id	sid	eid	entity	type
ejpam-6264	1	1	european journal	ORG
ejpam-6264	1	2	2025	DATE
ejpam-6264	1	3	18	CARDINAL
ejpam-6264	1	4	4	CARDINAL
ejpam-6264	1	5	6264	CARDINAL
ejpam-6264	1	6	1307-5543	DATE
ejpam-6264	1	7	new york	GPE
ejpam-6264	1	8	sherihatha r. ahamad1,2	PERSON
ejpam-6264	1	9	jerry boy g. cariaga1,2	PERSON
ejpam-6264	1	10	sheila m. menchavez1,2	PERSON
ejpam-6264	1	11	ferdinand p. jamil1,2,∗	ORG
ejpam-6264	2	1	1	CARDINAL
ejpam-6264	2	2	msu-iligan institute of technology	ORG
ejpam-6264	2	3	9200	CARDINAL
ejpam-6264	2	4	iligan city	GPE
ejpam-6264	2	5	2	CARDINAL
ejpam-6264	2	6	msu-iligan institute of technology	ORG
ejpam-6264	2	7	9200	CARDINAL
ejpam-6264	2	8	iligan city	GPE
ejpam-6264	2	9	philippines	GPE
ejpam-6264	4	1	0	CARDINAL
ejpam-6264	4	2	1	DATE
ejpam-6264	4	3	2	DATE
ejpam-6264	4	4	3	CARDINAL
ejpam-6264	4	5	0	CARDINAL
ejpam-6264	4	6	2	CARDINAL
ejpam-6264	4	7	3	CARDINAL
ejpam-6264	4	8	1	CARDINAL
ejpam-6264	4	9	∈	PERSON
ejpam-6264	5	1	2	CARDINAL
ejpam-6264	6	1	3	CARDINAL
ejpam-6264	7	1	∈	ORG
ejpam-6264	7	2	∑ v∈v	PERSON
ejpam-6264	10	1	2020	DATE
ejpam-6264	10	2	05c69	CARDINAL
ejpam-6264	10	3	1	CARDINAL
ejpam-6264	11	1	1	CARDINAL
ejpam-6264	11	2	2004	DATE
ejpam-6264	11	3	revelle	PERSON
ejpam-6264	12	1	3	CARDINAL
ejpam-6264	13	1	4],[5],[6],[7],[8],[9],[10	DATE
ejpam-6264	14	1	s. r. ahamad	PERSON
ejpam-6264	14	2	jerryboy.cariaga@g.msuiit.edu.ph	GPE
ejpam-6264	14	3	j. b. g. cariaga	PERSON
ejpam-6264	14	4	sheila.menchavez@g.msuiit.edu.ph	GPE
ejpam-6264	14	5	s. m. menchavez	PERSON
ejpam-6264	14	6	ferdinand.jamil@g.msuiit.edu.ph	ORG
ejpam-6264	14	7	f. p. jamil	PERSON
ejpam-6264	15	1	1	CARDINAL
ejpam-6264	15	2	2025	CARDINAL
ejpam-6264	16	1	s. ahamad et al	PERSON
ejpam-6264	17	1	j. pure	PERSON
ejpam-6264	17	2	18	CARDINAL
ejpam-6264	17	3	4	CARDINAL
ejpam-6264	17	4	2025	CARDINAL
ejpam-6264	17	5	6264 2	DATE
ejpam-6264	17	6	20	CARDINAL
ejpam-6264	18	1	5	CARDINAL
ejpam-6264	21	1	2.	CARDINAL
ejpam-6264	21	2	⊆	CARDINAL
ejpam-6264	21	3	15	CARDINAL
ejpam-6264	23	1	⊆	CARDINAL
ejpam-6264	25	1	⊆	CARDINAL
ejpam-6264	26	1	⊆	CARDINAL
ejpam-6264	27	1	\s	ORG
ejpam-6264	27	2	∈	PERSON
ejpam-6264	27	3	∈	ORG
ejpam-6264	28	1	γ(g	NORP
ejpam-6264	28	2	16	CARDINAL
ejpam-6264	29	1	integer k	PERSON
ejpam-6264	29	2	⊆	CARDINAL
ejpam-6264	29	3	\d	ORG
ejpam-6264	29	4	2	CARDINAL
ejpam-6264	29	5	2	CARDINAL
ejpam-6264	29	6	2	CARDINAL
ejpam-6264	30	1	8	CARDINAL
ejpam-6264	31	1	0	CARDINAL
ejpam-6264	31	2	1	DATE
ejpam-6264	31	3	2	CARDINAL
ejpam-6264	31	4	∈	ORG
ejpam-6264	32	1	0	CARDINAL
ejpam-6264	32	2	at least one	CARDINAL
ejpam-6264	33	1	2	CARDINAL
ejpam-6264	34	1	8	CARDINAL
ejpam-6264	35	1	0	CARDINAL
ejpam-6264	35	2	1	DATE
ejpam-6264	35	3	2	DATE
ejpam-6264	35	4	3	CARDINAL
ejpam-6264	35	5	0	CARDINAL
ejpam-6264	35	6	2	CARDINAL
ejpam-6264	35	7	3	CARDINAL
ejpam-6264	35	8	s. ahamad et al	PERSON
ejpam-6264	36	1	j. pure	PERSON
ejpam-6264	36	2	18	CARDINAL
ejpam-6264	36	3	4	CARDINAL
ejpam-6264	36	4	2025	CARDINAL
ejpam-6264	36	5	6264 3	DATE
ejpam-6264	37	1	1	CARDINAL
ejpam-6264	37	2	∈	PERSON
ejpam-6264	37	3	2	CARDINAL
ejpam-6264	38	1	3	CARDINAL
ejpam-6264	38	2	∑ v∈v	PERSON
ejpam-6264	38	3	5	CARDINAL
ejpam-6264	39	1	0	CARDINAL
ejpam-6264	39	2	1	DATE
ejpam-6264	39	3	2	DATE
ejpam-6264	39	4	3	CARDINAL
ejpam-6264	39	5	vi = {	PERSON
ejpam-6264	39	6	∈	ORG
ejpam-6264	40	1	0	CARDINAL
ejpam-6264	40	2	1	DATE
ejpam-6264	40	3	2	DATE
ejpam-6264	40	4	3	CARDINAL
ejpam-6264	43	1	3	CARDINAL
ejpam-6264	43	2	7	CARDINAL
ejpam-6264	46	1	v2	PRODUCT
ejpam-6264	48	1	2	CARDINAL
ejpam-6264	48	2	⟨v2 ∪	ORG
ejpam-6264	50	1	2	CARDINAL
ejpam-6264	51	1	v2 ̸=	ORG
ejpam-6264	51	2	g+h	ORG
ejpam-6264	52	1	∈	ORG
ejpam-6264	52	2	one	CARDINAL
ejpam-6264	52	3	∩	PERSON
ejpam-6264	52	4	v2 ∩	PERSON
ejpam-6264	52	5	v2 ∩	PERSON
ejpam-6264	52	6	∩	PERSON
ejpam-6264	53	1	∩	PERSON
ejpam-6264	54	1	∈	ORG
ejpam-6264	54	2	one	CARDINAL
ejpam-6264	54	3	1	CARDINAL
ejpam-6264	54	4	∩	PERSON
ejpam-6264	54	5	1	CARDINAL
ejpam-6264	54	6	v2 ∩	PERSON
ejpam-6264	54	7	h. s. ahamad et al	PERSON
ejpam-6264	55	1	j. pure	PERSON
ejpam-6264	55	2	18	CARDINAL
ejpam-6264	55	3	4	CARDINAL
ejpam-6264	55	4	2025	CARDINAL
ejpam-6264	55	5	6264 4	DATE
ejpam-6264	55	6	v2 ∩	PERSON
ejpam-6264	55	7	∩	PERSON
ejpam-6264	56	1	∩	PERSON
ejpam-6264	57	1	̸∈ mrdf	PERSON
ejpam-6264	57	2	̸∈ mrdf	PERSON
ejpam-6264	57	3	∩ v2 = ∅	PERSON
ejpam-6264	59	1	v2 ∩	PERSON
ejpam-6264	59	2	∃x ∈ v1	ORG
ejpam-6264	59	3	v2 ∩	PERSON
ejpam-6264	59	4	∩ v2 = ∅	PERSON
ejpam-6264	61	1	v2 ∩	PERSON
ejpam-6264	61	2	∃x ∈ v1	ORG
ejpam-6264	61	3	nh(x)∩ v2 = ∅	PRODUCT
ejpam-6264	61	4	4	CARDINAL
ejpam-6264	61	5	1	CARDINAL
ejpam-6264	62	1	∈	ORG
ejpam-6264	62	2	0	CARDINAL
ejpam-6264	63	1	∑ v∈v	PERSON
ejpam-6264	63	2	1	CARDINAL
ejpam-6264	63	3	1	CARDINAL
ejpam-6264	64	1	0	CARDINAL
ejpam-6264	64	2	1	DATE
ejpam-6264	64	3	2	DATE
ejpam-6264	64	4	3	CARDINAL
ejpam-6264	64	5	3	CARDINAL
ejpam-6264	64	6	2	CARDINAL
ejpam-6264	64	7	f(b	GPE
ejpam-6264	65	1	0	CARDINAL
ejpam-6264	65	2	6	CARDINAL
ejpam-6264	65	3	0	CARDINAL
ejpam-6264	66	1	1b	CARDINAL
ejpam-6264	67	1	j. pure	PERSON
ejpam-6264	67	2	18	CARDINAL
ejpam-6264	67	3	4	CARDINAL
ejpam-6264	67	4	2025	CARDINAL
ejpam-6264	67	5	6264 5	DATE
ejpam-6264	67	6	20	CARDINAL
ejpam-6264	67	7	1	CARDINAL
ejpam-6264	67	8	7	CARDINAL
ejpam-6264	67	9	6	CARDINAL
ejpam-6264	69	1	γ(g	GPE
ejpam-6264	71	1	1	CARDINAL
ejpam-6264	71	2	2	DATE
ejpam-6264	71	3	n. proof	PERSON
ejpam-6264	72	1	v2 ∪	GPE
ejpam-6264	80	1	v2	PRODUCT
ejpam-6264	83	1	one	CARDINAL
ejpam-6264	83	2	0	CARDINAL
ejpam-6264	83	3	0	CARDINAL
ejpam-6264	85	1	0	CARDINAL
ejpam-6264	86	1	⊆ v2 ∪	MONEY
ejpam-6264	86	2	2	CARDINAL
ejpam-6264	86	3	′ 3	DATE
ejpam-6264	86	4	0	CARDINAL
ejpam-6264	87	1	′ 1	CARDINAL
ejpam-6264	87	2	\d	ORG
ejpam-6264	87	3	2	CARDINAL
ejpam-6264	87	4	3	CARDINAL
ejpam-6264	87	5	∈	ORG
ejpam-6264	87	6	′ 1 |+ 2|v	DATE
ejpam-6264	91	1	0	CARDINAL
ejpam-6264	93	1	∈	ORG
ejpam-6264	93	2	∈	ORG
ejpam-6264	93	3	∩ ng(v3	PERSON
ejpam-6264	94	1	1	CARDINAL
ejpam-6264	94	2	∩ ng(v3	PERSON
ejpam-6264	94	3	′′	ORG
ejpam-6264	94	4	2	CARDINAL
ejpam-6264	94	5	∩ ng(v3	PERSON
ejpam-6264	95	1	1	CARDINAL
ejpam-6264	95	2	′′ 2	ORG
ejpam-6264	95	3	3	CARDINAL
ejpam-6264	96	1	2|v	ORDINAL
ejpam-6264	97	1	′′	ORG
ejpam-6264	97	2	2	CARDINAL
ejpam-6264	100	1	s. ahamad et al	PERSON
ejpam-6264	101	1	j. pure	PERSON
ejpam-6264	101	2	18	CARDINAL
ejpam-6264	101	3	4	CARDINAL
ejpam-6264	101	4	2025	CARDINAL
ejpam-6264	101	5	6264 6	DATE
ejpam-6264	101	6	20	CARDINAL
ejpam-6264	101	7	1	CARDINAL
ejpam-6264	105	1	0	CARDINAL
ejpam-6264	106	1	g. (ii	PRODUCT
ejpam-6264	106	2	|v1|	CARDINAL
ejpam-6264	108	1	0	CARDINAL
ejpam-6264	109	1	f(v	PERSON
ejpam-6264	109	2	∈	ORG
ejpam-6264	110	1	0	CARDINAL
ejpam-6264	110	2	0	CARDINAL
ejpam-6264	112	1	1	CARDINAL
ejpam-6264	113	1	2	CARDINAL
ejpam-6264	113	2	v2 ∪	GPE
ejpam-6264	113	3	⊆ v2 ∪	MONEY
ejpam-6264	113	4	∗ 1	DATE
ejpam-6264	113	5	2	CARDINAL
ejpam-6264	113	6	∗ 3	DATE
ejpam-6264	113	7	∗ 1	CARDINAL
ejpam-6264	113	8	\d	ORG
ejpam-6264	113	9	2	CARDINAL
ejpam-6264	113	10	∩ v2	PERSON
ejpam-6264	114	1	∈	ORG
ejpam-6264	114	2	∗ 1	DATE
ejpam-6264	114	3	∗ 2 |+3|v ∗ 3 |	QUANTITY
ejpam-6264	116	1	v2 ∪	GPE
ejpam-6264	116	2	v2 ∪	GPE
ejpam-6264	116	3	⊆	CARDINAL
ejpam-6264	117	1	1	CARDINAL
ejpam-6264	117	2	2	CARDINAL
ejpam-6264	117	3	∩ v2	PERSON
ejpam-6264	117	4	3	CARDINAL
ejpam-6264	118	1	2	CARDINAL
ejpam-6264	118	2	3	CARDINAL
ejpam-6264	118	3	2|v	CARDINAL
ejpam-6264	118	4	2	CARDINAL
ejpam-6264	120	1	v2 ∪	GPE
ejpam-6264	121	1	∈	ORG
ejpam-6264	121	2	∩ ng(z	ORG
ejpam-6264	122	1	∗ 1	DATE
ejpam-6264	122	2	2	CARDINAL
ejpam-6264	122	3	∗ 3	DATE
ejpam-6264	122	4	∗ 1 ̸=	CARDINAL
ejpam-6264	122	5	∗ 2	DATE
ejpam-6264	122	6	∗ 3	DATE
ejpam-6264	123	1	∈	ORG
ejpam-6264	124	1	3|v ∗ 3	TIME
ejpam-6264	124	2	2	CARDINAL
ejpam-6264	124	3	∗ 1	DATE
ejpam-6264	125	1	0	CARDINAL
ejpam-6264	127	1	n ≥ 2	ORG
ejpam-6264	128	1	3	CARDINAL
ejpam-6264	130	1	4	CARDINAL
ejpam-6264	133	1	g+h	ORG
ejpam-6264	134	1	3	CARDINAL
ejpam-6264	135	1	3	CARDINAL
ejpam-6264	136	1	3	CARDINAL
ejpam-6264	136	2	3	CARDINAL
ejpam-6264	136	3	1	CARDINAL
ejpam-6264	136	4	2	CARDINAL
ejpam-6264	143	1	∈	ORG
ejpam-6264	143	2	ωtmr	ORG
ejpam-6264	143	3	4	CARDINAL
ejpam-6264	143	4	4	CARDINAL
ejpam-6264	144	1	4	CARDINAL
ejpam-6264	144	2	4	CARDINAL
ejpam-6264	145	1	j. pure	PERSON
ejpam-6264	145	2	18	CARDINAL
ejpam-6264	145	3	4	CARDINAL
ejpam-6264	145	4	2025	CARDINAL
ejpam-6264	145	5	6264 7	DATE
ejpam-6264	145	6	20	CARDINAL
ejpam-6264	146	1	4	CARDINAL
ejpam-6264	147	1	1	CARDINAL
ejpam-6264	147	2	1	CARDINAL
ejpam-6264	148	1	2	CARDINAL
ejpam-6264	150	1	3	CARDINAL
ejpam-6264	151	1	0	CARDINAL
ejpam-6264	154	1	1	CARDINAL
ejpam-6264	154	2	2	CARDINAL
ejpam-6264	157	1	3	CARDINAL
ejpam-6264	159	1	8	CARDINAL
ejpam-6264	160	1	5	CARDINAL
ejpam-6264	160	2	4	CARDINAL
ejpam-6264	160	3	1 or	CARDINAL
ejpam-6264	160	4	2	CARDINAL
ejpam-6264	162	1	5	CARDINAL
ejpam-6264	162	2	|v3| ≤ 1	FAC
ejpam-6264	163	1	7 (ii	DATE
ejpam-6264	165	1	only two	CARDINAL
ejpam-6264	165	2	1 and |v2| ≤ 2	CARDINAL
ejpam-6264	166	1	2	CARDINAL
ejpam-6264	166	2	1	CARDINAL
ejpam-6264	166	3	3	CARDINAL
ejpam-6264	166	4	7 (ii	DATE
ejpam-6264	167	1	1	CARDINAL
ejpam-6264	167	2	3	CARDINAL
ejpam-6264	167	3	v2	PRODUCT
ejpam-6264	167	4	4	CARDINAL
ejpam-6264	168	1	1	CARDINAL
ejpam-6264	168	2	1	CARDINAL
ejpam-6264	169	1	2	CARDINAL
ejpam-6264	169	2	3	CARDINAL
ejpam-6264	170	1	7 (ii	DATE
ejpam-6264	171	1	1	CARDINAL
ejpam-6264	172	1	2	CARDINAL
ejpam-6264	172	2	v2 ∪	GPE
ejpam-6264	172	3	4	CARDINAL
ejpam-6264	172	4	2	CARDINAL
ejpam-6264	172	5	4	CARDINAL
ejpam-6264	173	1	1	CARDINAL
ejpam-6264	173	2	7 (ii	DATE
ejpam-6264	173	3	5	CARDINAL
ejpam-6264	175	1	∈	ORG
ejpam-6264	175	2	5	CARDINAL
ejpam-6264	177	1	5	CARDINAL
ejpam-6264	178	1	2	CARDINAL
ejpam-6264	180	1	3	CARDINAL
ejpam-6264	180	2	2	CARDINAL
ejpam-6264	180	3	0	CARDINAL
ejpam-6264	180	4	∈	ORG
ejpam-6264	180	5	\d	ORG
ejpam-6264	181	1	∈	ORG
ejpam-6264	181	2	5	CARDINAL
ejpam-6264	182	1	5	CARDINAL
ejpam-6264	183	1	5	CARDINAL
ejpam-6264	183	2	1	CARDINAL
ejpam-6264	184	1	4	CARDINAL
ejpam-6264	184	2	5	CARDINAL
ejpam-6264	186	1	8	CARDINAL
ejpam-6264	188	1	g1	ORG
ejpam-6264	188	2	gn	PERSON
ejpam-6264	190	1	i=1 γtmr(gi	PERSON
ejpam-6264	192	1	g1	ORG
ejpam-6264	192	2	gn	PERSON
ejpam-6264	192	3	f2	ORG
ejpam-6264	192	4	g1	ORG
ejpam-6264	192	5	gn	PERSON
ejpam-6264	193	1	0	CARDINAL
ejpam-6264	193	2	1	DATE
ejpam-6264	193	3	2	DATE
ejpam-6264	193	4	3	CARDINAL
ejpam-6264	193	5	s. ahamad et al	PERSON
ejpam-6264	194	1	j. pure	PERSON
ejpam-6264	194	2	18	CARDINAL
ejpam-6264	194	3	4	CARDINAL
ejpam-6264	194	4	2025	CARDINAL
ejpam-6264	194	5	6264 8	DATE
ejpam-6264	194	6	∈	ORG
ejpam-6264	194	7	g1	ORG
ejpam-6264	195	1	∈	ORG
ejpam-6264	196	1	∈	ORG
ejpam-6264	199	1	f |gi	PRODUCT
ejpam-6264	199	2	1	CARDINAL
ejpam-6264	199	3	2	DATE
ejpam-6264	200	1	1	CARDINAL
ejpam-6264	200	2	2	DATE
ejpam-6264	200	3	n. hence,∑n	PERSON
ejpam-6264	200	4	i=1 γtmr(gi	PERSON
ejpam-6264	204	1	i=1 γtmr(gi	PERSON
ejpam-6264	205	1	10	CARDINAL
ejpam-6264	206	1	3	CARDINAL
ejpam-6264	211	1	n ≡	ORG
ejpam-6264	212	1	vn−7	GPE
ejpam-6264	212	2	vn−4	ORG
ejpam-6264	213	1	1(mod 3	CARDINAL
ejpam-6264	215	1	3	CARDINAL
ejpam-6264	216	1	vn−6	GPE
ejpam-6264	217	1	3	CARDINAL
ejpam-6264	218	1	0	CARDINAL
ejpam-6264	219	1	3 ⌉ ≤	QUANTITY
ejpam-6264	221	1	3	CARDINAL
ejpam-6264	222	1	two	CARDINAL
ejpam-6264	222	2	2	CARDINAL
ejpam-6264	223	1	1 1 1 1	QUANTITY
ejpam-6264	223	2	2 2	CARDINAL
ejpam-6264	223	3	2	CARDINAL
ejpam-6264	223	4	2	CARDINAL
ejpam-6264	223	5	8 and γtmr(b5	DATE
ejpam-6264	224	1	10	CARDINAL
ejpam-6264	225	1	11	CARDINAL
ejpam-6264	226	1	n ≥ 3	DATE
ejpam-6264	226	2	γtmr(bn	GPE
ejpam-6264	226	3	8	CARDINAL
ejpam-6264	226	4	3	CARDINAL
ejpam-6264	226	5	10	CARDINAL
ejpam-6264	227	1	s. ahamad et al	PERSON
ejpam-6264	228	1	j. pure	PERSON
ejpam-6264	228	2	18	CARDINAL
ejpam-6264	228	3	4	CARDINAL
ejpam-6264	228	4	2025	CARDINAL
ejpam-6264	228	5	6264 9	DATE
ejpam-6264	228	6	20	CARDINAL
ejpam-6264	229	1	∈	ORG
ejpam-6264	229	2	two	CARDINAL
ejpam-6264	229	3	kn	PERSON
ejpam-6264	230	1	3	CARDINAL
ejpam-6264	230	2	f(x	ORG
ejpam-6264	231	1	2	CARDINAL
ejpam-6264	232	1	1	CARDINAL
ejpam-6264	235	1	8	CARDINAL
ejpam-6264	235	2	2	CARDINAL
ejpam-6264	236	1	3	CARDINAL
ejpam-6264	236	2	8	CARDINAL
ejpam-6264	238	1	8	CARDINAL
ejpam-6264	239	1	n ≥ 4	DATE
ejpam-6264	239	2	∈	ORG
ejpam-6264	240	1	f(x	ORG
ejpam-6264	243	1	3	CARDINAL
ejpam-6264	244	1	2	CARDINAL
ejpam-6264	246	1	10	CARDINAL
ejpam-6264	246	2	2	CARDINAL
ejpam-6264	247	1	γtmr(bn) ≥ 10	GPE
ejpam-6264	248	1	γtmr(bn	GPE
ejpam-6264	248	2	10	CARDINAL
ejpam-6264	249	1	k ≥ 2 and n ≥ 2	ORG
ejpam-6264	250	1	n(k − 1	PERSON
ejpam-6264	250	2	1 2nk(k	QUANTITY
ejpam-6264	250	3	1	CARDINAL
ejpam-6264	251	1	3	CARDINAL
ejpam-6264	251	2	dutch	NORP
ejpam-6264	251	3	3	CARDINAL
ejpam-6264	251	4	+ nk2	DATE
ejpam-6264	251	5	2	CARDINAL
ejpam-6264	251	6	3	CARDINAL
ejpam-6264	251	7	+2k2	DATE
ejpam-6264	252	1	3	CARDINAL
ejpam-6264	252	2	4	DATE
ejpam-6264	252	3	5	CARDINAL
ejpam-6264	252	4	2	CARDINAL
ejpam-6264	252	5	3	CARDINAL
ejpam-6264	252	6	3	CARDINAL
ejpam-6264	253	1	3 22	CARDINAL
ejpam-6264	253	2	0	CARDINAL
ejpam-6264	253	3	3	CARDINAL
ejpam-6264	253	4	2	CARDINAL
ejpam-6264	253	5	2	CARDINAL
ejpam-6264	254	1	2 1 1 1 1 11 1 1	TIME
ejpam-6264	254	2	4	CARDINAL
ejpam-6264	254	3	3	CARDINAL
ejpam-6264	254	4	4 3	DATE
ejpam-6264	255	1	10	CARDINAL
ejpam-6264	255	2	s. ahamad et al	PERSON
ejpam-6264	256	1	j. pure	PERSON
ejpam-6264	256	2	18	CARDINAL
ejpam-6264	256	3	4	CARDINAL
ejpam-6264	256	4	2025	CARDINAL
ejpam-6264	256	5	6264 10	DATE
ejpam-6264	256	6	5	CARDINAL
ejpam-6264	256	7	3	CARDINAL
ejpam-6264	256	8	2 3	DATE
ejpam-6264	256	9	6	CARDINAL
ejpam-6264	256	10	12	CARDINAL
ejpam-6264	257	1	k ≥ 4 and n ≥ 2, γtmr(g	ORG
ejpam-6264	257	2	2n+ 3	DATE
ejpam-6264	258	1	k ≥ 4 and n ≥ 2.	ORG
ejpam-6264	258	2	kk−1	ORG
ejpam-6264	258	3	f(x	ORG
ejpam-6264	260	1	3	CARDINAL
ejpam-6264	260	2	2	CARDINAL
ejpam-6264	262	1	∈	ORG
ejpam-6264	263	1	2n	CARDINAL
ejpam-6264	264	1	γ(g	NORP
ejpam-6264	264	2	1	CARDINAL
ejpam-6264	264	3	2	CARDINAL
ejpam-6264	264	4	3	CARDINAL
ejpam-6264	267	1	2n+ 3	CARDINAL
ejpam-6264	268	1	13	CARDINAL
ejpam-6264	269	1	2n+ 2	DATE
ejpam-6264	270	1	n ≥ 2	ORG
ejpam-6264	272	1	1 ≤	QUANTITY
ejpam-6264	273	1	2n+2	TIME
ejpam-6264	274	1	∈	ORG
ejpam-6264	274	2	2n	CARDINAL
ejpam-6264	276	1	1	CARDINAL
ejpam-6264	276	2	2	CARDINAL
ejpam-6264	276	3	3	CARDINAL
ejpam-6264	279	1	2n+ 2	DATE
ejpam-6264	279	2	2	CARDINAL
ejpam-6264	280	1	6	CARDINAL
ejpam-6264	281	1	13	CARDINAL
ejpam-6264	282	1	bipartite	ORG
ejpam-6264	282	2	two	CARDINAL
ejpam-6264	282	3	v2.	GPE
ejpam-6264	283	1	bipartite	NORP
ejpam-6264	283	2	g = km	PERSON
ejpam-6264	283	3	6	CARDINAL
ejpam-6264	283	4	bipartite	NORP
ejpam-6264	283	5	k7,5	ORG
ejpam-6264	283	6	14	DATE
ejpam-6264	284	1	bipartite	NORP
ejpam-6264	284	2	graph km	PERSON
ejpam-6264	284	3	n},m	NORP
ejpam-6264	284	4	n ≥ 2	DATE
ejpam-6264	285	1	γtmr(km,n	ORG
ejpam-6264	285	2	6	CARDINAL
ejpam-6264	285	3	2	CARDINAL
ejpam-6264	285	4	8	CARDINAL
ejpam-6264	285	5	3 9	DATE
ejpam-6264	285	6	4 10	DATE
ejpam-6264	285	7	5	CARDINAL
ejpam-6264	286	1	s. ahamad et al	PERSON
ejpam-6264	287	1	j. pure	PERSON
ejpam-6264	287	2	18	CARDINAL
ejpam-6264	287	3	4	CARDINAL
ejpam-6264	287	4	2025	CARDINAL
ejpam-6264	287	5	6264 11	DATE
ejpam-6264	287	6	20	CARDINAL
ejpam-6264	294	1	...........................................................................................................................................................................................................................................................................................................................................................................	PERSON
ejpam-6264	399	1	6	CARDINAL
ejpam-6264	399	2	bipartite	NORP
ejpam-6264	400	1	bipartite	NORP
ejpam-6264	400	2	graph km	PERSON
ejpam-6264	400	3	km,n	FAC
ejpam-6264	402	1	2	CARDINAL
ejpam-6264	402	2	 3	DATE
ejpam-6264	403	1	2	CARDINAL
ejpam-6264	404	1	1	CARDINAL
ejpam-6264	406	1	6	CARDINAL
ejpam-6264	406	2	3	CARDINAL
ejpam-6264	406	3	6	CARDINAL
ejpam-6264	408	1	6	CARDINAL
ejpam-6264	409	1	3	CARDINAL
ejpam-6264	409	2	 3	DATE
ejpam-6264	410	1	2	CARDINAL
ejpam-6264	411	1	1	CARDINAL
ejpam-6264	413	1	8	CARDINAL
ejpam-6264	413	2	3	CARDINAL
ejpam-6264	413	3	8	CARDINAL
ejpam-6264	415	1	8	CARDINAL
ejpam-6264	416	1	4	CARDINAL
ejpam-6264	416	2	x3	GPE
ejpam-6264	416	3	 3	DATE
ejpam-6264	417	1	2	CARDINAL
ejpam-6264	418	1	1	CARDINAL
ejpam-6264	418	2	x3, x4	ORG
ejpam-6264	420	1	9	CARDINAL
ejpam-6264	421	1	3	CARDINAL
ejpam-6264	421	2	9	CARDINAL
ejpam-6264	423	1	9	CARDINAL
ejpam-6264	424	1	5	CARDINAL
ejpam-6264	424	2	y = kn	PERSON
ejpam-6264	424	3	wlog	PERSON
ejpam-6264	424	4	s. ahamad et al	PERSON
ejpam-6264	425	1	j. pure	PERSON
ejpam-6264	425	2	18	CARDINAL
ejpam-6264	425	3	4	CARDINAL
ejpam-6264	425	4	2025	CARDINAL
ejpam-6264	425	5	6264 12	DATE
ejpam-6264	426	1	3	CARDINAL
ejpam-6264	427	1	2	CARDINAL
ejpam-6264	429	1	10	CARDINAL
ejpam-6264	430	1	3	CARDINAL
ejpam-6264	430	2	10	CARDINAL
ejpam-6264	432	1	10	CARDINAL
ejpam-6264	433	1	sn	ORG
ejpam-6264	433	2	1	CARDINAL
ejpam-6264	434	1	7	CARDINAL
ejpam-6264	434	2	s6	GPE
ejpam-6264	435	1	2 1 1 1 1 1 2	TIME
ejpam-6264	435	2	7	CARDINAL
ejpam-6264	435	3	s6	GPE
ejpam-6264	435	4	7	CARDINAL
ejpam-6264	435	5	15	CARDINAL
ejpam-6264	436	1	n ≥ 1	DATE
ejpam-6264	436	2	2	CARDINAL
ejpam-6264	437	1	f(x	ORG
ejpam-6264	438	1	2	CARDINAL
ejpam-6264	439	1	1	CARDINAL
ejpam-6264	440	1	∈	ORG
ejpam-6264	441	1	w0,w1,w2,w3	ORG
ejpam-6264	441	2	w3 =	GPE
ejpam-6264	441	3	1	CARDINAL
ejpam-6264	441	4	1 and |w3|	TIME
ejpam-6264	441	5	1	CARDINAL
ejpam-6264	443	1	2|w2|+	CARDINAL
ejpam-6264	443	2	2	CARDINAL
ejpam-6264	443	3	2	CARDINAL
ejpam-6264	443	4	16	CARDINAL
ejpam-6264	444	1	5	CARDINAL
ejpam-6264	447	1	y},∅	PERSON
ejpam-6264	450	1	1	CARDINAL
ejpam-6264	452	1	ωtmr kn	PERSON
ejpam-6264	452	2	+ 1 ≥ 5	DATE
ejpam-6264	453	1	1 and |v3| ≥ 1	TIME
ejpam-6264	455	1	ωtmr kn	PERSON
ejpam-6264	455	2	+ 3|v3| ≥ 5	DATE
ejpam-6264	457	1	5	CARDINAL
ejpam-6264	458	1	s. ahamad et al	PERSON
ejpam-6264	459	1	j. pure	PERSON
ejpam-6264	459	2	18	CARDINAL
ejpam-6264	459	3	4	CARDINAL
ejpam-6264	459	4	2025	CARDINAL
ejpam-6264	459	5	6264 13	DATE
ejpam-6264	459	6	20 5	DATE
ejpam-6264	460	1	two	CARDINAL
ejpam-6264	460	2	∈	ORG
ejpam-6264	461	1	8	CARDINAL
ejpam-6264	463	1	17	CARDINAL
ejpam-6264	465	1	v2 ̸=	ORG
ejpam-6264	465	2	∈	ORG
ejpam-6264	465	3	g+h	ORG
ejpam-6264	466	1	∈	ORG
ejpam-6264	466	2	one	CARDINAL
ejpam-6264	466	3	∩	PERSON
ejpam-6264	466	4	v2 ∩	PERSON
ejpam-6264	466	5	v2 ∩	PERSON
ejpam-6264	466	6	∩	PERSON
ejpam-6264	467	1	∩	PERSON
ejpam-6264	468	1	∈	ORG
ejpam-6264	468	2	one	CARDINAL
ejpam-6264	468	3	1	CARDINAL
ejpam-6264	468	4	∩	PERSON
ejpam-6264	468	5	1	CARDINAL
ejpam-6264	468	6	v2 ∩	PERSON
ejpam-6264	468	7	v2 ∩	PERSON
ejpam-6264	468	8	∩	PERSON
ejpam-6264	469	1	∩	PERSON
ejpam-6264	471	1	∩ v2 = ∅	PERSON
ejpam-6264	473	1	v2 ∩	PERSON
ejpam-6264	473	2	∃x ∈ v1	ORG
ejpam-6264	473	3	v2 ∩	PERSON
ejpam-6264	473	4	∩ v2 = ∅	PERSON
ejpam-6264	475	1	s. ahamad et al	PERSON
ejpam-6264	476	1	j. pure	PERSON
ejpam-6264	476	2	18	CARDINAL
ejpam-6264	476	3	4	CARDINAL
ejpam-6264	476	4	2025	CARDINAL
ejpam-6264	476	5	6264 14	DATE
ejpam-6264	476	6	v2 ∩	PERSON
ejpam-6264	476	7	∃x ∈ v1	ORG
ejpam-6264	476	8	nh(x)∩ v2 = ∅	PRODUCT
ejpam-6264	476	9	∈	ORG
ejpam-6264	476	10	⊆	CARDINAL
ejpam-6264	477	1	∈	ORG
ejpam-6264	477	2	⊆	CARDINAL
ejpam-6264	479	1	∈	ORG
ejpam-6264	482	1	∈ v2 ∩	PERSON
ejpam-6264	482	2	w ∈	PERSON
ejpam-6264	483	1	⊆	CARDINAL
ejpam-6264	485	1	∩	PERSON
ejpam-6264	487	1	vw ∈	ORG
ejpam-6264	488	1	∈	ORG
ejpam-6264	490	1	∈	ORG
ejpam-6264	490	2	∈	ORG
ejpam-6264	490	3	⊆	CARDINAL
ejpam-6264	491	1	∈	ORG
ejpam-6264	492	1	∩	PERSON
ejpam-6264	492	2	∈	PRODUCT
ejpam-6264	492	3	∈	PRODUCT
ejpam-6264	493	1	∈	ORG
ejpam-6264	494	1	∈	ORG
ejpam-6264	494	2	1	CARDINAL
ejpam-6264	494	3	∩	PERSON
ejpam-6264	494	4	1	CARDINAL
ejpam-6264	494	5	∈	ORG
ejpam-6264	494	6	g+h	ORG
ejpam-6264	496	1	∈	ORG
ejpam-6264	496	2	∩	PERSON
ejpam-6264	496	3	⊆	CARDINAL
ejpam-6264	498	1	∈ v2 ∩	PERSON
ejpam-6264	499	1	w ∈ v3 ∩	PRODUCT
ejpam-6264	500	1	vw	GPE
ejpam-6264	504	1	∈	ORG
ejpam-6264	510	1	∈	ORG
ejpam-6264	512	1	∈	ORG
ejpam-6264	512	2	∩	PERSON
ejpam-6264	512	3	⊆	CARDINAL
ejpam-6264	514	1	⊆	CARDINAL
ejpam-6264	516	1	∈	ORG
ejpam-6264	519	1	∈	ORG
ejpam-6264	520	1	⊆	CARDINAL
ejpam-6264	522	1	∈ v2 ∩	PERSON
ejpam-6264	523	1	∈	ORG
ejpam-6264	524	1	∈	ORG
ejpam-6264	525	1	∈	ORG
ejpam-6264	528	1	∈	ORG
ejpam-6264	529	1	⊆	CARDINAL
ejpam-6264	530	1	w ∈	PERSON
ejpam-6264	530	2	vw ∈	ORG
ejpam-6264	532	1	∩ v2 ̸=	PERSON
ejpam-6264	532	2	∈ v2 ∩	PERSON
ejpam-6264	532	3	∈	ORG
ejpam-6264	533	1	w ∈ v3 ∩	PERSON
ejpam-6264	533	2	vw ∈	ORG
ejpam-6264	535	1	v2 ∩	PERSON
ejpam-6264	535	2	∈ v2 ∩	PERSON
ejpam-6264	535	3	w ∈	PERSON
ejpam-6264	535	4	vw	GPE
ejpam-6264	536	1	wx ∈	PERSON
ejpam-6264	538	1	1	CARDINAL
ejpam-6264	539	1	∩ v2 = ∅	PERSON
ejpam-6264	539	2	∈	PRODUCT
ejpam-6264	541	1	∈	ORG
ejpam-6264	542	1	∈	ORG
ejpam-6264	542	2	0	CARDINAL
ejpam-6264	542	3	1	CARDINAL
ejpam-6264	542	4	∈	ORG
ejpam-6264	543	1	∈	ORG
ejpam-6264	544	1	∈	ORG
ejpam-6264	544	2	⊆	CARDINAL
ejpam-6264	544	3	∈	ORG
ejpam-6264	544	4	⊆	CARDINAL
ejpam-6264	545	1	s. ahamad et al	PERSON
ejpam-6264	546	1	j. pure	PERSON
ejpam-6264	546	2	18	CARDINAL
ejpam-6264	546	3	4	CARDINAL
ejpam-6264	546	4	2025	CARDINAL
ejpam-6264	546	5	6264 15	DATE
ejpam-6264	546	6	20	CARDINAL
ejpam-6264	547	1	∈	ORG
ejpam-6264	547	2	g+h	ORG
ejpam-6264	548	1	∈	ORG
ejpam-6264	548	2	g+h	ORG
ejpam-6264	549	1	1	CARDINAL
ejpam-6264	549	2	∈	ORG
ejpam-6264	552	1	v2 ∩	PERSON
ejpam-6264	552	2	v2 ∩	PERSON
ejpam-6264	552	3	∩	PERSON
ejpam-6264	553	1	∈	ORG
ejpam-6264	553	2	∈	ORG
ejpam-6264	555	1	v2 ∩	PERSON
ejpam-6264	555	2	v2 ⊆	PRODUCT
ejpam-6264	556	1	v2 ∩	PERSON
ejpam-6264	556	2	w ∈ v2	PRODUCT
ejpam-6264	557	1	∈	ORG
ejpam-6264	557	2	g+h	ORG
ejpam-6264	557	3	vw ∈ e(h	ORG
ejpam-6264	557	4	⊆	CARDINAL
ejpam-6264	559	1	∈	ORG
ejpam-6264	560	1	i)(c2	ORG
ejpam-6264	561	1	∈	ORG
ejpam-6264	562	1	2	CARDINAL
ejpam-6264	562	2	∈	ORG
ejpam-6264	563	1	1	CARDINAL
ejpam-6264	563	2	3	CARDINAL
ejpam-6264	566	1	∩ v2 = ∅	PERSON
ejpam-6264	566	2	∈	ORG
ejpam-6264	567	1	∈	ORG
ejpam-6264	567	2	y ∈ v2 ∩ ng+h(x	PERSON
ejpam-6264	568	1	∈	ORG
ejpam-6264	570	1	v2 ∩	PERSON
ejpam-6264	572	1	∩ v2 = ∅	PERSON
ejpam-6264	573	1	∈	ORG
ejpam-6264	573	2	y ∈ v2	PERSON
ejpam-6264	573	3	xy ∈	ORG
ejpam-6264	575	1	∈	ORG
ejpam-6264	576	1	y ∈ v2 ∩	PERSON
ejpam-6264	577	1	v2 ∩	PERSON
ejpam-6264	578	1	∪ v2 ∪	MONEY
ejpam-6264	578	2	g)⟩	ORG
ejpam-6264	580	1	⊆	CARDINAL
ejpam-6264	581	1	∈	ORG
ejpam-6264	581	2	g+h	ORG
ejpam-6264	584	1	3	CARDINAL
ejpam-6264	587	1	3 ≤	QUANTITY
ejpam-6264	589	1	g+h	PERSON
ejpam-6264	590	1	2	CARDINAL
ejpam-6264	590	2	3	CARDINAL
ejpam-6264	591	1	un	ORG
ejpam-6264	592	1	f(x	ORG
ejpam-6264	594	1	2	CARDINAL
ejpam-6264	595	1	3	CARDINAL
ejpam-6264	595	2	{v2	PERSON
ejpam-6264	596	1	∈	ORG
ejpam-6264	598	1	∈	ORG
ejpam-6264	598	2	g+h	ORG
ejpam-6264	599	1	ωtmr	ORG
ejpam-6264	600	1	10	CARDINAL
ejpam-6264	601	1	3 ≤	QUANTITY
ejpam-6264	603	1	γtmr(k1+g	PERSON
ejpam-6264	603	2	3+2γ(g	QUANTITY
ejpam-6264	605	1	s. ahamad et al	PERSON
ejpam-6264	606	1	j. pure	PERSON
ejpam-6264	606	2	18	CARDINAL
ejpam-6264	606	3	4	CARDINAL
ejpam-6264	606	4	2025	CARDINAL
ejpam-6264	606	5	6264 16	DATE
ejpam-6264	606	6	20	CARDINAL
ejpam-6264	606	7	∈	ORG
ejpam-6264	607	1	γtmr(k1	ORG
ejpam-6264	607	2	2(1	CARDINAL
ejpam-6264	607	3	2 + n.	DATE
ejpam-6264	607	4	2	CARDINAL
ejpam-6264	607	5	′ 3	DATE
ejpam-6264	608	1	\d	ORG
ejpam-6264	608	2	′ 1	CARDINAL
ejpam-6264	608	3	2	CARDINAL
ejpam-6264	609	1	∈	ORG
ejpam-6264	610	1	γtmr(k1	ORG
ejpam-6264	611	1	3|v ′ 3 |+ 2|v	TIME
ejpam-6264	612	1	3(1	CARDINAL
ejpam-6264	613	1	+ 2|d|	CARDINAL
ejpam-6264	613	2	3 + 2γ(g	QUANTITY
ejpam-6264	614	1	k1+g	GPE
ejpam-6264	614	2	g ∈ {kn	PERSON
ejpam-6264	616	1	2	CARDINAL
ejpam-6264	616	2	8	CARDINAL
ejpam-6264	616	3	9	CARDINAL
ejpam-6264	617	1	2b	CARDINAL
ejpam-6264	617	2	2	CARDINAL
ejpam-6264	617	3	0a	CARDINAL
ejpam-6264	617	4	3	CARDINAL
ejpam-6264	617	5	8	CARDINAL
ejpam-6264	617	6	γtmr(k1 + p7	ORG
ejpam-6264	617	7	8	CARDINAL
ejpam-6264	617	8	8	CARDINAL
ejpam-6264	617	9	0	CARDINAL
ejpam-6264	617	10	1	DATE
ejpam-6264	617	11	2	DATE
ejpam-6264	617	12	3	CARDINAL
ejpam-6264	617	13	3	CARDINAL
ejpam-6264	617	14	f(b	GPE
ejpam-6264	617	15	2	CARDINAL
ejpam-6264	617	16	0	CARDINAL
ejpam-6264	617	17	1	CARDINAL
ejpam-6264	618	1	3	CARDINAL
ejpam-6264	618	2	8	CARDINAL
ejpam-6264	619	1	8	CARDINAL
ejpam-6264	619	2	γtmr(k1 + p7	ORG
ejpam-6264	619	3	3 + 2(γ(p7	DATE
ejpam-6264	620	1	9	CARDINAL
ejpam-6264	621	1	3	CARDINAL
ejpam-6264	621	2	2	CARDINAL
ejpam-6264	622	1	9	CARDINAL
ejpam-6264	622	2	γtmr(k1 +k5	ORG
ejpam-6264	623	1	5	CARDINAL
ejpam-6264	624	1	s. ahamad et al	PERSON
ejpam-6264	625	1	j. pure	PERSON
ejpam-6264	625	2	18	CARDINAL
ejpam-6264	625	3	4	CARDINAL
ejpam-6264	625	4	2025	CARDINAL
ejpam-6264	625	5	6264 17	DATE
ejpam-6264	625	6	20	CARDINAL
ejpam-6264	625	7	9	CARDINAL
ejpam-6264	625	8	5	CARDINAL
ejpam-6264	626	1	γtmr(k1 +k5	ORG
ejpam-6264	626	2	3 + 2(γ(k1	DATE
ejpam-6264	626	3	5	CARDINAL
ejpam-6264	629	1	3	CARDINAL
ejpam-6264	631	1	4	CARDINAL
ejpam-6264	633	1	5	CARDINAL
ejpam-6264	635	1	1	CARDINAL
ejpam-6264	636	1	1	CARDINAL
ejpam-6264	636	2	2	CARDINAL
ejpam-6264	637	1	2	CARDINAL
ejpam-6264	638	1	17	CARDINAL
ejpam-6264	639	1	6	CARDINAL
ejpam-6264	641	1	one	CARDINAL
ejpam-6264	641	2	8	CARDINAL
ejpam-6264	641	3	g ◦ h corresponding	ORG
ejpam-6264	641	4	∈	ORG
ejpam-6264	642	1	18	CARDINAL
ejpam-6264	645	1	∈	ORG
ejpam-6264	645	2	g ◦ h	ORG
ejpam-6264	647	1	∈	ORG
ejpam-6264	647	2	2	CARDINAL
ejpam-6264	647	3	3	CARDINAL
ejpam-6264	648	1	1	CARDINAL
ejpam-6264	648	2	2	CARDINAL
ejpam-6264	648	3	3	CARDINAL
ejpam-6264	648	4	1	CARDINAL
ejpam-6264	648	5	v2 ∩	PERSON
ejpam-6264	649	1	∈	ORG
ejpam-6264	649	2	g ◦ h	ORG
ejpam-6264	650	1	0	CARDINAL
ejpam-6264	651	1	∈	ORG
ejpam-6264	651	2	w ∈ v2	PRODUCT
ejpam-6264	653	1	∈	ORG
ejpam-6264	654	1	w	ORG
ejpam-6264	654	2	∈	ORG
ejpam-6264	655	1	1	CARDINAL
ejpam-6264	656	1	∈ v2	MONEY
ejpam-6264	656	2	∈	ORG
ejpam-6264	656	3	2 ∪	PERCENT
ejpam-6264	656	4	3	CARDINAL
ejpam-6264	657	1	2 ∪	PERCENT
ejpam-6264	657	2	3	CARDINAL
ejpam-6264	658	1	z′ ∈	PERSON
ejpam-6264	659	1	0	CARDINAL
ejpam-6264	662	1	s. ahamad et al	PERSON
ejpam-6264	663	1	j. pure	PERSON
ejpam-6264	663	2	18	CARDINAL
ejpam-6264	663	3	4	CARDINAL
ejpam-6264	663	4	2025	CARDINAL
ejpam-6264	663	5	6264 18	DATE
ejpam-6264	663	6	20	CARDINAL
ejpam-6264	663	7	2	CARDINAL
ejpam-6264	663	8	3	CARDINAL
ejpam-6264	663	9	0	CARDINAL
ejpam-6264	665	1	∈	ORG
ejpam-6264	666	1	|ng(v)∩ v3| ≥ 1	ORG
ejpam-6264	666	2	3	CARDINAL
ejpam-6264	666	3	2	CARDINAL
ejpam-6264	667	1	0	CARDINAL
ejpam-6264	667	2	|ng(v)∩ v2| ≥ 1	ORG
ejpam-6264	669	1	∈ v2 ∩	PRODUCT
ejpam-6264	669	2	0	CARDINAL
ejpam-6264	670	1	⊆	CARDINAL
ejpam-6264	671	1	∈	PRODUCT
ejpam-6264	672	1	3	CARDINAL
ejpam-6264	673	1	3	CARDINAL
ejpam-6264	673	2	0	CARDINAL
ejpam-6264	677	1	∈	ORG
ejpam-6264	677	2	∈	ORG
ejpam-6264	678	1	1	CARDINAL
ejpam-6264	679	1	w	ORG
ejpam-6264	679	2	∈	ORG
ejpam-6264	679	3	2	CARDINAL
ejpam-6264	679	4	3	CARDINAL
ejpam-6264	680	1	w ∈ v2	PERSON
ejpam-6264	680	2	w	ORG
ejpam-6264	681	1	3	CARDINAL
ejpam-6264	681	2	2	CARDINAL
ejpam-6264	682	1	1	CARDINAL
ejpam-6264	683	1	3	CARDINAL
ejpam-6264	683	2	w ∈	ORG
ejpam-6264	683	3	∩ v2	PERSON
ejpam-6264	683	4	w	ORG
ejpam-6264	684	1	2	CARDINAL
ejpam-6264	684	2	3	CARDINAL
ejpam-6264	685	1	1	CARDINAL
ejpam-6264	686	1	w ∈	PERSON
ejpam-6264	686	2	2	CARDINAL
ejpam-6264	686	3	w	ORG
ejpam-6264	687	1	2	CARDINAL
ejpam-6264	687	2	∈	ORG
ejpam-6264	687	3	0	CARDINAL
ejpam-6264	689	1	g◦h	ORG
ejpam-6264	690	1	w	ORG
ejpam-6264	690	2	∈	ORG
ejpam-6264	690	3	2	CARDINAL
ejpam-6264	690	4	3	CARDINAL
ejpam-6264	691	1	∈ v2 ∩	PRODUCT
ejpam-6264	692	1	3	CARDINAL
ejpam-6264	692	2	0	CARDINAL
ejpam-6264	693	1	∈	ORG
ejpam-6264	693	2	3	CARDINAL
ejpam-6264	694	1	∈	PRODUCT
ejpam-6264	695	1	2	CARDINAL
ejpam-6264	695	2	0	CARDINAL
ejpam-6264	696	1	∈	ORG
ejpam-6264	696	2	2	CARDINAL
ejpam-6264	697	1	1	CARDINAL
ejpam-6264	697	2	2	CARDINAL
ejpam-6264	697	3	w ∈ v2	PERSON
ejpam-6264	697	4	w	ORG
ejpam-6264	699	1	∈	ORG
ejpam-6264	699	2	2 ∪	PERCENT
ejpam-6264	699	3	3	CARDINAL
ejpam-6264	699	4	∈	ORG
ejpam-6264	699	5	hu	PERSON
ejpam-6264	700	1	∈ v2 ∪	MONEY
ejpam-6264	701	1	∈	ORG
ejpam-6264	702	1	∈	ORG
ejpam-6264	703	1	∈	PRODUCT
ejpam-6264	703	2	w ∈	PERSON
ejpam-6264	703	3	2 ∪v	PERCENT
ejpam-6264	703	4	3	CARDINAL
ejpam-6264	704	1	w ∈	ORG
ejpam-6264	704	2	w ∈	ORG
ejpam-6264	705	1	∈	ORG
ejpam-6264	705	2	g◦h	ORG
ejpam-6264	706	1	6	CARDINAL
ejpam-6264	708	1	3n ≤ ∑	QUANTITY
ejpam-6264	710	1	∈	ORG
ejpam-6264	711	1	∈ v2 ∪	MONEY
ejpam-6264	711	2	3n ≤ ∑	QUANTITY
ejpam-6264	711	3	∈	ORG
ejpam-6264	712	1	18	CARDINAL
ejpam-6264	713	1	3n	CARDINAL
ejpam-6264	715	1	3n ≤ ∑	QUANTITY
ejpam-6264	719	1	4n	CARDINAL
ejpam-6264	719	2	2. 5n	CARDINAL
ejpam-6264	719	3	3	CARDINAL
ejpam-6264	721	1	1	CARDINAL
ejpam-6264	722	1	2	CARDINAL
ejpam-6264	722	2	4	CARDINAL
ejpam-6264	722	3	7 (ii	DATE
ejpam-6264	723	1	4	CARDINAL
ejpam-6264	723	2	5	CARDINAL
ejpam-6264	723	3	8.	DATE
ejpam-6264	724	1	1	CARDINAL
ejpam-6264	724	2	s. ahamad et al	PERSON
ejpam-6264	725	1	j. pure	PERSON
ejpam-6264	725	2	18	CARDINAL
ejpam-6264	725	3	4	CARDINAL
ejpam-6264	725	4	2025	CARDINAL
ejpam-6264	725	5	6264 19	DATE
ejpam-6264	725	6	2	CARDINAL
ejpam-6264	726	1	v∈v	PERSON
ejpam-6264	727	1	∈	ORG
ejpam-6264	729	1	w0,w1,w2,w3	ORG
ejpam-6264	730	1	w3 =	GPE
ejpam-6264	730	2	4n	CARDINAL
ejpam-6264	731	1	1 and |w3|	TIME
ejpam-6264	731	2	1	CARDINAL
ejpam-6264	732	1	2|w2|+3|w3|	CARDINAL
ejpam-6264	732	2	4n	CARDINAL
ejpam-6264	734	1	4n	CARDINAL
ejpam-6264	735	1	3	CARDINAL
ejpam-6264	735	2	∈	ORG
ejpam-6264	736	1	f(x	ORG
ejpam-6264	738	1	3	CARDINAL
ejpam-6264	738	2	∈	ORG
ejpam-6264	739	1	2	CARDINAL
ejpam-6264	739	2	∈	ORG
ejpam-6264	741	1	∈	ORG
ejpam-6264	743	1	w0,w1,w2,w3	ORG
ejpam-6264	744	1	w3 =	GPE
ejpam-6264	744	2	5n	CARDINAL
ejpam-6264	745	1	1 and |w3|	TIME
ejpam-6264	745	2	1	CARDINAL
ejpam-6264	747	1	2|w2|	CARDINAL
ejpam-6264	747	2	5n	CARDINAL
ejpam-6264	748	1	5n	CARDINAL
ejpam-6264	749	1	8	CARDINAL
ejpam-6264	750	1	kn	PERSON
ejpam-6264	750	2	γtmr(k1 ◦kn	ORG
ejpam-6264	751	1	2	CARDINAL
ejpam-6264	752	1	3n	CARDINAL
ejpam-6264	754	1	sn	ORG
ejpam-6264	754	2	15	CARDINAL
ejpam-6264	754	3	γtmr(k1 ◦kn	ORG
ejpam-6264	754	4	= γtmr(sn	PERSON
ejpam-6264	754	5	n + 2	ORG
ejpam-6264	754	6	kn ◦k1	PERSON
ejpam-6264	755	1	9	CARDINAL
ejpam-6264	755	2	γtmr(kn ◦k1	ORG
ejpam-6264	756	1	3n	CARDINAL
ejpam-6264	757	1	s. ahamad	PERSON
ejpam-6264	758	1	1	CARDINAL
ejpam-6264	758	2	e. j. cockayne	PERSON
ejpam-6264	758	3	m. dreyer sr.	PERSON
ejpam-6264	758	4	s. m. hedetniemi	PERSON
ejpam-6264	758	5	s. t. hedetniemi	PERSON
ejpam-6264	760	1	278(1	CARDINAL
ejpam-6264	760	2	2004	DATE
ejpam-6264	761	1	2	CARDINAL
ejpam-6264	761	2	c. s. revelle	PERSON
ejpam-6264	761	3	k. e. rosing	PERSON
ejpam-6264	762	1	defendens imperium romanum	PERSON
ejpam-6264	763	1	american	NORP
ejpam-6264	763	2	monthly	DATE
ejpam-6264	763	3	107(7):585–594, 2000	DATE
ejpam-6264	764	1	3	CARDINAL
ejpam-6264	764	2	i. stewart	PERSON
ejpam-6264	766	1	american	NORP
ejpam-6264	766	2	281(6):136–139, 1999	DATE
ejpam-6264	767	1	4	CARDINAL
ejpam-6264	767	2	a. a. hossein	PERSON
ejpam-6264	767	3	a. h. michael	PERSON
ejpam-6264	767	4	s. vladimir	PERSON
ejpam-6264	767	5	g. y. ismael	PERSON
ejpam-6264	769	1	10(2):501–517	DATE
ejpam-6264	769	2	2016	DATE
ejpam-6264	770	1	s. ahamad et al	PERSON
ejpam-6264	771	1	j. pure	PERSON
ejpam-6264	771	2	18	CARDINAL
ejpam-6264	771	3	4	CARDINAL
ejpam-6264	771	4	2025	CARDINAL
ejpam-6264	771	5	6264 20	DATE
ejpam-6264	772	1	5	CARDINAL
ejpam-6264	772	2	a. h. hassan	PERSON
ejpam-6264	772	3	a. o. ahmed	PERSON
ejpam-6264	774	1	basrah journal of agricultural sciences	ORG
ejpam-6264	774	2	august 2018	DATE
ejpam-6264	775	1	6	CARDINAL
ejpam-6264	775	2	a. o. ahmed	PERSON
ejpam-6264	775	3	n. a. manal	PERSON
ejpam-6264	777	1	june 2022	DATE
ejpam-6264	778	1	7	CARDINAL
ejpam-6264	778	2	e. w.	PERSON
ejpam-6264	778	3	extremal	GPE
ejpam-6264	779	1	siam journal	ORG
ejpam-6264	779	2	2004	DATE
ejpam-6264	780	1	8	CARDINAL
ejpam-6264	780	2	j. b. cariaga	PERSON
ejpam-6264	780	3	f. p. jamil	PERSON
ejpam-6264	782	1	european journal	ORG
ejpam-6264	782	2	16(2):847–863	CARDINAL
ejpam-6264	782	3	2023	CARDINAL
ejpam-6264	783	1	9	CARDINAL
ejpam-6264	783	2	l. m. paleta	PERSON
ejpam-6264	783	3	f. p. jamil	PERSON
ejpam-6264	785	1	european journal	ORG
ejpam-6264	785	2	13(3):529–548	DATE
ejpam-6264	785	3	2020	DATE
ejpam-6264	786	1	10	CARDINAL
ejpam-6264	786	2	m. a. henning	PERSON
ejpam-6264	786	3	s. t. hedetniemi	PERSON
ejpam-6264	788	1	266(1-3	CARDINAL
ejpam-6264	788	2	2003	DATE
ejpam-6264	789	1	11	CARDINAL
ejpam-6264	789	2	r. j. fortosa	PERSON
ejpam-6264	789	3	f. p. jamil	PERSON
ejpam-6264	789	4	s. r. canoy	PERSON
ejpam-6264	791	1	european journal	ORG
ejpam-6264	791	2	17(2):1335–1351	CARDINAL
ejpam-6264	791	3	2024	DATE
ejpam-6264	792	1	12	CARDINAL
ejpam-6264	792	2	s. r. canoy jr, f. p. jamil	PERSON
ejpam-6264	792	3	s. m. menchavez.	PERSON
ejpam-6264	793	1	italian	NORP
ejpam-6264	794	1	european journal	ORG
ejpam-6264	794	2	16(4):2431–2449	DATE
ejpam-6264	794	3	2023	CARDINAL
ejpam-6264	795	1	13	CARDINAL
ejpam-6264	795	2	s. salah	PERSON
ejpam-6264	795	3	a. a. omran	PERSON
ejpam-6264	795	4	m. n. al-harere	PERSON
ejpam-6264	796	1	two	CARDINAL
ejpam-6264	797	1	aip	ORG
ejpam-6264	797	2	2386	CARDINAL
ejpam-6264	797	3	060014	DATE
ejpam-6264	797	4	2022	CARDINAL
ejpam-6264	798	1	14	CARDINAL
ejpam-6264	798	2	s. s. majeed	PERSON
ejpam-6264	798	3	a. a. omran	PERSON
ejpam-6264	798	4	m. n. yaqoob	PERSON
ejpam-6264	800	1	january 2022	DATE
ejpam-6264	801	1	15	CARDINAL
ejpam-6264	801	2	f. buckley	PERSON
ejpam-6264	801	3	f. harary	PERSON
ejpam-6264	803	1	addison-wesley	ORG
ejpam-6264	803	2	redwood city	GPE
ejpam-6264	803	3	1990	DATE
ejpam-6264	804	1	16	CARDINAL
ejpam-6264	804	2	e. j. cockayne	PERSON
ejpam-6264	804	3	s. t. hedetniemi	PERSON
ejpam-6264	806	1	1977	DATE