The circuit basis in binary matroids

AbstractThe concept of a circuit basis for a matroid is introduced, as an algorithmically rapid way of determining several characteristics of a given matroid. It is used to give a short search for planarity in graphs, and also to begin the answer to a question of G.-C. Rota about “dependency among dependencies.” A circuit basis for a matroid is a least set of circuits which will generate all the circuits of the matroid by repeated use of symmetric differences of cells