Longest Paths in Random Hypergraphs

Oliver Cooley, Frederik Garbe, Eng Keat Hng, Mihyun Kang, Nicolás Sanhueza-Matamala, Julian Zalla

Research output: Contribution to journalArticlepeer-review


Given integers $k,j$ with $1\le j \le k-1$, we consider the length of the longest $j$-tight path in the binomial random $k$-uniform hypergraph $H^k(n,p)$. We show that this length undergoes a phase transition from logarithmic length to linear and determine the critical threshold, as well as proving upper and lower bounds on the length in the subcritical and supercritical ranges. In particular, for the supercritical case we introduce the \tt Pathfinder algorithm, a depth-first search algorithm which discovers $j$-tight paths in a $k$-uniform hypergraph. We prove that, in the supercritical case, with high probability this algorithm will find a long $j$-tight path.
Original languageEnglish
Pages (from-to)2430-2458
JournalSIAM Journal on Discrete Mathematics
Issue number4
Publication statusPublished - 2021

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Fields of Expertise

  • Information, Communication & Computing


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