Covering contractible edges in 2-connected graphs

In this paper we prove that, for any 2-connected graph G nonisomorphic to K-3, the set of contractible edges EC(G) cannot be covered by one vertex. All 2-connected graphs whose contractible edges can be covered by exactly two vertices are characterized. We also prove that if a vertex subset S covers E-C(G) such that vertical bar V (G)vertical bar >= 2 vertical bar S vertical bar + 1, then G - S is not connected. Finally, we provide tight upper bounds for the order, size and number of non-trivial components of G-S (components having more than one vertex) in terms of vertical bar S vertical bar, and characterize all the extremal graphs.