This groundbreaking, yet accessible book explores the interaction between graph theory and computational complexity using methods from finite model theory.
This groundbreaking, yet accessible book explores the interaction between graph theory and computational complexity using methods from finite model theory.
Martin Grohe is a Professor of Theoretical Computer Science at RTWH Aachen University, Germany, where he holds the Chair for Logic and the Theory of Discrete Systems. His research interests are in theoretical computer science interpreted broadly, including logic, algorithms and complexity, graph theory, and database theory.
Inhaltsangabe
1. Introduction Part I. The Basic Theory: 2. Background from graph theory and logic 3. Descriptive complexity 4. Treelike decompositions 5. Definable decompositions 6. Graphs of bounded tree width 7. Ordered treelike decompositions 8. 3-Connected components 9. Graphs embeddable in a surface Part II. Definable Decompositions of Graphs with Excluded Minors: 10. Quasi-4-connected components 11. K5-minor free graphs 12. Completions of pre-decompositions 13. Almost planar graphs 14. Almost planar completions 15. Almost embeddable graphs 16. Decompositions of almost embeddable graphs 17. Graphs with excluded minors 18. Bits and pieces Appendix. Robertson and Seymour's version of the local structure theorem References Symbol index Index.
1. Introduction Part I. The Basic Theory: 2. Background from graph theory and logic 3. Descriptive complexity 4. Treelike decompositions 5. Definable decompositions 6. Graphs of bounded tree width 7. Ordered treelike decompositions 8. 3-Connected components 9. Graphs embeddable in a surface Part II. Definable Decompositions of Graphs with Excluded Minors: 10. Quasi-4-connected components 11. K5-minor free graphs 12. Completions of pre-decompositions 13. Almost planar graphs 14. Almost planar completions 15. Almost embeddable graphs 16. Decompositions of almost embeddable graphs 17. Graphs with excluded minors 18. Bits and pieces Appendix. Robertson and Seymour's version of the local structure theorem References Symbol index Index.
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