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arXiv · 1603.09713

Excluded minors are almost fragile

Nick Brettell·Ben Clark·James Oxley·Charles Semple·Geoff Whittle
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Abstract

Let $M$ be an excluded minor for the class of $\mathbb{P}$-representable matroids for some partial field $\mathbb P$, and let $N$ be a $3$-connected strong $\mathbb{P}$-stabilizer that is non-binary. We prove that either $M$ is bounded relative to $N$, or, up to replacing $M$ by a $Δ$-$Y$-equivalent excluded minor, we can choose a pair of elements $\{a,b\}$ such that either $M\backslash \{a,b\}$ is $N$-fragile, or $M^* \backslash \{a,b\}$ is $N^*$-fragile.

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Nick Brettell, Ben Clark, James Oxley, Charles Semple, Geoff Whittle. 2018-09-20. Excluded minors are almost fragile. https://doi.org/10.1016/j.jctb.2019.05.008

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