Lichiardopol's conjecture on disjoint cycles in tournaments

Lichiardopol's conjecture on disjoint cycles in tournaments

In 2010, N. Lichiardopol conjectured for \(q \geq 3\) and \(k \geq 1\) that any tournament with minimum out-degree at least \((q-1)k-1\) contains \(k\) disjoint cycles of length \(q\). We prove this conjecture for \(q \geq 5\). Since it is already known to hold for \(q\le4\), this completes the proo...

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Veröffentlicht in:arXiv.org 2019-10
Hauptverfasser: Ma, Fuhong, West, Douglas B, Jin, Yan
Format: Artikel
Sprache:eng
Schlagworte:
Graph theory
Integers
Tournaments & championships
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Zusammenfassung:In 2010, N. Lichiardopol conjectured for \(q \geq 3\) and \(k \geq 1\) that any tournament with minimum out-degree at least \((q-1)k-1\) contains \(k\) disjoint cycles of length \(q\). We prove this conjecture for \(q \geq 5\). Since it is already known to hold for \(q\le4\), this completes the proof of the conjecture.
ISSN:2331-8422