Extending Simple Drawings

Alan Arroyo, Martin Derka, Irene Parada

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

Simple drawings of graphs are those in which each pair of edges share at most one point, either a common endpoint or a proper crossing. In this paper we study the problem of extending a simple drawing D(G) of a graph G by inserting a set of edges from the complement of G into D(G) such that the result is a simple drawing. In the context of rectilinear drawings, the problem is trivial. For pseudolinear drawings, the existence of such an extension follows from Levi’s enlargement lemma. In contrast, we prove that deciding if a given set of edges can be inserted into a simple drawing is NP-complete. Moreover, we show that the maximization version of the problem is APX-hard. We also present a polynomial-time algorithm for deciding whether one edge uv can be inserted into D(G) when {u,v} is a dominating set for the graph G.
Original languageEnglish
Title of host publicationGraph Drawing and Network Visualization
Subtitle of host publication 27th International Symposium on Graph Drawing and Network Visualization (GD 2019), Proceedings
PublisherSpringer, Cham
Pages230-243
DOIs
Publication statusPublished - 2019
Event27th International Symposium on Graph Drawing and Network Visualization - Hotel Floret, Pruhonice, Czech Republic
Duration: 17 Sep 201920 Sep 2019
https://kam.mff.cuni.cz/gd2019/index.html
https://kam.mff.cuni.cz/gd2019/

Publication series

NameLNCS
Volume11904

Conference

Conference27th International Symposium on Graph Drawing and Network Visualization
Abbreviated titleGD 2019
CountryCzech Republic
CityPruhonice
Period17/09/1920/09/19
Internet address

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Arroyo, A., Derka, M., & Parada, I. (2019). Extending Simple Drawings. In Graph Drawing and Network Visualization : 27th International Symposium on Graph Drawing and Network Visualization (GD 2019), Proceedings (pp. 230-243). (LNCS; Vol. 11904). Springer, Cham. https://doi.org/10.1007/978-3-030-35802-0_18