Additional PC-Tree Planarity Conditions
Recent research efforts have produced new algorithms for solving planarity-related problems. One such method performs vertex addition using the PC-tree data structure, which is similar to but simpler than the well-known PQ-tree. For each vertex, the PC-tree is first checked to see if the new vertex can be added without violating certain planarity conditions; if the conditions hold, the PC-tree is adjusted to add the new vertex and processing continues. The full set of planarity conditions are required for a PC-tree planarity tester to report only planar graphs as planar. This paper provides further analyses and new planarity conditions needed to produce a correct planarity algorithm with a PC-tree.
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