000 03779nam a22005055i 4500
001 978-3-540-75859-4
003 DE-He213
005 20190213151551.0
007 cr nn 008mamaa
008 100301s2008 gw | s |||| 0|eng d
020 _a9783540758594
_9978-3-540-75859-4
024 7 _a10.1007/978-3-540-75859-4
_2doi
050 4 _aQA150-272
072 7 _aPBD
_2bicssc
072 7 _aMAT008000
_2bisacsh
072 7 _aPBD
_2thema
082 0 4 _a511.1
_223
100 1 _aJonsson, Jakob.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSimplicial Complexes of Graphs
_h[electronic resource] /
_cby Jakob Jonsson.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2008.
300 _aXIV, 382 p. 34 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1928
505 0 _aand Basic Concepts -- and 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.
520 _aA 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.
650 0 _aCombinatorics.
650 0 _aAlgebraic topology.
650 0 _aAlgebra.
650 1 4 _aDiscrete Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M29000
650 2 4 _aCombinatorics.
_0http://scigraph.springernature.com/things/product-market-codes/M29010
650 2 4 _aAlgebraic Topology.
_0http://scigraph.springernature.com/things/product-market-codes/M28019
650 2 4 _aOrder, Lattices, Ordered Algebraic Structures.
_0http://scigraph.springernature.com/things/product-market-codes/M11124
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540845249
776 0 8 _iPrinted edition:
_z9783540758587
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1928
856 4 0 _uhttps://doi.org/10.1007/978-3-540-75859-4
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11125
_d11125