Random Graphs / Edition 2

by Béla Bollobás

Overview

This is a new 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 an up-to-date and comprehensive account of random graph theory. The theory estimates 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.

Product Details

ISBN-13:	9780521797221
Publisher:	Cambridge University Press
Publication date:	08/30/2001
Series:	Cambridge Studies in Advanced Mathematics , #73
Edition description:	Second Edition
Pages:	518
Product dimensions:	6.06(w) x 8.94(h) x 0.91(d)

About the Author

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. Bollobás has previously written over 250 research papers in extremal and probabilistic combinatorics, functional analysis, probability theory, isoperimetric inequalities and polynomials of graphs.

Table of Contents

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.

Editorial Reviews

"An up-to-date, comprehensive account of the random graph theory, this edition of what's considered a "classic" text contians two new sections, numerous new results, and over 150 references."
Poptronics

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

From the Publisher

Probabilistic concepts have proven important in the study of graphs since Erdós and Rényi's founding of the theory of random graphs in the early 1960s. Their student, Bollobás (U. of Memphis; Trinity College, Cambridge), treats random graphs as evolving over time. "Our task is to determine at what stage of the evolution a particular property of the graph is likely to arise." Includes exercises of varying difficulty, and 38 pages of references relevant to such branches of math as number theory, combinatorics, and computer science. First published in 1985 by Academic Press. Annotation c. Book News, Inc., Portland, OR (booknews.com)