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arXiv · 1908.09971

A note on the connectivity of 2-polymatroid minors

Zachary Gershkoff·James Oxley
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Abstract

Brylawski and Seymour independently proved that if $M$ is a connected matroid with a connected minor $N$, and $e \in E(M) - E(N)$, then $M \backslash e$ or $M / e$ is connected having $N$ as a minor. This paper proves an analogous but somewhat weaker result for $2$-polymatroids. Specifically, if $M$ is a connected $2$-polymatroid with a proper connected minor $N$, then there is an element $e$ of $E(M) - E(N)$ such that $M \backslash e$ or $M / e$ is connected having $N$ as a minor. We also consider what can be said about the uniqueness of the way in which the elements of $E(M) - E(N)$ can be removed so that connectedness is always maintained.

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Zachary Gershkoff, James Oxley. 2019-08-27. A note on the connectivity of 2-polymatroid minors. https://arxiv.org/abs/1908.09971

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