On Binary Matroids Not Isomorphic to Their Base Matroids

Abstract

Let $M=(E,\mathcal{F})$ be a matroid on a set $E$, $B$ one of its bases, and $M_B$ the base matroid associated to $B$. In this paper, we determine a characterization of simple binary matroids $M$ which are not isomorphic to $M_B$, for every base $B$ of $M$. We also extend to matroids some graph notions.