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arXiv · 2504.12196

Loose paths in random ordered hypergraphs

Andrzej Dudek·Alan Frieze·Wesley Pegden
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Abstract

We consider the length of {\em ordered loose paths} in the random $r$-uniform hypergraph $H=H^{(r)}(n, p)$. A ordered loose path is a sequence of edges $E_1,E_2,\ldots,E_\ell$ where $\max\{j\in E_i\}=\min\{j\in E_{i+1}\}$ for $1\leq i<\ell$. We establish fairly tight bounds on the length of the longest ordered loose path in $H$ that hold with high probability.

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Andrzej Dudek, Alan Frieze, Wesley Pegden. 2026-04-02. Loose paths in random ordered hypergraphs. https://arxiv.org/abs/2504.12196

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