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A signed graph G is a graph associated with a mapping (sigma: E(G) -> {+1, -1). An edge e is an element of E(G) is positive if sigma(e) = 1 and negative if sigma(e) = -1. A circuit in G is balanced if it contains an even number of negative edges, and unbalanced otherwise. A barbell consists of two unbalanced circuits joined by a path. A signed circuit of G is either a balanced circuit or a barbell. A signed graph is coverable if each edge is contained in some signed circuit. An oriented signed" graph (bidirected graph) has a nowhere-zero integer flow if and only if it is coverable. A signed circuit cover of G is a collection.F of signed circuits in G such that each edge e is an element of E(G) is contained in at least one signed circuit of.T; The length of.F is the sum of the lengths of the signed circuits in it. The minimum length of a signed circuit cover of G is denoted by scc(G). The first nontrivial bound on scc(G) was established by Mgajova et al., who proved that scc(G) <= 11|E(G)| for every coverable signed graph G, which was recently improved by Cheng et al. to scc(G) <= 14/3 |E(G)|. In this paper, we prove that scc(G) <= 25/6 |E(G)| for every coverable signed graph G. (C) 2017 Elsevier B.V. All rights reserved.
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DISCRETE APPLIED MATHEMATICS
ISSN: 0166-218X
Year: 2018
Volume: 235
Page: 51-58
0 . 9 8 3
JCR@2018
1 . 0 0 0
JCR@2023
ESI Discipline: ENGINEERING;
ESI HC Threshold:170
JCR Journal Grade:3
CAS Journal Grade:4
Cited Count:
WoS CC Cited Count: 5
SCOPUS Cited Count: 5
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1
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