Contractible edges in minimally kk-connected graphs

An edge of a kk-connected graph is said to be kk-contractible if the contraction of the edge results in a kk-connected graph. In this paper, we prove that a (K1+C4)(K1+C4)-free minimally k-connected graph has a k-contractible edge, if incident to each vertex of degree k, there is an edge which is not contained in a triangle. This implies two previous results, one due to Thomassen and the other due to Kawarabayashi.