Approximate Min-max Relations for Odd Cycles in Planar Graphs

摘要

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, Kral and Voss recently proved that this ratio is at most 2; we also give a short proof of their result.