# 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} }

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…

## 33 Citations

### Simple Realizability of Complete Abstract Topological Graphs Simplified

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This work characterize simply realizable complete AT-graphs by a finite set of forbidden AT-subgraphs, each with at most six vertices, which implies a straightforward polynomial algorithm for testing simple realizability of complete AT -graphs.

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