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A chordless cycle, or equivalently a hole, in a graph $G$ is an inducedsubgraph of $G$ which is a cycle of length at least $4$. We prove that theErd\H{o}s-P\'osa property holds for chordless cycles, which resolves the majoropen question concerning the Erd\H{o}s-P\'osa property. Our proof for chordlesscycles is constructive: in polynomial time, one can find either $k+1$vertex-disjoint chordless cycles, or $c_1k^2 \log k+c_2$ vertices hitting everychordless cycle for some constants $c_1$ and $c_2$. It immediately implies anapproximation algorithm of factor $\mathcal{O}(\sf{opt}\log {\sf opt})$ forChordal Vertex Deletion. We complement our main result by showing thatchordless cycles of length at least $\ell$ for any fixed $\ell\ge 5$ do nothave the Erd\H{o}s-P\'osa property.

Erd\H{o}s-P\'osa property of chordless cycles and its applications