Estimating the Number of Disjoint Edges in Simple Topological Graphs via Cylindrical Drawings
Radoslav Fulek · SIAM Journal on Discrete Mathematics · 2014
A topological graph drawn on a cylinder whose base is horizontal is angularly monotone if every vertical line intersects every edge at most once. Let $c(n)$ denote the maximum number $c$ such that every simple angularly monotone drawing of a complete graph on $n$ vertices contains at least $c$ pairwise disjoint edges. We show that for every simple complete topological graph $G$ there exists $\Delta$, $0<\Delta