Book:J.A. Bondy/Graph Theory With Applications

Subject Matter

 * Graph Theory

Contents

 * Preface


 * 1 Graphs and Subgraphs
 * 1.1 Graphs and Simple Graphs
 * 1.2 Graph Isomorphism
 * 1.3 The Incidence and Adjacency Matrices
 * 1.4 Subgraphs
 * 1.5 Vertex Degrees
 * 1.6 Paths and Connection
 * 1.7 Cycles
 * Applications
 * 1.8 The Shortest Path Problem
 * 1.9 Sperner's Lemma


 * 2 Trees
 * 2.1 Trees
 * 2.2 Cut Edges and Bonds
 * 2.3 Cut Vertices
 * 2.4 Cayley's Formula
 * Applications
 * 2.5 The Connector Problem


 * 3 Connectivity
 * 3.1 Connectivity
 * 3.2 Blocks
 * Applications
 * 3.3 Construction of Reliable Communication Networks


 * 4 Euler Tours and Hamilton Cycles
 * 4.1 Euler Tours
 * 4.2 Hamilton Cycles
 * Applications
 * 4.3 The Chinese Postman Problem
 * 4.4 The Travelling Salesman Problem


 * 5 Matchings
 * 5.1 Matchings
 * 5.2 Matchings and Coverings in Bipartite Graphs
 * 5.3 Perfect Matchings
 * Applications
 * 5.4 The Personnel Assignment Problem
 * 5.5 The Optimal Assignment Problem


 * 6 Edge Colourings
 * 6.1 Edge Chromatic Number
 * 6.2 Vizing's Theorem
 * Applications
 * 6.3 The Timetabling Problem


 * 7 Independent Sets and Cliques
 * 7.1 Independent Sets
 * 7.2 Ramsey's Theorem
 * 7.3 Turán's Theorem
 * Applications
 * 7.4 Schur's Theorem
 * 7.5 A Geometry Problem


 * 8 Vertex Colourings
 * 8.1 Chromatic Number
 * 8.2 Brooks' Theorem
 * 8.3 Hajós' Conjecture
 * 8.4 Chromatic Polynomials
 * 8.5 Girth and Chromatic Number
 * Applications
 * 8.6 A Storage Problem


 * 9 Planar Graphs
 * 9.1 Plane and Planar Graphs
 * 9.2 Dual Graphs
 * 9.3 Euler's Formula
 * 9.4 Bridges
 * 9.5 Kuratowski's Theorem
 * 9.6 The Five-Colour Theorem and the Four-Colour Conjecture
 * 9.7 Nonhamiltonian Planar Graphs
 * Applications
 * 9.8 A Planarity Algorithm


 * 10 Directed Graphs
 * 10.1 Directed Graphs
 * 10.2 Directed Paths
 * 10.3 Directed Cycles
 * Applications
 * 10.4 A Job Sequencing Problem
 * 10.5 Designing an Efficient Computer Drum
 * 10.6 Making a Road System One-Way
 * 10.7 Ranking the Participants in a Tournament


 * 11 Networks
 * 11.1 Flows
 * 11.2 Cuts
 * 11.3 The Max-Flow Min-Cut Theorem
 * Applications
 * 11.4 Menger's Theorems
 * 11.5 Feasible Flows


 * 12 The Cycle Space and Bond Space
 * 12.1 Circulations and Potential Differences
 * 12.2 The Number of Spanning Trees
 * Applications
 * 12.3 Perfect Squares


 * Appendix I: Hints to Starred Exercises
 * Appendix II: Four Graphs and a Table of their Properties
 * Appendix III: Some Interesting Graphs
 * Appendix IV: Unsolved Problems
 * Appendix V: Suggestions for Further Reading


 * Glossary of Symbols
 * Index