English

An improved bound for disjoint directed cycles

Combinatorics 2018-12-11 v2

Abstract

We show that every directed graph with minimum out-degree at least 18k18k contains at least kk vertex disjoint cycles. This is an improvement over the result of Alon who showed this result for digraphs of minimum out-degree at least 64k64k. The main benefit of the argument is that getting better results for small values of kk allows for further improvements to the constant.

Keywords

Cite

@article{arxiv.1701.06364,
  title  = {An improved bound for disjoint directed cycles},
  author = {Matija Bucić},
  journal= {arXiv preprint arXiv:1701.06364},
  year   = {2018}
}
R2 v1 2026-06-22T17:57:03.281Z