Longest Paths in Random Hypergraphs

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

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung

Abstract

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.
Originalspracheenglisch
Seiten (von - bis)2430-2458
FachzeitschriftSIAM Journal on Discrete Mathematics
Jahrgang35
Ausgabenummer4
DOIs
PublikationsstatusVeröffentlicht - 2021

ASJC Scopus subject areas

  • Diskrete Mathematik und Kombinatorik

Fields of Expertise

  • Information, Communication & Computing

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