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Random Graphs, Geometry and Asymptotic Structure

£24.99

Part of London Mathematical Society Student Texts

  • Date Published: May 2016
  • availability: In stock
  • format: Paperback
  • isbn: 9781316501917

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About the Authors
  • 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.

    • An introduction to state-of-the-art developments in the theory of random graphs particularly related to topological, geometric and analytic aspects
    • Written by established researchers this book brings together in a single volume very different aspects of the theory of random graphs
    • Covers theoretical background which has applications in various scientific disciplines including telecommunications, astronomy, statistical physics, biology, and computer science, as well as much more recent developments such as the study of social and biological networks
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    Reviews & endorsements

    '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.' Miklós Bóna, MAA Reviews (www.maa.org)

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    Product details

    • Date Published: May 2016
    • format: Paperback
    • isbn: 9781316501917
    • length: 127 pages
    • dimensions: 227 x 152 x 70 mm
    • weight: 0.18kg
    • contains: 2 b/w illus. 1 table
    • availability: In stock
  • Table of Contents

    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.

  • Authors

    Michael Krivelevich, Tel-Aviv University

    Konstantinos Panagiotou, Universität Munchen

    Mathew Penrose, University of Bath

    Colin McDiarmid, University of Oxford

    Editors

    Nikolaos Fountoulakis, University of Birmingham

    Dan Hefetz, University of Birmingham

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