### Abstract

Caccetta and Häggkvist [1] conjectured that every digraph with n vertices and minimum outdegree k contains a directed cycle of length at most {plus 45 degree rule}n/k. With regard to this conjecture, Chvátal and Szemerédi [2] proved that if G is a digraph with n vertices and if each of these vertices has outdegree at least k, then G contains a cycle of length at most (n/k) + 2500. Our result is an improvement of this result.

Original language | English |
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Pages (from-to) | 295-298 |

Number of pages | 4 |

Journal | Discrete Mathematics |

Volume | 72 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 1988 Dec |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Nishimura, T. (1988). Short cycles in digraphs.

*Discrete Mathematics*,*72*(1-3), 295-298. https://doi.org/10.1016/0012-365X(88)90219-1