Simplicial Complexes of Graphs
(Sprache: Englisch)
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence...
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Klappentext zu „Simplicial Complexes of Graphs “
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.
Inhaltsverzeichnis zu „Simplicial Complexes of Graphs “
- Basic Concepts- Overview
- Abstract Graphs and Set Systems
- Simplicial Topology
- Tools
- Discrete Morse Theory
- Decision Trees
- Miscellaneous Results
- Overview of Graph Complexes
- Graph Properties
- Dihedral Graph Properties
- Digraph Properties
- Main Goals and Proof Techniques
- Vertex Degree
- Matchings
- Graphs of Bounded Degree
- Cycles and Crossings
- Forests and Matroids
- Bipartite Graphs
- Directed Variants of Forests and Bipartite Graphs
- Noncrossing Graphs
- Non-Hamiltonian Graphs
- Connectivity
- Disconnected Graphs
- Not 2-connected Graphs
- Not 3-connected Graphs and Beyond
- Dihedral Variants of k-connected Graphs
- Directed Variants of Connected Graphs
- Not 2-edge-connected Graphs
- Cliques and Stable Sets
- Graphs Avoiding k-matchings
- t-colorable Graphs
- Graphs and Hypergraphs with Bounded Covering Number
- Open Problems
- Open Problems
Bibliographische Angaben
- Autor: Jakob Jonsson
- 2008, 400 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer Berlin Heidelberg
- ISBN-10: 3540758585
- ISBN-13: 9783540758587
- Erscheinungsdatum: 15.11.2007
Sprache:
Englisch
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