On matroids of the greatestW-connectivity

AbstractThe Whitney connectivity (W-connectivity) of a matroidM is defined by T. Inukai and L. Weinberg as the least integerk for which there exists a subsetS of the ground setE ofM such that ϱ(S) ≥ k, ϱ(E − S) ≥ k, andp(S)+p(E-S)-pM+1=k where ϱ is the rank function ofM.Mis called a Whitney matroid if there exists no such integer. In this case, theW-connectivity ofM to be the rank ofM is defined. In this paper, several properties of Whitney matroids are demonstrated. In addition, the Whitney matroids whose duals are also Whitney matroids are characterized, and an interpretation of binaryW-matroids is given