Ordering Circuits of Matroids

The cycles of a graph give natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges adjacent one cycle if only they every which appear together. An orderable matroid is whose set circuits admits such ordering. In this paper, we consider the question determining matroids orderable. Although able answer for non-binary matroids, it remains open binary matroids. We examples provide insight into potential difficulty general. also show that, by requiring preserves three arcs theta-graph restriction $M$, guarantee $M$ graphic.