576	12	31	for	for	ADP
cana-2576	12	32	double	double	ADJ
cana-2576	12	33	alternate	alternate	ADJ
cana-2576	12	34	quadrilateral	quadrilateral	ADJ
cana-2576	12	35	snake	snake	NOUN
cana-2576	12	36	graphs	graph	NOUN
cana-2576	12	37	,	,	PUNCT
cana-2576	12	38	it	it	PRON
cana-2576	12	39	is	be	AUX
cana-2576	12	40	2	2	NUM
cana-2576	12	41	,	,	PUNCT
cana-2576	12	42	3	3	NUM
cana-2576	12	43	,	,	PUNCT
cana-2576	12	44	4	4	NUM
cana-2576	12	45	or	or	CCONJ
cana-2576	12	46	5	5	NUM
cana-2576	12	47	.	.	PUNCT
cana-2576	13	1	notably	notably	ADV
cana-2576	13	2	,	,	PUNCT
cana-2576	13	3	the	the	DET
cana-2576	13	4	complements	complement	NOUN
cana-2576	13	5	of	of	ADP
cana-2576	13	6	quadrilateral	quadrilateral	ADJ
cana-2576	13	7	,	,	PUNCT
cana-2576	13	8	alternate	alternate	ADJ
cana-2576	13	9	quadrilateral	quadrilateral	NOUN
cana-2576	13	10	,	,	PUNCT
cana-2576	13	11	double	double	ADJ
cana-2576	13	12	quadrilateral	quadrilateral	NOUN
cana-2576	13	13	,	,	PUNCT
cana-2576	13	14	and	and	CCONJ
cana-2576	13	15	double	double	ADJ
cana-2576	13	16	alternate	alternate	ADJ
cana-2576	13	17	quadrilateral	quadrilateral	ADJ
cana-2576	13	18	snake	snake	NOUN
cana-2576	13	19	graphs	graph	NOUN
cana-2576	13	20	exhibit	exhibit	VERB
cana-2576	13	21	a	a	DET
cana-2576	13	22	relatively	relatively	ADV
cana-2576	13	23	prime	prime	ADJ
cana-2576	13	24	domination	domination	NOUN
cana-2576	13	25	number	number	NOUN
cana-2576	13	26	of	of	ADP
cana-2576	13	27	2	2	NUM
cana-2576	13	28	.	.	PUNCT
cana-2576	14	1	keywords	keyword	NOUN
cana-2576	14	2	:	:	PUNCT
cana-2576	14	3	dominating	dominate	VERB
cana-2576	14	4	set	set	NOUN
cana-2576	14	5	,	,	PUNCT
cana-2576	14	6	domination	domination	NOUN
cana-2576	14	7	number	number	NOUN
cana-2576	14	8	,	,	PUNCT
cana-2576	14	9	relatively	relatively	ADV
cana-2576	14	10	prime	prime	ADJ
cana-2576	14	11	dominating	dominating	NOUN
cana-2576	14	12	set	set	NOUN
cana-2576	14	13	,	,	PUNCT
cana-2576	14	14	relatively	relatively	ADV
cana-2576	14	15	prime	prime	ADJ
cana-2576	14	16	dominating	dominating	NOUN
cana-2576	14	17	number	number	NOUN
cana-2576	14	18	1	1	NUM
cana-2576	14	19	.	.	PUNCT
cana-2576	14	20	introduction	introduction	NOUN
cana-2576	14	21	by	by	ADP
cana-2576	14	22	a	a	DET
cana-2576	14	23	graph	graph	NOUN
cana-2576	14	24	g	g	NOUN
cana-2576	14	25	=	=	SYM
cana-2576	14	26	(	(	PUNCT
cana-2576	14	27	v	v	NOUN
cana-2576	14	28	,	,	PUNCT
cana-2576	14	29	e	e	NOUN
cana-2576	14	30	)	)	PUNCT
cana-2576	14	31	we	we	PRON
cana-2576	14	32	mean	mean	VERB
cana-2576	14	33	a	a	DET
cana-2576	14	34	finite	finite	ADJ
cana-2576	14	35	undirected	undirected	ADJ
cana-2576	14	36	graph	graph	NOUN
cana-2576	14	37	without	without	ADP
cana-2576	14	38	loops	loop	NOUN
cana-2576	14	39	and	and	CCONJ
cana-2576	14	40	multiple	multiple	ADJ
cana-2576	14	41	edges	edge	NOUN
cana-2576	14	42	.	.	PUNCT
cana-2576	15	1	the	the	DET
cana-2576	15	2	order	order	NOUN
cana-2576	15	3	and	and	CCONJ
cana-2576	15	4	size	size	NOUN
cana-2576	15	5	of	of	ADP
cana-2576	15	6	g	g	PROPN
cana-2576	15	7	are	be	AUX
cana-2576	15	8	denoted	denote	VERB
cana-2576	15	9	by	by	ADP
cana-2576	15	10	p	p	NOUN
cana-2576	15	11	and	and	CCONJ
cana-2576	15	12	q	q	NOUN
cana-2576	15	13	respectively	respectively	ADV
cana-2576	15	14	.	.	PUNCT
cana-2576	16	1	for	for	ADP
cana-2576	16	2	graph	graph	NOUN
cana-2576	16	3	theoretical	theoretical	ADJ
cana-2576	16	4	terms	term	NOUN
cana-2576	16	5	,	,	PUNCT
cana-2576	16	6	we	we	PRON
cana-2576	16	7	refer	refer	VERB
cana-2576	16	8	to	to	ADP
cana-2576	16	9	harary	harary	NOUN
cana-2576	16	10	[	[	X
cana-2576	16	11	2	2	NUM
cana-2576	16	12	]	]	PUNCT
cana-2576	16	13	and	and	CCONJ
cana-2576	16	14	for	for	ADP
cana-2576	16	15	terms	term	NOUN
cana-2576	16	16	related	relate	VERB
cana-2576	16	17	to	to	ADP
cana-2576	16	18	domination	domination	NOUN
cana-2576	16	19	we	we	PRON
cana-2576	16	20	refer	refer	VERB
cana-2576	16	21	to	to	ADP
cana-2576	16	22	haynes	haynes	PROPN
cana-2576	16	23	[	[	X
cana-2576	16	24	7	7	NUM
cana-2576	16	25	]	]	PUNCT
cana-2576	16	26	.	.	PUNCT
cana-2576	17	1	a	a	DET
cana-2576	17	2	subset	subset	NOUN
cana-2576	17	3	s	s	NOUN
cana-2576	17	4	of	of	ADP
cana-2576	17	5	v	v	NOUN
cana-2576	17	6	is	be	AUX
cana-2576	17	7	said	say	VERB
cana-2576	17	8	to	to	PART
cana-2576	17	9	be	be	AUX
cana-2576	17	10	a	a	DET
cana-2576	17	11	dominating	dominating	NOUN
cana-2576	17	12	set	set	VERB
cana-2576	17	13	in	in	ADP
cana-2576	17	14	g	g	PROPN
cana-2576	17	15	if	if	SCONJ
cana-2576	17	16	every	every	DET
cana-2576	17	17	vertex	vertex	NOUN
cana-2576	17	18	in	in	ADP
cana-2576	17	19	v	v	NOUN
cana-2576	17	20	–	–	PUNCT
cana-2576	17	21	s	s	VERB
cana-2576	17	22	is	be	AUX
cana-2576	17	23	adjacent	adjacent	ADJ
cana-2576	17	24	to	to	ADP
cana-2576	17	25	at	at	ADV
cana-2576	17	26	least	least	ADV
cana-2576	17	27	one	one	NUM
cana-2576	17	28	vertex	vertex	NOUN
cana-2576	17	29	in	in	ADP
cana-2576	17	30	s.	s.	PROPN
cana-2576	17	31	the	the	DET
cana-2576	17	32	domination	domination	NOUN
cana-2576	17	33	number	number	NOUN
cana-2576	17	34	𝛾(g	𝛾(g	PROPN
cana-2576	17	35	)	)	PUNCT
cana-2576	17	36	is	be	AUX
cana-2576	17	37	the	the	DET
cana-2576	17	38	minimum	minimum	ADJ
cana-2576	17	39	cardinality	cardinality	NOUN
cana-2576	17	40	of	of	ADP
cana-2576	17	41	a	a	DET
cana-2576	17	42	dominating	dominating	NOUN
cana-2576	17	43	set	set	VERB
cana-2576	17	44	in	in	ADP
cana-2576	17	45	g.	g.	PROPN
cana-2576	17	46	berge	berge	NOUN
cana-2576	18	1	[	[	X
cana-2576	18	2	1	1	X
cana-2576	18	3	]	]	PUNCT
cana-2576	18	4	and	and	CCONJ
cana-2576	18	5	ore	ore	NOUN
cana-2576	18	6	[	[	X
cana-2576	18	7	6	6	NUM
cana-2576	18	8	]	]	PUNCT
cana-2576	18	9	formulated	formulate	VERB
cana-2576	18	10	the	the	DET
cana-2576	18	11	concept	concept	NOUN
cana-2576	18	12	of	of	ADP
cana-2576	18	13	domination	domination	NOUN
cana-2576	18	14	in	in	ADP
cana-2576	18	15	graphs	graph	NOUN
cana-2576	18	16	.	.	PUNCT
cana-2576	19	1	it	it	PRON
cana-2576	19	2	was	be	AUX
cana-2576	19	3	further	far	ADV
cana-2576	19	4	extended	extend	VERB
cana-2576	19	5	to	to	PART
cana-2576	19	6	define	define	VERB
cana-2576	19	7	many	many	ADJ
cana-2576	19	8	other	other	ADJ
cana-2576	19	9	dominations	domination	NOUN
cana-2576	19	10	related	relate	VERB
cana-2576	19	11	parameters	parameter	NOUN
cana-2576	19	12	in	in	ADP
cana-2576	19	13	graphs	graph	NOUN
cana-2576	19	14	.	.	PUNCT
cana-2576	20	1	in	in	ADP
cana-2576	20	2	2017	2017	NUM
cana-2576	20	3	,	,	PUNCT
cana-2576	20	4	c.	c.	PROPN
cana-2576	20	5	jayasekaran	jayasekaran	PROPN
cana-2576	20	6	and	and	CCONJ
cana-2576	20	7	a.	a.	NOUN
cana-2576	20	8	jancy	jancy	PROPN
cana-2576	20	9	vini	vini	PROPN
cana-2576	21	1	[	[	X
cana-2576	21	2	3	3	X
cana-2576	21	3	]	]	PUNCT
cana-2576	21	4	have	have	AUX
cana-2576	21	5	introduced	introduce	VERB
cana-2576	21	6	the	the	DET
cana-2576	21	7	concept	concept	NOUN
cana-2576	21	8	of	of	ADP
cana-2576	21	9	relatively	relatively	ADV
cana-2576	21	10	prime	prime	ADJ
cana-2576	21	11	domination	domination	NOUN
cana-2576	21	12	number	number	NOUN
cana-2576	21	13	in	in	ADP
cana-2576	21	14	graph	graph	NOUN
cana-2576	21	15	theory	theory	NOUN
cana-2576	21	16	.	.	PUNCT
cana-2576	22	1	let	let	VERB
cana-2576	22	2	g	g	PRON
cana-2576	22	3	be	be	AUX
cana-2576	22	4	a	a	DET
cana-2576	22	5	non	non	ADJ
cana-2576	22	6	–	–	PUNCT
cana-2576	22	7	trivial	trivial	ADJ
cana-2576	22	8	graph	graph	NOUN
cana-2576	22	9	.	.	PUNCT
cana-2576	23	1	a	a	DET
cana-2576	23	2	set	set	NOUN
cana-2576	23	3	s	s	PART
cana-2576	23	4	v	v	NOUN
cana-2576	23	5	is	be	AUX
cana-2576	23	6	said	say	VERB
cana-2576	23	7	to	to	PART
cana-2576	23	8	be	be	AUX
cana-2576	23	9	a	a	DET
cana-2576	23	10	relatively	relatively	ADV
cana-2576	23	11	prime	prime	ADJ
cana-2576	23	12	dominating	dominating	NOUN
cana-2576	23	13	set	set	NOUN
cana-2576	23	14	if	if	SCONJ
cana-2576	23	15	it	it	PRON
cana-2576	23	16	is	be	AUX
cana-2576	23	17	a	a	DET
cana-2576	23	18	dominating	dominating	NOUN
cana-2576	23	19	set	set	NOUN
cana-2576	23	20	and	and	CCONJ
cana-2576	23	21	for	for	ADP
cana-2576	23	22	every	every	DET
cana-2576	23	23	pair	pair	NOUN
cana-2576	23	24	of	of	ADP
cana-2576	23	25	vertices	vertex	NOUN
cana-2576	23	26	u	u	NOUN
cana-2576	23	27	and	and	CCONJ
cana-2576	23	28	v	v	NOUN
cana-2576	23	29	in	in	ADP
cana-2576	23	30	s	s	PRON
cana-2576	23	31	such	such	ADJ
cana-2576	23	32	that	that	SCONJ
cana-2576	23	33	(	(	PUNCT
cana-2576	23	34	d(u	d(u	PROPN
cana-2576	23	35	)	)	PUNCT
cana-2576	23	36	,	,	PUNCT
cana-2576	23	37	d(v	d(v	PROPN
cana-2576	23	38	)	)	PUNCT
cana-2576	23	39	)	)	PUNCT
cana-2576	24	1	=	=	PUNCT
cana-2576	24	2	1	1	X
cana-2576	24	3	.	.	PUNCT
cana-2576	25	1	the	the	DET
cana-2576	25	2	minimum	minimum	ADJ
cana-2576	25	3	cardinality	cardinality	NOUN
cana-2576	25	4	of	of	ADP
cana-2576	25	5	a	a	DET
cana-2576	25	6	relatively	relatively	ADV
cana-2576	25	7	prime	prime	ADJ
cana-2576	25	8	dominating	dominating	NOUN
cana-2576	25	9	set	set	NOUN
cana-2576	25	10	is	be	AUX
cana-2576	25	11	called	call	VERB
cana-2576	25	12	the	the	DET
cana-2576	25	13	relatively	relatively	ADV
cana-2576	25	14	prime	prime	ADJ
cana-2576	25	15	domination	domination	NOUN
cana-2576	25	16	number	number	NOUN
cana-2576	25	17	and	and	CCONJ
cana-2576	25	18	it	it	PRON
cana-2576	25	19	is	be	AUX
cana-2576	25	20	denoted	denote	VERB
cana-2576	25	21	by	by	ADP
cana-2576	25	22	rpdγ	rpdγ	NOUN
cana-2576	25	23	(	(	PUNCT
cana-2576	25	24	g	g	NOUN
cana-2576	25	25	)	)	PUNCT
cana-2576	25	26	.	.	PUNCT
cana-2576	26	1	further	far	ADV
cana-2576	26	2	they	they	PRON
cana-2576	26	3	have	have	AUX
cana-2576	26	4	introduced	introduce	VERB
cana-2576	26	5	the	the	DET
cana-2576	26	6	concept	concept	NOUN
cana-2576	26	7	of	of	ADP
cana-2576	26	8	relatively	relatively	ADV
cana-2576	26	9	prime	prime	ADJ
cana-2576	26	10	dominating	dominating	NOUN
cana-2576	26	11	polynomial	polynomial	NOUN
cana-2576	26	12	in	in	ADP
cana-2576	26	13	[	[	X
cana-2576	26	14	4	4	NUM
cana-2576	26	15	]	]	PUNCT
cana-2576	26	16	.	.	PUNCT
cana-2576	27	1	switching	switch	VERB
cana-2576	27	2	in	in	ADP
cana-2576	27	3	graphs	graph	NOUN
cana-2576	27	4	was	be	AUX
cana-2576	27	5	introduced	introduce	VERB
cana-2576	27	6	by	by	ADP
cana-2576	27	7	lint	lint	NOUN
cana-2576	27	8	and	and	CCONJ
cana-2576	27	9	seidel	seidel	NOUN
cana-2576	28	1	[	[	X
cana-2576	28	2	5	5	NUM
cana-2576	28	3	]	]	PUNCT
cana-2576	28	4	.	.	PUNCT
cana-2576	29	1	for	for	ADP
cana-2576	29	2	a	a	DET
cana-2576	29	3	finite	finite	ADJ
cana-2576	29	4	undirected	undirected	ADJ
cana-2576	29	5	graph	graph	NOUN
cana-2576	29	6	g(v	g(v	NOUN
cana-2576	29	7	,	,	PUNCT
cana-2576	29	8	e	e	NOUN
cana-2576	29	9	)	)	PUNCT
cana-2576	29	10	and	and	CCONJ
cana-2576	29	11	a	a	DET
cana-2576	29	12	subset	subset	NOUN
cana-2576	29	13			PROPN
cana-2576	29	14	v	v	PROPN
cana-2576	29	15	,	,	PUNCT
cana-2576	29	16	the	the	DET
cana-2576	29	17	switching	switching	NOUN
cana-2576	29	18	of	of	ADP
cana-2576	29	19	g	g	NOUN
cana-2576	29	20	by	by	ADP
cana-2576	29	21			PROPN
cana-2576	29	22	is	be	AUX
cana-2576	29	23	defined	define	VERB
cana-2576	29	24	as	as	ADP
cana-2576	29	25	the	the	DET
cana-2576	29	26	graph	graph	NOUN
cana-2576	29	27	communications	communication	NOUN
cana-2576	29	28	on	on	ADP
cana-2576	29	29	applied	apply	VERB
cana-2576	29	30	nonlinear	nonlinear	ADJ
cana-2576	29	31	analysis	analysis	NOUN
cana-2576	29	32	issn	issn	NOUN
cana-2576	29	33	:	:	PUNCT
cana-2576	29	34	1074	1074	NUM
cana-2576	29	35	-	-	PUNCT
cana-2576	29	36	133x	133x	NUM
cana-2576	29	37	vol	vol	NOUN
cana-2576	29	38	32	32	NUM
cana-2576	29	39	no	no	NOUN
cana-2576	29	40	.	.	PUNCT
cana-2576	30	1	3s	3s	NUM
cana-2576	30	2	(	(	PUNCT
cana-2576	30	3	2025	2025	NUM
cana-2576	30	4	)	)	PUNCT
cana-2576	30	5	155	155	NUM
cana-2576	30	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2576	30	7	g	g	PROPN
cana-2576	30	8	(	(	PUNCT
cana-2576	30	9	v	v	NOUN
cana-2576	30	10	,	,	PUNCT
cana-2576	30	11	e	e	ADJ
cana-2576	30	12	)	)	PUNCT
cana-2576	30	13	which	which	PRON
cana-2576	30	14	is	be	AUX
cana-2576	30	15	obtained	obtain	VERB
cana-2576	30	16	from	from	ADP
cana-2576	30	17	g	g	NOUN
cana-2576	30	18	by	by	ADP
cana-2576	30	19	removing	remove	VERB
cana-2576	30	20	all	all	DET
cana-2576	30	21	edges	edge	NOUN
cana-2576	30	22	between	between	ADP
cana-2576	30	23			PROPN
cana-2576	30	24	and	and	CCONJ
cana-2576	30	25	its	its	PRON
cana-2576	30	26	complement	complement	NOUN
cana-2576	30	27	v–	v–	NOUN
cana-2576	30	28	and	and	CCONJ
cana-2576	30	29	adding	add	VERB
cana-2576	30	30	as	as	ADP
cana-2576	30	31	edges	edge	NOUN
cana-2576	30	32	all	all	DET
cana-2576	30	33	non	non	NOUN
cana-2576	30	34	-	-	NOUN
cana-2576	30	35	edges	edge	NOUN
cana-2576	30	36	between	between	ADP
cana-2576	30	37			PROPN
cana-2576	30	38	and	and	CCONJ
cana-2576	30	39	v–	v–	NOUN
cana-2576	30	40	.	.	PUNCT
cana-2576	31	1	for	for	ADP
cana-2576	31	2			PROPN
cana-2576	31	3	=	=	SYM
cana-2576	31	4	{	{	PUNCT
cana-2576	31	5	v	v	NOUN
cana-2576	31	6	}	}	PUNCT
cana-2576	31	7	,	,	PUNCT
cana-2576	31	8	we	we	PRON
cana-2576	31	9	write	write	VERB
cana-2576	31	10	gv	gv	ADP
cana-2576	31	11	instead	instead	ADV
cana-2576	31	12	of	of	ADP
cana-2576	31	13	g{v	g{v	NOUN
cana-2576	31	14	}	}	PUNCT
cana-2576	31	15	and	and	CCONJ
cana-2576	31	16	the	the	DET
cana-2576	31	17	corresponding	corresponding	ADJ
cana-2576	31	18	switching	switching	NOUN
cana-2576	31	19	is	be	AUX
cana-2576	31	20	called	call	VERB
cana-2576	31	21	as	as	ADP
cana-2576	31	22	vertex	vertex	NOUN
cana-2576	31	23	switching	switching	NOUN
cana-2576	31	24	.	.	PUNCT
cana-2576	32	1	in	in	ADP
cana-2576	32	2	this	this	DET
cana-2576	32	3	paper	paper	NOUN
cana-2576	32	4	we	we	PRON
cana-2576	32	5	determine	determine	VERB
cana-2576	32	6	the	the	DET
cana-2576	32	7	relatively	relatively	ADV
cana-2576	32	8	prime	prime	ADJ
cana-2576	32	9	domination	domination	NOUN
cana-2576	32	10	number	number	NOUN
cana-2576	32	11	v	v	NOUN
cana-2576	32	12	rpdγ	rpdγ	NOUN
cana-2576	32	13	(	(	PUNCT
cana-2576	32	14	g	g	NOUN
cana-2576	32	15	)	)	PUNCT
cana-2576	32	16	and	and	CCONJ
cana-2576	32	17	rpdγ	rpdγ	ADJ
cana-2576	32	18	(	(	PUNCT
cana-2576	32	19	g	g	NOUN
cana-2576	32	20	)	)	PUNCT
cana-2576	32	21	,	,	PUNCT
cana-2576	32	22	where	where	SCONJ
cana-2576	32	23	g	g	PROPN
cana-2576	32	24	is	be	AUX
cana-2576	32	25	a	a	DET
cana-2576	32	26	quadrilateral	quadrilateral	ADJ
cana-2576	32	27	snake	snake	NOUN
cana-2576	32	28	graph	graph	NOUN
cana-2576	32	29	.	.	PUNCT
cana-2576	33	1	2	2	X
cana-2576	33	2	.	.	X
cana-2576	33	3	preliminaries	preliminary	NOUN
cana-2576	33	4	definition	definition	NOUN
cana-2576	33	5	2.1	2.1	NUM
cana-2576	33	6	.	.	PUNCT
cana-2576	34	1	a	a	DET
cana-2576	34	2	quadrilateral	quadrilateral	ADJ
cana-2576	34	3	snake	snake	NOUN
cana-2576	34	4	is	be	AUX
cana-2576	34	5	obtained	obtain	VERB
cana-2576	34	6	from	from	ADP
cana-2576	34	7	a	a	DET
cana-2576	34	8	path	path	NOUN
cana-2576	34	9	𝑎1,𝑎2	𝑎1,𝑎2	PROPN
cana-2576	34	10	,	,	PUNCT
cana-2576	34	11	…	…	PUNCT
cana-2576	34	12	,	,	PUNCT
cana-2576	34	13	𝑎𝑛	𝑎𝑛	PRON
cana-2576	34	14	by	by	ADP
cana-2576	34	15	joining	join	VERB
cana-2576	34	16	𝑎𝑖	𝑎𝑖	ADV
cana-2576	34	17	and	and	CCONJ
cana-2576	34	18	𝑎𝑖+1	𝑎𝑖+1	NUM
cana-2576	34	19	to	to	ADP
cana-2576	34	20	new	new	ADJ
cana-2576	34	21	vertices	vertex	NOUN
cana-2576	34	22	𝑏𝑖	𝑏𝑖	ADP
cana-2576	34	23	and	and	CCONJ
cana-2576	34	24	𝑐𝑖	𝑐𝑖	NOUN
cana-2576	34	25	respectively	respectively	ADV
cana-2576	34	26	and	and	CCONJ
cana-2576	34	27	joining	join	VERB
cana-2576	34	28	the	the	DET
cana-2576	34	29	vertices	vertex	NOUN
cana-2576	34	30	𝑏𝑖	𝑏𝑖	ADP
cana-2576	34	31	and	and	CCONJ
cana-2576	34	32	𝑐𝑖	𝑐𝑖	NOUN
cana-2576	34	33	for	for	ADP
cana-2576	34	34	i	i	PROPN
cana-2576	34	35	=	=	SYM
cana-2576	34	36	1,2	1,2	NUM
cana-2576	34	37	,	,	PUNCT
cana-2576	34	38	…	…	PUNCT
cana-2576	34	39	,	,	PUNCT
cana-2576	34	40	n	n	CCONJ
cana-2576	34	41	–	–	PUNCT
cana-2576	35	1	1	1	X
cana-2576	35	2	.	.	X
cana-2576	35	3	that	that	PRON
cana-2576	35	4	is	be	AUX
cana-2576	35	5	every	every	DET
cana-2576	35	6	edge	edge	NOUN
cana-2576	35	7	is	be	AUX
cana-2576	35	8	of	of	ADP
cana-2576	35	9	a	a	DET
cana-2576	35	10	path	path	NOUN
cana-2576	35	11	is	be	AUX
cana-2576	35	12	replaced	replace	VERB
cana-2576	35	13	by	by	ADP
cana-2576	35	14	a	a	DET
cana-2576	35	15	cycle	cycle	NOUN
cana-2576	35	16	𝐶4	𝐶4	NOUN
cana-2576	35	17	.	.	PUNCT
cana-2576	36	1	definition	definition	NOUN
cana-2576	36	2	2.2	2.2	NUM
cana-2576	36	3	.	.	PUNCT
cana-2576	37	1	an	an	DET
cana-2576	37	2	alternate	alternate	ADJ
cana-2576	37	3	quadrilateral	quadrilateral	ADJ
cana-2576	37	4	snake	snake	NOUN
cana-2576	37	5	is	be	AUX
cana-2576	37	6	obtained	obtain	VERB
cana-2576	37	7	from	from	ADP
cana-2576	37	8	a	a	DET
cana-2576	37	9	path	path	NOUN
cana-2576	37	10	𝑎1,𝑎2	𝑎1,𝑎2	PROPN
cana-2576	37	11	,	,	PUNCT
cana-2576	37	12	…	…	PUNCT
cana-2576	37	13	,	,	PUNCT
cana-2576	37	14	𝑎𝑛by	𝑎𝑛by	NOUN
cana-2576	37	15	joining	join	VERB
cana-2576	37	16	𝑎𝑖	𝑎𝑖	ADV
cana-2576	37	17	and	and	CCONJ
cana-2576	37	18	𝑎𝑖+1	𝑎𝑖+1	NUM
cana-2576	37	19	to	to	ADP
cana-2576	37	20	new	new	ADJ
cana-2576	37	21	vertices	vertex	NOUN
cana-2576	37	22	𝑏𝑖	𝑏𝑖	ADP
cana-2576	37	23	and	and	CCONJ
cana-2576	37	24	𝑐𝑖	𝑐𝑖	NOUN
cana-2576	37	25	respectively	respectively	ADV
cana-2576	37	26	and	and	CCONJ
cana-2576	37	27	joining	join	VERB
cana-2576	37	28	the	the	DET
cana-2576	37	29	vertices	vertex	NOUN
cana-2576	37	30	𝑏𝑖	𝑏𝑖	ADP
cana-2576	37	31	and	and	CCONJ
cana-2576	37	32	𝑐𝑖	𝑐𝑖	VERB
cana-2576	37	33	for	for	ADP
cana-2576	37	34	𝑖	𝑖	PROPN
cana-2576	37	35	≡	≡	PROPN
cana-2576	37	36	1(mod	1(mod	NUM
cana-2576	37	37	2	2	X
cana-2576	37	38	)	)	PUNCT
cana-2576	37	39	and	and	CCONJ
cana-2576	37	40	i	i	PRON
cana-2576	37	41	≤	≤	PUNCT
cana-2576	37	42	n	n	CCONJ
cana-2576	37	43	–	–	PUNCT
cana-2576	37	44	1	1	NUM
cana-2576	37	45	and	and	CCONJ
cana-2576	37	46	then	then	ADV
cana-2576	37	47	joining	join	VERB
cana-2576	37	48	𝑏𝑖	𝑏𝑖	ADV
cana-2576	37	49	and	and	CCONJ
cana-2576	37	50	𝑐𝑖.	𝑐𝑖.	NOUN
cana-2576	37	51	that	that	PRON
cana-2576	37	52	is	be	AUX
cana-2576	37	53	every	every	DET
cana-2576	37	54	alternate	alternate	ADJ
cana-2576	37	55	edge	edge	NOUN
cana-2576	37	56	of	of	ADP
cana-2576	37	57	a	a	DET
cana-2576	37	58	path	path	NOUN
cana-2576	37	59	is	be	AUX
cana-2576	37	60	replaced	replace	VERB
cana-2576	37	61	by	by	ADP
cana-2576	37	62	a	a	DET
cana-2576	37	63	cycle	cycle	NOUN
cana-2576	37	64	𝐶4	𝐶4	NOUN
cana-2576	37	65	.	.	PUNCT
cana-2576	38	1	it	it	PRON
cana-2576	38	2	is	be	AUX
cana-2576	38	3	denoted	denote	VERB
cana-2576	38	4	by	by	ADP
cana-2576	38	5	𝐴(𝑄𝑛	𝐴(𝑄𝑛	NOUN
cana-2576	38	6	)	)	PUNCT
cana-2576	38	7	.	.	PUNCT
cana-2576	39	1	definition	definition	NOUN
cana-2576	39	2	2.3	2.3	NUM
cana-2576	39	3	.	.	PUNCT
cana-2576	40	1	a	a	DET
cana-2576	40	2	double	double	ADJ
cana-2576	40	3	quadrilateral	quadrilateral	ADJ
cana-2576	40	4	snake	snake	NOUN
cana-2576	40	5	is	be	AUX
cana-2576	40	6	obtained	obtain	VERB
cana-2576	40	7	from	from	ADP
cana-2576	40	8	two	two	NUM
cana-2576	40	9	quadrilateral	quadrilateral	ADJ
cana-2576	40	10	snakes	snake	NOUN
cana-2576	40	11	that	that	PRON
cana-2576	40	12	have	have	VERB
cana-2576	40	13	a	a	DET
cana-2576	40	14	common	common	ADJ
cana-2576	40	15	path	path	NOUN
cana-2576	40	16	.	.	PUNCT
cana-2576	41	1	it	it	PRON
cana-2576	41	2	is	be	AUX
cana-2576	41	3	denoted	denote	VERB
cana-2576	41	4	by	by	ADP
cana-2576	41	5	𝐷(𝑄𝑛	𝐷(𝑄𝑛	PROPN
cana-2576	41	6	)	)	PUNCT
cana-2576	41	7	.	.	PUNCT
cana-2576	42	1	definition	definition	NOUN
cana-2576	42	2	2.4	2.4	NUM
cana-2576	42	3	.	.	PUNCT
cana-2576	43	1	an	an	DET
cana-2576	43	2	alternate	alternate	ADJ
cana-2576	43	3	double	double	ADJ
cana-2576	43	4	quadrilateral	quadrilateral	ADJ
cana-2576	43	5	snake	snake	NOUN
cana-2576	43	6	is	be	AUX
cana-2576	43	7	obtained	obtain	VERB
cana-2576	43	8	from	from	ADP
cana-2576	43	9	two	two	NUM
cana-2576	43	10	alternative	alternative	ADJ
cana-2576	43	11	quadrilateral	quadrilateral	ADJ
cana-2576	43	12	snakes	snake	NOUN
cana-2576	43	13	that	that	PRON
cana-2576	43	14	have	have	VERB
cana-2576	43	15	a	a	DET
cana-2576	43	16	common	common	ADJ
cana-2576	43	17	path	path	NOUN
cana-2576	43	18	.	.	PUNCT
cana-2576	44	1	it	it	PRON
cana-2576	44	2	is	be	AUX
cana-2576	44	3	denoted	denote	VERB
cana-2576	44	4	by	by	ADP
cana-2576	44	5	𝐴(𝐷(𝑄𝑛	𝐴(𝐷(𝑄𝑛	NOUN
cana-2576	44	6	)	)	PUNCT
cana-2576	44	7	)	)	PUNCT
cana-2576	44	8	.	.	PUNCT
cana-2576	45	1	3	3	X
cana-2576	45	2	.	.	X
cana-2576	45	3	relatively	relatively	ADV
cana-2576	45	4	prime	prime	ADJ
cana-2576	45	5	domination	domination	NOUN
cana-2576	45	6	number	number	NOUN
cana-2576	45	7	of	of	ADP
cana-2576	45	8	quadrilateral	quadrilateral	ADJ
cana-2576	45	9	snake	snake	NOUN
cana-2576	45	10	graph	graph	NOUN
cana-2576	45	11	in	in	ADP
cana-2576	45	12	this	this	DET
cana-2576	45	13	section	section	NOUN
cana-2576	45	14	we	we	PRON
cana-2576	45	15	have	have	AUX
cana-2576	45	16	discussed	discuss	VERB
cana-2576	45	17	the	the	DET
cana-2576	45	18	relatively	relatively	ADV
cana-2576	45	19	prime	prime	ADJ
cana-2576	45	20	domination	domination	NOUN
cana-2576	45	21	number	number	NOUN
cana-2576	45	22	for	for	ADP
cana-2576	45	23	snake	snake	NOUN
cana-2576	45	24	graphs	graph	NOUN
cana-2576	45	25	.	.	PUNCT
cana-2576	46	1	theorem	theorem	VERB
cana-2576	46	2	3.1	3.1	NUM
cana-2576	46	3	.	.	PUNCT
cana-2576	47	1	let	let	VERB
cana-2576	47	2	g	g	PRON
cana-2576	47	3	be	be	AUX
cana-2576	47	4	a	a	DET
cana-2576	47	5	quadrilateral	quadrilateral	ADJ
cana-2576	47	6	snake	snake	NOUN
cana-2576	47	7	graph	graph	NOUN
cana-2576	47	8	with	with	ADP
cana-2576	47	9	p	p	ADJ
cana-2576	47	10	vertices	vertex	NOUN
cana-2576	47	11	,	,	PUNCT
cana-2576	47	12	where	where	SCONJ
cana-2576	47	13	p	p	PROPN
cana-2576	47	14	=	=	PROPN
cana-2576	47	15	3n+1	3n+1	PROPN
cana-2576	47	16	,	,	PUNCT
cana-2576	47	17	n	n	PRON
cana-2576	47	18	≥	≥	NOUN
cana-2576	47	19	2	2	NUM
cana-2576	47	20	.	.	PUNCT
cana-2576	48	1	then	then	ADV
cana-2576	48	2	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	48	3	)	)	PUNCT
cana-2576	48	4	=	=	PUNCT
cana-2576	48	5	2	2	NUM
cana-2576	48	6	,	,	PUNCT
cana-2576	48	7	3	3	NUM
cana-2576	48	8	or	or	CCONJ
cana-2576	48	9	4	4	NUM
cana-2576	48	10	.	.	X
cana-2576	49	1	proof	proof	NOUN
cana-2576	49	2	:	:	PUNCT
cana-2576	49	3	let	let	VERB
cana-2576	49	4	g	g	PRON
cana-2576	49	5	be	be	AUX
cana-2576	49	6	a	a	DET
cana-2576	49	7	quadrilateral	quadrilateral	ADJ
cana-2576	49	8	snake	snake	NOUN
cana-2576	49	9	graph	graph	NOUN
cana-2576	49	10	with	with	ADP
cana-2576	49	11	p	p	NOUN
cana-2576	49	12	vertices	vertex	NOUN
cana-2576	49	13	.	.	PUNCT
cana-2576	50	1	let	let	VERB
cana-2576	50	2	the	the	DET
cana-2576	50	3	vertices	vertex	NOUN
cana-2576	50	4	in	in	ADP
cana-2576	50	5	the	the	DET
cana-2576	50	6	path	path	NOUN
cana-2576	50	7	be	be	AUX
cana-2576	50	8	𝑣1	𝑣1	PROPN
cana-2576	50	9	,	,	PUNCT
cana-2576	50	10	𝑣2	𝑣2	PROPN
cana-2576	50	11	,	,	PUNCT
cana-2576	50	12	…	…	PUNCT
cana-2576	50	13	,	,	PUNCT
cana-2576	50	14	𝑣𝑝	𝑣𝑝	NOUN
cana-2576	50	15	and	and	CCONJ
cana-2576	50	16	the	the	DET
cana-2576	50	17	vertices	vertex	NOUN
cana-2576	50	18	in	in	ADP
cana-2576	50	19	the	the	DET
cana-2576	50	20	quadrilateral	quadrilateral	ADJ
cana-2576	50	21	be	be	AUX
cana-2576	50	22	𝑢1	𝑢1	PROPN
cana-2576	50	23	,	,	PUNCT
cana-2576	50	24	𝑢2	𝑢2	PROPN
cana-2576	50	25	,	,	PUNCT
cana-2576	50	26	𝑤2	𝑤2	NOUN
cana-2576	50	27	,	,	PUNCT
cana-2576	50	28	𝑢3	𝑢3	PROPN
cana-2576	50	29	,	,	PUNCT
cana-2576	50	30	𝑤3	𝑤3	PROPN
cana-2576	50	31	,	,	PUNCT
cana-2576	50	32	…	…	PUNCT
cana-2576	50	33	,	,	PUNCT
cana-2576	50	34	𝑢𝑚−1	𝑢𝑚−1	PROPN
cana-2576	50	35	,	,	PUNCT
cana-2576	50	36	𝑤𝑚−1	𝑤𝑚−1	PROPN
cana-2576	50	37	,	,	PUNCT
cana-2576	50	38	𝑢𝑚	𝑢𝑚	NOUN
cana-2576	50	39	,	,	PUNCT
cana-2576	50	40	𝑤𝑚.	𝑤𝑚.	NOUN
cana-2576	50	41	then	then	ADV
cana-2576	50	42	the	the	DET
cana-2576	50	43	degree	degree	NOUN
cana-2576	50	44	of	of	ADP
cana-2576	50	45	vertices	vertex	NOUN
cana-2576	50	46	in	in	ADP
cana-2576	50	47	the	the	DET
cana-2576	50	48	path	path	NOUN
cana-2576	50	49	except	except	SCONJ
cana-2576	50	50	the	the	DET
cana-2576	50	51	initial	initial	NOUN
cana-2576	50	52	and	and	CCONJ
cana-2576	50	53	the	the	DET
cana-2576	50	54	end	end	NOUN
cana-2576	50	55	vertex	vertex	NOUN
cana-2576	50	56	is	be	AUX
cana-2576	50	57	4	4	NUM
cana-2576	50	58	;	;	PUNCT
cana-2576	50	59	the	the	DET
cana-2576	50	60	degree	degree	NOUN
cana-2576	50	61	of	of	ADP
cana-2576	50	62	initial	initial	ADJ
cana-2576	50	63	and	and	CCONJ
cana-2576	50	64	the	the	DET
cana-2576	50	65	end	end	NOUN
cana-2576	50	66	vertex	vertex	NOUN
cana-2576	50	67	is	be	AUX
cana-2576	50	68	2	2	NUM
cana-2576	50	69	;	;	PUNCT
cana-2576	50	70	the	the	DET
cana-2576	50	71	degree	degree	NOUN
cana-2576	50	72	of	of	ADP
cana-2576	50	73	vertices	vertex	NOUN
cana-2576	50	74	in	in	ADP
cana-2576	50	75	the	the	DET
cana-2576	50	76	quadrilateral	quadrilateral	NOUN
cana-2576	50	77	is	be	AUX
cana-2576	50	78	2	2	NUM
cana-2576	50	79	.	.	PUNCT
cana-2576	51	1	let	let	VERB
cana-2576	51	2	v	v	PART
cana-2576	51	3	be	be	AUX
cana-2576	51	4	a	a	DET
cana-2576	51	5	vertex	vertex	NOUN
cana-2576	51	6	in	in	ADP
cana-2576	51	7	g.	g.	PROPN
cana-2576	52	1	we	we	PRON
cana-2576	52	2	have	have	VERB
cana-2576	52	3	the	the	DET
cana-2576	52	4	following	follow	VERB
cana-2576	52	5	cases	case	NOUN
cana-2576	52	6	.	.	PUNCT
cana-2576	53	1	case	case	NOUN
cana-2576	53	2	1	1	NUM
cana-2576	53	3	:	:	SYM
cana-2576	53	4	v	v	NOUN
cana-2576	53	5	is	be	AUX
cana-2576	53	6	any	any	DET
cana-2576	53	7	vertex	vertex	NOUN
cana-2576	53	8	from	from	ADP
cana-2576	53	9	{	{	PUNCT
cana-2576	53	10	𝑢1	𝑢1	PROPN
cana-2576	53	11	,	,	PUNCT
cana-2576	53	12	𝑢2	𝑢2	PROPN
cana-2576	53	13	,	,	PUNCT
cana-2576	53	14	𝑤2	𝑤2	NOUN
cana-2576	53	15	,	,	PUNCT
cana-2576	53	16	𝑢3	𝑢3	PROPN
cana-2576	53	17	,	,	PUNCT
cana-2576	53	18	𝑤3	𝑤3	PROPN
cana-2576	53	19	,	,	PUNCT
cana-2576	53	20	…	…	PUNCT
cana-2576	53	21	,	,	PUNCT
cana-2576	53	22	𝑢𝑚−1	𝑢𝑚−1	PROPN
cana-2576	53	23	,	,	PUNCT
cana-2576	53	24	𝑤𝑚−1	𝑤𝑚−1	PROPN
cana-2576	53	25	,	,	PUNCT
cana-2576	53	26	𝑢𝑚	𝑢𝑚	NOUN
cana-2576	53	27	}	}	PUNCT
cana-2576	53	28	.	.	PUNCT
cana-2576	54	1	without	without	ADP
cana-2576	54	2	loss	loss	NOUN
cana-2576	54	3	of	of	ADP
cana-2576	54	4	generality	generality	NOUN
cana-2576	54	5	,	,	PUNCT
cana-2576	54	6	let	let	VERB
cana-2576	54	7	v	v	NOUN
cana-2576	54	8	=	=	SYM
cana-2576	54	9	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	54	10	,	,	PUNCT
cana-2576	54	11	i	i	PRON
cana-2576	54	12	=	=	NOUN
cana-2576	54	13	1	1	NUM
cana-2576	54	14	,	,	PUNCT
cana-2576	54	15	2	2	NUM
cana-2576	54	16	,	,	PUNCT
cana-2576	54	17	…	…	PUNCT
cana-2576	54	18	,	,	PUNCT
cana-2576	54	19	m-1	m-1	PROPN
cana-2576	54	20	.	.	PUNCT
cana-2576	55	1	then	then	ADV
cana-2576	55	2	d(𝑢𝑖	d(𝑢𝑖	PROPN
cana-2576	55	3	)	)	PUNCT
cana-2576	55	4	=	=	SYM
cana-2576	56	1	p–3	p–3	NOUN
cana-2576	56	2	.	.	PUNCT
cana-2576	57	1	clearly	clearly	ADV
cana-2576	57	2	,	,	PUNCT
cana-2576	57	3	this	this	DET
cana-2576	57	4	vertex	vertex	NOUN
cana-2576	57	5	covers	cover	VERB
cana-2576	57	6	all	all	DET
cana-2576	57	7	the	the	DET
cana-2576	57	8	vertices	vertex	NOUN
cana-2576	57	9	except	except	SCONJ
cana-2576	57	10	two	two	NUM
cana-2576	57	11	vertices	vertex	NOUN
cana-2576	57	12	,	,	PUNCT
cana-2576	57	13	say	say	VERB
cana-2576	57	14	𝑤𝑖−1	𝑤𝑖−1	NOUN
cana-2576	57	15	and	and	CCONJ
cana-2576	57	16	𝑣𝑖.	𝑣𝑖.	NOUN
cana-2576	57	17	then	then	ADV
cana-2576	57	18	d(𝑤𝑖−1	d(𝑤𝑖−1	NOUN
cana-2576	57	19	)	)	PUNCT
cana-2576	57	20	=	=	SYM
cana-2576	57	21	1	1	NUM
cana-2576	57	22	and	and	CCONJ
cana-2576	57	23	d(𝑣𝑖	d(𝑣𝑖	NUM
cana-2576	57	24	)	)	PUNCT
cana-2576	57	25	=	=	SYM
cana-2576	57	26	1	1	NUM
cana-2576	57	27	if	if	SCONJ
cana-2576	57	28	𝑣𝑖	𝑣𝑖	ADV
cana-2576	57	29	is	be	AUX
cana-2576	57	30	an	an	DET
cana-2576	57	31	initial(end	initial(end	NOUN
cana-2576	57	32	)	)	PUNCT
cana-2576	57	33	vertex	vertex	NOUN
cana-2576	57	34	,	,	PUNCT
cana-2576	57	35	otherwise	otherwise	ADV
cana-2576	57	36	d(𝑣𝑖	d(𝑣𝑖	ADJ
cana-2576	57	37	)	)	PUNCT
cana-2576	57	38	=	=	SYM
cana-2576	57	39	3	3	X
cana-2576	57	40	.	.	PUNCT
cana-2576	57	41	to	to	PART
cana-2576	57	42	cover	cover	VERB
cana-2576	57	43	the	the	DET
cana-2576	57	44	vertex	vertex	NOUN
cana-2576	57	45	𝑤𝑖−1	𝑤𝑖−1	NOUN
cana-2576	57	46	and	and	CCONJ
cana-2576	57	47	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	57	48	,	,	PUNCT
cana-2576	57	49	either	either	CCONJ
cana-2576	57	50	we	we	PRON
cana-2576	57	51	have	have	VERB
cana-2576	57	52	to	to	PART
cana-2576	57	53	take	take	VERB
cana-2576	57	54	these	these	DET
cana-2576	57	55	two	two	NUM
cana-2576	57	56	vertices	vertex	NOUN
cana-2576	57	57	or	or	CCONJ
cana-2576	57	58	take	take	VERB
cana-2576	57	59	a	a	DET
cana-2576	57	60	vertex	vertex	NOUN
cana-2576	57	61	which	which	PRON
cana-2576	57	62	is	be	AUX
cana-2576	57	63	adjacent	adjacent	ADJ
cana-2576	57	64	to	to	ADP
cana-2576	57	65	both	both	CCONJ
cana-2576	57	66	𝑤𝑖−1	𝑤𝑖−1	NOUN
cana-2576	57	67	and	and	CCONJ
cana-2576	57	68	𝑣𝑖.	𝑣𝑖.	NOUN
cana-2576	57	69	such	such	DET
cana-2576	57	70	a	a	DET
cana-2576	57	71	vertex	vertex	NOUN
cana-2576	57	72	always	always	ADV
cana-2576	57	73	will	will	AUX
cana-2576	57	74	exist	exist	VERB
cana-2576	57	75	,	,	PUNCT
cana-2576	57	76	since	since	SCONJ
cana-2576	57	77	it	it	PRON
cana-2576	57	78	is	be	AUX
cana-2576	57	79	a	a	DET
cana-2576	57	80	quadrilateral	quadrilateral	ADJ
cana-2576	57	81	graph	graph	NOUN
cana-2576	57	82	and	and	CCONJ
cana-2576	57	83	|v|	|v|	NUM
cana-2576	57	84	≥	≥	NUM
cana-2576	57	85	6	6	NUM
cana-2576	57	86	.	.	PUNCT
cana-2576	58	1	let	let	VERB
cana-2576	58	2	the	the	DET
cana-2576	58	3	vertex	vertex	NOUN
cana-2576	58	4	be	be	AUX
cana-2576	58	5	𝑣𝑡	𝑣𝑡	ADP
cana-2576	58	6	.	.	PUNCT
cana-2576	59	1	then	then	ADV
cana-2576	59	2	d(𝑣𝑡	d(𝑣𝑡	VERB
cana-2576	59	3	)	)	PUNCT
cana-2576	59	4	=	=	SYM
cana-2576	59	5	5	5	NUM
cana-2576	59	6	if	if	SCONJ
cana-2576	59	7	it	it	PRON
cana-2576	59	8	is	be	AUX
cana-2576	59	9	an	an	DET
cana-2576	59	10	internal	internal	ADJ
cana-2576	59	11	path	path	NOUN
cana-2576	59	12	vertex	vertex	NOUN
cana-2576	59	13	;	;	PUNCT
cana-2576	59	14	otherwise	otherwise	ADV
cana-2576	59	15	d(𝑣𝑡	d(𝑣𝑡	PROPN
cana-2576	59	16	)	)	PUNCT
cana-2576	59	17	=	=	SYM
cana-2576	60	1	3	3	X
cana-2576	60	2	.	.	X
cana-2576	61	1	we	we	PRON
cana-2576	61	2	have	have	VERB
cana-2576	61	3	two	two	NUM
cana-2576	61	4	more	more	ADJ
cana-2576	61	5	subcases	subcase	NOUN
cana-2576	61	6	.	.	PUNCT
cana-2576	62	1	case	case	NOUN
cana-2576	62	2	1.1	1.1	NUM
cana-2576	62	3	:	:	PUNCT
cana-2576	62	4	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	62	5	is	be	AUX
cana-2576	62	6	an	an	DET
cana-2576	62	7	initial(end	initial(end	NOUN
cana-2576	62	8	)	)	PUNCT
cana-2576	62	9	vertex	vertex	NOUN
cana-2576	62	10	.	.	PUNCT
cana-2576	63	1	if	if	SCONJ
cana-2576	63	2	d(v	d(v	PROPN
cana-2576	63	3	)	)	PUNCT
cana-2576	63	4	is	be	AUX
cana-2576	63	5	not	not	PART
cana-2576	63	6	a	a	DET
cana-2576	63	7	multiple	multiple	NOUN
cana-2576	63	8	of	of	ADP
cana-2576	63	9	5	5	NUM
cana-2576	63	10	,	,	PUNCT
cana-2576	63	11	then	then	ADV
cana-2576	63	12	{	{	PUNCT
cana-2576	63	13	𝑣	𝑣	NOUN
cana-2576	63	14	,	,	PUNCT
cana-2576	63	15	𝑣𝑡	𝑣𝑡	ADP
cana-2576	63	16	}	}	PUNCT
cana-2576	63	17	is	be	AUX
cana-2576	63	18	a	a	DET
cana-2576	63	19	relatively	relatively	ADV
cana-2576	63	20	prime	prime	ADJ
cana-2576	63	21	dominating	dominating	NOUN
cana-2576	63	22	set	set	NOUN
cana-2576	63	23	.	.	PUNCT
cana-2576	64	1	hence	hence	ADV
cana-2576	64	2	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	64	3	)	)	PUNCT
cana-2576	65	1	=	=	SYM
cana-2576	65	2	2	2	NUM
cana-2576	65	3	in	in	ADP
cana-2576	65	4	this	this	DET
cana-2576	65	5	case	case	NOUN
cana-2576	65	6	.	.	PUNCT
cana-2576	66	1	if	if	SCONJ
cana-2576	66	2	d(v	d(v	PROPN
cana-2576	66	3	)	)	PUNCT
cana-2576	66	4	is	be	AUX
cana-2576	66	5	multiple	multiple	ADJ
cana-2576	66	6	of	of	ADP
cana-2576	66	7	5	5	NUM
cana-2576	66	8	,	,	PUNCT
cana-2576	66	9	then	then	ADV
cana-2576	66	10	the	the	DET
cana-2576	66	11	set	set	NOUN
cana-2576	66	12	{	{	PUNCT
cana-2576	66	13	𝑣	𝑣	NOUN
cana-2576	66	14	,	,	PUNCT
cana-2576	66	15	𝑤𝑖−1	𝑤𝑖−1	NOUN
cana-2576	66	16	,	,	PUNCT
cana-2576	66	17	𝑣𝑖	𝑣𝑖	ADP
cana-2576	66	18	}	}	PUNCT
cana-2576	66	19	is	be	AUX
cana-2576	66	20	our	our	PRON
cana-2576	66	21	required	require	VERB
cana-2576	66	22	relatively	relatively	ADV
cana-2576	66	23	prime	prime	ADJ
cana-2576	66	24	dominating	dominating	NOUN
cana-2576	66	25	set	set	NOUN
cana-2576	66	26	.	.	PUNCT
cana-2576	67	1	therefore	therefore	ADV
cana-2576	67	2	,	,	PUNCT
cana-2576	67	3	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	67	4	)	)	PUNCT
cana-2576	67	5	=	=	SYM
cana-2576	67	6	3	3	NUM
cana-2576	67	7	in	in	ADP
cana-2576	67	8	this	this	DET
cana-2576	67	9	case	case	NOUN
cana-2576	67	10	.	.	PUNCT
cana-2576	68	1	communications	communication	NOUN
cana-2576	68	2	on	on	ADP
cana-2576	68	3	applied	apply	VERB
cana-2576	68	4	nonlinear	nonlinear	ADJ
cana-2576	68	5	analysis	analysis	NOUN
cana-2576	68	6	issn	issn	NOUN
cana-2576	68	7	:	:	PUNCT
cana-2576	68	8	1074	1074	NUM
cana-2576	68	9	-	-	PUNCT
cana-2576	68	10	133x	133x	NUM
cana-2576	68	11	vol	vol	NOUN
cana-2576	68	12	32	32	NUM
cana-2576	68	13	no	no	NOUN
cana-2576	68	14	.	.	PUNCT
cana-2576	69	1	3s	3s	NUM
cana-2576	69	2	(	(	PUNCT
cana-2576	69	3	2025	2025	NUM
cana-2576	69	4	)	)	PUNCT
cana-2576	69	5	156	156	NUM
cana-2576	69	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2576	69	7	case	case	NOUN
cana-2576	69	8	1.2	1.2	NUM
cana-2576	69	9	:	:	PUNCT
cana-2576	69	10	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	69	11	is	be	AUX
cana-2576	69	12	not	not	PART
cana-2576	69	13	an	an	DET
cana-2576	69	14	initial(end	initial(end	NOUN
cana-2576	69	15	)	)	PUNCT
cana-2576	69	16	vertex	vertex	NOUN
cana-2576	69	17	.	.	PUNCT
cana-2576	70	1	then	then	ADV
cana-2576	70	2	d(𝑣𝑡	d(𝑣𝑡	NOUN
cana-2576	70	3	)	)	PUNCT
cana-2576	70	4	=	=	SYM
cana-2576	71	1	3	3	X
cana-2576	71	2	.	.	PUNCT
cana-2576	71	3	since	since	SCONJ
cana-2576	71	4	|v|	|v|	NOUN
cana-2576	71	5	=	=	SYM
cana-2576	71	6	3n+1	3n+1	PROPN
cana-2576	71	7	and	and	CCONJ
cana-2576	71	8	d(v	d(v	ADJ
cana-2576	71	9	)	)	PUNCT
cana-2576	71	10	=	=	SYM
cana-2576	71	11	p–3	p–3	NOUN
cana-2576	71	12	,	,	PUNCT
cana-2576	71	13	the	the	DET
cana-2576	71	14	degree	degree	NOUN
cana-2576	71	15	of	of	ADP
cana-2576	71	16	v	v	NOUN
cana-2576	71	17	can	can	AUX
cana-2576	71	18	not	not	PART
cana-2576	71	19	be	be	AUX
cana-2576	71	20	a	a	DET
cana-2576	71	21	multiple	multiple	NOUN
cana-2576	71	22	of	of	ADP
cana-2576	71	23	3	3	NUM
cana-2576	71	24	and	and	CCONJ
cana-2576	71	25	so	so	ADV
cana-2576	71	26	(	(	PUNCT
cana-2576	71	27	p	p	X
cana-2576	71	28	–	–	PUNCT
cana-2576	71	29	3	3	NUM
cana-2576	71	30	,	,	PUNCT
cana-2576	71	31	3	3	NUM
cana-2576	71	32	)	)	PUNCT
cana-2576	71	33	=	=	SYM
cana-2576	71	34	1	1	X
cana-2576	71	35	.	.	PUNCT
cana-2576	72	1	thus	thus	ADV
cana-2576	72	2	,	,	PUNCT
cana-2576	72	3	the	the	DET
cana-2576	72	4	set	set	NOUN
cana-2576	72	5	{	{	PUNCT
cana-2576	72	6	𝑣	𝑣	NOUN
cana-2576	72	7	,	,	PUNCT
cana-2576	72	8	𝑣𝑡	𝑣𝑡	ADP
cana-2576	72	9	}	}	PUNCT
cana-2576	72	10	is	be	AUX
cana-2576	72	11	our	our	PRON
cana-2576	72	12	required	require	VERB
cana-2576	72	13	relatively	relatively	ADV
cana-2576	72	14	prime	prime	ADJ
cana-2576	72	15	dominating	dominating	NOUN
cana-2576	72	16	set	set	NOUN
cana-2576	72	17	.	.	PUNCT
cana-2576	73	1	therefore	therefore	ADV
cana-2576	73	2	,	,	PUNCT
cana-2576	73	3	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	73	4	)	)	PUNCT
cana-2576	73	5	=	=	SYM
cana-2576	73	6	2	2	NUM
cana-2576	73	7	in	in	ADP
cana-2576	73	8	this	this	DET
cana-2576	73	9	case	case	NOUN
cana-2576	73	10	.	.	PUNCT
cana-2576	74	1	case	case	NOUN
cana-2576	74	2	2	2	NUM
cana-2576	74	3	:	:	SYM
cana-2576	74	4	v	v	NOUN
cana-2576	74	5	is	be	AUX
cana-2576	74	6	an	an	DET
cana-2576	74	7	initial	initial	ADJ
cana-2576	74	8	or	or	CCONJ
cana-2576	74	9	an	an	DET
cana-2576	74	10	end	end	NOUN
cana-2576	74	11	vertex	vertex	NOUN
cana-2576	74	12	of	of	ADP
cana-2576	74	13	a	a	DET
cana-2576	74	14	path	path	NOUN
cana-2576	74	15	.	.	PUNCT
cana-2576	75	1	without	without	ADP
cana-2576	75	2	loss	loss	NOUN
cana-2576	75	3	of	of	ADP
cana-2576	75	4	generality	generality	NOUN
cana-2576	75	5	,	,	PUNCT
cana-2576	75	6	let	let	VERB
cana-2576	75	7	it	it	PRON
cana-2576	75	8	be	be	AUX
cana-2576	75	9	𝑣1	𝑣1	PROPN
cana-2576	75	10	.	.	PUNCT
cana-2576	76	1	then	then	ADV
cana-2576	76	2	d(v	d(v	PROPN
cana-2576	76	3	)	)	PUNCT
cana-2576	76	4	=	=	PUNCT
cana-2576	76	5	p-3	p-3	NOUN
cana-2576	76	6	.	.	PUNCT
cana-2576	77	1	this	this	DET
cana-2576	77	2	vertex	vertex	NOUN
cana-2576	77	3	does	do	AUX
cana-2576	77	4	not	not	PART
cana-2576	77	5	cover	cover	VERB
cana-2576	77	6	the	the	DET
cana-2576	77	7	two	two	NUM
cana-2576	77	8	vertices	vertex	NOUN
cana-2576	77	9	𝑢1	𝑢1	PROPN
cana-2576	77	10	and	and	CCONJ
cana-2576	77	11	𝑣2	𝑣2	PROPN
cana-2576	77	12	.	.	PUNCT
cana-2576	78	1	then	then	ADV
cana-2576	78	2	d(𝑣2	d(𝑣2	ADV
cana-2576	78	3	)	)	PUNCT
cana-2576	78	4	=	=	SYM
cana-2576	78	5	3	3	NUM
cana-2576	78	6	and	and	CCONJ
cana-2576	78	7	d(𝑢1	d(𝑢1	NOUN
cana-2576	78	8	)	)	PUNCT
cana-2576	78	9	=	=	SYM
cana-2576	79	1	1	1	X
cana-2576	79	2	.	.	PUNCT
cana-2576	79	3	to	to	PART
cana-2576	79	4	cover	cover	VERB
cana-2576	79	5	the	the	DET
cana-2576	79	6	vertices	vertex	NOUN
cana-2576	79	7	𝑢1	𝑢1	PROPN
cana-2576	79	8	and	and	CCONJ
cana-2576	79	9	𝑣2	𝑣2	PROPN
cana-2576	79	10	,	,	PUNCT
cana-2576	79	11	two	two	NUM
cana-2576	79	12	possibilities	possibility	NOUN
cana-2576	79	13	are	be	AUX
cana-2576	79	14	there	there	ADV
cana-2576	79	15	.	.	PUNCT
cana-2576	80	1	either	either	CCONJ
cana-2576	80	2	we	we	PRON
cana-2576	80	3	have	have	VERB
cana-2576	80	4	to	to	PART
cana-2576	80	5	take	take	VERB
cana-2576	80	6	these	these	DET
cana-2576	80	7	two	two	NUM
cana-2576	80	8	vertices	vertex	NOUN
cana-2576	80	9	or	or	CCONJ
cana-2576	80	10	a	a	DET
cana-2576	80	11	vertex	vertex	NOUN
cana-2576	80	12	which	which	PRON
cana-2576	80	13	is	be	AUX
cana-2576	80	14	adjacent	adjacent	ADJ
cana-2576	80	15	to	to	ADP
cana-2576	80	16	both	both	CCONJ
cana-2576	80	17	𝑢1	𝑢1	PROPN
cana-2576	80	18	and	and	CCONJ
cana-2576	80	19	𝑣2	𝑣2	PROPN
cana-2576	80	20	.	.	PUNCT
cana-2576	81	1	such	such	DET
cana-2576	81	2	a	a	DET
cana-2576	81	3	vertex	vertex	NOUN
cana-2576	81	4	always	always	ADV
cana-2576	81	5	exists	exist	VERB
cana-2576	81	6	,	,	PUNCT
cana-2576	81	7	since	since	SCONJ
cana-2576	81	8	g	g	PROPN
cana-2576	81	9	is	be	AUX
cana-2576	81	10	a	a	DET
cana-2576	81	11	quadrilateral	quadrilateral	ADJ
cana-2576	81	12	snake	snake	NOUN
cana-2576	81	13	graph	graph	NOUN
cana-2576	81	14	and	and	CCONJ
cana-2576	81	15	|v|	|v|	NUM
cana-2576	81	16	≥	≥	NUM
cana-2576	81	17	6	6	NUM
cana-2576	81	18	.	.	PUNCT
cana-2576	82	1	then	then	ADV
cana-2576	82	2	the	the	DET
cana-2576	82	3	vertex	vertex	NOUN
cana-2576	82	4	must	must	AUX
cana-2576	82	5	be	be	AUX
cana-2576	82	6	𝑢2	𝑢2	PROPN
cana-2576	82	7	and	and	CCONJ
cana-2576	82	8	d(𝑢2	d(𝑢2	NOUN
cana-2576	82	9	)	)	PUNCT
cana-2576	82	10	=	=	SYM
cana-2576	83	1	3	3	X
cana-2576	83	2	.	.	PUNCT
cana-2576	83	3	since	since	SCONJ
cana-2576	83	4	p–3	p–3	NOUN
cana-2576	83	5	is	be	AUX
cana-2576	83	6	not	not	PART
cana-2576	83	7	a	a	DET
cana-2576	83	8	multiple	multiple	NOUN
cana-2576	83	9	of	of	ADP
cana-2576	83	10	3	3	NUM
cana-2576	83	11	,	,	PUNCT
cana-2576	83	12	we	we	PRON
cana-2576	83	13	have	have	VERB
cana-2576	83	14	the	the	DET
cana-2576	83	15	set	set	NOUN
cana-2576	83	16	{	{	PUNCT
cana-2576	83	17	𝑣	𝑣	NOUN
cana-2576	83	18	,	,	PUNCT
cana-2576	83	19	𝑢2	𝑢2	PROPN
cana-2576	83	20	}	}	PUNCT
cana-2576	83	21	is	be	AUX
cana-2576	83	22	our	our	PRON
cana-2576	83	23	required	require	VERB
cana-2576	83	24	relatively	relatively	ADV
cana-2576	83	25	prime	prime	ADJ
cana-2576	83	26	dominating	dominating	NOUN
cana-2576	83	27	set	set	NOUN
cana-2576	83	28	and	and	CCONJ
cana-2576	83	29	hence	hence	ADV
cana-2576	83	30	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	83	31	)	)	PUNCT
cana-2576	84	1	=	=	SYM
cana-2576	84	2	2	2	X
cana-2576	84	3	.	.	X
cana-2576	84	4	case	case	NOUN
cana-2576	84	5	3	3	NUM
cana-2576	84	6	:	:	SYM
cana-2576	84	7	v	v	NOUN
cana-2576	84	8	is	be	AUX
cana-2576	84	9	any	any	DET
cana-2576	84	10	internal	internal	ADJ
cana-2576	84	11	path	path	NOUN
cana-2576	84	12	vertex	vertex	NOUN
cana-2576	84	13	.	.	PUNCT
cana-2576	85	1	without	without	ADP
cana-2576	85	2	loss	loss	NOUN
cana-2576	85	3	of	of	ADP
cana-2576	85	4	generality	generality	NOUN
cana-2576	85	5	,	,	PUNCT
cana-2576	85	6	let	let	VERB
cana-2576	85	7	it	it	PRON
cana-2576	85	8	be	be	AUX
cana-2576	85	9	𝑣𝑖.	𝑣𝑖.	NOUN
cana-2576	85	10	then	then	ADV
cana-2576	85	11	d(𝑣𝑖	d(𝑣𝑖	ADJ
cana-2576	85	12	)	)	PUNCT
cana-2576	86	1	=	=	SYM
cana-2576	86	2	p-5	p-5	PROPN
cana-2576	86	3	.	.	PUNCT
cana-2576	87	1	this	this	DET
cana-2576	87	2	vertex	vertex	NOUN
cana-2576	87	3	does	do	AUX
cana-2576	87	4	not	not	PART
cana-2576	87	5	cover	cover	VERB
cana-2576	87	6	four	four	NUM
cana-2576	87	7	vertices	vertex	NOUN
cana-2576	87	8	;	;	PUNCT
cana-2576	87	9	namely	namely	ADV
cana-2576	87	10	,	,	PUNCT
cana-2576	87	11	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	87	12	,	,	PUNCT
cana-2576	87	13	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	87	14	,	,	PUNCT
cana-2576	87	15	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	87	16	and	and	CCONJ
cana-2576	87	17	𝑤𝑖.	𝑤𝑖.	VERB
cana-2576	87	18	then	then	ADV
cana-2576	87	19	d(𝑢𝑖	d(𝑢𝑖	NOUN
cana-2576	87	20	)	)	PUNCT
cana-2576	87	21	=	=	SYM
cana-2576	87	22	d(𝑤𝑖	d(𝑤𝑖	NOUN
cana-2576	87	23	)	)	PUNCT
cana-2576	87	24	=	=	SYM
cana-2576	87	25	1	1	NUM
cana-2576	87	26	and	and	CCONJ
cana-2576	87	27	d(𝑣𝑖−1	d(𝑣𝑖−1	NUM
cana-2576	87	28	)	)	PUNCT
cana-2576	87	29	=	=	SYM
cana-2576	87	30	1	1	NUM
cana-2576	87	31	if	if	SCONJ
cana-2576	87	32	it	it	PRON
cana-2576	87	33	is	be	AUX
cana-2576	87	34	an	an	DET
cana-2576	87	35	initial	initial	ADJ
cana-2576	87	36	vertex	vertex	NOUN
cana-2576	87	37	and	and	CCONJ
cana-2576	87	38	d(𝑣𝑖+1	d(𝑣𝑖+1	NOUN
cana-2576	87	39	)	)	PUNCT
cana-2576	87	40	=	=	SYM
cana-2576	87	41	3	3	NUM
cana-2576	87	42	;	;	PUNCT
cana-2576	87	43	similarly	similarly	ADV
cana-2576	87	44	d(𝑣𝑖−1	d(𝑣𝑖−1	PUNCT
cana-2576	87	45	)	)	PUNCT
cana-2576	87	46	=	=	SYM
cana-2576	87	47	3	3	NUM
cana-2576	87	48	and	and	CCONJ
cana-2576	87	49	d(𝑣𝑖+1	d(𝑣𝑖+1	NOUN
cana-2576	87	50	)	)	PUNCT
cana-2576	87	51	=	=	SYM
cana-2576	87	52	1	1	NUM
cana-2576	87	53	if	if	SCONJ
cana-2576	87	54	it	it	PRON
cana-2576	87	55	is	be	AUX
cana-2576	87	56	an	an	DET
cana-2576	87	57	end	end	NOUN
cana-2576	87	58	vertex	vertex	NOUN
cana-2576	87	59	.	.	PUNCT
cana-2576	88	1	to	to	PART
cana-2576	88	2	cover	cover	VERB
cana-2576	88	3	these	these	DET
cana-2576	88	4	four	four	NUM
cana-2576	88	5	vertices	vertex	NOUN
cana-2576	88	6	,	,	PUNCT
cana-2576	88	7	either	either	CCONJ
cana-2576	88	8	we	we	PRON
cana-2576	88	9	have	have	VERB
cana-2576	88	10	to	to	PART
cana-2576	88	11	take	take	VERB
cana-2576	88	12	these	these	DET
cana-2576	88	13	four	four	NUM
cana-2576	88	14	vertices	vertex	NOUN
cana-2576	88	15	or	or	CCONJ
cana-2576	88	16	the	the	DET
cana-2576	88	17	vertices	vertex	NOUN
cana-2576	88	18	which	which	PRON
cana-2576	88	19	are	be	AUX
cana-2576	88	20	adjacent	adjacent	ADJ
cana-2576	88	21	to	to	ADP
cana-2576	88	22	these	these	DET
cana-2576	88	23	four	four	NUM
cana-2576	88	24	vertices	vertex	NOUN
cana-2576	88	25	.	.	PUNCT
cana-2576	89	1	since	since	SCONJ
cana-2576	89	2	g	g	PROPN
cana-2576	89	3	is	be	AUX
cana-2576	89	4	a	a	DET
cana-2576	89	5	quadrilateral	quadrilateral	ADJ
cana-2576	89	6	graph	graph	NOUN
cana-2576	89	7	,	,	PUNCT
cana-2576	89	8	such	such	DET
cana-2576	89	9	a	a	DET
cana-2576	89	10	vertex	vertex	NOUN
cana-2576	89	11	always	always	ADV
cana-2576	89	12	exists	exist	VERB
cana-2576	89	13	as	as	ADP
cana-2576	89	14	in	in	ADP
cana-2576	89	15	case	case	NOUN
cana-2576	89	16	2	2	X
cana-2576	89	17	.	.	PUNCT
cana-2576	89	18	let	let	VERB
cana-2576	89	19	them	they	PRON
cana-2576	89	20	be	be	AUX
cana-2576	89	21	𝑤𝑖−1	𝑤𝑖−1	ADJ
cana-2576	89	22	and	and	CCONJ
cana-2576	89	23	𝑢𝑖+2	𝑢𝑖+2	NUM
cana-2576	89	24	and	and	CCONJ
cana-2576	89	25	degree	degree	NOUN
cana-2576	89	26	of	of	ADP
cana-2576	89	27	these	these	DET
cana-2576	89	28	two	two	NUM
cana-2576	89	29	vertices	vertex	NOUN
cana-2576	89	30	is	be	AUX
cana-2576	89	31	three	three	NUM
cana-2576	89	32	and	and	CCONJ
cana-2576	89	33	hence	hence	ADV
cana-2576	89	34	we	we	PRON
cana-2576	89	35	can	can	AUX
cana-2576	89	36	not	not	PART
cana-2576	89	37	take	take	VERB
cana-2576	89	38	these	these	DET
cana-2576	89	39	two	two	NUM
cana-2576	89	40	vertices	vertex	NOUN
cana-2576	89	41	together	together	ADV
cana-2576	89	42	.	.	PUNCT
cana-2576	90	1	suppose	suppose	VERB
cana-2576	90	2	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	90	3	is	be	AUX
cana-2576	90	4	an	an	DET
cana-2576	90	5	initial	initial	ADJ
cana-2576	90	6	vertex	vertex	NOUN
cana-2576	90	7	,	,	PUNCT
cana-2576	90	8	then	then	ADV
cana-2576	90	9	the	the	DET
cana-2576	90	10	set	set	NOUN
cana-2576	90	11	{	{	PUNCT
cana-2576	90	12	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	90	13	,	,	PUNCT
cana-2576	90	14	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	90	15	,	,	PUNCT
cana-2576	90	16	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	90	17	,	,	PUNCT
cana-2576	90	18	𝑢𝑖+2	𝑢𝑖+2	NUM
cana-2576	90	19	}	}	PUNCT
cana-2576	90	20	is	be	AUX
cana-2576	90	21	a	a	DET
cana-2576	90	22	relatively	relatively	ADV
cana-2576	90	23	prime	prime	ADJ
cana-2576	90	24	dominating	dominating	NOUN
cana-2576	90	25	set	set	NOUN
cana-2576	90	26	and	and	CCONJ
cana-2576	90	27	hence	hence	ADV
cana-2576	90	28	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	90	29	)	)	PUNCT
cana-2576	91	1	=	=	PUNCT
cana-2576	91	2	4	4	X
cana-2576	91	3	.	.	X
cana-2576	91	4	similarly	similarly	ADV
cana-2576	91	5	,	,	PUNCT
cana-2576	91	6	if	if	SCONJ
cana-2576	91	7	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	91	8	is	be	AUX
cana-2576	91	9	an	an	DET
cana-2576	91	10	end	end	NOUN
cana-2576	91	11	vertex	vertex	NOUN
cana-2576	91	12	.	.	PUNCT
cana-2576	92	1	hence	hence	ADV
cana-2576	92	2	assume	assume	VERB
cana-2576	92	3	that	that	SCONJ
cana-2576	92	4	neither	neither	DET
cana-2576	92	5	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	92	6	is	be	AUX
cana-2576	92	7	an	an	DET
cana-2576	92	8	initial	initial	ADJ
cana-2576	92	9	vertex	vertex	NOUN
cana-2576	92	10	nor	nor	CCONJ
cana-2576	92	11	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	92	12	is	be	AUX
cana-2576	92	13	an	an	DET
cana-2576	92	14	end	end	NOUN
cana-2576	92	15	vertex	vertex	NOUN
cana-2576	92	16	.	.	PUNCT
cana-2576	93	1	since	since	SCONJ
cana-2576	93	2	we	we	PRON
cana-2576	93	3	can	can	AUX
cana-2576	93	4	not	not	PART
cana-2576	93	5	take	take	VERB
cana-2576	93	6	the	the	DET
cana-2576	93	7	vertices	vertex	NOUN
cana-2576	93	8	𝑤𝑖−1	𝑤𝑖−1	NOUN
cana-2576	93	9	and	and	CCONJ
cana-2576	93	10	𝑢𝑖+2	𝑢𝑖+2	NUM
cana-2576	93	11	together	together	ADV
cana-2576	93	12	,	,	PUNCT
cana-2576	93	13	we	we	PRON
cana-2576	93	14	have	have	VERB
cana-2576	93	15	to	to	PART
cana-2576	93	16	choose	choose	VERB
cana-2576	93	17	a	a	DET
cana-2576	93	18	vertex	vertex	NOUN
cana-2576	93	19	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	93	20	or	or	CCONJ
cana-2576	93	21	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	93	22	.	.	PUNCT
cana-2576	94	1	but	but	CCONJ
cana-2576	94	2	both	both	PRON
cana-2576	94	3	of	of	ADP
cana-2576	94	4	them	they	PRON
cana-2576	94	5	has	have	VERB
cana-2576	94	6	degree	degree	NOUN
cana-2576	94	7	3	3	NUM
cana-2576	94	8	.	.	PUNCT
cana-2576	95	1	therefore	therefore	ADV
cana-2576	95	2	,	,	PUNCT
cana-2576	95	3	relatively	relatively	ADV
cana-2576	95	4	prime	prime	ADJ
cana-2576	95	5	dominating	dominating	NOUN
cana-2576	95	6	set	set	NOUN
cana-2576	95	7	does	do	AUX
cana-2576	95	8	not	not	PART
cana-2576	95	9	exist	exist	VERB
cana-2576	95	10	in	in	ADP
cana-2576	95	11	this	this	DET
cana-2576	95	12	case	case	NOUN
cana-2576	95	13	.	.	PUNCT
cana-2576	96	1	theorem	theorem	VERB
cana-2576	96	2	3.2	3.2	NUM
cana-2576	96	3	.	.	PUNCT
cana-2576	97	1	let	let	VERB
cana-2576	97	2	g	g	PRON
cana-2576	97	3	be	be	AUX
cana-2576	97	4	an	an	DET
cana-2576	97	5	alternate	alternate	ADJ
cana-2576	97	6	quadrilateral	quadrilateral	ADJ
cana-2576	97	7	snake	snake	NOUN
cana-2576	97	8	graph	graph	NOUN
cana-2576	97	9	with	with	ADP
cana-2576	97	10	p	p	ADJ
cana-2576	97	11	vertices	vertex	NOUN
cana-2576	97	12	,	,	PUNCT
cana-2576	97	13	where	where	SCONJ
cana-2576	97	14	p	p	NOUN
cana-2576	97	15	=	=	NOUN
cana-2576	97	16	4n	4n	X
cana-2576	97	17	,	,	PUNCT
cana-2576	97	18	n	n	PRON
cana-2576	97	19	≥	≥	NOUN
cana-2576	97	20	2	2	NUM
cana-2576	97	21	.	.	PUNCT
cana-2576	98	1	then	then	ADV
cana-2576	98	2	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	98	3	)	)	PUNCT
cana-2576	98	4	=	=	PUNCT
cana-2576	98	5	2	2	NUM
cana-2576	98	6	,	,	PUNCT
cana-2576	98	7	3	3	NUM
cana-2576	98	8	or	or	CCONJ
cana-2576	98	9	4	4	NUM
cana-2576	98	10	.	.	X
cana-2576	99	1	proof	proof	NOUN
cana-2576	99	2	:	:	PUNCT
cana-2576	99	3	let	let	VERB
cana-2576	99	4	g	g	PRON
cana-2576	99	5	be	be	AUX
cana-2576	99	6	an	an	DET
cana-2576	99	7	alternate	alternate	ADJ
cana-2576	99	8	quadrilateral	quadrilateral	ADJ
cana-2576	99	9	snake	snake	NOUN
cana-2576	99	10	graph	graph	NOUN
cana-2576	99	11	with	with	ADP
cana-2576	99	12	p	p	NOUN
cana-2576	99	13	vertices	vertex	NOUN
cana-2576	99	14	.	.	PUNCT
cana-2576	100	1	let	let	VERB
cana-2576	100	2	the	the	DET
cana-2576	100	3	vertices	vertex	NOUN
cana-2576	100	4	in	in	ADP
cana-2576	100	5	the	the	DET
cana-2576	100	6	path	path	NOUN
cana-2576	100	7	be	be	AUX
cana-2576	100	8	𝑣1,𝑣2,𝑣6,	𝑣1,𝑣2,𝑣6,	NOUN
cana-2576	100	9	…	…	PUNCT
cana-2576	100	10	,𝑣𝑚	,𝑣𝑚	PUNCT
cana-2576	100	11	and	and	CCONJ
cana-2576	100	12	the	the	DET
cana-2576	100	13	vertices	vertex	NOUN
cana-2576	100	14	in	in	ADP
cana-2576	100	15	the	the	DET
cana-2576	100	16	quadrilateral	quadrilateral	ADJ
cana-2576	100	17	be	be	AUX
cana-2576	100	18	𝑢1	𝑢1	PROPN
cana-2576	100	19	,	,	PUNCT
cana-2576	100	20	𝑢2	𝑢2	PROPN
cana-2576	100	21	,	,	PUNCT
cana-2576	100	22	𝑢3,	𝑢3,	NOUN
cana-2576	100	23	…	…	SYM
cana-2576	100	24	,𝑢𝑚.	,𝑢𝑚.	PUNCT
cana-2576	100	25	then	then	ADV
cana-2576	100	26	degree	degree	NOUN
cana-2576	100	27	of	of	ADP
cana-2576	100	28	each	each	DET
cana-2576	100	29	vertex	vertex	NOUN
cana-2576	100	30	in	in	ADP
cana-2576	100	31	the	the	DET
cana-2576	100	32	path	path	NOUN
cana-2576	100	33	except	except	SCONJ
cana-2576	100	34	the	the	DET
cana-2576	100	35	initial	initial	ADJ
cana-2576	100	36	and	and	CCONJ
cana-2576	100	37	end	end	VERB
cana-2576	100	38	vertex	vertex	NOUN
cana-2576	100	39	is	be	AUX
cana-2576	100	40	3	3	NUM
cana-2576	100	41	;	;	PUNCT
cana-2576	100	42	degree	degree	NOUN
cana-2576	100	43	of	of	ADP
cana-2576	100	44	initial	initial	ADJ
cana-2576	100	45	and	and	CCONJ
cana-2576	100	46	end	end	VERB
cana-2576	100	47	vertex	vertex	NOUN
cana-2576	100	48	is	be	AUX
cana-2576	100	49	2	2	NUM
cana-2576	100	50	;	;	PUNCT
cana-2576	100	51	degree	degree	NOUN
cana-2576	100	52	of	of	ADP
cana-2576	100	53	vertices	vertex	NOUN
cana-2576	100	54	in	in	ADP
cana-2576	100	55	the	the	DET
cana-2576	100	56	quadrilateral	quadrilateral	NOUN
cana-2576	100	57	is	be	AUX
cana-2576	100	58	2	2	NUM
cana-2576	100	59	.	.	PUNCT
cana-2576	101	1	let	let	VERB
cana-2576	101	2	v	v	PART
cana-2576	101	3	be	be	AUX
cana-2576	101	4	any	any	DET
cana-2576	101	5	vertex	vertex	NOUN
cana-2576	101	6	in	in	ADP
cana-2576	101	7	g.	g.	PROPN
cana-2576	102	1	we	we	PRON
cana-2576	102	2	have	have	VERB
cana-2576	102	3	the	the	DET
cana-2576	102	4	following	follow	VERB
cana-2576	102	5	cases	case	NOUN
cana-2576	102	6	:	:	PUNCT
cana-2576	102	7	case	case	NOUN
cana-2576	102	8	1	1	NUM
cana-2576	102	9	:	:	SYM
cana-2576	102	10	v	v	NOUN
cana-2576	102	11	is	be	AUX
cana-2576	102	12	any	any	DET
cana-2576	102	13	vertex	vertex	NOUN
cana-2576	102	14	from	from	ADP
cana-2576	102	15	{	{	PUNCT
cana-2576	102	16	𝑢1	𝑢1	PROPN
cana-2576	102	17	,	,	PUNCT
cana-2576	102	18	𝑢2	𝑢2	PROPN
cana-2576	102	19	,	,	PUNCT
cana-2576	102	20	…	…	PUNCT
cana-2576	102	21	,	,	PUNCT
cana-2576	102	22	𝑢𝑚	𝑢𝑚	ADP
cana-2576	102	23	}	}	PUNCT
cana-2576	102	24	.	.	PUNCT
cana-2576	103	1	without	without	ADP
cana-2576	103	2	loss	loss	NOUN
cana-2576	103	3	of	of	ADP
cana-2576	103	4	generality	generality	NOUN
cana-2576	103	5	,	,	PUNCT
cana-2576	103	6	we	we	PRON
cana-2576	103	7	take	take	VERB
cana-2576	103	8	v	v	NOUN
cana-2576	103	9	=	=	NOUN
cana-2576	103	10	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	103	11	,	,	PUNCT
cana-2576	103	12	𝑖	𝑖	X
cana-2576	103	13	=	=	SYM
cana-2576	103	14	1,2	1,2	NUM
cana-2576	103	15	,	,	PUNCT
cana-2576	103	16	…	…	PUNCT
cana-2576	103	17	,	,	PUNCT
cana-2576	103	18	𝑚.	𝑚.	ADV
cana-2576	103	19	then	then	ADV
cana-2576	103	20	d(v	d(v	PROPN
cana-2576	103	21	)	)	PUNCT
cana-2576	103	22	=	=	PUNCT
cana-2576	104	1	p-3	p-3	NOUN
cana-2576	104	2	.	.	PUNCT
cana-2576	105	1	this	this	DET
cana-2576	105	2	vertex	vertex	NOUN
cana-2576	105	3	covers	cover	VERB
cana-2576	105	4	all	all	DET
cana-2576	105	5	the	the	DET
cana-2576	105	6	vertices	vertex	NOUN
cana-2576	105	7	of	of	ADP
cana-2576	105	8	𝐺𝑣	𝐺𝑣	PROPN
cana-2576	105	9	,	,	PUNCT
cana-2576	105	10	except	except	SCONJ
cana-2576	105	11	the	the	DET
cana-2576	105	12	two	two	NUM
cana-2576	105	13	vertices	vertex	NOUN
cana-2576	105	14	,	,	PUNCT
cana-2576	105	15	namely	namely	ADV
cana-2576	105	16	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	105	17	and	and	CCONJ
cana-2576	105	18	𝑢𝑖−1	𝑢𝑖−1	PROPN
cana-2576	105	19	.	.	PROPN
cana-2576	106	1	then	then	ADV
cana-2576	106	2	d(𝑣𝑖	d(𝑣𝑖	NUM
cana-2576	106	3	)	)	PUNCT
cana-2576	107	1	=	=	SYM
cana-2576	107	2	1	1	NUM
cana-2576	107	3	if	if	SCONJ
cana-2576	107	4	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	107	5	is	be	AUX
cana-2576	107	6	initial	initial	ADJ
cana-2576	107	7	or	or	CCONJ
cana-2576	107	8	end	end	VERB
cana-2576	107	9	vertex	vertex	NOUN
cana-2576	107	10	,	,	PUNCT
cana-2576	107	11	otherwise	otherwise	ADV
cana-2576	107	12	2	2	NUM
cana-2576	107	13	.	.	PUNCT
cana-2576	107	14	to	to	PART
cana-2576	107	15	cover	cover	VERB
cana-2576	107	16	the	the	DET
cana-2576	107	17	vertices	vertex	NOUN
cana-2576	107	18	𝑣𝑖and	𝑣𝑖and	NOUN
cana-2576	107	19	𝑢𝑖−1,either	𝑢𝑖−1,either	NOUN
cana-2576	107	20	we	we	PRON
cana-2576	107	21	have	have	VERB
cana-2576	107	22	to	to	PART
cana-2576	107	23	take	take	VERB
cana-2576	107	24	these	these	DET
cana-2576	107	25	two	two	NUM
cana-2576	107	26	vertices	vertex	NOUN
cana-2576	107	27	or	or	CCONJ
cana-2576	107	28	choose	choose	VERB
cana-2576	107	29	a	a	DET
cana-2576	107	30	vertex	vertex	NOUN
cana-2576	107	31	which	which	PRON
cana-2576	107	32	is	be	AUX
cana-2576	107	33	adjacent	adjacent	ADJ
cana-2576	107	34	to	to	ADP
cana-2576	107	35	both	both	PRON
cana-2576	107	36	𝑣𝑖	𝑣𝑖	ADP
cana-2576	107	37	and	and	CCONJ
cana-2576	107	38	𝑢𝑖−1	𝑢𝑖−1	PROPN
cana-2576	107	39	.	.	PUNCT
cana-2576	108	1	such	such	DET
cana-2576	108	2	a	a	DET
cana-2576	108	3	vertex	vertex	NOUN
cana-2576	108	4	always	always	ADV
cana-2576	108	5	exists	exist	VERB
cana-2576	108	6	in	in	ADP
cana-2576	108	7	alternate	alternate	ADJ
cana-2576	108	8	quadrilateral	quadrilateral	ADJ
cana-2576	108	9	snake	snake	NOUN
cana-2576	108	10	graph	graph	NOUN
cana-2576	108	11	.	.	PUNCT
cana-2576	109	1	let	let	VERB
cana-2576	109	2	the	the	DET
cana-2576	109	3	vertex	vertex	NOUN
cana-2576	109	4	be	be	AUX
cana-2576	109	5	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	109	6	and	and	CCONJ
cana-2576	109	7	d(𝑣𝑖+1	d(𝑣𝑖+1	NOUN
cana-2576	109	8	)	)	PUNCT
cana-2576	109	9	=	=	SYM
cana-2576	110	1	4	4	X
cana-2576	110	2	.	.	PUNCT
cana-2576	110	3	since	since	SCONJ
cana-2576	110	4	d(𝑣𝑖	d(𝑣𝑖	NUM
cana-2576	110	5	)	)	PUNCT
cana-2576	110	6	=	=	SYM
cana-2576	110	7	p-3	p-3	NOUN
cana-2576	110	8	and	and	CCONJ
cana-2576	110	9	|𝑉|	|𝑉|	NOUN
cana-2576	110	10	=	=	PUNCT
cana-2576	110	11	4n	4n	NOUN
cana-2576	110	12	,	,	PUNCT
cana-2576	110	13	it	it	PRON
cana-2576	110	14	can	can	AUX
cana-2576	110	15	not	not	PART
cana-2576	110	16	be	be	AUX
cana-2576	110	17	multiple	multiple	ADJ
cana-2576	110	18	of	of	ADP
cana-2576	110	19	4	4	NUM
cana-2576	110	20	and	and	CCONJ
cana-2576	110	21	hence	hence	ADV
cana-2576	110	22	(	(	PUNCT
cana-2576	110	23	d(𝑣𝑖	d(𝑣𝑖	NUM
cana-2576	110	24	)	)	PUNCT
cana-2576	110	25	,	,	PUNCT
cana-2576	110	26	d(𝑣𝑖+1	d(𝑣𝑖+1	NUM
cana-2576	110	27	)	)	PUNCT
cana-2576	110	28	)	)	PUNCT
cana-2576	111	1	=	=	PRON
cana-2576	111	2	(	(	PUNCT
cana-2576	111	3	p-3	p-3	NOUN
cana-2576	111	4	,	,	PUNCT
cana-2576	111	5	4	4	NUM
cana-2576	111	6	)	)	PUNCT
cana-2576	111	7	=	=	SYM
cana-2576	111	8	1	1	NUM
cana-2576	111	9	and	and	CCONJ
cana-2576	111	10	these	these	DET
cana-2576	111	11	two	two	NUM
cana-2576	111	12	vertices	vertex	NOUN
cana-2576	111	13	covers	cover	VERB
cana-2576	111	14	all	all	DET
cana-2576	111	15	the	the	DET
cana-2576	111	16	vertices	vertex	NOUN
cana-2576	111	17	of	of	ADP
cana-2576	111	18	𝐺𝑣.	𝐺𝑣.	ADJ
cana-2576	111	19	hence	hence	ADV
cana-2576	111	20	relatively	relatively	ADV
cana-2576	111	21	prime	prime	ADJ
cana-2576	111	22	dominating	dominating	NOUN
cana-2576	111	23	set	set	NOUN
cana-2576	111	24	is	be	AUX
cana-2576	111	25	{	{	PUNCT
cana-2576	111	26	𝑢𝑖,𝑣𝑖+1	𝑢𝑖,𝑣𝑖+1	NOUN
cana-2576	111	27	}	}	PUNCT
cana-2576	111	28	and	and	CCONJ
cana-2576	111	29	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	111	30	)	)	PUNCT
cana-2576	112	1	=	=	SYM
cana-2576	112	2	2	2	X
cana-2576	112	3	.	.	X
cana-2576	112	4	communications	communication	NOUN
cana-2576	112	5	on	on	ADP
cana-2576	112	6	applied	apply	VERB
cana-2576	112	7	nonlinear	nonlinear	ADJ
cana-2576	112	8	analysis	analysis	NOUN
cana-2576	112	9	issn	issn	NOUN
cana-2576	112	10	:	:	PUNCT
cana-2576	112	11	1074	1074	NUM
cana-2576	112	12	-	-	PUNCT
cana-2576	112	13	133x	133x	NUM
cana-2576	112	14	vol	vol	NOUN
cana-2576	112	15	32	32	NUM
cana-2576	112	16	no	no	NOUN
cana-2576	112	17	.	.	PUNCT
cana-2576	113	1	3s	3s	NUM
cana-2576	113	2	(	(	PUNCT
cana-2576	113	3	2025	2025	NUM
cana-2576	113	4	)	)	PUNCT
cana-2576	113	5	157	157	NUM
cana-2576	113	6	https://internationalpubls.com	https://internationalpubls.com	NOUN
cana-2576	113	7	case	case	NOUN
cana-2576	113	8	2	2	NUM
cana-2576	113	9	:	:	PUNCT
cana-2576	113	10	v	v	NOUN
cana-2576	113	11	is	be	AUX
cana-2576	113	12	an	an	DET
cana-2576	113	13	initial	initial	ADJ
cana-2576	113	14	vertex	vertex	NOUN
cana-2576	113	15	or	or	CCONJ
cana-2576	113	16	an	an	DET
cana-2576	113	17	end	end	NOUN
cana-2576	113	18	vertex	vertex	NOUN
cana-2576	113	19	.	.	PUNCT
cana-2576	114	1	without	without	ADP
cana-2576	114	2	loss	loss	NOUN
cana-2576	114	3	of	of	ADP
cana-2576	114	4	generality	generality	NOUN
cana-2576	114	5	,	,	PUNCT
cana-2576	114	6	let	let	VERB
cana-2576	114	7	v	v	NOUN
cana-2576	114	8	=	=	SYM
cana-2576	114	9	𝑣1	𝑣1	PROPN
cana-2576	114	10	.	.	PUNCT
cana-2576	115	1	then	then	ADV
cana-2576	115	2	d(v	d(v	PROPN
cana-2576	115	3	)	)	PUNCT
cana-2576	115	4	=	=	PUNCT
cana-2576	115	5	p-3	p-3	NOUN
cana-2576	115	6	.	.	PUNCT
cana-2576	116	1	this	this	DET
cana-2576	116	2	vertex	vertex	NOUN
cana-2576	116	3	covers	cover	VERB
cana-2576	116	4	all	all	DET
cana-2576	116	5	the	the	DET
cana-2576	116	6	vertices	vertex	NOUN
cana-2576	116	7	except	except	SCONJ
cana-2576	116	8	two	two	NUM
cana-2576	116	9	vertices	vertex	NOUN
cana-2576	116	10	,	,	PUNCT
cana-2576	116	11	namely	namely	ADV
cana-2576	116	12	𝑢1	𝑢1	PROPN
cana-2576	116	13	and	and	CCONJ
cana-2576	116	14	𝑣2	𝑣2	PROPN
cana-2576	116	15	and	and	CCONJ
cana-2576	116	16	d(𝑢1	d(𝑢1	NOUN
cana-2576	116	17	)	)	PUNCT
cana-2576	116	18	=	=	SYM
cana-2576	116	19	1	1	NUM
cana-2576	116	20	and	and	CCONJ
cana-2576	116	21	d(𝑣2	d(𝑣2	ADJ
cana-2576	116	22	)	)	PUNCT
cana-2576	117	1	=	=	SYM
cana-2576	117	2	2	2	X
cana-2576	117	3	.	.	PUNCT
cana-2576	117	4	to	to	PART
cana-2576	117	5	cover	cover	VERB
cana-2576	117	6	the	the	DET
cana-2576	117	7	vertices	vertex	NOUN
cana-2576	117	8	𝑢1	𝑢1	PROPN
cana-2576	117	9	and	and	CCONJ
cana-2576	117	10	𝑣2	𝑣2	PROPN
cana-2576	117	11	,	,	PUNCT
cana-2576	117	12	either	either	CCONJ
cana-2576	117	13	we	we	PRON
cana-2576	117	14	have	have	VERB
cana-2576	117	15	to	to	PART
cana-2576	117	16	choose	choose	VERB
cana-2576	117	17	these	these	DET
cana-2576	117	18	two	two	NUM
cana-2576	117	19	vertices	vertex	NOUN
cana-2576	117	20	or	or	CCONJ
cana-2576	117	21	a	a	DET
cana-2576	117	22	vertex	vertex	NOUN
cana-2576	117	23	which	which	PRON
cana-2576	117	24	is	be	AUX
cana-2576	117	25	adjacent	adjacent	ADJ
cana-2576	117	26	to	to	ADP
cana-2576	117	27	both	both	DET
cana-2576	117	28	𝑢1	𝑢1	PROPN
cana-2576	117	29	of	of	ADP
cana-2576	117	30	𝑣2	𝑣2	PROPN
cana-2576	117	31	.	.	PUNCT
cana-2576	118	1	such	such	DET
cana-2576	118	2	a	a	DET
cana-2576	118	3	vertex	vertex	NOUN
cana-2576	118	4	is	be	AUX
cana-2576	118	5	always	always	ADV
cana-2576	118	6	existing	exist	VERB
cana-2576	118	7	,	,	PUNCT
cana-2576	118	8	since	since	SCONJ
cana-2576	118	9	g	g	PROPN
cana-2576	118	10	is	be	AUX
cana-2576	118	11	an	an	DET
cana-2576	118	12	alternate	alternate	ADJ
cana-2576	118	13	quadrilateral	quadrilateral	ADJ
cana-2576	118	14	snake	snake	NOUN
cana-2576	118	15	graph	graph	NOUN
cana-2576	118	16	.	.	PUNCT
cana-2576	119	1	let	let	VERB
cana-2576	119	2	the	the	DET
cana-2576	119	3	vertex	vertex	NOUN
cana-2576	119	4	be	be	AUX
cana-2576	119	5	𝑢2	𝑢2	PROPN
cana-2576	119	6	and	and	CCONJ
cana-2576	119	7	d(𝑢2	d(𝑢2	NOUN
cana-2576	119	8	)	)	PUNCT
cana-2576	119	9	=	=	SYM
cana-2576	120	1	3	3	X
cana-2576	120	2	.	.	NOUN
cana-2576	120	3	if	if	SCONJ
cana-2576	120	4	d(v	d(v	PROPN
cana-2576	120	5	)	)	PUNCT
cana-2576	120	6	is	be	AUX
cana-2576	120	7	not	not	PART
cana-2576	120	8	a	a	DET
cana-2576	120	9	multiple	multiple	NOUN
cana-2576	120	10	of	of	ADP
cana-2576	120	11	3	3	NUM
cana-2576	120	12	,	,	PUNCT
cana-2576	120	13	the	the	DET
cana-2576	120	14	set	set	NOUN
cana-2576	120	15	{	{	PUNCT
cana-2576	120	16	v,𝑢2	v,𝑢2	PROPN
cana-2576	120	17	}	}	PUNCT
cana-2576	120	18	satisfies	satisfy	VERB
cana-2576	120	19	all	all	DET
cana-2576	120	20	the	the	DET
cana-2576	120	21	condition	condition	NOUN
cana-2576	120	22	for	for	ADP
cana-2576	120	23	being	be	AUX
cana-2576	120	24	a	a	DET
cana-2576	120	25	relatively	relatively	ADV
cana-2576	120	26	prime	prime	ADJ
cana-2576	120	27	dominating	dominating	NOUN
cana-2576	120	28	set	set	NOUN
cana-2576	120	29	.	.	PUNCT
cana-2576	121	1	hence	hence	ADV
cana-2576	121	2	𝛾𝑟𝑝𝑑=	𝛾𝑟𝑝𝑑=	PUNCT
cana-2576	121	3	2	2	NUM
cana-2576	121	4	in	in	ADP
cana-2576	121	5	this	this	DET
cana-2576	121	6	case	case	NOUN
cana-2576	121	7	.	.	PUNCT
cana-2576	121	8	suppose	suppose	VERB
cana-2576	121	9	that	that	SCONJ
cana-2576	121	10	d(v	d(v	PROPN
cana-2576	121	11	)	)	PUNCT
cana-2576	121	12	is	be	AUX
cana-2576	121	13	a	a	DET
cana-2576	121	14	multiple	multiple	NOUN
cana-2576	121	15	of	of	ADP
cana-2576	121	16	3	3	NUM
cana-2576	121	17	.	.	PUNCT
cana-2576	122	1	since	since	SCONJ
cana-2576	122	2	|𝑉|	|𝑉|	NOUN
cana-2576	122	3	=	=	SYM
cana-2576	122	4	4n	4n	NOUN
cana-2576	122	5	,	,	PUNCT
cana-2576	122	6	p-3	p-3	PROPN
cana-2576	122	7	is	be	AUX
cana-2576	122	8	always	always	ADV
cana-2576	122	9	odd	odd	ADJ
cana-2576	122	10	.	.	PUNCT
cana-2576	123	1	hence	hence	ADV
cana-2576	123	2	{	{	PUNCT
cana-2576	123	3	v	v	NOUN
cana-2576	123	4	,	,	PUNCT
cana-2576	123	5	𝑢1	𝑢1	PROPN
cana-2576	123	6	,	,	PUNCT
cana-2576	123	7	𝑣2	𝑣2	PROPN
cana-2576	123	8	}	}	PUNCT
cana-2576	123	9	is	be	AUX
cana-2576	123	10	a	a	DET
cana-2576	123	11	relatively	relatively	ADV
cana-2576	123	12	prime	prime	ADJ
cana-2576	123	13	dominating	dominating	NOUN
cana-2576	123	14	set	set	NOUN
cana-2576	123	15	.	.	PUNCT
cana-2576	124	1	thus	thus	ADV
cana-2576	124	2	𝛾𝑟𝑝𝑑=	𝛾𝑟𝑝𝑑=	CCONJ
cana-2576	124	3	3	3	NUM
cana-2576	124	4	in	in	ADP
cana-2576	124	5	this	this	DET
cana-2576	124	6	case	case	NOUN
cana-2576	124	7	.	.	PUNCT
cana-2576	125	1	case	case	NOUN
cana-2576	125	2	3	3	NUM
cana-2576	125	3	:	:	SYM
cana-2576	125	4	v	v	NOUN
cana-2576	125	5	is	be	AUX
cana-2576	125	6	any	any	DET
cana-2576	125	7	internal	internal	ADJ
cana-2576	125	8	path	path	NOUN
cana-2576	125	9	vertex	vertex	NOUN
cana-2576	125	10	.	.	PUNCT
cana-2576	126	1	let	let	VERB
cana-2576	126	2	it	it	PRON
cana-2576	126	3	be	be	AUX
cana-2576	126	4	𝑣𝑖.	𝑣𝑖.	NOUN
cana-2576	126	5	then	then	ADV
cana-2576	126	6	d(𝑣𝑖	d(𝑣𝑖	ADJ
cana-2576	126	7	)	)	PUNCT
cana-2576	127	1	=	=	NOUN
cana-2576	127	2	p-4	p-4	NOUN
cana-2576	127	3	.	.	PUNCT
cana-2576	128	1	this	this	DET
cana-2576	128	2	vertex	vertex	NOUN
cana-2576	128	3	covers	cover	VERB
cana-2576	128	4	all	all	DET
cana-2576	128	5	the	the	DET
cana-2576	128	6	vertices	vertex	NOUN
cana-2576	128	7	of	of	ADP
cana-2576	128	8	𝐺𝑣	𝐺𝑣	PROPN
cana-2576	128	9	,	,	PUNCT
cana-2576	128	10	except	except	SCONJ
cana-2576	128	11	the	the	DET
cana-2576	128	12	3	3	NUM
cana-2576	128	13	vertices	vertex	NOUN
cana-2576	128	14	,	,	PUNCT
cana-2576	128	15	namely	namely	ADV
cana-2576	128	16	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	128	17	,	,	PUNCT
cana-2576	128	18	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	128	19	,	,	PUNCT
cana-2576	128	20	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	128	21	and	and	CCONJ
cana-2576	128	22	d(𝑢𝑖	d(𝑢𝑖	PROPN
cana-2576	128	23	)	)	PUNCT
cana-2576	128	24	=	=	SYM
cana-2576	128	25	1	1	NUM
cana-2576	128	26	;	;	PUNCT
cana-2576	128	27	d(𝑣𝑖−1	d(𝑣𝑖−1	NUM
cana-2576	128	28	)	)	PUNCT
cana-2576	128	29	=	=	SYM
cana-2576	128	30	1	1	NUM
cana-2576	128	31	if	if	SCONJ
cana-2576	128	32	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	128	33	is	be	AUX
cana-2576	128	34	an	an	DET
cana-2576	128	35	initial	initial	ADJ
cana-2576	128	36	vertex	vertex	NOUN
cana-2576	128	37	,	,	PUNCT
cana-2576	128	38	otherwise	otherwise	ADV
cana-2576	128	39	2	2	NUM
cana-2576	128	40	.	.	NOUN
cana-2576	128	41	similarly	similarly	ADV
cana-2576	128	42	d(𝑣𝑖+1	d(𝑣𝑖+1	NOUN
cana-2576	128	43	)	)	PUNCT
cana-2576	128	44	=	=	SYM
cana-2576	128	45	1	1	NUM
cana-2576	128	46	if	if	SCONJ
cana-2576	128	47	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	128	48	is	be	AUX
cana-2576	128	49	an	an	DET
cana-2576	128	50	initial	initial	ADJ
cana-2576	128	51	vertex	vertex	NOUN
cana-2576	128	52	,	,	PUNCT
cana-2576	128	53	otherwise	otherwise	ADV
cana-2576	128	54	2	2	X
cana-2576	128	55	.	.	PUNCT
cana-2576	129	1	since	since	SCONJ
cana-2576	129	2	g	g	PROPN
cana-2576	129	3	is	be	AUX
cana-2576	129	4	an	an	DET
cana-2576	129	5	alternate	alternate	ADJ
cana-2576	129	6	quadrilateral	quadrilateral	ADJ
cana-2576	129	7	snake	snake	NOUN
cana-2576	129	8	graph	graph	NOUN
cana-2576	129	9	,	,	PUNCT
cana-2576	129	10	let	let	VERB
cana-2576	129	11	the	the	DET
cana-2576	129	12	vertex	vertex	NOUN
cana-2576	129	13	adjacent	adjacent	ADJ
cana-2576	129	14	to	to	ADP
cana-2576	129	15	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	129	16	and	and	CCONJ
cana-2576	129	17	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	129	18	be	be	AUX
cana-2576	129	19	𝑢𝑖−1	𝑢𝑖−1	ADJ
cana-2576	129	20	and	and	CCONJ
cana-2576	129	21	the	the	DET
cana-2576	129	22	vertex	vertex	NOUN
cana-2576	129	23	adjacent	adjacent	ADJ
cana-2576	129	24	to	to	ADP
cana-2576	129	25	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	129	26	be	be	AUX
cana-2576	129	27	𝑢𝑖+1	𝑢𝑖+1	NUM
cana-2576	129	28	and	and	CCONJ
cana-2576	129	29	𝑣𝑖+2	𝑣𝑖+2	NUM
cana-2576	129	30	and	and	CCONJ
cana-2576	129	31	d(𝑢𝑖−1	d(𝑢𝑖−1	NUM
cana-2576	129	32	)	)	PUNCT
cana-2576	129	33	=	=	PUNCT
cana-2576	130	1	d(𝑢𝑖+1	d(𝑢𝑖+1	X
cana-2576	130	2	)	)	PUNCT
cana-2576	130	3	=	=	SYM
cana-2576	130	4	3	3	NUM
cana-2576	130	5	;	;	PUNCT
cana-2576	130	6	d(𝑣𝑖+2	d(𝑣𝑖+2	NOUN
cana-2576	130	7	)	)	PUNCT
cana-2576	130	8	=	=	SYM
cana-2576	130	9	4	4	X
cana-2576	130	10	.	.	NOUN
cana-2576	130	11	since	since	SCONJ
cana-2576	130	12	d(v	d(v	PROPN
cana-2576	130	13	)	)	PUNCT
cana-2576	130	14	is	be	AUX
cana-2576	130	15	a	a	DET
cana-2576	130	16	multiple	multiple	NOUN
cana-2576	130	17	of	of	ADP
cana-2576	130	18	4	4	NUM
cana-2576	130	19	,	,	PUNCT
cana-2576	130	20	we	we	PRON
cana-2576	130	21	can	can	AUX
cana-2576	130	22	not	not	PART
cana-2576	130	23	take	take	VERB
cana-2576	130	24	the	the	DET
cana-2576	130	25	vertex	vertex	NOUN
cana-2576	130	26	𝑣𝑖+2	𝑣𝑖+2	PRON
cana-2576	130	27	.	.	PUNCT
cana-2576	131	1	we	we	PRON
cana-2576	131	2	have	have	VERB
cana-2576	131	3	the	the	DET
cana-2576	131	4	following	follow	VERB
cana-2576	131	5	subcases	subcase	NOUN
cana-2576	131	6	.	.	PUNCT
cana-2576	132	1	case	case	NOUN
cana-2576	132	2	3.1	3.1	NUM
cana-2576	132	3	:	:	PUNCT
cana-2576	132	4	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	132	5	is	be	AUX
cana-2576	132	6	an	an	DET
cana-2576	132	7	initial	initial	ADJ
cana-2576	132	8	vertex	vertex	NOUN
cana-2576	132	9	and	and	CCONJ
cana-2576	132	10	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	132	11	is	be	AUX
cana-2576	132	12	not	not	PART
cana-2576	132	13	an	an	DET
cana-2576	132	14	end	end	NOUN
cana-2576	132	15	vertex	vertex	NOUN
cana-2576	132	16	.	.	PUNCT
cana-2576	133	1	if	if	SCONJ
cana-2576	133	2	d(v	d(v	PROPN
cana-2576	133	3	)	)	PUNCT
cana-2576	133	4	is	be	AUX
cana-2576	133	5	not	not	PART
cana-2576	133	6	a	a	DET
cana-2576	133	7	multiple	multiple	NOUN
cana-2576	133	8	of	of	ADP
cana-2576	133	9	3	3	NUM
cana-2576	133	10	,	,	PUNCT
cana-2576	133	11	then	then	ADV
cana-2576	133	12	the	the	DET
cana-2576	133	13	set	set	NOUN
cana-2576	133	14	{	{	PUNCT
cana-2576	133	15	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	133	16	,	,	PUNCT
cana-2576	133	17	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	133	18	,	,	PUNCT
cana-2576	133	19	𝑣𝑖−1¸𝑢𝑖+1	𝑣𝑖−1¸𝑢𝑖+1	NOUN
cana-2576	133	20	}	}	PUNCT
cana-2576	133	21	is	be	AUX
cana-2576	133	22	a	a	DET
cana-2576	133	23	relatively	relatively	ADV
cana-2576	133	24	prime	prime	ADJ
cana-2576	133	25	dominating	dominating	NOUN
cana-2576	133	26	set	set	NOUN
cana-2576	133	27	and	and	CCONJ
cana-2576	133	28	hence	hence	ADV
cana-2576	133	29	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	133	30	)	)	PUNCT
cana-2576	134	1	=	=	PUNCT
cana-2576	135	1	4	4	X
cana-2576	135	2	.	.	NOUN
cana-2576	135	3	if	if	SCONJ
cana-2576	135	4	d(v	d(v	PROPN
cana-2576	135	5	)	)	PUNCT
cana-2576	135	6	is	be	AUX
cana-2576	135	7	a	a	DET
cana-2576	135	8	multiple	multiple	NOUN
cana-2576	135	9	of	of	ADP
cana-2576	135	10	3	3	NUM
cana-2576	135	11	,	,	PUNCT
cana-2576	135	12	then	then	ADV
cana-2576	135	13	relatively	relatively	ADV
cana-2576	135	14	prime	prime	ADJ
cana-2576	135	15	dominating	dominating	NOUN
cana-2576	135	16	set	set	NOUN
cana-2576	135	17	does	do	AUX
cana-2576	135	18	not	not	PART
cana-2576	135	19	exist	exist	VERB
cana-2576	135	20	.	.	PUNCT
cana-2576	136	1	case	case	NOUN
cana-2576	136	2	3.2	3.2	NUM
cana-2576	136	3	:	:	SYM
cana-2576	136	4	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	136	5	is	be	AUX
cana-2576	136	6	an	an	DET
cana-2576	136	7	end	end	NOUN
cana-2576	136	8	vertex	vertex	NOUN
cana-2576	136	9	and	and	CCONJ
cana-2576	136	10	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	136	11	is	be	AUX
cana-2576	136	12	not	not	PART
cana-2576	136	13	an	an	DET
cana-2576	136	14	initial	initial	ADJ
cana-2576	136	15	vertex	vertex	NOUN
cana-2576	136	16	.	.	PUNCT
cana-2576	137	1	same	same	ADJ
cana-2576	137	2	as	as	ADP
cana-2576	137	3	case	case	NOUN
cana-2576	137	4	3.1	3.1	NUM
cana-2576	137	5	.	.	PUNCT
cana-2576	137	6	case	case	NOUN
cana-2576	137	7	3.3	3.3	NUM
cana-2576	137	8	:	:	PUNCT
cana-2576	137	9	neither	neither	CCONJ
cana-2576	137	10	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	137	11	is	be	AUX
cana-2576	137	12	an	an	DET
cana-2576	137	13	initial	initial	ADJ
cana-2576	137	14	vertex	vertex	NOUN
cana-2576	137	15	nor	nor	CCONJ
cana-2576	137	16	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	137	17	is	be	AUX
cana-2576	137	18	an	an	DET
cana-2576	137	19	end	end	NOUN
cana-2576	137	20	vertex	vertex	NOUN
cana-2576	137	21	.	.	PUNCT
cana-2576	138	1	then	then	ADV
cana-2576	138	2	d(𝑣𝑖−1	d(𝑣𝑖−1	NUM
cana-2576	138	3	)	)	PUNCT
cana-2576	138	4	=	=	SYM
cana-2576	138	5	d(𝑣𝑖+1	d(𝑣𝑖+1	PROPN
cana-2576	138	6	)	)	PUNCT
cana-2576	138	7	=	=	SYM
cana-2576	139	1	2	2	X
cana-2576	139	2	.	.	PUNCT
cana-2576	139	3	therefore	therefore	ADV
cana-2576	139	4	,	,	PUNCT
cana-2576	139	5	we	we	PRON
cana-2576	139	6	can	can	AUX
cana-2576	139	7	not	not	PART
cana-2576	139	8	choose	choose	VERB
cana-2576	139	9	these	these	DET
cana-2576	139	10	two	two	NUM
cana-2576	139	11	vertices	vertex	NOUN
cana-2576	139	12	.	.	PUNCT
cana-2576	140	1	also	also	ADV
cana-2576	140	2	note	note	VERB
cana-2576	140	3	that	that	SCONJ
cana-2576	140	4	the	the	DET
cana-2576	140	5	vertices	vertex	NOUN
cana-2576	140	6	which	which	PRON
cana-2576	140	7	are	be	AUX
cana-2576	140	8	adjacent	adjacent	ADJ
cana-2576	140	9	to	to	ADP
cana-2576	140	10	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	140	11	and	and	CCONJ
cana-2576	140	12	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	140	13	of	of	ADP
cana-2576	140	14	degree	degree	NOUN
cana-2576	140	15	3	3	NUM
cana-2576	140	16	and	and	CCONJ
cana-2576	140	17	4	4	NUM
cana-2576	140	18	.	.	PUNCT
cana-2576	141	1	therefore	therefore	ADV
cana-2576	141	2	,	,	PUNCT
cana-2576	141	3	relatively	relatively	ADV
cana-2576	141	4	prime	prime	ADJ
cana-2576	141	5	dominating	dominating	NOUN
cana-2576	141	6	set	set	NOUN
cana-2576	141	7	does	do	AUX
cana-2576	141	8	not	not	PART
cana-2576	141	9	exist	exist	VERB
cana-2576	141	10	.	.	PUNCT
cana-2576	142	1	theorem	theorem	VERB
cana-2576	142	2	3.3	3.3	NUM
cana-2576	142	3	.	.	PUNCT
cana-2576	143	1	let	let	VERB
cana-2576	143	2	g	g	PRON
cana-2576	143	3	be	be	AUX
cana-2576	143	4	a	a	DET
cana-2576	143	5	double	double	ADJ
cana-2576	143	6	quadrilateral	quadrilateral	ADJ
cana-2576	143	7	snake	snake	NOUN
cana-2576	143	8	graph	graph	NOUN
cana-2576	143	9	with	with	ADP
cana-2576	143	10	p	p	ADJ
cana-2576	143	11	vertices	vertex	NOUN
cana-2576	143	12	,	,	PUNCT
cana-2576	144	1	where	where	SCONJ
cana-2576	144	2	p	p	PROPN
cana-2576	144	3	=	=	SYM
cana-2576	144	4	5n+1	5n+1	PROPN
cana-2576	144	5	,	,	PUNCT
cana-2576	144	6	n	n	PRON
cana-2576	144	7	≥	≥	NOUN
cana-2576	144	8	2	2	NUM
cana-2576	144	9	.	.	PUNCT
cana-2576	144	10	then	then	ADV
cana-2576	144	11	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	144	12	)	)	PUNCT
cana-2576	144	13	=	=	SYM
cana-2576	144	14	2	2	NUM
cana-2576	144	15	,	,	PUNCT
cana-2576	144	16	3	3	NUM
cana-2576	144	17	,	,	PUNCT
cana-2576	144	18	4	4	NUM
cana-2576	144	19	,	,	PUNCT
cana-2576	144	20	6	6	NUM
cana-2576	144	21	or	or	CCONJ
cana-2576	144	22	7	7	NUM
cana-2576	144	23	.	.	X
cana-2576	144	24	proof	proof	NOUN
cana-2576	144	25	:	:	PUNCT
cana-2576	144	26	let	let	VERB
cana-2576	144	27	g	g	PRON
cana-2576	144	28	be	be	AUX
cana-2576	144	29	a	a	DET
cana-2576	144	30	double	double	ADJ
cana-2576	144	31	quadrilateral	quadrilateral	ADJ
cana-2576	144	32	snake	snake	NOUN
cana-2576	144	33	graph	graph	NOUN
cana-2576	144	34	with	with	ADP
cana-2576	144	35	p	p	NOUN
cana-2576	144	36	vertices	vertex	NOUN
cana-2576	144	37	.	.	PUNCT
cana-2576	145	1	let	let	VERB
cana-2576	145	2	the	the	DET
cana-2576	145	3	vertices	vertex	NOUN
cana-2576	145	4	in	in	ADP
cana-2576	145	5	the	the	DET
cana-2576	145	6	path	path	NOUN
cana-2576	145	7	be	be	AUX
cana-2576	145	8	𝑣1	𝑣1	PROPN
cana-2576	145	9	,	,	PUNCT
cana-2576	145	10	𝑣2	𝑣2	PROPN
cana-2576	145	11	,	,	PUNCT
cana-2576	145	12	…	…	PUNCT
cana-2576	145	13	,	,	PUNCT
cana-2576	145	14	𝑣𝑚	𝑣𝑚	ADJ
cana-2576	145	15	and	and	CCONJ
cana-2576	145	16	the	the	DET
cana-2576	145	17	vertices	vertex	NOUN
cana-2576	145	18	in	in	ADP
cana-2576	145	19	the	the	DET
cana-2576	145	20	upper	upper	ADJ
cana-2576	145	21	quadrilateral	quadrilateral	NOUN
cana-2576	145	22	be	be	AUX
cana-2576	145	23	𝑢1	𝑢1	PROPN
cana-2576	145	24	,	,	PUNCT
cana-2576	145	25	𝑢2	𝑢2	PROPN
cana-2576	145	26	,	,	PUNCT
cana-2576	145	27	𝑤2	𝑤2	NOUN
cana-2576	145	28	,	,	PUNCT
cana-2576	145	29	𝑢3	𝑢3	PROPN
cana-2576	145	30	,	,	PUNCT
cana-2576	145	31	𝑤3	𝑤3	PROPN
cana-2576	145	32	,	,	PUNCT
cana-2576	145	33	…	…	PUNCT
cana-2576	145	34	,	,	PUNCT
cana-2576	145	35	𝑢𝑚−1	𝑢𝑚−1	PROPN
cana-2576	145	36	,	,	PUNCT
cana-2576	145	37	𝑤𝑚−1	𝑤𝑚−1	PROPN
cana-2576	145	38	,	,	PUNCT
cana-2576	145	39	𝑢𝑚	𝑢𝑚	NOUN
cana-2576	145	40	and	and	CCONJ
cana-2576	145	41	the	the	DET
cana-2576	145	42	vertices	vertex	NOUN
cana-2576	145	43	in	in	ADP
cana-2576	145	44	the	the	DET
cana-2576	145	45	lower	low	ADJ
cana-2576	145	46	quadrilateral	quadrilateral	ADJ
cana-2576	145	47	be	be	PROPN
cana-2576	145	48	𝑥1	𝑥1	NOUN
cana-2576	145	49	,	,	PUNCT
cana-2576	145	50	𝑥2	𝑥2	NOUN
cana-2576	145	51	,	,	PUNCT
cana-2576	145	52	𝑦2	𝑦2	NOUN
cana-2576	145	53	,	,	PUNCT
cana-2576	145	54	𝑥3	𝑥3	NOUN
cana-2576	145	55	,	,	PUNCT
cana-2576	145	56	𝑦3	𝑦3	PROPN
cana-2576	145	57	,	,	PUNCT
cana-2576	145	58	…	…	PUNCT
cana-2576	145	59	,	,	PUNCT
cana-2576	145	60	𝑥𝑚−1	𝑥𝑚−1	NOUN
cana-2576	145	61	,	,	PUNCT
cana-2576	145	62	𝑦𝑚−1	𝑦𝑚−1	NOUN
cana-2576	145	63	,	,	PUNCT
cana-2576	145	64	𝑥𝑚.	𝑥𝑚.	NOUN
cana-2576	145	65	then	then	ADV
cana-2576	145	66	degree	degree	NOUN
cana-2576	145	67	of	of	ADP
cana-2576	145	68	each	each	DET
cana-2576	145	69	internal	internal	ADJ
cana-2576	145	70	vertex	vertex	NOUN
cana-2576	145	71	is	be	AUX
cana-2576	145	72	6	6	NUM
cana-2576	145	73	;	;	PUNCT
cana-2576	145	74	degree	degree	NOUN
cana-2576	145	75	of	of	ADP
cana-2576	145	76	initial	initial	ADJ
cana-2576	145	77	and	and	CCONJ
cana-2576	145	78	end	end	VERB
cana-2576	145	79	vertex	vertex	NOUN
cana-2576	145	80	is	be	AUX
cana-2576	145	81	3	3	NUM
cana-2576	145	82	;	;	PUNCT
cana-2576	145	83	degree	degree	NOUN
cana-2576	145	84	of	of	ADP
cana-2576	145	85	vertices	vertex	NOUN
cana-2576	145	86	in	in	ADP
cana-2576	145	87	the	the	DET
cana-2576	145	88	upper	upper	ADJ
cana-2576	145	89	and	and	CCONJ
cana-2576	145	90	lower	low	ADJ
cana-2576	145	91	quadrilateral	quadrilateral	NOUN
cana-2576	145	92	is	be	AUX
cana-2576	145	93	2	2	NUM
cana-2576	145	94	.	.	PUNCT
cana-2576	146	1	let	let	VERB
cana-2576	146	2	v	v	PART
cana-2576	146	3	be	be	AUX
cana-2576	146	4	any	any	DET
cana-2576	146	5	vertex	vertex	NOUN
cana-2576	146	6	in	in	ADP
cana-2576	146	7	g.	g.	PROPN
cana-2576	146	8	we	we	PRON
cana-2576	146	9	consider	consider	VERB
cana-2576	146	10	the	the	DET
cana-2576	146	11	following	follow	VERB
cana-2576	146	12	cases	case	NOUN
cana-2576	146	13	:	:	PUNCT
cana-2576	146	14	case	case	NOUN
cana-2576	146	15	1	1	NUM
cana-2576	146	16	:	:	SYM
cana-2576	146	17	v	v	NOUN
cana-2576	146	18	is	be	AUX
cana-2576	146	19	any	any	DET
cana-2576	146	20	vertex	vertex	NOUN
cana-2576	146	21	from	from	ADP
cana-2576	146	22	{	{	PUNCT
cana-2576	146	23	𝑢1	𝑢1	PROPN
cana-2576	146	24	,	,	PUNCT
cana-2576	146	25	𝑢2	𝑢2	PROPN
cana-2576	146	26	,	,	PUNCT
cana-2576	146	27	𝑤2	𝑤2	NOUN
cana-2576	146	28	,	,	PUNCT
cana-2576	146	29	𝑢3	𝑢3	PROPN
cana-2576	146	30	,	,	PUNCT
cana-2576	146	31	𝑤3	𝑤3	PROPN
cana-2576	146	32	,	,	PUNCT
cana-2576	146	33	…	…	PUNCT
cana-2576	146	34	,	,	PUNCT
cana-2576	146	35	𝑢𝑚−1	𝑢𝑚−1	PROPN
cana-2576	146	36	,	,	PUNCT
cana-2576	146	37	𝑤𝑚−1	𝑤𝑚−1	PROPN
cana-2576	146	38	,	,	PUNCT
cana-2576	146	39	𝑢𝑚	𝑢𝑚	NOUN
cana-2576	146	40	,	,	PUNCT
cana-2576	146	41	𝑥1	𝑥1	NOUN
cana-2576	146	42	,	,	PUNCT
cana-2576	146	43	𝑥2	𝑥2	NOUN
cana-2576	146	44	,	,	PUNCT
cana-2576	146	45	𝑦2	𝑦2	NOUN
cana-2576	146	46	,	,	PUNCT
cana-2576	146	47	𝑥3	𝑥3	NOUN
cana-2576	146	48	,	,	PUNCT
cana-2576	146	49	𝑦3	𝑦3	PROPN
cana-2576	146	50	,	,	PUNCT
cana-2576	146	51	…	…	PUNCT
cana-2576	146	52	,	,	PUNCT
cana-2576	146	53	𝑥𝑚−1	𝑥𝑚−1	NOUN
cana-2576	146	54	,	,	PUNCT
cana-2576	146	55	𝑦𝑚−1	𝑦𝑚−1	NOUN
cana-2576	146	56	,	,	PUNCT
cana-2576	146	57	𝑥𝑚	𝑥𝑚	NOUN
cana-2576	146	58	}	}	PUNCT
cana-2576	146	59	.	.	PUNCT
cana-2576	147	1	without	without	ADP
cana-2576	147	2	loss	loss	NOUN
cana-2576	147	3	of	of	ADP
cana-2576	147	4	generality	generality	NOUN
cana-2576	147	5	,	,	PUNCT
cana-2576	147	6	let	let	VERB
cana-2576	147	7	v	v	VERB
cana-2576	147	8	=	=	NOUN
cana-2576	147	9	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	147	10	,	,	PUNCT
cana-2576	147	11	𝑖	𝑖	X
cana-2576	147	12	=	=	SYM
cana-2576	147	13	1,2	1,2	NUM
cana-2576	147	14	,	,	PUNCT
cana-2576	147	15	…	…	PUNCT
cana-2576	147	16	,	,	PUNCT
cana-2576	147	17	𝑚.	𝑚.	ADV
cana-2576	147	18	then	then	ADV
cana-2576	147	19	d(v	d(v	PROPN
cana-2576	147	20	)	)	PUNCT
cana-2576	148	1	=	=	PUNCT
cana-2576	148	2	p-3	p-3	NOUN
cana-2576	148	3	in	in	ADP
cana-2576	148	4	𝐺𝑣.	𝐺𝑣.	ADP
cana-2576	148	5	this	this	DET
cana-2576	148	6	vertex	vertex	NOUN
cana-2576	148	7	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	148	8	covers	cover	VERB
cana-2576	148	9	all	all	DET
cana-2576	148	10	the	the	DET
cana-2576	148	11	vertices	vertex	NOUN
cana-2576	148	12	in	in	ADP
cana-2576	148	13	𝐺𝑣	𝐺𝑣	PROPN
cana-2576	148	14	other	other	ADJ
cana-2576	148	15	than	than	ADP
cana-2576	148	16	the	the	DET
cana-2576	148	17	two	two	NUM
cana-2576	148	18	vertices	vertex	NOUN
cana-2576	148	19	which	which	PRON
cana-2576	148	20	are	be	AUX
cana-2576	148	21	adjacent	adjacent	ADJ
cana-2576	148	22	to	to	ADP
cana-2576	148	23	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	148	24	in	in	ADP
cana-2576	148	25	g	g	NOUN
cana-2576	148	26	,	,	PUNCT
cana-2576	148	27	namely	namely	ADV
cana-2576	148	28	𝑣𝑖	𝑣𝑖	ADP
cana-2576	148	29	,	,	PUNCT
cana-2576	148	30	𝑤𝑖−1	𝑤𝑖−1	PROPN
cana-2576	148	31	.	.	PUNCT
cana-2576	149	1	since	since	SCONJ
cana-2576	149	2	g	g	PROPN
cana-2576	149	3	is	be	AUX
cana-2576	149	4	a	a	DET
cana-2576	149	5	quadrilateral	quadrilateral	ADJ
cana-2576	149	6	snake	snake	NOUN
cana-2576	149	7	graph	graph	NOUN
cana-2576	149	8	,	,	PUNCT
cana-2576	149	9	the	the	DET
cana-2576	149	10	vertices	vertex	NOUN
cana-2576	149	11	𝑣𝑖	𝑣𝑖	ADV
cana-2576	149	12	and	and	CCONJ
cana-2576	149	13	𝑤𝑖−1	𝑤𝑖−1	NOUN
cana-2576	149	14	are	be	AUX
cana-2576	149	15	adjacent	adjacent	ADJ
cana-2576	149	16	with	with	ADP
cana-2576	149	17	a	a	DET
cana-2576	149	18	vertex	vertex	NOUN
cana-2576	149	19	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	149	20	.	.	PUNCT
cana-2576	150	1	to	to	PART
cana-2576	150	2	cover	cover	VERB
cana-2576	150	3	the	the	DET
cana-2576	150	4	communications	communication	NOUN
cana-2576	150	5	on	on	ADP
cana-2576	150	6	applied	apply	VERB
cana-2576	150	7	nonlinear	nonlinear	ADJ
cana-2576	150	8	analysis	analysis	NOUN
cana-2576	150	9	issn	issn	NOUN
cana-2576	150	10	:	:	PUNCT
cana-2576	150	11	1074	1074	NUM
cana-2576	150	12	-	-	PUNCT
cana-2576	150	13	133x	133x	NUM
cana-2576	150	14	vol	vol	NOUN
cana-2576	150	15	32	32	NUM
cana-2576	150	16	no	no	NOUN
cana-2576	150	17	.	.	PUNCT
cana-2576	151	1	3s	3s	NUM
cana-2576	151	2	(	(	PUNCT
cana-2576	151	3	2025	2025	NUM
cana-2576	151	4	)	)	PUNCT
cana-2576	151	5	158	158	NUM
cana-2576	152	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2576	152	2	vertices	vertice	VERB
cana-2576	152	3	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	152	4	and	and	CCONJ
cana-2576	152	5	𝑤𝑖−1	𝑤𝑖−1	NOUN
cana-2576	152	6	,	,	PUNCT
cana-2576	152	7	either	either	CCONJ
cana-2576	152	8	we	we	PRON
cana-2576	152	9	have	have	VERB
cana-2576	152	10	to	to	PART
cana-2576	152	11	take	take	VERB
cana-2576	152	12	these	these	DET
cana-2576	152	13	two	two	NUM
cana-2576	152	14	vertices	vertex	NOUN
cana-2576	152	15	or	or	CCONJ
cana-2576	152	16	which	which	PRON
cana-2576	152	17	is	be	AUX
cana-2576	152	18	adjacent	adjacent	ADJ
cana-2576	152	19	to	to	ADP
cana-2576	152	20	both	both	PRON
cana-2576	152	21	𝑣𝑖	𝑣𝑖	ADP
cana-2576	152	22	and	and	CCONJ
cana-2576	152	23	𝑤𝑖−1	𝑤𝑖−1	NOUN
cana-2576	152	24	,	,	PUNCT
cana-2576	152	25	that	that	ADV
cana-2576	152	26	is	is	ADV
cana-2576	152	27	,	,	PUNCT
cana-2576	152	28	the	the	DET
cana-2576	152	29	vertex	vertex	NOUN
cana-2576	152	30	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	152	31	.	.	PUNCT
cana-2576	153	1	note	note	VERB
cana-2576	153	2	that	that	SCONJ
cana-2576	153	3	if	if	SCONJ
cana-2576	153	4	n	n	PRON
cana-2576	153	5	is	be	AUX
cana-2576	153	6	even	even	ADV
cana-2576	153	7	and	and	CCONJ
cana-2576	153	8	odd	odd	ADJ
cana-2576	153	9	,	,	PUNCT
cana-2576	153	10	then	then	ADV
cana-2576	153	11	d(v	d(v	PROPN
cana-2576	153	12	)	)	PUNCT
cana-2576	153	13	is	be	AUX
cana-2576	153	14	odd	odd	ADJ
cana-2576	153	15	and	and	CCONJ
cana-2576	153	16	even	even	ADV
cana-2576	153	17	respectively	respectively	ADV
cana-2576	153	18	.	.	PUNCT
cana-2576	154	1	here	here	ADV
cana-2576	154	2	,	,	PUNCT
cana-2576	154	3	d(𝑤𝑖−1	d(𝑤𝑖−1	NOUN
cana-2576	154	4	)	)	PUNCT
cana-2576	154	5	=	=	SYM
cana-2576	154	6	1	1	NUM
cana-2576	154	7	;	;	PUNCT
cana-2576	154	8	d(𝑣𝑖	d(𝑣𝑖	NUM
cana-2576	154	9	)	)	PUNCT
cana-2576	154	10	=	=	SYM
cana-2576	154	11	2	2	NUM
cana-2576	154	12	if	if	SCONJ
cana-2576	154	13	𝑣𝑖	𝑣𝑖	ADV
cana-2576	154	14	is	be	AUX
cana-2576	154	15	a	a	DET
cana-2576	154	16	initial	initial	ADJ
cana-2576	154	17	vertex	vertex	NOUN
cana-2576	154	18	or	or	CCONJ
cana-2576	154	19	end	end	VERB
cana-2576	154	20	vertex	vertex	NOUN
cana-2576	154	21	,	,	PUNCT
cana-2576	154	22	otherwise	otherwise	ADV
cana-2576	154	23	5	5	NUM
cana-2576	154	24	.	.	PUNCT
cana-2576	154	25	and	and	CCONJ
cana-2576	154	26	d(𝑣𝑖−1	d(𝑣𝑖−1	PUNCT
cana-2576	154	27	)	)	PUNCT
cana-2576	154	28	=	=	SYM
cana-2576	154	29	7	7	NUM
cana-2576	154	30	if	if	SCONJ
cana-2576	154	31	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	154	32	is	be	AUX
cana-2576	154	33	an	an	DET
cana-2576	154	34	internal	internal	ADJ
cana-2576	154	35	path	path	NOUN
cana-2576	154	36	vertex	vertex	NOUN
cana-2576	154	37	,	,	PUNCT
cana-2576	154	38	otherwise	otherwise	ADV
cana-2576	154	39	4	4	X
cana-2576	154	40	.	.	X
cana-2576	155	1	we	we	PRON
cana-2576	155	2	have	have	VERB
cana-2576	155	3	the	the	DET
cana-2576	155	4	following	follow	VERB
cana-2576	155	5	subcases	subcase	NOUN
cana-2576	155	6	.	.	PUNCT
cana-2576	156	1	case	case	NOUN
cana-2576	156	2	1.1	1.1	NUM
cana-2576	156	3	:	:	PUNCT
cana-2576	156	4	𝑣𝑖	𝑣𝑖	ADV
cana-2576	156	5	is	be	AUX
cana-2576	156	6	an	an	DET
cana-2576	156	7	initial	initial	ADJ
cana-2576	156	8	or	or	CCONJ
cana-2576	156	9	an	an	DET
cana-2576	156	10	end	end	NOUN
cana-2576	156	11	vertex	vertex	NOUN
cana-2576	156	12	.	.	PUNCT
cana-2576	157	1	then	then	ADV
cana-2576	157	2	d(𝑣𝑖	d(𝑣𝑖	NUM
cana-2576	157	3	)	)	PUNCT
cana-2576	157	4	=	=	SYM
cana-2576	158	1	2	2	X
cana-2576	158	2	.	.	X
cana-2576	158	3	if	if	SCONJ
cana-2576	158	4	d(v	d(v	PROPN
cana-2576	158	5	)	)	PUNCT
cana-2576	158	6	is	be	AUX
cana-2576	158	7	odd	odd	ADJ
cana-2576	158	8	and	and	CCONJ
cana-2576	158	9	not	not	PART
cana-2576	158	10	a	a	DET
cana-2576	158	11	multiple	multiple	NOUN
cana-2576	158	12	of	of	ADP
cana-2576	158	13	7	7	NUM
cana-2576	158	14	,	,	PUNCT
cana-2576	158	15	then	then	ADV
cana-2576	158	16	{	{	PUNCT
cana-2576	158	17	𝑣	𝑣	NOUN
cana-2576	158	18	,	,	PUNCT
cana-2576	158	19	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	158	20	}	}	PUNCT
cana-2576	158	21	is	be	AUX
cana-2576	158	22	a	a	DET
cana-2576	158	23	relatively	relatively	ADV
cana-2576	158	24	prime	prime	ADJ
cana-2576	158	25	dominating	dominating	NOUN
cana-2576	158	26	set	set	NOUN
cana-2576	158	27	and	and	CCONJ
cana-2576	158	28	hence	hence	ADV
cana-2576	158	29	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	158	30	)	)	PUNCT
cana-2576	159	1	=	=	SYM
cana-2576	159	2	2	2	NUM
cana-2576	159	3	in	in	ADP
cana-2576	159	4	this	this	DET
cana-2576	159	5	case	case	NOUN
cana-2576	159	6	.	.	PUNCT
cana-2576	160	1	if	if	SCONJ
cana-2576	160	2	d(v	d(v	PROPN
cana-2576	160	3	)	)	PUNCT
cana-2576	160	4	is	be	AUX
cana-2576	160	5	odd	odd	ADJ
cana-2576	160	6	and	and	CCONJ
cana-2576	160	7	a	a	DET
cana-2576	160	8	multiple	multiple	NOUN
cana-2576	160	9	of	of	ADP
cana-2576	160	10	7	7	NUM
cana-2576	160	11	,	,	PUNCT
cana-2576	160	12	then	then	ADV
cana-2576	160	13	the	the	DET
cana-2576	160	14	set	set	NOUN
cana-2576	160	15	{	{	PUNCT
cana-2576	160	16	𝑣	𝑣	NOUN
cana-2576	160	17	,	,	PUNCT
cana-2576	160	18	𝑣𝑖	𝑣𝑖	ADV
cana-2576	160	19	,	,	PUNCT
cana-2576	160	20	𝑤𝑖−1	𝑤𝑖−1	PROPN
cana-2576	160	21	}	}	PUNCT
cana-2576	160	22	is	be	AUX
cana-2576	160	23	a	a	DET
cana-2576	160	24	relatively	relatively	ADV
cana-2576	160	25	prime	prime	ADJ
cana-2576	160	26	dominating	dominating	NOUN
cana-2576	160	27	set	set	NOUN
cana-2576	160	28	and	and	CCONJ
cana-2576	160	29	hence	hence	ADV
cana-2576	160	30	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	160	31	)	)	PUNCT
cana-2576	161	1	=	=	SYM
cana-2576	161	2	3	3	NUM
cana-2576	161	3	in	in	ADP
cana-2576	161	4	this	this	DET
cana-2576	161	5	case	case	NOUN
cana-2576	161	6	.	.	PUNCT
cana-2576	162	1	if	if	SCONJ
cana-2576	162	2	d(v	d(v	PROPN
cana-2576	162	3	)	)	PUNCT
cana-2576	162	4	is	be	AUX
cana-2576	162	5	even	even	ADV
cana-2576	162	6	and	and	CCONJ
cana-2576	162	7	not	not	PART
cana-2576	162	8	multiple	multiple	NOUN
cana-2576	162	9	of	of	ADP
cana-2576	162	10	7	7	NUM
cana-2576	162	11	,	,	PUNCT
cana-2576	162	12	then	then	ADV
cana-2576	162	13	the	the	DET
cana-2576	162	14	set	set	NOUN
cana-2576	162	15	{	{	PUNCT
cana-2576	162	16	𝑣	𝑣	NOUN
cana-2576	162	17	,	,	PUNCT
cana-2576	162	18	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	162	19	}	}	PUNCT
cana-2576	162	20	is	be	AUX
cana-2576	162	21	a	a	DET
cana-2576	162	22	relatively	relatively	ADV
cana-2576	162	23	prime	prime	ADJ
cana-2576	162	24	dominating	dominating	NOUN
cana-2576	162	25	set	set	NOUN
cana-2576	162	26	and	and	CCONJ
cana-2576	162	27	hence	hence	ADV
cana-2576	162	28	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	162	29	)	)	PUNCT
cana-2576	163	1	=	=	PUNCT
cana-2576	163	2	2	2	X
cana-2576	163	3	.	.	X
cana-2576	163	4	if	if	SCONJ
cana-2576	163	5	d(v	d(v	PROPN
cana-2576	163	6	)	)	PUNCT
cana-2576	163	7	is	be	AUX
cana-2576	163	8	even	even	ADV
cana-2576	163	9	and	and	CCONJ
cana-2576	163	10	multiple	multiple	ADJ
cana-2576	163	11	of	of	ADP
cana-2576	163	12	7	7	NUM
cana-2576	163	13	,	,	PUNCT
cana-2576	163	14	then	then	ADV
cana-2576	163	15	relatively	relatively	ADV
cana-2576	163	16	prime	prime	ADJ
cana-2576	163	17	dominating	dominating	NOUN
cana-2576	163	18	set	set	NOUN
cana-2576	163	19	does	do	AUX
cana-2576	163	20	not	not	PART
cana-2576	163	21	exist	exist	VERB
cana-2576	163	22	in	in	ADP
cana-2576	163	23	this	this	DET
cana-2576	163	24	case	case	NOUN
cana-2576	163	25	.	.	PUNCT
cana-2576	164	1	case	case	NOUN
cana-2576	164	2	1.2	1.2	NUM
cana-2576	164	3	:	:	PUNCT
cana-2576	164	4	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	164	5	is	be	AUX
cana-2576	164	6	neither	neither	CCONJ
cana-2576	164	7	an	an	DET
cana-2576	164	8	initial	initial	ADJ
cana-2576	164	9	nor	nor	CCONJ
cana-2576	164	10	an	an	DET
cana-2576	164	11	end	end	NOUN
cana-2576	164	12	vertex	vertex	NOUN
cana-2576	164	13	.	.	PUNCT
cana-2576	165	1	then	then	ADV
cana-2576	165	2	d(𝑣𝑖	d(𝑣𝑖	NUM
cana-2576	165	3	)	)	PUNCT
cana-2576	165	4	=	=	SYM
cana-2576	166	1	5	5	X
cana-2576	166	2	.	.	NOUN
cana-2576	166	3	since	since	SCONJ
cana-2576	166	4	d(v	d(v	PROPN
cana-2576	166	5	)	)	PUNCT
cana-2576	166	6	=	=	PUNCT
cana-2576	166	7	p-3	p-3	NOUN
cana-2576	166	8	and	and	CCONJ
cana-2576	166	9	|v|	|v|	NOUN
cana-2576	166	10	=	=	SYM
cana-2576	166	11	5n+1	5n+1	PROPN
cana-2576	166	12	,	,	PUNCT
cana-2576	166	13	degree	degree	NOUN
cana-2576	166	14	of	of	ADP
cana-2576	166	15	v	v	NOUN
cana-2576	166	16	can	can	AUX
cana-2576	166	17	not	not	PART
cana-2576	166	18	be	be	AUX
cana-2576	166	19	a	a	DET
cana-2576	166	20	multiple	multiple	NOUN
cana-2576	166	21	of	of	ADP
cana-2576	166	22	5	5	NUM
cana-2576	166	23	.	.	PUNCT
cana-2576	167	1	suppose	suppose	VERB
cana-2576	167	2	that	that	SCONJ
cana-2576	167	3	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	167	4	is	be	AUX
cana-2576	167	5	an	an	DET
cana-2576	167	6	initial	initial	ADJ
cana-2576	167	7	or	or	CCONJ
cana-2576	167	8	end	end	ADJ
cana-2576	167	9	vertex	vertex	NOUN
cana-2576	167	10	.	.	PUNCT
cana-2576	168	1	then	then	ADV
cana-2576	168	2	d(𝑣𝑖−1	d(𝑣𝑖−1	PUNCT
cana-2576	168	3	)	)	PUNCT
cana-2576	168	4	=	=	SYM
cana-2576	169	1	4	4	X
cana-2576	169	2	.	.	NOUN
cana-2576	169	3	if	if	SCONJ
cana-2576	169	4	d(v	d(v	PROPN
cana-2576	169	5	)	)	PUNCT
cana-2576	169	6	is	be	AUX
cana-2576	169	7	odd	odd	ADJ
cana-2576	169	8	,	,	PUNCT
cana-2576	169	9	then	then	ADV
cana-2576	169	10	the	the	DET
cana-2576	169	11	set	set	NOUN
cana-2576	169	12	{	{	PUNCT
cana-2576	169	13	𝑣	𝑣	NOUN
cana-2576	169	14	,	,	PUNCT
cana-2576	169	15	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	169	16	}	}	PUNCT
cana-2576	169	17	is	be	AUX
cana-2576	169	18	a	a	DET
cana-2576	169	19	relatively	relatively	ADV
cana-2576	169	20	prime	prime	ADJ
cana-2576	169	21	dominating	dominating	NOUN
cana-2576	169	22	set	set	NOUN
cana-2576	169	23	and	and	CCONJ
cana-2576	169	24	hence	hence	ADV
cana-2576	169	25	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	169	26	)	)	PUNCT
cana-2576	170	1	=	=	PUNCT
cana-2576	170	2	2	2	X
cana-2576	170	3	.	.	X
cana-2576	170	4	if	if	SCONJ
cana-2576	170	5	d(v	d(v	PROPN
cana-2576	170	6	)	)	PUNCT
cana-2576	170	7	is	be	AUX
cana-2576	170	8	even	even	ADV
cana-2576	170	9	and	and	CCONJ
cana-2576	170	10	not	not	PART
cana-2576	170	11	a	a	DET
cana-2576	170	12	multiple	multiple	NOUN
cana-2576	170	13	of	of	ADP
cana-2576	170	14	4	4	NUM
cana-2576	170	15	,	,	PUNCT
cana-2576	170	16	then	then	ADV
cana-2576	170	17	the	the	DET
cana-2576	170	18	set	set	NOUN
cana-2576	170	19	{	{	PUNCT
cana-2576	170	20	𝑣	𝑣	NOUN
cana-2576	170	21	,	,	PUNCT
cana-2576	170	22	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	170	23	}	}	PUNCT
cana-2576	170	24	is	be	AUX
cana-2576	170	25	a	a	DET
cana-2576	170	26	relatively	relatively	ADV
cana-2576	170	27	prime	prime	ADJ
cana-2576	170	28	dominating	dominating	NOUN
cana-2576	170	29	set	set	NOUN
cana-2576	170	30	and	and	CCONJ
cana-2576	170	31	hence	hence	ADV
cana-2576	170	32	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	170	33	)	)	PUNCT
cana-2576	171	1	=	=	PUNCT
cana-2576	171	2	2	2	X
cana-2576	171	3	.	.	X
cana-2576	171	4	if	if	SCONJ
cana-2576	171	5	d(v	d(v	PROPN
cana-2576	171	6	)	)	PUNCT
cana-2576	171	7	is	be	AUX
cana-2576	171	8	even	even	ADV
cana-2576	171	9	and	and	CCONJ
cana-2576	171	10	multiple	multiple	ADJ
cana-2576	171	11	of	of	ADP
cana-2576	171	12	4	4	NUM
cana-2576	171	13	,	,	PUNCT
cana-2576	171	14	then	then	ADV
cana-2576	171	15	the	the	DET
cana-2576	171	16	set	set	NOUN
cana-2576	171	17	{	{	PUNCT
cana-2576	171	18	𝑣	𝑣	NOUN
cana-2576	171	19	,	,	PUNCT
cana-2576	171	20	𝑣𝑖	𝑣𝑖	ADV
cana-2576	171	21	,	,	PUNCT
cana-2576	171	22	𝑤𝑖−1	𝑤𝑖−1	PROPN
cana-2576	171	23	}	}	PUNCT
cana-2576	171	24	is	be	AUX
cana-2576	171	25	a	a	DET
cana-2576	171	26	relatively	relatively	ADV
cana-2576	171	27	prime	prime	ADJ
cana-2576	171	28	dominating	dominating	NOUN
cana-2576	171	29	set	set	NOUN
cana-2576	171	30	and	and	CCONJ
cana-2576	171	31	hence	hence	ADV
cana-2576	171	32	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	171	33	)	)	PUNCT
cana-2576	172	1	=	=	SYM
cana-2576	172	2	3	3	X
cana-2576	172	3	.	.	X
cana-2576	172	4	case	case	NOUN
cana-2576	172	5	2	2	NUM
cana-2576	172	6	:	:	SYM
cana-2576	172	7	v	v	NOUN
cana-2576	172	8	is	be	AUX
cana-2576	172	9	an	an	DET
cana-2576	172	10	initial	initial	ADJ
cana-2576	172	11	vertex	vertex	NOUN
cana-2576	172	12	or	or	CCONJ
cana-2576	172	13	an	an	DET
cana-2576	172	14	end	end	NOUN
cana-2576	172	15	vertex	vertex	NOUN
cana-2576	172	16	.	.	PUNCT
cana-2576	173	1	without	without	ADP
cana-2576	173	2	loss	loss	NOUN
cana-2576	173	3	of	of	ADP
cana-2576	173	4	generality	generality	NOUN
cana-2576	173	5	,	,	PUNCT
cana-2576	173	6	let	let	VERB
cana-2576	173	7	v	v	NOUN
cana-2576	173	8	=	=	SYM
cana-2576	173	9	𝑣1	𝑣1	PROPN
cana-2576	173	10	.	.	PUNCT
cana-2576	174	1	then	then	ADV
cana-2576	174	2	d(v	d(v	PROPN
cana-2576	174	3	)	)	PUNCT
cana-2576	175	1	=	=	NOUN
cana-2576	175	2	p-4	p-4	NOUN
cana-2576	175	3	in	in	ADP
cana-2576	175	4	𝐺𝑣.	𝐺𝑣.	PROPN
cana-2576	175	5	then	then	ADV
cana-2576	175	6	the	the	DET
cana-2576	175	7	vertex	vertex	NOUN
cana-2576	175	8	𝑣1	𝑣1	NOUN
cana-2576	175	9	covers	cover	VERB
cana-2576	175	10	all	all	DET
cana-2576	175	11	the	the	DET
cana-2576	175	12	vertices	vertex	NOUN
cana-2576	175	13	except	except	SCONJ
cana-2576	175	14	the	the	DET
cana-2576	175	15	three	three	NUM
cana-2576	175	16	vertices	vertex	NOUN
cana-2576	175	17	,	,	PUNCT
cana-2576	175	18	namely	namely	ADV
cana-2576	175	19	,	,	PUNCT
cana-2576	175	20	𝑢1	𝑢1	PROPN
cana-2576	175	21	,	,	PUNCT
cana-2576	175	22	𝑥1	𝑥1	NOUN
cana-2576	175	23	and	and	CCONJ
cana-2576	175	24	𝑣2	𝑣2	PROPN
cana-2576	175	25	and	and	CCONJ
cana-2576	175	26	d(𝑢1	d(𝑢1	NOUN
cana-2576	175	27	)	)	PUNCT
cana-2576	175	28	=	=	SYM
cana-2576	175	29	d(𝑥1	d(𝑥1	X
cana-2576	175	30	)	)	PUNCT
cana-2576	175	31	=	=	SYM
cana-2576	175	32	1	1	NUM
cana-2576	175	33	;	;	PUNCT
cana-2576	175	34	d(𝑣2	d(𝑣2	ADV
cana-2576	175	35	)	)	PUNCT
cana-2576	175	36	=	=	SYM
cana-2576	176	1	5	5	X
cana-2576	176	2	.	.	PUNCT
cana-2576	177	1	if	if	SCONJ
cana-2576	177	2	n	n	PRON
cana-2576	177	3	is	be	AUX
cana-2576	177	4	even	even	ADV
cana-2576	177	5	and	and	CCONJ
cana-2576	177	6	odd	odd	ADJ
cana-2576	177	7	,	,	PUNCT
cana-2576	177	8	then	then	ADV
cana-2576	177	9	d(v	d(v	PROPN
cana-2576	177	10	)	)	PUNCT
cana-2576	178	1	=	=	NOUN
cana-2576	178	2	p-4	p-4	NOUN
cana-2576	178	3	is	be	AUX
cana-2576	178	4	even	even	ADV
cana-2576	178	5	and	and	CCONJ
cana-2576	178	6	odd	odd	ADJ
cana-2576	178	7	respectively	respectively	ADV
cana-2576	178	8	.	.	PUNCT
cana-2576	179	1	to	to	PART
cana-2576	179	2	cover	cover	VERB
cana-2576	179	3	the	the	DET
cana-2576	179	4	vertices	vertex	NOUN
cana-2576	179	5	𝑢1	𝑢1	PROPN
cana-2576	179	6	,	,	PUNCT
cana-2576	179	7	𝑥1	𝑥1	NOUN
cana-2576	179	8	and	and	CCONJ
cana-2576	179	9	𝑣2	𝑣2	PROPN
cana-2576	179	10	,	,	PUNCT
cana-2576	179	11	either	either	CCONJ
cana-2576	179	12	we	we	PRON
cana-2576	179	13	have	have	VERB
cana-2576	179	14	to	to	PART
cana-2576	179	15	choose	choose	VERB
cana-2576	179	16	these	these	DET
cana-2576	179	17	vertices	vertex	NOUN
cana-2576	179	18	or	or	CCONJ
cana-2576	179	19	a	a	DET
cana-2576	179	20	vertex	vertex	NOUN
cana-2576	179	21	which	which	PRON
cana-2576	179	22	are	be	AUX
cana-2576	179	23	adjacent	adjacent	ADJ
cana-2576	179	24	to	to	PART
cana-2576	179	25	𝑢1	𝑢1	VERB
cana-2576	179	26	,	,	PUNCT
cana-2576	179	27	𝑥1	𝑥1	NOUN
cana-2576	179	28	and	and	CCONJ
cana-2576	179	29	𝑣2	𝑣2	PROPN
cana-2576	179	30	.	.	PUNCT
cana-2576	180	1	note	note	VERB
cana-2576	180	2	that	that	SCONJ
cana-2576	180	3	there	there	PRON
cana-2576	180	4	is	be	VERB
cana-2576	180	5	no	no	DET
cana-2576	180	6	vertex	vertex	NOUN
cana-2576	180	7	which	which	PRON
cana-2576	180	8	is	be	AUX
cana-2576	180	9	adjacent	adjacent	ADJ
cana-2576	180	10	to	to	ADP
cana-2576	180	11	these	these	DET
cana-2576	180	12	three	three	NUM
cana-2576	180	13	vertices	vertex	NOUN
cana-2576	180	14	,	,	PUNCT
cana-2576	180	15	since	since	SCONJ
cana-2576	180	16	g	g	PROPN
cana-2576	180	17	is	be	AUX
cana-2576	180	18	a	a	DET
cana-2576	180	19	double	double	ADJ
cana-2576	180	20	quadrilateral	quadrilateral	ADJ
cana-2576	180	21	snake	snake	NOUN
cana-2576	180	22	graph	graph	NOUN
cana-2576	180	23	.	.	PUNCT
cana-2576	181	1	but	but	CCONJ
cana-2576	181	2	𝑢1	𝑢1	PROPN
cana-2576	181	3	,	,	PUNCT
cana-2576	181	4	𝑣2	𝑣2	PROPN
cana-2576	181	5	and	and	CCONJ
cana-2576	181	6	𝑥1	𝑥1	PROPN
cana-2576	181	7	,	,	PUNCT
cana-2576	181	8	𝑣2	𝑣2	NUM
cana-2576	181	9	are	be	AUX
cana-2576	181	10	connected	connect	VERB
cana-2576	181	11	by	by	ADP
cana-2576	181	12	a	a	DET
cana-2576	181	13	vertex	vertex	NOUN
cana-2576	181	14	.	.	PUNCT
cana-2576	182	1	they	they	PRON
cana-2576	182	2	are	be	AUX
cana-2576	182	3	𝑢2	𝑢2	NOUN
cana-2576	182	4	and	and	CCONJ
cana-2576	182	5	𝑥2	𝑥2	NOUN
cana-2576	182	6	and	and	CCONJ
cana-2576	182	7	d(𝑢2	d(𝑢2	NOUN
cana-2576	182	8	)	)	PUNCT
cana-2576	182	9	=	=	SYM
cana-2576	182	10	d(𝑥2	d(𝑥2	NUM
cana-2576	182	11	)	)	PUNCT
cana-2576	182	12	=	=	SYM
cana-2576	182	13	3	3	X
cana-2576	182	14	.	.	X
cana-2576	182	15	note	note	VERB
cana-2576	182	16	that	that	SCONJ
cana-2576	182	17	,	,	PUNCT
cana-2576	182	18	since	since	SCONJ
cana-2576	182	19	|v|	|v|	INTJ
cana-2576	182	20	=	=	SYM
cana-2576	182	21	5n+1	5n+1	PROPN
cana-2576	182	22	and	and	CCONJ
cana-2576	182	23	d(v	d(v	ADJ
cana-2576	182	24	)	)	PUNCT
cana-2576	182	25	=	=	NOUN
cana-2576	182	26	p-4	p-4	NOUN
cana-2576	182	27	,	,	PUNCT
cana-2576	182	28	degree	degree	NOUN
cana-2576	182	29	of	of	ADP
cana-2576	182	30	v	v	NOUN
cana-2576	182	31	can	can	AUX
cana-2576	182	32	not	not	PART
cana-2576	182	33	be	be	AUX
cana-2576	182	34	a	a	DET
cana-2576	182	35	multiple	multiple	NOUN
cana-2576	182	36	of	of	ADP
cana-2576	182	37	5	5	NUM
cana-2576	182	38	.	.	PUNCT
cana-2576	183	1	if	if	SCONJ
cana-2576	183	2	d(v	d(v	PROPN
cana-2576	183	3	)	)	PUNCT
cana-2576	183	4	is	be	AUX
cana-2576	183	5	odd	odd	ADJ
cana-2576	183	6	and	and	CCONJ
cana-2576	183	7	not	not	PART
cana-2576	183	8	a	a	DET
cana-2576	183	9	multiple	multiple	NOUN
cana-2576	183	10	of	of	ADP
cana-2576	183	11	3	3	NUM
cana-2576	183	12	,	,	PUNCT
cana-2576	183	13	then	then	ADV
cana-2576	183	14	the	the	DET
cana-2576	183	15	set	set	NOUN
cana-2576	183	16	{	{	PUNCT
cana-2576	183	17	𝑣	𝑣	NOUN
cana-2576	183	18	,	,	PUNCT
cana-2576	183	19	𝑢2	𝑢2	PROPN
cana-2576	183	20	,	,	PUNCT
cana-2576	183	21	𝑥1	𝑥1	PROPN
cana-2576	183	22	}	}	PUNCT
cana-2576	183	23	is	be	AUX
cana-2576	183	24	a	a	DET
cana-2576	183	25	relatively	relatively	ADV
cana-2576	183	26	prime	prime	ADJ
cana-2576	183	27	dominating	dominating	NOUN
cana-2576	183	28	set	set	NOUN
cana-2576	183	29	and	and	CCONJ
cana-2576	183	30	hence	hence	ADV
cana-2576	183	31	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	183	32	)	)	PUNCT
cana-2576	184	1	=	=	PUNCT
cana-2576	185	1	3	3	X
cana-2576	185	2	.	.	NOUN
cana-2576	185	3	if	if	SCONJ
cana-2576	185	4	d(v	d(v	PROPN
cana-2576	185	5	)	)	PUNCT
cana-2576	185	6	is	be	AUX
cana-2576	185	7	odd	odd	ADJ
cana-2576	185	8	and	and	CCONJ
cana-2576	185	9	a	a	DET
cana-2576	185	10	multiple	multiple	NOUN
cana-2576	185	11	of	of	ADP
cana-2576	185	12	3	3	NUM
cana-2576	185	13	,	,	PUNCT
cana-2576	185	14	then	then	ADV
cana-2576	185	15	the	the	DET
cana-2576	185	16	set	set	NOUN
cana-2576	185	17	{	{	PUNCT
cana-2576	185	18	𝑣	𝑣	NOUN
cana-2576	185	19	,	,	PUNCT
cana-2576	185	20	𝑢1	𝑢1	PROPN
cana-2576	185	21	,	,	PUNCT
cana-2576	185	22	𝑥1	𝑥1	PROPN
cana-2576	185	23	,	,	PUNCT
cana-2576	185	24	𝑣2	𝑣2	PROPN
cana-2576	185	25	}	}	PUNCT
cana-2576	185	26	is	be	AUX
cana-2576	185	27	a	a	DET
cana-2576	185	28	relatively	relatively	ADV
cana-2576	185	29	prime	prime	ADJ
cana-2576	185	30	dominating	dominating	NOUN
cana-2576	185	31	set	set	NOUN
cana-2576	185	32	and	and	CCONJ
cana-2576	185	33	hence	hence	ADV
cana-2576	185	34	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	185	35	)	)	PUNCT
cana-2576	186	1	=	=	PUNCT
cana-2576	187	1	4	4	X
cana-2576	187	2	.	.	NOUN
cana-2576	187	3	if	if	SCONJ
cana-2576	187	4	d(v	d(v	PROPN
cana-2576	187	5	)	)	PUNCT
cana-2576	187	6	is	be	AUX
cana-2576	187	7	even	even	ADV
cana-2576	187	8	and	and	CCONJ
cana-2576	187	9	not	not	PART
cana-2576	187	10	multiple	multiple	NOUN
cana-2576	187	11	of	of	ADP
cana-2576	187	12	3	3	NUM
cana-2576	187	13	,	,	PUNCT
cana-2576	187	14	then	then	ADV
cana-2576	187	15	the	the	DET
cana-2576	187	16	set	set	NOUN
cana-2576	187	17	{	{	PUNCT
cana-2576	187	18	𝑣	𝑣	NOUN
cana-2576	187	19	,	,	PUNCT
cana-2576	187	20	𝑢2	𝑢2	PROPN
cana-2576	187	21	,	,	PUNCT
cana-2576	187	22	𝑥1	𝑥1	PROPN
cana-2576	187	23	}	}	PUNCT
cana-2576	187	24	is	be	AUX
cana-2576	187	25	a	a	DET
cana-2576	187	26	relatively	relatively	ADV
cana-2576	187	27	prime	prime	ADJ
cana-2576	187	28	dominating	dominating	NOUN
cana-2576	187	29	set	set	NOUN
cana-2576	187	30	and	and	CCONJ
cana-2576	187	31	hence	hence	ADV
cana-2576	187	32	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	187	33	)	)	PUNCT
cana-2576	188	1	=	=	PUNCT
cana-2576	189	1	3	3	X
cana-2576	189	2	.	.	NOUN
cana-2576	189	3	if	if	SCONJ
cana-2576	189	4	d(v	d(v	PROPN
cana-2576	189	5	)	)	PUNCT
cana-2576	189	6	is	be	AUX
cana-2576	189	7	even	even	ADV
cana-2576	189	8	and	and	CCONJ
cana-2576	189	9	multiple	multiple	ADJ
cana-2576	189	10	of	of	ADP
cana-2576	189	11	3	3	NUM
cana-2576	189	12	,	,	PUNCT
cana-2576	189	13	then	then	ADV
cana-2576	189	14	the	the	DET
cana-2576	189	15	set	set	NOUN
cana-2576	189	16	{	{	PUNCT
cana-2576	189	17	𝑣	𝑣	NOUN
cana-2576	189	18	,	,	PUNCT
cana-2576	189	19	𝑢1	𝑢1	PROPN
cana-2576	189	20	,	,	PUNCT
cana-2576	189	21	𝑥1	𝑥1	PROPN
cana-2576	189	22	,	,	PUNCT
cana-2576	189	23	𝑣2	𝑣2	PROPN
cana-2576	189	24	}	}	PUNCT
cana-2576	189	25	is	be	AUX
cana-2576	189	26	a	a	DET
cana-2576	189	27	relatively	relatively	ADV
cana-2576	189	28	prime	prime	ADJ
cana-2576	189	29	dominating	dominating	NOUN
cana-2576	189	30	set	set	NOUN
cana-2576	189	31	and	and	CCONJ
cana-2576	189	32	hence	hence	ADV
cana-2576	189	33	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	189	34	)	)	PUNCT
cana-2576	190	1	=	=	PUNCT
cana-2576	190	2	4	4	X
cana-2576	190	3	.	.	X
cana-2576	190	4	case	case	NOUN
cana-2576	190	5	3	3	NUM
cana-2576	190	6	:	:	SYM
cana-2576	190	7	v	v	NOUN
cana-2576	190	8	is	be	AUX
cana-2576	190	9	any	any	DET
cana-2576	190	10	internal	internal	ADJ
cana-2576	190	11	path	path	NOUN
cana-2576	190	12	vertex	vertex	NOUN
cana-2576	190	13	.	.	PUNCT
cana-2576	191	1	without	without	ADP
cana-2576	191	2	loss	loss	NOUN
cana-2576	191	3	of	of	ADP
cana-2576	191	4	generality	generality	NOUN
cana-2576	191	5	,	,	PUNCT
cana-2576	191	6	let	let	VERB
cana-2576	191	7	it	it	PRON
cana-2576	191	8	be	be	AUX
cana-2576	191	9	𝑣𝑖	𝑣𝑖	ADP
cana-2576	191	10	,	,	PUNCT
cana-2576	191	11	𝑖	𝑖	X
cana-2576	191	12	=	=	SYM
cana-2576	191	13	2,3	2,3	NUM
cana-2576	191	14	,	,	PUNCT
cana-2576	191	15	…	…	PUNCT
cana-2576	191	16	,	,	PUNCT
cana-2576	191	17	𝑚	𝑚	ADP
cana-2576	191	18	−	−	PROPN
cana-2576	191	19	1	1	NUM
cana-2576	191	20	.	.	PUNCT
cana-2576	192	1	then	then	ADV
cana-2576	192	2	d(𝑣𝑖	d(𝑣𝑖	NUM
cana-2576	192	3	)	)	PUNCT
cana-2576	192	4	=	=	SYM
cana-2576	192	5	p-7	p-7	NOUN
cana-2576	192	6	in	in	ADP
cana-2576	192	7	𝐺𝑣.	𝐺𝑣.	PROPN
cana-2576	192	8	then	then	ADV
cana-2576	192	9	the	the	DET
cana-2576	192	10	vertex	vertex	NOUN
cana-2576	192	11	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	192	12	covers	cover	VERB
cana-2576	192	13	all	all	DET
cana-2576	192	14	the	the	DET
cana-2576	192	15	vertices	vertex	NOUN
cana-2576	192	16	except	except	SCONJ
cana-2576	192	17	the	the	DET
cana-2576	192	18	six	six	NUM
cana-2576	192	19	vertices	vertex	NOUN
cana-2576	192	20	,	,	PUNCT
cana-2576	192	21	namely	namely	ADV
cana-2576	192	22	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	192	23	,	,	PUNCT
cana-2576	192	24	𝑤𝑖	𝑤𝑖	ADP
cana-2576	192	25	,	,	PUNCT
cana-2576	192	26	𝑥𝑖	𝑥𝑖	PROPN
cana-2576	192	27	,	,	PUNCT
cana-2576	192	28	𝑦𝑖	𝑦𝑖	PROPN
cana-2576	192	29	,	,	PUNCT
cana-2576	192	30	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	192	31	,	,	PUNCT
cana-2576	192	32	𝑣𝑖+1	𝑣𝑖+1	PROPN
cana-2576	192	33	.	.	PUNCT
cana-2576	192	34	then	then	ADV
cana-2576	192	35	d(𝑢𝑖	d(𝑢𝑖	NOUN
cana-2576	192	36	)	)	PUNCT
cana-2576	192	37	=	=	SYM
cana-2576	192	38	d(𝑤𝑖	d(𝑤𝑖	NOUN
cana-2576	192	39	)	)	PUNCT
cana-2576	192	40	=	=	PUNCT
cana-2576	192	41	d(𝑥𝑖	d(𝑥𝑖	X
cana-2576	192	42	)	)	PUNCT
cana-2576	192	43	=	=	PUNCT
cana-2576	192	44	d(𝑦𝑖	d(𝑦𝑖	ADJ
cana-2576	192	45	)	)	PUNCT
cana-2576	192	46	=	=	SYM
cana-2576	192	47	1	1	NUM
cana-2576	192	48	and	and	CCONJ
cana-2576	192	49	d(𝑣𝑖−1	d(𝑣𝑖−1	NUM
cana-2576	192	50	)	)	PUNCT
cana-2576	192	51	=	=	SYM
cana-2576	192	52	2	2	NUM
cana-2576	192	53	if	if	SCONJ
cana-2576	192	54	it	it	PRON
cana-2576	192	55	is	be	AUX
cana-2576	192	56	an	an	DET
cana-2576	192	57	initial	initial	ADJ
cana-2576	192	58	vertex	vertex	NOUN
cana-2576	192	59	,	,	PUNCT
cana-2576	192	60	otherwise	otherwise	ADV
cana-2576	192	61	5	5	NUM
cana-2576	192	62	.	.	PUNCT
cana-2576	192	63	similarly	similarly	ADV
cana-2576	192	64	for	for	ADP
cana-2576	192	65	the	the	DET
cana-2576	192	66	vertex	vertex	NOUN
cana-2576	192	67	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	192	68	.	.	PUNCT
cana-2576	192	69	to	to	PART
cana-2576	192	70	cover	cover	VERB
cana-2576	192	71	these	these	DET
cana-2576	192	72	six	six	NUM
cana-2576	192	73	vertices	vertex	NOUN
cana-2576	192	74	,	,	PUNCT
cana-2576	192	75	either	either	CCONJ
cana-2576	192	76	we	we	PRON
cana-2576	192	77	have	have	VERB
cana-2576	192	78	to	to	PART
cana-2576	192	79	take	take	VERB
cana-2576	192	80	these	these	DET
cana-2576	192	81	six	six	NUM
cana-2576	192	82	vertices	vertex	NOUN
cana-2576	192	83	or	or	CCONJ
cana-2576	192	84	vertices	vertex	NOUN
cana-2576	192	85	which	which	PRON
cana-2576	192	86	are	be	AUX
cana-2576	192	87	adjacent	adjacent	ADJ
cana-2576	192	88	to	to	ADP
cana-2576	192	89	these	these	DET
cana-2576	192	90	six	six	NUM
cana-2576	192	91	vertices	vertex	NOUN
cana-2576	192	92	.	.	PUNCT
cana-2576	193	1	as	as	ADP
cana-2576	193	2	in	in	ADP
cana-2576	193	3	case	case	NOUN
cana-2576	193	4	2	2	NUM
cana-2576	193	5	,	,	PUNCT
cana-2576	193	6	the	the	DET
cana-2576	193	7	vertices	vertex	NOUN
cana-2576	193	8	which	which	PRON
cana-2576	193	9	are	be	AUX
cana-2576	193	10	adjacent	adjacent	ADJ
cana-2576	193	11	to	to	ADP
cana-2576	193	12	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	193	13	and	and	CCONJ
cana-2576	193	14	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	193	15	,	,	PUNCT
cana-2576	193	16	𝑤𝑖	𝑤𝑖	NOUN
cana-2576	193	17	and	and	CCONJ
cana-2576	193	18	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	193	19	,	,	PUNCT
cana-2576	193	20	𝑥𝑖	𝑥𝑖	PROPN
cana-2576	193	21	and	and	CCONJ
cana-2576	193	22	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	193	23	,	,	PUNCT
cana-2576	193	24	𝑦𝑖	𝑦𝑖	NUM
cana-2576	193	25	and	and	CCONJ
cana-2576	193	26	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	193	27	are	be	AUX
cana-2576	193	28	𝑤𝑖−1	𝑤𝑖−1	ADJ
cana-2576	193	29	,	,	PUNCT
cana-2576	193	30	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-2576	193	31	,	,	PUNCT
cana-2576	193	32	𝑥𝑖−1	𝑥𝑖−1	NOUN
cana-2576	193	33	,	,	PUNCT
cana-2576	193	34	𝑦𝑖+1	𝑦𝑖+1	X
cana-2576	193	35	respectively	respectively	ADV
cana-2576	193	36	.	.	PUNCT
cana-2576	194	1	then	then	ADV
cana-2576	194	2	d(𝑤𝑖−1	d(𝑤𝑖−1	NOUN
cana-2576	194	3	)	)	PUNCT
cana-2576	194	4	=	=	PUNCT
cana-2576	194	5	d(𝑢𝑖+1	d(𝑢𝑖+1	X
cana-2576	194	6	)	)	PUNCT
cana-2576	194	7	=	=	SYM
cana-2576	194	8	d(𝑥𝑖−1	d(𝑥𝑖−1	NOUN
cana-2576	194	9	)	)	PUNCT
cana-2576	194	10	=	=	SYM
cana-2576	194	11	d(𝑦𝑖+1	d(𝑦𝑖+1	PROPN
cana-2576	194	12	)	)	PUNCT
cana-2576	194	13	=	=	SYM
cana-2576	194	14	3	3	X
cana-2576	194	15	.	.	PUNCT
cana-2576	194	16	to	to	PART
cana-2576	194	17	obtain	obtain	VERB
cana-2576	194	18	a	a	DET
cana-2576	194	19	relatively	relatively	ADV
cana-2576	194	20	prime	prime	ADJ
cana-2576	194	21	dominating	dominating	NOUN
cana-2576	194	22	set	set	NOUN
cana-2576	194	23	,	,	PUNCT
cana-2576	194	24	we	we	PRON
cana-2576	194	25	can	can	AUX
cana-2576	194	26	take	take	VERB
cana-2576	194	27	only	only	ADV
cana-2576	194	28	one	one	NUM
cana-2576	194	29	of	of	ADP
cana-2576	194	30	these	these	DET
cana-2576	194	31	four	four	NUM
cana-2576	194	32	vertices	vertex	NOUN
cana-2576	194	33	.	.	PUNCT
cana-2576	195	1	we	we	PRON
cana-2576	195	2	have	have	VERB
cana-2576	195	3	the	the	DET
cana-2576	195	4	following	follow	VERB
cana-2576	195	5	subcases	subcase	NOUN
cana-2576	195	6	.	.	PUNCT
cana-2576	196	1	communications	communication	NOUN
cana-2576	196	2	on	on	ADP
cana-2576	196	3	applied	apply	VERB
cana-2576	196	4	nonlinear	nonlinear	ADJ
cana-2576	196	5	analysis	analysis	NOUN
cana-2576	196	6	issn	issn	NOUN
cana-2576	196	7	:	:	PUNCT
cana-2576	196	8	1074	1074	NUM
cana-2576	196	9	-	-	PUNCT
cana-2576	196	10	133x	133x	NUM
cana-2576	196	11	vol	vol	NOUN
cana-2576	196	12	32	32	NUM
cana-2576	196	13	no	no	NOUN
cana-2576	196	14	.	.	PUNCT
cana-2576	197	1	3s	3s	NUM
cana-2576	197	2	(	(	PUNCT
cana-2576	197	3	2025	2025	NUM
cana-2576	197	4	)	)	PUNCT
cana-2576	197	5	159	159	NUM
cana-2576	197	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2576	197	7	case	case	NOUN
cana-2576	197	8	3.1	3.1	NUM
cana-2576	197	9	:	:	PUNCT
cana-2576	197	10	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	197	11	is	be	AUX
cana-2576	197	12	an	an	DET
cana-2576	197	13	initial	initial	ADJ
cana-2576	197	14	vertex	vertex	NOUN
cana-2576	197	15	.	.	PUNCT
cana-2576	198	1	then	then	ADV
cana-2576	198	2	d(𝑣𝑖−1	d(𝑣𝑖−1	NOUN
cana-2576	198	3	)	)	PUNCT
cana-2576	198	4	=	=	SYM
cana-2576	198	5	2	2	X
cana-2576	198	6	.	.	X
cana-2576	198	7	note	note	VERB
cana-2576	198	8	that	that	SCONJ
cana-2576	198	9	d(v	d(v	PROPN
cana-2576	198	10	)	)	PUNCT
cana-2576	198	11	can	can	AUX
cana-2576	198	12	not	not	PART
cana-2576	198	13	be	be	AUX
cana-2576	198	14	a	a	DET
cana-2576	198	15	multiple	multiple	NOUN
cana-2576	198	16	of	of	ADP
cana-2576	198	17	5	5	NUM
cana-2576	198	18	.	.	PUNCT
cana-2576	199	1	if	if	SCONJ
cana-2576	199	2	d(v	d(v	PROPN
cana-2576	199	3	)	)	PUNCT
cana-2576	199	4	is	be	AUX
cana-2576	199	5	odd	odd	ADJ
cana-2576	199	6	and	and	CCONJ
cana-2576	199	7	not	not	PART
cana-2576	199	8	a	a	DET
cana-2576	199	9	multiple	multiple	NOUN
cana-2576	199	10	of	of	ADP
cana-2576	199	11	3	3	NUM
cana-2576	199	12	,	,	PUNCT
cana-2576	199	13	then	then	ADV
cana-2576	199	14	the	the	DET
cana-2576	199	15	set	set	NOUN
cana-2576	199	16	{	{	PUNCT
cana-2576	199	17	𝑣	𝑣	NOUN
cana-2576	199	18	,	,	PUNCT
cana-2576	199	19	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	199	20	,	,	PUNCT
cana-2576	199	21	𝑥𝑖	𝑥𝑖	PROPN
cana-2576	199	22	,	,	PUNCT
cana-2576	199	23	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	199	24	,	,	PUNCT
cana-2576	199	25	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-2576	199	26	,	,	PUNCT
cana-2576	199	27	𝑦𝑖	𝑦𝑖	VERB
cana-2576	199	28	}	}	PUNCT
cana-2576	199	29	is	be	AUX
cana-2576	199	30	a	a	DET
cana-2576	199	31	relatively	relatively	ADV
cana-2576	199	32	prime	prime	ADJ
cana-2576	199	33	dominating	dominating	NOUN
cana-2576	199	34	set	set	NOUN
cana-2576	199	35	and	and	CCONJ
cana-2576	199	36	hence	hence	ADV
cana-2576	199	37	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	199	38	)	)	PUNCT
cana-2576	200	1	=	=	PUNCT
cana-2576	200	2	6	6	X
cana-2576	200	3	.	.	PUNCT
cana-2576	201	1	if	if	SCONJ
cana-2576	201	2	d(v	d(v	PROPN
cana-2576	201	3	)	)	PUNCT
cana-2576	201	4	is	be	AUX
cana-2576	201	5	odd	odd	ADJ
cana-2576	201	6	and	and	CCONJ
cana-2576	201	7	a	a	DET
cana-2576	201	8	multiple	multiple	NOUN
cana-2576	201	9	of	of	ADP
cana-2576	201	10	3	3	NUM
cana-2576	201	11	,	,	PUNCT
cana-2576	201	12	then	then	ADV
cana-2576	201	13	the	the	DET
cana-2576	201	14	set	set	NOUN
cana-2576	201	15	{	{	PUNCT
cana-2576	201	16	𝑣	𝑣	NOUN
cana-2576	201	17	,	,	PUNCT
cana-2576	201	18	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	201	19	,	,	PUNCT
cana-2576	201	20	𝑥𝑖	𝑥𝑖	X
cana-2576	201	21	,	,	PUNCT
cana-2576	201	22	𝑤𝑖	𝑤𝑖	PRON
cana-2576	201	23	,	,	PUNCT
cana-2576	201	24	𝑦𝑖¸𝑣𝑖+1	𝑦𝑖¸𝑣𝑖+1	NOUN
cana-2576	201	25	,	,	PUNCT
cana-2576	201	26	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	201	27	}	}	PUNCT
cana-2576	201	28	is	be	AUX
cana-2576	201	29	a	a	DET
cana-2576	201	30	relatively	relatively	ADV
cana-2576	201	31	prime	prime	ADJ
cana-2576	201	32	dominating	dominating	NOUN
cana-2576	201	33	set	set	NOUN
cana-2576	201	34	and	and	CCONJ
cana-2576	201	35	hence	hence	ADV
cana-2576	201	36	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	201	37	)	)	PUNCT
cana-2576	202	1	=	=	PUNCT
cana-2576	202	2	7	7	X
cana-2576	202	3	.	.	X
cana-2576	202	4	case	case	NOUN
cana-2576	202	5	3.2	3.2	NUM
cana-2576	202	6	:	:	SYM
cana-2576	202	7	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	202	8	is	be	AUX
cana-2576	202	9	an	an	DET
cana-2576	202	10	end	end	NOUN
cana-2576	202	11	vertex	vertex	NOUN
cana-2576	202	12	same	same	ADJ
cana-2576	202	13	as	as	ADP
cana-2576	202	14	case	case	NOUN
cana-2576	202	15	3.1	3.1	NUM
cana-2576	202	16	.	.	PUNCT
cana-2576	202	17	case	case	NOUN
cana-2576	202	18	3.3	3.3	NUM
cana-2576	202	19	:	:	PUNCT
cana-2576	202	20	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	202	21	is	be	AUX
cana-2576	202	22	an	an	DET
cana-2576	202	23	initial	initial	ADJ
cana-2576	202	24	vertex	vertex	NOUN
cana-2576	202	25	and	and	CCONJ
cana-2576	202	26	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	202	27	is	be	AUX
cana-2576	202	28	an	an	DET
cana-2576	202	29	end	end	NOUN
cana-2576	202	30	vertex	vertex	NOUN
cana-2576	202	31	.	.	PUNCT
cana-2576	203	1	then	then	ADV
cana-2576	203	2	|v|	|v|	INTJ
cana-2576	203	3	must	must	AUX
cana-2576	203	4	be	be	AUX
cana-2576	203	5	11	11	NUM
cana-2576	203	6	and	and	CCONJ
cana-2576	203	7	hence	hence	ADV
cana-2576	203	8	d(v	d(v	ADJ
cana-2576	203	9	)	)	PUNCT
cana-2576	203	10	=	=	SYM
cana-2576	203	11	4	4	X
cana-2576	203	12	.	.	PUNCT
cana-2576	204	1	hence	hence	ADV
cana-2576	204	2	the	the	DET
cana-2576	204	3	set	set	NOUN
cana-2576	204	4	{	{	PUNCT
cana-2576	204	5	𝑣	𝑣	NOUN
cana-2576	204	6	,	,	PUNCT
cana-2576	204	7	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	204	8	,	,	PUNCT
cana-2576	204	9	𝑥𝑖	𝑥𝑖	PROPN
cana-2576	204	10	,	,	PUNCT
cana-2576	204	11	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	204	12	,	,	PUNCT
cana-2576	204	13	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-2576	204	14	,	,	PUNCT
cana-2576	204	15	𝑦𝑖	𝑦𝑖	VERB
cana-2576	204	16	}	}	PUNCT
cana-2576	204	17	is	be	AUX
cana-2576	204	18	a	a	DET
cana-2576	204	19	relatively	relatively	ADV
cana-2576	204	20	prime	prime	ADJ
cana-2576	204	21	dominating	dominating	NOUN
cana-2576	204	22	set	set	NOUN
cana-2576	204	23	and	and	CCONJ
cana-2576	204	24	hence	hence	ADV
cana-2576	204	25	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	204	26	)	)	PUNCT
cana-2576	205	1	=	=	PUNCT
cana-2576	205	2	6	6	X
cana-2576	205	3	.	.	PUNCT
cana-2576	205	4	case	case	NOUN
cana-2576	205	5	3.4	3.4	NUM
cana-2576	205	6	:	:	PUNCT
cana-2576	205	7	neither	neither	CCONJ
cana-2576	205	8	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	205	9	is	be	AUX
cana-2576	205	10	an	an	DET
cana-2576	205	11	initial	initial	ADJ
cana-2576	205	12	vertex	vertex	NOUN
cana-2576	205	13	nor	nor	CCONJ
cana-2576	205	14	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	205	15	is	be	AUX
cana-2576	205	16	an	an	DET
cana-2576	205	17	end	end	NOUN
cana-2576	205	18	vertex	vertex	NOUN
cana-2576	205	19	.	.	PUNCT
cana-2576	206	1	then	then	ADV
cana-2576	206	2	d(𝑣𝑖−1	d(𝑣𝑖−1	NUM
cana-2576	206	3	)	)	PUNCT
cana-2576	206	4	=	=	SYM
cana-2576	206	5	d(𝑣𝑖+1	d(𝑣𝑖+1	X
cana-2576	206	6	)	)	PUNCT
cana-2576	206	7	=	=	SYM
cana-2576	206	8	5	5	X
cana-2576	206	9	.	.	PUNCT
cana-2576	206	10	since	since	SCONJ
cana-2576	206	11	degree	degree	NOUN
cana-2576	206	12	of	of	ADP
cana-2576	206	13	these	these	DET
cana-2576	206	14	two	two	NUM
cana-2576	206	15	vertices	vertex	NOUN
cana-2576	206	16	are	be	AUX
cana-2576	206	17	5	5	NUM
cana-2576	206	18	,	,	PUNCT
cana-2576	206	19	we	we	PRON
cana-2576	206	20	can	can	AUX
cana-2576	206	21	not	not	PART
cana-2576	206	22	take	take	VERB
cana-2576	206	23	these	these	DET
cana-2576	206	24	vertices	vertex	NOUN
cana-2576	206	25	together	together	ADV
cana-2576	206	26	.	.	PUNCT
cana-2576	207	1	so	so	ADV
cana-2576	207	2	we	we	PRON
cana-2576	207	3	consider	consider	VERB
cana-2576	207	4	the	the	DET
cana-2576	207	5	vertices	vertex	NOUN
cana-2576	207	6	which	which	PRON
cana-2576	207	7	are	be	AUX
cana-2576	207	8	adjacent	adjacent	ADJ
cana-2576	207	9	to	to	ADP
cana-2576	207	10	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	207	11	,	,	PUNCT
cana-2576	207	12	namely	namely	ADV
cana-2576	207	13	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-2576	207	14	,	,	PUNCT
cana-2576	207	15	𝑥𝑖+1	𝑥𝑖+1	ADV
cana-2576	207	16	,	,	PUNCT
cana-2576	207	17	𝑤𝑖+1	𝑤𝑖+1	NUM
cana-2576	207	18	,	,	PUNCT
cana-2576	207	19	𝑦𝑖+1	𝑦𝑖+1	NOUN
cana-2576	207	20	,	,	PUNCT
cana-2576	207	21	𝑣𝑖+2	𝑣𝑖+2	NUM
cana-2576	207	22	.	.	NOUN
cana-2576	207	23	then	then	ADV
cana-2576	207	24	d(𝑢𝑖+1	d(𝑢𝑖+1	NOUN
cana-2576	207	25	)	)	PUNCT
cana-2576	207	26	=	=	SYM
cana-2576	207	27	d(𝑥𝑖+1	d(𝑥𝑖+1	PROPN
cana-2576	207	28	)	)	PUNCT
cana-2576	207	29	=	=	SYM
cana-2576	207	30	d(𝑤𝑖+1	d(𝑤𝑖+1	NUM
cana-2576	207	31	)	)	PUNCT
cana-2576	207	32	=	=	SYM
cana-2576	207	33	d(𝑦𝑖+1	d(𝑦𝑖+1	PROPN
cana-2576	207	34	)	)	PUNCT
cana-2576	207	35	=	=	SYM
cana-2576	207	36	3	3	NUM
cana-2576	207	37	and	and	CCONJ
cana-2576	207	38	d(𝑣𝑖+2	d(𝑣𝑖+2	NOUN
cana-2576	207	39	)	)	PUNCT
cana-2576	207	40	=	=	SYM
cana-2576	207	41	4	4	NUM
cana-2576	207	42	if	if	SCONJ
cana-2576	207	43	𝑣𝑖+2	𝑣𝑖+2	PRON
cana-2576	207	44	is	be	AUX
cana-2576	207	45	an	an	DET
cana-2576	207	46	end	end	NOUN
cana-2576	207	47	vertex	vertex	NOUN
cana-2576	207	48	,	,	PUNCT
cana-2576	207	49	otherwise	otherwise	ADV
cana-2576	207	50	7	7	X
cana-2576	207	51	.	.	PUNCT
cana-2576	208	1	if	if	SCONJ
cana-2576	208	2	d(v	d(v	PROPN
cana-2576	208	3	)	)	PUNCT
cana-2576	208	4	is	be	AUX
cana-2576	208	5	odd	odd	ADJ
cana-2576	208	6	and	and	CCONJ
cana-2576	208	7	not	not	PART
cana-2576	208	8	a	a	DET
cana-2576	208	9	multiple	multiple	NOUN
cana-2576	208	10	of	of	ADP
cana-2576	208	11	3	3	NUM
cana-2576	208	12	,	,	PUNCT
cana-2576	208	13	then	then	ADV
cana-2576	208	14	the	the	DET
cana-2576	208	15	set	set	NOUN
cana-2576	208	16	{	{	PUNCT
cana-2576	208	17	𝑣	𝑣	NOUN
cana-2576	208	18	,	,	PUNCT
cana-2576	208	19	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	208	20	,	,	PUNCT
cana-2576	208	21	𝑥𝑖	𝑥𝑖	PROPN
cana-2576	208	22	,	,	PUNCT
cana-2576	208	23	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	208	24	,	,	PUNCT
cana-2576	208	25	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-2576	208	26	,	,	PUNCT
cana-2576	208	27	𝑦𝑖	𝑦𝑖	VERB
cana-2576	208	28	}	}	PUNCT
cana-2576	208	29	is	be	AUX
cana-2576	208	30	a	a	DET
cana-2576	208	31	relatively	relatively	ADV
cana-2576	208	32	prime	prime	ADJ
cana-2576	208	33	dominating	dominating	NOUN
cana-2576	208	34	set	set	NOUN
cana-2576	208	35	and	and	CCONJ
cana-2576	208	36	hence	hence	ADV
cana-2576	208	37	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	208	38	)	)	PUNCT
cana-2576	209	1	=	=	SYM
cana-2576	209	2	6	6	X
cana-2576	209	3	.	.	PUNCT
cana-2576	209	4	suppose	suppose	VERB
cana-2576	209	5	that	that	SCONJ
cana-2576	209	6	d(v	d(v	PROPN
cana-2576	209	7	)	)	PUNCT
cana-2576	209	8	is	be	AUX
cana-2576	209	9	odd	odd	ADJ
cana-2576	209	10	and	and	CCONJ
cana-2576	209	11	a	a	DET
cana-2576	209	12	multiple	multiple	ADJ
cana-2576	209	13	3	3	NUM
cana-2576	209	14	.	.	PUNCT
cana-2576	210	1	here	here	ADV
cana-2576	210	2	we	we	PRON
cana-2576	210	3	can	can	AUX
cana-2576	210	4	not	not	PART
cana-2576	210	5	choose	choose	VERB
cana-2576	210	6	a	a	DET
cana-2576	210	7	vertex	vertex	NOUN
cana-2576	210	8	of	of	ADP
cana-2576	210	9	degree	degree	NOUN
cana-2576	210	10	3	3	NUM
cana-2576	210	11	.	.	PUNCT
cana-2576	211	1	the	the	DET
cana-2576	211	2	only	only	ADJ
cana-2576	211	3	possibility	possibility	NOUN
cana-2576	211	4	is	be	AUX
cana-2576	211	5	choose	choose	VERB
cana-2576	211	6	the	the	DET
cana-2576	211	7	vertex	vertex	NOUN
cana-2576	211	8	𝑣𝑖+2	𝑣𝑖+2	NUM
cana-2576	211	9	.	.	PUNCT
cana-2576	212	1	if	if	SCONJ
cana-2576	212	2	𝑣𝑖+2	𝑣𝑖+2	PROPN
cana-2576	212	3	is	be	AUX
cana-2576	212	4	an	an	DET
cana-2576	212	5	end	end	NOUN
cana-2576	212	6	vertex	vertex	NOUN
cana-2576	212	7	,	,	PUNCT
cana-2576	212	8	then	then	ADV
cana-2576	212	9	the	the	DET
cana-2576	212	10	set	set	NOUN
cana-2576	212	11	{	{	PUNCT
cana-2576	212	12	𝑣	𝑣	NOUN
cana-2576	212	13	,	,	PUNCT
cana-2576	212	14	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	212	15	,	,	PUNCT
cana-2576	212	16	𝑥𝑖	𝑥𝑖	PROPN
cana-2576	212	17	,	,	PUNCT
cana-2576	212	18	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	212	19	,	,	PUNCT
cana-2576	212	20	𝑤𝑖	𝑤𝑖	PRON
cana-2576	212	21	,	,	PUNCT
cana-2576	212	22	𝑦𝑖	𝑦𝑖	PROPN
cana-2576	212	23	,	,	PUNCT
cana-2576	212	24	𝑣𝑖+2	𝑣𝑖+2	PROPN
cana-2576	212	25	}	}	PUNCT
cana-2576	212	26	is	be	AUX
cana-2576	212	27	a	a	DET
cana-2576	212	28	relatively	relatively	ADV
cana-2576	212	29	prime	prime	ADJ
cana-2576	212	30	dominating	dominating	NOUN
cana-2576	212	31	set	set	NOUN
cana-2576	212	32	and	and	CCONJ
cana-2576	212	33	hence	hence	ADV
cana-2576	212	34	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	212	35	)	)	PUNCT
cana-2576	213	1	=	=	PUNCT
cana-2576	213	2	7	7	X
cana-2576	213	3	.	.	X
cana-2576	213	4	if	if	SCONJ
cana-2576	213	5	𝑣𝑖+2	𝑣𝑖+2	NOUN
cana-2576	213	6	is	be	AUX
cana-2576	213	7	not	not	PART
cana-2576	213	8	an	an	DET
cana-2576	213	9	end	end	NOUN
cana-2576	213	10	vertex	vertex	NOUN
cana-2576	213	11	and	and	CCONJ
cana-2576	213	12	d(v	d(v	PROPN
cana-2576	213	13	)	)	PUNCT
cana-2576	213	14	is	be	AUX
cana-2576	213	15	not	not	PART
cana-2576	213	16	a	a	DET
cana-2576	213	17	multiple	multiple	NOUN
cana-2576	213	18	of	of	ADP
cana-2576	213	19	7	7	NUM
cana-2576	213	20	,	,	PUNCT
cana-2576	213	21	then	then	ADV
cana-2576	213	22	set	set	VERB
cana-2576	213	23	{	{	PUNCT
cana-2576	213	24	𝑣	𝑣	NOUN
cana-2576	213	25	,	,	PUNCT
cana-2576	213	26	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	213	27	,	,	PUNCT
cana-2576	213	28	𝑥𝑖	𝑥𝑖	PROPN
cana-2576	213	29	,	,	PUNCT
cana-2576	213	30	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	213	31	,	,	PUNCT
cana-2576	213	32	𝑤𝑖	𝑤𝑖	PRON
cana-2576	213	33	,	,	PUNCT
cana-2576	213	34	𝑦𝑖	𝑦𝑖	PROPN
cana-2576	213	35	,	,	PUNCT
cana-2576	213	36	𝑣𝑖+2	𝑣𝑖+2	NOUN
cana-2576	213	37	}	}	PUNCT
cana-2576	213	38	is	be	AUX
cana-2576	213	39	a	a	DET
cana-2576	213	40	relatively	relatively	ADV
cana-2576	213	41	prime	prime	ADJ
cana-2576	213	42	dominating	dominating	NOUN
cana-2576	213	43	set	set	NOUN
cana-2576	213	44	and	and	CCONJ
cana-2576	213	45	hence	hence	ADV
cana-2576	213	46	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	213	47	)	)	PUNCT
cana-2576	214	1	=	=	PUNCT
cana-2576	214	2	7	7	X
cana-2576	214	3	.	.	X
cana-2576	214	4	if	if	SCONJ
cana-2576	214	5	d(v	d(v	PROPN
cana-2576	214	6	)	)	PUNCT
cana-2576	214	7	is	be	AUX
cana-2576	214	8	odd	odd	ADJ
cana-2576	214	9	and	and	CCONJ
cana-2576	214	10	a	a	DET
cana-2576	214	11	multiple	multiple	NOUN
cana-2576	214	12	of	of	ADP
cana-2576	214	13	3	3	NUM
cana-2576	214	14	and	and	CCONJ
cana-2576	214	15	7	7	NUM
cana-2576	214	16	,	,	PUNCT
cana-2576	214	17	then	then	ADV
cana-2576	214	18	relatively	relatively	ADV
cana-2576	214	19	prime	prime	ADJ
cana-2576	214	20	dominating	dominating	NOUN
cana-2576	214	21	set	set	NOUN
cana-2576	214	22	does	do	AUX
cana-2576	214	23	not	not	PART
cana-2576	214	24	exist	exist	VERB
cana-2576	214	25	.	.	PUNCT
cana-2576	215	1	if	if	SCONJ
cana-2576	215	2	d(v	d(v	PROPN
cana-2576	215	3	)	)	PUNCT
cana-2576	215	4	is	be	AUX
cana-2576	215	5	even	even	ADV
cana-2576	215	6	and	and	CCONJ
cana-2576	215	7	not	not	PART
cana-2576	215	8	a	a	DET
cana-2576	215	9	multiple	multiple	NOUN
cana-2576	215	10	of	of	ADP
cana-2576	215	11	3	3	NUM
cana-2576	215	12	,	,	PUNCT
cana-2576	215	13	then	then	ADV
cana-2576	215	14	the	the	DET
cana-2576	215	15	set	set	NOUN
cana-2576	215	16	{	{	PUNCT
cana-2576	215	17	𝑣	𝑣	NOUN
cana-2576	215	18	,	,	PUNCT
cana-2576	215	19	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	215	20	,	,	PUNCT
cana-2576	215	21	𝑥𝑖	𝑥𝑖	PROPN
cana-2576	215	22	,	,	PUNCT
cana-2576	215	23	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	215	24	,	,	PUNCT
cana-2576	215	25	𝑤𝑖	𝑤𝑖	PRON
cana-2576	215	26	,	,	PUNCT
cana-2576	215	27	𝑢𝑖+1	𝑢𝑖+1	AUX
cana-2576	215	28	}	}	PUNCT
cana-2576	215	29	is	be	AUX
cana-2576	215	30	a	a	DET
cana-2576	215	31	relatively	relatively	ADV
cana-2576	215	32	prime	prime	ADJ
cana-2576	215	33	dominating	dominating	NOUN
cana-2576	215	34	set	set	NOUN
cana-2576	215	35	and	and	CCONJ
cana-2576	215	36	hence	hence	ADV
cana-2576	215	37	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	215	38	)	)	PUNCT
cana-2576	216	1	=	=	SYM
cana-2576	216	2	6	6	X
cana-2576	216	3	.	.	PUNCT
cana-2576	216	4	suppose	suppose	VERB
cana-2576	216	5	that	that	SCONJ
cana-2576	216	6	d(v	d(v	PROPN
cana-2576	216	7	)	)	PUNCT
cana-2576	216	8	is	be	AUX
cana-2576	216	9	even	even	ADV
cana-2576	216	10	and	and	CCONJ
cana-2576	216	11	a	a	DET
cana-2576	216	12	multiple	multiple	NOUN
cana-2576	216	13	of	of	ADP
cana-2576	216	14	3	3	NUM
cana-2576	216	15	.	.	PUNCT
cana-2576	217	1	as	as	SCONJ
cana-2576	217	2	said	say	VERB
cana-2576	217	3	above	above	ADV
cana-2576	217	4	,	,	PUNCT
cana-2576	217	5	we	we	PRON
cana-2576	217	6	can	can	AUX
cana-2576	217	7	not	not	PART
cana-2576	217	8	take	take	VERB
cana-2576	217	9	the	the	DET
cana-2576	217	10	vertices	vertex	NOUN
cana-2576	217	11	of	of	ADP
cana-2576	217	12	degree	degree	NOUN
cana-2576	217	13	3	3	X
cana-2576	217	14	.	.	PUNCT
cana-2576	218	1	we	we	PRON
cana-2576	218	2	can	can	AUX
cana-2576	218	3	cover	cover	VERB
cana-2576	218	4	the	the	DET
cana-2576	218	5	vertices	vertex	NOUN
cana-2576	218	6	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	218	7	,	,	PUNCT
cana-2576	218	8	𝑤𝑖	𝑤𝑖	INTJ
cana-2576	218	9	,	,	PUNCT
cana-2576	218	10	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	218	11	,	,	PUNCT
cana-2576	218	12	𝑥𝑖	𝑥𝑖	PRON
cana-2576	218	13	,	,	PUNCT
cana-2576	218	14	𝑦𝑖.	𝑦𝑖.	VERB
cana-2576	218	15	we	we	PRON
cana-2576	218	16	have	have	VERB
cana-2576	218	17	only	only	ADV
cana-2576	218	18	one	one	NUM
cana-2576	218	19	vertex	vertex	NOUN
cana-2576	218	20	to	to	PART
cana-2576	218	21	cover	cover	VERB
cana-2576	218	22	is	be	AUX
cana-2576	218	23	𝑣𝑖+1	𝑣𝑖+1	X
cana-2576	218	24	.	.	PUNCT
cana-2576	219	1	if	if	SCONJ
cana-2576	219	2	𝑣𝑖+2	𝑣𝑖+2	PROPN
cana-2576	219	3	is	be	AUX
cana-2576	219	4	an	an	DET
cana-2576	219	5	end	end	NOUN
cana-2576	219	6	vertex	vertex	NOUN
cana-2576	219	7	,	,	PUNCT
cana-2576	219	8	then	then	ADV
cana-2576	219	9	the	the	DET
cana-2576	219	10	set	set	NOUN
cana-2576	219	11	{	{	PUNCT
cana-2576	219	12	𝑣	𝑣	NOUN
cana-2576	219	13	,	,	PUNCT
cana-2576	219	14	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	219	15	,	,	PUNCT
cana-2576	219	16	𝑥𝑖	𝑥𝑖	PROPN
cana-2576	219	17	,	,	PUNCT
cana-2576	219	18	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	219	19	,	,	PUNCT
cana-2576	219	20	𝑤𝑖	𝑤𝑖	PRON
cana-2576	219	21	,	,	PUNCT
cana-2576	219	22	𝑦𝑖	𝑦𝑖	PROPN
cana-2576	219	23	,	,	PUNCT
cana-2576	219	24	𝑣𝑖+2	𝑣𝑖+2	PROPN
cana-2576	219	25	}	}	PUNCT
cana-2576	219	26	is	be	AUX
cana-2576	219	27	a	a	DET
cana-2576	219	28	relatively	relatively	ADV
cana-2576	219	29	prime	prime	ADJ
cana-2576	219	30	dominating	dominating	NOUN
cana-2576	219	31	set	set	NOUN
cana-2576	219	32	and	and	CCONJ
cana-2576	219	33	hence	hence	ADV
cana-2576	219	34	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	219	35	)	)	PUNCT
cana-2576	220	1	=	=	PUNCT
cana-2576	220	2	7	7	X
cana-2576	220	3	.	.	X
cana-2576	220	4	if	if	SCONJ
cana-2576	220	5	𝑣𝑖+2	𝑣𝑖+2	NOUN
cana-2576	220	6	is	be	AUX
cana-2576	220	7	not	not	PART
cana-2576	220	8	an	an	DET
cana-2576	220	9	end	end	NOUN
cana-2576	220	10	vertex	vertex	NOUN
cana-2576	220	11	and	and	CCONJ
cana-2576	220	12	d(v	d(v	PROPN
cana-2576	220	13	)	)	PUNCT
cana-2576	220	14	is	be	AUX
cana-2576	220	15	not	not	PART
cana-2576	220	16	a	a	DET
cana-2576	220	17	multiple	multiple	NOUN
cana-2576	220	18	of	of	ADP
cana-2576	220	19	7	7	NUM
cana-2576	220	20	,	,	PUNCT
cana-2576	220	21	then	then	ADV
cana-2576	220	22	set	set	VERB
cana-2576	220	23	{	{	PUNCT
cana-2576	220	24	𝑣	𝑣	NOUN
cana-2576	220	25	,	,	PUNCT
cana-2576	220	26	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	220	27	,	,	PUNCT
cana-2576	220	28	𝑥𝑖	𝑥𝑖	PROPN
cana-2576	220	29	,	,	PUNCT
cana-2576	220	30	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	220	31	,	,	PUNCT
cana-2576	220	32	𝑤𝑖	𝑤𝑖	PRON
cana-2576	220	33	,	,	PUNCT
cana-2576	220	34	𝑦𝑖	𝑦𝑖	PROPN
cana-2576	220	35	,	,	PUNCT
cana-2576	220	36	𝑣𝑖+2	𝑣𝑖+2	NOUN
cana-2576	220	37	}	}	PUNCT
cana-2576	220	38	is	be	AUX
cana-2576	220	39	a	a	DET
cana-2576	220	40	relatively	relatively	ADV
cana-2576	220	41	prime	prime	ADJ
cana-2576	220	42	dominating	dominating	NOUN
cana-2576	220	43	set	set	NOUN
cana-2576	220	44	and	and	CCONJ
cana-2576	220	45	hence	hence	ADV
cana-2576	220	46	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	220	47	)	)	PUNCT
cana-2576	221	1	=	=	PUNCT
cana-2576	221	2	7	7	X
cana-2576	221	3	.	.	X
cana-2576	221	4	if	if	SCONJ
cana-2576	221	5	d(v	d(v	PROPN
cana-2576	221	6	)	)	PUNCT
cana-2576	221	7	is	be	AUX
cana-2576	221	8	odd	odd	ADJ
cana-2576	221	9	and	and	CCONJ
cana-2576	221	10	a	a	DET
cana-2576	221	11	multiple	multiple	NOUN
cana-2576	221	12	of	of	ADP
cana-2576	221	13	3	3	NUM
cana-2576	221	14	and	and	CCONJ
cana-2576	221	15	7	7	NUM
cana-2576	221	16	,	,	PUNCT
cana-2576	221	17	then	then	ADV
cana-2576	221	18	relatively	relatively	ADV
cana-2576	221	19	prime	prime	ADJ
cana-2576	221	20	dominating	dominating	NOUN
cana-2576	221	21	set	set	NOUN
cana-2576	221	22	does	do	AUX
cana-2576	221	23	not	not	PART
cana-2576	221	24	exist	exist	VERB
cana-2576	221	25	.	.	PUNCT
cana-2576	222	1	theorem	theorem	VERB
cana-2576	222	2	3.4	3.4	NUM
cana-2576	222	3	.	.	PUNCT
cana-2576	223	1	let	let	VERB
cana-2576	223	2	g	g	PRON
cana-2576	223	3	be	be	AUX
cana-2576	223	4	a	a	DET
cana-2576	223	5	double	double	ADJ
cana-2576	223	6	alternate	alternate	ADJ
cana-2576	223	7	quadrilateral	quadrilateral	ADJ
cana-2576	223	8	snake	snake	NOUN
cana-2576	223	9	graph	graph	NOUN
cana-2576	223	10	with	with	ADP
cana-2576	223	11	p	p	ADJ
cana-2576	223	12	vertices	vertex	NOUN
cana-2576	223	13	,	,	PUNCT
cana-2576	223	14	where	where	SCONJ
cana-2576	223	15	p	p	NOUN
cana-2576	223	16	=	=	SYM
cana-2576	223	17	6n	6n	PROPN
cana-2576	223	18	,	,	PUNCT
cana-2576	223	19	n	n	PRON
cana-2576	223	20	≥	≥	NOUN
cana-2576	223	21	2	2	NUM
cana-2576	223	22	.	.	PUNCT
cana-2576	224	1	then	then	ADV
cana-2576	224	2	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	224	3	)	)	PUNCT
cana-2576	224	4	=	=	SYM
cana-2576	224	5	2	2	NUM
cana-2576	224	6	,	,	PUNCT
cana-2576	224	7	3	3	NUM
cana-2576	224	8	,	,	PUNCT
cana-2576	224	9	4	4	NUM
cana-2576	224	10	or	or	CCONJ
cana-2576	224	11	5	5	NUM
cana-2576	224	12	.	.	PUNCT
cana-2576	225	1	proof	proof	NOUN
cana-2576	225	2	:	:	PUNCT
cana-2576	225	3	let	let	VERB
cana-2576	225	4	g	g	PRON
cana-2576	225	5	be	be	AUX
cana-2576	225	6	a	a	DET
cana-2576	225	7	double	double	ADJ
cana-2576	225	8	alternate	alternate	ADJ
cana-2576	225	9	quadrilateral	quadrilateral	ADJ
cana-2576	225	10	snake	snake	NOUN
cana-2576	225	11	graph	graph	NOUN
cana-2576	225	12	with	with	ADP
cana-2576	225	13	p	p	NOUN
cana-2576	225	14	vertices	vertex	NOUN
cana-2576	225	15	.	.	PUNCT
cana-2576	226	1	let	let	VERB
cana-2576	226	2	the	the	DET
cana-2576	226	3	vertices	vertex	NOUN
cana-2576	226	4	in	in	ADP
cana-2576	226	5	the	the	DET
cana-2576	226	6	path	path	NOUN
cana-2576	226	7	be	be	AUX
cana-2576	226	8	𝑣1,𝑣2	𝑣1,𝑣2	PROPN
cana-2576	226	9	,	,	PUNCT
cana-2576	226	10	…	…	PUNCT
cana-2576	226	11	,	,	PUNCT
cana-2576	226	12	𝑣𝑚	𝑣𝑚	VERB
cana-2576	226	13	,	,	PUNCT
cana-2576	226	14	where	where	SCONJ
cana-2576	226	15	𝑣1	𝑣1	NOUN
cana-2576	226	16	and	and	CCONJ
cana-2576	226	17	𝑣𝑚	𝑣𝑚	VERB
cana-2576	226	18	denote	denote	VERB
cana-2576	226	19	the	the	DET
cana-2576	226	20	initial	initial	ADJ
cana-2576	226	21	and	and	CCONJ
cana-2576	226	22	end	end	VERB
cana-2576	226	23	vertex	vertex	NOUN
cana-2576	226	24	respectively	respectively	ADV
cana-2576	226	25	.	.	PUNCT
cana-2576	227	1	let	let	VERB
cana-2576	227	2	the	the	DET
cana-2576	227	3	vertices	vertex	NOUN
cana-2576	227	4	in	in	ADP
cana-2576	227	5	the	the	DET
cana-2576	227	6	upper	upper	ADJ
cana-2576	227	7	quadrilateral	quadrilateral	NOUN
cana-2576	227	8	be	be	AUX
cana-2576	227	9	𝑢1,𝑢2	𝑢1,𝑢2	PROPN
cana-2576	227	10	,	,	PUNCT
cana-2576	227	11	…	…	PUNCT
cana-2576	227	12	,	,	PUNCT
cana-2576	227	13	𝑢𝑚	𝑢𝑚	NOUN
cana-2576	227	14	and	and	CCONJ
cana-2576	227	15	the	the	DET
cana-2576	227	16	vertices	vertex	NOUN
cana-2576	227	17	in	in	ADP
cana-2576	227	18	the	the	DET
cana-2576	227	19	lower	low	ADJ
cana-2576	227	20	quadrilateral	quadrilateral	NOUN
cana-2576	227	21	be	be	AUX
cana-2576	227	22	𝑤1,𝑤2,	𝑤1,𝑤2,	NOUN
cana-2576	227	23	…	…	SYM
cana-2576	227	24	,𝑤𝑚.	,𝑤𝑚.	NOUN
cana-2576	227	25	then	then	ADV
cana-2576	227	26	degree	degree	NOUN
cana-2576	227	27	of	of	ADP
cana-2576	227	28	each	each	DET
cana-2576	227	29	internal	internal	ADJ
cana-2576	227	30	path	path	NOUN
cana-2576	227	31	vertex	vertex	NOUN
cana-2576	227	32	is	be	AUX
cana-2576	227	33	4	4	NUM
cana-2576	227	34	;	;	PUNCT
cana-2576	227	35	degree	degree	NOUN
cana-2576	227	36	of	of	ADP
cana-2576	227	37	initial	initial	ADJ
cana-2576	227	38	and	and	CCONJ
cana-2576	227	39	end	end	VERB
cana-2576	227	40	vertex	vertex	NOUN
cana-2576	227	41	is	be	AUX
cana-2576	227	42	3	3	NUM
cana-2576	227	43	;	;	PUNCT
cana-2576	227	44	degree	degree	NOUN
cana-2576	227	45	of	of	ADP
cana-2576	227	46	vertices	vertex	NOUN
cana-2576	227	47	in	in	ADP
cana-2576	227	48	the	the	DET
cana-2576	227	49	quadrilateral	quadrilateral	NOUN
cana-2576	227	50	is	be	AUX
cana-2576	227	51	2	2	NUM
cana-2576	227	52	.	.	PUNCT
cana-2576	228	1	let	let	VERB
cana-2576	228	2	v	v	PART
cana-2576	228	3	be	be	AUX
cana-2576	228	4	any	any	DET
cana-2576	228	5	vertex	vertex	NOUN
cana-2576	228	6	in	in	ADP
cana-2576	228	7	g.	g.	PROPN
cana-2576	229	1	we	we	PRON
cana-2576	229	2	have	have	VERB
cana-2576	229	3	the	the	DET
cana-2576	229	4	following	follow	VERB
cana-2576	229	5	cases	case	NOUN
cana-2576	229	6	.	.	PUNCT
cana-2576	230	1	case	case	NOUN
cana-2576	230	2	1	1	NUM
cana-2576	230	3	:	:	PUNCT
cana-2576	230	4	v	v	NOUN
cana-2576	230	5	is	be	AUX
cana-2576	230	6	any	any	DET
cana-2576	230	7	vertex	vertex	NOUN
cana-2576	230	8	from	from	ADP
cana-2576	230	9	{	{	PUNCT
cana-2576	230	10	𝑢1,𝑢2	𝑢1,𝑢2	PROPN
cana-2576	230	11	,	,	PUNCT
cana-2576	230	12	…	…	PUNCT
cana-2576	230	13	,	,	PUNCT
cana-2576	230	14	𝑢𝑚−1	𝑢𝑚−1	PROPN
cana-2576	230	15	,	,	PUNCT
cana-2576	230	16	𝑤1,𝑤2,	𝑤1,𝑤2,	ADP
cana-2576	230	17	…	…	SYM
cana-2576	230	18	,𝑤𝑚−1	,𝑤𝑚−1	PRON
cana-2576	230	19	}	}	PUNCT
cana-2576	230	20	.	.	PUNCT
cana-2576	231	1	communications	communication	NOUN
cana-2576	231	2	on	on	ADP
cana-2576	231	3	applied	apply	VERB
cana-2576	231	4	nonlinear	nonlinear	ADJ
cana-2576	231	5	analysis	analysis	NOUN
cana-2576	231	6	issn	issn	NOUN
cana-2576	231	7	:	:	PUNCT
cana-2576	231	8	1074	1074	NUM
cana-2576	231	9	-	-	PUNCT
cana-2576	231	10	133x	133x	NUM
cana-2576	231	11	vol	vol	NOUN
cana-2576	231	12	32	32	NUM
cana-2576	231	13	no	no	NOUN
cana-2576	231	14	.	.	PUNCT
cana-2576	232	1	3s	3s	NUM
cana-2576	232	2	(	(	PUNCT
cana-2576	232	3	2025	2025	NUM
cana-2576	232	4	)	)	PUNCT
cana-2576	232	5	160	160	NUM
cana-2576	232	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2576	232	7	without	without	ADP
cana-2576	232	8	loss	loss	NOUN
cana-2576	232	9	of	of	ADP
cana-2576	232	10	generality	generality	NOUN
cana-2576	232	11	,	,	PUNCT
cana-2576	232	12	let	let	VERB
cana-2576	232	13	v	v	VERB
cana-2576	232	14	=	=	NOUN
cana-2576	232	15	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	232	16	,	,	PUNCT
cana-2576	232	17	𝑖	𝑖	X
cana-2576	232	18	=	=	SYM
cana-2576	232	19	1,2	1,2	NUM
cana-2576	232	20	,	,	PUNCT
cana-2576	232	21	…	…	PUNCT
cana-2576	232	22	,	,	PUNCT
cana-2576	232	23	𝑚.	𝑚.	ADV
cana-2576	232	24	then	then	ADV
cana-2576	232	25	d(v	d(v	PROPN
cana-2576	232	26	)	)	PUNCT
cana-2576	233	1	=	=	SYM
cana-2576	233	2	p–3	p–3	NOUN
cana-2576	233	3	.	.	PUNCT
cana-2576	234	1	this	this	DET
cana-2576	234	2	vertex	vertex	NOUN
cana-2576	234	3	covers	cover	VERB
cana-2576	234	4	all	all	DET
cana-2576	234	5	the	the	DET
cana-2576	234	6	vertices	vertex	NOUN
cana-2576	234	7	in	in	ADP
cana-2576	234	8	𝐺𝑣	𝐺𝑣	PROPN
cana-2576	234	9	except	except	SCONJ
cana-2576	234	10	the	the	DET
cana-2576	234	11	two	two	NUM
cana-2576	234	12	vertices	vertex	NOUN
cana-2576	234	13	,	,	PUNCT
cana-2576	234	14	namely	namely	ADV
cana-2576	234	15	𝑣𝑖	𝑣𝑖	ADV
cana-2576	234	16	and	and	CCONJ
cana-2576	234	17	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-2576	234	18	or	or	CCONJ
cana-2576	234	19	𝑣𝑖	𝑣𝑖	ADV
cana-2576	234	20	and	and	CCONJ
cana-2576	234	21	𝑢𝑖−𝑖.	𝑢𝑖−𝑖.	NUM
cana-2576	234	22	without	without	ADP
cana-2576	234	23	loss	loss	NOUN
cana-2576	234	24	of	of	ADP
cana-2576	234	25	generality	generality	NOUN
cana-2576	234	26	,	,	PUNCT
cana-2576	234	27	let	let	VERB
cana-2576	234	28	us	we	PRON
cana-2576	234	29	take	take	VERB
cana-2576	234	30	𝑣𝑖	𝑣𝑖	ADV
cana-2576	234	31	and	and	CCONJ
cana-2576	234	32	𝑢𝑖+1	𝑢𝑖+1	NOUN
cana-2576	234	33	.	.	NOUN
cana-2576	234	34	to	to	PART
cana-2576	234	35	find	find	VERB
cana-2576	234	36	the	the	DET
cana-2576	234	37	relatively	relatively	ADV
cana-2576	234	38	prime	prime	ADJ
cana-2576	234	39	dominating	dominating	NOUN
cana-2576	234	40	set	set	NOUN
cana-2576	234	41	,	,	PUNCT
cana-2576	234	42	we	we	PRON
cana-2576	234	43	have	have	VERB
cana-2576	234	44	to	to	PART
cana-2576	234	45	cover	cover	VERB
cana-2576	234	46	these	these	DET
cana-2576	234	47	two	two	NUM
cana-2576	234	48	vertices	vertex	NOUN
cana-2576	234	49	.	.	PUNCT
cana-2576	235	1	either	either	CCONJ
cana-2576	235	2	we	we	PRON
cana-2576	235	3	have	have	VERB
cana-2576	235	4	to	to	PART
cana-2576	235	5	choose	choose	VERB
cana-2576	235	6	these	these	DET
cana-2576	235	7	two	two	NUM
cana-2576	235	8	vertices	vertex	NOUN
cana-2576	235	9	or	or	CCONJ
cana-2576	235	10	a	a	DET
cana-2576	235	11	vertex	vertex	NOUN
cana-2576	235	12	which	which	PRON
cana-2576	235	13	is	be	AUX
cana-2576	235	14	adjacent	adjacent	ADJ
cana-2576	235	15	to	to	ADP
cana-2576	235	16	both	both	CCONJ
cana-2576	235	17	the	the	DET
cana-2576	235	18	vertices	vertex	NOUN
cana-2576	235	19	𝑣𝑖	𝑣𝑖	ADV
cana-2576	235	20	and	and	CCONJ
cana-2576	235	21	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	235	22	.	.	NOUN
cana-2576	235	23	such	such	DET
cana-2576	235	24	a	a	DET
cana-2576	235	25	vertex	vertex	NOUN
cana-2576	235	26	always	always	ADV
cana-2576	235	27	exists	exist	VERB
cana-2576	235	28	,	,	PUNCT
cana-2576	235	29	since	since	SCONJ
cana-2576	235	30	g	g	PROPN
cana-2576	235	31	is	be	AUX
cana-2576	235	32	a	a	DET
cana-2576	235	33	double	double	ADJ
cana-2576	235	34	alternative	alternative	ADJ
cana-2576	235	35	quadrilateral	quadrilateral	ADJ
cana-2576	235	36	snake	snake	NOUN
cana-2576	235	37	graph	graph	NOUN
cana-2576	235	38	and	and	CCONJ
cana-2576	235	39	let	let	VERB
cana-2576	235	40	the	the	DET
cana-2576	235	41	vertex	vertex	NOUN
cana-2576	235	42	be	be	AUX
cana-2576	235	43	𝑣𝑖+1	𝑣𝑖+1	PROPN
cana-2576	235	44	.	.	PUNCT
cana-2576	235	45	then	then	ADV
cana-2576	235	46	d(𝑣𝑖+1	d(𝑣𝑖+1	NUM
cana-2576	235	47	)	)	PUNCT
cana-2576	235	48	=	=	SYM
cana-2576	236	1	4	4	X
cana-2576	236	2	,	,	PUNCT
cana-2576	236	3	if	if	SCONJ
cana-2576	236	4	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	236	5	is	be	AUX
cana-2576	236	6	an	an	DET
cana-2576	236	7	end	end	NOUN
cana-2576	236	8	vertex	vertex	NOUN
cana-2576	236	9	,	,	PUNCT
cana-2576	236	10	otherwise	otherwise	ADV
cana-2576	236	11	4	4	X
cana-2576	236	12	.	.	PUNCT
cana-2576	237	1	since	since	SCONJ
cana-2576	237	2	|v|	|v|	PROPN
cana-2576	237	3	=	=	SYM
cana-2576	237	4	6n	6n	PROPN
cana-2576	237	5	,	,	PUNCT
cana-2576	237	6	d(v	d(v	PROPN
cana-2576	237	7	)	)	PUNCT
cana-2576	237	8	is	be	AUX
cana-2576	237	9	always	always	ADV
cana-2576	237	10	odd	odd	ADJ
cana-2576	237	11	and	and	CCONJ
cana-2576	237	12	it	it	PRON
cana-2576	237	13	is	be	AUX
cana-2576	237	14	a	a	DET
cana-2576	237	15	multiple	multiple	NOUN
cana-2576	237	16	of	of	ADP
cana-2576	237	17	3	3	NUM
cana-2576	237	18	.	.	PUNCT
cana-2576	238	1	we	we	PRON
cana-2576	238	2	consider	consider	VERB
cana-2576	238	3	the	the	DET
cana-2576	238	4	following	follow	VERB
cana-2576	238	5	subcases	subcase	NOUN
cana-2576	238	6	.	.	PUNCT
cana-2576	239	1	case	case	NOUN
cana-2576	239	2	1.1	1.1	NUM
cana-2576	239	3	:	:	PUNCT
cana-2576	239	4	𝑣𝑖	𝑣𝑖	ADV
cana-2576	239	5	is	be	AUX
cana-2576	239	6	an	an	DET
cana-2576	239	7	initial	initial	ADJ
cana-2576	239	8	vertex	vertex	NOUN
cana-2576	239	9	.	.	PUNCT
cana-2576	240	1	then	then	ADV
cana-2576	240	2	the	the	DET
cana-2576	240	3	set	set	NOUN
cana-2576	240	4	{	{	PUNCT
cana-2576	240	5	𝑣	𝑣	NOUN
cana-2576	240	6	,	,	PUNCT
cana-2576	240	7	𝑣𝑖	𝑣𝑖	ADV
cana-2576	240	8	,	,	PUNCT
cana-2576	240	9	𝑢𝑖+1	𝑢𝑖+1	AUX
cana-2576	240	10	}	}	PUNCT
cana-2576	240	11	is	be	AUX
cana-2576	240	12	a	a	DET
cana-2576	240	13	relatively	relatively	ADV
cana-2576	240	14	prime	prime	ADJ
cana-2576	240	15	dominating	dominating	NOUN
cana-2576	240	16	set	set	NOUN
cana-2576	240	17	,	,	PUNCT
cana-2576	240	18	since	since	SCONJ
cana-2576	240	19	(	(	PUNCT
cana-2576	240	20	p-3	p-3	NOUN
cana-2576	240	21	,	,	PUNCT
cana-2576	240	22	4	4	NUM
cana-2576	240	23	)	)	PUNCT
cana-2576	240	24	=	=	SYM
cana-2576	241	1	1	1	X
cana-2576	241	2	.	.	X
cana-2576	241	3	therefore	therefore	ADV
cana-2576	241	4	,	,	PUNCT
cana-2576	241	5	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	241	6	)	)	PUNCT
cana-2576	241	7	=	=	SYM
cana-2576	242	1	3	3	X
cana-2576	242	2	.	.	X
cana-2576	242	3	case	case	NOUN
cana-2576	242	4	1.2	1.2	NUM
cana-2576	242	5	:	:	PUNCT
cana-2576	242	6	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	242	7	is	be	AUX
cana-2576	242	8	not	not	PART
cana-2576	242	9	an	an	DET
cana-2576	242	10	initial	initial	ADJ
cana-2576	242	11	vertex	vertex	NOUN
cana-2576	242	12	.	.	PUNCT
cana-2576	243	1	consider	consider	VERB
cana-2576	243	2	the	the	DET
cana-2576	243	3	vertex	vertex	NOUN
cana-2576	243	4	𝑣𝑖+1	𝑣𝑖+1	PRON
cana-2576	243	5	.	.	PUNCT
cana-2576	244	1	if	if	SCONJ
cana-2576	244	2	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	244	3	is	be	AUX
cana-2576	244	4	an	an	DET
cana-2576	244	5	end	end	NOUN
cana-2576	244	6	vertex	vertex	NOUN
cana-2576	244	7	,	,	PUNCT
cana-2576	244	8	then	then	ADV
cana-2576	244	9	the	the	DET
cana-2576	244	10	set	set	NOUN
cana-2576	244	11	{	{	PUNCT
cana-2576	244	12	𝑣	𝑣	NOUN
cana-2576	244	13	,	,	PUNCT
cana-2576	244	14	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	244	15	}	}	PUNCT
cana-2576	244	16	is	be	AUX
cana-2576	244	17	a	a	DET
cana-2576	244	18	relatively	relatively	ADV
cana-2576	244	19	prime	prime	ADJ
cana-2576	244	20	dominating	dominating	NOUN
cana-2576	244	21	set	set	NOUN
cana-2576	244	22	and	and	CCONJ
cana-2576	244	23	hence	hence	ADV
cana-2576	244	24	.	.	PUNCT
cana-2576	245	1	otherwise	otherwise	ADV
cana-2576	245	2	,	,	PUNCT
cana-2576	245	3	we	we	PRON
cana-2576	245	4	have	have	VERB
cana-2576	245	5	degree	degree	NOUN
cana-2576	245	6	of	of	ADP
cana-2576	245	7	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	245	8	is	be	AUX
cana-2576	245	9	5	5	NUM
cana-2576	245	10	.	.	PUNCT
cana-2576	246	1	if	if	SCONJ
cana-2576	246	2	d(v	d(v	PROPN
cana-2576	246	3	)	)	PUNCT
cana-2576	246	4	is	be	AUX
cana-2576	246	5	not	not	PART
cana-2576	246	6	a	a	DET
cana-2576	246	7	multiple	multiple	NOUN
cana-2576	246	8	of	of	ADP
cana-2576	246	9	5	5	NUM
cana-2576	246	10	,	,	PUNCT
cana-2576	246	11	then	then	ADV
cana-2576	246	12	the	the	DET
cana-2576	246	13	set	set	NOUN
cana-2576	246	14	{	{	PUNCT
cana-2576	246	15	𝑣	𝑣	NOUN
cana-2576	246	16	,	,	PUNCT
cana-2576	246	17	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	246	18	}	}	PUNCT
cana-2576	246	19	is	be	AUX
cana-2576	246	20	a	a	DET
cana-2576	246	21	relatively	relatively	ADV
cana-2576	246	22	prime	prime	ADJ
cana-2576	246	23	dominating	dominating	NOUN
cana-2576	246	24	set	set	NOUN
cana-2576	246	25	and	and	CCONJ
cana-2576	246	26	hence	hence	ADV
cana-2576	246	27	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	246	28	)	)	PUNCT
cana-2576	247	1	=	=	PUNCT
cana-2576	247	2	2	2	X
cana-2576	247	3	.	.	X
cana-2576	247	4	if	if	SCONJ
cana-2576	247	5	d(v	d(v	PROPN
cana-2576	247	6	)	)	PUNCT
cana-2576	247	7	is	be	AUX
cana-2576	247	8	not	not	PART
cana-2576	247	9	multiple	multiple	ADJ
cana-2576	247	10	of	of	ADP
cana-2576	247	11	5	5	NUM
cana-2576	247	12	,	,	PUNCT
cana-2576	247	13	then	then	ADV
cana-2576	247	14	relatively	relatively	ADV
cana-2576	247	15	prime	prime	ADJ
cana-2576	247	16	dominating	dominating	NOUN
cana-2576	247	17	set	set	NOUN
cana-2576	247	18	does	do	AUX
cana-2576	247	19	not	not	PART
cana-2576	247	20	exist	exist	VERB
cana-2576	247	21	.	.	PUNCT
cana-2576	248	1	case	case	NOUN
cana-2576	248	2	2	2	NUM
cana-2576	248	3	:	:	SYM
cana-2576	248	4	v	v	NOUN
cana-2576	248	5	is	be	AUX
cana-2576	248	6	an	an	DET
cana-2576	248	7	initial	initial	ADJ
cana-2576	248	8	vertex	vertex	NOUN
cana-2576	248	9	or	or	CCONJ
cana-2576	248	10	an	an	DET
cana-2576	248	11	end	end	NOUN
cana-2576	248	12	vertex	vertex	NOUN
cana-2576	248	13	.	.	PUNCT
cana-2576	249	1	without	without	ADP
cana-2576	249	2	loss	loss	NOUN
cana-2576	249	3	of	of	ADP
cana-2576	249	4	generality	generality	NOUN
cana-2576	249	5	,	,	PUNCT
cana-2576	249	6	let	let	VERB
cana-2576	249	7	v	v	NOUN
cana-2576	249	8	=	=	SYM
cana-2576	249	9	𝑣1	𝑣1	PROPN
cana-2576	249	10	.	.	PUNCT
cana-2576	250	1	then	then	ADV
cana-2576	250	2	d(𝑣1	d(𝑣1	ADJ
cana-2576	250	3	)	)	PUNCT
cana-2576	250	4	=	=	SYM
cana-2576	250	5	p–4	p–4	NOUN
cana-2576	250	6	.	.	PUNCT
cana-2576	251	1	this	this	DET
cana-2576	251	2	vertex	vertex	NOUN
cana-2576	251	3	covers	cover	VERB
cana-2576	251	4	all	all	DET
cana-2576	251	5	the	the	DET
cana-2576	251	6	vertices	vertex	NOUN
cana-2576	251	7	of	of	ADP
cana-2576	251	8	𝐺𝑣	𝐺𝑣	PROPN
cana-2576	251	9	except	except	SCONJ
cana-2576	251	10	three	three	NUM
cana-2576	251	11	vertices	vertex	NOUN
cana-2576	251	12	,	,	PUNCT
cana-2576	251	13	namely	namely	ADV
cana-2576	251	14	𝑢1	𝑢1	PROPN
cana-2576	251	15	,	,	PUNCT
cana-2576	251	16	𝑤1	𝑤1	VERB
cana-2576	251	17	,	,	PUNCT
cana-2576	251	18	and	and	CCONJ
cana-2576	251	19	𝑣2	𝑣2	PROPN
cana-2576	251	20	.	.	PUNCT
cana-2576	252	1	note	note	VERB
cana-2576	252	2	that	that	SCONJ
cana-2576	252	3	there	there	PRON
cana-2576	252	4	is	be	VERB
cana-2576	252	5	no	no	DET
cana-2576	252	6	vertex	vertex	NOUN
cana-2576	252	7	which	which	PRON
cana-2576	252	8	covers	cover	VERB
cana-2576	252	9	all	all	DET
cana-2576	252	10	these	these	DET
cana-2576	252	11	three	three	NUM
cana-2576	252	12	vertices	vertex	NOUN
cana-2576	252	13	.	.	PUNCT
cana-2576	253	1	but	but	CCONJ
cana-2576	253	2	the	the	DET
cana-2576	253	3	vertices	vertex	NOUN
cana-2576	253	4	𝑢1	𝑢1	PROPN
cana-2576	253	5	and	and	CCONJ
cana-2576	253	6	𝑣2	𝑣2	PROPN
cana-2576	253	7	,	,	PUNCT
cana-2576	253	8	𝑤1	𝑤1	VERB
cana-2576	253	9	and	and	CCONJ
cana-2576	253	10	𝑣2	𝑣2	PRON
cana-2576	253	11	are	be	AUX
cana-2576	253	12	connected	connect	VERB
cana-2576	253	13	by	by	ADP
cana-2576	253	14	a	a	DET
cana-2576	253	15	vertex	vertex	NOUN
cana-2576	253	16	,	,	PUNCT
cana-2576	253	17	namely	namely	ADV
cana-2576	253	18	𝑢2	𝑢2	PROPN
cana-2576	253	19	and	and	CCONJ
cana-2576	253	20	𝑤2	𝑤2	NOUN
cana-2576	253	21	.	.	PUNCT
cana-2576	254	1	then	then	ADV
cana-2576	254	2	d(𝑢2	d(𝑢2	X
cana-2576	254	3	)	)	PUNCT
cana-2576	254	4	=	=	SYM
cana-2576	254	5	d(𝑤2	d(𝑤2	NOUN
cana-2576	254	6	)	)	PUNCT
cana-2576	254	7	=	=	SYM
cana-2576	255	1	3	3	X
cana-2576	255	2	.	.	PUNCT
cana-2576	255	3	since	since	SCONJ
cana-2576	255	4	d(𝑣1	d(𝑣1	ADJ
cana-2576	255	5	)	)	PUNCT
cana-2576	255	6	=	=	NOUN
cana-2576	255	7	p-4	p-4	NOUN
cana-2576	255	8	,	,	PUNCT
cana-2576	255	9	it	it	PRON
cana-2576	255	10	can	can	AUX
cana-2576	255	11	not	not	PART
cana-2576	255	12	be	be	AUX
cana-2576	255	13	multiple	multiple	ADJ
cana-2576	255	14	of	of	ADP
cana-2576	255	15	3	3	NUM
cana-2576	255	16	.	.	PUNCT
cana-2576	256	1	hence	hence	ADV
cana-2576	256	2	the	the	DET
cana-2576	256	3	set	set	NOUN
cana-2576	256	4	{	{	PUNCT
cana-2576	256	5	𝑣1	𝑣1	PROPN
cana-2576	256	6	,	,	PUNCT
cana-2576	256	7	𝑢2	𝑢2	PROPN
cana-2576	256	8	,	,	PUNCT
cana-2576	256	9	𝑤1	𝑤1	VERB
cana-2576	256	10	}	}	PUNCT
cana-2576	256	11	is	be	AUX
cana-2576	256	12	a	a	DET
cana-2576	256	13	relatively	relatively	ADV
cana-2576	256	14	prime	prime	ADJ
cana-2576	256	15	dominating	dominating	NOUN
cana-2576	256	16	set	set	NOUN
cana-2576	256	17	and	and	CCONJ
cana-2576	256	18	hence	hence	ADV
cana-2576	256	19	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	256	20	)	)	PUNCT
cana-2576	257	1	=	=	SYM
cana-2576	257	2	3	3	X
cana-2576	257	3	.	.	X
cana-2576	257	4	case	case	NOUN
cana-2576	257	5	3	3	NUM
cana-2576	257	6	:	:	SYM
cana-2576	257	7	v	v	NOUN
cana-2576	257	8	is	be	AUX
cana-2576	257	9	anyone	anyone	PRON
cana-2576	257	10	of	of	ADP
cana-2576	257	11	internal	internal	ADJ
cana-2576	257	12	path	path	NOUN
cana-2576	257	13	vertex	vertex	NOUN
cana-2576	257	14	.	.	PUNCT
cana-2576	258	1	without	without	ADP
cana-2576	258	2	loss	loss	NOUN
cana-2576	258	3	of	of	ADP
cana-2576	258	4	generality	generality	NOUN
cana-2576	258	5	,	,	PUNCT
cana-2576	258	6	let	let	VERB
cana-2576	258	7	v	v	NOUN
cana-2576	258	8	=	=	SYM
cana-2576	258	9	𝑣𝑖	𝑣𝑖	ADV
cana-2576	258	10	,	,	PUNCT
cana-2576	258	11	𝑖	𝑖	X
cana-2576	258	12	=	=	SYM
cana-2576	258	13	2,3	2,3	NUM
cana-2576	258	14	,	,	PUNCT
cana-2576	258	15	…	…	PUNCT
cana-2576	258	16	,	,	PUNCT
cana-2576	258	17	𝑚	𝑚	ADP
cana-2576	258	18	−	−	PROPN
cana-2576	258	19	1	1	NUM
cana-2576	258	20	.	.	PUNCT
cana-2576	259	1	then	then	ADV
cana-2576	259	2	d(v	d(v	PROPN
cana-2576	259	3	)	)	PUNCT
cana-2576	259	4	=	=	PUNCT
cana-2576	260	1	p–5	p–5	NOUN
cana-2576	260	2	.	.	PUNCT
cana-2576	261	1	this	this	DET
cana-2576	261	2	vertex	vertex	NOUN
cana-2576	261	3	covers	cover	VERB
cana-2576	261	4	all	all	DET
cana-2576	261	5	the	the	DET
cana-2576	261	6	vertices	vertex	NOUN
cana-2576	261	7	of	of	ADP
cana-2576	261	8	𝐺𝑣	𝐺𝑣	PROPN
cana-2576	261	9	except	except	SCONJ
cana-2576	261	10	four	four	NUM
cana-2576	261	11	vertices	vertex	NOUN
cana-2576	261	12	,	,	PUNCT
cana-2576	261	13	namely	namely	ADV
cana-2576	261	14	,	,	PUNCT
cana-2576	261	15	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	261	16	,	,	PUNCT
cana-2576	261	17	𝑤𝑖	𝑤𝑖	NOUN
cana-2576	261	18	,	,	PUNCT
cana-2576	261	19	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	261	20	and	and	CCONJ
cana-2576	261	21	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	261	22	.	.	PUNCT
cana-2576	262	1	then	then	ADV
cana-2576	262	2	d(𝑢𝑖	d(𝑢𝑖	NOUN
cana-2576	262	3	)	)	PUNCT
cana-2576	262	4	=	=	SYM
cana-2576	262	5	d(𝑤𝑖	d(𝑤𝑖	NOUN
cana-2576	262	6	)	)	PUNCT
cana-2576	262	7	=	=	SYM
cana-2576	262	8	1	1	NUM
cana-2576	262	9	,	,	PUNCT
cana-2576	262	10	d(𝑣𝑖−1	d(𝑣𝑖−1	PUNCT
cana-2576	262	11	)	)	PUNCT
cana-2576	262	12	=	=	SYM
cana-2576	262	13	2	2	NUM
cana-2576	262	14	if	if	SCONJ
cana-2576	262	15	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	262	16	is	be	AUX
cana-2576	262	17	an	an	DET
cana-2576	262	18	initial	initial	ADJ
cana-2576	262	19	vertex	vertex	NOUN
cana-2576	262	20	,	,	PUNCT
cana-2576	262	21	otherwise	otherwise	ADV
cana-2576	262	22	3	3	X
cana-2576	262	23	.	.	PUNCT
cana-2576	262	24	similarly	similarly	ADV
cana-2576	262	25	,	,	PUNCT
cana-2576	262	26	d(𝑣𝑖+1	d(𝑣𝑖+1	ADJ
cana-2576	262	27	)	)	PUNCT
cana-2576	262	28	=	=	SYM
cana-2576	262	29	2	2	NUM
cana-2576	262	30	if	if	SCONJ
cana-2576	262	31	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	262	32	is	be	AUX
cana-2576	262	33	an	an	DET
cana-2576	262	34	end	end	NOUN
cana-2576	262	35	vertex	vertex	NOUN
cana-2576	262	36	,	,	PUNCT
cana-2576	262	37	otherwise	otherwise	ADV
cana-2576	262	38	3	3	X
cana-2576	262	39	.	.	X
cana-2576	263	1	we	we	PRON
cana-2576	263	2	consider	consider	VERB
cana-2576	263	3	the	the	DET
cana-2576	263	4	following	follow	VERB
cana-2576	263	5	subcases	subcase	NOUN
cana-2576	263	6	.	.	PUNCT
cana-2576	264	1	case	case	NOUN
cana-2576	264	2	3.1	3.1	NUM
cana-2576	264	3	:	:	PUNCT
cana-2576	264	4	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	264	5	is	be	AUX
cana-2576	264	6	an	an	DET
cana-2576	264	7	initial	initial	ADJ
cana-2576	264	8	vertex	vertex	NOUN
cana-2576	264	9	.	.	PUNCT
cana-2576	265	1	note	note	VERB
cana-2576	265	2	that	that	SCONJ
cana-2576	265	3	d(v	d(v	PROPN
cana-2576	265	4	)	)	PUNCT
cana-2576	265	5	=	=	PUNCT
cana-2576	266	1	p-5	p-5	NOUN
cana-2576	266	2	is	be	AUX
cana-2576	266	3	always	always	ADV
cana-2576	266	4	odd	odd	ADJ
cana-2576	266	5	and	and	CCONJ
cana-2576	266	6	not	not	PART
cana-2576	266	7	multiple	multiple	NOUN
cana-2576	266	8	of	of	ADP
cana-2576	266	9	3	3	NUM
cana-2576	266	10	.	.	PUNCT
cana-2576	267	1	as	as	SCONJ
cana-2576	267	2	said	say	VERB
cana-2576	267	3	in	in	ADP
cana-2576	267	4	case	case	NOUN
cana-2576	267	5	2	2	NUM
cana-2576	267	6	,	,	PUNCT
cana-2576	267	7	the	the	DET
cana-2576	267	8	vertex	vertex	NOUN
cana-2576	267	9	which	which	PRON
cana-2576	267	10	is	be	AUX
cana-2576	267	11	adjacent	adjacent	ADJ
cana-2576	267	12	to	to	ADP
cana-2576	267	13	𝑢𝑖	𝑢𝑖	NOUN
cana-2576	267	14	and	and	CCONJ
cana-2576	267	15	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	267	16	is	be	AUX
cana-2576	267	17	𝑢𝑖−1	𝑢𝑖−1	ADJ
cana-2576	267	18	,	,	PUNCT
cana-2576	267	19	is	be	AUX
cana-2576	267	20	of	of	ADP
cana-2576	267	21	degree	degree	NOUN
cana-2576	267	22	3	3	NUM
cana-2576	267	23	and	and	CCONJ
cana-2576	267	24	the	the	DET
cana-2576	267	25	vertex	vertex	NOUN
cana-2576	267	26	adjacent	adjacent	ADJ
cana-2576	267	27	to	to	ADP
cana-2576	267	28	the	the	DET
cana-2576	267	29	vertex	vertex	NOUN
cana-2576	267	30	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	267	31	in	in	ADP
cana-2576	267	32	the	the	DET
cana-2576	267	33	paths	path	NOUN
cana-2576	267	34	is	be	AUX
cana-2576	267	35	𝑣𝑖+2	𝑣𝑖+2	NOUN
cana-2576	267	36	,	,	PUNCT
cana-2576	267	37	is	be	AUX
cana-2576	267	38	of	of	ADP
cana-2576	267	39	degree	degree	NOUN
cana-2576	267	40	5	5	NUM
cana-2576	267	41	,	,	PUNCT
cana-2576	267	42	if	if	SCONJ
cana-2576	267	43	𝑣𝑖+2	𝑣𝑖+2	PRON
cana-2576	267	44	is	be	AUX
cana-2576	267	45	not	not	PART
cana-2576	267	46	an	an	DET
cana-2576	267	47	end	end	NOUN
cana-2576	267	48	vertex	vertex	NOUN
cana-2576	267	49	,	,	PUNCT
cana-2576	267	50	otherwise	otherwise	ADV
cana-2576	267	51	4	4	X
cana-2576	267	52	.	.	PUNCT
cana-2576	268	1	if	if	SCONJ
cana-2576	268	2	𝑣𝑖+2	𝑣𝑖+2	PROPN
cana-2576	268	3	is	be	AUX
cana-2576	268	4	an	an	DET
cana-2576	268	5	end	end	NOUN
cana-2576	268	6	vertex	vertex	NOUN
cana-2576	268	7	,	,	PUNCT
cana-2576	268	8	then	then	ADV
cana-2576	268	9	the	the	DET
cana-2576	268	10	set	set	NOUN
cana-2576	268	11	{	{	PUNCT
cana-2576	268	12	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	268	13	,	,	PUNCT
cana-2576	268	14	𝑣𝑖+2	𝑣𝑖+2	NUM
cana-2576	268	15	,	,	PUNCT
cana-2576	268	16	𝑢𝑖−1	𝑢𝑖−1	NOUN
cana-2576	268	17	,	,	PUNCT
cana-2576	268	18	𝑤𝑖	𝑤𝑖	ADP
cana-2576	268	19	}	}	PUNCT
cana-2576	268	20	is	be	AUX
cana-2576	268	21	a	a	DET
cana-2576	268	22	relatively	relatively	ADV
cana-2576	268	23	prime	prime	ADJ
cana-2576	268	24	dominating	dominating	NOUN
cana-2576	268	25	set	set	NOUN
cana-2576	268	26	and	and	CCONJ
cana-2576	268	27	hence	hence	ADV
cana-2576	268	28	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	268	29	)	)	PUNCT
cana-2576	269	1	=	=	PUNCT
cana-2576	269	2	4	4	X
cana-2576	269	3	.	.	X
cana-2576	270	1	if	if	SCONJ
cana-2576	270	2	𝑣𝑖+2	𝑣𝑖+2	NOUN
cana-2576	270	3	is	be	AUX
cana-2576	270	4	not	not	PART
cana-2576	270	5	an	an	DET
cana-2576	270	6	end	end	NOUN
cana-2576	270	7	vertex	vertex	NOUN
cana-2576	270	8	and	and	CCONJ
cana-2576	270	9	d(v	d(v	PROPN
cana-2576	270	10	)	)	PUNCT
cana-2576	270	11	is	be	AUX
cana-2576	270	12	not	not	PART
cana-2576	270	13	a	a	DET
cana-2576	270	14	multiple	multiple	NOUN
cana-2576	270	15	of	of	ADP
cana-2576	270	16	5	5	NUM
cana-2576	270	17	,	,	PUNCT
cana-2576	270	18	then	then	ADV
cana-2576	270	19	the	the	DET
cana-2576	270	20	set	set	NOUN
cana-2576	270	21	{	{	PUNCT
cana-2576	270	22	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	270	23	,	,	PUNCT
cana-2576	270	24	𝑣𝑖+2	𝑣𝑖+2	NUM
cana-2576	270	25	,	,	PUNCT
cana-2576	270	26	𝑢𝑖−1	𝑢𝑖−1	NOUN
cana-2576	270	27	,	,	PUNCT
cana-2576	270	28	𝑤𝑖	𝑤𝑖	ADP
cana-2576	270	29	}	}	PUNCT
cana-2576	270	30	is	be	AUX
cana-2576	270	31	a	a	DET
cana-2576	270	32	relatively	relatively	ADV
cana-2576	270	33	prime	prime	ADJ
cana-2576	270	34	dominating	dominating	NOUN
cana-2576	270	35	set	set	NOUN
cana-2576	270	36	and	and	CCONJ
cana-2576	270	37	hence	hence	ADV
cana-2576	270	38	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	270	39	)	)	PUNCT
cana-2576	271	1	=	=	PUNCT
cana-2576	271	2	4	4	X
cana-2576	271	3	.	.	X
cana-2576	272	1	if	if	SCONJ
cana-2576	272	2	𝑣𝑖+2	𝑣𝑖+2	NOUN
cana-2576	272	3	is	be	AUX
cana-2576	272	4	not	not	PART
cana-2576	272	5	an	an	DET
cana-2576	272	6	end	end	NOUN
cana-2576	272	7	vertex	vertex	NOUN
cana-2576	272	8	and	and	CCONJ
cana-2576	272	9	d(v	d(v	PROPN
cana-2576	272	10	)	)	PUNCT
cana-2576	272	11	is	be	AUX
cana-2576	272	12	a	a	DET
cana-2576	272	13	multiple	multiple	NOUN
cana-2576	272	14	of	of	ADP
cana-2576	272	15	5	5	NUM
cana-2576	272	16	,	,	PUNCT
cana-2576	272	17	then	then	ADV
cana-2576	272	18	the	the	DET
cana-2576	272	19	set	set	NOUN
cana-2576	272	20	{	{	PUNCT
cana-2576	272	21	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	272	22	,	,	PUNCT
cana-2576	272	23	𝑢𝑖	𝑢𝑖	INTJ
cana-2576	272	24	,	,	PUNCT
cana-2576	272	25	𝑤𝑖	𝑤𝑖	NOUN
cana-2576	272	26	,	,	PUNCT
cana-2576	272	27	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	272	28	,	,	PUNCT
cana-2576	272	29	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	272	30	}	}	PUNCT
cana-2576	272	31	is	be	AUX
cana-2576	272	32	a	a	DET
cana-2576	272	33	relatively	relatively	ADV
cana-2576	272	34	prime	prime	ADJ
cana-2576	272	35	dominating	dominating	NOUN
cana-2576	272	36	set	set	NOUN
cana-2576	272	37	and	and	CCONJ
cana-2576	272	38	hence	hence	ADV
cana-2576	272	39	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	272	40	)	)	PUNCT
cana-2576	273	1	=	=	SYM
cana-2576	273	2	5	5	X
cana-2576	273	3	.	.	PUNCT
cana-2576	273	4	case	case	NOUN
cana-2576	273	5	3.2	3.2	NUM
cana-2576	273	6	:	:	PUNCT
cana-2576	273	7	same	same	ADJ
cana-2576	273	8	as	as	ADP
cana-2576	273	9	case	case	NOUN
cana-2576	273	10	3.1	3.1	NUM
cana-2576	273	11	.	.	PUNCT
cana-2576	274	1	communications	communication	NOUN
cana-2576	274	2	on	on	ADP
cana-2576	274	3	applied	apply	VERB
cana-2576	274	4	nonlinear	nonlinear	ADJ
cana-2576	274	5	analysis	analysis	NOUN
cana-2576	274	6	issn	issn	NOUN
cana-2576	274	7	:	:	PUNCT
cana-2576	274	8	1074	1074	NUM
cana-2576	274	9	-	-	PUNCT
cana-2576	274	10	133x	133x	NUM
cana-2576	274	11	vol	vol	NOUN
cana-2576	274	12	32	32	NUM
cana-2576	274	13	no	no	NOUN
cana-2576	274	14	.	.	PUNCT
cana-2576	275	1	3s	3s	NUM
cana-2576	275	2	(	(	PUNCT
cana-2576	275	3	2025	2025	NUM
cana-2576	275	4	)	)	PUNCT
cana-2576	275	5	161	161	NUM
cana-2576	275	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-2576	275	7	case	case	NOUN
cana-2576	275	8	3.3	3.3	NUM
cana-2576	275	9	:	:	PUNCT
cana-2576	275	10	neither	neither	CCONJ
cana-2576	275	11	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	275	12	is	be	AUX
cana-2576	275	13	an	an	DET
cana-2576	275	14	initial	initial	ADJ
cana-2576	275	15	vertex	vertex	NOUN
cana-2576	275	16	nor	nor	CCONJ
cana-2576	275	17	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	275	18	is	be	AUX
cana-2576	275	19	an	an	DET
cana-2576	275	20	end	end	NOUN
cana-2576	275	21	vertex	vertex	NOUN
cana-2576	275	22	.	.	PUNCT
cana-2576	276	1	then	then	ADV
cana-2576	276	2	d(𝑣𝑖−1	d(𝑣𝑖−1	NUM
cana-2576	276	3	)	)	PUNCT
cana-2576	276	4	=	=	SYM
cana-2576	276	5	d(𝑣𝑖+1	d(𝑣𝑖+1	PROPN
cana-2576	276	6	)	)	PUNCT
cana-2576	276	7	=	=	SYM
cana-2576	277	1	3	3	X
cana-2576	277	2	.	.	PUNCT
cana-2576	278	1	so	so	ADV
cana-2576	278	2	,	,	PUNCT
cana-2576	278	3	we	we	PRON
cana-2576	278	4	can	can	AUX
cana-2576	278	5	not	not	PART
cana-2576	278	6	take	take	VERB
cana-2576	278	7	these	these	DET
cana-2576	278	8	two	two	NUM
cana-2576	278	9	vertices	vertex	NOUN
cana-2576	278	10	together	together	ADV
cana-2576	278	11	.	.	PUNCT
cana-2576	279	1	consider	consider	VERB
cana-2576	279	2	the	the	DET
cana-2576	279	3	vertices	vertex	NOUN
cana-2576	279	4	adjacent	adjacent	ADJ
cana-2576	279	5	to	to	ADP
cana-2576	279	6	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-2576	279	7	and	and	CCONJ
cana-2576	279	8	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-2576	279	9	in	in	ADP
cana-2576	279	10	the	the	DET
cana-2576	279	11	path	path	NOUN
cana-2576	279	12	.	.	PUNCT
cana-2576	280	1	let	let	VERB
cana-2576	280	2	them	they	PRON
cana-2576	280	3	be	be	AUX
cana-2576	280	4	𝑣𝑖−2	𝑣𝑖−2	ADJ
cana-2576	280	5	and	and	CCONJ
cana-2576	280	6	𝑣𝑖+2	𝑣𝑖+2	NOUN
cana-2576	280	7	.	.	PROPN
cana-2576	280	8	then	then	ADV
cana-2576	280	9	d(𝑣𝑖−2	d(𝑣𝑖−2	PROPN
cana-2576	280	10	)	)	PUNCT
cana-2576	281	1	=	=	SYM
cana-2576	281	2	4	4	NUM
cana-2576	281	3	if	if	SCONJ
cana-2576	281	4	it	it	PRON
cana-2576	281	5	is	be	AUX
cana-2576	281	6	an	an	DET
cana-2576	281	7	initial	initial	ADJ
cana-2576	281	8	vertex	vertex	NOUN
cana-2576	281	9	,	,	PUNCT
cana-2576	281	10	otherwise	otherwise	ADV
cana-2576	281	11	5	5	NUM
cana-2576	281	12	.	.	PUNCT
cana-2576	282	1	then	then	ADV
cana-2576	282	2	the	the	DET
cana-2576	282	3	set	set	NOUN
cana-2576	282	4	{	{	PUNCT
cana-2576	282	5	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	282	6	,	,	PUNCT
cana-2576	282	7	𝑣𝑖−2	𝑣𝑖−2	PROPN
cana-2576	282	8	,	,	PUNCT
cana-2576	282	9	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-2576	282	10	,	,	PUNCT
cana-2576	282	11	𝑤𝑖	𝑤𝑖	PRON
cana-2576	282	12	}	}	PUNCT
cana-2576	282	13	is	be	AUX
cana-2576	282	14	a	a	DET
cana-2576	282	15	relatively	relatively	ADV
cana-2576	282	16	prime	prime	ADJ
cana-2576	282	17	dominating	dominating	NOUN
cana-2576	282	18	set	set	NOUN
cana-2576	282	19	if	if	SCONJ
cana-2576	282	20	𝑣𝑖−2	𝑣𝑖−2	PROPN
cana-2576	282	21	is	be	AUX
cana-2576	282	22	an	an	DET
cana-2576	282	23	initial	initial	ADJ
cana-2576	282	24	vertex	vertex	NOUN
cana-2576	282	25	and	and	CCONJ
cana-2576	282	26	hence	hence	ADV
cana-2576	282	27	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	282	28	)	)	PUNCT
cana-2576	283	1	=	=	PUNCT
cana-2576	283	2	4	4	X
cana-2576	283	3	.	.	X
cana-2576	284	1	if	if	SCONJ
cana-2576	284	2	𝑣𝑖−2	𝑣𝑖−2	PROPN
cana-2576	284	3	is	be	AUX
cana-2576	284	4	not	not	PART
cana-2576	284	5	an	an	DET
cana-2576	284	6	initial	initial	ADJ
cana-2576	284	7	vertex	vertex	NOUN
cana-2576	284	8	,	,	PUNCT
cana-2576	284	9	𝑣𝑖+2	𝑣𝑖+2	PROPN
cana-2576	284	10	is	be	AUX
cana-2576	284	11	not	not	PART
cana-2576	284	12	an	an	DET
cana-2576	284	13	end	end	NOUN
cana-2576	284	14	vertex	vertex	NOUN
cana-2576	284	15	and	and	CCONJ
cana-2576	284	16	d(v	d(v	PROPN
cana-2576	284	17	)	)	PUNCT
cana-2576	284	18	is	be	AUX
cana-2576	284	19	not	not	PART
cana-2576	284	20	a	a	DET
cana-2576	284	21	multiple	multiple	NOUN
cana-2576	284	22	of	of	ADP
cana-2576	284	23	5	5	NUM
cana-2576	284	24	,	,	PUNCT
cana-2576	284	25	then	then	ADV
cana-2576	284	26	the	the	DET
cana-2576	284	27	set	set	NOUN
cana-2576	284	28	{	{	PUNCT
cana-2576	284	29	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	284	30	,	,	PUNCT
cana-2576	284	31	𝑣𝑖−2	𝑣𝑖−2	PROPN
cana-2576	284	32	,	,	PUNCT
cana-2576	284	33	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-2576	284	34	,	,	PUNCT
cana-2576	284	35	𝑤𝑖	𝑤𝑖	PRON
cana-2576	284	36	}	}	PUNCT
cana-2576	284	37	is	be	AUX
cana-2576	284	38	a	a	DET
cana-2576	284	39	relatively	relatively	ADV
cana-2576	284	40	prime	prime	ADJ
cana-2576	284	41	dominating	dominating	NOUN
cana-2576	284	42	set	set	NOUN
cana-2576	284	43	and	and	CCONJ
cana-2576	284	44	hence	hence	ADV
cana-2576	284	45	𝛾𝑟𝑝𝑑(𝐺𝑣	𝛾𝑟𝑝𝑑(𝐺𝑣	PROPN
cana-2576	284	46	)	)	PUNCT
cana-2576	285	1	=	=	PUNCT
cana-2576	286	1	4	4	X
cana-2576	286	2	.	.	PUNCT
cana-2576	286	3	otherwise	otherwise	ADV
cana-2576	286	4	,	,	PUNCT
cana-2576	286	5	relatively	relatively	ADV
cana-2576	286	6	prime	prime	ADJ
cana-2576	286	7	dominating	dominating	NOUN
cana-2576	286	8	set	set	NOUN
cana-2576	286	9	does	do	AUX
cana-2576	286	10	not	not	PART
cana-2576	286	11	exist	exist	VERB
cana-2576	286	12	.	.	PUNCT
cana-2576	287	1	4	4	X
cana-2576	287	2	.	.	X
cana-2576	287	3	relatively	relatively	ADV
cana-2576	287	4	prime	prime	ADJ
cana-2576	287	5	domination	domination	NOUN
cana-2576	287	6	number	number	NOUN
cana-2576	287	7	on	on	ADP
cana-2576	287	8	complement	complement	NOUN
cana-2576	287	9	of	of	ADP
cana-2576	287	10	quadrilateral	quadrilateral	ADJ
cana-2576	287	11	snake	snake	NOUN
cana-2576	287	12	graph	graph	NOUN
cana-2576	287	13	in	in	ADP
cana-2576	287	14	this	this	DET
cana-2576	287	15	section	section	NOUN
cana-2576	287	16	we	we	PRON
cana-2576	287	17	have	have	AUX
cana-2576	287	18	shown	show	VERB
cana-2576	287	19	that	that	SCONJ
cana-2576	287	20	the	the	DET
cana-2576	287	21	relatively	relatively	ADV
cana-2576	287	22	prime	prime	ADJ
cana-2576	287	23	domination	domination	NOUN
cana-2576	287	24	number	number	NOUN
cana-2576	287	25	for	for	ADP
cana-2576	287	26	complement	complement	NOUN
cana-2576	287	27	of	of	ADP
cana-2576	287	28	quadrilateral	quadrilateral	ADJ
cana-2576	287	29	type	type	NOUN
cana-2576	287	30	graphs	graph	NOUN
cana-2576	287	31	is	be	AUX
cana-2576	287	32	2	2	NUM
cana-2576	287	33	.	.	PUNCT
cana-2576	287	34	theorem	theorem	VERB
cana-2576	287	35	4.1	4.1	NUM
cana-2576	287	36	.	.	PUNCT
cana-2576	288	1	let	let	VERB
cana-2576	288	2	g	g	PRON
cana-2576	288	3	be	be	AUX
cana-2576	288	4	a	a	DET
cana-2576	288	5	quadrilateral	quadrilateral	ADJ
cana-2576	288	6	snake	snake	NOUN
cana-2576	288	7	graph	graph	NOUN
cana-2576	288	8	with	with	ADP
cana-2576	288	9	p	p	NOUN
cana-2576	288	10	vertices	vertex	NOUN
cana-2576	288	11	.	.	PUNCT
cana-2576	289	1	then	then	ADV
cana-2576	289	2	for	for	ADP
cana-2576	289	3	p	p	NOUN
cana-2576	289	4	is	be	AUX
cana-2576	289	5	even	even	ADV
cana-2576	289	6	,	,	PUNCT
cana-2576	289	7	𝛾𝑟𝑝𝑑(	𝛾𝑟𝑝𝑑(	PROPN
cana-2576	289	8	�	�	PROPN
cana-2576	289	9	̅	̅	NOUN
cana-2576	289	10	�	�	NOUN
cana-2576	289	11	)	)	PUNCT
cana-2576	289	12	=	=	SYM
cana-2576	289	13	2	2	X
cana-2576	289	14	.	.	X
cana-2576	289	15	proof	proof	NOUN
cana-2576	289	16	:	:	PUNCT
cana-2576	289	17	let	let	VERB
cana-2576	289	18	g	g	PRON
cana-2576	289	19	be	be	AUX
cana-2576	289	20	a	a	DET
cana-2576	289	21	quadrilateral	quadrilateral	ADJ
cana-2576	289	22	snake	snake	NOUN
cana-2576	289	23	graph	graph	NOUN
cana-2576	289	24	with	with	ADP
cana-2576	289	25	p	p	NOUN
cana-2576	289	26	vertices	vertex	NOUN
cana-2576	289	27	.	.	PUNCT
cana-2576	290	1	let	let	VERB
cana-2576	290	2	the	the	DET
cana-2576	290	3	vertices	vertex	NOUN
cana-2576	290	4	be	be	AUX
cana-2576	290	5	𝑣1,𝑣2	𝑣1,𝑣2	PROPN
cana-2576	290	6	,	,	PUNCT
cana-2576	290	7	…	…	PUNCT
cana-2576	290	8	𝑣𝑝.	𝑣𝑝.	NOUN
cana-2576	290	9	since	since	SCONJ
cana-2576	290	10	degree	degree	NOUN
cana-2576	290	11	of	of	ADP
cana-2576	290	12	each	each	DET
cana-2576	290	13	vertex	vertex	NOUN
cana-2576	290	14	in	in	ADP
cana-2576	290	15	the	the	DET
cana-2576	290	16	quadrilateral	quadrilateral	ADJ
cana-2576	290	17	snake	snake	NOUN
cana-2576	290	18	graph	graph	NOUN
cana-2576	290	19	g	g	PROPN
cana-2576	290	20	is	be	AUX
cana-2576	290	21	either	either	PRON
cana-2576	290	22	2	2	NUM
cana-2576	290	23	or	or	CCONJ
cana-2576	290	24	4	4	NUM
cana-2576	290	25	,	,	PUNCT
cana-2576	290	26	degree	degree	NOUN
cana-2576	290	27	of	of	ADP
cana-2576	290	28	each	each	DET
cana-2576	290	29	vertex	vertex	NOUN
cana-2576	290	30	in	in	ADP
cana-2576	290	31	the	the	DET
cana-2576	290	32	complement	complement	NOUN
cana-2576	290	33	of	of	ADP
cana-2576	290	34	quadrilateral	quadrilateral	ADJ
cana-2576	290	35	graph	graph	NOUN
cana-2576	290	36	�	�	NOUN
cana-2576	290	37	̅	̅	NOUN
cana-2576	290	38	�	�	NOUN
cana-2576	290	39	is	be	AUX
cana-2576	290	40	either	either	CCONJ
cana-2576	290	41	p–3	p–3	NOUN
cana-2576	290	42	or	or	CCONJ
cana-2576	290	43	p–5	p–5	NOUN
cana-2576	290	44	.	.	PUNCT
cana-2576	291	1	note	note	VERB
cana-2576	291	2	that	that	SCONJ
cana-2576	291	3	if	if	SCONJ
cana-2576	291	4	either	either	PRON
cana-2576	291	5	n	n	ADV
cana-2576	291	6	is	be	AUX
cana-2576	291	7	even	even	ADV
cana-2576	291	8	or	or	CCONJ
cana-2576	291	9	odd	odd	ADJ
cana-2576	291	10	,	,	PUNCT
cana-2576	291	11	then	then	ADV
cana-2576	291	12	p	p	X
cana-2576	291	13	–	–	PUNCT
cana-2576	291	14	3	3	NUM
cana-2576	291	15	and	and	CCONJ
cana-2576	291	16	p–5	p–5	NOUN
cana-2576	291	17	are	be	AUX
cana-2576	291	18	always	always	ADV
cana-2576	291	19	odd	odd	ADJ
cana-2576	291	20	and	and	CCONJ
cana-2576	291	21	hence	hence	ADV
cana-2576	291	22	(	(	PUNCT
cana-2576	291	23	p–3	p–3	NOUN
cana-2576	291	24	,	,	PUNCT
cana-2576	291	25	p–5	p–5	NOUN
cana-2576	291	26	)	)	PUNCT
cana-2576	291	27	=	=	SYM
cana-2576	292	1	1	1	X
cana-2576	292	2	.	.	X
cana-2576	292	3	consider	consider	VERB
cana-2576	292	4	a	a	DET
cana-2576	292	5	vertex	vertex	NOUN
cana-2576	292	6	which	which	PRON
cana-2576	292	7	has	have	VERB
cana-2576	292	8	degree	degree	NOUN
cana-2576	292	9	p–3	p–3	NOUN
cana-2576	292	10	.	.	PUNCT
cana-2576	293	1	then	then	ADV
cana-2576	293	2	this	this	DET
cana-2576	293	3	vertex	vertex	NOUN
cana-2576	293	4	,	,	PUNCT
cana-2576	293	5	say	say	VERB
cana-2576	293	6	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	293	7	covers	cover	VERB
cana-2576	293	8	all	all	DET
cana-2576	293	9	the	the	DET
cana-2576	293	10	vertices	vertex	NOUN
cana-2576	293	11	of	of	ADP
cana-2576	293	12	�	�	NOUN
cana-2576	293	13	̅	̅	NOUN
cana-2576	293	14	�	�	NOUN
cana-2576	293	15	except	except	SCONJ
cana-2576	293	16	the	the	DET
cana-2576	293	17	vertices	vertex	NOUN
cana-2576	293	18	,	,	PUNCT
cana-2576	293	19	say	say	VERB
cana-2576	293	20	𝑣𝑘	𝑣𝑘	ADV
cana-2576	293	21	and	and	CCONJ
cana-2576	293	22	𝑣𝑙.	𝑣𝑙.	VERB
cana-2576	293	23	in	in	ADP
cana-2576	293	24	order	order	NOUN
cana-2576	293	25	to	to	PART
cana-2576	293	26	find	find	VERB
cana-2576	293	27	a	a	DET
cana-2576	293	28	relatively	relatively	ADV
cana-2576	293	29	prime	prime	ADJ
cana-2576	293	30	dominating	dominating	NOUN
cana-2576	293	31	set	set	NOUN
cana-2576	293	32	,	,	PUNCT
cana-2576	293	33	choose	choose	VERB
cana-2576	293	34	a	a	DET
cana-2576	293	35	vertex	vertex	NOUN
cana-2576	293	36	of	of	ADP
cana-2576	293	37	degree	degree	NOUN
cana-2576	293	38	p–4	p–4	NOUN
cana-2576	293	39	,	,	PUNCT
cana-2576	293	40	say	say	VERB
cana-2576	293	41	𝑣𝑗	𝑣𝑗	ADP
cana-2576	293	42	which	which	PRON
cana-2576	293	43	has	have	VERB
cana-2576	293	44	adjacency	adjacency	NOUN
cana-2576	293	45	with	with	ADP
cana-2576	293	46	the	the	DET
cana-2576	293	47	vertices	vertex	NOUN
cana-2576	293	48	𝑣𝑘	𝑣𝑘	ADV
cana-2576	293	49	and	and	CCONJ
cana-2576	293	50	𝑣𝑙.	𝑣𝑙.	VERB
cana-2576	293	51	note	note	VERB
cana-2576	293	52	that	that	SCONJ
cana-2576	293	53	such	such	DET
cana-2576	293	54	a	a	DET
cana-2576	293	55	vertex	vertex	NOUN
cana-2576	293	56	is	be	AUX
cana-2576	293	57	always	always	ADV
cana-2576	293	58	exist	exist	VERB
cana-2576	293	59	,	,	PUNCT
cana-2576	293	60	since	since	SCONJ
cana-2576	293	61	|v|	|v|	NUM
cana-2576	293	62	≥	≥	NUM
cana-2576	293	63	6	6	NUM
cana-2576	293	64	.	.	PUNCT
cana-2576	294	1	since	since	SCONJ
cana-2576	294	2	these	these	DET
cana-2576	294	3	two	two	NUM
cana-2576	294	4	vertices	vertex	NOUN
cana-2576	294	5	𝑣𝑖	𝑣𝑖	ADV
cana-2576	294	6	and	and	CCONJ
cana-2576	294	7	𝑣𝑗	𝑣𝑗	ADP
cana-2576	294	8	satisfies	satisfie	NOUN
cana-2576	294	9	the	the	DET
cana-2576	294	10	conditions	condition	NOUN
cana-2576	294	11	for	for	ADP
cana-2576	294	12	being	be	AUX
cana-2576	294	13	a	a	DET
cana-2576	294	14	relatively	relatively	ADV
cana-2576	294	15	prime	prime	ADJ
cana-2576	294	16	dominating	dominating	NOUN
cana-2576	294	17	set	set	NOUN
cana-2576	294	18	,	,	PUNCT
cana-2576	294	19	we	we	PRON
cana-2576	294	20	have	have	VERB
cana-2576	294	21	𝛾𝑟𝑝𝑑(	𝛾𝑟𝑝𝑑(	PROPN
cana-2576	294	22	�	�	NOUN
cana-2576	294	23	̅	̅	NOUN
cana-2576	294	24	�	�	NOUN
cana-2576	294	25	)	)	PUNCT
cana-2576	294	26	=	=	SYM
cana-2576	295	1	2	2	X
cana-2576	295	2	.	.	X
cana-2576	295	3	theorem	theorem	VERB
cana-2576	295	4	4.2	4.2	NUM
cana-2576	295	5	.	.	PUNCT
cana-2576	296	1	for	for	ADP
cana-2576	296	2	any	any	DET
cana-2576	296	3	alternate	alternate	ADJ
cana-2576	296	4	quadrilateral	quadrilateral	ADJ
cana-2576	296	5	snake	snake	NOUN
cana-2576	296	6	graph	graph	NOUN
cana-2576	296	7	g	g	PROPN
cana-2576	296	8	,	,	PUNCT
cana-2576	296	9	𝛾𝑟𝑝𝑑(	𝛾𝑟𝑝𝑑(	PROPN
cana-2576	296	10	�	�	PROPN
cana-2576	296	11	̅	̅	NOUN
cana-2576	296	12	�	�	NOUN
cana-2576	296	13	)	)	PUNCT
cana-2576	296	14	=	=	SYM
cana-2576	296	15	2	2	NUM
cana-2576	296	16	proof	proof	NOUN
cana-2576	296	17	:	:	PUNCT
cana-2576	296	18	let	let	VERB
cana-2576	296	19	g	g	PRON
cana-2576	296	20	be	be	AUX
cana-2576	296	21	alternate	alternate	ADJ
cana-2576	296	22	quadrilateral	quadrilateral	ADJ
cana-2576	296	23	snake	snake	NOUN
cana-2576	296	24	graph	graph	NOUN
cana-2576	296	25	with	with	ADP
cana-2576	296	26	p	p	NOUN
cana-2576	296	27	vertices	vertex	NOUN
cana-2576	296	28	.let	.let	PUNCT
cana-2576	297	1	the	the	DET
cana-2576	297	2	vertices	vertex	NOUN
cana-2576	297	3	in	in	ADP
cana-2576	297	4	the	the	DET
cana-2576	297	5	path	path	NOUN
cana-2576	297	6	be	be	AUX
cana-2576	297	7	𝑣1,𝑣2	𝑣1,𝑣2	PROPN
cana-2576	297	8	,	,	PUNCT
cana-2576	297	9	…	…	PUNCT
cana-2576	297	10	,	,	PUNCT
cana-2576	297	11	𝑣𝑝.	𝑣𝑝.	NOUN
cana-2576	297	12	since	since	SCONJ
cana-2576	297	13	degree	degree	NOUN
cana-2576	297	14	of	of	ADP
cana-2576	297	15	each	each	DET
cana-2576	297	16	vertex	vertex	NOUN
cana-2576	297	17	in	in	ADP
cana-2576	297	18	an	an	DET
cana-2576	297	19	alternate	alternate	ADJ
cana-2576	297	20	quadrilateral	quadrilateral	ADJ
cana-2576	297	21	snake	snake	NOUN
cana-2576	297	22	graph	graph	NOUN
cana-2576	297	23	is	be	AUX
cana-2576	297	24	either	either	PRON
cana-2576	297	25	2	2	NUM
cana-2576	297	26	or	or	CCONJ
cana-2576	297	27	3	3	NUM
cana-2576	297	28	,	,	PUNCT
cana-2576	297	29	degree	degree	NOUN
cana-2576	297	30	of	of	ADP
cana-2576	297	31	each	each	DET
cana-2576	297	32	vertex	vertex	NOUN
cana-2576	297	33	in	in	ADP
cana-2576	297	34	the	the	DET
cana-2576	297	35	complement	complement	NOUN
cana-2576	297	36	of	of	ADP
cana-2576	297	37	alternate	alternate	ADJ
cana-2576	297	38	quadrilateral	quadrilateral	ADJ
cana-2576	297	39	snake	snake	NOUN
cana-2576	297	40	graph	graph	NOUN
cana-2576	297	41	is	be	AUX
cana-2576	297	42	either	either	CCONJ
cana-2576	297	43	p-3	p-3	NOUN
cana-2576	297	44	or	or	CCONJ
cana-2576	297	45	p-4	p-4	NOUN
cana-2576	297	46	.	.	PUNCT
cana-2576	298	1	choose	choose	VERB
cana-2576	298	2	a	a	DET
cana-2576	298	3	vertex	vertex	NOUN
cana-2576	298	4	of	of	ADP
cana-2576	298	5	degree	degree	NOUN
cana-2576	298	6	p-3	p-3	NOUN
cana-2576	298	7	,	,	PUNCT
cana-2576	298	8	say	say	VERB
cana-2576	298	9	𝑣𝑖.	𝑣𝑖.	NOUN
cana-2576	298	10	this	this	DET
cana-2576	298	11	vertex	vertex	NOUN
cana-2576	298	12	cover	cover	VERB
cana-2576	298	13	all	all	DET
cana-2576	298	14	the	the	DET
cana-2576	298	15	vertices	vertex	NOUN
cana-2576	298	16	of	of	ADP
cana-2576	298	17	�	�	NOUN
cana-2576	298	18	̅	̅	NOUN
cana-2576	298	19	�	�	NOUN
cana-2576	298	20	except	except	SCONJ
cana-2576	298	21	two	two	NUM
cana-2576	298	22	vertices	vertex	NOUN
cana-2576	298	23	,	,	PUNCT
cana-2576	298	24	namely	namely	ADV
cana-2576	298	25	𝑣𝑘	𝑣𝑘	ADV
cana-2576	298	26	and	and	CCONJ
cana-2576	298	27	𝑣𝑙.	𝑣𝑙.	VERB
cana-2576	298	28	now	now	ADV
cana-2576	298	29	,	,	PUNCT
cana-2576	298	30	choose	choose	VERB
cana-2576	298	31	a	a	DET
cana-2576	298	32	vertex	vertex	NOUN
cana-2576	298	33	of	of	ADP
cana-2576	298	34	degree	degree	NOUN
cana-2576	298	35	p-4	p-4	NOUN
cana-2576	298	36	,	,	PUNCT
cana-2576	298	37	say	say	VERB
cana-2576	298	38	𝑣𝑗	𝑣𝑗	ADP
cana-2576	298	39	such	such	ADJ
cana-2576	298	40	that	that	SCONJ
cana-2576	298	41	it	it	PRON
cana-2576	298	42	has	have	AUX
cana-2576	298	43	adjacent	adjacent	ADJ
cana-2576	298	44	with	with	ADP
cana-2576	298	45	the	the	DET
cana-2576	298	46	vertices	vertex	NOUN
cana-2576	298	47	𝑣𝑘	𝑣𝑘	ADV
cana-2576	298	48	and	and	CCONJ
cana-2576	298	49	𝑣𝑙.	𝑣𝑙.	VERB
cana-2576	298	50	such	such	DET
cana-2576	298	51	a	a	DET
cana-2576	298	52	vertex	vertex	NOUN
cana-2576	298	53	always	always	ADV
cana-2576	298	54	exists	exist	VERB
cana-2576	298	55	,	,	PUNCT
cana-2576	298	56	since|𝑉|	since|𝑉|	X
cana-2576	298	57	≥	≥	NUM
cana-2576	298	58	6	6	NUM
cana-2576	298	59	.	.	PUNCT
cana-2576	299	1	since	since	SCONJ
cana-2576	299	2	these	these	DET
cana-2576	299	3	two	two	NUM
cana-2576	299	4	vertices	vertex	NOUN
cana-2576	299	5	𝑣𝑖	𝑣𝑖	ADV
cana-2576	299	6	and	and	CCONJ
cana-2576	299	7	𝑣𝑗	𝑣𝑗	ADP
cana-2576	299	8	satisfies	satisfie	NOUN
cana-2576	299	9	the	the	DET
cana-2576	299	10	conditions	condition	NOUN
cana-2576	299	11	for	for	ADP
cana-2576	299	12	being	be	AUX
cana-2576	299	13	a	a	DET
cana-2576	299	14	relatively	relatively	ADV
cana-2576	299	15	prime	prime	ADJ
cana-2576	299	16	dominating	dominating	NOUN
cana-2576	299	17	set	set	NOUN
cana-2576	299	18	,	,	PUNCT
cana-2576	299	19	we	we	PRON
cana-2576	299	20	have	have	VERB
cana-2576	299	21	𝛾𝑟𝑝𝑑(	𝛾𝑟𝑝𝑑(	PROPN
cana-2576	299	22	�	�	NOUN
cana-2576	299	23	̅	̅	NOUN
cana-2576	299	24	�	�	NOUN
cana-2576	299	25	)	)	PUNCT
cana-2576	299	26	=	=	SYM
cana-2576	300	1	2	2	X
cana-2576	300	2	.	.	X
cana-2576	300	3	theorem	theorem	VERB
cana-2576	300	4	4.3	4.3	NUM
cana-2576	300	5	.	.	PUNCT
cana-2576	301	1	for	for	ADP
cana-2576	301	2	any	any	DET
cana-2576	301	3	double	double	ADJ
cana-2576	301	4	quadrilateral	quadrilateral	ADJ
cana-2576	301	5	snake	snake	NOUN
cana-2576	301	6	graph	graph	NOUN
cana-2576	301	7	g	g	PROPN
cana-2576	301	8	,	,	PUNCT
cana-2576	301	9	𝛾𝑟𝑝𝑑(	𝛾𝑟𝑝𝑑(	PROPN
cana-2576	301	10	�	�	PROPN
cana-2576	301	11	̅	̅	NOUN
cana-2576	301	12	�	�	NOUN
cana-2576	301	13	)	)	PUNCT
cana-2576	301	14	=	=	SYM
cana-2576	301	15	2	2	X
cana-2576	301	16	.	.	X
cana-2576	301	17	proof	proof	NOUN
cana-2576	301	18	:	:	PUNCT
cana-2576	301	19	let	let	VERB
cana-2576	301	20	g	g	PRON
cana-2576	301	21	be	be	AUX
cana-2576	301	22	a	a	DET
cana-2576	301	23	double	double	ADJ
cana-2576	301	24	quadrilateral	quadrilateral	ADJ
cana-2576	301	25	snake	snake	NOUN
cana-2576	301	26	graph	graph	NOUN
cana-2576	301	27	with	with	ADP
cana-2576	301	28	p	p	NOUN
cana-2576	301	29	vertices	vertex	NOUN
cana-2576	301	30	.	.	PUNCT
cana-2576	302	1	let	let	VERB
cana-2576	302	2	the	the	DET
cana-2576	302	3	vertices	vertex	NOUN
cana-2576	302	4	be	be	AUX
cana-2576	302	5	𝑣1,𝑣2	𝑣1,𝑣2	PROPN
cana-2576	302	6	,	,	PUNCT
cana-2576	302	7	…	…	PUNCT
cana-2576	302	8	𝑣𝑝.	𝑣𝑝.	NOUN
cana-2576	302	9	we	we	PRON
cana-2576	302	10	know	know	VERB
cana-2576	302	11	that	that	SCONJ
cana-2576	302	12	,	,	PUNCT
cana-2576	302	13	in	in	ADP
cana-2576	302	14	the	the	DET
cana-2576	302	15	double	double	ADJ
cana-2576	302	16	quadrilateral	quadrilateral	ADJ
cana-2576	302	17	snake	snake	NOUN
cana-2576	302	18	graph	graph	NOUN
cana-2576	302	19	,	,	PUNCT
cana-2576	302	20	degree	degree	NOUN
cana-2576	302	21	of	of	ADP
cana-2576	302	22	each	each	DET
cana-2576	302	23	vertex	vertex	NOUN
cana-2576	302	24	is	be	AUX
cana-2576	302	25	either	either	CCONJ
cana-2576	302	26	2,3	2,3	NUM
cana-2576	302	27	or	or	CCONJ
cana-2576	302	28	6	6	NUM
cana-2576	302	29	.	.	PUNCT
cana-2576	303	1	hence	hence	ADV
cana-2576	303	2	in	in	ADP
cana-2576	303	3	the	the	DET
cana-2576	303	4	complement	complement	NOUN
cana-2576	303	5	graph	graph	NOUN
cana-2576	303	6	�	�	NOUN
cana-2576	303	7	̅	̅	NOUN
cana-2576	303	8	�	�	NOUN
cana-2576	303	9	,	,	PUNCT
cana-2576	303	10	degree	degree	NOUN
cana-2576	303	11	of	of	ADP
cana-2576	303	12	each	each	DET
cana-2576	303	13	vertex	vertex	NOUN
cana-2576	303	14	is	be	AUX
cana-2576	303	15	either	either	PRON
cana-2576	303	16	p–3	p–3	NOUN
cana-2576	303	17	,	,	PUNCT
cana-2576	303	18	p–4	p–4	NOUN
cana-2576	303	19	or	or	CCONJ
cana-2576	303	20	p–7	p–7	PROPN
cana-2576	303	21	.	.	PUNCT
cana-2576	304	1	choose	choose	VERB
cana-2576	304	2	a	a	DET
cana-2576	304	3	vertex	vertex	NOUN
cana-2576	304	4	of	of	ADP
cana-2576	304	5	degree	degree	NOUN
cana-2576	304	6	p–3	p–3	NOUN
cana-2576	304	7	,	,	PUNCT
cana-2576	304	8	say	say	VERB
cana-2576	304	9	𝑣𝑖.	𝑣𝑖.	NOUN
cana-2576	304	10	since	since	SCONJ
cana-2576	304	11	this	this	DET
cana-2576	304	12	vertex	vertex	NOUN
cana-2576	304	13	cover	cover	VERB
cana-2576	304	14	all	all	DET
cana-2576	304	15	the	the	DET
cana-2576	304	16	vertices	vertex	NOUN
cana-2576	304	17	of	of	ADP
cana-2576	304	18	�	�	NOUN
cana-2576	304	19	̅	̅	NOUN
cana-2576	304	20	�	�	NOUN
cana-2576	304	21	except	except	SCONJ
cana-2576	304	22	two	two	NUM
cana-2576	304	23	vertices	vertex	NOUN
cana-2576	304	24	say	say	VERB
cana-2576	304	25	,	,	PUNCT
cana-2576	304	26	𝑣𝑘	𝑣𝑘	ADV
cana-2576	304	27	and	and	CCONJ
cana-2576	304	28	𝑣𝑙	𝑣𝑙	NOUN
cana-2576	304	29	,	,	PUNCT
cana-2576	304	30	we	we	PRON
cana-2576	304	31	have	have	VERB
cana-2576	304	32	to	to	PART
cana-2576	304	33	choose	choose	VERB
cana-2576	304	34	a	a	DET
cana-2576	304	35	vertex	vertex	NOUN
cana-2576	304	36	of	of	ADP
cana-2576	304	37	degree	degree	NOUN
cana-2576	304	38	n	n	CCONJ
cana-2576	304	39	–	–	PUNCT
cana-2576	304	40	4	4	NUM
cana-2576	304	41	such	such	ADJ
cana-2576	304	42	that	that	SCONJ
cana-2576	304	43	it	it	PRON
cana-2576	304	44	has	have	VERB
cana-2576	304	45	adjacency	adjacency	NOUN
cana-2576	304	46	with	with	ADP
cana-2576	304	47	the	the	DET
cana-2576	304	48	two	two	NUM
cana-2576	304	49	vertices	vertex	NOUN
cana-2576	304	50	𝑣𝑘	𝑣𝑘	ADV
cana-2576	304	51	and	and	CCONJ
cana-2576	304	52	𝑣𝑙.	𝑣𝑙.	VERB
cana-2576	304	53	such	such	DET
cana-2576	304	54	a	a	DET
cana-2576	304	55	vertex	vertex	NOUN
cana-2576	304	56	always	always	ADV
cana-2576	304	57	exists	exist	VERB
cana-2576	304	58	,	,	PUNCT
cana-2576	304	59	since	since	SCONJ
cana-2576	304	60	|v|	|v|	NUM
cana-2576	304	61	≥	≥	NUM
cana-2576	304	62	6	6	NUM
cana-2576	304	63	.	.	PUNCT
cana-2576	305	1	let	let	VERB
cana-2576	305	2	the	the	DET
cana-2576	305	3	vertex	vertex	NOUN
cana-2576	305	4	which	which	PRON
cana-2576	305	5	has	have	VERB
cana-2576	305	6	degree	degree	NOUN
cana-2576	305	7	p–4	p–4	NOUN
cana-2576	305	8	be	be	AUX
cana-2576	305	9	𝑣𝑗	𝑣𝑗	ADP
cana-2576	305	10	.	.	PUNCT
cana-2576	306	1	now	now	ADV
cana-2576	306	2	,	,	PUNCT
cana-2576	306	3	clearly	clearly	ADV
cana-2576	306	4	the	the	DET
cana-2576	306	5	two	two	NUM
cana-2576	306	6	vertices	vertex	NOUN
cana-2576	306	7	𝑣𝑖	𝑣𝑖	ADV
cana-2576	306	8	and	and	CCONJ
cana-2576	306	9	𝑣𝑗	𝑣𝑗	AUX
cana-2576	306	10	cover	cover	VERB
cana-2576	306	11	all	all	DET
cana-2576	306	12	the	the	DET
cana-2576	306	13	vertices	vertex	NOUN
cana-2576	306	14	of	of	ADP
cana-2576	306	15	�	�	NOUN
cana-2576	306	16	̅	̅	NOUN
cana-2576	306	17	�	�	PROPN
cana-2576	306	18	and	and	CCONJ
cana-2576	306	19	(	(	PUNCT
cana-2576	306	20	d(𝑣𝑖),d(𝑣𝑗	d(𝑣𝑖),d(𝑣𝑗	PROPN
cana-2576	306	21	)	)	PUNCT
cana-2576	306	22	)	)	PUNCT
cana-2576	307	1	=	=	PRON
cana-2576	307	2	(	(	PUNCT
cana-2576	307	3	p–3	p–3	NOUN
cana-2576	307	4	,	,	PUNCT
cana-2576	307	5	p–4	p–4	NOUN
cana-2576	307	6	)	)	PUNCT
cana-2576	307	7	=	=	SYM
cana-2576	308	1	1	1	X
cana-2576	308	2	.	.	PUNCT
cana-2576	308	3	therefore	therefore	ADV
cana-2576	308	4	,	,	PUNCT
cana-2576	308	5	relatively	relatively	ADV
cana-2576	308	6	prime	prime	ADJ
cana-2576	308	7	dominating	dominating	NOUN
cana-2576	308	8	set	set	NOUN
cana-2576	308	9	is	be	AUX
cana-2576	308	10	{	{	PUNCT
cana-2576	308	11	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	308	12	,	,	PUNCT
cana-2576	308	13	𝑣𝑗	𝑣𝑗	ADP
cana-2576	308	14	}	}	PUNCT
cana-2576	308	15	and	and	CCONJ
cana-2576	308	16	hence	hence	ADV
cana-2576	308	17	𝛾𝑟𝑝𝑑(	𝛾𝑟𝑝𝑑(	ADV
cana-2576	308	18	�	�	PROPN
cana-2576	308	19	̅	̅	NOUN
cana-2576	308	20	�	�	NOUN
cana-2576	308	21	)	)	PUNCT
cana-2576	308	22	=	=	SYM
cana-2576	308	23	2	2	X
cana-2576	308	24	.	.	X
cana-2576	308	25	communications	communication	NOUN
cana-2576	308	26	on	on	ADP
cana-2576	308	27	applied	apply	VERB
cana-2576	308	28	nonlinear	nonlinear	ADJ
cana-2576	308	29	analysis	analysis	NOUN
cana-2576	308	30	issn	issn	NOUN
cana-2576	308	31	:	:	PUNCT
cana-2576	308	32	1074	1074	NUM
cana-2576	308	33	-	-	PUNCT
cana-2576	308	34	133x	133x	NUM
cana-2576	308	35	vol	vol	NOUN
cana-2576	308	36	32	32	NUM
cana-2576	308	37	no	no	NOUN
cana-2576	308	38	.	.	PUNCT
cana-2576	309	1	3s	3s	NUM
cana-2576	309	2	(	(	PUNCT
cana-2576	309	3	2025	2025	NUM
cana-2576	309	4	)	)	PUNCT
cana-2576	309	5	162	162	NUM
cana-2576	309	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2576	309	7	theorem	theorem	VERB
cana-2576	309	8	4.4	4.4	NUM
cana-2576	309	9	.	.	PUNCT
cana-2576	310	1	for	for	ADP
cana-2576	310	2	any	any	DET
cana-2576	310	3	double	double	ADJ
cana-2576	310	4	alternate	alternate	ADJ
cana-2576	310	5	quadrilateral	quadrilateral	ADJ
cana-2576	310	6	snake	snake	NOUN
cana-2576	310	7	graph	graph	NOUN
cana-2576	310	8	g	g	PROPN
cana-2576	310	9	,	,	PUNCT
cana-2576	310	10	𝛾𝑟𝑝𝑑(	𝛾𝑟𝑝𝑑(	PROPN
cana-2576	310	11	�	�	PROPN
cana-2576	310	12	̅	̅	NOUN
cana-2576	310	13	�	�	NOUN
cana-2576	310	14	)	)	PUNCT
cana-2576	310	15	=	=	SYM
cana-2576	310	16	2	2	X
cana-2576	310	17	.	.	X
cana-2576	310	18	proof	proof	NOUN
cana-2576	310	19	:	:	PUNCT
cana-2576	310	20	let	let	VERB
cana-2576	310	21	g	g	PRON
cana-2576	310	22	be	be	AUX
cana-2576	310	23	a	a	DET
cana-2576	310	24	double	double	ADJ
cana-2576	310	25	alternate	alternate	ADJ
cana-2576	310	26	quadrilateral	quadrilateral	ADJ
cana-2576	310	27	snake	snake	NOUN
cana-2576	310	28	graph	graph	NOUN
cana-2576	310	29	with	with	ADP
cana-2576	310	30	p	p	NOUN
cana-2576	310	31	vertices	vertex	NOUN
cana-2576	310	32	.	.	PUNCT
cana-2576	311	1	let	let	VERB
cana-2576	311	2	the	the	DET
cana-2576	311	3	vertices	vertex	NOUN
cana-2576	311	4	in	in	ADP
cana-2576	311	5	g	g	PROPN
cana-2576	311	6	be	be	AUX
cana-2576	311	7	𝑣1	𝑣1	PROPN
cana-2576	311	8	,	,	PUNCT
cana-2576	311	9	𝑣2	𝑣2	PROPN
cana-2576	311	10	,	,	PUNCT
cana-2576	311	11	…	…	PUNCT
cana-2576	311	12	,	,	PUNCT
cana-2576	311	13	𝑣𝑝.	𝑣𝑝.	NOUN
cana-2576	311	14	then	then	ADV
cana-2576	311	15	degree	degree	VERB
cana-2576	311	16	of	of	ADP
cana-2576	311	17	each	each	DET
cana-2576	311	18	vertex	vertex	NOUN
cana-2576	311	19	in	in	ADP
cana-2576	311	20	the	the	DET
cana-2576	311	21	complement	complement	NOUN
cana-2576	311	22	of	of	ADP
cana-2576	311	23	double	double	ADJ
cana-2576	311	24	alternative	alternative	ADJ
cana-2576	311	25	quadrilateral	quadrilateral	ADJ
cana-2576	311	26	snake	snake	NOUN
cana-2576	311	27	graph	graph	NOUN
cana-2576	311	28	�	�	PROPN
cana-2576	311	29	̅	̅	NOUN
cana-2576	311	30	�	�	NOUN
cana-2576	311	31	is	be	AUX
cana-2576	311	32	either	either	CCONJ
cana-2576	311	33	p-3	p-3	NOUN
cana-2576	311	34	,	,	PUNCT
cana-2576	311	35	p-4	p-4	NOUN
cana-2576	311	36	or	or	CCONJ
cana-2576	311	37	p-5	p-5	PROPN
cana-2576	311	38	,	,	PUNCT
cana-2576	311	39	since	since	SCONJ
cana-2576	311	40	degree	degree	NOUN
cana-2576	311	41	of	of	ADP
cana-2576	311	42	each	each	DET
cana-2576	311	43	vertex	vertex	NOUN
cana-2576	311	44	in	in	ADP
cana-2576	311	45	a	a	DET
cana-2576	311	46	double	double	ADJ
cana-2576	311	47	alternate	alternate	ADJ
cana-2576	311	48	quadrilateral	quadrilateral	ADJ
cana-2576	311	49	snake	snake	NOUN
cana-2576	311	50	graph	graph	NOUN
cana-2576	311	51	is	be	AUX
cana-2576	311	52	2	2	NUM
cana-2576	311	53	,	,	PUNCT
cana-2576	311	54	3	3	NUM
cana-2576	311	55	or	or	CCONJ
cana-2576	311	56	4	4	NUM
cana-2576	311	57	.	.	X
cana-2576	311	58	consider	consider	VERB
cana-2576	311	59	a	a	DET
cana-2576	311	60	vertex	vertex	NOUN
cana-2576	311	61	which	which	PRON
cana-2576	311	62	has	have	VERB
cana-2576	311	63	degree	degree	NOUN
cana-2576	311	64	p-3	p-3	NOUN
cana-2576	311	65	,	,	PUNCT
cana-2576	311	66	say	say	VERB
cana-2576	311	67	𝑣𝑖.	𝑣𝑖.	NOUN
cana-2576	311	68	this	this	DET
cana-2576	311	69	vertex	vertex	NOUN
cana-2576	311	70	covers	cover	VERB
cana-2576	311	71	all	all	DET
cana-2576	311	72	the	the	DET
cana-2576	311	73	vertices	vertex	NOUN
cana-2576	311	74	of	of	ADP
cana-2576	311	75	𝐺	𝐺	PROPN
cana-2576	311	76	̅except	̅except	VERB
cana-2576	311	77	two	two	NUM
cana-2576	311	78	vertices	vertex	NOUN
cana-2576	311	79	,	,	PUNCT
cana-2576	311	80	say	say	VERB
cana-2576	311	81	𝑣𝑘	𝑣𝑘	ADV
cana-2576	311	82	and	and	CCONJ
cana-2576	311	83	𝑣𝑙.	𝑣𝑙.	VERB
cana-2576	311	84	now	now	ADV
cana-2576	311	85	,	,	PUNCT
cana-2576	311	86	choose	choose	VERB
cana-2576	311	87	a	a	DET
cana-2576	311	88	vertex	vertex	NOUN
cana-2576	311	89	degree	degree	NOUN
cana-2576	311	90	p-4	p-4	NOUN
cana-2576	311	91	such	such	ADJ
cana-2576	311	92	that	that	SCONJ
cana-2576	311	93	it	it	PRON
cana-2576	311	94	has	have	VERB
cana-2576	311	95	adjacency	adjacency	NOUN
cana-2576	311	96	with	with	ADP
cana-2576	311	97	the	the	DET
cana-2576	311	98	vertices	vertex	NOUN
cana-2576	311	99	𝑣𝑘	𝑣𝑘	ADV
cana-2576	311	100	and	and	CCONJ
cana-2576	311	101	𝑣𝑙	𝑣𝑙	PROPN
cana-2576	311	102	.	.	PUNCT
cana-2576	312	1	such	such	DET
cana-2576	312	2	a	a	DET
cana-2576	312	3	vertex	vertex	NOUN
cana-2576	312	4	is	be	AUX
cana-2576	312	5	always	always	ADV
cana-2576	312	6	possible	possible	ADJ
cana-2576	312	7	,	,	PUNCT
cana-2576	312	8	since	since	SCONJ
cana-2576	312	9	|𝑉|	|𝑉|	NOUN
cana-2576	312	10	>	>	X
cana-2576	312	11	6	6	NUM
cana-2576	312	12	.	.	PUNCT
cana-2576	313	1	let	let	VERB
cana-2576	313	2	the	the	DET
cana-2576	313	3	vertex	vertex	NOUN
cana-2576	313	4	which	which	PRON
cana-2576	313	5	has	have	VERB
cana-2576	313	6	degree	degree	NOUN
cana-2576	313	7	p-4	p-4	NOUN
cana-2576	313	8	be	be	AUX
cana-2576	313	9	𝑣𝑗	𝑣𝑗	ADP
cana-2576	313	10	.	.	PUNCT
cana-2576	314	1	hence	hence	ADV
cana-2576	314	2	the	the	DET
cana-2576	314	3	relatively	relatively	ADV
cana-2576	314	4	prime	prime	ADJ
cana-2576	314	5	dominating	dominating	NOUN
cana-2576	314	6	set	set	NOUN
cana-2576	314	7	is	be	AUX
cana-2576	314	8	{	{	PUNCT
cana-2576	314	9	𝑣𝑖	𝑣𝑖	NOUN
cana-2576	314	10	,	,	PUNCT
cana-2576	314	11	𝑣𝑗	𝑣𝑗	ADP
cana-2576	314	12	}	}	PUNCT
cana-2576	314	13	and	and	CCONJ
cana-2576	314	14	the	the	DET
cana-2576	314	15	relatively	relatively	ADV
cana-2576	314	16	prime	prime	ADJ
cana-2576	314	17	domination	domination	NOUN
cana-2576	314	18	number	number	NOUN
cana-2576	314	19	is	be	AUX
cana-2576	314	20	2	2	NUM
cana-2576	314	21	.	.	NOUN
cana-2576	314	22	5	5	NUM
cana-2576	314	23	.	.	X
cana-2576	314	24	conclusion	conclusion	NOUN
cana-2576	314	25	dominations	domination	NOUN
cana-2576	314	26	in	in	ADP
cana-2576	314	27	graph	graph	NOUN
cana-2576	314	28	theory	theory	NOUN
cana-2576	314	29	is	be	AUX
cana-2576	314	30	a	a	DET
cana-2576	314	31	wide	wide	ADJ
cana-2576	314	32	area	area	NOUN
cana-2576	314	33	with	with	ADP
cana-2576	314	34	more	more	ADJ
cana-2576	314	35	applications	application	NOUN
cana-2576	314	36	to	to	ADP
cana-2576	314	37	real	real	ADJ
cana-2576	314	38	life	life	NOUN
cana-2576	314	39	which	which	PRON
cana-2576	314	40	helps	help	VERB
cana-2576	314	41	the	the	DET
cana-2576	314	42	researchers	researcher	NOUN
cana-2576	314	43	to	to	PART
cana-2576	314	44	get	get	VERB
cana-2576	314	45	more	more	ADJ
cana-2576	314	46	ideas	idea	NOUN
cana-2576	314	47	to	to	PART
cana-2576	314	48	manage	manage	VERB
cana-2576	314	49	the	the	DET
cana-2576	314	50	problems	problem	NOUN
cana-2576	314	51	in	in	ADP
cana-2576	314	52	real	real	ADJ
cana-2576	314	53	life	life	NOUN
cana-2576	314	54	situation	situation	NOUN
cana-2576	314	55	.	.	PUNCT
cana-2576	315	1	the	the	DET
cana-2576	315	2	standard	standard	ADJ
cana-2576	315	3	purpose	purpose	NOUN
cana-2576	315	4	of	of	ADP
cana-2576	315	5	the	the	DET
cana-2576	315	6	paper	paper	NOUN
cana-2576	315	7	is	be	AUX
cana-2576	315	8	to	to	PART
cana-2576	315	9	explain	explain	VERB
cana-2576	315	10	the	the	DET
cana-2576	315	11	significance	significance	NOUN
cana-2576	315	12	of	of	ADP
cana-2576	315	13	dominating	dominating	NOUN
cana-2576	315	14	sets	set	NOUN
cana-2576	315	15	and	and	CCONJ
cana-2576	315	16	relatively	relatively	ADV
cana-2576	315	17	prime	prime	ADJ
cana-2576	315	18	domination	domination	NOUN
cana-2576	315	19	number	number	NOUN
cana-2576	315	20	.	.	PUNCT
cana-2576	316	1	we	we	PRON
cana-2576	316	2	have	have	AUX
cana-2576	316	3	examined	examine	VERB
cana-2576	316	4	the	the	DET
cana-2576	316	5	idea	idea	NOUN
cana-2576	316	6	of	of	ADP
cana-2576	316	7	relatively	relatively	ADV
cana-2576	316	8	prime	prime	ADJ
cana-2576	316	9	dominations	domination	NOUN
cana-2576	316	10	in	in	ADP
cana-2576	316	11	various	various	ADJ
cana-2576	316	12	types	type	NOUN
cana-2576	316	13	of	of	ADP
cana-2576	316	14	quadrilateral	quadrilateral	ADJ
cana-2576	316	15	snake	snake	NOUN
cana-2576	316	16	graphs	graph	NOUN
cana-2576	316	17	and	and	CCONJ
cana-2576	316	18	also	also	ADV
cana-2576	316	19	their	their	PRON
cana-2576	316	20	complements	complement	NOUN
cana-2576	316	21	.	.	PUNCT
cana-2576	317	1	references	reference	NOUN
cana-2576	317	2	[	[	X
cana-2576	317	3	1	1	NUM
cana-2576	317	4	]	]	PUNCT
cana-2576	317	5	berge	berge	NOUN
cana-2576	317	6	c.	c.	PROPN
cana-2576	317	7	1962	1962	NUM
cana-2576	317	8	.	.	PUNCT
cana-2576	318	1	theory	theory	NOUN
cana-2576	318	2	of	of	ADP
cana-2576	318	3	graphs	graph	NOUN
cana-2576	318	4	and	and	CCONJ
cana-2576	318	5	its	its	PRON
cana-2576	318	6	applications	application	NOUN
cana-2576	318	7	.	.	PUNCT
cana-2576	319	1	london	london	PROPN
cana-2576	319	2	:	:	PUNCT
cana-2576	319	3	methuen	methuen	PROPN
cana-2576	319	4	.	.	PUNCT
cana-2576	320	1	[	[	X
cana-2576	320	2	2	2	NUM
cana-2576	320	3	]	]	X
cana-2576	320	4	harary	harary	PROPN
cana-2576	320	5	f.	f.	PROPN
cana-2576	320	6	1972	1972	NUM
cana-2576	320	7	.	.	PUNCT
cana-2576	321	1	graph	graph	NOUN
cana-2576	321	2	theory	theory	NOUN
cana-2576	321	3	.	.	PUNCT
cana-2576	322	1	california	california	PROPN
cana-2576	322	2	:	:	PUNCT
cana-2576	322	3	addison	addison	PROPN
cana-2576	322	4	-	-	PUNCT
cana-2576	322	5	wesley	wesley	PROPN
cana-2576	322	6	publishing	publishing	NOUN
cana-2576	322	7	company	company	NOUN
cana-2576	322	8	reading	reading	NOUN
cana-2576	322	9	,	,	PUNCT
cana-2576	322	10	massachusetts	massachusetts	PROPN
cana-2576	322	11	.	.	PUNCT
cana-2576	323	1	[	[	X
cana-2576	323	2	3	3	X
cana-2576	323	3	]	]	PUNCT
cana-2576	323	4	jayasekaran	jayasekaran	PROPN
cana-2576	323	5	c.	c.	PROPN
cana-2576	323	6	,	,	PUNCT
cana-2576	323	7	and	and	CCONJ
cana-2576	323	8	jancy	jancy	PROPN
cana-2576	323	9	vini	vini	PROPN
cana-2576	323	10	a.	a.	PROPN
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cana-2576	323	12	.	.	PUNCT
cana-2576	324	1	relatively	relatively	ADV
cana-2576	324	2	prime	prime	ADJ
cana-2576	324	3	dominating	dominating	NOUN
cana-2576	324	4	sets	set	NOUN
cana-2576	324	5	in	in	ADP
cana-2576	324	6	graphs	graph	NOUN
cana-2576	324	7	.	.	PUNCT
cana-2576	325	1	annals	annal	NOUN
cana-2576	325	2	of	of	ADP
cana-2576	325	3	pure	pure	ADJ
cana-2576	325	4	and	and	CCONJ
cana-2576	325	5	applied	applied	ADJ
cana-2576	325	6	mathematics	mathematic	NOUN
cana-2576	325	7	.	.	PUNCT
cana-2576	326	1	https://dx.doi.org/10.22457/apam.v14n3a2	https://dx.doi.org/10.22457/apam.v14n3a2	X
cana-2576	326	2	.	.	PUNCT
cana-2576	327	1	[	[	X
cana-2576	327	2	4	4	X
cana-2576	327	3	]	]	PUNCT
cana-2576	327	4	jayasekaran	jayasekaran	PROPN
cana-2576	327	5	c.	c.	PROPN
cana-2576	327	6	,	,	PUNCT
cana-2576	327	7	and	and	CCONJ
cana-2576	327	8	jancy	jancy	PROPN
cana-2576	327	9	vini	vini	PROPN
cana-2576	327	10	a.	a.	PROPN
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cana-2576	327	12	.	.	PUNCT
cana-2576	328	1	relatively	relatively	ADV
cana-2576	328	2	prime	prime	ADJ
cana-2576	328	3	dominating	dominating	NOUN
cana-2576	328	4	polynomial	polynomial	NOUN
cana-2576	328	5	in	in	ADP
cana-2576	328	6	graphs	graph	NOUN
cana-2576	328	7	.	.	PUNCT
cana-2576	329	1	malaya	malaya	PROPN
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cana-2576	330	1	https://doi.org/	https://doi.org/	VERB
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cana-2576	330	3	/	/	SYM
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cana-2576	330	5	[	[	NOUN
cana-2576	330	6	5	5	NUM
cana-2576	330	7	]	]	PUNCT
cana-2576	330	8	lint	lint	NOUN
cana-2576	330	9	j.	j.	PROPN
cana-2576	330	10	h.	h.	PROPN
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cana-2576	330	15	j.	j.	PROPN
cana-2576	330	16	1966	1966	PROPN
cana-2576	330	17	.	.	PUNCT
cana-2576	331	1	equilateral	equilateral	ADJ
cana-2576	331	2	points	point	NOUN
cana-2576	331	3	in	in	ADP
cana-2576	331	4	elliptic	elliptic	ADJ
cana-2576	331	5	geometry	geometry	NOUN
cana-2576	331	6	.	.	PUNCT
cana-2576	332	1	in	in	ADP
cana-2576	332	2	proc	proc	NOUN
cana-2576	332	3	.	.	PUNCT
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cana-2576	333	2	.	.	PUNCT
cana-2576	334	1	nede	nede	PROPN
cana-2576	334	2	.	.	PUNCT
cana-2576	335	1	acad	acad	PROPN
cana-2576	335	2	.	.	PUNCT
cana-2576	336	1	wetensch	wetensch	PROPN
cana-2576	336	2	.	.	PUNCT
cana-2576	337	1	ser	ser	PROPN
cana-2576	337	2	.	.	PUNCT
cana-2576	338	1	a	a	DET
cana-2576	338	2	,	,	PUNCT
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cana-2576	338	4	.	.	PROPN
cana-2576	339	1	69	69	NUM
cana-2576	339	2	,	,	PUNCT
cana-2576	339	3	pp	pp	ADJ
cana-2576	339	4	.	.	PUNCT
cana-2576	340	1	335	335	NUM
cana-2576	340	2	-	-	SYM
cana-2576	340	3	348	348	NUM
cana-2576	340	4	.	.	PUNCT
cana-2576	341	1	[	[	X
cana-2576	341	2	6	6	NUM
cana-2576	341	3	]	]	PUNCT
cana-2576	341	4	ore	ore	NOUN
cana-2576	341	5	o.	o.	NOUN
cana-2576	341	6	1962	1962	NUM
cana-2576	341	7	.	.	PUNCT
cana-2576	342	1	theory	theory	NOUN
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cana-2576	342	3	graphs	graph	NOUN
cana-2576	342	4	.	.	PUNCT
cana-2576	343	1	american	american	PROPN
cana-2576	343	2	mathematical	mathematical	PROPN
cana-2576	343	3	society	society	NOUN
cana-2576	343	4	colloquium	colloquium	NOUN
cana-2576	343	5	publications	publication	NOUN
cana-2576	343	6	,	,	PUNCT
cana-2576	343	7	vol	vol	NOUN
cana-2576	343	8	.	.	PROPN
cana-2576	344	1	38	38	NUM
cana-2576	344	2	(	(	PUNCT
cana-2576	344	3	amer	amer	PROPN
cana-2576	344	4	.	.	PROPN
cana-2576	344	5	math	math	PROPN
cana-2576	344	6	.	.	PUNCT
cana-2576	345	1	soc	soc	PROPN
cana-2576	345	2	.	.	PUNCT
cana-2576	345	3	,	,	PUNCT
cana-2576	345	4	providence	providence	NOUN
cana-2576	345	5	,	,	PUNCT
cana-2576	345	6	ri	ri	PROPN
cana-2576	345	7	)	)	PUNCT
cana-2576	345	8	.	.	PUNCT
cana-2576	346	1	[	[	X
cana-2576	346	2	7	7	X
cana-2576	346	3	]	]	X
cana-2576	346	4	teresa	teresa	PROPN
cana-2576	346	5	w.	w.	PROPN
cana-2576	346	6	haynes	haynes	PROPN
cana-2576	346	7	,	,	PUNCT
cana-2576	346	8	stephen	stephen	PROPN
cana-2576	346	9	hedetniemi	hedetniemi	PROPN
cana-2576	346	10	,	,	PUNCT
cana-2576	346	11	and	and	CCONJ
cana-2576	346	12	peter	peter	PROPN
cana-2576	346	13	slater	slater	PROPN
cana-2576	346	14	.	.	PUNCT
cana-2576	347	1	1998	1998	NUM
cana-2576	347	2	.	.	PUNCT
cana-2576	348	1	fundamentals	fundamental	NOUN
cana-2576	348	2	of	of	ADP
cana-2576	348	3	domination	domination	NOUN
cana-2576	348	4	in	in	ADP
cana-2576	348	5	graphs	graph	NOUN
cana-2576	348	6	.	.	PUNCT
cana-2576	349	1	new	new	PROPN
cana-2576	349	2	york	york	PROPN
cana-2576	349	3	:	:	PUNCT
cana-2576	349	4	marcel	marcel	PROPN
cana-2576	349	5	dekker	dekker	PROPN
cana-2576	349	6	,	,	PUNCT
cana-2576	349	7	inc	inc	PROPN
cana-2576	349	8	..	..	PUNCT
cana-2576	350	1	[	[	X
cana-2576	350	2	8	8	NUM
cana-2576	350	3	]	]	PUNCT
cana-2576	350	4	anat	anat	PROPN
cana-2576	350	5	jaslin	jaslin	PROPN
cana-2576	350	6	jini	jini	PROPN
cana-2576	350	7	,	,	PUNCT
cana-2576	350	8	a	a	PRON
cana-2576	350	9	,	,	PUNCT
cana-2576	350	10	jancy	jancy	PROPN
cana-2576	350	11	vini	vini	PROPN
cana-2576	350	12	a	a	X
cana-2576	350	13	,	,	PUNCT
cana-2576	350	14	manikanda	manikanda	NOUN
cana-2576	350	15	prabhu	prabhu	PROPN
cana-2576	350	16	s	s	PROPN
cana-2576	350	17	,	,	PUNCT
cana-2576	350	18	suresh	suresh	PROPN
cana-2576	350	19	k	k	PROPN
cana-2576	350	20	and	and	CCONJ
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cana-2576	350	22	p	p	PRON
cana-2576	350	23	,	,	PUNCT
cana-2576	350	24	“	"	PUNCT
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cana-2576	350	26	prime	prime	ADJ
cana-2576	350	27	domination	domination	NOUN
cana-2576	350	28	number	number	NOUN
cana-2576	350	29	in	in	ADP
cana-2576	350	30	quadrilateral	quadrilateral	ADJ
cana-2576	350	31	snake	snake	NOUN
cana-2576	350	32	graphs	graph	NOUN
cana-2576	350	33	”	"	PUNCT
cana-2576	350	34	,	,	PUNCT
cana-2576	350	35	advances	advance	NOUN
cana-2576	350	36	in	in	ADP
cana-2576	350	37	nonlinear	nonlinear	ADJ
cana-2576	350	38	variational	variational	ADJ
cana-2576	350	39	inequalities	inequality	NOUN
cana-2576	350	40	.	.	PUNCT
cana-2576	351	1	vol	vol	NOUN
cana-2576	351	2	28	28	NUM
cana-2576	351	3	,	,	PUNCT
cana-2576	351	4	no	no	INTJ
cana-2576	351	5	.	.	NOUN
cana-2576	351	6	2	2	NUM
cana-2576	351	7	(	(	PUNCT
cana-2576	351	8	2025	2025	NUM
cana-2576	351	9	)	)	PUNCT
cana-2576	351	10	.	.	PUNCT
cana-2576	352	1	https://dx.doi.org/10.22457/apam.v14n3a2	https://dx.doi.org/10.22457/apam.v14n3a2	PROPN