A step toward the Bermond-Thomassen conjecture about disjoint cycles in digraphs

Abstract

In 1981, Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k - 1 contains k disjoint cycles. This conjecture is trivial for k = 1, and was established for k = 2 by Thomassen in 1983.

We verify it for the next case, proving that every digraph with minimum out-degree at least five contains three disjoint cycles.

Keywords

• toward
• Bermond-Thomassen
• conjecture
• about
• disjoint
• cycles
• digraphs