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arXiv · 2309.11677

Cycle Partitions in Dense Regular Digraphs and Oriented Graphs

Allan Lo·Viresh Patel·Mehmet Akif Yıldız
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Abstract

A conjecture of Jackson from 1981 states that every $d$-regular oriented graph on $n$ vertices with $n\leq 4d+1$ is Hamiltonian. We prove this conjecture for sufficiently large $n$. In fact we prove a more general result that for all $α>0$, there exists $n_0=n_0(α)$ such that every $d$-regular digraph on $n\geq n_0$ vertices with $d \geq αn $ can be covered by at most $n/(d+1)$ vertex-disjoint cycles, and moreover that if $G$ is an oriented graph, then at most $n/(2d+1)$ cycles suffice.

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Allan Lo, Viresh Patel, Mehmet Akif Yıldız. 2025-01-23. Cycle Partitions in Dense Regular Digraphs and Oriented Graphs. https://doi.org/10.1017/fms.2025.28

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