24 search results - page 1 / 5 » Extending a matroid by a cocircuit |
DM
2006
13 years 6 months ago
2006
Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view Dowling lattices and ne...
EJC
2011
13 years 1 months ago
2011
We present an algorithm which takes a graph as input and decides in cubic time if the graph is the cocircuit graph of a uniform oriented matroid. In the affirmative case the algor...
JCT
2006
13 years 6 months ago
2006
The cocircuit graph of an oriented matroid is the 1-skeleton of the cellular decomposition induced by the Topological Representation Theorem due to Folkman and Lawrence (1978) [J....
DCG
2000
13 years 6 months ago
2000
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 dete...
DCG
2002
13 years 6 months ago
2002
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 theoretica...