## Graphs and Their Uses, Volume 34In 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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### Contents

Introduction | 3 |

Connected Graphs | 24 |

Trees | 37 |

Matchings | 53 |

Directed Graphs | 63 |

Questions Concerning Games and Puzzles | 83 |

Relations | 95 |

Planar Graphs | 109 |

Map Coloring | 125 |

Solutions | 136 |

146 | |

### Common terms and phrases

applicants basis graph Betty boundary edges called Color Theorem committees complete graph completely regular graphs connected components connected graph consider consists cyclic trail denote diagonal braces directed edges directed graph directed path diversity condition dodecahedron draw drawn dual graph economy tree edges connecting edges correspond elements endpoint equivalence relation Euler's formula Eulerian trail example four color framework graph G graph in Figure graph theory Hamiltonian cycle illustrate indeg(a infinite face initial vertex instance integers intersections interval graph isomorphic jugs large number matches mathematical mathematician moves null graph number of edges number of vertices obtain odd number odd vertices pair planar graph plane played polygonal graph possible Problem Set puzzle regular of degree result road Section set Ra shortest solution streets strict partial order Suppose teams temporary label three edges tournament travelling salesman problem undirected whole graph winning positions