Gabow–Kajitani–Ueno–Miyano cyclic ordering conjecture for matroids

Let $M$ be a matroid of rank $r(M)$ whose ground set is the union of two disjoint bases.

Cyclic ordering conjecture. It is possible to place the elements of the ground set of $M$ on a circle so that every $r(M)$ consecutive elements form a basis of $M$.

This conjecture connects matroid basis exchange properties with cyclic orderings. The source attributes its formulation to Kajitani, Ueno, and Miyano, following an earlier suspicion of Gabow; its general status is not resolved in the provided text.