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
Author
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
Member of
Cataloging source
EBLCP
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
LC call number
QA166.195
LC item number
.L58 2017eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Topological graph theory
  • MATHEMATICS
  • Topological graph theory
  • Graphentheorie
  • Topologie
Label
Topological theory of graphs, Yanpei Liu
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
978572048
Dimensions
unknown
Edition
  • DG edition.
  • USTC edition.
Extent
1 online resource (370 pages)
File format
unknown
Form of item
online
Isbn
9783110479492
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
  • 10.1515/9783110479492
  • 9783110479492
  • urn:nbn:de:101:1-2017040528062
  • 9783110479225
  • urn:nbn:de:101:1-201704192965
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
1000764
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
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
978572048
Dimensions
unknown
Edition
  • DG edition.
  • USTC edition.
Extent
1 online resource (370 pages)
File format
unknown
Form of item
online
Isbn
9783110479492
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
  • 10.1515/9783110479492
  • 9783110479492
  • urn:nbn:de:101:1-2017040528062
  • 9783110479225
  • urn:nbn:de:101:1-201704192965
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
1000764
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)978572048

Library Locations

    • Curtis Laws Wilson LibraryBorrow it
      400 West 14th Street, Rolla, MO, 65409, US
      37.955220 -91.772210
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