The Complexity of Several Realizability Problems for Abstract Topological GraphsKynčl, Jan (2008) The Complexity of Several Realizability Problems for Abstract Topological Graphs. In: Graph Drawing 15th International Symposium, GD 2007, September 2426, 2007 , pp. 137158(Official URL: http://dx.doi.org/10.1007/9783540775379_16). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783540775379_16
AbstractAn $abstract topological graph$ (briefly an $ATgraph$) is a pair $A=(G,R)$ where $G=(V,E)$ is a graph and $Rsubseteq E choose 2$ is a set of pairs of its edges. An ATgraph $A$ 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 ATgraph is simply realizable. On the other hand, we show that other similar realizability problems for (complete) ATgraphs are NPhard.
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