A linear algorithm for minimum dominator colorings of orientations of paths

In this paper we present an algorithm for finding a minimum dominator coloring of orientations of paths. To date this is the first algorithm for dominator colorings of digraphs in any capacity. We prove that the algorithm always provides a minimum dominator coloring of an oriented path and show that it runs in O ( n ) time. The algorithm is available at https://github.com/cat-astrophic/MDC-orientations_of_paths/.