Short Cycles in Digraphs

Tsuyoshi Nishimura

doi:10.1016/S0167-5060(08)70796-9

Short Cycles in Digraphs

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

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
Pages (from-to)	295-298
Number of pages	4
Journal	Annals of Discrete Mathematics
Volume	38
Issue number	C
DOIs	https://doi.org/10.1016/S0167-5060(08)70796-9
Publication status	Published - 1988 Jan 1
Externally published	Yes

ASJC Scopus subject areas

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 [n/k]. With regard to this conjecture, Chv{\'a}tal and Szem{\'e}rldi [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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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.

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