Extending drawings of complete graphs into arrangements of pseudocircles

@article{Arroyo2021ExtendingDO,
  title={Extending drawings of complete graphs into arrangements of pseudocircles},
  author={Alan Arroyo and R. Richter and M. Sunohara},
  journal={SIAM J. Discret. Math.},
  year={2021},
  volume={35},
  pages={1050-1076}
}
We prove three principal results. First we exhibit a drawing of $K_{10}$ in the plane for which there do not exist extensions of the edges to simple closed curves with any two curves intersecting at most twice. Second, we exhibit a drawing of $K_9$ that has an extension of its edges to simple closed curves such that any two curves intersect in at most two points, but no extension to simple closed curves has every two curves intersecting in exactly two points. Third, we show that every h-convex… Expand
1 Citations
Topological Drawings meet Classical Theorems from Convex Geometry
In this article we discuss classical theorems from Convex Geometry in the context of topological drawings. In a simple topological drawing of the complete graph $K_n$, any two edges share at most oneExpand

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