Complexity of two coloring problems in cubic planar bipartite mixed graphs

In this note we consider two coloring problems in mixed graphs, i.e., graphs containing edges and arcs, which arise from scheduling problems where disjunctive and precedence constraints have to be taken into account. We show that they are both image-complete in cubic planar bipartite mixed graphs, which strengthens some results of Ries and de Werra (2008) .