The vertex Folkman number F(r, n, m), n < m, is the smallest integer t such that there exists a Km-free graph of order t with the property that every r-coloring of its vertices...
Secure multi-party computation (MPC) is a central problem in cryptography. Unfortunately, it is well known that MPC is possible if and only if the underlying communication network...
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.
Abstract. A random iteration algorithm for graph-directed sets is defined and discussed. Similarly to the Barnsley-Elton’s theorem, it is shown that almost all sequences obtaine...
This paper explores the fundamental question of how many iterations the celebrated HITS algorithm requires on a general graph to converge in score and, perhaps more importantly, in...