id	sid	eid	entity	type
ejpam-6904	1	1	european journal	ORG
ejpam-6904	1	2	2025	DATE
ejpam-6904	1	3	18	CARDINAL
ejpam-6904	1	4	4	CARDINAL
ejpam-6904	1	5	6904	CARDINAL
ejpam-6904	1	6	1307-5543	DATE
ejpam-6904	1	7	new york	GPE
ejpam-6904	1	8	2	CARDINAL
ejpam-6904	1	9	aziz b. tapeing1,2	PERSON
ejpam-6904	1	10	sergio r. canoy	PERSON
ejpam-6904	1	11	jr.1,2,∗ 1	ORG
ejpam-6904	1	12	msu-iligan institute of technology	ORG
ejpam-6904	1	13	iligan city	GPE
ejpam-6904	1	14	2	CARDINAL
ejpam-6904	1	15	msu-iligan institute of technology	ORG
ejpam-6904	1	16	iligan city	GPE
ejpam-6904	1	17	philippines	GPE
ejpam-6904	2	1	⊆	CARDINAL
ejpam-6904	2	2	2	CARDINAL
ejpam-6904	3	1	w ∈ s	PERSON
ejpam-6904	3	2	2	CARDINAL
ejpam-6904	3	3	∈	ORG
ejpam-6904	3	4	w	GPE
ejpam-6904	4	1	2	CARDINAL
ejpam-6904	4	2	2	CARDINAL
ejpam-6904	4	3	two	CARDINAL
ejpam-6904	4	4	2 ≤	QUANTITY
ejpam-6904	4	5	2	CARDINAL
ejpam-6904	5	1	2	CARDINAL
ejpam-6904	6	1	2	CARDINAL
ejpam-6904	7	1	2	CARDINAL
ejpam-6904	8	1	2020	DATE
ejpam-6904	8	2	05c69	CARDINAL
ejpam-6904	8	3	1	CARDINAL
ejpam-6904	8	4	1	CARDINAL
ejpam-6904	8	5	2	CARDINAL
ejpam-6904	8	6	3	CARDINAL
ejpam-6904	8	7	4	CARDINAL
ejpam-6904	9	1	5	CARDINAL
ejpam-6904	12	1	6	CARDINAL
ejpam-6904	14	1	7	CARDINAL
ejpam-6904	15	1	∗corresponding	PERSON
ejpam-6904	16	1	https://doi.org/10.29020/nybg.ejpam.v18i4.6904	DATE
ejpam-6904	17	1	aziz.tapeing@g.msuiit.edu.ph (a. b. tapeing	ORG
ejpam-6904	17	2	sergio.canoy@g.msuiit.edu.ph	ORG
ejpam-6904	17	3	s. r. canoy jr.	PERSON
ejpam-6904	18	1	1	CARDINAL
ejpam-6904	18	2	2025	CARDINAL
ejpam-6904	19	1	a. b. tapeing	PERSON
ejpam-6904	19	2	s. r. canoy	PERSON
ejpam-6904	20	1	j. pure	PERSON
ejpam-6904	20	2	18	CARDINAL
ejpam-6904	20	3	4	CARDINAL
ejpam-6904	20	4	2025	CARDINAL
ejpam-6904	20	5	6904 2	DATE
ejpam-6904	20	6	14	CARDINAL
ejpam-6904	21	1	8	CARDINAL
ejpam-6904	21	2	9	CARDINAL
ejpam-6904	22	1	10	CARDINAL
ejpam-6904	22	2	11	CARDINAL
ejpam-6904	23	1	recent years	DATE
ejpam-6904	23	2	5	CARDINAL
ejpam-6904	23	3	12	CARDINAL
ejpam-6904	23	4	13	CARDINAL
ejpam-6904	23	5	14	CARDINAL
ejpam-6904	23	6	15	CARDINAL
ejpam-6904	23	7	1	CARDINAL
ejpam-6904	23	8	16	CARDINAL
ejpam-6904	23	9	17	CARDINAL
ejpam-6904	23	10	18	CARDINAL
ejpam-6904	24	1	2	CARDINAL
ejpam-6904	25	1	two	CARDINAL
ejpam-6904	25	2	2	CARDINAL
ejpam-6904	26	1	2	CARDINAL
ejpam-6904	26	2	19	CARDINAL
ejpam-6904	26	3	20	CARDINAL
ejpam-6904	26	4	21	CARDINAL
ejpam-6904	26	5	22	CARDINAL
ejpam-6904	27	1	2	CARDINAL
ejpam-6904	29	1	∈	ORG
ejpam-6904	30	1	⊆	CARDINAL
ejpam-6904	31	1	∈	ORG
ejpam-6904	32	1	1	CARDINAL
ejpam-6904	33	1	wv	GPE
ejpam-6904	33	2	w	ORG
ejpam-6904	34	1	i(g	PERSON
ejpam-6904	34	2	l(g	PERSON
ejpam-6904	34	3	s(g	PERSON
ejpam-6904	36	1	α(g	PERSON
ejpam-6904	36	2	α(g	PERSON
ejpam-6904	36	3	⊆	CARDINAL
ejpam-6904	37	1	2	CARDINAL
ejpam-6904	37	2	2	CARDINAL
ejpam-6904	39	1	2	CARDINAL
ejpam-6904	41	1	2	CARDINAL
ejpam-6904	41	2	2	CARDINAL
ejpam-6904	43	1	⊆	CARDINAL
ejpam-6904	43	2	∈	ORG
ejpam-6904	43	3	w ∈ s	PERSON
ejpam-6904	43	4	∈	ORG
ejpam-6904	43	5	ig[u	ORG
ejpam-6904	43	6	w	ORG
ejpam-6904	43	7	ig[u	ORG
ejpam-6904	43	8	w	ORG
ejpam-6904	43	9	w	GPE
ejpam-6904	43	10	w	GPE
ejpam-6904	43	11	w	GPE
ejpam-6904	43	12	u-w	ORG
ejpam-6904	44	1	⊆	CARDINAL
ejpam-6904	44	2	2	CARDINAL
ejpam-6904	44	3	2	CARDINAL
ejpam-6904	45	1	∈	ORG
ejpam-6904	45	2	∈	ORG
ejpam-6904	45	3	2	CARDINAL
ejpam-6904	46	1	2	CARDINAL
ejpam-6904	46	2	g2p(g	ORG
ejpam-6904	46	3	2	CARDINAL
ejpam-6904	46	4	2	CARDINAL
ejpam-6904	46	5	2	CARDINAL
ejpam-6904	46	6	2	CARDINAL
ejpam-6904	46	7	2	CARDINAL
ejpam-6904	46	8	2	CARDINAL
ejpam-6904	46	9	2	CARDINAL
ejpam-6904	46	10	a. b. tapeing	PERSON
ejpam-6904	46	11	s. r. canoy	PERSON
ejpam-6904	47	1	j. pure	PERSON
ejpam-6904	47	2	18	CARDINAL
ejpam-6904	47	3	4	CARDINAL
ejpam-6904	47	4	2025	CARDINAL
ejpam-6904	47	5	6904 3	DATE
ejpam-6904	47	6	14	DATE
ejpam-6904	47	7	2	CARDINAL
ejpam-6904	47	8	2	CARDINAL
ejpam-6904	47	9	2	CARDINAL
ejpam-6904	47	10	2	CARDINAL
ejpam-6904	48	1	∈	ORG
ejpam-6904	48	2	∈	PERSON
ejpam-6904	48	3	∈	ORG
ejpam-6904	50	1	⊆	CARDINAL
ejpam-6904	50	2	2	CARDINAL
ejpam-6904	50	3	2	CARDINAL
ejpam-6904	50	4	2	CARDINAL
ejpam-6904	50	5	2	CARDINAL
ejpam-6904	50	6	2	CARDINAL
ejpam-6904	51	1	1	CARDINAL
ejpam-6904	53	1	∈	ORG
ejpam-6904	54	1	2	CARDINAL
ejpam-6904	54	2	2	CARDINAL
ejpam-6904	54	3	less than 3	CARDINAL
ejpam-6904	54	4	3	CARDINAL
ejpam-6904	54	5	1	CARDINAL
ejpam-6904	54	6	3	CARDINAL
ejpam-6904	54	7	two	CARDINAL
ejpam-6904	55	1	+ h	GPE
ejpam-6904	56	1	∈	ORG
ejpam-6904	57	1	two	CARDINAL
ejpam-6904	57	2	g1	ORG
ejpam-6904	57	3	∈	ORG
ejpam-6904	57	4	g1	ORG
ejpam-6904	58	1	23	CARDINAL
ejpam-6904	59	1	3	CARDINAL
ejpam-6904	59	2	2	CARDINAL
ejpam-6904	59	3	2	CARDINAL
ejpam-6904	60	1	1	CARDINAL
ejpam-6904	61	1	2	CARDINAL
ejpam-6904	61	2	2	CARDINAL
ejpam-6904	62	1	2	CARDINAL
ejpam-6904	63	1	{v2	PERSON
ejpam-6904	64	1	2	CARDINAL
ejpam-6904	65	1	2	CARDINAL
ejpam-6904	65	2	g2p(g	ORG
ejpam-6904	66	1	4	CARDINAL
ejpam-6904	66	2	a. b. tapeing	PERSON
ejpam-6904	66	3	s. r. canoy	PERSON
ejpam-6904	67	1	j. pure	PERSON
ejpam-6904	67	2	18	CARDINAL
ejpam-6904	67	3	4	CARDINAL
ejpam-6904	67	4	2025	CARDINAL
ejpam-6904	67	5	6904 4	DATE
ejpam-6904	68	1	2	CARDINAL
ejpam-6904	69	1	v1 v2 v3 w1	PERSON
ejpam-6904	69	2	w3 g	PERSON
ejpam-6904	69	3	2	CARDINAL
ejpam-6904	69	4	2	CARDINAL
ejpam-6904	69	5	g2p(g	ORG
ejpam-6904	70	1	4	CARDINAL
ejpam-6904	70	2	2	CARDINAL
ejpam-6904	74	1	α(g	PERSON
ejpam-6904	76	1	2	CARDINAL
ejpam-6904	76	2	i(g	PERSON
ejpam-6904	77	1	⊆	CARDINAL
ejpam-6904	78	1	2	CARDINAL
ejpam-6904	80	1	2	CARDINAL
ejpam-6904	81	1	⊆	CARDINAL
ejpam-6904	82	1	\s	ORG
ejpam-6904	83	1	2	CARDINAL
ejpam-6904	83	2	∈	ORG
ejpam-6904	83	3	2	CARDINAL
ejpam-6904	83	4	∈	ORG
ejpam-6904	84	1	2	CARDINAL
ejpam-6904	85	1	1(i	CARDINAL
ejpam-6904	86	1	1	CARDINAL
ejpam-6904	89	1	1	CARDINAL
ejpam-6904	90	1	g1	ORG
ejpam-6904	90	2	gk	PERSON
ejpam-6904	90	3	k ≥ 1	ORG
ejpam-6904	90	4	2	CARDINAL
ejpam-6904	91	1	2	CARDINAL
ejpam-6904	92	1	1	CARDINAL
ejpam-6904	92	2	2	DATE
ejpam-6904	95	1	2	CARDINAL
ejpam-6904	96	1	1	CARDINAL
ejpam-6904	96	2	2	DATE
ejpam-6904	98	1	2	CARDINAL
ejpam-6904	100	1	j ∈	PERSON
ejpam-6904	101	1	ab ∈ e(gj	ORG
ejpam-6904	102	1	∈	ORG
ejpam-6904	102	2	∈	ORG
ejpam-6904	102	3	∈	ORG
ejpam-6904	102	4	gj	PERSON
ejpam-6904	104	1	2	CARDINAL
ejpam-6904	104	2	2	CARDINAL
ejpam-6904	105	1	a. b. tapeing	PERSON
ejpam-6904	105	2	s. r. canoy	PERSON
ejpam-6904	106	1	j. pure	PERSON
ejpam-6904	106	2	18	CARDINAL
ejpam-6904	106	3	4	CARDINAL
ejpam-6904	106	4	2025	CARDINAL
ejpam-6904	106	5	6904 5	DATE
ejpam-6904	106	6	14	CARDINAL
ejpam-6904	106	7	2	CARDINAL
ejpam-6904	106	8	∈	ORG
ejpam-6904	108	1	2	CARDINAL
ejpam-6904	111	1	2	CARDINAL
ejpam-6904	112	1	1	CARDINAL
ejpam-6904	112	2	2	DATE
ejpam-6904	115	1	j ∈	PERSON
ejpam-6904	116	1	pq ∈ e(gj	ORG
ejpam-6904	117	1	gj	ORG
ejpam-6904	117	2	∈	ORG
ejpam-6904	118	1	∈	ORG
ejpam-6904	120	1	∈	ORG
ejpam-6904	120	2	st.	GPE
ejpam-6904	120	3	st	GPE
ejpam-6904	120	4	2	CARDINAL
ejpam-6904	120	5	w ∈	PERSON
ejpam-6904	120	6	2	CARDINAL
ejpam-6904	120	7	w	GPE
ejpam-6904	120	8	w	GPE
ejpam-6904	121	1	2	CARDINAL
ejpam-6904	121	2	gj	PERSON
ejpam-6904	123	1	2	CARDINAL
ejpam-6904	124	1	g2p(g	ORG
ejpam-6904	127	1	g. (ii	PRODUCT
ejpam-6904	127	2	2	CARDINAL
ejpam-6904	128	1	2	CARDINAL
ejpam-6904	128	2	2	CARDINAL
ejpam-6904	128	3	g2p(g	ORG
ejpam-6904	129	1	g2p(g	ORG
ejpam-6904	131	1	2	CARDINAL
ejpam-6904	132	1	first	ORDINAL
ejpam-6904	134	1	2	CARDINAL
ejpam-6904	134	2	2	CARDINAL
ejpam-6904	135	1	first	ORDINAL
ejpam-6904	136	1	3	CARDINAL
ejpam-6904	137	1	1	CARDINAL
ejpam-6904	137	2	2	CARDINAL
ejpam-6904	137	3	k2,k2,k2,n−2} a. b. tapeing	ORG
ejpam-6904	137	4	s. r. canoy	PERSON
ejpam-6904	138	1	j. pure	PERSON
ejpam-6904	138	2	18	CARDINAL
ejpam-6904	138	3	4	CARDINAL
ejpam-6904	138	4	2025	CARDINAL
ejpam-6904	138	5	6904 6	DATE
ejpam-6904	138	6	3	CARDINAL
ejpam-6904	138	7	k3,k3, p1 ∪	ORG
ejpam-6904	139	1	one	CARDINAL
ejpam-6904	140	1	2	CARDINAL
ejpam-6904	140	2	z}⟩	ORG
ejpam-6904	140	3	z}⟩	ORG
ejpam-6904	140	4	∈	ORG
ejpam-6904	141	1	z}⟩	ORG
ejpam-6904	142	1	∈	ORG
ejpam-6904	144	1	1	CARDINAL
ejpam-6904	144	2	2	CARDINAL
ejpam-6904	146	1	1.	CARDINAL
ejpam-6904	146	2	2	CARDINAL
ejpam-6904	147	1	2	CARDINAL
ejpam-6904	148	1	n ≥ 3	DATE
ejpam-6904	150	1	2	CARDINAL
ejpam-6904	150	2	2	CARDINAL
ejpam-6904	151	1	s⟩.	NORP
ejpam-6904	151	2	2	CARDINAL
ejpam-6904	154	1	3	CARDINAL
ejpam-6904	155	1	2	CARDINAL
ejpam-6904	155	2	3	CARDINAL
ejpam-6904	156	1	2	CARDINAL
ejpam-6904	159	1	3	CARDINAL
ejpam-6904	159	2	k3,k3, p1 ∪	ORG
ejpam-6904	161	1	∈	ORG
ejpam-6904	163	1	2	CARDINAL
ejpam-6904	163	2	2	CARDINAL
ejpam-6904	166	1	z}⟩	ORG
ejpam-6904	166	2	2	CARDINAL
ejpam-6904	166	3	∈	ORG
ejpam-6904	168	1	z}⟩	ORG
ejpam-6904	169	1	∈	ORG
ejpam-6904	170	1	2	CARDINAL
ejpam-6904	170	2	∈	ORG
ejpam-6904	171	1	∈	ORG
ejpam-6904	171	2	2	CARDINAL
ejpam-6904	172	1	3	CARDINAL
ejpam-6904	172	2	w ∈	PERSON
ejpam-6904	176	1	first	ORDINAL
ejpam-6904	176	2	k3,k3, p1 ∪	ORG
ejpam-6904	178	1	3	CARDINAL
ejpam-6904	182	1	∈	ORG
ejpam-6904	182	2	∈	ORG
ejpam-6904	183	1	2	CARDINAL
ejpam-6904	183	2	2	CARDINAL
ejpam-6904	183	3	3	CARDINAL
ejpam-6904	187	1	∈	ORG
ejpam-6904	188	1	2	CARDINAL
ejpam-6904	188	2	3	CARDINAL
ejpam-6904	191	1	∈	ORG
ejpam-6904	192	1	∈	ORG
ejpam-6904	192	2	∈	ORG
ejpam-6904	193	1	2	CARDINAL
ejpam-6904	193	2	a. b. tapeing	PERSON
ejpam-6904	193	3	s. r. canoy	PERSON
ejpam-6904	194	1	j. pure	PERSON
ejpam-6904	194	2	18	CARDINAL
ejpam-6904	194	3	4	CARDINAL
ejpam-6904	194	4	2025	CARDINAL
ejpam-6904	194	5	6904 7	DATE
ejpam-6904	194	6	14	CARDINAL
ejpam-6904	196	1	3	CARDINAL
ejpam-6904	196	2	4	CARDINAL
ejpam-6904	198	1	g′	PERSON
ejpam-6904	198	2	g′	PERSON
ejpam-6904	199	1	g′	PERSON
ejpam-6904	201	1	∈	ORG
ejpam-6904	201	2	2	CARDINAL
ejpam-6904	203	1	2	CARDINAL
ejpam-6904	203	2	1	CARDINAL
ejpam-6904	203	3	1	CARDINAL
ejpam-6904	203	4	1	CARDINAL
ejpam-6904	206	1	1	CARDINAL
ejpam-6904	206	2	g′	PERSON
ejpam-6904	206	3	theorem1	PERSON
ejpam-6904	206	4	5	CARDINAL
ejpam-6904	207	1	1	CARDINAL
ejpam-6904	211	1	g1	ORG
ejpam-6904	211	2	gk	PERSON
ejpam-6904	212	1	1	CARDINAL
ejpam-6904	212	2	4	CARDINAL
ejpam-6904	213	1	1	CARDINAL
ejpam-6904	213	2	1	CARDINAL
ejpam-6904	214	1	1	CARDINAL
ejpam-6904	214	2	2	DATE
ejpam-6904	214	3	k}	PERSON
ejpam-6904	215	1	h∗	ORG
ejpam-6904	216	1	h∗	ORG
ejpam-6904	217	1	h∗	ORG
ejpam-6904	219	1	∈	ORG
ejpam-6904	219	2	h∗	ORG
ejpam-6904	220	1	2	CARDINAL
ejpam-6904	222	1	2	CARDINAL
ejpam-6904	223	1	h∗	ORG
ejpam-6904	224	1	gj	PERSON
ejpam-6904	224	2	1	CARDINAL
ejpam-6904	224	3	2	DATE
ejpam-6904	224	4	1	CARDINAL
ejpam-6904	224	5	1	CARDINAL
ejpam-6904	224	6	h∗	ORG
ejpam-6904	226	1	1	CARDINAL
ejpam-6904	226	2	1	CARDINAL
ejpam-6904	226	3	2	DATE
ejpam-6904	226	4	4	CARDINAL
ejpam-6904	227	1	⊆	CARDINAL
ejpam-6904	227	2	1(i	CARDINAL
ejpam-6904	228	1	h∗	ORG
ejpam-6904	229	1	1	CARDINAL
ejpam-6904	229	2	h∗	ORG
ejpam-6904	230	1	h∗	ORG
ejpam-6904	231	1	∈	ORG
ejpam-6904	231	2	h∗	ORG
ejpam-6904	231	3	\d	ORG
ejpam-6904	232	1	pq ∈ e(h	ORG
ejpam-6904	232	2	h∗	ORG
ejpam-6904	234	1	∩	PERSON
ejpam-6904	235	1	1	CARDINAL
ejpam-6904	235	2	1	CARDINAL
ejpam-6904	235	3	1	CARDINAL
ejpam-6904	235	4	1	CARDINAL
ejpam-6904	235	5	6	CARDINAL
ejpam-6904	236	1	2 ≤ m1 ≤	QUANTITY
ejpam-6904	241	1	k−1∪	PERSON
ejpam-6904	241	2	i=1 si	PERSON
ejpam-6904	241	3	2	CARDINAL
ejpam-6904	243	1	a. b. tapeing	PERSON
ejpam-6904	243	2	s. r. canoy	PERSON
ejpam-6904	244	1	j. pure	PERSON
ejpam-6904	244	2	18	CARDINAL
ejpam-6904	244	3	4	CARDINAL
ejpam-6904	244	4	2025	CARDINAL
ejpam-6904	244	5	6904 8	DATE
ejpam-6904	245	1	∈	ORG
ejpam-6904	245	2	1	CARDINAL
ejpam-6904	245	3	2	DATE
ejpam-6904	247	1	∈	ORG
ejpam-6904	248	1	vw	GPE
ejpam-6904	249	1	j ̸=r si	PERSON
ejpam-6904	249	2	⊆	CARDINAL
ejpam-6904	255	1	2	CARDINAL
ejpam-6904	257	1	2	CARDINAL
ejpam-6904	257	2	2	CARDINAL
ejpam-6904	258	1	7	CARDINAL
ejpam-6904	258	2	two	CARDINAL
ejpam-6904	258	3	3 ≤	QUANTITY
ejpam-6904	258	4	g2p(g	ORG
ejpam-6904	261	1	g2p(g	ORG
ejpam-6904	261	2	= a.	PERSON
ejpam-6904	261	3	3	CARDINAL
ejpam-6904	261	4	ka−1	PERSON
ejpam-6904	261	5	kb−a+1	PERSON
ejpam-6904	263	1	kb−a+1	PERSON
ejpam-6904	266	1	xb−a+1}	GPE
ejpam-6904	269	1	g2p(g	ORG
ejpam-6904	271	1	va−2	GPE
ejpam-6904	271	2	1(i	CARDINAL
ejpam-6904	272	1	va−1 /∈ d0	PERSON
ejpam-6904	272	2	⊆	CARDINAL
ejpam-6904	272	3	d0 = ext(g	ORG
ejpam-6904	272	4	kb−a+1	PERSON
ejpam-6904	274	1	∈	ORG
ejpam-6904	275	1	kb−a+1	PERSON
ejpam-6904	277	1	a. ka−1	PERSON
ejpam-6904	278	1	xb−a+1 va−1 g	PERSON
ejpam-6904	278	2	3	CARDINAL
ejpam-6904	278	3	g2p(g	ORG
ejpam-6904	280	1	7	CARDINAL
ejpam-6904	280	2	2	CARDINAL
ejpam-6904	282	1	− g2p(g	PERSON
ejpam-6904	283	1	− g2p(g	PERSON
ejpam-6904	284	1	a. b. tapeing	PERSON
ejpam-6904	284	2	s. r. canoy	PERSON
ejpam-6904	285	1	j. pure	PERSON
ejpam-6904	285	2	18	CARDINAL
ejpam-6904	285	3	4	CARDINAL
ejpam-6904	285	4	2025	CARDINAL
ejpam-6904	285	5	6904 9	DATE
ejpam-6904	285	6	14	CARDINAL
ejpam-6904	286	1	two	CARDINAL
ejpam-6904	286	2	2 ≤	QUANTITY
ejpam-6904	287	1	= a. next	PERSON
ejpam-6904	287	2	4	CARDINAL
ejpam-6904	294	1	a−2	PERSON
ejpam-6904	297	1	= a. hence	PERSON
ejpam-6904	297	2	= a.	PERSON
ejpam-6904	301	1	⊆	CARDINAL
ejpam-6904	301	2	1(i	CARDINAL
ejpam-6904	302	1	|{x, va	GPE
ejpam-6904	302	2	1	CARDINAL
ejpam-6904	302	3	1	CARDINAL
ejpam-6904	304	1	b. ka	PERSON
ejpam-6904	307	1	4	CARDINAL
ejpam-6904	309	1	8	CARDINAL
ejpam-6904	309	2	3	CARDINAL
ejpam-6904	313	1	g1	ORG
ejpam-6904	314	1	∈	ORG
ejpam-6904	314	2	g1	ORG
ejpam-6904	315	1	9	CARDINAL
ejpam-6904	317	1	⊆	CARDINAL
ejpam-6904	318	1	sg1 ∪ sg2	DATE
ejpam-6904	318	2	sg1 ∪ sg2	DATE
ejpam-6904	318	3	sg1	PRODUCT
ejpam-6904	318	4	sg2	ORG
ejpam-6904	318	5	g1	ORG
ejpam-6904	319	1	w ∈ sg1	PERSON
ejpam-6904	319	2	w′ ∈ sg2	ORG
ejpam-6904	320	1	∈	PRODUCT
ejpam-6904	320	2	ng2(p ′	DATE
ejpam-6904	323	1	sg1	DATE
ejpam-6904	323	2	g1	ORG
ejpam-6904	323	3	g1	ORG
ejpam-6904	325	1	g1	ORG
ejpam-6904	326	1	sg1	PRODUCT
ejpam-6904	326	2	g1	ORG
ejpam-6904	326	3	w ∈ sg1	PERSON
ejpam-6904	327	1	∈	ORG
ejpam-6904	327	2	a. b. tapeing	PERSON
ejpam-6904	327	3	s. r. canoy	PERSON
ejpam-6904	328	1	j. pure	PERSON
ejpam-6904	328	2	18	CARDINAL
ejpam-6904	328	3	4	CARDINAL
ejpam-6904	328	4	2025	CARDINAL
ejpam-6904	328	5	6904 10	DATE
ejpam-6904	328	6	14	CARDINAL
ejpam-6904	329	1	w′ ∈ sg2	ORG
ejpam-6904	333	1	1	CARDINAL
ejpam-6904	334	1	xy ∈	PERSON
ejpam-6904	335	1	xy ∈	ORG
ejpam-6904	335	2	y ∈ sg1	PERSON
ejpam-6904	335	3	sg1	PRODUCT
ejpam-6904	335	4	g1	ORG
ejpam-6904	336	1	∈ sg2	ORG
ejpam-6904	336	2	∈	ORG
ejpam-6904	336	3	xy ∈	ORG
ejpam-6904	337	1	2	CARDINAL
ejpam-6904	337	2	∈	ORG
ejpam-6904	337	3	g1	ORG
ejpam-6904	338	1	z′	PERSON
ejpam-6904	338	2	g1	ORG
ejpam-6904	340	1	∈	ORG
ejpam-6904	341	1	∈	ORG
ejpam-6904	341	2	z′ ∈ sg2	ORG
ejpam-6904	343	1	10	CARDINAL
ejpam-6904	345	1	⊆	CARDINAL
ejpam-6904	346	1	2	CARDINAL
ejpam-6904	349	1	sg1 ∪ sg2	DATE
ejpam-6904	349	2	9	CARDINAL
ejpam-6904	349	3	∈	ORG
ejpam-6904	349	4	g1	ORG
ejpam-6904	350	1	w ∈	ORG
ejpam-6904	350	2	g1	ORG
ejpam-6904	350	3	ng1(v	PERSON
ejpam-6904	351	1	w	GPE
ejpam-6904	351	2	w′ ∈ s	PERSON
ejpam-6904	353	1	2	CARDINAL
ejpam-6904	354	1	∈	ORG
ejpam-6904	355	1	z′	PERSON
ejpam-6904	355	2	g1	ORG
ejpam-6904	355	3	x′	CARDINAL
ejpam-6904	356	1	x′	CARDINAL
ejpam-6904	356	2	dd2(g)(x	ORG
ejpam-6904	356	3	2	CARDINAL
ejpam-6904	357	1	2	CARDINAL
ejpam-6904	363	1	2β(g	TIME
ejpam-6904	365	1	g1	ORG
ejpam-6904	367	1	9	CARDINAL
ejpam-6904	368	1	10	CARDINAL
ejpam-6904	368	2	2β(g	TIME
ejpam-6904	370	1	sg1	PRODUCT
ejpam-6904	370	2	sg2	ORG
ejpam-6904	370	3	g1	ORG
ejpam-6904	370	4	9	CARDINAL
ejpam-6904	370	5	10	CARDINAL
ejpam-6904	373	1	2β(g	TIME
ejpam-6904	375	1	11	CARDINAL
ejpam-6904	377	1	⊆	CARDINAL
ejpam-6904	377	2	2	CARDINAL
ejpam-6904	378	1	a. b. tapeing	PERSON
ejpam-6904	378	2	s. r. canoy	PERSON
ejpam-6904	379	1	j. pure	PERSON
ejpam-6904	379	2	18	CARDINAL
ejpam-6904	379	3	4	CARDINAL
ejpam-6904	379	4	2025	CARDINAL
ejpam-6904	379	5	6904 11	DATE
ejpam-6904	379	6	14	CARDINAL
ejpam-6904	379	7	2	CARDINAL
ejpam-6904	380	1	2	CARDINAL
ejpam-6904	380	2	km+g	LOC
ejpam-6904	381	1	∈	ORG
ejpam-6904	382	1	km + g	PRODUCT
ejpam-6904	382	2	⊆	CARDINAL
ejpam-6904	382	3	1	CARDINAL
ejpam-6904	384	1	\s	ORG
ejpam-6904	386	1	km + g	PRODUCT
ejpam-6904	386	2	sg	GPE
ejpam-6904	387	1	2	CARDINAL
ejpam-6904	387	2	km+g	GPE
ejpam-6904	388	1	w ∈	ORG
ejpam-6904	388	2	2	CARDINAL
ejpam-6904	388	3	w ∈	PERSON
ejpam-6904	388	4	2	CARDINAL
ejpam-6904	388	5	sg	GPE
ejpam-6904	388	6	2	CARDINAL
ejpam-6904	388	7	first	ORDINAL
ejpam-6904	390	1	2	CARDINAL
ejpam-6904	390	2	km+g	LOC
ejpam-6904	391	1	km)∪sg	PRODUCT
ejpam-6904	391	2	2	CARDINAL
ejpam-6904	391	3	∈	ORG
ejpam-6904	392	1	∈	ORG
ejpam-6904	394	1	sg	GPE
ejpam-6904	394	2	∈	ORG
ejpam-6904	394	3	∈	ORG
ejpam-6904	395	1	∈	ORG
ejpam-6904	397	1	∈	ORG
ejpam-6904	397	2	2	CARDINAL
ejpam-6904	397	3	w ∈	ORG
ejpam-6904	398	1	2	CARDINAL
ejpam-6904	399	1	11	CARDINAL
ejpam-6904	400	1	5	CARDINAL
ejpam-6904	403	1	min{(m− 1	PERSON
ejpam-6904	404	1	6	CARDINAL
ejpam-6904	406	1	β2pg(k1	PRODUCT
ejpam-6904	408	1	+ 1	DATE
ejpam-6904	412	1	2	CARDINAL
ejpam-6904	413	1	⌈n2 ⌉+ 1	DATE
ejpam-6904	416	1	k ≥ 2	ORG
ejpam-6904	416	2	12	CARDINAL
ejpam-6904	418	1	⊆	CARDINAL
ejpam-6904	418	2	2	CARDINAL
ejpam-6904	418	3	g+h	ORG
ejpam-6904	419	1	h. (ii	ORG
ejpam-6904	419	2	sg	GPE
ejpam-6904	419	3	g. a. b. tapeing	PERSON
ejpam-6904	419	4	s. r. canoy	PERSON
ejpam-6904	420	1	j. pure	PERSON
ejpam-6904	420	2	18	CARDINAL
ejpam-6904	420	3	4	CARDINAL
ejpam-6904	420	4	2025	CARDINAL
ejpam-6904	420	5	6904 12	DATE
ejpam-6904	420	6	14	CARDINAL
ejpam-6904	421	1	2	CARDINAL
ejpam-6904	424	1	xy ∈	ORG
ejpam-6904	424	2	y /∈ s.	PERSON
ejpam-6904	425	1	g+h	ORG
ejpam-6904	427	1	⊆	CARDINAL
ejpam-6904	427	2	ab ∈ e(h	ORG
ejpam-6904	428	1	∈	ORG
ejpam-6904	428	2	∈	ORG
ejpam-6904	431	1	st ∈	PERSON
ejpam-6904	432	1	∈	ORG
ejpam-6904	432	2	st	GPE
ejpam-6904	432	3	s.	GPE
ejpam-6904	432	4	st ∈ e(h	ORG
ejpam-6904	433	1	∈	ORG
ejpam-6904	438	1	∈	ORG
ejpam-6904	439	1	∈	ORG
ejpam-6904	439	2	dg+h(p	NORP
ejpam-6904	439	3	2	CARDINAL
ejpam-6904	439	4	∈	ORG
ejpam-6904	440	1	2	CARDINAL
ejpam-6904	440	2	g+h	ORG
ejpam-6904	442	1	12	CARDINAL
ejpam-6904	445	1	min{m+ β(h	PERSON
ejpam-6904	447	1	2	CARDINAL
ejpam-6904	449	1	n ≥ 3	DATE
ejpam-6904	450	1	n ≥ 4. 4	DATE
ejpam-6904	450	2	2	CARDINAL
ejpam-6904	451	1	− β(g	PERSON
ejpam-6904	453	1	2	CARDINAL
ejpam-6904	455	1	2	CARDINAL
ejpam-6904	457	1	a. b. tapeing	PERSON
ejpam-6904	457	2	s. r. canoy	PERSON
ejpam-6904	458	1	j. pure	PERSON
ejpam-6904	458	2	18	CARDINAL
ejpam-6904	458	3	4	CARDINAL
ejpam-6904	458	4	2025	CARDINAL
ejpam-6904	458	5	6904 13	DATE
ejpam-6904	458	6	14	CARDINAL
ejpam-6904	458	7	msu-iligan institute of technology	ORG
ejpam-6904	458	8	iligan city	GPE
ejpam-6904	459	1	1	CARDINAL
ejpam-6904	459	2	m. henning	PERSON
ejpam-6904	459	3	a. yeo	PERSON
ejpam-6904	461	1	the electric journal	ORG
ejpam-6904	461	2	2012	DATE
ejpam-6904	462	1	2	CARDINAL
ejpam-6904	462	2	s. canoy jr	PERSON
ejpam-6904	462	3	r. artes jr.	PERSON
ejpam-6904	463	1	congressus numerantium	PERSON
ejpam-6904	463	2	167:65, 2004	DATE
ejpam-6904	464	1	3	CARDINAL
ejpam-6904	464	2	s. sitthiwirattham	PERSON
ejpam-6904	466	1	77(4):543–547	ORG
ejpam-6904	466	2	2012	DATE
ejpam-6904	467	1	4	CARDINAL
ejpam-6904	467	2	j. uy and v. abregana	PERSON
ejpam-6904	469	1	5714	CARDINAL
ejpam-6904	469	2	2015	DATE
ejpam-6904	470	1	5	CARDINAL
ejpam-6904	470	2	d. angel	PERSON
ejpam-6904	470	3	a. amutha	PERSON
ejpam-6904	472	1	procedia computer science	ORG
ejpam-6904	472	2	87:164–171	CARDINAL
ejpam-6904	472	3	2016	DATE
ejpam-6904	473	1	6	CARDINAL
ejpam-6904	473	2	r. swain	PERSON
ejpam-6904	473	3	c. revelle	PERSON
ejpam-6904	473	4	l. bercman	PERSON
ejpam-6904	475	1	america	GPE
ejpam-6904	475	2	1971	DATE
ejpam-6904	476	1	7	CARDINAL
ejpam-6904	478	1	plenum press	ORG
ejpam-6904	478	2	new york	GPE
ejpam-6904	478	3	85–103	DATE
ejpam-6904	478	4	1972	DATE
ejpam-6904	479	1	8	CARDINAL
ejpam-6904	479	2	garey	ORG
ejpam-6904	479	3	johnson	PERSON
ejpam-6904	481	1	siam journal	ORG
ejpam-6904	481	2	32:826–834, 1977	DATE
ejpam-6904	482	1	9	CARDINAL
ejpam-6904	482	2	garey	ORG
ejpam-6904	482	3	d.s. johnson	PERSON
ejpam-6904	482	4	l. stockmeyer	PERSON
ejpam-6904	484	1	sixth	ORDINAL
ejpam-6904	484	2	annual	DATE
ejpam-6904	484	3	47	CARDINAL
ejpam-6904	484	4	63, 1974	DATE
ejpam-6904	485	1	10	CARDINAL
ejpam-6904	485	2	mahmoodian	NORP
ejpam-6904	486	1	generalized petersen	ORG
ejpam-6904	487	1	australian	NORP
ejpam-6904	487	2	combinatorics	ORG
ejpam-6904	487	3	40:253–264, 2008	DATE
ejpam-6904	488	1	11	CARDINAL
ejpam-6904	488	2	j. uy	PERSON
ejpam-6904	489	1	journal of research	ORG
ejpam-6904	489	2	1:49–53, 2003	DATE
ejpam-6904	490	1	12	CARDINAL
ejpam-6904	490	2	m.a.	PERSON
ejpam-6904	490	3	bonsocan	NORP
ejpam-6904	490	4	j. hassan	PERSON
ejpam-6904	490	5	s. dagondon.	PERSON
ejpam-6904	493	1	j. pure	PERSON
ejpam-6904	493	2	17(1):93–104	DATE
ejpam-6904	493	3	2024	DATE
ejpam-6904	494	1	13	CARDINAL
ejpam-6904	494	2	j. hassan	PERSON
ejpam-6904	494	3	m. a. bonsocan	PERSON
ejpam-6904	494	4	r. rasid	PERSON
ejpam-6904	494	5	a. sappari	PERSON
ejpam-6904	497	1	j.	PERSON
ejpam-6904	497	2	17(2):1038–1045	CARDINAL
ejpam-6904	497	3	2024	DATE
ejpam-6904	498	1	14	CARDINAL
ejpam-6904	498	2	j. hassan	PERSON
ejpam-6904	498	3	s. canoy jr, a. gamorez	PERSON
ejpam-6904	498	4	e. ahmad	PERSON
ejpam-6904	498	5	a. sappari	PERSON
ejpam-6904	499	1	2	CARDINAL
ejpam-6904	500	1	european journal	ORG
ejpam-6904	500	2	pure & applied	ORG
ejpam-6904	500	3	2025	DATE
ejpam-6904	501	1	15	CARDINAL
ejpam-6904	501	2	s. canoy jr, m.a.	PERSON
ejpam-6904	501	3	bonsocan	NORP
ejpam-6904	501	4	j. hassan	PERSON
ejpam-6904	501	5	v. bilar	ORG
ejpam-6904	503	1	european journal	ORG
ejpam-6904	503	2	pure & applied	ORG
ejpam-6904	503	3	18(1	CARDINAL
ejpam-6904	503	4	2025	DATE
ejpam-6904	504	1	16	CARDINAL
ejpam-6904	504	2	r. ravi	PERSON
ejpam-6904	506	1	39:87–93, 1992	DATE
ejpam-6904	507	1	17	CARDINAL
ejpam-6904	507	2	c. suseendran	PERSON
ejpam-6904	509	1	9(2	CARDINAL
ejpam-6904	509	2	2017	DATE
ejpam-6904	510	1	18	CARDINAL
ejpam-6904	510	2	l. sathikala	PERSON
ejpam-6904	510	3	k. k. basari	PERSON
ejpam-6904	510	4	k. subramanian	PERSON
ejpam-6904	512	1	turkish	NORP
ejpam-6904	512	2	12(2):2180	CARDINAL
ejpam-6904	512	3	2185	CARDINAL
ejpam-6904	512	4	2021	DATE
ejpam-6904	513	1	a. b. tapeing	PERSON
ejpam-6904	513	2	s. r. canoy	PERSON
ejpam-6904	514	1	j. pure	PERSON
ejpam-6904	514	2	18	CARDINAL
ejpam-6904	514	3	4	CARDINAL
ejpam-6904	514	4	2025	CARDINAL
ejpam-6904	514	5	6904 14	DATE
ejpam-6904	514	6	19	CARDINAL
ejpam-6904	514	7	g. cagaanan	PERSON
ejpam-6904	514	8	s. canoy jr.	PERSON
ejpam-6904	514	9	cartesian	NORP
ejpam-6904	515	1	utilitas mathematica	PERSON
ejpam-6904	515	2	79:91–98, 2009	GPE
ejpam-6904	516	1	20	CARDINAL
ejpam-6904	516	2	g. cagaanan	PERSON
ejpam-6904	516	3	jr.	PERSON
ejpam-6904	516	4	s. canoy.	PERSON
ejpam-6904	518	1	asia pacific journal	ORG
ejpam-6904	518	2	19(1	CARDINAL
ejpam-6904	518	3	2005	DATE
ejpam-6904	519	1	21	CARDINAL
ejpam-6904	519	2	f. jamil	PERSON
ejpam-6904	519	3	i. aniversario	PERSON
ejpam-6904	519	4	s. canoy jr.	PERSON
ejpam-6904	520	1	84:191–204	GPE
ejpam-6904	520	2	2007	DATE
ejpam-6904	521	1	22	CARDINAL
ejpam-6904	521	2	s. canoy jr, g. cagaanan	PERSON
ejpam-6904	521	3	s. gervacio.	PERSON
ejpam-6904	523	1	2006	DATE
ejpam-6904	524	1	23	CARDINAL
ejpam-6904	524	2	f. buckley	PERSON
ejpam-6904	524	3	f. harary	PERSON
ejpam-6904	526	1	addison-wesley	ORG
ejpam-6904	526	2	redwood city	GPE
ejpam-6904	526	3	1990	DATE