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author:

Chen, Jing (Chen, Jing.) [1] | Fan, Genghua (Fan, Genghua.) [2] (Scholars:范更华)

Indexed by:

EI Scopus SCIE

Abstract:

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.

Keyword:

Circuit cover Minimum circuit cover Signed circuit Signed graph

Community:

  • [ 1 ] [Chen, Jing]Hunan First Normal Univ, Sch Math, Changsha, Hunan, Peoples R China
  • [ 2 ] [Fan, Genghua]Fuzhou Univ, Ctr Discrete Math, Fuzhou, Fujian, Peoples R China

Reprint 's Address:

  • 范更华

    [Fan, Genghua]Fuzhou Univ, Ctr Discrete Math, Fuzhou, Fujian, Peoples R China

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Source :

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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