Orientations of Self-complementary Graphs and the Relation of Sperner and Shannon Capacities

We prove that the edges of a self-complementary graph and its complement can be oriented in such a way that they remain isomorphic as digraphs and their union is a transitive tournament. This result is used to explore the relation between the Shannon and Sperner capacity of certain graphs. In particular, using results of Lovلsz, we show that the maximum Sperner capacity over all orientations of the edges of a vertex-transitive self-complementary graph equals its Shannon capacity.