Empty Triangles in Generalized Twisted Drawings of $K_n$
DOI:
https://doi.org/10.7155/jgaa.00637Abstract
Simple drawings are drawings of graphs in the plane such that vertices are distinct points, edges are Jordan arcs connecting their endpoints, and edges intersect at most once (either in a proper crossing or in a shared endpoint). Simple drawings are generalized twisted if there is a point $O$ such that every ray emanating from $O$ crosses every edge of the drawing at most once, and there is a ray emanating from $O$ which crosses every edge exactly once. We show that all generalized twisted drawings of $K_n$ contain exactly $2n-4$ empty triangles, by this making a substantial step towards proving the conjecture that any simple drawing of $K_n$ contains at least $2n-4$ empty triangles.Downloads
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Published
2023-11-01
How to Cite
García, A., Tejel, J., Vogtenhuber, B., & Weinberger, A. (2023). Empty Triangles in Generalized Twisted Drawings of $K_n$. Journal of Graph Algorithms and Applications, 27(8), 721–735. https://doi.org/10.7155/jgaa.00637
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Copyright (c) 2023 Alfredo García, Javier Tejel, Birgit Vogtenhuber, Alexandra Weinberger
This work is licensed under a Creative Commons Attribution 4.0 International License.