10.1007/978-3-030-35802-0_18
Arroyo Guevara, Alan M
Alan M
Arroyo Guevara
Derka, Martin
Martin
Derka
Parada, Irene
Irene
Parada
Extending simple drawings
LNCS
Springer Nature
2019
2020-01-05T23:00:47Z
2020-01-16T12:38:22Z
conference
https://research-explorer.app.ist.ac.at/record/7230
https://research-explorer.app.ist.ac.at/record/7230.json
9783030358013
03029743
1908.08129
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.