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arXiv · 2507.23182

Binary matroids and degree-boundedness for pivot-minors

Rutger Campbell·James Davies·Robert Hickingbotham
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Abstract

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.

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Rutger Campbell, James Davies, Robert Hickingbotham. 2026-03-22. Binary matroids and degree-boundedness for pivot-minors. https://arxiv.org/abs/2507.23182

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