
Random Graphs, Geometry and Asymptotic Structure
Cambridge University Press
Will be published approx. on 5. May 2016
Book
Paperback/Softback
127 pages
978-1-316-50191-7 (ISBN)
Description
The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.
Reviews / Votes
'The chapter on geometric graphs has plenty of exercises ... the book will help many novices make their first steps in the field of random graphs.' Miklos Bona, MAA Reviews (www.maa.org)More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Product notice
Paperback (trade)
Illustrations
1 Tables, black and white; 2 Line drawings, unspecified
Dimensions
Height: 226 mm
Width: 151 mm
Thickness: 10 mm
Weight
194 gr
ISBN-13
978-1-316-50191-7 (9781316501917)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Michael Krivelevich | Konstantinos Panagiotou | Mathew Penrose
Random Graphs, Geometry and Asymptotic Structure
E-Book
05/2016
Cambridge University Press
€32.49
Available for download

Michael Krivelevich | Konstantinos Panagiotou | Mathew Penrose
Random Graphs, Geometry and Asymptotic Structure
Book
04/2016
Cambridge University Press
€90.50
Shipment within 15-20 days
Persons
Professor Michael Krivelevich is a renowned expert on the theory of random graphs. He has written over 170 research papers, more than 100 of them in the last ten years. Most of his publications are on random graphs and related fields, such as extremal combinatorics, positional games theory and theoretical computer science. Professor Konstantinos Panagiotou received the Richard Rado Prize in 2010. He is an expert on the relatively new theory of Boltzmann samplers and its relations to the study of random planar graphs as well as random graphs with constraints. Professor Mathew Penrose is a leading expert on the theory of random geometric graphs. His research interests cover a variety of topics in modern probability theory, often motivated by questions from the physical sciences. These include interacting particle systems, percolation, stochastic analysis and extreme value theory. Professor Colin McDiarmid is a leading expert on probabilistic combinatorics and discrete probability theory, with several participations in editorial boards of leading combinatorics journals. He has published over 80 papers on these areas. He is one of the pioneers of the theory of random planar graphs and random graphs with constraints.
Author
Tel-Aviv University
Universitaet Munchen
University of Bath
University of Oxford
Editor
University of Birmingham
University of Birmingham
Content
Editors' introduction; Part I. Long Paths and Hamiltonicity in Random Graphs: 1. Introduction; 2. Tools; 3. Long paths in random graphs; 4. The appearance of Hamilton cycles in random graphs; References for Part I; Part II. Random Graphs from Restricted Classes: 1. Introduction; 2. Random trees; 3. Random graphs from block-stable classes; References for Part II; Part III. Lectures on Random Geometric Graphs: 1. Introduction; 2. Edge counts; 3. Edge counts: normal approximation; 4. The maximum degree; 5. A sufficient condition for connectivity; 6. Connectivity and Hamiltonicity; 7. Solutions to exercises; References for Part III; Part IV. On Random Graphs from a Minor-closed Class: 1. Introduction; 2. Properties of graph classes; 3. Bridge-addability, being connected and the fragment; 4 Growth constants; 5. Unlabelled graphs; 6. Smoothness; 7. Concluding remarks; References for Part IV; Index.