A Note About the Closing \(S^3\) Recognition Algorithm

In \([V_2]\), Vince outlined three potential graph algorithms for \(S^3\) recognition, namely shelling, reducing, and closing; on the other hand, he conjectured that the graph \(H_0\ ) of Fig.1 – which proves the first two to fail – could be a counterexample for the third one, too. This note shows that the conjecture is false; so, the validity of the closing algorithm is still an open problem.