Abstract
We investigate the problem of determining if a given graph corresponds to the dual of a triangulation of a simple polygon. This is a graph recognition problem, where in our particular case we wish to recognize a graph which corresponds to the dual of a triangulation of a simple polygon with or without holes and interior points. We show that the difficulty of this problem depends critically on the amount of information given and we give a sharp boundary between the various tractable and intractable versions of the problem.
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