Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1928)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (27 chapters)
-
Front Matter
-
Introduction and Basic Concepts
-
Overview of Graph Complexes
-
Vertex Degree
-
Connectivity
Keywords
About this book
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, including commutative algebra, geometry, and knot theory. 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. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Reviews
From the reviews:
"The subject of this book is the topology of graph complexes. A graph complex is a family of graphs … which is closed under deletion of edges. … Topological and enumerative properties of monotone graph properties such as matchings, forests, bipartite graphs, non-Hamiltonian graphs, not-k-connected graphs are discussed. … Researchers, who find any of the stated problems intriguing, will be enticed to read the book." (Herman J. Servatius, Zentralblatt MATH, Vol. 1152, 2009)
Authors and Affiliations
Bibliographic Information
Book Title: Simplicial Complexes of Graphs
Authors: Jakob Jonsson
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-75859-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Softcover ISBN: 978-3-540-75858-7Published: 15 November 2007
eBook ISBN: 978-3-540-75859-4Published: 10 December 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIV, 382
Number of Illustrations: 34 b/w illustrations
Topics: Discrete Mathematics, Combinatorics, Algebraic Topology, Order, Lattices, Ordered Algebraic Structures