On matroids of the greatestW-connectivity

In this paper, M is a matroid with the rank function p on a finite set E of II elements. For an element e of E, the restriction of M to E e will be denoted by M e, and the contraction of M to E e will be denoted by M/e. For the terminology and notation not specified here, see [4]. According to Inukai and Weinberg [3], the Whitney connectivity (IV connectivity) of M, denoted by A(M), is defined as the least integer k for which there is a subset 5’ of E such that p(S) > k, p(E S) 2 k, and