Local 2-separators

2020/08/07 by Johannes Carmesin, Carmesin, Johannes · 1 citation
Computer Science · Mathematics · #05C40 #05C75 #05C82 #05C83 #05C85 #05C90 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems

paper · doi:10.48550/arxiv.2008.03032

openalex publication_date 2020/08/07 · openalex created_date 2024/02/14 · openalex updated_date 2026/07/28

Abstract

How can sparse graph theory be extended to large networks, where algorithms whose running time is estimated using the number of vertices are not good enough? I address this question by introducing 'Local Separators' of graphs. Applications include: 1. A unique decomposition theorem for graphs along their local 2-separators analogous to the 2-separator theorem; 2. an exact characterisation of graphs with no bounded subdivision of a wheel.

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