Coverart for item
The Resource Topological theory of graphs, Yanpei Liu

Topological theory of graphs, Yanpei Liu

Label
Topological theory of graphs
Title
Topological theory of graphs
Statement of responsibility
Yanpei Liu
Creator
Subject
Language
eng
Summary
"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 (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 includes the Jordan of axiom in polyhedral forms, efficient methods for extremality 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"--Back cover
http://library.link/vocab/creatorDate
1939-
http://library.link/vocab/creatorName
Liu, Yanpei
Dewey number
511.5
Illustrations
illustrations
Index
index present
Language note
In English
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
Topological graph theory
Label
Topological theory of graphs, Yanpei Liu
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Color
multicolored
Contents
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
Control code
ocn978572048
Dimensions
unknown
Edition
  • DG edition
  • USTC edition
Extent
1 online resource (370 pages)
File format
unknown
Form of item
online
Isbn
9783110479508
Level of compression
unknown
Note
eBooks on EBSCOhost
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)978572048
Label
Topological theory of graphs, Yanpei Liu
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Color
multicolored
Contents
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
Control code
ocn978572048
Dimensions
unknown
Edition
  • DG edition
  • USTC edition
Extent
1 online resource (370 pages)
File format
unknown
Form of item
online
Isbn
9783110479508
Level of compression
unknown
Note
eBooks on EBSCOhost
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)978572048

Library Locations

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