Unavoidable Configurations in Complete Topological Graphs

@article{Pach2000UnavoidableCI,
  title={Unavoidable Configurations in Complete Topological Graphs},
  author={J{\'a}nos Pach and J{\'o}zsef Solymosi and G{\'e}za T{\'o}th},
  journal={Discrete & Computational Geometry},
  year={2000},
  volume={30},
  pages={311-320}
}
Abstract A topological graph is a graph drawn in the plane so that its vertices are represented by points, and its edges are represented by Jordan curves connecting the corresponding points, with the property that any two curves have at most one point in common. We define two canonical classes of topological complete graphs, and prove that every topological complete graph with n vertices has a canonical subgraph of size at least clog1/8n, which belongs to one of these classes. We also show that… CONTINUE READING

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References

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SHOWING 1-10 OF 23 REFERENCES

Bounds for generalized thrackles

S. Even Ehrlich, R. E. Tarjan
  • Discrete Comput . Geom .
  • 2000

Nikolayevsky: Bounds for generalized thrackles

Y. G. Cairns
  • Discrete Comput. Geom
  • 2000

Agarwal: Combinatorial Geometry

J. Pach, K P.
  • Wiley-Interscience, New York,
  • 1995
VIEW 1 EXCERPT

Thürmann: Minimum number of edges with at most s crossings in drawings of the complete graph

H. Harborth, Ch
  • in: Proceedings of the Twenty-Fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL,
  • 1994

Törőcsik: Some geometric applications of Dilworth’s theorem

J. J. Pach
  • Discrete Comput. Geom
  • 1994

Drawings of the complete graph with maximum number of crossings

H. Harborth, I. Mengersen
  • in: Proceedings of the Twenty-Third Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL,
  • 1992