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4-Connected Triangulations on Few Lines

  • Stefan FelsnerEmail author
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)

Abstract

We show that 4-connected plane triangulations can be redrawn such that edges are represented by straight segments and the vertices are covered by a set of at most \(\sqrt{2n}\) lines each of them horizontal or vertical. The same holds for all subgraphs of such triangulations.

The proof is based on a corresponding result for diagrams of planar lattices which makes use of orthogonal chain and antichain families.

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Notes

Acknowledgments

Work on this problem began at the 2018 Bertinoro Workshop of Graph Drawing. I thank the organizers of the event for making this possible. Special thanks go to Pavel Valtr, Alex Pilz and Torsten Ueckerdt for helpful discussions.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany

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