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Journals ACM SIGACT News Volume 40 Issue 3

Review of Random Graphs (Second Edition)8 Author of Book: B la Bollob s e a Cambridge Press, 500 pages, $134 on amazon (used $100.00) Review by Mikl s B na 2009 o o Introduction Random graphs can be studied using various models. Perhaps the most popular one is Gp . In this model, one considers n labeled vertices, and connects any pair of vertices by an edge with probability p. Summary After a purely probabilistic introduction in Chapter 1, the author uses Chapter 2 to introduce this, and the other 3-4 basic models he will use in this impressive book. Chapter 3 is about the ordered degree sequence of a random graph. Here by ordered, we mean that the degrees are arranged in a non-increasing order. It turns out that depending on the value of p = p(n), the elements of the degree sequence are, to a large extent, determined. For instance, there are results explaining that for certain values of p, almost no graphs Gp will contain a vertex of degree k, or, for other values of p, almost all such Gp will contain at least t vertices of degree k, where k and t are arbitrary,

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Review of Random graphs: (second edition) by Béla Bollobás

Bóna, Miklós
ACM SIGACT News , Volume 40 (3)
Association for Computing Machinery – Sep 25, 2009

More Info
  • Publisher Association for Computing Machinery
  • Copyright The ACM Portal is published by the Association for Computing Machinery. Copyright © 2010 ACM, Inc.
  • ISSN 0163-5700
  • D.O.I. 10.1145/1620491.1620499
  • Publisher site Get PDF  

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