Choe–Oxley–Sokal–Wagner's rank-three transversal matroid conjecture

A transversal matroid is a matroid obtained from a family of subsets by declaring a set independent when it can be matched injectively to distinct members of the family. A matroid has the half-plane property when its basis generating polynomial is nonvanishing whenever all variables lie in a common open half-plane.

Rank-three transversal matroid conjecture. Every transversal matroid of rank $3$ has the half-plane property.

The conjecture was first posed in the cited earlier work and is described by the source as still open. It is directly related to the paper's investigation of half-plane properties for classes of transversal matroids.