Summary
This paper presents two efficient algorithms for drawing plane graphs nicely. Both draw all edges of a graph as straight line segments without crossing lines. The first draws a plane graph “convex” if possible, that is, in a way that every inner face and the complement of the outer face are convex polygons. The second, using the first, produces a pleasing drawing of a given plane graph that satisfies the following property as far as possible: the complements of 3-connected components, together with inner faces and the complement of the outer face, are convex polygons. The running time and storage space of both algorithms are linear in the number of vertices of the graph.
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Chiba, N., Nishizeki, T., Abe, S., Ozawa, T.: A linear algorithm for embedding planar graphs using PQ-trees. J. Comput. Syst. Sci. (To appear)
Chiba, N., Yamanouchi, T., Nishizeki, T.: Linear algorithms for convex drawings of planar graphs. In: Progress in Graph Theory (J.A. Bondy, U.S.R. Murty, eds.), pp. 153–173. Toronto: Academic Press 1984
Fary, I.: On straight representations of planar graphs. Acta Sci. Math. Szeged 11, 229–233 (1948)
Hopcroft, J.E., Tarjan, R.E.: Dividing a graph into triconnected components. SIAM J. Comput. 2, 3, 135–158 (1973)
Hopcroft, J.E., Tarjan, R.E.: Efficient planarity testing. J. ACM 21, 549–568 (1974)
Lipton, R.J., Rose, D.J., Tarjan, R.E.: Generalized nested dissection. SIAM J. Numer. Anal. 16, 2, 346–358 (1979)
Reingold, E.M., Tilford, J.S.: Tidier drawings of trees. IEEE Trans. Software Eng. 3, 223–228 (1981)
Supowit, K.J., Reingold, E.M.: The complexity of drawing trees nicely. Acta Inf. 18, 377–392 (1983)
Thomassen, C.: Planarity and duality of finite and infinite graphs. J. Comb. Theory, Ser. B 29, 244–271 (1980)
Tutte, W.T.: Convex representations of graphs. Proc. Lond. Math. Soc., (3) 10, 304–320 (1960)
Tutte, W.T.: How to draw a graph. Proc. Lond. Math. Soc. 13, 743–768 (1963)
Vaucher, J.G.: Pretty-printing of trees. Software, Pract. Exper. 10, 553���561 (1980)
Wetherell, C., Shannon, A.: Tidy drawings of trees. IEEE Trans. Software Eng. 5, 514–520 (1970)
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Chiba, N., Onoguchi, K. & Nishizeki, T. Drawing plane graphs nicely. Acta Informatica 22, 187–201 (1985). https://doi.org/10.1007/BF00264230
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DOI: https://doi.org/10.1007/BF00264230