Descriptive Complexity, Canonisation, and Definable Graph Structure Theory - Martin Grohe

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Résumé :
This groundbreaking, yet accessible book explores the interaction between graph theory and computational complexity using methods from finite model theory.

Biographie:
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.

Sommaire:
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.