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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 Erdoes and Renyi 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. Random Graphs, 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
Béla Bollobás has taught at Cambridge University's Department of Pure Maths and Mathematical Statistics for over 25 years and has been a fellow of Trinity College for 30 years. Since 1996, he has held the unique Chair of Excellence in the Department of Mathematical Sciences at the University of Memphis. Bollobas 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 Scientiarum Mathematicarum
"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
