  For a number $\ell\geq 2$, let $\mathcal{G}_{\ell}$ denote the family of
graphs which have girth $2\ell+1$ and have no odd hole with length greater than
$2\ell+1$. Plummer and Zha conjectured that every 3-connected and internally
4-connected graph in $\mathcal{G}_2$ is 3-colorable. Wu, Xu, and Xu conjectured
that every graph in $\bigcup_{\ell\geq2}\mathcal{G}_{\ell}$ is 3-colorable.
Chudnovsky et al. and Wu et al., respectively, proved that every graph in
$\mathcal{G}_2$ and $\mathcal{G}_3$ is 3-colorable. In this paper, we prove
that every graph in $\bigcup_{\ell\geq5}\mathcal{G}_{\ell}$ is 3-colorable.
