Short cycles in digraphs

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 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.