Hamilton Cycles in Dense Regular Digraphs and Oriented Graphs

Allan Lo; Viresh Patel; Mehmet Akif Yıldız

Hamilton Cycles in Dense Regular Digraphs and Oriented Graphs

Combinatorics 2023-09-15 v2

Authors: Allan Lo , Viresh Patel , Mehmet Akif Yıldız

Abstract

We prove that for every $\varepsilon > 0$ there exists $n_0=n_0(\varepsilon)$ such that every regular oriented graph on $n > n_0$ vertices and degree at least $(1/4 + \varepsilon)n$ has a Hamilton cycle. This establishes an approximate version of a conjecture of Jackson from 1981. We also establish a result related to a conjecture of K\"uhn and Osthus about the Hamiltonicity of regular directed graphs with suitable degree and connectivity conditions.

Keywords

hamilton cycles graph cycles hadwiger conjecture

Cite

@article{arxiv.2203.10112,
  title  = {Hamilton Cycles in Dense Regular Digraphs and Oriented Graphs},
  author = {Allan Lo and Viresh Patel and Mehmet Akif Yıldız},
  journal= {arXiv preprint arXiv:2203.10112},
  year   = {2023}
}

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33 pages, 7 figures

Hamilton Cycles in Dense Regular Digraphs and Oriented Graphs

Abstract

Keywords

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