Loose paths in random ordered hypergraphs Article Swipe
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Andrzej Dudek
,
Alan Frieze
,
Wesley Pegden
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2504.12196
· OA: W4416543903
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2504.12196
· OA: W4416543903
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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