English

Two disjoint cycles in digraphs

Combinatorics 2022-08-18 v2

Abstract

Bermond and Thomassen conjectured that every digraph with minimum outdegree at least 2k12k-1 contains kk vertex disjoint cycles. So far the conjecture was verified for k3k\le 3. Here we generalise the question asking for all outdegree sequences which force kk vertex disjoint cycles and give the full answer for k2k\le 2.

Keywords

Cite

@article{arxiv.2205.10826,
  title  = {Two disjoint cycles in digraphs},
  author = {Mikołaj Lewandowski and Joanna Polcyn and Christian Reiher},
  journal= {arXiv preprint arXiv:2205.10826},
  year   = {2022}
}
R2 v1 2026-06-24T11:24:45.100Z