Simple Realizability of Complete Abstract Topological Graphs in P

  title={Simple Realizability of Complete Abstract Topological Graphs in P},
  author={Jan Kyn{\vc}l},
  journal={Discrete \& Computational Geometry},
  • 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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