id	sid	eid	entity	type
ejpam-5555	1	1	european journal	ORG
ejpam-5555	1	2	2025	DATE
ejpam-5555	1	3	18	CARDINAL
ejpam-5555	1	4	1	CARDINAL
ejpam-5555	1	5	5555	CARDINAL
ejpam-5555	1	6	1307-5543	DATE
ejpam-5555	1	7	new york	GPE
ejpam-5555	1	8	clint	PERSON
ejpam-5555	1	9	m. quije1,2	PERSON
ejpam-5555	1	10	rochelleo e. mariano3	PERSON
ejpam-5555	1	11	eman c. ahmad3,∗	PERSON
ejpam-5555	1	12	1	CARDINAL
ejpam-5555	1	13	ateneo de zamboanga university	ORG
ejpam-5555	1	14	zamboanga city	GPE
ejpam-5555	1	15	philippines 2 institute of arts	ORG
ejpam-5555	1	16	3	CARDINAL
ejpam-5555	1	17	university, zamboanga city	ORG
ejpam-5555	1	18	philippines	GPE
ejpam-5555	3	1	at least one	CARDINAL
ejpam-5555	3	2	⊆	CARDINAL
ejpam-5555	7	1	2 ≤	MONEY
ejpam-5555	8	1	2020	DATE
ejpam-5555	8	2	05c69	CARDINAL
ejpam-5555	8	3	05c76	CARDINAL
ejpam-5555	8	4	1	CARDINAL
ejpam-5555	10	1	asdain et al	PERSON
ejpam-5555	11	1	1	CARDINAL
ejpam-5555	11	2	chartrand et al	ORG
ejpam-5555	12	1	3	CARDINAL
ejpam-5555	12	2	mariano	ORG
ejpam-5555	12	3	8	CARDINAL
ejpam-5555	12	4	john	PERSON
ejpam-5555	13	1	12	CARDINAL
ejpam-5555	14	1	cartesian	NORP
ejpam-5555	16	1	cjquije@gadtc.edu.ph (c.j. quije	ORG
ejpam-5555	16	2	r. mariano	PERSON
ejpam-5555	16	3	e. ahmad	PERSON
ejpam-5555	17	1	1	CARDINAL
ejpam-5555	17	2	2025	CARDINAL
ejpam-5555	18	1	c.j. quije	GPE
ejpam-5555	18	2	r. mariano	PERSON
ejpam-5555	18	3	e. ahmad	PERSON
ejpam-5555	19	1	j. pure	PERSON
ejpam-5555	19	2	18	CARDINAL
ejpam-5555	19	3	1	CARDINAL
ejpam-5555	19	4	2025	CARDINAL
ejpam-5555	19	5	5555 2	CARDINAL
ejpam-5555	19	6	8	CARDINAL
ejpam-5555	20	1	13	CARDINAL
ejpam-5555	20	2	at least one	CARDINAL
ejpam-5555	21	1	al	PERSON
ejpam-5555	21	2	2	CARDINAL
ejpam-5555	27	1	escuadra et al	PERSON
ejpam-5555	28	1	4	CARDINAL
ejpam-5555	28	2	vijayan et al	PERSON
ejpam-5555	29	1	15	CARDINAL
ejpam-5555	31	1	stalin et al	PERSON
ejpam-5555	32	1	13	CARDINAL
ejpam-5555	33	1	9	CARDINAL
ejpam-5555	38	1	stalin et al	PERSON
ejpam-5555	39	1	13	CARDINAL
ejpam-5555	41	1	two	CARDINAL
ejpam-5555	41	2	2	CARDINAL
ejpam-5555	41	3	1	CARDINAL
ejpam-5555	41	4	0	CARDINAL
ejpam-5555	41	5	γg1(g	PERSON
ejpam-5555	44	1	1–15	CARDINAL
ejpam-5555	47	1	⊆	CARDINAL
ejpam-5555	48	1	xy ∈	ORG
ejpam-5555	49	1	∈	ORG
ejpam-5555	50	1	n(v	ORG
ejpam-5555	51	1	∈	ORG
ejpam-5555	52	1	n(v	ORG
ejpam-5555	53	1	at least one	CARDINAL
ejpam-5555	53	2	⊆	CARDINAL
ejpam-5555	53	3	g(g	PERSON
ejpam-5555	54	1	⊆	CARDINAL
ejpam-5555	54	2	c.j.	GPE
ejpam-5555	54	3	r. mariano	PERSON
ejpam-5555	54	4	e. ahmad	PERSON
ejpam-5555	55	1	j. pure	PERSON
ejpam-5555	55	2	18	CARDINAL
ejpam-5555	55	3	1	CARDINAL
ejpam-5555	55	4	2025	CARDINAL
ejpam-5555	55	5	5555 3	CARDINAL
ejpam-5555	55	6	8	CARDINAL
ejpam-5555	55	7	ge	ORG
ejpam-5555	63	1	ext(g	ORG
ejpam-5555	67	1	⟨g−	ORG
ejpam-5555	68	1	\x	ORG
ejpam-5555	68	2	g1	ORG
ejpam-5555	70	1	subgraph kr	PERSON
ejpam-5555	70	2	1	CARDINAL
ejpam-5555	71	1	one	CARDINAL
ejpam-5555	72	1	g1	ORG
ejpam-5555	75	1	1	CARDINAL
ejpam-5555	75	2	2	CARDINAL
ejpam-5555	75	3	g1	ORG
ejpam-5555	77	1	2.	PERCENT
ejpam-5555	78	1	1	CARDINAL
ejpam-5555	79	1	8	CARDINAL
ejpam-5555	80	1	g. theorem 1	ORG
ejpam-5555	81	1	13	CARDINAL
ejpam-5555	81	2	at least two	CARDINAL
ejpam-5555	81	3	1	CARDINAL
ejpam-5555	82	1	2	DATE
ejpam-5555	83	1	13	CARDINAL
ejpam-5555	83	2	n ≥ 2, γge(kn	ORG
ejpam-5555	83	3	3	CARDINAL
ejpam-5555	84	1	12	CARDINAL
ejpam-5555	84	2	4	CARDINAL
ejpam-5555	85	1	13	CARDINAL
ejpam-5555	85	2	one	CARDINAL
ejpam-5555	85	3	1	CARDINAL
ejpam-5555	86	1	1	CARDINAL
ejpam-5555	87	1	c.j. quije	ORG
ejpam-5555	87	2	r. mariano	PERSON
ejpam-5555	87	3	e. ahmad	PERSON
ejpam-5555	88	1	j. pure	PERSON
ejpam-5555	88	2	18	CARDINAL
ejpam-5555	88	3	1	CARDINAL
ejpam-5555	88	4	2025	CARDINAL
ejpam-5555	88	5	5555 4	DATE
ejpam-5555	88	6	3.1	CARDINAL
ejpam-5555	89	1	5	CARDINAL
ejpam-5555	90	1	n ≥ 4	ORG
ejpam-5555	91	1	⊆	CARDINAL
ejpam-5555	91	2	g. i.	PERSON
ejpam-5555	95	1	1	CARDINAL
ejpam-5555	95	2	h. iii	PERSON
ejpam-5555	98	1	n ≥ 4	ORG
ejpam-5555	98	2	1 ≤	QUANTITY
ejpam-5555	98	3	two	CARDINAL
ejpam-5555	99	1	1	CARDINAL
ejpam-5555	99	2	∈	ORG
ejpam-5555	100	1	1	CARDINAL
ejpam-5555	100	2	1	CARDINAL
ejpam-5555	104	1	2	CARDINAL
ejpam-5555	105	1	∈	ORG
ejpam-5555	105	2	1	CARDINAL
ejpam-5555	106	1	1	CARDINAL
ejpam-5555	106	2	1	CARDINAL
ejpam-5555	106	3	3	CARDINAL
ejpam-5555	107	1	1	CARDINAL
ejpam-5555	110	1	xy ∈ e(h	ORG
ejpam-5555	110	2	1	CARDINAL
ejpam-5555	110	3	xy	ORG
ejpam-5555	111	1	2	CARDINAL
ejpam-5555	111	2	∈	ORG
ejpam-5555	111	3	zy /∈	ORG
ejpam-5555	113	1	∈ e(h	ORG
ejpam-5555	118	1	⊆	CARDINAL
ejpam-5555	119	1	3	CARDINAL
ejpam-5555	120	1	∈	ORG
ejpam-5555	122	1	∈	ORG
ejpam-5555	122	2	vz ∈ e(h	ORG
ejpam-5555	125	1	c.j. quije	PERSON
ejpam-5555	125	2	r. mariano	PERSON
ejpam-5555	125	3	e. ahmad	PERSON
ejpam-5555	126	1	j. pure	PERSON
ejpam-5555	126	2	18	CARDINAL
ejpam-5555	126	3	1	CARDINAL
ejpam-5555	126	4	2025	CARDINAL
ejpam-5555	126	5	5555 5	DATE
ejpam-5555	126	6	8	CARDINAL
ejpam-5555	129	1	1	CARDINAL
ejpam-5555	129	2	2	CARDINAL
ejpam-5555	129	3	3.2	CARDINAL
ejpam-5555	130	1	6	CARDINAL
ejpam-5555	131	1	1 ≤	QUANTITY
ejpam-5555	131	2	kp	ORG
ejpam-5555	131	3	kq	PERSON
ejpam-5555	132	1	1	CARDINAL
ejpam-5555	132	2	g. ii	PERSON
ejpam-5555	132	3	1	CARDINAL
ejpam-5555	132	4	g. iii	PERSON
ejpam-5555	133	1	1	CARDINAL
ejpam-5555	134	1	kp	ORG
ejpam-5555	135	1	1	CARDINAL
ejpam-5555	136	1	4	CARDINAL
ejpam-5555	137	1	g. ii	PERSON
ejpam-5555	138	1	1	CARDINAL
ejpam-5555	138	2	∈	ORG
ejpam-5555	139	1	1	CARDINAL
ejpam-5555	139	2	more than one	CARDINAL
ejpam-5555	140	1	1	CARDINAL
ejpam-5555	140	2	g. iii	PERSON
ejpam-5555	141	1	1	CARDINAL
ejpam-5555	142	1	kq	PERSON
ejpam-5555	142	2	2	CARDINAL
ejpam-5555	142	3	g. corollary 2	PERSON
ejpam-5555	143	1	1 ≤	QUANTITY
ejpam-5555	143	2	kp	ORG
ejpam-5555	143	3	kq	PERSON
ejpam-5555	144	1	1	CARDINAL
ejpam-5555	144	2	1	CARDINAL
ejpam-5555	144	3	1	CARDINAL
ejpam-5555	144	4	1	CARDINAL
ejpam-5555	144	5	3.3	CARDINAL
ejpam-5555	145	1	7	CARDINAL
ejpam-5555	145	2	2 ≤	MONEY
ejpam-5555	147	1	b. c.j. quije	PERSON
ejpam-5555	147	2	r. mariano	PERSON
ejpam-5555	147	3	e. ahmad	PERSON
ejpam-5555	148	1	j. pure	PERSON
ejpam-5555	148	2	18	CARDINAL
ejpam-5555	148	3	1	CARDINAL
ejpam-5555	148	4	2025	CARDINAL
ejpam-5555	148	5	5555 6	CARDINAL
ejpam-5555	149	1	2	CARDINAL
ejpam-5555	151	1	2	CARDINAL
ejpam-5555	151	2	2	CARDINAL
ejpam-5555	152	1	3	CARDINAL
ejpam-5555	154	1	u7	PERSON
ejpam-5555	155	1	4	CARDINAL
ejpam-5555	155	2	seven	CARDINAL
ejpam-5555	157	1	three	CARDINAL
ejpam-5555	159	1	1	CARDINAL
ejpam-5555	159	2	2	DATE
ejpam-5555	159	3	3	CARDINAL
ejpam-5555	159	4	1 ≤	QUANTITY
ejpam-5555	160	1	3	CARDINAL
ejpam-5555	162	1	v1(b−3	GPE
ejpam-5555	162	2	j ̸= k	PERSON
ejpam-5555	162	3	1	CARDINAL
ejpam-5555	162	4	2	DATE
ejpam-5555	162	5	3	DATE
ejpam-5555	163	1	3	CARDINAL
ejpam-5555	164	1	1	CARDINAL
ejpam-5555	164	2	1	CARDINAL
ejpam-5555	165	1	2	CARDINAL
ejpam-5555	165	2	u7	ORG
ejpam-5555	166	1	u4, u5	ORG
ejpam-5555	166	2	1	CARDINAL
ejpam-5555	166	3	2	DATE
ejpam-5555	166	4	3	CARDINAL
ejpam-5555	166	5	1 ≤ j ≤	QUANTITY
ejpam-5555	166	6	3	CARDINAL
ejpam-5555	169	1	2 + b−	MONEY
ejpam-5555	170	1	2	CARDINAL
ejpam-5555	170	2	eight	CARDINAL
ejpam-5555	172	1	u8	CARDINAL
ejpam-5555	172	2	a−	ORG
ejpam-5555	172	3	2	CARDINAL
ejpam-5555	173	1	wa−2	ORG
ejpam-5555	174	1	a−2	PERSON
ejpam-5555	175	1	eight	CARDINAL
ejpam-5555	177	1	u8	CARDINAL
ejpam-5555	177	2	a−2 vertices	ORG
ejpam-5555	178	1	wa−2	ORG
ejpam-5555	178	2	three	CARDINAL
ejpam-5555	181	1	1	CARDINAL
ejpam-5555	181	2	2	DATE
ejpam-5555	181	3	3	DATE
ejpam-5555	181	4	u7	ORG
ejpam-5555	181	5	u7	ORG
ejpam-5555	182	1	j ̸= k	PERSON
ejpam-5555	182	2	1	CARDINAL
ejpam-5555	182	3	2	DATE
ejpam-5555	182	4	3	DATE
ejpam-5555	184	1	1	CARDINAL
ejpam-5555	184	2	2	CARDINAL
ejpam-5555	185	1	2	CARDINAL
ejpam-5555	186	1	u8	ORG
ejpam-5555	188	1	wa−2	ORG
ejpam-5555	190	1	= a. moreover	PERSON
ejpam-5555	190	2	u7	ORG
ejpam-5555	190	3	u8	ORG
ejpam-5555	190	4	wi	GPE
ejpam-5555	191	1	1	CARDINAL
ejpam-5555	191	2	2	DATE
ejpam-5555	191	3	3	CARDINAL
ejpam-5555	191	4	1 ≤ j ≤	QUANTITY
ejpam-5555	192	1	1 ≤ j ≤ b− a−	QUANTITY
ejpam-5555	192	2	1	CARDINAL
ejpam-5555	194	1	1	CARDINAL
ejpam-5555	194	2	1 + 1	QUANTITY
ejpam-5555	194	3	b. c.j. quije	PERSON
ejpam-5555	194	4	r. mariano	PERSON
ejpam-5555	194	5	e. ahmad	PERSON
ejpam-5555	195	1	j. pure	PERSON
ejpam-5555	195	2	18	CARDINAL
ejpam-5555	195	3	1	CARDINAL
ejpam-5555	195	4	2025	CARDINAL
ejpam-5555	195	5	5555 7	DATE
ejpam-5555	195	6	8	CARDINAL
ejpam-5555	195	7	2	CARDINAL
ejpam-5555	195	8	4	CARDINAL
ejpam-5555	197	1	cartesian	NORP
ejpam-5555	200	1	ateneo de zamboanga university	ORG
ejpam-5555	200	2	university for supporting this research	ORG
ejpam-5555	201	1	1	CARDINAL
ejpam-5555	201	2	a. asdain	PERSON
ejpam-5555	201	3	j. i. salim	PERSON
ejpam-5555	201	4	r. g. artes jr.	PERSON
ejpam-5555	202	1	18(4):767–771	ORG
ejpam-5555	202	2	2023	CARDINAL
ejpam-5555	203	1	2	CARDINAL
ejpam-5555	203	2	a. t. castaneda	PERSON
ejpam-5555	203	3	m. a. medina	PERSON
ejpam-5555	203	4	l. ruivivar	PERSON
ejpam-5555	205	1	dlsu research congress	ORG
ejpam-5555	205	2	2016	DATE
ejpam-5555	206	1	3	CARDINAL
ejpam-5555	206	2	f. harary	PERSON
ejpam-5555	206	3	p. zhang	PERSON
ejpam-5555	208	1	20(1):129–138, 2000	DATE
ejpam-5555	209	1	c.j. quije	ORG
ejpam-5555	209	2	r. mariano	PERSON
ejpam-5555	209	3	e. ahmad	PERSON
ejpam-5555	210	1	j. pure	PERSON
ejpam-5555	210	2	18	CARDINAL
ejpam-5555	210	3	1	CARDINAL
ejpam-5555	210	4	2025	CARDINAL
ejpam-5555	210	5	5555 8	DATE
ejpam-5555	210	6	4	CARDINAL
ejpam-5555	210	7	h. escuadro	PERSON
ejpam-5555	210	8	r. gera	PERSON
ejpam-5555	210	9	a. hansberg	PERSON
ejpam-5555	210	10	n. jafari rad	PERSON
ejpam-5555	210	11	l. volkmann	PERSON
ejpam-5555	212	1	77:89–101, 2011	DATE
ejpam-5555	213	1	5	CARDINAL
ejpam-5555	213	2	a. gamorez	PERSON
ejpam-5555	213	3	s. canoy jr.	PERSON
ejpam-5555	214	1	european journal	ORG
ejpam-5555	214	2	15(2):635–645	DATE
ejpam-5555	214	3	2022	CARDINAL
ejpam-5555	215	1	6	CARDINAL
ejpam-5555	215	2	a. hansberg	PERSON
ejpam-5555	215	3	l. volkmann	PERSON
ejpam-5555	216	1	310(15–16):2140–2146	CARDINAL
ejpam-5555	216	2	2010	DATE
ejpam-5555	217	1	7	CARDINAL
ejpam-5555	217	2	j. harris	PERSON
ejpam-5555	217	3	j. hirst	PERSON
ejpam-5555	217	4	m. mossinghoff	PERSON
ejpam-5555	217	5	combinatorics	ORG
ejpam-5555	218	1	lawrence university	ORG
ejpam-5555	218	2	2008	DATE
ejpam-5555	219	1	8	CARDINAL
ejpam-5555	219	2	r. mariano	PERSON
ejpam-5555	219	3	s. canoy jr.	PERSON
ejpam-5555	220	1	4:2301–2310, 2009	DATE
ejpam-5555	221	1	9	CARDINAL
ejpam-5555	222	1	5:41–54	DATE
ejpam-5555	222	2	2020	DATE
ejpam-5555	223	1	10	CARDINAL
ejpam-5555	223	2	e. sandueta	PERSON
ejpam-5555	223	3	s. canoy jr.	PERSON
ejpam-5555	224	1	6:1031–1035, 2011	DATE
ejpam-5555	225	1	11	CARDINAL
ejpam-5555	225	2	a. p. santhakumaran	PERSON
ejpam-5555	227	1	34:343–350	CARDINAL
ejpam-5555	227	2	2015	DATE
ejpam-5555	228	1	12	CARDINAL
ejpam-5555	228	2	a. p. santhakumaran	PERSON
ejpam-5555	228	3	j. john	PERSON
ejpam-5555	230	1	10:415–432, 2007	DATE
ejpam-5555	231	1	13	CARDINAL
ejpam-5555	231	2	d. stalin	PERSON
ejpam-5555	231	3	j. john	PERSON
ejpam-5555	232	1	116:31–40	CARDINAL
ejpam-5555	232	2	2017	DATE
ejpam-5555	233	1	14	CARDINAL
ejpam-5555	233	2	a. ajitha	PERSON
ejpam-5555	233	3	a. subramanian	PERSON
ejpam-5555	235	1	4:45–50	GPE
ejpam-5555	235	2	2016	DATE
ejpam-5555	236	1	15	CARDINAL
ejpam-5555	236	2	a. vijayan	PERSON
ejpam-5555	236	3	n. jaspin beaula	PERSON
ejpam-5555	238	1	6:3774–3779	CARDINAL
ejpam-5555	238	2	2016	DATE