id	sid	eid	entity	type
ejpam-4461	1	1	european journal	ORG
ejpam-4461	2	1	15	CARDINAL
ejpam-4461	2	2	3	CARDINAL
ejpam-4461	2	3	2022	CARDINAL
ejpam-4461	2	4	1265	CARDINAL
ejpam-4461	2	5	1307-5543	CARDINAL
ejpam-4461	2	6	new york	GPE
ejpam-4461	2	7	ahadi aradais1,∗	PERSON
ejpam-4461	3	1	ferdinand p.	ORG
ejpam-4461	3	2	jamil2,3 1	ORG
ejpam-4461	3	3	msu tawi-tawi college of technology	ORG
ejpam-4461	3	4	2	CARDINAL
ejpam-4461	3	5	3	CARDINAL
ejpam-4461	3	6	msu-iligan institute of technology	ORG
ejpam-4461	3	7	9200	CARDINAL
ejpam-4461	3	8	iligan city	GPE
ejpam-4461	3	9	philippines	GPE
ejpam-4461	5	1	2	CARDINAL
ejpam-4461	5	2	s.	GPE
ejpam-4461	7	1	first	ORDINAL
ejpam-4461	9	1	2020	DATE
ejpam-4461	9	2	05c69	CARDINAL
ejpam-4461	9	3	1	CARDINAL
ejpam-4461	9	4	2014	DATE
ejpam-4461	9	5	w. goddard	PERSON
ejpam-4461	9	6	m. henning	PERSON
ejpam-4461	9	7	c. mcpillan	GPE
ejpam-4461	9	8	6	CARDINAL
ejpam-4461	11	1	m. henning	PERSON
ejpam-4461	11	2	a. marcon	PERSON
ejpam-4461	11	3	8	CARDINAL
ejpam-4461	11	4	2014	DATE
ejpam-4461	11	5	2016	DATE
ejpam-4461	11	6	g. hao	PERSON
ejpam-4461	11	7	w. zhuang	PERSON
ejpam-4461	11	8	2018	DATE
ejpam-4461	11	9	i. aniversario et al	PERSON
ejpam-4461	12	1	1	CARDINAL
ejpam-4461	12	2	2019	DATE
ejpam-4461	13	1	j. cyman	PERSON
ejpam-4461	13	2	4	CARDINAL
ejpam-4461	16	1	alkajimaradais@msutawi-tawi.edu.ph	GPE
ejpam-4461	16	2	a. aradais	PERSON
ejpam-4461	16	3	ferdinand.jamil@g.msuiit.edu.ph	ORG
ejpam-4461	16	4	f. jamil	PERSON
ejpam-4461	16	5	1265	CARDINAL
ejpam-4461	17	1	2022	CARDINAL
ejpam-4461	18	1	a. aradais	PERSON
ejpam-4461	18	2	f. jamil	PERSON
ejpam-4461	19	1	j. pure	PERSON
ejpam-4461	19	2	15	CARDINAL
ejpam-4461	19	3	3	CARDINAL
ejpam-4461	19	4	2022	CARDINAL
ejpam-4461	19	5	1265-1279	CARDINAL
ejpam-4461	19	6	⊆	CARDINAL
ejpam-4461	19	7	∈	ORG
ejpam-4461	20	1	∈	ORG
ejpam-4461	21	1	2	CARDINAL
ejpam-4461	22	1	two	CARDINAL
ejpam-4461	22	2	∈	ORG
ejpam-4461	23	1	one	CARDINAL
ejpam-4461	23	2	g[h	ORG
ejpam-4461	24	1	v1)(u2	GPE
ejpam-4461	27	1	⊆	CARDINAL
ejpam-4461	31	1	⊆	CARDINAL
ejpam-4461	33	1	∈	PERSON
ejpam-4461	33	2	∈	ORG
ejpam-4461	34	1	⊆	CARDINAL
ejpam-4461	34	2	∈	PERSON
ejpam-4461	34	3	∈	ORG
ejpam-4461	36	1	γ(g	NORP
ejpam-4461	36	2	γt(g	ORG
ejpam-4461	40	1	3	CARDINAL
ejpam-4461	41	1	⊆	CARDINAL
ejpam-4461	44	1	γ̃(g	ORG
ejpam-4461	45	1	⊆	CARDINAL
ejpam-4461	48	1	4	CARDINAL
ejpam-4461	48	2	5	CARDINAL
ejpam-4461	50	1	⊆	CARDINAL
ejpam-4461	50	2	γt2(g	ORG
ejpam-4461	51	1	a. aradais	PERSON
ejpam-4461	51	2	f. jamil	PERSON
ejpam-4461	52	1	j. pure	PERSON
ejpam-4461	52	2	15	CARDINAL
ejpam-4461	52	3	3	CARDINAL
ejpam-4461	52	4	2022	CARDINAL
ejpam-4461	52	5	1265-1279 1267	DATE
ejpam-4461	52	6	1, 6–8	CARDINAL
ejpam-4461	56	1	γ̃t2	CARDINAL
ejpam-4461	57	1	n2 g(v	ORG
ejpam-4461	58	1	⊆	CARDINAL
ejpam-4461	58	2	2	CARDINAL
ejpam-4461	59	1	3	CARDINAL
ejpam-4461	61	1	γ̃(g	ORG
ejpam-4461	62	1	1	CARDINAL
ejpam-4461	62	2	1	CARDINAL
ejpam-4461	63	1	1	CARDINAL
ejpam-4461	64	1	w	GPE
ejpam-4461	64	2	γ̃t2	CARDINAL
ejpam-4461	65	1	γ̃(g	ORG
ejpam-4461	65	2	4	CARDINAL
ejpam-4461	65	3	6 and γ̃t(g	CARDINAL
ejpam-4461	66	1	7	CARDINAL
ejpam-4461	73	1	1	CARDINAL
ejpam-4461	73	2	1	CARDINAL
ejpam-4461	74	1	2	CARDINAL
ejpam-4461	76	1	2	CARDINAL
ejpam-4461	76	2	1	CARDINAL
ejpam-4461	76	3	3 ≤ n ≤ 5	QUANTITY
ejpam-4461	76	4	2	CARDINAL
ejpam-4461	78	1	2	CARDINAL
ejpam-4461	79	1	n ≥ 3	DATE
ejpam-4461	80	1	⊆	CARDINAL
ejpam-4461	80	2	γ̃t2	ORG
ejpam-4461	81	1	⟨v	DATE
ejpam-4461	82	1	a a. aradais	PERSON
ejpam-4461	82	2	f. jamil	PERSON
ejpam-4461	83	1	j. pure	PERSON
ejpam-4461	83	2	15	CARDINAL
ejpam-4461	83	3	3	CARDINAL
ejpam-4461	83	4	2022	CARDINAL
ejpam-4461	83	5	1265-1279 1268	CARDINAL
ejpam-4461	84	1	y /∈ npn	PERSON
ejpam-4461	85	1	1 or	CARDINAL
ejpam-4461	85	2	2	CARDINAL
ejpam-4461	87	1	3 ≤ n ≤ 5	QUANTITY
ejpam-4461	89	1	1	CARDINAL
ejpam-4461	89	2	n ≥ 6	DATE
ejpam-4461	95	1	2	CARDINAL
ejpam-4461	96	1	2	CARDINAL
ejpam-4461	96	2	2	CARDINAL
ejpam-4461	97	1	3	CARDINAL
ejpam-4461	98	1	2	CARDINAL
ejpam-4461	98	2	3	CARDINAL
ejpam-4461	98	3	2	CARDINAL
ejpam-4461	98	4	n ≥ 4	DATE
ejpam-4461	100	1	3	CARDINAL
ejpam-4461	101	1	n ≥ 4	DATE
ejpam-4461	104	1	xn	ORG
ejpam-4461	105	1	x4	PERSON
ejpam-4461	107	1	2	CARDINAL
ejpam-4461	108	1	⊆	CARDINAL
ejpam-4461	108	2	⟨v	DATE
ejpam-4461	108	3	1 ≤	CARDINAL
ejpam-4461	110	1	2	CARDINAL
ejpam-4461	110	2	3	CARDINAL
ejpam-4461	111	1	1 ≤ n1 ≤ n2 ≤	QUANTITY
ejpam-4461	111	2	2	CARDINAL
ejpam-4461	111	3	2	CARDINAL
ejpam-4461	111	4	1	CARDINAL
ejpam-4461	111	5	2 2	DATE
ejpam-4461	115	1	first	ORDINAL
ejpam-4461	115	2	1	CARDINAL
ejpam-4461	115	3	γ̃t2(g	ORG
ejpam-4461	115	4	2	CARDINAL
ejpam-4461	115	5	2	CARDINAL
ejpam-4461	116	1	1	CARDINAL
ejpam-4461	116	2	1	CARDINAL
ejpam-4461	117	1	1.1	CARDINAL
ejpam-4461	117	2	2	CARDINAL
ejpam-4461	117	3	2	CARDINAL
ejpam-4461	119	1	⊆	CARDINAL
ejpam-4461	119	2	1.2	CARDINAL
ejpam-4461	119	3	t ≥ 3	DATE
ejpam-4461	119	4	1	CARDINAL
ejpam-4461	120	1	∈	ORG
ejpam-4461	122	1	2	CARDINAL
ejpam-4461	122	2	1.3	CARDINAL
ejpam-4461	122	3	t ≥ 3	DATE
ejpam-4461	122	4	2	CARDINAL
ejpam-4461	123	1	2	CARDINAL
ejpam-4461	123	2	2	CARDINAL
ejpam-4461	123	3	2	CARDINAL
ejpam-4461	123	4	nk ≥ 2	ORG
ejpam-4461	123	5	1	CARDINAL
ejpam-4461	123	6	2	DATE
ejpam-4461	128	1	n ≥ 2	ORG
ejpam-4461	129	1	2	CARDINAL
ejpam-4461	129	2	2	CARDINAL
ejpam-4461	129	3	1 or	CARDINAL
ejpam-4461	129	4	2	DATE
ejpam-4461	130	1	a. aradais	PERSON
ejpam-4461	130	2	f. jamil	PERSON
ejpam-4461	131	1	j. pure	PERSON
ejpam-4461	131	2	15	CARDINAL
ejpam-4461	131	3	3	CARDINAL
ejpam-4461	131	4	2022	CARDINAL
ejpam-4461	131	5	1265-1279 1269	CARDINAL
ejpam-4461	135	1	2	CARDINAL
ejpam-4461	136	1	2	CARDINAL
ejpam-4461	136	2	n ≥ 3	DATE
ejpam-4461	140	1	1	CARDINAL
ejpam-4461	141	1	2	CARDINAL
ejpam-4461	147	1	nk	ORG
ejpam-4461	148	1	1	CARDINAL
ejpam-4461	148	2	2	DATE
ejpam-4461	152	1	1	CARDINAL
ejpam-4461	152	2	2	DATE
ejpam-4461	154	1	j ∈	PERSON
ejpam-4461	154	2	1	CARDINAL
ejpam-4461	154	3	2	DATE
ejpam-4461	156	1	k}	PERSON
ejpam-4461	156	2	γ̃t2	CARDINAL
ejpam-4461	157	1	ci	PERSON
ejpam-4461	157	2	= γ̃t2(cj	PERSON
ejpam-4461	162	1	⊆	CARDINAL
ejpam-4461	162	2	1	CARDINAL
ejpam-4461	162	3	2	DATE
ejpam-4461	165	1	first	ORDINAL
ejpam-4461	165	2	j ∈	PERSON
ejpam-4461	165	3	1	CARDINAL
ejpam-4461	165	4	2	DATE
ejpam-4461	166	1	ci	PERSON
ejpam-4461	166	2	j.	PERSON
ejpam-4461	166	3	j ∈	PERSON
ejpam-4461	166	4	1	CARDINAL
ejpam-4461	166	5	2	DATE
ejpam-4461	168	1	ci	PERSON
ejpam-4461	169	1	∈	ORG
ejpam-4461	169	2	ci	PERSON
ejpam-4461	171	1	∈	ORG
ejpam-4461	174	1	ci	PERSON
ejpam-4461	183	1	6	CARDINAL
ejpam-4461	187	1	2	CARDINAL
ejpam-4461	190	1	nk	ORG
ejpam-4461	190	2	a. aradais	PERSON
ejpam-4461	190	3	f. jamil	PERSON
ejpam-4461	191	1	j. pure	PERSON
ejpam-4461	191	2	15	CARDINAL
ejpam-4461	191	3	3	CARDINAL
ejpam-4461	191	4	2022	CARDINAL
ejpam-4461	191	5	1265-1279 1270	CARDINAL
ejpam-4461	192	1	2	CARDINAL
ejpam-4461	196	1	at least two	CARDINAL
ejpam-4461	198	1	1	CARDINAL
ejpam-4461	198	2	2	CARDINAL
ejpam-4461	201	1	nk	ORG
ejpam-4461	204	1	nk = 1	PERSON
ejpam-4461	206	1	nk ≥ 2.	ORG
ejpam-4461	207	1	first	ORDINAL
ejpam-4461	207	2	⊆	CARDINAL
ejpam-4461	207	3	1	CARDINAL
ejpam-4461	207	4	2	DATE
ejpam-4461	209	1	k.	PERSON
ejpam-4461	210	1	∈	ORG
ejpam-4461	212	1	∈	ORG
ejpam-4461	215	1	2	CARDINAL
ejpam-4461	216	1	⊆	CARDINAL
ejpam-4461	216	2	γ̃t2	CARDINAL
ejpam-4461	217	1	1	CARDINAL
ejpam-4461	217	2	2	DATE
ejpam-4461	220	1	u /∈ s	PERSON
ejpam-4461	222	1	a. aradais	PERSON
ejpam-4461	222	2	f. jamil	PERSON
ejpam-4461	223	1	j. pure	PERSON
ejpam-4461	223	2	15	CARDINAL
ejpam-4461	223	3	3	CARDINAL
ejpam-4461	223	4	2022	CARDINAL
ejpam-4461	223	5	1265-1279 1271	CARDINAL
ejpam-4461	223	6	j. moreover	PERSON
ejpam-4461	223	7	γ̃t2	CARDINAL
ejpam-4461	223	8	j = k.	PERSON
ejpam-4461	224	1	ci	PERSON
ejpam-4461	225	1	1 +	CARDINAL
ejpam-4461	225	2	2	CARDINAL
ejpam-4461	226	1	2	CARDINAL
ejpam-4461	227	1	1	CARDINAL
ejpam-4461	227	2	2	DATE
ejpam-4461	229	1	1	CARDINAL
ejpam-4461	229	2	3	CARDINAL
ejpam-4461	230	1	1	CARDINAL
ejpam-4461	230	2	2 +	CARDINAL
ejpam-4461	230	3	nj	ORG
ejpam-4461	231	1	3	CARDINAL
ejpam-4461	232	1	2	CARDINAL
ejpam-4461	233	1	nj	ORG
ejpam-4461	233	2	2	CARDINAL
ejpam-4461	233	3	1	CARDINAL
ejpam-4461	234	1	1	CARDINAL
ejpam-4461	234	2	⊆	CARDINAL
ejpam-4461	235	1	g+h	ORG
ejpam-4461	236	1	⊆	CARDINAL
ejpam-4461	236	2	⊆	CARDINAL
ejpam-4461	236	3	2	CARDINAL
ejpam-4461	238	1	⊆	CARDINAL
ejpam-4461	238	2	g+h	ORG
ejpam-4461	239	1	⊆	CARDINAL
ejpam-4461	239	2	one	CARDINAL
ejpam-4461	239	3	g. (ii	PERSON
ejpam-4461	239	4	⊆	CARDINAL
ejpam-4461	239	5	one	CARDINAL
ejpam-4461	239	6	a. aradais	PERSON
ejpam-4461	239	7	f. jamil	PERSON
ejpam-4461	240	1	j. pure	PERSON
ejpam-4461	240	2	15	CARDINAL
ejpam-4461	240	3	3	CARDINAL
ejpam-4461	240	4	2022	CARDINAL
ejpam-4461	240	5	1265-1279 1272	CARDINAL
ejpam-4461	240	6	⊆	CARDINAL
ejpam-4461	241	1	⊆	CARDINAL
ejpam-4461	245	1	⊆	CARDINAL
ejpam-4461	247	1	⟨v	DATE
ejpam-4461	247	2	g+h	NORP
ejpam-4461	251	1	⊆	CARDINAL
ejpam-4461	253	1	⊆	CARDINAL
ejpam-4461	253	2	g+h	NORP
ejpam-4461	254	1	⟨v	DATE
ejpam-4461	255	1	⊆	CARDINAL
ejpam-4461	257	1	g+h	ORG
ejpam-4461	258	1	⊆	CARDINAL
ejpam-4461	258	2	1	CARDINAL
ejpam-4461	260	1	g+h	NORP
ejpam-4461	261	1	⟨(v	ORG
ejpam-4461	263	1	1	CARDINAL
ejpam-4461	263	2	⊆	CARDINAL
ejpam-4461	264	1	⟨v	DATE
ejpam-4461	265	1	g+h	ORG
ejpam-4461	266	1	g+h	ORG
ejpam-4461	267	1	1	CARDINAL
ejpam-4461	269	1	2	CARDINAL
ejpam-4461	270	1	∈	ORG
ejpam-4461	270	2	∈	ORG
ejpam-4461	271	1	2	CARDINAL
ejpam-4461	272	1	γ̃t2(g + h	ORG
ejpam-4461	273	1	1	CARDINAL
ejpam-4461	273	2	2	CARDINAL
ejpam-4461	273	3	3	CARDINAL
ejpam-4461	274	1	⊆	CARDINAL
ejpam-4461	275	1	∪v∈v	PERSON
ejpam-4461	275	2	1	CARDINAL
ejpam-4461	275	3	⊆	CARDINAL
ejpam-4461	275	4	g. a. aradais	PERSON
ejpam-4461	275	5	f. jamil	PERSON
ejpam-4461	276	1	j. pure	PERSON
ejpam-4461	276	2	15	CARDINAL
ejpam-4461	276	3	3	CARDINAL
ejpam-4461	276	4	2022	CARDINAL
ejpam-4461	276	5	1265-1279 1273	CARDINAL
ejpam-4461	280	1	two	CARDINAL
ejpam-4461	280	2	1	CARDINAL
ejpam-4461	281	1	∈	ORG
ejpam-4461	281	2	∈	ORG
ejpam-4461	281	3	\s	ORG
ejpam-4461	282	1	\s⟩	ORG
ejpam-4461	282	2	\s	ORG
ejpam-4461	285	1	2	CARDINAL
ejpam-4461	285	2	∈	ORG
ejpam-4461	285	3	∈	ORG
ejpam-4461	287	1	∪v∈v (g){xv}	ORG
ejpam-4461	288	1	first	ORDINAL
ejpam-4461	289	1	∈	ORG
ejpam-4461	292	1	s.	PERSON
ejpam-4461	294	1	∪v∈v	PERSON
ejpam-4461	295	1	1	CARDINAL
ejpam-4461	296	1	∈	ORG
ejpam-4461	296	2	∈	ORG
ejpam-4461	297	1	w ∈	PERSON
ejpam-4461	297	2	⊆	CARDINAL
ejpam-4461	298	1	k1(u	GPE
ejpam-4461	298	2	w	GPE
ejpam-4461	298	3	2	CARDINAL
ejpam-4461	298	4	w	GPE
ejpam-4461	299	1	2	CARDINAL
ejpam-4461	300	1	xu ∈ s.	PERSON
ejpam-4461	300	2	∈	ORG
ejpam-4461	302	1	⟨v	DATE
ejpam-4461	304	1	2	CARDINAL
ejpam-4461	307	1	3	CARDINAL
ejpam-4461	307	2	1	CARDINAL
ejpam-4461	308	1	4	CARDINAL
ejpam-4461	309	1	⊆	CARDINAL
ejpam-4461	311	1	a. aradais	PERSON
ejpam-4461	311	2	f. jamil	PERSON
ejpam-4461	312	1	j. pure	PERSON
ejpam-4461	312	2	15	CARDINAL
ejpam-4461	312	3	3	CARDINAL
ejpam-4461	312	4	2022	CARDINAL
ejpam-4461	312	5	1265-1279 1274	CARDINAL
ejpam-4461	312	6	∈	ORG
ejpam-4461	312	7	⊆	CARDINAL
ejpam-4461	314	1	2	CARDINAL
ejpam-4461	314	2	⊆	CARDINAL
ejpam-4461	314	3	sx ⊆	ORG
ejpam-4461	315	1	sx	ORG
ejpam-4461	316	1	1	CARDINAL
ejpam-4461	319	1	two	CARDINAL
ejpam-4461	319	2	1	CARDINAL
ejpam-4461	319	3	⊆	CARDINAL
ejpam-4461	319	4	h)\s⟩	GPE
ejpam-4461	319	5	∈	ORG
ejpam-4461	319	6	⊆	CARDINAL
ejpam-4461	321	1	2	CARDINAL
ejpam-4461	322	1	2	CARDINAL
ejpam-4461	323	1	g ◦ h	ORG
ejpam-4461	324	1	⊆	CARDINAL
ejpam-4461	325	1	2	CARDINAL
ejpam-4461	325	2	s.	PERSON
ejpam-4461	325	3	g ◦h	ORG
ejpam-4461	326	1	\sx	NORP
ejpam-4461	327	1	g◦h and	ORG
ejpam-4461	327	2	w ∈ s	PERSON
ejpam-4461	329	1	1	CARDINAL
ejpam-4461	330	1	g ◦ h	ORG
ejpam-4461	330	2	w ∈ s	PERSON
ejpam-4461	330	3	h(u	GPE
ejpam-4461	331	1	w /∈ sx	PERSON
ejpam-4461	331	2	∩	ORG
ejpam-4461	333	1	⊆	CARDINAL
ejpam-4461	336	1	g ◦h. now	ORG
ejpam-4461	336	2	sx	ORG
ejpam-4461	337	1	≤ 2	CARDINAL
ejpam-4461	338	1	⊆	CARDINAL
ejpam-4461	338	2	h)\s⟩	GPE
ejpam-4461	339	1	∈	ORG
ejpam-4461	339	2	⊆	CARDINAL
ejpam-4461	339	3	∈	ORG
ejpam-4461	340	1	a. aradais	PERSON
ejpam-4461	340	2	f. jamil	PERSON
ejpam-4461	341	1	j. pure	PERSON
ejpam-4461	341	2	15	CARDINAL
ejpam-4461	341	3	3	CARDINAL
ejpam-4461	341	4	2022	CARDINAL
ejpam-4461	341	5	1265-1279 1275	CARDINAL
ejpam-4461	341	6	h(x	GPE
ejpam-4461	342	1	1	CARDINAL
ejpam-4461	343	1	∈	ORG
ejpam-4461	344	1	∈	ORG
ejpam-4461	345	1	2	CARDINAL
ejpam-4461	346	1	∈	ORG
ejpam-4461	346	2	h(x	GPE
ejpam-4461	347	1	1	CARDINAL
ejpam-4461	348	1	∈	PRODUCT
ejpam-4461	350	1	2	CARDINAL
ejpam-4461	352	1	1	CARDINAL
ejpam-4461	352	2	γ̃t2(g ◦h) ≤ min{2n	ORG
ejpam-4461	353	1	γ(h	ORG
ejpam-4461	353	2	2	CARDINAL
ejpam-4461	353	3	γ̃t2(g ◦h	ORG
ejpam-4461	353	4	γ̃(g	ORG
ejpam-4461	353	5	1 +	CARDINAL
ejpam-4461	355	1	⊆	CARDINAL
ejpam-4461	356	1	sv ⊆	ORG
ejpam-4461	357	1	⋃	DATE
ejpam-4461	357	2	 ⋃	PERSON
ejpam-4461	358	1	4(ii	DATE
ejpam-4461	358	2	γ̃t2(g ◦h	ORG
ejpam-4461	358	3	n− |a|	ORG
ejpam-4461	358	4	1 +	CARDINAL
ejpam-4461	360	1	γ(h	ORG
ejpam-4461	360	2	1	CARDINAL
ejpam-4461	360	3	γ̃t2(g ◦h) ≤ n+mγ̃(g	ORG
ejpam-4461	361	1	γ(h	ORG
ejpam-4461	362	1	1	CARDINAL
ejpam-4461	364	1	∈	ORG
ejpam-4461	365	1	γ(h	ORG
ejpam-4461	365	2	2	CARDINAL
ejpam-4461	365	3	sv ⊆	ORG
ejpam-4461	365	4	∈	ORG
ejpam-4461	366	1	⋃ v∈v	PERSON
ejpam-4461	366	2	4(ii	CARDINAL
ejpam-4461	367	1	γ(h	ORG
ejpam-4461	367	2	1	CARDINAL
ejpam-4461	367	3	γ̃t2(g ◦h	ORG
ejpam-4461	367	4	2n	CARDINAL
ejpam-4461	368	1	γ(h	ORG
ejpam-4461	368	2	2	CARDINAL
ejpam-4461	368	3	γ̃t2(g ◦h	ORG
ejpam-4461	371	1	a. aradais	PERSON
ejpam-4461	371	2	f. jamil	PERSON
ejpam-4461	372	1	j. pure	PERSON
ejpam-4461	372	2	15	CARDINAL
ejpam-4461	372	3	3	CARDINAL
ejpam-4461	372	4	2022	CARDINAL
ejpam-4461	372	5	1265-1279 1276	CARDINAL
ejpam-4461	373	1	1	CARDINAL
ejpam-4461	373	2	γ̃t2	CARDINAL
ejpam-4461	374	1	1	CARDINAL
ejpam-4461	375	1	γ(h	ORG
ejpam-4461	375	2	2	CARDINAL
ejpam-4461	375	3	γ̃t2	CARDINAL
ejpam-4461	375	4	1)γ(h	CARDINAL
ejpam-4461	375	5	γ̃(g	ORG
ejpam-4461	375	6	1 +	CARDINAL
ejpam-4461	378	1	3	CARDINAL
ejpam-4461	378	2	1	CARDINAL
ejpam-4461	380	1	⊆	CARDINAL
ejpam-4461	380	2	k.	PERSON
ejpam-4461	381	1	first	ORDINAL
ejpam-4461	381	2	4(ii	DATE
ejpam-4461	382	1	2(n	CARDINAL
ejpam-4461	382	2	2n	CARDINAL
ejpam-4461	384	1	⊆	CARDINAL
ejpam-4461	385	1	⊆	CARDINAL
ejpam-4461	386	1	⊆	CARDINAL
ejpam-4461	386	2	1 + n ≥	FAC
ejpam-4461	389	1	4	CARDINAL
ejpam-4461	389	2	5	CARDINAL
ejpam-4461	390	1	1	CARDINAL
ejpam-4461	390	2	⊆	CARDINAL
ejpam-4461	391	1	tx	ORG
ejpam-4461	391	2	tx	ORG
ejpam-4461	391	3	2	CARDINAL
ejpam-4461	392	1	⊆	CARDINAL
ejpam-4461	394	1	6	CARDINAL
ejpam-4461	395	1	n ≥ 2	ORG
ejpam-4461	396	1	one	CARDINAL
ejpam-4461	396	2	g. a. aradais	PERSON
ejpam-4461	396	3	f. jamil	PERSON
ejpam-4461	397	1	j. pure	PERSON
ejpam-4461	397	2	15	CARDINAL
ejpam-4461	397	3	3	CARDINAL
ejpam-4461	397	4	2022	CARDINAL
ejpam-4461	397	5	1265-1279 1277	CARDINAL
ejpam-4461	397	6	2	CARDINAL
ejpam-4461	399	1	|cg|	CARDINAL
ejpam-4461	399	2	2	CARDINAL
ejpam-4461	399	3	∈	ORG
ejpam-4461	399	4	∈	PRODUCT
ejpam-4461	402	1	kn	PERSON
ejpam-4461	402	2	5	CARDINAL
ejpam-4461	402	3	|cg|	CARDINAL
ejpam-4461	402	4	1	CARDINAL
ejpam-4461	403	1	|cg|	CARDINAL
ejpam-4461	403	2	2	CARDINAL
ejpam-4461	403	3	∈	ORG
ejpam-4461	403	4	w ∈	PERSON
ejpam-4461	403	5	z)-(v	PERSON
ejpam-4461	403	6	w	GPE
ejpam-4461	404	1	xn	ORG
ejpam-4461	406	1	1	CARDINAL
ejpam-4461	406	2	2	DATE
ejpam-4461	408	1	1	CARDINAL
ejpam-4461	408	2	2	DATE
ejpam-4461	409	1	xkr = v]	PERSON
ejpam-4461	410	1	∩	PERSON
ejpam-4461	411	1	xkj ∈ s ∩v	ORG
ejpam-4461	415	1	5	CARDINAL
ejpam-4461	417	1	tx	ORG
ejpam-4461	417	2	∈	ORG
ejpam-4461	417	3	g[h	ORG
ejpam-4461	419	1	w	ORG
ejpam-4461	419	2	∈	ORG
ejpam-4461	421	1	1	CARDINAL
ejpam-4461	421	2	∈	ORG
ejpam-4461	429	1	xn−1	GPE
ejpam-4461	429	2	z)-(v	PERSON
ejpam-4461	429	3	w	GPE
ejpam-4461	429	4	⟨v	DATE
ejpam-4461	430	1	2	CARDINAL
ejpam-4461	431	1	yk ∈	ORG
ejpam-4461	434	1	xn−1	GPE
ejpam-4461	434	2	xn	ORG
ejpam-4461	434	3	z)-(v	PERSON
ejpam-4461	434	4	w	GPE
ejpam-4461	434	5	⟨v	DATE
ejpam-4461	434	6	2	CARDINAL
ejpam-4461	437	1	xn−1	GPE
ejpam-4461	439	1	xn−1 ∈	PERSON
ejpam-4461	440	1	xn−1	GPE
ejpam-4461	442	1	xn−1	GPE
ejpam-4461	442	2	z)-(v	PERSON
ejpam-4461	442	3	w	GPE
ejpam-4461	442	4	⟨v	DATE
ejpam-4461	446	1	lemma	ORG
ejpam-4461	446	2	1	CARDINAL
ejpam-4461	447	1	a. aradais	PERSON
ejpam-4461	447	2	f. jamil	PERSON
ejpam-4461	448	1	j. pure	PERSON
ejpam-4461	448	2	15	CARDINAL
ejpam-4461	448	3	3	CARDINAL
ejpam-4461	448	4	2022	CARDINAL
ejpam-4461	448	5	1265-1279 1278	CARDINAL
ejpam-4461	448	6	1	CARDINAL
ejpam-4461	449	1	1	CARDINAL
ejpam-4461	449	2	⊆	CARDINAL
ejpam-4461	451	1	⊆	CARDINAL
ejpam-4461	451	2	∈	ORG
ejpam-4461	451	3	xux ∈	PERSON
ejpam-4461	452	1	|s∗|	PRODUCT
ejpam-4461	454	1	5	CARDINAL
ejpam-4461	455	1	n ≥ 2.	ORG
ejpam-4461	458	1	⊆	CARDINAL
ejpam-4461	458	2	∈	ORG
ejpam-4461	459	1	6	CARDINAL
ejpam-4461	461	1	⋃	PERSON
ejpam-4461	461	2	⊆	CARDINAL
ejpam-4461	462	1	6	CARDINAL
ejpam-4461	463	1	6	CARDINAL
ejpam-4461	463	2	 ⋃	PERSON
ejpam-4461	463	3		GPE
ejpam-4461	463	4	⋃ x∈s2	DATE
ejpam-4461	463	5	2	CARDINAL
ejpam-4461	464	1	x∈s1	FAC
ejpam-4461	464	2	2|s1|+	CARDINAL
ejpam-4461	465	1	lemma 1,	ORG
ejpam-4461	467	1	1279	CARDINAL
ejpam-4461	468	1	msu-iligan institute of technology	ORG
ejpam-4461	469	1	msu-iit	ORG
ejpam-4461	469	2	msu	ORG
ejpam-4461	470	1	1	CARDINAL
ejpam-4461	470	2	i. aniversario	PERSON
ejpam-4461	470	3	jr.	PERSON
ejpam-4461	470	4	s. canoy	PERSON
ejpam-4461	470	5	jamil	GPE
ejpam-4461	472	1	european journal	ORG
ejpam-4461	472	2	12(4):1410–1425,	DATE
ejpam-4461	472	3	2019	DATE
ejpam-4461	473	1	2	CARDINAL
ejpam-4461	473	2	f. buckley	PERSON
ejpam-4461	473	3	f. harary	PERSON
ejpam-4461	475	1	addison-wesley	ORG
ejpam-4461	475	2	1990	DATE
ejpam-4461	476	1	3	CARDINAL
ejpam-4461	476	2	cockayne	ORG
ejpam-4461	476	3	s.t.	PERSON
ejpam-4461	476	4	hedetniemi	PERSON
ejpam-4461	478	1	1997	DATE
ejpam-4461	479	1	4	CARDINAL
ejpam-4461	479	2	j. cyman	PERSON
ejpam-4461	481	1	j. combin	PERSON
ejpam-4461	481	2	38:35–46,	DATE
ejpam-4461	481	3	2007	DATE
ejpam-4461	482	1	5	CARDINAL
ejpam-4461	482	2	j. cyman	PERSON
ejpam-4461	482	3	j. raczek	PERSON
ejpam-4461	484	1	157:3198–3202,	DATE
ejpam-4461	484	2	2009	DATE
ejpam-4461	485	1	6	CARDINAL
ejpam-4461	485	2	w. goddard	PERSON
ejpam-4461	485	3	m. henning	PERSON
ejpam-4461	485	4	c. mcpil	PERSON
ejpam-4461	487	1	mathematica	PERSON
ejpam-4461	487	2	94:67–81, 2004	DATE
ejpam-4461	488	1	7	CARDINAL
ejpam-4461	488	2	g. hao	PERSON
ejpam-4461	488	3	w. zhuang	PERSON
ejpam-4461	490	1	20(2):1–11	CARDINAL
ejpam-4461	490	2	2018	DATE
ejpam-4461	491	1	8	CARDINAL
ejpam-4461	491	2	h. henning	PERSON
ejpam-4461	491	3	a. marcon	PERSON
ejpam-4461	493	1	combinatorics	ORG
ejpam-4461	493	2	20(4):799–813	DATE
ejpam-4461	493	3	2016	DATE