id	sid	eid	entity	type
ejpam-6188	1	1	european journal	ORG
ejpam-6188	1	2	2025	DATE
ejpam-6188	1	3	18	CARDINAL
ejpam-6188	1	4	3	CARDINAL
ejpam-6188	1	5	6188	CARDINAL
ejpam-6188	1	6	new york	GPE
ejpam-6188	1	7	chaiyakhot4	GPE
ejpam-6188	1	8	sinthuket3 1	ORG
ejpam-6188	1	9	thailand 2	ORG
ejpam-6188	1	10	thailand 3	ORG
ejpam-6188	1	11	science, mahasarakham university	ORG
ejpam-6188	1	12	thailand 4	ORG
ejpam-6188	1	13	kaen university	ORG
ejpam-6188	1	14	khon kaen	PERSON
ejpam-6188	1	15	thailand	GPE
ejpam-6188	2	1	at least one	CARDINAL
ejpam-6188	6	1	1	CARDINAL
ejpam-6188	7	1	9	DATE
ejpam-6188	8	1	10 ≤ n ≤ 15	QUANTITY
ejpam-6188	9	1	2020	DATE
ejpam-6188	9	2	05c15	CARDINAL
ejpam-6188	9	3	05c76	CARDINAL
ejpam-6188	9	4	05c69	CARDINAL
ejpam-6188	9	5	1	CARDINAL
ejpam-6188	10	1	k}	PERSON
ejpam-6188	11	1	1	CARDINAL
ejpam-6188	12	1	k.	PERSON
ejpam-6188	12	2	c(s	ORG
ejpam-6188	14	1	j ̸= i.	PERSON
ejpam-6188	15	1	r. w. irving	PERSON
ejpam-6188	15	2	d. f. manlove	PERSON
ejpam-6188	16	1	2	CARDINAL
ejpam-6188	16	2	integer k	PERSON
ejpam-6188	18	1	w. tangjai	PERSON
ejpam-6188	18	2	63010213002@msu.ac.th	CARDINAL
ejpam-6188	18	3	r.	NORP
ejpam-6188	18	4	1	CARDINAL
ejpam-6188	19	1	2025	CARDINAL
ejpam-6188	22	1	j. pure	PERSON
ejpam-6188	22	2	18	CARDINAL
ejpam-6188	22	3	3	CARDINAL
ejpam-6188	22	4	2025	CARDINAL
ejpam-6188	22	5	6188 2	CARDINAL
ejpam-6188	22	6	13	CARDINAL
ejpam-6188	23	1	6	CARDINAL
ejpam-6188	24	1	7	CARDINAL
ejpam-6188	25	1	1989	DATE
ejpam-6188	26	1	8	CARDINAL
ejpam-6188	27	1	9	CARDINAL
ejpam-6188	28	1	2015	DATE
ejpam-6188	29	1	10	CARDINAL
ejpam-6188	30	1	∑ v∈v c(v	PERSON
ejpam-6188	33	1	11	CARDINAL
ejpam-6188	33	2	12	CARDINAL
ejpam-6188	35	1	two	CARDINAL
ejpam-6188	36	1	∪u	CARDINAL
ejpam-6188	39	1	un	ORG
ejpam-6188	39	2	vi	PERSON
ejpam-6188	40	1	µ(g	ORG
ejpam-6188	40	2	⊂	GPE
ejpam-6188	40	3	1 ≤ i ≤ n	QUANTITY
ejpam-6188	40	4	2011	DATE
ejpam-6188	41	1	al	PERSON
ejpam-6188	42	1	13	CARDINAL
ejpam-6188	43	1	2017	DATE
ejpam-6188	43	2	1	CARDINAL
ejpam-6188	44	1	n ≥ 2	DATE
ejpam-6188	44	2	7 or n ≥ 9	DATE
ejpam-6188	45	1	9	CARDINAL
ejpam-6188	45	2	10 ≤ n ≤ 15	QUANTITY
ejpam-6188	46	1	2	CARDINAL
ejpam-6188	47	1	1	CARDINAL
ejpam-6188	48	1	14	CARDINAL
ejpam-6188	52	1	mycielskian	NORP
ejpam-6188	53	1	un	ORG
ejpam-6188	53	2	e(µ(g	DATE
ejpam-6188	54	1	1 ≤ i ≤ n	QUANTITY
ejpam-6188	54	2	1 ≤ i ≤ n	QUANTITY
ejpam-6188	54	3	∈	PRODUCT
ejpam-6188	55	1	un	ORG
ejpam-6188	55	2	1 ≤ i ≤ n	QUANTITY
ejpam-6188	56	1	un	ORG
ejpam-6188	56	2	1	CARDINAL
ejpam-6188	56	3	1	CARDINAL
ejpam-6188	58	1	1 degree	QUANTITY
ejpam-6188	60	1	j. pure	PERSON
ejpam-6188	60	2	18	CARDINAL
ejpam-6188	60	3	3	CARDINAL
ejpam-6188	60	4	2025	CARDINAL
ejpam-6188	60	5	6188 3	DATE
ejpam-6188	60	6	13	CARDINAL
ejpam-6188	60	7	u4 u5	PERSON
ejpam-6188	61	1	un v1 v2 v3 v4 v5 ·	PERSON
ejpam-6188	62	1	1	CARDINAL
ejpam-6188	62	2	1	CARDINAL
ejpam-6188	63	1	15	CARDINAL
ejpam-6188	64	1	mycielskian	NORP
ejpam-6188	65	1	3	CARDINAL
ejpam-6188	65	2	2 ≤ n ≤ 4	QUANTITY
ejpam-6188	65	3	4	CARDINAL
ejpam-6188	65	4	5	DATE
ejpam-6188	65	5	n ≥ 8	DATE
ejpam-6188	66	1	1	CARDINAL
ejpam-6188	67	1	3	CARDINAL
ejpam-6188	68	1	n ≥ 9	DATE
ejpam-6188	71	1	2	CARDINAL
ejpam-6188	71	2	2	CARDINAL
ejpam-6188	72	1	1	CARDINAL
ejpam-6188	74	1	 4	DATE
ejpam-6188	74	2	1	CARDINAL
ejpam-6188	74	3	3	CARDINAL
ejpam-6188	74	4	2⌊n2	CARDINAL
ejpam-6188	75	1	2	CARDINAL
ejpam-6188	75	2	3	DATE
ejpam-6188	75	3	4	DATE
ejpam-6188	75	4	6 +	DATE
ejpam-6188	75	5	3⌊n−1 2	CARDINAL
ejpam-6188	75	6	2⌈n−1 2	QUANTITY
ejpam-6188	75	7	5	CARDINAL
ejpam-6188	75	8	6	DATE
ejpam-6188	75	9	44	DATE
ejpam-6188	75	10	8	CARDINAL
ejpam-6188	75	11	3	CARDINAL
ejpam-6188	76	1	1	CARDINAL
ejpam-6188	78	1	28	CARDINAL
ejpam-6188	78	2	7	CARDINAL
ejpam-6188	78	3	48	DATE
ejpam-6188	78	4	9	CARDINAL
ejpam-6188	78	5	45 +	DATE
ejpam-6188	78	6	n ≥ 10	DATE
ejpam-6188	79	1	n ≥ 10	DATE
ejpam-6188	79	2	3n+ 21	DATE
ejpam-6188	79	3	3n+ 22	CARDINAL
ejpam-6188	80	1	3	CARDINAL
ejpam-6188	80	2	n = 7,	ORG
ejpam-6188	80	3	9	DATE
ejpam-6188	80	4	10 ≤ n ≤ 15	QUANTITY
ejpam-6188	83	1	27	CARDINAL
ejpam-6188	84	1	46	CARDINAL
ejpam-6188	84	2	3n+	CARDINAL
ejpam-6188	84	3	18 ≤	QUANTITY
ejpam-6188	85	1	3n+ 19	CARDINAL
ejpam-6188	85	2	10 ≤ n ≤ 15	QUANTITY
ejpam-6188	86	1	3n+ 19	DATE
ejpam-6188	88	1	j. pure	PERSON
ejpam-6188	88	2	18	CARDINAL
ejpam-6188	88	3	3	CARDINAL
ejpam-6188	88	4	2025	CARDINAL
ejpam-6188	88	5	6188 4 of 13 3	DATE
ejpam-6188	88	6	1	CARDINAL
ejpam-6188	90	1	n ≥ 9	DATE
ejpam-6188	93	1	1	CARDINAL
ejpam-6188	94	1	9	DATE
ejpam-6188	94	2	10 ≤ n ≤ 15	QUANTITY
ejpam-6188	95	1	4	CARDINAL
ejpam-6188	97	1	4	CARDINAL
ejpam-6188	98	1	27	CARDINAL
ejpam-6188	100	1	1	CARDINAL
ejpam-6188	101	1	4	CARDINAL
ejpam-6188	101	2	1	CARDINAL
ejpam-6188	101	3	2	DATE
ejpam-6188	101	4	3	DATE
ejpam-6188	101	5	4	CARDINAL
ejpam-6188	102	1	first	ORDINAL
ejpam-6188	102	2	7	CARDINAL
ejpam-6188	102	3	1	CARDINAL
ejpam-6188	102	4	at least 8	CARDINAL
ejpam-6188	102	5	1	CARDINAL
ejpam-6188	103	1	at least three	CARDINAL
ejpam-6188	104	1	c(u	GPE
ejpam-6188	105	1	1	CARDINAL
ejpam-6188	105	2	1	CARDINAL
ejpam-6188	106	1	|c1|	GPE
ejpam-6188	106	2	2	CARDINAL
ejpam-6188	106	3	5	CARDINAL
ejpam-6188	108	1	4	CARDINAL
ejpam-6188	108	2	1	CARDINAL
ejpam-6188	108	3	at least 4	CARDINAL
ejpam-6188	108	4	1	CARDINAL
ejpam-6188	108	5	u7	GPE
ejpam-6188	109	1	∩	PERSON
ejpam-6188	109	2	4	CARDINAL
ejpam-6188	109	3	∩	PERSON
ejpam-6188	109	4	4	CARDINAL
ejpam-6188	112	1	j = 1	PERSON
ejpam-6188	112	2	2	DATE
ejpam-6188	112	3	3	DATE
ejpam-6188	112	4	∩	PERSON
ejpam-6188	112	5	4 + j	DATE
ejpam-6188	112	6	|np7(c1 ∩	GPE
ejpam-6188	112	7	∩	PERSON
ejpam-6188	112	8	4 + j.	TIME
ejpam-6188	112	9	3	CARDINAL
ejpam-6188	112	10	1	CARDINAL
ejpam-6188	112	11	|c1| ≤ 7	DATE
ejpam-6188	113	1	1	CARDINAL
ejpam-6188	113	2	2	CARDINAL
ejpam-6188	113	3	1	CARDINAL
ejpam-6188	114	1	3	CARDINAL
ejpam-6188	115	1	1	CARDINAL
ejpam-6188	115	2	2	CARDINAL
ejpam-6188	116	1	1	CARDINAL
ejpam-6188	116	2	2	CARDINAL
ejpam-6188	117	1	1	CARDINAL
ejpam-6188	117	2	∑ v∈v	PERSON
ejpam-6188	117	3	4|c4|+	CARDINAL
ejpam-6188	117	4	2|c2|+	CARDINAL
ejpam-6188	117	5	4	CARDINAL
ejpam-6188	117	6	1 + 3	DATE
ejpam-6188	117	7	2 + 2	DATE
ejpam-6188	117	8	5 + 1	DATE
ejpam-6188	117	9	7	CARDINAL
ejpam-6188	117	10	27	CARDINAL
ejpam-6188	118	1	2	CARDINAL
ejpam-6188	118	2	∑ v∈v	PERSON
ejpam-6188	118	3	4	CARDINAL
ejpam-6188	120	1	5 + 1	DATE
ejpam-6188	120	2	7	CARDINAL
ejpam-6188	120	3	28	CARDINAL
ejpam-6188	121	1	27	CARDINAL
ejpam-6188	122	1	2	CARDINAL
ejpam-6188	124	1	j. pure	PERSON
ejpam-6188	124	2	18	CARDINAL
ejpam-6188	124	3	3	CARDINAL
ejpam-6188	124	4	2025	CARDINAL
ejpam-6188	124	5	6188 5 of 13	DATE
ejpam-6188	125	1	c7	PERSON
ejpam-6188	126	1	1	CARDINAL
ejpam-6188	126	2	2	DATE
ejpam-6188	126	3	3	DATE
ejpam-6188	126	4	4	CARDINAL
ejpam-6188	126	5	u7	ORG
ejpam-6188	126	6	2	CARDINAL
ejpam-6188	126	7	u4	ORG
ejpam-6188	126	8	3	CARDINAL
ejpam-6188	126	9	4	CARDINAL
ejpam-6188	127	1	1	CARDINAL
ejpam-6188	127	2	c7	PERSON
ejpam-6188	128	1	27	CARDINAL
ejpam-6188	129	1	3	CARDINAL
ejpam-6188	129	2	1	CARDINAL
ejpam-6188	129	3	1	CARDINAL
ejpam-6188	129	4	1	CARDINAL
ejpam-6188	129	5	1	CARDINAL
ejpam-6188	129	6	2	CARDINAL
ejpam-6188	129	7	3	CARDINAL
ejpam-6188	129	8	2	CARDINAL
ejpam-6188	129	9	2	CARDINAL
ejpam-6188	129	10	4	CARDINAL
ejpam-6188	130	1	5	CARDINAL
ejpam-6188	131	1	1	CARDINAL
ejpam-6188	131	2	1	CARDINAL
ejpam-6188	132	1	1	CARDINAL
ejpam-6188	133	1	n ≥ 8	DATE
ejpam-6188	133	2	un	ORG
ejpam-6188	134	1	1	CARDINAL
ejpam-6188	134	2	n ≥ 8	DATE
ejpam-6188	135	1	5	CARDINAL
ejpam-6188	135	2	4	CARDINAL
ejpam-6188	136	1	3	CARDINAL
ejpam-6188	136	2	1 ≤ i ≤ n	QUANTITY
ejpam-6188	137	1	2	CARDINAL
ejpam-6188	137	2	∈	ORG
ejpam-6188	137	3	pn)∪un	ORG
ejpam-6188	137	4	1	CARDINAL
ejpam-6188	138	1	2	CARDINAL
ejpam-6188	138	2	3	DATE
ejpam-6188	138	3	4	DATE
ejpam-6188	138	4	5	DATE
ejpam-6188	138	5	at least three	CARDINAL
ejpam-6188	139	1	three	CARDINAL
ejpam-6188	139	2	x.	GPE
ejpam-6188	139	3	two	CARDINAL
ejpam-6188	140	1	2	CARDINAL
ejpam-6188	140	2	n ≥ 8	DATE
ejpam-6188	143	1	j. pure	PERSON
ejpam-6188	143	2	18	CARDINAL
ejpam-6188	143	3	3	CARDINAL
ejpam-6188	143	4	2025	CARDINAL
ejpam-6188	143	5	6188 6	CARDINAL
ejpam-6188	143	6	13	CARDINAL
ejpam-6188	144	1	1	CARDINAL
ejpam-6188	144	2	un	ORG
ejpam-6188	145	1	5	CARDINAL
ejpam-6188	145	2	2	CARDINAL
ejpam-6188	145	3	vi	PERSON
ejpam-6188	145	4	2	CARDINAL
ejpam-6188	146	1	un	ORG
ejpam-6188	147	1	3	CARDINAL
ejpam-6188	147	2	n ≥ 8	DATE
ejpam-6188	147	3	1	CARDINAL
ejpam-6188	147	4	2	DATE
ejpam-6188	147	5	3	DATE
ejpam-6188	147	6	4	DATE
ejpam-6188	147	7	5	CARDINAL
ejpam-6188	147	8	|cm|	DATE
ejpam-6188	147	9	2	CARDINAL
ejpam-6188	147	10	3	CARDINAL
ejpam-6188	148	1	1	CARDINAL
ejpam-6188	149	1	5	CARDINAL
ejpam-6188	149	2	2	CARDINAL
ejpam-6188	149	3	lemma 1	ORG
ejpam-6188	150	1	5	CARDINAL
ejpam-6188	151	1	1	CARDINAL
ejpam-6188	152	1	k ∈	PERSON
ejpam-6188	152	2	2	CARDINAL
ejpam-6188	154	1	5	CARDINAL
ejpam-6188	154	2	j ∈	PERSON
ejpam-6188	154	3	1	CARDINAL
ejpam-6188	156	1	5	CARDINAL
ejpam-6188	157	1	at least one	CARDINAL
ejpam-6188	157	2	vk−1	ORG
ejpam-6188	158	1	4	CARDINAL
ejpam-6188	158	2	3	CARDINAL
ejpam-6188	158	3	3	CARDINAL
ejpam-6188	159	1	cn(vk+2	ORG
ejpam-6188	159	2	3	CARDINAL
ejpam-6188	159	3	cn({uk−1	ORG
ejpam-6188	159	4	1	CARDINAL
ejpam-6188	159	5	2	CARDINAL
ejpam-6188	160	1	3	CARDINAL
ejpam-6188	161	1	3	CARDINAL
ejpam-6188	162	1	3	CARDINAL
ejpam-6188	163	1	un	ORG
ejpam-6188	163	2	1	CARDINAL
ejpam-6188	163	3	2	CARDINAL
ejpam-6188	164	1	|c1| ≥ 3 and |c2| ≥ 3	DATE
ejpam-6188	165	1	2	CARDINAL
ejpam-6188	165	2	5	CARDINAL
ejpam-6188	165	3	vk−1	ORG
ejpam-6188	165	4	1	CARDINAL
ejpam-6188	165	5	2	CARDINAL
ejpam-6188	165	6	j ∈	PERSON
ejpam-6188	165	7	2	CARDINAL
ejpam-6188	165	8	3	DATE
ejpam-6188	166	1	1	CARDINAL
ejpam-6188	166	2	2	CARDINAL
ejpam-6188	167	1	3	CARDINAL
ejpam-6188	167	2	4	CARDINAL
ejpam-6188	168	1	at least 2	CARDINAL
ejpam-6188	168	2	4	CARDINAL
ejpam-6188	169	1	3	CARDINAL
ejpam-6188	170	1	3	CARDINAL
ejpam-6188	170	2	1	CARDINAL
ejpam-6188	173	1	4	CARDINAL
ejpam-6188	174	1	3	CARDINAL
ejpam-6188	174	2	uk−2	ORG
ejpam-6188	174	3	1	CARDINAL
ejpam-6188	174	4	1	CARDINAL
ejpam-6188	174	5	2	CARDINAL
ejpam-6188	174	6	2	CARDINAL
ejpam-6188	174	7	3	CARDINAL
ejpam-6188	174	8	4	CARDINAL
ejpam-6188	174	9	3	CARDINAL
ejpam-6188	174	10	3	CARDINAL
ejpam-6188	174	11	3	CARDINAL
ejpam-6188	174	12	n ≥ 8	DATE
ejpam-6188	175	1	2	CARDINAL
ejpam-6188	175	2	∑ v∈v	PERSON
ejpam-6188	175	3	5	CARDINAL
ejpam-6188	175	4	2 + 4	DATE
ejpam-6188	175	5	3 + 3	DATE
ejpam-6188	175	6	3 + 2	DATE
ejpam-6188	175	7	2n−	DATE
ejpam-6188	175	8	+ |c1|	PERCENT
ejpam-6188	176	1	|c5|	GPE
ejpam-6188	176	2	3	CARDINAL
ejpam-6188	176	3	5	CARDINAL
ejpam-6188	177	1	2 + 3	DATE
ejpam-6188	177	2	3 + 2	DATE
ejpam-6188	177	3	2n−	DATE
ejpam-6188	178	1	+ |c1|	PERCENT
ejpam-6188	180	1	j. pure	PERSON
ejpam-6188	180	2	18	CARDINAL
ejpam-6188	180	3	3	CARDINAL
ejpam-6188	180	4	2025	CARDINAL
ejpam-6188	180	5	6188 7	DATE
ejpam-6188	180	6	13	CARDINAL
ejpam-6188	180	7	4	CARDINAL
ejpam-6188	180	8	n ≥ 8	DATE
ejpam-6188	181	1	|cm|	CARDINAL
ejpam-6188	181	2	2	CARDINAL
ejpam-6188	181	3	4	CARDINAL
ejpam-6188	182	1	|cm|	CARDINAL
ejpam-6188	182	2	2	CARDINAL
ejpam-6188	182	3	lemma 1	ORG
ejpam-6188	183	1	2	CARDINAL
ejpam-6188	184	1	3	CARDINAL
ejpam-6188	184	2	3	CARDINAL
ejpam-6188	184	3	|ck|	ORG
ejpam-6188	184	4	3	CARDINAL
ejpam-6188	186	1	3	CARDINAL
ejpam-6188	187	1	3 ̸∈ cn(un	QUANTITY
ejpam-6188	188	1	vi	PERSON
ejpam-6188	190	1	3	CARDINAL
ejpam-6188	191	1	5	CARDINAL
ejpam-6188	191	2	c(vj−1	PERSON
ejpam-6188	192	1	5	CARDINAL
ejpam-6188	192	2	2	CARDINAL
ejpam-6188	192	3	5	CARDINAL
ejpam-6188	193	1	3	CARDINAL
ejpam-6188	193	2	5	CARDINAL
ejpam-6188	194	1	1–4	CARDINAL
ejpam-6188	194	2	|c5|	GPE
ejpam-6188	194	3	2	CARDINAL
ejpam-6188	195	1	3	CARDINAL
ejpam-6188	195	2	lemmas 2 and	ORG
ejpam-6188	195	3	4	DATE
ejpam-6188	195	4	c8(u	GPE
ejpam-6188	195	5	1	CARDINAL
ejpam-6188	195	6	2	CARDINAL
ejpam-6188	195	7	4 ≤ |cc8(u)| ≤	MONEY
ejpam-6188	195	8	5	CARDINAL
ejpam-6188	196	1	4	CARDINAL
ejpam-6188	196	2	5	CARDINAL
ejpam-6188	198	1	5	CARDINAL
ejpam-6188	199	1	3 + 3	DATE
ejpam-6188	199	2	3 + 2	QUANTITY
ejpam-6188	199	3	4 + 1	DATE
ejpam-6188	199	4	5	CARDINAL
ejpam-6188	199	5	44	CARDINAL
ejpam-6188	199	6	1	CARDINAL
ejpam-6188	201	1	44	DATE
ejpam-6188	201	2	1	CARDINAL
ejpam-6188	202	1	n ≥ 9	DATE
ejpam-6188	202	2	5	CARDINAL
ejpam-6188	202	3	1–4	CARDINAL
ejpam-6188	202	4	5	CARDINAL
ejpam-6188	202	5	n ≥ 9	DATE
ejpam-6188	203	1	1	CARDINAL
ejpam-6188	203	2	1	CARDINAL
ejpam-6188	204	1	∈	PERSON
ejpam-6188	204	2	|c1|	GPE
ejpam-6188	204	3	1	CARDINAL
ejpam-6188	204	4	∈	PERSON
ejpam-6188	205	1	3	CARDINAL
ejpam-6188	205	2	2 ≤ k ≤ n	QUANTITY
ejpam-6188	206	1	nµ(pn)(vk	GPE
ejpam-6188	207	1	vk−1	ORG
ejpam-6188	207	2	uk−1	GPE
ejpam-6188	207	3	1	CARDINAL
ejpam-6188	208	1	two	CARDINAL
ejpam-6188	208	2	1	CARDINAL
ejpam-6188	208	3	4	CARDINAL
ejpam-6188	209	1	1	CARDINAL
ejpam-6188	212	1	2	CARDINAL
ejpam-6188	214	1	1	CARDINAL
ejpam-6188	215	1	1	CARDINAL
ejpam-6188	216	1	1 or cn(vk+1	CARDINAL
ejpam-6188	216	2	1	CARDINAL
ejpam-6188	216	3	1	CARDINAL
ejpam-6188	216	4	4	CARDINAL
ejpam-6188	217	1	1	CARDINAL
ejpam-6188	218	1	1	CARDINAL
ejpam-6188	219	1	|c1|	GPE
ejpam-6188	219	2	1	CARDINAL
ejpam-6188	219	3	2	CARDINAL
ejpam-6188	219	4	1 or	CARDINAL
ejpam-6188	219	5	1	CARDINAL
ejpam-6188	219	6	1	CARDINAL
ejpam-6188	219	7	4	CARDINAL
ejpam-6188	220	1	1	CARDINAL
ejpam-6188	220	2	1	CARDINAL
ejpam-6188	222	1	1	CARDINAL
ejpam-6188	222	2	|c1|	GPE
ejpam-6188	223	1	1	CARDINAL
ejpam-6188	224	1	1	CARDINAL
ejpam-6188	224	2	5	CARDINAL
ejpam-6188	225	1	4	CARDINAL
ejpam-6188	225	2	5	CARDINAL
ejpam-6188	226	1	4	CARDINAL
ejpam-6188	227	1	1	CARDINAL
ejpam-6188	228	1	j. pure	PERSON
ejpam-6188	228	2	18	CARDINAL
ejpam-6188	228	3	3	CARDINAL
ejpam-6188	228	4	2025	CARDINAL
ejpam-6188	228	5	6188 8 of 13	DATE
ejpam-6188	228	6	4	CARDINAL
ejpam-6188	228	7	5	DATE
ejpam-6188	228	8	6	CARDINAL
ejpam-6188	230	1	|c1| ≤ n−	ORG
ejpam-6188	230	2	1	CARDINAL
ejpam-6188	231	1	uk−1	ORG
ejpam-6188	231	2	uk	GPE
ejpam-6188	231	3	3	CARDINAL
ejpam-6188	231	4	1 vk+2	QUANTITY
ejpam-6188	231	5	1	CARDINAL
ejpam-6188	231	6	3	CARDINAL
ejpam-6188	231	7	4	CARDINAL
ejpam-6188	231	8	1	CARDINAL
ejpam-6188	231	9	1 u2 x	QUANTITY
ejpam-6188	231	10	1 u4 x	QUANTITY
ejpam-6188	232	1	1	CARDINAL
ejpam-6188	232	2	1 v2 x v3	QUANTITY
ejpam-6188	232	3	1 v4	QUANTITY
ejpam-6188	233	1	5	CARDINAL
ejpam-6188	233	2	1	CARDINAL
ejpam-6188	233	3	1	CARDINAL
ejpam-6188	234	1	1 1 x	QUANTITY
ejpam-6188	234	2	1	CARDINAL
ejpam-6188	234	3	1 x	QUANTITY
ejpam-6188	234	4	1	CARDINAL
ejpam-6188	234	5	1	CARDINAL
ejpam-6188	234	6	6	CARDINAL
ejpam-6188	234	7	1	CARDINAL
ejpam-6188	234	8	n ≥ 9	DATE
ejpam-6188	234	9	5	CARDINAL
ejpam-6188	234	10	n ≥ 9	DATE
ejpam-6188	234	11	3n+ 18	DATE
ejpam-6188	234	12	10 ≤ n ≤ 15	QUANTITY
ejpam-6188	234	13	3n+ 19	DATE
ejpam-6188	234	14	9	CARDINAL
ejpam-6188	236	1	1	CARDINAL
ejpam-6188	236	2	2	DATE
ejpam-6188	236	3	3	DATE
ejpam-6188	236	4	4	DATE
ejpam-6188	236	5	5	CARDINAL
ejpam-6188	236	6	n ≥ 9	DATE
ejpam-6188	238	1	1	CARDINAL
ejpam-6188	238	2	3	CARDINAL
ejpam-6188	238	3	4	DATE
ejpam-6188	238	4	5	CARDINAL
ejpam-6188	239	1	lemmas 1,	ORG
ejpam-6188	239	2	3	DATE
ejpam-6188	239	3	4	DATE
ejpam-6188	239	4	3	CARDINAL
ejpam-6188	239	5	3	CARDINAL
ejpam-6188	239	6	3	CARDINAL
ejpam-6188	239	7	2	CARDINAL
ejpam-6188	239	8	|cj	GPE
ejpam-6188	239	9	3	CARDINAL
ejpam-6188	239	10	4	CARDINAL
ejpam-6188	239	11	3	CARDINAL
ejpam-6188	239	12	4	DATE
ejpam-6188	239	13	5	CARDINAL
ejpam-6188	240	1	5|c5| +	DATE
ejpam-6188	242	1	j. pure	PERSON
ejpam-6188	242	2	18	CARDINAL
ejpam-6188	242	3	3	CARDINAL
ejpam-6188	242	4	2025	CARDINAL
ejpam-6188	242	5	6188 9	DATE
ejpam-6188	243	1	3 + 3	DATE
ejpam-6188	243	2	4	CARDINAL
ejpam-6188	243	3	34	CARDINAL
ejpam-6188	244	1	lemma 5	ORG
ejpam-6188	244	2	|c1|	GPE
ejpam-6188	244	3	1	CARDINAL
ejpam-6188	245	1	7	CARDINAL
ejpam-6188	246	1	34 + 2(n− 7	DATE
ejpam-6188	246	2	1	CARDINAL
ejpam-6188	246	3	3n+ 19	DATE
ejpam-6188	246	4	2	CARDINAL
ejpam-6188	247	1	1	CARDINAL
ejpam-6188	247	2	lemma 2	ORG
ejpam-6188	248	1	|c1|	GPE
ejpam-6188	248	2	|c3|	CARDINAL
ejpam-6188	248	3	|c4|	ORG
ejpam-6188	248	4	|c5|	GPE
ejpam-6188	249	1	|c1|	GPE
ejpam-6188	250	1	3	CARDINAL
ejpam-6188	250	2	2	CARDINAL
ejpam-6188	252	1	that∑	NORP
ejpam-6188	252	2	5	CARDINAL
ejpam-6188	253	1	3 + 3	DATE
ejpam-6188	254	1	2	CARDINAL
ejpam-6188	255	1	2	CARDINAL
ejpam-6188	255	2	3n+	CARDINAL
ejpam-6188	255	3	2	CARDINAL
ejpam-6188	255	4	3n+ 19	DATE
ejpam-6188	256	1	3	CARDINAL
ejpam-6188	258	1	2	CARDINAL
ejpam-6188	258	2	first	ORDINAL
ejpam-6188	258	3	|c1|	GPE
ejpam-6188	258	4	|c3|	CARDINAL
ejpam-6188	258	5	|c4|	ORG
ejpam-6188	258	6	|c5|	GPE
ejpam-6188	260	1	3	CARDINAL
ejpam-6188	260	2	2	CARDINAL
ejpam-6188	262	1	5	CARDINAL
ejpam-6188	263	1	3 + 3	DATE
ejpam-6188	264	1	1	CARDINAL
ejpam-6188	264	2	3n+ 18	DATE
ejpam-6188	265	1	two	CARDINAL
ejpam-6188	266	1	8	CARDINAL
ejpam-6188	266	2	4	CARDINAL
ejpam-6188	266	3	3	CARDINAL
ejpam-6188	266	4	2	CARDINAL
ejpam-6188	267	1	|c1|	CARDINAL
ejpam-6188	267	2	7	CARDINAL
ejpam-6188	267	3	4	CARDINAL
ejpam-6188	267	4	5	CARDINAL
ejpam-6188	268	1	3 + 3	DATE
ejpam-6188	268	2	3 + 2	QUANTITY
ejpam-6188	268	3	4 + 1	DATE
ejpam-6188	268	4	7	CARDINAL
ejpam-6188	268	5	46	CARDINAL
ejpam-6188	268	6	3n+ 19. •	DATE
ejpam-6188	268	7	|c1|	CARDINAL
ejpam-6188	268	8	1	CARDINAL
ejpam-6188	268	9	3	CARDINAL
ejpam-6188	268	10	2	CARDINAL
ejpam-6188	268	11	lemma 2	ORG
ejpam-6188	269	1	2n+ 1)− 2− 3−	DATE
ejpam-6188	269	2	2	CARDINAL
ejpam-6188	270	1	1	CARDINAL
ejpam-6188	270	2	2	CARDINAL
ejpam-6188	270	3	4	CARDINAL
ejpam-6188	271	1	5	CARDINAL
ejpam-6188	272	1	3 + 3	DATE
ejpam-6188	272	2	2	CARDINAL
ejpam-6188	272	3	2	CARDINAL
ejpam-6188	273	1	1	CARDINAL
ejpam-6188	273	2	3n+	CARDINAL
ejpam-6188	273	3	2	CARDINAL
ejpam-6188	273	4	3n+ 19	DATE
ejpam-6188	273	5	three	CARDINAL
ejpam-6188	273	6	3n+ 18	DATE
ejpam-6188	273	7	10 ≤ n ≤ 15	QUANTITY
ejpam-6188	274	1	3n+ 19	DATE
ejpam-6188	274	2	9	CARDINAL
ejpam-6188	275	1	5	CARDINAL
ejpam-6188	277	1	j. pure	PERSON
ejpam-6188	277	2	18	CARDINAL
ejpam-6188	277	3	3	CARDINAL
ejpam-6188	277	4	2025	CARDINAL
ejpam-6188	277	5	6188 10	DATE
ejpam-6188	277	6	13	CARDINAL
ejpam-6188	277	7	2	CARDINAL
ejpam-6188	277	8	1 u2 1	CARDINAL
ejpam-6188	277	9	5	CARDINAL
ejpam-6188	277	10	3	CARDINAL
ejpam-6188	277	11	1	CARDINAL
ejpam-6188	277	12	1 u8 3	CARDINAL
ejpam-6188	277	13	4	CARDINAL
ejpam-6188	277	14	1	CARDINAL
ejpam-6188	277	15	4	CARDINAL
ejpam-6188	277	16	2	CARDINAL
ejpam-6188	277	17	1	CARDINAL
ejpam-6188	277	18	7	CARDINAL
ejpam-6188	277	19	2	CARDINAL
ejpam-6188	277	20	5	CARDINAL
ejpam-6188	277	21	3	CARDINAL
ejpam-6188	277	22	1	CARDINAL
ejpam-6188	277	23	1 u8 3	CARDINAL
ejpam-6188	277	24	1	CARDINAL
ejpam-6188	277	25	4	CARDINAL
ejpam-6188	277	26	1	CARDINAL
ejpam-6188	277	27	5	CARDINAL
ejpam-6188	277	28	4	CARDINAL
ejpam-6188	277	29	2	CARDINAL
ejpam-6188	277	30	2	CARDINAL
ejpam-6188	277	31	8	CARDINAL
ejpam-6188	277	32	µ(p10	LANGUAGE
ejpam-6188	277	33	1	CARDINAL
ejpam-6188	278	1	10 ≤ n ≤ 15	QUANTITY
ejpam-6188	278	2	3n+18	CARDINAL
ejpam-6188	278	3	2	CARDINAL
ejpam-6188	278	4	6	CARDINAL
ejpam-6188	278	5	3	CARDINAL
ejpam-6188	278	6	2	CARDINAL
ejpam-6188	278	7	6	CARDINAL
ejpam-6188	278	8	n ≥ 9	DATE
ejpam-6188	278	9	3n+ 19	DATE
ejpam-6188	280	1	µ(p10	GPE
ejpam-6188	280	2	µ(p11	PERSON
ejpam-6188	280	3	7	CARDINAL
ejpam-6188	280	4	8	DATE
ejpam-6188	281	1	∑ v∈v	PERSON
ejpam-6188	281	2	3n + 19	DATE
ejpam-6188	281	3	9 ≤ n ≤ 11	QUANTITY
ejpam-6188	283	1	3n+ 19	DATE
ejpam-6188	283	2	9 ≤ n ≤ 11	QUANTITY
ejpam-6188	284	1	1	CARDINAL
ejpam-6188	284	2	2	DATE
ejpam-6188	284	3	3	DATE
ejpam-6188	284	4	4	DATE
ejpam-6188	284	5	5	CARDINAL
ejpam-6188	286	1	∈	ORG
ejpam-6188	286	2	vi	PERSON
ejpam-6188	286	3	2	CARDINAL
ejpam-6188	287	1	12	CARDINAL
ejpam-6188	287	2	1	CARDINAL
ejpam-6188	287	3	vi	PERSON
ejpam-6188	287	4	14	CARDINAL
ejpam-6188	287	5	2	CARDINAL
ejpam-6188	288	1	vi	PERSON
ejpam-6188	288	2	odd i ≥ 13	DATE
ejpam-6188	289	1	1	CARDINAL
ejpam-6188	289	2	2	DATE
ejpam-6188	289	3	3	DATE
ejpam-6188	289	4	4	DATE
ejpam-6188	289	5	5	CARDINAL
ejpam-6188	291	1	∈	ORG
ejpam-6188	291	2	vi	PERSON
ejpam-6188	291	3	1	CARDINAL
ejpam-6188	292	1	11	CARDINAL
ejpam-6188	292	2	2	CARDINAL
ejpam-6188	292	3	∈	ORG
ejpam-6188	292	4	vi	PERSON
ejpam-6188	292	5	12	CARDINAL
ejpam-6188	292	6	1	CARDINAL
ejpam-6188	292	7	∈	ORG
ejpam-6188	292	8	vi	PERSON
ejpam-6188	292	9	odd i ≥ 13	DATE
ejpam-6188	295	1	3n+19	CARDINAL
ejpam-6188	295	2	n ≥ 12	DATE
ejpam-6188	297	1	n ≥ 12	DATE
ejpam-6188	298	1	n ≥ 9	DATE
ejpam-6188	299	1	theorems 4	ORG
ejpam-6188	299	2	5	DATE
ejpam-6188	299	3	6	CARDINAL
ejpam-6188	301	1	j. pure	PERSON
ejpam-6188	301	2	18	CARDINAL
ejpam-6188	301	3	3	CARDINAL
ejpam-6188	301	4	2025	CARDINAL
ejpam-6188	301	5	6188 11	DATE
ejpam-6188	301	6	13	CARDINAL
ejpam-6188	301	7	3	CARDINAL
ejpam-6188	301	8	5	CARDINAL
ejpam-6188	301	9	1	CARDINAL
ejpam-6188	301	10	1	CARDINAL
ejpam-6188	301	11	1	CARDINAL
ejpam-6188	301	12	1	CARDINAL
ejpam-6188	301	13	1	CARDINAL
ejpam-6188	301	14	4	CARDINAL
ejpam-6188	301	15	3	CARDINAL
ejpam-6188	301	16	2	CARDINAL
ejpam-6188	301	17	1	CARDINAL
ejpam-6188	301	18	9	CARDINAL
ejpam-6188	301	19	µ(p11	GPE
ejpam-6188	301	20	7	CARDINAL
ejpam-6188	302	1	•	CARDINAL
ejpam-6188	303	1	27	CARDINAL
ejpam-6188	304	1	3n+ 19	CARDINAL
ejpam-6188	304	2	10 ≤ n ≤ 15	QUANTITY
ejpam-6188	305	1	3n+ 19	DATE
ejpam-6188	305	2	9	CARDINAL
ejpam-6188	306	1	4	CARDINAL
ejpam-6188	307	1	1	CARDINAL
ejpam-6188	308	1	44	CARDINAL
ejpam-6188	309	1	n ≥ 9	DATE
ejpam-6188	311	1	one	CARDINAL
ejpam-6188	311	2	1	CARDINAL
ejpam-6188	311	3	1	CARDINAL
ejpam-6188	311	4	5	CARDINAL
ejpam-6188	314	1	5	CARDINAL
ejpam-6188	315	1	5	CARDINAL
ejpam-6188	315	2	1	CARDINAL
ejpam-6188	316	1	10 ≤ n ≤ 15	QUANTITY
ejpam-6188	318	1	27	CARDINAL
ejpam-6188	319	1	3n	CARDINAL
ejpam-6188	321	1	9	CARDINAL
ejpam-6188	321	2	1	CARDINAL
ejpam-6188	322	1	1	CARDINAL
ejpam-6188	324	1	1	CARDINAL
ejpam-6188	324	2	n ≥ 9	DATE
ejpam-6188	325	1	3n+ 19	DATE
ejpam-6188	327	1	mycielskian	NORP
ejpam-6188	328	1	one	CARDINAL
ejpam-6188	331	1	j. pure	PERSON
ejpam-6188	331	2	18	CARDINAL
ejpam-6188	331	3	3	CARDINAL
ejpam-6188	331	4	2025	CARDINAL
ejpam-6188	331	5	6188 12	DATE
ejpam-6188	331	6	13 n	QUANTITY
ejpam-6188	331	7	1	CARDINAL
ejpam-6188	331	8	7 27 27	DATE
ejpam-6188	331	9	8 44	DATE
ejpam-6188	331	10	19	CARDINAL
ejpam-6188	331	11	19	CARDINAL
ejpam-6188	331	12	21 10, 12	DATE
ejpam-6188	331	13	14	CARDINAL
ejpam-6188	331	14	18	CARDINAL
ejpam-6188	331	15	19	CARDINAL
ejpam-6188	331	16	21 11, 13	DATE
ejpam-6188	331	17	15	CARDINAL
ejpam-6188	331	18	16 3n+	CARDINAL
ejpam-6188	331	19	19	CARDINAL
ejpam-6188	331	20	21 odd	DATE
ejpam-6188	331	21	19	CARDINAL
ejpam-6188	331	22	19 3n+	CARDINAL
ejpam-6188	331	23	22	CARDINAL
ejpam-6188	331	24	1	CARDINAL
ejpam-6188	331	25	n ≥ 7	ORG
ejpam-6188	336	1	1	CARDINAL
ejpam-6188	336	2	p. c. lisna	PERSON
ejpam-6188	336	3	m. s. sunitha	PERSON
ejpam-6188	338	1	63:407–414	CARDINAL
ejpam-6188	338	2	2017	DATE
ejpam-6188	339	1	2	CARDINAL
ejpam-6188	339	2	r. w. irving	PERSON
ejpam-6188	339	3	d. f. manlove	PERSON
ejpam-6188	341	1	91(1-3):127–141, 1999	ORG
ejpam-6188	342	1	3	CARDINAL
ejpam-6188	342	2	m. alkhateeb and	PERSON
ejpam-6188	342	3	a. kohl	PERSON
ejpam-6188	346	1	31:709–735, 2011	DATE
ejpam-6188	347	1	4	CARDINAL
ejpam-6188	347	2	c. guo	PERSON
ejpam-6188	347	3	m. newman	PERSON
ejpam-6188	348	1	cartesian	NORP
ejpam-6188	349	1	239:82–93, 2018	DATE
ejpam-6188	350	1	5	CARDINAL
ejpam-6188	350	2	k. kouider	PERSON
ejpam-6188	350	3	m. zaker	PERSON
ejpam-6188	352	1	2006	DATE
ejpam-6188	353	1	6	CARDINAL
ejpam-6188	353	2	m. jakovac	PERSON
ejpam-6188	353	3	i. peterin	PERSON
ejpam-6188	355	1	2018	DATE
ejpam-6188	356	1	7	CARDINAL
ejpam-6188	356	2	h. kheddouci	PERSON
ejpam-6188	356	3	a. dussauchoy	PERSON
ejpam-6188	358	1	2008	DATE
ejpam-6188	359	1	8	CARDINAL
ejpam-6188	359	2	a. j. schwenk	PERSON
ejpam-6188	361	1	17th	ORDINAL
ejpam-6188	361	2	csc	ORG
ejpam-6188	361	3	89	CARDINAL
ejpam-6188	361	4	39–45	DATE
ejpam-6188	361	5	new york	GPE
ejpam-6188	361	6	ny, usa, 1989	ORG
ejpam-6188	363	1	9	CARDINAL
ejpam-6188	363	2	m. bellare	PERSON
ejpam-6188	363	3	m. m. halldórsson	PERSON
ejpam-6188	363	4	h. shachnai	PERSON
ejpam-6188	363	5	t. tamir	PERSON
ejpam-6188	365	1	140(2):183	CARDINAL
ejpam-6188	365	2	202	CARDINAL
ejpam-6188	365	3	1998	DATE
ejpam-6188	367	1	j. pure	PERSON
ejpam-6188	367	2	18	CARDINAL
ejpam-6188	367	3	3	CARDINAL
ejpam-6188	367	4	2025	CARDINAL
ejpam-6188	367	5	6188 13	DATE
ejpam-6188	367	6	13	CARDINAL
ejpam-6188	367	7	10	CARDINAL
ejpam-6188	367	8	p. c. lisna	PERSON
ejpam-6188	367	9	m. s. sunitha	PERSON
ejpam-6188	369	1	7(3):1550040	CARDINAL
ejpam-6188	369	2	2015	DATE
ejpam-6188	370	1	11	CARDINAL
ejpam-6188	370	2	p. c. lisna	PERSON
ejpam-6188	370	3	m. s. sunitha	PERSON
ejpam-6188	372	1	2015	DATE
ejpam-6188	373	1	12	CARDINAL
ejpam-6188	373	2	p. c. lisna	PERSON
ejpam-6188	373	3	m. s. sunitha	PERSON
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ejpam-6188	377	1	235(1	CARDINAL
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ejpam-6188	378	1	14	CARDINAL
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ejpam-6188	379	1	sur le coloriage des graphs	ORG
ejpam-6188	380	1	3	CARDINAL
ejpam-6188	380	2	1955	DATE
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ejpam-6188	381	2	p. c. lisna	PERSON
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ejpam-6188	383	1	2(1):23–40	DATE
ejpam-6188	383	2	2016	DATE