Longest paths in random hypergraphs

Cooley, Oliver, Garbe, Frederik, Hng, Eng Keat, Kang, Mihyun, Sanhueza-Matama, Nicolás and Zalla, Julian (2021) Longest paths in random hypergraphs. SIAM Journal on Discrete Mathematics, 35 (4). 2430 – 2458. ISSN 0895-4801

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Abstract

Given integers k, j with 1 ≤ j ≤ k -1, we consider the length of the longest j-tight path in the binomial random k-uniform hypergraph Hk(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 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.

Item Type:	Article
Official URL:	https://epubs.siam.org/journal/sjdmec
Additional Information:	© 2021 Society for Industrial and Applied Mathematics
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	13 Apr 2022 09:30
Last Modified:	30 Nov 2024 18:03
URI:	http://eprints.lse.ac.uk/id/eprint/114877

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