## A First Look at Graph TheoryThis book is intended to be an introductory text for mathematics and computer science students at the second and third year levels in universities. It gives an introduction to the subject with sufficient theory for students at those levels, with emphasis on algorithms and applications. |

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I have taught undergraduate graph theory from this book many times, and I very much like its level, exposition, and problem selection. It is neither the most basic nor the most advanced introduction I've seen, but probably somewhere on the low side of middle. I supplement it with excellent texts (Bondy & Murty, Diestel) that are available for free online.

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Textbook

### Contents

An Introduction to Graphs | 1 |

Trees and Connectivity | 47 |

Euler Tours and Hamiltonian Cycles | 83 |

Matchings | 121 |

Planar Graphs | 157 |

Directed Graphs | 229 |

Networks | 261 |

Ramsey Theory | 291 |

Reconstruction | 303 |

321 | |

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### Common terms and phrases

9raph adjacency matrix algorithm assigned blue bridge choose chromatic index colour the edges colouring of G complete bipartite graph complete graph component of G connected components connected graph corresponding cut vertex cycle of length degree denote the number digraph disconnected distinct vertices ed9es edge colouring edges incident edges of G Euler graph Euler tour Euler trail example Exercises for Section G is called G is connected G of Figure given gives graph G graph of Figure Hamiltonian cycle Hamiltonian graph Hamiltonian path Hence induction internally disjoint isomorphic Kempe chain least Let G loop maximum monochromatic triangle nonempty number of edges number of vertices odd vertices outdegree path in G perfect matching planar plane graph problem shortest path shown in Figure shows simple graph Step strongly connected subgraph G subgraph of G subset supergraph suppose that G tournament tree H vertex set vertices of G weighted graph