Counting maximal cycles in binary matroids


It is shown that each binary matroid contains an odd number of maximal cycles and, as a result of this, that each element of an Eulerian binary matroid is contained in an odd number of circuits. Let M be a binary matroid with circuits ~ (M) and cycles .~(M), and let ~e(M) be the set of circuits containing an element e in the underlying set E(M). (For… (More)
DOI: 10.1016/0012-365X(95)00240-W