The Resource Topological theory of graphs, Yanpei Liu
Topological theory of graphs, Yanpei Liu
Resource Information
The item Topological theory of graphs, Yanpei Liu represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Missouri University of Science & Technology Library.This item is available to borrow from 1 library branch.
Resource Information
The item Topological theory of graphs, Yanpei Liu represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Missouri University of Science & Technology Library.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Edition
-
- DG edition.
- USTC edition.
- Extent
- 1 online resource (370 pages)
- 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
- Isbn
- 9783110479508
- Label
- Topological theory of graphs
- Title
- Topological theory of graphs
- Statement of responsibility
- Yanpei Liu
- Subject
-
- (BISAC Subject Heading)MAT012000: MAT012000 MATHEMATICS / Geometry / General
- (BISAC Subject Heading)MAT038000: MAT038000 MATHEMATICS / Topology
- (Produktform)Electronic book text
- (Produktrabattgruppe)PR: rabattbeschränkt/Bibliothekswerke
- (VLB-WN)9620
- (Zielgruppe)Fachpublikum/ Wissenschaft
- Graphentheorie
- MATHEMATICS -- General
- Topological graph theory
- Topological graph theory
- Topologie
- Electronic books
- (BISAC Subject Heading)MAT008000
- 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
- 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
- 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
- 9783110479508
- 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
- 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
- 9783110479508
- 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
Subject
- (BISAC Subject Heading)MAT012000: MAT012000 MATHEMATICS / Geometry / General
- (BISAC Subject Heading)MAT038000: MAT038000 MATHEMATICS / Topology
- (Produktform)Electronic book text
- (Produktrabattgruppe)PR: rabattbeschränkt/Bibliothekswerke
- (VLB-WN)9620
- (Zielgruppe)Fachpublikum/ Wissenschaft
- Graphentheorie
- MATHEMATICS -- General
- Topological graph theory
- Topological graph theory
- Topologie
- Electronic books
- (BISAC Subject Heading)MAT008000
Genre
Member of
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.mst.edu/portal/Topological-theory-of-graphs-Yanpei-Liu/9OoQS1Mi6uU/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.mst.edu/portal/Topological-theory-of-graphs-Yanpei-Liu/9OoQS1Mi6uU/">Topological theory of graphs, Yanpei Liu</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.mst.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.mst.edu/">Missouri University of Science & Technology Library</a></span></span></span></span></div>
