id	sid	eid	entity	type
ejpam-5332	1	1	european journal	ORG
ejpam-5332	2	1	17	CARDINAL
ejpam-5332	2	2	4	CARDINAL
ejpam-5332	2	3	2024	DATE
ejpam-5332	2	4	2930-2938	CARDINAL
ejpam-5332	2	5	new york	GPE
ejpam-5332	2	6	harold b. samson1,∗	PERSON
ejpam-5332	2	7	imelda s. aniversario2	PERSON
ejpam-5332	2	8	mary joy f. luga3	PERSON
ejpam-5332	2	9	mindanao	GPE
ejpam-5332	2	10	university-iligan institute of technology	ORG
ejpam-5332	2	11	9200	CARDINAL
ejpam-5332	2	12	iligan city	GPE
ejpam-5332	2	13	philippines 2 department	ORG
ejpam-5332	2	14	mindanao state university-iligan institute of technology	ORG
ejpam-5332	2	15	9200	CARDINAL
ejpam-5332	2	16	iligan city	GPE
ejpam-5332	2	17	philippines 3	ORG
ejpam-5332	2	18	mindanao state university-iligan institute of technology	ORG
ejpam-5332	2	19	9200	CARDINAL
ejpam-5332	2	20	iligan city	GPE
ejpam-5332	2	21	philippines	GPE
ejpam-5332	3	1	cartesian	NORP
ejpam-5332	4	1	cartesian	NORP
ejpam-5332	7	1	2020	DATE
ejpam-5332	7	2	05c12	CARDINAL
ejpam-5332	7	3	1	CARDINAL
ejpam-5332	7	4	r. g. artes	PERSON
ejpam-5332	7	5	jr.	PERSON
ejpam-5332	7	6	m.j. f. luga	PERSON
ejpam-5332	8	1	3	CARDINAL
ejpam-5332	8	2	2	CARDINAL
ejpam-5332	8	3	2014	DATE
ejpam-5332	9	1	cartesian	NORP
ejpam-5332	10	1	1	CARDINAL
ejpam-5332	13	1	harold.samson@g.msuiit.edu.ph	DATE
ejpam-5332	13	2	h. samson	PERSON
ejpam-5332	13	3	imelda.aniverario@g.msuiit.edu.ph	PERSON
ejpam-5332	13	4	i. aniversario	PERSON
ejpam-5332	14	1	2930	CARDINAL
ejpam-5332	15	1	2024	CARDINAL
ejpam-5332	16	1	h. b. samson	PERSON
ejpam-5332	16	2	i. s. aniversario	PERSON
ejpam-5332	16	3	m. j. f. luga	PERSON
ejpam-5332	17	1	j. pure	PERSON
ejpam-5332	17	2	17	CARDINAL
ejpam-5332	17	3	4	CARDINAL
ejpam-5332	17	4	2024	CARDINAL
ejpam-5332	17	5	2930	CARDINAL
ejpam-5332	17	6	∈	ORG
ejpam-5332	17	7	the subgraph h	ORG
ejpam-5332	22	1	1	CARDINAL
ejpam-5332	26	1	⊆	CARDINAL
ejpam-5332	27	1	two	CARDINAL
ejpam-5332	28	1	two	CARDINAL
ejpam-5332	29	1	∈	ORG
ejpam-5332	30	1	∈	ORG
ejpam-5332	31	1	ig[u	ORG
ejpam-5332	31	2	ig[u	ORG
ejpam-5332	31	3	ig[u	ORG
ejpam-5332	32	1	g. subgraph h	ORG
ejpam-5332	32	2	subgraph h∗	PERSON
ejpam-5332	32	3	∈	ORG
ejpam-5332	33	1	k ∈ n.	PERSON
ejpam-5332	35	1	two	CARDINAL
ejpam-5332	35	2	ḡ	GPE
ejpam-5332	35	3	cartesian	NORP
ejpam-5332	36	1	⊠h	CARDINAL
ejpam-5332	36	2	cartesian	NORP
ejpam-5332	36	3	u, u′	ORG
ejpam-5332	36	4	⊂	GPE
ejpam-5332	36	5	∈	PRODUCT
ejpam-5332	37	1	∈	ORG
ejpam-5332	38	1	h. b. samson	PERSON
ejpam-5332	38	2	i. s. aniversario	PERSON
ejpam-5332	38	3	m. j. f. luga	PERSON
ejpam-5332	39	1	j. pure	PERSON
ejpam-5332	39	2	17	CARDINAL
ejpam-5332	39	3	4	CARDINAL
ejpam-5332	39	4	2024	CARDINAL
ejpam-5332	39	5	2930-2938 2932	QUANTITY
ejpam-5332	39	6	5	CARDINAL
ejpam-5332	40	1	g′	PERSON
ejpam-5332	40	2	h′	PERSON
ejpam-5332	40	3	cartesian	NORP
ejpam-5332	40	4	g′	PERSON
ejpam-5332	40	5	h′	GPE
ejpam-5332	42	1	h′	ORG
ejpam-5332	43	1	4	CARDINAL
ejpam-5332	44	1	g ⊠ h	ORG
ejpam-5332	44	2	dg⊠h((u	GPE
ejpam-5332	46	1	4	CARDINAL
ejpam-5332	47	1	2	CARDINAL
ejpam-5332	48	1	1	CARDINAL
ejpam-5332	53	1	n ≥ 4	DATE
ejpam-5332	54	1	2	CARDINAL
ejpam-5332	55	1	1	CARDINAL
ejpam-5332	57	1	x3	GPE
ejpam-5332	59	1	x2][x2	GPE
ejpam-5332	60	1	x3, x4]	ORG
ejpam-5332	63	1	xn−1	GPE
ejpam-5332	64	1	1	CARDINAL
ejpam-5332	67	1	xi+1	PERSON
ejpam-5332	68	1	∈	ORG
ejpam-5332	68	2	1	CARDINAL
ejpam-5332	69	1	2	CARDINAL
ejpam-5332	71	1	2	CARDINAL
ejpam-5332	71	2	γk1(g	PERSON
ejpam-5332	72	1	2	CARDINAL
ejpam-5332	72	2	2	CARDINAL
ejpam-5332	74	1	1	CARDINAL
ejpam-5332	75	1	dg(xi−1	ORG
ejpam-5332	75	2	2	CARDINAL
ejpam-5332	76	1	2	CARDINAL
ejpam-5332	77	1	2	CARDINAL
ejpam-5332	77	2	2	CARDINAL
ejpam-5332	77	3	3	CARDINAL
ejpam-5332	79	1	1	CARDINAL
ejpam-5332	79	2	1	CARDINAL
ejpam-5332	81	1	2	CARDINAL
ejpam-5332	84	1	2	CARDINAL
ejpam-5332	86	1	1	CARDINAL
ejpam-5332	87	1	1	CARDINAL
ejpam-5332	87	2	h. b. samson	PERSON
ejpam-5332	87	3	i. s. aniversario	PERSON
ejpam-5332	87	4	m. j. f. luga	PERSON
ejpam-5332	88	1	j. pure	PERSON
ejpam-5332	88	2	17	CARDINAL
ejpam-5332	88	3	4	CARDINAL
ejpam-5332	88	4	2024	CARDINAL
ejpam-5332	88	5	2930-2938 2933	QUANTITY
ejpam-5332	88	6	1	CARDINAL
ejpam-5332	88	7	2	CARDINAL
ejpam-5332	89	1	n ≥ 5	DATE
ejpam-5332	90	1	2	CARDINAL
ejpam-5332	90	2	1	CARDINAL
ejpam-5332	94	1	un	ORG
ejpam-5332	97	1	un−1	ORG
ejpam-5332	97	2	un	ORG
ejpam-5332	97	3	un	ORG
ejpam-5332	101	1	dcn	ORG
ejpam-5332	102	1	ui+1	CARDINAL
ejpam-5332	102	2	dcn	ORG
ejpam-5332	102	3	2	CARDINAL
ejpam-5332	102	4	ui+1	CARDINAL
ejpam-5332	102	5	dcn	ORG
ejpam-5332	102	6	2	CARDINAL
ejpam-5332	103	1	2	CARDINAL
ejpam-5332	104	1	1	CARDINAL
ejpam-5332	104	2	bipartite	ORG
ejpam-5332	106	1	3	CARDINAL
ejpam-5332	106	2	cartesian	NORP
ejpam-5332	106	3	cartesian	NORP
ejpam-5332	107	1	3	CARDINAL
ejpam-5332	108	1	g1	ORG
ejpam-5332	108	2	g1	ORG
ejpam-5332	109	1	g1	ORG
ejpam-5332	110	1	5	CARDINAL
ejpam-5332	110	2	g1	ORG
ejpam-5332	111	1	h. b. samson	PERSON
ejpam-5332	111	2	i. s. aniversario	PERSON
ejpam-5332	111	3	m. j. f. luga	PERSON
ejpam-5332	112	1	j. pure	PERSON
ejpam-5332	112	2	17	CARDINAL
ejpam-5332	112	3	4	CARDINAL
ejpam-5332	112	4	2024	CARDINAL
ejpam-5332	112	5	2930	CARDINAL
ejpam-5332	114	1	dg1□g2((u	PERSON
ejpam-5332	116	1	g1	ORG
ejpam-5332	128	1	cartesian	NORP
ejpam-5332	128	2	2	CARDINAL
ejpam-5332	129	1	2 + 2	CARDINAL
ejpam-5332	129	2	4	CARDINAL
ejpam-5332	129	3	4	CARDINAL
ejpam-5332	130	1	h. b. samson	PERSON
ejpam-5332	130	2	i. s. aniversario	PERSON
ejpam-5332	130	3	m. j. f. luga	PERSON
ejpam-5332	131	1	j. pure	PERSON
ejpam-5332	131	2	17	CARDINAL
ejpam-5332	131	3	4	CARDINAL
ejpam-5332	131	4	2024	CARDINAL
ejpam-5332	131	5	2930	CARDINAL
ejpam-5332	131	6	2	CARDINAL
ejpam-5332	131	7	cartesian	NORP
ejpam-5332	131	8	4	CARDINAL
ejpam-5332	133	1	⊂	GPE
ejpam-5332	135	1	⊂	GPE
ejpam-5332	136	1	ch ⊂	PERSON
ejpam-5332	138	1	two	CARDINAL
ejpam-5332	139	1	one	CARDINAL
ejpam-5332	139	2	1	CARDINAL
ejpam-5332	139	3	u-u′	ORG
ejpam-5332	141	1	2	CARDINAL
ejpam-5332	143	1	3	CARDINAL
ejpam-5332	148	1	5	CARDINAL
ejpam-5332	150	1	⊂	GPE
ejpam-5332	152	1	∈	ORG
ejpam-5332	152	2	g ⊠ h	ORG
ejpam-5332	152	3	u u′	ORG
ejpam-5332	152	4	oru	PERSON
ejpam-5332	153	1	∈	PRODUCT
ejpam-5332	153	2	h. b. samson	PERSON
ejpam-5332	153	3	i. s. aniversario	PERSON
ejpam-5332	153	4	m. j. f. luga	PERSON
ejpam-5332	154	1	j. pure	PERSON
ejpam-5332	154	2	17	CARDINAL
ejpam-5332	154	3	4	CARDINAL
ejpam-5332	154	4	2024	CARDINAL
ejpam-5332	154	5	2930-2938 2936	QUANTITY
ejpam-5332	154	6	b′	PRODUCT
ejpam-5332	154	7	⊆	CARDINAL
ejpam-5332	156	1	∈	ORG
ejpam-5332	157	1	j = n	PERSON
ejpam-5332	158	1	⊆	CARDINAL
ejpam-5332	159	1	1	CARDINAL
ejpam-5332	161	1	∈	ORG
ejpam-5332	161	2	g ⊠ h	ORG
ejpam-5332	161	3	g ⊠ h	ORG
ejpam-5332	164	1	two	CARDINAL
ejpam-5332	165	1	4	CARDINAL
ejpam-5332	165	2	5	CARDINAL
ejpam-5332	165	3	6	CARDINAL
ejpam-5332	166	1	g1	ORG
ejpam-5332	166	2	⊠h2	ORG
ejpam-5332	166	3	g1	ORG
ejpam-5332	168	1	g1	ORG
ejpam-5332	168	2	g1	ORG
ejpam-5332	169	1	g1	ORG
ejpam-5332	172	1	4	CARDINAL
ejpam-5332	173	1	max	PERSON
ejpam-5332	173	2	dg1(u	PERSON
ejpam-5332	173	3	dg2(v	NORP
ejpam-5332	174	1	3	CARDINAL
ejpam-5332	175	1	max	PERSON
ejpam-5332	175	2	max	PERSON
ejpam-5332	175	3	dg1(u	GPE
ejpam-5332	175	4	dg2(v	NORP
ejpam-5332	176	1	max	PERSON
ejpam-5332	178	1	dg1⊠g2((u	ORG
ejpam-5332	181	1	h. b. samson	PERSON
ejpam-5332	181	2	i. s. aniversario	PERSON
ejpam-5332	181	3	m. j. f. luga	PERSON
ejpam-5332	182	1	j. pure	PERSON
ejpam-5332	182	2	17	CARDINAL
ejpam-5332	182	3	4	CARDINAL
ejpam-5332	182	4	2024	CARDINAL
ejpam-5332	182	5	2930	CARDINAL
ejpam-5332	182	6	3	CARDINAL
ejpam-5332	184	1	3	CARDINAL
ejpam-5332	186	1	max	PERSON
ejpam-5332	186	2	2	CARDINAL
ejpam-5332	186	3	3	CARDINAL
ejpam-5332	186	4	3	CARDINAL
ejpam-5332	191	1	msu-iligan institute of technology	ORG
ejpam-5332	192	1	2938	CARDINAL
ejpam-5332	192	2	1	CARDINAL
ejpam-5332	194	1	addison-weasley	ORG
ejpam-5332	194	2	boston, usa, 1969	ORG
ejpam-5332	195	1	2	CARDINAL
ejpam-5332	195	2	mj luga	PERSON
ejpam-5332	197	1	hikari ltd	ORG
ejpam-5332	197	2	2014	DATE
ejpam-5332	198	1	3	CARDINAL
ejpam-5332	198	2	mj luga	PERSON
ejpam-5332	200	1	hikari ltd	ORG
ejpam-5332	200	2	8(88):4361–4366	CARDINAL
ejpam-5332	200	3	2014	DATE
ejpam-5332	201	1	4	CARDINAL
ejpam-5332	201	2	w imrich	PERSON
ejpam-5332	201	3	hammack	PERSON
ejpam-5332	203	1	taylor	PERSON
ejpam-5332	203	2	francis	PERSON
ejpam-5332	203	3	england	GPE
ejpam-5332	203	4	united kingdom,	GPE
ejpam-5332	203	5	2011	DATE
ejpam-5332	204	1	5	CARDINAL
ejpam-5332	204	2	jr s	PERSON
ejpam-5332	204	3	ijl garces	ORG
ejpam-5332	206	1	combinatorics	ORG
ejpam-5332	206	2	18:787–793, 2002	DATE