Oriented chromatic number for Cartesian products P_m\Box P_n and C_m\Box P_n

Abstract

We consider oriented chromatic number of Cartesian products of two paths P m P n and of Cartesian products of paths and cycles, C m P n. We say that the oriented graph − → G is colored by an oriented graph − → H if there is a homomorphism from − → G to − → H. In this paper we show that there exists an oriented tournament − → H 10 with ten vertices which colors every orientation of P 8 P n and every orientation of C m P n , for m = 3, 4, 5, 6, 7 and n ≥ 1. We also show that there exists an oriented graph − → T 16 with sixteen vertices which colors every orientation of C m P n .