7 problems

Let $\Gamma$ be a finite group. A $\Gamma$-gainable quasi-graphic matroid is a quasi-graphic matroid represented by a $\Gamma$-gainable biased framework. An excluded minor is a mat…

Quasi-graphic matroid conjectures. The list of excluded minors for the class of quasi-graphic matroids is finite, and there is a polynomial-time algorithm for recognition of $3$-co…

Finite excluded-minor conjecture. There are, up to isomorphism, only finitely many excluded minors for the class of quasi-graphic matroids.

Let $H$ be a group. A lift matroid is a matroid in Zaslavsky's class of lift matroids, and a quasi-graphic matroid is a matroid in the class of quasi-graphic matroids. The monadic…

A quasi-graphic matroid is a matroid having a framework: a graph $G$ with $E(G)=E(M)$ such that, for each component $H$ of $G$, $r(E(H))\leq |V(H)|$; for each vertex $v$,…

In [? Let $M$ be a matroid. A framework for $M$ is a graph $G$ satisfying: $E(G)=E(M)$; for each component $H$ of $G$, $r(E(H))\leq |V(H)|$; for each vertex $v\in V(G)$,…

Recognition conjecture. There is a polynomial-time algorithm that, given a $3$-connected matroid $M$ via its rank oracle, decides whether or not $M$ is quasi-graphic.