Almost All 3-Connected Graphs Contain a Contractible Set of k Vertices

McCuaig and Ota conjectured that every sufficiently large 3-connected graph G contains a connected subgraph H on k vertices such that G−V(H) is 2-connected. We prove the weaker statement that every sufficiently large 3-connected graph G contains a not necessarily connected subgraph H on k vertices such that G−V(H) is 2-connected.