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arXiv · 1806.04188

The structure of binary matroids with no induced claw or Fano plane restriction

Marthe Bonamy·Frantisek Kardos·Tom Kelly·Peter Nelson·Luke Postle
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Abstract

An 'induced restriction' of a simple binary matroid $M$ is a restriction $M|F$, where $F$ is a flat of $M$. We consider the class $\mathcal{M}$ of all simple binary matroids $M$ containing neither a free matroid on three elements (which we call a 'claw'), nor a Fano plane as an induced restriction. We give an exact structure theorem for this class; two of its consequences are that the matroids in $\mathcal{M}$ have unbounded critical number, while the matroids in $\mathcal{M}$ not containing the clique $M(K_5)$ as an induced restriction have critical number at most $2$.

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Marthe Bonamy, Frantisek Kardos, Tom Kelly, Peter Nelson, Luke Postle. 2018-06-11. The structure of binary matroids with no induced claw or Fano plane restriction. https://arxiv.org/abs/1806.04188

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