ABSTRACT: Let G(n, c/n) and Gr(n) be an n-node sparse random graph and a sparse random rregular graph, respectively, and let I(n, r) and I(n, c) be the sizes of the largest indepen...
Given d (0, ) let kd be the smallest integer k such that d < 2k log k. We prove that the chromatic number of a random graph G(n, d/n) is either kd or kd + 1 almost surely.
In this paper we consider the classical Erd˝os-R´enyi model of random graphs Gn,p. We show that for p = p(n) ≤ n−3/4−δ , for any fixed δ > 0, the chromatic number χ...
Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1...
We introduce a graph Laplacian based algorithm for the tomography reconstruction of a planar object from its projections taken at random unknown directions. The algorithm is shown ...
Ronald R. Coifman, Yoel Shkolnisky, Fred J. Sigwor...