Let G = G(n, r) be a random geometric graph resulting from placing n nodes uniformly at random in the unit square (disk) and connecting every two nodes if and only if their Euclide...
The main aim of this short paper is to answer the following question. Given a fixed graph H, for which values of the degree d does a random d-regular graph on n vertices contain ...
In this paper, we prove that there exists a function k = (4 + o(1))k such that G(n, /n) contains a k-regular graph with high probability whenever > k. In the case of k = 3, it...
We examine the relationship of a graph G and its random subgraphs which are defined by independently choosing each edge with probability p. Suppose that G has a spectral gap λ (...
Motivated by a problem that arises in the study of mirrored storage systems, we describe, for any fixed , > 0 and any integer d 2, explicit or randomized constructions of d-r...