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Drawing plane graphs nicely. (English) Zbl 0545.68057

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, procedures a pleasing 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.

MSC:

68R10 Graph theory (including graph drawing) in computer science
68Q25 Analysis of algorithms and problem complexity
05C10 Planar graphs; geometric and topological aspects of graph theory
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