### 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 |

Externally published | Yes |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

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

**Short cycles in digraphs.** / Nishimura, Tsuyoshi.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 72, no. 1-3, pp. 295-298. https://doi.org/10.1016/0012-365X(88)90219-1

}

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 {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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0013011158&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0013011158&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(88)90219-1

DO - 10.1016/0012-365X(88)90219-1

M3 - Article

AN - SCOPUS:0013011158

VL - 72

SP - 295

EP - 298

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -