Matroids with the Circuit Cover Property

Abstract

We verify a conjecture regarding circuits of a binary matroid. Acircuit coverof a integer-weighted matroid (M,p) is a list of circuits ofMsuch that each elementeis in exactlyp(e) circuits from the list. We characterize those binary matroids for which two obvious necessary conditions for a weighting (M,p) to have a circuit cover are also sufficient.