A note on the number of edges guaranteeing a C4 in Eulerian bipartite digraphs

Jian Shen, Raphael Yuster

Research output: Contribution to journalArticlepeer-review

Abstract

Let G be an Eulerian bipartite digraph with vertex partition sizes m, n. We prove the following Turán-type result: If e(G) > 2mn/3 then G contains a directed cycle of length at most 4. The result is sharp. We also show that if e(G) = 2mn/3 and no directed cycle of length at most 4 exists, then G must be biregular. We apply this result in order to obtain an improved upper bound for the diameter of interchange graphs.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalElectronic Journal of Combinatorics
Volume9
Issue number1 N
DOIs
StatePublished - 2002

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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