## Algorithmic Graph Theory and Perfect Graphs: Second EditionAlgorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails. The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. These are surveyed in the new Epilogue chapter in this second edition. · New edition of the "Classic" book on the topic · Wonderful introduction to a rich research area · Leading author in the field of algorithmic graph theory · Beautifully written for the new mathematician or computer scientist · Comprehensive treatment |

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### Contents

Chapter 1 Graph Theoretic Foundations | 1 |

Chapter 2 The Design of Efficient Algorithms | 22 |

Chapter 3 Perfect Graphs | 51 |

Chapter 4 Triangulated Graphs | 81 |

Chapter 5 Comparability Graphs | 105 |

Chapter 6 Split Graphs | 149 |

Chapter 7 Permutation Graphs | 157 |

Chapter 8 Interval Graphs | 171 |

### Common terms and phrases

acyclic Adj(v adjacency sets algorithm assume bisimplicial called Chapter characterization chordal bipartite graph chordal graphs chordless cycle chords Chvatal circle graphs circular 1’s circular-arc graphs clique cover clique matrix clique of G cograph color classes columns comparability graph complement complete Corollary corresponding data structure decomposition deﬁned deﬁnition denote derived graph Discrete Math efﬁcient endpoint equivalent example exists ﬁnd ﬁnite ﬁrst Golumbic graph G graph in Figure Graph Theory implication class implies induced subgraph integer intersection graph interval graph isomorphic labeling Lemma Let G linear maximal maximum clique maximum stable set minimal minimum multiplex NP-complete obtain orientation of G p-critical partially ordered sets partition path perfect elimination scheme permutation graph polynomial problem Proof Prove the following queue representation satisﬁes Section semiorder sequence simplex split graph subset subtrees superperfect Theorem threshold graph tolerance graphs topological sorting transitive orientation tree triangulated graphs undirected graph Univ vertices