Algorithmic Graph Theory and Perfect Graphs

¿ForewordPrefaceAcknowledgmentsList of SymbolsChapter 1 Graph Theoretic Foundations 1. Basic Definitions and Notations 2. Intersection Graphs 3. Interval Graphs-A Sneak Preview of the Notions Coming Up 4. Summary Exercises BibliographyChapter 2 The Design of Efficient Algorithms 1. The Complexity of Computer Algorithms 2. Data Structures 3. How to Explore a Graph 4. Transitive Tournaments and Topological Sorting Exercises BibliographyChapter 3 Perfect Graphs 1. The Star of the Show 2. The Perfect Graph Theorem 3. p-Critical and Partitionable Graphs 4. A Polyhedral Characterization of Perfect Graphs 5. A Polyhedral Characterization of p-Critical Graphs 6. The Strong Perfect Graph Conjecture Exercises BibliographyChapter 4 Triangulated Graphs 1. Introduction 2. Characterizing Triangulated Graphs 3. Recognizing Triangulated Graphs by Lexicographic Breadth-First Search 4. The Complexity of Recognizing Triangulated Graphs 5. Triangulated Graphs as Intersection Graphs 6. Triangulated Graphs Are Perfect 7. Fast Algorithms for the Coloring, Clique, Stable Set, and Clique-Cover Problems on Triangulated Graphs Exercises BibliographyChapter 5 Comparability Graphs 1. G-Chains and Implication Classes 2. Uniquely Partially Orderable Graphs 3. The Number of Transitive Orientations 4. Schemes and G-Decompositions-An Algorithm for Assigning Transitive Orientations 5. The G-Matroid of a Graph 6. The Complexity of Comparability Graph Recognition 7. Coloring and Other Problems on Comparability Graphs 8. The Dimension of Partial Orders Exercises BibliographyChapter 6 Split Graphs 1. An Introduction to Chapters 6-8: Interval,Permutation, and Split Graphs 2. Characterizing Split Graphs 3. Degree Sequences and Split Graphs Exercises BibliographyChapter 7 Permutation Graphs 1. Introduction 2. Characterizing Permutation Graphs 3. Permutation Labelings 4. Applications 5. Sorting a Permutation Using Queues in Parallel Exercises BibliographyChapter 8 Interval Graphs 1. How It All Started 2. Some Characterizations of Interval Graphs 3. The Complexity of Consecutive 1's Testing 4. Applications of Interval Graphs 5. Preference and Indifference 6. Circular-Arc Graphs Exercises BibliographyChapter 9 Superperfect Graphs 1. Coloring Weighted Graphs 2. Superperfection 3. An Infinite Class of Superperfect Noncomparability Graphs 4. When Does Superperfect Equal Comparability? 5. Composition of Superperfect Graphs 6. A Representation Using the Consecutive 1's Property Exercises BibliographyChapter 10 Threshold Graphs 1. The Threshold Dimension 2. Degree Partition of Threshold Graphs 3. A Characterization Using Permutations 4. An Application to Synchronizing Parallel Processes Exercises BibliographyChapter 11 Not So Perfect Graphs 1. Sorting a Permutation Using Stacks in Parallel 2. Intersecting Chords of a Circle 3. Overlap Graphs 4. Fast Algorithms for Maximum Stable Set and Maximum Clique of These Not So Perfect Graphs 5. A Graph Theoretic Characterization of Overlap Graphs Exercises BibliographyChapter 12 Perfect Gaussian Elimination 1. Perfect Elimination Matrices 2. Symmetric Matrices 3. Perfect Elimination Bipartite Graphs 4. Chordal Bipartite Graphs Exercises BibliographyAppendix A. A Small Collection of NP-Complete Problems B. An Algorithm for Set Union, Intersection, Difference, and Symmetric Difference of Two Subsets C. Topological Sorting: An Example of Algorithm 2.4 D. An Illustration of the Decomposition Algorithm E. The Properties P.E.B., C.B., (P.E.B.)', (C.B.)' Illustrated F. The Properties C, C, T, T IllustratedIndex