Approximate Min-max Relations for Odd Cycles in Planar Graphs
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- Fiorini S., Hardy N., Reed B., Vetta A. (2005) Approximate Min-max Relations for Odd Cycles in Planar Graphs. In: Jünger M., Kaibel V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg
We study the ratio between the minimum size of an odd cycle vertex transversal and the maximum size of a collection of vertex-disjoint odd cycles in a planar graph. We show that this ratio is at most 10. For the corresponding edge version of this problem, Král and Voss  recently proved that this ratio is at most 2; we also give a short proof of their result.
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