About this product

Product Identifiers

PublisherCambridge University Press

ISBN-101316501914

ISBN-139781316501917

eBay Product ID (ePID)219472683

Product Key Features

Number of Pages127 Pages

Publication NameRandom Graphs, Geometry and Asymptotic Structure

LanguageEnglish

SubjectGraphic Methods, Topology, Geometry / Algebraic, Discrete Mathematics

Publication Year2016

TypeTextbook

Subject AreaMathematics

AuthorKonstantinos Panagiotou, Mathew Penrose, Michael Krivelevich, Colin Mcdiarmid

SeriesLondon Mathematical Society Student Texts

FormatTrade Paperback

Dimensions

Item Height2.1 in

Item Weight6.7 Oz

Item Length8.9 in

Item Width6 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2015-043108

Reviews'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.' Mikls Bna, MAA Reviews (www.maa.org)

Dewey Edition23

Series Volume NumberSeries Number 84

IllustratedYes

Dewey Decimal511/.5

Table Of ContentEditors' 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.

SynopsisThe 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., A self-contained and concise introduction to recent developments, particularly those of a geometric and topological nature, in the theory of random graphs. Such material is seldom covered in the formative study of young combinatorialists and probabilists, making this essential reading for beginning researchers in these fields.

LC Classification NumberQA166.17.R37 2016