TY - JOUR
AU - GarcĂa, Alfredo
AU - Tejel, Javier
AU - Vogtenhuber, Birgit
AU - Weinberger, Alexandra
PY - 2023/11/01
Y2 - 2024/11/01
TI - Empty Triangles in Generalized Twisted Drawings of $K_n$
JF - Journal of Graph Algorithms and Applications
JA - JGAA
VL - 27
IS - 8
SE -
DO - 10.7155/jgaa.00637
UR - https://jgaa.info/index.php/jgaa/article/view/paper637
SP - 721-735
AB - 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 thatany simple drawing of $K_n$ contains at least $2n-4$ empty triangles.
ER -