Abstract
Let $\nu(G)$ be the maximum number of vertex-disjoint odd cycles of a graph $G$ and $\tau(G)$ the minimum number of vertices whose removal makes $G$ bipartite. We show that $\tau(G)\le 6\nu(G)$ if $G$ is planar. This improves the previous bound $\tau(G)\le 10\nu(G)$ by Fiorini et al. [Math. Program. Ser. B, 110 (2007), pp. 71--91].
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