On the cocircuit graph of an oriented matroid

• Type: Article in International Scientific Journal
• Date: 2000

Authors

Cordovil, R (Author) Other; Fukuda, K (Author) Other; de Oliveira, AG (Author) FCUP

Journal

Title: Discrete and Computational Geometry

Vol. 24

Pages: 257-265

ISSN: 0179-5376

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 6 Citations

Scientific classification

FOS: Natural sciences > Computer and information sciences

Other information

Authenticus ID: P-000-Z21

DOI: 10.1007/s004540010031

Abstract (EN): 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 GM 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 9