LEADER 03788nam 2200661 450 001 9910484516703321 005 20210217150637.0 010 $a3-540-75859-3 024 7 $a10.1007/978-3-540-75859-4 035 $a(CKB)1000000000437244 035 $a(SSID)ssj0000320043 035 $a(PQKBManifestationID)11244785 035 $a(PQKBTitleCode)TC0000320043 035 $a(PQKBWorkID)10360910 035 $a(PQKB)10453328 035 $a(DE-He213)978-3-540-75859-4 035 $a(MiAaPQ)EBC3062070 035 $a(MiAaPQ)EBC337074 035 $a(MiAaPQ)EBC6351800 035 $a(Au-PeEL)EBL337074 035 $a(OCoLC)808680584 035 $a(PPN)123739950 035 $a(EXLCZ)991000000000437244 100 $a20210217d2008 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aSimplicial complexes of graphs /$fJakob Jonsson 205 $a1st ed. 2008. 210 1$aBerlin, Germany :$cSpringer,$d[2008] 210 4$dİ2008 215 $a1 online resource (XIV, 382 p. 34 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1928 300 $aOriginally issued as the author's thesis (Ph. D.)--Royal Institute of Technology, Stockholm, 2005. 311 $a3-540-75858-5 320 $aIncludes bibliographical references (pages [363]-369) and index. 327 $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. 330 $aA graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1928 606 $aDecision trees 606 $aGraph theory 606 $aMorse theory 606 $aAlgebra, Homological 615 0$aDecision trees. 615 0$aGraph theory. 615 0$aMorse theory. 615 0$aAlgebra, Homological. 676 $a511.5 700 $aJonsson$b Jakob$f1972-$01221120 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484516703321 996 $aSimplicial complexes of graphs$92831249 997 $aUNINA