Author 
Jonsson, Jakob, 1972

Series 
Lecture notes in mathematics, 00758434 ; 1928 

Lecture notes in mathematics (SpringerVerlag) ;
1928.

Subject 
Topological graph theory.


Graph theory.


Morse theory.


Decision trees.


Algebra, Homological.

Description 
1 online resource (xiv, 378 pages) : illustrations. 

polychrome rdacc 
Bibliography Note 
Includes bibliographical references (pages 363369) and index. 
Contents 
Introduction and overview  Abstract and set systems  Simplicial topology  Discrete Morse theory  Decision trees  Miscellaneous results  Graph properties  Dihedral graph properties  Diagraph properties  Main goals and proof techniques  Matchings  Graphs of bounded degree  Forests and matroids  Bipartite graphs  Directed variants of forests and bipartite graphs  Noncrossing graphs  Non Hamiltonian graphs  Disconnected graphs  Not 2connected graphs  Not 3connected graphs and beyond  Dihedral variants of kconnected graphs  Directed variants of connected graphs  Not 2edgeconnected graphs  Graphs avoiding kmatching  tcolorable graphs  Graphs and hypergraphs with bounded covering number. 
Summary 
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. 
Note 
Print version record. 
ISBN 
9783540758594 

3540758593 

3540758585 (softcover ; alk. paper) 

9783540758587 (softcover ; alk. paper) 
ISBN/ISSN 
10.1007/9783540758594 
OCLC # 
233973602 
Additional Format 
Print version: Jonsson, Jakob, 1972 Simplicial complexes of graphs. Berlin ; New York : Springer, 2008 3540758585 (DLC) 2007937408 (OCoLC)181090547 
