Hamilton Cycles in Dense Regular Digraphs and Oriented Graphs

Hamilton Cycles in Dense Regular Digraphs and Oriented Graphs

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 a...

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Veröffentlicht in:arXiv.org 2023-09
Hauptverfasser: Lo, Allan, Patel, Viresh, Yıldız, Mehmet Akif
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Graph theory
Graphs
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Zusammenfassung: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.
ISSN:2331-8422