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For a number $l\geq 2$, let ${\cal{G}}_l$ denote the family of graphs whichhave girth $2l+1$ and have no odd hole with length greater than $2l+1$. Wu, Xuand Xu conjectured that every graph in $\bigcup_{l\geq 2} {\cal{G}}_{l}$ is$3$-colorable. Chudnovsky et al., Wu et al., and Chen showed that every graphin ${\cal{G}}_2$, ${\cal{G}}_3$ and $\bigcup_{l\geq 5} {\cal{G}}_{l}$ is$3$-colorable respectively. In this paper, we prove that every graph in${\cal{G}}_4$ is $3$-colorable. This confirms Wu, Xu and Xu's conjecture.

Graphs with girth 9 and without longer odd holes are 3-colorable