Abstract
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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Kynčl, J. (2008). The Complexity of Several Realizability Problems for Abstract Topological Graphs. In: Hong, SH., Nishizeki, T., Quan, W. (eds) Graph Drawing. GD 2007. Lecture Notes in Computer Science, vol 4875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77537-9_16
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DOI: https://doi.org/10.1007/978-3-540-77537-9_16
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