Random Graphs

Przednia okładka
John Wiley & Sons, 30 wrz 2011 - 348
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A unified, modern treatment of the theory of randomgraphs-including recent results and techniques
Since its inception in the 1960s, the theory of random graphs hasevolved into a dynamic branch of discrete mathematics. Yet despitethe lively activity and important applications, the lastcomprehensive volume on the subject is Bollobas's well-known 1985book. Poised to stimulate research for years to come, this new workcovers developments of the last decade, providing a much-needed,modern overview of this fast-growing area of combinatorics. Writtenby three highly respected members of the discrete mathematicscommunity, the book incorporates many disparate results from acrossthe literature, including results obtained by the authors and somecompletely new results. Current tools and techniques are alsothoroughly emphasized. Clear, easily accessible presentations makeRandom Graphs an ideal introduction for newcomers to the field andan excellent reference for scientists interested in discretemathematics and theoretical computer science. Special featuresinclude:
* A focus on the fundamental theory as well as basic models ofrandom graphs
* A detailed description of the phase transition phenomenon
* Easy-to-apply exponential inequalities for large deviationbounds
* An extensive study of the problem of containing smallsubgraphs
* Results by Bollobas and others on the chromatic number of randomgraphs
* The result by Robinson and Wormald on the existence of Hamiltoncycles in random regular graphs
* A gentle introduction to the zero-one laws
* Ample exercises, figures, and bibliographic references
 

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Spis treści

1 Preliminaries
1
2 Exponentially Small Probabilities
25
3 Small Subgraphs
53
4 Matchings
81
5 The Phase Transition
103
6 Asymptotic Distributions
139
7 The Chromatic Number
179
8 Extremal and Ramsey Properties
201
9 Random Regular Graphs
233
10 ZeroOne Laws
271
References
307
Index of Notation
327
Index
331
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Informacje o autorze (2011)

SVANTE JANSON, PhD, is Professor of Mathematics at UppsalaUniversity, Sweden.

TOMASZ LUCZAK, PhD, is Professor of Mathematics at Adam MickiewiczUniversity, Poland, and a visiting professor at Emory University,Atlanta, Georgia.

ANDRZEJ RUCINSKI, PhD, is Professor of Mathematics at AdamMickiewicz University and a visiting professor at Emory University.

Informacje bibliograficzne