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On Point Set Embeddings for k-Planar Graphs with Few Bends per Edge

  • Michael KaufmannEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11376)

Abstract

We consider the point set embedding problem (PSE) for 1-, 2- and k-planar graphs where at most 1, 2, or k crossings resp. are allowed for each edge which greatly extends the well-researched class of planar graphs. For any set of n points and any given embedded graph that belongs to one of the above graph classes, we compute a 1-to-1 mapping of the vertices to the points such that the edges can be routed using only a limited number of bends according to the given embedding and the sequences of crossings. Surprisingly, for the class of 1-planar graphs the same results can be achieved as the best known results for planar graphs. Additionally for k-planar graphs, the bounds are also much better than expected from the first sight.

Notes

Acknowledgement

The author wishes to thanks the participants of the GNV workshop in Heiligkreuztal 2018 for inspiring discussions.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Wilhelm-Schickhard-Institut für InformatikUniversität TübingenTübingenGermany

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