4 problems

Let $(G,\mathcal{B})$ be a biased graph, let $M$ be an elementary lift of the frame matroid $F(G,\mathcal{B})$, and suppose that $M$ is $3$-connected. Let $\mathbb{F}$ be a field a…

Let $G$ be a graph, let $\mathcal{B}$ be a bias set, and let $F(G,\mathcal{B})$ and $L(G,\mathcal{B})$ denote the associated frame and lifted-graphic matroids. Representations of t…

A matroid is a finite set system with an independence structure, and a frame matroid is a matroid arising from a biased graph; the monadic second-order language of matroids is the…

A matroid $M$ is a frame matroid if there is a matroid $M'$ with a basis $V$ such that … and, for each $e\in E(M)$, the unique circuit in $V\cup\{e\}$ has size at most $3$. An excl…