Aravind's induced rainbow path conjecture

A graph is properly colored if adjacent vertices receive distinct colors, and a vertex-colored graph is rainbow if no two vertices have the same color. A graph is triangle-free if it contains no triangle. Aravind's conjecture. Every properly colored triangle-free graph $G$ contains an induced rainbow path on $\chi(G)$ vertices. This is a rainbow strengthening of the known theorem that every triangle-free graph contains an induced path on $\chi(G)$ vertices; the supplied text does not state whether the conjecture has been resolved.