On the regularity of orientable matroids

  title={On the regularity of orientable matroids},
  author={Libby Taylor},
  journal={Discret. Math.},
  • Libby Taylor
  • Published 2019
  • Mathematics, Computer Science
  • Discret. Math.
We present two characterizations of regular matroids among orientable matroids and use them to give a measure of "how far" an orientable matroid is from being regular. 

Topics from this paper

The circuit and cocircuit lattices of a regular matroid
A matroid abstracts the notions of dependence common to linear algebra, graph theory, and geometry. We show the equivalence of some of the various axiom systems which define a matroid and examine theExpand


Decomposition of regular matroids
  • P. Seymour
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1980
Abstract It is proved that every regular matroid may be constructed by piecing together graphic and cographic matroids and copies of a certain 10-element matroid.
Lifts of matroid representations over partial fields
This paper proves the following theorem by Vertigan: if a matroid is representable over both GF(4) and GF(5), then it is representsable over the real numbers by a matrix such that the absolute value of the determinant of every nonsingular square submatrix is a power of the golden ratio. Expand
On the number of circuit-cocircuit reversal classes of an oriented matroid
The circuit-cocircuit reversal system of an oriented matroid is extended to an equivalence of matroidal properties, thereby giving a new characterization of regular matroids. Expand
Algebraic Potential Theory on Graphs
This paper encompasses a motley collection of ideas from several areas of mathematics, including, in no particular order, random walks, the Picard group, exchange rate networks, chip-firing games,Expand
Flows and colorings in oriented matroids
Wir werden uns in dieser Arbeit mit einer Struktur beschaftigen, deren Starke darin liegt, verschiedenste Gebiete der Mathematik zusammenzufuhren wie Lineare Optimierung, affine/projektive Geometrie,Expand
Mixed integer reformulations of integer programs and the affine TU-dimension of a matrix
A generalization of total unimodularity called the affine TU-dimension of a matrix is introduced and related theory and algorithms for determining the affinity of a matrices are studied, showing bounds on the number of integer variables needed to represent certain integer hulls. Expand
Oriented Matroids, volume 46 of Encyclopedia of Mathematics and its Applications
  • 1999
Combinatorial geometries, volume 29 of of Encyclopedia of Mathematics and its Applications
  • 1987
On the axiomatic foundations of the theories of directed linear graphs, electrical networks and network programming
  • Journal of Mathematics and Mechanics,
  • 1966
Lectures on matroids