Density Theorems for Intersection Graphs of t-Monotone Curves

  • Andrew Suk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)


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.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andrew Suk
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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