Transversals and Matroid Partition

Abstract

Abstract : A matroid M = (E, F) is a finite set E of elements and a family F of subsets of E, called independent sets, such that (1) every subset of an independent set is independent, and (2) for every set A belonging to E, all maximal independent subsets of A have the same cardinality, called the rank r(A) of A. The concept of 'matroid' thus generalizes that of 'matrix' or, in particular, that of 'graph.' This paper treats a variety of partition problems involving independent sets of matroids.