id	sid	eid	entity	type
ejpam-6383	1	1	european journal	ORG
ejpam-6383	1	2	2025	DATE
ejpam-6383	1	3	18	CARDINAL
ejpam-6383	1	4	3	CARDINAL
ejpam-6383	1	5	6383	CARDINAL
ejpam-6383	1	6	1307-5543	DATE
ejpam-6383	1	7	new york	GPE
ejpam-6383	1	8	kaimar jay s. maharajul1	PERSON
ejpam-6383	1	9	javier a. hassan1,2,∗	PERSON
ejpam-6383	1	10	ladznar	GPE
ejpam-6383	1	11	s. laja1	ORG
ejpam-6383	2	1	msu	ORG
ejpam-6383	2	2	2department	TIME
ejpam-6383	2	3	korea university	ORG
ejpam-6383	2	4	seoul	GPE
ejpam-6383	2	5	south korea	GPE
ejpam-6383	6	1	1	CARDINAL
ejpam-6383	6	2	j ∈	PERSON
ejpam-6383	6	3	1	CARDINAL
ejpam-6383	6	4	2	DATE
ejpam-6383	8	1	2	CARDINAL
ejpam-6383	10	1	two	CARDINAL
ejpam-6383	13	1	2020	DATE
ejpam-6383	13	2	05c69	CARDINAL
ejpam-6383	14	1	l-grundy	PERSON
ejpam-6383	14	2	1	CARDINAL
ejpam-6383	14	3	first	ORDINAL
ejpam-6383	14	4	leonhard euler	PERSON
ejpam-6383	14	5	1735	CARDINAL
ejpam-6383	16	1	one	CARDINAL
ejpam-6383	17	1	⊆	CARDINAL
ejpam-6383	18	1	α(g	PERSON
ejpam-6383	18	2	1	CARDINAL
ejpam-6383	20	1	kaimarjaymaharajul@msutawi-tawi.edu.ph	ORG
ejpam-6383	20	2	k. j. maharajul	PERSON
ejpam-6383	20	3	j. a. hassan	PERSON
ejpam-6383	21	1	ladznarlaja@msutawi-tawi.edu.ph	PERSON
ejpam-6383	21	2	l. s. laja	PERSON
ejpam-6383	22	1	1	CARDINAL
ejpam-6383	22	2	2025	CARDINAL
ejpam-6383	23	1	k. maharajul	PERSON
ejpam-6383	23	2	j. a. hassan	PERSON
ejpam-6383	23	3	l. laja	PERSON
ejpam-6383	24	1	j. pure	PERSON
ejpam-6383	24	2	18	CARDINAL
ejpam-6383	24	3	3	CARDINAL
ejpam-6383	24	4	2025	CARDINAL
ejpam-6383	24	5	6383 2	DATE
ejpam-6383	24	6	10	CARDINAL
ejpam-6383	26	1	2022	CARDINAL
ejpam-6383	26	2	j. hassan et al	PERSON
ejpam-6383	27	1	2	CARDINAL
ejpam-6383	28	1	⊆	CARDINAL
ejpam-6383	28	2	w ∈ s.	PERSON
ejpam-6383	31	1	3–11	CARDINAL
ejpam-6383	34	1	two	CARDINAL
ejpam-6383	38	1	2	CARDINAL
ejpam-6383	39	1	two	CARDINAL
ejpam-6383	40	1	α(g	PERSON
ejpam-6383	40	2	α(g	PERSON
ejpam-6383	40	3	two	CARDINAL
ejpam-6383	42	1	2	CARDINAL
ejpam-6383	42	2	3	DATE
ejpam-6383	42	3	k	PERSON
ejpam-6383	44	1	[vi]\ i−1⋃ j=1 n(vj	PERSON
ejpam-6383	45	1	2	CARDINAL
ejpam-6383	45	2	3	DATE
ejpam-6383	45	3	k}	PERSON
ejpam-6383	49	1	two	CARDINAL
ejpam-6383	49	2	s1 ⊕ s2	ORG
ejpam-6383	49	3	s1 ⊕	PERSON
ejpam-6383	54	1	1 or l	CARDINAL
ejpam-6383	55	1	2	CARDINAL
ejpam-6383	55	2	k}	PERSON
ejpam-6383	56	1	k. maharajul	PERSON
ejpam-6383	56	2	j. a. hassan	PERSON
ejpam-6383	56	3	l. laja	PERSON
ejpam-6383	57	1	j. pure	PERSON
ejpam-6383	57	2	18	CARDINAL
ejpam-6383	57	3	3	CARDINAL
ejpam-6383	57	4	2025	CARDINAL
ejpam-6383	57	5	6383 3	DATE
ejpam-6383	57	6	10	CARDINAL
ejpam-6383	58	1	kn	PERSON
ejpam-6383	59	1	⊆	CARDINAL
ejpam-6383	60	1	ω(g	ORG
ejpam-6383	61	1	two	CARDINAL
ejpam-6383	62	1	+ h	GPE
ejpam-6383	63	1	∈	ORG
ejpam-6383	64	1	3	CARDINAL
ejpam-6383	64	2	1	CARDINAL
ejpam-6383	68	1	1	CARDINAL
ejpam-6383	68	2	j ∈	PERSON
ejpam-6383	68	3	1	CARDINAL
ejpam-6383	68	4	2	DATE
ejpam-6383	70	1	2	CARDINAL
ejpam-6383	72	1	1	CARDINAL
ejpam-6383	72	2	1	CARDINAL
ejpam-6383	74	1	1	CARDINAL
ejpam-6383	76	1	2	CARDINAL
ejpam-6383	76	2	2	CARDINAL
ejpam-6383	77	1	2	CARDINAL
ejpam-6383	78	1	2	CARDINAL
ejpam-6383	78	2	1	CARDINAL
ejpam-6383	78	3	4	CARDINAL
ejpam-6383	78	4	k. maharajul	PERSON
ejpam-6383	78	5	j. a. hassan	PERSON
ejpam-6383	78	6	l. laja	PERSON
ejpam-6383	79	1	j. pure	PERSON
ejpam-6383	79	2	18	CARDINAL
ejpam-6383	79	3	3	CARDINAL
ejpam-6383	79	4	2025	CARDINAL
ejpam-6383	79	5	6383 4	DATE
ejpam-6383	79	6	10	CARDINAL
ejpam-6383	81	1	i. αlh(g	PERSON
ejpam-6383	81	2	1 ≤	QUANTITY
ejpam-6383	84	1	i.	PERSON
ejpam-6383	84	2	d̂	GPE
ejpam-6383	84	3	d̂	GPE
ejpam-6383	86	1	∈	ORG
ejpam-6383	86	2	1	CARDINAL
ejpam-6383	88	1	1 ≤	QUANTITY
ejpam-6383	94	1	2	CARDINAL
ejpam-6383	94	2	3	DATE
ejpam-6383	95	1	⊆	CARDINAL
ejpam-6383	95	2	∈	ORG
ejpam-6383	95	3	∅ ̸= ng[vi]\ i−1⋃ j=1 ng[vj	ORG
ejpam-6383	96	1	⊆	CARDINAL
ejpam-6383	96	2	ng(vj	PRODUCT
ejpam-6383	97	1	2	CARDINAL
ejpam-6383	97	2	3	DATE
ejpam-6383	98	1	αlh(g	GPE
ejpam-6383	99	1	1	CARDINAL
ejpam-6383	100	1	1(i	CARDINAL
ejpam-6383	102	1	two	CARDINAL
ejpam-6383	102	2	2	CARDINAL
ejpam-6383	104	1	x3	GPE
ejpam-6383	106	1	4	CARDINAL
ejpam-6383	108	1	ng[x2	GPE
ejpam-6383	108	2	x3	GPE
ejpam-6383	109	1	ng[x2	GPE
ejpam-6383	109	2	ng(xi	TIME
ejpam-6383	109	3	j ∈	PERSON
ejpam-6383	109	4	1	CARDINAL
ejpam-6383	109	5	2	DATE
ejpam-6383	109	6	3	DATE
ejpam-6383	109	7	4	CARDINAL
ejpam-6383	111	1	2	CARDINAL
ejpam-6383	111	2	k. maharajul	PERSON
ejpam-6383	111	3	j. a. hassan	PERSON
ejpam-6383	111	4	l. laja	PERSON
ejpam-6383	112	1	j. pure	PERSON
ejpam-6383	112	2	18	CARDINAL
ejpam-6383	112	3	3	CARDINAL
ejpam-6383	112	4	2025	CARDINAL
ejpam-6383	112	5	6383 5	DATE
ejpam-6383	112	6	10	CARDINAL
ejpam-6383	114	1	x3 x4	PERSON
ejpam-6383	116	1	g′	PERSON
ejpam-6383	116	2	8	CARDINAL
ejpam-6383	117	1	2	CARDINAL
ejpam-6383	123	1	1	CARDINAL
ejpam-6383	123	2	1 2	CARDINAL
ejpam-6383	126	1	1	CARDINAL
ejpam-6383	126	2	2	CARDINAL
ejpam-6383	128	1	nk2	CARDINAL
ejpam-6383	129	1	1	CARDINAL
ejpam-6383	131	1	2	CARDINAL
ejpam-6383	132	1	n ≥ 3	DATE
ejpam-6383	138	1	2	CARDINAL
ejpam-6383	138	2	3	CARDINAL
ejpam-6383	139	1	3	CARDINAL
ejpam-6383	141	1	i=1 nkn(vi	PERSON
ejpam-6383	142	1	2	CARDINAL
ejpam-6383	143	1	2	CARDINAL
ejpam-6383	147	1	k. maharajul	PERSON
ejpam-6383	147	2	j. a. hassan	PERSON
ejpam-6383	147	3	l. laja	PERSON
ejpam-6383	148	1	j. pure	PERSON
ejpam-6383	148	2	18	CARDINAL
ejpam-6383	148	3	3	CARDINAL
ejpam-6383	148	4	2025	CARDINAL
ejpam-6383	148	5	6383 6	DATE
ejpam-6383	148	6	10	CARDINAL
ejpam-6383	149	1	1	CARDINAL
ejpam-6383	151	1	k5	ORG
ejpam-6383	151	2	k5	ORG
ejpam-6383	152	1	x3	GPE
ejpam-6383	152	2	x4	GPE
ejpam-6383	153	1	dk5(xi	GPE
ejpam-6383	153	2	xj	GPE
ejpam-6383	153	3	1	CARDINAL
ejpam-6383	153	4	j ∈	PERSON
ejpam-6383	153	5	1	CARDINAL
ejpam-6383	153	6	2	DATE
ejpam-6383	153	7	3	DATE
ejpam-6383	153	8	4	DATE
ejpam-6383	153	9	5	DATE
ejpam-6383	153	10	k5	ORG
ejpam-6383	153	11	k5	ORG
ejpam-6383	154	1	5	CARDINAL
ejpam-6383	154	2	2	CARDINAL
ejpam-6383	155	1	2	CARDINAL
ejpam-6383	156	1	2	CARDINAL
ejpam-6383	157	1	i.	PERSON
ejpam-6383	159	1	n ≥ 3	DATE
ejpam-6383	159	2	∈	ORG
ejpam-6383	160	1	3	CARDINAL
ejpam-6383	165	1	2	CARDINAL
ejpam-6383	166	1	2(i	CARDINAL
ejpam-6383	168	1	n ≥ 3	DATE
ejpam-6383	168	2	2	CARDINAL
ejpam-6383	173	1	1	CARDINAL
ejpam-6383	173	2	1	CARDINAL
ejpam-6383	174	1	i=1 αlh(k1	PERSON
ejpam-6383	177	1	2	CARDINAL
ejpam-6383	179	1	2s	CARDINAL
ejpam-6383	181	1	1	CARDINAL
ejpam-6383	185	1	two	CARDINAL
ejpam-6383	185	2	first	ORDINAL
ejpam-6383	185	3	2	CARDINAL
ejpam-6383	189	1	1	CARDINAL
ejpam-6383	189	2	l̂	GPE
ejpam-6383	190	1	l̂	GPE
ejpam-6383	190	2	g. k. maharajul	PERSON
ejpam-6383	190	3	j. a. hassan	PERSON
ejpam-6383	190	4	l. laja	PERSON
ejpam-6383	191	1	j. pure	PERSON
ejpam-6383	191	2	18	CARDINAL
ejpam-6383	191	3	3	CARDINAL
ejpam-6383	191	4	2025	CARDINAL
ejpam-6383	191	5	6383 7	DATE
ejpam-6383	191	6	10	CARDINAL
ejpam-6383	193	1	l-grundy	PERSON
ejpam-6383	193	2	l̂	GPE
ejpam-6383	193	3	l-grundy	PERSON
ejpam-6383	193	4	l-grundy	ORG
ejpam-6383	193	5	l̂	GPE
ejpam-6383	193	6	g. theorem 4	ORG
ejpam-6383	194	1	2]let	CARDINAL
ejpam-6383	195	1	g+h	ORG
ejpam-6383	195	2	g. (ii	PERSON
ejpam-6383	196	1	5	CARDINAL
ejpam-6383	197	1	12	CARDINAL
ejpam-6383	197	2	two	CARDINAL
ejpam-6383	198	1	+ h	GPE
ejpam-6383	200	1	⊕	PERSON
ejpam-6383	200	2	w ∈	PERSON
ejpam-6383	201	1	⊕	PERSON
ejpam-6383	201	2	∈	ORG
ejpam-6383	202	1	6	CARDINAL
ejpam-6383	203	1	two	CARDINAL
ejpam-6383	206	1	∈	ORG
ejpam-6383	208	1	∈	ORG
ejpam-6383	211	1	â ⊆	ORG
ejpam-6383	212	1	â	GPE
ejpam-6383	212	2	4	CARDINAL
ejpam-6383	212	3	5	CARDINAL
ejpam-6383	212	4	k. maharajul	PERSON
ejpam-6383	212	5	j. a. hassan	PERSON
ejpam-6383	212	6	l. laja	PERSON
ejpam-6383	213	1	j. pure	PERSON
ejpam-6383	213	2	18	CARDINAL
ejpam-6383	213	3	3	CARDINAL
ejpam-6383	213	4	2025	CARDINAL
ejpam-6383	213	5	6383 8	DATE
ejpam-6383	214	1	â ⊆	ORG
ejpam-6383	217	1	⊕	PERSON
ejpam-6383	217	2	∈	ORG
ejpam-6383	217	3	5	CARDINAL
ejpam-6383	218	1	4	CARDINAL
ejpam-6383	219	1	4	CARDINAL
ejpam-6383	219	2	5	CARDINAL
ejpam-6383	220	1	l-grundy	PERSON
ejpam-6383	220	2	k. conversely	PERSON
ejpam-6383	221	1	4	DATE
ejpam-6383	221	2	â	GPE
ejpam-6383	226	1	∈	ORG
ejpam-6383	229	1	⊕	PERSON
ejpam-6383	231	1	∈	ORG
ejpam-6383	232	1	12]let	CARDINAL
ejpam-6383	236	1	⊕	PERSON
ejpam-6383	236	2	∈	ORG
ejpam-6383	237	1	8	CARDINAL
ejpam-6383	239	1	r.	NORP
ejpam-6383	239	2	⊕	PERSON
ejpam-6383	239	3	w ∈	PERSON
ejpam-6383	240	1	∈	ORG
ejpam-6383	243	1	b̂ ⊆	ORG
ejpam-6383	244	1	b̂	PERSON
ejpam-6383	244	2	q+	GPE
ejpam-6383	244	3	b̂	PERSON
ejpam-6383	244	4	4	CARDINAL
ejpam-6383	246	1	b̂ ⊆	ORG
ejpam-6383	247	1	k. maharajul	PERSON
ejpam-6383	247	2	j. a. hassan	PERSON
ejpam-6383	247	3	l. laja	PERSON
ejpam-6383	248	1	j. pure	PERSON
ejpam-6383	248	2	18	CARDINAL
ejpam-6383	248	3	3	CARDINAL
ejpam-6383	248	4	2025	CARDINAL
ejpam-6383	248	5	6383 9 of 10	DATE
ejpam-6383	248	6	⊕	PERSON
ejpam-6383	248	7	neighborhhood	CARDINAL
ejpam-6383	248	8	w ∈	PERSON
ejpam-6383	249	1	r. hence	GPE
ejpam-6383	252	1	9	CARDINAL
ejpam-6383	255	1	r.	NORP
ejpam-6383	255	2	∈	ORG
ejpam-6383	256	1	1	CARDINAL
ejpam-6383	256	2	6	CARDINAL
ejpam-6383	256	3	8	CARDINAL
ejpam-6383	256	4	9	CARDINAL
ejpam-6383	256	5	2	CARDINAL
ejpam-6383	257	1	two	CARDINAL
ejpam-6383	258	1	2 ≤	MONEY
ejpam-6383	259	1	2	CARDINAL
ejpam-6383	260	1	4.	CARDINAL
ejpam-6383	261	1	two	CARDINAL
ejpam-6383	263	1	mindanao	GPE
ejpam-6383	263	2	korea university	ORG
ejpam-6383	264	1	1	CARDINAL
ejpam-6383	264	2	e. davies	PERSON
ejpam-6383	264	3	m. jenssen	PERSON
ejpam-6383	264	4	w. perkins	PERSON
ejpam-6383	264	5	b. roberts	PERSON
ejpam-6383	265	1	matchings	ORG
ejpam-6383	266	1	london	GPE
ejpam-6383	266	2	96(1):47–66	CARDINAL
ejpam-6383	266	3	2017	DATE
ejpam-6383	267	1	k. maharajul	PERSON
ejpam-6383	267	2	j. a. hassan	PERSON
ejpam-6383	267	3	l. laja	PERSON
ejpam-6383	268	1	j. pure	PERSON
ejpam-6383	268	2	18	CARDINAL
ejpam-6383	268	3	3	CARDINAL
ejpam-6383	268	4	2025	CARDINAL
ejpam-6383	268	5	6383 10	DATE
ejpam-6383	268	6	2	CARDINAL
ejpam-6383	268	7	j. hassan	PERSON
ejpam-6383	268	8	s. canoy jr.	PERSON
ejpam-6383	268	9	a. aradais	PERSON
ejpam-6383	270	1	european journal	ORG
ejpam-6383	270	2	15(2):467–477	ORG
ejpam-6383	270	3	2022	CARDINAL
ejpam-6383	271	1	3	CARDINAL
ejpam-6383	271	2	z. furedi	PERSON
ejpam-6383	273	1	11(4):463–470, 1987	DATE
ejpam-6383	274	1	4	CARDINAL
ejpam-6383	274	2	j. r. griggs	PERSON
ejpam-6383	274	3	c. m. grinstead	PERSON
ejpam-6383	274	4	d. r.	NORP
ejpam-6383	275	1	68:211–220, 1988	DATE
ejpam-6383	276	1	5	CARDINAL
ejpam-6383	276	2	j. hassan	PERSON
ejpam-6383	276	3	m. langamin	PERSON
ejpam-6383	276	4	a. laja	PERSON
ejpam-6383	276	5	b. amiruddin	PERSON
ejpam-6383	276	6	e. ahmad	PERSON
ejpam-6383	276	7	j. manditong	PERSON
ejpam-6383	278	1	european journal	ORG
ejpam-6383	278	2	17(2):725–735	DATE
ejpam-6383	278	3	2024	DATE
ejpam-6383	279	1	6	CARDINAL
ejpam-6383	279	2	s. kaida	PERSON
ejpam-6383	279	3	k. j. maharajul	PERSON
ejpam-6383	279	4	j. hassan	PERSON
ejpam-6383	279	5	l. laja	PERSON
ejpam-6383	279	6	a. lintasan	PERSON
ejpam-6383	279	7	a. pablo	PERSON
ejpam-6383	281	1	european journal	ORG
ejpam-6383	281	2	17(1):435–444	CARDINAL
ejpam-6383	281	3	2024	DATE
ejpam-6383	282	1	7	CARDINAL
ejpam-6383	282	2	w. staton	PERSON
ejpam-6383	284	1	57:245–251	CARDINAL
ejpam-6383	284	2	1985	DATE
ejpam-6383	285	1	8	CARDINAL
ejpam-6383	285	2	d. g. c. horrocks	PERSON
ejpam-6383	287	1	australasian journal of combinatorics	ORG
ejpam-6383	287	2	22:105–116	CARDINAL
ejpam-6383	287	3	2000	DATE
ejpam-6383	288	1	9	CARDINAL
ejpam-6383	288	2	m. jou	PERSON
ejpam-6383	288	3	g. chang	PERSON
ejpam-6383	290	1	taiwanese	NORP
ejpam-6383	290	2	4(4):685–695	CARDINAL
ejpam-6383	290	3	2000	DATE
ejpam-6383	291	1	10	CARDINAL
ejpam-6383	291	2	h. s. wilf	PERSON
ejpam-6383	293	1	siam	GPE
ejpam-6383	293	2	algebraic	PERSON
ejpam-6383	293	3	1986	DATE
ejpam-6383	294	1	11	CARDINAL
ejpam-6383	294	2	j. zito	PERSON
ejpam-6383	296	1	15(2):207–221, 1991	DATE
ejpam-6383	297	1	12	CARDINAL
ejpam-6383	297	2	j. hassan	PERSON
ejpam-6383	297	3	s. canoy jr.	PERSON
ejpam-6383	298	1	grundy	PERSON
ejpam-6383	298	2	grundy	PERSON
ejpam-6383	299	1	european journal	ORG
ejpam-6383	299	2	16(2):1154–1166	CARDINAL
ejpam-6383	299	3	2023	CARDINAL