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arXiv · 2205.10826

Two disjoint cycles in digraphs

Mikołaj Lewandowski·Joanna Polcyn·Christian Reiher
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Abstract

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

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Mikołaj Lewandowski, Joanna Polcyn, Christian Reiher. 2022-08-17. Two disjoint cycles in digraphs. https://arxiv.org/abs/2205.10826

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