On the oriented chromatic number of Halin graphs
Résumé
An oriented k-coloring of an oriented graph G is a mapping c from V(G) to { 1, 2, \ldots , k} such that (i) if xy \in E(G) then c (x) \neq c(y) and (ii) if xy, zt \in E(G) then c(x) = c(t) implies c(y) \neq c(z). The oriented chromatic number ocn(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 Halin graph has oriented chromatic number at most 9, improving a previous bound proposed by Vignal.