On the oriented chromatic number of Halin graphs
An oriented k-coloring of an oriented graph G is a mapping c: V(G) {1, 2, ... k) such that (i) if xy is an element of E(G) their c(x) not equal c(y) and (ii) if xy.zi is an element of E(G) then c(x) = c(t) double right arrow c(y) not equal c(z). The oriented chromatic number (chi) over bar (G) of an oriented graph G is defined as the smallest k such that G admits an oriented k-coloring. We prove in this paper that every Hahn graph has oriented chromatic number at most 9. improving a previous bound proposed by Vignal. (c) 2006 Elsevier B.V. All rights reserved.
graph coloring oriented graph coloring graph homomorphism combinatorial problems