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 ≥ 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.
@InProceedings{katheder_et_al:LIPIcs.GD.2024.35, author = {Katheder, Julia and Kindermann, Philipp and Klute, Fabian and Parada, Irene and Rutter, Ignaz}, title = {{On k-Plane Insertion into Plane Drawings}}, booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)}, pages = {35:1--35:11}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-343-0}, ISSN = {1868-8969}, year = {2024}, volume = {320}, editor = {Felsner, Stefan and Klein, Karsten}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.35}, URN = {urn:nbn:de:0030-drops-213190}, doi = {10.4230/LIPIcs.GD.2024.35}, annote = {Keywords: Graph drawing, edge insertion, k-planarity} }
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