Improved Erd\H{o}s-P\'osa inequalities for odd cycles in planar graphs
Combinatorics
2025-12-30 v1
Abstract
In an undirected graph, the odd cycle packing number is the maximum number of pairwise vertex-disjoint odd cycles. The odd cycle transversal number is the minimum number of vertices that hit every odd cycle. The maximum ratio between transversal and packing number is called Erd\H{o}s-P\'osa ratio. We show that in planar graphs, this ratio does not exceed 4. This improves on the previously best known bound of 6 by Kr\'al', Sereni and Stacho.
Cite
@article{arxiv.2512.22865,
title = {Improved Erd\H{o}s-P\'osa inequalities for odd cycles in planar graphs},
author = {Luise Puhlmann and Niklas Schlomberg},
journal= {arXiv preprint arXiv:2512.22865},
year = {2025}
}