New bounds for chromatic polynomials and chromatic roots

摘要

If G is a k-chromatic graph of order n then it is known that the chromatic polynomial of G, pi (G, x), is at most x(x - 1) ... (x - (k - 1))x(n-k) = (x)(down arrow k)Xn-k for every x is an element of N. We improve here this bound by showing that