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Introduction and Overview

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1928)

This book focuses on families of graphs on a fixed vertex set. We are particularly interested in graph complexes, which are graph families closed under deletion of edges. Equivalently, a graph complex Α has the property that if G ∈ Α and e is an edge in G, then the graph obtained from G by removing e is also in Α. Since the vertex set is fixed, we may identify each graph in Α with its edge set and hence interpret Α as a simplicial complex. In particular, we may realize Α as a geometric object and hence analyze its topology. Indeed, this is the main purpose of the book.

Keywords

  • Bipartite Graph
  • Simplicial Complex
  • Vertex Cover
  • Homotopy Type
  • Graph Property

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2008 Springer-Verlag Berlin Heidelberg

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(2008). Introduction and Overview. In: Simplicial Complexes of Graphs. Lecture Notes in Mathematics, vol 1928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75859-4_1

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