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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/2507.23182 |
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| _version_ | 1866911533148143616 |
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| author | Campbell, Rutger Davies, James Hickingbotham, Robert |
| author_facet | Campbell, Rutger Davies, James Hickingbotham, Robert |
| contents | We prove that for every bipartite graph $H$ and positive integer $s$, the class of $K_{s,s}$-subgraph-free graphs excluding $H$ as a pivot-minor has bounded average degree. Our proof relies on the announced binary matroid structure theorem of Geelen, Gerards, and Whittle. Along the way, we also prove that every $K_{s,t}$-free bipartite circle graph with $s\le t$ has a vertex of degree at most $\max\{2s-2, t-1\}$ and provide examples showing that this is tight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Binary matroids and degree-boundedness for pivot-minors Campbell, Rutger Davies, James Hickingbotham, Robert Combinatorics We prove that for every bipartite graph $H$ and positive integer $s$, the class of $K_{s,s}$-subgraph-free graphs excluding $H$ as a pivot-minor has bounded average degree. Our proof relies on the announced binary matroid structure theorem of Geelen, Gerards, and Whittle. Along the way, we also prove that every $K_{s,t}$-free bipartite circle graph with $s\le t$ has a vertex of degree at most $\max\{2s-2, t-1\}$ and provide examples showing that this is tight. |
| title | Binary matroids and degree-boundedness for pivot-minors |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.23182 |