Bondy proved that an n-vertex simple Hamiltonian graph with at least n2/4 edges has cycles of every length unless it is isomorphic to Kn/2,n/2. This paper considers finding circuits of every size in GF(q)-representable matroids with large numbers of elements. A consequence of the main result is that a rank-r simple binary matroid with at least 2r-1 elements either has circuits of all sizes or is isomorphic to AG(r-1,2). © 2005 Elsevier B.V. All rights reserved.
Publication Source (Journal or Book title)
Beavers, B., & Oxley, J. (2005). On pancyclic representable matroids. Discrete Mathematics, 305 (1-3), 337-343. https://doi.org/10.1016/j.disc.2005.10.008