On pancyclic representable matroids

Bondy proved that an n-vertex simple Hamiltonian graph with at least image edges has cycles of every length unless it is isomorphic to image. This paper considers finding circuits of every size in image-representable matroids with large numbers of elements. A consequence of the main result is that a rank-r simple binary matroid with at least image elements either has circuits of all sizes or is isomorphic to image.