id	sid	tid	token	lemma	pos
ejpam-5038	1	1	european	european	PROPN
ejpam-5038	1	2	journal	journal	PROPN
ejpam-5038	1	3	of	of	ADP
ejpam-5038	1	4	pure	pure	ADJ
ejpam-5038	1	5	and	and	CCONJ
ejpam-5038	1	6	applied	apply	VERB
ejpam-5038	1	7	mathematics	mathematic	NOUN
ejpam-5038	1	8	vol	vol	NOUN
ejpam-5038	1	9	.	.	PROPN
ejpam-5038	2	1	17	17	NUM
ejpam-5038	2	2	,	,	PUNCT
ejpam-5038	2	3	no	no	INTJ
ejpam-5038	2	4	.	.	NOUN
ejpam-5038	2	5	2	2	NUM
ejpam-5038	2	6	,	,	PUNCT
ejpam-5038	2	7	2024	2024	NUM
ejpam-5038	2	8	,	,	PUNCT
ejpam-5038	2	9	1082	1082	NUM
ejpam-5038	2	10	-	-	SYM
ejpam-5038	2	11	1093	1093	NUM
ejpam-5038	2	12	issn	issn	PROPN
ejpam-5038	2	13	1307	1307	NUM
ejpam-5038	2	14	-	-	SYM
ejpam-5038	2	15	5543	5543	NUM
ejpam-5038	2	16	–	–	PUNCT
ejpam-5038	2	17	ejpam.com	ejpam.com	X
ejpam-5038	2	18	published	publish	VERB
ejpam-5038	2	19	by	by	ADP
ejpam-5038	2	20	new	new	PROPN
ejpam-5038	2	21	york	york	PROPN
ejpam-5038	2	22	business	business	PROPN
ejpam-5038	2	23	global	global	ADJ
ejpam-5038	2	24	inverse	inverse	NOUN
ejpam-5038	2	25	domination	domination	NOUN
ejpam-5038	2	26	in	in	ADP
ejpam-5038	2	27	x	x	NOUN
ejpam-5038	2	28	-	-	NOUN
ejpam-5038	2	29	trees	tree	NOUN
ejpam-5038	2	30	and	and	CCONJ
ejpam-5038	2	31	sibling	sible	VERB
ejpam-5038	2	32	trees	tree	NOUN
ejpam-5038	2	33	v.	v.	ADP
ejpam-5038	2	34	shalini1	shalini1	NOUN
ejpam-5038	2	35	,	,	PUNCT
ejpam-5038	2	36	indra	indra	PROPN
ejpam-5038	2	37	rajasingh1,∗	rajasingh1,∗	NOUN
ejpam-5038	2	38	1	1	NUM
ejpam-5038	2	39	division	division	NOUN
ejpam-5038	2	40	of	of	ADP
ejpam-5038	2	41	mathematics	mathematic	NOUN
ejpam-5038	2	42	,	,	PUNCT
ejpam-5038	2	43	school	school	NOUN
ejpam-5038	2	44	of	of	ADP
ejpam-5038	2	45	advanced	advanced	ADJ
ejpam-5038	2	46	sciences	science	NOUN
ejpam-5038	2	47	,	,	PUNCT
ejpam-5038	2	48	vellore	vellore	PROPN
ejpam-5038	2	49	institute	institute	PROPN
ejpam-5038	2	50	of	of	ADP
ejpam-5038	2	51	technology	technology	PROPN
ejpam-5038	2	52	,	,	PUNCT
ejpam-5038	2	53	chennai	chennai	PROPN
ejpam-5038	2	54	,	,	PUNCT
ejpam-5038	2	55	tamilnadu	tamilnadu	NOUN
ejpam-5038	2	56	,	,	PUNCT
ejpam-5038	2	57	india	india	PROPN
ejpam-5038	2	58	abstract	abstract	PROPN
ejpam-5038	2	59	.	.	PUNCT
ejpam-5038	3	1	a	a	DET
ejpam-5038	3	2	set	set	ADJ
ejpam-5038	3	3	d	d	NOUN
ejpam-5038	3	4	of	of	ADP
ejpam-5038	3	5	vertices	vertex	NOUN
ejpam-5038	3	6	in	in	ADP
ejpam-5038	3	7	a	a	DET
ejpam-5038	3	8	graph	graph	NOUN
ejpam-5038	3	9	g	g	NOUN
ejpam-5038	3	10	is	be	AUX
ejpam-5038	3	11	a	a	DET
ejpam-5038	3	12	dominating	dominating	NOUN
ejpam-5038	3	13	set	set	NOUN
ejpam-5038	3	14	if	if	SCONJ
ejpam-5038	3	15	every	every	DET
ejpam-5038	3	16	vertex	vertex	NOUN
ejpam-5038	3	17	not	not	PART
ejpam-5038	3	18	in	in	ADP
ejpam-5038	3	19	d	d	PROPN
ejpam-5038	3	20	is	be	AUX
ejpam-5038	3	21	adjacent	adjacent	ADJ
ejpam-5038	3	22	to	to	ADP
ejpam-5038	3	23	at	at	ADV
ejpam-5038	3	24	least	least	ADV
ejpam-5038	3	25	one	one	NUM
ejpam-5038	3	26	vertex	vertex	NOUN
ejpam-5038	3	27	in	in	ADP
ejpam-5038	3	28	d.	d.	PROPN
ejpam-5038	3	29	the	the	DET
ejpam-5038	3	30	minimum	minimum	ADJ
ejpam-5038	3	31	cardinality	cardinality	NOUN
ejpam-5038	3	32	of	of	ADP
ejpam-5038	3	33	a	a	DET
ejpam-5038	3	34	dominating	dominating	NOUN
ejpam-5038	3	35	set	set	NOUN
ejpam-5038	3	36	in	in	ADP
ejpam-5038	3	37	g	g	PROPN
ejpam-5038	3	38	is	be	AUX
ejpam-5038	3	39	called	call	VERB
ejpam-5038	3	40	the	the	DET
ejpam-5038	3	41	domination	domination	NOUN
ejpam-5038	3	42	number	number	NOUN
ejpam-5038	3	43	and	and	CCONJ
ejpam-5038	3	44	is	be	AUX
ejpam-5038	3	45	denoted	denote	VERB
ejpam-5038	3	46	by	by	ADP
ejpam-5038	3	47	γ(g	γ(g	PROPN
ejpam-5038	3	48	)	)	PUNCT
ejpam-5038	3	49	.	.	PUNCT
ejpam-5038	4	1	letd	letd	PROPN
ejpam-5038	4	2	be	be	AUX
ejpam-5038	4	3	a	a	DET
ejpam-5038	4	4	minimum	minimum	ADJ
ejpam-5038	4	5	dominating	dominating	NOUN
ejpam-5038	4	6	set	set	NOUN
ejpam-5038	4	7	of	of	ADP
ejpam-5038	4	8	g.	g.	PROPN
ejpam-5038	4	9	if	if	SCONJ
ejpam-5038	4	10	v	v	PROPN
ejpam-5038	4	11	−d	−d	PROPN
ejpam-5038	4	12	contains	contain	VERB
ejpam-5038	4	13	a	a	DET
ejpam-5038	4	14	dominating	dominating	NOUN
ejpam-5038	4	15	set	set	NOUN
ejpam-5038	4	16	say	say	VERB
ejpam-5038	4	17	d	d	ADP
ejpam-5038	4	18	′	′	NUM
ejpam-5038	4	19	of	of	ADP
ejpam-5038	4	20	g	g	NOUN
ejpam-5038	4	21	,	,	PUNCT
ejpam-5038	4	22	then	then	ADV
ejpam-5038	4	23	d	d	ADP
ejpam-5038	4	24	′	′	NOUN
ejpam-5038	4	25	is	be	AUX
ejpam-5038	4	26	called	call	VERB
ejpam-5038	4	27	an	an	DET
ejpam-5038	4	28	inverse	inverse	NOUN
ejpam-5038	4	29	dominating	dominating	NOUN
ejpam-5038	4	30	set	set	VERB
ejpam-5038	4	31	with	with	ADP
ejpam-5038	4	32	respect	respect	NOUN
ejpam-5038	4	33	to	to	ADP
ejpam-5038	4	34	d.	d.	NOUN
ejpam-5038	4	35	the	the	DET
ejpam-5038	4	36	inverse	inverse	NOUN
ejpam-5038	4	37	domination	domination	NOUN
ejpam-5038	4	38	number	number	NOUN
ejpam-5038	4	39	γ	γ	NOUN
ejpam-5038	4	40	′	′	NUM
ejpam-5038	4	41	(	(	PUNCT
ejpam-5038	4	42	g	g	NOUN
ejpam-5038	4	43	)	)	PUNCT
ejpam-5038	4	44	is	be	AUX
ejpam-5038	4	45	the	the	DET
ejpam-5038	4	46	cardinality	cardinality	NOUN
ejpam-5038	4	47	of	of	ADP
ejpam-5038	4	48	a	a	DET
ejpam-5038	4	49	minimum	minimum	ADJ
ejpam-5038	4	50	inverse	inverse	NOUN
ejpam-5038	4	51	dominating	dominating	NOUN
ejpam-5038	4	52	set	set	NOUN
ejpam-5038	4	53	of	of	ADP
ejpam-5038	4	54	g.	g.	PROPN
ejpam-5038	4	55	a	a	DET
ejpam-5038	4	56	dominating	dominating	NOUN
ejpam-5038	4	57	set	set	NOUN
ejpam-5038	4	58	d	d	NOUN
ejpam-5038	4	59	is	be	AUX
ejpam-5038	4	60	called	call	VERB
ejpam-5038	4	61	a	a	DET
ejpam-5038	4	62	connected	connect	VERB
ejpam-5038	4	63	dominating	dominating	NOUN
ejpam-5038	4	64	set	set	NOUN
ejpam-5038	4	65	or	or	CCONJ
ejpam-5038	4	66	an	an	DET
ejpam-5038	4	67	independent	independent	ADJ
ejpam-5038	4	68	dominating	dominating	NOUN
ejpam-5038	4	69	set	set	NOUN
ejpam-5038	4	70	of	of	ADP
ejpam-5038	4	71	g	g	NOUN
ejpam-5038	4	72	according	accord	VERB
ejpam-5038	4	73	as	as	SCONJ
ejpam-5038	4	74	the	the	DET
ejpam-5038	4	75	induced	induced	ADJ
ejpam-5038	4	76	subgraph	subgraph	NOUN
ejpam-5038	4	77	⟨d⟩	⟨d⟩	PROPN
ejpam-5038	4	78	is	be	AUX
ejpam-5038	4	79	connected	connect	VERB
ejpam-5038	4	80	or	or	CCONJ
ejpam-5038	4	81	independent	independent	ADJ
ejpam-5038	4	82	in	in	ADP
ejpam-5038	4	83	g.	g.	PROPN
ejpam-5038	4	84	the	the	DET
ejpam-5038	4	85	minimum	minimum	NOUN
ejpam-5038	4	86	of	of	ADP
ejpam-5038	4	87	the	the	DET
ejpam-5038	4	88	cardinalities	cardinality	NOUN
ejpam-5038	4	89	of	of	ADP
ejpam-5038	4	90	the	the	DET
ejpam-5038	4	91	connected	connected	ADJ
ejpam-5038	4	92	dominating	dominating	NOUN
ejpam-5038	4	93	sets	set	NOUN
ejpam-5038	4	94	of	of	ADP
ejpam-5038	4	95	g	g	NOUN
ejpam-5038	4	96	or	or	CCONJ
ejpam-5038	4	97	the	the	DET
ejpam-5038	4	98	independent	independent	ADJ
ejpam-5038	4	99	dominating	dominating	NOUN
ejpam-5038	4	100	sets	set	NOUN
ejpam-5038	4	101	of	of	ADP
ejpam-5038	4	102	g	g	PROPN
ejpam-5038	4	103	is	be	AUX
ejpam-5038	4	104	called	call	VERB
ejpam-5038	4	105	the	the	DET
ejpam-5038	4	106	connected	connected	ADJ
ejpam-5038	4	107	domination	domination	NOUN
ejpam-5038	4	108	number	number	NOUN
ejpam-5038	4	109	γc(g	γc(g	NUM
ejpam-5038	4	110	)	)	PUNCT
ejpam-5038	4	111	or	or	CCONJ
ejpam-5038	4	112	the	the	DET
ejpam-5038	4	113	independent	independent	ADJ
ejpam-5038	4	114	domination	domination	NOUN
ejpam-5038	4	115	number	number	NOUN
ejpam-5038	4	116	γi(g	γi(g	NOUN
ejpam-5038	4	117	)	)	PUNCT
ejpam-5038	4	118	respectively	respectively	ADV
ejpam-5038	4	119	.	.	PUNCT
ejpam-5038	5	1	in	in	ADP
ejpam-5038	5	2	this	this	DET
ejpam-5038	5	3	paper	paper	NOUN
ejpam-5038	5	4	,	,	PUNCT
ejpam-5038	5	5	we	we	PRON
ejpam-5038	5	6	determine	determine	VERB
ejpam-5038	5	7	the	the	DET
ejpam-5038	5	8	inverse	inverse	NOUN
ejpam-5038	5	9	domination	domination	NOUN
ejpam-5038	5	10	numbers	number	NOUN
ejpam-5038	5	11	in	in	ADP
ejpam-5038	5	12	x	x	NOUN
ejpam-5038	5	13	-	-	NOUN
ejpam-5038	5	14	trees	tree	NOUN
ejpam-5038	5	15	and	and	CCONJ
ejpam-5038	5	16	sibling	sible	VERB
ejpam-5038	5	17	trees	tree	NOUN
ejpam-5038	5	18	.	.	PUNCT
ejpam-5038	6	1	we	we	PRON
ejpam-5038	6	2	have	have	AUX
ejpam-5038	6	3	also	also	ADV
ejpam-5038	6	4	determined	determine	VERB
ejpam-5038	6	5	the	the	DET
ejpam-5038	6	6	independent	independent	ADJ
ejpam-5038	6	7	domination	domination	NOUN
ejpam-5038	6	8	numbers	number	NOUN
ejpam-5038	6	9	of	of	ADP
ejpam-5038	6	10	both	both	CCONJ
ejpam-5038	6	11	the	the	DET
ejpam-5038	6	12	trees	tree	NOUN
ejpam-5038	6	13	and	and	CCONJ
ejpam-5038	6	14	the	the	DET
ejpam-5038	6	15	connected	connected	ADJ
ejpam-5038	6	16	domination	domination	NOUN
ejpam-5038	6	17	number	number	NOUN
ejpam-5038	6	18	of	of	ADP
ejpam-5038	6	19	sibling	sible	VERB
ejpam-5038	6	20	trees	tree	NOUN
ejpam-5038	6	21	.	.	PUNCT
ejpam-5038	7	1	a	a	DET
ejpam-5038	7	2	result	result	NOUN
ejpam-5038	7	3	on	on	ADP
ejpam-5038	7	4	inverse	inverse	ADJ
ejpam-5038	7	5	domination	domination	NOUN
ejpam-5038	7	6	number	number	NOUN
ejpam-5038	7	7	of	of	ADP
ejpam-5038	7	8	some	some	DET
ejpam-5038	7	9	classes	class	NOUN
ejpam-5038	7	10	of	of	ADP
ejpam-5038	7	11	hypertrees	hypertree	NOUN
ejpam-5038	7	12	is	be	AUX
ejpam-5038	7	13	also	also	ADV
ejpam-5038	7	14	included	include	VERB
ejpam-5038	7	15	.	.	PUNCT
ejpam-5038	8	1	2020	2020	NUM
ejpam-5038	8	2	mathematics	mathematic	NOUN
ejpam-5038	8	3	subject	subject	NOUN
ejpam-5038	8	4	classifications	classification	NOUN
ejpam-5038	8	5	:	:	PUNCT
ejpam-5038	8	6	05c69	05c69	X
ejpam-5038	8	7	key	key	ADJ
ejpam-5038	8	8	words	word	NOUN
ejpam-5038	8	9	and	and	CCONJ
ejpam-5038	8	10	phrases	phrase	NOUN
ejpam-5038	8	11	:	:	PUNCT
ejpam-5038	8	12	domination	domination	NOUN
ejpam-5038	8	13	,	,	PUNCT
ejpam-5038	8	14	inverse	inverse	ADJ
ejpam-5038	8	15	domination	domination	NOUN
ejpam-5038	8	16	,	,	PUNCT
ejpam-5038	8	17	connected	connected	ADJ
ejpam-5038	8	18	domination	domination	NOUN
ejpam-5038	8	19	,	,	PUNCT
ejpam-5038	8	20	hypertrees	hypertree	NOUN
ejpam-5038	8	21	,	,	PUNCT
ejpam-5038	8	22	sibling	sible	VERB
ejpam-5038	8	23	trees	tree	NOUN
ejpam-5038	8	24	1	1	NUM
ejpam-5038	8	25	.	.	PUNCT
ejpam-5038	9	1	introduction	introduction	NOUN
ejpam-5038	9	2	domination	domination	NOUN
ejpam-5038	9	3	problems	problem	NOUN
ejpam-5038	9	4	are	be	AUX
ejpam-5038	9	5	studied	study	VERB
ejpam-5038	9	6	to	to	PART
ejpam-5038	9	7	find	find	VERB
ejpam-5038	9	8	sets	set	NOUN
ejpam-5038	9	9	of	of	ADP
ejpam-5038	9	10	representatives	representative	NOUN
ejpam-5038	9	11	to	to	PART
ejpam-5038	9	12	monitor	monitor	VERB
ejpam-5038	9	13	communication	communication	NOUN
ejpam-5038	9	14	or	or	CCONJ
ejpam-5038	9	15	electrical	electrical	ADJ
ejpam-5038	9	16	networks	network	NOUN
ejpam-5038	9	17	and	and	CCONJ
ejpam-5038	9	18	in	in	ADP
ejpam-5038	9	19	land	land	NOUN
ejpam-5038	9	20	surveying	surveying	NOUN
ejpam-5038	9	21	where	where	SCONJ
ejpam-5038	9	22	it	it	PRON
ejpam-5038	9	23	is	be	AUX
ejpam-5038	9	24	necessary	necessary	ADJ
ejpam-5038	9	25	to	to	PART
ejpam-5038	9	26	minimize	minimize	VERB
ejpam-5038	9	27	the	the	DET
ejpam-5038	9	28	number	number	NOUN
ejpam-5038	9	29	of	of	ADP
ejpam-5038	9	30	places	place	NOUN
ejpam-5038	9	31	a	a	DET
ejpam-5038	9	32	surveyor	surveyor	NOUN
ejpam-5038	9	33	must	must	AUX
ejpam-5038	9	34	stand	stand	VERB
ejpam-5038	9	35	to	to	PART
ejpam-5038	9	36	take	take	VERB
ejpam-5038	9	37	height	height	NOUN
ejpam-5038	9	38	measurements	measurement	NOUN
ejpam-5038	9	39	for	for	ADP
ejpam-5038	9	40	an	an	DET
ejpam-5038	9	41	entire	entire	ADJ
ejpam-5038	9	42	region	region	NOUN
ejpam-5038	9	43	[	[	X
ejpam-5038	9	44	24	24	NUM
ejpam-5038	9	45	]	]	PUNCT
ejpam-5038	9	46	.	.	PUNCT
ejpam-5038	10	1	it	it	PRON
ejpam-5038	10	2	also	also	ADV
ejpam-5038	10	3	plays	play	VERB
ejpam-5038	10	4	a	a	DET
ejpam-5038	10	5	vital	vital	ADJ
ejpam-5038	10	6	role	role	NOUN
ejpam-5038	10	7	in	in	ADP
ejpam-5038	10	8	parallel	parallel	ADJ
ejpam-5038	10	9	processing	processing	NOUN
ejpam-5038	10	10	and	and	CCONJ
ejpam-5038	10	11	supercomputing	supercomputing	NOUN
ejpam-5038	10	12	,	,	PUNCT
ejpam-5038	10	13	which	which	PRON
ejpam-5038	10	14	continue	continue	VERB
ejpam-5038	10	15	to	to	PART
ejpam-5038	10	16	exert	exert	VERB
ejpam-5038	10	17	great	great	ADJ
ejpam-5038	10	18	influence	influence	NOUN
ejpam-5038	10	19	on	on	ADP
ejpam-5038	10	20	the	the	DET
ejpam-5038	10	21	development	development	NOUN
ejpam-5038	10	22	of	of	ADP
ejpam-5038	10	23	modern	modern	ADJ
ejpam-5038	10	24	science	science	NOUN
ejpam-5038	10	25	and	and	CCONJ
ejpam-5038	10	26	engineering	engineering	NOUN
ejpam-5038	10	27	.	.	PUNCT
ejpam-5038	11	1	in	in	ADP
ejpam-5038	11	2	any	any	DET
ejpam-5038	11	3	network	network	NOUN
ejpam-5038	11	4	,	,	PUNCT
ejpam-5038	11	5	dominating	dominating	NOUN
ejpam-5038	11	6	sets	set	NOUN
ejpam-5038	11	7	are	be	AUX
ejpam-5038	11	8	central	central	ADJ
ejpam-5038	11	9	sets	set	NOUN
ejpam-5038	11	10	and	and	CCONJ
ejpam-5038	11	11	hence	hence	ADV
ejpam-5038	11	12	they	they	PRON
ejpam-5038	11	13	play	play	VERB
ejpam-5038	11	14	a	a	DET
ejpam-5038	11	15	key	key	ADJ
ejpam-5038	11	16	role	role	NOUN
ejpam-5038	11	17	in	in	ADP
ejpam-5038	11	18	routing	route	VERB
ejpam-5038	11	19	problems	problem	NOUN
ejpam-5038	11	20	associated	associate	VERB
ejpam-5038	11	21	with	with	ADP
ejpam-5038	11	22	parallel	parallel	ADJ
ejpam-5038	11	23	computing	computing	NOUN
ejpam-5038	12	1	[	[	X
ejpam-5038	12	2	22	22	NUM
ejpam-5038	12	3	]	]	PUNCT
ejpam-5038	12	4	.	.	PUNCT
ejpam-5038	13	1	a	a	DET
ejpam-5038	13	2	non	non	ADJ
ejpam-5038	13	3	-	-	ADJ
ejpam-5038	13	4	empty	empty	ADJ
ejpam-5038	13	5	subset	subset	NOUN
ejpam-5038	13	6	d	d	X
ejpam-5038	13	7	⊆	⊆	NUM
ejpam-5038	13	8	v	v	ADP
ejpam-5038	13	9	(	(	PUNCT
ejpam-5038	13	10	g	g	NOUN
ejpam-5038	13	11	)	)	PUNCT
ejpam-5038	13	12	is	be	AUX
ejpam-5038	13	13	a	a	DET
ejpam-5038	13	14	dominating	dominating	NOUN
ejpam-5038	13	15	set	set	NOUN
ejpam-5038	13	16	if	if	SCONJ
ejpam-5038	13	17	each	each	DET
ejpam-5038	13	18	vertex	vertex	NOUN
ejpam-5038	13	19	in	in	ADP
ejpam-5038	13	20	v	v	NOUN
ejpam-5038	13	21	(	(	PUNCT
ejpam-5038	13	22	g	g	NOUN
ejpam-5038	13	23	)	)	PUNCT
ejpam-5038	13	24	−	−	PROPN
ejpam-5038	14	1	d	d	NOUN
ejpam-5038	14	2	is	be	AUX
ejpam-5038	14	3	adjacent	adjacent	ADJ
ejpam-5038	14	4	to	to	ADP
ejpam-5038	14	5	at	at	ADV
ejpam-5038	14	6	least	least	ADV
ejpam-5038	14	7	one	one	NUM
ejpam-5038	14	8	vertex	vertex	NOUN
ejpam-5038	14	9	in	in	ADP
ejpam-5038	14	10	d.	d.	PROPN
ejpam-5038	14	11	such	such	DET
ejpam-5038	14	12	a	a	DET
ejpam-5038	14	13	set	set	NOUN
ejpam-5038	14	14	with	with	ADP
ejpam-5038	14	15	minimum	minimum	ADJ
ejpam-5038	14	16	cardinality	cardinality	NOUN
ejpam-5038	14	17	yields	yield	VERB
ejpam-5038	14	18	the	the	DET
ejpam-5038	14	19	domination	domination	NOUN
ejpam-5038	14	20	number	number	NOUN
ejpam-5038	14	21	of	of	ADP
ejpam-5038	14	22	a	a	DET
ejpam-5038	14	23	graph	graph	NOUN
ejpam-5038	14	24	g	g	NOUN
ejpam-5038	14	25	and	and	CCONJ
ejpam-5038	14	26	is	be	AUX
ejpam-5038	14	27	denoted	denote	VERB
ejpam-5038	14	28	by	by	ADP
ejpam-5038	14	29	γ(g	γ(g	PROPN
ejpam-5038	14	30	)	)	PUNCT
ejpam-5038	14	31	∗corresponding	∗corresponde	VERB
ejpam-5038	14	32	author	author	NOUN
ejpam-5038	14	33	.	.	PUNCT
ejpam-5038	15	1	doi	doi	NOUN
ejpam-5038	15	2	:	:	PUNCT
ejpam-5038	15	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5038	https://doi.org/10.29020/nybg.ejpam.v17i2.5038	PUNCT
ejpam-5038	15	4	email	email	NOUN
ejpam-5038	15	5	addresses	address	NOUN
ejpam-5038	15	6	:	:	PUNCT
ejpam-5038	15	7	shalu.maths@gmail.com	shalu.maths@gmail.com	X
ejpam-5038	15	8	(	(	PUNCT
ejpam-5038	15	9	v.	v.	X
ejpam-5038	15	10	shalini	shalini	PROPN
ejpam-5038	15	11	)	)	PUNCT
ejpam-5038	15	12	,	,	PUNCT
ejpam-5038	15	13	indrarajasingh@yahoo.com	indrarajasingh@yahoo.com	X
ejpam-5038	15	14	(	(	PUNCT
ejpam-5038	15	15	i.	i.	PROPN
ejpam-5038	15	16	rajasingh	rajasingh	PROPN
ejpam-5038	15	17	)	)	PUNCT
ejpam-5038	15	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5038	15	19	1082	1082	NUM
ejpam-5038	16	1	©	©	PROPN
ejpam-5038	16	2	2024	2024	NUM
ejpam-5038	16	3	ejpam	ejpam	NOUN
ejpam-5038	16	4	all	all	DET
ejpam-5038	16	5	rights	right	NOUN
ejpam-5038	16	6	reserved	reserve	VERB
ejpam-5038	16	7	.	.	PUNCT
ejpam-5038	17	1	v.	v.	PROPN
ejpam-5038	17	2	shalini	shalini	PROPN
ejpam-5038	17	3	,	,	PUNCT
ejpam-5038	17	4	i.	i.	PROPN
ejpam-5038	17	5	rajasingh	rajasingh	PROPN
ejpam-5038	17	6	/	/	SYM
ejpam-5038	17	7	eur	eur	PROPN
ejpam-5038	17	8	.	.	PUNCT
ejpam-5038	18	1	j.	j.	PROPN
ejpam-5038	18	2	pure	pure	PROPN
ejpam-5038	18	3	appl	appl	PROPN
ejpam-5038	18	4	.	.	PROPN
ejpam-5038	18	5	math	math	PROPN
ejpam-5038	18	6	,	,	PUNCT
ejpam-5038	18	7	17	17	NUM
ejpam-5038	18	8	(	(	PUNCT
ejpam-5038	18	9	2	2	NUM
ejpam-5038	18	10	)	)	PUNCT
ejpam-5038	18	11	(	(	PUNCT
ejpam-5038	18	12	2024	2024	NUM
ejpam-5038	18	13	)	)	PUNCT
ejpam-5038	18	14	,	,	PUNCT
ejpam-5038	18	15	1082	1082	NUM
ejpam-5038	18	16	-	-	SYM
ejpam-5038	18	17	1093	1093	NUM
ejpam-5038	18	18	1083	1083	NUM
ejpam-5038	19	1	[	[	X
ejpam-5038	19	2	13	13	NUM
ejpam-5038	19	3	]	]	PUNCT
ejpam-5038	19	4	.	.	PUNCT
ejpam-5038	20	1	a	a	DET
ejpam-5038	20	2	dominating	dominating	NOUN
ejpam-5038	20	3	set	set	NOUN
ejpam-5038	20	4	d	d	NOUN
ejpam-5038	20	5	is	be	AUX
ejpam-5038	20	6	said	say	VERB
ejpam-5038	20	7	to	to	PART
ejpam-5038	20	8	be	be	AUX
ejpam-5038	20	9	a	a	DET
ejpam-5038	20	10	connected	connected	ADJ
ejpam-5038	20	11	dominating	dominating	NOUN
ejpam-5038	20	12	set	set	NOUN
ejpam-5038	20	13	or	or	CCONJ
ejpam-5038	20	14	an	an	DET
ejpam-5038	20	15	independent	independent	ADJ
ejpam-5038	20	16	dominating	dominating	NOUN
ejpam-5038	20	17	set	set	NOUN
ejpam-5038	20	18	if	if	SCONJ
ejpam-5038	20	19	the	the	DET
ejpam-5038	20	20	induced	induced	ADJ
ejpam-5038	20	21	subgraph	subgraph	NOUN
ejpam-5038	20	22	⟨d⟩	⟨d⟩	PROPN
ejpam-5038	20	23	is	be	AUX
ejpam-5038	20	24	connected	connect	VERB
ejpam-5038	20	25	or	or	CCONJ
ejpam-5038	20	26	independent	independent	ADJ
ejpam-5038	20	27	in	in	ADP
ejpam-5038	20	28	g.	g.	PROPN
ejpam-5038	20	29	the	the	DET
ejpam-5038	20	30	minimum	minimum	NOUN
ejpam-5038	20	31	of	of	ADP
ejpam-5038	20	32	the	the	DET
ejpam-5038	20	33	cardinalities	cardinality	NOUN
ejpam-5038	20	34	of	of	ADP
ejpam-5038	20	35	the	the	DET
ejpam-5038	20	36	connected	connected	ADJ
ejpam-5038	20	37	dominating	dominating	NOUN
ejpam-5038	20	38	sets	set	NOUN
ejpam-5038	20	39	of	of	ADP
ejpam-5038	20	40	g	g	NOUN
ejpam-5038	20	41	or	or	CCONJ
ejpam-5038	20	42	independent	independent	ADJ
ejpam-5038	20	43	dominating	dominating	NOUN
ejpam-5038	20	44	sets	set	NOUN
ejpam-5038	20	45	of	of	ADP
ejpam-5038	20	46	g	g	PROPN
ejpam-5038	20	47	is	be	AUX
ejpam-5038	20	48	called	call	VERB
ejpam-5038	20	49	the	the	DET
ejpam-5038	20	50	connected	connected	ADJ
ejpam-5038	20	51	domination	domination	NOUN
ejpam-5038	20	52	number	number	NOUN
ejpam-5038	20	53	of	of	ADP
ejpam-5038	20	54	g	g	NOUN
ejpam-5038	20	55	denoted	denote	VERB
ejpam-5038	20	56	by	by	ADP
ejpam-5038	20	57	γc(g	γc(g	NOUN
ejpam-5038	20	58	)	)	PUNCT
ejpam-5038	20	59	or	or	CCONJ
ejpam-5038	20	60	the	the	DET
ejpam-5038	20	61	independent	independent	ADJ
ejpam-5038	20	62	domination	domination	NOUN
ejpam-5038	20	63	number	number	NOUN
ejpam-5038	20	64	denoted	denote	VERB
ejpam-5038	20	65	by	by	ADP
ejpam-5038	20	66	γi(g)[18	γi(g)[18	NOUN
ejpam-5038	20	67	]	]	PUNCT
ejpam-5038	20	68	.	.	PUNCT
ejpam-5038	21	1	the	the	DET
ejpam-5038	21	2	study	study	NOUN
ejpam-5038	21	3	of	of	ADP
ejpam-5038	21	4	connected	connected	ADJ
ejpam-5038	21	5	domination	domination	NOUN
ejpam-5038	21	6	has	have	VERB
ejpam-5038	21	7	extensive	extensive	ADJ
ejpam-5038	21	8	application	application	NOUN
ejpam-5038	21	9	in	in	ADP
ejpam-5038	21	10	the	the	DET
ejpam-5038	21	11	study	study	NOUN
ejpam-5038	21	12	of	of	ADP
ejpam-5038	21	13	routing	route	VERB
ejpam-5038	21	14	problems	problem	NOUN
ejpam-5038	21	15	and	and	CCONJ
ejpam-5038	21	16	virtual	virtual	ADJ
ejpam-5038	21	17	backbone	backbone	NOUN
ejpam-5038	21	18	based	base	VERB
ejpam-5038	21	19	routing	routing	NOUN
ejpam-5038	21	20	in	in	ADP
ejpam-5038	21	21	wireless	wireless	ADJ
ejpam-5038	21	22	networks[4	networks[4	PROPN
ejpam-5038	21	23	,	,	PUNCT
ejpam-5038	21	24	15	15	NUM
ejpam-5038	21	25	,	,	PUNCT
ejpam-5038	21	26	25	25	NUM
ejpam-5038	21	27	]	]	PUNCT
ejpam-5038	21	28	.	.	PUNCT
ejpam-5038	22	1	determining	determine	VERB
ejpam-5038	22	2	if	if	SCONJ
ejpam-5038	22	3	an	an	DET
ejpam-5038	22	4	arbitrary	arbitrary	ADJ
ejpam-5038	22	5	graph	graph	NOUN
ejpam-5038	22	6	has	have	VERB
ejpam-5038	22	7	a	a	DET
ejpam-5038	22	8	dominating	dominating	NOUN
ejpam-5038	22	9	set	set	NOUN
ejpam-5038	22	10	of	of	ADP
ejpam-5038	22	11	a	a	DET
ejpam-5038	22	12	given	give	VERB
ejpam-5038	22	13	size	size	NOUN
ejpam-5038	22	14	is	be	AUX
ejpam-5038	22	15	a	a	DET
ejpam-5038	22	16	well	well	ADV
ejpam-5038	22	17	-	-	PUNCT
ejpam-5038	22	18	known	know	VERB
ejpam-5038	22	19	np	np	NOUN
ejpam-5038	22	20	-complete	-complete	ADJ
ejpam-5038	22	21	problem	problem	NOUN
ejpam-5038	22	22	[	[	X
ejpam-5038	22	23	10	10	NUM
ejpam-5038	22	24	]	]	PUNCT
ejpam-5038	22	25	.	.	PUNCT
ejpam-5038	23	1	finding	find	VERB
ejpam-5038	23	2	optimum	optimum	ADJ
ejpam-5038	23	3	dominating	dominating	NOUN
ejpam-5038	23	4	sets	set	NOUN
ejpam-5038	23	5	in	in	ADP
ejpam-5038	23	6	networks	network	NOUN
ejpam-5038	23	7	has	have	AUX
ejpam-5038	23	8	always	always	ADV
ejpam-5038	23	9	been	be	AUX
ejpam-5038	23	10	challenging	challenge	VERB
ejpam-5038	23	11	.	.	PUNCT
ejpam-5038	24	1	let	let	VERB
ejpam-5038	24	2	d	d	PRON
ejpam-5038	24	3	be	be	AUX
ejpam-5038	24	4	a	a	DET
ejpam-5038	24	5	minimum	minimum	ADJ
ejpam-5038	24	6	dominating	dominating	NOUN
ejpam-5038	24	7	set	set	NOUN
ejpam-5038	24	8	of	of	ADP
ejpam-5038	24	9	g.	g.	PROPN
ejpam-5038	24	10	if	if	SCONJ
ejpam-5038	24	11	v	v	NUM
ejpam-5038	24	12	−	−	PROPN
ejpam-5038	24	13	d	d	NOUN
ejpam-5038	24	14	contains	contain	VERB
ejpam-5038	24	15	a	a	DET
ejpam-5038	24	16	dominating	dominating	NOUN
ejpam-5038	24	17	set	set	NOUN
ejpam-5038	24	18	say	say	VERB
ejpam-5038	24	19	d	d	ADP
ejpam-5038	24	20	′	′	NUM
ejpam-5038	24	21	of	of	ADP
ejpam-5038	24	22	g	g	NOUN
ejpam-5038	24	23	,	,	PUNCT
ejpam-5038	24	24	then	then	ADV
ejpam-5038	24	25	d	d	ADP
ejpam-5038	24	26	′	′	NOUN
ejpam-5038	24	27	is	be	AUX
ejpam-5038	24	28	called	call	VERB
ejpam-5038	24	29	an	an	DET
ejpam-5038	24	30	inverse	inverse	NOUN
ejpam-5038	24	31	dominating	dominating	NOUN
ejpam-5038	24	32	set	set	VERB
ejpam-5038	24	33	with	with	ADP
ejpam-5038	24	34	respect	respect	NOUN
ejpam-5038	24	35	to	to	ADP
ejpam-5038	24	36	d.	d.	NOUN
ejpam-5038	24	37	the	the	DET
ejpam-5038	24	38	inverse	inverse	NOUN
ejpam-5038	24	39	domination	domination	NOUN
ejpam-5038	24	40	number	number	NOUN
ejpam-5038	24	41	γ	γ	NOUN
ejpam-5038	24	42	′	′	NUM
ejpam-5038	24	43	(	(	PUNCT
ejpam-5038	24	44	g	g	NOUN
ejpam-5038	24	45	)	)	PUNCT
ejpam-5038	24	46	is	be	AUX
ejpam-5038	24	47	the	the	DET
ejpam-5038	24	48	order	order	NOUN
ejpam-5038	24	49	of	of	ADP
ejpam-5038	24	50	a	a	DET
ejpam-5038	24	51	smallest	small	ADJ
ejpam-5038	24	52	inverse	inverse	NOUN
ejpam-5038	24	53	dominating	dominating	NOUN
ejpam-5038	24	54	set	set	VERB
ejpam-5038	24	55	in	in	ADP
ejpam-5038	24	56	g	g	PROPN
ejpam-5038	25	1	[	[	X
ejpam-5038	25	2	14	14	NUM
ejpam-5038	25	3	]	]	SYM
ejpam-5038	25	4	.	.	PUNCT
ejpam-5038	26	1	inverse	inverse	ADJ
ejpam-5038	26	2	domination	domination	NOUN
ejpam-5038	26	3	in	in	ADP
ejpam-5038	26	4	graphs	graph	NOUN
ejpam-5038	26	5	introduced	introduce	VERB
ejpam-5038	26	6	by	by	ADP
ejpam-5038	26	7	kulli	kulli	PROPN
ejpam-5038	26	8	and	and	CCONJ
ejpam-5038	26	9	sigarkanti	sigarkanti	ADJ
ejpam-5038	26	10	[	[	X
ejpam-5038	26	11	14	14	NUM
ejpam-5038	26	12	]	]	PUNCT
ejpam-5038	26	13	in	in	ADP
ejpam-5038	26	14	1991	1991	NUM
ejpam-5038	26	15	plays	play	VERB
ejpam-5038	26	16	a	a	DET
ejpam-5038	26	17	major	major	ADJ
ejpam-5038	26	18	role	role	NOUN
ejpam-5038	26	19	in	in	ADP
ejpam-5038	26	20	reliable	reliable	ADJ
ejpam-5038	26	21	communication	communication	NOUN
ejpam-5038	26	22	and	and	CCONJ
ejpam-5038	26	23	electrical	electrical	ADJ
ejpam-5038	26	24	networks	network	NOUN
ejpam-5038	26	25	.	.	PUNCT
ejpam-5038	27	1	suppose	suppose	VERB
ejpam-5038	27	2	d	d	X
ejpam-5038	27	3	is	be	AUX
ejpam-5038	27	4	a	a	DET
ejpam-5038	27	5	minimum	minimum	ADJ
ejpam-5038	27	6	dominating	dominating	NOUN
ejpam-5038	27	7	set	set	VERB
ejpam-5038	27	8	in	in	ADP
ejpam-5038	27	9	a	a	DET
ejpam-5038	27	10	graph	graph	NOUN
ejpam-5038	27	11	g	g	NOUN
ejpam-5038	27	12	and	and	CCONJ
ejpam-5038	27	13	some	some	DET
ejpam-5038	27	14	nodes	node	NOUN
ejpam-5038	27	15	of	of	ADP
ejpam-5038	27	16	d	d	NOUN
ejpam-5038	27	17	fail	fail	ADJ
ejpam-5038	27	18	,	,	PUNCT
ejpam-5038	27	19	the	the	DET
ejpam-5038	27	20	inverse	inverse	NOUN
ejpam-5038	27	21	dominating	dominating	NOUN
ejpam-5038	27	22	set	set	NOUN
ejpam-5038	27	23	plays	play	VERB
ejpam-5038	27	24	the	the	DET
ejpam-5038	27	25	role	role	NOUN
ejpam-5038	27	26	of	of	ADP
ejpam-5038	27	27	d.	d.	PROPN
ejpam-5038	27	28	domke	domke	PROPN
ejpam-5038	27	29	,	,	PUNCT
ejpam-5038	27	30	dunbar	dunbar	NOUN
ejpam-5038	27	31	,	,	PUNCT
ejpam-5038	27	32	and	and	CCONJ
ejpam-5038	27	33	markus	markus	NOUN
ejpam-5038	27	34	(	(	PUNCT
ejpam-5038	27	35	ars	ar	NOUN
ejpam-5038	27	36	combin	combin	NOUN
ejpam-5038	27	37	.	.	PUNCT
ejpam-5038	28	1	72	72	NUM
ejpam-5038	28	2	(	(	PUNCT
ejpam-5038	28	3	2004	2004	NUM
ejpam-5038	28	4	)	)	PUNCT
ejpam-5038	28	5	,	,	PUNCT
ejpam-5038	28	6	149–160)[6	149–160)[6	NUM
ejpam-5038	28	7	]	]	PUNCT
ejpam-5038	28	8	conjectured	conjecture	VERB
ejpam-5038	28	9	that	that	SCONJ
ejpam-5038	28	10	the	the	DET
ejpam-5038	28	11	inverse	inverse	NOUN
ejpam-5038	28	12	domination	domination	NOUN
ejpam-5038	28	13	number	number	NOUN
ejpam-5038	28	14	of	of	ADP
ejpam-5038	28	15	g	g	PROPN
ejpam-5038	28	16	is	be	AUX
ejpam-5038	28	17	at	at	ADP
ejpam-5038	28	18	most	most	ADJ
ejpam-5038	28	19	the	the	DET
ejpam-5038	28	20	independence	independence	NOUN
ejpam-5038	28	21	number	number	NOUN
ejpam-5038	28	22	of	of	ADP
ejpam-5038	28	23	g.	g.	PROPN
ejpam-5038	28	24	the	the	DET
ejpam-5038	28	25	above	above	ADJ
ejpam-5038	28	26	conjecture	conjecture	NOUN
ejpam-5038	28	27	has	have	AUX
ejpam-5038	28	28	been	be	AUX
ejpam-5038	28	29	proved	prove	VERB
ejpam-5038	28	30	for	for	ADP
ejpam-5038	28	31	special	special	ADJ
ejpam-5038	28	32	families	family	NOUN
ejpam-5038	28	33	of	of	ADP
ejpam-5038	28	34	graphs	graph	NOUN
ejpam-5038	28	35	,	,	PUNCT
ejpam-5038	28	36	including	include	VERB
ejpam-5038	28	37	claw	claw	NOUN
ejpam-5038	28	38	-	-	PUNCT
ejpam-5038	28	39	free	free	ADJ
ejpam-5038	28	40	graphs	graph	NOUN
ejpam-5038	28	41	,	,	PUNCT
ejpam-5038	28	42	bipartite	bipartite	NOUN
ejpam-5038	28	43	graphs	graph	NOUN
ejpam-5038	28	44	,	,	PUNCT
ejpam-5038	28	45	split	split	ADJ
ejpam-5038	28	46	graphs	graph	NOUN
ejpam-5038	28	47	,	,	PUNCT
ejpam-5038	28	48	very	very	ADV
ejpam-5038	28	49	well	well	ADV
ejpam-5038	28	50	covered	cover	VERB
ejpam-5038	28	51	graphs	graph	NOUN
ejpam-5038	28	52	,	,	PUNCT
ejpam-5038	28	53	chordal	chordal	NOUN
ejpam-5038	28	54	graphs	graph	NOUN
ejpam-5038	28	55	and	and	CCONJ
ejpam-5038	28	56	cactus	cactus	NOUN
ejpam-5038	28	57	graphs	graph	NOUN
ejpam-5038	28	58	in[8	in[8	NOUN
ejpam-5038	28	59	]	]	PUNCT
ejpam-5038	28	60	.	.	PUNCT
ejpam-5038	29	1	there	there	PRON
ejpam-5038	29	2	are	be	VERB
ejpam-5038	29	3	some	some	DET
ejpam-5038	29	4	graphs	graph	NOUN
ejpam-5038	29	5	with	with	ADP
ejpam-5038	29	6	equal	equal	ADJ
ejpam-5038	29	7	domination	domination	NOUN
ejpam-5038	29	8	and	and	CCONJ
ejpam-5038	29	9	inverse	inverse	NOUN
ejpam-5038	29	10	domination	domination	NOUN
ejpam-5038	29	11	numbers	number	NOUN
ejpam-5038	29	12	are	be	AUX
ejpam-5038	29	13	identified	identify	VERB
ejpam-5038	29	14	by	by	ADP
ejpam-5038	29	15	t.tamizhchelvam	t.tamizhchelvam	ADJ
ejpam-5038	29	16	[	[	X
ejpam-5038	29	17	2	2	NUM
ejpam-5038	29	18	]	]	PUNCT
ejpam-5038	29	19	.	.	PUNCT
ejpam-5038	30	1	inverse	inverse	ADJ
ejpam-5038	30	2	domination	domination	NOUN
ejpam-5038	30	3	number	number	NOUN
ejpam-5038	30	4	of	of	ADP
ejpam-5038	30	5	circulant	circulant	ADJ
ejpam-5038	30	6	graph	graph	NOUN
ejpam-5038	30	7	proved	prove	VERB
ejpam-5038	30	8	by	by	ADP
ejpam-5038	30	9	v.cynthiya	v.cynthiya	NOUN
ejpam-5038	30	10	in	in	ADP
ejpam-5038	30	11	[	[	X
ejpam-5038	30	12	3	3	NUM
ejpam-5038	30	13	]	]	PUNCT
ejpam-5038	30	14	.	.	PUNCT
ejpam-5038	31	1	also	also	ADV
ejpam-5038	31	2	we	we	PRON
ejpam-5038	31	3	identified	identify	VERB
ejpam-5038	31	4	domination	domination	NOUN
ejpam-5038	31	5	and	and	CCONJ
ejpam-5038	31	6	inverse	inverse	NOUN
ejpam-5038	31	7	domination	domination	NOUN
ejpam-5038	31	8	numbers	number	NOUN
ejpam-5038	31	9	for	for	ADP
ejpam-5038	31	10	wrapped	wrap	VERB
ejpam-5038	31	11	butterfly	butterfly	NOUN
ejpam-5038	31	12	network	network	NOUN
ejpam-5038	31	13	,	,	PUNCT
ejpam-5038	31	14	lollipop	lollipop	NOUN
ejpam-5038	31	15	graph	graph	NOUN
ejpam-5038	31	16	,	,	PUNCT
ejpam-5038	31	17	fly	fly	VERB
ejpam-5038	31	18	graph	graph	NOUN
ejpam-5038	31	19	and	and	CCONJ
ejpam-5038	31	20	jellyfish	jellyfish	ADJ
ejpam-5038	31	21	graph	graph	NOUN
ejpam-5038	31	22	in	in	ADP
ejpam-5038	31	23	[	[	X
ejpam-5038	31	24	19–21	19–21	NUM
ejpam-5038	31	25	]	]	PUNCT
ejpam-5038	31	26	.	.	PUNCT
ejpam-5038	32	1	in	in	ADP
ejpam-5038	32	2	this	this	DET
ejpam-5038	32	3	paper	paper	NOUN
ejpam-5038	32	4	,	,	PUNCT
ejpam-5038	32	5	we	we	PRON
ejpam-5038	32	6	determine	determine	VERB
ejpam-5038	32	7	the	the	DET
ejpam-5038	32	8	inverse	inverse	NOUN
ejpam-5038	32	9	domination	domination	NOUN
ejpam-5038	32	10	,	,	PUNCT
ejpam-5038	32	11	independent	independent	ADJ
ejpam-5038	32	12	domination	domination	NOUN
ejpam-5038	32	13	and	and	CCONJ
ejpam-5038	32	14	connected	connected	ADJ
ejpam-5038	32	15	domination	domination	NOUN
ejpam-5038	32	16	numbers	number	NOUN
ejpam-5038	32	17	in	in	ADP
ejpam-5038	32	18	sibling	sible	VERB
ejpam-5038	32	19	tree	tree	NOUN
ejpam-5038	32	20	networks	network	NOUN
ejpam-5038	32	21	and	and	CCONJ
ejpam-5038	32	22	also	also	ADV
ejpam-5038	32	23	find	find	VERB
ejpam-5038	32	24	the	the	DET
ejpam-5038	32	25	domination	domination	NOUN
ejpam-5038	32	26	,	,	PUNCT
ejpam-5038	32	27	independent	independent	ADJ
ejpam-5038	32	28	domination	domination	NOUN
ejpam-5038	32	29	and	and	CCONJ
ejpam-5038	32	30	inverse	inverse	NOUN
ejpam-5038	32	31	domination	domination	NOUN
ejpam-5038	32	32	numbers	number	NOUN
ejpam-5038	32	33	for	for	ADP
ejpam-5038	32	34	the	the	DET
ejpam-5038	32	35	x	x	ADJ
ejpam-5038	32	36	-	-	ADJ
ejpam-5038	32	37	tree	tree	ADJ
ejpam-5038	32	38	networks	network	NOUN
ejpam-5038	32	39	.	.	PUNCT
ejpam-5038	33	1	the	the	DET
ejpam-5038	33	2	inverse	inverse	ADJ
ejpam-5038	33	3	domination	domination	NOUN
ejpam-5038	33	4	number	number	NOUN
ejpam-5038	33	5	of	of	ADP
ejpam-5038	33	6	some	some	DET
ejpam-5038	33	7	classes	class	NOUN
ejpam-5038	33	8	of	of	ADP
ejpam-5038	33	9	hypertrees	hypertree	NOUN
ejpam-5038	33	10	is	be	AUX
ejpam-5038	33	11	included	include	VERB
ejpam-5038	33	12	.	.	PUNCT
ejpam-5038	34	1	2	2	X
ejpam-5038	34	2	.	.	X
ejpam-5038	34	3	domination	domination	NOUN
ejpam-5038	34	4	and	and	CCONJ
ejpam-5038	34	5	inverse	inverse	NOUN
ejpam-5038	34	6	domination	domination	NOUN
ejpam-5038	34	7	in	in	ADP
ejpam-5038	34	8	x	x	NOUN
ejpam-5038	34	9	-	-	ADJ
ejpam-5038	34	10	trees	tree	NOUN
ejpam-5038	34	11	efficient	efficient	ADJ
ejpam-5038	34	12	inter	inter	ADJ
ejpam-5038	34	13	-	-	ADJ
ejpam-5038	34	14	processor	processor	ADJ
ejpam-5038	34	15	communication	communication	NOUN
ejpam-5038	34	16	is	be	AUX
ejpam-5038	34	17	one	one	NUM
ejpam-5038	34	18	of	of	ADP
ejpam-5038	34	19	the	the	DET
ejpam-5038	34	20	crucial	crucial	ADJ
ejpam-5038	34	21	issues	issue	NOUN
ejpam-5038	34	22	in	in	ADP
ejpam-5038	34	23	multiprocessor	multiprocessor	NOUN
ejpam-5038	34	24	systems	system	NOUN
ejpam-5038	34	25	[	[	X
ejpam-5038	34	26	1	1	NUM
ejpam-5038	34	27	,	,	PUNCT
ejpam-5038	34	28	7	7	NUM
ejpam-5038	34	29	,	,	PUNCT
ejpam-5038	34	30	9	9	NUM
ejpam-5038	34	31	,	,	PUNCT
ejpam-5038	34	32	12	12	NUM
ejpam-5038	34	33	,	,	PUNCT
ejpam-5038	34	34	23	23	NUM
ejpam-5038	34	35	]	]	PUNCT
ejpam-5038	34	36	.	.	PUNCT
ejpam-5038	35	1	multiple	multiple	ADJ
ejpam-5038	35	2	processors	processor	NOUN
ejpam-5038	35	3	are	be	AUX
ejpam-5038	35	4	interconnected	interconnect	VERB
ejpam-5038	35	5	in	in	ADP
ejpam-5038	35	6	a	a	DET
ejpam-5038	35	7	tightly	tightly	ADV
ejpam-5038	35	8	coupled	couple	VERB
ejpam-5038	35	9	,	,	PUNCT
ejpam-5038	35	10	hierarchical	hierarchical	ADJ
ejpam-5038	35	11	,	,	PUNCT
ejpam-5038	35	12	tree	tree	NOUN
ejpam-5038	35	13	-	-	PUNCT
ejpam-5038	35	14	structured	structure	VERB
ejpam-5038	35	15	network	network	NOUN
ejpam-5038	35	16	.	.	PUNCT
ejpam-5038	36	1	an	an	DET
ejpam-5038	36	2	x	x	NOUN
ejpam-5038	36	3	-	-	NOUN
ejpam-5038	36	4	tree	tree	NOUN
ejpam-5038	36	5	[	[	X
ejpam-5038	36	6	5	5	NUM
ejpam-5038	36	7	]	]	PUNCT
ejpam-5038	36	8	is	be	AUX
ejpam-5038	36	9	a	a	DET
ejpam-5038	36	10	complete	complete	ADJ
ejpam-5038	36	11	binary	binary	ADJ
ejpam-5038	36	12	tree	tree	NOUN
ejpam-5038	36	13	with	with	ADP
ejpam-5038	36	14	additional	additional	ADJ
ejpam-5038	36	15	edges	edge	NOUN
ejpam-5038	36	16	to	to	PART
ejpam-5038	36	17	connect	connect	VERB
ejpam-5038	36	18	consecutive	consecutive	ADJ
ejpam-5038	36	19	nodes	node	NOUN
ejpam-5038	36	20	on	on	ADP
ejpam-5038	36	21	the	the	DET
ejpam-5038	36	22	same	same	ADJ
ejpam-5038	36	23	level	level	NOUN
ejpam-5038	36	24	of	of	ADP
ejpam-5038	36	25	the	the	DET
ejpam-5038	36	26	tree	tree	NOUN
ejpam-5038	36	27	so	so	SCONJ
ejpam-5038	36	28	that	that	SCONJ
ejpam-5038	36	29	the	the	DET
ejpam-5038	36	30	vertices	vertex	NOUN
ejpam-5038	36	31	on	on	ADP
ejpam-5038	36	32	each	each	DET
ejpam-5038	36	33	level	level	NOUN
ejpam-5038	36	34	induce	induce	VERB
ejpam-5038	36	35	a	a	DET
ejpam-5038	36	36	path	path	NOUN
ejpam-5038	36	37	.	.	PUNCT
ejpam-5038	37	1	edges	edge	NOUN
ejpam-5038	37	2	on	on	ADP
ejpam-5038	37	3	such	such	ADJ
ejpam-5038	37	4	paths	path	NOUN
ejpam-5038	37	5	are	be	AUX
ejpam-5038	37	6	called	call	VERB
ejpam-5038	37	7	horizontal	horizontal	ADJ
ejpam-5038	37	8	edges	edge	NOUN
ejpam-5038	37	9	.	.	PUNCT
ejpam-5038	38	1	horizontal	horizontal	ADJ
ejpam-5038	38	2	edges	edge	NOUN
ejpam-5038	38	3	are	be	AUX
ejpam-5038	38	4	of	of	ADP
ejpam-5038	38	5	two	two	NUM
ejpam-5038	38	6	types	type	NOUN
ejpam-5038	38	7	:	:	PUNCT
ejpam-5038	38	8	sibling	sible	VERB
ejpam-5038	38	9	edges	edge	NOUN
ejpam-5038	38	10	and	and	CCONJ
ejpam-5038	38	11	cousin	cousin	NOUN
ejpam-5038	38	12	edges	edge	NOUN
ejpam-5038	38	13	.	.	PUNCT
ejpam-5038	39	1	a	a	DET
ejpam-5038	39	2	sibling	sible	VERB
ejpam-5038	39	3	edge	edge	NOUN
ejpam-5038	39	4	denotes	denote	NOUN
ejpam-5038	39	5	a	a	DET
ejpam-5038	39	6	horizontal	horizontal	ADJ
ejpam-5038	39	7	edge	edge	NOUN
ejpam-5038	39	8	that	that	PRON
ejpam-5038	39	9	connects	connect	VERB
ejpam-5038	39	10	two	two	NUM
ejpam-5038	39	11	vertices	vertex	NOUN
ejpam-5038	39	12	with	with	ADP
ejpam-5038	39	13	the	the	DET
ejpam-5038	39	14	same	same	ADJ
ejpam-5038	39	15	parent	parent	NOUN
ejpam-5038	39	16	and	and	CCONJ
ejpam-5038	39	17	a	a	DET
ejpam-5038	39	18	cousin	cousin	NOUN
ejpam-5038	39	19	edge	edge	NOUN
ejpam-5038	39	20	denotes	denote	NOUN
ejpam-5038	39	21	any	any	PRON
ejpam-5038	39	22	of	of	ADP
ejpam-5038	39	23	the	the	DET
ejpam-5038	39	24	remaining	remain	VERB
ejpam-5038	39	25	horizontal	horizontal	ADJ
ejpam-5038	39	26	edges	edge	NOUN
ejpam-5038	39	27	.	.	PUNCT
ejpam-5038	40	1	two	two	NUM
ejpam-5038	40	2	sibling	sible	VERB
ejpam-5038	40	3	edges	edge	NOUN
ejpam-5038	40	4	are	be	AUX
ejpam-5038	40	5	said	say	VERB
ejpam-5038	40	6	to	to	PART
ejpam-5038	40	7	be	be	AUX
ejpam-5038	40	8	adjacent	adjacent	ADJ
ejpam-5038	40	9	if	if	SCONJ
ejpam-5038	40	10	there	there	PRON
ejpam-5038	40	11	is	be	VERB
ejpam-5038	40	12	exactly	exactly	ADV
ejpam-5038	40	13	one	one	NUM
ejpam-5038	40	14	cousin	cousin	NOUN
ejpam-5038	40	15	edge	edge	NOUN
ejpam-5038	40	16	between	between	ADP
ejpam-5038	40	17	them	they	PRON
ejpam-5038	40	18	.	.	PUNCT
ejpam-5038	41	1	the	the	DET
ejpam-5038	41	2	tree	tree	NOUN
ejpam-5038	41	3	edges	edge	NOUN
ejpam-5038	41	4	are	be	AUX
ejpam-5038	41	5	addressed	address	VERB
ejpam-5038	41	6	as	as	ADP
ejpam-5038	41	7	vertical	vertical	ADJ
ejpam-5038	41	8	edges	edge	NOUN
ejpam-5038	41	9	.	.	PUNCT
ejpam-5038	42	1	the	the	DET
ejpam-5038	42	2	structural	structural	ADJ
ejpam-5038	42	3	characteristic	characteristic	NOUN
ejpam-5038	42	4	of	of	ADP
ejpam-5038	42	5	x	x	NOUN
ejpam-5038	42	6	-	-	NOUN
ejpam-5038	42	7	tree	tree	NOUN
ejpam-5038	42	8	was	be	AUX
ejpam-5038	42	9	identified	identify	VERB
ejpam-5038	42	10	in	in	ADP
ejpam-5038	42	11	[	[	X
ejpam-5038	42	12	5	5	NUM
ejpam-5038	42	13	]	]	PUNCT
ejpam-5038	42	14	.	.	PUNCT
ejpam-5038	43	1	the	the	DET
ejpam-5038	43	2	root	root	NOUN
ejpam-5038	43	3	of	of	ADP
ejpam-5038	43	4	x(k	x(k	PROPN
ejpam-5038	43	5	)	)	PUNCT
ejpam-5038	43	6	is	be	AUX
ejpam-5038	43	7	considered	consider	VERB
ejpam-5038	43	8	to	to	PART
ejpam-5038	43	9	be	be	AUX
ejpam-5038	43	10	at	at	ADP
ejpam-5038	43	11	level	level	NOUN
ejpam-5038	43	12	0	0	NUM
ejpam-5038	43	13	.	.	PUNCT
ejpam-5038	43	14	vertices	vertex	NOUN
ejpam-5038	43	15	at	at	ADP
ejpam-5038	43	16	level	level	NOUN
ejpam-5038	43	17	k	k	PROPN
ejpam-5038	43	18	are	be	AUX
ejpam-5038	43	19	called	call	VERB
ejpam-5038	43	20	leaf	leaf	NOUN
ejpam-5038	43	21	vertices	vertex	NOUN
ejpam-5038	43	22	.	.	PUNCT
ejpam-5038	44	1	the	the	DET
ejpam-5038	44	2	vertices	vertex	NOUN
ejpam-5038	44	3	of	of	ADP
ejpam-5038	44	4	x(k	x(k	NOUN
ejpam-5038	44	5	)	)	PUNCT
ejpam-5038	44	6	other	other	ADJ
ejpam-5038	44	7	than	than	ADP
ejpam-5038	44	8	the	the	DET
ejpam-5038	44	9	root	root	NOUN
ejpam-5038	44	10	and	and	CCONJ
ejpam-5038	44	11	the	the	DET
ejpam-5038	44	12	leaf	leaf	NOUN
ejpam-5038	44	13	vertices	vertex	NOUN
ejpam-5038	44	14	are	be	AUX
ejpam-5038	44	15	called	call	VERB
ejpam-5038	44	16	internal	internal	ADJ
ejpam-5038	44	17	vertices	vertex	NOUN
ejpam-5038	44	18	.	.	PUNCT
ejpam-5038	45	1	a	a	DET
ejpam-5038	45	2	k	k	NOUN
ejpam-5038	45	3	-	-	PUNCT
ejpam-5038	45	4	level	level	NOUN
ejpam-5038	45	5	x	x	NOUN
ejpam-5038	45	6	-	-	NOUN
ejpam-5038	45	7	tree	tree	NOUN
ejpam-5038	45	8	or	or	CCONJ
ejpam-5038	45	9	a	a	DET
ejpam-5038	45	10	2k	2k	NUM
ejpam-5038	45	11	-	-	PUNCT
ejpam-5038	45	12	leaf	leaf	NOUN
ejpam-5038	45	13	x	x	NOUN
ejpam-5038	45	14	-	-	NOUN
ejpam-5038	45	15	tree	tree	NOUN
ejpam-5038	45	16	will	will	AUX
ejpam-5038	45	17	be	be	AUX
ejpam-5038	45	18	denoted	denote	VERB
ejpam-5038	45	19	by	by	ADP
ejpam-5038	45	20	x(k	x(k	NOUN
ejpam-5038	45	21	)	)	PUNCT
ejpam-5038	45	22	.	.	PUNCT
ejpam-5038	46	1	a	a	DET
ejpam-5038	46	2	k	k	NOUN
ejpam-5038	46	3	-	-	PUNCT
ejpam-5038	46	4	level	level	NOUN
ejpam-5038	46	5	x	x	NOUN
ejpam-5038	46	6	-	-	NOUN
ejpam-5038	46	7	tree	tree	NOUN
ejpam-5038	46	8	has	have	AUX
ejpam-5038	46	9	2k+1	2k+1	NOUN
ejpam-5038	46	10	−	−	NOUN
ejpam-5038	46	11	1	1	NUM
ejpam-5038	46	12	vertices	vertex	NOUN
ejpam-5038	46	13	and	and	CCONJ
ejpam-5038	46	14	2k+2	2k+2	NUM
ejpam-5038	46	15	−	−	PROPN
ejpam-5038	47	1	k	k	NOUN
ejpam-5038	47	2	−	−	PROPN
ejpam-5038	47	3	4	4	NUM
ejpam-5038	47	4	edges	edge	NOUN
ejpam-5038	47	5	v.	v.	ADP
ejpam-5038	47	6	shalini	shalini	PROPN
ejpam-5038	47	7	,	,	PUNCT
ejpam-5038	47	8	i.	i.	PROPN
ejpam-5038	47	9	rajasingh	rajasingh	PROPN
ejpam-5038	47	10	/	/	SYM
ejpam-5038	47	11	eur	eur	PROPN
ejpam-5038	47	12	.	.	PUNCT
ejpam-5038	48	1	j.	j.	PROPN
ejpam-5038	48	2	pure	pure	PROPN
ejpam-5038	48	3	appl	appl	PROPN
ejpam-5038	48	4	.	.	PROPN
ejpam-5038	48	5	math	math	PROPN
ejpam-5038	48	6	,	,	PUNCT
ejpam-5038	48	7	17	17	NUM
ejpam-5038	48	8	(	(	PUNCT
ejpam-5038	48	9	2	2	NUM
ejpam-5038	48	10	)	)	PUNCT
ejpam-5038	48	11	(	(	PUNCT
ejpam-5038	48	12	2024	2024	NUM
ejpam-5038	48	13	)	)	PUNCT
ejpam-5038	48	14	,	,	PUNCT
ejpam-5038	48	15	1082	1082	NUM
ejpam-5038	48	16	-	-	SYM
ejpam-5038	48	17	1093	1093	NUM
ejpam-5038	48	18	1084	1084	NUM
ejpam-5038	48	19	figure	figure	NOUN
ejpam-5038	48	20	1	1	NUM
ejpam-5038	48	21	:	:	PUNCT
ejpam-5038	48	22	(	(	PUNCT
ejpam-5038	48	23	a	a	X
ejpam-5038	48	24	)	)	PUNCT
ejpam-5038	48	25	x(3	x(3	NOUN
ejpam-5038	48	26	)	)	PUNCT
ejpam-5038	48	27	with	with	ADP
ejpam-5038	48	28	labels	label	NOUN
ejpam-5038	48	29	.	.	PUNCT
ejpam-5038	49	1	(	(	PUNCT
ejpam-5038	49	2	b	b	X
ejpam-5038	49	3	)	)	PUNCT
ejpam-5038	49	4	subgraph	subgraph	NOUN
ejpam-5038	49	5	h	h	PROPN
ejpam-5038	49	6	in	in	ADP
ejpam-5038	49	7	lemma	lemma	PROPN
ejpam-5038	49	8	2	2	NUM
ejpam-5038	49	9	.	.	PUNCT
ejpam-5038	50	1	[	[	X
ejpam-5038	50	2	16	16	NUM
ejpam-5038	50	3	]	]	PUNCT
ejpam-5038	50	4	.	.	PUNCT
ejpam-5038	51	1	x	x	NOUN
ejpam-5038	51	2	-	-	NOUN
ejpam-5038	51	3	trees	tree	NOUN
ejpam-5038	51	4	are	be	AUX
ejpam-5038	51	5	fault	fault	VERB
ejpam-5038	51	6	tolerant	tolerant	ADJ
ejpam-5038	51	7	variants	variant	NOUN
ejpam-5038	51	8	of	of	ADP
ejpam-5038	51	9	the	the	DET
ejpam-5038	51	10	basic	basic	ADJ
ejpam-5038	51	11	tree	tree	NOUN
ejpam-5038	51	12	network	network	NOUN
ejpam-5038	51	13	and	and	CCONJ
ejpam-5038	51	14	have	have	AUX
ejpam-5038	51	15	been	be	AUX
ejpam-5038	51	16	the	the	DET
ejpam-5038	51	17	focus	focus	NOUN
ejpam-5038	51	18	of	of	ADP
ejpam-5038	51	19	more	more	ADV
ejpam-5038	51	20	recent	recent	ADJ
ejpam-5038	51	21	implementation	implementation	NOUN
ejpam-5038	51	22	in	in	ADP
ejpam-5038	51	23	massively	massively	ADV
ejpam-5038	51	24	parallel	parallel	ADJ
ejpam-5038	51	25	systems	system	NOUN
ejpam-5038	51	26	.	.	PUNCT
ejpam-5038	52	1	in	in	ADP
ejpam-5038	52	2	this	this	DET
ejpam-5038	52	3	section	section	NOUN
ejpam-5038	52	4	,	,	PUNCT
ejpam-5038	52	5	we	we	PRON
ejpam-5038	52	6	determine	determine	VERB
ejpam-5038	52	7	the	the	DET
ejpam-5038	52	8	domination	domination	NOUN
ejpam-5038	52	9	number	number	NOUN
ejpam-5038	52	10	of	of	ADP
ejpam-5038	52	11	x(k	x(k	PROPN
ejpam-5038	52	12	)	)	PUNCT
ejpam-5038	52	13	,	,	PUNCT
ejpam-5038	53	1	k	k	PROPN
ejpam-5038	53	2	≥	≥	NUM
ejpam-5038	53	3	1	1	NUM
ejpam-5038	53	4	.	.	PUNCT
ejpam-5038	54	1	for	for	ADP
ejpam-5038	54	2	convenience	convenience	NOUN
ejpam-5038	54	3	,	,	PUNCT
ejpam-5038	54	4	we	we	PRON
ejpam-5038	54	5	label	label	VERB
ejpam-5038	54	6	the	the	DET
ejpam-5038	54	7	vertices	vertex	NOUN
ejpam-5038	54	8	of	of	ADP
ejpam-5038	54	9	x(3	x(3	NOUN
ejpam-5038	54	10	)	)	PUNCT
ejpam-5038	54	11	as	as	ADP
ejpam-5038	54	12	in	in	ADP
ejpam-5038	54	13	figure	figure	NOUN
ejpam-5038	54	14	1(a	1(a	NUM
ejpam-5038	54	15	)	)	PUNCT
ejpam-5038	54	16	.	.	PUNCT
ejpam-5038	55	1	lemma	lemma	PROPN
ejpam-5038	55	2	1	1	NUM
ejpam-5038	55	3	.	.	PUNCT
ejpam-5038	56	1	the	the	DET
ejpam-5038	56	2	domination	domination	NOUN
ejpam-5038	56	3	number	number	NOUN
ejpam-5038	56	4	of	of	ADP
ejpam-5038	56	5	x(3	x(3	PROPN
ejpam-5038	56	6	)	)	PUNCT
ejpam-5038	56	7	is	be	AUX
ejpam-5038	56	8	given	give	VERB
ejpam-5038	56	9	by	by	ADP
ejpam-5038	56	10	γ(x(3	γ(x(3	NOUN
ejpam-5038	56	11	)	)	PUNCT
ejpam-5038	56	12	)	)	PUNCT
ejpam-5038	57	1	=	=	SYM
ejpam-5038	57	2	4	4	X
ejpam-5038	57	3	.	.	X
ejpam-5038	57	4	proof	proof	NOUN
ejpam-5038	57	5	.	.	PUNCT
ejpam-5038	58	1	let	let	VERB
ejpam-5038	58	2	d	d	PRON
ejpam-5038	58	3	be	be	AUX
ejpam-5038	58	4	a	a	DET
ejpam-5038	58	5	dominating	dominating	NOUN
ejpam-5038	58	6	set	set	NOUN
ejpam-5038	58	7	of	of	ADP
ejpam-5038	58	8	x(3	x(3	PROPN
ejpam-5038	58	9	)	)	PUNCT
ejpam-5038	58	10	.	.	PUNCT
ejpam-5038	59	1	three	three	NUM
ejpam-5038	59	2	distinct	distinct	ADJ
ejpam-5038	59	3	vertices	vertex	NOUN
ejpam-5038	59	4	are	be	AUX
ejpam-5038	59	5	necessary	necessary	ADJ
ejpam-5038	59	6	in	in	SCONJ
ejpam-5038	59	7	d	d	PROPN
ejpam-5038	59	8	to	to	PART
ejpam-5038	59	9	dominate	dominate	VERB
ejpam-5038	59	10	the	the	DET
ejpam-5038	59	11	degree	degree	NOUN
ejpam-5038	59	12	2	2	NUM
ejpam-5038	59	13	vertices	vertex	NOUN
ejpam-5038	59	14	u	u	NOUN
ejpam-5038	59	15	,	,	PUNCT
ejpam-5038	59	16	l3	l3	PROPN
ejpam-5038	59	17	and	and	CCONJ
ejpam-5038	59	18	r3	r3	PROPN
ejpam-5038	59	19	.	.	PUNCT
ejpam-5038	60	1	refer	refer	VERB
ejpam-5038	60	2	figure	figure	NOUN
ejpam-5038	60	3	1(a	1(a	NUM
ejpam-5038	60	4	)	)	PUNCT
ejpam-5038	60	5	.	.	PUNCT
ejpam-5038	61	1	to	to	PART
ejpam-5038	61	2	optimize	optimize	VERB
ejpam-5038	61	3	the	the	DET
ejpam-5038	61	4	cardinality	cardinality	NOUN
ejpam-5038	61	5	of	of	ADP
ejpam-5038	61	6	the	the	DET
ejpam-5038	61	7	neighbourhoods	neighbourhood	NOUN
ejpam-5038	61	8	of	of	ADP
ejpam-5038	61	9	vertices	vertex	NOUN
ejpam-5038	61	10	adjacent	adjacent	ADJ
ejpam-5038	61	11	to	to	ADP
ejpam-5038	61	12	u	u	PROPN
ejpam-5038	61	13	,	,	PUNCT
ejpam-5038	61	14	l3	l3	PROPN
ejpam-5038	61	15	and	and	CCONJ
ejpam-5038	61	16	r2	r2	PROPN
ejpam-5038	61	17	,	,	PUNCT
ejpam-5038	61	18	we	we	PRON
ejpam-5038	61	19	choose	choose	VERB
ejpam-5038	61	20	l1	l1	PROPN
ejpam-5038	61	21	,	,	PUNCT
ejpam-5038	61	22	r2	r2	PROPN
ejpam-5038	61	23	(	(	PUNCT
ejpam-5038	61	24	or	or	CCONJ
ejpam-5038	61	25	8)	8)	NUM
ejpam-5038	61	26	and	and	CCONJ
ejpam-5038	61	27	l2	l2	NOUN
ejpam-5038	61	28	(	(	PUNCT
ejpam-5038	61	29	or	or	CCONJ
ejpam-5038	61	30	3	3	NUM
ejpam-5038	61	31	)	)	PUNCT
ejpam-5038	61	32	in	in	ADP
ejpam-5038	61	33	d.	d.	PROPN
ejpam-5038	61	34	another	another	DET
ejpam-5038	61	35	possibility	possibility	NOUN
ejpam-5038	61	36	is	be	AUX
ejpam-5038	61	37	r1	r1	NOUN
ejpam-5038	61	38	,	,	PUNCT
ejpam-5038	61	39	l2	l2	NOUN
ejpam-5038	61	40	(	(	PUNCT
ejpam-5038	61	41	or	or	CCONJ
ejpam-5038	61	42	3	3	NUM
ejpam-5038	61	43	)	)	PUNCT
ejpam-5038	61	44	and	and	CCONJ
ejpam-5038	61	45	r2	r2	PROPN
ejpam-5038	61	46	(	(	PUNCT
ejpam-5038	61	47	or	or	CCONJ
ejpam-5038	61	48	8)	8)	NUM
ejpam-5038	61	49	.	.	PUNCT
ejpam-5038	62	1	in	in	ADP
ejpam-5038	62	2	either	either	DET
ejpam-5038	62	3	case	case	NOUN
ejpam-5038	62	4	,	,	PUNCT
ejpam-5038	62	5	the	the	DET
ejpam-5038	62	6	number	number	NOUN
ejpam-5038	62	7	of	of	ADP
ejpam-5038	62	8	dominated	dominate	VERB
ejpam-5038	62	9	vertices	vertex	NOUN
ejpam-5038	62	10	is	be	AUX
ejpam-5038	62	11	7	7	NUM
ejpam-5038	62	12	.	.	PUNCT
ejpam-5038	62	13	to	to	PART
ejpam-5038	62	14	dominate	dominate	VERB
ejpam-5038	62	15	the	the	DET
ejpam-5038	62	16	subgraph	subgraph	NOUN
ejpam-5038	62	17	induced	induce	VERB
ejpam-5038	62	18	by	by	ADP
ejpam-5038	62	19	the	the	DET
ejpam-5038	62	20	remaining	remain	VERB
ejpam-5038	62	21	5	5	NUM
ejpam-5038	62	22	vertices	vertex	NOUN
ejpam-5038	62	23	,	,	PUNCT
ejpam-5038	62	24	we	we	PRON
ejpam-5038	62	25	require	require	VERB
ejpam-5038	62	26	at	at	ADV
ejpam-5038	62	27	least	least	ADV
ejpam-5038	62	28	one	one	NUM
ejpam-5038	62	29	more	more	ADJ
ejpam-5038	62	30	vertex	vertex	NOUN
ejpam-5038	62	31	in	in	ADP
ejpam-5038	62	32	d.	d.	PROPN
ejpam-5038	62	33	thus	thus	ADV
ejpam-5038	62	34	|d|≥	|d|≥	PROPN
ejpam-5038	62	35	4	4	NUM
ejpam-5038	62	36	.	.	PUNCT
ejpam-5038	63	1	it	it	PRON
ejpam-5038	63	2	is	be	AUX
ejpam-5038	63	3	easy	easy	ADJ
ejpam-5038	63	4	to	to	PART
ejpam-5038	63	5	verify	verify	VERB
ejpam-5038	63	6	that	that	SCONJ
ejpam-5038	63	7	{	{	PUNCT
ejpam-5038	63	8	l1	l1	PROPN
ejpam-5038	63	9	,	,	PUNCT
ejpam-5038	63	10	r2	r2	PROPN
ejpam-5038	63	11	,	,	PUNCT
ejpam-5038	63	12	3	3	NUM
ejpam-5038	63	13	,	,	PUNCT
ejpam-5038	63	14	6	6	NUM
ejpam-5038	63	15	}	}	PUNCT
ejpam-5038	63	16	is	be	AUX
ejpam-5038	63	17	a	a	DET
ejpam-5038	63	18	dominating	dominating	NOUN
ejpam-5038	63	19	set	set	NOUN
ejpam-5038	63	20	of	of	ADP
ejpam-5038	63	21	x(3	x(3	PROPN
ejpam-5038	63	22	)	)	PUNCT
ejpam-5038	63	23	.	.	PUNCT
ejpam-5038	64	1	hence	hence	ADV
ejpam-5038	64	2	γ(x(3	γ(x(3	NOUN
ejpam-5038	64	3	)	)	PUNCT
ejpam-5038	64	4	)	)	PUNCT
ejpam-5038	65	1	=	=	SYM
ejpam-5038	65	2	4	4	X
ejpam-5038	65	3	.	.	NOUN
ejpam-5038	65	4	remark	remark	NOUN
ejpam-5038	65	5	1	1	NUM
ejpam-5038	65	6	.	.	PUNCT
ejpam-5038	66	1	{	{	PUNCT
ejpam-5038	66	2	r1	r1	NOUN
ejpam-5038	66	3	,	,	PUNCT
ejpam-5038	66	4	l2	l2	NOUN
ejpam-5038	66	5	,	,	PUNCT
ejpam-5038	66	6	5	5	NUM
ejpam-5038	66	7	,	,	PUNCT
ejpam-5038	66	8	8	8	NUM
ejpam-5038	66	9	}	}	PUNCT
ejpam-5038	66	10	is	be	AUX
ejpam-5038	66	11	also	also	ADV
ejpam-5038	66	12	a	a	DET
ejpam-5038	66	13	minimum	minimum	ADJ
ejpam-5038	66	14	dominating	dominating	NOUN
ejpam-5038	66	15	set	set	NOUN
ejpam-5038	66	16	of	of	ADP
ejpam-5038	66	17	x(3	x(3	PROPN
ejpam-5038	66	18	)	)	PUNCT
ejpam-5038	66	19	.	.	PUNCT
ejpam-5038	67	1	lemma	lemma	PROPN
ejpam-5038	67	2	2	2	NUM
ejpam-5038	67	3	.	.	PUNCT
ejpam-5038	67	4	a	a	DET
ejpam-5038	67	5	minimal	minimal	ADJ
ejpam-5038	67	6	dominating	dominating	NOUN
ejpam-5038	67	7	set	set	NOUN
ejpam-5038	67	8	of	of	ADP
ejpam-5038	67	9	x(3	x(3	PROPN
ejpam-5038	67	10	)	)	PUNCT
ejpam-5038	67	11	that	that	PRON
ejpam-5038	67	12	contains	contain	VERB
ejpam-5038	67	13	the	the	DET
ejpam-5038	67	14	root	root	NOUN
ejpam-5038	67	15	of	of	ADP
ejpam-5038	67	16	x(3	x(3	NOUN
ejpam-5038	67	17	)	)	PUNCT
ejpam-5038	67	18	is	be	AUX
ejpam-5038	67	19	of	of	ADP
ejpam-5038	67	20	cardinality	cardinality	NOUN
ejpam-5038	67	21	5	5	NUM
ejpam-5038	67	22	.	.	PUNCT
ejpam-5038	68	1	proof	proof	NOUN
ejpam-5038	68	2	.	.	PUNCT
ejpam-5038	69	1	let	let	VERB
ejpam-5038	69	2	d	d	PRON
ejpam-5038	69	3	be	be	AUX
ejpam-5038	69	4	a	a	DET
ejpam-5038	69	5	dominating	dominating	NOUN
ejpam-5038	69	6	set	set	NOUN
ejpam-5038	69	7	of	of	ADP
ejpam-5038	69	8	x(3	x(3	PROPN
ejpam-5038	69	9	)	)	PUNCT
ejpam-5038	69	10	that	that	PRON
ejpam-5038	69	11	contains	contain	VERB
ejpam-5038	69	12	u.	u.	PROPN
ejpam-5038	69	13	then	then	ADV
ejpam-5038	69	14	u	u	NOUN
ejpam-5038	69	15	dominates	dominate	VERB
ejpam-5038	69	16	l1	l1	PROPN
ejpam-5038	69	17	and	and	CCONJ
ejpam-5038	69	18	r1	r1	PROPN
ejpam-5038	69	19	.	.	PUNCT
ejpam-5038	70	1	consider	consider	VERB
ejpam-5038	70	2	the	the	DET
ejpam-5038	70	3	subgraph	subgraph	NOUN
ejpam-5038	70	4	h	h	NOUN
ejpam-5038	70	5	induced	induce	VERB
ejpam-5038	70	6	by	by	ADP
ejpam-5038	70	7	level	level	NOUN
ejpam-5038	70	8	2	2	NUM
ejpam-5038	70	9	and	and	CCONJ
ejpam-5038	70	10	level	level	NOUN
ejpam-5038	70	11	3	3	NUM
ejpam-5038	70	12	vertices	vertex	NOUN
ejpam-5038	70	13	of	of	ADP
ejpam-5038	70	14	x(3	x(3	NOUN
ejpam-5038	70	15	)	)	PUNCT
ejpam-5038	70	16	which	which	PRON
ejpam-5038	70	17	are	be	AUX
ejpam-5038	70	18	yet	yet	ADV
ejpam-5038	70	19	to	to	PART
ejpam-5038	70	20	be	be	AUX
ejpam-5038	70	21	dominated	dominate	VERB
ejpam-5038	70	22	.	.	PUNCT
ejpam-5038	71	1	see	see	VERB
ejpam-5038	71	2	figure	figure	NOUN
ejpam-5038	71	3	1(b	1(b	NUM
ejpam-5038	71	4	)	)	PUNCT
ejpam-5038	71	5	.	.	PUNCT
ejpam-5038	72	1	to	to	PART
ejpam-5038	72	2	dominate	dominate	VERB
ejpam-5038	72	3	the	the	DET
ejpam-5038	72	4	degree	degree	NOUN
ejpam-5038	72	5	2	2	NUM
ejpam-5038	72	6	vertices	vertex	NOUN
ejpam-5038	72	7	l3	l3	NOUN
ejpam-5038	72	8	and	and	CCONJ
ejpam-5038	72	9	r3	r3	PROPN
ejpam-5038	72	10	,	,	PUNCT
ejpam-5038	72	11	it	it	PRON
ejpam-5038	72	12	is	be	AUX
ejpam-5038	72	13	necessary	necessary	ADJ
ejpam-5038	72	14	to	to	PART
ejpam-5038	72	15	include	include	VERB
ejpam-5038	72	16	2	2	NUM
ejpam-5038	72	17	vertices	vertex	NOUN
ejpam-5038	72	18	of	of	ADP
ejpam-5038	72	19	h	h	NOUN
ejpam-5038	72	20	in	in	ADP
ejpam-5038	72	21	d.	d.	PROPN
ejpam-5038	72	22	the	the	DET
ejpam-5038	72	23	possibilities	possibility	NOUN
ejpam-5038	72	24	that	that	PRON
ejpam-5038	72	25	do	do	AUX
ejpam-5038	72	26	not	not	PART
ejpam-5038	72	27	include	include	VERB
ejpam-5038	72	28	l3	l3	NOUN
ejpam-5038	72	29	or	or	CCONJ
ejpam-5038	72	30	r3	r3	PROPN
ejpam-5038	72	31	are	be	AUX
ejpam-5038	72	32	{	{	PUNCT
ejpam-5038	72	33	l2	l2	NOUN
ejpam-5038	72	34	,	,	PUNCT
ejpam-5038	72	35	r2	r2	PROPN
ejpam-5038	72	36	}	}	PUNCT
ejpam-5038	72	37	,	,	PUNCT
ejpam-5038	72	38	{	{	PUNCT
ejpam-5038	72	39	l2	l2	NOUN
ejpam-5038	72	40	,	,	PUNCT
ejpam-5038	72	41	8	8	NUM
ejpam-5038	72	42	}	}	PUNCT
ejpam-5038	72	43	,	,	PUNCT
ejpam-5038	72	44	{	{	PUNCT
ejpam-5038	72	45	r2	r2	NOUN
ejpam-5038	72	46	,	,	PUNCT
ejpam-5038	72	47	3	3	NUM
ejpam-5038	72	48	}	}	PUNCT
ejpam-5038	72	49	and	and	CCONJ
ejpam-5038	72	50	{	{	PUNCT
ejpam-5038	72	51	3	3	NUM
ejpam-5038	72	52	,	,	PUNCT
ejpam-5038	72	53	8	8	NUM
ejpam-5038	72	54	}	}	PUNCT
ejpam-5038	72	55	.	.	PUNCT
ejpam-5038	73	1	in	in	ADP
ejpam-5038	73	2	all	all	DET
ejpam-5038	73	3	cases	case	NOUN
ejpam-5038	73	4	,	,	PUNCT
ejpam-5038	73	5	the	the	DET
ejpam-5038	73	6	remaining	remain	VERB
ejpam-5038	73	7	vertices	vertex	NOUN
ejpam-5038	73	8	to	to	PART
ejpam-5038	73	9	be	be	AUX
ejpam-5038	73	10	dominated	dominate	VERB
ejpam-5038	73	11	induce	induce	VERB
ejpam-5038	73	12	a	a	DET
ejpam-5038	73	13	path	path	NOUN
ejpam-5038	73	14	of	of	ADP
ejpam-5038	73	15	length	length	NOUN
ejpam-5038	73	16	3	3	NUM
ejpam-5038	73	17	.	.	PUNCT
ejpam-5038	74	1	as	as	SCONJ
ejpam-5038	74	2	there	there	PRON
ejpam-5038	74	3	are	be	VERB
ejpam-5038	74	4	two	two	NUM
ejpam-5038	74	5	pendant	pendant	ADJ
ejpam-5038	74	6	vertices	vertex	NOUN
ejpam-5038	74	7	,	,	PUNCT
ejpam-5038	74	8	two	two	NUM
ejpam-5038	74	9	more	more	ADJ
ejpam-5038	74	10	vertices	vertex	NOUN
ejpam-5038	74	11	from	from	ADP
ejpam-5038	74	12	the	the	DET
ejpam-5038	74	13	path	path	NOUN
ejpam-5038	74	14	are	be	AUX
ejpam-5038	74	15	to	to	PART
ejpam-5038	74	16	be	be	AUX
ejpam-5038	74	17	included	include	VERB
ejpam-5038	74	18	in	in	ADP
ejpam-5038	74	19	d.	d.	PROPN
ejpam-5038	74	20	on	on	ADP
ejpam-5038	74	21	the	the	DET
ejpam-5038	74	22	otherhand	otherhand	PROPN
ejpam-5038	74	23	,	,	PUNCT
ejpam-5038	74	24	the	the	DET
ejpam-5038	74	25	possibilities	possibility	NOUN
ejpam-5038	74	26	that	that	PRON
ejpam-5038	74	27	include	include	VERB
ejpam-5038	74	28	l3	l3	NOUN
ejpam-5038	74	29	or	or	CCONJ
ejpam-5038	74	30	r3	r3	PROPN
ejpam-5038	74	31	are	be	AUX
ejpam-5038	74	32	{	{	PUNCT
ejpam-5038	74	33	l3	l3	PROPN
ejpam-5038	74	34	,	,	PUNCT
ejpam-5038	74	35	r3	r3	PROPN
ejpam-5038	74	36	}	}	PUNCT
ejpam-5038	74	37	,	,	PUNCT
ejpam-5038	74	38	{	{	PUNCT
ejpam-5038	74	39	l3	l3	NOUN
ejpam-5038	74	40	,	,	PUNCT
ejpam-5038	74	41	r2	r2	PROPN
ejpam-5038	74	42	}	}	PUNCT
ejpam-5038	74	43	,	,	PUNCT
ejpam-5038	74	44	and	and	CCONJ
ejpam-5038	74	45	{	{	PUNCT
ejpam-5038	74	46	l2	l2	NOUN
ejpam-5038	74	47	,	,	PUNCT
ejpam-5038	74	48	r3	r3	PROPN
ejpam-5038	74	49	}	}	PUNCT
ejpam-5038	74	50	.	.	PUNCT
ejpam-5038	75	1	in	in	ADP
ejpam-5038	75	2	all	all	DET
ejpam-5038	75	3	these	these	DET
ejpam-5038	75	4	cases	case	NOUN
ejpam-5038	75	5	,	,	PUNCT
ejpam-5038	75	6	the	the	DET
ejpam-5038	75	7	remaining	remain	VERB
ejpam-5038	75	8	vertices	vertex	NOUN
ejpam-5038	75	9	to	to	PART
ejpam-5038	75	10	be	be	AUX
ejpam-5038	75	11	dominated	dominate	VERB
ejpam-5038	75	12	are	be	AUX
ejpam-5038	75	13	1,2,4,5,6	1,2,4,5,6	NUM
ejpam-5038	75	14	and	and	CCONJ
ejpam-5038	75	15	7	7	NUM
ejpam-5038	75	16	.	.	PUNCT
ejpam-5038	76	1	the	the	DET
ejpam-5038	76	2	subgraph	subgraph	NOUN
ejpam-5038	76	3	induced	induce	VERB
ejpam-5038	76	4	by	by	ADP
ejpam-5038	76	5	these	these	DET
ejpam-5038	76	6	vertices	vertex	NOUN
ejpam-5038	76	7	require	require	VERB
ejpam-5038	76	8	2	2	NUM
ejpam-5038	76	9	vertices	vertex	NOUN
ejpam-5038	76	10	to	to	PART
ejpam-5038	76	11	be	be	AUX
ejpam-5038	76	12	included	include	VERB
ejpam-5038	76	13	in	in	ADP
ejpam-5038	76	14	d.	d.	PROPN
ejpam-5038	76	15	thus	thus	ADV
ejpam-5038	76	16	|d|=	|d|=	PROPN
ejpam-5038	76	17	5	5	NUM
ejpam-5038	76	18	.	.	PUNCT
ejpam-5038	77	1	v.	v.	PROPN
ejpam-5038	77	2	shalini	shalini	PROPN
ejpam-5038	77	3	,	,	PUNCT
ejpam-5038	77	4	i.	i.	PROPN
ejpam-5038	77	5	rajasingh	rajasingh	PROPN
ejpam-5038	77	6	/	/	SYM
ejpam-5038	77	7	eur	eur	PROPN
ejpam-5038	77	8	.	.	PUNCT
ejpam-5038	78	1	j.	j.	PROPN
ejpam-5038	78	2	pure	pure	PROPN
ejpam-5038	78	3	appl	appl	PROPN
ejpam-5038	78	4	.	.	PROPN
ejpam-5038	78	5	math	math	PROPN
ejpam-5038	78	6	,	,	PUNCT
ejpam-5038	78	7	17	17	NUM
ejpam-5038	78	8	(	(	PUNCT
ejpam-5038	78	9	2	2	NUM
ejpam-5038	78	10	)	)	PUNCT
ejpam-5038	78	11	(	(	PUNCT
ejpam-5038	78	12	2024	2024	NUM
ejpam-5038	78	13	)	)	PUNCT
ejpam-5038	78	14	,	,	PUNCT
ejpam-5038	78	15	1082	1082	NUM
ejpam-5038	78	16	-	-	SYM
ejpam-5038	78	17	1093	1093	NUM
ejpam-5038	78	18	1085	1085	NUM
ejpam-5038	78	19	figure	figure	NOUN
ejpam-5038	78	20	2	2	NUM
ejpam-5038	78	21	:	:	PUNCT
ejpam-5038	78	22	(	(	PUNCT
ejpam-5038	78	23	a	a	X
ejpam-5038	78	24	)	)	PUNCT
ejpam-5038	78	25	subgraph	subgraph	NOUN
ejpam-5038	78	26	h1	h1	PROPN
ejpam-5038	78	27	dominated	dominate	VERB
ejpam-5038	78	28	by	by	ADP
ejpam-5038	78	29	circled	circle	VERB
ejpam-5038	78	30	vertices	vertex	NOUN
ejpam-5038	78	31	.	.	PUNCT
ejpam-5038	79	1	(	(	PUNCT
ejpam-5038	79	2	b)subgraph	b)subgraph	PROPN
ejpam-5038	79	3	h2	h2	PROPN
ejpam-5038	79	4	dominated	dominate	VERB
ejpam-5038	79	5	by	by	ADP
ejpam-5038	79	6	circled	circle	VERB
ejpam-5038	79	7	vertices	vertex	NOUN
ejpam-5038	79	8	.	.	PUNCT
ejpam-5038	80	1	lemma	lemma	PROPN
ejpam-5038	80	2	3	3	NUM
ejpam-5038	80	3	.	.	PUNCT
ejpam-5038	80	4	a	a	DET
ejpam-5038	80	5	minimal	minimal	ADJ
ejpam-5038	80	6	dominating	dominating	NOUN
ejpam-5038	80	7	set	set	NOUN
ejpam-5038	80	8	of	of	ADP
ejpam-5038	80	9	x(3	x(3	PROPN
ejpam-5038	80	10	)	)	PUNCT
ejpam-5038	81	1	containing	contain	VERB
ejpam-5038	81	2	(	(	PUNCT
ejpam-5038	81	3	i	i	NOUN
ejpam-5038	81	4	)	)	PUNCT
ejpam-5038	81	5	{	{	PUNCT
ejpam-5038	81	6	l1	l1	PROPN
ejpam-5038	81	7	,	,	PUNCT
ejpam-5038	81	8	l2	l2	NOUN
ejpam-5038	81	9	}	}	PUNCT
ejpam-5038	81	10	,	,	PUNCT
ejpam-5038	81	11	(	(	PUNCT
ejpam-5038	81	12	ii){l2	ii){l2	NOUN
ejpam-5038	81	13	,	,	PUNCT
ejpam-5038	81	14	l3	l3	NOUN
ejpam-5038	81	15	}	}	PUNCT
ejpam-5038	81	16	,	,	PUNCT
ejpam-5038	81	17	or	or	CCONJ
ejpam-5038	81	18	(	(	PUNCT
ejpam-5038	81	19	iii	iii	NOUN
ejpam-5038	81	20	)	)	PUNCT
ejpam-5038	81	21	{	{	PUNCT
ejpam-5038	81	22	l3	l3	PROPN
ejpam-5038	81	23	,	,	PUNCT
ejpam-5038	81	24	l1	l1	PROPN
ejpam-5038	81	25	}	}	PUNCT
ejpam-5038	81	26	is	be	AUX
ejpam-5038	81	27	of	of	ADP
ejpam-5038	81	28	cardinality	cardinality	NOUN
ejpam-5038	81	29	5	5	NUM
ejpam-5038	81	30	.	.	PUNCT
ejpam-5038	82	1	proof	proof	NOUN
ejpam-5038	82	2	.	.	PUNCT
ejpam-5038	83	1	let	let	VERB
ejpam-5038	83	2	d	d	PRON
ejpam-5038	83	3	be	be	AUX
ejpam-5038	83	4	a	a	DET
ejpam-5038	83	5	minimal	minimal	ADJ
ejpam-5038	83	6	dominating	dominating	NOUN
ejpam-5038	83	7	set	set	NOUN
ejpam-5038	83	8	of	of	ADP
ejpam-5038	83	9	x(3	x(3	PROPN
ejpam-5038	83	10	)	)	PUNCT
ejpam-5038	83	11	.	.	PUNCT
ejpam-5038	84	1	suppose	suppose	VERB
ejpam-5038	84	2	d	d	NOUN
ejpam-5038	84	3	contains	contain	VERB
ejpam-5038	84	4	{	{	PUNCT
ejpam-5038	84	5	l1	l1	PROPN
ejpam-5038	84	6	,	,	PUNCT
ejpam-5038	84	7	l2	l2	NOUN
ejpam-5038	84	8	}	}	PUNCT
ejpam-5038	84	9	or	or	CCONJ
ejpam-5038	84	10	{	{	PUNCT
ejpam-5038	84	11	l3	l3	PROPN
ejpam-5038	84	12	,	,	PUNCT
ejpam-5038	84	13	l1	l1	PROPN
ejpam-5038	84	14	}	}	PUNCT
ejpam-5038	84	15	.	.	PUNCT
ejpam-5038	85	1	now	now	ADV
ejpam-5038	85	2	if	if	SCONJ
ejpam-5038	85	3	n	n	PRON
ejpam-5038	85	4	[	[	X
ejpam-5038	85	5	s	s	X
ejpam-5038	85	6	]	]	X
ejpam-5038	85	7	denotes	denote	VERB
ejpam-5038	85	8	the	the	DET
ejpam-5038	85	9	closed	closed	ADJ
ejpam-5038	85	10	neighbourhood	neighbourhood	NOUN
ejpam-5038	85	11	of	of	ADP
ejpam-5038	85	12	a	a	DET
ejpam-5038	85	13	set	set	NOUN
ejpam-5038	85	14	s	s	NOUN
ejpam-5038	85	15	of	of	ADP
ejpam-5038	85	16	vertices	vertex	NOUN
ejpam-5038	85	17	,	,	PUNCT
ejpam-5038	85	18	then	then	ADV
ejpam-5038	85	19	n	n	CCONJ
ejpam-5038	85	20	[	[	X
ejpam-5038	85	21	{	{	PUNCT
ejpam-5038	85	22	l1	l1	PROPN
ejpam-5038	85	23	,	,	PUNCT
ejpam-5038	85	24	l2	l2	NOUN
ejpam-5038	85	25	}	}	PUNCT
ejpam-5038	85	26	]	]	PUNCT
ejpam-5038	85	27	=	=	PUNCT
ejpam-5038	85	28	{	{	PUNCT
ejpam-5038	85	29	u	u	PROPN
ejpam-5038	85	30	,	,	PUNCT
ejpam-5038	85	31	l1	l1	PROPN
ejpam-5038	85	32	,	,	PUNCT
ejpam-5038	85	33	l2	l2	NOUN
ejpam-5038	85	34	,	,	PUNCT
ejpam-5038	85	35	l3	l3	PROPN
ejpam-5038	85	36	,	,	PUNCT
ejpam-5038	85	37	r1	r1	PROPN
ejpam-5038	85	38	,	,	PUNCT
ejpam-5038	85	39	1	1	NUM
ejpam-5038	85	40	,	,	PUNCT
ejpam-5038	85	41	3	3	NUM
ejpam-5038	85	42	}	}	PUNCT
ejpam-5038	85	43	=	=	SYM
ejpam-5038	85	44	n	n	PRON
ejpam-5038	85	45	[	[	X
ejpam-5038	85	46	{	{	PUNCT
ejpam-5038	85	47	l3	l3	NOUN
ejpam-5038	85	48	,	,	PUNCT
ejpam-5038	85	49	l1	l1	PROPN
ejpam-5038	85	50	}	}	PUNCT
ejpam-5038	85	51	]	]	PUNCT
ejpam-5038	85	52	.	.	PUNCT
ejpam-5038	86	1	the	the	DET
ejpam-5038	86	2	subgraphh1	subgraphh1	NOUN
ejpam-5038	86	3	induced	induce	VERB
ejpam-5038	86	4	by	by	ADP
ejpam-5038	86	5	the	the	DET
ejpam-5038	86	6	remaining	remain	VERB
ejpam-5038	86	7	vertices	vertex	NOUN
ejpam-5038	86	8	require	require	VERB
ejpam-5038	86	9	3	3	NUM
ejpam-5038	86	10	vertices	vertex	NOUN
ejpam-5038	86	11	to	to	PART
ejpam-5038	86	12	be	be	AUX
ejpam-5038	86	13	included	include	VERB
ejpam-5038	86	14	in	in	ADP
ejpam-5038	86	15	d	d	PROPN
ejpam-5038	86	16	to	to	PART
ejpam-5038	86	17	dominate	dominate	VERB
ejpam-5038	86	18	all	all	DET
ejpam-5038	86	19	vertices	vertex	NOUN
ejpam-5038	86	20	of	of	ADP
ejpam-5038	86	21	the	the	DET
ejpam-5038	86	22	subgraph	subgraph	NOUN
ejpam-5038	86	23	.	.	PUNCT
ejpam-5038	87	1	see	see	VERB
ejpam-5038	87	2	figure	figure	NOUN
ejpam-5038	87	3	2(a	2(a	NUM
ejpam-5038	87	4	)	)	PUNCT
ejpam-5038	87	5	.	.	PUNCT
ejpam-5038	88	1	again	again	ADV
ejpam-5038	88	2	,	,	PUNCT
ejpam-5038	88	3	suppose	suppose	VERB
ejpam-5038	88	4	d	d	X
ejpam-5038	88	5	contains	contain	VERB
ejpam-5038	88	6	{	{	PUNCT
ejpam-5038	88	7	l2	l2	NOUN
ejpam-5038	88	8	,	,	PUNCT
ejpam-5038	88	9	l3	l3	PROPN
ejpam-5038	88	10	}	}	PUNCT
ejpam-5038	88	11	.	.	PUNCT
ejpam-5038	89	1	we	we	PRON
ejpam-5038	89	2	have	have	VERB
ejpam-5038	89	3	n	n	PRON
ejpam-5038	89	4	[	[	X
ejpam-5038	89	5	{	{	PUNCT
ejpam-5038	89	6	l2	l2	NOUN
ejpam-5038	89	7	,	,	PUNCT
ejpam-5038	89	8	l3	l3	PROPN
ejpam-5038	89	9	}	}	PUNCT
ejpam-5038	89	10	]	]	PUNCT
ejpam-5038	90	1	=	=	PRON
ejpam-5038	90	2	{	{	PUNCT
ejpam-5038	90	3	l1	l1	PROPN
ejpam-5038	90	4	,	,	PUNCT
ejpam-5038	90	5	l2	l2	NOUN
ejpam-5038	90	6	,	,	PUNCT
ejpam-5038	90	7	l3	l3	PROPN
ejpam-5038	90	8	,	,	PUNCT
ejpam-5038	90	9	1	1	NUM
ejpam-5038	90	10	,	,	PUNCT
ejpam-5038	90	11	3	3	NUM
ejpam-5038	90	12	}	}	PUNCT
ejpam-5038	90	13	.	.	PUNCT
ejpam-5038	91	1	the	the	DET
ejpam-5038	91	2	subgraph	subgraph	PROPN
ejpam-5038	91	3	h2	h2	NOUN
ejpam-5038	91	4	induced	induce	VERB
ejpam-5038	91	5	by	by	ADP
ejpam-5038	91	6	the	the	DET
ejpam-5038	91	7	remaining	remain	VERB
ejpam-5038	91	8	vertices	vertex	NOUN
ejpam-5038	91	9	require	require	VERB
ejpam-5038	91	10	3	3	NUM
ejpam-5038	91	11	vertices	vertex	NOUN
ejpam-5038	91	12	to	to	PART
ejpam-5038	91	13	be	be	AUX
ejpam-5038	91	14	included	include	VERB
ejpam-5038	91	15	in	in	ADP
ejpam-5038	91	16	d	d	PROPN
ejpam-5038	91	17	to	to	PART
ejpam-5038	91	18	dominate	dominate	VERB
ejpam-5038	91	19	all	all	DET
ejpam-5038	91	20	vertices	vertex	NOUN
ejpam-5038	91	21	of	of	ADP
ejpam-5038	91	22	the	the	DET
ejpam-5038	91	23	subgraph	subgraph	NOUN
ejpam-5038	91	24	.	.	PUNCT
ejpam-5038	92	1	see	see	VERB
ejpam-5038	92	2	figure	figure	NOUN
ejpam-5038	92	3	2(b	2(b	NUM
ejpam-5038	92	4	)	)	PUNCT
ejpam-5038	92	5	.	.	PUNCT
ejpam-5038	93	1	in	in	ADP
ejpam-5038	93	2	either	either	DET
ejpam-5038	93	3	cases	case	NOUN
ejpam-5038	93	4	,	,	PUNCT
ejpam-5038	93	5	we	we	PRON
ejpam-5038	93	6	have	have	VERB
ejpam-5038	93	7	|d|=	|d|=	NOUN
ejpam-5038	93	8	5	5	NUM
ejpam-5038	93	9	.	.	PUNCT
ejpam-5038	94	1	we	we	PRON
ejpam-5038	94	2	now	now	ADV
ejpam-5038	94	3	proceed	proceed	VERB
ejpam-5038	94	4	to	to	PART
ejpam-5038	94	5	determine	determine	VERB
ejpam-5038	94	6	the	the	DET
ejpam-5038	94	7	domination	domination	NOUN
ejpam-5038	94	8	number	number	NOUN
ejpam-5038	94	9	of	of	ADP
ejpam-5038	94	10	x(k	x(k	PROPN
ejpam-5038	94	11	)	)	PUNCT
ejpam-5038	94	12	,	,	PUNCT
ejpam-5038	94	13	k	k	PROPN
ejpam-5038	94	14	≥	≥	NUM
ejpam-5038	95	1	3	3	X
ejpam-5038	95	2	.	.	PUNCT
ejpam-5038	96	1	let	let	VERB
ejpam-5038	96	2	h	h	NOUN
ejpam-5038	96	3	be	be	AUX
ejpam-5038	96	4	the	the	DET
ejpam-5038	96	5	subgraph	subgraph	NOUN
ejpam-5038	96	6	induced	induce	VERB
ejpam-5038	96	7	by	by	ADP
ejpam-5038	96	8	the	the	DET
ejpam-5038	96	9	vertices	vertex	NOUN
ejpam-5038	96	10	in	in	ADP
ejpam-5038	96	11	levels	level	NOUN
ejpam-5038	96	12	k	k	PROPN
ejpam-5038	96	13	,	,	PUNCT
ejpam-5038	96	14	k	k	PROPN
ejpam-5038	97	1	−	−	PROPN
ejpam-5038	97	2	1	1	NUM
ejpam-5038	97	3	,	,	PUNCT
ejpam-5038	97	4	k	k	PROPN
ejpam-5038	97	5	−	−	PROPN
ejpam-5038	97	6	2	2	NUM
ejpam-5038	97	7	and	and	CCONJ
ejpam-5038	97	8	k	k	NOUN
ejpam-5038	97	9	−	−	PROPN
ejpam-5038	97	10	3	3	NUM
ejpam-5038	97	11	of	of	ADP
ejpam-5038	97	12	x(k	x(k	PROPN
ejpam-5038	97	13	)	)	PUNCT
ejpam-5038	97	14	,	,	PUNCT
ejpam-5038	97	15	k	k	PROPN
ejpam-5038	97	16	≥	≥	NUM
ejpam-5038	97	17	3	3	X
ejpam-5038	97	18	.	.	PUNCT
ejpam-5038	97	19	h	h	PROPN
ejpam-5038	97	20	has	have	VERB
ejpam-5038	97	21	the	the	DET
ejpam-5038	97	22	following	follow	VERB
ejpam-5038	97	23	properties	property	NOUN
ejpam-5038	97	24	:	:	PUNCT
ejpam-5038	97	25	(	(	PUNCT
ejpam-5038	97	26	i	i	NOUN
ejpam-5038	97	27	)	)	PUNCT
ejpam-5038	97	28	v	v	PROPN
ejpam-5038	97	29	(	(	PUNCT
ejpam-5038	97	30	h	h	NOUN
ejpam-5038	97	31	)	)	PUNCT
ejpam-5038	98	1	=	=	PUNCT
ejpam-5038	98	2	⋃2k−3	⋃2k−3	PROPN
ejpam-5038	98	3	i=1	i=1	PROPN
ejpam-5038	98	4	vi	vi	PROPN
ejpam-5038	99	1	such	such	ADJ
ejpam-5038	99	2	that	that	SCONJ
ejpam-5038	99	3	the	the	DET
ejpam-5038	99	4	subgraph	subgraph	NOUN
ejpam-5038	99	5	induced	induce	VERB
ejpam-5038	99	6	by	by	ADP
ejpam-5038	99	7	vi	vi	PROPN
ejpam-5038	99	8	is	be	AUX
ejpam-5038	99	9	isomorphic	isomorphic	ADJ
ejpam-5038	99	10	to	to	ADP
ejpam-5038	99	11	x(3	x(3	NOUN
ejpam-5038	99	12	)	)	PUNCT
ejpam-5038	99	13	,	,	PUNCT
ejpam-5038	99	14	1	1	NUM
ejpam-5038	99	15	≤	≤	NUM
ejpam-5038	99	16	i	i	PRON
ejpam-5038	99	17	≤	≤	ADJ
ejpam-5038	99	18	2k−3	2k−3	NOUN
ejpam-5038	99	19	.	.	PUNCT
ejpam-5038	100	1	let	let	VERB
ejpam-5038	100	2	these	these	DET
ejpam-5038	100	3	copies	copy	NOUN
ejpam-5038	100	4	of	of	ADP
ejpam-5038	100	5	x(3	x(3	NOUN
ejpam-5038	100	6	)	)	PUNCT
ejpam-5038	100	7	be	be	AUX
ejpam-5038	100	8	named	name	VERB
ejpam-5038	100	9	h1	h1	PROPN
ejpam-5038	100	10	,	,	PUNCT
ejpam-5038	100	11	h2	h2	PROPN
ejpam-5038	100	12	,	,	PUNCT
ejpam-5038	100	13	...	...	PUNCT
ejpam-5038	100	14	,	,	PUNCT
ejpam-5038	100	15	h2k−3	h2k−3	PROPN
ejpam-5038	100	16	from	from	ADP
ejpam-5038	100	17	left	left	ADJ
ejpam-5038	100	18	to	to	ADP
ejpam-5038	100	19	right	right	ADV
ejpam-5038	100	20	as	as	SCONJ
ejpam-5038	100	21	shown	show	VERB
ejpam-5038	100	22	in	in	ADP
ejpam-5038	100	23	figure	figure	NOUN
ejpam-5038	100	24	3	3	NUM
ejpam-5038	100	25	.	.	PUNCT
ejpam-5038	101	1	let	let	VERB
ejpam-5038	101	2	the	the	DET
ejpam-5038	101	3	roots	root	NOUN
ejpam-5038	101	4	of	of	ADP
ejpam-5038	101	5	hi	hi	INTJ
ejpam-5038	101	6	,	,	PUNCT
ejpam-5038	101	7	1	1	NUM
ejpam-5038	101	8	≤	≤	NUM
ejpam-5038	101	9	i	i	PRON
ejpam-5038	101	10	≤	≤	NOUN
ejpam-5038	101	11	2k−3	2k−3	NUM
ejpam-5038	101	12	be	be	AUX
ejpam-5038	101	13	labeled	label	VERB
ejpam-5038	101	14	u1	u1	NOUN
ejpam-5038	101	15	,	,	PUNCT
ejpam-5038	101	16	u2	u2	NOUN
ejpam-5038	101	17	,	,	PUNCT
ejpam-5038	101	18	...	...	PUNCT
ejpam-5038	101	19	,	,	PUNCT
ejpam-5038	101	20	u2k−3	u2k−3	PROPN
ejpam-5038	101	21	respectively	respectively	ADV
ejpam-5038	101	22	.	.	PUNCT
ejpam-5038	102	1	figure	figure	VERB
ejpam-5038	102	2	3	3	NUM
ejpam-5038	102	3	:	:	PUNCT
ejpam-5038	102	4	subgraph	subgraph	NOUN
ejpam-5038	102	5	induced	induce	VERB
ejpam-5038	102	6	by	by	ADP
ejpam-5038	102	7	vertices	vertex	NOUN
ejpam-5038	102	8	in	in	ADP
ejpam-5038	102	9	levels	level	NOUN
ejpam-5038	102	10	2,3,4,5	2,3,4,5	NUM
ejpam-5038	102	11	of	of	ADP
ejpam-5038	102	12	x(5	x(5	PROPN
ejpam-5038	102	13	)	)	PUNCT
ejpam-5038	102	14	let	let	VERB
ejpam-5038	102	15	the	the	DET
ejpam-5038	102	16	leftmost	leftmost	ADJ
ejpam-5038	102	17	descendants	descendant	NOUN
ejpam-5038	102	18	of	of	ADP
ejpam-5038	102	19	ui	ui	PROPN
ejpam-5038	102	20	be	be	AUX
ejpam-5038	102	21	labeled	label	VERB
ejpam-5038	102	22	li1	li1	NOUN
ejpam-5038	102	23	,	,	PUNCT
ejpam-5038	102	24	li2	li2	PROPN
ejpam-5038	102	25	and	and	CCONJ
ejpam-5038	102	26	li3	li3	PROPN
ejpam-5038	102	27	;	;	PUNCT
ejpam-5038	102	28	similarly	similarly	ADV
ejpam-5038	102	29	let	let	VERB
ejpam-5038	102	30	the	the	DET
ejpam-5038	102	31	rightmost	rightmost	ADJ
ejpam-5038	102	32	descendants	descendant	NOUN
ejpam-5038	102	33	of	of	ADP
ejpam-5038	102	34	ui	ui	PROPN
ejpam-5038	102	35	be	be	AUX
ejpam-5038	102	36	labeled	label	VERB
ejpam-5038	102	37	ri1	ri1	NOUN
ejpam-5038	102	38	,	,	PUNCT
ejpam-5038	102	39	ri2	ri2	NOUN
ejpam-5038	102	40	and	and	CCONJ
ejpam-5038	102	41	ri3	ri3	PROPN
ejpam-5038	102	42	,	,	PUNCT
ejpam-5038	102	43	1	1	NUM
ejpam-5038	102	44	≤	≤	NUM
ejpam-5038	102	45	i	i	PRON
ejpam-5038	102	46	≤	≤	ADJ
ejpam-5038	102	47	2k−3	2k−3	NOUN
ejpam-5038	102	48	.	.	PUNCT
ejpam-5038	103	1	see	see	VERB
ejpam-5038	103	2	figure	figure	NOUN
ejpam-5038	103	3	3	3	NUM
ejpam-5038	103	4	.	.	PUNCT
ejpam-5038	104	1	let	let	VERB
ejpam-5038	104	2	the	the	DET
ejpam-5038	104	3	2	2	NUM
ejpam-5038	104	4	unlabeled	unlabele	VERB
ejpam-5038	104	5	vertices	vertex	NOUN
ejpam-5038	104	6	in	in	ADP
ejpam-5038	104	7	level	level	NOUN
ejpam-5038	104	8	k−	k−	NOUN
ejpam-5038	104	9	1	1	NUM
ejpam-5038	104	10	in	in	ADP
ejpam-5038	104	11	each	each	DET
ejpam-5038	104	12	hi	hi	INTJ
ejpam-5038	104	13	be	be	AUX
ejpam-5038	104	14	labeled	label	VERB
ejpam-5038	104	15	as	as	ADP
ejpam-5038	104	16	(	(	PUNCT
ejpam-5038	104	17	i−	i−	PROPN
ejpam-5038	104	18	1)8	1)8	PROPN
ejpam-5038	104	19	+	+	NUM
ejpam-5038	104	20	1	1	NUM
ejpam-5038	104	21	and	and	CCONJ
ejpam-5038	104	22	(	(	PUNCT
ejpam-5038	104	23	i−	i−	PROPN
ejpam-5038	104	24	1)8	1)8	PROPN
ejpam-5038	104	25	+	+	NUM
ejpam-5038	104	26	2	2	NUM
ejpam-5038	104	27	and	and	CCONJ
ejpam-5038	104	28	the	the	DET
ejpam-5038	104	29	6	6	NUM
ejpam-5038	104	30	unlabeled	unlabele	VERB
ejpam-5038	104	31	vertices	vertex	NOUN
ejpam-5038	104	32	in	in	ADP
ejpam-5038	104	33	level	level	NOUN
ejpam-5038	104	34	k	k	PROPN
ejpam-5038	104	35	of	of	ADP
ejpam-5038	104	36	each	each	DET
ejpam-5038	104	37	hi	hi	INTJ
ejpam-5038	104	38	as	as	ADP
ejpam-5038	104	39	(	(	PUNCT
ejpam-5038	104	40	i−	i−	PROPN
ejpam-5038	104	41	1)8	1)8	PROPN
ejpam-5038	104	42	+	+	CCONJ
ejpam-5038	104	43	3	3	NUM
ejpam-5038	104	44	,	,	PUNCT
ejpam-5038	104	45	(	(	PUNCT
ejpam-5038	104	46	i−	i−	PROPN
ejpam-5038	104	47	1)8	1)8	PROPN
ejpam-5038	104	48	+	+	CCONJ
ejpam-5038	104	49	4	4	NUM
ejpam-5038	104	50	,	,	PUNCT
ejpam-5038	104	51	...	...	PUNCT
ejpam-5038	104	52	,	,	PUNCT
ejpam-5038	104	53	(	(	PUNCT
ejpam-5038	104	54	i−	i−	PROPN
ejpam-5038	104	55	1)8	1)8	PROPN
ejpam-5038	104	56	+	+	CCONJ
ejpam-5038	104	57	8	8	NUM
ejpam-5038	104	58	v.	v.	ADP
ejpam-5038	104	59	shalini	shalini	PROPN
ejpam-5038	104	60	,	,	PUNCT
ejpam-5038	104	61	i.	i.	PROPN
ejpam-5038	104	62	rajasingh	rajasingh	PROPN
ejpam-5038	104	63	/	/	SYM
ejpam-5038	104	64	eur	eur	PROPN
ejpam-5038	104	65	.	.	PUNCT
ejpam-5038	105	1	j.	j.	PROPN
ejpam-5038	105	2	pure	pure	PROPN
ejpam-5038	105	3	appl	appl	PROPN
ejpam-5038	105	4	.	.	PROPN
ejpam-5038	105	5	math	math	PROPN
ejpam-5038	105	6	,	,	PUNCT
ejpam-5038	105	7	17	17	NUM
ejpam-5038	105	8	(	(	PUNCT
ejpam-5038	105	9	2	2	NUM
ejpam-5038	105	10	)	)	PUNCT
ejpam-5038	105	11	(	(	PUNCT
ejpam-5038	105	12	2024	2024	NUM
ejpam-5038	105	13	)	)	PUNCT
ejpam-5038	105	14	,	,	PUNCT
ejpam-5038	105	15	1082	1082	NUM
ejpam-5038	105	16	-	-	SYM
ejpam-5038	105	17	1093	1093	NUM
ejpam-5038	105	18	1086	1086	NUM
ejpam-5038	105	19	figure	figure	NOUN
ejpam-5038	105	20	4	4	NUM
ejpam-5038	105	21	:	:	PUNCT
ejpam-5038	105	22	(	(	PUNCT
ejpam-5038	105	23	a	a	X
ejpam-5038	105	24	)	)	PUNCT
ejpam-5038	105	25	subgraph	subgraph	NOUN
ejpam-5038	105	26	h1	h1	NOUN
ejpam-5038	105	27	in	in	ADP
ejpam-5038	105	28	case	case	NOUN
ejpam-5038	105	29	1	1	NUM
ejpam-5038	105	30	.	.	PUNCT
ejpam-5038	106	1	(	(	PUNCT
ejpam-5038	106	2	b	b	X
ejpam-5038	106	3	)	)	PUNCT
ejpam-5038	106	4	subgraph	subgraph	NOUN
ejpam-5038	106	5	h2	h2	NOUN
ejpam-5038	106	6	in	in	ADP
ejpam-5038	106	7	case	case	NOUN
ejpam-5038	106	8	1.(c	1.(c	NOUN
ejpam-5038	106	9	)	)	PUNCT
ejpam-5038	106	10	subgraph	subgraph	NOUN
ejpam-5038	106	11	h2	h2	NOUN
ejpam-5038	106	12	in	in	ADP
ejpam-5038	106	13	case	case	NOUN
ejpam-5038	106	14	2	2	NUM
ejpam-5038	106	15	.	.	PUNCT
ejpam-5038	106	16	from	from	ADP
ejpam-5038	106	17	left	left	ADJ
ejpam-5038	106	18	to	to	ADP
ejpam-5038	106	19	right	right	NOUN
ejpam-5038	106	20	,	,	PUNCT
ejpam-5038	106	21	1	1	NUM
ejpam-5038	106	22	≤	≤	NUM
ejpam-5038	106	23	i	i	PRON
ejpam-5038	106	24	≤	≤	ADJ
ejpam-5038	106	25	2k−3	2k−3	NOUN
ejpam-5038	106	26	.	.	PUNCT
ejpam-5038	107	1	lemma	lemma	PROPN
ejpam-5038	107	2	4	4	X
ejpam-5038	107	3	.	.	PUNCT
ejpam-5038	108	1	let	let	VERB
ejpam-5038	108	2	h	h	NOUN
ejpam-5038	108	3	be	be	AUX
ejpam-5038	108	4	the	the	DET
ejpam-5038	108	5	subgraph	subgraph	NOUN
ejpam-5038	108	6	of	of	ADP
ejpam-5038	108	7	x(k	x(k	PROPN
ejpam-5038	108	8	)	)	PUNCT
ejpam-5038	108	9	induced	induce	VERB
ejpam-5038	108	10	by	by	ADP
ejpam-5038	108	11	levels	level	NOUN
ejpam-5038	108	12	k	k	PROPN
ejpam-5038	108	13	,	,	PUNCT
ejpam-5038	108	14	k	k	PROPN
ejpam-5038	109	1	−	−	PROPN
ejpam-5038	109	2	1	1	NUM
ejpam-5038	109	3	,	,	PUNCT
ejpam-5038	109	4	k	k	PROPN
ejpam-5038	109	5	−	−	PROPN
ejpam-5038	109	6	2	2	NUM
ejpam-5038	109	7	and	and	CCONJ
ejpam-5038	109	8	k	k	NOUN
ejpam-5038	109	9	−	−	PROPN
ejpam-5038	109	10	3	3	NUM
ejpam-5038	109	11	of	of	ADP
ejpam-5038	109	12	x(k	x(k	PROPN
ejpam-5038	109	13	)	)	PUNCT
ejpam-5038	109	14	,	,	PUNCT
ejpam-5038	109	15	k	k	PROPN
ejpam-5038	109	16	≥	≥	NUM
ejpam-5038	109	17	3	3	NUM
ejpam-5038	109	18	.	.	PUNCT
ejpam-5038	109	19	then	then	ADV
ejpam-5038	109	20	γ(h	γ(h	NOUN
ejpam-5038	109	21	)	)	PUNCT
ejpam-5038	109	22	=	=	SYM
ejpam-5038	109	23	2k−1	2k−1	NUM
ejpam-5038	109	24	.	.	PUNCT
ejpam-5038	110	1	proof	proof	NOUN
ejpam-5038	110	2	.	.	PUNCT
ejpam-5038	111	1	due	due	ADP
ejpam-5038	111	2	to	to	ADP
ejpam-5038	111	3	symmetricity	symmetricity	NOUN
ejpam-5038	111	4	and	and	CCONJ
ejpam-5038	111	5	the	the	DET
ejpam-5038	111	6	fact	fact	NOUN
ejpam-5038	111	7	that	that	SCONJ
ejpam-5038	111	8	vertices	vertex	NOUN
ejpam-5038	111	9	of	of	ADP
ejpam-5038	111	10	hi−1	hi−1	PROPN
ejpam-5038	111	11	and	and	CCONJ
ejpam-5038	111	12	hi+1	hi+1	PRON
ejpam-5038	111	13	can	can	AUX
ejpam-5038	111	14	dominate	dominate	VERB
ejpam-5038	111	15	vertices	vertex	NOUN
ejpam-5038	111	16	in	in	ADP
ejpam-5038	111	17	hi	hi	ADV
ejpam-5038	111	18	,	,	PUNCT
ejpam-5038	111	19	it	it	PRON
ejpam-5038	111	20	is	be	AUX
ejpam-5038	111	21	enough	enough	ADJ
ejpam-5038	111	22	to	to	PART
ejpam-5038	111	23	consider	consider	VERB
ejpam-5038	111	24	the	the	DET
ejpam-5038	111	25	domination	domination	NOUN
ejpam-5038	111	26	parameter	parameter	NOUN
ejpam-5038	111	27	in	in	ADP
ejpam-5038	111	28	the	the	DET
ejpam-5038	111	29	subgroup	subgroup	NOUN
ejpam-5038	111	30	h1	h1	PROPN
ejpam-5038	111	31	∪	∪	PROPN
ejpam-5038	111	32	h2	h2	PROPN
ejpam-5038	111	33	∪h3	∪h3	NOUN
ejpam-5038	111	34	.	.	PUNCT
ejpam-5038	112	1	case	case	NOUN
ejpam-5038	112	2	1	1	X
ejpam-5038	112	3	.	.	X
ejpam-5038	112	4	consider	consider	VERB
ejpam-5038	112	5	h1	h1	VERB
ejpam-5038	112	6	∪h2	∪h2	PROPN
ejpam-5038	112	7	.	.	PUNCT
ejpam-5038	113	1	suppose	suppose	VERB
ejpam-5038	113	2	u1	u1	NOUN
ejpam-5038	113	3	,	,	PUNCT
ejpam-5038	113	4	r11	r11	NOUN
ejpam-5038	113	5	,	,	PUNCT
ejpam-5038	113	6	r12	r12	NOUN
ejpam-5038	113	7	and	and	CCONJ
ejpam-5038	113	8	r13	r13	NOUN
ejpam-5038	113	9	are	be	AUX
ejpam-5038	113	10	dominated	dominate	VERB
ejpam-5038	113	11	by	by	ADP
ejpam-5038	113	12	vertices	vertex	NOUN
ejpam-5038	113	13	that	that	PRON
ejpam-5038	113	14	are	be	AUX
ejpam-5038	113	15	not	not	PART
ejpam-5038	113	16	in	in	ADP
ejpam-5038	113	17	h1	h1	PROPN
ejpam-5038	113	18	.	.	PUNCT
ejpam-5038	114	1	then	then	ADV
ejpam-5038	114	2	the	the	DET
ejpam-5038	114	3	subgraph	subgraph	NOUN
ejpam-5038	114	4	of	of	ADP
ejpam-5038	114	5	h1	h1	PROPN
ejpam-5038	114	6	induced	induce	VERB
ejpam-5038	114	7	by	by	ADP
ejpam-5038	114	8	the	the	DET
ejpam-5038	114	9	remaining	remain	VERB
ejpam-5038	114	10	vertices	vertex	NOUN
ejpam-5038	114	11	of	of	ADP
ejpam-5038	114	12	h1	h1	PROPN
ejpam-5038	114	13	require	require	VERB
ejpam-5038	114	14	3	3	NUM
ejpam-5038	114	15	vertices	vertex	NOUN
ejpam-5038	114	16	of	of	ADP
ejpam-5038	114	17	h1	h1	NOUN
ejpam-5038	114	18	in	in	ADP
ejpam-5038	114	19	any	any	DET
ejpam-5038	114	20	dominating	dominating	NOUN
ejpam-5038	114	21	set	set	NOUN
ejpam-5038	114	22	d	d	PROPN
ejpam-5038	114	23	of	of	ADP
ejpam-5038	114	24	h.	h.	PROPN
ejpam-5038	114	25	see	see	PROPN
ejpam-5038	114	26	figure	figure	NOUN
ejpam-5038	114	27	4(a	4(a	NUM
ejpam-5038	114	28	)	)	PUNCT
ejpam-5038	114	29	.	.	PUNCT
ejpam-5038	115	1	in	in	ADP
ejpam-5038	115	2	this	this	DET
ejpam-5038	115	3	case	case	NOUN
ejpam-5038	115	4	necessarily	necessarily	ADV
ejpam-5038	115	5	{	{	PUNCT
ejpam-5038	115	6	u2	u2	PROPN
ejpam-5038	115	7	,	,	PUNCT
ejpam-5038	115	8	l21	l21	NOUN
ejpam-5038	115	9	,	,	PUNCT
ejpam-5038	115	10	l22	l22	NOUN
ejpam-5038	115	11	,	,	PUNCT
ejpam-5038	115	12	l23	l23	NOUN
ejpam-5038	115	13	}	}	PUNCT
ejpam-5038	115	14	⊆	⊆	NUM
ejpam-5038	115	15	d.	d.	NOUN
ejpam-5038	115	16	to	to	PART
ejpam-5038	115	17	dominate	dominate	VERB
ejpam-5038	115	18	the	the	DET
ejpam-5038	115	19	remaining	remain	VERB
ejpam-5038	115	20	vertices	vertex	NOUN
ejpam-5038	115	21	in	in	ADP
ejpam-5038	115	22	h2	h2	NOUN
ejpam-5038	115	23	,	,	PUNCT
ejpam-5038	115	24	3	3	NUM
ejpam-5038	115	25	more	more	ADJ
ejpam-5038	115	26	vertices	vertex	NOUN
ejpam-5038	115	27	in	in	ADP
ejpam-5038	115	28	h2	h2	NOUN
ejpam-5038	115	29	are	be	AUX
ejpam-5038	115	30	to	to	PART
ejpam-5038	115	31	be	be	AUX
ejpam-5038	115	32	included	include	VERB
ejpam-5038	115	33	in	in	ADP
ejpam-5038	115	34	d.	d.	PROPN
ejpam-5038	115	35	see	see	VERB
ejpam-5038	115	36	figure	figure	NOUN
ejpam-5038	115	37	4(b	4(b	NUM
ejpam-5038	115	38	)	)	PUNCT
ejpam-5038	115	39	.	.	PUNCT
ejpam-5038	116	1	thus	thus	ADV
ejpam-5038	116	2	to	to	PART
ejpam-5038	116	3	dominate	dominate	VERB
ejpam-5038	116	4	h1	h1	PRON
ejpam-5038	116	5	∪h2	∪h2	PROPN
ejpam-5038	116	6	at	at	ADP
ejpam-5038	116	7	least	least	ADJ
ejpam-5038	116	8	9	9	NUM
ejpam-5038	116	9	vertices	vertex	NOUN
ejpam-5038	116	10	of	of	ADP
ejpam-5038	116	11	h1	h1	NOUN
ejpam-5038	116	12	∪h2	∪h2	PROPN
ejpam-5038	116	13	are	be	AUX
ejpam-5038	116	14	to	to	PART
ejpam-5038	116	15	be	be	AUX
ejpam-5038	116	16	included	include	VERB
ejpam-5038	116	17	in	in	ADP
ejpam-5038	116	18	d.	d.	PROPN
ejpam-5038	116	19	case	case	NOUN
ejpam-5038	116	20	2	2	NUM
ejpam-5038	116	21	:	:	PUNCT
ejpam-5038	116	22	consider	consider	VERB
ejpam-5038	116	23	h1	h1	PROPN
ejpam-5038	116	24	∪	∪	VERB
ejpam-5038	116	25	h2	h2	PROPN
ejpam-5038	116	26	∪	∪	NOUN
ejpam-5038	116	27	h3	h3	NOUN
ejpam-5038	116	28	.	.	PUNCT
ejpam-5038	117	1	suppose	suppose	VERB
ejpam-5038	117	2	u2	u2	NOUN
ejpam-5038	117	3	,	,	PUNCT
ejpam-5038	117	4	l21	l21	NOUN
ejpam-5038	117	5	,	,	PUNCT
ejpam-5038	117	6	l22	l22	NOUN
ejpam-5038	117	7	,	,	PUNCT
ejpam-5038	117	8	l23	l23	NOUN
ejpam-5038	117	9	,	,	PUNCT
ejpam-5038	117	10	r21	r21	NOUN
ejpam-5038	117	11	,	,	PUNCT
ejpam-5038	117	12	r22	r22	NOUN
ejpam-5038	117	13	and	and	CCONJ
ejpam-5038	117	14	r23	r23	NOUN
ejpam-5038	117	15	are	be	AUX
ejpam-5038	117	16	already	already	ADV
ejpam-5038	117	17	dominated	dominate	VERB
ejpam-5038	117	18	by	by	ADP
ejpam-5038	117	19	vertices	vertex	NOUN
ejpam-5038	117	20	that	that	PRON
ejpam-5038	117	21	are	be	AUX
ejpam-5038	117	22	not	not	PART
ejpam-5038	117	23	in	in	ADP
ejpam-5038	117	24	h2	h2	NOUN
ejpam-5038	117	25	.	.	PUNCT
ejpam-5038	118	1	then	then	ADV
ejpam-5038	118	2	the	the	DET
ejpam-5038	118	3	subgraph	subgraph	NOUN
ejpam-5038	118	4	of	of	ADP
ejpam-5038	118	5	h2	h2	NOUN
ejpam-5038	118	6	induced	induce	VERB
ejpam-5038	118	7	by	by	ADP
ejpam-5038	118	8	the	the	DET
ejpam-5038	118	9	remaining	remain	VERB
ejpam-5038	118	10	vertices	vertex	NOUN
ejpam-5038	118	11	of	of	ADP
ejpam-5038	118	12	h2	h2	NOUN
ejpam-5038	118	13	require	require	VERB
ejpam-5038	118	14	2	2	NUM
ejpam-5038	118	15	vertices	vertex	NOUN
ejpam-5038	118	16	of	of	ADP
ejpam-5038	118	17	h2	h2	PROPN
ejpam-5038	118	18	in	in	ADP
ejpam-5038	118	19	d.	d.	PROPN
ejpam-5038	118	20	see	see	VERB
ejpam-5038	118	21	figure	figure	NOUN
ejpam-5038	118	22	4(c	4(c	NUM
ejpam-5038	118	23	)	)	PUNCT
ejpam-5038	118	24	.	.	PUNCT
ejpam-5038	119	1	in	in	ADP
ejpam-5038	119	2	this	this	DET
ejpam-5038	119	3	case	case	NOUN
ejpam-5038	119	4	necessarily	necessarily	ADV
ejpam-5038	119	5	{	{	PUNCT
ejpam-5038	119	6	r11	r11	NOUN
ejpam-5038	119	7	,	,	PUNCT
ejpam-5038	119	8	r12	r12	NOUN
ejpam-5038	119	9	,	,	PUNCT
ejpam-5038	119	10	r13	r13	PROPN
ejpam-5038	119	11	,	,	PUNCT
ejpam-5038	119	12	l31	l31	NOUN
ejpam-5038	119	13	,	,	PUNCT
ejpam-5038	119	14	l32	l32	NOUN
ejpam-5038	119	15	,	,	PUNCT
ejpam-5038	119	16	l33	l33	PROPN
ejpam-5038	119	17	}	}	PUNCT
ejpam-5038	119	18	⊆	⊆	NUM
ejpam-5038	119	19	d.	d.	NOUN
ejpam-5038	119	20	three	three	NUM
ejpam-5038	119	21	more	more	ADJ
ejpam-5038	119	22	vertices	vertex	NOUN
ejpam-5038	119	23	in	in	ADP
ejpam-5038	119	24	each	each	PRON
ejpam-5038	119	25	of	of	ADP
ejpam-5038	119	26	h1	h1	NOUN
ejpam-5038	119	27	and	and	CCONJ
ejpam-5038	119	28	h3	h3	NOUN
ejpam-5038	119	29	are	be	AUX
ejpam-5038	119	30	to	to	PART
ejpam-5038	119	31	be	be	AUX
ejpam-5038	119	32	included	include	VERB
ejpam-5038	119	33	in	in	ADP
ejpam-5038	119	34	d	d	PROPN
ejpam-5038	119	35	to	to	PART
ejpam-5038	119	36	dominate	dominate	VERB
ejpam-5038	119	37	all	all	DET
ejpam-5038	119	38	the	the	DET
ejpam-5038	119	39	vertices	vertex	NOUN
ejpam-5038	119	40	in	in	ADP
ejpam-5038	119	41	h1	h1	PROPN
ejpam-5038	119	42	∪	∪	PROPN
ejpam-5038	119	43	h2	h2	PROPN
ejpam-5038	119	44	∪	∪	NOUN
ejpam-5038	119	45	h3	h3	NOUN
ejpam-5038	119	46	.	.	PUNCT
ejpam-5038	120	1	thus	thus	ADV
ejpam-5038	120	2	to	to	PART
ejpam-5038	120	3	dominate	dominate	VERB
ejpam-5038	120	4	h1	h1	PROPN
ejpam-5038	120	5	∪h2	∪h2	PROPN
ejpam-5038	120	6	∪h3	∪h3	PROPN
ejpam-5038	120	7	at	at	ADV
ejpam-5038	120	8	least	least	ADV
ejpam-5038	120	9	6	6	NUM
ejpam-5038	120	10	+	+	SYM
ejpam-5038	120	11	2	2	NUM
ejpam-5038	120	12	+	+	NUM
ejpam-5038	120	13	6	6	NUM
ejpam-5038	120	14	=	=	SYM
ejpam-5038	120	15	14	14	NUM
ejpam-5038	120	16	vertices	vertex	NOUN
ejpam-5038	120	17	of	of	ADP
ejpam-5038	120	18	h1	h1	PROPN
ejpam-5038	120	19	∪h2	∪h2	PROPN
ejpam-5038	120	20	∪h3	∪h3	PROPN
ejpam-5038	120	21	are	be	AUX
ejpam-5038	120	22	to	to	PART
ejpam-5038	120	23	be	be	AUX
ejpam-5038	120	24	included	include	VERB
ejpam-5038	120	25	in	in	ADP
ejpam-5038	120	26	d.	d.	PROPN
ejpam-5038	120	27	by	by	ADP
ejpam-5038	120	28	virtue	virtue	NOUN
ejpam-5038	120	29	of	of	ADP
ejpam-5038	120	30	lemmas	lemmas	PROPN
ejpam-5038	120	31	2	2	NUM
ejpam-5038	120	32	and	and	CCONJ
ejpam-5038	120	33	3	3	NUM
ejpam-5038	120	34	and	and	CCONJ
ejpam-5038	120	35	arguments	argument	NOUN
ejpam-5038	120	36	similar	similar	ADJ
ejpam-5038	120	37	to	to	ADP
ejpam-5038	120	38	the	the	DET
ejpam-5038	120	39	above	above	ADJ
ejpam-5038	120	40	cases	case	NOUN
ejpam-5038	120	41	,	,	PUNCT
ejpam-5038	120	42	we	we	PRON
ejpam-5038	120	43	claim	claim	VERB
ejpam-5038	120	44	that	that	SCONJ
ejpam-5038	120	45	selecting	select	VERB
ejpam-5038	120	46	4	4	NUM
ejpam-5038	120	47	vertices	vertex	NOUN
ejpam-5038	120	48	in	in	ADP
ejpam-5038	120	49	each	each	DET
ejpam-5038	120	50	hi	hi	ADJ
ejpam-5038	120	51	,	,	PUNCT
ejpam-5038	120	52	1	1	NUM
ejpam-5038	120	53	≤	≤	NUM
ejpam-5038	120	54	i	i	PRON
ejpam-5038	120	55	≤	≤	ADJ
ejpam-5038	120	56	2k−3	2k−3	NOUN
ejpam-5038	120	57	as	as	ADP
ejpam-5038	120	58	in	in	ADP
ejpam-5038	120	59	lemma	lemma	PROPN
ejpam-5038	120	60	1	1	NUM
ejpam-5038	120	61	yields	yield	NOUN
ejpam-5038	120	62	a	a	DET
ejpam-5038	120	63	minimum	minimum	ADJ
ejpam-5038	120	64	dominating	dominating	NOUN
ejpam-5038	120	65	set	set	NOUN
ejpam-5038	120	66	d	d	NOUN
ejpam-5038	120	67	of	of	ADP
ejpam-5038	120	68	x(k	x(k	PROPN
ejpam-5038	120	69	)	)	PUNCT
ejpam-5038	120	70	.	.	PUNCT
ejpam-5038	121	1	by	by	ADP
ejpam-5038	121	2	lemma	lemma	PROPN
ejpam-5038	121	3	1	1	NUM
ejpam-5038	121	4	,	,	PUNCT
ejpam-5038	121	5	d	d	PRON
ejpam-5038	121	6	is	be	AUX
ejpam-5038	121	7	a	a	DET
ejpam-5038	121	8	dominating	dominating	NOUN
ejpam-5038	121	9	set	set	NOUN
ejpam-5038	121	10	of	of	ADP
ejpam-5038	121	11	h.	h.	NOUN
ejpam-5038	121	12	to	to	PART
ejpam-5038	121	13	prove	prove	VERB
ejpam-5038	121	14	that	that	SCONJ
ejpam-5038	121	15	d	d	NOUN
ejpam-5038	121	16	is	be	AUX
ejpam-5038	121	17	a	a	DET
ejpam-5038	121	18	minimum	minimum	ADJ
ejpam-5038	121	19	dominating	dominating	NOUN
ejpam-5038	121	20	set	set	NOUN
ejpam-5038	121	21	,	,	PUNCT
ejpam-5038	121	22	we	we	PRON
ejpam-5038	121	23	need	need	VERB
ejpam-5038	121	24	to	to	PART
ejpam-5038	121	25	consider	consider	VERB
ejpam-5038	121	26	only	only	ADV
ejpam-5038	121	27	h1	h1	VERB
ejpam-5038	121	28	∪	∪	VERB
ejpam-5038	121	29	h2	h2	PROPN
ejpam-5038	121	30	∪	∪	NOUN
ejpam-5038	121	31	h3	h3	NOUN
ejpam-5038	121	32	and	and	CCONJ
ejpam-5038	121	33	consider	consider	VERB
ejpam-5038	121	34	the	the	DET
ejpam-5038	121	35	dominating	dominating	NOUN
ejpam-5038	121	36	sets	set	NOUN
ejpam-5038	121	37	d1	d1	PROPN
ejpam-5038	121	38	=	=	SYM
ejpam-5038	121	39	{	{	PUNCT
ejpam-5038	121	40	l11	l11	PROPN
ejpam-5038	121	41	,	,	PUNCT
ejpam-5038	121	42	r12	r12	NOUN
ejpam-5038	121	43	,	,	PUNCT
ejpam-5038	121	44	3	3	NUM
ejpam-5038	121	45	,	,	PUNCT
ejpam-5038	121	46	6	6	NUM
ejpam-5038	121	47	}	}	PUNCT
ejpam-5038	121	48	,	,	PUNCT
ejpam-5038	121	49	d′	d′	NOUN
ejpam-5038	121	50	1	1	NUM
ejpam-5038	121	51	=	=	SYM
ejpam-5038	121	52	{	{	PUNCT
ejpam-5038	121	53	r11	r11	NOUN
ejpam-5038	121	54	,	,	PUNCT
ejpam-5038	121	55	l12	l12	NOUN
ejpam-5038	121	56	,	,	PUNCT
ejpam-5038	121	57	5	5	NUM
ejpam-5038	121	58	,	,	PUNCT
ejpam-5038	121	59	8	8	NUM
ejpam-5038	121	60	}	}	PUNCT
ejpam-5038	121	61	of	of	ADP
ejpam-5038	121	62	h1	h1	NOUN
ejpam-5038	121	63	and	and	CCONJ
ejpam-5038	121	64	d3	d3	PROPN
ejpam-5038	121	65	=	=	SYM
ejpam-5038	121	66	{	{	PUNCT
ejpam-5038	121	67	l31	l31	NOUN
ejpam-5038	121	68	,	,	PUNCT
ejpam-5038	121	69	r32	r32	NOUN
ejpam-5038	121	70	,	,	PUNCT
ejpam-5038	121	71	19	19	NUM
ejpam-5038	121	72	,	,	PUNCT
ejpam-5038	121	73	22	22	NUM
ejpam-5038	121	74	}	}	PUNCT
ejpam-5038	121	75	,	,	PUNCT
ejpam-5038	121	76	d′	d′	NOUN
ejpam-5038	121	77	3	3	NUM
ejpam-5038	121	78	=	=	SYM
ejpam-5038	121	79	{	{	PUNCT
ejpam-5038	121	80	r31	r31	NOUN
ejpam-5038	121	81	,	,	PUNCT
ejpam-5038	121	82	l32	l32	NOUN
ejpam-5038	121	83	,	,	PUNCT
ejpam-5038	121	84	21	21	NUM
ejpam-5038	121	85	,	,	PUNCT
ejpam-5038	121	86	24	24	NUM
ejpam-5038	121	87	}	}	PUNCT
ejpam-5038	121	88	of	of	ADP
ejpam-5038	121	89	h3	h3	NOUN
ejpam-5038	121	90	.	.	PUNCT
ejpam-5038	122	1	if	if	SCONJ
ejpam-5038	122	2	d1	d1	PROPN
ejpam-5038	122	3	and	and	CCONJ
ejpam-5038	122	4	d′	d′	PRON
ejpam-5038	122	5	3	3	NUM
ejpam-5038	122	6	are	be	AUX
ejpam-5038	122	7	in	in	ADP
ejpam-5038	122	8	d	d	PROPN
ejpam-5038	122	9	,	,	PUNCT
ejpam-5038	122	10	then	then	ADV
ejpam-5038	122	11	we	we	PRON
ejpam-5038	122	12	observe	observe	VERB
ejpam-5038	122	13	that	that	SCONJ
ejpam-5038	122	14	r12	r12	PROPN
ejpam-5038	122	15	dominates	dominate	VERB
ejpam-5038	122	16	l22	l22	NOUN
ejpam-5038	122	17	and	and	CCONJ
ejpam-5038	122	18	l32	l32	NOUN
ejpam-5038	122	19	dominates	dominate	VERB
ejpam-5038	122	20	r22	r22	NOUN
ejpam-5038	122	21	.	.	PUNCT
ejpam-5038	123	1	the	the	DET
ejpam-5038	123	2	subgraph	subgraph	NOUN
ejpam-5038	123	3	of	of	ADP
ejpam-5038	123	4	h2	h2	NOUN
ejpam-5038	123	5	induced	induce	VERB
ejpam-5038	123	6	by	by	ADP
ejpam-5038	123	7	the	the	DET
ejpam-5038	123	8	remaining	remain	VERB
ejpam-5038	123	9	vertices	vertex	NOUN
ejpam-5038	123	10	requires	require	VERB
ejpam-5038	123	11	more	more	ADJ
ejpam-5038	123	12	than	than	ADP
ejpam-5038	123	13	4	4	NUM
ejpam-5038	123	14	vertices	vertex	NOUN
ejpam-5038	123	15	to	to	PART
ejpam-5038	123	16	dominate	dominate	VERB
ejpam-5038	123	17	the	the	DET
ejpam-5038	123	18	subgraph	subgraph	NOUN
ejpam-5038	123	19	.	.	PUNCT
ejpam-5038	124	1	see	see	VERB
ejpam-5038	124	2	figure	figure	NOUN
ejpam-5038	124	3	5(a	5(a	NUM
ejpam-5038	124	4	)	)	PUNCT
ejpam-5038	124	5	.	.	PUNCT
ejpam-5038	125	1	on	on	ADP
ejpam-5038	125	2	the	the	DET
ejpam-5038	125	3	other	other	ADJ
ejpam-5038	125	4	hand	hand	NOUN
ejpam-5038	125	5	if	if	SCONJ
ejpam-5038	125	6	d1	d1	PROPN
ejpam-5038	125	7	and	and	CCONJ
ejpam-5038	125	8	d3	d3	PROPN
ejpam-5038	125	9	are	be	AUX
ejpam-5038	125	10	in	in	ADP
ejpam-5038	125	11	d	d	PROPN
ejpam-5038	125	12	then	then	ADV
ejpam-5038	125	13	r12	r12	PROPN
ejpam-5038	125	14	dominates	dominate	VERB
ejpam-5038	125	15	l22	l22	NOUN
ejpam-5038	125	16	and	and	CCONJ
ejpam-5038	125	17	l31	l31	VERB
ejpam-5038	125	18	dominates	dominate	VERB
ejpam-5038	125	19	r21	r21	NOUN
ejpam-5038	125	20	.	.	PUNCT
ejpam-5038	126	1	in	in	ADP
ejpam-5038	126	2	this	this	DET
ejpam-5038	126	3	case	case	NOUN
ejpam-5038	126	4	,	,	PUNCT
ejpam-5038	126	5	the	the	DET
ejpam-5038	126	6	subgraph	subgraph	NOUN
ejpam-5038	126	7	of	of	ADP
ejpam-5038	126	8	h2	h2	NOUN
ejpam-5038	126	9	induced	induce	VERB
ejpam-5038	126	10	by	by	ADP
ejpam-5038	126	11	the	the	DET
ejpam-5038	126	12	remaining	remain	VERB
ejpam-5038	126	13	vertices	vertex	NOUN
ejpam-5038	126	14	require	require	VERB
ejpam-5038	126	15	4	4	NUM
ejpam-5038	126	16	vertices	vertex	NOUN
ejpam-5038	126	17	to	to	PART
ejpam-5038	126	18	dominate	dominate	VERB
ejpam-5038	126	19	the	the	DET
ejpam-5038	126	20	subgraph	subgraph	NOUN
ejpam-5038	126	21	.	.	PUNCT
ejpam-5038	127	1	see	see	VERB
ejpam-5038	127	2	figure	figure	NOUN
ejpam-5038	127	3	5(b	5(b	NUM
ejpam-5038	127	4	)	)	PUNCT
ejpam-5038	127	5	.	.	PUNCT
ejpam-5038	128	1	in	in	ADP
ejpam-5038	128	2	either	either	DET
ejpam-5038	128	3	case	case	NOUN
ejpam-5038	128	4	,	,	PUNCT
ejpam-5038	128	5	the	the	DET
ejpam-5038	128	6	number	number	NOUN
ejpam-5038	128	7	of	of	ADP
ejpam-5038	128	8	vertices	vertex	NOUN
ejpam-5038	128	9	dominating	dominating	NOUN
ejpam-5038	128	10	h2	h2	NOUN
ejpam-5038	128	11	,	,	PUNCT
ejpam-5038	128	12	considering	consider	VERB
ejpam-5038	128	13	the	the	DET
ejpam-5038	128	14	already	already	ADV
ejpam-5038	128	15	dominated	dominate	VERB
ejpam-5038	128	16	vertices	vertex	NOUN
ejpam-5038	128	17	of	of	ADP
ejpam-5038	128	18	h2	h2	NOUN
ejpam-5038	128	19	,	,	PUNCT
ejpam-5038	128	20	is	be	AUX
ejpam-5038	128	21	not	not	PART
ejpam-5038	128	22	less	less	ADJ
ejpam-5038	128	23	than	than	ADP
ejpam-5038	128	24	4	4	NUM
ejpam-5038	128	25	.	.	PUNCT
ejpam-5038	129	1	thus	thus	ADV
ejpam-5038	129	2	4	4	NUM
ejpam-5038	129	3	vertices	vertex	NOUN
ejpam-5038	129	4	from	from	ADP
ejpam-5038	129	5	each	each	DET
ejpam-5038	129	6	hi	hi	NOUN
ejpam-5038	129	7	,	,	PUNCT
ejpam-5038	129	8	1	1	NUM
ejpam-5038	129	9	≤	≤	NUM
ejpam-5038	129	10	i	i	PRON
ejpam-5038	129	11	≤	≤	ADJ
ejpam-5038	129	12	2k−3	2k−3	NOUN
ejpam-5038	129	13	is	be	AUX
ejpam-5038	129	14	a	a	DET
ejpam-5038	129	15	minimum	minimum	ADJ
ejpam-5038	129	16	count	count	NOUN
ejpam-5038	129	17	in	in	ADP
ejpam-5038	129	18	d.	d.	PROPN
ejpam-5038	129	19	hence	hence	ADV
ejpam-5038	129	20	d	d	PROPN
ejpam-5038	129	21	is	be	AUX
ejpam-5038	129	22	a	a	DET
ejpam-5038	129	23	minimum	minimum	ADJ
ejpam-5038	129	24	dominating	dominating	NOUN
ejpam-5038	129	25	set	set	NOUN
ejpam-5038	129	26	and	and	CCONJ
ejpam-5038	129	27	|d|=	|d|=	NOUN
ejpam-5038	129	28	4×	4×	NOUN
ejpam-5038	129	29	2k−3	2k−3	NUM
ejpam-5038	129	30	=	=	SYM
ejpam-5038	129	31	2k−1	2k−1	NUM
ejpam-5038	129	32	.	.	PUNCT
ejpam-5038	130	1	v.	v.	PROPN
ejpam-5038	130	2	shalini	shalini	PROPN
ejpam-5038	130	3	,	,	PUNCT
ejpam-5038	130	4	i.	i.	PROPN
ejpam-5038	130	5	rajasingh	rajasingh	PROPN
ejpam-5038	130	6	/	/	SYM
ejpam-5038	130	7	eur	eur	PROPN
ejpam-5038	130	8	.	.	PUNCT
ejpam-5038	131	1	j.	j.	PROPN
ejpam-5038	131	2	pure	pure	PROPN
ejpam-5038	131	3	appl	appl	PROPN
ejpam-5038	131	4	.	.	PROPN
ejpam-5038	131	5	math	math	PROPN
ejpam-5038	131	6	,	,	PUNCT
ejpam-5038	131	7	17	17	NUM
ejpam-5038	131	8	(	(	PUNCT
ejpam-5038	131	9	2	2	NUM
ejpam-5038	131	10	)	)	PUNCT
ejpam-5038	131	11	(	(	PUNCT
ejpam-5038	131	12	2024	2024	NUM
ejpam-5038	131	13	)	)	PUNCT
ejpam-5038	131	14	,	,	PUNCT
ejpam-5038	131	15	1082	1082	NUM
ejpam-5038	131	16	-	-	SYM
ejpam-5038	131	17	1093	1093	NUM
ejpam-5038	131	18	1087	1087	NUM
ejpam-5038	131	19	figure	figure	NOUN
ejpam-5038	131	20	5	5	NUM
ejpam-5038	131	21	:	:	PUNCT
ejpam-5038	131	22	(	(	PUNCT
ejpam-5038	131	23	a	a	X
ejpam-5038	131	24	)	)	PUNCT
ejpam-5038	131	25	l22	l22	NOUN
ejpam-5038	131	26	and	and	CCONJ
ejpam-5038	131	27	r22	r22	NOUN
ejpam-5038	131	28	of	of	ADP
ejpam-5038	131	29	h2	h2	NOUN
ejpam-5038	131	30	are	be	AUX
ejpam-5038	131	31	already	already	ADV
ejpam-5038	131	32	dominated	dominate	VERB
ejpam-5038	131	33	.	.	PUNCT
ejpam-5038	132	1	(	(	PUNCT
ejpam-5038	132	2	b	b	X
ejpam-5038	132	3	)	)	PUNCT
ejpam-5038	132	4	l22	l22	NOUN
ejpam-5038	132	5	and	and	CCONJ
ejpam-5038	132	6	r21	r21	NOUN
ejpam-5038	132	7	of	of	ADP
ejpam-5038	132	8	h2	h2	NOUN
ejpam-5038	132	9	are	be	AUX
ejpam-5038	132	10	already	already	ADV
ejpam-5038	132	11	dominated	dominate	VERB
ejpam-5038	132	12	.	.	PUNCT
ejpam-5038	133	1	theorem	theorem	NOUN
ejpam-5038	133	2	1	1	NUM
ejpam-5038	133	3	.	.	PUNCT
ejpam-5038	134	1	let	let	VERB
ejpam-5038	134	2	g	g	NOUN
ejpam-5038	134	3	be	be	AUX
ejpam-5038	134	4	the	the	DET
ejpam-5038	134	5	x	x	NOUN
ejpam-5038	134	6	-	-	NOUN
ejpam-5038	134	7	tree	tree	NOUN
ejpam-5038	134	8	of	of	ADP
ejpam-5038	134	9	dimension	dimension	NOUN
ejpam-5038	135	1	k	k	PROPN
ejpam-5038	136	1	and	and	CCONJ
ejpam-5038	136	2	it	it	PRON
ejpam-5038	136	3	is	be	AUX
ejpam-5038	136	4	denoted	denote	VERB
ejpam-5038	136	5	by	by	ADP
ejpam-5038	136	6	x(k	x(k	NOUN
ejpam-5038	136	7	)	)	PUNCT
ejpam-5038	136	8	,	,	PUNCT
ejpam-5038	136	9	k	k	PROPN
ejpam-5038	136	10	≥	≥	PROPN
ejpam-5038	136	11	0	0	NUM
ejpam-5038	136	12	,	,	PUNCT
ejpam-5038	136	13	then	then	ADV
ejpam-5038	136	14	γ(x(k	γ(x(k	NOUN
ejpam-5038	136	15	)	)	PUNCT
ejpam-5038	136	16	)	)	PUNCT
ejpam-5038	137	1	=	=	PUNCT
ejpam-5038	137	2			NOUN
ejpam-5038	137	3	2k+3−4	2k+3−4	NUM
ejpam-5038	137	4	15	15	NUM
ejpam-5038	137	5	;	;	PUNCT
ejpam-5038	137	6	k	k	PROPN
ejpam-5038	138	1	+	+	PROPN
ejpam-5038	138	2	1	1	NUM
ejpam-5038	138	3	≡	≡	PROPN
ejpam-5038	138	4	0	0	NUM
ejpam-5038	138	5	(	(	PUNCT
ejpam-5038	138	6	mod	mod	NOUN
ejpam-5038	138	7	4	4	NUM
ejpam-5038	138	8	)	)	PUNCT
ejpam-5038	138	9	2k+3	2k+3	PROPN
ejpam-5038	139	1	+	+	PROPN
ejpam-5038	139	2	7	7	NUM
ejpam-5038	139	3	15	15	NUM
ejpam-5038	140	1	;	;	PUNCT
ejpam-5038	140	2	k	k	PROPN
ejpam-5038	141	1	+	+	CCONJ
ejpam-5038	141	2	1	1	NUM
ejpam-5038	141	3	≡	≡	PROPN
ejpam-5038	141	4	1	1	NUM
ejpam-5038	141	5	(	(	PUNCT
ejpam-5038	141	6	mod	mod	NOUN
ejpam-5038	141	7	4	4	NUM
ejpam-5038	141	8	)	)	PUNCT
ejpam-5038	141	9	2k+3−1	2k+3−1	NUM
ejpam-5038	141	10	15	15	NUM
ejpam-5038	141	11	;	;	PUNCT
ejpam-5038	141	12	k	k	PROPN
ejpam-5038	141	13	+	+	CCONJ
ejpam-5038	141	14	1	1	NUM
ejpam-5038	141	15	≡	≡	PROPN
ejpam-5038	141	16	2	2	NUM
ejpam-5038	141	17	(	(	PUNCT
ejpam-5038	141	18	mod	mod	NOUN
ejpam-5038	141	19	4	4	NUM
ejpam-5038	141	20	)	)	PUNCT
ejpam-5038	141	21	2k+3−2	2k+3−2	NUM
ejpam-5038	141	22	15	15	NUM
ejpam-5038	141	23	;	;	PUNCT
ejpam-5038	141	24	k	k	PROPN
ejpam-5038	141	25	+	+	CCONJ
ejpam-5038	141	26	1	1	NUM
ejpam-5038	141	27	≡	≡	PROPN
ejpam-5038	141	28	3	3	NUM
ejpam-5038	141	29	(	(	PUNCT
ejpam-5038	141	30	mod	mod	NOUN
ejpam-5038	141	31	4	4	NUM
ejpam-5038	141	32	)	)	PUNCT
ejpam-5038	141	33	proof	proof	NOUN
ejpam-5038	141	34	.	.	PUNCT
ejpam-5038	142	1	by	by	ADP
ejpam-5038	142	2	lemma	lemma	PROPN
ejpam-5038	142	3	2	2	PROPN
ejpam-5038	142	4	and	and	CCONJ
ejpam-5038	142	5	lemma	lemma	PROPN
ejpam-5038	142	6	4	4	NUM
ejpam-5038	142	7	,	,	PUNCT
ejpam-5038	142	8	it	it	PRON
ejpam-5038	142	9	is	be	AUX
ejpam-5038	142	10	clear	clear	ADJ
ejpam-5038	142	11	that	that	SCONJ
ejpam-5038	142	12	a	a	DET
ejpam-5038	142	13	count	count	NOUN
ejpam-5038	142	14	of	of	ADP
ejpam-5038	142	15	4	4	NUM
ejpam-5038	142	16	levels	level	NOUN
ejpam-5038	142	17	starting	start	VERB
ejpam-5038	142	18	from	from	ADP
ejpam-5038	142	19	the	the	DET
ejpam-5038	142	20	last	last	ADJ
ejpam-5038	142	21	level	level	NOUN
ejpam-5038	142	22	k	k	PROPN
ejpam-5038	142	23	of	of	ADP
ejpam-5038	142	24	x(k	x(k	PROPN
ejpam-5038	142	25	)	)	PUNCT
ejpam-5038	142	26	contributes	contribute	VERB
ejpam-5038	142	27	2k−1	2k−1	NUM
ejpam-5038	142	28	vertices	vertex	NOUN
ejpam-5038	142	29	to	to	ADP
ejpam-5038	142	30	any	any	DET
ejpam-5038	142	31	minimum	minimum	ADJ
ejpam-5038	142	32	dominating	dominating	NOUN
ejpam-5038	142	33	set	set	NOUN
ejpam-5038	142	34	d	d	NOUN
ejpam-5038	142	35	of	of	ADP
ejpam-5038	142	36	x(k	x(k	PROPN
ejpam-5038	142	37	)	)	PUNCT
ejpam-5038	142	38	.	.	PUNCT
ejpam-5038	143	1	deleting	delete	VERB
ejpam-5038	143	2	these	these	DET
ejpam-5038	143	3	4	4	NUM
ejpam-5038	143	4	levels	level	NOUN
ejpam-5038	143	5	from	from	ADP
ejpam-5038	143	6	x(k	x(k	NOUN
ejpam-5038	143	7	)	)	PUNCT
ejpam-5038	143	8	yields	yield	NOUN
ejpam-5038	143	9	x(k	x(k	PROPN
ejpam-5038	143	10	−	−	PROPN
ejpam-5038	143	11	4	4	NUM
ejpam-5038	143	12	)	)	PUNCT
ejpam-5038	143	13	.	.	PUNCT
ejpam-5038	144	1	applying	apply	VERB
ejpam-5038	144	2	lemma	lemma	PROPN
ejpam-5038	144	3	4	4	NUM
ejpam-5038	144	4	and	and	CCONJ
ejpam-5038	144	5	deleting	delete	VERB
ejpam-5038	144	6	the	the	DET
ejpam-5038	144	7	last	last	ADJ
ejpam-5038	144	8	4	4	NUM
ejpam-5038	144	9	levels	level	NOUN
ejpam-5038	144	10	repeatedly	repeatedly	ADV
ejpam-5038	144	11	we	we	PRON
ejpam-5038	144	12	are	be	AUX
ejpam-5038	144	13	left	leave	VERB
ejpam-5038	144	14	with	with	ADP
ejpam-5038	144	15	x(0	x(0	PROPN
ejpam-5038	144	16	)	)	PUNCT
ejpam-5038	144	17	,	,	PUNCT
ejpam-5038	144	18	x(1	x(1	PROPN
ejpam-5038	144	19	)	)	PUNCT
ejpam-5038	144	20	,	,	PUNCT
ejpam-5038	144	21	x(2	x(2	PROPN
ejpam-5038	144	22	)	)	PUNCT
ejpam-5038	144	23	or	or	CCONJ
ejpam-5038	144	24	x(3	x(3	PROPN
ejpam-5038	144	25	)	)	PUNCT
ejpam-5038	144	26	according	accord	VERB
ejpam-5038	144	27	as	as	ADP
ejpam-5038	144	28	k	k	PROPN
ejpam-5038	144	29	+	+	PROPN
ejpam-5038	144	30	1	1	NUM
ejpam-5038	144	31	≡	≡	PROPN
ejpam-5038	144	32	0	0	NUM
ejpam-5038	144	33	,	,	PUNCT
ejpam-5038	144	34	1	1	NUM
ejpam-5038	144	35	,	,	PUNCT
ejpam-5038	144	36	2	2	NUM
ejpam-5038	144	37	or	or	CCONJ
ejpam-5038	144	38	3	3	NUM
ejpam-5038	144	39	(	(	PUNCT
ejpam-5038	144	40	mod	mod	NOUN
ejpam-5038	144	41	4	4	NUM
ejpam-5038	144	42	)	)	PUNCT
ejpam-5038	144	43	respectively	respectively	ADV
ejpam-5038	144	44	.	.	PUNCT
ejpam-5038	145	1	we	we	PRON
ejpam-5038	145	2	have	have	VERB
ejpam-5038	145	3	γ(x(0	γ(x(0	NUM
ejpam-5038	145	4	)	)	PUNCT
ejpam-5038	145	5	)	)	PUNCT
ejpam-5038	146	1	=	=	SYM
ejpam-5038	146	2	γ(x(1	γ(x(1	PROPN
ejpam-5038	146	3	)	)	PUNCT
ejpam-5038	146	4	)	)	PUNCT
ejpam-5038	147	1	=	=	SYM
ejpam-5038	147	2	1	1	X
ejpam-5038	147	3	,	,	PUNCT
ejpam-5038	147	4	γ(x(2	γ(x(2	NOUN
ejpam-5038	147	5	)	)	PUNCT
ejpam-5038	147	6	)	)	PUNCT
ejpam-5038	147	7	=	=	SYM
ejpam-5038	148	1	2	2	X
ejpam-5038	148	2	.	.	PUNCT
ejpam-5038	148	3	thus	thus	ADV
ejpam-5038	148	4	we	we	PRON
ejpam-5038	148	5	compute	compute	VERB
ejpam-5038	148	6	the	the	DET
ejpam-5038	148	7	domination	domination	NOUN
ejpam-5038	148	8	number	number	NOUN
ejpam-5038	148	9	of	of	ADP
ejpam-5038	148	10	x(k	x(k	PROPN
ejpam-5038	148	11	)	)	PUNCT
ejpam-5038	148	12	as	as	SCONJ
ejpam-5038	148	13	follows	follow	VERB
ejpam-5038	148	14	.	.	PUNCT
ejpam-5038	149	1	when	when	SCONJ
ejpam-5038	149	2	k	k	PROPN
ejpam-5038	149	3	+	+	PROPN
ejpam-5038	149	4	1	1	NUM
ejpam-5038	149	5	≡	≡	PROPN
ejpam-5038	149	6	0	0	NUM
ejpam-5038	149	7	(	(	PUNCT
ejpam-5038	149	8	mod	mod	PROPN
ejpam-5038	149	9	4	4	NUM
ejpam-5038	149	10	)	)	PUNCT
ejpam-5038	149	11	,	,	PUNCT
ejpam-5038	149	12	|d|=	|d|=	NOUN
ejpam-5038	149	13	2k−1	2k−1	NUM
ejpam-5038	149	14	+	+	CCONJ
ejpam-5038	149	15	2k−5	2k−5	NUM
ejpam-5038	149	16	+	+	CCONJ
ejpam-5038	149	17	...	...	PUNCT
ejpam-5038	149	18	+	+	X
ejpam-5038	149	19	210	210	NUM
ejpam-5038	149	20	+	+	CCONJ
ejpam-5038	149	21	26	26	NUM
ejpam-5038	149	22	+	+	CCONJ
ejpam-5038	149	23	22	22	NUM
ejpam-5038	149	24	=	=	SYM
ejpam-5038	149	25	2k+3−4	2k+3−4	NUM
ejpam-5038	149	26	15	15	NUM
ejpam-5038	149	27	when	when	SCONJ
ejpam-5038	149	28	k	k	PROPN
ejpam-5038	149	29	+	+	CCONJ
ejpam-5038	149	30	1	1	NUM
ejpam-5038	149	31	≡	≡	PROPN
ejpam-5038	149	32	1	1	NUM
ejpam-5038	149	33	(	(	PUNCT
ejpam-5038	149	34	mod	mod	NOUN
ejpam-5038	149	35	4	4	NUM
ejpam-5038	149	36	)	)	PUNCT
ejpam-5038	149	37	,	,	PUNCT
ejpam-5038	149	38	|d|=	|d|=	NOUN
ejpam-5038	149	39	(	(	PUNCT
ejpam-5038	149	40	2k−1	2k−1	NUM
ejpam-5038	149	41	+	+	SYM
ejpam-5038	149	42	2k−5	2k−5	NUM
ejpam-5038	149	43	+	+	CCONJ
ejpam-5038	149	44	...	...	PUNCT
ejpam-5038	149	45	+	+	CCONJ
ejpam-5038	149	46	27	27	NUM
ejpam-5038	149	47	+	+	NUM
ejpam-5038	149	48	25	25	NUM
ejpam-5038	149	49	)	)	PUNCT
ejpam-5038	149	50	+	+	CCONJ
ejpam-5038	149	51	1	1	NUM
ejpam-5038	149	52	=	=	SYM
ejpam-5038	149	53	2k+3	2k+3	NUM
ejpam-5038	149	54	+	+	NOUN
ejpam-5038	149	55	7	7	NUM
ejpam-5038	149	56	15	15	NUM
ejpam-5038	149	57	when	when	SCONJ
ejpam-5038	149	58	k	k	PROPN
ejpam-5038	149	59	+	+	CCONJ
ejpam-5038	149	60	1	1	NUM
ejpam-5038	149	61	≡	≡	PROPN
ejpam-5038	149	62	2	2	NUM
ejpam-5038	149	63	(	(	PUNCT
ejpam-5038	149	64	mod	mod	NOUN
ejpam-5038	149	65	4	4	NUM
ejpam-5038	149	66	)	)	PUNCT
ejpam-5038	149	67	,	,	PUNCT
ejpam-5038	149	68	|d|=	|d|=	NOUN
ejpam-5038	149	69	(	(	PUNCT
ejpam-5038	149	70	2k−1	2k−1	NUM
ejpam-5038	149	71	+	+	SYM
ejpam-5038	149	72	2k−5	2k−5	NUM
ejpam-5038	149	73	+	+	CCONJ
ejpam-5038	149	74	...	...	PUNCT
ejpam-5038	149	75	+	+	NUM
ejpam-5038	149	76	28	28	NUM
ejpam-5038	149	77	+	+	NUM
ejpam-5038	149	78	24	24	NUM
ejpam-5038	149	79	)	)	PUNCT
ejpam-5038	149	80	+	+	CCONJ
ejpam-5038	149	81	1	1	NUM
ejpam-5038	149	82	=	=	SYM
ejpam-5038	149	83	2k+3−1	2k+3−1	NUM
ejpam-5038	149	84	15	15	NUM
ejpam-5038	149	85	and	and	CCONJ
ejpam-5038	149	86	when	when	SCONJ
ejpam-5038	149	87	k	k	PROPN
ejpam-5038	149	88	+	+	PROPN
ejpam-5038	149	89	1	1	NUM
ejpam-5038	149	90	≡	≡	PROPN
ejpam-5038	149	91	3	3	NUM
ejpam-5038	149	92	(	(	PUNCT
ejpam-5038	149	93	mod	mod	NOUN
ejpam-5038	149	94	4	4	NUM
ejpam-5038	149	95	)	)	PUNCT
ejpam-5038	149	96	,	,	PUNCT
ejpam-5038	149	97	|d|=	|d|=	NOUN
ejpam-5038	149	98	(	(	PUNCT
ejpam-5038	149	99	2k−1	2k−1	NUM
ejpam-5038	149	100	+	+	SYM
ejpam-5038	149	101	2k−5	2k−5	NUM
ejpam-5038	149	102	+	+	CCONJ
ejpam-5038	149	103	...	...	PUNCT
ejpam-5038	149	104	+	+	CCONJ
ejpam-5038	149	105	211	211	NUM
ejpam-5038	149	106	+	+	NUM
ejpam-5038	149	107	27	27	NUM
ejpam-5038	149	108	)	)	PUNCT
ejpam-5038	149	109	+	+	CCONJ
ejpam-5038	149	110	2	2	NUM
ejpam-5038	149	111	=	=	SYM
ejpam-5038	149	112	2k+3−2	2k+3−2	NUM
ejpam-5038	149	113	15	15	NUM
ejpam-5038	149	114	notations	notation	NOUN
ejpam-5038	149	115	:	:	PUNCT
ejpam-5038	149	116	the	the	DET
ejpam-5038	149	117	sets	set	NOUN
ejpam-5038	149	118	of	of	ADP
ejpam-5038	149	119	vertices	vertex	NOUN
ejpam-5038	149	120	{	{	PUNCT
ejpam-5038	149	121	l1	l1	PROPN
ejpam-5038	149	122	,	,	PUNCT
ejpam-5038	149	123	r2	r2	PROPN
ejpam-5038	149	124	,	,	PUNCT
ejpam-5038	149	125	3	3	NUM
ejpam-5038	149	126	,	,	PUNCT
ejpam-5038	149	127	6	6	NUM
ejpam-5038	149	128	}	}	PUNCT
ejpam-5038	149	129	and	and	CCONJ
ejpam-5038	149	130	{	{	PUNCT
ejpam-5038	149	131	r1	r1	NOUN
ejpam-5038	149	132	,	,	PUNCT
ejpam-5038	149	133	l2	l2	NOUN
ejpam-5038	149	134	,	,	PUNCT
ejpam-5038	149	135	5	5	NUM
ejpam-5038	149	136	,	,	PUNCT
ejpam-5038	149	137	8	8	NUM
ejpam-5038	149	138	}	}	PUNCT
ejpam-5038	149	139	in	in	ADP
ejpam-5038	149	140	a	a	DET
ejpam-5038	149	141	copy	copy	NOUN
ejpam-5038	149	142	of	of	ADP
ejpam-5038	149	143	x(3	x(3	NOUN
ejpam-5038	149	144	)	)	PUNCT
ejpam-5038	149	145	as	as	ADP
ejpam-5038	149	146	in	in	ADP
ejpam-5038	149	147	figure	figure	NOUN
ejpam-5038	149	148	1(a	1(a	NUM
ejpam-5038	149	149	)	)	PUNCT
ejpam-5038	149	150	are	be	AUX
ejpam-5038	149	151	disjoint	disjoint	ADJ
ejpam-5038	149	152	dominating	dominating	NOUN
ejpam-5038	149	153	sets	set	NOUN
ejpam-5038	149	154	of	of	ADP
ejpam-5038	149	155	x(3	x(3	PROPN
ejpam-5038	149	156	)	)	PUNCT
ejpam-5038	149	157	.	.	PUNCT
ejpam-5038	150	1	we	we	PRON
ejpam-5038	150	2	refer	refer	VERB
ejpam-5038	150	3	to	to	ADP
ejpam-5038	150	4	them	they	PRON
ejpam-5038	150	5	as	as	ADP
ejpam-5038	150	6	d	d	ADJ
ejpam-5038	150	7	-	-	ADJ
ejpam-5038	150	8	twin	twin	ADJ
ejpam-5038	150	9	sets	set	NOUN
ejpam-5038	150	10	.	.	PUNCT
ejpam-5038	151	1	theorem	theorem	NOUN
ejpam-5038	151	2	2	2	NUM
ejpam-5038	151	3	.	.	PUNCT
ejpam-5038	152	1	let	let	AUX
ejpam-5038	152	2	x(k	x(k	PUNCT
ejpam-5038	152	3	)	)	PUNCT
ejpam-5038	152	4	be	be	AUX
ejpam-5038	152	5	the	the	DET
ejpam-5038	152	6	x	x	NOUN
ejpam-5038	152	7	-	-	NOUN
ejpam-5038	152	8	tree	tree	NOUN
ejpam-5038	152	9	of	of	ADP
ejpam-5038	152	10	dimension	dimension	NOUN
ejpam-5038	152	11	k	k	PROPN
ejpam-5038	152	12	≥	≥	PROPN
ejpam-5038	152	13	0	0	NUM
ejpam-5038	152	14	.	.	PUNCT
ejpam-5038	153	1	then	then	ADV
ejpam-5038	153	2	γ′(x(k	γ′(x(k	NUM
ejpam-5038	153	3	)	)	PUNCT
ejpam-5038	153	4	)	)	PUNCT
ejpam-5038	154	1	=	=	PUNCT
ejpam-5038	154	2	γ(x(k	γ(x(k	PROPN
ejpam-5038	154	3	)	)	PUNCT
ejpam-5038	154	4	)	)	PUNCT
ejpam-5038	154	5	,	,	PUNCT
ejpam-5038	154	6	k	k	PROPN
ejpam-5038	154	7	≥	≥	NOUN
ejpam-5038	154	8	0	0	NUM
ejpam-5038	154	9	.	.	PUNCT
ejpam-5038	155	1	proof	proof	NOUN
ejpam-5038	155	2	.	.	PUNCT
ejpam-5038	156	1	we	we	PRON
ejpam-5038	156	2	construct	construct	VERB
ejpam-5038	156	3	two	two	NUM
ejpam-5038	156	4	minimum	minimum	ADJ
ejpam-5038	156	5	dominating	dominating	NOUN
ejpam-5038	156	6	sets	set	NOUN
ejpam-5038	156	7	d	d	NOUN
ejpam-5038	156	8	and	and	CCONJ
ejpam-5038	156	9	d′	d′	NUM
ejpam-5038	156	10	of	of	ADP
ejpam-5038	156	11	x(k	x(k	PROPN
ejpam-5038	156	12	)	)	PUNCT
ejpam-5038	156	13	,	,	PUNCT
ejpam-5038	156	14	k	k	X
ejpam-5038	156	15	≥	≥	X
ejpam-5038	156	16	0	0	PUNCT
ejpam-5038	156	17	as	as	SCONJ
ejpam-5038	156	18	follows	follow	VERB
ejpam-5038	156	19	:	:	PUNCT
ejpam-5038	156	20	include	include	VERB
ejpam-5038	156	21	one	one	NUM
ejpam-5038	156	22	set	set	NOUN
ejpam-5038	156	23	of	of	ADP
ejpam-5038	156	24	d	d	ADJ
ejpam-5038	156	25	-	-	ADJ
ejpam-5038	156	26	twin	twin	ADJ
ejpam-5038	156	27	vertices	vertex	NOUN
ejpam-5038	156	28	in	in	ADP
ejpam-5038	156	29	d	d	PROPN
ejpam-5038	156	30	and	and	CCONJ
ejpam-5038	156	31	the	the	DET
ejpam-5038	156	32	other	other	ADJ
ejpam-5038	156	33	set	set	NOUN
ejpam-5038	156	34	of	of	ADP
ejpam-5038	156	35	d	d	ADJ
ejpam-5038	156	36	-	-	ADJ
ejpam-5038	156	37	twin	twin	ADJ
ejpam-5038	156	38	vertices	vertex	NOUN
ejpam-5038	156	39	in	in	ADP
ejpam-5038	156	40	d′	d′	NUM
ejpam-5038	156	41	from	from	ADP
ejpam-5038	156	42	each	each	DET
ejpam-5038	156	43	copy	copy	NOUN
ejpam-5038	156	44	of	of	ADP
ejpam-5038	156	45	x(3	x(3	PROPN
ejpam-5038	156	46	)	)	PUNCT
ejpam-5038	156	47	considered	consider	VERB
ejpam-5038	156	48	in	in	ADP
ejpam-5038	156	49	theorem	theorem	NOUN
ejpam-5038	156	50	1	1	NUM
ejpam-5038	156	51	.	.	PUNCT
ejpam-5038	157	1	the	the	DET
ejpam-5038	157	2	vertices	vertex	NOUN
ejpam-5038	157	3	that	that	PRON
ejpam-5038	157	4	are	be	AUX
ejpam-5038	157	5	not	not	PART
ejpam-5038	157	6	covered	cover	VERB
ejpam-5038	157	7	by	by	ADP
ejpam-5038	157	8	these	these	DET
ejpam-5038	157	9	copies	copy	NOUN
ejpam-5038	157	10	of	of	ADP
ejpam-5038	157	11	x(3	x(3	NOUN
ejpam-5038	157	12	)	)	PUNCT
ejpam-5038	157	13	induce	induce	VERB
ejpam-5038	157	14	x(0	x(0	PROPN
ejpam-5038	157	15	)	)	PUNCT
ejpam-5038	157	16	,	,	PUNCT
ejpam-5038	157	17	x(1	x(1	PROPN
ejpam-5038	157	18	)	)	PUNCT
ejpam-5038	157	19	or	or	CCONJ
ejpam-5038	157	20	x(2	x(2	PROPN
ejpam-5038	157	21	)	)	PUNCT
ejpam-5038	157	22	according	accord	VERB
ejpam-5038	157	23	as	as	ADP
ejpam-5038	157	24	k	k	PROPN
ejpam-5038	157	25	+	+	PROPN
ejpam-5038	157	26	1	1	NUM
ejpam-5038	157	27	≡	≡	PROPN
ejpam-5038	157	28	1	1	NUM
ejpam-5038	157	29	,	,	PUNCT
ejpam-5038	157	30	2	2	NUM
ejpam-5038	157	31	or	or	CCONJ
ejpam-5038	157	32	3(mod	3(mod	NUM
ejpam-5038	157	33	4	4	NUM
ejpam-5038	157	34	)	)	PUNCT
ejpam-5038	157	35	.	.	PUNCT
ejpam-5038	158	1	see	see	VERB
ejpam-5038	158	2	figure	figure	NOUN
ejpam-5038	158	3	6	6	NUM
ejpam-5038	158	4	.	.	PUNCT
ejpam-5038	159	1	when	when	SCONJ
ejpam-5038	159	2	k	k	PROPN
ejpam-5038	159	3	+	+	PROPN
ejpam-5038	159	4	1	1	NUM
ejpam-5038	159	5	≡	≡	PROPN
ejpam-5038	159	6	1	1	NUM
ejpam-5038	159	7	or	or	CCONJ
ejpam-5038	159	8	2(mod	2(mod	NUM
ejpam-5038	159	9	4	4	NUM
ejpam-5038	159	10	)	)	PUNCT
ejpam-5038	159	11	,	,	PUNCT
ejpam-5038	159	12	no	no	DET
ejpam-5038	159	13	d	d	ADJ
ejpam-5038	159	14	-	-	ADJ
ejpam-5038	159	15	twin	twin	ADJ
ejpam-5038	159	16	set	set	NOUN
ejpam-5038	159	17	includes	include	VERB
ejpam-5038	159	18	l	l	PROPN
ejpam-5038	159	19	or	or	CCONJ
ejpam-5038	159	20	r.	r.	PROPN
ejpam-5038	159	21	hence	hence	ADV
ejpam-5038	159	22	put	put	VERB
ejpam-5038	159	23	l	l	NOUN
ejpam-5038	159	24	in	in	ADP
ejpam-5038	159	25	d	d	PROPN
ejpam-5038	159	26	and	and	CCONJ
ejpam-5038	159	27	r	r	NOUN
ejpam-5038	159	28	in	in	ADP
ejpam-5038	159	29	d′.	d′.	NOUN
ejpam-5038	159	30	on	on	ADP
ejpam-5038	159	31	the	the	DET
ejpam-5038	159	32	otherhand	otherhand	NOUN
ejpam-5038	159	33	,	,	PUNCT
ejpam-5038	159	34	when	when	SCONJ
ejpam-5038	159	35	k	k	PROPN
ejpam-5038	159	36	+	+	PROPN
ejpam-5038	159	37	1	1	NUM
ejpam-5038	159	38	≡	≡	PROPN
ejpam-5038	159	39	3(mod	3(mod	NUM
ejpam-5038	159	40	4	4	NUM
ejpam-5038	159	41	)	)	PUNCT
ejpam-5038	159	42	,	,	PUNCT
ejpam-5038	159	43	none	none	NOUN
ejpam-5038	159	44	of	of	ADP
ejpam-5038	159	45	the	the	DET
ejpam-5038	159	46	level	level	NOUN
ejpam-5038	159	47	2	2	NUM
ejpam-5038	159	48	vertices	vertex	NOUN
ejpam-5038	159	49	in	in	ADV
ejpam-5038	159	50	v.	v.	ADP
ejpam-5038	159	51	shalini	shalini	PROPN
ejpam-5038	159	52	,	,	PUNCT
ejpam-5038	159	53	i.	i.	PROPN
ejpam-5038	159	54	rajasingh	rajasingh	PROPN
ejpam-5038	159	55	/	/	SYM
ejpam-5038	159	56	eur	eur	PROPN
ejpam-5038	159	57	.	.	PUNCT
ejpam-5038	160	1	j.	j.	PROPN
ejpam-5038	160	2	pure	pure	PROPN
ejpam-5038	160	3	appl	appl	PROPN
ejpam-5038	160	4	.	.	PROPN
ejpam-5038	160	5	math	math	PROPN
ejpam-5038	160	6	,	,	PUNCT
ejpam-5038	160	7	17	17	NUM
ejpam-5038	160	8	(	(	PUNCT
ejpam-5038	160	9	2	2	NUM
ejpam-5038	160	10	)	)	PUNCT
ejpam-5038	160	11	(	(	PUNCT
ejpam-5038	160	12	2024	2024	NUM
ejpam-5038	160	13	)	)	PUNCT
ejpam-5038	160	14	,	,	PUNCT
ejpam-5038	160	15	1082	1082	NUM
ejpam-5038	160	16	-	-	SYM
ejpam-5038	160	17	1093	1093	NUM
ejpam-5038	160	18	1088	1088	NUM
ejpam-5038	160	19	figure	figure	NOUN
ejpam-5038	160	20	6	6	NUM
ejpam-5038	160	21	:	:	PUNCT
ejpam-5038	160	22	subgraph	subgraph	NOUN
ejpam-5038	160	23	induced	induce	VERB
ejpam-5038	160	24	by	by	ADP
ejpam-5038	160	25	leftout	leftout	ADJ
ejpam-5038	160	26	vertices	vertex	NOUN
ejpam-5038	160	27	when	when	SCONJ
ejpam-5038	160	28	k	k	PROPN
ejpam-5038	160	29	+	+	PROPN
ejpam-5038	160	30	1	1	NUM
ejpam-5038	160	31	≡	≡	PROPN
ejpam-5038	160	32	1	1	NUM
ejpam-5038	160	33	,	,	PUNCT
ejpam-5038	160	34	2	2	NUM
ejpam-5038	160	35	,	,	PUNCT
ejpam-5038	160	36	3	3	NUM
ejpam-5038	160	37	or	or	CCONJ
ejpam-5038	160	38	(	(	PUNCT
ejpam-5038	160	39	mod	mod	ADJ
ejpam-5038	160	40	4	4	NUM
ejpam-5038	160	41	)	)	PUNCT
ejpam-5038	160	42	figure	figure	NOUN
ejpam-5038	160	43	7	7	NUM
ejpam-5038	160	44	:	:	PUNCT
ejpam-5038	160	45	(	(	PUNCT
ejpam-5038	160	46	a	a	X
ejpam-5038	160	47	)	)	PUNCT
ejpam-5038	160	48	levels	level	NOUN
ejpam-5038	160	49	of	of	ADP
ejpam-5038	160	50	st	st	PROPN
ejpam-5038	160	51	(	(	PUNCT
ejpam-5038	160	52	3	3	NUM
ejpam-5038	160	53	)	)	PUNCT
ejpam-5038	160	54	.	.	PUNCT
ejpam-5038	161	1	(	(	PUNCT
ejpam-5038	161	2	b	b	X
ejpam-5038	161	3	)	)	PUNCT
ejpam-5038	161	4	st	st	NOUN
ejpam-5038	161	5	(	(	PUNCT
ejpam-5038	161	6	2	2	NUM
ejpam-5038	161	7	)	)	PUNCT
ejpam-5038	161	8	with	with	ADP
ejpam-5038	161	9	labels	label	NOUN
ejpam-5038	161	10	.	.	PUNCT
ejpam-5038	162	1	x(2	x(2	NOUN
ejpam-5038	162	2	)	)	PUNCT
ejpam-5038	162	3	is	be	AUX
ejpam-5038	162	4	included	include	VERB
ejpam-5038	162	5	in	in	ADP
ejpam-5038	162	6	any	any	DET
ejpam-5038	162	7	d	d	ADJ
ejpam-5038	162	8	-	-	ADJ
ejpam-5038	162	9	twin	twin	ADJ
ejpam-5038	162	10	set	set	NOUN
ejpam-5038	162	11	.	.	PUNCT
ejpam-5038	163	1	hence	hence	ADV
ejpam-5038	163	2	include	include	VERB
ejpam-5038	163	3	{	{	PUNCT
ejpam-5038	163	4	l1	l1	PROPN
ejpam-5038	163	5	,	,	PUNCT
ejpam-5038	163	6	r2	r2	PROPN
ejpam-5038	163	7	}	}	PUNCT
ejpam-5038	163	8	in	in	ADP
ejpam-5038	163	9	d	d	PROPN
ejpam-5038	163	10	and	and	CCONJ
ejpam-5038	163	11	{	{	PUNCT
ejpam-5038	163	12	r1	r1	NOUN
ejpam-5038	163	13	,	,	PUNCT
ejpam-5038	163	14	l2	l2	NOUN
ejpam-5038	163	15	}	}	PUNCT
ejpam-5038	163	16	in	in	ADP
ejpam-5038	163	17	d′.	d′.	NOUN
ejpam-5038	163	18	thus	thus	ADV
ejpam-5038	163	19	d	d	NOUN
ejpam-5038	163	20	and	and	CCONJ
ejpam-5038	163	21	d′	d′	PRON
ejpam-5038	163	22	are	be	AUX
ejpam-5038	163	23	dominating	dominate	VERB
ejpam-5038	163	24	sets	set	NOUN
ejpam-5038	163	25	of	of	ADP
ejpam-5038	163	26	the	the	DET
ejpam-5038	163	27	same	same	ADJ
ejpam-5038	163	28	cardinality	cardinality	NOUN
ejpam-5038	163	29	as	as	ADP
ejpam-5038	163	30	the	the	DET
ejpam-5038	163	31	one	one	NOUN
ejpam-5038	163	32	constructed	construct	VERB
ejpam-5038	163	33	in	in	ADP
ejpam-5038	163	34	theorem	theorem	NOUN
ejpam-5038	163	35	1	1	NUM
ejpam-5038	163	36	.	.	PUNCT
ejpam-5038	163	37	thus	thus	ADV
ejpam-5038	163	38	γ′(x(k	γ′(x(k	NOUN
ejpam-5038	163	39	)	)	PUNCT
ejpam-5038	163	40	)	)	PUNCT
ejpam-5038	164	1	=	=	PUNCT
ejpam-5038	164	2	γ(x(k	γ(x(k	PROPN
ejpam-5038	164	3	)	)	PUNCT
ejpam-5038	164	4	)	)	PUNCT
ejpam-5038	164	5	,	,	PUNCT
ejpam-5038	164	6	k	k	PROPN
ejpam-5038	164	7	≥	≥	PROPN
ejpam-5038	164	8	0	0	NUM
ejpam-5038	164	9	.	.	PUNCT
ejpam-5038	165	1	we	we	PRON
ejpam-5038	165	2	note	note	VERB
ejpam-5038	165	3	that	that	SCONJ
ejpam-5038	165	4	the	the	DET
ejpam-5038	165	5	dominating	dominating	NOUN
ejpam-5038	165	6	set	set	NOUN
ejpam-5038	165	7	d	d	NOUN
ejpam-5038	165	8	of	of	ADP
ejpam-5038	165	9	x(k	x(k	PROPN
ejpam-5038	165	10	)	)	PUNCT
ejpam-5038	165	11	,	,	PUNCT
ejpam-5038	165	12	k	k	PROPN
ejpam-5038	165	13	≥	≥	X
ejpam-5038	165	14	0	0	NUM
ejpam-5038	165	15	constructed	construct	VERB
ejpam-5038	165	16	in	in	ADP
ejpam-5038	165	17	theorem	theorem	NOUN
ejpam-5038	165	18	1	1	NUM
ejpam-5038	165	19	is	be	AUX
ejpam-5038	165	20	an	an	DET
ejpam-5038	165	21	independent	independent	ADJ
ejpam-5038	165	22	dominating	dominating	NOUN
ejpam-5038	165	23	set	set	NOUN
ejpam-5038	165	24	.	.	PUNCT
ejpam-5038	166	1	thus	thus	ADV
ejpam-5038	166	2	we	we	PRON
ejpam-5038	166	3	have	have	VERB
ejpam-5038	166	4	the	the	DET
ejpam-5038	166	5	following	follow	VERB
ejpam-5038	166	6	result	result	NOUN
ejpam-5038	166	7	.	.	PUNCT
ejpam-5038	167	1	theorem	theorem	NOUN
ejpam-5038	167	2	3	3	X
ejpam-5038	167	3	.	.	PUNCT
ejpam-5038	168	1	let	let	AUX
ejpam-5038	168	2	x(k	x(k	PUNCT
ejpam-5038	168	3	)	)	PUNCT
ejpam-5038	168	4	be	be	AUX
ejpam-5038	168	5	the	the	DET
ejpam-5038	168	6	x	x	NOUN
ejpam-5038	168	7	-	-	NOUN
ejpam-5038	168	8	tree	tree	NOUN
ejpam-5038	168	9	of	of	ADP
ejpam-5038	168	10	dimension	dimension	NOUN
ejpam-5038	168	11	k.	k.	PROPN
ejpam-5038	169	1	then	then	ADV
ejpam-5038	169	2	γ(x(k	γ(x(k	PROPN
ejpam-5038	169	3	)	)	PUNCT
ejpam-5038	169	4	)	)	PUNCT
ejpam-5038	170	1	=	=	SYM
ejpam-5038	170	2	γ′(x(k	γ′(x(k	NUM
ejpam-5038	170	3	)	)	PUNCT
ejpam-5038	170	4	)	)	PUNCT
ejpam-5038	171	1	=	=	SYM
ejpam-5038	171	2	γi(x(k	γi(x(k	NOUN
ejpam-5038	171	3	)	)	PUNCT
ejpam-5038	171	4	)	)	PUNCT
ejpam-5038	171	5	.	.	PUNCT
ejpam-5038	172	1	3	3	X
ejpam-5038	172	2	.	.	X
ejpam-5038	172	3	inverse	inverse	NOUN
ejpam-5038	172	4	and	and	CCONJ
ejpam-5038	172	5	connected	connected	ADJ
ejpam-5038	172	6	domination	domination	NOUN
ejpam-5038	172	7	in	in	ADP
ejpam-5038	172	8	sibling	sible	VERB
ejpam-5038	172	9	trees	tree	NOUN
ejpam-5038	172	10	a	a	DET
ejpam-5038	172	11	sibling	sible	VERB
ejpam-5038	172	12	tree	tree	NOUN
ejpam-5038	172	13	st	st	NOUN
ejpam-5038	172	14	(	(	PUNCT
ejpam-5038	172	15	r	r	NOUN
ejpam-5038	172	16	)	)	PUNCT
ejpam-5038	172	17	of	of	ADP
ejpam-5038	172	18	dimension	dimension	NOUN
ejpam-5038	172	19	r	r	NOUN
ejpam-5038	172	20	is	be	AUX
ejpam-5038	172	21	obtained	obtain	VERB
ejpam-5038	172	22	from	from	ADP
ejpam-5038	172	23	the	the	DET
ejpam-5038	172	24	complete	complete	ADJ
ejpam-5038	172	25	binary	binary	NOUN
ejpam-5038	172	26	tree	tree	NOUN
ejpam-5038	172	27	t	t	PROPN
ejpam-5038	172	28	(	(	PUNCT
ejpam-5038	172	29	r	r	NOUN
ejpam-5038	172	30	)	)	PUNCT
ejpam-5038	172	31	of	of	ADP
ejpam-5038	172	32	height	height	NOUN
ejpam-5038	172	33	r	r	NOUN
ejpam-5038	172	34	by	by	ADP
ejpam-5038	172	35	adding	add	VERB
ejpam-5038	172	36	edges	edge	NOUN
ejpam-5038	172	37	called	call	VERB
ejpam-5038	172	38	sibling	sible	VERB
ejpam-5038	172	39	edges	edge	NOUN
ejpam-5038	172	40	joining	join	VERB
ejpam-5038	172	41	left	leave	VERB
ejpam-5038	172	42	and	and	CCONJ
ejpam-5038	172	43	right	right	ADJ
ejpam-5038	172	44	children	child	NOUN
ejpam-5038	172	45	of	of	ADP
ejpam-5038	172	46	the	the	DET
ejpam-5038	172	47	same	same	ADJ
ejpam-5038	172	48	parent	parent	NOUN
ejpam-5038	172	49	node	node	NOUN
ejpam-5038	172	50	.	.	PUNCT
ejpam-5038	173	1	the	the	DET
ejpam-5038	173	2	root	root	NOUN
ejpam-5038	173	3	node	node	NOUN
ejpam-5038	173	4	is	be	AUX
ejpam-5038	173	5	at	at	ADP
ejpam-5038	173	6	level	level	NOUN
ejpam-5038	173	7	0	0	NUM
ejpam-5038	173	8	.	.	PUNCT
ejpam-5038	174	1	level	level	NOUN
ejpam-5038	174	2	i	i	PRON
ejpam-5038	174	3	vertices	vertice	VERB
ejpam-5038	174	4	are	be	AUX
ejpam-5038	174	5	the	the	DET
ejpam-5038	174	6	children	child	NOUN
ejpam-5038	174	7	of	of	ADP
ejpam-5038	174	8	vertices	vertex	NOUN
ejpam-5038	174	9	in	in	ADP
ejpam-5038	174	10	level	level	NOUN
ejpam-5038	174	11	i−	i−	PROPN
ejpam-5038	174	12	1	1	NUM
ejpam-5038	174	13	,	,	PUNCT
ejpam-5038	174	14	1	1	NUM
ejpam-5038	174	15	≤	≤	NUM
ejpam-5038	174	16	i	i	PRON
ejpam-5038	174	17	≤	≤	PROPN
ejpam-5038	174	18	r.	r.	PROPN
ejpam-5038	174	19	st	st	PROPN
ejpam-5038	175	1	(	(	PUNCT
ejpam-5038	175	2	r	r	NOUN
ejpam-5038	175	3	)	)	PUNCT
ejpam-5038	175	4	has	have	AUX
ejpam-5038	175	5	2r+1	2r+1	VERB
ejpam-5038	175	6	−	−	ADJ
ejpam-5038	175	7	1	1	NUM
ejpam-5038	175	8	vertices	vertex	NOUN
ejpam-5038	175	9	and	and	CCONJ
ejpam-5038	175	10	3(2r	3(2r	NUM
ejpam-5038	175	11	−	−	NOUN
ejpam-5038	175	12	1	1	NUM
ejpam-5038	175	13	)	)	PUNCT
ejpam-5038	175	14	edges	edge	NOUN
ejpam-5038	175	15	,	,	PUNCT
ejpam-5038	175	16	see	see	VERB
ejpam-5038	175	17	figure	figure	NOUN
ejpam-5038	175	18	7(a	7(a	NUM
ejpam-5038	175	19	)	)	PUNCT
ejpam-5038	175	20	.	.	PUNCT
ejpam-5038	176	1	notation	notation	NOUN
ejpam-5038	176	2	:	:	PUNCT
ejpam-5038	176	3	let	let	VERB
ejpam-5038	176	4	h	h	NOUN
ejpam-5038	176	5	be	be	AUX
ejpam-5038	176	6	a	a	DET
ejpam-5038	176	7	graph	graph	NOUN
ejpam-5038	176	8	,	,	PUNCT
ejpam-5038	176	9	isomorphic	isomorphic	ADJ
ejpam-5038	176	10	to	to	ADP
ejpam-5038	176	11	st	st	PROPN
ejpam-5038	176	12	(	(	PUNCT
ejpam-5038	176	13	2	2	NUM
ejpam-5038	176	14	)	)	PUNCT
ejpam-5038	176	15	as	as	SCONJ
ejpam-5038	176	16	shown	show	VERB
ejpam-5038	176	17	in	in	ADP
ejpam-5038	176	18	the	the	DET
ejpam-5038	176	19	figure	figure	NOUN
ejpam-5038	176	20	7(b	7(b	NOUN
ejpam-5038	176	21	)	)	PUNCT
ejpam-5038	176	22	.	.	PUNCT
ejpam-5038	177	1	we	we	PRON
ejpam-5038	177	2	call	call	VERB
ejpam-5038	177	3	the	the	DET
ejpam-5038	177	4	pair	pair	NOUN
ejpam-5038	177	5	of	of	ADP
ejpam-5038	177	6	vertices	vertex	NOUN
ejpam-5038	177	7	u	u	NOUN
ejpam-5038	177	8	and	and	CCONJ
ejpam-5038	177	9	v	v	NOUN
ejpam-5038	177	10	as	as	ADP
ejpam-5038	177	11	irregular	irregular	ADJ
ejpam-5038	177	12	d	d	NOUN
ejpam-5038	177	13	-	-	PUNCT
ejpam-5038	177	14	twins	twin	NOUN
ejpam-5038	177	15	as	as	SCONJ
ejpam-5038	177	16	u	u	NOUN
ejpam-5038	177	17	and	and	CCONJ
ejpam-5038	177	18	v	v	NOUN
ejpam-5038	177	19	together	together	ADV
ejpam-5038	177	20	dominate	dominate	VERB
ejpam-5038	177	21	all	all	DET
ejpam-5038	177	22	the	the	DET
ejpam-5038	177	23	vertices	vertex	NOUN
ejpam-5038	177	24	of	of	ADP
ejpam-5038	177	25	h.	h.	NOUN
ejpam-5038	177	26	similarly	similarly	ADV
ejpam-5038	177	27	,	,	PUNCT
ejpam-5038	177	28	x	x	PUNCT
ejpam-5038	177	29	and	and	CCONJ
ejpam-5038	177	30	y	y	PROPN
ejpam-5038	177	31	form	form	VERB
ejpam-5038	177	32	another	another	DET
ejpam-5038	177	33	pair	pair	NOUN
ejpam-5038	177	34	of	of	ADP
ejpam-5038	177	35	irregular	irregular	ADJ
ejpam-5038	177	36	d	d	NOUN
ejpam-5038	177	37	-	-	PUNCT
ejpam-5038	177	38	twins	twin	NOUN
ejpam-5038	177	39	.	.	PUNCT
ejpam-5038	178	1	incidentally	incidentally	ADV
ejpam-5038	178	2	,	,	PUNCT
ejpam-5038	178	3	the	the	DET
ejpam-5038	178	4	vertices	vertex	NOUN
ejpam-5038	178	5	u	u	NOUN
ejpam-5038	178	6	and	and	CCONJ
ejpam-5038	178	7	x	x	NOUN
ejpam-5038	178	8	form	form	VERB
ejpam-5038	178	9	a	a	DET
ejpam-5038	178	10	pair	pair	NOUN
ejpam-5038	178	11	of	of	ADP
ejpam-5038	178	12	regular	regular	ADJ
ejpam-5038	178	13	of	of	ADP
ejpam-5038	178	14	d	d	NOUN
ejpam-5038	178	15	-	-	PUNCT
ejpam-5038	178	16	twins	twin	NOUN
ejpam-5038	178	17	.	.	PUNCT
ejpam-5038	179	1	we	we	PRON
ejpam-5038	179	2	refer	refer	VERB
ejpam-5038	179	3	to	to	ADP
ejpam-5038	179	4	vertex	vertex	NOUN
ejpam-5038	179	5	w	w	NOUN
ejpam-5038	179	6	as	as	ADP
ejpam-5038	179	7	the	the	DET
ejpam-5038	179	8	apex	apex	NOUN
ejpam-5038	179	9	vertex	vertex	NOUN
ejpam-5038	179	10	of	of	ADP
ejpam-5038	179	11	h.	h.	PROPN
ejpam-5038	179	12	remark	remark	PROPN
ejpam-5038	179	13	2	2	NUM
ejpam-5038	179	14	.	.	PUNCT
ejpam-5038	180	1	the	the	DET
ejpam-5038	180	2	domination	domination	NOUN
ejpam-5038	180	3	number	number	NOUN
ejpam-5038	180	4	of	of	ADP
ejpam-5038	180	5	st	st	PROPN
ejpam-5038	180	6	(	(	PUNCT
ejpam-5038	180	7	r	r	NOUN
ejpam-5038	180	8	)	)	PUNCT
ejpam-5038	180	9	,	,	PUNCT
ejpam-5038	180	10	r	r	NOUN
ejpam-5038	180	11	≥	≥	NOUN
ejpam-5038	180	12	0	0	NUM
ejpam-5038	180	13	,	,	PUNCT
ejpam-5038	180	14	has	have	AUX
ejpam-5038	180	15	been	be	AUX
ejpam-5038	180	16	determined	determine	VERB
ejpam-5038	180	17	in	in	ADP
ejpam-5038	180	18	[	[	X
ejpam-5038	180	19	17	17	NUM
ejpam-5038	180	20	]	]	X
ejpam-5038	180	21	making	make	VERB
ejpam-5038	180	22	use	use	NOUN
ejpam-5038	180	23	of	of	ADP
ejpam-5038	180	24	regular	regular	ADJ
ejpam-5038	180	25	d	d	NOUN
ejpam-5038	180	26	-	-	PUNCT
ejpam-5038	180	27	twins	twin	NOUN
ejpam-5038	180	28	.	.	PUNCT
ejpam-5038	181	1	in	in	ADP
ejpam-5038	181	2	this	this	DET
ejpam-5038	181	3	section	section	NOUN
ejpam-5038	181	4	,	,	PUNCT
ejpam-5038	181	5	we	we	PRON
ejpam-5038	181	6	make	make	VERB
ejpam-5038	181	7	use	use	NOUN
ejpam-5038	181	8	of	of	ADP
ejpam-5038	181	9	irregular	irregular	ADJ
ejpam-5038	181	10	d	d	NOUN
ejpam-5038	181	11	-	-	PUNCT
ejpam-5038	181	12	twins	twin	NOUN
ejpam-5038	181	13	,	,	PUNCT
ejpam-5038	181	14	leading	lead	VERB
ejpam-5038	181	15	to	to	ADP
ejpam-5038	181	16	the	the	DET
ejpam-5038	181	17	computation	computation	NOUN
ejpam-5038	181	18	of	of	ADP
ejpam-5038	181	19	inverse	inverse	ADJ
ejpam-5038	181	20	domination	domination	NOUN
ejpam-5038	181	21	number	number	NOUN
ejpam-5038	181	22	of	of	ADP
ejpam-5038	181	23	st	st	PROPN
ejpam-5038	181	24	(	(	PUNCT
ejpam-5038	181	25	r	r	NOUN
ejpam-5038	181	26	)	)	PUNCT
ejpam-5038	181	27	.	.	PUNCT
ejpam-5038	182	1	v.	v.	PROPN
ejpam-5038	182	2	shalini	shalini	PROPN
ejpam-5038	182	3	,	,	PUNCT
ejpam-5038	182	4	i.	i.	PROPN
ejpam-5038	182	5	rajasingh	rajasingh	PROPN
ejpam-5038	182	6	/	/	SYM
ejpam-5038	182	7	eur	eur	PROPN
ejpam-5038	182	8	.	.	PUNCT
ejpam-5038	183	1	j.	j.	PROPN
ejpam-5038	183	2	pure	pure	PROPN
ejpam-5038	183	3	appl	appl	PROPN
ejpam-5038	183	4	.	.	PROPN
ejpam-5038	183	5	math	math	PROPN
ejpam-5038	183	6	,	,	PUNCT
ejpam-5038	183	7	17	17	NUM
ejpam-5038	183	8	(	(	PUNCT
ejpam-5038	183	9	2	2	NUM
ejpam-5038	183	10	)	)	PUNCT
ejpam-5038	183	11	(	(	PUNCT
ejpam-5038	183	12	2024	2024	NUM
ejpam-5038	183	13	)	)	PUNCT
ejpam-5038	183	14	,	,	PUNCT
ejpam-5038	183	15	1082	1082	NUM
ejpam-5038	183	16	-	-	SYM
ejpam-5038	183	17	1093	1093	NUM
ejpam-5038	183	18	1089	1089	NUM
ejpam-5038	183	19	lemma	lemma	PROPN
ejpam-5038	183	20	5	5	NUM
ejpam-5038	183	21	.	.	PUNCT
ejpam-5038	184	1	let	let	VERB
ejpam-5038	184	2	h	h	PRON
ejpam-5038	184	3	be	be	AUX
ejpam-5038	184	4	an	an	DET
ejpam-5038	184	5	induced	induced	ADJ
ejpam-5038	184	6	subgraph	subgraph	NOUN
ejpam-5038	184	7	from	from	ADP
ejpam-5038	184	8	the	the	DET
ejpam-5038	184	9	last	last	ADJ
ejpam-5038	184	10	three	three	NUM
ejpam-5038	184	11	levels	level	NOUN
ejpam-5038	184	12	of	of	ADP
ejpam-5038	184	13	st	st	PROPN
ejpam-5038	184	14	(	(	PUNCT
ejpam-5038	184	15	r	r	NOUN
ejpam-5038	184	16	)	)	PUNCT
ejpam-5038	184	17	,	,	PUNCT
ejpam-5038	184	18	r	r	NOUN
ejpam-5038	184	19	≥	≥	NOUN
ejpam-5038	184	20	2	2	NUM
ejpam-5038	184	21	,	,	PUNCT
ejpam-5038	184	22	isomorphic	isomorphic	ADJ
ejpam-5038	184	23	to	to	ADP
ejpam-5038	184	24	st	st	PROPN
ejpam-5038	184	25	(	(	PUNCT
ejpam-5038	184	26	2	2	NUM
ejpam-5038	184	27	)	)	PUNCT
ejpam-5038	184	28	.	.	PUNCT
ejpam-5038	185	1	then	then	ADV
ejpam-5038	185	2	γ(h	γ(h	PROPN
ejpam-5038	185	3	)	)	PUNCT
ejpam-5038	185	4	=	=	SYM
ejpam-5038	185	5	2	2	X
ejpam-5038	185	6	.	.	PUNCT
ejpam-5038	185	7	proof	proof	NOUN
ejpam-5038	185	8	.	.	PUNCT
ejpam-5038	186	1	even	even	ADV
ejpam-5038	186	2	if	if	SCONJ
ejpam-5038	186	3	the	the	DET
ejpam-5038	186	4	apex	apex	PROPN
ejpam-5038	186	5	vertex	vertex	PROPN
ejpam-5038	186	6	w	w	PROPN
ejpam-5038	186	7	of	of	ADP
ejpam-5038	186	8	h	h	NOUN
ejpam-5038	186	9	is	be	AUX
ejpam-5038	186	10	already	already	ADV
ejpam-5038	186	11	dominated	dominate	VERB
ejpam-5038	186	12	by	by	ADP
ejpam-5038	186	13	some	some	DET
ejpam-5038	186	14	vertex	vertex	NOUN
ejpam-5038	186	15	from	from	ADP
ejpam-5038	186	16	v	v	NUM
ejpam-5038	186	17	(	(	PUNCT
ejpam-5038	186	18	st	st	PROPN
ejpam-5038	186	19	(	(	PUNCT
ejpam-5038	186	20	r	r	NOUN
ejpam-5038	186	21	)	)	PUNCT
ejpam-5038	186	22	)	)	PUNCT
ejpam-5038	187	1	−	−	PROPN
ejpam-5038	187	2	v	v	X
ejpam-5038	187	3	(	(	PUNCT
ejpam-5038	187	4	h	h	NOUN
ejpam-5038	187	5	)	)	PUNCT
ejpam-5038	187	6	,	,	PUNCT
ejpam-5038	187	7	there	there	PRON
ejpam-5038	187	8	is	be	VERB
ejpam-5038	187	9	no	no	DET
ejpam-5038	187	10	vertex	vertex	NOUN
ejpam-5038	187	11	of	of	ADP
ejpam-5038	187	12	degree	degree	NOUN
ejpam-5038	187	13	5	5	NUM
ejpam-5038	187	14	in	in	ADP
ejpam-5038	187	15	h	h	NOUN
ejpam-5038	187	16	that	that	PRON
ejpam-5038	187	17	dominates	dominate	VERB
ejpam-5038	187	18	the	the	DET
ejpam-5038	187	19	remaining	remain	VERB
ejpam-5038	187	20	vertices	vertex	NOUN
ejpam-5038	187	21	.	.	PUNCT
ejpam-5038	188	1	thus	thus	ADV
ejpam-5038	188	2	γ(h	γ(h	NOUN
ejpam-5038	188	3	)	)	PUNCT
ejpam-5038	188	4	≥	≥	NOUN
ejpam-5038	188	5	2	2	NUM
ejpam-5038	188	6	.	.	PUNCT
ejpam-5038	188	7	further	far	ADV
ejpam-5038	188	8	,	,	PUNCT
ejpam-5038	188	9	any	any	DET
ejpam-5038	188	10	pair	pair	NOUN
ejpam-5038	188	11	of	of	ADP
ejpam-5038	188	12	irregular	irregular	ADJ
ejpam-5038	188	13	d	d	ADJ
ejpam-5038	188	14	-	-	ADJ
ejpam-5038	188	15	twin	twin	ADJ
ejpam-5038	188	16	vertices	vertex	NOUN
ejpam-5038	188	17	in	in	ADP
ejpam-5038	188	18	h	h	NOUN
ejpam-5038	188	19	dominates	dominate	VERB
ejpam-5038	188	20	all	all	DET
ejpam-5038	188	21	vertices	vertex	NOUN
ejpam-5038	188	22	in	in	ADP
ejpam-5038	188	23	h.	h.	PROPN
ejpam-5038	188	24	hence	hence	ADV
ejpam-5038	188	25	γ(h	γ(h	PROPN
ejpam-5038	188	26	)	)	PUNCT
ejpam-5038	188	27	=	=	SYM
ejpam-5038	188	28	2	2	X
ejpam-5038	188	29	.	.	X
ejpam-5038	188	30	theorem	theorem	NOUN
ejpam-5038	188	31	4	4	NUM
ejpam-5038	188	32	.	.	PUNCT
ejpam-5038	189	1	let	let	VERB
ejpam-5038	189	2	g	g	NOUN
ejpam-5038	189	3	be	be	AUX
ejpam-5038	189	4	the	the	DET
ejpam-5038	189	5	sibling	sible	VERB
ejpam-5038	189	6	tree	tree	NOUN
ejpam-5038	189	7	st	st	PROPN
ejpam-5038	189	8	(	(	PUNCT
ejpam-5038	189	9	r	r	NOUN
ejpam-5038	189	10	)	)	PUNCT
ejpam-5038	189	11	of	of	ADP
ejpam-5038	189	12	dimension	dimension	NOUN
ejpam-5038	189	13	r	r	NOUN
ejpam-5038	189	14	≥	≥	NOUN
ejpam-5038	189	15	0	0	NUM
ejpam-5038	189	16	.	.	PUNCT
ejpam-5038	190	1	then	then	ADV
ejpam-5038	190	2	γ(st	γ(st	PROPN
ejpam-5038	190	3	(	(	PUNCT
ejpam-5038	190	4	r	r	NOUN
ejpam-5038	190	5	)	)	PUNCT
ejpam-5038	190	6	)	)	PUNCT
ejpam-5038	191	1	=	=	PUNCT
ejpam-5038	192	1			NOUN
ejpam-5038	192	2	1	1	NUM
ejpam-5038	192	3	7(2	7(2	NUM
ejpam-5038	192	4	r+2	r+2	NUM
ejpam-5038	192	5	+	+	NOUN
ejpam-5038	192	6	3	3	NUM
ejpam-5038	192	7	)	)	PUNCT
ejpam-5038	192	8	;	;	PUNCT
ejpam-5038	192	9	r	r	NOUN
ejpam-5038	192	10	≡	≡	PROPN
ejpam-5038	192	11	0	0	PUNCT
ejpam-5038	193	1	(	(	PUNCT
ejpam-5038	193	2	mod	mod	NOUN
ejpam-5038	193	3	3	3	NUM
ejpam-5038	193	4	)	)	PUNCT
ejpam-5038	193	5	1	1	NUM
ejpam-5038	193	6	7(2	7(2	NUM
ejpam-5038	193	7	r+2	r+2	NUM
ejpam-5038	193	8	−	−	PROPN
ejpam-5038	193	9	1	1	NUM
ejpam-5038	193	10	)	)	PUNCT
ejpam-5038	193	11	;	;	PUNCT
ejpam-5038	193	12	r	r	NOUN
ejpam-5038	193	13	≡	≡	PROPN
ejpam-5038	193	14	1	1	NUM
ejpam-5038	193	15	(	(	PUNCT
ejpam-5038	193	16	mod	mod	NOUN
ejpam-5038	193	17	3	3	NUM
ejpam-5038	193	18	)	)	PUNCT
ejpam-5038	193	19	1	1	NUM
ejpam-5038	193	20	7(2	7(2	NUM
ejpam-5038	193	21	r+2	r+2	NUM
ejpam-5038	193	22	−	−	PROPN
ejpam-5038	193	23	2	2	NUM
ejpam-5038	193	24	)	)	PUNCT
ejpam-5038	193	25	;	;	PUNCT
ejpam-5038	193	26	r	r	NOUN
ejpam-5038	193	27	≡	≡	PROPN
ejpam-5038	193	28	2	2	NUM
ejpam-5038	193	29	(	(	PUNCT
ejpam-5038	193	30	mod	mod	NOUN
ejpam-5038	193	31	3	3	NUM
ejpam-5038	193	32	)	)	PUNCT
ejpam-5038	193	33	proof	proof	NOUN
ejpam-5038	193	34	.	.	PUNCT
ejpam-5038	194	1	we	we	PRON
ejpam-5038	194	2	partition	partition	VERB
ejpam-5038	194	3	the	the	DET
ejpam-5038	194	4	levels	level	NOUN
ejpam-5038	194	5	l0	l0	PROPN
ejpam-5038	194	6	,	,	PUNCT
ejpam-5038	194	7	l1	l1	PROPN
ejpam-5038	194	8	,	,	PUNCT
ejpam-5038	194	9	l2	l2	NOUN
ejpam-5038	194	10	,	,	PUNCT
ejpam-5038	194	11	l3	l3	PROPN
ejpam-5038	194	12	,	,	PUNCT
ejpam-5038	194	13	...	...	PUNCT
ejpam-5038	194	14	,	,	PUNCT
ejpam-5038	194	15	lr	lr	PROPN
ejpam-5038	194	16	of	of	ADP
ejpam-5038	194	17	st	st	PROPN
ejpam-5038	194	18	(	(	PUNCT
ejpam-5038	194	19	r	r	NOUN
ejpam-5038	194	20	)	)	PUNCT
ejpam-5038	194	21	into	into	ADP
ejpam-5038	194	22	maximum	maximum	ADJ
ejpam-5038	194	23	number	number	NOUN
ejpam-5038	194	24	of	of	ADP
ejpam-5038	194	25	disjoint	disjoint	ADJ
ejpam-5038	194	26	3	3	NUM
ejpam-5038	194	27	-	-	NOUN
ejpam-5038	194	28	levels	level	NOUN
ejpam-5038	194	29	,	,	PUNCT
ejpam-5038	194	30	beginning	begin	VERB
ejpam-5038	194	31	from	from	ADP
ejpam-5038	194	32	lr	lr	PROPN
ejpam-5038	194	33	.	.	PROPN
ejpam-5038	195	1	clearly	clearly	ADV
ejpam-5038	195	2	the	the	DET
ejpam-5038	195	3	left	leave	VERB
ejpam-5038	195	4	out	out	ADP
ejpam-5038	195	5	levels	level	NOUN
ejpam-5038	195	6	will	will	AUX
ejpam-5038	195	7	be	be	AUX
ejpam-5038	195	8	l0	l0	VERB
ejpam-5038	196	1	when	when	SCONJ
ejpam-5038	196	2	r	r	NOUN
ejpam-5038	196	3	(	(	PUNCT
ejpam-5038	196	4	mod	mod	NOUN
ejpam-5038	196	5	3	3	NUM
ejpam-5038	196	6	)	)	PUNCT
ejpam-5038	196	7	=	=	SYM
ejpam-5038	196	8	0	0	NUM
ejpam-5038	196	9	;	;	PUNCT
ejpam-5038	196	10	l0	l0	PROPN
ejpam-5038	196	11	and	and	CCONJ
ejpam-5038	196	12	l1	l1	PROPN
ejpam-5038	196	13	when	when	SCONJ
ejpam-5038	196	14	r	r	NOUN
ejpam-5038	196	15	(	(	PUNCT
ejpam-5038	196	16	mod	mod	NOUN
ejpam-5038	196	17	3	3	NUM
ejpam-5038	196	18	)	)	PUNCT
ejpam-5038	196	19	=	=	SYM
ejpam-5038	196	20	1	1	X
ejpam-5038	196	21	.	.	X
ejpam-5038	196	22	in	in	ADP
ejpam-5038	196	23	otherwords	otherword	NOUN
ejpam-5038	196	24	,	,	PUNCT
ejpam-5038	196	25	we	we	PRON
ejpam-5038	196	26	have	have	VERB
ejpam-5038	196	27	the	the	DET
ejpam-5038	196	28	partitioning	partition	VERB
ejpam-5038	196	29	set	set	NOUN
ejpam-5038	196	30	p	p	NOUN
ejpam-5038	196	31	of	of	ADP
ejpam-5038	196	32	the	the	DET
ejpam-5038	196	33	levels	level	NOUN
ejpam-5038	196	34	of	of	ADP
ejpam-5038	196	35	st	st	PROPN
ejpam-5038	196	36	(	(	PUNCT
ejpam-5038	196	37	r	r	NOUN
ejpam-5038	196	38	)	)	PUNCT
ejpam-5038	196	39	as	as	SCONJ
ejpam-5038	196	40	follows	follow	VERB
ejpam-5038	196	41	:	:	PUNCT
ejpam-5038	196	42	(	(	PUNCT
ejpam-5038	196	43	i	i	NOUN
ejpam-5038	196	44	)	)	PUNCT
ejpam-5038	196	45	when	when	SCONJ
ejpam-5038	196	46	r	r	NOUN
ejpam-5038	196	47	(	(	PUNCT
ejpam-5038	196	48	mod	mod	NOUN
ejpam-5038	196	49	3	3	NUM
ejpam-5038	196	50	)	)	PUNCT
ejpam-5038	196	51	=	=	SYM
ejpam-5038	196	52	0	0	NUM
ejpam-5038	196	53	,	,	PUNCT
ejpam-5038	196	54	p	p	NOUN
ejpam-5038	196	55	=	=	PUNCT
ejpam-5038	196	56	{	{	PUNCT
ejpam-5038	196	57	l0	l0	NOUN
ejpam-5038	196	58	}	}	PUNCT
ejpam-5038	196	59	∪	∪	NOUN
ejpam-5038	196	60	⋃⌊	⋃⌊	PROPN
ejpam-5038	196	61	r	r	NOUN
ejpam-5038	196	62	3	3	NUM
ejpam-5038	196	63	⌋−1	⌋−1	NOUN
ejpam-5038	196	64	i=0	i=0	PROPN
ejpam-5038	196	65	{	{	PUNCT
ejpam-5038	196	66	lr−3i−2	lr−3i−2	PROPN
ejpam-5038	196	67	,	,	PUNCT
ejpam-5038	196	68	lr−3i−1	lr−3i−1	PROPN
ejpam-5038	196	69	,	,	PUNCT
ejpam-5038	196	70	lr−3i	lr−3i	PROPN
ejpam-5038	196	71	}	}	PUNCT
ejpam-5038	196	72	;	;	PUNCT
ejpam-5038	196	73	(	(	PUNCT
ejpam-5038	196	74	ii	ii	NOUN
ejpam-5038	196	75	)	)	PUNCT
ejpam-5038	196	76	when	when	SCONJ
ejpam-5038	196	77	r	r	NOUN
ejpam-5038	196	78	(	(	PUNCT
ejpam-5038	196	79	mod	mod	NOUN
ejpam-5038	196	80	3	3	NUM
ejpam-5038	196	81	)	)	PUNCT
ejpam-5038	196	82	=	=	SYM
ejpam-5038	196	83	1	1	NUM
ejpam-5038	196	84	,	,	PUNCT
ejpam-5038	196	85	p	p	NOUN
ejpam-5038	196	86	=	=	PUNCT
ejpam-5038	196	87	{	{	PUNCT
ejpam-5038	196	88	l0	l0	PROPN
ejpam-5038	196	89	,	,	PUNCT
ejpam-5038	196	90	l1	l1	PROPN
ejpam-5038	196	91	}	}	PUNCT
ejpam-5038	196	92	∪	∪	VERB
ejpam-5038	196	93	⋃⌊	⋃⌊	PROPN
ejpam-5038	196	94	r	r	NOUN
ejpam-5038	196	95	3	3	NUM
ejpam-5038	196	96	⌋−1	⌋−1	NOUN
ejpam-5038	196	97	i=0	i=0	PROPN
ejpam-5038	196	98	{	{	PUNCT
ejpam-5038	196	99	lr−3i−2	lr−3i−2	PROPN
ejpam-5038	196	100	,	,	PUNCT
ejpam-5038	196	101	lr−3i−1	lr−3i−1	PROPN
ejpam-5038	196	102	,	,	PUNCT
ejpam-5038	196	103	lr−3i	lr−3i	PROPN
ejpam-5038	196	104	}	}	PUNCT
ejpam-5038	196	105	;	;	PUNCT
ejpam-5038	196	106	(	(	PUNCT
ejpam-5038	196	107	iii	iii	X
ejpam-5038	196	108	)	)	PUNCT
ejpam-5038	196	109	when	when	SCONJ
ejpam-5038	196	110	r	r	NOUN
ejpam-5038	196	111	(	(	PUNCT
ejpam-5038	196	112	mod	mod	NOUN
ejpam-5038	196	113	3	3	NUM
ejpam-5038	196	114	)	)	PUNCT
ejpam-5038	196	115	=	=	SYM
ejpam-5038	196	116	2	2	NUM
ejpam-5038	196	117	,	,	PUNCT
ejpam-5038	196	118	p	p	NOUN
ejpam-5038	196	119	=	=	PROPN
ejpam-5038	196	120	⋃⌊	⋃⌊	PROPN
ejpam-5038	196	121	r	r	NOUN
ejpam-5038	196	122	3	3	NUM
ejpam-5038	196	123	⌋	⌋	NOUN
ejpam-5038	196	124	i=0{lr−3i−2	i=0{lr−3i−2	ADP
ejpam-5038	196	125	,	,	PUNCT
ejpam-5038	196	126	lr−3i−1	lr−3i−1	PROPN
ejpam-5038	196	127	,	,	PUNCT
ejpam-5038	196	128	lr−3i	lr−3i	PROPN
ejpam-5038	196	129	}	}	PUNCT
ejpam-5038	196	130	.	.	PUNCT
ejpam-5038	197	1	we	we	PRON
ejpam-5038	197	2	note	note	VERB
ejpam-5038	197	3	that	that	SCONJ
ejpam-5038	197	4	lr−3i−2	lr−3i−2	NOUN
ejpam-5038	197	5	has	have	VERB
ejpam-5038	197	6	2r−3i−2	2r−3i−2	NUM
ejpam-5038	197	7	vertices	vertex	NOUN
ejpam-5038	197	8	for	for	ADP
ejpam-5038	197	9	any	any	DET
ejpam-5038	197	10	i	i	PROPN
ejpam-5038	197	11	,	,	PUNCT
ejpam-5038	197	12	0	0	NUM
ejpam-5038	197	13	≤	≤	NUM
ejpam-5038	198	1	i	i	PRON
ejpam-5038	198	2	≤	≤	PUNCT
ejpam-5038	198	3	⌊	⌊	AUX
ejpam-5038	198	4	r3⌋	r3⌋	NOUN
ejpam-5038	198	5	−	−	PROPN
ejpam-5038	198	6	1	1	NUM
ejpam-5038	198	7	.	.	PUNCT
ejpam-5038	198	8	hence	hence	ADV
ejpam-5038	198	9	lr−3i−2	lr−3i−2	PROPN
ejpam-5038	198	10	,	,	PUNCT
ejpam-5038	198	11	lr−3i−1	lr−3i−1	PROPN
ejpam-5038	198	12	,	,	PUNCT
ejpam-5038	198	13	lr−3i	lr−3i	VERB
ejpam-5038	198	14	together	together	ADV
ejpam-5038	198	15	induce	induce	VERB
ejpam-5038	198	16	2r−3i−2	2r−3i−2	NUM
ejpam-5038	198	17	disjoint	disjoint	NOUN
ejpam-5038	198	18	copies	copy	NOUN
ejpam-5038	198	19	of	of	ADP
ejpam-5038	198	20	st	st	PROPN
ejpam-5038	198	21	(	(	PUNCT
ejpam-5038	198	22	2	2	NUM
ejpam-5038	198	23	)	)	PUNCT
ejpam-5038	198	24	,	,	PUNCT
ejpam-5038	198	25	0	0	NUM
ejpam-5038	198	26	≤	≤	NUM
ejpam-5038	198	27	i	i	PRON
ejpam-5038	198	28	≤	≤	PUNCT
ejpam-5038	198	29	⌊	⌊	AUX
ejpam-5038	198	30	r3⌋	r3⌋	NOUN
ejpam-5038	198	31	−	−	PROPN
ejpam-5038	198	32	1	1	NUM
ejpam-5038	198	33	.	.	PUNCT
ejpam-5038	199	1	thus	thus	ADV
ejpam-5038	199	2	the	the	DET
ejpam-5038	199	3	number	number	NOUN
ejpam-5038	199	4	α	α	NOUN
ejpam-5038	199	5	of	of	ADP
ejpam-5038	199	6	vertex	vertex	NOUN
ejpam-5038	199	7	disjoint	disjoint	NOUN
ejpam-5038	199	8	copies	copy	NOUN
ejpam-5038	199	9	of	of	ADP
ejpam-5038	199	10	st	st	PROPN
ejpam-5038	199	11	(	(	PUNCT
ejpam-5038	199	12	2	2	NUM
ejpam-5038	199	13	)	)	PUNCT
ejpam-5038	199	14	in	in	ADP
ejpam-5038	199	15	st	st	PROPN
ejpam-5038	199	16	(	(	PUNCT
ejpam-5038	199	17	r	r	NOUN
ejpam-5038	199	18	)	)	PUNCT
ejpam-5038	199	19	,	,	PUNCT
ejpam-5038	199	20	r	r	NOUN
ejpam-5038	199	21	≥	≥	NOUN
ejpam-5038	199	22	3	3	NUM
ejpam-5038	199	23	,	,	PUNCT
ejpam-5038	199	24	is	be	AUX
ejpam-5038	199	25	α	α	NOUN
ejpam-5038	199	26	=	=	PUNCT
ejpam-5038	199	27	⌊	⌊	NOUN
ejpam-5038	199	28	r	r	NOUN
ejpam-5038	199	29	3	3	NUM
ejpam-5038	199	30	⌋−1∑	⌋−1∑	ADP
ejpam-5038	199	31	i=0	i=0	PROPN
ejpam-5038	199	32	2r−3i−2	2r−3i−2	NUM
ejpam-5038	199	33	=	=	SYM
ejpam-5038	199	34	2r+1	2r+1	NUM
ejpam-5038	199	35	7	7	NUM
ejpam-5038	199	36	(	(	PUNCT
ejpam-5038	199	37	23⌊	23⌊	NOUN
ejpam-5038	199	38	r	r	NOUN
ejpam-5038	199	39	3	3	NUM
ejpam-5038	199	40	⌋	⌋	NOUN
ejpam-5038	199	41	−	−	NOUN
ejpam-5038	199	42	1	1	NUM
ejpam-5038	199	43	2⌊	2⌊	NUM
ejpam-5038	199	44	r	r	NOUN
ejpam-5038	199	45	3	3	NUM
ejpam-5038	199	46	⌋	⌋	NOUN
ejpam-5038	199	47	)	)	PUNCT
ejpam-5038	199	48	=	=	PUNCT
ejpam-5038	200	1	1	1	NUM
ejpam-5038	200	2	7	7	NUM
ejpam-5038	200	3	(	(	PUNCT
ejpam-5038	200	4	2r+1	2r+1	NOUN
ejpam-5038	200	5	−	−	PROPN
ejpam-5038	200	6	2r(mod	2r(mod	NUM
ejpam-5038	200	7	3)+1	3)+1	NOUN
ejpam-5038	200	8	)	)	PUNCT
ejpam-5038	200	9	by	by	ADP
ejpam-5038	200	10	lemma	lemma	PROPN
ejpam-5038	200	11	5	5	NUM
ejpam-5038	200	12	,	,	PUNCT
ejpam-5038	200	13	each	each	DET
ejpam-5038	200	14	st	st	PROPN
ejpam-5038	200	15	(	(	PUNCT
ejpam-5038	200	16	2	2	NUM
ejpam-5038	200	17	)	)	PUNCT
ejpam-5038	200	18	contributes	contribute	VERB
ejpam-5038	200	19	2	2	NUM
ejpam-5038	200	20	vertices	vertex	NOUN
ejpam-5038	200	21	to	to	ADP
ejpam-5038	200	22	any	any	DET
ejpam-5038	200	23	minimum	minimum	ADJ
ejpam-5038	200	24	dominating	dominating	NOUN
ejpam-5038	200	25	set	set	NOUN
ejpam-5038	200	26	d	d	PROPN
ejpam-5038	200	27	of	of	ADP
ejpam-5038	200	28	st	st	PROPN
ejpam-5038	200	29	(	(	PUNCT
ejpam-5038	200	30	r	r	NOUN
ejpam-5038	200	31	)	)	PUNCT
ejpam-5038	200	32	.	.	PUNCT
ejpam-5038	201	1	hence	hence	ADV
ejpam-5038	201	2	γ(st	γ(st	PROPN
ejpam-5038	201	3	(	(	PUNCT
ejpam-5038	201	4	r	r	NOUN
ejpam-5038	201	5	)	)	PUNCT
ejpam-5038	201	6	)	)	PUNCT
ejpam-5038	202	1	=	=	NOUN
ejpam-5038	203	1	2α	2α	NOUN
ejpam-5038	203	2	+	+	CCONJ
ejpam-5038	203	3	1	1	NUM
ejpam-5038	203	4	for	for	ADP
ejpam-5038	203	5	r	r	NOUN
ejpam-5038	203	6	≡	≡	PROPN
ejpam-5038	203	7	0	0	NUM
ejpam-5038	203	8	,	,	PUNCT
ejpam-5038	203	9	1(mod	1(mod	NUM
ejpam-5038	203	10	3	3	NUM
ejpam-5038	203	11	)	)	PUNCT
ejpam-5038	203	12	and	and	CCONJ
ejpam-5038	203	13	γ(st	γ(st	PROPN
ejpam-5038	203	14	(	(	PUNCT
ejpam-5038	203	15	r	r	NOUN
ejpam-5038	203	16	)	)	PUNCT
ejpam-5038	203	17	)	)	PUNCT
ejpam-5038	204	1	=	=	NOUN
ejpam-5038	205	1	2α	2α	NOUN
ejpam-5038	205	2	+	+	CCONJ
ejpam-5038	205	3	2	2	NUM
ejpam-5038	205	4	for	for	ADP
ejpam-5038	205	5	r	r	NOUN
ejpam-5038	205	6	≡	≡	PROPN
ejpam-5038	205	7	2(mod	2(mod	NUM
ejpam-5038	205	8	3	3	NUM
ejpam-5038	205	9	)	)	PUNCT
ejpam-5038	205	10	.	.	PUNCT
ejpam-5038	206	1	hence	hence	ADV
ejpam-5038	206	2	the	the	DET
ejpam-5038	206	3	result	result	NOUN
ejpam-5038	206	4	.	.	PUNCT
ejpam-5038	207	1	theorem	theorem	ADJ
ejpam-5038	207	2	5	5	NUM
ejpam-5038	207	3	.	.	PUNCT
ejpam-5038	208	1	let	let	VERB
ejpam-5038	208	2	g	g	NOUN
ejpam-5038	208	3	be	be	AUX
ejpam-5038	208	4	the	the	DET
ejpam-5038	208	5	sibling	sible	VERB
ejpam-5038	208	6	tree	tree	NOUN
ejpam-5038	208	7	st	st	PROPN
ejpam-5038	208	8	(	(	PUNCT
ejpam-5038	208	9	r	r	NOUN
ejpam-5038	208	10	)	)	PUNCT
ejpam-5038	208	11	of	of	ADP
ejpam-5038	208	12	dimension	dimension	NOUN
ejpam-5038	208	13	r	r	NOUN
ejpam-5038	208	14	≥	≥	NOUN
ejpam-5038	208	15	0	0	NUM
ejpam-5038	208	16	.	.	PUNCT
ejpam-5038	209	1	then	then	ADV
ejpam-5038	209	2	γ′(st	γ′(st	NOUN
ejpam-5038	209	3	(	(	PUNCT
ejpam-5038	209	4	r	r	NOUN
ejpam-5038	209	5	)	)	PUNCT
ejpam-5038	209	6	)	)	PUNCT
ejpam-5038	210	1	=	=	SYM
ejpam-5038	210	2	γ(st	γ(st	PROPN
ejpam-5038	210	3	(	(	PUNCT
ejpam-5038	210	4	r	r	NOUN
ejpam-5038	210	5	)	)	PUNCT
ejpam-5038	210	6	)	)	PUNCT
ejpam-5038	210	7	,	,	PUNCT
ejpam-5038	210	8	r	r	NOUN
ejpam-5038	210	9	≥	≥	NOUN
ejpam-5038	210	10	0	0	NUM
ejpam-5038	210	11	.	.	PUNCT
ejpam-5038	211	1	proof	proof	NOUN
ejpam-5038	211	2	.	.	PUNCT
ejpam-5038	212	1	we	we	PRON
ejpam-5038	212	2	construct	construct	VERB
ejpam-5038	212	3	two	two	NUM
ejpam-5038	212	4	minimum	minimum	ADJ
ejpam-5038	212	5	dominating	dominating	NOUN
ejpam-5038	212	6	sets	set	NOUN
ejpam-5038	212	7	d	d	NOUN
ejpam-5038	212	8	and	and	CCONJ
ejpam-5038	212	9	d′	d′	PROPN
ejpam-5038	212	10	of	of	ADP
ejpam-5038	212	11	st	st	PROPN
ejpam-5038	212	12	(	(	PUNCT
ejpam-5038	212	13	r	r	NOUN
ejpam-5038	212	14	)	)	PUNCT
ejpam-5038	212	15	,	,	PUNCT
ejpam-5038	212	16	r	r	NOUN
ejpam-5038	212	17	≥	≥	NOUN
ejpam-5038	212	18	0	0	PUNCT
ejpam-5038	212	19	as	as	SCONJ
ejpam-5038	212	20	follows	follow	VERB
ejpam-5038	212	21	.	.	PUNCT
ejpam-5038	213	1	include	include	VERB
ejpam-5038	213	2	one	one	NUM
ejpam-5038	213	3	pair	pair	NOUN
ejpam-5038	213	4	of	of	ADP
ejpam-5038	213	5	irregular	irregular	ADJ
ejpam-5038	213	6	d	d	ADJ
ejpam-5038	213	7	-	-	ADJ
ejpam-5038	213	8	twin	twin	ADJ
ejpam-5038	213	9	vertices	vertex	NOUN
ejpam-5038	213	10	in	in	ADP
ejpam-5038	213	11	d	d	PROPN
ejpam-5038	213	12	and	and	CCONJ
ejpam-5038	213	13	the	the	DET
ejpam-5038	213	14	other	other	ADJ
ejpam-5038	213	15	pair	pair	NOUN
ejpam-5038	213	16	of	of	ADP
ejpam-5038	213	17	d	d	ADJ
ejpam-5038	213	18	-	-	ADJ
ejpam-5038	213	19	twin	twin	ADJ
ejpam-5038	213	20	vertices	vertex	NOUN
ejpam-5038	213	21	in	in	ADP
ejpam-5038	213	22	d′	d′	NUM
ejpam-5038	213	23	from	from	ADP
ejpam-5038	213	24	each	each	PRON
ejpam-5038	213	25	of	of	ADP
ejpam-5038	213	26	the	the	DET
ejpam-5038	213	27	copies	copy	NOUN
ejpam-5038	213	28	of	of	ADP
ejpam-5038	213	29	st	st	PROPN
ejpam-5038	213	30	(	(	PUNCT
ejpam-5038	213	31	2	2	NUM
ejpam-5038	213	32	)	)	PUNCT
ejpam-5038	213	33	considered	consider	VERB
ejpam-5038	213	34	in	in	ADP
ejpam-5038	213	35	theorem	theorem	NOUN
ejpam-5038	213	36	4	4	NUM
ejpam-5038	213	37	.	.	PUNCT
ejpam-5038	214	1	the	the	DET
ejpam-5038	214	2	vertices	vertex	NOUN
ejpam-5038	214	3	of	of	ADP
ejpam-5038	214	4	st	st	PROPN
ejpam-5038	214	5	(	(	PUNCT
ejpam-5038	214	6	r	r	NOUN
ejpam-5038	214	7	)	)	PUNCT
ejpam-5038	214	8	that	that	PRON
ejpam-5038	214	9	are	be	AUX
ejpam-5038	214	10	not	not	PART
ejpam-5038	214	11	covered	cover	VERB
ejpam-5038	214	12	by	by	ADP
ejpam-5038	214	13	these	these	DET
ejpam-5038	214	14	copies	copy	NOUN
ejpam-5038	214	15	of	of	ADP
ejpam-5038	214	16	st	st	PROPN
ejpam-5038	214	17	(	(	PUNCT
ejpam-5038	214	18	2	2	NUM
ejpam-5038	214	19	)	)	PUNCT
ejpam-5038	214	20	induce	induce	VERB
ejpam-5038	214	21	st	st	PROPN
ejpam-5038	214	22	(	(	PUNCT
ejpam-5038	214	23	0	0	NUM
ejpam-5038	214	24	)	)	PUNCT
ejpam-5038	214	25	or	or	CCONJ
ejpam-5038	214	26	st	st	PROPN
ejpam-5038	214	27	(	(	PUNCT
ejpam-5038	214	28	1	1	NUM
ejpam-5038	214	29	)	)	PUNCT
ejpam-5038	214	30	according	accord	VERB
ejpam-5038	214	31	as	as	ADP
ejpam-5038	214	32	r	r	NOUN
ejpam-5038	214	33	≡	≡	PROPN
ejpam-5038	214	34	0	0	NUM
ejpam-5038	214	35	or	or	CCONJ
ejpam-5038	214	36	1	1	NUM
ejpam-5038	214	37	mod	mod	NOUN
ejpam-5038	214	38	3	3	NUM
ejpam-5038	214	39	.	.	PUNCT
ejpam-5038	215	1	since	since	SCONJ
ejpam-5038	215	2	the	the	DET
ejpam-5038	215	3	children	child	NOUN
ejpam-5038	215	4	u	u	NOUN
ejpam-5038	215	5	and	and	CCONJ
ejpam-5038	215	6	x	x	PROPN
ejpam-5038	215	7	of	of	ADP
ejpam-5038	215	8	the	the	DET
ejpam-5038	215	9	root	root	NOUN
ejpam-5038	215	10	node	node	PROPN
ejpam-5038	215	11	w	w	PROPN
ejpam-5038	215	12	(	(	PUNCT
ejpam-5038	215	13	refer	refer	VERB
ejpam-5038	215	14	figure	figure	NOUN
ejpam-5038	215	15	7(b	7(b	NOUN
ejpam-5038	215	16	)	)	PUNCT
ejpam-5038	215	17	)	)	PUNCT
ejpam-5038	215	18	of	of	ADP
ejpam-5038	215	19	st	st	PROPN
ejpam-5038	215	20	(	(	PUNCT
ejpam-5038	215	21	r	r	NOUN
ejpam-5038	215	22	)	)	PUNCT
ejpam-5038	215	23	do	do	AUX
ejpam-5038	215	24	not	not	PART
ejpam-5038	215	25	belong	belong	VERB
ejpam-5038	215	26	to	to	ADP
ejpam-5038	215	27	any	any	DET
ejpam-5038	215	28	d	d	ADJ
ejpam-5038	215	29	-	-	ADJ
ejpam-5038	215	30	twin	twin	ADJ
ejpam-5038	215	31	set	set	NOUN
ejpam-5038	215	32	include	include	VERB
ejpam-5038	215	33	u	u	NOUN
ejpam-5038	215	34	in	in	ADP
ejpam-5038	215	35	d	d	PROPN
ejpam-5038	215	36	and	and	CCONJ
ejpam-5038	215	37	x	x	X
ejpam-5038	215	38	in	in	ADP
ejpam-5038	215	39	d′.	d′.	NOUN
ejpam-5038	215	40	thus	thus	ADV
ejpam-5038	215	41	d	d	NOUN
ejpam-5038	215	42	and	and	CCONJ
ejpam-5038	215	43	d′	d′	PRON
ejpam-5038	215	44	are	be	AUX
ejpam-5038	215	45	dominating	dominate	VERB
ejpam-5038	215	46	sets	set	NOUN
ejpam-5038	215	47	of	of	ADP
ejpam-5038	215	48	the	the	DET
ejpam-5038	215	49	same	same	ADJ
ejpam-5038	215	50	cardinality	cardinality	NOUN
ejpam-5038	215	51	as	as	ADP
ejpam-5038	215	52	the	the	DET
ejpam-5038	215	53	one	one	NOUN
ejpam-5038	215	54	constructed	construct	VERB
ejpam-5038	215	55	in	in	ADP
ejpam-5038	215	56	theorem	theorem	NOUN
ejpam-5038	215	57	4	4	NUM
ejpam-5038	215	58	.	.	PUNCT
ejpam-5038	215	59	thus	thus	ADV
ejpam-5038	215	60	γ	γ	X
ejpam-5038	215	61	′	′	NUM
ejpam-5038	215	62	(	(	PUNCT
ejpam-5038	215	63	st	st	PROPN
ejpam-5038	215	64	(	(	PUNCT
ejpam-5038	215	65	r	r	NOUN
ejpam-5038	215	66	)	)	PUNCT
ejpam-5038	215	67	)	)	PUNCT
ejpam-5038	216	1	=	=	SYM
ejpam-5038	216	2	γ(st	γ(st	PROPN
ejpam-5038	216	3	(	(	PUNCT
ejpam-5038	216	4	r	r	NOUN
ejpam-5038	216	5	)	)	PUNCT
ejpam-5038	216	6	)	)	PUNCT
ejpam-5038	216	7	,	,	PUNCT
ejpam-5038	216	8	r	r	NOUN
ejpam-5038	216	9	≥	≥	NOUN
ejpam-5038	216	10	0	0	NUM
ejpam-5038	216	11	.	.	PUNCT
ejpam-5038	217	1	v.	v.	PROPN
ejpam-5038	217	2	shalini	shalini	PROPN
ejpam-5038	217	3	,	,	PUNCT
ejpam-5038	217	4	i.	i.	PROPN
ejpam-5038	217	5	rajasingh	rajasingh	PROPN
ejpam-5038	217	6	/	/	SYM
ejpam-5038	217	7	eur	eur	PROPN
ejpam-5038	217	8	.	.	PUNCT
ejpam-5038	218	1	j.	j.	PROPN
ejpam-5038	218	2	pure	pure	PROPN
ejpam-5038	218	3	appl	appl	PROPN
ejpam-5038	218	4	.	.	PROPN
ejpam-5038	218	5	math	math	PROPN
ejpam-5038	218	6	,	,	PUNCT
ejpam-5038	218	7	17	17	NUM
ejpam-5038	218	8	(	(	PUNCT
ejpam-5038	218	9	2	2	NUM
ejpam-5038	218	10	)	)	PUNCT
ejpam-5038	218	11	(	(	PUNCT
ejpam-5038	218	12	2024	2024	NUM
ejpam-5038	218	13	)	)	PUNCT
ejpam-5038	218	14	,	,	PUNCT
ejpam-5038	218	15	1082	1082	NUM
ejpam-5038	218	16	-	-	SYM
ejpam-5038	218	17	1093	1093	NUM
ejpam-5038	218	18	1090	1090	NUM
ejpam-5038	218	19	we	we	PRON
ejpam-5038	218	20	note	note	VERB
ejpam-5038	218	21	that	that	SCONJ
ejpam-5038	218	22	the	the	DET
ejpam-5038	218	23	dominating	dominating	NOUN
ejpam-5038	218	24	set	set	NOUN
ejpam-5038	218	25	of	of	ADP
ejpam-5038	218	26	st	st	PROPN
ejpam-5038	218	27	(	(	PUNCT
ejpam-5038	218	28	r	r	NOUN
ejpam-5038	218	29	)	)	PUNCT
ejpam-5038	218	30	constructed	construct	VERB
ejpam-5038	218	31	in	in	ADP
ejpam-5038	218	32	theorem	theorem	NOUN
ejpam-5038	218	33	4	4	NUM
ejpam-5038	218	34	is	be	AUX
ejpam-5038	218	35	an	an	DET
ejpam-5038	218	36	independent	independent	ADJ
ejpam-5038	218	37	dominating	dominating	NOUN
ejpam-5038	218	38	set	set	NOUN
ejpam-5038	218	39	.	.	PUNCT
ejpam-5038	219	1	thus	thus	ADV
ejpam-5038	219	2	we	we	PRON
ejpam-5038	219	3	have	have	VERB
ejpam-5038	219	4	the	the	DET
ejpam-5038	219	5	following	follow	VERB
ejpam-5038	219	6	result	result	NOUN
ejpam-5038	219	7	.	.	PUNCT
ejpam-5038	220	1	theorem	theorem	ADJ
ejpam-5038	220	2	6	6	NUM
ejpam-5038	220	3	.	.	PUNCT
ejpam-5038	221	1	let	let	VERB
ejpam-5038	221	2	g	g	NOUN
ejpam-5038	221	3	be	be	AUX
ejpam-5038	221	4	the	the	DET
ejpam-5038	221	5	sibling	sible	VERB
ejpam-5038	221	6	tree	tree	NOUN
ejpam-5038	221	7	st	st	PROPN
ejpam-5038	221	8	(	(	PUNCT
ejpam-5038	221	9	r	r	NOUN
ejpam-5038	221	10	)	)	PUNCT
ejpam-5038	221	11	of	of	ADP
ejpam-5038	221	12	dimension	dimension	NOUN
ejpam-5038	221	13	r	r	NOUN
ejpam-5038	221	14	≥	≥	NOUN
ejpam-5038	221	15	0	0	NUM
ejpam-5038	221	16	.	.	PUNCT
ejpam-5038	222	1	then	then	ADV
ejpam-5038	222	2	γ(st	γ(st	PROPN
ejpam-5038	222	3	(	(	PUNCT
ejpam-5038	222	4	r	r	NOUN
ejpam-5038	222	5	)	)	PUNCT
ejpam-5038	222	6	)	)	PUNCT
ejpam-5038	223	1	=	=	SYM
ejpam-5038	223	2	γ	γ	X
ejpam-5038	223	3	′	′	NUM
ejpam-5038	223	4	(	(	PUNCT
ejpam-5038	223	5	st	st	PROPN
ejpam-5038	223	6	(	(	PUNCT
ejpam-5038	223	7	r	r	NOUN
ejpam-5038	223	8	)	)	PUNCT
ejpam-5038	223	9	)	)	PUNCT
ejpam-5038	224	1	=	=	SYM
ejpam-5038	224	2	γi(st	γi(st	NOUN
ejpam-5038	224	3	(	(	PUNCT
ejpam-5038	224	4	r	r	NOUN
ejpam-5038	224	5	)	)	PUNCT
ejpam-5038	224	6	)	)	PUNCT
ejpam-5038	224	7	.	.	PUNCT
ejpam-5038	225	1	theorem	theorem	VERB
ejpam-5038	225	2	7	7	NUM
ejpam-5038	225	3	.	.	PUNCT
ejpam-5038	226	1	let	let	VERB
ejpam-5038	226	2	g	g	NOUN
ejpam-5038	226	3	be	be	AUX
ejpam-5038	226	4	the	the	DET
ejpam-5038	226	5	sibling	sible	VERB
ejpam-5038	226	6	tree	tree	NOUN
ejpam-5038	226	7	st	st	PROPN
ejpam-5038	226	8	(	(	PUNCT
ejpam-5038	226	9	r	r	NOUN
ejpam-5038	226	10	)	)	PUNCT
ejpam-5038	226	11	,	,	PUNCT
ejpam-5038	226	12	r	r	NOUN
ejpam-5038	226	13	≥	≥	NOUN
ejpam-5038	226	14	2	2	NUM
ejpam-5038	226	15	,	,	PUNCT
ejpam-5038	226	16	then	then	ADV
ejpam-5038	226	17	γc(g	γc(g	PUNCT
ejpam-5038	226	18	)	)	PUNCT
ejpam-5038	227	1	=	=	SYM
ejpam-5038	227	2	2r	2r	NUM
ejpam-5038	228	1	−	−	NOUN
ejpam-5038	229	1	2	2	X
ejpam-5038	229	2	.	.	PUNCT
ejpam-5038	229	3	proof	proof	NOUN
ejpam-5038	229	4	.	.	PUNCT
ejpam-5038	230	1	let	let	VERB
ejpam-5038	230	2	d	d	PRON
ejpam-5038	230	3	be	be	AUX
ejpam-5038	230	4	a	a	DET
ejpam-5038	230	5	connected	connect	VERB
ejpam-5038	230	6	dominating	dominating	NOUN
ejpam-5038	230	7	set	set	NOUN
ejpam-5038	230	8	of	of	ADP
ejpam-5038	230	9	st	st	PROPN
ejpam-5038	230	10	(	(	PUNCT
ejpam-5038	230	11	r	r	NOUN
ejpam-5038	230	12	)	)	PUNCT
ejpam-5038	230	13	,	,	PUNCT
ejpam-5038	230	14	r	r	NOUN
ejpam-5038	230	15	≥	≥	NOUN
ejpam-5038	230	16	2	2	NUM
ejpam-5038	230	17	.	.	PUNCT
ejpam-5038	231	1	let	let	VERB
ejpam-5038	231	2	v	v	PART
ejpam-5038	231	3	be	be	AUX
ejpam-5038	231	4	an	an	DET
ejpam-5038	231	5	arbitrary	arbitrary	ADJ
ejpam-5038	231	6	vertex	vertex	NOUN
ejpam-5038	231	7	of	of	ADP
ejpam-5038	231	8	st	st	PROPN
ejpam-5038	231	9	(	(	PUNCT
ejpam-5038	231	10	r	r	NOUN
ejpam-5038	231	11	)	)	PUNCT
ejpam-5038	231	12	in	in	ADP
ejpam-5038	231	13	level	level	NOUN
ejpam-5038	231	14	i	i	NOUN
ejpam-5038	231	15	,	,	PUNCT
ejpam-5038	231	16	1	1	NUM
ejpam-5038	231	17	≤	≤	NUM
ejpam-5038	231	18	i	i	NOUN
ejpam-5038	232	1	≤	≤	NOUN
ejpam-5038	232	2	r	r	NOUN
ejpam-5038	232	3	−	−	NOUN
ejpam-5038	232	4	1	1	NUM
ejpam-5038	232	5	.	.	PUNCT
ejpam-5038	233	1	then	then	ADV
ejpam-5038	233	2	v	v	NOUN
ejpam-5038	233	3	is	be	AUX
ejpam-5038	233	4	a	a	DET
ejpam-5038	233	5	cut	cut	ADJ
ejpam-5038	233	6	vertex	vertex	NOUN
ejpam-5038	233	7	of	of	ADP
ejpam-5038	233	8	st	st	PROPN
ejpam-5038	233	9	(	(	PUNCT
ejpam-5038	233	10	r	r	NOUN
ejpam-5038	233	11	)	)	PUNCT
ejpam-5038	233	12	.	.	PUNCT
ejpam-5038	234	1	let	let	VERB
ejpam-5038	234	2	gv	gv	INTJ
ejpam-5038	234	3	and	and	CCONJ
ejpam-5038	234	4	g′	g′	NOUN
ejpam-5038	234	5	v	v	NOUN
ejpam-5038	234	6	be	be	AUX
ejpam-5038	234	7	the	the	DET
ejpam-5038	234	8	components	component	NOUN
ejpam-5038	234	9	of	of	ADP
ejpam-5038	234	10	st	st	PROPN
ejpam-5038	234	11	(	(	PUNCT
ejpam-5038	234	12	r	r	NOUN
ejpam-5038	234	13	)	)	PUNCT
ejpam-5038	234	14	\	\	NOUN
ejpam-5038	234	15	{	{	PUNCT
ejpam-5038	234	16	v	v	NOUN
ejpam-5038	234	17	}	}	PUNCT
ejpam-5038	234	18	.	.	PUNCT
ejpam-5038	235	1	suppose	suppose	VERB
ejpam-5038	235	2	v	v	AUX
ejpam-5038	235	3	/∈	/∈	PUNCT
ejpam-5038	235	4	d.	d.	PROPN
ejpam-5038	235	5	let	let	VERB
ejpam-5038	235	6	d(gv	d(gv	ADJ
ejpam-5038	235	7	)	)	PUNCT
ejpam-5038	235	8	=	=	SYM
ejpam-5038	235	9	v	v	X
ejpam-5038	235	10	(	(	PUNCT
ejpam-5038	235	11	gv	gv	NOUN
ejpam-5038	235	12	)	)	PUNCT
ejpam-5038	235	13	∩	∩	ADJ
ejpam-5038	235	14	d	d	NOUN
ejpam-5038	235	15	and	and	CCONJ
ejpam-5038	235	16	d(g′	d(g′	PROPN
ejpam-5038	235	17	v	v	NOUN
ejpam-5038	235	18	)	)	PUNCT
ejpam-5038	235	19	=	=	SYM
ejpam-5038	235	20	v	v	X
ejpam-5038	235	21	(	(	PUNCT
ejpam-5038	235	22	g′	g′	NOUN
ejpam-5038	235	23	v)∩d	v)∩d	PROPN
ejpam-5038	235	24	.	.	PUNCT
ejpam-5038	236	1	thend	thend	VERB
ejpam-5038	236	2	=	=	PUNCT
ejpam-5038	236	3	d(gv)∪d(g′	d(gv)∪d(g′	NOUN
ejpam-5038	236	4	v	v	NOUN
ejpam-5038	236	5	)	)	PUNCT
ejpam-5038	236	6	.	.	PUNCT
ejpam-5038	237	1	choose	choose	VERB
ejpam-5038	237	2	x	x	PUNCT
ejpam-5038	237	3	∈	∈	PROPN
ejpam-5038	237	4	d(gv	d(gv	ADJ
ejpam-5038	237	5	)	)	PUNCT
ejpam-5038	237	6	and	and	CCONJ
ejpam-5038	237	7	y	y	PROPN
ejpam-5038	237	8	∈	∈	PROPN
ejpam-5038	237	9	d(g′	d(g′	PROPN
ejpam-5038	237	10	v	v	NOUN
ejpam-5038	237	11	)	)	PUNCT
ejpam-5038	237	12	.	.	PUNCT
ejpam-5038	238	1	since	since	SCONJ
ejpam-5038	238	2	d	d	PROPN
ejpam-5038	238	3	is	be	AUX
ejpam-5038	238	4	connected	connect	VERB
ejpam-5038	238	5	,	,	PUNCT
ejpam-5038	238	6	there	there	PRON
ejpam-5038	238	7	exists	exist	VERB
ejpam-5038	238	8	a	a	DET
ejpam-5038	238	9	path	path	NOUN
ejpam-5038	238	10	between	between	ADP
ejpam-5038	238	11	x	x	PROPN
ejpam-5038	238	12	and	and	CCONJ
ejpam-5038	238	13	y	y	PROPN
ejpam-5038	238	14	in	in	ADP
ejpam-5038	238	15	d.	d.	PROPN
ejpam-5038	238	16	this	this	DET
ejpam-5038	238	17	path	path	NOUN
ejpam-5038	238	18	has	have	VERB
ejpam-5038	238	19	to	to	PART
ejpam-5038	238	20	necessarily	necessarily	ADV
ejpam-5038	238	21	pass	pass	VERB
ejpam-5038	238	22	through	through	ADP
ejpam-5038	238	23	v.	v.	ADP
ejpam-5038	239	1	but	but	CCONJ
ejpam-5038	239	2	v	v	ADP
ejpam-5038	239	3	/∈	/∈	PUNCT
ejpam-5038	240	1	d	d	NOUN
ejpam-5038	240	2	and	and	CCONJ
ejpam-5038	240	3	hence	hence	ADV
ejpam-5038	240	4	there	there	PRON
ejpam-5038	240	5	is	be	VERB
ejpam-5038	240	6	no	no	DET
ejpam-5038	240	7	path	path	NOUN
ejpam-5038	240	8	between	between	ADP
ejpam-5038	240	9	x	x	PROPN
ejpam-5038	240	10	and	and	CCONJ
ejpam-5038	240	11	y	y	PROPN
ejpam-5038	240	12	in	in	ADP
ejpam-5038	240	13	d	d	PROPN
ejpam-5038	240	14	,	,	PUNCT
ejpam-5038	240	15	a	a	DET
ejpam-5038	240	16	contradiction	contradiction	NOUN
ejpam-5038	240	17	to	to	ADP
ejpam-5038	240	18	the	the	DET
ejpam-5038	240	19	connectedness	connectedness	NOUN
ejpam-5038	240	20	of	of	ADP
ejpam-5038	240	21	d.	d.	PROPN
ejpam-5038	240	22	this	this	PRON
ejpam-5038	240	23	implies	imply	VERB
ejpam-5038	240	24	v	v	ADP
ejpam-5038	240	25	∈	∈	PROPN
ejpam-5038	240	26	d.	d.	NOUN
ejpam-5038	240	27	thus	thus	ADV
ejpam-5038	240	28	any	any	DET
ejpam-5038	240	29	internal	internal	ADJ
ejpam-5038	240	30	vertex	vertex	NOUN
ejpam-5038	240	31	v	v	NOUN
ejpam-5038	240	32	in	in	ADP
ejpam-5038	240	33	level	level	NOUN
ejpam-5038	240	34	i	i	PRON
ejpam-5038	240	35	,	,	PUNCT
ejpam-5038	240	36	1	1	NUM
ejpam-5038	240	37	≤	≤	NUM
ejpam-5038	240	38	i	i	NOUN
ejpam-5038	241	1	≤	≤	NOUN
ejpam-5038	241	2	r	r	NOUN
ejpam-5038	241	3	−	−	NOUN
ejpam-5038	241	4	1	1	NUM
ejpam-5038	241	5	is	be	AUX
ejpam-5038	241	6	a	a	DET
ejpam-5038	241	7	member	member	NOUN
ejpam-5038	241	8	of	of	ADP
ejpam-5038	241	9	d.	d.	PROPN
ejpam-5038	241	10	obviously	obviously	ADV
ejpam-5038	241	11	,	,	PUNCT
ejpam-5038	241	12	these	these	DET
ejpam-5038	241	13	vertices	vertex	NOUN
ejpam-5038	241	14	also	also	ADV
ejpam-5038	241	15	dominate	dominate	VERB
ejpam-5038	241	16	g.	g.	NOUN
ejpam-5038	241	17	hence	hence	ADV
ejpam-5038	241	18	γc(g	γc(g	PUNCT
ejpam-5038	241	19	)	)	PUNCT
ejpam-5038	241	20	=	=	SYM
ejpam-5038	242	1	(	(	PUNCT
ejpam-5038	242	2	2r+1	2r+1	PROPN
ejpam-5038	242	3	−	−	PROPN
ejpam-5038	243	1	1)−	1)−	PROPN
ejpam-5038	243	2	1−	1−	NUM
ejpam-5038	243	3	2r	2r	NUM
ejpam-5038	243	4	=	=	SYM
ejpam-5038	243	5	2r	2r	NUM
ejpam-5038	243	6	−	−	NOUN
ejpam-5038	244	1	2	2	NUM
ejpam-5038	244	2	.	.	SYM
ejpam-5038	244	3	4	4	NUM
ejpam-5038	244	4	.	.	NOUN
ejpam-5038	244	5	inverse	inverse	ADJ
ejpam-5038	244	6	domination	domination	NOUN
ejpam-5038	244	7	in	in	ADP
ejpam-5038	244	8	hypertree	hypertree	PROPN
ejpam-5038	244	9	networks	network	NOUN
ejpam-5038	244	10	the	the	DET
ejpam-5038	244	11	fundamental	fundamental	ADJ
ejpam-5038	244	12	skeleton	skeleton	NOUN
ejpam-5038	244	13	of	of	ADP
ejpam-5038	244	14	a	a	DET
ejpam-5038	244	15	hypertree	hypertree	NOUN
ejpam-5038	244	16	is	be	AUX
ejpam-5038	244	17	a	a	DET
ejpam-5038	244	18	complete	complete	ADJ
ejpam-5038	244	19	binary	binary	ADJ
ejpam-5038	244	20	tree	tree	NOUN
ejpam-5038	244	21	tn	tn	PROPN
ejpam-5038	244	22	of	of	ADP
ejpam-5038	244	23	height	height	NOUN
ejpam-5038	244	24	n.	n.	PROPN
ejpam-5038	244	25	here	here	ADV
ejpam-5038	244	26	the	the	DET
ejpam-5038	244	27	nodes	node	NOUN
ejpam-5038	244	28	of	of	ADP
ejpam-5038	244	29	the	the	DET
ejpam-5038	244	30	tree	tree	NOUN
ejpam-5038	244	31	are	be	AUX
ejpam-5038	244	32	numbered	number	VERB
ejpam-5038	244	33	as	as	SCONJ
ejpam-5038	244	34	follows	follow	VERB
ejpam-5038	244	35	:	:	PUNCT
ejpam-5038	244	36	the	the	DET
ejpam-5038	244	37	root	root	NOUN
ejpam-5038	244	38	node	node	NOUN
ejpam-5038	244	39	has	have	AUX
ejpam-5038	244	40	label	label	NOUN
ejpam-5038	244	41	1	1	NUM
ejpam-5038	244	42	.	.	PUNCT
ejpam-5038	245	1	the	the	DET
ejpam-5038	245	2	root	root	NOUN
ejpam-5038	245	3	is	be	AUX
ejpam-5038	245	4	supposed	suppose	VERB
ejpam-5038	245	5	to	to	PART
ejpam-5038	245	6	be	be	AUX
ejpam-5038	245	7	at	at	ADP
ejpam-5038	245	8	level	level	NOUN
ejpam-5038	245	9	0	0	NUM
ejpam-5038	245	10	.	.	PUNCT
ejpam-5038	246	1	labels	label	NOUN
ejpam-5038	246	2	of	of	ADP
ejpam-5038	246	3	left	left	ADJ
ejpam-5038	246	4	and	and	CCONJ
ejpam-5038	246	5	right	right	ADJ
ejpam-5038	246	6	children	child	NOUN
ejpam-5038	246	7	are	be	AUX
ejpam-5038	246	8	formed	form	VERB
ejpam-5038	246	9	by	by	ADP
ejpam-5038	246	10	appending	append	VERB
ejpam-5038	246	11	0	0	NUM
ejpam-5038	246	12	and	and	CCONJ
ejpam-5038	246	13	1	1	NUM
ejpam-5038	246	14	,	,	PUNCT
ejpam-5038	246	15	respectively	respectively	ADV
ejpam-5038	246	16	to	to	ADP
ejpam-5038	246	17	the	the	DET
ejpam-5038	246	18	labels	label	NOUN
ejpam-5038	246	19	of	of	ADP
ejpam-5038	246	20	the	the	DET
ejpam-5038	246	21	parent	parent	NOUN
ejpam-5038	246	22	node	node	NOUN
ejpam-5038	246	23	.	.	PUNCT
ejpam-5038	247	1	the	the	DET
ejpam-5038	247	2	decimal	decimal	ADJ
ejpam-5038	247	3	and	and	CCONJ
ejpam-5038	247	4	binary	binary	ADJ
ejpam-5038	247	5	labels	label	NOUN
ejpam-5038	247	6	of	of	ADP
ejpam-5038	247	7	the	the	DET
ejpam-5038	247	8	hypertree	hypertree	NOUN
ejpam-5038	247	9	are	be	AUX
ejpam-5038	247	10	given	give	VERB
ejpam-5038	247	11	in	in	ADP
ejpam-5038	247	12	figure	figure	NOUN
ejpam-5038	247	13	8	8	NUM
ejpam-5038	247	14	.	.	PUNCT
ejpam-5038	248	1	here	here	ADV
ejpam-5038	248	2	the	the	DET
ejpam-5038	248	3	children	child	NOUN
ejpam-5038	248	4	of	of	ADP
ejpam-5038	248	5	the	the	DET
ejpam-5038	248	6	node	node	NOUN
ejpam-5038	248	7	x	x	PUNCT
ejpam-5038	248	8	are	be	AUX
ejpam-5038	248	9	labelled	label	VERB
ejpam-5038	248	10	as	as	ADP
ejpam-5038	248	11	2x	2x	NUM
ejpam-5038	248	12	and	and	CCONJ
ejpam-5038	248	13	2x+1	2x+1	NOUN
ejpam-5038	248	14	.	.	PUNCT
ejpam-5038	249	1	additional	additional	ADJ
ejpam-5038	249	2	links	link	NOUN
ejpam-5038	249	3	in	in	ADP
ejpam-5038	249	4	a	a	DET
ejpam-5038	249	5	hypertree	hypertree	NOUN
ejpam-5038	249	6	are	be	AUX
ejpam-5038	249	7	horizontal	horizontal	ADJ
ejpam-5038	249	8	and	and	CCONJ
ejpam-5038	249	9	two	two	NUM
ejpam-5038	249	10	nodes	node	NOUN
ejpam-5038	249	11	are	be	AUX
ejpam-5038	249	12	joined	join	VERB
ejpam-5038	249	13	in	in	ADP
ejpam-5038	249	14	the	the	DET
ejpam-5038	249	15	same	same	ADJ
ejpam-5038	249	16	level	level	NOUN
ejpam-5038	249	17	i	i	PRON
ejpam-5038	249	18	of	of	ADP
ejpam-5038	249	19	the	the	DET
ejpam-5038	249	20	tree	tree	NOUN
ejpam-5038	249	21	if	if	SCONJ
ejpam-5038	249	22	their	their	PRON
ejpam-5038	249	23	label	label	NOUN
ejpam-5038	249	24	difference	difference	NOUN
ejpam-5038	249	25	is	be	AUX
ejpam-5038	249	26	2i−1	2i−1	NUM
ejpam-5038	249	27	.	.	PUNCT
ejpam-5038	250	1	we	we	PRON
ejpam-5038	250	2	denote	denote	VERB
ejpam-5038	250	3	an	an	DET
ejpam-5038	250	4	n	n	NUM
ejpam-5038	250	5	-	-	PUNCT
ejpam-5038	250	6	level	level	NOUN
ejpam-5038	250	7	hypertree	hypertree	NOUN
ejpam-5038	250	8	as	as	ADP
ejpam-5038	250	9	ht	ht	PROPN
ejpam-5038	250	10	(	(	PUNCT
ejpam-5038	250	11	n	n	CCONJ
ejpam-5038	250	12	)	)	PUNCT
ejpam-5038	250	13	.	.	PUNCT
ejpam-5038	251	1	it	it	PRON
ejpam-5038	251	2	has	have	VERB
ejpam-5038	251	3	2n+1−	2n+1−	PROPN
ejpam-5038	251	4	1	1	NUM
ejpam-5038	251	5	vertices	vertex	NOUN
ejpam-5038	251	6	and	and	CCONJ
ejpam-5038	251	7	3(2n−	3(2n−	DET
ejpam-5038	251	8	1)edges	1)edge	NOUN
ejpam-5038	251	9	.	.	PUNCT
ejpam-5038	252	1	hypertree	hypertree	NOUN
ejpam-5038	252	2	is	be	AUX
ejpam-5038	252	3	a	a	DET
ejpam-5038	252	4	multiprocessor	multiprocessor	NOUN
ejpam-5038	252	5	interconnection	interconnection	NOUN
ejpam-5038	252	6	topology	topology	NOUN
ejpam-5038	252	7	which	which	PRON
ejpam-5038	252	8	has	have	VERB
ejpam-5038	252	9	a	a	DET
ejpam-5038	252	10	frequent	frequent	ADJ
ejpam-5038	252	11	data	datum	NOUN
ejpam-5038	252	12	exchange	exchange	NOUN
ejpam-5038	252	13	in	in	ADP
ejpam-5038	252	14	algorithms	algorithm	NOUN
ejpam-5038	252	15	such	such	ADJ
ejpam-5038	252	16	as	as	ADP
ejpam-5038	252	17	sorting	sort	VERB
ejpam-5038	252	18	and	and	CCONJ
ejpam-5038	252	19	fast	fast	ADJ
ejpam-5038	252	20	and	and	CCONJ
ejpam-5038	252	21	fourier	fourier	NOUN
ejpam-5038	252	22	transforms	transform	VERB
ejpam-5038	252	23	(	(	PUNCT
ejpam-5038	252	24	fft	fft	PROPN
ejpam-5038	252	25	’s	’s	PART
ejpam-5038	252	26	)	)	PUNCT
ejpam-5038	253	1	[	[	X
ejpam-5038	253	2	11	11	NUM
ejpam-5038	253	3	]	]	PUNCT
ejpam-5038	253	4	.	.	PUNCT
ejpam-5038	254	1	figure	figure	NOUN
ejpam-5038	254	2	8	8	NUM
ejpam-5038	254	3	:	:	PUNCT
ejpam-5038	254	4	ht	ht	PROPN
ejpam-5038	254	5	(	(	PUNCT
ejpam-5038	254	6	3	3	NUM
ejpam-5038	254	7	)	)	PUNCT
ejpam-5038	254	8	with	with	ADP
ejpam-5038	254	9	decimal	decimal	ADJ
ejpam-5038	254	10	and	and	CCONJ
ejpam-5038	254	11	binary	binary	ADJ
ejpam-5038	254	12	labels	label	NOUN
ejpam-5038	254	13	.	.	PUNCT
ejpam-5038	255	1	following	follow	VERB
ejpam-5038	255	2	the	the	DET
ejpam-5038	255	3	lines	line	NOUN
ejpam-5038	255	4	of	of	ADP
ejpam-5038	255	5	theorem	theorem	NOUN
ejpam-5038	255	6	4	4	NUM
ejpam-5038	255	7	,	,	PUNCT
ejpam-5038	255	8	we	we	PRON
ejpam-5038	255	9	have	have	AUX
ejpam-5038	255	10	obtained	obtain	VERB
ejpam-5038	255	11	γ′(ht	γ′(ht	NOUN
ejpam-5038	255	12	(	(	PUNCT
ejpam-5038	255	13	n	n	CCONJ
ejpam-5038	255	14	)	)	PUNCT
ejpam-5038	255	15	)	)	PUNCT
ejpam-5038	255	16	for	for	ADP
ejpam-5038	255	17	n	n	PRON
ejpam-5038	255	18	≡	≡	PROPN
ejpam-5038	255	19	0	0	NUM
ejpam-5038	255	20	,	,	PUNCT
ejpam-5038	255	21	1(mod	1(mod	NUM
ejpam-5038	255	22	3	3	NUM
ejpam-5038	255	23	)	)	PUNCT
ejpam-5038	255	24	.	.	PUNCT
ejpam-5038	256	1	an	an	DET
ejpam-5038	256	2	independent	independent	ADJ
ejpam-5038	256	3	proof	proof	NOUN
ejpam-5038	256	4	has	have	AUX
ejpam-5038	256	5	been	be	AUX
ejpam-5038	256	6	given	give	VERB
ejpam-5038	256	7	in	in	ADP
ejpam-5038	256	8	[	[	X
ejpam-5038	256	9	17	17	NUM
ejpam-5038	256	10	]	]	PUNCT
ejpam-5038	256	11	to	to	PART
ejpam-5038	256	12	obtain	obtain	VERB
ejpam-5038	256	13	γ(ht	γ(ht	NOUN
ejpam-5038	256	14	(	(	PUNCT
ejpam-5038	256	15	n	n	CCONJ
ejpam-5038	256	16	)	)	PUNCT
ejpam-5038	256	17	)	)	PUNCT
ejpam-5038	256	18	.	.	PUNCT
ejpam-5038	257	1	v.	v.	PROPN
ejpam-5038	257	2	shalini	shalini	PROPN
ejpam-5038	257	3	,	,	PUNCT
ejpam-5038	257	4	i.	i.	PROPN
ejpam-5038	257	5	rajasingh	rajasingh	PROPN
ejpam-5038	257	6	/	/	SYM
ejpam-5038	257	7	eur	eur	PROPN
ejpam-5038	257	8	.	.	PUNCT
ejpam-5038	258	1	j.	j.	PROPN
ejpam-5038	258	2	pure	pure	PROPN
ejpam-5038	258	3	appl	appl	PROPN
ejpam-5038	258	4	.	.	PROPN
ejpam-5038	258	5	math	math	PROPN
ejpam-5038	258	6	,	,	PUNCT
ejpam-5038	258	7	17	17	NUM
ejpam-5038	258	8	(	(	PUNCT
ejpam-5038	258	9	2	2	NUM
ejpam-5038	258	10	)	)	PUNCT
ejpam-5038	258	11	(	(	PUNCT
ejpam-5038	258	12	2024	2024	NUM
ejpam-5038	258	13	)	)	PUNCT
ejpam-5038	258	14	,	,	PUNCT
ejpam-5038	258	15	1082	1082	NUM
ejpam-5038	258	16	-	-	SYM
ejpam-5038	258	17	1093	1093	NUM
ejpam-5038	258	18	1091	1091	NUM
ejpam-5038	258	19	theorem	theorem	NOUN
ejpam-5038	258	20	8	8	NUM
ejpam-5038	258	21	.	.	PUNCT
ejpam-5038	259	1	let	let	VERB
ejpam-5038	259	2	g	g	NOUN
ejpam-5038	259	3	be	be	AUX
ejpam-5038	259	4	the	the	DET
ejpam-5038	259	5	hypertree	hypertree	NOUN
ejpam-5038	259	6	ht	ht	PROPN
ejpam-5038	259	7	(	(	PUNCT
ejpam-5038	259	8	r	r	NOUN
ejpam-5038	259	9	)	)	PUNCT
ejpam-5038	259	10	of	of	ADP
ejpam-5038	259	11	dimension	dimension	NOUN
ejpam-5038	259	12	r	r	NOUN
ejpam-5038	259	13	≥	≥	NOUN
ejpam-5038	259	14	0	0	NUM
ejpam-5038	259	15	.	.	PUNCT
ejpam-5038	260	1	then	then	ADV
ejpam-5038	260	2	γ′(ht	γ′(ht	NOUN
ejpam-5038	260	3	(	(	PUNCT
ejpam-5038	260	4	r	r	NOUN
ejpam-5038	260	5	)	)	PUNCT
ejpam-5038	260	6	)	)	PUNCT
ejpam-5038	261	1	=	=	PUNCT
ejpam-5038	261	2	γ(ht	γ(ht	NOUN
ejpam-5038	261	3	(	(	PUNCT
ejpam-5038	261	4	r	r	NOUN
ejpam-5038	261	5	)	)	PUNCT
ejpam-5038	261	6	)	)	PUNCT
ejpam-5038	262	1	=	=	PRON
ejpam-5038	262	2	{	{	PUNCT
ejpam-5038	262	3	1	1	NUM
ejpam-5038	262	4	7(2	7(2	NUM
ejpam-5038	262	5	r+2	r+2	NUM
ejpam-5038	262	6	+	+	NOUN
ejpam-5038	262	7	3	3	NUM
ejpam-5038	262	8	)	)	PUNCT
ejpam-5038	262	9	;	;	PUNCT
ejpam-5038	262	10	r	r	NOUN
ejpam-5038	262	11	≡	≡	PROPN
ejpam-5038	262	12	0	0	PUNCT
ejpam-5038	262	13	(	(	PUNCT
ejpam-5038	262	14	mod	mod	NOUN
ejpam-5038	262	15	3	3	NUM
ejpam-5038	262	16	)	)	PUNCT
ejpam-5038	262	17	1	1	NUM
ejpam-5038	262	18	7(2	7(2	NUM
ejpam-5038	262	19	r+2	r+2	NUM
ejpam-5038	262	20	−	−	PROPN
ejpam-5038	262	21	1	1	NUM
ejpam-5038	262	22	)	)	PUNCT
ejpam-5038	262	23	;	;	PUNCT
ejpam-5038	262	24	r	r	NOUN
ejpam-5038	262	25	≡	≡	PROPN
ejpam-5038	262	26	1	1	NUM
ejpam-5038	262	27	(	(	PUNCT
ejpam-5038	262	28	mod	mod	NOUN
ejpam-5038	262	29	3	3	NUM
ejpam-5038	262	30	)	)	PUNCT
ejpam-5038	262	31	conjecture	conjecture	NOUN
ejpam-5038	262	32	8.1	8.1	NUM
ejpam-5038	262	33	.	.	PUNCT
ejpam-5038	263	1	let	let	VERB
ejpam-5038	263	2	g	g	PRON
ejpam-5038	263	3	be	be	AUX
ejpam-5038	263	4	the	the	DET
ejpam-5038	263	5	hypertree	hypertree	NOUN
ejpam-5038	263	6	ht	ht	INTJ
ejpam-5038	263	7	(	(	PUNCT
ejpam-5038	263	8	r	r	NOUN
ejpam-5038	263	9	)	)	PUNCT
ejpam-5038	263	10	,	,	PUNCT
ejpam-5038	263	11	r	r	NOUN
ejpam-5038	263	12	≥	≥	NOUN
ejpam-5038	263	13	0	0	NUM
ejpam-5038	263	14	.	.	PUNCT
ejpam-5038	264	1	then	then	ADV
ejpam-5038	264	2	γ′(ht	γ′(ht	NOUN
ejpam-5038	264	3	(	(	PUNCT
ejpam-5038	264	4	r	r	NOUN
ejpam-5038	264	5	)	)	PUNCT
ejpam-5038	264	6	)	)	PUNCT
ejpam-5038	265	1	=	=	PUNCT
ejpam-5038	265	2	γ(ht	γ(ht	NOUN
ejpam-5038	265	3	(	(	PUNCT
ejpam-5038	265	4	r	r	NOUN
ejpam-5038	265	5	)	)	PUNCT
ejpam-5038	265	6	)	)	PUNCT
ejpam-5038	266	1	+	+	CCONJ
ejpam-5038	266	2	1	1	NUM
ejpam-5038	266	3	=	=	SYM
ejpam-5038	266	4	1	1	NUM
ejpam-5038	266	5	7(2	7(2	NUM
ejpam-5038	266	6	r+2	r+2	NUM
ejpam-5038	266	7	−	−	PROPN
ejpam-5038	266	8	2	2	NUM
ejpam-5038	266	9	)	)	PUNCT
ejpam-5038	266	10	+	+	NUM
ejpam-5038	266	11	1	1	NUM
ejpam-5038	266	12	,	,	PUNCT
ejpam-5038	266	13	for	for	ADP
ejpam-5038	266	14	r	r	NOUN
ejpam-5038	266	15	≡	≡	PROPN
ejpam-5038	266	16	2	2	NUM
ejpam-5038	266	17	(	(	PUNCT
ejpam-5038	266	18	mod	mod	NOUN
ejpam-5038	266	19	3	3	NUM
ejpam-5038	266	20	)	)	PUNCT
ejpam-5038	266	21	.	.	PUNCT
ejpam-5038	267	1	figure	figure	VERB
ejpam-5038	267	2	9	9	NUM
ejpam-5038	267	3	:	:	PUNCT
ejpam-5038	267	4	plotting	plot	VERB
ejpam-5038	267	5	of	of	ADP
ejpam-5038	267	6	domination	domination	NOUN
ejpam-5038	267	7	numbers	number	NOUN
ejpam-5038	267	8	.	.	PUNCT
ejpam-5038	268	1	5	5	X
ejpam-5038	268	2	.	.	X
ejpam-5038	268	3	conclusion	conclusion	NOUN
ejpam-5038	268	4	in	in	ADP
ejpam-5038	268	5	this	this	DET
ejpam-5038	268	6	paper	paper	NOUN
ejpam-5038	268	7	,	,	PUNCT
ejpam-5038	268	8	we	we	PRON
ejpam-5038	268	9	have	have	AUX
ejpam-5038	268	10	obtained	obtain	VERB
ejpam-5038	268	11	domination	domination	NOUN
ejpam-5038	268	12	,	,	PUNCT
ejpam-5038	268	13	inverse	inverse	ADJ
ejpam-5038	268	14	domination	domination	NOUN
ejpam-5038	268	15	and	and	CCONJ
ejpam-5038	268	16	independent	independent	ADJ
ejpam-5038	268	17	domination	domination	NOUN
ejpam-5038	268	18	numbers	number	NOUN
ejpam-5038	268	19	of	of	ADP
ejpam-5038	268	20	the	the	DET
ejpam-5038	268	21	x	x	ADJ
ejpam-5038	268	22	-	-	ADJ
ejpam-5038	268	23	tree	tree	ADJ
ejpam-5038	268	24	networks	network	NOUN
ejpam-5038	268	25	.	.	PUNCT
ejpam-5038	269	1	similarly	similarly	ADV
ejpam-5038	269	2	,	,	PUNCT
ejpam-5038	269	3	we	we	PRON
ejpam-5038	269	4	have	have	AUX
ejpam-5038	269	5	obtained	obtain	VERB
ejpam-5038	269	6	the	the	DET
ejpam-5038	269	7	domination	domination	NOUN
ejpam-5038	269	8	,	,	PUNCT
ejpam-5038	269	9	inverse	inverse	ADJ
ejpam-5038	269	10	domination	domination	NOUN
ejpam-5038	269	11	,	,	PUNCT
ejpam-5038	269	12	independent	independent	ADJ
ejpam-5038	269	13	domination	domination	NOUN
ejpam-5038	269	14	and	and	CCONJ
ejpam-5038	269	15	connected	connected	ADJ
ejpam-5038	269	16	domination	domination	NOUN
ejpam-5038	269	17	numbers	number	NOUN
ejpam-5038	269	18	of	of	ADP
ejpam-5038	269	19	sibling	sible	VERB
ejpam-5038	269	20	tree	tree	NOUN
ejpam-5038	269	21	networks	network	NOUN
ejpam-5038	269	22	.	.	PUNCT
ejpam-5038	270	1	we	we	PRON
ejpam-5038	270	2	have	have	AUX
ejpam-5038	270	3	also	also	ADV
ejpam-5038	270	4	obtained	obtain	VERB
ejpam-5038	270	5	the	the	DET
ejpam-5038	270	6	inverse	inverse	NOUN
ejpam-5038	270	7	domination	domination	NOUN
ejpam-5038	270	8	number	number	NOUN
ejpam-5038	270	9	of	of	ADP
ejpam-5038	270	10	a	a	DET
ejpam-5038	270	11	few	few	ADJ
ejpam-5038	270	12	classes	class	NOUN
ejpam-5038	270	13	of	of	ADP
ejpam-5038	270	14	hypertree	hypertree	NOUN
ejpam-5038	270	15	networks	network	NOUN
ejpam-5038	270	16	.	.	PUNCT
ejpam-5038	271	1	all	all	DET
ejpam-5038	271	2	its	its	PRON
ejpam-5038	271	3	tree	tree	NOUN
ejpam-5038	271	4	networks	network	NOUN
ejpam-5038	271	5	have	have	VERB
ejpam-5038	271	6	the	the	DET
ejpam-5038	271	7	same	same	ADJ
ejpam-5038	271	8	basic	basic	ADJ
ejpam-5038	271	9	structure	structure	NOUN
ejpam-5038	271	10	as	as	ADP
ejpam-5038	271	11	the	the	DET
ejpam-5038	271	12	complete	complete	ADJ
ejpam-5038	271	13	binary	binary	ADJ
ejpam-5038	271	14	tree	tree	NOUN
ejpam-5038	271	15	and	and	CCONJ
ejpam-5038	271	16	the	the	DET
ejpam-5038	271	17	number	number	NOUN
ejpam-5038	271	18	of	of	ADP
ejpam-5038	271	19	vertices	vertex	NOUN
ejpam-5038	271	20	in	in	ADP
ejpam-5038	271	21	x(k	x(k	NOUN
ejpam-5038	271	22	)	)	PUNCT
ejpam-5038	271	23	and	and	CCONJ
ejpam-5038	271	24	st	st	PROPN
ejpam-5038	271	25	(	(	PUNCT
ejpam-5038	271	26	k	k	NOUN
ejpam-5038	271	27	)	)	PUNCT
ejpam-5038	271	28	and	and	CCONJ
ejpam-5038	271	29	ht	ht	INTJ
ejpam-5038	271	30	(	(	PUNCT
ejpam-5038	271	31	k	k	NOUN
ejpam-5038	271	32	)	)	PUNCT
ejpam-5038	271	33	k	k	PROPN
ejpam-5038	271	34	≥	≥	NOUN
ejpam-5038	271	35	0	0	NUM
ejpam-5038	271	36	,	,	PUNCT
ejpam-5038	271	37	are	be	AUX
ejpam-5038	271	38	equal	equal	ADJ
ejpam-5038	271	39	.	.	PUNCT
ejpam-5038	272	1	hence	hence	ADV
ejpam-5038	272	2	,	,	PUNCT
ejpam-5038	272	3	it	it	PRON
ejpam-5038	272	4	is	be	AUX
ejpam-5038	272	5	worth	worth	ADJ
ejpam-5038	272	6	comparing	compare	VERB
ejpam-5038	272	7	the	the	DET
ejpam-5038	272	8	domination	domination	NOUN
ejpam-5038	272	9	numbers	number	NOUN
ejpam-5038	272	10	of	of	ADP
ejpam-5038	272	11	x(k	x(k	PROPN
ejpam-5038	272	12	)	)	PUNCT
ejpam-5038	272	13	and	and	CCONJ
ejpam-5038	272	14	st	st	PROPN
ejpam-5038	272	15	(	(	PUNCT
ejpam-5038	272	16	k	k	NOUN
ejpam-5038	272	17	)	)	PUNCT
ejpam-5038	272	18	of	of	ADP
ejpam-5038	272	19	the	the	DET
ejpam-5038	272	20	same	same	ADJ
ejpam-5038	272	21	dimension	dimension	NOUN
ejpam-5038	272	22	k.	k.	PROPN
ejpam-5038	273	1	see	see	VERB
ejpam-5038	273	2	figure	figure	NOUN
ejpam-5038	273	3	9	9	NUM
ejpam-5038	273	4	.	.	PUNCT
ejpam-5038	274	1	we	we	PRON
ejpam-5038	274	2	conclude	conclude	VERB
ejpam-5038	274	3	that	that	SCONJ
ejpam-5038	274	4	,	,	PUNCT
ejpam-5038	274	5	as	as	ADV
ejpam-5038	274	6	far	far	ADV
ejpam-5038	274	7	as	as	SCONJ
ejpam-5038	274	8	domination	domination	NOUN
ejpam-5038	274	9	parameter	parameter	NOUN
ejpam-5038	274	10	is	be	AUX
ejpam-5038	274	11	concerned	concern	VERB
ejpam-5038	274	12	,	,	PUNCT
ejpam-5038	274	13	x(k	x(k	PROPN
ejpam-5038	274	14	)	)	PUNCT
ejpam-5038	274	15	is	be	AUX
ejpam-5038	274	16	a	a	DET
ejpam-5038	274	17	better	well	ADJ
ejpam-5038	274	18	architecture	architecture	NOUN
ejpam-5038	274	19	than	than	ADP
ejpam-5038	274	20	st	st	PROPN
ejpam-5038	274	21	(	(	PUNCT
ejpam-5038	274	22	k	k	PROPN
ejpam-5038	274	23	)	)	PUNCT
ejpam-5038	274	24	,	,	PUNCT
ejpam-5038	274	25	k	k	PROPN
ejpam-5038	274	26	≥	≥	PROPN
ejpam-5038	274	27	0	0	NUM
ejpam-5038	274	28	.	.	PROPN
ejpam-5038	275	1	6	6	NUM
ejpam-5038	275	2	.	.	X
ejpam-5038	275	3	future	future	ADJ
ejpam-5038	275	4	work	work	NOUN
ejpam-5038	275	5	it	it	PRON
ejpam-5038	275	6	is	be	AUX
ejpam-5038	275	7	worth	worth	ADJ
ejpam-5038	275	8	studying	study	VERB
ejpam-5038	275	9	the	the	DET
ejpam-5038	275	10	domination	domination	NOUN
ejpam-5038	275	11	and	and	CCONJ
ejpam-5038	275	12	inverse	inverse	NOUN
ejpam-5038	275	13	domination	domination	NOUN
ejpam-5038	275	14	numbers	number	NOUN
ejpam-5038	275	15	of	of	ADP
ejpam-5038	275	16	architectures	architecture	NOUN
ejpam-5038	275	17	like	like	ADP
ejpam-5038	275	18	benes	bene	NOUN
ejpam-5038	275	19	networks	network	NOUN
ejpam-5038	275	20	and	and	CCONJ
ejpam-5038	275	21	hyper	hyper	ADJ
ejpam-5038	275	22	-	-	ADJ
ejpam-5038	275	23	butterfly	butterfly	NOUN
ejpam-5038	275	24	networks	network	NOUN
ejpam-5038	275	25	.	.	PUNCT
ejpam-5038	276	1	it	it	PRON
ejpam-5038	276	2	would	would	AUX
ejpam-5038	276	3	be	be	AUX
ejpam-5038	276	4	an	an	DET
ejpam-5038	276	5	interesting	interesting	ADJ
ejpam-5038	276	6	line	line	NOUN
ejpam-5038	276	7	of	of	ADP
ejpam-5038	276	8	research	research	NOUN
ejpam-5038	276	9	to	to	PART
ejpam-5038	276	10	explore	explore	VERB
ejpam-5038	276	11	domination	domination	NOUN
ejpam-5038	276	12	parameters	parameter	NOUN
ejpam-5038	276	13	in	in	ADP
ejpam-5038	276	14	tree	tree	NOUN
ejpam-5038	276	15	-	-	PUNCT
ejpam-5038	276	16	like	like	ADJ
ejpam-5038	276	17	architectures	architecture	NOUN
ejpam-5038	276	18	like	like	ADP
ejpam-5038	276	19	christmas	christmas	NOUN
ejpam-5038	276	20	trees	tree	NOUN
ejpam-5038	276	21	and	and	CCONJ
ejpam-5038	276	22	slim	slim	ADJ
ejpam-5038	276	23	trees	tree	NOUN
ejpam-5038	276	24	.	.	PUNCT
ejpam-5038	277	1	references	reference	NOUN
ejpam-5038	277	2	1092	1092	NUM
ejpam-5038	277	3	references	reference	NOUN
ejpam-5038	277	4	[	[	X
ejpam-5038	277	5	1	1	NUM
ejpam-5038	277	6	]	]	X
ejpam-5038	277	7	robert	robert	PROPN
ejpam-5038	277	8	glen	glen	PROPN
ejpam-5038	277	9	arnold	arnold	PROPN
ejpam-5038	277	10	and	and	CCONJ
ejpam-5038	277	11	ew	ew	PROPN
ejpam-5038	277	12	page	page	NOUN
ejpam-5038	277	13	.	.	PUNCT
ejpam-5038	278	1	a	a	DET
ejpam-5038	278	2	hierarchical	hierarchical	ADJ
ejpam-5038	278	3	,	,	PUNCT
ejpam-5038	278	4	restructurable	restructurable	ADJ
ejpam-5038	278	5	multimicroprocessor	multimicroprocessor	NOUN
ejpam-5038	278	6	architecture	architecture	NOUN
ejpam-5038	278	7	.	.	PUNCT
ejpam-5038	279	1	in	in	ADP
ejpam-5038	279	2	proceedings	proceeding	NOUN
ejpam-5038	279	3	of	of	ADP
ejpam-5038	279	4	the	the	DET
ejpam-5038	279	5	3rd	3rd	ADJ
ejpam-5038	279	6	annual	annual	ADJ
ejpam-5038	279	7	symposium	symposium	NOUN
ejpam-5038	279	8	on	on	ADP
ejpam-5038	279	9	computer	computer	NOUN
ejpam-5038	279	10	architecture	architecture	NOUN
ejpam-5038	279	11	,	,	PUNCT
ejpam-5038	279	12	pages	page	NOUN
ejpam-5038	279	13	40–45	40–45	NUM
ejpam-5038	279	14	,	,	PUNCT
ejpam-5038	279	15	1976	1976	NUM
ejpam-5038	279	16	.	.	PUNCT
ejpam-5038	280	1	[	[	X
ejpam-5038	280	2	2	2	NUM
ejpam-5038	280	3	]	]	PUNCT
ejpam-5038	280	4	t	t	PROPN
ejpam-5038	280	5	tamizh	tamizh	PROPN
ejpam-5038	280	6	chelvam	chelvam	PROPN
ejpam-5038	280	7	and	and	CCONJ
ejpam-5038	280	8	gs	gs	INTJ
ejpam-5038	280	9	grace	grace	NOUN
ejpam-5038	280	10	prema	prema	NOUN
ejpam-5038	280	11	.	.	PUNCT
ejpam-5038	281	1	equality	equality	NOUN
ejpam-5038	281	2	of	of	ADP
ejpam-5038	281	3	domination	domination	NOUN
ejpam-5038	281	4	and	and	CCONJ
ejpam-5038	281	5	inverse	inverse	NOUN
ejpam-5038	281	6	domination	domination	NOUN
ejpam-5038	281	7	numbers	number	NOUN
ejpam-5038	281	8	.	.	PUNCT
ejpam-5038	282	1	ars	ars	PROPN
ejpam-5038	282	2	combinatoria	combinatoria	PROPN
ejpam-5038	282	3	,	,	PUNCT
ejpam-5038	282	4	95:103–111	95:103–111	PROPN
ejpam-5038	282	5	,	,	PUNCT
ejpam-5038	282	6	2010	2010	NUM
ejpam-5038	282	7	.	.	PUNCT
ejpam-5038	283	1	[	[	X
ejpam-5038	283	2	3	3	X
ejpam-5038	283	3	]	]	SYM
ejpam-5038	283	4	v	v	ADP
ejpam-5038	283	5	cynthia	cynthia	NOUN
ejpam-5038	283	6	and	and	CCONJ
ejpam-5038	283	7	a	a	DET
ejpam-5038	283	8	kavitha	kavitha	PROPN
ejpam-5038	283	9	.	.	PUNCT
ejpam-5038	284	1	inverse	inverse	PROPN
ejpam-5038	284	2	domination	domination	NOUN
ejpam-5038	284	3	number	number	NOUN
ejpam-5038	284	4	of	of	ADP
ejpam-5038	284	5	circulant	circulant	ADJ
ejpam-5038	284	6	graph	graph	NOUN
ejpam-5038	284	7	g	g	PROPN
ejpam-5038	284	8	(	(	PUNCT
ejpam-5038	284	9	n;±{1	n;±{1	PROPN
ejpam-5038	284	10	,	,	PUNCT
ejpam-5038	284	11	2	2	NUM
ejpam-5038	284	12	,	,	PUNCT
ejpam-5038	284	13	3	3	NUM
ejpam-5038	284	14	}	}	PUNCT
ejpam-5038	284	15	)	)	PUNCT
ejpam-5038	284	16	.	.	PUNCT
ejpam-5038	285	1	advances	advance	NOUN
ejpam-5038	285	2	&	&	CCONJ
ejpam-5038	285	3	applications	application	NOUN
ejpam-5038	285	4	in	in	ADP
ejpam-5038	285	5	discrete	discrete	ADJ
ejpam-5038	285	6	mathematics	mathematic	NOUN
ejpam-5038	285	7	,	,	PUNCT
ejpam-5038	285	8	23(2	23(2	NOUN
ejpam-5038	285	9	)	)	PUNCT
ejpam-5038	285	10	,	,	PUNCT
ejpam-5038	285	11	2020	2020	NUM
ejpam-5038	285	12	.	.	PUNCT
ejpam-5038	286	1	[	[	X
ejpam-5038	286	2	4	4	NUM
ejpam-5038	286	3	]	]	X
ejpam-5038	286	4	bevan	bevan	PROPN
ejpam-5038	286	5	das	das	PROPN
ejpam-5038	286	6	and	and	CCONJ
ejpam-5038	286	7	vaduvur	vaduvur	PROPN
ejpam-5038	286	8	bharghavan	bharghavan	PROPN
ejpam-5038	286	9	.	.	PUNCT
ejpam-5038	287	1	routing	route	VERB
ejpam-5038	287	2	in	in	ADP
ejpam-5038	287	3	ad	ad	NOUN
ejpam-5038	287	4	-	-	PUNCT
ejpam-5038	287	5	hoc	hoc	ADJ
ejpam-5038	287	6	networks	network	NOUN
ejpam-5038	287	7	using	use	VERB
ejpam-5038	287	8	minimum	minimum	NOUN
ejpam-5038	287	9	connected	connect	VERB
ejpam-5038	287	10	dominating	dominating	NOUN
ejpam-5038	287	11	sets	set	NOUN
ejpam-5038	287	12	.	.	PUNCT
ejpam-5038	288	1	in	in	ADP
ejpam-5038	288	2	proceedings	proceeding	NOUN
ejpam-5038	288	3	of	of	ADP
ejpam-5038	288	4	icc’97	icc’97	PROPN
ejpam-5038	288	5	-	-	PUNCT
ejpam-5038	288	6	international	international	ADJ
ejpam-5038	288	7	conference	conference	NOUN
ejpam-5038	288	8	on	on	ADP
ejpam-5038	288	9	communications	communication	NOUN
ejpam-5038	288	10	,	,	PUNCT
ejpam-5038	288	11	volume	volume	NOUN
ejpam-5038	288	12	1	1	NUM
ejpam-5038	288	13	,	,	PUNCT
ejpam-5038	288	14	pages	page	NOUN
ejpam-5038	288	15	376–380	376–380	NUM
ejpam-5038	288	16	.	.	PUNCT
ejpam-5038	289	1	ieee	ieee	NOUN
ejpam-5038	289	2	,	,	PUNCT
ejpam-5038	289	3	1997	1997	NUM
ejpam-5038	289	4	.	.	PUNCT
ejpam-5038	290	1	[	[	X
ejpam-5038	290	2	5	5	X
ejpam-5038	290	3	]	]	X
ejpam-5038	290	4	alvin	alvin	PROPN
ejpam-5038	290	5	m	m	PROPN
ejpam-5038	290	6	despain	despain	PROPN
ejpam-5038	290	7	and	and	CCONJ
ejpam-5038	290	8	david	david	PROPN
ejpam-5038	290	9	a	a	DET
ejpam-5038	290	10	patterson	patterson	PROPN
ejpam-5038	290	11	.	.	PUNCT
ejpam-5038	291	1	x	x	X
ejpam-5038	291	2	-	-	PUNCT
ejpam-5038	291	3	tree	tree	NOUN
ejpam-5038	291	4	:	:	PUNCT
ejpam-5038	291	5	a	a	DET
ejpam-5038	291	6	tree	tree	NOUN
ejpam-5038	291	7	structured	structure	VERB
ejpam-5038	291	8	multi	multi	ADJ
ejpam-5038	291	9	-	-	ADJ
ejpam-5038	291	10	processor	processor	ADJ
ejpam-5038	291	11	computer	computer	NOUN
ejpam-5038	291	12	architecture	architecture	NOUN
ejpam-5038	291	13	.	.	PUNCT
ejpam-5038	292	1	in	in	ADP
ejpam-5038	292	2	proceedings	proceeding	NOUN
ejpam-5038	292	3	of	of	ADP
ejpam-5038	292	4	the	the	DET
ejpam-5038	292	5	5th	5th	ADJ
ejpam-5038	292	6	annual	annual	ADJ
ejpam-5038	292	7	symposium	symposium	NOUN
ejpam-5038	292	8	on	on	ADP
ejpam-5038	292	9	computer	computer	NOUN
ejpam-5038	292	10	architecture	architecture	NOUN
ejpam-5038	292	11	,	,	PUNCT
ejpam-5038	292	12	pages	page	NOUN
ejpam-5038	292	13	144–151	144–151	NUM
ejpam-5038	292	14	,	,	PUNCT
ejpam-5038	292	15	1978	1978	NUM
ejpam-5038	292	16	.	.	PUNCT
ejpam-5038	293	1	[	[	X
ejpam-5038	293	2	6	6	NUM
ejpam-5038	293	3	]	]	PUNCT
ejpam-5038	293	4	gayla	gayla	NOUN
ejpam-5038	293	5	s	s	NOUN
ejpam-5038	293	6	domke	domke	NOUN
ejpam-5038	293	7	,	,	PUNCT
ejpam-5038	293	8	jean	jean	PROPN
ejpam-5038	293	9	e	e	PROPN
ejpam-5038	293	10	dunbar	dunbar	PROPN
ejpam-5038	293	11	,	,	PUNCT
ejpam-5038	293	12	and	and	CCONJ
ejpam-5038	293	13	lisa	lisa	PROPN
ejpam-5038	293	14	r	r	NOUN
ejpam-5038	293	15	markus	marku	NOUN
ejpam-5038	293	16	.	.	PUNCT
ejpam-5038	294	1	the	the	DET
ejpam-5038	294	2	inverse	inverse	ADJ
ejpam-5038	294	3	domination	domination	NOUN
ejpam-5038	294	4	number	number	NOUN
ejpam-5038	294	5	of	of	ADP
ejpam-5038	294	6	a	a	DET
ejpam-5038	294	7	graph	graph	NOUN
ejpam-5038	294	8	.	.	PUNCT
ejpam-5038	295	1	ars	ars	PROPN
ejpam-5038	295	2	combinatoria	combinatoria	PROPN
ejpam-5038	295	3	,	,	PUNCT
ejpam-5038	295	4	72:149–160	72:149–160	PROPN
ejpam-5038	295	5	,	,	PUNCT
ejpam-5038	295	6	2004	2004	NUM
ejpam-5038	295	7	.	.	PUNCT
ejpam-5038	296	1	[	[	X
ejpam-5038	296	2	7	7	X
ejpam-5038	296	3	]	]	X
ejpam-5038	296	4	philip	philip	PROPN
ejpam-5038	296	5	enslow	enslow	PROPN
ejpam-5038	296	6	.	.	PUNCT
ejpam-5038	297	1	multiprocessor	multiprocessor	NOUN
ejpam-5038	297	2	organization	organization	NOUN
ejpam-5038	297	3	—	—	PUNCT
ejpam-5038	297	4	a	a	DET
ejpam-5038	297	5	survey	survey	NOUN
ejpam-5038	297	6	.	.	PUNCT
ejpam-5038	298	1	acm	acm	PROPN
ejpam-5038	298	2	comput	comput	NOUN
ejpam-5038	298	3	.	.	PUNCT
ejpam-5038	299	1	surv	surv	PROPN
ejpam-5038	299	2	.	.	PUNCT
ejpam-5038	299	3	,	,	PUNCT
ejpam-5038	300	1	9(1):103–129	9(1):103–129	NUM
ejpam-5038	300	2	,	,	PUNCT
ejpam-5038	300	3	mar	mar	PROPN
ejpam-5038	300	4	1977	1977	NUM
ejpam-5038	300	5	.	.	PUNCT
ejpam-5038	301	1	[	[	X
ejpam-5038	301	2	8	8	NUM
ejpam-5038	301	3	]	]	PUNCT
ejpam-5038	301	4	allan	allan	PROPN
ejpam-5038	301	5	frendrup	frendrup	PROPN
ejpam-5038	301	6	,	,	PUNCT
ejpam-5038	301	7	michael	michael	PROPN
ejpam-5038	301	8	a	a	DET
ejpam-5038	301	9	henning	henning	PROPN
ejpam-5038	301	10	,	,	PUNCT
ejpam-5038	301	11	bert	bert	PROPN
ejpam-5038	301	12	randerath	randerath	PROPN
ejpam-5038	301	13	,	,	PUNCT
ejpam-5038	301	14	and	and	CCONJ
ejpam-5038	301	15	preben	preben	PROPN
ejpam-5038	301	16	d	d	AUX
ejpam-5038	301	17	vestergaard	vestergaard	PROPN
ejpam-5038	301	18	.	.	PUNCT
ejpam-5038	302	1	on	on	ADP
ejpam-5038	302	2	a	a	DET
ejpam-5038	302	3	conjecture	conjecture	NOUN
ejpam-5038	302	4	about	about	ADP
ejpam-5038	302	5	inverse	inverse	NOUN
ejpam-5038	302	6	domination	domination	NOUN
ejpam-5038	302	7	in	in	ADP
ejpam-5038	302	8	graphs	graph	NOUN
ejpam-5038	302	9	.	.	PUNCT
ejpam-5038	303	1	2009	2009	NUM
ejpam-5038	303	2	.	.	PUNCT
ejpam-5038	304	1	[	[	X
ejpam-5038	304	2	9	9	NUM
ejpam-5038	304	3	]	]	X
ejpam-5038	304	4	samuel	samuel	PROPN
ejpam-5038	304	5	h	h	PROPN
ejpam-5038	304	6	fuller	full	ADJ
ejpam-5038	304	7	,	,	PUNCT
ejpam-5038	304	8	john	john	PROPN
ejpam-5038	304	9	k	k	PROPN
ejpam-5038	304	10	ousterhout	ousterhout	PROPN
ejpam-5038	304	11	,	,	PUNCT
ejpam-5038	304	12	levy	levy	VERB
ejpam-5038	304	13	raskin	raskin	NOUN
ejpam-5038	304	14	,	,	PUNCT
ejpam-5038	304	15	paul	paul	PROPN
ejpam-5038	304	16	i	i	PRON
ejpam-5038	304	17	rubinfeld	rubinfeld	VERB
ejpam-5038	304	18	,	,	PUNCT
ejpam-5038	304	19	pj	pj	PROPN
ejpam-5038	304	20	sindhu	sindhu	PROPN
ejpam-5038	304	21	,	,	PUNCT
ejpam-5038	304	22	and	and	CCONJ
ejpam-5038	304	23	richard	richard	PROPN
ejpam-5038	304	24	j	j	PROPN
ejpam-5038	304	25	swan	swan	PROPN
ejpam-5038	304	26	.	.	PUNCT
ejpam-5038	305	1	multi	multi	ADJ
ejpam-5038	305	2	-	-	NOUN
ejpam-5038	305	3	microprocessors	microprocessor	NOUN
ejpam-5038	305	4	:	:	PUNCT
ejpam-5038	305	5	an	an	DET
ejpam-5038	305	6	overview	overview	NOUN
ejpam-5038	305	7	and	and	CCONJ
ejpam-5038	305	8	working	work	VERB
ejpam-5038	305	9	example	example	NOUN
ejpam-5038	305	10	.	.	PUNCT
ejpam-5038	306	1	proceedings	proceeding	NOUN
ejpam-5038	306	2	of	of	ADP
ejpam-5038	306	3	the	the	DET
ejpam-5038	306	4	ieee	ieee	NOUN
ejpam-5038	306	5	,	,	PUNCT
ejpam-5038	306	6	66(2):216–228	66(2):216–228	PROPN
ejpam-5038	306	7	,	,	PUNCT
ejpam-5038	306	8	1978	1978	NUM
ejpam-5038	306	9	.	.	PUNCT
ejpam-5038	307	1	[	[	X
ejpam-5038	307	2	10	10	NUM
ejpam-5038	307	3	]	]	PUNCT
ejpam-5038	307	4	m.	m.	PROPN
ejpam-5038	307	5	r.	r.	PROPN
ejpam-5038	307	6	garey	garey	PROPN
ejpam-5038	307	7	and	and	CCONJ
ejpam-5038	307	8	david	david	PROPN
ejpam-5038	307	9	s.	s.	PROPN
ejpam-5038	307	10	johnson	johnson	PROPN
ejpam-5038	307	11	.	.	PUNCT
ejpam-5038	308	1	computers	computer	NOUN
ejpam-5038	308	2	and	and	CCONJ
ejpam-5038	308	3	intractability	intractability	NOUN
ejpam-5038	308	4	:	:	PUNCT
ejpam-5038	308	5	a	a	DET
ejpam-5038	308	6	guide	guide	NOUN
ejpam-5038	308	7	to	to	ADP
ejpam-5038	308	8	the	the	DET
ejpam-5038	308	9	theory	theory	NOUN
ejpam-5038	308	10	of	of	ADP
ejpam-5038	308	11	np	np	NOUN
ejpam-5038	308	12	-	-	NOUN
ejpam-5038	308	13	completeness	completeness	NOUN
ejpam-5038	308	14	.	.	PUNCT
ejpam-5038	309	1	1978	1978	NUM
ejpam-5038	309	2	.	.	PUNCT
ejpam-5038	310	1	[	[	X
ejpam-5038	310	2	11	11	NUM
ejpam-5038	310	3	]	]	X
ejpam-5038	310	4	james	james	PROPN
ejpam-5038	310	5	r.	r.	PROPN
ejpam-5038	310	6	goodman	goodman	PROPN
ejpam-5038	310	7	and	and	CCONJ
ejpam-5038	310	8	carlo	carlo	PROPN
ejpam-5038	310	9	h.	h.	PROPN
ejpam-5038	310	10	séquin	séquin	PROPN
ejpam-5038	310	11	.	.	PUNCT
ejpam-5038	310	12	hypertree	hypertree	PROPN
ejpam-5038	310	13	:	:	PUNCT
ejpam-5038	310	14	a	a	DET
ejpam-5038	310	15	multiprocessor	multiprocessor	NOUN
ejpam-5038	310	16	interconnection	interconnection	NOUN
ejpam-5038	310	17	topology	topology	NOUN
ejpam-5038	310	18	.	.	PUNCT
ejpam-5038	311	1	ieee	ieee	NOUN
ejpam-5038	311	2	transactions	transaction	NOUN
ejpam-5038	311	3	on	on	ADP
ejpam-5038	311	4	computers	computer	NOUN
ejpam-5038	311	5	,	,	PUNCT
ejpam-5038	311	6	c-30:923–933	c-30:923–933	NOUN
ejpam-5038	311	7	,	,	PUNCT
ejpam-5038	311	8	1981	1981	NUM
ejpam-5038	311	9	.	.	PUNCT
ejpam-5038	312	1	[	[	X
ejpam-5038	312	2	12	12	NUM
ejpam-5038	312	3	]	]	X
ejpam-5038	312	4	wolfgang	wolfgang	PROPN
ejpam-5038	312	5	händler	händler	PROPN
ejpam-5038	312	6	,	,	PUNCT
ejpam-5038	312	7	fridolin	fridolin	PROPN
ejpam-5038	312	8	hofmann	hofmann	PROPN
ejpam-5038	312	9	,	,	PUNCT
ejpam-5038	312	10	and	and	CCONJ
ejpam-5038	312	11	hans	hans	PROPN
ejpam-5038	312	12	jorgen	jorgen	PROPN
ejpam-5038	312	13	schneider	schneider	PROPN
ejpam-5038	312	14	.	.	PUNCT
ejpam-5038	313	1	a	a	DET
ejpam-5038	313	2	general	general	ADJ
ejpam-5038	313	3	purpose	purpose	NOUN
ejpam-5038	313	4	array	array	NOUN
ejpam-5038	313	5	with	with	ADP
ejpam-5038	313	6	a	a	DET
ejpam-5038	313	7	broad	broad	ADJ
ejpam-5038	313	8	spectrum	spectrum	NOUN
ejpam-5038	313	9	of	of	ADP
ejpam-5038	313	10	applications	application	NOUN
ejpam-5038	313	11	.	.	PUNCT
ejpam-5038	314	1	in	in	ADP
ejpam-5038	314	2	computer	computer	NOUN
ejpam-5038	314	3	architecture	architecture	NOUN
ejpam-5038	314	4	:	:	PUNCT
ejpam-5038	314	5	workshop	workshop	NOUN
ejpam-5038	314	6	of	of	ADP
ejpam-5038	314	7	the	the	DET
ejpam-5038	314	8	gesellschaft	gesellschaft	NOUN
ejpam-5038	314	9	für	für	NOUN
ejpam-5038	314	10	informatik	informatik	PROPN
ejpam-5038	314	11	erlangen	erlangen	PROPN
ejpam-5038	314	12	,	,	PUNCT
ejpam-5038	314	13	may	may	PROPN
ejpam-5038	314	14	22–23	22–23	NUM
ejpam-5038	314	15	,	,	PUNCT
ejpam-5038	314	16	1975	1975	NUM
ejpam-5038	314	17	,	,	PUNCT
ejpam-5038	314	18	pages	page	NOUN
ejpam-5038	314	19	311–335	311–335	NUM
ejpam-5038	314	20	.	.	PUNCT
ejpam-5038	314	21	springer	springer	NOUN
ejpam-5038	314	22	,	,	PUNCT
ejpam-5038	314	23	1976	1976	NUM
ejpam-5038	314	24	.	.	PUNCT
ejpam-5038	315	1	[	[	X
ejpam-5038	315	2	13	13	NUM
ejpam-5038	315	3	]	]	X
ejpam-5038	315	4	teresa	teresa	PROPN
ejpam-5038	315	5	w.	w.	PROPN
ejpam-5038	315	6	haynes	haynes	PROPN
ejpam-5038	315	7	,	,	PUNCT
ejpam-5038	315	8	stephen	stephen	PROPN
ejpam-5038	315	9	t.	t.	PROPN
ejpam-5038	315	10	hedetniemi	hedetniemi	PROPN
ejpam-5038	315	11	,	,	PUNCT
ejpam-5038	315	12	and	and	CCONJ
ejpam-5038	315	13	peter	peter	PROPN
ejpam-5038	315	14	j.	j.	PROPN
ejpam-5038	315	15	slater	slater	PROPN
ejpam-5038	315	16	.	.	PUNCT
ejpam-5038	316	1	fundamentals	fundamental	NOUN
ejpam-5038	316	2	of	of	ADP
ejpam-5038	316	3	domination	domination	NOUN
ejpam-5038	316	4	in	in	ADP
ejpam-5038	316	5	graphs	graph	NOUN
ejpam-5038	316	6	.	.	PUNCT
ejpam-5038	317	1	pure	pure	ADJ
ejpam-5038	317	2	and	and	CCONJ
ejpam-5038	317	3	applied	applied	ADJ
ejpam-5038	317	4	mathematics	mathematic	NOUN
ejpam-5038	317	5	,	,	PUNCT
ejpam-5038	317	6	1998	1998	NUM
ejpam-5038	317	7	.	.	PUNCT
ejpam-5038	318	1	references	reference	NOUN
ejpam-5038	318	2	1093	1093	NUM
ejpam-5038	319	1	[	[	X
ejpam-5038	319	2	14	14	NUM
ejpam-5038	319	3	]	]	X
ejpam-5038	319	4	v.	v.	CCONJ
ejpam-5038	319	5	kulli	kulli	PROPN
ejpam-5038	319	6	and	and	CCONJ
ejpam-5038	319	7	s.c	s.c	PROPN
ejpam-5038	319	8	.	.	PROPN
ejpam-5038	319	9	sigarkanti	sigarkanti	PROPN
ejpam-5038	319	10	.	.	PROPN
ejpam-5038	319	11	inverse	inverse	ADJ
ejpam-5038	319	12	domination	domination	NOUN
ejpam-5038	319	13	in	in	ADP
ejpam-5038	319	14	graphs	graph	NOUN
ejpam-5038	319	15	.	.	PUNCT
ejpam-5038	320	1	national	national	PROPN
ejpam-5038	320	2	academy	academy	PROPN
ejpam-5038	320	3	science	science	PROPN
ejpam-5038	320	4	letters	letter	NOUN
ejpam-5038	320	5	,	,	PUNCT
ejpam-5038	320	6	14	14	NUM
ejpam-5038	320	7	,	,	PUNCT
ejpam-5038	320	8	01	01	NUM
ejpam-5038	320	9	1991	1991	NUM
ejpam-5038	320	10	.	.	PUNCT
ejpam-5038	321	1	[	[	X
ejpam-5038	321	2	15	15	NUM
ejpam-5038	321	3	]	]	X
ejpam-5038	321	4	deying	deye	VERB
ejpam-5038	321	5	li	li	PROPN
ejpam-5038	321	6	,	,	PUNCT
ejpam-5038	321	7	hongwei	hongwei	PROPN
ejpam-5038	321	8	du	du	PROPN
ejpam-5038	321	9	,	,	PUNCT
ejpam-5038	321	10	peng	peng	PROPN
ejpam-5038	321	11	-	-	PUNCT
ejpam-5038	321	12	jun	jun	PROPN
ejpam-5038	321	13	wan	wan	PROPN
ejpam-5038	321	14	,	,	PUNCT
ejpam-5038	321	15	xiaofeng	xiaofeng	PROPN
ejpam-5038	321	16	gao	gao	PROPN
ejpam-5038	321	17	,	,	PUNCT
ejpam-5038	321	18	zhao	zhao	PROPN
ejpam-5038	321	19	zhang	zhang	PROPN
ejpam-5038	321	20	,	,	PUNCT
ejpam-5038	321	21	and	and	CCONJ
ejpam-5038	321	22	weili	weili	PROPN
ejpam-5038	321	23	wu	wu	PROPN
ejpam-5038	321	24	.	.	PUNCT
ejpam-5038	322	1	construction	construction	NOUN
ejpam-5038	322	2	of	of	ADP
ejpam-5038	322	3	strongly	strongly	ADV
ejpam-5038	322	4	connected	connect	VERB
ejpam-5038	322	5	dominating	dominating	NOUN
ejpam-5038	322	6	sets	set	NOUN
ejpam-5038	322	7	in	in	ADP
ejpam-5038	322	8	asymmetric	asymmetric	ADJ
ejpam-5038	322	9	multihop	multihop	NOUN
ejpam-5038	322	10	wireless	wireless	NOUN
ejpam-5038	322	11	networks	network	NOUN
ejpam-5038	322	12	.	.	PUNCT
ejpam-5038	323	1	theoretical	theoretical	ADJ
ejpam-5038	323	2	computer	computer	NOUN
ejpam-5038	323	3	science	science	NOUN
ejpam-5038	323	4	,	,	PUNCT
ejpam-5038	323	5	410(8	410(8	NUM
ejpam-5038	323	6	-	-	SYM
ejpam-5038	323	7	10):661–669	10):661–669	NUM
ejpam-5038	323	8	,	,	PUNCT
ejpam-5038	323	9	2009	2009	NUM
ejpam-5038	323	10	.	.	PUNCT
ejpam-5038	324	1	[	[	X
ejpam-5038	324	2	16	16	NUM
ejpam-5038	324	3	]	]	X
ejpam-5038	324	4	arthur	arthur	PROPN
ejpam-5038	324	5	l	l	PROPN
ejpam-5038	324	6	liestman	liestman	PROPN
ejpam-5038	324	7	and	and	CCONJ
ejpam-5038	324	8	thomas	thomas	PROPN
ejpam-5038	324	9	c	c	PROPN
ejpam-5038	324	10	shermer	shermer	PROPN
ejpam-5038	324	11	.	.	PUNCT
ejpam-5038	324	12	degree	degree	NOUN
ejpam-5038	324	13	-	-	PUNCT
ejpam-5038	324	14	constrained	constrain	VERB
ejpam-5038	324	15	network	network	NOUN
ejpam-5038	324	16	spanners	spanner	NOUN
ejpam-5038	324	17	with	with	ADP
ejpam-5038	324	18	nonconstant	nonconstant	ADJ
ejpam-5038	324	19	delay	delay	NOUN
ejpam-5038	324	20	.	.	PUNCT
ejpam-5038	325	1	siam	siam	PROPN
ejpam-5038	325	2	journal	journal	PROPN
ejpam-5038	325	3	on	on	ADP
ejpam-5038	325	4	discrete	discrete	ADJ
ejpam-5038	325	5	mathematics	mathematic	NOUN
ejpam-5038	325	6	,	,	PUNCT
ejpam-5038	325	7	8(2):291–321	8(2):291–321	NUM
ejpam-5038	325	8	,	,	PUNCT
ejpam-5038	325	9	1995	1995	NUM
ejpam-5038	325	10	.	.	PUNCT
ejpam-5038	326	1	[	[	X
ejpam-5038	326	2	17	17	NUM
ejpam-5038	326	3	]	]	X
ejpam-5038	326	4	indra	indra	PROPN
ejpam-5038	326	5	rajasingh	rajasingh	PROPN
ejpam-5038	326	6	,	,	PUNCT
ejpam-5038	326	7	r	r	NOUN
ejpam-5038	326	8	jayagopal	jayagopal	ADJ
ejpam-5038	326	9	,	,	PUNCT
ejpam-5038	326	10	and	and	CCONJ
ejpam-5038	326	11	r	r	PROPN
ejpam-5038	326	12	sundara	sundara	PROPN
ejpam-5038	326	13	rajan	rajan	PROPN
ejpam-5038	326	14	.	.	PUNCT
ejpam-5038	327	1	domination	domination	NOUN
ejpam-5038	327	2	parameters	parameter	NOUN
ejpam-5038	327	3	in	in	ADP
ejpam-5038	327	4	hypertrees	hypertree	NOUN
ejpam-5038	327	5	and	and	CCONJ
ejpam-5038	327	6	sibling	sible	VERB
ejpam-5038	327	7	trees	tree	NOUN
ejpam-5038	327	8	.	.	PUNCT
ejpam-5038	328	1	discrete	discrete	ADJ
ejpam-5038	328	2	applied	apply	VERB
ejpam-5038	328	3	mathematics	mathematic	NOUN
ejpam-5038	328	4	,	,	PUNCT
ejpam-5038	328	5	280:237–245	280:237–245	NUM
ejpam-5038	328	6	,	,	PUNCT
ejpam-5038	328	7	2020	2020	NUM
ejpam-5038	328	8	.	.	PUNCT
ejpam-5038	329	1	[	[	X
ejpam-5038	329	2	18	18	NUM
ejpam-5038	329	3	]	]	X
ejpam-5038	329	4	e	e	X
ejpam-5038	329	5	sampathkumar	sampathkumar	PROPN
ejpam-5038	329	6	and	and	CCONJ
ejpam-5038	329	7	hb	hb	NOUN
ejpam-5038	329	8	walikar	walikar	NOUN
ejpam-5038	329	9	.	.	PUNCT
ejpam-5038	330	1	the	the	DET
ejpam-5038	330	2	connected	connected	ADJ
ejpam-5038	330	3	domination	domination	NOUN
ejpam-5038	330	4	number	number	NOUN
ejpam-5038	330	5	of	of	ADP
ejpam-5038	330	6	a	a	DET
ejpam-5038	330	7	graph	graph	NOUN
ejpam-5038	330	8	.	.	PUNCT
ejpam-5038	331	1	j.	j.	PROPN
ejpam-5038	331	2	math	math	PROPN
ejpam-5038	331	3	.	.	PUNCT
ejpam-5038	332	1	phys	phy	NOUN
ejpam-5038	332	2	,	,	PUNCT
ejpam-5038	332	3	1979	1979	NUM
ejpam-5038	332	4	.	.	PUNCT
ejpam-5038	333	1	[	[	X
ejpam-5038	333	2	19	19	NUM
ejpam-5038	333	3	]	]	SYM
ejpam-5038	333	4	v	v	X
ejpam-5038	333	5	shalini	shalini	PROPN
ejpam-5038	333	6	and	and	CCONJ
ejpam-5038	333	7	indra	indra	PROPN
ejpam-5038	333	8	rajasingh	rajasingh	PROPN
ejpam-5038	333	9	.	.	PUNCT
ejpam-5038	334	1	domination	domination	NOUN
ejpam-5038	334	2	and	and	CCONJ
ejpam-5038	334	3	inverse	inverse	NOUN
ejpam-5038	334	4	domination	domination	NOUN
ejpam-5038	334	5	in	in	ADP
ejpam-5038	334	6	wrapped	wrap	VERB
ejpam-5038	334	7	butterfly	butterfly	NOUN
ejpam-5038	334	8	networks	network	NOUN
ejpam-5038	334	9	.	.	PUNCT
ejpam-5038	335	1	computer	computer	NOUN
ejpam-5038	335	2	science	science	NOUN
ejpam-5038	335	3	,	,	PUNCT
ejpam-5038	335	4	15(4):1055–1063	15(4):1055–1063	NUM
ejpam-5038	335	5	,	,	PUNCT
ejpam-5038	335	6	2020	2020	NUM
ejpam-5038	335	7	.	.	PUNCT
ejpam-5038	336	1	[	[	X
ejpam-5038	336	2	20	20	NUM
ejpam-5038	336	3	]	]	SYM
ejpam-5038	336	4	v	v	X
ejpam-5038	336	5	shalini	shalini	PROPN
ejpam-5038	336	6	and	and	CCONJ
ejpam-5038	336	7	indra	indra	PROPN
ejpam-5038	336	8	rajasingh	rajasingh	PROPN
ejpam-5038	336	9	.	.	PUNCT
ejpam-5038	337	1	domination	domination	NOUN
ejpam-5038	337	2	and	and	CCONJ
ejpam-5038	337	3	total	total	ADJ
ejpam-5038	337	4	domination	domination	NOUN
ejpam-5038	337	5	in	in	ADP
ejpam-5038	337	6	wrapped	wrap	VERB
ejpam-5038	337	7	butterfly	butterfly	NOUN
ejpam-5038	337	8	networks	network	NOUN
ejpam-5038	337	9	.	.	PUNCT
ejpam-5038	338	1	procedia	procedia	PROPN
ejpam-5038	338	2	computer	computer	NOUN
ejpam-5038	338	3	science	science	NOUN
ejpam-5038	338	4	,	,	PUNCT
ejpam-5038	338	5	172:66–70	172:66–70	NUM
ejpam-5038	338	6	,	,	PUNCT
ejpam-5038	338	7	2020	2020	NUM
ejpam-5038	338	8	.	.	PUNCT
ejpam-5038	339	1	[	[	X
ejpam-5038	339	2	21	21	NUM
ejpam-5038	339	3	]	]	SYM
ejpam-5038	339	4	v	v	X
ejpam-5038	339	5	shalini	shalini	PROPN
ejpam-5038	339	6	and	and	CCONJ
ejpam-5038	339	7	indra	indra	PROPN
ejpam-5038	339	8	rajasingh	rajasingh	PROPN
ejpam-5038	339	9	.	.	PUNCT
ejpam-5038	340	1	total	total	ADJ
ejpam-5038	340	2	and	and	CCONJ
ejpam-5038	340	3	inverse	inverse	NOUN
ejpam-5038	340	4	domination	domination	NOUN
ejpam-5038	340	5	numbers	number	NOUN
ejpam-5038	340	6	of	of	ADP
ejpam-5038	340	7	certain	certain	ADJ
ejpam-5038	340	8	graphs	graph	NOUN
ejpam-5038	340	9	.	.	PUNCT
ejpam-5038	341	1	in	in	ADP
ejpam-5038	341	2	iop	iop	PROPN
ejpam-5038	341	3	conference	conference	NOUN
ejpam-5038	341	4	series	series	NOUN
ejpam-5038	341	5	:	:	PUNCT
ejpam-5038	341	6	materials	material	NOUN
ejpam-5038	341	7	science	science	NOUN
ejpam-5038	341	8	and	and	CCONJ
ejpam-5038	341	9	engineering	engineering	NOUN
ejpam-5038	341	10	,	,	PUNCT
ejpam-5038	341	11	volume	volume	NOUN
ejpam-5038	341	12	1012	1012	NUM
ejpam-5038	341	13	,	,	PUNCT
ejpam-5038	341	14	page	page	NOUN
ejpam-5038	341	15	012066	012066	NUM
ejpam-5038	341	16	.	.	PUNCT
ejpam-5038	342	1	iop	iop	PROPN
ejpam-5038	342	2	publishing	publishing	NOUN
ejpam-5038	342	3	,	,	PUNCT
ejpam-5038	342	4	2021	2021	NUM
ejpam-5038	342	5	.	.	PUNCT
ejpam-5038	343	1	[	[	X
ejpam-5038	343	2	22	22	NUM
ejpam-5038	343	3	]	]	X
ejpam-5038	343	4	howard	howard	PROPN
ejpam-5038	343	5	jay	jay	PROPN
ejpam-5038	343	6	siegel	siegel	PROPN
ejpam-5038	343	7	and	and	CCONJ
ejpam-5038	343	8	craig	craig	PROPN
ejpam-5038	343	9	b.	b.	PROPN
ejpam-5038	343	10	stunkel	stunkel	PROPN
ejpam-5038	343	11	.	.	PUNCT
ejpam-5038	344	1	inside	inside	ADP
ejpam-5038	344	2	parallel	parallel	ADJ
ejpam-5038	344	3	computers	computer	NOUN
ejpam-5038	344	4	:	:	PUNCT
ejpam-5038	344	5	trends	trend	NOUN
ejpam-5038	344	6	in	in	ADP
ejpam-5038	344	7	interconnection	interconnection	NOUN
ejpam-5038	344	8	networks	network	NOUN
ejpam-5038	344	9	.	.	PUNCT
ejpam-5038	345	1	ieee	ieee	NOUN
ejpam-5038	345	2	comput	comput	PROPN
ejpam-5038	345	3	.	.	PUNCT
ejpam-5038	346	1	sci	sci	PROPN
ejpam-5038	346	2	.	.	PUNCT
ejpam-5038	347	1	eng	eng	PROPN
ejpam-5038	347	2	.	.	PROPN
ejpam-5038	347	3	,	,	PUNCT
ejpam-5038	347	4	3(3):69–71	3(3):69–71	NUM
ejpam-5038	347	5	,	,	PUNCT
ejpam-5038	347	6	sep	sep	PROPN
ejpam-5038	347	7	1996	1996	NUM
ejpam-5038	347	8	.	.	PUNCT
ejpam-5038	348	1	[	[	X
ejpam-5038	348	2	23	23	NUM
ejpam-5038	348	3	]	]	X
ejpam-5038	348	4	richard	richard	PROPN
ejpam-5038	348	5	j	j	PROPN
ejpam-5038	348	6	swan	swan	PROPN
ejpam-5038	348	7	,	,	PUNCT
ejpam-5038	348	8	samuel	samuel	PROPN
ejpam-5038	348	9	h	h	PROPN
ejpam-5038	348	10	fuller	full	ADJ
ejpam-5038	348	11	,	,	PUNCT
ejpam-5038	348	12	and	and	CCONJ
ejpam-5038	348	13	daniel	daniel	PROPN
ejpam-5038	348	14	p	p	PROPN
ejpam-5038	348	15	siewiorek	siewiorek	NOUN
ejpam-5038	348	16	.	.	PUNCT
ejpam-5038	349	1	cm	cm	X
ejpam-5038	349	2	*	*	PUNCT
ejpam-5038	349	3	a	a	DET
ejpam-5038	349	4	modular	modular	ADJ
ejpam-5038	349	5	,	,	PUNCT
ejpam-5038	349	6	multimicroprocessor	multimicroprocessor	NOUN
ejpam-5038	349	7	.	.	PUNCT
ejpam-5038	350	1	in	in	ADP
ejpam-5038	350	2	proceedings	proceeding	NOUN
ejpam-5038	350	3	of	of	ADP
ejpam-5038	350	4	the	the	DET
ejpam-5038	350	5	june	june	PROPN
ejpam-5038	350	6	13	13	NUM
ejpam-5038	350	7	-	-	SYM
ejpam-5038	350	8	16	16	NUM
ejpam-5038	350	9	,	,	PUNCT
ejpam-5038	350	10	1977	1977	NUM
ejpam-5038	350	11	,	,	PUNCT
ejpam-5038	350	12	national	national	ADJ
ejpam-5038	350	13	computer	computer	NOUN
ejpam-5038	350	14	conference	conference	NOUN
ejpam-5038	350	15	,	,	PUNCT
ejpam-5038	350	16	pages	page	NOUN
ejpam-5038	350	17	637–644	637–644	NUM
ejpam-5038	350	18	,	,	PUNCT
ejpam-5038	350	19	1977	1977	NUM
ejpam-5038	350	20	.	.	PUNCT
ejpam-5038	351	1	[	[	X
ejpam-5038	351	2	24	24	NUM
ejpam-5038	351	3	]	]	X
ejpam-5038	351	4	yahya	yahya	PROPN
ejpam-5038	351	5	talebi	talebi	PROPN
ejpam-5038	351	6	and	and	CCONJ
ejpam-5038	351	7	hossein	hossein	PROPN
ejpam-5038	351	8	rashmanlou	rashmanlou	PROPN
ejpam-5038	351	9	.	.	PUNCT
ejpam-5038	352	1	new	new	ADJ
ejpam-5038	352	2	concepts	concept	NOUN
ejpam-5038	352	3	of	of	ADP
ejpam-5038	352	4	domination	domination	NOUN
ejpam-5038	352	5	sets	set	NOUN
ejpam-5038	352	6	in	in	ADP
ejpam-5038	352	7	vague	vague	ADJ
ejpam-5038	352	8	graphs	graph	NOUN
ejpam-5038	352	9	with	with	ADP
ejpam-5038	352	10	applications	application	NOUN
ejpam-5038	352	11	.	.	PUNCT
ejpam-5038	353	1	international	international	ADJ
ejpam-5038	353	2	journal	journal	PROPN
ejpam-5038	353	3	of	of	ADP
ejpam-5038	353	4	computing	compute	VERB
ejpam-5038	353	5	science	science	NOUN
ejpam-5038	353	6	and	and	CCONJ
ejpam-5038	353	7	mathematics	mathematic	NOUN
ejpam-5038	353	8	,	,	PUNCT
ejpam-5038	353	9	10(4):375–389	10(4):375–389	NUM
ejpam-5038	353	10	,	,	PUNCT
ejpam-5038	353	11	2019	2019	NUM
ejpam-5038	353	12	.	.	PUNCT
ejpam-5038	354	1	[	[	X
ejpam-5038	354	2	25	25	NUM
ejpam-5038	354	3	]	]	X
ejpam-5038	354	4	jie	jie	PROPN
ejpam-5038	354	5	wu	wu	PROPN
ejpam-5038	354	6	and	and	CCONJ
ejpam-5038	354	7	hailan	hailan	PROPN
ejpam-5038	354	8	li	li	PROPN
ejpam-5038	354	9	.	.	PROPN
ejpam-5038	355	1	on	on	ADP
ejpam-5038	355	2	calculating	calculate	VERB
ejpam-5038	355	3	connected	connect	VERB
ejpam-5038	355	4	dominating	dominating	NOUN
ejpam-5038	355	5	set	set	NOUN
ejpam-5038	355	6	for	for	ADP
ejpam-5038	355	7	efficient	efficient	ADJ
ejpam-5038	355	8	routing	routing	NOUN
ejpam-5038	355	9	in	in	ADP
ejpam-5038	355	10	ad	ad	X
ejpam-5038	355	11	hoc	hoc	X
ejpam-5038	355	12	wireless	wireless	NOUN
ejpam-5038	355	13	networks	network	NOUN
ejpam-5038	355	14	.	.	PUNCT
ejpam-5038	356	1	in	in	ADP
ejpam-5038	356	2	proceedings	proceeding	NOUN
ejpam-5038	356	3	of	of	ADP
ejpam-5038	356	4	the	the	DET
ejpam-5038	356	5	3rd	3rd	ADJ
ejpam-5038	356	6	international	international	ADJ
ejpam-5038	356	7	workshop	workshop	NOUN
ejpam-5038	356	8	on	on	ADP
ejpam-5038	356	9	discrete	discrete	ADJ
ejpam-5038	356	10	algorithms	algorithm	NOUN
ejpam-5038	356	11	and	and	CCONJ
ejpam-5038	356	12	methods	method	NOUN
ejpam-5038	356	13	for	for	ADP
ejpam-5038	356	14	mobile	mobile	ADJ
ejpam-5038	356	15	computing	computing	NOUN
ejpam-5038	356	16	and	and	CCONJ
ejpam-5038	356	17	communications	communication	NOUN
ejpam-5038	356	18	,	,	PUNCT
ejpam-5038	356	19	pages	page	NOUN
ejpam-5038	356	20	7–14	7–14	PROPN
ejpam-5038	356	21	,	,	PUNCT
ejpam-5038	356	22	1999	1999	NUM
ejpam-5038	356	23	.	.	PUNCT