Title: Coloring ($P_6$, diamond, $K_4$)-free graphs,
Abstract: We show that every ($P_6$, diamond, $K_4$)-free graph is $6$-colorable.
Moreover, we give an example of a ($P_6$, diamond, $K_4$)-free graph $G$ with
$\chi(G) = 6$. This generalizes some known results in the literature.