@inproceedings{2a4c6f08e7a542a6957265cda9c961d3,
title = "Empty Triangles in Generalized Twisted Drawings of Kn",
abstract = "Simple drawings are drawings of graphs in the plane or on the sphere 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 Kn contain exactly 2 n- 4 empty triangles, by this making a substantial step towards proving the conjecture that this is the case for every simple drawing of Kn.",
keywords = "Empty triangles, Simple drawings, Simple topological graphs",
author = "Alfredo Garc{\'i}a and Javier Tejel and Birgit Vogtenhuber and Alexandra Weinberger",
note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 30th International Symposium on Graph Drawing and Network Visualization : GD 2022, GD 2022 ; Conference date: 13-09-2022 Through 16-01-2023",
year = "2023",
doi = "10.1007/978-3-031-22203-0\_4",
language = "English",
isbn = "9783031222023",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "40--48",
editor = "Patrizio Angelini and \{von Hanxleden\}, Reinhard",
booktitle = "Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Revised Selected Papers",
address = "Germany",
}