id	sid	eid	entity	type
ejpam-3812	1	1	european journal	ORG
ejpam-3812	2	1	13	CARDINAL
ejpam-3812	2	2	4, 2020	DATE
ejpam-3812	2	3	779	CARDINAL
ejpam-3812	2	4	new york	GPE
ejpam-3812	2	5	marivir m. ortega1,∗	PERSON
ejpam-3812	2	6	rowena t. isla1,2 1	PERSON
ejpam-3812	2	7	mindanao state university-iligan institute of technology	ORG
ejpam-3812	2	8	9200	CARDINAL
ejpam-3812	2	9	iligan city	GPE
ejpam-3812	2	10	2	CARDINAL
ejpam-3812	2	11	institute of science	ORG
ejpam-3812	2	12	mindanao state university-iligan institute of technology	ORG
ejpam-3812	2	13	9200	CARDINAL
ejpam-3812	2	14	iligan city	GPE
ejpam-3812	2	15	philippines	GPE
ejpam-3812	4	1	1	CARDINAL
ejpam-3812	4	2	1	CARDINAL
ejpam-3812	5	1	2020	DATE
ejpam-3812	5	2	05c69	CARDINAL
ejpam-3812	5	3	05c76	CARDINAL
ejpam-3812	5	4	1	CARDINAL
ejpam-3812	6	1	∈	ORG
ejpam-3812	8	1	∈	ORG
ejpam-3812	9	1	⊆	CARDINAL
ejpam-3812	10	1	⋃	PERSON
ejpam-3812	11	1	x.	PERSON
ejpam-3812	12	1	⊆	CARDINAL
ejpam-3812	14	1	γ(g	NORP
ejpam-3812	14	2	γ(g	NORP
ejpam-3812	14	3	1	CARDINAL
ejpam-3812	14	4	9	CARDINAL
ejpam-3812	14	5	1962	DATE
ejpam-3812	15	1	2	CARDINAL
ejpam-3812	18	1	https://doi.org/10.29020/nybg.ejpam.v13i4.3812	ORG
ejpam-3812	18	2	m. ortega	PERSON
ejpam-3812	19	1	2020	DATE
ejpam-3812	20	1	m. ortega	PERSON
ejpam-3812	20	2	r. isla	PERSON
ejpam-3812	21	1	j. pure	PERSON
ejpam-3812	21	2	13	CARDINAL
ejpam-3812	21	3	4	CARDINAL
ejpam-3812	21	4	2020	DATE
ejpam-3812	21	5	779-793	CARDINAL
ejpam-3812	21	6	two	CARDINAL
ejpam-3812	23	1	henning	PERSON
ejpam-3812	24	1	4	CARDINAL
ejpam-3812	24	2	2012	DATE
ejpam-3812	25	1	1	CARDINAL
ejpam-3812	25	2	⊆	CARDINAL
ejpam-3812	27	1	k ≤ γkfd(g	PERSON
ejpam-3812	28	1	2014	DATE
ejpam-3812	28	2	maravilla	ORG
ejpam-3812	28	3	isla	PERSON
ejpam-3812	28	4	6	CARDINAL
ejpam-3812	29	1	two	CARDINAL
ejpam-3812	29	2	gomisong	PERSON
ejpam-3812	30	1	3	CARDINAL
ejpam-3812	30	2	2018	DATE
ejpam-3812	30	3	isla	PERSON
ejpam-3812	31	1	7	CARDINAL
ejpam-3812	31	2	2019	DATE
ejpam-3812	32	1	goddard, henning	ORG
ejpam-3812	32	2	5	CARDINAL
ejpam-3812	32	3	2014	DATE
ejpam-3812	33	1	⊆	CARDINAL
ejpam-3812	33	2	2019	DATE
ejpam-3812	33	3	jamil	PERSON
ejpam-3812	34	1	8	CARDINAL
ejpam-3812	36	1	⊆	CARDINAL
ejpam-3812	36	2	y ∈ s	PERSON
ejpam-3812	36	3	d(x	ORG
ejpam-3812	40	1	⊆	CARDINAL
ejpam-3812	40	2	two	CARDINAL
ejpam-3812	43	1	two	CARDINAL
ejpam-3812	44	1	∈	ORG
ejpam-3812	45	1	two	CARDINAL
ejpam-3812	45	2	g ◦ h	ORG
ejpam-3812	45	3	one	CARDINAL
ejpam-3812	45	4	∈	ORG
ejpam-3812	45	5	g ◦ h	ORG
ejpam-3812	46	1	two	CARDINAL
ejpam-3812	46	2	g[h	ORG
ejpam-3812	46	3	v1)(u2	GPE
ejpam-3812	47	1	cartesian	NORP
ejpam-3812	47	2	two	CARDINAL
ejpam-3812	47	3	m. ortega	PERSON
ejpam-3812	47	4	r. isla	PERSON
ejpam-3812	48	1	j. pure	PERSON
ejpam-3812	48	2	13	CARDINAL
ejpam-3812	48	3	4	CARDINAL
ejpam-3812	48	4	2020	DATE
ejpam-3812	48	5	779-793 781	QUANTITY
ejpam-3812	48	6	v1)(u2	GPE
ejpam-3812	49	1	2	CARDINAL
ejpam-3812	49	2	1	CARDINAL
ejpam-3812	51	1	1	CARDINAL
ejpam-3812	53	1	2	CARDINAL
ejpam-3812	57	1	2	CARDINAL
ejpam-3812	57	2	1fd	ORDINAL
ejpam-3812	57	3	∈	ORG
ejpam-3812	57	4	\s	ORG
ejpam-3812	57	5	∈	ORG
ejpam-3812	62	1	1	CARDINAL
ejpam-3812	63	1	∪h	PRODUCT
ejpam-3812	66	1	2	CARDINAL
ejpam-3812	67	1	1	CARDINAL
ejpam-3812	68	1	6	CARDINAL
ejpam-3812	68	2	k ≤ n.	ORG
ejpam-3812	70	1	= k.	PERSON
ejpam-3812	70	2	degree k. theorem 2	PERSON
ejpam-3812	71	1	n ≥ 2	ORG
ejpam-3812	71	2	2 ≤ k ≤ n.	QUANTITY
ejpam-3812	72	1	k. proof	PERSON
ejpam-3812	73	1	= k.	PERSON
ejpam-3812	76	1	〉	CARDINAL
ejpam-3812	77	1	⊆	CARDINAL
ejpam-3812	78	1	y ∈ s	PERSON
ejpam-3812	78	2	6=	CARDINAL
ejpam-3812	79	1	xy /∈ e(g	PERSON
ejpam-3812	81	1	∈	ORG
ejpam-3812	83	1	2	CARDINAL
ejpam-3812	83	2	1	CARDINAL
ejpam-3812	83	3	= k. � corollary	PERSON
ejpam-3812	83	4	2	CARDINAL
ejpam-3812	85	1	2	CARDINAL
ejpam-3812	85	2	h. m. ortega	PERSON
ejpam-3812	85	3	r. isla	PERSON
ejpam-3812	86	1	j. pure	PERSON
ejpam-3812	86	2	13	CARDINAL
ejpam-3812	86	3	4	CARDINAL
ejpam-3812	86	4	2020	DATE
ejpam-3812	86	5	779	CARDINAL
ejpam-3812	87	1	2	CARDINAL
ejpam-3812	88	1	leth = 〈v	PERSON
ejpam-3812	89	1	〉	CARDINAL
ejpam-3812	90	1	2	CARDINAL
ejpam-3812	91	1	⊆	CARDINAL
ejpam-3812	92	1	2	CARDINAL
ejpam-3812	92	2	2	CARDINAL
ejpam-3812	95	1	2	CARDINAL
ejpam-3812	95	2	3	CARDINAL
ejpam-3812	96	1	n ≥ 2	ORG
ejpam-3812	96	2	2	CARDINAL
ejpam-3812	97	1	⊆	CARDINAL
ejpam-3812	101	1	1	CARDINAL
ejpam-3812	103	1	∩	ORG
ejpam-3812	103	2	6=	CARDINAL
ejpam-3812	103	3	w ∈ s	PERSON
ejpam-3812	103	4	1.	CARDINAL
ejpam-3812	103	5	∩	ORG
ejpam-3812	103	6	∈	ORG
ejpam-3812	104	1	∈	ORG
ejpam-3812	105	1	k ≥ 2	ORG
ejpam-3812	105	2	∈	ORG
ejpam-3812	106	1	2	CARDINAL
ejpam-3812	108	1	2	CARDINAL
ejpam-3812	108	2	1 ≤ k ≤ α(g	QUANTITY
ejpam-3812	108	3	α(g	PERSON
ejpam-3812	109	1	2	CARDINAL
ejpam-3812	109	2	1fd	CARDINAL
ejpam-3812	110	1	4	CARDINAL
ejpam-3812	111	1	1 ≤ k ≤ α(g	QUANTITY
ejpam-3812	118	1	〉	CARDINAL
ejpam-3812	120	1	⊆	CARDINAL
ejpam-3812	120	2	1	CARDINAL
ejpam-3812	120	3	2	DATE
ejpam-3812	120	4	6=	CARDINAL
ejpam-3812	120	5	j.	PERSON
ejpam-3812	122	1	5	CARDINAL
ejpam-3812	123	1	1fd	CARDINAL
ejpam-3812	124	1	1 ≤ γi1f	QUANTITY
ejpam-3812	124	2	α(g	PERSON
ejpam-3812	125	1	γi1f	PERSON
ejpam-3812	125	2	1	CARDINAL
ejpam-3812	126	1	γi1f	PERSON
ejpam-3812	126	2	α(g	PERSON
ejpam-3812	126	3	2	CARDINAL
ejpam-3812	126	4	3	CARDINAL
ejpam-3812	126	5	y ∈ s	PERSON
ejpam-3812	126	6	6=	CARDINAL
ejpam-3812	128	1	γi1f	ORG
ejpam-3812	129	1	1 ≤	CARDINAL
ejpam-3812	129	2	γi1f	PERSON
ejpam-3812	129	3	α(g	PERSON
ejpam-3812	130	1	4	CARDINAL
ejpam-3812	130	2	γi1f	PERSON
ejpam-3812	130	3	α(g	PERSON
ejpam-3812	130	4	2	CARDINAL
ejpam-3812	131	1	γi1f	ORG
ejpam-3812	131	2	y ∈ s	PERSON
ejpam-3812	131	3	6=	CARDINAL
ejpam-3812	131	4	1fd	CARDINAL
ejpam-3812	131	5	3	CARDINAL
ejpam-3812	131	6	m. ortega	PERSON
ejpam-3812	131	7	r. isla	PERSON
ejpam-3812	132	1	j. pure	PERSON
ejpam-3812	132	2	13	CARDINAL
ejpam-3812	132	3	4	CARDINAL
ejpam-3812	132	4	2020	DATE
ejpam-3812	132	5	779-793 783	QUANTITY
ejpam-3812	132	6	3	CARDINAL
ejpam-3812	132	7	y ∈ s	PERSON
ejpam-3812	132	8	6=	CARDINAL
ejpam-3812	134	1	∈	ORG
ejpam-3812	135	1	3	CARDINAL
ejpam-3812	135	2	1	CARDINAL
ejpam-3812	135	3	1fd	CARDINAL
ejpam-3812	135	4	γi1f	PERSON
ejpam-3812	135	5	α(g	PERSON
ejpam-3812	136	1	γi1f	PERSON
ejpam-3812	136	2	α(g	PERSON
ejpam-3812	137	1	kn = k1	PERSON
ejpam-3812	137	2	+kn−1	GPE
ejpam-3812	138	1	1	CARDINAL
ejpam-3812	139	1	3	CARDINAL
ejpam-3812	140	1	1	CARDINAL
ejpam-3812	140	2	3	CARDINAL
ejpam-3812	142	1	6	CARDINAL
ejpam-3812	143	1	1fd	CARDINAL
ejpam-3812	144	1	γi1f	PERSON
ejpam-3812	144	2	2	CARDINAL
ejpam-3812	145	1	γi1f	ORG
ejpam-3812	147	1	dg(a	GPE
ejpam-3812	147	2	2	CARDINAL
ejpam-3812	147	3	3	CARDINAL
ejpam-3812	147	4	1fd	CARDINAL
ejpam-3812	150	1	γi1f	PERSON
ejpam-3812	150	2	2	CARDINAL
ejpam-3812	150	3	7	CARDINAL
ejpam-3812	151	1	γi1f	PERSON
ejpam-3812	153	1	γi1f	PERSON
ejpam-3812	153	2	γi1f	PERSON
ejpam-3812	153	3	γi1f	PERSON
ejpam-3812	154	1	1	CARDINAL
ejpam-3812	154	2	3	CARDINAL
ejpam-3812	154	3	1	CARDINAL
ejpam-3812	154	4	3r	CARDINAL
ejpam-3812	154	5	first	ORDINAL
ejpam-3812	154	6	3r	CARDINAL
ejpam-3812	155	1	sr−1	PERSON
ejpam-3812	155	2	v3r	PERSON
ejpam-3812	156	1	〉	CARDINAL
ejpam-3812	156	2	1	CARDINAL
ejpam-3812	156	3	4	DATE
ejpam-3812	156	4	3r−2	CARDINAL
ejpam-3812	156	5	1	CARDINAL
ejpam-3812	157	1	1	CARDINAL
ejpam-3812	158	1	γi1f	PERSON
ejpam-3812	158	2	r.	NORP
ejpam-3812	158	3	three	CARDINAL
ejpam-3812	159	1	1	CARDINAL
ejpam-3812	160	1	γi1f	PERSON
ejpam-3812	160	2	r.	NORP
ejpam-3812	160	3	γi1f	PERSON
ejpam-3812	160	4	e. m. ortega	PERSON
ejpam-3812	160	5	r. isla	PERSON
ejpam-3812	161	1	j. pure	PERSON
ejpam-3812	161	2	13	CARDINAL
ejpam-3812	161	3	4	CARDINAL
ejpam-3812	161	4	2020	DATE
ejpam-3812	161	5	779	CARDINAL
ejpam-3812	161	6	793 784	CARDINAL
ejpam-3812	161	7	2	CARDINAL
ejpam-3812	161	8	3r	CARDINAL
ejpam-3812	161	9	1	CARDINAL
ejpam-3812	161	10	γi1f	ORG
ejpam-3812	161	11	〉	CARDINAL
ejpam-3812	162	1	γi1f	ORG
ejpam-3812	163	1	γi1f	PERSON
ejpam-3812	163	2	1	CARDINAL
ejpam-3812	163	3	3	CARDINAL
ejpam-3812	163	4	3	CARDINAL
ejpam-3812	163	5	3r	CARDINAL
ejpam-3812	163	6	first	ORDINAL
ejpam-3812	163	7	3r	CARDINAL
ejpam-3812	163	8	1	CARDINAL
ejpam-3812	164	1	1	CARDINAL
ejpam-3812	165	1	γi1f	PERSON
ejpam-3812	165	2	+ 1	DATE
ejpam-3812	165	3	+ 1	CARDINAL
ejpam-3812	165	4	3r+1 3	DATE
ejpam-3812	165	5	first	ORDINAL
ejpam-3812	165	6	1	CARDINAL
ejpam-3812	165	7	v3r	ORG
ejpam-3812	165	8	v3r+1	DATE
ejpam-3812	166	1	1	CARDINAL
ejpam-3812	166	2	1	CARDINAL
ejpam-3812	166	3	+ 1	CARDINAL
ejpam-3812	166	4	3r+1 3	DATE
ejpam-3812	167	1	γi1f	PERSON
ejpam-3812	168	1	γi1f	PERSON
ejpam-3812	169	1	4	CARDINAL
ejpam-3812	170	1	γi1f	PERSON
ejpam-3812	170	2	3	CARDINAL
ejpam-3812	172	1	1	CARDINAL
ejpam-3812	172	2	7	CARDINAL
ejpam-3812	173	1	8	CARDINAL
ejpam-3812	174	1	6	CARDINAL
ejpam-3812	174	2	1 ≤ k ≤ max{m	QUANTITY
ejpam-3812	175	1	⊆	CARDINAL
ejpam-3812	175	2	g+h	ORG
ejpam-3812	176	1	⊆	CARDINAL
ejpam-3812	176	2	= k	PERSON
ejpam-3812	176	3	⊆	CARDINAL
ejpam-3812	176	4	= k	PERSON
ejpam-3812	178	1	9	CARDINAL
ejpam-3812	179	1	6	CARDINAL
ejpam-3812	179	2	k ≤	ORG
ejpam-3812	180	1	⊆	CARDINAL
ejpam-3812	181	1	⋃ v∈v	PERSON
ejpam-3812	181	2	sv	ORG
ejpam-3812	184	1	⋃ v∈v	PERSON
ejpam-3812	184	2	sv	ORG
ejpam-3812	184	3	|sv| = k. theorem 10	PERSON
ejpam-3812	185	1	6	CARDINAL
ejpam-3812	186	1	⋃	PERSON
ejpam-3812	186	2	⊆	CARDINAL
ejpam-3812	187	1	m. ortega	PERSON
ejpam-3812	187	2	r. isla	PERSON
ejpam-3812	188	1	j. pure	PERSON
ejpam-3812	188	2	13	CARDINAL
ejpam-3812	188	3	4	CARDINAL
ejpam-3812	188	4	2020	DATE
ejpam-3812	188	5	779	CARDINAL
ejpam-3812	188	6	tx	ORG
ejpam-3812	190	1	6=	CARDINAL
ejpam-3812	190	2	tx	ORG
ejpam-3812	190	3	∑ z∈ng(x)∩s |tz|	PERSON
ejpam-3812	191	1	k − r.	PERSON
ejpam-3812	191	2	∈	ORG
ejpam-3812	191	3	tx	ORG
ejpam-3812	191	4	tx	ORG
ejpam-3812	191	5	∑ v∈ng(y)∩s	PERSON
ejpam-3812	191	6	5	CARDINAL
ejpam-3812	192	1	6	CARDINAL
ejpam-3812	193	1	⋃	PERSON
ejpam-3812	193	2	⊆	CARDINAL
ejpam-3812	193	3	1fd	ORDINAL
ejpam-3812	194	1	1fd	ORDINAL
ejpam-3812	194	2	tx	ORG
ejpam-3812	194	3	1	CARDINAL
ejpam-3812	194	4	11	CARDINAL
ejpam-3812	195	1	6	CARDINAL
ejpam-3812	195	2	1 ≤ k ≤	QUANTITY
ejpam-3812	197	1	⊆	CARDINAL
ejpam-3812	197	2	h)\tx ⊆ nh(tx	ORG
ejpam-3812	197	3	⋃ z∈ng(x	PERSON
ejpam-3812	197	4	tx	ORG
ejpam-3812	197	5	∈	ORG
ejpam-3812	197	6	h)\tx	ORG
ejpam-3812	197	7	∈	ORG
ejpam-3812	197	8	∈	ORG
ejpam-3812	197	9	0	CARDINAL
ejpam-3812	197	10	∈	ORG
ejpam-3812	197	11	∈	ORG
ejpam-3812	197	12	1	CARDINAL
ejpam-3812	197	13	2	DATE
ejpam-3812	198	1	k −	PERSON
ejpam-3812	199	1	6	CARDINAL
ejpam-3812	200	1	6	CARDINAL
ejpam-3812	200	2	k ≤ min{m	ORG
ejpam-3812	202	1	3	CARDINAL
ejpam-3812	202	2	1	CARDINAL
ejpam-3812	202	3	3	CARDINAL
ejpam-3812	202	4	k ≥ 2	ORG
ejpam-3812	202	5	1	CARDINAL
ejpam-3812	203	1	1	CARDINAL
ejpam-3812	203	2	1	CARDINAL
ejpam-3812	203	3	4	CARDINAL
ejpam-3812	204	1	n ≥ 2	ORG
ejpam-3812	204	2	2	CARDINAL
ejpam-3812	205	1	two	CARDINAL
ejpam-3812	206	1	m. ortega	PERSON
ejpam-3812	206	2	r. isla	PERSON
ejpam-3812	207	1	j. pure	PERSON
ejpam-3812	207	2	13	CARDINAL
ejpam-3812	207	3	4	CARDINAL
ejpam-3812	207	4	2020	DATE
ejpam-3812	207	5	779	CARDINAL
ejpam-3812	209	1	1	CARDINAL
ejpam-3812	209	2	2	CARDINAL
ejpam-3812	209	3	2 ≤ n ≤ 4 2r	QUANTITY
ejpam-3812	209	4	4r	CARDINAL
ejpam-3812	209	5	2r + 1	DATE
ejpam-3812	209	6	4r	CARDINAL
ejpam-3812	209	7	4r + 2	DATE
ejpam-3812	209	8	4r + 3	DATE
ejpam-3812	209	9	2	CARDINAL
ejpam-3812	210	1	n ≥ 3	DATE
ejpam-3812	210	2	1	CARDINAL
ejpam-3812	210	3	3	CARDINAL
ejpam-3812	210	4	3 2r	CARDINAL
ejpam-3812	210	5	4r	CARDINAL
ejpam-3812	210	6	2r + 1	DATE
ejpam-3812	210	7	4r	CARDINAL
ejpam-3812	210	8	4r	CARDINAL
ejpam-3812	210	9	4r + 3	DATE
ejpam-3812	210	10	12	CARDINAL
ejpam-3812	211	1	2 ≤	QUANTITY
ejpam-3812	214	1	1	CARDINAL
ejpam-3812	215	1	1	CARDINAL
ejpam-3812	231	1	•	CARDINAL
ejpam-3812	233	1	x3 x4	PERSON
ejpam-3812	233	2	xa−1 xa	PERSON
ejpam-3812	233	3	1	CARDINAL
ejpam-3812	234	1	1f	CARDINAL
ejpam-3812	235	1	xa−1	PERSON
ejpam-3812	235	2	xa	PERSON
ejpam-3812	235	3	g1	ORG
ejpam-3812	237	1	2	CARDINAL
ejpam-3812	237	2	2	CARDINAL
ejpam-3812	239	1	x2 x3 ·	PERSON
ejpam-3812	257	1	• • • • y1 y2 y3 yb−a	TIME
ejpam-3812	257	2	2	CARDINAL
ejpam-3812	258	1	1f	CARDINAL
ejpam-3812	260	1	{y1	PERSON
ejpam-3812	262	1	a− 1	ORG
ejpam-3812	262	2	m. ortega	PERSON
ejpam-3812	262	3	r. isla	PERSON
ejpam-3812	263	1	j. pure	PERSON
ejpam-3812	263	2	13	CARDINAL
ejpam-3812	263	3	4	CARDINAL
ejpam-3812	263	4	2020	DATE
ejpam-3812	263	5	779-793 787	MONEY
ejpam-3812	263	6	7	CARDINAL
ejpam-3812	265	1	1	CARDINAL
ejpam-3812	266	1	1	CARDINAL
ejpam-3812	267	1	13	CARDINAL
ejpam-3812	268	1	two	CARDINAL
ejpam-3812	269	1	⊆	CARDINAL
ejpam-3812	269	2	1fd	ORDINAL
ejpam-3812	269	3	g+h	ORG
ejpam-3812	272	1	g+h	ORG
ejpam-3812	272	2	2	CARDINAL
ejpam-3812	272	3	8	CARDINAL
ejpam-3812	272	4	8	CARDINAL
ejpam-3812	274	1	g+ h	ORG
ejpam-3812	274	2	2	CARDINAL
ejpam-3812	274	3	g+h	ORG
ejpam-3812	277	1	14	DATE
ejpam-3812	279	1	⊆	CARDINAL
ejpam-3812	279	2	1fd	ORDINAL
ejpam-3812	282	1	⊆	CARDINAL
ejpam-3812	282	2	1fd	ORDINAL
ejpam-3812	283	1	1fd	ORDINAL
ejpam-3812	283	2	9	CARDINAL
ejpam-3812	285	1	9	CARDINAL
ejpam-3812	287	1	g ◦h	ORG
ejpam-3812	288	1	15	CARDINAL
ejpam-3812	290	1	⊆	CARDINAL
ejpam-3812	290	2	1fd	ORDINAL
ejpam-3812	290	3	g[h	ORG
ejpam-3812	293	1	⋃	PERSON
ejpam-3812	293	2	1fd	ORDINAL
ejpam-3812	293	3	g[h	ORG
ejpam-3812	294	1	1fd	ORDINAL
ejpam-3812	295	1	tx	ORG
ejpam-3812	295	2	1	CARDINAL
ejpam-3812	295	3	∈	ORG
ejpam-3812	295	4	5	CARDINAL
ejpam-3812	295	5	6=	CARDINAL
ejpam-3812	298	1	1	CARDINAL
ejpam-3812	298	2	1fd	ORDINAL
ejpam-3812	299	1	1fd	ORDINAL
ejpam-3812	299	2	g[h	ORG
ejpam-3812	299	3	w	ORG
ejpam-3812	299	4	w	ORG
ejpam-3812	301	1	w ∈ s	PERSON
ejpam-3812	301	2	2	CARDINAL
ejpam-3812	301	3	w	ORG
ejpam-3812	302	1	2	CARDINAL
ejpam-3812	303	1	∈	ORG
ejpam-3812	304	1	∈	ORG
ejpam-3812	304	2	w ∈	ORG
ejpam-3812	304	3	∩ s	PERSON
ejpam-3812	304	4	1fd	ORDINAL
ejpam-3812	306	1	1	CARDINAL
ejpam-3812	306	2	1fd	ORDINAL
ejpam-3812	306	3	g[h	ORG
ejpam-3812	307	1	1	CARDINAL
ejpam-3812	307	2	2	CARDINAL
ejpam-3812	308	1	∈	ORG
ejpam-3812	308	2	2	CARDINAL
ejpam-3812	308	3	1fd	ORDINAL
ejpam-3812	310	1	10	CARDINAL
ejpam-3812	312	1	g[h	ORG
ejpam-3812	312	2	n. m. ortega	PERSON
ejpam-3812	312	3	r. isla	PERSON
ejpam-3812	313	1	j. pure	PERSON
ejpam-3812	313	2	13	CARDINAL
ejpam-3812	313	3	4	CARDINAL
ejpam-3812	313	4	2020	DATE
ejpam-3812	313	5	779	CARDINAL
ejpam-3812	313	6	793 788	CARDINAL
ejpam-3812	313	7	16	CARDINAL
ejpam-3812	316	1	⊆	CARDINAL
ejpam-3812	316	2	1fd	ORDINAL
ejpam-3812	316	3	h)\tx ⊆ nh(tx	ORG
ejpam-3812	316	4	⋃ z∈ng(x	PERSON
ejpam-3812	316	5	tx	ORG
ejpam-3812	316	6	∈	ORG
ejpam-3812	316	7	h)\tx	ORG
ejpam-3812	316	8	1	CARDINAL
ejpam-3812	316	9	∈	ORG
ejpam-3812	316	10	∩ tx = ∅	PERSON
ejpam-3812	316	11	∈	ORG
ejpam-3812	316	12	one	CARDINAL
ejpam-3812	316	13	∈	ORG
ejpam-3812	316	14	∈	ORG
ejpam-3812	316	15	tx	ORG
ejpam-3812	316	16	tx	ORG
ejpam-3812	316	17	ab ∈ e(h	ORG
ejpam-3812	316	18	∈	ORG
ejpam-3812	316	19	∈	ORG
ejpam-3812	317	1	⊆	CARDINAL
ejpam-3812	317	2	1fd	ORDINAL
ejpam-3812	317	3	1fd	ORDINAL
ejpam-3812	317	4	11	CARDINAL
ejpam-3812	319	1	∈	ORG
ejpam-3812	319	2	tx	ORG
ejpam-3812	319	3	tx	ORG
ejpam-3812	319	4	ab /∈ e(h	ORG
ejpam-3812	319	5	∈	ORG
ejpam-3812	322	1	2	CARDINAL
ejpam-3812	323	1	2	CARDINAL
ejpam-3812	324	1	2	CARDINAL
ejpam-3812	324	2	d)∩	ORG
ejpam-3812	324	3	2	CARDINAL
ejpam-3812	324	4	1fd	ORDINAL
ejpam-3812	327	1	11	CARDINAL
ejpam-3812	327	2	1fd	ORDINAL
ejpam-3812	328	1	1fd	ORDINAL
ejpam-3812	328	2	11	CARDINAL
ejpam-3812	330	1	c1 =	PERSON
ejpam-3812	331	1	1fd	ORDINAL
ejpam-3812	332	1	1fd	CARDINAL
ejpam-3812	333	1	11	CARDINAL
ejpam-3812	334	1	12	CARDINAL
ejpam-3812	336	1	γ1fd(h	ORG
ejpam-3812	337	1	5	CARDINAL
ejpam-3812	338	1	12	CARDINAL
ejpam-3812	339	1	3	CARDINAL
ejpam-3812	341	1	8	CARDINAL
ejpam-3812	341	2	2	DATE
ejpam-3812	341	3	4	CARDINAL
ejpam-3812	341	4	2	CARDINAL
ejpam-3812	343	1	m. ortega	PERSON
ejpam-3812	343	2	r. isla	PERSON
ejpam-3812	344	1	j. pure	PERSON
ejpam-3812	344	2	13	CARDINAL
ejpam-3812	344	3	4	CARDINAL
ejpam-3812	344	4	2020	DATE
ejpam-3812	344	5	779	CARDINAL
ejpam-3812	344	6	793 789	CARDINAL
ejpam-3812	365	1	3	CARDINAL
ejpam-3812	365	2	1f	CARDINAL
ejpam-3812	365	3	8	CARDINAL
ejpam-3812	365	4	4	CARDINAL
ejpam-3812	368	1	17	CARDINAL
ejpam-3812	369	1	1 ≤ k	QUANTITY
ejpam-3812	370	1	g+h	ORG
ejpam-3812	371	1	g+h	ORG
ejpam-3812	371	2	= k	PERSON
ejpam-3812	371	3	= k	PERSON
ejpam-3812	372	1	g+h	PERSON
ejpam-3812	372	2	1 ≤ k	QUANTITY
ejpam-3812	374	1	∈	ORG
ejpam-3812	374	2	∈	ORG
ejpam-3812	375	1	g+h	ORG
ejpam-3812	377	1	∈	ORG
ejpam-3812	378	1	= k.	PERSON
ejpam-3812	385	1	= k	PERSON
ejpam-3812	385	2	∈	ORG
ejpam-3812	388	1	17	CARDINAL
ejpam-3812	388	2	13	CARDINAL
ejpam-3812	389	1	1 ≤ k	QUANTITY
ejpam-3812	390	1	= k	PERSON
ejpam-3812	390	2	g+h	ORG
ejpam-3812	390	3	k. theorem 18	PERSON
ejpam-3812	391	1	k ≤	ORG
ejpam-3812	392	1	2	CARDINAL
ejpam-3812	394	1	k vertices	ORG
ejpam-3812	395	1	m. ortega	PERSON
ejpam-3812	395	2	r. isla	PERSON
ejpam-3812	396	1	j. pure	PERSON
ejpam-3812	396	2	13	CARDINAL
ejpam-3812	396	3	4	CARDINAL
ejpam-3812	396	4	2020	DATE
ejpam-3812	396	5	779-793 790	QUANTITY
ejpam-3812	397	1	k ≤ ⌈	ORG
ejpam-3812	397	2	2	CARDINAL
ejpam-3812	398	1	6=	CARDINAL
ejpam-3812	399	1	hv)∩c	NORP
ejpam-3812	399	2	1	CARDINAL
ejpam-3812	400	1	1	CARDINAL
ejpam-3812	400	2	w ∈	ORG
ejpam-3812	401	1	w /∈ c.	NORP
ejpam-3812	401	2	1	CARDINAL
ejpam-3812	401	3	∩ ng◦	PERSON
ejpam-3812	403	1	⋃ v∈v	PERSON
ejpam-3812	403	2	sv	ORG
ejpam-3812	403	3	|sv| = k	PERSON
ejpam-3812	404	1	k vertices	ORG
ejpam-3812	405	1	k vertices	ORG
ejpam-3812	407	1	⋃ v∈v	PERSON
ejpam-3812	407	2	sv	ORG
ejpam-3812	407	3	|sv| = k.	PERSON
ejpam-3812	407	4	9	CARDINAL
ejpam-3812	408	1	18	CARDINAL
ejpam-3812	408	2	14	DATE
ejpam-3812	409	1	k ≤ ⌈ n 2 ⌉ .	ORG
ejpam-3812	410	1	= k	PERSON
ejpam-3812	410	2	19	CARDINAL
ejpam-3812	411	1	1 ≤ k ≤	QUANTITY
ejpam-3812	412	1	2	CARDINAL
ejpam-3812	413	1	⋃	PERSON
ejpam-3812	413	2	1fd	CARDINAL
ejpam-3812	413	3	∈	ORG
ejpam-3812	414	1	tx	ORG
ejpam-3812	415	1	⋃	PERSON
ejpam-3812	415	2	g[h	ORG
ejpam-3812	416	1	10	CARDINAL
ejpam-3812	416	2	10	CARDINAL
ejpam-3812	416	3	∑ v∈ng(y)∩s	PERSON
ejpam-3812	416	4	1	CARDINAL
ejpam-3812	417	1	1fd	CARDINAL
ejpam-3812	418	1	tx	ORG
ejpam-3812	418	2	10	CARDINAL
ejpam-3812	418	3	k ≤ ⌈	ORG
ejpam-3812	418	4	2	CARDINAL
ejpam-3812	419	1	∈	ORG
ejpam-3812	419	2	tx	ORG
ejpam-3812	419	3	tx	ORG
ejpam-3812	421	1	tx	ORG
ejpam-3812	423	1	tx	ORG
ejpam-3812	423	2	∈	ORG
ejpam-3812	423	3	∑ v∈ng(y)∩s	PERSON
ejpam-3812	424	1	10	CARDINAL
ejpam-3812	425	1	tx	ORG
ejpam-3812	427	1	tx	ORG
ejpam-3812	427	2	ab ∈ e(h	ORG
ejpam-3812	427	3	m. ortega	PERSON
ejpam-3812	427	4	r. isla	PERSON
ejpam-3812	428	1	j. pure	PERSON
ejpam-3812	428	2	13	CARDINAL
ejpam-3812	428	3	4	CARDINAL
ejpam-3812	428	4	2020	DATE
ejpam-3812	428	5	779	CARDINAL
ejpam-3812	428	6	tx	ORG
ejpam-3812	429	1	6=	CARDINAL
ejpam-3812	429	2	a)(y	PERSON
ejpam-3812	430	1	∈	ORG
ejpam-3812	430	2	∩ s	ORG
ejpam-3812	430	3	g[h	ORG
ejpam-3812	431	1	15	CARDINAL
ejpam-3812	433	1	2	CARDINAL
ejpam-3812	435	1	γi1f	PERSON
ejpam-3812	437	1	γi1f	ORG
ejpam-3812	437	2	tx	ORG
ejpam-3812	438	1	⋃	PERSON
ejpam-3812	438	2	19	CARDINAL
ejpam-3812	439	1	γi1f	PERSON
ejpam-3812	440	1	g[h	ORG
ejpam-3812	441	1	19	CARDINAL
ejpam-3812	442	1	⋃	DATE
ejpam-3812	443	1	x}×qx	ORG
ejpam-3812	443	2	1fd	CARDINAL
ejpam-3812	443	3	= k	PERSON
ejpam-3812	443	4	∈	ORG
ejpam-3812	444	1	≥ k	PERSON
ejpam-3812	444	2	γi1f	PERSON
ejpam-3812	446	1	20	CARDINAL
ejpam-3812	447	1	1 ≤ k ≤	QUANTITY
ejpam-3812	449	1	tx	ORG
ejpam-3812	449	2	∈	ORG
ejpam-3812	449	3	tx	ORG
ejpam-3812	449	4	∈	PRODUCT
ejpam-3812	449	5	∈	ORG
ejpam-3812	449	6	∈	ORG
ejpam-3812	449	7	0	CARDINAL
ejpam-3812	449	8	h)\tx ⊆ nh(tx	ORG
ejpam-3812	449	9	⋃	PERSON
ejpam-3812	449	10	∈	ORG
ejpam-3812	449	11	∈	ORG
ejpam-3812	450	1	0	CARDINAL
ejpam-3812	450	2	∈	ORG
ejpam-3812	450	3	k−r⋂ i=1 txi	PERSON
ejpam-3812	450	4	∈	ORG
ejpam-3812	450	5	1	CARDINAL
ejpam-3812	450	6	2	DATE
ejpam-3812	450	7	k − r. proof	PERSON
ejpam-3812	451	1	11	CARDINAL
ejpam-3812	452	1	∈	ORG
ejpam-3812	452	2	tx	ORG
ejpam-3812	452	3	tx	ORG
ejpam-3812	454	1	tx	ORG
ejpam-3812	455	1	∈	ORG
ejpam-3812	455	2	tx	ORG
ejpam-3812	455	3	∈	ORG
ejpam-3812	455	4	∈	ORG
ejpam-3812	459	1	792 11	DATE
ejpam-3812	460	1	3	CARDINAL
ejpam-3812	460	2	6	CARDINAL
ejpam-3812	461	1	16	CARDINAL
ejpam-3812	462	1	1 ≤ k ≤	QUANTITY
ejpam-3812	464	1	6	CARDINAL
ejpam-3812	465	1	16	CARDINAL
ejpam-3812	467	1	4	CARDINAL
ejpam-3812	469	1	γi1f	PERSON
ejpam-3812	469	2	2	CARDINAL
ejpam-3812	469	3	1	CARDINAL
ejpam-3812	469	4	3	CARDINAL
ejpam-3812	469	5	1	CARDINAL
ejpam-3812	469	6	γi3f	ORG
ejpam-3812	469	7	5	CARDINAL
ejpam-3812	469	8	3	CARDINAL
ejpam-3812	469	9	3	CARDINAL
ejpam-3812	469	10	3	CARDINAL
ejpam-3812	476	1	4	CARDINAL
ejpam-3812	477	1	1f	CARDINAL
ejpam-3812	477	2	2	CARDINAL
ejpam-3812	477	3	3f	CARDINAL
ejpam-3812	477	4	5	CARDINAL
ejpam-3812	477	5	the department of science and technology	ORG
ejpam-3812	477	6	mindanao	LOC
ejpam-3812	477	7	university-iligan institute of technology	ORG
ejpam-3812	479	1	1	CARDINAL
ejpam-3812	481	1	methuen	GPE
ejpam-3812	481	2	london	GPE
ejpam-3812	481	3	1962	DATE
ejpam-3812	482	1	2	CARDINAL
ejpam-3812	482	2	e. cockayne	PERSON
ejpam-3812	482	3	s. hedetniemi	PERSON
ejpam-3812	485	1	numer	PERSON
ejpam-3812	485	2	1974	DATE
ejpam-3812	486	1	3	CARDINAL
ejpam-3812	486	2	w. bent-usman	PERSON
ejpam-3812	487	1	d. gomisong	PERSON
ejpam-3812	487	2	r. isla	PERSON
ejpam-3812	488	1	cartesian	NORP
ejpam-3812	489	1	12(27):1341–1355	DATE
ejpam-3812	489	2	2018	DATE
ejpam-3812	490	1	793	CARDINAL
ejpam-3812	490	2	4	CARDINAL
ejpam-3812	491	1	a. hansberg	PERSON
ejpam-3812	491	2	m. henning	PERSON
ejpam-3812	493	1	312(19):2905–2914	DATE
ejpam-3812	493	2	2012	DATE
ejpam-3812	494	1	5	CARDINAL
ejpam-3812	494	2	w. goddard	PERSON
ejpam-3812	494	3	m. henning	PERSON
ejpam-3812	494	4	c. mcpillan	GPE
ejpam-3812	496	1	utilitas mathematica	PERSON
ejpam-3812	496	2	94:67–81, 2014	DATE
ejpam-3812	497	1	6	CARDINAL
ejpam-3812	497	2	r. isla	PERSON
ejpam-3812	497	3	s. canoy jr.	PERSON
ejpam-3812	499	1	8(178):8863–8874,	DATE
ejpam-3812	499	2	2014	DATE
ejpam-3812	500	1	7	CARDINAL
ejpam-3812	500	2	w. bent-usman	PERSON
ejpam-3812	501	1	r. isla	PERSON
ejpam-3812	501	2	s. canoy jr.	PERSON
ejpam-3812	502	1	european journal	ORG
ejpam-3812	502	2	12(3):1337–1349	DATE
ejpam-3812	502	3	2019	DATE
ejpam-3812	503	1	8	CARDINAL
ejpam-3812	503	2	i. aniversario	PERSON
ejpam-3812	504	1	s. canoy jr and f. jamil	PERSON
ejpam-3812	506	1	european journal	ORG
ejpam-3812	506	2	2019	DATE
ejpam-3812	507	1	9	CARDINAL
ejpam-3812	508	1	amer	PERSON
ejpam-3812	509	1	colloq	PERSON
ejpam-3812	511	1	38:206–212	CARDINAL
ejpam-3812	511	2	1962	DATE