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arXiv · 2403.14518

Tight Hamiltonicity from dense links of triples

Richard Lang·Mathias Schacht·Jan Volec
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Abstract

We show that for all $k\geq 4$, $\varepsilon >0$, and $n$ sufficiently large, every $k$-uniform hypergraph on $n$ vertices in which each set of $k-3$ vertices is contained in at least $(5/8 + \varepsilon) \binom{n}{3}$ edges contains a tight Hamilton cycle. This is asymptotically best possible.

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Richard Lang, Mathias Schacht, Jan Volec. 2025-07-30. Tight Hamiltonicity from dense links of triples. https://arxiv.org/abs/2403.14518

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