id	sid	eid	entity	type
ejpam-6951	1	1	european journal	ORG
ejpam-6951	1	2	2025	DATE
ejpam-6951	1	3	18	CARDINAL
ejpam-6951	1	4	4	CARDINAL
ejpam-6951	1	5	6951	CARDINAL
ejpam-6951	1	6	1307-5543	DATE
ejpam-6951	1	7	new york	GPE
ejpam-6951	1	8	bipartite	ORG
ejpam-6951	1	9	gino derek m. sepillo1,∗	PERSON
ejpam-6951	1	10	joyce g. valdez1	PERSON
ejpam-6951	1	11	meguilito y. eyao1	PERSON
ejpam-6951	1	12	neil m. mame1 1	PERSON
ejpam-6951	1	13	batangas state university	ORG
ejpam-6951	1	14	the national engineering university	ORG
ejpam-6951	1	15	batangas city	GPE
ejpam-6951	1	16	batangas	GPE
ejpam-6951	1	17	philippines	GPE
ejpam-6951	6	1	0	CARDINAL
ejpam-6951	6	2	1	CARDINAL
ejpam-6951	9	1	1	CARDINAL
ejpam-6951	9	2	0	CARDINAL
ejpam-6951	9	3	∈	ORG
ejpam-6951	10	1	the subgraph g⟨s⟩	PRODUCT
ejpam-6951	12	1	bipartite	NORP
ejpam-6951	12	2	graph km	PERSON
ejpam-6951	12	3	m. 2020	PERSON
ejpam-6951	12	4	05c50	CARDINAL
ejpam-6951	15	1	1	CARDINAL
ejpam-6951	16	1	∗corresponding	PERSON
ejpam-6951	17	1	21-58341@g.batstate-u.edu.ph	CARDINAL
ejpam-6951	17	2	20-59247@g.batstate-u.edu.ph	CARDINAL
ejpam-6951	17	3	m. j. valdez	PERSON
ejpam-6951	17	4	15-52878@g.batstate-u.edu.ph	CARDINAL
ejpam-6951	17	5	m. y. eyao	PERSON
ejpam-6951	17	6	neil.mame@g.batstate-u.edu.ph	ORG
ejpam-6951	17	7	n. m. mame	PERSON
ejpam-6951	18	1	1	CARDINAL
ejpam-6951	18	2	2025	CARDINAL
ejpam-6951	19	1	g. d. sepillo et al	PERSON
ejpam-6951	20	1	j. pure	PERSON
ejpam-6951	20	2	18	CARDINAL
ejpam-6951	20	3	4	CARDINAL
ejpam-6951	20	4	2025	CARDINAL
ejpam-6951	20	5	6951 2	DATE
ejpam-6951	20	6	23	CARDINAL
ejpam-6951	20	7	0	CARDINAL
ejpam-6951	20	8	1	CARDINAL
ejpam-6951	20	9	0	CARDINAL
ejpam-6951	20	10	1	CARDINAL
ejpam-6951	23	1	2	CARDINAL
ejpam-6951	24	1	3	CARDINAL
ejpam-6951	24	2	first	ORDINAL
ejpam-6951	24	3	4	CARDINAL
ejpam-6951	24	4	5	CARDINAL
ejpam-6951	26	1	generator subgraphs	ORG
ejpam-6951	26	2	mame	PERSON
ejpam-6951	31	1	7→	CARDINAL
ejpam-6951	37	1	7→	CARDINAL
ejpam-6951	38	1	⊆	CARDINAL
ejpam-6951	38	2	⊆	CARDINAL
ejpam-6951	39	1	g⟨s⟩	ORG
ejpam-6951	41	1	y ∈ s	PERSON
ejpam-6951	42	1	⊆	CARDINAL
ejpam-6951	42	2	mame	PERSON
ejpam-6951	43	1	3	CARDINAL
ejpam-6951	44	1	bipartite	ORG
ejpam-6951	45	1	bipartite	ORG
ejpam-6951	45	2	graph km	PERSON
ejpam-6951	45	3	6	CARDINAL
ejpam-6951	46	1	∈	ORG
ejpam-6951	46	2	0	CARDINAL
ejpam-6951	46	3	1	CARDINAL
ejpam-6951	47	1	bipartite	ORG
ejpam-6951	48	1	8	CARDINAL
ejpam-6951	49	1	9	CARDINAL
ejpam-6951	49	2	chartrand	GPE
ejpam-6951	49	3	lesniak	PERSON
ejpam-6951	50	1	10	CARDINAL
ejpam-6951	51	1	6	CARDINAL
ejpam-6951	51	2	g. d. sepillo et	PERSON
ejpam-6951	52	1	j. pure	PERSON
ejpam-6951	52	2	18	CARDINAL
ejpam-6951	52	3	4	CARDINAL
ejpam-6951	52	4	2025	CARDINAL
ejpam-6951	52	5	6951 3	DATE
ejpam-6951	52	6	23	CARDINAL
ejpam-6951	53	1	11	CARDINAL
ejpam-6951	53	2	larson	ORG
ejpam-6951	54	1	12	CARDINAL
ejpam-6951	55	1	bipartite	ORG
ejpam-6951	56	1	first	ORDINAL
ejpam-6951	56	2	two	CARDINAL
ejpam-6951	56	3	two	CARDINAL
ejpam-6951	57	1	3	CARDINAL
ejpam-6951	59	1	2	CARDINAL
ejpam-6951	59	2	2.1	CARDINAL
ejpam-6951	60	1	vertex-generator	ORG
ejpam-6951	62	1	3	CARDINAL
ejpam-6951	63	1	1	CARDINAL
ejpam-6951	64	1	1	CARDINAL
ejpam-6951	65	1	0	CARDINAL
ejpam-6951	65	2	1	CARDINAL
ejpam-6951	65	3	1	CARDINAL
ejpam-6951	65	4	0	CARDINAL
ejpam-6951	66	1	1	CARDINAL
ejpam-6951	66	2	1	CARDINAL
ejpam-6951	67	1	1	CARDINAL
ejpam-6951	67	2	x3	GPE
ejpam-6951	71	1	2	CARDINAL
ejpam-6951	72	1	3	CARDINAL
ejpam-6951	72	2	3	CARDINAL
ejpam-6951	73	1	3	CARDINAL
ejpam-6951	75	1	∈	ORG
ejpam-6951	78	1	ci ∈	PERSON
ejpam-6951	78	2	0	CARDINAL
ejpam-6951	78	3	1	CARDINAL
ejpam-6951	79	1	g. d. sepillo et	PERSON
ejpam-6951	80	1	j. pure	PERSON
ejpam-6951	80	2	18	CARDINAL
ejpam-6951	80	3	4	CARDINAL
ejpam-6951	80	4	2025	CARDINAL
ejpam-6951	80	5	6951 4	DATE
ejpam-6951	80	6	23	CARDINAL
ejpam-6951	80	7	4	CARDINAL
ejpam-6951	81	1	3	CARDINAL
ejpam-6951	82	1	1	CARDINAL
ejpam-6951	82	2	⊆	CARDINAL
ejpam-6951	83	1	⊆	CARDINAL
ejpam-6951	84	1	⊆	CARDINAL
ejpam-6951	86	1	1	CARDINAL
ejpam-6951	87	1	3	CARDINAL
ejpam-6951	87	2	x3	GPE
ejpam-6951	90	1	1	CARDINAL
ejpam-6951	92	1	a5 c5	PERSON
ejpam-6951	92	2	1	CARDINAL
ejpam-6951	92	3	c5.	ORG
ejpam-6951	93	1	first	ORDINAL
ejpam-6951	93	2	c5	ORG
ejpam-6951	94	1	{a1	PERSON
ejpam-6951	94	2	a5}	PERSON
ejpam-6951	94	3	a5}	PERSON
ejpam-6951	95	1	⊆	CARDINAL
ejpam-6951	96	1	{a1	PERSON
ejpam-6951	98	1	1	CARDINAL
ejpam-6951	98	2	c5	ORG
ejpam-6951	99	1	g. d. sepillo et	PERSON
ejpam-6951	100	1	j. pure	PERSON
ejpam-6951	100	2	18	CARDINAL
ejpam-6951	100	3	4	CARDINAL
ejpam-6951	100	4	2025	CARDINAL
ejpam-6951	100	5	6951 5	DATE
ejpam-6951	100	6	23 2.1.1	CARDINAL
ejpam-6951	101	1	first	ORDINAL
ejpam-6951	102	1	2	CARDINAL
ejpam-6951	103	1	3	CARDINAL
ejpam-6951	105	1	3	CARDINAL
ejpam-6951	106	1	3	CARDINAL
ejpam-6951	107	1	4	CARDINAL
ejpam-6951	108	1	3	CARDINAL
ejpam-6951	110	1	5	CARDINAL
ejpam-6951	111	1	3	CARDINAL
ejpam-6951	113	1	≃ k1	WORK_OF_ART
ejpam-6951	115	1	3	CARDINAL
ejpam-6951	117	1	6	CARDINAL
ejpam-6951	118	1	3	CARDINAL
ejpam-6951	120	1	1	CARDINAL
ejpam-6951	121	1	1	CARDINAL
ejpam-6951	121	2	7	CARDINAL
ejpam-6951	122	1	3	CARDINAL
ejpam-6951	122	2	x3	PERSON
ejpam-6951	125	1	8	CARDINAL
ejpam-6951	126	1	3	CARDINAL
ejpam-6951	126	2	⊆	CARDINAL
ejpam-6951	127	1	⊆	CARDINAL
ejpam-6951	128	1	1	CARDINAL
ejpam-6951	128	2	g. d. sepillo et	PERSON
ejpam-6951	129	1	j. pure	PERSON
ejpam-6951	129	2	18	CARDINAL
ejpam-6951	129	3	4	CARDINAL
ejpam-6951	129	4	2025	CARDINAL
ejpam-6951	129	5	6951 6	DATE
ejpam-6951	129	6	23	CARDINAL
ejpam-6951	129	7	2	CARDINAL
ejpam-6951	130	1	3	CARDINAL
ejpam-6951	130	2	x3	GPE
ejpam-6951	135	1	9	CARDINAL
ejpam-6951	136	1	3	CARDINAL
ejpam-6951	137	1	kn	ORG
ejpam-6951	137	2	kn	ORG
ejpam-6951	138	1	1 ≤	QUANTITY
ejpam-6951	138	2	1	CARDINAL
ejpam-6951	138	3	3	CARDINAL
ejpam-6951	138	4	3.1	CARDINAL
ejpam-6951	138	5	vertex-generator	ORG
ejpam-6951	138	6	bipartite	ORG
ejpam-6951	138	7	graph km	PERSON
ejpam-6951	138	8	bipartite	NORP
ejpam-6951	138	9	graph km	PERSON
ejpam-6951	138	10	bipartite	NORP
ejpam-6951	139	1	∪n	CARDINAL
ejpam-6951	139	2	x3	GPE
ejpam-6951	139	3	xm−1	ORG
ejpam-6951	139	4	xm	ORG
ejpam-6951	140	1	1 ≤	QUANTITY
ejpam-6951	140	2	2	CARDINAL
ejpam-6951	140	3	bipartite	NORP
ejpam-6951	143	1	2	CARDINAL
ejpam-6951	143	2	bipartite	NORP
ejpam-6951	143	3	graph km	PERSON
ejpam-6951	143	4	1	CARDINAL
ejpam-6951	145	1	xm	ORG
ejpam-6951	147	1	j. pure	PERSON
ejpam-6951	147	2	18	CARDINAL
ejpam-6951	147	3	4	CARDINAL
ejpam-6951	147	4	2025	CARDINAL
ejpam-6951	147	5	6951 7	DATE
ejpam-6951	147	6	23	CARDINAL
ejpam-6951	148	1	1	CARDINAL
ejpam-6951	150	1	7	CARDINAL
ejpam-6951	150	2	xm	ORG
ejpam-6951	152	1	m+	CARDINAL
ejpam-6951	152	2	1	CARDINAL
ejpam-6951	152	3	6	CARDINAL
ejpam-6951	152	4	2	CARDINAL
ejpam-6951	152	5	k1,1	PERSON
ejpam-6951	152	6	k2,2	ORG
ejpam-6951	153	1	theorem 5	DATE
ejpam-6951	155	1	km,n	ORG
ejpam-6951	155	2	2	CARDINAL
ejpam-6951	155	3	m+n ≥ 5	ORG
ejpam-6951	156	1	10	CARDINAL
ejpam-6951	157	1	2	CARDINAL
ejpam-6951	159	1	kt	ORG
ejpam-6951	160	1	bipartite	NORP
ejpam-6951	161	1	3	CARDINAL
ejpam-6951	168	1	3	CARDINAL
ejpam-6951	168	2	kn	PERSON
ejpam-6951	169	1	9	CARDINAL
ejpam-6951	170	1	9	CARDINAL
ejpam-6951	171	1	kt	ORG
ejpam-6951	171	2	9	CARDINAL
ejpam-6951	172	1	kt	ORG
ejpam-6951	172	2	kn	PERSON
ejpam-6951	173	1	1 ≤	QUANTITY
ejpam-6951	173	2	1 ≤ j ≤ n	QUANTITY
ejpam-6951	173	3	1	CARDINAL
ejpam-6951	179	1	1	CARDINAL
ejpam-6951	179	2	kt	ORG
ejpam-6951	179	3	n. g. d. sepillo et	PERSON
ejpam-6951	180	1	j. pure	PERSON
ejpam-6951	180	2	18	CARDINAL
ejpam-6951	180	3	4	CARDINAL
ejpam-6951	180	4	2025	CARDINAL
ejpam-6951	180	5	6951 8	DATE
ejpam-6951	180	6	23	CARDINAL
ejpam-6951	181	1	2	CARDINAL
ejpam-6951	182	1	1	CARDINAL
ejpam-6951	182	2	3	CARDINAL
ejpam-6951	183	1	1	CARDINAL
ejpam-6951	183	2	3	CARDINAL
ejpam-6951	183	3	2	CARDINAL
ejpam-6951	183	4	1 ≤	QUANTITY
ejpam-6951	183	5	bipartite	NORP
ejpam-6951	183	6	graph km	PERSON
ejpam-6951	184	1	1 ≤	QUANTITY
ejpam-6951	184	2	∈	CARDINAL
ejpam-6951	184	3	4	CARDINAL
ejpam-6951	190	1	xm−1 xm	FAC
ejpam-6951	191	1	4	CARDINAL
ejpam-6951	191	2	1	CARDINAL
ejpam-6951	191	3	2	DATE
ejpam-6951	191	4	3	DATE
ejpam-6951	192	1	1 ≤ j ≤ n	QUANTITY
ejpam-6951	192	2	partite	ORG
ejpam-6951	192	3	bipartite	NORP
ejpam-6951	192	4	graph km	PERSON
ejpam-6951	193	1	1 ≤ j ≤ n.	QUANTITY
ejpam-6951	193	2	5	CARDINAL
ejpam-6951	193	3	g. d. sepillo et	PERSON
ejpam-6951	194	1	j. pure	PERSON
ejpam-6951	194	2	18	CARDINAL
ejpam-6951	194	3	4	CARDINAL
ejpam-6951	194	4	2025	CARDINAL
ejpam-6951	194	5	6951 9	DATE
ejpam-6951	194	6	23	CARDINAL
ejpam-6951	201	1	yn km	PERSON
ejpam-6951	201	2	n⟨f ⟩	PERSON
ejpam-6951	201	3	5	CARDINAL
ejpam-6951	201	4	1	CARDINAL
ejpam-6951	201	5	2	DATE
ejpam-6951	201	6	3	DATE
ejpam-6951	202	1	km,n	ORG
ejpam-6951	202	2	1	CARDINAL
ejpam-6951	203	1	km,n	ORG
ejpam-6951	206	1	12	CARDINAL
ejpam-6951	207	1	2	CARDINAL
ejpam-6951	208	1	t ≤ min{m	GPE
ejpam-6951	208	2	st	GPE
ejpam-6951	210	1	1 ≤	QUANTITY
ejpam-6951	210	2	bipartite	ORG
ejpam-6951	210	3	1 ≤	MONEY
ejpam-6951	210	4	x3	GPE
ejpam-6951	210	5	1 ≤	MONEY
ejpam-6951	210	6	1 ≤	QUANTITY
ejpam-6951	210	7	∈	PRODUCT
ejpam-6951	210	8	6	CARDINAL
ejpam-6951	211	1	1	CARDINAL
ejpam-6951	211	2	2	DATE
ejpam-6951	211	3	3	DATE
ejpam-6951	213	1	j. pure	PERSON
ejpam-6951	213	2	18	CARDINAL
ejpam-6951	213	3	4	CARDINAL
ejpam-6951	213	4	2025	CARDINAL
ejpam-6951	213	5	6951 10	DATE
ejpam-6951	213	6	23	CARDINAL
ejpam-6951	216	1	xt+1	ORG
ejpam-6951	217	1	xm−1 xm	PERSON
ejpam-6951	222	1	xm−2 xm−1	ORG
ejpam-6951	225	1	6	CARDINAL
ejpam-6951	225	2	a1 △a2 △a3 △ ·	PRODUCT
ejpam-6951	226	1	1 ≤ j ≤ n	QUANTITY
ejpam-6951	226	2	partite	ORG
ejpam-6951	226	3	bipartite	NORP
ejpam-6951	226	4	graph km	PERSON
ejpam-6951	226	5	1 ≤	QUANTITY
ejpam-6951	226	6	xq	ORG
ejpam-6951	226	7	1 ≤	QUANTITY
ejpam-6951	226	8	x3	GPE
ejpam-6951	226	9	1 ≤ j ≤ n.	QUANTITY
ejpam-6951	226	10	bq	ORG
ejpam-6951	226	11	7	CARDINAL
ejpam-6951	229	1	xt+1	ORG
ejpam-6951	230	1	xm−1 xm	PERSON
ejpam-6951	234	1	xt+1	ORG
ejpam-6951	235	1	xm−1 xm	PERSON
ejpam-6951	236	1	7	CARDINAL
ejpam-6951	236	2	b g. d. sepillo et	PERSON
ejpam-6951	237	1	j. pure	PERSON
ejpam-6951	237	2	18	CARDINAL
ejpam-6951	237	3	4	CARDINAL
ejpam-6951	237	4	2025	CARDINAL
ejpam-6951	237	5	6951 11	DATE
ejpam-6951	237	6	23	CARDINAL
ejpam-6951	237	7	1	CARDINAL
ejpam-6951	237	8	2	DATE
ejpam-6951	237	9	3	DATE
ejpam-6951	239	1	x3	GPE
ejpam-6951	239	2	x3	GPE
ejpam-6951	240	1	1	CARDINAL
ejpam-6951	240	2	st	GPE
ejpam-6951	240	3	bipartite	NORP
ejpam-6951	240	4	graph kr	PERSON
ejpam-6951	240	5	r+1	ORG
ejpam-6951	240	6	13	CARDINAL
ejpam-6951	241	1	2	CARDINAL
ejpam-6951	241	2	m+n ≥ 5	ORG
ejpam-6951	242	1	kr	ORG
ejpam-6951	242	2	r+1	ORG
ejpam-6951	244	1	1	CARDINAL
ejpam-6951	245	1	1	CARDINAL
ejpam-6951	245	2	k1,2 of km	PRODUCT
ejpam-6951	245	3	k1,2	ORG
ejpam-6951	246	1	11	CARDINAL
ejpam-6951	246	2	km,n	ORG
ejpam-6951	246	3	k1,2	ORG
ejpam-6951	247	1	2	CARDINAL
ejpam-6951	247	2	2	CARDINAL
ejpam-6951	248	1	2 ≤	MONEY
ejpam-6951	249	1	xq	ORG
ejpam-6951	249	2	partite	ORG
ejpam-6951	249	3	bipartite	NORP
ejpam-6951	249	4	graph km	PERSON
ejpam-6951	250	1	xm−r+3	GPE
ejpam-6951	250	2	xm	ORG
ejpam-6951	250	3	r+1 vertices︷ ︸︸	PERSON
ejpam-6951	250	4	2 ≤	MONEY
ejpam-6951	250	5	m−	NORP
ejpam-6951	251	1	xm−r+2	ORG
ejpam-6951	251	2	xm	ORG
ejpam-6951	251	3	r+1 vertices︷ ︸︸	PERSON
ejpam-6951	251	4	xq	ORG
ejpam-6951	251	5	m−	NORP
ejpam-6951	251	6	8	CARDINAL
ejpam-6951	252	1	2	CARDINAL
ejpam-6951	252	2	3	DATE
ejpam-6951	252	3	4	DATE
ejpam-6951	252	4	m−	PERSON
ejpam-6951	253	1	xq	ORG
ejpam-6951	254	1	2 ≤	MONEY
ejpam-6951	254	2	m−	PERSON
ejpam-6951	255	1	1 ≤ s ≤ n	QUANTITY
ejpam-6951	255	2	g. d. sepillo et	PERSON
ejpam-6951	257	1	j. pure	PERSON
ejpam-6951	257	2	18	CARDINAL
ejpam-6951	257	3	4	CARDINAL
ejpam-6951	257	4	2025	CARDINAL
ejpam-6951	257	5	6951 12	DATE
ejpam-6951	257	6	23	CARDINAL
ejpam-6951	258	1	xm−r+1xm−r+2xm−r+3 xm	FAC
ejpam-6951	262	1	yn km	ORG
ejpam-6951	262	2	xm−r+1xm−r+2xm−r+3 xm	FAC
ejpam-6951	266	1	yn km	PERSON
ejpam-6951	266	2	xm−r+1xm−r+2xm−r+3 xm	FAC
ejpam-6951	271	1	xm−r+1xm−r+2xm−r+3 xm	FAC
ejpam-6951	275	1	8	CARDINAL
ejpam-6951	275	2	partite	ORG
ejpam-6951	275	3	bipartite	NORP
ejpam-6951	275	4	graph km	PERSON
ejpam-6951	276	1	x3	GPE
ejpam-6951	277	1	1 ≤ s ≤	QUANTITY
ejpam-6951	277	2	x3	GPE
ejpam-6951	277	3	r+1 vertices︷ ︸︸	PERSON
ejpam-6951	277	4	yn−r+1	ORG
ejpam-6951	277	5	n−	NORP
ejpam-6951	277	6	w	ORG
ejpam-6951	277	7	∈	PRODUCT
ejpam-6951	277	8	9	CARDINAL
ejpam-6951	278	1	1	CARDINAL
ejpam-6951	278	2	2	DATE
ejpam-6951	278	3	3	DATE
ejpam-6951	278	4	r+1	ORG
ejpam-6951	278	5	n− r+2	ORG
ejpam-6951	280	1	g. d. sepillo et	PERSON
ejpam-6951	281	1	j. pure	PERSON
ejpam-6951	281	2	18	CARDINAL
ejpam-6951	281	3	4	CARDINAL
ejpam-6951	281	4	2025	CARDINAL
ejpam-6951	281	5	6951 13	DATE
ejpam-6951	281	6	23	CARDINAL
ejpam-6951	285	1	xm−1 xm	PERSON
ejpam-6951	286	1	n⟨w ⟩	PERSON
ejpam-6951	289	1	xm−1 xm	PERSON
ejpam-6951	294	1	xm−1 xm	PERSON
ejpam-6951	298	1	xm−1 xm	PERSON
ejpam-6951	299	1	9	CARDINAL
ejpam-6951	300	1	2	CARDINAL
ejpam-6951	300	2	kr	ORG
ejpam-6951	300	3	r+1	ORG
ejpam-6951	300	4	km,n	ORG
ejpam-6951	300	5	2	CARDINAL
ejpam-6951	301	1	kr	ORG
ejpam-6951	301	2	r+1	ORG
ejpam-6951	301	3	3.2	CARDINAL
ejpam-6951	302	1	vertex-generator	ORG
ejpam-6951	302	2	m. let tn	PERSON
ejpam-6951	303	1	x3	GPE
ejpam-6951	303	2	xn−1	GPE
ejpam-6951	304	1	10	CARDINAL
ejpam-6951	305	1	1	CARDINAL
ejpam-6951	307	1	g. d. sepillo et	PERSON
ejpam-6951	308	1	j. pure	PERSON
ejpam-6951	308	2	18	CARDINAL
ejpam-6951	308	3	4	CARDINAL
ejpam-6951	308	4	2025	CARDINAL
ejpam-6951	308	5	6951 14	DATE
ejpam-6951	308	6	23	CARDINAL
ejpam-6951	309	1	x3 x4 x5	PERSON
ejpam-6951	309	2	xn−2	GPE
ejpam-6951	310	1	10	CARDINAL
ejpam-6951	313	1	{ym−1}	PERSON
ejpam-6951	314	1	n+m	DATE
ejpam-6951	314	2	1	CARDINAL
ejpam-6951	314	3	2	CARDINAL
ejpam-6951	314	4	tn	ORG
ejpam-6951	314	5	tn	ORG
ejpam-6951	314	6	m. theorem 14	PERSON
ejpam-6951	315	1	3	CARDINAL
ejpam-6951	315	2	2	CARDINAL
ejpam-6951	316	1	1 ≤	CARDINAL
ejpam-6951	316	2	tn	ORG
ejpam-6951	316	3	m. proof	PERSON
ejpam-6951	318	1	1 ≤	QUANTITY
ejpam-6951	318	2	1 ≤	MONEY
ejpam-6951	318	3	t vertices︷ ︸︸	ORG
ejpam-6951	318	4	x3	GPE
ejpam-6951	318	5	x4	PERSON
ejpam-6951	318	6	xt+1	ORG
ejpam-6951	318	7	1 ≤	MONEY
ejpam-6951	319	1	1 ≤	QUANTITY
ejpam-6951	319	2	∈	ORG
ejpam-6951	319	3	11	CARDINAL
ejpam-6951	320	1	1	CARDINAL
ejpam-6951	320	2	2	DATE
ejpam-6951	320	3	3	DATE
ejpam-6951	321	1	a1 △a2 △a3 △ ·	PRODUCT
ejpam-6951	322	1	g. d. sepillo et	PERSON
ejpam-6951	323	1	j. pure	PERSON
ejpam-6951	323	2	18	CARDINAL
ejpam-6951	323	3	4	CARDINAL
ejpam-6951	323	4	2025	CARDINAL
ejpam-6951	323	5	6951 15	DATE
ejpam-6951	324	1	x3 x4 xt+1	PERSON
ejpam-6951	325	1	xn−2	GPE
ejpam-6951	325	2	xn−1	GPE
ejpam-6951	327	1	xn−2	GPE
ejpam-6951	328	1	11	CARDINAL
ejpam-6951	328	2	1 ≤ j ≤ m	QUANTITY
ejpam-6951	328	3	1 ≤	QUANTITY
ejpam-6951	329	1	1 ≤	QUANTITY
ejpam-6951	329	2	t vertices︷ ︸︸	ORG
ejpam-6951	330	1	x3	GPE
ejpam-6951	330	2	x4	PERSON
ejpam-6951	330	3	xt+1	GPE
ejpam-6951	330	4	1 ≤ j ≤ m.	QUANTITY
ejpam-6951	330	5	bq	ORG
ejpam-6951	330	6	12	CARDINAL
ejpam-6951	333	1	xn−2	GPE
ejpam-6951	333	2	xn−1	GPE
ejpam-6951	334	1	ym−1 ym	PERSON
ejpam-6951	335	1	x3 x4 xt+1	PERSON
ejpam-6951	336	1	xn−2	GPE
ejpam-6951	336	2	xn−1	GPE
ejpam-6951	337	1	12	CARDINAL
ejpam-6951	337	2	bq	ORG
ejpam-6951	337	3	j = 1	WORK_OF_ART
ejpam-6951	337	4	2	DATE
ejpam-6951	337	5	3	DATE
ejpam-6951	338	1	g. d. sepillo et	PERSON
ejpam-6951	339	1	j. pure	PERSON
ejpam-6951	339	2	18	CARDINAL
ejpam-6951	339	3	4	CARDINAL
ejpam-6951	339	4	2025	CARDINAL
ejpam-6951	339	5	6951 16	DATE
ejpam-6951	339	6	23	CARDINAL
ejpam-6951	339	7	x3	GPE
ejpam-6951	339	8	x4	PERSON
ejpam-6951	339	9	xt+1	ORG
ejpam-6951	339	10	x3	GPE
ejpam-6951	339	11	x4	PERSON
ejpam-6951	339	12	xt+1	GPE
ejpam-6951	340	1	1	CARDINAL
ejpam-6951	340	2	tn	ORG
ejpam-6951	340	3	tn	ORG
ejpam-6951	340	4	m. theorem 15	PERSON
ejpam-6951	341	1	4	CARDINAL
ejpam-6951	341	2	3	CARDINAL
ejpam-6951	342	1	2t−	CARDINAL
ejpam-6951	342	2	2 ≤	QUANTITY
ejpam-6951	342	3	kt	ORG
ejpam-6951	342	4	tn	ORG
ejpam-6951	342	5	m. proof	PERSON
ejpam-6951	343	1	2 ≤	QUANTITY
ejpam-6951	344	1	1 ≤	QUANTITY
ejpam-6951	344	2	1 ≤	MONEY
ejpam-6951	344	3	1	CARDINAL
ejpam-6951	345	1	t−1 vertices︷ ︸︸	ORG
ejpam-6951	346	1	x4	PERSON
ejpam-6951	346	2	x2t−2	PERSON
ejpam-6951	346	3	1 ≤	MONEY
ejpam-6951	346	4	1	CARDINAL
ejpam-6951	347	1	1 ≤	QUANTITY
ejpam-6951	347	2	∈	ORG
ejpam-6951	347	3	13	CARDINAL
ejpam-6951	352	1	xn−1	GPE
ejpam-6951	354	1	x2 x3 x4x5	PERSON
ejpam-6951	355	1	xn−1	GPE
ejpam-6951	356	1	13	CARDINAL
ejpam-6951	356	2	1	CARDINAL
ejpam-6951	356	3	2	DATE
ejpam-6951	356	4	3	DATE
ejpam-6951	358	1	j. pure	PERSON
ejpam-6951	358	2	18	CARDINAL
ejpam-6951	358	3	4	CARDINAL
ejpam-6951	358	4	2025	CARDINAL
ejpam-6951	358	5	6951 17	DATE
ejpam-6951	358	6	23	CARDINAL
ejpam-6951	358	7	a1 △a2 △a3 △ ·	PRODUCT
ejpam-6951	359	1	△at−1)	PERSON
ejpam-6951	360	1	1 ≤ j ≤ m	QUANTITY
ejpam-6951	360	2	1 ≤	QUANTITY
ejpam-6951	360	3	1	CARDINAL
ejpam-6951	360	4	t−1 vertices︷ ︸︸	ORG
ejpam-6951	361	1	1 ≤	QUANTITY
ejpam-6951	361	2	1	CARDINAL
ejpam-6951	361	3	t−1 vertices︷ ︸︸	ORG
ejpam-6951	362	1	x4	PERSON
ejpam-6951	362	2	x2t−2	PERSON
ejpam-6951	362	3	1 ≤ j ≤ m.	QUANTITY
ejpam-6951	362	4	bq	ORG
ejpam-6951	362	5	∈	ORG
ejpam-6951	362	6	14	CARDINAL
ejpam-6951	367	1	xn−1	GPE
ejpam-6951	373	1	xn−1	GPE
ejpam-6951	374	1	m⟨b⟩	ORG
ejpam-6951	374	2	14	CARDINAL
ejpam-6951	374	3	j = 1	WORK_OF_ART
ejpam-6951	374	4	2	DATE
ejpam-6951	374	5	3	DATE
ejpam-6951	374	6	q=1 bq	PERSON
ejpam-6951	375	1	x4	PERSON
ejpam-6951	375	2	x4	PERSON
ejpam-6951	375	3	x2t−2	PERSON
ejpam-6951	376	1	1	CARDINAL
ejpam-6951	376	2	kt	ORG
ejpam-6951	376	3	tn	ORG
ejpam-6951	376	4	m. g. d.	PERSON
ejpam-6951	377	1	j. pure	PERSON
ejpam-6951	377	2	18	CARDINAL
ejpam-6951	377	3	4	CARDINAL
ejpam-6951	377	4	2025	CARDINAL
ejpam-6951	377	5	6951 18	DATE
ejpam-6951	377	6	23	CARDINAL
ejpam-6951	377	7	tn	ORG
ejpam-6951	377	8	m. theorem 16	PERSON
ejpam-6951	379	1	3k ≤	QUANTITY
ejpam-6951	379	2	tn	ORG
ejpam-6951	379	3	m. proof	PERSON
ejpam-6951	380	1	3k ≤	QUANTITY
ejpam-6951	381	1	1 ≤	QUANTITY
ejpam-6951	381	2	1 ≤	MONEY
ejpam-6951	382	1	p2︷ ︸︸	ORG
ejpam-6951	382	2	x3	GPE
ejpam-6951	382	3	x3k−1	GPE
ejpam-6951	382	4	1 ≤	MONEY
ejpam-6951	382	5	y3p−1	ORG
ejpam-6951	382	6	{y3p	PERSON
ejpam-6951	382	7	1 ≤	MONEY
ejpam-6951	382	8	p2︷ ︸︸	ORG
ejpam-6951	383	1	1 ≤	QUANTITY
ejpam-6951	383	2	a2p−1	ORG
ejpam-6951	383	3	∈	ORG
ejpam-6951	383	4	15	CARDINAL
ejpam-6951	384	1	1	CARDINAL
ejpam-6951	384	2	2	DATE
ejpam-6951	384	3	3	DATE
ejpam-6951	388	1	a1 △a2 △a3 △a4	PRODUCT
ejpam-6951	389	1	1 ≤ j ≤ m	QUANTITY
ejpam-6951	389	2	1 ≤	QUANTITY
ejpam-6951	390	1	p2︷ ︸︸	ORG
ejpam-6951	391	1	1 ≤	QUANTITY
ejpam-6951	391	2	1 ≤	QUANTITY
ejpam-6951	391	3	p2︷ ︸︸	ORG
ejpam-6951	392	1	x3	GPE
ejpam-6951	393	1	x3k−1	GPE
ejpam-6951	393	2	1 ≤ j ≤ m.	QUANTITY
ejpam-6951	393	3	16	CARDINAL
ejpam-6951	394	1	g. d. sepillo et	PERSON
ejpam-6951	395	1	j. pure	PERSON
ejpam-6951	395	2	18	CARDINAL
ejpam-6951	395	3	4	CARDINAL
ejpam-6951	395	4	2025	CARDINAL
ejpam-6951	395	5	6951 19	DATE
ejpam-6951	395	6	23	CARDINAL
ejpam-6951	399	1	xn−1	GPE
ejpam-6951	400	1	x2 x3 x4x5	PERSON
ejpam-6951	403	1	xn−1	GPE
ejpam-6951	406	1	xn−1	GPE
ejpam-6951	407	1	15	CARDINAL
ejpam-6951	407	2	j = 1	WORK_OF_ART
ejpam-6951	407	3	2	DATE
ejpam-6951	407	4	3	DATE
ejpam-6951	407	5	q=1	PERSON
ejpam-6951	410	1	+b2k	PERSON
ejpam-6951	411	1	+b2k	PERSON
ejpam-6951	412	1	x3	GPE
ejpam-6951	412	2	x3k−1	GPE
ejpam-6951	412	3	x3	GPE
ejpam-6951	412	4	x3k−1	GPE
ejpam-6951	413	1	1	CARDINAL
ejpam-6951	413	2	tn	ORG
ejpam-6951	413	3	tn	ORG
ejpam-6951	413	4	m. theorem 17	PERSON
ejpam-6951	414	1	3	CARDINAL
ejpam-6951	415	1	2t+1 ≤	MONEY
ejpam-6951	415	2	tn	ORG
ejpam-6951	415	3	m. g. d.	PERSON
ejpam-6951	417	1	j. pure	PERSON
ejpam-6951	417	2	18	CARDINAL
ejpam-6951	417	3	4	CARDINAL
ejpam-6951	417	4	2025	CARDINAL
ejpam-6951	417	5	6951 20	DATE
ejpam-6951	421	1	xn−1	GPE
ejpam-6951	425	1	xn−1	GPE
ejpam-6951	426	1	m⟨b2q⟩	ORG
ejpam-6951	427	1	x2 x3 x4x5	PERSON
ejpam-6951	428	1	xn−1	GPE
ejpam-6951	429	1	m⟨b⟩	ORG
ejpam-6951	429	2	16	CARDINAL
ejpam-6951	430	1	1 ≤	QUANTITY
ejpam-6951	431	1	1 ≤	QUANTITY
ejpam-6951	431	2	1 ≤	MONEY
ejpam-6951	431	3	p2︷ ︸︸	ORG
ejpam-6951	431	4	x3	GPE
ejpam-6951	432	1	x2t+1	GPE
ejpam-6951	432	2	1 ≤	MONEY
ejpam-6951	433	1	y2t+1	GPE
ejpam-6951	433	2	1 ≤	QUANTITY
ejpam-6951	433	3	∈	ORG
ejpam-6951	433	4	17	CARDINAL
ejpam-6951	434	1	1	CARDINAL
ejpam-6951	434	2	2	DATE
ejpam-6951	434	3	3	DATE
ejpam-6951	434	4	a1 + t∑ p=1 ap+1	PRODUCT
ejpam-6951	435	1	+at+1	PERSON
ejpam-6951	436	1	+at+1	PERSON
ejpam-6951	437	1	a1 △a2 △a3 △a4	PRODUCT
ejpam-6951	438	1	j. pure	PERSON
ejpam-6951	438	2	18	CARDINAL
ejpam-6951	438	3	4	CARDINAL
ejpam-6951	438	4	2025	CARDINAL
ejpam-6951	438	5	6951 21	DATE
ejpam-6951	438	6	23	CARDINAL
ejpam-6951	441	1	xn−1	GPE
ejpam-6951	443	1	y2t+1	GPE
ejpam-6951	444	1	ym−1 ym tn	PERSON
ejpam-6951	449	1	xn−1	GPE
ejpam-6951	451	1	y2t+1	GPE
ejpam-6951	452	1	ym−1 ym tn	PERSON
ejpam-6951	452	2	m⟨ap+1⟩	PERSON
ejpam-6951	452	3	x2 x3 x4x5	PERSON
ejpam-6951	453	1	xn−1	GPE
ejpam-6951	455	1	y2t+1	GPE
ejpam-6951	456	1	ym−1 ym tn	PERSON
ejpam-6951	456	2	17	CARDINAL
ejpam-6951	456	3	y2t+1	GPE
ejpam-6951	457	1	1 ≤ j ≤ m	QUANTITY
ejpam-6951	457	2	1 ≤	QUANTITY
ejpam-6951	458	1	y2t+1	GPE
ejpam-6951	458	2	1 ≤	QUANTITY
ejpam-6951	458	3	p2︷ ︸︸	ORG
ejpam-6951	458	4	x3	GPE
ejpam-6951	458	5	x2t+1	GPE
ejpam-6951	458	6	1 ≤ j ≤ m.	QUANTITY
ejpam-6951	458	7	∈	ORG
ejpam-6951	458	8	18	CARDINAL
ejpam-6951	459	1	j = 1	WORK_OF_ART
ejpam-6951	459	2	2	DATE
ejpam-6951	459	3	3	DATE
ejpam-6951	460	1	+bt+1	PERSON
ejpam-6951	461	1	g. d. sepillo et	PERSON
ejpam-6951	462	1	j. pure	PERSON
ejpam-6951	462	2	18	CARDINAL
ejpam-6951	462	3	4	CARDINAL
ejpam-6951	462	4	2025	CARDINAL
ejpam-6951	462	5	6951 22	DATE
ejpam-6951	462	6	23	CARDINAL
ejpam-6951	465	1	xn−1	GPE
ejpam-6951	467	1	y2t+1	GPE
ejpam-6951	468	1	ym−1 ym tn	PERSON
ejpam-6951	473	1	xn−1	GPE
ejpam-6951	475	1	y2t+1	GPE
ejpam-6951	476	1	ym−1 ym tn	PERSON
ejpam-6951	481	1	xn−1	GPE
ejpam-6951	482	1	m⟨b⟩	ORG
ejpam-6951	482	2	18	CARDINAL
ejpam-6951	482	3	+bt+1	PERSON
ejpam-6951	483	1	△bt+1)	ORG
ejpam-6951	483	2	x3	GPE
ejpam-6951	483	3	x5	GPE
ejpam-6951	483	4	x2t+1	GPE
ejpam-6951	483	5	x3	GPE
ejpam-6951	483	6	x5	GPE
ejpam-6951	483	7	x2t+1	GPE
ejpam-6951	484	1	1	CARDINAL
ejpam-6951	484	2	kt	ORG
ejpam-6951	484	3	tn	ORG
ejpam-6951	484	4	m. 4	PERSON
ejpam-6951	485	1	km,n	ORG
ejpam-6951	485	2	bipartite	NORP
ejpam-6951	485	3	graph kr	PERSON
ejpam-6951	487	1	km,n	ORG
ejpam-6951	487	2	tn	GPE
ejpam-6951	487	3	two	CARDINAL
ejpam-6951	488	1	g. d. sepillo et	PERSON
ejpam-6951	489	1	j. pure	PERSON
ejpam-6951	489	2	18	CARDINAL
ejpam-6951	489	3	4	CARDINAL
ejpam-6951	489	4	2025	CARDINAL
ejpam-6951	489	5	6951 23	DATE
ejpam-6951	489	6	23	CARDINAL
ejpam-6951	489	7	the batangas state university	ORG
ejpam-6951	489	8	the national engineering university	ORG
ejpam-6951	489	9	neu	PERSON
ejpam-6951	490	1	first	ORDINAL
ejpam-6951	492	1	1	CARDINAL
ejpam-6951	492	2	r. diestel	PERSON
ejpam-6951	493	1	173	CARDINAL
ejpam-6951	494	1	springerverlag	PERSON
ejpam-6951	494	2	new york	GPE
ejpam-6951	494	3	second	ORDINAL
ejpam-6951	494	4	2000	DATE
ejpam-6951	495	1	2	CARDINAL
ejpam-6951	495	2	s. butenko	PERSON
ejpam-6951	495	3	p. festa	PERSON
ejpam-6951	497	1	109:69–82, 2001	DATE
ejpam-6951	498	1	3	CARDINAL
ejpam-6951	498	2	j. torino	PERSON
ejpam-6951	498	3	n. mame	PERSON
ejpam-6951	499	1	asian	NORP
ejpam-6951	499	2	chiang mai,	GPE
ejpam-6951	499	3	thailand	GPE
ejpam-6951	499	4	august 3-7, 2025	DATE
ejpam-6951	500	1	4	CARDINAL
ejpam-6951	500	2	n. mame	PERSON
ejpam-6951	500	3	s. gervacio	PERSON
ejpam-6951	502	1	8(1):17–27	CARDINAL
ejpam-6951	502	2	2020	DATE
ejpam-6951	503	1	5	CARDINAL
ejpam-6951	503	2	r. mame	PERSON
ejpam-6951	505	1	17(4):3815–3825	DATE
ejpam-6951	505	2	2024	DATE
ejpam-6951	506	1	6	CARDINAL
ejpam-6951	506	2	f. harary	PERSON
ejpam-6951	508	1	addison-wesley	PERSON
ejpam-6951	509	1	addison-wesley publishing company, inc.	ORG
ejpam-6951	509	2	new york	GPE
ejpam-6951	509	3	1969	DATE
ejpam-6951	510	1	7	CARDINAL
ejpam-6951	510	2	h. komarullah	PERSON
ejpam-6951	510	3	j. halilim	PERSON
ejpam-6951	510	4	k. santoso	PERSON
ejpam-6951	512	1	41	CARDINAL
ejpam-6951	512	2	2021	DATE
ejpam-6951	513	1	8	CARDINAL
ejpam-6951	515	1	73	CARDINAL
ejpam-6951	515	2	cambridge	GPE
ejpam-6951	516	1	cambridge university press	ORG
ejpam-6951	516	2	new york	GPE
ejpam-6951	516	3	second	ORDINAL
ejpam-6951	516	4	2001	DATE
ejpam-6951	517	1	9	CARDINAL
ejpam-6951	517	2	j. a. bondy	PERSON
ejpam-6951	517	3	u. s. r. murty	PERSON
ejpam-6951	518	1	244	CARDINAL
ejpam-6951	519	1	london	GPE
ejpam-6951	519	2	first	ORDINAL
ejpam-6951	519	3	2008	DATE
ejpam-6951	520	1	10	CARDINAL
ejpam-6951	520	2	g. chartrand	PERSON
ejpam-6951	520	3	l. d. lesniak	PERSON
ejpam-6951	520	4	p. zhang	PERSON
ejpam-6951	521	1	39	CARDINAL
ejpam-6951	522	1	crc press	ORG
ejpam-6951	522	2	taylor & francis group	ORG
ejpam-6951	522	3	boca raton	GPE
ejpam-6951	522	4	sixth	ORDINAL
ejpam-6951	522	5	2016	DATE
ejpam-6951	523	1	11	CARDINAL
ejpam-6951	525	1	john wiley & sons, inc.	ORG
ejpam-6951	525	2	new york	GPE
ejpam-6951	525	3	second	ORDINAL
ejpam-6951	525	4	1970	DATE
ejpam-6951	526	1	12	CARDINAL
ejpam-6951	526	2	r. larson	PERSON
ejpam-6951	526	3	d. c. falvo	PERSON
ejpam-6951	527	1	179–230	CARDINAL
ejpam-6951	528	1	houghton mifflin harcourt publishing company	ORG
ejpam-6951	528	2	boston	GPE
ejpam-6951	528	3	sixth	ORDINAL
ejpam-6951	528	4	2009	DATE