Topology of matching, chessboard, and general bounded degree graph complexes

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Abstract

We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen in a variety of contexts in the literature. The most well-known examples are the matching complex and the chessboard complex. The topics covered here include computation of Betti numbers, representations of the symmetric group on rational homology, torsion in integral homology, homotopy properties, and connections with other fields.

Original languageEnglish (US)
Pages (from-to)345-385
Number of pages41
JournalAlgebra Universalis
Volume49
Issue number4
DOIs
StatePublished - Nov 3 2003

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Keywords

  • Chessboard complex
  • Matching complex
  • Simplicial complex

ASJC Scopus subject areas

  • Algebra and Number Theory

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