Positive-coline conjecture for gammoids

A positive coline of a matroid is a coline whose copoint partition has more singular classes than multiple classes. A gammoid is a matroid arising from a directed graph by the gammoid construction. Positive-coline conjecture for gammoids. Every simple gammoid of rank at least two has a positive coline. This conjecture was proposed as a route toward proving the oriented-matroid version of Hadwiger's conjecture, because positive colines imply that all orientations in the relevant minor-closed class are generalized series-parallel. The paper's abstract states that this conjecture is disproved by an infinite class of strict gammoids without positive colines.