Note on inseparability graphs of matroids having exactly one class of orientations (Q1363689)

The oriented matroids whose inseparability graph is complete are identified as the oriented matroids of series-parallel graphs. Furthermore, the signed inseparability graph of such an oriented matroid, which records which pairs of elements are covariant resp.\ contravariant, determines the network. Reviewer's remark: The two conjectures at the end of the paper are false on the extension of \(R_{10}\) with a parallel element, whose inseparability graph has only one edge.