Topics in structural graph theory /

Topics in structural graph theory /

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Bibliographic Details
Imprint:Cambridge ; New York : Cambridge University Press, 2013.
Description:xiv, 327 p. : ill. ; 24 cm.
Language:English
Series:Encyclopedia of mathematics and its applications ; 147
Encyclopedia of mathematics and its applications ; v. 147.
Subject:
Graph theory -- Data processing.
Graph theory -- Data processing.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/9041479
Hidden Bibliographic Details
Other authors / contributors:Beineke, Lowell W.
Wilson, Robin J.
ISBN:9780521802314 (hardback)
0521802318 (hardback)
Notes:Includes bibliographical references and index.
Summary:"The rapidly expanding area of structural graph theory uses ideas of connectivity to explore various aspects of graph theory and vice versa. It has links with other areas of mathematics, such as design theory and is increasingly used in such areas as computer networks where connectivity algorithms are an important feature. Although other books cover parts of this material, none has a similarly wide scope. Ortrud R. Oellermann (Winnipeg), internationally recognised for her substantial contributions to structural graph theory, acted as academic consultant for this volume, helping shape its coverage of key topics. The result is a collection of thirteen expository chapters, each written by acknowledged experts. These contributions have been carefully edited to enhance readability and to standardise the chapter structure, terminology and notation throughout. An introductory chapter details the background material in graph theory and network flows and each chapter concludes with an extensive list of references"--
Table of Contents:
  • Foreword
  • Preface
  • Introduction
  • 1. Graph theory
  • 2. Graphs in the plane
  • 3. Surfaces
  • 4. Graphs on surfaces
  • 1. Embedding graphs on surfaces
  • 1. Introduction
  • 2. Graphs and surfaces
  • 3. Embeddings
  • 4. Rotation systems
  • 5. Covering spaces and voltage graphs
  • 6. Enumeration
  • 7. Algorithms
  • 8. Graph minors
  • 2. Maximum genus
  • 1. Introduction
  • 2. Characterizations and complexity
  • 3. Kuratowski-type theorems
  • 4. Upper-embeddability
  • 5. Lower bounds
  • 3. Distribution of embeddings
  • 1. Introduction
  • 2. Enumerating embeddings by surface type
  • 3. Total embedding distributions
  • 4. Congruence classes
  • 5. The unimodality problem
  • 6. Average genus
  • 7. Stratification of embeddings
  • 4. Algorithms and obstructions for embeddings
  • 1. Introduction
  • 2. Planarity
  • 3. Outerplanarity and face covers
  • 4. Disc embeddings and the 2-path problem
  • 5. Graph minors and obstructions
  • 6. Algorithms for embeddability in general surfaces
  • 7. Computing the genus
  • 5. Graph minors: generalizing Kuratowski's theorem
  • 1. Introduction
  • 2. Graph decompositions
  • 3. Linked decompositions
  • 4. Graphs with bounded tree-width
  • 5. Finding large grids
  • 6. Embedding large grids
  • 6. Colouring graphs on surfaces
  • 1. Introduction
  • 2. High-end colouring
  • 3. A transition from high-end to low-end colouring
  • 4. Colouring graphs with few colours
  • 5. Girth and chromatic number
  • 6. List-colouring graphs
  • 7. More colouring extensions
  • 8. An open problem
  • 7. Crossing numbers
  • 1. Introduction
  • 2. What is the crossing number?
  • 3. General bounds
  • 4. Applications to geometry
  • 5. Crossing-critical graphs
  • 6. Other families of graphs
  • 7. Algorithmic questions
  • 8. Drawings in other surfaces
  • 9. Conclusion
  • 8. Representing graphs and maps
  • 1. Introduction
  • 2. Representations of graphs
  • 3. Energy and optimal representations
  • 4. Representations of maps
  • 5. Representations of maps in the plane
  • 6. Representations of incidence geometries and related topics
  • 9. Enumerating coverings
  • 1. Introduction
  • 2. Graph coverings
  • 3. Regular coverings
  • 4. Surface branched coverings
  • 5. Regular surface branched coverings
  • 6. Distribution of surface branched coverings
  • 7. Further remarks
  • 10. Symmetric maps
  • 1. Introduction
  • 2. Representing maps algebraically
  • 3. Regular maps
  • 4. Cayley maps
  • 5. Regular Cayley maps
  • 6. Edge-transitive maps
  • 7. Maps and mathematics
  • 11. The genus of a group
  • 1. Introduction
  • 2. Symmetric embeddings and groups acting on surfaces
  • 3. Quotient embeddings and voltage graphs
  • 4. Inequalities
  • 5. Groups of low genus
  • 6. Genera of families of groups
  • 12. Embeddings and geometries
  • 1. Introduction
  • 2. Surface models
  • 3. Projective geometries
  • 4. Affine geometries
  • 5. 3-configurations
  • 6. Partial geometries
  • 7. Regular embeddings for PG(2,n)
  • 8. Problems
  • 13. Embeddings and designs
  • 1. Introduction
  • 2. Steiner triple systems and triangulations
  • 3. Recursive constructions
  • 4. Small systems
  • 5. Cyclic embeddings
  • 6. Concluding remarks
  • 14. Infinite graphs and planar maps
  • 1. Introduction
  • 2. Ends
  • 3. Automorphisms
  • 4. Connectivities
  • 5. Growth
  • 6. Infinite planar graphs and maps
  • 15. Open problems
  • 1. Introduction
  • 2. Drawings and crossings
  • 3. Genus and obstructions
  • 4. Cycles and factors
  • 5. Colourings and flows
  • 6. Local planarity
  • 7. Thickness, book embeddings and-covering graphs
  • 8. Geometrical topics
  • 9. Algorithms
  • 10. Infinite graphs
  • Notes on contributors
  • Index

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