Sparsity

• Part I Presentation: 1. Introduction.- 2. A Few Problems.- 3. Commented Contents.- Part II. The Theory: 4. Prolegomena.- 5. Measuring Sparsity.- 6. Classes and their Classification.- 7. Bounded Height Trees and Tree-Depth.- 8. Decomposition.- 9. Independence.- 10. First-Order Constraint Satisfaction Problems and Homomorphism Dualities.- 11. Restricted Homomorphism Dualities.- 12. Counting.- 13. Back to Classes.- Part III Applications: 14. Classes with Bounded Expansion – Examples.- 15. Property Testing, Hyperfiniteness and Separators.- 16. Algorithmic Applications.- 17. Other Applications.- 18. Conclusion.- Bibliography.- Index.- List of Symbols​.

From the reviews: "This well-crafted and well-written work ... brings the authors' vast knowledge, expertise, taste, and judgment to bear on an increasingly important and mainstream subject. ... This is a much-needed book devoted to the systematic study of sparse graphs and sparse classes of structures. ... This is an important and useful book. It contains a wealth of up-to-date material, some of which is not readily available in research papers. ... A researcher in graph theory or related fields will find this an excellent reference work." (Jozsef Balogh, Mathematical Reviews, March, 2013) "This is an excellent and useful book for all researchers in mathematics, computer science, logic, and even in any field in physical science, who seek the tools available for analysis of the properties of discrete structures, and particularly, sparse structures." (Tadashi Sakuma, zbMATH, Vol. 1268, 2013) "The book is very well written and diagrammed to beautifully present the theory supporting the study of sparse and dense objects. ... the book contains up-to-date research topics laid out in an amazing chain of thoughts. Almost every chapter ends with exercises, aiding professors in advanced graduate courses. The extensive list of references, together with conjectures and open problems, offers professors, students, and researchers ... profound knowledge on the sparsity of graphs, all in one great book." (Andre Maximo, Computing Reviews, October, 2012)