### Abstract

Caccetta and Häggkvist [1] conjectured that every digraph with n vertices and minimum outdegree k contains a directed cycle of length at most [n/k]. With regard to this conjecture, Chvátal and Szemérldi [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 | Annals of Discrete Mathematics |

Volume | 38 |

Issue number | C |

DOIs | |

Publication status | Published - 1988 |

Externally published | Yes |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Annals of Discrete Mathematics*,

*38*(C), 295-298. https://doi.org/10.1016/S0167-5060(08)70796-9

**Short Cycles in Digraphs.** / Nishimura, Tsuyoshi.

Research output: Contribution to journal › Article

*Annals of Discrete Mathematics*, vol. 38, no. C, pp. 295-298. https://doi.org/10.1016/S0167-5060(08)70796-9

}

TY - JOUR

T1 - Short Cycles in Digraphs

AU - Nishimura, Tsuyoshi

PY - 1988

Y1 - 1988

N2 - Caccetta and Häggkvist [1] conjectured that every digraph with n vertices and minimum outdegree k contains a directed cycle of length at most [n/k]. With regard to this conjecture, Chvátal and Szemérldi [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.

AB - Caccetta and Häggkvist [1] conjectured that every digraph with n vertices and minimum outdegree k contains a directed cycle of length at most [n/k]. With regard to this conjecture, Chvátal and Szemérldi [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.

UR - http://www.scopus.com/inward/record.url?scp=77957045838&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957045838&partnerID=8YFLogxK

U2 - 10.1016/S0167-5060(08)70796-9

DO - 10.1016/S0167-5060(08)70796-9

M3 - Article

AN - SCOPUS:77957045838

VL - 38

SP - 295

EP - 298

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

SN - 0167-5060

IS - C

ER -