Transversal Matroids and Related Structures

There is an extensive body of literature on the subject of transversal matroids (with the partial transversals of a family of sets as independent sets) and the more general theory of matroids induced from graphs. This paper reviews the known results and some still unsolved problems. The topics discussed include: characterizations of transversal matroids and of their presentations, standard operations applied to transversal matroids, gammoids and strict gammoids, base-orderability of matroids. The notion of a complete class of matroids (the gammoids being the simplest such class) is introduced and discussed.

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