id	sid	eid	entity	type
ejpam-6326	1	1	european journal	ORG
ejpam-6326	1	2	2025	DATE
ejpam-6326	1	3	18	CARDINAL
ejpam-6326	1	4	4	CARDINAL
ejpam-6326	1	5	6326	CARDINAL
ejpam-6326	1	6	1307-5543	DATE
ejpam-6326	1	7	new york	GPE
ejpam-6326	1	8	s. cabahug	PERSON
ejpam-6326	1	9	jr.1,∗	GPE
ejpam-6326	1	10	rolito g. eballe1	PERSON
ejpam-6326	1	11	reynard t. fernandez1	ORG
ejpam-6326	2	1	1	CARDINAL
ejpam-6326	2	2	central mindanao university	ORG
ejpam-6326	2	3	8714	CARDINAL
ejpam-6326	2	4	philippines	GPE
ejpam-6326	3	1	two	CARDINAL
ejpam-6326	5	1	first	ORDINAL
ejpam-6326	5	2	one	CARDINAL
ejpam-6326	5	3	two	CARDINAL
ejpam-6326	6	1	two	CARDINAL
ejpam-6326	9	1	two	CARDINAL
ejpam-6326	10	1	2020	DATE
ejpam-6326	10	2	05c69	CARDINAL
ejpam-6326	10	3	1	CARDINAL
ejpam-6326	11	1	the eighteenth century	DATE
ejpam-6326	12	1	1	CARDINAL
ejpam-6326	12	2	2	CARDINAL
ejpam-6326	13	1	one	CARDINAL
ejpam-6326	14	1	henning	PERSON
ejpam-6326	14	2	yeo	PERSON
ejpam-6326	15	1	3	CARDINAL
ejpam-6326	16	1	haynes	ORG
ejpam-6326	16	2	henning	PERSON
ejpam-6326	17	1	4	CARDINAL
ejpam-6326	22	1	9–12	CARDINAL
ejpam-6326	24	1	isaganicabahugjr@cmu.edu.ph (i. s. cabahug, jr.	ORG
ejpam-6326	24	2	rgeballe@cmu.edu.ph	PERSON
ejpam-6326	24	3	r. g. eballe	PERSON
ejpam-6326	24	4	r. t. fernandez	PERSON
ejpam-6326	25	1	1	CARDINAL
ejpam-6326	25	2	2025	CARDINAL
ejpam-6326	26	1	i. s. cabahug, jr.	PERSON
ejpam-6326	26	2	r. g. eballe	PERSON
ejpam-6326	26	3	r. t. fernandez	PERSON
ejpam-6326	27	1	j. pure	PERSON
ejpam-6326	27	2	18	CARDINAL
ejpam-6326	27	3	4	CARDINAL
ejpam-6326	27	4	2025	CARDINAL
ejpam-6326	27	5	6326 2	CARDINAL
ejpam-6326	28	1	one	CARDINAL
ejpam-6326	28	2	13	CARDINAL
ejpam-6326	31	1	14	CARDINAL
ejpam-6326	33	1	one	CARDINAL
ejpam-6326	33	2	two	CARDINAL
ejpam-6326	35	1	two	CARDINAL
ejpam-6326	38	1	2.	CARDINAL
ejpam-6326	38	2	∈	ORG
ejpam-6326	38	3	n(v	ORG
ejpam-6326	38	4	n(v	ORG
ejpam-6326	41	1	n(v	ORG
ejpam-6326	42	1	⊆	CARDINAL
ejpam-6326	42	2	n(s	GPE
ejpam-6326	42	3	⋃	DATE
ejpam-6326	42	4	n(v	ORG
ejpam-6326	42	5	n(s	GPE
ejpam-6326	43	1	s.	PERSON
ejpam-6326	44	1	⊆	CARDINAL
ejpam-6326	45	1	∈	ORG
ejpam-6326	45	2	n(v	ORG
ejpam-6326	47	1	1	CARDINAL
ejpam-6326	50	1	⊆	CARDINAL
ejpam-6326	50	2	⊆	CARDINAL
ejpam-6326	50	3	at least one	CARDINAL
ejpam-6326	50	4	d. equivalently	ORG
ejpam-6326	50	5	⋃	DATE
ejpam-6326	52	1	⊆	CARDINAL
ejpam-6326	53	1	1	CARDINAL
ejpam-6326	53	2	15	CARDINAL
ejpam-6326	53	3	⊆	CARDINAL
ejpam-6326	54	1	degf	PERSON
ejpam-6326	55	1	haynes	ORG
ejpam-6326	55	2	henning	PERSON
ejpam-6326	55	3	i. s. cabahug, jr.	PERSON
ejpam-6326	55	4	r. g. eballe	PERSON
ejpam-6326	55	5	r. t. fernandez	PERSON
ejpam-6326	56	1	j. pure	PERSON
ejpam-6326	56	2	18	CARDINAL
ejpam-6326	56	3	4	CARDINAL
ejpam-6326	56	4	2025	CARDINAL
ejpam-6326	56	5	6326 3	DATE
ejpam-6326	56	6	15	CARDINAL
ejpam-6326	57	1	4	CARDINAL
ejpam-6326	58	1	1	CARDINAL
ejpam-6326	58	2	2	DATE
ejpam-6326	58	3	15	CARDINAL
ejpam-6326	60	1	4	CARDINAL
ejpam-6326	61	1	two	CARDINAL
ejpam-6326	61	2	g ∨ h	ORG
ejpam-6326	61	3	first	ORDINAL
ejpam-6326	61	4	g and h (so no vertex	ORG
ejpam-6326	61	5	two	CARDINAL
ejpam-6326	61	6	∈	ORG
ejpam-6326	62	1	two	CARDINAL
ejpam-6326	62	2	one	CARDINAL
ejpam-6326	63	1	1	CARDINAL
ejpam-6326	63	2	15	CARDINAL
ejpam-6326	63	3	two	CARDINAL
ejpam-6326	63	4	one	CARDINAL
ejpam-6326	65	1	16	CARDINAL
ejpam-6326	65	2	1{a	CARDINAL
ejpam-6326	65	3	1	CARDINAL
ejpam-6326	65	4	0	CARDINAL
ejpam-6326	66	1	1	CARDINAL
ejpam-6326	66	2	0	CARDINAL
ejpam-6326	66	3	1{x/∈s	CARDINAL
ejpam-6326	66	4	1	CARDINAL
ejpam-6326	66	5	0	CARDINAL
ejpam-6326	67	1	one	CARDINAL
ejpam-6326	67	2	two	CARDINAL
ejpam-6326	67	3	1	CARDINAL
ejpam-6326	67	4	0	CARDINAL
ejpam-6326	70	1	an)1/n	PERSON
ejpam-6326	71	1	an)1/n	FAC
ejpam-6326	71	2	17	CARDINAL
ejpam-6326	72	1	3	CARDINAL
ejpam-6326	72	2	1	CARDINAL
ejpam-6326	74	1	⊆	CARDINAL
ejpam-6326	75	1	degf	PERSON
ejpam-6326	77	1	1	CARDINAL
ejpam-6326	77	2	v2, v3	GPE
ejpam-6326	78	1	i. s. cabahug, jr.	PERSON
ejpam-6326	78	2	r. g. eballe	PERSON
ejpam-6326	78	3	r. t. fernandez	PERSON
ejpam-6326	79	1	j. pure	PERSON
ejpam-6326	79	2	18	CARDINAL
ejpam-6326	79	3	4	CARDINAL
ejpam-6326	79	4	2025	CARDINAL
ejpam-6326	79	5	6326 4	DATE
ejpam-6326	79	6	15	CARDINAL
ejpam-6326	81	1	1 ≤	MONEY
ejpam-6326	82	1	1	CARDINAL
ejpam-6326	82	2	1 ≤	MONEY
ejpam-6326	83	1	1	CARDINAL
ejpam-6326	84	1	2	CARDINAL
ejpam-6326	84	2	3.1	CARDINAL
ejpam-6326	86	1	1	CARDINAL
ejpam-6326	94	1	2	CARDINAL
ejpam-6326	96	1	g. theorem 1	ORG
ejpam-6326	97	1	⊆	CARDINAL
ejpam-6326	99	1	⊆	CARDINAL
ejpam-6326	99	2	∈	ORG
ejpam-6326	101	1	one	CARDINAL
ejpam-6326	101	2	w.	PERSON
ejpam-6326	101	3	w ∈	PERSON
ejpam-6326	102	1	1	CARDINAL
ejpam-6326	105	1	1	CARDINAL
ejpam-6326	106	1	0	CARDINAL
ejpam-6326	108	1	2	CARDINAL
ejpam-6326	109	1	⊆	CARDINAL
ejpam-6326	111	1	i. s. cabahug, jr.	PERSON
ejpam-6326	111	2	r. g. eballe	PERSON
ejpam-6326	111	3	r. t. fernandez	PERSON
ejpam-6326	112	1	j. pure	PERSON
ejpam-6326	112	2	18	CARDINAL
ejpam-6326	112	3	4	CARDINAL
ejpam-6326	112	4	2025	CARDINAL
ejpam-6326	112	5	6326 5	DATE
ejpam-6326	112	6	15	CARDINAL
ejpam-6326	113	1	w.	PERSON
ejpam-6326	113	2	w ∈	ORG
ejpam-6326	114	1	0	CARDINAL
ejpam-6326	115	1	1	CARDINAL
ejpam-6326	116	1	1 ≤	CARDINAL
ejpam-6326	116	2	0	CARDINAL
ejpam-6326	118	1	3	CARDINAL
ejpam-6326	119	1	2	CARDINAL
ejpam-6326	120	1	1	CARDINAL
ejpam-6326	120	2	∈	ORG
ejpam-6326	120	3	at least one	CARDINAL
ejpam-6326	122	1	1	CARDINAL
ejpam-6326	122	2	⊆	CARDINAL
ejpam-6326	123	1	1	CARDINAL
ejpam-6326	127	1	1	CARDINAL
ejpam-6326	128	1	∈	ORG
ejpam-6326	129	1	1	CARDINAL
ejpam-6326	130	1	1	CARDINAL
ejpam-6326	130	2	at least one	CARDINAL
ejpam-6326	130	3	∈	ORG
ejpam-6326	130	4	1	CARDINAL
ejpam-6326	130	5	1	CARDINAL
ejpam-6326	131	1	1	CARDINAL
ejpam-6326	132	1	degf	PERSON
ejpam-6326	132	2	1 ≤	MONEY
ejpam-6326	134	1	1	CARDINAL
ejpam-6326	135	1	1	CARDINAL
ejpam-6326	135	2	1	CARDINAL
ejpam-6326	136	1	w1,m	NORP
ejpam-6326	136	2	2	CARDINAL
ejpam-6326	136	3	w1,m	NORP
ejpam-6326	136	4	1	CARDINAL
ejpam-6326	137	1	3	CARDINAL
ejpam-6326	137	2	4	CARDINAL
ejpam-6326	139	1	2	CARDINAL
ejpam-6326	139	2	three	CARDINAL
ejpam-6326	142	1	1	CARDINAL
ejpam-6326	142	2	two	CARDINAL
ejpam-6326	142	3	∈	ORG
ejpam-6326	142	4	at least one	CARDINAL
ejpam-6326	142	5	∈	ORG
ejpam-6326	143	1	y}(v	PERSON
ejpam-6326	146	1	2	CARDINAL
ejpam-6326	146	2	⊆	CARDINAL
ejpam-6326	146	3	two	CARDINAL
ejpam-6326	147	1	at least one	CARDINAL
ejpam-6326	148	1	degf	PERSON
ejpam-6326	149	1	i. s. cabahug, jr.	PERSON
ejpam-6326	149	2	r. g. eballe	PERSON
ejpam-6326	149	3	r. t. fernandez	PERSON
ejpam-6326	150	1	j. pure	PERSON
ejpam-6326	150	2	18	CARDINAL
ejpam-6326	150	3	4	CARDINAL
ejpam-6326	150	4	2025	CARDINAL
ejpam-6326	150	5	6326 6	CARDINAL
ejpam-6326	150	6	15	CARDINAL
ejpam-6326	150	7	1	CARDINAL
ejpam-6326	150	8	2	CARDINAL
ejpam-6326	150	9	three	CARDINAL
ejpam-6326	154	1	1	CARDINAL
ejpam-6326	154	2	2	CARDINAL
ejpam-6326	154	3	2	CARDINAL
ejpam-6326	154	4	2	CARDINAL
ejpam-6326	155	1	2	CARDINAL
ejpam-6326	155	2	∆(h	NORP
ejpam-6326	155	3	1	CARDINAL
ejpam-6326	157	1	2	CARDINAL
ejpam-6326	157	2	bipartite	NORP
ejpam-6326	157	3	graph km	PERSON
ejpam-6326	157	4	2	CARDINAL
ejpam-6326	158	1	2	CARDINAL
ejpam-6326	159	1	4	CARDINAL
ejpam-6326	159	2	5	CARDINAL
ejpam-6326	160	1	γ(g	NORP
ejpam-6326	164	1	1	CARDINAL
ejpam-6326	164	2	1	CARDINAL
ejpam-6326	165	1	xi|i	DATE
ejpam-6326	165	2	1	CARDINAL
ejpam-6326	165	3	2	DATE
ejpam-6326	165	4	3	DATE
ejpam-6326	170	1	xa−1 xa	PERSON
ejpam-6326	170	2	1	CARDINAL
ejpam-6326	171	1	2	CARDINAL
ejpam-6326	171	2	2	CARDINAL
ejpam-6326	171	3	x3	GPE
ejpam-6326	173	1	xa−1	PERSON
ejpam-6326	173	2	xa	PERSON
ejpam-6326	176	1	γ(g	PERSON
ejpam-6326	180	1	yb−a}| = a+ b−	PERSON
ejpam-6326	182	1	3	CARDINAL
ejpam-6326	186	1	5	CARDINAL
ejpam-6326	186	2	γ(h	ORG
ejpam-6326	187	1	1	CARDINAL
ejpam-6326	187	2	i. s. cabahug, jr.	PERSON
ejpam-6326	187	3	r. g. eballe	PERSON
ejpam-6326	187	4	r. t. fernandez	PERSON
ejpam-6326	188	1	j. pure	PERSON
ejpam-6326	188	2	18	CARDINAL
ejpam-6326	188	3	4	CARDINAL
ejpam-6326	188	4	2025	CARDINAL
ejpam-6326	188	5	6326 7	DATE
ejpam-6326	190	1	xa−1 xa y1 y2 y3	PERSON
ejpam-6326	190	2	2	CARDINAL
ejpam-6326	191	1	+ 1	DATE
ejpam-6326	192	1	− γ(g	PERSON
ejpam-6326	193	1	1	CARDINAL
ejpam-6326	194	1	6	CARDINAL
ejpam-6326	195	1	2	CARDINAL
ejpam-6326	195	2	⊆	CARDINAL
ejpam-6326	197	1	∈	ORG
ejpam-6326	198	1	1	CARDINAL
ejpam-6326	198	2	one	CARDINAL
ejpam-6326	199	1	∈	ORG
ejpam-6326	199	2	1	CARDINAL
ejpam-6326	201	1	⊆	CARDINAL
ejpam-6326	201	2	1	CARDINAL
ejpam-6326	201	3	∈	ORG
ejpam-6326	201	4	1	CARDINAL
ejpam-6326	202	1	2	CARDINAL
ejpam-6326	204	1	two	CARDINAL
ejpam-6326	204	2	2	CARDINAL
ejpam-6326	204	3	0	CARDINAL
ejpam-6326	207	1	1	CARDINAL
ejpam-6326	208	1	1	CARDINAL
ejpam-6326	209	1	one	CARDINAL
ejpam-6326	210	1	2	CARDINAL
ejpam-6326	210	2	one	CARDINAL
ejpam-6326	210	3	one	CARDINAL
ejpam-6326	210	4	1	CARDINAL
ejpam-6326	210	5	1 ≤ 1	QUANTITY
ejpam-6326	211	1	g. corollary 4	PERSON
ejpam-6326	212	1	2	CARDINAL
ejpam-6326	213	1	i. s. cabahug, jr.	PERSON
ejpam-6326	213	2	r. g. eballe	PERSON
ejpam-6326	213	3	r. t. fernandez	PERSON
ejpam-6326	214	1	j. pure	PERSON
ejpam-6326	214	2	18	CARDINAL
ejpam-6326	214	3	4	CARDINAL
ejpam-6326	214	4	2025	CARDINAL
ejpam-6326	214	5	6326 8	DATE
ejpam-6326	214	6	15	CARDINAL
ejpam-6326	215	1	 n+ 6 3	DATE
ejpam-6326	215	2	n ≡ 0	ORG
ejpam-6326	215	3	2 3	DATE
ejpam-6326	215	4	n ≡ 1	ORG
ejpam-6326	215	5	4 3	DATE
ejpam-6326	215	6	n ≡ 2	ORG
ejpam-6326	220	1	vn−1	ORG
ejpam-6326	221	1	1	CARDINAL
ejpam-6326	222	1	3	CARDINAL
ejpam-6326	223	1	6 3	CARDINAL
ejpam-6326	223	2	3	CARDINAL
ejpam-6326	223	3	3	CARDINAL
ejpam-6326	224	1	3	CARDINAL
ejpam-6326	226	1	2 + n 3	DATE
ejpam-6326	226	2	6 3	DATE
ejpam-6326	227	1	6	CARDINAL
ejpam-6326	228	1	6 3	DATE
ejpam-6326	229	1	6 3	DATE
ejpam-6326	230	1	6 3	CARDINAL
ejpam-6326	231	1	2	CARDINAL
ejpam-6326	231	2	n ≡ 2	ORG
ejpam-6326	231	3	1	CARDINAL
ejpam-6326	234	1	2 + n−	DATE
ejpam-6326	234	2	4 3	DATE
ejpam-6326	234	3	2 3	CARDINAL
ejpam-6326	234	4	n ≡ 1	ORG
ejpam-6326	237	1	2 + n−	DATE
ejpam-6326	237	2	2 3	DATE
ejpam-6326	237	3	4 3	CARDINAL
ejpam-6326	237	4	n ≡ 2	ORG
ejpam-6326	238	1	5	CARDINAL
ejpam-6326	239	1	3	CARDINAL
ejpam-6326	240	1	3	CARDINAL
ejpam-6326	242	1	one	CARDINAL
ejpam-6326	243	1	one	CARDINAL
ejpam-6326	243	2	3	CARDINAL
ejpam-6326	244	1	3	CARDINAL
ejpam-6326	245	1	3.2	CARDINAL
ejpam-6326	246	1	7	CARDINAL
ejpam-6326	248	1	0 ≤	MONEY
ejpam-6326	248	2	1	CARDINAL
ejpam-6326	251	1	i. s. cabahug, jr.	PERSON
ejpam-6326	251	2	r. g. eballe	PERSON
ejpam-6326	251	3	r. t. fernandez	PERSON
ejpam-6326	252	1	j. pure	PERSON
ejpam-6326	252	2	18	CARDINAL
ejpam-6326	252	3	4	CARDINAL
ejpam-6326	252	4	2025	CARDINAL
ejpam-6326	252	5	6326 9	DATE
ejpam-6326	252	6	at least 1	CARDINAL
ejpam-6326	253	1	1	CARDINAL
ejpam-6326	253	2	0 ≤	MONEY
ejpam-6326	254	1	≤ n−	ORG
ejpam-6326	254	2	1	CARDINAL
ejpam-6326	255	1	1	CARDINAL
ejpam-6326	256	1	1	CARDINAL
ejpam-6326	256	2	kn	PERSON
ejpam-6326	256	3	kn	ORG
ejpam-6326	257	1	kn	PERSON
ejpam-6326	258	1	1	CARDINAL
ejpam-6326	258	2	1	CARDINAL
ejpam-6326	259	1	∣∣γf	ORG
ejpam-6326	259	2	0	CARDINAL
ejpam-6326	261	1	1	CARDINAL
ejpam-6326	264	1	1	CARDINAL
ejpam-6326	265	1	at least two	CARDINAL
ejpam-6326	268	1	2	CARDINAL
ejpam-6326	272	1	ℓn−1	ORG
ejpam-6326	273	1	⊆	CARDINAL
ejpam-6326	276	1	1	CARDINAL
ejpam-6326	277	1	∈	ORG
ejpam-6326	278	1	1	CARDINAL
ejpam-6326	280	1	8	CARDINAL
ejpam-6326	281	1	4	CARDINAL
ejpam-6326	284	1	lemma 1	ORG
ejpam-6326	284	2	2n	CARDINAL
ejpam-6326	285	1	6	CARDINAL
ejpam-6326	286	1	4	CARDINAL
ejpam-6326	287	1	i. s. cabahug, jr.	PERSON
ejpam-6326	287	2	r. g. eballe	PERSON
ejpam-6326	287	3	r. t. fernandez	PERSON
ejpam-6326	288	1	j. pure	PERSON
ejpam-6326	288	2	18	CARDINAL
ejpam-6326	288	3	4	CARDINAL
ejpam-6326	288	4	2025	CARDINAL
ejpam-6326	288	5	6326 10	DATE
ejpam-6326	288	6	15	CARDINAL
ejpam-6326	289	1	8	CARDINAL
ejpam-6326	293	1	2	CARDINAL
ejpam-6326	293	2	2	CARDINAL
ejpam-6326	296	1	2n 2	CARDINAL
ejpam-6326	296	2	2	CARDINAL
ejpam-6326	297	1	3.3	CARDINAL
ejpam-6326	298	1	3	CARDINAL
ejpam-6326	299	1	⊆	CARDINAL
ejpam-6326	300	1	⊆	CARDINAL
ejpam-6326	300	2	⊆	CARDINAL
ejpam-6326	301	1	9	CARDINAL
ejpam-6326	303	1	⊆	CARDINAL
ejpam-6326	303	2	⊆	CARDINAL
ejpam-6326	306	1	2	CARDINAL
ejpam-6326	306	2	2	CARDINAL
ejpam-6326	309	1	f1	PERSON
ejpam-6326	309	2	f2	ORG
ejpam-6326	311	1	∈	ORG
ejpam-6326	311	2	g∨h)\f	ORG
ejpam-6326	313	1	2	CARDINAL
ejpam-6326	314	1	∈	ORG
ejpam-6326	314	2	2	CARDINAL
ejpam-6326	315	1	2	CARDINAL
ejpam-6326	315	2	2	CARDINAL
ejpam-6326	315	3	f1	PERSON
ejpam-6326	315	4	f2	ORG
ejpam-6326	321	1	n2−|f2|	PERSON
ejpam-6326	322	1	g∨h)\f	ORG
ejpam-6326	323	1	2	CARDINAL
ejpam-6326	324	1	degf	PERSON
ejpam-6326	324	2	g∨h)\f	ORG
ejpam-6326	325	1	w ∈	ORG
ejpam-6326	325	2	g∨h)\f	ORG
ejpam-6326	328	1	10	CARDINAL
ejpam-6326	329	1	⊆	CARDINAL
ejpam-6326	330	1	three	CARDINAL
ejpam-6326	332	1	δ(h	PERSON
ejpam-6326	332	2	i. s. cabahug, jr.	PERSON
ejpam-6326	332	3	r. g. eballe	PERSON
ejpam-6326	332	4	r. t. fernandez	PERSON
ejpam-6326	333	1	j. pure	PERSON
ejpam-6326	333	2	18	CARDINAL
ejpam-6326	333	3	4	CARDINAL
ejpam-6326	333	4	2025	CARDINAL
ejpam-6326	333	5	6326 11	DATE
ejpam-6326	335	1	g ∨ h.	ORG
ejpam-6326	336	1	∈	ORG
ejpam-6326	338	1	g∨h)\f	ORG
ejpam-6326	339	1	δ(h	PERSON
ejpam-6326	341	1	δ(h	PERSON
ejpam-6326	349	1	two	CARDINAL
ejpam-6326	350	1	1	CARDINAL
ejpam-6326	352	1	g∨h)\f	ORG
ejpam-6326	355	1	δ(h	PERSON
ejpam-6326	355	2	g∨h)\f	ORG
ejpam-6326	356	1	2	CARDINAL
ejpam-6326	359	1	g∨h)\f	ORG
ejpam-6326	362	1	11	CARDINAL
ejpam-6326	363	1	⊆	CARDINAL
ejpam-6326	364	1	three	CARDINAL
ejpam-6326	367	1	10	CARDINAL
ejpam-6326	367	2	12	CARDINAL
ejpam-6326	369	1	⊆	CARDINAL
ejpam-6326	369	2	⊆	CARDINAL
ejpam-6326	369	3	f2	ORG
ejpam-6326	370	1	g ∨ h	ORG
ejpam-6326	371	1	two	CARDINAL
ejpam-6326	372	1	− 2|f2|	PERSON
ejpam-6326	372	2	deghf2	PERSON
ejpam-6326	373	1	− 2|f1|	ORG
ejpam-6326	377	1	∈	ORG
ejpam-6326	380	1	deggf1	PERSON
ejpam-6326	380	2	− 2|f2|	PERSON
ejpam-6326	381	1	deghf2	PERSON
ejpam-6326	382	1	− 2|f1|	ORG
ejpam-6326	384	1	f1	PERSON
ejpam-6326	385	1	f2	PERSON
ejpam-6326	385	2	at least one	CARDINAL
ejpam-6326	387	1	i. s. cabahug, jr.	PERSON
ejpam-6326	387	2	r. g. eballe	PERSON
ejpam-6326	387	3	r. t. fernandez	PERSON
ejpam-6326	388	1	j. pure	PERSON
ejpam-6326	388	2	18	CARDINAL
ejpam-6326	388	3	4	CARDINAL
ejpam-6326	388	4	2025	CARDINAL
ejpam-6326	388	5	6326 12	DATE
ejpam-6326	388	6	15	CARDINAL
ejpam-6326	391	1	deggf1	PERSON
ejpam-6326	392	1	deggf1	PERSON
ejpam-6326	395	1	g∨h)\f	ORG
ejpam-6326	398	1	3.4	CARDINAL
ejpam-6326	398	2	13	CARDINAL
ejpam-6326	400	1	⊆	CARDINAL
ejpam-6326	400	2	⊆	CARDINAL
ejpam-6326	404	1	first	ORDINAL
ejpam-6326	404	2	∈	ORG
ejpam-6326	406	1	h /∈	FAC
ejpam-6326	412	1	one	CARDINAL
ejpam-6326	413	1	1	CARDINAL
ejpam-6326	416	1	1	CARDINAL
ejpam-6326	416	2	1 ≤	MONEY
ejpam-6326	419	1	14	DATE
ejpam-6326	420	1	⊆	CARDINAL
ejpam-6326	421	1	⊆	CARDINAL
ejpam-6326	421	2	⋃	PRODUCT
ejpam-6326	423	1	2	CARDINAL
ejpam-6326	426	1	∈	ORG
ejpam-6326	426	2	∈	ORG
ejpam-6326	427	1	degg(x)+|v	ORG
ejpam-6326	427	2	2	CARDINAL
ejpam-6326	430	1	ng◦h	ORG
ejpam-6326	433	1	∈	ORG
ejpam-6326	435	1	∈	ORG
ejpam-6326	435	2	2	CARDINAL
ejpam-6326	437	1	1	CARDINAL
ejpam-6326	437	2	2|px|	ORG
ejpam-6326	437	3	2a ≤	MONEY
ejpam-6326	438	1	i. s. cabahug, jr.	PERSON
ejpam-6326	438	2	r. g. eballe	PERSON
ejpam-6326	438	3	r. t. fernandez	PERSON
ejpam-6326	439	1	j. pure	PERSON
ejpam-6326	439	2	18	CARDINAL
ejpam-6326	439	3	4	CARDINAL
ejpam-6326	439	4	2025	CARDINAL
ejpam-6326	439	5	6326 13	DATE
ejpam-6326	439	6	15	CARDINAL
ejpam-6326	439	7	2	CARDINAL
ejpam-6326	439	8	+ 1	CARDINAL
ejpam-6326	441	1	g ◦h. theorem 15	ORG
ejpam-6326	442	1	⊆	CARDINAL
ejpam-6326	443	1	f0 ⊆	CARDINAL
ejpam-6326	443	2	⊆	PRODUCT
ejpam-6326	443	3	̸=	PERSON
ejpam-6326	443	4	at least one	CARDINAL
ejpam-6326	443	5	⋃	PRODUCT
ejpam-6326	446	1	f0	PRODUCT
ejpam-6326	446	2	̸=	PERSON
ejpam-6326	447	1	nhx	ORG
ejpam-6326	449	1	∈	ORG
ejpam-6326	449	2	degf0	PRODUCT
ejpam-6326	452	1	degpx	PERSON
ejpam-6326	457	1	f0	PRODUCT
ejpam-6326	462	1	px dominates hx	PERSON
ejpam-6326	470	1	1{x∈f0	CARDINAL
ejpam-6326	473	1	∈	ORG
ejpam-6326	474	1	f0	PRODUCT
ejpam-6326	475	1	⊆	PRODUCT
ejpam-6326	476	1	ng◦h	ORG
ejpam-6326	482	1	∈	ORG
ejpam-6326	483	1	∈ hx \px	ORG
ejpam-6326	487	1	i. s. cabahug, jr.	PERSON
ejpam-6326	487	2	r. g. eballe	PERSON
ejpam-6326	487	3	r. t. fernandez	PERSON
ejpam-6326	488	1	j. pure	PERSON
ejpam-6326	488	2	18	CARDINAL
ejpam-6326	488	3	4	CARDINAL
ejpam-6326	488	4	2025	CARDINAL
ejpam-6326	488	5	6326 14	DATE
ejpam-6326	488	6	15	CARDINAL
ejpam-6326	489	1	13	CARDINAL
ejpam-6326	489	2	g◦h	ORG
ejpam-6326	491	1	14	CARDINAL
ejpam-6326	491	2	15	CARDINAL
ejpam-6326	491	3	at least one	CARDINAL
ejpam-6326	493	1	g ◦h	ORG
ejpam-6326	494	1	4.	CARDINAL
ejpam-6326	495	1	1 or	CARDINAL
ejpam-6326	495	2	2	CARDINAL
ejpam-6326	495	3	− γ	PERSON
ejpam-6326	496	1	two	CARDINAL
ejpam-6326	497	1	two	CARDINAL
ejpam-6326	498	1	cartesian	NORP
ejpam-6326	501	1	central mindanao university	ORG
ejpam-6326	503	1	1	CARDINAL
ejpam-6326	503	2	j. a. bondy	PERSON
ejpam-6326	503	3	u. s. r. murty	PERSON
ejpam-6326	505	1	berlin	GPE
ejpam-6326	505	2	germany	GPE
ejpam-6326	505	3	2008	DATE
ejpam-6326	506	1	2	CARDINAL
ejpam-6326	506	2	d. b. west	PERSON
ejpam-6326	508	1	prentice hall	ORG
ejpam-6326	508	2	nj	GPE
ejpam-6326	508	3	2001	DATE
ejpam-6326	509	1	3	CARDINAL
ejpam-6326	509	2	m. a. henning	PERSON
ejpam-6326	509	3	a. yeo	PERSON
ejpam-6326	511	1	new york	GPE
ejpam-6326	511	2	usa	GPE
ejpam-6326	511	3	2013	DATE
ejpam-6326	512	1	4	CARDINAL
ejpam-6326	512	2	w. haynes	PERSON
ejpam-6326	512	3	s. t. hedetniemi	PERSON
ejpam-6326	512	4	m. a. henning	PERSON
ejpam-6326	514	1	cham	GPE
ejpam-6326	514	2	switzerland	GPE
ejpam-6326	514	3	2021	DATE
ejpam-6326	515	1	5	CARDINAL
ejpam-6326	515	2	j. m. sigarreta	PERSON
ejpam-6326	515	3	j. a. rodŕıguez-velázquez	PERSON
ejpam-6326	517	1	2009	DATE
ejpam-6326	518	1	i. s. cabahug, jr.	PERSON
ejpam-6326	518	2	r. g. eballe	PERSON
ejpam-6326	518	3	r. t. fernandez	PERSON
ejpam-6326	519	1	j. pure	PERSON
ejpam-6326	519	2	18	CARDINAL
ejpam-6326	519	3	4	CARDINAL
ejpam-6326	519	4	2025	CARDINAL
ejpam-6326	519	5	6326 15	DATE
ejpam-6326	519	6	6	CARDINAL
ejpam-6326	519	7	o. favaron	PERSON
ejpam-6326	519	8	g. fricke	PERSON
ejpam-6326	519	9	w. goddard	PERSON
ejpam-6326	519	10	s. m. hedetniemi	PERSON
ejpam-6326	519	11	s. t. hedetniemi	PERSON
ejpam-6326	519	12	p. kristiansen	PERSON
ejpam-6326	519	13	r. c. laskar	PERSON
ejpam-6326	519	14	r. d. skaggs	PERSON
ejpam-6326	521	1	24(2):263–275	ORG
ejpam-6326	521	2	2004	DATE
ejpam-6326	522	1	7	CARDINAL
ejpam-6326	522	2	m. s. hablo	PERSON
ejpam-6326	522	3	i. s. cabahug jr.	PERSON
ejpam-6326	522	4	2	CARDINAL
ejpam-6326	522	5	42(4):391–399	DATE
ejpam-6326	522	6	2025	DATE
ejpam-6326	523	1	8	CARDINAL
ejpam-6326	523	2	k. s. r. tan	PERSON
ejpam-6326	523	3	i. s. cabahug jr.	PERSON
ejpam-6326	525	1	42(3):191–204	ORG
ejpam-6326	525	2	2025	DATE
ejpam-6326	526	1	9	CARDINAL
ejpam-6326	526	2	w. haynes	PERSON
ejpam-6326	526	3	s. t. hedetniemi	PERSON
ejpam-6326	526	4	m. a. henning	PERSON
ejpam-6326	528	1	journal of combinatorics	ORG
ejpam-6326	528	2	10(1):r47, 2003	DATE
ejpam-6326	529	1	10	CARDINAL
ejpam-6326	529	2	j. m. sigarreta	PERSON
ejpam-6326	529	3	j. a. rodŕıguez-velázquez	PERSON
ejpam-6326	531	1	19(12):1345–1350, 2006	DATE
ejpam-6326	532	1	11	CARDINAL
ejpam-6326	532	2	w. haynes	PERSON
ejpam-6326	532	3	s. t. hedetniemi	PERSON
ejpam-6326	532	4	m. a. henning	PERSON
ejpam-6326	534	1	17th	ORDINAL
ejpam-6326	534	2	303–307	CARDINAL
ejpam-6326	535	1	crc press / taylor & francis	ORG
ejpam-6326	535	2	2022	CARDINAL
ejpam-6326	536	1	12	CARDINAL
ejpam-6326	536	2	l. f. consistente	PERSON
ejpam-6326	536	3	i.s.	GPE
ejpam-6326	536	4	cabahug jr.	PERSON
ejpam-6326	537	1	european journal	ORG
ejpam-6326	537	2	17(3):2196–2209	CARDINAL
ejpam-6326	537	3	2024	DATE
ejpam-6326	538	1	13	CARDINAL
ejpam-6326	538	2	a. hansberg	PERSON
ejpam-6326	538	3	m. a. henning	PERSON
ejpam-6326	540	1	312:2905–2914	CARDINAL
ejpam-6326	540	2	2012	DATE
ejpam-6326	541	1	14	CARDINAL
ejpam-6326	541	2	f. harary	PERSON
ejpam-6326	541	3	w. haynes	PERSON
ejpam-6326	542	1	nordhaus	ORG
ejpam-6326	543	1	155(1	CARDINAL
ejpam-6326	543	2	1996	DATE
ejpam-6326	544	1	15	CARDINAL
ejpam-6326	544	2	l. lesniak	PERSON
ejpam-6326	545	1	crc press	ORG
ejpam-6326	545	2	boca raton	GPE
ejpam-6326	545	3	fl, usa	ORG
ejpam-6326	545	4	6th	ORDINAL
ejpam-6326	545	5	2016	DATE
ejpam-6326	546	1	16	CARDINAL
ejpam-6326	546	2	r. frucht	PERSON
ejpam-6326	546	3	f. harary	PERSON
ejpam-6326	547	1	two	CARDINAL
ejpam-6326	548	1	aequationes mathematicae	PERSON
ejpam-6326	548	2	4:322–325, 1970	DATE
ejpam-6326	549	1	17	CARDINAL
ejpam-6326	549	2	g. h. hardy	PERSON
ejpam-6326	549	3	j. e. littlewood	PERSON
ejpam-6326	551	1	cambridge university press	ORG
ejpam-6326	551	2	cambridge	GPE
ejpam-6326	551	3	uk	GPE
ejpam-6326	551	4	2nd	ORDINAL
ejpam-6326	551	5	1952	DATE