On $k$-Plane Insertion into Plane Drawings
Julia Katheder, Philipp Kindermann, Fabian Klute, Irene Parada, Ignaz Rutter · arXiv (Cornell University) · 2024
We introduce the $k$-Plane Insertion into Plane drawing ($k$-PIP) problem: given a plane drawing of a planar graph $G$ and a set $F$ of edges, insert the edges in $F$ into the drawing such that the resulting drawing is $k$-plane. In this paper, we show that the problem is NP-complete for every $k\ge 1$, even when $G$ is biconnected and the set $F$ of edges forms a matching or a path. On the positive side, we present a linear-time algorithm for the case that $k=1$ and $G$ is a triangulation.