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Random Graphs, Geometry and Asymptotic Structure

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: 0.19kg
    • 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
    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.

    Konstantinos Panagiotou, Universität Munchen
    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.

    Mathew Penrose, University of Bath
    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.

    Colin McDiarmid, University of Oxford
    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.

    Editors

    Nikolaos Fountoulakis, University of Birmingham

    Dan Hefetz, University of Birmingham

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