Introduction to the Theory of Matroids
A presentation of the basic concepts and methods of matroid theory. The report defines a matroid axiomatically and introduces the matroids associated with the structures of graphs and chain-groups. It discusses the subgraphs and contractions of a graph, exhibits corresponding simplifications of chain-groups and matroids, and studies the rank of a matroid. It also examines a property of matroids called "connection" and shows that it corresponds to the property of nonseparability for graphs. It further treats the detailed structure of a matroid (that is, it studies the relation between a given circuit and the rest of the matroid), and concludes by considering the regular matroids and their associated chain-groups. The regular matroids mark an interesting half-way stage between the matroids corresponding to graphs on the one hand, and the binary matroids, corresponding to chain-groups over GF(2), on the other.