On matroid separations of graphs

Let K be a connected and undirected graph, and M be the polygon matroid of K. Assume that, for some k ⩾ 1, the matroid M is k-separable and k-connected according to the matroid separability and connectivity definitions of W. T. Tutte. In this paper we classify the matroid k-separations of M in terms of subgraphs of K.