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001 | 978-3-540-75859-4 | ||
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007 | cr nn 008mamaa | ||
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_a9783540758594 _9978-3-540-75859-4 |
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_a10.1007/978-3-540-75859-4 _2doi |
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_aPBD _2bicssc |
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_aMAT008000 _2bisacsh |
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_aPBD _2thema |
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_a511.1 _223 |
100 | 1 |
_aJonsson, Jakob. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aSimplicial Complexes of Graphs _h[electronic resource] / _cby Jakob Jonsson. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2008. |
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300 |
_aXIV, 382 p. 34 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1928 |
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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 |
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773 | 0 | _tSpringer eBooks | |
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_iPrinted edition: _z9783540845249 |
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_iPrinted edition: _z9783540758587 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1928 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-540-75859-4 |
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