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The Foundations of Topological Graph Theory

  • C. Paul Bonnington
  • Charles H. C. Little
Book

Table of contents

  1. Front Matter
    Pages i-ix
  2. C. Paul Bonnington, Charles H. C. Little
    Pages 1-21
  3. C. Paul Bonnington, Charles H. C. Little
    Pages 23-37
  4. C. Paul Bonnington, Charles H. C. Little
    Pages 39-51
  5. C. Paul Bonnington, Charles H. C. Little
    Pages 53-62
  6. C. Paul Bonnington, Charles H. C. Little
    Pages 63-81
  7. C. Paul Bonnington, Charles H. C. Little
    Pages 83-96
  8. C. Paul Bonnington, Charles H. C. Little
    Pages 97-109
  9. C. Paul Bonnington, Charles H. C. Little
    Pages 111-141
  10. C. Paul Bonnington, Charles H. C. Little
    Pages 143-152
  11. C. Paul Bonnington, Charles H. C. Little
    Pages 153-159
  12. Back Matter
    Pages 161-178

About this book

Introduction

This is not a traditional work on topological graph theory. No current graph or voltage graph adorns its pages. Its readers will not compute the genus (orientable or non-orientable) of a single non-planar graph. Their muscles will not flex under the strain of lifting walks from base graphs to derived graphs. What is it, then? It is an attempt to place topological graph theory on a purely combinatorial yet rigorous footing. The vehicle chosen for this purpose is the con­ cept of a 3-graph, which is a combinatorial generalisation of an imbedding. These properly edge-coloured cubic graphs are used to classify surfaces, to generalise the Jordan curve theorem, and to prove Mac Lane's characterisation of planar graphs. Thus they playa central role in this book, but it is not being suggested that they are necessarily the most effective tool in areas of topological graph theory not dealt with in this volume. Fruitful though 3-graphs have been for our investigations, other jewels must be examined with a different lens. The sole requirement for understanding the logical development in this book is some elementary knowledge of vector spaces over the field Z2 of residue classes modulo 2. Groups are occasionally mentioned, but no expertise in group theory is required. The treatment will be appreciated best, however, by readers acquainted with topology. A modicum of topology is required in order to comprehend much of the motivation we supply for some of the concepts introduced.

Keywords

Graph theory Partition Permutation classification graphs

Authors and affiliations

  • C. Paul Bonnington
    • 1
  • Charles H. C. Little
    • 2
  1. 1.Department of MathematicsUniversity of AucklandAucklandNew Zealand
  2. 2.Department of MathematicsMassey UniversityPalmerston NorthNew Zealand

Bibliographic information