Closure matroid properties

Abstract EN

A closure matroid is defined to be a matroid in which A u B = A u B for all subsets A and B of its ground set.

In this paper, we characterize closure matroids via the rank function and circuits and we show that the class of all closure matroids is the smallest minor-closed class that contains all transversal matroids, which is an improvement of the well- known result: The class of all gammoids is the smallest minor-closed class that contains all transversal matroids, In addition, we show that the closure matroid property is preserved under both series and parallel connection operation.