Abstract.
In this paper we consider the cocircuit graph G M of an oriented matroid M , the 1 -skeleton of the cell complex W formed by the span of the cocircuits of M . In general, W is not determined by G M . However, we show that if the vertex set (resp. edge set) of G M is properly labeled by the hyperplanes (resp. colines) of M , G M determines W . Also we prove that, when M is uniform, the cocircuit graph together with all antipodal pairs of vertices being marked determines W . These results can be considered as variations of Blind—Mani's theorem that says the 1-skeleton of a simple convex polytope determines its face lattice.
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Received August 14, 1998, and in revised form March 2, 1999.
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Cordovil, R., Fukuda, K. & Guedes de Oliveira, A. On the Cocircuit Graph of an Oriented Matroid . Discrete Comput Geom 24, 257–266 (2000). https://doi.org/10.1007/s004540010031
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DOI: https://doi.org/10.1007/s004540010031