Odd Cycle Packing

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, Kr?al and Voss recently proved that this ratio is at most 2; we also give a short proof of their result. Keywords Odd cycle transversal ? Odd cycle packing ? Planar graph

• Type: Conference
• Year: 2010
• Where: STOC
• Authors: Ken-ichi Kawarabayashi and Bruce Reed
• Keywords: Algorithms, Odd Cycle Packing, Odd Cycle Transversal, Odd Cycle Vertex, STOC 2010