zbMATH — the first resource for mathematics

A linear algorithm for embedding planar graphs using PQ-trees. (English) Zbl 0605.68060
This paper presents a simple linear algorithm for embedding (or drawing) a planar graph in the plane. The algorithm is based on the ”vertex- addition” algorithm of A. Lempel, S. Even, and I. Cederbaum [Theory of graphs, Int. Symp. Rome 1966, 215-232 (1967; Zbl 0197.502)] for the planarity testing, and is a modification of K. S. Booth and G. S. Lueker’s [J. Comput. Syst. Sci. 13, 335-379 (1976; Zbl 0367.68034)] implementation of the testing algorithm using a PQ-tree. Compared with the known embedding algorithm of J. E. Hopcroft and R. E. Tarjan [J. Assoc. Comput. Mach. 21, 549-568 (1974; Zbl 0307.68025)], this algorithm is conceptually simple and easy to understand or implement. Moreover this embedding algorithm can find all the embeddings of a planar graph.

68R10 Graph theory (including graph drawing) in computer science
05C10 Planar graphs; geometric and topological aspects of graph theory
Full Text: DOI
[1] Auslander, L.; Parter, S.V., On imbedding graphs in plane, J. math. mech., 11, No. 3, 517-523, (1961) · Zbl 0101.16704
[2] Booth, K.S.; Lueker, G.S., Testing the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. comput. system sci., 13, 335-379, (1976) · Zbl 0367.68034
[3] {\scN. Chiba, T. Yamanouchi and T. Nishizeki}, Linear algorithms for convex drawings of planar graphs, in “Proceedings of Silver Jubilee Conference on Combinatorics,” Academic Press, in press. · Zbl 0556.05023
[4] Even, S., Graph algorithms, (1979), Computer Sci. Press Potomac, M · Zbl 0441.68072
[5] Even, S.; Tartan, R.E., Computing an st-numbering, Theoret. comput. sci., 2, 339-344, (1976) · Zbl 0341.68029
[6] Goldstein, A.J., An efficient and constructive algorithm for testing whether a graph can be embedded in a plane, ()
[7] Harary, F., Graph theory, (1972), Addison-Wesley Reading, Mass, (revised) · Zbl 0797.05064
[8] Hopcroft, J.E.; Tartan, R.E., Dividing a graph into triconnected components, SIAM J. comput., 2, No. 3, 135-158, (1973) · Zbl 0281.05111
[9] Hopcroft, J.E.; Tartan, R.E., Efficient planarity testing, J. assoc. comput. Mach., 21, No. 4, 549-568, (1974) · Zbl 0307.68025
[10] Lempel, A.; Even, S.; Cederbaum, I., An algorithm for planarity testing of graphs, (), 215-232 · Zbl 0197.50204
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.