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Topological Theory of Graphs

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Title: Topological Theory of Graphs
Description: This book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and nonorientable) with given genus, the Gauss crossing conjecture, the graphicness and cographicness of a matroid, and so forth. Notably, the specific case of embeddability on a surface of genus zero leads to a number of corollaries, including the theorems of Lefschetz (on double coverings), of MacLane (on cycle bases), and of Whitney (on duality) for planarity. Relevant problems include the Jordan axiom in polyhedral forms, efficient methods for extremality and for recognizing a variety of embeddings (including rectilinear layouts in VLSI), and pan-polynomials, including those of Jones, Kauffman (on knots), and Tutte (on graphs), among others. Contents Preliminaries Polyhedra Surfaces Homology on Polyhedra Polyhedra on the Sphere Automorphisms of a Polyhedron Gauss Crossing Sequences Cohomology on Graphs Embeddability on Surfaces Embeddings on Sphere Orthogonality on Surfaces Net Embeddings Extremality on Surfaces Matroidal Graphicness Knot Polynomials
Authors: Yanpei Liu
Resource Type: eBook.
Subjects: Topological graph theory
Categories: MATHEMATICS / Discrete Mathematics, MATHEMATICS / Geometry / General, MATHEMATICS / Topology
Database: eBook Collection (EBSCOhost)
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DbLabel: eBook Collection (EBSCOhost)
An: 1484790
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PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1077.00524902344
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  Group: Ti
  Data: Topological Theory of Graphs
– Name: Abstract
  Label: Description
  Group: Ab
  Data: This book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and nonorientable) with given genus, the Gauss crossing conjecture, the graphicness and cographicness of a matroid, and so forth. Notably, the specific case of embeddability on a surface of genus zero leads to a number of corollaries, including the theorems of Lefschetz (on double coverings), of MacLane (on cycle bases), and of Whitney (on duality) for planarity. Relevant problems include the Jordan axiom in polyhedral forms, efficient methods for extremality and for recognizing a variety of embeddings (including rectilinear layouts in VLSI), and pan-polynomials, including those of Jones, Kauffman (on knots), and Tutte (on graphs), among others. Contents Preliminaries Polyhedra Surfaces Homology on Polyhedra Polyhedra on the Sphere Automorphisms of a Polyhedron Gauss Crossing Sequences Cohomology on Graphs Embeddability on Surfaces Embeddings on Sphere Orthogonality on Surfaces Net Embeddings Extremality on Surfaces Matroidal Graphicness Knot Polynomials
– Name: Author
  Label: Authors
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  Data: <searchLink fieldCode="AR" term="%22Yanpei+Liu%22">Yanpei Liu</searchLink>
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  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Discrete+Mathematics%22">MATHEMATICS / Discrete Mathematics</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Geometry+%2F+General%22">MATHEMATICS / Geometry / General</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Topology%22">MATHEMATICS / Topology</searchLink>
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RecordInfo BibRecord:
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    Classifications:
      – Code: 511.5
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Topological graph theory
        Type: general
    Titles:
      – TitleFull: Topological Theory of Graphs
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Yanpei Liu
      – PersonEntity:
          Name:
            NameFull: Yanpei Liu
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      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2017
            – D: 30
              M: 08
              Type: profile
              Y: 2017
          Identifiers:
            – Type: isbn-print
              Value: 9783110476699
            – Type: isbn-electronic
              Value: 9783110479225
            – Type: isbn-electronic
              Value: 9783110479492
          Titles:
            – TitleFull: Topological Theory of Graphs
              Type: main
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