A graph-theoretical axiomatization of oriented matroids

A graph-theoretical axiomatization of oriented matroids

We characterize which systems of sign vectors are the cocircuits of an oriented matroid in terms of the cocircuit graph.

Generation of Oriented Matroids - A Graph Theoretical Approach

We discuss methods for the generation of oriented matroids and of isomorphism classes of oriented matroids. Our methods are based on single element extensions and graph theoretical representations of oriented matroids, and all these methods work in general rank and for nonuniform and uniform oriented matroids as well. We consider two types of graphs, cocircuit graphs and tope graphs, and discus...

An Independent Set Axiomatization of Symplectic Matroids

Fachbereich 3 Mathematik Oriented Matroids Oriented Matroids

Oriented matroids and complete-graph embeddings on surfaces

We provide a link between topological graph theory and pseudoline arrangements from the theory of oriented matroids. We investigate and generalize a function f that assigns to each simple pseudoline arrangement with an even number of elements a pair of complete-graph embeddings on a surface. Each element of the pair keeps the information of the oriented matroid we started with. We call a simple...