The Complexity of Several Realizability Problems for Abstract Topological Graphs

(Extended Abstract)
  • Jan Kynčl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)


An abstract topological graph (briefly an AT-graph) is a pair A = (G,R) where G = (V,E) is a graph and \(R\subseteq {E \choose 2}\) is a set of pairs of its edges. An AT-graph A is simply realizable if G can be drawn in the plane in such a way that each pair of edges from R crosses exactly once and no other pair crosses. We present a polynomial algorithm which decides whether a given complete AT-graph is simply realizable. On the other hand, we show that other similar realizability problems for (complete) AT-graphs are NP-hard.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jan Kynčl
    • 1
  1. 1.Department of Applied Mathematics and Institute for Theoretical Computer Science, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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