ALGORITHMIC GRAPH THEORY AND PERFECT GRAPHS SECOND EDITION【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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CHAPTER 1 Graph Theoretic Foundations1

1.Basic Definitions and Notations1

2.Intersection Graphs9

3.Interval Graphs—A Sneak Preview of the Notions Coming Up13

4.Summary17

Exercises18

Bibliography20

CHAPTER 2 The Design of Efficient Algorithms22

1.The Complexity of Computer Algorithms22

2.Data Structures31

3.How to Explore a Graph37

4.Transitive Tournaments and Topological Sorting42

Exercises45

Bibliography48

CHAPTER 3 Perfect Graphs51

1.The Star of the Show51

2.The Perfect Graph Theorem53

3.p-Critical and Partitionable Graphs58

4.A Polyhedral Characterization of Perfect Graphs62

5.A Polyhedral Characterization of p-Critical Graphs65

6.The Strong Perfect Graph Conjecture71

Exercises75

Bibliography77

CHAPTER 4 Triangulated Graphs81

1.Introduction81

2.Characterizing Triangulated Graphs81

3.Recognizing Triangulated Graphs by Lexicographic Breadth-First Search84

4.The Complexity of Recognizing Triangulated Graphs87

5.Triangulated Graphs as Intersection Graphs91

6.Triangulated Graphs Are Perfect94

7.Fast Algorithms for the COLORING，CLIQUE， STABLE SET， and CLIQUE-COVER Problems on Triangulated Graphs98

Exercises100

Bibliography102

CHAPTER 5 Comparability Graphs105

1.Γ-Chains and Implication Classes105

2.Uniquely Partially Orderable Graphs109

3.The Number of Transitive Orientations113

4.Schemes and G-Decompositions—An Algorithm for Assigning Transitive Orientations120

5.The 1*-Matroid of a Graph124

6.The Complexity of Comparability Graph Recognition129

7.Coloring and Other Problems on Comparability Graphs132

8.The Dimension of Partial Orders135

Exercises139

Bibliography142

CHAPTER 6 Split Graphs149

1.An Introduction to Chapters 6-8： Interval，Permutation， and Split Graphs149

2.Characterizing Split Graphs149

3.Degree Sequences and Split Graphs152

Exercises155

Bibliography156

CHAPTER 7 Permutation Graphs157

1.Introduction157

2.Characterizing Permutation Graphs158

3.Permutation Labelings160

4.Applications162

5.Sorting a Permutation Using Queues in Parallel164

Exercises168

Bibliography169

CHAPTER 8 Interal Graphs171

1.How It All Started171

2.Some Characterizations of Interval Graphs172

3.The Complexity of Consecutive l’s Testing175

4.Applications of Interval Graphs181

5.Preference and Indifference185

6.Circular-Arc Graphs188

Exercises193

Bibliography197

CHAPTER 9 Superperfect Graphs203

1.Coloring Weighted Graphs203

2.Superperfection206

3.An Infinite Class of Superperfect Noncom parability Graphs209

4.When Does Superperfect Equal Comparability？212

5.Composition of Superperfect Graphs214

6.A Representation Using the Consecutive l’s Property215

Exercises218

Bibliography218

CHAPTER 10 Threshold Graphs219

1.The Threshold Dimension219

2.Degree Partition of Threshold Graphs223

3.A Characterization Using Permutations227

4.An Application to Synchronizing Parallel Processes229

Exercises231

Bibliography234

CHAPTER 11 Not So Perfect Graphs235

1.Sorting a Permutation Using Stacks in Parallel235

2.Intersecting Chords of a Circle237

3.Overlap Graphs242

4.Fast Algorithms for Maximum Stable Set and Maximum Clique of These Not So Perfect Graphs244

5.A Graph Theoretic Characterization of Overlap Graphs248

Exercises251

Bibliography253

CHAPTER 12 Perfect Gaussian Elimination254

1.Perfect Elimination Matrices254

2.Symmetric Matrices256

3.Perfect Elimination Bipartite Graphs259

4.Chordal Bipartite Graphs261

Exercises264

Bibliography266

Appendix269

A.A Small Collection of NP-Complete Problems269

B.An Algorithm for Set Union， Intersection，Difference， and Symmetric Difference of Two Subsets270

C.Topological Sorting： An Example of Algorithm 2.4271

D.An Illustration of the Decomposition Algorithm273

E.The Properties P.E.B.， C.B.，（P.E.B.）’，（C.B.）’ Illustrated273

F.The Properties C， C —， T， T — llustrated275

Epilogue 2004277

Index307