id	sid	eid	entity	type
ejpam-5251	1	1	european journal	ORG
ejpam-5251	2	1	17	CARDINAL
ejpam-5251	2	2	3	CARDINAL
ejpam-5251	2	3	2024	DATE
ejpam-5251	2	4	1737-1750	CARDINAL
ejpam-5251	2	5	1307-5543	DATE
ejpam-5251	2	6	new york	GPE
ejpam-5251	2	7	imelda s. aniversario1	PERSON
ejpam-5251	3	1	ferdinand p.	PERSON
ejpam-5251	4	1	1	CARDINAL
ejpam-5251	4	2	msu-iligan institute of technology	ORG
ejpam-5251	4	3	9200	CARDINAL
ejpam-5251	4	4	iligan city	GPE
ejpam-5251	4	5	philippines	GPE
ejpam-5251	6	1	⊆	CARDINAL
ejpam-5251	6	2	two	CARDINAL
ejpam-5251	6	3	1	CARDINAL
ejpam-5251	6	4	∈	ORG
ejpam-5251	6	5	2	CARDINAL
ejpam-5251	6	6	2	CARDINAL
ejpam-5251	6	7	s.	GPE
ejpam-5251	7	1	γ+ hg(g	ORG
ejpam-5251	9	1	2 ≤	MONEY
ejpam-5251	11	1	2020	DATE
ejpam-5251	11	2	05c69	CARDINAL
ejpam-5251	11	3	2	CARDINAL
ejpam-5251	11	4	1	CARDINAL
ejpam-5251	11	5	2021	CARDINAL
ejpam-5251	11	6	d.	NORP
ejpam-5251	12	1	17	CARDINAL
ejpam-5251	13	1	d.	NORP
ejpam-5251	14	1	3	CARDINAL
ejpam-5251	14	2	2022	CARDINAL
ejpam-5251	14	3	c.j.	ORG
ejpam-5251	14	4	s.r. canoy jr.	PERSON
ejpam-5251	15	1	26	CARDINAL
ejpam-5251	15	2	27	CARDINAL
ejpam-5251	15	3	2023	CARDINAL
ejpam-5251	15	4	d. anusha et al	LOC
ejpam-5251	16	1	4	CARDINAL
ejpam-5251	19	1	6	CARDINAL
ejpam-5251	19	2	11	CARDINAL
ejpam-5251	20	1	two	CARDINAL
ejpam-5251	20	2	∈	ORG
ejpam-5251	21	1	h. ∗corresponding	ORG
ejpam-5251	22	1	catian	NORP
ejpam-5251	22	2	imelda.aniversario@g.msuiit.edu.ph	GPE
ejpam-5251	22	3	i. aniversario	PERSON
ejpam-5251	22	4	ferdinand.jamil@g.msuiit.edu.ph	ORG
ejpam-5251	22	5	f. jamil	PERSON
ejpam-5251	22	6	2024	CARDINAL
ejpam-5251	23	1	d. catian	NORP
ejpam-5251	23	2	i. s. aniversario	PERSON
ejpam-5251	23	3	f. p. jamil	PERSON
ejpam-5251	24	1	j. pure	PERSON
ejpam-5251	24	2	17	CARDINAL
ejpam-5251	24	3	3	CARDINAL
ejpam-5251	24	4	2024	CARDINAL
ejpam-5251	24	5	1737-1750 1738	CARDINAL
ejpam-5251	24	6	v)(w	PERSON
ejpam-5251	24	7	vz ∈ e(h	ORG
ejpam-5251	26	1	two	CARDINAL
ejpam-5251	28	1	1	CARDINAL
ejpam-5251	29	1	ω(g	NORP
ejpam-5251	29	2	⊆	CARDINAL
ejpam-5251	30	1	∈	ORG
ejpam-5251	32	1	⊆	CARDINAL
ejpam-5251	32	2	s.	PERSON
ejpam-5251	33	1	∈	ORG
ejpam-5251	33	2	ig[u	ORG
ejpam-5251	34	1	⊆	CARDINAL
ejpam-5251	35	1	⊆	CARDINAL
ejpam-5251	36	1	g(g	PERSON
ejpam-5251	38	1	1	CARDINAL
ejpam-5251	38	2	2	DATE
ejpam-5251	38	3	7	DATE
ejpam-5251	38	4	8	DATE
ejpam-5251	38	5	10	DATE
ejpam-5251	38	6	12	DATE
ejpam-5251	38	7	15	DATE
ejpam-5251	38	8	16	DATE
ejpam-5251	38	9	18	DATE
ejpam-5251	38	10	19	DATE
ejpam-5251	38	11	28	CARDINAL
ejpam-5251	39	1	⊆	CARDINAL
ejpam-5251	39	2	2	CARDINAL
ejpam-5251	39	3	p2[s]g	ORG
ejpam-5251	39	4	p2[s]g	WORK_OF_ART
ejpam-5251	39	5	w ∈	PERSON
ejpam-5251	39	6	w ∈	PERSON
ejpam-5251	39	7	ig[u	ORG
ejpam-5251	39	8	∈	ORG
ejpam-5251	40	1	2	CARDINAL
ejpam-5251	40	2	2	CARDINAL
ejpam-5251	41	1	2	CARDINAL
ejpam-5251	42	1	2	CARDINAL
ejpam-5251	42	2	2	CARDINAL
ejpam-5251	42	3	2	CARDINAL
ejpam-5251	43	1	2	CARDINAL
ejpam-5251	44	1	2	CARDINAL
ejpam-5251	44	2	15	CARDINAL
ejpam-5251	44	3	18	DATE
ejpam-5251	44	4	19	CARDINAL
ejpam-5251	45	1	n2 g(v	ORG
ejpam-5251	45	2	2	CARDINAL
ejpam-5251	47	1	⊆	CARDINAL
ejpam-5251	48	1	s.	PERSON
ejpam-5251	48	2	⊆	CARDINAL
ejpam-5251	49	1	4	CARDINAL
ejpam-5251	49	2	5	DATE
ejpam-5251	49	3	9	DATE
ejpam-5251	49	4	13	DATE
ejpam-5251	49	5	14	DATE
ejpam-5251	49	6	20–25	CARDINAL
ejpam-5251	50	1	⊆	CARDINAL
ejpam-5251	51	1	d. catian	NORP
ejpam-5251	51	2	i. s. aniversario	PERSON
ejpam-5251	51	3	f. p. jamil	PERSON
ejpam-5251	52	1	j. pure	PERSON
ejpam-5251	52	2	17	CARDINAL
ejpam-5251	52	3	3	CARDINAL
ejpam-5251	52	4	2024	CARDINAL
ejpam-5251	52	5	1737-1750	CARDINAL
ejpam-5251	52	6	2.1	CARDINAL
ejpam-5251	58	1	2 ≤	MONEY
ejpam-5251	64	1	w	GPE
ejpam-5251	65	1	w ∈	PERSON
ejpam-5251	65	2	w	GPE
ejpam-5251	65	3	2	CARDINAL
ejpam-5251	66	1	second	ORDINAL
ejpam-5251	66	2	1	CARDINAL
ejpam-5251	66	3	1	CARDINAL
ejpam-5251	69	1	1	CARDINAL
ejpam-5251	72	1	i.	PERSON
ejpam-5251	73	1	g = kn	PERSON
ejpam-5251	74	1	g ̸= kn	PERSON
ejpam-5251	76	1	g = kn	PERSON
ejpam-5251	76	2	g ̸= kn	PERSON
ejpam-5251	77	1	\s⟩	ORG
ejpam-5251	78	1	first	ORDINAL
ejpam-5251	78	2	⊆	CARDINAL
ejpam-5251	78	3	⊆	CARDINAL
ejpam-5251	79	1	s⟩.	NORP
ejpam-5251	79	2	⊆	CARDINAL
ejpam-5251	80	1	∈	ORG
ejpam-5251	80	2	∈	ORG
ejpam-5251	80	3	∈	ORG
ejpam-5251	81	1	∈	ORG
ejpam-5251	81	2	∈	ORG
ejpam-5251	82	1	∈	ORG
ejpam-5251	82	2	∈	ORG
ejpam-5251	82	3	∈	ORG
ejpam-5251	84	1	⊆	CARDINAL
ejpam-5251	85	1	⊆	CARDINAL
ejpam-5251	86	1	⊆	CARDINAL
ejpam-5251	91	1	g = kn	PERSON
ejpam-5251	92	1	g ̸= kn	PERSON
ejpam-5251	93	1	1	CARDINAL
ejpam-5251	93	2	⊆	CARDINAL
ejpam-5251	95	1	w	GPE
ejpam-5251	96	1	d. catian	NORP
ejpam-5251	96	2	i. s. aniversario	PERSON
ejpam-5251	96	3	f. p. jamil	PERSON
ejpam-5251	97	1	j. pure	PERSON
ejpam-5251	97	2	17	CARDINAL
ejpam-5251	97	3	3	CARDINAL
ejpam-5251	97	4	2024	CARDINAL
ejpam-5251	97	5	1737-1750	CARDINAL
ejpam-5251	97	6	w	ORG
ejpam-5251	98	1	∈	ORG
ejpam-5251	99	1	w	GPE
ejpam-5251	99	2	2	CARDINAL
ejpam-5251	106	1	∈	ORG
ejpam-5251	107	1	at least two	CARDINAL
ejpam-5251	108	1	2	CARDINAL
ejpam-5251	110	1	2	CARDINAL
ejpam-5251	110	2	3	CARDINAL
ejpam-5251	112	1	2	CARDINAL
ejpam-5251	113	1	w ∈	PERSON
ejpam-5251	114	1	w	GPE
ejpam-5251	115	1	2	CARDINAL
ejpam-5251	116	1	2	CARDINAL
ejpam-5251	116	2	w	GPE
ejpam-5251	116	3	⊆	CARDINAL
ejpam-5251	117	1	2	CARDINAL
ejpam-5251	118	1	2	CARDINAL
ejpam-5251	120	1	∈	ORG
ejpam-5251	121	1	∈	ORG
ejpam-5251	123	1	g	GPE
ejpam-5251	123	2	dg(a	GPE
ejpam-5251	123	3	2	CARDINAL
ejpam-5251	124	1	3	CARDINAL
ejpam-5251	124	2	u /∈ ext(g	ORG
ejpam-5251	125	1	two	CARDINAL
ejpam-5251	125	2	1	CARDINAL
ejpam-5251	125	3	3	CARDINAL
ejpam-5251	125	4	w ∈	ORG
ejpam-5251	126	1	z. clearly	PERSON
ejpam-5251	126	2	3	CARDINAL
ejpam-5251	127	1	z.	PERSON
ejpam-5251	127	2	w /∈	GPE
ejpam-5251	129	1	3	CARDINAL
ejpam-5251	130	1	2	CARDINAL
ejpam-5251	131	1	2	CARDINAL
ejpam-5251	133	1	w	GPE
ejpam-5251	133	2	w ̸= z. consequently	PERSON
ejpam-5251	135	1	6	CARDINAL
ejpam-5251	135	2	g ̸= c6	PERSON
ejpam-5251	135	3	at least one	CARDINAL
ejpam-5251	136	1	3	CARDINAL
ejpam-5251	138	1	u ∈ ext(g	ORG
ejpam-5251	139	1	∈ ext(g	ORG
ejpam-5251	139	2	2	CARDINAL
ejpam-5251	140	1		ORG
ejpam-5251	141	1	1	CARDINAL
ejpam-5251	141	2	2	DATE
ejpam-5251	141	3	3	CARDINAL
ejpam-5251	141	4	4k	CARDINAL
ejpam-5251	141	5	4	CARDINAL
ejpam-5251	141	6	d. catian	NORP
ejpam-5251	141	7	i. s. aniversario	PERSON
ejpam-5251	141	8	f. p. jamil	PERSON
ejpam-5251	142	1	j. pure	PERSON
ejpam-5251	142	2	17	CARDINAL
ejpam-5251	142	3	3	CARDINAL
ejpam-5251	142	4	2024	CARDINAL
ejpam-5251	142	5	1737-1750 1741	DATE
ejpam-5251	143	1	3	CARDINAL
ejpam-5251	143	2	3	CARDINAL
ejpam-5251	143	3	4	DATE
ejpam-5251	143	4	5 2	CARDINAL
ejpam-5251	143	5	6 2k + 1	DATE
ejpam-5251	143	6	4	CARDINAL
ejpam-5251	143	7	γ+hg(p	PERSON
ejpam-5251	144	1	6	CARDINAL
ejpam-5251	145	1	1	CARDINAL
ejpam-5251	149	1	1	CARDINAL
ejpam-5251	149	2	2	DATE
ejpam-5251	149	3	3	DATE
ejpam-5251	149	4	k ≥ 1	ORG
ejpam-5251	151	1	2k+1	CARDINAL
ejpam-5251	153	1	3	CARDINAL
ejpam-5251	153	2	two	CARDINAL
ejpam-5251	153	3	xj	GPE
ejpam-5251	153	4	xj+2	LANGUAGE
ejpam-5251	155	1	γ+hg(pn	PRODUCT
ejpam-5251	155	2	2k + 1	DATE
ejpam-5251	156	1	third	ORDINAL
ejpam-5251	156	2	n ̸= 4k+1	LAW
ejpam-5251	157	1	4k	CARDINAL
ejpam-5251	161	1	4k 2	CARDINAL
ejpam-5251	161	2	2k	CARDINAL
ejpam-5251	161	3	2	CARDINAL
ejpam-5251	162	1	4k	CARDINAL
ejpam-5251	164	1	xn−1	GPE
ejpam-5251	165	1	2	CARDINAL
ejpam-5251	166	1	2	CARDINAL
ejpam-5251	170	1	first	ORDINAL
ejpam-5251	170	2	second	ORDINAL
ejpam-5251	171	1	1	CARDINAL
ejpam-5251	172	1	third	ORDINAL
ejpam-5251	172	2	+ 3	DATE
ejpam-5251	172	3	v2, v5	GPE
ejpam-5251	175	1	3	CARDINAL
ejpam-5251	175	2	∈	ORG
ejpam-5251	176	1	∈	ORG
ejpam-5251	176	2	vi ∈ n2	PERSON
ejpam-5251	176	3	∈	PRODUCT
ejpam-5251	177	1	4k	CARDINAL
ejpam-5251	177	2	2 + 1	TIME
ejpam-5251	177	3	2k + 1 ≤ γ+hg(g	MONEY
ejpam-5251	180	1	2k+1	CARDINAL
ejpam-5251	181	1	fourth	ORDINAL
ejpam-5251	181	2	k ≥ 2.	ORG
ejpam-5251	182	1	v2, v5	GPE
ejpam-5251	184	1	vn−3	ORG
ejpam-5251	186	1	4k 2	CARDINAL
ejpam-5251	186	2	2k	CARDINAL
ejpam-5251	186	3	2	CARDINAL
ejpam-5251	187	1	1	CARDINAL
ejpam-5251	188	1	1	CARDINAL
ejpam-5251	190	1	6	CARDINAL
ejpam-5251	191	1	w	GPE
ejpam-5251	191	2	2	CARDINAL
ejpam-5251	193	1	⊆	CARDINAL
ejpam-5251	194	1	w d. catian	NORP
ejpam-5251	194	2	i. s. aniversario	PERSON
ejpam-5251	194	3	f. p. jamil	PERSON
ejpam-5251	195	1	j. pure	PERSON
ejpam-5251	195	2	17	CARDINAL
ejpam-5251	195	3	3	CARDINAL
ejpam-5251	195	4	2024	CARDINAL
ejpam-5251	195	5	1737-1750 1742	DATE
ejpam-5251	196	1	∈	ORG
ejpam-5251	196	2	w	ORG
ejpam-5251	196	3	∈	ORG
ejpam-5251	196	4	w	ORG
ejpam-5251	196	5	n ≥ 3	DATE
ejpam-5251	198	1	s ∩ w ̸=	ORG
ejpam-5251	198	2	⊆	CARDINAL
ejpam-5251	198	3	w ∈ s	PERSON
ejpam-5251	199	1	w ⊆ s	PRODUCT
ejpam-5251	199	2	∈	PERSON
ejpam-5251	200	1	\s ̸=	PERSON
ejpam-5251	200	2	w \s ̸=	ORG
ejpam-5251	200	3	2	CARDINAL
ejpam-5251	201	1	2	CARDINAL
ejpam-5251	201	2	∈	ORG
ejpam-5251	201	3	w	ORG
ejpam-5251	201	4	∈	ORG
ejpam-5251	202	1	w	ORG
ejpam-5251	202	2	w	ORG
ejpam-5251	203	1	2	CARDINAL
ejpam-5251	204	1	2	CARDINAL
ejpam-5251	205	1	n}+ 1	ORG
ejpam-5251	206	1	2	CARDINAL
ejpam-5251	206	2	3	CARDINAL
ejpam-5251	207	1	n ≥ 3 or m ≥ 3	DATE
ejpam-5251	207	2	4	CARDINAL
ejpam-5251	209	1	1 +max{m	MONEY
ejpam-5251	210	1	3	CARDINAL
ejpam-5251	210	2	3	CARDINAL
ejpam-5251	210	3	2 ≤	MONEY
ejpam-5251	213	1	2	CARDINAL
ejpam-5251	213	2	2	CARDINAL
ejpam-5251	213	3	k + 2	ORG
ejpam-5251	214	1	2	CARDINAL
ejpam-5251	214	2	3	CARDINAL
ejpam-5251	214	3	2	CARDINAL
ejpam-5251	214	4	w2i−1,	GPE
ejpam-5251	214	5	z2i	GPE
ejpam-5251	215	1	1	CARDINAL
ejpam-5251	215	2	2	DATE
ejpam-5251	215	3	3	DATE
ejpam-5251	216	1	w1, w2i+1	ORG
ejpam-5251	216	2	z2i	GPE
ejpam-5251	217	1	1	CARDINAL
ejpam-5251	217	2	2	DATE
ejpam-5251	217	3	3	DATE
ejpam-5251	218	1	2	CARDINAL
ejpam-5251	218	2	k	PERSON
ejpam-5251	220	1	3	CARDINAL
ejpam-5251	220	2	g1	ORG
ejpam-5251	220	3	2	CARDINAL
ejpam-5251	220	4	j = 1	PERSON
ejpam-5251	220	5	2	DATE
ejpam-5251	222	1	2	CARDINAL
ejpam-5251	222	2	d. catian	NORP
ejpam-5251	222	3	i. s. aniversario	PERSON
ejpam-5251	222	4	f. p. jamil	PERSON
ejpam-5251	223	1	j. pure	PERSON
ejpam-5251	223	2	17	CARDINAL
ejpam-5251	223	3	3	CARDINAL
ejpam-5251	223	4	2024	CARDINAL
ejpam-5251	223	5	1737-1750 1743	CARDINAL
ejpam-5251	226	1	xa−2	GPE
ejpam-5251	226	2	3	CARDINAL
ejpam-5251	226	3	3	CARDINAL
ejpam-5251	226	4	3	CARDINAL
ejpam-5251	227	1	1	CARDINAL
ejpam-5251	227	2	2	DATE
ejpam-5251	229	1	2	CARDINAL
ejpam-5251	229	2	w2i−1,	GPE
ejpam-5251	229	3	z2i	GPE
ejpam-5251	229	4	xj	GPE
ejpam-5251	229	5	1	CARDINAL
ejpam-5251	229	6	2	DATE
ejpam-5251	229	7	3	DATE
ejpam-5251	230	1	+ 1	DATE
ejpam-5251	230	2	1	CARDINAL
ejpam-5251	230	3	2	DATE
ejpam-5251	232	1	2	CARDINAL
ejpam-5251	232	2	w1, w2i+1	ORG
ejpam-5251	232	3	z2i	GPE
ejpam-5251	232	4	xj	GPE
ejpam-5251	233	1	1	CARDINAL
ejpam-5251	233	2	2	DATE
ejpam-5251	233	3	3	DATE
ejpam-5251	234	1	2	CARDINAL
ejpam-5251	234	2	j = 1	PERSON
ejpam-5251	234	3	2	DATE
ejpam-5251	236	1	2	CARDINAL
ejpam-5251	241	1	3	CARDINAL
ejpam-5251	243	1	4	CARDINAL
ejpam-5251	244	1	⊆	CARDINAL
ejpam-5251	244	2	⊆	CARDINAL
ejpam-5251	244	3	2	CARDINAL
ejpam-5251	244	4	2	CARDINAL
ejpam-5251	244	5	2	CARDINAL
ejpam-5251	244	6	2	CARDINAL
ejpam-5251	244	7	2	CARDINAL
ejpam-5251	245	1	2	CARDINAL
ejpam-5251	245	2	2	CARDINAL
ejpam-5251	245	3	ρ+2pnd	ORG
ejpam-5251	246	1	4	CARDINAL
ejpam-5251	247	1	26	CARDINAL
ejpam-5251	247	2	two	CARDINAL
ejpam-5251	248	1	⊆	CARDINAL
ejpam-5251	249	1	2	CARDINAL
ejpam-5251	249	2	2	CARDINAL
ejpam-5251	249	3	g. proposition 4.	PERSON
ejpam-5251	250	1	⊆	CARDINAL
ejpam-5251	250	2	g+h	ORG
ejpam-5251	250	3	sg ⊆	ORG
ejpam-5251	250	4	⊆	CARDINAL
ejpam-5251	250	5	2	CARDINAL
ejpam-5251	251	1	d. catian	NORP
ejpam-5251	251	2	i. s. aniversario	PERSON
ejpam-5251	251	3	f. p. jamil	PERSON
ejpam-5251	252	1	j. pure	PERSON
ejpam-5251	252	2	17	CARDINAL
ejpam-5251	252	3	3	CARDINAL
ejpam-5251	252	4	2024	CARDINAL
ejpam-5251	252	5	1737-1750 1744	CARDINAL
ejpam-5251	252	6	2	CARDINAL
ejpam-5251	253	1	4	CARDINAL
ejpam-5251	254	1	4	DATE
ejpam-5251	254	2	sg	GPE
ejpam-5251	254	3	⊆	CARDINAL
ejpam-5251	254	4	2	CARDINAL
ejpam-5251	255	1	4	CARDINAL
ejpam-5251	255	2	g+h	ORG
ejpam-5251	256	1	2	CARDINAL
ejpam-5251	258	1	1	CARDINAL
ejpam-5251	259	1	1	CARDINAL
ejpam-5251	259	2	⊆	CARDINAL
ejpam-5251	260	1	2	CARDINAL
ejpam-5251	262	1	⊆	CARDINAL
ejpam-5251	262	2	sg ⊆	ORG
ejpam-5251	262	3	⊆	CARDINAL
ejpam-5251	262	4	one	CARDINAL
ejpam-5251	262	5	2	CARDINAL
ejpam-5251	262	6	g. (ii	PERSON
ejpam-5251	262	7	2	CARDINAL
ejpam-5251	263	1	g+h	ORG
ejpam-5251	266	1	g+h	ORG
ejpam-5251	268	1	s.	PERSON
ejpam-5251	268	2	∈	ORG
ejpam-5251	268	3	sg	GPE
ejpam-5251	268	4	2	CARDINAL
ejpam-5251	268	5	2	CARDINAL
ejpam-5251	269	1	2	CARDINAL
ejpam-5251	269	2	⊆	CARDINAL
ejpam-5251	270	1	∈	ORG
ejpam-5251	270	2	lemma 1	ORG
ejpam-5251	271	1	∈	ORG
ejpam-5251	272	1	2	CARDINAL
ejpam-5251	273	1	2	CARDINAL
ejpam-5251	274	1	g+h	ORG
ejpam-5251	275	1	g+h	PRODUCT
ejpam-5251	276	1	⊆	CARDINAL
ejpam-5251	277	1	tg	ORG
ejpam-5251	278	1	tg	PERSON
ejpam-5251	278	2	4	CARDINAL
ejpam-5251	278	3	tg ⊆	ORG
ejpam-5251	278	4	⊆	CARDINAL
ejpam-5251	280	1	xy ∈	ORG
ejpam-5251	282	1	4	CARDINAL
ejpam-5251	282	2	tg	ORG
ejpam-5251	282	3	2	CARDINAL
ejpam-5251	282	4	tg ⊆	ORG
ejpam-5251	283	1	g+h	ORG
ejpam-5251	284	1	g+h	ORG
ejpam-5251	286	1	1	CARDINAL
ejpam-5251	286	2	⊆	CARDINAL
ejpam-5251	288	1	kp	ORG
ejpam-5251	288	2	sg ⊆	ORG
ejpam-5251	288	3	2	CARDINAL
ejpam-5251	289	1	d. catian	PERSON
ejpam-5251	289	2	i. s. aniversario	PERSON
ejpam-5251	289	3	f. p. jamil	PERSON
ejpam-5251	290	1	j. pure	PERSON
ejpam-5251	290	2	17	CARDINAL
ejpam-5251	290	3	3	CARDINAL
ejpam-5251	290	4	2024	CARDINAL
ejpam-5251	290	5	1737-1750 1745	CARDINAL
ejpam-5251	291	1	+ h	GPE
ejpam-5251	294	1	kp	ORG
ejpam-5251	294	2	kp	ORG
ejpam-5251	296	1	kp	ORG
ejpam-5251	296	2	sg	GPE
ejpam-5251	296	3	2	CARDINAL
ejpam-5251	296	4	sg	GPE
ejpam-5251	296	5	2	CARDINAL
ejpam-5251	296	6	g+h	ORG
ejpam-5251	297	1	6	CARDINAL
ejpam-5251	302	1	⊆	CARDINAL
ejpam-5251	302	2	ρ+2pnd	ORG
ejpam-5251	302	3	⊆	CARDINAL
ejpam-5251	303	1	∈	ORG
ejpam-5251	304	1	xy /∈ e(h	ORG
ejpam-5251	305	1	4	CARDINAL
ejpam-5251	305	2	g+h	ORG
ejpam-5251	307	1	ρ+hg(h	DATE
ejpam-5251	308	1	5	CARDINAL
ejpam-5251	308	2	+ ω(p3	PERSON
ejpam-5251	308	3	6	CARDINAL
ejpam-5251	309	1	5	CARDINAL
ejpam-5251	309	2	5	CARDINAL
ejpam-5251	310	1	27	CARDINAL
ejpam-5251	310	2	two	CARDINAL
ejpam-5251	311	1	⊆	CARDINAL
ejpam-5251	312	1	∪v∈v (g)sv	ORG
ejpam-5251	312	2	⊆	CARDINAL
ejpam-5251	312	3	sv ⊆	ORG
ejpam-5251	312	4	one	CARDINAL
ejpam-5251	312	5	dhw(a	ORG
ejpam-5251	312	6	∃x	ORG
ejpam-5251	312	7	w ∈	PERSON
ejpam-5251	312	8	t ∈ a.	ORG
ejpam-5251	312	9	2	CARDINAL
ejpam-5251	312	10	∈	ORG
ejpam-5251	313	1	5	CARDINAL
ejpam-5251	314	1	5	CARDINAL
ejpam-5251	315	1	two	CARDINAL
ejpam-5251	316	1	⊆	CARDINAL
ejpam-5251	317	1	∪v∈v (g)sv	ORG
ejpam-5251	317	2	⊆	CARDINAL
ejpam-5251	317	3	sv ⊆	ORG
ejpam-5251	317	4	d. catian	NORP
ejpam-5251	317	5	i. s. aniversario	PERSON
ejpam-5251	317	6	f. p. jamil	PERSON
ejpam-5251	318	1	j. pure	PERSON
ejpam-5251	318	2	17	CARDINAL
ejpam-5251	318	3	3	CARDINAL
ejpam-5251	318	4	2024	CARDINAL
ejpam-5251	318	5	1737-1750 1746	DATE
ejpam-5251	318	6	sv	PERSON
ejpam-5251	318	7	2	CARDINAL
ejpam-5251	318	8	∈	ORG
ejpam-5251	320	1	5	CARDINAL
ejpam-5251	320	2	9	CARDINAL
ejpam-5251	320	3	5	CARDINAL
ejpam-5251	320	4	∈	ORG
ejpam-5251	320	5	w ∈ ig+h(u	ORG
ejpam-5251	321	1	w ∈	PERSON
ejpam-5251	322	1	∈	ORG
ejpam-5251	323	1	∈	ORG
ejpam-5251	324	1	w ∈	ORG
ejpam-5251	326	1	two	CARDINAL
ejpam-5251	326	2	n ≥ 2.	ORG
ejpam-5251	329	1	∈	ORG
ejpam-5251	329	2	sv ⊆	ORG
ejpam-5251	329	3	ρ+2pnd	ORG
ejpam-5251	329	4	5	CARDINAL
ejpam-5251	329	5	∪v∈v	PERSON
ejpam-5251	329	6	⊆	CARDINAL
ejpam-5251	329	7	5	CARDINAL
ejpam-5251	329	8	t ⊆ s	DATE
ejpam-5251	329	9	⊆	CARDINAL
ejpam-5251	329	10	2	CARDINAL
ejpam-5251	330	1	sv	ORG
ejpam-5251	330	2	∈	ORG
ejpam-5251	332	1	4	CARDINAL
ejpam-5251	334	1	two	CARDINAL
ejpam-5251	335	1	⊆	CARDINAL
ejpam-5251	335	2	∪v∈v (g)sv	ORG
ejpam-5251	335	3	⊆	CARDINAL
ejpam-5251	335	4	sv ⊆	ORG
ejpam-5251	335	5	2	CARDINAL
ejpam-5251	335	6	sv	PERSON
ejpam-5251	335	7	2	CARDINAL
ejpam-5251	335	8	∈	ORG
ejpam-5251	337	1	5	CARDINAL
ejpam-5251	338	1	∈	ORG
ejpam-5251	339	1	⊆	CARDINAL
ejpam-5251	339	2	2	CARDINAL
ejpam-5251	340	1	∪u∈v (g)\{v}su ) ∪d	ORG
ejpam-5251	340	2	⊆	CARDINAL
ejpam-5251	340	3	t = s.	ORG
ejpam-5251	340	4	sv	ORG
ejpam-5251	340	5	2	CARDINAL
ejpam-5251	342	1	6	CARDINAL
ejpam-5251	343	1	two	CARDINAL
ejpam-5251	347	1	1	CARDINAL
ejpam-5251	347	2	kp	ORG
ejpam-5251	347	3	d. catian	PERSON
ejpam-5251	347	4	i. s. aniversario	PERSON
ejpam-5251	347	5	f. p. jamil	PERSON
ejpam-5251	348	1	j. pure	PERSON
ejpam-5251	348	2	17	CARDINAL
ejpam-5251	348	3	3	CARDINAL
ejpam-5251	348	4	2024	CARDINAL
ejpam-5251	348	5	1737-1750 1747	CARDINAL
ejpam-5251	349	1	∪v∈v (g)sv	ORG
ejpam-5251	349	2	⊆	CARDINAL
ejpam-5251	349	3	sv ⊆	ORG
ejpam-5251	349	4	∈	ORG
ejpam-5251	349	5	sv	ORG
ejpam-5251	349	6	2	CARDINAL
ejpam-5251	349	7	sv	ORG
ejpam-5251	349	8	2	CARDINAL
ejpam-5251	349	9	∈	ORG
ejpam-5251	350	1	∈	ORG
ejpam-5251	353	1	6	CARDINAL
ejpam-5251	353	2	6	CARDINAL
ejpam-5251	354	1	27	CARDINAL
ejpam-5251	355	1	⊆	CARDINAL
ejpam-5251	355	2	⊆	CARDINAL
ejpam-5251	355	3	sx ⊆	ORG
ejpam-5251	355	4	2	CARDINAL
ejpam-5251	356	1	6	CARDINAL
ejpam-5251	358	1	⊆	CARDINAL
ejpam-5251	358	2	⊆	CARDINAL
ejpam-5251	358	3	sx ⊆	ORG
ejpam-5251	358	4	2	CARDINAL
ejpam-5251	359	1	g[h	ORG
ejpam-5251	361	1	6	CARDINAL
ejpam-5251	361	2	g[h	ORG
ejpam-5251	362	1	g[h	ORG
ejpam-5251	363	1	6	CARDINAL
ejpam-5251	363	2	tx	ORG
ejpam-5251	363	3	⊆	PRODUCT
ejpam-5251	363	4	∈	ORG
ejpam-5251	364	1	tx	ORG
ejpam-5251	364	2	g(t	NORP
ejpam-5251	364	3	tx	ORG
ejpam-5251	364	4	2	CARDINAL
ejpam-5251	365	1	c∗ ⊆ c	ORG
ejpam-5251	365	2	⊆	CARDINAL
ejpam-5251	365	3	tx	ORG
ejpam-5251	365	4	⊆	PRODUCT
ejpam-5251	365	5	∈	ORG
ejpam-5251	366	1	t = s. consequently	ORG
ejpam-5251	366	2	sx = tx	ORG
ejpam-5251	366	3	∈	ORG
ejpam-5251	366	4	g(t	NORP
ejpam-5251	366	5	tx	ORG
ejpam-5251	366	6	∈	ORG
ejpam-5251	367	1	g[h	ORG
ejpam-5251	368	1	8	CARDINAL
ejpam-5251	369	1	2	CARDINAL
ejpam-5251	370	1	γ+hg(g	DATE
ejpam-5251	373	1	1748	CARDINAL
ejpam-5251	374	1	⊆	CARDINAL
ejpam-5251	374	2	kp	ORG
ejpam-5251	377	1	γ+hg(g	DATE
ejpam-5251	378	1	⊆	CARDINAL
ejpam-5251	379	1	6	CARDINAL
ejpam-5251	379	2	kp	ORG
ejpam-5251	381	1	|s| ≤ p	FAC
ejpam-5251	381	2	γ+hg(g	DATE
ejpam-5251	383	1	⊆	CARDINAL
ejpam-5251	384	1	6	CARDINAL
ejpam-5251	384	2	kp	ORG
ejpam-5251	384	3	sx	ORG
ejpam-5251	384	4	2	CARDINAL
ejpam-5251	384	5	sx	ORG
ejpam-5251	384	6	2	CARDINAL
ejpam-5251	387	1	⊆	CARDINAL
ejpam-5251	387	2	ρ+2pnd	ORG
ejpam-5251	388	1	kp	ORG
ejpam-5251	391	1	first	ORDINAL
ejpam-5251	391	2	the department of science and technology	ORG
ejpam-5251	391	3	philippines	GPE
ejpam-5251	392	1	first	ORDINAL
ejpam-5251	392	2	1	CARDINAL
ejpam-5251	392	3	jamil	PERSON
ejpam-5251	394	1	utilitas mathematica	PERSON
ejpam-5251	394	2	79	DATE
ejpam-5251	394	3	2009	DATE
ejpam-5251	395	1	2	CARDINAL
ejpam-5251	395	2	f.p. jamil	PERSON
ejpam-5251	395	3	s.r.	PERSON
ejpam-5251	397	1	utilitas mathematica	PERSON
ejpam-5251	397	2	74, 2007	DATE
ejpam-5251	398	1	3	CARDINAL
ejpam-5251	401	1	4	CARDINAL
ejpam-5251	401	2	j. john	PERSON
ejpam-5251	401	3	s. joseph robin	PERSON
ejpam-5251	403	1	boletim da	PERSON
ejpam-5251	403	2	42:1–12	CARDINAL
ejpam-5251	403	3	2024	DATE
ejpam-5251	404	1	5	CARDINAL
ejpam-5251	404	2	natarajan chidambaram	PERSON
ejpam-5251	404	3	venkatakrishnan yanamandram	PERSON
ejpam-5251	406	1	2022	CARDINAL
ejpam-5251	407	1	1749	CARDINAL
ejpam-5251	407	2	6	CARDINAL
ejpam-5251	409	1	methuen co. ltd	ORG
ejpam-5251	409	2	london	GPE
ejpam-5251	409	3	john wiley & sons inc	ORG
ejpam-5251	409	4	new york	GPE
ejpam-5251	409	5	1962	DATE
ejpam-5251	410	1	7	CARDINAL
ejpam-5251	410	2	aleksandra	ORG
ejpam-5251	411	1	197–218	CARDINAL
ejpam-5251	411	2	1 1970	DATE
ejpam-5251	412	1	8	CARDINAL
ejpam-5251	412	2	g. cagaanan	PERSON
ejpam-5251	412	3	s.r. canoy jr.	PERSON
ejpam-5251	413	1	79, 2006	DATE
ejpam-5251	414	1	9	CARDINAL
ejpam-5251	414	2	salasalan	PERSON
ejpam-5251	416	1	european journal	ORG
ejpam-5251	416	2	15(2):342–353	CARDINAL
ejpam-5251	416	3	2022	CARDINAL
ejpam-5251	417	1	10	CARDINAL
ejpam-5251	417	2	g. chartrand	PERSON
ejpam-5251	417	3	f. harary	PERSON
ejpam-5251	417	4	p. zhang	PERSON
ejpam-5251	419	1	39(1):1–6, 2002	DATE
ejpam-5251	420	1	11	CARDINAL
ejpam-5251	420	2	f. harary	PERSON
ejpam-5251	422	1	addison-wesley publishing company	ORG
ejpam-5251	422	2	1991	DATE
ejpam-5251	423	1	12	CARDINAL
ejpam-5251	423	2	f. harary	PERSON
ejpam-5251	425	1	mathl	PERSON
ejpam-5251	426	1	comput	PERSON
ejpam-5251	427	1	17(11):89–95, 1993	DATE
ejpam-5251	428	1	13	CARDINAL
ejpam-5251	428	2	m. henning	PERSON
ejpam-5251	428	3	s. pal	PERSON
ejpam-5251	428	4	d. pradhan	PERSON
ejpam-5251	430	1	2019	DATE
ejpam-5251	431	1	14	CARDINAL
ejpam-5251	431	2	m. henning	PERSON
ejpam-5251	431	3	n. jafari rad	PERSON
ejpam-5251	432	1	2	CARDINAL
ejpam-5251	433	1	combinatorics	ORG
ejpam-5251	433	2	33:1–15	CARDINAL
ejpam-5251	433	3	2017	DATE
ejpam-5251	434	1	15	CARDINAL
ejpam-5251	434	2	jamil	GPE
ejpam-5251	434	3	i.s. aniversario	PERSON
ejpam-5251	434	4	s.r.	PERSON
ejpam-5251	436	1	utilitas mathematica	PERSON
ejpam-5251	436	2	82, 2010	DATE
ejpam-5251	437	1	16	CARDINAL
ejpam-5251	437	2	jamil	PERSON
ejpam-5251	437	3	h. nuenay-maglanque	PERSON
ejpam-5251	439	1	2015	DATE
ejpam-5251	440	1	17	CARDINAL
ejpam-5251	440	2	j. john	PERSON
ejpam-5251	442	1	2020	DATE
ejpam-5251	443	1	18	CARDINAL
ejpam-5251	443	2	canoy jr and g. cagaanan	PERSON
ejpam-5251	445	1	congressus numerantium	PERSON
ejpam-5251	445	2	2003	DATE
ejpam-5251	446	1	19	CARDINAL
ejpam-5251	446	2	s.r. canoy jr.	PERSON
ejpam-5251	446	3	g. cagaanan	PERSON
ejpam-5251	446	4	s. gervacio.	PERSON
ejpam-5251	448	1	utilitas mathematica	PERSON
ejpam-5251	448	2	71, 2006	DATE
ejpam-5251	449	1	20	CARDINAL
ejpam-5251	449	2	canoy jr	PERSON
ejpam-5251	449	3	r. mollejon	PERSON
ejpam-5251	449	4	j. canoy.	PERSON
ejpam-5251	451	1	european journal	ORG
ejpam-5251	451	2	11	DATE
ejpam-5251	451	3	2019	DATE
ejpam-5251	452	1	21	CARDINAL
ejpam-5251	452	2	s.k.	GPE
ejpam-5251	454	1	analele universitatii	PERSON
ejpam-5251	454	2	constanta seria matematica	PERSON
ejpam-5251	454	3	2015	DATE
ejpam-5251	455	1	22	CARDINAL
ejpam-5251	455	2	h. rara	PERSON
ejpam-5251	457	1	asian-european journal of mathematics,	ORG
ejpam-5251	457	2	11	DATE
ejpam-5251	457	3	2017	DATE
ejpam-5251	458	1	23	CARDINAL
ejpam-5251	458	2	g. salasalan	PERSON
ejpam-5251	458	3	s.r.	GPE
ejpam-5251	458	4	canoy jr.	PERSON
ejpam-5251	459	1	european journal	ORG
ejpam-5251	459	2	14:112–125	CARDINAL
ejpam-5251	459	3	2021	DATE
ejpam-5251	460	1	24	CARDINAL
ejpam-5251	460	2	g. salasalan	PERSON
ejpam-5251	460	3	s.r.	GPE
ejpam-5251	460	4	canoy jr.	PERSON
ejpam-5251	461	1	european journal	ORG
ejpam-5251	461	2	14:1415–1428	CARDINAL
ejpam-5251	461	3	2021	CARDINAL
ejpam-5251	462	1	1750	CARDINAL
ejpam-5251	462	2	25	CARDINAL
ejpam-5251	462	3	c.j.	ORG
ejpam-5251	462	4	s.r. canoy	PERSON
ejpam-5251	464	1	european journal	ORG
ejpam-5251	464	2	15:1966–1981	CARDINAL
ejpam-5251	464	3	2022	CARDINAL
ejpam-5251	465	1	26	CARDINAL
ejpam-5251	465	2	c.j.	ORG
ejpam-5251	465	3	s.r. canoy	PERSON
ejpam-5251	467	1	european journal	ORG
ejpam-5251	467	2	2023	CARDINAL
ejpam-5251	468	1	27	CARDINAL
ejpam-5251	468	2	c.j.	ORG
ejpam-5251	468	3	s.r. canoy	PERSON
ejpam-5251	470	1	european journal	ORG
ejpam-5251	470	2	2023	CARDINAL
ejpam-5251	471	1	28	CARDINAL
ejpam-5251	471	2	jamil	GPE
ejpam-5251	471	3	s.r. canoy jr.	GPE
ejpam-5251	472	1	ars combinatoria	ORG
ejpam-5251	472	2	112:13–31,	DATE
ejpam-5251	472	3	2013	DATE