On the Cocircuit Graph of an Oriented Matroid

In this paper we consider the cocircuit graph GM 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 GM. However, we show that if the vertex set (resp. edge set) of GM is properly labeled by the hyperplanes (resp. colines) ofM, GM 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

• Type: Journal
• Year: 2000
• Where: DCG
• Authors: Raul Cordovil, Komei Fukuda, António Guedes de Oliveira
• Keywords: Cocircuit Graph, Cocircuit Graph Gm, DCG 2000, Oriented Matroid