The Binding Number of a Digraph

Genjiu Xu, Xueliang Li, Shenggui Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Caccetta-Häggkvist's Conjecture discusses the relation between the girth g(D) of a digraph D and the minimum outdegree δ +(D) of D. The special case when g(D) = 3 has lately attracted wide attention. For an undirected graph G, the binding number is a sufficient condition for G to have a triangle (cycle with length 3). In this paper we generalize the concept of binding numbers to digraphs and give some corresponding results. In particular, the value range of binding numbers is given, and the existence of digraphs with a given binding number is confirmed. By using the binding number of a digraph we give a condition that guarantees the existence of a directed triangle in the digraph. The relationship between binding number and connectivity is also discussed.

Original languageEnglish
Title of host publicationDiscrete Geometry, Combinatorics and Graph Theory 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, Xi'an, China, November 22-24, 2005, Revised Selected Papers
Pages221-227
Number of pages7
DOIs
StatePublished - 2007
Event7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005 - Xi'an, China
Duration: 22 Nov 200524 Nov 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4381 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005
Country/TerritoryChina
CityXi'an
Period22/11/0524/11/05

Keywords

  • Binding number
  • Caccetta-Häggkvist Conjecture
  • Directed graph
  • Girth

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