We show that the number of halving sets of a set of n points in R4 is O n4−1/18 , improving the previous bound of [9] with a simpler (albeit similar) proof.
We study a problem on edge percolation on product graphs G× K2. Here G is any finite graph and K2 consists of two vertices {0, 1} connected by an edge. Every edge in G × K2 is p...
Consider a randomly oriented graph G = (V, E) and let a, s and b be three distinct vertices in V . We study the correlation between the events {a → s} and {s → b}. We show that...
Let X be the random variable that counts the number of triangles in the binomial random graph G(n, p). We show that for some positive constant c, the probability that X deviates f...