Topological theory of graphs /

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"This book presents a topological approach to combinatorial configuration, in particular graphs, by introducing a new pair of homology and cohomology via polyhedral. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientabl...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Liu, Yanpei, 1939- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston : De Gruyter, 2017.
Edición:DG edition.
Temas:
Topological graph theory.
Théorie des graphes topologiques.
MATHEMATICS > General.
Graphentheorie
Topologie
(Produktform)Electronic book text
(Zielgruppe)Fachpublikum/ Wissenschaft
(BISAC Subject Heading)MAT008000
(BISAC Subject Heading)MAT038000: MAT038000 MATHEMATICS / Topology
(BISAC Subject Heading)MAT012000: MAT012000 MATHEMATICS / Geometry / General
(VLB-WN)9620
(Produktrabattgruppe)PR: rabattbeschränkt/Bibliothekswerke
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface to DG Edition
  • Preface to USTC Edition
  • 1 Preliminaries ; 1.1 Sets and relations ; 1.2 Partitions and permutations ; 1.3 Graphs and networks ; 1.4 Groups and spaces ; 1.5 Notes
  • 2 Polyhedra ; 2.1 Polygon double covers ; 2.2 Supports and skeletons ; 2.3 Orientable polyhedra ; 2.4 Non-orientable polyhedra ; 2.5 Classic polyhedra ; 2.6 Notes
  • 3 Surfaces ; 3.1 Polyhegons ; 3.2 Surface closed curve axiom ; 3.3 Topological transformations ; 3.4 Complete invariants ; 3.5 Graphs on surfaces ; 3.6 Up-embeddability ; 3.7 Notes
  • 4 Homology on Polyhedra ; 4.1 Double cover by travels ; 4.2 Homology ; 4.3 Cohomology ; 4.4 Bicycles ; 4.5 Notes
  • 5 Polyhedra on the Sphere ; 5.1 Planar polyhedra ; 5.2 Jordan closed-curve axiom ; 5.3 Uniqueness ; 5.4 Straight-line representations ; 5.5 Convex representation ; 5.6 Notes
  • 6 Automorphisms of a Polyhedron ; 6.1 Automorphisms of polyhedra ; 6.2 Eulerian and non-Eulerian codes ; 6.3 Determination of automorphisms ; 6.4 Asymmetrization ; 6.5 Notes
  • 7 Gauss Crossing Sequences ; 7.1 Crossing polyhegons ; 7.2 Dehn's transformation ; 7.3 Algebraic principles ; 7.4 Gauss crossing problem ; 7.5 Notes
  • 8 Cohomology on Graphs ; 8.1 Immersions ; 8.2 Realization of planarity ; 8.3 Reductions ; 8.4 Planarity auxiliary graphs ; 8.5 Basic conclusions ; 8.6 Notes
  • 9 Embeddability on Surfaces ; 9.1 Joint tree model ; 9.2 Associate polyhegons ; 9.4 Criteria of embeddability ; 9.5 Notes
  • 10 Embeddings on Sphere ; 10.1 Left and right determinations ; 10.2 Forbidden configurations ; 10.3 Basic order characterization ; 10.4 Number of planar embeddings ; 10.5 Notes
  • 11 Orthogonality on Surfaces
  • 11.1 Definitions ; 11.2 On surfaces of genus zero ; 11.3 Surface models ; 11.4 On surfaces of genus not zero ; 11.5 Notes
  • 12 Net Embeddings ; 12.1 Definitions ; 12.2 Face admissibility ; 12.3 General criterion ; 12.4 Special criterion ; 12.4 Special criteria ; 12.5 Notes
  • 13 Extremality on Surfaces ; 13.1 Maximal genus ; 13.2 Minimal genus ; 13.3 Shortest embedding ; 13.4 Thickness ; 13.5 Crossing number ; 13.6 Minimal bend ; 13.8 Notes
  • 14 Matroidal Graphicness ; 14.1 Definitions ; 14.2 Binary matroids ; 14.3 Regularity ; 14.4 Graphicness ; 14.5 Cographicness ; 14.6 Notes
  • 15 Knot Polynomials ; 15.1 Definitions ; 15.2 Knot diagram ; 15.3 Tutte polynomial ; 15.4 Pan-polynomial ; 15.5 Jones Polynomial ; 15.6 Notes
  • Bibliography
  • Subject Index
  • Author Index.

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