2019/09/27 by Jakob Kneip, Kneip, Jay Lilian
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1909.12628
openalex publication_date 2019/09/27 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Every end of an infinite graph G defines a tangle of infinite order in G . These tangles indicate a highly cohesive substructure in the graph if and only if they are closed in some natural topology. We characterize, for every finite k , the ends ω whose induced tangles of order k are closed. They are precisely the tangles τ for which there is a set of k vertices that decides τ by majority vote. Such a set exists if and only if the vertex degree plus the number of dominating vertices of ω is at least k .