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Author Jonsson, Jakob, 1972-
Title Simplicial complexes of graphs / Jakob Jonsson.
Imprint Berlin ; New York : Springer, 2008.

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Author Jonsson, Jakob, 1972-
Series Lecture notes in mathematics, 0075-8434 ; 1928
Lecture notes in mathematics (Springer-Verlag) ; 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 363-369) 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 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 -- Graphs avoiding k-matching -- t-colorable 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
3540758585 (softcover ; alk. paper)
9783540758587 (softcover ; alk. paper)
ISBN/ISSN 10.1007/978-3-540-75859-4
OCLC # 233973602
Additional Format Print version: Jonsson, Jakob, 1972- Simplicial complexes of graphs. Berlin ; New York : Springer, 2008 3540758585 (DLC) 2007937408 (OCoLC)181090547

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