id	sid	eid	entity	type
ejpam-4144	1	1	european journal	ORG
ejpam-4144	2	1	14	DATE
ejpam-4144	2	2	4	CARDINAL
ejpam-4144	2	3	2021	DATE
ejpam-4144	2	4	1415-1428	CARDINAL
ejpam-4144	2	5	new york	GPE
ejpam-4144	2	6	gemma salasalan1,∗	PERSON
ejpam-4144	2	7	sergio r. canoy	PERSON
ejpam-4144	2	8	1	CARDINAL
ejpam-4144	2	9	davao del sur state college	ORG
ejpam-4144	2	10	matti	ORG
ejpam-4144	2	11	digos city	GPE
ejpam-4144	2	12	davao del sur	GPE
ejpam-4144	2	13	philippines 2 department	ORG
ejpam-4144	2	14	msu-iligan institute of technology	ORG
ejpam-4144	2	15	9200 iligan city	GPE
ejpam-4144	2	16	3	CARDINAL
ejpam-4144	2	17	institute of science	ORG
ejpam-4144	2	18	msu-iligan institute of technology	ORG
ejpam-4144	2	19	9200	CARDINAL
ejpam-4144	2	20	iligan city	GPE
ejpam-4144	2	21	philippines	GPE
ejpam-4144	3	1	⊆	CARDINAL
ejpam-4144	4	1	w ∈ s	PERSON
ejpam-4144	5	1	2	CARDINAL
ejpam-4144	10	1	2020	DATE
ejpam-4144	10	2	05c69	CARDINAL
ejpam-4144	10	3	1	CARDINAL
ejpam-4144	14	1	1	CARDINAL
ejpam-4144	14	2	2	CARDINAL
ejpam-4144	14	3	3	CARDINAL
ejpam-4144	14	4	4	CARDINAL
ejpam-4144	14	5	6	CARDINAL
ejpam-4144	14	6	8	CARDINAL
ejpam-4144	14	7	9	CARDINAL
ejpam-4144	14	8	10	CARDINAL
ejpam-4144	14	9	14	CARDINAL
ejpam-4144	15	1	natarajan	PERSON
ejpam-4144	15	2	13	CARDINAL
ejpam-4144	16	1	5	CARDINAL
ejpam-4144	16	2	11	CARDINAL
ejpam-4144	16	3	12	CARDINAL
ejpam-4144	16	4	15	CARDINAL
ejpam-4144	16	5	16	CARDINAL
ejpam-4144	19	1	g. salasalan	PERSON
ejpam-4144	19	2	sergio.canoy@g.msuiit.edu.ph	ORG
ejpam-4144	19	3	s. canoy, jr.	PERSON
ejpam-4144	20	1	2021	CARDINAL
ejpam-4144	21	1	g. salasalan	PERSON
ejpam-4144	21	2	s. canoy, jr.	PERSON
ejpam-4144	22	1	j. pure	PERSON
ejpam-4144	22	2	14	CARDINAL
ejpam-4144	22	3	4	CARDINAL
ejpam-4144	22	4	2021	CARDINAL
ejpam-4144	22	5	1415-1428 1416	CARDINAL
ejpam-4144	23	1	16	CARDINAL
ejpam-4144	26	1	two	CARDINAL
ejpam-4144	28	1	∈	ORG
ejpam-4144	29	1	s. the degree of	PERSON
ejpam-4144	31	1	1	CARDINAL
ejpam-4144	32	1	2	CARDINAL
ejpam-4144	32	2	w ∈	PERSON
ejpam-4144	32	3	2	CARDINAL
ejpam-4144	32	4	2	CARDINAL
ejpam-4144	32	5	2	CARDINAL
ejpam-4144	33	1	2	CARDINAL
ejpam-4144	33	2	2	CARDINAL
ejpam-4144	33	3	2	CARDINAL
ejpam-4144	33	4	2	CARDINAL
ejpam-4144	33	5	s.	PERSON
ejpam-4144	33	6	⊆	CARDINAL
ejpam-4144	34	1	γ(g	NORP
ejpam-4144	34	2	⊆	CARDINAL
ejpam-4144	36	1	∈	ORG
ejpam-4144	36	2	2	CARDINAL
ejpam-4144	36	3	⊆	CARDINAL
ejpam-4144	36	4	2	CARDINAL
ejpam-4144	38	1	first	ORDINAL
ejpam-4144	39	1	1	CARDINAL
ejpam-4144	41	1	1	CARDINAL
ejpam-4144	42	1	1	CARDINAL
ejpam-4144	44	1	kn+1	GPE
ejpam-4144	45	1	γ(g	NORP
ejpam-4144	45	2	1	CARDINAL
ejpam-4144	49	1	1	CARDINAL
ejpam-4144	49	2	2	CARDINAL
ejpam-4144	54	1	g. salasalan	PERSON
ejpam-4144	54	2	s. canoy, jr.	PERSON
ejpam-4144	55	1	j. pure	PERSON
ejpam-4144	55	2	14	CARDINAL
ejpam-4144	55	3	4	CARDINAL
ejpam-4144	55	4	2021	CARDINAL
ejpam-4144	55	5	1415-1428 1417	CARDINAL
ejpam-4144	67	1	w3	PRODUCT
ejpam-4144	68	1	1	CARDINAL
ejpam-4144	70	1	γ(g)−	ORG
ejpam-4144	70	2	2)− 2	CARDINAL
ejpam-4144	71	1	1	CARDINAL
ejpam-4144	74	1	2 ≤	QUANTITY
ejpam-4144	75	1	3 ≤	QUANTITY
ejpam-4144	75	2	γ(h	ORG
ejpam-4144	76	1	first	ORDINAL
ejpam-4144	76	2	2	CARDINAL
ejpam-4144	77	1	xa	PERSON
ejpam-4144	80	1	= a.	PERSON
ejpam-4144	85	1	y3 ya−1 ya	PERSON
ejpam-4144	86	1	xa−1 xa	PERSON
ejpam-4144	87	1	2	CARDINAL
ejpam-4144	88	1	− a.	PERSON
ejpam-4144	88	2	3	CARDINAL
ejpam-4144	90	1	xa	PERSON
ejpam-4144	90	2	= a.	PERSON
ejpam-4144	94	1	|s′|	PERSON
ejpam-4144	94	2	b. g. salasalan	PERSON
ejpam-4144	94	3	s. canoy, jr.	PERSON
ejpam-4144	95	1	j. pure	PERSON
ejpam-4144	95	2	14	CARDINAL
ejpam-4144	95	3	4	CARDINAL
ejpam-4144	95	4	2021	CARDINAL
ejpam-4144	95	5	1415-1428 1418	CARDINAL
ejpam-4144	118	1	y3 ya−1 ya	PERSON
ejpam-4144	120	1	xa−1 xa	PERSON
ejpam-4144	120	2	z2 zm	ORG
ejpam-4144	122	1	3 (ii	CARDINAL
ejpam-4144	122	2	first	ORDINAL
ejpam-4144	124	1	− a.	PERSON
ejpam-4144	124	2	km+1	PERSON
ejpam-4144	124	3	km+1	PERSON
ejpam-4144	126	1	4	CARDINAL
ejpam-4144	128	1	ya−1	PERSON
ejpam-4144	130	1	xa−1}∪	PERSON
ejpam-4144	145	1	xa−1	PERSON
ejpam-4144	146	1	4 v	QUANTITY
ejpam-4144	146	2	km+1	PERSON
ejpam-4144	146	3	ofh	GPE
ejpam-4144	147	1	γ(h	ORG
ejpam-4144	147	2	a−1+m+1	DATE
ejpam-4144	150	1	1	CARDINAL
ejpam-4144	152	1	16	CARDINAL
ejpam-4144	152	2	1	CARDINAL
ejpam-4144	153	1	3.3	CARDINAL
ejpam-4144	153	2	16	CARDINAL
ejpam-4144	154	1	2	CARDINAL
ejpam-4144	154	2	3.3	CARDINAL
ejpam-4144	154	3	16	CARDINAL
ejpam-4144	157	1	∈	ORG
ejpam-4144	159	1	first	ORDINAL
ejpam-4144	161	1	2	CARDINAL
ejpam-4144	162	1	g. salasalan	PERSON
ejpam-4144	162	2	s. canoy, jr.	PERSON
ejpam-4144	163	1	j. pure	PERSON
ejpam-4144	163	2	14	CARDINAL
ejpam-4144	163	3	4	CARDINAL
ejpam-4144	163	4	2021	CARDINAL
ejpam-4144	163	5	1415-1428 1419	CARDINAL
ejpam-4144	163	6	w ∈	ORG
ejpam-4144	163	7	2	CARDINAL
ejpam-4144	169	1	∈	ORG
ejpam-4144	169	2	2	CARDINAL
ejpam-4144	171	1	2	CARDINAL
ejpam-4144	172	1	∈	ORG
ejpam-4144	173	1	2	CARDINAL
ejpam-4144	176	1	first	ORDINAL
ejpam-4144	177	1	first	ORDINAL
ejpam-4144	181	1	∈	ORG
ejpam-4144	182	1	∈	ORG
ejpam-4144	182	2	g)\ng(v	PERSON
ejpam-4144	182	3	dg(a	GPE
ejpam-4144	182	4	2	CARDINAL
ejpam-4144	183	1	dg(a	GPE
ejpam-4144	183	2	w	GPE
ejpam-4144	183	3	2	CARDINAL
ejpam-4144	187	1	∈	ORG
ejpam-4144	188	1	cv	PERSON
ejpam-4144	189	1	∈	ORG
ejpam-4144	189	2	cv	ORG
ejpam-4144	191	1	2	CARDINAL
ejpam-4144	191	2	1	CARDINAL
ejpam-4144	192	1	2	CARDINAL
ejpam-4144	192	2	3	CARDINAL
ejpam-4144	193	1	2 ≤	QUANTITY
ejpam-4144	195	1	1	CARDINAL
ejpam-4144	197	1	2	CARDINAL
ejpam-4144	197	2	2	CARDINAL
ejpam-4144	198	1	k = b− a.	PERSON
ejpam-4144	199	1	xa−1	PERSON
ejpam-4144	199	2	5	CARDINAL
ejpam-4144	199	3	+ ka−1	PERSON
ejpam-4144	199	4	1	CARDINAL
ejpam-4144	199	5	2	DATE
ejpam-4144	201	1	j ∈	PERSON
ejpam-4144	201	2	1	CARDINAL
ejpam-4144	201	3	2	DATE
ejpam-4144	203	1	g. salasalan	PERSON
ejpam-4144	203	2	s. canoy, jr.	PERSON
ejpam-4144	204	1	j. pure	PERSON
ejpam-4144	204	2	14	CARDINAL
ejpam-4144	204	3	4	CARDINAL
ejpam-4144	204	4	2021	CARDINAL
ejpam-4144	204	5	1415-1428 1420	CARDINAL
ejpam-4144	275	1	xa−1	PERSON
ejpam-4144	276	1	y1 y2 yk	PERSON
ejpam-4144	277	1	5	CARDINAL
ejpam-4144	279	1	xa−1	PERSON
ejpam-4144	280	1	1 ≤ i ≤	QUANTITY
ejpam-4144	280	2	1	CARDINAL
ejpam-4144	280	3	2	CARDINAL
ejpam-4144	280	4	1	CARDINAL
ejpam-4144	280	5	2	DATE
ejpam-4144	282	1	k}	PERSON
ejpam-4144	283	1	ka−1	PERSON
ejpam-4144	284	1	2	CARDINAL
ejpam-4144	284	2	1	CARDINAL
ejpam-4144	284	3	2	CARDINAL
ejpam-4144	287	1	3	CARDINAL
ejpam-4144	288	1	1	CARDINAL
ejpam-4144	291	1	∈	ORG
ejpam-4144	291	2	∪g	CARDINAL
ejpam-4144	291	3	∈	ORG
ejpam-4144	293	1	4	CARDINAL
ejpam-4144	294	1	10	CARDINAL
ejpam-4144	296	1	5	CARDINAL
ejpam-4144	298	1	γ(g	NORP
ejpam-4144	299	1	1	CARDINAL
ejpam-4144	300	1	1 + γ(g	MONEY
ejpam-4144	301	1	n ≥ 1	DATE
ejpam-4144	302	1	2	CARDINAL
ejpam-4144	303	1	n ≥ 2	DATE
ejpam-4144	303	2	2γgh(g	CARDINAL
ejpam-4144	306	1	⊆	CARDINAL
ejpam-4144	306	2	ngg(v	ORG
ejpam-4144	307	1	1 + γ(g	MONEY
ejpam-4144	308	1	g. salasalan	PERSON
ejpam-4144	308	2	s. canoy, jr.	PERSON
ejpam-4144	309	1	j. pure	PERSON
ejpam-4144	309	2	14	CARDINAL
ejpam-4144	309	3	4	CARDINAL
ejpam-4144	309	4	2021	CARDINAL
ejpam-4144	309	5	1415-1428 1421	CARDINAL
ejpam-4144	309	6	s0	ORG
ejpam-4144	311	1	∈	ORG
ejpam-4144	311	2	∈	ORG
ejpam-4144	312	1	∈	ORG
ejpam-4144	312	2	ngg(w)∩v	PERSON
ejpam-4144	313	1	1+γ(g\v	CARDINAL
ejpam-4144	314	1	∩	PERSON
ejpam-4144	317	1	w ∈	PERSON
ejpam-4144	317	2	w ∈	PERSON
ejpam-4144	319	1	1+ |s1|+	MONEY
ejpam-4144	319	2	1+γ(g\v	CARDINAL
ejpam-4144	320	1	∈	ORG
ejpam-4144	321	1	s0	ORG
ejpam-4144	328	1	2	CARDINAL
ejpam-4144	328	2	∈	ORG
ejpam-4144	328	3	2	CARDINAL
ejpam-4144	328	4	2|	CARDINAL
ejpam-4144	329	1	d′ = d2 ∪d∗ 2	PERSON
ejpam-4144	329	2	1+	CARDINAL
ejpam-4144	329	3	1+ |d′|	DATE
ejpam-4144	329	4	1 + γ(g	QUANTITY
ejpam-4144	331	1	g = kn	PERSON
ejpam-4144	334	1	2	CARDINAL
ejpam-4144	334	2	n ≥ 2	ORG
ejpam-4144	335	1	∈	ORG
ejpam-4144	336	1	w ∈	PERSON
ejpam-4144	337	1	wv	GPE
ejpam-4144	338	1	wv	GPE
ejpam-4144	339	1	w	GPE
ejpam-4144	345	1	2	CARDINAL
ejpam-4144	345	2	n ≥ 2	ORG
ejpam-4144	347	1	w ∈	ORG
ejpam-4144	349	1	w	GPE
ejpam-4144	350	1	2	CARDINAL
ejpam-4144	352	1	yy	GPE
ejpam-4144	354	1	xy ∈	ORG
ejpam-4144	355	1	yx ∈	ORG
ejpam-4144	356	1	2	CARDINAL
ejpam-4144	357	1	xy	ORG
ejpam-4144	359	1	xy ∈	ORG
ejpam-4144	360	1	xy ∈	ORG
ejpam-4144	360	2	2	CARDINAL
ejpam-4144	363	1	sg	GPE
ejpam-4144	365	1	2γgh(g	CARDINAL
ejpam-4144	366	1	first	ORDINAL
ejpam-4144	370	1	3	CARDINAL
ejpam-4144	370	2	4	CARDINAL
ejpam-4144	370	3	5	CARDINAL
ejpam-4144	370	4	6	CARDINAL
ejpam-4144	371	1	m1 ≤ m2 ≤ g. salasalan	QUANTITY
ejpam-4144	371	2	s. canoy, jr.	PERSON
ejpam-4144	372	1	j. pure	PERSON
ejpam-4144	372	2	14	CARDINAL
ejpam-4144	372	3	4	CARDINAL
ejpam-4144	372	4	2021	CARDINAL
ejpam-4144	372	5	1415-1428 1422	CARDINAL
ejpam-4144	373	1	k ≥ 2.	ORG
ejpam-4144	375	1	1	CARDINAL
ejpam-4144	375	2	2	CARDINAL
ejpam-4144	378	1	uk	GPE
ejpam-4144	378	2	|ui|	NORP
ejpam-4144	378	3	1	CARDINAL
ejpam-4144	378	4	2	DATE
ejpam-4144	381	1	1	CARDINAL
ejpam-4144	381	2	2	DATE
ejpam-4144	382	1	k}	PERSON
ejpam-4144	384	1	uk	GPE
ejpam-4144	385	1	first	ORDINAL
ejpam-4144	385	2	1	CARDINAL
ejpam-4144	386	1	5(i	CARDINAL
ejpam-4144	386	2	1+ γ(g	MONEY
ejpam-4144	391	1	1	CARDINAL
ejpam-4144	392	1	2	CARDINAL
ejpam-4144	393	1	4	CARDINAL
ejpam-4144	394	1	k + 2	ORG
ejpam-4144	396	1	2	CARDINAL
ejpam-4144	397	1	k}	PERSON
ejpam-4144	397	2	vi ∈	PERSON
ejpam-4144	397	3	{vi :	PERSON
ejpam-4144	397	4	2	CARDINAL
ejpam-4144	397	5	3	DATE
ejpam-4144	401	1	2 +	DATE
ejpam-4144	403	1	s′ ∩	WORK_OF_ART
ejpam-4144	403	2	|s′|	GPE
ejpam-4144	405	1	s′ ∩	WORK_OF_ART
ejpam-4144	405	2	1	CARDINAL
ejpam-4144	405	3	2	DATE
ejpam-4144	407	1	s′ ∩ u1 ̸=	WORK_OF_ART
ejpam-4144	407	2	∩	WORK_OF_ART
ejpam-4144	407	3	1	CARDINAL
ejpam-4144	407	4	∈	ORG
ejpam-4144	407	5	s′	PRODUCT
ejpam-4144	408	1	⊆	CARDINAL
ejpam-4144	408	2	ngg(v	ORG
ejpam-4144	409	1	∩	ORG
ejpam-4144	409	2	1	CARDINAL
ejpam-4144	410	1	j ∈	PERSON
ejpam-4144	410	2	2	CARDINAL
ejpam-4144	410	3	3	DATE
ejpam-4144	411	1	⊆	CARDINAL
ejpam-4144	411	2	w ∈	ORG
ejpam-4144	412	1	sw	ORG
ejpam-4144	413	1	|uj | ≥	DATE
ejpam-4144	413	2	2	CARDINAL
ejpam-4144	413	3	|s′|	PERSON
ejpam-4144	414	1	j ̸=	PERSON
ejpam-4144	414	2	2	CARDINAL
ejpam-4144	414	3	3	DATE
ejpam-4144	417	1	1	CARDINAL
ejpam-4144	417	2	2	CARDINAL
ejpam-4144	417	3	3	DATE
ejpam-4144	421	1	∩	WORK_OF_ART
ejpam-4144	421	2	2	CARDINAL
ejpam-4144	421	3	s′ ∩	WORK_OF_ART
ejpam-4144	421	4	2	CARDINAL
ejpam-4144	422	1	k}	PERSON
ejpam-4144	423	1	∩	WORK_OF_ART
ejpam-4144	423	2	1	CARDINAL
ejpam-4144	423	3	j ̸= 1	PERSON
ejpam-4144	423	4	∩	PERSON
ejpam-4144	423	5	1	CARDINAL
ejpam-4144	424	1	s′ ∩	WORK_OF_ART
ejpam-4144	424	2	2	CARDINAL
ejpam-4144	425	1	j − 1	PERSON
ejpam-4144	425	2	j + 2	PRODUCT
ejpam-4144	427	1	k}	PERSON
ejpam-4144	429	1	∩	PERSON
ejpam-4144	429	2	2	CARDINAL
ejpam-4144	432	1	+ 1	DATE
ejpam-4144	434	1	4	CARDINAL
ejpam-4144	436	1	1	CARDINAL
ejpam-4144	436	2	2	DATE
ejpam-4144	439	1	∩	WORK_OF_ART
ejpam-4144	439	2	3	CARDINAL
ejpam-4144	439	3	≥ k	PERSON
ejpam-4144	441	1	j ̸= 1	PERSON
ejpam-4144	441	2	≥ k	PERSON
ejpam-4144	443	1	|s∩u1|	CARDINAL
ejpam-4144	443	2	2	CARDINAL
ejpam-4144	443	3	|s∩u1|	CARDINAL
ejpam-4144	443	4	1	CARDINAL
ejpam-4144	443	5	u j)| = 2.	ORG
ejpam-4144	443	6	u r)| ≥ 2	PERSON
ejpam-4144	444	1	≥ k	PERSON
ejpam-4144	445	1	∩	WORK_OF_ART
ejpam-4144	446	1	⊆	CARDINAL
ejpam-4144	446	2	1	CARDINAL
ejpam-4144	447	1	3	CARDINAL
ejpam-4144	447	2	+3	DATE
ejpam-4144	448	1	1+	DATE
ejpam-4144	448	2	≥ k+3	PERSON
ejpam-4144	449	1	j ≥ 2	PERSON
ejpam-4144	449	2	u j)| ≥ 2.	ORG
ejpam-4144	450	1	2	CARDINAL
ejpam-4144	450	2	s g. salasalan	PERSON
ejpam-4144	450	3	s. canoy, jr.	PERSON
ejpam-4144	451	1	j. pure	PERSON
ejpam-4144	451	2	14	CARDINAL
ejpam-4144	451	3	4	CARDINAL
ejpam-4144	451	4	2021	CARDINAL
ejpam-4144	451	5	1415-1428 1423	CARDINAL
ejpam-4144	452	1	3	CARDINAL
ejpam-4144	454	1	1	CARDINAL
ejpam-4144	454	2	dom(g	NORP
ejpam-4144	454	3	∈	ORG
ejpam-4144	455	1	1	CARDINAL
ejpam-4144	456	1	1	CARDINAL
ejpam-4144	457	1	∈	ORG
ejpam-4144	457	2	∈	ORG
ejpam-4144	458	1	∈	ORG
ejpam-4144	459	1	∈	ORG
ejpam-4144	460	1	∈	ORG
ejpam-4144	461	1	2	CARDINAL
ejpam-4144	462	1	1	CARDINAL
ejpam-4144	464	1	∈	ORG
ejpam-4144	464	2	∈	ORG
ejpam-4144	464	3	s.	PERSON
ejpam-4144	464	4	3	CARDINAL
ejpam-4144	465	1	2	DATE
ejpam-4144	466	1	γgh(knkn	ORG
ejpam-4144	467	1	kn	PERSON
ejpam-4144	467	2	γgh(knkn	ORG
ejpam-4144	467	3	1	CARDINAL
ejpam-4144	467	4	γgh(knkn	ORG
ejpam-4144	468	1	1 ≤ m1 ≤ m2 ≤	QUANTITY
ejpam-4144	469	1	k ≥ 2	ORG
ejpam-4144	469	2	2	CARDINAL
ejpam-4144	469	3	j ≤ k.	PERSON
ejpam-4144	471	1	k ≥ 4 k + 1	ORG
ejpam-4144	475	1	uk	GPE
ejpam-4144	475	2	|ui|	NORP
ejpam-4144	475	3	1	CARDINAL
ejpam-4144	475	4	2	DATE
ejpam-4144	478	1	1	CARDINAL
ejpam-4144	478	2	2	DATE
ejpam-4144	479	1	k}	PERSON
ejpam-4144	480	1	vi ∈	PERSON
ejpam-4144	480	2	1	CARDINAL
ejpam-4144	480	3	2	DATE
ejpam-4144	483	1	m1 = m2 = 1 and	PERSON
ejpam-4144	483	2	k ≥ 4	ORG
ejpam-4144	487	1	dgg(v1, v2	GPE
ejpam-4144	487	2	2	CARDINAL
ejpam-4144	488	1	2	CARDINAL
ejpam-4144	488	2	3	CARDINAL
ejpam-4144	488	3	4	DATE
ejpam-4144	489	1	k}	PERSON
ejpam-4144	489	2	2	CARDINAL
ejpam-4144	489	3	2	CARDINAL
ejpam-4144	489	4	3	CARDINAL
ejpam-4144	490	1	2	CARDINAL
ejpam-4144	491	1	2	CARDINAL
ejpam-4144	491	2	3	CARDINAL
ejpam-4144	491	3	4	DATE
ejpam-4144	492	1	k}	PERSON
ejpam-4144	492	2	2	CARDINAL
ejpam-4144	492	3	2	CARDINAL
ejpam-4144	492	4	∈	ORG
ejpam-4144	494	1	= k. next	PERSON
ejpam-4144	494	2	j ∈	PERSON
ejpam-4144	494	3	1	CARDINAL
ejpam-4144	494	4	2	DATE
ejpam-4144	496	1	s0∩(uj∪u j	ORG
ejpam-4144	497	1	1	CARDINAL
ejpam-4144	498	1	2	CARDINAL
ejpam-4144	499	1	s0∩(uj∪u j	PERSON
ejpam-4144	499	2	1	CARDINAL
ejpam-4144	499	3	2	DATE
ejpam-4144	501	1	≥ k.	PERSON
ejpam-4144	501	2	k. g. salasalan	PERSON
ejpam-4144	501	3	s. canoy, jr.	PERSON
ejpam-4144	502	1	j. pure	PERSON
ejpam-4144	502	2	14	CARDINAL
ejpam-4144	502	3	4	CARDINAL
ejpam-4144	502	4	2021	CARDINAL
ejpam-4144	502	5	1415-1428 1424	CARDINAL
ejpam-4144	502	6	k ≥ 4	ORG
ejpam-4144	505	1	5(ii	CARDINAL
ejpam-4144	507	1	j ∈	PERSON
ejpam-4144	507	2	1	CARDINAL
ejpam-4144	507	3	2	DATE
ejpam-4144	511	1	2	CARDINAL
ejpam-4144	511	2	j ∈	PERSON
ejpam-4144	511	3	1	CARDINAL
ejpam-4144	511	4	2	DATE
ejpam-4144	513	1	1	CARDINAL
ejpam-4144	513	2	2	DATE
ejpam-4144	516	1	j \{vj}	PERSON
ejpam-4144	516	2	vi	PERSON
ejpam-4144	517	1	2	CARDINAL
ejpam-4144	521	1	+ 1	DATE
ejpam-4144	522	1	∩	WORK_OF_ART
ejpam-4144	522	2	1	CARDINAL
ejpam-4144	522	3	2	DATE
ejpam-4144	524	1	k}.	PERSON
ejpam-4144	525	1	j ∈	PERSON
ejpam-4144	525	2	1	CARDINAL
ejpam-4144	525	3	2	DATE
ejpam-4144	526	1	2	CARDINAL
ejpam-4144	526	2	∩	PERSON
ejpam-4144	527	1	∈	ORG
ejpam-4144	528	1	1	CARDINAL
ejpam-4144	528	2	∩	PERSON
ejpam-4144	528	3	∈	ORG
ejpam-4144	529	1	⊆	CARDINAL
ejpam-4144	530	1	2	CARDINAL
ejpam-4144	531	1	∩	PERSON
ejpam-4144	531	2	2	CARDINAL
ejpam-4144	532	1	∩	PERSON
ejpam-4144	532	2	2	CARDINAL
ejpam-4144	532	3	2	CARDINAL
ejpam-4144	534	1	∩	PERSON
ejpam-4144	534	2	1	CARDINAL
ejpam-4144	534	3	2	CARDINAL
ejpam-4144	535	1	∈	ORG
ejpam-4144	537	1	2	CARDINAL
ejpam-4144	538	1	2	CARDINAL
ejpam-4144	539	1	2	CARDINAL
ejpam-4144	540	1	1	CARDINAL
ejpam-4144	540	2	1	CARDINAL
ejpam-4144	540	3	2	CARDINAL
ejpam-4144	544	1	∈	ORG
ejpam-4144	544	2	∩	ORG
ejpam-4144	544	3	2	CARDINAL
ejpam-4144	544	4	dgg(z	ORG
ejpam-4144	545	1	2	CARDINAL
ejpam-4144	546	1	1	CARDINAL
ejpam-4144	546	2	2	CARDINAL
ejpam-4144	547	1	3	CARDINAL
ejpam-4144	549	1	∩	PERSON
ejpam-4144	550	1	s0	ORG
ejpam-4144	550	2	3	CARDINAL
ejpam-4144	552	1	2	CARDINAL
ejpam-4144	553	1	2	CARDINAL
ejpam-4144	554	1	k+1	TIME
ejpam-4144	555	1	two	CARDINAL
ejpam-4144	555	2	g1	ORG
ejpam-4144	555	3	∈	ORG
ejpam-4144	555	4	g1	ORG
ejpam-4144	556	1	2	CARDINAL
ejpam-4144	558	1	w ∈	PERSON
ejpam-4144	558	2	g1	ORG
ejpam-4144	558	3	w′ ∈	PERSON
ejpam-4144	558	4	w	GPE
ejpam-4144	558	5	2	CARDINAL
ejpam-4144	559	1	2	CARDINAL
ejpam-4144	560	1	2	CARDINAL
ejpam-4144	560	2	2	CARDINAL
ejpam-4144	563	1	2	CARDINAL
ejpam-4144	564	1	2	CARDINAL
ejpam-4144	564	2	2	CARDINAL
ejpam-4144	565	1	2	CARDINAL
ejpam-4144	566	1	2	CARDINAL
ejpam-4144	566	2	first	ORDINAL
ejpam-4144	566	3	∈	ORG
ejpam-4144	566	4	g1	ORG
ejpam-4144	568	1	2	CARDINAL
ejpam-4144	569	1	2	CARDINAL
ejpam-4144	570	1	g1	ORG
ejpam-4144	571	1	∈	ORG
ejpam-4144	572	1	∈	ORG
ejpam-4144	572	2	g1	ORG
ejpam-4144	572	3	g1	ORG
ejpam-4144	574	1	2	CARDINAL
ejpam-4144	575	1	z′ ∈	PERSON
ejpam-4144	576	1	g1	ORG
ejpam-4144	576	2	w′	GPE
ejpam-4144	576	3	z′	PERSON
ejpam-4144	577	1	∈	ORG
ejpam-4144	578	1	z′	PERSON
ejpam-4144	580	1	2	CARDINAL
ejpam-4144	581	1	2	CARDINAL
ejpam-4144	581	2	⊆	CARDINAL
ejpam-4144	581	3	2	CARDINAL
ejpam-4144	582	1	2	CARDINAL
ejpam-4144	582	2	g. salasalan	PERSON
ejpam-4144	582	3	s. canoy, jr.	PERSON
ejpam-4144	583	1	j. pure	PERSON
ejpam-4144	583	2	14	CARDINAL
ejpam-4144	583	3	4	CARDINAL
ejpam-4144	583	4	2021	CARDINAL
ejpam-4144	583	5	1415-1428 1425 nd2(g)[w	CARDINAL
ejpam-4144	583	6	2	CARDINAL
ejpam-4144	583	7	⊆	CARDINAL
ejpam-4144	583	8	2	CARDINAL
ejpam-4144	584	1	2	CARDINAL
ejpam-4144	585	1	2	CARDINAL
ejpam-4144	585	2	⊆	CARDINAL
ejpam-4144	585	3	2	CARDINAL
ejpam-4144	586	1	2	CARDINAL
ejpam-4144	587	1	2	CARDINAL
ejpam-4144	588	1	2	CARDINAL
ejpam-4144	589	1	2	CARDINAL
ejpam-4144	589	2	2	CARDINAL
ejpam-4144	590	1	13	CARDINAL
ejpam-4144	594	1	2	CARDINAL
ejpam-4144	594	2	γh(d2(h	DATE
ejpam-4144	595	1	6	CARDINAL
ejpam-4144	596	1	8	CARDINAL
ejpam-4144	601	1	g3	ORG
ejpam-4144	602	1	gk	PERSON
ejpam-4144	603	1	2r	CARDINAL
ejpam-4144	606	1	two	CARDINAL
ejpam-4144	607	1	g1	ORG
ejpam-4144	608	1	∈	ORG
ejpam-4144	608	2	g1	ORG
ejpam-4144	608	3	dd2(g)(v	GPE
ejpam-4144	609	1	2	CARDINAL
ejpam-4144	609	2	g1	ORG
ejpam-4144	609	3	w ∈ s	PERSON
ejpam-4144	609	4	dg1(v	GPE
ejpam-4144	609	5	w	GPE
ejpam-4144	609	6	2	CARDINAL
ejpam-4144	609	7	g1	ORG
ejpam-4144	610	1	∈	ORG
ejpam-4144	612	1	dd2(g)(w	PERSON
ejpam-4144	613	1	2	CARDINAL
ejpam-4144	615	1	g1	ORG
ejpam-4144	616	1	g1	ORG
ejpam-4144	617	1	|s′|	PERSON
ejpam-4144	617	2	g1	ORG
ejpam-4144	618	1	two	CARDINAL
ejpam-4144	619	1	∈	ORG
ejpam-4144	619	2	g1	ORG
ejpam-4144	620	1	2	CARDINAL
ejpam-4144	620	2	g1	ORG
ejpam-4144	621	1	2	CARDINAL
ejpam-4144	621	2	∈	ORG
ejpam-4144	621	3	g1	ORG
ejpam-4144	622	1	∈ sg	ORG
ejpam-4144	624	1	2	CARDINAL
ejpam-4144	624	2	2	CARDINAL
ejpam-4144	624	3	lemma 2.	ORG
ejpam-4144	624	4	g1	ORG
ejpam-4144	626	1	2	CARDINAL
ejpam-4144	627	1	w ∈	PERSON
ejpam-4144	627	2	z′ ∈ s2	PERSON
ejpam-4144	627	3	w ∈	ORG
ejpam-4144	627	4	2	CARDINAL
ejpam-4144	628	1	lemma 2	ORG
ejpam-4144	628	2	w ∈ nd2(g)[z	ORG
ejpam-4144	628	3	2	CARDINAL
ejpam-4144	629	1	2	CARDINAL
ejpam-4144	630	1	⊆	CARDINAL
ejpam-4144	630	2	2	CARDINAL
ejpam-4144	630	3	sg	GPE
ejpam-4144	630	4	g1	ORG
ejpam-4144	634	1	9	CARDINAL
ejpam-4144	639	1	g1	ORG
ejpam-4144	639	2	two	CARDINAL
ejpam-4144	640	1	g1	ORG
ejpam-4144	643	1	g1	ORG
ejpam-4144	644	1	2γgh(g	CARDINAL
ejpam-4144	646	1	g. salasalan	PERSON
ejpam-4144	646	2	s. canoy, jr.	PERSON
ejpam-4144	647	1	j. pure	PERSON
ejpam-4144	647	2	14	CARDINAL
ejpam-4144	647	3	4	CARDINAL
ejpam-4144	647	4	2021	CARDINAL
ejpam-4144	647	5	1415-1428 1426	CARDINAL
ejpam-4144	647	6	3	CARDINAL
ejpam-4144	651	1	d2(g	PERSON
ejpam-4144	652	1	4	CARDINAL
ejpam-4144	654	1	g = kn	PERSON
ejpam-4144	655	1	g = kn	PERSON
ejpam-4144	655	2	i=1 mi = n. proof	PERSON
ejpam-4144	656	1	g1	ORG
ejpam-4144	656	2	two	CARDINAL
ejpam-4144	658	1	3	CARDINAL
ejpam-4144	659	1	g = kn	PERSON
ejpam-4144	663	1	g = kn	PERSON
ejpam-4144	667	1	1	CARDINAL
ejpam-4144	667	2	2	DATE
ejpam-4144	668	1	k}	PERSON
ejpam-4144	668	2	s1,i	ORG
ejpam-4144	668	3	g1	ORG
ejpam-4144	668	4	ci	PERSON
ejpam-4144	669	1	s2,i	GPE
ejpam-4144	669	2	ci	PERSON
ejpam-4144	670	1	∈ s1,i	ORG
ejpam-4144	670	2	∈ s2,i	ORG
ejpam-4144	670	3	ci =	PERSON
ejpam-4144	671	1	1	CARDINAL
ejpam-4144	671	2	2	DATE
ejpam-4144	674	1	j ∈	PERSON
ejpam-4144	674	2	1	CARDINAL
ejpam-4144	674	3	2	DATE
ejpam-4144	676	1	ci	PERSON
ejpam-4144	676	2	s1,i	ORG
ejpam-4144	676	3	s1,j	GPE
ejpam-4144	676	4	g1	ORG
ejpam-4144	676	5	xy ∈	ORG
ejpam-4144	676	6	y ∈ s1,j	ORG
ejpam-4144	677	1	g1	ORG
ejpam-4144	677	2	partite	ORG
ejpam-4144	677	3	s1,1	GPE
ejpam-4144	680	1	s1,k	ORG
ejpam-4144	683	1	10	CARDINAL
ejpam-4144	685	1	2n	CARDINAL
ejpam-4144	685	2	g = kn	PERSON
ejpam-4144	685	3	i=1 mi = n. proof	PERSON
ejpam-4144	686	1	2	CARDINAL
ejpam-4144	687	1	2n	CARDINAL
ejpam-4144	688	1	lemma 4, γgh(d2(g	ORG
ejpam-4144	689	1	2n	CARDINAL
ejpam-4144	689	2	g = kn	PERSON
ejpam-4144	689	3	i=1 mi = n.	PERSON
ejpam-4144	689	4	10	CARDINAL
ejpam-4144	689	5	9	CARDINAL
ejpam-4144	693	1	1427	CARDINAL
ejpam-4144	693	2	2γgh(g	CARDINAL
ejpam-4144	693	3	9	CARDINAL
ejpam-4144	696	1	philippines	GPE
ejpam-4144	696	2	msu-iligan institute of technology	ORG
ejpam-4144	697	1	1	CARDINAL
ejpam-4144	697	2	s. jr.	PERSON
ejpam-4144	698	1	canoy	PERSON
ejpam-4144	700	1	8:1571–1580	CARDINAL
ejpam-4144	700	2	2014	DATE
ejpam-4144	701	1	2	CARDINAL
ejpam-4144	701	2	a. cabaro	PERSON
ejpam-4144	701	3	s. jr.	PERSON
ejpam-4144	701	4	canoy	PERSON
ejpam-4144	701	5	i. aniversario	PERSON
ejpam-4144	703	1	8(42):2065–2074	ORG
ejpam-4144	703	2	2014	DATE
ejpam-4144	704	1	3	CARDINAL
ejpam-4144	704	2	s. jr.	PERSON
ejpam-4144	704	3	canoy, s.a. canoy	PERSON
ejpam-4144	704	4	m. cruzate	PERSON
ejpam-4144	706	1	19(4):401–408	DATE
ejpam-4144	706	2	2018	DATE
ejpam-4144	707	1	4	CARDINAL
ejpam-4144	707	2	s. jr.	PERSON
ejpam-4144	707	3	canoy	PERSON
ejpam-4144	707	4	g. malacas	PERSON
ejpam-4144	709	1	nrcp research journal.	ORG
ejpam-4144	709	2	13(1):1–8	DATE
ejpam-4144	709	3	2013	DATE
ejpam-4144	710	1	5	CARDINAL
ejpam-4144	710	2	s. jr.	PERSON
ejpam-4144	710	3	canoy	PERSON
ejpam-4144	710	4	r. mollejon	PERSON
ejpam-4144	710	5	canoy.	PERSON
ejpam-4144	712	1	european journal	ORG
ejpam-4144	712	2	12(4):1455	CARDINAL
ejpam-4144	712	3	1463	DATE
ejpam-4144	712	4	2019	DATE
ejpam-4144	713	1	6	CARDINAL
ejpam-4144	713	2	r. gera	PERSON
ejpam-4144	713	3	a. hansberg	PERSON
ejpam-4144	713	4	a.j. rad	PERSON
ejpam-4144	713	5	l. volkman	PERSON
ejpam-4144	715	1	77:89–101, 2011	DATE
ejpam-4144	716	1	7	CARDINAL
ejpam-4144	716	2	s. hedetniemi	PERSON
ejpam-4144	716	3	slater	PERSON
ejpam-4144	718	1	marcell dekker	PERSON
ejpam-4144	718	2	new york	GPE
ejpam-4144	718	3	usa	GPE
ejpam-4144	718	4	1998	DATE
ejpam-4144	719	1	8	CARDINAL
ejpam-4144	719	2	s. hedetniemi	PERSON
ejpam-4144	719	3	slater	PERSON
ejpam-4144	721	1	marcell dekker	PERSON
ejpam-4144	721	2	new york	GPE
ejpam-4144	721	3	usa	GPE
ejpam-4144	721	4	1998	DATE
ejpam-4144	722	1	9	CARDINAL
ejpam-4144	722	2	m. henning	PERSON
ejpam-4144	722	3	j. howard	PERSON
ejpam-4144	724	1	154(8):1293–1300, 2006	DATE
ejpam-4144	725	1	10	CARDINAL
ejpam-4144	725	2	m. henning	PERSON
ejpam-4144	725	3	l. van der merwe	PERSON
ejpam-4144	726	1	18:23–37	CARDINAL
ejpam-4144	726	2	2009	DATE
ejpam-4144	727	1	1428	CARDINAL
ejpam-4144	727	2	11	CARDINAL
ejpam-4144	727	3	m. henning	PERSON
ejpam-4144	727	4	n.j	GPE
ejpam-4144	728	1	2	CARDINAL
ejpam-4144	729	1	combinatorics	ORG
ejpam-4144	729	2	33(4):913–927	DATE
ejpam-4144	729	3	2017	DATE
ejpam-4144	730	1	12	CARDINAL
ejpam-4144	730	2	g. mahadevan	PERSON
ejpam-4144	730	3	v. vijayalakshmi	PERSON
ejpam-4144	732	1	22(5):719–729	ORG
ejpam-4144	732	2	2019	DATE
ejpam-4144	733	1	13	CARDINAL
ejpam-4144	733	2	c. natarajan	PERSON
ejpam-4144	733	3	s. ayyaswamy	ORG
ejpam-4144	734	1	versita	PERSON
ejpam-4144	734	2	23(2):187	CARDINAL
ejpam-4144	734	3	199	CARDINAL
ejpam-4144	734	4	2015	DATE
ejpam-4144	735	1	14	CARDINAL
ejpam-4144	735	2	b. omamalin	PERSON
ejpam-4144	735	3	s. jr.	PERSON
ejpam-4144	735	4	canoy	PERSON
ejpam-4144	735	5	h. rara	PERSON
ejpam-4144	737	1	8(48):2363–2374	CARDINAL
ejpam-4144	737	2	2014	DATE
ejpam-4144	738	1	15	CARDINAL
ejpam-4144	738	2	h. rara	PERSON
ejpam-4144	740	1	asian-european journal of mathematics	ORG
ejpam-4144	740	2	11(5):1850075–1–1850075–11	DATE
ejpam-4144	740	3	2018	DATE
ejpam-4144	741	1	16	CARDINAL
ejpam-4144	741	2	g. salasalan	PERSON
ejpam-4144	741	3	s. jr.	PERSON
ejpam-4144	741	4	canoy	PERSON
ejpam-4144	743	1	european journal	ORG
ejpam-4144	743	2	14(1):112–125	DATE
ejpam-4144	743	3	2021	DATE