Abstract
In this paper we present two O(n2) planarization algorithms—PLANARIZE and MAXIMAL-PLANARIZE. These algorithms are based on Lempel, Even, and Cederbaum's planarity testing algorithm [9] and its implementation using PQ-trees [8, 13]. Algorithm PLANARIZE is for the construction of a spanning planar subgraph of an n-vertex nonplanar graph. This algorithm proceeds by embedding one vertex at a time and, at each step, adds the maximum number of edges possible without creating nonplanarity of the resultant graph. Given a biconnected spanning planar subgraph Gp of a nonplanar graph G, algorithm MAXIMAL-PLANARIZE constructs a maximal planar subgraph of G which contains Gp. This latter algorithm can also be used to maximally planarize a biconnected planar graph.
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© 1989 Springer-Verlag Berlin Heidelberg
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Jayakumar, R., Thulasiraman, K., Swamy, M.N.S. (1989). O(n2) algorithms for graph planarization. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1988. Lecture Notes in Computer Science, vol 344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50728-0_56
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DOI: https://doi.org/10.1007/3-540-50728-0_56
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