On -Plane Insertion into Plane Drawings
arXiv preprint arXiv:2402.14552, 2024•arxiv.org
We introduce the $ k $-Plane Insertion into Plane drawing ($ k $-PIP) problem: given a plane
drawing of a planar graph $ G $ and a set of edges $ F $, insert the edges in $ F $ into the
drawing such that the resulting drawing is $ k $-plane. In this paper, we focus on the $1 $-
PIP scenario. We present a linear-time algorithm for the case that $ G $ is a triangulation,
while proving NP-completeness for the case that $ G $ is biconnected and $ F $ forms a path
or a matching.
drawing of a planar graph $ G $ and a set of edges $ F $, insert the edges in $ F $ into the
drawing such that the resulting drawing is $ k $-plane. In this paper, we focus on the $1 $-
PIP scenario. We present a linear-time algorithm for the case that $ G $ is a triangulation,
while proving NP-completeness for the case that $ G $ is biconnected and $ F $ forms a path
or a matching.
We introduce the -Plane Insertion into Plane drawing (-PIP) problem: given a plane drawing of a planar graph and a set of edges , insert the edges in into the drawing such that the resulting drawing is -plane. In this paper, we focus on the -PIP scenario. We present a linear-time algorithm for the case that is a triangulation, while proving NP-completeness for the case that is biconnected and forms a path or a matching.
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