Random graphs. (Q2723297)

The book is devoted to random graphs, random permutations, systems of random linear equations in finite fields, and equations involving a permutation as an unknown variable. These topics are presented under an unified approach based on the generalized placement scheme where many combinatorial problems are reduced to some estimations of the sums of independent random variables. NEWLINENEWLINENEWLINEThe book consists of five chapters. The first chapter entitled ``Generalized placement scheme and components of random graphs'' is devoted to the introduction to the computational combinatorial methods. These methods are applied to computing the size of the components in a random forest and to some problems on graphs with components of special type. The second chapter ``Random graph evolution'' contains various results on precritical and critical graphs and graphs with independent edges. NEWLINENEWLINENEWLINEThe third chapter ``Systems of random linear equations in \(\mathrm{GF}(2)\)'' is devoted to the problems related to the rank of a random matrix, consistency of systems of random linear equations and their applications to cycles and hypercycles in related graphs. The last two chapters study various aspects of random permutations and equations involving random permutations.