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We present an algorithm which takes a graph as input and decides in cubictime if the graph is the cocircuit graph of a uniform oriented matroid. In theaffirmative case the algorithm returns the set of signed cocircuits of theoriented matroid. This improves an algorithm proposed by Babson, Finschi andFukuda.  Moreover we strengthen a result of Montellano-Ballesteros and Strausz aboutcrabbed connectivity of cocircuit graphs of uniform oriented matroids.

Cubic Time Recognition of Cocircuit Graphs of Uniform Oriented Matroids