1-perfectly orientable K4-minor-free and outerplanar graphs

A graph G is said to be 1-perfectly orientable if it has an orientation D such that for every vertex v∈V(G), the out-neighborhood of v in D is a clique in G. We characterize the class of 1-perfectly orientable K4-minor-free graphs. As a consequence we obtain a characterization of 1-perfectly orientable outerplanar graphs.