Short cycles in digraphs

Tsuyoshi Nishimura

doi:10.1016/0012-365X(88)90219-1

Short cycles in digraphs

Tsuyoshi Nishimura

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

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
Pages (from-to)	295-298
Number of pages	4
Journal	Discrete Mathematics
Volume	72
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(88)90219-1
Publication status	Published - 1988 Dec
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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title = "Short cycles in digraphs",

abstract = "Caccetta and H{\"a}ggkvist [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, Chv{\'a}tal and Szemer{\'e}di [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.",

author = "Tsuyoshi Nishimura",

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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.

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