We consider two problems, namely Min Split-coloring and Min Cocoloring, that generalize the classical Min Coloring problem by using not only stable sets but also cliques to cover ...
Let G be a regular graph and H a subgraph on the same vertex set. We give surprisingly compact formulas for the number of copies of H one expects to find in a random subgraph of G...
The classical zero-one law for first-order logic on random graphs says that for every first-order property in the theory of graphs and every p (0, 1), the probability that the r...
Abstract. In this paper we present the set of base algorithms for generating connected random graphs (RG). RG can be used for testing different algorithms on networks. The fast al...
We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than w...