In [V2], 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.
A note about the closing S3 recognition algorithm / Casali, Maria Rita. - In: ARS COMBINATORIA. - ISSN 0381-7032. - STAMPA. - 39:(1995), pp. 155-160.
A note about the closing S3 recognition algorithm
CASALI, Maria Rita
1995-01-01
Abstract
In [V2], 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.
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