Random Graphs

This is a revised and updated version of the classic first edition.

Béla Bollobás (Author)

9780521809207, Cambridge University Press

Hardback, published 30 August 2001

520 pages, 10 b/w illus. 8 tables
22.9 x 15.2 x 3.3 cm, 0.93 kg

'The book is very impressive in the wealth of information it offers. It is bound to become a reference material on random graphs.' SIGACT News

In this second edition of the now classic text, the already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents a comprehensive account of random graph theory. The theory (founded by Erdös and Rényi in the late fifties) aims to estimate the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self-contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study.

1. Probability theoretic preliminaries
2. Models of random graphs
3. The degree sequence
4. Small subgraphs
5. The evolution of random graphs - sparse components
6. The evolution of random graphs-the giant component
7. Connectivity and components
8. Long paths and cycles
9. The automorphism group
10. The diameter
11. Cliques, independent sets and colouring
12. Ramsey theory
13. Explicit constructions
14. Sequences, matrices and permutations
15. Sorting algorithms
16. Random graphs of small order.

Subject Areas: Combinatorics & graph theory [PBV], Probability & statistics [PBT]