id	sid	eid	entity	type
ejpam-4356	1	1	european journal	ORG
ejpam-4356	2	1	15	CARDINAL
ejpam-4356	2	2	2	CARDINAL
ejpam-4356	2	3	2022	CARDINAL
ejpam-4356	2	4	736	CARDINAL
ejpam-4356	2	5	1307-5543	DATE
ejpam-4356	2	6	new york	GPE
ejpam-4356	2	7	jamil j. hamja1,∗	PERSON
ejpam-4356	2	8	imelda s. aniversario2	PERSON
ejpam-4356	3	1	helen m. rara2	PERSON
ejpam-4356	3	2	1	CARDINAL
ejpam-4356	3	3	msu	ORG
ejpam-4356	3	4	7500	CARDINAL
ejpam-4356	3	5	2	CARDINAL
ejpam-4356	3	6	msu-iligan institute of technology	ORG
ejpam-4356	3	7	9200	CARDINAL
ejpam-4356	3	8	iligan city	GPE
ejpam-4356	3	9	philippines	GPE
ejpam-4356	5	1	⊆	CARDINAL
ejpam-4356	5	2	two	CARDINAL
ejpam-4356	6	1	v2 ̸=	FAC
ejpam-4356	7	1	vi	PERSON
ejpam-4356	7	2	1	CARDINAL
ejpam-4356	7	3	2	DATE
ejpam-4356	10	1	cartesian	NORP
ejpam-4356	10	2	two	CARDINAL
ejpam-4356	13	1	2020	DATE
ejpam-4356	13	2	05c69	CARDINAL
ejpam-4356	14	1	1	CARDINAL
ejpam-4356	15	1	two	CARDINAL
ejpam-4356	17	1	j. hamja	PERSON
ejpam-4356	17	2	imelda.aniversario@g.msuiit.edu.ph	GPE
ejpam-4356	17	3	i. aniversario	PERSON
ejpam-4356	17	4	helen.rara@g.msuiit.edu.ph	GPE
ejpam-4356	17	5	h. rara	PERSON
ejpam-4356	18	1	736	CARDINAL
ejpam-4356	19	1	2022	CARDINAL
ejpam-4356	20	1	j. hamja	PERSON
ejpam-4356	20	2	i. aniversario	PERSON
ejpam-4356	20	3	h. rara	PERSON
ejpam-4356	21	1	j. pure	PERSON
ejpam-4356	21	2	15	CARDINAL
ejpam-4356	21	3	2	CARDINAL
ejpam-4356	21	4	2022	CARDINAL
ejpam-4356	21	5	736-752 737	QUANTITY
ejpam-4356	25	1	al	PERSON
ejpam-4356	26	1	12	CARDINAL
ejpam-4356	27	1	1	CARDINAL
ejpam-4356	28	1	al	PERSON
ejpam-4356	29	1	6	CARDINAL
ejpam-4356	29	2	dunbar	GPE
ejpam-4356	29	3	7	CARDINAL
ejpam-4356	29	4	jamil	GPE
ejpam-4356	30	1	11	CARDINAL
ejpam-4356	30	2	sandueta	ORG
ejpam-4356	30	3	13	CARDINAL
ejpam-4356	33	1	2	CARDINAL
ejpam-4356	34	1	γ(g	NORP
ejpam-4356	36	1	14	CARDINAL
ejpam-4356	36	2	8	CARDINAL
ejpam-4356	37	1	⊆	CARDINAL
ejpam-4356	38	1	∈	ORG
ejpam-4356	40	1	12	CARDINAL
ejpam-4356	41	1	⊆	CARDINAL
ejpam-4356	42	1	sandueta	ORG
ejpam-4356	42	2	13	CARDINAL
ejpam-4356	43	1	∈	ORG
ejpam-4356	44	1	ig[u	ORG
ejpam-4356	45	1	⋃	DATE
ejpam-4356	45	2	chartrand	GPE
ejpam-4356	45	3	4	CARDINAL
ejpam-4356	46	1	⊆	CARDINAL
ejpam-4356	47	1	g(g	PERSON
ejpam-4356	49	1	g(g	PERSON
ejpam-4356	50	1	ig[u	ORG
ejpam-4356	51	1	⊆	CARDINAL
ejpam-4356	53	1	j. hamja	PERSON
ejpam-4356	53	2	i. aniversario	PERSON
ejpam-4356	53	3	h. rara	PERSON
ejpam-4356	54	1	j. pure	PERSON
ejpam-4356	54	2	15	CARDINAL
ejpam-4356	54	3	2	CARDINAL
ejpam-4356	54	4	2022	CARDINAL
ejpam-4356	54	5	736-752 738	QUANTITY
ejpam-4356	56	1	9	CARDINAL
ejpam-4356	56	2	et.al	DATE
ejpam-4356	56	3	12	CARDINAL
ejpam-4356	56	4	15	CARDINAL
ejpam-4356	57	1	3 ≤	QUANTITY
ejpam-4356	59	1	vi	PERSON
ejpam-4356	59	2	1	CARDINAL
ejpam-4356	59	3	2	DATE
ejpam-4356	59	4	⊆	CARDINAL
ejpam-4356	63	1	cgb(g) aniversario	ORG
ejpam-4356	63	2	1	CARDINAL
ejpam-4356	63	3	12	CARDINAL
ejpam-4356	64	1	n(v	ORG
ejpam-4356	64	2	ext(g	ORG
ejpam-4356	65	1	n(v	ORG
ejpam-4356	66	1	⊆	CARDINAL
ejpam-4356	67	1	w ∈ n(v	ORG
ejpam-4356	67	2	2	CARDINAL
ejpam-4356	67	3	3	CARDINAL
ejpam-4356	67	4	1	CARDINAL
ejpam-4356	68	1	⊆	CARDINAL
ejpam-4356	69	1	2	CARDINAL
ejpam-4356	69	2	p2[s]g	ORG
ejpam-4356	69	3	p2[s]g	WORK_OF_ART
ejpam-4356	69	4	w ∈	PERSON
ejpam-4356	69	5	w ∈	PERSON
ejpam-4356	69	6	ig[u	ORG
ejpam-4356	69	7	∈	ORG
ejpam-4356	69	8	2	CARDINAL
ejpam-4356	70	1	2	CARDINAL
ejpam-4356	70	2	5	CARDINAL
ejpam-4356	70	3	1	CARDINAL
ejpam-4356	73	1	∈	ORG
ejpam-4356	73	2	∈	PERSON
ejpam-4356	74	1	1	CARDINAL
ejpam-4356	74	2	2	DATE
ejpam-4356	74	3	12	CARDINAL
ejpam-4356	75	1	3	CARDINAL
ejpam-4356	75	2	1	CARDINAL
ejpam-4356	76	1	j. hamja	PERSON
ejpam-4356	76	2	i. aniversario	PERSON
ejpam-4356	76	3	h. rara	PERSON
ejpam-4356	77	1	j. pure	PERSON
ejpam-4356	77	2	15	CARDINAL
ejpam-4356	77	3	2	CARDINAL
ejpam-4356	77	4	2022	CARDINAL
ejpam-4356	77	5	736	CARDINAL
ejpam-4356	79	1	1	CARDINAL
ejpam-4356	80	1	1	CARDINAL
ejpam-4356	81	1	u2 ̸= u4	PERSON
ejpam-4356	82	1	ig[u2	ORG
ejpam-4356	82	2	u4}	PERSON
ejpam-4356	82	3	ig[u2	ORG
ejpam-4356	82	4	u4, u5	ORG
ejpam-4356	83	1	u4, u5	ORG
ejpam-4356	85	1	s.	PERSON
ejpam-4356	87	1	u6 /∈	ORG
ejpam-4356	90	1	1	CARDINAL
ejpam-4356	90	2	3	CARDINAL
ejpam-4356	90	3	1	CARDINAL
ejpam-4356	93	1	2	CARDINAL
ejpam-4356	94	1	wcg(g	GPE
ejpam-4356	94	2	3	CARDINAL
ejpam-4356	96	1	1	CARDINAL
ejpam-4356	98	1	1	CARDINAL
ejpam-4356	101	1	j. hamja	PERSON
ejpam-4356	101	2	i. aniversario	PERSON
ejpam-4356	101	3	h. rara	PERSON
ejpam-4356	102	1	j. pure	PERSON
ejpam-4356	102	2	15	CARDINAL
ejpam-4356	102	3	2	CARDINAL
ejpam-4356	102	4	2022	CARDINAL
ejpam-4356	102	5	736-752 740	QUANTITY
ejpam-4356	105	1	lemma 1	ORG
ejpam-4356	106	1	g. (ii	PRODUCT
ejpam-4356	106	2	1	CARDINAL
ejpam-4356	106	3	∈	ORG
ejpam-4356	108	1	ig[u	ORG
ejpam-4356	108	2	w	ORG
ejpam-4356	108	3	w ∈ s	PERSON
ejpam-4356	111	1	2	CARDINAL
ejpam-4356	112	1	1	CARDINAL
ejpam-4356	112	2	1	CARDINAL
ejpam-4356	114	1	2	CARDINAL
ejpam-4356	116	1	n ≥ 4	DATE
ejpam-4356	116	2	3	CARDINAL
ejpam-4356	118	1	n has γwcg(fn	ORG
ejpam-4356	118	2	n ≥ 4	DATE
ejpam-4356	118	3	vi	PERSON
ejpam-4356	119	1	2	CARDINAL
ejpam-4356	119	2	n ≥ 5	DATE
ejpam-4356	119	3	4	CARDINAL
ejpam-4356	119	4	j. hamja	PERSON
ejpam-4356	119	5	i. aniversario	PERSON
ejpam-4356	119	6	h. rara	PERSON
ejpam-4356	120	1	j. pure	PERSON
ejpam-4356	120	2	15	CARDINAL
ejpam-4356	120	3	2	CARDINAL
ejpam-4356	120	4	2022	CARDINAL
ejpam-4356	120	5	736-752 741	QUANTITY
ejpam-4356	120	6	2	CARDINAL
ejpam-4356	122	1	g = kn	PERSON
ejpam-4356	125	1	2	CARDINAL
ejpam-4356	126	1	ig[v1	GPE
ejpam-4356	126	2	vi ∈	PERSON
ejpam-4356	126	3	3	CARDINAL
ejpam-4356	126	4	2	DATE
ejpam-4356	126	5	4	DATE
ejpam-4356	130	1	g = kn	PERSON
ejpam-4356	132	1	2	CARDINAL
ejpam-4356	133	1	w	GPE
ejpam-4356	136	1	∈	ORG
ejpam-4356	137	1	3	CARDINAL
ejpam-4356	138	1	w	GPE
ejpam-4356	138	2	γwcg(km,n	PERSON
ejpam-4356	141	1	w	GPE
ejpam-4356	141	2	lemma 2	ORG
ejpam-4356	141	3	γwcg(km,n	ORG
ejpam-4356	141	4	∈	ORG
ejpam-4356	142	1	2	CARDINAL
ejpam-4356	143	1	w	GPE
ejpam-4356	143	2	γwcg(km,n	PERSON
ejpam-4356	144	1	4	CARDINAL
ejpam-4356	146	1	wcg	PERSON
ejpam-4356	146	2	5	CARDINAL
ejpam-4356	146	3	bipartite km	PRODUCT
ejpam-4356	146	4	2	CARDINAL
ejpam-4356	146	5	1	CARDINAL
ejpam-4356	146	6	n ≥ 2	DATE
ejpam-4356	146	7	1	CARDINAL
ejpam-4356	146	8	2	CARDINAL
ejpam-4356	146	9	1	CARDINAL
ejpam-4356	146	10	3	CARDINAL
ejpam-4356	148	1	1	CARDINAL
ejpam-4356	149	1	j. hamja	PERSON
ejpam-4356	149	2	i. aniversario	PERSON
ejpam-4356	149	3	h. rara	PERSON
ejpam-4356	150	1	j. pure	PERSON
ejpam-4356	150	2	15	CARDINAL
ejpam-4356	150	3	2	CARDINAL
ejpam-4356	150	4	2022	CARDINAL
ejpam-4356	150	5	736	CARDINAL
ejpam-4356	150	6	6	CARDINAL
ejpam-4356	150	7	γwcg(hn	PERSON
ejpam-4356	150	8	1	CARDINAL
ejpam-4356	152	1	1	CARDINAL
ejpam-4356	152	2	2	DATE
ejpam-4356	152	3	3	DATE
ejpam-4356	152	4	vi	PERSON
ejpam-4356	152	5	1	CARDINAL
ejpam-4356	152	6	2	DATE
ejpam-4356	152	7	3	DATE
ejpam-4356	155	1	sn ∈	ORG
ejpam-4356	156	1	sn	ORG
ejpam-4356	157	1	sn	ORG
ejpam-4356	157	2	sn	ORG
ejpam-4356	161	1	∈	ORG
ejpam-4356	166	1	γwcg(hn	PERSON
ejpam-4356	167	1	1	CARDINAL
ejpam-4356	168	1	γw(g	PERSON
ejpam-4356	170	1	n ≥ 2	ORG
ejpam-4356	170	2	2	CARDINAL
ejpam-4356	171	1	2	CARDINAL
ejpam-4356	171	2	8	CARDINAL
ejpam-4356	172	1	1	CARDINAL
ejpam-4356	174	1	1	CARDINAL
ejpam-4356	175	1	bipartite	NORP
ejpam-4356	175	2	graph km	PERSON
ejpam-4356	175	3	γwcg(km,n	ORG
ejpam-4356	176	1	9	CARDINAL
ejpam-4356	183	1	u1}|	ORG
ejpam-4356	186	1	10	CARDINAL
ejpam-4356	187	1	n ≥ 2	DATE
ejpam-4356	188	1	g = kn	PERSON
ejpam-4356	190	1	4	CARDINAL
ejpam-4356	191	1	3	CARDINAL
ejpam-4356	191	2	n ≥ 5	DATE
ejpam-4356	192	1	j. hamja	PERSON
ejpam-4356	192	2	i. aniversario	PERSON
ejpam-4356	192	3	h. rara	PERSON
ejpam-4356	193	1	j. pure	PERSON
ejpam-4356	193	2	15	CARDINAL
ejpam-4356	193	3	2	CARDINAL
ejpam-4356	193	4	2022	CARDINAL
ejpam-4356	193	5	736-752 743	QUANTITY
ejpam-4356	194	1	1	CARDINAL
ejpam-4356	197	1	2	CARDINAL
ejpam-4356	197	2	n ≥ 5	DATE
ejpam-4356	197	3	11	CARDINAL
ejpam-4356	198	1	bipartite	ORG
ejpam-4356	198	2	2	CARDINAL
ejpam-4356	198	3	2	CARDINAL
ejpam-4356	199	1	2	CARDINAL
ejpam-4356	201	1	3	CARDINAL
ejpam-4356	203	1	12	CARDINAL
ejpam-4356	204	1	n ≥ 4	DATE
ejpam-4356	204	2	13	CARDINAL
ejpam-4356	205	1	2 ≤	QUANTITY
ejpam-4356	205	2	n ≤ 4	FAC
ejpam-4356	206	1	γwcg(km,n	ORG
ejpam-4356	207	1	5	CARDINAL
ejpam-4356	208	1	n ≥ 5	DATE
ejpam-4356	208	2	γwcg(km,n	ORG
ejpam-4356	209	1	two	CARDINAL
ejpam-4356	209	2	•	CARDINAL
ejpam-4356	209	3	∈	ORG
ejpam-4356	210	1	2	CARDINAL
ejpam-4356	211	1	3	CARDINAL
ejpam-4356	211	2	1	CARDINAL
ejpam-4356	212	1	2	CARDINAL
ejpam-4356	212	2	2	CARDINAL
ejpam-4356	212	3	14	DATE
ejpam-4356	213	1	1	CARDINAL
ejpam-4356	215	1	⊆	CARDINAL
ejpam-4356	216	1	2	CARDINAL
ejpam-4356	216	2	s ∈ c∗(h	ORG
ejpam-4356	217	1	15	CARDINAL
ejpam-4356	221	1	2	CARDINAL
ejpam-4356	221	2	w(g	TIME
ejpam-4356	224	1	2	CARDINAL
ejpam-4356	224	2	w(h	PRODUCT
ejpam-4356	225	1	14	DATE
ejpam-4356	226	1	∈	ORG
ejpam-4356	226	2	2	CARDINAL
ejpam-4356	226	3	kp	ORG
ejpam-4356	228	1	∈	ORG
ejpam-4356	229	1	∈	ORG
ejpam-4356	229	2	mx	PRODUCT
ejpam-4356	230	1	kp	ORG
ejpam-4356	230	2	mx	PRODUCT
ejpam-4356	230	3	∈	ORG
ejpam-4356	232	1	mx	PRODUCT
ejpam-4356	232	2	∈	ORG
ejpam-4356	233	1	∈	ORG
ejpam-4356	233	2	kp	ORG
ejpam-4356	233	3	j. hamja	PERSON
ejpam-4356	233	4	i. aniversario	PERSON
ejpam-4356	233	5	h. rara	PERSON
ejpam-4356	234	1	j. pure	PERSON
ejpam-4356	234	2	15	CARDINAL
ejpam-4356	234	3	2	CARDINAL
ejpam-4356	234	4	2022	CARDINAL
ejpam-4356	234	5	736-752 744	QUANTITY
ejpam-4356	234	6	mx	PRODUCT
ejpam-4356	234	7	∈	ORG
ejpam-4356	235	1	mx	PRODUCT
ejpam-4356	235	2	∈	ORG
ejpam-4356	237	1	kp	ORG
ejpam-4356	237	2	∈	ORG
ejpam-4356	237	3	dh(u	ORG
ejpam-4356	237	4	2	CARDINAL
ejpam-4356	237	5	kp	NORP
ejpam-4356	238	1	2	CARDINAL
ejpam-4356	238	2	kp	ORG
ejpam-4356	238	3	⊆	CARDINAL
ejpam-4356	239	1	kp	ORG
ejpam-4356	239	2	⊆	CARDINAL
ejpam-4356	240	1	w(g	TIME
ejpam-4356	241	1	16	CARDINAL
ejpam-4356	243	1	⊆	CARDINAL
ejpam-4356	243	2	2	CARDINAL
ejpam-4356	243	3	6	CARDINAL
ejpam-4356	245	1	⊆	CARDINAL
ejpam-4356	245	2	w(g	TIME
ejpam-4356	247	1	ω	CARDINAL
ejpam-4356	247	2	⊆	CARDINAL
ejpam-4356	247	3	w(g	TIME
ejpam-4356	248	1	1	CARDINAL
ejpam-4356	249	1	2	CARDINAL
ejpam-4356	249	2	w(g	TIME
ejpam-4356	250	1	⊆	CARDINAL
ejpam-4356	250	2	16	CARDINAL
ejpam-4356	250	3	⊆	CARDINAL
ejpam-4356	250	4	2	CARDINAL
ejpam-4356	252	1	two	CARDINAL
ejpam-4356	255	1	2	CARDINAL
ejpam-4356	259	1	2	CARDINAL
ejpam-4356	259	2	1	CARDINAL
ejpam-4356	260	1	⊆	CARDINAL
ejpam-4356	260	2	w(g	TIME
ejpam-4356	261	1	6	CARDINAL
ejpam-4356	262	1	2	CARDINAL
ejpam-4356	263	1	16	CARDINAL
ejpam-4356	263	2	⊆	CARDINAL
ejpam-4356	263	3	2	CARDINAL
ejpam-4356	263	4	15	CARDINAL
ejpam-4356	263	5	w(g	TIME
ejpam-4356	264	1	6	CARDINAL
ejpam-4356	266	1	two	CARDINAL
ejpam-4356	267	1	17	CARDINAL
ejpam-4356	270	1	i.	PERSON
ejpam-4356	270	2	⊆	CARDINAL
ejpam-4356	270	3	2	CARDINAL
ejpam-4356	270	4	⊆	CARDINAL
ejpam-4356	270	5	2	CARDINAL
ejpam-4356	270	6	k. proof	PERSON
ejpam-4356	275	1	∈	ORG
ejpam-4356	275	2	w(g	TIME
ejpam-4356	278	1	j. hamja	PERSON
ejpam-4356	278	2	i. aniversario	PERSON
ejpam-4356	278	3	h. rara	PERSON
ejpam-4356	279	1	j. pure	PERSON
ejpam-4356	279	2	15	CARDINAL
ejpam-4356	279	3	2	CARDINAL
ejpam-4356	279	4	2022	CARDINAL
ejpam-4356	279	5	736-752 745 1 ≤	QUANTITY
ejpam-4356	282	1	2	CARDINAL
ejpam-4356	282	2	∈	PRODUCT
ejpam-4356	282	3	∈	PRODUCT
ejpam-4356	283	1	∈	PRODUCT
ejpam-4356	285	1	xk−1	ORG
ejpam-4356	288	1	yn	ORG
ejpam-4356	288	2	1 ≤ n ≤ l	QUANTITY
ejpam-4356	289	1	1	CARDINAL
ejpam-4356	290	1	1	CARDINAL
ejpam-4356	290	2	1	CARDINAL
ejpam-4356	290	3	2	DATE
ejpam-4356	292	1	∈	ORG
ejpam-4356	293	1	xj	ORG
ejpam-4356	294	1	2	CARDINAL
ejpam-4356	298	1	∩	PERSON
ejpam-4356	298	2	2	CARDINAL
ejpam-4356	298	3	two	CARDINAL
ejpam-4356	298	4	1	CARDINAL
ejpam-4356	298	5	1	CARDINAL
ejpam-4356	298	6	2	CARDINAL
ejpam-4356	298	7	2	CARDINAL
ejpam-4356	298	8	1	CARDINAL
ejpam-4356	300	1	1	CARDINAL
ejpam-4356	300	2	2	DATE
ejpam-4356	301	1	xk−l	NORP
ejpam-4356	301	2	xm = yq	ORG
ejpam-4356	301	3	1	CARDINAL
ejpam-4356	301	4	2	DATE
ejpam-4356	301	5	⊆	CARDINAL
ejpam-4356	301	6	ig[s ∗	PERSON
ejpam-4356	304	1	xz	ORG
ejpam-4356	306	1	k-l	PERSON
ejpam-4356	307	1	2	CARDINAL
ejpam-4356	307	2	∈	PRODUCT
ejpam-4356	308	1	2	CARDINAL
ejpam-4356	308	2	⊆	CARDINAL
ejpam-4356	308	3	∈	PRODUCT
ejpam-4356	312	1	sn	ORG
ejpam-4356	312	2	w(g	TIME
ejpam-4356	313	1	2	CARDINAL
ejpam-4356	313	2	⊆	CARDINAL
ejpam-4356	314	1	16	CARDINAL
ejpam-4356	314	2	3	CARDINAL
ejpam-4356	317	1	∈	ORG
ejpam-4356	318	1	2	CARDINAL
ejpam-4356	319	1	2	CARDINAL
ejpam-4356	319	2	2	CARDINAL
ejpam-4356	319	3	∈	PRODUCT
ejpam-4356	319	4	⊆	CARDINAL
ejpam-4356	320	1	⊆	CARDINAL
ejpam-4356	320	2	2	CARDINAL
ejpam-4356	320	3	k. theorem 18	PERSON
ejpam-4356	324	1	i.	PERSON
ejpam-4356	324	2	⊆	CARDINAL
ejpam-4356	324	3	2	CARDINAL
ejpam-4356	324	4	w(h	PRODUCT
ejpam-4356	324	5	⊆	CARDINAL
ejpam-4356	324	6	2	CARDINAL
ejpam-4356	324	7	w(g	TIME
ejpam-4356	325	1	j. hamja	PERSON
ejpam-4356	325	2	i. aniversario	PERSON
ejpam-4356	325	3	h. rara	PERSON
ejpam-4356	326	1	j. pure	PERSON
ejpam-4356	326	2	15	CARDINAL
ejpam-4356	326	3	2	CARDINAL
ejpam-4356	326	4	2022	CARDINAL
ejpam-4356	326	5	736-752 746	QUANTITY
ejpam-4356	326	6	19	DATE
ejpam-4356	330	1	= min{γ(h),γ(k	PERSON
ejpam-4356	330	2	γ(h	ORG
ejpam-4356	330	3	⊆	CARDINAL
ejpam-4356	330	4	w(g	TIME
ejpam-4356	330	5	γ(k	PERSON
ejpam-4356	331	1	⊆	CARDINAL
ejpam-4356	331	2	w(g	TIME
ejpam-4356	335	1	⊆	CARDINAL
ejpam-4356	335	2	17	CARDINAL
ejpam-4356	335	3	⊆	CARDINAL
ejpam-4356	335	4	2	CARDINAL
ejpam-4356	335	5	2	CARDINAL
ejpam-4356	335	6	k. hence	PERSON
ejpam-4356	335	7	≥ min{γ(h),γ(k	PERSON
ejpam-4356	335	8	γ(h	ORG
ejpam-4356	335	9	⊆	CARDINAL
ejpam-4356	335	10	w(g	TIME
ejpam-4356	335	11	γ(k	PERSON
ejpam-4356	336	1	⊆	CARDINAL
ejpam-4356	336	2	w(g	TIME
ejpam-4356	337	1	18	CARDINAL
ejpam-4356	337	2	min{γ(h),γ(k	PERSON
ejpam-4356	338	1	= min{γ(h),γ(k	PERSON
ejpam-4356	339	1	8	CARDINAL
ejpam-4356	340	1	bipartite	NORP
ejpam-4356	340	2	graph km	PERSON
ejpam-4356	341	1	i.	PERSON
ejpam-4356	342	1	2	CARDINAL
ejpam-4356	342	2	2	CARDINAL
ejpam-4356	342	3	2	CARDINAL
ejpam-4356	343	1	3	CARDINAL
ejpam-4356	344	1	γwcg(km,n	PERSON
ejpam-4356	344	2	2	CARDINAL
ejpam-4356	345	1	γwcg(km,n +kp	PERSON
ejpam-4356	345	2	2	CARDINAL
ejpam-4356	347	1	+ k.	PERSON
ejpam-4356	348	1	2	CARDINAL
ejpam-4356	350	1	one	CARDINAL
ejpam-4356	350	2	one	CARDINAL
ejpam-4356	350	3	∈	ORG
ejpam-4356	351	1	2	CARDINAL
ejpam-4356	352	1	20	CARDINAL
ejpam-4356	353	1	jamil	PERSON
ejpam-4356	353	2	11	CARDINAL
ejpam-4356	353	3	⊆	CARDINAL
ejpam-4356	354	1	⋃ v∈v	PERSON
ejpam-4356	354	2	sv ⊆	ORG
ejpam-4356	354	3	sv ∈	PERSON
ejpam-4356	355	1	4	CARDINAL
ejpam-4356	357	1	w(g	TIME
ejpam-4356	357	2	∈	ORG
ejpam-4356	358	1	5	CARDINAL
ejpam-4356	360	1	sv ⊆	ORG
ejpam-4356	360	2	∈	ORG
ejpam-4356	361	1	sv ∈ w(v	PERSON
ejpam-4356	361	2	∈	ORG
ejpam-4356	361	3	⋃ v∈v	PERSON
ejpam-4356	361	4	w(g	TIME
ejpam-4356	362	1	j. hamja	PERSON
ejpam-4356	362	2	i. aniversario	PERSON
ejpam-4356	362	3	h. rara	PERSON
ejpam-4356	363	1	j. pure	PERSON
ejpam-4356	363	2	15	CARDINAL
ejpam-4356	363	3	2	CARDINAL
ejpam-4356	363	4	2022	CARDINAL
ejpam-4356	363	5	736-752 747	QUANTITY
ejpam-4356	363	6	21	DATE
ejpam-4356	364	1	sv ⊆	ORG
ejpam-4356	365	1	w(g	TIME
ejpam-4356	365	2	⋃ v∈v	PERSON
ejpam-4356	365	3	sv ⊆	ORG
ejpam-4356	365	4	sv ∈ w(v +kv	PERSON
ejpam-4356	367	1	w(g	TIME
ejpam-4356	369	1	20	CARDINAL
ejpam-4356	369	2	⋃ v∈v	PERSON
ejpam-4356	370	1	sv ⊆	PERSON
ejpam-4356	370	2	sv ∈ c∗(v + kv	PERSON
ejpam-4356	371	1	lemma 4	ORG
ejpam-4356	371	2	∈	ORG
ejpam-4356	371	3	∈	ORG
ejpam-4356	374	1	sv	ORG
ejpam-4356	375	1	xz	ORG
ejpam-4356	375	2	e(v+kv	CARDINAL
ejpam-4356	376	1	sv ∈ w(v +kv	PERSON
ejpam-4356	377	1	⋃ v∈v	PERSON
ejpam-4356	378	1	sv ⊆	ORG
ejpam-4356	378	2	sv ∈	ORG
ejpam-4356	379	1	lemma 5	ORG
ejpam-4356	379	2	⋃ v∈v	PERSON
ejpam-4356	379	3	w(g	TIME
ejpam-4356	381	1	20	CARDINAL
ejpam-4356	381	2	3	CARDINAL
ejpam-4356	381	3	⋃ v∈v	PERSON
ejpam-4356	381	4	s0	ORG
ejpam-4356	381	5	∈	ORG
ejpam-4356	381	6	⋃ v∈v	PERSON
ejpam-4356	384	1	⋃ v∈v	PERSON
ejpam-4356	384	2	∈	ORG
ejpam-4356	384	3	w(g	TIME
ejpam-4356	385	1	10	CARDINAL
ejpam-4356	387	1	⋃ v∈v	PERSON
ejpam-4356	389	1	11	CARDINAL
ejpam-4356	393	1	22	CARDINAL
ejpam-4356	394	1	m. if n ≥ 3	PERSON
ejpam-4356	397	1	11	CARDINAL
ejpam-4356	397	2	j. hamja	PERSON
ejpam-4356	397	3	i. aniversario	PERSON
ejpam-4356	397	4	h. rara	PERSON
ejpam-4356	398	1	j. pure	PERSON
ejpam-4356	398	2	15	CARDINAL
ejpam-4356	398	3	2	CARDINAL
ejpam-4356	398	4	2022	CARDINAL
ejpam-4356	398	5	736-752 748	QUANTITY
ejpam-4356	399	1	1	CARDINAL
ejpam-4356	399	2	2	CARDINAL
ejpam-4356	399	3	12	CARDINAL
ejpam-4356	402	1	n ≥ 3	DATE
ejpam-4356	402	2	23	CARDINAL
ejpam-4356	403	1	m. if n ≥ 3	PERSON
ejpam-4356	403	2	2 ⌋.	PERCENT
ejpam-4356	406	1	11	CARDINAL
ejpam-4356	408	1	1	CARDINAL
ejpam-4356	408	2	13	CARDINAL
ejpam-4356	409	1	2	CARDINAL
ejpam-4356	409	2	n ≥ 3	DATE
ejpam-4356	409	3	24	CARDINAL
ejpam-4356	410	1	k = kn	PERSON
ejpam-4356	411	1	⋃ v∈v	PERSON
ejpam-4356	413	1	k = kn	PERSON
ejpam-4356	413	2	⋃ v∈v	PERSON
ejpam-4356	413	3	sv =	PERSON
ejpam-4356	414	1	lemma 5	ORG
ejpam-4356	414	2	⋃ v∈v	PERSON
ejpam-4356	415	1	w(h ◦ kn	PERSON
ejpam-4356	416	1	10	CARDINAL
ejpam-4356	416	2	⋃ v∈v	PERSON
ejpam-4356	416	3	14	DATE
ejpam-4356	417	1	k = kn	PERSON
ejpam-4356	417	2	n ≥ 4	DATE
ejpam-4356	417	3	1	CARDINAL
ejpam-4356	418	1	cartesian	NORP
ejpam-4356	418	2	two	CARDINAL
ejpam-4356	418	3	g□h	ORG
ejpam-4356	418	4	v1)(u2	GPE
ejpam-4356	419	1	2	CARDINAL
ejpam-4356	420	1	j. hamja	PERSON
ejpam-4356	420	2	i. aniversario	PERSON
ejpam-4356	420	3	h. rara	PERSON
ejpam-4356	421	1	j. pure	PERSON
ejpam-4356	421	2	15	CARDINAL
ejpam-4356	421	3	2	CARDINAL
ejpam-4356	421	4	2022	CARDINAL
ejpam-4356	421	5	736	CARDINAL
ejpam-4356	421	6	6	CARDINAL
ejpam-4356	421	7	chellathurai, et.al	PERSON
ejpam-4356	421	8	6	CARDINAL
ejpam-4356	421	9	cartesian	NORP
ejpam-4356	422	1	⊆	CARDINAL
ejpam-4356	422	2	⊆	CARDINAL
ejpam-4356	423	1	7	CARDINAL
ejpam-4356	423	2	chellathurai, et.al	PERSON
ejpam-4356	423	3	6	CARDINAL
ejpam-4356	423	4	cartesian	NORP
ejpam-4356	424	1	⊆	CARDINAL
ejpam-4356	424	2	⊆	CARDINAL
ejpam-4356	424	3	8	CARDINAL
ejpam-4356	425	1	cartesian	NORP
ejpam-4356	426	1	i.	PERSON
ejpam-4356	427	1	⊆	CARDINAL
ejpam-4356	428	1	⊆	CARDINAL
ejpam-4356	428	2	∈	ORG
ejpam-4356	430	1	⊆	CARDINAL
ejpam-4356	431	1	4	CARDINAL
ejpam-4356	432	1	cartesian	NORP
ejpam-4356	433	1	⊆	CARDINAL
ejpam-4356	434	1	25	CARDINAL
ejpam-4356	439	1	⊆	CARDINAL
ejpam-4356	440	1	6	CARDINAL
ejpam-4356	440	2	7	DATE
ejpam-4356	440	3	⊆	CARDINAL
ejpam-4356	440	4	⊆	CARDINAL
ejpam-4356	441	1	vy ∈ e(h□j	ORG
ejpam-4356	441	2	∈	ORG
ejpam-4356	441	3	∈	PRODUCT
ejpam-4356	442	1	⊆	CARDINAL
ejpam-4356	446	1	15	CARDINAL
ejpam-4356	447	1	□kn	PERSON
ejpam-4356	448	1	26	CARDINAL
ejpam-4356	449	1	at least 3	CARDINAL
ejpam-4356	449	2	2	CARDINAL
ejpam-4356	455	1	two	CARDINAL
ejpam-4356	460	1	first	ORDINAL
ejpam-4356	460	2	∈	ORG
ejpam-4356	461	1	diam(h1	ORG
ejpam-4356	463	1	j. hamja	PERSON
ejpam-4356	463	2	i. aniversario	PERSON
ejpam-4356	463	3	h. rara	PERSON
ejpam-4356	464	1	j. pure	PERSON
ejpam-4356	464	2	15	CARDINAL
ejpam-4356	464	3	2	CARDINAL
ejpam-4356	464	4	2022	CARDINAL
ejpam-4356	464	5	736-752 750	QUANTITY
ejpam-4356	464	6	∈	ORG
ejpam-4356	466	1	∈	ORG
ejpam-4356	467	1	diam(h1	ORG
ejpam-4356	467	2	∈	ORG
ejpam-4356	470	1	∈	ORG
ejpam-4356	470	2	d.	NORP
ejpam-4356	472	1	⊆	CARDINAL
ejpam-4356	473	1	∈	ORG
ejpam-4356	475	1	⊆	CARDINAL
ejpam-4356	477	1	∈	ORG
ejpam-4356	480	1	15	CARDINAL
ejpam-4356	481	1	two	CARDINAL
ejpam-4356	482	1	1	CARDINAL
ejpam-4356	482	2	2	CARDINAL
ejpam-4356	482	3	∈	ORG
ejpam-4356	485	1	∈	ORG
ejpam-4356	488	1	∈	ORG
ejpam-4356	490	1	d(u	PERSON
ejpam-4356	490	2	d(u	PERSON
ejpam-4356	490	3	+ d(u	PERSON
ejpam-4356	490	4	2	CARDINAL
ejpam-4356	490	5	diam(h1	ORG
ejpam-4356	490	6	cartesian	NORP
ejpam-4356	490	7	two	CARDINAL
ejpam-4356	493	1	two	CARDINAL
ejpam-4356	493	2	two	CARDINAL
ejpam-4356	495	1	the department of science and technology	ORG
ejpam-4356	496	1	751	CARDINAL
ejpam-4356	496	2	1	CARDINAL
ejpam-4356	496	3	i. aniversario	PERSON
ejpam-4356	496	4	f. jamil	PERSON
ejpam-4356	496	5	jr.	PERSON
ejpam-4356	496	6	s. canoy	PERSON
ejpam-4356	496	7	utilitas mathematica	PERSON
ejpam-4356	496	8	74	DATE
ejpam-4356	496	9	2007	DATE
ejpam-4356	498	1	3 18	DATE
ejpam-4356	499	1	2	CARDINAL
ejpam-4356	499	2	f. harary	PERSON
ejpam-4356	499	3	addison-wesley publishing company, inc.	ORG
ejpam-4356	499	4	usa	GPE
ejpam-4356	499	5	1969	DATE
ejpam-4356	500	1	3	CARDINAL
ejpam-4356	500	2	g. cagaanan	PERSON
ejpam-4356	502	1	msu-iligan institute of technology	ORG
ejpam-4356	502	2	march 2004	DATE
ejpam-4356	503	1	4	CARDINAL
ejpam-4356	503	2	g. chartrand	PERSON
ejpam-4356	503	3	f. harary	PERSON
ejpam-4356	503	4	p. zhang	PERSON
ejpam-4356	503	5	20	CARDINAL
ejpam-4356	503	6	129	CARDINAL
ejpam-4356	503	7	5	CARDINAL
ejpam-4356	503	8	s. canoy	PERSON
ejpam-4356	503	9	g. cagaanan	PERSON
ejpam-4356	503	10	s. gervacio	PERSON
ejpam-4356	504	1	mathematica 71 (	PERSON
ejpam-4356	504	2	2006	DATE
ejpam-4356	505	1	6	CARDINAL
ejpam-4356	505	2	s. padma vijaya	PERSON
ejpam-4356	505	3	combinatorics	ORG
ejpam-4356	505	4	issn	PERSON
ejpam-4356	505	5	2251-8657	DATE
ejpam-4356	505	6	issn	PERSON
ejpam-4356	505	7	2251-8665	DATE
ejpam-4356	505	8	3 no.	CARDINAL
ejpam-4356	505	9	2014	DATE
ejpam-4356	506	1	19-30	CARDINAL
ejpam-4356	507	1	7	CARDINAL
ejpam-4356	507	2	j. dunbar	PERSON
ejpam-4356	507	3	j. grossman	PERSON
ejpam-4356	507	4	j. hattingh	PERSON
ejpam-4356	507	5	s. hedetniemi	PERSON
ejpam-4356	507	6	a. mcrae	PERSON
ejpam-4356	507	7	1997	DATE
ejpam-4356	507	8	261	CARDINAL
ejpam-4356	507	9	8	CARDINAL
ejpam-4356	507	10	w. duckworth	PERSON
ejpam-4356	507	11	b. mans	PERSON
ejpam-4356	507	12	309	CARDINAL
ejpam-4356	507	13	2009	DATE
ejpam-4356	507	14	2305–2322	CARDINAL
ejpam-4356	508	1	9	CARDINAL
ejpam-4356	508	2	h. escuadro	PERSON
ejpam-4356	508	3	r. gera	PERSON
ejpam-4356	508	4	a. hansberg	PERSON
ejpam-4356	508	5	n. jafari rad	PERSON
ejpam-4356	508	6	l. volkmann	PERSON
ejpam-4356	509	1	j. combin	PERSON
ejpam-4356	510	1	77 (2011	DATE
ejpam-4356	510	2	89	CARDINAL
ejpam-4356	510	3	10	CARDINAL
ejpam-4356	510	4	a. hansberg	PERSON
ejpam-4356	510	5	l. volkmann	PERSON
ejpam-4356	510	6	lehrstuhl ii für mathematik	PERSON
ejpam-4356	510	7	52056	CARDINAL
ejpam-4356	510	8	germany	GPE
ejpam-4356	510	9	310	CARDINAL
ejpam-4356	510	10	2010	DATE
ejpam-4356	510	11	2140–2146	CARDINAL
ejpam-4356	511	1	11	CARDINAL
ejpam-4356	511	2	f. jamil	PERSON
ejpam-4356	511	3	i. aniversario	PERSON
ejpam-4356	511	4	jr.	PERSON
ejpam-4356	511	5	s. canoy	PERSON
ejpam-4356	511	6	msu iligan institute of technology	ORG
ejpam-4356	511	7	9200	CARDINAL
ejpam-4356	511	8	iligan city	GPE
ejpam-4356	511	9	mathematica	PERSON
ejpam-4356	511	10	74(2007	DATE
ejpam-4356	511	11	pp.3	ORG
ejpam-4356	512	1	12	CARDINAL
ejpam-4356	512	2	r. patangan	PERSON
ejpam-4356	512	3	i. aniversario	PERSON
ejpam-4356	512	4	jr. a. rosalio	PERSON
ejpam-4356	512	5	10	CARDINAL
ejpam-4356	512	6	2016	DATE
ejpam-4356	512	7	6	CARDINAL
ejpam-4356	512	8	257 270	CARDINAL
ejpam-4356	513	1	13	CARDINAL
ejpam-4356	513	2	e. sandueta	PERSON
ejpam-4356	513	3	jr.	PERSON
ejpam-4356	513	4	s. canoy	PERSON
ejpam-4356	513	5	6, 2011	DATE
ejpam-4356	513	6	21	CARDINAL
ejpam-4356	513	7	1035	CARDINAL
ejpam-4356	514	1	14	CARDINAL
ejpam-4356	514	2	j. tarr	PERSON
ejpam-4356	514	3	s. suen	PERSON
ejpam-4356	514	4	university of south florida	ORG
ejpam-4356	514	5	5	CARDINAL
ejpam-4356	514	6	752	CARDINAL
ejpam-4356	514	7	15	CARDINAL
ejpam-4356	514	8	tejaswini	PERSON
ejpam-4356	514	9	m. goudar	PERSON
ejpam-4356	515	1	9	CARDINAL
ejpam-4356	515	2	7, 2014	DATE
ejpam-4356	515	3	2812-2816	CARDINAL