An improved bound for disjoint directed cycles

Abstract

We show that every directed graph with minimum out-degree at least $18k$ contains at least $k$ vertex disjoint cycles. This is an improvement over the result of Alon who showed this result for digraphs of minimum out-degree at least $64k$. The main benefit of the argument is that getting better results for small values of $k$ allows for further improvements to the constant.

Cited by in corpus (4)

• On sufficient conditions for rainbow cycles in edge-colored graphs
• Disjoint cycles with length constraints in digraphs of large connectivity or minimum degree
• A note on digraph splitting
• Lichiardopol's conjecture on disjoint cycles in tournaments