Isomorphisms between random d-hypergraphs

2024/05/07 by Théo Lenoir, Lenoir, Théo
Mathematics · #05C65 #05C80 #60C05 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2405.04670

openalex publication_date 2024/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the size of the largest common induced subgraph of two independent random uniform d-hypergraphs of different sizes with d≥ 3. More precisely, its distribution is asymptotically concentrated on two points, and we obtain as a consequence a phase transition for the inclusion of the smallest hypergraph in the largest one. This generalizes to uniform random d-hypergraphs the results of Chatterjee and Diaconis for uniform random graphs. Our proofs rely on the first and second moment methods.

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