## Pearls in Graph Theory: A Comprehensive Introduction"Innovative introductory text . . . clear exposition of unusual and more advanced topics . . . Develops material to substantial level."-- American Mathematical Monthly"Refreshingly different . . . an ideal training ground for the mathematical process of investigation, generalization, and conjecture leading to the discovery of proofs and counterexamples."-- American Mathematical Monthly" . . . An excellent textbook for an undergraduate course."-- Australian Computer JournalA stimulating view of mathematics that appeals to students as well as teachers, this undergraduate-level text is written in an informal style that does not sacrifice depth or challenge. Based on 20 years of teaching by the leading researcher in graph theory, it offers a solid foundation on the subject. This revised and augmented edition features new exercises, simplifications, and other improvements suggested by classroom users and reviewers. Topics include basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 ed. |

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#### Review: Pearls in Graph Theory: A Comprehensive Introduction

User Review - GoodreadsSkimmed through most of this; it looked good, and there were several wonderful examples I'd never seen before (generally, results I'd seen achieved with trivial topological results, but not through a "pure" graph theory methodology). Read full review

#### Review: Pearls in Graph Theory: A Comprehensive Introduction

User Review - Nick Black - GoodreadsSkimmed through most of this; it looked good, and there were several wonderful examples I'd never seen before (generally, results I'd seen achieved with trivial topological results, but not through a "pure" graph theory methodology). Read full review

### Contents

Colorings of Graphs | 23 |

Circuits and Cycles | 49 |

Extremal Problems | 70 |

Chapters Counting | 87 |

Cayleys Spanning Tree Formula | 94 |

Labeling Graphs | 104 |

Conservative Graphs | 114 |

Applications and Algorithms | 125 |

Matchings in Graphs Scheduling Problems | 133 |

Chapters Drawings of Graphs | 149 |

Measurements of Closeness to Planarity | 179 |

Thickness and Splitting Number | 190 |

Graphs on Surfaces | 208 |

241 | |

### Common terms and phrases

1-factor 2-pires algorithm antimagic assume binary tree blue edges blue vertices bridge called circuit induced codeword Color Theorem complete bipartite graph complete graph connected graph consider countries crossing number cubic graph decomposable degree sequence edge coloring edges incident edges of G endpoints Eulerian circuit example Exercises Find a graph four colors four vertices G contains graph G graph of Figure graph theory Hamilton cycle Hamilton path Heawood Hence integer isomorphic subgraphs largest graph Let G magic maximal planar graph maximal rotation multiset mutually adjacent normal map number of edges number of vertices obtain odd degree path of length Petersen graph planar graph plane drawing problem proof of Theorem pseudograph q edges red and blue red edges red vertex red vertices region regular of degree Ringel shown in Figure shows simple drawing spanning trees strongly conservative subgraphs isomorphic three colors triangle vertices and q vertices of degree vertices of G