New upper bounds for the greatest number of proper colorings of a (V,E)‐graph
Felix Lazebnik · Journal of Graph Theory · 1990
Abstract Let 𝒻 denote the family of simple undirected graphs on v vertices having e edges ((v, e)‐graphs) and P(G; λ) be the chromatic polynomial of a graph G. For the given integers v, e, and λ, let f(v, e, λ) denote the greatest number of proper colorings in λ or less colors that a (v, e)‐graph G can have, i.e., f(v, e, λ) = max{P(G; λ): G ∈ 𝒻}. In this paper we determine some new upper bounds for f(v, e, λ).