Optimal $\chi$-boundness of $\mathrm{\ell }$-holed graphs

A graph is {\em{$\mathrm{\ell }$-holed}} if all of its induced cycles of length at least four have length exactly $\mathrm{\ell }$. In the paper, we prove that if $G$ is an $\mathrm{\ell }$-holed graph with odd $\mathrm{\ell }\ge 7$, then $\chi (G)\le \lceil \frac{\mathrm{\ell }}{\mathrm{\ell }-1}\omega (G)\rceil$. This result is sharp.