A remark on the connectivity of the complement of a 3-connected graph Original Research Article

A graph G is said to be bi-3-connected if not only G but also its complement G are 3-connected and a two-vertex set whose contraction results in a bi-3-connected graph is called a bi-contractible pair of G. We prove that every bi-3-connected graph of order at least 22 has a bi-contractible pair.