On excluded minors of connectivity 2 for the class of frame matroids

TL;DR

This paper characterizes all excluded minors of connectivity 2 for frame matroids, identifying 18 specific cases and describing the structure of others as 2-sums involving a known non-binary frame matroid.

Contribution

The paper provides a complete list of excluded minors of connectivity 2 for frame matroids and describes their structural composition.

Findings

Identified 18 specific excluded minors of connectivity 2.

Showed that other excluded minors are 2-sums of U_{2,4} and a 3-connected non-binary frame matroid.

Established a structural characterization of all such excluded minors.

Abstract

We investigate the set of excluded minors of connectivity 2 for the class of frame matroids. We exhibit a list $\mathcal{E}$ of 18 such matroids, and show that if $N$ is such an excluded minor, then either $N \in \mathcal{E}$ or $N$ is a 2-sum of $U_{2,4}$ and a 3-connected non-binary frame matroid.