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High-order bootstrap percolation in hypergraphs

2022/01/24 by Oliver Cooley, Cooley, Oliver, Julian Zalla +1
Mathematics · Physics and Astronomy · #05C65 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #math.CO #msc:05C65

paper · pdf · doi:10.48550/arxiv.2201.09718

arxiv created 2022/01/24 · openalex publication_date 2022/01/24 · arxiv updated 2022/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by the bootstrap percolation process for graphs, we define a new, high-order generalisation to k-uniform hypergraphs, in which we infect j-sets of vertices for some integer 1≤ j ≤ k-1. We investigate the smallest possible size of an initially infected set which ultimately percolates and determine the exact size in almost all cases of k and j.

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