id	sid	eid	entity	type
ejpam-6040	1	1	european journal	ORG
ejpam-6040	1	2	2025	DATE
ejpam-6040	1	3	18	CARDINAL
ejpam-6040	1	4	2	CARDINAL
ejpam-6040	1	5	6040	CARDINAL
ejpam-6040	1	6	new york	GPE
ejpam-6040	1	7	sergio r. canoy	PERSON
ejpam-6040	1	8	jesica m. anoche1,2,∗	PERSON
ejpam-6040	1	9	1	CARDINAL
ejpam-6040	1	10	msu-iligan institute of technology	ORG
ejpam-6040	1	11	9200	CARDINAL
ejpam-6040	1	12	iligan city	GPE
ejpam-6040	1	13	2	CARDINAL
ejpam-6040	1	14	msu-iligan institute of technology	ORG
ejpam-6040	1	15	9200	CARDINAL
ejpam-6040	1	16	iligan city	GPE
ejpam-6040	1	17	philippines	GPE
ejpam-6040	5	1	at least one	CARDINAL
ejpam-6040	5	2	two	CARDINAL
ejpam-6040	5	3	s.	GPE
ejpam-6040	5	4	k	PERSON
ejpam-6040	5	5	k ≤	ORG
ejpam-6040	8	1	⊆	CARDINAL
ejpam-6040	11	1	2020	DATE
ejpam-6040	11	2	05c69	CARDINAL
ejpam-6040	11	3	1	CARDINAL
ejpam-6040	12	1	1	CARDINAL
ejpam-6040	12	2	2	CARDINAL
ejpam-6040	13	1	at least one	CARDINAL
ejpam-6040	13	2	s.	GPE
ejpam-6040	13	3	das et al	PERSON
ejpam-6040	14	1	3	CARDINAL
ejpam-6040	15	1	sergio.canoy@g.msuiit.edu.ph	ORG
ejpam-6040	15	2	s. canoy, jr.	PERSON
ejpam-6040	16	1	jesica.anoche@g.msuiit.edu.ph	PERSON
ejpam-6040	16	2	j. anoche	PERSON
ejpam-6040	17	1	1	CARDINAL
ejpam-6040	17	2	2025	CARDINAL
ejpam-6040	18	1	s. canoy, jr.	PERSON
ejpam-6040	18	2	j. anoche	PERSON
ejpam-6040	19	1	j. pure	PERSON
ejpam-6040	19	2	18	CARDINAL
ejpam-6040	19	3	2	CARDINAL
ejpam-6040	19	4	2025	CARDINAL
ejpam-6040	19	5	6040 2	CARDINAL
ejpam-6040	19	6	16	CARDINAL
ejpam-6040	21	1	two	CARDINAL
ejpam-6040	23	1	8–12	CARDINAL
ejpam-6040	25	1	13	CARDINAL
ejpam-6040	26	1	14	CARDINAL
ejpam-6040	26	2	15	CARDINAL
ejpam-6040	26	3	16	CARDINAL
ejpam-6040	26	4	17	CARDINAL
ejpam-6040	26	5	18	CARDINAL
ejpam-6040	26	6	19	CARDINAL
ejpam-6040	27	1	at least one	CARDINAL
ejpam-6040	27	2	two	CARDINAL
ejpam-6040	31	1	two	CARDINAL
ejpam-6040	35	1	unevaluated	ORG
ejpam-6040	37	1	2	CARDINAL
ejpam-6040	37	2	two	CARDINAL
ejpam-6040	38	1	two	CARDINAL
ejpam-6040	38	2	two	CARDINAL
ejpam-6040	38	3	∈	ORG
ejpam-6040	40	1	⊆	CARDINAL
ejpam-6040	40	2	⋃	PERSON
ejpam-6040	40	3	0	CARDINAL
ejpam-6040	41	1	i(g	PERSON
ejpam-6040	42	1	⊆	CARDINAL
ejpam-6040	42	2	s. canoy, jr.	PERSON
ejpam-6040	42	3	j. anoche	PERSON
ejpam-6040	43	1	j. pure	PERSON
ejpam-6040	43	2	18	CARDINAL
ejpam-6040	43	3	2	CARDINAL
ejpam-6040	43	4	2025	CARDINAL
ejpam-6040	43	5	6040 3	CARDINAL
ejpam-6040	43	6	16	CARDINAL
ejpam-6040	43	7	∈	ORG
ejpam-6040	43	8	∈	ORG
ejpam-6040	44	1	⊆	CARDINAL
ejpam-6040	45	1	γ(g	NORP
ejpam-6040	45	2	two	CARDINAL
ejpam-6040	47	1	⊆	CARDINAL
ejpam-6040	47	2	ig[u	ORG
ejpam-6040	49	1	g(g	PERSON
ejpam-6040	49	2	g(g	PERSON
ejpam-6040	49	3	⊆	CARDINAL
ejpam-6040	51	1	1 ≤	QUANTITY
ejpam-6040	53	1	⊆	CARDINAL
ejpam-6040	55	1	ζgk(g	PERSON
ejpam-6040	55	2	⊆	CARDINAL
ejpam-6040	56	1	⊆	CARDINAL
ejpam-6040	56	2	− k	PERSON
ejpam-6040	57	1	〈 ng g[s	PERSON
ejpam-6040	57	2	ng g[s	ORG
ejpam-6040	57	3	− k.	PERSON
ejpam-6040	57	4	1	CARDINAL
ejpam-6040	59	1	4	CARDINAL
ejpam-6040	60	1	1	CARDINAL
ejpam-6040	60	2	7	CARDINAL
ejpam-6040	60	3	1	CARDINAL
ejpam-6040	62	1	ζg1	PERSON
ejpam-6040	63	1	8	CARDINAL
ejpam-6040	63	2	6	CARDINAL
ejpam-6040	63	3	2	CARDINAL
ejpam-6040	64	1	2	CARDINAL
ejpam-6040	67	1	8	CARDINAL
ejpam-6040	67	2	6	CARDINAL
ejpam-6040	67	3	2	CARDINAL
ejpam-6040	68	1	3	CARDINAL
ejpam-6040	68	2	1	CARDINAL
ejpam-6040	68	3	1	CARDINAL
ejpam-6040	68	4	7	CARDINAL
ejpam-6040	74	1	1	CARDINAL
ejpam-6040	74	2	4	CARDINAL
ejpam-6040	74	3	1	CARDINAL
ejpam-6040	74	4	2	CARDINAL
ejpam-6040	74	5	7	CARDINAL
ejpam-6040	74	6	s. canoy, jr.	PERSON
ejpam-6040	74	7	j. anoche	PERSON
ejpam-6040	75	1	j. pure	PERSON
ejpam-6040	75	2	18	CARDINAL
ejpam-6040	75	3	2	CARDINAL
ejpam-6040	75	4	2025	CARDINAL
ejpam-6040	75	5	6040 4	CARDINAL
ejpam-6040	76	1	1	CARDINAL
ejpam-6040	76	2	20	CARDINAL
ejpam-6040	80	1	γg(k1,n−1	ORG
ejpam-6040	80	2	1	CARDINAL
ejpam-6040	80	3	bipartite	NORP
ejpam-6040	80	4	graph km	PERSON
ejpam-6040	80	5	4	CARDINAL
ejpam-6040	82	1	2	CARDINAL
ejpam-6040	82	2	n ≥ 5	DATE
ejpam-6040	84	1	n ≥ 6	DATE
ejpam-6040	85	1	vi	PERSON
ejpam-6040	87	1	3 ⌉.	QUANTITY
ejpam-6040	88	1	4	CARDINAL
ejpam-6040	88	2	1	CARDINAL
ejpam-6040	89	1	g1	ORG
ejpam-6040	93	1	aj ⊆	PERSON
ejpam-6040	94	1	1	CARDINAL
ejpam-6040	94	2	2	DATE
ejpam-6040	95	1	2	CARDINAL
ejpam-6040	95	2	g1	ORG
ejpam-6040	95	3	1	CARDINAL
ejpam-6040	96	1	1	CARDINAL
ejpam-6040	96	2	2	DATE
ejpam-6040	102	1	1(i	CARDINAL
ejpam-6040	106	1	|di| =	GPE
ejpam-6040	107	1	1	CARDINAL
ejpam-6040	110	1	j ∈	PERSON
ejpam-6040	117	1	1	CARDINAL
ejpam-6040	120	1	s. canoy, jr.	PERSON
ejpam-6040	120	2	j. anoche	PERSON
ejpam-6040	121	1	j. pure	PERSON
ejpam-6040	121	2	18	CARDINAL
ejpam-6040	121	3	2	CARDINAL
ejpam-6040	121	4	2025	CARDINAL
ejpam-6040	121	5	6040 5	CARDINAL
ejpam-6040	121	6	16	CARDINAL
ejpam-6040	123	1	1	CARDINAL
ejpam-6040	123	2	⊆	CARDINAL
ejpam-6040	123	3	1	CARDINAL
ejpam-6040	124	1	⊆	CARDINAL
ejpam-6040	126	1	γg(g)−1	ORG
ejpam-6040	126	2	at least one	CARDINAL
ejpam-6040	126	3	1(i	CARDINAL
ejpam-6040	128	1	1	CARDINAL
ejpam-6040	130	1	i=1	PERSON
ejpam-6040	134	1	3	CARDINAL
ejpam-6040	135	1	i(g	PERSON
ejpam-6040	136	1	ζgj	GPE
ejpam-6040	137	1	1	CARDINAL
ejpam-6040	137	2	2	DATE
ejpam-6040	137	3	r+ζgk−r(g ′	ORG
ejpam-6040	137	4	r+1	ORG
ejpam-6040	137	5	γg(g)−1}	GPE
ejpam-6040	137	6	g′	PERSON
ejpam-6040	138	1	i(g	PERSON
ejpam-6040	140	1	⊆	CARDINAL
ejpam-6040	142	1	v2	PERSON
ejpam-6040	142	2	− j. hence	PERSON
ejpam-6040	144	1	k ∈	PERSON
ejpam-6040	144	2	r+1	ORG
ejpam-6040	144	3	γg(g)−1}	GPE
ejpam-6040	145	1	ing′	CARDINAL
ejpam-6040	145	2	⟨v	DATE
ejpam-6040	147	1	k ≤ γg(g)−1	FAC
ejpam-6040	149	1	|s′|	GPE
ejpam-6040	150	1	ζgk−r(g ′	ORG
ejpam-6040	155	1	4	CARDINAL
ejpam-6040	156	1	1	CARDINAL
ejpam-6040	156	2	1 ≤ ζgk(g	QUANTITY
ejpam-6040	156	3	1	CARDINAL
ejpam-6040	159	1	− k. hence	PERSON
ejpam-6040	159	2	1	CARDINAL
ejpam-6040	160	1	1	CARDINAL
ejpam-6040	162	1	5	CARDINAL
ejpam-6040	164	1	1	CARDINAL
ejpam-6040	164	2	∈	ORG
ejpam-6040	164	3	1	CARDINAL
ejpam-6040	166	1	1	CARDINAL
ejpam-6040	167	1	1	CARDINAL
ejpam-6040	167	2	∈	ORG
ejpam-6040	170	1	〈 ng g[s	PERSON
ejpam-6040	170	2	1	CARDINAL
ejpam-6040	171	1	⊆	CARDINAL
ejpam-6040	171	2	γg(g)−1 andng g[d	ORG
ejpam-6040	173	1	1	CARDINAL
ejpam-6040	174	1	1	CARDINAL
ejpam-6040	174	2	s. canoy, jr.	PERSON
ejpam-6040	174	3	j. anoche	PERSON
ejpam-6040	175	1	j. pure	PERSON
ejpam-6040	175	2	18	CARDINAL
ejpam-6040	175	3	2	CARDINAL
ejpam-6040	175	4	2025	CARDINAL
ejpam-6040	175	5	6040 6	CARDINAL
ejpam-6040	175	6	16	CARDINAL
ejpam-6040	175	7	1	CARDINAL
ejpam-6040	178	1	1	CARDINAL
ejpam-6040	178	2	1	CARDINAL
ejpam-6040	180	1	1	CARDINAL
ejpam-6040	181	1	2	CARDINAL
ejpam-6040	182	1	⊆	CARDINAL
ejpam-6040	186	1	= s.	PERSON
ejpam-6040	187	1	6	CARDINAL
ejpam-6040	188	1	kn	PERSON
ejpam-6040	188	2	n ≥ 2	ORG
ejpam-6040	188	3	1 ≤ k ≤ n	QUANTITY
ejpam-6040	189	1	k. proof	PERSON
ejpam-6040	190	1	k ≤ γg(kn)−	ORG
ejpam-6040	191	1	1	CARDINAL
ejpam-6040	192	1	kn	PERSON
ejpam-6040	194	1	lemma 2	ORG
ejpam-6040	198	1	2	CARDINAL
ejpam-6040	199	1	k ≤ γg(g)− 1,	ORG
ejpam-6040	200	1	⊆	CARDINAL
ejpam-6040	201	1	2	CARDINAL
ejpam-6040	202	1	k ≤ γg(g)− 1.	ORG
ejpam-6040	203	1	2	CARDINAL
ejpam-6040	205	1	3	CARDINAL
ejpam-6040	205	2	1	CARDINAL
ejpam-6040	206	1	ng g[s ′	ORG
ejpam-6040	207	1	6	CARDINAL
ejpam-6040	207	2	4	CARDINAL
ejpam-6040	207	3	2	CARDINAL
ejpam-6040	207	4	1	CARDINAL
ejpam-6040	208	1	dg(b	DATE
ejpam-6040	208	2	3	CARDINAL
ejpam-6040	208	3	0	CARDINAL
ejpam-6040	210	1	2	CARDINAL
ejpam-6040	210	2	g. s. canoy, jr.	PERSON
ejpam-6040	210	3	j. anoche	PERSON
ejpam-6040	211	1	j. pure	PERSON
ejpam-6040	211	2	18	CARDINAL
ejpam-6040	211	3	2	CARDINAL
ejpam-6040	211	4	2025	CARDINAL
ejpam-6040	211	5	6040 7	CARDINAL
ejpam-6040	211	6	16	CARDINAL
ejpam-6040	216	1	2	CARDINAL
ejpam-6040	216	2	3	CARDINAL
ejpam-6040	216	3	1	CARDINAL
ejpam-6040	216	4	5	CARDINAL
ejpam-6040	217	1	⊆	CARDINAL
ejpam-6040	218	1	⊆ ng g[s	QUANTITY
ejpam-6040	219	1	2	CARDINAL
ejpam-6040	220	1	2	CARDINAL
ejpam-6040	220	2	k ≤ γg(g)− 1,	ORG
ejpam-6040	224	1	i2g(s	ORG
ejpam-6040	224	2	⊆ ng g[s	QUANTITY
ejpam-6040	225	1	⊆ ng g[s	QUANTITY
ejpam-6040	226	1	2	CARDINAL
ejpam-6040	228	1	∈	ORG
ejpam-6040	228	2	∈	ORG
ejpam-6040	229	1	∈	ORG
ejpam-6040	230	1	2	CARDINAL
ejpam-6040	230	2	2	CARDINAL
ejpam-6040	231	1	⊆	CARDINAL
ejpam-6040	236	1	ζgk(s ′	ORG
ejpam-6040	245	1	8	CARDINAL
ejpam-6040	246	1	k ≤ γg(g)− 1.	ORG
ejpam-6040	249	1	2(g	CARDINAL
ejpam-6040	249	2	1	CARDINAL
ejpam-6040	249	3	1 ≤ diam(g	QUANTITY
ejpam-6040	251	1	k ≤ γg(g)−1	ORG
ejpam-6040	251	2	2(g	CARDINAL
ejpam-6040	253	1	7(i	CARDINAL
ejpam-6040	253	2	⊆ ng g[s	QUANTITY
ejpam-6040	255	1	|i2g(s)|	NORP
ejpam-6040	257	1	2(g	CARDINAL
ejpam-6040	258	1	k = γg(g)−1.	PERSON
ejpam-6040	259	1	1	CARDINAL
ejpam-6040	260	1	2	CARDINAL
ejpam-6040	260	2	0	CARDINAL
ejpam-6040	261	1	1	CARDINAL
ejpam-6040	263	1	2(g	CARDINAL
ejpam-6040	264	1	1 ≤ diam(g) ≤ 2	QUANTITY
ejpam-6040	264	2	1	CARDINAL
ejpam-6040	265	1	s. canoy, jr.	PERSON
ejpam-6040	265	2	j. anoche	PERSON
ejpam-6040	266	1	j. pure	PERSON
ejpam-6040	266	2	18	CARDINAL
ejpam-6040	266	3	2	CARDINAL
ejpam-6040	266	4	2025	CARDINAL
ejpam-6040	266	5	6040 8	CARDINAL
ejpam-6040	266	6	0	CARDINAL
ejpam-6040	268	1	0	CARDINAL
ejpam-6040	269	1	ng g[s	PERSON
ejpam-6040	269	2	lemma 2	ORG
ejpam-6040	274	1	2	CARDINAL
ejpam-6040	274	2	7(ii	CARDINAL
ejpam-6040	282	1	2(g	CARDINAL
ejpam-6040	284	1	3	CARDINAL
ejpam-6040	284	2	8	CARDINAL
ejpam-6040	285	1	3	CARDINAL
ejpam-6040	285	2	1(vi	CARDINAL
ejpam-6040	286	1	4	CARDINAL
ejpam-6040	287	1	1	CARDINAL
ejpam-6040	288	1	3	CARDINAL
ejpam-6040	288	2	ng h	ORG
ejpam-6040	290	1	1	CARDINAL
ejpam-6040	291	1	2	CARDINAL
ejpam-6040	291	2	1	CARDINAL
ejpam-6040	293	1	2	CARDINAL
ejpam-6040	293	2	ng h	ORG
ejpam-6040	295	1	2(h	CARDINAL
ejpam-6040	295	2	1	CARDINAL
ejpam-6040	296	1	ζg2 (h	ORG
ejpam-6040	296	2	4	CARDINAL
ejpam-6040	297	1	+ 2−	DATE
ejpam-6040	303	1	v1 v2 v3 v4 v5 v6	PERSON
ejpam-6040	303	2	3	CARDINAL
ejpam-6040	304	1	4	CARDINAL
ejpam-6040	304	2	1	CARDINAL
ejpam-6040	304	3	k1,n, ζgk(k1,n	ORG
ejpam-6040	304	4	1 k	QUANTITY
ejpam-6040	304	5	1	CARDINAL
ejpam-6040	307	1	k ≤ n−	ORG
ejpam-6040	307	2	1	CARDINAL
ejpam-6040	308	1	k = n−	PERSON
ejpam-6040	308	2	1	CARDINAL
ejpam-6040	308	3	1	CARDINAL
ejpam-6040	309	1	1	CARDINAL
ejpam-6040	309	2	1	CARDINAL
ejpam-6040	311	1	k1,n	ORG
ejpam-6040	311	2	2(k1,n	CARDINAL
ejpam-6040	311	3	1	CARDINAL
ejpam-6040	311	4	1− n+	TIME
ejpam-6040	313	1	8	CARDINAL
ejpam-6040	313	2	2	CARDINAL
ejpam-6040	314	1	n ≥ 5	DATE
ejpam-6040	316	1	1	CARDINAL
ejpam-6040	316	2	1 2k	CARDINAL
ejpam-6040	317	1	s. canoy, jr.	PERSON
ejpam-6040	317	2	j. anoche	PERSON
ejpam-6040	318	1	j. pure	PERSON
ejpam-6040	318	2	18	CARDINAL
ejpam-6040	318	3	2	CARDINAL
ejpam-6040	318	4	2025	CARDINAL
ejpam-6040	318	5	6040 9	CARDINAL
ejpam-6040	318	6	16	CARDINAL
ejpam-6040	319	1	1	CARDINAL
ejpam-6040	319	2	1(iv	CARDINAL
ejpam-6040	320	1	2	CARDINAL
ejpam-6040	320	2	2	CARDINAL
ejpam-6040	320	3	1	CARDINAL
ejpam-6040	321	1	1 ≤	QUANTITY
ejpam-6040	322	1	2	CARDINAL
ejpam-6040	324	1	2	CARDINAL
ejpam-6040	325	1	2	CARDINAL
ejpam-6040	327	1	n−2k−1 2	DATE
ejpam-6040	328	1	8	CARDINAL
ejpam-6040	330	1	2 +	DATE
ejpam-6040	331	1	n−2k−1 2	DATE
ejpam-6040	331	2	2k + 1	DATE
ejpam-6040	332	1	2k + 1	DATE
ejpam-6040	335	1	2	CARDINAL
ejpam-6040	336	1	8	CARDINAL
ejpam-6040	336	2	2	CARDINAL
ejpam-6040	336	3	2k	CARDINAL
ejpam-6040	337	1	3	CARDINAL
ejpam-6040	339	1	4	CARDINAL
ejpam-6040	339	2	1 7	DATE
ejpam-6040	339	3	2 9	DATE
ejpam-6040	339	4	3	CARDINAL
ejpam-6040	342	1	1(vii	DATE
ejpam-6040	343	1	4	CARDINAL
ejpam-6040	344	1	3	CARDINAL
ejpam-6040	344	2	9	CARDINAL
ejpam-6040	344	3	1	CARDINAL
ejpam-6040	345	1	1 ≤ k ≤ 2	QUANTITY
ejpam-6040	346	1	4	CARDINAL
ejpam-6040	349	1	|i2p	ORG
ejpam-6040	349	2	3	CARDINAL
ejpam-6040	350	1	|i2p	ORG
ejpam-6040	350	2	1	CARDINAL
ejpam-6040	351	1	8	CARDINAL
ejpam-6040	351	2	10−	CARDINAL
ejpam-6040	351	3	3	CARDINAL
ejpam-6040	351	4	4	CARDINAL
ejpam-6040	374	1	w1 w5 w4	ORG
ejpam-6040	374	2	• • •	DATE
ejpam-6040	408	1	w1 w5 w4	ORG
ejpam-6040	408	2	• •	CARDINAL
ejpam-6040	408	3	4	CARDINAL
ejpam-6040	408	4	w3	DATE
ejpam-6040	408	5	ζg2 (p	ORG
ejpam-6040	409	1	10−	CARDINAL
ejpam-6040	409	2	7	CARDINAL
ejpam-6040	411	1	9	CARDINAL
ejpam-6040	411	2	9	CARDINAL
ejpam-6040	412	1	g = km1,m2	PERSON
ejpam-6040	412	2	2 ≤ m1 ≤ m2 ≤	QUANTITY
ejpam-6040	414	1	2	CARDINAL
ejpam-6040	415	1	2	CARDINAL
ejpam-6040	415	2	2 3	DATE
ejpam-6040	415	3	3 4	DATE
ejpam-6040	415	4	4	CARDINAL
ejpam-6040	415	5	10	CARDINAL
ejpam-6040	416	1	km1,m2	PERSON
ejpam-6040	416	2	2	CARDINAL
ejpam-6040	416	3	2 ≤	QUANTITY
ejpam-6040	417	1	s. canoy, jr.	PERSON
ejpam-6040	417	2	j. anoche	PERSON
ejpam-6040	418	1	j. pure	PERSON
ejpam-6040	418	2	18	CARDINAL
ejpam-6040	418	3	2	CARDINAL
ejpam-6040	418	4	2025	CARDINAL
ejpam-6040	418	5	6040 10	CARDINAL
ejpam-6040	418	6	16 ζgk(g	QUANTITY
ejpam-6040	419	1	1	CARDINAL
ejpam-6040	419	2	1 1	CARDINAL
ejpam-6040	419	3	3	CARDINAL
ejpam-6040	419	4	1	CARDINAL
ejpam-6040	421	1	4	CARDINAL
ejpam-6040	425	1	1	CARDINAL
ejpam-6040	425	2	1	CARDINAL
ejpam-6040	425	3	lemma 1	ORG
ejpam-6040	425	4	1	CARDINAL
ejpam-6040	425	5	2	CARDINAL
ejpam-6040	425	6	1	CARDINAL
ejpam-6040	425	7	9	CARDINAL
ejpam-6040	426	1	3	CARDINAL
ejpam-6040	426	2	2	CARDINAL
ejpam-6040	431	1	1	CARDINAL
ejpam-6040	431	2	3	CARDINAL
ejpam-6040	431	3	9	CARDINAL
ejpam-6040	431	4	4	CARDINAL
ejpam-6040	431	5	4	CARDINAL
ejpam-6040	431	6	{q11	PERSON
ejpam-6040	431	7	4−k 1	CARDINAL
ejpam-6040	431	8	1	CARDINAL
ejpam-6040	431	9	2	DATE
ejpam-6040	431	10	4−k	CARDINAL
ejpam-6040	437	1	j=2	PERSON
ejpam-6040	439	1	4	CARDINAL
ejpam-6040	441	1	10	CARDINAL
ejpam-6040	441	2	4	CARDINAL
ejpam-6040	441	3	bipartite	NORP
ejpam-6040	441	4	graph km	PERSON
ejpam-6040	441	5	2 ≤ m ≤ n	QUANTITY
ejpam-6040	442	1	m+	CARDINAL
ejpam-6040	442	2	1	CARDINAL
ejpam-6040	442	3	1 1	CARDINAL
ejpam-6040	442	4	4	CARDINAL
ejpam-6040	442	5	4	CARDINAL
ejpam-6040	443	1	s. canoy, jr.	PERSON
ejpam-6040	443	2	j. anoche	PERSON
ejpam-6040	444	1	j. pure	PERSON
ejpam-6040	444	2	18	CARDINAL
ejpam-6040	444	3	2	CARDINAL
ejpam-6040	444	4	2025	CARDINAL
ejpam-6040	444	5	6040 11	CARDINAL
ejpam-6040	444	6	16	CARDINAL
ejpam-6040	444	7	11	DATE
ejpam-6040	445	1	n ≥ 2 vertices	ORG
ejpam-6040	445	2	3k	CARDINAL
ejpam-6040	446	1	2	CARDINAL
ejpam-6040	446	2	2	CARDINAL
ejpam-6040	446	3	3r	CARDINAL
ejpam-6040	446	4	k ≤ r	FAC
ejpam-6040	447	1	1	CARDINAL
ejpam-6040	447	2	k ≤ r 3k	ORG
ejpam-6040	448	1	3r	CARDINAL
ejpam-6040	448	2	k ≤ r. proof	PERSON
ejpam-6040	450	1	1	CARDINAL
ejpam-6040	450	2	theorem 1(vi	DATE
ejpam-6040	451	1	3	CARDINAL
ejpam-6040	452	1	2	CARDINAL
ejpam-6040	453	1	2	CARDINAL
ejpam-6040	453	2	1	CARDINAL
ejpam-6040	453	3	n ≥ 3	DATE
ejpam-6040	453	4	1	CARDINAL
ejpam-6040	453	5	3r	CARDINAL
ejpam-6040	454	1	theorem 1(vi	DATE
ejpam-6040	455	1	3	CARDINAL
ejpam-6040	456	1	+ 1	DATE
ejpam-6040	457	1	k ≤ r and γg(pn	ORG
ejpam-6040	460	1	− k	ORG
ejpam-6040	462	1	ng g[s1	PERSON
ejpam-6040	463	1	3r	CARDINAL
ejpam-6040	463	2	3r	CARDINAL
ejpam-6040	463	3	3k	CARDINAL
ejpam-6040	463	4	3k	CARDINAL
ejpam-6040	464	1	1	CARDINAL
ejpam-6040	464	2	2	CARDINAL
ejpam-6040	464	3	theorem 1(vi	DATE
ejpam-6040	465	1	3	CARDINAL
ejpam-6040	466	1	+ 1	DATE
ejpam-6040	466	2	k ≤ r.	PERSON
ejpam-6040	466	3	− k	ORG
ejpam-6040	468	1	ng g[s2	PERSON
ejpam-6040	469	1	3r + 1)−	DATE
ejpam-6040	469	2	3r	CARDINAL
ejpam-6040	469	3	3k	CARDINAL
ejpam-6040	470	1	3k	CARDINAL
ejpam-6040	471	1	3	CARDINAL
ejpam-6040	471	2	3r	CARDINAL
ejpam-6040	471	3	1(vi	CARDINAL
ejpam-6040	472	1	3	CARDINAL
ejpam-6040	473	1	+ 2	DATE
ejpam-6040	473	2	k ≤ r + 1	FAC
ejpam-6040	475	1	− k	ORG
ejpam-6040	476	1	v3r−3k+4	ORG
ejpam-6040	477	1	v3r−3k+4	ORG
ejpam-6040	479	1	3r + 2−	DATE
ejpam-6040	479	2	3r	CARDINAL
ejpam-6040	479	3	3k	CARDINAL
ejpam-6040	480	1	3k	CARDINAL
ejpam-6040	480	2	2	CARDINAL
ejpam-6040	480	3	s. canoy, jr.	PERSON
ejpam-6040	480	4	j. anoche	PERSON
ejpam-6040	481	1	j. pure	PERSON
ejpam-6040	481	2	18	CARDINAL
ejpam-6040	481	3	2	CARDINAL
ejpam-6040	481	4	2025	CARDINAL
ejpam-6040	481	5	6040 12	CARDINAL
ejpam-6040	481	6	16	CARDINAL
ejpam-6040	481	7	12	CARDINAL
ejpam-6040	482	1	k ≤ γg(cn)− 1	FAC
ejpam-6040	484	1	3r	CARDINAL
ejpam-6040	484	2	2	CARDINAL
ejpam-6040	485	1	1	CARDINAL
ejpam-6040	485	2	3	CARDINAL
ejpam-6040	486	1	2 3k + 1	CARDINAL
ejpam-6040	486	2	3r	CARDINAL
ejpam-6040	486	3	2	CARDINAL
ejpam-6040	486	4	k = γg(cn)− 1 or	PERSON
ejpam-6040	486	5	3	CARDINAL
ejpam-6040	487	1	2 3k	CARDINAL
ejpam-6040	487	2	3r	CARDINAL
ejpam-6040	487	3	4	CARDINAL
ejpam-6040	487	4	1 ≤ k ≤ γg(cn)−	QUANTITY
ejpam-6040	487	5	3	CARDINAL
ejpam-6040	487	6	3r	CARDINAL
ejpam-6040	487	7	4	CARDINAL
ejpam-6040	488	1	2	CARDINAL
ejpam-6040	488	2	3r	CARDINAL
ejpam-6040	488	3	k =	PERSON
ejpam-6040	489	1	1	CARDINAL
ejpam-6040	490	1	2 3k	CARDINAL
ejpam-6040	490	2	2	CARDINAL
ejpam-6040	490	3	3r	CARDINAL
ejpam-6040	490	4	3	CARDINAL
ejpam-6040	490	5	1 ≤ k ≤	QUANTITY
ejpam-6040	491	1	3	CARDINAL
ejpam-6040	491	2	3	CARDINAL
ejpam-6040	492	1	2	CARDINAL
ejpam-6040	492	2	2 3k	CARDINAL
ejpam-6040	492	3	1	CARDINAL
ejpam-6040	492	4	3r	CARDINAL
ejpam-6040	492	5	1	CARDINAL
ejpam-6040	492	6	3r	CARDINAL
ejpam-6040	492	7	k =	PERSON
ejpam-6040	493	1	2	CARDINAL
ejpam-6040	493	2	3r	CARDINAL
ejpam-6040	493	3	4	CARDINAL
ejpam-6040	493	4	3	CARDINAL
ejpam-6040	494	1	1 k	QUANTITY
ejpam-6040	497	1	1	CARDINAL
ejpam-6040	498	1	3	CARDINAL
ejpam-6040	499	1	6	CARDINAL
ejpam-6040	500	1	5	CARDINAL
ejpam-6040	500	2	2	CARDINAL
ejpam-6040	500	3	3k− 1	DATE
ejpam-6040	501	1	4	CARDINAL
ejpam-6040	501	2	3k− 2	DATE
ejpam-6040	502	1	4	CARDINAL
ejpam-6040	503	1	1	CARDINAL
ejpam-6040	503	2	2	CARDINAL
ejpam-6040	503	3	1(v	CARDINAL
ejpam-6040	504	1	r.	NORP
ejpam-6040	504	2	k ≤ r−1	PERSON
ejpam-6040	505	1	1	CARDINAL
ejpam-6040	506	1	1	CARDINAL
ejpam-6040	506	2	1	CARDINAL
ejpam-6040	506	3	lemma 1	ORG
ejpam-6040	507	1	1	CARDINAL
ejpam-6040	507	2	3r	CARDINAL
ejpam-6040	507	3	1	CARDINAL
ejpam-6040	507	4	3k	CARDINAL
ejpam-6040	507	5	2	CARDINAL
ejpam-6040	507	6	k =	PERSON
ejpam-6040	508	1	2	CARDINAL
ejpam-6040	508	2	2	CARDINAL
ejpam-6040	512	1	ζgk(cn	PERSON
ejpam-6040	513	1	3r	CARDINAL
ejpam-6040	513	2	3r	CARDINAL
ejpam-6040	513	3	− 4	PERSON
ejpam-6040	513	4	3k	CARDINAL
ejpam-6040	513	5	3	CARDINAL
ejpam-6040	513	6	4	CARDINAL
ejpam-6040	514	1	3	CARDINAL
ejpam-6040	514	2	2	CARDINAL
ejpam-6040	515	1	d3	ORG
ejpam-6040	515	2	s. canoy, jr.	PERSON
ejpam-6040	515	3	j. anoche	PERSON
ejpam-6040	516	1	j. pure	PERSON
ejpam-6040	516	2	18	CARDINAL
ejpam-6040	516	3	2	CARDINAL
ejpam-6040	516	4	2025	CARDINAL
ejpam-6040	516	5	6040 13	CARDINAL
ejpam-6040	516	6	16 cn	QUANTITY
ejpam-6040	516	7	v3r	ORG
ejpam-6040	517	1	ζgk(cn	PERSON
ejpam-6040	519	1	3r	CARDINAL
ejpam-6040	520	1	3r	CARDINAL
ejpam-6040	520	2	3k	CARDINAL
ejpam-6040	520	3	2	CARDINAL
ejpam-6040	520	4	3k	CARDINAL
ejpam-6040	521	1	2	CARDINAL
ejpam-6040	522	1	3	CARDINAL
ejpam-6040	522	2	d4	ORG
ejpam-6040	522	3	2	CARDINAL
ejpam-6040	523	1	d4	ORG
ejpam-6040	523	2	3r+2 2	CARDINAL
ejpam-6040	523	3	2	CARDINAL
ejpam-6040	523	4	3r+2 2	CARDINAL
ejpam-6040	525	1	3r	CARDINAL
ejpam-6040	526	1	3r	CARDINAL
ejpam-6040	526	2	3k	CARDINAL
ejpam-6040	526	3	4	CARDINAL
ejpam-6040	526	4	3k	CARDINAL
ejpam-6040	527	1	4	CARDINAL
ejpam-6040	527	2	4	CARDINAL
ejpam-6040	527	3	k =	PERSON
ejpam-6040	528	1	2	CARDINAL
ejpam-6040	528	2	− 2	PERSON
ejpam-6040	529	1	3r+2 2	CARDINAL
ejpam-6040	530	1	ng g[d5	PERSON
ejpam-6040	531	1	3r 2	CARDINAL
ejpam-6040	531	2	3r+4 2	DATE
ejpam-6040	531	3	v3r	ORG
ejpam-6040	532	1	3r	CARDINAL
ejpam-6040	532	2	− |ng	PERSON
ejpam-6040	532	3	3r	CARDINAL
ejpam-6040	532	4	6	CARDINAL
ejpam-6040	532	5	3k	CARDINAL
ejpam-6040	533	1	2	CARDINAL
ejpam-6040	533	2	1(v	CARDINAL
ejpam-6040	535	1	k ≤ r. consider	PERSON
ejpam-6040	535	2	1	CARDINAL
ejpam-6040	536	1	1	CARDINAL
ejpam-6040	536	2	1	CARDINAL
ejpam-6040	537	1	1	CARDINAL
ejpam-6040	537	2	3r	CARDINAL
ejpam-6040	537	3	+ 1− 1	TIME
ejpam-6040	537	4	3r	CARDINAL
ejpam-6040	537	5	3k	CARDINAL
ejpam-6040	538	1	2	CARDINAL
ejpam-6040	538	2	k =	PERSON
ejpam-6040	539	1	2	CARDINAL
ejpam-6040	539	2	1	CARDINAL
ejpam-6040	543	1	3r	CARDINAL
ejpam-6040	543	2	3r	CARDINAL
ejpam-6040	543	3	3k	CARDINAL
ejpam-6040	543	4	3	CARDINAL
ejpam-6040	544	1	3	CARDINAL
ejpam-6040	544	2	3	CARDINAL
ejpam-6040	545	1	2	CARDINAL
ejpam-6040	547	1	= ζgk(d8	PERSON
ejpam-6040	550	1	3k− 2	DATE
ejpam-6040	552	1	3k	CARDINAL
ejpam-6040	554	1	2	CARDINAL
ejpam-6040	555	1	2	CARDINAL
ejpam-6040	556	1	3	CARDINAL
ejpam-6040	556	2	− k + 1)element	PERSON
ejpam-6040	556	3	d9	ORG
ejpam-6040	557	1	d9	ORG
ejpam-6040	557	2	3r+3 2	CARDINAL
ejpam-6040	560	1	3k− 2	DATE
ejpam-6040	562	1	3k	CARDINAL
ejpam-6040	563	1	2	CARDINAL
ejpam-6040	563	2	s. canoy, jr.	PERSON
ejpam-6040	563	3	j. anoche	PERSON
ejpam-6040	564	1	j. pure	PERSON
ejpam-6040	564	2	18	CARDINAL
ejpam-6040	564	3	2	CARDINAL
ejpam-6040	564	4	2025	CARDINAL
ejpam-6040	564	5	6040 14	CARDINAL
ejpam-6040	564	6	16	CARDINAL
ejpam-6040	564	7	4	CARDINAL
ejpam-6040	564	8	3	CARDINAL
ejpam-6040	564	9	k =	PERSON
ejpam-6040	565	1	2	CARDINAL
ejpam-6040	565	2	1	CARDINAL
ejpam-6040	566	1	3r+3 2	CARDINAL
ejpam-6040	568	1	3r+1 2	DATE
ejpam-6040	568	2	3r+3 2	DATE
ejpam-6040	568	3	3r+5 2 , v3r+1	CARDINAL
ejpam-6040	570	1	3r	CARDINAL
ejpam-6040	570	2	3r	CARDINAL
ejpam-6040	570	3	+ 1− 6	TIME
ejpam-6040	570	4	3k	CARDINAL
ejpam-6040	571	1	2	CARDINAL
ejpam-6040	571	2	3	CARDINAL
ejpam-6040	571	3	2	CARDINAL
ejpam-6040	571	4	1(v	CARDINAL
ejpam-6040	572	1	k ≤ r. consider	PERSON
ejpam-6040	572	2	1	CARDINAL
ejpam-6040	573	1	1	CARDINAL
ejpam-6040	576	1	d11	ORG
ejpam-6040	577	1	d11	ORG
ejpam-6040	578	1	|ng g[d11]|	DATE
ejpam-6040	578	2	3r + 2−	DATE
ejpam-6040	579	1	3r	CARDINAL
ejpam-6040	579	2	1	CARDINAL
ejpam-6040	579	3	2	CARDINAL
ejpam-6040	579	4	3k	CARDINAL
ejpam-6040	579	5	1	CARDINAL
ejpam-6040	579	6	2	CARDINAL
ejpam-6040	579	7	1	CARDINAL
ejpam-6040	579	8	1	CARDINAL
ejpam-6040	580	1	1	CARDINAL
ejpam-6040	580	2	3r	CARDINAL
ejpam-6040	580	3	+ 2− 1	CARDINAL
ejpam-6040	580	4	3r	CARDINAL
ejpam-6040	580	5	3k	CARDINAL
ejpam-6040	581	1	3	CARDINAL
ejpam-6040	581	2	k =	PERSON
ejpam-6040	582	1	2	CARDINAL
ejpam-6040	582	2	1	CARDINAL
ejpam-6040	586	1	3r + 2−	QUANTITY
ejpam-6040	586	2	3r	CARDINAL
ejpam-6040	586	3	+ 2− 4	CARDINAL
ejpam-6040	586	4	3k	CARDINAL
ejpam-6040	587	1	4	CARDINAL
ejpam-6040	587	2	k =	PERSON
ejpam-6040	588	1	2	CARDINAL
ejpam-6040	588	2	− 1	ORG
ejpam-6040	588	3	letd14	ORG
ejpam-6040	588	4	3r+4 2	CARDINAL
ejpam-6040	588	5	andng g[d14	PERSON
ejpam-6040	588	6	3r+2 2	DATE
ejpam-6040	588	7	3r+4 2	DATE
ejpam-6040	588	8	3r+6 2	DATE
ejpam-6040	590	1	3r + 2−	CARDINAL
ejpam-6040	590	2	3r + 2− 6	DATE
ejpam-6040	590	3	3k	CARDINAL
ejpam-6040	590	4	1	CARDINAL
ejpam-6040	590	5	5	CARDINAL
ejpam-6040	590	6	4	CARDINAL
ejpam-6040	591	1	3	CARDINAL
ejpam-6040	592	1	2	CARDINAL
ejpam-6040	593	1	ng g[d15	PERSON
ejpam-6040	595	1	ζgk(cn	PERSON
ejpam-6040	596	1	3r+2−	CARDINAL
ejpam-6040	597	1	3r−3k+2)+1	CARDINAL
ejpam-6040	597	2	3k−1	CARDINAL
ejpam-6040	598	1	2	CARDINAL
ejpam-6040	598	2	k ≤ γg(cn)−3	ORG
ejpam-6040	599	1	− k	ORG
ejpam-6040	600	1	3r+5	CARDINAL
ejpam-6040	600	2	2	CARDINAL
ejpam-6040	601	1	ng g[d16	PERSON
ejpam-6040	602	1	3r+5 2	CARDINAL
ejpam-6040	602	2	3r+5	CARDINAL
ejpam-6040	602	3	2	CARDINAL
ejpam-6040	602	4	3r+5	CARDINAL
ejpam-6040	602	5	2	CARDINAL
ejpam-6040	603	1	s. canoy, jr.	PERSON
ejpam-6040	603	2	j. anoche	PERSON
ejpam-6040	604	1	j. pure	PERSON
ejpam-6040	604	2	18	CARDINAL
ejpam-6040	604	3	2	CARDINAL
ejpam-6040	604	4	2025	CARDINAL
ejpam-6040	604	5	6040 15	CARDINAL
ejpam-6040	604	6	16	CARDINAL
ejpam-6040	605	1	3r + 2−	DATE
ejpam-6040	606	1	3r	CARDINAL
ejpam-6040	606	2	3k	CARDINAL
ejpam-6040	606	3	1	CARDINAL
ejpam-6040	606	4	3k	CARDINAL
ejpam-6040	607	1	1	CARDINAL
ejpam-6040	609	1	4.	CARDINAL
ejpam-6040	613	1	msu-iligan institute of technology	ORG
ejpam-6040	614	1	1	CARDINAL
ejpam-6040	614	2	e. cockayne	PERSON
ejpam-6040	614	3	s. hedetniemi	PERSON
ejpam-6040	616	1	marcel dekker	PERSON
ejpam-6040	616	2	new york	GPE
ejpam-6040	616	3	7(3):247–261, 1977	DATE
ejpam-6040	617	1	2	CARDINAL
ejpam-6040	617	2	haynes	ORG
ejpam-6040	617	3	s.t.	PERSON
ejpam-6040	617	4	hedetniemi	PERSON
ejpam-6040	617	5	slater	PERSON
ejpam-6040	619	1	1998	DATE
ejpam-6040	620	1	3	CARDINAL
ejpam-6040	620	2	a. das	PERSON
ejpam-6040	620	3	w. j. desormeaux	PERSON
ejpam-6040	622	1	indian	NORP
ejpam-6040	623	1	49(2):349–364, 2018	DATE
ejpam-6040	624	1	4	CARDINAL
ejpam-6040	624	2	a. miranda	PERSON
ejpam-6040	624	3	r. eballe	PERSON
ejpam-6040	626	1	15(12):615	CARDINAL
ejpam-6040	626	2	623	CARDINAL
ejpam-6040	626	3	2021	DATE
ejpam-6040	627	1	5	CARDINAL
ejpam-6040	627	2	a. miranda	PERSON
ejpam-6040	627	3	r. eballe	PERSON
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ejpam-6040	629	2	18(12):95–101	ORG
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ejpam-6040	639	1	utilitas mathematica	PERSON
ejpam-6040	639	2	74:3–18	DATE
ejpam-6040	639	3	2007	DATE
ejpam-6040	640	1	9	CARDINAL
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ejpam-6040	643	1	ars combinatoria	PERSON
ejpam-6040	643	2	84:191–203, 2007	DATE
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ejpam-6040	649	1	12	CARDINAL
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ejpam-6040	653	1	mathl	PERSON
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ejpam-6040	656	2	g. cagaanan	PERSON
ejpam-6040	656	3	s. canoy jr.	PERSON
ejpam-6040	657	1	congresus numerantium	PERSON
ejpam-6040	657	2	161:97–104, 2003	DATE
ejpam-6040	658	1	15	CARDINAL
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ejpam-6040	658	4	79:33–45,	DATE
ejpam-6040	658	5	2006	DATE
ejpam-6040	659	1	16	CARDINAL
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ejpam-6040	660	1	utilitas mathematica	PERSON
ejpam-6040	660	2	79:9	CARDINAL
ejpam-6040	660	3	2009	DATE
ejpam-6040	661	1	17	CARDINAL
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ejpam-6040	667	1	combin	PERSON
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ejpam-6040	672	1	utilitas mathematica	PERSON
ejpam-6040	672	2	71:143–159, 2006	DATE
ejpam-6040	673	1	20	CARDINAL
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ejpam-6040	675	1	combinatorics	ORG
ejpam-6040	675	2	3(4):19–30, 2014	DATE