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E-BOOK
Title Topological theory of graphs / Yanpei Liu.
Imprint Boston : De Gruyter, 2017.

Copies/Volumes

LOCATION CALL # STATUS
 Internet  Electronic Book    AVAILABLE
Edition DG edition.
USTC edition.
Description 1 online resource (370 pages) : illustrations
Bibliog. Includes bibliographical references and index.
Note Available only to authorized UTEP users.
In English.
Print version record.
Subject Topological graph theory.
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.
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.
Other Title Print version : Liu, Yanpei, 1939- Topological theory of graphs. Berlin ; Boston : De Gruyter, [2017] 9783110476699