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 language | English |
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Title of host publication | Graph Drawing and Network Visualization |
Subtitle of host publication | 27th International Symposium on Graph Drawing and Network Visualization (GD 2019), Proceedings |
Publisher | Springer, Cham |
Pages | 230-243 |
DOIs | |
Publication status | Published - 2019 |
Event | 27th International Symposium on Graph Drawing and Network Visualization: GD 2019 - Hotel Floret, Pruhonice, Czech Republic Duration: 17 Sept 2019 → 20 Sept 2019 https://kam.mff.cuni.cz/gd2019/index.html https://kam.mff.cuni.cz/gd2019/ |
Publication series
Name | LNCS |
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Volume | 11904 |
Conference
Conference | 27th International Symposium on Graph Drawing and Network Visualization |
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Abbreviated title | GD 2019 |
Country/Territory | Czech Republic |
City | Pruhonice |
Period | 17/09/19 → 20/09/19 |
Internet address |