Drawing planar partitions III: Two constrained embedding problems

In two previous papers, we studied the following problem: Given a planar graph G = (V; E) and a partition V = A B of the vertices. Can we draw G without crossing such that the partition is clearly visible? For three models used to display the partition, we developed necessary and suucient conditions for the existence of such a drawing. The time to test these conditions was dominated by verifying whether there exists a planar embedding of G that satisses certain additional properties. In this paper, we study how these constrained embedding tests can be done in linear time.

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