University of IsfahanTransactions on Combinatorics2251-86572220130601On the complexity of the colorful directed paths in vertex coloring of digraphs17284010.22108/toc.2013.2840ENS.SaqaeeyanAbadan Branch, Islamic Azad UniversityEsmaeilMollaahmadiSharif University of Technology .AliDehghanAmirkabir University of Technology, Tehran, IranJournal Article20121016The 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.https://toc.ui.ac.ir/article_2840_6a5c24f33fd5a66915e473e2c44ca4aa.pdf