Extending Simple Drawings

Alan Arroyo, Martin Derka, Irene Parada

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


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
Publication statusPublished - 2019
Event27th International Symposium on Graph Drawing and Network Visualization: GD 2019 - Hotel Floret, Pruhonice, Czech Republic
Duration: 17 Sept 201920 Sept 2019

Publication series



Conference27th International Symposium on Graph Drawing and Network Visualization
Abbreviated titleGD 2019
Country/TerritoryCzech Republic
Internet address


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