Matroids with the circuit cover property

Abstract

We verify a conjecture regarding circuits of a binary matroid. A circuit cover of a integer-weighted matroid (M, p) is a list of circuits of M such that each element e is in exactly p(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. © 1999 Academic Press.