Linear-size Universal Point Sets for One-bend Drawings

Abstract

For every integer $n ge 4$, we construct a planar point set $S_n$ of size $6n-10$ such that every $n$-vertex planar graph $G$ admits a plane embedding in which the vertices are mapped to points in $S_n$, and every edge is either a line segment or a polyline with one bend, where the bend point is also in $S_n$.