## The Complexity of Several Realizability Problems for Abstract Topological Graphs
Kynčl, Jan
(2008)
Full text not available from this repository. ## AbstractAn $abstract topological graph$ (briefly an $AT-graph$) 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 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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