A note on computing a maximal planar subgraph using PQ-trees

The problem of computing a maximal planar subgraph of a nonplanar graph has been deeply investigated over the last 20 years. Several attempts have been tried to solve the problem with the help of PQ-trees. The latest attempt has been reported by Jayakumar et al. In this paper we show that the algorithm presented by Jayakumar et al. is not correct. We show that it does not necessarily compute a maximal planar subgraph and we note that the same holds for a modified version of the algorithm presented by Kant. Our conclusions most likely suggest not to use PQ-trees at all for this specific problem.