Graphs and Their Uses.

Front Cover -- Graphs and Their Uses -- Copyright Page -- Contents -- Introduction -- Chapter 1. What Is a Graph? -- 1.1 Team Competitions -- I .2 Null Graphs and Complete Graphs -- 1.3 Isomorphic Graphs -- I .4 Planar Graphs -- 1.5 Planar Problems -- 1.6 The Number of Edges in a Graph -- I .7 Interval Graphs -- Chapter 2. Connected Graphs -- 2.1 Connected Components -- 2.2 The Problem of the Bridges of Königsberg -- 2.3 Eulerian Graphs -- 2.4 Finding Your Way -- 2.5 Hamiltonian Cycles -- 2.6 Puzzles and Graphs -- Chapter 3. Trees -- 3.1 Trees and Forests -- 3.2 Cycles and Trees -- 3.3 The Connector Problem -- 3.4 The Travelling Salesman Problem Revisited -- 3.5 Bracing Frameworks -- 3.6 Streets and Squares -- Chapter 4. Matchings -- 4.1 The Jobs and the Applicants -- 4.2 Other Formulations -- 4.3 Round-Robin Matchings -- Chapter 5. Directed Graphs -- 5.1 Team Competitions Re-examined -- 5.2 The Problems of One-way Traffic -- 5.3 Degrees -- 5.4 Genetic Graphs -- 5.5 Finding the Shortest Route -- Chapter 6. Questions Concerning Games and Puzzles -- 6.1 Puzzles and Directed Graphs -- 6.2 The Theory of Games -- 6.3 The Sportswriter's Paradox -- Chapter 7. Relations -- 7.1 Relations and Graphs -- 7.2 Special Conditions -- 7.3 Equivalence Relations -- 7.4 Partial Orders -- Chapter 8. Planar Graphs -- 8.1 Conditions for Planar Graphs -- 8.2 Euler's Formula -- 8.3 Graph Relations and Dual Graphs -- 8.4 The Platonic Solids -- 8.5 Mosaics -- Chapter 9. Map Coloring -- 9.1 The Four Color Problem -- 9.2 The Five Color Theorem -- 9.3 Coloring Maps on Other Surfaces -- Solutions -- Bibliography -- Glossary -- Index -- Back Cover.

In 1963, Oystein Ore wrote this classic volume, which was published in the New Mathematical Library Series. This elegant book has provided students and teachers with an excellent introduction to the field of graph theory for close to thirty years.Robin Wilson's revision adds strength to the book by updating the terminology and notation, bringing them in line with contemporary usage. Wilson has added new material on interval graphs, the traveling salesman problem, bracing frameworks, shortest route problems, and coloring maps on surfaces. Most of the diagrams in the book have been redrawn.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.