id	sid	eid	entity	type
ejpam-4506	1	1	european journal	ORG
ejpam-4506	2	1	16	CARDINAL
ejpam-4506	2	2	1	CARDINAL
ejpam-4506	2	3	2023	CARDINAL
ejpam-4506	2	4	169	CARDINAL
ejpam-4506	2	5	new york	GPE
ejpam-4506	2	6	jesica m. anoche1,∗	PERSON
ejpam-4506	2	7	imelda s. aniversario1	PERSON
ejpam-4506	2	8	catherine i. merca1	PERSON
ejpam-4506	3	1	mindanao state university-iligan institute of technology	ORG
ejpam-4506	3	2	9200	CARDINAL
ejpam-4506	3	3	iligan city	GPE
ejpam-4506	3	4	philippines	GPE
ejpam-4506	5	1	two	CARDINAL
ejpam-4506	7	1	2020	DATE
ejpam-4506	7	2	05c69	CARDINAL
ejpam-4506	7	3	1	CARDINAL
ejpam-4506	9	1	first	ORDINAL
ejpam-4506	9	2	the late 1950’s	DATE
ejpam-4506	9	3	1960	DATE
ejpam-4506	9	4	c. berge	PERSON
ejpam-4506	9	5	1958	DATE
ejpam-4506	11	1	1962	DATE
ejpam-4506	12	1	years later	DATE
ejpam-4506	13	1	2011	DATE
ejpam-4506	15	1	i. aniversario	PERSON
ejpam-4506	16	1	3	CARDINAL
ejpam-4506	17	1	buckley	PERSON
ejpam-4506	17	2	2	CARDINAL
ejpam-4506	17	3	1	CARDINAL
ejpam-4506	20	1	jesica.anoche@g.msuiit.edu.ph (j.anoche	ORG
ejpam-4506	20	2	imelda.aniversario@g.msuiit.edu.ph	GPE
ejpam-4506	20	3	i. aniversario	PERSON
ejpam-4506	20	4	catherine.merca@g.msuiit.edu.ph (c. merca	ORG
ejpam-4506	20	5	169	CARDINAL
ejpam-4506	21	1	2023	CARDINAL
ejpam-4506	22	1	j. anoche	PERSON
ejpam-4506	22	2	i. aniversario	PERSON
ejpam-4506	22	3	c. merca	PERSON
ejpam-4506	23	1	j. pure	PERSON
ejpam-4506	23	2	16	CARDINAL
ejpam-4506	23	3	1	CARDINAL
ejpam-4506	23	4	2023	CARDINAL
ejpam-4506	23	5	169	CARDINAL
ejpam-4506	23	6	179 170	CARDINAL
ejpam-4506	25	1	⊆	CARDINAL
ejpam-4506	26	1	two	CARDINAL
ejpam-4506	33	1	gn	ORG
ejpam-4506	35	1	3 ≤	QUANTITY
ejpam-4506	37	1	vi	PERSON
ejpam-4506	37	2	1	CARDINAL
ejpam-4506	37	3	2	DATE
ejpam-4506	37	4	k.	PERSON
ejpam-4506	38	1	cgn	CARDINAL
ejpam-4506	38	2	1	CARDINAL
ejpam-4506	39	1	2	CARDINAL
ejpam-4506	39	2	1	CARDINAL
ejpam-4506	40	1	2	CARDINAL
ejpam-4506	40	2	∖	PERSON
ejpam-4506	41	1	g∖	DATE
ejpam-4506	42	1	2	CARDINAL
ejpam-4506	43	1	2	CARDINAL
ejpam-4506	43	2	ω	CARDINAL
ejpam-4506	44	1	3	CARDINAL
ejpam-4506	45	1	2	CARDINAL
ejpam-4506	45	2	∈	ORG
ejpam-4506	45	3	∈	PRODUCT
ejpam-4506	46	1	∈	ORG
ejpam-4506	46	2	4	CARDINAL
ejpam-4506	47	1	2	CARDINAL
ejpam-4506	49	1	5	CARDINAL
ejpam-4506	50	1	2	CARDINAL
ejpam-4506	52	1	6	CARDINAL
ejpam-4506	53	1	2	CARDINAL
ejpam-4506	54	1	7	CARDINAL
ejpam-4506	55	1	6	CARDINAL
ejpam-4506	55	2	g ⋄ h of g and h	ORG
ejpam-4506	55	3	one	CARDINAL
ejpam-4506	55	4	h. j. anoche	PERSON
ejpam-4506	55	5	i. aniversario	PERSON
ejpam-4506	55	6	c. merca	PERSON
ejpam-4506	56	1	j. pure	PERSON
ejpam-4506	56	2	16	CARDINAL
ejpam-4506	56	3	1	CARDINAL
ejpam-4506	56	4	2023	CARDINAL
ejpam-4506	56	5	169	CARDINAL
ejpam-4506	56	6	8	CARDINAL
ejpam-4506	57	1	4	CARDINAL
ejpam-4506	57	2	⊆	CARDINAL
ejpam-4506	58	1	2	CARDINAL
ejpam-4506	58	2	p2[s]g	ORG
ejpam-4506	58	3	p2[s]g	WORK_OF_ART
ejpam-4506	58	4	w ∈	PERSON
ejpam-4506	59	1	w ∈	PERSON
ejpam-4506	59	2	∈	ORG
ejpam-4506	59	3	2	CARDINAL
ejpam-4506	60	1	2	CARDINAL
ejpam-4506	61	1	2	CARDINAL
ejpam-4506	62	1	9	CARDINAL
ejpam-4506	63	1	3	CARDINAL
ejpam-4506	67	1	10	CARDINAL
ejpam-4506	87	1	c1 c2 d1	PERSON
ejpam-4506	87	2	1	CARDINAL
ejpam-4506	87	3	1	CARDINAL
ejpam-4506	87	4	1	CARDINAL
ejpam-4506	88	1	{c1	PERSON
ejpam-4506	89	1	{c1	PERSON
ejpam-4506	89	2	{c1	PERSON
ejpam-4506	89	3	{c1	PERSON
ejpam-4506	89	4	{c1	PERSON
ejpam-4506	90	1	{c1	PERSON
ejpam-4506	93	1	c1	ORG
ejpam-4506	95	1	less than 3	CARDINAL
ejpam-4506	97	1	3	CARDINAL
ejpam-4506	97	2	j. anoche	PERSON
ejpam-4506	97	3	i. aniversario	PERSON
ejpam-4506	97	4	c. merca	PERSON
ejpam-4506	98	1	j. pure	PERSON
ejpam-4506	98	2	16	CARDINAL
ejpam-4506	98	3	1	CARDINAL
ejpam-4506	98	4	2023	CARDINAL
ejpam-4506	98	5	169	CARDINAL
ejpam-4506	98	6	∖	PERSON
ejpam-4506	99	1	at least two	CARDINAL
ejpam-4506	99	2	3	CARDINAL
ejpam-4506	99	3	1	CARDINAL
ejpam-4506	100	1	7	CARDINAL
ejpam-4506	101	1	2 ≤	QUANTITY
ejpam-4506	102	1	1	CARDINAL
ejpam-4506	103	1	3	CARDINAL
ejpam-4506	104	1	n 2 + 1	ORG
ejpam-4506	104	2	2 + 1	DATE
ejpam-4506	105	1	2	CARDINAL
ejpam-4506	106	1	3	CARDINAL
ejpam-4506	107	1	⊆	CARDINAL
ejpam-4506	107	2	g∖	DATE
ejpam-4506	107	3	s.	GPE
ejpam-4506	107	4	2	CARDINAL
ejpam-4506	108	1	3	CARDINAL
ejpam-4506	108	2	3	CARDINAL
ejpam-4506	109	1	3	CARDINAL
ejpam-4506	110	1	two	CARDINAL
ejpam-4506	110	2	4	CARDINAL
ejpam-4506	111	1	3	CARDINAL
ejpam-4506	112	1	2	CARDINAL
ejpam-4506	113	1	5	CARDINAL
ejpam-4506	114	1	3	CARDINAL
ejpam-4506	115	1	m. theorem 6	PERSON
ejpam-4506	116	1	3	CARDINAL
ejpam-4506	119	1	3	CARDINAL
ejpam-4506	119	2	9	CARDINAL
ejpam-4506	120	1	2	CARDINAL
ejpam-4506	121	1	c8	GPE
ejpam-4506	124	1	j. anoche	PERSON
ejpam-4506	124	2	i. aniversario	PERSON
ejpam-4506	124	3	c. merca	PERSON
ejpam-4506	125	1	j. pure	PERSON
ejpam-4506	125	2	16	CARDINAL
ejpam-4506	125	3	1	CARDINAL
ejpam-4506	125	4	2023	CARDINAL
ejpam-4506	125	5	169	CARDINAL
ejpam-4506	125	6	179 173	CARDINAL
ejpam-4506	134	1	c8 v8 v1 v2 v3	PERSON
ejpam-4506	134	2	2	CARDINAL
ejpam-4506	134	3	3	CARDINAL
ejpam-4506	135	1	4	CARDINAL
ejpam-4506	136	1	10	CARDINAL
ejpam-4506	149	1	v1 v2 v3v4 :	ORG
ejpam-4506	149	2	3	CARDINAL
ejpam-4506	149	3	2	CARDINAL
ejpam-4506	149	4	k1,5	ORG
ejpam-4506	149	5	3	CARDINAL
ejpam-4506	149	6	k1,5	ORG
ejpam-4506	149	7	k1,5	ORG
ejpam-4506	149	8	k1,5	ORG
ejpam-4506	151	1	k1,5	ORG
ejpam-4506	152	1	k1,n	ORG
ejpam-4506	153	1	7	CARDINAL
ejpam-4506	155	1	⊆	CARDINAL
ejpam-4506	155	2	g∖	DATE
ejpam-4506	155	3	s. j. anoche	PERSON
ejpam-4506	155	4	i. aniversario	PERSON
ejpam-4506	155	5	c. merca	PERSON
ejpam-4506	156	1	j. pure	PERSON
ejpam-4506	156	2	16	CARDINAL
ejpam-4506	156	3	1	CARDINAL
ejpam-4506	156	4	2023	CARDINAL
ejpam-4506	156	5	169	CARDINAL
ejpam-4506	156	6	⊆	CARDINAL
ejpam-4506	156	7	4	CARDINAL
ejpam-4506	157	1	2	CARDINAL
ejpam-4506	157	2	g∖	DATE
ejpam-4506	157	3	s. ■	ORG
ejpam-4506	157	4	2	CARDINAL
ejpam-4506	157	5	3	CARDINAL
ejpam-4506	157	6	4	CARDINAL
ejpam-4506	158	1	5	CARDINAL
ejpam-4506	159	1	g. theorem 8	ORG
ejpam-4506	161	1	2	CARDINAL
ejpam-4506	161	2	3	CARDINAL
ejpam-4506	173	1	•	CARDINAL
ejpam-4506	173	2	4	CARDINAL
ejpam-4506	173	3	4	CARDINAL
ejpam-4506	173	4	8	CARDINAL
ejpam-4506	173	5	3	CARDINAL
ejpam-4506	174	1	9	CARDINAL
ejpam-4506	176	1	2	CARDINAL
ejpam-4506	177	1	9	CARDINAL
ejpam-4506	177	2	three	CARDINAL
ejpam-4506	178	1	5	CARDINAL
ejpam-4506	178	2	9	CARDINAL
ejpam-4506	178	3	three	CARDINAL
ejpam-4506	179	1	j. anoche	PERSON
ejpam-4506	179	2	i. aniversario	PERSON
ejpam-4506	179	3	c. merca	PERSON
ejpam-4506	180	1	j. pure	PERSON
ejpam-4506	180	2	16	CARDINAL
ejpam-4506	180	3	1	CARDINAL
ejpam-4506	180	4	2023	CARDINAL
ejpam-4506	180	5	169	CARDINAL
ejpam-4506	201	1	•	CARDINAL
ejpam-4506	201	2	bb2 b3 v1 v2v3	PERSON
ejpam-4506	201	3	5	CARDINAL
ejpam-4506	201	4	1	CARDINAL
ejpam-4506	201	5	6	CARDINAL
ejpam-4506	202	1	2 ≤	QUANTITY
ejpam-4506	203	1	10	CARDINAL
ejpam-4506	205	1	2	CARDINAL
ejpam-4506	206	1	10	DATE
ejpam-4506	211	1	2	CARDINAL
ejpam-4506	211	2	2	CARDINAL
ejpam-4506	211	3	7	CARDINAL
ejpam-4506	213	1	g. j. changa et al	PERSON
ejpam-4506	214	1	5	CARDINAL
ejpam-4506	216	1	1	CARDINAL
ejpam-4506	217	1	m. theorem 11	PERSON
ejpam-4506	219	1	m. proof	PERSON
ejpam-4506	219	2	3	CARDINAL
ejpam-4506	219	3	∈	ORG
ejpam-4506	220	1	5	CARDINAL
ejpam-4506	220	2	∈	ORG
ejpam-4506	222	1	m. ■ j. anoche	PERSON
ejpam-4506	222	2	i. aniversario	PERSON
ejpam-4506	222	3	c. merca	PERSON
ejpam-4506	223	1	j. pure	PERSON
ejpam-4506	223	2	16	CARDINAL
ejpam-4506	223	3	1	CARDINAL
ejpam-4506	223	4	2023	CARDINAL
ejpam-4506	223	5	169	CARDINAL
ejpam-4506	223	6	8	CARDINAL
ejpam-4506	228	1	1	CARDINAL
ejpam-4506	232	1	m. ■	PERSON
ejpam-4506	233	1	12	CARDINAL
ejpam-4506	237	1	10	CARDINAL
ejpam-4506	238	1	6	CARDINAL
ejpam-4506	240	1	1	CARDINAL
ejpam-4506	241	1	4	CARDINAL
ejpam-4506	241	2	two	CARDINAL
ejpam-4506	242	1	two	CARDINAL
ejpam-4506	243	1	6	CARDINAL
ejpam-4506	261	1	..............................................................................................................................................................................................................	PERSON
ejpam-4506	289	1	6	CARDINAL
ejpam-4506	289	2	j. anoche	PERSON
ejpam-4506	289	3	i. aniversario	PERSON
ejpam-4506	289	4	c. merca	PERSON
ejpam-4506	290	1	j. pure	PERSON
ejpam-4506	290	2	16	CARDINAL
ejpam-4506	290	3	1	CARDINAL
ejpam-4506	290	4	2023	CARDINAL
ejpam-4506	290	5	169	CARDINAL
ejpam-4506	292	1	first	ORDINAL
ejpam-4506	293	1	⊆	CARDINAL
ejpam-4506	294	1	9	CARDINAL
ejpam-4506	295	1	2	CARDINAL
ejpam-4506	297	1	13	CARDINAL
ejpam-4506	298	1	bothk andh	ORG
ejpam-4506	298	2	∈	ORG
ejpam-4506	298	3	∈	ORG
ejpam-4506	299	1	k⋄h	PERSON
ejpam-4506	300	1	⋃ uv∈e(k	PERSON
ejpam-4506	300	2	∪a	CARDINAL
ejpam-4506	300	3	⊆	CARDINAL
ejpam-4506	300	4	∈	ORG
ejpam-4506	300	5	⊆	CARDINAL
ejpam-4506	300	6	ωhuv	ORG
ejpam-4506	301	1	k ⋄ h	ORG
ejpam-4506	302	1	⊆	CARDINAL
ejpam-4506	302	2	⊆	CARDINAL
ejpam-4506	303	1	⋃ uv∈e(k	PERSON
ejpam-4506	303	2	a.	PERSON
ejpam-4506	303	3	7	DATE
ejpam-4506	303	4	huv copy	PERSON
ejpam-4506	303	5	∈	ORG
ejpam-4506	304	1	huv	ORG
ejpam-4506	304	2	ωhuv	GPE
ejpam-4506	305	1	ωhuv	ORG
ejpam-4506	307	1	⋃ uv∈e(k	PERSON
ejpam-4506	307	2	∪a	CARDINAL
ejpam-4506	308	1	2	CARDINAL
ejpam-4506	310	1	7	CARDINAL
ejpam-4506	311	1	2	CARDINAL
ejpam-4506	311	2	k)∖a	PERSON
ejpam-4506	311	3	at least two	CARDINAL
ejpam-4506	311	4	k.	PERSON
ejpam-4506	311	5	g. ■ theorem	ORG
ejpam-4506	311	6	14	DATE
ejpam-4506	312	1	≥ 3	DATE
ejpam-4506	312	2	∈	ORG
ejpam-4506	312	3	∈	ORG
ejpam-4506	316	1	∈	ORG
ejpam-4506	318	1	j. anoche	PERSON
ejpam-4506	318	2	i. aniversario	PERSON
ejpam-4506	318	3	c. merca	PERSON
ejpam-4506	319	1	j. pure	PERSON
ejpam-4506	319	2	16	CARDINAL
ejpam-4506	319	3	1	CARDINAL
ejpam-4506	319	4	2023	CARDINAL
ejpam-4506	319	5	169	CARDINAL
ejpam-4506	319	6	∈	ORG
ejpam-4506	319	7	∈	ORG
ejpam-4506	320	1	3	CARDINAL
ejpam-4506	320	2	13	CARDINAL
ejpam-4506	320	3	⋃ uv∈e(k	PERSON
ejpam-4506	320	4	∪a	CARDINAL
ejpam-4506	320	5	⊆	CARDINAL
ejpam-4506	320	6	∈	ORG
ejpam-4506	320	7	⊆	CARDINAL
ejpam-4506	320	8	ωhuv	ORG
ejpam-4506	321	1	ωhuv	LOC
ejpam-4506	323	1	∈	ORG
ejpam-4506	325	1	∈	ORG
ejpam-4506	327	1	∈	ORG
ejpam-4506	328	1	∈	ORG
ejpam-4506	329	1	2	CARDINAL
ejpam-4506	330	1	3	CARDINAL
ejpam-4506	332	1	|e(pn)|	GPE
ejpam-4506	332	2	n ≥ 1	DATE
ejpam-4506	332	3	14	DATE
ejpam-4506	332	4	|e(pn)|	GPE
ejpam-4506	332	5	skm ∈ ωkm}+min{|spn	PERSON
ejpam-4506	332	6	spn ∈	PERSON
ejpam-4506	332	7	1	CARDINAL
ejpam-4506	332	8	1	CARDINAL
ejpam-4506	332	9	m+	CARDINAL
ejpam-4506	332	10	n. ■ theorem 15	ORG
ejpam-4506	333	1	2	CARDINAL
ejpam-4506	335	1	2	CARDINAL
ejpam-4506	336	1	9	CARDINAL
ejpam-4506	336	2	∈	ORG
ejpam-4506	337	1	2	CARDINAL
ejpam-4506	337	2	y ∈ s	PERSON
ejpam-4506	341	1	2	CARDINAL
ejpam-4506	341	2	8	DATE
ejpam-4506	341	3	∈	ORG
ejpam-4506	341	4	at least two	CARDINAL
ejpam-4506	343	1	3	CARDINAL
ejpam-4506	343	2	3	CARDINAL
ejpam-4506	344	1	179	CARDINAL
ejpam-4506	344	2	15	CARDINAL
ejpam-4506	344	3	γpicg(k2 ⋄	ORG
ejpam-4506	345	1	4	CARDINAL
ejpam-4506	347	1	2	CARDINAL
ejpam-4506	349	1	2	CARDINAL
ejpam-4506	349	2	∈	ORG
ejpam-4506	349	3	dh(u	ORG
ejpam-4506	352	1	15	CARDINAL
ejpam-4506	354	1	3	CARDINAL
ejpam-4506	355	1	diam(fn	PERSON
ejpam-4506	355	2	2	CARDINAL
ejpam-4506	355	3	diam(wm	PERSON
ejpam-4506	355	4	2	CARDINAL
ejpam-4506	355	5	4	CARDINAL
ejpam-4506	355	6	4	CARDINAL
ejpam-4506	356	1	4	CARDINAL
ejpam-4506	356	2	the department of science and technology	ORG
ejpam-4506	356	3	philippines	GPE
ejpam-4506	357	1	1	CARDINAL
ejpam-4506	357	2	i. s. aniversario	PERSON
ejpam-4506	357	3	f. p. jamil	PERSON
ejpam-4506	357	4	s. r. canoy jr.	PERSON
ejpam-4506	359	1	utilitas mathematica	PERSON
ejpam-4506	359	2	74:3–18	DATE
ejpam-4506	359	3	2007	DATE
ejpam-4506	360	1	2	CARDINAL
ejpam-4506	360	2	f. buckley	PERSON
ejpam-4506	360	3	f. harary	PERSON
ejpam-4506	362	1	addison-wesley	ORG
ejpam-4506	362	2	1990	DATE
ejpam-4506	363	1	3	CARDINAL
ejpam-4506	363	2	i. cauntongan	PERSON
ejpam-4506	363	3	i. s. aniversario	PERSON
ejpam-4506	365	1	22(1):41–53	CARDINAL
ejpam-4506	365	2	2019	DATE
ejpam-4506	366	1	4	CARDINAL
ejpam-4506	366	2	jamil	PERSON
ejpam-4506	366	3	m. b. macababat	PERSON
ejpam-4506	368	1	26:1277–1290, 2010	DATE
ejpam-4506	369	1	5	CARDINAL
ejpam-4506	369	2	l.d. tong g. j. changa	PERSON
ejpam-4506	369	3	wang	PERSON
ejpam-4506	370	1	25	CARDINAL
ejpam-4506	370	2	2004	DATE
ejpam-4506	371	1	6	CARDINAL
ejpam-4506	371	2	h. rara	PERSON
ejpam-4506	373	1	2017	DATE
ejpam-4506	374	1	7	CARDINAL
ejpam-4506	374	2	r. n. villarante	PERSON
ejpam-4506	374	3	i. s. aniversario	PERSON
ejpam-4506	375	1	29(5	CARDINAL
ejpam-4506	376	1	2017	CARDINAL