The class of quasi-graphic matroids, recently introduced by Geelen, Gerards, and Whittle, is minor closed and contains both the class of lifted-graphic matroids and the class of frame matroids, each of which generalizes the class of graphic matroids. In this paper, we prove that the matroids $U_{3,7}$ and $U_{4,7}$ are the only 9-connected excluded minors for the class of quasi-graphic matroids.

Let $M$ be a matroid and let $Q$, $R$, $S$, and $T$ be subsets of the ground set such that the smallest separation that separates $Q$ from $R$ has order $k$ and the smallest separation that separates $S$ from $T$ has order $\ell$. We prove that if $E(M)-(Q\cup R\cup S\cup T)$ is sufficiently large, then there is an element $e$ of $M$ such that, in one of $M\backslash e$ or $M/e$, both connectivities are preserved.