Combinatorics, Probability and Computing

One of the exciting phenomena in mathematics in recent years has been the widespread and surprisingly effective use of probabilistic methods in diverse areas. The probabilistic point of view has turned out to b

On the independence number and Hamiltonicity of uniform random intersection graphs

AbstractIn the uniform random intersection graphs model, denoted by Gn,m,λ, to each vertex v we assign exactly λ randomly chosen labels of some label set M of m labels and we connect every pair of vertices that has at least one label in common. In this model, we estimate the independence number α(Gn,m,λ), for the wide range m=⌊nα⌋,α<1 and λ=O(m1/4). We also prove the Hamiltonicity of this model by an interesting combinatorial construction. Finally, we give a brief note concerning the independence number of Gn,m,p random intersection graphs, in which each vertex chooses labels with probability p

An extensive English language bibliography on graph theory and its applications, supplement 1

Graph theory and its applications - bibliography, supplement