RSA
2011
13 years 2 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
13 years 6 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
13 years 6 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
13 years 6 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
13 years 6 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
13 years 6 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
13 years 6 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
13 years 6 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
13 years 6 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
13 years 6 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...