ON THE COMPLEXITY OF THE COLORFUL DIRECTED PATHS IN VERTEX COLORING OF DIGRAPHS

The colorful paths and rainbow paths have been considered by several authors. A colorful directed path in a digraph G is a directed path with chi(G) vertices whose colors are different. A v-colorful directed path is such a directed path, starting from v. We prove that for a given 3-regular triangle-free digraph G determining whether there is a proper chi(G)-coloring of G such that for every v epsilon V(G), there exists a v-colorful directed path is NP-complete.