Almost given length cycles in digraphs

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A digraph is called k-cyclic if it cannot be made acyclic by removing less than k arcs. It is proved that for every ε > 0 there are constants K and δ so that for every d (0, δn), every ε n 2-cyclic digraph with n vertices contains a directed cycle whose length is between d and d + K. A more general result of the same form is obtained for blow-ups of directed cycles.

Original languageEnglish
Pages (from-to)59-65
Number of pages7
JournalGraphs and Combinatorics
Issue number1
StatePublished - Feb 2008


  • Directed cycle
  • Directed graph
  • Regularity lemma

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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