id	sid	eid	entity	type
ejpam-6046	1	1	european journal	ORG
ejpam-6046	1	2	2025	DATE
ejpam-6046	1	3	18	CARDINAL
ejpam-6046	1	4	2	CARDINAL
ejpam-6046	1	5	6046	CARDINAL
ejpam-6046	1	6	new york	GPE
ejpam-6046	1	7	s. ontulan1,∗	PERSON
ejpam-6046	1	8	cherry mae r.	ORG
ejpam-6046	1	9	1	CARDINAL
ejpam-6046	1	10	central mindanao university	ORG
ejpam-6046	1	11	8710	CARDINAL
ejpam-6046	1	12	bukidnon	GPE
ejpam-6046	1	13	philippines	GPE
ejpam-6046	7	1	2020	DATE
ejpam-6046	7	2	54a05	CARDINAL
ejpam-6046	7	3	54a25	CARDINAL
ejpam-6046	7	4	05c75	DATE
ejpam-6046	7	5	bipartite	ORG
ejpam-6046	7	6	1	CARDINAL
ejpam-6046	7	7	two	CARDINAL
ejpam-6046	9	1	1	CARDINAL
ejpam-6046	13	1	2	CARDINAL
ejpam-6046	14	1	2018	DATE
ejpam-6046	14	2	abdu	PERSON
ejpam-6046	15	1	two	CARDINAL
ejpam-6046	17	1	j. n. ontulan	PERSON
ejpam-6046	17	2	f.cherrymae.balingit@cmu.edu.ph	GPE
ejpam-6046	17	3	c. m. balingit	PERSON
ejpam-6046	18	1	1	CARDINAL
ejpam-6046	18	2	2025	CARDINAL
ejpam-6046	19	1	j. n. ontulan	PERSON
ejpam-6046	19	2	c. m. balingit	PERSON
ejpam-6046	20	1	j. pure	PERSON
ejpam-6046	20	2	18	CARDINAL
ejpam-6046	20	3	2	CARDINAL
ejpam-6046	20	4	2025	CARDINAL
ejpam-6046	20	5	6046 2	DATE
ejpam-6046	20	6	14	CARDINAL
ejpam-6046	20	7	3	CARDINAL
ejpam-6046	22	1	4	CARDINAL
ejpam-6046	23	1	at least one	CARDINAL
ejpam-6046	24	1	1	CARDINAL
ejpam-6046	25	1	two	CARDINAL
ejpam-6046	26	1	5	CARDINAL
ejpam-6046	27	1	2020	DATE
ejpam-6046	27	2	hassan	PERSON
ejpam-6046	28	1	6	CARDINAL
ejpam-6046	30	1	7	CARDINAL
ejpam-6046	33	1	matchings	ORG
ejpam-6046	33	2	more than one	CARDINAL
ejpam-6046	33	3	5	CARDINAL
ejpam-6046	35	1	two	CARDINAL
ejpam-6046	37	1	8	CARDINAL
ejpam-6046	38	1	2	CARDINAL
ejpam-6046	38	2	1	CARDINAL
ejpam-6046	39	1	9	CARDINAL
ejpam-6046	39	2	2element	CARDINAL
ejpam-6046	40	1	two	CARDINAL
ejpam-6046	40	2	two	CARDINAL
ejpam-6046	41	1	0	CARDINAL
ejpam-6046	42	1	two	CARDINAL
ejpam-6046	43	1	nonempty	ORG
ejpam-6046	43	2	one	CARDINAL
ejpam-6046	44	1	two	CARDINAL
ejpam-6046	44	2	j. n. ontulan	PERSON
ejpam-6046	44	3	c. m. balingit	PERSON
ejpam-6046	45	1	j. pure	PERSON
ejpam-6046	45	2	18	CARDINAL
ejpam-6046	45	3	2	CARDINAL
ejpam-6046	45	4	2025	CARDINAL
ejpam-6046	45	5	6046 3	DATE
ejpam-6046	45	6	14	CARDINAL
ejpam-6046	46	1	n ∈ n	ORG
ejpam-6046	46	2	{vα1 , vα2	PERSON
ejpam-6046	50	1	1	CARDINAL
ejpam-6046	50	2	2	DATE
ejpam-6046	52	1	j	PERSON
ejpam-6046	52	2	j ∈	PERSON
ejpam-6046	54	1	two	CARDINAL
ejpam-6046	56	1	1	CARDINAL
ejpam-6046	59	1	two	CARDINAL
ejpam-6046	59	2	i2	ORG
ejpam-6046	59	3	1	CARDINAL
ejpam-6046	60	1	two	CARDINAL
ejpam-6046	61	1	v1 v2 v3 v4 v5 v6g	PERSON
ejpam-6046	61	2	e1,2 e2,3e3,4 e1,4 e4,5	ORG
ejpam-6046	61	3	1	CARDINAL
ejpam-6046	61	4	2	CARDINAL
ejpam-6046	62	1	9	CARDINAL
ejpam-6046	62	2	k(g	GPE
ejpam-6046	63	1	k(g	PERSON
ejpam-6046	64	1	1	CARDINAL
ejpam-6046	64	2	2	CARDINAL
ejpam-6046	64	3	3	CARDINAL
ejpam-6046	65	1	3	CARDINAL
ejpam-6046	65	2	2	CARDINAL
ejpam-6046	65	3	3	CARDINAL
ejpam-6046	65	4	3	CARDINAL
ejpam-6046	66	1	9	CARDINAL
ejpam-6046	66	2	two	CARDINAL
ejpam-6046	66	3	g ∼= h	ORG
ejpam-6046	66	4	two	CARDINAL
ejpam-6046	66	5	j. n. ontulan	PERSON
ejpam-6046	66	6	c. m. balingit	PERSON
ejpam-6046	67	1	j. pure	PERSON
ejpam-6046	67	2	18	CARDINAL
ejpam-6046	67	3	2	CARDINAL
ejpam-6046	67	4	2025	CARDINAL
ejpam-6046	67	5	6046 4 of 14	DATE
ejpam-6046	68	1	3	CARDINAL
ejpam-6046	73	1	u7 g : v1 v2 v3 v4 v5 v6 v7 h :	PERSON
ejpam-6046	73	2	3	CARDINAL
ejpam-6046	73	3	4	CARDINAL
ejpam-6046	74	1	10	CARDINAL
ejpam-6046	75	1	two	CARDINAL
ejpam-6046	78	1	5	CARDINAL
ejpam-6046	79	1	11	CARDINAL
ejpam-6046	80	1	i. ∅	PERSON
ejpam-6046	81	1	⊂ τ	PERSON
ejpam-6046	81	2	⋃	DATE
ejpam-6046	81	3	∈	ORG
ejpam-6046	84	1	un ∈ τ	ORG
ejpam-6046	90	1	p(x	PERSON
ejpam-6046	92	1	x.	GPE
ejpam-6046	92	2	1	CARDINAL
ejpam-6046	93	1	11	CARDINAL
ejpam-6046	93	2	p(x	PERSON
ejpam-6046	94	1	j. n. ontulan	PERSON
ejpam-6046	94	2	c. m. balingit	PERSON
ejpam-6046	95	1	j. pure	PERSON
ejpam-6046	95	2	18	CARDINAL
ejpam-6046	95	3	2	CARDINAL
ejpam-6046	95	4	2025	CARDINAL
ejpam-6046	95	5	6046 5	DATE
ejpam-6046	95	6	14	DATE
ejpam-6046	95	7	6	CARDINAL
ejpam-6046	96	1	12	CARDINAL
ejpam-6046	97	1	τ(σ	ORG
ejpam-6046	98	1	τ(σ	GPE
ejpam-6046	99	1	σ	ORG
ejpam-6046	99	2	τ(σ	GPE
ejpam-6046	99	3	τ(σ	GPE
ejpam-6046	99	4	σ	ORG
ejpam-6046	100	1	1	CARDINAL
ejpam-6046	101	1	6	CARDINAL
ejpam-6046	101	2	τ(σ	NORP
ejpam-6046	101	3	p(x	PERSON
ejpam-6046	102	1	τ(σ	GPE
ejpam-6046	102	2	x. 3	DATE
ejpam-6046	102	3	7	CARDINAL
ejpam-6046	105	1	2	CARDINAL
ejpam-6046	105	2	4	CARDINAL
ejpam-6046	106	1	e1,2, e1,3, e1,4	ORG
ejpam-6046	106	2	e2,3	ORG
ejpam-6046	107	1	e1,4	GPE
ejpam-6046	107	2	6	CARDINAL
ejpam-6046	107	3	e1,4	GPE
ejpam-6046	107	4	e1,2, e1,3	ORG
ejpam-6046	107	5	e1,3, e1,4	ORG
ejpam-6046	107	6	e1,2, e1,4	ORG
ejpam-6046	107	7	e2,3	ORG
ejpam-6046	108	1	v1 v2 v3 v4	PERSON
ejpam-6046	108	2	1,2	CARDINAL
ejpam-6046	108	3	2	CARDINAL
ejpam-6046	108	4	3	CARDINAL
ejpam-6046	108	5	4	CARDINAL
ejpam-6046	108	6	1	CARDINAL
ejpam-6046	108	7	3	CARDINAL
ejpam-6046	108	8	4	CARDINAL
ejpam-6046	108	9	2	CARDINAL
ejpam-6046	111	1	1	CARDINAL
ejpam-6046	113	1	at least 2	CARDINAL
ejpam-6046	114	1	s.	PERSON
ejpam-6046	114	2	∈	ORG
ejpam-6046	114	3	⊆	CARDINAL
ejpam-6046	116	1	j. n. ontulan	PERSON
ejpam-6046	116	2	c. m. balingit	PERSON
ejpam-6046	117	1	j. pure	PERSON
ejpam-6046	117	2	18	CARDINAL
ejpam-6046	117	3	2	CARDINAL
ejpam-6046	117	4	2025	CARDINAL
ejpam-6046	117	5	6046 6	DATE
ejpam-6046	119	1	3	CARDINAL
ejpam-6046	119	2	5	CARDINAL
ejpam-6046	119	3	e1,2, e4,5}	ORG
ejpam-6046	120	1	e1,2, e4,5	ORG
ejpam-6046	120	2	2	CARDINAL
ejpam-6046	122	1	v1 v2 v3 v4 v5 h :	PERSON
ejpam-6046	122	2	1	CARDINAL
ejpam-6046	122	3	2	CARDINAL
ejpam-6046	122	4	4	CARDINAL
ejpam-6046	122	5	5	CARDINAL
ejpam-6046	122	6	5	CARDINAL
ejpam-6046	122	7	4	CARDINAL
ejpam-6046	122	8	8	CARDINAL
ejpam-6046	123	1	9	CARDINAL
ejpam-6046	123	2	two	CARDINAL
ejpam-6046	124	1	kn	PERSON
ejpam-6046	125	1	kn	PERSON
ejpam-6046	126	1	two	CARDINAL
ejpam-6046	126	2	kn	ORG
ejpam-6046	126	3	kn	ORG
ejpam-6046	126	4	1	CARDINAL
ejpam-6046	126	5	2	CARDINAL
ejpam-6046	127	1	kn	PERSON
ejpam-6046	127	2	i.	PERSON
ejpam-6046	129	1	vi	PERSON
ejpam-6046	129	2	∈	ORG
ejpam-6046	130	1	k5	ORG
ejpam-6046	130	2	6	CARDINAL
ejpam-6046	131	1	v1 v2 v3v4 v5 k5	PERSON
ejpam-6046	131	2	1,2	CARDINAL
ejpam-6046	131	3	3e 1	CARDINAL
ejpam-6046	131	4	4	CARDINAL
ejpam-6046	131	5	2	CARDINAL
ejpam-6046	131	6	3	CARDINAL
ejpam-6046	131	7	4 e2,5 e3,4 e	QUANTITY
ejpam-6046	131	8	3,5	CARDINAL
ejpam-6046	131	9	4,5	CARDINAL
ejpam-6046	131	10	6	CARDINAL
ejpam-6046	131	11	k5 j. n. ontulan	PERSON
ejpam-6046	131	12	c. m. balingit	PERSON
ejpam-6046	132	1	j. pure	PERSON
ejpam-6046	132	2	18	CARDINAL
ejpam-6046	132	3	2	CARDINAL
ejpam-6046	132	4	2025	CARDINAL
ejpam-6046	132	5	6046 7	DATE
ejpam-6046	132	6	14	CARDINAL
ejpam-6046	133	1	kn	PERSON
ejpam-6046	133	2	n ≥ 2	ORG
ejpam-6046	135	1	∈	ORG
ejpam-6046	136	1	eik	PERSON
ejpam-6046	137	1	̸= ik ̸= j1 ̸=	PERSON
ejpam-6046	142	1	eik	PERSON
ejpam-6046	143	1	̸= ik ̸= j1 ̸=	PERSON
ejpam-6046	144	1	1	CARDINAL
ejpam-6046	145	1	∈	ORG
ejpam-6046	146	1	1 2	DATE
ejpam-6046	146	2	|{i1	ORG
ejpam-6046	148	1	ik	PERSON
ejpam-6046	150	1	jk}|	PERSON
ejpam-6046	150	2	2k	CARDINAL
ejpam-6046	151	1	i1	ORG
ejpam-6046	153	1	ik	PERSON
ejpam-6046	155	1	s.	GPE
ejpam-6046	157	1	ik	PERSON
ejpam-6046	161	1	ik	PERSON
ejpam-6046	162	1	i1	ORG
ejpam-6046	164	1	ik	PERSON
ejpam-6046	165	1	1 ep	QUANTITY
ejpam-6046	165	2	s.	GPE
ejpam-6046	165	3	k = n 2	PERSON
ejpam-6046	165	4	|{i1	ORG
ejpam-6046	166	1	ik	PERSON
ejpam-6046	168	1	jk}|	PERSON
ejpam-6046	168	2	2k	CARDINAL
ejpam-6046	169	1	|{i1	ORG
ejpam-6046	171	1	ik	PERSON
ejpam-6046	173	1	jk}|	PERSON
ejpam-6046	176	1	i1	ORG
ejpam-6046	176	2	ik	PERSON
ejpam-6046	178	1	1	CARDINAL
ejpam-6046	178	2	s. hence	GPE
ejpam-6046	178	3	kn	PERSON
ejpam-6046	181	1	2	CARDINAL
ejpam-6046	181	2	|{i1	ORG
ejpam-6046	181	3	ik	PERSON
ejpam-6046	182	1	jk}| =	PERSON
ejpam-6046	182	2	2k	CARDINAL
ejpam-6046	182	3	two	CARDINAL
ejpam-6046	183	1	1	CARDINAL
ejpam-6046	184	1	2	CARDINAL
ejpam-6046	184	2	|{i1	ORG
ejpam-6046	185	1	ik	PERSON
ejpam-6046	187	1	jk}| =	PERSON
ejpam-6046	187	2	2k ≤ n − 2	QUANTITY
ejpam-6046	191	1	eik	PERSON
ejpam-6046	194	1	s. therefore	PERSON
ejpam-6046	194	2	kn	PERSON
ejpam-6046	194	3	i2	ORG
ejpam-6046	195	1	4	CARDINAL
ejpam-6046	195	2	n ≥ 2	ORG
ejpam-6046	196	1	k =	PERSON
ejpam-6046	196	2	2	CARDINAL
ejpam-6046	198	1	3	CARDINAL
ejpam-6046	198	2	kn	PERSON
ejpam-6046	198	3	2	CARDINAL
ejpam-6046	198	4	i2	ORG
ejpam-6046	198	5	j2}	PERSON
ejpam-6046	199	1	{ik	PERSON
ejpam-6046	200	1	2	CARDINAL
ejpam-6046	200	2	2 2	DATE
ejpam-6046	200	3	2	CARDINAL
ejpam-6046	202	1	2k + 2 2	QUANTITY
ejpam-6046	202	2	2	CARDINAL
ejpam-6046	202	3	2k + 2	DATE
ejpam-6046	203	1	2k	CARDINAL
ejpam-6046	203	2	0	CARDINAL
ejpam-6046	203	3	1	CARDINAL
ejpam-6046	203	4	2 2	DATE
ejpam-6046	203	5	2− 2 2	DATE
ejpam-6046	203	6	2k + 2 2	QUANTITY
ejpam-6046	205	1	2k(n− 2k	CARDINAL
ejpam-6046	208	1	j. n. ontulan	PERSON
ejpam-6046	208	2	c. m. balingit	PERSON
ejpam-6046	209	1	j. pure	PERSON
ejpam-6046	209	2	18	CARDINAL
ejpam-6046	209	3	2	CARDINAL
ejpam-6046	209	4	2025	CARDINAL
ejpam-6046	209	5	6046 8	DATE
ejpam-6046	211	1	4	CARDINAL
ejpam-6046	211	2	k5	ORG
ejpam-6046	211	3	6	CARDINAL
ejpam-6046	212	1	e1,2, e1,3, e1,4	ORG
ejpam-6046	212	2	e1,5	ORG
ejpam-6046	212	3	e2,3	ORG
ejpam-6046	212	4	e2,4	ORG
ejpam-6046	213	1	k5	ORG
ejpam-6046	213	2	e1,3	ORG
ejpam-6046	213	3	e1,3	ORG
ejpam-6046	213	4	e1,3	ORG
ejpam-6046	213	5	e4,5	GPE
ejpam-6046	213	6	e1,4	GPE
ejpam-6046	213	7	e1,4	GPE
ejpam-6046	213	8	e1,4	GPE
ejpam-6046	213	9	e1,5	ORG
ejpam-6046	213	10	e1,5	ORG
ejpam-6046	213	11	e1,5	ORG
ejpam-6046	213	12	e2,3	ORG
ejpam-6046	213	13	e4,5	GPE
ejpam-6046	214	1	2	CARDINAL
ejpam-6046	214	2	2	CARDINAL
ejpam-6046	214	3	5	CARDINAL
ejpam-6046	214	4	22	CARDINAL
ejpam-6046	214	5	2	CARDINAL
ejpam-6046	215	1	15	CARDINAL
ejpam-6046	215	2	2	CARDINAL
ejpam-6046	216	1	2	CARDINAL
ejpam-6046	217	1	⊆	CARDINAL
ejpam-6046	217	2	1	CARDINAL
ejpam-6046	218	1	τeid(k4	PRODUCT
ejpam-6046	220	1	e1,2, e1,4	ORG
ejpam-6046	220	2	e1,3	ORG
ejpam-6046	220	3	e2,3	ORG
ejpam-6046	220	4	e1,4	GPE
ejpam-6046	220	5	e1,3	ORG
ejpam-6046	220	6	τeid(k4	PRODUCT
ejpam-6046	221	1	e1,4	GPE
ejpam-6046	221	2	e1,3	ORG
ejpam-6046	221	3	e1,4	GPE
ejpam-6046	221	4	e1,3	ORG
ejpam-6046	221	5	e1,4	GPE
ejpam-6046	221	6	e2,3	ORG
ejpam-6046	221	7	e1,3	ORG
ejpam-6046	222	1	5	CARDINAL
ejpam-6046	223	1	kn	PERSON
ejpam-6046	223	2	n ≥ 5	DATE
ejpam-6046	225	1	∈	ORG
ejpam-6046	225	2	5	CARDINAL
ejpam-6046	226	1	3	CARDINAL
ejpam-6046	226	2	k =	PERSON
ejpam-6046	226	3	2 ⌋ ≥ 3	DATE
ejpam-6046	227	1	k =	PERSON
ejpam-6046	228	1	kn	PERSON
ejpam-6046	229	1	∈	ORG
ejpam-6046	231	1	5	CARDINAL
ejpam-6046	233	1	5	CARDINAL
ejpam-6046	233	2	i1	ORG
ejpam-6046	233	3	j1	ORG
ejpam-6046	233	4	k5	ORG
ejpam-6046	233	5	1	CARDINAL
ejpam-6046	234	1	∈	ORG
ejpam-6046	234	2	∈	ORG
ejpam-6046	235	1	1	CARDINAL
ejpam-6046	235	2	5	CARDINAL
ejpam-6046	236	1	1	CARDINAL
ejpam-6046	237	1	n ≥ 2	ORG
ejpam-6046	238	1	2	CARDINAL
ejpam-6046	238	2	2 8	DATE
ejpam-6046	238	3	3	CARDINAL
ejpam-6046	238	4	4 2	CARDINAL
ejpam-6046	238	5	2	CARDINAL
ejpam-6046	238	6	9	CARDINAL
ejpam-6046	239	1	13	CARDINAL
ejpam-6046	239	2	n ≥ 2	ORG
ejpam-6046	239	3	frn	ORG
ejpam-6046	240	1	j. n. ontulan	PERSON
ejpam-6046	240	2	c. m. balingit	PERSON
ejpam-6046	241	1	j. pure	PERSON
ejpam-6046	241	2	18	CARDINAL
ejpam-6046	241	3	2	CARDINAL
ejpam-6046	241	4	2025	CARDINAL
ejpam-6046	241	5	6046 9	DATE
ejpam-6046	241	6	14	CARDINAL
ejpam-6046	241	7	frn	ORG
ejpam-6046	241	8	n ≥ 2	ORG
ejpam-6046	241	9	i.	PERSON
ejpam-6046	242	1	first	ORDINAL
ejpam-6046	242	2	c3	ORG
ejpam-6046	242	3	second	ORDINAL
ejpam-6046	242	4	c3	ORG
ejpam-6046	242	5	c3 ii	PERSON
ejpam-6046	243	1	e(frn	PERSON
ejpam-6046	244	1	e0,1b	GPE
ejpam-6046	244	2	e0,2a	GPE
ejpam-6046	244	3	e0,2b	ORG
ejpam-6046	244	4	e2a,2b	GPE
ejpam-6046	246	1	ena	GPE
ejpam-6046	247	1	fr3	ORG
ejpam-6046	247	2	7	CARDINAL
ejpam-6046	249	1	e0,2a	GPE
ejpam-6046	249	2	e2a,2b	GPE
ejpam-6046	249	3	7	CARDINAL
ejpam-6046	249	4	fr4	CARDINAL
ejpam-6046	249	5	6	CARDINAL
ejpam-6046	250	1	frn	ORG
ejpam-6046	250	2	n ≥ 2	ORG
ejpam-6046	250	3	⊆	CARDINAL
ejpam-6046	252	1	∈	ORG
ejpam-6046	252	2	one	CARDINAL
ejpam-6046	252	3	i. s1 =	PERSON
ejpam-6046	254	1	ena	PERSON
ejpam-6046	256	1	ena	PERSON
ejpam-6046	256	2	nb	ORG
ejpam-6046	256	3	kb	ORG
ejpam-6046	260	1	ena	PERSON
ejpam-6046	260	2	nb	ORG
ejpam-6046	260	3	kb	ORG
ejpam-6046	263	1	1	CARDINAL
ejpam-6046	264	1	ena	PERSON
ejpam-6046	264	2	nb	ORG
ejpam-6046	265	1	∈	ORG
ejpam-6046	266	1	kb	ORG
ejpam-6046	268	1	1	CARDINAL
ejpam-6046	269	1	∈	ORG
ejpam-6046	271	1	ena	PERSON
ejpam-6046	271	2	nb	ORG
ejpam-6046	271	3	kb	PERSON
ejpam-6046	271	4	kb	ORG
ejpam-6046	271	5	kb	ORG
ejpam-6046	272	1	∈	ORG
ejpam-6046	273	1	∈	ORG
ejpam-6046	274	1	kb	ORG
ejpam-6046	276	1	∈	ORG
ejpam-6046	276	2	frn	ORG
ejpam-6046	277	1	j. n. ontulan	PERSON
ejpam-6046	277	2	c. m. balingit	PERSON
ejpam-6046	278	1	j. pure	PERSON
ejpam-6046	278	2	18	CARDINAL
ejpam-6046	278	3	2	CARDINAL
ejpam-6046	278	4	2025	CARDINAL
ejpam-6046	278	5	6046 10	DATE
ejpam-6046	279	1	⊆	CARDINAL
ejpam-6046	280	1	k ∈	PERSON
ejpam-6046	281	1	two	CARDINAL
ejpam-6046	281	2	kb	ORG
ejpam-6046	282	1	k ∈	PERSON
ejpam-6046	283	1	kb	ORG
ejpam-6046	284	1	kb	ORG
ejpam-6046	284	2	frn	ORG
ejpam-6046	285	1	k, k′ ∈	ORG
ejpam-6046	286	1	∈	ORG
ejpam-6046	286	2	1	CARDINAL
ejpam-6046	287	1	2	CARDINAL
ejpam-6046	288	1	frn	ORG
ejpam-6046	288	2	n ≥ 2, |ide	ORG
ejpam-6046	289	1	2n+ 1	DATE
ejpam-6046	289	2	5	CARDINAL
ejpam-6046	289	3	7	CARDINAL
ejpam-6046	289	4	e0,1b	GPE
ejpam-6046	289	5	e0,2a	GPE
ejpam-6046	289	6	e0,2b	ORG
ejpam-6046	289	7	e2a,2b	GPE
ejpam-6046	289	8	e0,4a	CARDINAL
ejpam-6046	290	1	6	CARDINAL
ejpam-6046	290	2	e0,4a	CARDINAL
ejpam-6046	290	3	e0,1b	GPE
ejpam-6046	291	1	2(4	CARDINAL
ejpam-6046	292	1	+ 1	DATE
ejpam-6046	292	2	9	CARDINAL
ejpam-6046	292	3	7	CARDINAL
ejpam-6046	293	1	frn	ORG
ejpam-6046	295	1	ena	PERSON
ejpam-6046	295	2	nb	ORG
ejpam-6046	296	1	⊆	CARDINAL
ejpam-6046	296	2	i. s ⊆	PERSON
ejpam-6046	297	1	∈	ORG
ejpam-6046	297	2	∈	ORG
ejpam-6046	298	1	kb	ORG
ejpam-6046	298	2	⊆	CARDINAL
ejpam-6046	300	1	⊆	CARDINAL
ejpam-6046	301	1	⊆	CARDINAL
ejpam-6046	302	1	⊆	CARDINAL
ejpam-6046	303	1	∈	ORG
ejpam-6046	304	1	∈	ORG
ejpam-6046	305	1	k ∈	PERSON
ejpam-6046	306	1	kb	ORG
ejpam-6046	309	1	6	CARDINAL
ejpam-6046	310	1	⊆	CARDINAL
ejpam-6046	311	1	k, k′	ORG
ejpam-6046	311	2	∈	ORG
ejpam-6046	312	1	kb	ORG
ejpam-6046	312	2	∈	ORG
ejpam-6046	312	3	e0,k∗b	ORG
ejpam-6046	312	4	6	CARDINAL
ejpam-6046	313	1	⊆	CARDINAL
ejpam-6046	313	2	⊆	CARDINAL
ejpam-6046	313	3	⊆	CARDINAL
ejpam-6046	315	1	3	CARDINAL
ejpam-6046	316	1	frn	ORG
ejpam-6046	316	2	⊆	CARDINAL
ejpam-6046	316	3	n ≥ 2.	ORG
ejpam-6046	318	1	3	CARDINAL
ejpam-6046	319	1	frn	ORG
ejpam-6046	319	2	n ≥ 2	ORG
ejpam-6046	319	3	22n + 2n	DATE
ejpam-6046	320	1	j. n. ontulan	PERSON
ejpam-6046	320	2	c. m. balingit	PERSON
ejpam-6046	321	1	j. pure	PERSON
ejpam-6046	321	2	18	CARDINAL
ejpam-6046	321	3	2	CARDINAL
ejpam-6046	321	4	2025	CARDINAL
ejpam-6046	321	5	6046 11	DATE
ejpam-6046	321	6	14	CARDINAL
ejpam-6046	322	1	7	CARDINAL
ejpam-6046	323	1	6	CARDINAL
ejpam-6046	323	2	bipartite	ORG
ejpam-6046	323	3	10	CARDINAL
ejpam-6046	324	1	14	CARDINAL
ejpam-6046	324	2	bipartite	ORG
ejpam-6046	324	3	two	CARDINAL
ejpam-6046	324	4	two	CARDINAL
ejpam-6046	324	5	∈ va	LOC
ejpam-6046	325	1	bipartite	NORP
ejpam-6046	325	2	graph km	PERSON
ejpam-6046	325	3	two	CARDINAL
ejpam-6046	325	4	i. va(km	PERSON
ejpam-6046	327	1	vma	PERSON
ejpam-6046	328	1	vb(km,	PERSON
ejpam-6046	330	1	j = viavjb	PERSON
ejpam-6046	330	2	∈	PRODUCT
ejpam-6046	331	1	bipartite	NORP
ejpam-6046	331	2	k2,3	ORG
ejpam-6046	331	3	8	CARDINAL
ejpam-6046	332	1	k2,3	ORG
ejpam-6046	332	2	2a	CARDINAL
ejpam-6046	332	3	1	CARDINAL
ejpam-6046	332	4	2b	CARDINAL
ejpam-6046	332	5	1	CARDINAL
ejpam-6046	332	6	3	CARDINAL
ejpam-6046	332	7	3b	CARDINAL
ejpam-6046	332	8	8	CARDINAL
ejpam-6046	332	9	bipartite	NORP
ejpam-6046	332	10	k2,3	ORG
ejpam-6046	332	11	8	CARDINAL
ejpam-6046	333	1	bipartite	NORP
ejpam-6046	336	1	eik	PERSON
ejpam-6046	336	2	= k = min{m	PERSON
ejpam-6046	337	1	̸= ik	PERSON
ejpam-6046	338	1	i1	PERSON
ejpam-6046	340	1	ik ∈	PERSON
ejpam-6046	340	2	1a	CARDINAL
ejpam-6046	341	1	ma	PERSON
ejpam-6046	341	2	j1	ORG
ejpam-6046	343	1	1b	CARDINAL
ejpam-6046	343	2	nb	ORG
ejpam-6046	345	1	1	CARDINAL
ejpam-6046	346	1	= k	PERSON
ejpam-6046	346	2	1a	CARDINAL
ejpam-6046	347	1	ma	PERSON
ejpam-6046	347	2	s. hence	GPE
ejpam-6046	347	3	1a	CARDINAL
ejpam-6046	348	1	ma	PERSON
ejpam-6046	350	1	eca	ORG
ejpam-6046	350	2	∈	ORG
ejpam-6046	350	3	1	CARDINAL
ejpam-6046	350	4	eca	ORG
ejpam-6046	350	5	n. j. n. ontulan	PERSON
ejpam-6046	350	6	c. m. balingit	PERSON
ejpam-6046	351	1	j. pure	PERSON
ejpam-6046	351	2	18	CARDINAL
ejpam-6046	351	3	2	CARDINAL
ejpam-6046	351	4	2025	CARDINAL
ejpam-6046	351	5	6046 12	DATE
ejpam-6046	351	6	14	CARDINAL
ejpam-6046	351	7	k = min{m	PERSON
ejpam-6046	352	1	at least two	CARDINAL
ejpam-6046	352	2	first	ORDINAL
ejpam-6046	353	1	1	CARDINAL
ejpam-6046	356	1	s. hence	GPE
ejpam-6046	356	2	1	CARDINAL
ejpam-6046	358	1	̸= ik	PERSON
ejpam-6046	359	1	1	CARDINAL
ejpam-6046	359	2	9	CARDINAL
ejpam-6046	360	1	bipartite	NORP
ejpam-6046	360	2	graph km	PERSON
ejpam-6046	362	1	1a	CARDINAL
ejpam-6046	362	2	2a	CARDINAL
ejpam-6046	364	1	ma	PERSON
ejpam-6046	364	2	s of km	PRODUCT
ejpam-6046	364	3	one	CARDINAL
ejpam-6046	364	4	1b	CARDINAL
ejpam-6046	366	1	nb	ORG
ejpam-6046	367	1	1a	CARDINAL
ejpam-6046	367	2	1	CARDINAL
ejpam-6046	367	3	2a	CARDINAL
ejpam-6046	369	1	n −m + 1	ORG
ejpam-6046	369	2	ma	PERSON
ejpam-6046	370	1	2	CARDINAL
ejpam-6046	373	1	6	CARDINAL
ejpam-6046	374	1	bipartite	NORP
ejpam-6046	374	2	k2,3	ORG
ejpam-6046	374	3	8	CARDINAL
ejpam-6046	374	4	e1a,1b	GPE
ejpam-6046	374	5	e1a,2b	GPE
ejpam-6046	374	6	e1a,3b	DATE
ejpam-6046	374	7	e2a,2b	GPE
ejpam-6046	375	1	k2,3	ORG
ejpam-6046	375	2	e1a,3b	DATE
ejpam-6046	375	3	e1a,3b	TIME
ejpam-6046	376	1	6	CARDINAL
ejpam-6046	376	2	4	CARDINAL
ejpam-6046	376	3	i. τeid(k1,1	PERSON
ejpam-6046	376	4	2. ii	CARDINAL
ejpam-6046	379	1	k2,2	ORG
ejpam-6046	381	1	10	CARDINAL
ejpam-6046	382	1	bipartite	NORP
ejpam-6046	382	2	k1,n	ORG
ejpam-6046	382	3	n ≥ 2	ORG
ejpam-6046	384	1	⊆	CARDINAL
ejpam-6046	384	2	8	CARDINAL
ejpam-6046	384	3	1	CARDINAL
ejpam-6046	385	1	e(km,n	ORG
ejpam-6046	385	2	τeid(km	PERSON
ejpam-6046	385	3	1	CARDINAL
ejpam-6046	385	4	τeid(km	GPE
ejpam-6046	386	1	11	CARDINAL
ejpam-6046	387	1	bipartite	NORP
ejpam-6046	387	2	2	CARDINAL
ejpam-6046	387	3	τeid(km	GPE
ejpam-6046	387	4	e(km,n	ORG
ejpam-6046	388	1	j. n. ontulan	PERSON
ejpam-6046	388	2	c. m. balingit	PERSON
ejpam-6046	389	1	j. pure	PERSON
ejpam-6046	389	2	18	CARDINAL
ejpam-6046	389	3	2	CARDINAL
ejpam-6046	389	4	2025	CARDINAL
ejpam-6046	389	5	6046 13	DATE
ejpam-6046	389	6	14	CARDINAL
ejpam-6046	390	1	bipartite	NORP
ejpam-6046	390	2	graph km	PERSON
ejpam-6046	390	3	2	CARDINAL
ejpam-6046	395	1	1a	CARDINAL
ejpam-6046	395	2	2a	CARDINAL
ejpam-6046	396	1	ma}	PERSON
ejpam-6046	398	1	jm−1 ∈	PERSON
ejpam-6046	398	2	1b	CARDINAL
ejpam-6046	398	3	2b	CARDINAL
ejpam-6046	399	1	nb	ORG
ejpam-6046	401	1	̸= jm−1.	PERSON
ejpam-6046	403	1	2	CARDINAL
ejpam-6046	403	2	j2 ̸= q ̸=	ORG
ejpam-6046	407	1	τeid(km	GPE
ejpam-6046	407	2	e(km,n	ORG
ejpam-6046	408	1	4	CARDINAL
ejpam-6046	409	1	bipartite	NORP
ejpam-6046	409	2	graph km	PERSON
ejpam-6046	409	3	n)| =  2	ORG
ejpam-6046	409	4	1	CARDINAL
ejpam-6046	409	5	1 4	DATE
ejpam-6046	409	6	2	CARDINAL
ejpam-6046	409	7	2 2n	DATE
ejpam-6046	409	8	1	CARDINAL
ejpam-6046	409	9	2	CARDINAL
ejpam-6046	409	10	n ≥ 3	DATE
ejpam-6046	410	1	central mindanao university	ORG
ejpam-6046	411	1	1	CARDINAL
ejpam-6046	411	2	j yellen	PERSON
ejpam-6046	413	1	crc press	ORG
ejpam-6046	413	2	2nd	ORDINAL
ejpam-6046	413	3	2005	DATE
ejpam-6046	414	1	2	CARDINAL
ejpam-6046	414	2	j.b macaso	PERSON
ejpam-6046	414	3	c.m balingit	PERSON
ejpam-6046	416	1	european journal	ORG
ejpam-6046	416	2	17(2):663–675	CARDINAL
ejpam-6046	416	3	2024	DATE
ejpam-6046	417	1	3	CARDINAL
ejpam-6046	417	2	k.a abdu	PERSON
ejpam-6046	419	1	2018	DATE
ejpam-6046	420	1	4	CARDINAL
ejpam-6046	423	1	bull	ORG
ejpam-6046	423	2	12(3):3273–3279	CARDINAL
ejpam-6046	423	3	2023	CARDINAL
ejpam-6046	424	1	5	CARDINAL
ejpam-6046	426	1	3rd	ORDINAL
ejpam-6046	426	2	2006	DATE
ejpam-6046	427	1	6	CARDINAL
ejpam-6046	427	2	a.f hassan	PERSON
ejpam-6046	427	3	z.i abed	PERSON
ejpam-6046	429	1	1591(1):1–10, 2020	DATE
ejpam-6046	430	1	7	CARDINAL
ejpam-6046	430	2	t.w haynes	PERSON
ejpam-6046	430	3	s.t hedetniemi	PERSON
ejpam-6046	430	4	p.j slater	GPE
ejpam-6046	432	1	marcel dekker	PERSON
ejpam-6046	432	2	inc.	ORG
ejpam-6046	432	3	1998	DATE
ejpam-6046	433	1	j. n. ontulan	PERSON
ejpam-6046	433	2	c. m. balingit	PERSON
ejpam-6046	434	1	j. pure	PERSON
ejpam-6046	434	2	18	CARDINAL
ejpam-6046	434	3	2	CARDINAL
ejpam-6046	434	4	2025	CARDINAL
ejpam-6046	434	5	6046 14 of 14	DATE
ejpam-6046	435	1	8	CARDINAL
ejpam-6046	435	2	c.e leiserson	GPE
ejpam-6046	435	3	r.l rivest	PERSON
ejpam-6046	437	1	3rd	ORDINAL
ejpam-6046	437	2	2009	DATE
ejpam-6046	438	1	9	CARDINAL
ejpam-6046	438	2	l lesniak	PERSON
ejpam-6046	438	3	p zhang	PERSON
ejpam-6046	439	1	crc press	ORG
ejpam-6046	439	2	6th	ORDINAL
ejpam-6046	439	3	2015	DATE
ejpam-6046	440	1	10	CARDINAL
ejpam-6046	440	2	d.a mojdeh	PERSON
ejpam-6046	442	1	2(7):315–320, 2007	DATE
ejpam-6046	443	1	11	CARDINAL
ejpam-6046	445	1	prentice hall, inc.	ORG
ejpam-6046	445	2	2nd	ORDINAL
ejpam-6046	445	3	1966	DATE
ejpam-6046	446	1	12	CARDINAL
ejpam-6046	448	1	allyn	ORG
ejpam-6046	448	2	bacon, inc.	ORG
ejpam-6046	448	3	1966	DATE
ejpam-6046	449	1	13	CARDINAL
ejpam-6046	449	2	c.m balingit	PERSON
ejpam-6046	451	1	asian research journal	ORG
ejpam-6046	451	2	2024	DATE
ejpam-6046	452	1	14	CARDINAL
ejpam-6046	452	2	r.s kumar	PERSON
ejpam-6046	452	3	kannan	GPE
ejpam-6046	452	4	jathavedan	GPE
ejpam-6046	454	1	international journal of combinatorics	ORG
ejpam-6046	454	2	1–12, 2014	DATE