Some approaches to a conjecture on short cycles in digraphs

Haitze J. Broersma, Xueliang Li, Xueliang Li

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3 Citations (Scopus)
14 Downloads (Pure)

Abstract

We consider the following special case of a conjecture due to Caccetta and Häggkvist: Let D be a digraph on n vertices that all have in-degree and out-degree at least n/3. Then, D contains a directed cycle of length 2 or 3. We discuss several necessary conditions for possible counterexamples to this conjecture, in terms of cycle structure, diameter, maximum degree, clique number, toughness, and local structure. These conditions have not enabled us to prove or refute the conjecture, but they lead to proofs of special instances of the conjecture.
Original languageEnglish
Pages (from-to)45-93
Number of pages9
JournalDiscrete applied mathematics
Volume120
Issue number1-3
DOIs
Publication statusPublished - 2002

Keywords

  • Digraph
  • Directed triangle
  • Degree condition
  • Girth

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