On Stratified Domination in Oriented Graphs

An oriented graph is 2-stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let H be a 2-stratified oriented graph rooted at some blue vertex. An H-coloring of an oriented graph D is a red-blue coloring of the vertices of D in which every blue vertex v belongs to a copy of H rooted at v in D. The Hdomination number γH(D) is the minimum number of red vertices in an H-coloring of D. We investigate H-colorings in oriented graphs where H is the red-red-blue directed path of order 3.