A characterization of cocircuit graphs of uniform oriented matroids (Q2496197)

Given an oriented matroid \({\mathcal M}\), the authors define the cocircuit graph as the 1-skeleton of the cellular decomposition of the sphere induced by the pseudospheres that realizes \({\mathcal M}\) via the well-known topological representation theorem of Folkman and Lawrence. In this paper, it is presented a complete characterization of such graphs in the case when \({\mathcal M}\) is uniform. This characterization is given in terms of embeddings into the 1-skeleton of the \(n\)-cube's \(k\)-skeleton's dual complex where \(n\) denotes the number of elements of \({\mathcal M}\).