For a graph G and k a real number, we consider the sum of the k-th powers of the degrees of the vertices of G. We present some general bounds on this sum for various values of k. ...
For graphs G and H, let G H denote their Cartesian sum. This paper investigates the chromatic number and the circular chromatic number for GH. It is proved that (G H) max{ c(G)...
In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on ...
Richard Kenyon, James Gary Propp, David Bruce Wils...
We prove the following inequality: for every positive integer n and every collection X1, . . . , Xn of nonnegative independent random variables that each has expectation 1, the pr...