Document Type

Article

Publication Date

12-6-2005

Abstract

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)

Discrete Mathematics

First Page

337

Last Page

343

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