Random Graphs

Results of research on classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields.

V. F. Kolchin (Author)

9780521119689, Cambridge University Press

Paperback, published 17 September 2009

268 pages
23.4 x 15.6 x 1.4 cm, 0.38 kg

Review of the hardback: 'Many of the results appear here for the first time in an English translation. The book is therefore to be welcomed for bringing this material to a wider audience.' W. T. Gowers, Bulletin of the London Mathematical Society

This book is devoted to the study of classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields. The author shows how the application of the generalized scheme of allocation in the study of random graphs and permutations reduces the combinatorial problems to classical problems of probability theory on the summation of independent random variables. He concentrates on research by Russian mathematicians, including a discussion of equations containing an unknown permutation and a presentation of techniques for solving systems of random linear equations in finite fields. These results will interest specialists in combinatorics and probability theory and will also be useful in applied areas of probabilistic combinatorics such as communication theory, cryptology, and mathematical genetics.

Preface
1. The generalized scheme of allocation and the components of random graphs
2. Evolution of random graphs
3. Systems of random linear equations in GF(2)
4. Random permutations
5. Equations containing an unknown permutation
Bibliography
Index.

Subject Areas: Combinatorics & graph theory [PBV]