RSA
2011
12 years 7 months ago
2011
We consider a conditioned Galton–Watson tree and prove an estimate of the number of pairs of vertices with a given distance, or, equivalently, the number of paths of a given leng...
RSA
2011
12 years 11 months ago
2011
Abstract. In this paper we study the minimal number τ(S, G) of translates of an arbitrary subset S of a group G needed to cover the group, and related notions of the efficiency of...
RSA
2011
12 years 11 months ago
2011
We study the cover time of random geometric graphs. Let I(d) = [0, 1]d denote the unit torus in d dimensions. Let D(x, r) denote the ball (disc) of radius r. Let Υd be the volume...
RSA
2011
12 years 11 months ago
2011
Abstract. Consider a set of n random axis parallel boxes in the unit hypercube in Rd , where d is fixed and n tends to infinity. We show that the minimum number of points one nee...
RSA
2011
12 years 11 months ago
2011
Determining the cardinality and describing the structure of H-free graphs is wellinvestigated for many graphs H. In the nineties, Prömel and Steger proved that for a graph H with...
RSA
2011
12 years 11 months ago
2011
: We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small...
RSA
2011
12 years 11 months ago
2011
: The classical result in the theory of random graphs, proved by Erd˝os and Rényi in 1960, concerns the threshold for the appearance of the giant component in the random graph pr...
RSA
2011
12 years 11 months ago
2011
We prove game-theoretic versions of several classical results on nonrepetitive sequences, showing the existence of winning strategies using an extension of the Local Lemma which c...
RSA
2011
12 years 11 months ago
2011
We prove that for fixed integer D and positive reals α and γ, there exists a constant C0 such that for all p satisfying p(n) ≥ C0/n, the random graph G(n, p) asymptotically a...
RSA
2011
12 years 11 months ago
2011
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edge...