id	sid	eid	entity	type
ejpam-3443	1	1	european journal	ORG
ejpam-3443	2	1	12	CARDINAL
ejpam-3443	2	2	3, 2019	DATE
ejpam-3443	2	3	978	CARDINAL
ejpam-3443	2	4	new york	GPE
ejpam-3443	2	5	jamil1	GPE
ejpam-3443	2	6	1	CARDINAL
ejpam-3443	2	7	msu-iligan institute of technology	ORG
ejpam-3443	2	8	9200	CARDINAL
ejpam-3443	2	9	iligan city	GPE
ejpam-3443	2	10	philippines 2 department	ORG
ejpam-3443	2	11	university of science and technology of southern philippines	ORG
ejpam-3443	2	12	9000 cagayan de oro city	FAC
ejpam-3443	3	1	philippines	GPE
ejpam-3443	5	1	at least one	CARDINAL
ejpam-3443	5	2	s.	GPE
ejpam-3443	7	1	2010	DATE
ejpam-3443	7	2	05c12	CARDINAL
ejpam-3443	7	3	1	CARDINAL
ejpam-3443	8	1	1	CARDINAL
ejpam-3443	9	1	⊆	CARDINAL
ejpam-3443	9	2	g. ∗corresponding	PERSON
ejpam-3443	10	1	ferdinand.jamil@g.msuiit.edu.ph	ORG
ejpam-3443	10	2	f. jamil	PERSON
ejpam-3443	11	1	h. nuenay-maglanque	PERSON
ejpam-3443	11	2	978	CARDINAL
ejpam-3443	12	1	2019	CARDINAL
ejpam-3443	13	1	h. nuenay-maglanque	PERSON
ejpam-3443	14	1	j. pure	PERSON
ejpam-3443	14	2	12	CARDINAL
ejpam-3443	14	3	3	CARDINAL
ejpam-3443	14	4	2019	DATE
ejpam-3443	14	5	978	CARDINAL
ejpam-3443	14	6	∈	ORG
ejpam-3443	15	1	one	CARDINAL
ejpam-3443	16	1	u = u′	ORG
ejpam-3443	16	2	∈ e(h	ORG
ejpam-3443	17	1	∈	ORG
ejpam-3443	18	1	∈	ORG
ejpam-3443	19	1	∈	ORG
ejpam-3443	19	2	∈	ORG
ejpam-3443	20	1	zero	CARDINAL
ejpam-3443	21	1	⊆	CARDINAL
ejpam-3443	23	1	γ(g	PERSON
ejpam-3443	24	1	two	CARDINAL
ejpam-3443	24	2	∈	ORG
ejpam-3443	25	1	i(g	PERSON
ejpam-3443	26	1	2–7	CARDINAL
ejpam-3443	27	1	8, 9	DATE
ejpam-3443	27	2	13	CARDINAL
ejpam-3443	28	1	⊆	CARDINAL
ejpam-3443	29	1	⊆	CARDINAL
ejpam-3443	29	2	∈	ORG
ejpam-3443	30	1	⊆	CARDINAL
ejpam-3443	33	1	γ+ce(g	DATE
ejpam-3443	35	1	11	CARDINAL
ejpam-3443	35	2	12	CARDINAL
ejpam-3443	36	1	⊆	CARDINAL
ejpam-3443	39	1	γmce	PERSON
ejpam-3443	39	2	γ+ce(g	DATE
ejpam-3443	41	1	h. nuenay-maglanque	PERSON
ejpam-3443	42	1	j. pure	PERSON
ejpam-3443	42	2	12	CARDINAL
ejpam-3443	42	3	3	CARDINAL
ejpam-3443	42	4	2019	DATE
ejpam-3443	42	5	978	CARDINAL
ejpam-3443	43	1	2	CARDINAL
ejpam-3443	43	2	1	CARDINAL
ejpam-3443	44	1	two	CARDINAL
ejpam-3443	44	2	s of g+h	PRODUCT
ejpam-3443	44	3	⊆	CARDINAL
ejpam-3443	44	4	1	CARDINAL
ejpam-3443	45	1	1	CARDINAL
ejpam-3443	46	1	1	CARDINAL
ejpam-3443	46	2	v1 v2 v3 v4 v5 u	PERSON
ejpam-3443	46	3	1	CARDINAL
ejpam-3443	46	4	⊆	CARDINAL
ejpam-3443	49	1	⊆	CARDINAL
ejpam-3443	49	2	g+h	ORG
ejpam-3443	51	1	⊆	CARDINAL
ejpam-3443	52	1	g+h	ORG
ejpam-3443	53	1	∈	ORG
ejpam-3443	55	1	g+h	ORG
ejpam-3443	56	1	1	CARDINAL
ejpam-3443	57	1	⊆	CARDINAL
ejpam-3443	58	1	g+h	ORG
ejpam-3443	58	2	⊆	CARDINAL
ejpam-3443	58	3	∈	ORG
ejpam-3443	58	4	⊆	CARDINAL
ejpam-3443	58	5	∈	ORG
ejpam-3443	58	6	6=	CARDINAL
ejpam-3443	58	7	6=	CARDINAL
ejpam-3443	58	8	∈	ORG
ejpam-3443	58	9	∩ v (	LAW
ejpam-3443	58	10	∈	ORG
ejpam-3443	59	1	h. nuenay-maglanque	PERSON
ejpam-3443	60	1	j. pure	PERSON
ejpam-3443	60	2	12	CARDINAL
ejpam-3443	60	3	3	CARDINAL
ejpam-3443	60	4	2019	DATE
ejpam-3443	60	5	978	CARDINAL
ejpam-3443	61	1	⊆	CARDINAL
ejpam-3443	62	1	g+h	ORG
ejpam-3443	63	1	⊆	CARDINAL
ejpam-3443	63	2	∈	ORG
ejpam-3443	65	1	⊆	CARDINAL
ejpam-3443	65	2	∈	ORG
ejpam-3443	66	1	+ |nh(v	PERSON
ejpam-3443	66	2	6=	CARDINAL
ejpam-3443	66	3	6=	CARDINAL
ejpam-3443	69	1	2|s2|	CARDINAL
ejpam-3443	70	1	∈	ORG
ejpam-3443	70	2	|nh(v) ∩	ORG
ejpam-3443	70	3	2|s1| ≤	MONEY
ejpam-3443	73	1	g+h	ORG
ejpam-3443	74	1	g+h	PRODUCT
ejpam-3443	76	1	g+h	ORG
ejpam-3443	77	1	∈	ORG
ejpam-3443	80	1	∈	ORG
ejpam-3443	80	2	g+h	ORG
ejpam-3443	81	1	1	CARDINAL
ejpam-3443	82	1	g+h	PERSON
ejpam-3443	83	1	h. nuenay-maglanque	PERSON
ejpam-3443	84	1	j. pure	PERSON
ejpam-3443	84	2	12	CARDINAL
ejpam-3443	84	3	3	CARDINAL
ejpam-3443	84	4	2019	DATE
ejpam-3443	84	5	978	CARDINAL
ejpam-3443	85	1	1	CARDINAL
ejpam-3443	85	2	1 or	CARDINAL
ejpam-3443	85	3	1 2	CARDINAL
ejpam-3443	87	1	γ(g	NORP
ejpam-3443	87	2	1	CARDINAL
ejpam-3443	88	1	γve(g	PRODUCT
ejpam-3443	89	1	1	CARDINAL
ejpam-3443	89	2	γ(h	ORG
ejpam-3443	90	1	1	CARDINAL
ejpam-3443	91	1	1	CARDINAL
ejpam-3443	91	2	γ(g	GPE
ejpam-3443	91	3	2	CARDINAL
ejpam-3443	91	4	γ(h	ORG
ejpam-3443	91	5	2	CARDINAL
ejpam-3443	91	6	∈	ORG
ejpam-3443	91	7	∈	ORG
ejpam-3443	92	1	1(iii	CARDINAL
ejpam-3443	92	2	g+h	ORG
ejpam-3443	93	1	2	CARDINAL
ejpam-3443	93	2	2	CARDINAL
ejpam-3443	94	1	⊆	CARDINAL
ejpam-3443	96	1	⊆	CARDINAL
ejpam-3443	97	1	∈	ORG
ejpam-3443	97	2	⊆	CARDINAL
ejpam-3443	97	3	∈	ORG
ejpam-3443	97	4	∈	ORG
ejpam-3443	97	5	∈	ORG
ejpam-3443	99	1	⊆	CARDINAL
ejpam-3443	100	1	1	CARDINAL
ejpam-3443	101	1	1	CARDINAL
ejpam-3443	101	2	∈	ORG
ejpam-3443	101	3	⊆	CARDINAL
ejpam-3443	101	4	|s∗| ≤	MONEY
ejpam-3443	103	1	⊆	CARDINAL
ejpam-3443	104	1	6=	CARDINAL
ejpam-3443	104	2	6=	CARDINAL
ejpam-3443	104	3	∈	PERSON
ejpam-3443	104	4	∈	ORG
ejpam-3443	105	1	1(iii	CARDINAL
ejpam-3443	105	2	g+h	ORG
ejpam-3443	105	3	∈	ORG
ejpam-3443	107	1	∈	ORG
ejpam-3443	107	2	∈	ORG
ejpam-3443	108	1	1	CARDINAL
ejpam-3443	108	2	g+h	ORG
ejpam-3443	109	1	h. nuenay-maglanque	PERSON
ejpam-3443	110	1	j. pure	PERSON
ejpam-3443	110	2	12	CARDINAL
ejpam-3443	110	3	3	CARDINAL
ejpam-3443	110	4	2019	DATE
ejpam-3443	110	5	978	CARDINAL
ejpam-3443	110	6	2	CARDINAL
ejpam-3443	112	1	max{γm(g	PERSON
ejpam-3443	114	1	⊆	CARDINAL
ejpam-3443	114	2	2	CARDINAL
ejpam-3443	114	3	2	CARDINAL
ejpam-3443	115	1	⊆	CARDINAL
ejpam-3443	116	1	⊆	CARDINAL
ejpam-3443	117	1	max{γm(g	PERSON
ejpam-3443	118	1	1	CARDINAL
ejpam-3443	118	2	1	CARDINAL
ejpam-3443	118	3	g+h	ORG
ejpam-3443	124	1	max{γm(g	PERSON
ejpam-3443	125	1	3	CARDINAL
ejpam-3443	126	1	1	CARDINAL
ejpam-3443	128	1	kr	PERSON
ejpam-3443	130	1	3	CARDINAL
ejpam-3443	130	2	10	CARDINAL
ejpam-3443	130	3	2	CARDINAL
ejpam-3443	131	1	1	CARDINAL
ejpam-3443	131	2	2	CARDINAL
ejpam-3443	134	1	0	CARDINAL
ejpam-3443	135	1	1 2	CARDINAL
ejpam-3443	135	2	2k	CARDINAL
ejpam-3443	138	1	+ 1	DATE
ejpam-3443	138	2	kn+1	GPE
ejpam-3443	138	3	1	CARDINAL
ejpam-3443	139	1	γ+ce(g+k1	ORG
ejpam-3443	141	1	2k + 1 + 1	DATE
ejpam-3443	142	1	2k	CARDINAL
ejpam-3443	144	1	γ+ce(g	DATE
ejpam-3443	145	1	2	CARDINAL
ejpam-3443	146	1	2	CARDINAL
ejpam-3443	147	1	h. nuenay-maglanque	PERSON
ejpam-3443	148	1	j. pure	PERSON
ejpam-3443	148	2	12	CARDINAL
ejpam-3443	148	3	3	CARDINAL
ejpam-3443	148	4	2019	DATE
ejpam-3443	148	5	978	CARDINAL
ejpam-3443	148	6	984 v2 v4 v3 v1 v5 v6	PRODUCT
ejpam-3443	148	7	2	CARDINAL
ejpam-3443	148	8	2	CARDINAL
ejpam-3443	152	1	2	CARDINAL
ejpam-3443	152	2	v6	GPE
ejpam-3443	153	1	γ+ce(g	DATE
ejpam-3443	153	2	3	CARDINAL
ejpam-3443	154	1	2	CARDINAL
ejpam-3443	155	1	11	CARDINAL
ejpam-3443	155	2	n ≥ 2	ORG
ejpam-3443	155	3	2	CARDINAL
ejpam-3443	156	1	3	CARDINAL
ejpam-3443	159	1	max	PERSON
ejpam-3443	159	2	γ+ce(g	DATE
ejpam-3443	159	3	max	PERSON
ejpam-3443	159	4	⊆	CARDINAL
ejpam-3443	159	5	2	CARDINAL
ejpam-3443	159	6	max	PERSON
ejpam-3443	159	7	⊆	CARDINAL
ejpam-3443	159	8	2	CARDINAL
ejpam-3443	161	1	first	ORDINAL
ejpam-3443	161	2	2	CARDINAL
ejpam-3443	161	3	1	CARDINAL
ejpam-3443	161	4	1	CARDINAL
ejpam-3443	161	5	g+h	ORG
ejpam-3443	164	1	2	CARDINAL
ejpam-3443	164	2	⊆	CARDINAL
ejpam-3443	165	1	2|s2| ≤	QUANTITY
ejpam-3443	166	1	2	CARDINAL
ejpam-3443	166	2	2	CARDINAL
ejpam-3443	167	1	∈	ORG
ejpam-3443	167	2	2|s1| ≤	MONEY
ejpam-3443	168	1	1	CARDINAL
ejpam-3443	175	1	h. nuenay-maglanque	PERSON
ejpam-3443	176	1	j. pure	PERSON
ejpam-3443	176	2	12	CARDINAL
ejpam-3443	176	3	3	CARDINAL
ejpam-3443	176	4	2019	DATE
ejpam-3443	176	5	978	CARDINAL
ejpam-3443	176	6	4	CARDINAL
ejpam-3443	177	1	m.	PERSON
ejpam-3443	178	1	1 2	CARDINAL
ejpam-3443	180	1	⊆	CARDINAL
ejpam-3443	181	1	1(i	CARDINAL
ejpam-3443	181	2	⊆	CARDINAL
ejpam-3443	182	1	⊆	CARDINAL
ejpam-3443	183	1	kn	PERSON
ejpam-3443	183	2	∈	ORG
ejpam-3443	183	3	1	CARDINAL
ejpam-3443	186	1	6=	CARDINAL
ejpam-3443	186	2	6=	CARDINAL
ejpam-3443	186	3	1	CARDINAL
ejpam-3443	186	4	∈	ORG
ejpam-3443	186	5	2|s1| ≤ m+	MONEY
ejpam-3443	187	1	m+	CARDINAL
ejpam-3443	187	2	2|s2|+ 1	DATE
ejpam-3443	187	3	1 2	CARDINAL
ejpam-3443	188	1	3	CARDINAL
ejpam-3443	188	2	5	CARDINAL
ejpam-3443	189	1	8	CARDINAL
ejpam-3443	189	2	m.	PERSON
ejpam-3443	189	3	⊆	CARDINAL
ejpam-3443	192	1	⊆	CARDINAL
ejpam-3443	193	1	g ◦h	ORG
ejpam-3443	194	1	4	CARDINAL
ejpam-3443	194	2	g ◦ h	ORG
ejpam-3443	194	3	6=	CARDINAL
ejpam-3443	194	4	∈	ORG
ejpam-3443	195	1	3	CARDINAL
ejpam-3443	197	1	sv ⊆	ORG
ejpam-3443	198	1	∈	ORG
ejpam-3443	198	2	sv ⊆	ORG
ejpam-3443	199	1	sv	ORG
ejpam-3443	203	1	h. nuenay-maglanque	PERSON
ejpam-3443	204	1	j. pure	PERSON
ejpam-3443	204	2	12	CARDINAL
ejpam-3443	204	3	3	CARDINAL
ejpam-3443	204	4	2019	DATE
ejpam-3443	204	5	978	CARDINAL
ejpam-3443	205	1	n ≥ 2	ORG
ejpam-3443	206	1	∈	ORG
ejpam-3443	206	2	sv ⊆	ORG
ejpam-3443	207	1	∪v∈v	PERSON
ejpam-3443	207	2	∈	ORG
ejpam-3443	210	1	∈	ORG
ejpam-3443	212	1	sv	ORG
ejpam-3443	213	1	sv	ORG
ejpam-3443	216	1	5	CARDINAL
ejpam-3443	219	1	⊆	CARDINAL
ejpam-3443	220	1	g. a kn	PERSON
ejpam-3443	221	1	γ+knce	PERSON
ejpam-3443	222	1	3	CARDINAL
ejpam-3443	223	1	γ+ce(g	DATE
ejpam-3443	224	1	γ+knce	PERSON
ejpam-3443	225	1	4	CARDINAL
ejpam-3443	229	1	1	CARDINAL
ejpam-3443	229	2	2	DATE
ejpam-3443	231	1	n. lemma 1	PERSON
ejpam-3443	232	1	⊆	CARDINAL
ejpam-3443	232	2	∈	ORG
ejpam-3443	233	1	g◦h	ORG
ejpam-3443	234	1	h. nuenay-maglanque	PERSON
ejpam-3443	235	1	j. pure	PERSON
ejpam-3443	235	2	12	CARDINAL
ejpam-3443	235	3	3	CARDINAL
ejpam-3443	235	4	2019	DATE
ejpam-3443	235	5	978	CARDINAL
ejpam-3443	235	6	g◦h and v ∈	ORG
ejpam-3443	237	1	|nhv+v(u)∩sv|	PERSON
ejpam-3443	237	2	6	CARDINAL
ejpam-3443	238	1	⊆	CARDINAL
ejpam-3443	240	1	∈	ORG
ejpam-3443	240	2	hv)| ≤ 1 2	DATE
ejpam-3443	243	1	4	CARDINAL
ejpam-3443	244	1	∈	ORG
ejpam-3443	245	1	sv	ORG
ejpam-3443	247	1	1 + |nhv(u	QUANTITY
ejpam-3443	251	1	sv	ORG
ejpam-3443	252	1	∈	ORG
ejpam-3443	254	1	1 2	CARDINAL
ejpam-3443	256	1	1	CARDINAL
ejpam-3443	257	1	∈	ORG
ejpam-3443	257	2	5	CARDINAL
ejpam-3443	258	1	4	CARDINAL
ejpam-3443	260	1	1 2	CARDINAL
ejpam-3443	262	1	∩	ORG
ejpam-3443	262	2	|sv| ≤ |ng(u	PERSON
ejpam-3443	262	3	− |sv| = |ng(v	PERSON
ejpam-3443	264	1	h. nuenay-maglanque	PERSON
ejpam-3443	265	1	j. pure	PERSON
ejpam-3443	265	2	12	CARDINAL
ejpam-3443	265	3	3	CARDINAL
ejpam-3443	265	4	2019	DATE
ejpam-3443	265	5	978	CARDINAL
ejpam-3443	269	1	sv = s ∩	PERSON
ejpam-3443	271	1	5	CARDINAL
ejpam-3443	272	1	6	CARDINAL
ejpam-3443	275	1	2	CARDINAL
ejpam-3443	278	1	⊆	CARDINAL
ejpam-3443	279	1	\ng[s	PERSON
ejpam-3443	281	1	ng(u)∩s∗	ORG
ejpam-3443	281	2	\s	ORG
ejpam-3443	282	1	0 ≤	MONEY
ejpam-3443	284	1	g. corollary 6	PERSON
ejpam-3443	289	1	mγk1mce(h	ORDINAL
ejpam-3443	289	2	γ+ce(g	DATE
ejpam-3443	289	3	∈	ORG
ejpam-3443	292	1	6=	CARDINAL
ejpam-3443	292	2	∈	ORG
ejpam-3443	292	3	\d	ORG
ejpam-3443	292	4	sv ⊆	ORG
ejpam-3443	294	1	⋃	PRODUCT
ejpam-3443	295	1	∈	ORG
ejpam-3443	296	1	∩	PERSON
ejpam-3443	296	2	hv)|	DATE
ejpam-3443	296	3	0 ≤	MONEY
ejpam-3443	297	1	h. nuenay-maglanque	PERSON
ejpam-3443	298	1	j. pure	PERSON
ejpam-3443	298	2	12	CARDINAL
ejpam-3443	298	3	3	CARDINAL
ejpam-3443	298	4	2019	DATE
ejpam-3443	298	5	978	CARDINAL
ejpam-3443	299	1	\d	GPE
ejpam-3443	301	1	6	CARDINAL
ejpam-3443	301	2	g ◦h	ORG
ejpam-3443	302	1	∑ v∈v	PERSON
ejpam-3443	306	1	⊆	CARDINAL
ejpam-3443	306	2	6	CARDINAL
ejpam-3443	306	3	1 +	CARDINAL
ejpam-3443	306	4	hv)|	DATE
ejpam-3443	306	5	γk1ce(h	ORG
ejpam-3443	307	1	∈	ORG
ejpam-3443	309	1	2	CARDINAL
ejpam-3443	309	2	∑ v∈v	PERSON
ejpam-3443	309	3	γk1ce(h	ORG
ejpam-3443	310	1	γ+ce(g	DATE
ejpam-3443	313	1	⋃ v∈v	PERSON
ejpam-3443	313	2	sv ⊆	ORG
ejpam-3443	314	1	6	CARDINAL
ejpam-3443	314	2	sv	ORG
ejpam-3443	315	1	⊆	CARDINAL
ejpam-3443	315	2	∈	ORG
ejpam-3443	316	1	theorem 6(ii	PERSON
ejpam-3443	317	1	∈	ORG
ejpam-3443	318	1	6(i	CARDINAL
ejpam-3443	318	2	sv = s ∩	PERSON
ejpam-3443	318	3	1 2	CARDINAL
ejpam-3443	319	1	2	CARDINAL
ejpam-3443	320	1	2|sv|	CARDINAL
ejpam-3443	323	1	∈	ORG
ejpam-3443	323	2	h. nuenay-maglanque	PERSON
ejpam-3443	324	1	j. pure	PERSON
ejpam-3443	324	2	12	CARDINAL
ejpam-3443	324	3	3	CARDINAL
ejpam-3443	324	4	2019	DATE
ejpam-3443	324	5	978	CARDINAL
ejpam-3443	326	1	∑ v∈v	PERSON
ejpam-3443	326	2	hv)| ≤ ∑ v∈v	QUANTITY
ejpam-3443	328	1	∈	ORG
ejpam-3443	328	2	sv ⊆	ORG
ejpam-3443	329	1	γ+ce(g	DATE
ejpam-3443	330	1	γ+ce(g	DATE
ejpam-3443	330	2	⊆	CARDINAL
ejpam-3443	330	3	∈	ORG
ejpam-3443	330	4	∩	PERSON
ejpam-3443	330	5	1 + γ+k1ce	CARDINAL
ejpam-3443	331	1	sv = s ∩	PERSON
ejpam-3443	331	2	γ+k1ce	CARDINAL
ejpam-3443	331	3	γ+k1ce	CARDINAL
ejpam-3443	332	1	γ+ce(g	DATE
ejpam-3443	332	2	1 + γ+k1ce	CARDINAL
ejpam-3443	333	1	m−	NORP
ejpam-3443	333	2	γ+k1ce (h	ORG
ejpam-3443	334	1	6	CARDINAL
ejpam-3443	337	1	9	CARDINAL
ejpam-3443	337	2	3γ+k1ce	CARDINAL
ejpam-3443	339	1	10	CARDINAL
ejpam-3443	339	2	1 + 3γ+k1ce	DATE
ejpam-3443	341	1	2	CARDINAL
ejpam-3443	342	1	γ+ce(g	DATE
ejpam-3443	342	2	2	CARDINAL
ejpam-3443	344	1	5	CARDINAL
ejpam-3443	344	2	6	CARDINAL
ejpam-3443	345	1	6	CARDINAL
ejpam-3443	345	2	1	CARDINAL
ejpam-3443	345	3	1	CARDINAL
ejpam-3443	345	4	γ+k1ce	CARDINAL
ejpam-3443	346	1	2	CARDINAL
ejpam-3443	347	1	h. nuenay-maglanque	PERSON
ejpam-3443	348	1	j. pure	PERSON
ejpam-3443	348	2	12	CARDINAL
ejpam-3443	348	3	3	CARDINAL
ejpam-3443	348	4	2019	DATE
ejpam-3443	348	5	978	CARDINAL
ejpam-3443	348	6	991	CARDINAL
ejpam-3443	349	1	3	CARDINAL
ejpam-3443	350	1	2	CARDINAL
ejpam-3443	352	1	γ+ce(g	DATE
ejpam-3443	353	1	2	CARDINAL
ejpam-3443	355	1	4	CARDINAL
ejpam-3443	355	2	n ≥ 2 and m	ORG
ejpam-3443	355	3	2	CARDINAL
ejpam-3443	356	1	2	CARDINAL
ejpam-3443	364	1	1	CARDINAL
ejpam-3443	365	1	γ+ce(g	DATE
ejpam-3443	369	1	∈	ORG
ejpam-3443	371	1	⊆	CARDINAL
ejpam-3443	371	2	⊆	CARDINAL
ejpam-3443	371	3	kv	ORG
ejpam-3443	372	1	∈	ORG
ejpam-3443	373	1	hv)|	CARDINAL
ejpam-3443	373	2	∩	PERSON
ejpam-3443	373	3	hv)|	DATE
ejpam-3443	373	4	0 ≤	MONEY
ejpam-3443	374	1	∈	ORG
ejpam-3443	375	1	\d	GPE
ejpam-3443	377	1	6	CARDINAL
ejpam-3443	377	2	g ◦h	ORG
ejpam-3443	378	1	∑ v∈v	PERSON
ejpam-3443	383	1	⊆	CARDINAL
ejpam-3443	383	2	6	CARDINAL
ejpam-3443	383	3	1 +	CARDINAL
ejpam-3443	383	4	hv)|	DATE
ejpam-3443	384	1	+ k.	PERSON
ejpam-3443	385	1	∈	ORG
ejpam-3443	389	1	∑ v∈v	PERSON
ejpam-3443	389	2	+ k	PERSON
ejpam-3443	389	3	h. nuenay-maglanque	PERSON
ejpam-3443	390	1	j. pure	PERSON
ejpam-3443	390	2	12	CARDINAL
ejpam-3443	390	3	3	CARDINAL
ejpam-3443	390	4	2019	DATE
ejpam-3443	390	5	978	CARDINAL
ejpam-3443	394	1	1	CARDINAL
ejpam-3443	396	1	sv = lv∪pv	PERSON
ejpam-3443	396	2	⊆	CARDINAL
ejpam-3443	396	3	⊆	CARDINAL
ejpam-3443	396	4	kv	ORG
ejpam-3443	397	1	6	CARDINAL
ejpam-3443	397	2	sv	ORG
ejpam-3443	398	1	⊆	CARDINAL
ejpam-3443	398	2	∈	ORG
ejpam-3443	399	1	theorem 6(ii	PERSON
ejpam-3443	400	1	∈	ORG
ejpam-3443	403	1	6(i	CARDINAL
ejpam-3443	403	2	sv = s ∩	PERSON
ejpam-3443	403	3	1 2	CARDINAL
ejpam-3443	404	1	2	CARDINAL
ejpam-3443	405	1	2|sv|	CARDINAL
ejpam-3443	408	1	∈	ORG
ejpam-3443	410	1	∑ v∈v	PERSON
ejpam-3443	410	2	hv)| ≤ ∑ v∈v	QUANTITY
ejpam-3443	413	1	∈	ORG
ejpam-3443	413	2	sv ⊆	ORG
ejpam-3443	414	1	⊆	CARDINAL
ejpam-3443	414	2	h. nuenay-maglanque	PERSON
ejpam-3443	415	1	j. pure	PERSON
ejpam-3443	415	2	12	CARDINAL
ejpam-3443	415	3	3	CARDINAL
ejpam-3443	415	4	2019	DATE
ejpam-3443	415	5	978	CARDINAL
ejpam-3443	415	6	⊆	CARDINAL
ejpam-3443	415	7	γ+k1ce	CARDINAL
ejpam-3443	415	8	kv	ORG
ejpam-3443	416	1	6	CARDINAL
ejpam-3443	416	2	γ+ce(g	DATE
ejpam-3443	416	3	∑ v∈v	PERSON
ejpam-3443	418	1	⊆	CARDINAL
ejpam-3443	418	2	γ+ce(g	DATE
ejpam-3443	419	1	γ+k1ce (k	ORG
ejpam-3443	420	1	γ+ce(g	DATE
ejpam-3443	421	1	γ+k1ce (k	ORG
ejpam-3443	422	1	γ+knce	PERSON
ejpam-3443	425	1	4.	CARDINAL
ejpam-3443	425	2	7	CARDINAL
ejpam-3443	426	1	9	CARDINAL
ejpam-3443	427	1	⋃	PERSON
ejpam-3443	427	2	⊆	CARDINAL
ejpam-3443	427	3	⊆	CARDINAL
ejpam-3443	427	4	tx	ORG
ejpam-3443	427	5	⊆	PRODUCT
ejpam-3443	427	6	g[h	ORG
ejpam-3443	428	1	tx	ORG
ejpam-3443	429	1	8	CARDINAL
ejpam-3443	430	1	9	CARDINAL
ejpam-3443	430	2	γ(h	ORG
ejpam-3443	431	1	1	CARDINAL
ejpam-3443	431	2	1	CARDINAL
ejpam-3443	431	3	7	CARDINAL
ejpam-3443	433	1	⊆	CARDINAL
ejpam-3443	433	2	|ng[h]((u	ORG
ejpam-3443	433	3	∑ x∈s∩ng(u	PERSON
ejpam-3443	433	4	2	CARDINAL
ejpam-3443	433	5	|ng[h]((u	ORG
ejpam-3443	435	1	3	CARDINAL
ejpam-3443	437	1	h. nuenay-maglanque	PERSON
ejpam-3443	438	1	j. pure	PERSON
ejpam-3443	438	2	12	CARDINAL
ejpam-3443	438	3	3	CARDINAL
ejpam-3443	438	4	2019	DATE
ejpam-3443	438	5	978	CARDINAL
ejpam-3443	438	6	998 994	CARDINAL
ejpam-3443	439	1	⊆	CARDINAL
ejpam-3443	439	2	⊆	CARDINAL
ejpam-3443	439	3	tx	ORG
ejpam-3443	439	4	⊆	PRODUCT
ejpam-3443	439	5	tx	ORG
ejpam-3443	439	6	∈	ORG
ejpam-3443	439	7	g[h	ORG
ejpam-3443	441	1	tx	ORG
ejpam-3443	441	2	g[h	ORG
ejpam-3443	442	1	∈	ORG
ejpam-3443	444	1	6=	CARDINAL
ejpam-3443	444	2	2	CARDINAL
ejpam-3443	444	3	3	CARDINAL
ejpam-3443	445	1	|ng[h]((u	ORG
ejpam-3443	447	1	g[h	ORG
ejpam-3443	448	1	8	CARDINAL
ejpam-3443	450	1	9	CARDINAL
ejpam-3443	452	1	10	CARDINAL
ejpam-3443	453	1	⊆	CARDINAL
ejpam-3443	454	1	tx	ORG
ejpam-3443	454	2	tx	ORG
ejpam-3443	454	3	g[h	ORG
ejpam-3443	456	1	7	CARDINAL
ejpam-3443	456	2	g[h	ORG
ejpam-3443	458	1	6=	CARDINAL
ejpam-3443	458	2	2	CARDINAL
ejpam-3443	458	3	3	DATE
ejpam-3443	460	1	2	CARDINAL
ejpam-3443	460	2	3	CARDINAL
ejpam-3443	461	1	∑ x∈s∩ng(u	PERSON
ejpam-3443	462	1	h. nuenay-maglanque	PERSON
ejpam-3443	463	1	j. pure	PERSON
ejpam-3443	463	2	12	CARDINAL
ejpam-3443	463	3	3	CARDINAL
ejpam-3443	463	4	2019	DATE
ejpam-3443	463	5	978	CARDINAL
ejpam-3443	468	1	g[h	ORG
ejpam-3443	470	1	k1,4	ORG
ejpam-3443	470	2	4	CARDINAL
ejpam-3443	471	1	8	CARDINAL
ejpam-3443	471	2	|ng((x	ORG
ejpam-3443	472	1	3	CARDINAL
ejpam-3443	474	1	11	CARDINAL
ejpam-3443	475	1	2	CARDINAL
ejpam-3443	477	1	2	CARDINAL
ejpam-3443	479	1	⊆	CARDINAL
ejpam-3443	479	2	kp	ORG
ejpam-3443	481	1	7	CARDINAL
ejpam-3443	482	1	∈	ORG
ejpam-3443	483	1	1	CARDINAL
ejpam-3443	483	2	1)|ng(u	DATE
ejpam-3443	486	1	8	CARDINAL
ejpam-3443	487	1	10	CARDINAL
ejpam-3443	490	1	w ∈ s∗.	GPE
ejpam-3443	490	2	∩	PERSON
ejpam-3443	491	1	∈	ORG
ejpam-3443	491	2	∩	PERSON
ejpam-3443	492	1	1	CARDINAL
ejpam-3443	492	2	h. nuenay-maglanque	PERSON
ejpam-3443	493	1	j. pure	PERSON
ejpam-3443	493	2	12	CARDINAL
ejpam-3443	493	3	3	CARDINAL
ejpam-3443	493	4	2019	DATE
ejpam-3443	493	5	978	CARDINAL
ejpam-3443	493	6	7	CARDINAL
ejpam-3443	495	1	⊆	CARDINAL
ejpam-3443	496	1	1	CARDINAL
ejpam-3443	496	2	2	CARDINAL
ejpam-3443	497	1	kp	ORG
ejpam-3443	497	2	kp	ORG
ejpam-3443	497	3	7	CARDINAL
ejpam-3443	498	1	1	CARDINAL
ejpam-3443	498	2	2	CARDINAL
ejpam-3443	498	3	c∗| ≥	GPE
ejpam-3443	500	1	c∗	PERSON
ejpam-3443	501	1	c∗	ORG
ejpam-3443	502	1	1	CARDINAL
ejpam-3443	502	2	kp	ORG
ejpam-3443	502	3	∈ s. clearly	PERSON
ejpam-3443	504	1	⊆	CARDINAL
ejpam-3443	504	2	∈	PRODUCT
ejpam-3443	504	3	⊆	CARDINAL
ejpam-3443	504	4	kp	ORG
ejpam-3443	504	5	kp	ORG
ejpam-3443	504	6	kp	ORG
ejpam-3443	505	1	10	CARDINAL
ejpam-3443	505	2	g[h	ORG
ejpam-3443	510	1	γ(h	ORG
ejpam-3443	510	2	1	CARDINAL
ejpam-3443	512	1	12	CARDINAL
ejpam-3443	513	1	3	CARDINAL
ejpam-3443	514	1	1	CARDINAL
ejpam-3443	514	2	1 2	CARDINAL
ejpam-3443	516	1	2	CARDINAL
ejpam-3443	518	1	kp	ORG
ejpam-3443	518	2	∈	ORG
ejpam-3443	519	1	10	CARDINAL
ejpam-3443	520	1	2	CARDINAL
ejpam-3443	520	2	h. nuenay-maglanque	PERSON
ejpam-3443	521	1	j. pure	PERSON
ejpam-3443	521	2	12	CARDINAL
ejpam-3443	521	3	3	CARDINAL
ejpam-3443	521	4	2019	DATE
ejpam-3443	521	5	978	CARDINAL
ejpam-3443	521	6	10	CARDINAL
ejpam-3443	521	7	kp	ORG
ejpam-3443	521	8	⊆	CARDINAL
ejpam-3443	523	1	2	CARDINAL
ejpam-3443	524	1	first	ORDINAL
ejpam-3443	525	1	2	CARDINAL
ejpam-3443	525	2	⊆	CARDINAL
ejpam-3443	525	3	kp	ORG
ejpam-3443	529	1	⊆	CARDINAL
ejpam-3443	530	1	ia	GPE
ejpam-3443	530	2	kp	ORG
ejpam-3443	530	3	kp	ORG
ejpam-3443	531	1	kp	ORG
ejpam-3443	531	2	∈	ORG
ejpam-3443	531	3	kp	ORG
ejpam-3443	532	1	kp	ORG
ejpam-3443	534	1	⊆	CARDINAL
ejpam-3443	534	2	kp	NORP
ejpam-3443	534	3	ia	GPE
ejpam-3443	534	4	kp	ORG
ejpam-3443	535	1	10	CARDINAL
ejpam-3443	538	1	10	CARDINAL
ejpam-3443	538	2	2	CARDINAL
ejpam-3443	538	3	3	CARDINAL
ejpam-3443	538	4	1	CARDINAL
ejpam-3443	542	1	∈	ORG
ejpam-3443	543	1	1	CARDINAL
ejpam-3443	543	2	2|s||v	CARDINAL
ejpam-3443	543	3	1)|v	CARDINAL
ejpam-3443	543	4	∈	ORG
ejpam-3443	544	1	1 2	CARDINAL
ejpam-3443	544	2	1	CARDINAL
ejpam-3443	545	1	|s||v	PERSON
ejpam-3443	546	1	1 2	CARDINAL
ejpam-3443	547	1	998	CARDINAL
ejpam-3443	547	2	1	CARDINAL
ejpam-3443	547	3	fred and frank harary	PERSON
ejpam-3443	547	4	1990	DATE
ejpam-3443	548	1	2	CARDINAL
ejpam-3443	548	2	methuen	GPE
ejpam-3443	548	3	london	GPE
ejpam-3443	548	4	1962	DATE
ejpam-3443	549	1	3	CARDINAL
ejpam-3443	549	2	bondy	PERSON
ejpam-3443	549	3	geng-hau	PERSON
ejpam-3443	550	1	205	CARDINAL
ejpam-3443	550	2	4	CARDINAL
ejpam-3443	550	3	cockayne	ORG
ejpam-3443	550	4	s.t.	PERSON
ejpam-3443	551	1	7(3	CARDINAL
ejpam-3443	551	2	247	CARDINAL
ejpam-3443	552	1	5	CARDINAL
ejpam-3443	552	2	haynes	ORG
ejpam-3443	552	3	s.t.	PERSON
ejpam-3443	552	4	hedetniemi	PERSON
ejpam-3443	552	5	p.j.	GPE
ejpam-3443	552	6	slater	PERSON
ejpam-3443	553	1	marcel dekker	PERSON
ejpam-3443	553	2	inc.	ORG
ejpam-3443	553	3	new york	GPE
ejpam-3443	553	4	1998	DATE
ejpam-3443	554	1	6	CARDINAL
ejpam-3443	554	2	s. hedetniemi	PERSON
ejpam-3443	554	3	m. henning	PERSON
ejpam-3443	554	4	j. discrete	PERSON
ejpam-3443	554	5	15(4	CARDINAL
ejpam-3443	554	6	2000	DATE
ejpam-3443	555	1	7	CARDINAL
ejpam-3443	555	2	amer	PERSON
ejpam-3443	558	1	38	DATE
ejpam-3443	558	2	amer	PERSON
ejpam-3443	559	1	ri	GPE
ejpam-3443	559	2	1962	DATE
ejpam-3443	559	3	206	CARDINAL
ejpam-3443	560	1	8	CARDINAL
ejpam-3443	560	2	s. canoy jr	PERSON
ejpam-3443	561	1	6(16	CARDINAL
ejpam-3443	561	2	763	CARDINAL
ejpam-3443	561	3	771, 2011	DATE
ejpam-3443	562	1	9	CARDINAL
ejpam-3443	562	2	s. canoy jr	PERSON
ejpam-3443	563	1	10	CARDINAL
ejpam-3443	563	2	fomin	ORG
ejpam-3443	563	3	f. gradoni	PERSON
ejpam-3443	563	4	a. pyatkin	PERSON
ejpam-3443	563	5	a. stepanov	PERSON
ejpam-3443	563	6	22:157-162, 2005	DATE
ejpam-3443	564	1	11	CARDINAL
ejpam-3443	564	2	haynes	ORG
ejpam-3443	564	3	s.m.	GPE
ejpam-3443	564	4	hedetniemi	GPE
ejpam-3443	564	5	s.t.	PERSON
ejpam-3443	564	6	hedetniemi	PERSON
ejpam-3443	564	7	mccoy	PERSON
ejpam-3443	564	8	i. vasylieva	PERSON
ejpam-3443	565	1	211	CARDINAL
ejpam-3443	565	2	2012	DATE
ejpam-3443	565	3	197 209	CARDINAL
ejpam-3443	566	1	12	CARDINAL
ejpam-3443	566	2	haynes	ORG
ejpam-3443	566	3	s.t.	PERSON
ejpam-3443	566	4	hedetniemi	PERSON
ejpam-3443	566	5	mccoy	PERSON
ejpam-3443	566	6	t.k. rodriguez	PERSON
ejpam-3443	566	7	quaestiones mathematicae	ORG
ejpam-3443	567	1	773	CARDINAL
ejpam-3443	567	2	2016	DATE
ejpam-3443	568	1	13	CARDINAL
ejpam-3443	568	2	h. nuenay	PERSON
ejpam-3443	568	3	f. jamil	PERSON
ejpam-3443	569	1	403	CARDINAL
ejpam-3443	569	2	2015	DATE