Descriptive Complexity, Canonisation, and Definable Graph Structure Theory

ISBN-13: 9781107014527 / Angielski / Twarda / 2017 / 554 str.

Martin Grohe

Opis

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

Recenzje

'The book is divided evenly into two parts. Part I gives background and definitions of the main notions, and makes the book self-contained. Many results from descriptive complexity theory, and the author's earlier results, are clearly presented. Part II is devoted to the main theorem about graphs with excluded minors. The book ends with a symbol index and an index.' Pascal Michel, Mathematical Reviews

Spis treści

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.