Caccetta and Häggkvist  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  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.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics