An improved bound for disjoint directed cycles

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11 Scopus citations


We show that every directed graph with minimum out-degree at least 18k contains at least k vertex disjoint cycles. This is an improvement over the result of Alon who showed this result for digraphs of minimum out-degree at least 64k. The main benefit of the argument is that getting better results for small values of k allows for further improvements to the constant.

Original languageEnglish (US)
Pages (from-to)2231-2236
Number of pages6
JournalDiscrete Mathematics
Issue number8
StatePublished - Aug 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


  • Directed graph
  • Disjoint cycles
  • Minimal out-degree


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