Lecture Notes in Mathematics

Simplicial Complexes of Graphs

Authors: Jonsson, Jakob

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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.

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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)


Table of contents (27 chapters)

Table of contents (27 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-540-75859-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-3-540-75858-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Simplicial Complexes of Graphs
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1928
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-75859-4
DOI
10.1007/978-3-540-75859-4
Softcover ISBN
978-3-540-75858-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 382
Number of Illustrations
34 b/w illustrations
Topics