id	sid	eid	entity	type
ejpam-6536	1	1	european journal	ORG
ejpam-6536	1	2	2025	DATE
ejpam-6536	1	3	18	CARDINAL
ejpam-6536	1	4	3	CARDINAL
ejpam-6536	1	5	6536	CARDINAL
ejpam-6536	1	6	1307-5543	DATE
ejpam-6536	1	7	new york	GPE
ejpam-6536	1	8	viralou abrille b. besana1,2,∗	GPE
ejpam-6536	2	1	ferdinand p. jamil1,2	ORG
ejpam-6536	2	2	sergio r. canoy	PERSON
ejpam-6536	2	3	1	CARDINAL
ejpam-6536	2	4	mindanao state university iligan institute of technology	ORG
ejpam-6536	2	5	9200	CARDINAL
ejpam-6536	2	6	iligan city	GPE
ejpam-6536	2	7	2	CARDINAL
ejpam-6536	2	8	institute of science	ORG
ejpam-6536	2	9	mindanao state university iligan institute of technology	ORG
ejpam-6536	2	10	9200	CARDINAL
ejpam-6536	2	11	iligan city	GPE
ejpam-6536	2	12	philippines	GPE
ejpam-6536	4	1	2	CARDINAL
ejpam-6536	4	2	s.	GPE
ejpam-6536	5	1	+ |t	PERSON
ejpam-6536	8	1	2 ≤ m ≤ n	QUANTITY
ejpam-6536	9	1	integer n ≥ 4	PRODUCT
ejpam-6536	12	1	2020	DATE
ejpam-6536	12	2	05c69	CARDINAL
ejpam-6536	12	3	1	CARDINAL
ejpam-6536	15	1	1	CARDINAL
ejpam-6536	17	1	∈	ORG
ejpam-6536	18	1	one	CARDINAL
ejpam-6536	19	1	v.a besana	PERSON
ejpam-6536	19	2	ferdinand.jamil@g.msuiit.edu.ph	ORG
ejpam-6536	19	3	s. canoy jr.	PERSON
ejpam-6536	20	1	1	CARDINAL
ejpam-6536	20	2	2025	CARDINAL
ejpam-6536	21	1	besana	GPE
ejpam-6536	21	2	f. jamil	PERSON
ejpam-6536	21	3	s. canoy jr.	PERSON
ejpam-6536	22	1	j. pure	PERSON
ejpam-6536	22	2	18	CARDINAL
ejpam-6536	22	3	3	CARDINAL
ejpam-6536	22	4	2025	CARDINAL
ejpam-6536	22	5	6536 2	DATE
ejpam-6536	22	6	17	DATE
ejpam-6536	24	1	u = u′	ORG
ejpam-6536	24	2	∈ e(h	ORG
ejpam-6536	26	1	∈	ORG
ejpam-6536	27	1	0	CARDINAL
ejpam-6536	29	1	⊆	CARDINAL
ejpam-6536	30	1	⊆	CARDINAL
ejpam-6536	31	1	γ(g	NORP
ejpam-6536	32	1	2–6	CARDINAL
ejpam-6536	33	1	⊆	CARDINAL
ejpam-6536	33	2	1	CARDINAL
ejpam-6536	34	1	1	CARDINAL
ejpam-6536	35	1	∈	ORG
ejpam-6536	35	2	2	CARDINAL
ejpam-6536	35	3	1	CARDINAL
ejpam-6536	36	1	1	CARDINAL
ejpam-6536	36	2	γ∗	ORG
ejpam-6536	36	3	γ∗t	GPE
ejpam-6536	36	4	1	CARDINAL
ejpam-6536	37	1	1	CARDINAL
ejpam-6536	37	2	1	CARDINAL
ejpam-6536	38	1	1	CARDINAL
ejpam-6536	38	2	γ∗	ORG
ejpam-6536	38	3	γ∗t	GPE
ejpam-6536	39	1	γ∗	ORG
ejpam-6536	40	1	γ∗t	GPE
ejpam-6536	40	2	1,2	CARDINAL
ejpam-6536	40	3	1	CARDINAL
ejpam-6536	40	4	1	CARDINAL
ejpam-6536	41	1	⊆	CARDINAL
ejpam-6536	42	1	∈	PERSON
ejpam-6536	48	1	γpnd	PERSON
ejpam-6536	50	1	⊆	CARDINAL
ejpam-6536	51	1	γ̃(g	ORG
ejpam-6536	52	1	kulli	PERSON
ejpam-6536	52	2	s.c.	GPE
ejpam-6536	53	1	8	CARDINAL
ejpam-6536	53	2	1991	DATE
ejpam-6536	55	1	9–12	CARDINAL
ejpam-6536	56	1	p.g.	GPE
ejpam-6536	56	2	bhat	GPE
ejpam-6536	56	3	s.r.	GPE
ejpam-6536	56	4	9	CARDINAL
ejpam-6536	59	1	besana	GPE
ejpam-6536	59	2	f. jamil	PERSON
ejpam-6536	59	3	s. canoy jr.	PERSON
ejpam-6536	60	1	j. pure	PERSON
ejpam-6536	60	2	18	CARDINAL
ejpam-6536	60	3	3	CARDINAL
ejpam-6536	60	4	2025	CARDINAL
ejpam-6536	60	5	6536 3	DATE
ejpam-6536	60	6	17	CARDINAL
ejpam-6536	60	7	11–13	CARDINAL
ejpam-6536	61	1	⊆	CARDINAL
ejpam-6536	64	1	∈	ORG
ejpam-6536	65	1	2	CARDINAL
ejpam-6536	67	1	γth(g	PERSON
ejpam-6536	69	1	γth(g	PERSON
ejpam-6536	72	1	∈	PRODUCT
ejpam-6536	73	1	c. natarajan	PERSON
ejpam-6536	74	1	14	CARDINAL
ejpam-6536	74	2	2015	DATE
ejpam-6536	74	3	7	CARDINAL
ejpam-6536	74	4	15–19	CARDINAL
ejpam-6536	75	1	2	CARDINAL
ejpam-6536	75	2	2	CARDINAL
ejpam-6536	75	3	⊆	CARDINAL
ejpam-6536	75	4	2	CARDINAL
ejpam-6536	75	5	2	CARDINAL
ejpam-6536	75	6	2	CARDINAL
ejpam-6536	75	7	2	CARDINAL
ejpam-6536	75	8	s. precisely	PERSON
ejpam-6536	77	1	2	CARDINAL
ejpam-6536	77	2	ng(s	ORG
ejpam-6536	77	3	2	CARDINAL
ejpam-6536	78	1	20	CARDINAL
ejpam-6536	80	1	two	CARDINAL
ejpam-6536	82	1	two	CARDINAL
ejpam-6536	84	1	first	ORDINAL
ejpam-6536	85	1	two	CARDINAL
ejpam-6536	85	2	•	CARDINAL
ejpam-6536	85	3	second	ORDINAL
ejpam-6536	85	4	first	ORDINAL
ejpam-6536	85	5	•	CARDINAL
ejpam-6536	85	6	second	ORDINAL
ejpam-6536	85	7	first	ORDINAL
ejpam-6536	86	1	2	CARDINAL
ejpam-6536	87	1	1	CARDINAL
ejpam-6536	88	1	14	CARDINAL
ejpam-6536	89	1	bipartite	NORP
ejpam-6536	89	2	graph km	PERSON
ejpam-6536	89	3	n, γh(km	DATE
ejpam-6536	89	4	2	CARDINAL
ejpam-6536	90	1	besana	GPE
ejpam-6536	90	2	f. jamil	PERSON
ejpam-6536	90	3	s. canoy jr.	PERSON
ejpam-6536	91	1	j. pure	PERSON
ejpam-6536	91	2	18	CARDINAL
ejpam-6536	91	3	3	CARDINAL
ejpam-6536	91	4	2025	CARDINAL
ejpam-6536	91	5	6536 4	DATE
ejpam-6536	91	6		ORG
ejpam-6536	91	7	2r	PRODUCT
ejpam-6536	91	8	6r	CARDINAL
ejpam-6536	92	1	2r	CARDINAL
ejpam-6536	92	2	+ 1	DATE
ejpam-6536	92	3	6r + 1	CARDINAL
ejpam-6536	92	4	2r	CARDINAL
ejpam-6536	92	5	2 ≤ s ≤ 5	QUANTITY
ejpam-6536	93	1		ORG
ejpam-6536	93	2	2r	PRODUCT
ejpam-6536	93	3	6r	CARDINAL
ejpam-6536	93	4	2r	CARDINAL
ejpam-6536	93	5	+ 1	DATE
ejpam-6536	93	6	6r + 1	CARDINAL
ejpam-6536	93	7	2r	CARDINAL
ejpam-6536	93	8	2 ≤ s ≤ 5	QUANTITY
ejpam-6536	95	1	2	CARDINAL
ejpam-6536	95	2	2	CARDINAL
ejpam-6536	96	1	1 ≤	QUANTITY
ejpam-6536	98	1	g = kn	PERSON
ejpam-6536	98	2	1	CARDINAL
ejpam-6536	99	1	2	CARDINAL
ejpam-6536	100	1	1	CARDINAL
ejpam-6536	101	1	two	CARDINAL
ejpam-6536	102	1	⊆	CARDINAL
ejpam-6536	104	1	2	CARDINAL
ejpam-6536	105	1	two	CARDINAL
ejpam-6536	106	1	⊆	CARDINAL
ejpam-6536	108	1	∪v∈v (g)∩ng(a)sv ) ∪	ORG
ejpam-6536	108	2	∪w∈v	GPE
ejpam-6536	108	3	⊆	CARDINAL
ejpam-6536	109	1	2	CARDINAL
ejpam-6536	110	1	⊆	CARDINAL
ejpam-6536	111	1	3	CARDINAL
ejpam-6536	113	1	1 + pnd(h)]γ(g	QUANTITY
ejpam-6536	114	1	2	CARDINAL
ejpam-6536	114	2	2	CARDINAL
ejpam-6536	115	1	besana	GPE
ejpam-6536	115	2	f. jamil	PERSON
ejpam-6536	115	3	s. canoy jr.	PERSON
ejpam-6536	116	1	j. pure	PERSON
ejpam-6536	116	2	18	CARDINAL
ejpam-6536	116	3	3	CARDINAL
ejpam-6536	116	4	2025	CARDINAL
ejpam-6536	116	5	6536 5	DATE
ejpam-6536	116	6	2	CARDINAL
ejpam-6536	117	1	1	CARDINAL
ejpam-6536	118	1	4	CARDINAL
ejpam-6536	120	1	g[h	ORG
ejpam-6536	121	1	tx	ORG
ejpam-6536	121	2	2	CARDINAL
ejpam-6536	122	1	0	CARDINAL
ejpam-6536	123	1	1	CARDINAL
ejpam-6536	126	1	1	CARDINAL
ejpam-6536	126	2	2)| + pnd(h)|s \	MONEY
ejpam-6536	126	3	2)|	CARDINAL
ejpam-6536	128	1	3	CARDINAL
ejpam-6536	131	1	max{dg(u	TIME
ejpam-6536	132	1	∈	ORG
ejpam-6536	134	1	∈	ORG
ejpam-6536	134	2	∈	ORG
ejpam-6536	136	1	2	CARDINAL
ejpam-6536	137	1	⊆	CARDINAL
ejpam-6536	137	2	⊆	CARDINAL
ejpam-6536	137	3	∈	ORG
ejpam-6536	138	1	r(g	GPE
ejpam-6536	138	2	2	CARDINAL
ejpam-6536	138	3	∈	ORG
ejpam-6536	138	4	2	CARDINAL
ejpam-6536	140	1	|s∗|	PRODUCT
ejpam-6536	141	1	2	CARDINAL
ejpam-6536	141	2	3.1	CARDINAL
ejpam-6536	142	1	⊆	CARDINAL
ejpam-6536	144	1	2	CARDINAL
ejpam-6536	145	1	1	CARDINAL
ejpam-6536	145	2	besana	GPE
ejpam-6536	145	3	f. jamil	PERSON
ejpam-6536	145	4	s. canoy jr.	PERSON
ejpam-6536	146	1	j. pure	PERSON
ejpam-6536	146	2	18	CARDINAL
ejpam-6536	146	3	3	CARDINAL
ejpam-6536	146	4	2025	CARDINAL
ejpam-6536	146	5	6536 6	DATE
ejpam-6536	146	6	17	CARDINAL
ejpam-6536	146	7	5	CARDINAL
ejpam-6536	147	1	2	CARDINAL
ejpam-6536	147	2	2	CARDINAL
ejpam-6536	147	3	two	CARDINAL
ejpam-6536	149	1	2	CARDINAL
ejpam-6536	151	1	1	CARDINAL
ejpam-6536	151	2	2	CARDINAL
ejpam-6536	151	3	2	CARDINAL
ejpam-6536	154	1	2	CARDINAL
ejpam-6536	155	1	1	CARDINAL
ejpam-6536	155	2	2	CARDINAL
ejpam-6536	156	1	y ∈ s	PERSON
ejpam-6536	157	1	2	CARDINAL
ejpam-6536	158	1	first	ORDINAL
ejpam-6536	158	2	2	CARDINAL
ejpam-6536	159	1	∈	ORG
ejpam-6536	159	2	2	CARDINAL
ejpam-6536	160	1	∈	ORG
ejpam-6536	160	2	2	CARDINAL
ejpam-6536	160	3	2	CARDINAL
ejpam-6536	160	4	2	CARDINAL
ejpam-6536	162	1	w	GPE
ejpam-6536	165	1	2	CARDINAL
ejpam-6536	165	2	y ∈ s	PERSON
ejpam-6536	165	3	2	CARDINAL
ejpam-6536	166	1	1	CARDINAL
ejpam-6536	166	2	g1	ORG
ejpam-6536	166	3	2	CARDINAL
ejpam-6536	166	4	5(ii	CARDINAL
ejpam-6536	166	5	3	CARDINAL
ejpam-6536	166	6	2	CARDINAL
ejpam-6536	167	1	1	CARDINAL
ejpam-6536	168	1	5(ii	CARDINAL
ejpam-6536	170	1	2	CARDINAL
ejpam-6536	170	2	6	CARDINAL
ejpam-6536	170	3	2	CARDINAL
ejpam-6536	170	4	4	CARDINAL
ejpam-6536	180	1	•	CARDINAL
ejpam-6536	181	1	u vx y z	PERSON
ejpam-6536	191	1	•	CARDINAL
ejpam-6536	192	1	1	CARDINAL
ejpam-6536	192	2	5	CARDINAL
ejpam-6536	192	3	1	CARDINAL
ejpam-6536	193	1	1	CARDINAL
ejpam-6536	194	1	2 ≤	QUANTITY
ejpam-6536	195	1	4	CARDINAL
ejpam-6536	195	2	2r	CARDINAL
ejpam-6536	197	1	2r	CARDINAL
ejpam-6536	198	1	0 ≤	MONEY
ejpam-6536	199	1	besana	GPE
ejpam-6536	199	2	f. jamil	PERSON
ejpam-6536	199	3	s. canoy jr.	PERSON
ejpam-6536	200	1	j. pure	PERSON
ejpam-6536	200	2	18	CARDINAL
ejpam-6536	200	3	3	CARDINAL
ejpam-6536	200	4	2025	CARDINAL
ejpam-6536	200	5	6536 7	DATE
ejpam-6536	200	6	4	CARDINAL
ejpam-6536	200	7		ORG
ejpam-6536	201	1	3r	CARDINAL
ejpam-6536	201	2	2r	CARDINAL
ejpam-6536	202	1	+ 1	DATE
ejpam-6536	202	2	6r + 1	CARDINAL
ejpam-6536	202	3	2r	CARDINAL
ejpam-6536	203	1	2	CARDINAL
ejpam-6536	203	2	4	DATE
ejpam-6536	203	3	5	DATE
ejpam-6536	204	1	2	CARDINAL
ejpam-6536	204	2	6	CARDINAL
ejpam-6536	204	3	2 ≤ m ≤ n	QUANTITY
ejpam-6536	204	4	g ∈	PERSON
ejpam-6536	204	5	2 ≤	QUANTITY
ejpam-6536	205	1	+ k	PERSON
ejpam-6536	206	1	2	CARDINAL
ejpam-6536	206	2	2	CARDINAL
ejpam-6536	206	3	2	CARDINAL
ejpam-6536	207	1	3	CARDINAL
ejpam-6536	208	1	+ kr1,r2,	PERSON
ejpam-6536	208	2	,rm−1	ORG
ejpam-6536	209	1	2	CARDINAL
ejpam-6536	209	2	2	CARDINAL
ejpam-6536	210	1	{y1 rj	PERSON
ejpam-6536	210	2	y2 rj	PERSON
ejpam-6536	210	3	1	CARDINAL
ejpam-6536	210	4	2	DATE
ejpam-6536	212	1	m−1	PERSON
ejpam-6536	212	2	kr1,r2,	PERSON
ejpam-6536	213	1	1	CARDINAL
ejpam-6536	213	2	2	DATE
ejpam-6536	214	1	m−1}	PERSON
ejpam-6536	214	2	kk+1)∪{y2 rj	PERSON
ejpam-6536	214	3	j = 1	PERSON
ejpam-6536	214	4	2	DATE
ejpam-6536	216	1	m−1}	PERSON
ejpam-6536	217	1	1	CARDINAL
ejpam-6536	222	1	• • • • • •	CARDINAL
ejpam-6536	247	1	• • • • • • • •	CARDINAL
ejpam-6536	269	1	...................................................................................................................................................................................................................................................................	PERSON
ejpam-6536	281	1	2	CARDINAL
ejpam-6536	281	2	6	CARDINAL
ejpam-6536	281	3	2	CARDINAL
ejpam-6536	283	1	3.2	CARDINAL
ejpam-6536	284	1	3	CARDINAL
ejpam-6536	286	1	besana	GPE
ejpam-6536	286	2	f. jamil	PERSON
ejpam-6536	286	3	s. canoy jr.	PERSON
ejpam-6536	287	1	j. pure	PERSON
ejpam-6536	287	2	18	CARDINAL
ejpam-6536	287	3	3	CARDINAL
ejpam-6536	287	4	2025	CARDINAL
ejpam-6536	287	5	6536 8	DATE
ejpam-6536	288	1	2	CARDINAL
ejpam-6536	288	2	2	CARDINAL
ejpam-6536	289	1	3	CARDINAL
ejpam-6536	289	2	c3	PERSON
ejpam-6536	289	3	b3	GPE
ejpam-6536	303	1	•	CARDINAL
ejpam-6536	303	2	c2 c3 g:	PERSON
ejpam-6536	303	3	3	CARDINAL
ejpam-6536	303	4	4	CARDINAL
ejpam-6536	304	1	3	CARDINAL
ejpam-6536	305	1	1	CARDINAL
ejpam-6536	305	2	4	CARDINAL
ejpam-6536	305	3	4r + 4	DATE
ejpam-6536	306	1	2 ≤	QUANTITY
ejpam-6536	306	2	4r + 2	DATE
ejpam-6536	306	3	6r	CARDINAL
ejpam-6536	306	4	4r + 3	DATE
ejpam-6536	306	5	6r	CARDINAL
ejpam-6536	307	1	4r + 5	DATE
ejpam-6536	308	1	3	CARDINAL
ejpam-6536	309	1	1 +	CARDINAL
ejpam-6536	310	1	1+2γh(g	DATE
ejpam-6536	312	1	1+2γh(g	DATE
ejpam-6536	313	1	2	CARDINAL
ejpam-6536	314	1	besana	GPE
ejpam-6536	314	2	f. jamil	PERSON
ejpam-6536	314	3	s. canoy jr.	PERSON
ejpam-6536	315	1	j. pure	PERSON
ejpam-6536	315	2	18	CARDINAL
ejpam-6536	315	3	3	CARDINAL
ejpam-6536	315	4	2025	CARDINAL
ejpam-6536	315	5	6536 9	DATE
ejpam-6536	315	6	17	CARDINAL
ejpam-6536	315	7	+ kr1,r2,	PERSON
ejpam-6536	315	8	,rm−1	ORG
ejpam-6536	316	1	2	CARDINAL
ejpam-6536	316	2	6	CARDINAL
ejpam-6536	316	3	2	CARDINAL
ejpam-6536	316	4	+ k	PERSON
ejpam-6536	317	1	2	CARDINAL
ejpam-6536	317	2	1 +	CARDINAL
ejpam-6536	318	1	1	CARDINAL
ejpam-6536	318	2	1	CARDINAL
ejpam-6536	319	1	5	CARDINAL
ejpam-6536	319	2	integer n ≥ 4	PRODUCT
ejpam-6536	319	3	g ∈	PERSON
ejpam-6536	320	1	4	CARDINAL
ejpam-6536	320	2	w	ORG
ejpam-6536	320	3	three	CARDINAL
ejpam-6536	320	4	w	ORG
ejpam-6536	323	1	xn−2	ORG
ejpam-6536	323	2	........	PERSON
ejpam-6536	328	1	•	CARDINAL
ejpam-6536	356	1	• •	CARDINAL
ejpam-6536	366	1	c2 c3 c4 ............................................................................................................	PERSON
ejpam-6536	372	1	• •	CARDINAL
ejpam-6536	383	1	a a1 a2 a3 a4	PERSON
ejpam-6536	383	2	4	CARDINAL
ejpam-6536	384	1	c3	PERSON
ejpam-6536	384	2	wc ∈	PERSON
ejpam-6536	385	1	w	ORG
ejpam-6536	387	1	xn−2	ORG
ejpam-6536	387	2	c3	PERSON
ejpam-6536	388	1	4 +	DATE
ejpam-6536	389	1	11	CARDINAL
ejpam-6536	389	2	n. ■	ORG
ejpam-6536	389	3	3	CARDINAL
ejpam-6536	392	1	3.3	CARDINAL
ejpam-6536	393	1	3	CARDINAL
ejpam-6536	394	1	1	CARDINAL
ejpam-6536	396	1	⊆	CARDINAL
ejpam-6536	396	2	g. lemma 1	PERSON
ejpam-6536	398	1	⊆	CARDINAL
ejpam-6536	399	1	besana	GPE
ejpam-6536	399	2	f. jamil	PERSON
ejpam-6536	399	3	s. canoy jr.	PERSON
ejpam-6536	400	1	j. pure	PERSON
ejpam-6536	400	2	18	CARDINAL
ejpam-6536	400	3	3	CARDINAL
ejpam-6536	400	4	2025	CARDINAL
ejpam-6536	400	5	6536 10	DATE
ejpam-6536	400	6	17	CARDINAL
ejpam-6536	402	1	g+h	ORG
ejpam-6536	403	1	first	ORDINAL
ejpam-6536	408	1	1	CARDINAL
ejpam-6536	411	1	sg ⊆	ORG
ejpam-6536	411	2	⊆	CARDINAL
ejpam-6536	412	1	⊆	CARDINAL
ejpam-6536	412	2	⊆	CARDINAL
ejpam-6536	412	3	1	CARDINAL
ejpam-6536	412	4	g + h. ■	ORG
ejpam-6536	412	5	4	CARDINAL
ejpam-6536	415	1	4	CARDINAL
ejpam-6536	415	2	⊆	CARDINAL
ejpam-6536	415	3	1	CARDINAL
ejpam-6536	419	1	⊆	CARDINAL
ejpam-6536	420	1	∈	ORG
ejpam-6536	421	1	∈	ORG
ejpam-6536	422	1	∈	ORG
ejpam-6536	423	1	1	CARDINAL
ejpam-6536	426	1	5	CARDINAL
ejpam-6536	429	1	5	CARDINAL
ejpam-6536	429	2	besana	GPE
ejpam-6536	429	3	f. jamil	PERSON
ejpam-6536	429	4	s. canoy jr.	PERSON
ejpam-6536	430	1	j. pure	PERSON
ejpam-6536	430	2	18	CARDINAL
ejpam-6536	430	3	3	CARDINAL
ejpam-6536	430	4	2025	CARDINAL
ejpam-6536	430	5	6536 11	DATE
ejpam-6536	430	6	17 3.4	CARDINAL
ejpam-6536	431	1	3	CARDINAL
ejpam-6536	431	2	γ∗t	GPE
ejpam-6536	431	3	1 + pnd(h)]γ(g	QUANTITY
ejpam-6536	433	1	1	CARDINAL
ejpam-6536	433	2	γ(a	PERSON
ejpam-6536	434	1	∈	ORG
ejpam-6536	436	1	one	CARDINAL
ejpam-6536	436	2	∈	ORG
ejpam-6536	438	1	6	CARDINAL
ejpam-6536	441	1	1 +	CARDINAL
ejpam-6536	442	1	γ∗t	GPE
ejpam-6536	443	1	3	CARDINAL
ejpam-6536	445	1	1 + pnd(h)]γ(g	QUANTITY
ejpam-6536	446	1	1 + pnd(h)]γ̃(g	CARDINAL
ejpam-6536	448	1	sv ⊆	ORG
ejpam-6536	449	1	∈	ORG
ejpam-6536	449	2	⊆	CARDINAL
ejpam-6536	451	1	∈	ORG
ejpam-6536	453	1	∈	ORG
ejpam-6536	454	1	y ∈ su	PERSON
ejpam-6536	455	1	y ∈ s	ORG
ejpam-6536	455	2	2	CARDINAL
ejpam-6536	455	3	sv	ORG
ejpam-6536	455	4	y ∈	PERSON
ejpam-6536	456	1	2	CARDINAL
ejpam-6536	459	1	1 + pnd(h	DATE
ejpam-6536	460	1	γhh(p4 ◦ h	ORG
ejpam-6536	460	2	4	CARDINAL
ejpam-6536	460	3	2γγ(g	CARDINAL
ejpam-6536	462	1	⊆	CARDINAL
ejpam-6536	462	2	∩	PRODUCT
ejpam-6536	462	3	sv ⊆	ORG
ejpam-6536	463	1	∈	ORG
ejpam-6536	463	2	⊆	CARDINAL
ejpam-6536	464	1	∪v∈v	PERSON
ejpam-6536	465	1	besana	GPE
ejpam-6536	465	2	f. jamil	PERSON
ejpam-6536	465	3	s. canoy jr.	PERSON
ejpam-6536	466	1	j. pure	PERSON
ejpam-6536	466	2	18	CARDINAL
ejpam-6536	466	3	3	CARDINAL
ejpam-6536	466	4	2025	CARDINAL
ejpam-6536	466	5	6536 12	DATE
ejpam-6536	466	6	17	CARDINAL
ejpam-6536	466	7	∈	ORG
ejpam-6536	468	1	1	CARDINAL
ejpam-6536	468	2	⊆	CARDINAL
ejpam-6536	468	3	w ∈	ORG
ejpam-6536	468	4	∩	ORG
ejpam-6536	469	1	first	ORDINAL
ejpam-6536	469	2	w ∈ γ(a	PERSON
ejpam-6536	470	1	y /∈	PERSON
ejpam-6536	471	1	2	CARDINAL
ejpam-6536	472	1	w /∈ γ(a	PERSON
ejpam-6536	473	1	w /∈ ng(a◦	NORP
ejpam-6536	473	2	tw	ORG
ejpam-6536	474	1	y ∈	PERSON
ejpam-6536	475	1	∩ c.	PERSON
ejpam-6536	475	2	2	CARDINAL
ejpam-6536	476	1	w ∈	PERSON
ejpam-6536	476	2	∩	ORG
ejpam-6536	478	1	w ∈ γ(a	PERSON
ejpam-6536	479	1	vy	ORG
ejpam-6536	479	2	2	CARDINAL
ejpam-6536	480	1	∈	PRODUCT
ejpam-6536	480	2	y /∈ ng(a◦	PERSON
ejpam-6536	480	3	2	CARDINAL
ejpam-6536	482	1	2	CARDINAL
ejpam-6536	482	2	1+(n−1)pnd(h	CARDINAL
ejpam-6536	482	3	1	CARDINAL
ejpam-6536	483	1	1+(n−1)pnd(h	CARDINAL
ejpam-6536	484	1	⊆	CARDINAL
ejpam-6536	484	2	⊆	CARDINAL
ejpam-6536	484	3	sv ⊆	ORG
ejpam-6536	485	1	∈	ORG
ejpam-6536	485	2	⊆	CARDINAL
ejpam-6536	489	1	1 + pnd(h)]γ(g	QUANTITY
ejpam-6536	491	1	1 + pnd(h)]γ̃(g	DATE
ejpam-6536	492	1	2	CARDINAL
ejpam-6536	492	2	5	CARDINAL
ejpam-6536	493	1	g ◦ h and γ̃h(g ◦ h	ORG
ejpam-6536	493	2	2 + pnd(h	DATE
ejpam-6536	496	1	4	CARDINAL
ejpam-6536	496	2	1 + 2pnd(h	CARDINAL
ejpam-6536	502	1	g x y	PERSON
ejpam-6536	502	2	5	CARDINAL
ejpam-6536	502	3	proposition 6(ii	LAW
ejpam-6536	503	1	n ≥ 2	DATE
ejpam-6536	503	2	2n	CARDINAL
ejpam-6536	505	1	1 +	CARDINAL
ejpam-6536	507	1	besana	GPE
ejpam-6536	507	2	f. jamil	PERSON
ejpam-6536	507	3	s. canoy jr.	PERSON
ejpam-6536	508	1	j. pure	PERSON
ejpam-6536	508	2	18	CARDINAL
ejpam-6536	508	3	3	CARDINAL
ejpam-6536	508	4	2025	CARDINAL
ejpam-6536	508	5	6536 13	DATE
ejpam-6536	508	6	17 3.5	CARDINAL
ejpam-6536	509	1	⊆	CARDINAL
ejpam-6536	509	2	∩	PERSON
ejpam-6536	509	3	2)| + pnd(h)|s \	MONEY
ejpam-6536	509	4	2)|	CARDINAL
ejpam-6536	510	1	9	CARDINAL
ejpam-6536	514	1	⊆	CARDINAL
ejpam-6536	514	2	∈	ORG
ejpam-6536	514	3	4	CARDINAL
ejpam-6536	514	4	g[h	ORG
ejpam-6536	515	1	g[h	ORG
ejpam-6536	515	2	1	CARDINAL
ejpam-6536	516	1	g[h	ORG
ejpam-6536	520	1	10	CARDINAL
ejpam-6536	521	1	1	CARDINAL
ejpam-6536	522	1	⊆	CARDINAL
ejpam-6536	522	2	tx ̸=	ORG
ejpam-6536	522	3	g[h	ORG
ejpam-6536	522	4	tx	ORG
ejpam-6536	522	5	2	CARDINAL
ejpam-6536	522	6	2	CARDINAL
ejpam-6536	522	7	tx	ORG
ejpam-6536	522	8	pnd	ORG
ejpam-6536	522	9	2	CARDINAL
ejpam-6536	522	10	ng(s∗,	GPE
ejpam-6536	522	11	2	CARDINAL
ejpam-6536	522	12	tx	ORG
ejpam-6536	522	13	first	ORDINAL
ejpam-6536	522	14	g[h	ORG
ejpam-6536	523	1	4	CARDINAL
ejpam-6536	523	2	s.	PERSON
ejpam-6536	523	3	c∗ = ∪x∈s∗	PERSON
ejpam-6536	523	4	⊆	CARDINAL
ejpam-6536	523	5	1	CARDINAL
ejpam-6536	523	6	2	CARDINAL
ejpam-6536	524	1	2	CARDINAL
ejpam-6536	525	1	⊆	CARDINAL
ejpam-6536	525	2	tx	ORG
ejpam-6536	526	1	∈	ORG
ejpam-6536	526	2	ng(s	ORG
ejpam-6536	526	3	2	CARDINAL
ejpam-6536	526	4	ng(s∗,	GPE
ejpam-6536	526	5	2	CARDINAL
ejpam-6536	526	6	tx	ORG
ejpam-6536	526	7	tx	ORG
ejpam-6536	526	8	⊆	PRODUCT
ejpam-6536	526	9	tx	ORG
ejpam-6536	528	1	4	CARDINAL
ejpam-6536	528	2	g[h	ORG
ejpam-6536	529	1	c∗ = ∪x∈s∗	PERSON
ejpam-6536	529	2	⊆	CARDINAL
ejpam-6536	529	3	1	CARDINAL
ejpam-6536	529	4	ng(s∗	PRODUCT
ejpam-6536	529	5	2	CARDINAL
ejpam-6536	529	6	∈	ORG
ejpam-6536	529	7	h)\tx	ORG
ejpam-6536	530	1	2	CARDINAL
ejpam-6536	530	2	tx	ORG
ejpam-6536	530	3	⊆	PRODUCT
ejpam-6536	531	1	2	CARDINAL
ejpam-6536	532	1	ng(s∗	PRODUCT
ejpam-6536	532	2	2	CARDINAL
ejpam-6536	534	1	2	CARDINAL
ejpam-6536	534	2	pnd	ORG
ejpam-6536	534	3	besana	GPE
ejpam-6536	534	4	f. jamil	PERSON
ejpam-6536	534	5	s. canoy jr.	PERSON
ejpam-6536	535	1	j. pure	PERSON
ejpam-6536	535	2	18	CARDINAL
ejpam-6536	535	3	3	CARDINAL
ejpam-6536	535	4	2025	CARDINAL
ejpam-6536	535	5	6536 14	DATE
ejpam-6536	535	6	17	CARDINAL
ejpam-6536	535	7	c∗ = ∪x∈s∗	PERSON
ejpam-6536	536	1	c∗	PERSON
ejpam-6536	536	2	g[h	ORG
ejpam-6536	536	3	4	CARDINAL
ejpam-6536	541	1	∩	PERSON
ejpam-6536	541	2	2)| + pnd(h)|s∗ \ ng(s∗	QUANTITY
ejpam-6536	541	3	2)|	CARDINAL
ejpam-6536	542	1	g[h	ORG
ejpam-6536	543	1	6	CARDINAL
ejpam-6536	545	1	1	CARDINAL
ejpam-6536	546	1	2)| + ipnd(h)|s	MONEY
ejpam-6536	546	2	2)|	CARDINAL
ejpam-6536	546	3	∈	PRODUCT
ejpam-6536	548	1	2)| + ipnd(h)|s	MONEY
ejpam-6536	548	2	2)|	CARDINAL
ejpam-6536	548	3	∈	PRODUCT
ejpam-6536	549	1	⊆	CARDINAL
ejpam-6536	549	2	⊆	CARDINAL
ejpam-6536	549	3	tx	ORG
ejpam-6536	549	4	∈	ORG
ejpam-6536	549	5	2	CARDINAL
ejpam-6536	549	6	tx	ORG
ejpam-6536	549	7	2	CARDINAL
ejpam-6536	550	1	10	CARDINAL
ejpam-6536	550	2	g[h	ORG
ejpam-6536	551	1	∩	PERSON
ejpam-6536	551	2	2)| + ipnd(h)|s	MONEY
ejpam-6536	551	3	2)|	CARDINAL
ejpam-6536	553	1	7	CARDINAL
ejpam-6536	554	1	2	CARDINAL
ejpam-6536	555	1	first	ORDINAL
ejpam-6536	555	2	2	CARDINAL
ejpam-6536	555	3	6	CARDINAL
ejpam-6536	557	1	⊆	CARDINAL
ejpam-6536	558	1	10	CARDINAL
ejpam-6536	558	2	tx	ORG
ejpam-6536	558	3	⊆	PRODUCT
ejpam-6536	559	1	γ̃h(km[h	PERSON
ejpam-6536	560	1	6	CARDINAL
ejpam-6536	562	1	only three	CARDINAL
ejpam-6536	563	1	2	CARDINAL
ejpam-6536	564	1	2 + ipnd(h	DATE
ejpam-6536	567	1	2γth(g	CARDINAL
ejpam-6536	568	1	besana	GPE
ejpam-6536	568	2	f. jamil	PERSON
ejpam-6536	568	3	s. canoy jr.	PERSON
ejpam-6536	569	1	j. pure	PERSON
ejpam-6536	569	2	18	CARDINAL
ejpam-6536	569	3	3	CARDINAL
ejpam-6536	569	4	2025	CARDINAL
ejpam-6536	569	5	6536 15	DATE
ejpam-6536	569	6	17	CARDINAL
ejpam-6536	569	7	1	CARDINAL
ejpam-6536	569	8	9	CARDINAL
ejpam-6536	569	9	2γth(g	CARDINAL
ejpam-6536	569	10	2γh(g[h	CARDINAL
ejpam-6536	570	1	2γth(g	CARDINAL
ejpam-6536	571	1	4	CARDINAL
ejpam-6536	571	2	11	CARDINAL
ejpam-6536	572	1	1	CARDINAL
ejpam-6536	573	1	c∗ = ∪x∈s∗	PERSON
ejpam-6536	573	2	⊆	CARDINAL
ejpam-6536	573	3	tx ̸=	ORG
ejpam-6536	574	1	4	CARDINAL
ejpam-6536	574	2	tx	PERSON
ejpam-6536	574	3	∈	ORG
ejpam-6536	574	4	tx	ORG
ejpam-6536	574	5	ng(s	ORG
ejpam-6536	574	6	2	CARDINAL
ejpam-6536	574	7	ng(s∗,	GPE
ejpam-6536	574	8	2	CARDINAL
ejpam-6536	575	1	8	CARDINAL
ejpam-6536	576	1	2	CARDINAL
ejpam-6536	576	2	ppnd(h	PERSON
ejpam-6536	577	1	c∗ = ∪x∈s	PERSON
ejpam-6536	578	1	tx	ORG
ejpam-6536	579	1	4	CARDINAL
ejpam-6536	580	1	ppnd(h	PERSON
ejpam-6536	582	1	c∗ = ∪x∈s∗	PERSON
ejpam-6536	582	2	tx	ORG
ejpam-6536	582	3	2	CARDINAL
ejpam-6536	582	4	2	CARDINAL
ejpam-6536	583	1	2	CARDINAL
ejpam-6536	583	2	2	CARDINAL
ejpam-6536	583	3	11(ii	CARDINAL
ejpam-6536	583	4	tx	ORG
ejpam-6536	586	1	philippines	GPE
ejpam-6536	586	2	philippines	GPE
ejpam-6536	588	1	besana	GPE
ejpam-6536	588	2	f. jamil	PERSON
ejpam-6536	588	3	s. canoy jr.	PERSON
ejpam-6536	589	1	j. pure	PERSON
ejpam-6536	589	2	18	CARDINAL
ejpam-6536	589	3	3	CARDINAL
ejpam-6536	589	4	2025	CARDINAL
ejpam-6536	589	5	6536 16	DATE
ejpam-6536	589	6	17	CARDINAL
ejpam-6536	589	7	1	CARDINAL
ejpam-6536	589	8	f. buckley	PERSON
ejpam-6536	589	9	f. harary	PERSON
ejpam-6536	591	1	addison-wesley	ORG
ejpam-6536	591	2	redwood city	GPE
ejpam-6536	591	3	1990	DATE
ejpam-6536	592	1	2	CARDINAL
ejpam-6536	594	1	wiley	ORG
ejpam-6536	594	2	new york	GPE
ejpam-6536	594	3	1962	DATE
ejpam-6536	595	1	3	CARDINAL
ejpam-6536	595	2	e. cockayne	PERSON
ejpam-6536	595	3	s. hedetniemi	PERSON
ejpam-6536	597	1	7(3):247–261	CARDINAL
ejpam-6536	597	2	1977	DATE
ejpam-6536	598	1	4	CARDINAL
ejpam-6536	598	2	haynes	ORG
ejpam-6536	598	3	s.t.	PERSON
ejpam-6536	598	4	hedetniemi	PERSON
ejpam-6536	598	5	slater	PERSON
ejpam-6536	600	1	marcel dekker	PERSON
ejpam-6536	600	2	inc.	ORG
ejpam-6536	600	3	new york	GPE
ejpam-6536	600	4	1998	DATE
ejpam-6536	601	1	5	CARDINAL
ejpam-6536	601	2	jamil	GPE
ejpam-6536	603	1	european journal	ORG
ejpam-6536	603	2	12(3):978–998	DATE
ejpam-6536	603	3	2019	DATE
ejpam-6536	604	1	6	CARDINAL
ejpam-6536	605	1	38	CARDINAL
ejpam-6536	605	2	american	NORP
ejpam-6536	606	1	american mathematical society	ORG
ejpam-6536	606	2	ri	GPE
ejpam-6536	606	3	1962	DATE
ejpam-6536	607	1	7	CARDINAL
ejpam-6536	607	2	s.r canoy jr.	PERSON
ejpam-6536	607	3	canoy.	PERSON
ejpam-6536	609	1	european journal	ORG
ejpam-6536	609	2	12(4):1455–1463,	DATE
ejpam-6536	609	3	2019	DATE
ejpam-6536	610	1	8	CARDINAL
ejpam-6536	610	2	kulli	PERSON
ejpam-6536	610	3	s.c.	GPE
ejpam-6536	611	1	national academy science letters	ORG
ejpam-6536	611	2	14:473–475, 1991	DATE
ejpam-6536	612	1	9	CARDINAL
ejpam-6536	612	2	bhat	GPE
ejpam-6536	612	3	s.r.	GPE
ejpam-6536	614	1	42(5	CARDINAL
ejpam-6536	614	2	2012	DATE
ejpam-6536	615	1	10	CARDINAL
ejpam-6536	615	2	g.s. domke	PERSON
ejpam-6536	615	3	j.e. dunbar	GPE
ejpam-6536	615	4	l.r	DATE
ejpam-6536	615	5	markus	PERSON
ejpam-6536	617	1	72:149–160	CARDINAL
ejpam-6536	617	2	2004	DATE
ejpam-6536	618	1	11	CARDINAL
ejpam-6536	618	2	kiunisala	GPE
ejpam-6536	618	3	f.p. jamil	GPE
ejpam-6536	620	1	8(107):5303–5315	DATE
ejpam-6536	620	2	2014	DATE
ejpam-6536	621	1	12	CARDINAL
ejpam-6536	621	2	kiunisala	GPE
ejpam-6536	621	3	f.p. jamil	GPE
ejpam-6536	623	1	10(13):623–637	CARDINAL
ejpam-6536	623	2	2016	DATE
ejpam-6536	624	1	13	CARDINAL
ejpam-6536	624	2	hedetniemi	GPE
ejpam-6536	624	3	s.t.	PERSON
ejpam-6536	624	4	hedetniemi	GPE
ejpam-6536	624	5	r.c. laskar	PERSON
ejpam-6536	624	6	l. markus	PERSON
ejpam-6536	624	7	slater	PERSON
ejpam-6536	626	1	7	CARDINAL
ejpam-6536	626	2	2008	DATE
ejpam-6536	627	1	14	CARDINAL
ejpam-6536	627	2	c. natarajan	PERSON
ejpam-6536	628	1	versita	PERSON
ejpam-6536	628	2	23(2):187–199	DATE
ejpam-6536	628	3	2015	DATE
ejpam-6536	629	1	15	CARDINAL
ejpam-6536	629	2	bonsocan	NORP
ejpam-6536	629	3	jamil	GPE
ejpam-6536	631	1	european journal	ORG
ejpam-6536	631	2	16(1):192–206	DATE
ejpam-6536	631	3	2023	CARDINAL
ejpam-6536	632	1	16	CARDINAL
ejpam-6536	632	2	henning	PERSON
ejpam-6536	632	3	s. pal	PERSON
ejpam-6536	632	4	d. pradhan	PERSON
ejpam-6536	634	1	153:105872	CARDINAL
ejpam-6536	634	2	2020	DATE
ejpam-6536	635	1	17	CARDINAL
ejpam-6536	635	2	henning	PERSON
ejpam-6536	635	3	n.j	GPE
ejpam-6536	636	1	2	CARDINAL
ejpam-6536	637	1	combinatorics	ORG
ejpam-6536	637	2	33:913–927	CARDINAL
ejpam-6536	637	3	2017	DATE
ejpam-6536	638	1	18	CARDINAL
ejpam-6536	638	2	c. natarajan	PERSON
ejpam-6536	638	3	s.k.	GPE
ejpam-6536	638	4	g. sathiamoorthy	PERSON
ejpam-6536	640	1	119(12):14165–14171, 2018	DATE
ejpam-6536	641	1	besana	GPE
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ejpam-6536	642	1	j. pure	PERSON
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ejpam-6536	642	3	3	CARDINAL
ejpam-6536	642	4	2025	CARDINAL
ejpam-6536	642	5	6536 17	DATE
ejpam-6536	642	6	19	CARDINAL
ejpam-6536	642	7	s. shanmugavelan	PERSON
ejpam-6536	642	8	c. natarajan	PERSON
ejpam-6536	644	1	ural mathematical journal	ORG
ejpam-6536	644	2	7(2):121–135	DATE
ejpam-6536	644	3	2021	DATE
ejpam-6536	645	1	20	CARDINAL
ejpam-6536	645	2	w. desormeaux	PERSON
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ejpam-6536	645	4	m. a. henning	PERSON
ejpam-6536	647	1	36:1043–1050	CARDINAL
ejpam-6536	647	2	2016	DATE