Clones in 3-Connected Frame Matroids
We determine the structure of clonal classes of 3-connected frame matroids in terms of the structure of biased graphs. Robbins has conjectured that a 3-connected non-uniform matroid with a clonal class of size q−1 is not GF(q)-representable. We confirm the conjecture for the class of frame matroids.
& Zhou, X.
(2016). Clones in 3-Connected Frame Matroids. Discrete Mathematics, 339 (4), 1329-1334.