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4-Connected Triangulations on Few Lines

  • Stefan FelsnerEmail author
Conference paper
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.

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany

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