Trees contained in every orientation of a graph

For every graph G, let t(G) denote the largest integer t such that every oriented tree of order t appears in every orientation of G. In 1980, Burr conjectured that t(G) > 1 + ??(G)/2 for all G, and showed that t(G) > 1 + L ??(G)]; this bound remains the state of the art, apart from the multiplicative constant. We present an elementary argument that improves this bound whenever G has somewhat large chromatic number, showing that t(G) > L??(G)/ log2 v(G)] for all G.