Oriented vertex and arc colorings of outerplanar graphs
A homomorphism from an oriented graph G to an oriented graph H is an arc-preserving mapping phi from V(G) to V(H), that is phi(x)phi(y) is an arc in H whenever xy is an arc in G. The oriented chromatic number of G is the minimum order of an oriented graph H such that G has a homomorphism to H. The oriented chromatic index of G is the minimum order of an oriented graph H such that the line-digraph of G has a homomorphism to H. In this paper, we determine for every k >= 3 the oriented chromatic number and the oriented chromatic index of the class of oriented outerplanar graphs with girth at least k. (c) 2006 Elsevier B.V. All rights reserved.
outerplanar graph oriented chromatic number oriented chromatic index girth combinatorial problems