Goddyn–Hochstättler–Neudauer positive-coline conjecture for gammoids

Let $M$ be a matroid. A gammoid is a matroid arising from linkages in a directed graph; $M$ is simple if it has no loops or parallel elements, and a coline is a rank-$r(M)-2$ flat. A coline is positive when its copoint partition has more singular than multiple classes. Goddyn–Hochstättler–Neudauer's positive-coline conjecture. Every simple gammoid of rank at least two has a positive coline. Equivalently, every cosimple gammoid of corank at least two has a positive double circuit. The conjecture was proposed in connection with proving the oriented-matroid version of Hadwiger's conjecture and is refuted in this paper by a large class of bicircular matroids without positive double circuits.