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.
This is a revised and updated version of the classic first edition.
Has taught at Cambridge department of pure maths and mathematical statistics for over 25 years and has been a fellow of Trinity College for 30 years. Since 1996 has held the unique Chair of Excellence in the dept of mathematical sciences at the university of Memphis. The author has previously written over 250 research papers in extremal and probabilistic combinatorics, functional analysis, probability theory, isoperimetric inequalities and polynomials of graphs.
'... contains an enormous amount of material, assembled by one who has played a leading role in the development of the area.' Zentralblatt MATH 'This book, written by one of the leaders in the field, has become the bible of random graphs. This book is primarily for mathematicians interested in graph theory and combinatorics with probability and computing, but it could also be of interest to computer scientists. It is self-contained and lists numerous exercises in each chapter. As such, it is an excellent textbook for advanced courses or for self-study.' EMS 'There are many beautiful results in the theory of random graphs, and the main aim of the book is to introduce the reader and extensive account of a substantial body of methods and results from the theory of random graphs. This is a classic textbook suitable not only for mathematicians. It has clearly passed the test of time.' Internationale Mathematische Nachrichten '... a very good and handy guidebhook for researchers.' Acta Sci. Math.