On the complexity of the colorful directed paths in vertex coloring of digraphs
نویسندگان
1 Abadan Branch, Islamic Azad University
2 Sharif University of Technology .
3 Amirkabir University of Technology, Tehran, Iran
doi
10.22108/toc.2013.2840چکیده
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 $v \in V (G)$, there exists a $v$-colorful directed path is $ \mathbf{NP} $-complete.
