Journal of Graph Algorithms and Applications
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Selected Papers from the 1999 Symposium on Graph Drawing
Embedding Vertices at Points: Few Bends Suffice for Planar Graphs
Vol. 6, no. 1, pp. 115-129, 2002. Regular paper.
Abstract The existing literature gives efficient algorithms for mapping trees or less restrictively outerplanar graphs on a given set of points in a plane, so that the edges are drawn planar and as straight lines. We relax the latter requirement and allow very few bends on each edge while considering general plane graphs. Our results show two algorithms for mapping four-connected plane graphs with at most one bend per edge and for mapping general plane graphs with at most two bends per edge. Furthermore we give a point set, where for arbitrary plane graphs it is NP-complete to decide whether there is an mapping such that each edge has at most one bend.