Density theorems for intersection graphs of t-monotone curves

  • Authors:

  • Andrew Suk

  • Affiliations:

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA

  • Venue:
  • GD'12 Proceedings of the 20th international conference on Graph Drawing
  • Year:
  • 2012

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Abstract

A curve γ in the plane is t-monotone if its interior has at most t−1 vertical tangent points. A family of t-monotone curves F is simple if any two members intersect at most once. It is shown that if F is a simple family of nt-monotone curves with at least εn2 intersecting pairs (disjoint pairs), then there exists two subfamilies F1,F2⊂F of size δn each, such that every curve in F1 intersects (is disjoint to) every curve in F2, where δ depends only on ε. We apply these results to find pairwise disjoint edges in simple topological graphs.