A matroid is a combinatorial structure that possesses important combinatorial properties of a wide variety of mathematical structures. Such varied structures as vector spaces, transversals, certain ployhedral corner points , cycles in a graph, spanning trees, and the source arcs used by a network flow are all special cases of matroids. Matroid theory provides a convenient way to summarize these scattered results and to extend them simultaneously [1, Ch. 21],1 [2-5], [8], [11].

/pdf/finding-the-circuits-of-a-matroid-39v5qa0hfl.pdf

Finding the circuits of a matroid

The survey is devoted to certain current problems in general combinatorial mathematics. The contemporary state-of-the-art of the theory of permanents, questions on the existence and the enumeration of matrices with nonnegative elements, and a number of problems connected with latin rectangles (enumeration, problem of completing a latin square, equidistant arrays) are examined. The main directions in combinatorial theory in connection with selection problems also are analyzed: matroid theory, transversals, extremal problems (coverings, depth of a matrix, Sperner families). Principal attention is paid to the papers reviewed in Referativnyi Zhurnal “Matematika” during 1975–1979.

Combinatorial analysis (matrix problems, order theory)

A note on some algorithms for matroids

Matroid bases, opposite families and some related algorithms

One generalization of ordinary matroids is symplectic matroids While symplectic matroids were initially defined by their collections of bases, there has been no cryptomorphic definition of symplectic matroids in terms of circuits We give a definition of symplectic matroids by collections of circuits As an application, we construct a class of examples of symplectic matroids from graphs in terms of circuits

Symplectic Matroids, Circuits, and Signed Graphs

t('r)(T of variou s lcxicographic network fl o ws. Second , a n independenc e prope rl y o f m axi mum flow s is proved and thi s prop e rt y is r (' la ted to a n ind e pe nd e nce property of Rru aldi and S crimger.

/pdf/maximal-network-flows-matroids-and-matchings-5faunvtmnx.pdf

Maximal network flows, matroids and matchings

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Finding the circuits of a matroid

Maximal network flows, matroids and matchings