id	sid	eid	entity	type
ejpam-5943	1	1	european journal	ORG
ejpam-5943	1	2	2025	DATE
ejpam-5943	1	3	18	CARDINAL
ejpam-5943	1	4	2	CARDINAL
ejpam-5943	1	5	5943	CARDINAL
ejpam-5943	1	6	1307-5543	DATE
ejpam-5943	1	7	new york	GPE
ejpam-5943	1	8	lysandra a. toladro1,∗	PERSON
ejpam-5943	1	9	isagani s. cabahug	PERSON
ejpam-5943	1	10	jr.2 1	ORG
ejpam-5943	1	11	central mindanao university	ORG
ejpam-5943	1	12	bukidnon	GPE
ejpam-5943	1	13	8710	CARDINAL
ejpam-5943	1	14	philippines	GPE
ejpam-5943	5	1	bipartite	ORG
ejpam-5943	6	1	2020	DATE
ejpam-5943	6	2	91d30	CARDINAL
ejpam-5943	6	3	1	CARDINAL
ejpam-5943	8	1	one	CARDINAL
ejpam-5943	12	1	linton freeman	PERSON
ejpam-5943	12	2	1976	DATE
ejpam-5943	12	3	1	CARDINAL
ejpam-5943	13	1	freeman	ORG
ejpam-5943	13	2	1970	DATE
ejpam-5943	16	1	https://doi.org/10.29020/nybg.ejpam.v18i2.5943	PERSON
ejpam-5943	16	2	isaganicabahugjr@cmu.edu.ph (i. cabahug, jr.	ORG
ejpam-5943	17	1	1	CARDINAL
ejpam-5943	17	2	2025	CARDINAL
ejpam-5943	18	1	i. cabahug / eur	PERSON
ejpam-5943	19	1	j. pure	PERSON
ejpam-5943	19	2	18	CARDINAL
ejpam-5943	19	3	2	CARDINAL
ejpam-5943	19	4	2025	CARDINAL
ejpam-5943	19	5	5943 2	DATE
ejpam-5943	19	6	13	CARDINAL
ejpam-5943	20	1	2015	DATE
ejpam-5943	20	2	freeman	ORG
ejpam-5943	21	1	1	CARDINAL
ejpam-5943	21	2	2	CARDINAL
ejpam-5943	22	1	zhao et al	PERSON
ejpam-5943	23	1	2	CARDINAL
ejpam-5943	26	1	3	CARDINAL
ejpam-5943	26	2	4	CARDINAL
ejpam-5943	27	1	5	CARDINAL
ejpam-5943	27	2	6	CARDINAL
ejpam-5943	29	1	2.	CARDINAL
ejpam-5943	29	2	2.1	CARDINAL
ejpam-5943	30	1	2	CARDINAL
ejpam-5943	35	1	deg v.	PERSON
ejpam-5943	36	1	7	CARDINAL
ejpam-5943	38	1	two	CARDINAL
ejpam-5943	39	1	n(v	ORG
ejpam-5943	40	1	n(v	ORG
ejpam-5943	40	2	vw	GPE
ejpam-5943	40	3	vw	GPE
ejpam-5943	43	1	1	CARDINAL
ejpam-5943	44	1	two	CARDINAL
ejpam-5943	45	1	0	CARDINAL
ejpam-5943	46	1	nonempty	ORG
ejpam-5943	46	2	one	CARDINAL
ejpam-5943	47	1	two	CARDINAL
ejpam-5943	48	1	u−	ORG
ejpam-5943	49	1	u−	ORG
ejpam-5943	51	1	the graph l. toladro	ORG
ejpam-5943	51	2	i. cabahug / eur	PERSON
ejpam-5943	52	1	j. pure	PERSON
ejpam-5943	52	2	18	CARDINAL
ejpam-5943	52	3	2	CARDINAL
ejpam-5943	52	4	2025	CARDINAL
ejpam-5943	52	5	5943 3	DATE
ejpam-5943	52	6	d(u	PERSON
ejpam-5943	53	1	u−	ORG
ejpam-5943	53	2	d(u	PERSON
ejpam-5943	54	1	1	CARDINAL
ejpam-5943	54	2	1	CARDINAL
ejpam-5943	54	3	1	CARDINAL
ejpam-5943	54	4	2	DATE
ejpam-5943	54	5	1	CARDINAL
ejpam-5943	55	1	3	CARDINAL
ejpam-5943	55	2	1	CARDINAL
ejpam-5943	55	3	2	DATE
ejpam-5943	55	4	1	CARDINAL
ejpam-5943	58	1	n ≥ 2	ORG
ejpam-5943	58	2	kn	PERSON
ejpam-5943	59	1	frn	ORG
ejpam-5943	59	2	8	CARDINAL
ejpam-5943	60	1	bipartite	NORP
ejpam-5943	60	2	two	CARDINAL
ejpam-5943	60	3	two	CARDINAL
ejpam-5943	60	4	∈	PRODUCT
ejpam-5943	63	1	9	CARDINAL
ejpam-5943	64	1	k1,n	ORG
ejpam-5943	64	2	1	CARDINAL
ejpam-5943	64	3	one	CARDINAL
ejpam-5943	64	4	1	CARDINAL
ejpam-5943	64	5	6	CARDINAL
ejpam-5943	65	1	n ≥ 2	DATE
ejpam-5943	65	2	1	CARDINAL
ejpam-5943	66	1	6	CARDINAL
ejpam-5943	67	1	n + 1	PRODUCT
ejpam-5943	67	2	n ≥ 3	DATE
ejpam-5943	68	1	6	CARDINAL
ejpam-5943	69	1	3	CARDINAL
ejpam-5943	70	1	asv	PERSON
ejpam-5943	71	1	1	CARDINAL
ejpam-5943	73	1	vi ∈	PERSON
ejpam-5943	73	2	vertex vi	ORG
ejpam-5943	73	3	•	CARDINAL
ejpam-5943	73	4	•	CARDINAL
ejpam-5943	74	1	l. toladro	PERSON
ejpam-5943	74	2	i. cabahug / eur	PERSON
ejpam-5943	75	1	j. pure	PERSON
ejpam-5943	75	2	18	CARDINAL
ejpam-5943	75	3	2	CARDINAL
ejpam-5943	75	4	2025	CARDINAL
ejpam-5943	75	5	5943 4	DATE
ejpam-5943	75	6	13	CARDINAL
ejpam-5943	75	7	1	CARDINAL
ejpam-5943	76	1	1 + 1 + 1	DATE
ejpam-5943	77	1	5 5	CARDINAL
ejpam-5943	77	2	1	CARDINAL
ejpam-5943	77	3	3.1	CARDINAL
ejpam-5943	77	4	d(2	PERSON
ejpam-5943	77	5	d(1	PERSON
ejpam-5943	77	6	frn	ORG
ejpam-5943	77	7	bipartite	ORG
ejpam-5943	77	8	k1,n	PERSON
ejpam-5943	78	1	1	CARDINAL
ejpam-5943	82	1	n ≥ 2	ORG
ejpam-5943	82	2	1 ≤ i ≤ n	QUANTITY
ejpam-5943	82	3	n(vi	ORG
ejpam-5943	82	4	1 or i	CARDINAL
ejpam-5943	82	5	2n	CARDINAL
ejpam-5943	83	1	n−	ORG
ejpam-5943	83	2	2n	CARDINAL
ejpam-5943	83	3	2 ≤	QUANTITY
ejpam-5943	83	4	i. proof	PERSON
ejpam-5943	86	1	n ≥ 2	ORG
ejpam-5943	87	1	n(vn	ORG
ejpam-5943	88	1	1 + 2 + 3 +	DATE
ejpam-5943	89	1	1 n	QUANTITY
ejpam-5943	90	1	2 ≤	MONEY
ejpam-5943	90	2	1	CARDINAL
ejpam-5943	90	3	i=2	PERSON
ejpam-5943	90	4	n(vi	ORG
ejpam-5943	90	5	i=2	PERSON
ejpam-5943	90	6	n(vi	ORG
ejpam-5943	91	1	n(vi	ORG
ejpam-5943	92	1	1 + 2 +	CARDINAL
ejpam-5943	94	1	1 + 2 +	DATE
ejpam-5943	96	1	1	CARDINAL
ejpam-5943	96	2	n−	ORG
ejpam-5943	96	3	2	CARDINAL
ejpam-5943	96	4	n(vi	ORG
ejpam-5943	96	5	1	CARDINAL
ejpam-5943	97	1	n−	ORG
ejpam-5943	97	2	2n	CARDINAL
ejpam-5943	98	1	l. toladro	ORG
ejpam-5943	98	2	i. cabahug / eur	PERSON
ejpam-5943	99	1	j. pure	PERSON
ejpam-5943	99	2	18	CARDINAL
ejpam-5943	99	3	2	CARDINAL
ejpam-5943	99	4	2025	CARDINAL
ejpam-5943	99	5	5943 5	DATE
ejpam-5943	99	6	13	CARDINAL
ejpam-5943	99	7	n(vi	ORG
ejpam-5943	99	8	1 or i	CARDINAL
ejpam-5943	99	9	2n	CARDINAL
ejpam-5943	100	1	n−	ORG
ejpam-5943	100	2	2n	CARDINAL
ejpam-5943	100	3	2 ≤	QUANTITY
ejpam-5943	100	4	i. ■ theorem 2	ORG
ejpam-5943	106	1	1 ≤ i ≤ n	QUANTITY
ejpam-5943	106	2	ppcn(vi	ORG
ejpam-5943	107	1	4	CARDINAL
ejpam-5943	107	2	1 4n	CARDINAL
ejpam-5943	109	1	first	ORDINAL
ejpam-5943	115	1	1 + 1 + 2 + 2 +	DATE
ejpam-5943	116	1	2	CARDINAL
ejpam-5943	116	2	1	CARDINAL
ejpam-5943	117	1	2	CARDINAL
ejpam-5943	117	2	1 + 2 +	DATE
ejpam-5943	118	1	1	CARDINAL
ejpam-5943	119	1	4	CARDINAL
ejpam-5943	120	1	ppcn(vi	ORG
ejpam-5943	122	1	1 + 1 + 2 + 2 +	DATE
ejpam-5943	123	1	2	CARDINAL
ejpam-5943	123	2	1 2	DATE
ejpam-5943	124	1	2	CARDINAL
ejpam-5943	124	2	1 + 2 +	DATE
ejpam-5943	125	1	1 2	CARDINAL
ejpam-5943	125	2	1 4	DATE
ejpam-5943	126	1	ppcn(vi	ORG
ejpam-5943	126	2	1 4n	CARDINAL
ejpam-5943	127	1	l. toladro	PERSON
ejpam-5943	127	2	i. cabahug / eur	PERSON
ejpam-5943	128	1	j. pure	PERSON
ejpam-5943	128	2	18	CARDINAL
ejpam-5943	128	3	2	CARDINAL
ejpam-5943	128	4	2025	CARDINAL
ejpam-5943	128	5	5943 6	DATE
ejpam-5943	128	6	13	CARDINAL
ejpam-5943	128	7	ppcn(vi	NORP
ejpam-5943	129	1	4	CARDINAL
ejpam-5943	129	2	1 4n	CARDINAL
ejpam-5943	130	1	3	CARDINAL
ejpam-5943	131	1	1 ≤ i ≤ n	QUANTITY
ejpam-5943	131	2	ppkn(vi	NORP
ejpam-5943	131	3	1 n	QUANTITY
ejpam-5943	133	1	1 + 1 +	DATE
ejpam-5943	135	1	1︸	CARDINAL
ejpam-5943	135	2	1	CARDINAL
ejpam-5943	136	1	ppkn(vi	NORP
ejpam-5943	136	2	1 n	CARDINAL
ejpam-5943	137	1	4	CARDINAL
ejpam-5943	138	1	frn	ORG
ejpam-5943	142	1	2n	CARDINAL
ejpam-5943	142	2	1 ≤	QUANTITY
ejpam-5943	142	3	2n 2n+ 1	CARDINAL
ejpam-5943	142	4	2n	CARDINAL
ejpam-5943	143	1	2 2n+ 1	CARDINAL
ejpam-5943	143	2	2	CARDINAL
ejpam-5943	144	1	the center vertex v2n+1	ORG
ejpam-5943	145	1	frn	ORG
ejpam-5943	145	2	2n+ 1	DATE
ejpam-5943	145	3	one	CARDINAL
ejpam-5943	145	4	2n	CARDINAL
ejpam-5943	145	5	2	CARDINAL
ejpam-5943	145	6	1	CARDINAL
ejpam-5943	145	7	2n	CARDINAL
ejpam-5943	146	1	one	CARDINAL
ejpam-5943	146	2	2n	CARDINAL
ejpam-5943	146	3	2n	CARDINAL
ejpam-5943	147	1	1	CARDINAL
ejpam-5943	148	1	thus,∑ dfrn(vi	PERSON
ejpam-5943	148	2	1 + 1 +	DATE
ejpam-5943	150	1	1︸	CARDINAL
ejpam-5943	150	2	2n	CARDINAL
ejpam-5943	150	3	2n	CARDINAL
ejpam-5943	151	1	2n	CARDINAL
ejpam-5943	152	1	l. toladro	PERSON
ejpam-5943	152	2	i. cabahug / eur	PERSON
ejpam-5943	153	1	j. pure	PERSON
ejpam-5943	153	2	18	CARDINAL
ejpam-5943	153	3	2	CARDINAL
ejpam-5943	153	4	2025	CARDINAL
ejpam-5943	153	5	5943 7	DATE
ejpam-5943	153	6	13	CARDINAL
ejpam-5943	153	7	2	CARDINAL
ejpam-5943	154	1	2	CARDINAL
ejpam-5943	154	2	= d(v1, v2n+1	PERSON
ejpam-5943	155	1	+ d(v1	PERSON
ejpam-5943	157	1	d(v1, v2n+1	PERSON
ejpam-5943	157	2	d(v1	PERSON
ejpam-5943	157	3	2	CARDINAL
ejpam-5943	157	4	2	CARDINAL
ejpam-5943	158	1	2 + 2 +	DATE
ejpam-5943	159	1	2︸	CARDINAL
ejpam-5943	159	2	2n-2	CARDINAL
ejpam-5943	159	3	2(2n−	CARDINAL
ejpam-5943	160	1	4n− 4	DATE
ejpam-5943	160	2	∑ dfrn(v1	PERSON
ejpam-5943	160	3	1 + 1 + 2 + 2 +	DATE
ejpam-5943	161	1	2︸	CARDINAL
ejpam-5943	161	2	2n-2	CARDINAL
ejpam-5943	161	3	2 +	DATE
ejpam-5943	162	1	2	CARDINAL
ejpam-5943	163	1	2 2n+ 1	CARDINAL
ejpam-5943	165	1	2n 2n+ 1	CARDINAL
ejpam-5943	165	2	2n	CARDINAL
ejpam-5943	166	1	2 2n+ 1	CARDINAL
ejpam-5943	166	2	2	CARDINAL
ejpam-5943	166	3	5	CARDINAL
ejpam-5943	171	1	1 ≤	QUANTITY
ejpam-5943	171	2	ppf	GPE
ejpam-5943	171	3	n(vi	ORG
ejpam-5943	171	4	2	CARDINAL
ejpam-5943	171	5	2	CARDINAL
ejpam-5943	171	6	3	CARDINAL
ejpam-5943	171	7	3	CARDINAL
ejpam-5943	174	1	three	CARDINAL
ejpam-5943	175	1	1	CARDINAL
ejpam-5943	175	2	n. l. toladro	PERSON
ejpam-5943	175	3	i. cabahug / eur	PERSON
ejpam-5943	176	1	j. pure	PERSON
ejpam-5943	176	2	18	CARDINAL
ejpam-5943	176	3	2	CARDINAL
ejpam-5943	176	4	2025	CARDINAL
ejpam-5943	176	5	5943 8 of 13	DATE
ejpam-5943	176	6	one	CARDINAL
ejpam-5943	177	1	1	CARDINAL
ejpam-5943	178	1	n(vi	ORG
ejpam-5943	178	2	1 + 1 +	DATE
ejpam-5943	180	1	1︸	CARDINAL
ejpam-5943	180	2	ppf n(vi	GPE
ejpam-5943	180	3	2	CARDINAL
ejpam-5943	180	4	2	CARDINAL
ejpam-5943	180	5	2	CARDINAL
ejpam-5943	180	6	only two	CARDINAL
ejpam-5943	180	7	2	CARDINAL
ejpam-5943	180	8	1	CARDINAL
ejpam-5943	182	1	= d(v1	PERSON
ejpam-5943	184	1	d(v1, v2	PERSON
ejpam-5943	184	2	1	CARDINAL
ejpam-5943	184	3	d(v1	PERSON
ejpam-5943	184	4	2	CARDINAL
ejpam-5943	184	5	2	CARDINAL
ejpam-5943	185	1	1	CARDINAL
ejpam-5943	186	1	2 + 2 +	DATE
ejpam-5943	187	1	2︸	CARDINAL
ejpam-5943	187	2	2(n− 2	ORG
ejpam-5943	188	1	4	CARDINAL
ejpam-5943	189	1	∑ dfn(v1	PERSON
ejpam-5943	190	1	1 + 1 + (	DATE
ejpam-5943	190	2	4	CARDINAL
ejpam-5943	190	3	2 +	DATE
ejpam-5943	190	4	4	CARDINAL
ejpam-5943	191	1	2	DATE
ejpam-5943	192	1	ppf n(vi	GPE
ejpam-5943	193	1	2	CARDINAL
ejpam-5943	193	2	3	CARDINAL
ejpam-5943	193	3	3	CARDINAL
ejpam-5943	193	4	v2 ∈	PERSON
ejpam-5943	198	1	2	CARDINAL
ejpam-5943	198	2	1	CARDINAL
ejpam-5943	198	3	3	DATE
ejpam-5943	198	4	1	CARDINAL
ejpam-5943	199	1	2 + 2 +	DATE
ejpam-5943	200	1	2︸	CARDINAL
ejpam-5943	200	2	2(n− 3	ORG
ejpam-5943	201	1	6	CARDINAL
ejpam-5943	201	2	∑ df	GPE
ejpam-5943	201	3	n(v2	DATE
ejpam-5943	204	1	2︸	CARDINAL
ejpam-5943	204	2	3 + (2n−	DATE
ejpam-5943	204	3	6	CARDINAL
ejpam-5943	205	1	3	CARDINAL
ejpam-5943	205	2	l. toladro	ORG
ejpam-5943	205	3	i. cabahug / eur	PERSON
ejpam-5943	206	1	j. pure	PERSON
ejpam-5943	206	2	18	CARDINAL
ejpam-5943	206	3	2	CARDINAL
ejpam-5943	206	4	2025	CARDINAL
ejpam-5943	206	5	5943 9	DATE
ejpam-5943	206	6	13	CARDINAL
ejpam-5943	206	7	n(vi	ORG
ejpam-5943	207	1	3	CARDINAL
ejpam-5943	208	1	ppf n(vi	GPE
ejpam-5943	208	2	2	CARDINAL
ejpam-5943	208	3	2	CARDINAL
ejpam-5943	208	4	3	CARDINAL
ejpam-5943	208	5	3	CARDINAL
ejpam-5943	209	1	6	CARDINAL
ejpam-5943	214	1	1 ≤	QUANTITY
ejpam-5943	214	2	ppwn(vi	PERSON
ejpam-5943	215	1	3	CARDINAL
ejpam-5943	215	2	3	CARDINAL
ejpam-5943	220	1	1	CARDINAL
ejpam-5943	221	1	vi = vn+1	PERSON
ejpam-5943	222	1	one	CARDINAL
ejpam-5943	222	2	1	CARDINAL
ejpam-5943	222	3	1	CARDINAL
ejpam-5943	224	1	thus,∑ dwn(vi	DATE
ejpam-5943	225	1	1 + 1 +	DATE
ejpam-5943	227	1	1︸	CARDINAL
ejpam-5943	228	1	2	CARDINAL
ejpam-5943	228	2	3	CARDINAL
ejpam-5943	229	1	vi	PERSON
ejpam-5943	231	1	1 ≤ i ≤ n	QUANTITY
ejpam-5943	231	2	1	CARDINAL
ejpam-5943	231	3	two	CARDINAL
ejpam-5943	231	4	1	CARDINAL
ejpam-5943	232	1	l. toladro	GPE
ejpam-5943	232	2	i. cabahug / eur	PERSON
ejpam-5943	233	1	j. pure	PERSON
ejpam-5943	233	2	18	CARDINAL
ejpam-5943	233	3	2	CARDINAL
ejpam-5943	233	4	2025	CARDINAL
ejpam-5943	233	5	5943 10	DATE
ejpam-5943	233	6	13	CARDINAL
ejpam-5943	233	7	2	CARDINAL
ejpam-5943	234	1	d(vi	PRODUCT
ejpam-5943	234	2	+ d(vi	DATE
ejpam-5943	236	1	3	CARDINAL
ejpam-5943	236	2	1	CARDINAL
ejpam-5943	236	3	d(vi	PRODUCT
ejpam-5943	236	4	d(vi	PRODUCT
ejpam-5943	236	5	d(vi	ORG
ejpam-5943	237	1	3	CARDINAL
ejpam-5943	237	2	2	CARDINAL
ejpam-5943	238	1	1 + 1 + 1 + 2 + 2 +	DATE
ejpam-5943	239	1	2︸	CARDINAL
ejpam-5943	239	2	3 +	DATE
ejpam-5943	240	1	6	CARDINAL
ejpam-5943	240	2	3	CARDINAL
ejpam-5943	241	1	3	CARDINAL
ejpam-5943	243	1	3	CARDINAL
ejpam-5943	243	2	3	CARDINAL
ejpam-5943	244	1	bipartite km	PRODUCT
ejpam-5943	244	2	1 ≤	QUANTITY
ejpam-5943	245	1	ppkm	PERSON
ejpam-5943	245	2	n(vi	ORG
ejpam-5943	245	3	m+	CARDINAL
ejpam-5943	245	4	2	CARDINAL
ejpam-5943	245	5	m. proof	PERSON
ejpam-5943	246	1	bipartite	ORG
ejpam-5943	246	2	two	CARDINAL
ejpam-5943	246	3	two	CARDINAL
ejpam-5943	247	1	1	CARDINAL
ejpam-5943	247	2	dkm	PERSON
ejpam-5943	247	3	n(vi	ORG
ejpam-5943	247	4	1≤q≤n d(vi	CARDINAL
ejpam-5943	248	1	l. toladro	PERSON
ejpam-5943	248	2	i. cabahug / eur	PERSON
ejpam-5943	249	1	j. pure	PERSON
ejpam-5943	249	2	18	CARDINAL
ejpam-5943	249	3	2	CARDINAL
ejpam-5943	249	4	2025	CARDINAL
ejpam-5943	249	5	5943 11	DATE
ejpam-5943	249	6	13	CARDINAL
ejpam-5943	249	7	1≤q≤n d(vi	CARDINAL
ejpam-5943	249	8	1 + 1 +	DATE
ejpam-5943	251	1	1︸	CARDINAL
ejpam-5943	251	2	2 + 2 +	DATE
ejpam-5943	252	1	2︸	CARDINAL
ejpam-5943	252	2	2(m− 1	DATE
ejpam-5943	253	1	2m− 2	DATE
ejpam-5943	254	1	dkm	PERSON
ejpam-5943	254	2	n(vi	ORG
ejpam-5943	256	1	2m− 2	DATE
ejpam-5943	257	1	ppkm	GPE
ejpam-5943	257	2	n(vm	ORG
ejpam-5943	259	1	2m−	CARDINAL
ejpam-5943	260	1	2	CARDINAL
ejpam-5943	260	2	dkm	PERSON
ejpam-5943	260	3	n(vi	ORG
ejpam-5943	260	4	1≤k≤m d(vi	DATE
ejpam-5943	261	1	1 + 1 +	DATE
ejpam-5943	263	1	1︸	CARDINAL
ejpam-5943	263	2	2 + 2 +	DATE
ejpam-5943	264	1	2︸	CARDINAL
ejpam-5943	264	2	2(n− 1	ORG
ejpam-5943	265	1	2	CARDINAL
ejpam-5943	266	1	dkm	PERSON
ejpam-5943	266	2	n(vi	ORG
ejpam-5943	266	3	vj	ORG
ejpam-5943	266	4	m+	CARDINAL
ejpam-5943	266	5	2	CARDINAL
ejpam-5943	267	1	l. toladro	PERSON
ejpam-5943	267	2	i. cabahug / eur	PERSON
ejpam-5943	268	1	j. pure	PERSON
ejpam-5943	268	2	18	CARDINAL
ejpam-5943	268	3	2	CARDINAL
ejpam-5943	268	4	2025	CARDINAL
ejpam-5943	268	5	5943 12	DATE
ejpam-5943	268	6	13	CARDINAL
ejpam-5943	268	7	ppkm	GPE
ejpam-5943	268	8	n(vn	ORG
ejpam-5943	269	1	m+	CARDINAL
ejpam-5943	269	2	2	CARDINAL
ejpam-5943	270	1	ppkm	GPE
ejpam-5943	270	2	n(vi	ORG
ejpam-5943	271	1	m+	CARDINAL
ejpam-5943	271	2	2	CARDINAL
ejpam-5943	271	3	m. ■ theorem	PERSON
ejpam-5943	272	1	k1,n	ORG
ejpam-5943	275	1	1 ≤	QUANTITY
ejpam-5943	276	1	1 n+ 1	CARDINAL
ejpam-5943	276	2	1	CARDINAL
ejpam-5943	277	1	first	ORDINAL
ejpam-5943	277	2	one	CARDINAL
ejpam-5943	277	3	k1,n	GPE
ejpam-5943	277	4	d(vi	PRODUCT
ejpam-5943	277	5	1	CARDINAL
ejpam-5943	277	6	j ̸= n+ 1	PERSON
ejpam-5943	283	1	1︸	CARDINAL
ejpam-5943	284	1	1	CARDINAL
ejpam-5943	285	1	1 + 2 + 2 +	DATE
ejpam-5943	286	1	2︸	CARDINAL
ejpam-5943	286	2	1 + 2(n− 1	DATE
ejpam-5943	287	1	1	CARDINAL
ejpam-5943	288	1	1 n+ 1	CARDINAL
ejpam-5943	290	1	1 n+ 1	CARDINAL
ejpam-5943	290	2	1	CARDINAL
ejpam-5943	290	3	i. cabahug / eur	PERSON
ejpam-5943	291	1	j. pure	PERSON
ejpam-5943	291	2	18	CARDINAL
ejpam-5943	291	3	2	CARDINAL
ejpam-5943	291	4	2025	CARDINAL
ejpam-5943	291	5	5943 13	DATE
ejpam-5943	291	6	13 4	DATE
ejpam-5943	295	1	the department of science and technology-science education institute science and technology regional alliance	ORG
ejpam-5943	297	1	1	CARDINAL
ejpam-5943	299	1	1(3):215–239, 1979	DATE
ejpam-5943	300	1	2	CARDINAL
ejpam-5943	300	2	y zhao	PERSON
ejpam-5943	302	1	5(2):177–188	CARDINAL
ejpam-5943	302	2	2015	DATE
ejpam-5943	303	1	3	CARDINAL
ejpam-5943	304	1	16(4):127–134	DATE
ejpam-5943	304	2	2021	DATE
ejpam-5943	305	1	4	CARDINAL
ejpam-5943	305	2	cm balingit	PERSON
ejpam-5943	305	3	al flores	PERSON
ejpam-5943	305	4	nalosa	ORG
ejpam-5943	305	5	ga	ORG
ejpam-5943	307	1	2023	CARDINAL
ejpam-5943	308	1	5	CARDINAL
ejpam-5943	310	1	addison-wesley publishing company	ORG
ejpam-5943	310	2	redwood city	GPE
ejpam-5943	310	3	1990	DATE
ejpam-5943	311	1	6	CARDINAL
ejpam-5943	313	1	addison-wesly publiching company inc.	PERSON
ejpam-5943	313	2	united states of america	GPE
ejpam-5943	313	3	1969	DATE
ejpam-5943	314	1	7	CARDINAL
ejpam-5943	314	2	l lesniak	PERSON
ejpam-5943	314	3	p zhang	PERSON
ejpam-5943	315	1	new york	GPE
ejpam-5943	315	2	6th	ORDINAL
ejpam-5943	315	3	2015	DATE
ejpam-5943	316	1	8	CARDINAL
ejpam-5943	316	2	k vaithilingan	PERSON
ejpam-5943	318	1	2(6):37–43, 2014	GPE
ejpam-5943	319	1	9	CARDINAL
ejpam-5943	319	2	kannan	GPE
ejpam-5943	319	3	jathavedan	GPE
ejpam-5943	321	1	international journal of combinatorics	ORG
ejpam-5943	321	2	1–12, 2014	DATE