Cycles of even length in graphs

J. A. Bondy, M. Simonovits

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191 Citations (Scopus)

Abstract

In this paper we solve a conjecture of P. Erdös by showing that if a graph Gn has n vertices and at least 100kn1+ 1 k edges, then G contains a cycle C2l of length 2l for every integer l ∈ [k, kn 1 k]. Apart from the value of the constant this result is best possible. It is obtained from a more general theorem which also yields corresponding results in the case where Gn has only cn(log n)α edges (α ≥ 1).

Original languageEnglish
Pages (from-to)97-105
Number of pages9
JournalJournal of Combinatorial Theory, Series B
Volume16
Issue number2
DOIs
Publication statusPublished - Apr 1974

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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