Almost-graphic matroids
A matroid which is not graphic is termed almost graphic if, for each element of the matroid, either the matroid obtained by deletion of the element is graphic, or the matroid obtained by contraction of the element is graphic. In this paper, the almost graphic matroids are explicitly determined, thereby solving a problem of James Oxley. Additionally, a characterization of the ``almost regular matroids having at least one regular element'' is given.
scientific article; zbMATH DE number 1800217