Combinatorics and Probability

This volume celebrating the 60th birthday of Béla Bollobás presents the state of the art in combinatorics.

Graham Brightwell (Edited by), Imre Leader (Edited by), Alex Scott (Edited by), Andrew Thomason (Edited by)

9780521872072, Cambridge University Press

Hardback, published 8 March 2007

660 pages, 31 b/w illus. 4 tables 6 exercises
25.3 x 17.8 x 3.7 cm, 1.452 kg

'… this reviewer was very impressed, and even surprised, by the breadth of the articles of the collection. (Of course, the depth is impressive, too, but that is not surprising, given the pedigree of the contributors.)' MAA Reviews

Combinatorics is an area of mathematics involving an impressive breadth of ideas, and it encompasses topics ranging from codes and circuit design to algorithmic complexity and algebraic graph theory. In a highly distinguished career Béla Bollobás has made, and continues to make, many significant contributions to combinatorics, and this volume reflects the wide range of topics on which his work has had a major influence. It arises from a conference organized to mark his 60th birthday and the thirty-one articles contained here are of the highest calibre. That so many excellent mathematicians have contributed is testament to the very high regard in which Béla Bollobás is held. Students and researchers across combinatorics and related fields will find that this volume provides a wealth of insight to the state of the art.

1. Measures of pseudorandomness for finite sequences: minimal values N. Alon, Y. Kohayakawa, C. Mauduit and V. R. Rödl
2. MaxCut in H-Free graphs Noga Alon, Michael Krivelevich and Benny Sudakov
3. A tale of three couplings: Poisson–Dirichlet and GEM approximations for random permutations Richard Arratia, A. D. Barbour and Simon Tavaré
4. Positional games József Beck
5. Degree distribution of competition-induced preferential attachment graphs N. Berger, C. Borgs, J. T. Chayes, R. M. D'Souza and R. D. Kleinberg
6. On two conjectures on packing of graphs Béla Bollobás, Alexandr Kostochka and Kittikorn Nakprasit
7. Approximate counting and quantum computation M. Bordewich, M. Freedman, L. Lovász and D. Welsh
8. Absence of zeros for the chromatic polynomial on bounded degree graphs Christian Borgs
9. Duality in infinite graphs Henning Bruhn and Reinhard Diestel
10. Homomorphism-homogeneous relational structures Peter J. Cameron and Jaroslav Ne?etril
11. A spectral Turán theorem Fan Chung
12. Automorphism groups of metacirculant graphs of order a product of two distinct primes Edward Dobson
13. On the number of Hamiltonian cycles in a tournament Ehud Friedgut and Jeff Kahn
14. The game of JumbleG Alan Frieze, Michael Krivelevich, Oleg Pikhurko and Tibor Szabó
15. 2-Bases of quadruples Zoltán Füredi and Gyula O. H. Katona
16. On triple systems with independent neighbourhoods Zoltán Füredi, Oleg Pikhurko and Miklós Simonovits
17. Quasirandomness, counting and regularity for 3-uniform hypergraphs W. T. Gowers
18. Triangle-free hypergraphs Ervin Gyori
19. Odd independent transversals are odd Penny Haxell and Tibor Szabó
20. The first eigenvalue of random graphs Svante Janson
21. On the number of monochromatic solutions of x + y = z2 Ayman Khalfalah and Endre Szemerédi
22. Rapid Steiner symmetrization of most of a convex body and the slicing problem B. Klartag and V. Milman
23. A note on bipartite graphs wthout 2k-cycles Assaf Naor and Jacques Verstraëte
24. Book Ramsey numbers and quasi-eandomness V. Nikiforov, C. C. Rousseau and R. H. Schelp
25. Homomorphism and dimension Patrice Ossona de Mendez and Pierre Rosenstiehl
26. The distance of a permutation from a subgroup of Sn Richard G. E. Pinch
27. On dimensions of a random solid diagram Boris Pittel
28. The small giant component in scale-free random graphs Oliver Riordan
29. A Dirac-type theorem for 3-uniform hypergraphs Vojtech Rödl, Andrzej Rucinski and Endre Szemerédi
30. On dependency graphs and the lattice gas Alexander D. Scott and Alan D. Sokal
31. Solving sparse random instances of max cut and max 2-CSP in linear expected time Alexander D. Scott and Gregory B. Sorkin.

Subject Areas: Communications engineering / telecommunications [TJK], Combinatorics & graph theory [PBV], Probability & statistics [PBT]