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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.22865 |
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| _version_ | 1866909977026756608 |
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| author | Puhlmann, Luise Schlomberg, Niklas |
| author_facet | Puhlmann, Luise Schlomberg, Niklas |
| contents | 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 Erdős-Pósa ratio. We show that in planar graphs, this ratio does not exceed 4. This improves on the previously best known bound of 6 by Král', Sereni and Stacho. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved Erdős-Pósa inequalities for odd cycles in planar graphs Puhlmann, Luise Schlomberg, Niklas Combinatorics 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 Erdős-Pósa ratio. We show that in planar graphs, this ratio does not exceed 4. This improves on the previously best known bound of 6 by Král', Sereni and Stacho. |
| title | Improved Erdős-Pósa inequalities for odd cycles in planar graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.22865 |