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 nonuniform matroid with a clonal class of size q − 1 is not GF(q)-representable. We confirm the conjecture for the class of frame matroids.

• Type: Journal
• Year: 2016
• Where: DM
• Authors: Jakayla R. Robbins, Daniel C. Slilaty, Xiangqian Zhou
• Keywords: DM 2016