Description
Book SynopsisSince its inception in the 1960s, the theory of random graphs has evolved into a dynamic branch of discrete mathematics. Yet despite the lively activity and important applications, the last comprehensive volume on the subject is Bollobas's well-known 1985 book.
Trade Review"Details developments in the theory of random graphs over the past decade, providing a much-needed overview of this area of combinatorics." (SciTech Book News, Vol. 24, No. 4, December 2000)
The book is well written, and the material is well chosen. (Bulletin of the London Mathematical Society, Volume 33, 2001)
"It is fifteen years since Bollobas's monograph appeared, and this new definitive work should take us through the next fifteen. Such is the importance and appeal of this book that is should find its way onto the shelves no only of those working directly in the area of random graphs, but also anyone with a more general interest in combinatorics, probability theory, or certain aspects of computer science." (Mathematical Reviews, Issue 2001k)
"...a beautiful presentation of new developments in the asymptotic theory of random graphs." (Zentralblatt MATH, Vol. 968, 2001/18)
"An introduction to the subject as well as a resource for those working in the field." (American Mathematical Monthly, January 2002)
Table of ContentsPreliminaries.
Exponentially Small Probabilities.
Small Subgraphs.
Matchings.
The Phase Transition.
Asymptotic Distributions.
The Chromatic Number.
Extremal and Ramsey Properties.
Random Regular Graphs.
Zero-One Laws.
References.
Indexes.
