Abstract
We prove that every 4-connected planar triangulation admits a contact representation by homothetic triangles.
There is a known proof of this result that is based on the Convex Packing Theorem by Schramm, a general result about contact representations of planar triangulations by convex shapes. But our approach makes use of the combinatorial structure of triangle contact representations in terms of Schnyder woods. We start with an arbitrary Schnyder wood and produce a sequence of Schnyder woods via face flips. We show that at some point the sequence has to reach a Schnyder wood describing a representation by homothetic triangles.
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Notes
- 1.
The journal version [6] does not contain this proof.
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Schrezenmaier, H. (2017). Homothetic Triangle Contact Representations. In: Bodlaender, H., Woeginger, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2017. Lecture Notes in Computer Science(), vol 10520. Springer, Cham. https://doi.org/10.1007/978-3-319-68705-6_32
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DOI: https://doi.org/10.1007/978-3-319-68705-6_32
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