Introduction to the Theory of Matroids

by W. T. Tutte

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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.

This report is part of the RAND Corporation Report series. The report was a product of the RAND Corporation from 1948 to 1993 that represented the principal publication documenting and transmitting RAND's major research findings and final research.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.