In this paper we prove the following conjecture by Bollobás and Komlós: For every γ > 0 and integers r ≥ 1 and ∆, there exists β > 0 with the following property. If G is a sufficiently large graph… (More)

We prove sufficient and essentially necessary conditions in terms of the minimum degree for a graph to contain planar subgraphs with many edges. For example, for all positive γ every sufficiently… (More)

Random intersection graphs naturally exhibit a certain amount of transitivity and hence can be used to model real–world networks. We study the evolution of the chromatic number of a random… (More)

A conjecture by Bollobás and Komlós states the following: For every γ > 0 and integers r ≥ 2 and ∆, there exists β > 0 with the following property. If G is a sufficiently large graph with n vertices… (More)

We provide suucient conditions for packing two hypergraphs. The emphasis is on the asymptotic case when one of the hypergraphs has a bounded degree and the other is dense. As an application, we give… (More)

We describe a polynomial time algorithm for covering graphs with cliques, prove its asymptotic optimality in a random intersection graph model and present experimental results on complex real–world… (More)

Let F be a fixed graph of chromatic number r+1. We prove that for all large n the degree sequence of any F -free graph of order n is, in a sense, close to being dominated by the degree sequence of… (More)