Rl. Hemminger et Xx. Yu, COVERING CONTRACTILE EDGES IN 3-CONNECTED GRAPHS .2. CHARACTERIZING THOSE WITH COVERS OF SIZE 3, Journal of graph theory, 17(2), 1993, pp. 247-252
It is shown that if G is a 3-connected graph with \V(G)\ greater-than-
or-equal-to 10, then, with the exception of one infinite class based o
n K3,p, it takes at least four vertices to cover the set of contractib
le edges of G.