# Simple Realizability of Complete Abstract Topological Graphs in P

@article{Kynl2011SimpleRO,
title={Simple Realizability of Complete Abstract Topological Graphs in P},
author={Jan Kyn{\vc}l},
journal={Discrete \& Computational Geometry},
year={2011},
volume={45},
pages={383-399}
}
• J. Kynčl
• Published 1 April 2011
• Mathematics, Computer Science
• Discrete & Computational Geometry
An abstract topological graph (briefly an AT-graph) is a pair $A=(G,\mathcal{R})$ where G=(V,E) is a graph and $\mathcal {R}\subseteq {E \choose 2}$ 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 $\mathcal{R}$ 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…

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