ISSN:
1432-0444
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004540010031
